LMFDB - Embedded newform 160.2.z.a.69.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [160,2,Mod(29,160)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(160, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("160.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 160 = 2^{5} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	160.z (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:	$1.27760643234$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			69.12
Character	$\chi$	$=$	160.69
Dual form			160.2.z.a.109.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.125510 - 1.40863i) q^{2} +(-1.86499 + 0.772505i) q^{3} +(-1.96849 - 0.353596i) q^{4} +(0.0190434 + 2.23599i) q^{5} +(0.854100 + 2.72405i) q^{6} +(-0.798508 + 0.798508i) q^{7} +(-0.745154 + 2.72851i) q^{8} +(0.760109 - 0.760109i) q^{9} +O(q^{10})$	\(q+(0.125510 - 1.40863i) q^{2} +(-1.86499 + 0.772505i) q^{3} +(-1.96849 - 0.353596i) q^{4} +(0.0190434 + 2.23599i) q^{5} +(0.854100 + 2.72405i) q^{6} +(-0.798508 + 0.798508i) q^{7} +(-0.745154 + 2.72851i) q^{8} +(0.760109 - 0.760109i) q^{9} +(3.15208 + 0.253815i) q^{10} +(-1.21174 + 2.92539i) q^{11} +(3.94438 - 0.861217i) q^{12} +(-0.175830 - 0.424491i) q^{13} +(1.02458 + 1.22503i) q^{14} +(-1.76283 - 4.15539i) q^{15} +(3.74994 + 1.39210i) q^{16} +3.66556 q^{17} +(-0.975313 - 1.16612i) q^{18} +(-5.39199 + 2.23343i) q^{19} +(0.753150 - 4.40826i) q^{20} +(0.872360 - 2.10606i) q^{21} +(3.96871 + 2.07406i) q^{22} +(-3.04392 - 3.04392i) q^{23} +(-0.718078 - 5.66428i) q^{24} +(-4.99927 + 0.0851615i) q^{25} +(-0.620020 + 0.194402i) q^{26} +(1.48711 - 3.59019i) q^{27} +(1.85421 - 1.28951i) q^{28} +(0.995872 + 2.40425i) q^{29} +(-6.07467 + 1.96163i) q^{30} -2.13401 q^{31} +(2.43162 - 5.10756i) q^{32} -6.39190i q^{33} +(0.460066 - 5.16343i) q^{34} +(-1.80066 - 1.77025i) q^{35} +(-1.76504 + 1.22750i) q^{36} +(-4.33444 + 10.4643i) q^{37} +(2.46934 + 7.87565i) q^{38} +(0.655842 + 0.655842i) q^{39} +(-6.11509 - 1.61420i) q^{40} +(6.79854 - 6.79854i) q^{41} +(-2.85718 - 1.49317i) q^{42} +(9.19158 + 3.80728i) q^{43} +(3.41970 - 5.33015i) q^{44} +(1.71407 + 1.68512i) q^{45} +(-4.66981 + 3.90572i) q^{46} +2.81155 q^{47} +(-8.06901 + 0.300582i) q^{48} +5.72477i q^{49} +(-0.507500 + 7.05283i) q^{50} +(-6.83623 + 2.83166i) q^{51} +(0.196022 + 0.897781i) q^{52} +(-0.347970 - 0.144134i) q^{53} +(-4.87061 - 2.54539i) q^{54} +(-6.56421 - 2.65372i) q^{55} +(-1.58372 - 2.77375i) q^{56} +(8.33067 - 8.33067i) q^{57} +(3.51170 - 1.10106i) q^{58} +(10.0632 + 4.16829i) q^{59} +(2.00078 + 8.80318i) q^{60} +(-5.16229 - 12.4629i) q^{61} +(-0.267840 + 3.00603i) q^{62} +1.21391i q^{63} +(-6.88949 - 4.06632i) q^{64} +(0.945808 - 0.401237i) q^{65} +(-9.00384 - 0.802250i) q^{66} +(7.97969 - 3.30530i) q^{67} +(-7.21563 - 1.29613i) q^{68} +(8.02832 + 3.32544i) q^{69} +(-2.71963 + 2.31429i) q^{70} +(5.88607 + 5.88607i) q^{71} +(1.50756 + 2.64036i) q^{72} +(-4.50108 - 4.50108i) q^{73} +(14.1963 + 7.41901i) q^{74} +(9.25782 - 4.02079i) q^{75} +(11.4038 - 2.48992i) q^{76} +(-1.36837 - 3.30353i) q^{77} +(1.00616 - 0.841526i) q^{78} +5.05155i q^{79} +(-3.04132 + 8.41133i) q^{80} +11.0693i q^{81} +(-8.72336 - 10.4299i) q^{82} +(2.81897 + 6.80560i) q^{83} +(-2.46193 + 3.83731i) q^{84} +(0.0698046 + 8.19614i) q^{85} +(6.51669 - 12.4697i) q^{86} +(-3.71459 - 3.71459i) q^{87} +(-7.07901 - 5.48609i) q^{88} +(7.44423 + 7.44423i) q^{89} +(2.58885 - 2.20299i) q^{90} +(0.479361 + 0.198558i) q^{91} +(4.91562 + 7.06825i) q^{92} +(3.97991 - 1.64853i) q^{93} +(0.352879 - 3.96044i) q^{94} +(-5.09661 - 12.0139i) q^{95} +(-0.589336 + 11.4040i) q^{96} +1.85143i q^{97} +(8.06410 + 0.718518i) q^{98} +(1.30256 + 3.14467i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9}+O(q^{10}) $ 88 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9	$ 88 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9} - 4 q^{10} - 8 q^{11} - 24 q^{14} - 8 q^{16} - 8 q^{19} - 4 q^{20} - 8 q^{21} - 16 q^{24} - 4 q^{25} + 32 q^{26} - 8 q^{29} - 52 q^{30} - 64 q^{31} - 24 q^{34} + 20 q^{35} + 72 q^{36} - 8 q^{39} - 56 q^{40} - 8 q^{41} - 8 q^{44} - 16 q^{45} - 8 q^{46} - 44 q^{50} - 48 q^{51} + 24 q^{54} + 28 q^{55} - 56 q^{56} + 24 q^{59} + 32 q^{60} + 24 q^{61} + 64 q^{64} - 8 q^{65} - 8 q^{66} - 40 q^{69} + 80 q^{70} - 40 q^{71} + 128 q^{74} + 28 q^{75} - 8 q^{76} + 48 q^{80} + 200 q^{84} - 24 q^{85} + 24 q^{86} - 8 q^{89} + 80 q^{90} - 8 q^{91} + 120 q^{94} - 8 q^{95} - 56 q^{96} - 48 q^{99}+O(q^{100}) $ 88 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9 - 4 * q^10 - 8 * q^11 - 24 * q^14 - 8 * q^16 - 8 * q^19 - 4 * q^20 - 8 * q^21 - 16 * q^24 - 4 * q^25 + 32 * q^26 - 8 * q^29 - 52 * q^30 - 64 * q^31 - 24 * q^34 + 20 * q^35 + 72 * q^36 - 8 * q^39 - 56 * q^40 - 8 * q^41 - 8 * q^44 - 16 * q^45 - 8 * q^46 - 44 * q^50 - 48 * q^51 + 24 * q^54 + 28 * q^55 - 56 * q^56 + 24 * q^59 + 32 * q^60 + 24 * q^61 + 64 * q^64 - 8 * q^65 - 8 * q^66 - 40 * q^69 + 80 * q^70 - 40 * q^71 + 128 * q^74 + 28 * q^75 - 8 * q^76 + 48 * q^80 + 200 * q^84 - 24 * q^85 + 24 * q^86 - 8 * q^89 + 80 * q^90 - 8 * q^91 + 120 * q^94 - 8 * q^95 - 56 * q^96 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/160\mathbb{Z}\right)^\times$.

$n$	$31$	$97$	$101$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{8}\right)$

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 $

$2$	0.125510	−	1.40863i	0.0887493	−	0.996054i
$2$	0.125510	−	1.40863i	0.0887493	−	0.996054i
$3$	−1.86499	+	0.772505i	−1.07675	+	0.446006i	−0.849369	−	0.527799i	$-0.823017\pi$
$3$	−1.86499	+	0.772505i	−1.07675	+	0.446006i	−0.227384	+	0.973805i	$0.573017\pi$
$4$	−1.96849	−	0.353596i	−0.984247	−	0.176798i
$5$	0.0190434	+	2.23599i	0.00851646	+	0.999964i
$5$	0.0190434	+	2.23599i	0.00851646	+	0.999964i
$6$	0.854100	+	2.72405i	0.348685	+	1.11209i
$7$	−0.798508	+	0.798508i	−0.301808	+	0.301808i	−0.841721	−	0.539913i	$-0.818457\pi$
$7$	−0.798508	+	0.798508i	−0.301808	+	0.301808i	0.539913	+	0.841721i	$0.318457\pi$
$8$	−0.745154	+	2.72851i	−0.263452	+	0.964673i
$9$	0.760109	−	0.760109i	0.253370	−	0.253370i
$10$	3.15208	+	0.253815i	0.996774	+	0.0802632i
$11$	−1.21174	+	2.92539i	−0.365352	+	0.882038i	0.629146	+	0.777287i	$0.283405\pi$
$11$	−1.21174	+	2.92539i	−0.365352	+	0.882038i	−0.994498	+	0.104751i	$0.966595\pi$
$12$	3.94438	−	0.861217i	1.13864	−	0.248612i
$13$	−0.175830	−	0.424491i	−0.0487664	−	0.117733i	0.897619	−	0.440772i	$-0.145295\pi$
$13$	−0.175830	−	0.424491i	−0.0487664	−	0.117733i	−0.946385	+	0.323040i	$0.895295\pi$
$14$	1.02458	+	1.22503i	0.273832	+	0.327402i
$15$	−1.76283	−	4.15539i	−0.455160	−	1.07292i
$16$	3.74994	+	1.39210i	0.937485	+	0.348026i
$17$	3.66556			0.889028			0.444514	−	0.895772i	$-0.353376\pi$
$17$	3.66556			0.889028			0.444514	+	0.895772i	$0.353376\pi$
$18$	−0.975313	−	1.16612i	−0.229884	−	0.274856i
$19$	−5.39199	+	2.23343i	−1.23701	+	0.512385i	−0.902778	−	0.430107i	$-0.858476\pi$
$19$	−5.39199	+	2.23343i	−1.23701	+	0.512385i	−0.334229	+	0.942492i	$0.608476\pi$
$20$	0.753150	−	4.40826i	0.168409	−	0.985717i
$21$	0.872360	−	2.10606i	0.190364	−	0.459581i
$22$	3.96871	+	2.07406i	0.846133	+	0.442191i
$23$	−3.04392	−	3.04392i	−0.634701	−	0.634701i	0.314543	−	0.949243i	$-0.398149\pi$
$23$	−3.04392	−	3.04392i	−0.634701	−	0.634701i	−0.949243	+	0.314543i	$0.898149\pi$
$24$	−0.718078	−	5.66428i	−0.146577	−	1.15622i
$25$	−4.99927	+	0.0851615i	−0.999855	+	0.0170323i
$26$	−0.620020	+	0.194402i	−0.121596	+	0.0381253i
$27$	1.48711	−	3.59019i	0.286194	−	0.690932i
$28$	1.85421	−	1.28951i	0.350413	−	0.243694i
$29$	0.995872	+	2.40425i	0.184929	+	0.446458i	0.988970	−	0.148116i	$-0.0473209\pi$
$29$	0.995872	+	2.40425i	0.184929	+	0.446458i	−0.804041	+	0.594574i	$0.797321\pi$
$30$	−6.07467	+	1.96163i	−1.10908	+	0.358143i
$31$	−2.13401			−0.383279			−0.191640	−	0.981465i	$-0.561380\pi$
$31$	−2.13401			−0.383279			−0.191640	+	0.981465i	$0.561380\pi$
$32$	2.43162	−	5.10756i	0.429854	−	0.902898i
$33$		−	6.39190i		−	1.11269i
$34$	0.460066	−	5.16343i	0.0789007	−	0.885520i
$35$	−1.80066	−	1.77025i	−0.304367	−	0.299226i
$36$	−1.76504	+	1.22750i	−0.294174	+	0.204583i
$37$	−4.33444	+	10.4643i	−0.712578	+	1.72032i	−0.0191211	+	0.999817i	$0.506087\pi$
$37$	−4.33444	+	10.4643i	−0.712578	+	1.72032i	−0.693457	+	0.720498i	$0.743913\pi$
$38$	2.46934	+	7.87565i	0.400580	+	1.27760i
$39$	0.655842	+	0.655842i	0.105019	+	0.105019i
$40$	−6.11509	−	1.61420i	−0.966881	−	0.255227i
$41$	6.79854	−	6.79854i	1.06175	−	1.06175i	0.0637899	−	0.997963i	$-0.479681\pi$
$41$	6.79854	−	6.79854i	1.06175	−	1.06175i	0.997963	−	0.0637899i	$-0.0203187\pi$
$42$	−2.85718	−	1.49317i	−0.440872	−	0.230401i
$43$	9.19158	+	3.80728i	1.40170	+	0.580604i	0.950193	−	0.311662i	$-0.100886\pi$
$43$	9.19158	+	3.80728i	1.40170	+	0.580604i	0.451509	+	0.892266i	$0.350886\pi$
$44$	3.41970	−	5.33015i	0.515540	−	0.803550i
$45$	1.71407	+	1.68512i	0.255518	+	0.251203i
$46$	−4.66981	+	3.90572i	−0.688525	+	0.575867i
$47$	2.81155			0.410106			0.205053	−	0.978751i	$-0.434263\pi$
$47$	2.81155			0.410106			0.205053	+	0.978751i	$0.434263\pi$
$48$	−8.06901	+	0.300582i	−1.16466	+	0.0433853i
$49$			5.72477i			0.817824i
$50$	−0.507500	+	7.05283i	−0.0717713	+	0.997421i
$51$	−6.83623	+	2.83166i	−0.957264	+	0.396512i
$52$	0.196022	+	0.897781i	0.0271833	+	0.124500i
$53$	−0.347970	−	0.144134i	−0.0477974	−	0.0197983i	0.358657	−	0.933470i	$-0.383235\pi$
$53$	−0.347970	−	0.144134i	−0.0477974	−	0.0197983i	−0.406454	+	0.913671i	$0.633235\pi$
$54$	−4.87061	−	2.54539i	−0.662806	−	0.346384i
$55$	−6.56421	−	2.65372i	−0.885118	−	0.357827i
$56$	−1.58372	−	2.77375i	−0.211634	−	0.370657i
$57$	8.33067	−	8.33067i	1.10342	−	1.10342i
$58$	3.51170	−	1.10106i	0.461108	−	0.144576i
$59$	10.0632	+	4.16829i	1.31011	+	0.542666i	0.924917	−	0.380170i	$-0.124135\pi$
$59$	10.0632	+	4.16829i	1.31011	+	0.542666i	0.385194	+	0.922836i	$0.374135\pi$
$60$	2.00078	+	8.80318i	0.258300	+	1.13649i
$61$	−5.16229	−	12.4629i	−0.660964	−	1.59571i	−0.796296	−	0.604908i	$-0.793210\pi$
$61$	−5.16229	−	12.4629i	−0.660964	−	1.59571i	0.135332	−	0.990800i	$-0.456790\pi$
$62$	−0.267840	+	3.00603i	−0.0340157	+	0.381767i
$63$			1.21391i			0.152938i
$64$	−6.88949	−	4.06632i	−0.861186	−	0.508289i
$65$	0.945808	−	0.401237i	0.117313	−	0.0497673i
$66$	−9.00384	−	0.802250i	−1.10830	−	0.0987502i
$67$	7.97969	−	3.30530i	0.974874	−	0.403806i	0.162350	−	0.986733i	$-0.448093\pi$
$67$	7.97969	−	3.30530i	0.974874	−	0.403806i	0.812524	+	0.582927i	$0.198093\pi$
$68$	−7.21563	−	1.29613i	−0.875024	−	0.157179i
$69$	8.02832	+	3.32544i	0.966496	+	0.400336i
$70$	−2.71963	+	2.31429i	−0.325058	+	0.276610i
$71$	5.88607	+	5.88607i	0.698548	+	0.698548i	0.964097	−	0.265549i	$-0.0855532\pi$
$71$	5.88607	+	5.88607i	0.698548	+	0.698548i	−0.265549	+	0.964097i	$0.585553\pi$
$72$	1.50756	+	2.64036i	0.177668	+	0.311170i
$73$	−4.50108	−	4.50108i	−0.526812	−	0.526812i	0.392808	−	0.919620i	$-0.371504\pi$
$73$	−4.50108	−	4.50108i	−0.526812	−	0.526812i	−0.919620	+	0.392808i	$0.871504\pi$
$74$	14.1963	+	7.41901i	1.65029	+	0.862443i
$75$	9.25782	−	4.02079i	1.06900	−	0.464281i
$76$	11.4038	−	2.48992i	1.30811	−	0.285613i
$77$	−1.36837	−	3.30353i	−0.155940	−	0.376472i
$78$	1.00616	−	0.841526i	0.113925	−	0.0952841i
$79$			5.05155i			0.568344i	0.958773	+	0.284172i	$0.0917187\pi$
$79$			5.05155i			0.568344i	−0.958773	+	0.284172i	$0.908281\pi$
$80$	−3.04132	+	8.41133i	−0.340030	+	0.940415i
$81$			11.0693i			1.22993i
$82$	−8.72336	−	10.4299i	−0.963334	−	1.15179i
$83$	2.81897	+	6.80560i	0.309422	+	0.747012i	0.999724	+	0.0234902i	$0.00747785\pi$
$83$	2.81897	+	6.80560i	0.309422	+	0.747012i	−0.690302	+	0.723522i	$0.742522\pi$
$84$	−2.46193	+	3.83731i	−0.268619	+	0.418685i
$85$	0.0698046	+	8.19614i	0.00757138	+	0.888996i
$86$	6.51669	−	12.4697i	0.702713	−	1.34464i
$87$	−3.71459	−	3.71459i	−0.398245	−	0.398245i
$88$	−7.07901	−	5.48609i	−0.754625	−	0.584820i
$89$	7.44423	+	7.44423i	0.789087	+	0.789087i	0.981345	−	0.192257i	$-0.0615809\pi$
$89$	7.44423	+	7.44423i	0.789087	+	0.789087i	−0.192257	+	0.981345i	$0.561581\pi$
$90$	2.58885	−	2.20299i	0.272889	−	0.232216i
$91$	0.479361	+	0.198558i	0.0502507	+	0.0208145i
$92$	4.91562	+	7.06825i	0.512488	+	0.736916i
$93$	3.97991	−	1.64853i	0.412697	−	0.170945i
$94$	0.352879	−	3.96044i	0.0363966	−	0.408488i
$95$	−5.09661	−	12.0139i	−0.522901	−	1.23260i
$96$	−0.589336	+	11.4040i	−0.0601488	+	1.16392i
$97$			1.85143i			0.187984i	0.995573	+	0.0939920i	$0.0299628\pi$
$97$			1.85143i			0.187984i	−0.995573	+	0.0939920i	$0.970037\pi$
$98$	8.06410	+	0.718518i	0.814597	+	0.0725813i
$99$	1.30256	+	3.14467i	0.130913	+	0.316051i
$100$	9.87116	+	1.60009i	0.987116	+	0.160009i
$101$	−5.38144	−	2.22907i	−0.535474	−	0.221800i	0.0985250	−	0.995135i	$-0.468588\pi$
$101$	−5.38144	−	2.22907i	−0.535474	−	0.221800i	−0.633999	+	0.773334i	$0.718588\pi$
$102$	3.13075	+	9.98515i	0.309991	+	0.988677i
$103$	−9.17653	+	9.17653i	−0.904190	+	0.904190i	−0.995795	−	0.0916051i	$-0.970800\pi$
$103$	−9.17653	+	9.17653i	−0.904190	+	0.904190i	0.0916051	+	0.995795i	$0.470800\pi$
$104$	1.28925	−	0.163442i	0.126421	−	0.0160268i
$105$	4.72574	+	1.91048i	0.461185	+	0.186444i
$106$	−0.246706	+	0.472072i	−0.0239622	+	0.0458517i
$107$	−9.71062	−	4.02227i	−0.938761	−	0.388848i	−0.139766	−	0.990185i	$-0.544635\pi$
$107$	−9.71062	−	4.02227i	−0.938761	−	0.388848i	−0.798996	+	0.601337i	$0.794635\pi$
$108$	−4.19684	+	6.54143i	−0.403841	+	0.629450i
$109$	−18.0950	+	7.49520i	−1.73319	+	0.717910i	−0.733936	+	0.679219i	$0.762319\pi$
$109$	−18.0950	+	7.49520i	−1.73319	+	0.717910i	−0.999251	+	0.0386910i	$0.987681\pi$
$110$	−4.56199	+	8.91349i	−0.434969	+	0.849868i
$111$		−	22.8642i		−	2.17017i
$112$	−4.10596	+	1.88275i	−0.387977	+	0.177903i
$113$	−1.66682			−0.156801			−0.0784004	−	0.996922i	$-0.524981\pi$
$113$	−1.66682			−0.156801			−0.0784004	+	0.996922i	$0.524981\pi$
$114$	−10.6893	−	12.7804i	−1.00114	−	1.19700i
$115$	6.74819	−	6.86413i	0.629272	−	0.640083i
$116$	−1.11024	−	5.08489i	−0.103083	−	0.472120i
$117$	−0.456309	−	0.189010i	−0.0421858	−	0.0174739i
$118$	7.13463	−	13.6521i	0.656796	−	1.25678i
$119$	−2.92698	+	2.92698i	−0.268316	+	0.268316i
$120$	12.6516	−	1.71348i	1.15493	−	0.156419i
$121$	0.688576	+	0.688576i	0.0625978	+	0.0625978i
$122$	−18.2035	+	5.70755i	−1.64807	+	0.516738i
$123$	−7.42731	+	17.9311i	−0.669698	+	1.61679i
$124$	4.20078	+	0.754577i	0.377241	+	0.0677630i
$125$	−0.285623	−	11.1767i	−0.0255469	−	0.999674i
$126$	1.70995	+	0.152358i	0.152334	+	0.0135731i
$127$			11.9791i			1.06297i	0.847066	+	0.531487i	$0.178367\pi$
$127$			11.9791i			1.06297i	−0.847066	+	0.531487i	$0.821633\pi$
$128$	−6.59265	+	9.19440i	−0.582713	+	0.812678i
$129$	−20.0834			−1.76824
$130$	−0.446487	−	1.38266i	−0.0391595	−	0.121267i
$131$	1.07279	+	2.58995i	0.0937303	+	0.226285i	0.963791	−	0.266660i	$-0.0859202\pi$
$131$	1.07279	+	2.58995i	0.0937303	+	0.226285i	−0.870060	+	0.492945i	$0.835920\pi$
$132$	−2.26015	+	12.5824i	−0.196721	+	1.09516i
$133$	2.52213	−	6.08896i	0.218697	−	0.527980i
$134$	−3.65441	−	11.6553i	−0.315693	−	1.00686i
$135$	8.05594	+	3.25678i	0.693345	+	0.280299i
$136$	−2.73141	+	10.0015i	−0.234216	+	0.857621i
$137$	7.11033	+	7.11033i	0.607476	+	0.607476i	0.942286	−	0.334810i	$-0.108672\pi$
$137$	7.11033	+	7.11033i	0.607476	+	0.607476i	−0.334810	+	0.942286i	$0.608672\pi$
$138$	5.69196	−	10.8916i	0.484532	−	0.927153i
$139$	7.78228	−	18.7881i	0.660084	−	1.59358i	−0.137585	−	0.990490i	$-0.543934\pi$
$139$	7.78228	−	18.7881i	0.660084	−	1.59358i	0.797669	−	0.603095i	$-0.206066\pi$
$140$	2.91864	+	4.12143i	0.246670	+	0.348324i
$141$	−5.24351	+	2.17193i	−0.441583	+	0.182910i
$142$	9.03008	−	7.55255i	0.757788	−	0.633796i
$143$	1.45486			0.121662
$144$	3.90851	−	1.79221i	0.325710	−	0.149351i
$145$	−5.35690	+	2.27254i	−0.444867	+	0.188724i
$146$	−6.90531	+	5.77544i	−0.571487	+	0.477979i
$147$	−4.42241	−	10.6766i	−0.364754	−	0.880595i
$148$	12.2325	−	19.0662i	1.00550	−	1.56723i
$149$	1.78543	−	4.31042i	0.146268	−	0.353123i	−0.833717	−	0.552192i	$-0.813792\pi$
$149$	1.78543	−	4.31042i	0.146268	−	0.353123i	0.979986	+	0.199068i	$0.0637916\pi$
$150$	−4.50186	−	13.5455i	−0.367576	−	1.10599i
$151$	8.74596	−	8.74596i	0.711736	−	0.711736i	−0.255162	−	0.966898i	$-0.582129\pi$
$151$	8.74596	−	8.74596i	0.711736	−	0.711736i	0.966898	+	0.255162i	$0.0821288\pi$
$152$	−2.07608	−	16.3763i	−0.168392	−	1.32830i
$153$	2.78622	−	2.78622i	0.225253	−	0.225253i
$154$	−4.82520	+	1.51290i	−0.388826	+	0.121913i
$155$	−0.0406387	−	4.77161i	−0.00326418	−	0.383265i
$156$	−1.05912	−	1.52293i	−0.0847973	−	0.121932i
$157$	−16.0091	+	6.63117i	−1.27766	+	0.529225i	−0.915285	−	0.402806i	$-0.868035\pi$
$157$	−16.0091	+	6.63117i	−1.27766	+	0.529225i	−0.362377	+	0.932032i	$0.618035\pi$
$158$	7.11579	+	0.634023i	0.566102	+	0.0504402i
$159$	0.760305			0.0602961
$160$	11.4668	+	5.33981i	0.906526	+	0.422149i
$161$	4.86119			0.383115
$162$	15.5926	+	1.38932i	1.22507	+	0.109155i
$163$	2.28807	−	0.947748i	0.179215	−	0.0742334i	−0.291272	−	0.956640i	$-0.594078\pi$
$163$	2.28807	−	0.947748i	0.179215	−	0.0742334i	0.470487	+	0.882407i	$0.344078\pi$
$164$	−15.7868	+	10.9789i	−1.23274	+	0.857311i
$165$	14.2922	−	0.121723i	1.11265	−	0.00947615i
$166$	9.94041	−	3.11672i	0.771525	−	0.241905i
$167$	2.97405	−	2.97405i	0.230139	−	0.230139i	−0.582612	−	0.812750i	$-0.697969\pi$
$167$	2.97405	−	2.97405i	0.230139	−	0.230139i	0.812750	+	0.582612i	$0.197969\pi$
$168$	5.09636	+	3.94958i	0.393193	+	0.304717i
$169$	9.04311	−	9.04311i	0.695624	−	0.695624i
$170$	11.5541	+	0.930372i	0.886160	+	0.0713563i
$171$	−2.40085	+	5.79615i	−0.183597	+	0.443243i
$172$	−16.7473	−	10.7447i	−1.27697	−	0.819276i
$173$	−3.72322	−	8.98865i	−0.283071	−	0.683394i	0.716833	−	0.697245i	$-0.245591\pi$
$173$	−3.72322	−	8.98865i	−0.283071	−	0.683394i	−0.999904	+	0.0138508i	$0.995591\pi$
$174$	−5.69871	+	4.76627i	−0.432018	+	0.361330i
$175$	3.92396	−	4.05996i	0.296624	−	0.306904i
$176$	−8.61638	+	9.28317i	−0.649484	+	0.699745i
$177$	−21.9877			−1.65270
$178$	11.4205	−	9.55186i	0.856004	−	0.715942i
$179$	−12.4973	+	5.17653i	−0.934089	+	0.386912i	−0.797228	−	0.603678i	$-0.793701\pi$
$179$	−12.4973	+	5.17653i	−0.934089	+	0.386912i	−0.136861	+	0.990590i	$0.543701\pi$
$180$	−2.77828	−	3.92324i	−0.207081	−	0.292421i
$181$	−2.52860	+	6.10459i	−0.187950	+	0.453751i	−0.989565	−	0.144090i	$-0.953975\pi$
$181$	−2.52860	+	6.10459i	−0.187950	+	0.453751i	0.801615	+	0.597841i	$0.203975\pi$
$182$	0.339860	−	0.650323i	0.0251921	−	0.0482051i
$183$	19.2553	+	19.2553i	1.42339	+	1.42339i
$184$	10.5735	−	6.03716i	0.779491	−	0.445065i
$185$	−23.4805	−	9.49248i	−1.72632	−	0.697901i
$186$	−1.82266	−	5.81313i	−0.133644	−	0.426240i
$187$	−4.44169	+	10.7232i	−0.324808	+	0.784157i
$188$	−5.53451	−	0.994153i	−0.403646	−	0.0725060i
$189$	1.67933	+	4.05426i	0.122153	+	0.294904i
$190$	−17.5628	+	5.67139i	−1.27414	+	0.411446i
$191$	15.4267			1.11624			0.558120	−	0.829760i	$-0.311523\pi$
$191$	15.4267			1.11624			0.558120	+	0.829760i	$0.311523\pi$
$192$	15.9901	+	2.26148i	1.15399	+	0.163208i
$193$		−	7.08523i		−	0.510006i	−0.966940	−	0.255003i	$-0.917923\pi$
$193$		−	7.08523i		−	0.510006i	0.966940	−	0.255003i	$-0.0820765\pi$
$194$	2.60798	+	0.232373i	0.187242	+	0.0166834i
$195$	−1.45397	+	1.47894i	−0.104121	+	0.105909i
$196$	2.02426	−	11.2692i	0.144590	−	0.804941i
$197$	−0.344992	+	0.832884i	−0.0245797	+	0.0593405i	−0.935693	−	0.352816i	$-0.885224\pi$
$197$	−0.344992	+	0.832884i	−0.0245797	+	0.0593405i	0.911113	+	0.412156i	$0.135224\pi$
$198$	4.59317	−	1.44015i	0.326422	−	0.102347i
$199$	−2.91076	−	2.91076i	−0.206338	−	0.206338i	0.596371	−	0.802709i	$-0.296609\pi$
$199$	−2.91076	−	2.91076i	−0.206338	−	0.206338i	−0.802709	+	0.596371i	$0.796609\pi$
$200$	3.49287	−	13.7040i	0.246983	−	0.969020i
$201$	−12.3287	+	12.3287i	−0.869599	+	0.869599i
$202$	−3.81536	+	7.30071i	−0.268448	+	0.513676i
$203$	−2.71502	−	1.12460i	−0.190557	−	0.0789314i
$204$	14.4584	−	3.15684i	1.01229	−	0.221023i
$205$	15.3309	+	15.0720i	1.07076	+	1.05267i
$206$	11.7746	+	14.0781i	0.820376	+	0.980869i
$207$	−4.62742			−0.321628
$208$	−0.0684155	−	1.83659i	−0.00474376	−	0.127345i
$209$		−	18.4800i		−	1.27829i
$210$	3.28429	−	6.41705i	0.226638	−	0.442819i
$211$	−7.92698	+	3.28346i	−0.545716	+	0.226043i	−0.638471	−	0.769646i	$-0.720433\pi$
$211$	−7.92698	+	3.28346i	−0.545716	+	0.226043i	0.0927548	+	0.995689i	$0.470433\pi$
$212$	0.634012	+	0.406768i	0.0435441	+	0.0279369i
$213$	−15.5245	−	6.43046i	−1.06372	−	0.440608i
$214$	−6.88469	+	13.1739i	−0.470628	+	0.900547i
$215$	−8.33798	+	20.6247i	−0.568646	+	1.40660i
$216$	8.68773	+	6.73282i	0.591125	+	0.458110i
$217$	1.70402	−	1.70402i	0.115677	−	0.115677i
$218$	8.28687	+	26.4299i	0.561258	+	1.79006i
$219$	11.8716	+	4.91737i	0.802208	+	0.332285i
$220$	11.9833	+	7.54491i	0.807911	+	0.508677i
$221$	−0.644515	−	1.55600i	−0.0433547	−	0.104668i
$222$	−32.2072	−	2.86969i	−2.16161	−	0.192601i
$223$		−	5.77501i		−	0.386723i	−0.981128	−	0.193362i	$-0.938061\pi$
$223$		−	5.77501i		−	0.386723i	0.981128	−	0.193362i	$-0.0619390\pi$
$224$	2.13676	+	6.02010i	0.142768	+	0.402235i
$225$	−3.73526	+	3.86473i	−0.249018	+	0.257648i
$226$	−0.209203	+	2.34793i	−0.0139160	+	0.156182i
$227$	2.95889	−	1.22561i	0.196389	−	0.0813469i	−0.282321	−	0.959320i	$-0.591104\pi$
$227$	2.95889	−	1.22561i	0.196389	−	0.0813469i	0.478710	+	0.877973i	$0.341104\pi$
$228$	−19.3446	+	13.4532i	−1.28113	+	0.890959i
$229$	15.2062	+	6.29862i	1.00485	+	0.416224i	0.823575	−	0.567207i	$-0.191976\pi$
$229$	15.2062	+	6.29862i	1.00485	+	0.416224i	0.181279	+	0.983432i	$0.441976\pi$
$230$	−8.82207	−	10.3672i	−0.581710	−	0.683596i
$231$	5.10398	+	5.10398i	0.335817	+	0.335817i
$232$	−7.30208	+	0.925708i	−0.479405	+	0.0607757i
$233$	5.63270	+	5.63270i	0.369010	+	0.369010i	0.867116	−	0.498106i	$-0.165971\pi$
$233$	5.63270	+	5.63270i	0.369010	+	0.369010i	−0.498106	+	0.867116i	$0.665971\pi$
$234$	−0.323517	+	0.619050i	−0.0211489	+	0.0404685i
$235$	0.0535414	+	6.28658i	0.00349265	+	0.410091i
$236$	−18.3354	−	11.7636i	−1.19353	−	0.765742i
$237$	−3.90235	−	9.42111i	−0.253485	−	0.611967i
$238$	3.75567	+	4.49041i	0.243444	+	0.291070i
$239$			9.70011i			0.627448i	0.949514	+	0.313724i	$0.101577\pi$
$239$			9.70011i			0.627448i	−0.949514	+	0.313724i	$0.898423\pi$
$240$	−0.825759	−	18.0365i	−0.0533025	−	1.16425i
$241$			16.7088i			1.07631i	0.842847	+	0.538154i	$0.180878\pi$
$241$			16.7088i			1.07631i	−0.842847	+	0.538154i	$0.819122\pi$
$242$	1.05637	−	0.883527i	0.0679063	−	0.0567953i
$243$	−4.08980	−	9.87365i	−0.262361	−	0.633395i
$244$	5.75512	+	26.3585i	0.368433	+	1.68743i
$245$	−12.8005	+	0.109019i	−0.817794	+	0.00696497i
$246$	24.3262	+	12.7129i	1.55098	+	0.810545i
$247$	1.89615	+	1.89615i	0.120649	+	0.120649i
$248$	1.59016	−	5.82265i	0.100976	−	0.369739i
$249$	−10.5147	−	10.5147i	−0.666343	−	0.666343i
$250$	−15.7797	−	1.00045i	−0.997996	−	0.0632742i
$251$	−6.61061	−	2.73821i	−0.417258	−	0.172834i	0.164169	−	0.986432i	$-0.447506\pi$
$251$	−6.61061	−	2.73821i	−0.417258	−	0.172834i	−0.581428	+	0.813598i	$0.697506\pi$
$252$	0.429233	−	2.38957i	0.0270391	−	0.150529i
$253$	12.5931	−	5.21622i	0.791719	−	0.327941i
$254$	16.8742	+	1.50350i	1.05878	+	0.0943383i
$255$	−6.46174	−	15.2318i	−0.404650	−	0.953853i
$256$	12.1241	+	10.4406i	0.757755	+	0.652539i
$257$			10.2334i			0.638344i	0.947697	+	0.319172i	$0.103405\pi$
$257$			10.2334i			0.638344i	−0.947697	+	0.319172i	$0.896595\pi$
$258$	−2.52067	+	28.2901i	−0.156930	+	1.76126i
$259$	−4.89472	−	11.8169i	−0.304143	−	0.734266i
$260$	−2.00369	+	0.455399i	−0.124264	+	0.0282426i
$261$	2.58446	+	1.07052i	0.159974	+	0.0662635i
$262$	3.78294	−	1.18610i	0.233711	−	0.0732778i
$263$	1.31205	−	1.31205i	0.0809045	−	0.0809045i	−0.665496	−	0.746401i	$-0.731780\pi$
$263$	1.31205	−	1.31205i	0.0809045	−	0.0809045i	0.746401	+	0.665496i	$0.231780\pi$
$264$	17.4403	+	4.76295i	1.07338	+	0.293139i
$265$	0.315655	−	0.780801i	0.0193905	−	0.0479642i
$266$	−8.26056	−	4.31699i	−0.506488	−	0.264691i
$267$	−19.6341	−	8.13273i	−1.20159	−	0.497715i
$268$	−16.8767	+	3.68487i	−1.03091	+	0.225089i
$269$	16.4601	−	6.81801i	1.00359	−	0.415701i	0.180479	−	0.983579i	$-0.442235\pi$
$269$	16.4601	−	6.81801i	1.00359	−	0.415701i	0.823113	+	0.567878i	$0.192235\pi$
$270$	5.59871	−	10.9391i	0.340727	−	0.665732i
$271$		−	9.45666i		−	0.574451i	−0.957863	−	0.287226i	$-0.907267\pi$
$271$		−	9.45666i		−	0.574451i	0.957863	−	0.287226i	$-0.0927329\pi$
$272$	13.7456	+	5.10284i	0.833451	+	0.309405i
$273$	−1.04739			−0.0633910
$274$	10.9083	−	9.12342i	0.658992	−	0.551166i
$275$	5.80867	−	14.7280i	0.350276	−	0.888133i
$276$	−14.6278	−	9.38489i	−0.880492	−	0.564904i
$277$	26.2678	+	10.8805i	1.57828	+	0.653743i	0.988139	−	0.153560i	$-0.0490738\pi$
$277$	26.2678	+	10.8805i	1.57828	+	0.653743i	0.590137	+	0.807303i	$0.299074\pi$
$278$	−25.4888	−	13.3205i	−1.52871	−	0.798909i
$279$	−1.62208	+	1.62208i	−0.0971113	+	0.0971113i
$280$	6.17190	−	3.59401i	0.368842	−	0.214783i
$281$	13.8016	+	13.8016i	0.823332	+	0.823332i	0.986584	−	0.163253i	$-0.0521985\pi$
$281$	13.8016	+	13.8016i	0.823332	+	0.823332i	−0.163253	+	0.986584i	$0.552199\pi$
$282$	2.40134	+	7.65878i	0.142998	+	0.456074i
$283$	9.13571	−	22.0556i	0.543062	−	1.31107i	−0.379491	−	0.925196i	$-0.623901\pi$
$283$	9.13571	−	22.0556i	0.543062	−	1.31107i	0.922553	−	0.385872i	$-0.126099\pi$
$284$	−9.50541	−	13.6680i	−0.564042	−	0.811046i
$285$	18.7859	+	18.4686i	1.11278	+	1.09399i
$286$	0.182600	−	2.04936i	0.0107974	−	0.121181i
$287$			10.8574i			0.640891i
$288$	−2.03401	−	5.73060i	−0.119855	−	0.337679i
$289$	−3.56368			−0.209628
$290$	2.52883	+	7.83114i	0.148498	+	0.459860i
$291$	−1.43024	−	3.45290i	−0.0838419	−	0.202412i
$292$	7.26879	+	10.4519i	0.425374	+	0.611653i
$293$	7.20694	−	17.3991i	0.421034	−	1.01647i	−0.561009	−	0.827809i	$-0.689587\pi$
$293$	7.20694	−	17.3991i	0.421034	−	1.01647i	0.982043	−	0.188656i	$-0.0604132\pi$
$294$	−15.5945	+	4.88952i	−0.909492	+	0.285163i
$295$	−9.12861	+	22.5805i	−0.531488	+	1.31468i
$296$	−25.3220	−	19.6240i	−1.47181	−	1.14062i
$297$	8.70072	+	8.70072i	0.504867	+	0.504867i
$298$	−5.84771	−	3.05602i	−0.338749	−	0.177031i
$299$	−0.756903	+	1.82733i	−0.0437729	+	0.105677i
$300$	−19.6457	+	4.64137i	−1.13424	+	0.267970i
$301$	−10.3797	+	4.29941i	−0.598276	+	0.247814i
$302$	−11.2221	−	13.4176i	−0.645762	−	0.772094i
$303$	11.7583			0.675497
$304$	−23.3288	+	0.869031i	−1.33800	+	0.0498423i
$305$	27.7685	−	11.7802i	1.59002	−	0.674530i
$306$	−3.57507	−	4.27447i	−0.204373	−	0.244355i
$307$	4.47505	+	10.8037i	0.255404	+	0.616601i	0.998624	−	0.0524470i	$-0.0167021\pi$
$307$	4.47505	+	10.8037i	0.255404	+	0.616601i	−0.743219	+	0.669048i	$0.766702\pi$
$308$	1.52551	+	6.98683i	0.0869238	+	0.398111i
$309$	10.0252	−	24.2031i	0.570316	−	1.37686i
$310$	−6.72655	−	0.541642i	−0.382042	−	0.0307632i
$311$	−5.50620	+	5.50620i	−0.312228	+	0.312228i	−0.845772	−	0.533544i	$-0.820860\pi$
$311$	−5.50620	+	5.50620i	−0.312228	+	0.312228i	0.533544	+	0.845772i	$0.320860\pi$
$312$	−2.27817	+	1.30077i	−0.128976	+	0.0736414i
$313$	−5.15295	+	5.15295i	−0.291262	+	0.291262i	−0.837579	−	0.546317i	$-0.816029\pi$
$313$	−5.15295	+	5.15295i	−0.291262	+	0.291262i	0.546317	+	0.837579i	$0.316029\pi$
$314$	7.33158	+	23.3832i	0.413745	+	1.31959i
$315$	−2.71428	+	0.0231169i	−0.152932	+	0.00130249i
$316$	1.78621	−	9.94396i	0.100482	−	0.559391i
$317$	18.5382	−	7.67876i	1.04121	−	0.431282i	0.204462	−	0.978874i	$-0.434455\pi$
$317$	18.5382	−	7.67876i	1.04121	−	0.431282i	0.836745	+	0.547592i	$0.184455\pi$
$318$	0.0954263	−	1.07099i	0.00535124	−	0.0600582i
$319$	−8.24010			−0.461357
$320$	8.96103	−	15.4822i	0.500937	−	0.865484i
$321$	21.2175			1.18424
$322$	0.610130	−	6.84763i	0.0340012	−	0.381603i
$323$	−19.7646	+	8.18679i	−1.09973	+	0.455525i
$324$	3.91408	−	21.7899i	0.217449	−	1.21055i
$325$	0.915172	+	2.10717i	0.0507646	+	0.116885i
$326$	−1.04785	−	3.34200i	−0.0580352	−	0.185096i
$327$	27.9570	−	27.9570i	1.54602	−	1.54602i
$328$	13.4839	+	23.6158i	0.744523	+	1.30396i
$329$	−2.24504	+	2.24504i	−0.123773	+	0.123773i
$330$	1.62236	−	20.1477i	0.0893078	−	1.10910i
$331$	−1.58035	+	3.81529i	−0.0868637	+	0.209708i	−0.961342	−	0.275357i	$-0.911204\pi$
$331$	−1.58035	+	3.81529i	−0.0868637	+	0.209708i	0.874478	+	0.485065i	$0.161204\pi$
$332$	−3.14270	−	14.3936i	−0.172478	−	0.789950i
$333$	4.65934	+	11.2486i	0.255330	+	0.616422i
$334$	−3.81607	−	4.56261i	−0.208806	−	0.249655i
$335$	7.54256	+	17.7795i	0.412094	+	0.971400i
$336$	6.20316	−	6.68319i	0.338410	−	0.364598i
$337$	−7.45730			−0.406225			−0.203112	−	0.979155i	$-0.565106\pi$
$337$	−7.45730			−0.406225			−0.203112	+	0.979155i	$0.565106\pi$
$338$	−11.6034	−	13.8734i	−0.631143	−	0.754615i
$339$	3.10860	−	1.28762i	0.168836	−	0.0699341i
$340$	2.76072	−	16.1587i	0.149721	−	0.876331i
$341$	2.58585	−	6.24280i	0.140032	−	0.338067i
$342$	7.86332	+	4.10939i	0.425200	+	0.222210i
$343$	−10.1608	−	10.1608i	−0.548633	−	0.548633i
$344$	−17.2373	+	22.2423i	−0.929374	+	1.19922i
$345$	−7.28275	+	18.0145i	−0.392090	+	0.969871i
$346$	−13.1290	+	4.11648i	−0.705820	+	0.221303i
$347$	2.98151	−	7.19799i	0.160056	−	0.386409i	−0.823424	−	0.567426i	$-0.807939\pi$
$347$	2.98151	−	7.19799i	0.160056	−	0.386409i	0.983480	+	0.181018i	$0.0579392\pi$
$348$	5.99868	+	8.62561i	0.321563	+	0.462381i
$349$	4.45368	+	10.7521i	0.238400	+	0.575548i	0.997118	−	0.0758714i	$-0.0241738\pi$
$349$	4.45368	+	10.7521i	0.238400	+	0.575548i	−0.758718	+	0.651419i	$0.774174\pi$
$350$	−5.22650	−	6.03699i	−0.279368	−	0.322691i
$351$	−1.78548			−0.0953019
$352$	11.9951	+	13.3025i	0.639343	+	0.709023i
$353$		−	0.146505i		−	0.00779766i	−0.999992	−	0.00389883i	$-0.998759\pi$
$353$		−	0.146505i		−	0.00779766i	0.999992	−	0.00389883i	$-0.00124104\pi$
$354$	−2.75969	+	30.9726i	−0.146676	+	1.64618i
$355$	−13.0491	+	13.2733i	−0.692574	+	0.704472i
$356$	−12.0217	−	17.2862i	−0.637148	−	0.916166i
$357$	3.19769	−	7.71990i	0.169239	−	0.408580i
$358$	5.72330	+	18.2538i	0.302486	+	0.964741i
$359$	−20.8531	−	20.8531i	−1.10058	−	1.10058i	−0.994340	−	0.106242i	$-0.966118\pi$
$359$	−20.8531	−	20.8531i	−1.10058	−	1.10058i	−0.106242	−	0.994340i	$-0.533882\pi$
$360$	−5.87510	+	3.42117i	−0.309645	+	0.180312i
$361$	10.6503	−	10.6503i	0.560541	−	0.560541i
$362$	8.28176	+	4.32807i	0.435280	+	0.227478i
$363$	−1.81612	−	0.752260i	−0.0953214	−	0.0394834i
$364$	−0.873410	−	0.560360i	−0.0457791	−	0.0293709i
$365$	9.97865	−	10.1501i	0.522306	−	0.531279i
$366$	29.5403	−	24.7069i	1.54410	−	1.29145i
$367$	5.98845			0.312594			0.156297	−	0.987710i	$-0.450044\pi$
$367$	5.98845			0.312594			0.156297	+	0.987710i	$0.450044\pi$
$368$	−7.17705	−	15.6520i	−0.374130	−	0.815915i
$369$		−	10.3353i		−	0.538032i
$370$	−16.3185	+	31.8840i	−0.848357	+	1.65757i
$371$	0.392949	−	0.162765i	0.0204009	−	0.00845033i
$372$	−8.41734	+	1.83784i	−0.436419	+	0.0952877i
$373$	6.63539	+	2.74847i	0.343568	+	0.142310i	0.547794	−	0.836613i	$-0.315468\pi$
$373$	6.63539	+	2.74847i	0.343568	+	0.142310i	−0.204226	+	0.978924i	$0.565468\pi$
$374$	14.5476	+	7.60258i	0.752236	+	0.393120i
$375$	9.16673	+	20.6238i	0.473368	+	1.06501i
$376$	−2.09504	+	7.67132i	−0.108043	+	0.395618i
$377$	0.845477	−	0.845477i	0.0435443	−	0.0435443i
$378$	5.92174	−	1.85671i	0.304581	−	0.0954987i
$379$	−9.53326	−	3.94881i	−0.489691	−	0.202837i	0.124154	−	0.992263i	$-0.460378\pi$
$379$	−9.53326	−	3.94881i	−0.489691	−	0.202837i	−0.613845	+	0.789426i	$0.710378\pi$
$380$	5.78459	+	25.4514i	0.296743	+	1.30563i
$381$	−9.25393	−	22.3410i	−0.474093	−	1.14456i
$382$	1.93622	−	21.7306i	0.0990655	−	1.11184i
$383$			12.9567i			0.662057i	0.943621	+	0.331028i	$0.107396\pi$
$383$			12.9567i			0.662057i	−0.943621	+	0.331028i	$0.892604\pi$
$384$	5.19252	−	22.2403i	0.264980	−	1.13495i
$385$	7.36059	−	3.12256i	0.375130	−	0.159140i
$386$	−9.98049	−	0.889271i	−0.507994	−	0.0452627i
$387$	9.88055	−	4.09266i	0.502256	−	0.208041i
$388$	0.654658	−	3.64452i	0.0332352	−	0.185023i
$389$	−25.6596	−	10.6286i	−1.30099	−	0.538889i	−0.378751	−	0.925499i	$-0.623646\pi$
$389$	−25.6596	−	10.6286i	−1.30099	−	0.538889i	−0.922244	+	0.386609i	$0.873646\pi$
$390$	1.90080	+	2.23373i	0.0962509	+	0.113109i
$391$	−11.1577	−	11.1577i	−0.564267	−	0.564267i
$392$	−15.6201	−	4.26584i	−0.788933	−	0.215457i
$393$	−4.00150	−	4.00150i	−0.201849	−	0.201849i
$394$	1.12993	+	0.590503i	0.0569250	+	0.0297491i
$395$	−11.2952	+	0.0961987i	−0.568324	+	0.00484028i
$396$	−1.45215	−	6.65084i	−0.0729731	−	0.334217i
$397$	−13.4708	−	32.5215i	−0.676082	−	1.63221i	−0.771088	−	0.636729i	$-0.780287\pi$
$397$	−13.4708	−	32.5215i	−0.676082	−	1.63221i	0.0950060	−	0.995477i	$-0.469713\pi$
$398$	−4.46552	+	3.73486i	−0.223836	+	0.187211i
$399$			13.3042i			0.666044i
$400$	−18.8655	−	6.64016i	−0.943276	−	0.332008i
$401$		−	2.52062i		−	0.125874i	−0.998018	−	0.0629368i	$-0.979953\pi$
$401$		−	2.52062i		−	0.125874i	0.998018	−	0.0629368i	$-0.0200466\pi$
$402$	15.8192	+	18.9140i	0.788991	+	0.943344i
$403$	0.375222	+	0.905867i	0.0186912	+	0.0451244i
$404$	9.80515	+	6.29076i	0.487824	+	0.312977i
$405$	−24.7509	+	0.210798i	−1.22988	+	0.0104746i
$406$	−1.92491	+	3.68332i	−0.0955318	+	0.182800i
$407$	−25.3599	−	25.3599i	−1.25704	−	1.25704i
$408$	−2.63216	−	20.7627i	−0.130311	−	1.02791i
$409$	5.83443	+	5.83443i	0.288494	+	0.288494i	0.836484	−	0.547991i	$-0.184607\pi$
$409$	5.83443	+	5.83443i	0.288494	+	0.288494i	−0.547991	+	0.836484i	$0.684607\pi$
$410$	23.1551	−	19.7039i	1.14355	−	0.973108i
$411$	−18.7535	−	7.76794i	−0.925040	−	0.383164i
$412$	21.3087	−	14.8192i	1.04981	−	0.730087i
$413$	−11.3639	+	4.70709i	−0.559182	+	0.231621i
$414$	−0.580789	+	6.51834i	−0.0285442	+	0.320359i
$415$	−15.1636	+	6.43279i	−0.744350	+	0.315773i
$416$	−2.59567	−	0.134139i	−0.127263	−	0.00657669i
$417$			41.0515i			2.01030i
$418$	−26.0315	−	2.31943i	−1.27324	−	0.113447i
$419$	−5.75322	−	13.8895i	−0.281063	−	0.678546i	0.718798	−	0.695219i	$-0.244693\pi$
$419$	−5.75322	−	13.8895i	−0.281063	−	0.678546i	−0.999861	+	0.0166728i	$0.994693\pi$
$420$	−8.62706	−	5.43177i	−0.420957	−	0.265043i
$421$	−27.5675	−	11.4188i	−1.34356	−	0.556520i	−0.409066	−	0.912505i	$-0.634145\pi$
$421$	−27.5675	−	11.4188i	−1.34356	−	0.556520i	−0.934492	+	0.355985i	$0.884145\pi$
$422$	3.63028	+	11.5783i	0.176719	+	0.563624i
$423$	2.13708	−	2.13708i	0.103909	−	0.103909i
$424$	0.652561	−	0.842036i	0.0316912	−	0.0408929i
$425$	−18.3251	+	0.312164i	−0.888899	+	0.0151422i
$426$	−11.0066	+	21.0612i	−0.533274	+	1.02042i
$427$	14.0738	+	5.82958i	0.681081	+	0.282113i
$428$	17.6930	+	11.3515i	0.855226	+	0.548694i
$429$	−2.71330	+	1.12389i	−0.130999	+	0.0542618i
$430$	28.0062	+	14.3338i	1.35058	+	0.691236i
$431$			34.5185i			1.66270i	0.555750	+	0.831349i	$0.312431\pi$
$431$			34.5185i			1.66270i	−0.555750	+	0.831349i	$0.687569\pi$
$432$	10.5745	−	11.3928i	0.508765	−	0.548136i
$433$	16.9110			0.812690			0.406345	−	0.913720i	$-0.366803\pi$
$433$	16.9110			0.812690			0.406345	+	0.913720i	$0.366803\pi$
$434$	−2.18647	−	2.61422i	−0.104954	−	0.125486i
$435$	8.23503	−	8.37650i	0.394839	−	0.401623i
$436$	38.2702	−	8.35592i	1.83281	−	0.400176i
$437$	23.2112	+	9.61438i	1.11034	+	0.459918i
$438$	8.41678	−	16.1055i	0.402170	−	0.769552i
$439$	7.67146	−	7.67146i	0.366139	−	0.366139i	−0.499928	−	0.866067i	$-0.666640\pi$
$439$	7.67146	−	7.67146i	0.366139	−	0.366139i	0.866067	+	0.499928i	$0.166640\pi$
$440$	12.1320	−	15.9331i	0.578372	−	0.759578i
$441$	4.35145	+	4.35145i	0.207212	+	0.207212i
$442$	−2.27272	+	0.712591i	−0.108102	+	0.0338945i
$443$	1.56765	−	3.78465i	0.0744815	−	0.179814i	−0.882254	−	0.470774i	$-0.843975\pi$
$443$	1.56765	−	3.78465i	0.0744815	−	0.179814i	0.956735	+	0.290960i	$0.0939746\pi$
$444$	−8.08468	+	45.0080i	−0.383682	+	2.13598i
$445$	−16.5034	+	16.7870i	−0.782338	+	0.795779i
$446$	−8.13487	−	0.724824i	−0.385197	−	0.0343214i
$447$			9.41815i			0.445463i
$448$	8.74830	−	2.25433i	0.413318	−	0.106507i
$449$	3.12042			0.147262			0.0736309	−	0.997286i	$-0.476541\pi$
$449$	3.12042			0.147262			0.0736309	+	0.997286i	$0.476541\pi$
$450$	4.97517	+	5.74668i	0.234532	+	0.270901i
$451$	11.6503	+	28.1264i	0.548593	+	1.32442i
$452$	3.28112	+	0.589380i	0.154331	+	0.0277221i
$453$	−9.55485	+	23.0674i	−0.448926	+	1.08380i
$454$	−1.35507	−	4.32182i	−0.0635965	−	0.202833i
$455$	−0.434844	+	1.07563i	−0.0203858	+	0.0504261i
$456$	16.5227	+	28.9379i	0.773744	+	1.35514i
$457$	−28.7210	−	28.7210i	−1.34351	−	1.34351i	−0.892535	−	0.450978i	$-0.851075\pi$
$457$	−28.7210	−	28.7210i	−1.34351	−	1.34351i	−0.450978	−	0.892535i	$-0.648925\pi$
$458$	10.7810	−	20.6294i	0.503762	−	0.963950i
$459$	5.45107	−	13.1600i	0.254434	−	0.614258i
$460$	−15.7109	+	11.1259i	−0.732525	+	0.518746i
$461$	33.4225	−	13.8441i	1.55664	−	0.644782i	0.572139	−	0.820157i	$-0.306114\pi$
$461$	33.4225	−	13.8441i	1.55664	−	0.644782i	0.984502	+	0.175375i	$0.0561138\pi$
$462$	7.83024	−	6.54904i	0.364296	−	0.304689i
$463$	−13.9489			−0.648259			−0.324130	−	0.946013i	$-0.605071\pi$
$463$	−13.9489			−0.648259			−0.324130	+	0.946013i	$0.605071\pi$
$464$	0.387495	+	10.4021i	0.0179890	+	0.482907i
$465$	3.76188	+	8.86762i	0.174453	+	0.411226i
$466$	8.64136	−	7.22744i	0.400303	−	0.334805i
$467$	14.4737	+	34.9426i	0.669763	+	1.61695i	0.782006	+	0.623271i	$0.214197\pi$
$467$	14.4737	+	34.9426i	0.669763	+	1.61695i	−0.112243	+	0.993681i	$0.535803\pi$
$468$	0.831409	+	0.533413i	0.0384319	+	0.0246570i
$469$	−3.73254	+	9.01115i	−0.172353	+	0.416096i
$470$	8.86221	+	0.713612i	0.408783	+	0.0329164i
$471$	24.7342	−	24.7342i	1.13969	−	1.13969i
$472$	−18.8718	+	24.3513i	−0.868646	+	1.12086i
$473$	−22.2755	+	22.2755i	−1.02423	+	1.02423i
$474$	−13.7607	+	4.31453i	−0.632048	+	0.198173i
$475$	26.7658	−	11.6247i	1.22810	−	0.533380i
$476$	6.79671	−	4.72677i	0.311527	−	0.216651i
$477$	−0.374053	+	0.154938i	−0.0171267	+	0.00709411i
$478$	13.6639	+	1.21747i	0.624972	+	0.0556856i
$479$	−1.27470			−0.0582424			−0.0291212	−	0.999576i	$-0.509271\pi$
$479$	−1.27470			−0.0582424			−0.0291212	+	0.999576i	$0.509271\pi$
$480$	−25.5104	−	1.10058i	−1.16439	−	0.0502342i
$481$	5.20411			0.237287
$482$	23.5365	+	2.09713i	1.07206	+	0.0955215i
$483$	−9.06607	+	3.75529i	−0.412521	+	0.170872i
$484$	−1.11198	−	1.59894i	−0.0505445	−	0.0726789i
$485$	−4.13977	+	0.0352574i	−0.187977	+	0.00160096i
$486$	−14.4217	+	4.52178i	−0.654180	+	0.205112i
$487$	−5.87473	+	5.87473i	−0.266209	+	0.266209i	−0.827571	−	0.561361i	$-0.810278\pi$
$487$	−5.87473	+	5.87473i	−0.266209	+	0.266209i	0.561361	+	0.827571i	$0.310278\pi$
$488$	37.8517	−	4.79858i	1.71347	−	0.217222i
$489$	−3.53508	+	3.53508i	−0.159862	+	0.159862i
$490$	−1.45303	+	18.0449i	−0.0656412	+	0.815186i
$491$	−14.2233	+	34.3381i	−0.641889	+	1.54966i	0.182240	+	0.983254i	$0.441665\pi$
$491$	−14.2233	+	34.3381i	−0.641889	+	1.54966i	−0.824129	+	0.566403i	$0.808335\pi$
$492$	20.9610	−	32.6710i	0.944995	−	1.47292i
$493$	3.65043	+	8.81291i	0.164407	+	0.396914i
$494$	2.90896	−	2.43299i	0.130880	−	0.109465i
$495$	−7.00663	+	2.97240i	−0.314925	+	0.133599i
$496$	−8.00240	−	2.97076i	−0.359318	−	0.133391i
$497$	−9.40016			−0.421655
$498$	−16.1311	+	13.4917i	−0.722851	+	0.604576i
$499$	33.8195	−	14.0085i	1.51397	−	0.627107i	0.537597	−	0.843202i	$-0.319332\pi$
$499$	33.8195	−	14.0085i	1.51397	−	0.627107i	0.976372	+	0.216095i	$0.0693322\pi$
$500$	−3.38979	+	22.1022i	−0.151596	+	0.988443i
$501$	−3.24911	+	7.84403i	−0.145159	+	0.350446i
$502$	−4.68683	+	8.96825i	−0.209183	+	0.400273i
$503$	−0.844993	−	0.844993i	−0.0376764	−	0.0376764i	0.688018	−	0.725694i	$-0.258481\pi$
$503$	−0.844993	−	0.844993i	−0.0376764	−	0.0376764i	−0.725694	+	0.688018i	$0.758481\pi$
$504$	−3.31215	−	0.904548i	−0.147535	−	0.0402918i
$505$	4.88168	−	12.0753i	0.217232	−	0.537343i
$506$	−5.76718	−	18.3937i	−0.256382	−	0.817700i
$507$	−9.87948	+	23.8512i	−0.438763	+	1.05927i
$508$	4.23577	−	23.5808i	0.187932	−	1.04623i
$509$	0.698779	+	1.68700i	0.0309728	+	0.0747750i	0.938609	−	0.344982i	$-0.112115\pi$
$509$	0.698779	+	1.68700i	0.0309728	+	0.0747750i	−0.907636	+	0.419757i	$0.862115\pi$
$510$	−22.2670	+	7.19047i	−0.986001	+	0.318399i
$511$	7.18831			0.317992
$512$	16.2287	−	15.7680i	0.717214	−	0.696853i
$513$			22.6796i			1.00133i
$514$	14.4152	+	1.28440i	0.635825	+	0.0566526i
$515$	−20.6934	−	20.3438i	−0.911858	−	0.896457i
$516$	39.5340	+	7.10140i	1.74039	+	0.312622i
$517$	−3.40685	+	8.22487i	−0.149833	+	0.361729i
$518$	−17.2600	+	5.41172i	−0.758361	+	0.237777i
$519$	13.8875	+	13.8875i	0.609596	+	0.609596i
$520$	0.390005	+	2.87963i	0.0171029	+	0.126280i
$521$	−19.8057	+	19.8057i	−0.867706	+	0.867706i	−0.992218	−	0.124513i	$-0.960263\pi$
$521$	−19.8057	+	19.8057i	−0.867706	+	0.867706i	0.124513	+	0.992218i	$0.460263\pi$
$522$	1.83235	−	3.50620i	0.0801996	−	0.153462i
$523$	2.41194	+	0.999058i	0.105467	+	0.0436858i	0.434793	−	0.900530i	$-0.356822\pi$
$523$	2.41194	+	0.999058i	0.105467	+	0.0436858i	−0.329326	+	0.944216i	$0.606822\pi$
$524$	−1.19599	−	5.47764i	−0.0522470	−	0.239292i
$525$	−4.18181	+	10.6031i	−0.182509	+	0.462756i
$526$	−1.68352	−	2.01287i	−0.0734050	−	0.0877654i
$527$	−7.82233			−0.340746
$528$	8.89819	−	23.9692i	0.387244	−	1.04313i
$529$		−	4.46914i		−	0.194310i
$530$	−1.06024	−	0.542641i	−0.0460541	−	0.0235708i
$531$	10.8175	−	4.48074i	0.469437	−	0.194447i
$532$	−7.11784	+	11.0943i	−0.308597	+	0.480998i
$533$	−4.08130	−	1.69053i	−0.176781	−	0.0732250i
$534$	−13.9203	+	26.6366i	−0.602391	+	1.15268i
$535$	8.80882	−	21.7894i	0.380839	−	0.942039i
$536$	3.07242	+	24.2356i	0.132708	+	1.04682i
$537$	19.3084	−	19.3084i	0.833218	−	0.833218i
$538$	−7.53815	−	24.0420i	−0.324993	−	1.03652i
$539$	−16.7472	−	6.93691i	−0.721352	−	0.298794i
$540$	−14.7065	−	9.25950i	−0.632866	−	0.398465i
$541$	5.84464	+	14.1102i	0.251281	+	0.606645i	0.998308	−	0.0581482i	$-0.0185196\pi$
$541$	5.84464	+	14.1102i	0.251281	+	0.606645i	−0.747027	+	0.664793i	$0.768520\pi$
$542$	−13.3210	−	1.18691i	−0.572184	−	0.0509821i
$543$		−	13.3384i		−	0.572404i
$544$	8.91325	−	18.7221i	0.382152	−	0.802702i
$545$	−17.1038	−	40.3175i	−0.732644	−	1.72701i
$546$	−0.131459	+	1.47539i	−0.00562591	+	0.0631409i
$547$	33.2376	−	13.7675i	1.42114	−	0.588655i	0.465992	−	0.884789i	$-0.345698\pi$
$547$	33.2376	−	13.7675i	1.42114	−	0.588655i	0.955146	+	0.296134i	$0.0956976\pi$
$548$	−11.4825	−	16.5108i	−0.490506	−	0.705307i
$549$	−13.3971	−	5.54924i	−0.571772	−	0.236836i
$550$	−20.0173	−	10.0308i	−0.853542	−	0.427715i
$551$	−10.7395	−	10.7395i	−0.457517	−	0.457517i
$552$	−15.0558	+	19.4274i	−0.640818	+	0.826883i
$553$	−4.03371	−	4.03371i	−0.171531	−	0.171531i
$554$	18.6235	−	35.6360i	0.791235	−	1.51403i
$555$	51.1239	−	0.435411i	2.17009	−	0.0184822i
$556$	−21.9628	+	34.2325i	−0.931429	+	1.45178i
$557$	1.15386	+	2.78566i	0.0488905	+	0.118032i	0.946438	−	0.322886i	$-0.104653\pi$
$557$	1.15386	+	2.78566i	0.0488905	+	0.118032i	−0.897547	+	0.440918i	$0.854653\pi$
$558$	2.08133	+	2.48850i	0.0881096	+	0.105347i
$559$		−	4.57117i		−	0.193340i
$560$	−4.28800	−	9.14503i	−0.181201	−	0.386448i
$561$		−	23.4299i		−	0.989210i
$562$	21.1736	−	17.7091i	0.893153	−	0.747013i
$563$	−0.338542	−	0.817314i	−0.0142679	−	0.0344457i	0.916585	−	0.399840i	$-0.130934\pi$
$563$	−0.338542	−	0.817314i	−0.0142679	−	0.0344457i	−0.930853	+	0.365394i	$0.880934\pi$
$564$	11.0898	−	2.42135i	0.466965	−	0.101957i
$565$	−0.0317418	−	3.72698i	−0.00133539	−	0.156795i
$566$	−29.9216	−	15.6371i	−1.25770	−	0.657275i
$567$	−8.83896	−	8.83896i	−0.371201	−	0.371201i
$568$	−20.4462	+	11.6742i	−0.857904	+	0.489837i
$569$	−1.30773	−	1.30773i	−0.0548229	−	0.0548229i	0.679164	−	0.733987i	$-0.262343\pi$
$569$	−1.30773	−	1.30773i	−0.0548229	−	0.0548229i	−0.733987	+	0.679164i	$0.762343\pi$
$570$	28.3734	−	24.1445i	1.18843	−	1.01130i
$571$	−3.63704	−	1.50651i	−0.152206	−	0.0630456i	0.305280	−	0.952263i	$-0.401250\pi$
$571$	−3.63704	−	1.50651i	−0.152206	−	0.0630456i	−0.457486	+	0.889217i	$0.651250\pi$
$572$	−2.86388	−	0.514433i	−0.119745	−	0.0215095i
$573$	−28.7708	+	11.9172i	−1.20192	+	0.497850i
$574$	15.2941	+	1.36271i	0.638362	+	0.0568786i
$575$	15.4766	+	14.9582i	0.645419	+	0.623798i
$576$	−8.32761	+	2.14592i	−0.346984	+	0.0894134i
$577$		−	33.9400i		−	1.41294i	−0.707743	−	0.706470i	$-0.750286\pi$
$577$		−	33.9400i		−	1.41294i	0.707743	−	0.706470i	$-0.249714\pi$
$578$	−0.447280	+	5.01992i	−0.0186044	+	0.208801i
$579$	5.47338	+	13.2139i	0.227466	+	0.549151i
$580$	11.3486	−	2.57930i	0.471225	−	0.107100i
$581$	−7.68530	−	3.18336i	−0.318840	−	0.132068i
$582$	−5.04337	+	1.58130i	−0.209055	+	0.0655471i
$583$	0.843295	−	0.843295i	0.0349257	−	0.0349257i
$584$	15.6352	−	8.92723i	0.646991	−	0.369412i
$585$	0.413933	−	1.02390i	0.0171140	−	0.0423331i
$586$	−23.6044	−	12.3357i	−0.975088	−	0.509583i
$587$	−42.7204	−	17.6954i	−1.76326	−	0.730367i	−0.996032	−	0.0889930i	$-0.971635\pi$
$587$	−42.7204	−	17.6954i	−1.76326	−	0.730367i	−0.767229	−	0.641374i	$-0.778365\pi$
$588$	4.93027	+	22.5807i	0.203321	+	0.931211i
$589$	11.5065	−	4.76617i	0.474119	−	0.196386i
$590$	30.6618	+	15.6929i	1.26233	+	0.646069i
$591$		−	1.81983i		−	0.0748578i
$592$	−30.8213	+	33.2064i	−1.26675	+	1.36477i
$593$	24.2307			0.995036			0.497518	−	0.867454i	$-0.334245\pi$
$593$	24.2307			0.995036			0.497518	+	0.867454i	$0.334245\pi$
$594$	13.3482	−	11.1641i	0.547682	−	0.458068i
$595$	−6.60043	−	6.48895i	−0.270591	−	0.266021i
$596$	−5.03877	+	7.85371i	−0.206396	+	0.321701i
$597$	7.67711	+	3.17996i	0.314203	+	0.130147i
$598$	2.47903	+	1.29555i	0.101375	+	0.0529789i
$599$	13.7452	−	13.7452i	0.561614	−	0.561614i	−0.368152	−	0.929766i	$-0.620009\pi$
$599$	13.7452	−	13.7452i	0.561614	−	0.561614i	0.929766	+	0.368152i	$0.120009\pi$
$600$	4.07225	+	28.2561i	0.166249	+	1.15355i
$601$	−7.85659	−	7.85659i	−0.320477	−	0.320477i	0.528473	−	0.848950i	$-0.322765\pi$
$601$	−7.85659	−	7.85659i	−0.320477	−	0.320477i	−0.848950	+	0.528473i	$0.822765\pi$
$602$	4.75353	+	15.1608i	0.193739	+	0.617908i
$603$	3.55305	−	8.57782i	0.144691	−	0.349316i
$604$	−20.3089	+	14.1238i	−0.826358	+	0.574691i
$605$	−1.52653	+	1.55276i	−0.0620624	+	0.0631286i
$606$	1.47579	−	16.5631i	0.0599499	−	0.672832i
$607$			28.6943i			1.16467i	0.812950	+	0.582333i	$0.197860\pi$
$607$			28.6943i			1.16467i	−0.812950	+	0.582333i	$0.802140\pi$
$608$	−1.70386	+	32.9708i	−0.0691008	+	1.33714i
$609$	5.93226			0.240387
$610$	−13.1087	−	40.5942i	−0.530755	−	1.64361i
$611$	−0.494354	−	1.19348i	−0.0199994	−	0.0482829i
$612$	−6.46987	+	4.49947i	−0.261529	+	0.181880i
$613$	−7.04353	+	17.0046i	−0.284485	+	0.686808i	−0.999930	−	0.0118614i	$-0.996224\pi$
$613$	−7.04353	+	17.0046i	−0.284485	+	0.686808i	0.715444	+	0.698670i	$0.246224\pi$
$614$	15.7801	−	4.94772i	0.636835	−	0.199674i
$615$	−40.2352	−	16.2659i	−1.62244	−	0.655905i
$616$	10.0333	−	1.27196i	0.404255	−	0.0512486i
$617$	−5.61180	−	5.61180i	−0.225922	−	0.225922i	0.585064	−	0.810987i	$-0.301069\pi$
$617$	−5.61180	−	5.61180i	−0.225922	−	0.225922i	−0.810987	+	0.585064i	$0.801069\pi$
$618$	−32.8350	−	17.1596i	−1.32082	−	0.690261i
$619$	−10.2233	+	24.6813i	−0.410911	+	0.992027i	0.573983	+	0.818867i	$0.305398\pi$
$619$	−10.2233	+	24.6813i	−0.410911	+	0.992027i	−0.984894	+	0.173160i	$0.944602\pi$
$620$	−1.60723	+	9.40726i	−0.0645478	+	0.377805i
$621$	−15.4549	+	6.40161i	−0.620182	+	0.256888i
$622$	7.06513	+	8.44730i	0.283286	+	0.338706i
$623$	−11.8886			−0.476305
$624$	1.54637	+	3.37237i	0.0619043	+	0.135003i
$625$	24.9855	−	0.851492i	0.999420	−	0.0340597i
$626$	6.61186	+	7.90536i	0.264263	+	0.315962i
$627$	14.2759	+	34.4650i	0.570124	+	1.37640i
$628$	33.8585	−	7.39268i	1.35110	−	0.295000i
$629$	−15.8882	+	38.3574i	−0.633502	+	1.52941i
$630$	−0.308107	+	3.82633i	−0.0122753	+	0.152444i
$631$	−3.09520	+	3.09520i	−0.123218	+	0.123218i	−0.766027	−	0.642809i	$-0.777769\pi$
$631$	−3.09520	+	3.09520i	−0.123218	+	0.123218i	0.642809	+	0.766027i	$0.277769\pi$
$632$	−13.7832	−	3.76419i	−0.548266	−	0.149731i
$633$	12.2473	−	12.2473i	0.486785	−	0.486785i
$634$	−8.48982	−	27.0772i	−0.337174	−	1.07537i
$635$	−26.7852	+	0.228123i	−1.06294	+	0.00905278i
$636$	−1.49666	−	0.268841i	−0.0593463	−	0.0106602i
$637$	2.43011	−	1.00659i	0.0962845	−	0.0398824i
$638$	−1.03422	+	11.6073i	−0.0409451	+	0.459536i
$639$	8.94812			0.353982
$640$	−20.6841	−	14.5660i	−0.817611	−	0.575771i
$641$	−7.87672			−0.311112			−0.155556	−	0.987827i	$-0.549717\pi$
$641$	−7.87672			−0.311112			−0.155556	+	0.987827i	$0.549717\pi$
$642$	2.66301	−	29.8876i	0.105101	−	1.17957i
$643$	19.8362	−	8.21644i	0.782265	−	0.324025i	0.0444357	−	0.999012i	$-0.485851\pi$
$643$	19.8362	−	8.21644i	0.782265	−	0.324025i	0.737829	+	0.674988i	$0.235851\pi$
$644$	−9.56922	−	1.71890i	−0.377080	−	0.0677341i
$645$	−0.382455	−	44.9061i	−0.0150591	−	1.76818i
$646$	9.05151	+	28.8687i	0.356127	+	1.13582i
$647$	23.8640	−	23.8640i	0.938192	−	0.938192i	−0.0600057	−	0.998198i	$-0.519112\pi$
$647$	23.8640	−	23.8640i	0.938192	−	0.938192i	0.998198	+	0.0600057i	$0.0191119\pi$
$648$	−30.2028	−	8.24836i	−1.18648	−	0.324026i
$649$	−24.3878	+	24.3878i	−0.957303	+	0.957303i
$650$	3.08310	−	1.02467i	0.120929	−	0.0401908i
$651$	−1.86162	+	4.49435i	−0.0729627	+	0.176148i
$652$	−4.83917	+	1.05658i	−0.189516	+	0.0413791i
$653$	14.9873	+	36.1824i	0.586497	+	1.41593i	0.886831	+	0.462095i	$0.152902\pi$
$653$	14.9873	+	36.1824i	0.586497	+	1.41593i	−0.300334	+	0.953834i	$0.597098\pi$
$654$	−35.8722	−	42.8900i	−1.40271	−	1.67713i
$655$	−5.77066	+	2.44807i	−0.225478	+	0.0956540i
$656$	34.9584	−	16.0298i	1.36490	−	0.625860i
$657$	−6.84263			−0.266956
$658$	2.88067	+	3.44422i	0.112300	+	0.134270i
$659$	20.8508	−	8.63670i	0.812233	−	0.336438i	0.0623886	−	0.998052i	$-0.480128\pi$
$659$	20.8508	−	8.63670i	0.812233	−	0.336438i	0.749845	+	0.661614i	$0.230128\pi$
$660$	−28.1772	−	4.81406i	−1.09679	−	0.187387i
$661$	12.8313	−	30.9774i	0.499078	−	1.20488i	−0.450902	−	0.892573i	$-0.648898\pi$
$661$	12.8313	−	30.9774i	0.499078	−	1.20488i	0.949981	−	0.312308i	$-0.101102\pi$
$662$	5.17600	+	2.70499i	0.201171	+	0.105132i
$663$	2.40403	+	2.40403i	0.0933647	+	0.0933647i
$664$	−20.6697	+	2.62036i	−0.802140	+	0.101690i
$665$	13.6629	+	5.52350i	0.529824	+	0.214192i
$666$	16.4300	−	5.15148i	0.636650	−	0.199616i
$667$	4.28698	−	10.3497i	0.165993	−	0.400741i
$668$	−6.90600	+	4.80278i	−0.267201	+	0.185825i
$669$	4.46122	+	10.7703i	0.172481	+	0.416405i
$670$	25.9915	−	8.39318i	1.00414	−	0.324257i
$671$	42.7141			1.64896
$672$	−8.63560	−	9.57678i	−0.333126	−	0.369432i
$673$		−	31.7494i		−	1.22385i	−0.790916	−	0.611925i	$-0.790395\pi$
$673$		−	31.7494i		−	1.22385i	0.790916	−	0.611925i	$-0.209605\pi$
$674$	−0.935969	+	10.5046i	−0.0360522	+	0.404622i
$675$	−7.12870	+	18.0750i	−0.274384	+	0.695707i
$676$	−20.9989	+	14.6037i	−0.807651	+	0.561681i
$677$	−3.61070	+	8.71700i	−0.138770	+	0.335022i	−0.977952	−	0.208830i	$-0.933035\pi$
$677$	−3.61070	+	8.71700i	−0.138770	+	0.335022i	0.839182	+	0.543851i	$0.183035\pi$
$678$	−1.42363	−	4.54048i	−0.0546740	−	0.174376i
$679$	−1.47838	−	1.47838i	−0.0567350	−	0.0567350i
$680$	−22.4152	−	5.91693i	−0.859585	−	0.226904i
$681$	−4.57152	+	4.57152i	−0.175181	+	0.175181i
$682$	−8.46927	−	4.42606i	−0.324305	−	0.169482i
$683$	29.6789	+	12.2934i	1.13563	+	0.470394i	0.869692	−	0.493595i	$-0.164317\pi$
$683$	29.6789	+	12.2934i	1.13563	+	0.470394i	0.265941	+	0.963989i	$0.414317\pi$
$684$	6.77555	−	10.5608i	0.259070	−	0.403801i
$685$	−15.7632	+	16.0340i	−0.602281	+	0.612628i
$686$	−15.5882	+	13.0376i	−0.595159	+	0.497778i
$687$	−33.2252			−1.26762
$688$	29.1677	+	27.0727i	1.11201	+	1.03214i
$689$			0.173053i			0.00659280i
$690$	24.4618	+	12.5197i	0.931246	+	0.476618i
$691$	−36.7401	+	15.2182i	−1.39766	+	0.578929i	−0.949143	−	0.314846i	$-0.898047\pi$
$691$	−36.7401	+	15.2182i	−1.39766	+	0.578929i	−0.448516	+	0.893775i	$0.648047\pi$
$692$	4.15078	+	19.0106i	0.157789	+	0.722675i
$693$	−3.55115	−	1.47093i	−0.134897	−	0.0558762i
$694$	−9.76512	−	5.10327i	−0.370679	−	0.193718i
$695$	42.1581	+	17.0433i	1.59915	+	0.646489i
$696$	12.9032	−	7.36733i	0.489095	−	0.279258i
$697$	24.9204	−	24.9204i	0.943929	−	0.943929i
$698$	15.7048	−	4.92409i	0.594435	−	0.186380i
$699$	−14.8562	−	6.15365i	−0.561914	−	0.232752i
$700$	−9.15988	+	6.60452i	−0.346211	+	0.249627i
$701$	10.8619	+	26.2229i	0.410248	+	0.990427i	0.985071	+	0.172149i	$0.0550709\pi$
$701$	10.8619	+	26.2229i	0.410248	+	0.990427i	−0.574823	+	0.818278i	$0.694929\pi$
$702$	−0.224096	+	2.51509i	−0.00845797	+	0.0949258i
$703$		−	66.1039i		−	2.49316i
$704$	20.2438	−	15.2271i	0.762967	−	0.573894i
$705$	−4.95627	−	11.6831i	−0.186664	−	0.440009i
$706$	−0.206371	−	0.0183879i	−0.00776689	−	0.000692037i
$707$	6.07706	−	2.51720i	0.228551	−	0.0946690i
$708$	43.2827	+	7.77478i	1.62666	+	0.292194i
$709$	11.9035	+	4.93060i	0.447046	+	0.185172i	0.594837	−	0.803846i	$-0.297216\pi$
$709$	11.9035	+	4.93060i	0.447046	+	0.185172i	−0.147791	+	0.989019i	$0.547216\pi$
$710$	17.0594	+	20.0473i	0.640227	+	0.752362i
$711$	3.83973	+	3.83973i	0.144001	+	0.144001i
$712$	−25.8587	+	14.7645i	−0.969097	+	0.553324i
$713$	6.49574	+	6.49574i	0.243267	+	0.243267i
$714$	−10.4732	−	5.47329i	−0.391948	−	0.204833i
$715$	0.0277055	+	3.25305i	0.00103613	+	0.121657i
$716$	26.4312	−	5.77099i	0.987779	−	0.215672i
$717$	−7.49338	−	18.0906i	−0.279845	−	0.675607i
$718$	−31.9916	+	26.7570i	−1.19391	+	0.998563i
$719$		−	29.8520i		−	1.11329i	−0.830750	−	0.556645i	$-0.812088\pi$
$719$		−	29.8520i		−	1.11329i	0.830750	−	0.556645i	$-0.187912\pi$
$720$	4.08179	+	8.70526i	0.152119	+	0.324426i
$721$		−	14.6551i		−	0.545783i
$722$	−13.6656	−	16.3391i	−0.508582	−	0.608077i
$723$	−12.9076	−	31.1617i	−0.480039	−	1.15892i
$724$	7.13611	−	11.1227i	0.265211	−	0.413374i
$725$	−5.18339	−	11.9347i	−0.192506	−	0.443243i
$726$	−1.28760	+	2.46382i	−0.0477873	+	0.0914411i
$727$	−5.31546	−	5.31546i	−0.197139	−	0.197139i	0.601633	−	0.798773i	$-0.294517\pi$
$727$	−5.31546	−	5.31546i	−0.197139	−	0.197139i	−0.798773	+	0.601633i	$0.794517\pi$
$728$	−0.898964	+	1.15998i	−0.0333178	+	0.0429918i
$729$	−8.22672	−	8.22672i	−0.304693	−	0.304693i
$730$	−13.0453	−	15.3302i	−0.482829	−	0.567396i
$731$	33.6923	+	13.9558i	1.24615	+	0.516174i
$732$	−31.0953	−	44.7125i	−1.14931	−	1.65262i
$733$	21.0712	−	8.72796i	0.778281	−	0.322375i	0.0420595	−	0.999115i	$-0.486608\pi$
$733$	21.0712	−	8.72796i	0.778281	−	0.322375i	0.736222	+	0.676740i	$0.236608\pi$
$734$	0.751613	−	8.43552i	0.0277425	−	0.311361i
$735$	23.7886	−	10.0918i	0.877457	−	0.372241i
$736$	−22.9487	+	8.14535i	−0.845899	+	0.300242i
$737$			27.3488i			1.00741i
$738$	−14.5586	−	1.29718i	−0.535909	−	0.0477500i
$739$	12.8599	+	31.0465i	0.473059	+	1.14207i	0.962804	+	0.270200i	$0.0870898\pi$
$739$	12.8599	+	31.0465i	0.473059	+	1.14207i	−0.489745	+	0.871866i	$0.662910\pi$
$740$	42.8647	+	26.9885i	1.57574	+	0.992118i
$741$	−5.00108	−	2.07151i	−0.183719	−	0.0760990i
$742$	−0.179957	−	0.573950i	−0.00660642	−	0.0210704i
$743$	−5.20989	+	5.20989i	−0.191133	+	0.191133i	−0.796185	−	0.605053i	$-0.793152\pi$
$743$	−5.20989	+	5.20989i	−0.191133	+	0.191133i	0.605053	+	0.796185i	$0.293152\pi$
$744$	1.53238	+	12.0876i	0.0561799	+	0.443153i
$745$	9.67204	+	3.91012i	0.354356	+	0.143256i
$746$	4.70440	−	9.00187i	0.172240	−	0.329582i
$747$	7.31573	+	3.03027i	0.267669	+	0.110872i
$748$	12.5351	−	19.5380i	0.458329	−	0.714379i
$749$	10.9658	−	4.54220i	0.400683	−	0.165968i
$750$	30.2019	−	10.3241i	1.10282	−	0.376981i
$751$		−	13.7728i		−	0.502575i	−0.967913	−	0.251287i	$-0.919146\pi$
$751$		−	13.7728i		−	0.502575i	0.967913	−	0.251287i	$-0.0808539\pi$
$752$	10.5431	+	3.91397i	0.384468	+	0.142728i
$753$	14.4440			0.526369
$754$	−1.08485	−	1.29708i	−0.0395079	−	0.0472370i
$755$	19.7224	+	19.3893i	0.717772	+	0.705649i
$756$	−1.87218	−	8.57460i	−0.0680905	−	0.311855i
$757$	−13.2033	−	5.46900i	−0.479883	−	0.198774i	0.129611	−	0.991565i	$-0.458627\pi$
$757$	−13.2033	−	5.46900i	−0.479883	−	0.198774i	−0.609494	+	0.792791i	$0.708627\pi$
$758$	−6.75895	+	12.9333i	−0.245496	+	0.469757i
$759$	−19.4564	+	19.4564i	−0.706223	+	0.706223i
$760$	36.5777	−	4.95394i	1.32681	−	0.179698i
$761$	23.8131	+	23.8131i	0.863225	+	0.863225i	0.991711	−	0.128487i	$-0.0410119\pi$
$761$	23.8131	+	23.8131i	0.863225	+	0.863225i	−0.128487	+	0.991711i	$0.541012\pi$
$762$	−32.6317	+	10.2314i	−1.18212	+	0.370643i
$763$	8.46404	−	20.4340i	0.306419	−	0.739760i
$764$	−30.3675	−	5.45484i	−1.09866	−	0.197349i
$765$	6.28302	+	6.17690i	0.227163	+	0.223326i
$766$	18.2512	+	1.62620i	0.659444	+	0.0587571i
$767$		−	5.00463i		−	0.180707i
$768$	−30.6767	−	10.1057i	−1.10695	−	0.364660i
$769$	43.8494			1.58125			0.790626	−	0.612300i	$-0.209756\pi$
$769$	43.8494			1.58125			0.790626	+	0.612300i	$0.209756\pi$
$770$	−3.47471	−	10.7603i	−0.125220	−	0.387774i
$771$	−7.90538	−	19.0853i	−0.284705	−	0.687339i
$772$	−2.50531	+	13.9472i	−0.0901682	+	0.501972i
$773$	8.76014	−	21.1489i	0.315080	−	0.760672i	−0.684421	−	0.729087i	$-0.739945\pi$
$773$	8.76014	−	21.1489i	0.315080	−	0.760672i	0.999501	−	0.0315842i	$-0.0100552\pi$
$774$	−4.52494	−	14.4317i	−0.162646	−	0.518738i
$775$	10.6685	−	0.181735i	0.383223	−	0.00652812i
$776$	−5.05163	−	1.37960i	−0.181343	−	0.0495247i
$777$	18.2572	+	18.2572i	0.654974	+	0.654974i
$778$	−18.1923	+	34.8110i	−0.652225	+	1.24803i
$779$	−21.4735	+	51.8417i	−0.769370	+	1.85742i
$780$	3.38507	−	2.39718i	0.121205	−	0.0858327i
$781$	−24.3514	+	10.0867i	−0.871363	+	0.360930i
$782$	−17.1174	+	14.3166i	−0.612119	+	0.511962i
$783$	10.1127			0.361397
$784$	−7.96948	+	21.4675i	−0.284624	+	0.766698i
$785$	−15.1321	−	35.6698i	−0.540087	−	1.27311i
$786$	−6.13887	+	5.13441i	−0.218966	+	0.183138i
$787$	6.64829	+	16.0504i	0.236986	+	0.572134i	0.996968	−	0.0778092i	$-0.0247925\pi$
$787$	6.64829	+	16.0504i	0.236986	+	0.572134i	−0.759982	+	0.649944i	$0.774792\pi$
$788$	0.973619	−	1.51754i	0.0346838	−	0.0540601i
$789$	−1.43340	+	3.46053i	−0.0510303	+	0.123198i
$790$	−1.28216	+	15.9229i	−0.0456171	+	0.566511i
$791$	1.33097	−	1.33097i	0.0473237	−	0.0473237i
$792$	−9.55085	+	1.21079i	−0.339375	+	0.0430236i
$793$	−4.38269	+	4.38269i	−0.155634	+	0.155634i
$794$	−47.5015	+	14.8937i	−1.68577	+	0.528557i
$795$	0.0144788	+	1.70003i	0.000513509	+	0.0602939i
$796$	4.70057	+	6.75904i	0.166607	+	0.239568i
$797$	−48.1639	+	19.9501i	−1.70605	+	0.706670i	−0.999999	−	0.00148846i	$-0.999526\pi$
$797$	−48.1639	+	19.9501i	−1.70605	+	0.706670i	−0.706053	+	0.708159i	$0.749526\pi$
$798$	18.7408	+	1.66982i	0.663416	+	0.0591110i
$799$	10.3059			0.364596
$800$	−11.7214	+	25.7412i	−0.414413	+	0.910089i
$801$	11.3169			0.399862
$802$	−3.55062	−	0.316364i	−0.125377	−	0.0111712i
$803$	18.6215	−	7.71330i	0.657140	−	0.272196i
$804$	28.6283	−	19.9096i	1.00964	−	0.702157i
$805$	0.0925734	+	10.8695i	0.00326278	+	0.383101i
$806$	1.32313	−	0.414855i	0.0466052	−	0.0146126i
$807$	−25.4311	+	25.4311i	−0.895216	+	0.895216i
$808$	10.0920	−	13.0223i	0.355036	−	0.458123i
$809$	−11.9277	+	11.9277i	−0.419355	+	0.419355i	−0.884981	−	0.465626i	$-0.845829\pi$
$809$	−11.9277	+	11.9277i	−0.419355	+	0.419355i	0.465626	+	0.884981i	$0.345829\pi$
$810$	−2.80956	+	34.8914i	−0.0987179	+	1.22596i
$811$	13.7044	−	33.0853i	0.481225	−	1.16178i	−0.477802	−	0.878468i	$-0.658566\pi$
$811$	13.7044	−	33.0853i	0.481225	−	1.16178i	0.959027	−	0.283313i	$-0.0914337\pi$
$812$	4.94686	+	3.17379i	0.173601	+	0.111378i
$813$	7.30531	+	17.6366i	0.256209	+	0.618542i
$814$	−38.9057	+	32.5398i	−1.36364	+	1.14052i
$815$	2.16273	+	5.09804i	0.0757570	+	0.178576i
$816$	−29.5774	+	1.10180i	−1.03542	+	0.0385708i
$817$	−58.0642			−2.03141
$818$	8.95085	−	7.48628i	0.312959	−	0.261752i
$819$	0.515292	−	0.213441i	0.0180058	−	0.00745824i
$820$	−24.8494	−	35.0900i	−0.867779	−	1.22540i
$821$	3.61317	−	8.72295i	0.126100	−	0.304433i	−0.848204	−	0.529670i	$-0.822316\pi$
$821$	3.61317	−	8.72295i	0.126100	−	0.304433i	0.974304	+	0.225237i	$0.0723157\pi$
$822$	−13.2959	+	25.4418i	−0.463749	+	0.887384i
$823$	9.66407	+	9.66407i	0.336868	+	0.336868i	0.855187	−	0.518319i	$-0.173442\pi$
$823$	9.66407	+	9.66407i	0.336868	+	0.336868i	−0.518319	+	0.855187i	$0.673442\pi$
$824$	−18.2003	−	31.8761i	−0.634037	−	1.11046i
$825$	0.544344	+	31.9549i	0.0189516	+	1.11253i
$826$	5.20427	+	16.5984i	0.181080	+	0.577532i
$827$	−12.2671	+	29.6154i	−0.426569	+	1.02983i	0.553798	+	0.832651i	$0.313178\pi$
$827$	−12.2671	+	29.6154i	−0.426569	+	1.02983i	−0.980368	+	0.197178i	$0.936822\pi$
$828$	9.10905	+	1.63624i	0.316561	+	0.0568632i
$829$	−3.93773	−	9.50653i	−0.136763	−	0.330175i	0.840629	−	0.541612i	$-0.182186\pi$
$829$	−3.93773	−	9.50653i	−0.136763	−	0.330175i	−0.977392	+	0.211437i	$0.932186\pi$
$830$	7.15825	+	22.1673i	0.248467	+	0.769437i
$831$	−57.3943			−1.99099
$832$	−0.514736	+	3.63951i	−0.0178452	+	0.126177i
$833$			20.9845i			0.727069i
$834$	57.8265	+	5.15239i	2.00237	+	0.178413i
$835$	6.70656	+	6.59329i	0.232090	+	0.228170i
$836$	−6.53446	+	36.3778i	−0.225999	+	1.25815i
$837$	−3.17349	+	7.66149i	−0.109692	+	0.264820i
$838$	−20.2873	+	6.36090i	−0.700813	+	0.219733i
$839$	2.71963	+	2.71963i	0.0938921	+	0.0938921i	0.752493	−	0.658601i	$-0.228851\pi$
$839$	2.71963	+	2.71963i	0.0938921	+	0.0938921i	−0.658601	+	0.752493i	$0.728851\pi$
$840$	−8.73416	+	11.4706i	−0.301357	+	0.395774i
$841$	15.7174	−	15.7174i	0.541981	−	0.541981i
$842$	−19.5450	+	37.3993i	−0.673564	+	1.28887i
$843$	−36.4015	−	15.0780i	−1.25374	−	0.519314i
$844$	16.7652	−	3.66053i	0.577083	−	0.126001i
$845$	20.3925	+	20.0481i	0.701523	+	0.689675i
$846$	−2.74214	−	3.27859i	−0.0942767	−	0.112720i
$847$	−1.09967			−0.0377850
$848$	−1.10422	−	1.02490i	−0.0379190	−	0.0351953i
$849$			48.1908i			1.65390i
$850$	−1.86027	+	25.8526i	−0.0638068	+	0.886736i
$851$	45.0461	−	18.6587i	1.54416	−	0.639612i
$852$	28.2861	+	18.1477i	0.969066	+	0.621731i
$853$	0.490953	+	0.203359i	0.0168099	+	0.00696289i	0.391073	−	0.920360i	$-0.372104\pi$
$853$	0.490953	+	0.203359i	0.0168099	+	0.00696289i	−0.374263	+	0.927323i	$0.622104\pi$
$854$	9.97815	−	19.0932i	0.341445	−	0.653356i
$855$	−13.0058	−	5.25788i	−0.444791	−	0.179816i
$856$	18.2107	−	23.4983i	0.622429	−	0.803155i
$857$	9.02822	−	9.02822i	0.308398	−	0.308398i	−0.535890	−	0.844288i	$-0.680024\pi$
$857$	9.02822	−	9.02822i	0.308398	−	0.308398i	0.844288	+	0.535890i	$0.180024\pi$
$858$	1.24260	+	3.96311i	0.0424215	+	0.135298i
$859$	9.49187	+	3.93166i	0.323858	+	0.134147i	0.538689	−	0.842505i	$-0.318920\pi$
$859$	9.49187	+	3.93166i	0.323858	+	0.134147i	−0.214830	+	0.976651i	$0.568920\pi$
$860$	23.7061	−	37.6514i	0.808371	−	1.28390i
$861$	−8.38738	−	20.2489i	−0.285841	−	0.690081i
$862$	48.6239	+	4.33243i	1.65614	+	0.147563i
$863$			2.75061i			0.0936320i	0.998904	+	0.0468160i	$0.0149074\pi$
$863$			2.75061i			0.0936320i	−0.998904	+	0.0468160i	$0.985093\pi$
$864$	−14.7210	−	16.3255i	−0.500820	−	0.555404i
$865$	20.0276	−	8.49624i	0.680959	−	0.288881i
$866$	2.12251	−	23.8214i	0.0721257	−	0.809483i
$867$	6.64624	−	2.75296i	0.225718	−	0.0934955i
$868$	−3.95690	+	2.75182i	−0.134306	+	0.0934029i
$869$	−14.7778	−	6.12115i	−0.501301	−	0.207646i
$870$	−10.7658	−	12.6515i	−0.364996	−	0.428925i
$871$	−2.80614	−	2.80614i	−0.0950823	−	0.0950823i
$872$	−6.96712	−	54.9574i	−0.235936	−	1.86109i
$873$	1.40729	+	1.40729i	0.0476294	+	0.0476294i
$874$	16.4564	−	31.4893i	0.556645	−	1.06514i
$875$	9.15275	+	8.69661i	0.309420	+	0.293999i
$876$	−21.6304	−	13.8776i	−0.730823	−	0.468880i
$877$	6.36290	+	15.3614i	0.214860	+	0.518718i	0.994158	−	0.107936i	$-0.0344241\pi$
$877$	6.36290	+	15.3614i	0.214860	+	0.518718i	−0.779298	+	0.626654i	$0.784424\pi$
$878$	−9.84342	−	11.7691i	−0.332199	−	0.397189i
$879$			38.0165i			1.28227i
$880$	−20.9211	−	19.0893i	−0.705251	−	0.643502i
$881$		−	10.9358i		−	0.368435i	−0.982885	−	0.184218i	$-0.941025\pi$
$881$		−	10.9358i		−	0.368435i	0.982885	−	0.184218i	$-0.0589752\pi$
$882$	6.67575	−	5.58344i	0.224784	−	0.188004i
$883$	−0.828407	−	1.99995i	−0.0278781	−	0.0673037i	0.909327	−	0.416081i	$-0.136597\pi$
$883$	−0.828407	−	1.99995i	−0.0278781	−	0.0673037i	−0.937206	+	0.348778i	$0.886597\pi$
$884$	0.718529	+	3.29087i	0.0241667	+	0.110684i
$885$	−0.418721	−	49.1642i	−0.0140751	−	1.65264i
$886$	−5.13443	−	2.68326i	−0.172495	−	0.0901460i
$887$	26.2532	+	26.2532i	0.881497	+	0.881497i	0.993687	−	0.112189i	$-0.0357863\pi$
$887$	26.2532	+	26.2532i	0.881497	+	0.881497i	−0.112189	+	0.993687i	$0.535786\pi$
$888$	62.3850	+	17.0373i	2.09350	+	0.571735i
$889$	−9.56543	−	9.56543i	−0.320814	−	0.320814i
$890$	21.5753	+	25.3542i	0.723207	+	0.849876i
$891$	−32.3821	−	13.4131i	−1.08484	−	0.449356i
$892$	−2.04202	+	11.3681i	−0.0683720	+	0.380631i
$893$	−15.1598	+	6.27941i	−0.507304	+	0.210132i
$894$	13.2667	+	1.18208i	0.443706	+	0.0395346i
$895$	−11.8126	−	27.8451i	−0.394853	−	0.930760i
$896$	−2.07752	−	12.6061i	−0.0694050	−	0.421140i
$897$		−	3.99266i		−	0.133311i
$898$	0.391646	−	4.39553i	0.0130694	−	0.146681i
$899$	−2.12520	−	5.13068i	−0.0708793	−	0.171118i
$900$	8.71940	−	6.28692i	0.290647	−	0.209564i
$901$	−1.27550	−	0.528331i	−0.0424932	−	0.0176013i
$902$	41.0820	−	12.8809i	1.36788	−	0.428887i
$903$	16.0367	−	16.0367i	0.533669	−	0.533669i
$904$	1.24203	−	4.54792i	0.0413094	−	0.151261i
$905$	−13.6979	−	5.53768i	−0.455335	−	0.184079i
$906$	31.2943	+	16.3545i	1.03968	+	0.543341i
$907$	−25.9433	−	10.7461i	−0.861432	−	0.356817i	−0.0921648	−	0.995744i	$-0.529379\pi$
$907$	−25.9433	−	10.7461i	−0.861432	−	0.356817i	−0.769268	+	0.638927i	$0.779379\pi$
$908$	−6.25794	+	1.36636i	−0.207677	+	0.0453443i
$909$	−5.78482	+	2.39615i	−0.191870	+	0.0794753i
$910$	1.46059	+	0.747538i	0.0484179	+	0.0247806i
$911$			23.8049i			0.788691i	0.918962	+	0.394345i	$0.129029\pi$
$911$			23.8049i			0.788691i	−0.918962	+	0.394345i	$0.870971\pi$
$912$	42.8367	−	19.6423i	1.41846	−	0.650423i
$913$	−23.3249			−0.771941
$914$	−44.0622	+	36.8526i	−1.45745	+	1.21898i
$915$	−42.6878	+	43.4212i	−1.41122	+	1.43546i
$916$	−27.7062	−	17.7757i	−0.915437	−	0.587324i
$917$	−2.92473	−	1.21146i	−0.0965831	−	0.0400060i
$918$	−17.8535	−	9.33028i	−0.589254	−	0.307945i
$919$	−28.3643	+	28.3643i	−0.935652	+	0.935652i	−0.998051	−	0.0623993i	$-0.980125\pi$
$919$	−28.3643	+	28.3643i	−0.935652	+	0.935652i	0.0623993	+	0.998051i	$0.480125\pi$
$920$	13.7004	+	23.5273i	0.451688	+	0.775673i
$921$	−16.6919	−	16.6919i	−0.550015	−	0.550015i
$922$	−15.3063	−	48.8176i	−0.504087	−	1.60772i
$923$	1.46364	−	3.53353i	0.0481762	−	0.116308i
$924$	−8.24241	−	11.8519i	−0.271155	−	0.389899i
$925$	20.7779	−	52.6829i	0.683174	−	1.73220i
$926$	−1.75073	+	19.6489i	−0.0575326	+	0.645701i
$927$			13.9503i			0.458189i
$928$	14.7014	+	0.759740i	0.482598	+	0.0249397i
$929$	24.6748			0.809553			0.404777	−	0.914416i	$-0.367349\pi$
$929$	24.6748			0.809553			0.404777	+	0.914416i	$0.367349\pi$
$930$	12.9634	−	4.18614i	0.425086	−	0.137269i
$931$	−12.7859	−	30.8679i	−0.419041	−	1.01165i
$932$	−9.09623	−	13.0796i	−0.297957	−	0.428438i
$933$	6.01545	−	14.5226i	0.196937	−	0.475448i
$934$	51.0379	−	16.0025i	1.67001	−	0.523617i
$935$	−24.0615	−	9.72735i	−0.786895	−	0.318118i
$936$	0.855734	−	1.10420i	0.0279706	−	0.0360920i
$937$	−6.68724	−	6.68724i	−0.218463	−	0.218463i	0.589388	−	0.807850i	$-0.299369\pi$
$937$	−6.68724	−	6.68724i	−0.218463	−	0.218463i	−0.807850	+	0.589388i	$0.799369\pi$
$938$	12.2249	+	6.38878i	0.399158	+	0.208601i
$939$	5.62953	−	13.5909i	0.183713	−	0.443522i
$940$	2.11752	−	12.3940i	0.0690658	−	0.404249i
$941$	27.0354	−	11.1984i	0.881327	−	0.365058i	0.104316	−	0.994544i	$-0.466735\pi$
$941$	27.0354	−	11.1984i	0.881327	−	0.365058i	0.777011	+	0.629486i	$0.216735\pi$
$942$	−31.7370	−	37.9457i	−1.03405	−	1.23634i
$943$	−41.3884			−1.34779
$944$	31.9335	+	29.6398i	1.03935	+	0.964694i
$945$	−9.03330	+	3.83217i	−0.293853	+	0.124660i
$946$	28.5822	+	34.1739i	0.929289	+	1.11109i
$947$	−20.9971	−	50.6915i	−0.682314	−	1.64725i	−0.759719	−	0.650252i	$-0.774663\pi$
$947$	−20.9971	−	50.6915i	−0.682314	−	1.64725i	0.0774050	−	0.997000i	$-0.475337\pi$
$948$	4.35048	+	19.9252i	0.141297	+	0.647142i
$949$	−1.11924	+	2.70209i	−0.0363322	+	0.0877137i
$950$	−13.0156	−	39.1623i	−0.422282	−	1.27059i
$951$	−28.6417	+	28.6417i	−0.928769	+	0.928769i
$952$	−5.80523	−	10.1673i	−0.188149	−	0.329525i
$953$	−16.5754	+	16.5754i	−0.536931	+	0.536931i	−0.922626	−	0.385695i	$-0.873962\pi$
$953$	−16.5754	+	16.5754i	−0.536931	+	0.536931i	0.385695	+	0.922626i	$0.373962\pi$
$954$	0.171303	+	0.546349i	0.00554613	+	0.0176887i
$955$	0.293777	+	34.4940i	0.00950642	+	1.11620i
$956$	3.42992	−	19.0946i	0.110932	−	0.617564i
$957$	15.3677	−	6.36551i	0.496767	−	0.205768i
$958$	−0.159988	+	1.79558i	−0.00516897	+	0.0580126i
$959$	−11.3553			−0.366682
$960$	−4.75213	+	35.7967i	−0.153374	+	1.15533i
$961$	−26.4460			−0.853097
$962$	0.653170	−	7.33068i	0.0210591	−	0.236351i
$963$	−10.4385	+	4.32377i	−0.336376	+	0.139331i
$964$	5.90816	−	32.8911i	0.190289	−	1.05935i
$965$	15.8425	−	0.134927i	0.509988	−	0.00434345i
$966$	4.15194	+	13.2421i	0.133586	+	0.426057i
$967$	14.6698	−	14.6698i	0.471749	−	0.471749i	−0.430731	−	0.902480i	$-0.641744\pi$
$967$	14.6698	−	14.6698i	0.471749	−	0.471749i	0.902480	+	0.430731i	$0.141744\pi$
$968$	−2.39188	+	1.36569i	−0.0768779	+	0.0438949i
$969$	30.5366	−	30.5366i	0.980976	−	0.980976i
$970$	−0.469919	+	5.83584i	−0.0150882	+	0.187377i
$971$	17.8403	−	43.0702i	0.572521	−	1.38219i	−0.326881	−	0.945065i	$-0.605998\pi$
$971$	17.8403	−	43.0702i	0.572521	−	1.38219i	0.899402	−	0.437122i	$-0.144002\pi$
$972$	4.55946	+	20.8824i	0.146245	+	0.669802i
$973$	8.78823	+	21.2167i	0.281738	+	0.680175i
$974$	7.53800	+	9.01268i	0.241533	+	0.288785i
$975$	−3.33459	−	3.22288i	−0.106792	−	0.103215i
$976$	−2.00865	−	53.9215i	−0.0642954	−	1.72598i
$977$	43.7977			1.40121			0.700607	−	0.713548i	$-0.252913\pi$
$977$	43.7977			1.40121			0.700607	+	0.713548i	$0.252913\pi$
$978$	4.53595	+	5.42333i	0.145044	+	0.173419i
$979$	−30.7977	+	12.7568i	−0.984300	+	0.407710i
$980$	25.2363	+	4.31161i	0.806143	+	0.137729i
$981$	−8.05701	+	19.4513i	−0.257241	+	0.621034i
$982$	46.5846	+	24.3452i	1.48657	+	0.776887i
$983$	−34.5849	−	34.5849i	−1.10309	−	1.10309i	−0.994036	−	0.109050i	$-0.965219\pi$
$983$	−34.5849	−	34.5849i	−1.10309	−	1.10309i	−0.109050	−	0.994036i	$-0.534781\pi$
$984$	−43.3907	−	33.6269i	−1.38324	−	1.07199i
$985$	−1.86889	−	0.755536i	−0.0595477	−	0.0240734i
$986$	12.8723	−	4.03600i	0.409938	−	0.128532i
$987$	2.45268	−	5.92129i	0.0780697	−	0.188477i
$988$	−3.06208	−	4.40302i	−0.0974178	−	0.140079i
$989$	−16.3894	−	39.5674i	−0.521152	−	1.25817i
$990$	3.30762	+	10.2428i	0.105123	+	0.325539i
$991$	−27.5480			−0.875090			−0.437545	−	0.899196i	$-0.644152\pi$
$991$	−27.5480			−0.875090			−0.437545	+	0.899196i	$0.644152\pi$
$992$	−5.18910	+	10.8996i	−0.164754	+	0.346062i
$993$		−	8.33632i		−	0.264545i
$994$	−1.17982	+	13.2414i	−0.0374216	+	0.419991i
$995$	6.45298	−	6.56384i	0.204573	−	0.208088i
$996$	16.9802	+	24.4161i	0.538038	+	0.773655i
$997$	−2.33016	+	5.62550i	−0.0737968	+	0.178161i	−0.956473	−	0.291820i	$-0.905739\pi$
$997$	−2.33016	+	5.62550i	−0.0737968	+	0.178161i	0.882677	+	0.469981i	$0.155739\pi$
$998$	−15.4881	−	49.3975i	−0.490268	−	1.56365i
$999$	31.1229	+	31.1229i	0.984686	+	0.984686i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	160.2.z.a.69.12	yes	88
4.3	odd	2		640.2.z.a.369.18		88
5.2	odd	4		800.2.y.f.101.22		88
5.3	odd	4		800.2.y.f.101.1		88
5.4	even	2	inner	160.2.z.a.69.11	✓	88
20.19	odd	2		640.2.z.a.369.5		88
32.13	even	8	inner	160.2.z.a.109.11	yes	88
32.19	odd	8		640.2.z.a.529.5		88
160.13	odd	8		800.2.y.f.301.1		88
160.19	odd	8		640.2.z.a.529.18		88
160.77	odd	8		800.2.y.f.301.22		88
160.109	even	8	inner	160.2.z.a.109.12	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
160.2.z.a.69.11	✓	88	5.4	even	2	inner
160.2.z.a.69.12	yes	88	1.1	even	1	trivial
160.2.z.a.109.11	yes	88	32.13	even	8	inner
160.2.z.a.109.12	yes	88	160.109	even	8	inner
640.2.z.a.369.5		88	20.19	odd	2
640.2.z.a.369.18		88	4.3	odd	2
640.2.z.a.529.5		88	32.19	odd	8
640.2.z.a.529.18		88	160.19	odd	8
800.2.y.f.101.1		88	5.3	odd	4
800.2.y.f.101.22		88	5.2	odd	4
800.2.y.f.301.1		88	160.13	odd	8
800.2.y.f.301.22		88	160.77	odd	8

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:	\( N \)	\(=\)	\( 160 = 2^{5} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	160.z (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.125510 - 1.40863i) q^{2} +(-1.86499 + 0.772505i) q^{3} +(-1.96849 - 0.353596i) q^{4} +(0.0190434 + 2.23599i) q^{5} +(0.854100 + 2.72405i) q^{6} +(-0.798508 + 0.798508i) q^{7} +(-0.745154 + 2.72851i) q^{8} +(0.760109 - 0.760109i) q^{9} +O(q^{10})\)	\(q+(0.125510 - 1.40863i) q^{2} +(-1.86499 + 0.772505i) q^{3} +(-1.96849 - 0.353596i) q^{4} +(0.0190434 + 2.23599i) q^{5} +(0.854100 + 2.72405i) q^{6} +(-0.798508 + 0.798508i) q^{7} +(-0.745154 + 2.72851i) q^{8} +(0.760109 - 0.760109i) q^{9} +(3.15208 + 0.253815i) q^{10} +(-1.21174 + 2.92539i) q^{11} +(3.94438 - 0.861217i) q^{12} +(-0.175830 - 0.424491i) q^{13} +(1.02458 + 1.22503i) q^{14} +(-1.76283 - 4.15539i) q^{15} +(3.74994 + 1.39210i) q^{16} +3.66556 q^{17} +(-0.975313 - 1.16612i) q^{18} +(-5.39199 + 2.23343i) q^{19} +(0.753150 - 4.40826i) q^{20} +(0.872360 - 2.10606i) q^{21} +(3.96871 + 2.07406i) q^{22} +(-3.04392 - 3.04392i) q^{23} +(-0.718078 - 5.66428i) q^{24} +(-4.99927 + 0.0851615i) q^{25} +(-0.620020 + 0.194402i) q^{26} +(1.48711 - 3.59019i) q^{27} +(1.85421 - 1.28951i) q^{28} +(0.995872 + 2.40425i) q^{29} +(-6.07467 + 1.96163i) q^{30} -2.13401 q^{31} +(2.43162 - 5.10756i) q^{32} -6.39190i q^{33} +(0.460066 - 5.16343i) q^{34} +(-1.80066 - 1.77025i) q^{35} +(-1.76504 + 1.22750i) q^{36} +(-4.33444 + 10.4643i) q^{37} +(2.46934 + 7.87565i) q^{38} +(0.655842 + 0.655842i) q^{39} +(-6.11509 - 1.61420i) q^{40} +(6.79854 - 6.79854i) q^{41} +(-2.85718 - 1.49317i) q^{42} +(9.19158 + 3.80728i) q^{43} +(3.41970 - 5.33015i) q^{44} +(1.71407 + 1.68512i) q^{45} +(-4.66981 + 3.90572i) q^{46} +2.81155 q^{47} +(-8.06901 + 0.300582i) q^{48} +5.72477i q^{49} +(-0.507500 + 7.05283i) q^{50} +(-6.83623 + 2.83166i) q^{51} +(0.196022 + 0.897781i) q^{52} +(-0.347970 - 0.144134i) q^{53} +(-4.87061 - 2.54539i) q^{54} +(-6.56421 - 2.65372i) q^{55} +(-1.58372 - 2.77375i) q^{56} +(8.33067 - 8.33067i) q^{57} +(3.51170 - 1.10106i) q^{58} +(10.0632 + 4.16829i) q^{59} +(2.00078 + 8.80318i) q^{60} +(-5.16229 - 12.4629i) q^{61} +(-0.267840 + 3.00603i) q^{62} +1.21391i q^{63} +(-6.88949 - 4.06632i) q^{64} +(0.945808 - 0.401237i) q^{65} +(-9.00384 - 0.802250i) q^{66} +(7.97969 - 3.30530i) q^{67} +(-7.21563 - 1.29613i) q^{68} +(8.02832 + 3.32544i) q^{69} +(-2.71963 + 2.31429i) q^{70} +(5.88607 + 5.88607i) q^{71} +(1.50756 + 2.64036i) q^{72} +(-4.50108 - 4.50108i) q^{73} +(14.1963 + 7.41901i) q^{74} +(9.25782 - 4.02079i) q^{75} +(11.4038 - 2.48992i) q^{76} +(-1.36837 - 3.30353i) q^{77} +(1.00616 - 0.841526i) q^{78} +5.05155i q^{79} +(-3.04132 + 8.41133i) q^{80} +11.0693i q^{81} +(-8.72336 - 10.4299i) q^{82} +(2.81897 + 6.80560i) q^{83} +(-2.46193 + 3.83731i) q^{84} +(0.0698046 + 8.19614i) q^{85} +(6.51669 - 12.4697i) q^{86} +(-3.71459 - 3.71459i) q^{87} +(-7.07901 - 5.48609i) q^{88} +(7.44423 + 7.44423i) q^{89} +(2.58885 - 2.20299i) q^{90} +(0.479361 + 0.198558i) q^{91} +(4.91562 + 7.06825i) q^{92} +(3.97991 - 1.64853i) q^{93} +(0.352879 - 3.96044i) q^{94} +(-5.09661 - 12.0139i) q^{95} +(-0.589336 + 11.4040i) q^{96} +1.85143i q^{97} +(8.06410 + 0.718518i) q^{98} +(1.30256 + 3.14467i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9}+O(q^{10}) \) 88 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9	\( 88 q - 8 q^{4} - 4 q^{5} - 8 q^{6} - 8 q^{9} - 4 q^{10} - 8 q^{11} - 24 q^{14} - 8 q^{16} - 8 q^{19} - 4 q^{20} - 8 q^{21} - 16 q^{24} - 4 q^{25} + 32 q^{26} - 8 q^{29} - 52 q^{30} - 64 q^{31} - 24 q^{34} + 20 q^{35} + 72 q^{36} - 8 q^{39} - 56 q^{40} - 8 q^{41} - 8 q^{44} - 16 q^{45} - 8 q^{46} - 44 q^{50} - 48 q^{51} + 24 q^{54} + 28 q^{55} - 56 q^{56} + 24 q^{59} + 32 q^{60} + 24 q^{61} + 64 q^{64} - 8 q^{65} - 8 q^{66} - 40 q^{69} + 80 q^{70} - 40 q^{71} + 128 q^{74} + 28 q^{75} - 8 q^{76} + 48 q^{80} + 200 q^{84} - 24 q^{85} + 24 q^{86} - 8 q^{89} + 80 q^{90} - 8 q^{91} + 120 q^{94} - 8 q^{95} - 56 q^{96} - 48 q^{99}+O(q^{100}) \) 88 * q - 8 * q^4 - 4 * q^5 - 8 * q^6 - 8 * q^9 - 4 * q^10 - 8 * q^11 - 24 * q^14 - 8 * q^16 - 8 * q^19 - 4 * q^20 - 8 * q^21 - 16 * q^24 - 4 * q^25 + 32 * q^26 - 8 * q^29 - 52 * q^30 - 64 * q^31 - 24 * q^34 + 20 * q^35 + 72 * q^36 - 8 * q^39 - 56 * q^40 - 8 * q^41 - 8 * q^44 - 16 * q^45 - 8 * q^46 - 44 * q^50 - 48 * q^51 + 24 * q^54 + 28 * q^55 - 56 * q^56 + 24 * q^59 + 32 * q^60 + 24 * q^61 + 64 * q^64 - 8 * q^65 - 8 * q^66 - 40 * q^69 + 80 * q^70 - 40 * q^71 + 128 * q^74 + 28 * q^75 - 8 * q^76 + 48 * q^80 + 200 * q^84 - 24 * q^85 + 24 * q^86 - 8 * q^89 + 80 * q^90 - 8 * q^91 + 120 * q^94 - 8 * q^95 - 56 * q^96 - 48 * q^99

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