LMFDB - Embedded newform 966.2.be.a.145.13

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			145.13
Character	$\chi$	$=$	966.145
Dual form			966.2.be.a.493.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.327068 + 0.945001i) q^{2} +(0.458227 - 0.888835i) q^{3} +(-0.786053 + 0.618159i) q^{4} +(-0.000133721 - 1.27688e-5i) q^{5} +(0.989821 + 0.142315i) q^{6} +(1.26024 - 2.32633i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(-0.580057 - 0.814576i) q^{9} +(-3.16693e-5 - 0.000130543i) q^{10} +(-2.18789 - 0.757237i) q^{11} +(0.189251 + 0.981929i) q^{12} +(1.48591 - 5.06053i) q^{13} +(2.61057 + 0.430057i) q^{14} +(-7.26238e-5 + 0.000113005i) q^{15} +(0.235759 - 0.971812i) q^{16} +(-4.72591 + 1.89197i) q^{17} +(0.580057 - 0.814576i) q^{18} +(-2.45088 - 0.981185i) q^{19} +(0.000113005 - 7.26238e-5i) q^{20} +(-1.49025 - 2.18613i) q^{21} -2.31523i q^{22} +(3.59265 - 3.17693i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-4.90964 - 0.946256i) q^{25} +(5.26820 - 0.250955i) q^{26} +(-0.989821 + 0.142315i) q^{27} +(0.447428 + 2.60764i) q^{28} +(-0.0478048 + 0.332490i) q^{29} +(-0.000130543 - 3.16693e-5i) q^{30} +(0.479048 + 0.0228198i) q^{31} +(0.995472 - 0.0950560i) q^{32} +(-1.67561 + 1.59769i) q^{33} +(-3.33361 - 3.84719i) q^{34} +(-0.000198224 + 0.000294987i) q^{35} +(0.959493 + 0.281733i) q^{36} +(7.64991 - 5.44747i) q^{37} +(0.125616 - 2.63700i) q^{38} +(-3.81710 - 3.63959i) q^{39} +(0.000105590 + 8.30367e-5i) q^{40} +(-5.37037 + 2.45257i) q^{41} +(1.57848 - 2.12330i) q^{42} +(1.37656 + 2.14196i) q^{43} +(2.18789 - 0.757237i) q^{44} +(6.71645e-5 + 0.000116332i) q^{45} +(4.17724 + 2.35599i) q^{46} +(1.41674 + 0.817955i) q^{47} +(-0.755750 - 0.654861i) q^{48} +(-3.82361 - 5.86345i) q^{49} +(-0.711574 - 4.94911i) q^{50} +(-0.483889 + 5.06751i) q^{51} +(1.96021 + 4.89637i) q^{52} +(7.60876 - 7.97983i) q^{53} +(-0.458227 - 0.888835i) q^{54} +(0.000282898 + 0.000129195i) q^{55} +(-2.31789 + 1.27570i) q^{56} +(-1.99517 + 1.72883i) q^{57} +(-0.329839 + 0.0635712i) q^{58} +(-0.946867 + 0.229708i) q^{59} +(-1.27688e-5 - 0.000133721i) q^{60} +(5.85410 - 3.01800i) q^{61} +(0.135116 + 0.460164i) q^{62} +(-2.62598 + 0.322845i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-0.000263313 + 0.000657725i) q^{65} +(-2.05786 - 1.06090i) q^{66} +(0.312972 - 1.62385i) 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} +(0.0475819 + 0.998867i) q^{72} +(8.53497 + 10.8531i) q^{73} +(7.64991 + 5.44747i) q^{74} +(-3.09079 + 3.93027i) q^{75} +(2.53305 - 0.743771i) q^{76} +(-4.51884 + 4.13546i) q^{77} +(2.19097 - 4.79755i) q^{78} +(1.82034 + 1.90911i) q^{79} +(-4.39347e-5 + 0.000126941i) q^{80} +(-0.327068 + 0.945001i) q^{81} +(-4.07415 - 4.27285i) q^{82} +(-2.17121 + 4.75428i) q^{83} +(2.52279 + 0.797201i) q^{84} +(0.000656111 - 0.000192652i) q^{85} +(-1.57393 + 2.00141i) q^{86} +(0.273623 + 0.194846i) q^{87} +(1.43118 + 1.81989i) q^{88} +(-0.354172 - 7.43499i) 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} +(-0.309598 + 1.60635i) q^{94} +(0.000315205 + 0.000162500i) q^{95} +(0.371662 - 0.928368i) q^{96} +(-7.72358 - 16.9123i) q^{97} +(4.29038 - 5.53106i) 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 $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{19}{22}\right)$

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 $

$2$	0.327068	+	0.945001i	0.231272	+	0.668216i
$2$	0.327068	+	0.945001i	0.231272	+	0.668216i
$3$	0.458227	−	0.888835i	0.264557	−	0.513169i
$3$	0.458227	−	0.888835i	0.264557	−	0.513169i
$4$	−0.786053	+	0.618159i	−0.393027	+	0.309079i
$5$	−0.000133721	0	1.27688e-5i	−5.98018e−5	0	5.71038e-6i	0.0950261	−	0.995475i	$-0.469707\pi$
$5$	−0.000133721	0	1.27688e-5i	−5.98018e−5	0	5.71038e-6i	−0.0950859	+	0.995469i	$0.530313\pi$
$6$	0.989821	+	0.142315i	0.404093	+	0.0580998i
$7$	1.26024	−	2.32633i	0.476324	−	0.879270i
$7$	1.26024	−	2.32633i	0.476324	−	0.879270i
$8$	−0.841254	−	0.540641i	−0.297428	−	0.191145i
$9$	−0.580057	−	0.814576i	−0.193352	−	0.271525i
$10$	−3.16693e−5	0	0.000130543i	−1.00147e−5	0	4.12812e-5i
$11$	−2.18789	−	0.757237i	−0.659674	−	0.228316i	−0.0233385	−	0.999728i	$-0.507430\pi$
$11$	−2.18789	−	0.757237i	−0.659674	−	0.228316i	−0.636336	+	0.771412i	$0.719551\pi$
$12$	0.189251	+	0.981929i	0.0546321	+	0.283458i
$13$	1.48591	−	5.06053i	0.412116	−	1.40354i	−0.448271	−	0.893898i	$-0.647960\pi$
$13$	1.48591	−	5.06053i	0.412116	−	1.40354i	0.860387	−	0.509641i	$-0.170222\pi$
$14$	2.61057	+	0.430057i	0.697703	+	0.114937i
$15$	−7.26238e−5	0	0.000113005i	−1.87514e−5	0	2.91777e-5i
$16$	0.235759	−	0.971812i	0.0589397	−	0.242953i
$17$	−4.72591	+	1.89197i	−1.14620	+	0.458870i	−0.865492	−	0.500922i	$-0.832994\pi$
$17$	−4.72591	+	1.89197i	−1.14620	+	0.458870i	−0.280710	+	0.959793i	$0.590570\pi$
$18$	0.580057	−	0.814576i	0.136721	−	0.191997i
$19$	−2.45088	−	0.981185i	−0.562271	−	0.225099i	0.0730757	−	0.997326i	$-0.476719\pi$
$19$	−2.45088	−	0.981185i	−0.562271	−	0.225099i	−0.635347	+	0.772227i	$0.719143\pi$
$20$	0.000113005	0	7.26238e-5i	2.52686e−5	0	1.62392e-5i
$21$	−1.49025	−	2.18613i	−0.325199	−	0.477052i
$22$		−	2.31523i		−	0.493608i
$23$	3.59265	−	3.17693i	0.749119	−	0.662435i
$23$	3.59265	−	3.17693i	0.749119	−	0.662435i
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	−4.90964	−	0.946256i	−0.981929	−	0.189251i
$26$	5.26820	−	0.250955i	1.03318	−	0.0492164i
$27$	−0.989821	+	0.142315i	−0.190491	+	0.0273885i
$28$	0.447428	+	2.60764i	0.0845560	+	0.492798i
$29$	−0.0478048	+	0.332490i	−0.00887713	+	0.0617418i	−0.993778	−	0.111375i	$-0.964475\pi$
$29$	−0.0478048	+	0.332490i	−0.00887713	+	0.0617418i	0.984901	+	0.173117i	$0.0553837\pi$
$30$	−0.000130543	0	3.16693e-5i	−2.38337e−5	0	5.78199e-6i
$31$	0.479048	+	0.0228198i	0.0860395	+	0.00409857i	0.0905575	−	0.995891i	$-0.471135\pi$
$31$	0.479048	+	0.0228198i	0.0860395	+	0.00409857i	−0.00451802	+	0.999990i	$0.501438\pi$
$32$	0.995472	−	0.0950560i	0.175976	−	0.0168037i
$33$	−1.67561	+	1.59769i	−0.291686	+	0.278122i
$34$	−3.33361	−	3.84719i	−0.571709	−	0.659787i
$35$	−0.000198224	0	0.000294987i	−3.35060e−5	0	4.98619e-5i
$36$	0.959493	+	0.281733i	0.159915	+	0.0469554i
$37$	7.64991	−	5.44747i	1.25764	−	0.895559i	0.260092	−	0.965584i	$-0.416247\pi$
$37$	7.64991	−	5.44747i	1.25764	−	0.895559i	0.997545	+	0.0700246i	$0.0223078\pi$
$38$	0.125616	−	2.63700i	0.0203776	−	0.427778i
$39$	−3.81710	−	3.63959i	−0.611225	−	0.582802i
$40$	0.000105590	0	8.30367e-5i	1.66952e−5	0	1.31293e-5i
$41$	−5.37037	+	2.45257i	−0.838711	+	0.383027i	−0.787991	−	0.615686i	$-0.788879\pi$
$41$	−5.37037	+	2.45257i	−0.838711	+	0.383027i	−0.0507198	+	0.998713i	$0.516152\pi$
$42$	1.57848	−	2.12330i	0.243565	−	0.327632i
$43$	1.37656	+	2.14196i	0.209923	+	0.326646i	0.930209	−	0.367031i	$-0.119626\pi$
$43$	1.37656	+	2.14196i	0.209923	+	0.326646i	−0.720286	+	0.693677i	$0.755989\pi$
$44$	2.18789	−	0.757237i	0.329837	−	0.114158i
$45$	6.71645e−5	0	0.000116332i	1.00123e−5	0	1.73418e-5i
$46$	4.17724	+	2.35599i	0.615900	+	0.347371i
$47$	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
$49$	−3.82361	−	5.86345i	−0.546230	−	0.837635i
$50$	−0.711574	−	4.94911i	−0.100632	−	0.699909i
$51$	−0.483889	+	5.06751i	−0.0677579	+	0.709593i
$52$	1.96021	+	4.89637i	0.271832	+	0.679004i
$53$	7.60876	−	7.97983i	1.04514	−	1.09611i	0.0498939	−	0.998755i	$-0.484112\pi$
$53$	7.60876	−	7.97983i	1.04514	−	1.09611i	0.995249	−	0.0973601i	$-0.0310398\pi$
$54$	−0.458227	−	0.888835i	−0.0623567	−	0.120955i
$55$	0.000282898	0	0.000129195i	3.81459e−5	0	1.74207e-5i
$56$	−2.31789	+	1.27570i	−0.309741	+	0.170472i
$57$	−1.99517	+	1.72883i	−0.264267	+	0.228989i
$58$	−0.329839	+	0.0635712i	−0.0433099	+	0.00834730i
$59$	−0.946867	+	0.229708i	−0.123272	+	0.0299054i	−0.296920	−	0.954902i	$-0.595960\pi$
$59$	−0.946867	+	0.229708i	−0.123272	+	0.0299054i	0.173648	+	0.984808i	$0.444444\pi$
$60$	−1.27688e−5	0	0.000133721i	−1.64844e−6	0	1.72633e-5i
$61$	5.85410	−	3.01800i	0.749541	−	0.386415i	−0.0407320	−	0.999170i	$-0.512969\pi$
$61$	5.85410	−	3.01800i	0.749541	−	0.386415i	0.790273	+	0.612755i	$0.209939\pi$
$62$	0.135116	+	0.460164i	0.0171598	+	0.0584409i
$63$	−2.62598	+	0.322845i	−0.330842	+	0.0406746i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	−0.000263313	0	0.000657725i	−3.26600e−5	0	8.15808e-5i
$66$	−2.05786	−	1.06090i	−0.253305	−	0.130588i
$67$	0.312972	−	1.62385i	0.0382356	−	0.198385i	−0.957788	−	0.287476i	$-0.907184\pi$
$67$	0.312972	−	1.62385i	0.0382356	−	0.198385i	0.996024	+	0.0890905i	$0.0283960\pi$
$68$	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	−0.609814	−	0.792545i	$-0.708756\pi$
$71$	2.20301	−	2.54241i	0.261449	−	0.301729i	0.871263	+	0.490816i	$0.163301\pi$
$72$	0.0475819	+	0.998867i	0.00560758	+	0.117718i
$73$	8.53497	+	10.8531i	0.998943	+	1.27026i	0.962602	+	0.270920i	$0.0873279\pi$
$73$	8.53497	+	10.8531i	0.998943	+	1.27026i	0.0363413	+	0.999339i	$0.488430\pi$
$74$	7.64991	+	5.44747i	0.889284	+	0.633256i
$75$	−3.09079	+	3.93027i	−0.356894	+	0.453828i
$76$	2.53305	−	0.743771i	0.290561	−	0.0853164i
$77$	−4.51884	+	4.13546i	−0.514970	+	0.471279i
$78$	2.19097	−	4.79755i	0.248078	−	0.543216i
$79$	1.82034	+	1.90911i	0.204804	+	0.214792i	0.818123	−	0.575043i	$-0.195015\pi$
$79$	1.82034	+	1.90911i	0.204804	+	0.214792i	−0.613319	+	0.789835i	$0.710166\pi$
$80$	−4.39347e−5	0	0.000126941i	−4.91205e−6	0	1.41924e-5i
$81$	−0.327068	+	0.945001i	−0.0363409	+	0.105000i
$82$	−4.07415	−	4.27285i	−0.449915	−	0.471857i
$83$	−2.17121	+	4.75428i	−0.238321	+	0.521850i	−0.990567	−	0.137033i	$-0.956244\pi$
$83$	−2.17121	+	4.75428i	−0.238321	+	0.521850i	0.752245	+	0.658883i	$0.228971\pi$
$84$	2.52279	+	0.797201i	0.275259	+	0.0869818i
$85$	0.000656111	0	0.000192652i	7.11653e−5	0	2.08960e-5i
$86$	−1.57393	+	2.00141i	−0.169721	+	0.215818i
$87$	0.273623	+	0.194846i	0.0293355	+	0.0208897i
$88$	1.43118	+	1.81989i	0.152564	+	0.194001i
$89$	−0.354172	−	7.43499i	−0.0375422	−	0.788108i	−0.936626	−	0.350331i	$-0.886069\pi$
$89$	−0.354172	−	7.43499i	−0.0375422	−	0.788108i	0.899084	−	0.437777i	$-0.144234\pi$
$90$	−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
$94$	−0.309598	+	1.60635i	−0.0319326	+	0.165682i
$95$	0.000315205	0	0.000162500i	3.23394e−5	0	1.66721e-5i
$96$	0.371662	−	0.928368i	0.0379326	−	0.0947512i
$97$	−7.72358	−	16.9123i	−0.784211	−	1.71718i	−0.692524	−	0.721395i	$-0.743501\pi$
$97$	−7.72358	−	16.9123i	−0.784211	−	1.71718i	−0.0916874	−	0.995788i	$-0.529226\pi$
$98$	4.29038	−	5.53106i	0.433394	−	0.558721i
$99$	0.652275	+	2.22145i	0.0655561	+	0.223264i
$100$	4.44418	−	2.29113i	0.444418	−	0.229113i
$101$	0.702760	+	7.35963i	0.0699272	+	0.732311i	0.960650	+	0.277763i	$0.0895930\pi$
$101$	0.702760	+	7.35963i	0.0699272	+	0.732311i	−0.890722	+	0.454548i	$0.849801\pi$
$102$	−4.94707	+	1.20015i	−0.489832	+	0.118832i
$103$	0.547117	−	0.105448i	0.0539090	−	0.0103901i	−0.162225	−	0.986754i	$-0.551867\pi$
$103$	0.547117	−	0.105448i	0.0539090	−	0.0103901i	0.216134	+	0.976364i	$0.430655\pi$
$104$	−3.98595	+	3.45385i	−0.390855	+	0.338678i
$105$	0.000171363	0	0.000311360i	1.67233e−5	0	3.03856e-5i
$106$	10.0295	+	4.58033i	0.974154	+	0.444881i
$107$	4.08141	+	7.91682i	0.394564	+	0.765348i	0.999522	−	0.0309094i	$-0.00984033\pi$
$107$	4.08141	+	7.91682i	0.394564	+	0.765348i	−0.604958	+	0.796258i	$0.706810\pi$
$108$	0.690079	−	0.723734i	0.0664029	−	0.0696413i
$109$	−2.94495	−	7.35613i	−0.282075	−	0.704589i	−0.999964	−	0.00843219i	$-0.997316\pi$
$109$	−2.94495	−	7.35613i	−0.282075	−	0.704589i	0.717889	−	0.696157i	$-0.245108\pi$
$110$	−2.95627e−5	0	0.000309594i	−2.81869e−6	0	2.95187e-5i
$111$	−1.33652	−	9.29569i	−0.126857	−	0.882308i
$112$	−1.96364	−	1.77316i	−0.185547	−	0.167548i
$113$	10.4209	+	9.02976i	0.980316	+	0.849448i	0.988607	−	0.150517i	$-0.0480939\pi$
$113$	10.4209	+	9.02976i	0.980316	+	0.849448i	−0.00829180	+	0.999966i	$0.502639\pi$
$114$	−2.28630	−	1.32000i	−0.214131	−	0.123629i
$115$	−0.000520978	0	0.000378948i	−4.85814e−5	0	3.53370e-5i
$116$	−0.167954	−	0.290906i	−0.0155942	−	0.0270099i
$117$	−4.98410	+	1.72501i	−0.460780	+	0.159477i
$118$	−0.526764	−	0.819661i	−0.0484925	−	0.0754559i
$119$	−1.55442	+	13.3784i	−0.142494	+	1.22639i
$120$	0.000122190	0	5.58023e-5i	1.11544e−5	0	5.09403e-6i
$121$	−4.43312	−	3.48624i	−0.403011	−	0.316931i
$122$	4.76670	+	4.54504i	0.431557	+	0.411489i
$123$	−0.280919	+	5.89721i	−0.0253296	+	0.531733i
$124$	−0.390663	+	0.278190i	−0.0350826	+	0.0249822i
$125$	0.00128888		0.000378449i	0.000115281		3.38495e-5i
$126$	−1.16396	−	2.37596i	−0.103694	−	0.211667i
$127$	2.79517	+	3.22580i	0.248032	+	0.286244i	0.866090	−	0.499889i	$-0.166626\pi$
$127$	2.79517	+	3.22580i	0.248032	+	0.286244i	−0.618058	+	0.786132i	$0.712080\pi$
$128$	−0.723734	+	0.690079i	−0.0639697	+	0.0609949i
$129$	2.53463	−	0.242027i	0.223161	−	0.0213093i
$130$	−0.000707672	0	3.37106e-5i	−6.20669e−5	0	2.95661e-6i
$131$	10.8659	+	2.63604i	0.949359	+	0.230312i	0.680401	−	0.732840i	$-0.261806\pi$
$131$	10.8659	+	2.63604i	0.949359	+	0.230312i	0.268958	+	0.963152i	$0.413321\pi$
$132$	0.329491	−	2.29166i	0.0286785	−	0.199464i
$133$	−5.37125	+	4.46503i	−0.465746	+	0.387167i
$134$	1.63691	−	0.235352i	0.141407	−	0.0203313i
$135$	0.000134177	0	6.39164e-6i	1.15481e−5	0	5.50104e-7i
$136$	4.99857	+	0.963395i	0.428624	+	0.0826104i
$137$	−3.70400	+	2.13851i	−0.316454	+	0.182705i	−0.649811	−	0.760096i	$-0.725152\pi$
$137$	−3.70400	+	2.13851i	−0.316454	+	0.182705i	0.333357	+	0.942801i	$0.391819\pi$
$138$	4.00821	−	2.63330i	0.341201	−	0.224162i
$139$			2.24680i			0.190571i	0.995450	+	0.0952857i	$0.0303765\pi$
$139$			2.24680i			0.190571i	−0.995450	+	0.0952857i	$0.969624\pi$
$140$	−2.65340e−5	0	0.000354409i	−2.24254e−6	0	2.99531e-5i
$141$	1.37622	−	0.884440i	0.115898	−	0.0744833i
$142$	3.12312	+	1.25031i	0.262086	+	0.104923i
$143$	−7.08302	+	9.94671i	−0.592312	+	0.831786i
$144$	−0.928368	+	0.371662i	−0.0773640	+	0.0309719i
$145$	1.06380e−5	0	4.38504e-5i	8.83437e−7	0	3.64158e-6i
$146$	−7.46467	+	11.6153i	−0.617781	+	0.961286i
$147$	−6.96372	+	0.711773i	−0.574358	+	0.0587061i
$148$	−2.64583	+	9.01086i	−0.217486	+	0.740688i
$149$	2.38841	+	12.3923i	0.195666	+	1.01521i	0.938380	+	0.345605i	$0.112326\pi$
$149$	2.38841	+	12.3923i	0.195666	+	1.01521i	−0.742714	+	0.669609i	$0.766462\pi$
$150$	−4.72500	−	1.63534i	−0.385795	−	0.133525i
$151$	0.947097	+	3.90399i	0.0770737	+	0.317702i	0.997278	−	0.0737370i	$-0.0234925\pi$
$151$	0.947097	+	3.90399i	0.0770737	+	0.317702i	−0.920204	+	0.391439i	$0.871977\pi$
$152$	1.53134	+	2.15047i	0.124208	+	0.174426i
$153$	4.28245	+	2.75216i	0.346216	+	0.222499i
$154$	−5.38598	−	2.91773i	−0.434015	−	0.235118i
$155$	−6.37673e−5	0	9.16835e-6i	−5.12191e−6	0	7.36419e-7i
$156$	5.25029	+	0.501342i	0.420360	+	0.0401395i
$157$	−14.2984	+	11.2444i	−1.14114	+	0.897403i	−0.995761	−	0.0919734i	$-0.970683\pi$
$157$	−14.2984	+	11.2444i	−1.14114	+	0.897403i	−0.145379	+	0.989376i	$0.546440\pi$
$158$	−1.20874	+	2.34463i	−0.0961622	+	0.186529i
$159$	−3.60623	−	10.4195i	−0.285992	−	0.826320i
$160$	−0.000134329	0		−1.06196e−5	0
$161$	−2.86299	−	12.3614i	−0.225635	−	0.974212i
$162$	−1.00000			−0.0785674
$163$	6.17850	+	17.8516i	0.483938	+	1.39825i	0.877778	+	0.479067i	$0.159025\pi$
$163$	6.17850	+	17.8516i	0.483938	+	1.39825i	−0.393841	+	0.919179i	$0.628854\pi$
$164$	2.70532	−	5.24759i	0.211250	−	0.409768i
$165$	0.000244464	0	0.000192249i	1.90315e−5	0	1.49666e-5i
$166$	−5.20293	−	0.496820i	−0.403826	−	0.0385607i
$167$	1.83590	+	0.263963i	0.142067	+	0.0204261i	0.212981	−	0.977056i	$-0.431683\pi$
$167$	1.83590	+	0.263963i	0.142067	+	0.0204261i	−0.0709146	+	0.997482i	$0.522592\pi$
$168$	0.0717678	+	2.64478i	0.00553701	+	0.204049i
$169$	−12.4647	−	8.01061i	−0.958827	−	0.616201i
$170$	0.000396649	0	0.000557016i	3.04216e−5	0	4.27211e-5i
$171$	0.622401	+	2.56557i	0.0475962	+	0.196194i
$172$	−2.40612	−	0.832766i	−0.183465	−	0.0634978i
$173$	−1.13804	−	5.90471i	−0.0865235	−	0.448926i	−0.999191	−	0.0402230i	$-0.987193\pi$
$173$	−1.13804	−	5.90471i	−0.0865235	−	0.448926i	0.912667	−	0.408703i	$-0.134019\pi$
$174$	−0.0946365	+	0.322302i	−0.00717437	+	0.0244337i
$175$	−8.38861	+	10.2289i	−0.634120	+	0.773235i
$176$	−1.25171	+	1.94769i	−0.0943510	+	0.146813i
$177$	−0.229708	+	0.946867i	−0.0172659	+	0.0711709i
$178$	6.91023	−	2.76644i	0.517944	−	0.207353i
$179$	−12.7362	+	17.8855i	−0.951951	+	1.33683i	−0.0104035	+	0.999946i	$0.503312\pi$
$179$	−12.7362	+	17.8855i	−0.951951	+	1.33683i	−0.941547	+	0.336882i	$0.890628\pi$
$180$	−0.000124707	0	4.99251e-5i	−9.29510e−6	0	3.72120e-6i
$181$	−6.47611	+	4.16194i	−0.481365	+	0.309355i	−0.758725	−	0.651412i	$-0.774177\pi$
$181$	−6.47611	+	4.16194i	−0.481365	+	0.309355i	0.277359	+	0.960766i	$0.410541\pi$
$182$	6.05537	−	12.5718i	0.448854	−	0.931885i
$183$		−	6.58626i		−	0.486871i
$184$	−4.73991	+	0.730268i	−0.349430	+	0.0538361i
$185$	−0.00109251		0.000630761i	−8.03229e−5		4.63745e-5i
$186$	0.470924	+	0.0907632i	0.0345298	+	0.00665508i
$187$	11.7725	−	0.560791i	0.860888	−	0.0410091i
$188$	−1.61926	+	0.232814i	−0.118097	+	0.0169797i
$189$	−0.916338	+	2.48200i	−0.0666538	+	0.180539i
$190$	−5.04688e−5	0	0.000351018i	−3.66139e−6	0	2.54655e-5i
$191$	12.4605	+	3.02288i	0.901610	+	0.218728i	0.659663	−	0.751561i	$-0.270699\pi$
$191$	12.4605	+	3.02288i	0.901610	+	0.218728i	0.241947	+	0.970290i	$0.422214\pi$
$192$	0.998867	+	0.0475819i	0.0720870	+	0.00343393i
$193$	23.4789	−	2.24196i	1.69005	−	0.161380i	0.794777	−	0.606902i	$-0.207588\pi$
$193$	23.4789	−	2.24196i	1.69005	−	0.161380i	0.895271	+	0.445522i	$0.146982\pi$
$194$	13.4560	−	12.8303i	0.966084	−	0.921159i
$195$	0.000463952	0	0.000535429i	3.32243e−5	0	3.83429e-5i
$196$	6.63010	+	2.24538i	0.473579	+	0.160384i
$197$	18.9607	+	5.56736i	1.35089	+	0.396658i	0.875544	−	0.483139i	$-0.160503\pi$
$197$	18.9607	+	5.56736i	1.35089	+	0.396658i	0.475349	+	0.879797i	$0.342322\pi$
$198$	−1.88593	+	1.34296i	−0.134027	+	0.0954403i
$199$	0.597950	−	12.5525i	0.0423875	−	0.889824i	−0.873116	−	0.487513i	$-0.837904\pi$
$199$	0.597950	−	12.5525i	0.0423875	−	0.889824i	0.915503	−	0.402311i	$-0.131793\pi$
$200$	3.61867	+	3.45040i	0.255879	+	0.243980i
$201$	−1.29993	−	1.02227i	−0.0916898	−	0.0721056i
$202$	−6.72501	+	3.07121i	−0.473170	+	0.216089i
$203$	0.713235	+	0.530225i	0.0500593	+	0.0372145i
$204$	−2.75216	−	4.28245i	−0.192690	−	0.299832i
$205$	0.000749447	0	0.000259386i	5.23436e−5	0	1.81163e-5i
$206$	0.278593	+	0.482537i	0.0194105	+	0.0336199i
$207$	−4.67179	−	1.08369i	−0.324712	−	0.0753215i
$208$	−4.56757	−	2.63709i	−0.316704	−	0.182849i
$209$	4.61928	+	4.00263i	0.319522	+	0.276867i
$210$	−0.000238188	0	0.000263774i	−1.64365e−5	0	1.82021e-5i
$211$	−1.69789	−	11.8091i	−0.116888	−	0.812971i	−0.960949	−	0.276725i	$-0.910751\pi$
$211$	−1.69789	−	11.8091i	−0.116888	−	0.812971i	0.844062	−	0.536246i	$-0.180158\pi$
$212$	−1.04808	+	10.9760i	−0.0719825	+	0.753834i
$213$	−1.25031	−	3.12312i	−0.0856696	−	0.213992i
$214$	−6.14651	+	6.44627i	−0.420167	+	0.440658i
$215$	−0.000156724	0	0.000304002i	−1.06885e−5	0	2.07328e-5i
$216$	0.909632	+	0.415415i	0.0618926	+	0.0282654i
$217$	0.656800	−	1.08566i	0.0445865	−	0.0736997i
$218$	5.98835	−	5.18893i	0.405582	−	0.351439i
$219$	13.5576	−	2.61301i	0.916136	−	0.176571i
$220$	−0.000302236	0	7.33216e-5i	−2.03767e−5	0	4.94334e-6i
$221$	2.55211	+	26.7269i	0.171674	+	1.79785i
$222$	8.34730	−	4.30333i	0.560234	−	0.288821i
$223$	−7.05853	−	24.0391i	−0.472674	−	1.60978i	−0.758620	−	0.651533i	$-0.774126\pi$
$223$	−7.05853	−	24.0391i	−0.472674	−	1.60978i	0.285946	−	0.958246i	$-0.407692\pi$
$224$	1.03340	−	2.43559i	0.0690468	−	0.162735i
$225$	2.07708	+	4.54816i	0.138472	+	0.303211i
$226$	−5.12479	+	12.8011i	−0.340896	+	0.851517i
$227$	−20.8890	−	10.7690i	−1.38645	−	0.714766i	−0.406436	−	0.913679i	$-0.633229\pi$
$227$	−20.8890	−	10.7690i	−1.38645	−	0.714766i	−0.980017	+	0.198913i	$0.936259\pi$
$228$	0.499621	−	2.59228i	0.0330882	−	0.171678i
$229$	7.52635	−	13.0360i	0.497355	−	0.861445i	−0.502640	−	0.864496i	$-0.667638\pi$
$229$	7.52635	−	13.0360i	0.497355	−	0.861445i	0.999995	+	0.00305102i	$0.000971170\pi$
$230$	−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
$233$	−0.163171	−	3.42537i	−0.0106897	−	0.224404i	−0.997890	−	0.0649210i	$-0.979320\pi$
$233$	−0.163171	−	3.42537i	−0.0106897	−	0.224404i	0.987201	−	0.159483i	$-0.0509826\pi$
$234$	−3.26028	−	4.14578i	−0.213131	−	0.271018i
$235$	−0.000179003	0	0.000127468i	−1.16769e−5	0	8.31508e-6i
$236$	0.602292	−	0.765877i	0.0392059	−	0.0498543i
$237$	2.53101	−	0.743173i	0.164407	−	0.0482743i
$238$	−13.1510	+	2.90670i	−0.852450	+	0.188413i
$239$	−2.90958	+	6.37109i	−0.188205	+	0.412112i	−0.980089	−	0.198560i	$-0.936373\pi$
$239$	−2.90958	+	6.37109i	−0.188205	+	0.412112i	0.791884	+	0.610672i	$0.209101\pi$
$240$	9.26977e−5	0	9.72185e-5i	5.98361e−6	0	6.27543e-6i
$241$	4.04293	−	11.6813i	0.260428	−	0.752457i	−0.736665	−	0.676258i	$-0.763600\pi$
$241$	4.04293	−	11.6813i	0.260428	−	0.752457i	0.997093	−	0.0761991i	$-0.0242785\pi$
$242$	1.84457	−	5.32954i	0.118574	−	0.342596i
$243$	0.690079	+	0.723734i	0.0442686	+	0.0464276i
$244$	−2.73603	+	5.99107i	−0.175157	+	0.383539i
$245$	0.000436427	0	0.000832888i	2.78823e−5	0	5.32113e-5i
$246$	−5.66475	+	1.66332i	−0.361171	+	0.106049i
$247$	−8.60710	+	10.9448i	−0.547656	+	0.696402i
$248$	−0.390663	−	0.278190i	−0.0248071	−	0.0176651i
$249$	3.23087	+	4.10839i	0.204748	+	0.260358i
$250$	6.39164e−5		0.00134177i	4.04243e−6		8.48610e-5i
$251$	−17.6355	+	20.3524i	−1.11314	+	1.28463i	−0.158342	+	0.987384i	$0.550615\pi$
$251$	−17.6355	+	20.3524i	−1.11314	+	1.28463i	−0.954800	+	0.297249i	$0.903931\pi$
$252$	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
$255$	0.000129412	0	0.000671453i	8.10409e−6	0	4.20480e-5i
$256$	−0.888835	−	0.458227i	−0.0555522	−	0.0286392i
$257$	4.73055	−	11.8164i	0.295084	−	0.737084i	−0.704540	−	0.709664i	$-0.748847\pi$
$257$	4.73055	−	11.8164i	0.295084	−	0.737084i	0.999624	−	0.0274197i	$-0.00872904\pi$
$258$	1.05771	+	2.31606i	0.0658502	+	0.144192i
$259$	−3.03193	−	24.6613i	−0.188395	−	1.53238i
$260$	−0.000199600	0	0.000679776i	−1.23787e−5	0	4.21579e-5i
$261$	0.298568	−	0.153922i	0.0184809	−	0.00952755i
$262$	1.06283	+	11.1305i	0.0656619	+	0.687642i
$263$	−8.88093	+	2.15449i	−0.547622	+	0.132852i	−0.500018	−	0.866015i	$-0.666673\pi$
$263$	−8.88093	+	2.15449i	−0.547622	+	0.132852i	−0.0476032	+	0.998866i	$0.515158\pi$
$264$	2.27339	−	0.438160i	0.139917	−	0.0269669i
$265$	−0.00111934		0.000969916i	−6.87606e−5		5.95814e-5i
$266$	−5.97622	−	3.61547i	−0.366426	−	0.221678i
$267$	−6.77078	−	3.09211i	−0.414365	−	0.189234i
$268$	0.757787	+	1.46990i	0.0462892	+	0.0897886i
$269$	−2.83312	+	2.97129i	−0.172738	+	0.181163i	−0.804412	−	0.594071i	$-0.797520\pi$
$269$	−2.83312	+	2.97129i	−0.172738	+	0.181163i	0.631674	+	0.775234i	$0.282368\pi$
$270$	4.99251e−5	0	0.000124707i	3.03834e−6	0	7.58942e-6i
$271$	−2.14530	+	22.4666i	−0.130318	+	1.36475i	0.659636	+	0.751585i	$0.270710\pi$
$271$	−2.14530	+	22.4666i	−0.130318	+	1.36475i	−0.789954	+	0.613166i	$0.789896\pi$
$272$	0.724462	+	5.03875i	0.0439270	+	0.305519i
$273$	−13.2773	+	4.29307i	−0.803581	+	0.259829i
$274$	−3.23235	−	2.80085i	−0.195273	−	0.169205i
$275$	10.0252	+	5.78807i	0.604544	+	0.349034i
$276$	3.79943	+	2.92649i	0.228699	+	0.176154i
$277$	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	$0.800670\pi$
$278$	−2.12323	+	0.734858i	−0.127343	+	0.0440738i
$279$	−0.259286	−	0.403457i	−0.0155231	−	0.0241544i
$280$	0.000326239	0	0.000140991i	1.94965e−5	0	8.42580e-6i
$281$	−4.25856	+	1.94482i	−0.254044	+	0.116018i	−0.538367	−	0.842710i	$-0.680959\pi$
$281$	−4.25856	+	1.94482i	−0.254044	+	0.116018i	0.284323	+	0.958729i	$0.408231\pi$
$282$	1.28591	+	1.01125i	0.0765750	+	0.0602192i
$283$	−5.63076	−	5.36892i	−0.334714	−	0.319149i	0.504019	−	0.863693i	$-0.331854\pi$
$283$	−5.63076	−	5.36892i	−0.334714	−	0.319149i	−0.838732	+	0.544544i	$0.816703\pi$
$284$	−0.160070	+	3.36028i	−0.00949840	+	0.199396i
$285$	0.000288871	0	0.000205704i	1.71112e−5	0	1.21849e-5i
$286$	−11.7163	−	3.44021i	−0.692798	−	0.203424i
$287$	−1.06246	+	15.5841i	−0.0627151	+	0.919898i
$288$	−0.654861	−	0.755750i	−0.0385880	−	0.0445330i
$289$	6.45123	−	6.15123i	0.379484	−	0.361837i
$290$	4.49180e−5	0	4.28915e-6i	2.63768e−6	0	2.51868e-7i
$291$	−18.5714	−	0.884665i	−1.08867	−	0.0518600i
$292$	−13.4179	−	3.25514i	−0.785222	−	0.190493i
$293$	2.97340	−	20.6804i	0.173708	−	1.20816i	−0.697258	−	0.716821i	$-0.745597\pi$
$293$	2.97340	−	20.6804i	0.173708	−	1.20816i	0.870966	−	0.491344i	$-0.163494\pi$
$294$	−2.95024	−	6.34792i	−0.172061	−	0.370218i
$295$	0.000129549	0	1.86263e-5i	7.54263e−6	0	1.08447e-6i
$296$	−9.38064	+	0.446855i	−0.545239	+	0.0259729i
$297$	2.27339	+	0.438160i	0.131915	+	0.0254246i
$298$	−10.9295	+	6.31017i	−0.633131	+	0.365538i
$299$	−10.7386	−	22.9013i	−0.621029	−	1.32442i
$300$		−	5.00000i		−	0.288675i
$301$	6.71769	−	0.502942i	0.387201	−	0.0289891i
$302$	−3.37951	+	2.17188i	−0.194469	+	0.124977i
$303$	6.86353	+	2.74774i	0.394299	+	0.157854i
$304$	−1.53134	+	2.15047i	−0.0878286	+	0.123338i
$305$	−0.000821352	0	0.000328820i	−4.70305e−5	0	1.88282e-5i
$306$	−1.20015	+	4.94707i	−0.0686077	+	0.282805i
$307$	−17.5285	+	27.2749i	−1.00040	+	1.55666i	−0.180968	+	0.983489i	$0.557923\pi$
$307$	−17.5285	+	27.2749i	−1.00040	+	1.55666i	−0.819436	+	0.573170i	$0.805713\pi$
$308$	0.995679	−	6.04405i	0.0567341	−	0.344392i
$309$	0.156977	−	0.534616i	0.00893013	−	0.0304132i
$310$	−1.21921e−5	0	6.32588e-5i	−6.92467e−7	0	3.59286e-6i
$311$	−13.7220	−	4.74924i	−0.778104	−	0.269304i	−0.0909880	−	0.995852i	$-0.529002\pi$
$311$	−13.7220	−	4.74924i	−0.778104	−	0.269304i	−0.687116	+	0.726548i	$0.741124\pi$
$312$	1.24343	+	5.12550i	0.0703955	+	0.290174i
$313$	8.88859	+	12.4823i	0.502413	+	0.705540i	0.985432	−	0.170069i	$-0.0543992\pi$
$313$	8.88859	+	12.4823i	0.502413	+	0.705540i	−0.483019	+	0.875610i	$0.660460\pi$
$314$	−15.3026	−	9.83435i	−0.863573	−	0.554985i
$315$	0.000355271	0	9.64051e-6i	2.00172e−5	0	5.43181e-7i
$316$	−2.61102	−	0.375408i	−0.146881	−	0.0211183i
$317$	19.2280	+	1.83605i	1.07995	+	0.103123i	0.619833	−	0.784734i	$-0.287201\pi$
$317$	19.2280	+	1.83605i	1.07995	+	0.103123i	0.460119	+	0.887857i	$0.347807\pi$
$318$	8.66696	−	6.81577i	0.486019	−	0.382210i
$319$	0.356365	−	0.691252i	0.0199526	−	0.0387027i
$320$	−4.39347e−5	0	0.000126941i	−2.45603e−6	0	7.09622e-6i
$321$	8.90696			0.497138
$322$	10.7451	−	6.74853i	0.598801	−	0.376081i
$323$	13.4390			0.747768
$324$	−0.327068	−	0.945001i	−0.0181704	−	0.0525000i
$325$	−12.0838	+	23.4393i	−0.670290	+	1.30018i
$326$	−14.8490	+	11.6774i	−0.822410	+	0.646750i
$327$	−7.88784	−	0.753198i	−0.436199	−	0.0416519i
$328$	5.84380	+	0.840212i	0.322670	+	0.0463929i
$329$	3.68826	−	2.26499i	0.203340	−	0.124873i
$330$	0.000261632	0	0.000168141i	1.44024e−5	0	9.25584e-6i
$331$	13.1004	+	18.3970i	0.720064	+	1.01119i	0.998709	+	0.0507946i	$0.0161754\pi$
$331$	13.1004	+	18.3970i	0.720064	+	1.01119i	−0.278645	+	0.960394i	$0.589885\pi$
$332$	−1.23222	−	5.07927i	−0.0676267	−	0.278761i
$333$	−8.87476	−	3.07159i	−0.486334	−	0.168322i
$334$	0.351020	+	1.82126i	0.0192070	+	0.0996552i
$335$	−6.25856e−5	0	0.000213147i	−3.41942e−6	0	1.16455e-5i
$336$	−2.47584	+	0.932843i	−0.135068	+	0.0508907i
$337$	14.8679	−	23.1349i	0.809906	−	1.26024i	−0.152413	−	0.988317i	$-0.548705\pi$
$337$	14.8679	−	23.1349i	0.809906	−	1.26024i	0.962319	−	0.271922i	$-0.0876591\pi$
$338$	3.49321	−	14.3992i	0.190006	−	0.783214i
$339$	12.8011	−	5.12479i	0.695260	−	0.278340i
$340$	−0.000396649	0	0.000557016i	−2.15113e−5	0	3.02084e-5i
$341$	−1.03082	−	0.412680i	−0.0558223	−	0.0223479i
$342$	−2.22090	+	1.42729i	−0.120093	+	0.0771788i
$343$	−18.4590	+	1.50565i	−0.996690	+	0.0812972i
$344$		−	2.54616i		−	0.137280i
$345$	9.80963e−5	0	0.000636707i	5.28133e−6	0	3.42792e-5i
$346$	5.20774	−	3.00669i	0.279970	−	0.161641i
$347$	8.64797	+	1.66676i	0.464247	+	0.0894763i	0.416011	−	0.909360i	$-0.363428\pi$
$347$	8.64797	+	1.66676i	0.464247	+	0.0894763i	0.0482364	+	0.998836i	$0.484640\pi$
$348$	−0.335528	+	0.0159832i	−0.0179862	+	0.000856789i
$349$	24.7263	−	3.55511i	1.32357	−	0.190301i	0.555955	−	0.831212i	$-0.312353\pi$
$349$	24.7263	−	3.55511i	1.32357	−	0.190301i	0.767615	+	0.640912i	$0.221443\pi$
$350$	−12.4100	−	4.58169i	−0.663342	−	0.244902i
$351$	−0.750593	+	5.22049i	−0.0400637	+	0.278649i
$352$	−2.24997	−	0.545836i	−0.119924	−	0.0290931i
$353$	22.6717	+	1.07999i	1.20669	+	0.0574819i	0.641268	−	0.767317i	$-0.278409\pi$
$353$	22.6717	+	1.07999i	1.20669	+	0.0574819i	0.565426	+	0.824799i	$0.308712\pi$
$354$	−0.969921	+	0.0926162i	−0.0515507	+	0.00492249i
$355$	−0.000327052	0	0.000311844i	−1.73581e−5	0	1.65509e-5i
$356$	4.87441	+	5.62536i	0.258343	+	0.298144i
$357$	11.1789	+	7.51194i	0.591649	+	0.397574i
$358$	−21.0675	−	6.18596i	−1.11345	−	0.326938i
$359$	−12.2772	+	8.74253i	−0.647964	+	0.461413i	−0.856185	−	0.516669i	$-0.827172\pi$
$359$	−12.2772	+	8.74253i	−0.647964	+	0.461413i	0.208221	+	0.978082i	$0.433233\pi$
$360$	6.39164e−6	0	0.000134177i	3.36869e−7	0	7.07175e-6i
$361$	−8.70685	−	8.30196i	−0.458255	−	0.436945i
$362$	−6.05117	−	4.75869i	−0.318042	−	0.250111i
$363$	−5.13007	+	2.34282i	−0.269259	+	0.122966i
$364$	13.8609	+	1.61049i	0.726508	+	0.0844125i
$365$	−0.00100272	−	0.00156027i	−5.24849e−5	−	8.16681e-5i
$366$	6.22402	−	2.15416i	0.325335	−	0.112600i
$367$	2.66151	+	4.60988i	0.138930	+	0.240634i	0.927092	−	0.374834i	$-0.122300\pi$
$367$	2.66151	+	4.60988i	0.138930	+	0.240634i	−0.788162	+	0.615468i	$0.788967\pi$
$368$	−2.24038	−	4.24037i	−0.116788	−	0.221044i
$369$	5.11292	+	2.95195i	0.266168	+	0.153672i
$370$	−0.000953394	0	0.000826121i	−4.95646e−5	0	4.29480e-5i
$371$	−8.97489	−	27.7569i	−0.465953	−	1.44107i
$372$	0.0682529	+	0.474709i	0.00353875	+	0.0246125i
$373$	2.16102	−	22.6312i	0.111893	−	1.17180i	−0.748843	−	0.662747i	$-0.769390\pi$
$373$	2.16102	−	22.6312i	0.111893	−	1.17180i	0.860736	−	0.509051i	$-0.170004\pi$
$374$	4.38034	+	10.9416i	0.226502	+	0.565775i
$375$	0.000926977	0	0.000972185i	4.78689e−5	0	5.02034e-5i
$376$	−0.749617	−	1.45405i	−0.0386586	−	0.0749872i
$377$	1.61154	+	0.735966i	0.0829986	+	0.0379042i
$378$	−2.64520	−	0.0541571i	−0.136054	−	0.00278554i
$379$	7.07898	−	6.13397i	0.363623	−	0.315081i	−0.453817	−	0.891095i	$-0.649938\pi$
$379$	7.07898	−	6.13397i	0.363623	−	0.315081i	0.817440	+	0.576014i	$0.195393\pi$
$380$	−0.000348219	0	6.71137e-5i	−1.78633e−5	0	3.44286e-6i
$381$	4.14803	−	1.00630i	0.212510	−	0.0515544i
$382$	1.21880	+	12.7639i	0.0623593	+	0.653056i
$383$	19.3521	−	9.97669i	0.988845	−	0.509785i	0.113632	−	0.993523i	$-0.463751\pi$
$383$	19.3521	−	9.97669i	0.988845	−	0.509785i	0.875213	+	0.483738i	$0.160721\pi$
$384$	0.281733	+	0.959493i	0.0143771	+	0.0489639i
$385$	0.000657068	0	0.000495297i	3.34873e−5	0	2.52427e-5i
$386$	9.79785	+	21.4543i	0.498698	+	1.09200i
$387$	0.946310	−	2.36377i	0.0481037	−	0.120157i
$388$	16.5256	+	8.51956i	0.838962	+	0.432515i
$389$	5.55271	−	28.8102i	0.281533	−	1.46073i	−0.515548	−	0.856861i	$-0.672411\pi$
$389$	5.55271	−	28.8102i	0.281533	−	1.46073i	0.797081	−	0.603873i	$-0.206376\pi$
$390$	−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
$394$	0.940274	+	19.7388i	0.0473703	+	0.994425i
$395$	−0.000219040	0	0.000278532i	−1.10211e−5	0	1.40145e-5i
$396$	−1.88593	−	1.34296i	−0.0947715	−	0.0674865i
$397$	−8.41986	+	10.7067i	−0.422580	+	0.537355i	−0.950000	−	0.312250i	$-0.898917\pi$
$397$	−8.41986	+	10.7067i	−0.422580	+	0.537355i	0.527419	+	0.849605i	$0.323160\pi$
$398$	12.0577	−	3.54046i	0.604398	−	0.177467i
$399$	1.50743	+	6.82015i	0.0754659	+	0.341435i
$400$	−2.07708	+	4.54816i	−0.103854	+	0.227408i
$401$	−4.94056	−	5.18151i	−0.246720	−	0.258752i	0.588716	−	0.808340i	$-0.299633\pi$
$401$	−4.94056	−	5.18151i	−0.246720	−	0.258752i	−0.835436	+	0.549587i	$0.814785\pi$
$402$	0.540885	−	1.56279i	0.0269769	−	0.0779446i
$403$	0.827300	−	2.39033i	0.0412107	−	0.119071i
$404$	−5.10183	−	5.35064i	−0.253825	−	0.266205i
$405$	5.58023e−5	0	0.000122190i	2.77284e−6	0	6.07167e-6i
$406$	−0.267787	+	0.847428i	−0.0132900	+	0.0420571i
$407$	−20.8622	+	6.12570i	−1.03410	+	0.303639i
$408$	3.14678	−	4.00145i	0.155789	−	0.198101i
$409$	−1.12849	−	0.803595i	−0.0558003	−	0.0397352i	0.551816	−	0.833966i	$-0.313935\pi$
$409$	−1.12849	−	0.803595i	−0.0558003	−	0.0397352i	−0.607617	+	0.794230i	$0.707874\pi$
$410$	0.000490240	0	0.000623391i	2.42112e−5	0	3.07871e-5i
$411$	0.203508	+	4.27217i	0.0100383	+	0.210730i
$412$	−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
$416$	0.998143	−	5.17886i	0.0489380	−	0.253914i
$417$	1.99704	+	1.02955i	0.0977954	+	0.0504170i
$418$	−2.27167	+	5.67435i	−0.111111	+	0.277542i
$419$	0.0463027	+	0.101389i	0.00226204	+	0.00495317i	0.910760	−	0.412937i	$-0.135497\pi$
$419$	0.0463027	+	0.101389i	0.00226204	+	0.00495317i	−0.908498	+	0.417890i	$0.862770\pi$
$420$	−0.000327170	0	0.000138815i	−1.59643e−5	0	6.77350e-6i
$421$	3.42616	+	11.6684i	0.166981	+	0.568684i	0.999883	+	0.0152648i	$0.00485914\pi$
$421$	3.42616	+	11.6684i	0.166981	+	0.568684i	−0.832903	+	0.553419i	$0.813323\pi$
$422$	10.6043	−	5.46688i	0.516208	−	0.266124i
$423$	−0.155503	−	1.62850i	−0.00756082	−	0.0791805i
$424$	−10.7151	+	2.59946i	−0.520372	+	0.126241i
$425$	24.9928	−	4.81697i	1.21233	−	0.233658i
$426$	2.54241	−	2.20301i	0.123180	−	0.106736i
$427$	0.356693	−	17.4220i	0.0172616	−	0.843108i
$428$	−8.10206	−	3.70009i	−0.391628	−	0.178850i
$429$	5.59536	+	10.8535i	0.270147	+	0.524011i
$430$	0.000236023	0	0.000247534i	1.13820e−5	0	1.19371e-5i
$431$	−10.9772	−	27.4196i	−0.528752	−	1.32076i	−0.916884	−	0.399154i	$-0.869304\pi$
$431$	−10.9772	−	27.4196i	−0.528752	−	1.32076i	0.388132	−	0.921604i	$-0.373120\pi$
$432$	−0.0950560	+	0.995472i	−0.00457339	+	0.0478947i
$433$	−1.20848	−	8.40519i	−0.0580761	−	0.403928i	−0.998036	−	0.0626431i	$-0.980047\pi$
$433$	−1.20848	−	8.40519i	−0.0580761	−	0.403928i	0.939960	−	0.341285i	$-0.110862\pi$
$434$	1.24077	+	0.265590i	0.0595589	+	0.0127487i
$435$	−3.41012e−5	0	2.95488e-5i	−1.63503e−6	0	1.41676e-6i
$436$	6.86214	+	3.96186i	0.328637	+	0.189739i
$437$	−11.9223	+	4.26122i	−0.570322	+	0.203842i
$438$	6.90354	+	11.9573i	0.329864	+	0.571341i
$439$	16.0377	−	5.55071i	0.765439	−	0.264921i	0.0836747	−	0.996493i	$-0.473334\pi$
$439$	16.0377	−	5.55071i	0.765439	−	0.264921i	0.681764	+	0.731572i	$0.261213\pi$
$440$	−0.000168141	0	0.000261632i	−8.01579e−6	0	1.24728e-5i
$441$	−2.55831	+	6.51575i	−0.121824	+	0.310274i
$442$	−24.4222	+	11.1533i	−1.16165	+	0.530507i
$443$	−25.5575	−	20.0986i	−1.21427	−	0.954914i	−0.214509	−	0.976722i	$-0.568815\pi$
$443$	−25.5575	−	20.0986i	−1.21427	−	0.954914i	−0.999762	+	0.0218081i	$0.993058\pi$
$444$	6.79679	+	6.48072i	0.322561	+	0.307561i
$445$	−4.75756e−5	0	0.000998736i	−2.25530e−6	0	4.73446e-5i
$446$	20.4084	−	14.5327i	0.966365	−	0.688145i
$447$	12.1091	+	3.55556i	0.572742	+	0.168172i
$448$	2.63962	+	0.179959i	0.124711	+	0.00850228i
$449$	26.8987	+	31.0427i	1.26943	+	1.46500i	0.820734	+	0.571310i	$0.193565\pi$
$449$	26.8987	+	31.0427i	1.26943	+	1.46500i	0.448693	+	0.893686i	$0.351890\pi$
$450$	−3.61867	+	3.45040i	−0.170586	+	0.162653i
$451$	13.6070	−	1.29931i	0.640727	−	0.0611820i
$452$	−13.7732	−	0.656099i	−0.647837	−	0.0308603i
$453$	3.90399	+	0.947097i	0.183425	+	0.0444985i
$454$	3.34462	−	23.2624i	0.156971	−	1.09176i
$455$	0.00119825	+	0.00144144i	5.61747e−5	+	6.75759e-5i
$456$	2.61312	−	0.375710i	0.122371	−	0.0175942i
$457$	31.7296	−	1.51147i	1.48425	−	0.0707034i	0.710275	−	0.703924i	$-0.248571\pi$
$457$	31.7296	−	1.51147i	1.48425	−	0.0707034i	0.773971	+	0.633221i	$0.218267\pi$
$458$	14.7807	+	2.84874i	0.690656	+	0.133113i
$459$	4.40855	−	2.54528i	0.205774	−	0.118804i
$460$	0.000175266	0	0.000619920i	8.17183e−6	0	2.89039e-5i
$461$		−	16.7648i		−	0.780814i	−0.920642	−	0.390407i	$-0.872334\pi$
$461$		−	16.7648i		−	0.780814i	0.920642	−	0.390407i	$-0.127666\pi$
$462$	−5.06139	+	3.45027i	−0.235477	+	0.160521i
$463$	7.83270	−	5.03377i	0.364016	−	0.233939i	−0.345828	−	0.938298i	$-0.612402\pi$
$463$	7.83270	−	5.03377i	0.364016	−	0.233939i	0.709844	+	0.704359i	$0.248765\pi$
$464$	0.311847	+	0.124845i	0.0144771	+	0.00579577i
$465$	−3.73690e−5	0	5.24774e-5i	−1.73295e−6	0	2.43358e-6i
$466$	3.18361	−	1.27453i	0.147478	−	0.0590413i
$467$	4.21479	−	17.3736i	0.195037	−	0.803955i	−0.787259	−	0.616622i	$-0.788501\pi$
$467$	4.21479	−	17.3736i	0.195037	−	0.803955i	0.982297	−	0.187333i	$-0.0599842\pi$
$468$	2.85143	−	4.43691i	0.131807	−	0.205096i
$469$	−3.38320	−	2.77452i	−0.156222	−	0.128115i
$470$	6.19108e−5	0	0.000210849i	2.85573e−6	0	9.72573e-6i
$471$	3.44251	+	17.8615i	0.158623	+	0.823013i
$472$	0.920745	+	0.318673i	0.0423807	+	0.0146681i
$473$	−1.38978	−	5.72876i	−0.0639023	−	0.263409i
$474$	1.53011	+	2.14874i	0.0702804	+	0.0986950i
$475$	11.1045	+	7.13643i	0.509510	+	0.327442i
$476$	−7.04809	−	11.4770i	−0.323049	−	0.526046i
$477$	−10.9137	−	1.56915i	−0.499704	−	0.0718465i
$478$	−6.97232	−	0.665776i	−0.318906	−	0.0304519i
$479$	30.3012	−	23.8291i	1.38450	−	1.08878i	0.399401	−	0.916776i	$-0.369218\pi$
$479$	30.3012	−	23.8291i	1.38450	−	1.08878i	0.985096	−	0.172005i	$-0.0550244\pi$
$480$	−6.15532e−5	0	0.000119396i	−2.80950e−6	0	5.44968e-6i
$481$	−16.2001	−	46.8070i	−0.738659	−	2.13422i
$482$	12.3611			0.563034
$483$	−12.2991	−	3.11958i	−0.559629	−	0.141946i
$484$	5.63972			0.256351
$485$	0.000816855		0.00236015i	3.70915e−5		0.000107169i
$486$	−0.458227	+	0.888835i	−0.0207856	+	0.0403184i
$487$	−21.5868	+	16.9761i	−0.978193	+	0.769259i	−0.973018	−	0.230727i	$-0.925889\pi$
$487$	−21.5868	+	16.9761i	−0.978193	+	0.769259i	−0.00517421	+	0.999987i	$0.501647\pi$
$488$	−6.55644	−	0.626064i	−0.296796	−	0.0283406i
$489$	18.6983	+	2.68841i	0.845566	+	0.121574i
$490$	−0.000644338	0	0.000684835i	−2.91082e−5	0	3.09377e-5i
$491$	24.1917	+	15.5471i	1.09176	+	0.701630i	0.957244	−	0.289282i	$-0.0934165\pi$
$491$	24.1917	+	15.5471i	1.09176	+	0.701630i	0.134513	+	0.990912i	$0.457053\pi$
$492$	−3.42459	−	4.80917i	−0.154393	−	0.216814i
$493$	−0.403139	−	1.66176i	−0.0181565	−	0.0748420i
$494$	−13.1580	−	4.55402i	−0.592005	−	0.204895i
$495$	−5.88576e−5	0	0.000305382i	−2.64545e−6	0	1.37259e-5i
$496$	0.135116	−	0.460164i	0.00606690	−	0.0206620i
$497$	−3.13817	−	8.32897i	−0.140766	−	0.373605i
$498$	−2.82571	+	4.39690i	−0.126623	+	0.197030i
$499$	8.41651	−	34.6933i	0.376775	−	1.55309i	−0.395905	−	0.918291i	$-0.629569\pi$
$499$	8.41651	−	34.6933i	0.376775	−	1.55309i	0.772680	−	0.634795i	$-0.218916\pi$
$500$	−0.00124707		0.000499251i	−5.57706e−5		2.23272e-5i
$501$	1.07588	−	1.51086i	0.0480668	−	0.0675003i
$502$	−25.0011	−	10.0089i	−1.11585	−	0.446720i
$503$	22.8486	−	14.6839i	1.01877	−	0.654723i	0.0791202	−	0.996865i	$-0.474789\pi$
$503$	22.8486	−	14.6839i	1.01877	−	0.654723i	0.939648	+	0.342142i	$0.111153\pi$
$504$	2.38366	+	1.14812i	0.106177	+	0.0511412i
$505$		0	0.000993110i		0	4.41928e-5i
$506$	−7.35531	−	8.31780i	−0.326984	−	0.369771i
$507$	−12.8318	+	7.40844i	−0.569880	+	0.329020i
$508$	−4.19121	−	0.807790i	−0.185955	−	0.0358399i
$509$	−21.7927	+	1.03811i	−0.965943	+	0.0460136i	−0.524622	−	0.851335i	$-0.675793\pi$
$509$	−21.7927	+	1.03811i	−0.965943	+	0.0460136i	−0.441322	+	0.897349i	$0.645490\pi$
$510$	0.000676850	0	9.73164e-5i	2.99714e−5	0	4.30924e-6i
$511$	36.0040	−	6.17768i	1.59272	−	0.273285i
$512$	0.142315	−	0.989821i	0.00628949	−	0.0437443i
$513$	2.56557	+	0.622401i	0.113273	+	0.0274797i
$514$	12.7137	+	0.605627i	0.560776	+	0.0267131i
$515$	−7.45073e−5	0	7.11459e-6i	−3.28319e−6	0	3.13506e-7i
$516$	−1.84274	+	1.75705i	−0.0811221	+	0.0773497i
$517$	−2.48029	−	2.86241i	−0.109083	−	0.125888i
$518$	22.3133	−	10.9311i	0.980390	−	0.480285i
$519$	−5.76979	−	1.69416i	−0.253266	−	0.0743655i
$520$	0.000577106	0	0.000410956i	2.53078e−5	0	1.80216e-5i
$521$	0.837704	−	17.5856i	0.0367005	−	0.770437i	−0.903248	−	0.429120i	$-0.858824\pi$
$521$	0.837704	−	17.5856i	0.0367005	−	0.770437i	0.939948	−	0.341318i	$-0.110873\pi$
$522$	0.243109	+	0.231804i	0.0106406	+	0.0101458i
$523$	22.4049	+	17.6194i	0.979697	+	0.770442i	0.973300	−	0.229537i	$-0.0737213\pi$
$523$	22.4049	+	17.6194i	0.979697	+	0.770442i	0.00639712	+	0.999980i	$0.497964\pi$
$524$	−10.1707	+	4.64479i	−0.444308	+	0.202909i
$525$	5.24796	+	12.1433i	0.229040	+	0.529976i
$526$	−4.94066	−	7.68782i	−0.215423	−	0.335205i
$527$	−2.30711	+	0.798499i	−0.100499	+	0.0347832i
$528$	1.15761	+	2.00505i	0.0503787	+	0.0872584i
$529$	2.81426	−	22.8272i	0.122359	−	0.992486i
$530$	−0.00128267		0.000740551i	−5.57157e−5		3.21675e-5i
$531$	0.736351	+	0.638052i	0.0319549	+	0.0276891i
$532$	1.46199	−	6.83004i	0.0633852	−	0.296120i
$533$	4.43142	+	30.8212i	0.191946	+	1.33501i
$534$	0.707542	−	7.40972i	0.0306184	−	0.320650i
$535$	−0.000444681	−	0.00111076i	−1.92252e−5	−	4.80223e-5i
$536$	−1.14121	+	1.19687i	−0.0492928	+	0.0516968i
$537$	10.0612	+	19.5160i	0.434174	+	0.842179i
$538$	−3.73449	−	1.70548i	−0.161005	−	0.0735287i
$539$	3.92563	+	15.7240i	0.169089	+	0.677279i
$540$	−0.000101519	0	8.79669e-5i	−4.36869e−6	0	3.78549e-6i
$541$	16.7776	−	3.23362i	0.721326	−	0.139024i	0.184640	−	0.982806i	$-0.440888\pi$
$541$	16.7776	−	3.23362i	0.721326	−	0.139024i	0.536686	+	0.843782i	$0.319676\pi$
$542$	−21.9326	+	5.32080i	−0.942088	+	0.228548i
$543$	0.731757	+	7.66331i	0.0314027	+	0.328864i
$544$	−4.52467	+	2.33263i	−0.193994	+	0.100011i
$545$	0.000299872		0.00102127i	1.28451e−5		4.37465e-5i
$546$	−8.39955	−	11.1430i	−0.359467	−	0.476875i
$547$	15.3597	+	33.6332i	0.656735	+	1.43805i	0.885533	+	0.464576i	$0.153793\pi$
$547$	15.3597	+	33.6332i	0.656735	+	1.43805i	−0.228798	+	0.973474i	$0.573479\pi$
$548$	1.58960	−	3.97064i	0.0679045	−	0.169617i
$549$	−5.85410	−	3.01800i	−0.249847	−	0.128805i
$550$	−2.19080	+	11.3669i	−0.0934160	+	0.484688i
$551$	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
$555$	6.00256e−5		0.00126009i	2.54795e−6		5.34880e-5i
$556$	−1.38888	−	1.76611i	−0.0589017	−	0.0748996i
$557$	−21.9404	−	15.6237i	−0.929646	−	0.661998i	0.0115234	−	0.999934i	$-0.496332\pi$
$557$	−21.9404	−	15.6237i	−0.929646	−	0.661998i	−0.941169	+	0.337936i	$0.890271\pi$
$558$	0.296463	−	0.376984i	0.0125503	−	0.0159590i
$559$	12.8849	−	3.78335i	0.544973	−	0.160019i
$560$	0.000239939	0	0.000262182i	1.01393e−5	0	1.10792e-5i
$561$	4.89600	−	10.7207i	0.206709	−	0.452630i
$562$	−3.23069	−	3.38825i	−0.136279	−	0.142925i
$563$	5.58551	−	16.1383i	0.235401	−	0.680147i	−0.763989	−	0.645229i	$-0.776762\pi$
$563$	5.58551	−	16.1383i	0.235401	−	0.680147i	0.999390	−	0.0349178i	$-0.0111169\pi$
$564$	−0.535054	+	1.54594i	−0.0225298	+	0.0650957i
$565$	−0.00127819	−	0.00134053i	−5.37739e−5	−	5.63965e-5i
$566$	3.23199	−	7.07707i	0.135851	−	0.297471i
$567$	1.78620	+	1.95179i	0.0750133	+	0.0819675i
$568$	−3.22782	+	0.947774i	−0.135436	+	0.0397677i
$569$	11.3245	−	14.4003i	0.474749	−	0.603692i	−0.488414	−	0.872612i	$-0.662424\pi$
$569$	11.3245	−	14.4003i	0.474749	−	0.603692i	0.963162	+	0.268920i	$0.0866668\pi$
$570$	0.000288871	0	0.000205704i	1.20995e−5	0	8.61600e-6i
$571$	24.4342	+	31.0706i	1.02254	+	1.30027i	0.953092	+	0.302681i	$0.0978815\pi$
$571$	24.4342	+	31.0706i	1.02254	+	1.30027i	0.0694485	+	0.997586i	$0.477876\pi$
$572$	−0.581018	−	12.1971i	−0.0242936	−	0.509985i
$573$	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
$577$	−0.961878	+	4.99070i	−0.0400435	+	0.207765i	−0.996440	−	0.0843064i	$-0.973133\pi$
$577$	−0.961878	+	4.99070i	−0.0400435	+	0.207765i	0.956396	+	0.292072i	$0.0943447\pi$
$578$	7.92291	+	4.08454i	0.329549	+	0.169895i
$579$	8.76592	−	21.8962i	0.364299	−	0.909975i
$580$	1.87445e−5	0	4.10447e-5i	7.78323e−7	0	1.70429e-6i
$581$	8.32379	+	11.0425i	0.345329	+	0.458119i
$582$	−5.23810	−	17.8393i	−0.217126	−	0.739464i
$583$	−22.6898	+	11.6974i	−0.939714	+	0.484456i
$584$	−1.31245	−	13.7446i	−0.0543094	−	0.568754i
$585$	0.000688504	0	0.000167029i	2.84661e−5	0	6.90581e-6i
$586$	20.5155	−	3.95405i	0.847489	−	0.163340i
$587$	−21.1122	+	18.2938i	−0.871393	+	0.755066i	−0.970777	−	0.239983i	$-0.922858\pi$
$587$	−21.1122	+	18.2938i	−0.871393	+	0.755066i	0.0993845	+	0.995049i	$0.468313\pi$
$588$	5.03386	−	4.86418i	0.207593	−	0.200595i
$589$	−1.15170	−	0.525963i	−0.0474549	−	0.0216719i
$590$	5.99732e−5	0	0.000116332i	2.46906e−6	0	4.78931e-6i
$591$	13.6368	−	14.3018i	0.560941	−	0.588298i
$592$	−3.49038	−	8.71856i	−0.143454	−	0.358331i
$593$	1.37308	−	14.3795i	0.0563855	−	0.590496i	−0.922488	−	0.386027i	$-0.873847\pi$
$593$	1.37308	−	14.3795i	0.0563855	−	0.590496i	0.978873	−	0.204469i	$-0.0655467\pi$
$594$	0.329491	+	2.29166i	0.0135192	+	0.0940281i
$595$	0.000378684	−	0.00176912i	1.55245e−5	−	7.25267e-5i
$596$	−9.53781	−	8.26456i	−0.390684	−	0.338530i
$597$	−10.8831	−	6.28337i	−0.445417	−	0.257161i
$598$	18.1295	−	17.6383i	0.741371	−	0.721283i
$599$	−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	$0.870242\pi$
$600$	4.72500	−	1.63534i	0.192897	−	0.0667625i
$601$	6.99833	+	10.8896i	0.285468	+	0.444197i	0.954140	−	0.299361i	$-0.0967734\pi$
$601$	6.99833	+	10.8896i	0.285468	+	0.444197i	−0.668672	+	0.743557i	$0.733137\pi$
$602$	2.67242	+	6.18373i	0.108920	+	0.252030i
$603$	−1.50429	+	0.686988i	−0.0612596	+	0.0279763i
$604$	−3.15775	−	2.48329i	−0.128487	−	0.101043i
$605$	0.000548285	0	0.000522789i	2.22910e−5	0	2.12544e-5i
$606$	−0.351778	+	7.38474i	−0.0142900	+	0.299984i
$607$	2.00127	−	1.42510i	0.0812289	−	0.0578429i	−0.538721	−	0.842484i	$-0.681092\pi$
$607$	2.00127	−	1.42510i	0.0812289	−	0.0578429i	0.619950	+	0.784641i	$0.287153\pi$
$608$	−2.53305	−	0.743771i	−0.102729	−	0.0301639i
$609$	0.798106	−	0.390985i	0.0323409	−	0.0158435i
$610$	−0.000579373	0	0.000668632i	−2.34581e−5	0	2.70721e-5i
$611$	6.24443	−	5.95405i	0.252622	−	0.240875i
$612$	−5.06751	+	0.483889i	−0.204842	+	0.0195600i
$613$	16.7919	+	0.799897i	0.678219	+	0.0323076i	0.383865	−	0.923389i	$-0.374593\pi$
$613$	16.7919	+	0.799897i	0.678219	+	0.0323076i	0.294354	+	0.955697i	$0.404896\pi$
$614$	−31.5078	−	7.64371i	−1.27155	−	0.308475i
$615$	0.000112865	0	0.000784993i	4.55115e−6	0	3.16540e-5i
$616$	6.03729	−	1.03590i	0.243249	−	0.0417376i
$617$	−32.3583	+	4.65242i	−1.30270	+	0.187299i	−0.758508	−	0.651664i	$-0.774071\pi$
$617$	−32.3583	+	4.65242i	−1.30270	+	0.187299i	−0.544188	+	0.838963i	$0.683162\pi$
$618$	0.556554	−	0.0265120i	0.0223879	−	0.00106647i
$619$	−17.7187	−	3.41501i	−0.712177	−	0.137261i	−0.179720	−	0.983718i	$-0.557519\pi$
$619$	−17.7187	−	3.41501i	−0.712177	−	0.137261i	−0.532457	+	0.846457i	$0.678731\pi$
$620$	5.57920e−5	0	3.22115e-5i	2.24066e−6	0	1.29364e-6i
$621$	−3.10396	+	3.65588i	−0.124558	+	0.146705i
$622$		−	14.5206i		−	0.582225i
$623$	−17.7426	−	8.54592i	−0.710841	−	0.342385i
$624$	−4.43691	+	2.85143i	−0.177619	+	0.114149i
$625$	23.2092	+	9.29156i	0.928368	+	0.371662i
$626$	−8.88859	+	12.4823i	−0.355260	+	0.498892i
$627$	5.67435	−	2.27167i	0.226612	−	0.0907217i
$628$	4.28850	−	17.6774i	0.171130	−	0.705406i
$629$	−25.8463	+	40.2177i	−1.03056	+	1.60358i
$630$	0.000125308	0	0.000332578i	4.99239e−6	0	1.32502e-5i
$631$	−6.67316	+	22.7267i	−0.265654	+	0.904736i	0.713335	+	0.700824i	$0.247184\pi$
$631$	−6.67316	+	22.7267i	−0.265654	+	0.904736i	−0.978989	+	0.203912i	$0.934634\pi$
$632$	−0.499219	−	2.59020i	−0.0198579	−	0.103032i
$633$	−11.2744	−	3.90209i	−0.448115	−	0.155094i
$634$	4.55379	+	18.7710i	0.180854	+	0.745491i
$635$	−0.000332583	0	0.000467048i	−1.31982e−5	0	1.85342e-5i
$636$	9.27560	+	5.96106i	0.367801	+	0.236372i
$637$	−35.3537	+	10.6370i	−1.40076	+	0.421452i
$638$	0.769790	+	0.110679i	0.0304763	+	0.00438183i
$639$	−3.34886	−	0.319777i	−0.132479	−	0.0126502i
$640$	0.000105590	0	8.30367e-5i	4.17380e−6	0	3.28232e-6i
$641$	−1.22067	+	2.36778i	−0.0482137	+	0.0935215i	−0.911711	−	0.410831i	$-0.865239\pi$
$641$	−1.22067	+	2.36778i	−0.0482137	+	0.0935215i	0.863498	+	0.504353i	$0.168269\pi$
$642$	2.91318	+	8.41709i	0.114974	+	0.332196i
$643$	21.4780			0.847011			0.423505	−	0.905894i	$-0.360799\pi$
$643$	21.4780			0.847011			0.423505	+	0.905894i	$0.360799\pi$
$644$	9.89175	+	7.94690i	0.389790	+	0.313152i
$645$	−0.000342023	0		−1.34671e−5	0
$646$	4.39548	+	12.6999i	0.172938	+	0.499671i
$647$	−5.84700	+	11.3416i	−0.229869	+	0.445885i	−0.975356	−	0.220636i	$-0.929187\pi$
$647$	−5.84700	+	11.3416i	−0.229869	+	0.445885i	0.745487	+	0.666520i	$0.232217\pi$
$648$	0.786053	−	0.618159i	0.0308791	−	0.0242836i
$649$	2.24559	+	0.214428i	0.0881470	+	0.00841702i
$650$	−26.1024	−	3.75296i	−1.02382	−	0.147203i
$651$	−0.664013	−	1.08127i	−0.0260247	−	0.0423782i
$652$	−15.8918	−	10.2130i	−0.622369	−	0.399973i
$653$	13.8944	+	19.5119i	0.543729	+	0.763560i	0.991432	−	0.130622i	$-0.0416975\pi$
$653$	13.8944	+	19.5119i	0.543729	+	0.763560i	−0.447704	+	0.894182i	$0.647758\pi$
$654$	−1.86809	−	7.70036i	−0.0730480	−	0.301108i
$655$	−0.00141934		0.000491238i	−5.54582e−5		1.91943e-5i
$656$	1.11732	+	5.79720i	0.0436240	+	0.226343i
$657$	3.88991	−	13.2478i	0.151760	−	0.516846i
$658$	3.34672	+	2.74460i	0.130469	+	0.106996i
$659$	−15.6655	+	24.3761i	−0.610243	+	0.949556i	0.389352	+	0.921089i	$0.372699\pi$
$659$	−15.6655	+	24.3761i	−0.610243	+	0.949556i	−0.999595	+	0.0284673i	$0.990937\pi$
$660$	−7.33216e−5	0	0.000302236i	−2.85404e−6	0	1.17645e-5i
$661$	26.2943	−	10.5266i	1.02273	−	0.409439i	0.201167	−	0.979557i	$-0.435527\pi$
$661$	26.2943	−	10.5266i	1.02273	−	0.409439i	0.821563	+	0.570118i	$0.193103\pi$
$662$	−13.1004	+	18.3970i	−0.509162	+	0.715018i
$663$	24.9253	+	9.97857i	0.968017	+	0.387536i
$664$	4.39690	−	2.82571i	0.170633	−	0.109659i
$665$	0.000775261	0	0.000528484i	3.00633e−5	0	2.04937e-5i
$666$		−	9.39128i		−	0.363905i
$667$	0.884550	+	1.34639i	0.0342499	+	0.0521325i
$668$	−1.60629	+	0.927391i	−0.0621492	+	0.0358819i
$669$	−24.6012	−	4.74150i	−0.951139	−	0.183317i
$670$	−0.000221894	0	1.05701e-5i	−8.57250e−6	0	4.08359e-7i
$671$	−15.0935	+	2.17012i	−0.582678	+	0.0837764i
$672$	−1.69131	−	2.03457i	−0.0652436	−	0.0784853i
$673$	5.74720	−	39.9727i	0.221538	−	1.54083i	−0.510684	−	0.859768i	$-0.670608\pi$
$673$	5.74720	−	39.9727i	0.221538	−	1.54083i	0.732223	−	0.681065i	$-0.238483\pi$
$674$	26.7253	+	6.48349i	1.02942	+	0.249735i
$675$	4.99434	+	0.237910i	0.192232	+	0.00915714i
$676$	14.7498	−	1.40843i	0.567299	−	0.0541705i
$677$	−29.6481	+	28.2694i	−1.13947	+	1.08648i	−0.144177	+	0.989552i	$0.546053\pi$
$677$	−29.6481	+	28.2694i	−1.13947	+	1.08648i	−0.995291	+	0.0969285i	$0.969098\pi$
$678$	9.02976	+	10.4209i	0.346786	+	0.400212i
$679$	−49.0771	−	3.34588i	−1.88341	−	0.128403i
$680$	−0.000656111	0	0.000192652i	−2.51607e−5	0	7.38785e-6i
$681$	−19.1438	+	13.6322i	−0.733592	+	0.522389i
$682$	0.0528332	−	1.10910i	0.00202309	−	0.0424698i
$683$	−35.3891	−	33.7434i	−1.35413	−	1.29116i	−0.920862	−	0.389889i	$-0.872513\pi$
$683$	−35.3891	−	33.7434i	−1.35413	−	1.29116i	−0.433264	−	0.901267i	$-0.642638\pi$
$684$	−2.07517	−	1.63193i	−0.0793462	−	0.0623985i
$685$	0.000522608	0	0.000238667i	1.99678e−5	0	9.11900e-6i
$686$	−7.46017	−	16.9513i	−0.284831	−	0.647203i
$687$	−8.13811	−	12.6631i	−0.310488	−	0.483129i
$688$	2.40612	−	0.832766i	0.0917324	−	0.0317489i
$689$	−29.0763	−	50.3616i	−1.10772	−	1.91862i
$690$	−0.000569605	0	0.000300948i	−2.16845e−5	0	1.14569e-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
$693$	5.98983	+	1.28214i	0.227535	+	0.0487044i
$694$	1.25338	+	8.71748i	0.0475778	+	0.330911i
$695$	2.86890e−5	0	0.000300445i	1.08823e−6	0	1.13965e-5i
$696$	−0.124845	−	0.311847i	−0.00473223	−	0.0118205i
$697$	20.7397	−	21.7512i	0.785573	−	0.823885i
$698$	11.4468	+	22.2036i	0.433267	+	0.840420i
$699$	−3.11936	−	1.42456i	−0.117985	−	0.0538820i
$700$	0.270785	−	13.2260i	0.0102347	−	0.499895i
$701$	30.1968	−	26.1656i	1.14052	−	0.988262i	0.140517	−	0.990078i	$-0.455123\pi$
$701$	30.1968	−	26.1656i	1.14052	−	0.988262i	0.999998	+	0.00181584i	$0.000578002\pi$
$702$	−5.17886	+	0.998143i	−0.195463	+	0.0376725i
$703$	−24.0940	+	5.84514i	−0.908723	+	0.220454i
$704$	−0.220076	−	2.30474i	−0.00829444	−	0.0868633i
$705$	−0.000195322	0	0.000100695i	−7.35625e−6	0	3.79241e-6i
$706$	6.39461	+	21.7780i	0.240664	+	0.819627i
$707$	18.0066	+	7.64002i	0.677207	+	0.287333i
$708$	−0.404752	−	0.886284i	−0.0152115	−	0.0333086i
$709$	5.14844	−	12.8602i	0.193354	−	0.482975i	−0.799733	−	0.600356i	$-0.795026\pi$
$709$	5.14844	−	12.8602i	0.193354	−	0.482975i	0.993087	+	0.117381i	$0.0374499\pi$
$710$	−0.000401661	0	0.000207070i	−1.50741e−5	0	7.77122e-6i
$711$	0.499219	−	2.59020i	0.0187222	−	0.0971400i
$712$	−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
$716$	−1.04475	−	21.9320i	−0.0390441	−	0.819637i
$717$	4.32961	+	5.50554i	0.161692	+	0.205608i
$718$	−12.2772	−	8.74253i	−0.458180	−	0.326268i
$719$	12.6438	−	16.0780i	0.471536	−	0.599606i	−0.490867	−	0.871235i	$-0.663320\pi$
$719$	12.6438	−	16.0780i	0.471536	−	0.599606i	0.962402	+	0.271628i	$0.0875621\pi$
$720$	0.000128888	0	3.78449e-5i	4.80337e−6	0	1.41040e-6i
$721$	0.444189	−	1.40566i	0.0165425	−	0.0523496i
$722$	4.99763	−	10.9433i	0.185993	−	0.407267i
$723$	−8.53016	−	8.94617i	−0.317240	−	0.332712i
$724$	2.51782	−	7.27477i	0.0935742	−	0.270365i
$725$	0.549325	−	1.58717i	0.0204014	−	0.0589460i
$726$	−3.89185	−	4.08166i	−0.144440	−	0.151484i
$727$	−2.46500	+	5.39759i	−0.0914217	+	0.200186i	−0.949819	−	0.312800i	$-0.898733\pi$
$727$	−2.46500	+	5.39759i	−0.0914217	+	0.200186i	0.858397	+	0.512985i	$0.171460\pi$
$728$	3.01154	+	13.6253i	0.111615	+	0.504987i
$729$	0.959493	−	0.281733i	0.0355368	−	0.0104345i
$730$	0.00114650	−	0.00145789i	4.24337e−5	−	5.39588e-5i
$731$	−10.5580	−	7.51833i	−0.390502	−	0.278075i
$732$	4.07136	+	5.17715i	0.150482	+	0.191353i
$733$	0.957908	+	20.1090i	0.0353811	+	0.742742i	0.944955	+	0.327200i	$0.106105\pi$
$733$	0.957908	+	20.1090i	0.0353811	+	0.742742i	−0.909574	+	0.415542i	$0.863592\pi$
$734$	−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
$738$	−1.11732	+	5.79720i	−0.0411291	+	0.213398i
$739$	−7.06109	−	3.64025i	−0.259747	−	0.133909i	0.323435	−	0.946250i	$-0.395162\pi$
$739$	−7.06109	−	3.64025i	−0.259747	−	0.133909i	−0.583182	+	0.812342i	$0.698192\pi$
$740$	0.000468860	−	0.00117116i	1.72356e−5	−	4.30526e-5i
$741$	5.78414	+	12.6655i	0.212486	+	0.465279i
$742$	23.2949	−	17.5597i	0.855184	−	0.644636i
$743$	−0.840378	−	2.86206i	−0.0308305	−	0.104999i	0.942640	−	0.333810i	$-0.108334\pi$
$743$	−0.840378	−	2.86206i	−0.0308305	−	0.104999i	−0.973471	+	0.228811i	$0.926516\pi$
$744$	−0.426277	+	0.219761i	−0.0156281	+	0.00805684i
$745$	−0.000161146	−	0.00168760i	−5.90395e−6	−	6.18289e-5i
$746$	22.0933	−	5.35977i	0.808893	−	0.196235i
$747$	5.13215	−	0.989141i	0.187776	−	0.0361908i
$748$	−8.90712	+	7.71806i	−0.325677	+	0.282200i
$749$	23.5607	+	0.482375i	0.860888	+	0.0176256i
$750$	0.00122190		0.000558023i	4.46175e−5		2.03761e-5i
$751$	−9.28408	−	18.0086i	−0.338781	−	0.657143i	0.656484	−	0.754340i	$-0.272043\pi$
$751$	−9.28408	−	18.0086i	−0.338781	−	0.657143i	−0.995265	+	0.0971964i	$0.969013\pi$
$752$	1.12891	−	1.18396i	0.0411670	−	0.0431747i
$753$	10.0089	+	25.0011i	0.364745	+	0.911089i
$754$	−0.168405	+	1.76362i	−0.00613295	+	0.0642272i
$755$	−7.67974e−5	0	0.000534138i	−2.79494e−6	0	1.94393e-5i
$756$	−0.813981	−	2.51743i	−0.0296042	−	0.0915579i
$757$	−1.50636	−	1.30527i	−0.0547498	−	0.0474409i	0.627056	−	0.778974i	$-0.284260\pi$
$757$	−1.50636	−	1.30527i	−0.0547498	−	0.0474409i	−0.681806	+	0.731533i	$0.738805\pi$
$758$	8.11192	+	4.68342i	0.294638	+	0.170109i
$759$	−0.944131	+	11.0632i	−0.0342698	+	0.401570i
$760$	−0.000177314	0	0.000307116i	−6.43185e−6	0	1.11403e-5i
$761$	−43.2709	+	14.9762i	−1.56857	+	0.542887i	−0.966745	−	0.255741i	$-0.917680\pi$
$761$	−43.2709	+	14.9762i	−1.56857	+	0.542887i	−0.601824	+	0.798628i	$0.705559\pi$
$762$	2.30764	+	3.59076i	0.0835971	+	0.130080i
$763$	−20.8241	−	2.41954i	−0.753883	−	0.0875932i
$764$	−11.6632	+	5.32642i	−0.421961	+	0.192703i
$765$	−0.000537511	0	0.000422704i	−1.94338e−5	0	1.52829e-5i
$766$	15.7574	+	15.0247i	0.569339	+	0.542864i
$767$	−0.244514	+	5.13297i	−0.00882888	+	0.185341i
$768$	−0.814576	+	0.580057i	−0.0293935	+	0.0209310i
$769$	−25.0851	−	7.36564i	−0.904591	−	0.265612i	−0.203829	−	0.979007i	$-0.565339\pi$
$769$	−25.0851	−	7.36564i	−0.904591	−	0.265612i	−0.700762	+	0.713395i	$0.747157\pi$
$770$	0.000682962	0	0.000458934i	2.46122e−5	0	1.65388e-5i
$771$	−8.33513	−	9.61925i	−0.300182	−	0.346429i
$772$	−17.0698	+	16.2760i	−0.614355	+	0.585786i
$773$	−37.7246	+	3.60226i	−1.35686	+	0.129564i	−0.747992	−	0.663708i	$-0.768982\pi$
$773$	−37.7246	+	3.60226i	−1.35686	+	0.129564i	−0.608867	+	0.793272i	$0.708376\pi$
$774$	2.54327	+	0.121151i	0.0914160	+	0.00435468i
$775$	−2.33036	−	0.565339i	−0.0837090	−	0.0203076i
$776$	−2.64598	+	18.4032i	−0.0949852	+	0.660637i
$777$	−23.3091	−	8.60558i	−0.836211	−	0.308723i
$778$	29.0417	−	4.17557i	1.04120	−	0.149702i
$779$	15.5686	−	0.741622i	0.557802	−	0.0265714i
$780$	−0.000695672	0	0.000134080i	−2.49090e−5	0	4.80082e-6i
$781$	−6.74516	+	3.89432i	−0.241361	+	0.139350i
$782$	−24.1987	−	3.23097i	−0.865345	−	0.115539i
$783$		−	0.335909i		−	0.0120044i
$784$	−6.59962	+	2.33347i	−0.235701	+	0.0833382i
$785$	0.00205558	−	0.00132104i	7.33667e−5	−	4.71499e-5i
$786$	10.3802	+	4.15559i	0.370248	+	0.148225i
$787$	−25.0220	+	35.1385i	−0.891938	+	1.25255i	0.0749073	+	0.997190i	$0.476134\pi$
$787$	−25.0220	+	35.1385i	−0.891938	+	1.25255i	−0.966846	+	0.255362i	$0.917805\pi$
$788$	−18.3456	+	7.34448i	−0.653536	+	0.261636i
$789$	−2.15449	+	8.88093i	−0.0767019	+	0.316170i
$790$	0.000191572	0	0.000298092i	6.81582e−6	0	1.06056e-5i
$791$	34.1390	−	12.8628i	1.21384	−	0.457349i
$792$	0.652275	−	2.22145i	0.0231776	−	0.0789356i
$793$	−6.57403	−	34.1093i	−0.233451	−	1.21126i
$794$	−12.8717	−	4.45495i	−0.456800	−	0.158100i
$795$	0.000349183		0.00143935i	1.23842e−5		5.10486e-5i
$796$	7.28943	+	10.2366i	0.258367	+	0.362826i
$797$	30.3850	+	19.5272i	1.07629	+	0.691690i	0.953698	−	0.300767i	$-0.0972426\pi$
$797$	30.3850	+	19.5272i	1.07629	+	0.691690i	0.122593	+	0.992457i	$0.460879\pi$
$798$	−5.95202	+	3.65518i	−0.210699	+	0.129392i
$799$	−8.24294	−	1.18516i	−0.291614	−	0.0419278i
$800$	−4.97736	−	0.475280i	−0.175976	−	0.0168037i
$801$	−5.85093	+	4.60122i	−0.206732	+	0.162576i
$802$	3.28063	−	6.36354i	0.115843	−	0.224704i
$803$	−10.4552	−	30.2084i	−0.368957	−	1.06603i
$804$	1.65374			0.0583229
$805$	0.000225002		0.00168953i	7.93027e−6		5.95481e-5i
$806$	2.52944			0.0890958
$807$	1.34278	+	3.87970i	0.0472680	+	0.136572i
$808$	3.38772	−	6.57126i	0.119180	−	0.231176i
$809$	−21.6268	+	17.0075i	−0.760358	+	0.597952i	−0.921228	−	0.389023i	$-0.872813\pi$
$809$	−21.6268	+	17.0075i	−0.760358	+	0.597952i	0.160870	+	0.986976i	$0.448570\pi$
$810$	0.000133721	0	1.27688e-5i	4.69847e−6	0	4.48650e-7i
$811$	47.5021	+	6.82978i	1.66803	+	0.239826i	0.910657	−	0.413162i	$-0.135576\pi$
$811$	47.5021	+	6.82978i	1.66803	+	0.239826i	0.757368	+	0.652988i	$0.226485\pi$
$812$	−0.888404	+	0.0241074i	−0.0311769	+	0.000846005i
$813$	18.9861	+	12.2016i	0.665872	+	0.427930i
$814$	−12.6121	−	17.7113i	−0.442056	−	0.620780i
$815$	−0.000598251	−	0.00246602i	−2.09558e−5	−	8.63810e-5i
$816$	4.81058	+	1.66496i	0.168404	+	0.0582852i
$817$	−1.27211	−	6.60035i	−0.0445056	−	0.230917i
$818$	0.390305	−	1.32926i	0.0136467	−	0.0464763i
$819$	−2.26819	+	13.7686i	−0.0792570	+	0.481113i
$820$	−0.000428763	0	0.000667169i	−1.49731e−5	0	2.32985e-5i
$821$	−1.02773	+	4.23634i	−0.0358679	+	0.147849i	−0.986930	−	0.161151i	$-0.948479\pi$
$821$	−1.02773	+	4.23634i	−0.0358679	+	0.147849i	0.951062	+	0.309001i	$0.0999945\pi$
$822$	−3.97064	+	1.58960i	−0.138492	+	0.0554438i
$823$	−7.92029	+	11.1225i	−0.276084	+	0.387705i	−0.929215	−	0.369539i	$-0.879516\pi$
$823$	−7.92029	+	11.1225i	−0.276084	+	0.387705i	0.653131	+	0.757245i	$0.273455\pi$
$824$	−0.517273	−	0.207085i	−0.0180201	−	0.00721415i
$825$	9.73847	−	6.25853i	0.339050	−	0.217894i
$826$	−2.57065	+	0.192460i	−0.0894442	+	0.00669654i
$827$		−	15.0984i		−	0.525024i	−0.964929	−	0.262512i	$-0.915449\pi$
$827$		−	15.0984i		−	0.525024i	0.964929	−	0.262512i	$-0.0845509\pi$
$828$	4.34217	−	2.03607i	0.150901	−	0.0707584i
$829$	−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	$0.620012\pi$
$830$	0.000689397	0	0.000132870i	2.39293e−5	0	4.61200e-6i
$831$	3.40586	−	0.162241i	0.118148	−	0.00562808i
$832$	5.22049	−	0.750593i	0.180988	−	0.0260221i
$833$	29.1635	+	20.4760i	1.01046	+	0.709451i
$834$	−0.319754	+	2.22394i	−0.0110722	+	0.0770086i
$835$	−0.000242128	0	5.87397e-5i	−8.37919e−6	0	2.03277e-6i
$836$	−6.10526	−	0.290829i	−0.211155	−	0.0100585i
$837$	−0.477419	+	0.0455880i	−0.0165020	+	0.00157575i
$838$	−0.0806684	+	0.0769171i	−0.00278664	+	0.00265706i
$839$	−16.0244	−	18.4931i	−0.553223	−	0.638454i	0.408408	−	0.912800i	$-0.366084\pi$
$839$	−16.0244	−	18.4931i	−0.553223	−	0.638454i	−0.961631	+	0.274346i	$0.911539\pi$
$840$	2.41738e−5	0	0.000354578i	8.34074e−7	0	1.22341e-5i
$841$	27.7170	+	8.13845i	0.955760	+	0.280636i
$842$	−9.90609	+	7.05409i	−0.341386	+	0.243100i
$843$	−0.222761	+	4.67633i	−0.00767229	+	0.161061i
$844$	8.63452	+	8.23300i	0.297213	+	0.283392i
$845$	0.00156451	+	0.00123034i	5.38208e−5	+	4.23252e-5i
$846$	1.48808	−	0.679582i	0.0511611	−	0.0233645i
$847$	−13.6969	+	5.91940i	−0.470632	+	0.203393i
$848$	−5.96106	−	9.27560i	−0.204704	−	0.318525i
$849$	−7.35224	+	2.54464i	−0.252328	+	0.0873317i
$850$	12.7264	+	22.0428i	0.436512	+	0.756061i
$851$	10.1772	−	43.8741i	0.348870	−	1.50398i
$852$	2.91339	+	1.68205i	0.0998111	+	0.0576259i
$853$	−5.15630	−	4.46796i	−0.176548	−	0.152980i	0.562104	−	0.827067i	$-0.309992\pi$
$853$	−5.15630	−	4.46796i	−0.176548	−	0.152980i	−0.738652	+	0.674086i	$0.764538\pi$
$854$	16.5804	−	5.36109i	0.567371	−	0.183453i
$855$	−5.04688e−5	0	0.000351018i	−1.72600e−6	0	1.20046e-5i
$856$	0.846660	−	8.86663i	0.0289383	−	0.303055i
$857$	14.8985	+	37.2147i	0.508923	+	1.27123i	0.931116	+	0.364723i	$0.118836\pi$
$857$	14.8985	+	37.2147i	0.508923	+	1.27123i	−0.422193	+	0.906506i	$0.638739\pi$
$858$	−8.42649	+	8.83745i	−0.287676	+	0.301706i
$859$	14.5705	+	28.2628i	0.497139	+	0.964315i	0.995264	+	0.0972099i	$0.0309918\pi$
$859$	14.5705	+	28.2628i	0.497139	+	0.964315i	−0.498125	+	0.867105i	$0.665978\pi$
$860$	0.000311115	0	0.000142081i	1.06089e−5	0	4.84494e-6i
$861$	13.3648	+	8.08538i	0.455472	+	0.275549i
$862$	22.3213	−	19.3415i	0.760267	−	0.658775i
$863$	−55.7200	+	10.7392i	−1.89673	+	0.365565i	−0.997423	−	0.0717474i	$-0.977142\pi$
$863$	−55.7200	+	10.7392i	−1.89673	+	0.365565i	−0.899310	+	0.437313i	$0.855930\pi$
$864$	−0.971812	+	0.235759i	−0.0330617	+	0.00802068i
$865$	7.67835e−5	0	0.000804114i	2.61072e−6	0	2.73407e-5i
$866$	7.54766	−	3.89109i	0.256480	−	0.132225i
$867$	−2.51131	−	8.55273i	−0.0852885	−	0.290466i
$868$	0.154833	+	1.25940i	0.00525539	+	0.0427467i
$869$	−2.53705	−	5.55536i	−0.0860635	−	0.188453i
$870$	1.67703e−5	0	4.18901e-5i	5.68566e−7	0	1.42021e-6i
$871$	−7.75252	−	3.99670i	−0.262684	−	0.135423i
$872$	−1.49957	+	7.78053i	−0.0507820	+	0.263482i
$873$	−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
$877$	−1.68475	−	35.3673i	−0.0568900	−	1.19427i	−0.829174	−	0.558991i	$-0.811189\pi$
$877$	−1.68475	−	35.3673i	−0.0568900	−	1.19427i	0.772284	−	0.635277i	$-0.219114\pi$
$878$	10.4908	+	13.3402i	0.354049	+	0.450210i
$879$	−17.0190	−	12.1192i	−0.574037	−	0.408770i
$880$	0.000192249	0	0.000244464i	6.48071e−6	0	8.24090e-6i
$881$	−47.6911	+	14.0034i	−1.60675	+	0.471786i	−0.957416	−	0.288713i	$-0.906773\pi$
$881$	−47.6911	+	14.0034i	−1.60675	+	0.471786i	−0.649339	+	0.760499i	$0.724954\pi$
$882$	−6.99413	−	0.286512i	−0.235505	−	0.00964737i
$883$	−20.4753	+	44.8347i	−0.689049	+	1.50881i	0.163713	+	0.986508i	$0.447653\pi$
$883$	−20.4753	+	44.8347i	−0.689049	+	1.50881i	−0.852762	+	0.522299i	$0.825074\pi$
$884$	−18.5276	−	19.4312i	−0.623150	−	0.653541i
$885$	4.28070e−5	0	0.000123683i	1.43894e−6	0	4.15755e-6i
$886$	10.6342	−	30.7254i	0.357262	−	1.03224i
$887$	−11.0202	−	11.5577i	−0.370023	−	0.388069i	0.512227	−	0.858850i	$-0.328821\pi$
$887$	−11.0202	−	11.5577i	−0.370023	−	0.388069i	−0.882250	+	0.470781i	$0.843972\pi$
$888$	−3.90128	+	8.54261i	−0.130918	+	0.286671i
$889$	11.0269	−	2.43722i	0.369829	−	0.0817417i
$890$	−0.000959367	0	0.000281695i	−3.21580e−5	0	9.44245e-6i
$891$	1.43118	−	1.81989i	0.0479463	−	0.0609687i
$892$	20.4084	+	14.5327i	0.683323	+	0.486592i
$893$	−2.66970	−	3.39480i	−0.0893380	−	0.113603i
$894$	0.600500	+	12.6060i	0.0200837	+	0.421609i
$895$	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
$899$	−0.0304881	+	0.158188i	−0.00101684	+	0.00527585i
$900$	−4.44418	−	2.29113i	−0.148139	−	0.0763711i
$901$	−20.8607	+	52.1075i	−0.694971	+	1.73595i
$902$	5.67825	+	12.4336i	0.189065	+	0.413995i
$903$	2.63119	−	6.20139i	0.0875606	−	0.206369i
$904$	−3.88476	−	13.2303i	−0.129205	−	0.440033i
$905$	0.000919134	0	0.000473846i	3.05530e−5	0	1.57512e-5i
$906$	0.381862	+	3.99904i	0.0126865	+	0.132859i
$907$	−38.8731	+	9.43050i	−1.29076	+	0.313135i	−0.821643	−	0.570002i	$-0.806942\pi$
$907$	−38.8731	+	9.43050i	−1.29076	+	0.313135i	−0.469116	+	0.883137i	$0.655427\pi$
$908$	23.0769	−	4.44770i	0.765833	−	0.147602i
$909$	5.58734	−	4.84146i	0.185320	−	0.160581i
$910$	−0.000970256		0.00160379i	−3.21637e−5		5.31653e-5i
$911$	49.0993	+	22.4229i	1.62673	+	0.742904i	0.999359	−	0.0358127i	$-0.0114020\pi$
$911$	49.0993	+	22.4229i	1.62673	+	0.742904i	0.627375	+	0.778717i	$0.284129\pi$
$912$	1.20971	+	2.34652i	0.0400576	+	0.0777009i
$913$	8.35049	−	8.75774i	0.276361	−	0.289839i
$914$	11.8061	+	29.4901i	0.390510	+	0.975446i
$915$	−8.40986e−5	0	0.000880721i	−2.78021e−6	0	2.91157e-5i
$916$	2.14222	+	14.8995i	0.0707811	+	0.492293i
$917$	19.8259	−	21.9556i	0.654709	−	0.725039i
$918$	3.84719	+	3.33361i	0.126976	+	0.110025i
$919$	20.6184	+	11.9040i	0.680138	+	0.392678i	0.799907	−	0.600124i	$-0.204882\pi$
$919$	20.6184	+	11.9040i	0.680138	+	0.392678i	−0.119769	+	0.992802i	$0.538215\pi$
$920$	0.000643149	0	3.71292e-5i	2.12040e−5	0	1.22411e-6i
$921$	16.2109	+	28.0780i	0.534166	+	0.925202i
$922$	15.8427	−	5.48322i	0.521753	−	0.180580i
$923$	−9.59248	−	14.9262i	−0.315740	−	0.491301i
$924$	−4.91592	−	3.65454i	−0.161722	−	0.120226i
$925$	−42.7130	+	19.5064i	−1.40440	+	0.641366i
$926$	7.31874	+	5.75552i	0.240509	+	0.189138i
$927$	−0.403254	−	0.384502i	−0.0132446	−	0.0126287i
$928$	−0.0159832	+	0.335528i	−0.000524674	+	0.0110143i
$929$	29.5227	−	21.0230i	0.968608	−	0.689742i	0.0179028	−	0.999840i	$-0.494301\pi$
$929$	29.5227	−	21.0230i	0.968608	−	0.689742i	0.950705	+	0.310097i	$0.100362\pi$
$930$	−6.18134e−5	0	1.81501e-5i	−2.02694e−6	0	5.95164e-7i
$931$	3.61809	+	18.1223i	0.118578	+	0.593934i
$932$	2.24569	+	2.59166i	0.0735599	+	0.0848926i
$933$	−10.5091	+	10.0204i	−0.344052	+	0.328053i
$934$	17.7966	−	1.69937i	0.582322	−	0.0556050i
$935$	−0.00158138		7.53306e-5i	−5.17168e−5		2.46357e-6i
$936$	5.12550	+	1.24343i	0.167532	+	0.0406429i
$937$	2.55583	−	17.7762i	0.0834954	−	0.580724i	−0.904527	−	0.426416i	$-0.859776\pi$
$937$	2.55583	−	17.7762i	0.0834954	−	0.580724i	0.988023	−	0.154308i	$-0.0493148\pi$
$938$	1.51538	−	4.10458i	0.0494790	−	0.134019i
$939$	15.1677	−	2.18078i	0.494979	−	0.0711672i
$940$	0.000219501	0	1.04561e-5i	7.15935e−6	0	3.41042e-7i
$941$	−32.9964	−	6.35954i	−1.07565	−	0.207315i	−0.379488	−	0.925197i	$-0.623900\pi$
$941$	−32.9964	−	6.35954i	−1.07565	−	0.207315i	−0.696165	+	0.717882i	$0.745112\pi$
$942$	−15.7532	+	9.09509i	−0.513266	+	0.296334i
$943$	−11.5022	+	25.8725i	−0.374564	+	0.842524i
$944$			0.974332i			0.0317118i
$945$	0.000154226	0	0.000320195i	5.01696e−6	0	1.04159e-5i
$946$	4.95913	−	3.18704i	0.161235	−	0.103620i
$947$	6.15227	+	2.46300i	0.199922	+	0.0800366i	0.469463	−	0.882952i	$-0.344448\pi$
$947$	6.15227	+	2.46300i	0.199922	+	0.0800366i	−0.269541	+	0.962989i	$0.586872\pi$
$948$	−1.53011	+	2.14874i	−0.0496957	+	0.0697879i
$949$	67.6046	−	27.0648i	2.19454	−	0.878561i
$950$	−3.11201	+	12.8279i	−0.100967	+	0.416191i
$951$	10.4427	−	16.2492i	0.338629	−	0.526916i
$952$	8.54055	−	10.4142i	0.276801	−	0.337526i
$953$	4.50929	−	15.3572i	0.146070	−	0.497469i	−0.853657	−	0.520836i	$-0.825620\pi$
$953$	4.50929	−	15.3572i	0.146070	−	0.497469i	0.999727	+	0.0233666i	$0.00743850\pi$
$954$	−2.08667	−	10.8267i	−0.0675584	−	0.350526i
$955$	−0.00162763		0.000563328i	−5.26689e−5		1.82289e-5i
$956$	−1.65126	−	6.80660i	−0.0534057	−	0.220141i
$957$	−0.451114	−	0.633500i	−0.0145824	−	0.0204782i
$958$	32.4291	+	20.8409i	1.04774	+	0.673339i
$959$	0.306952	+	11.3117i	0.00991199	+	0.365275i
$960$	−0.000132962	0	1.91170e-5i	−4.29132e−6	0	6.16999e-7i
$961$	−30.6307	−	2.92487i	−0.988086	−	0.0943508i
$962$	38.9341	−	30.6182i	1.25529	−	0.987169i
$963$	4.08141	−	7.91682i	0.131521	−	0.255116i
$964$	4.04293	+	11.6813i	0.130214	+	0.376229i
$965$	−0.00316825			−0.000101989
$966$	−1.07464	−	12.6430i	−0.0345761	−	0.406781i
$967$	−15.7637			−0.506925			−0.253462	−	0.967345i	$-0.581569\pi$
$967$	−15.7637			−0.506925			−0.253462	+	0.967345i	$0.581569\pi$
$968$	1.84457	+	5.32954i	0.0592868	+	0.171298i
$969$	6.15812	−	11.9451i	0.197827	−	0.383731i
$970$	−0.00196317	+	0.00154386i	−6.30337e−5	+	4.95703e-5i
$971$	−13.8561	−	1.32309i	−0.444662	−	0.0424601i	−0.129676	−	0.991556i	$-0.541394\pi$
$971$	−13.8561	−	1.32309i	−0.444662	−	0.0424601i	−0.314986	+	0.949096i	$0.602000\pi$
$972$	−0.989821	−	0.142315i	−0.0317485	−	0.00456475i
$973$	5.22681	+	2.83150i	0.167564	+	0.0907738i
$974$	−23.1028	−	14.8472i	−0.740260	−	0.475736i
$975$	15.2966	+	21.4811i	0.489883	+	0.687945i
$976$	−1.55277	−	6.40061i	−0.0497030	−	0.204878i
$977$	8.20109	+	2.83843i	0.262376	+	0.0908093i	0.455089	−	0.890446i	$-0.349607\pi$
$977$	8.20109	+	2.83843i	0.262376	+	0.0908093i	−0.192713	+	0.981255i	$0.561729\pi$
$978$	3.57506	+	18.5492i	0.114318	+	0.593138i
$979$	−4.85516	+	16.5352i	−0.155172	+	0.528466i
$980$	−0.000857912	0	0.000384913i	−2.74050e−5	0	1.22956e-5i
$981$	−4.28389	+	6.66586i	−0.136774	+	0.212824i
$982$	−6.77966	+	27.9462i	−0.216348	+	0.891798i
$983$	−16.3309	+	6.53789i	−0.520873	+	0.208526i	−0.617175	−	0.786826i	$-0.711723\pi$
$983$	−16.3309	+	6.53789i	−0.520873	+	0.208526i	0.0963016	+	0.995352i	$0.469299\pi$
$984$	3.42459	−	4.80917i	0.109172	−	0.153311i
$985$	−0.00246435		0.000986577i	−7.85207e−5		3.14350e-5i
$986$	1.43851	−	0.924477i	0.0458116	−	0.0294413i
$987$	−0.323142	−	4.31613i	−0.0102857	−	0.137384i
$988$		−	13.9238i		−	0.442974i
$989$	11.7503	+	3.32210i	0.373639	+	0.105637i
$990$	0.000269336	0	0.000155501i	8.56006e−6	0	4.94215e-6i
$991$	−2.40632	−	0.463780i	−0.0764393	−	0.0147325i	0.150888	−	0.988551i	$-0.451787\pi$
$991$	−2.40632	−	0.463780i	−0.0764393	−	0.0147325i	−0.227327	+	0.973818i	$0.572999\pi$
$992$	0.479048	−	0.0228198i	0.0152098	−	0.000724531i
$993$	22.3548	−	3.21414i	0.709409	−	0.101998i
$994$	6.84449	−	5.68971i	0.217094	−	0.180467i
$995$	−0.000240239		0.00167090i	−7.61608e−6		5.29710e-5i
$996$	−5.07927	−	1.23222i	−0.160943	−	0.0390443i
$997$	9.30769	+	0.443380i	0.294778	+	0.0140420i	0.194450	−	0.980912i	$-0.437708\pi$
$997$	9.30769	+	0.443380i	0.294778	+	0.0140420i	0.100328	+	0.994954i	$0.468011\pi$
$998$	35.5380	−	3.39347i	1.12494	−	0.107418i
$999$	−6.79679	+	6.48072i	−0.215041	+	0.205041i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.a.145.13	✓	320	1.1	even	1	trivial
966.2.be.a.283.13	yes	320	7.3	odd	6	inner
966.2.be.a.355.13	yes	320	23.10	odd	22	inner
966.2.be.a.493.13	yes	320	161.10	even	66	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+(0.327068 + 0.945001i) q^{2} +(0.458227 - 0.888835i) q^{3} +(-0.786053 + 0.618159i) q^{4} +(-0.000133721 - 1.27688e-5i) q^{5} +(0.989821 + 0.142315i) q^{6} +(1.26024 - 2.32633i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(-0.580057 - 0.814576i) q^{9} +(-3.16693e-5 - 0.000130543i) q^{10} +(-2.18789 - 0.757237i) q^{11} +(0.189251 + 0.981929i) q^{12} +(1.48591 - 5.06053i) q^{13} +(2.61057 + 0.430057i) q^{14} +(-7.26238e-5 + 0.000113005i) q^{15} +(0.235759 - 0.971812i) q^{16} +(-4.72591 + 1.89197i) q^{17} +(0.580057 - 0.814576i) q^{18} +(-2.45088 - 0.981185i) q^{19} +(0.000113005 - 7.26238e-5i) q^{20} +(-1.49025 - 2.18613i) q^{21} -2.31523i q^{22} +(3.59265 - 3.17693i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-4.90964 - 0.946256i) q^{25} +(5.26820 - 0.250955i) q^{26} +(-0.989821 + 0.142315i) q^{27} +(0.447428 + 2.60764i) q^{28} +(-0.0478048 + 0.332490i) q^{29} +(-0.000130543 - 3.16693e-5i) q^{30} +(0.479048 + 0.0228198i) q^{31} +(0.995472 - 0.0950560i) q^{32} +(-1.67561 + 1.59769i) q^{33} +(-3.33361 - 3.84719i) q^{34} +(-0.000198224 + 0.000294987i) q^{35} +(0.959493 + 0.281733i) q^{36} +(7.64991 - 5.44747i) q^{37} +(0.125616 - 2.63700i) q^{38} +(-3.81710 - 3.63959i) q^{39} +(0.000105590 + 8.30367e-5i) q^{40} +(-5.37037 + 2.45257i) q^{41} +(1.57848 - 2.12330i) q^{42} +(1.37656 + 2.14196i) q^{43} +(2.18789 - 0.757237i) q^{44} +(6.71645e-5 + 0.000116332i) q^{45} +(4.17724 + 2.35599i) q^{46} +(1.41674 + 0.817955i) q^{47} +(-0.755750 - 0.654861i) q^{48} +(-3.82361 - 5.86345i) q^{49} +(-0.711574 - 4.94911i) q^{50} +(-0.483889 + 5.06751i) q^{51} +(1.96021 + 4.89637i) q^{52} +(7.60876 - 7.97983i) q^{53} +(-0.458227 - 0.888835i) q^{54} +(0.000282898 + 0.000129195i) q^{55} +(-2.31789 + 1.27570i) q^{56} +(-1.99517 + 1.72883i) q^{57} +(-0.329839 + 0.0635712i) q^{58} +(-0.946867 + 0.229708i) q^{59} +(-1.27688e-5 - 0.000133721i) q^{60} +(5.85410 - 3.01800i) q^{61} +(0.135116 + 0.460164i) q^{62} +(-2.62598 + 0.322845i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-0.000263313 + 0.000657725i) q^{65} +(-2.05786 - 1.06090i) q^{66} +(0.312972 - 1.62385i) 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} +(0.0475819 + 0.998867i) q^{72} +(8.53497 + 10.8531i) q^{73} +(7.64991 + 5.44747i) q^{74} +(-3.09079 + 3.93027i) q^{75} +(2.53305 - 0.743771i) q^{76} +(-4.51884 + 4.13546i) q^{77} +(2.19097 - 4.79755i) q^{78} +(1.82034 + 1.90911i) q^{79} +(-4.39347e-5 + 0.000126941i) q^{80} +(-0.327068 + 0.945001i) q^{81} +(-4.07415 - 4.27285i) q^{82} +(-2.17121 + 4.75428i) q^{83} +(2.52279 + 0.797201i) q^{84} +(0.000656111 - 0.000192652i) q^{85} +(-1.57393 + 2.00141i) q^{86} +(0.273623 + 0.194846i) q^{87} +(1.43118 + 1.81989i) q^{88} +(-0.354172 - 7.43499i) 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} +(-0.309598 + 1.60635i) q^{94} +(0.000315205 + 0.000162500i) q^{95} +(0.371662 - 0.928368i) q^{96} +(-7.72358 - 16.9123i) q^{97} +(4.29038 - 5.53106i) 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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