LMFDB - Embedded newform 966.2.be.a.355.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [966,2,Mod(19,966)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("966.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(966, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([0, 55, 45])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.be (of order $66$, degree $20$, minimal)

Newform invariants

comment:select newform

sage:traces = [320,-16] 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			355.13
Character	$\chi$	$=$	966.355
Dual form			966.2.be.a.283.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.981929 + 0.189251i) q^{2} +(0.998867 + 0.0475819i) q^{3} +(0.928368 - 0.371662i) q^{4} +(-7.79185e-5 - 0.000109421i) q^{5} +(-0.989821 + 0.142315i) q^{6} +(-2.31789 + 1.27570i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.995472 + 0.0950560i) q^{9} +(9.72185e-5 + 9.26977e-5i) q^{10} +(0.438160 - 2.27339i) q^{11} +(0.945001 - 0.327068i) q^{12} +(-1.48591 - 5.06053i) q^{13} +(2.03457 - 1.69131i) q^{14} +(-7.26238e-5 - 0.000113005i) q^{15} +(0.723734 - 0.690079i) q^{16} +(-4.00145 + 3.14678i) q^{17} +(-0.995472 + 0.0950560i) q^{18} +(-2.07517 - 1.63193i) q^{19} +(-0.000113005 - 7.26238e-5i) q^{20} +(-2.37596 + 1.16396i) q^{21} +2.31523i q^{22} +(0.954975 - 4.69979i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(1.63534 - 4.72500i) q^{25} +(2.41676 + 4.68787i) q^{26} +(0.989821 + 0.142315i) q^{27} +(-1.67772 + 2.04579i) q^{28} +(-0.0478048 - 0.332490i) q^{29} +(9.26977e-5 + 9.72185e-5i) q^{30} +(0.219761 - 0.426277i) q^{31} +(-0.580057 + 0.814576i) q^{32} +(0.545836 - 2.24997i) q^{33} +(3.33361 - 3.84719i) q^{34} +(0.000320195 + 0.000154226i) q^{35} +(0.959493 - 0.281733i) q^{36} +(0.892698 - 9.34875i) q^{37} +(2.34652 + 1.20971i) q^{38} +(-1.24343 - 5.12550i) q^{39} +(0.000124707 + 4.99251e-5i) q^{40} +(5.37037 + 2.45257i) q^{41} +(2.11274 - 1.59258i) q^{42} +(1.37656 - 2.14196i) q^{43} +(-0.438160 - 2.27339i) q^{44} +(-6.71645e-5 - 0.000116332i) q^{45} +(-0.0482765 + 4.79559i) q^{46} +(1.41674 + 0.817955i) q^{47} +(0.755750 - 0.654861i) q^{48} +(3.74519 - 5.91384i) q^{49} +(-0.711574 + 4.94911i) q^{50} +(-4.14665 + 2.95281i) q^{51} +(-3.26028 - 4.14578i) q^{52} +(-10.7151 + 2.59946i) q^{53} +(-0.998867 + 0.0475819i) q^{54} +(-0.000282898 + 0.000129195i) q^{55} +(1.26024 - 2.32633i) q^{56} +(-1.99517 - 1.72883i) q^{57} +(0.109865 + 0.317434i) q^{58} +(-0.672366 + 0.705158i) q^{59} +(-0.000109421 - 7.79185e-5i) q^{60} +(0.313387 + 6.57880i) q^{61} +(-0.135116 + 0.460164i) q^{62} +(-2.42865 + 1.04959i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-0.000437950 + 0.000556899i) q^{65} +(-0.110163 + 2.31261i) q^{66} +(-1.56279 - 0.540885i) q^{67} +(-2.54528 + 4.40855i) q^{68} +(1.17752 - 4.64903i) q^{69} +(-0.000343596 - 9.08413e-5i) q^{70} +(2.20301 + 2.54241i) q^{71} +(-0.888835 + 0.458227i) q^{72} +(-5.13158 - 12.8181i) q^{73} +(0.892698 + 9.34875i) q^{74} +(1.85831 - 4.64184i) q^{75} +(-2.53305 - 0.743771i) q^{76} +(1.88455 + 5.82842i) q^{77} +(2.19097 + 4.79755i) q^{78} +(-2.56351 - 0.621901i) q^{79} +(-0.000131902 - 2.54219e-5i) q^{80} +(0.981929 + 0.189251i) q^{81} +(-5.73747 - 1.39190i) q^{82} +(2.17121 + 4.75428i) q^{83} +(-1.77316 + 1.96364i) q^{84} +(0.000656111 + 0.000192652i) q^{85} +(-0.946310 + 2.36377i) q^{86} +(-0.0319302 - 0.334388i) q^{87} +(0.860483 + 2.14938i) q^{88} +(-6.61598 + 3.41077i) q^{89} +(8.79669e-5 + 0.000101519i) q^{90} +(9.89986 + 9.83417i) q^{91} +(-0.860167 - 4.71806i) q^{92} +(0.239795 - 0.415338i) q^{93} +(-1.54594 - 0.535054i) q^{94} +(-1.68739e-5 + 0.000354226i) q^{95} +(-0.618159 + 0.786053i) q^{96} +(7.72358 - 16.9123i) q^{97} +(-2.55831 + 6.51575i) q^{98} +(0.652275 - 2.22145i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9} - 22 q^{14} + 16 q^{16} + 66 q^{17} + 16 q^{18} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36}+ \cdots - 90 q^{98}+O(q^{100}) $ 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9 - 22 * q^14 + 16 * q^16 + 66 * q^17 + 16 * q^18 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{22}\right)$

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 $

$2$	−0.981929	+	0.189251i	−0.694328	+	0.133821i
$2$	−0.981929	+	0.189251i	−0.694328	+	0.133821i
$3$	0.998867	+	0.0475819i	0.576696	+	0.0274714i
$3$	0.998867	+	0.0475819i	0.576696	+	0.0274714i
$4$	0.928368	−	0.371662i	0.464184	−	0.185831i
$5$	−7.79185e−5	0	0.000109421i	−3.48462e−5	0	4.89347e-5i	0.814559	−	0.580081i	$-0.196979\pi$
$5$	−7.79185e−5	0	0.000109421i	−3.48462e−5	0	4.89347e-5i	−0.814593	+	0.580032i	$0.803040\pi$
$6$	−0.989821	+	0.142315i	−0.404093	+	0.0580998i
$7$	−2.31789	+	1.27570i	−0.876079	+	0.482168i
$7$	−2.31789	+	1.27570i	−0.876079	+	0.482168i
$8$	−0.841254	+	0.540641i	−0.297428	+	0.191145i
$9$	0.995472	+	0.0950560i	0.331824	+	0.0316853i
$10$	9.72185e−5	0	9.26977e-5i	3.07432e−5	0	2.93136e-5i
$11$	0.438160	−	2.27339i	0.132110	−	0.685453i	−0.854120	−	0.520076i	$-0.825904\pi$
$11$	0.438160	−	2.27339i	0.132110	−	0.685453i	0.986230	−	0.165377i	$-0.0528841\pi$
$12$	0.945001	−	0.327068i	0.272798	−	0.0944164i
$13$	−1.48591	−	5.06053i	−0.412116	−	1.40354i	−0.860387	−	0.509641i	$-0.829778\pi$
$13$	−1.48591	−	5.06053i	−0.412116	−	1.40354i	0.448271	−	0.893898i	$-0.352040\pi$
$14$	2.03457	−	1.69131i	0.543762	−	0.452021i
$15$	−7.26238e−5	0	0.000113005i	−1.87514e−5	0	2.91777e-5i
$16$	0.723734	−	0.690079i	0.180934	−	0.172520i
$17$	−4.00145	+	3.14678i	−0.970494	+	0.763205i	−0.971560	−	0.236794i	$-0.923903\pi$
$17$	−4.00145	+	3.14678i	−0.970494	+	0.763205i	0.00106544	+	0.999999i	$0.499661\pi$
$18$	−0.995472	+	0.0950560i	−0.234635	+	0.0224049i
$19$	−2.07517	−	1.63193i	−0.476077	−	0.374391i	0.351095	−	0.936340i	$-0.385809\pi$
$19$	−2.07517	−	1.63193i	−0.476077	−	0.374391i	−0.827172	+	0.561949i	$0.810052\pi$
$20$	−0.000113005	0	7.26238e-5i	−2.52686e−5	0	1.62392e-5i
$21$	−2.37596	+	1.16396i	−0.518477	+	0.253997i
$22$			2.31523i			0.493608i
$23$	0.954975	−	4.69979i	0.199126	−	0.979974i
$23$	0.954975	−	4.69979i	0.199126	−	0.979974i
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	1.63534	−	4.72500i	0.327068	−	0.945001i
$26$	2.41676	+	4.68787i	0.473967	+	0.919367i
$27$	0.989821	+	0.142315i	0.190491	+	0.0273885i
$28$	−1.67772	+	2.04579i	−0.317060	+	0.386618i
$29$	−0.0478048	−	0.332490i	−0.00887713	−	0.0617418i	0.984901	−	0.173117i	$-0.0553837\pi$
$29$	−0.0478048	−	0.332490i	−0.00887713	−	0.0617418i	−0.993778	+	0.111375i	$0.964475\pi$
$30$	9.26977e−5	0	9.72185e-5i	1.69242e−5	0	1.77496e-5i
$31$	0.219761	−	0.426277i	0.0394703	−	0.0765617i	−0.868276	−	0.496082i	$-0.834771\pi$
$31$	0.219761	−	0.426277i	0.0394703	−	0.0765617i	0.907746	+	0.419521i	$0.137802\pi$
$32$	−0.580057	+	0.814576i	−0.102541	+	0.143998i
$33$	0.545836	−	2.24997i	0.0950178	−	0.391669i
$34$	3.33361	−	3.84719i	0.571709	−	0.659787i
$35$	0.000320195	0	0.000154226i	5.41228e−5	0	2.60689e-5i
$36$	0.959493	−	0.281733i	0.159915	−	0.0469554i
$37$	0.892698	−	9.34875i	0.146759	−	1.53693i	−0.559416	−	0.828887i	$-0.688974\pi$
$37$	0.892698	−	9.34875i	0.146759	−	1.53693i	0.706174	−	0.708038i	$-0.250420\pi$
$38$	2.34652	+	1.20971i	0.380655	+	0.196241i
$39$	−1.24343	−	5.12550i	−0.199109	−	0.820737i
$40$	0.000124707	0	4.99251e-5i	1.97179e−5	0	7.89385e-6i
$41$	5.37037	+	2.45257i	0.838711	+	0.383027i	0.787991	−	0.615686i	$-0.211121\pi$
$41$	5.37037	+	2.45257i	0.838711	+	0.383027i	0.0507198	+	0.998713i	$0.483848\pi$
$42$	2.11274	−	1.59258i	0.326003	−	0.245741i
$43$	1.37656	−	2.14196i	0.209923	−	0.326646i	−0.720286	−	0.693677i	$-0.755989\pi$
$43$	1.37656	−	2.14196i	0.209923	−	0.326646i	0.930209	+	0.367031i	$0.119626\pi$
$44$	−0.438160	−	2.27339i	−0.0660551	−	0.342726i
$45$	−6.71645e−5	0	0.000116332i	−1.00123e−5	0	1.73418e-5i
$46$	−0.0482765	+	4.79559i	−0.00711798	+	0.707071i
$47$	1.41674	+	0.817955i	0.206653	+	0.119311i	0.599755	−	0.800184i	$-0.295265\pi$
$47$	1.41674	+	0.817955i	0.206653	+	0.119311i	−0.393102	+	0.919495i	$0.628598\pi$
$48$	0.755750	−	0.654861i	0.109083	−	0.0945210i
$49$	3.74519	−	5.91384i	0.535028	−	0.844835i
$50$	−0.711574	+	4.94911i	−0.100632	+	0.699909i
$51$	−4.14665	+	2.95281i	−0.580647	+	0.413477i
$52$	−3.26028	−	4.14578i	−0.452119	−	0.574916i
$53$	−10.7151	+	2.59946i	−1.47183	+	0.357063i	−0.889894	−	0.456168i	$-0.849222\pi$
$53$	−10.7151	+	2.59946i	−1.47183	+	0.357063i	−0.581941	+	0.813231i	$0.697707\pi$
$54$	−0.998867	+	0.0475819i	−0.135929	+	0.00647508i
$55$	−0.000282898	0	0.000129195i	−3.81459e−5	0	1.74207e-5i
$56$	1.26024	−	2.32633i	0.168406	−	0.310869i
$57$	−1.99517	−	1.72883i	−0.264267	−	0.228989i
$58$	0.109865	+	0.317434i	0.0144260	+	0.0416811i
$59$	−0.672366	+	0.705158i	−0.0875346	+	0.0918037i	−0.766044	−	0.642788i	$-0.777778\pi$
$59$	−0.672366	+	0.705158i	−0.0875346	+	0.0918037i	0.678510	+	0.734592i	$0.262626\pi$
$60$	−0.000109421	0	7.79185e-5i	−1.41262e−5	0	1.00592e-5i
$61$	0.313387	+	6.57880i	0.0401251	+	0.842329i	0.925798	+	0.378019i	$0.123395\pi$
$61$	0.313387	+	6.57880i	0.0401251	+	0.842329i	−0.885673	+	0.464310i	$0.846302\pi$
$62$	−0.135116	+	0.460164i	−0.0171598	+	0.0584409i
$63$	−2.42865	+	1.04959i	−0.305982	+	0.132236i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	−0.000437950	0	0.000556899i	−5.43210e−5	0	6.90748e-5i
$66$	−0.110163	+	2.31261i	−0.0135601	+	0.284662i
$67$	−1.56279	−	0.540885i	−0.190925	−	0.0660796i	0.229933	−	0.973207i	$-0.426149\pi$
$67$	−1.56279	−	0.540885i	−0.190925	−	0.0660796i	−0.420857	+	0.907127i	$0.638271\pi$
$68$	−2.54528	+	4.40855i	−0.308661	+	0.534616i
$69$	1.17752	−	4.64903i	0.141757	−	0.559677i
$70$	−0.000343596	0	9.08413e-5i	−4.10675e−5	0	1.08576e-5i
$71$	2.20301	+	2.54241i	0.261449	+	0.301729i	0.871263	−	0.490816i	$-0.163301\pi$
$71$	2.20301	+	2.54241i	0.261449	+	0.301729i	−0.609814	+	0.792545i	$0.708756\pi$
$72$	−0.888835	+	0.458227i	−0.104750	+	0.0540025i
$73$	−5.13158	−	12.8181i	−0.600605	−	1.50024i	−0.847283	−	0.531142i	$-0.821763\pi$
$73$	−5.13158	−	12.8181i	−0.600605	−	1.50024i	0.246677	−	0.969098i	$-0.420661\pi$
$74$	0.892698	+	9.34875i	0.103774	+	1.08677i
$75$	1.85831	−	4.64184i	0.214579	−	0.535993i
$76$	−2.53305	−	0.743771i	−0.290561	−	0.0853164i
$77$	1.88455	+	5.82842i	0.214765	+	0.664210i
$78$	2.19097	+	4.79755i	0.248078	+	0.543216i
$79$	−2.56351	−	0.621901i	−0.288417	−	0.0699693i	0.0889401	−	0.996037i	$-0.471652\pi$
$79$	−2.56351	−	0.621901i	−0.288417	−	0.0699693i	−0.377357	+	0.926068i	$0.623167\pi$
$80$	−0.000131902	0	2.54219e-5i	−1.47470e−5	0	2.84226e-6i
$81$	0.981929	+	0.189251i	0.109103	+	0.0210279i
$82$	−5.73747	−	1.39190i	−0.633598	−	0.153709i
$83$	2.17121	+	4.75428i	0.238321	+	0.521850i	0.990567	−	0.137033i	$-0.0437565\pi$
$83$	2.17121	+	4.75428i	0.238321	+	0.521850i	−0.752245	+	0.658883i	$0.771029\pi$
$84$	−1.77316	+	1.96364i	−0.193468	+	0.214251i
$85$	0.000656111	0	0.000192652i	7.11653e−5	0	2.08960e-5i
$86$	−0.946310	+	2.36377i	−0.102043	+	0.254892i
$87$	−0.0319302	−	0.334388i	−0.00342327	−	0.0358501i
$88$	0.860483	+	2.14938i	0.0917278	+	0.229125i
$89$	−6.61598	+	3.41077i	−0.701292	+	0.361541i	−0.771708	−	0.635976i	$-0.780598\pi$
$89$	−6.61598	+	3.41077i	−0.701292	+	0.361541i	0.0704162	+	0.997518i	$0.477567\pi$
$90$	8.79669e−5	0	0.000101519i	9.27252e−6	0	1.07011e-5i
$91$	9.89986	+	9.83417i	1.03779	+	1.03090i
$92$	−0.860167	−	4.71806i	−0.0896786	−	0.491892i
$93$	0.239795	−	0.415338i	0.0248656	−	0.0430685i
$94$	−1.54594	−	0.535054i	−0.159451	−	0.0551866i
$95$	−1.68739e−5	0	0.000354226i	−1.73122e−6	0	3.63428e-5i
$96$	−0.618159	+	0.786053i	−0.0630906	+	0.0802262i
$97$	7.72358	−	16.9123i	0.784211	−	1.71718i	0.0916874	−	0.995788i	$-0.470774\pi$
$97$	7.72358	−	16.9123i	0.784211	−	1.71718i	0.692524	−	0.721395i	$-0.256499\pi$
$98$	−2.55831	+	6.51575i	−0.258428	+	0.658190i
$99$	0.652275	−	2.22145i	0.0655561	−	0.223264i
$100$	−0.237910	−	4.99434i	−0.0237910	−	0.499434i
$101$	−6.02225	−	4.28842i	−0.599236	−	0.426714i	0.239775	−	0.970829i	$-0.422926\pi$
$101$	−6.02225	−	4.28842i	−0.599236	−	0.426714i	−0.839011	+	0.544114i	$0.816866\pi$
$102$	3.51289	−	3.68421i	0.347828	−	0.364791i
$103$	0.182238	+	0.526541i	0.0179564	+	0.0518816i	0.953623	−	0.301004i	$-0.0973217\pi$
$103$	0.182238	+	0.526541i	0.0179564	+	0.0518816i	−0.935667	+	0.352886i	$0.885201\pi$
$104$	3.98595	+	3.45385i	0.390855	+	0.338678i
$105$	0.000312494	0	0.000169286i	3.04963e−5	0	1.65207e-5i
$106$	10.0295	−	4.58033i	0.974154	−	0.444881i
$107$	−8.89687	+	0.423810i	−0.860093	+	0.0409713i	−0.472993	−	0.881066i	$-0.656826\pi$
$107$	−8.89687	+	0.423810i	−0.860093	+	0.0409713i	−0.387100	+	0.922038i	$0.626523\pi$
$108$	0.971812	−	0.235759i	0.0935126	−	0.0226859i
$109$	−4.89812	−	6.22847i	−0.469155	−	0.596579i	0.492680	−	0.870211i	$-0.336017\pi$
$109$	−4.89812	−	6.22847i	−0.469155	−	0.596579i	−0.961834	+	0.273632i	$0.911775\pi$
$110$	0.000253335	0	0.000180399i	2.41546e−5	0	1.72004e-5i
$111$	1.33652	−	9.29569i	0.126857	−	0.882308i
$112$	−0.797201	+	2.52279i	−0.0753285	+	0.238381i
$113$	10.4209	−	9.02976i	0.980316	−	0.849448i	−0.00829180	−	0.999966i	$-0.502639\pi$
$113$	10.4209	−	9.02976i	0.980316	−	0.849448i	0.988607	+	0.150517i	$0.0480939\pi$
$114$	2.28630	+	1.32000i	0.214131	+	0.123629i
$115$	−0.000588667	0	0.000261706i	−5.48935e−5	0	2.44042e-5i
$116$	−0.167954	−	0.290906i	−0.0155942	−	0.0270099i
$117$	−0.998143	−	5.17886i	−0.0922784	−	0.478786i
$118$	0.526764	−	0.819661i	0.0484925	−	0.0754559i
$119$	5.26058	−	12.3985i	0.482236	−	1.13657i
$120$	0.000122190	0	5.58023e-5i	1.11544e−5	0	5.09403e-6i
$121$	5.23573	+	2.09607i	0.475976	+	0.190552i
$122$	−1.55277	−	6.40061i	−0.140581	−	0.579484i
$123$	5.24759	+	2.70532i	0.473159	+	0.243931i
$124$	0.0455880	−	0.477419i	0.00409392	−	0.0428735i
$125$	−0.00128888		0.000378449i	−0.000115281		3.38495e-5i
$126$	2.18613	−	1.49025i	0.194756	−	0.132762i
$127$	2.79517	−	3.22580i	0.248032	−	0.286244i	−0.618058	−	0.786132i	$-0.712080\pi$
$127$	2.79517	−	3.22580i	0.248032	−	0.286244i	0.866090	+	0.499889i	$0.166626\pi$
$128$	−0.235759	+	0.971812i	−0.0208383	+	0.0858968i
$129$	1.47692	−	2.07404i	0.130035	−	0.182609i
$130$	0.000324642	0	0.000629717i	2.84730e−5	0	5.52299e-5i
$131$	7.71583	+	8.09213i	0.674136	+	0.707013i	0.968593	−	0.248652i	$-0.0799874\pi$
$131$	7.71583	+	8.09213i	0.674136	+	0.707013i	−0.294457	+	0.955665i	$0.595139\pi$
$132$	−0.329491	−	2.29166i	−0.0286785	−	0.199464i
$133$	6.89187	+	1.13535i	0.597601	+	0.0984469i
$134$	1.63691	+	0.235352i	0.141407	+	0.0203313i
$135$	−6.15532e−5	0	0.000119396i	−5.29765e−6	0	1.02760e-5i
$136$	1.66496	−	4.81058i	0.142769	−	0.412504i
$137$	3.70400	−	2.13851i	0.316454	−	0.182705i	−0.333357	−	0.942801i	$-0.608181\pi$
$137$	3.70400	−	2.13851i	0.316454	−	0.182705i	0.649811	+	0.760096i	$0.274848\pi$
$138$	−0.276405	+	4.78786i	−0.0235292	+	0.407570i
$139$			2.24680i			0.190571i	0.995450	+	0.0952857i	$0.0303765\pi$
$139$			2.24680i			0.190571i	−0.995450	+	0.0952857i	$0.969624\pi$
$140$	0.000354578	0	2.41738e-5i	2.99673e−5	0	2.04306e-6i
$141$	1.37622	+	0.884440i	0.115898	+	0.0744833i
$142$	−2.64435	−	2.07954i	−0.221909	−	0.174511i
$143$	−12.1556	+	1.16072i	−1.01650	+	0.0970643i
$144$	0.786053	−	0.618159i	0.0655044	−	0.0515132i
$145$	−3.26566e−5	0	3.11380e-5i	−2.71198e−6	0	2.58587e-6i
$146$	7.46467	+	11.6153i	0.617781	+	0.961286i
$147$	4.02234	−	5.72894i	0.331757	−	0.472515i
$148$	−2.64583	−	9.01086i	−0.217486	−	0.740688i
$149$	−11.9262	+	4.12771i	−0.977034	+	0.338155i	−0.768493	−	0.639859i	$-0.778993\pi$
$149$	−11.9262	+	4.12771i	−0.977034	+	0.338155i	−0.208542	+	0.978013i	$0.566872\pi$
$150$	−0.946256	+	4.90964i	−0.0772615	+	0.400871i
$151$	2.90740	+	2.77220i	0.236601	+	0.225599i	0.799098	−	0.601201i	$-0.205311\pi$
$151$	2.90740	+	2.77220i	0.236601	+	0.225599i	−0.562497	+	0.826799i	$0.690159\pi$
$152$	2.62804	+	0.250947i	0.213162	+	0.0203545i
$153$	−4.28245	+	2.75216i	−0.346216	+	0.222499i
$154$	−2.95353	−	5.36644i	−0.238002	−	0.432440i
$155$	−6.37673e−5	0	9.16835e-6i	−5.12191e−6	0	7.36419e-7i
$156$	−3.05932	−	4.29621i	−0.244942	−	0.343972i
$157$	−16.8872	+	6.76061i	−1.34774	+	0.539555i	−0.929514	−	0.368786i	$-0.879773\pi$
$157$	−16.8872	+	6.76061i	−1.34774	+	0.539555i	−0.418229	+	0.908341i	$0.637349\pi$
$158$	2.63488	+	0.125515i	0.209620	+	0.00998542i
$159$	−10.8267	+	2.08667i	−0.858611	+	0.165484i
$160$	0.000134329	0		1.06196e−5	0
$161$	3.78198	+	12.1118i	0.298062	+	0.954546i
$162$	−1.00000			−0.0785674
$163$	−18.5492	+	3.57506i	−1.45289	+	0.280021i	−0.853773	−	0.520645i	$-0.825692\pi$
$163$	−18.5492	+	3.57506i	−1.45289	+	0.280021i	−0.599112	+	0.800665i	$0.704479\pi$
$164$	5.89721	+	0.280919i	0.460495	+	0.0219361i
$165$	−0.000288725	0	0.000115588i	−2.24772e−5	0	8.99851e-6i
$166$	−3.03173	−	4.25746i	−0.235308	−	0.330443i
$167$	−1.83590	+	0.263963i	−0.142067	+	0.0204261i	−0.212981	−	0.977056i	$-0.568317\pi$
$167$	−1.83590	+	0.263963i	−0.142067	+	0.0204261i	0.0709146	+	0.997482i	$0.477408\pi$
$168$	1.36950	−	2.26373i	0.105659	−	0.174651i
$169$	−12.4647	+	8.01061i	−0.958827	+	0.616201i
$170$	−0.000680714	0	6.50003e-5i	−5.22084e−5	0	4.98530e-6i
$171$	−1.91065	−	1.82180i	−0.146111	−	0.139317i
$172$	0.481863	−	2.50014i	0.0367417	−	0.190634i
$173$	−5.68264	+	1.96678i	−0.432043	+	0.149532i	−0.534430	−	0.845213i	$-0.679474\pi$
$173$	−5.68264	+	1.96678i	−0.432043	+	0.149532i	0.102386	+	0.994745i	$0.467352\pi$
$174$	0.0946365	+	0.322302i	0.00717437	+	0.0244337i
$175$	2.23714	+	13.0382i	0.169112	+	0.985597i
$176$	−1.25171	−	1.94769i	−0.0943510	−	0.146813i
$177$	−0.705158	+	0.672366i	−0.0530029	+	0.0505381i
$178$	5.85093	−	4.60122i	0.438545	−	0.344876i
$179$	21.8574	−	2.08713i	1.63370	−	0.156000i	0.762522	−	0.646963i	$-0.223961\pi$
$179$	21.8574	−	2.08713i	1.63370	−	0.156000i	0.871180	+	0.490963i	$0.163355\pi$
$180$	−0.000105590	0	8.30367e-5i	−7.87020e−6	0	6.18919e-6i
$181$	6.47611	+	4.16194i	0.481365	+	0.309355i	0.758725	−	0.651412i	$-0.225823\pi$
$181$	6.47611	+	4.16194i	0.481365	+	0.309355i	−0.277359	+	0.960766i	$0.589459\pi$
$182$	−11.5821	−	7.78289i	−0.858521	−	0.576906i
$183$			6.58626i			0.486871i
$184$	1.73752	+	4.47001i	0.128092	+	0.329534i
$185$	−0.00109251		0.000630761i	−8.03229e−5		4.63745e-5i
$186$	−0.156859	+	0.453214i	−0.0115014	+	0.0332312i
$187$	5.40057	+	10.4756i	0.394929	+	0.766055i
$188$	1.61926	+	0.232814i	0.118097	+	0.0169797i
$189$	−2.47584	+	0.932843i	−0.180091	+	0.0678543i
$190$	−5.04688e−5	0	0.000351018i	−3.66139e−6	0	2.54655e-5i
$191$	−8.84814	−	9.27967i	−0.640229	−	0.671453i	0.321040	−	0.947066i	$-0.395968\pi$
$191$	−8.84814	−	9.27967i	−0.640229	−	0.671453i	−0.961269	+	0.275613i	$0.911119\pi$
$192$	0.458227	−	0.888835i	0.0330697	−	0.0641462i
$193$	−13.6810	+	19.2123i	−0.984783	+	1.38293i	−0.0618026	+	0.998088i	$0.519685\pi$
$193$	−13.6810	+	19.2123i	−0.984783	+	1.38293i	−0.922981	+	0.384846i	$0.874254\pi$
$194$	−4.38334	+	18.0684i	−0.314705	+	1.29723i
$195$	−0.000463952	0	0.000535429i	−3.32243e−5	0	3.83429e-5i
$196$	1.27897	−	6.88217i	0.0913546	−	0.491583i
$197$	18.9607	−	5.56736i	1.35089	−	0.396658i	0.475349	−	0.879797i	$-0.342322\pi$
$197$	18.9607	−	5.56736i	1.35089	−	0.396658i	0.875544	+	0.483139i	$0.160503\pi$
$198$	−0.220076	+	2.30474i	−0.0156402	+	0.163791i
$199$	11.1698	+	5.75842i	0.791804	+	0.408203i	0.806163	−	0.591694i	$-0.201540\pi$
$199$	11.1698	+	5.75842i	0.791804	+	0.408203i	−0.0143590	+	0.999897i	$0.504571\pi$
$200$	1.17879	+	4.85906i	0.0833534	+	0.343587i
$201$	−1.53528	−	0.614633i	−0.108290	−	0.0433529i
$202$	6.72501	+	3.07121i	0.473170	+	0.216089i
$203$	0.534962	+	0.709689i	0.0375470	+	0.0498104i
$204$	−2.75216	+	4.28245i	−0.192690	+	0.299832i
$205$	−0.000150089	0	0.000778733i	−1.04826e−5	0	5.43891e-5i
$206$	−0.278593	−	0.482537i	−0.0194105	−	0.0336199i
$207$	1.39739	−	4.58773i	0.0971256	−	0.318869i
$208$	−4.56757	−	2.63709i	−0.316704	−	0.182849i
$209$	−4.61928	+	4.00263i	−0.319522	+	0.276867i
$210$	−0.000338884	0	0.000107087i	−2.33852e−5	0	7.38973e-6i
$211$	−1.69789	+	11.8091i	−0.116888	+	0.812971i	0.844062	+	0.536246i	$0.180158\pi$
$211$	−1.69789	+	11.8091i	−0.116888	+	0.812971i	−0.960949	+	0.276725i	$0.910751\pi$
$212$	−8.98145	+	6.39566i	−0.616849	+	0.439256i
$213$	2.07954	+	2.64435i	0.142488	+	0.181188i
$214$	8.65589	−	2.09990i	0.591704	−	0.143546i
$215$	−0.000341635	0	1.62741e-5i	−2.32993e−5	0	1.10988e-6i
$216$	−0.909632	+	0.415415i	−0.0618926	+	0.0282654i
$217$	0.0344192	+	1.26841i	0.00233653	+	0.0861054i
$218$	5.98835	+	5.18893i	0.405582	+	0.351439i
$219$	−4.51586	−	13.0477i	−0.305153	−	0.881682i
$220$	−0.000214616	0	0.000225083i	−1.44694e−5	0	1.51751e-5i
$221$	21.8701	+	15.5736i	1.47114	+	1.04760i
$222$	0.446855	+	9.38064i	0.0299909	+	0.629587i
$223$	7.05853	−	24.0391i	0.472674	−	1.60978i	−0.285946	−	0.958246i	$-0.592308\pi$
$223$	7.05853	−	24.0391i	0.472674	−	1.60978i	0.758620	−	0.651533i	$-0.225874\pi$
$224$	0.305354	−	2.62807i	0.0204023	−	0.175595i
$225$	2.07708	−	4.54816i	0.138472	−	0.303211i
$226$	−8.52369	+	10.8387i	−0.566987	+	0.720983i
$227$	−1.11825	+	23.4749i	−0.0742208	+	1.55809i	0.588051	+	0.808824i	$0.299895\pi$
$227$	−1.11825	+	23.4749i	−0.0742208	+	1.55809i	−0.662272	+	0.749263i	$0.730408\pi$
$228$	−2.49479	−	0.863456i	−0.165222	−	0.0571838i
$229$	−7.52635	+	13.0360i	−0.497355	+	0.861445i	−0.999995	−	0.00305102i	$-0.999029\pi$
$229$	−7.52635	+	13.0360i	−0.497355	+	0.861445i	0.502640	+	0.864496i	$0.332362\pi$
$230$	0.000528501	0	0.000368383i	3.48483e−5	0	2.42904e-5i
$231$	1.60509	+	5.91149i	0.105607	+	0.388947i
$232$	0.219974	+	0.253863i	0.0144420	+	0.0166669i
$233$	3.04805	−	1.57138i	0.199684	−	0.102944i	−0.355484	−	0.934682i	$-0.615684\pi$
$233$	3.04805	−	1.57138i	0.199684	−	0.102944i	0.555168	+	0.831738i	$0.312654\pi$
$234$	1.96021	+	4.89637i	0.128143	+	0.320086i
$235$	−2.08886e−5	0	0.000218755i	−1.36262e−6	0	1.42700e-5i
$236$	−0.362123	+	0.904539i	−0.0235722	+	0.0588805i
$237$	−2.53101	−	0.743173i	−0.164407	−	0.0482743i
$238$	−2.81908	+	13.1700i	−0.182734	+	0.853686i
$239$	−2.90958	−	6.37109i	−0.188205	−	0.412112i	0.791884	−	0.610672i	$-0.209101\pi$
$239$	−2.90958	−	6.37109i	−0.188205	−	0.412112i	−0.980089	+	0.198560i	$0.936373\pi$
$240$	−0.000130543	0	3.16693e-5i	−8.42649e−6	0	2.04424e-6i
$241$	12.1378	+	2.33936i	0.781861	+	0.150691i	0.564537	−	0.825408i	$-0.309055\pi$
$241$	12.1378	+	2.33936i	0.781861	+	0.150691i	0.217325	+	0.976099i	$0.430267\pi$
$242$	−5.53780	−	1.06732i	−0.355983	−	0.0686102i
$243$	0.971812	+	0.235759i	0.0623417	+	0.0151239i
$244$	2.73603	+	5.99107i	0.175157	+	0.383539i
$245$	−0.000938920	0	5.09940e-5i	−5.99854e−5	0	3.25789e-6i
$246$	−5.66475	−	1.66332i	−0.361171	−	0.106049i
$247$	−5.17494	+	12.9264i	−0.329273	+	0.822485i
$248$	0.0455880	+	0.477419i	0.00289484	+	0.0303161i
$249$	1.94253	+	4.85221i	0.123103	+	0.307496i
$250$	0.00119396		0.000615532i	7.55130e−5		3.89296e-5i
$251$	17.6355	+	20.3524i	1.11314	+	1.28463i	0.954800	+	0.297249i	$0.0960693\pi$
$251$	17.6355	+	20.3524i	1.11314	+	1.28463i	0.158342	+	0.987384i	$0.449385\pi$
$252$	−1.86459	+	1.87705i	−0.117458	+	0.118243i
$253$	−10.2660	−	4.23029i	−0.645419	−	0.265956i
$254$	−2.13417	+	3.69650i	−0.133910	+	0.231939i
$255$	0.000646201	0	0.000223652i	4.04667e−5	0	1.40057e-5i
$256$	0.0475819	−	0.998867i	0.00297387	−	0.0624292i
$257$	−7.86798	+	10.0050i	−0.490791	+	0.624092i	−0.966857	−	0.255318i	$-0.917820\pi$
$257$	−7.86798	+	10.0050i	−0.490791	+	0.624092i	0.476066	+	0.879410i	$0.342062\pi$
$258$	−1.05771	+	2.31606i	−0.0658502	+	0.144192i
$259$	9.85700	+	22.8082i	0.612484	+	1.41723i
$260$	−0.000199600	0	0.000679776i	−1.23787e−5	0	4.21579e-5i
$261$	−0.0159832	−	0.335528i	−0.000989334	−	0.0207687i
$262$	−9.10785	−	6.48567i	−0.562685	−	0.400686i
$263$	6.30631	−	6.61387i	0.388864	−	0.407829i	−0.499982	−	0.866036i	$-0.666660\pi$
$263$	6.30631	−	6.61387i	0.388864	−	0.407829i	0.888845	+	0.458208i	$0.151508\pi$
$264$	0.757237	+	2.18789i	0.0466047	+	0.134655i
$265$	0.00111934		0.000969916i	6.87606e−5		5.95814e-5i
$266$	−6.98219	+	0.189466i	−0.428105	+	0.0116169i
$267$	−6.77078	+	3.09211i	−0.414365	+	0.189234i
$268$	−1.65187	+	0.0786881i	−0.100904	+	0.00480664i
$269$	−3.98977	+	0.967907i	−0.243261	+	0.0590144i	−0.355535	−	0.934663i	$-0.615701\pi$
$269$	−3.98977	+	0.967907i	−0.243261	+	0.0590144i	0.112275	+	0.993677i	$0.464186\pi$
$270$	8.30367e−5	0	0.000105590i	5.05345e−6	0	6.42599e-6i
$271$	18.3840	−	13.0912i	1.11675	−	0.795234i	0.136040	−	0.990703i	$-0.456562\pi$
$271$	18.3840	−	13.0912i	1.11675	−	0.795234i	0.980710	+	0.195469i	$0.0626230\pi$
$272$	−0.724462	+	5.03875i	−0.0439270	+	0.305519i
$273$	9.42072	+	10.2941i	0.570168	+	0.623026i
$274$	−3.23235	+	2.80085i	−0.195273	+	0.169205i
$275$	−10.0252	−	5.78807i	−0.604544	−	0.349034i
$276$	−0.634698	−	4.75365i	−0.0382043	−	0.286136i
$277$	1.70486	+	2.95290i	0.102435	+	0.177423i	0.912687	−	0.408658i	$-0.134003\pi$
$277$	1.70486	+	2.95290i	0.102435	+	0.177423i	−0.810252	+	0.586081i	$0.800670\pi$
$278$	−0.425210	−	2.20620i	−0.0255024	−	0.132319i
$279$	0.259286	−	0.403457i	0.0155231	−	0.0241544i
$280$	−0.000352746	0	4.33675e-5i	−2.10806e−5	0	2.59170e-6i
$281$	−4.25856	−	1.94482i	−0.254044	−	0.116018i	0.284323	−	0.958729i	$-0.408231\pi$
$281$	−4.25856	−	1.94482i	−0.254044	−	0.116018i	−0.538367	+	0.842710i	$0.680959\pi$
$282$	−1.51873	−	0.608006i	−0.0904388	−	0.0362063i
$283$	1.83424	+	7.56084i	0.109034	+	0.449445i	0.999989	−	0.00464655i	$-0.00147905\pi$
$283$	1.83424	+	7.56084i	0.109034	+	0.449445i	−0.890955	+	0.454092i	$0.849964\pi$
$284$	2.99012	+	1.54152i	0.177431	+	0.0914722i
$285$	−3.37095e−5	0	0.000353022i	−1.99678e−6	0	2.09112e-5i
$286$	11.7163	−	3.44021i	0.692798	−	0.203424i
$287$	−15.5766	+	1.16620i	−0.919460	+	0.0688384i
$288$	−0.654861	+	0.755750i	−0.0385880	+	0.0445330i
$289$	2.10151	−	8.66254i	0.123618	−	0.509561i
$290$	2.61735e−5	0	3.67556e-5i	1.53696e−6	0	2.15836e-6i
$291$	8.51956	−	16.5256i	0.499425	−	0.968750i
$292$	−9.52798	−	9.99266i	−0.557583	−	0.584776i
$293$	−2.97340	−	20.6804i	−0.173708	−	1.20816i	−0.870966	−	0.491344i	$-0.836506\pi$
$293$	−2.97340	−	20.6804i	−0.173708	−	1.20816i	0.697258	−	0.716821i	$-0.254403\pi$
$294$	−2.86545	+	6.38664i	−0.167116	+	0.372477i
$295$	0.000129549	0	1.86263e-5i	7.54263e−6	0	1.08447e-6i
$296$	4.30333	+	8.34730i	0.250126	+	0.485177i
$297$	0.757237	−	2.18789i	0.0439393	−	0.126954i
$298$	10.9295	−	6.31017i	0.633131	−	0.365538i
$299$	−25.2024	+	2.15076i	−1.45749	+	0.124382i
$300$		−	5.00000i		−	0.288675i
$301$	−0.458204	+	6.72089i	−0.0264105	+	0.387386i
$302$	−3.37951	−	2.17188i	−0.194469	−	0.124977i
$303$	−5.81138	−	4.57012i	−0.333855	−	0.262546i
$304$	−2.62804	+	0.250947i	−0.150728	+	0.0143928i
$305$	0.000695442	0	0.000546902i	3.98209e−5	0	3.13155e-5i
$306$	3.68421	−	3.51289i	0.210612	−	0.200818i
$307$	17.5285	+	27.2749i	1.00040	+	1.55666i	0.819436	+	0.573170i	$0.194287\pi$
$307$	17.5285	+	27.2749i	1.00040	+	1.55666i	0.180968	+	0.983489i	$0.442077\pi$
$308$	3.91576	+	4.71050i	0.223121	+	0.268406i
$309$	0.156977	+	0.534616i	0.00893013	+	0.0304132i
$310$	6.08798e−5	0	2.10707e-5i	3.45774e−6	0	1.19674e-6i
$311$	−2.74805	+	14.2582i	−0.155828	+	0.808510i	0.816939	+	0.576724i	$0.195669\pi$
$311$	−2.74805	+	14.2582i	−0.155828	+	0.808510i	−0.972767	+	0.231786i	$0.925543\pi$
$312$	3.81710	+	3.63959i	0.216101	+	0.206051i
$313$	15.2543	+	1.45661i	0.862222	+	0.0823323i	0.516791	−	0.856112i	$-0.327126\pi$
$313$	15.2543	+	1.45661i	0.862222	+	0.0823323i	0.345432	+	0.938444i	$0.387733\pi$
$314$	15.3026	−	9.83435i	0.863573	−	0.554985i
$315$	0.000304085	0	0.000183964i	1.71332e−5	0	1.03652e-5i
$316$	−2.61102	+	0.375408i	−0.146881	+	0.0211183i
$317$	−11.2041	−	15.7339i	−0.629283	−	0.883704i	0.369683	−	0.929158i	$-0.379466\pi$
$317$	−11.2041	−	15.7339i	−0.629283	−	0.883704i	−0.998966	+	0.0454534i	$0.985527\pi$
$318$	10.2361	−	4.09792i	0.574013	−	0.229800i
$319$	−0.776825	−	0.0370047i	−0.0434938	−	0.00207187i
$320$	−0.000131902	0	2.54219e-5i	−7.37352e−6	0	1.42113e-6i
$321$	−8.90696			−0.497138
$322$	−6.00582	−	11.1772i	−0.334691	−	0.622882i
$323$	13.4390			0.747768
$324$	0.981929	−	0.189251i	0.0545516	−	0.0105140i
$325$	−26.3410	−	1.25478i	−1.46113	−	0.0696024i
$326$	17.5374	−	7.02092i	0.971307	−	0.388853i
$327$	−4.59621	−	6.45447i	−0.254171	−	0.356933i
$328$	−5.84380	+	0.840212i	−0.322670	+	0.0463929i
$329$	−4.32730	−	0.0885961i	−0.238572	−	0.00488446i
$330$	0.000261632	0	0.000168141i	1.44024e−5	0	9.25584e-6i
$331$	−22.4825	−	2.14681i	−1.23575	−	0.118000i	−0.543344	−	0.839510i	$-0.682842\pi$
$331$	−22.4825	−	2.14681i	−1.23575	−	0.118000i	−0.692403	+	0.721511i	$0.743448\pi$
$332$	3.78267	+	3.60677i	0.207601	+	0.197947i
$333$	1.77731	−	9.22156i	0.0973960	−	0.505339i
$334$	1.75277	−	0.606640i	0.0959074	−	0.0331939i
$335$	6.25856e−5	0	0.000213147i	3.41942e−6	0	1.16455e-5i
$336$	−0.916338	+	2.48200i	−0.0499903	+	0.135404i
$337$	14.8679	+	23.1349i	0.809906	+	1.26024i	0.962319	+	0.271922i	$0.0876591\pi$
$337$	14.8679	+	23.1349i	0.809906	+	1.26024i	−0.152413	+	0.988317i	$0.548705\pi$
$338$	10.7235	−	10.2248i	0.583280	−	0.556157i
$339$	10.8387	−	8.52369i	0.588680	−	0.462943i
$340$	0.000680714	0	6.50003e-5i	3.69169e−5	0	3.52514e-6i
$341$	−0.872804	−	0.686380i	−0.0472650	−	0.0371696i
$342$	2.22090	+	1.42729i	0.120093	+	0.0771788i
$343$	−1.13666	+	18.4853i	−0.0613740	+	0.998115i
$344$			2.54616i			0.137280i
$345$	−0.000600453	0	0.000233400i	−3.23273e−5	0	1.25658e-5i
$346$	5.20774	−	3.00669i	0.279970	−	0.161641i
$347$	−2.88053	+	8.32274i	−0.154635	+	0.446788i	−0.995534	−	0.0944037i	$-0.969906\pi$
$347$	−2.88053	+	8.32274i	−0.154635	+	0.446788i	0.840899	+	0.541192i	$0.182027\pi$
$348$	−0.153922	−	0.298568i	−0.00825110	−	0.0160049i
$349$	−24.7263	−	3.55511i	−1.32357	−	0.190301i	−0.555955	−	0.831212i	$-0.687647\pi$
$349$	−24.7263	−	3.55511i	−1.32357	−	0.190301i	−0.767615	+	0.640912i	$0.778557\pi$
$350$	−4.66421	−	12.3792i	−0.249313	−	0.661697i
$351$	−0.750593	−	5.22049i	−0.0400637	−	0.278649i
$352$	1.59769	+	1.67561i	0.0851572	+	0.0893103i
$353$	10.4006	−	20.1743i	0.553566	−	1.07377i	−0.431584	−	0.902073i	$-0.642045\pi$
$353$	10.4006	−	20.1743i	0.553566	−	1.07377i	0.985150	−	0.171696i	$-0.0549247\pi$
$354$	0.565168	−	0.793668i	0.0300384	−	0.0421830i
$355$	0.000106538	0	0.000439157i	5.65447e−6	0	2.33080e-5i
$356$	−4.87441	+	5.62536i	−0.258343	+	0.298144i
$357$	5.84456	−	12.1342i	0.309327	−	0.642208i
$358$	−21.0675	+	6.18596i	−1.11345	+	0.326938i
$359$	−1.43267	+	15.0036i	−0.0756135	+	0.791860i	0.875541	+	0.483144i	$0.160505\pi$
$359$	−1.43267	+	15.0036i	−0.0756135	+	0.791860i	−0.951154	+	0.308716i	$0.900101\pi$
$360$	0.000119396	0	6.15532e-5i	6.29275e−6	0	3.24414e-6i
$361$	−2.83629	−	11.6913i	−0.149278	−	0.615333i
$362$	−7.14673	−	2.86112i	−0.375624	−	0.150377i
$363$	5.13007	+	2.34282i	0.269259	+	0.122966i
$364$	12.8457	+	5.45032i	0.673298	+	0.285674i
$365$	−0.00100272	+	0.00156027i	−5.24849e−5	+	8.16681e-5i
$366$	−1.24646	−	6.46724i	−0.0651534	−	0.338048i
$367$	−2.66151	−	4.60988i	−0.138930	−	0.240634i	0.788162	−	0.615468i	$-0.211033\pi$
$367$	−2.66151	−	4.60988i	−0.138930	−	0.240634i	−0.927092	+	0.374834i	$0.877700\pi$
$368$	−2.55208	−	4.06041i	−0.133036	−	0.211663i
$369$	5.11292	+	2.95195i	0.266168	+	0.153672i
$370$	0.000953394	0	0.000826121i	4.95646e−5	0	4.29480e-5i
$371$	21.5203	−	19.6945i	1.11728	−	1.02249i
$372$	0.0682529	−	0.474709i	0.00353875	−	0.0246125i
$373$	18.5187	−	13.1871i	0.958860	−	0.682801i	0.0104828	−	0.999945i	$-0.496663\pi$
$373$	18.5187	−	13.1871i	0.958860	−	0.682801i	0.948377	+	0.317144i	$0.102724\pi$
$374$	−7.28550	−	9.26427i	−0.376724	−	0.479044i
$375$	−0.00130543		0.000316693i	−6.74119e−5		1.63539e-5i
$376$	−1.63406	+	0.0778397i	−0.0842701	+	0.00401428i
$377$	−1.61154	+	0.735966i	−0.0829986	+	0.0379042i
$378$	2.25456	−	1.38454i	0.115962	−	0.0712131i
$379$	7.07898	+	6.13397i	0.363623	+	0.315081i	0.817440	−	0.576014i	$-0.195393\pi$
$379$	7.07898	+	6.13397i	0.363623	+	0.315081i	−0.453817	+	0.891095i	$0.649938\pi$
$380$	0.000115987	0	0.000335123i	5.95002e−6	0	1.71915e-5i
$381$	2.94550	−	3.08915i	0.150902	−	0.158262i
$382$	10.4444	+	7.43745i	0.534384	+	0.380533i
$383$	1.03597	+	21.7477i	0.0529357	+	1.11126i	0.856536	+	0.516088i	$0.172612\pi$
$383$	1.03597	+	21.7477i	0.0529357	+	1.11126i	−0.803600	+	0.595170i	$0.797085\pi$
$384$	−0.281733	+	0.959493i	−0.0143771	+	0.0489639i
$385$	0.000490911	0	0.000660352i	2.50192e−5	0	3.36546e-5i
$386$	9.79785	−	21.4543i	0.498698	−	1.09200i
$387$	1.57393	−	2.00141i	0.0800073	−	0.101738i
$388$	0.884665	−	18.5714i	0.0449120	−	0.942820i
$389$	−27.7267	−	9.59630i	−1.40580	−	0.486552i	−0.484290	−	0.874908i	$-0.660922\pi$
$389$	−27.7267	−	9.59630i	−1.40580	−	0.486552i	−0.921509	+	0.388356i	$0.873043\pi$
$390$	0.000354237	0	0.000613557i	1.79375e−5	0	3.10687e-5i
$391$	10.9679	+	21.8111i	0.554670	+	1.10303i
$392$	0.0466066	+	6.99984i	0.00235399	+	0.353546i
$393$	7.32206	+	8.45010i	0.369349	+	0.426251i
$394$	−17.5644	+	9.05508i	−0.884882	+	0.456189i
$395$	0.000131696	0	0.000328960i	6.62633e−6	0	1.65518e-5i
$396$	−0.220076	−	2.30474i	−0.0110593	−	0.115818i
$397$	5.06236	−	12.6452i	0.254073	−	0.634643i	−0.745417	−	0.666599i	$-0.767749\pi$
$397$	5.06236	−	12.6452i	0.254073	−	0.634643i	0.999489	+	0.0319561i	$0.0101737\pi$
$398$	−12.0577	−	3.54046i	−0.604398	−	0.177467i
$399$	6.83004	+	1.46199i	0.341930	+	0.0731909i
$400$	−2.07708	−	4.54816i	−0.103854	−	0.227408i
$401$	6.95760	+	1.68790i	0.347446	+	0.0842895i	0.405684	−	0.914013i	$-0.367033\pi$
$401$	6.95760	+	1.68790i	0.347446	+	0.0842895i	−0.0582384	+	0.998303i	$0.518548\pi$
$402$	1.62385	+	0.312972i	0.0809905	+	0.0156096i
$403$	−2.48373	−	0.478700i	−0.123724	−	0.0238458i
$404$	−7.18471	−	1.74299i	−0.357453	−	0.0867171i
$405$	−5.58023e−5	0	0.000122190i	−2.77284e−6	0	6.07167e-6i
$406$	−0.659604	−	0.595622i	−0.0327356	−	0.0295602i
$407$	−20.8622	−	6.12570i	−1.03410	−	0.303639i
$408$	1.89197	−	4.72591i	0.0936665	−	0.233968i
$409$	0.131688	+	1.37910i	0.00651156	+	0.0681921i	0.998144	−	0.0609042i	$-0.0193984\pi$
$409$	0.131688	+	1.37910i	0.00651156	+	0.0681921i	−0.991632	+	0.129096i	$0.958792\pi$
$410$	0.000294752	0	0.000736256i	1.45568e−5	0	3.63611e-5i
$411$	3.80156	−	1.95984i	0.187517	−	0.0966718i
$412$	0.364879	+	0.421093i	0.0179763	+	0.0207458i
$413$	0.658901	−	2.49221i	0.0324224	−	0.122634i
$414$	−0.503908	+	4.76928i	−0.0247657	+	0.234398i
$415$	0.000351042	0	0.000608023i	1.72320e−5	0	2.98467e-5i
$416$	4.98410	+	1.72501i	0.244365	+	0.0845757i
$417$	−0.106907	+	2.24426i	−0.00523527	+	0.109902i
$418$	3.77830	−	4.80450i	0.184803	−	0.234996i
$419$	−0.0463027	+	0.101389i	−0.00226204	+	0.00495317i	−0.910760	−	0.412937i	$-0.864503\pi$
$419$	−0.0463027	+	0.101389i	−0.00226204	+	0.00495317i	0.908498	+	0.417890i	$0.137230\pi$
$420$	0.000353026	0	4.10179e-5i	1.72259e−5	0	2.00147e-6i
$421$	3.42616	−	11.6684i	0.166981	−	0.568684i	−0.832903	−	0.553419i	$-0.813323\pi$
$421$	3.42616	−	11.6684i	0.166981	−	0.568684i	0.999883	−	0.0152648i	$-0.00485914\pi$
$422$	−0.567677	−	11.9170i	−0.0276341	−	0.580111i
$423$	1.33257	+	0.948921i	0.0647919	+	0.0461381i
$424$	7.60876	−	7.97983i	0.369514	−	0.387535i
$425$	8.32480	+	24.0529i	0.403812	+	1.16674i
$426$	−2.54241	−	2.20301i	−0.123180	−	0.106736i
$427$	−9.11895	−	14.8491i	−0.441297	−	0.718600i
$428$	−8.10206	+	3.70009i	−0.391628	+	0.178850i
$429$	−12.1971	+	0.581018i	−0.588880	+	0.0280518i
$430$	0.000332382	0	8.06349e-5i	1.60289e−5	0	3.88856e-6i
$431$	−18.2575	−	23.2163i	−0.879434	−	1.11829i	−0.992198	−	0.124670i	$-0.960213\pi$
$431$	−18.2575	−	23.2163i	−0.879434	−	1.11829i	0.112764	−	0.993622i	$-0.464029\pi$
$432$	0.814576	−	0.580057i	0.0391913	−	0.0279080i
$433$	1.20848	−	8.40519i	0.0580761	−	0.403928i	−0.939960	−	0.341285i	$-0.889138\pi$
$433$	1.20848	−	8.40519i	0.0580761	−	0.403928i	0.998036	−	0.0626431i	$-0.0199530\pi$
$434$	−0.273846	−	1.23898i	−0.0131450	−	0.0594727i
$435$	−3.41012e−5	0	2.95488e-5i	−1.63503e−6	0	1.41676e-6i
$436$	−6.86214	−	3.96186i	−0.328637	−	0.189739i
$437$	−9.65148	+	8.19442i	−0.461693	+	0.391992i
$438$	6.90354	+	11.9573i	0.329864	+	0.571341i
$439$	3.21181	+	16.6644i	0.153291	+	0.795350i	0.974442	+	0.224639i	$0.0721202\pi$
$439$	3.21181	+	16.6644i	0.153291	+	0.795350i	−0.821151	+	0.570711i	$0.806668\pi$
$440$	0.000168141	0	0.000261632i	8.01579e−6	0	1.24728e-5i
$441$	4.29038	−	5.53106i	0.204304	−	0.263384i
$442$	−24.4222	−	11.1533i	−1.16165	−	0.530507i
$443$	30.1846	+	12.0841i	1.43412	+	0.574133i	0.953121	−	0.302590i	$-0.0978514\pi$
$443$	30.1846	+	12.0841i	1.43412	+	0.574133i	0.480995	+	0.876723i	$0.340276\pi$
$444$	−2.21408	−	9.12655i	−0.105075	−	0.433127i
$445$	0.000888718	0	0.000458166i	4.21293e−5	0	2.17192e-5i
$446$	−2.38153	+	24.9405i	−0.112769	+	1.18097i
$447$	−12.1091	+	3.55556i	−0.572742	+	0.168172i
$448$	0.197530	+	2.63837i	0.00933242	+	0.124651i
$449$	26.8987	−	31.0427i	1.26943	−	1.46500i	0.448693	−	0.893686i	$-0.351890\pi$
$449$	26.8987	−	31.0427i	1.26943	−	1.46500i	0.820734	−	0.571310i	$-0.193565\pi$
$450$	−1.17879	+	4.85906i	−0.0555689	+	0.229058i
$451$	7.92872	−	11.1343i	0.373349	−	0.524295i
$452$	6.31840	−	12.2560i	0.297193	−	0.576474i
$453$	2.77220	+	2.90740i	0.130250	+	0.136602i
$454$	−3.34462	−	23.2624i	−0.156971	−	1.09176i
$455$	0.000304684	−	0.00184952i	1.42838e−5	−	8.67068e-5i
$456$	2.61312	+	0.375710i	0.122371	+	0.0175942i
$457$	−14.5558	−	28.2343i	−0.680892	−	1.32075i	−0.935371	−	0.353668i	$-0.884934\pi$
$457$	−14.5558	−	28.2343i	−0.680892	−	1.32075i	0.254479	−	0.967078i	$-0.418096\pi$
$458$	4.92326	−	14.2248i	0.230049	−	0.664682i
$459$	−4.40855	+	2.54528i	−0.205774	+	0.118804i
$460$	−0.000449233	0	0.000461745i	−2.09456e−5	0	2.15290e-5i
$461$		−	16.7648i		−	0.780814i	−0.920642	−	0.390407i	$-0.872334\pi$
$461$		−	16.7648i		−	0.780814i	0.920642	−	0.390407i	$-0.127666\pi$
$462$	−2.69484	−	5.50089i	−0.125375	−	0.255925i
$463$	7.83270	+	5.03377i	0.364016	+	0.233939i	0.709844	−	0.704359i	$-0.248765\pi$
$463$	7.83270	+	5.03377i	0.364016	+	0.233939i	−0.345828	+	0.938298i	$0.612402\pi$
$464$	−0.264042	−	0.207645i	−0.0122579	−	0.00963968i
$465$	−6.41313e−5	0	6.12380e-6i	−2.97402e−6	0	2.83984e-7i
$466$	−2.69558	+	2.11983i	−0.124870	+	0.0981990i
$467$	−12.9386	+	12.3369i	−0.598727	+	0.570885i	−0.927640	−	0.373475i	$-0.878166\pi$
$467$	−12.9386	+	12.3369i	−0.598727	+	0.570885i	0.328914	+	0.944360i	$0.393318\pi$
$468$	−2.85143	−	4.43691i	−0.131807	−	0.205096i
$469$	4.31236	−	0.739930i	0.199126	−	0.0341668i
$470$	6.19108e−5	0	0.000210849i	2.85573e−6	0	9.72573e-6i
$471$	−17.1897	+	5.94942i	−0.792061	+	0.274135i
$472$	0.184394	−	0.956725i	0.00848740	−	0.0440368i
$473$	−4.26636	−	4.06797i	−0.196168	−	0.187045i
$474$	2.62592	+	0.250745i	0.120613	+	0.0115171i
$475$	−11.1045	+	7.13643i	−0.509510	+	0.327442i
$476$	0.275690	−	13.4655i	0.0126362	−	0.617192i
$477$	−10.9137	+	1.56915i	−0.499704	+	0.0718465i
$478$	4.06274	+	5.70532i	0.185825	+	0.260955i
$479$	35.7872	−	14.3270i	1.63516	−	0.654620i	0.641508	−	0.767116i	$-0.278309\pi$
$479$	35.7872	−	14.3270i	1.63516	−	0.654620i	0.993652	+	0.112497i	$0.0358847\pi$
$480$	0.000134177	0	6.39164e-6i	6.12431e−6	0	2.91737e-7i
$481$	−48.6361	+	9.37384i	−2.21762	+	0.427410i
$482$	−12.3611			−0.563034
$483$	3.20140	+	12.2781i	0.145669	+	0.558672i
$484$	5.63972			0.256351
$485$	−0.00245237		0.000472656i	−0.000111357		2.14622e-5i
$486$	−0.998867	−	0.0475819i	−0.0453095	−	0.00215836i
$487$	25.4951	−	10.2067i	1.15529	−	0.462510i	0.286693	−	0.958022i	$-0.407444\pi$
$487$	25.4951	−	10.2067i	1.15529	−	0.462510i	0.868601	+	0.495512i	$0.165020\pi$
$488$	−3.82041	−	5.36501i	−0.172942	−	0.242863i
$489$	−18.6983	+	2.68841i	−0.845566	+	0.121574i
$490$	0.000912302	0	0.000227764i	4.12136e−5	0	1.02893e-5i
$491$	24.1917	−	15.5471i	1.09176	−	0.701630i	0.134513	−	0.990912i	$-0.457053\pi$
$491$	24.1917	−	15.5471i	1.09176	−	0.701630i	0.957244	+	0.289282i	$0.0934165\pi$
$492$	5.87716	+	0.561201i	0.264963	+	0.0253009i
$493$	1.23756	+	1.18001i	0.0557369	+	0.0531450i
$494$	2.63509	−	13.6721i	0.118558	−	0.615139i
$495$	−0.000293898	0	0.000101719i	−1.32097e−5	0	4.57193e-6i
$496$	−0.135116	−	0.460164i	−0.00606690	−	0.0206620i
$497$	−8.34968	−	3.08264i	−0.374534	−	0.138275i
$498$	−2.82571	−	4.39690i	−0.126623	−	0.197030i
$499$	25.8370	−	24.6356i	1.15663	−	1.10284i	0.163409	−	0.986558i	$-0.447751\pi$
$499$	25.8370	−	24.6356i	1.15663	−	1.10284i	0.993216	−	0.116281i	$-0.0370974\pi$
$500$	−0.00105590		0.000830367i	−4.72212e−5		3.71352e-5i
$501$	−1.84638	+	0.176308i	−0.0824904	+	0.00787688i
$502$	−21.1685	−	16.6471i	−0.944797	−	0.742996i
$503$	−22.8486	−	14.6839i	−1.01877	−	0.654723i	−0.0791202	−	0.996865i	$-0.525211\pi$
$503$	−22.8486	−	14.6839i	−1.01877	−	0.654723i	−0.939648	+	0.342142i	$0.888847\pi$
$504$	1.47566	−	2.19600i	0.0657312	−	0.0978177i
$505$		0	0.000993110i		0	4.41928e-5i
$506$	10.8811	+	2.21099i	0.483723	+	0.0982903i
$507$	−12.8318	+	7.40844i	−0.569880	+	0.329020i
$508$	1.39604	−	4.03359i	0.0619393	−	0.178962i
$509$	−9.99731	−	19.3921i	−0.443123	−	0.859538i	−0.999589	−	0.0286680i	$-0.990873\pi$
$509$	−9.99731	−	19.3921i	−0.443123	−	0.859538i	0.556466	−	0.830870i	$-0.312157\pi$
$510$	−0.000676850	0	9.73164e-5i	−2.99714e−5	0	4.30924e-6i
$511$	28.2464	+	23.1645i	1.24955	+	1.02474i
$512$	0.142315	+	0.989821i	0.00628949	+	0.0437443i
$513$	−1.82180	−	1.91065i	−0.0804345	−	0.0843573i
$514$	5.83235	−	11.3132i	0.257254	−	0.499003i
$515$	4.34151e−5	0	6.09679e-5i	1.91310e−6	0	2.68657e-6i
$516$	0.600279	−	2.47438i	0.0264258	−	0.108929i
$517$	2.48029	−	2.86241i	0.109083	−	0.125888i
$518$	−13.9953	−	20.5305i	−0.614920	−	0.902060i
$519$	−5.76979	+	1.69416i	−0.253266	+	0.0743655i
$520$	6.73448e−5	0	0.000705267i	2.95326e−6	0	3.09280e-5i
$521$	15.6484	+	8.06731i	0.685569	+	0.353435i	0.765564	−	0.643360i	$-0.222460\pi$
$521$	15.6484	+	8.06731i	0.685569	+	0.353435i	−0.0799951	+	0.996795i	$0.525490\pi$
$522$	0.0791935	+	0.326440i	0.00346621	+	0.0142879i
$523$	26.4613	+	10.5935i	1.15707	+	0.463221i	0.869206	−	0.494450i	$-0.164630\pi$
$523$	26.4613	+	10.5935i	1.15707	+	0.463221i	0.287865	+	0.957671i	$0.407055\pi$
$524$	10.1707	+	4.64479i	0.444308	+	0.202909i
$525$	1.61422	+	13.1299i	0.0704505	+	0.573036i
$526$	−4.94066	+	7.68782i	−0.215423	+	0.335205i
$527$	0.462035	+	2.39727i	0.0201266	+	0.104427i
$528$	−1.15761	−	2.00505i	−0.0503787	−	0.0872584i
$529$	−21.1760	−	8.97636i	−0.920698	−	0.390277i
$530$	−0.00128267		0.000740551i	−5.57157e−5		3.21675e-5i
$531$	−0.736351	+	0.638052i	−0.0319549	+	0.0276891i
$532$	6.82015	−	1.50743i	0.295691	−	0.0653554i
$533$	4.43142	−	30.8212i	0.191946	−	1.33501i
$534$	6.06323	−	4.31761i	0.262382	−	0.186841i
$535$	0.000739605	0	0.000940484i	3.19759e−5	0	4.06607e-5i
$536$	1.60712	−	0.389884i	0.0694172	−	0.0168404i
$537$	21.9320	−	1.04475i	0.946435	−	0.0450843i
$538$	3.73449	−	1.70548i	0.161005	−	0.0735287i
$539$	−11.8035	−	11.1055i	−0.508411	−	0.478347i
$540$	−0.000101519	0	8.79669e-5i	−4.36869e−6	0	3.78549e-6i
$541$	−5.58841	−	16.1467i	−0.240265	−	0.694199i	−0.999080	−	0.0428928i	$-0.986343\pi$
$541$	−5.58841	−	16.1467i	−0.240265	−	0.694199i	0.758815	−	0.651306i	$-0.225779\pi$
$542$	−15.5743	+	16.3338i	−0.668972	+	0.701598i
$543$	6.27074	+	4.46537i	0.269103	+	0.191628i
$544$	−0.242219	−	5.08479i	−0.0103850	−	0.218009i
$545$	−0.000299872		0.00102127i	−1.28451e−5		4.37465e-5i
$546$	−11.1986	−	8.32517i	−0.479258	−	0.356284i
$547$	15.3597	−	33.6332i	0.656735	−	1.43805i	−0.228798	−	0.973474i	$-0.573479\pi$
$547$	15.3597	−	33.6332i	0.656735	−	1.43805i	0.885533	−	0.464576i	$-0.153793\pi$
$548$	2.64387	−	3.36196i	0.112941	−	0.143616i
$549$	−0.313387	+	6.57880i	−0.0133750	+	0.280776i
$550$	10.9395	+	3.78618i	0.466460	+	0.161443i
$551$	−0.443398	+	0.767988i	−0.0188894	+	0.0327174i
$552$	1.52286	+	4.54762i	0.0648173	+	0.193560i
$553$	6.73528	−	1.82877i	0.286413	−	0.0777670i
$554$	−2.23289	−	2.57689i	−0.0948665	−	0.109482i
$555$	−0.00112129		0.000578063i	−4.75959e−5		2.45374e-5i
$556$	0.835053	+	2.08586i	0.0354141	+	0.0884602i
$557$	−2.56031	−	26.8128i	−0.108484	−	1.13610i	−0.871730	−	0.489987i	$-0.837001\pi$
$557$	−2.56031	−	26.8128i	−0.108484	−	1.13610i	0.763246	−	0.646108i	$-0.223605\pi$
$558$	−0.178246	+	0.445237i	−0.00754575	+	0.0188484i
$559$	−12.8849	−	3.78335i	−0.544973	−	0.160019i
$560$	0.000338164	0	0.000109341i	1.42900e−5	0	4.62051e-6i
$561$	4.89600	+	10.7207i	0.206709	+	0.452630i
$562$	4.54966	+	1.10374i	0.191916	+	0.0465583i
$563$	16.7689	+	3.23194i	0.706725	+	0.136210i	0.529935	−	0.848038i	$-0.322216\pi$
$563$	16.7689	+	3.23194i	0.706725	+	0.136210i	0.176790	+	0.984249i	$0.443429\pi$
$564$	1.60635	+	0.309598i	0.0676394	+	0.0130364i
$565$	−0.00180003		0.000436682i	−7.57278e−5		1.83714e-5i
$566$	−3.23199	−	7.07707i	−0.135851	−	0.297471i
$567$	−2.51743	+	0.813981i	−0.105722	+	0.0341840i
$568$	−3.22782	−	0.947774i	−0.135436	−	0.0397677i
$569$	6.80876	−	17.0075i	0.285438	−	0.712990i	−0.714473	−	0.699663i	$-0.753333\pi$
$569$	6.80876	−	17.0075i	0.285438	−	0.712990i	0.999911	−	0.0133272i	$-0.00424230\pi$
$570$	−3.37095e−5	0	0.000353022i	−1.41194e−6	0	1.47865e-5i
$571$	14.6909	+	36.6960i	0.614793	+	1.53568i	0.829210	+	0.558937i	$0.188791\pi$
$571$	14.6909	+	36.6960i	0.614793	+	1.53568i	−0.214417	+	0.976742i	$0.568785\pi$
$572$	−10.8535	+	5.59536i	−0.453807	+	0.233954i
$573$	−8.39658	−	9.69017i	−0.350772	−	0.404813i
$574$	15.0744	−	4.09302i	0.629195	−	0.170839i
$575$	−20.6448	−	12.1980i	−0.860948	−	0.508692i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−4.80301	−	1.66234i	−0.199952	−	0.0692040i	0.225256	−	0.974300i	$-0.427678\pi$
$577$	−4.80301	−	1.66234i	−0.199952	−	0.0692040i	−0.425208	+	0.905095i	$0.639799\pi$
$578$	−0.424136	+	8.90371i	−0.0176417	+	0.370346i
$579$	−14.5797	+	18.5396i	−0.605912	+	0.770480i
$580$	−1.87445e−5	0	4.10447e-5i	−7.78323e−7	0	1.70429e-6i
$581$	−11.0976	−	8.25008i	−0.460408	−	0.342271i
$582$	−5.23810	+	17.8393i	−0.217126	+	0.739464i
$583$	1.21465	+	25.4986i	0.0503056	+	1.05604i
$584$	11.2469	+	8.00890i	0.465401	+	0.331410i
$585$	−0.000488903	0	0.000512747i	−2.02137e−5	0	2.11995e-5i
$586$	6.83347	+	19.7440i	0.282288	+	0.815617i
$587$	21.1122	+	18.2938i	0.871393	+	0.755066i	0.970777	−	0.239983i	$-0.0771419\pi$
$587$	21.1122	+	18.2938i	0.871393	+	0.755066i	−0.0993845	+	0.995049i	$0.531687\pi$
$588$	1.60498	−	6.81352i	0.0661884	−	0.280985i
$589$	−1.15170	+	0.525963i	−0.0474549	+	0.0216719i
$590$	−0.000130733	0	6.22758e-6i	−5.38219e−6	0	2.56385e-7i
$591$	19.2041	−	4.65887i	0.789952	−	0.191640i
$592$	−5.80530	−	7.38204i	−0.238596	−	0.303400i
$593$	−11.7665	+	8.37887i	−0.483192	+	0.344079i	−0.795553	−	0.605884i	$-0.792819\pi$
$593$	−11.7665	+	8.37887i	−0.483192	+	0.344079i	0.312361	+	0.949963i	$0.398880\pi$
$594$	−0.329491	+	2.29166i	−0.0135192	+	0.0940281i
$595$	−0.00176656		0.000390455i	−7.24218e−5		1.60071e-5i
$596$	−9.53781	+	8.26456i	−0.390684	+	0.338530i
$597$	10.8831	+	6.28337i	0.445417	+	0.257161i
$598$	24.3400	−	6.88149i	0.995335	−	0.281405i
$599$	−2.83151	−	4.90433i	−0.115693	−	0.200385i	0.802364	−	0.596835i	$-0.203575\pi$
$599$	−2.83151	−	4.90433i	−0.115693	−	0.200385i	−0.918056	+	0.396450i	$0.870242\pi$
$600$	0.946256	+	4.90964i	0.0386307	+	0.200435i
$601$	−6.99833	+	10.8896i	−0.285468	+	0.444197i	−0.954140	−	0.299361i	$-0.903227\pi$
$601$	−6.99833	+	10.8896i	−0.285468	+	0.444197i	0.668672	+	0.743557i	$0.266863\pi$
$602$	−0.822013	−	6.68615i	−0.0335028	−	0.272507i
$603$	−1.50429	−	0.686988i	−0.0612596	−	0.0279763i
$604$	3.72947	+	1.49305i	0.151750	+	0.0607514i
$605$	−0.000178606	0	0.000736223i	−7.26136e−6	0	2.99317e-5i
$606$	6.57126	+	3.38772i	0.266939	+	0.137617i
$607$	−0.233536	+	2.44570i	−0.00947892	+	0.0992678i	−0.998973	−	0.0453039i	$-0.985574\pi$
$607$	−0.233536	+	2.44570i	−0.00947892	+	0.0992678i	0.989494	+	0.144572i	$0.0461804\pi$
$608$	2.53305	−	0.743771i	0.102729	−	0.0301639i
$609$	0.500588	+	0.734340i	0.0202849	+	0.0297569i
$610$	−0.000579373	0	0.000668632i	−2.34581e−5	0	2.70721e-5i
$611$	2.03414	−	8.38486i	0.0822927	−	0.339215i
$612$	−2.95281	+	4.14665i	−0.119360	+	0.167618i
$613$	−7.70322	+	14.9422i	−0.311130	+	0.603509i	−0.991611	−	0.129257i	$-0.958741\pi$
$613$	−7.70322	+	14.9422i	−0.311130	+	0.603509i	0.680481	+	0.732766i	$0.261771\pi$
$614$	−22.3735	−	23.4647i	−0.902923	−	0.946958i
$615$	−0.000112865	0	0.000784993i	−4.55115e−6	0	3.16540e-5i
$616$	−4.73647	−	3.88431i	−0.190838	−	0.156503i
$617$	−32.3583	−	4.65242i	−1.30270	−	0.187299i	−0.544188	−	0.838963i	$-0.683162\pi$
$617$	−32.3583	−	4.65242i	−1.30270	−	0.187299i	−0.758508	+	0.651664i	$0.774071\pi$
$618$	−0.255317	−	0.495246i	−0.0102704	−	0.0199217i
$619$	−5.90189	+	17.0524i	−0.237217	+	0.685393i	0.762065	+	0.647501i	$0.224186\pi$
$619$	−5.90189	+	17.0524i	−0.237217	+	0.685393i	−0.999282	+	0.0378927i	$0.987936\pi$
$620$	−5.57920e−5	0	3.22115e-5i	−2.24066e−6	0	1.29364e-6i
$621$	1.61410	−	4.51605i	0.0647718	−	0.181223i
$622$		−	14.5206i		−	0.582225i
$623$	10.9840	−	16.3458i	0.440063	−	0.654879i
$624$	−4.43691	−	2.85143i	−0.177619	−	0.114149i
$625$	−19.6513	−	15.4540i	−0.786053	−	0.618159i
$626$	−15.2543	+	1.45661i	−0.609683	+	0.0582177i
$627$	−4.80450	+	3.77830i	−0.191873	+	0.150891i
$628$	−13.1649	+	12.5527i	−0.525335	+	0.500906i
$629$	25.8463	+	40.2177i	1.03056	+	1.60358i
$630$	−0.000333405	0	0.000123091i	−1.32832e−5	0	4.90406e-6i
$631$	−6.67316	−	22.7267i	−0.265654	−	0.904736i	−0.978989	−	0.203912i	$-0.934634\pi$
$631$	−6.67316	−	22.7267i	−0.265654	−	0.904736i	0.713335	−	0.700824i	$-0.247184\pi$
$632$	2.49279	−	0.862762i	0.0991577	−	0.0343188i
$633$	−2.25787	+	11.7149i	−0.0897421	+	0.465626i
$634$	13.9793	+	13.3292i	0.555187	+	0.529370i
$635$	−0.000570767	0	5.45017e-5i	−2.26502e−5	0	2.16283e-6i
$636$	−9.27560	+	5.96106i	−0.367801	+	0.236372i
$637$	−35.4922	−	10.1653i	−1.40625	−	0.402762i
$638$	0.769790	−	0.110679i	0.0304763	−	0.00438183i
$639$	1.95136	+	2.74031i	0.0771948	+	0.108405i
$640$	0.000124707	0	4.99251e-5i	4.92947e−6	0	1.97346e-6i
$641$	2.66089	+	0.126754i	0.105099	+	0.00500647i	0.100065	−	0.994981i	$-0.468095\pi$
$641$	2.66089	+	0.126754i	0.105099	+	0.00500647i	0.00503340	+	0.999987i	$0.498398\pi$
$642$	8.74600	−	1.68565i	0.345177	−	0.0665274i
$643$	−21.4780			−0.847011			−0.423505	−	0.905894i	$-0.639201\pi$
$643$	−21.4780			−0.847011			−0.423505	+	0.905894i	$0.639201\pi$
$644$	8.01259	+	9.83862i	0.315740	+	0.387696i
$645$	−0.000342023	0		−1.34671e−5	0
$646$	−13.1962	+	2.54335i	−0.519196	+	0.100067i
$647$	−12.7456	−	0.607149i	−0.501082	−	0.0238695i	−0.204480	−	0.978871i	$-0.565550\pi$
$647$	−12.7456	−	0.607149i	−0.501082	−	0.0238695i	−0.296602	+	0.955001i	$0.595853\pi$
$648$	−0.928368	+	0.371662i	−0.0364697	+	0.0146003i
$649$	1.30849	+	1.83752i	0.0513629	+	0.0721290i
$650$	26.1024	−	3.75296i	1.02382	−	0.147203i
$651$	−0.0259732	+	1.26861i	−0.00101797	+	0.0497208i
$652$	−15.8918	+	10.2130i	−0.622369	+	0.399973i
$653$	−23.8450	−	2.27692i	−0.933126	−	0.0891028i	−0.382594	−	0.923917i	$-0.624969\pi$
$653$	−23.8450	−	2.27692i	−0.933126	−	0.0891028i	−0.550532	+	0.834814i	$0.685575\pi$
$654$	5.73467	+	5.46799i	0.224243	+	0.213815i
$655$	0.000284245	−	0.00147480i	1.11064e−5	−	5.76253e-5i
$656$	5.57919	−	1.93097i	0.217831	−	0.0753919i
$657$	−3.88991	−	13.2478i	−0.151760	−	0.516846i
$658$	4.26587	−	0.731953i	0.166301	−	0.0285345i
$659$	−15.6655	−	24.3761i	−0.610243	−	0.949556i	−0.999595	−	0.0284673i	$-0.990937\pi$
$659$	−15.6655	−	24.3761i	−0.610243	−	0.949556i	0.389352	−	0.921089i	$-0.372699\pi$
$660$	−0.000225083	0	0.000214616i	−8.76135e−6	0	8.35393e-6i
$661$	22.2635	−	17.5082i	0.865949	−	0.680990i	−0.0829553	−	0.996553i	$-0.526436\pi$
$661$	22.2635	−	17.5082i	0.865949	−	0.680990i	0.948905	+	0.315563i	$0.102193\pi$
$662$	22.4825	−	2.14681i	0.873805	−	0.0834383i
$663$	21.1043	+	16.5966i	0.819624	+	0.644560i
$664$	−4.39690	−	2.82571i	−0.170633	−	0.109659i
$665$	−0.000412773	0	0.000842581i	−1.60067e−5	0	3.26739e-5i
$666$			9.39128i			0.363905i
$667$	−1.60828	−	0.0928469i	−0.0622730	−	0.00359505i
$668$	−1.60629	+	0.927391i	−0.0621492	+	0.0358819i
$669$	8.19436	−	23.6760i	0.316812	−	0.915369i
$670$	−0.000101793	0	0.000197451i	−3.93260e−6	0	7.62818e-6i
$671$	15.0935	+	2.17012i	0.582678	+	0.0837764i
$672$	0.430057	−	2.61057i	0.0165898	−	0.100705i
$673$	5.74720	+	39.9727i	0.221538	+	1.54083i	0.732223	+	0.681065i	$0.238483\pi$
$673$	5.74720	+	39.9727i	0.221538	+	1.54083i	−0.510684	+	0.859768i	$0.670608\pi$
$674$	−18.9775	−	19.9031i	−0.730987	−	0.766637i
$675$	2.29113	−	4.44418i	0.0881857	−	0.171056i
$676$	−8.59463	+	12.0695i	−0.330563	+	0.464210i
$677$	9.65796	−	39.8107i	0.371186	−	1.53005i	−0.413703	−	0.910412i	$-0.635765\pi$
$677$	9.65796	−	39.8107i	0.371186	−	1.53005i	0.784889	−	0.619637i	$-0.212720\pi$
$678$	−9.02976	+	10.4209i	−0.346786	+	0.400212i
$679$	3.67257	+	49.0537i	0.140940	+	1.88251i
$680$	−0.000656111	0	0.000192652i	−2.51607e−5	0	7.38785e-6i
$681$	−2.23397	+	23.3952i	−0.0856058	+	0.896504i
$682$	0.986929	+	0.508797i	0.0377915	+	0.0194829i
$683$	−11.5281	−	47.5196i	−0.441111	−	1.81829i	−0.563888	−	0.825851i	$-0.690695\pi$
$683$	−11.5281	−	47.5196i	−0.441111	−	1.81829i	0.122777	−	0.992434i	$-0.460820\pi$
$684$	−2.45088	−	0.981185i	−0.0937118	−	0.0375166i
$685$	−0.000522608	0	0.000238667i	−1.99678e−5	0	9.11900e-6i
$686$	−2.38225	−	18.3664i	−0.0909548	−	0.701233i
$687$	−8.13811	+	12.6631i	−0.310488	+	0.483129i
$688$	−0.481863	−	2.50014i	−0.0183709	−	0.0953171i
$689$	29.0763	+	50.3616i	1.10772	+	1.91862i
$690$	0.000545431	0	0.000342818i	2.07642e−5	0	1.30509e-5i
$691$	11.1272	+	6.42431i	0.423300	+	0.244392i	0.696488	−	0.717568i	$-0.254745\pi$
$691$	11.1272	+	6.42431i	0.423300	+	0.244392i	−0.273188	+	0.961961i	$0.588078\pi$
$692$	−4.54461	+	3.93792i	−0.172760	+	0.149697i
$693$	1.32199	+	5.98116i	0.0502183	+	0.227206i
$694$	1.25338	−	8.71748i	0.0475778	−	0.330911i
$695$	0.000245848	0	0.000175068i	9.32555e−6	0	6.64069e-6i
$696$	0.207645	+	0.264042i	0.00787077	+	0.0100085i
$697$	−29.2070	+	7.08553i	−1.10629	+	0.268384i
$698$	24.9523	−	1.18862i	0.944459	−	0.0449901i
$699$	3.11936	−	1.42456i	0.117985	−	0.0538820i
$700$	6.92271	+	11.2728i	0.261654	+	0.426072i
$701$	30.1968	+	26.1656i	1.14052	+	0.988262i	0.999998	−	0.00181584i	$-0.000578002\pi$
$701$	30.1968	+	26.1656i	1.14052	+	0.988262i	0.140517	+	0.990078i	$0.455123\pi$
$702$	1.72501	+	4.98410i	0.0651064	+	0.188113i
$703$	−17.1090	+	17.9434i	−0.645280	+	0.676750i
$704$	−1.88593	−	1.34296i	−0.0710786	−	0.0506149i
$705$	−1.04561e−5	0	0.000219501i	−3.93801e−7	0	8.26690e-6i
$706$	−6.39461	+	21.7780i	−0.240664	+	0.819627i
$707$	19.4296	+	2.25751i	0.730726	+	0.0849025i
$708$	−0.404752	+	0.886284i	−0.0152115	+	0.0333086i
$709$	8.56303	−	10.8888i	0.321591	−	0.408937i	−0.598199	−	0.801348i	$-0.704117\pi$
$709$	8.56303	−	10.8888i	0.321591	−	0.408937i	0.919790	+	0.392411i	$0.128359\pi$
$710$	−2.15021e−5	0	0.000451384i	−8.06958e−7	0	1.69401e-5i
$711$	−2.49279	−	0.862762i	−0.0934868	−	0.0323561i
$712$	3.72171	−	6.44619i	0.139477	−	0.241581i
$713$	−1.79355	−	1.43992i	−0.0671689	−	0.0539253i
$714$	−3.44254	+	13.0210i	−0.128834	+	0.487297i
$715$	0.00107416	+	0.00123964i	4.01711e−5	+	4.63600e-5i
$716$	19.5160	−	10.0612i	0.729349	−	0.376005i
$717$	−2.60314	−	6.50232i	−0.0972159	−	0.242834i
$718$	−1.43267	−	15.0036i	−0.0534668	−	0.559930i
$719$	−7.60199	+	18.9889i	−0.283507	+	0.708165i	0.716438	+	0.697651i	$0.245771\pi$
$719$	−7.60199	+	18.9889i	−0.283507	+	0.708165i	−0.999945	+	0.0105145i	$0.996653\pi$
$720$	−0.000128888	0	3.78449e-5i	−4.80337e−6	0	1.41040e-6i
$721$	−1.09411	−	0.987982i	−0.0407469	−	0.0367944i
$722$	4.99763	+	10.9433i	0.185993	+	0.407267i
$723$	12.0127	+	2.91425i	0.446757	+	0.108382i
$724$	7.55905	+	1.45689i	0.280930	+	0.0541448i
$725$	−1.64919	−	0.317856i	−0.0612495	−	0.0118049i
$726$	−5.48074	−	1.32961i	−0.203409	−	0.0493466i
$727$	2.46500	+	5.39759i	0.0914217	+	0.200186i	0.949819	−	0.312800i	$-0.101267\pi$
$727$	2.46500	+	5.39759i	0.0914217	+	0.200186i	−0.858397	+	0.512985i	$0.828540\pi$
$728$	−13.6450	−	2.92076i	−0.505719	−	0.108250i
$729$	0.959493	+	0.281733i	0.0355368	+	0.0104345i
$730$	0.000689320	−	0.00172184i	2.55129e−5	−	6.37281e-5i
$731$	1.23206	+	12.9027i	0.0455692	+	0.477222i
$732$	2.44787	+	6.11447i	0.0904757	+	0.225997i
$733$	17.8938	−	9.22491i	0.660924	−	0.340730i	−0.0949172	−	0.995485i	$-0.530259\pi$
$733$	17.8938	−	9.22491i	0.660924	−	0.340730i	0.755841	+	0.654755i	$0.227228\pi$
$734$	3.48584	+	4.02287i	0.128665	+	0.148487i
$735$	−0.000940283	0	6.26062e-6i	−3.46829e−5	0	2.30926e-7i
$736$	3.27440	+	3.50405i	0.120696	+	0.129161i
$737$	−1.91439	+	3.31582i	−0.0705175	+	0.122140i
$738$	−5.57919	−	1.93097i	−0.205373	−	0.0710802i
$739$	0.378001	−	7.93521i	0.0139050	−	0.291901i	−0.981194	−	0.193022i	$-0.938171\pi$
$739$	0.378001	−	7.93521i	0.0139050	−	0.291901i	0.995099	−	0.0988795i	$-0.0315258\pi$
$740$	−0.000779821	0	0.000991623i	−2.86668e−5	0	3.64528e-5i
$741$	−5.78414	+	12.6655i	−0.212486	+	0.465279i
$742$	−17.4042	+	23.4113i	−0.638928	+	0.859457i
$743$	−0.840378	+	2.86206i	−0.0308305	+	0.104999i	−0.973471	−	0.228811i	$-0.926516\pi$
$743$	−0.840378	+	2.86206i	−0.0308305	+	0.104999i	0.942640	+	0.333810i	$0.108334\pi$
$744$	0.0228198	+	0.479048i	0.000836616	+	0.0175627i
$745$	0.00138093		0.000983358i	5.05935e−5		3.60274e-5i
$746$	−15.6883	+	16.4535i	−0.574391	+	0.602404i
$747$	1.70945	+	4.93914i	0.0625456	+	0.180714i
$748$	8.90712	+	7.71806i	0.325677	+	0.282200i
$749$	20.0813	−	12.3321i	0.733754	−	0.450604i
$750$	0.00122190		0.000558023i	4.46175e−5		2.03761e-5i
$751$	20.2379	−	0.964052i	0.738493	−	0.0351788i	0.325035	−	0.945702i	$-0.394624\pi$
$751$	20.2379	−	0.964052i	0.738493	−	0.0351788i	0.413458	+	0.910523i	$0.364321\pi$
$752$	1.58980	−	0.385680i	0.0579739	−	0.0140643i
$753$	16.6471	+	21.1685i	0.606654	+	0.771423i
$754$	1.44314	−	1.02765i	0.0525559	−	0.0374249i
$755$	7.67974e−5	0	0.000534138i	2.79494e−6	0	1.94393e-5i
$756$	−1.95179	+	1.78620i	−0.0709860	+	0.0649635i
$757$	−1.50636	+	1.30527i	−0.0547498	+	0.0474409i	−0.681806	−	0.731533i	$-0.738805\pi$
$757$	−1.50636	+	1.30527i	−0.0547498	+	0.0474409i	0.627056	+	0.778974i	$0.284260\pi$
$758$	−8.11192	−	4.68342i	−0.294638	−	0.170109i
$759$	−10.0531	−	4.71397i	−0.364905	−	0.171106i
$760$	−0.000177314	0	0.000307116i	−6.43185e−6	0	1.11403e-5i
$761$	−8.66568	−	44.9618i	−0.314131	−	1.62986i	−0.704851	−	0.709355i	$-0.748986\pi$
$761$	−8.66568	−	44.9618i	−0.314131	−	1.62986i	0.390720	−	0.920509i	$-0.372226\pi$
$762$	−2.30764	+	3.59076i	−0.0835971	+	0.130080i
$763$	19.2989	+	8.18836i	0.698668	+	0.296438i
$764$	−11.6632	−	5.32642i	−0.421961	−	0.192703i
$765$	0.000634828	0	0.000254147i	2.29522e−5	0	9.18869e-6i
$766$	−5.13304	−	21.1587i	−0.185464	−	0.764494i
$767$	4.56754	+	2.35473i	0.164924	+	0.0850245i
$768$	0.0950560	−	0.995472i	0.00343004	−	0.0359210i
$769$	25.0851	−	7.36564i	0.904591	−	0.265612i	0.203829	−	0.979007i	$-0.434661\pi$
$769$	25.0851	−	7.36564i	0.904591	−	0.265612i	0.700762	+	0.713395i	$0.252843\pi$
$770$	−0.000357067	0	0.000741324i	−1.28678e−5	0	2.67155e-5i
$771$	−8.33513	+	9.61925i	−0.300182	+	0.346429i
$772$	−5.56054	+	22.9209i	−0.200128	+	0.824940i
$773$	−21.9819	+	30.8693i	−0.790635	+	1.11029i	0.200792	+	0.979634i	$0.435648\pi$
$773$	−21.9819	+	30.8693i	−0.790635	+	1.11029i	−0.991428	+	0.130658i	$0.958291\pi$
$774$	−1.16672	+	2.26311i	−0.0419367	+	0.0813459i
$775$	−1.65478	−	1.73548i	−0.0594414	−	0.0623403i
$776$	2.64598	+	18.4032i	0.0949852	+	0.660637i
$777$	8.76058	+	23.2513i	0.314284	+	0.834137i
$778$	29.0417	+	4.17557i	1.04120	+	0.149702i
$779$	−7.14202	−	13.8536i	−0.255889	−	0.496356i
$780$	−0.000231719	0	0.000669509i	−8.29688e−6	0	2.39723e-5i
$781$	6.74516	−	3.89432i	0.241361	−	0.139350i
$782$	−14.8975	−	19.3412i	−0.532732	−	0.691641i
$783$		−	0.335909i		−	0.0120044i
$784$	−1.37049	−	6.86453i	−0.0489462	−	0.245162i
$785$	0.00205558	+	0.00132104i	7.33667e−5	+	4.71499e-5i
$786$	−8.78893	−	6.91169i	−0.313491	−	0.246532i
$787$	−42.9418	+	4.10045i	−1.53071	+	0.146165i	−0.826139	−	0.563467i	$-0.809467\pi$
$787$	−42.9418	+	4.10045i	−1.53071	+	0.146165i	−0.704572	+	0.709632i	$0.748861\pi$
$788$	15.5333	−	12.2155i	0.553351	−	0.435160i
$789$	6.61387	−	6.30631i	0.235460	−	0.224511i
$790$	−0.000191572	0	0.000298092i	−6.81582e−6	0	1.06056e-5i
$791$	−12.6352	+	34.2239i	−0.449257	+	1.21686i
$792$	0.652275	+	2.22145i	0.0231776	+	0.0789356i
$793$	32.8266	−	11.3614i	1.16571	−	0.403455i
$794$	−2.57776	+	13.3747i	−0.0914814	+	0.474651i
$795$	0.00107192	+	0.00102208i	3.80172e−5	+	3.62494e-5i
$796$	12.5098	+	1.19455i	0.443400	+	0.0423395i
$797$	−30.3850	+	19.5272i	−1.07629	+	0.691690i	−0.953698	−	0.300767i	$-0.902757\pi$
$797$	−30.3850	+	19.5272i	−1.07629	+	0.691690i	−0.122593	+	0.992457i	$0.539121\pi$
$798$	−6.98329	−	0.142974i	−0.247206	−	0.00506123i
$799$	−8.24294	+	1.18516i	−0.291614	+	0.0419278i
$800$	2.90028	+	4.07288i	0.102541	+	0.143998i
$801$	−6.91023	+	2.76644i	−0.244161	+	0.0977474i
$802$	−7.15131	−	0.340659i	−0.252521	−	0.0120291i
$803$	−31.3889	+	6.04971i	−1.10769	+	0.213490i
$804$	−1.65374			−0.0583229
$805$	0.00103061	−	0.00135757i	3.63241e−5	−	4.78479e-5i
$806$	2.52944			0.0890958
$807$	−4.03130	+	0.776970i	−0.141909	+	0.0273507i
$808$	7.38474	+	0.351778i	0.259794	+	0.0123755i
$809$	25.5423	−	10.2256i	0.898021	−	0.359513i	0.123710	−	0.992318i	$-0.460521\pi$
$809$	25.5423	−	10.2256i	0.898021	−	0.359513i	0.774311	+	0.632805i	$0.218097\pi$
$810$	7.79185e−5	0	0.000109421i	2.73778e−6	0	3.84467e-6i
$811$	−47.5021	+	6.82978i	−1.66803	+	0.239826i	−0.910657	−	0.413162i	$-0.864424\pi$
$811$	−47.5021	+	6.82978i	−1.66803	+	0.239826i	−0.757368	+	0.652988i	$0.773515\pi$
$812$	0.760407	+	0.460027i	0.0266850	+	0.0161438i
$813$	18.9861	−	12.2016i	0.665872	−	0.427930i
$814$	21.6445	+	2.06680i	0.758639	+	0.0724413i
$815$	0.00183651	+	0.00175111i	6.43303e−5	+	6.13388e-5i
$816$	−0.963395	+	4.99857i	−0.0337256	+	0.174985i
$817$	−6.35213	+	2.19849i	−0.222233	+	0.0769156i
$818$	−0.390305	−	1.32926i	−0.0136467	−	0.0464763i
$819$	8.92024	+	10.7307i	0.311698	+	0.374960i
$820$	−0.000428763	0	0.000667169i	−1.49731e−5	0	2.32985e-5i
$821$	−3.15492	+	3.00821i	−0.110107	+	0.104987i	−0.743133	−	0.669143i	$-0.766661\pi$
$821$	−3.15492	+	3.00821i	−0.110107	+	0.104987i	0.633026	+	0.774131i	$0.281813\pi$
$822$	−3.36196	+	2.64387i	−0.117262	+	0.0922157i
$823$	13.5925	−	1.29793i	0.473805	−	0.0452429i	0.144577	−	0.989494i	$-0.453818\pi$
$823$	13.5925	−	1.29793i	0.473805	−	0.0452429i	0.329227	+	0.944251i	$0.393212\pi$
$824$	−0.437977	−	0.344429i	−0.0152577	−	0.0119988i
$825$	−9.73847	−	6.25853i	−0.339050	−	0.217894i
$826$	−0.175340	+	2.57187i	−0.00610086	+	0.0894868i
$827$			15.0984i			0.525024i	0.964929	+	0.262512i	$0.0845509\pi$
$827$			15.0984i			0.525024i	−0.964929	+	0.262512i	$0.915449\pi$
$828$	−0.407792	−	4.77846i	−0.0141717	−	0.166063i
$829$	−39.0839	+	22.5651i	−1.35744	+	0.783718i	−0.989278	−	0.146044i	$-0.953346\pi$
$829$	−39.0839	+	22.5651i	−1.35744	+	0.783718i	−0.368161	+	0.929762i	$0.620012\pi$
$830$	−0.000229629	0	0.000663471i	−7.97055e−6	0	2.30294e-5i
$831$	1.56242	+	3.03068i	0.0541999	+	0.105133i
$832$	−5.22049	−	0.750593i	−0.180988	−	0.0260221i
$833$	3.62332	+	35.4492i	0.125541	+	1.22824i
$834$	−0.319754	−	2.22394i	−0.0110722	−	0.0770086i
$835$	0.000171934	0	0.000180319i	5.95002e−6	0	6.24021e-6i
$836$	−2.80076	+	5.43272i	−0.0968664	+	0.187895i
$837$	0.278190	−	0.390663i	0.00961565	−	0.0135033i
$838$	0.0262780	−	0.108319i	0.000907759	−	0.00374183i
$839$	16.0244	−	18.4931i	0.553223	−	0.638454i	−0.408408	−	0.912800i	$-0.633916\pi$
$839$	16.0244	−	18.4931i	0.553223	−	0.638454i	0.961631	+	0.274346i	$0.0884613\pi$
$840$	−0.000354409	0	2.65340e-5i	−1.22283e−5	0	9.15511e-7i
$841$	27.7170	−	8.13845i	0.955760	−	0.280636i
$842$	−1.15598	+	12.1060i	−0.0398377	+	0.417199i
$843$	−4.16120	−	2.14525i	−0.143319	−	0.0738862i
$844$	2.81273	+	11.5942i	0.0968180	+	0.399089i
$845$	0.00184777		0.000739734i	6.35651e−5		2.54476e-5i
$846$	−1.48808	−	0.679582i	−0.0511611	−	0.0233645i
$847$	−14.8098	+	1.82075i	−0.508870	+	0.0625619i
$848$	−5.96106	+	9.27560i	−0.204704	+	0.318525i
$849$	1.47240	+	7.63955i	0.0505327	+	0.262189i
$850$	−12.7264	−	22.0428i	−0.436512	−	0.756061i
$851$	−43.0847	−	13.1233i	−1.47692	−	0.449861i
$852$	2.91339	+	1.68205i	0.0998111	+	0.0576259i
$853$	5.15630	−	4.46796i	0.176548	−	0.152980i	−0.562104	−	0.827067i	$-0.690008\pi$
$853$	5.15630	−	4.46796i	0.176548	−	0.152980i	0.738652	+	0.674086i	$0.235462\pi$
$854$	11.7644	+	12.8550i	0.402569	+	0.439889i
$855$	−5.04688e−5	0	0.000351018i	−1.72600e−6	0	1.20046e-5i
$856$	7.25540	−	5.16654i	0.247984	−	0.176589i
$857$	−24.7796	−	31.5098i	−0.846455	−	1.07636i	−0.996154	−	0.0876236i	$-0.972073\pi$
$857$	−24.7796	−	31.5098i	−0.846455	−	1.07636i	0.149698	−	0.988732i	$-0.452170\pi$
$858$	11.8667	−	2.87883i	0.405123	−	0.0982817i
$859$	31.7616	−	1.51299i	1.08369	−	0.0516226i	0.501873	−	0.864941i	$-0.332645\pi$
$859$	31.7616	−	1.51299i	1.08369	−	0.0516226i	0.581818	+	0.813319i	$0.302342\pi$
$860$	−0.000311115	0	0.000142081i	−1.06089e−5	0	4.84494e-6i
$861$	−15.6145	+	0.423710i	−0.532140	+	0.0144400i
$862$	22.3213	+	19.3415i	0.760267	+	0.658775i
$863$	18.5596	+	53.6246i	0.631777	+	1.82540i	0.560847	+	0.827920i	$0.310476\pi$
$863$	18.5596	+	53.6246i	0.631777	+	1.82540i	0.0709309	+	0.997481i	$0.477403\pi$
$864$	−0.690079	+	0.723734i	−0.0234770	+	0.0246219i
$865$	0.000657991	0	0.000468553i	2.23724e−5	0	1.59313e-5i
$866$	0.404048	+	8.48201i	0.0137301	+	0.288230i
$867$	2.51131	−	8.55273i	0.0852885	−	0.290466i
$868$	0.503374	+	1.16476i	0.0170856	+	0.0395345i
$869$	−2.53705	+	5.55536i	−0.0860635	+	0.188453i
$870$	2.78928e−5	0	3.54685e-5i	9.45654e−7	0	1.20250e-6i
$871$	−0.415014	+	8.71223i	−0.0140622	+	0.295202i
$872$	7.48792	+	2.59160i	0.253573	+	0.0877625i
$873$	9.29623	−	16.1015i	0.314630	−	0.544954i
$874$	7.92626	−	9.87289i	0.268110	−	0.333955i
$875$	0.00250469	−	0.00252142i	8.46739e−5	−	8.52395e-5i
$876$	−9.04172	−	10.4347i	−0.305491	−	0.352556i
$877$	31.4713	−	16.2246i	1.06271	−	0.547866i	0.164024	−	0.986456i	$-0.447552\pi$
$877$	31.4713	−	16.2246i	1.06271	−	0.547866i	0.898687	+	0.438590i	$0.144522\pi$
$878$	−6.30753	−	15.7554i	−0.212869	−	0.531720i
$879$	−1.98602	−	20.7985i	−0.0669867	−	0.701516i
$880$	−0.000115588	0	0.000288725i	−3.89647e−6	0	9.73291e-6i
$881$	47.6911	+	14.0034i	1.60675	+	0.471786i	0.957416	−	0.288713i	$-0.0932275\pi$
$881$	47.6911	+	14.0034i	1.60675	+	0.471786i	0.649339	+	0.760499i	$0.275046\pi$
$882$	−3.16609	+	6.24307i	−0.106608	+	0.210215i
$883$	−20.4753	−	44.8347i	−0.689049	−	1.50881i	−0.852762	−	0.522299i	$-0.825074\pi$
$883$	−20.4753	−	44.8347i	−0.689049	−	1.50881i	0.163713	−	0.986508i	$-0.447653\pi$
$884$	26.0917	+	6.32977i	0.877558	+	0.212893i
$885$	0.000128516	0	2.47694e-5i	4.32002e−6	0	8.32615e-7i
$886$	−31.9261	−	6.15325i	−1.07258	−	0.206722i
$887$	−15.5194	−	3.76496i	−0.521089	−	0.126415i	−0.0334167	−	0.999442i	$-0.510639\pi$
$887$	−15.5194	−	3.76496i	−0.521089	−	0.126415i	−0.487673	+	0.873027i	$0.662154\pi$
$888$	3.90128	+	8.54261i	0.130918	+	0.286671i
$889$	−2.36375	+	11.0428i	−0.0792776	+	0.370365i
$890$	−0.000959367	0	0.000281695i	−3.21580e−5	0	9.44245e-6i
$891$	0.860483	−	2.14938i	0.0288273	−	0.0720071i
$892$	−2.38153	−	24.9405i	−0.0797396	−	0.835071i
$893$	−1.60513	−	4.00942i	−0.0537137	−	0.134170i
$894$	11.2174	−	5.78297i	0.375166	−	0.193412i
$895$	−0.00193148	−	0.00222904i	−6.45621e−5	−	7.45087e-5i
$896$	−0.693275	−	2.55331i	−0.0231607	−	0.0853000i
$897$	−25.2762	+	0.949148i	−0.843948	+	0.0316911i
$898$	−20.5377	+	35.5723i	−0.685352	+	1.18706i
$899$	−0.152238	−	0.0526903i	−0.00507744	−	0.00175732i
$900$	0.237910	−	4.99434i	0.00793032	−	0.166478i
$901$	34.6961	−	44.1197i	1.15589	−	1.46984i
$902$	−5.67825	+	12.4336i	−0.189065	+	0.413995i
$903$	−0.777478	+	6.69148i	−0.0258729	+	0.222678i
$904$	−3.88476	+	13.2303i	−0.129205	+	0.440033i
$905$	−4.92039e−5	−	0.00103292i	−1.63559e−6	−	3.43353e-5i
$906$	−3.27234	−	2.33022i	−0.108716	−	0.0774164i
$907$	27.6036	−	28.9498i	0.916562	−	0.961263i	−0.0828145	−	0.996565i	$-0.526391\pi$
$907$	27.6036	−	28.9498i	0.916562	−	0.961263i	0.999377	+	0.0353023i	$0.0112394\pi$
$908$	7.68661	+	22.2090i	0.255089	+	0.737032i
$909$	−5.58734	−	4.84146i	−0.185320	−	0.160581i
$910$	5.08457e−5		0.00187376i	1.68552e−6		6.21145e-5i
$911$	49.0993	−	22.4229i	1.62673	−	0.742904i	0.627375	−	0.778717i	$-0.284129\pi$
$911$	49.0993	−	22.4229i	1.62673	−	0.742904i	0.999359	+	0.0358127i	$0.0114020\pi$
$912$	−2.63700	+	0.125616i	−0.0873198	+	0.00415955i
$913$	11.7597	−	2.85287i	0.389188	−	0.0944161i
$914$	19.6362	+	24.9694i	0.649506	+	0.825914i
$915$	0.000720677	0	0.000513192i	2.38248e−5	0	1.69656e-5i
$916$	−2.14222	+	14.8995i	−0.0707811	+	0.492293i
$917$	−28.2075	−	8.91358i	−0.931495	−	0.294352i
$918$	3.84719	−	3.33361i	0.126976	−	0.110025i
$919$	−20.6184	−	11.9040i	−0.680138	−	0.392678i	0.119769	−	0.992802i	$-0.461785\pi$
$919$	−20.6184	−	11.9040i	−0.680138	−	0.392678i	−0.799907	+	0.600124i	$0.795118\pi$
$920$	0.000353729	0	0.000538419i	1.16621e−5	0	1.77511e-5i
$921$	16.2109	+	28.0780i	0.534166	+	0.925202i
$922$	3.17276	+	16.4618i	0.104489	+	0.542141i
$923$	9.59248	−	14.9262i	0.315740	−	0.491301i
$924$	3.68719	+	4.89148i	0.121300	+	0.160918i
$925$	−42.7130	−	19.5064i	−1.40440	−	0.641366i
$926$	−8.64380	−	3.46046i	−0.284053	−	0.113718i
$927$	0.131361	+	0.541479i	0.00431448	+	0.0177845i
$928$	0.298568	+	0.153922i	0.00980096	+	0.00505275i
$929$	−3.44512	+	36.0789i	−0.113031	+	1.18371i	0.743905	+	0.668286i	$0.232972\pi$
$929$	−3.44512	+	36.0789i	−0.113031	+	1.18371i	−0.856935	+	0.515424i	$0.827634\pi$
$930$	6.18134e−5	0	1.81501e-5i	2.02694e−6	0	5.95164e-7i
$931$	−17.4229	+	6.16033i	−0.571013	+	0.201897i
$932$	2.24569	−	2.59166i	0.0735599	−	0.0848926i
$933$	−3.42337	+	14.1113i	−0.112076	+	0.461984i
$934$	10.3700	−	14.5626i	0.339317	−	0.476503i
$935$	0.000725454	−	0.00140718i	2.37249e−5	−	4.60198e-5i
$936$	3.63959	+	3.81710i	0.118964	+	0.124766i
$937$	−2.55583	−	17.7762i	−0.0834954	−	0.580724i	−0.988023	−	0.154308i	$-0.950685\pi$
$937$	−2.55583	−	17.7762i	−0.0834954	−	0.580724i	0.904527	−	0.426416i	$-0.140224\pi$
$938$	−4.09440	+	1.54268i	−0.133687	+	0.0503703i
$939$	15.1677	+	2.18078i	0.494979	+	0.0711672i
$940$	−0.000100695	0	0.000195322i	−3.28432e−6	0	6.37070e-6i
$941$	−10.9907	+	31.7555i	−0.358286	+	1.03520i	0.611500	+	0.791244i	$0.290566\pi$
$941$	−10.9907	+	31.7555i	−0.358286	+	1.03520i	−0.969786	+	0.243956i	$0.921555\pi$
$942$	15.7532	−	9.09509i	0.513266	−	0.296334i
$943$	16.6551	−	22.8975i	0.542365	−	0.745644i
$944$			0.974332i			0.0317118i
$945$	0.000294987	0	0.000198224i	9.59593e−6	0	6.44824e-6i
$946$	4.95913	+	3.18704i	0.161235	+	0.103620i
$947$	−5.20915	−	4.09652i	−0.169275	−	0.133119i	0.529928	−	0.848043i	$-0.322219\pi$
$947$	−5.20915	−	4.09652i	−0.169275	−	0.133119i	−0.699203	+	0.714924i	$0.746461\pi$
$948$	−2.62592	+	0.250745i	−0.0852860	+	0.00814382i
$949$	−57.2411	+	45.0149i	−1.85813	+	1.46125i
$950$	9.55325	−	9.10901i	0.309948	−	0.295535i
$951$	−10.4427	−	16.2492i	−0.338629	−	0.526916i
$952$	2.27766	+	13.2744i	0.0738194	+	0.430225i
$953$	4.50929	+	15.3572i	0.146070	+	0.497469i	0.999727	−	0.0233666i	$-0.00743850\pi$
$953$	4.50929	+	15.3572i	0.146070	+	0.497469i	−0.853657	+	0.520836i	$0.825620\pi$
$954$	10.4195	−	3.60623i	0.337344	−	0.116756i
$955$	−0.000325958		0.00169123i	−1.05478e−5		5.47270e-5i
$956$	−5.06906	−	4.83334i	−0.163945	−	0.156321i
$957$	−0.774184	−	0.0739256i	−0.0250258	−	0.00238968i
$958$	−32.4291	+	20.8409i	−1.04774	+	0.673339i
$959$	−5.85737	+	9.68200i	−0.189144	+	0.312648i
$960$	−0.000132962	0	1.91170e-5i	−4.29132e−6	0	6.16999e-7i
$961$	17.8483	+	25.0645i	0.575753	+	0.808532i
$962$	45.9832	−	18.4089i	1.48256	−	0.593526i
$963$	−8.89687	−	0.423810i	−0.286698	−	0.0136571i
$964$	12.1378	−	2.33936i	0.390931	−	0.0753457i
$965$	0.00316825			0.000101989
$966$	−5.46718	−	11.4503i	−0.175904	−	0.368408i
$967$	−15.7637			−0.506925			−0.253462	−	0.967345i	$-0.581569\pi$
$967$	−15.7637			−0.506925			−0.253462	+	0.967345i	$0.581569\pi$
$968$	−5.53780	+	1.06732i	−0.177992	+	0.0343051i
$969$	13.4238	+	0.639455i	0.431235	+	0.0205422i
$970$	0.00231861		0.000928230i	7.44459e−5		2.98037e-5i
$971$	−8.07387	−	11.3382i	−0.259103	−	0.363859i	0.664448	−	0.747334i	$-0.268667\pi$
$971$	−8.07387	−	11.3382i	−0.259103	−	0.363859i	−0.923551	+	0.383475i	$0.874727\pi$
$972$	0.989821	−	0.142315i	0.0317485	−	0.00456475i
$973$	−2.86624	−	5.20784i	−0.0918875	−	0.166956i
$974$	−23.1028	+	14.8472i	−0.740260	+	0.475736i
$975$	−26.2514	−	2.50671i	−0.840719	−	0.0802789i
$976$	4.76670	+	4.54504i	0.152578	+	0.145483i
$977$	−1.64240	+	8.52157i	−0.0525449	+	0.272629i	−0.998693	−	0.0511042i	$-0.983726\pi$
$977$	−1.64240	+	8.52157i	−0.0525449	+	0.272629i	0.946148	+	0.323733i	$0.104938\pi$
$978$	17.8516	−	6.17850i	0.570831	−	0.197567i
$979$	4.85516	+	16.5352i	0.155172	+	0.528466i
$980$	−0.000852711	0	0.000396302i	−2.72388e−5	0	1.26594e-5i
$981$	−4.28389	−	6.66586i	−0.136774	−	0.212824i
$982$	−20.8122	+	19.8444i	−0.664145	+	0.633261i
$983$	−13.8274	+	10.8740i	−0.441026	+	0.346826i	−0.813849	−	0.581076i	$-0.802632\pi$
$983$	−13.8274	+	10.8740i	−0.441026	+	0.346826i	0.372824	+	0.927902i	$0.378390\pi$
$984$	−5.87716	+	0.561201i	−0.187357	+	0.0178904i
$985$	−0.00208658	−	0.00164090i	−6.64838e−5	−	5.22835e-5i
$986$	−1.43851	−	0.924477i	−0.0458116	−	0.0294413i
$987$	−4.31819	−	0.294397i	−0.137449	−	0.00937077i
$988$			13.9238i			0.442974i
$989$	−8.75220	−	8.51504i	−0.278304	−	0.270763i
$990$	0.000269336	0	0.000155501i	8.56006e−6	0	4.94215e-6i
$991$	0.801515	−	2.31583i	0.0254610	−	0.0735646i	−0.931554	−	0.363602i	$-0.881547\pi$
$991$	0.801515	−	2.31583i	0.0254610	−	0.0735646i	0.957015	+	0.290038i	$0.0936679\pi$
$992$	0.219761	+	0.426277i	0.00697743	+	0.0135343i
$993$	−22.3548	−	3.21414i	−0.709409	−	0.101998i
$994$	8.78218	+	1.44675i	0.278554	+	0.0458881i
$995$	−0.000240239	−	0.00167090i	−7.61608e−6	−	5.29710e-5i
$996$	3.60677	+	3.78267i	0.114285	+	0.119858i
$997$	4.26987	−	8.28239i	0.135228	−	0.262306i	−0.811492	−	0.584364i	$-0.801344\pi$
$997$	4.26987	−	8.28239i	0.135228	−	0.262306i	0.946720	+	0.322058i	$0.104375\pi$
$998$	−20.7078	+	29.0801i	−0.655495	+	0.920514i
$999$	2.21408	−	9.12655i	0.0700503	−	0.288751i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.a.355.13	yes	320
7.3	odd	6	inner	966.2.be.a.493.13	yes	320
23.7	odd	22	inner	966.2.be.a.145.13	✓	320
161.122	even	66	inner	966.2.be.a.283.13	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.a.145.13	✓	320	23.7	odd	22	inner
966.2.be.a.283.13	yes	320	161.122	even	66	inner
966.2.be.a.355.13	yes	320	1.1	even	1	trivial
966.2.be.a.493.13	yes	320	7.3	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.be (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.981929 + 0.189251i) q^{2} +(0.998867 + 0.0475819i) q^{3} +(0.928368 - 0.371662i) q^{4} +(-7.79185e-5 - 0.000109421i) q^{5} +(-0.989821 + 0.142315i) q^{6} +(-2.31789 + 1.27570i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(0.995472 + 0.0950560i) q^{9} +(9.72185e-5 + 9.26977e-5i) q^{10} +(0.438160 - 2.27339i) q^{11} +(0.945001 - 0.327068i) q^{12} +(-1.48591 - 5.06053i) q^{13} +(2.03457 - 1.69131i) q^{14} +(-7.26238e-5 - 0.000113005i) q^{15} +(0.723734 - 0.690079i) q^{16} +(-4.00145 + 3.14678i) q^{17} +(-0.995472 + 0.0950560i) q^{18} +(-2.07517 - 1.63193i) q^{19} +(-0.000113005 - 7.26238e-5i) q^{20} +(-2.37596 + 1.16396i) q^{21} +2.31523i q^{22} +(0.954975 - 4.69979i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(1.63534 - 4.72500i) q^{25} +(2.41676 + 4.68787i) q^{26} +(0.989821 + 0.142315i) q^{27} +(-1.67772 + 2.04579i) q^{28} +(-0.0478048 - 0.332490i) q^{29} +(9.26977e-5 + 9.72185e-5i) q^{30} +(0.219761 - 0.426277i) q^{31} +(-0.580057 + 0.814576i) q^{32} +(0.545836 - 2.24997i) q^{33} +(3.33361 - 3.84719i) q^{34} +(0.000320195 + 0.000154226i) q^{35} +(0.959493 - 0.281733i) q^{36} +(0.892698 - 9.34875i) q^{37} +(2.34652 + 1.20971i) q^{38} +(-1.24343 - 5.12550i) q^{39} +(0.000124707 + 4.99251e-5i) q^{40} +(5.37037 + 2.45257i) q^{41} +(2.11274 - 1.59258i) q^{42} +(1.37656 - 2.14196i) q^{43} +(-0.438160 - 2.27339i) q^{44} +(-6.71645e-5 - 0.000116332i) q^{45} +(-0.0482765 + 4.79559i) q^{46} +(1.41674 + 0.817955i) q^{47} +(0.755750 - 0.654861i) q^{48} +(3.74519 - 5.91384i) q^{49} +(-0.711574 + 4.94911i) q^{50} +(-4.14665 + 2.95281i) q^{51} +(-3.26028 - 4.14578i) q^{52} +(-10.7151 + 2.59946i) q^{53} +(-0.998867 + 0.0475819i) q^{54} +(-0.000282898 + 0.000129195i) q^{55} +(1.26024 - 2.32633i) q^{56} +(-1.99517 - 1.72883i) q^{57} +(0.109865 + 0.317434i) q^{58} +(-0.672366 + 0.705158i) q^{59} +(-0.000109421 - 7.79185e-5i) q^{60} +(0.313387 + 6.57880i) q^{61} +(-0.135116 + 0.460164i) q^{62} +(-2.42865 + 1.04959i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-0.000437950 + 0.000556899i) q^{65} +(-0.110163 + 2.31261i) q^{66} +(-1.56279 - 0.540885i) q^{67} +(-2.54528 + 4.40855i) q^{68} +(1.17752 - 4.64903i) q^{69} +(-0.000343596 - 9.08413e-5i) q^{70} +(2.20301 + 2.54241i) q^{71} +(-0.888835 + 0.458227i) q^{72} +(-5.13158 - 12.8181i) q^{73} +(0.892698 + 9.34875i) q^{74} +(1.85831 - 4.64184i) q^{75} +(-2.53305 - 0.743771i) q^{76} +(1.88455 + 5.82842i) q^{77} +(2.19097 + 4.79755i) q^{78} +(-2.56351 - 0.621901i) q^{79} +(-0.000131902 - 2.54219e-5i) q^{80} +(0.981929 + 0.189251i) q^{81} +(-5.73747 - 1.39190i) q^{82} +(2.17121 + 4.75428i) q^{83} +(-1.77316 + 1.96364i) q^{84} +(0.000656111 + 0.000192652i) q^{85} +(-0.946310 + 2.36377i) q^{86} +(-0.0319302 - 0.334388i) q^{87} +(0.860483 + 2.14938i) q^{88} +(-6.61598 + 3.41077i) q^{89} +(8.79669e-5 + 0.000101519i) q^{90} +(9.89986 + 9.83417i) q^{91} +(-0.860167 - 4.71806i) q^{92} +(0.239795 - 0.415338i) q^{93} +(-1.54594 - 0.535054i) q^{94} +(-1.68739e-5 + 0.000354226i) q^{95} +(-0.618159 + 0.786053i) q^{96} +(7.72358 - 16.9123i) q^{97} +(-2.55831 + 6.51575i) q^{98} +(0.652275 - 2.22145i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9} - 22 q^{14} + 16 q^{16} + 66 q^{17} + 16 q^{18} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36}+ \cdots - 90 q^{98}+O(q^{100}) \) 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9 - 22 * q^14 + 16 * q^16 + 66 * q^17 + 16 * q^18 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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