LMFDB - Embedded newform 672.2.bo.a.125.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(125,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 4, 4]))

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

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

chi := DirichletCharacter("672.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bo (of order $8$, degree $4$, 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$496$
Relative dimension:	$124$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			125.4
Character	$\chi$	$=$	672.125
Dual form			672.2.bo.a.629.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40652 - 0.147357i) q^{2} +(0.676569 - 1.59444i) q^{3} +(1.95657 + 0.414520i) q^{4} +(-1.32184 - 3.19120i) q^{5} +(-1.18656 + 2.14291i) q^{6} +(2.44227 + 1.01750i) q^{7} +(-2.69087 - 0.871344i) q^{8} +(-2.08451 - 2.15750i) q^{9} +O(q^{10})$	\(q+(-1.40652 - 0.147357i) q^{2} +(0.676569 - 1.59444i) q^{3} +(1.95657 + 0.414520i) q^{4} +(-1.32184 - 3.19120i) q^{5} +(-1.18656 + 2.14291i) q^{6} +(2.44227 + 1.01750i) q^{7} +(-2.69087 - 0.871344i) q^{8} +(-2.08451 - 2.15750i) q^{9} +(1.38894 + 4.68326i) q^{10} +(0.934109 + 2.25514i) q^{11} +(1.98469 - 2.83919i) q^{12} +(-6.23391 - 2.58217i) q^{13} +(-3.28516 - 1.79102i) q^{14} +(-5.98251 - 0.0514692i) q^{15} +(3.65635 + 1.62208i) q^{16} -5.84303i q^{17} +(2.61397 + 3.34173i) q^{18} +(1.55482 + 0.644029i) q^{19} +(-1.26346 - 6.79174i) q^{20} +(3.27472 - 3.20566i) q^{21} +(-0.981528 - 3.30953i) q^{22} +(1.53658 - 1.53658i) q^{23} +(-3.20987 + 3.70091i) q^{24} +(-4.90097 + 4.90097i) q^{25} +(8.38760 + 4.55048i) q^{26} +(-4.85034 + 1.86393i) q^{27} +(4.35671 + 3.00318i) q^{28} +(-2.60392 + 6.28642i) q^{29} +(8.40691 + 0.953957i) q^{30} -4.45356i q^{31} +(-4.90368 - 2.82026i) q^{32} +(4.22768 + 0.0363720i) q^{33} +(-0.861012 + 8.21832i) q^{34} +(0.0187613 - 9.13875i) q^{35} +(-3.18416 - 5.08538i) q^{36} +(-2.65934 - 6.42021i) q^{37} +(-2.09198 - 1.13495i) q^{38} +(-8.33481 + 8.19261i) q^{39} +(0.776258 + 9.73887i) q^{40} +(5.33031 + 5.33031i) q^{41} +(-5.07831 + 4.02625i) q^{42} +(-1.19034 + 0.493056i) q^{43} +(0.892851 + 4.79955i) q^{44} +(-4.12965 + 9.50396i) q^{45} +(-2.38764 + 1.93479i) q^{46} +8.51373i q^{47} +(5.06008 - 4.73239i) q^{48} +(4.92938 + 4.97003i) q^{49} +(7.61548 - 6.17110i) q^{50} +(-9.31639 - 3.95322i) q^{51} +(-11.1267 - 7.63629i) q^{52} +(-0.540062 - 1.30382i) q^{53} +(7.09674 - 1.90692i) q^{54} +(5.96186 - 5.96186i) q^{55} +(-5.68523 - 4.86602i) q^{56} +(2.07881 - 2.04335i) q^{57} +(4.58881 - 8.45825i) q^{58} +(-2.84358 - 6.86502i) q^{59} +(-11.6839 - 2.58057i) q^{60} +(3.81261 - 9.20445i) q^{61} +(-0.656264 + 6.26400i) q^{62} +(-2.89567 - 7.39020i) q^{63} +(6.48152 + 4.68934i) q^{64} +23.3069i q^{65} +(-5.94094 - 0.674137i) q^{66} +(-3.08997 - 1.27991i) q^{67} +(2.42205 - 11.4323i) q^{68} +(-1.41039 - 3.48958i) q^{69} +(-1.37305 + 12.8510i) q^{70} +(-5.53156 - 5.53156i) q^{71} +(3.72920 + 7.62188i) q^{72} +(-6.50929 + 6.50929i) q^{73} +(2.79434 + 9.42199i) q^{74} +(4.49848 + 11.1302i) q^{75} +(2.77516 + 1.90460i) q^{76} +(-0.0132581 + 6.45812i) q^{77} +(12.9303 - 10.2948i) q^{78} +4.06160i q^{79} +(0.343273 - 13.8123i) q^{80} +(-0.309650 + 8.99467i) q^{81} +(-6.71171 - 8.28263i) q^{82} +(1.03568 - 2.50036i) q^{83} +(7.73602 - 4.91466i) q^{84} +(-18.6463 + 7.72355i) q^{85} +(1.74689 - 0.518085i) q^{86} +(8.26162 + 8.40501i) q^{87} +(-0.548561 - 6.88220i) q^{88} +(1.72661 - 1.72661i) q^{89} +(7.20889 - 12.7589i) q^{90} +(-12.5976 - 12.6494i) q^{91} +(3.64336 - 2.36948i) q^{92} +(-7.10096 - 3.01314i) q^{93} +(1.25456 - 11.9747i) q^{94} -5.81306i q^{95} +(-7.81444 + 5.91055i) q^{96} +0.141625i q^{97} +(-6.20088 - 7.71680i) q^{98} +(2.91831 - 6.71620i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) $ 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9	$ 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9} - 48 q^{16} - 8 q^{18} - 4 q^{21} - 16 q^{22} - 16 q^{25} - 8 q^{28} - 64 q^{30} - 48 q^{36} - 16 q^{37} - 8 q^{39} + 56 q^{42} - 16 q^{43} - 16 q^{46} + 16 q^{51} - 8 q^{57} - 80 q^{58} + 24 q^{60} - 8 q^{63} - 112 q^{64} + 48 q^{67} - 8 q^{70} - 8 q^{72} - 160 q^{78} + 128 q^{84} + 64 q^{85} - 16 q^{88} - 56 q^{91} + 16 q^{93} - 8 q^{99}+O(q^{100}) $ 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9 - 48 * q^16 - 8 * q^18 - 4 * q^21 - 16 * q^22 - 16 * q^25 - 8 * q^28 - 64 * q^30 - 48 * q^36 - 16 * q^37 - 8 * q^39 + 56 * q^42 - 16 * q^43 - 16 * q^46 + 16 * q^51 - 8 * q^57 - 80 * q^58 + 24 * q^60 - 8 * q^63 - 112 * q^64 + 48 * q^67 - 8 * q^70 - 8 * q^72 - 160 * q^78 + 128 * q^84 + 64 * q^85 - 16 * q^88 - 56 * q^91 + 16 * q^93 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$-1$	$-1$

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 $

$2$	−1.40652	−	0.147357i	−0.994557	−	0.104197i
$2$	−1.40652	−	0.147357i	−0.994557	−	0.104197i
$3$	0.676569	−	1.59444i	0.390617	−	0.920553i
$3$	0.676569	−	1.59444i	0.390617	−	0.920553i
$4$	1.95657	+	0.414520i	0.978286	+	0.207260i
$5$	−1.32184	−	3.19120i	−0.591144	−	1.42715i	−0.882399	−	0.470503i	$-0.844073\pi$
$5$	−1.32184	−	3.19120i	−0.591144	−	1.42715i	0.291254	−	0.956646i	$-0.405927\pi$
$6$	−1.18656	+	2.14291i	−0.484410	+	0.874841i
$7$	2.44227	+	1.01750i	0.923092	+	0.384579i
$7$	2.44227	+	1.01750i	0.923092	+	0.384579i
$8$	−2.69087	−	0.871344i	−0.951365	−	0.308067i
$9$	−2.08451	−	2.15750i	−0.694836	−	0.719168i
$10$	1.38894	+	4.68326i	0.439221	+	1.48098i
$11$	0.934109	+	2.25514i	0.281644	+	0.679950i	0.999874	−	0.0158562i	$-0.00504739\pi$
$11$	0.934109	+	2.25514i	0.281644	+	0.679950i	−0.718230	+	0.695806i	$0.755047\pi$
$12$	1.98469	−	2.83919i	0.572929	−	0.819605i
$13$	−6.23391	−	2.58217i	−1.72898	−	0.716166i	−0.999482	−	0.0321793i	$-0.989755\pi$
$13$	−6.23391	−	2.58217i	−1.72898	−	0.716166i	−0.729495	−	0.683986i	$-0.760245\pi$
$14$	−3.28516	−	1.79102i	−0.877995	−	0.478670i
$15$	−5.98251	−	0.0514692i	−1.54468	−	0.0132893i
$16$	3.65635	+	1.62208i	0.914087	+	0.405519i
$17$		−	5.84303i		−	1.41714i	−0.705639	−	0.708572i	$-0.749340\pi$
$17$		−	5.84303i		−	1.41714i	0.705639	−	0.708572i	$-0.250660\pi$
$18$	2.61397	+	3.34173i	0.616119	+	0.787653i
$19$	1.55482	+	0.644029i	0.356701	+	0.147750i	0.553836	−	0.832626i	$-0.313164\pi$
$19$	1.55482	+	0.644029i	0.356701	+	0.147750i	−0.197135	+	0.980376i	$0.563164\pi$
$20$	−1.26346	−	6.79174i	−0.282517	−	1.51868i
$21$	3.27472	−	3.20566i	0.714601	−	0.699532i
$22$	−0.981528	−	3.30953i	−0.209262	−	0.705595i
$23$	1.53658	−	1.53658i	0.320398	−	0.320398i	−0.528522	−	0.848920i	$-0.677253\pi$
$23$	1.53658	−	1.53658i	0.320398	−	0.320398i	0.848920	+	0.528522i	$0.177253\pi$
$24$	−3.20987	+	3.70091i	−0.655211	+	0.755446i
$25$	−4.90097	+	4.90097i	−0.980194	+	0.980194i
$26$	8.38760	+	4.55048i	1.64494	+	0.892422i
$27$	−4.85034	+	1.86393i	−0.933448	+	0.358714i
$28$	4.35671	+	3.00318i	0.823340	+	0.567549i
$29$	−2.60392	+	6.28642i	−0.483536	+	1.16736i	0.474382	+	0.880319i	$0.342671\pi$
$29$	−2.60392	+	6.28642i	−0.483536	+	1.16736i	−0.957918	+	0.287041i	$0.907329\pi$
$30$	8.40691	+	0.953957i	1.53488	+	0.174168i
$31$		−	4.45356i		−	0.799883i	−0.916541	−	0.399942i	$-0.869030\pi$
$31$		−	4.45356i		−	0.799883i	0.916541	−	0.399942i	$-0.130970\pi$
$32$	−4.90368	−	2.82026i	−0.866857	−	0.498557i
$33$	4.22768	+	0.0363720i	0.735945	+	0.00633155i
$34$	−0.861012	+	8.21832i	−0.147662	+	1.40943i
$35$	0.0187613	−	9.13875i	0.00317123	−	1.54473i
$36$	−3.18416	−	5.08538i	−0.530694	−	0.847564i
$37$	−2.65934	−	6.42021i	−0.437192	−	1.05548i	−0.976914	−	0.213632i	$-0.931471\pi$
$37$	−2.65934	−	6.42021i	−0.437192	−	1.05548i	0.539722	−	0.841843i	$-0.318529\pi$
$38$	−2.09198	−	1.13495i	−0.339364	−	0.184113i
$39$	−8.33481	+	8.19261i	−1.33464	+	1.31187i
$40$	0.776258	+	9.73887i	0.122737	+	1.53985i
$41$	5.33031	+	5.33031i	0.832455	+	0.832455i	0.987852	−	0.155397i	$-0.0496658\pi$
$41$	5.33031	+	5.33031i	0.832455	+	0.832455i	−0.155397	+	0.987852i	$0.549666\pi$
$42$	−5.07831	+	4.02625i	−0.783601	+	0.621265i
$43$	−1.19034	+	0.493056i	−0.181526	+	0.0751903i	−0.471595	−	0.881815i	$-0.656322\pi$
$43$	−1.19034	+	0.493056i	−0.181526	+	0.0751903i	0.290069	+	0.957006i	$0.406322\pi$
$44$	0.892851	+	4.79955i	0.134602	+	0.723559i
$45$	−4.12965	+	9.50396i	−0.615611	+	1.41677i
$46$	−2.38764	+	1.93479i	−0.352039	+	0.285270i
$47$			8.51373i			1.24186i	0.783868	+	0.620928i	$0.213244\pi$
$47$			8.51373i			1.24186i	−0.783868	+	0.620928i	$0.786756\pi$
$48$	5.06008	−	4.73239i	0.730360	−	0.683062i
$49$	4.92938	+	4.97003i	0.704198	+	0.710004i
$50$	7.61548	−	6.17110i	1.07699	−	0.872725i
$51$	−9.31639	−	3.95322i	−1.30456	−	0.553561i
$52$	−11.1267	−	7.63629i	−1.54300	−	1.05896i
$53$	−0.540062	−	1.30382i	−0.0741832	−	0.179094i	0.882438	−	0.470429i	$-0.155901\pi$
$53$	−0.540062	−	1.30382i	−0.0741832	−	0.179094i	−0.956621	+	0.291335i	$0.905901\pi$
$54$	7.09674	−	1.90692i	0.965743	−	0.259499i
$55$	5.96186	−	5.96186i	0.803897	−	0.803897i
$56$	−5.68523	−	4.86602i	−0.759721	−	0.650249i
$57$	2.07881	−	2.04335i	0.275346	−	0.270648i
$58$	4.58881	−	8.45825i	0.602540	−	1.11062i
$59$	−2.84358	−	6.86502i	−0.370203	−	0.893750i	−0.993715	−	0.111936i	$-0.964295\pi$
$59$	−2.84358	−	6.86502i	−0.370203	−	0.893750i	0.623512	−	0.781814i	$-0.285705\pi$
$60$	−11.6839	−	2.58057i	−1.50838	−	0.333151i
$61$	3.81261	−	9.20445i	0.488155	−	1.17851i	−0.467493	−	0.883997i	$-0.654843\pi$
$61$	3.81261	−	9.20445i	0.488155	−	1.17851i	0.955648	−	0.294513i	$-0.0951573\pi$
$62$	−0.656264	+	6.26400i	−0.0833456	+	0.795529i
$63$	−2.89567	−	7.39020i	−0.364820	−	0.931078i
$64$	6.48152	+	4.68934i	0.810190	+	0.586167i
$65$			23.3069i			2.89086i
$66$	−5.94094	−	0.674137i	−0.731279	−	0.0829805i
$67$	−3.08997	−	1.27991i	−0.377500	−	0.156365i	0.185862	−	0.982576i	$-0.440492\pi$
$67$	−3.08997	−	1.27991i	−0.377500	−	0.156365i	−0.563362	+	0.826210i	$0.690492\pi$
$68$	2.42205	−	11.4323i	0.293717	−	1.38637i
$69$	−1.41039	−	3.48958i	−0.169790	−	0.420097i
$70$	−1.37305	+	12.8510i	−0.164111	+	1.53599i
$71$	−5.53156	−	5.53156i	−0.656476	−	0.656476i	0.298069	−	0.954544i	$-0.403658\pi$
$71$	−5.53156	−	5.53156i	−0.656476	−	0.656476i	−0.954544	+	0.298069i	$0.903658\pi$
$72$	3.72920	+	7.62188i	0.439491	+	0.898247i
$73$	−6.50929	+	6.50929i	−0.761855	+	0.761855i	−0.976658	−	0.214802i	$-0.931089\pi$
$73$	−6.50929	+	6.50929i	−0.761855	+	0.761855i	0.214802	+	0.976658i	$0.431089\pi$
$74$	2.79434	+	9.42199i	0.324835	+	1.09528i
$75$	4.49848	+	11.1302i	0.519440	+	1.28520i
$76$	2.77516	+	1.90460i	0.318333	+	0.218472i
$77$	−0.0132581	+	6.45812i	−0.00151090	+	0.735971i
$78$	12.9303	−	10.2948i	1.46407	−	1.16566i
$79$			4.06160i			0.456965i	0.973548	+	0.228483i	$0.0733764\pi$
$79$			4.06160i			0.456965i	−0.973548	+	0.228483i	$0.926624\pi$
$80$	0.343273	−	13.8123i	0.0383791	−	1.54426i
$81$	−0.309650	+	8.99467i	−0.0344055	+	0.999408i
$82$	−6.71171	−	8.28263i	−0.741184	−	0.914663i
$83$	1.03568	−	2.50036i	0.113681	−	0.274450i	−0.856791	−	0.515664i	$-0.827545\pi$
$83$	1.03568	−	2.50036i	0.113681	−	0.274450i	0.970472	+	0.241213i	$0.0775454\pi$
$84$	7.73602	−	4.91466i	0.844070	−	0.536234i
$85$	−18.6463	+	7.72355i	−2.02247	+	0.837736i
$86$	1.74689	−	0.518085i	0.188372	−	0.0558666i
$87$	8.26162	+	8.40501i	0.885739	+	0.901112i
$88$	−0.548561	−	6.88220i	−0.0584768	−	0.733645i
$89$	1.72661	−	1.72661i	0.183020	−	0.183020i	−0.609650	−	0.792670i	$-0.708690\pi$
$89$	1.72661	−	1.72661i	0.183020	−	0.183020i	0.792670	+	0.609650i	$0.208690\pi$
$90$	7.20889	−	12.7589i	0.759883	−	1.34491i
$91$	−12.5976	−	12.6494i	−1.32058	−	1.32602i
$92$	3.64336	−	2.36948i	0.379847	−	0.247035i
$93$	−7.10096	−	3.01314i	−0.736335	−	0.312448i
$94$	1.25456	−	11.9747i	0.129398	−	1.23510i
$95$		−	5.81306i		−	0.596407i
$96$	−7.81444	+	5.91055i	−0.797558	+	0.603243i
$97$			0.141625i			0.0143799i	0.999974	+	0.00718994i	$0.00228865\pi$
$97$			0.141625i			0.0143799i	−0.999974	+	0.00718994i	$0.997711\pi$
$98$	−6.20088	−	7.71680i	−0.626384	−	0.779515i
$99$	2.91831	−	6.71620i	0.293301	−	0.675003i
$100$	−11.6207	+	7.55755i	−1.16207	+	0.755755i
$101$	−3.50013	−	8.45006i	−0.348276	−	0.840812i	−0.996824	−	0.0796383i	$-0.974623\pi$
$101$	−3.50013	−	8.45006i	−0.348276	−	0.840812i	0.648548	−	0.761174i	$-0.275377\pi$
$102$	12.5211	+	6.93310i	1.23978	+	0.686479i
$103$	−1.95212	−	1.95212i	−0.192348	−	0.192348i	0.604362	−	0.796710i	$-0.293428\pi$
$103$	−1.95212	−	1.95212i	−0.192348	−	0.192348i	−0.796710	+	0.604362i	$0.793428\pi$
$104$	14.5247	+	12.3802i	1.42426	+	1.21397i
$105$	−14.5585	−	6.21291i	−1.42077	−	0.606318i
$106$	0.567477	+	1.91343i	0.0551183	+	0.185849i
$107$	−1.33802	−	3.23026i	−0.129351	−	0.312281i	0.845914	−	0.533319i	$-0.179055\pi$
$107$	−1.33802	−	3.23026i	−0.129351	−	0.312281i	−0.975265	+	0.221038i	$0.929055\pi$
$108$	−10.2627	+	1.63636i	−0.987526	+	0.157458i
$109$	0.894822	−	2.16029i	0.0857084	−	0.206918i	−0.875214	−	0.483736i	$-0.839280\pi$
$109$	0.894822	−	2.16029i	0.0857084	−	0.206918i	0.960923	+	0.276817i	$0.0892797\pi$
$110$	−9.26397	+	7.50692i	−0.883285	+	0.715757i
$111$	−12.0359	−	0.103548i	−1.14240	−	0.00982836i
$112$	7.27933	+	7.68189i	0.687832	+	0.725870i
$113$	4.73016			0.444976			0.222488	−	0.974935i	$-0.428582\pi$
$113$	4.73016			0.444976			0.222488	+	0.974935i	$0.428582\pi$
$114$	−3.22499	+	2.56768i	−0.302048	+	0.240485i
$115$	−6.93463	−	2.87242i	−0.646657	−	0.267854i
$116$	−7.70061	+	11.2205i	−0.714984	+	1.04179i
$117$	7.42360	+	18.8323i	0.686312	+	1.74104i
$118$	2.98794	+	10.0748i	0.275062	+	0.927459i
$119$	5.94529	−	14.2703i	0.545004	−	1.30815i
$120$	16.0533	+	5.35132i	1.46546	+	0.488506i
$121$	3.56509	−	3.56509i	0.324099	−	0.324099i
$122$	−6.71884	+	12.3844i	−0.608295	+	1.12123i
$123$	12.1052	−	4.89256i	1.09149	−	0.441148i
$124$	1.84609	−	8.71371i	0.165784	−	0.782514i
$125$	6.16227	+	2.55249i	0.551170	+	0.228302i
$126$	2.98381	+	10.8211i	0.265819	+	0.964023i
$127$	−7.19265			−0.638245			−0.319122	−	0.947714i	$-0.603388\pi$
$127$	−7.19265			−0.638245			−0.319122	+	0.947714i	$0.603388\pi$
$128$	−8.42535	−	7.55073i	−0.744703	−	0.667396i
$129$	−0.0191984	+	2.23152i	−0.00169033	+	0.196475i
$130$	3.43444	−	32.7815i	0.301220	−	2.87513i
$131$	12.0622	+	4.99634i	1.05388	+	0.436532i	0.841276	−	0.540606i	$-0.181805\pi$
$131$	12.0622	+	4.99634i	1.05388	+	0.436532i	0.212606	+	0.977138i	$0.431805\pi$
$132$	8.25669	+	1.82362i	0.718652	+	0.158726i
$133$	3.14200	+	3.15493i	0.272446	+	0.273567i
$134$	4.15748	+	2.25554i	0.359152	+	0.194849i
$135$	12.3595	+	13.0146i	1.06374	+	1.12012i
$136$	−5.09129	+	15.7228i	−0.436575	+	1.34822i
$137$	14.6624	−	14.6624i	1.25269	−	1.25269i	0.298183	−	0.954509i	$-0.403619\pi$
$137$	14.6624	−	14.6624i	1.25269	−	1.25269i	0.954509	−	0.298183i	$-0.0963807\pi$
$138$	1.46951	+	5.11599i	0.125093	+	0.435502i
$139$	3.03305	+	7.32244i	0.257260	+	0.621081i	0.998755	−	0.0498771i	$-0.0158830\pi$
$139$	3.03305	+	7.32244i	0.257260	+	0.621081i	−0.741495	+	0.670958i	$0.765883\pi$
$140$	3.82490	−	17.8728i	0.323263	−	1.51053i
$141$	13.5747	+	5.76013i	1.14319	+	0.485090i
$142$	6.96511	+	8.59534i	0.584499	+	0.721305i
$143$		−	16.4704i		−	1.37732i
$144$	−4.12205	−	11.2698i	−0.343504	−	0.939151i
$145$	23.5032			1.95183
$146$	10.1146	−	8.19623i	0.837091	−	0.678325i
$147$	11.2595	−	4.49706i	0.928668	−	0.370911i
$148$	−2.54188	−	13.6639i	−0.208941	−	1.12317i
$149$	0.163403	+	0.394491i	0.0133865	+	0.0323180i	0.930431	−	0.366466i	$-0.119432\pi$
$149$	0.163403	+	0.394491i	0.0133865	+	0.0323180i	−0.917045	+	0.398784i	$0.869432\pi$
$150$	−4.68707	−	16.3176i	−0.382698	−	1.33233i
$151$	13.6089	+	13.6089i	1.10748	+	1.10748i	0.993481	+	0.113995i	$0.0363647\pi$
$151$	13.6089	+	13.6089i	1.10748	+	1.10748i	0.113995	+	0.993481i	$0.463635\pi$
$152$	−3.62265	−	3.08778i	−0.293836	−	0.250452i
$153$	−12.6064	+	12.1799i	−1.01916	+	0.984683i
$154$	0.970297	−	9.08149i	0.0781888	−	0.731807i
$155$	−14.2122	+	5.88689i	−1.14155	+	0.472846i
$156$	−19.7036	+	12.5745i	−1.57755	+	1.00677i
$157$	4.22676	−	10.2043i	0.337332	−	0.814393i	−0.660637	−	0.750705i	$-0.729714\pi$
$157$	4.22676	−	10.2043i	0.337332	−	0.814393i	0.997970	−	0.0636874i	$-0.0202861\pi$
$158$	0.598505	−	5.71270i	0.0476145	−	0.454478i
$159$	−2.44426	−	0.0210287i	−0.193843	−	0.00166768i
$160$	−2.51815	+	19.3766i	−0.199078	+	1.53185i
$161$	5.31620	−	2.18927i	0.418976	−	0.172538i
$162$	1.76096	−	12.6055i	0.138354	−	0.990383i
$163$	19.7942	+	8.19902i	1.55040	+	0.642197i	0.983389	−	0.181513i	$-0.0580995\pi$
$163$	19.7942	+	8.19902i	1.55040	+	0.642197i	0.567012	+	0.823710i	$0.308099\pi$
$164$	8.21962	+	12.6387i	0.641844	+	0.986913i
$165$	−5.47224	−	13.5395i	−0.426014	−	1.05405i
$166$	−1.82515	+	3.36418i	−0.141659	+	0.261111i
$167$	9.16515	−	9.16515i	0.709220	−	0.709220i	−0.257151	−	0.966371i	$-0.582784\pi$
$167$	9.16515	−	9.16515i	0.709220	−	0.709220i	0.966371	+	0.257151i	$0.0827838\pi$
$168$	−11.6050	+	5.77259i	−0.895349	+	0.445365i
$169$	23.0017	+	23.0017i	1.76936	+	1.76936i
$170$	27.3644	−	8.11562i	2.09875	−	0.622440i
$171$	−1.85155	−	4.69702i	−0.141591	−	0.359190i
$172$	−2.53337	+	0.471279i	−0.193168	+	0.0359346i
$173$	2.98589	−	7.20858i	0.227013	−	0.548059i	−0.768798	−	0.639492i	$-0.779145\pi$
$173$	2.98589	−	7.20858i	0.227013	−	0.548059i	0.995811	+	0.0914333i	$0.0291448\pi$
$174$	−10.3816	−	13.0392i	−0.787024	−	0.988498i
$175$	−16.9562	+	6.98276i	−1.28177	+	0.527847i
$176$	−0.242582	+	9.76076i	−0.0182853	+	0.735745i
$177$	−12.8698	−	0.110722i	−0.967352	−	0.00832240i
$178$	−2.68293	+	2.17407i	−0.201094	+	0.162953i
$179$	11.4577	+	4.74595i	0.856392	+	0.354729i	0.767295	−	0.641294i	$-0.221602\pi$
$179$	11.4577	+	4.74595i	0.856392	+	0.354729i	0.0890964	+	0.996023i	$0.471602\pi$
$180$	−12.0195	+	16.8834i	−0.895883	+	1.25841i
$181$	−7.39199	−	17.8459i	−0.549443	−	1.32647i	−0.917894	−	0.396825i	$-0.870112\pi$
$181$	−7.39199	−	17.8459i	−0.549443	−	1.32647i	0.368452	−	0.929647i	$-0.379888\pi$
$182$	15.8547	+	19.6479i	1.17523	+	1.45640i
$183$	−12.0965	−	12.3064i	−0.894199	−	0.909719i
$184$	−5.47361	+	2.79583i	−0.403520	+	0.206112i
$185$	−16.9730	+	16.9730i	−1.24788	+	1.24788i
$186$	9.54360	+	5.28441i	0.699771	+	0.387472i
$187$	13.1768	−	5.45803i	0.963586	−	0.399131i
$188$	−3.52911	+	16.6577i	−0.257387	+	1.21489i
$189$	−13.7424	−	0.382992i	−0.999612	−	0.0278585i
$190$	−0.856595	+	8.17616i	−0.0621440	+	0.593161i
$191$		−	22.6638i		−	1.63989i	−0.572439	−	0.819947i	$-0.694003\pi$
$191$		−	22.6638i		−	1.63989i	0.572439	−	0.819947i	$-0.305997\pi$
$192$	11.8621	−	7.16176i	0.856072	−	0.516856i
$193$	5.84063			0.420417			0.210209	−	0.977657i	$-0.432586\pi$
$193$	5.84063			0.420417			0.210209	+	0.977657i	$0.432586\pi$
$194$	0.0208695	−	0.199198i	0.00149834	−	0.0143016i
$195$	37.1615	+	15.7687i	2.66119	+	1.12922i
$196$	7.58451	+	11.7675i	0.541751	+	0.840539i
$197$	−6.60728	+	2.73683i	−0.470749	+	0.194991i	−0.605430	−	0.795898i	$-0.706999\pi$
$197$	−6.60728	+	2.73683i	−0.470749	+	0.194991i	0.134681	+	0.990889i	$0.456999\pi$
$198$	−5.09433	+	9.01640i	−0.362038	+	0.640768i
$199$	0.622396	+	0.622396i	0.0441205	+	0.0441205i	0.728823	−	0.684702i	$-0.240068\pi$
$199$	0.622396	+	0.622396i	0.0441205	+	0.0441205i	−0.684702	+	0.728823i	$0.740068\pi$
$200$	17.4583	−	8.91742i	1.23449	−	0.630557i
$201$	−4.13132	+	4.06084i	−0.291401	+	0.286429i
$202$	3.67781	+	12.4009i	0.258770	+	0.872524i
$203$	−12.7559	+	12.7037i	−0.895291	+	0.891622i
$204$	−16.5895	−	11.5966i	−1.16150	−	0.811923i
$205$	9.96428	−	24.0559i	0.695936	−	1.68014i
$206$	2.45802	+	3.03334i	0.171259	+	0.211343i
$207$	−6.51817	−	0.112164i	−0.453044	−	0.00779592i
$208$	−18.6049	−	19.5532i	−1.29002	−	1.35577i
$209$			4.10794i			0.284152i
$210$	19.5613	+	10.8839i	1.34986	+	0.751058i
$211$	6.90345	−	16.6664i	0.475253	−	1.14736i	−0.486558	−	0.873648i	$-0.661748\pi$
$211$	6.90345	−	16.6664i	0.475253	−	1.14736i	0.961811	−	0.273714i	$-0.0882522\pi$
$212$	−0.516208	−	2.77489i	−0.0354533	−	0.190580i
$213$	−12.5623	+	5.07729i	−0.860751	+	0.347890i
$214$	1.40594	+	4.74057i	0.0961081	+	0.324059i
$215$	3.14688	+	3.14688i	0.214616	+	0.214616i
$216$	14.6757	−	0.789283i	0.998557	−	0.0537039i
$217$	4.53150	−	10.8768i	0.307618	−	0.738366i
$218$	−1.57692	+	2.90662i	−0.106802	+	0.196861i
$219$	5.97472	+	14.7827i	0.403734	+	0.998922i
$220$	14.1361	−	9.19349i	0.953056	−	0.619825i
$221$	−15.0877	+	36.4250i	−1.01491	+	2.45021i
$222$	16.9134	+	1.91922i	1.13515	+	0.128809i
$223$		−	20.8927i		−	1.39908i	−0.714593	−	0.699540i	$-0.753388\pi$
$223$		−	20.8927i		−	1.39908i	0.714593	−	0.699540i	$-0.246612\pi$
$224$	−9.10650	−	11.8774i	−0.608454	−	0.793589i
$225$	20.7900	+	0.357751i	1.38600	+	0.0238500i
$226$	−6.65305	−	0.697023i	−0.442554	−	0.0463653i
$227$	−1.03981	−	0.430703i	−0.0690145	−	0.0285868i	0.347909	−	0.937528i	$-0.386892\pi$
$227$	−1.03981	−	0.430703i	−0.0690145	−	0.0285868i	−0.416924	+	0.908941i	$0.636892\pi$
$228$	4.91436	−	3.13625i	0.325461	−	0.207703i
$229$	−18.5599	+	7.68778i	−1.22648	+	0.508023i	−0.899463	−	0.436997i	$-0.856042\pi$
$229$	−18.5599	+	7.68778i	−1.22648	+	0.508023i	−0.327013	+	0.945020i	$0.606042\pi$
$230$	9.33039	+	5.06196i	0.615228	+	0.333776i
$231$	10.2881	+	4.39050i	0.676910	+	0.288874i
$232$	12.4844	−	14.6470i	0.819644	−	0.961624i
$233$	11.9458	−	11.9458i	0.782592	−	0.782592i	−0.197675	−	0.980268i	$-0.563339\pi$
$233$	11.9458	−	11.9458i	0.782592	−	0.782592i	0.980268	+	0.197675i	$0.0633392\pi$
$234$	−7.66634	−	27.5818i	−0.501164	−	1.80308i
$235$	27.1690	−	11.2538i	1.77231	−	0.734116i
$236$	−2.71799	−	14.6106i	−0.176926	−	0.951071i
$237$	6.47599	+	2.74795i	0.420661	+	0.178499i
$238$	−10.4650	+	19.1953i	−0.678343	+	1.24425i
$239$	−12.0001			−0.776223			−0.388111	−	0.921612i	$-0.626872\pi$
$239$	−12.0001			−0.776223			−0.388111	+	0.921612i	$0.626872\pi$
$240$	−21.7906	−	9.89228i	−1.40658	−	0.638544i
$241$	−19.7131			−1.26983			−0.634917	−	0.772580i	$-0.718966\pi$
$241$	−19.7131			−1.26983			−0.634917	+	0.772580i	$0.718966\pi$
$242$	−5.53969	+	4.48901i	−0.356105	+	0.288564i
$243$	14.1320	+	6.57924i	0.906569	+	0.422058i
$244$	11.2751	−	16.4288i	0.721813	−	1.05174i
$245$	9.34451	−	22.3002i	0.596999	−	1.42471i
$246$	−17.7471	+	5.09768i	−1.13152	+	0.325016i
$247$	−8.02965	−	8.02965i	−0.510914	−	0.510914i
$248$	−3.88058	+	11.9839i	−0.246417	+	0.760981i
$249$	−3.28598	−	3.34301i	−0.208240	−	0.211855i
$250$	−8.29120	−	4.49818i	−0.524381	−	0.284490i
$251$	−1.77377	−	4.28226i	−0.111959	−	0.270294i	0.857962	−	0.513714i	$-0.171731\pi$
$251$	−1.77377	−	4.28226i	−0.111959	−	0.270294i	−0.969921	+	0.243420i	$0.921731\pi$
$252$	−2.60220	−	15.6598i	−0.163923	−	0.986473i
$253$	4.90052	+	2.02986i	0.308093	+	0.127616i
$254$	10.1166	+	1.05989i	0.634771	+	0.0665033i
$255$	−0.300736	+	34.9560i	−0.0188328	+	2.18903i
$256$	10.7377	+	11.8617i	0.671108	+	0.741359i
$257$	−7.64748			−0.477037			−0.238518	−	0.971138i	$-0.576662\pi$
$257$	−7.64748			−0.477037			−0.238518	+	0.971138i	$0.576662\pi$
$258$	0.355834	−	3.13584i	0.0221532	−	0.195229i
$259$	0.0377448	−	18.3858i	0.00234535	−	1.14244i
$260$	−9.66117	+	45.6016i	−0.599161	+	2.82809i
$261$	18.9909	−	7.48613i	1.17551	−	0.463380i
$262$	−16.2295	−	8.80489i	−1.00266	−	0.543968i
$263$	−6.53300	−	6.53300i	−0.402842	−	0.402842i	0.476391	−	0.879233i	$-0.341945\pi$
$263$	−6.53300	−	6.53300i	−0.402842	−	0.402842i	−0.879233	+	0.476391i	$0.841945\pi$
$264$	−11.3444	−	3.78164i	−0.698202	−	0.232744i
$265$	−3.44689	+	3.44689i	−0.211741	+	0.211741i
$266$	−3.95437	−	4.90045i	−0.242458	−	0.300466i
$267$	−1.58481	−	3.92115i	−0.0969888	−	0.239970i
$268$	−5.51519	−	3.78508i	−0.336894	−	0.231211i
$269$	−2.89525	+	6.98976i	−0.176527	+	0.426173i	−0.987234	−	0.159279i	$-0.949083\pi$
$269$	−2.89525	+	6.98976i	−0.176527	+	0.426173i	0.810707	+	0.585452i	$0.199083\pi$
$270$	−15.4661	−	20.1265i	−0.941237	−	1.22486i
$271$	25.8028			1.56741			0.783705	−	0.621134i	$-0.213328\pi$
$271$	25.8028			1.56741			0.783705	+	0.621134i	$0.213328\pi$
$272$	9.47785	−	21.3641i	0.574679	−	1.29539i
$273$	−28.6919	+	11.5279i	−1.73651	+	0.697701i
$274$	−22.7835	+	18.4623i	−1.37640	+	1.11535i
$275$	−15.6304	−	6.47432i	−0.942549	−	0.390416i
$276$	−1.31302	−	7.41226i	−0.0790343	−	0.446165i
$277$	14.3849	−	5.95842i	0.864305	−	0.358007i	0.0939153	−	0.995580i	$-0.470062\pi$
$277$	14.3849	−	5.95842i	0.864305	−	0.358007i	0.770390	+	0.637573i	$0.220062\pi$
$278$	−3.18702	−	10.7461i	−0.191145	−	0.644506i
$279$	−9.60858	+	9.28348i	−0.575250	+	0.555788i
$280$	−8.01348	+	24.5748i	−0.478897	+	1.46863i
$281$	11.2092	+	11.2092i	0.668687	+	0.668687i	0.957412	−	0.288725i	$-0.0932315\pi$
$281$	11.2092	+	11.2092i	0.668687	+	0.668687i	−0.288725	+	0.957412i	$0.593231\pi$
$282$	−18.2442	−	10.1020i	−1.08643	−	0.601568i
$283$	−1.92051	+	0.795501i	−0.114162	+	0.0472876i	−0.439034	−	0.898471i	$-0.644679\pi$
$283$	−1.92051	+	0.795501i	−0.114162	+	0.0472876i	0.324871	+	0.945758i	$0.394679\pi$
$284$	−8.52995	−	13.1158i	−0.506160	−	0.778282i
$285$	−9.26860	−	3.93294i	−0.549024	−	0.232967i
$286$	−2.42703	+	23.1658i	−0.143513	+	1.36982i
$287$	7.59447	+	18.4417i	0.448287	+	1.08858i
$288$	4.13703	+	16.4586i	0.243777	+	0.969831i
$289$	−17.1410			−1.00830
$290$	−33.0576	−	3.46336i	−1.94121	−	0.203376i
$291$	0.225814	+	0.0958194i	0.0132374	+	0.00561703i
$292$	−15.4341	+	10.0377i	−0.903214	+	0.587410i
$293$	8.52328	+	20.5770i	0.497935	+	1.20212i	0.950594	+	0.310438i	$0.100476\pi$
$293$	8.52328	+	20.5770i	0.497935	+	1.20212i	−0.452658	+	0.891684i	$0.649524\pi$
$294$	−16.4993	+	4.66602i	−0.962261	+	0.272128i
$295$	−18.1489	+	18.1489i	−1.05667	+	1.05667i
$296$	1.56171	+	19.5931i	0.0907726	+	1.13883i
$297$	−8.73417	−	9.19706i	−0.506808	−	0.533668i
$298$	−0.171699	−	0.578936i	−0.00994623	−	0.0335369i
$299$	−13.5466	+	5.61118i	−0.783419	+	0.324503i
$300$	4.18792	+	23.6417i	0.241790	+	1.36495i
$301$	−3.40882	−	0.00699810i	−0.196481	−	0.000403364i
$302$	−17.1358	−	21.1465i	−0.986052	−	1.21684i
$303$	−15.8412	−	0.136287i	−0.910055	−	0.00782946i
$304$	4.64031	+	4.87684i	0.266140	+	0.279706i
$305$	−34.4129			−1.97048
$306$	19.5258	−	15.2735i	1.11622	−	0.873128i
$307$	−0.291062	−	0.120562i	−0.0166118	−	0.00688083i	0.374362	−	0.927283i	$-0.377862\pi$
$307$	−0.291062	−	0.120562i	−0.0166118	−	0.00688083i	−0.390974	+	0.920402i	$0.627862\pi$
$308$	−2.70296	+	12.6303i	−0.154015	+	0.719677i
$309$	−4.43329	+	1.79180i	−0.252201	+	0.101932i
$310$	20.8572	−	6.18573i	1.18461	−	0.351326i
$311$	−18.1982	−	18.1982i	−1.03192	−	1.03192i	−0.999473	−	0.0324507i	$-0.989669\pi$
$311$	−18.1982	−	18.1982i	−1.03192	−	1.03192i	−0.0324507	−	0.999473i	$-0.510331\pi$
$312$	29.5664	−	14.7827i	1.67387	−	0.836908i
$313$	1.44585	+	1.44585i	0.0817245	+	0.0817245i	0.746787	−	0.665063i	$-0.231595\pi$
$313$	1.44585	+	1.44585i	0.0817245	+	0.0817245i	−0.665063	+	0.746787i	$0.731595\pi$
$314$	−7.44869	+	13.7297i	−0.420354	+	0.774810i
$315$	−19.7560	+	19.0093i	−1.11312	+	1.07105i
$316$	−1.68361	+	7.94681i	−0.0947107	+	0.447043i
$317$	7.91660	−	19.1124i	0.444640	−	1.07346i	−0.529661	−	0.848209i	$-0.677681\pi$
$317$	7.91660	−	19.1124i	0.444640	−	1.07346i	0.974302	−	0.225248i	$-0.0723191\pi$
$318$	3.43480	+	0.389757i	0.192614	+	0.0218565i
$319$	−16.6091			−0.929931
$320$	6.39710	−	26.8824i	0.357609	−	1.50277i
$321$	−6.05573	−	0.0520992i	−0.337998	−	0.00290789i
$322$	−7.79993	+	2.29586i	−0.434673	+	0.127943i
$323$	3.76308	−	9.08489i	0.209384	−	0.505497i
$324$	−4.33432	+	17.4704i	−0.240796	+	0.970576i
$325$	43.2074	−	17.8971i	2.39671	−	0.992751i
$326$	−26.6326	−	14.4489i	−1.47505	−	0.800248i
$327$	−2.83906	−	2.88833i	−0.157000	−	0.159725i
$328$	−9.69862	−	18.9877i	−0.535517	−	1.04842i
$329$	−8.66273	+	20.7929i	−0.477592	+	1.14635i
$330$	5.70166	+	19.8498i	0.313866	+	1.09270i
$331$	1.35712	−	0.562136i	0.0745938	−	0.0308978i	−0.345075	−	0.938575i	$-0.612146\pi$
$331$	1.35712	−	0.562136i	0.0745938	−	0.0308978i	0.419668	+	0.907678i	$0.362146\pi$
$332$	3.06284	−	4.46283i	0.168095	−	0.244929i
$333$	−8.30821	+	19.1205i	−0.455287	+	1.04780i
$334$	−14.2415	+	11.5404i	−0.779258	+	0.631461i
$335$			11.5525i			0.631182i
$336$	17.1733	−	6.40915i	0.936881	−	0.349648i
$337$		−	18.1860i		−	0.990653i	−0.868707	−	0.495327i	$-0.835048\pi$
$337$		−	18.1860i		−	0.990653i	0.868707	−	0.495327i	$-0.164952\pi$
$338$	−28.9628	−	35.7417i	−1.57537	−	1.94409i
$339$	3.20028	−	7.54198i	0.173815	−	0.409624i
$340$	−39.6844	+	7.38241i	−2.15219	+	0.400367i
$341$	10.0434	−	4.16011i	0.543880	−	0.225283i
$342$	1.91209	+	6.87928i	0.103394	+	0.371989i
$343$	6.98188	+	17.1538i	0.376986	+	0.926219i
$344$	3.63267	−	0.289550i	0.195861	−	0.0156115i
$345$	−9.27166	+	9.11349i	−0.499170	+	0.490654i
$346$	−5.26194	+	9.69899i	−0.282884	+	0.521421i
$347$	16.8768	−	6.99061i	0.905995	−	0.375275i	0.119473	−	0.992837i	$-0.461880\pi$
$347$	16.8768	−	6.99061i	0.905995	−	0.375275i	0.786522	+	0.617562i	$0.211880\pi$
$348$	12.6804	+	19.8696i	0.679741	+	1.06512i
$349$	−5.44280	+	13.1401i	−0.291346	+	0.703372i	−0.999998	−	0.00218687i	$-0.999304\pi$
$349$	−5.44280	+	13.1401i	−0.291346	+	0.703372i	0.708651	+	0.705559i	$0.249304\pi$
$350$	24.8782	−	7.32273i	1.32979	−	0.391417i
$351$	35.0496	+	0.904803i	1.87081	+	0.0482948i
$352$	1.77951	−	13.6929i	0.0948484	−	0.729835i
$353$	−8.05008			−0.428463			−0.214231	−	0.976783i	$-0.568725\pi$
$353$	−8.05008			−0.428463			−0.214231	+	0.976783i	$0.568725\pi$
$354$	18.0852	+	2.05219i	0.961219	+	0.109072i
$355$	−10.3405	+	24.9642i	−0.548816	+	1.32496i
$356$	4.09394	−	2.66252i	0.216978	−	0.141113i
$357$	−18.7308	−	19.1343i	−0.991337	−	1.01269i
$358$	−15.4161	−	8.36363i	−0.814768	−	0.442032i
$359$	25.1289	+	25.1289i	1.32625	+	1.32625i	0.908612	+	0.417642i	$0.137143\pi$
$359$	25.1289	+	25.1289i	1.32625	+	1.32625i	0.417642	+	0.908612i	$0.362857\pi$
$360$	19.3935	−	21.9755i	1.02213	−	1.15821i
$361$	−11.4323	−	11.4323i	−0.601701	−	0.601701i
$362$	7.76724	+	26.1897i	0.408237	+	1.37650i
$363$	−3.27231	−	8.09636i	−0.171752	−	0.424949i
$364$	−19.4046	−	29.9714i	−1.01708	−	1.57093i
$365$	29.3767	+	12.1682i	1.53765	+	0.636914i
$366$	15.2005	+	19.0917i	0.794541	+	0.997940i
$367$	14.5372			0.758838			0.379419	−	0.925225i	$-0.376124\pi$
$367$	14.5372			0.758838			0.379419	+	0.925225i	$0.376124\pi$
$368$	8.11070	−	3.12581i	0.422799	−	0.162944i
$369$	0.389091	−	22.6112i	0.0202553	−	1.17709i
$370$	26.3738	−	21.3716i	1.37111	−	1.11106i
$371$	0.00766526	−	3.73381i	0.000397961	−	0.193850i
$372$	−12.6445	−	8.83892i	−0.655588	−	0.458277i
$373$	9.87235	−	4.08926i	0.511171	−	0.211734i	−0.112163	−	0.993690i	$-0.535778\pi$
$373$	9.87235	−	4.08926i	0.511171	−	0.211734i	0.623334	+	0.781956i	$0.285778\pi$
$374$	−19.3377	+	5.73510i	−0.999929	+	0.296555i
$375$	8.23901	−	8.09845i	0.425461	−	0.418202i
$376$	7.41839	−	22.9093i	0.382574	−	1.18146i
$377$	32.4653	−	32.4653i	1.67205	−	1.67205i
$378$	19.2724	+	2.56372i	0.991268	+	0.131864i
$379$	−0.521108	−	1.25807i	−0.0267675	−	0.0646225i	0.909931	−	0.414761i	$-0.136135\pi$
$379$	−0.521108	−	1.25807i	−0.0267675	−	0.0646225i	−0.936698	+	0.350138i	$0.886135\pi$
$380$	2.40963	−	11.3737i	0.123611	−	0.583457i
$381$	−4.86633	+	11.4683i	−0.249310	+	0.587538i
$382$	−3.33967	+	31.8770i	−0.170872	+	1.63097i
$383$	−27.2489			−1.39235			−0.696176	−	0.717871i	$-0.745117\pi$
$383$	−27.2489			−1.39235			−0.696176	+	0.717871i	$0.745117\pi$
$384$	−17.7395	+	8.32517i	−0.905268	+	0.424842i
$385$	20.6267	−	8.49428i	1.05123	−	0.432909i
$386$	−8.21493	−	0.860658i	−0.418129	−	0.0438063i
$387$	3.54505	+	1.54039i	0.180205	+	0.0783024i
$388$	−0.0587066	+	0.277100i	−0.00298038	+	0.0140676i
$389$	−29.5883	+	12.2559i	−1.50019	+	0.621397i	−0.973505	−	0.228666i	$-0.926563\pi$
$389$	−29.5883	+	12.2559i	−1.50019	+	0.621397i	−0.526680	+	0.850063i	$0.676563\pi$
$390$	−49.9447	−	27.6550i	−2.52905	−	1.40036i
$391$	−8.97826	−	8.97826i	−0.454050	−	0.454050i
$392$	−8.93371	−	17.6689i	−0.451220	−	0.892413i
$393$	16.1273	−	15.8522i	0.813516	−	0.799637i
$394$	9.69653	−	2.87576i	0.488504	−	0.144879i
$395$	12.9614	−	5.36878i	0.652157	−	0.270132i
$396$	8.49389	−	11.9310i	0.426834	−	0.599557i
$397$	14.3326	+	5.93676i	0.719333	+	0.297958i	0.712161	−	0.702017i	$-0.247717\pi$
$397$	14.3326	+	5.93676i	0.719333	+	0.297958i	0.00717280	+	0.999974i	$0.497717\pi$
$398$	−0.783695	−	0.967124i	−0.0392831	−	0.0484776i
$399$	7.15614	−	2.87522i	0.358255	−	0.143941i
$400$	−25.8694	+	9.96989i	−1.29347	+	0.498495i
$401$	5.51540			0.275426			0.137713	−	0.990472i	$-0.456025\pi$
$401$	5.51540			0.275426			0.137713	+	0.990472i	$0.456025\pi$
$402$	6.40915	−	5.10285i	0.319659	−	0.254507i
$403$	−11.4999	+	27.7631i	−0.572849	+	1.38298i
$404$	−3.34553	−	17.9840i	−0.166446	−	0.894738i
$405$	29.1131	−	10.9013i	1.44664	−	0.541692i
$406$	19.8134	−	15.9882i	0.983322	−	0.793482i
$407$	11.9943	−	11.9943i	0.594538	−	0.594538i
$408$	21.6246	+	18.7554i	1.07057	+	0.928528i
$409$	12.6157	+	12.6157i	0.623807	+	0.623807i	0.946503	−	0.322695i	$-0.104589\pi$
$409$	12.6157	+	12.6157i	0.623807	+	0.623807i	−0.322695	+	0.946503i	$0.604589\pi$
$410$	−17.5597	+	32.3667i	−0.867213	+	1.59848i
$411$	−13.4582	−	33.2985i	−0.663846	−	1.64249i
$412$	−3.01027	−	4.62865i	−0.148305	−	0.228037i
$413$	0.0403599	−	19.6596i	0.00198598	−	0.967386i
$414$	9.15138	+	1.11826i	0.449766	+	0.0549594i
$415$	−9.34816			−0.458883
$416$	23.2867	+	30.2434i	1.14173	+	1.48281i
$417$	13.7273	+	0.118100i	0.672229	+	0.00578337i
$418$	0.605334	−	5.77788i	0.0296078	−	0.282605i
$419$	−32.4501	−	13.4413i	−1.58529	−	0.656650i	−0.596051	−	0.802946i	$-0.703265\pi$
$419$	−32.4501	−	13.4413i	−1.58529	−	0.656650i	−0.989241	+	0.146297i	$0.953265\pi$
$420$	−25.9095	−	18.1908i	−1.26425	−	0.887621i
$421$	−5.99689	−	14.4778i	−0.292271	−	0.705604i	0.707729	−	0.706484i	$-0.249720\pi$
$421$	−5.99689	−	14.4778i	−0.292271	−	0.705604i	−1.00000		0.000880407i	$0.999720\pi$
$422$	−12.1657	+	22.4243i	−0.592218	+	1.09160i
$423$	18.3684	−	17.7469i	0.893103	−	0.862886i
$424$	0.317154	+	3.97899i	0.0154024	+	0.193237i
$425$	28.6365	+	28.6365i	1.38908	+	1.38908i
$426$	18.4172	−	5.29014i	0.892315	−	0.256308i
$427$	18.6770	−	18.6004i	0.903842	−	0.900139i
$428$	−1.27892	−	6.87487i	−0.0618189	−	0.332309i
$429$	−26.2611	−	11.1433i	−1.26790	−	0.538006i
$430$	−3.96242	−	4.88985i	−0.191085	−	0.235810i
$431$	−22.3699			−1.07752			−0.538761	−	0.842459i	$-0.681107\pi$
$431$	−22.3699			−1.07752			−0.538761	+	0.842459i	$0.681107\pi$
$432$	−20.7579	−	1.05243i	−0.998717	−	0.0506352i
$433$	−26.3881			−1.26813			−0.634065	−	0.773280i	$-0.718615\pi$
$433$	−26.3881			−1.26813			−0.634065	+	0.773280i	$0.718615\pi$
$434$	−7.97640	+	14.6306i	−0.382880	+	0.702293i
$435$	15.9015	−	37.4746i	0.762421	−	1.79677i
$436$	2.64627	−	3.85584i	0.126733	−	0.184661i
$437$	3.37870	−	1.39951i	0.161625	−	0.0669474i
$438$	−6.22520	−	21.6725i	−0.297452	−	1.03555i
$439$	5.05535	−	5.05535i	0.241279	−	0.241279i	−0.576100	−	0.817379i	$-0.695426\pi$
$439$	5.05535	−	5.05535i	0.241279	−	0.241279i	0.817379	+	0.576100i	$0.195426\pi$
$440$	−21.2374	+	10.8477i	−1.01245	+	0.517145i
$441$	0.447518	−	20.9952i	0.0213104	−	0.999773i
$442$	26.5886	−	49.0090i	1.26469	−	2.33112i
$443$	−11.7454	+	4.86509i	−0.558039	+	0.231147i	−0.643834	−	0.765166i	$-0.722657\pi$
$443$	−11.7454	+	4.86509i	−0.558039	+	0.231147i	0.0857946	+	0.996313i	$0.472657\pi$
$444$	−23.5062	−	5.19172i	−1.11555	−	0.246388i
$445$	−7.79224	−	3.22765i	−0.369388	−	0.153005i
$446$	−3.07869	+	29.3859i	−0.145780	+	1.39146i
$447$	0.739548	+	0.00636254i	0.0349794	+	0.000300938i
$448$	11.0582	+	18.0476i	0.522452	+	0.852669i
$449$			0.278239i			0.0131309i	0.999978	+	0.00656547i	$0.00208987\pi$
$449$			0.278239i			0.0131309i	−0.999978	+	0.00656547i	$0.997910\pi$
$450$	−29.1887	−	3.56673i	−1.37597	−	0.168137i
$451$	−7.04150	+	16.9997i	−0.331571	+	0.800484i
$452$	9.25490	+	1.96075i	0.435314	+	0.0922258i
$453$	30.9060	−	12.4913i	1.45209	−	0.586891i
$454$	1.39904	+	0.759014i	0.0656602	+	0.0356223i
$455$	−23.7148	+	56.9218i	−1.11177	+	2.66853i
$456$	−7.37427	+	3.68702i	−0.345332	+	0.172661i
$457$	15.1793	+	15.1793i	0.710058	+	0.710058i	0.966547	−	0.256490i	$-0.0825659\pi$
$457$	15.1793	+	15.1793i	0.710058	+	0.710058i	−0.256490	+	0.966547i	$0.582566\pi$
$458$	27.2377	−	8.07804i	1.27273	−	0.377462i
$459$	10.8910	+	28.3407i	0.508349	+	1.32283i
$460$	−12.3774	−	8.49463i	−0.577100	−	0.396064i
$461$	−4.53928	+	10.9588i	−0.211416	+	0.510402i	−0.993641	−	0.112593i	$-0.964084\pi$
$461$	−4.53928	+	10.9588i	−0.211416	+	0.510402i	0.782226	+	0.622995i	$0.214084\pi$
$462$	−13.8235	−	7.69134i	−0.643125	−	0.357834i
$463$			34.0126i			1.58070i	0.612657	+	0.790349i	$0.290101\pi$
$463$			34.0126i			1.58070i	−0.612657	+	0.790349i	$0.709899\pi$
$464$	−19.7179	+	18.7616i	−0.915381	+	0.870984i
$465$	−0.229221	+	26.6435i	−0.0106299	+	1.23556i
$466$	−18.5622	+	15.0416i	−0.859876	+	0.696788i
$467$	−12.7518	+	30.7855i	−0.590082	+	1.42458i	0.293341	+	0.956008i	$0.405233\pi$
$467$	−12.7518	+	30.7855i	−0.590082	+	1.42458i	−0.883423	+	0.468576i	$0.844767\pi$
$468$	6.71846	+	39.9239i	0.310561	+	1.84548i
$469$	−6.24423	−	6.26992i	−0.288332	−	0.289518i
$470$	−39.8720	+	11.8251i	−1.83916	+	0.545450i
$471$	−13.4105	−	13.6433i	−0.617924	−	0.628648i
$472$	1.66991	+	20.9506i	0.0768639	+	0.964329i
$473$	−2.22382	−	2.22382i	−0.102251	−	0.102251i
$474$	−8.70365	−	4.81932i	−0.399772	−	0.221359i
$475$	−10.7765	+	4.46378i	−0.494460	+	0.204812i
$476$	17.5477	−	25.4564i	0.804298	−	1.16679i
$477$	−1.68724	+	3.88302i	−0.0772535	+	0.177791i
$478$	16.8783	+	1.76830i	0.771998	+	0.0808803i
$479$	20.9380			0.956681			0.478340	−	0.878174i	$-0.341239\pi$
$479$	20.9380			0.956681			0.478340	+	0.878174i	$0.341239\pi$
$480$	29.1912	+	17.1246i	1.33239	+	0.781630i
$481$			46.8899i			2.13799i
$482$	27.7268	+	2.90487i	1.26292	+	0.132313i
$483$	0.106112	−	9.95758i	0.00482827	−	0.453086i
$484$	8.45315	−	5.49755i	0.384234	−	0.249888i
$485$	0.451955	−	0.187206i	0.0205222	−	0.00850059i
$486$	−18.9074	−	11.3362i	−0.857657	−	0.514223i
$487$	16.1529	−	16.1529i	0.731960	−	0.731960i	−0.239048	−	0.971008i	$-0.576835\pi$
$487$	16.1529	−	16.1529i	0.731960	−	0.731960i	0.971008	+	0.239048i	$0.0768353\pi$
$488$	−18.2795	+	21.4459i	−0.827473	+	0.970808i
$489$	26.4650	−	26.0135i	1.19679	−	1.17637i
$490$	−16.4293	+	29.9886i	−0.742200	+	1.35475i
$491$	8.07180	+	19.4870i	0.364275	+	0.879438i	0.994665	+	0.103159i	$0.0328951\pi$
$491$	8.07180	+	19.4870i	0.364275	+	0.879438i	−0.630390	+	0.776279i	$0.717105\pi$
$492$	25.7128	−	4.55480i	1.15922	−	0.205346i
$493$	36.7318	+	15.2148i	1.65432	+	0.685240i
$494$	10.1106	+	12.4770i	0.454897	+	0.561369i
$495$	−25.2903	−	0.435191i	−1.13671	−	0.0195604i
$496$	7.22402	−	16.2838i	0.324368	−	0.731162i
$497$	−7.88121	−	19.1379i	−0.353520	−	0.858454i
$498$	4.12916	+	5.18621i	0.185032	+	0.232399i
$499$	6.51405	−	15.7263i	0.291609	−	0.704006i	−0.708389	−	0.705822i	$-0.750578\pi$
$499$	6.51405	−	15.7263i	0.291609	−	0.704006i	0.999998	+	0.00181551i	$0.000577895\pi$
$500$	10.9989	+	7.54852i	0.491884	+	0.337580i
$501$	−8.41246	−	20.8142i	−0.375841	−	0.929909i
$502$	1.86381	+	6.28444i	0.0831861	+	0.280488i
$503$	10.7244	+	10.7244i	0.478178	+	0.478178i	0.904548	−	0.426371i	$-0.140208\pi$
$503$	10.7244	+	10.7244i	0.478178	+	0.478178i	−0.426371	+	0.904548i	$0.640208\pi$
$504$	1.35246	+	22.4092i	0.0602434	+	0.998184i
$505$	−22.3392	+	22.3392i	−0.994082	+	0.994082i
$506$	−6.59354	−	3.57716i	−0.293119	−	0.159024i
$507$	52.2372	−	21.1127i	2.31993	−	0.937648i
$508$	−14.0729	−	2.98150i	−0.624386	−	0.132283i
$509$	31.6877	+	13.1255i	1.40453	+	0.581777i	0.950924	−	0.309424i	$-0.100136\pi$
$509$	31.6877	+	13.1255i	1.40453	+	0.581777i	0.453609	+	0.891201i	$0.350136\pi$
$510$	5.57400	−	49.1218i	0.246821	−	2.17515i
$511$	−22.5207	+	9.27425i	−0.996256	+	0.410269i
$512$	−13.3549	−	18.2660i	−0.590208	−	0.807251i
$513$	−8.74184	−	0.225670i	−0.385962	−	0.00996359i
$514$	10.7563	+	1.12691i	0.474440	+	0.0497059i
$515$	−3.64921	+	8.80998i	−0.160804	+	0.388214i
$516$	−0.962574	+	4.35817i	−0.0423750	+	0.191858i
$517$	−19.1996	+	7.95275i	−0.844399	+	0.349762i
$518$	−2.76236	+	25.8543i	−0.121371	+	1.13597i
$519$	−9.47353	−	9.63795i	−0.415842	−	0.423059i
$520$	20.3083	−	62.7157i	0.890578	−	2.75027i
$521$	20.5664	+	20.5664i	0.901031	+	0.901031i	0.995525	−	0.0944943i	$-0.0301234\pi$
$521$	20.5664	+	20.5664i	0.901031	+	0.901031i	−0.0944943	+	0.995525i	$0.530123\pi$
$522$	−27.8141	+	7.73092i	−1.21739	+	0.338373i
$523$	−1.64420	−	3.96944i	−0.0718956	−	0.173571i	0.883847	−	0.467777i	$-0.154945\pi$
$523$	−1.64420	−	3.96944i	−0.0718956	−	0.173571i	−0.955742	+	0.294206i	$0.904945\pi$
$524$	21.5295	+	14.7757i	0.940522	+	0.645481i
$525$	−0.338449	+	31.7601i	−0.0147711	+	1.38612i
$526$	8.22609	+	10.1515i	0.358674	+	0.442624i
$527$	−26.0223			−1.13355
$528$	15.3989	+	6.99061i	0.670150	+	0.304227i
$529$			18.2779i			0.794690i
$530$	5.35603	−	4.34018i	0.232651	−	0.188525i
$531$	−8.88384	+	20.4452i	−0.385526	+	0.887248i
$532$	4.83977	+	7.47527i	0.209831	+	0.324094i
$533$	−19.4649	−	46.9925i	−0.843120	−	2.03547i
$534$	1.65125	+	5.74869i	0.0714566	+	0.248770i
$535$	−8.53976	+	8.53976i	−0.369206	+	0.369206i
$536$	7.19945	+	6.13648i	0.310969	+	0.265056i
$537$	15.3191	−	15.0578i	0.661068	−	0.649791i
$538$	5.10221	−	9.40457i	0.219972	−	0.405460i
$539$	−6.60352	+	15.7590i	−0.284434	+	0.678788i
$540$	18.7875	+	30.5872i	0.808487	+	1.31626i
$541$	6.16702	+	2.55446i	0.265141	+	0.109825i	0.511294	−	0.859406i	$-0.329166\pi$
$541$	6.16702	+	2.55446i	0.265141	+	0.109825i	−0.246153	+	0.969231i	$0.579166\pi$
$542$	−36.2921	−	3.80223i	−1.55888	−	0.163320i
$543$	−33.4554	−	0.287827i	−1.43571	−	0.0123518i
$544$	−16.4789	+	28.6524i	−0.706527	+	1.22846i
$545$	−8.07673			−0.345969
$546$	42.0543	−	11.9862i	1.79976	−	0.512964i
$547$	−16.5591	−	6.85901i	−0.708017	−	0.293270i	−0.000533071	−	1.00000i	$-0.500170\pi$
$547$	−16.5591	−	6.85901i	−0.708017	−	0.293270i	−0.707484	+	0.706730i	$0.750170\pi$
$548$	34.7659	−	22.6102i	1.48512	−	0.965858i
$549$	−27.8061	+	10.9610i	−1.18673	+	0.467806i
$550$	21.0304	+	11.4095i	0.896738	+	0.486502i
$551$	−8.09728	+	8.09728i	−0.344956	+	0.344956i
$552$	0.754530	+	10.6189i	0.0321149	+	0.451972i
$553$	−4.13268	+	9.91953i	−0.175739	+	0.421821i
$554$	−21.1106	+	6.26089i	−0.896904	+	0.266000i
$555$	15.5791	+	38.5458i	0.661294	+	1.63618i
$556$	2.89909	+	15.5841i	0.122949	+	0.660915i
$557$	34.2131	+	14.1715i	1.44966	+	0.600467i	0.962118	−	0.272634i	$-0.0878948\pi$
$557$	34.2131	+	14.1715i	1.44966	+	0.600467i	0.487539	+	0.873101i	$0.337895\pi$
$558$	14.8826	−	11.6415i	0.630031	−	0.492823i
$559$	8.69365			0.367702
$560$	14.8924	−	33.3840i	0.629317	−	1.41073i
$561$	0.212523	−	24.7025i	0.00897271	−	1.04294i
$562$	−14.1142	−	17.4177i	−0.595371	−	0.734722i
$563$	16.0113	−	38.6547i	0.674796	−	1.62910i	−0.0985600	−	0.995131i	$-0.531424\pi$
$563$	16.0113	−	38.6547i	0.674796	−	1.62910i	0.773356	−	0.633972i	$-0.218576\pi$
$564$	24.1721	+	16.8971i	1.01783	+	0.711496i
$565$	−6.25251	−	15.0949i	−0.263045	−	0.635047i
$566$	2.81845	−	0.835884i	0.118468	−	0.0351348i
$567$	−9.90834	+	21.6524i	−0.416111	+	0.909314i
$568$	10.0648	+	19.7046i	0.422310	+	0.826786i
$569$	−6.20686	−	6.20686i	−0.260205	−	0.260205i	0.564932	−	0.825137i	$-0.308902\pi$
$569$	−6.20686	−	6.20686i	−0.260205	−	0.260205i	−0.825137	+	0.564932i	$0.808902\pi$
$570$	12.4569	+	6.89753i	0.521761	+	0.288906i
$571$	−9.61177	−	23.2049i	−0.402240	−	0.971093i	−0.987121	−	0.159974i	$-0.948859\pi$
$571$	−9.61177	−	23.2049i	−0.402240	−	0.971093i	0.584881	−	0.811119i	$-0.301141\pi$
$572$	6.82730	−	32.2255i	0.285464	−	1.34741i
$573$	−36.1362	−	15.3336i	−1.50961	−	0.640571i
$574$	−7.96423	−	27.0576i	−0.332421	−	1.12936i
$575$			15.0614i			0.628105i
$576$	−3.39351	−	23.7589i	−0.141396	−	0.989953i
$577$			1.64323i			0.0684087i	0.999415	+	0.0342043i	$0.0108897\pi$
$577$			1.64323i			0.0684087i	−0.999415	+	0.0342043i	$0.989110\pi$
$578$	24.1091	+	2.52585i	1.00281	+	0.105062i
$579$	3.95159	−	9.31256i	0.164222	−	0.387017i
$580$	45.9857	+	9.74255i	1.90945	+	0.404537i
$581$	5.07354	−	5.05275i	0.210486	−	0.209624i
$582$	−0.303491	−	0.168047i	−0.0125801	−	0.00696576i
$583$	2.43583	−	2.43583i	0.100882	−	0.100882i
$584$	23.1875	−	11.8438i	0.959504	−	0.490100i
$585$	50.2847	−	48.5834i	2.07902	−	2.00868i
$586$	−8.95596	−	30.1979i	−0.369967	−	1.24746i
$587$	−24.8622	+	10.2983i	−1.02617	+	0.425055i	−0.831330	−	0.555779i	$-0.812420\pi$
$587$	−24.8622	+	10.2983i	−1.02617	+	0.425055i	−0.194844	+	0.980834i	$0.562420\pi$
$588$	23.8942	−	4.13153i	0.985378	−	0.170381i
$589$	2.86822	−	6.92450i	0.118183	−	0.285319i
$590$	28.2011	−	22.8523i	1.16102	−	0.940816i
$591$	−0.106565	+	12.3866i	−0.00438352	+	0.509516i
$592$	0.690613	−	27.7881i	0.0283840	−	1.14209i
$593$		−	26.1227i		−	1.07273i	−0.843986	−	0.536365i	$-0.819797\pi$
$593$		−	26.1227i		−	1.07273i	0.843986	−	0.536365i	$-0.180203\pi$
$594$	10.9295	+	14.2228i	0.448442	+	0.583571i
$595$	−53.3980	−	0.109623i	−2.18911	−	0.00449409i
$596$	0.156186	+	0.839584i	0.00639764	+	0.0343907i
$597$	1.41347	−	0.571282i	0.0578495	−	0.0233810i
$598$	19.8803	−	5.89602i	0.812967	−	0.241106i
$599$	−17.6443	+	17.6443i	−0.720927	+	0.720927i	−0.968794	−	0.247867i	$-0.920270\pi$
$599$	−17.6443	+	17.6443i	−0.720927	+	0.720927i	0.247867	+	0.968794i	$0.420270\pi$
$600$	−2.40660	−	33.8695i	−0.0982492	−	1.38272i
$601$	20.5736	+	20.5736i	0.839215	+	0.839215i	0.988756	−	0.149540i	$-0.0477793\pi$
$601$	20.5736	+	20.5736i	0.839215	+	0.839215i	−0.149540	+	0.988756i	$0.547779\pi$
$602$	4.79353	+	0.512158i	0.195370	+	0.0208740i
$603$	3.67966	+	9.33459i	0.149847	+	0.380134i
$604$	20.9856	+	32.2679i	0.853893	+	1.31296i
$605$	−16.0894	−	6.66444i	−0.654126	−	0.270948i
$606$	22.2608	+	2.52601i	0.904285	+	0.102612i
$607$			21.0802i			0.855618i	0.903869	+	0.427809i	$0.140714\pi$
$607$			21.0802i			0.855618i	−0.903869	+	0.427809i	$0.859286\pi$
$608$	−5.80803	−	7.54313i	−0.235547	−	0.305914i
$609$	11.6250	+	28.9335i	0.471070	+	1.17245i
$610$	48.4023	+	5.07099i	1.95975	+	0.205318i
$611$	21.9839	−	53.0739i	0.889374	−	2.14714i
$612$	−29.7141	+	18.6052i	−1.20112	+	0.752069i
$613$	4.15844	+	10.0394i	0.167958	+	0.405486i	0.985338	−	0.170612i	$-0.0545746\pi$
$613$	4.15844	+	10.0394i	0.167958	+	0.405486i	−0.817380	+	0.576098i	$0.804575\pi$
$614$	0.391618	+	0.212462i	0.0158044	+	0.00857428i
$615$	−31.6143	−	32.1630i	−1.27481	−	1.29694i
$616$	5.66292	−	17.3664i	0.228165	−	0.699711i
$617$	14.7262	−	14.7262i	0.592854	−	0.592854i	−0.345548	−	0.938401i	$-0.612307\pi$
$617$	14.7262	−	14.7262i	0.592854	−	0.592854i	0.938401	+	0.345548i	$0.112307\pi$
$618$	6.49952	−	1.86692i	0.261449	−	0.0750985i
$619$	−3.72391	−	8.99031i	−0.149676	−	0.361351i	0.831202	−	0.555970i	$-0.187653\pi$
$619$	−3.72391	−	8.99031i	−0.149676	−	0.361351i	−0.980879	+	0.194619i	$0.937653\pi$
$620$	−30.2474	+	5.62687i	−1.21477	+	0.225981i
$621$	−4.58883	+	10.3170i	−0.184144	+	0.414006i
$622$	22.9144	+	28.2777i	0.918783	+	1.13383i
$623$	5.97366	−	2.46002i	0.239330	−	0.0985585i
$624$	−43.7640	+	16.4353i	−1.75196	+	0.657940i
$625$			11.6161i			0.464643i
$626$	−1.82056	−	2.24667i	−0.0727642	−	0.0897952i
$627$	6.54988	+	2.77930i	0.261577	+	0.110995i
$628$	12.4999	−	18.2134i	0.498799	−	0.726793i
$629$	−37.5135	+	15.5386i	−1.49576	+	0.619564i
$630$	30.5883	−	23.8257i	1.21867	−	0.949240i
$631$	5.77138	+	5.77138i	0.229755	+	0.229755i	0.812590	−	0.582835i	$-0.198057\pi$
$631$	5.77138	+	5.77138i	0.229755	+	0.229755i	−0.582835	+	0.812590i	$0.698057\pi$
$632$	3.53905	−	10.9292i	0.140776	−	0.434741i
$633$	−21.9030	−	22.2831i	−0.870566	−	0.885675i
$634$	−13.9512	+	25.7153i	−0.554071	+	1.02128i
$635$	9.50753	+	22.9532i	0.377295	+	0.910870i
$636$	−4.77366	−	1.05434i	−0.189288	−	0.0418073i
$637$	−17.8959	−	43.7112i	−0.709061	−	1.73190i
$638$	23.3610	+	2.44747i	0.924869	+	0.0968962i
$639$	−0.403781	+	23.4650i	−0.0159733	+	0.928259i
$640$	−12.9589	+	36.8678i	−0.512247	+	1.45733i
$641$			0.146112i			0.00577107i	0.999996	+	0.00288554i	$0.000918496\pi$
$641$			0.146112i			0.00577107i	−0.999996	+	0.00288554i	$0.999082\pi$
$642$	8.50980	+	0.965633i	0.335855	+	0.0381105i
$643$	−8.67574	+	20.9451i	−0.342138	+	0.825994i	0.655361	+	0.755316i	$0.272516\pi$
$643$	−8.67574	+	20.9451i	−0.342138	+	0.825994i	−0.997499	+	0.0706785i	$0.977484\pi$
$644$	11.3090	−	2.07979i	0.445638	−	0.0819551i
$645$	7.14661	−	2.88845i	0.281398	−	0.113732i
$646$	−6.63156	+	12.2235i	−0.260915	+	0.480928i
$647$	−26.1219	+	26.1219i	−1.02696	+	1.02696i	−0.0273318	+	0.999626i	$0.508701\pi$
$647$	−26.1219	+	26.1219i	−1.02696	+	1.02696i	−0.999626	+	0.0273318i	$0.991299\pi$
$648$	8.67068	−	23.9336i	0.340616	−	0.940202i
$649$	12.8254	−	12.8254i	0.503439	−	0.503439i
$650$	−63.4091	+	18.8056i	−2.48711	+	0.737617i
$651$	−14.2766	−	14.5841i	−0.559544	−	0.571598i
$652$	35.3301	+	24.2471i	1.38363	+	0.949588i
$653$	30.3469	+	12.5701i	1.18757	+	0.491907i	0.886962	−	0.461842i	$-0.152811\pi$
$653$	30.3469	+	12.5701i	1.18757	+	0.491907i	0.300606	+	0.953749i	$0.402811\pi$
$654$	3.56756	+	4.48084i	0.139503	+	0.175215i
$655$		−	45.0974i		−	1.76210i
$656$	10.8433	+	28.1356i	0.423359	+	1.09851i
$657$	27.6125	+	0.475152i	1.07727	+	0.0185374i
$658$	15.2482	−	27.9690i	0.594438	−	1.09034i
$659$	−1.85537	−	0.768518i	−0.0722748	−	0.0299372i	0.346253	−	0.938141i	$-0.387454\pi$
$659$	−1.85537	−	0.768518i	−0.0722748	−	0.0299372i	−0.418528	+	0.908204i	$0.637454\pi$
$660$	−5.09446	−	28.7593i	−0.198301	−	1.11945i
$661$	−4.69879	−	11.3439i	−0.182762	−	0.441226i	0.805772	−	0.592226i	$-0.201751\pi$
$661$	−4.69879	−	11.3439i	−0.182762	−	0.441226i	−0.988534	+	0.151000i	$0.951751\pi$
$662$	−1.99164	+	0.590672i	−0.0774072	+	0.0229571i
$663$	47.8697	+	48.7005i	1.85911	+	1.89137i
$664$	−4.96556	+	5.82570i	−0.192701	+	0.226081i
$665$	5.91479	−	14.1971i	0.229366	−	0.550539i
$666$	14.5032	−	25.6690i	0.561987	−	0.994654i
$667$	5.65844	+	13.6607i	0.219096	+	0.528944i
$668$	21.7314	−	14.1331i	0.840813	−	0.546827i
$669$	−33.3123	−	14.1354i	−1.28793	−	0.546505i
$670$	1.70235	−	16.2488i	0.0657674	−	0.627747i
$671$	24.3187			0.938813
$672$	−25.0990	+	6.48396i	−0.968214	+	0.250124i
$673$	−48.3023			−1.86192			−0.930959	−	0.365124i	$-0.881026\pi$
$673$	−48.3023			−1.86192			−0.930959	+	0.365124i	$0.881026\pi$
$674$	−2.67983	+	25.5789i	−0.103223	+	0.985261i
$675$	14.6363	−	32.9064i	0.563350	−	1.26657i
$676$	35.4698	+	54.5391i	1.36422	+	2.09766i
$677$	7.08612	+	17.1074i	0.272342	+	0.657491i	0.999583	−	0.0288911i	$-0.00919761\pi$
$677$	7.08612	+	17.1074i	0.272342	+	0.657491i	−0.727241	+	0.686383i	$0.759198\pi$
$678$	−5.61261	+	10.1363i	−0.215551	+	0.389284i
$679$	−0.144104	+	0.345888i	−0.00553021	+	0.0132740i
$680$	56.9045	−	4.53570i	2.18219	−	0.173936i
$681$	−1.39023	+	1.36652i	−0.0532739	+	0.0523651i
$682$	−14.7392	+	4.37129i	−0.564394	+	0.167385i
$683$	5.06055	+	12.2172i	0.193636	+	0.467480i	0.990641	−	0.136494i	$-0.0435833\pi$
$683$	5.06055	+	12.2172i	0.193636	+	0.467480i	−0.797004	+	0.603973i	$0.793583\pi$
$684$	−1.67568	−	9.95757i	−0.0640710	−	0.380737i
$685$	−66.1719	−	27.4093i	−2.52830	−	1.04726i
$686$	−7.29239	−	25.1559i	−0.278425	−	0.960458i
$687$	−0.299344	+	34.7941i	−0.0114207	+	1.32748i
$688$	−5.15208	−	0.128044i	−0.196421	−	0.00488162i
$689$			9.52246i			0.362777i
$690$	14.3837	−	11.4520i	0.547577	−	0.435971i
$691$	12.9952	+	5.38280i	0.494362	+	0.204771i	0.615913	−	0.787814i	$-0.288787\pi$
$691$	12.9952	+	5.38280i	0.494362	+	0.204771i	−0.121552	+	0.992585i	$0.538787\pi$
$692$	8.83022	−	12.8664i	0.335675	−	0.489107i
$693$	13.9611	−	13.4334i	0.530336	−	0.510292i
$694$	−24.7676	+	7.34548i	−0.940166	+	0.278831i
$695$	19.3582	−	19.3582i	0.734297	−	0.734297i
$696$	−14.9073	−	29.8155i	−0.565058	−	1.13015i
$697$	31.1452	−	31.1452i	1.17971	−	1.17971i
$698$	9.59166	−	17.6797i	0.363050	−	0.669186i
$699$	−10.9647	−	27.1290i	−0.414724	−	1.02611i
$700$	−36.0706	+	6.63356i	−1.36334	+	0.250725i
$701$	−0.169272	+	0.408659i	−0.00639332	+	0.0154348i	−0.927044	−	0.374953i	$-0.877659\pi$
$701$	−0.169272	+	0.408659i	−0.00639332	+	0.0154348i	0.920651	+	0.390387i	$0.127659\pi$
$702$	−49.1644	−	6.43742i	−1.85559	−	0.242965i
$703$		−	11.6950i		−	0.441085i
$704$	−4.52066	+	18.9971i	−0.170379	+	0.715979i
$705$	0.438195	−	50.9335i	0.0165034	−	1.91827i
$706$	11.3226	+	1.18624i	0.426130	+	0.0446446i
$707$	0.0496784	−	24.1987i	0.00186835	−	0.910086i
$708$	−25.1347	−	5.55142i	−0.944622	−	0.208635i
$709$	6.58167	+	15.8896i	0.247180	+	0.596745i	0.997962	−	0.0638044i	$-0.0203234\pi$
$709$	6.58167	+	15.8896i	0.247180	+	0.596745i	−0.750783	+	0.660549i	$0.770323\pi$
$710$	18.2227	−	33.5887i	0.683886	−	1.26056i
$711$	8.76291	−	8.46643i	0.328635	−	0.317516i
$712$	−6.15053	+	3.14160i	−0.230501	+	0.117736i
$713$	−6.84323	−	6.84323i	−0.256281	−	0.256281i
$714$	23.5255	+	29.6728i	0.880421	+	1.11047i
$715$	−52.5602	+	21.7712i	−1.96564	+	0.814195i
$716$	20.4506	+	14.0353i	0.764275	+	0.524522i
$717$	−8.11891	+	19.1335i	−0.303206	+	0.714554i
$718$	−31.6413	−	39.0471i	−1.18084	−	1.45723i
$719$		−	37.7092i		−	1.40631i	−0.711034	−	0.703157i	$-0.751773\pi$
$719$		−	37.7092i		−	1.40631i	0.711034	−	0.703157i	$-0.248227\pi$
$720$	−30.5156	+	28.0512i	−1.13725	+	1.04540i
$721$	−2.78132	−	6.75388i	−0.103582	−	0.251528i
$722$	14.3951	+	17.7644i	0.535730	+	0.661122i
$723$	−13.3373	+	31.4315i	−0.496019	+	1.16895i
$724$	−7.06550	−	37.9808i	−0.262587	−	1.41155i
$725$	−18.0478	−	43.5713i	−0.670280	−	1.61820i
$726$	3.40949	+	11.8699i	0.126538	+	0.440532i
$727$	30.0556	−	30.0556i	1.11470	−	1.11470i	0.122195	−	0.992506i	$-0.461007\pi$
$727$	30.0556	−	30.0556i	1.11470	−	1.11470i	0.992506	−	0.122195i	$-0.0389934\pi$
$728$	22.8764	+	45.0146i	0.847854	+	1.66835i
$729$	20.0515	−	18.0814i	0.742649	−	0.669681i
$730$	−39.5257	−	21.4437i	−1.46291	−	0.793666i
$731$	2.88094	+	6.95521i	0.106555	+	0.257248i
$732$	−18.5664	−	29.0927i	−0.686234	−	1.07530i
$733$	−6.41674	+	15.4914i	−0.237008	+	0.572188i	−0.996971	−	0.0777790i	$-0.975217\pi$
$733$	−6.41674	+	15.4914i	−0.237008	+	0.572188i	0.759963	+	0.649967i	$0.225217\pi$
$734$	−20.4469	−	2.14217i	−0.754707	−	0.0790688i
$735$	−29.2343	−	29.9869i	−1.07832	−	1.10609i
$736$	−11.8684	+	3.20133i	−0.437476	+	0.118003i
$737$		−	8.16387i		−	0.300720i
$738$	−3.87919	+	31.7457i	−0.142795	+	1.16858i
$739$	18.0230	+	7.46536i	0.662986	+	0.274618i	0.688695	−	0.725052i	$-0.258184\pi$
$739$	18.0230	+	7.46536i	0.662986	+	0.274618i	−0.0257084	+	0.999669i	$0.508184\pi$
$740$	−40.2444	+	26.1732i	−1.47941	+	0.962145i
$741$	−18.2354	+	7.37022i	−0.669896	+	0.270752i
$742$	−0.560984	+	5.25053i	−0.0205944	+	0.192753i
$743$	21.6861	+	21.6861i	0.795588	+	0.795588i	0.982396	−	0.186809i	$-0.0598145\pi$
$743$	21.6861	+	21.6861i	0.795588	+	0.795588i	−0.186809	+	0.982396i	$0.559814\pi$
$744$	16.4822	+	14.2953i	0.604268	+	0.524092i
$745$	1.04291	−	1.04291i	0.0382091	−	0.0382091i
$746$	−14.4882	+	4.29685i	−0.530451	+	0.157319i
$747$	−7.55343	+	2.97753i	−0.276366	+	0.108942i
$748$	28.0439	−	5.21696i	1.02539	−	0.190751i
$749$	0.0189909	−	9.25060i	0.000693912	−	0.338010i
$750$	−12.7817	+	10.1765i	−0.466720	+	0.371594i
$751$			0.713669i			0.0260422i	0.999915	+	0.0130211i	$0.00414486\pi$
$751$			0.713669i			0.0260422i	−0.999915	+	0.0130211i	$0.995855\pi$
$752$	−13.8099	+	31.1292i	−0.503596	+	1.13516i
$753$	−8.02790	−	0.0690663i	−0.292553	−	0.00251692i
$754$	−50.4469	+	40.8789i	−1.83717	+	1.48872i
$755$	25.4399	−	61.4175i	0.925855	−	2.23521i
$756$	−26.7292	−	6.44585i	−0.972132	−	0.234433i
$757$	−46.2904	+	19.1741i	−1.68245	+	0.696896i	−0.999438	−	0.0335073i	$-0.989332\pi$
$757$	−46.2904	+	19.1741i	−1.68245	+	0.696896i	−0.683016	+	0.730403i	$0.739332\pi$
$758$	0.547562	+	1.84628i	0.0198883	+	0.0670599i
$759$	6.55204	−	6.44027i	0.237824	−	0.233767i
$760$	−5.06517	+	15.6422i	−0.183733	+	0.567401i
$761$	1.08863	−	1.08863i	0.0394626	−	0.0394626i	−0.687100	−	0.726563i	$-0.741117\pi$
$761$	1.08863	−	1.08863i	0.0394626	−	0.0394626i	0.726563	+	0.687100i	$0.241117\pi$
$762$	8.53450	−	15.4132i	0.309172	−	0.558363i
$763$	4.38350	−	4.36554i	0.158693	−	0.158043i
$764$	9.39460	−	44.3433i	0.339885	−	1.60429i
$765$	55.5319	+	24.1297i	2.00776	+	0.872409i
$766$	38.3259	+	4.01531i	1.38477	+	0.145079i
$767$			50.1386i			1.81040i
$768$	26.1777	−	9.09543i	0.944607	−	0.328203i
$769$		−	20.4010i		−	0.735679i	−0.929889	−	0.367840i	$-0.880098\pi$
$769$		−	20.4010i		−	0.735679i	0.929889	−	0.367840i	$-0.119902\pi$
$770$	−30.2634	+	8.90785i	−1.09062	+	0.321017i
$771$	−5.17405	+	12.1935i	−0.186339	+	0.439138i
$772$	11.4276	+	2.42106i	0.411288	+	0.0871357i
$773$	18.2059	+	43.9530i	0.654822	+	1.58088i	0.805697	+	0.592328i	$0.201791\pi$
$773$	18.2059	+	43.9530i	0.654822	+	1.58088i	−0.150874	+	0.988553i	$0.548209\pi$
$774$	−4.75918	−	2.68897i	−0.171065	−	0.0966530i
$775$	21.8268	+	21.8268i	0.784041	+	0.784041i
$776$	0.123404	−	0.381095i	0.00442996	−	0.0136805i
$777$	−29.2896	−	12.4994i	−1.05076	−	0.448414i
$778$	43.4224	−	12.8780i	1.55677	−	0.461699i
$779$	4.85482	+	11.7206i	0.173942	+	0.419933i
$780$	66.1728	+	46.2568i	2.36937	+	1.65626i
$781$	7.30736	−	17.6415i	0.261478	−	0.631263i
$782$	11.3051	+	13.9511i	0.404268	+	0.498889i
$783$	0.912424	−	35.3448i	0.0326074	−	1.26312i
$784$	9.96176	+	26.1680i	0.355777	+	0.934571i
$785$	−38.1511			−1.36167
$786$	−25.0193	+	19.9199i	−0.892408	+	0.710519i
$787$	19.6264	+	8.12952i	0.699605	+	0.289786i	0.703996	−	0.710204i	$-0.251397\pi$
$787$	19.6264	+	8.12952i	0.699605	+	0.289786i	−0.00439031	+	0.999990i	$0.501397\pi$
$788$	−14.0621	+	2.61594i	−0.500941	+	0.0931891i
$789$	−14.8365	+	5.99648i	−0.528195	+	0.213480i
$790$	−19.0215	+	5.64132i	−0.676755	+	0.200709i
$791$	11.5523	+	4.81295i	0.410754	+	0.171129i
$792$	−13.7049	+	15.5295i	−0.486983	+	0.551818i
$793$	−47.5350	+	47.5350i	−1.68802	+	1.68802i
$794$	−19.2842	−	10.4622i	−0.684371	−	0.371288i
$795$	3.16382	+	7.82793i	0.112209	+	0.277628i
$796$	0.959767	+	1.47576i	0.0340180	+	0.0523069i
$797$	−3.07891	−	1.27533i	−0.109061	−	0.0451744i	0.327486	−	0.944856i	$-0.393799\pi$
$797$	−3.07891	−	1.27533i	−0.109061	−	0.0451744i	−0.436547	+	0.899682i	$0.643799\pi$
$798$	−10.4889	+	2.98953i	−0.371303	+	0.105828i
$799$	49.7460			1.75989
$800$	37.8548	−	10.2108i	1.33837	−	0.361005i
$801$	−7.32428	−	0.126035i	−0.258791	−	0.00445323i
$802$	−7.75750	−	0.812734i	−0.273927	−	0.0286986i
$803$	−20.7597	−	8.59897i	−0.732595	−	0.303451i
$804$	−9.76651	+	6.23280i	−0.344438	+	0.219814i
$805$	−14.0136	−	14.0712i	−0.493913	−	0.495945i
$806$	20.2658	−	37.3547i	0.713833	−	1.31576i
$807$	9.18595	+	9.34538i	0.323361	+	0.328973i
$808$	2.05547	+	25.7878i	0.0723112	+	0.907211i
$809$	2.50551	−	2.50551i	0.0880889	−	0.0880889i	−0.661689	−	0.749778i	$-0.730160\pi$
$809$	2.50551	−	2.50551i	0.0880889	−	0.0880889i	0.749778	+	0.661689i	$0.230160\pi$
$810$	−42.5544	+	11.0429i	−1.49521	+	0.388008i
$811$	17.0335	+	41.1225i	0.598126	+	1.44401i	0.875488	+	0.483239i	$0.160540\pi$
$811$	17.0335	+	41.1225i	0.598126	+	1.44401i	−0.277362	+	0.960766i	$0.589460\pi$
$812$	−30.2238	+	19.5680i	−1.06065	+	0.686703i
$813$	17.4574	−	41.1412i	0.612257	−	1.44288i
$814$	−18.6377	+	15.1028i	−0.653250	+	0.529352i
$815$		−	74.0050i		−	2.59228i
$816$	−27.6515	−	29.5662i	−0.967997	−	1.03503i
$817$	−2.16832			−0.0758598
$818$	−15.8852	−	19.6032i	−0.555413	−	0.685411i
$819$	−1.03139	+	53.5470i	−0.0360398	+	1.87108i
$820$	29.4675	−	42.9367i	1.02905	−	1.49941i
$821$	4.01965	+	9.70430i	0.140287	+	0.338682i	0.978371	−	0.206859i	$-0.0663241\pi$
$821$	4.01965	+	9.70430i	0.140287	+	0.338682i	−0.838084	+	0.545541i	$0.816324\pi$
$822$	14.0225	+	48.8180i	0.489090	+	1.70272i
$823$	−24.2528	−	24.2528i	−0.845399	−	0.845399i	0.144156	−	0.989555i	$-0.453953\pi$
$823$	−24.2528	−	24.2528i	−0.845399	−	0.845399i	−0.989555	+	0.144156i	$0.953953\pi$
$824$	3.55192	+	6.95385i	0.123737	+	0.242249i
$825$	−20.8980	+	20.5415i	−0.727575	+	0.715163i
$826$	−2.95375	+	27.6456i	−0.102774	+	0.961913i
$827$	−5.56590	+	2.30547i	−0.193545	+	0.0801692i	−0.477351	−	0.878713i	$-0.658403\pi$
$827$	−5.56590	+	2.30547i	−0.193545	+	0.0801692i	0.283806	+	0.958882i	$0.408403\pi$
$828$	−12.7068	−	2.92137i	−0.441591	−	0.101525i
$829$	−12.1579	+	29.3518i	−0.422262	+	1.01943i	0.559417	+	0.828887i	$0.311025\pi$
$829$	−12.1579	+	29.3518i	−0.422262	+	1.01943i	−0.981679	+	0.190544i	$0.938975\pi$
$830$	13.1483	+	1.37752i	0.456385	+	0.0478144i
$831$	0.232007	−	26.9672i	0.00804822	−	0.935482i
$832$	−28.2966	−	45.9693i	−0.981007	−	1.59370i
$833$	29.0400	−	28.8025i	1.00618	−	0.997949i
$834$	−19.2903	−	2.18892i	−0.667967	−	0.0757962i
$835$	−41.3627	−	17.1330i	−1.43141	−	0.592911i
$836$	−1.70282	+	8.03747i	−0.0588933	+	0.277982i
$837$	8.30114	+	21.6013i	0.286929	+	0.746649i
$838$	43.6609	+	23.6871i	1.50824	+	0.818258i
$839$	−22.5937	+	22.5937i	−0.780020	+	0.780020i	−0.979834	−	0.199814i	$-0.935966\pi$
$839$	−22.5937	+	22.5937i	−0.780020	+	0.780020i	0.199814	+	0.979834i	$0.435966\pi$
$840$	33.7615	+	29.4036i	1.16488	+	1.01452i
$841$	−12.2326	−	12.2326i	−0.421814	−	0.421814i
$842$	6.30132	+	21.2469i	0.217158	+	0.732216i
$843$	25.4563	−	10.2887i	0.876762	−	0.354361i
$844$	20.4156	−	29.7474i	0.702736	−	1.02395i
$845$	42.9985	−	103.808i	1.47919	−	3.57109i
$846$	−28.4506	+	22.2546i	−0.978152	+	0.765130i
$847$	12.3344	−	5.07943i	0.423815	−	0.174531i
$848$	0.140251	−	5.64325i	0.00481623	−	0.193790i
$849$	−0.0309749	+	3.60036i	−0.00106306	+	0.123564i
$850$	−36.0579	−	44.4975i	−1.23678	−	1.52625i
$851$	−13.9514	−	5.77886i	−0.478248	−	0.198097i
$852$	−26.6836	+	4.72677i	−0.914165	+	0.161936i
$853$	−5.36687	−	12.9568i	−0.183758	−	0.443631i	0.804977	−	0.593306i	$-0.202177\pi$
$853$	−5.36687	−	12.9568i	−0.183758	−	0.443631i	−0.988735	+	0.149675i	$0.952177\pi$
$854$	−29.0104	+	23.4096i	−0.992714	+	0.801061i
$855$	−12.5417	+	12.1174i	−0.428917	+	0.414405i
$856$	0.785758	+	9.85806i	0.0268567	+	0.336942i
$857$	−10.5589	+	10.5589i	−0.360686	+	0.360686i	−0.864065	−	0.503379i	$-0.832090\pi$
$857$	−10.5589	+	10.5589i	−0.360686	+	0.360686i	0.503379	+	0.864065i	$0.332090\pi$
$858$	35.2946	+	19.5430i	1.20494	+	0.667188i
$859$	−17.7244	+	7.34170i	−0.604750	+	0.250496i	−0.663982	−	0.747749i	$-0.731135\pi$
$859$	−17.7244	+	7.34170i	−0.604750	+	0.250496i	0.0592320	+	0.998244i	$0.481135\pi$
$860$	4.85265	+	7.46154i	0.165474	+	0.254437i
$861$	34.5424	+	0.368098i	1.17720	+	0.0125447i
$862$	31.4637	+	3.29637i	1.07166	+	0.112275i
$863$			0.423310i			0.0144096i	0.999974	+	0.00720481i	$0.00229338\pi$
$863$			0.423310i			0.0144096i	−0.999974	+	0.00720481i	$0.997707\pi$
$864$	29.0413	+	4.53910i	0.988005	+	0.154423i
$865$	−26.9509			−0.916358
$866$	37.1152	+	3.88847i	1.26123	+	0.132136i
$867$	−11.5971	+	27.3304i	−0.393858	+	0.928190i
$868$	13.3749	−	19.4029i	0.453973	−	0.658576i
$869$	−9.15946	+	3.79397i	−0.310714	+	0.128702i
$870$	−27.8879	+	50.3653i	−0.945489	+	1.70755i
$871$	15.9577	+	15.9577i	0.540704	+	0.540704i
$872$	−4.29020	+	5.03336i	−0.145285	+	0.170451i
$873$	0.305558	−	0.295219i	0.0103416	−	0.00999166i
$874$	−4.95843	+	1.47055i	−0.167721	+	0.0497421i
$875$	12.4528	+	12.5040i	0.420980	+	0.422712i
$876$	5.56225	+	31.4000i	0.187931	+	1.06091i
$877$	−17.3060	+	41.7803i	−0.584381	+	1.41082i	0.304425	+	0.952536i	$0.401536\pi$
$877$	−17.3060	+	41.7803i	−0.584381	+	1.41082i	−0.888806	+	0.458284i	$0.848464\pi$
$878$	−7.85537	+	6.36548i	−0.265106	+	0.214825i
$879$	38.5755	+	0.331876i	1.30112	+	0.0111939i
$880$	31.4692	−	12.1280i	1.06083	−	0.408836i
$881$			12.6396i			0.425840i	0.977070	+	0.212920i	$0.0682974\pi$
$881$			12.6396i			0.425840i	−0.977070	+	0.212920i	$0.931703\pi$
$882$	−3.72324	+	29.4642i	−0.125368	+	0.992110i
$883$	6.16930	−	14.8940i	0.207613	−	0.501223i	−0.785433	−	0.618947i	$-0.787560\pi$
$883$	6.16930	−	14.8940i	0.207613	−	0.501223i	0.993046	+	0.117724i	$0.0375597\pi$
$884$	−44.6191	+	65.0139i	−1.50070	+	2.18665i
$885$	16.6584	+	41.2164i	0.559967	+	1.38547i
$886$	17.2369	−	5.11206i	0.579086	−	0.171743i
$887$	−30.8381	−	30.8381i	−1.03544	−	1.03544i	−0.999348	−	0.0360936i	$-0.988509\pi$
$887$	−30.8381	−	30.8381i	−1.03544	−	1.03544i	−0.0360936	−	0.999348i	$-0.511491\pi$
$888$	32.2967	+	10.7660i	1.08381	+	0.361284i
$889$	−17.5664	−	7.31853i	−0.589159	−	0.245456i
$890$	10.4843	+	5.68798i	0.351434	+	0.190662i
$891$	−20.5735	+	7.70370i	−0.689237	+	0.258084i
$892$	8.66046	−	40.8781i	0.289974	−	1.36870i
$893$	−5.48309	+	13.2374i	−0.183485	+	0.442971i
$894$	−1.03925	−	0.117927i	−0.0347576	−	0.00394406i
$895$		−	42.8373i		−	1.43189i
$896$	−12.8941	−	27.0137i	−0.430762	−	0.902465i
$897$	−0.218486	+	25.3956i	−0.00729503	+	0.847936i
$898$	0.0410006	−	0.391348i	0.00136821	−	0.0130595i
$899$	27.9970	+	11.5967i	0.933751	+	0.386772i
$900$	40.5288	+	9.31783i	1.35096	+	0.310594i
$901$	−7.61828	+	3.15560i	−0.253802	+	0.105128i
$902$	12.4090	−	22.8727i	0.413174	−	0.761578i
$903$	−2.31746	+	5.43045i	−0.0771204	+	0.180714i
$904$	−12.7282	−	4.12160i	−0.423335	−	0.137082i
$905$	−47.1787	+	47.1787i	−1.56827	+	1.56827i
$906$	−45.3104	+	13.0150i	−1.50534	+	0.432393i
$907$	−17.1931	+	7.12164i	−0.570889	+	0.236470i	−0.649405	−	0.760443i	$-0.724982\pi$
$907$	−17.1931	+	7.12164i	−0.570889	+	0.236470i	0.0785157	+	0.996913i	$0.474982\pi$
$908$	−1.85593	−	1.27372i	−0.0615911	−	0.0422700i
$909$	−10.9350	+	25.1658i	−0.362691	+	0.834695i
$910$	41.7430	−	76.5668i	1.38377	−	2.53816i
$911$	5.17400			0.171422			0.0857111	−	0.996320i	$-0.472684\pi$
$911$	5.17400			0.171422			0.0857111	+	0.996320i	$0.472684\pi$
$912$	10.9153	−	4.09920i	0.361443	−	0.135738i
$913$	6.60610			0.218630
$914$	−19.1131	−	23.5867i	−0.632206	−	0.780178i
$915$	−23.2827	+	54.8695i	−0.769703	+	1.81393i
$916$	−39.5006	+	7.34822i	−1.30514	+	0.242792i
$917$	24.3755	+	24.4758i	0.804949	+	0.808261i
$918$	−11.1422	−	41.4665i	−0.367747	−	1.36860i
$919$	−20.4634	−	20.4634i	−0.675024	−	0.675024i	0.283846	−	0.958870i	$-0.408389\pi$
$919$	−20.4634	−	20.4634i	−0.675024	−	0.675024i	−0.958870	+	0.283846i	$0.908389\pi$
$920$	16.1573	+	13.7717i	0.532690	+	0.454041i
$921$	−0.389153	+	0.382514i	−0.0128230	+	0.0126043i
$922$	7.99943	−	14.7448i	0.263447	−	0.485595i
$923$	20.1998	+	48.7667i	0.664886	+	1.60518i
$924$	18.3095	+	12.8550i	0.602339	+	0.422898i
$925$	44.4986	+	18.4319i	1.46310	+	0.606038i
$926$	5.01199	−	47.8392i	0.164704	−	1.57209i
$927$	−0.142497	+	8.28091i	−0.00468020	+	0.271981i
$928$	30.4982	−	23.4829i	1.00115	−	0.770863i
$929$	−55.9138			−1.83447			−0.917235	−	0.398345i	$-0.869585\pi$
$929$	−55.9138			−1.83447			−0.917235	+	0.398345i	$0.869585\pi$
$930$	4.24851	−	37.4407i	0.139314	−	1.22773i
$931$	4.46348	+	10.9022i	0.146285	+	0.357305i
$932$	28.3245	−	18.4210i	0.927799	−	0.603399i
$933$	−41.3283	+	16.7037i	−1.35303	+	0.546853i
$934$	22.4720	−	41.4213i	0.735308	−	1.35534i
$935$	−34.8353	−	34.8353i	−1.13924	−	1.13924i
$936$	−3.56654	−	57.1436i	−0.116576	−	1.86780i
$937$	−9.69697	+	9.69697i	−0.316786	+	0.316786i	−0.847531	−	0.530745i	$-0.821912\pi$
$937$	−9.69697	+	9.69697i	−0.316786	+	0.316786i	0.530745	+	0.847531i	$0.321912\pi$
$938$	7.85869	+	9.73888i	0.256595	+	0.317986i
$939$	3.28356	−	1.32711i	0.107155	−	0.0433088i
$940$	57.8231	−	10.7567i	1.88598	−	0.350845i
$941$	−8.05009	+	19.4346i	−0.262425	+	0.633551i	−0.999088	−	0.0427100i	$-0.986401\pi$
$941$	−8.05009	+	19.4346i	−0.262425	+	0.633551i	0.736662	+	0.676261i	$0.236401\pi$
$942$	16.8517	+	21.1656i	0.549057	+	0.689612i
$943$	16.3809			0.533434
$944$	0.738461	−	29.7134i	0.0240349	−	0.967089i
$945$	16.9430	+	44.3610i	0.551156	+	1.44306i
$946$	2.80014	+	3.45553i	0.0910404	+	0.112349i
$947$	17.4915	+	7.24522i	0.568398	+	0.235438i	0.648326	−	0.761363i	$-0.275469\pi$
$947$	17.4915	+	7.24522i	0.568398	+	0.235438i	−0.0799287	+	0.996801i	$0.525469\pi$
$948$	11.5317	+	8.06099i	0.374531	+	0.261809i
$949$	57.3865	−	23.7703i	1.86284	−	0.771615i
$950$	15.8151	−	4.69038i	0.513110	−	0.152176i
$951$	−25.1175	−	25.5534i	−0.814490	−	0.828626i
$952$	−28.4323	+	33.2190i	−0.921496	+	1.07663i
$953$	−24.7395	−	24.7395i	−0.801391	−	0.801391i	0.181922	−	0.983313i	$-0.441768\pi$
$953$	−24.7395	−	24.7395i	−0.801391	−	0.801391i	−0.983313	+	0.181922i	$0.941768\pi$
$954$	2.94532	−	5.21290i	0.0953584	−	0.168774i
$955$	−72.3247	+	29.9579i	−2.34037	+	0.969414i
$956$	−23.4791	−	4.97429i	−0.759368	−	0.160880i
$957$	−11.2372	+	26.4823i	−0.363247	+	0.856051i
$958$	−29.4496	−	3.08536i	−0.951473	−	0.0996835i
$959$	50.7285	−	20.8905i	1.63811	−	0.674591i
$960$	−38.5344	−	28.3876i	−1.24369	−	0.916206i
$961$	11.1658			0.360187
$962$	6.90956	−	65.9514i	0.222773	−	2.12636i
$963$	−4.18019	+	9.62028i	−0.134705	+	0.310009i
$964$	−38.5701	−	8.17149i	−1.24226	−	0.263186i
$965$	−7.72036	−	18.6386i	−0.248527	−	0.599998i
$966$	−1.61657	+	13.9899i	−0.0520123	+	0.450116i
$967$	1.55319	−	1.55319i	0.0499472	−	0.0499472i	−0.681692	−	0.731639i	$-0.738756\pi$
$967$	1.55319	−	1.55319i	0.0499472	−	0.0499472i	0.731639	+	0.681692i	$0.238756\pi$
$968$	−12.6996	+	6.48675i	−0.408180	+	0.208492i
$969$	−11.9394	−	12.1466i	−0.383548	−	0.390204i
$970$	−0.663268	+	0.196709i	−0.0212963	+	0.00631596i
$971$	25.0709	−	10.3847i	0.804564	−	0.333261i	0.0577814	−	0.998329i	$-0.481597\pi$
$971$	25.0709	−	10.3847i	0.804564	−	0.333261i	0.746783	+	0.665068i	$0.231597\pi$
$972$	24.9231	+	18.7308i	0.799408	+	0.600789i
$973$	−0.0430491	+	20.9695i	−0.00138009	+	0.672252i
$974$	−25.0996	+	20.3391i	−0.804244	+	0.651707i
$975$	0.696869	−	81.0004i	0.0223177	−	2.59409i
$976$	28.8706	−	27.4703i	0.924124	−	0.879304i
$977$	−21.9870			−0.703426			−0.351713	−	0.936108i	$-0.614401\pi$
$977$	−21.9870			−0.703426			−0.351713	+	0.936108i	$0.614401\pi$
$978$	−41.0567	+	32.6886i	−1.31285	+	1.04527i
$979$	5.50657	+	2.28090i	0.175991	+	0.0728978i
$980$	27.5271	−	39.7585i	0.879321	−	1.27004i
$981$	−6.52610	+	2.57256i	−0.208362	+	0.0821356i
$982$	−8.48155	−	28.5983i	−0.270657	−	0.912607i
$983$	36.3877	+	36.3877i	1.16059	+	1.16059i	0.984347	+	0.176241i	$0.0563938\pi$
$983$	36.3877	+	36.3877i	1.16059	+	1.16059i	0.176241	+	0.984347i	$0.443606\pi$
$984$	−36.8366	+	2.61743i	−1.17431	+	0.0834406i
$985$	17.4675	+	17.4675i	0.556561	+	0.556561i
$986$	−49.4218	−	26.8125i	−1.57391	−	0.853885i
$987$	27.2921	+	27.8801i	0.868718	+	0.887432i
$988$	−12.3821	−	19.0390i	−0.393928	−	0.605712i
$989$	−1.07143	+	2.58667i	−0.0340696	+	0.0822513i
$990$	35.5070	+	4.33880i	1.12849	+	0.137896i
$991$	41.2828			1.31139			0.655695	−	0.755026i	$-0.272376\pi$
$991$	41.2828			1.31139			0.655695	+	0.755026i	$0.272376\pi$
$992$	−12.5602	+	21.8388i	−0.398787	+	0.693384i
$993$	0.0218882	−	2.54417i	0.000694601	−	0.0807368i
$994$	8.26493	+	28.0792i	0.262148	+	0.890617i
$995$	1.16348	−	2.80890i	0.0368849	−	0.0890481i
$996$	−5.04351	−	7.90294i	−0.159810	−	0.250414i
$997$	3.47876	−	1.44095i	0.110174	−	0.0456354i	−0.326916	−	0.945053i	$-0.606009\pi$
$997$	3.47876	−	1.44095i	0.110174	−	0.0456354i	0.437089	+	0.899418i	$0.356009\pi$
$998$	−11.4795	+	21.1594i	−0.363377	+	0.669789i
$999$	24.8655	+	26.1833i	0.786710	+	0.828404i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bo.a.125.4	yes	496
3.2	odd	2	inner	672.2.bo.a.125.122	yes	496
7.6	odd	2	inner	672.2.bo.a.125.3	✓	496
21.20	even	2	inner	672.2.bo.a.125.121	yes	496
32.21	even	8	inner	672.2.bo.a.629.121	yes	496
96.53	odd	8	inner	672.2.bo.a.629.3	yes	496
224.181	odd	8	inner	672.2.bo.a.629.122	yes	496
672.629	even	8	inner	672.2.bo.a.629.4	yes	496

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.bo.a.125.3	✓	496	7.6	odd	2	inner
672.2.bo.a.125.4	yes	496	1.1	even	1	trivial
672.2.bo.a.125.121	yes	496	21.20	even	2	inner
672.2.bo.a.125.122	yes	496	3.2	odd	2	inner
672.2.bo.a.629.3	yes	496	96.53	odd	8	inner
672.2.bo.a.629.4	yes	496	672.629	even	8	inner
672.2.bo.a.629.121	yes	496	32.21	even	8	inner
672.2.bo.a.629.122	yes	496	224.181	odd	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bo (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40652 - 0.147357i) q^{2} +(0.676569 - 1.59444i) q^{3} +(1.95657 + 0.414520i) q^{4} +(-1.32184 - 3.19120i) q^{5} +(-1.18656 + 2.14291i) q^{6} +(2.44227 + 1.01750i) q^{7} +(-2.69087 - 0.871344i) q^{8} +(-2.08451 - 2.15750i) q^{9} +O(q^{10})\)	\(q+(-1.40652 - 0.147357i) q^{2} +(0.676569 - 1.59444i) q^{3} +(1.95657 + 0.414520i) q^{4} +(-1.32184 - 3.19120i) q^{5} +(-1.18656 + 2.14291i) q^{6} +(2.44227 + 1.01750i) q^{7} +(-2.69087 - 0.871344i) q^{8} +(-2.08451 - 2.15750i) q^{9} +(1.38894 + 4.68326i) q^{10} +(0.934109 + 2.25514i) q^{11} +(1.98469 - 2.83919i) q^{12} +(-6.23391 - 2.58217i) q^{13} +(-3.28516 - 1.79102i) q^{14} +(-5.98251 - 0.0514692i) q^{15} +(3.65635 + 1.62208i) q^{16} -5.84303i q^{17} +(2.61397 + 3.34173i) q^{18} +(1.55482 + 0.644029i) q^{19} +(-1.26346 - 6.79174i) q^{20} +(3.27472 - 3.20566i) q^{21} +(-0.981528 - 3.30953i) q^{22} +(1.53658 - 1.53658i) q^{23} +(-3.20987 + 3.70091i) q^{24} +(-4.90097 + 4.90097i) q^{25} +(8.38760 + 4.55048i) q^{26} +(-4.85034 + 1.86393i) q^{27} +(4.35671 + 3.00318i) q^{28} +(-2.60392 + 6.28642i) q^{29} +(8.40691 + 0.953957i) q^{30} -4.45356i q^{31} +(-4.90368 - 2.82026i) q^{32} +(4.22768 + 0.0363720i) q^{33} +(-0.861012 + 8.21832i) q^{34} +(0.0187613 - 9.13875i) q^{35} +(-3.18416 - 5.08538i) q^{36} +(-2.65934 - 6.42021i) q^{37} +(-2.09198 - 1.13495i) q^{38} +(-8.33481 + 8.19261i) q^{39} +(0.776258 + 9.73887i) q^{40} +(5.33031 + 5.33031i) q^{41} +(-5.07831 + 4.02625i) q^{42} +(-1.19034 + 0.493056i) q^{43} +(0.892851 + 4.79955i) q^{44} +(-4.12965 + 9.50396i) q^{45} +(-2.38764 + 1.93479i) q^{46} +8.51373i q^{47} +(5.06008 - 4.73239i) q^{48} +(4.92938 + 4.97003i) q^{49} +(7.61548 - 6.17110i) q^{50} +(-9.31639 - 3.95322i) q^{51} +(-11.1267 - 7.63629i) q^{52} +(-0.540062 - 1.30382i) q^{53} +(7.09674 - 1.90692i) q^{54} +(5.96186 - 5.96186i) q^{55} +(-5.68523 - 4.86602i) q^{56} +(2.07881 - 2.04335i) q^{57} +(4.58881 - 8.45825i) q^{58} +(-2.84358 - 6.86502i) q^{59} +(-11.6839 - 2.58057i) q^{60} +(3.81261 - 9.20445i) q^{61} +(-0.656264 + 6.26400i) q^{62} +(-2.89567 - 7.39020i) q^{63} +(6.48152 + 4.68934i) q^{64} +23.3069i q^{65} +(-5.94094 - 0.674137i) q^{66} +(-3.08997 - 1.27991i) q^{67} +(2.42205 - 11.4323i) q^{68} +(-1.41039 - 3.48958i) q^{69} +(-1.37305 + 12.8510i) q^{70} +(-5.53156 - 5.53156i) q^{71} +(3.72920 + 7.62188i) q^{72} +(-6.50929 + 6.50929i) q^{73} +(2.79434 + 9.42199i) q^{74} +(4.49848 + 11.1302i) q^{75} +(2.77516 + 1.90460i) q^{76} +(-0.0132581 + 6.45812i) q^{77} +(12.9303 - 10.2948i) q^{78} +4.06160i q^{79} +(0.343273 - 13.8123i) q^{80} +(-0.309650 + 8.99467i) q^{81} +(-6.71171 - 8.28263i) q^{82} +(1.03568 - 2.50036i) q^{83} +(7.73602 - 4.91466i) q^{84} +(-18.6463 + 7.72355i) q^{85} +(1.74689 - 0.518085i) q^{86} +(8.26162 + 8.40501i) q^{87} +(-0.548561 - 6.88220i) q^{88} +(1.72661 - 1.72661i) q^{89} +(7.20889 - 12.7589i) q^{90} +(-12.5976 - 12.6494i) q^{91} +(3.64336 - 2.36948i) q^{92} +(-7.10096 - 3.01314i) q^{93} +(1.25456 - 11.9747i) q^{94} -5.81306i q^{95} +(-7.81444 + 5.91055i) q^{96} +0.141625i q^{97} +(-6.20088 - 7.71680i) q^{98} +(2.91831 - 6.71620i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9	\( 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9} - 48 q^{16} - 8 q^{18} - 4 q^{21} - 16 q^{22} - 16 q^{25} - 8 q^{28} - 64 q^{30} - 48 q^{36} - 16 q^{37} - 8 q^{39} + 56 q^{42} - 16 q^{43} - 16 q^{46} + 16 q^{51} - 8 q^{57} - 80 q^{58} + 24 q^{60} - 8 q^{63} - 112 q^{64} + 48 q^{67} - 8 q^{70} - 8 q^{72} - 160 q^{78} + 128 q^{84} + 64 q^{85} - 16 q^{88} - 56 q^{91} + 16 q^{93} - 8 q^{99}+O(q^{100}) \) 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9 - 48 * q^16 - 8 * q^18 - 4 * q^21 - 16 * q^22 - 16 * q^25 - 8 * q^28 - 64 * q^30 - 48 * q^36 - 16 * q^37 - 8 * q^39 + 56 * q^42 - 16 * q^43 - 16 * q^46 + 16 * q^51 - 8 * q^57 - 80 * q^58 + 24 * q^60 - 8 * q^63 - 112 * q^64 + 48 * q^67 - 8 * q^70 - 8 * q^72 - 160 * q^78 + 128 * q^84 + 64 * q^85 - 16 * q^88 - 56 * q^91 + 16 * q^93 - 8 * q^99

Introduction

L-functions

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