LMFDB - Embedded newform 990.2.t.a.131.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(131,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.131"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.t (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.6
Character	$\chi$	$=$	990.131
Dual form			990.2.t.a.461.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.28087 + 1.16592i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +(1.65015 + 0.526309i) q^{6} +(-0.700188 + 0.404254i) q^{7} +1.00000 q^{8} +(0.281268 - 2.98679i) q^{9} -1.00000i q^{10} +(-2.19142 + 2.48951i) q^{11} +(-0.369279 - 1.69223i) q^{12} +(1.59171 + 0.918976i) q^{13} +(0.700188 + 0.404254i) q^{14} +(-1.69223 + 0.369279i) q^{15} +(-0.500000 - 0.866025i) q^{16} +6.50173 q^{17} +(-2.72727 + 1.24981i) q^{18} +1.87055i q^{19} +(-0.866025 + 0.500000i) q^{20} +(0.425524 - 1.33416i) q^{21} +(3.25169 + 0.653075i) q^{22} +(-4.50121 - 2.59877i) q^{23} +(-1.28087 + 1.16592i) q^{24} +(0.500000 + 0.866025i) q^{25} -1.83795i q^{26} +(3.12208 + 4.15363i) q^{27} -0.808507i q^{28} +(-0.0530153 - 0.0918253i) q^{29} +(1.16592 + 1.28087i) q^{30} +(-3.25998 + 5.64645i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.0956298 - 5.74377i) q^{33} +(-3.25087 - 5.63067i) q^{34} -0.808507 q^{35} +(2.44600 + 1.73698i) q^{36} -4.15951 q^{37} +(1.61995 - 0.935276i) q^{38} +(-3.11023 + 0.678717i) q^{39} +(0.866025 + 0.500000i) q^{40} +(-1.74087 + 3.01528i) q^{41} +(-1.36818 + 0.298565i) q^{42} +(1.09708 - 0.633401i) q^{43} +(-1.06027 - 3.14258i) q^{44} +(1.73698 - 2.44600i) q^{45} +5.19755i q^{46} +(-4.05652 + 2.34204i) q^{47} +(1.65015 + 0.526309i) q^{48} +(-3.17316 + 5.49607i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-8.32789 + 7.58049i) q^{51} +(-1.59171 + 0.918976i) q^{52} -11.0936i q^{53} +(2.03611 - 4.78061i) q^{54} +(-3.14258 + 1.06027i) q^{55} +(-0.700188 + 0.404254i) q^{56} +(-2.18091 - 2.39594i) q^{57} +(-0.0530153 + 0.0918253i) q^{58} +(-1.38435 - 0.799257i) q^{59} +(0.526309 - 1.65015i) q^{60} +(-10.7598 + 6.21219i) q^{61} +6.51996 q^{62} +(1.01048 + 2.20501i) q^{63} +1.00000 q^{64} +(0.918976 + 1.59171i) q^{65} +(-4.92643 + 2.95470i) q^{66} +(-0.221611 + 0.383842i) q^{67} +(-3.25087 + 5.63067i) q^{68} +(8.79543 - 1.91934i) q^{69} +(0.404254 + 0.700188i) q^{70} +8.87630i q^{71} +(0.281268 - 2.98679i) q^{72} +14.6450i q^{73} +(2.07976 + 3.60224i) q^{74} +(-1.65015 - 0.526309i) q^{75} +(-1.61995 - 0.935276i) q^{76} +(0.528016 - 2.62902i) q^{77} +(2.14290 + 2.35418i) q^{78} +(-10.8062 + 6.23895i) q^{79} -1.00000i q^{80} +(-8.84178 - 1.68017i) q^{81} +3.48175 q^{82} +(-5.77334 - 9.99972i) q^{83} +(0.942653 + 1.03559i) q^{84} +(5.63067 + 3.25087i) q^{85} +(-1.09708 - 0.633401i) q^{86} +(0.174967 + 0.0558049i) q^{87} +(-2.19142 + 2.48951i) q^{88} +7.20794i q^{89} +(-2.98679 - 0.281268i) q^{90} -1.48600 q^{91} +(4.50121 - 2.59877i) q^{92} +(-2.40768 - 11.0333i) q^{93} +(4.05652 + 2.34204i) q^{94} +(-0.935276 + 1.61995i) q^{95} +(-0.369279 - 1.69223i) q^{96} +(5.63450 + 9.75924i) q^{97} +6.34632 q^{98} +(6.81925 + 7.24553i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 24 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{6} + 48 q^{8} + 10 q^{9} - 6 q^{11} + 4 q^{12} + 24 q^{13} - 4 q^{15} - 24 q^{16} - 12 q^{17} - 8 q^{18} - 16 q^{21} + 12 q^{22} + 36 q^{23} - 2 q^{24} + 24 q^{25}+ \cdots - 48 q^{99}+O(q^{100}) $ 48 * q - 24 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^6 + 48 * q^8 + 10 * q^9 - 6 * q^11 + 4 * q^12 + 24 * q^13 - 4 * q^15 - 24 * q^16 - 12 * q^17 - 8 * q^18 - 16 * q^21 + 12 * q^22 + 36 * q^23 - 2 * q^24 + 24 * q^25 - 8 * q^27 + 8 * q^30 - 24 * q^32 + 2 * q^33 + 6 * q^34 - 2 * q^36 - 6 * q^38 - 40 * q^39 - 6 * q^41 + 8 * q^42 + 30 * q^43 - 6 * q^44 - 2 * q^48 + 24 * q^49 + 24 * q^50 + 22 * q^51 - 24 * q^52 + 22 * q^54 + 40 * q^57 - 54 * q^59 - 4 * q^60 - 38 * q^63 + 48 * q^64 + 8 * q^66 - 6 * q^67 + 6 * q^68 + 76 * q^69 + 10 * q^72 + 2 * q^75 + 6 * q^76 + 6 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 + 36 * q^83 + 8 * q^84 - 30 * q^86 - 44 * q^87 - 6 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 + 4 * q^96 + 6 * q^97 - 48 * q^98 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.28087	+	1.16592i	−0.739512	+	0.673143i
$3$	−1.28087	+	1.16592i	−0.739512	+	0.673143i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$	1.65015	+	0.526309i	0.673671	+	0.214865i
$7$	−0.700188	+	0.404254i	−0.264646	+	0.152793i	−0.626452	−	0.779460i	$-0.715494\pi$
$7$	−0.700188	+	0.404254i	−0.264646	+	0.152793i	0.361806	+	0.932253i	$0.382160\pi$
$8$	1.00000			0.353553
$9$	0.281268	−	2.98679i	0.0937559	−	0.995595i
$10$		−	1.00000i		−	0.316228i
$11$	−2.19142	+	2.48951i	−0.660739	+	0.750615i
$11$	−2.19142	+	2.48951i	−0.660739	+	0.750615i
$12$	−0.369279	−	1.69223i	−0.106602	−	0.488504i
$13$	1.59171	+	0.918976i	0.441462	+	0.254878i	0.704218	−	0.709984i	$-0.251298\pi$
$13$	1.59171	+	0.918976i	0.441462	+	0.254878i	−0.262756	+	0.964862i	$0.584631\pi$
$14$	0.700188	+	0.404254i	0.187133	+	0.108041i
$15$	−1.69223	+	0.369279i	−0.436931	+	0.0953474i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	6.50173			1.57690			0.788451	−	0.615098i	$-0.210883\pi$
$17$	6.50173			1.57690			0.788451	+	0.615098i	$0.210883\pi$
$18$	−2.72727	+	1.24981i	−0.642823	+	0.294583i
$19$			1.87055i			0.429134i	0.976709	+	0.214567i	$0.0688340\pi$
$19$			1.87055i			0.429134i	−0.976709	+	0.214567i	$0.931166\pi$
$20$	−0.866025	+	0.500000i	−0.193649	+	0.111803i
$21$	0.425524	−	1.33416i	0.0928570	−	0.291137i
$22$	3.25169	+	0.653075i	0.693263	+	0.139236i
$23$	−4.50121	−	2.59877i	−0.938567	−	0.541882i	−0.0490560	−	0.998796i	$-0.515621\pi$
$23$	−4.50121	−	2.59877i	−0.938567	−	0.541882i	−0.889511	+	0.456914i	$0.848955\pi$
$24$	−1.28087	+	1.16592i	−0.261457	+	0.237992i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$		−	1.83795i		−	0.360452i
$27$	3.12208	+	4.15363i	0.600845	+	0.799366i
$28$		−	0.808507i		−	0.152793i
$29$	−0.0530153	−	0.0918253i	−0.00984470	−	0.0170515i	0.861061	−	0.508502i	$-0.169800\pi$
$29$	−0.0530153	−	0.0918253i	−0.00984470	−	0.0170515i	−0.870906	+	0.491450i	$0.836467\pi$
$30$	1.16592	+	1.28087i	0.212867	+	0.233854i
$31$	−3.25998	+	5.64645i	−0.585510	+	1.01413i	0.409302	+	0.912399i	$0.365772\pi$
$31$	−3.25998	+	5.64645i	−0.585510	+	1.01413i	−0.994812	+	0.101733i	$0.967561\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−0.0956298	−	5.74377i	−0.0166470	−	0.999861i
$34$	−3.25087	−	5.63067i	−0.557519	−	0.965651i
$35$	−0.808507			−0.136663
$36$	2.44600	+	1.73698i	0.407666	+	0.289496i
$37$	−4.15951			−0.683820			−0.341910	−	0.939733i	$-0.611074\pi$
$37$	−4.15951			−0.683820			−0.341910	+	0.939733i	$0.611074\pi$
$38$	1.61995	−	0.935276i	0.262790	−	0.151722i
$39$	−3.11023	+	0.678717i	−0.498036	+	0.108682i
$40$	0.866025	+	0.500000i	0.136931	+	0.0790569i
$41$	−1.74087	+	3.01528i	−0.271879	+	0.470908i	−0.969343	−	0.245712i	$-0.920978\pi$
$41$	−1.74087	+	3.01528i	−0.271879	+	0.470908i	0.697464	+	0.716620i	$0.254312\pi$
$42$	−1.36818	+	0.298565i	−0.211114	+	0.0460695i
$43$	1.09708	−	0.633401i	0.167304	−	0.0965928i	−0.414010	−	0.910272i	$-0.635872\pi$
$43$	1.09708	−	0.633401i	0.167304	−	0.0965928i	0.581314	+	0.813679i	$0.302539\pi$
$44$	−1.06027	−	3.14258i	−0.159841	−	0.473762i
$45$	1.73698	−	2.44600i	0.258933	−	0.364628i
$46$			5.19755i			0.766336i
$47$	−4.05652	+	2.34204i	−0.591705	+	0.341621i	−0.765771	−	0.643113i	$-0.777643\pi$
$47$	−4.05652	+	2.34204i	−0.591705	+	0.341621i	0.174066	+	0.984734i	$0.444309\pi$
$48$	1.65015	+	0.526309i	0.238179	+	0.0759661i
$49$	−3.17316	+	5.49607i	−0.453308	+	0.785153i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−8.32789	+	7.58049i	−1.16614	+	1.06148i
$52$	−1.59171	+	0.918976i	−0.220731	+	0.127439i
$53$		−	11.0936i		−	1.52382i	−0.647682	−	0.761911i	$-0.724261\pi$
$53$		−	11.0936i		−	1.52382i	0.647682	−	0.761911i	$-0.275739\pi$
$54$	2.03611	−	4.78061i	0.277079	−	0.650559i
$55$	−3.14258	+	1.06027i	−0.423746	+	0.142966i
$56$	−0.700188	+	0.404254i	−0.0935665	+	0.0540207i
$57$	−2.18091	−	2.39594i	−0.288869	−	0.317350i
$58$	−0.0530153	+	0.0918253i	−0.00696125	+	0.0120572i
$59$	−1.38435	−	0.799257i	−0.180228	−	0.104054i	0.407172	−	0.913351i	$-0.366515\pi$
$59$	−1.38435	−	0.799257i	−0.180228	−	0.104054i	−0.587400	+	0.809297i	$0.699848\pi$
$60$	0.526309	−	1.65015i	0.0679462	−	0.213034i
$61$	−10.7598	+	6.21219i	−1.37766	+	0.795390i	−0.991877	−	0.127201i	$-0.959401\pi$
$61$	−10.7598	+	6.21219i	−1.37766	+	0.795390i	−0.385779	+	0.922591i	$0.626067\pi$
$62$	6.51996			0.828036
$63$	1.01048	+	2.20501i	0.127308	+	0.277806i
$64$	1.00000			0.125000
$65$	0.918976	+	1.59171i	0.113985	+	0.197428i
$66$	−4.92643	+	2.95470i	−0.606402	+	0.363699i
$67$	−0.221611	+	0.383842i	−0.0270741	+	0.0468937i	−0.879245	−	0.476370i	$-0.841952\pi$
$67$	−0.221611	+	0.383842i	−0.0270741	+	0.0468937i	0.852171	+	0.523264i	$0.175286\pi$
$68$	−3.25087	+	5.63067i	−0.394225	+	0.682819i
$69$	8.79543	−	1.91934i	1.05885	−	0.231062i
$70$	0.404254	+	0.700188i	0.0483175	+	0.0836884i
$71$			8.87630i			1.05342i	0.850044	+	0.526711i	$0.176575\pi$
$71$			8.87630i			1.05342i	−0.850044	+	0.526711i	$0.823425\pi$
$72$	0.281268	−	2.98679i	0.0331477	−	0.351996i
$73$			14.6450i			1.71407i	0.515262	+	0.857033i	$0.327695\pi$
$73$			14.6450i			1.71407i	−0.515262	+	0.857033i	$0.672305\pi$
$74$	2.07976	+	3.60224i	0.241767	+	0.418752i
$75$	−1.65015	−	0.526309i	−0.190543	−	0.0607729i
$76$	−1.61995	−	0.935276i	−0.185820	−	0.107283i
$77$	0.528016	−	2.62902i	0.0601730	−	0.299604i
$78$	2.14290	+	2.35418i	0.242636	+	0.266559i
$79$	−10.8062	+	6.23895i	−1.21579	+	0.701937i	−0.964015	−	0.265848i	$-0.914348\pi$
$79$	−10.8062	+	6.23895i	−1.21579	+	0.701937i	−0.251776	+	0.967786i	$0.581015\pi$
$80$		−	1.00000i		−	0.111803i
$81$	−8.84178	−	1.68017i	−0.982420	−	0.186686i
$82$	3.48175			0.384495
$83$	−5.77334	−	9.99972i	−0.633707	−	1.09761i	−0.986788	−	0.162019i	$-0.948199\pi$
$83$	−5.77334	−	9.99972i	−0.633707	−	1.09761i	0.353081	−	0.935593i	$-0.385134\pi$
$84$	0.942653	+	1.03559i	0.102852	+	0.112993i
$85$	5.63067	+	3.25087i	0.610732	+	0.352606i
$86$	−1.09708	−	0.633401i	−0.118302	−	0.0683014i
$87$	0.174967	+	0.0558049i	0.0187584	+	0.00598291i
$88$	−2.19142	+	2.48951i	−0.233607	+	0.265383i
$89$			7.20794i			0.764040i	0.924154	+	0.382020i	$0.124771\pi$
$89$			7.20794i			0.764040i	−0.924154	+	0.382020i	$0.875229\pi$
$90$	−2.98679	−	0.281268i	−0.314835	−	0.0296482i
$91$	−1.48600			−0.155775
$92$	4.50121	−	2.59877i	0.469283	−	0.270941i
$93$	−2.40768	−	11.0333i	−0.249665	−	1.14409i
$94$	4.05652	+	2.34204i	0.418399	+	0.241563i
$95$	−0.935276	+	1.61995i	−0.0959573	+	0.166203i
$96$	−0.369279	−	1.69223i	−0.0376894	−	0.172712i
$97$	5.63450	+	9.75924i	0.572097	+	0.990901i	0.996350	+	0.0853575i	$0.0272032\pi$
$97$	5.63450	+	9.75924i	0.572097	+	0.990901i	−0.424253	+	0.905543i	$0.639463\pi$
$98$	6.34632			0.641075
$99$	6.81925	+	7.24553i	0.685361	+	0.728204i
$100$	−1.00000			−0.100000
$101$	5.71591	+	9.90025i	0.568755	+	0.985112i	0.996689	+	0.0813024i	$0.0259080\pi$
$101$	5.71591	+	9.90025i	0.568755	+	0.985112i	−0.427935	+	0.903810i	$0.640759\pi$
$102$	10.7288	+	3.42192i	1.06231	+	0.338820i
$103$	−6.50932	+	11.2745i	−0.641382	+	1.11091i	0.343742	+	0.939064i	$0.388305\pi$
$103$	−6.50932	+	11.2745i	−0.641382	+	1.11091i	−0.985124	+	0.171842i	$0.945028\pi$
$104$	1.59171	+	0.918976i	0.156080	+	0.0901130i
$105$	1.03559	−	0.942653i	0.101064	−	0.0919936i
$106$	−9.60733	+	5.54680i	−0.933147	+	0.538753i
$107$	19.5145			1.88654			0.943268	−	0.332032i	$-0.107734\pi$
$107$	19.5145			1.88654			0.943268	+	0.332032i	$0.107734\pi$
$108$	−5.15819	+	0.626989i	−0.496347	+	0.0603320i
$109$		−	3.12788i		−	0.299596i	−0.988717	−	0.149798i	$-0.952138\pi$
$109$		−	3.12788i		−	0.299596i	0.988717	−	0.149798i	$-0.0478624\pi$
$110$	2.48951	+	2.19142i	0.237365	+	0.208944i
$111$	5.32781	−	4.84965i	0.505693	−	0.460309i
$112$	0.700188	+	0.404254i	0.0661615	+	0.0381984i
$113$	−0.700012	−	0.404152i	−0.0658516	−	0.0380194i	0.466713	−	0.884409i	$-0.345438\pi$
$113$	−0.700012	−	0.404152i	−0.0658516	−	0.0380194i	−0.532564	+	0.846390i	$0.678772\pi$
$114$	−0.984487	+	3.08669i	−0.0922057	+	0.289095i
$115$	−2.59877	−	4.50121i	−0.242337	−	0.419740i
$116$	0.106031			0.00984470
$117$	3.19248	−	4.49563i	0.295145	−	0.415621i
$118$			1.59851i			0.147155i
$119$	−4.55243	+	2.62835i	−0.417321	+	0.240940i
$120$	−1.69223	+	0.369279i	−0.154479	+	0.0337104i
$121$	−1.39531	−	10.9111i	−0.126847	−	0.991922i
$122$	10.7598	+	6.21219i	0.974150	+	0.562426i
$123$	−1.28574	−	5.89191i	−0.115931	−	0.531255i
$124$	−3.25998	−	5.64645i	−0.292755	−	0.507066i
$125$			1.00000i			0.0894427i
$126$	1.40436	−	1.97761i	0.125110	−	0.176179i
$127$		−	21.3573i		−	1.89516i	−0.319523	−	0.947579i	$-0.603523\pi$
$127$		−	21.3573i		−	1.89516i	0.319523	−	0.947579i	$-0.396477\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−0.666729	+	2.09042i	−0.0587022	+	0.184051i
$130$	0.918976	−	1.59171i	0.0805995	−	0.139603i
$131$	3.08156	−	5.33742i	0.269237	−	0.466332i	−0.699428	−	0.714703i	$-0.746562\pi$
$131$	3.08156	−	5.33742i	0.269237	−	0.466332i	0.968665	+	0.248371i	$0.0798952\pi$
$132$	5.02206	+	2.78907i	0.437114	+	0.242757i
$133$	−0.756177	−	1.30974i	−0.0655689	−	0.113569i
$134$	0.443222			0.0382886
$135$	0.626989	+	5.15819i	0.0539626	+	0.443946i
$136$	6.50173			0.557519
$137$	−8.74723	+	5.05022i	−0.747326	+	0.431469i	−0.824727	−	0.565531i	$-0.808671\pi$
$137$	−8.74723	+	5.05022i	−0.747326	+	0.431469i	0.0774007	+	0.997000i	$0.475338\pi$
$138$	−6.05992	−	6.65739i	−0.515854	−	0.566715i
$139$	10.7266	+	6.19303i	0.909821	+	0.525286i	0.880374	−	0.474281i	$-0.157292\pi$
$139$	10.7266	+	6.19303i	0.909821	+	0.525286i	0.0294478	+	0.999566i	$0.490625\pi$
$140$	0.404254	−	0.700188i	0.0341657	−	0.0591767i
$141$	2.46527	−	7.72943i	0.207613	−	0.650935i
$142$	7.68710	−	4.43815i	0.645087	−	0.372441i
$143$	−5.77592	+	1.94872i	−0.483007	+	0.162960i
$144$	−2.72727	+	1.24981i	−0.227272	+	0.104151i
$145$		−	0.106031i		−	0.00880537i
$146$	12.6829	−	7.32249i	1.04965	−	0.606014i
$147$	−2.34356	−	10.7394i	−0.193294	−	0.885772i
$148$	2.07976	−	3.60224i	0.170955	−	0.296103i
$149$	10.3389	−	17.9074i	0.846992	−	1.46703i	−0.0368876	−	0.999319i	$-0.511744\pi$
$149$	10.3389	−	17.9074i	0.846992	−	1.46703i	0.883880	−	0.467714i	$-0.154922\pi$
$150$	0.369279	+	1.69223i	0.0301515	+	0.138170i
$151$	−17.5811	+	10.1504i	−1.43073	+	0.826031i	−0.997176	−	0.0750981i	$-0.976073\pi$
$151$	−17.5811	+	10.1504i	−1.43073	+	0.826031i	−0.433551	+	0.901129i	$0.642740\pi$
$152$			1.87055i			0.151722i
$153$	1.82873	−	19.4193i	0.147844	−	1.56996i
$154$	−2.54080	+	0.857232i	−0.204744	+	0.0690778i
$155$	−5.64645	+	3.25998i	−0.453534	+	0.261848i
$156$	0.967330	−	3.03290i	0.0774484	−	0.242826i
$157$	1.07419	−	1.86056i	0.0857301	−	0.148489i	−0.819972	−	0.572404i	$-0.806011\pi$
$157$	1.07419	−	1.86056i	0.0857301	−	0.148489i	0.905702	+	0.423915i	$0.139344\pi$
$158$	10.8062	+	6.23895i	0.859694	+	0.496345i
$159$	12.9342	+	14.2095i	1.02575	+	1.12688i
$160$	−0.866025	+	0.500000i	−0.0684653	+	0.0395285i
$161$	4.20225			0.331184
$162$	2.96582	+	8.49729i	0.233017	+	0.667610i
$163$	−11.8388			−0.927287			−0.463643	−	0.886022i	$-0.653458\pi$
$163$	−11.8388			−0.927287			−0.463643	+	0.886022i	$0.653458\pi$
$164$	−1.74087	−	3.01528i	−0.135939	−	0.235454i
$165$	2.78907	−	5.02206i	0.217128	−	0.390967i
$166$	−5.77334	+	9.99972i	−0.448098	+	0.776129i
$167$	11.4316	−	19.8001i	0.884604	−	1.53218i	0.0384373	−	0.999261i	$-0.487762\pi$
$167$	11.4316	−	19.8001i	0.884604	−	1.53218i	0.846167	−	0.532918i	$-0.178905\pi$
$168$	0.425524	−	1.33416i	0.0328299	−	0.102933i
$169$	−4.81097	−	8.33284i	−0.370074	−	0.640987i
$170$		−	6.50173i		−	0.498660i
$171$	5.58694	+	0.526125i	0.427244	+	0.0402338i
$172$			1.26680i			0.0965928i
$173$	2.53267	+	4.38671i	0.192555	+	0.333515i	0.946096	−	0.323886i	$-0.104989\pi$
$173$	2.53267	+	4.38671i	0.192555	+	0.333515i	−0.753541	+	0.657401i	$0.771656\pi$
$174$	−0.0391549	−	0.179428i	−0.00296833	−	0.0136024i
$175$	−0.700188	−	0.404254i	−0.0529292	−	0.0305587i
$176$	3.25169	+	0.653075i	0.245105	+	0.0492274i
$177$	2.70505	−	0.590298i	0.203324	−	0.0443695i
$178$	6.24226	−	3.60397i	0.467877	−	0.270129i
$179$		−	0.683164i		−	0.0510621i	−0.999674	−	0.0255310i	$-0.991872\pi$
$179$		−	0.683164i		−	0.0510621i	0.999674	−	0.0255310i	$-0.00812767\pi$
$180$	1.24981	+	2.72727i	0.0931552	+	0.203278i
$181$	−9.74615			−0.724425			−0.362213	−	0.932095i	$-0.617979\pi$
$181$	−9.74615			−0.724425			−0.362213	+	0.932095i	$0.617979\pi$
$182$	0.742999	+	1.28691i	0.0550747	+	0.0953922i
$183$	6.53906	−	20.5021i	0.483381	−	1.51556i
$184$	−4.50121	−	2.59877i	−0.331833	−	0.191584i
$185$	−3.60224	−	2.07976i	−0.264842	−	0.152907i
$186$	−8.35123	+	7.60174i	−0.612342	+	0.557387i
$187$	−14.2481	+	16.1861i	−1.04192	+	1.18365i
$188$		−	4.68407i		−	0.341621i
$189$	−3.86516	−	1.64621i	−0.281149	−	0.119744i
$190$	1.87055			0.135704
$191$	−5.09125	+	2.93944i	−0.368390	+	0.212690i	−0.672755	−	0.739865i	$-0.734889\pi$
$191$	−5.09125	+	2.93944i	−0.368390	+	0.212690i	0.304365	+	0.952556i	$0.401556\pi$
$192$	−1.28087	+	1.16592i	−0.0924390	+	0.0841429i
$193$	1.52540	+	0.880691i	0.109801	+	0.0633935i	0.553895	−	0.832587i	$-0.313141\pi$
$193$	1.52540	+	0.880691i	0.109801	+	0.0633935i	−0.444094	+	0.895980i	$0.646474\pi$
$194$	5.63450	−	9.75924i	0.404534	−	0.700673i
$195$	−3.03290	−	0.967330i	−0.217190	−	0.0692720i
$196$	−3.17316	−	5.49607i	−0.226654	−	0.392577i
$197$	−2.26771			−0.161568			−0.0807839	−	0.996732i	$-0.525742\pi$
$197$	−2.26771			−0.161568			−0.0807839	+	0.996732i	$0.525742\pi$
$198$	2.86519	−	9.52841i	0.203620	−	0.677155i
$199$	23.0129			1.63134			0.815669	−	0.578519i	$-0.196369\pi$
$199$	23.0129			1.63134			0.815669	+	0.578519i	$0.196369\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	−0.163673	−	0.750033i	−0.0115446	−	0.0529032i
$202$	5.71591	−	9.90025i	0.402170	−	0.696579i
$203$	0.0742414	+	0.0428633i	0.00521072	+	0.00300841i
$204$	−2.40095	−	11.0024i	−0.168100	−	0.770323i
$205$	−3.01528	+	1.74087i	−0.210596	+	0.121588i
$206$	13.0186			0.907051
$207$	−9.02802	+	12.7132i	−0.627491	+	0.883628i
$208$		−	1.83795i		−	0.127439i
$209$	−4.65676	−	4.09917i	−0.322115	−	0.283546i
$210$	−1.33416	−	0.425524i	−0.0920657	−	0.0293640i
$211$	6.07694	+	3.50852i	0.418354	+	0.241537i	0.694373	−	0.719616i	$-0.255682\pi$
$211$	6.07694	+	3.50852i	0.418354	+	0.241537i	−0.276019	+	0.961152i	$0.589015\pi$
$212$	9.60733	+	5.54680i	0.659834	+	0.380956i
$213$	−10.3490	−	11.3694i	−0.709104	−	0.779018i
$214$	−9.75724	−	16.9000i	−0.666991	−	1.15526i
$215$	1.26680			0.0863952
$216$	3.12208	+	4.15363i	0.212431	+	0.282618i
$217$		−	5.27143i		−	0.357848i
$218$	−2.70882	+	1.56394i	−0.183465	+	0.105923i
$219$	−17.0749	−	18.7584i	−1.15381	−	1.26757i
$220$	0.653075	−	3.25169i	0.0440303	−	0.219229i
$221$	10.3489	+	5.97494i	0.696142	+	0.401918i
$222$	−6.86383	−	2.18919i	−0.460670	−	0.146929i
$223$	8.66329	+	15.0053i	0.580136	+	1.00483i	0.995463	+	0.0951533i	$0.0303341\pi$
$223$	8.66329	+	15.0053i	0.580136	+	1.00483i	−0.415326	+	0.909673i	$0.636333\pi$
$224$		−	0.808507i		−	0.0540207i
$225$	2.72727	−	1.24981i	0.181818	−	0.0833205i
$226$			0.808304i			0.0537676i
$227$	−3.93984	−	6.82400i	−0.261496	−	0.452925i	0.705144	−	0.709065i	$-0.250883\pi$
$227$	−3.93984	−	6.82400i	−0.261496	−	0.452925i	−0.966640	+	0.256140i	$0.917549\pi$
$228$	3.16540	−	0.690755i	0.209634	−	0.0457464i
$229$	3.92425	−	6.79701i	0.259322	−	0.449159i	−0.706739	−	0.707475i	$-0.749834\pi$
$229$	3.92425	−	6.79701i	0.259322	−	0.449159i	0.966060	+	0.258316i	$0.0831676\pi$
$230$	−2.59877	+	4.50121i	−0.171358	+	0.296801i
$231$	2.38890	+	3.98306i	0.157178	+	0.262066i
$232$	−0.0530153	−	0.0918253i	−0.00348063	−	0.00602862i
$233$	6.38805			0.418495			0.209247	−	0.977863i	$-0.432899\pi$
$233$	6.38805			0.418495			0.209247	+	0.977863i	$0.432899\pi$
$234$	−5.48957	−	0.516956i	−0.358864	−	0.0337945i
$235$	−4.68407			−0.305555
$236$	1.38435	−	0.799257i	0.0901138	−	0.0520272i
$237$	6.56723	−	20.5904i	0.426587	−	1.33749i
$238$	4.55243	+	2.62835i	0.295090	+	0.170371i
$239$	−7.14471	+	12.3750i	−0.462153	+	0.800472i	−0.999068	−	0.0431641i	$-0.986256\pi$
$239$	−7.14471	+	12.3750i	−0.462153	+	0.800472i	0.536915	+	0.843636i	$0.319590\pi$
$240$	1.16592	+	1.28087i	0.0752597	+	0.0826799i
$241$	5.57754	−	3.22019i	0.359281	−	0.207431i	−0.309484	−	0.950905i	$-0.600156\pi$
$241$	5.57754	−	3.22019i	0.359281	−	0.207431i	0.668765	+	0.743474i	$0.266823\pi$
$242$	−8.75167	+	6.66395i	−0.562579	+	0.428375i
$243$	13.2841	−	8.15671i	0.852177	−	0.523253i
$244$		−	12.4244i		−	0.795390i
$245$	−5.49607	+	3.17316i	−0.351131	+	0.202726i
$246$	−4.45967	+	4.05943i	−0.284338	+	0.258820i
$247$	−1.71899	+	2.97738i	−0.109377	+	0.189446i
$248$	−3.25998	+	5.64645i	−0.207009	+	0.358550i
$249$	19.0538	+	6.07712i	1.20748	+	0.385122i
$250$	0.866025	−	0.500000i	0.0547723	−	0.0316228i
$251$		−	3.07565i		−	0.194134i	−0.995278	−	0.0970668i	$-0.969054\pi$
$251$		−	3.07565i		−	0.194134i	0.995278	−	0.0970668i	$-0.0309460\pi$
$252$	−2.41484	−	0.227407i	−0.152120	−	0.0143253i
$253$	16.3337	−	5.51078i	1.02689	−	0.346460i
$254$	−18.4960	+	10.6787i	−1.16054	+	0.670039i
$255$	−11.0024	+	2.40095i	−0.688998	+	0.150354i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.2896	−	7.09539i	−0.766603	−	0.442598i	0.0650588	−	0.997881i	$-0.479277\pi$
$257$	−12.2896	−	7.09539i	−0.766603	−	0.442598i	−0.831661	+	0.555283i	$0.812610\pi$
$258$	2.14372	−	0.467804i	0.133462	−	0.0291242i
$259$	2.91244	−	1.68150i	0.180970	−	0.104483i
$260$	−1.83795			−0.113985
$261$	−0.289174	+	0.132518i	−0.0178994	+	0.00820266i
$262$	−6.16312			−0.380759
$263$	13.1025	+	22.6943i	0.807938	+	1.39939i	0.914290	+	0.405061i	$0.132750\pi$
$263$	13.1025	+	22.6943i	0.807938	+	1.39939i	−0.106352	+	0.994329i	$0.533917\pi$
$264$	−0.0956298	−	5.74377i	−0.00588561	−	0.353504i
$265$	5.54680	−	9.60733i	0.340737	−	0.590174i
$266$	−0.756177	+	1.30974i	−0.0463642	+	0.0803051i
$267$	−8.40387	−	9.23244i	−0.514308	−	0.565016i
$268$	−0.221611	−	0.383842i	−0.0135371	−	0.0234469i
$269$			6.72917i			0.410285i	0.978732	+	0.205142i	$0.0657658\pi$
$269$			6.72917i			0.410285i	−0.978732	+	0.205142i	$0.934234\pi$
$270$	4.15363	−	3.12208i	0.252782	−	0.190004i
$271$			11.8647i			0.720730i	0.932811	+	0.360365i	$0.117348\pi$
$271$			11.8647i			0.720730i	−0.932811	+	0.360365i	$0.882652\pi$
$272$	−3.25087	−	5.63067i	−0.197113	−	0.341409i
$273$	1.90337	−	1.73255i	0.115197	−	0.104859i
$274$	8.74723	+	5.05022i	0.528440	+	0.305095i
$275$	−3.25169	−	0.653075i	−0.196084	−	0.0393819i
$276$	−2.73551	+	8.57674i	−0.164659	+	0.516259i
$277$	5.70227	−	3.29221i	0.342616	−	0.197810i	−0.318812	−	0.947818i	$-0.603284\pi$
$277$	5.70227	−	3.29221i	0.342616	−	0.197810i	0.661428	+	0.750008i	$0.269951\pi$
$278$		−	12.3861i		−	0.742866i
$279$	15.9478	+	11.3250i	0.954770	+	0.678011i
$280$	−0.808507			−0.0483175
$281$	−12.5438	−	21.7265i	−0.748302	−	1.29610i	−0.948636	−	0.316369i	$-0.897536\pi$
$281$	−12.5438	−	21.7265i	−0.748302	−	1.29610i	0.200334	−	0.979728i	$-0.435797\pi$
$282$	−7.92651	+	1.72973i	−0.472017	+	0.103004i
$283$	18.9030	+	10.9137i	1.12367	+	0.648751i	0.942335	−	0.334671i	$-0.108625\pi$
$283$	18.9030	+	10.9137i	1.12367	+	0.648751i	0.181334	+	0.983421i	$0.441958\pi$
$284$	−7.68710	−	4.43815i	−0.456145	−	0.263356i
$285$	−0.690755	−	3.16540i	−0.0409168	−	0.187502i
$286$	4.57560	+	4.02774i	0.270561	+	0.238165i
$287$		−	2.81502i		−	0.166165i
$288$	2.44600	+	1.73698i	0.144132	+	0.102352i
$289$	25.2725			1.48662
$290$	−0.0918253	+	0.0530153i	−0.00539216	+	0.00311317i
$291$	−18.5956	−	5.93097i	−1.09009	−	0.347680i
$292$	−12.6829	−	7.32249i	−0.742212	−	0.428516i
$293$	−5.87689	+	10.1791i	−0.343331	+	0.594667i	−0.985049	−	0.172274i	$-0.944889\pi$
$293$	−5.87689	+	10.1791i	−0.343331	+	0.594667i	0.641718	+	0.766941i	$0.278222\pi$
$294$	−8.12882	+	7.39929i	−0.474082	+	0.431535i
$295$	−0.799257	−	1.38435i	−0.0465346	−	0.0806002i
$296$	−4.15951			−0.241767
$297$	−17.1823	−	1.32991i	−0.997018	−	0.0771692i
$298$	−20.6777			−1.19783
$299$	−4.77642	−	8.27301i	−0.276228	−	0.478440i
$300$	1.28087	−	1.16592i	0.0739512	−	0.0673143i
$301$	−0.512110	+	0.887000i	−0.0295175	+	0.0511258i
$302$	17.5811	+	10.1504i	1.01168	+	0.584092i
$303$	−18.8642	−	6.01667i	−1.08372	−	0.345649i
$304$	1.61995	−	0.935276i	0.0929102	−	0.0536417i
$305$	−12.4244			−0.711418
$306$	−17.7320	+	8.12592i	−1.01367	+	0.464528i
$307$		−	4.46253i		−	0.254690i	−0.991858	−	0.127345i	$-0.959354\pi$
$307$		−	4.46253i		−	0.254690i	0.991858	−	0.127345i	$-0.0406456\pi$
$308$	2.01279	+	1.77178i	0.114689	+	0.100957i
$309$	−4.80751	−	22.0305i	−0.273490	−	1.25327i
$310$	5.64645	+	3.25998i	0.320697	+	0.185154i
$311$	7.44194	+	4.29660i	0.421993	+	0.243638i	0.695930	−	0.718110i	$-0.254992\pi$
$311$	7.44194	+	4.29660i	0.421993	+	0.243638i	−0.273936	+	0.961748i	$0.588326\pi$
$312$	−3.11023	+	0.678717i	−0.176082	+	0.0384248i
$313$	−1.02823	−	1.78094i	−0.0581189	−	0.100665i	0.835502	−	0.549487i	$-0.185177\pi$
$313$	−1.02823	−	1.78094i	−0.0581189	−	0.100665i	−0.893621	+	0.448822i	$0.851844\pi$
$314$	−2.14839			−0.121241
$315$	−0.227407	+	2.41484i	−0.0128129	+	0.136061i
$316$		−	12.4779i		−	0.701937i
$317$	3.40370	−	1.96513i	0.191171	−	0.110373i	−0.401360	−	0.915920i	$-0.631462\pi$
$317$	3.40370	−	1.96513i	0.191171	−	0.110373i	0.592531	+	0.805548i	$0.298129\pi$
$318$	5.83865	−	18.3061i	0.327415	−	1.02656i
$319$	0.344779	+	0.0692460i	0.0193039	+	0.00387703i
$320$	0.866025	+	0.500000i	0.0484123	+	0.0279508i
$321$	−24.9956	+	22.7523i	−1.39512	+	1.26991i
$322$	−2.10113	−	3.63926i	−0.117091	−	0.202808i
$323$			12.1618i			0.676702i
$324$	5.87596	−	6.81712i	0.326442	−	0.378729i
$325$			1.83795i			0.101951i
$326$	5.91940	+	10.2527i	0.327845	+	0.567845i
$327$	3.64685	+	4.00641i	0.201671	+	0.221555i
$328$	−1.74087	+	3.01528i	−0.0961237	+	0.166491i
$329$	1.89355	−	3.27973i	0.104395	−	0.180817i
$330$	−5.74377	+	0.0956298i	−0.316184	+	0.00526425i
$331$	−7.61257	−	13.1854i	−0.418424	−	0.724732i	0.577357	−	0.816492i	$-0.304084\pi$
$331$	−7.61257	−	13.1854i	−0.418424	−	0.724732i	−0.995781	+	0.0917596i	$0.970751\pi$
$332$	11.5467			0.633707
$333$	−1.16994	+	12.4236i	−0.0641121	+	0.680808i
$334$	−22.8632			−1.25102
$335$	−0.383842	+	0.221611i	−0.0209715	+	0.0121079i
$336$	−1.36818	+	0.298565i	−0.0746402	+	0.0162880i
$337$	5.77401	+	3.33363i	0.314530	+	0.181594i	0.648952	−	0.760829i	$-0.275208\pi$
$337$	5.77401	+	3.33363i	0.314530	+	0.181594i	−0.334422	+	0.942424i	$0.608541\pi$
$338$	−4.81097	+	8.33284i	−0.261682	+	0.453247i
$339$	1.36783	−	0.298490i	0.0742905	−	0.0162117i
$340$	−5.63067	+	3.25087i	−0.305366	+	0.176303i
$341$	−6.91289	−	20.4895i	−0.374354	−	1.10957i
$342$	−2.33783	−	5.10149i	−0.126415	−	0.275857i
$343$		−	10.7906i		−	0.582637i
$344$	1.09708	−	0.633401i	0.0591508	−	0.0341507i
$345$	8.57674	+	2.73551i	0.461756	+	0.147275i
$346$	2.53267	−	4.38671i	0.136157	−	0.235831i
$347$	3.74402	−	6.48484i	0.200990	−	0.348124i	−0.747858	−	0.663859i	$-0.768918\pi$
$347$	3.74402	−	6.48484i	0.200990	−	0.348124i	0.948848	+	0.315735i	$0.102251\pi$
$348$	−0.135812	+	0.123623i	−0.00728027	+	0.00662690i
$349$	−13.6389	+	7.87442i	−0.730073	+	0.421508i	−0.818449	−	0.574579i	$-0.805166\pi$
$349$	−13.6389	+	7.87442i	−0.730073	+	0.421508i	0.0883758	+	0.996087i	$0.471832\pi$
$350$			0.808507i			0.0432165i
$351$	1.15238	+	9.48050i	0.0615092	+	0.506032i
$352$	−1.06027	−	3.14258i	−0.0565124	−	0.167500i
$353$	14.8221	−	8.55757i	0.788903	−	0.455473i	−0.0506732	−	0.998715i	$-0.516137\pi$
$353$	14.8221	−	8.55757i	0.788903	−	0.455473i	0.839576	+	0.543242i	$0.182803\pi$
$354$	−1.86374	−	2.04749i	−0.0990566	−	0.108823i
$355$	−4.43815	+	7.68710i	−0.235552	+	0.407989i
$356$	−6.24226	−	3.60397i	−0.330839	−	0.191010i
$357$	2.76665	−	8.67435i	0.146426	−	0.459095i
$358$	−0.591638	+	0.341582i	−0.0312690	+	0.0180532i
$359$	10.8139			0.570738			0.285369	−	0.958418i	$-0.407884\pi$
$359$	10.8139			0.570738			0.285369	+	0.958418i	$0.407884\pi$
$360$	1.73698	−	2.44600i	0.0915468	−	0.128915i
$361$	15.5010			0.815844
$362$	4.87307	+	8.44041i	0.256123	+	0.443618i
$363$	14.5087	+	12.3490i	0.761511	+	0.648152i
$364$	0.742999	−	1.28691i	0.0389437	−	0.0674525i
$365$	−7.32249	+	12.6829i	−0.383277	+	0.663855i
$366$	−21.0249	+	4.58807i	−1.09899	+	0.239822i
$367$	−0.210501	−	0.364599i	−0.0109881	−	0.0190319i	0.860479	−	0.509486i	$-0.170164\pi$
$367$	−0.210501	−	0.364599i	−0.0109881	−	0.0190319i	−0.871467	+	0.490454i	$0.836831\pi$
$368$			5.19755i			0.270941i
$369$	8.51635	+	6.04772i	0.443343	+	0.314832i
$370$			4.15951i			0.216243i
$371$	4.48462	+	7.76760i	0.232830	+	0.403274i
$372$	10.7589	+	3.43151i	0.557824	+	0.177916i
$373$	26.9995	+	15.5882i	1.39798	+	0.807125i	0.994181	−	0.107721i	$-0.0343554\pi$
$373$	26.9995	+	15.5882i	1.39798	+	0.807125i	0.403801	+	0.914847i	$0.367689\pi$
$374$	21.1416	+	4.24612i	1.09321	+	0.219562i
$375$	−1.16592	−	1.28087i	−0.0602078	−	0.0661440i
$376$	−4.05652	+	2.34204i	−0.209199	+	0.120781i
$377$		−	0.194879i		−	0.0100368i
$378$	0.506925	+	4.17043i	0.0260734	+	0.214504i
$379$	−13.7409			−0.705820			−0.352910	−	0.935657i	$-0.614808\pi$
$379$	−13.7409			−0.705820			−0.352910	+	0.935657i	$0.614808\pi$
$380$	−0.935276	−	1.61995i	−0.0479786	−	0.0831014i
$381$	24.9009	+	27.3560i	1.27571	+	1.40149i
$382$	5.09125	+	2.93944i	0.260491	+	0.150395i
$383$	−8.00915	−	4.62409i	−0.409248	−	0.236280i	0.281218	−	0.959644i	$-0.409261\pi$
$383$	−8.00915	−	4.62409i	−0.409248	−	0.236280i	−0.690467	+	0.723364i	$0.742595\pi$
$384$	1.65015	+	0.526309i	0.0842089	+	0.0268581i
$385$	1.77178	−	2.01279i	0.0902984	−	0.102581i
$386$		−	1.76138i		−	0.0896520i
$387$	−1.58326	−	3.45491i	−0.0804816	−	0.175623i
$388$	−11.2690			−0.572097
$389$	4.41058	−	2.54645i	0.223625	−	0.129110i	−0.384003	−	0.923332i	$-0.625455\pi$
$389$	4.41058	−	2.54645i	0.223625	−	0.129110i	0.607628	+	0.794222i	$0.292121\pi$
$390$	0.678717	+	3.11023i	0.0343682	+	0.157493i
$391$	−29.2657	−	16.8965i	−1.48003	−	0.854494i
$392$	−3.17316	+	5.49607i	−0.160269	+	0.277594i
$393$	2.27591	+	10.4294i	0.114804	+	0.526093i
$394$	1.13386	+	1.96390i	0.0571228	+	0.0989396i
$395$	−12.4779			−0.627832
$396$	−9.68444	+	2.28288i	−0.486662	+	0.114719i
$397$	18.0972			0.908273			0.454137	−	0.890932i	$-0.349948\pi$
$397$	18.0972			0.908273			0.454137	+	0.890932i	$0.349948\pi$
$398$	−11.5064	−	19.9297i	−0.576765	−	0.998987i
$399$	2.49561	+	0.795965i	0.124937	+	0.0398481i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	−6.36615	−	3.67550i	−0.317910	−	0.183546i	0.332550	−	0.943085i	$-0.392091\pi$
$401$	−6.36615	−	3.67550i	−0.317910	−	0.183546i	−0.650461	+	0.759540i	$0.725424\pi$
$402$	−0.567711	+	0.516761i	−0.0283148	+	0.0257737i
$403$	−10.3779	+	5.99169i	−0.516960	+	0.298467i
$404$	−11.4318			−0.568755
$405$	−6.81712	−	5.87596i	−0.338745	−	0.291979i
$406$		−	0.0857266i		−	0.00425454i
$407$	9.11526	−	10.3551i	0.451827	−	0.513286i
$408$	−8.32789	+	7.58049i	−0.412292	+	0.375290i
$409$	7.31309	+	4.22222i	0.361609	+	0.208775i	0.669786	−	0.742554i	$-0.266386\pi$
$409$	7.31309	+	4.22222i	0.361609	+	0.208775i	−0.308177	+	0.951329i	$0.599719\pi$
$410$	3.01528	+	1.74087i	0.148914	+	0.0859756i
$411$	5.31594	−	16.6672i	0.262216	−	0.822134i
$412$	−6.50932	−	11.2745i	−0.320691	−	0.555453i
$413$	1.29241			0.0635954
$414$	15.5240	+	1.46190i	0.762961	+	0.0718485i
$415$		−	11.5467i		−	0.566804i
$416$	−1.59171	+	0.918976i	−0.0780402	+	0.0450565i
$417$	−20.9600	+	4.57391i	−1.02642	+	0.223985i
$418$	−1.22161	+	6.08246i	−0.0597509	+	0.297503i
$419$	25.9408	+	14.9769i	1.26729	+	0.731672i	0.974475	−	0.224496i	$-0.0720737\pi$
$419$	25.9408	+	14.9769i	1.26729	+	0.731672i	0.292818	+	0.956168i	$0.405407\pi$
$420$	0.298565	+	1.36818i	0.0145685	+	0.0667602i
$421$	4.82963	+	8.36516i	0.235382	+	0.407693i	0.959384	−	0.282105i	$-0.0910326\pi$
$421$	4.82963	+	8.36516i	0.235382	+	0.407693i	−0.724002	+	0.689798i	$0.757699\pi$
$422$		−	7.01704i		−	0.341584i
$423$	5.85419	+	12.7747i	0.284640	+	0.621128i
$424$		−	11.0936i		−	0.538753i
$425$	3.25087	+	5.63067i	0.157690	+	0.273127i
$426$	−4.67167	+	14.6472i	−0.226343	+	0.709661i
$427$	5.02260	−	8.69940i	0.243061	−	0.420994i
$428$	−9.75724	+	16.9000i	−0.471634	+	0.816894i
$429$	5.12617	−	9.23031i	0.247494	−	0.445644i
$430$	−0.633401	−	1.09708i	−0.0305453	−	0.0529061i
$431$	7.43225			0.357999			0.178999	−	0.983849i	$-0.442714\pi$
$431$	7.43225			0.357999			0.178999	+	0.983849i	$0.442714\pi$
$432$	2.03611	−	4.78061i	0.0979622	−	0.230007i
$433$	38.6060			1.85529			0.927644	−	0.373466i	$-0.121831\pi$
$433$	38.6060			1.85529			0.927644	+	0.373466i	$0.121831\pi$
$434$	−4.56519	+	2.63572i	−0.219136	+	0.126518i
$435$	0.123623	+	0.135812i	0.00592728	+	0.00651168i
$436$	2.70882	+	1.56394i	0.129729	+	0.0748991i
$437$	4.86114	−	8.41974i	0.232540	−	0.402771i
$438$	−7.70778	+	24.1664i	−0.368292	+	1.15472i
$439$	30.8607	−	17.8174i	1.47290	−	0.850380i	0.473367	−	0.880865i	$-0.343039\pi$
$439$	30.8607	−	17.8174i	1.47290	−	0.850380i	0.999535	+	0.0304850i	$0.00970518\pi$
$440$	−3.14258	+	1.06027i	−0.149817	+	0.0505462i
$441$	15.5231	+	11.0234i	0.739194	+	0.524924i
$442$		−	11.9499i		−	0.568398i
$443$	19.2694	−	11.1252i	0.915517	−	0.528574i	0.0333149	−	0.999445i	$-0.489394\pi$
$443$	19.2694	−	11.1252i	0.915517	−	0.528574i	0.882202	+	0.470871i	$0.156060\pi$
$444$	1.53602	+	7.03884i	0.0728963	+	0.334049i
$445$	−3.60397	+	6.24226i	−0.170844	+	0.295911i
$446$	8.66329	−	15.0053i	0.410218	−	0.710519i
$447$	7.63585	+	34.9914i	0.361163	+	1.65504i
$448$	−0.700188	+	0.404254i	−0.0330808	+	0.0190992i
$449$			24.9351i			1.17676i	0.808585	+	0.588379i	$0.200234\pi$
$449$			24.9351i			1.17676i	−0.808585	+	0.588379i	$0.799766\pi$
$450$	−2.44600	−	1.73698i	−0.115305	−	0.0818819i
$451$	−3.69158	−	10.9417i	−0.173830	−	0.515224i
$452$	0.700012	−	0.404152i	0.0329258	−	0.0190097i
$453$	10.6845	−	33.4995i	0.502003	−	1.57394i
$454$	−3.93984	+	6.82400i	−0.184906	+	0.320266i
$455$	−1.28691	−	0.742999i	−0.0603314	−	0.0348323i
$456$	−2.18091	−	2.39594i	−0.102131	−	0.112200i
$457$	−3.35432	+	1.93662i	−0.156909	+	0.0905912i	−0.576398	−	0.817169i	$-0.695542\pi$
$457$	−3.35432	+	1.93662i	−0.156909	+	0.0905912i	0.419490	+	0.907760i	$0.362209\pi$
$458$	−7.84851			−0.366737
$459$	20.2989	+	27.0058i	0.947473	+	1.26052i
$460$	5.19755			0.242337
$461$	4.36386	+	7.55843i	0.203245	+	0.352031i	0.949572	−	0.313548i	$-0.101518\pi$
$461$	4.36386	+	7.55843i	0.203245	+	0.352031i	−0.746327	+	0.665580i	$0.768184\pi$
$462$	2.25498	−	4.06037i	0.104911	−	0.188906i
$463$	−15.2101	+	26.3447i	−0.706873	+	1.22434i	0.259138	+	0.965840i	$0.416562\pi$
$463$	−15.2101	+	26.3447i	−0.706873	+	1.22434i	−0.966011	+	0.258500i	$0.916772\pi$
$464$	−0.0530153	+	0.0918253i	−0.00246118	+	0.00426288i
$465$	3.43151	−	10.7589i	0.159132	−	0.498933i
$466$	−3.19402	−	5.53221i	−0.147960	−	0.256275i
$467$			14.3264i			0.662946i	0.943465	+	0.331473i	$0.107546\pi$
$467$			14.3264i			0.662946i	−0.943465	+	0.331473i	$0.892454\pi$
$468$	2.29709	+	5.01259i	0.106183	+	0.231707i
$469$		−	0.358348i		−	0.0165470i
$470$	2.34204	+	4.05652i	0.108030	+	0.187114i
$471$	0.793355	+	3.63556i	0.0365559	+	0.167518i
$472$	−1.38435	−	0.799257i	−0.0637201	−	0.0367888i
$473$	−0.827317	+	4.11925i	−0.0380401	+	0.189403i
$474$	−21.1155	+	4.60783i	−0.969865	+	0.211645i
$475$	−1.61995	+	0.935276i	−0.0743282	+	0.0429134i
$476$		−	5.25670i		−	0.240940i
$477$	−33.1342	−	3.12027i	−1.51711	−	0.142867i
$478$	14.2894			0.653583
$479$	−4.21713	−	7.30428i	−0.192686	−	0.333741i	0.753454	−	0.657501i	$-0.228386\pi$
$479$	−4.21713	−	7.30428i	−0.192686	−	0.333741i	−0.946139	+	0.323760i	$0.895053\pi$
$480$	0.526309	−	1.65015i	0.0240226	−	0.0753188i
$481$	−6.62075	−	3.82249i	−0.301880	−	0.174291i
$482$	−5.57754	−	3.22019i	−0.254050	−	0.146676i
$483$	−5.38255	+	4.89949i	−0.244915	+	0.222934i
$484$	10.1470	+	4.24720i	0.461227	+	0.193054i
$485$			11.2690i			0.511699i
$486$	−13.7060	−	7.42604i	−0.621716	−	0.336852i
$487$	8.04981			0.364772			0.182386	−	0.983227i	$-0.441618\pi$
$487$	8.04981			0.364772			0.182386	+	0.983227i	$0.441618\pi$
$488$	−10.7598	+	6.21219i	−0.487075	+	0.281213i
$489$	15.1640	−	13.8031i	0.685740	−	0.624197i
$490$	5.49607	+	3.17316i	0.248287	+	0.143349i
$491$	0.370909	−	0.642433i	0.0167389	−	0.0289926i	−0.857535	−	0.514426i	$-0.828005\pi$
$491$	0.370909	−	0.642433i	0.0167389	−	0.0289926i	0.874274	+	0.485434i	$0.161338\pi$
$492$	5.74541	+	1.83247i	0.259023	+	0.0826143i
$493$	−0.344692	−	0.597023i	−0.0155241	−	0.0268886i
$494$	3.43798			0.154682
$495$	2.28288	+	9.68444i	0.102608	+	0.435283i
$496$	6.51996			0.292755
$497$	−3.58827	−	6.21507i	−0.160956	−	0.278784i
$498$	−4.26395	−	19.5396i	−0.191072	−	0.875591i
$499$	2.80828	−	4.86409i	0.125716	−	0.217747i	−0.796297	−	0.604906i	$-0.793211\pi$
$499$	2.80828	−	4.86409i	0.125716	−	0.217747i	0.922013	+	0.387160i	$0.126544\pi$
$500$	−0.866025	−	0.500000i	−0.0387298	−	0.0223607i
$501$	8.44290	+	38.6897i	0.377201	+	1.72853i
$502$	−2.66359	+	1.53783i	−0.118882	+	0.0686366i
$503$	−28.1297			−1.25424			−0.627121	−	0.778922i	$-0.715767\pi$
$503$	−28.1297			−1.25424			−0.627121	+	0.778922i	$0.715767\pi$
$504$	1.01048	+	2.20501i	0.0450103	+	0.0982191i
$505$			11.4318i			0.508710i
$506$	−12.9393	−	11.3900i	−0.575224	−	0.506349i
$507$	15.8776	+	5.06411i	0.705151	+	0.224905i
$508$	18.4960	+	10.6787i	0.820627	+	0.473789i
$509$	−36.2515	−	20.9298i	−1.60682	−	0.927698i	−0.990076	−	0.140535i	$-0.955118\pi$
$509$	−36.2515	−	20.9298i	−1.60682	−	0.927698i	−0.616745	−	0.787163i	$-0.711549\pi$
$510$	7.58049	+	8.32789i	0.335670	+	0.368765i
$511$	−5.92029	−	10.2542i	−0.261898	−	0.453621i
$512$	1.00000			0.0441942
$513$	−7.76957	+	5.84001i	−0.343035	+	0.257843i
$514$			14.1908i			0.625928i
$515$	−11.2745	+	6.50932i	−0.496812	+	0.286835i
$516$	−1.47699	−	1.62261i	−0.0650208	−	0.0714315i
$517$	3.05905	−	15.2312i	0.134537	−	0.669865i
$518$	−2.91244	−	1.68150i	−0.127965	−	0.0738808i
$519$	−8.35856	−	2.66593i	−0.366900	−	0.117021i
$520$	0.918976	+	1.59171i	0.0402998	+	0.0698013i
$521$			42.0815i			1.84362i	0.387638	+	0.921812i	$0.373291\pi$
$521$			42.0815i			1.84362i	−0.387638	+	0.921812i	$0.626709\pi$
$522$	0.259351	+	0.184173i	0.0113515	+	0.00806103i
$523$			9.18729i			0.401732i	0.979619	+	0.200866i	$0.0643756\pi$
$523$			9.18729i			0.401732i	−0.979619	+	0.200866i	$0.935624\pi$
$524$	3.08156	+	5.33742i	0.134619	+	0.233166i
$525$	1.36818	−	0.298565i	0.0597122	−	0.0130304i
$526$	13.1025	−	22.6943i	0.571298	−	0.989518i
$527$	−21.1955	+	36.7117i	−0.923291	+	1.59919i
$528$	−4.92643	+	2.95470i	−0.214395	+	0.128587i
$529$	2.00725	+	3.47665i	0.0872716	+	0.151159i
$530$	−11.0936			−0.481875
$531$	−2.77658	+	3.90996i	−0.120494	+	0.169678i
$532$	1.51235			0.0655689
$533$	−5.54194	+	3.19964i	−0.240048	+	0.138592i
$534$	−3.79360	+	11.8942i	−0.164165	+	0.514712i
$535$	16.9000	+	9.75724i	0.730652	+	0.421842i
$536$	−0.221611	+	0.383842i	−0.00957214	+	0.0165794i
$537$	0.796514	+	0.875046i	0.0343721	+	0.0377610i
$538$	5.82763	−	3.36459i	0.251247	−	0.145058i
$539$	−6.72878	−	19.9438i	−0.289829	−	0.859042i
$540$	−4.78061	−	2.03611i	−0.205725	−	0.0876200i
$541$		−	8.40554i		−	0.361382i	−0.983540	−	0.180691i	$-0.942167\pi$
$541$		−	8.40554i		−	0.361382i	0.983540	−	0.180691i	$-0.0578335\pi$
$542$	10.2751	−	5.93236i	0.441355	−	0.254817i
$543$	12.4836	−	11.3632i	0.535721	−	0.487642i
$544$	−3.25087	+	5.63067i	−0.139380	+	0.241413i
$545$	1.56394	−	2.70882i	0.0669918	−	0.116033i
$546$	−2.45212	−	0.782093i	−0.104941	−	0.0334705i
$547$	0.617106	−	0.356286i	0.0263855	−	0.0152337i	−0.486749	−	0.873542i	$-0.661817\pi$
$547$	0.617106	−	0.356286i	0.0263855	−	0.0152337i	0.513135	+	0.858308i	$0.328484\pi$
$548$		−	10.1004i		−	0.431469i
$549$	15.5281	+	33.8846i	0.662723	+	1.44616i
$550$	1.06027	+	3.14258i	0.0452099	+	0.134000i
$551$	0.171764	−	0.0991679i	0.00731739	−	0.00422470i
$552$	8.79543	−	1.91934i	0.374358	−	0.0816927i
$553$	5.04424	−	8.73688i	0.214503	−	0.371530i
$554$	−5.70227	−	3.29221i	−0.242266	−	0.139872i
$555$	7.03884	−	1.53602i	0.298782	−	0.0652005i
$556$	−10.7266	+	6.19303i	−0.454911	+	0.262643i
$557$	−3.99124			−0.169114			−0.0845571	−	0.996419i	$-0.526948\pi$
$557$	−3.99124			−0.169114			−0.0845571	+	0.996419i	$0.526948\pi$
$558$	1.83385	−	19.4737i	0.0776332	−	0.824388i
$559$	2.32832			0.0984776
$560$	0.404254	+	0.700188i	0.0170828	+	0.0295883i
$561$	−0.621759	−	37.3444i	−0.0262507	−	1.57668i
$562$	−12.5438	+	21.7265i	−0.529129	+	0.916479i
$563$	−23.4366	+	40.5933i	−0.987734	+	1.71081i	−0.358639	+	0.933476i	$0.616759\pi$
$563$	−23.4366	+	40.5933i	−0.987734	+	1.71081i	−0.629094	+	0.777329i	$0.716574\pi$
$564$	5.46125	+	5.99970i	0.229960	+	0.252633i
$565$	−0.404152	−	0.700012i	−0.0170028	−	0.0294497i
$566$		−	21.8274i		−	0.917472i
$567$	6.87012	−	2.39788i	0.288518	−	0.100702i
$568$			8.87630i			0.372441i
$569$	13.8231	+	23.9422i	0.579493	+	1.00371i	0.995537	+	0.0943670i	$0.0300827\pi$
$569$	13.8231	+	23.9422i	0.579493	+	1.00371i	−0.416044	+	0.909344i	$0.636584\pi$
$570$	−2.39594	+	2.18091i	−0.100355	+	0.0913483i
$571$	0.0760954	+	0.0439337i	0.00318449	+	0.00183857i	0.501591	−	0.865105i	$-0.332748\pi$
$571$	0.0760954	+	0.0439337i	0.00318449	+	0.00183857i	−0.498407	+	0.866943i	$0.666081\pi$
$572$	1.20032	−	5.97645i	0.0501879	−	0.249888i
$573$	3.09410	−	9.70103i	0.129258	−	0.405266i
$574$	−2.43788	+	1.40751i	−0.101755	+	0.0587483i
$575$		−	5.19755i		−	0.216753i
$576$	0.281268	−	2.98679i	0.0117195	−	0.124449i
$577$	−34.7807			−1.44794			−0.723970	−	0.689831i	$-0.757685\pi$
$577$	−34.7807			−1.44794			−0.723970	+	0.689831i	$0.757685\pi$
$578$	−12.6363	−	21.8867i	−0.525599	−	0.910365i
$579$	−2.98066	+	0.650442i	−0.123872	+	0.0270314i
$580$	0.0918253	+	0.0530153i	0.00381284	+	0.00220134i
$581$	8.08485	+	4.66779i	0.335416	+	0.193652i
$582$	4.16141	+	19.0697i	0.172496	+	0.790465i
$583$	27.6176	+	24.3108i	1.14380	+	1.00685i
$584$			14.6450i			0.606014i
$585$	5.01259	−	2.29709i	0.207245	−	0.0949729i
$586$	11.7538			0.485544
$587$	6.79402	−	3.92253i	0.280419	−	0.161900i	−0.353194	−	0.935550i	$-0.614904\pi$
$587$	6.79402	−	3.92253i	0.280419	−	0.161900i	0.633613	+	0.773650i	$0.281571\pi$
$588$	10.4724	+	3.34012i	0.431874	+	0.137744i
$589$	−10.5620	−	6.09796i	−0.435199	−	0.251262i
$590$	−0.799257	+	1.38435i	−0.0329049	+	0.0569930i
$591$	2.90465	−	2.64397i	0.119481	−	0.108758i
$592$	2.07976	+	3.60224i	0.0854775	+	0.148051i
$593$	−33.3620			−1.37001			−0.685006	−	0.728538i	$-0.740200\pi$
$593$	−33.3620			−1.37001			−0.685006	+	0.728538i	$0.740200\pi$
$594$	7.43941	+	15.5453i	0.305243	+	0.637830i
$595$	−5.25670			−0.215504
$596$	10.3389	+	17.9074i	0.423496	+	0.733517i
$597$	−29.4765	+	26.8311i	−1.20639	+	1.09812i
$598$	−4.77642	+	8.27301i	−0.195322	+	0.338308i
$599$	−4.28378	−	2.47324i	−0.175031	−	0.101054i	0.409925	−	0.912119i	$-0.365555\pi$
$599$	−4.28378	−	2.47324i	−0.175031	−	0.101054i	−0.584956	+	0.811065i	$0.698888\pi$
$600$	−1.65015	−	0.526309i	−0.0673671	−	0.0214865i
$601$	−21.5660	+	12.4512i	−0.879697	+	0.507893i	−0.870559	−	0.492065i	$-0.836242\pi$
$601$	−21.5660	+	12.4512i	−0.879697	+	0.507893i	−0.00913864	+	0.999958i	$0.502909\pi$
$602$	1.02422			0.0417441
$603$	1.08412	+	0.769867i	0.0441488	+	0.0313514i
$604$		−	20.3009i		−	0.826031i
$605$	4.24720	−	10.1470i	0.172673	−	0.412534i
$606$	4.22153	+	19.3453i	0.171488	+	0.785847i
$607$	−11.0145	−	6.35925i	−0.447066	−	0.258114i	0.259524	−	0.965737i	$-0.416434\pi$
$607$	−11.0145	−	6.35925i	−0.447066	−	0.258114i	−0.706590	+	0.707623i	$0.749768\pi$
$608$	−1.61995	−	0.935276i	−0.0656975	−	0.0379304i
$609$	−0.145069	+	0.0316570i	−0.00587848	+	0.00128281i
$610$	6.21219	+	10.7598i	0.251524	+	0.435653i
$611$	−8.60910			−0.348287
$612$	15.9032	+	11.2934i	0.642850	+	0.456507i
$613$		−	0.697036i		−	0.0281530i	−0.999901	−	0.0140765i	$-0.995519\pi$
$613$		−	0.697036i		−	0.0281530i	0.999901	−	0.0140765i	$-0.00448084\pi$
$614$	−3.86467	+	2.23127i	−0.155965	+	0.0900466i
$615$	1.83247	−	5.74541i	0.0738925	−	0.231677i
$616$	0.528016	−	2.62902i	0.0212744	−	0.105926i
$617$	−21.7066	−	12.5323i	−0.873876	−	0.504532i	−0.00524151	−	0.999986i	$-0.501668\pi$
$617$	−21.7066	−	12.5323i	−0.873876	−	0.504532i	−0.868634	+	0.495454i	$0.835002\pi$
$618$	−16.6752	+	15.1787i	−0.670775	+	0.610576i
$619$	−7.63117	−	13.2176i	−0.306723	−	0.531259i	0.670921	−	0.741529i	$-0.265899\pi$
$619$	−7.63117	−	13.2176i	−0.306723	−	0.531259i	−0.977643	+	0.210270i	$0.932566\pi$
$620$		−	6.51996i		−	0.261848i
$621$	−3.25880	−	26.8099i	−0.130771	−	1.07584i
$622$		−	8.59321i		−	0.344556i
$623$	−2.91383	−	5.04691i	−0.116740	−	0.202200i
$624$	2.14290	+	2.35418i	0.0857848	+	0.0942427i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−1.02823	+	1.78094i	−0.0410963	+	0.0711808i
$627$	10.7440	−	0.178880i	0.429074	−	0.00714380i
$628$	1.07419	+	1.86056i	0.0428650	+	0.0742444i
$629$	−27.0441			−1.07832
$630$	2.20501	−	1.01048i	0.0878499	−	0.0402584i
$631$	−16.4855			−0.656278			−0.328139	−	0.944629i	$-0.606421\pi$
$631$	−16.4855			−0.656278			−0.328139	+	0.944629i	$0.606421\pi$
$632$	−10.8062	+	6.23895i	−0.429847	+	0.248172i
$633$	−11.8744	+	2.59125i	−0.471966	+	0.102993i
$634$	−3.40370	−	1.96513i	−0.135178	−	0.0780452i
$635$	10.6787	−	18.4960i	0.423770	−	0.733991i
$636$	−18.7729	+	4.09663i	−0.744393	+	0.162442i
$637$	−10.1015	+	5.83211i	−0.400237	+	0.231077i
$638$	−0.112421	−	0.333210i	−0.00445078	−	0.0131919i
$639$	26.5116	+	2.49661i	1.04878	+	0.0987645i
$640$		−	1.00000i		−	0.0395285i
$641$	−5.30661	+	3.06377i	−0.209599	+	0.121012i	−0.601125	−	0.799155i	$-0.705281\pi$
$641$	−5.30661	+	3.06377i	−0.209599	+	0.121012i	0.391526	+	0.920167i	$0.371947\pi$
$642$	32.2019	+	10.2706i	1.27091	+	0.405350i
$643$	−7.76854	+	13.4555i	−0.306361	+	0.530634i	−0.977564	−	0.210641i	$-0.932445\pi$
$643$	−7.76854	+	13.4555i	−0.306361	+	0.530634i	0.671202	+	0.741274i	$0.265778\pi$
$644$	−2.10113	+	3.63926i	−0.0827960	+	0.143407i
$645$	−1.62261	+	1.47699i	−0.0638903	+	0.0581564i
$646$	10.5325	−	6.08091i	0.414394	−	0.239250i
$647$		−	39.4895i		−	1.55249i	−0.630430	−	0.776246i	$-0.717121\pi$
$647$		−	39.4895i		−	1.55249i	0.630430	−	0.776246i	$-0.282879\pi$
$648$	−8.84178	−	1.68017i	−0.347338	−	0.0660034i
$649$	5.02347	−	1.69485i	0.197188	−	0.0665287i
$650$	1.59171	−	0.918976i	0.0624321	−	0.0360452i
$651$	6.14606	+	6.75203i	0.240883	+	0.264633i
$652$	5.91940	−	10.2527i	0.231822	−	0.401527i
$653$	−18.3721	−	10.6071i	−0.718954	−	0.415088i	0.0954134	−	0.995438i	$-0.469583\pi$
$653$	−18.3721	−	10.6071i	−0.718954	−	0.415088i	−0.814368	+	0.580349i	$0.802916\pi$
$654$	1.64623	−	5.16147i	0.0643727	−	0.201830i
$655$	5.33742	−	3.08156i	0.208550	−	0.120406i
$656$	3.48175			0.135939
$657$	43.7414	+	4.11916i	1.70652	+	0.160704i
$658$	−3.78710			−0.147637
$659$	21.5484	+	37.3230i	0.839407	+	1.45390i	0.890391	+	0.455197i	$0.150431\pi$
$659$	21.5484	+	37.3230i	0.839407	+	1.45390i	−0.0509836	+	0.998699i	$0.516236\pi$
$660$	2.95470	+	4.92643i	0.115012	+	0.191761i
$661$	4.38090	−	7.58794i	0.170397	−	0.295137i	−0.768162	−	0.640256i	$-0.778828\pi$
$661$	4.38090	−	7.58794i	0.170397	−	0.295137i	0.938559	+	0.345119i	$0.112162\pi$
$662$	−7.61257	+	13.1854i	−0.295871	+	0.512463i
$663$	−20.2219	+	4.41284i	−0.785354	+	0.171380i
$664$	−5.77334	−	9.99972i	−0.224049	−	0.388064i
$665$		−	1.51235i		−	0.0586466i
$666$	11.3441	−	5.19859i	0.439575	−	0.201441i
$667$			0.551099i			0.0213387i
$668$	11.4316	+	19.8001i	0.442302	+	0.766090i
$669$	−28.5915	−	9.11912i	−1.10541	−	0.352566i
$670$	0.383842	+	0.221611i	0.0148291	+	0.00856158i
$671$	8.11406	−	40.4003i	0.313240	−	1.55964i
$672$	0.942653	+	1.03559i	0.0363636	+	0.0399489i
$673$	34.2563	−	19.7779i	1.32049	−	0.762382i	0.336679	−	0.941619i	$-0.390696\pi$
$673$	34.2563	−	19.7779i	1.32049	−	0.762382i	0.983806	+	0.179237i	$0.0573629\pi$
$674$		−	6.66725i		−	0.256813i
$675$	−2.03611	+	4.78061i	−0.0783697	+	0.184006i
$676$	9.62193			0.370074
$677$	−17.5285	−	30.3603i	−0.673676	−	1.16684i	−0.976854	−	0.213907i	$-0.931381\pi$
$677$	−17.5285	−	30.3603i	−0.673676	−	1.16684i	0.303178	−	0.952934i	$-0.401952\pi$
$678$	−0.942417	−	1.03533i	−0.0361933	−	0.0397618i
$679$	−7.89042	−	4.55553i	−0.302806	−	0.174825i
$680$	5.63067	+	3.25087i	0.215926	+	0.124665i
$681$	13.0027	+	4.14714i	0.498263	+	0.158919i
$682$	−14.2880	+	16.2315i	−0.547116	+	0.621536i
$683$		−	46.3667i		−	1.77417i	−0.461602	−	0.887087i	$-0.652725\pi$
$683$		−	46.3667i		−	1.77417i	0.461602	−	0.887087i	$-0.347275\pi$
$684$	−3.24911	+	4.57537i	−0.124233	+	0.174944i
$685$	−10.1004			−0.385918
$686$	−9.34493	+	5.39530i	−0.356791	+	0.205993i
$687$	2.89829	+	13.2815i	0.110577	+	0.506719i
$688$	−1.09708	−	0.633401i	−0.0418259	−	0.0241482i
$689$	10.1947	−	17.6578i	0.388389	−	0.672709i
$690$	−1.91934	−	8.79543i	−0.0730682	−	0.334836i
$691$	6.18944	+	10.7204i	0.235457	+	0.407824i	0.959405	−	0.282030i	$-0.0910079\pi$
$691$	6.18944	+	10.7204i	0.235457	+	0.407824i	−0.723948	+	0.689854i	$0.757675\pi$
$692$	−5.06533			−0.192555
$693$	−7.70379	−	2.31653i	−0.292643	−	0.0879976i
$694$	−7.48804			−0.284242
$695$	6.19303	+	10.7266i	0.234915	+	0.406885i
$696$	0.174967	+	0.0558049i	0.00663209	+	0.00211528i
$697$	−11.3187	+	19.6046i	−0.428726	+	0.742575i
$698$	13.6389	+	7.87442i	0.516240	+	0.298051i
$699$	−8.18227	+	7.44794i	−0.309482	+	0.281707i
$700$	0.700188	−	0.404254i	0.0264646	−	0.0152793i
$701$	41.3363			1.56125			0.780626	−	0.624999i	$-0.214900\pi$
$701$	41.3363			1.56125			0.780626	+	0.624999i	$0.214900\pi$
$702$	7.63417	−	5.73824i	0.288133	−	0.216576i
$703$		−	7.78059i		−	0.293450i
$704$	−2.19142	+	2.48951i	−0.0825924	+	0.0938269i
$705$	5.99970	−	5.46125i	0.225962	−	0.205682i
$706$	−14.8221	−	8.55757i	−0.557839	−	0.322068i
$707$	−8.00443	−	4.62136i	−0.301037	−	0.173804i
$708$	−0.841312	+	2.63779i	−0.0316184	+	0.0991343i
$709$	5.28407	+	9.15227i	0.198447	+	0.343721i	0.948025	−	0.318195i	$-0.103077\pi$
$709$	5.28407	+	9.15227i	0.198447	+	0.343721i	−0.749578	+	0.661916i	$0.769743\pi$
$710$	8.87630			0.333121
$711$	15.5950	+	34.0306i	0.584858	+	1.27625i
$712$			7.20794i			0.270129i
$713$	29.3477	−	16.9439i	1.09908	−	0.634554i
$714$	−8.89553	+	1.94119i	−0.332907	+	0.0726471i
$715$	−5.97645	−	1.20032i	−0.223507	−	0.0448895i
$716$	0.591638	+	0.341582i	0.0221105	+	0.0127655i
$717$	−5.27678	−	24.1809i	−0.197065	−	0.903054i
$718$	−5.40697	−	9.36515i	−0.201786	−	0.349504i
$719$		−	31.7377i		−	1.18362i	−0.806079	−	0.591809i	$-0.798414\pi$
$719$		−	31.7377i		−	1.18362i	0.806079	−	0.591809i	$-0.201586\pi$
$720$	−2.98679	−	0.281268i	−0.111311	−	0.0104822i
$721$		−	10.5257i		−	0.391996i
$722$	−7.75052	−	13.4243i	−0.288444	−	0.499600i
$723$	−3.38963	+	10.6276i	−0.126062	+	0.395245i
$724$	4.87307	−	8.44041i	0.181106	−	0.313685i
$725$	0.0530153	−	0.0918253i	0.00196894	−	0.00341030i
$726$	3.44015	−	18.7394i	0.127676	−	0.695485i
$727$	−11.1834	−	19.3702i	−0.414770	−	0.718402i	0.580635	−	0.814164i	$-0.302804\pi$
$727$	−11.1834	−	19.3702i	−0.414770	−	0.718402i	−0.995404	+	0.0957623i	$0.969471\pi$
$728$	−1.48600			−0.0550747
$729$	−7.50522	+	25.9359i	−0.277971	+	0.960589i
$730$	14.6450			0.542035
$731$	7.13294	−	4.11821i	0.263821	−	0.152317i
$732$	14.4858	+	15.9141i	0.535412	+	0.588200i
$733$	7.78084	+	4.49227i	0.287392	+	0.165926i	0.636765	−	0.771058i	$-0.280272\pi$
$733$	7.78084	+	4.49227i	0.287392	+	0.165926i	−0.349373	+	0.936984i	$0.613605\pi$
$734$	−0.210501	+	0.364599i	−0.00776974	+	0.0134576i
$735$	3.34012	−	10.4724i	0.123202	−	0.386280i
$736$	4.50121	−	2.59877i	0.165917	−	0.0957921i
$737$	−0.469933	−	1.39286i	−0.0173102	−	0.0513068i
$738$	0.979302	−	10.3992i	0.0360486	−	0.382801i
$739$		−	34.8736i		−	1.28285i	−0.767187	−	0.641423i	$-0.778344\pi$
$739$		−	34.8736i		−	1.28285i	0.767187	−	0.641423i	$-0.221656\pi$
$740$	3.60224	−	2.07976i	0.132421	−	0.0764534i
$741$	−1.26958	−	5.81785i	−0.0466390	−	0.213724i
$742$	4.48462	−	7.76760i	0.164636	−	0.285157i
$743$	−17.2037	+	29.7977i	−0.631142	+	1.09317i	0.356176	+	0.934419i	$0.384080\pi$
$743$	−17.2037	+	29.7977i	−0.631142	+	1.09317i	−0.987319	+	0.158752i	$0.949253\pi$
$744$	−2.40768	−	11.0333i	−0.0882700	−	0.404499i
$745$	17.9074	−	10.3389i	0.656077	−	0.378786i
$746$		−	31.1764i		−	1.14145i
$747$	−31.4909	+	14.4311i	−1.15219	+	0.528008i
$748$	−6.89357	−	20.4322i	−0.252054	−	0.747077i
$749$	−13.6638	+	7.88880i	−0.499264	+	0.288250i
$750$	−0.526309	+	1.65015i	−0.0192181	+	0.0602550i
$751$	−10.4865	+	18.1631i	−0.382657	+	0.662782i	−0.991441	−	0.130554i	$-0.958324\pi$
$751$	−10.4865	+	18.1631i	−0.382657	+	0.662782i	0.608784	+	0.793336i	$0.291658\pi$
$752$	4.05652	+	2.34204i	0.147926	+	0.0854052i
$753$	3.58596	+	3.93952i	0.130680	+	0.143564i
$754$	−0.168770	+	0.0974397i	−0.00614626	+	0.00354854i
$755$	−20.3009			−0.738824
$756$	3.35824	−	2.52422i	0.122138	−	0.0918052i
$757$	10.1082			0.367387			0.183694	−	0.982984i	$-0.441195\pi$
$757$	10.1082			0.367387			0.183694	+	0.982984i	$0.441195\pi$
$758$	6.87043	+	11.8999i	0.249545	+	0.432225i
$759$	−14.4963	+	26.1024i	−0.526182	+	0.947457i
$760$	−0.935276	+	1.61995i	−0.0339260	+	0.0587616i
$761$	4.66276	−	8.07613i	0.169025	−	0.292759i	−0.769052	−	0.639186i	$-0.779272\pi$
$761$	4.66276	−	8.07613i	0.169025	−	0.292759i	0.938077	+	0.346426i	$0.112605\pi$
$762$	11.2406	−	35.2428i	0.407202	−	1.27671i
$763$	1.26446	+	2.19010i	0.0457764	+	0.0792870i
$764$		−	5.87887i		−	0.212690i
$765$	11.2934	−	15.9032i	0.408312	−	0.574982i
$766$			9.24817i			0.334150i
$767$	−1.46900	−	2.54438i	−0.0530424	−	0.0918722i
$768$	−0.369279	−	1.69223i	−0.0133252	−	0.0610630i
$769$	−2.46917	−	1.42557i	−0.0890404	−	0.0514075i	0.454819	−	0.890584i	$-0.349704\pi$
$769$	−2.46917	−	1.42557i	−0.0890404	−	0.0514075i	−0.543859	+	0.839177i	$0.683037\pi$
$770$	−2.62902	−	0.528016i	−0.0947431	−	0.0190284i
$771$	24.0140	−	5.24036i	0.864844	−	0.188727i
$772$	−1.52540	+	0.880691i	−0.0549004	+	0.0316968i
$773$			39.7303i			1.42900i	0.699635	+	0.714500i	$0.253346\pi$
$773$			39.7303i			1.42900i	−0.699635	+	0.714500i	$0.746654\pi$
$774$	−2.20041	+	3.09860i	−0.0790920	+	0.111377i
$775$	−6.51996			−0.234204
$776$	5.63450	+	9.75924i	0.202267	+	0.350336i
$777$	−1.76997	+	5.54945i	−0.0634975	+	0.199086i
$778$	−4.41058	−	2.54645i	−0.158127	−	0.0912945i
$779$	−5.64024	−	3.25639i	−0.202083	−	0.116672i
$780$	2.35418	−	2.14290i	0.0842933	−	0.0767282i
$781$	−22.0976	−	19.4517i	−0.790715	−	0.696038i
$782$			33.7931i			1.20844i
$783$	0.215890	−	0.506892i	0.00771526	−	0.0181148i
$784$	6.34632			0.226654
$785$	1.86056	−	1.07419i	0.0664062	−	0.0383397i
$786$	7.89417	−	7.18569i	0.281576	−	0.256305i
$787$	8.69628	+	5.02080i	0.309989	+	0.178972i	0.646921	−	0.762557i	$-0.276056\pi$
$787$	8.69628	+	5.02080i	0.309989	+	0.178972i	−0.336933	+	0.941529i	$0.609389\pi$
$788$	1.13386	−	1.96390i	0.0403919	−	0.0699609i
$789$	−43.2424	−	13.7920i	−1.53947	−	0.491007i
$790$	6.23895	+	10.8062i	0.221972	+	0.384467i
$791$	0.653519			0.0232365
$792$	6.81925	+	7.24553i	0.242312	+	0.257459i
$793$	−22.8354			−0.810910
$794$	−9.04861	−	15.6726i	−0.321123	−	0.556201i
$795$	4.09663	+	18.7729i	0.145293	+	0.665805i
$796$	−11.5064	+	19.9297i	−0.407835	+	0.706390i
$797$	−14.5687	−	8.41127i	−0.516051	−	0.297942i	0.219266	−	0.975665i	$-0.429634\pi$
$797$	−14.5687	−	8.41127i	−0.516051	−	0.297942i	−0.735318	+	0.677723i	$0.762967\pi$
$798$	−0.558481	−	2.55925i	−0.0197700	−	0.0905964i
$799$	−26.3744	+	15.2273i	−0.933061	+	0.538703i
$800$	−1.00000			−0.0353553
$801$	21.5286	+	2.02736i	0.760674	+	0.0716332i
$802$			7.35100i			0.259573i
$803$	−36.4588	−	32.0934i	−1.28660	−	1.13255i
$804$	0.731384	+	0.233272i	0.0257939	+	0.00822686i
$805$	3.63926	+	2.10113i	0.128267	+	0.0740550i
$806$	10.3779	+	5.99169i	0.365546	+	0.211048i
$807$	−7.84567	−	8.61921i	−0.276181	−	0.303411i
$808$	5.71591	+	9.90025i	0.201085	+	0.348290i
$809$	−36.9210			−1.29807			−0.649037	−	0.760757i	$-0.724828\pi$
$809$	−36.9210			−1.29807			−0.649037	+	0.760757i	$0.724828\pi$
$810$	−1.68017	+	8.84178i	−0.0590352	+	0.310668i
$811$		−	56.0473i		−	1.96809i	−0.177925	−	0.984044i	$-0.556938\pi$
$811$		−	56.0473i		−	1.96809i	0.177925	−	0.984044i	$-0.443062\pi$
$812$	−0.0742414	+	0.0428633i	−0.00260536	+	0.00150421i
$813$	−13.8333	−	15.1972i	−0.485155	−	0.532988i
$814$	−13.5255	−	2.71647i	−0.474067	−	0.0952124i
$815$	−10.2527	−	5.91940i	−0.359137	−	0.207348i
$816$	10.7288	+	3.42192i	0.375585	+	0.119791i
$817$	1.18481	+	2.05215i	0.0414513	+	0.0717957i
$818$		−	8.44443i		−	0.295253i
$819$	−0.417963	+	4.43836i	−0.0146048	+	0.155089i
$820$		−	3.48175i		−	0.121588i
$821$	−13.8065	−	23.9135i	−0.481850	−	0.834589i	0.517933	−	0.855421i	$-0.326702\pi$
$821$	−13.8065	−	23.9135i	−0.481850	−	0.834589i	−0.999783	+	0.0208325i	$0.993368\pi$
$822$	−17.0922	+	3.72988i	−0.596160	+	0.130094i
$823$	−24.0282	+	41.6180i	−0.837570	+	1.45071i	0.0543515	+	0.998522i	$0.482691\pi$
$823$	−24.0282	+	41.6180i	−0.837570	+	1.45071i	−0.891921	+	0.452191i	$0.850642\pi$
$824$	−6.50932	+	11.2745i	−0.226763	+	0.392765i
$825$	4.92643	−	2.95470i	0.171516	−	0.102869i
$826$	−0.646205	−	1.11926i	−0.0224844	−	0.0389440i
$827$	18.7015			0.650316			0.325158	−	0.945660i	$-0.394582\pi$
$827$	18.7015			0.650316			0.325158	+	0.945660i	$0.394582\pi$
$828$	−6.49594	−	14.1751i	−0.225749	−	0.492619i
$829$	23.4767			0.815378			0.407689	−	0.913121i	$-0.366335\pi$
$829$	23.4767			0.815378			0.407689	+	0.913121i	$0.366335\pi$
$830$	−9.99972	+	5.77334i	−0.347095	+	0.200396i
$831$	−3.46543	+	10.8653i	−0.120215	+	0.376912i
$832$	1.59171	+	0.918976i	0.0551827	+	0.0318598i
$833$	−20.6310	+	35.7340i	−0.714823	+	1.23811i
$834$	14.4411	+	15.8650i	0.500055	+	0.549358i
$835$	19.8001	−	11.4316i	0.685211	−	0.395607i
$836$	5.87837	−	1.98328i	0.203308	−	0.0685932i
$837$	−33.6312	+	4.08794i	−1.16246	+	0.141300i
$838$		−	29.9539i		−	1.03474i
$839$	−2.82819	+	1.63286i	−0.0976399	+	0.0563724i	−0.548025	−	0.836462i	$-0.684620\pi$
$839$	−2.82819	+	1.63286i	−0.0976399	+	0.0563724i	0.450385	+	0.892834i	$0.351287\pi$
$840$	1.03559	−	0.942653i	0.0357314	−	0.0325246i
$841$	14.4944	−	25.1050i	0.499806	−	0.865690i
$842$	4.82963	−	8.36516i	0.166440	−	0.288283i
$843$	41.3984	+	13.2038i	1.42584	+	0.454765i
$844$	−6.07694	+	3.50852i	−0.209177	+	0.120768i
$845$		−	9.62193i		−	0.331004i
$846$	8.13613	−	11.4572i	0.279726	−	0.393908i
$847$	5.38785	+	7.07579i	0.185129	+	0.243127i
$848$	−9.60733	+	5.54680i	−0.329917	+	0.190478i
$849$	−36.9369	+	8.06039i	−1.26767	+	0.276632i
$850$	3.25087	−	5.63067i	0.111504	−	0.193130i
$851$	18.7228	+	10.8096i	0.641811	+	0.370550i
$852$	15.0207	−	3.27783i	0.514601	−	0.112297i
$853$	−31.3363	+	18.0920i	−1.07293	+	0.619459i	−0.928982	−	0.370125i	$-0.879315\pi$
$853$	−31.3363	+	18.0920i	−1.07293	+	0.619459i	−0.143953	+	0.989585i	$0.545981\pi$
$854$	−10.0452			−0.343740
$855$	4.57537	+	3.24911i	0.156474	+	0.111117i
$856$	19.5145			0.666991
$857$	22.9067	+	39.6755i	0.782477	+	1.35529i	0.930495	+	0.366306i	$0.119378\pi$
$857$	22.9067	+	39.6755i	0.782477	+	1.35529i	−0.148017	+	0.988985i	$0.547289\pi$
$858$	−10.5568	+	0.175763i	−0.360402	+	0.00600045i
$859$	25.7231	−	44.5537i	0.877661	−	1.52015i	0.0237611	−	0.999718i	$-0.492436\pi$
$859$	25.7231	−	44.5537i	0.877661	−	1.52015i	0.853900	−	0.520437i	$-0.174231\pi$
$860$	−0.633401	+	1.09708i	−0.0215988	+	0.0374102i
$861$	3.28208	+	3.60568i	0.111853	+	0.122881i
$862$	−3.71613	−	6.43652i	−0.126572	−	0.219229i
$863$			40.1888i			1.36804i	0.729462	+	0.684021i	$0.239771\pi$
$863$			40.1888i			1.36804i	−0.729462	+	0.684021i	$0.760229\pi$
$864$	−5.15819	+	0.626989i	−0.175485	+	0.0213306i
$865$			5.06533i			0.172226i
$866$	−19.3030	−	33.4338i	−0.655943	−	1.13613i
$867$	−32.3709	+	29.4657i	−1.09937	+	1.00071i
$868$	4.56519	+	2.63572i	0.154953	+	0.0894620i
$869$	8.14901	−	40.5743i	0.276436	−	1.37639i
$870$	0.0558049	−	0.174967i	0.00189196	−	0.00593193i
$871$	−0.705483	+	0.407311i	−0.0239044	+	0.0138012i
$872$		−	3.12788i		−	0.105923i
$873$	30.7336	−	14.0841i	1.04017	−	0.476674i
$874$	−9.72228			−0.328861
$875$	−0.404254	−	0.700188i	−0.0136663	−	0.0236707i
$876$	24.7826	−	5.40808i	0.837328	−	0.182722i
$877$	7.65282	+	4.41836i	0.258417	+	0.149197i	0.623612	−	0.781734i	$-0.285664\pi$
$877$	7.65282	+	4.41836i	0.258417	+	0.149197i	−0.365195	+	0.930931i	$0.618998\pi$
$878$	−30.8607	−	17.8174i	−1.04150	−	0.601310i
$879$	−4.34042	−	19.8901i	−0.146399	−	0.670875i
$880$	2.48951	+	2.19142i	0.0839213	+	0.0738729i
$881$			28.9530i			0.975451i	0.872997	+	0.487725i	$0.162173\pi$
$881$			28.9530i			0.975451i	−0.872997	+	0.487725i	$0.837827\pi$
$882$	1.78501	−	18.9551i	0.0601045	−	0.638251i
$883$	22.1157			0.744253			0.372127	−	0.928182i	$-0.378629\pi$
$883$	22.1157			0.744253			0.372127	+	0.928182i	$0.378629\pi$
$884$	−10.3489	+	5.97494i	−0.348071	+	0.200959i
$885$	2.63779	+	0.841312i	0.0886684	+	0.0282804i
$886$	−19.2694	−	11.1252i	−0.647368	−	0.373758i
$887$	17.5830	−	30.4547i	0.590380	−	1.02257i	−0.403802	−	0.914847i	$-0.632311\pi$
$887$	17.5830	−	30.4547i	0.590380	−	1.02257i	0.994181	−	0.107721i	$-0.0343553\pi$
$888$	5.32781	−	4.84965i	0.178789	−	0.162744i
$889$	8.63378	+	14.9541i	0.289568	+	0.501546i
$890$	7.20794			0.241611
$891$	23.5589	−	18.3297i	0.789253	−	0.614069i
$892$	−17.3266			−0.580136
$893$	−4.38090	−	7.58794i	−0.146601	−	0.253921i
$894$	26.4855	−	24.1085i	0.885808	−	0.806310i
$895$	0.341582	−	0.591638i	0.0114178	−	0.0197763i
$896$	0.700188	+	0.404254i	0.0233916	+	0.0135052i
$897$	15.7636	+	5.02774i	0.526333	+	0.167871i
$898$	21.5944	−	12.4675i	0.720615	−	0.416047i
$899$	0.691316			0.0230567
$900$	−0.281268	+	2.98679i	−0.00937559	+	0.0995595i
$901$		−	72.1276i		−	2.40292i
$902$	−7.62999	+	8.66784i	−0.254051	+	0.288608i
$903$	−0.378223	−	1.73321i	−0.0125865	−	0.0576777i
$904$	−0.700012	−	0.404152i	−0.0232820	−	0.0134419i
$905$	−8.44041	−	4.87307i	−0.280569	−	0.161986i
$906$	−34.3537	+	7.49669i	−1.14132	+	0.249061i
$907$	23.6311	+	40.9302i	0.784657	+	1.35907i	0.929204	+	0.369567i	$0.120494\pi$
$907$	23.6311	+	40.9302i	0.784657	+	1.35907i	−0.144547	+	0.989498i	$0.546173\pi$
$908$	7.87967			0.261496
$909$	31.1776	−	14.2876i	1.03410	−	0.473889i
$910$			1.48600i			0.0492603i
$911$	30.5270	−	17.6248i	1.01141	−	0.583935i	0.0998029	−	0.995007i	$-0.468179\pi$
$911$	30.5270	−	17.6248i	1.01141	−	0.583935i	0.911603	+	0.411072i	$0.134845\pi$
$912$	−0.984487	+	3.08669i	−0.0325996	+	0.102211i
$913$	37.5462	+	7.54085i	1.24260	+	0.249566i
$914$	3.35432	+	1.93662i	0.110951	+	0.0640577i
$915$	15.9141	−	14.4858i	0.526102	−	0.478887i
$916$	3.92425	+	6.79701i	0.129661	+	0.224579i
$917$			4.98292i			0.164551i
$918$	13.2382	−	31.0823i	0.436926	−	1.02587i
$919$			11.7900i			0.388916i	0.980911	+	0.194458i	$0.0622948\pi$
$919$			11.7900i			0.388916i	−0.980911	+	0.194458i	$0.937705\pi$
$920$	−2.59877	−	4.50121i	−0.0856790	−	0.148400i
$921$	5.20295	+	5.71594i	0.171443	+	0.188346i
$922$	4.36386	−	7.55843i	0.143716	−	0.248924i
$923$	−8.15710	+	14.1285i	−0.268494	+	0.465046i
$924$	−4.64388	+	0.0773173i	−0.152772	+	0.00254355i
$925$	−2.07976	−	3.60224i	−0.0683820	−	0.118441i
$926$	30.4202			0.999670
$927$	31.8436	+	22.6131i	1.04588	+	0.742711i
$928$	0.106031			0.00348063
$929$	10.4435	−	6.02956i	0.342640	−	0.197823i	−0.318799	−	0.947822i	$-0.603279\pi$
$929$	10.4435	−	6.02956i	0.342640	−	0.197823i	0.661439	+	0.749999i	$0.269946\pi$
$930$	−11.0333	+	2.40768i	−0.361795	+	0.0789511i
$931$	−10.2807	−	5.93556i	−0.336936	−	0.194530i
$932$	−3.19402	+	5.53221i	−0.104624	+	0.181214i
$933$	−14.5417	+	3.17329i	−0.476073	+	0.103889i
$934$	12.4070	−	7.16319i	0.405970	−	0.234387i
$935$	−20.4322	+	6.89357i	−0.668206	+	0.225444i
$936$	3.19248	−	4.49563i	0.104350	−	0.146944i
$937$		−	53.5358i		−	1.74894i	−0.485080	−	0.874470i	$-0.661209\pi$
$937$		−	53.5358i		−	1.74894i	0.485080	−	0.874470i	$-0.338791\pi$
$938$	−0.310339	+	0.179174i	−0.0101329	+	0.00585024i
$939$	3.39347	+	1.08233i	0.110742	+	0.0353205i
$940$	2.34204	−	4.05652i	0.0763888	−	0.132309i
$941$	−4.14260	+	7.17519i	−0.135045	+	0.233904i	−0.925615	−	0.378468i	$-0.876451\pi$
$941$	−4.14260	+	7.17519i	−0.135045	+	0.233904i	0.790570	+	0.612372i	$0.209784\pi$
$942$	2.75181	−	2.50485i	0.0896589	−	0.0816123i
$943$	15.6721	−	9.04827i	0.510353	−	0.294652i
$944$			1.59851i			0.0520272i
$945$	−2.52422	−	3.35824i	−0.0821130	−	0.109243i
$946$	3.98103	−	1.34315i	0.129435	−	0.0436695i
$947$	44.3316	−	25.5949i	1.44058	−	0.831722i	0.442696	−	0.896672i	$-0.354022\pi$
$947$	44.3316	−	25.5949i	1.44058	−	0.831722i	0.997889	+	0.0649501i	$0.0206888\pi$
$948$	14.5482	+	15.9826i	0.472504	+	0.519091i
$949$	−13.4584	+	23.3106i	−0.436878	+	0.756695i
$950$	1.61995	+	0.935276i	0.0525580	+	0.0303444i
$951$	−2.06853	+	6.48551i	−0.0670766	+	0.210307i
$952$	−4.55243	+	2.62835i	−0.147545	+	0.0851853i
$953$	17.2842			0.559891			0.279945	−	0.960016i	$-0.409684\pi$
$953$	17.2842			0.559891			0.279945	+	0.960016i	$0.409684\pi$
$954$	13.8649	+	30.2552i	0.448891	+	0.979548i
$955$	−5.87887			−0.190236
$956$	−7.14471	−	12.3750i	−0.231076	−	0.400236i
$957$	−0.522353	+	0.313289i	−0.0168853	+	0.0101272i
$958$	−4.21713	+	7.30428i	−0.136249	+	0.235991i
$959$	4.08314	−	7.07220i	0.131851	−	0.228373i
$960$	−1.69223	+	0.369279i	−0.0546164	+	0.0119184i
$961$	−5.75493	−	9.96783i	−0.185643	−	0.321543i
$962$			7.64499i			0.246484i
$963$	5.48879	−	58.2856i	0.176874	−	1.87823i
$964$			6.44039i			0.207431i
$965$	0.880691	+	1.52540i	0.0283505	+	0.0491044i
$966$	6.93435	+	2.21168i	0.223109	+	0.0711597i
$967$	11.2321	+	6.48486i	0.361200	+	0.208539i	0.669607	−	0.742715i	$-0.266462\pi$
$967$	11.2321	+	6.48486i	0.361200	+	0.208539i	−0.308407	+	0.951255i	$0.599796\pi$
$968$	−1.39531	−	10.9111i	−0.0448471	−	0.350698i
$969$	−14.1797	−	15.5777i	−0.455518	−	0.500429i
$970$	9.75924	−	5.63450i	0.313350	−	0.180913i
$971$			0.242751i			0.00779026i	0.999992	+	0.00389513i	$0.00123986\pi$
$971$			0.242751i			0.00779026i	−0.999992	+	0.00389513i	$0.998760\pi$
$972$	0.421850	+	15.5827i	0.0135308	+	0.499817i
$973$	−10.0142			−0.321041
$974$	−4.02490	−	6.97134i	−0.128966	−	0.223376i
$975$	−2.14290	−	2.35418i	−0.0686278	−	0.0753942i
$976$	10.7598	+	6.21219i	0.344414	+	0.198847i
$977$	25.4078	+	14.6692i	0.812866	+	0.469309i	0.847950	−	0.530076i	$-0.177837\pi$
$977$	25.4078	+	14.6692i	0.812866	+	0.469309i	−0.0350839	+	0.999384i	$0.511170\pi$
$978$	−19.5358	−	6.23086i	−0.624687	−	0.199241i
$979$	−17.9442	−	15.7956i	−0.573500	−	0.504831i
$980$		−	6.34632i		−	0.202726i
$981$	−9.34230	−	0.879771i	−0.298277	−	0.0280889i
$982$	−0.741818			−0.0236724
$983$	46.8439	−	27.0453i	1.49409	−	0.862612i	0.494112	−	0.869398i	$-0.335493\pi$
$983$	46.8439	−	27.0453i	1.49409	−	0.862612i	0.999977	+	0.00678602i	$0.00216007\pi$
$984$	−1.28574	−	5.89191i	−0.0409878	−	0.187827i
$985$	−1.96390	−	1.13386i	−0.0625749	−	0.0361276i
$986$	−0.344692	+	0.597023i	−0.0109772	+	0.0190131i
$987$	1.39850	+	6.40864i	0.0445147	+	0.203989i
$988$	−1.71899	−	2.97738i	−0.0546884	−	0.0947232i
$989$	−6.58427			−0.209368
$990$	7.24553	−	6.81925i	0.230278	−	0.216730i
$991$	−26.7484			−0.849690			−0.424845	−	0.905266i	$-0.639671\pi$
$991$	−26.7484			−0.849690			−0.424845	+	0.905266i	$0.639671\pi$
$992$	−3.25998	−	5.64645i	−0.103504	−	0.179275i
$993$	25.1238	+	8.01312i	0.797279	+	0.254289i
$994$	−3.58827	+	6.21507i	−0.113813	+	0.197130i
$995$	19.9297	+	11.5064i	0.631815	+	0.364778i
$996$	−14.7898	+	13.4625i	−0.468634	+	0.426575i
$997$	−19.4039	+	11.2028i	−0.614526	+	0.354797i	−0.774735	−	0.632286i	$-0.782117\pi$
$997$	−19.4039	+	11.2028i	−0.614526	+	0.354797i	0.160209	+	0.987083i	$0.448783\pi$
$998$	−5.61657			−0.177789
$999$	−12.9863	−	17.2771i	−0.410870	−	0.546622i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.t.a.131.6	✓	48
3.2	odd	2		2970.2.t.b.2771.5		48
9.2	odd	6		990.2.t.b.461.6	yes	48
9.7	even	3		2970.2.t.a.791.5		48
11.10	odd	2		990.2.t.b.131.6	yes	48
33.32	even	2		2970.2.t.a.2771.5		48
99.43	odd	6		2970.2.t.b.791.5		48
99.65	even	6	inner	990.2.t.a.461.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.t.a.131.6	✓	48	1.1	even	1	trivial
990.2.t.a.461.6	yes	48	99.65	even	6	inner
990.2.t.b.131.6	yes	48	11.10	odd	2
990.2.t.b.461.6	yes	48	9.2	odd	6
2970.2.t.a.791.5		48	9.7	even	3
2970.2.t.a.2771.5		48	33.32	even	2
2970.2.t.b.791.5		48	99.43	odd	6
2970.2.t.b.2771.5		48	3.2	odd	2

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:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-1.28087 + 1.16592i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +(1.65015 + 0.526309i) q^{6} +(-0.700188 + 0.404254i) q^{7} +1.00000 q^{8} +(0.281268 - 2.98679i) q^{9} -1.00000i q^{10} +(-2.19142 + 2.48951i) q^{11} +(-0.369279 - 1.69223i) q^{12} +(1.59171 + 0.918976i) q^{13} +(0.700188 + 0.404254i) q^{14} +(-1.69223 + 0.369279i) q^{15} +(-0.500000 - 0.866025i) q^{16} +6.50173 q^{17} +(-2.72727 + 1.24981i) q^{18} +1.87055i q^{19} +(-0.866025 + 0.500000i) q^{20} +(0.425524 - 1.33416i) q^{21} +(3.25169 + 0.653075i) q^{22} +(-4.50121 - 2.59877i) q^{23} +(-1.28087 + 1.16592i) q^{24} +(0.500000 + 0.866025i) q^{25} -1.83795i q^{26} +(3.12208 + 4.15363i) q^{27} -0.808507i q^{28} +(-0.0530153 - 0.0918253i) q^{29} +(1.16592 + 1.28087i) q^{30} +(-3.25998 + 5.64645i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-0.0956298 - 5.74377i) q^{33} +(-3.25087 - 5.63067i) q^{34} -0.808507 q^{35} +(2.44600 + 1.73698i) q^{36} -4.15951 q^{37} +(1.61995 - 0.935276i) q^{38} +(-3.11023 + 0.678717i) q^{39} +(0.866025 + 0.500000i) q^{40} +(-1.74087 + 3.01528i) q^{41} +(-1.36818 + 0.298565i) q^{42} +(1.09708 - 0.633401i) q^{43} +(-1.06027 - 3.14258i) q^{44} +(1.73698 - 2.44600i) q^{45} +5.19755i q^{46} +(-4.05652 + 2.34204i) q^{47} +(1.65015 + 0.526309i) q^{48} +(-3.17316 + 5.49607i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-8.32789 + 7.58049i) q^{51} +(-1.59171 + 0.918976i) q^{52} -11.0936i q^{53} +(2.03611 - 4.78061i) q^{54} +(-3.14258 + 1.06027i) q^{55} +(-0.700188 + 0.404254i) q^{56} +(-2.18091 - 2.39594i) q^{57} +(-0.0530153 + 0.0918253i) q^{58} +(-1.38435 - 0.799257i) q^{59} +(0.526309 - 1.65015i) q^{60} +(-10.7598 + 6.21219i) q^{61} +6.51996 q^{62} +(1.01048 + 2.20501i) q^{63} +1.00000 q^{64} +(0.918976 + 1.59171i) q^{65} +(-4.92643 + 2.95470i) q^{66} +(-0.221611 + 0.383842i) q^{67} +(-3.25087 + 5.63067i) q^{68} +(8.79543 - 1.91934i) q^{69} +(0.404254 + 0.700188i) q^{70} +8.87630i q^{71} +(0.281268 - 2.98679i) q^{72} +14.6450i q^{73} +(2.07976 + 3.60224i) q^{74} +(-1.65015 - 0.526309i) q^{75} +(-1.61995 - 0.935276i) q^{76} +(0.528016 - 2.62902i) q^{77} +(2.14290 + 2.35418i) q^{78} +(-10.8062 + 6.23895i) q^{79} -1.00000i q^{80} +(-8.84178 - 1.68017i) q^{81} +3.48175 q^{82} +(-5.77334 - 9.99972i) q^{83} +(0.942653 + 1.03559i) q^{84} +(5.63067 + 3.25087i) q^{85} +(-1.09708 - 0.633401i) q^{86} +(0.174967 + 0.0558049i) q^{87} +(-2.19142 + 2.48951i) q^{88} +7.20794i q^{89} +(-2.98679 - 0.281268i) q^{90} -1.48600 q^{91} +(4.50121 - 2.59877i) q^{92} +(-2.40768 - 11.0333i) q^{93} +(4.05652 + 2.34204i) q^{94} +(-0.935276 + 1.61995i) q^{95} +(-0.369279 - 1.69223i) q^{96} +(5.63450 + 9.75924i) q^{97} +6.34632 q^{98} +(6.81925 + 7.24553i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 24 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{6} + 48 q^{8} + 10 q^{9} - 6 q^{11} + 4 q^{12} + 24 q^{13} - 4 q^{15} - 24 q^{16} - 12 q^{17} - 8 q^{18} - 16 q^{21} + 12 q^{22} + 36 q^{23} - 2 q^{24} + 24 q^{25}+ \cdots - 48 q^{99}+O(q^{100}) \) 48 * q - 24 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^6 + 48 * q^8 + 10 * q^9 - 6 * q^11 + 4 * q^12 + 24 * q^13 - 4 * q^15 - 24 * q^16 - 12 * q^17 - 8 * q^18 - 16 * q^21 + 12 * q^22 + 36 * q^23 - 2 * q^24 + 24 * q^25 - 8 * q^27 + 8 * q^30 - 24 * q^32 + 2 * q^33 + 6 * q^34 - 2 * q^36 - 6 * q^38 - 40 * q^39 - 6 * q^41 + 8 * q^42 + 30 * q^43 - 6 * q^44 - 2 * q^48 + 24 * q^49 + 24 * q^50 + 22 * q^51 - 24 * q^52 + 22 * q^54 + 40 * q^57 - 54 * q^59 - 4 * q^60 - 38 * q^63 + 48 * q^64 + 8 * q^66 - 6 * q^67 + 6 * q^68 + 76 * q^69 + 10 * q^72 + 2 * q^75 + 6 * q^76 + 6 * q^77 + 32 * q^78 + 10 * q^81 + 12 * q^82 + 36 * q^83 + 8 * q^84 - 30 * q^86 - 44 * q^87 - 6 * q^88 + 24 * q^91 - 36 * q^92 - 68 * q^93 + 4 * q^96 + 6 * q^97 - 48 * q^98 - 48 * q^99

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