LMFDB - Embedded newform 656.2.n.g.493.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [656,2,Mod(165,656)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("656.165"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(656, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 656 = 2^{4} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	656.n (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [80,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$5.23818637260$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			493.15
Character	$\chi$	$=$	656.493
Dual form			656.2.n.g.165.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.508120 + 1.31978i) q^{2} +(-0.665472 - 0.665472i) q^{3} +(-1.48363 - 1.34121i) q^{4} +(-2.95032 + 2.95032i) q^{5} +(1.21641 - 0.540135i) q^{6} -0.781538i q^{7} +(2.52396 - 1.27656i) q^{8} -2.11429i q^{9} +(-2.39465 - 5.39288i) q^{10} +(-0.497263 + 0.497263i) q^{11} +(0.0947744 + 1.87985i) q^{12} +(-2.65132 - 2.65132i) q^{13} +(1.03146 + 0.397115i) q^{14} +3.92671 q^{15} +(0.402305 + 3.97972i) q^{16} +5.16483 q^{17} +(2.79040 + 1.07432i) q^{18} +(-0.814684 - 0.814684i) q^{19} +(8.33417 - 0.420175i) q^{20} +(-0.520092 + 0.520092i) q^{21} +(-0.403607 - 0.908945i) q^{22} +6.09207i q^{23} +(-2.52914 - 0.830109i) q^{24} -12.4087i q^{25} +(4.84634 - 2.15196i) q^{26} +(-3.40342 + 3.40342i) q^{27} +(-1.04821 + 1.15951i) q^{28} +(1.90872 + 1.90872i) q^{29} +(-1.99524 + 5.18238i) q^{30} +10.7974 q^{31} +(-5.45676 - 1.49122i) q^{32} +0.661828 q^{33} +(-2.62435 + 6.81643i) q^{34} +(2.30579 + 2.30579i) q^{35} +(-2.83572 + 3.13683i) q^{36} +(-0.128405 + 0.128405i) q^{37} +(1.48916 - 0.661244i) q^{38} +3.52876i q^{39} +(-3.68022 + 11.2128i) q^{40} +1.00000i q^{41} +(-0.422137 - 0.950675i) q^{42} +(2.14235 - 2.14235i) q^{43} +(1.40469 - 0.0708186i) q^{44} +(6.23784 + 6.23784i) q^{45} +(-8.04017 - 3.09550i) q^{46} +2.63309 q^{47} +(2.38067 - 2.91611i) q^{48} +6.38920 q^{49} +(16.3768 + 6.30513i) q^{50} +(-3.43705 - 3.43705i) q^{51} +(0.377593 + 7.48955i) q^{52} +(9.40074 - 9.40074i) q^{53} +(-2.76241 - 6.22110i) q^{54} -2.93416i q^{55} +(-0.997683 - 1.97257i) q^{56} +1.08430i q^{57} +(-3.48894 + 1.54922i) q^{58} +(4.35411 - 4.35411i) q^{59} +(-5.82577 - 5.26654i) q^{60} +(2.58265 + 2.58265i) q^{61} +(-5.48637 + 14.2502i) q^{62} -1.65240 q^{63} +(4.74077 - 6.44400i) q^{64} +15.6445 q^{65} +(-0.336288 + 0.873467i) q^{66} +(1.97446 + 1.97446i) q^{67} +(-7.66269 - 6.92713i) q^{68} +(4.05410 - 4.05410i) q^{69} +(-4.21474 + 1.87151i) q^{70} +5.20438i q^{71} +(-2.69903 - 5.33640i) q^{72} -9.21315i q^{73} +(-0.104221 - 0.234712i) q^{74} +(-8.25767 + 8.25767i) q^{75} +(0.116025 + 2.30135i) q^{76} +(0.388630 + 0.388630i) q^{77} +(-4.65718 - 1.79303i) q^{78} -13.9264 q^{79} +(-12.9284 - 10.5545i) q^{80} -1.81313 q^{81} +(-1.31978 - 0.508120i) q^{82} +(-10.7817 - 10.7817i) q^{83} +(1.46918 - 0.0740698i) q^{84} +(-15.2379 + 15.2379i) q^{85} +(1.73886 + 3.91600i) q^{86} -2.54039i q^{87} +(-0.620285 + 1.88986i) q^{88} -7.19641i q^{89} +(-11.4021 + 5.06299i) q^{90} +(-2.07211 + 2.07211i) q^{91} +(8.17075 - 9.03836i) q^{92} +(-7.18536 - 7.18536i) q^{93} +(-1.33793 + 3.47510i) q^{94} +4.80715 q^{95} +(2.63896 + 4.62369i) q^{96} +13.2406 q^{97} +(-3.24648 + 8.43232i) q^{98} +(1.05136 + 1.05136i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{4} + 4 q^{10} - 4 q^{11} + 14 q^{12} + 6 q^{14} - 48 q^{15} + 6 q^{16} + 40 q^{18} - 8 q^{19} - 42 q^{20} + 2 q^{22} - 2 q^{24} - 48 q^{26} + 42 q^{28} - 8 q^{29} - 14 q^{30} + 80 q^{31} - 20 q^{32}+ \cdots + 12 q^{99}+O(q^{100}) $ 80 * q - 2 * q^4 + 4 * q^10 - 4 * q^11 + 14 * q^12 + 6 * q^14 - 48 * q^15 + 6 * q^16 + 40 * q^18 - 8 * q^19 - 42 * q^20 + 2 * q^22 - 2 * q^24 - 48 * q^26 + 42 * q^28 - 8 * q^29 - 14 * q^30 + 80 * q^31 - 20 * q^32 + 12 * q^34 - 60 * q^36 - 8 * q^37 + 26 * q^40 - 46 * q^42 + 4 * q^43 + 82 * q^44 - 56 * q^47 + 10 * q^48 - 80 * q^49 + 70 * q^50 - 12 * q^51 - 28 * q^52 + 8 * q^53 + 38 * q^54 + 14 * q^56 - 60 * q^58 + 16 * q^59 + 144 * q^60 + 16 * q^61 - 40 * q^62 + 104 * q^63 - 14 * q^64 + 58 * q^66 + 20 * q^67 - 84 * q^68 - 40 * q^69 + 34 * q^70 + 6 * q^72 - 48 * q^74 - 28 * q^75 + 50 * q^76 + 8 * q^77 - 12 * q^78 - 144 * q^79 - 14 * q^80 - 80 * q^81 + 2 * q^82 - 112 * q^84 - 16 * q^85 + 2 * q^86 - 10 * q^88 - 116 * q^90 - 16 * q^91 + 64 * q^92 + 24 * q^94 + 96 * q^95 - 6 * q^96 + 178 * q^98 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/656\mathbb{Z}\right)^\times$.

$n$	$129$	$165$	$575$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.508120	+	1.31978i	−0.359295	+	0.933224i
$2$	−0.508120	+	1.31978i	−0.359295	+	0.933224i
$3$	−0.665472	−	0.665472i	−0.384210	−	0.384210i	0.488406	−	0.872616i	$-0.337578\pi$
$3$	−0.665472	−	0.665472i	−0.384210	−	0.384210i	−0.872616	+	0.488406i	$0.837578\pi$
$4$	−1.48363	−	1.34121i	−0.741814	−	0.670606i
$5$	−2.95032	+	2.95032i	−1.31942	+	1.31942i	−0.405189	+	0.914233i	$0.632794\pi$
$5$	−2.95032	+	2.95032i	−1.31942	+	1.31942i	−0.914233	+	0.405189i	$0.867206\pi$
$6$	1.21641	−	0.540135i	0.496599	−	0.220509i
$7$		−	0.781538i		−	0.295394i	−0.989033	−	0.147697i	$-0.952814\pi$
$7$		−	0.781538i		−	0.295394i	0.989033	−	0.147697i	$-0.0471860\pi$
$8$	2.52396	−	1.27656i	0.892355	−	0.451333i
$9$		−	2.11429i		−	0.704765i
$10$	−2.39465	−	5.39288i	−0.757254	−	1.70538i
$11$	−0.497263	+	0.497263i	−0.149930	+	0.149930i	−0.778087	−	0.628157i	$-0.783810\pi$
$11$	−0.497263	+	0.497263i	−0.149930	+	0.149930i	0.628157	+	0.778087i	$0.283810\pi$
$12$	0.0947744	+	1.87985i	0.0273590	+	0.542666i
$13$	−2.65132	−	2.65132i	−0.735344	−	0.735344i	0.236329	−	0.971673i	$-0.424056\pi$
$13$	−2.65132	−	2.65132i	−0.735344	−	0.735344i	−0.971673	+	0.236329i	$0.924056\pi$
$14$	1.03146	+	0.397115i	0.275669	+	0.106134i
$15$	3.92671			1.01387
$16$	0.402305	+	3.97972i	0.100576	+	0.994929i
$17$	5.16483			1.25266			0.626328	−	0.779560i	$-0.284557\pi$
$17$	5.16483			1.25266			0.626328	+	0.779560i	$0.284557\pi$
$18$	2.79040	+	1.07432i	0.657704	+	0.253219i
$19$	−0.814684	−	0.814684i	−0.186901	−	0.186901i	0.607454	−	0.794355i	$-0.292191\pi$
$19$	−0.814684	−	0.814684i	−0.186901	−	0.186901i	−0.794355	+	0.607454i	$0.792191\pi$
$20$	8.33417	−	0.420175i	1.86358	−	0.0939539i
$21$	−0.520092	+	0.520092i	−0.113493	+	0.113493i
$22$	−0.403607	−	0.908945i	−0.0860493	−	0.193788i
$23$			6.09207i			1.27028i	0.772396	+	0.635142i	$0.219058\pi$
$23$			6.09207i			1.27028i	−0.772396	+	0.635142i	$0.780942\pi$
$24$	−2.52914	−	0.830109i	−0.516259	−	0.169445i
$25$		−	12.4087i		−	2.48175i
$26$	4.84634	−	2.15196i	0.950446	−	0.422035i
$27$	−3.40342	+	3.40342i	−0.654988	+	0.654988i
$28$	−1.04821	+	1.15951i	−0.198093	+	0.219127i
$29$	1.90872	+	1.90872i	0.354440	+	0.354440i	0.861758	−	0.507319i	$-0.169363\pi$
$29$	1.90872	+	1.90872i	0.354440	+	0.354440i	−0.507319	+	0.861758i	$0.669363\pi$
$30$	−1.99524	+	5.18238i	−0.364279	+	0.946169i
$31$	10.7974			1.93927			0.969635	−	0.244557i	$-0.0786425\pi$
$31$	10.7974			1.93927			0.969635	+	0.244557i	$0.0786425\pi$
$32$	−5.45676	−	1.49122i	−0.964628	−	0.263613i
$33$	0.661828			0.115210
$34$	−2.62435	+	6.81643i	−0.450073	+	1.16901i
$35$	2.30579	+	2.30579i	0.389749	+	0.389749i
$36$	−2.83572	+	3.13683i	−0.472619	+	0.522805i
$37$	−0.128405	+	0.128405i	−0.0211097	+	0.0211097i	−0.717583	−	0.696473i	$-0.754752\pi$
$37$	−0.128405	+	0.128405i	−0.0211097	+	0.0211097i	0.696473	+	0.717583i	$0.254752\pi$
$38$	1.48916	−	0.661244i	0.241573	−	0.107268i
$39$			3.52876i			0.565053i
$40$	−3.68022	+	11.2128i	−0.581894	+	1.77289i
$41$			1.00000i			0.156174i
$41$			1.00000i			0.156174i
$42$	−0.422137	−	0.950675i	−0.0651371	−	0.146692i
$43$	2.14235	−	2.14235i	0.326705	−	0.326705i	−0.524627	−	0.851332i	$-0.675795\pi$
$43$	2.14235	−	2.14235i	0.326705	−	0.326705i	0.851332	+	0.524627i	$0.175795\pi$
$44$	1.40469	−	0.0708186i	0.211765	−	0.0106763i
$45$	6.23784	+	6.23784i	0.929882	+	0.929882i
$46$	−8.04017	−	3.09550i	−1.18546	−	0.456407i
$47$	2.63309			0.384076			0.192038	−	0.981388i	$-0.438490\pi$
$47$	2.63309			0.384076			0.192038	+	0.981388i	$0.438490\pi$
$48$	2.38067	−	2.91611i	0.343620	−	0.420904i
$49$	6.38920			0.912743
$50$	16.3768	+	6.30513i	2.31603	+	0.891680i
$51$	−3.43705	−	3.43705i	−0.481283	−	0.481283i
$52$	0.377593	+	7.48955i	0.0523627	+	1.03861i
$53$	9.40074	−	9.40074i	1.29129	−	1.29129i	0.357303	−	0.933989i	$-0.383697\pi$
$53$	9.40074	−	9.40074i	1.29129	−	1.29129i	0.933989	−	0.357303i	$-0.116303\pi$
$54$	−2.76241	−	6.22110i	−0.375917	−	0.846585i
$55$		−	2.93416i		−	0.395643i
$56$	−0.997683	−	1.97257i	−0.133321	−	0.263596i
$57$			1.08430i			0.143619i
$58$	−3.48894	+	1.54922i	−0.458120	+	0.203423i
$59$	4.35411	−	4.35411i	0.566857	−	0.566857i	−0.364389	−	0.931247i	$-0.618722\pi$
$59$	4.35411	−	4.35411i	0.566857	−	0.566857i	0.931247	+	0.364389i	$0.118722\pi$
$60$	−5.82577	−	5.26654i	−0.752104	−	0.679908i
$61$	2.58265	+	2.58265i	0.330674	+	0.330674i	0.852843	−	0.522168i	$-0.174877\pi$
$61$	2.58265	+	2.58265i	0.330674	+	0.330674i	−0.522168	+	0.852843i	$0.674877\pi$
$62$	−5.48637	+	14.2502i	−0.696770	+	1.80977i
$63$	−1.65240			−0.208183
$64$	4.74077	−	6.44400i	0.592596	−	0.805500i
$65$	15.6445			1.94046
$66$	−0.336288	+	0.873467i	−0.0413942	+	0.107516i
$67$	1.97446	+	1.97446i	0.241218	+	0.241218i	0.817354	−	0.576136i	$-0.195440\pi$
$67$	1.97446	+	1.97446i	0.241218	+	0.241218i	−0.576136	+	0.817354i	$0.695440\pi$
$68$	−7.66269	−	6.92713i	−0.929237	−	0.840038i
$69$	4.05410	−	4.05410i	0.488056	−	0.488056i
$70$	−4.21474	+	1.87151i	−0.503758	+	0.223688i
$71$			5.20438i			0.617646i	0.951120	+	0.308823i	$0.0999351\pi$
$71$			5.20438i			0.617646i	−0.951120	+	0.308823i	$0.900065\pi$
$72$	−2.69903	−	5.33640i	−0.318084	−	0.628901i
$73$		−	9.21315i		−	1.07832i	−0.842204	−	0.539159i	$-0.818742\pi$
$73$		−	9.21315i		−	1.07832i	0.842204	−	0.539159i	$-0.181258\pi$
$74$	−0.104221	−	0.234712i	−0.0121155	−	0.0272847i
$75$	−8.25767	+	8.25767i	−0.953514	+	0.953514i
$76$	0.116025	+	2.30135i	0.0133089	+	0.263983i
$77$	0.388630	+	0.388630i	0.0442885	+	0.0442885i
$78$	−4.65718	−	1.79303i	−0.527321	−	0.203021i
$79$	−13.9264			−1.56684			−0.783422	−	0.621490i	$-0.786528\pi$
$79$	−13.9264			−1.56684			−0.783422	+	0.621490i	$0.786528\pi$
$80$	−12.9284	−	10.5545i	−1.44543	−	1.18003i
$81$	−1.81313			−0.201458
$82$	−1.31978	−	0.508120i	−0.145745	−	0.0561125i
$83$	−10.7817	−	10.7817i	−1.18345	−	1.18345i	−0.978846	−	0.204599i	$-0.934411\pi$
$83$	−10.7817	−	10.7817i	−1.18345	−	1.18345i	−0.204599	−	0.978846i	$-0.565589\pi$
$84$	1.46918	−	0.0740698i	0.160300	−	0.00808168i
$85$	−15.2379	+	15.2379i	−1.65278	+	1.65278i
$86$	1.73886	+	3.91600i	0.187506	+	0.422273i
$87$		−	2.54039i		−	0.272359i
$88$	−0.620285	+	1.88986i	−0.0661226	+	0.201460i
$89$		−	7.19641i		−	0.762818i	−0.924406	−	0.381409i	$-0.875439\pi$
$89$		−	7.19641i		−	0.762818i	0.924406	−	0.381409i	$-0.124561\pi$
$90$	−11.4021	+	5.06299i	−1.20189	+	0.533686i
$91$	−2.07211	+	2.07211i	−0.217216	+	0.217216i
$92$	8.17075	−	9.03836i	0.851859	−	0.942314i
$93$	−7.18536	−	7.18536i	−0.745087	−	0.745087i
$94$	−1.33793	+	3.47510i	−0.137997	+	0.358429i
$95$	4.80715			0.493203
$96$	2.63896	+	4.62369i	0.269337	+	0.471903i
$97$	13.2406			1.34438			0.672191	−	0.740378i	$-0.265353\pi$
$97$	13.2406			1.34438			0.672191	+	0.740378i	$0.265353\pi$
$98$	−3.24648	+	8.43232i	−0.327944	+	0.851793i
$99$	1.05136	+	1.05136i	0.105666	+	0.105666i
$100$	−16.6427	+	18.4100i	−1.66427	+	1.84100i
$101$	4.14691	−	4.14691i	0.412633	−	0.412633i	−0.470022	−	0.882655i	$-0.655754\pi$
$101$	4.14691	−	4.14691i	0.412633	−	0.412633i	0.882655	+	0.470022i	$0.155754\pi$
$102$	6.28258	−	2.78971i	0.622068	−	0.276222i
$103$			7.76734i			0.765339i	0.923885	+	0.382670i	$0.124995\pi$
$103$			7.76734i			0.765339i	−0.923885	+	0.382670i	$0.875005\pi$
$104$	−10.0764	−	3.30725i	−0.988073	−	0.324303i
$105$		−	3.06887i		−	0.299491i
$106$	7.63019	+	17.1836i	0.741109	+	1.66902i
$107$	−0.478770	+	0.478770i	−0.0462844	+	0.0462844i	−0.729870	−	0.683586i	$-0.760420\pi$
$107$	−0.478770	+	0.478770i	−0.0462844	+	0.0462844i	0.683586	+	0.729870i	$0.260420\pi$
$108$	9.61411	−	0.484704i	0.925118	−	0.0466407i
$109$	−3.57967	−	3.57967i	−0.342870	−	0.342870i	0.514575	−	0.857445i	$-0.327950\pi$
$109$	−3.57967	−	3.57967i	−0.342870	−	0.342870i	−0.857445	+	0.514575i	$0.827950\pi$
$110$	3.87245	+	1.49091i	0.369223	+	0.142152i
$111$	0.170900			0.0162212
$112$	3.11030	−	0.314417i	0.293896	−	0.0297096i
$113$	0.583947			0.0549331			0.0274665	−	0.999623i	$-0.491256\pi$
$113$	0.583947			0.0549331			0.0274665	+	0.999623i	$0.491256\pi$
$114$	−1.43103	−	0.550953i	−0.134028	−	0.0516015i
$115$	−17.9735	−	17.9735i	−1.67604	−	1.67604i
$116$	−0.271833	−	5.39181i	−0.0252391	−	0.500617i
$117$	−5.60567	+	5.60567i	−0.518245	+	0.518245i
$118$	3.53405	+	7.95887i	0.325336	+	0.732674i
$119$		−	4.03651i		−	0.370027i
$120$	9.91086	−	5.01269i	0.904733	−	0.457594i
$121$			10.5055i			0.955042i
$122$	−4.72082	+	2.09623i	−0.427403	+	0.189784i
$123$	0.665472	−	0.665472i	0.0600036	−	0.0600036i
$124$	−16.0193	−	14.4816i	−1.43858	−	1.30049i
$125$	21.8582	+	21.8582i	1.95505	+	1.95505i
$126$	0.839619	−	2.18080i	0.0747992	−	0.194282i
$127$	−15.7848			−1.40068			−0.700338	−	0.713811i	$-0.746968\pi$
$127$	−15.7848			−1.40068			−0.700338	+	0.713811i	$0.746968\pi$
$128$	6.09576	+	9.53109i	0.538794	+	0.842437i
$129$	−2.85135			−0.251047
$130$	−7.94927	+	20.6472i	−0.697197	+	1.81088i
$131$	9.92464	+	9.92464i	0.867120	+	0.867120i	0.992153	−	0.125033i	$-0.0399036\pi$
$131$	9.92464	+	9.92464i	0.867120	+	0.867120i	−0.125033	+	0.992153i	$0.539904\pi$
$132$	−0.981907	−	0.887652i	−0.0854640	−	0.0772602i
$133$	−0.636706	+	0.636706i	−0.0552095	+	0.0552095i
$134$	−3.60911	+	1.60259i	−0.311780	+	0.138442i
$135$		−	20.0823i		−	1.72841i
$136$	13.0358	−	6.59323i	1.11781	−	0.565365i
$137$		−	15.5763i		−	1.33077i	−0.746500	−	0.665386i	$-0.768267\pi$
$137$		−	15.5763i		−	1.33077i	0.746500	−	0.665386i	$-0.231733\pi$
$138$	3.29054	+	7.41048i	0.280109	+	0.630822i
$139$	9.77232	−	9.77232i	0.828877	−	0.828877i	−0.158484	−	0.987362i	$-0.550661\pi$
$139$	9.77232	−	9.77232i	0.828877	−	0.828877i	0.987362	+	0.158484i	$0.0506607\pi$
$140$	−0.328383	−	6.51348i	−0.0277534	−	0.550489i
$141$	−1.75225	−	1.75225i	−0.147566	−	0.147566i
$142$	−6.86862	−	2.64445i	−0.576402	−	0.221917i
$143$	2.63680			0.220501
$144$	8.41430	−	0.850591i	0.701191	−	0.0708825i
$145$	−11.2626			−0.935311
$146$	12.1593	+	4.68139i	1.00631	+	0.387434i
$147$	−4.25183	−	4.25183i	−0.350685	−	0.350685i
$148$	0.362725	−	0.0182871i	0.0298158	−	0.00150319i
$149$	0.466427	−	0.466427i	0.0382112	−	0.0382112i	−0.687743	−	0.725954i	$-0.741398\pi$
$149$	0.466427	−	0.466427i	0.0382112	−	0.0382112i	0.725954	+	0.687743i	$0.241398\pi$
$150$	−6.70240	−	15.0942i	−0.547249	−	1.23243i
$151$		−	13.6213i		−	1.10848i	−0.832356	−	0.554241i	$-0.813008\pi$
$151$		−	13.6213i		−	1.10848i	0.832356	−	0.554241i	$-0.186992\pi$
$152$	−3.09623	−	1.01624i	−0.251137	−	0.0824276i
$153$		−	10.9200i		−	0.882828i
$154$	−0.710376	+	0.315434i	−0.0572437	+	0.0254184i
$155$	−31.8558	+	31.8558i	−2.55872	+	2.55872i
$156$	4.73281	−	5.23536i	0.378928	−	0.419164i
$157$	10.0786	+	10.0786i	0.804359	+	0.804359i	0.983774	−	0.179415i	$-0.0574203\pi$
$157$	10.0786	+	10.0786i	0.804359	+	0.804359i	−0.179415	+	0.983774i	$0.557420\pi$
$158$	7.07629	−	18.3798i	0.562959	−	1.46222i
$159$	−12.5119			−0.992255
$160$	20.4988	−	11.6996i	1.62057	−	0.924935i
$161$	4.76118			0.375234
$162$	0.921286	−	2.39292i	0.0723830	−	0.188006i
$163$	−7.73389	−	7.73389i	−0.605765	−	0.605765i	0.336071	−	0.941837i	$-0.390902\pi$
$163$	−7.73389	−	7.73389i	−0.605765	−	0.605765i	−0.941837	+	0.336071i	$0.890902\pi$
$164$	1.34121	−	1.48363i	0.104731	−	0.115852i
$165$	−1.95260	+	1.95260i	−0.152010	+	0.152010i
$166$	19.7078	−	8.75105i	1.52963	−	0.679213i
$167$		−	1.41969i		−	0.109859i	−0.998490	−	0.0549295i	$-0.982507\pi$
$167$		−	1.41969i		−	0.109859i	0.998490	−	0.0549295i	$-0.0174934\pi$
$168$	−0.648762	+	1.97662i	−0.0500531	+	0.152500i
$169$			1.05899i			0.0814611i
$170$	−12.3680	−	27.8533i	−0.948579	−	2.13625i
$171$	−1.72248	+	1.72248i	−0.131721	+	0.131721i
$172$	−6.05180	+	0.305107i	−0.461445	+	0.0232642i
$173$	4.12952	+	4.12952i	0.313961	+	0.313961i	0.846442	−	0.532481i	$-0.178740\pi$
$173$	4.12952	+	4.12952i	0.313961	+	0.313961i	−0.532481	+	0.846442i	$0.678740\pi$
$174$	3.35275	+	1.29082i	0.254172	+	0.0978571i
$175$	−9.69791			−0.733093
$176$	−2.17902	−	1.77891i	−0.164249	−	0.134091i
$177$	−5.79508			−0.435585
$178$	9.49767	+	3.65664i	0.711880	+	0.274077i
$179$	−1.71277	−	1.71277i	−0.128018	−	0.128018i	0.640194	−	0.768213i	$-0.278854\pi$
$179$	−1.71277	−	1.71277i	−0.128018	−	0.128018i	−0.768213	+	0.640194i	$0.778854\pi$
$180$	−0.888373	−	17.6209i	−0.0662154	−	1.31338i
$181$	8.59404	−	8.59404i	0.638790	−	0.638790i	−0.311467	−	0.950257i	$-0.600820\pi$
$181$	8.59404	−	8.59404i	0.638790	−	0.638790i	0.950257	+	0.311467i	$0.100820\pi$
$182$	−1.68184	−	3.78760i	−0.124667	−	0.280756i
$183$		−	3.43736i		−	0.254097i
$184$	7.77691	+	15.3761i	0.573321	+	1.13354i
$185$		−	0.757674i		−	0.0557053i
$186$	13.1341	−	5.83206i	0.963040	−	0.427627i
$187$	−2.56828	+	2.56828i	−0.187811	+	0.187811i
$188$	−3.90653	−	3.53153i	−0.284913	−	0.257563i
$189$	2.65990	+	2.65990i	0.193479	+	0.193479i
$190$	−2.44261	+	6.34437i	−0.177205	+	0.460269i
$191$	8.50146			0.615144			0.307572	−	0.951525i	$-0.400483\pi$
$191$	8.50146			0.615144			0.307572	+	0.951525i	$0.400483\pi$
$192$	−7.44315	+	1.13345i	−0.537163	+	0.0817996i
$193$	−14.0737			−1.01305			−0.506525	−	0.862225i	$-0.669070\pi$
$193$	−14.0737			−1.01305			−0.506525	+	0.862225i	$0.669070\pi$
$194$	−6.72783	+	17.4747i	−0.483030	+	1.25461i
$195$	−10.4110	−	10.4110i	−0.745544	−	0.745544i
$196$	−9.47919	−	8.56926i	−0.677085	−	0.612090i
$197$	−2.02716	+	2.02716i	−0.144429	+	0.144429i	−0.775624	−	0.631195i	$-0.782565\pi$
$197$	−2.02716	+	2.02716i	−0.144429	+	0.144429i	0.631195	+	0.775624i	$0.282565\pi$
$198$	−1.92178	+	0.853344i	−0.136575	+	0.0606445i
$199$		−	10.3610i		−	0.734473i	−0.930128	−	0.367237i	$-0.880304\pi$
$199$		−	10.3610i		−	0.734473i	0.930128	−	0.367237i	$-0.119696\pi$
$200$	−15.8406	−	31.3192i	−1.12010	−	2.21460i
$201$		−	2.62789i		−	0.185357i
$202$	3.36587	+	7.58013i	0.236822	+	0.533336i
$203$	1.49173	−	1.49173i	0.104699	−	0.104699i
$204$	0.489494	+	9.70911i	0.0342714	+	0.679774i
$205$	−2.95032	−	2.95032i	−0.206059	−	0.206059i
$206$	−10.2512	−	3.94674i	−0.714233	−	0.274983i
$207$	12.8804			0.895251
$208$	9.48487	−	11.6181i	0.657657	−	0.805573i
$209$	0.810223			0.0560443
$210$	4.05023	+	1.55935i	0.279492	+	0.107606i
$211$	18.2627	+	18.2627i	1.25726	+	1.25726i	0.952396	+	0.304863i	$0.0986108\pi$
$211$	18.2627	+	18.2627i	1.25726	+	1.25726i	0.304863	+	0.952396i	$0.401389\pi$
$212$	−26.5556	+	1.33882i	−1.82385	+	0.0919508i
$213$	3.46337	−	3.46337i	0.237306	−	0.237306i
$214$	−0.388597	−	0.875142i	−0.0265640	−	0.0598235i
$215$			12.6412i			0.862125i
$216$	−4.24542	+	12.9348i	−0.288864	+	0.880100i
$217$		−	8.43858i		−	0.572848i
$218$	6.54327	−	2.90547i	0.443166	−	0.196783i
$219$	−6.13109	+	6.13109i	−0.414301	+	0.414301i
$220$	−3.93533	+	4.35321i	−0.265320	+	0.293493i
$221$	−13.6936	−	13.6936i	−0.921132	−	0.921132i
$222$	−0.0868379	+	0.225551i	−0.00582818	+	0.0151380i
$223$	5.05448			0.338473			0.169237	−	0.985575i	$-0.445870\pi$
$223$	5.05448			0.338473			0.169237	+	0.985575i	$0.445870\pi$
$224$	−1.16545	+	4.26467i	−0.0778697	+	0.284945i
$225$	−26.2357			−1.74905
$226$	−0.296715	+	0.770680i	−0.0197372	+	0.0512649i
$227$	17.2665	+	17.2665i	1.14602	+	1.14602i	0.987328	+	0.158691i	$0.0507273\pi$
$227$	17.2665	+	17.2665i	1.14602	+	1.14602i	0.158691	+	0.987328i	$0.449273\pi$
$228$	1.45427	−	1.60869i	0.0963115	−	0.106538i
$229$	18.8092	−	18.8092i	1.24295	−	1.24295i	0.284172	−	0.958773i	$-0.408281\pi$
$229$	18.8092	−	18.8092i	1.24295	−	1.24295i	0.958773	−	0.284172i	$-0.0917188\pi$
$230$	32.8538	−	14.5884i	2.16631	−	0.961928i
$231$		−	0.517244i		−	0.0340322i
$232$	7.25412	+	2.38093i	0.476256	+	0.156316i
$233$		−	17.3892i		−	1.13921i	−0.821920	−	0.569603i	$-0.807097\pi$
$233$		−	17.3892i		−	1.13921i	0.821920	−	0.569603i	$-0.192903\pi$
$234$	−4.54989	−	10.2466i	−0.297435	−	0.669841i
$235$	−7.76846	+	7.76846i	−0.506758	+	0.506758i
$236$	−12.2997	+	0.620099i	−0.800640	+	0.0403650i
$237$	9.26763	+	9.26763i	0.601998	+	0.601998i
$238$	5.32730	+	2.05103i	0.345318	+	0.132949i
$239$	19.1104			1.23615			0.618073	−	0.786121i	$-0.287914\pi$
$239$	19.1104			1.23615			0.618073	+	0.786121i	$0.287914\pi$
$240$	1.57973	+	15.6272i	0.101971	+	1.00873i
$241$	12.9537			0.834420			0.417210	−	0.908810i	$-0.363008\pi$
$241$	12.9537			0.834420			0.417210	+	0.908810i	$0.363008\pi$
$242$	−13.8649	−	5.33803i	−0.891268	−	0.343142i
$243$	11.4168	+	11.4168i	0.732391	+	0.732391i
$244$	−0.367813	−	7.29557i	−0.0235468	−	0.467051i
$245$	−18.8502	+	18.8502i	−1.20429	+	1.20429i
$246$	0.540135	+	1.21641i	0.0344378	+	0.0775558i
$247$			4.31997i			0.274873i
$248$	27.2522	−	13.7836i	1.73052	−	0.875257i
$249$			14.3498i			0.909384i
$250$	−39.9545	+	17.7413i	−2.52694	+	1.12206i
$251$	−7.81247	+	7.81247i	−0.493119	+	0.493119i	−0.909287	−	0.416169i	$-0.863373\pi$
$251$	−7.81247	+	7.81247i	−0.493119	+	0.493119i	0.416169	+	0.909287i	$0.363373\pi$
$252$	2.45155	+	2.21622i	0.154433	+	0.139609i
$253$	−3.02936	−	3.02936i	−0.190454	−	0.190454i
$254$	8.02059	−	20.8325i	0.503256	−	1.30715i
$255$	20.2808			1.27003
$256$	−15.6763	+	3.20212i	−0.979769	+	0.200132i
$257$	−11.9532			−0.745620			−0.372810	−	0.927908i	$-0.621606\pi$
$257$	−11.9532			−0.745620			−0.372810	+	0.927908i	$0.621606\pi$
$258$	1.44883	−	3.76315i	0.0902000	−	0.234283i
$259$	0.100354	+	0.100354i	0.00623568	+	0.00623568i
$260$	−23.2106	−	20.9825i	−1.43946	−	1.30128i
$261$	4.03559	−	4.03559i	0.249797	−	0.249797i
$262$	−18.1412	+	8.05542i	−1.12077	+	0.497665i
$263$			19.8681i			1.22512i	0.790423	+	0.612561i	$0.209861\pi$
$263$			19.8681i			1.22512i	−0.790423	+	0.612561i	$0.790139\pi$
$264$	1.67043	−	0.844866i	0.102808	−	0.0519979i
$265$			55.4703i			3.40752i
$266$	−0.516788	−	1.16383i	−0.0316863	−	0.0713593i
$267$	−4.78901	+	4.78901i	−0.293083	+	0.293083i
$268$	−0.281196	−	5.57753i	−0.0171768	−	0.340702i
$269$	8.21676	+	8.21676i	0.500984	+	0.500984i	0.911744	−	0.410759i	$-0.134736\pi$
$269$	8.21676	+	8.21676i	0.500984	+	0.500984i	−0.410759	+	0.911744i	$0.634736\pi$
$270$	26.5042	+	10.2042i	1.61300	+	0.621010i
$271$	1.21193			0.0736194			0.0368097	−	0.999322i	$-0.488280\pi$
$271$	1.21193			0.0736194			0.0368097	+	0.999322i	$0.488280\pi$
$272$	2.07784	+	20.5546i	0.125987	+	1.24630i
$273$	2.75786			0.166913
$274$	20.5572	+	7.91462i	1.24191	+	0.478140i
$275$	6.17040	+	6.17040i	0.372089	+	0.372089i
$276$	−11.4522	+	0.577372i	−0.689340	+	0.0347537i
$277$	−16.4683	+	16.4683i	−0.989485	+	0.989485i	−0.999945	−	0.0104604i	$-0.996670\pi$
$277$	−16.4683	+	16.4683i	−0.989485	+	0.989485i	0.0104604	+	0.999945i	$0.496670\pi$
$278$	7.93178	+	17.8628i	0.475717	+	1.07134i
$279$		−	22.8289i		−	1.36673i
$280$	8.76320	+	2.87624i	0.523701	+	0.171888i
$281$		−	16.5400i		−	0.986696i	−0.869832	−	0.493348i	$-0.835773\pi$
$281$		−	16.5400i		−	0.986696i	0.869832	−	0.493348i	$-0.164227\pi$
$282$	3.20293	−	1.42223i	0.190732	−	0.0846923i
$283$	0.347513	−	0.347513i	0.0206575	−	0.0206575i	−0.696703	−	0.717360i	$-0.745350\pi$
$283$	0.347513	−	0.347513i	0.0206575	−	0.0206575i	0.717360	+	0.696703i	$0.245350\pi$
$284$	6.98017	−	7.72136i	0.414197	−	0.458178i
$285$	−3.19902	−	3.19902i	−0.189494	−	0.189494i
$286$	−1.33981	+	3.48000i	−0.0792248	+	0.205776i
$287$	0.781538			0.0461328
$288$	−3.15288	+	11.5372i	−0.185785	+	0.679836i
$289$	9.67548			0.569146
$290$	5.72277	−	14.8642i	0.336053	−	0.872854i
$291$	−8.81126	−	8.81126i	−0.516525	−	0.516525i
$292$	−12.3568	+	13.6689i	−0.723126	+	0.799911i
$293$	5.85813	−	5.85813i	0.342235	−	0.342235i	−0.514972	−	0.857207i	$-0.672198\pi$
$293$	5.85813	−	5.85813i	0.342235	−	0.342235i	0.857207	+	0.514972i	$0.172198\pi$
$294$	7.77191	−	3.45103i	0.453267	−	0.201268i
$295$			25.6920i			1.49585i
$296$	−0.160173	+	0.488008i	−0.00930986	+	0.0283649i
$297$		−	3.38479i		−	0.196405i
$298$	0.378579	+	0.852580i	0.0219305	+	0.0493887i
$299$	16.1520	−	16.1520i	0.934095	−	0.934095i
$300$	23.3266	−	1.17603i	1.34676	−	0.0678982i
$301$	−1.67433	−	1.67433i	−0.0965067	−	0.0965067i
$302$	17.9770	+	6.92124i	1.03446	+	0.398272i
$303$	−5.51930			−0.317076
$304$	2.91446	−	3.56996i	0.167156	−	0.204751i
$305$	−15.2393			−0.872598
$306$	14.4119	+	5.54866i	0.823876	+	0.317196i
$307$	4.14787	+	4.14787i	0.236731	+	0.236731i	0.815495	−	0.578764i	$-0.196465\pi$
$307$	4.14787	+	4.14787i	0.236731	+	0.236731i	−0.578764	+	0.815495i	$0.696465\pi$
$308$	−0.0553474	−	1.09782i	−0.00315371	−	0.0625539i
$309$	5.16895	−	5.16895i	0.294051	−	0.294051i
$310$	−25.8560	−	58.2291i	−1.46852	−	3.30719i
$311$			30.7362i			1.74289i	0.490496	+	0.871444i	$0.336816\pi$
$311$			30.7362i			1.74289i	−0.490496	+	0.871444i	$0.663184\pi$
$312$	4.50468	+	8.90645i	0.255027	+	0.504228i
$313$			27.6078i			1.56049i	0.625476	+	0.780244i	$0.284905\pi$
$313$			27.6078i			1.56049i	−0.625476	+	0.780244i	$0.715095\pi$
$314$	−18.4226	+	8.18037i	−1.03965	+	0.461645i
$315$	4.87511	−	4.87511i	0.274681	−	0.274681i
$316$	20.6616	+	18.6783i	1.16231	+	1.05073i
$317$	−15.3889	−	15.3889i	−0.864327	−	0.864327i	0.127511	−	0.991837i	$-0.459301\pi$
$317$	−15.3889	−	15.3889i	−0.864327	−	0.864327i	−0.991837	+	0.127511i	$0.959301\pi$
$318$	6.35752	−	16.5129i	0.356512	−	0.925996i
$319$	−1.89827			−0.106282
$320$	5.02505	+	32.9986i	0.280909	+	1.84468i
$321$	0.637215			0.0355659
$322$	−2.41925	+	6.28370i	−0.134820	+	0.350177i
$323$	−4.20770	−	4.20770i	−0.234123	−	0.234123i
$324$	2.69000	+	2.43179i	0.149445	+	0.135099i
$325$	−32.8996	+	32.8996i	−1.82494	+	1.82494i
$326$	14.1368	−	6.27727i	0.782963	−	0.347666i
$327$			4.76434i			0.263468i
$328$	1.27656	+	2.52396i	0.0704864	+	0.139363i
$329$		−	2.05786i		−	0.113454i
$330$	−1.58485	−	3.56916i	−0.0872429	−	0.196476i
$331$	22.7706	−	22.7706i	1.25158	−	1.25158i	0.296574	−	0.955010i	$-0.404156\pi$
$331$	22.7706	−	22.7706i	1.25158	−	1.25158i	0.955010	−	0.296574i	$-0.0958440\pi$
$332$	1.53550	+	30.4566i	0.0842712	+	1.67152i
$333$	0.271487	+	0.271487i	0.0148774	+	0.0148774i
$334$	1.87368	+	0.721373i	0.102523	+	0.0394718i
$335$	−11.6506			−0.636538
$336$	−2.27905	−	1.86058i	−0.124333	−	0.101503i
$337$	−2.69516			−0.146815			−0.0734073	−	0.997302i	$-0.523387\pi$
$337$	−2.69516			−0.146815			−0.0734073	+	0.997302i	$0.523387\pi$
$338$	−1.39764	−	0.538096i	−0.0760214	−	0.0292686i
$339$	−0.388600	−	0.388600i	−0.0211059	−	0.0211059i
$340$	43.0446	−	2.17013i	2.33442	−	0.117692i
$341$	−5.36914	+	5.36914i	−0.290755	+	0.290755i
$342$	−1.39807	−	3.14852i	−0.0755987	−	0.170252i
$343$		−	10.4642i		−	0.565012i
$344$	2.67237	−	8.14206i	0.144084	−	0.438990i
$345$			23.9217i			1.28790i
$346$	−7.54833	+	3.35175i	−0.405801	+	0.180191i
$347$	−21.0538	+	21.0538i	−1.13023	+	1.13023i	−0.140089	+	0.990139i	$0.544739\pi$
$347$	−21.0538	+	21.0538i	−1.13023	+	1.13023i	−0.990139	+	0.140089i	$0.955261\pi$
$348$	−3.40720	+	3.76900i	−0.182645	+	0.202039i
$349$	−4.54203	−	4.54203i	−0.243129	−	0.243129i	0.575014	−	0.818143i	$-0.304997\pi$
$349$	−4.54203	−	4.54203i	−0.243129	−	0.243129i	−0.818143	+	0.575014i	$0.804997\pi$
$350$	4.92770	−	12.7991i	0.263397	−	0.684140i
$351$	18.0471			0.963283
$352$	3.45497	−	1.97192i	0.184151	−	0.105103i
$353$	−0.635620			−0.0338307			−0.0169153	−	0.999857i	$-0.505385\pi$
$353$	−0.635620			−0.0338307			−0.0169153	+	0.999857i	$0.505385\pi$
$354$	2.94460	−	7.64822i	0.156503	−	0.406498i
$355$	−15.3546	−	15.3546i	−0.814936	−	0.814936i
$356$	−9.65191	+	10.6768i	−0.511550	+	0.565869i
$357$	−2.68619	+	2.68619i	−0.142168	+	0.142168i
$358$	3.13077	−	1.39018i	0.165466	−	0.0734735i
$359$			24.8946i			1.31389i	0.753939	+	0.656945i	$0.228151\pi$
$359$			24.8946i			1.31389i	−0.753939	+	0.656945i	$0.771849\pi$
$360$	23.7071	+	7.78108i	1.24947	+	0.410099i
$361$		−	17.6726i		−	0.930136i
$362$	6.97542	+	15.7090i	0.366620	+	0.825648i
$363$	6.99109	−	6.99109i	0.366937	−	0.366937i
$364$	5.85337	−	0.295103i	0.306800	−	0.0154676i
$365$	27.1817	+	27.1817i	1.42276	+	1.42276i
$366$	4.53655	+	1.74659i	0.237129	+	0.0912958i
$367$	−29.3027			−1.52959			−0.764794	−	0.644275i	$-0.777159\pi$
$367$	−29.3027			−1.52959			−0.764794	+	0.644275i	$0.777159\pi$
$368$	−24.2447	+	2.45087i	−1.26384	+	0.127760i
$369$	2.11429			0.110066
$370$	0.999961	+	0.384989i	0.0519855	+	0.0200146i
$371$	−7.34704	−	7.34704i	−0.381439	−	0.381439i
$372$	1.02332	+	20.2975i	0.0530565	+	1.05238i
$373$	−12.4740	+	12.4740i	−0.645879	+	0.645879i	−0.951994	−	0.306116i	$-0.900971\pi$
$373$	−12.4740	+	12.4740i	−0.645879	+	0.645879i	0.306116	+	0.951994i	$0.400971\pi$
$374$	−2.08456	−	4.69455i	−0.107790	−	0.242749i
$375$		−	29.0920i		−	1.50230i
$376$	6.64582	−	3.36131i	0.342732	−	0.173346i
$377$		−	10.1212i		−	0.521270i
$378$	−4.86203	+	2.15893i	−0.250076	+	0.111043i
$379$	−19.0270	+	19.0270i	−0.977350	+	0.977350i	−0.999749	−	0.0223995i	$-0.992869\pi$
$379$	−19.0270	+	19.0270i	−0.977350	+	0.977350i	0.0223995	+	0.999749i	$0.492869\pi$
$380$	−7.13202	−	6.44740i	−0.365865	−	0.330745i
$381$	10.5044	+	10.5044i	0.538154	+	0.538154i
$382$	−4.31976	+	11.2200i	−0.221018	+	0.574067i
$383$	2.95184			0.150832			0.0754160	−	0.997152i	$-0.475972\pi$
$383$	2.95184			0.150832			0.0754160	+	0.997152i	$0.475972\pi$
$384$	2.28611	−	10.3992i	0.116663	−	0.530683i
$385$	−2.29316			−0.116870
$386$	7.15115	−	18.5742i	0.363984	−	0.945403i
$387$	−4.52956	−	4.52956i	−0.230251	−	0.230251i
$388$	−19.6442	−	17.7585i	−0.997281	−	0.901550i
$389$	22.8492	−	22.8492i	1.15850	−	1.15850i	0.173703	−	0.984798i	$-0.444427\pi$
$389$	22.8492	−	22.8492i	1.15850	−	1.15850i	0.984798	−	0.173703i	$-0.0555732\pi$
$390$	19.0302	−	8.45013i	0.963630	−	0.427889i
$391$			31.4645i			1.59123i
$392$	16.1261	−	8.15622i	0.814491	−	0.411951i
$393$		−	13.2091i		−	0.666313i
$394$	−1.64536	−	3.70543i	−0.0828919	−	0.186677i
$395$	41.0873	−	41.0873i	2.06733	−	2.06733i
$396$	−0.149731	−	2.96992i	−0.00752428	−	0.149244i
$397$	−17.9687	−	17.9687i	−0.901822	−	0.901822i	0.0937714	−	0.995594i	$-0.470108\pi$
$397$	−17.9687	−	17.9687i	−0.901822	−	0.901822i	−0.995594	+	0.0937714i	$0.970108\pi$
$398$	13.6742	+	5.26464i	0.685428	+	0.263893i
$399$	0.847420			0.0424241
$400$	49.3833	−	4.99210i	2.46917	−	0.249605i
$401$	−9.33978			−0.466406			−0.233203	−	0.972428i	$-0.574921\pi$
$401$	−9.33978			−0.466406			−0.233203	+	0.972428i	$0.574921\pi$
$402$	3.46824	+	1.33528i	0.172980	+	0.0665980i
$403$	−28.6274	−	28.6274i	−1.42603	−	1.42603i
$404$	−11.7144	+	0.590589i	−0.582811	+	0.0293829i
$405$	5.34930	−	5.34930i	0.265809	−	0.265809i
$406$	1.21078	+	2.72674i	0.0600899	+	0.135326i
$407$		−	0.127702i		−	0.00632998i
$408$	−13.0626	−	4.28737i	−0.646695	−	0.212256i
$409$		−	8.99628i		−	0.444838i	−0.974951	−	0.222419i	$-0.928605\pi$
$409$		−	8.99628i		−	0.444838i	0.974951	−	0.222419i	$-0.0713952\pi$
$410$	5.39288	−	2.39465i	0.266335	−	0.118263i
$411$	−10.3656	+	10.3656i	−0.511296	+	0.511296i
$412$	10.4176	−	11.5238i	0.513241	−	0.567739i
$413$	−3.40291	−	3.40291i	−0.167446	−	0.167446i
$414$	−6.54480	+	16.9993i	−0.321659	+	0.835470i
$415$	63.6189			3.12293
$416$	10.5139	+	18.4213i	0.515487	+	0.903180i
$417$	−13.0064			−0.636926
$418$	−0.411691	+	1.06931i	−0.0201364	+	0.0523019i
$419$	5.09895	+	5.09895i	0.249100	+	0.249100i	0.820601	−	0.571501i	$-0.193639\pi$
$419$	5.09895	+	5.09895i	0.249100	+	0.249100i	−0.571501	+	0.820601i	$0.693639\pi$
$420$	−4.11600	+	4.55306i	−0.200840	+	0.222167i
$421$	21.8730	−	21.8730i	1.06602	−	1.06602i	0.0683634	−	0.997660i	$-0.478222\pi$
$421$	21.8730	−	21.8730i	1.06602	−	1.06602i	0.997660	−	0.0683634i	$-0.0217777\pi$
$422$	−33.3824	+	14.8231i	−1.62503	+	0.721578i
$423$		−	5.56713i		−	0.270683i
$424$	11.7265	−	35.7278i	0.569488	−	1.73509i
$425$		−	64.0891i		−	3.10878i
$426$	2.81107	+	6.33068i	0.136197	+	0.306722i
$427$	2.01844	−	2.01844i	0.0976792	−	0.0976792i
$428$	1.35245	−	0.0681848i	0.0653730	−	0.00329584i
$429$	−1.75472	−	1.75472i	−0.0847186	−	0.0847186i
$430$	−16.6836	−	6.42326i	−0.804555	−	0.309757i
$431$	−0.407184			−0.0196134			−0.00980668	−	0.999952i	$-0.503122\pi$
$431$	−0.407184			−0.0196134			−0.00980668	+	0.999952i	$0.503122\pi$
$432$	−14.9139	−	12.1754i	−0.717543	−	0.585791i
$433$	−15.8088			−0.759724			−0.379862	−	0.925043i	$-0.624028\pi$
$433$	−15.8088			−0.759724			−0.379862	+	0.925043i	$0.624028\pi$
$434$	11.1371	+	4.28781i	0.534596	+	0.205822i
$435$	7.49496	+	7.49496i	0.359356	+	0.359356i
$436$	0.509805	+	10.1120i	0.0244152	+	0.484276i
$437$	4.96311	−	4.96311i	0.237418	−	0.237418i
$438$	−4.97635	−	11.2070i	−0.237779	−	0.535492i
$439$			14.5933i			0.696498i	0.937402	+	0.348249i	$0.113224\pi$
$439$			14.5933i			0.696498i	−0.937402	+	0.348249i	$0.886776\pi$
$440$	−3.74565	−	7.40572i	−0.178567	−	0.353054i
$441$		−	13.5086i		−	0.643269i
$442$	25.0305	−	11.1145i	1.19058	−	0.528665i
$443$	−15.0573	+	15.0573i	−0.715396	+	0.715396i	−0.967659	−	0.252263i	$-0.918825\pi$
$443$	−15.0573	+	15.0573i	−0.715396	+	0.715396i	0.252263	+	0.967659i	$0.418825\pi$
$444$	−0.253553	−	0.229214i	−0.0120331	−	0.0108780i
$445$	21.2317	+	21.2317i	1.00648	+	1.00648i
$446$	−2.56828	+	6.67080i	−0.121612	+	0.315871i
$447$	−0.620788			−0.0293622
$448$	−5.03623	−	3.70509i	−0.237940	−	0.175049i
$449$	5.45868			0.257611			0.128806	−	0.991670i	$-0.458886\pi$
$449$	5.45868			0.257611			0.128806	+	0.991670i	$0.458886\pi$
$450$	13.3309	−	34.6254i	0.628425	−	1.63226i
$451$	−0.497263	−	0.497263i	−0.0234152	−	0.0234152i
$452$	−0.866359	−	0.783196i	−0.0407501	−	0.0368384i
$453$	−9.06457	+	9.06457i	−0.425890	+	0.425890i
$454$	−31.5614	+	14.0145i	−1.48125	+	0.657734i
$455$		−	12.2268i		−	0.573199i
$456$	1.38417	+	2.73673i	0.0648199	+	0.128159i
$457$			23.4134i			1.09523i	0.836729	+	0.547617i	$0.184465\pi$
$457$			23.4134i			1.09523i	−0.836729	+	0.547617i	$0.815535\pi$
$458$	15.2666	+	34.3813i	0.713362	+	1.60653i
$459$	−17.5781	+	17.5781i	−0.820475	+	0.820475i
$460$	2.55973	+	50.7723i	0.119348	+	2.36727i
$461$	−2.08007	−	2.08007i	−0.0968786	−	0.0968786i	0.657006	−	0.753885i	$-0.271822\pi$
$461$	−2.08007	−	2.08007i	−0.0968786	−	0.0968786i	−0.753885	+	0.657006i	$0.771822\pi$
$462$	0.682648	+	0.262822i	0.0317596	+	0.0122276i
$463$	−10.0817			−0.468537			−0.234268	−	0.972172i	$-0.575269\pi$
$463$	−10.0817			−0.468537			−0.234268	+	0.972172i	$0.575269\pi$
$464$	−6.82826	+	8.36403i	−0.316994	+	0.388290i
$465$	42.3982			1.96617
$466$	22.9499	+	8.83581i	1.06313	+	0.409311i
$467$	−17.7583	−	17.7583i	−0.821758	−	0.821758i	0.164602	−	0.986360i	$-0.447366\pi$
$467$	−17.7583	−	17.7583i	−0.821758	−	0.821758i	−0.986360	+	0.164602i	$0.947366\pi$
$468$	15.8351	−	0.798342i	0.731979	−	0.0369034i
$469$	1.54312	−	1.54312i	0.0712544	−	0.0712544i
$470$	−6.30533	−	14.1999i	−0.290843	−	0.654995i
$471$		−	13.4140i		−	0.618086i
$472$	5.43132	−	16.5479i	0.249997	−	0.761680i
$473$			2.13062i			0.0979661i
$474$	−16.9403	+	7.52215i	−0.778093	+	0.345504i
$475$	−10.1092	+	10.1092i	−0.463842	+	0.463842i
$476$	−5.41382	+	5.98868i	−0.248142	+	0.274491i
$477$	−19.8759	−	19.8759i	−0.910057	−	0.910057i
$478$	−9.71035	+	25.2214i	−0.444141	+	1.15360i
$479$	−1.08003			−0.0493477			−0.0246738	−	0.999696i	$-0.507855\pi$
$479$	−1.08003			−0.0493477			−0.0246738	+	0.999696i	$0.507855\pi$
$480$	−21.4271	−	5.85559i	−0.978009	−	0.267270i
$481$	0.680888			0.0310458
$482$	−6.58203	+	17.0960i	−0.299803	+	0.778701i
$483$	−3.16843	−	3.16843i	−0.144169	−	0.144169i
$484$	14.0900	−	15.5862i	0.640456	−	0.708463i
$485$	−39.0641	+	39.0641i	−1.77381	+	1.77381i
$486$	−20.8688	+	9.26657i	−0.946629	+	0.420340i
$487$		−	13.2600i		−	0.600866i	−0.953803	−	0.300433i	$-0.902869\pi$
$487$		−	13.2600i		−	0.600866i	0.953803	−	0.300433i	$-0.0971312\pi$
$488$	9.81543	+	3.22159i	0.444324	+	0.145835i
$489$			10.2934i			0.465482i
$490$	−15.2999	−	34.4562i	−0.691178	−	1.55657i
$491$	−25.0860	+	25.0860i	−1.13212	+	1.13212i	−0.142293	+	0.989825i	$0.545448\pi$
$491$	−25.0860	+	25.0860i	−1.13212	+	1.13212i	−0.989825	+	0.142293i	$0.954552\pi$
$492$	−1.87985	+	0.0947744i	−0.0847502	+	0.00427276i
$493$	9.85819	+	9.85819i	0.443991	+	0.443991i
$494$	−5.70141	−	2.19506i	−0.256518	−	0.0987606i
$495$	−6.20369			−0.278835
$496$	4.34384	+	42.9706i	0.195044	+	1.92944i
$497$	4.06742			0.182449
$498$	−18.9386	−	7.29144i	−0.848659	−	0.326737i
$499$	18.7250	+	18.7250i	0.838245	+	0.838245i	0.988628	−	0.150383i	$-0.0480505\pi$
$499$	18.7250	+	18.7250i	0.838245	+	0.838245i	−0.150383	+	0.988628i	$0.548051\pi$
$500$	−3.11297	−	61.7458i	−0.139216	−	2.76135i
$501$	−0.944764	+	0.944764i	−0.0422089	+	0.0422089i
$502$	−6.34105	−	14.2804i	−0.283015	−	0.637365i
$503$		−	37.5056i		−	1.67229i	−0.548505	−	0.836147i	$-0.684803\pi$
$503$		−	37.5056i		−	1.67229i	0.548505	−	0.836147i	$-0.315197\pi$
$504$	−4.17060	+	2.10940i	−0.185773	+	0.0939600i
$505$			24.4694i			1.08887i
$506$	5.53735	−	2.45880i	0.246165	−	0.109307i
$507$	0.704730	−	0.704730i	0.0312982	−	0.0312982i
$508$	23.4188	+	21.1708i	1.03904	+	0.939302i
$509$	6.84315	+	6.84315i	0.303317	+	0.303317i	0.842310	−	0.538993i	$-0.181195\pi$
$509$	6.84315	+	6.84315i	0.303317	+	0.303317i	−0.538993	+	0.842310i	$0.681195\pi$
$510$	−10.3051	+	26.7661i	−0.456316	+	1.18522i
$511$	−7.20043			−0.318528
$512$	3.73936	−	22.3163i	0.165258	−	0.986250i
$513$	5.54542			0.244836
$514$	6.07366	−	15.7756i	0.267898	−	0.695830i
$515$	−22.9161	−	22.9161i	−1.00981	−	1.00981i
$516$	4.23034	+	3.82426i	0.186230	+	0.168354i
$517$	−1.30934	+	1.30934i	−0.0575846	+	0.0575846i
$518$	−0.183437	+	0.0814530i	−0.00805974	+	0.00357884i
$519$		−	5.49615i		−	0.241254i
$520$	39.4861	−	19.9712i	1.73158	−	0.875793i
$521$			20.3262i			0.890506i	0.895405	+	0.445253i	$0.146886\pi$
$521$			20.3262i			0.890506i	−0.895405	+	0.445253i	$0.853114\pi$
$522$	3.27552	+	7.37664i	0.143365	+	0.322867i
$523$	27.9704	−	27.9704i	1.22306	−	1.22306i	0.256522	−	0.966538i	$-0.417423\pi$
$523$	27.9704	−	27.9704i	1.22306	−	1.22306i	0.966538	−	0.256522i	$-0.0825766\pi$
$524$	−1.41344	−	28.0355i	−0.0617462	−	1.22474i
$525$	6.45369	+	6.45369i	0.281662	+	0.281662i
$526$	−26.2215	−	10.0954i	−1.14331	−	0.440181i
$527$	55.7667			2.42924
$528$	0.266257	+	2.63389i	0.0115873	+	0.114625i
$529$	−14.1133			−0.613620
$530$	−73.2085	−	28.1856i	−3.17998	−	1.22430i
$531$	−9.20588	−	9.20588i	−0.399501	−	0.399501i
$532$	1.79859	−	0.0906777i	0.0779789	−	0.00393138i
$533$	2.65132	−	2.65132i	0.114841	−	0.114841i
$534$	−3.88704	−	8.75382i	−0.168209	−	0.378815i
$535$		−	2.82504i		−	0.122137i
$536$	7.50398	+	2.46294i	0.324123	+	0.106383i
$537$			2.27960i			0.0983720i
$538$	−15.0194	+	6.66920i	−0.647532	+	0.287529i
$539$	−3.17711	+	3.17711i	−0.136848	+	0.136848i
$540$	−26.9346	+	29.7947i	−1.15908	+	1.28216i
$541$	17.3536	+	17.3536i	0.746088	+	0.746088i	0.973742	−	0.227654i	$-0.0731056\pi$
$541$	17.3536	+	17.3536i	0.746088	+	0.746088i	−0.227654	+	0.973742i	$0.573106\pi$
$542$	−0.615805	+	1.59948i	−0.0264511	+	0.0687033i
$543$	−11.4382			−0.490859
$544$	−28.1833	−	7.70191i	−1.20835	−	0.330216i
$545$	21.1223			0.904781
$546$	−1.40132	+	3.63976i	−0.0599711	+	0.155767i
$547$	3.72205	+	3.72205i	0.159143	+	0.159143i	0.782187	−	0.623044i	$-0.214104\pi$
$547$	3.72205	+	3.72205i	0.159143	+	0.159143i	−0.623044	+	0.782187i	$0.714104\pi$
$548$	−20.8911	+	23.1094i	−0.892423	+	0.987185i
$549$	5.46048	−	5.46048i	0.233048	−	0.233048i
$550$	−11.2789	+	5.00826i	−0.480933	+	0.213553i
$551$		−	3.11000i		−	0.132490i
$552$	5.05708	−	15.4077i	0.215243	−	0.655795i
$553$			10.8840i			0.462836i
$554$	−13.3666	−	30.1024i	−0.567894	−	1.27893i
$555$	−0.504211	+	0.504211i	−0.0214025	+	0.0214025i
$556$	−27.6052	+	1.39174i	−1.17072	+	0.0590230i
$557$	−4.10936	−	4.10936i	−0.174119	−	0.174119i	0.614667	−	0.788786i	$-0.289290\pi$
$557$	−4.10936	−	4.10936i	−0.174119	−	0.174119i	−0.788786	+	0.614667i	$0.789290\pi$
$558$	30.1291	+	11.5998i	1.27546	+	0.491059i
$559$	−11.3601			−0.480482
$560$	−8.24875	+	10.1040i	−0.348573	+	0.426972i
$561$	3.41823			0.144318
$562$	21.8292	+	8.40433i	0.920808	+	0.354515i
$563$	−4.74122	−	4.74122i	−0.199819	−	0.199819i	0.600104	−	0.799922i	$-0.295126\pi$
$563$	−4.74122	−	4.74122i	−0.199819	−	0.199819i	−0.799922	+	0.600104i	$0.795126\pi$
$564$	0.249550	+	4.94982i	0.0105079	+	0.208425i
$565$	−1.72283	+	1.72283i	−0.0724799	+	0.0724799i
$566$	0.282062	+	0.635219i	0.0118559	+	0.0267002i
$567$			1.41703i			0.0595096i
$568$	6.64372	+	13.1357i	0.278764	+	0.551160i
$569$		−	9.86330i		−	0.413491i	−0.978395	−	0.206746i	$-0.933713\pi$
$569$		−	9.86330i		−	0.413491i	0.978395	−	0.206746i	$-0.0662872\pi$
$570$	5.84749	−	2.59651i	0.244924	−	0.108756i
$571$	19.1305	−	19.1305i	0.800585	−	0.800585i	−0.182602	−	0.983187i	$-0.558452\pi$
$571$	19.1305	−	19.1305i	0.800585	−	0.800585i	0.983187	+	0.182602i	$0.0584518\pi$
$572$	−3.91204	−	3.53651i	−0.163570	−	0.147869i
$573$	−5.65748	−	5.65748i	−0.236345	−	0.236345i
$574$	−0.397115	+	1.03146i	−0.0165753	+	0.0430522i
$575$	75.5949			3.15253
$576$	−13.6245	−	10.0234i	−0.567688	−	0.417641i
$577$	21.2355			0.884045			0.442023	−	0.897004i	$-0.354261\pi$
$577$	21.2355			0.884045			0.442023	+	0.897004i	$0.354261\pi$
$578$	−4.91630	+	12.7695i	−0.204491	+	0.531140i
$579$	9.36568	+	9.36568i	0.389224	+	0.389224i
$580$	16.7096	+	15.1056i	0.693827	+	0.627225i
$581$	−8.42631	+	8.42631i	−0.349582	+	0.349582i
$582$	16.1061	−	7.15173i	0.667619	−	0.296449i
$583$			9.34927i			0.387207i
$584$	−11.7612	−	23.2536i	−0.486681	−	0.962243i
$585$		−	33.0770i		−	1.36757i
$586$	4.75480	+	10.7081i	0.196419	+	0.442346i
$587$	3.81769	−	3.81769i	0.157573	−	0.157573i	−0.623917	−	0.781490i	$-0.714460\pi$
$587$	3.81769	−	3.81769i	0.157573	−	0.157573i	0.781490	+	0.623917i	$0.214460\pi$
$588$	0.605532	+	12.0107i	0.0249717	+	0.495315i
$589$	−8.79646	−	8.79646i	−0.362452	−	0.362452i
$590$	−33.9078	−	13.0546i	−1.39596	−	0.537451i
$591$	2.69803			0.110982
$592$	−0.562676	−	0.459359i	−0.0231258	−	0.0188796i
$593$	35.2913			1.44924			0.724621	−	0.689148i	$-0.242015\pi$
$593$	35.2913			1.44924			0.724621	+	0.689148i	$0.242015\pi$
$594$	4.46717	+	1.71988i	0.183290	+	0.0705674i
$595$	11.9090	+	11.9090i	0.488221	+	0.488221i
$596$	−1.31758	+	0.0664270i	−0.0539702	+	0.00272096i
$597$	−6.89497	+	6.89497i	−0.282192	+	0.282192i
$598$	13.1099	+	29.5242i	0.536104	+	1.20734i
$599$			18.9714i			0.775150i	0.921838	+	0.387575i	$0.126687\pi$
$599$			18.9714i			0.775150i	−0.921838	+	0.387575i	$0.873313\pi$
$600$	−10.3006	+	31.3835i	−0.420521	+	1.28123i
$601$		−	23.7444i		−	0.968555i	−0.874915	−	0.484277i	$-0.839083\pi$
$601$		−	23.7444i		−	0.968555i	0.874915	−	0.484277i	$-0.160917\pi$
$602$	3.06050	−	1.35898i	0.124737	−	0.0553880i
$603$	4.17459	−	4.17459i	0.170002	−	0.170002i
$604$	−18.2690	+	20.2089i	−0.743355	+	0.822288i
$605$	−30.9944	−	30.9944i	−1.26010	−	1.26010i
$606$	2.80447	−	7.28425i	0.113924	−	0.295903i
$607$	34.1619			1.38659			0.693295	−	0.720654i	$-0.256158\pi$
$607$	34.1619			1.38659			0.693295	+	0.720654i	$0.256158\pi$
$608$	3.23066	+	5.66041i	0.131021	+	0.229560i
$609$	−1.98541			−0.0804530
$610$	7.74338	−	20.1125i	0.313520	−	0.814330i
$611$	−6.98117	−	6.98117i	−0.282428	−	0.282428i
$612$	−14.6460	+	16.2012i	−0.592029	+	0.654894i
$613$	−15.8354	+	15.8354i	−0.639586	+	0.639586i	−0.950453	−	0.310867i	$-0.899381\pi$
$613$	−15.8354	+	15.8354i	−0.639586	+	0.639586i	0.310867	+	0.950453i	$0.399381\pi$
$614$	−7.58188	+	3.36665i	−0.305980	+	0.135867i
$615$			3.92671i			0.158340i
$616$	1.47700	+	0.484776i	0.0595099	+	0.0195322i
$617$		−	13.1474i		−	0.529294i	−0.964345	−	0.264647i	$-0.914745\pi$
$617$		−	13.1474i		−	0.529294i	0.964345	−	0.264647i	$-0.0852554\pi$
$618$	4.19542	+	9.44831i	0.168764	+	0.380067i
$619$	30.7070	−	30.7070i	1.23422	−	1.23422i	0.271892	−	0.962328i	$-0.412351\pi$
$619$	30.7070	−	30.7070i	1.23422	−	1.23422i	0.962328	−	0.271892i	$-0.0876493\pi$
$620$	89.9874	−	4.53679i	3.61398	−	0.182202i
$621$	−20.7338	−	20.7338i	−0.832021	−	0.832021i
$622$	−40.5649	−	15.6177i	−1.62650	−	0.626211i
$623$	−5.62427			−0.225332
$624$	−14.0435	+	1.41964i	−0.562188	+	0.0568309i
$625$	−66.9332			−2.67733
$626$	−36.4362	−	14.0281i	−1.45628	−	0.560676i
$627$	−0.539181	−	0.539181i	−0.0215328	−	0.0215328i
$628$	−1.43536	−	28.4704i	−0.0572771	−	1.13609i
$629$	−0.663193	+	0.663193i	−0.0264432	+	0.0264432i
$630$	3.95692	+	8.91121i	0.157648	+	0.355031i
$631$		−	40.8063i		−	1.62447i	−0.583327	−	0.812237i	$-0.698250\pi$
$631$		−	40.8063i		−	1.62447i	0.583327	−	0.812237i	$-0.301750\pi$
$632$	−35.1497	+	17.7779i	−1.39818	+	0.707169i
$633$		−	24.3067i		−	0.966104i
$634$	28.1293	−	12.4905i	1.11716	−	0.496062i
$635$	46.5702	−	46.5702i	1.84808	−	1.84808i
$636$	18.5629	+	16.7810i	0.736069	+	0.665412i
$637$	−16.9398	−	16.9398i	−0.671180	−	0.671180i
$638$	0.964547	−	2.50529i	0.0381868	−	0.0991853i
$639$	11.0036			0.435295
$640$	−46.1042	−	10.1353i	−1.82243	−	0.400633i
$641$	18.4702			0.729527			0.364764	−	0.931100i	$-0.381150\pi$
$641$	18.4702			0.729527			0.364764	+	0.931100i	$0.381150\pi$
$642$	−0.323782	+	0.840983i	−0.0127787	+	0.0331909i
$643$	−26.1036	−	26.1036i	−1.02943	−	1.02943i	−0.999554	−	0.0298727i	$-0.990490\pi$
$643$	−26.1036	−	26.1036i	−1.02943	−	1.02943i	−0.0298727	−	0.999554i	$-0.509510\pi$
$644$	−7.06382	−	6.38575i	−0.278354	−	0.251634i
$645$	8.41238	−	8.41238i	0.331237	−	0.331237i
$646$	7.69125	−	3.41522i	0.302608	−	0.134370i
$647$			9.36709i			0.368258i	0.982902	+	0.184129i	$0.0589464\pi$
$647$			9.36709i			0.368258i	−0.982902	+	0.184129i	$0.941054\pi$
$648$	−4.57626	+	2.31457i	−0.179773	+	0.0909249i
$649$			4.33027i			0.169978i
$650$	−26.7032	−	60.1370i	−1.04739	−	2.35877i
$651$	−5.61564	+	5.61564i	−0.220094	+	0.220094i
$652$	1.10144	+	21.8470i	0.0431356	+	0.855595i
$653$	15.0265	+	15.0265i	0.588032	+	0.588032i	0.937098	−	0.349066i	$-0.113501\pi$
$653$	15.0265	+	15.0265i	0.588032	+	0.588032i	−0.349066	+	0.937098i	$0.613501\pi$
$654$	−6.28787	−	2.42085i	−0.245875	−	0.0946629i
$655$	−58.5617			−2.28819
$656$	−3.97972	+	0.402305i	−0.155382	+	0.0157074i
$657$	−19.4793			−0.759961
$658$	2.71592	+	1.04564i	0.105878	+	0.0407633i
$659$	14.5192	+	14.5192i	0.565586	+	0.565586i	0.930889	−	0.365303i	$-0.119035\pi$
$659$	14.5192	+	14.5192i	0.565586	+	0.565586i	−0.365303	+	0.930889i	$0.619035\pi$
$660$	5.51579	−	0.278084i	0.214702	−	0.0108244i
$661$	−2.32494	+	2.32494i	−0.0904298	+	0.0904298i	−0.750875	−	0.660445i	$-0.770368\pi$
$661$	−2.32494	+	2.32494i	−0.0904298	+	0.0904298i	0.660445	+	0.750875i	$0.270368\pi$
$662$	18.4819	+	41.6223i	0.718320	+	1.61770i
$663$			18.2254i			0.707817i
$664$	−40.9761	−	13.4491i	−1.59018	−	0.521925i
$665$		−	3.75697i		−	0.145689i
$666$	−0.496251	+	0.220355i	−0.0192293	+	0.00853857i
$667$	−11.6280	+	11.6280i	−0.450239	+	0.450239i
$668$	−1.90410	+	2.10629i	−0.0736720	+	0.0814949i
$669$	−3.36362	−	3.36362i	−0.130045	−	0.130045i
$670$	5.91988	−	15.3762i	0.228705	−	0.594033i
$671$	−2.56851			−0.0991562
$672$	3.61359	−	2.06245i	0.139397	−	0.0795606i
$673$	−18.7756			−0.723747			−0.361874	−	0.932227i	$-0.617863\pi$
$673$	−18.7756			−0.723747			−0.361874	+	0.932227i	$0.617863\pi$
$674$	1.36946	−	3.55701i	0.0527498	−	0.137011i
$675$	42.2322	+	42.2322i	1.62552	+	1.62552i
$676$	1.42033	−	1.57115i	0.0546282	−	0.0604290i
$677$	−17.3451	+	17.3451i	−0.666625	+	0.666625i	−0.956933	−	0.290308i	$-0.906242\pi$
$677$	−17.3451	+	17.3451i	−0.666625	+	0.666625i	0.290308	+	0.956933i	$0.406242\pi$
$678$	0.710321	−	0.315410i	0.0272797	−	0.0121133i
$679$		−	10.3481i		−	0.397122i
$680$	−19.0077	+	57.9120i	−0.728913	+	2.22082i
$681$		−	22.9808i		−	0.880625i
$682$	−4.35791	−	9.81424i	−0.166873	−	0.375807i
$683$	12.2208	−	12.2208i	0.467615	−	0.467615i	−0.433526	−	0.901141i	$-0.642731\pi$
$683$	12.2208	−	12.2208i	0.467615	−	0.467615i	0.901141	+	0.433526i	$0.142731\pi$
$684$	4.86573	−	0.245310i	0.186046	−	0.00937967i
$685$	45.9550	+	45.9550i	1.75585	+	1.75585i
$686$	13.8104	+	5.31706i	0.527283	+	0.203006i
$687$	−25.0340			−0.955105
$688$	9.38783	+	7.66407i	0.357908	+	0.292190i
$689$	−49.8487			−1.89909
$690$	−31.5714	−	12.1551i	−1.20190	−	0.462737i
$691$	0.148909	+	0.148909i	0.00566475	+	0.00566475i	0.709933	−	0.704269i	$-0.248725\pi$
$691$	0.148909	+	0.148909i	0.00566475	+	0.00566475i	−0.704269	+	0.709933i	$0.748725\pi$
$692$	−0.588112	−	11.6652i	−0.0223567	−	0.443445i
$693$	0.821678	−	0.821678i	0.0312130	−	0.0312130i
$694$	−17.0885	−	38.4842i	−0.648671	−	1.46084i
$695$			57.6629i			2.18728i
$696$	−3.24297	−	6.41185i	−0.122925	−	0.243041i
$697$			5.16483i			0.195632i
$698$	8.30237	−	3.68657i	0.314249	−	0.139539i
$699$	−11.5720	+	11.5720i	−0.437695	+	0.437695i
$700$	14.3881	+	13.0069i	0.543819	+	0.491616i
$701$	−9.91692	−	9.91692i	−0.374557	−	0.374557i	0.494577	−	0.869134i	$-0.335323\pi$
$701$	−9.91692	−	9.91692i	−0.374557	−	0.374557i	−0.869134	+	0.494577i	$0.835323\pi$
$702$	−9.17009	+	23.8182i	−0.346103	+	0.898959i
$703$	0.209220			0.00789087
$704$	0.846950	+	5.56177i	0.0319206	+	0.209617i
$705$	10.3394			0.389403
$706$	0.322971	−	0.838878i	0.0121552	−	0.0315716i
$707$	−3.24097	−	3.24097i	−0.121889	−	0.121889i
$708$	8.59774	+	7.77242i	0.323123	+	0.292106i
$709$	8.87875	−	8.87875i	0.333449	−	0.333449i	−0.520446	−	0.853895i	$-0.674234\pi$
$709$	8.87875	−	8.87875i	0.333449	−	0.333449i	0.853895	+	0.520446i	$0.174234\pi$
$710$	28.0666	−	12.4627i	1.05332	−	0.467715i
$711$			29.4445i			1.10426i
$712$	−9.18668	−	18.1635i	−0.344285	−	0.680705i
$713$			65.7785i			2.46342i
$714$	−2.18026	−	4.91007i	−0.0815943	−	0.183755i
$715$	−7.77941	+	7.77941i	−0.290933	+	0.290933i
$716$	0.243927	+	4.83830i	0.00911599	+	0.180816i
$717$	−12.7174	−	12.7174i	−0.474940	−	0.474940i
$718$	−32.8554	−	12.6495i	−1.22615	−	0.472074i
$719$	−23.9693			−0.893903			−0.446951	−	0.894558i	$-0.647490\pi$
$719$	−23.9693			−0.893903			−0.446951	+	0.894558i	$0.647490\pi$
$720$	−22.3153	+	27.3344i	−0.831643	+	1.01869i
$721$	6.07048			0.226076
$722$	23.3239	+	8.97979i	0.868025	+	0.334193i
$723$	−8.62031	−	8.62031i	−0.320593	−	0.320593i
$724$	−24.2768	+	1.22394i	−0.902240	+	0.0454872i
$725$	23.6848	−	23.6848i	0.879630	−	0.879630i
$726$	5.67437	+	12.7790i	0.210596	+	0.474273i
$727$			45.8657i			1.70107i	0.525921	+	0.850533i	$0.323721\pi$
$727$			45.8657i			1.70107i	−0.525921	+	0.850533i	$0.676279\pi$
$728$	−2.58475	+	7.87510i	−0.0957970	+	0.291871i
$729$		−	9.75579i		−	0.361326i
$730$	−49.6854	+	22.0623i	−1.83894	+	0.816561i
$731$	11.0649	−	11.0649i	0.409249	−	0.409249i
$732$	−4.61023	+	5.09977i	−0.170399	+	0.188493i
$733$	−21.2625	−	21.2625i	−0.785348	−	0.785348i	0.195380	−	0.980728i	$-0.437406\pi$
$733$	−21.2625	−	21.2625i	−0.785348	−	0.785348i	−0.980728	+	0.195380i	$0.937406\pi$
$734$	14.8893	−	38.6730i	0.549573	−	1.42745i
$735$	25.0885			0.925403
$736$	9.08462	−	33.2430i	0.334863	−	1.22535i
$737$	−1.96365			−0.0723319
$738$	−1.07432	+	2.79040i	−0.0395461	+	0.102716i
$739$	−11.5895	−	11.5895i	−0.426326	−	0.426326i	0.461049	−	0.887375i	$-0.347473\pi$
$739$	−11.5895	−	11.5895i	−0.426326	−	0.426326i	−0.887375	+	0.461049i	$0.847473\pi$
$740$	−1.01620	+	1.12411i	−0.0373563	+	0.0413230i
$741$	2.87482	−	2.87482i	0.105609	−	0.105609i
$742$	13.4296	−	5.96328i	0.493018	−	0.218919i
$743$		−	47.2376i		−	1.73298i	−0.499194	−	0.866490i	$-0.666371\pi$
$743$		−	47.2376i		−	1.73298i	0.499194	−	0.866490i	$-0.333629\pi$
$744$	−27.3082	−	8.96301i	−1.00117	−	0.328600i
$745$			2.75221i			0.100833i
$746$	−10.1246	−	22.8012i	−0.370688	−	0.834811i
$747$	−22.7957	+	22.7957i	−0.834051	+	0.834051i
$748$	7.25497	−	0.365766i	0.265268	−	0.0133737i
$749$	0.374177	+	0.374177i	0.0136721	+	0.0136721i
$750$	38.3949	+	14.7822i	1.40198	+	0.539770i
$751$	−38.4635			−1.40355			−0.701777	−	0.712396i	$-0.747610\pi$
$751$	−38.4635			−1.40355			−0.701777	+	0.712396i	$0.747610\pi$
$752$	1.05930	+	10.4790i	0.0386289	+	0.382128i
$753$	10.3980			0.378923
$754$	13.3578	+	5.14280i	0.486462	+	0.187290i
$755$	40.1871	+	40.1871i	1.46256	+	1.46256i
$756$	−0.378815	−	7.51380i	−0.0137774	−	0.273274i
$757$	23.9302	−	23.9302i	0.869756	−	0.869756i	−0.122689	−	0.992445i	$-0.539152\pi$
$757$	23.9302	−	23.9302i	0.869756	−	0.869756i	0.992445	+	0.122689i	$0.0391518\pi$
$758$	−15.4434	−	34.7794i	−0.560929	−	1.26324i
$759$			4.03190i			0.146349i
$760$	12.1331	−	6.13663i	0.440113	−	0.222599i
$761$			46.2595i			1.67691i	0.544974	+	0.838453i	$0.316539\pi$
$761$			46.2595i			1.67691i	−0.544974	+	0.838453i	$0.683461\pi$
$762$	−19.2009	+	8.52594i	−0.695575	+	0.308862i
$763$	−2.79765	+	2.79765i	−0.101282	+	0.101282i
$764$	−12.6130	−	11.4023i	−0.456323	−	0.412519i
$765$	32.2174	+	32.2174i	1.16482	+	1.16482i
$766$	−1.49989	+	3.89577i	−0.0541932	+	0.140760i
$767$	−23.0883			−0.833670
$768$	12.5631	+	8.30122i	0.453330	+	0.299544i
$769$	38.0775			1.37311			0.686555	−	0.727078i	$-0.259122\pi$
$769$	38.0775			1.37311			0.686555	+	0.727078i	$0.259122\pi$
$770$	1.16520	−	3.02647i	0.0419910	−	0.109066i
$771$	7.95451	+	7.95451i	0.286475	+	0.286475i
$772$	20.8802	+	18.8759i	0.751495	+	0.679357i
$773$	−15.3045	+	15.3045i	−0.550464	+	0.550464i	−0.926575	−	0.376111i	$-0.877261\pi$
$773$	−15.3045	+	15.3045i	−0.550464	+	0.550464i	0.376111	+	0.926575i	$0.377261\pi$
$774$	8.27958	−	3.67645i	0.297603	−	0.132147i
$775$		−	133.982i		−	4.81278i
$776$	33.4188	−	16.9025i	1.19967	−	0.606764i
$777$		−	0.133565i		−	0.00479163i
$778$	18.5457	+	41.7660i	0.664897	+	1.49738i
$779$	0.814684	−	0.814684i	0.0291891	−	0.0291891i
$780$	1.48269	+	29.4093i	0.0530890	+	1.05302i
$781$	−2.58794	−	2.58794i	−0.0926038	−	0.0926038i
$782$	−41.5261	−	15.9877i	−1.48497	−	0.571720i
$783$	−12.9923			−0.464307
$784$	2.57040	+	25.4272i	0.0918001	+	0.908114i
$785$	−59.4701			−2.12258
$786$	17.4331	+	6.71183i	0.621819	+	0.239403i
$787$	14.8471	+	14.8471i	0.529241	+	0.529241i	0.920346	−	0.391105i	$-0.127907\pi$
$787$	14.8471	+	14.8471i	0.529241	+	0.529241i	−0.391105	+	0.920346i	$0.627907\pi$
$788$	5.72639	−	0.288701i	0.203994	−	0.0102845i
$789$	13.2217	−	13.2217i	0.470705	−	0.470705i
$790$	33.3489	+	75.1035i	1.18650	+	2.67206i
$791$		−	0.456377i		−	0.0162269i
$792$	3.99572	+	1.31146i	0.141982	+	0.0466009i
$793$		−	13.6949i		−	0.486319i
$794$	32.8449	−	14.5844i	1.16562	−	0.517582i
$795$	36.9139	−	36.9139i	1.30920	−	1.30920i
$796$	−13.8963	+	15.3719i	−0.492542	+	0.544843i
$797$	−19.1463	−	19.1463i	−0.678196	−	0.678196i	0.281396	−	0.959592i	$-0.409203\pi$
$797$	−19.1463	−	19.1463i	−0.678196	−	0.678196i	−0.959592	+	0.281396i	$0.909203\pi$
$798$	−0.430591	+	1.11841i	−0.0152428	+	0.0395912i
$799$	13.5995			0.481115
$800$	−18.5042	+	67.7116i	−0.654222	+	2.39397i
$801$	−15.2153			−0.537608
$802$	4.74573	−	12.3264i	0.167577	−	0.435261i
$803$	4.58136	+	4.58136i	0.161673	+	0.161673i
$804$	−3.52456	+	3.89882i	−0.124302	+	0.137501i
$805$	−14.0470	+	14.0470i	−0.495092	+	0.495092i
$806$	52.3279	−	23.2356i	1.84317	−	0.818440i
$807$		−	10.9360i		−	0.384967i
$808$	5.17285	−	15.7604i	0.181980	−	0.554450i
$809$			14.7225i			0.517615i	0.965929	+	0.258808i	$0.0833296\pi$
$809$			14.7225i			0.517615i	−0.965929	+	0.258808i	$0.916670\pi$
$810$	4.34180	+	9.77797i	0.152555	+	0.343563i
$811$	3.97743	−	3.97743i	0.139666	−	0.139666i	−0.633817	−	0.773483i	$-0.718513\pi$
$811$	3.97743	−	3.97743i	0.139666	−	0.139666i	0.773483	+	0.633817i	$0.218513\pi$
$812$	−4.21391	+	0.212448i	−0.147879	+	0.00745546i
$813$	−0.806504	−	0.806504i	−0.0282853	−	0.0282853i
$814$	0.168539	+	0.0648882i	0.00590729	+	0.00227433i
$815$	45.6349			1.59852
$816$	12.2957	−	15.0612i	0.430437	−	0.527248i
$817$	−3.49068			−0.122123
$818$	11.8731	+	4.57119i	0.415133	+	0.159828i
$819$	4.38105	+	4.38105i	0.153086	+	0.153086i
$820$	0.420175	+	8.33417i	0.0146731	+	0.291042i
$821$	−28.3427	+	28.3427i	−0.989167	+	0.989167i	−0.999942	−	0.0107747i	$-0.996570\pi$
$821$	−28.3427	+	28.3427i	−0.989167	+	0.989167i	0.0107747	+	0.999942i	$0.496570\pi$
$822$	−8.41330	−	18.9472i	−0.293448	−	0.660860i
$823$			28.7208i			1.00115i	0.865694	+	0.500573i	$0.166877\pi$
$823$			28.7208i			1.00115i	−0.865694	+	0.500573i	$0.833123\pi$
$824$	9.91551	+	19.6045i	0.345423	+	0.682954i
$825$		−	8.21246i		−	0.285921i
$826$	6.22017	−	2.76200i	0.216427	−	0.0961021i
$827$	−0.724566	+	0.724566i	−0.0251956	+	0.0251956i	−0.719592	−	0.694397i	$-0.755671\pi$
$827$	−0.724566	+	0.724566i	−0.0251956	+	0.0251956i	0.694397	+	0.719592i	$0.255671\pi$
$828$	−19.1098	−	17.2754i	−0.664110	−	0.600361i
$829$	−11.8827	−	11.8827i	−0.412703	−	0.412703i	0.469976	−	0.882679i	$-0.344263\pi$
$829$	−11.8827	−	11.8827i	−0.412703	−	0.412703i	−0.882679	+	0.469976i	$0.844263\pi$
$830$	−32.3260	+	83.9628i	−1.12205	+	2.91439i
$831$	21.9184			0.760341
$832$	−29.6544	+	4.51579i	−1.02808	+	0.156557i
$833$	32.9991			1.14335
$834$	6.60881	−	17.1656i	0.228845	−	0.594395i
$835$	4.18854	+	4.18854i	0.144950	+	0.144950i
$836$	−1.20207	−	1.08668i	−0.0415745	−	0.0375836i
$837$	−36.7481	+	36.7481i	−1.27020	+	1.27020i
$838$	−9.32036	+	4.13860i	−0.321966	+	0.142966i
$839$			22.9832i			0.793468i	0.917934	+	0.396734i	$0.129856\pi$
$839$			22.9832i			0.793468i	−0.917934	+	0.396734i	$0.870144\pi$
$840$	−3.91761	−	7.74572i	−0.135170	−	0.267253i
$841$		−	21.7136i		−	0.748745i
$842$	17.7534	+	39.9816i	0.611822	+	1.37786i
$843$	−11.0069	+	11.0069i	−0.379099	+	0.379099i
$844$	−2.60092	−	51.5893i	−0.0895274	−	1.77578i
$845$	−3.12437	−	3.12437i	−0.107482	−	0.107482i
$846$	7.34738	+	2.82877i	0.252608	+	0.0972552i
$847$	8.21042			0.282113
$848$	41.1943	+	33.6303i	1.41462	+	1.15487i
$849$	−0.462521			−0.0158737
$850$	84.5834	+	32.5649i	2.90118	+	1.11697i
$851$	−0.782255	−	0.782255i	−0.0268153	−	0.0268153i
$852$	−9.78345	+	0.493242i	−0.335176	+	0.0168982i
$853$	−10.2294	+	10.2294i	−0.350247	+	0.350247i	−0.860201	−	0.509954i	$-0.829662\pi$
$853$	−10.2294	+	10.2294i	−0.350247	+	0.350247i	0.509954	+	0.860201i	$0.329662\pi$
$854$	1.63828	+	3.68950i	0.0560609	+	0.126252i
$855$		−	10.1637i		−	0.347592i
$856$	−0.597217	+	1.81958i	−0.0204124	+	0.0621918i
$857$			43.8184i			1.49681i	0.663243	+	0.748404i	$0.269180\pi$
$857$			43.8184i			1.49681i	−0.663243	+	0.748404i	$0.730820\pi$
$858$	3.20745	−	1.42423i	0.109500	−	0.0486225i
$859$	15.9770	−	15.9770i	0.545129	−	0.545129i	−0.379899	−	0.925028i	$-0.624041\pi$
$859$	15.9770	−	15.9770i	0.545129	−	0.545129i	0.925028	+	0.379899i	$0.124041\pi$
$860$	16.9546	−	18.7549i	0.578146	−	0.639536i
$861$	−0.520092	−	0.520092i	−0.0177247	−	0.0177247i
$862$	0.206898	−	0.537392i	0.00704698	−	0.0183037i
$863$	−33.0529			−1.12513			−0.562567	−	0.826752i	$-0.690186\pi$
$863$	−33.0529			−1.12513			−0.562567	+	0.826752i	$0.690186\pi$
$864$	23.6469	−	13.4964i	0.804484	−	0.459157i
$865$	−24.3668			−0.828495
$866$	8.03278	−	20.8641i	0.272965	−	0.708992i
$867$	−6.43876	−	6.43876i	−0.218672	−	0.218672i
$868$	−11.3179	+	12.5197i	−0.384155	+	0.424947i
$869$	6.92508	−	6.92508i	0.234917	−	0.234917i
$870$	−13.7000	+	6.08335i	−0.464474	+	0.206245i
$871$		−	10.4698i		−	0.354757i
$872$	−13.6046	−	4.46527i	−0.460711	−	0.151213i
$873$		−	27.9946i		−	0.947473i
$874$	4.02834	+	9.07205i	0.136261	+	0.306867i
$875$	17.0830	−	17.0830i	0.577510	−	0.577510i
$876$	17.3193	−	0.873171i	0.585167	−	0.0295017i
$877$	−29.3424	−	29.3424i	−0.990821	−	0.990821i	0.00913711	−	0.999958i	$-0.497092\pi$
$877$	−29.3424	−	29.3424i	−0.990821	−	0.990821i	−0.999958	+	0.00913711i	$0.997092\pi$
$878$	−19.2599	−	7.41513i	−0.649989	−	0.250248i
$879$	−7.79684			−0.262981
$880$	11.6771	−	1.18043i	0.393637	−	0.0397922i
$881$	24.2467			0.816891			0.408445	−	0.912783i	$-0.366071\pi$
$881$	24.2467			0.816891			0.408445	+	0.912783i	$0.366071\pi$
$882$	17.8284	+	6.86401i	0.600314	+	0.231123i
$883$	17.1652	+	17.1652i	0.577656	+	0.577656i	0.934257	−	0.356601i	$-0.116064\pi$
$883$	17.1652	+	17.1652i	0.577656	+	0.577656i	−0.356601	+	0.934257i	$0.616064\pi$
$884$	1.95020	+	38.6823i	0.0655924	+	1.30103i
$885$	17.0973	−	17.0973i	0.574720	−	0.574720i
$886$	−12.2214	−	27.5233i	−0.410586	−	0.924663i
$887$		−	5.17050i		−	0.173608i	−0.996225	−	0.0868042i	$-0.972335\pi$
$887$		−	5.17050i		−	0.173608i	0.996225	−	0.0868042i	$-0.0276655\pi$
$888$	0.431346	−	0.218165i	0.0144750	−	0.00732115i
$889$			12.3364i			0.413751i
$890$	−38.8094	+	17.2329i	−1.30089	+	0.577647i
$891$	0.901600	−	0.901600i	0.0302047	−	0.0302047i
$892$	−7.49897	−	6.77913i	−0.251084	−	0.226982i
$893$	−2.14514	−	2.14514i	−0.0717843	−	0.0717843i
$894$	0.315435	−	0.819302i	0.0105497	−	0.0274015i
$895$	10.1064			0.337821
$896$	7.44891	−	4.76407i	0.248851	−	0.159157i
$897$	−21.4974			−0.717778
$898$	−2.77367	+	7.20425i	−0.0925584	+	0.240409i
$899$	20.6092	+	20.6092i	0.687354	+	0.687354i
$900$	38.9241	+	35.1877i	1.29747	+	1.17292i
$901$	48.5532	−	48.5532i	1.61754	−	1.61754i
$902$	0.908945	−	0.403607i	0.0302646	−	0.0134386i
$903$			2.22844i			0.0741578i
$904$	1.47386	−	0.745445i	0.0490198	−	0.0247931i
$905$			50.7103i			1.68567i
$906$	−7.35733	−	16.5691i	−0.244431	−	0.550472i
$907$	20.8166	−	20.8166i	0.691205	−	0.691205i	−0.271292	−	0.962497i	$-0.587451\pi$
$907$	20.8166	−	20.8166i	0.691205	−	0.691205i	0.962497	+	0.271292i	$0.0874508\pi$
$908$	−2.45904	−	48.7751i	−0.0816062	−	1.61866i
$909$	−8.76779	−	8.76779i	−0.290809	−	0.290809i
$910$	16.1366	+	6.21266i	0.534923	+	0.205948i
$911$	−54.1497			−1.79406			−0.897030	−	0.441970i	$-0.854280\pi$
$911$	−54.1497			−1.79406			−0.897030	+	0.441970i	$0.854280\pi$
$912$	−4.31520	+	0.436218i	−0.142891	+	0.0144446i
$913$	10.7227			0.354869
$914$	−30.9005	−	11.8968i	−1.02210	−	0.393512i
$915$	10.1413	+	10.1413i	0.335261	+	0.335261i
$916$	−53.1329	+	2.67874i	−1.75556	+	0.0885082i
$917$	7.75649	−	7.75649i	0.256142	−	0.256142i
$918$	−14.2674	−	32.1309i	−0.470894	−	1.06048i
$919$		−	15.3723i		−	0.507086i	−0.967324	−	0.253543i	$-0.918404\pi$
$919$		−	15.3723i		−	0.507086i	0.967324	−	0.253543i	$-0.0815959\pi$
$920$	−68.3089	−	22.4202i	−2.25208	−	0.739171i
$921$		−	5.52058i		−	0.181909i
$922$	3.80216	−	1.68831i	0.125218	−	0.0556015i
$923$	13.7985	−	13.7985i	0.454182	−	0.454182i
$924$	−0.693734	+	0.767398i	−0.0228222	+	0.0252455i
$925$	1.59335	+	1.59335i	0.0523891	+	0.0523891i
$926$	5.12272	−	13.3056i	0.168343	−	0.437250i
$927$	16.4225			0.539384
$928$	−7.56909	−	13.2617i	−0.248468	−	0.435337i
$929$	−6.29873			−0.206654			−0.103327	−	0.994647i	$-0.532949\pi$
$929$	−6.29873			−0.206654			−0.103327	+	0.994647i	$0.532949\pi$
$930$	−21.5434	+	55.9562i	−0.706435	+	1.83488i
$931$	−5.20517	−	5.20517i	−0.170593	−	0.170593i
$932$	−23.3226	+	25.7991i	−0.763958	+	0.845079i
$933$	20.4540	−	20.4540i	0.669635	−	0.669635i
$934$	32.4604	−	14.4137i	1.06214	−	0.471631i
$935$		−	15.1545i		−	0.495604i
$936$	−6.99251	+	21.3045i	−0.228557	+	0.696359i
$937$			55.9371i			1.82739i	0.406405	+	0.913693i	$0.366782\pi$
$937$			55.9371i			1.82739i	−0.406405	+	0.913693i	$0.633218\pi$
$938$	1.25248	+	2.82066i	0.0408950	+	0.0920977i
$939$	18.3722	−	18.3722i	0.599555	−	0.599555i
$940$	21.9446	−	1.10636i	0.715755	−	0.0360854i
$941$	−26.4956	−	26.4956i	−0.863733	−	0.863733i	0.128037	−	0.991769i	$-0.459132\pi$
$941$	−26.4956	−	26.4956i	−0.863733	−	0.863733i	−0.991769	+	0.128037i	$0.959132\pi$
$942$	17.7035	+	6.81594i	0.576813	+	0.222075i
$943$	−6.09207			−0.198385
$944$	19.0798	+	15.5765i	0.620995	+	0.506971i
$945$	−15.6951			−0.510562
$946$	−2.81195	−	1.08261i	−0.0914243	−	0.0351987i
$947$	2.08109	+	2.08109i	0.0676263	+	0.0676263i	0.740111	−	0.672485i	$-0.234773\pi$
$947$	2.08109	+	2.08109i	0.0676263	+	0.0676263i	−0.672485	+	0.740111i	$0.734773\pi$
$948$	−1.31987	−	26.1796i	−0.0428673	−	0.850273i
$949$	−24.4270	+	24.4270i	−0.792934	+	0.792934i
$950$	−8.20521	−	18.4786i	−0.266212	−	0.599525i
$951$			20.4818i			0.664166i
$952$	−5.15287	−	10.1880i	−0.167005	−	0.330195i
$953$		−	10.3341i		−	0.334754i	−0.985893	−	0.167377i	$-0.946470\pi$
$953$		−	10.3341i		−	0.334754i	0.985893	−	0.167377i	$-0.0535296\pi$
$954$	36.3312	−	16.1325i	1.17627	−	0.522308i
$955$	−25.0820	+	25.0820i	−0.811635	+	0.811635i
$956$	−28.3527	−	25.6310i	−0.916990	−	0.828966i
$957$	1.26324	+	1.26324i	0.0408348	+	0.0408348i
$958$	0.548783	−	1.42540i	0.0177304	−	0.0460524i
$959$	−12.1735			−0.393101
$960$	18.6156	−	25.3037i	0.600816	−	0.816673i
$961$	85.5838			2.76077
$962$	−0.345973	+	0.898621i	−0.0111546	+	0.0289727i
$963$	1.01226	+	1.01226i	0.0326196	+	0.0326196i
$964$	−19.2185	−	17.3736i	−0.618985	−	0.559567i
$965$	41.5220	−	41.5220i	1.33664	−	1.33664i
$966$	5.79157	−	2.57168i	0.186341	−	0.0827426i
$967$		−	11.1837i		−	0.359644i	−0.983699	−	0.179822i	$-0.942448\pi$
$967$		−	11.1837i		−	0.359644i	0.983699	−	0.179822i	$-0.0575522\pi$
$968$	13.4109	+	26.5154i	0.431042	+	0.852237i
$969$			5.60021i			0.179905i
$970$	−31.7067	−	71.4051i	−1.01804	−	2.29268i
$971$	39.8387	−	39.8387i	1.27848	−	1.27848i	0.336969	−	0.941516i	$-0.390598\pi$
$971$	39.8387	−	39.8387i	1.27848	−	1.27848i	0.941516	−	0.336969i	$-0.109402\pi$
$972$	−1.62595	−	32.2507i	−0.0521524	−	1.03444i
$973$	−7.63744	−	7.63744i	−0.244845	−	0.244845i
$974$	17.5002	+	6.73765i	0.560743	+	0.215888i
$975$	43.7874			1.40232
$976$	−9.23921	+	11.3172i	−0.295740	+	0.362256i
$977$	−0.699752			−0.0223870			−0.0111935	−	0.999937i	$-0.503563\pi$
$977$	−0.699752			−0.0223870			−0.0111935	+	0.999937i	$0.503563\pi$
$978$	−13.5850	−	5.23027i	−0.434399	−	0.167246i
$979$	3.57851	+	3.57851i	0.114370	+	0.114370i
$980$	53.2487	−	2.68458i	1.70097	−	0.0857558i
$981$	−7.56847	+	7.56847i	−0.241643	+	0.241643i
$982$	−20.3613	−	45.8547i	−0.649755	−	1.46328i
$983$		−	41.8235i		−	1.33396i	−0.745074	−	0.666981i	$-0.767586\pi$
$983$		−	41.8235i		−	1.33396i	0.745074	−	0.666981i	$-0.232414\pi$
$984$	0.830109	−	2.52914i	0.0264629	−	0.0806261i
$985$		−	11.9615i		−	0.381125i
$986$	−18.0198	+	8.00148i	−0.573866	+	0.254819i
$987$	−1.36945	+	1.36945i	−0.0435900	+	0.0435900i
$988$	5.79400	−	6.40923i	0.184332	−	0.203905i
$989$	13.0513	+	13.0513i	0.415009	+	0.415009i
$990$	3.15222	−	8.18749i	0.100184	−	0.260216i
$991$	−27.3857			−0.869937			−0.434968	−	0.900446i	$-0.643240\pi$
$991$	−27.3857			−0.869937			−0.434968	+	0.900446i	$0.643240\pi$
$992$	−58.9188	−	16.1013i	−1.87067	−	0.511217i
$993$	−30.3063			−0.961743
$994$	−2.06674	+	5.36809i	−0.0655529	+	0.170266i
$995$	30.5683	+	30.5683i	0.969080	+	0.969080i
$996$	19.2462	−	21.2898i	0.609838	−	0.674594i
$997$	34.0443	−	34.0443i	1.07819	−	1.07819i	0.0815215	−	0.996672i	$-0.474022\pi$
$997$	34.0443	−	34.0443i	1.07819	−	1.07819i	0.996672	−	0.0815215i	$-0.0259779\pi$
$998$	−34.2274	+	15.1983i	−1.08345	+	0.481093i
$999$		−	0.874035i		−	0.0276532i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	656.2.n.g.493.15	yes	80
16.5	even	4	inner	656.2.n.g.165.15	✓	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
656.2.n.g.165.15	✓	80	16.5	even	4	inner
656.2.n.g.493.15	yes	80	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 656 = 2^{4} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	656.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.508120 + 1.31978i) q^{2} +(-0.665472 - 0.665472i) q^{3} +(-1.48363 - 1.34121i) q^{4} +(-2.95032 + 2.95032i) q^{5} +(1.21641 - 0.540135i) q^{6} -0.781538i q^{7} +(2.52396 - 1.27656i) q^{8} -2.11429i q^{9} +(-2.39465 - 5.39288i) q^{10} +(-0.497263 + 0.497263i) q^{11} +(0.0947744 + 1.87985i) q^{12} +(-2.65132 - 2.65132i) q^{13} +(1.03146 + 0.397115i) q^{14} +3.92671 q^{15} +(0.402305 + 3.97972i) q^{16} +5.16483 q^{17} +(2.79040 + 1.07432i) q^{18} +(-0.814684 - 0.814684i) q^{19} +(8.33417 - 0.420175i) q^{20} +(-0.520092 + 0.520092i) q^{21} +(-0.403607 - 0.908945i) q^{22} +6.09207i q^{23} +(-2.52914 - 0.830109i) q^{24} -12.4087i q^{25} +(4.84634 - 2.15196i) q^{26} +(-3.40342 + 3.40342i) q^{27} +(-1.04821 + 1.15951i) q^{28} +(1.90872 + 1.90872i) q^{29} +(-1.99524 + 5.18238i) q^{30} +10.7974 q^{31} +(-5.45676 - 1.49122i) q^{32} +0.661828 q^{33} +(-2.62435 + 6.81643i) q^{34} +(2.30579 + 2.30579i) q^{35} +(-2.83572 + 3.13683i) q^{36} +(-0.128405 + 0.128405i) q^{37} +(1.48916 - 0.661244i) q^{38} +3.52876i q^{39} +(-3.68022 + 11.2128i) q^{40} +1.00000i q^{41} +(-0.422137 - 0.950675i) q^{42} +(2.14235 - 2.14235i) q^{43} +(1.40469 - 0.0708186i) q^{44} +(6.23784 + 6.23784i) q^{45} +(-8.04017 - 3.09550i) q^{46} +2.63309 q^{47} +(2.38067 - 2.91611i) q^{48} +6.38920 q^{49} +(16.3768 + 6.30513i) q^{50} +(-3.43705 - 3.43705i) q^{51} +(0.377593 + 7.48955i) q^{52} +(9.40074 - 9.40074i) q^{53} +(-2.76241 - 6.22110i) q^{54} -2.93416i q^{55} +(-0.997683 - 1.97257i) q^{56} +1.08430i q^{57} +(-3.48894 + 1.54922i) q^{58} +(4.35411 - 4.35411i) q^{59} +(-5.82577 - 5.26654i) q^{60} +(2.58265 + 2.58265i) q^{61} +(-5.48637 + 14.2502i) q^{62} -1.65240 q^{63} +(4.74077 - 6.44400i) q^{64} +15.6445 q^{65} +(-0.336288 + 0.873467i) q^{66} +(1.97446 + 1.97446i) q^{67} +(-7.66269 - 6.92713i) q^{68} +(4.05410 - 4.05410i) q^{69} +(-4.21474 + 1.87151i) q^{70} +5.20438i q^{71} +(-2.69903 - 5.33640i) q^{72} -9.21315i q^{73} +(-0.104221 - 0.234712i) q^{74} +(-8.25767 + 8.25767i) q^{75} +(0.116025 + 2.30135i) q^{76} +(0.388630 + 0.388630i) q^{77} +(-4.65718 - 1.79303i) q^{78} -13.9264 q^{79} +(-12.9284 - 10.5545i) q^{80} -1.81313 q^{81} +(-1.31978 - 0.508120i) q^{82} +(-10.7817 - 10.7817i) q^{83} +(1.46918 - 0.0740698i) q^{84} +(-15.2379 + 15.2379i) q^{85} +(1.73886 + 3.91600i) q^{86} -2.54039i q^{87} +(-0.620285 + 1.88986i) q^{88} -7.19641i q^{89} +(-11.4021 + 5.06299i) q^{90} +(-2.07211 + 2.07211i) q^{91} +(8.17075 - 9.03836i) q^{92} +(-7.18536 - 7.18536i) q^{93} +(-1.33793 + 3.47510i) q^{94} +4.80715 q^{95} +(2.63896 + 4.62369i) q^{96} +13.2406 q^{97} +(-3.24648 + 8.43232i) q^{98} +(1.05136 + 1.05136i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{4} + 4 q^{10} - 4 q^{11} + 14 q^{12} + 6 q^{14} - 48 q^{15} + 6 q^{16} + 40 q^{18} - 8 q^{19} - 42 q^{20} + 2 q^{22} - 2 q^{24} - 48 q^{26} + 42 q^{28} - 8 q^{29} - 14 q^{30} + 80 q^{31} - 20 q^{32}+ \cdots + 12 q^{99}+O(q^{100}) \) 80 * q - 2 * q^4 + 4 * q^10 - 4 * q^11 + 14 * q^12 + 6 * q^14 - 48 * q^15 + 6 * q^16 + 40 * q^18 - 8 * q^19 - 42 * q^20 + 2 * q^22 - 2 * q^24 - 48 * q^26 + 42 * q^28 - 8 * q^29 - 14 * q^30 + 80 * q^31 - 20 * q^32 + 12 * q^34 - 60 * q^36 - 8 * q^37 + 26 * q^40 - 46 * q^42 + 4 * q^43 + 82 * q^44 - 56 * q^47 + 10 * q^48 - 80 * q^49 + 70 * q^50 - 12 * q^51 - 28 * q^52 + 8 * q^53 + 38 * q^54 + 14 * q^56 - 60 * q^58 + 16 * q^59 + 144 * q^60 + 16 * q^61 - 40 * q^62 + 104 * q^63 - 14 * q^64 + 58 * q^66 + 20 * q^67 - 84 * q^68 - 40 * q^69 + 34 * q^70 + 6 * q^72 - 48 * q^74 - 28 * q^75 + 50 * q^76 + 8 * q^77 - 12 * q^78 - 144 * q^79 - 14 * q^80 - 80 * q^81 + 2 * q^82 - 112 * q^84 - 16 * q^85 + 2 * q^86 - 10 * q^88 - 116 * q^90 - 16 * q^91 + 64 * q^92 + 24 * q^94 + 96 * q^95 - 6 * q^96 + 178 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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