LMFDB - Embedded newform 484.2.g.f.475.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [484,2,Mod(215,484)] 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("484.215"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(484, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 484 = 2^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	484.g (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,-5,0,-1,4,10,0,-5,10] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$3.86475945783$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} + 13 x^{14} - 25 x^{13} + 35 x^{12} - 30 x^{11} - 2 x^{10} + 60 x^{9} - 116 x^{8} + \cdots + 256 $ x^16 - 5x^15 + 13x^14 - 25x^13 + 35x^12 - 30x^11 - 2x^10 + 60x^9 - 116x^8 + 120x^7 - 8x^6 - 240x^5 + 560x^4 - 800x^3 + 832x^2 - 640*x + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 44)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			475.4
Root			$1.40958 + 0.114404i$ of defining polynomial
Character	$\chi$	$=$	484.475
Dual form			484.2.g.f.215.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.07313 - 0.921084i) q^{2} +(0.435358 + 0.599219i) q^{3} +(0.303207 - 1.97688i) q^{4} +(-0.416683 - 1.28242i) q^{5} +(1.01913 + 0.242037i) q^{6} +(-1.31738 - 0.957131i) q^{7} +(-1.49550 - 2.40073i) q^{8} +(0.757524 - 2.33142i) q^{9} +(-1.62837 - 0.992398i) q^{10} +(1.31659 - 0.678965i) q^{12} +(3.38313 + 1.09925i) q^{13} +(-2.29531 + 0.186292i) q^{14} +(0.587043 - 0.807995i) q^{15} +(-3.81613 - 1.19881i) q^{16} +(0.0665412 - 0.0216205i) q^{17} +(-1.33451 - 3.19966i) q^{18} +(-6.43293 + 4.67380i) q^{19} +(-2.66153 + 0.434895i) q^{20} -1.20609i q^{21} -5.30988i q^{23} +(0.787485 - 1.94131i) q^{24} +(2.57411 - 1.87020i) q^{25} +(4.64303 - 1.93652i) q^{26} +(3.84010 - 1.24772i) q^{27} +(-2.29157 + 2.31409i) q^{28} +(2.31370 - 3.18453i) q^{29} +(-0.114260 - 1.40780i) q^{30} +(3.51309 + 1.14147i) q^{31} +(-5.19940 + 2.22850i) q^{32} +(0.0514928 - 0.0844916i) q^{34} +(-0.678513 + 2.08825i) q^{35} +(-4.37926 - 2.20444i) q^{36} +(5.56491 + 4.04314i) q^{37} +(-2.59840 + 10.9409i) q^{38} +(0.814185 + 2.50580i) q^{39} +(-2.45559 + 2.91819i) q^{40} +(3.40107 + 4.68117i) q^{41} +(-1.11091 - 1.29429i) q^{42} +1.89516 q^{43} -3.30550 q^{45} +(-4.89084 - 5.69818i) q^{46} +(5.76344 + 7.93270i) q^{47} +(-0.943034 - 2.80861i) q^{48} +(-1.34373 - 4.13559i) q^{49} +(1.03974 - 4.37794i) q^{50} +(0.0419247 + 0.0304601i) q^{51} +(3.19887 - 6.35475i) q^{52} +(-1.20135 + 3.69738i) q^{53} +(2.97166 - 4.87602i) q^{54} +(-0.327678 + 4.59405i) q^{56} +(-5.60126 - 1.81996i) q^{57} +(-0.450329 - 5.54852i) q^{58} +(-2.85758 + 3.93312i) q^{59} +(-1.41932 - 1.40551i) q^{60} +(-1.28015 + 0.415944i) q^{61} +(4.82139 - 2.01091i) q^{62} +(-3.22942 + 2.34631i) q^{63} +(-3.52698 + 7.18056i) q^{64} -4.79662i q^{65} +4.91303i q^{67} +(-0.0225655 - 0.138100i) q^{68} +(3.18178 - 2.31170i) q^{69} +(1.19532 + 2.86593i) q^{70} +(6.63416 - 2.15557i) q^{71} +(-6.72998 + 1.66802i) q^{72} +(-5.94967 + 8.18902i) q^{73} +(9.69594 - 0.786941i) q^{74} +(2.24132 + 0.728250i) q^{75} +(7.28904 + 14.1343i) q^{76} +(3.18178 + 1.93911i) q^{78} +(-1.85551 + 5.71067i) q^{79} +(0.0527412 + 5.39340i) q^{80} +(-3.53019 - 2.56484i) q^{81} +(7.96154 + 1.89082i) q^{82} +(-1.11615 - 3.43515i) q^{83} +(-2.38430 - 0.365696i) q^{84} +(-0.0554531 - 0.0763247i) q^{85} +(2.03375 - 1.74560i) q^{86} +2.91552 q^{87} -5.39711 q^{89} +(-3.54723 + 3.04465i) q^{90} +(-3.40474 - 4.68622i) q^{91} +(-10.4970 - 1.60999i) q^{92} +(0.845462 + 2.60206i) q^{93} +(13.4916 + 3.20418i) q^{94} +(8.67425 + 6.30221i) q^{95} +(-3.59896 - 2.14538i) q^{96} +(2.26393 - 6.96767i) q^{97} +(-5.25122 - 3.20032i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 5 q^{2} - q^{4} + 4 q^{5} + 10 q^{6} - 5 q^{8} + 10 q^{9} - 22 q^{12} - 2 q^{14} - 17 q^{16} - 10 q^{17} - 15 q^{18} - 24 q^{20} + 40 q^{24} - 4 q^{25} + 16 q^{26} - 30 q^{28} + 40 q^{29} + 30 q^{30}+ \cdots + 72 q^{97}+O(q^{100}) $ 16 * q - 5 * q^2 - q^4 + 4 * q^5 + 10 * q^6 - 5 * q^8 + 10 * q^9 - 22 * q^12 - 2 * q^14 - 17 * q^16 - 10 * q^17 - 15 * q^18 - 24 * q^20 + 40 * q^24 - 4 * q^25 + 16 * q^26 - 30 * q^28 + 40 * q^29 + 30 * q^30 - 6 * q^34 + 5 * q^36 - 12 * q^37 + 17 * q^38 - 50 * q^41 + 24 * q^42 + 40 * q^45 - 40 * q^46 - q^48 + 16 * q^49 + 25 * q^50 - 20 * q^52 - 12 * q^53 - 12 * q^56 - 50 * q^57 - 48 * q^60 + 20 * q^61 - 30 * q^62 - 37 * q^64 + 35 * q^68 + 4 * q^69 + 22 * q^70 - 10 * q^72 - 30 * q^73 + 60 * q^74 + 4 * q^78 + 32 * q^80 + 16 * q^81 + 46 * q^82 - 10 * q^84 + 60 * q^85 + 46 * q^86 - 36 * q^89 - 40 * q^90 - 54 * q^92 + 2 * q^93 + 60 * q^94 - 55 * q^96 + 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/484\mathbb{Z}\right)^\times$.

$n$	$243$	$365$
$\chi(n)$	$-1$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$	1.07313	−	0.921084i	0.758816	−	0.651305i
$2$	1.07313	−	0.921084i	0.758816	−	0.651305i
$3$	0.435358	+	0.599219i	0.251354	+	0.345959i	0.915985	−	0.401213i	$-0.131411\pi$
$3$	0.435358	+	0.599219i	0.251354	+	0.345959i	−0.664631	+	0.747172i	$0.731411\pi$
$4$	0.303207	−	1.97688i	0.151604	−	0.988441i
$5$	−0.416683	−	1.28242i	−0.186346	−	0.573515i	0.813623	−	0.581393i	$-0.197492\pi$
$5$	−0.416683	−	1.28242i	−0.186346	−	0.573515i	−0.999969	+	0.00787847i	$0.997492\pi$
$6$	1.01913	+	0.242037i	0.416057	+	0.0988113i
$7$	−1.31738	−	0.957131i	−0.497922	−	0.361762i	0.310301	−	0.950638i	$-0.399570\pi$
$7$	−1.31738	−	0.957131i	−0.497922	−	0.361762i	−0.808223	+	0.588877i	$0.799570\pi$
$8$	−1.49550	−	2.40073i	−0.528738	−	0.848785i
$9$	0.757524	−	2.33142i	0.252508	−	0.777140i
$10$	−1.62837	−	0.992398i	−0.514936	−	0.313824i
$11$		0			0
$11$		0			0
$12$	1.31659	−	0.678965i	0.380067	−	0.196000i
$13$	3.38313	+	1.09925i	0.938312	+	0.304876i	0.737957	−	0.674848i	$-0.235791\pi$
$13$	3.38313	+	1.09925i	0.938312	+	0.304876i	0.200354	+	0.979723i	$0.435791\pi$
$14$	−2.29531	+	0.186292i	−0.613449	+	0.0497887i
$15$	0.587043	−	0.807995i	0.151574	−	0.208624i
$16$	−3.81613	−	1.19881i	−0.954033	−	0.299702i
$17$	0.0665412	−	0.0216205i	0.0161386	−	0.00524375i	−0.300937	−	0.953644i	$-0.597299\pi$
$17$	0.0665412	−	0.0216205i	0.0161386	−	0.00524375i	0.317075	+	0.948400i	$0.397299\pi$
$18$	−1.33451	−	3.19966i	−0.314548	−	0.754166i
$19$	−6.43293	+	4.67380i	−1.47582	+	1.07224i	−0.496940	+	0.867785i	$0.665543\pi$
$19$	−6.43293	+	4.67380i	−1.47582	+	1.07224i	−0.978875	+	0.204458i	$0.934457\pi$
$20$	−2.66153	+	0.434895i	−0.595136	+	0.0972455i
$21$		−	1.20609i		−	0.263191i
$22$		0			0
$23$		−	5.30988i		−	1.10719i	−0.832787	−	0.553593i	$-0.813256\pi$
$23$		−	5.30988i		−	1.10719i	0.832787	−	0.553593i	$-0.186744\pi$
$24$	0.787485	−	1.94131i	0.160745	−	0.396267i
$25$	2.57411	−	1.87020i	0.514823	−	0.374041i
$26$	4.64303	−	1.93652i	0.910573	−	0.379782i
$27$	3.84010	−	1.24772i	0.739027	−	0.240125i
$28$	−2.29157	+	2.31409i	−0.433067	+	0.437323i
$29$	2.31370	−	3.18453i	0.429643	−	0.591353i	−0.538228	−	0.842799i	$-0.680906\pi$
$29$	2.31370	−	3.18453i	0.429643	−	0.591353i	0.967871	+	0.251446i	$0.0809062\pi$
$30$	−0.114260	−	1.40780i	−0.0208609	−	0.257028i
$31$	3.51309	+	1.14147i	0.630970	+	0.205015i	0.607005	−	0.794698i	$-0.292371\pi$
$31$	3.51309	+	1.14147i	0.630970	+	0.205015i	0.0239654	+	0.999713i	$0.492371\pi$
$32$	−5.19940	+	2.22850i	−0.919133	+	0.393947i
$33$		0			0
$34$	0.0514928	−	0.0844916i	0.00883095	−	0.0144902i
$35$	−0.678513	+	2.08825i	−0.114690	+	0.352979i
$36$	−4.37926	−	2.20444i	−0.729876	−	0.367407i
$37$	5.56491	+	4.04314i	0.914866	+	0.664689i	0.942241	−	0.334936i	$-0.108715\pi$
$37$	5.56491	+	4.04314i	0.914866	+	0.664689i	−0.0273751	+	0.999625i	$0.508715\pi$
$38$	−2.59840	+	10.9409i	−0.421515	+	1.77484i
$39$	0.814185	+	2.50580i	0.130374	+	0.401250i
$40$	−2.45559	+	2.91819i	−0.388263	+	0.461407i
$41$	3.40107	+	4.68117i	0.531158	+	0.731076i	0.987306	−	0.158827i	$-0.0507713\pi$
$41$	3.40107	+	4.68117i	0.531158	+	0.731076i	−0.456148	+	0.889904i	$0.650771\pi$
$42$	−1.11091	−	1.29429i	−0.171418	−	0.199714i
$43$	1.89516			0.289009			0.144505	−	0.989504i	$-0.453841\pi$
$43$	1.89516			0.289009			0.144505	+	0.989504i	$0.453841\pi$
$44$		0			0
$45$	−3.30550			−0.492755
$46$	−4.89084	−	5.69818i	−0.721116	−	0.840150i
$47$	5.76344	+	7.93270i	0.840685	+	1.15710i	0.985839	+	0.167694i	$0.0536322\pi$
$47$	5.76344	+	7.93270i	0.840685	+	1.15710i	−0.145154	+	0.989409i	$0.546368\pi$
$48$	−0.943034	−	2.80861i	−0.136115	−	0.405388i
$49$	−1.34373	−	4.13559i	−0.191962	−	0.590798i
$50$	1.03974	−	4.37794i	0.147041	−	0.619135i
$51$	0.0419247	+	0.0304601i	0.00587063	+	0.00426526i
$52$	3.19887	−	6.35475i	0.443603	−	0.881246i
$53$	−1.20135	+	3.69738i	−0.165018	+	0.507874i	−0.999038	−	0.0438612i	$-0.986034\pi$
$53$	−1.20135	+	3.69738i	−0.165018	+	0.507874i	0.834019	+	0.551735i	$0.186034\pi$
$54$	2.97166	−	4.87602i	0.404391	−	0.663543i
$55$		0			0
$56$	−0.327678	+	4.59405i	−0.0437878	+	0.613906i
$57$	−5.60126	−	1.81996i	−0.741905	−	0.241059i
$58$	−0.450329	−	5.54852i	−0.0591311	−	0.728556i
$59$	−2.85758	+	3.93312i	−0.372025	+	0.512049i	−0.953450	−	0.301551i	$-0.902496\pi$
$59$	−2.85758	+	3.93312i	−0.372025	+	0.512049i	0.581425	+	0.813600i	$0.302496\pi$
$60$	−1.41932	−	1.40551i	−0.183233	−	0.181450i
$61$	−1.28015	+	0.415944i	−0.163906	+	0.0532562i	−0.389820	−	0.920891i	$-0.627463\pi$
$61$	−1.28015	+	0.415944i	−0.163906	+	0.0532562i	0.225915	+	0.974147i	$0.427463\pi$
$62$	4.82139	−	2.01091i	0.612317	−	0.255386i
$63$	−3.22942	+	2.34631i	−0.406869	+	0.295607i
$64$	−3.52698	+	7.18056i	−0.440873	+	0.897569i
$65$		−	4.79662i		−	0.594948i
$66$		0			0
$67$			4.91303i			0.600223i	0.953904	+	0.300111i	$0.0970238\pi$
$67$			4.91303i			0.600223i	−0.953904	+	0.300111i	$0.902976\pi$
$68$	−0.0225655	−	0.138100i	−0.00273647	−	0.0167470i
$69$	3.18178	−	2.31170i	0.383041	−	0.278296i
$70$	1.19532	+	2.86593i	0.142868	+	0.342544i
$71$	6.63416	−	2.15557i	0.787330	−	0.255819i	0.112363	−	0.993667i	$-0.464158\pi$
$71$	6.63416	−	2.15557i	0.787330	−	0.255819i	0.674967	+	0.737848i	$0.264158\pi$
$72$	−6.72998	+	1.66802i	−0.793135	+	0.196578i
$73$	−5.94967	+	8.18902i	−0.696356	+	0.958452i	0.303628	+	0.952791i	$0.401802\pi$
$73$	−5.94967	+	8.18902i	−0.696356	+	0.958452i	−0.999984	+	0.00566160i	$0.998198\pi$
$74$	9.69594	−	0.786941i	1.12713	−	0.0914801i
$75$	2.24132	+	0.728250i	0.258806	+	0.0840911i
$76$	7.28904	+	14.1343i	0.836110	+	1.62131i
$77$		0			0
$78$	3.18178	+	1.93911i	0.360266	+	0.219561i
$79$	−1.85551	+	5.71067i	−0.208761	+	0.642501i	0.790777	+	0.612105i	$0.209677\pi$
$79$	−1.85551	+	5.71067i	−0.208761	+	0.642501i	−0.999538	+	0.0303963i	$0.990323\pi$
$80$	0.0527412	+	5.39340i	0.00589664	+	0.603000i
$81$	−3.53019	−	2.56484i	−0.392244	−	0.284982i
$82$	7.96154	+	1.89082i	0.879205	+	0.208807i
$83$	−1.11615	−	3.43515i	−0.122513	−	0.377057i	0.870927	−	0.491413i	$-0.163519\pi$
$83$	−1.11615	−	3.43515i	−0.122513	−	0.377057i	−0.993440	+	0.114356i	$0.963519\pi$
$84$	−2.38430	−	0.365696i	−0.260149	−	0.0399007i
$85$	−0.0554531	−	0.0763247i	−0.00601473	−	0.00827857i
$86$	2.03375	−	1.74560i	0.219305	−	0.188233i
$87$	2.91552			0.312576
$88$		0			0
$89$	−5.39711			−0.572093			−0.286046	−	0.958216i	$-0.592341\pi$
$89$	−5.39711			−0.572093			−0.286046	+	0.958216i	$0.592341\pi$
$90$	−3.54723	+	3.04465i	−0.373910	+	0.320934i
$91$	−3.40474	−	4.68622i	−0.356914	−	0.491250i
$92$	−10.4970	−	1.60999i	−1.09439	−	0.167853i
$93$	0.845462	+	2.60206i	0.0876703	+	0.269821i
$94$	13.4916	+	3.20418i	1.39155	+	0.330486i
$95$	8.67425	+	6.30221i	0.889960	+	0.646594i
$96$	−3.59896	−	2.14538i	−0.367318	−	0.218962i
$97$	2.26393	−	6.96767i	0.229867	−	0.707459i	−0.767893	−	0.640578i	$-0.778695\pi$
$97$	2.26393	−	6.96767i	0.229867	−	0.707459i	0.997761	−	0.0668817i	$-0.0213050\pi$
$98$	−5.25122	−	3.20032i	−0.530454	−	0.323281i
$99$		0			0
$100$	−2.91668	−	5.65578i	−0.291668	−	0.565578i
$101$	9.10415	+	2.95812i	0.905897	+	0.294344i	0.724669	−	0.689097i	$-0.241993\pi$
$101$	9.10415	+	2.95812i	0.905897	+	0.294344i	0.181228	+	0.983441i	$0.441993\pi$
$102$	0.0730468	−	0.00592862i	0.00723271	−	0.000587021i
$103$	−6.06681	+	8.35025i	−0.597781	+	0.822775i	−0.995503	−	0.0947311i	$-0.969801\pi$
$103$	−6.06681	+	8.35025i	−0.597781	+	0.822775i	0.397722	+	0.917506i	$0.369801\pi$
$104$	−2.42047	−	9.76589i	−0.237346	−	0.957625i
$105$	−1.54672	+	0.502558i	−0.150944	+	0.0490447i
$106$	2.11639	+	5.07431i	0.205562	+	0.492860i
$107$	8.96161	−	6.51099i	0.866352	−	0.629441i	−0.0632539	−	0.997997i	$-0.520148\pi$
$107$	8.96161	−	6.51099i	0.866352	−	0.629441i	0.929605	+	0.368556i	$0.120148\pi$
$108$	−1.30226	−	7.96974i	−0.125310	−	0.766889i
$109$			8.95933i			0.858149i	0.903269	+	0.429074i	$0.141160\pi$
$109$			8.95933i			0.858149i	−0.903269	+	0.429074i	$0.858840\pi$
$110$		0			0
$111$			5.09482i			0.483579i
$112$	3.87987	+	5.23182i	0.366613	+	0.494361i
$113$	−8.91785	+	6.47920i	−0.838921	+	0.609511i	−0.922069	−	0.387026i	$-0.873502\pi$
$113$	−8.91785	+	6.47920i	−0.838921	+	0.609511i	0.0831484	+	0.996537i	$0.473502\pi$
$114$	−7.68720	+	3.20618i	−0.719972	+	0.300286i
$115$	−6.80948	+	2.21253i	−0.634987	+	0.206320i
$116$	−5.59391	−	5.53948i	−0.519382	−	0.514328i
$117$	5.12561	−	7.05479i	0.473863	−	0.652216i
$118$	0.556188	+	6.85282i	0.0512013	+	0.630853i
$119$	−0.108354	−	0.0352062i	−0.00993275	−	0.00322735i
$120$	−2.81770	−	0.200977i	−0.257219	−	0.0183466i
$121$		0			0
$122$	−0.990640	+	1.62548i	−0.0896883	+	0.147164i
$123$	−1.32436	+	4.07597i	−0.119414	+	0.367518i
$124$	3.32175	−	6.59887i	0.298302	−	0.592596i
$125$	−8.92542	−	6.48470i	−0.798314	−	0.580009i
$126$	−1.30443	+	5.49246i	−0.116208	+	0.489307i
$127$	−3.18051	−	9.78860i	−0.282225	−	0.868598i	−0.987217	−	0.159383i	$-0.949050\pi$
$127$	−3.18051	−	9.78860i	−0.282225	−	0.868598i	0.704992	−	0.709215i	$-0.250950\pi$
$128$	2.82899	+	10.9543i	0.250050	+	0.968233i
$129$	0.825073	+	1.13562i	0.0726436	+	0.0999854i
$130$	−4.41810	−	5.14739i	−0.387493	−	0.451456i
$131$	1.86768			0.163180			0.0815901	−	0.996666i	$-0.474000\pi$
$131$	1.86768			0.163180			0.0815901	+	0.996666i	$0.474000\pi$
$132$		0			0
$133$	12.9480			1.12274
$134$	4.52532	+	5.27231i	0.390928	+	0.455459i
$135$	−3.20021	−	4.40471i	−0.275430	−	0.379097i
$136$	−0.151417	−	0.127414i	−0.0129839	−	0.0109256i
$137$	−0.387654	−	1.19308i	−0.0331195	−	0.101931i	0.933130	−	0.359539i	$-0.117066\pi$
$137$	−0.387654	−	1.19308i	−0.0331195	−	0.101931i	−0.966250	+	0.257607i	$0.917066\pi$
$138$	1.28519	−	5.41144i	0.109402	−	0.460652i
$139$	−5.08964	−	3.69784i	−0.431698	−	0.313647i	0.350630	−	0.936514i	$-0.385968\pi$
$139$	−5.08964	−	3.69784i	−0.431698	−	0.313647i	−0.782327	+	0.622867i	$0.785968\pi$
$140$	3.92249	+	1.97451i	0.331511	+	0.166877i
$141$	−2.24426	+	6.90713i	−0.189001	+	0.581686i
$142$	5.13384	−	8.42382i	0.430822	−	0.706912i
$143$		0			0
$144$	−5.68574	+	7.98888i	−0.473812	+	0.665740i
$145$	−5.04798	−	1.64019i	−0.419212	−	0.136210i
$146$	1.15802	+	14.2680i	0.0958384	+	1.18083i
$147$	1.89312	−	2.60565i	0.156142	−	0.214911i
$148$	9.68014	−	9.77527i	0.795703	−	0.803522i
$149$	16.3160	−	5.30140i	1.33666	−	0.434307i	0.448477	−	0.893795i	$-0.351967\pi$
$149$	16.3160	−	5.30140i	1.33666	−	0.434307i	0.888184	+	0.459487i	$0.151967\pi$
$150$	3.07601	−	1.28294i	0.251155	−	0.104752i
$151$	9.83626	−	7.14646i	0.800464	−	0.581571i	−0.110586	−	0.993867i	$-0.535273\pi$
$151$	9.83626	−	7.14646i	0.800464	−	0.581571i	0.911050	+	0.412295i	$0.135273\pi$
$152$	20.8409	+	8.45407i	1.69042	+	0.685715i
$153$		−	0.171513i		−	0.0138660i
$154$		0			0
$155$		−	4.98089i		−	0.400074i
$156$	5.20054	−	0.849770i	0.416377	−	0.0680361i
$157$	4.28919	−	3.11628i	0.342315	−	0.248706i	−0.403323	−	0.915058i	$-0.632145\pi$
$157$	4.28919	−	3.11628i	0.342315	−	0.248706i	0.745638	+	0.666351i	$0.232145\pi$
$158$	3.26881	+	7.83737i	0.260053	+	0.623507i
$159$	−2.73856	+	0.889811i	−0.217182	+	0.0705666i
$160$	5.02437	+	5.73923i	0.397212	+	0.453726i
$161$	−5.08225	+	6.99512i	−0.400537	+	0.551292i
$162$	−6.15078	+	0.499209i	−0.483251	+	0.0392216i
$163$	−9.56530	−	3.10795i	−0.749212	−	0.243434i	−0.0905700	−	0.995890i	$-0.528869\pi$
$163$	−9.56530	−	3.10795i	−0.749212	−	0.243434i	−0.658642	+	0.752456i	$0.728869\pi$
$164$	10.2854	−	5.30415i	0.803152	−	0.414185i
$165$		0			0
$166$	−4.36183	−	2.65829i	−0.338544	−	0.206323i
$167$	6.76983	−	20.8354i	0.523865	−	1.61229i	−0.242683	−	0.970106i	$-0.578028\pi$
$167$	6.76983	−	20.8354i	0.523865	−	1.61229i	0.766549	−	0.642186i	$-0.221972\pi$
$168$	−2.89550	+	1.80371i	−0.223393	+	0.139159i
$169$	−0.279988	−	0.203423i	−0.0215375	−	0.0156479i
$170$	−0.129810	−	0.0308291i	−0.00995595	−	0.00236449i
$171$	6.02348	+	18.5384i	0.460627	+	1.41766i
$172$	0.574626	−	3.74651i	0.0438148	−	0.285669i
$173$	−6.95480	−	9.57246i	−0.528763	−	0.727780i	0.458178	−	0.888861i	$-0.348502\pi$
$173$	−6.95480	−	9.57246i	−0.528763	−	0.727780i	−0.986941	+	0.161080i	$0.948502\pi$
$174$	3.12872	−	2.68544i	0.237188	−	0.203583i
$175$	−5.18111			−0.391655
$176$		0			0
$177$	−3.60087			−0.270658
$178$	−5.79179	+	4.97120i	−0.434113	+	0.372607i
$179$	0.548801	+	0.755360i	0.0410193	+	0.0564582i	0.829034	−	0.559198i	$-0.188891\pi$
$179$	0.548801	+	0.755360i	0.0410193	+	0.0564582i	−0.788015	+	0.615656i	$0.788891\pi$
$180$	−1.00225	+	6.53459i	−0.0747034	+	0.487060i
$181$	5.82171	+	17.9174i	0.432725	+	1.33179i	0.895400	+	0.445262i	$0.146889\pi$
$181$	5.82171	+	17.9174i	0.432725	+	1.33179i	−0.462676	+	0.886528i	$0.653111\pi$
$182$	−7.97013	−	1.89286i	−0.590785	−	0.140308i
$183$	−0.806564	−	0.586003i	−0.0596229	−	0.0433186i
$184$	−12.7476	+	7.94090i	−0.939763	+	0.585411i
$185$	2.86620	−	8.82125i	0.210727	−	0.648551i
$186$	3.30401	+	2.01361i	0.242262	+	0.147645i
$187$		0			0
$188$	17.4295	−	8.98840i	1.27118	−	0.655547i
$189$	−6.25310	−	2.03175i	−0.454846	−	0.147788i
$190$	15.1135	−	1.22664i	1.09645	−	0.0889896i
$191$	12.0167	−	16.5396i	0.869501	−	1.19676i	−0.109719	−	0.993963i	$-0.534995\pi$
$191$	12.0167	−	16.5396i	0.869501	−	1.19676i	0.979220	−	0.202802i	$-0.0650049\pi$
$192$	−5.83823	+	1.01268i	−0.421338	+	0.0730837i
$193$	−16.4922	+	5.35865i	−1.18714	+	0.385724i	−0.835013	−	0.550230i	$-0.814540\pi$
$193$	−16.4922	+	5.35865i	−1.18714	+	0.385724i	−0.352123	+	0.935954i	$0.614540\pi$
$194$	−3.98832	−	9.56247i	−0.286345	−	0.686545i
$195$	2.87423	−	2.08825i	0.205828	−	0.149543i
$196$	−8.58300	+	1.40246i	−0.613072	+	0.100176i
$197$			3.49133i			0.248747i	0.992235	+	0.124374i	$0.0396921\pi$
$197$			3.49133i			0.248747i	−0.992235	+	0.124374i	$0.960308\pi$
$198$		0			0
$199$			11.2660i			0.798625i	0.916815	+	0.399313i	$0.130751\pi$
$199$			11.2660i			0.798625i	−0.916815	+	0.399313i	$0.869249\pi$
$200$	−8.33942	−	3.38286i	−0.589686	−	0.239205i
$201$	−2.94398	+	2.13893i	−0.207653	+	0.150868i
$202$	12.4946	−	5.21125i	0.879117	−	0.366662i
$203$	−6.09603	+	1.98072i	−0.427857	+	0.139019i
$204$	0.0729278	−	0.0736445i	0.00510597	−	0.00515614i
$205$	4.58605	−	6.31216i	0.320304	−	0.440860i
$206$	1.18082	+	14.5489i	0.0822717	+	1.01367i
$207$	−12.3796	−	4.02236i	−0.860438	−	0.279573i
$208$	−11.5927	−	8.25060i	−0.803808	−	0.572076i
$209$		0			0
$210$	−1.19693	+	1.96397i	−0.0825957	+	0.135526i
$211$	0.847619	−	2.60870i	0.0583525	−	0.179590i	−0.917632	−	0.397432i	$-0.869902\pi$
$211$	0.847619	−	2.60870i	0.0583525	−	0.179590i	0.975984	+	0.217841i	$0.0699015\pi$
$212$	6.94503	+	3.49600i	0.476986	+	0.240106i
$213$	4.17989	+	3.03687i	0.286402	+	0.208083i
$214$	3.61978	−	15.2415i	0.247443	−	1.04189i
$215$	−0.789680	−	2.43039i	−0.0538558	−	0.165751i
$216$	−8.73830	−	7.35306i	−0.594566	−	0.500313i
$217$	−3.53553	−	4.86624i	−0.240008	−	0.330342i
$218$	8.25230	+	9.61451i	0.558916	+	0.651177i
$219$	−7.49726			−0.506618
$220$		0			0
$221$	0.248884			0.0167417
$222$	4.69276	+	5.46739i	0.314957	+	0.366947i
$223$	−13.9457	−	19.1946i	−0.933871	−	1.28536i	−0.958330	−	0.285662i	$-0.907787\pi$
$223$	−13.9457	−	19.1946i	−0.933871	−	1.28536i	0.0244597	−	0.999701i	$-0.492213\pi$
$224$	8.98255	+	2.04073i	0.600172	+	0.136352i
$225$	−2.41027	−	7.41806i	−0.160685	−	0.494538i
$226$	−3.60211	+	15.1671i	−0.239608	+	1.00890i
$227$	−0.647893	−	0.470721i	−0.0430021	−	0.0312429i	0.566077	−	0.824353i	$-0.308461\pi$
$227$	−0.647893	−	0.470721i	−0.0430021	−	0.0312429i	−0.609079	+	0.793110i	$0.708461\pi$
$228$	−5.29619	+	10.5212i	−0.350749	+	0.696784i
$229$	−7.28939	+	22.4344i	−0.481696	+	1.48251i	0.355013	+	0.934861i	$0.384476\pi$
$229$	−7.28939	+	22.4344i	−0.481696	+	1.48251i	−0.836709	+	0.547647i	$0.815524\pi$
$230$	−5.26951	+	8.64644i	−0.347461	+	0.570129i
$231$		0			0
$232$	−11.1053	−	0.792103i	−0.729100	−	0.0520041i
$233$	−16.6354	−	5.40517i	−1.08982	−	0.354105i	−0.291644	−	0.956527i	$-0.594202\pi$
$233$	−16.6354	−	5.40517i	−1.08982	−	0.354105i	−0.798178	+	0.602422i	$0.794202\pi$
$234$	−0.997627	−	12.2918i	−0.0652169	−	0.803541i
$235$	7.77151	−	10.6966i	0.506957	−	0.697767i
$236$	6.90888	+	6.84165i	0.449730	+	0.445354i
$237$	−4.22976	+	1.37433i	−0.274752	+	0.0892724i
$238$	−0.148705	+	0.0620220i	−0.00963912	+	0.00402029i
$239$	5.40825	−	3.92933i	0.349831	−	0.254167i	−0.398967	−	0.916965i	$-0.630631\pi$
$239$	5.40825	−	3.92933i	0.349831	−	0.254167i	0.748798	+	0.662798i	$0.230631\pi$
$240$	−3.20887	+	2.37966i	−0.207131	+	0.153607i
$241$		−	4.28655i		−	0.276121i	−0.990424	−	0.138061i	$-0.955913\pi$
$241$		−	4.28655i		−	0.276121i	0.990424	−	0.138061i	$-0.0440868\pi$
$242$		0			0
$243$		−	15.3451i		−	0.984391i
$244$	0.434124	+	2.65681i	0.0277920	+	0.170085i
$245$	−4.74364	+	3.44646i	−0.303060	+	0.220186i
$246$	2.33310	+	5.59389i	0.148753	+	0.356654i
$247$	−26.9011	+	8.74070i	−1.71168	+	0.556157i
$248$	−2.51345	−	10.1410i	−0.159604	−	0.643957i
$249$	1.57248	−	2.16434i	0.0996521	−	0.137159i
$250$	−15.5511	+	1.26216i	−0.983536	+	0.0798257i
$251$	4.65797	+	1.51346i	0.294008	+	0.0955291i	0.452307	−	0.891862i	$-0.350601\pi$
$251$	4.65797	+	1.51346i	0.294008	+	0.0955291i	−0.158299	+	0.987391i	$0.550601\pi$
$252$	3.65920	+	7.09560i	0.230508	+	0.446981i
$253$		0			0
$254$	−12.4292	−	7.57491i	−0.779879	−	0.475292i
$255$	0.0215932	−	0.0664571i	0.00135222	−	0.00416171i
$256$	13.1257	+	9.14963i	0.820357	+	0.571852i
$257$	10.0191	+	7.27931i	0.624975	+	0.454071i	0.854656	−	0.519195i	$-0.173768\pi$
$257$	10.0191	+	7.27931i	0.624975	+	0.454071i	−0.229681	+	0.973266i	$0.573768\pi$
$258$	1.93141	+	0.458699i	0.120244	+	0.0285574i
$259$	−3.46127	−	10.6527i	−0.215073	−	0.661927i
$260$	−9.48236	−	1.45437i	−0.588071	−	0.0901962i
$261$	−5.67180	−	7.80656i	−0.351075	−	0.483214i
$262$	2.00426	−	1.72029i	0.123824	−	0.106280i
$263$	−16.9489			−1.04511			−0.522556	−	0.852605i	$-0.675021\pi$
$263$	−16.9489			−1.04511			−0.522556	+	0.852605i	$0.675021\pi$
$264$		0			0
$265$	5.24217			0.322024
$266$	13.8949	−	11.9262i	0.851951	−	0.731245i
$267$	−2.34968	−	3.23405i	−0.143798	−	0.197921i
$268$	9.71249	+	1.48967i	0.593285	+	0.0909959i
$269$	1.22209	+	3.76120i	0.0745120	+	0.229324i	0.981375	−	0.192101i	$-0.0615300\pi$
$269$	1.22209	+	3.76120i	0.0745120	+	0.229324i	−0.906863	+	0.421425i	$0.861530\pi$
$270$	−7.49134	−	1.77915i	−0.455908	−	0.108276i
$271$	−19.2040	−	13.9525i	−1.16656	−	0.847556i	−0.175968	−	0.984396i	$-0.556305\pi$
$271$	−19.2040	−	13.9525i	−1.16656	−	0.847556i	−0.990593	+	0.136840i	$0.956305\pi$
$272$	−0.279849	+	0.00273659i	−0.0169683	+	0.000165930i
$273$	1.32579	−	4.08037i	0.0802406	−	0.246955i
$274$	−1.51493	−	0.923261i	−0.0915200	−	0.0557763i
$275$		0			0
$276$	−3.60522	−	6.99093i	−0.217009	−	0.420804i
$277$	14.2764	+	4.63868i	0.857784	+	0.278711i	0.704703	−	0.709503i	$-0.251080\pi$
$277$	14.2764	+	4.63868i	0.857784	+	0.278711i	0.153081	+	0.988214i	$0.451080\pi$
$278$	−8.86786	+	0.719733i	−0.531859	+	0.0431667i
$279$	5.32251	−	7.32580i	0.318650	−	0.438584i
$280$	6.02803	−	1.49404i	0.360244	−	0.0892861i
$281$	−5.46035	+	1.77417i	−0.325737	+	0.105838i	−0.467321	−	0.884088i	$-0.654781\pi$
$281$	−5.46035	+	1.77417i	−0.325737	+	0.105838i	0.141584	+	0.989926i	$0.454781\pi$
$282$	3.95367	+	9.47939i	0.235438	+	0.564490i
$283$	−9.05676	+	6.58012i	−0.538369	+	0.391148i	−0.823479	−	0.567347i	$-0.807970\pi$
$283$	−9.05676	+	6.58012i	−0.538369	+	0.391148i	0.285110	+	0.958495i	$0.407970\pi$
$284$	−2.24978	−	13.7685i	−0.133500	−	0.817013i
$285$			7.94150i			0.470414i
$286$		0			0
$287$		−	9.42215i		−	0.556172i
$288$	1.25690	+	13.8101i	0.0740637	+	0.813770i
$289$	−13.7493	+	9.98947i	−0.808784	+	0.587616i
$290$	−6.92788	+	2.88948i	−0.406819	+	0.169676i
$291$	5.16078	−	1.67684i	0.302530	−	0.0982981i
$292$	14.3848	+	14.2448i	0.841804	+	0.833612i
$293$	3.11697	−	4.29014i	0.182095	−	0.250632i	−0.708205	−	0.706007i	$-0.750495\pi$
$293$	3.11697	−	4.29014i	0.182095	−	0.250632i	0.890300	+	0.455375i	$0.150495\pi$
$294$	−0.368469	−	4.53992i	−0.0214895	−	0.264774i
$295$	6.23461	+	2.02575i	0.362993	+	0.117944i
$296$	1.38419	−	19.4063i	0.0804542	−	1.12797i
$297$		0			0
$298$	12.6261	−	20.7175i	0.731413	−	1.20013i
$299$	5.83686	−	17.9640i	0.337554	−	1.03889i
$300$	2.11925	−	4.21002i	0.122355	−	0.243066i
$301$	−2.49664	−	1.81392i	−0.143904	−	0.104552i
$302$	3.97307	−	16.7291i	0.228625	−	0.962652i
$303$	2.19101	+	6.74322i	0.125870	+	0.387388i
$304$	30.1519	−	10.1240i	1.72933	−	0.580649i
$305$	1.06683	+	1.46836i	0.0610865	+	0.0840783i
$306$	−0.157978	−	0.184056i	−0.00903102	−	0.0105218i
$307$	−2.27014			−0.129564			−0.0647820	−	0.997899i	$-0.520635\pi$
$307$	−2.27014			−0.129564			−0.0647820	+	0.997899i	$0.520635\pi$
$308$		0			0
$309$	−7.64487			−0.434901
$310$	−4.58782	−	5.34513i	−0.260571	−	0.303583i
$311$	11.8536	+	16.3151i	0.672155	+	0.925143i	0.999807	−	0.0196560i	$-0.00625712\pi$
$311$	11.8536	+	16.3151i	0.672155	+	0.925143i	−0.327651	+	0.944799i	$0.606257\pi$
$312$	4.79814	−	5.70205i	0.271641	−	0.322815i
$313$	0.476468	+	1.46642i	0.0269316	+	0.0828869i	0.963619	−	0.267280i	$-0.0861249\pi$
$313$	0.476468	+	1.46642i	0.0269316	+	0.0828869i	−0.936687	+	0.350167i	$0.886125\pi$
$314$	1.73249	−	7.29487i	0.0977703	−	0.411674i
$315$	4.35460	+	3.16380i	0.245354	+	0.178260i
$316$	10.7267	+	5.39964i	0.603426	+	0.303754i
$317$	−5.21071	+	16.0369i	−0.292663	+	0.900723i	0.691334	+	0.722536i	$0.257023\pi$
$317$	−5.21071	+	16.0369i	−0.292663	+	0.900723i	−0.983997	+	0.178188i	$0.942977\pi$
$318$	−2.11923	+	3.47732i	−0.118841	+	0.194999i
$319$		0			0
$320$	10.6781	+	1.53105i	0.596924	+	0.0855885i
$321$	7.80302	+	2.53535i	0.435522	+	0.141510i
$322$	0.989189	+	12.1878i	0.0551253	+	0.679201i
$323$	−0.327005	+	0.450083i	−0.0181950	+	0.0250433i
$324$	−6.14076	+	6.20110i	−0.341153	+	0.344506i
$325$	10.7644	−	3.49756i	0.597100	−	0.194010i
$326$	−13.1275	+	5.47522i	−0.727064	+	0.303244i
$327$	−5.36860	+	3.90052i	−0.296885	+	0.215699i
$328$	6.15193	−	15.1657i	0.339684	−	0.837387i
$329$		−	15.9667i		−	0.880275i
$330$		0			0
$331$			33.9735i			1.86735i	0.358115	+	0.933677i	$0.383419\pi$
$331$			33.9735i			1.86735i	−0.358115	+	0.933677i	$0.616581\pi$
$332$	−7.12931	+	1.16493i	−0.391272	+	0.0639339i
$333$	13.6418	−	9.91136i	0.747567	−	0.543139i
$334$	−11.9263	−	28.5946i	−0.652576	−	1.56463i
$335$	6.30056	−	2.04718i	0.344237	−	0.111849i
$336$	−1.44588	+	4.60261i	−0.0788790	+	0.251093i
$337$	−10.0486	+	13.8307i	−0.547382	+	0.753407i	−0.989654	−	0.143474i	$-0.954173\pi$
$337$	−10.0486	+	13.8307i	−0.547382	+	0.753407i	0.442272	+	0.896881i	$0.354173\pi$
$338$	−0.487833	+	0.0395935i	−0.0265346	+	0.00215360i
$339$	−7.76492	−	2.52297i	−0.421732	−	0.137029i
$340$	−0.167699	+	0.0864821i	−0.00909474	+	0.00469015i
$341$		0			0
$342$	23.5394	+	14.3459i	1.27286	+	0.775738i
$343$	−5.71045	+	17.5750i	−0.308335	+	0.948959i
$344$	−2.83420	−	4.54976i	−0.152810	−	0.245307i
$345$	−4.29036	−	3.11713i	−0.230985	−	0.167820i
$346$	−16.2804	−	3.86652i	−0.875241	−	0.207865i
$347$	0.772260	+	2.37677i	0.0414571	+	0.127592i	0.969643	−	0.244525i	$-0.0786321\pi$
$347$	0.772260	+	2.37677i	0.0414571	+	0.127592i	−0.928186	+	0.372117i	$0.878632\pi$
$348$	0.884006	−	5.76364i	0.0473877	−	0.308963i
$349$	−4.12112	−	5.67223i	−0.220598	−	0.303628i	0.684346	−	0.729157i	$-0.260088\pi$
$349$	−4.12112	−	5.67223i	−0.220598	−	0.303628i	−0.904944	+	0.425530i	$0.860088\pi$
$350$	−5.56000	+	4.77224i	−0.297194	+	0.255087i
$351$	14.3631			0.766646
$352$		0			0
$353$	17.9431			0.955017			0.477509	−	0.878627i	$-0.341540\pi$
$353$	17.9431			0.955017			0.477509	+	0.878627i	$0.341540\pi$
$354$	−3.86420	+	3.31671i	−0.205380	+	0.176281i
$355$	−5.52868	−	7.60958i	−0.293432	−	0.403874i
$356$	−1.63644	+	10.6695i	−0.0867313	+	0.565480i
$357$	−0.0260764	−	0.0802548i	−0.00138011	−	0.00424754i
$358$	1.28468	+	0.305106i	0.0678977	+	0.0161253i
$359$	7.83085	+	5.68945i	0.413297	+	0.300278i	0.774935	−	0.632041i	$-0.217783\pi$
$359$	7.83085	+	5.68945i	0.413297	+	0.300278i	−0.361638	+	0.932318i	$0.617783\pi$
$360$	4.94336	+	7.93561i	0.260538	+	0.418243i
$361$	13.6669	−	42.0624i	0.719310	−	2.21381i
$362$	22.7509	+	13.8654i	1.19576	+	0.728748i
$363$		0			0
$364$	−10.2965	+	5.30988i	−0.539681	+	0.278313i
$365$	12.9809	+	4.21774i	0.679450	+	0.220767i
$366$	−1.40530	+	0.114057i	−0.0734564	+	0.00596187i
$367$	−18.1903	+	25.0368i	−0.949524	+	1.30691i	0.00221435	+	0.999998i	$0.499295\pi$
$367$	−18.1903	+	25.0368i	−0.949524	+	1.30691i	−0.951738	+	0.306910i	$0.900705\pi$
$368$	−6.36553	+	20.2632i	−0.331826	+	1.05629i
$369$	13.4902	−	4.38322i	0.702270	−	0.228181i
$370$	−5.04932	−	12.1063i	−0.262502	−	0.629379i
$371$	5.12151	−	3.72100i	0.265896	−	0.193184i
$372$	5.40032	−	0.882414i	0.279994	−	0.0457511i
$373$		−	4.92658i		−	0.255088i	−0.991833	−	0.127544i	$-0.959291\pi$
$373$		−	4.92658i		−	0.255088i	0.991833	−	0.127544i	$-0.0407095\pi$
$374$		0			0
$375$		−	8.17145i		−	0.421972i
$376$	10.4250	−	25.6998i	0.537631	−	1.32537i
$377$	11.3281	−	8.23036i	0.583428	−	0.423885i
$378$	−8.58179	+	3.57930i	−0.441400	+	0.184099i
$379$	3.82815	−	1.24384i	0.196639	−	0.0638918i	−0.209042	−	0.977907i	$-0.567035\pi$
$379$	3.82815	−	1.24384i	0.196639	−	0.0638918i	0.405681	+	0.914015i	$0.367035\pi$
$380$	15.0888	−	15.2371i	0.774041	−	0.781647i
$381$	4.48086	−	6.16737i	0.229561	−	0.315964i
$382$	−2.33889	−	28.8176i	−0.119668	−	1.47443i
$383$	11.4021	+	3.70477i	0.582621	+	0.189305i	0.585474	−	0.810691i	$-0.300908\pi$
$383$	11.4021	+	3.70477i	0.582621	+	0.189305i	−0.00285329	+	0.999996i	$0.500908\pi$
$384$	−5.33240	+	6.46423i	−0.272118	+	0.329877i
$385$		0			0
$386$	−12.7625	+	20.9412i	−0.649594	+	1.06588i
$387$	1.43563	−	4.41841i	0.0729771	−	0.224600i
$388$	−13.0878	−	6.58817i	−0.664433	−	0.334464i
$389$	−11.1135	−	8.07444i	−0.563477	−	0.409390i	0.269253	−	0.963070i	$-0.413223\pi$
$389$	−11.1135	−	8.07444i	−0.563477	−	0.409390i	−0.832730	+	0.553679i	$0.813223\pi$
$390$	1.16096	−	4.88837i	0.0587876	−	0.247532i
$391$	−0.114802	−	0.353325i	−0.00580580	−	0.0178684i
$392$	−7.91887	+	9.41069i	−0.399963	+	0.475312i
$393$	0.813111	+	1.11915i	0.0410160	+	0.0564537i
$394$	3.21581	+	3.74664i	0.162010	+	0.188753i
$395$	8.09663			0.407386
$396$		0			0
$397$	−12.1547			−0.610027			−0.305014	−	0.952348i	$-0.598661\pi$
$397$	−12.1547			−0.610027			−0.305014	+	0.952348i	$0.598661\pi$
$398$	10.3769	+	12.0899i	0.520149	+	0.606010i
$399$	5.63704	+	7.75871i	0.282205	+	0.388422i
$400$	−12.0652	+	4.05107i	−0.603259	+	0.202553i
$401$	−8.89366	−	27.3719i	−0.444128	−	1.36689i	−0.883437	−	0.468550i	$-0.844777\pi$
$401$	−8.89366	−	27.3719i	−0.444128	−	1.36689i	0.439309	−	0.898336i	$-0.355223\pi$
$402$	−1.18914	+	5.00700i	−0.0593088	+	0.249727i
$403$	10.6305	+	7.72351i	0.529543	+	0.384735i
$404$	8.60830	−	17.1009i	0.428279	−	0.850802i
$405$	−1.81822	+	5.59591i	−0.0903481	+	0.278063i
$406$	−4.71741	+	7.74052i	−0.234121	+	0.384156i
$407$		0			0
$408$	0.0104281	−	0.146203i	0.000516269	−	0.00723811i
$409$	−18.0275	−	5.85749i	−0.891402	−	0.289634i	−0.172718	−	0.984971i	$-0.555255\pi$
$409$	−18.0275	−	5.85749i	−0.891402	−	0.289634i	−0.718684	+	0.695337i	$0.755255\pi$
$410$	−0.892611	−	10.9979i	−0.0440829	−	0.543147i
$411$	0.546146	−	0.751705i	0.0269394	−	0.0370789i
$412$	14.6680	+	14.5252i	0.722639	+	0.715607i
$413$	7.52903	−	2.44633i	0.370479	−	0.120376i
$414$	−16.9898	+	7.08610i	−0.835002	+	0.348263i
$415$	−3.94022	+	2.86274i	−0.193418	+	0.140526i
$416$	−20.0399	+	1.82389i	−0.982538	+	0.0894238i
$417$		−	4.65970i		−	0.228186i
$418$		0			0
$419$		−	15.3705i		−	0.750898i	−0.926843	−	0.375449i	$-0.877488\pi$
$419$		−	15.3705i		−	0.750898i	0.926843	−	0.375449i	$-0.122512\pi$
$420$	0.524524	+	3.21005i	0.0255941	+	0.156635i
$421$	−15.6309	+	11.3565i	−0.761803	+	0.553482i	−0.899463	−	0.436997i	$-0.856042\pi$
$421$	−15.6309	+	11.3565i	−0.761803	+	0.553482i	0.137660	+	0.990480i	$0.456042\pi$
$422$	−1.49323	−	3.58020i	−0.0726894	−	0.174281i
$423$	22.8604	−	7.42780i	1.11151	−	0.361152i
$424$	10.6730	−	2.64530i	0.518327	−	0.128467i
$425$	0.130850	−	0.180099i	0.00634714	−	0.00873609i
$426$	7.28278	−	0.591084i	0.352852	−	0.0286381i
$427$	2.08455	+	0.677311i	0.100878	+	0.0327774i
$428$	−10.1542	−	19.6902i	−0.490824	−	0.951763i
$429$		0			0
$430$	−3.08602	−	1.88075i	−0.148821	−	0.0906980i
$431$	−8.37559	+	25.7774i	−0.403438	+	1.24165i	0.518754	+	0.854923i	$0.326396\pi$
$431$	−8.37559	+	25.7774i	−0.403438	+	1.24165i	−0.922192	+	0.386732i	$0.873604\pi$
$432$	−16.1501	+	0.157929i	−0.777022	+	0.00759837i
$433$	−3.52419	−	2.56048i	−0.169362	−	0.123049i	0.499876	−	0.866097i	$-0.333379\pi$
$433$	−3.52419	−	2.56048i	−0.169362	−	0.123049i	−0.669237	+	0.743049i	$0.733379\pi$
$434$	−8.27630	−	1.96558i	−0.397275	−	0.0943508i
$435$	−1.21485	−	3.73891i	−0.0582474	−	0.179267i
$436$	17.7116	+	2.71653i	0.848230	+	0.130098i
$437$	24.8173	+	34.1581i	1.18717	+	1.63400i
$438$	−8.04552	+	6.90561i	−0.384430	+	0.329963i
$439$	24.0996			1.15021			0.575105	−	0.818080i	$-0.304961\pi$
$439$	24.0996			1.15021			0.575105	+	0.818080i	$0.304961\pi$
$440$		0			0
$441$	−10.6597			−0.507605
$442$	0.267084	−	0.229243i	0.0127039	−	0.0109040i
$443$	13.5454	+	18.6436i	0.643561	+	0.885786i	0.998799	−	0.0489896i	$-0.0156001\pi$
$443$	13.5454	+	18.6436i	0.643561	+	0.885786i	−0.355238	+	0.934776i	$0.615600\pi$
$444$	10.0719	+	1.54478i	0.477989	+	0.0733122i
$445$	2.24888	+	6.92135i	0.106607	+	0.328104i
$446$	−32.6453	−	7.75308i	−1.54580	−	0.367119i
$447$	10.2800	+	7.46887i	0.486228	+	0.353265i
$448$	11.5191	−	6.08372i	0.544227	−	0.287429i
$449$	−1.16607	+	3.58880i	−0.0550303	+	0.169366i	−0.974794	−	0.223107i	$-0.928380\pi$
$449$	−1.16607	+	3.58880i	−0.0550303	+	0.169366i	0.919764	+	0.392473i	$0.128380\pi$
$450$	−9.41920	−	5.74046i	−0.444025	−	0.270608i
$451$		0			0
$452$	10.1047	+	19.5941i	0.475283	+	0.921628i
$453$	8.56460	+	2.78281i	0.402400	+	0.130748i
$454$	−1.12885	+	0.0916193i	−0.0529794	+	0.00429991i
$455$	−4.59100	+	6.31897i	−0.215229	+	0.296238i
$456$	4.00743	+	16.1688i	0.187665	+	0.757175i
$457$	−33.5315	+	10.8950i	−1.56854	+	0.509649i	−0.959072	−	0.283164i	$-0.908616\pi$
$457$	−33.5315	+	10.8950i	−1.56854	+	0.509649i	−0.609466	+	0.792812i	$0.708616\pi$
$458$	12.8416	+	30.7891i	0.600046	+	1.43868i
$459$	0.228548	−	0.166050i	0.0106677	−	0.00775055i
$460$	2.30924	+	14.1324i	0.107669	+	0.658927i
$461$			38.5074i			1.79347i	0.442571	+	0.896734i	$0.354067\pi$
$461$			38.5074i			1.79347i	−0.442571	+	0.896734i	$0.645933\pi$
$462$		0			0
$463$		−	10.7672i		−	0.500394i	−0.968195	−	0.250197i	$-0.919505\pi$
$463$		−	10.7672i		−	0.500394i	0.968195	−	0.250197i	$-0.0804954\pi$
$464$	−12.6470	+	9.37890i	−0.587123	+	0.435405i
$465$	2.98464	−	2.16847i	0.138409	−	0.100560i
$466$	−22.8305	+	9.52218i	−1.05760	+	0.441106i
$467$	19.6677	−	6.39043i	0.910114	−	0.295714i	0.183709	−	0.982981i	$-0.441190\pi$
$467$	19.6677	−	6.39043i	0.910114	−	0.295714i	0.726405	+	0.687267i	$0.241190\pi$
$468$	−12.3924	−	12.2718i	−0.572838	−	0.567264i
$469$	4.70242	−	6.47232i	0.217138	−	0.298864i
$470$	−1.51262	−	18.6370i	−0.0697717	−	0.859661i
$471$	3.73467	+	1.21347i	0.172084	+	0.0559136i
$472$	13.7159	+	0.978304i	0.631323	+	0.0450301i
$473$		0			0
$474$	−3.27320	+	5.37080i	−0.150343	+	0.246689i
$475$	−7.81814	+	24.0618i	−0.358721	+	1.10403i
$476$	−0.102452	+	0.203528i	−0.00469588	+	0.00932867i
$477$	7.71009	+	5.60171i	0.353021	+	0.256485i
$478$	2.18451	−	9.19813i	0.0999170	−	0.420713i
$479$	3.52707	+	10.8552i	0.161156	+	0.495986i	0.998732	−	0.0503333i	$-0.0160284\pi$
$479$	3.52707	+	10.8552i	0.161156	+	0.495986i	−0.837577	+	0.546320i	$0.816028\pi$
$480$	−1.25165	+	5.50932i	−0.0571299	+	0.251465i
$481$	14.3824	+	19.7957i	0.655781	+	0.902606i
$482$	−3.94828	−	4.60002i	−0.179839	−	0.209525i
$483$	−6.40421			−0.291401
$484$		0			0
$485$	−9.87880			−0.448573
$486$	−14.1342	−	16.4673i	−0.641139	−	0.746972i
$487$	2.35405	+	3.24008i	0.106672	+	0.146822i	0.859016	−	0.511949i	$-0.171076\pi$
$487$	2.35405	+	3.24008i	0.106672	+	0.146822i	−0.752343	+	0.658771i	$0.771076\pi$
$488$	2.91302	+	2.45124i	0.131866	+	0.110962i
$489$	−2.30199	−	7.08479i	−0.104099	−	0.320385i
$490$	−1.91606	+	8.06778i	−0.0865586	+	0.364465i
$491$	9.05615	+	6.57968i	0.408698	+	0.296937i	0.773075	−	0.634315i	$-0.218718\pi$
$491$	9.05615	+	6.57968i	0.408698	+	0.296937i	−0.364376	+	0.931252i	$0.618718\pi$
$492$	7.65617	+	3.85398i	0.345167	+	0.173751i
$493$	0.0851048	−	0.261926i	0.00383293	−	0.0117965i
$494$	−20.8174	+	34.1581i	−0.936619	+	1.53684i
$495$		0			0
$496$	−12.0380	−	8.56754i	−0.540523	−	0.384694i
$497$	−10.8029	−	3.51006i	−0.484575	−	0.157448i
$498$	−0.306062	−	3.77100i	−0.0137150	−	0.168983i
$499$	−23.1385	+	31.8474i	−1.03582	+	1.42569i	−0.135336	+	0.990800i	$0.543211\pi$
$499$	−23.1385	+	31.8474i	−1.03582	+	1.42569i	−0.900485	+	0.434886i	$0.856789\pi$
$500$	−15.5257	+	15.6783i	−0.694332	+	0.701155i
$501$	15.4323	−	5.01425i	0.689463	−	0.224020i
$502$	6.39262	−	2.66624i	0.285317	−	0.119000i
$503$	−15.6439	+	11.3660i	−0.697527	+	0.506783i	−0.879126	−	0.476589i	$-0.841873\pi$
$503$	−15.6439	+	11.3660i	−0.697527	+	0.506783i	0.181599	+	0.983373i	$0.441873\pi$
$504$	10.4624	+	4.24406i	0.466034	+	0.189045i
$505$		−	12.9079i		−	0.574395i
$506$		0			0
$507$		−	0.256336i		−	0.0113843i
$508$	−20.3153	+	3.31952i	−0.901345	+	0.147280i
$509$	34.7849	−	25.2727i	1.54181	−	1.12019i	0.592628	−	0.805476i	$-0.298090\pi$
$509$	34.7849	−	25.2727i	1.54181	−	1.12019i	0.949186	−	0.314717i	$-0.101910\pi$
$510$	−0.0380403	−	0.0912062i	−0.00168445	−	0.00403868i
$511$	15.6759	−	5.09342i	0.693463	−	0.225320i
$512$	22.5131	−	2.27116i	0.994950	−	0.100372i
$513$	−18.8715	+	25.9744i	−0.833196	+	1.14680i
$514$	17.4566	−	1.41681i	0.769979	−	0.0624930i
$515$	13.2365	+	4.30078i	0.583268	+	0.189515i
$516$	2.49515	−	1.28675i	0.109843	−	0.0566458i
$517$		0			0
$518$	−13.5264	−	8.24359i	−0.594317	−	0.362202i
$519$	2.70817	−	8.33490i	0.118876	−	0.365861i
$520$	−11.5154	+	7.17333i	−0.504983	+	0.314571i
$521$	11.9178	+	8.65882i	0.522130	+	0.379350i	0.817406	−	0.576062i	$-0.195411\pi$
$521$	11.9178	+	8.65882i	0.522130	+	0.379350i	−0.295275	+	0.955412i	$0.595411\pi$
$522$	−13.2771	−	3.15323i	−0.581121	−	0.138013i
$523$	−12.5006	−	38.4729i	−0.546614	−	1.68230i	−0.717122	−	0.696948i	$-0.754541\pi$
$523$	−12.5006	−	38.4729i	−0.546614	−	1.68230i	0.170508	−	0.985356i	$-0.445459\pi$
$524$	0.566295	−	3.69219i	0.0247387	−	0.161294i
$525$	−2.25564	−	3.10462i	−0.0984442	−	0.135497i
$526$	−18.1883	+	15.6113i	−0.793047	+	0.680686i
$527$	0.258445			0.0112580
$528$		0			0
$529$	−5.19479			−0.225860
$530$	5.62552	−	4.82848i	0.244357	−	0.209736i
$531$	7.00507	+	9.64165i	0.303994	+	0.418412i
$532$	3.92594	−	25.5968i	0.170211	−	1.10976i
$533$	6.36051	+	19.5756i	0.275504	+	0.847915i
$534$	−5.50034	−	1.30630i	−0.238023	−	0.0565292i
$535$	−12.0840	−	8.77951i	−0.522435	−	0.379571i
$536$	11.7949	−	7.34742i	0.509460	−	0.317360i
$537$	−0.213701	+	0.657704i	−0.00922188	+	0.0283820i
$538$	4.77584	+	2.91060i	0.205901	+	0.125485i
$539$		0			0
$540$	−9.67791	+	4.99089i	−0.416471	+	0.214774i
$541$	15.9160	+	5.17141i	0.684281	+	0.222336i	0.630469	−	0.776215i	$-0.282863\pi$
$541$	15.9160	+	5.17141i	0.684281	+	0.222336i	0.0538123	+	0.998551i	$0.482863\pi$
$542$	−33.4598	+	2.71567i	−1.43722	+	0.116648i
$543$	−8.20192	+	11.2890i	−0.351978	+	0.484456i
$544$	−0.297793	+	0.260701i	−0.0127678	+	0.0111775i
$545$	11.4896	−	3.73320i	0.492161	−	0.159913i
$546$	−2.33562	−	5.59993i	−0.0999553	−	0.239655i
$547$	−7.51580	+	5.46055i	−0.321352	+	0.233476i	−0.736752	−	0.676163i	$-0.763642\pi$
$547$	−7.51580	+	5.46055i	−0.321352	+	0.233476i	0.415400	+	0.909639i	$0.363642\pi$
$548$	−2.47611	+	0.404597i	−0.105774	+	0.0172835i
$549$			3.29964i			0.140825i
$550$		0			0
$551$			31.2996i			1.33341i
$552$	−10.3081	−	4.18145i	−0.438742	−	0.177974i
$553$	7.91027	−	5.74715i	0.336379	−	0.244394i
$554$	19.5930	−	8.17185i	0.832426	−	0.347189i
$555$	6.53368	−	2.12292i	0.277339	−	0.0901131i
$556$	−8.85341	+	8.94041i	−0.375468	+	0.379158i
$557$	7.79519	−	10.7292i	0.330293	−	0.454609i	−0.611282	−	0.791413i	$-0.709346\pi$
$557$	7.79519	−	10.7292i	0.330293	−	0.454609i	0.941575	+	0.336804i	$0.109346\pi$
$558$	−1.03595	−	12.7640i	−0.0438553	−	0.540343i
$559$	6.41157	+	2.08325i	0.271181	+	0.0881119i
$560$	5.09271	−	7.15563i	0.215206	−	0.302380i
$561$		0			0
$562$	−4.22549	+	6.93336i	−0.178241	+	0.292466i
$563$	−7.26327	+	22.3541i	−0.306110	+	0.942111i	0.673150	+	0.739506i	$0.264941\pi$
$563$	−7.26327	+	22.3541i	−0.306110	+	0.942111i	−0.979260	+	0.202605i	$0.935059\pi$
$564$	12.9741	+	6.53094i	0.546309	+	0.275002i
$565$	12.0250	+	8.73664i	0.505893	+	0.367553i
$566$	−3.65822	+	15.4034i	−0.153766	+	0.647451i
$567$	2.19572	+	6.75772i	0.0922114	+	0.283797i
$568$	−15.0963	−	12.7032i	−0.633426	−	0.533013i
$569$	−7.57056	−	10.4200i	−0.317374	−	0.436828i	0.620289	−	0.784373i	$-0.287015\pi$
$569$	−7.57056	−	10.4200i	−0.317374	−	0.436828i	−0.937663	+	0.347545i	$0.887015\pi$
$570$	7.31479	+	8.52224i	0.306383	+	0.356958i
$571$	20.4261			0.854806			0.427403	−	0.904061i	$-0.359429\pi$
$571$	20.4261			0.854806			0.427403	+	0.904061i	$0.359429\pi$
$572$		0			0
$573$	15.1424			0.632585
$574$	−8.67859	−	10.1112i	−0.362238	−	0.422032i
$575$	−9.93055	−	13.6682i	−0.414132	−	0.570004i
$576$	14.0691	+	13.6623i	0.586213	+	0.569264i
$577$	2.11524	+	6.51003i	0.0880585	+	0.271016i	0.985383	−	0.170356i	$-0.0544918\pi$
$577$	2.11524	+	6.51003i	0.0880585	+	0.271016i	−0.897324	+	0.441372i	$0.854492\pi$
$578$	−5.55364	+	23.3843i	−0.231001	+	0.972658i
$579$	−10.3910	−	7.54952i	−0.431836	−	0.313747i
$580$	−4.77304	+	9.48194i	−0.198190	+	0.393716i
$581$	−1.81750	+	5.59369i	−0.0754026	+	0.232065i
$582$	3.99367	−	6.55298i	0.165543	−	0.271630i
$583$		0			0
$584$	28.5573	+	2.03689i	1.18171	+	0.0842873i
$585$	−11.1829	−	3.63356i	−0.462358	−	0.150229i
$586$	−0.606674	−	7.47485i	−0.0250615	−	0.308783i
$587$	−0.375476	+	0.516798i	−0.0154975	+	0.0213305i	−0.816695	−	0.577069i	$-0.804196\pi$
$587$	−0.375476	+	0.516798i	−0.0154975	+	0.0213305i	0.801198	+	0.598399i	$0.204196\pi$
$588$	−4.57706	−	4.53252i	−0.188755	−	0.186918i
$589$	−27.9345	+	9.07647i	−1.15102	+	0.373989i
$590$	8.55642	−	3.56872i	0.352262	−	0.146922i
$591$	−2.09207	+	1.51998i	−0.0860564	+	0.0625236i
$592$	−16.3895	−	22.1004i	−0.673603	−	0.908322i
$593$		−	17.0480i		−	0.700077i	−0.936735	−	0.350039i	$-0.886168\pi$
$593$		−	17.0480i		−	0.700077i	0.936735	−	0.350039i	$-0.113832\pi$
$594$		0			0
$595$			0.153624i			0.00629799i
$596$	−5.53311	−	33.8623i	−0.226645	−	1.38705i
$597$	−6.75080	+	4.90474i	−0.276292	+	0.200738i
$598$	−10.2827	−	24.6539i	−0.420490	−	1.00817i
$599$	1.88754	−	0.613298i	0.0771227	−	0.0250587i	−0.270202	−	0.962804i	$-0.587090\pi$
$599$	1.88754	−	0.613298i	0.0771227	−	0.0250587i	0.347324	+	0.937745i	$0.387090\pi$
$600$	−1.60356	−	6.46990i	−0.0654650	−	0.264133i
$601$	9.67660	−	13.3187i	0.394717	−	0.543281i	−0.564692	−	0.825302i	$-0.691005\pi$
$601$	9.67660	−	13.3187i	0.394717	−	0.543281i	0.959408	+	0.282021i	$0.0910049\pi$
$602$	−4.34999	+	0.353053i	−0.177292	+	0.0143894i
$603$	11.4543	+	3.72174i	0.466457	+	0.151561i
$604$	−11.1453	−	21.6120i	−0.453496	−	0.879380i
$605$		0			0
$606$	8.56231	+	5.21824i	0.347820	+	0.211976i
$607$	8.87509	−	27.3147i	0.360229	−	1.10867i	−0.592686	−	0.805433i	$-0.701933\pi$
$607$	8.87509	−	27.3147i	0.360229	−	1.10867i	0.952915	−	0.303237i	$-0.0980674\pi$
$608$	23.0318	−	38.6368i	0.934064	−	1.56693i
$609$	−3.84084	−	2.79053i	−0.155639	−	0.113078i
$610$	2.49733	+	0.593103i	0.101114	+	0.0240140i
$611$	10.7785	+	33.1728i	0.436051	+	1.34203i
$612$	−0.339062	−	0.0520041i	−0.0137058	−	0.00210214i
$613$	3.91099	+	5.38302i	0.157964	+	0.217418i	0.880662	−	0.473745i	$-0.157098\pi$
$613$	3.91099	+	5.38302i	0.157964	+	0.217418i	−0.722698	+	0.691164i	$0.757098\pi$
$614$	−2.43616	+	2.09100i	−0.0983153	+	0.0843857i
$615$	5.77894			0.233029
$616$		0			0
$617$	−17.8948			−0.720416			−0.360208	−	0.932872i	$-0.617294\pi$
$617$	−17.8948			−0.720416			−0.360208	+	0.932872i	$0.617294\pi$
$618$	−8.20392	+	7.04157i	−0.330010	+	0.283253i
$619$	13.6588	+	18.7998i	0.548995	+	0.755627i	0.989875	−	0.141939i	$-0.0453336\pi$
$619$	13.6588	+	18.7998i	0.548995	+	0.755627i	−0.440880	+	0.897566i	$0.645334\pi$
$620$	−9.84663	−	1.51024i	−0.395450	−	0.0606527i
$621$	−6.62526	−	20.3904i	−0.265862	−	0.818241i
$622$	27.7480	+	6.59000i	1.11259	+	0.264235i
$623$	7.11004	+	5.16574i	0.284858	+	0.206961i
$624$	−0.103054	−	10.5385i	−0.00412548	−	0.421879i
$625$	0.319097	−	0.982080i	0.0127639	−	0.0392832i
$626$	1.86201	+	1.13479i	0.0744208	+	0.0453552i
$627$		0			0
$628$	−4.86001	−	9.42411i	−0.193935	−	0.376063i
$629$	0.457710	+	0.148719i	0.0182501	+	0.00592982i
$630$	7.58716	−	0.615789i	0.302280	−	0.0245336i
$631$	27.2272	−	37.4750i	1.08390	−	1.49186i	0.228739	−	0.973488i	$-0.426540\pi$
$631$	27.2272	−	37.4750i	1.08390	−	1.49186i	0.855158	−	0.518368i	$-0.173460\pi$
$632$	16.4847	−	4.08571i	0.655725	−	0.162521i
$633$	1.93220	−	0.627811i	0.0767981	−	0.0249532i
$634$	9.17960	+	22.0092i	0.364568	+	0.874096i
$635$	−11.2278	+	8.15749i	−0.445562	+	0.323720i
$636$	0.928703	+	5.68361i	0.0368255	+	0.225370i
$637$		−	15.4683i		−	0.612877i
$638$		0			0
$639$		−	17.0999i		−	0.676462i
$640$	12.8692	−	8.19242i	0.508700	−	0.323834i
$641$	−21.9856	+	15.9734i	−0.868377	+	0.630913i	−0.930151	−	0.367177i	$-0.880324\pi$
$641$	−21.9856	+	15.9734i	−0.868377	+	0.630913i	0.0617738	+	0.998090i	$0.480324\pi$
$642$	10.7089	−	4.46648i	0.422647	−	0.176278i
$643$	−29.5052	+	9.58683i	−1.16357	+	0.378068i	−0.826240	−	0.563318i	$-0.809525\pi$
$643$	−29.5052	+	9.58683i	−1.16357	+	0.378068i	−0.337333	+	0.941386i	$0.609525\pi$
$644$	12.2876	+	12.1680i	0.484197	+	0.479486i
$645$	1.11254	−	1.53128i	0.0438062	−	0.0602941i
$646$	0.0636469	+	0.784196i	0.00250415	+	0.0308538i
$647$	−40.1073	−	13.0317i	−1.57678	−	0.512327i	−0.615557	−	0.788093i	$-0.711069\pi$
$647$	−40.1073	−	13.0317i	−1.57678	−	0.512327i	−0.961225	+	0.275765i	$0.911069\pi$
$648$	−0.878082	+	12.3107i	−0.0344943	+	0.483611i
$649$		0			0
$650$	8.33001	−	13.6682i	0.326730	−	0.536112i
$651$	1.37672	−	4.23712i	0.0539580	−	0.166066i
$652$	−9.04433	+	17.9671i	−0.354203	+	0.703647i
$653$	3.27455	+	2.37910i	0.128143	+	0.0931015i	0.650011	−	0.759925i	$-0.274764\pi$
$653$	3.27455	+	2.37910i	0.128143	+	0.0931015i	−0.521867	+	0.853027i	$0.674764\pi$
$654$	−2.16849	+	9.13069i	−0.0847947	+	0.357038i
$655$	−0.778232	−	2.39515i	−0.0304080	−	0.0935863i
$656$	−7.36710	−	21.9412i	−0.287637	−	0.856660i
$657$	14.5850	+	20.0746i	0.569016	+	0.783183i
$658$	−14.7067	−	17.1344i	−0.573328	−	0.667967i
$659$	−6.46292			−0.251760			−0.125880	−	0.992045i	$-0.540175\pi$
$659$	−6.46292			−0.251760			−0.125880	+	0.992045i	$0.540175\pi$
$660$		0			0
$661$	26.6232			1.03552			0.517761	−	0.855525i	$-0.326766\pi$
$661$	26.6232			1.03552			0.517761	+	0.855525i	$0.326766\pi$
$662$	31.2925	+	36.4580i	1.21622	+	1.41698i
$663$	0.108354	+	0.149136i	0.00420810	+	0.00579196i
$664$	−6.57766	+	7.81682i	−0.255263	+	0.303351i
$665$	−5.39523	−	16.6048i	−0.209218	−	0.643907i
$666$	5.51022	−	23.2014i	0.213517	−	0.899037i
$667$	−16.9095	−	12.2854i	−0.654737	−	0.475694i
$668$	−39.1365	−	19.7006i	−1.51424	−	0.762239i
$669$	5.43039	−	16.7130i	0.209951	−	0.646163i
$670$	4.87569	−	8.00023i	0.188364	−	0.309076i
$671$		0			0
$672$	2.68778	+	6.27096i	0.103683	+	0.241908i
$673$	7.91272	+	2.57100i	0.305013	+	0.0991047i	0.457525	−	0.889197i	$-0.348736\pi$
$673$	7.91272	+	2.57100i	0.305013	+	0.0991047i	−0.152512	+	0.988302i	$0.548736\pi$
$674$	1.95582	+	24.0977i	0.0753353	+	0.928210i
$675$	7.55135	−	10.3935i	0.290652	−	0.400048i
$676$	−0.487038	+	0.491824i	−0.0187322	+	0.0189163i
$677$	14.5159	−	4.71650i	0.557891	−	0.181270i	−0.0164808	−	0.999864i	$-0.505246\pi$
$677$	14.5159	−	4.71650i	0.557891	−	0.181270i	0.574372	+	0.818594i	$0.305246\pi$
$678$	−10.6566	+	4.44467i	−0.409265	+	0.170696i
$679$	−9.65143	+	7.01217i	−0.370388	+	0.269102i
$680$	−0.100305	+	0.247271i	−0.00384651	+	0.00948241i
$681$		−	0.593162i		−	0.0227300i
$682$		0			0
$683$		−	32.9156i		−	1.25948i	−0.776806	−	0.629740i	$-0.783161\pi$
$683$		−	32.9156i		−	1.25948i	0.776806	−	0.629740i	$-0.216839\pi$
$684$	38.4746	−	6.28675i	1.47111	−	0.240380i
$685$	−1.36849	+	0.994269i	−0.0522875	+	0.0379891i
$686$	10.0600	+	24.1200i	0.384092	+	0.920905i
$687$	−16.6166	+	5.39907i	−0.633964	+	0.205987i
$688$	−7.23218	−	2.27194i	−0.275724	−	0.0866167i
$689$	−8.12866	+	11.1881i	−0.309677	+	0.426234i
$690$	−7.47524	+	0.606705i	−0.284577	+	0.0230969i
$691$	43.2897	+	14.0657i	1.64682	+	0.535083i	0.978047	−	0.208385i	$-0.0668208\pi$
$691$	43.2897	+	14.0657i	1.64682	+	0.535083i	0.668771	+	0.743469i	$0.266821\pi$
$692$	−21.0324	+	10.8464i	−0.799531	+	0.412318i
$693$		0			0
$694$	3.01794	+	1.83926i	0.114559	+	0.0698175i
$695$	−2.62141	+	8.06787i	−0.0994358	+	0.306032i
$696$	−4.36015	−	6.99937i	−0.165271	−	0.265310i
$697$	0.327521	+	0.237958i	0.0124057	+	0.00901329i
$698$	−9.64709	−	2.29113i	−0.365148	−	0.0867207i
$699$	−4.00348	−	12.3214i	−0.151426	−	0.466040i
$700$	−1.57095	+	10.2425i	−0.0593763	+	0.387128i
$701$	−29.4388	−	40.5191i	−1.11189	−	1.53038i	−0.818604	−	0.574359i	$-0.805252\pi$
$701$	−29.4388	−	40.5191i	−1.11189	−	1.53038i	−0.293285	−	0.956025i	$-0.594748\pi$
$702$	15.4135	−	13.2296i	0.581743	−	0.499320i
$703$	−54.6955			−2.06288
$704$		0			0
$705$	9.79298			0.368825
$706$	19.2553	−	16.5272i	0.724682	−	0.622008i
$707$	−9.16230	−	12.6108i	−0.344584	−	0.474279i
$708$	−1.09181	+	7.11850i	−0.0410327	+	0.267530i
$709$	−2.62623	−	8.08270i	−0.0986301	−	0.303552i	0.889553	−	0.456833i	$-0.151016\pi$
$709$	−2.62623	−	8.08270i	−0.0986301	−	0.303552i	−0.988183	+	0.153280i	$0.951016\pi$
$710$	−12.9420	−	3.07367i	−0.485706	−	0.115353i
$711$	11.9084	+	8.65195i	0.446599	+	0.324473i
$712$	8.07136	+	12.9570i	0.302487	+	0.485584i
$713$	6.06108	−	18.6541i	0.226989	−	0.698601i
$714$	−0.101905	−	0.0621052i	−0.00381369	−	0.00232423i
$715$		0			0
$716$	1.65966	−	0.855885i	0.0620243	−	0.0319859i
$717$	4.70905	+	1.53006i	0.175863	+	0.0571413i
$718$	13.6440	−	1.10737i	0.509188	−	0.0413267i
$719$	4.28927	−	5.90368i	0.159963	−	0.220170i	−0.721511	−	0.692403i	$-0.756552\pi$
$719$	4.28927	−	5.90368i	0.159963	−	0.220170i	0.881474	+	0.472233i	$0.156552\pi$
$720$	12.6142	+	3.96267i	0.470104	+	0.147680i
$721$	15.9846	−	5.19370i	0.595297	−	0.193424i
$722$	−24.0767	−	57.7266i	−0.896041	−	2.14836i
$723$	2.56858	−	1.86619i	0.0955266	−	0.0694042i
$724$	37.1858	−	6.07617i	1.38200	−	0.225819i
$725$		−	12.5244i		−	0.465146i
$726$		0			0
$727$		−	1.85004i		−	0.0686140i	−0.999411	−	0.0343070i	$-0.989078\pi$
$727$		−	1.85004i		−	0.0686140i	0.999411	−	0.0343070i	$-0.0109224\pi$
$728$	−6.15857	+	15.1821i	−0.228252	+	0.562685i
$729$	−1.39548	+	1.01388i	−0.0516845	+	0.0375510i
$730$	17.8150	−	7.43030i	0.659364	−	0.275008i
$731$	0.126106	−	0.0409743i	0.00466420	−	0.00151549i
$732$	−1.40301	+	1.41680i	−0.0518569	+	0.0523665i
$733$	11.1055	−	15.2854i	0.410190	−	0.564578i	−0.553075	−	0.833132i	$-0.686546\pi$
$733$	11.1055	−	15.2854i	0.410190	−	0.564578i	0.963265	+	0.268554i	$0.0865456\pi$
$734$	3.54048	+	43.6224i	0.130682	+	1.61013i
$735$	−4.13037	−	1.34204i	−0.152351	−	0.0495018i
$736$	11.8331	+	27.6082i	0.436173	+	1.01765i
$737$		0			0
$738$	10.4394	−	17.1293i	0.384278	−	0.630540i
$739$	4.85731	−	14.9493i	0.178679	−	0.549918i	−0.821103	−	0.570780i	$-0.806641\pi$
$739$	4.85731	−	14.9493i	0.178679	−	0.549918i	0.999782	+	0.0208619i	$0.00664102\pi$
$740$	−16.5695	−	8.34080i	−0.609108	−	0.306614i
$741$	−16.9492	−	12.3143i	−0.622645	−	0.452378i
$742$	2.06869	−	8.71045i	0.0759438	−	0.319771i
$743$	1.79427	+	5.52219i	0.0658253	+	0.202590i	0.978559	−	0.205964i	$-0.0660331\pi$
$743$	1.79427	+	5.52219i	0.0658253	+	0.202590i	−0.912734	+	0.408554i	$0.866033\pi$
$744$	4.98246	−	5.92110i	0.182666	−	0.217078i
$745$	−13.5972	−	18.7150i	−0.498163	−	0.685663i
$746$	−4.53779	−	5.28685i	−0.166140	−	0.193565i
$747$	−8.85428			−0.323961
$748$		0			0
$749$	−18.0377			−0.659083
$750$	−7.52659	−	8.76901i	−0.274832	−	0.320199i
$751$	−1.76537	−	2.42982i	−0.0644193	−	0.0886655i	0.775592	−	0.631235i	$-0.217452\pi$
$751$	−1.76537	−	2.42982i	−0.0644193	−	0.0886655i	−0.840011	+	0.542569i	$0.817452\pi$
$752$	−12.4843	−	37.1815i	−0.455254	−	1.35587i
$753$	1.12099	+	3.45004i	0.0408510	+	0.125727i
$754$	4.57567	−	19.2664i	0.166636	−	0.701641i
$755$	−13.2634	−	9.63639i	−0.482703	−	0.350704i
$756$	−5.91252	+	11.7456i	−0.215036	+	0.427183i
$757$	−8.06136	+	24.8103i	−0.292995	+	0.901746i	0.690892	+	0.722958i	$0.257218\pi$
$757$	−8.06136	+	24.8103i	−0.292995	+	0.901746i	−0.983888	+	0.178789i	$0.942782\pi$
$758$	2.96241	−	4.86085i	0.107600	−	0.176554i
$759$		0			0
$760$	2.15759	−	30.2495i	0.0782639	−	1.09726i
$761$	30.3887	+	9.87389i	1.10159	+	0.357928i	0.802714	−	0.596364i	$-0.203388\pi$
$761$	30.3887	+	9.87389i	1.10159	+	0.357928i	0.298876	+	0.954292i	$0.403388\pi$
$762$	−0.872136	−	10.7456i	−0.0315942	−	0.389273i
$763$	8.57526	−	11.8028i	0.310445	−	0.427291i
$764$	−29.0533	−	28.7706i	−1.05111	−	1.04088i
$765$	−0.219952	+	0.0714667i	−0.00795238	+	0.00258388i
$766$	15.6483	−	6.52662i	0.565398	−	0.235816i
$767$	−13.9910	+	10.1651i	−0.505187	+	0.367040i
$768$	0.231752	+	11.8485i	0.00836263	+	0.427547i
$769$			22.3560i			0.806176i	0.915161	+	0.403088i	$0.132063\pi$
$769$			22.3560i			0.806176i	−0.915161	+	0.403088i	$0.867937\pi$
$770$		0			0
$771$			9.17275i			0.330348i
$772$	5.59286	+	34.2280i	0.201291	+	1.23189i
$773$	−4.10741	+	2.98421i	−0.147733	+	0.107335i	−0.659197	−	0.751970i	$-0.729104\pi$
$773$	−4.10741	+	2.98421i	−0.147733	+	0.107335i	0.511463	+	0.859305i	$0.329104\pi$
$774$	−2.52912	−	6.06386i	−0.0909072	−	0.217961i
$775$	11.1779	−	3.63192i	0.401522	−	0.130462i
$776$	−20.1132	+	4.98503i	−0.722021	+	0.178952i
$777$	4.87641	−	6.71180i	0.174940	−	0.240785i
$778$	−19.3635	+	1.57158i	−0.694214	+	0.0563437i
$779$	−43.7577	−	14.2177i	−1.56778	−	0.509404i
$780$	−3.25674	−	6.31519i	−0.116610	−	0.226120i
$781$		0			0
$782$	−0.448640	−	0.273421i	−0.0160433	−	0.00977750i
$783$	4.91141	−	15.1158i	0.175519	−	0.540193i
$784$	0.170082	+	17.3928i	0.00607434	+	0.621172i
$785$	−5.78361	−	4.20204i	−0.206426	−	0.149977i
$786$	1.90341	+	0.452049i	0.0678922	+	0.0161240i
$787$	0.909670	+	2.79968i	0.0324262	+	0.0997977i	0.965960	−	0.258693i	$-0.0832916\pi$
$787$	0.909670	+	2.79968i	0.0324262	+	0.0997977i	−0.933533	+	0.358490i	$0.883292\pi$
$788$	6.90195	+	1.05860i	0.245872	+	0.0377109i
$789$	−7.37882	−	10.1561i	−0.262693	−	0.361566i
$790$	8.68872	−	7.45768i	0.309131	−	0.265332i
$791$	17.9496			0.638215
$792$		0			0
$793$	−4.78812			−0.170031
$794$	−13.0436	+	11.1955i	−0.462899	+	0.397314i
$795$	2.28222	+	3.14121i	0.0809420	+	0.111407i
$796$	22.2716	+	3.41593i	0.789394	+	0.121074i
$797$	2.31514	+	7.12526i	0.0820064	+	0.252390i	0.983650	−	0.180090i	$-0.0576388\pi$
$797$	2.31514	+	7.12526i	0.0820064	+	0.252390i	−0.901644	+	0.432479i	$0.857639\pi$
$798$	13.1957	+	3.13391i	0.467122	+	0.110939i
$799$	0.555015	+	0.403242i	0.0196350	+	0.0142657i
$800$	−9.21610	+	15.4604i	−0.325838	+	0.546606i
$801$	−4.08844	+	12.5829i	−0.144458	+	0.444596i
$802$	−34.7558	−	21.1817i	−1.22727	−	0.747952i
$803$		0			0
$804$	3.33578	+	6.46845i	0.117644	+	0.228125i
$805$	11.0883	+	3.60282i	0.390813	+	0.126983i
$806$	18.5219	−	1.50327i	0.652406	−	0.0529505i
$807$	−1.72174	+	2.36977i	−0.0606080	+	0.0834197i
$808$	−6.51358	−	26.2804i	−0.229147	−	0.924543i
$809$	−37.8768	+	12.3069i	−1.33168	+	0.432688i	−0.886489	−	0.462749i	$-0.846863\pi$
$809$	−37.8768	+	12.3069i	−1.33168	+	0.432688i	−0.445188	+	0.895437i	$0.646863\pi$
$810$	3.20312	+	7.67986i	0.112546	+	0.269843i
$811$	34.5030	−	25.0679i	1.21157	−	0.880254i	0.216193	−	0.976351i	$-0.430636\pi$
$811$	34.5030	−	25.0679i	1.21157	−	0.880254i	0.995372	+	0.0960970i	$0.0306359\pi$
$812$	2.06729	+	12.6517i	0.0725477	+	0.443988i
$813$		−	17.5818i		−	0.616619i
$814$		0			0
$815$			13.5617i			0.475047i
$816$	−0.123474	−	0.166499i	−0.00432246	−	0.00582864i
$817$	−12.1914	+	8.85759i	−0.426524	+	0.309888i
$818$	−24.7410	+	10.3190i	−0.865050	+	0.360796i
$819$	−13.5047	+	4.38795i	−0.471893	+	0.153327i
$820$	−11.0879	−	10.9800i	−0.387205	−	0.383438i
$821$	−11.3507	+	15.6229i	−0.396142	+	0.545243i	−0.959771	−	0.280785i	$-0.909405\pi$
$821$	−11.3507	+	15.6229i	−0.396142	+	0.545243i	0.563628	+	0.826029i	$0.309405\pi$
$822$	−0.106300	−	1.30972i	−0.00370762	−	0.0456818i
$823$	−9.43380	−	3.06523i	−0.328842	−	0.106847i	0.139943	−	0.990160i	$-0.455308\pi$
$823$	−9.43380	−	3.06523i	−0.328842	−	0.106847i	−0.468785	+	0.883312i	$0.655308\pi$
$824$	29.1196	+	2.07700i	1.01443	+	0.0723557i
$825$		0			0
$826$	5.82633	−	9.56010i	0.202724	−	0.332638i
$827$	13.4827	−	41.4953i	0.468838	−	1.44293i	−0.385253	−	0.922811i	$-0.625886\pi$
$827$	13.4827	−	41.4953i	0.468838	−	1.44293i	0.854091	−	0.520124i	$-0.174114\pi$
$828$	−11.7053	+	23.2533i	−0.406787	+	0.808108i
$829$	22.7735	+	16.5459i	0.790957	+	0.574664i	0.908247	−	0.418434i	$-0.137421\pi$
$829$	22.7735	+	16.5459i	0.790957	+	0.574664i	−0.117290	+	0.993098i	$0.537421\pi$
$830$	−1.59154	+	6.70135i	−0.0552430	+	0.232607i
$831$	3.43575	+	10.5742i	0.119185	+	0.366814i
$832$	−19.8254	+	20.4157i	−0.687324	+	0.707788i
$833$	−0.178827	−	0.246135i	−0.00619600	−	0.00852806i
$834$	−4.29197	−	5.00045i	−0.148619	−	0.173151i
$835$	−29.5406			−1.02229
$836$		0			0
$837$	14.9149			0.515533
$838$	−14.1575	−	16.4945i	−0.489064	−	0.569794i
$839$	−20.5447	−	28.2774i	−0.709283	−	0.976244i	−0.999812	−	0.0193779i	$-0.993831\pi$
$839$	−20.5447	−	28.2774i	−0.709283	−	0.976244i	0.290529	−	0.956866i	$-0.406169\pi$
$840$	3.51961	+	2.96167i	0.121438	+	0.102187i
$841$	4.17345	+	12.8446i	0.143912	+	0.442916i
$842$	−6.31364	+	26.5844i	−0.217583	+	0.916157i
$843$	−3.44033	−	2.49954i	−0.118491	−	0.0860889i
$844$	−4.90009	−	2.46662i	−0.168668	−	0.0849046i
$845$	−0.144207	+	0.443825i	−0.00496089	+	0.0152680i
$846$	17.6905	−	29.0273i	0.608212	−	0.997980i
$847$		0			0
$848$	9.01697	−	12.6695i	0.309644	−	0.435072i
$849$	−7.88587	−	2.56227i	−0.270642	−	0.0879371i
$850$	−0.0254681	−	0.313793i	−0.000873547	−	0.0107630i
$851$	21.4686	−	29.5490i	0.735934	−	1.01293i
$852$	7.27091	−	7.34236i	0.249097	−	0.251545i
$853$	25.8841	−	8.41026i	0.886255	−	0.287962i	0.169703	−	0.985495i	$-0.445719\pi$
$853$	25.8841	−	8.41026i	0.886255	−	0.287962i	0.716552	+	0.697533i	$0.245719\pi$
$854$	2.86085	−	1.19320i	0.0978962	−	0.0408306i
$855$	21.2641	−	15.4492i	0.727216	−	0.528353i
$856$	−29.0332	−	11.7772i	−0.992333	−	0.402537i
$857$			37.5541i			1.28282i	0.767197	+	0.641412i	$0.221651\pi$
$857$			37.5541i			1.28282i	−0.767197	+	0.641412i	$0.778349\pi$
$858$		0			0
$859$			4.50293i			0.153638i	0.997045	+	0.0768190i	$0.0244764\pi$
$859$			4.50293i			0.153638i	−0.997045	+	0.0768190i	$0.975524\pi$
$860$	−5.04403	+	0.824195i	−0.172000	+	0.0281048i
$861$	5.64593	−	4.10201i	0.192413	−	0.139796i
$862$	14.7551	+	35.3771i	0.502561	+	1.20495i
$863$	−17.1534	+	5.57348i	−0.583908	+	0.189723i	−0.586051	−	0.810274i	$-0.699318\pi$
$863$	−17.1534	+	5.57348i	−0.583908	+	0.189723i	0.00214238	+	0.999998i	$0.499318\pi$
$864$	−17.1857	+	15.0451i	−0.584668	+	0.511844i
$865$	−9.37795	+	12.9076i	−0.318860	+	0.438873i
$866$	−6.14032	+	0.498361i	−0.208657	+	0.0169350i
$867$	−11.9718	−	3.88986i	−0.406582	−	0.132107i
$868$	−10.6920	+	5.51386i	−0.362910	+	0.187152i
$869$		0			0
$870$	−4.74754	−	2.89336i	−0.160957	−	0.0980940i
$871$	−5.40063	+	16.6214i	−0.182993	+	0.563196i
$872$	21.5089	−	13.3986i	0.728384	−	0.453735i
$873$	−14.5296	−	10.5564i	−0.491751	−	0.357278i
$874$	58.0946	+	13.7972i	1.96508	+	0.466696i
$875$	5.55145	+	17.0856i	0.187673	+	0.577599i
$876$	−2.27322	+	14.8212i	−0.0768050	+	0.500762i
$877$	−8.00606	−	11.0194i	−0.270345	−	0.372099i	0.652161	−	0.758081i	$-0.273863\pi$
$877$	−8.00606	−	11.0194i	−0.270345	−	0.372099i	−0.922506	+	0.385982i	$0.873863\pi$
$878$	25.8619	−	22.1977i	0.872797	−	0.749137i
$879$	3.92773			0.132479
$880$		0			0
$881$	5.44549			0.183463			0.0917317	−	0.995784i	$-0.470760\pi$
$881$	5.44549			0.183463			0.0917317	+	0.995784i	$0.470760\pi$
$882$	−11.4392	+	9.81848i	−0.385179	+	0.330606i
$883$	−16.5930	−	22.8383i	−0.558399	−	0.768570i	0.432723	−	0.901527i	$-0.357553\pi$
$883$	−16.5930	−	22.8383i	−0.558399	−	0.768570i	−0.991122	+	0.132957i	$0.957553\pi$
$884$	0.0754633	−	0.492014i	0.00253811	−	0.0165482i
$885$	1.50042	+	4.61782i	0.0504361	+	0.155226i
$886$	31.7083	+	7.53056i	1.06526	+	0.252994i
$887$	−34.3342	−	24.9453i	−1.15283	−	0.837580i	−0.163975	−	0.986464i	$-0.552432\pi$
$887$	−34.3342	−	24.9453i	−1.15283	−	0.837580i	−0.988855	+	0.148885i	$0.952432\pi$
$888$	12.2313	−	7.61928i	0.410454	−	0.255686i
$889$	−5.17904	+	15.9395i	−0.173700	+	0.534592i
$890$	8.78849	+	5.35608i	0.294591	+	0.179536i
$891$		0			0
$892$	−42.1738	+	21.7490i	−1.41208	+	0.728211i
$893$	−74.1517	−	24.0933i	−2.48139	−	0.806253i
$894$	17.9112	−	1.45371i	0.599041	−	0.0486194i
$895$	0.740011	−	1.01854i	0.0247358	−	0.0340460i
$896$	6.75786	−	17.1387i	0.225764	−	0.572563i
$897$	13.3055	−	4.32322i	0.444258	−	0.144348i
$898$	2.05424	+	4.92529i	0.0685510	+	0.164359i
$899$	11.7633	−	8.54653i	0.392328	−	0.285043i
$900$	−15.3955	+	2.51562i	−0.513182	+	0.0838541i
$901$			0.272002i			0.00906169i
$902$		0			0
$903$		−	2.28574i		−	0.0760646i
$904$	28.8914	+	11.7197i	0.960913	+	0.389792i
$905$	20.5518	−	14.9317i	0.683164	−	0.496348i
$906$	11.7541	−	4.90241i	0.390504	−	0.162872i
$907$	−32.9920	+	10.7198i	−1.09548	+	0.355944i	−0.800363	−	0.599516i	$-0.795360\pi$
$907$	−32.9920	+	10.7198i	−1.09548	+	0.355944i	−0.295120	+	0.955460i	$0.595360\pi$
$908$	−1.12701	+	1.13808i	−0.0374010	+	0.0377686i
$909$	13.7932	−	18.9847i	0.457492	−	0.629684i
$910$	0.893574	+	11.0098i	0.0296217	+	0.364970i
$911$	28.2154	+	9.16772i	0.934816	+	0.303740i	0.736531	−	0.676404i	$-0.236463\pi$
$911$	28.2154	+	9.16772i	0.934816	+	0.303740i	0.198286	+	0.980144i	$0.436463\pi$
$912$	19.1933	+	13.6600i	0.635555	+	0.452329i
$913$		0			0
$914$	−25.9483	+	42.5771i	−0.858294	+	1.40833i
$915$	−0.415419	+	1.27853i	−0.0137333	+	0.0422669i
$916$	42.1400	+	21.2125i	1.39235	+	0.700882i
$917$	−2.46045	−	1.78762i	−0.0812511	−	0.0590324i
$918$	0.0923154	−	0.388705i	0.00304686	−	0.0128292i
$919$	−6.67764	−	20.5517i	−0.220275	−	0.677937i	−0.998737	−	0.0502448i	$-0.984000\pi$
$919$	−6.67764	−	20.5517i	−0.220275	−	0.677937i	0.778462	−	0.627692i	$-0.216000\pi$
$920$	15.4952	+	13.0389i	0.510863	+	0.429879i
$921$	−0.988326	−	1.36031i	−0.0325665	−	0.0448239i
$922$	35.4685	+	41.3233i	1.16809	+	1.36091i
$923$	24.8137			0.816754
$924$		0			0
$925$	21.8862			0.719614
$926$	−9.91749	−	11.5546i	−0.325909	−	0.379707i
$927$	14.8722	+	20.4698i	0.488467	+	0.672317i
$928$	−4.93311	+	21.7137i	−0.161937	+	0.712788i
$929$	14.5920	+	44.9097i	0.478749	+	1.47344i	0.840834	+	0.541293i	$0.182065\pi$
$929$	14.5920	+	44.9097i	0.478749	+	1.47344i	−0.362085	+	0.932145i	$0.617935\pi$
$930$	1.20556	−	5.07615i	0.0395319	−	0.166454i
$931$	27.9730	+	20.3236i	0.916780	+	0.666079i
$932$	−15.7294	+	31.2474i	−0.515233	+	1.02354i
$933$	−4.61574	+	14.2058i	−0.151113	+	0.465077i
$934$	15.2199	−	24.9734i	0.498009	−	0.817154i
$935$		0			0
$936$	−24.6020	−	1.75477i	−0.804140	−	0.0573565i
$937$	−44.1171	−	14.3345i	−1.44124	−	0.468289i	−0.518959	−	0.854799i	$-0.673680\pi$
$937$	−44.1171	−	14.3345i	−1.44124	−	0.468289i	−0.922285	+	0.386510i	$0.873680\pi$
$938$	−0.915260	−	11.2770i	−0.0298843	−	0.368206i
$939$	−0.671272	+	0.923926i	−0.0219061	+	0.0301512i
$940$	−18.7895	−	18.6066i	−0.612845	−	0.606882i
$941$	−37.4912	+	12.1816i	−1.22218	+	0.397109i	−0.847874	−	0.530197i	$-0.822118\pi$
$941$	−37.4912	+	12.1816i	−1.22218	+	0.397109i	−0.374303	+	0.927307i	$0.622118\pi$
$942$	5.12548	−	2.13774i	0.166997	−	0.0696513i
$943$	24.8565	−	18.0593i	0.809438	−	0.588091i
$944$	15.6200	−	11.5836i	0.508387	−	0.377015i
$945$			8.86568i			0.288401i
$946$		0			0
$947$			24.9488i			0.810725i	0.914156	+	0.405363i	$0.132855\pi$
$947$			24.9488i			0.810725i	−0.914156	+	0.405363i	$0.867145\pi$
$948$	1.43440	+	8.77844i	0.0465871	+	0.285111i
$949$	−29.1303	+	21.1644i	−0.945608	+	0.687025i
$950$	13.7731	+	33.0225i	0.446857	+	1.07139i
$951$	−11.8782	+	3.85945i	−0.385176	+	0.125151i
$952$	0.0775218	+	0.312778i	0.00251250	+	0.0101372i
$953$	24.0471	−	33.0979i	0.778961	−	1.07215i	−0.216435	−	0.976297i	$-0.569443\pi$
$953$	24.0471	−	33.0979i	0.778961	−	1.07215i	0.995396	−	0.0958506i	$-0.0305571\pi$
$954$	13.4336	−	1.09029i	0.434927	−	0.0352996i
$955$	−26.2179	−	8.51870i	−0.848391	−	0.275659i
$956$	−6.12800	−	11.8829i	−0.198194	−	0.384320i
$957$		0			0
$958$	13.7835	+	8.40029i	0.445326	+	0.271401i
$959$	−0.631244	+	1.94277i	−0.0203839	+	0.0627353i
$960$	3.73136	+	7.06508i	0.120429	+	0.228025i
$961$	−14.0407	−	10.2011i	−0.452924	−	0.329069i
$962$	33.6677	+	7.99589i	1.08549	+	0.257798i
$963$	−8.39122	−	25.8255i	−0.270403	−	0.832215i
$964$	−8.47401	−	1.29971i	−0.272929	−	0.0418609i
$965$	13.7440	+	18.9171i	0.442437	+	0.608962i
$966$	−6.87253	+	5.89881i	−0.221120	+	0.189791i
$967$	23.6696			0.761164			0.380582	−	0.924747i	$-0.375724\pi$
$967$	23.6696			0.761164			0.380582	+	0.924747i	$0.375724\pi$
$968$		0			0
$969$	−0.412063			−0.0132374
$970$	−10.6012	+	9.09921i	−0.340385	+	0.292158i
$971$	−31.7005	−	43.6320i	−1.01732	−	1.40022i	−0.914067	−	0.405563i	$-0.867076\pi$
$971$	−31.7005	−	43.6320i	−1.01732	−	1.40022i	−0.103251	−	0.994655i	$-0.532924\pi$
$972$	−30.3355	−	4.65275i	−0.973013	−	0.149237i
$973$	3.16566	+	9.74291i	0.101487	+	0.312343i
$974$	5.51059	+	1.30874i	0.176571	+	0.0419346i
$975$	6.78216	+	4.92753i	0.217203	+	0.157807i
$976$	5.38384	−	0.0526477i	0.172333	−	0.00168521i
$977$	−2.96528	+	9.12620i	−0.0948678	+	0.291973i	−0.987219	−	0.159368i	$-0.949054\pi$
$977$	−2.96528	+	9.12620i	−0.0948678	+	0.291973i	0.892351	+	0.451341i	$0.149054\pi$
$978$	−8.99601	−	5.48256i	−0.287661	−	0.175313i
$979$		0			0
$980$	5.37494	+	10.4226i	0.171696	+	0.332938i
$981$	20.8880	+	6.78691i	0.666901	+	0.216689i
$982$	15.7788	−	1.28064i	0.503523	−	0.0408669i
$983$	−20.7503	+	28.5603i	−0.661831	+	0.910932i	−0.999540	−	0.0303182i	$-0.990348\pi$
$983$	−20.7503	+	28.5603i	−0.661831	+	0.910932i	0.337709	+	0.941250i	$0.390348\pi$
$984$	11.7659	−	2.91617i	0.375083	−	0.0929639i
$985$	4.47735	−	1.45478i	0.142660	−	0.0463531i
$986$	−0.149927	−	0.359469i	−0.00477466	−	0.0114478i
$987$	9.56758	−	6.95125i	0.304539	−	0.221261i
$988$	9.12273	+	55.8306i	0.290233	+	1.77621i
$989$		−	10.0631i		−	0.319987i
$990$		0			0
$991$			17.8021i			0.565502i	0.959193	+	0.282751i	$0.0912471\pi$
$991$			17.8021i			0.565502i	−0.959193	+	0.282751i	$0.908753\pi$
$992$	−20.8098	+	1.89396i	−0.660711	+	0.0601333i
$993$	−20.3576	+	14.7907i	−0.646029	+	0.469367i
$994$	−14.8259	+	6.18360i	−0.470250	+	0.196132i
$995$	14.4477	−	4.69435i	0.458023	−	0.148821i
$996$	−3.80185	−	3.76486i	−0.120466	−	0.119294i
$997$	−36.9946	+	50.9188i	−1.17163	+	1.61261i	−0.519648	+	0.854380i	$0.673937\pi$
$997$	−36.9946	+	50.9188i	−1.17163	+	1.61261i	−0.651984	+	0.758233i	$0.726063\pi$
$998$	4.50358	+	55.4889i	0.142558	+	1.75647i
$999$	26.4145	+	8.58260i	0.835719	+	0.271542i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	484.2.g.f.475.4		16
4.3	odd	2	inner	484.2.g.f.475.3		16
11.2	odd	10		484.2.g.i.239.4		16
11.3	even	5		484.2.g.i.403.2		16
11.4	even	5		484.2.c.d.483.14		16
11.5	even	5		484.2.g.j.215.2		16
11.6	odd	10	inner	484.2.g.f.215.3		16
11.7	odd	10		484.2.c.d.483.3		16
11.8	odd	10		44.2.g.a.7.3	yes	16
11.9	even	5		44.2.g.a.19.1	yes	16
11.10	odd	2		484.2.g.j.475.1		16
33.8	even	10		396.2.r.a.271.2		16
33.20	odd	10		396.2.r.a.19.4		16
44.3	odd	10		484.2.g.i.403.4		16
44.7	even	10		484.2.c.d.483.13		16
44.15	odd	10		484.2.c.d.483.4		16
44.19	even	10		44.2.g.a.7.1	✓	16
44.27	odd	10		484.2.g.j.215.1		16
44.31	odd	10		44.2.g.a.19.3	yes	16
44.35	even	10		484.2.g.i.239.2		16
44.39	even	10	inner	484.2.g.f.215.4		16
44.43	even	2		484.2.g.j.475.2		16
88.19	even	10		704.2.u.c.447.2		16
88.53	even	10		704.2.u.c.63.2		16
88.75	odd	10		704.2.u.c.63.3		16
88.85	odd	10		704.2.u.c.447.3		16
132.107	odd	10		396.2.r.a.271.4		16
132.119	even	10		396.2.r.a.19.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
44.2.g.a.7.1	✓	16	44.19	even	10
44.2.g.a.7.3	yes	16	11.8	odd	10
44.2.g.a.19.1	yes	16	11.9	even	5
44.2.g.a.19.3	yes	16	44.31	odd	10
396.2.r.a.19.2		16	132.119	even	10
396.2.r.a.19.4		16	33.20	odd	10
396.2.r.a.271.2		16	33.8	even	10
396.2.r.a.271.4		16	132.107	odd	10
484.2.c.d.483.3		16	11.7	odd	10
484.2.c.d.483.4		16	44.15	odd	10
484.2.c.d.483.13		16	44.7	even	10
484.2.c.d.483.14		16	11.4	even	5
484.2.g.f.215.3		16	11.6	odd	10	inner
484.2.g.f.215.4		16	44.39	even	10	inner
484.2.g.f.475.3		16	4.3	odd	2	inner
484.2.g.f.475.4		16	1.1	even	1	trivial
484.2.g.i.239.2		16	44.35	even	10
484.2.g.i.239.4		16	11.2	odd	10
484.2.g.i.403.2		16	11.3	even	5
484.2.g.i.403.4		16	44.3	odd	10
484.2.g.j.215.1		16	44.27	odd	10
484.2.g.j.215.2		16	11.5	even	5
484.2.g.j.475.1		16	11.10	odd	2
484.2.g.j.475.2		16	44.43	even	2
704.2.u.c.63.2		16	88.53	even	10
704.2.u.c.63.3		16	88.75	odd	10
704.2.u.c.447.2		16	88.19	even	10
704.2.u.c.447.3		16	88.85	odd	10

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:	\( N \)	\(=\)	\( 484 = 2^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	484.g (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.07313 - 0.921084i) q^{2} +(0.435358 + 0.599219i) q^{3} +(0.303207 - 1.97688i) q^{4} +(-0.416683 - 1.28242i) q^{5} +(1.01913 + 0.242037i) q^{6} +(-1.31738 - 0.957131i) q^{7} +(-1.49550 - 2.40073i) q^{8} +(0.757524 - 2.33142i) q^{9} +(-1.62837 - 0.992398i) q^{10} +(1.31659 - 0.678965i) q^{12} +(3.38313 + 1.09925i) q^{13} +(-2.29531 + 0.186292i) q^{14} +(0.587043 - 0.807995i) q^{15} +(-3.81613 - 1.19881i) q^{16} +(0.0665412 - 0.0216205i) q^{17} +(-1.33451 - 3.19966i) q^{18} +(-6.43293 + 4.67380i) q^{19} +(-2.66153 + 0.434895i) q^{20} -1.20609i q^{21} -5.30988i q^{23} +(0.787485 - 1.94131i) q^{24} +(2.57411 - 1.87020i) q^{25} +(4.64303 - 1.93652i) q^{26} +(3.84010 - 1.24772i) q^{27} +(-2.29157 + 2.31409i) q^{28} +(2.31370 - 3.18453i) q^{29} +(-0.114260 - 1.40780i) q^{30} +(3.51309 + 1.14147i) q^{31} +(-5.19940 + 2.22850i) q^{32} +(0.0514928 - 0.0844916i) q^{34} +(-0.678513 + 2.08825i) q^{35} +(-4.37926 - 2.20444i) q^{36} +(5.56491 + 4.04314i) q^{37} +(-2.59840 + 10.9409i) q^{38} +(0.814185 + 2.50580i) q^{39} +(-2.45559 + 2.91819i) q^{40} +(3.40107 + 4.68117i) q^{41} +(-1.11091 - 1.29429i) q^{42} +1.89516 q^{43} -3.30550 q^{45} +(-4.89084 - 5.69818i) q^{46} +(5.76344 + 7.93270i) q^{47} +(-0.943034 - 2.80861i) q^{48} +(-1.34373 - 4.13559i) q^{49} +(1.03974 - 4.37794i) q^{50} +(0.0419247 + 0.0304601i) q^{51} +(3.19887 - 6.35475i) q^{52} +(-1.20135 + 3.69738i) q^{53} +(2.97166 - 4.87602i) q^{54} +(-0.327678 + 4.59405i) q^{56} +(-5.60126 - 1.81996i) q^{57} +(-0.450329 - 5.54852i) q^{58} +(-2.85758 + 3.93312i) q^{59} +(-1.41932 - 1.40551i) q^{60} +(-1.28015 + 0.415944i) q^{61} +(4.82139 - 2.01091i) q^{62} +(-3.22942 + 2.34631i) q^{63} +(-3.52698 + 7.18056i) q^{64} -4.79662i q^{65} +4.91303i q^{67} +(-0.0225655 - 0.138100i) q^{68} +(3.18178 - 2.31170i) q^{69} +(1.19532 + 2.86593i) q^{70} +(6.63416 - 2.15557i) q^{71} +(-6.72998 + 1.66802i) q^{72} +(-5.94967 + 8.18902i) q^{73} +(9.69594 - 0.786941i) q^{74} +(2.24132 + 0.728250i) q^{75} +(7.28904 + 14.1343i) q^{76} +(3.18178 + 1.93911i) q^{78} +(-1.85551 + 5.71067i) q^{79} +(0.0527412 + 5.39340i) q^{80} +(-3.53019 - 2.56484i) q^{81} +(7.96154 + 1.89082i) q^{82} +(-1.11615 - 3.43515i) q^{83} +(-2.38430 - 0.365696i) q^{84} +(-0.0554531 - 0.0763247i) q^{85} +(2.03375 - 1.74560i) q^{86} +2.91552 q^{87} -5.39711 q^{89} +(-3.54723 + 3.04465i) q^{90} +(-3.40474 - 4.68622i) q^{91} +(-10.4970 - 1.60999i) q^{92} +(0.845462 + 2.60206i) q^{93} +(13.4916 + 3.20418i) q^{94} +(8.67425 + 6.30221i) q^{95} +(-3.59896 - 2.14538i) q^{96} +(2.26393 - 6.96767i) q^{97} +(-5.25122 - 3.20032i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 5 q^{2} - q^{4} + 4 q^{5} + 10 q^{6} - 5 q^{8} + 10 q^{9} - 22 q^{12} - 2 q^{14} - 17 q^{16} - 10 q^{17} - 15 q^{18} - 24 q^{20} + 40 q^{24} - 4 q^{25} + 16 q^{26} - 30 q^{28} + 40 q^{29} + 30 q^{30}+ \cdots + 72 q^{97}+O(q^{100}) \) 16 * q - 5 * q^2 - q^4 + 4 * q^5 + 10 * q^6 - 5 * q^8 + 10 * q^9 - 22 * q^12 - 2 * q^14 - 17 * q^16 - 10 * q^17 - 15 * q^18 - 24 * q^20 + 40 * q^24 - 4 * q^25 + 16 * q^26 - 30 * q^28 + 40 * q^29 + 30 * q^30 - 6 * q^34 + 5 * q^36 - 12 * q^37 + 17 * q^38 - 50 * q^41 + 24 * q^42 + 40 * q^45 - 40 * q^46 - q^48 + 16 * q^49 + 25 * q^50 - 20 * q^52 - 12 * q^53 - 12 * q^56 - 50 * q^57 - 48 * q^60 + 20 * q^61 - 30 * q^62 - 37 * q^64 + 35 * q^68 + 4 * q^69 + 22 * q^70 - 10 * q^72 - 30 * q^73 + 60 * q^74 + 4 * q^78 + 32 * q^80 + 16 * q^81 + 46 * q^82 - 10 * q^84 + 60 * q^85 + 46 * q^86 - 36 * q^89 - 40 * q^90 - 54 * q^92 + 2 * q^93 + 60 * q^94 - 55 * q^96 + 72 * q^97

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