LMFDB - Embedded newform 637.2.q.h.491.2

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			491.2
Root			$0.759479 - 1.19298i$ of defining polynomial
Character	$\chi$	$=$	637.491
Dual form			637.2.q.h.589.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20027 + 0.692976i) q^{2} +(-1.41289 - 2.44719i) q^{3} +(-0.0395678 + 0.0685334i) q^{4} +0.518957i q^{5} +(3.39169 + 1.95819i) q^{6} -2.88158i q^{8} +(-2.49250 + 4.31714i) q^{9} +O(q^{10})$	\(q+(-1.20027 + 0.692976i) q^{2} +(-1.41289 - 2.44719i) q^{3} +(-0.0395678 + 0.0685334i) q^{4} +0.518957i q^{5} +(3.39169 + 1.95819i) q^{6} -2.88158i q^{8} +(-2.49250 + 4.31714i) q^{9} +(-0.359625 - 0.622889i) q^{10} +(1.40656 - 0.812080i) q^{11} +0.223619 q^{12} +(-1.42641 - 3.31140i) q^{13} +(1.26999 - 0.733228i) q^{15} +(1.91773 + 3.32161i) q^{16} +(-0.974127 + 1.68724i) q^{17} -6.90897i q^{18} +(-2.15740 - 1.24558i) q^{19} +(-0.0355659 - 0.0205340i) q^{20} +(-1.12550 + 1.94943i) q^{22} +(-4.57029 - 7.91598i) q^{23} +(-7.05179 + 4.07135i) q^{24} +4.73068 q^{25} +(4.00680 + 2.98610i) q^{26} +5.60916 q^{27} +(2.61498 + 4.52928i) q^{29} +(-1.01622 + 1.76014i) q^{30} +5.79391i q^{31} +(0.387453 + 0.223696i) q^{32} +(-3.97463 - 2.29475i) q^{33} -2.70019i q^{34} +(-0.197245 - 0.341639i) q^{36} +(-8.85879 + 5.11463i) q^{37} +3.45262 q^{38} +(-6.08826 + 8.16934i) q^{39} +1.49542 q^{40} +(-3.64513 + 2.10452i) q^{41} +(-0.498655 + 0.863697i) q^{43} +0.128529i q^{44} +(-2.24041 - 1.29350i) q^{45} +(10.9712 + 6.33421i) q^{46} +4.51725i q^{47} +(5.41908 - 9.38612i) q^{48} +(-5.67810 + 3.27825i) q^{50} +5.50532 q^{51} +(0.283381 + 0.0332676i) q^{52} -8.89651 q^{53} +(-6.73251 + 3.88701i) q^{54} +(0.421434 + 0.729946i) q^{55} +7.03944i q^{57} +(-6.27736 - 3.62424i) q^{58} +(5.37392 + 3.10263i) q^{59} +0.116049i q^{60} +(-6.73536 + 11.6660i) q^{61} +(-4.01504 - 6.95426i) q^{62} -8.29100 q^{64} +(1.71847 - 0.740247i) q^{65} +6.36084 q^{66} +(-7.25094 + 4.18633i) q^{67} +(-0.0770880 - 0.133520i) q^{68} +(-12.9146 + 22.3688i) q^{69} +(-4.50168 - 2.59905i) q^{71} +(12.4402 + 7.18234i) q^{72} +11.8395i q^{73} +(7.08863 - 12.2779i) q^{74} +(-6.68392 - 11.5769i) q^{75} +(0.170727 - 0.0985694i) q^{76} +(1.64640 - 14.0244i) q^{78} +0.982310 q^{79} +(-1.72377 + 0.995221i) q^{80} +(-0.447609 - 0.775281i) q^{81} +(2.91676 - 5.05197i) q^{82} -8.91851i q^{83} +(-0.875603 - 0.505530i) q^{85} -1.38223i q^{86} +(7.38934 - 12.7987i) q^{87} +(-2.34008 - 4.05313i) q^{88} +(10.4087 - 6.00949i) q^{89} +3.58546 q^{90} +0.723345 q^{92} +(14.1788 - 8.18614i) q^{93} +(-3.13035 - 5.42193i) q^{94} +(0.646401 - 1.11960i) q^{95} -1.26423i q^{96} +(-3.82981 - 2.21114i) q^{97} +8.09643i 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 $

$2$	−1.20027	+	0.692976i	−0.848719	+	0.490008i	−0.860218	−	0.509926i	$-0.829673\pi$
$2$	−1.20027	+	0.692976i	−0.848719	+	0.490008i	0.0114993	+	0.999934i	$0.496340\pi$
$3$	−1.41289	−	2.44719i	−0.815731	−	1.41289i	−0.908802	−	0.417228i	$-0.863002\pi$
$3$	−1.41289	−	2.44719i	−0.815731	−	1.41289i	0.0930713	−	0.995659i	$-0.470332\pi$
$4$	−0.0395678	+	0.0685334i	−0.0197839	+	0.0342667i
$5$			0.518957i			0.232085i	0.993244	+	0.116042i	$0.0370208\pi$
$5$			0.518957i			0.232085i	−0.993244	+	0.116042i	$0.962979\pi$
$6$	3.39169	+	1.95819i	1.38465	+	0.799429i
$7$		0			0
$7$		0			0
$8$		−	2.88158i		−	1.01879i
$9$	−2.49250	+	4.31714i	−0.830833	+	1.43905i
$10$	−0.359625	−	0.622889i	−0.113723	−	0.196975i
$11$	1.40656	−	0.812080i	0.424095	−	0.244851i	−0.272733	−	0.962090i	$-0.587928\pi$
$11$	1.40656	−	0.812080i	0.424095	−	0.244851i	0.696828	+	0.717239i	$0.254594\pi$
$12$	0.223619			0.0645533
$13$	−1.42641	−	3.31140i	−0.395616	−	0.918416i
$13$	−1.42641	−	3.31140i	−0.395616	−	0.918416i
$14$		0			0
$15$	1.26999	−	0.733228i	0.327909	−	0.189319i
$16$	1.91773	+	3.32161i	0.479433	+	0.830403i
$17$	−0.974127	+	1.68724i	−0.236260	+	0.409215i	−0.959638	−	0.281237i	$-0.909255\pi$
$17$	−0.974127	+	1.68724i	−0.236260	+	0.409215i	0.723378	+	0.690452i	$0.242589\pi$
$18$		−	6.90897i		−	1.62846i
$19$	−2.15740	−	1.24558i	−0.494942	−	0.285755i	0.231680	−	0.972792i	$-0.425578\pi$
$19$	−2.15740	−	1.24558i	−0.494942	−	0.285755i	−0.726622	+	0.687037i	$0.758911\pi$
$20$	−0.0355659	−	0.0205340i	−0.00795277	−	0.00459154i
$21$		0			0
$22$	−1.12550	+	1.94943i	−0.239958	+	0.415620i
$23$	−4.57029	−	7.91598i	−0.952971	−	1.65059i	−0.738943	−	0.673767i	$-0.764675\pi$
$23$	−4.57029	−	7.91598i	−0.952971	−	1.65059i	−0.214028	−	0.976828i	$-0.568658\pi$
$24$	−7.05179	+	4.07135i	−1.43944	+	0.831061i
$25$	4.73068			0.946137
$26$	4.00680	+	2.98610i	0.785798	+	0.585622i
$27$	5.60916			1.07948
$28$		0			0
$29$	2.61498	+	4.52928i	0.485589	+	0.841065i	0.999863	−	0.0165608i	$-0.00527172\pi$
$29$	2.61498	+	4.52928i	0.485589	+	0.841065i	−0.514274	+	0.857626i	$0.671938\pi$
$30$	−1.01622	+	1.76014i	−0.185535	+	0.321357i
$31$			5.79391i			1.04062i	0.853978	+	0.520308i	$0.174183\pi$
$31$			5.79391i			1.04062i	−0.853978	+	0.520308i	$0.825817\pi$
$32$	0.387453	+	0.223696i	0.0684926	+	0.0395442i
$33$	−3.97463	−	2.29475i	−0.691894	−	0.399465i
$34$		−	2.70019i		−	0.463078i
$35$		0			0
$36$	−0.197245	−	0.341639i	−0.0328742	−	0.0569398i
$37$	−8.85879	+	5.11463i	−1.45638	+	0.840840i	−0.998831	−	0.0483462i	$-0.984605\pi$
$37$	−8.85879	+	5.11463i	−1.45638	+	0.840840i	−0.457546	+	0.889186i	$0.651272\pi$
$38$	3.45262			0.560089
$39$	−6.08826	+	8.16934i	−0.974902	+	1.30814i
$40$	1.49542			0.236446
$41$	−3.64513	+	2.10452i	−0.569273	+	0.328670i	−0.756859	−	0.653578i	$-0.773267\pi$
$41$	−3.64513	+	2.10452i	−0.569273	+	0.328670i	0.187586	+	0.982248i	$0.439934\pi$
$42$		0			0
$43$	−0.498655	+	0.863697i	−0.0760442	+	0.131712i	−0.901540	−	0.432696i	$-0.857562\pi$
$43$	−0.498655	+	0.863697i	−0.0760442	+	0.131712i	0.825496	+	0.564408i	$0.190896\pi$
$44$			0.128529i			0.0193764i
$45$	−2.24041	−	1.29350i	−0.333980	−	0.192824i
$46$	10.9712	+	6.33421i	1.61761	+	0.933928i
$47$			4.51725i			0.658909i	0.944171	+	0.329455i	$0.106865\pi$
$47$			4.51725i			0.658909i	−0.944171	+	0.329455i	$0.893135\pi$
$48$	5.41908	−	9.38612i	0.782177	−	1.35477i
$49$		0			0
$50$	−5.67810	+	3.27825i	−0.803004	+	0.463615i
$51$	5.50532			0.770899
$52$	0.283381	+	0.0332676i	0.0392979	+	0.00461339i
$53$	−8.89651			−1.22203			−0.611015	−	0.791619i	$-0.709238\pi$
$53$	−8.89651			−1.22203			−0.611015	+	0.791619i	$0.709238\pi$
$54$	−6.73251	+	3.88701i	−0.916178	+	0.528956i
$55$	0.421434	+	0.729946i	0.0568262	+	0.0984259i
$56$		0			0
$57$			7.03944i			0.932397i
$58$	−6.27736	−	3.62424i	−0.824258	−	0.475886i
$59$	5.37392	+	3.10263i	0.699624	+	0.403928i	0.807207	−	0.590268i	$-0.200978\pi$
$59$	5.37392	+	3.10263i	0.699624	+	0.403928i	−0.107583	+	0.994196i	$0.534311\pi$
$60$			0.116049i			0.0149818i
$61$	−6.73536	+	11.6660i	−0.862375	+	1.49368i	0.00725571	+	0.999974i	$0.497690\pi$
$61$	−6.73536	+	11.6660i	−0.862375	+	1.49368i	−0.869630	+	0.493703i	$0.835643\pi$
$62$	−4.01504	−	6.95426i	−0.509911	−	0.883191i
$63$		0			0
$64$	−8.29100			−1.03637
$65$	1.71847	−	0.740247i	0.213150	−	0.0918164i
$66$	6.36084			0.782965
$67$	−7.25094	+	4.18633i	−0.885843	+	0.511442i	−0.872580	−	0.488470i	$-0.837555\pi$
$67$	−7.25094	+	4.18633i	−0.885843	+	0.511442i	−0.0132624	+	0.999912i	$0.504222\pi$
$68$	−0.0770880	−	0.133520i	−0.00934830	−	0.0161917i
$69$	−12.9146	+	22.3688i	−1.55474	+	2.69288i
$70$		0			0
$71$	−4.50168	−	2.59905i	−0.534251	−	0.308450i	0.208495	−	0.978023i	$-0.433144\pi$
$71$	−4.50168	−	2.59905i	−0.534251	−	0.308450i	−0.742746	+	0.669573i	$0.766477\pi$
$72$	12.4402	+	7.18234i	1.46609	+	0.846447i
$73$			11.8395i			1.38571i	0.721076	+	0.692856i	$0.243648\pi$
$73$			11.8395i			1.38571i	−0.721076	+	0.692856i	$0.756352\pi$
$74$	7.08863	−	12.2779i	0.824037	−	1.42727i
$75$	−6.68392	−	11.5769i	−0.771793	−	1.33678i
$76$	0.170727	−	0.0985694i	0.0195838	−	0.0113067i
$77$		0			0
$78$	1.64640	−	14.0244i	0.186418	−	1.58795i
$79$	0.982310			0.110518			0.0552592	−	0.998472i	$-0.482401\pi$
$79$	0.982310			0.110518			0.0552592	+	0.998472i	$0.482401\pi$
$80$	−1.72377	+	0.995221i	−0.192724	+	0.111269i
$81$	−0.447609	−	0.775281i	−0.0497343	−	0.0861423i
$82$	2.91676	−	5.05197i	0.322102	−	0.557897i
$83$		−	8.91851i		−	0.978934i	−0.872022	−	0.489467i	$-0.837191\pi$
$83$		−	8.91851i		−	0.978934i	0.872022	−	0.489467i	$-0.162809\pi$
$84$		0			0
$85$	−0.875603	−	0.505530i	−0.0949725	−	0.0548324i
$86$		−	1.38223i		−	0.149049i
$87$	7.38934	−	12.7987i	0.792220	−	1.37217i
$88$	−2.34008	−	4.05313i	−0.249453	−	0.432065i
$89$	10.4087	−	6.00949i	1.10332	−	0.637005i	0.166233	−	0.986087i	$-0.446840\pi$
$89$	10.4087	−	6.00949i	1.10332	−	0.637005i	0.937092	+	0.349082i	$0.113506\pi$
$90$	3.58546			0.377941
$91$		0			0
$92$	0.723345			0.0754139
$93$	14.1788	−	8.18614i	1.47027	−	0.848863i
$94$	−3.13035	−	5.42193i	−0.322871	−	0.559229i
$95$	0.646401	−	1.11960i	0.0663194	−	0.114869i
$96$		−	1.26423i		−	0.129030i
$97$	−3.82981	−	2.21114i	−0.388858	−	0.224507i	0.292807	−	0.956172i	$-0.405411\pi$
$97$	−3.82981	−	2.21114i	−0.388858	−	0.224507i	−0.681665	+	0.731664i	$0.738744\pi$
$98$		0			0
$99$			8.09643i			0.813722i
$100$	−0.187183	+	0.324210i	−0.0187183	+	0.0324210i
$101$	−9.15132	−	15.8506i	−0.910591	−	1.57719i	−0.813231	−	0.581940i	$-0.802294\pi$
$101$	−9.15132	−	15.8506i	−0.910591	−	1.57719i	−0.0973594	−	0.995249i	$-0.531040\pi$
$102$	−6.60787	+	3.81506i	−0.654277	+	0.377747i
$103$	5.02046			0.494680			0.247340	−	0.968929i	$-0.420444\pi$
$103$	5.02046			0.494680			0.247340	+	0.968929i	$0.420444\pi$
$104$	−9.54206	+	4.11033i	−0.935676	+	0.403051i
$105$		0			0
$106$	10.6782	−	6.16507i	1.03716	−	0.598804i
$107$	−3.07228	−	5.32134i	−0.297008	−	0.514434i	0.678442	−	0.734654i	$-0.262656\pi$
$107$	−3.07228	−	5.32134i	−0.297008	−	0.514434i	−0.975450	+	0.220221i	$0.929322\pi$
$108$	−0.221942	+	0.384415i	−0.0213564	+	0.0369903i
$109$		−	11.8962i		−	1.13945i	−0.821834	−	0.569727i	$-0.807049\pi$
$109$		−	11.8962i		−	1.13945i	0.821834	−	0.569727i	$-0.192951\pi$
$110$	−1.01167	−	0.584088i	−0.0964590	−	0.0556906i
$111$	25.0330	+	14.4528i	2.37602	+	1.37180i
$112$		0			0
$113$	−1.77806	+	3.07969i	−0.167266	+	0.289713i	−0.937458	−	0.348099i	$-0.886827\pi$
$113$	−1.77806	+	3.07969i	−0.167266	+	0.289713i	0.770192	+	0.637812i	$0.220161\pi$
$114$	−4.87817	−	8.44923i	−0.456882	−	0.791343i
$115$	4.10805	−	2.37178i	0.383078	−	0.221170i
$116$	−0.413875			−0.0384274
$117$	17.8511	+	2.09563i	1.65033	+	0.193741i
$118$	−8.60020			−0.791713
$119$		0			0
$120$	−2.11286	−	3.65957i	−0.192877	−	0.334072i
$121$	−4.18105	+	7.24180i	−0.380096	+	0.658345i
$122$		−	18.6698i		−	1.69028i
$123$	10.3003	+	5.94689i	0.928748	+	0.536213i
$124$	−0.397076	−	0.229252i	−0.0356585	−	0.0205874i
$125$			5.04981i			0.451668i
$126$		0			0
$127$	−0.711749	−	1.23279i	−0.0631575	−	0.109392i	0.832718	−	0.553698i	$-0.186784\pi$
$127$	−0.711749	−	1.23279i	−0.0631575	−	0.109392i	−0.895875	+	0.444306i	$0.853450\pi$
$128$	9.17653	−	5.29807i	0.811098	−	0.468288i
$129$	2.81818			0.248127
$130$	−1.54966	+	2.07936i	−0.135914	+	0.182372i
$131$	−8.67374			−0.757828			−0.378914	−	0.925432i	$-0.623702\pi$
$131$	−8.67374			−0.757828			−0.378914	+	0.925432i	$0.623702\pi$
$132$	0.314535	−	0.181597i	0.0273767	−	0.0158060i
$133$		0			0
$134$	5.80205	−	10.0495i	0.501221	−	0.868141i
$135$			2.91091i			0.250531i
$136$	4.86191	+	2.80703i	0.416906	+	0.240701i
$137$	7.37667	+	4.25892i	0.630231	+	0.363864i	0.780842	−	0.624729i	$-0.214791\pi$
$137$	7.37667	+	4.25892i	0.630231	+	0.363864i	−0.150611	+	0.988593i	$0.548124\pi$
$138$		−	35.7981i		−	3.04733i
$139$	−2.51922	+	4.36342i	−0.213677	+	0.370100i	−0.952863	−	0.303402i	$-0.901877\pi$
$139$	−2.51922	+	4.36342i	−0.213677	+	0.370100i	0.739185	+	0.673502i	$0.235211\pi$
$140$		0			0
$141$	11.0546	−	6.38237i	0.930964	−	0.537493i
$142$	7.20431			0.604572
$143$	−4.69546	−	3.49933i	−0.392654	−	0.292628i
$144$	−19.1198			−1.59332
$145$	−2.35050	+	1.35706i	−0.195198	+	0.112698i
$146$	−8.20451	−	14.2106i	−0.679010	−	1.17608i
$147$		0			0
$148$		−	0.809498i		−	0.0665403i
$149$	2.91409	+	1.68245i	0.238732	+	0.137832i	0.614594	−	0.788844i	$-0.289320\pi$
$149$	2.91409	+	1.68245i	0.238732	+	0.137832i	−0.375862	+	0.926676i	$0.622653\pi$
$150$	16.0450	+	9.26360i	1.31007	+	0.756370i
$151$			12.6566i			1.02998i	0.857196	+	0.514991i	$0.172205\pi$
$151$			12.6566i			1.02998i	−0.857196	+	0.514991i	$0.827795\pi$
$152$	−3.58924	+	6.21674i	−0.291125	+	0.504244i
$153$	−4.85602	−	8.41087i	−0.392586	−	0.679979i
$154$		0			0
$155$	−3.00679			−0.241511
$156$	−0.318973	−	0.740492i	−0.0255383	−	0.0592868i
$157$	−10.3691			−0.827547			−0.413773	−	0.910380i	$-0.635789\pi$
$157$	−10.3691			−0.827547			−0.413773	+	0.910380i	$0.635789\pi$
$158$	−1.17904	+	0.680717i	−0.0937992	+	0.0541550i
$159$	12.5698	+	21.7715i	0.996847	+	1.72659i
$160$	−0.116089	+	0.201071i	−0.00917761	+	0.0158961i
$161$		0			0
$162$	1.07450	+	0.620364i	0.0844209	+	0.0487404i
$163$	13.6428	+	7.87669i	1.06859	+	0.616950i	0.927796	−	0.373089i	$-0.121701\pi$
$163$	13.6428	+	7.87669i	1.06859	+	0.616950i	0.140794	+	0.990039i	$0.455035\pi$
$164$		−	0.333084i		−	0.0260095i
$165$	1.19088	−	2.06266i	0.0927098	−	0.160578i
$166$	6.18032	+	10.7046i	0.479686	+	0.830840i
$167$	14.2016	−	8.19930i	1.09895	−	0.634481i	0.163007	−	0.986625i	$-0.447881\pi$
$167$	14.2016	−	8.19930i	1.09895	−	0.634481i	0.935946	+	0.352144i	$0.114547\pi$
$168$		0			0
$169$	−8.93069	+	9.44684i	−0.686976	+	0.726680i
$170$	1.40128			0.107473
$171$	10.7547	−	6.20920i	0.822429	−	0.474830i
$172$	−0.0394614	−	0.0683491i	−0.00300890	−	0.00521157i
$173$	0.150677	−	0.260981i	0.0114558	−	0.0198420i	−0.860241	−	0.509888i	$-0.829687\pi$
$173$	0.150677	−	0.260981i	0.0114558	−	0.0198420i	0.871696	+	0.490046i	$0.163020\pi$
$174$			20.4825i			1.55278i
$175$		0			0
$176$	5.39483	+	3.11470i	0.406650	+	0.234780i
$177$		−	17.5347i		−	1.31799i
$178$	−8.32887	+	14.4260i	−0.624275	+	1.08128i
$179$	−4.90791	−	8.50075i	−0.366834	−	0.635376i	0.622234	−	0.782831i	$-0.286225\pi$
$179$	−4.90791	−	8.50075i	−0.366834	−	0.635376i	−0.989069	+	0.147455i	$0.952892\pi$
$180$	0.177296	−	0.102362i	0.0132149	−	0.00762960i
$181$	−12.4320			−0.924062			−0.462031	−	0.886864i	$-0.652879\pi$
$181$	−12.4320			−0.924062			−0.462031	+	0.886864i	$0.652879\pi$
$182$		0			0
$183$	38.0652			2.81386
$184$	−22.8105	+	13.1697i	−1.68162	+	0.970881i
$185$	−2.65427	−	4.59733i	−0.195146	−	0.338003i
$186$	−11.3456	+	19.6512i	−0.831900	+	1.44089i
$187$			3.16427i			0.231395i
$188$	−0.309583	−	0.178738i	−0.0225786	−	0.0130358i
$189$		0			0
$190$			1.79176i			0.129988i
$191$	6.12346	−	10.6061i	0.443078	−	0.767434i	−0.554838	−	0.831958i	$-0.687220\pi$
$191$	6.12346	−	10.6061i	0.443078	−	0.767434i	0.997916	+	0.0645248i	$0.0205531\pi$
$192$	11.7142	+	20.2897i	0.845403	+	1.46428i
$193$	−10.0752	+	5.81692i	−0.725229	+	0.418711i	−0.816674	−	0.577099i	$-0.804185\pi$
$193$	−10.0752	+	5.81692i	−0.725229	+	0.418711i	0.0914452	+	0.995810i	$0.470851\pi$
$194$	6.12908			0.440042
$195$	−4.23953	−	3.15955i	−0.303599	−	0.226260i
$196$		0			0
$197$	−1.55984	+	0.900572i	−0.111134	+	0.0641631i	−0.554537	−	0.832159i	$-0.687104\pi$
$197$	−1.55984	+	0.900572i	−0.111134	+	0.0641631i	0.443403	+	0.896322i	$0.353771\pi$
$198$	−5.61064	−	9.71791i	−0.398731	−	0.690622i
$199$	−3.29657	+	5.70982i	−0.233687	+	0.404759i	−0.958890	−	0.283777i	$-0.908413\pi$
$199$	−3.29657	+	5.70982i	−0.233687	+	0.404759i	0.725203	+	0.688535i	$0.241746\pi$
$200$		−	13.6319i		−	0.963918i
$201$	20.4895	+	11.8296i	1.44522	+	0.834397i
$202$	21.9681	+	12.6833i	1.54567	+	0.892394i
$203$		0			0
$204$	−0.217833	+	0.377298i	−0.0152514	+	0.0264162i
$205$	−1.09215	−	1.89166i	−0.0762793	−	0.132120i
$206$	−6.02590	+	3.47906i	−0.419845	+	0.242397i
$207$	45.5658			3.16704
$208$	8.26369	−	11.0884i	0.572984	−	0.768840i
$209$	−4.04603			−0.279870
$210$		0			0
$211$	−5.35996	−	9.28373i	−0.368995	−	0.639118i	0.620414	−	0.784275i	$-0.286965\pi$
$211$	−5.35996	−	9.28373i	−0.368995	−	0.639118i	−0.989409	+	0.145157i	$0.953631\pi$
$212$	0.352015	−	0.609708i	0.0241765	−	0.0418749i
$213$			14.6886i			1.00645i
$214$	7.37513	+	4.25803i	0.504154	+	0.291073i
$215$	−0.448221	−	0.258781i	−0.0305684	−	0.0176487i
$216$		−	16.1633i		−	1.09977i
$217$		0			0
$218$	8.24382	+	14.2787i	0.558342	+	0.967076i
$219$	28.9736	−	16.7279i	1.95785	−	1.13037i
$220$	−0.0667009			−0.00449697
$221$	6.97662	+	0.819021i	0.469298	+	0.0550933i
$222$	−40.0617			−2.68877
$223$	11.1612	−	6.44392i	0.747409	−	0.431517i	−0.0773480	−	0.997004i	$-0.524645\pi$
$223$	11.1612	−	6.44392i	0.747409	−	0.431517i	0.824757	+	0.565487i	$0.191312\pi$
$224$		0			0
$225$	−11.7912	+	20.4230i	−0.786082	+	1.36153i
$226$		−	4.92862i		−	0.327847i
$227$	0.605486	+	0.349577i	0.0401875	+	0.0232023i	0.519959	−	0.854191i	$-0.325947\pi$
$227$	0.605486	+	0.349577i	0.0401875	+	0.0232023i	−0.479772	+	0.877393i	$0.659280\pi$
$228$	−0.482437	−	0.278535i	−0.0319502	−	0.0184464i
$229$		−	18.2868i		−	1.20843i	−0.796822	−	0.604214i	$-0.793487\pi$
$229$		−	18.2868i		−	1.20843i	0.796822	−	0.604214i	$-0.206513\pi$
$230$	−3.28718	+	5.69356i	−0.216750	+	0.375422i
$231$		0			0
$232$	13.0515	−	7.53528i	0.856872	−	0.494715i
$233$	−26.7796			−1.75439			−0.877194	−	0.480137i	$-0.840587\pi$
$233$	−26.7796			−1.75439			−0.877194	+	0.480137i	$0.840587\pi$
$234$	−22.8783	+	9.85505i	−1.49560	+	0.644245i
$235$	−2.34426			−0.152923
$236$	−0.425268	+	0.245528i	−0.0276826	+	0.0159825i
$237$	−1.38789	−	2.40390i	−0.0901533	−	0.156150i
$238$		0			0
$239$			16.6177i			1.07491i	0.843293	+	0.537454i	$0.180614\pi$
$239$			16.6177i			1.07491i	−0.843293	+	0.537454i	$0.819386\pi$
$240$	4.87099	+	2.81227i	0.314421	+	0.181531i
$241$	−15.0800	−	8.70643i	−0.971387	−	0.560830i	−0.0717279	−	0.997424i	$-0.522851\pi$
$241$	−15.0800	−	8.70643i	−0.971387	−	0.560830i	−0.899659	+	0.436594i	$0.856185\pi$
$242$		−	11.5895i		−	0.745000i
$243$	7.14890	−	12.3823i	0.458602	−	0.794322i
$244$	−0.533007	−	0.923194i	−0.0341222	−	0.0591015i
$245$		0			0
$246$	−16.4842			−1.05099
$247$	−1.04725	+	8.92073i	−0.0666350	+	0.567612i
$248$	16.6956			1.06017
$249$	−21.8253	+	12.6008i	−1.38312	+	0.798546i
$250$	−3.49940	−	6.06113i	−0.221321	−	0.383340i
$251$	3.22491	−	5.58571i	0.203554	−	0.352567i	−0.746117	−	0.665815i	$-0.768084\pi$
$251$	3.22491	−	5.58571i	0.203554	−	0.352567i	0.949671	+	0.313249i	$0.101417\pi$
$252$		0			0
$253$	−12.8568	−	7.42288i	−0.808300	−	0.466672i
$254$	1.70858	+	0.986451i	0.107206	+	0.0618954i
$255$			2.85703i			0.178914i
$256$	0.948120	−	1.64219i	0.0592575	−	0.102637i
$257$	1.83578	+	3.17966i	0.114513	+	0.198342i	0.917585	−	0.397540i	$-0.130136\pi$
$257$	1.83578	+	3.17966i	0.114513	+	0.198342i	−0.803072	+	0.595882i	$0.796803\pi$
$258$	−3.38257	+	1.95293i	−0.210590	+	0.121584i
$259$		0			0
$260$	−0.0172645	+	0.147063i	−0.00107070	+	0.00912044i
$261$	−26.0713			−1.61377
$262$	10.4108	−	6.01070i	0.643183	−	0.371342i
$263$	−9.15964	−	15.8650i	−0.564807	−	0.978275i	−0.997068	−	0.0765263i	$-0.975617\pi$
$263$	−9.15964	−	15.8650i	−0.564807	−	0.978275i	0.432260	−	0.901749i	$-0.357716\pi$
$264$	−6.61252	+	11.4532i	−0.406973	+	0.704897i
$265$		−	4.61690i		−	0.283614i
$266$		0			0
$267$	−29.4128	−	16.9815i	−1.80003	−	1.03925i
$268$		−	0.662575i		−	0.0404732i
$269$	13.7715	−	23.8529i	0.839661	−	1.45434i	−0.0505171	−	0.998723i	$-0.516087\pi$
$269$	13.7715	−	23.8529i	0.839661	−	1.45434i	0.890178	−	0.455613i	$-0.150580\pi$
$270$	−2.01719	−	3.49388i	−0.122762	−	0.212631i
$271$	−5.64582	+	3.25961i	−0.342959	+	0.198007i	−0.661580	−	0.749875i	$-0.730114\pi$
$271$	−5.64582	+	3.25961i	−0.342959	+	0.198007i	0.318621	+	0.947882i	$0.396780\pi$
$272$	−7.47246			−0.453084
$273$		0			0
$274$	−11.8053			−0.713186
$275$	6.65401	−	3.84169i	0.401252	−	0.231663i
$276$	−1.02200	−	1.77016i	−0.0615174	−	0.106551i
$277$	2.72093	−	4.71279i	0.163485	−	0.283164i	−0.772631	−	0.634855i	$-0.781060\pi$
$277$	2.72093	−	4.71279i	0.163485	−	0.283164i	0.936116	+	0.351691i	$0.114393\pi$
$278$		−	6.98304i		−	0.418815i
$279$	−25.0131	−	14.4413i	−1.49749	−	0.864579i
$280$		0			0
$281$			3.54237i			0.211320i	0.994402	+	0.105660i	$0.0336955\pi$
$281$			3.54237i			0.211320i	−0.994402	+	0.105660i	$0.966304\pi$
$282$	−8.84566	+	15.3211i	−0.526752	+	0.912360i
$283$	7.06956	+	12.2448i	0.420242	+	0.727880i	0.995963	−	0.0897658i	$-0.0286119\pi$
$283$	7.06956	+	12.2448i	0.420242	+	0.727880i	−0.575721	+	0.817646i	$0.695279\pi$
$284$	0.356243	−	0.205677i	0.0211391	−	0.0122047i
$285$	−3.65317			−0.216395
$286$	8.06077	+	0.946296i	0.476643	+	0.0559556i
$287$		0			0
$288$	−1.93145	+	1.11512i	−0.113812	+	0.0657093i
$289$	6.60215	+	11.4353i	0.388362	+	0.672663i
$290$	1.88082	−	3.25768i	0.110446	−	0.191298i
$291$			12.4964i			0.732551i
$292$	−0.811403	−	0.468464i	−0.0474838	−	0.0274148i
$293$	7.23071	+	4.17465i	0.422423	+	0.243886i	0.696113	−	0.717932i	$-0.254911\pi$
$293$	7.23071	+	4.17465i	0.422423	+	0.243886i	−0.273691	+	0.961818i	$0.588244\pi$
$294$		0			0
$295$	−1.61013	+	2.78883i	−0.0937455	+	0.162372i
$296$	14.7382	+	25.5274i	0.856642	+	1.48375i
$297$	7.88964	−	4.55508i	0.457803	−	0.264313i
$298$	−4.66359			−0.270155
$299$	−19.6938	+	26.4255i	−1.13892	+	1.52823i
$300$	1.05787			0.0610762
$301$		0			0
$302$	−8.77074	−	15.1914i	−0.504699	−	0.874165i
$303$	−25.8596	+	44.7901i	−1.48559	+	2.57312i
$304$		−	9.55474i		−	0.548002i
$305$	−6.05415	−	3.49536i	−0.346659	−	0.200144i
$306$	11.6571	+	6.73021i	0.666390	+	0.384741i
$307$			8.33362i			0.475625i	0.971311	+	0.237813i	$0.0764304\pi$
$307$			8.33362i			0.475625i	−0.971311	+	0.237813i	$0.923570\pi$
$308$		0			0
$309$	−7.09334	−	12.2860i	−0.403526	−	0.698927i
$310$	3.60896	−	2.08363i	0.204975	−	0.118342i
$311$	−14.6227			−0.829176			−0.414588	−	0.910009i	$-0.636074\pi$
$311$	−14.6227			−0.829176			−0.414588	+	0.910009i	$0.636074\pi$
$312$	23.5406	+	17.5438i	1.33273	+	0.993224i
$313$	−17.1328			−0.968404			−0.484202	−	0.874956i	$-0.660890\pi$
$313$	−17.1328			−0.968404			−0.484202	+	0.874956i	$0.660890\pi$
$314$	12.4458	−	7.18556i	0.702355	−	0.405505i
$315$		0			0
$316$	−0.0388678	+	0.0673210i	−0.00218649	+	0.00378710i
$317$			14.0000i			0.786320i	0.919470	+	0.393160i	$0.128618\pi$
$317$			14.0000i			0.786320i	−0.919470	+	0.393160i	$0.871382\pi$
$318$	−30.1742	−	17.4211i	−1.69209	−	0.976926i
$319$	7.35627	+	4.24714i	0.411872	+	0.237794i
$320$		−	4.30267i		−	0.240527i
$321$	−8.68157	+	15.0369i	−0.484558	+	0.839279i
$322$		0			0
$323$	4.20317	−	2.42670i	0.233871	−	0.135025i
$324$	0.0708435			0.00393575
$325$	−6.74791	−	15.6652i	−0.374307	−	0.868947i
$326$	−21.8334			−1.20924
$327$	−29.1124	+	16.8081i	−1.60992	+	0.929487i
$328$	6.06434	+	10.5037i	0.334847	+	0.579972i
$329$		0			0
$330$			3.30100i			0.181714i
$331$	5.99286	+	3.45998i	0.329397	+	0.190178i	0.655574	−	0.755131i	$-0.272427\pi$
$331$	5.99286	+	3.45998i	0.329397	+	0.190178i	−0.326176	+	0.945309i	$0.605760\pi$
$332$	0.611216	+	0.352886i	0.0335448	+	0.0193671i
$333$		−	50.9928i		−	2.79439i
$334$	−11.3638	+	19.6827i	−0.621801	+	1.07699i
$335$	−2.17253	−	3.76292i	−0.118698	−	0.205591i
$336$		0			0
$337$	11.1559			0.607703			0.303852	−	0.952719i	$-0.401727\pi$
$337$	11.1559			0.607703			0.303852	+	0.952719i	$0.401727\pi$
$338$	4.17280	−	17.5275i	0.226970	−	0.953371i
$339$	10.0488			0.545776
$340$	0.0692913	−	0.0400054i	0.00375785	−	0.00216960i
$341$	4.70512	+	8.14950i	0.254796	+	0.441320i
$342$	−8.60566	+	14.9054i	−0.465341	+	0.805994i
$343$		0			0
$344$	2.48881	+	1.43692i	0.134188	+	0.0774734i
$345$	−11.6084	−	6.70213i	−0.624977	−	0.360830i
$346$			0.417663i			0.0224537i
$347$	2.46255	−	4.26527i	0.132197	−	0.228971i	−0.792326	−	0.610097i	$-0.791130\pi$
$347$	2.46255	−	4.26527i	0.132197	−	0.228971i	0.924523	+	0.381126i	$0.124464\pi$
$348$	0.584759	+	1.01283i	0.0313464	+	0.0542935i
$349$	−1.31926	+	0.761675i	−0.0706183	+	0.0407715i	−0.534893	−	0.844920i	$-0.679648\pi$
$349$	−1.31926	+	0.761675i	−0.0706183	+	0.0407715i	0.464275	+	0.885691i	$0.346315\pi$
$350$		0			0
$351$	−8.00098	−	18.5741i	−0.427061	−	0.991415i
$352$	0.726636			0.0387298
$353$	−15.5261	+	8.96401i	−0.826372	+	0.477106i	−0.852609	−	0.522550i	$-0.824981\pi$
$353$	−15.5261	+	8.96401i	−0.826372	+	0.477106i	0.0262367	+	0.999656i	$0.491648\pi$
$354$	12.1511	+	21.0463i	0.645824	+	1.11860i
$355$	1.34879	−	2.33618i	0.0715865	−	0.123991i
$356$			0.951129i			0.0504097i
$357$		0			0
$358$	11.7816	+	6.80213i	0.622679	+	0.359504i
$359$		−	20.0014i		−	1.05563i	−0.849359	−	0.527816i	$-0.823011\pi$
$359$		−	20.0014i		−	1.05563i	0.849359	−	0.527816i	$-0.176989\pi$
$360$	−3.72733	+	6.45592i	−0.196447	+	0.340257i
$361$	−6.39707	−	11.0801i	−0.336688	−	0.583161i
$362$	14.9217	−	8.61507i	0.784269	−	0.452798i
$363$	23.6294			1.24022
$364$		0			0
$365$	−6.14421			−0.321602
$366$	−45.6885	+	26.3783i	−2.38818	+	1.37882i
$367$	13.7078	+	23.7427i	0.715544	+	1.23936i	0.962749	+	0.270395i	$0.0871543\pi$
$367$	13.7078	+	23.7427i	0.715544	+	1.23936i	−0.247206	+	0.968963i	$0.579512\pi$
$368$	17.5292	−	30.3615i	0.913772	−	1.58270i
$369$		−	20.9820i		−	1.09228i
$370$	6.37169	+	3.67870i	0.331248	+	0.191246i
$371$		0			0
$372$			1.29563i			0.0671752i
$373$	7.94643	−	13.7636i	0.411451	−	0.712653i	−0.583598	−	0.812043i	$-0.698356\pi$
$373$	7.94643	−	13.7636i	0.411451	−	0.712653i	0.995049	+	0.0993893i	$0.0316889\pi$
$374$	−2.19277	−	3.79798i	−0.113385	−	0.196389i
$375$	12.3578	−	7.13481i	0.638156	−	0.368440i
$376$	13.0168			0.671292
$377$	11.2682	−	15.1199i	0.580341	−	0.778712i
$378$		0			0
$379$	7.60284	−	4.38950i	0.390532	−	0.225474i	−0.291859	−	0.956461i	$-0.594274\pi$
$379$	7.60284	−	4.38950i	0.390532	−	0.225474i	0.682390	+	0.730988i	$0.260940\pi$
$380$	0.0511533	+	0.0886001i	0.00262411	+	0.00454509i
$381$	−2.01124	+	3.48357i	−0.103039	+	0.178469i
$382$			16.9736i			0.868447i
$383$	−6.89562	−	3.98119i	−0.352349	−	0.203429i	0.313370	−	0.949631i	$-0.398542\pi$
$383$	−6.89562	−	3.98119i	−0.352349	−	0.203429i	−0.665720	+	0.746202i	$0.731875\pi$
$384$	−25.9308	−	14.9712i	−1.32328	−	0.763994i
$385$		0			0
$386$	8.06198	−	13.9638i	0.410344	−	0.710736i
$387$	−2.48580	−	4.30553i	−0.126360	−	0.218862i
$388$	0.303074	−	0.174980i	0.0153863	−	0.00888326i
$389$	−32.0434			−1.62467			−0.812333	−	0.583194i	$-0.801803\pi$
$389$	−32.0434			−1.62467			−0.812333	+	0.583194i	$0.801803\pi$
$390$	7.27808	+	0.854411i	0.368540	+	0.0432648i
$391$	17.8082			0.900598
$392$		0			0
$393$	12.2550	+	21.2263i	0.618184	+	1.07073i
$394$	1.24815	−	2.16186i	0.0628809	−	0.108913i
$395$			0.509777i			0.0256496i
$396$	−0.554876	−	0.320358i	−0.0278836	−	0.0160986i
$397$	−5.57251	−	3.21729i	−0.279676	−	0.161471i	0.353601	−	0.935396i	$-0.384957\pi$
$397$	−5.57251	−	3.21729i	−0.279676	−	0.161471i	−0.633277	+	0.773925i	$0.718290\pi$
$398$		−	9.13777i		−	0.458035i
$399$		0			0
$400$	9.07219	+	15.7135i	0.453609	+	0.785675i
$401$	−0.462092	+	0.266789i	−0.0230758	+	0.0133228i	−0.511494	−	0.859287i	$-0.670908\pi$
$401$	−0.462092	+	0.266789i	−0.0230758	+	0.0133228i	0.488418	+	0.872610i	$0.337574\pi$
$402$	−32.7906			−1.63545
$403$	19.1859	−	8.26451i	0.955719	−	0.411685i
$404$	1.44839			0.0720601
$405$	0.402337	−	0.232290i	0.0199923	−	0.0115426i
$406$		0			0
$407$	−8.30697	+	14.3881i	−0.411761	+	0.713191i
$408$		−	15.8640i		−	0.785387i
$409$	34.4269	+	19.8764i	1.70230	+	0.982824i	0.943424	+	0.331590i	$0.107585\pi$
$409$	34.4269	+	19.8764i	1.70230	+	0.982824i	0.758877	+	0.651234i	$0.225748\pi$
$410$	2.62176	+	1.51367i	0.129479	+	0.0747550i
$411$		−	24.0695i		−	1.18726i
$412$	−0.198648	+	0.344069i	−0.00978670	+	0.0169511i
$413$		0			0
$414$	−54.6913	+	31.5760i	−2.68793	+	1.55188i
$415$	4.62832			0.227195
$416$	0.188078	−	1.60209i	0.00922128	−	0.0785490i
$417$	14.2375			0.697213
$418$	4.85633	−	2.80380i	0.237531	−	0.137139i
$419$	11.9088	+	20.6266i	0.581783	+	1.00768i	0.995268	+	0.0971665i	$0.0309779\pi$
$419$	11.9088	+	20.6266i	0.581783	+	1.00768i	−0.413485	+	0.910511i	$0.635689\pi$
$420$		0			0
$421$		−	23.2419i		−	1.13274i	−0.824151	−	0.566370i	$-0.808347\pi$
$421$		−	23.2419i		−	1.13274i	0.824151	−	0.566370i	$-0.191653\pi$
$422$	12.8668	+	7.42865i	0.626346	+	0.361621i
$423$	−19.5016	−	11.2593i	−0.948200	−	0.547444i
$424$			25.6360i			1.24500i
$425$	−4.60828	+	7.98178i	−0.223535	+	0.387173i
$426$	−10.1789	−	17.6303i	−0.493168	−	0.854192i
$427$		0			0
$428$	0.486253			0.0235039
$429$	−1.92937	+	16.4348i	−0.0931510	+	0.793482i
$430$	0.717316			0.0345920
$431$	−2.34424	+	1.35345i	−0.112918	+	0.0651932i	−0.555395	−	0.831586i	$-0.687433\pi$
$431$	−2.34424	+	1.35345i	−0.112918	+	0.0651932i	0.442477	+	0.896780i	$0.354100\pi$
$432$	10.7569	+	18.6314i	0.517540	+	0.896406i
$433$	2.90945	−	5.03932i	0.139819	−	0.242174i	−0.787609	−	0.616176i	$-0.788681\pi$
$433$	2.90945	−	5.03932i	0.139819	−	0.242174i	0.927428	+	0.374002i	$0.122015\pi$
$434$		0			0
$435$	6.64198	+	3.83475i	0.318459	+	0.183862i
$436$	0.815290	+	0.470708i	0.0390453	+	0.0225428i
$437$			22.7706i			1.08927i
$438$	−23.1841	+	40.1560i	−1.10778	+	1.91873i
$439$	−19.0851	−	33.0563i	−0.910882	−	1.57769i	−0.812822	−	0.582513i	$-0.802070\pi$
$439$	−19.0851	−	33.0563i	−0.910882	−	1.57769i	−0.0980599	−	0.995181i	$-0.531264\pi$
$440$	2.10340	−	1.21440i	0.100276	−	0.0578942i
$441$		0			0
$442$	−8.94139	+	3.85158i	−0.425298	+	0.183201i
$443$	−31.6740			−1.50488			−0.752440	−	0.658661i	$-0.771123\pi$
$443$	−31.6740			−1.50488			−0.752440	+	0.658661i	$0.771123\pi$
$444$	−1.98100	+	1.14373i	−0.0940139	+	0.0542790i
$445$	3.11867	+	5.40169i	0.147839	+	0.256065i
$446$	−8.93097	+	15.4689i	−0.422894	+	0.732473i
$447$		−	9.50845i		−	0.449734i
$448$		0			0
$449$	27.1975	+	15.7025i	1.28353	+	0.741045i	0.977491	−	0.210975i	$-0.0676638\pi$
$449$	27.1975	+	15.7025i	1.28353	+	0.741045i	0.306036	+	0.952020i	$0.400997\pi$
$450$		−	32.6842i		−	1.54075i
$451$	−3.41807	+	5.92027i	−0.160951	+	0.278775i
$452$	−0.140708	−	0.243713i	−0.00661834	−	0.0114633i
$453$	30.9732	−	17.8824i	1.45525	−	0.840187i
$454$	−0.968995			−0.0454772
$455$		0			0
$456$	20.2847			0.949920
$457$	27.5640	−	15.9141i	1.28939	−	0.744429i	0.310844	−	0.950461i	$-0.399388\pi$
$457$	27.5640	−	15.9141i	1.28939	−	0.744429i	0.978545	+	0.206032i	$0.0660551\pi$
$458$	12.6723	+	21.9491i	0.592140	+	1.02562i
$459$	−5.46403	+	9.46398i	−0.255039	+	0.441741i
$460$			0.375385i			0.0175024i
$461$	−1.01005	−	0.583153i	−0.0470427	−	0.0271601i	0.476294	−	0.879286i	$-0.341980\pi$
$461$	−1.01005	−	0.583153i	−0.0470427	−	0.0271601i	−0.523337	+	0.852126i	$0.675313\pi$
$462$		0			0
$463$			20.3441i			0.945469i	0.881205	+	0.472734i	$0.156733\pi$
$463$			20.3441i			0.945469i	−0.881205	+	0.472734i	$0.843267\pi$
$464$	−10.0297	+	17.3719i	−0.465615	+	0.806470i
$465$	4.24825	+	7.35819i	0.197008	+	0.341228i
$466$	32.1427	−	18.5576i	1.48898	−	0.859664i
$467$	−1.56939			−0.0726229			−0.0363114	−	0.999341i	$-0.511561\pi$
$467$	−1.56939			−0.0726229			−0.0363114	+	0.999341i	$0.511561\pi$
$468$	−0.849948	+	1.14048i	−0.0392889	+	0.0527185i
$469$		0			0
$470$	2.81375	−	1.62452i	0.129788	−	0.0749334i
$471$	14.6504	+	25.3753i	0.675055	+	1.16923i
$472$	8.94049	−	15.4854i	0.411519	−	0.712773i
$473$			1.61979i			0.0744781i
$474$	3.33169	+	1.92355i	0.153030	+	0.0883517i
$475$	−10.2060	−	5.89243i	−0.468283	−	0.270363i
$476$		0			0
$477$	22.1745	−	38.4074i	1.01530	−	1.75856i
$478$	−11.5157	−	19.9457i	−0.526714	−	0.912295i
$479$	−6.68501	+	3.85959i	−0.305446	+	0.176349i	−0.644887	−	0.764278i	$-0.723095\pi$
$479$	−6.68501	+	3.85959i	−0.305446	+	0.176349i	0.339441	+	0.940627i	$0.389762\pi$
$480$	0.656080			0.0299458
$481$	29.5729	+	22.0394i	1.34841	+	1.00491i
$482$	24.1334			1.09925
$483$		0			0
$484$	−0.330870	−	0.573083i	−0.0150395	−	0.0260492i
$485$	1.14749	−	1.98751i	0.0521047	−	0.0902481i
$486$			19.8161i			0.898875i
$487$	−0.0659739	−	0.0380900i	−0.00298956	−	0.00172602i	0.498504	−	0.866887i	$-0.333883\pi$
$487$	−0.0659739	−	0.0380900i	−0.00298956	−	0.00172602i	−0.501494	+	0.865161i	$0.667216\pi$
$488$	33.6165	+	19.4085i	1.52175	+	0.878582i
$489$		−	44.5155i		−	2.01306i
$490$		0			0
$491$	0.893574	+	1.54772i	0.0403264	+	0.0698474i	0.885484	−	0.464670i	$-0.153827\pi$
$491$	0.893574	+	1.54772i	0.0403264	+	0.0698474i	−0.845158	+	0.534517i	$0.820494\pi$
$492$	−0.815121	+	0.470610i	−0.0367485	+	0.0212167i
$493$	−10.1893			−0.458902
$494$	−4.92487	−	11.4330i	−0.221580	−	0.514395i
$495$	−4.20170			−0.188852
$496$	−19.2451	+	11.1112i	−0.864131	+	0.498906i
$497$		0			0
$498$	17.4642	−	30.2488i	0.782589	−	1.35548i
$499$		−	8.33493i		−	0.373123i	−0.982443	−	0.186561i	$-0.940266\pi$
$499$		−	8.33493i		−	0.373123i	0.982443	−	0.186561i	$-0.0597343\pi$
$500$	−0.346080	−	0.199810i	−0.0154772	−	0.00893576i
$501$	−40.1305	−	23.1694i	−1.79290	−	1.03513i
$502$			8.93914i			0.398973i
$503$	0.720238	−	1.24749i	0.0321138	−	0.0556228i	−0.849522	−	0.527554i	$-0.823109\pi$
$503$	0.720238	−	1.24749i	0.0321138	−	0.0556228i	0.881636	+	0.471931i	$0.156443\pi$
$504$		0			0
$505$	8.22576	−	4.74914i	0.366041	−	0.211334i
$506$	20.5755			0.914693
$507$	35.7363	+	8.50779i	1.58710	+	0.377844i
$508$	0.112649			0.00499801
$509$	−12.8394	+	7.41282i	−0.569096	+	0.328568i	−0.756788	−	0.653660i	$-0.773233\pi$
$509$	−12.8394	+	7.41282i	−0.569096	+	0.328568i	0.187692	+	0.982228i	$0.439899\pi$
$510$	−1.97985	−	3.42920i	−0.0876693	−	0.151848i
$511$		0			0
$512$			23.8204i			1.05272i
$513$	−12.1012	−	6.98664i	−0.534282	−	0.308468i
$514$	−4.40686	−	2.54430i	−0.194378	−	0.112224i
$515$			2.60540i			0.114808i
$516$	−0.111509	+	0.193139i	−0.00490891	+	0.00850248i
$517$	3.66837	+	6.35380i	0.161335	+	0.279440i
$518$		0			0
$519$	−0.851561			−0.0373794
$520$	−2.13308	−	4.95192i	−0.0935419	−	0.217156i
$521$	0.334388			0.0146498			0.00732489	−	0.999973i	$-0.497668\pi$
$521$	0.334388			0.0146498			0.00732489	+	0.999973i	$0.497668\pi$
$522$	31.2926	−	18.0668i	1.36964	−	0.790763i
$523$	−16.2533	−	28.1515i	−0.710705	−	1.23098i	−0.964593	−	0.263744i	$-0.915043\pi$
$523$	−16.2533	−	28.1515i	−0.710705	−	1.23098i	0.253887	−	0.967234i	$-0.418291\pi$
$524$	0.343201	−	0.594441i	0.0149928	−	0.0259683i
$525$		0			0
$526$	21.9881	+	12.6948i	0.958726	+	0.553521i
$527$	−9.77570	−	5.64400i	−0.425836	−	0.245857i
$528$		−	17.6029i		−	0.766068i
$529$	−30.2751	+	52.4380i	−1.31631	+	2.27991i
$530$	3.19941	+	5.54153i	0.138973	+	0.240709i
$531$	−26.7890	+	15.4666i	−1.16254	+	0.671194i
$532$		0			0
$533$	12.1683	+	9.06855i	0.527070	+	0.392803i
$534$	47.0710			2.03696
$535$	2.76155	−	1.59438i	0.119392	−	0.0689311i
$536$	12.0633	+	20.8942i	0.521053	+	0.902491i
$537$	−13.8686	+	24.0212i	−0.598476	+	1.03659i
$538$			38.1732i			1.64576i
$539$		0			0
$540$	−0.199495	−	0.115178i	−0.00858488	−	0.00495649i
$541$			10.6015i			0.455796i	0.973685	+	0.227898i	$0.0731852\pi$
$541$			10.6015i			0.455796i	−0.973685	+	0.227898i	$0.926815\pi$
$542$	4.51767	−	7.82483i	0.194051	−	0.336105i
$543$	17.5650	+	30.4235i	0.753786	+	1.30560i
$544$	−0.754856	+	0.435816i	−0.0323642	+	0.0186855i
$545$	6.17364			0.264450
$546$		0			0
$547$	10.2327			0.437519			0.218760	−	0.975779i	$-0.429799\pi$
$547$	10.2327			0.437519			0.218760	+	0.975779i	$0.429799\pi$
$548$	−0.583756	+	0.337032i	−0.0249368	+	0.0143973i
$549$	−33.5758	−	58.1549i	−1.43298	−	2.48199i
$550$	−5.32440	+	9.22214i	−0.227033	+	0.393233i
$551$		−	13.0286i		−	0.555038i
$552$	64.4574	+	37.2145i	2.74349	+	1.58396i
$553$		0			0
$554$			7.54216i			0.320436i
$555$	−7.50037	+	12.9910i	−0.318373	+	0.551438i
$556$	−0.199360	−	0.345301i	−0.00845474	−	0.0146440i
$557$	27.7067	−	15.9965i	1.17397	−	0.677793i	0.219359	−	0.975644i	$-0.429603\pi$
$557$	27.7067	−	15.9965i	1.17397	−	0.677793i	0.954612	+	0.297851i	$0.0962700\pi$
$558$	40.0300			1.69460
$559$	3.57133	+	0.419257i	0.151051	+	0.0177327i
$560$		0			0
$561$	7.74359	−	4.47076i	0.326934	−	0.188756i
$562$	−2.45478	−	4.25180i	−0.103549	−	0.179351i
$563$	−5.39566	+	9.34556i	−0.227400	+	0.393868i	−0.957037	−	0.289967i	$-0.906356\pi$
$563$	−5.39566	+	9.34556i	−0.227400	+	0.393868i	0.729637	+	0.683835i	$0.239689\pi$
$564$			1.01014i			0.0425348i
$565$	−1.59823	−	0.922737i	−0.0672380	−	0.0388199i
$566$	−16.9708	−	9.79808i	−0.713335	−	0.411844i
$567$		0			0
$568$	−7.48937	+	12.9720i	−0.314247	+	0.544292i
$569$	−12.3007	−	21.3054i	−0.515672	−	0.893170i	−0.999835	−	0.0181917i	$-0.994209\pi$
$569$	−12.3007	−	21.3054i	−0.515672	−	0.893170i	0.484163	−	0.874978i	$-0.339124\pi$
$570$	4.38479	−	2.53156i	0.183659	−	0.106035i
$571$	−16.5724			−0.693534			−0.346767	−	0.937951i	$-0.612721\pi$
$571$	−16.5724			−0.693534			−0.346767	+	0.937951i	$0.612721\pi$
$572$	0.425610	−	0.183335i	0.0177956	−	0.00766563i
$573$	−34.6070			−1.44573
$574$		0			0
$575$	−21.6206	−	37.4480i	−0.901641	−	1.56169i
$576$	20.6653	−	35.7934i	0.861054	−	1.49139i
$577$			14.6611i			0.610348i	0.952297	+	0.305174i	$0.0987147\pi$
$577$			14.6611i			0.610348i	−0.952297	+	0.305174i	$0.901285\pi$
$578$	−15.8487	−	9.15027i	−0.659221	−	0.380601i
$579$	28.4702	+	16.4373i	1.18318	+	0.683111i
$580$		−	0.214784i		−	0.00891840i
$581$		0			0
$582$	−8.65969	−	14.9990i	−0.358956	−	0.621730i
$583$	−12.5135	+	7.22467i	−0.518256	+	0.299215i
$584$	34.1166			1.41175
$585$	−1.08754	+	9.26394i	−0.0449644	+	0.383017i
$586$	−11.5717			−0.478024
$587$	−30.5998	+	17.6668i	−1.26299	+	0.729186i	−0.973652	−	0.228041i	$-0.926768\pi$
$587$	−30.5998	+	17.6668i	−1.26299	+	0.729186i	−0.289336	+	0.957227i	$0.593435\pi$
$588$		0			0
$589$	7.21676	−	12.4998i	0.297362	−	0.515045i
$590$		−	4.46313i		−	0.183744i
$591$	4.40775	+	2.54481i	0.181310	+	0.104680i
$592$	−33.9776	−	19.6170i	−1.39647	−	0.806253i
$593$		−	16.4294i		−	0.674675i	−0.941384	−	0.337338i	$-0.890474\pi$
$593$		−	16.4294i		−	0.674675i	0.941384	−	0.337338i	$-0.109526\pi$
$594$	−6.31313	+	10.9347i	−0.259031	+	0.448655i
$595$		0			0
$596$	−0.230608	+	0.133142i	−0.00944608	+	0.00545370i
$597$	18.6307			0.762504
$598$	5.32564	−	45.3651i	0.217782	−	1.85512i
$599$	12.0819			0.493653			0.246826	−	0.969060i	$-0.420612\pi$
$599$	12.0819			0.493653			0.246826	+	0.969060i	$0.420612\pi$
$600$	−33.3598	+	19.2603i	−1.36191	+	0.786297i
$601$	3.90743	+	6.76787i	0.159387	+	0.276067i	0.934648	−	0.355574i	$-0.115715\pi$
$601$	3.90743	+	6.76787i	0.159387	+	0.276067i	−0.775261	+	0.631642i	$0.782381\pi$
$602$		0			0
$603$		−	41.7377i		−	1.69969i
$604$	−0.867401	−	0.500794i	−0.0352941	−	0.0203770i
$605$	−3.75818	−	2.16979i	−0.152792	−	0.0882144i
$606$		−	71.6803i		−	2.91181i
$607$	17.7825	−	30.8001i	0.721768	−	1.25014i	−0.238523	−	0.971137i	$-0.576663\pi$
$607$	17.7825	−	30.8001i	0.721768	−	1.25014i	0.960291	−	0.279002i	$-0.0900035\pi$
$608$	−0.557261	−	0.965205i	−0.0225999	−	0.0391442i
$609$		0			0
$610$	9.68882			0.392289
$611$	14.9584	−	6.44347i	0.605153	−	0.260675i
$612$	0.768568			0.0310675
$613$	−10.3376	+	5.96839i	−0.417530	+	0.241061i	−0.694020	−	0.719956i	$-0.744162\pi$
$613$	−10.3376	+	5.96839i	−0.417530	+	0.241061i	0.276490	+	0.961017i	$0.410829\pi$
$614$	−5.77500	−	10.0026i	−0.233060	−	0.403672i
$615$	−3.08618	+	5.34542i	−0.124447	+	0.215548i
$616$		0			0
$617$	−20.4124	−	11.7851i	−0.821772	−	0.474450i	0.0292550	−	0.999572i	$-0.490687\pi$
$617$	−20.4124	−	11.7851i	−0.821772	−	0.474450i	−0.851027	+	0.525122i	$0.824020\pi$
$618$	17.0278	+	9.83103i	0.684960	+	0.395462i
$619$		−	28.5571i		−	1.14781i	−0.818923	−	0.573904i	$-0.805428\pi$
$619$		−	28.5571i		−	1.14781i	0.818923	−	0.573904i	$-0.194572\pi$
$620$	0.118972	−	0.206066i	0.00477803	−	0.00827579i
$621$	−25.6355	−	44.4020i	−1.02872	−	1.78179i
$622$	17.5512	−	10.1332i	0.703738	−	0.406303i
$623$		0			0
$624$	−38.8110	−	4.55623i	−1.55368	−	0.182395i
$625$	21.0328			0.841311
$626$	20.5640	−	11.8726i	0.821903	−	0.474526i
$627$	5.71659	+	9.90142i	0.228298	+	0.395425i
$628$	0.410283	−	0.710632i	0.0163721	−	0.0283573i
$629$		−	19.9292i		−	0.794628i
$630$		0			0
$631$	−38.9646	−	22.4962i	−1.55116	−	0.895561i	−0.998048	−	0.0624526i	$-0.980108\pi$
$631$	−38.9646	−	22.4962i	−1.55116	−	0.895561i	−0.553109	−	0.833109i	$-0.686559\pi$
$632$		−	2.83061i		−	0.112596i
$633$	−15.1460	+	26.2337i	−0.602001	+	1.04270i
$634$	−9.70169	−	16.8038i	−0.385303	−	0.667365i
$635$	0.639763	−	0.369367i	0.0253882	−	0.0146579i
$636$	−1.98943			−0.0788860
$637$		0			0
$638$	−11.7727			−0.466085
$639$	22.4409	−	12.9562i	0.887747	−	0.512541i
$640$	2.74947	+	4.76222i	0.108682	+	0.188243i
$641$	−1.26650	+	2.19364i	−0.0500238	+	0.0866437i	−0.889953	−	0.456052i	$-0.849263\pi$
$641$	−1.26650	+	2.19364i	−0.0500238	+	0.0866437i	0.839929	+	0.542696i	$0.182596\pi$
$642$		−	24.0645i		−	0.949749i
$643$	−15.9150	−	9.18853i	−0.627627	−	0.362360i	0.152206	−	0.988349i	$-0.451362\pi$
$643$	−15.9150	−	9.18853i	−0.627627	−	0.362360i	−0.779832	+	0.625988i	$0.784696\pi$
$644$		0			0
$645$			1.46251i			0.0575863i
$646$	−3.36329	+	5.82539i	−0.132327	+	0.229197i
$647$	−10.4643	−	18.1248i	−0.411396	−	0.712558i	0.583647	−	0.812008i	$-0.301625\pi$
$647$	−10.4643	−	18.1248i	−0.411396	−	0.712558i	−0.995043	+	0.0994494i	$0.968292\pi$
$648$	−2.23404	+	1.28982i	−0.0877612	+	0.0506690i
$649$	10.0783			0.395609
$650$	18.9549	+	14.1263i	0.743473	+	0.554079i
$651$		0			0
$652$	−1.07963	+	0.623326i	−0.0422817	+	0.0244113i
$653$	24.0580	+	41.6696i	0.941461	+	1.63066i	0.762686	+	0.646769i	$0.223880\pi$
$653$	24.0580	+	41.6696i	0.941461	+	1.63066i	0.178775	+	0.983890i	$0.442786\pi$
$654$	23.2952	−	40.3484i	0.910913	−	1.57775i
$655$		−	4.50130i		−	0.175880i
$656$	−13.9808	−	8.07180i	−0.545857	−	0.315151i
$657$	−51.1129	−	29.5100i	−1.99410	−	1.15130i
$658$		0			0
$659$	1.10819	−	1.91944i	0.0431690	−	0.0747708i	−0.843634	−	0.536919i	$-0.819588\pi$
$659$	1.10819	−	1.91944i	0.0431690	−	0.0747708i	0.886803	+	0.462148i	$0.152921\pi$
$660$	0.0942408	+	0.163230i	0.00366832	+	0.00635371i
$661$	0.552034	−	0.318717i	0.0214716	−	0.0123966i	−0.489226	−	0.872157i	$-0.662721\pi$
$661$	0.552034	−	0.318717i	0.0214716	−	0.0123966i	0.510697	+	0.859761i	$0.329387\pi$
$662$	−9.59073			−0.372754
$663$	−7.85287	−	18.2303i	−0.304980	−	0.708006i
$664$	−25.6994			−0.997331
$665$		0			0
$666$	35.3368	+	61.2052i	1.36927	+	2.37165i
$667$	23.9024	−	41.4002i	0.925506	−	1.60302i
$668$			1.29771i			0.0502100i
$669$	−31.5390	−	18.2091i	−1.21937	−	0.704003i
$670$	5.21523	+	3.01102i	0.201482	+	0.116326i
$671$			21.8786i			0.844614i
$672$		0			0
$673$	7.70343	+	13.3427i	0.296945	+	0.514324i	0.975436	−	0.220285i	$-0.0706988\pi$
$673$	7.70343	+	13.3427i	0.296945	+	0.514324i	−0.678490	+	0.734609i	$0.737365\pi$
$674$	−13.3901	+	7.73081i	−0.515769	+	0.297780i
$675$	26.5352			1.02134
$676$	−0.294057	−	0.985841i	−0.0113099	−	0.0379170i
$677$	11.6812			0.448945			0.224473	−	0.974480i	$-0.427934\pi$
$677$	11.6812			0.448945			0.224473	+	0.974480i	$0.427934\pi$
$678$	−12.0613	+	6.96358i	−0.463210	+	0.267435i
$679$		0			0
$680$	−1.45673	+	2.52312i	−0.0558629	+	0.0967574i
$681$		−	1.97565i		−	0.0757072i
$682$	−11.2948	−	6.52107i	−0.432501	−	0.249705i
$683$	19.8419	+	11.4557i	0.759227	+	0.438340i	0.829018	−	0.559221i	$-0.188900\pi$
$683$	19.8419	+	11.4557i	0.759227	+	0.438340i	−0.0697909	+	0.997562i	$0.522233\pi$
$684$			0.982737i			0.0375759i
$685$	−2.21020	+	3.82817i	−0.0844473	+	0.146267i
$686$		0			0
$687$	−44.7514	+	25.8372i	−1.70737	+	0.985752i
$688$	−3.82515			−0.145833
$689$	12.6901	+	29.4599i	0.483454	+	1.12233i
$690$	18.5777			0.707239
$691$	40.9046	−	23.6163i	1.55608	−	0.898405i	0.558458	−	0.829533i	$-0.311393\pi$
$691$	40.9046	−	23.6163i	1.55608	−	0.898405i	0.997625	−	0.0688729i	$-0.0219403\pi$
$692$	0.0119239	+	0.0206529i	0.000453280	+	0.000785104i
$693$		0			0
$694$			6.82596i			0.259110i
$695$	−2.26443	−	1.30737i	−0.0858946	−	0.0495913i
$696$	−36.8805	−	21.2930i	−1.39795	−	0.807109i
$697$		−	8.20026i		−	0.310607i
$698$	1.05565	−	1.82843i	0.0399568	−	0.0692071i
$699$	37.8365	+	65.5347i	1.43111	+	2.47875i
$700$		0			0
$701$	12.2098			0.461158			0.230579	−	0.973054i	$-0.425938\pi$
$701$	12.2098			0.461158			0.230579	+	0.973054i	$0.425938\pi$
$702$	22.4748	+	16.7495i	0.848256	+	0.632169i
$703$	25.4827			0.961097
$704$	−11.6618	+	6.73295i	−0.439521	+	0.253758i
$705$	3.31218	+	5.73686i	0.124744	+	0.216063i
$706$	12.4237	−	21.5185i	0.467572	−	0.809858i
$707$		0			0
$708$	1.20171	+	0.693808i	0.0451630	+	0.0260749i
$709$	−15.4910	−	8.94374i	−0.581777	−	0.335889i	0.180062	−	0.983655i	$-0.442370\pi$
$709$	−15.4910	−	8.94374i	−0.581777	−	0.335889i	−0.761839	+	0.647766i	$0.775703\pi$
$710$			3.73873i			0.140312i
$711$	−2.44841	+	4.24076i	−0.0918224	+	0.159041i
$712$	−17.3169	−	29.9937i	−0.648977	−	1.12406i
$713$	45.8644	−	26.4798i	1.71764	−	0.991678i
$714$		0			0
$715$	1.81600	−	2.43674i	0.0679146	−	0.0911290i
$716$	0.776780			0.0290296
$717$	40.6667	−	23.4789i	1.51872	−	0.876836i
$718$	13.8605	+	24.0070i	0.517268	+	0.895935i
$719$	−4.56317	+	7.90364i	−0.170178	+	0.294756i	−0.938482	−	0.345329i	$-0.887767\pi$
$719$	−4.56317	+	7.90364i	−0.170178	+	0.294756i	0.768304	+	0.640085i	$0.221101\pi$
$720$		−	9.92235i		−	0.369784i
$721$		0			0
$722$	15.3564	+	8.86604i	0.571507	+	0.329960i
$723$			49.2048i			1.82995i
$724$	0.491906	−	0.852006i	0.0182815	−	0.0316646i
$725$	12.3706	+	21.4266i	0.459434	+	0.795763i
$726$	−28.3617	+	16.3746i	−1.05260	+	0.607719i
$727$	−33.6859			−1.24934			−0.624670	−	0.780889i	$-0.714767\pi$
$727$	−33.6859			−1.24934			−0.624670	+	0.780889i	$0.714767\pi$
$728$		0			0
$729$	−43.0880			−1.59585
$730$	7.37471	−	4.25779i	0.272950	−	0.157588i
$731$	−0.971507	−	1.68270i	−0.0359325	−	0.0622369i
$732$	−1.50616	+	2.60874i	−0.0556691	+	0.0964218i
$733$			46.4344i			1.71509i	0.514406	+	0.857547i	$0.328013\pi$
$733$			46.4344i			1.71509i	−0.514406	+	0.857547i	$0.671987\pi$
$734$	−32.9062	−	18.9984i	−1.21459	−	0.701245i
$735$		0			0
$736$		−	4.08942i		−	0.150738i
$737$	−6.79927	+	11.7767i	−0.250454	+	0.433799i
$738$	14.5400	+	25.1841i	0.535226	+	0.927039i
$739$	−1.60237	+	0.925127i	−0.0589440	+	0.0340314i	−0.529182	−	0.848508i	$-0.677501\pi$
$739$	−1.60237	+	0.925127i	−0.0589440	+	0.0340314i	0.470238	+	0.882539i	$0.344168\pi$
$740$	0.420095			0.0154430
$741$	23.3104	−	10.0412i	0.856328	−	0.368871i
$742$		0			0
$743$	28.7095	−	16.5755i	1.05325	−	0.608094i	0.129693	−	0.991554i	$-0.458601\pi$
$743$	28.7095	−	16.5755i	1.05325	−	0.608094i	0.923558	+	0.383460i	$0.125268\pi$
$744$	−23.5890	−	40.8574i	−0.864816	−	1.49791i
$745$	−0.873120	+	1.51229i	−0.0319886	+	0.0554059i
$746$			22.0268i			0.806457i
$747$	38.5024	+	22.2294i	1.40873	+	0.813331i
$748$	−0.216858	−	0.125203i	−0.00792913	−	0.00457788i
$749$		0			0
$750$	−9.88850	+	17.1274i	−0.361077	+	0.625404i
$751$	−10.3871	−	17.9910i	−0.379032	−	0.656503i	0.611890	−	0.790943i	$-0.290410\pi$
$751$	−10.3871	−	17.9910i	−0.379032	−	0.656503i	−0.990922	+	0.134441i	$0.957076\pi$
$752$	−15.0046	+	8.66289i	−0.547160	+	0.315903i
$753$	−18.2257			−0.664182
$754$	−3.04717	+	25.9565i	−0.110971	+	0.945280i
$755$	−6.56824			−0.239043
$756$		0			0
$757$	−21.8075	−	37.7717i	−0.792607	−	1.37283i	−0.924348	−	0.381551i	$-0.875390\pi$
$757$	−21.8075	−	37.7717i	−0.792607	−	1.37283i	0.131741	−	0.991284i	$-0.457943\pi$
$758$	−6.08364	+	10.5372i	−0.220968	+	0.382727i
$759$			41.9508i			1.52272i
$760$	−3.22622	−	1.86266i	−0.117027	−	0.0675657i
$761$	−10.7302	−	6.19511i	−0.388971	−	0.224573i	0.292743	−	0.956191i	$-0.405432\pi$
$761$	−10.7302	−	6.19511i	−0.388971	−	0.224573i	−0.681714	+	0.731619i	$0.738765\pi$
$762$		−	5.57497i		−	0.201960i
$763$		0			0
$764$	0.484583	+	0.839323i	0.0175316	+	0.0303656i
$765$	4.36488	−	2.52007i	0.157813	−	0.0911132i
$766$	11.0355			0.398728
$767$	2.60862	−	22.2208i	0.0941917	−	0.802347i
$768$	−5.35835			−0.193353
$769$	4.80955	−	2.77680i	0.173437	−	0.100134i	−0.410769	−	0.911740i	$-0.634740\pi$
$769$	4.80955	−	2.77680i	0.173437	−	0.100134i	0.584205	+	0.811606i	$0.301406\pi$
$770$		0			0
$771$	5.18750	−	8.98501i	0.186823	−	0.323587i
$772$		−	0.920651i		−	0.0331349i
$773$	−37.9355	−	21.9021i	−1.36445	−	0.787764i	−0.374235	−	0.927334i	$-0.622095\pi$
$773$	−37.9355	−	21.9021i	−1.36445	−	0.787764i	−0.990212	+	0.139570i	$0.955428\pi$
$774$	5.96726	+	3.44520i	0.214489	+	0.123835i
$775$			27.4092i			0.984566i
$776$	−6.37159	+	11.0359i	−0.228727	+	0.396166i
$777$		0			0
$778$	38.4608	−	22.2053i	1.37889	−	0.796100i
$779$	10.4853			0.375677
$780$	0.384283	−	0.165534i	0.0137596	−	0.00592705i
$781$	−8.44253			−0.302098
$782$	−21.3746	+	12.3406i	−0.764354	+	0.441300i
$783$	14.6678	+	25.4054i	0.524185	+	0.907916i
$784$		0			0
$785$		−	5.38113i		−	0.192061i
$786$	−29.4187	−	16.9849i	−1.04933	−	0.605830i
$787$	−21.4782	−	12.4005i	−0.765616	−	0.442029i	0.0656923	−	0.997840i	$-0.479074\pi$
$787$	−21.4782	−	12.4005i	−0.765616	−	0.442029i	−0.831309	+	0.555811i	$0.812408\pi$
$788$		−	0.142535i		−	0.00507758i
$789$	−25.8831	+	44.8308i	−0.921462	+	1.59602i
$790$	−0.353263	−	0.611870i	−0.0125685	−	0.0217693i
$791$		0			0
$792$	23.3305			0.829015
$793$	48.2381	+	5.66293i	1.71299	+	0.201096i
$794$	8.91801			0.316489
$795$	−11.2985	+	6.52316i	−0.400715	+	0.231353i
$796$	−0.260876	−	0.451850i	−0.00924649	−	0.0160154i
$797$	8.23575	−	14.2647i	0.291725	−	0.505283i	−0.682492	−	0.730893i	$-0.739104\pi$
$797$	8.23575	−	14.2647i	0.291725	−	0.505283i	0.974218	+	0.225610i	$0.0724373\pi$
$798$		0			0
$799$	−7.62168	−	4.40038i	−0.269636	−	0.155674i
$800$	1.83292	+	1.05823i	0.0648034	+	0.0374142i
$801$			59.9146i			2.11698i
$802$	0.369756	−	0.640437i	0.0130566	−	0.0226146i
$803$	9.61464	+	16.6530i	0.339293	+	0.587673i
$804$	−1.62145	+	0.936144i	−0.0571841	+	0.0330152i
$805$		0			0
$806$	−17.3012	+	23.2150i	−0.609408	+	0.817715i
$807$	−77.8301			−2.73975
$808$	−45.6747	+	26.3703i	−1.60683	+	0.927704i
$809$	−0.690968	−	1.19679i	−0.0242932	−	0.0420770i	0.853623	−	0.520891i	$-0.174400\pi$
$809$	−0.690968	−	1.19679i	−0.0242932	−	0.0420770i	−0.877916	+	0.478814i	$0.841067\pi$
$810$	−0.321942	+	0.557621i	−0.0113119	+	0.0195928i
$811$		−	6.83571i		−	0.240034i	−0.992772	−	0.120017i	$-0.961705\pi$
$811$		−	6.83571i		−	0.240034i	0.992772	−	0.120017i	$-0.0382950\pi$
$812$		0			0
$813$	15.9538	+	9.21093i	0.559524	+	0.323041i
$814$		−	23.0261i		−	0.807066i
$815$	−4.08767	+	7.08004i	−0.143185	+	0.248003i
$816$	10.5577	+	18.2865i	0.369595	+	0.640157i
$817$	2.15160	−	1.24223i	0.0752750	−	0.0434601i
$818$	−55.0954			−1.92637
$819$		0			0
$820$	0.172856			0.00603640
$821$	−9.13009	+	5.27126i	−0.318642	+	0.183968i	−0.650787	−	0.759260i	$-0.725561\pi$
$821$	−9.13009	+	5.27126i	−0.318642	+	0.183968i	0.332145	+	0.943228i	$0.392228\pi$
$822$	16.6796	+	28.8899i	0.581767	+	1.00765i
$823$	7.41652	−	12.8458i	0.258524	−	0.447776i	−0.707323	−	0.706891i	$-0.750097\pi$
$823$	7.41652	−	12.8458i	0.258524	−	0.447776i	0.965847	+	0.259114i	$0.0834307\pi$
$824$		−	14.4669i		−	0.503977i
$825$	−18.8027	−	10.8558i	−0.654627	−	0.377949i
$826$		0			0
$827$			55.6758i			1.93604i	0.250879	+	0.968018i	$0.419280\pi$
$827$			55.6758i			1.93604i	−0.250879	+	0.968018i	$0.580720\pi$
$828$	−1.80294	+	3.12278i	−0.0626564	+	0.108524i
$829$	0.0232424	+	0.0402570i	0.000807242	+	0.00139818i	0.866429	−	0.499301i	$-0.166410\pi$
$829$	0.0232424	+	0.0402570i	0.000807242	+	0.00139818i	−0.865622	+	0.500699i	$0.833076\pi$
$830$	−5.55524	+	3.20732i	−0.192825	+	0.111328i
$831$	−15.3775			−0.533438
$832$	11.8264	+	27.4548i	0.410006	+	0.951823i
$833$		0			0
$834$	−17.0888	+	9.86624i	−0.591738	+	0.341640i
$835$	4.25508	+	7.37002i	0.147253	+	0.255050i
$836$	0.160092	−	0.277288i	0.00553691	−	0.00959022i
$837$			32.4990i			1.12333i
$838$	−28.5875	−	16.5050i	−0.987540	−	0.570157i
$839$	−22.1248	−	12.7738i	−0.763833	−	0.440999i	0.0668370	−	0.997764i	$-0.478709\pi$
$839$	−22.1248	−	12.7738i	−0.763833	−	0.440999i	−0.830670	+	0.556765i	$0.812043\pi$
$840$		0			0
$841$	0.823775	−	1.42682i	0.0284060	−	0.0492007i
$842$	16.1061	+	27.8965i	0.555052	+	0.961378i
$843$	8.66886	−	5.00497i	0.298572	−	0.172380i
$844$	0.848327			0.0292006
$845$	−4.90250	−	4.63464i	−0.168651	−	0.159437i
$846$	31.2096			1.07301
$847$		0			0
$848$	−17.0611	−	29.5507i	−0.585881	−	1.01478i
$849$	19.9770	−	34.6012i	0.685609	−	1.18751i
$850$		−	12.7737i		−	0.438135i
$851$	80.9745	+	46.7507i	2.77577	+	1.60259i
$852$	−1.00666	−	0.581197i	−0.0344877	−	0.0199115i
$853$			22.6671i			0.776105i	0.921637	+	0.388053i	$0.126852\pi$
$853$			22.6671i			0.776105i	−0.921637	+	0.388053i	$0.873148\pi$
$854$		0			0
$855$	3.22231	+	5.58120i	0.110201	+	0.190873i
$856$	−15.3339	+	8.85303i	−0.524102	+	0.302590i
$857$	−37.0535			−1.26572			−0.632862	−	0.774264i	$-0.718120\pi$
$857$	−37.0535			−1.26572			−0.632862	+	0.774264i	$0.718120\pi$
$858$	−9.07319	−	21.0633i	−0.309754	−	0.719088i
$859$	4.24339			0.144782			0.0723912	−	0.997376i	$-0.476937\pi$
$859$	4.24339			0.144782			0.0723912	+	0.997376i	$0.476937\pi$
$860$	0.0354702	−	0.0204788i	0.00120953	−	0.000698320i
$861$		0			0
$862$	1.87581	−	3.24900i	0.0638904	−	0.110661i
$863$			7.50051i			0.255320i	0.991818	+	0.127660i	$0.0407467\pi$
$863$			7.50051i			0.255320i	−0.991818	+	0.127660i	$0.959253\pi$
$864$	2.17328	+	1.25475i	0.0739366	+	0.0426873i
$865$	0.135438	+	0.0781951i	0.00460503	+	0.00265871i
$866$			8.06472i			0.274050i
$867$	18.6562	−	32.3135i	0.633598	−	1.09742i
$868$		0			0
$869$	1.38168	−	0.797714i	0.0468703	−	0.0270606i
$870$	−10.6296			−0.360376
$871$	24.2054	+	18.0393i	0.820170	+	0.611238i
$872$	−34.2800			−1.16087
$873$	19.0916	−	11.0225i	0.646153	−	0.373057i
$874$	−15.7795	−	27.3309i	−0.533749	−	0.924481i
$875$		0			0
$876$			2.64755i			0.0894523i
$877$	−24.4996	−	14.1448i	−0.827291	−	0.477637i	0.0256330	−	0.999671i	$-0.491840\pi$
$877$	−24.4996	−	14.1448i	−0.827291	−	0.477637i	−0.852924	+	0.522035i	$0.825173\pi$
$878$	45.8145	+	26.4510i	1.54617	+	0.892679i
$879$		−	23.5933i		−	0.795781i
$880$	−1.61640	+	2.79968i	−0.0544888	+	0.0943773i
$881$	19.7860	+	34.2704i	0.666609	+	1.15460i	0.978846	+	0.204596i	$0.0655882\pi$
$881$	19.7860	+	34.2704i	0.666609	+	1.15460i	−0.312238	+	0.950004i	$0.601079\pi$
$882$		0			0
$883$	−28.3609			−0.954419			−0.477209	−	0.878790i	$-0.658352\pi$
$883$	−28.3609			−0.954419			−0.477209	+	0.878790i	$0.658352\pi$
$884$	−0.332179	+	0.445724i	−0.0111724	+	0.0149913i
$885$	9.09974			0.305884
$886$	38.0174	−	21.9494i	1.27722	−	0.737403i
$887$	−21.8593	−	37.8614i	−0.733963	−	1.27126i	−0.955177	−	0.296036i	$-0.904335\pi$
$887$	−21.8593	−	37.8614i	−0.733963	−	1.27126i	0.221214	−	0.975225i	$-0.428998\pi$
$888$	41.6469	−	72.1345i	1.39758	−	2.42068i
$889$		0			0
$890$	−7.48649	−	4.32233i	−0.250948	−	0.144885i
$891$	−1.25918	−	0.726988i	−0.0421841	−	0.0243550i
$892$			1.01989i			0.0341483i
$893$	5.62659	−	9.74554i	0.188287	−	0.326122i
$894$	6.58913	+	11.4127i	0.220374	+	0.381698i
$895$	4.41152	−	2.54699i	0.147461	−	0.0851366i
$896$		0			0
$897$	92.4934	+	10.8583i	3.08826	+	0.362547i
$898$	−43.5257			−1.45247
$899$	−26.2422	+	15.1509i	−0.875227	+	0.505312i
$900$	−0.933105	−	1.61619i	−0.0311035	−	0.0538728i
$901$	8.66632	−	15.0105i	0.288717	−	0.500073i
$902$		−	9.47456i		−	0.315468i
$903$		0			0
$904$	8.87439	+	5.12363i	0.295158	+	0.170409i
$905$		−	6.45167i		−	0.214461i
$906$	−24.7841	+	42.9274i	−0.823397	+	1.42617i
$907$	−18.3493	−	31.7818i	−0.609277	−	1.05530i	−0.991360	−	0.131171i	$-0.958126\pi$
$907$	−18.3493	−	31.7818i	−0.609277	−	1.05530i	0.382083	−	0.924128i	$-0.375207\pi$
$908$	−0.0479154	+	0.0276640i	−0.00159013	+	0.000918062i
$909$	91.2387			3.02620
$910$		0			0
$911$	−35.5211			−1.17686			−0.588432	−	0.808546i	$-0.700255\pi$
$911$	−35.5211			−1.17686			−0.588432	+	0.808546i	$0.700255\pi$
$912$	−23.3823	+	13.4998i	−0.774265	+	0.447022i
$913$	−7.24254	−	12.5444i	−0.239693	−	0.415161i
$914$	−22.0562	+	38.2024i	−0.729553	+	1.26362i
$915$			19.7542i			0.653054i
$916$	1.25326	+	0.723569i	0.0414088	+	0.0239074i
$917$		0			0
$918$		−	15.1458i		−	0.499885i
$919$	−10.9667	+	18.9949i	−0.361758	+	0.626583i	−0.988250	−	0.152844i	$-0.951157\pi$
$919$	−10.9667	+	18.9949i	−0.361758	+	0.626583i	0.626492	+	0.779428i	$0.284490\pi$
$920$	−6.83449	−	11.8377i	−0.225327	−	0.390277i
$921$	20.3940	−	11.7745i	0.672005	−	0.387982i
$922$	1.61644			0.0532348
$923$	−2.18521	+	18.6142i	−0.0719272	+	0.612693i
$924$		0			0
$925$	−41.9082	+	24.1957i	−1.37793	+	0.795549i
$926$	−14.0980	−	24.4184i	−0.463287	−	0.802437i
$927$	−12.5135	+	21.6740i	−0.410997	+	0.711867i
$928$			2.33984i			0.0768090i
$929$	13.4383	+	7.75858i	0.440895	+	0.254551i	0.703977	−	0.710223i	$-0.251406\pi$
$929$	13.4383	+	7.75858i	0.440895	+	0.254551i	−0.263082	+	0.964773i	$0.584739\pi$
$930$	−10.1981	−	5.88788i	−0.334409	−	0.193071i
$931$		0			0
$932$	1.05961	−	1.83529i	0.0347086	−	0.0601171i
$933$	20.6602	+	35.7845i	0.676385	+	1.17153i
$934$	1.88370	−	1.08755i	0.0616364	−	0.0355858i
$935$	−1.64212			−0.0537031
$936$	6.03874	−	51.4394i	0.197382	−	1.68135i
$937$	−40.8110			−1.33324			−0.666618	−	0.745399i	$-0.732259\pi$
$937$	−40.8110			−1.33324			−0.666618	+	0.745399i	$0.732259\pi$
$938$		0			0
$939$	24.2067	+	41.9273i	0.789957	+	1.36825i
$940$	0.0927572	−	0.160660i	0.00302541	−	0.00524016i
$941$		−	51.5936i		−	1.68190i	−0.541109	−	0.840952i	$-0.681996\pi$
$941$		−	51.5936i		−	1.68190i	0.541109	−	0.840952i	$-0.318004\pi$
$942$	−35.1689	−	20.3048i	−1.14586	−	0.661565i
$943$	33.3186	+	19.2365i	1.08500	+	0.626427i
$944$			23.8001i			0.774627i
$945$		0			0
$946$	−1.12248	−	1.94419i	−0.0364949	−	0.0632110i
$947$	−4.31462	+	2.49105i	−0.140206	+	0.0809482i	−0.568462	−	0.822709i	$-0.692461\pi$
$947$	−4.31462	+	2.49105i	−0.140206	+	0.0809482i	0.428256	+	0.903657i	$0.359128\pi$
$948$	0.219663			0.00713433
$949$	39.2054	−	16.8881i	1.27266	−	0.548210i
$950$	16.3333			0.529921
$951$	34.2608	−	19.7805i	1.11098	−	0.641426i
$952$		0			0
$953$	15.1163	−	26.1822i	0.489664	−	0.848123i	−0.510265	−	0.860017i	$-0.670453\pi$
$953$	15.1163	−	26.1822i	0.489664	−	0.848123i	0.999929	+	0.0118941i	$0.00378608\pi$
$954$			61.4657i			1.99003i
$955$	5.50413	+	3.17781i	0.178110	+	0.102832i
$956$	−1.13887	−	0.657525i	−0.0368336	−	0.0212659i
$957$		−	24.0029i		−	0.775904i
$958$	5.34921	−	9.26511i	0.172825	−	0.299342i
$959$		0			0
$960$	−10.5295	+	6.07919i	−0.339837	+	0.196205i
$961$	−2.56939			−0.0828835
$962$	−50.7682	−	5.95995i	−1.63683	−	0.192156i
$963$	30.6306			0.987058
$964$	1.19336	−	0.688988i	0.0384356	−	0.0221908i
$965$	−3.01873	−	5.22860i	−0.0971764	−	0.168315i
$966$		0			0
$967$			29.9990i			0.964703i	0.875978	+	0.482352i	$0.160217\pi$
$967$			29.9990i			0.964703i	−0.875978	+	0.482352i	$0.839783\pi$
$968$	20.8678	+	12.0481i	0.670718	+	0.387239i
$969$	−11.8772	−	6.85731i	−0.381551	−	0.220288i
$970$			3.18073i			0.102127i
$971$	22.0620	−	38.2125i	0.708003	−	1.22630i	−0.257594	−	0.966253i	$-0.582930\pi$
$971$	22.0620	−	38.2125i	0.708003	−	1.22630i	0.965597	−	0.260044i	$-0.0837371\pi$
$972$	0.565732	+	0.979876i	0.0181459	+	0.0314295i
$973$		0			0
$974$	0.105582			0.00338306
$975$	−28.8016	+	38.6465i	−0.922391	+	1.23768i
$976$	−51.6665			−1.65380
$977$	−12.9925	+	7.50121i	−0.415666	+	0.239985i	−0.693221	−	0.720725i	$-0.743809\pi$
$977$	−12.9925	+	7.50121i	−0.415666	+	0.239985i	0.277555	+	0.960710i	$0.410476\pi$
$978$	30.8482	+	53.4306i	0.986417	+	1.70852i
$979$	9.76037	−	16.9055i	0.311943	−	0.540301i
$980$		0			0
$981$	51.3577	+	29.6514i	1.63973	+	0.946696i
$982$	−2.14506	−	1.23845i	−0.0684516	−	0.0395206i
$983$			6.01856i			0.191962i	0.995383	+	0.0959812i	$0.0305989\pi$
$983$			6.01856i			0.191962i	−0.995383	+	0.0959812i	$0.969401\pi$
$984$	17.1364	−	29.6812i	0.546290	−	0.946202i
$985$	−0.467358	−	0.809488i	−0.0148913	−	0.0257924i
$986$	12.2299	−	7.06093i	0.389479	−	0.224866i
$987$		0			0
$988$	−0.569930	−	0.424745i	−0.0181319	−	0.0135129i
$989$	9.11600			0.289872
$990$	5.04318	−	2.91168i	0.160283	−	0.0925392i
$991$	−16.9200	−	29.3063i	−0.537482	−	0.930946i	−0.999039	−	0.0438356i	$-0.986042\pi$
$991$	−16.9200	−	29.3063i	−0.537482	−	0.930946i	0.461557	−	0.887111i	$-0.347291\pi$
$992$	−1.29607	+	2.24487i	−0.0411504	+	0.0712746i
$993$		−	19.5542i		−	0.620535i
$994$		0			0
$995$	−2.96315	−	1.71078i	−0.0939382	−	0.0542353i
$996$		−	1.99435i		−	0.0631934i
$997$	13.1608	−	22.7951i	0.416805	−	0.721928i	−0.578811	−	0.815462i	$-0.696483\pi$
$997$	13.1608	−	22.7951i	0.416805	−	0.721928i	0.995616	+	0.0935340i	$0.0298164\pi$
$998$	5.77591	+	10.0042i	0.182833	+	0.316676i
$999$	−49.6904	+	28.6888i	−1.57213	+	0.907672i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.q.h.491.2		12
7.2	even	3		637.2.u.i.361.5		12
7.3	odd	6		637.2.k.h.569.2		12
7.4	even	3		637.2.k.g.569.2		12
7.5	odd	6		637.2.u.h.361.5		12
7.6	odd	2		91.2.q.a.36.2	✓	12
13.2	odd	12		8281.2.a.ch.1.1		6
13.4	even	6	inner	637.2.q.h.589.2		12
13.11	odd	12		8281.2.a.by.1.6		6
21.20	even	2		819.2.ct.a.127.5		12
28.27	even	2		1456.2.cc.c.673.1		12
91.4	even	6		637.2.u.i.30.5		12
91.17	odd	6		637.2.u.h.30.5		12
91.30	even	6		637.2.k.g.459.5		12
91.41	even	12		1183.2.a.p.1.1		6
91.55	odd	6		1183.2.c.i.337.3		12
91.62	odd	6		1183.2.c.i.337.10		12
91.69	odd	6		91.2.q.a.43.2	yes	12
91.76	even	12		1183.2.a.m.1.6		6
91.82	odd	6		637.2.k.h.459.5		12
273.251	even	6		819.2.ct.a.316.5		12
364.251	even	6		1456.2.cc.c.225.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.q.a.36.2	✓	12	7.6	odd	2
91.2.q.a.43.2	yes	12	91.69	odd	6
637.2.k.g.459.5		12	91.30	even	6
637.2.k.g.569.2		12	7.4	even	3
637.2.k.h.459.5		12	91.82	odd	6
637.2.k.h.569.2		12	7.3	odd	6
637.2.q.h.491.2		12	1.1	even	1	trivial
637.2.q.h.589.2		12	13.4	even	6	inner
637.2.u.h.30.5		12	91.17	odd	6
637.2.u.h.361.5		12	7.5	odd	6
637.2.u.i.30.5		12	91.4	even	6
637.2.u.i.361.5		12	7.2	even	3
819.2.ct.a.127.5		12	21.20	even	2
819.2.ct.a.316.5		12	273.251	even	6
1183.2.a.m.1.6		6	91.76	even	12
1183.2.a.p.1.1		6	91.41	even	12
1183.2.c.i.337.3		12	91.55	odd	6
1183.2.c.i.337.10		12	91.62	odd	6
1456.2.cc.c.225.1		12	364.251	even	6
1456.2.cc.c.673.1		12	28.27	even	2
8281.2.a.by.1.6		6	13.11	odd	12
8281.2.a.ch.1.1		6	13.2	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)

\(f(q)\)	\(=\)	\(q+(-1.20027 + 0.692976i) q^{2} +(-1.41289 - 2.44719i) q^{3} +(-0.0395678 + 0.0685334i) q^{4} +0.518957i q^{5} +(3.39169 + 1.95819i) q^{6} -2.88158i q^{8} +(-2.49250 + 4.31714i) q^{9} +O(q^{10})\)	\(q+(-1.20027 + 0.692976i) q^{2} +(-1.41289 - 2.44719i) q^{3} +(-0.0395678 + 0.0685334i) q^{4} +0.518957i q^{5} +(3.39169 + 1.95819i) q^{6} -2.88158i q^{8} +(-2.49250 + 4.31714i) q^{9} +(-0.359625 - 0.622889i) q^{10} +(1.40656 - 0.812080i) q^{11} +0.223619 q^{12} +(-1.42641 - 3.31140i) q^{13} +(1.26999 - 0.733228i) q^{15} +(1.91773 + 3.32161i) q^{16} +(-0.974127 + 1.68724i) q^{17} -6.90897i q^{18} +(-2.15740 - 1.24558i) q^{19} +(-0.0355659 - 0.0205340i) q^{20} +(-1.12550 + 1.94943i) q^{22} +(-4.57029 - 7.91598i) q^{23} +(-7.05179 + 4.07135i) q^{24} +4.73068 q^{25} +(4.00680 + 2.98610i) q^{26} +5.60916 q^{27} +(2.61498 + 4.52928i) q^{29} +(-1.01622 + 1.76014i) q^{30} +5.79391i q^{31} +(0.387453 + 0.223696i) q^{32} +(-3.97463 - 2.29475i) q^{33} -2.70019i q^{34} +(-0.197245 - 0.341639i) q^{36} +(-8.85879 + 5.11463i) q^{37} +3.45262 q^{38} +(-6.08826 + 8.16934i) q^{39} +1.49542 q^{40} +(-3.64513 + 2.10452i) q^{41} +(-0.498655 + 0.863697i) q^{43} +0.128529i q^{44} +(-2.24041 - 1.29350i) q^{45} +(10.9712 + 6.33421i) q^{46} +4.51725i q^{47} +(5.41908 - 9.38612i) q^{48} +(-5.67810 + 3.27825i) q^{50} +5.50532 q^{51} +(0.283381 + 0.0332676i) q^{52} -8.89651 q^{53} +(-6.73251 + 3.88701i) q^{54} +(0.421434 + 0.729946i) q^{55} +7.03944i q^{57} +(-6.27736 - 3.62424i) q^{58} +(5.37392 + 3.10263i) q^{59} +0.116049i q^{60} +(-6.73536 + 11.6660i) q^{61} +(-4.01504 - 6.95426i) q^{62} -8.29100 q^{64} +(1.71847 - 0.740247i) q^{65} +6.36084 q^{66} +(-7.25094 + 4.18633i) q^{67} +(-0.0770880 - 0.133520i) q^{68} +(-12.9146 + 22.3688i) q^{69} +(-4.50168 - 2.59905i) q^{71} +(12.4402 + 7.18234i) q^{72} +11.8395i q^{73} +(7.08863 - 12.2779i) q^{74} +(-6.68392 - 11.5769i) q^{75} +(0.170727 - 0.0985694i) q^{76} +(1.64640 - 14.0244i) q^{78} +0.982310 q^{79} +(-1.72377 + 0.995221i) q^{80} +(-0.447609 - 0.775281i) q^{81} +(2.91676 - 5.05197i) q^{82} -8.91851i q^{83} +(-0.875603 - 0.505530i) q^{85} -1.38223i q^{86} +(7.38934 - 12.7987i) q^{87} +(-2.34008 - 4.05313i) q^{88} +(10.4087 - 6.00949i) q^{89} +3.58546 q^{90} +0.723345 q^{92} +(14.1788 - 8.18614i) q^{93} +(-3.13035 - 5.42193i) q^{94} +(0.646401 - 1.11960i) q^{95} -1.26423i q^{96} +(-3.82981 - 2.21114i) q^{97} +8.09643i 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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