LMFDB - Embedded newform 624.2.u.a.5.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(5,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2, 3]))

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

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

chi := DirichletCharacter("624.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.u (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 9 $ x^4 - 5*x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.2
Root			$-1.65831 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	624.5
Dual form			624.2.u.a.125.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.00000i) q^{2} +(1.65831 + 0.500000i) q^{3} -2.00000i q^{4} -1.00000i q^{5} +(-2.15831 + 1.15831i) q^{6} +(-0.158312 + 0.158312i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.50000 + 1.65831i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.00000i) q^{2} +(1.65831 + 0.500000i) q^{3} -2.00000i q^{4} -1.00000i q^{5} +(-2.15831 + 1.15831i) q^{6} +(-0.158312 + 0.158312i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.50000 + 1.65831i) q^{9} +(1.00000 + 1.00000i) q^{10} +4.31662 q^{11} +(1.00000 - 3.31662i) q^{12} +(-3.00000 - 2.00000i) q^{13} -0.316625i q^{14} +(0.500000 - 1.65831i) q^{15} -4.00000 q^{16} +1.31662 q^{17} +(-4.15831 + 0.841688i) q^{18} -4.31662i q^{19} -2.00000 q^{20} +(-0.341688 + 0.183375i) q^{21} +(-4.31662 + 4.31662i) q^{22} +4.00000i q^{23} +(2.31662 + 4.31662i) q^{24} +4.00000 q^{25} +(5.00000 - 1.00000i) q^{26} +(3.31662 + 4.00000i) q^{27} +(0.316625 + 0.316625i) q^{28} +(1.31662 + 1.31662i) q^{29} +(1.15831 + 2.15831i) q^{30} +(5.31662 - 5.31662i) q^{31} +(4.00000 - 4.00000i) q^{32} +(7.15831 + 2.15831i) q^{33} +(-1.31662 + 1.31662i) q^{34} +(0.158312 + 0.158312i) q^{35} +(3.31662 - 5.00000i) q^{36} +1.63325i q^{37} +(4.31662 + 4.31662i) q^{38} +(-3.97494 - 4.81662i) q^{39} +(2.00000 - 2.00000i) q^{40} +(0.316625 - 0.316625i) q^{41} +(0.158312 - 0.525063i) q^{42} +(2.47494 - 2.47494i) q^{43} -8.63325i q^{44} +(1.65831 - 2.50000i) q^{45} +(-4.00000 - 4.00000i) q^{46} +(-4.47494 + 4.47494i) q^{47} +(-6.63325 - 2.00000i) q^{48} +6.94987i q^{49} +(-4.00000 + 4.00000i) q^{50} +(2.18338 + 0.658312i) q^{51} +(-4.00000 + 6.00000i) q^{52} +(-0.316625 + 0.316625i) q^{53} +(-7.31662 - 0.683375i) q^{54} -4.31662i q^{55} -0.633250 q^{56} +(2.15831 - 7.15831i) q^{57} -2.63325 q^{58} +0.316625 q^{59} +(-3.31662 - 1.00000i) q^{60} +(-4.00000 + 4.00000i) q^{61} +10.6332i q^{62} +(-0.658312 + 0.133250i) q^{63} +8.00000i q^{64} +(-2.00000 + 3.00000i) q^{65} +(-9.31662 + 5.00000i) q^{66} -2.31662i q^{67} -2.63325i q^{68} +(-2.00000 + 6.63325i) q^{69} -0.316625 q^{70} +(-1.15831 + 1.15831i) q^{71} +(1.68338 + 8.31662i) q^{72} +(9.31662 - 9.31662i) q^{73} +(-1.63325 - 1.63325i) q^{74} +(6.63325 + 2.00000i) q^{75} -8.63325 q^{76} +(-0.683375 + 0.683375i) q^{77} +(8.79156 + 0.841688i) q^{78} -1.36675 q^{79} +4.00000i q^{80} +(3.50000 + 8.29156i) q^{81} +0.633250i q^{82} -12.6332 q^{83} +(0.366750 + 0.683375i) q^{84} -1.31662i q^{85} +4.94987i q^{86} +(1.52506 + 2.84169i) q^{87} +(8.63325 + 8.63325i) q^{88} +(-7.00000 - 7.00000i) q^{89} +(0.841688 + 4.15831i) q^{90} +(0.791562 - 0.158312i) q^{91} +8.00000 q^{92} +(11.4749 - 6.15831i) q^{93} -8.94987i q^{94} -4.31662 q^{95} +(8.63325 - 4.63325i) q^{96} +(-11.3166 + 11.3166i) q^{97} +(-6.94987 - 6.94987i) q^{98} +(10.7916 + 7.15831i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 2 q^{6} + 6 q^{7} + 8 q^{8} + 10 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 2 * q^6 + 6 * q^7 + 8 * q^8 + 10 * q^9	$ 4 q - 4 q^{2} - 2 q^{6} + 6 q^{7} + 8 q^{8} + 10 q^{9} + 4 q^{10} + 4 q^{11} + 4 q^{12} - 12 q^{13} + 2 q^{15} - 16 q^{16} - 8 q^{17} - 10 q^{18} - 8 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{24} + 16 q^{25} + 20 q^{26} - 12 q^{28} - 8 q^{29} - 2 q^{30} + 8 q^{31} + 16 q^{32} + 22 q^{33} + 8 q^{34} - 6 q^{35} + 4 q^{38} + 4 q^{39} + 8 q^{40} - 12 q^{41} - 6 q^{42} - 10 q^{43} - 16 q^{46} + 2 q^{47} - 16 q^{50} + 22 q^{51} - 16 q^{52} + 12 q^{53} - 16 q^{54} + 24 q^{56} + 2 q^{57} + 16 q^{58} - 12 q^{59} - 16 q^{61} + 4 q^{63} - 8 q^{65} - 24 q^{66} - 8 q^{69} + 12 q^{70} + 2 q^{71} + 20 q^{72} + 24 q^{73} + 20 q^{74} - 8 q^{76} - 16 q^{77} + 2 q^{78} - 32 q^{79} + 14 q^{81} - 24 q^{83} + 28 q^{84} + 26 q^{87} + 8 q^{88} - 28 q^{89} + 10 q^{90} - 30 q^{91} + 32 q^{92} + 26 q^{93} - 4 q^{95} + 8 q^{96} - 32 q^{97} + 12 q^{98} + 10 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 2 * q^6 + 6 * q^7 + 8 * q^8 + 10 * q^9 + 4 * q^10 + 4 * q^11 + 4 * q^12 - 12 * q^13 + 2 * q^15 - 16 * q^16 - 8 * q^17 - 10 * q^18 - 8 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^24 + 16 * q^25 + 20 * q^26 - 12 * q^28 - 8 * q^29 - 2 * q^30 + 8 * q^31 + 16 * q^32 + 22 * q^33 + 8 * q^34 - 6 * q^35 + 4 * q^38 + 4 * q^39 + 8 * q^40 - 12 * q^41 - 6 * q^42 - 10 * q^43 - 16 * q^46 + 2 * q^47 - 16 * q^50 + 22 * q^51 - 16 * q^52 + 12 * q^53 - 16 * q^54 + 24 * q^56 + 2 * q^57 + 16 * q^58 - 12 * q^59 - 16 * q^61 + 4 * q^63 - 8 * q^65 - 24 * q^66 - 8 * q^69 + 12 * q^70 + 2 * q^71 + 20 * q^72 + 24 * q^73 + 20 * q^74 - 8 * q^76 - 16 * q^77 + 2 * q^78 - 32 * q^79 + 14 * q^81 - 24 * q^83 + 28 * q^84 + 26 * q^87 + 8 * q^88 - 28 * q^89 + 10 * q^90 - 30 * q^91 + 32 * q^92 + 26 * q^93 - 4 * q^95 + 8 * q^96 - 32 * q^97 + 12 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$2$	−1.00000	+	1.00000i	−0.707107	+	0.707107i
$3$	1.65831	+	0.500000i	0.957427	+	0.288675i
$3$	1.65831	+	0.500000i	0.957427	+	0.288675i
$4$		−	2.00000i		−	1.00000i
$5$		−	1.00000i		−	0.447214i	−0.974679	−	0.223607i	$-0.928217\pi$
$5$		−	1.00000i		−	0.447214i	0.974679	−	0.223607i	$-0.0717831\pi$
$6$	−2.15831	+	1.15831i	−0.881127	+	0.472879i
$7$	−0.158312	+	0.158312i	−0.0598365	+	0.0598365i	−0.736392	−	0.676555i	$-0.763472\pi$
$7$	−0.158312	+	0.158312i	−0.0598365	+	0.0598365i	0.676555	+	0.736392i	$0.263472\pi$
$8$	2.00000	+	2.00000i	0.707107	+	0.707107i
$9$	2.50000	+	1.65831i	0.833333	+	0.552771i
$10$	1.00000	+	1.00000i	0.316228	+	0.316228i
$11$	4.31662			1.30151			0.650756	−	0.759287i	$-0.274452\pi$
$11$	4.31662			1.30151			0.650756	+	0.759287i	$0.274452\pi$
$12$	1.00000	−	3.31662i	0.288675	−	0.957427i
$13$	−3.00000	−	2.00000i	−0.832050	−	0.554700i
$13$	−3.00000	−	2.00000i	−0.832050	−	0.554700i
$14$		−	0.316625i		−	0.0846215i
$15$	0.500000	−	1.65831i	0.129099	−	0.428174i
$16$	−4.00000			−1.00000
$17$	1.31662			0.319328			0.159664	−	0.987171i	$-0.448959\pi$
$17$	1.31662			0.319328			0.159664	+	0.987171i	$0.448959\pi$
$18$	−4.15831	+	0.841688i	−0.980124	+	0.198388i
$19$		−	4.31662i		−	0.990302i	−0.868807	−	0.495151i	$-0.835113\pi$
$19$		−	4.31662i		−	0.990302i	0.868807	−	0.495151i	$-0.164887\pi$
$20$	−2.00000			−0.447214
$21$	−0.341688	+	0.183375i	−0.0745623	+	0.0400158i
$22$	−4.31662	+	4.31662i	−0.920307	+	0.920307i
$23$			4.00000i			0.834058i	0.908893	+	0.417029i	$0.136929\pi$
$23$			4.00000i			0.834058i	−0.908893	+	0.417029i	$0.863071\pi$
$24$	2.31662	+	4.31662i	0.472879	+	0.881127i
$25$	4.00000			0.800000
$26$	5.00000	−	1.00000i	0.980581	−	0.196116i
$27$	3.31662	+	4.00000i	0.638285	+	0.769800i
$28$	0.316625	+	0.316625i	0.0598365	+	0.0598365i
$29$	1.31662	+	1.31662i	0.244491	+	0.244491i	0.818705	−	0.574214i	$-0.194692\pi$
$29$	1.31662	+	1.31662i	0.244491	+	0.244491i	−0.574214	+	0.818705i	$0.694692\pi$
$30$	1.15831	+	2.15831i	0.211478	+	0.394052i
$31$	5.31662	−	5.31662i	0.954894	−	0.954894i	−0.0441317	−	0.999026i	$-0.514052\pi$
$31$	5.31662	−	5.31662i	0.954894	−	0.954894i	0.999026	+	0.0441317i	$0.0140521\pi$
$32$	4.00000	−	4.00000i	0.707107	−	0.707107i
$33$	7.15831	+	2.15831i	1.24610	+	0.375714i
$34$	−1.31662	+	1.31662i	−0.225799	+	0.225799i
$35$	0.158312	+	0.158312i	0.0267597	+	0.0267597i
$36$	3.31662	−	5.00000i	0.552771	−	0.833333i
$37$			1.63325i			0.268505i	0.990947	+	0.134252i	$0.0428633\pi$
$37$			1.63325i			0.268505i	−0.990947	+	0.134252i	$0.957137\pi$
$38$	4.31662	+	4.31662i	0.700249	+	0.700249i
$39$	−3.97494	−	4.81662i	−0.636499	−	0.771277i
$40$	2.00000	−	2.00000i	0.316228	−	0.316228i
$41$	0.316625	−	0.316625i	0.0494485	−	0.0494485i	−0.681950	−	0.731399i	$-0.738868\pi$
$41$	0.316625	−	0.316625i	0.0494485	−	0.0494485i	0.731399	+	0.681950i	$0.238868\pi$
$42$	0.158312	−	0.525063i	0.0244281	−	0.0810190i
$43$	2.47494	−	2.47494i	0.377424	−	0.377424i	−0.492748	−	0.870172i	$-0.664007\pi$
$43$	2.47494	−	2.47494i	0.377424	−	0.377424i	0.870172	+	0.492748i	$0.164007\pi$
$44$		−	8.63325i		−	1.30151i
$45$	1.65831	−	2.50000i	0.247207	−	0.372678i
$46$	−4.00000	−	4.00000i	−0.589768	−	0.589768i
$47$	−4.47494	+	4.47494i	−0.652737	+	0.652737i	−0.953651	−	0.300914i	$-0.902708\pi$
$47$	−4.47494	+	4.47494i	−0.652737	+	0.652737i	0.300914	+	0.953651i	$0.402708\pi$
$48$	−6.63325	−	2.00000i	−0.957427	−	0.288675i
$49$			6.94987i			0.992839i
$50$	−4.00000	+	4.00000i	−0.565685	+	0.565685i
$51$	2.18338	+	0.658312i	0.305734	+	0.0921822i
$52$	−4.00000	+	6.00000i	−0.554700	+	0.832050i
$53$	−0.316625	+	0.316625i	−0.0434918	+	0.0434918i	−0.728518	−	0.685026i	$-0.759791\pi$
$53$	−0.316625	+	0.316625i	−0.0434918	+	0.0434918i	0.685026	+	0.728518i	$0.259791\pi$
$54$	−7.31662	−	0.683375i	−0.995667	−	0.0929956i
$55$		−	4.31662i		−	0.582054i
$56$	−0.633250			−0.0846215
$57$	2.15831	−	7.15831i	0.285875	−	0.948142i
$58$	−2.63325			−0.345763
$59$	0.316625			0.0412210			0.0206105	−	0.999788i	$-0.493439\pi$
$59$	0.316625			0.0412210			0.0206105	+	0.999788i	$0.493439\pi$
$60$	−3.31662	−	1.00000i	−0.428174	−	0.129099i
$61$	−4.00000	+	4.00000i	−0.512148	+	0.512148i	−0.915184	−	0.403036i	$-0.867955\pi$
$61$	−4.00000	+	4.00000i	−0.512148	+	0.512148i	0.403036	+	0.915184i	$0.367955\pi$
$62$			10.6332i			1.35042i
$63$	−0.658312	+	0.133250i	−0.0829396	+	0.0167879i
$64$			8.00000i			1.00000i
$65$	−2.00000	+	3.00000i	−0.248069	+	0.372104i
$66$	−9.31662	+	5.00000i	−1.14680	+	0.615457i
$67$		−	2.31662i		−	0.283021i	−0.989937	−	0.141510i	$-0.954804\pi$
$67$		−	2.31662i		−	0.283021i	0.989937	−	0.141510i	$-0.0451959\pi$
$68$		−	2.63325i		−	0.319328i
$69$	−2.00000	+	6.63325i	−0.240772	+	0.798549i
$70$	−0.316625			−0.0378439
$71$	−1.15831	+	1.15831i	−0.137466	+	0.137466i	−0.772491	−	0.635025i	$-0.780990\pi$
$71$	−1.15831	+	1.15831i	−0.137466	+	0.137466i	0.635025	+	0.772491i	$0.280990\pi$
$72$	1.68338	+	8.31662i	0.198388	+	0.980124i
$73$	9.31662	−	9.31662i	1.09043	−	1.09043i	0.0949460	−	0.995482i	$-0.469732\pi$
$73$	9.31662	−	9.31662i	1.09043	−	1.09043i	0.995482	−	0.0949460i	$-0.0302679\pi$
$74$	−1.63325	−	1.63325i	−0.189861	−	0.189861i
$75$	6.63325	+	2.00000i	0.765942	+	0.230940i
$76$	−8.63325			−0.990302
$77$	−0.683375	+	0.683375i	−0.0778778	+	0.0778778i
$78$	8.79156	+	0.841688i	0.995448	+	0.0953024i
$79$	−1.36675			−0.153771			−0.0768857	−	0.997040i	$-0.524498\pi$
$79$	−1.36675			−0.153771			−0.0768857	+	0.997040i	$0.524498\pi$
$80$			4.00000i			0.447214i
$81$	3.50000	+	8.29156i	0.388889	+	0.921285i
$82$			0.633250i			0.0699307i
$83$	−12.6332			−1.38668			−0.693340	−	0.720611i	$-0.743861\pi$
$83$	−12.6332			−1.38668			−0.693340	+	0.720611i	$0.743861\pi$
$84$	0.366750	+	0.683375i	0.0400158	+	0.0745623i
$85$		−	1.31662i		−	0.142808i
$86$			4.94987i			0.533759i
$87$	1.52506	+	2.84169i	0.163504	+	0.304661i
$88$	8.63325	+	8.63325i	0.920307	+	0.920307i
$89$	−7.00000	−	7.00000i	−0.741999	−	0.741999i	0.230964	−	0.972962i	$-0.425812\pi$
$89$	−7.00000	−	7.00000i	−0.741999	−	0.741999i	−0.972962	+	0.230964i	$0.925812\pi$
$90$	0.841688	+	4.15831i	0.0887217	+	0.438325i
$91$	0.791562	−	0.158312i	0.0829782	−	0.0165956i
$92$	8.00000			0.834058
$93$	11.4749	−	6.15831i	1.18990	−	0.638587i
$94$		−	8.94987i		−	0.923109i
$95$	−4.31662			−0.442876
$96$	8.63325	−	4.63325i	0.881127	−	0.472879i
$97$	−11.3166	+	11.3166i	−1.14903	+	1.14903i	−0.162285	+	0.986744i	$0.551886\pi$
$97$	−11.3166	+	11.3166i	−1.14903	+	1.14903i	−0.986744	+	0.162285i	$0.948114\pi$
$98$	−6.94987	−	6.94987i	−0.702043	−	0.702043i
$99$	10.7916	+	7.15831i	1.08459	+	0.719437i
$100$		−	8.00000i		−	0.800000i
$101$	12.6332	+	12.6332i	1.25706	+	1.25706i	0.952492	+	0.304563i	$0.0985105\pi$
$101$	12.6332	+	12.6332i	1.25706	+	1.25706i	0.304563	+	0.952492i	$0.401490\pi$
$102$	−2.84169	+	1.52506i	−0.281369	+	0.151004i
$103$	−12.6332			−1.24479			−0.622396	−	0.782703i	$-0.713840\pi$
$103$	−12.6332			−1.24479			−0.622396	+	0.782703i	$0.713840\pi$
$104$	−2.00000	−	10.0000i	−0.196116	−	0.980581i
$105$	0.183375	+	0.341688i	0.0178956	+	0.0333453i
$106$		−	0.633250i		−	0.0615066i
$107$	−3.63325	+	3.63325i	−0.351239	+	0.351239i	−0.860571	−	0.509331i	$-0.829893\pi$
$107$	−3.63325	+	3.63325i	−0.351239	+	0.351239i	0.509331	+	0.860571i	$0.329893\pi$
$108$	8.00000	−	6.63325i	0.769800	−	0.638285i
$109$		−	13.6332i		−	1.30583i	−0.757432	−	0.652914i	$-0.773546\pi$
$109$		−	13.6332i		−	1.30583i	0.757432	−	0.652914i	$-0.226454\pi$
$110$	4.31662	+	4.31662i	0.411574	+	0.411574i
$111$	−0.816625	+	2.70844i	−0.0775106	+	0.257074i
$112$	0.633250	−	0.633250i	0.0598365	−	0.0598365i
$113$			13.2665i			1.24801i	0.781421	+	0.624004i	$0.214495\pi$
$113$			13.2665i			1.24801i	−0.781421	+	0.624004i	$0.785505\pi$
$114$	5.00000	+	9.31662i	0.468293	+	0.872582i
$115$	4.00000			0.373002
$116$	2.63325	−	2.63325i	0.244491	−	0.244491i
$117$	−4.18338	−	9.97494i	−0.386753	−	0.922183i
$118$	−0.316625	+	0.316625i	−0.0291477	+	0.0291477i
$119$	−0.208438	+	0.208438i	−0.0191075	+	0.0191075i
$120$	4.31662	−	2.31662i	0.394052	−	0.211478i
$121$	7.63325			0.693932
$122$		−	8.00000i		−	0.724286i
$123$	0.683375	−	0.366750i	0.0616179	−	0.0330688i
$124$	−10.6332	−	10.6332i	−0.954894	−	0.954894i
$125$		−	9.00000i		−	0.804984i
$126$	0.525063	−	0.791562i	0.0467763	−	0.0705179i
$127$		−	8.00000i		−	0.709885i	−0.934888	−	0.354943i	$-0.884500\pi$
$127$		−	8.00000i		−	0.709885i	0.934888	−	0.354943i	$-0.115500\pi$
$128$	−8.00000	−	8.00000i	−0.707107	−	0.707107i
$129$	5.34169	−	2.86675i	0.470309	−	0.252403i
$130$	−1.00000	−	5.00000i	−0.0877058	−	0.438529i
$131$	−5.47494	−	5.47494i	−0.478347	−	0.478347i	0.426255	−	0.904603i	$-0.359832\pi$
$131$	−5.47494	−	5.47494i	−0.478347	−	0.478347i	−0.904603	+	0.426255i	$0.859832\pi$
$132$	4.31662	−	14.3166i	0.375714	−	1.24610i
$133$	0.683375	+	0.683375i	0.0592561	+	0.0592561i
$134$	2.31662	+	2.31662i	0.200126	+	0.200126i
$135$	4.00000	−	3.31662i	0.344265	−	0.285450i
$136$	2.63325	+	2.63325i	0.225799	+	0.225799i
$137$	−4.31662	−	4.31662i	−0.368794	−	0.368794i	0.498243	−	0.867037i	$-0.333979\pi$
$137$	−4.31662	−	4.31662i	−0.368794	−	0.368794i	−0.867037	+	0.498243i	$0.833979\pi$
$138$	−4.63325	−	8.63325i	−0.394408	−	0.734911i
$139$	−13.7916	−	13.7916i	−1.16979	−	1.16979i	−0.982260	−	0.187525i	$-0.939953\pi$
$139$	−13.7916	−	13.7916i	−1.16979	−	1.16979i	−0.187525	−	0.982260i	$-0.560047\pi$
$140$	0.316625	−	0.316625i	0.0267597	−	0.0267597i
$141$	−9.65831	+	5.18338i	−0.813377	+	0.436519i
$142$		−	2.31662i		−	0.194407i
$143$	−12.9499	−	8.63325i	−1.08292	−	0.721949i
$144$	−10.0000	−	6.63325i	−0.833333	−	0.552771i
$145$	1.31662	−	1.31662i	0.109340	−	0.109340i
$146$			18.6332i			1.54210i
$147$	−3.47494	+	11.5251i	−0.286608	+	0.950571i
$148$	3.26650			0.268505
$149$			10.0000i			0.819232i	0.912258	+	0.409616i	$0.134337\pi$
$149$			10.0000i			0.819232i	−0.912258	+	0.409616i	$0.865663\pi$
$150$	−8.63325	+	4.63325i	−0.704902	+	0.378303i
$151$	1.15831	−	1.15831i	0.0942621	−	0.0942621i	−0.658403	−	0.752665i	$-0.728768\pi$
$151$	1.15831	−	1.15831i	0.0942621	−	0.0942621i	0.752665	+	0.658403i	$0.228768\pi$
$152$	8.63325	−	8.63325i	0.700249	−	0.700249i
$153$	3.29156	+	2.18338i	0.266107	+	0.176515i
$154$		−	1.36675i		−	0.110136i
$155$	−5.31662	−	5.31662i	−0.427042	−	0.427042i
$156$	−9.63325	+	7.94987i	−0.771277	+	0.636499i
$157$	−12.2665	+	12.2665i	−0.978973	+	0.978973i	−0.999783	−	0.0208102i	$-0.993375\pi$
$157$	−12.2665	+	12.2665i	−0.978973	+	0.978973i	0.0208102	+	0.999783i	$0.493375\pi$
$158$	1.36675	−	1.36675i	0.108733	−	0.108733i
$159$	−0.683375	+	0.366750i	−0.0541952	+	0.0290852i
$160$	−4.00000	−	4.00000i	−0.316228	−	0.316228i
$161$	−0.633250	−	0.633250i	−0.0499071	−	0.0499071i
$162$	−11.7916	−	4.79156i	−0.926433	−	0.376461i
$163$	−14.6332			−1.14616			−0.573082	−	0.819498i	$-0.694252\pi$
$163$	−14.6332			−1.14616			−0.573082	+	0.819498i	$0.694252\pi$
$164$	−0.633250	−	0.633250i	−0.0494485	−	0.0494485i
$165$	2.15831	−	7.15831i	0.168024	−	0.557274i
$166$	12.6332	−	12.6332i	0.980530	−	0.980530i
$167$	−13.6332	−	13.6332i	−1.05497	−	1.05497i	−0.998398	−	0.0565741i	$-0.981982\pi$
$167$	−13.6332	−	13.6332i	−1.05497	−	1.05497i	−0.0565741	−	0.998398i	$-0.518018\pi$
$168$	−1.05013	−	0.316625i	−0.0810190	−	0.0244281i
$169$	5.00000	+	12.0000i	0.384615	+	0.923077i
$170$	1.31662	+	1.31662i	0.100981	+	0.100981i
$171$	7.15831	−	10.7916i	0.547410	−	0.825251i
$172$	−4.94987	−	4.94987i	−0.377424	−	0.377424i
$173$	17.5831	−	17.5831i	1.33682	−	1.33682i	0.437698	−	0.899122i	$-0.355794\pi$
$173$	17.5831	−	17.5831i	1.33682	−	1.33682i	0.899122	−	0.437698i	$-0.144206\pi$
$174$	−4.36675	−	1.31662i	−0.331042	−	0.0998131i
$175$	−0.633250	+	0.633250i	−0.0478692	+	0.0478692i
$176$	−17.2665			−1.30151
$177$	0.525063	+	0.158312i	0.0394661	+	0.0118995i
$178$	14.0000			1.04934
$179$	5.52506	−	5.52506i	0.412963	−	0.412963i	−0.469807	−	0.882769i	$-0.655676\pi$
$179$	5.52506	−	5.52506i	0.412963	−	0.412963i	0.882769	+	0.469807i	$0.155676\pi$
$180$	−5.00000	−	3.31662i	−0.372678	−	0.247207i
$181$	12.6332	−	12.6332i	0.939022	−	0.939022i	−0.0592227	−	0.998245i	$-0.518862\pi$
$181$	12.6332	−	12.6332i	0.939022	−	0.939022i	0.998245	+	0.0592227i	$0.0188622\pi$
$182$	−0.633250	+	0.949874i	−0.0469396	+	0.0704094i
$183$	−8.63325	+	4.63325i	−0.638188	+	0.342500i
$184$	−8.00000	+	8.00000i	−0.589768	+	0.589768i
$185$	1.63325			0.120079
$186$	−5.31662	+	17.6332i	−0.389834	+	1.29293i
$187$	5.68338			0.415610
$188$	8.94987	+	8.94987i	0.652737	+	0.652737i
$189$	−1.15831	−	0.108187i	−0.0842548	−	0.00786943i
$190$	4.31662	−	4.31662i	0.313161	−	0.313161i
$191$		−	5.68338i		−	0.411235i	−0.978632	−	0.205617i	$-0.934080\pi$
$191$		−	5.68338i		−	0.411235i	0.978632	−	0.205617i	$-0.0659202\pi$
$192$	−4.00000	+	13.2665i	−0.288675	+	0.957427i
$193$	16.9499	+	16.9499i	1.22008	+	1.22008i	0.967603	+	0.252475i	$0.0812447\pi$
$193$	16.9499	+	16.9499i	1.22008	+	1.22008i	0.252475	+	0.967603i	$0.418755\pi$
$194$		−	22.6332i		−	1.62497i
$195$	−4.81662	+	3.97494i	−0.344926	+	0.284651i
$196$	13.8997			0.992839
$197$			2.68338i			0.191183i	0.995421	+	0.0955913i	$0.0304742\pi$
$197$			2.68338i			0.191183i	−0.995421	+	0.0955913i	$0.969526\pi$
$198$	−17.9499	+	3.63325i	−1.27564	+	0.258204i
$199$	−21.5831			−1.52999			−0.764994	−	0.644038i	$-0.777258\pi$
$199$	−21.5831			−1.52999			−0.764994	+	0.644038i	$0.777258\pi$
$200$	8.00000	+	8.00000i	0.565685	+	0.565685i
$201$	1.15831	−	3.84169i	0.0817011	−	0.270972i
$202$	−25.2665			−1.77774
$203$	−0.416876			−0.0292590
$204$	1.31662	−	4.36675i	0.0921822	−	0.305734i
$205$	−0.316625	−	0.316625i	−0.0221140	−	0.0221140i
$206$	12.6332	−	12.6332i	0.880200	−	0.880200i
$207$	−6.63325	+	10.0000i	−0.461043	+	0.695048i
$208$	12.0000	+	8.00000i	0.832050	+	0.554700i
$209$		−	18.6332i		−	1.28889i
$210$	−0.525063	−	0.158312i	−0.0362328	−	0.0109246i
$211$	8.15831	−	8.15831i	0.561641	−	0.561641i	−0.368132	−	0.929773i	$-0.620003\pi$
$211$	8.15831	−	8.15831i	0.561641	−	0.561641i	0.929773	+	0.368132i	$0.120003\pi$
$212$	0.633250	+	0.633250i	0.0434918	+	0.0434918i
$213$	−2.50000	+	1.34169i	−0.171297	+	0.0919309i
$214$		−	7.26650i		−	0.496728i
$215$	−2.47494	−	2.47494i	−0.168789	−	0.168789i
$216$	−1.36675	+	14.6332i	−0.0929956	+	0.995667i
$217$			1.68338i			0.114275i
$218$	13.6332	+	13.6332i	0.923360	+	0.923360i
$219$	20.1082	−	10.7916i	1.35879	−	0.729226i
$220$	−8.63325			−0.582054
$221$	−3.94987	−	2.63325i	−0.265697	−	0.177132i
$222$	−1.89181	−	3.52506i	−0.126970	−	0.236587i
$223$	−7.15831	+	7.15831i	−0.479356	+	0.479356i	−0.904926	−	0.425570i	$-0.860074\pi$
$223$	−7.15831	+	7.15831i	−0.479356	+	0.479356i	0.425570	+	0.904926i	$0.360074\pi$
$224$			1.26650i			0.0846215i
$225$	10.0000	+	6.63325i	0.666667	+	0.442217i
$226$	−13.2665	−	13.2665i	−0.882474	−	0.882474i
$227$	−10.6332			−0.705754			−0.352877	−	0.935670i	$-0.614797\pi$
$227$	−10.6332			−0.705754			−0.352877	+	0.935670i	$0.614797\pi$
$228$	−14.3166	−	4.31662i	−0.948142	−	0.285875i
$229$		−	6.58312i		−	0.435025i	−0.976058	−	0.217513i	$-0.930206\pi$
$229$		−	6.58312i		−	0.435025i	0.976058	−	0.217513i	$-0.0697943\pi$
$230$	−4.00000	+	4.00000i	−0.263752	+	0.263752i
$231$	−1.47494	+	0.791562i	−0.0970437	+	0.0520810i
$232$			5.26650i			0.345763i
$233$			23.5330i			1.54170i	0.637018	+	0.770849i	$0.280168\pi$
$233$			23.5330i			1.54170i	−0.637018	+	0.770849i	$0.719832\pi$
$234$	14.1583	+	5.79156i	0.925558	+	0.378606i
$235$	4.47494	+	4.47494i	0.291913	+	0.291913i
$236$		−	0.633250i		−	0.0412210i
$237$	−2.26650	−	0.683375i	−0.147225	−	0.0443900i
$238$		−	0.416876i		−	0.0270221i
$239$	−15.1583	−	15.1583i	−0.980510	−	0.980510i	0.0193039	−	0.999814i	$-0.493855\pi$
$239$	−15.1583	−	15.1583i	−0.980510	−	0.980510i	−0.999814	+	0.0193039i	$0.993855\pi$
$240$	−2.00000	+	6.63325i	−0.129099	+	0.428174i
$241$	1.00000	+	1.00000i	0.0644157	+	0.0644157i	0.738581	−	0.674165i	$-0.235496\pi$
$241$	1.00000	+	1.00000i	0.0644157	+	0.0644157i	−0.674165	+	0.738581i	$0.735496\pi$
$242$	−7.63325	+	7.63325i	−0.490684	+	0.490684i
$243$	1.65831	+	15.5000i	0.106381	+	0.994325i
$244$	8.00000	+	8.00000i	0.512148	+	0.512148i
$245$	6.94987			0.444011
$246$	−0.316625	+	1.05013i	−0.0201873	+	0.0669536i
$247$	−8.63325	+	12.9499i	−0.549321	+	0.823981i
$248$	21.2665			1.35042
$249$	−20.9499	−	6.31662i	−1.32764	−	0.400300i
$250$	9.00000	+	9.00000i	0.569210	+	0.569210i
$251$	11.9499	+	11.9499i	0.754269	+	0.754269i	0.975273	−	0.221004i	$-0.0709333\pi$
$251$	11.9499	+	11.9499i	0.754269	+	0.754269i	−0.221004	+	0.975273i	$0.570933\pi$
$252$	0.266499	+	1.31662i	0.0167879	+	0.0829396i
$253$			17.2665i			1.08554i
$254$	8.00000	+	8.00000i	0.501965	+	0.501965i
$255$	0.658312	−	2.18338i	0.0412251	−	0.136728i
$256$	16.0000			1.00000
$257$	−24.5831			−1.53345			−0.766727	−	0.641974i	$-0.778116\pi$
$257$	−24.5831			−1.53345			−0.766727	+	0.641974i	$0.778116\pi$
$258$	−2.47494	+	8.20844i	−0.154083	+	0.511035i
$259$	−0.258564	−	0.258564i	−0.0160664	−	0.0160664i
$260$	6.00000	+	4.00000i	0.372104	+	0.248069i
$261$	1.10819	+	5.47494i	0.0685950	+	0.338890i
$262$	10.9499			0.676485
$263$	−4.63325			−0.285698			−0.142849	−	0.989744i	$-0.545626\pi$
$263$	−4.63325			−0.285698			−0.142849	+	0.989744i	$0.545626\pi$
$264$	10.0000	+	18.6332i	0.615457	+	1.14680i
$265$	0.316625	+	0.316625i	0.0194501	+	0.0194501i
$266$	−1.36675			−0.0838008
$267$	−8.10819	−	15.1082i	−0.496213	−	0.924606i
$268$	−4.63325			−0.283021
$269$	−8.00000	−	8.00000i	−0.487769	−	0.487769i	0.419833	−	0.907601i	$-0.362089\pi$
$269$	−8.00000	−	8.00000i	−0.487769	−	0.487769i	−0.907601	+	0.419833i	$0.862089\pi$
$270$	−0.683375	+	7.31662i	−0.0415889	+	0.445276i
$271$	8.84169	+	8.84169i	0.537094	+	0.537094i	0.922674	−	0.385580i	$-0.125999\pi$
$271$	8.84169	+	8.84169i	0.537094	+	0.537094i	−0.385580	+	0.922674i	$0.625999\pi$
$272$	−5.26650			−0.319328
$273$	1.39181	+	0.133250i	0.0842364	+	0.00806463i
$274$	8.63325			0.521554
$275$	17.2665			1.04121
$276$	13.2665	+	4.00000i	0.798549	+	0.240772i
$277$	1.36675	−	1.36675i	0.0821201	−	0.0821201i	−0.664854	−	0.746974i	$-0.731506\pi$
$277$	1.36675	−	1.36675i	0.0821201	−	0.0821201i	0.746974	+	0.664854i	$0.231506\pi$
$278$	27.5831			1.65433
$279$	22.1082	−	4.47494i	1.32358	−	0.267907i
$280$			0.633250i			0.0378439i
$281$	2.36675	+	2.36675i	0.141188	+	0.141188i	0.774168	−	0.632980i	$-0.218168\pi$
$281$	2.36675	+	2.36675i	0.141188	+	0.141188i	−0.632980	+	0.774168i	$0.718168\pi$
$282$	4.47494	−	14.8417i	0.266479	−	0.883810i
$283$	11.0000	−	11.0000i	0.653882	−	0.653882i	−0.300043	−	0.953926i	$-0.597001\pi$
$283$	11.0000	−	11.0000i	0.653882	−	0.653882i	0.953926	+	0.300043i	$0.0970012\pi$
$284$	2.31662	+	2.31662i	0.137466	+	0.137466i
$285$	−7.15831	−	2.15831i	−0.424022	−	0.127847i
$286$	21.5831	−	4.31662i	1.27624	−	0.255247i
$287$			0.100251i			0.00591764i
$288$	16.6332	−	3.36675i	0.980124	−	0.198388i
$289$	−15.2665			−0.898029
$290$			2.63325i			0.154630i
$291$	−24.4248	+	13.1082i	−1.43181	+	0.768416i
$292$	−18.6332	−	18.6332i	−1.09043	−	1.09043i
$293$	−22.5831			−1.31932			−0.659660	−	0.751564i	$-0.729300\pi$
$293$	−22.5831			−1.31932			−0.659660	+	0.751564i	$0.729300\pi$
$294$	−8.05013	−	15.0000i	−0.469493	−	0.874818i
$295$		−	0.316625i		−	0.0184346i
$296$	−3.26650	+	3.26650i	−0.189861	+	0.189861i
$297$	14.3166	+	17.2665i	0.830735	+	1.00190i
$298$	−10.0000	−	10.0000i	−0.579284	−	0.579284i
$299$	8.00000	−	12.0000i	0.462652	−	0.693978i
$300$	4.00000	−	13.2665i	0.230940	−	0.765942i
$301$			0.783626i			0.0451675i
$302$			2.31662i			0.133307i
$303$	14.6332	+	27.2665i	0.840658	+	1.56642i
$304$			17.2665i			0.990302i
$305$	4.00000	+	4.00000i	0.229039	+	0.229039i
$306$	−5.47494	+	1.10819i	−0.312981	+	0.0633508i
$307$	24.9499			1.42396			0.711982	−	0.702197i	$-0.247798\pi$
$307$	24.9499			1.42396			0.711982	+	0.702197i	$0.247798\pi$
$308$	1.36675	+	1.36675i	0.0778778	+	0.0778778i
$309$	−20.9499	−	6.31662i	−1.19180	−	0.359340i
$310$	10.6332			0.603928
$311$			24.3166i			1.37887i	0.724348	+	0.689435i	$0.242141\pi$
$311$			24.3166i			1.37887i	−0.724348	+	0.689435i	$0.757859\pi$
$312$	1.68338	−	17.5831i	0.0953024	−	0.995448i
$313$			31.2164i			1.76445i	0.470825	+	0.882227i	$0.343956\pi$
$313$			31.2164i			1.76445i	−0.470825	+	0.882227i	$0.656044\pi$
$314$		−	24.5330i		−	1.38448i
$315$	0.133250	+	0.658312i	0.00750776	+	0.0370917i
$316$			2.73350i			0.153771i
$317$	16.6332			0.934216			0.467108	−	0.884200i	$-0.345296\pi$
$317$	16.6332			0.934216			0.467108	+	0.884200i	$0.345296\pi$
$318$	0.316625	−	1.05013i	0.0177554	−	0.0588881i
$319$	5.68338	+	5.68338i	0.318208	+	0.318208i
$320$	8.00000			0.447214
$321$	−7.84169	+	4.20844i	−0.437680	+	0.234892i
$322$	1.26650			0.0705792
$323$		−	5.68338i		−	0.316231i
$324$	16.5831	−	7.00000i	0.921285	−	0.388889i
$325$	−12.0000	−	8.00000i	−0.665640	−	0.443760i
$326$	14.6332	−	14.6332i	0.810461	−	0.810461i
$327$	6.81662	−	22.6082i	0.376960	−	1.25024i
$328$	1.26650			0.0699307
$329$		−	1.41688i		−	0.0781149i
$330$	5.00000	+	9.31662i	0.275241	+	0.512863i
$331$		0			0			−	1.00000i	$-0.5\pi$
$331$		0			0				1.00000i	$0.5\pi$
$332$			25.2665i			1.38668i
$333$	−2.70844	+	4.08312i	−0.148421	+	0.223754i
$334$	27.2665			1.49196
$335$	−2.31662			−0.126571
$336$	1.36675	−	0.733501i	0.0745623	−	0.0400158i
$337$			9.94987i			0.542004i	0.962579	+	0.271002i	$0.0873550\pi$
$337$			9.94987i			0.542004i	−0.962579	+	0.271002i	$0.912645\pi$
$338$	−17.0000	−	7.00000i	−0.924678	−	0.380750i
$339$	−6.63325	+	22.0000i	−0.360269	+	1.19488i
$340$	−2.63325			−0.142808
$341$	22.9499	−	22.9499i	1.24281	−	1.24281i
$342$	3.63325	+	17.9499i	0.196464	+	0.970618i
$343$	−2.20844	−	2.20844i	−0.119244	−	0.119244i
$344$	9.89975			0.533759
$345$	6.63325	+	2.00000i	0.357122	+	0.107676i
$346$			35.1662i			1.89055i
$347$	−13.5251	+	13.5251i	−0.726063	+	0.726063i	−0.969833	−	0.243770i	$-0.921616\pi$
$347$	−13.5251	+	13.5251i	−0.726063	+	0.726063i	0.243770	+	0.969833i	$0.421616\pi$
$348$	5.68338	−	3.05013i	0.304661	−	0.163504i
$349$	−3.31662			−0.177535			−0.0887674	−	0.996052i	$-0.528293\pi$
$349$	−3.31662			−0.177535			−0.0887674	+	0.996052i	$0.528293\pi$
$350$		−	1.26650i		−	0.0676972i
$351$	−1.94987	−	18.6332i	−0.104077	−	0.994569i
$352$	17.2665	−	17.2665i	0.920307	−	0.920307i
$353$	−18.3166	−	18.3166i	−0.974896	−	0.974896i	0.0247969	−	0.999693i	$-0.492106\pi$
$353$	−18.3166	−	18.3166i	−0.974896	−	0.974896i	−0.999693	+	0.0247969i	$0.992106\pi$
$354$	−0.683375	+	0.366750i	−0.0363210	+	0.0194926i
$355$	1.15831	+	1.15831i	0.0614768	+	0.0614768i
$356$	−14.0000	+	14.0000i	−0.741999	+	0.741999i
$357$	−0.449874	+	0.241436i	−0.0238099	+	0.0127782i
$358$			11.0501i			0.584017i
$359$	21.6332	+	21.6332i	1.14176	+	1.14176i	0.988128	+	0.153631i	$0.0490967\pi$
$359$	21.6332	+	21.6332i	1.14176	+	1.14176i	0.153631	+	0.988128i	$0.450903\pi$
$360$	8.31662	−	1.68338i	0.438325	−	0.0887217i
$361$	0.366750			0.0193027
$362$			25.2665i			1.32798i
$363$	12.6583	+	3.81662i	0.664389	+	0.200321i
$364$	−0.316625	−	1.58312i	−0.0165956	−	0.0829782i
$365$	−9.31662	−	9.31662i	−0.487654	−	0.487654i
$366$	4.00000	−	13.2665i	0.209083	−	0.693451i
$367$	−6.31662			−0.329725			−0.164863	−	0.986317i	$-0.552718\pi$
$367$	−6.31662			−0.329725			−0.164863	+	0.986317i	$0.552718\pi$
$368$		−	16.0000i		−	0.834058i
$369$	1.31662	−	0.266499i	0.0685407	−	0.0138734i
$370$	−1.63325	+	1.63325i	−0.0849086	+	0.0849086i
$371$		−	0.100251i		−	0.00520479i
$372$	−12.3166	−	22.9499i	−0.638587	−	1.18990i
$373$	2.94987	+	2.94987i	0.152739	+	0.152739i	0.779340	−	0.626601i	$-0.215555\pi$
$373$	2.94987	+	2.94987i	0.152739	+	0.152739i	−0.626601	+	0.779340i	$0.715555\pi$
$374$	−5.68338	+	5.68338i	−0.293880	+	0.293880i
$375$	4.50000	−	14.9248i	0.232379	−	0.770714i
$376$	−17.8997			−0.923109
$377$	−1.31662	−	6.58312i	−0.0678096	−	0.339048i
$378$	1.26650	−	1.05013i	0.0651417	−	0.0540126i
$379$	−7.36675			−0.378405			−0.189202	−	0.981938i	$-0.560590\pi$
$379$	−7.36675			−0.378405			−0.189202	+	0.981938i	$0.560590\pi$
$380$			8.63325i			0.442876i
$381$	4.00000	−	13.2665i	0.204926	−	0.679663i
$382$	5.68338	+	5.68338i	0.290787	+	0.290787i
$383$	25.4248	+	25.4248i	1.29915	+	1.29915i	0.928955	+	0.370192i	$0.120708\pi$
$383$	25.4248	+	25.4248i	1.29915	+	1.29915i	0.370192	+	0.928955i	$0.379292\pi$
$384$	−9.26650	−	17.2665i	−0.472879	−	0.881127i
$385$	0.683375	+	0.683375i	0.0348280	+	0.0348280i
$386$	−33.8997			−1.72545
$387$	10.2916	−	2.08312i	0.523149	−	0.105891i
$388$	22.6332	+	22.6332i	1.14903	+	1.14903i
$389$	3.00000	+	3.00000i	0.152106	+	0.152106i	0.779058	−	0.626952i	$-0.215698\pi$
$389$	3.00000	+	3.00000i	0.152106	+	0.152106i	−0.626952	+	0.779058i	$0.715698\pi$
$390$	0.841688	−	8.79156i	0.0426205	−	0.445178i
$391$			5.26650i			0.266338i
$392$	−13.8997	+	13.8997i	−0.702043	+	0.702043i
$393$	−6.34169	−	11.8166i	−0.319896	−	0.596070i
$394$	−2.68338	−	2.68338i	−0.135186	−	0.135186i
$395$			1.36675i			0.0687687i
$396$	14.3166	−	21.5831i	0.719437	−	1.08459i
$397$	13.3668			0.670858			0.335429	−	0.942065i	$-0.391119\pi$
$397$	13.3668			0.670858			0.335429	+	0.942065i	$0.391119\pi$
$398$	21.5831	−	21.5831i	1.08186	−	1.08186i
$399$	0.791562	+	1.47494i	0.0396277	+	0.0738392i
$400$	−16.0000			−0.800000
$401$	−16.0000	+	16.0000i	−0.799002	+	0.799002i	−0.982938	−	0.183936i	$-0.941116\pi$
$401$	−16.0000	+	16.0000i	−0.799002	+	0.799002i	0.183936	+	0.982938i	$0.441116\pi$
$402$	2.68338	+	5.00000i	0.133835	+	0.249377i
$403$	−26.5831	+	5.31662i	−1.32420	+	0.264840i
$404$	25.2665	−	25.2665i	1.25706	−	1.25706i
$405$	8.29156	−	3.50000i	0.412011	−	0.173916i
$406$	0.416876	−	0.416876i	0.0206892	−	0.0206892i
$407$			7.05013i			0.349462i
$408$	3.05013	+	5.68338i	0.151004	+	0.281369i
$409$	2.00000	+	2.00000i	0.0988936	+	0.0988936i	0.754823	−	0.655929i	$-0.227723\pi$
$409$	2.00000	+	2.00000i	0.0988936	+	0.0988936i	−0.655929	+	0.754823i	$0.727723\pi$
$410$	0.633250			0.0312740
$411$	−5.00000	−	9.31662i	−0.246632	−	0.459555i
$412$			25.2665i			1.24479i
$413$	−0.0501256	+	0.0501256i	−0.00246652	+	0.00246652i
$414$	−3.36675	−	16.6332i	−0.165467	−	0.817480i
$415$			12.6332i			0.620142i
$416$	−20.0000	+	4.00000i	−0.980581	+	0.196116i
$417$	−15.9749	−	29.7665i	−0.782296	−	1.45767i
$418$	18.6332	+	18.6332i	0.911382	+	0.911382i
$419$	−4.47494	−	4.47494i	−0.218615	−	0.218615i	0.589300	−	0.807915i	$-0.299404\pi$
$419$	−4.47494	−	4.47494i	−0.218615	−	0.218615i	−0.807915	+	0.589300i	$0.799404\pi$
$420$	0.683375	−	0.366750i	0.0333453	−	0.0178956i
$421$	19.3166			0.941435			0.470717	−	0.882284i	$-0.343995\pi$
$421$	19.3166			0.941435			0.470717	+	0.882284i	$0.343995\pi$
$422$			16.3166i			0.794281i
$423$	−18.6082	+	3.76650i	−0.904761	+	0.183133i
$424$	−1.26650			−0.0615066
$425$	5.26650			0.255463
$426$	1.15831	−	3.84169i	0.0561204	−	0.186130i
$427$		−	1.26650i		−	0.0612902i
$428$	7.26650	+	7.26650i	0.351239	+	0.351239i
$429$	−17.1583	−	20.7916i	−0.828411	−	1.00383i
$430$	4.94987			0.238704
$431$	22.7414	+	22.7414i	1.09542	+	1.09542i	0.994939	+	0.100477i	$0.0320369\pi$
$431$	22.7414	+	22.7414i	1.09542	+	1.09542i	0.100477	+	0.994939i	$0.467963\pi$
$432$	−13.2665	−	16.0000i	−0.638285	−	0.769800i
$433$			10.5831i			0.508592i	0.967126	+	0.254296i	$0.0818438\pi$
$433$			10.5831i			0.508592i	−0.967126	+	0.254296i	$0.918156\pi$
$434$	−1.68338	−	1.68338i	−0.0808046	−	0.0808046i
$435$	2.84169	−	1.52506i	0.136248	−	0.0731212i
$436$	−27.2665			−1.30583
$437$	17.2665			0.825969
$438$	−9.31662	+	30.8997i	−0.445166	+	1.47645i
$439$	−34.3166			−1.63784			−0.818922	−	0.573905i	$-0.805428\pi$
$439$	−34.3166			−1.63784			−0.818922	+	0.573905i	$0.805428\pi$
$440$	8.63325	−	8.63325i	0.411574	−	0.411574i
$441$	−11.5251	+	17.3747i	−0.548813	+	0.827366i
$442$	6.58312	−	1.31662i	0.313127	−	0.0626255i
$443$	2.52506	−	2.52506i	0.119969	−	0.119969i	−0.644573	−	0.764543i	$-0.722965\pi$
$443$	2.52506	−	2.52506i	0.119969	−	0.119969i	0.764543	+	0.644573i	$0.222965\pi$
$444$	5.41688	+	1.63325i	0.257074	+	0.0775106i
$445$	−7.00000	+	7.00000i	−0.331832	+	0.331832i
$446$		−	14.3166i		−	0.677912i
$447$	−5.00000	+	16.5831i	−0.236492	+	0.784355i
$448$	−1.26650	−	1.26650i	−0.0598365	−	0.0598365i
$449$	−24.2665	+	24.2665i	−1.14521	+	1.14521i	−0.157724	+	0.987483i	$0.550416\pi$
$449$	−24.2665	+	24.2665i	−1.14521	+	1.14521i	−0.987483	+	0.157724i	$0.949584\pi$
$450$	−16.6332	+	3.36675i	−0.784099	+	0.158710i
$451$	1.36675	−	1.36675i	0.0643578	−	0.0643578i
$452$	26.5330			1.24801
$453$	2.50000	−	1.34169i	0.117460	−	0.0630380i
$454$	10.6332	−	10.6332i	0.499043	−	0.499043i
$455$	−0.158312	−	0.791562i	−0.00742180	−	0.0371090i
$456$	18.6332	−	10.0000i	0.872582	−	0.468293i
$457$	−20.8997	−	20.8997i	−0.977649	−	0.977649i	0.0221066	−	0.999756i	$-0.492963\pi$
$457$	−20.8997	−	20.8997i	−0.977649	−	0.977649i	−0.999756	+	0.0221066i	$0.992963\pi$
$458$	6.58312	+	6.58312i	0.307609	+	0.307609i
$459$	4.36675	+	5.26650i	0.203822	+	0.245819i
$460$		−	8.00000i		−	0.373002i
$461$	−32.4829			−1.51288			−0.756439	−	0.654064i	$-0.773063\pi$
$461$	−32.4829			−1.51288			−0.756439	+	0.654064i	$0.773063\pi$
$462$	0.683375	−	2.26650i	0.0317935	−	0.105447i
$463$	−2.36675	−	2.36675i	−0.109992	−	0.109992i	0.649969	−	0.759961i	$-0.274782\pi$
$463$	−2.36675	−	2.36675i	−0.109992	−	0.109992i	−0.759961	+	0.649969i	$0.774782\pi$
$464$	−5.26650	−	5.26650i	−0.244491	−	0.244491i
$465$	−6.15831	−	11.4749i	−0.285585	−	0.532137i
$466$	−23.5330	−	23.5330i	−1.09015	−	1.09015i
$467$	23.6332	−	23.6332i	1.09362	−	1.09362i	0.0984770	−	0.995139i	$-0.468603\pi$
$467$	23.6332	−	23.6332i	1.09362	−	1.09362i	0.995139	−	0.0984770i	$-0.0313971\pi$
$468$	−19.9499	+	8.36675i	−0.922183	+	0.386753i
$469$	0.366750	+	0.366750i	0.0169350	+	0.0169350i
$470$	−8.94987			−0.412827
$471$	−26.4749	+	14.2084i	−1.21990	+	0.654690i
$472$	0.633250	+	0.633250i	0.0291477	+	0.0291477i
$473$	10.6834	−	10.6834i	0.491222	−	0.491222i
$474$	2.94987	−	1.58312i	0.135492	−	0.0727153i
$475$		−	17.2665i		−	0.792241i
$476$	0.416876	+	0.416876i	0.0191075	+	0.0191075i
$477$	−1.31662	+	0.266499i	−0.0602841	+	0.0122022i
$478$	30.3166			1.38665
$479$	8.79156	−	8.79156i	0.401697	−	0.401697i	−0.477134	−	0.878831i	$-0.658324\pi$
$479$	8.79156	−	8.79156i	0.401697	−	0.401697i	0.878831	+	0.477134i	$0.158324\pi$
$480$	−4.63325	−	8.63325i	−0.211478	−	0.394052i
$481$	3.26650	−	4.89975i	0.148940	−	0.223409i
$482$	−2.00000			−0.0910975
$483$	−0.733501	−	1.36675i	−0.0333754	−	0.0621893i
$484$		−	15.2665i		−	0.693932i
$485$	11.3166	+	11.3166i	0.513861	+	0.513861i
$486$	−17.1583	−	13.8417i	−0.778317	−	0.627872i
$487$	−3.63325	−	3.63325i	−0.164638	−	0.164638i	0.619980	−	0.784618i	$-0.287141\pi$
$487$	−3.63325	−	3.63325i	−0.164638	−	0.164638i	−0.784618	+	0.619980i	$0.787141\pi$
$488$	−16.0000			−0.724286
$489$	−24.2665	−	7.31662i	−1.09737	−	0.330869i
$490$	−6.94987	+	6.94987i	−0.313963	+	0.313963i
$491$	−17.4749	−	17.4749i	−0.788633	−	0.788633i	0.192637	−	0.981270i	$-0.438296\pi$
$491$	−17.4749	−	17.4749i	−0.788633	−	0.788633i	−0.981270	+	0.192637i	$0.938296\pi$
$492$	−0.733501	−	1.36675i	−0.0330688	−	0.0616179i
$493$	1.73350	+	1.73350i	0.0780730	+	0.0780730i
$494$	−4.31662	−	21.5831i	−0.194214	−	0.971071i
$495$	7.15831	−	10.7916i	0.321742	−	0.485045i
$496$	−21.2665	+	21.2665i	−0.954894	+	0.954894i
$497$		−	0.366750i		−	0.0164510i
$498$	27.2665	−	14.6332i	1.22184	−	0.655732i
$499$		−	27.2665i		−	1.22062i	−0.792164	−	0.610308i	$-0.791046\pi$
$499$		−	27.2665i		−	1.22062i	0.792164	−	0.610308i	$-0.208954\pi$
$500$	−18.0000			−0.804984
$501$	−15.7916	−	29.4248i	−0.705515	−	1.31460i
$502$	−23.8997			−1.06670
$503$	−8.94987			−0.399055			−0.199528	−	0.979892i	$-0.563941\pi$
$503$	−8.94987			−0.399055			−0.199528	+	0.979892i	$0.563941\pi$
$504$	−1.58312	−	1.05013i	−0.0705179	−	0.0467763i
$505$	12.6332	−	12.6332i	0.562172	−	0.562172i
$506$	−17.2665	−	17.2665i	−0.767590	−	0.767590i
$507$	2.29156	+	22.3997i	0.101772	+	0.994808i
$508$	−16.0000			−0.709885
$509$	−6.00000			−0.265945			−0.132973	−	0.991120i	$-0.542452\pi$
$509$	−6.00000			−0.265945			−0.132973	+	0.991120i	$0.542452\pi$
$510$	1.52506	+	2.84169i	0.0675309	+	0.125832i
$511$			2.94987i			0.130495i
$512$	−16.0000	+	16.0000i	−0.707107	+	0.707107i
$513$	17.2665	−	14.3166i	0.762335	−	0.632094i
$514$	24.5831	−	24.5831i	1.08432	−	1.08432i
$515$			12.6332i			0.556687i
$516$	−5.73350	−	10.6834i	−0.252403	−	0.470309i
$517$	−19.3166	+	19.3166i	−0.849544	+	0.849544i
$518$	0.517127			0.0227213
$519$	37.9499	−	20.3668i	1.66581	−	0.894001i
$520$	−10.0000	+	2.00000i	−0.438529	+	0.0877058i
$521$	−10.2665			−0.449783			−0.224892	−	0.974384i	$-0.572203\pi$
$521$	−10.2665			−0.449783			−0.224892	+	0.974384i	$0.572203\pi$
$522$	−6.58312	−	4.36675i	−0.288136	−	0.191127i
$523$	5.00000	+	5.00000i	0.218635	+	0.218635i	0.807923	−	0.589288i	$-0.200592\pi$
$523$	5.00000	+	5.00000i	0.218635	+	0.218635i	−0.589288	+	0.807923i	$0.700592\pi$
$524$	−10.9499	+	10.9499i	−0.478347	+	0.478347i
$525$	−1.36675	+	0.733501i	−0.0596499	+	0.0320126i
$526$	4.63325	−	4.63325i	0.202019	−	0.202019i
$527$	7.00000	−	7.00000i	0.304925	−	0.304925i
$528$	−28.6332	−	8.63325i	−1.24610	−	0.375714i
$529$	7.00000			0.304348
$530$	−0.633250			−0.0275066
$531$	0.791562	+	0.525063i	0.0343509	+	0.0227858i
$532$	1.36675	−	1.36675i	0.0592561	−	0.0592561i
$533$	−1.58312	+	0.316625i	−0.0685727	+	0.0137145i
$534$	23.2164	+	7.00000i	1.00467	+	0.302920i
$535$	3.63325	+	3.63325i	0.157079	+	0.157079i
$536$	4.63325	−	4.63325i	0.200126	−	0.200126i
$537$	11.9248	−	6.39975i	0.514594	−	0.276170i
$538$	16.0000			0.689809
$539$			30.0000i			1.29219i
$540$	−6.63325	−	8.00000i	−0.285450	−	0.344265i
$541$	39.5330			1.69966			0.849828	−	0.527060i	$-0.176706\pi$
$541$	39.5330			1.69966			0.849828	+	0.527060i	$0.176706\pi$
$542$	−17.6834			−0.759566
$543$	27.2665	−	14.6332i	1.17012	−	0.627973i
$544$	5.26650	−	5.26650i	0.225799	−	0.225799i
$545$	−13.6332			−0.583984
$546$	−1.52506	+	1.25856i	−0.0652667	+	0.0538616i
$547$	8.74144	−	8.74144i	0.373757	−	0.373757i	−0.495087	−	0.868844i	$-0.664864\pi$
$547$	8.74144	−	8.74144i	0.373757	−	0.373757i	0.868844	+	0.495087i	$0.164864\pi$
$548$	−8.63325	+	8.63325i	−0.368794	+	0.368794i
$549$	−16.6332	+	3.36675i	−0.709890	+	0.143689i
$550$	−17.2665	+	17.2665i	−0.736246	+	0.736246i
$551$	5.68338	−	5.68338i	0.242120	−	0.242120i
$552$	−17.2665	+	9.26650i	−0.734911	+	0.394408i
$553$	0.216374	−	0.216374i	0.00920114	−	0.00920114i
$554$			2.73350i			0.116135i
$555$	2.70844	+	0.816625i	0.114967	+	0.0346638i
$556$	−27.5831	+	27.5831i	−1.16979	+	1.16979i
$557$			24.5831i			1.04162i	0.853673	+	0.520810i	$0.174370\pi$
$557$			24.5831i			1.04162i	−0.853673	+	0.520810i	$0.825630\pi$
$558$	−17.6332	+	26.5831i	−0.746475	+	1.12535i
$559$	−12.3747	+	2.47494i	−0.523393	+	0.104679i
$560$	−0.633250	−	0.633250i	−0.0267597	−	0.0267597i
$561$	9.42481	+	2.84169i	0.397916	+	0.119976i
$562$	−4.73350			−0.199671
$563$	12.4749	−	12.4749i	0.525756	−	0.525756i	−0.393548	−	0.919304i	$-0.628753\pi$
$563$	12.4749	−	12.4749i	0.525756	−	0.525756i	0.919304	+	0.393548i	$0.128753\pi$
$564$	10.3668	+	19.3166i	0.436519	+	0.813377i
$565$	13.2665			0.558126
$566$			22.0000i			0.924729i
$567$	−1.86675	−	0.758564i	−0.0783961	−	0.0318567i
$568$	−4.63325			−0.194407
$569$		−	30.5831i		−	1.28211i	−0.767494	−	0.641056i	$-0.778497\pi$
$569$		−	30.5831i		−	1.28211i	0.767494	−	0.641056i	$-0.221503\pi$
$570$	9.31662	−	5.00000i	0.390230	−	0.209427i
$571$	15.4749	−	15.4749i	0.647606	−	0.647606i	−0.304808	−	0.952414i	$-0.598592\pi$
$571$	15.4749	−	15.4749i	0.647606	−	0.647606i	0.952414	+	0.304808i	$0.0985923\pi$
$572$	−17.2665	+	25.8997i	−0.721949	+	1.08292i
$573$	2.84169	−	9.42481i	0.118713	−	0.393727i
$574$	−0.100251	−	0.100251i	−0.00418441	−	0.00418441i
$575$			16.0000i			0.667246i
$576$	−13.2665	+	20.0000i	−0.552771	+	0.833333i
$577$	20.2665	−	20.2665i	0.843705	−	0.843705i	−0.145633	−	0.989339i	$-0.546522\pi$
$577$	20.2665	−	20.2665i	0.843705	−	0.843705i	0.989339	+	0.145633i	$0.0465219\pi$
$578$	15.2665	−	15.2665i	0.635003	−	0.635003i
$579$	19.6332	+	36.5831i	0.815930	+	1.52034i
$580$	−2.63325	−	2.63325i	−0.109340	−	0.109340i
$581$	2.00000	−	2.00000i	0.0829740	−	0.0829740i
$582$	11.3166	−	37.5330i	0.469089	−	1.55579i
$583$	−1.36675	+	1.36675i	−0.0566050	+	0.0566050i
$584$	37.2665			1.54210
$585$	−9.97494	+	4.18338i	−0.412413	+	0.172961i
$586$	22.5831	−	22.5831i	0.932900	−	0.932900i
$587$		−	28.0000i		−	1.15568i	−0.816149	−	0.577842i	$-0.803895\pi$
$587$		−	28.0000i		−	1.15568i	0.816149	−	0.577842i	$-0.196105\pi$
$588$	23.0501	+	6.94987i	0.950571	+	0.286608i
$589$	−22.9499	−	22.9499i	−0.945633	−	0.945633i
$590$	0.316625	+	0.316625i	0.0130352	+	0.0130352i
$591$	−1.34169	+	4.44987i	−0.0551897	+	0.183043i
$592$		−	6.53300i		−	0.268505i
$593$	5.00000	−	5.00000i	0.205325	−	0.205325i	−0.596952	−	0.802277i	$-0.703622\pi$
$593$	5.00000	−	5.00000i	0.205325	−	0.205325i	0.802277	+	0.596952i	$0.203622\pi$
$594$	−31.5831	−	2.94987i	−1.29587	−	0.121035i
$595$	0.208438	+	0.208438i	0.00854513	+	0.00854513i
$596$	20.0000			0.819232
$597$	−35.7916	−	10.7916i	−1.46485	−	0.441669i
$598$	4.00000	+	20.0000i	0.163572	+	0.817861i
$599$	25.6834			1.04939			0.524697	−	0.851289i	$-0.324179\pi$
$599$	25.6834			1.04939			0.524697	+	0.851289i	$0.324179\pi$
$600$	9.26650	+	17.2665i	0.378303	+	0.704902i
$601$			3.63325i			0.148203i	0.997251	+	0.0741017i	$0.0236089\pi$
$601$			3.63325i			0.148203i	−0.997251	+	0.0741017i	$0.976391\pi$
$602$	−0.783626	−	0.783626i	−0.0319382	−	0.0319382i
$603$	3.84169	−	5.79156i	0.156446	−	0.235851i
$604$	−2.31662	−	2.31662i	−0.0942621	−	0.0942621i
$605$		−	7.63325i		−	0.310336i
$606$	−41.8997	−	12.6332i	−1.70206	−	0.513191i
$607$	46.8496			1.90157			0.950784	−	0.309855i	$-0.100281\pi$
$607$	46.8496			1.90157			0.950784	+	0.309855i	$0.100281\pi$
$608$	−17.2665	−	17.2665i	−0.700249	−	0.700249i
$609$	−0.691311	−	0.208438i	−0.0280133	−	0.00844633i
$610$	−8.00000			−0.323911
$611$	22.3747	−	4.47494i	0.905183	−	0.181037i
$612$	4.36675	−	6.58312i	0.176515	−	0.266107i
$613$	8.73350			0.352743			0.176371	−	0.984324i	$-0.443564\pi$
$613$	8.73350			0.352743			0.176371	+	0.984324i	$0.443564\pi$
$614$	−24.9499	+	24.9499i	−1.00689	+	1.00689i
$615$	−0.366750	−	0.683375i	−0.0147888	−	0.0275563i
$616$	−2.73350			−0.110136
$617$	−17.6834	+	17.6834i	−0.711906	+	0.711906i	−0.966934	−	0.255028i	$-0.917915\pi$
$617$	−17.6834	+	17.6834i	−0.711906	+	0.711906i	0.255028	+	0.966934i	$0.417915\pi$
$618$	27.2665	−	14.6332i	1.09682	−	0.588636i
$619$			37.2665i			1.49787i	0.662645	+	0.748934i	$0.269434\pi$
$619$			37.2665i			1.49787i	−0.662645	+	0.748934i	$0.730566\pi$
$620$	−10.6332	+	10.6332i	−0.427042	+	0.427042i
$621$	−16.0000	+	13.2665i	−0.642058	+	0.532366i
$622$	−24.3166	−	24.3166i	−0.975008	−	0.975008i
$623$	2.21637			0.0887971
$624$	15.8997	+	19.2665i	0.636499	+	0.771277i
$625$	11.0000			0.440000
$626$	−31.2164	−	31.2164i	−1.24766	−	1.24766i
$627$	9.31662	−	30.8997i	0.372070	−	1.23402i
$628$	24.5330	+	24.5330i	0.978973	+	0.978973i
$629$			2.15038i			0.0857411i
$630$	−0.791562	−	0.525063i	−0.0315366	−	0.0209190i
$631$	28.4248	−	28.4248i	1.13157	−	1.13157i	0.141658	−	0.989916i	$-0.454757\pi$
$631$	28.4248	−	28.4248i	1.13157	−	1.13157i	0.989916	−	0.141658i	$-0.0452434\pi$
$632$	−2.73350	−	2.73350i	−0.108733	−	0.108733i
$633$	17.6082	−	9.44987i	0.699863	−	0.375599i
$634$	−16.6332	+	16.6332i	−0.660591	+	0.660591i
$635$	−8.00000			−0.317470
$636$	0.733501	+	1.36675i	0.0290852	+	0.0541952i
$637$	13.8997	−	20.8496i	0.550728	−	0.826092i
$638$	−11.3668			−0.450014
$639$	−4.81662	+	0.974937i	−0.190543	+	0.0385679i
$640$	−8.00000	+	8.00000i	−0.316228	+	0.316228i
$641$	−9.26650			−0.366005			−0.183002	−	0.983112i	$-0.558582\pi$
$641$	−9.26650			−0.366005			−0.183002	+	0.983112i	$0.558582\pi$
$642$	3.63325	−	12.0501i	0.143393	−	0.475581i
$643$			44.8496i			1.76870i	0.466828	+	0.884348i	$0.345397\pi$
$643$			44.8496i			1.76870i	−0.466828	+	0.884348i	$0.654603\pi$
$644$	−1.26650	+	1.26650i	−0.0499071	+	0.0499071i
$645$	−2.86675	−	5.34169i	−0.112878	−	0.210329i
$646$	5.68338	+	5.68338i	0.223609	+	0.223609i
$647$		−	9.58312i		−	0.376751i	−0.982097	−	0.188376i	$-0.939678\pi$
$647$		−	9.58312i		−	0.376751i	0.982097	−	0.188376i	$-0.0603223\pi$
$648$	−9.58312	+	23.5831i	−0.376461	+	0.926433i
$649$	1.36675			0.0536496
$650$	20.0000	−	4.00000i	0.784465	−	0.156893i
$651$	−0.841688	+	2.79156i	−0.0329883	+	0.109410i
$652$			29.2665i			1.14616i
$653$	28.6332	+	28.6332i	1.12051	+	1.12051i	0.991665	+	0.128840i	$0.0411255\pi$
$653$	28.6332	+	28.6332i	1.12051	+	1.12051i	0.128840	+	0.991665i	$0.458875\pi$
$654$	15.7916	+	29.4248i	0.617499	+	1.15060i
$655$	−5.47494	+	5.47494i	−0.213923	+	0.213923i
$656$	−1.26650	+	1.26650i	−0.0494485	+	0.0494485i
$657$	38.7414	−	7.84169i	1.51145	−	0.305933i
$658$	1.41688	+	1.41688i	0.0552356	+	0.0552356i
$659$	14.2665	+	14.2665i	0.555744	+	0.555744i	0.928093	−	0.372349i	$-0.121448\pi$
$659$	14.2665	+	14.2665i	0.555744	+	0.555744i	−0.372349	+	0.928093i	$0.621448\pi$
$660$	−14.3166	−	4.31662i	−0.557274	−	0.168024i
$661$		−	6.63325i		−	0.258004i	−0.991644	−	0.129002i	$-0.958823\pi$
$661$		−	6.63325i		−	0.258004i	0.991644	−	0.129002i	$-0.0411773\pi$
$662$		0			0
$663$	−5.23350	−	6.34169i	−0.203252	−	0.246291i
$664$	−25.2665	−	25.2665i	−0.980530	−	0.980530i
$665$	0.683375	−	0.683375i	0.0265002	−	0.0265002i
$666$	−1.37469	−	6.79156i	−0.0532680	−	0.263168i
$667$	−5.26650	+	5.26650i	−0.203920	+	0.203920i
$668$	−27.2665	+	27.2665i	−1.05497	+	1.05497i
$669$	−15.4499	+	8.29156i	−0.597327	+	0.320570i
$670$	2.31662	−	2.31662i	0.0894990	−	0.0894990i
$671$	−17.2665	+	17.2665i	−0.666566	+	0.666566i
$672$	−0.633250	+	2.10025i	−0.0244281	+	0.0810190i
$673$		−	28.2665i		−	1.08959i	−0.838568	−	0.544797i	$-0.816607\pi$
$673$		−	28.2665i		−	1.08959i	0.838568	−	0.544797i	$-0.183393\pi$
$674$	−9.94987	−	9.94987i	−0.383255	−	0.383255i
$675$	13.2665	+	16.0000i	0.510628	+	0.615840i
$676$	24.0000	−	10.0000i	0.923077	−	0.384615i
$677$	10.0000	−	10.0000i	0.384331	−	0.384331i	−0.488329	−	0.872660i	$-0.662393\pi$
$677$	10.0000	−	10.0000i	0.384331	−	0.384331i	0.872660	+	0.488329i	$0.162393\pi$
$678$	−15.3668	−	28.6332i	−0.590156	−	1.09965i
$679$		−	3.58312i		−	0.137508i
$680$	2.63325	−	2.63325i	0.100981	−	0.100981i
$681$	−17.6332	−	5.31662i	−0.675708	−	0.203734i
$682$			45.8997i			1.75759i
$683$	−3.26650			−0.124989			−0.0624946	−	0.998045i	$-0.519906\pi$
$683$	−3.26650			−0.124989			−0.0624946	+	0.998045i	$0.519906\pi$
$684$	−21.5831	−	14.3166i	−0.825251	−	0.547410i
$685$	−4.31662	+	4.31662i	−0.164930	+	0.164930i
$686$	4.41688			0.168637
$687$	3.29156	−	10.9169i	0.125581	−	0.416505i
$688$	−9.89975	+	9.89975i	−0.377424	+	0.377424i
$689$	1.58312	−	0.316625i	0.0603122	−	0.0120624i
$690$	−8.63325	+	4.63325i	−0.328662	+	0.176385i
$691$		−	23.3668i		−	0.888913i	−0.895800	−	0.444457i	$-0.853397\pi$
$691$		−	23.3668i		−	0.888913i	0.895800	−	0.444457i	$-0.146603\pi$
$692$	−35.1662	−	35.1662i	−1.33682	−	1.33682i
$693$	−2.84169	+	0.575188i	−0.107947	+	0.0218496i
$694$		−	27.0501i		−	1.02681i
$695$	−13.7916	+	13.7916i	−0.523144	+	0.523144i
$696$	−2.63325	+	8.73350i	−0.0998131	+	0.331042i
$697$	0.416876	−	0.416876i	0.0157903	−	0.0157903i
$698$	3.31662	−	3.31662i	0.125536	−	0.125536i
$699$	−11.7665	+	39.0251i	−0.445050	+	1.47606i
$700$	1.26650	+	1.26650i	0.0478692	+	0.0478692i
$701$	−7.58312	+	7.58312i	−0.286411	+	0.286411i	−0.835659	−	0.549248i	$-0.814914\pi$
$701$	−7.58312	+	7.58312i	−0.286411	+	0.286411i	0.549248	+	0.835659i	$0.314914\pi$
$702$	20.5831	+	16.6834i	0.776860	+	0.629673i
$703$	7.05013			0.265901
$704$			34.5330i			1.30151i
$705$	5.18338	+	9.65831i	0.195217	+	0.363753i
$706$	36.6332			1.37871
$707$	−4.00000			−0.150435
$708$	0.316625	−	1.05013i	0.0118995	−	0.0394661i
$709$			7.26650i			0.272899i	0.990647	+	0.136450i	$0.0435692\pi$
$709$			7.26650i			0.272899i	−0.990647	+	0.136450i	$0.956431\pi$
$710$	−2.31662			−0.0869414
$711$	−3.41688	−	2.26650i	−0.128143	−	0.0850004i
$712$		−	28.0000i		−	1.04934i
$713$	21.2665	+	21.2665i	0.796437	+	0.796437i
$714$	0.208438	−	0.691311i	0.00780060	−	0.0258717i
$715$	−8.63325	+	12.9499i	−0.322865	+	0.484298i
$716$	−11.0501	−	11.0501i	−0.412963	−	0.412963i
$717$	−17.5581	−	32.7164i	−0.655718	−	1.22182i
$718$	−43.2665			−1.61469
$719$	−41.5831			−1.55079			−0.775394	−	0.631477i	$-0.782449\pi$
$719$	−41.5831			−1.55079			−0.775394	+	0.631477i	$0.782449\pi$
$720$	−6.63325	+	10.0000i	−0.247207	+	0.372678i
$721$	2.00000	−	2.00000i	0.0744839	−	0.0744839i
$722$	−0.366750	+	0.366750i	−0.0136490	+	0.0136490i
$723$	1.15831	+	2.15831i	0.0430781	+	0.0802685i
$724$	−25.2665	−	25.2665i	−0.939022	−	0.939022i
$725$	5.26650	+	5.26650i	0.195593	+	0.195593i
$726$	−16.4749	+	8.84169i	−0.611442	+	0.328146i
$727$	29.4829			1.09346			0.546730	−	0.837309i	$-0.315873\pi$
$727$	29.4829			1.09346			0.546730	+	0.837309i	$0.315873\pi$
$728$	1.89975	+	1.26650i	0.0704094	+	0.0469396i
$729$	−5.00000	+	26.5330i	−0.185185	+	0.982704i
$730$	18.6332			0.689648
$731$	3.25856	−	3.25856i	0.120522	−	0.120522i
$732$	9.26650	+	17.2665i	0.342500	+	0.638188i
$733$			21.2164i			0.783645i	0.920041	+	0.391822i	$0.128155\pi$
$733$			21.2164i			0.783645i	−0.920041	+	0.391822i	$0.871845\pi$
$734$	6.31662	−	6.31662i	0.233151	−	0.233151i
$735$	11.5251	+	3.47494i	0.425108	+	0.128175i
$736$	16.0000	+	16.0000i	0.589768	+	0.589768i
$737$		−	10.0000i		−	0.368355i
$738$	−1.05013	+	1.58312i	−0.0386557	+	0.0582756i
$739$	14.6332			0.538293			0.269146	−	0.963099i	$-0.413258\pi$
$739$	14.6332			0.538293			0.269146	+	0.963099i	$0.413258\pi$
$740$		−	3.26650i		−	0.120079i
$741$	−20.7916	+	17.1583i	−0.763797	+	0.630326i
$742$	0.100251	+	0.100251i	0.00368034	+	0.00368034i
$743$	28.0581	−	28.0581i	1.02935	−	1.02935i	0.0297944	−	0.999556i	$-0.490515\pi$
$743$	28.0581	−	28.0581i	1.02935	−	1.02935i	0.999556	−	0.0297944i	$-0.00948525\pi$
$744$	35.2665	+	10.6332i	1.29293	+	0.389834i
$745$	10.0000			0.366372
$746$	−5.89975			−0.216005
$747$	−31.5831	−	20.9499i	−1.15557	−	0.766516i
$748$		−	11.3668i		−	0.415610i
$749$		−	1.15038i		−	0.0420339i
$750$	10.4248	+	19.4248i	0.380660	+	0.709294i
$751$		−	45.8997i		−	1.67491i	−0.546510	−	0.837453i	$-0.684044\pi$
$751$		−	45.8997i		−	1.67491i	0.546510	−	0.837453i	$-0.315956\pi$
$752$	17.8997	−	17.8997i	0.652737	−	0.652737i
$753$	13.8417	+	25.7916i	0.504419	+	0.939897i
$754$	7.89975	+	5.26650i	0.287692	+	0.191795i
$755$	−1.15831	−	1.15831i	−0.0421553	−	0.0421553i
$756$	−0.216374	+	2.31662i	−0.00786943	+	0.0842548i
$757$	22.5330	+	22.5330i	0.818976	+	0.818976i	0.985960	−	0.166984i	$-0.0534028\pi$
$757$	22.5330	+	22.5330i	0.818976	+	0.818976i	−0.166984	+	0.985960i	$0.553403\pi$
$758$	7.36675	−	7.36675i	0.267572	−	0.267572i
$759$	−8.63325	+	28.6332i	−0.313367	+	1.03932i
$760$	−8.63325	−	8.63325i	−0.313161	−	0.313161i
$761$	−1.73350	−	1.73350i	−0.0628394	−	0.0628394i	0.674989	−	0.737828i	$-0.264148\pi$
$761$	−1.73350	−	1.73350i	−0.0628394	−	0.0628394i	−0.737828	+	0.674989i	$0.764148\pi$
$762$	9.26650	+	17.2665i	0.335690	+	0.625499i
$763$	2.15831	+	2.15831i	0.0781362	+	0.0781362i
$764$	−11.3668			−0.411235
$765$	2.18338	−	3.29156i	0.0789401	−	0.119007i
$766$	−50.8496			−1.83727
$767$	−0.949874	−	0.633250i	−0.0342980	−	0.0228653i
$768$	26.5330	+	8.00000i	0.957427	+	0.288675i
$769$	7.89975	−	7.89975i	0.284872	−	0.284872i	−0.550176	−	0.835049i	$-0.685439\pi$
$769$	7.89975	−	7.89975i	0.284872	−	0.284872i	0.835049	+	0.550176i	$0.185439\pi$
$770$	−1.36675			−0.0492543
$771$	−40.7665	−	12.2916i	−1.46817	−	0.442670i
$772$	33.8997	−	33.8997i	1.22008	−	1.22008i
$773$			44.1662i			1.58855i	0.607559	+	0.794275i	$0.292149\pi$
$773$			44.1662i			1.58855i	−0.607559	+	0.794275i	$0.707851\pi$
$774$	−8.20844	+	12.3747i	−0.295046	+	0.444799i
$775$	21.2665	−	21.2665i	0.763915	−	0.763915i
$776$	−45.2665			−1.62497
$777$	−0.299497	−	0.558061i	−0.0107444	−	0.0200203i
$778$	−6.00000			−0.215110
$779$	−1.36675	−	1.36675i	−0.0489689	−	0.0489689i
$780$	7.94987	+	9.63325i	0.284651	+	0.344926i
$781$	−5.00000	+	5.00000i	−0.178914	+	0.178914i
$782$	−5.26650	−	5.26650i	−0.188330	−	0.188330i
$783$	−0.899749	+	9.63325i	−0.0321544	+	0.344264i
$784$		−	27.7995i		−	0.992839i
$785$	12.2665	+	12.2665i	0.437810	+	0.437810i
$786$	18.1583	+	5.47494i	0.647686	+	0.195285i
$787$	−43.8997			−1.56486			−0.782429	−	0.622740i	$-0.786019\pi$
$787$	−43.8997			−1.56486			−0.782429	+	0.622740i	$0.786019\pi$
$788$	5.36675			0.191183
$789$	−7.68338	−	2.31662i	−0.273535	−	0.0824740i
$790$	−1.36675	−	1.36675i	−0.0486268	−	0.0486268i
$791$	−2.10025	−	2.10025i	−0.0746763	−	0.0746763i
$792$	7.26650	+	35.8997i	0.258204	+	1.27564i
$793$	20.0000	−	4.00000i	0.710221	−	0.142044i
$794$	−13.3668	+	13.3668i	−0.474368	+	0.474368i
$795$	0.366750	+	0.683375i	0.0130073	+	0.0242368i
$796$			43.1662i			1.52999i
$797$	26.5831	−	26.5831i	0.941623	−	0.941623i	−0.0567650	−	0.998388i	$-0.518079\pi$
$797$	26.5831	−	26.5831i	0.941623	−	0.941623i	0.998388	+	0.0567650i	$0.0180786\pi$
$798$	−2.26650	−	0.683375i	−0.0802332	−	0.0241912i
$799$	−5.89181	+	5.89181i	−0.208437	+	0.208437i
$800$	16.0000	−	16.0000i	0.565685	−	0.565685i
$801$	−5.89181	−	29.1082i	−0.208177	−	1.02849i
$802$		−	32.0000i		−	1.12996i
$803$	40.2164	−	40.2164i	1.41921	−	1.41921i
$804$	−7.68338	−	2.31662i	−0.270972	−	0.0817011i
$805$	−0.633250	+	0.633250i	−0.0223191	+	0.0223191i
$806$	21.2665	−	31.8997i	0.749080	−	1.12362i
$807$	−9.26650	−	17.2665i	−0.326196	−	0.607810i
$808$			50.5330i			1.77774i
$809$	−9.53300			−0.335162			−0.167581	−	0.985858i	$-0.553596\pi$
$809$	−9.53300			−0.335162			−0.167581	+	0.985858i	$0.553596\pi$
$810$	−4.79156	+	11.7916i	−0.168358	+	0.414313i
$811$	−37.2665			−1.30860			−0.654302	−	0.756233i	$-0.727037\pi$
$811$	−37.2665			−1.30860			−0.654302	+	0.756233i	$0.727037\pi$
$812$			0.833752i			0.0292590i
$813$	10.2414	+	19.0831i	0.359183	+	0.669274i
$814$	−7.05013	−	7.05013i	−0.247107	−	0.247107i
$815$			14.6332i			0.512580i
$816$	−8.73350	−	2.63325i	−0.305734	−	0.0921822i
$817$	−10.6834	−	10.6834i	−0.373764	−	0.373764i
$818$	−4.00000			−0.139857
$819$	2.24144	+	0.916876i	0.0783221	+	0.0320382i
$820$	−0.633250	+	0.633250i	−0.0221140	+	0.0221140i
$821$		−	15.6332i		−	0.545604i	−0.962070	−	0.272802i	$-0.912050\pi$
$821$		−	15.6332i		−	0.545604i	0.962070	−	0.272802i	$-0.0879504\pi$
$822$	14.3166	+	4.31662i	0.499350	+	0.150560i
$823$	−30.1161			−1.04978			−0.524891	−	0.851169i	$-0.675894\pi$
$823$	−30.1161			−1.04978			−0.524891	+	0.851169i	$0.675894\pi$
$824$	−25.2665	−	25.2665i	−0.880200	−	0.880200i
$825$	28.6332	+	8.63325i	0.996882	+	0.300571i
$826$		−	0.100251i		−	0.00348819i
$827$	0.416876			0.0144962			0.00724810	−	0.999974i	$-0.497693\pi$
$827$	0.416876			0.0144962			0.00724810	+	0.999974i	$0.497693\pi$
$828$	20.0000	+	13.2665i	0.695048	+	0.461043i
$829$	−21.3166	−	21.3166i	−0.740357	−	0.740357i	0.232290	−	0.972647i	$-0.425378\pi$
$829$	−21.3166	−	21.3166i	−0.740357	−	0.740357i	−0.972647	+	0.232290i	$0.925378\pi$
$830$	−12.6332	−	12.6332i	−0.438506	−	0.438506i
$831$	2.94987	−	1.58312i	0.102330	−	0.0549180i
$832$	16.0000	−	24.0000i	0.554700	−	0.832050i
$833$			9.15038i			0.317042i
$834$	45.7414	+	13.7916i	1.58390	+	0.477563i
$835$	−13.6332	+	13.6332i	−0.471798	+	0.471798i
$836$	−37.2665			−1.28889
$837$	38.8997	+	3.63325i	1.34457	+	0.125583i
$838$	8.94987			0.309168
$839$	37.5330	+	37.5330i	1.29578	+	1.29578i	0.931152	+	0.364631i	$0.118805\pi$
$839$	37.5330	+	37.5330i	1.29578	+	1.29578i	0.364631	+	0.931152i	$0.381195\pi$
$840$	−0.316625	+	1.05013i	−0.0109246	+	0.0362328i
$841$		−	25.5330i		−	0.880448i
$842$	−19.3166	+	19.3166i	−0.665695	+	0.665695i
$843$	2.74144	+	5.10819i	0.0944201	+	0.175935i
$844$	−16.3166	−	16.3166i	−0.561641	−	0.561641i
$845$	12.0000	−	5.00000i	0.412813	−	0.172005i
$846$	14.8417	−	22.3747i	0.510268	−	0.769258i
$847$	−1.20844	+	1.20844i	−0.0415224	+	0.0415224i
$848$	1.26650	−	1.26650i	0.0434918	−	0.0434918i
$849$	23.7414	−	12.7414i	0.814804	−	0.437285i
$850$	−5.26650	+	5.26650i	−0.180639	+	0.180639i
$851$	−6.53300			−0.223948
$852$	2.68338	+	5.00000i	0.0919309	+	0.171297i
$853$			4.68338i			0.160356i	0.996781	+	0.0801779i	$0.0255488\pi$
$853$			4.68338i			0.160356i	−0.996781	+	0.0801779i	$0.974451\pi$
$854$	1.26650	+	1.26650i	0.0433387	+	0.0433387i
$855$	−10.7916	−	7.15831i	−0.369064	−	0.244809i
$856$	−14.5330			−0.496728
$857$			2.00000i			0.0683187i	0.999416	+	0.0341593i	$0.0108754\pi$
$857$			2.00000i			0.0683187i	−0.999416	+	0.0341593i	$0.989125\pi$
$858$	37.9499	+	3.63325i	1.29559	+	0.124037i
$859$	14.2665	+	14.2665i	0.486767	+	0.486767i	0.907284	−	0.420518i	$-0.138152\pi$
$859$	14.2665	+	14.2665i	0.486767	+	0.486767i	−0.420518	+	0.907284i	$0.638152\pi$
$860$	−4.94987	+	4.94987i	−0.168789	+	0.168789i
$861$	−0.0501256	+	0.166248i	−0.00170828	+	0.00566571i
$862$	−45.4829			−1.54915
$863$	0.424812	+	0.424812i	0.0144608	+	0.0144608i	0.714300	−	0.699839i	$-0.246745\pi$
$863$	0.424812	+	0.424812i	0.0144608	+	0.0144608i	−0.699839	+	0.714300i	$0.746745\pi$
$864$	29.2665	+	2.73350i	0.995667	+	0.0929956i
$865$	−17.5831	−	17.5831i	−0.597844	−	0.597844i
$866$	−10.5831	−	10.5831i	−0.359629	−	0.359629i
$867$	−25.3166	−	7.63325i	−0.859798	−	0.259239i
$868$	3.36675			0.114275
$869$	−5.89975			−0.200135
$870$	−1.31662	+	4.36675i	−0.0446378	+	0.148047i
$871$	−4.63325	+	6.94987i	−0.156992	+	0.235488i
$872$	27.2665	−	27.2665i	0.923360	−	0.923360i
$873$	−47.0581	+	9.52506i	−1.59267	+	0.322375i
$874$	−17.2665	+	17.2665i	−0.584048	+	0.584048i
$875$	1.42481	+	1.42481i	0.0481674	+	0.0481674i
$876$	−21.5831	−	40.2164i	−0.729226	−	1.35879i
$877$			28.5831i			0.965184i	0.875845	+	0.482592i	$0.160305\pi$
$877$			28.5831i			0.965184i	−0.875845	+	0.482592i	$0.839695\pi$
$878$	34.3166	−	34.3166i	1.15813	−	1.15813i
$879$	−37.4499	−	11.2916i	−1.26315	−	0.380855i
$880$			17.2665i			0.582054i
$881$	20.4829			0.690086			0.345043	−	0.938587i	$-0.387864\pi$
$881$	20.4829			0.690086			0.345043	+	0.938587i	$0.387864\pi$
$882$	−5.84962	−	28.8997i	−0.196967	−	0.973105i
$883$	13.7414	+	13.7414i	0.462436	+	0.462436i	0.899453	−	0.437017i	$-0.143965\pi$
$883$	13.7414	+	13.7414i	0.462436	+	0.462436i	−0.437017	+	0.899453i	$0.643965\pi$
$884$	−5.26650	+	7.89975i	−0.177132	+	0.265697i
$885$	0.158312	−	0.525063i	0.00532161	−	0.0176498i
$886$			5.05013i			0.169662i
$887$	0.733501			0.0246285			0.0123143	−	0.999924i	$-0.496080\pi$
$887$	0.733501			0.0246285			0.0123143	+	0.999924i	$0.496080\pi$
$888$	−7.05013	+	3.78363i	−0.236587	+	0.126970i
$889$	1.26650	+	1.26650i	0.0424770	+	0.0424770i
$890$		−	14.0000i		−	0.469281i
$891$	15.1082	+	35.7916i	0.506143	+	1.19906i
$892$	14.3166	+	14.3166i	0.479356	+	0.479356i
$893$	19.3166	+	19.3166i	0.646406	+	0.646406i
$894$	−11.5831	−	21.5831i	−0.387398	−	0.721848i
$895$	−5.52506	−	5.52506i	−0.184682	−	0.184682i
$896$	2.53300			0.0846215
$897$	19.2665	−	15.8997i	0.643290	−	0.530877i
$898$		−	48.5330i		−	1.61957i
$899$	14.0000			0.466926
$900$	13.2665	−	20.0000i	0.442217	−	0.666667i
$901$	−0.416876	+	0.416876i	−0.0138882	+	0.0138882i
$902$			2.73350i			0.0910156i
$903$	−0.391813	+	1.29950i	−0.0130387	+	0.0432446i
$904$	−26.5330	+	26.5330i	−0.882474	+	0.882474i
$905$	−12.6332	−	12.6332i	−0.419943	−	0.419943i
$906$	−1.15831	+	3.84169i	−0.0384824	+	0.127632i
$907$	−38.0581	+	38.0581i	−1.26370	+	1.26370i	−0.314410	+	0.949287i	$0.601807\pi$
$907$	−38.0581	+	38.0581i	−1.26370	+	1.26370i	−0.949287	+	0.314410i	$0.898193\pi$
$908$			21.2665i			0.705754i
$909$	10.6332	+	52.5330i	0.352683	+	1.74241i
$910$	0.949874	+	0.633250i	0.0314880	+	0.0209920i
$911$		−	31.5831i		−	1.04640i	−0.852211	−	0.523198i	$-0.824739\pi$
$911$		−	31.5831i		−	1.04640i	0.852211	−	0.523198i	$-0.175261\pi$
$912$	−8.63325	+	28.6332i	−0.285875	+	0.948142i
$913$	−54.5330			−1.80478
$914$	41.7995			1.38260
$915$	4.63325	+	8.63325i	0.153171	+	0.285406i
$916$	−13.1662			−0.435025
$917$	1.73350			0.0572452
$918$	−9.63325	−	0.899749i	−0.317945	−	0.0296961i
$919$		−	37.3668i		−	1.23262i	−0.787505	−	0.616308i	$-0.788628\pi$
$919$		−	37.3668i		−	1.23262i	0.787505	−	0.616308i	$-0.211372\pi$
$920$	8.00000	+	8.00000i	0.263752	+	0.263752i
$921$	41.3747	+	12.4749i	1.36334	+	0.411063i
$922$	32.4829	−	32.4829i	1.06977	−	1.06977i
$923$	5.79156	−	1.15831i	0.190632	−	0.0381263i
$924$	1.58312	+	2.94987i	0.0520810	+	0.0970437i
$925$			6.53300i			0.214804i
$926$	4.73350			0.155552
$927$	−31.5831	−	20.9499i	−1.03733	−	0.688084i
$928$	10.5330			0.345763
$929$	−15.0501	−	15.0501i	−0.493779	−	0.493779i	0.415716	−	0.909495i	$-0.363531\pi$
$929$	−15.0501	−	15.0501i	−0.493779	−	0.493779i	−0.909495	+	0.415716i	$0.863531\pi$
$930$	17.6332	+	5.31662i	0.578217	+	0.174339i
$931$	30.0000			0.983210
$932$	47.0660			1.54170
$933$	−12.1583	+	40.3246i	−0.398045	+	1.32017i
$934$			47.2665i			1.54661i
$935$		−	5.68338i		−	0.185866i
$936$	11.5831	−	28.3166i	0.378606	−	0.925558i
$937$			41.1662i			1.34484i	0.740169	+	0.672421i	$0.234746\pi$
$937$			41.1662i			1.34484i	−0.740169	+	0.672421i	$0.765254\pi$
$938$	−0.733501			−0.0239497
$939$	−15.6082	+	51.7665i	−0.509354	+	1.68934i
$940$	8.94987	−	8.94987i	0.291913	−	0.291913i
$941$	−10.8997			−0.355322			−0.177661	−	0.984092i	$-0.556853\pi$
$941$	−10.8997			−0.355322			−0.177661	+	0.984092i	$0.556853\pi$
$942$	12.2665	−	40.6834i	0.399664	−	1.32554i
$943$	1.26650	+	1.26650i	0.0412429	+	0.0412429i
$944$	−1.26650			−0.0412210
$945$	−0.108187	+	1.15831i	−0.00351932	+	0.0376799i
$946$			21.3668i			0.694693i
$947$		−	56.7494i		−	1.84411i	−0.387063	−	0.922053i	$-0.626510\pi$
$947$		−	56.7494i		−	1.84411i	0.387063	−	0.922053i	$-0.373490\pi$
$948$	−1.36675	+	4.53300i	−0.0443900	+	0.147225i
$949$	−46.5831	+	9.31662i	−1.51215	+	0.302430i
$950$	17.2665	+	17.2665i	0.560199	+	0.560199i
$951$	27.5831	+	8.31662i	0.894444	+	0.269685i
$952$	−0.833752			−0.0270221
$953$		−	57.1161i		−	1.85017i	−0.379757	−	0.925086i	$-0.623992\pi$
$953$		−	57.1161i		−	1.85017i	0.379757	−	0.925086i	$-0.376008\pi$
$954$	1.05013	−	1.58312i	0.0339991	−	0.0512555i
$955$	−5.68338			−0.183910
$956$	−30.3166	+	30.3166i	−0.980510	+	0.980510i
$957$	6.58312	+	12.2665i	0.212802	+	0.396520i
$958$			17.5831i			0.568085i
$959$	1.36675			0.0441347
$960$	13.2665	+	4.00000i	0.428174	+	0.129099i
$961$		−	25.5330i		−	0.823645i
$962$	1.63325	+	8.16625i	0.0526581	+	0.263290i
$963$	−15.1082	+	3.05806i	−0.486855	+	0.0985446i
$964$	2.00000	−	2.00000i	0.0644157	−	0.0644157i
$965$	16.9499	−	16.9499i	0.545636	−	0.545636i
$966$	2.10025	+	0.633250i	0.0675745	+	0.0203745i
$967$	20.7916	+	20.7916i	0.668612	+	0.668612i	0.957395	−	0.288783i	$-0.0932506\pi$
$967$	20.7916	+	20.7916i	0.668612	+	0.668612i	−0.288783	+	0.957395i	$0.593251\pi$
$968$	15.2665	+	15.2665i	0.490684	+	0.490684i
$969$	2.84169	−	9.42481i	0.0912882	−	0.302769i
$970$	−22.6332			−0.726710
$971$	27.6913	−	27.6913i	0.888656	−	0.888656i	−0.105738	−	0.994394i	$-0.533720\pi$
$971$	27.6913	−	27.6913i	0.888656	−	0.888656i	0.994394	+	0.105738i	$0.0337204\pi$
$972$	31.0000	−	3.31662i	0.994325	−	0.106381i
$973$	4.36675			0.139992
$974$	7.26650			0.232834
$975$	−15.8997	−	19.2665i	−0.509199	−	0.617022i
$976$	16.0000	−	16.0000i	0.512148	−	0.512148i
$977$	26.3668	+	26.3668i	0.843547	+	0.843547i	0.989318	−	0.145771i	$-0.0465663\pi$
$977$	26.3668	+	26.3668i	0.843547	+	0.843547i	−0.145771	+	0.989318i	$0.546566\pi$
$978$	31.5831	−	16.9499i	1.00992	−	0.541997i
$979$	−30.2164	−	30.2164i	−0.965719	−	0.965719i
$980$		−	13.8997i		−	0.444011i
$981$	22.6082	−	34.0831i	0.721824	−	1.08819i
$982$	34.9499			1.11530
$983$	18.4248	+	18.4248i	0.587660	+	0.587660i	0.936997	−	0.349337i	$-0.113593\pi$
$983$	18.4248	+	18.4248i	0.587660	+	0.587660i	−0.349337	+	0.936997i	$0.613593\pi$
$984$	2.10025	+	0.633250i	0.0669536	+	0.0201873i
$985$	2.68338			0.0854994
$986$	−3.46700			−0.110412
$987$	0.708438	−	2.34962i	0.0225498	−	0.0747893i
$988$	25.8997	+	17.2665i	0.823981	+	0.549321i
$989$	9.89975	+	9.89975i	0.314794	+	0.314794i
$990$	3.63325	+	17.9499i	0.115472	+	0.570484i
$991$	−53.6834			−1.70531			−0.852654	−	0.522475i	$-0.825009\pi$
$991$	−53.6834			−1.70531			−0.852654	+	0.522475i	$0.825009\pi$
$992$		−	42.5330i		−	1.35042i
$993$		0			0
$994$	0.366750	+	0.366750i	0.0116326	+	0.0116326i
$995$			21.5831i			0.684231i
$996$	−12.6332	+	41.8997i	−0.400300	+	1.32764i
$997$	−9.94987	−	9.94987i	−0.315116	−	0.315116i	0.531772	−	0.846888i	$-0.321526\pi$
$997$	−9.94987	−	9.94987i	−0.315116	−	0.315116i	−0.846888	+	0.531772i	$0.821526\pi$
$998$	27.2665	+	27.2665i	0.863106	+	0.863106i
$999$	−6.53300	+	5.41688i	−0.206695	+	0.171382i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.u.a.5.2	✓	4
3.2	odd	2		624.2.u.b.5.1	yes	4
13.8	odd	4		624.2.bm.a.437.2	yes	4
16.13	even	4		624.2.bm.b.317.2	yes	4
39.8	even	4		624.2.bm.b.437.1	yes	4
48.29	odd	4		624.2.bm.a.317.2	yes	4
208.125	odd	4		624.2.u.b.125.2	yes	4
624.125	even	4	inner	624.2.u.a.125.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
624.2.u.a.5.2	✓	4	1.1	even	1	trivial
624.2.u.a.125.2	yes	4	624.125	even	4	inner
624.2.u.b.5.1	yes	4	3.2	odd	2
624.2.u.b.125.2	yes	4	208.125	odd	4
624.2.bm.a.317.2	yes	4	48.29	odd	4
624.2.bm.a.437.2	yes	4	13.8	odd	4
624.2.bm.b.317.2	yes	4	16.13	even	4
624.2.bm.b.437.1	yes	4	39.8	even	4

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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.65831 + 0.500000i) q^{3} -2.00000i q^{4} -1.00000i q^{5} +(-2.15831 + 1.15831i) q^{6} +(-0.158312 + 0.158312i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.50000 + 1.65831i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.00000i) q^{2} +(1.65831 + 0.500000i) q^{3} -2.00000i q^{4} -1.00000i q^{5} +(-2.15831 + 1.15831i) q^{6} +(-0.158312 + 0.158312i) q^{7} +(2.00000 + 2.00000i) q^{8} +(2.50000 + 1.65831i) q^{9} +(1.00000 + 1.00000i) q^{10} +4.31662 q^{11} +(1.00000 - 3.31662i) q^{12} +(-3.00000 - 2.00000i) q^{13} -0.316625i q^{14} +(0.500000 - 1.65831i) q^{15} -4.00000 q^{16} +1.31662 q^{17} +(-4.15831 + 0.841688i) q^{18} -4.31662i q^{19} -2.00000 q^{20} +(-0.341688 + 0.183375i) q^{21} +(-4.31662 + 4.31662i) q^{22} +4.00000i q^{23} +(2.31662 + 4.31662i) q^{24} +4.00000 q^{25} +(5.00000 - 1.00000i) q^{26} +(3.31662 + 4.00000i) q^{27} +(0.316625 + 0.316625i) q^{28} +(1.31662 + 1.31662i) q^{29} +(1.15831 + 2.15831i) q^{30} +(5.31662 - 5.31662i) q^{31} +(4.00000 - 4.00000i) q^{32} +(7.15831 + 2.15831i) q^{33} +(-1.31662 + 1.31662i) q^{34} +(0.158312 + 0.158312i) q^{35} +(3.31662 - 5.00000i) q^{36} +1.63325i q^{37} +(4.31662 + 4.31662i) q^{38} +(-3.97494 - 4.81662i) q^{39} +(2.00000 - 2.00000i) q^{40} +(0.316625 - 0.316625i) q^{41} +(0.158312 - 0.525063i) q^{42} +(2.47494 - 2.47494i) q^{43} -8.63325i q^{44} +(1.65831 - 2.50000i) q^{45} +(-4.00000 - 4.00000i) q^{46} +(-4.47494 + 4.47494i) q^{47} +(-6.63325 - 2.00000i) q^{48} +6.94987i q^{49} +(-4.00000 + 4.00000i) q^{50} +(2.18338 + 0.658312i) q^{51} +(-4.00000 + 6.00000i) q^{52} +(-0.316625 + 0.316625i) q^{53} +(-7.31662 - 0.683375i) q^{54} -4.31662i q^{55} -0.633250 q^{56} +(2.15831 - 7.15831i) q^{57} -2.63325 q^{58} +0.316625 q^{59} +(-3.31662 - 1.00000i) q^{60} +(-4.00000 + 4.00000i) q^{61} +10.6332i q^{62} +(-0.658312 + 0.133250i) q^{63} +8.00000i q^{64} +(-2.00000 + 3.00000i) q^{65} +(-9.31662 + 5.00000i) q^{66} -2.31662i q^{67} -2.63325i q^{68} +(-2.00000 + 6.63325i) q^{69} -0.316625 q^{70} +(-1.15831 + 1.15831i) q^{71} +(1.68338 + 8.31662i) q^{72} +(9.31662 - 9.31662i) q^{73} +(-1.63325 - 1.63325i) q^{74} +(6.63325 + 2.00000i) q^{75} -8.63325 q^{76} +(-0.683375 + 0.683375i) q^{77} +(8.79156 + 0.841688i) q^{78} -1.36675 q^{79} +4.00000i q^{80} +(3.50000 + 8.29156i) q^{81} +0.633250i q^{82} -12.6332 q^{83} +(0.366750 + 0.683375i) q^{84} -1.31662i q^{85} +4.94987i q^{86} +(1.52506 + 2.84169i) q^{87} +(8.63325 + 8.63325i) q^{88} +(-7.00000 - 7.00000i) q^{89} +(0.841688 + 4.15831i) q^{90} +(0.791562 - 0.158312i) q^{91} +8.00000 q^{92} +(11.4749 - 6.15831i) q^{93} -8.94987i q^{94} -4.31662 q^{95} +(8.63325 - 4.63325i) q^{96} +(-11.3166 + 11.3166i) q^{97} +(-6.94987 - 6.94987i) q^{98} +(10.7916 + 7.15831i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 2 q^{6} + 6 q^{7} + 8 q^{8} + 10 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 2 * q^6 + 6 * q^7 + 8 * q^8 + 10 * q^9	\( 4 q - 4 q^{2} - 2 q^{6} + 6 q^{7} + 8 q^{8} + 10 q^{9} + 4 q^{10} + 4 q^{11} + 4 q^{12} - 12 q^{13} + 2 q^{15} - 16 q^{16} - 8 q^{17} - 10 q^{18} - 8 q^{20} - 8 q^{21} - 4 q^{22} - 4 q^{24} + 16 q^{25} + 20 q^{26} - 12 q^{28} - 8 q^{29} - 2 q^{30} + 8 q^{31} + 16 q^{32} + 22 q^{33} + 8 q^{34} - 6 q^{35} + 4 q^{38} + 4 q^{39} + 8 q^{40} - 12 q^{41} - 6 q^{42} - 10 q^{43} - 16 q^{46} + 2 q^{47} - 16 q^{50} + 22 q^{51} - 16 q^{52} + 12 q^{53} - 16 q^{54} + 24 q^{56} + 2 q^{57} + 16 q^{58} - 12 q^{59} - 16 q^{61} + 4 q^{63} - 8 q^{65} - 24 q^{66} - 8 q^{69} + 12 q^{70} + 2 q^{71} + 20 q^{72} + 24 q^{73} + 20 q^{74} - 8 q^{76} - 16 q^{77} + 2 q^{78} - 32 q^{79} + 14 q^{81} - 24 q^{83} + 28 q^{84} + 26 q^{87} + 8 q^{88} - 28 q^{89} + 10 q^{90} - 30 q^{91} + 32 q^{92} + 26 q^{93} - 4 q^{95} + 8 q^{96} - 32 q^{97} + 12 q^{98} + 10 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 2 * q^6 + 6 * q^7 + 8 * q^8 + 10 * q^9 + 4 * q^10 + 4 * q^11 + 4 * q^12 - 12 * q^13 + 2 * q^15 - 16 * q^16 - 8 * q^17 - 10 * q^18 - 8 * q^20 - 8 * q^21 - 4 * q^22 - 4 * q^24 + 16 * q^25 + 20 * q^26 - 12 * q^28 - 8 * q^29 - 2 * q^30 + 8 * q^31 + 16 * q^32 + 22 * q^33 + 8 * q^34 - 6 * q^35 + 4 * q^38 + 4 * q^39 + 8 * q^40 - 12 * q^41 - 6 * q^42 - 10 * q^43 - 16 * q^46 + 2 * q^47 - 16 * q^50 + 22 * q^51 - 16 * q^52 + 12 * q^53 - 16 * q^54 + 24 * q^56 + 2 * q^57 + 16 * q^58 - 12 * q^59 - 16 * q^61 + 4 * q^63 - 8 * q^65 - 24 * q^66 - 8 * q^69 + 12 * q^70 + 2 * q^71 + 20 * q^72 + 24 * q^73 + 20 * q^74 - 8 * q^76 - 16 * q^77 + 2 * q^78 - 32 * q^79 + 14 * q^81 - 24 * q^83 + 28 * q^84 + 26 * q^87 + 8 * q^88 - 28 * q^89 + 10 * q^90 - 30 * q^91 + 32 * q^92 + 26 * q^93 - 4 * q^95 + 8 * q^96 - 32 * q^97 + 12 * q^98 + 10 * q^99

Introduction

L-functions

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