LMFDB - Embedded newform 1110.2.bb.d.1009.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(1009,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1110.1009");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.bb (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1009.9
Character	$\chi$	$=$	1110.1009
Dual form			1110.2.bb.d.1099.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.13568 + 0.662460i) q^{5} +1.00000 q^{6} +(-1.09384 + 0.631530i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.13568 + 0.662460i) q^{5} +1.00000 q^{6} +(-1.09384 + 0.631530i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.18079 - 0.494135i) q^{10} -4.99195 q^{11} +(0.866025 + 0.500000i) q^{12} +(-4.64326 + 2.68079i) q^{13} -1.26306 q^{14} +(-1.51833 + 1.64155i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.69192 + 2.13153i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-3.67492 - 6.36515i) q^{19} +(-1.64155 - 1.51833i) q^{20} +(-0.631530 + 1.09384i) q^{21} +(-4.32315 - 2.49597i) q^{22} -7.94839i q^{23} +(0.500000 + 0.866025i) q^{24} +(4.12229 - 2.82961i) q^{25} -5.36157 q^{26} -1.00000i q^{27} +(-1.09384 - 0.631530i) q^{28} +0.263060 q^{29} +(-2.13568 + 0.662460i) q^{30} -8.35352 q^{31} +(-0.866025 + 0.500000i) q^{32} +(-4.32315 + 2.49597i) q^{33} +(2.13153 + 3.69192i) q^{34} +(1.91774 - 2.07338i) q^{35} +1.00000 q^{36} +(-5.93579 - 1.32904i) q^{37} -7.34984i q^{38} +(-2.68079 + 4.64326i) q^{39} +(-0.662460 - 2.13568i) q^{40} +(3.74009 + 6.47803i) q^{41} +(-1.09384 + 0.631530i) q^{42} +11.0032i q^{43} +(-2.49597 - 4.32315i) q^{44} +(-0.494135 + 2.18079i) q^{45} +(3.97419 - 6.88350i) q^{46} +3.66980i q^{47} +1.00000i q^{48} +(-2.70234 + 4.68059i) q^{49} +(4.98482 - 0.389366i) q^{50} +4.26306 q^{51} +(-4.64326 - 2.68079i) q^{52} +(7.06383 + 4.07831i) q^{53} +(0.500000 - 0.866025i) q^{54} +(10.6612 - 3.30696i) q^{55} +(-0.631530 - 1.09384i) q^{56} +(-6.36515 - 3.67492i) q^{57} +(0.227817 + 0.131530i) q^{58} +(-2.45264 + 4.24810i) q^{59} +(-2.18079 - 0.494135i) q^{60} +(0.390022 + 0.675539i) q^{61} +(-7.23436 - 4.17676i) q^{62} +1.26306i q^{63} -1.00000 q^{64} +(8.14062 - 8.80129i) q^{65} -4.99195 q^{66} +(-3.05829 + 1.76570i) q^{67} +4.26306i q^{68} +(-3.97419 - 6.88350i) q^{69} +(2.69750 - 0.836727i) q^{70} +(-0.141422 - 0.244950i) q^{71} +(0.866025 + 0.500000i) q^{72} +1.54371i q^{73} +(-4.47603 - 4.11888i) q^{74} +(2.15521 - 4.51166i) q^{75} +(3.67492 - 6.36515i) q^{76} +(5.46040 - 3.15256i) q^{77} +(-4.64326 + 2.68079i) q^{78} +(-4.05244 - 7.01903i) q^{79} +(0.494135 - 2.18079i) q^{80} +(-0.500000 - 0.866025i) q^{81} +7.48019i q^{82} +(11.9301 + 6.88783i) q^{83} -1.26306 q^{84} +(-9.29683 - 2.10653i) q^{85} +(-5.50161 + 9.52907i) q^{86} +(0.227817 - 0.131530i) q^{87} -4.99195i q^{88} +(6.52339 - 11.2988i) q^{89} +(-1.51833 + 1.64155i) q^{90} +(3.38600 - 5.86472i) q^{91} +(6.88350 - 3.97419i) q^{92} +(-7.23436 + 4.17676i) q^{93} +(-1.83490 + 3.17814i) q^{94} +(12.0651 + 11.1595i) q^{95} +(-0.500000 + 0.866025i) q^{96} +6.02010i q^{97} +(-4.68059 + 2.70234i) q^{98} +(-2.49597 + 4.32315i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9}+O(q^{10}) $ 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9	$ 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9} + 4 q^{10} - 12 q^{11} + 8 q^{14} + 2 q^{15} - 14 q^{16} - 20 q^{19} - 2 q^{20} + 4 q^{21} + 14 q^{24} - 8 q^{25} - 20 q^{26} - 36 q^{29} + 2 q^{30} + 24 q^{31} + 38 q^{34} - 2 q^{35} + 28 q^{36} - 10 q^{39} + 2 q^{40} - 6 q^{44} + 4 q^{45} + 8 q^{46} + 50 q^{49} - 4 q^{50} + 76 q^{51} + 14 q^{54} - 28 q^{55} + 4 q^{56} - 26 q^{59} + 4 q^{60} - 28 q^{61} - 28 q^{64} + 60 q^{65} - 12 q^{66} - 8 q^{69} - 10 q^{70} - 64 q^{71} + 24 q^{74} - 8 q^{75} + 20 q^{76} + 32 q^{79} - 4 q^{80} - 14 q^{81} + 8 q^{84} + 16 q^{85} - 8 q^{86} + 76 q^{89} + 2 q^{90} - 8 q^{91} - 38 q^{94} - 70 q^{95} - 14 q^{96} - 6 q^{99}+O(q^{100}) $ 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9 + 4 * q^10 - 12 * q^11 + 8 * q^14 + 2 * q^15 - 14 * q^16 - 20 * q^19 - 2 * q^20 + 4 * q^21 + 14 * q^24 - 8 * q^25 - 20 * q^26 - 36 * q^29 + 2 * q^30 + 24 * q^31 + 38 * q^34 - 2 * q^35 + 28 * q^36 - 10 * q^39 + 2 * q^40 - 6 * q^44 + 4 * q^45 + 8 * q^46 + 50 * q^49 - 4 * q^50 + 76 * q^51 + 14 * q^54 - 28 * q^55 + 4 * q^56 - 26 * q^59 + 4 * q^60 - 28 * q^61 - 28 * q^64 + 60 * q^65 - 12 * q^66 - 8 * q^69 - 10 * q^70 - 64 * q^71 + 24 * q^74 - 8 * q^75 + 20 * q^76 + 32 * q^79 - 4 * q^80 - 14 * q^81 + 8 * q^84 + 16 * q^85 - 8 * q^86 + 76 * q^89 + 2 * q^90 - 8 * q^91 - 38 * q^94 - 70 * q^95 - 14 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−2.13568	+	0.662460i	−0.955107	+	0.296261i
$5$	−2.13568	+	0.662460i	−0.955107	+	0.296261i
$6$	1.00000			0.408248
$7$	−1.09384	+	0.631530i	−0.413434	+	0.238696i	−0.692264	−	0.721644i	$-0.743387\pi$
$7$	−1.09384	+	0.631530i	−0.413434	+	0.238696i	0.278830	+	0.960340i	$0.410053\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−2.18079	−	0.494135i	−0.689625	−	0.156259i
$11$	−4.99195			−1.50513			−0.752564	−	0.658519i	$-0.771183\pi$
$11$	−4.99195			−1.50513			−0.752564	+	0.658519i	$0.771183\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$	−4.64326	+	2.68079i	−1.28781	+	0.743516i	−0.978263	−	0.207368i	$-0.933510\pi$
$13$	−4.64326	+	2.68079i	−1.28781	+	0.743516i	−0.309545	+	0.950885i	$0.600177\pi$
$14$	−1.26306			−0.337567
$15$	−1.51833	+	1.64155i	−0.392030	+	0.423846i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.69192	+	2.13153i	0.895422	+	0.516972i	0.875712	−	0.482834i	$-0.160392\pi$
$17$	3.69192	+	2.13153i	0.895422	+	0.516972i	0.0197097	+	0.999806i	$0.493726\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−3.67492	−	6.36515i	−0.843085	−	1.46027i	−0.887274	−	0.461243i	$-0.847404\pi$
$19$	−3.67492	−	6.36515i	−0.843085	−	1.46027i	0.0441891	−	0.999023i	$-0.485930\pi$
$20$	−1.64155	−	1.51833i	−0.367062	−	0.339508i
$21$	−0.631530	+	1.09384i	−0.137811	+	0.238696i
$22$	−4.32315	−	2.49597i	−0.921699	−	0.532143i
$23$		−	7.94839i		−	1.65735i	−0.559728	−	0.828677i	$-0.689094\pi$
$23$		−	7.94839i		−	1.65735i	0.559728	−	0.828677i	$-0.310906\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	4.12229	−	2.82961i	0.824459	−	0.565922i
$26$	−5.36157			−1.05149
$27$		−	1.00000i		−	0.192450i
$28$	−1.09384	−	0.631530i	−0.206717	−	0.119348i
$29$	0.263060			0.0488491			0.0244245	−	0.999702i	$-0.492225\pi$
$29$	0.263060			0.0488491			0.0244245	+	0.999702i	$0.492225\pi$
$30$	−2.13568	+	0.662460i	−0.389921	+	0.120948i
$31$	−8.35352			−1.50034			−0.750168	−	0.661247i	$-0.770027\pi$
$31$	−8.35352			−1.50034			−0.750168	+	0.661247i	$0.770027\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−4.32315	+	2.49597i	−0.752564	+	0.434493i
$34$	2.13153	+	3.69192i	0.365554	+	0.633159i
$35$	1.91774	−	2.07338i	0.324157	−	0.350464i
$36$	1.00000			0.166667
$37$	−5.93579	−	1.32904i	−0.975839	−	0.218492i
$37$	−5.93579	−	1.32904i	−0.975839	−	0.218492i
$38$		−	7.34984i		−	1.19230i
$39$	−2.68079	+	4.64326i	−0.429269	+	0.743516i
$40$	−0.662460	−	2.13568i	−0.104744	−	0.337681i
$41$	3.74009	+	6.47803i	0.584104	+	1.01170i	0.994986	+	0.100010i	$0.0318875\pi$
$41$	3.74009	+	6.47803i	0.584104	+	1.01170i	−0.410882	+	0.911689i	$0.634779\pi$
$42$	−1.09384	+	0.631530i	−0.168784	+	0.0974472i
$43$			11.0032i			1.67798i	0.544150	+	0.838988i	$0.316852\pi$
$43$			11.0032i			1.67798i	−0.544150	+	0.838988i	$0.683148\pi$
$44$	−2.49597	−	4.32315i	−0.376282	−	0.651740i
$45$	−0.494135	+	2.18079i	−0.0736613	+	0.325092i
$46$	3.97419	−	6.88350i	0.585963	−	1.01492i
$47$			3.66980i			0.535296i	0.963517	+	0.267648i	$0.0862464\pi$
$47$			3.66980i			0.535296i	−0.963517	+	0.267648i	$0.913754\pi$
$48$			1.00000i			0.144338i
$49$	−2.70234	+	4.68059i	−0.386048	+	0.668656i
$50$	4.98482	−	0.389366i	0.704959	−	0.0550647i
$51$	4.26306			0.596948
$52$	−4.64326	−	2.68079i	−0.643904	−	0.371758i
$53$	7.06383	+	4.07831i	0.970292	+	0.560198i	0.899325	−	0.437280i	$-0.144058\pi$
$53$	7.06383	+	4.07831i	0.970292	+	0.560198i	0.0709668	+	0.997479i	$0.477392\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	10.6612	−	3.30696i	1.43756	−	0.445911i
$56$	−0.631530	−	1.09384i	−0.0843918	−	0.146171i
$57$	−6.36515	−	3.67492i	−0.843085	−	0.486755i
$58$	0.227817	+	0.131530i	0.0299138	+	0.0172708i
$59$	−2.45264	+	4.24810i	−0.319307	+	0.553055i	−0.980344	−	0.197298i	$-0.936783\pi$
$59$	−2.45264	+	4.24810i	−0.319307	+	0.553055i	0.661037	+	0.750353i	$0.270117\pi$
$60$	−2.18079	−	0.494135i	−0.281538	−	0.0637926i
$61$	0.390022	+	0.675539i	0.0499373	+	0.0864939i	0.889914	−	0.456129i	$-0.150765\pi$
$61$	0.390022	+	0.675539i	0.0499373	+	0.0864939i	−0.839976	+	0.542623i	$0.817431\pi$
$62$	−7.23436	−	4.17676i	−0.918765	−	0.530449i
$63$			1.26306i			0.159131i
$64$	−1.00000			−0.125000
$65$	8.14062	−	8.80129i	1.00972	−	1.09167i
$66$	−4.99195			−0.614466
$67$	−3.05829	+	1.76570i	−0.373629	+	0.215715i	−0.675043	−	0.737779i	$-0.735875\pi$
$67$	−3.05829	+	1.76570i	−0.373629	+	0.215715i	0.301414	+	0.953494i	$0.402542\pi$
$68$			4.26306i			0.516972i
$69$	−3.97419	−	6.88350i	−0.478437	−	0.828677i
$70$	2.69750	−	0.836727i	0.322413	−	0.100008i
$71$	−0.141422	−	0.244950i	−0.0167837	−	0.0290702i	0.857512	−	0.514465i	$-0.172009\pi$
$71$	−0.141422	−	0.244950i	−0.0167837	−	0.0290702i	−0.874295	+	0.485394i	$0.838676\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$			1.54371i			0.180677i	0.995911	+	0.0903387i	$0.0287950\pi$
$73$			1.54371i			0.180677i	−0.995911	+	0.0903387i	$0.971205\pi$
$74$	−4.47603	−	4.11888i	−0.520328	−	0.478810i
$75$	2.15521	−	4.51166i	0.248862	−	0.520962i
$76$	3.67492	−	6.36515i	0.421542	−	0.730133i
$77$	5.46040	−	3.15256i	0.622271	−	0.359268i
$78$	−4.64326	+	2.68079i	−0.525746	+	0.303539i
$79$	−4.05244	−	7.01903i	−0.455935	−	0.789703i	0.542806	−	0.839858i	$-0.317362\pi$
$79$	−4.05244	−	7.01903i	−0.455935	−	0.789703i	−0.998741	+	0.0501551i	$0.984028\pi$
$80$	0.494135	−	2.18079i	0.0552460	−	0.243819i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$			7.48019i			0.826048i
$83$	11.9301	+	6.88783i	1.30950	+	0.756038i	0.982012	−	0.188819i	$-0.0604659\pi$
$83$	11.9301	+	6.88783i	1.30950	+	0.756038i	0.327484	+	0.944857i	$0.393799\pi$
$84$	−1.26306			−0.137811
$85$	−9.29683	−	2.10653i	−1.00838	−	0.228485i
$86$	−5.50161	+	9.52907i	−0.593254	+	1.02755i
$87$	0.227817	−	0.131530i	0.0244245	−	0.0141015i
$88$		−	4.99195i		−	0.532143i
$89$	6.52339	−	11.2988i	0.691478	−	1.19768i	−0.279876	−	0.960036i	$-0.590293\pi$
$89$	6.52339	−	11.2988i	0.691478	−	1.19768i	0.971354	−	0.237639i	$-0.0763734\pi$
$90$	−1.51833	+	1.64155i	−0.160046	+	0.173034i
$91$	3.38600	−	5.86472i	0.354949	−	0.614789i
$92$	6.88350	−	3.97419i	0.717655	−	0.414338i
$93$	−7.23436	+	4.17676i	−0.750168	+	0.433110i
$94$	−1.83490	+	3.17814i	−0.189256	+	0.327800i
$95$	12.0651	+	11.1595i	1.23786	+	1.14494i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$			6.02010i			0.611249i	0.952152	+	0.305624i	$0.0988651\pi$
$97$			6.02010i			0.611249i	−0.952152	+	0.305624i	$0.901135\pi$
$98$	−4.68059	+	2.70234i	−0.472811	+	0.272977i
$99$	−2.49597	+	4.32315i	−0.250855	+	0.434493i
$100$	4.51166	+	2.15521i	0.451166	+	0.215521i
$101$	−19.5101			−1.94133			−0.970665	−	0.240435i	$-0.922710\pi$
$101$	−19.5101			−1.94133			−0.970665	+	0.240435i	$0.922710\pi$
$102$	3.69192	+	2.13153i	0.365554	+	0.211053i
$103$		−	8.49192i		−	0.836733i	−0.908278	−	0.418367i	$-0.862603\pi$
$103$		−	8.49192i		−	0.836733i	0.908278	−	0.418367i	$-0.137397\pi$
$104$	−2.68079	−	4.64326i	−0.262873	−	0.455309i
$105$	0.624123	−	2.75447i	0.0609081	−	0.268808i
$106$	4.07831	+	7.06383i	0.396120	+	0.686100i
$107$	−13.5483	+	7.82214i	−1.30977	+	0.756195i	−0.982057	−	0.188583i	$-0.939610\pi$
$107$	−13.5483	+	7.82214i	−1.30977	+	0.756195i	−0.327711	+	0.944778i	$0.606277\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	5.13717	−	8.89784i	0.492051	−	0.852258i	−0.507907	−	0.861412i	$-0.669581\pi$
$109$	5.13717	−	8.89784i	0.492051	−	0.852258i	0.999958	+	0.00915400i	$0.00291385\pi$
$110$	10.8864	+	2.46670i	1.03797	+	0.235190i
$111$	−5.80507	+	1.81692i	−0.550993	+	0.172454i
$112$		−	1.26306i		−	0.119348i
$113$	15.6594	+	9.04098i	1.47312	+	0.850503i	0.999542	−	0.0302513i	$-0.00963074\pi$
$113$	15.6594	+	9.04098i	1.47312	+	0.850503i	0.473573	+	0.880755i	$0.342964\pi$
$114$	−3.67492	−	6.36515i	−0.344188	−	0.596151i
$115$	5.26549	+	16.9752i	0.491009	+	1.58295i
$116$	0.131530	+	0.227817i	0.0122123	+	0.0211523i
$117$			5.36157i			0.495678i
$118$	−4.24810	+	2.45264i	−0.391069	+	0.225784i
$119$	−5.38450			−0.493597
$120$	−1.64155	−	1.51833i	−0.149852	−	0.138604i
$121$	13.9195			1.26541
$122$			0.780045i			0.0706219i
$123$	6.47803	+	3.74009i	0.584104	+	0.337233i
$124$	−4.17676	−	7.23436i	−0.375084	−	0.649665i
$125$	−6.92942	+	8.77401i	−0.619786	+	0.784771i
$126$	−0.631530	+	1.09384i	−0.0562612	+	0.0974472i
$127$	3.82426	+	2.20794i	0.339348	+	0.195923i	0.659984	−	0.751280i	$-0.270563\pi$
$127$	3.82426	+	2.20794i	0.339348	+	0.195923i	−0.320635	+	0.947203i	$0.603896\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	5.50161	+	9.52907i	0.484390	+	0.838988i
$130$	11.4506	−	3.55183i	1.00429	−	0.311516i
$131$	4.83306	−	8.37111i	0.422267	−	0.731388i	−0.573894	−	0.818930i	$-0.694568\pi$
$131$	4.83306	−	8.37111i	0.422267	−	0.731388i	0.996161	+	0.0875420i	$0.0279012\pi$
$132$	−4.32315	−	2.49597i	−0.376282	−	0.217247i
$133$	8.03957	+	4.64165i	0.697119	+	0.402482i
$134$	−3.53141			−0.305067
$135$	0.662460	+	2.13568i	0.0570155	+	0.183810i
$136$	−2.13153	+	3.69192i	−0.182777	+	0.316579i
$137$		−	14.3318i		−	1.22445i	−0.790684	−	0.612225i	$-0.790275\pi$
$137$		−	14.3318i		−	1.22445i	0.790684	−	0.612225i	$-0.209725\pi$
$138$		−	7.94839i		−	0.676612i
$139$	−3.79794	+	6.57823i	−0.322137	+	0.557958i	−0.980929	−	0.194367i	$-0.937735\pi$
$139$	−3.79794	+	6.57823i	−0.322137	+	0.557958i	0.658791	+	0.752326i	$0.271068\pi$
$140$	2.75447	+	0.624123i	0.232795	+	0.0527480i
$141$	1.83490	+	3.17814i	0.154527	+	0.267648i
$142$		−	0.282844i		−	0.0237357i
$143$	23.1789	−	13.3823i	1.93832	−	1.11909i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−0.561814	+	0.174267i	−0.0466561	+	0.0144721i
$146$	−0.771854	+	1.33689i	−0.0638791	+	0.110642i
$147$			5.40468i			0.445770i
$148$	−1.81692	−	5.80507i	−0.149350	−	0.477174i
$149$	−2.64733			−0.216877			−0.108439	−	0.994103i	$-0.534585\pi$
$149$	−2.64733			−0.216877			−0.108439	+	0.994103i	$0.534585\pi$
$150$	4.12229	−	2.82961i	0.336584	−	0.231037i
$151$	−2.35137	−	4.07269i	−0.191352	−	0.331431i	0.754347	−	0.656476i	$-0.227954\pi$
$151$	−2.35137	−	4.07269i	−0.191352	−	0.331431i	−0.945698	+	0.325045i	$0.894620\pi$
$152$	6.36515	−	3.67492i	0.516282	−	0.298076i
$153$	3.69192	−	2.13153i	0.298474	−	0.172324i
$154$	6.30513			0.508082
$155$	17.8405	−	5.53387i	1.43298	−	0.444491i
$156$	−5.36157			−0.429269
$157$	−11.7867	−	6.80507i	−0.940683	−	0.543104i	−0.0505086	−	0.998724i	$-0.516084\pi$
$157$	−11.7867	−	6.80507i	−0.940683	−	0.543104i	−0.890174	+	0.455620i	$0.849418\pi$
$158$		−	8.10488i		−	0.644790i
$159$	8.15661			0.646861
$160$	1.51833	−	1.64155i	0.120034	−	0.129776i
$161$	5.01965	+	8.69428i	0.395604	+	0.685205i
$162$		−	1.00000i		−	0.0785674i
$163$	−10.5279	−	6.07828i	−0.824609	−	0.476088i	0.0273945	−	0.999625i	$-0.491279\pi$
$163$	−10.5279	−	6.07828i	−0.824609	−	0.476088i	−0.852003	+	0.523537i	$0.824612\pi$
$164$	−3.74009	+	6.47803i	−0.292052	+	0.505849i
$165$	7.57941	−	8.19452i	0.590056	−	0.637943i
$166$	6.88783	+	11.9301i	0.534600	+	0.925954i
$167$	−17.1266	+	9.88805i	−1.32530	+	0.765160i	−0.984568	−	0.175001i	$-0.944007\pi$
$167$	−17.1266	+	9.88805i	−1.32530	+	0.765160i	−0.340728	+	0.940162i	$0.610674\pi$
$168$	−1.09384	−	0.631530i	−0.0843918	−	0.0487236i
$169$	7.87323	−	13.6368i	0.605633	−	1.04899i
$170$	−6.99802	−	6.47272i	−0.536724	−	0.496435i
$171$	−7.34984			−0.562057
$172$	−9.52907	+	5.50161i	−0.726585	+	0.419494i
$173$	−4.03173	−	2.32772i	−0.306527	−	0.176973i	0.338844	−	0.940842i	$-0.389964\pi$
$173$	−4.03173	−	2.32772i	−0.306527	−	0.176973i	−0.645371	+	0.763869i	$0.723297\pi$
$174$	0.263060			0.0199426
$175$	−2.72216	+	5.69850i	−0.205776	+	0.430766i
$176$	2.49597	−	4.32315i	0.188141	−	0.325870i
$177$			4.90528i			0.368704i
$178$	11.2988	−	6.52339i	0.846884	−	0.488949i
$179$	18.0339			1.34792			0.673958	−	0.738770i	$-0.264593\pi$
$179$	18.0339			1.34792			0.673958	+	0.738770i	$0.264593\pi$
$180$	−2.13568	+	0.662460i	−0.159185	+	0.0493768i
$181$	6.41934	+	11.1186i	0.477146	+	0.826440i	0.999657	−	0.0261920i	$-0.00833811\pi$
$181$	6.41934	+	11.1186i	0.477146	+	0.826440i	−0.522511	+	0.852632i	$0.675005\pi$
$182$	5.86472	−	3.38600i	0.434722	−	0.250987i
$183$	0.675539	+	0.390022i	0.0499373	+	0.0288313i
$184$	7.94839			0.585963
$185$	13.5574	−	1.09382i	0.996761	−	0.0804194i
$186$	−8.35352			−0.612510
$187$	−18.4299	−	10.6405i	−1.34772	−	0.778109i
$188$	−3.17814	+	1.83490i	−0.231790	+	0.133824i
$189$	0.631530	+	1.09384i	0.0459371	+	0.0795653i
$190$	4.86898	+	15.6969i	0.353233	+	1.13878i
$191$	−4.45352			−0.322246			−0.161123	−	0.986934i	$-0.551512\pi$
$191$	−4.45352			−0.322246			−0.161123	+	0.986934i	$0.551512\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$			8.79974i			0.633419i	0.948523	+	0.316709i	$0.102578\pi$
$193$			8.79974i			0.633419i	−0.948523	+	0.316709i	$0.897422\pi$
$194$	−3.01005	+	5.21356i	−0.216109	+	0.374312i
$195$	2.64934	−	11.6924i	0.189723	−	0.837314i
$196$	−5.40468			−0.386048
$197$	−7.01557	−	4.05044i	−0.499839	−	0.288582i	0.228808	−	0.973472i	$-0.426517\pi$
$197$	−7.01557	−	4.05044i	−0.499839	−	0.288582i	−0.728647	+	0.684889i	$0.759851\pi$
$198$	−4.32315	+	2.49597i	−0.307233	+	0.177381i
$199$	0.881703			0.0625023			0.0312511	−	0.999512i	$-0.490051\pi$
$199$	0.881703			0.0625023			0.0312511	+	0.999512i	$0.490051\pi$
$200$	2.82961	+	4.12229i	0.200084	+	0.291490i
$201$	−1.76570	+	3.05829i	−0.124543	+	0.215715i
$202$	−16.8963	−	9.75507i	−1.18882	−	0.686364i
$203$	−0.287747	+	0.166131i	−0.0201959	+	0.0116601i
$204$	2.13153	+	3.69192i	0.149237	+	0.258486i
$205$	−12.2791	−	11.3574i	−0.857609	−	0.793233i
$206$	4.24596	−	7.35421i	0.295830	−	0.512392i
$207$	−6.88350	−	3.97419i	−0.478437	−	0.276226i
$208$		−	5.36157i		−	0.371758i
$209$	18.3450	+	31.7745i	1.26895	+	2.19789i
$210$	1.91774	−	2.07338i	0.132337	−	0.143077i
$211$	−20.2451			−1.39373			−0.696866	−	0.717201i	$-0.745423\pi$
$211$	−20.2451			−1.39373			−0.696866	+	0.717201i	$0.745423\pi$
$212$			8.15661i			0.560198i
$213$	−0.244950	−	0.141422i	−0.0167837	−	0.00969008i
$214$	−15.6443			−1.06942
$215$	−7.28919	−	23.4994i	−0.497119	−	1.60265i
$216$	1.00000			0.0680414
$217$	9.13743	−	5.27550i	0.620289	−	0.358124i
$218$	8.89784	−	5.13717i	0.602637	−	0.347933i
$219$	0.771854	+	1.33689i	0.0521571	+	0.0903387i
$220$	8.19452	+	7.57941i	0.552475	+	0.511003i
$221$	−22.8567			−1.53751
$222$	−5.93579	−	1.32904i	−0.398384	−	0.0891991i
$223$		−	18.1705i		−	1.21679i	−0.793635	−	0.608394i	$-0.791814\pi$
$223$		−	18.1705i		−	1.21679i	0.793635	−	0.608394i	$-0.208186\pi$
$224$	0.631530	−	1.09384i	0.0421959	−	0.0730854i
$225$	−0.389366	−	4.98482i	−0.0259578	−	0.332321i
$226$	9.04098	+	15.6594i	0.601397	+	1.04165i
$227$	−9.88733	+	5.70845i	−0.656245	+	0.378883i	−0.790845	−	0.612017i	$-0.790358\pi$
$227$	−9.88733	+	5.70845i	−0.656245	+	0.378883i	0.134600	+	0.990900i	$0.457025\pi$
$228$		−	7.34984i		−	0.486755i
$229$	7.27924	+	12.6080i	0.481026	+	0.833161i	0.999763	−	0.0217727i	$-0.00693103\pi$
$229$	7.27924	+	12.6080i	0.481026	+	0.833161i	−0.518737	+	0.854934i	$0.673598\pi$
$230$	−3.92758	+	17.3337i	−0.258977	+	1.14295i
$231$	3.15256	−	5.46040i	0.207424	−	0.359268i
$232$			0.263060i			0.0172708i
$233$			2.82229i			0.184895i	0.995718	+	0.0924473i	$0.0294690\pi$
$233$			2.82229i			0.184895i	−0.995718	+	0.0924473i	$0.970531\pi$
$234$	−2.68079	+	4.64326i	−0.175249	+	0.303539i
$235$	−2.43110	−	7.83754i	−0.158587	−	0.511265i
$236$	−4.90528			−0.319307
$237$	−7.01903	−	4.05244i	−0.455935	−	0.263234i
$238$	−4.66312	−	2.69225i	−0.302265	−	0.174513i
$239$	11.2761	−	19.5308i	0.729390	−	1.26334i	−0.227751	−	0.973719i	$-0.573137\pi$
$239$	11.2761	−	19.5308i	0.729390	−	1.26334i	0.957141	−	0.289621i	$-0.0935294\pi$
$240$	−0.662460	−	2.13568i	−0.0427616	−	0.137858i
$241$	−2.91315	−	5.04572i	−0.187652	−	0.325023i	0.756815	−	0.653629i	$-0.226754\pi$
$241$	−2.91315	−	5.04572i	−0.187652	−	0.325023i	−0.944467	+	0.328606i	$0.893421\pi$
$242$	12.0547	+	6.95976i	0.774903	+	0.447390i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−0.390022	+	0.675539i	−0.0249686	+	0.0432469i
$245$	2.67064	−	11.7865i	0.170621	−	0.753009i
$246$	3.74009	+	6.47803i	0.238460	+	0.413024i
$247$	34.1272	+	19.7034i	2.17146	+	1.25369i
$248$		−	8.35352i		−	0.530449i
$249$	13.7757			0.872997
$250$	−10.3881	+	4.13380i	−0.656998	+	0.261445i
$251$	20.3308			1.28327			0.641633	−	0.767012i	$-0.278257\pi$
$251$	20.3308			1.28327			0.641633	+	0.767012i	$0.278257\pi$
$252$	−1.09384	+	0.631530i	−0.0689056	+	0.0397827i
$253$			39.6779i			2.49453i
$254$	2.20794	+	3.82426i	0.138538	+	0.239956i
$255$	−9.10455	+	2.82411i	−0.570149	+	0.176852i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	8.32463	+	4.80623i	0.519276	+	0.299804i	0.736638	−	0.676287i	$-0.236412\pi$
$257$	8.32463	+	4.80623i	0.519276	+	0.299804i	−0.217362	+	0.976091i	$0.569745\pi$
$258$			11.0032i			0.685031i
$259$	7.33215	−	2.29488i	0.455598	−	0.142597i
$260$	11.6924	+	2.64934i	0.725135	+	0.164305i
$261$	0.131530	−	0.227817i	0.00814151	−	0.0141015i
$262$	8.37111	−	4.83306i	0.517169	−	0.298588i
$263$	−4.05962	+	2.34382i	−0.250327	+	0.144526i	−0.619914	−	0.784670i	$-0.712832\pi$
$263$	−4.05962	+	2.34382i	−0.250327	+	0.144526i	0.369587	+	0.929196i	$0.379499\pi$
$264$	−2.49597	−	4.32315i	−0.153617	−	0.266072i
$265$	−17.7878	−	4.03047i	−1.09270	−	0.247590i
$266$	4.64165	+	8.03957i	0.284598	+	0.492938i
$267$		−	13.0468i		−	0.798450i
$268$	−3.05829	−	1.76570i	−0.186815	−	0.107857i
$269$	18.0324			1.09945			0.549727	−	0.835344i	$-0.314732\pi$
$269$	18.0324			1.09945			0.549727	+	0.835344i	$0.314732\pi$
$270$	−0.494135	+	2.18079i	−0.0300721	+	0.132718i
$271$	1.40902	−	2.44050i	0.0855920	−	0.148250i	−0.820051	−	0.572290i	$-0.806055\pi$
$271$	1.40902	−	2.44050i	0.0855920	−	0.148250i	0.905643	+	0.424040i	$0.139389\pi$
$272$	−3.69192	+	2.13153i	−0.223855	+	0.129243i
$273$		−	6.77199i		−	0.409860i
$274$	7.16590	−	12.4117i	0.432908	−	0.749819i
$275$	−20.5783	+	14.1253i	−1.24092	+	0.851785i
$276$	3.97419	−	6.88350i	0.239218	−	0.414338i
$277$	16.3046	−	9.41347i	0.979649	−	0.565601i	0.0774850	−	0.996994i	$-0.475311\pi$
$277$	16.3046	−	9.41347i	0.979649	−	0.565601i	0.902164	+	0.431393i	$0.141978\pi$
$278$	−6.57823	+	3.79794i	−0.394536	+	0.227786i
$279$	−4.17676	+	7.23436i	−0.250056	+	0.433110i
$280$	2.07338	+	1.91774i	0.123908	+	0.114607i
$281$	8.14090	−	14.1005i	0.485646	−	0.841163i	−0.514218	−	0.857659i	$-0.671918\pi$
$281$	8.14090	−	14.1005i	0.485646	−	0.841163i	0.999864	+	0.0164965i	$0.00525125\pi$
$282$			3.66980i			0.218534i
$283$	−9.11635	+	5.26333i	−0.541911	+	0.312872i	−0.745853	−	0.666111i	$-0.767958\pi$
$283$	−9.11635	+	5.26333i	−0.541911	+	0.312872i	0.203942	+	0.978983i	$0.434624\pi$
$284$	0.141422	−	0.244950i	0.00839185	−	0.0145351i
$285$	16.0284	+	3.63182i	0.949443	+	0.215130i
$286$	26.7647			1.58263
$287$	−8.18214	−	4.72396i	−0.482977	−	0.278847i
$288$			1.00000i			0.0589256i
$289$	0.586842	+	1.01644i	0.0345201	+	0.0597906i
$290$	−0.573679	−	0.129987i	−0.0336876	−	0.00763312i
$291$	3.01005	+	5.21356i	0.176452	+	0.305624i
$292$	−1.33689	+	0.771854i	−0.0782356	+	0.0451693i
$293$	−4.47258	+	2.58224i	−0.261291	+	0.150856i	−0.624923	−	0.780686i	$-0.714870\pi$
$293$	−4.47258	+	2.58224i	−0.261291	+	0.150856i	0.363632	+	0.931542i	$0.381536\pi$
$294$	−2.70234	+	4.68059i	−0.157604	+	0.272977i
$295$	2.42387	−	10.6974i	0.141123	−	0.622825i
$296$	1.32904	−	5.93579i	0.0772487	−	0.345011i
$297$			4.99195i			0.289662i
$298$	−2.29265	−	1.32366i	−0.132810	−	0.0766778i
$299$	21.3079	+	36.9064i	1.23227	+	2.13435i
$300$	4.98482	−	0.389366i	0.287799	−	0.0224801i
$301$	−6.94887	−	12.0358i	−0.400526	−	0.693731i
$302$		−	4.70273i		−	0.270612i
$303$	−16.8963	+	9.75507i	−0.970665	+	0.560414i
$304$	7.34984			0.421542
$305$	−1.28048	−	1.18436i	−0.0733202	−	0.0678164i
$306$	4.26306			0.243703
$307$		−	15.5648i		−	0.888333i	−0.895944	−	0.444166i	$-0.853500\pi$
$307$		−	15.5648i		−	0.888333i	0.895944	−	0.444166i	$-0.146500\pi$
$308$	5.46040	+	3.15256i	0.311135	+	0.179634i
$309$	−4.24596	−	7.35421i	−0.241544	−	0.418367i
$310$	18.2172	+	4.12777i	1.03467	+	0.234441i
$311$	−8.92380	+	15.4565i	−0.506022	+	0.876456i	0.493954	+	0.869488i	$0.335551\pi$
$311$	−8.92380	+	15.4565i	−0.506022	+	0.876456i	−0.999976	+	0.00696784i	$0.997782\pi$
$312$	−4.64326	−	2.68079i	−0.262873	−	0.151770i
$313$	−5.50514	−	3.17839i	−0.311169	−	0.179653i	0.336281	−	0.941762i	$-0.390831\pi$
$313$	−5.50514	−	3.17839i	−0.311169	−	0.179653i	−0.647449	+	0.762108i	$0.724164\pi$
$314$	−6.80507	−	11.7867i	−0.384032	−	0.665163i
$315$	−0.836727	−	2.69750i	−0.0471442	−	0.151987i
$316$	4.05244	−	7.01903i	0.227968	−	0.394851i
$317$	−13.7824	−	7.95728i	−0.774097	−	0.446925i	0.0602370	−	0.998184i	$-0.480814\pi$
$317$	−13.7824	−	7.95728i	−0.774097	−	0.446925i	−0.834334	+	0.551259i	$0.814148\pi$
$318$	7.06383	+	4.07831i	0.396120	+	0.228700i
$319$	−1.31318			−0.0735241
$320$	2.13568	−	0.662460i	0.119388	−	0.0370326i
$321$	−7.82214	+	13.5483i	−0.436589	+	0.756195i
$322$			10.0393i			0.559468i
$323$		−	31.3328i		−	1.74341i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−11.5553	+	24.1896i	−0.640973	+	1.34180i
$326$	−6.07828	−	10.5279i	−0.336645	−	0.583086i
$327$		−	10.2743i		−	0.568172i
$328$	−6.47803	+	3.74009i	−0.357689	+	0.206512i
$329$	−2.31759	−	4.01419i	−0.127773	−	0.221309i
$330$	10.6612	−	3.30696i	0.586881	−	0.182042i
$331$	3.96108	−	6.86079i	0.217721	−	0.377103i	−0.736390	−	0.676557i	$-0.763471\pi$
$331$	3.96108	−	6.86079i	0.217721	−	0.377103i	0.954111	+	0.299454i	$0.0968045\pi$
$332$			13.7757i			0.756038i
$333$	−4.11888	+	4.47603i	−0.225713	+	0.245285i
$334$	−19.7761			−1.08210
$335$	5.36183	−	5.79698i	0.292948	−	0.316723i
$336$	−0.631530	−	1.09384i	−0.0344528	−	0.0596740i
$337$	−30.5973	+	17.6654i	−1.66674	+	0.962295i	−0.697367	+	0.716714i	$0.745645\pi$
$337$	−30.5973	+	17.6654i	−1.66674	+	0.962295i	−0.969376	+	0.245581i	$0.921021\pi$
$338$	13.6368	−	7.87323i	0.741746	−	0.428247i
$339$	18.0820			0.982077
$340$	−2.82411	−	9.10455i	−0.153159	−	0.493764i
$341$	41.7003			2.25820
$342$	−6.36515	−	3.67492i	−0.344188	−	0.198717i
$343$		−	15.6679i		−	0.845985i
$344$	−11.0032			−0.593254
$345$	13.0477	+	12.0682i	0.702463	+	0.649733i
$346$	−2.32772	−	4.03173i	−0.125139	−	0.216747i
$347$		−	3.87172i		−	0.207845i	−0.994585	−	0.103923i	$-0.966861\pi$
$347$		−	3.87172i		−	0.207845i	0.994585	−	0.103923i	$-0.0331394\pi$
$348$	0.227817	+	0.131530i	0.0122123	+	0.00705076i
$349$	−7.16648	+	12.4127i	−0.383613	+	0.664437i	−0.991576	−	0.129528i	$-0.958654\pi$
$349$	−7.16648	+	12.4127i	−0.383613	+	0.664437i	0.607963	+	0.793966i	$0.291987\pi$
$350$	−5.20671	+	3.57397i	−0.278310	+	0.191037i
$351$	2.68079	+	4.64326i	0.143090	+	0.247839i
$352$	4.32315	−	2.49597i	0.230425	−	0.133036i
$353$	1.29700	+	0.748825i	0.0690325	+	0.0398559i	0.534119	−	0.845409i	$-0.320643\pi$
$353$	1.29700	+	0.748825i	0.0690325	+	0.0398559i	−0.465086	+	0.885265i	$0.653977\pi$
$354$	−2.45264	+	4.24810i	−0.130356	+	0.225784i
$355$	0.464302	+	0.429450i	0.0246426	+	0.0227928i
$356$	13.0468			0.691478
$357$	−4.66312	+	2.69225i	−0.246798	+	0.142489i
$358$	15.6178	+	9.01694i	0.825426	+	0.476560i
$359$	−8.83396			−0.466239			−0.233119	−	0.972448i	$-0.574893\pi$
$359$	−8.83396			−0.466239			−0.233119	+	0.972448i	$0.574893\pi$
$360$	−2.18079	−	0.494135i	−0.114938	−	0.0260432i
$361$	−17.5101	+	30.3284i	−0.921584	+	1.59623i
$362$			12.8387i			0.674786i
$363$	12.0547	−	6.95976i	0.632706	−	0.365293i
$364$	6.77199			0.354949
$365$	−1.02264	−	3.29687i	−0.0535277	−	0.172566i
$366$	0.390022	+	0.675539i	0.0203868	+	0.0353110i
$367$	−15.9066	+	9.18365i	−0.830315	+	0.479383i	−0.853961	−	0.520338i	$-0.825806\pi$
$367$	−15.9066	+	9.18365i	−0.830315	+	0.479383i	0.0236452	+	0.999720i	$0.492473\pi$
$368$	6.88350	+	3.97419i	0.358827	+	0.207169i
$369$	7.48019			0.389403
$370$	12.2880	+	5.83143i	0.638822	+	0.303162i
$371$	−10.3023			−0.534868
$372$	−7.23436	−	4.17676i	−0.375084	−	0.216555i
$373$	−7.08648	+	4.09138i	−0.366924	+	0.211844i	−0.672114	−	0.740448i	$-0.734613\pi$
$373$	−7.08648	+	4.09138i	−0.366924	+	0.211844i	0.305190	+	0.952292i	$0.401280\pi$
$374$	−10.6405	−	18.4299i	−0.550206	−	0.952985i
$375$	−1.61405	+	11.0632i	−0.0833491	+	0.571302i
$376$	−3.66980			−0.189256
$377$	−1.22146	+	0.705209i	−0.0629083	+	0.0363201i
$378$			1.26306i			0.0649648i
$379$	−13.6863	+	23.7054i	−0.703019	+	1.21766i	0.264383	+	0.964418i	$0.414832\pi$
$379$	−13.6863	+	23.7054i	−0.703019	+	1.21766i	−0.967402	+	0.253247i	$0.918502\pi$
$380$	−3.63182	+	16.0284i	−0.186308	+	0.822242i
$381$	4.41588			0.226232
$382$	−3.85686	−	2.22676i	−0.197334	−	0.113931i
$383$	29.9910	−	17.3153i	1.53247	−	0.884771i	0.533222	−	0.845975i	$-0.320981\pi$
$383$	29.9910	−	17.3153i	1.53247	−	0.884771i	0.999247	−	0.0387959i	$-0.0123522\pi$
$384$	−1.00000			−0.0510310
$385$	−9.57325	+	10.3502i	−0.487898	+	0.527494i
$386$	−4.39987	+	7.62080i	−0.223947	+	0.387888i
$387$	9.52907	+	5.50161i	0.484390	+	0.279663i
$388$	−5.21356	+	3.01005i	−0.264678	+	0.152812i
$389$	−10.0409	−	17.3913i	−0.509093	−	0.881775i	−0.999945	−	0.0105319i	$-0.996648\pi$
$389$	−10.0409	−	17.3913i	−0.509093	−	0.881775i	0.490851	−	0.871243i	$-0.336686\pi$
$390$	8.14062	−	8.80129i	0.412216	−	0.445670i
$391$	16.9422	−	29.3448i	0.856805	−	1.48403i
$392$	−4.68059	−	2.70234i	−0.236405	−	0.136489i
$393$		−	9.66613i		−	0.487592i
$394$	−4.05044	−	7.01557i	−0.204058	−	0.353440i
$395$	13.3046	+	12.3059i	0.669425	+	0.619175i
$396$	−4.99195			−0.250855
$397$			19.1670i			0.961964i	0.876730	+	0.480982i	$0.159720\pi$
$397$			19.1670i			0.961964i	−0.876730	+	0.480982i	$0.840280\pi$
$398$	0.763578	+	0.440852i	0.0382747	+	0.0220979i
$399$	9.28330			0.464746
$400$	0.389366	+	4.98482i	0.0194683	+	0.249241i
$401$	−2.28974			−0.114344			−0.0571721	−	0.998364i	$-0.518208\pi$
$401$	−2.28974			−0.114344			−0.0571721	+	0.998364i	$0.518208\pi$
$402$	−3.05829	+	1.76570i	−0.152533	+	0.0880653i
$403$	38.7876	−	22.3940i	1.93215	−	1.11552i
$404$	−9.75507	−	16.8963i	−0.485333	−	0.840621i
$405$	1.64155	+	1.51833i	0.0815692	+	0.0754463i
$406$	−0.332261			−0.0164898
$407$	29.6312	+	6.63448i	1.46876	+	0.328859i
$408$			4.26306i			0.211053i
$409$	−18.8834	+	32.7070i	−0.933724	+	1.61726i	−0.156831	+	0.987625i	$0.550128\pi$
$409$	−18.8834	+	32.7070i	−0.933724	+	1.61726i	−0.776893	+	0.629632i	$0.783206\pi$
$410$	−4.95532	−	15.9753i	−0.244726	−	0.788965i
$411$	−7.16590	−	12.4117i	−0.353468	−	0.612225i
$412$	7.35421	−	4.24596i	0.362316	−	0.209183i
$413$		−	6.19567i		−	0.304869i
$414$	−3.97419	−	6.88350i	−0.195321	−	0.338306i
$415$	−30.0418	−	6.80704i	−1.47469	−	0.334145i
$416$	2.68079	−	4.64326i	0.131436	−	0.227654i
$417$			7.59589i			0.371972i
$418$			36.6900i			1.79457i
$419$	8.70163	−	15.0717i	0.425103	−	0.736299i	−0.571327	−	0.820722i	$-0.693571\pi$
$419$	8.70163	−	15.0717i	0.425103	−	0.736299i	0.996430	+	0.0844228i	$0.0269047\pi$
$420$	2.69750	−	0.836727i	0.131624	−	0.0408281i
$421$	6.81109			0.331952			0.165976	−	0.986130i	$-0.446923\pi$
$421$	6.81109			0.331952			0.165976	+	0.986130i	$0.446923\pi$
$422$	−17.5328	−	10.1226i	−0.853484	−	0.492759i
$423$	3.17814	+	1.83490i	0.154527	+	0.0892159i
$424$	−4.07831	+	7.06383i	−0.198060	+	0.343050i
$425$	21.2506	−	1.65989i	1.03080	−	0.0805166i
$426$	−0.141422	−	0.244950i	−0.00685192	−	0.0118679i
$427$	−0.853246	−	0.492622i	−0.0412915	−	0.0238396i
$428$	−13.5483	−	7.82214i	−0.654884	−	0.378097i
$429$	13.3823	−	23.1789i	0.646106	−	1.11909i
$430$	5.43708	−	23.9957i	0.262199	−	1.15717i
$431$	10.8020	+	18.7097i	0.520316	+	0.901214i	0.999721	+	0.0236199i	$0.00751915\pi$
$431$	10.8020	+	18.7097i	0.520316	+	0.901214i	−0.479405	+	0.877594i	$0.659148\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$			4.55525i			0.218911i	0.993992	+	0.109456i	$0.0349108\pi$
$433$			4.55525i			0.218911i	−0.993992	+	0.109456i	$0.965089\pi$
$434$	10.5510			0.506464
$435$	−0.399412	+	0.431826i	−0.0191503	+	0.0207045i
$436$	10.2743			0.492051
$437$	−50.5927	+	29.2097i	−2.42018	+	1.39729i
$438$			1.54371i			0.0737612i
$439$	6.18014	+	10.7043i	0.294962	+	0.510889i	0.974976	−	0.222310i	$-0.0713597\pi$
$439$	6.18014	+	10.7043i	0.294962	+	0.510889i	−0.680014	+	0.733199i	$0.738026\pi$
$440$	3.30696	+	10.6612i	0.157653	+	0.508254i
$441$	2.70234	+	4.68059i	0.128683	+	0.222885i
$442$	−19.7945	−	11.4284i	−0.941528	−	0.543591i
$443$			13.2381i			0.628960i	0.949264	+	0.314480i	$0.101830\pi$
$443$			13.2381i			0.628960i	−0.949264	+	0.314480i	$0.898170\pi$
$444$	−4.47603	−	4.11888i	−0.212423	−	0.195473i
$445$	−6.44687	+	28.4522i	−0.305611	+	1.34877i
$446$	9.08526	−	15.7361i	0.430200	−	0.745127i
$447$	−2.29265	+	1.32366i	−0.108439	+	0.0626071i
$448$	1.09384	−	0.631530i	0.0516792	−	0.0298370i
$449$	−18.3409	−	31.7673i	−0.865559	−	1.49919i	−0.866492	−	0.499192i	$-0.833630\pi$
$449$	−18.3409	−	31.7673i	−0.865559	−	1.49919i	0.000932977	−	1.00000i	$-0.499703\pi$
$450$	2.15521	−	4.51166i	0.101597	−	0.212682i
$451$	−18.6703	−	32.3380i	−0.879152	−	1.52274i
$452$			18.0820i			0.850503i
$453$	−4.07269	−	2.35137i	−0.191352	−	0.110477i
$454$	−11.4169			−0.535822
$455$	−3.34628	+	14.7683i	−0.156876	+	0.692347i
$456$	3.67492	−	6.36515i	0.172094	−	0.298076i
$457$	−32.3173	+	18.6584i	−1.51174	+	0.872803i	−0.511833	+	0.859085i	$0.671033\pi$
$457$	−32.3173	+	18.6584i	−1.51174	+	0.872803i	−0.999906	+	0.0137183i	$0.995633\pi$
$458$			14.5585i			0.680273i
$459$	2.13153	−	3.69192i	0.0994913	−	0.172324i
$460$	−12.0682	+	13.0477i	−0.562685	+	0.608351i
$461$	−11.8742	+	20.5667i	−0.553036	+	0.957887i	0.445017	+	0.895522i	$0.353198\pi$
$461$	−11.8742	+	20.5667i	−0.553036	+	0.957887i	−0.998053	+	0.0623650i	$0.980136\pi$
$462$	5.46040	−	3.15256i	0.254041	−	0.146671i
$463$	−24.5010	+	14.1457i	−1.13866	+	0.657405i	−0.946098	−	0.323880i	$-0.895013\pi$
$463$	−24.5010	+	14.1457i	−1.13866	+	0.657405i	−0.192561	+	0.981285i	$0.561679\pi$
$464$	−0.131530	+	0.227817i	−0.00610614	+	0.0105761i
$465$	12.6834	−	13.7127i	0.588177	−	0.635912i
$466$	−1.41115	+	2.44418i	−0.0653701	+	0.113224i
$467$		−	19.4357i		−	0.899378i	−0.893185	−	0.449689i	$-0.851535\pi$
$467$		−	19.4357i		−	0.899378i	0.893185	−	0.449689i	$-0.148465\pi$
$468$	−4.64326	+	2.68079i	−0.214635	+	0.123919i
$469$	2.23019	−	3.86280i	0.102981	−	0.178368i
$470$	1.81338	−	8.00306i	0.0836449	−	0.369153i
$471$	−13.6101			−0.627122
$472$	−4.24810	−	2.45264i	−0.195535	−	0.112892i
$473$		−	54.9275i		−	2.52557i
$474$	−4.05244	−	7.01903i	−0.186135	−	0.322395i
$475$	−33.1600	−	15.8404i	−1.52149	−	0.726809i
$476$	−2.69225	−	4.66312i	−0.123399	−	0.213734i
$477$	7.06383	−	4.07831i	0.323431	−	0.186733i
$478$	19.5308	−	11.2761i	0.893317	−	0.515757i
$479$	−18.7548	+	32.4842i	−0.856926	+	1.48424i	0.0179197	+	0.999839i	$0.494296\pi$
$479$	−18.7548	+	32.4842i	−0.856926	+	1.48424i	−0.874846	+	0.484401i	$0.839038\pi$
$480$	0.494135	−	2.18079i	0.0225541	−	0.0995388i
$481$	31.1243	−	9.74154i	1.41915	−	0.444176i
$482$		−	5.82630i		−	0.265380i
$483$	8.69428	+	5.01965i	0.395604	+	0.228402i
$484$	6.95976	+	12.0547i	0.316353	+	0.547939i
$485$	−3.98807	−	12.8570i	−0.181089	−	0.583808i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$		−	17.3440i		−	0.785931i	−0.919553	−	0.392965i	$-0.871449\pi$
$487$		−	17.3440i		−	0.785931i	0.919553	−	0.392965i	$-0.128551\pi$
$488$	−0.675539	+	0.390022i	−0.0305802	+	0.0176555i
$489$	−12.1566			−0.549739
$490$	8.20607	−	8.87204i	0.370712	−	0.400798i
$491$	−2.30071			−0.103829			−0.0519147	−	0.998652i	$-0.516532\pi$
$491$	−2.30071			−0.103829			−0.0519147	+	0.998652i	$0.516532\pi$
$492$			7.48019i			0.337233i
$493$	0.971197	+	0.560721i	0.0437405	+	0.0252536i
$494$	19.7034	+	34.1272i	0.886496	+	1.53546i
$495$	2.46670	−	10.8864i	0.110870	−	0.489306i
$496$	4.17676	−	7.23436i	0.187542	−	0.324832i
$497$	0.309387	+	0.178625i	0.0138779	+	0.00801241i
$498$	11.9301	+	6.88783i	0.534600	+	0.308651i
$499$	−2.18307	−	3.78119i	−0.0977276	−	0.169269i	0.813016	−	0.582241i	$-0.197824\pi$
$499$	−2.18307	−	3.78119i	−0.0977276	−	0.169269i	−0.910744	+	0.412972i	$0.864491\pi$
$500$	−11.0632	−	1.61405i	−0.494762	−	0.0721824i
$501$	−9.88805	+	17.1266i	−0.441766	+	0.765160i
$502$	17.6070	+	10.1654i	0.785837	+	0.453703i
$503$	−18.1801	−	10.4963i	−0.810608	−	0.468005i	0.0365587	−	0.999332i	$-0.488360\pi$
$503$	−18.1801	−	10.4963i	−0.810608	−	0.468005i	−0.847167	+	0.531327i	$0.821694\pi$
$504$	−1.26306			−0.0562612
$505$	41.6675	−	12.9247i	1.85418	−	0.575140i
$506$	−19.8390	+	34.3621i	−0.881949	+	1.52758i
$507$		−	15.7465i		−	0.699325i
$508$			4.41588i			0.195923i
$509$	−18.8359	+	32.6247i	−0.834886	+	1.44607i	0.0592368	+	0.998244i	$0.481133\pi$
$509$	−18.8359	+	32.6247i	−0.834886	+	1.44607i	−0.894123	+	0.447821i	$0.852200\pi$
$510$	−9.29683	−	2.10653i	−0.411670	−	0.0932786i
$511$	−0.974898	−	1.68857i	−0.0431270	−	0.0746981i
$512$		−	1.00000i		−	0.0441942i
$513$	−6.36515	+	3.67492i	−0.281028	+	0.162252i
$514$	4.80623	+	8.32463i	0.211993	+	0.367184i
$515$	5.62555	+	18.1361i	0.247891	+	0.799170i
$516$	−5.50161	+	9.52907i	−0.242195	+	0.419494i
$517$		−	18.3195i		−	0.805689i
$518$	7.49727	+	1.67865i	0.329411	+	0.0737558i
$519$	−4.65544			−0.204351
$520$	8.80129	+	8.14062i	0.385962	+	0.356990i
$521$	−18.1788	−	31.4866i	−0.796428	−	1.37945i	−0.921929	−	0.387360i	$-0.873387\pi$
$521$	−18.1788	−	31.4866i	−0.796428	−	1.37945i	0.125501	−	0.992094i	$-0.459946\pi$
$522$	0.227817	−	0.131530i	0.00997128	−	0.00575692i
$523$	35.0328	−	20.2262i	1.53188	−	0.884430i	0.532602	−	0.846366i	$-0.321214\pi$
$523$	35.0328	−	20.2262i	1.53188	−	0.884430i	0.999275	−	0.0380645i	$-0.0121192\pi$
$524$	9.66613			0.422267
$525$	0.491793	+	6.29612i	0.0214636	+	0.274785i
$526$	−4.68764			−0.204391
$527$	−30.8405	−	17.8058i	−1.34343	−	0.775632i
$528$		−	4.99195i		−	0.217247i
$529$	−40.1769			−1.74682
$530$	−13.3895	−	12.3844i	−0.581602	−	0.537944i
$531$	2.45264	+	4.24810i	0.106436	+	0.184352i
$532$			9.28330i			0.402482i
$533$	−34.7324	−	20.0528i	−1.50443	−	0.868582i
$534$	6.52339	−	11.2988i	0.282295	−	0.488949i
$535$	23.7531	−	25.6809i	1.02694	−	1.11028i
$536$	−1.76570	−	3.05829i	−0.0762667	−	0.132098i
$537$	15.6178	−	9.01694i	0.673958	−	0.389110i
$538$	15.6165	+	9.01620i	0.673276	+	0.388716i
$539$	13.4899	−	23.3652i	0.581052	−	1.00641i
$540$	−1.51833	+	1.64155i	−0.0653384	+	0.0706410i
$541$	13.0090			0.559299			0.279649	−	0.960102i	$-0.409782\pi$
$541$	13.0090			0.559299			0.279649	+	0.960102i	$0.409782\pi$
$542$	2.44050	−	1.40902i	0.104828	−	0.0605227i
$543$	11.1186	+	6.41934i	0.477146	+	0.275480i
$544$	−4.26306			−0.182777
$545$	−5.07691	+	22.4061i	−0.217471	+	0.959773i
$546$	3.38600	−	5.86472i	0.144907	−	0.250987i
$547$		−	24.6188i		−	1.05262i	−0.850292	−	0.526312i	$-0.823574\pi$
$547$		−	24.6188i		−	1.05262i	0.850292	−	0.526312i	$-0.176426\pi$
$548$	12.4117	−	7.16590i	0.530202	−	0.306112i
$549$	0.780045			0.0332915
$550$	−24.8839	+	1.94370i	−1.06105	+	0.0828795i
$551$	−0.966726	−	1.67442i	−0.0411839	−	0.0713327i
$552$	6.88350	−	3.97419i	0.292981	−	0.169153i
$553$	8.86546	+	5.11848i	0.376998	+	0.217660i
$554$	18.8269			0.799880
$555$	11.1942	−	7.72599i	0.475165	−	0.327950i
$556$	−7.59589			−0.322137
$557$	12.1937	+	7.04001i	0.516662	+	0.298295i	0.735568	−	0.677451i	$-0.236915\pi$
$557$	12.1937	+	7.04001i	0.516662	+	0.298295i	−0.218906	+	0.975746i	$0.570249\pi$
$558$	−7.23436	+	4.17676i	−0.306255	+	0.176816i
$559$	−29.4973	−	51.0908i	−1.24760	−	2.16091i
$560$	0.836727	+	2.69750i	0.0353582	+	0.113990i
$561$	−21.2810			−0.898483
$562$	14.1005	−	8.14090i	0.594792	−	0.343403i
$563$			18.2964i			0.771101i	0.922687	+	0.385551i	$0.125989\pi$
$563$			18.2964i			0.771101i	−0.922687	+	0.385551i	$0.874011\pi$
$564$	−1.83490	+	3.17814i	−0.0772633	+	0.133824i
$565$	−39.4329	−	8.93493i	−1.65895	−	0.375895i
$566$	−10.5267			−0.442468
$567$	1.09384	+	0.631530i	0.0459371	+	0.0265218i
$568$	0.244950	−	0.141422i	0.0102779	−	0.00593394i
$569$	25.3625			1.06325			0.531625	−	0.846980i	$-0.321581\pi$
$569$	25.3625			1.06325			0.531625	+	0.846980i	$0.321581\pi$
$570$	12.0651	+	11.1595i	0.505353	+	0.467419i
$571$	21.1056	−	36.5560i	0.883241	−	1.52982i	0.0355254	−	0.999369i	$-0.488690\pi$
$571$	21.1056	−	36.5560i	0.883241	−	1.52982i	0.847716	−	0.530450i	$-0.177977\pi$
$572$	23.1789	+	13.3823i	0.969158	+	0.559544i
$573$	−3.85686	+	2.22676i	−0.161123	+	0.0930243i
$574$	−4.72396	−	8.18214i	−0.197174	−	0.341516i
$575$	−22.4908	−	32.7656i	−0.937932	−	1.36642i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−0.213185	−	0.123082i	−0.00887501	−	0.00512399i	0.495556	−	0.868576i	$-0.334964\pi$
$577$	−0.213185	−	0.123082i	−0.00887501	−	0.00512399i	−0.504431	+	0.863452i	$0.668298\pi$
$578$			1.17368i			0.0488188i
$579$	4.39987	+	7.62080i	0.182852	+	0.316709i
$580$	−0.431826	−	0.399412i	−0.0179306	−	0.0165847i
$581$	−17.3995			−0.721853
$582$			6.02010i			0.249541i
$583$	−35.2623	−	20.3587i	−1.46041	−	0.843171i
$584$	−1.54371			−0.0638791
$585$	−3.55183	−	11.4506i	−0.146850	−	0.473425i
$586$	−5.16449			−0.213343
$587$	−24.5330	+	14.1641i	−1.01258	+	0.584616i	−0.911947	−	0.410307i	$-0.865421\pi$
$587$	−24.5330	+	14.1641i	−1.01258	+	0.584616i	−0.100637	+	0.994923i	$0.532088\pi$
$588$	−4.68059	+	2.70234i	−0.193024	+	0.111443i
$589$	30.6985	+	53.1714i	1.26491	+	2.19089i
$590$	7.44782	−	8.05226i	0.306622	−	0.331506i
$591$	−8.10089			−0.333226
$592$	4.11888	−	4.47603i	0.169285	−	0.183964i
$593$			32.0201i			1.31491i	0.753494	+	0.657455i	$0.228367\pi$
$593$			32.0201i			1.31491i	−0.753494	+	0.657455i	$0.771633\pi$
$594$	−2.49597	+	4.32315i	−0.102411	+	0.177381i
$595$	11.4996	−	3.56702i	0.471438	−	0.146233i
$596$	−1.32366	−	2.29265i	−0.0542194	−	0.0939107i
$597$	0.763578	−	0.440852i	0.0312511	−	0.0180429i
$598$			42.6159i			1.74269i
$599$	8.52695	+	14.7691i	0.348402	+	0.603449i	0.985966	−	0.166948i	$-0.0533912\pi$
$599$	8.52695	+	14.7691i	0.348402	+	0.603449i	−0.637564	+	0.770397i	$0.720058\pi$
$600$	4.51166	+	2.15521i	0.184188	+	0.0879860i
$601$	−5.27568	+	9.13774i	−0.215199	+	0.372736i	−0.953334	−	0.301917i	$-0.902373\pi$
$601$	−5.27568	+	9.13774i	−0.215199	+	0.372736i	0.738135	+	0.674653i	$0.235707\pi$
$602$		−	13.8977i		−	0.566429i
$603$			3.53141i			0.143810i
$604$	2.35137	−	4.07269i	0.0956758	−	0.165715i
$605$	−29.7277	+	9.22112i	−1.20860	+	0.374892i
$606$	−19.5101			−0.792545
$607$	−9.55271	−	5.51526i	−0.387733	−	0.223858i	0.293445	−	0.955976i	$-0.405198\pi$
$607$	−9.55271	−	5.51526i	−0.387733	−	0.223858i	−0.681177	+	0.732118i	$0.738532\pi$
$608$	6.36515	+	3.67492i	0.258141	+	0.149038i
$609$	−0.166131	+	0.287747i	−0.00673195	+	0.0116601i
$610$	−0.516748	−	1.66593i	−0.0209225	−	0.0674515i
$611$	−9.83796	−	17.0398i	−0.398001	−	0.689358i
$612$	3.69192	+	2.13153i	0.149237	+	0.0861620i
$613$	18.5126	+	10.6883i	0.747717	+	0.431695i	0.824869	−	0.565325i	$-0.191249\pi$
$613$	18.5126	+	10.6883i	0.747717	+	0.431695i	−0.0771512	+	0.997019i	$0.524582\pi$
$614$	7.78242	−	13.4796i	0.314073	−	0.543990i
$615$	−16.3127	−	3.69622i	−0.657791	−	0.149046i
$616$	3.15256	+	5.46040i	0.127020	+	0.220006i
$617$	2.11476	+	1.22095i	0.0851368	+	0.0491538i	0.541964	−	0.840402i	$-0.317681\pi$
$617$	2.11476	+	1.22095i	0.0851368	+	0.0491538i	−0.456827	+	0.889555i	$0.651014\pi$
$618$		−	8.49192i		−	0.341595i
$619$	41.1110			1.65239			0.826196	−	0.563382i	$-0.190500\pi$
$619$	41.1110			1.65239			0.826196	+	0.563382i	$0.190500\pi$
$620$	13.7127	+	12.6834i	0.550716	+	0.509377i
$621$	−7.94839			−0.318958
$622$	−15.4565	+	8.92380i	−0.619748	+	0.357812i
$623$			16.4789i			0.660212i
$624$	−2.68079	−	4.64326i	−0.107317	−	0.185879i
$625$	8.98662	−	23.3290i	0.359465	−	0.933159i
$626$	−3.17839	−	5.50514i	−0.127034	−	0.220029i
$627$	31.7745	+	18.3450i	1.26895	+	0.732629i
$628$		−	13.6101i		−	0.543104i
$629$	−19.0816	−	17.5590i	−0.760833	−	0.700124i
$630$	0.624123	−	2.75447i	0.0248656	−	0.109741i
$631$	8.88206	−	15.3842i	0.353589	−	0.612434i	−0.633286	−	0.773918i	$-0.718294\pi$
$631$	8.88206	−	15.3842i	0.353589	−	0.612434i	0.986875	+	0.161483i	$0.0516278\pi$
$632$	7.01903	−	4.05244i	0.279202	−	0.161197i
$633$	−17.5328	+	10.1226i	−0.696866	+	0.402336i
$634$	−7.95728	−	13.7824i	−0.316024	−	0.547369i
$635$	−9.63009	−	2.18204i	−0.382158	−	0.0865917i
$636$	4.07831	+	7.06383i	0.161715	+	0.280099i
$637$		−	28.9776i		−	1.14813i
$638$	−1.13725	−	0.656592i	−0.0450242	−	0.0259947i
$639$	−0.282844			−0.0111891
$640$	2.18079	+	0.494135i	0.0862032	+	0.0195324i
$641$	10.1835	−	17.6384i	0.402225	−	0.696674i	−0.591769	−	0.806108i	$-0.701570\pi$
$641$	10.1835	−	17.6384i	0.402225	−	0.696674i	0.993994	+	0.109433i	$0.0349036\pi$
$642$	−13.5483	+	7.82214i	−0.534710	+	0.308715i
$643$			3.70473i			0.146100i	0.997328	+	0.0730502i	$0.0232733\pi$
$643$			3.70473i			0.146100i	−0.997328	+	0.0730502i	$0.976727\pi$
$644$	−5.01965	+	8.69428i	−0.197802	+	0.342603i
$645$	−18.0623	−	16.7065i	−0.711203	−	0.657817i
$646$	15.6664	−	27.1350i	0.616387	−	1.06761i
$647$	−3.89440	+	2.24843i	−0.153105	+	0.0883950i	−0.574595	−	0.818438i	$-0.694840\pi$
$647$	−3.89440	+	2.24843i	−0.153105	+	0.0883950i	0.421490	+	0.906833i	$0.361507\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	12.2434	−	21.2063i	0.480597	−	0.832419i
$650$	−22.1020	+	15.1712i	−0.866911	+	0.595062i
$651$	5.27550	−	9.13743i	0.206763	−	0.358124i
$652$		−	12.1566i		−	0.476088i
$653$	19.3934	−	11.1968i	0.758921	−	0.438163i	−0.0699875	−	0.997548i	$-0.522296\pi$
$653$	19.3934	−	11.1968i	0.758921	−	0.438163i	0.828908	+	0.559385i	$0.188963\pi$
$654$	5.13717	−	8.89784i	0.200879	−	0.347933i
$655$	−4.77637	+	21.0798i	−0.186628	+	0.823655i
$656$	−7.48019			−0.292052
$657$	1.33689	+	0.771854i	0.0521571	+	0.0301129i
$658$		−	4.63518i		−	0.180698i
$659$	1.35816	+	2.35241i	0.0529065	+	0.0916368i	0.891266	−	0.453481i	$-0.149818\pi$
$659$	1.35816	+	2.35241i	0.0529065	+	0.0916368i	−0.838359	+	0.545118i	$0.816485\pi$
$660$	10.8864	+	2.46670i	0.423751	+	0.0960160i
$661$	3.15588	+	5.46614i	0.122749	+	0.212608i	0.920851	−	0.389915i	$-0.127495\pi$
$661$	3.15588	+	5.46614i	0.122749	+	0.212608i	−0.798102	+	0.602523i	$0.794162\pi$
$662$	6.86079	−	3.96108i	0.266652	−	0.153952i
$663$	−19.7945	+	11.4284i	−0.768754	+	0.443841i
$664$	−6.88783	+	11.9301i	−0.267300	+	0.462977i
$665$	−20.2449	−	4.58720i	−0.785063	−	0.177884i
$666$	−5.80507	+	1.81692i	−0.224942	+	0.0704042i
$667$		−	2.09091i		−	0.0809602i
$668$	−17.1266	−	9.88805i	−0.662648	−	0.382580i
$669$	−9.08526	−	15.7361i	−0.351256	−	0.608394i
$670$	7.54197	−	2.33941i	0.291372	−	0.0903794i
$671$	−1.94697	−	3.37225i	−0.0751620	−	0.130184i
$672$		−	1.26306i		−	0.0487236i
$673$	3.67729	−	2.12308i	0.141749	−	0.0818388i	−0.427448	−	0.904040i	$-0.640587\pi$
$673$	3.67729	−	2.12308i	0.141749	−	0.0818388i	0.569197	+	0.822201i	$0.307254\pi$
$674$	−35.3308			−1.36089
$675$	−2.82961	−	4.12229i	−0.108912	−	0.158667i
$676$	15.7465			0.605633
$677$			38.4405i			1.47739i	0.674041	+	0.738693i	$0.264557\pi$
$677$			38.4405i			1.47739i	−0.674041	+	0.738693i	$0.735443\pi$
$678$	15.6594	+	9.04098i	0.601397	+	0.347217i
$679$	−3.80187	−	6.58504i	−0.145903	−	0.252711i
$680$	2.10653	−	9.29683i	0.0807817	−	0.356517i
$681$	−5.70845	+	9.88733i	−0.218748	+	0.378883i
$682$	36.1135	+	20.8502i	1.38286	+	0.798394i
$683$	−41.5997	−	24.0176i	−1.59177	−	0.919009i	−0.993004	−	0.118085i	$-0.962325\pi$
$683$	−41.5997	−	24.0176i	−1.59177	−	0.919009i	−0.598766	−	0.800924i	$-0.704342\pi$
$684$	−3.67492	−	6.36515i	−0.140514	−	0.243378i
$685$	9.49425	+	30.6082i	0.362756	+	1.16948i
$686$	7.83393	−	13.5688i	0.299101	−	0.518058i
$687$	12.6080	+	7.27924i	0.481026	+	0.277720i
$688$	−9.52907	−	5.50161i	−0.363292	−	0.209747i
$689$	−43.7323			−1.66607
$690$	5.26549	+	16.9752i	0.200454	+	0.646237i
$691$	15.9446	−	27.6169i	0.606561	−	1.05060i	−0.385241	−	0.922816i	$-0.625882\pi$
$691$	15.9446	−	27.6169i	0.606561	−	1.05060i	0.991803	−	0.127779i	$-0.0407849\pi$
$692$		−	4.65544i		−	0.176973i
$693$		−	6.30513i		−	0.239512i
$694$	1.93586	−	3.35301i	0.0734843	−	0.127279i
$695$	3.75340	−	16.5650i	0.142374	−	0.628347i
$696$	0.131530	+	0.227817i	0.00498564	+	0.00863538i
$697$			31.8885i			1.20786i
$698$	−12.4127	+	7.16648i	−0.469828	+	0.271255i
$699$	1.41115	+	2.44418i	0.0533745	+	0.0924473i
$700$	−6.29612	+	0.491793i	−0.237971	+	0.0185880i
$701$	−1.65838	+	2.87241i	−0.0626363	+	0.108489i	−0.895643	−	0.444774i	$-0.853284\pi$
$701$	−1.65838	+	2.87241i	−0.0626363	+	0.108489i	0.833007	+	0.553263i	$0.186617\pi$
$702$			5.36157i			0.202360i
$703$	13.3541	+	42.6663i	0.503658	+	1.60919i
$704$	4.99195			0.188141
$705$	−6.02416	−	5.57196i	−0.226883	−	0.209852i
$706$	0.748825	+	1.29700i	0.0281824	+	0.0488134i
$707$	21.3410	−	12.3212i	0.802611	−	0.463388i
$708$	−4.24810	+	2.45264i	−0.159653	+	0.0921759i
$709$	−17.1332			−0.643449			−0.321724	−	0.946833i	$-0.604262\pi$
$709$	−17.1332			−0.643449			−0.321724	+	0.946833i	$0.604262\pi$
$710$	0.187373	+	0.604066i	0.00703197	+	0.0226702i
$711$	−8.10488			−0.303957
$712$	11.2988	+	6.52339i	0.423442	+	0.244474i
$713$			66.3970i			2.48659i
$714$	−5.38450			−0.201510
$715$	−40.6375	+	43.9355i	−1.51976	+	1.64310i
$716$	9.01694	+	15.6178i	0.336979	+	0.583664i
$717$		−	22.5522i		−	0.842227i
$718$	−7.65044	−	4.41698i	−0.285512	−	0.164840i
$719$	−4.90657	+	8.49843i	−0.182984	+	0.316938i	−0.942895	−	0.333089i	$-0.891909\pi$
$719$	−4.90657	+	8.49843i	−0.182984	+	0.316938i	0.759911	+	0.650027i	$0.225242\pi$
$720$	−1.64155	−	1.51833i	−0.0611769	−	0.0565847i
$721$	5.36290	+	9.28882i	0.199725	+	0.345934i
$722$	−30.3284	+	17.5101i	−1.12871	+	0.651658i
$723$	−5.04572	−	2.91315i	−0.187652	−	0.108341i
$724$	−6.41934	+	11.1186i	−0.238573	+	0.413220i
$725$	1.08441	−	0.744358i	0.0402741	−	0.0276448i
$726$	13.9195			0.516602
$727$	17.4136	−	10.0537i	0.645835	−	0.372873i	−0.141024	−	0.990006i	$-0.545039\pi$
$727$	17.4136	−	10.0537i	0.645835	−	0.372873i	0.786859	+	0.617133i	$0.211706\pi$
$728$	5.86472	+	3.38600i	0.217361	+	0.125493i
$729$	−1.00000			−0.0370370
$730$	0.762801	−	3.36650i	0.0282325	−	0.124600i
$731$	−23.4537	+	40.6230i	−0.867466	+	1.50250i
$732$			0.780045i			0.0288313i
$733$	15.5016	−	8.94984i	0.572564	−	0.330570i	−0.185609	−	0.982624i	$-0.559426\pi$
$733$	15.5016	−	8.94984i	0.572564	−	0.330570i	0.758173	+	0.652054i	$0.226092\pi$
$734$	−18.3673			−0.677950
$735$	−3.58038	−	11.5427i	−0.132064	−	0.425758i
$736$	3.97419	+	6.88350i	0.146491	+	0.253729i
$737$	15.2668	−	8.81429i	0.562360	−	0.324679i
$738$	6.47803	+	3.74009i	0.238460	+	0.137675i
$739$	20.5194			0.754818			0.377409	−	0.926047i	$-0.376815\pi$
$739$	20.5194			0.754818			0.377409	+	0.926047i	$0.376815\pi$
$740$	7.72599	+	11.1942i	0.284013	+	0.411505i
$741$	39.4067			1.44764
$742$	−8.92205	−	5.15115i	−0.327539	−	0.189105i
$743$	−5.03166	+	2.90503i	−0.184594	+	0.106575i	−0.589449	−	0.807805i	$-0.700655\pi$
$743$	−5.03166	+	2.90503i	−0.184594	+	0.106575i	0.404855	+	0.914381i	$0.367322\pi$
$744$	−4.17676	−	7.23436i	−0.153127	−	0.265224i
$745$	5.65385	−	1.75375i	0.207141	−	0.0642523i
$746$	−8.18276			−0.299592
$747$	11.9301	−	6.88783i	0.436499	−	0.252013i
$748$		−	21.2810i		−	0.778109i
$749$	9.87983	−	17.1124i	0.361001	−	0.625273i
$750$	−6.92942	+	8.77401i	−0.253027	+	0.320381i
$751$	21.8875			0.798687			0.399343	−	0.916801i	$-0.369238\pi$
$751$	21.8875			0.798687			0.399343	+	0.916801i	$0.369238\pi$
$752$	−3.17814	−	1.83490i	−0.115895	−	0.0669120i
$753$	17.6070	−	10.1654i	0.641633	−	0.370447i
$754$	−1.41042			−0.0513644
$755$	7.71977	+	7.14029i	0.280951	+	0.259862i
$756$	−0.631530	+	1.09384i	−0.0229685	+	0.0397827i
$757$	−2.78518	−	1.60802i	−0.101229	−	0.0584445i	0.448531	−	0.893767i	$-0.351947\pi$
$757$	−2.78518	−	1.60802i	−0.101229	−	0.0584445i	−0.549760	+	0.835323i	$0.685281\pi$
$758$	−23.7054	+	13.6863i	−0.861019	+	0.497110i
$759$	19.8390	+	34.3621i	0.720109	+	1.24726i
$760$	−11.1595	+	12.0651i	−0.404796	+	0.437648i
$761$	3.34598	−	5.79541i	0.121292	−	0.210083i	−0.798986	−	0.601350i	$-0.794630\pi$
$761$	3.34598	−	5.79541i	0.121292	−	0.210083i	0.920277	+	0.391267i	$0.127963\pi$
$762$	3.82426	+	2.20794i	0.138538	+	0.0799852i
$763$			12.9771i			0.469803i
$764$	−2.22676	−	3.85686i	−0.0805614	−	0.139536i
$765$	−6.47272	+	6.99802i	−0.234022	+	0.253014i
$766$	34.6306			1.25126
$767$		−	26.3000i		−	0.949639i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	26.6101			0.959585			0.479793	−	0.877382i	$-0.340712\pi$
$769$	26.6101			0.959585			0.479793	+	0.877382i	$0.340712\pi$
$770$	−13.4658	+	4.17689i	−0.485272	+	0.150525i
$771$	9.61245			0.346184
$772$	−7.62080	+	4.39987i	−0.274278	+	0.158355i
$773$	−24.3315	+	14.0478i	−0.875145	+	0.505265i	−0.869054	−	0.494716i	$-0.835272\pi$
$773$	−24.3315	+	14.0478i	−0.875145	+	0.505265i	−0.00609016	+	0.999981i	$0.501939\pi$
$774$	5.50161	+	9.52907i	0.197751	+	0.342515i
$775$	−34.4357	+	23.6372i	−1.23697	+	0.849073i
$776$	−6.02010			−0.216109
$777$	5.20239	−	5.65350i	0.186635	−	0.202818i
$778$		−	20.0818i		−	0.719966i
$779$	27.4891	−	47.6125i	0.984899	−	1.70590i
$780$	11.4506	−	3.55183i	0.409998	−	0.127176i
$781$	0.705971	+	1.22278i	0.0252616	+	0.0437544i
$782$	29.3448	−	16.9422i	1.04937	−	0.605853i
$783$		−	0.263060i		−	0.00940101i
$784$	−2.70234	−	4.68059i	−0.0965121	−	0.167164i
$785$	29.6808	+	6.72525i	1.05935	+	0.240034i
$786$	4.83306	−	8.37111i	0.172390	−	0.298588i
$787$			50.6929i			1.80701i	0.428579	+	0.903504i	$0.359014\pi$
$787$			50.6929i			1.80701i	−0.428579	+	0.903504i	$0.640986\pi$
$788$		−	8.10089i		−	0.288582i
$789$	−2.34382	+	4.05962i	−0.0834422	+	0.144526i
$790$	5.36916	+	17.3095i	0.191026	+	0.615843i
$791$	−22.8386			−0.812047
$792$	−4.32315	−	2.49597i	−0.153617	−	0.0886905i
$793$	−3.62195	−	2.09113i	−0.128619	−	0.0742583i
$794$	−9.58350	+	16.5991i	−0.340106	+	0.589081i
$795$	−17.4199	+	5.40343i	−0.617822	+	0.191640i
$796$	0.440852	+	0.763578i	0.0156256	+	0.0270643i
$797$	−19.0649	−	11.0071i	−0.675312	−	0.389892i	0.122774	−	0.992435i	$-0.460821\pi$
$797$	−19.0649	−	11.0071i	−0.675312	−	0.389892i	−0.798086	+	0.602543i	$0.794154\pi$
$798$	8.03957	+	4.64165i	0.284598	+	0.164313i
$799$	−7.82229	+	13.5486i	−0.276733	+	0.479315i
$800$	−2.15521	+	4.51166i	−0.0761981	+	0.159511i
$801$	−6.52339	−	11.2988i	−0.230493	−	0.399225i
$802$	−1.98297	−	1.14487i	−0.0700212	−	0.0404268i
$803$		−	7.70611i		−	0.271943i
$804$	−3.53141			−0.124543
$805$	−16.4800	−	15.2429i	−0.580843	−	0.537243i
$806$	44.7880			1.57759
$807$	15.6165	−	9.01620i	0.549727	−	0.317385i
$808$		−	19.5101i		−	0.686364i
$809$	−1.43253	−	2.48122i	−0.0503652	−	0.0872350i	0.839744	−	0.542983i	$-0.182705\pi$
$809$	−1.43253	−	2.48122i	−0.0503652	−	0.0872350i	−0.890109	+	0.455748i	$0.849372\pi$
$810$	0.662460	+	2.13568i	0.0232765	+	0.0750403i
$811$	−15.7472	−	27.2749i	−0.552958	−	0.957752i	−0.998059	−	0.0622713i	$-0.980166\pi$
$811$	−15.7472	−	27.2749i	−0.552958	−	0.957752i	0.445101	−	0.895480i	$-0.353168\pi$
$812$	−0.287747	−	0.166131i	−0.0100979	−	0.00583004i
$813$		−	2.81804i		−	0.0988331i
$814$	22.3441	+	20.5612i	0.783160	+	0.720670i
$815$	26.5109	+	6.00699i	0.928636	+	0.210416i
$816$	−2.13153	+	3.69192i	−0.0746185	+	0.129243i
$817$	70.0372	−	40.4360i	2.45029	−	1.41468i
$818$	−32.7070	+	18.8834i	−1.14357	+	0.660243i
$819$	−3.38600	−	5.86472i	−0.118316	−	0.204930i
$820$	3.69622	−	16.3127i	0.129078	−	0.569664i
$821$	1.88493	+	3.26480i	0.0657846	+	0.113942i	0.897042	−	0.441946i	$-0.145712\pi$
$821$	1.88493	+	3.26480i	0.0657846	+	0.113942i	−0.831257	+	0.555888i	$0.812378\pi$
$822$		−	14.3318i		−	0.499879i
$823$	0.802289	+	0.463202i	0.0279660	+	0.0161462i	0.513918	−	0.857839i	$-0.328194\pi$
$823$	0.802289	+	0.463202i	0.0279660	+	0.0161462i	−0.485952	+	0.873986i	$0.661527\pi$
$824$	8.49192			0.295830
$825$	−10.7587	+	22.5220i	−0.374569	+	0.784114i
$826$	3.09783	−	5.36560i	0.107787	−	0.186693i
$827$	−18.2258	+	10.5227i	−0.633773	+	0.365909i	−0.782212	−	0.623012i	$-0.785909\pi$
$827$	−18.2258	+	10.5227i	−0.633773	+	0.365909i	0.148439	+	0.988922i	$0.452575\pi$
$828$		−	7.94839i		−	0.276226i
$829$	22.5048	−	38.9795i	0.781624	−	1.35381i	−0.149371	−	0.988781i	$-0.547725\pi$
$829$	22.5048	−	38.9795i	0.781624	−	1.35381i	0.930995	−	0.365032i	$-0.118942\pi$
$830$	−22.6134	−	20.9160i	−0.784924	−	0.726004i
$831$	9.41347	−	16.3046i	0.326550	−	0.565601i
$832$	4.64326	−	2.68079i	0.160976	−	0.0929396i
$833$	−19.9536	+	11.5202i	−0.691352	+	0.399152i
$834$	−3.79794	+	6.57823i	−0.131512	+	0.227786i
$835$	30.0266	−	32.4634i	1.03911	−	1.12344i
$836$	−18.3450	+	31.7745i	−0.634475	+	1.09894i
$837$			8.35352i			0.288740i
$838$	15.0717	−	8.70163i	0.520642	−	0.300593i
$839$	−6.26844	+	10.8572i	−0.216410	+	0.374834i	−0.953708	−	0.300734i	$-0.902768\pi$
$839$	−6.26844	+	10.8572i	−0.216410	+	0.374834i	0.737298	+	0.675568i	$0.236102\pi$
$840$	2.75447	+	0.624123i	0.0950381	+	0.0215343i
$841$	−28.9308			−0.997614
$842$	5.89858	+	3.40555i	0.203278	+	0.117363i
$843$		−	16.2818i		−	0.560775i
$844$	−10.1226	−	17.5328i	−0.348433	−	0.603504i
$845$	−7.78088	+	34.3397i	−0.267671	+	1.18132i
$846$	1.83490	+	3.17814i	0.0630852	+	0.109267i
$847$	−15.2258	+	8.79060i	−0.523163	+	0.302049i
$848$	−7.06383	+	4.07831i	−0.242573	+	0.140050i
$849$	−5.26333	+	9.11635i	−0.180637	+	0.312872i
$850$	19.2335	+	9.18778i	0.659703	+	0.315138i
$851$	−10.5637	+	47.1800i	−0.362119	+	1.61731i
$852$		−	0.282844i		−	0.00969008i
$853$	−20.5299	−	11.8529i	−0.702930	−	0.405837i	0.105508	−	0.994418i	$-0.466353\pi$
$853$	−20.5299	−	11.8529i	−0.702930	−	0.405837i	−0.808438	+	0.588582i	$0.799686\pi$
$854$	−0.492622	−	0.853246i	−0.0168572	−	0.0291975i
$855$	15.6969	−	4.86898i	0.536824	−	0.166515i
$856$	−7.82214	−	13.5483i	−0.267355	−	0.463073i
$857$		−	28.1064i		−	0.960096i	−0.877242	−	0.480048i	$-0.840619\pi$
$857$		−	28.1064i		−	0.960096i	0.877242	−	0.480048i	$-0.159381\pi$
$858$	23.1789	−	13.3823i	0.791314	−	0.456866i
$859$	−55.4336			−1.89137			−0.945685	−	0.325085i	$-0.894607\pi$
$859$	−55.4336			−1.89137			−0.945685	+	0.325085i	$0.894607\pi$
$860$	16.7065	−	18.0623i	0.569687	−	0.615920i
$861$	−9.44793			−0.321984
$862$			21.6041i			0.735838i
$863$	−4.37677	−	2.52693i	−0.148987	−	0.0860177i	0.423653	−	0.905824i	$-0.360748\pi$
$863$	−4.37677	−	2.52693i	−0.148987	−	0.0860177i	−0.572640	+	0.819807i	$0.694081\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	10.1525	+	2.30042i	0.345196	+	0.0782165i
$866$	−2.27763	+	3.94496i	−0.0773969	+	0.134055i
$867$	1.01644	+	0.586842i	0.0345201	+	0.0199302i
$868$	9.13743	+	5.27550i	0.310145	+	0.179062i
$869$	20.2296	+	35.0386i	0.686241	+	1.18860i
$870$	−0.561814	+	0.174267i	−0.0190473	+	0.00590820i
$871$	9.46695	−	16.3972i	0.320775	−	0.555599i
$872$	8.89784	+	5.13717i	0.301319	+	0.173966i
$873$	5.21356	+	3.01005i	0.176452	+	0.101875i
$874$	−58.4194			−1.97607
$875$	2.03864	−	13.9735i	0.0689186	−	0.472391i
$876$	−0.771854	+	1.33689i	−0.0260785	+	0.0451693i
$877$		−	21.0116i		−	0.709511i	−0.934959	−	0.354755i	$-0.884564\pi$
$877$		−	21.0116i		−	0.709511i	0.934959	−	0.354755i	$-0.115436\pi$
$878$			12.3603i			0.417139i
$879$	−2.58224	+	4.47258i	−0.0870969	+	0.150856i
$880$	−2.46670	+	10.8864i	−0.0831523	+	0.366979i
$881$	−2.01042	−	3.48216i	−0.0677329	−	0.117317i	0.830170	−	0.557510i	$-0.188243\pi$
$881$	−2.01042	−	3.48216i	−0.0677329	−	0.117317i	−0.897903	+	0.440193i	$0.854910\pi$
$882$			5.40468i			0.181985i
$883$	−36.6621	+	21.1669i	−1.23378	+	0.712323i	−0.967816	−	0.251661i	$-0.919023\pi$
$883$	−36.6621	+	21.1669i	−1.23378	+	0.712323i	−0.265963	+	0.963983i	$0.585690\pi$
$884$	−11.4284	−	19.7945i	−0.384377	−	0.665761i
$885$	−3.24955	−	10.4761i	−0.109232	−	0.352151i
$886$	−6.61903	+	11.4645i	−0.222371	+	0.385158i
$887$			55.2976i			1.85671i	0.371694	+	0.928355i	$0.378777\pi$
$887$			55.2976i			1.85671i	−0.371694	+	0.928355i	$0.621223\pi$
$888$	−1.81692	−	5.80507i	−0.0609718	−	0.194805i
$889$	−5.57752			−0.187064
$890$	−19.8093	+	21.4169i	−0.664009	+	0.717897i
$891$	2.49597	+	4.32315i	0.0836182	+	0.144831i
$892$	15.7361	−	9.08526i	0.526885	−	0.304197i
$893$	23.3588	−	13.4862i	0.781674	−	0.451300i
$894$	−2.64733			−0.0885399
$895$	−38.5147	+	11.9467i	−1.28740	+	0.399335i
$896$	1.26306			0.0421959
$897$	36.9064	+	21.3079i	1.23227	+	0.711451i
$898$		−	36.6817i		−	1.22408i
$899$	−2.19748			−0.0732901
$900$	4.12229	−	2.82961i	0.137410	−	0.0943203i
$901$	17.3861	+	30.1135i	0.579214	+	1.00323i
$902$		−	37.3407i		−	1.24331i
$903$	−12.0358	−	6.94887i	−0.400526	−	0.231244i
$904$	−9.04098	+	15.6594i	−0.300698	+	0.520825i
$905$	−21.0753	−	19.4933i	−0.700567	−	0.647979i
$906$	−2.35137	−	4.07269i	−0.0781189	−	0.135306i
$907$	5.91799	−	3.41675i	0.196504	−	0.113451i	−0.398520	−	0.917160i	$-0.630476\pi$
$907$	5.91799	−	3.41675i	0.196504	−	0.113451i	0.595024	+	0.803708i	$0.297143\pi$
$908$	−9.88733	−	5.70845i	−0.328123	−	0.189442i
$909$	−9.75507	+	16.8963i	−0.323555	+	0.560414i
$910$	−10.2821	+	11.1166i	−0.340848	+	0.368510i
$911$	−16.0278			−0.531025			−0.265513	−	0.964107i	$-0.585541\pi$
$911$	−16.0278			−0.531025			−0.265513	+	0.964107i	$0.585541\pi$
$912$	6.36515	−	3.67492i	0.210771	−	0.121689i
$913$	−59.5543	−	34.3837i	−1.97096	−	1.13793i
$914$	−37.3168			−1.23433
$915$	−1.70111	−	0.385448i	−0.0562370	−	0.0127425i
$916$	−7.27924	+	12.6080i	−0.240513	+	0.416580i
$917$			12.2089i			0.403174i
$918$	3.69192	−	2.13153i	0.121851	−	0.0703510i
$919$	18.8381			0.621412			0.310706	−	0.950506i	$-0.399434\pi$
$919$	18.8381			0.621412			0.310706	+	0.950506i	$0.399434\pi$
$920$	−16.9752	+	5.26549i	−0.559657	+	0.173598i
$921$	−7.78242	−	13.4796i	−0.256440	−	0.444166i
$922$	−20.5667	+	11.8742i	−0.677328	+	0.391056i
$923$	1.31332	+	0.758245i	0.0432284	+	0.0249579i
$924$	6.30513			0.207424
$925$	−28.2297	+	11.3173i	−0.928188	+	0.372111i
$926$	−28.2913			−0.929711
$927$	−7.35421	−	4.24596i	−0.241544	−	0.139456i
$928$	−0.227817	+	0.131530i	−0.00747846	+	0.00431769i
$929$	23.3315	+	40.4114i	0.765482	+	1.32585i	0.939991	+	0.341199i	$0.110833\pi$
$929$	23.3315	+	40.4114i	0.765482	+	1.32585i	−0.174509	+	0.984656i	$0.555834\pi$
$930$	17.8405	−	5.53387i	0.585012	−	0.181463i
$931$	39.7235			1.30189
$932$	−2.44418	+	1.41115i	−0.0800617	+	0.0462236i
$933$			17.8476i			0.584304i
$934$	9.71786	−	16.8318i	0.317978	−	0.550754i
$935$	46.4092	+	10.5157i	1.51774	+	0.343899i
$936$	−5.36157			−0.175249
$937$	42.9876	+	24.8189i	1.40434	+	0.810798i	0.994835	−	0.101507i	$-0.0323666\pi$
$937$	42.9876	+	24.8189i	1.40434	+	0.810798i	0.409509	+	0.912306i	$0.365700\pi$
$938$	3.86280	−	2.23019i	0.126125	−	0.0728183i
$939$	−6.35678			−0.207446
$940$	5.57196	−	6.02416i	0.181737	−	0.196486i
$941$	−13.5062	+	23.3935i	−0.440291	+	0.762606i	−0.997711	−	0.0676245i	$-0.978458\pi$
$941$	−13.5062	+	23.3935i	−0.440291	+	0.762606i	0.557420	+	0.830231i	$0.311791\pi$
$942$	−11.7867	−	6.80507i	−0.384032	−	0.221721i
$943$	51.4899	−	29.7277i	1.67674	−	0.968067i
$944$	−2.45264	−	4.24810i	−0.0798267	−	0.138264i
$945$	−2.07338	−	1.91774i	−0.0674469	−	0.0623840i
$946$	27.4637	−	47.5686i	0.892923	−	1.54659i
$947$	8.58103	+	4.95426i	0.278846	+	0.160992i	0.632901	−	0.774233i	$-0.281864\pi$
$947$	8.58103	+	4.95426i	0.278846	+	0.160992i	−0.354055	+	0.935225i	$0.615197\pi$
$948$		−	8.10488i		−	0.263234i
$949$	−4.13835	−	7.16784i	−0.134337	−	0.232678i
$950$	−20.7972	−	30.2982i	−0.674750	−	0.983004i
$951$	−15.9146			−0.516065
$952$		−	5.38450i		−	0.174513i
$953$	−21.1411	−	12.2058i	−0.684828	−	0.395386i	0.116844	−	0.993150i	$-0.462722\pi$
$953$	−21.1411	−	12.2058i	−0.684828	−	0.395386i	−0.801672	+	0.597765i	$0.796056\pi$
$954$	8.15661			0.264080
$955$	9.51132	−	2.95028i	0.307779	−	0.0954688i
$956$	22.5522			0.729390
$957$	−1.13725	+	0.656592i	−0.0367621	+	0.0212246i
$958$	−32.4842	+	18.7548i	−1.04952	+	0.605939i
$959$	9.05097	+	15.6767i	0.292271	+	0.506228i
$960$	1.51833	−	1.64155i	0.0490038	−	0.0529808i
$961$	38.7813			1.25101
$962$	31.8252	+	7.12573i	1.02609	+	0.229743i
$963$			15.6443i			0.504130i
$964$	2.91315	−	5.04572i	0.0938262	−	0.162512i
$965$	−5.82947	−	18.7935i	−0.187657	−	0.604983i
$966$	5.01965	+	8.69428i	0.161504	+	0.279734i
$967$	−1.75442	+	1.01292i	−0.0564184	+	0.0325732i	−0.527944	−	0.849279i	$-0.677037\pi$
$967$	−1.75442	+	1.01292i	−0.0564184	+	0.0325732i	0.471525	+	0.881852i	$0.343704\pi$
$968$			13.9195i			0.447390i
$969$	−15.6664	−	27.1350i	−0.503278	−	0.871703i
$970$	2.97474	−	13.1286i	0.0955133	−	0.421532i
$971$	−2.26173	+	3.91744i	−0.0725824	+	0.125716i	−0.900032	−	0.435823i	$-0.856457\pi$
$971$	−2.26173	+	3.91744i	−0.0725824	+	0.125716i	0.827450	+	0.561539i	$0.189791\pi$
$972$		−	1.00000i		−	0.0320750i
$973$		−	9.59407i		−	0.307572i
$974$	8.67199	−	15.0203i	0.277868	−	0.481282i
$975$	2.08762	+	26.7265i	0.0668572	+	0.855932i
$976$	−0.780045			−0.0249686
$977$	−11.9433	−	6.89545i	−0.382099	−	0.220605i	0.296632	−	0.954992i	$-0.404137\pi$
$977$	−11.9433	−	6.89545i	−0.382099	−	0.220605i	−0.678731	+	0.734387i	$0.737470\pi$
$978$	−10.5279	−	6.07828i	−0.336645	−	0.194362i
$979$	−32.5644	+	56.4032i	−1.04076	+	1.80265i
$980$	11.5427	−	3.58038i	0.368718	−	0.114371i
$981$	−5.13717	−	8.89784i	−0.164017	−	0.284086i
$982$	−1.99247	−	1.15035i	−0.0635823	−	0.0367092i
$983$	35.1161	+	20.2743i	1.12003	+	0.646649i	0.941408	−	0.337269i	$-0.109503\pi$
$983$	35.1161	+	20.2743i	1.12003	+	0.646649i	0.178621	+	0.983918i	$0.442837\pi$
$984$	−3.74009	+	6.47803i	−0.119230	+	0.206512i
$985$	17.6663	+	4.00293i	0.562895	+	0.127544i
$986$	0.560721	+	0.971197i	0.0178570	+	0.0309292i
$987$	−4.01419	−	2.31759i	−0.127773	−	0.0737697i
$988$			39.4067i			1.25369i
$989$	87.4579			2.78100
$990$	7.57941	−	8.19452i	0.240889	−	0.260439i
$991$	3.39031			0.107697			0.0538483	−	0.998549i	$-0.482851\pi$
$991$	3.39031			0.107697			0.0538483	+	0.998549i	$0.482851\pi$
$992$	7.23436	−	4.17676i	0.229691	−	0.132612i
$993$		−	7.92216i		−	0.251402i
$994$	0.178625	+	0.309387i	0.00566563	+	0.00981315i
$995$	−1.88304	+	0.584093i	−0.0596964	+	0.0185170i
$996$	6.88783	+	11.9301i	0.218249	+	0.378019i
$997$	−17.2302	−	9.94785i	−0.545686	−	0.315052i	0.201694	−	0.979448i	$-0.435355\pi$
$997$	−17.2302	−	9.94785i	−0.545686	−	0.315052i	−0.747380	+	0.664397i	$0.768689\pi$
$998$		−	4.36614i		−	0.138208i
$999$	−1.32904	+	5.93579i	−0.0420489	+	0.187800i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.bb.d.1009.9	yes	28
5.4	even	2	inner	1110.2.bb.d.1009.6	✓	28
37.26	even	3	inner	1110.2.bb.d.1099.6	yes	28
185.174	even	6	inner	1110.2.bb.d.1099.9	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.bb.d.1009.6	✓	28	5.4	even	2	inner
1110.2.bb.d.1009.9	yes	28	1.1	even	1	trivial
1110.2.bb.d.1099.6	yes	28	37.26	even	3	inner
1110.2.bb.d.1099.9	yes	28	185.174	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.13568 + 0.662460i) q^{5} +1.00000 q^{6} +(-1.09384 + 0.631530i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.13568 + 0.662460i) q^{5} +1.00000 q^{6} +(-1.09384 + 0.631530i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.18079 - 0.494135i) q^{10} -4.99195 q^{11} +(0.866025 + 0.500000i) q^{12} +(-4.64326 + 2.68079i) q^{13} -1.26306 q^{14} +(-1.51833 + 1.64155i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.69192 + 2.13153i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-3.67492 - 6.36515i) q^{19} +(-1.64155 - 1.51833i) q^{20} +(-0.631530 + 1.09384i) q^{21} +(-4.32315 - 2.49597i) q^{22} -7.94839i q^{23} +(0.500000 + 0.866025i) q^{24} +(4.12229 - 2.82961i) q^{25} -5.36157 q^{26} -1.00000i q^{27} +(-1.09384 - 0.631530i) q^{28} +0.263060 q^{29} +(-2.13568 + 0.662460i) q^{30} -8.35352 q^{31} +(-0.866025 + 0.500000i) q^{32} +(-4.32315 + 2.49597i) q^{33} +(2.13153 + 3.69192i) q^{34} +(1.91774 - 2.07338i) q^{35} +1.00000 q^{36} +(-5.93579 - 1.32904i) q^{37} -7.34984i q^{38} +(-2.68079 + 4.64326i) q^{39} +(-0.662460 - 2.13568i) q^{40} +(3.74009 + 6.47803i) q^{41} +(-1.09384 + 0.631530i) q^{42} +11.0032i q^{43} +(-2.49597 - 4.32315i) q^{44} +(-0.494135 + 2.18079i) q^{45} +(3.97419 - 6.88350i) q^{46} +3.66980i q^{47} +1.00000i q^{48} +(-2.70234 + 4.68059i) q^{49} +(4.98482 - 0.389366i) q^{50} +4.26306 q^{51} +(-4.64326 - 2.68079i) q^{52} +(7.06383 + 4.07831i) q^{53} +(0.500000 - 0.866025i) q^{54} +(10.6612 - 3.30696i) q^{55} +(-0.631530 - 1.09384i) q^{56} +(-6.36515 - 3.67492i) q^{57} +(0.227817 + 0.131530i) q^{58} +(-2.45264 + 4.24810i) q^{59} +(-2.18079 - 0.494135i) q^{60} +(0.390022 + 0.675539i) q^{61} +(-7.23436 - 4.17676i) q^{62} +1.26306i q^{63} -1.00000 q^{64} +(8.14062 - 8.80129i) q^{65} -4.99195 q^{66} +(-3.05829 + 1.76570i) q^{67} +4.26306i q^{68} +(-3.97419 - 6.88350i) q^{69} +(2.69750 - 0.836727i) q^{70} +(-0.141422 - 0.244950i) q^{71} +(0.866025 + 0.500000i) q^{72} +1.54371i q^{73} +(-4.47603 - 4.11888i) q^{74} +(2.15521 - 4.51166i) q^{75} +(3.67492 - 6.36515i) q^{76} +(5.46040 - 3.15256i) q^{77} +(-4.64326 + 2.68079i) q^{78} +(-4.05244 - 7.01903i) q^{79} +(0.494135 - 2.18079i) q^{80} +(-0.500000 - 0.866025i) q^{81} +7.48019i q^{82} +(11.9301 + 6.88783i) q^{83} -1.26306 q^{84} +(-9.29683 - 2.10653i) q^{85} +(-5.50161 + 9.52907i) q^{86} +(0.227817 - 0.131530i) q^{87} -4.99195i q^{88} +(6.52339 - 11.2988i) q^{89} +(-1.51833 + 1.64155i) q^{90} +(3.38600 - 5.86472i) q^{91} +(6.88350 - 3.97419i) q^{92} +(-7.23436 + 4.17676i) q^{93} +(-1.83490 + 3.17814i) q^{94} +(12.0651 + 11.1595i) q^{95} +(-0.500000 + 0.866025i) q^{96} +6.02010i q^{97} +(-4.68059 + 2.70234i) q^{98} +(-2.49597 + 4.32315i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9}+O(q^{10}) \) 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9	\( 28 q + 14 q^{4} + 2 q^{5} + 28 q^{6} + 14 q^{9} + 4 q^{10} - 12 q^{11} + 8 q^{14} + 2 q^{15} - 14 q^{16} - 20 q^{19} - 2 q^{20} + 4 q^{21} + 14 q^{24} - 8 q^{25} - 20 q^{26} - 36 q^{29} + 2 q^{30} + 24 q^{31} + 38 q^{34} - 2 q^{35} + 28 q^{36} - 10 q^{39} + 2 q^{40} - 6 q^{44} + 4 q^{45} + 8 q^{46} + 50 q^{49} - 4 q^{50} + 76 q^{51} + 14 q^{54} - 28 q^{55} + 4 q^{56} - 26 q^{59} + 4 q^{60} - 28 q^{61} - 28 q^{64} + 60 q^{65} - 12 q^{66} - 8 q^{69} - 10 q^{70} - 64 q^{71} + 24 q^{74} - 8 q^{75} + 20 q^{76} + 32 q^{79} - 4 q^{80} - 14 q^{81} + 8 q^{84} + 16 q^{85} - 8 q^{86} + 76 q^{89} + 2 q^{90} - 8 q^{91} - 38 q^{94} - 70 q^{95} - 14 q^{96} - 6 q^{99}+O(q^{100}) \) 28 * q + 14 * q^4 + 2 * q^5 + 28 * q^6 + 14 * q^9 + 4 * q^10 - 12 * q^11 + 8 * q^14 + 2 * q^15 - 14 * q^16 - 20 * q^19 - 2 * q^20 + 4 * q^21 + 14 * q^24 - 8 * q^25 - 20 * q^26 - 36 * q^29 + 2 * q^30 + 24 * q^31 + 38 * q^34 - 2 * q^35 + 28 * q^36 - 10 * q^39 + 2 * q^40 - 6 * q^44 + 4 * q^45 + 8 * q^46 + 50 * q^49 - 4 * q^50 + 76 * q^51 + 14 * q^54 - 28 * q^55 + 4 * q^56 - 26 * q^59 + 4 * q^60 - 28 * q^61 - 28 * q^64 + 60 * q^65 - 12 * q^66 - 8 * q^69 - 10 * q^70 - 64 * q^71 + 24 * q^74 - 8 * q^75 + 20 * q^76 + 32 * q^79 - 4 * q^80 - 14 * q^81 + 8 * q^84 + 16 * q^85 - 8 * q^86 + 76 * q^89 + 2 * q^90 - 8 * q^91 - 38 * q^94 - 70 * q^95 - 14 * q^96 - 6 * q^99

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