LMFDB - Embedded newform 966.2.j.a.137.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(137,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("966.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$64$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			137.5
Character	$\chi$	$=$	966.137
Dual form			966.2.j.a.275.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-1.58146 - 0.706395i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.53878 - 2.66525i) q^{5} +(1.72278 - 0.178972i) q^{6} +(-0.379647 - 2.61837i) q^{7} +1.00000i q^{8} +(2.00201 + 2.23427i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.58146 - 0.706395i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.53878 - 2.66525i) q^{5} +(1.72278 - 0.178972i) q^{6} +(-0.379647 - 2.61837i) q^{7} +1.00000i q^{8} +(2.00201 + 2.23427i) q^{9} +(2.66525 + 1.53878i) q^{10} +(2.20065 - 3.81164i) q^{11} +(-1.40248 + 1.01638i) q^{12} +3.82174 q^{13} +(1.63797 + 2.07775i) q^{14} +(0.550799 + 5.30197i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.52209 - 4.36839i) q^{17} +(-2.85093 - 0.933927i) q^{18} +(2.68548 - 1.55046i) q^{19} -3.07757 q^{20} +(-1.24921 + 4.40902i) q^{21} +4.40131i q^{22} +(4.41722 + 1.86767i) q^{23} +(0.706395 - 1.58146i) q^{24} +(-2.23572 + 3.87238i) q^{25} +(-3.30972 + 1.91087i) q^{26} +(-1.58782 - 4.94761i) q^{27} +(-2.45740 - 0.980401i) q^{28} +2.98764i q^{29} +(-3.12799 - 4.31624i) q^{30} +(4.90706 - 8.49927i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-6.17277 + 4.47342i) q^{33} +5.04418i q^{34} +(-6.39443 + 5.04097i) q^{35} +(2.93594 - 0.616659i) q^{36} +(-0.921124 + 0.531811i) q^{37} +(-1.55046 + 2.68548i) q^{38} +(-6.04392 - 2.69966i) q^{39} +(2.66525 - 1.53878i) q^{40} -4.96539i q^{41} +(-1.12266 - 4.44293i) q^{42} -4.16427i q^{43} +(-2.20065 - 3.81164i) q^{44} +(2.87423 - 8.77392i) q^{45} +(-4.75926 + 0.591162i) q^{46} +(-9.79033 + 5.65245i) q^{47} +(0.178972 + 1.72278i) q^{48} +(-6.71174 + 1.98811i) q^{49} -4.47144i q^{50} +(-7.07439 + 5.12682i) q^{51} +(1.91087 - 3.30972i) q^{52} +(-2.59692 + 4.49800i) q^{53} +(3.84889 + 3.49085i) q^{54} -13.5453 q^{55} +(2.61837 - 0.379647i) q^{56} +(-5.34221 + 0.554979i) q^{57} +(-1.49382 - 2.58737i) q^{58} +(8.75632 + 5.05546i) q^{59} +(4.86704 + 2.17398i) q^{60} +(2.22589 - 1.28512i) q^{61} +9.81411i q^{62} +(5.09008 - 6.09024i) q^{63} -1.00000 q^{64} +(-5.88084 - 10.1859i) q^{65} +(3.10906 - 6.96048i) q^{66} +(2.97353 + 1.71677i) q^{67} +(-2.52209 - 4.36839i) q^{68} +(-5.66633 - 6.07394i) q^{69} +(3.01725 - 7.56282i) q^{70} -9.54983i q^{71} +(-2.23427 + 2.00201i) q^{72} +(-5.38750 + 9.33143i) q^{73} +(0.531811 - 0.921124i) q^{74} +(6.27112 - 4.54470i) q^{75} -3.10093i q^{76} +(-10.8158 - 4.31505i) q^{77} +(6.58402 - 0.683984i) q^{78} +(2.71811 - 1.56930i) q^{79} +(-1.53878 + 2.66525i) q^{80} +(-0.983904 + 8.94606i) q^{81} +(2.48270 + 4.30015i) q^{82} +8.64133 q^{83} +(3.19372 + 3.28636i) q^{84} -15.5238 q^{85} +(2.08214 + 3.60637i) q^{86} +(2.11046 - 4.72482i) q^{87} +(3.81164 + 2.20065i) q^{88} +(0.175628 + 0.304196i) q^{89} +(1.89781 + 9.03555i) q^{90} +(-1.45091 - 10.0067i) q^{91} +(3.82606 - 2.89159i) q^{92} +(-13.7641 + 9.97491i) q^{93} +(5.65245 - 9.79033i) q^{94} +(-8.26476 - 4.77166i) q^{95} +(-1.01638 - 1.40248i) q^{96} -16.3857i q^{97} +(4.81848 - 5.07763i) q^{98} +(12.9220 - 2.71410i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9}+O(q^{10}) $ 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9	$ 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9} - 64 q^{16} + 4 q^{24} - 72 q^{25} + 24 q^{27} - 8 q^{36} + 4 q^{39} + 12 q^{46} + 72 q^{49} + 4 q^{54} - 96 q^{55} - 128 q^{64} - 56 q^{69} + 32 q^{70} - 40 q^{73} - 40 q^{75} - 16 q^{78} + 36 q^{81} - 32 q^{82} - 64 q^{85} - 24 q^{87} + 32 q^{93} - 8 q^{94} - 4 q^{96}+O(q^{100}) $ 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9 - 64 * q^16 + 4 * q^24 - 72 * q^25 + 24 * q^27 - 8 * q^36 + 4 * q^39 + 12 * q^46 + 72 * q^49 + 4 * q^54 - 96 * q^55 - 128 * q^64 - 56 * q^69 + 32 * q^70 - 40 * q^73 - 40 * q^75 - 16 * q^78 + 36 * q^81 - 32 * q^82 - 64 * q^85 - 24 * q^87 + 32 * q^93 - 8 * q^94 - 4 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.58146	−	0.706395i	−0.913054	−	0.407838i
$3$	−1.58146	−	0.706395i	−0.913054	−	0.407838i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−1.53878	−	2.66525i	−0.688166	−	1.19194i	−0.972431	−	0.233192i	$-0.925083\pi$
$5$	−1.53878	−	2.66525i	−0.688166	−	1.19194i	0.284265	−	0.958746i	$-0.408250\pi$
$6$	1.72278	−	0.178972i	0.703322	−	0.0730650i
$7$	−0.379647	−	2.61837i	−0.143493	−	0.989651i
$7$	−0.379647	−	2.61837i	−0.143493	−	0.989651i
$8$			1.00000i			0.353553i
$9$	2.00201	+	2.23427i	0.667337	+	0.744756i
$10$	2.66525	+	1.53878i	0.842827	+	0.486607i
$11$	2.20065	−	3.81164i	0.663522	−	1.14925i	−0.316162	−	0.948705i	$-0.602394\pi$
$11$	2.20065	−	3.81164i	0.663522	−	1.14925i	0.979684	−	0.200548i	$-0.0642724\pi$
$12$	−1.40248	+	1.01638i	−0.404862	+	0.293405i
$13$	3.82174			1.05996			0.529980	−	0.848010i	$-0.322199\pi$
$13$	3.82174			1.05996			0.529980	+	0.848010i	$0.322199\pi$
$14$	1.63797	+	2.07775i	0.437766	+	0.555303i
$15$	0.550799	+	5.30197i	0.142216	+	1.36896i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.52209	−	4.36839i	0.611697	−	1.05949i	−0.379258	−	0.925291i	$-0.623821\pi$
$17$	2.52209	−	4.36839i	0.611697	−	1.05949i	0.990954	−	0.134199i	$-0.0428460\pi$
$18$	−2.85093	−	0.933927i	−0.671970	−	0.220129i
$19$	2.68548	−	1.55046i	0.616092	−	0.355701i	−0.159254	−	0.987238i	$-0.550909\pi$
$19$	2.68548	−	1.55046i	0.616092	−	0.355701i	0.775346	+	0.631537i	$0.217576\pi$
$20$	−3.07757			−0.688166
$21$	−1.24921	+	4.40902i	−0.272600	+	0.962127i
$22$			4.40131i			0.938362i
$23$	4.41722	+	1.86767i	0.921054	+	0.389436i
$23$	4.41722	+	1.86767i	0.921054	+	0.389436i
$24$	0.706395	−	1.58146i	0.144192	−	0.322814i
$25$	−2.23572	+	3.87238i	−0.447144	+	0.774476i
$26$	−3.30972	+	1.91087i	−0.649090	+	0.374752i
$27$	−1.58782	−	4.94761i	−0.305576	−	0.952168i
$28$	−2.45740	−	0.980401i	−0.464405	−	0.185278i
$29$			2.98764i			0.554791i	0.960756	+	0.277395i	$0.0894712\pi$
$29$			2.98764i			0.554791i	−0.960756	+	0.277395i	$0.910529\pi$
$30$	−3.12799	−	4.31624i	−0.571091	−	0.788035i
$31$	4.90706	−	8.49927i	0.881334	−	1.52651i	0.0314744	−	0.999505i	$-0.489980\pi$
$31$	4.90706	−	8.49927i	0.881334	−	1.52651i	0.849859	−	0.527010i	$-0.176687\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−6.17277	+	4.47342i	−1.07454	+	0.778722i
$34$			5.04418i			0.865070i
$35$	−6.39443	+	5.04097i	−1.08086	+	0.852079i
$36$	2.93594	−	0.616659i	0.489323	−	0.102776i
$37$	−0.921124	+	0.531811i	−0.151432	+	0.0874292i	−0.573801	−	0.818995i	$-0.694532\pi$
$37$	−0.921124	+	0.531811i	−0.151432	+	0.0874292i	0.422369	+	0.906424i	$0.361198\pi$
$38$	−1.55046	+	2.68548i	−0.251518	+	0.435643i
$39$	−6.04392	−	2.69966i	−0.967801	−	0.432292i
$40$	2.66525	−	1.53878i	0.421414	−	0.243303i
$41$		−	4.96539i		−	0.775464i	−0.921772	−	0.387732i	$-0.873259\pi$
$41$		−	4.96539i		−	0.775464i	0.921772	−	0.387732i	$-0.126741\pi$
$42$	−1.12266	−	4.44293i	−0.173231	−	0.685559i
$43$		−	4.16427i		−	0.635046i	−0.948251	−	0.317523i	$-0.897149\pi$
$43$		−	4.16427i		−	0.635046i	0.948251	−	0.317523i	$-0.102851\pi$
$44$	−2.20065	−	3.81164i	−0.331761	−	0.574627i
$45$	2.87423	−	8.77392i	0.428464	−	1.30794i
$46$	−4.75926	+	0.591162i	−0.701714	+	0.0871621i
$47$	−9.79033	+	5.65245i	−1.42807	+	0.824495i	−0.996968	−	0.0778099i	$-0.975207\pi$
$47$	−9.79033	+	5.65245i	−1.42807	+	0.824495i	−0.431099	+	0.902305i	$0.641874\pi$
$48$	0.178972	+	1.72278i	0.0258324	+	0.248662i
$49$	−6.71174	+	1.98811i	−0.958819	+	0.284016i
$50$		−	4.47144i		−	0.632357i
$51$	−7.07439	+	5.12682i	−0.990612	+	0.717899i
$52$	1.91087	−	3.30972i	0.264990	−	0.458976i
$53$	−2.59692	+	4.49800i	−0.356715	+	0.617848i	−0.987410	−	0.158182i	$-0.949437\pi$
$53$	−2.59692	+	4.49800i	−0.356715	+	0.617848i	0.630695	+	0.776031i	$0.282770\pi$
$54$	3.84889	+	3.49085i	0.523768	+	0.475044i
$55$	−13.5453			−1.82645
$56$	2.61837	−	0.379647i	0.349895	−	0.0507325i
$57$	−5.34221	+	0.554979i	−0.707593	+	0.0735088i
$58$	−1.49382	−	2.58737i	−0.196148	−	0.339739i
$59$	8.75632	+	5.05546i	1.13998	+	0.658165i	0.946424	−	0.322925i	$-0.104666\pi$
$59$	8.75632	+	5.05546i	1.13998	+	0.658165i	0.193551	+	0.981090i	$0.438000\pi$
$60$	4.86704	+	2.17398i	0.628333	+	0.280660i
$61$	2.22589	−	1.28512i	0.284996	−	0.164543i	−0.350687	−	0.936493i	$-0.614052\pi$
$61$	2.22589	−	1.28512i	0.284996	−	0.164543i	0.635683	+	0.771950i	$0.280719\pi$
$62$			9.81411i			1.24639i
$63$	5.09008	−	6.09024i	0.641290	−	0.767298i
$64$	−1.00000			−0.125000
$65$	−5.88084	−	10.1859i	−0.729428	−	1.26341i
$66$	3.10906	−	6.96048i	0.382699	−	0.856775i
$67$	2.97353	+	1.71677i	0.363274	+	0.209736i	0.670516	−	0.741895i	$-0.266073\pi$
$67$	2.97353	+	1.71677i	0.363274	+	0.209736i	−0.307242	+	0.951631i	$0.599406\pi$
$68$	−2.52209	−	4.36839i	−0.305848	−	0.529745i
$69$	−5.66633	−	6.07394i	−0.682146	−	0.731216i
$70$	3.01725	−	7.56282i	0.360631	−	0.903930i
$71$		−	9.54983i		−	1.13336i	−0.823939	−	0.566678i	$-0.808228\pi$
$71$		−	9.54983i		−	1.13336i	0.823939	−	0.566678i	$-0.191772\pi$
$72$	−2.23427	+	2.00201i	−0.263311	+	0.235939i
$73$	−5.38750	+	9.33143i	−0.630559	+	1.09216i	0.356878	+	0.934151i	$0.383841\pi$
$73$	−5.38750	+	9.33143i	−0.630559	+	1.09216i	−0.987438	+	0.158010i	$0.949492\pi$
$74$	0.531811	−	0.921124i	0.0618218	−	0.107078i
$75$	6.27112	−	4.54470i	0.724127	−	0.524776i
$76$		−	3.10093i		−	0.355701i
$77$	−10.8158	−	4.31505i	−1.23257	−	0.491745i
$78$	6.58402	−	0.683984i	0.745493	−	0.0774460i
$79$	2.71811	−	1.56930i	0.305811	−	0.176560i	−0.339239	−	0.940700i	$-0.610170\pi$
$79$	2.71811	−	1.56930i	0.305811	−	0.176560i	0.645051	+	0.764140i	$0.276836\pi$
$80$	−1.53878	+	2.66525i	−0.172041	+	0.297984i
$81$	−0.983904	+	8.94606i	−0.109323	+	0.994006i
$82$	2.48270	+	4.30015i	0.274168	+	0.474873i
$83$	8.64133			0.948509			0.474255	−	0.880388i	$-0.342718\pi$
$83$	8.64133			0.948509			0.474255	+	0.880388i	$0.342718\pi$
$84$	3.19372	+	3.28636i	0.348463	+	0.358571i
$85$	−15.5238			−1.68379
$86$	2.08214	+	3.60637i	0.224523	+	0.388884i
$87$	2.11046	−	4.72482i	0.226265	−	0.506554i
$88$	3.81164	+	2.20065i	0.406323	+	0.234590i
$89$	0.175628	+	0.304196i	0.0186165	+	0.0322447i	0.875184	−	0.483791i	$-0.160741\pi$
$89$	0.175628	+	0.304196i	0.0186165	+	0.0322447i	−0.856567	+	0.516036i	$0.827407\pi$
$90$	1.89781	+	9.03555i	0.200047	+	0.952431i
$91$	−1.45091	−	10.0067i	−0.152097	−	1.04899i
$92$	3.82606	−	2.89159i	0.398894	−	0.301469i
$93$	−13.7641	+	9.97491i	−1.42728	+	1.03435i
$94$	5.65245	−	9.79033i	0.583006	−	1.00980i
$95$	−8.26476	−	4.77166i	−0.847946	−	0.489562i
$96$	−1.01638	−	1.40248i	−0.103734	−	0.143141i
$97$		−	16.3857i		−	1.66372i	−0.554989	−	0.831858i	$-0.687277\pi$
$97$		−	16.3857i		−	1.66372i	0.554989	−	0.831858i	$-0.312723\pi$
$98$	4.81848	−	5.07763i	0.486740	−	0.512918i
$99$	12.9220	−	2.71410i	1.29871	−	0.272778i
$100$	2.23572	+	3.87238i	0.223572	+	0.387238i
$101$	12.1304	+	7.00352i	1.20702	+	0.696876i	0.962108	−	0.272668i	$-0.0879061\pi$
$101$	12.1304	+	7.00352i	1.20702	+	0.696876i	0.244917	+	0.969544i	$0.421239\pi$
$102$	3.56319	−	7.97715i	0.352808	−	0.789856i
$103$	−0.310672	+	0.179367i	−0.0306114	+	0.0176735i	−0.515228	−	0.857053i	$-0.672293\pi$
$103$	−0.310672	+	0.179367i	−0.0306114	+	0.0176735i	0.484616	+	0.874727i	$0.338959\pi$
$104$			3.82174i			0.374752i
$105$	13.6734	−	3.45508i	1.33439	−	0.337181i
$106$		−	5.19385i		−	0.504471i
$107$	2.57772	+	4.46475i	0.249198	+	0.431623i	0.963303	−	0.268415i	$-0.0864997\pi$
$107$	2.57772	+	4.46475i	0.249198	+	0.431623i	−0.714106	+	0.700038i	$0.753166\pi$
$108$	−5.07866	−	1.09871i	−0.488695	−	0.105724i
$109$	8.92907	+	5.15520i	0.855250	+	0.493779i	0.862419	−	0.506196i	$-0.168949\pi$
$109$	8.92907	+	5.15520i	0.855250	+	0.493779i	−0.00716890	+	0.999974i	$0.502282\pi$
$110$	11.7306	−	6.77266i	1.11847	−	0.645748i
$111$	1.83239	−	0.190359i	0.173922	−	0.0180680i
$112$	−2.07775	+	1.63797i	−0.196329	+	0.154774i
$113$	−14.9630			−1.40760			−0.703800	−	0.710398i	$-0.748515\pi$
$113$	−14.9630			−1.40760			−0.703800	+	0.710398i	$0.748515\pi$
$114$	4.34900	−	3.15173i	0.407321	−	0.295187i
$115$	−1.81934	−	14.6469i	−0.169655	−	1.36583i
$116$	2.58737	+	1.49382i	0.240231	+	0.138698i
$117$	7.65117	+	8.53879i	0.707351	+	0.789411i
$118$	−10.1109			−0.930786
$119$	−12.3956	−	4.94532i	−1.13630	−	0.453337i
$120$	−5.30197	+	0.550799i	−0.484002	+	0.0502808i
$121$	−4.18575	−	7.24993i	−0.380523	−	0.659085i
$122$	−1.28512	+	2.22589i	−0.116349	+	0.201523i
$123$	−3.50753	+	7.85255i	−0.316263	+	0.708041i
$124$	−4.90706	−	8.49927i	−0.440667	−	0.763257i
$125$	−1.62669			−0.145496
$126$	−1.36302	+	7.81935i	−0.121428	+	0.696603i
$127$	−9.98686			−0.886191			−0.443095	−	0.896475i	$-0.646120\pi$
$127$	−9.98686			−0.886191			−0.443095	+	0.896475i	$0.646120\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−2.94162	+	6.58562i	−0.258995	+	0.579831i
$130$	10.1859	+	5.88084i	0.893363	+	0.515783i
$131$	−4.44217	+	2.56469i	−0.388114	+	0.224078i	−0.681343	−	0.731965i	$-0.738604\pi$
$131$	−4.44217	+	2.56469i	−0.388114	+	0.224078i	0.293229	+	0.956042i	$0.405270\pi$
$132$	0.787711	+	7.58248i	0.0685614	+	0.659970i
$133$	−5.07922	−	6.44296i	−0.440425	−	0.558675i
$134$	−3.43353			−0.296612
$135$	−10.7433	+	11.8452i	−0.924638	+	1.01948i
$136$	4.36839	+	2.52209i	0.374586	+	0.216267i
$137$	−7.07976	+	12.2625i	−0.604864	+	1.04766i	0.387208	+	0.921992i	$0.373439\pi$
$137$	−7.07976	+	12.2625i	−0.604864	+	1.04766i	−0.992073	+	0.125664i	$0.959894\pi$
$138$	7.94415	+	2.42702i	0.676251	+	0.206602i
$139$	3.53316			0.299678			0.149839	−	0.988710i	$-0.452124\pi$
$139$	3.53316			0.299678			0.149839	+	0.988710i	$0.452124\pi$
$140$	1.16839	+	8.05822i	0.0987471	+	0.681044i
$141$	19.4759	−	2.02326i	1.64016	−	0.170389i
$142$	4.77491	+	8.27039i	0.400702	+	0.694036i
$143$	8.41032	−	14.5671i	0.703307	−	1.21816i
$144$	0.933927	−	2.85093i	0.0778273	−	0.237577i
$145$	7.96282	−	4.59734i	0.661276	−	0.381788i
$146$		−	10.7750i		−	0.891746i
$147$	12.0187	+	1.59702i	0.991287	+	0.131720i
$148$			1.06362i			0.0874292i
$149$	8.36840	+	14.4945i	0.685566	+	1.18744i	0.973259	+	0.229712i	$0.0737786\pi$
$149$	8.36840	+	14.4945i	0.685566	+	1.18744i	−0.287692	+	0.957723i	$0.592888\pi$
$150$	−3.15860	+	7.07138i	−0.257899	+	0.577376i
$151$	0.793561	−	1.37449i	0.0645791	−	0.111854i	−0.831928	−	0.554883i	$-0.812763\pi$
$151$	0.793561	−	1.37449i	0.0645791	−	0.111854i	0.896507	+	0.443029i	$0.146096\pi$
$152$	1.55046	+	2.68548i	0.125759	+	0.217821i
$153$	14.8094	−	3.11054i	1.19727	−	0.251472i
$154$	11.5243	−	1.67094i	0.928651	−	0.134649i
$155$	−30.2036			−2.42601
$156$	−5.35993	+	3.88436i	−0.429138	+	0.310997i
$157$	−17.6982	−	10.2181i	−1.41247	−	0.815491i	−0.416850	−	0.908975i	$-0.636866\pi$
$157$	−17.6982	−	10.2181i	−1.41247	−	0.815491i	−0.995621	+	0.0934845i	$0.970199\pi$
$158$	−1.56930	+	2.71811i	−0.124847	+	0.216241i
$159$	7.28429	−	5.27894i	0.577682	−	0.418647i
$160$		−	3.07757i		−	0.243303i
$161$	3.21326	−	12.2750i	0.253240	−	0.967403i
$162$	−3.62094	−	8.23946i	−0.284488	−	0.647353i
$163$	3.30511	+	5.72462i	0.258876	+	0.448387i	0.965941	−	0.258762i	$-0.0833145\pi$
$163$	3.30511	+	5.72462i	0.258876	+	0.448387i	−0.707065	+	0.707149i	$0.749981\pi$
$164$	−4.30015	−	2.48270i	−0.335786	−	0.193866i
$165$	21.4214	+	9.56836i	1.66765	+	0.744896i
$166$	−7.48361	+	4.32066i	−0.580841	+	0.335349i
$167$			19.7950i			1.53179i	0.642968	+	0.765893i	$0.277703\pi$
$167$			19.7950i			1.53179i	−0.642968	+	0.765893i	$0.722297\pi$
$168$	−4.40902	−	1.24921i	−0.340163	−	0.0963786i
$169$	1.60570			0.123515
$170$	13.4440	−	7.76191i	1.03111	−	0.595311i
$171$	8.84051	+	2.89604i	0.676051	+	0.221466i
$172$	−3.60637	−	2.08214i	−0.274983	−	0.158761i
$173$	14.9303	−	8.62002i	1.13513	−	0.655368i	0.189911	−	0.981801i	$-0.439180\pi$
$173$	14.9303	−	8.62002i	1.13513	−	0.655368i	0.945220	+	0.326433i	$0.105847\pi$
$174$	0.534704	+	5.14704i	0.0405358	+	0.390196i
$175$	10.9881	+	4.38380i	0.830623	+	0.331384i
$176$	−4.40131			−0.331761
$177$	−10.2766	−	14.1804i	−0.772435	−	1.06587i
$178$	−0.304196	−	0.175628i	−0.0228005	−	0.0131638i
$179$	9.22798	+	5.32777i	0.689731	+	0.398217i	0.803511	−	0.595289i	$-0.202963\pi$
$179$	9.22798	+	5.32777i	0.689731	+	0.398217i	−0.113780	+	0.993506i	$0.536296\pi$
$180$	−6.16133	−	6.87611i	−0.459238	−	0.512515i
$181$			25.8661i			1.92261i	0.275481	+	0.961306i	$0.411163\pi$
$181$			25.8661i			1.92261i	−0.275481	+	0.961306i	$0.588837\pi$
$182$	6.25989	+	7.94063i	0.464014	+	0.588599i
$183$	−4.42795	+	0.460001i	−0.327324	+	0.0340042i
$184$	−1.86767	+	4.41722i	−0.137686	+	0.325642i
$185$	2.83482	+	1.63669i	0.208420	+	0.120332i
$186$	6.93265	−	15.5206i	0.508326	−	1.13803i
$187$	−11.1005	−	19.2266i	−0.811748	−	1.40599i
$188$			11.3049i			0.824495i
$189$	−12.3519	+	6.03584i	−0.898466	+	0.439043i
$190$	9.54332			0.692345
$191$	7.91755	+	13.7136i	0.572894	+	0.992281i	0.996267	+	0.0863258i	$0.0275126\pi$
$191$	7.91755	+	13.7136i	0.572894	+	0.992281i	−0.423373	+	0.905955i	$0.639154\pi$
$192$	1.58146	+	0.706395i	0.114132	+	0.0509797i
$193$	−11.6949	+	20.2562i	−0.841818	+	1.45807i	0.0465385	+	0.998916i	$0.485181\pi$
$193$	−11.6949	+	20.2562i	−0.841818	+	1.45807i	−0.888356	+	0.459155i	$0.848152\pi$
$194$	8.19285	+	14.1904i	0.588212	+	1.01881i
$195$	2.10501	+	20.2628i	0.150743	+	1.45105i
$196$	−1.63411	+	6.80659i	−0.116722	+	0.486185i
$197$			9.03343i			0.643605i	0.946807	+	0.321803i	$0.104289\pi$
$197$			9.03343i			0.643605i	−0.946807	+	0.321803i	$0.895711\pi$
$198$	−9.83370	+	8.81146i	−0.698850	+	0.626203i
$199$	1.13615	+	0.655958i	0.0805398	+	0.0464997i	0.539729	−	0.841839i	$-0.318527\pi$
$199$	1.13615	+	0.655958i	0.0805398	+	0.0464997i	−0.459189	+	0.888338i	$0.651860\pi$
$200$	−3.87238	−	2.23572i	−0.273818	−	0.158089i
$201$	−3.48979	−	4.81548i	−0.246151	−	0.339658i
$202$	−14.0070			−0.985531
$203$	7.82275	−	1.13425i	0.549049	−	0.0796087i
$204$	0.902767	+	8.69001i	0.0632063	+	0.608422i
$205$	−13.2340	+	7.64067i	−0.924305	+	0.533647i
$206$	0.179367	−	0.310672i	0.0124971	−	0.0216456i
$207$	4.67045	+	13.6083i	0.324619	+	0.945845i
$208$	−1.91087	−	3.30972i	−0.132495	−	0.229488i
$209$		−	13.6481i		−	0.944061i
$210$	−10.1140	+	9.82890i	−0.697932	+	0.678258i
$211$	11.1259			0.765937			0.382969	−	0.923761i	$-0.374902\pi$
$211$	11.1259			0.765937			0.382969	+	0.923761i	$0.374902\pi$
$212$	2.59692	+	4.49800i	0.178357	+	0.308924i
$213$	−6.74596	+	15.1026i	−0.462225	+	1.03482i
$214$	−4.46475	−	2.57772i	−0.305204	−	0.176209i
$215$	−11.0988	+	6.40792i	−0.756935	+	0.437017i
$216$	4.94761	−	1.58782i	0.336642	−	0.108037i
$217$	−24.1172	−	9.62177i	−1.63718	−	0.653168i
$218$	−10.3104			−0.698309
$219$	15.1118	−	10.9515i	1.02116	−	0.740037i
$220$	−6.77266	+	11.7306i	−0.456613	+	0.790877i
$221$	9.63877	−	16.6948i	0.648374	−	1.12302i
$222$	−1.49171	+	1.08105i	−0.100117	+	0.0725552i
$223$	10.0607			0.673712			0.336856	−	0.941556i	$-0.390636\pi$
$223$	10.0607			0.673712			0.336856	+	0.941556i	$0.390636\pi$
$224$	0.980401	−	2.45740i	0.0655058	−	0.164192i
$225$	−13.1279	+	2.75735i	−0.875191	+	0.183823i
$226$	12.9583	−	7.48150i	0.861976	−	0.497662i
$227$	13.6383	−	23.6222i	0.905205	−	1.56786i	0.0845638	−	0.996418i	$-0.473050\pi$
$227$	13.6383	−	23.6222i	0.905205	−	1.56786i	0.820641	−	0.571443i	$-0.193616\pi$
$228$	−2.19048	+	4.90398i	−0.145068	+	0.324774i
$229$	−1.48222	+	0.855761i	−0.0979480	+	0.0565503i	−0.548174	−	0.836364i	$-0.684677\pi$
$229$	−1.48222	+	0.855761i	−0.0979480	+	0.0565503i	0.450226	+	0.892915i	$0.351343\pi$
$230$	8.89907	+	11.7750i	0.586787	+	0.776418i
$231$	14.0565	+	14.4643i	0.924853	+	0.951679i
$232$	−2.98764			−0.196148
$233$	−2.47869	+	1.43108i	−0.162385	+	0.0937528i	−0.578990	−	0.815335i	$-0.696553\pi$
$233$	−2.47869	+	1.43108i	−0.162385	+	0.0937528i	0.416605	+	0.909087i	$0.363220\pi$
$234$	−10.8955	−	3.56923i	−0.712261	−	0.233328i
$235$	30.1304	+	17.3958i	1.96549	+	1.13478i
$236$	8.75632	−	5.05546i	0.569988	−	0.329082i
$237$	−5.40712	+	0.561722i	−0.351230	+	0.0364878i
$238$	13.2075	−	1.91501i	0.856117	−	0.124132i
$239$		−	20.2584i		−	1.31041i	−0.755451	−	0.655205i	$-0.772582\pi$
$239$		−	20.2584i		−	1.31041i	0.755451	−	0.655205i	$-0.227418\pi$
$240$	4.31624	−	3.12799i	0.278612	−	0.201911i
$241$	2.64764	+	1.52862i	0.170549	+	0.0984668i	0.582845	−	0.812583i	$-0.301940\pi$
$241$	2.64764	+	1.52862i	0.170549	+	0.0984668i	−0.412295	+	0.911050i	$0.635273\pi$
$242$	7.24993	+	4.18575i	0.466043	+	0.269070i
$243$	7.87545	−	13.4528i	0.505211	−	0.862996i
$244$		−	2.57024i		−	0.164543i
$245$	15.6267	+	14.8292i	0.998356	+	0.947403i
$246$	−0.888666	−	8.55427i	−0.0566593	−	0.545401i
$247$	10.2632	−	5.92547i	0.653032	−	0.377028i
$248$	8.49927	+	4.90706i	0.539704	+	0.311598i
$249$	−13.6659	−	6.10420i	−0.866040	−	0.386838i
$250$	1.40876	−	0.813346i	0.0890976	−	0.0514405i
$251$	−24.0931			−1.52074			−0.760371	−	0.649489i	$-0.774983\pi$
$251$	−24.0931			−1.52074			−0.760371	+	0.649489i	$0.774983\pi$
$252$	−2.72926	−	7.45326i	−0.171927	−	0.469511i
$253$	16.8396	−	12.7268i	1.05870	−	0.800125i
$254$	8.64888	−	4.99343i	0.542679	−	0.313316i
$255$	24.5502	+	10.9660i	1.53740	+	0.686715i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−12.7268	+	7.34781i	−0.793875	+	0.458344i	−0.841325	−	0.540530i	$-0.818224\pi$
$257$	−12.7268	+	7.34781i	−0.793875	+	0.458344i	0.0474500	+	0.998874i	$0.484891\pi$
$258$	−0.745288	−	7.17412i	−0.0463996	−	0.446641i
$259$	1.74218	+	2.20994i	0.108254	+	0.137319i
$260$	−11.7617			−0.729428
$261$	−6.67519	+	5.98129i	−0.413184	+	0.370232i
$262$	2.56469	−	4.44217i	0.158447	−	0.274438i
$263$	5.73754	−	9.93770i	0.353792	−	0.612785i	−0.633119	−	0.774055i	$-0.718226\pi$
$263$	5.73754	−	9.93770i	0.353792	−	0.612785i	0.986910	+	0.161270i	$0.0515589\pi$
$264$	−4.47342	−	6.17277i	−0.275320	−	0.379907i
$265$	15.9844			0.981916
$266$	7.62022	+	3.04015i	0.467225	+	0.186404i
$267$	−0.0628649	−	0.605135i	−0.00384727	−	0.0370337i
$268$	2.97353	−	1.71677i	0.181637	−	0.104868i
$269$	5.99245	+	3.45974i	0.365366	+	0.210944i	0.671432	−	0.741066i	$-0.265680\pi$
$269$	5.99245	+	3.45974i	0.365366	+	0.210944i	−0.306066	+	0.952010i	$0.599013\pi$
$270$	3.38137	−	15.6299i	0.205784	−	0.951208i
$271$	11.7984	+	20.4355i	0.716704	+	1.24137i	0.962299	+	0.271995i	$0.0876834\pi$
$271$	11.7984	+	20.4355i	0.716704	+	1.24137i	−0.245595	+	0.969373i	$0.578983\pi$
$272$	−5.04418			−0.305848
$273$	−4.77415	+	16.8501i	−0.288945	+	1.01982i
$274$		−	14.1595i		−	0.855408i
$275$	9.84008	+	17.0435i	0.593379	+	1.02776i
$276$	−8.09335	+	1.87022i	−0.487162	+	0.112574i
$277$	1.87920	−	3.25487i	0.112910	−	0.195566i	−0.804032	−	0.594586i	$-0.797316\pi$
$277$	1.87920	−	3.25487i	0.112910	−	0.195566i	0.916942	+	0.399019i	$0.130649\pi$
$278$	−3.05980	+	1.76658i	−0.183515	+	0.105952i
$279$	28.8136	−	6.05196i	1.72503	−	0.362321i
$280$	−5.04097	−	6.39443i	−0.301255	−	0.382140i
$281$	−10.8110			−0.644931			−0.322466	−	0.946581i	$-0.604512\pi$
$281$	−10.8110			−0.644931			−0.322466	+	0.946581i	$0.604512\pi$
$282$	−15.8550	+	11.4901i	−0.944149	+	0.684227i
$283$	−8.71160	−	5.02964i	−0.517851	−	0.298981i	0.218204	−	0.975903i	$-0.429980\pi$
$283$	−8.71160	−	5.02964i	−0.517851	−	0.298981i	−0.736055	+	0.676922i	$0.763313\pi$
$284$	−8.27039	−	4.77491i	−0.490758	−	0.283339i
$285$	9.69968	+	13.3844i	0.574559	+	0.792821i
$286$			16.8206i			0.994626i
$287$	−13.0012	+	1.88510i	−0.767439	+	0.111274i
$288$	0.616659	+	2.93594i	0.0363370	+	0.173002i
$289$	−4.22188	−	7.31251i	−0.248346	−	0.430147i
$290$	−4.59734	+	7.96282i	−0.269965	+	0.467593i
$291$	−11.5748	+	25.9133i	−0.678526	+	1.51906i
$292$	5.38750	+	9.33143i	0.315280	+	0.546080i
$293$	20.3492			1.18881			0.594405	−	0.804166i	$-0.297388\pi$
$293$	20.3492			1.18881			0.594405	+	0.804166i	$0.297388\pi$
$294$	−11.2070	+	4.62630i	−0.653607	+	0.269811i
$295$		−	31.1171i		−	1.81171i
$296$	−0.531811	−	0.921124i	−0.0309109	−	0.0535392i
$297$	−22.3528	−	4.83578i	−1.29704	−	0.280600i
$298$	−14.4945	−	8.36840i	−0.839644	−	0.484768i
$299$	16.8815	+	7.13774i	0.976280	+	0.412786i
$300$	−0.800262	−	7.70330i	−0.0462031	−	0.444750i
$301$	−10.9036	+	1.58095i	−0.628474	+	0.0911247i
$302$			1.58712i			0.0913286i
$303$	−14.2365	−	19.6447i	−0.817867	−	1.12856i
$304$	−2.68548	−	1.55046i	−0.154023	−	0.0889252i
$305$	−6.85034	−	3.95504i	−0.392249	−	0.226465i
$306$	−11.2700	+	10.0985i	−0.644266	+	0.577293i
$307$	−24.7883			−1.41474			−0.707371	−	0.706842i	$-0.750119\pi$
$307$	−24.7883			−1.41474			−0.707371	+	0.706842i	$0.750119\pi$
$308$	−9.14483	+	7.20921i	−0.521075	+	0.410783i
$309$	0.618018	−	0.0642032i	0.0351578	−	0.00365239i
$310$	26.1571	−	15.1018i	1.48562	−	0.857725i
$311$	11.1110	+	6.41495i	0.630049	+	0.363759i	0.780771	−	0.624817i	$-0.214827\pi$
$311$	11.1110	+	6.41495i	0.630049	+	0.363759i	−0.150722	+	0.988576i	$0.548160\pi$
$312$	2.69966	−	6.04392i	0.152838	−	0.342169i
$313$	−1.79490	+	1.03629i	−0.101454	+	0.0585743i	−0.549868	−	0.835251i	$-0.685322\pi$
$313$	−1.79490	+	1.03629i	−0.101454	+	0.0585743i	0.448415	+	0.893826i	$0.351989\pi$
$314$	20.4361			1.15328
$315$	−24.0646	−	4.19479i	−1.35589	−	0.236350i
$316$		−	3.13860i		−	0.176560i
$317$	−6.72351	+	3.88182i	−0.377630	+	0.218025i	−0.676787	−	0.736179i	$-0.736628\pi$
$317$	−6.72351	+	3.88182i	−0.377630	+	0.218025i	0.299157	+	0.954204i	$0.403295\pi$
$318$	−3.66891	+	8.21385i	−0.205742	+	0.460610i
$319$	11.3878	+	6.57476i	0.637595	+	0.368116i
$320$	1.53878	+	2.66525i	0.0860207	+	0.148992i
$321$	−0.922680	−	8.88169i	−0.0514990	−	0.495728i
$322$	3.35472	+	12.2371i	0.186951	+	0.681945i
$323$		−	15.6416i		−	0.870324i
$324$	7.25556	+	5.32511i	0.403087	+	0.295840i
$325$	−8.54433	+	14.7992i	−0.473954	+	0.820913i
$326$	−5.72462	−	3.30511i	−0.317057	−	0.183053i
$327$	−10.4793	−	14.4602i	−0.579508	−	0.799650i
$328$	4.96539			0.274168
$329$	18.5171	+	23.4888i	1.02088	+	1.29498i
$330$	−23.3356	+	2.42423i	−1.28458	+	0.133450i
$331$	−11.8453	−	20.5166i	−0.651075	−	1.12769i	−0.982863	−	0.184340i	$-0.940985\pi$
$331$	−11.8453	−	20.5166i	−0.651075	−	1.12769i	0.331788	−	0.943354i	$-0.392348\pi$
$332$	4.32066	−	7.48361i	0.237127	−	0.410716i
$333$	−3.03231	−	0.993346i	−0.166170	−	0.0544350i
$334$	−9.89751	−	17.1430i	−0.541568	−	0.938023i
$335$		−	10.5669i		−	0.577334i
$336$	4.44293	−	1.12266i	0.242382	−	0.0612463i
$337$			15.6832i			0.854320i	0.904176	+	0.427160i	$0.140486\pi$
$337$			15.6832i			0.854320i	−0.904176	+	0.427160i	$0.859514\pi$
$338$	−1.39057	+	0.802849i	−0.0756373	+	0.0436692i
$339$	23.6633	+	10.5698i	1.28522	+	0.574072i
$340$	−7.76191	+	13.4440i	−0.420949	+	0.729104i
$341$	−21.5975	−	37.4079i	−1.16957	−	2.02575i
$342$	−9.10413	+	1.91221i	−0.492295	+	0.103401i
$343$	7.75372	+	16.8190i	0.418661	+	0.908142i
$344$	4.16427			0.224523
$345$	−7.46932	+	24.4487i	−0.402135	+	1.31627i
$346$	−8.62002	+	14.9303i	−0.463415	+	0.802659i
$347$	−11.1697	−	6.44883i	−0.599621	−	0.346191i	0.169272	−	0.985569i	$-0.445858\pi$
$347$	−11.1697	−	6.44883i	−0.599621	−	0.346191i	−0.768892	+	0.639378i	$0.779192\pi$
$348$	−3.03659	−	4.19012i	−0.162778	−	0.224614i
$349$	10.8173			0.579036			0.289518	−	0.957173i	$-0.406505\pi$
$349$	10.8173			0.579036			0.289518	+	0.957173i	$0.406505\pi$
$350$	−11.7079	+	1.69757i	−0.625813	+	0.0907389i
$351$	−6.06823	−	18.9085i	−0.323898	−	1.00926i
$352$	3.81164	−	2.20065i	0.203161	−	0.117295i
$353$	−18.4975	−	10.6795i	−0.984520	−	0.568413i	−0.0808885	−	0.996723i	$-0.525776\pi$
$353$	−18.4975	−	10.6795i	−0.984520	−	0.568413i	−0.903632	+	0.428310i	$0.859109\pi$
$354$	15.9900	+	7.14231i	0.849858	+	0.379609i
$355$	−25.4527	+	14.6951i	−1.35089	+	0.779937i
$356$	0.351255			0.0186165
$357$	16.1097	+	16.5770i	0.852616	+	0.877347i
$358$	−10.6555			−0.563163
$359$	−1.49189	−	2.58402i	−0.0787387	−	0.136379i	0.823967	−	0.566637i	$-0.191756\pi$
$359$	−1.49189	−	2.58402i	−0.0787387	−	0.136379i	−0.902706	+	0.430258i	$0.858423\pi$
$360$	8.77392	+	2.87423i	0.462426	+	0.151485i
$361$	−4.69213	+	8.12700i	−0.246954	+	0.427737i
$362$	−12.9331	−	22.4007i	−0.679746	−	1.17736i
$363$	1.49826	+	14.4222i	0.0786385	+	0.756972i
$364$	−9.39154	−	3.74684i	−0.492251	−	0.196388i
$365$	33.1608			1.73572
$366$	3.60472	−	2.61235i	0.188422	−	0.136550i
$367$	9.45430	+	5.45844i	0.493510	+	0.284928i	0.726030	−	0.687664i	$-0.241364\pi$
$367$	9.45430	+	5.45844i	0.493510	+	0.284928i	−0.232519	+	0.972592i	$0.574697\pi$
$368$	−0.591162	−	4.75926i	−0.0308164	−	0.248093i
$369$	11.0940	−	9.94077i	0.577531	−	0.517496i
$370$	−3.27337			−0.170175
$371$	12.7634	+	5.09206i	0.662641	+	0.264366i
$372$	1.75645	+	16.9076i	0.0910678	+	0.876616i
$373$	−22.7421	+	13.1302i	−1.17754	+	0.679854i	−0.955445	−	0.295171i	$-0.904623\pi$
$373$	−22.7421	+	13.1302i	−1.17754	+	0.679854i	−0.222097	+	0.975025i	$0.571290\pi$
$374$	19.2266	+	11.1005i	0.994185	+	0.573993i
$375$	2.57254	+	1.14909i	0.132846	+	0.0593386i
$376$	−5.65245	−	9.79033i	−0.291503	−	0.504898i
$377$			11.4180i			0.588056i
$378$	7.67911	−	11.4031i	0.394971	−	0.586514i
$379$		−	3.02838i		−	0.155557i	−0.996971	−	0.0777787i	$-0.975217\pi$
$379$		−	3.02838i		−	0.155557i	0.996971	−	0.0777787i	$-0.0247828\pi$
$380$	−8.26476	+	4.77166i	−0.423973	+	0.244781i
$381$	15.7938	+	7.05467i	0.809140	+	0.361422i
$382$	−13.7136	−	7.91755i	−0.701649	−	0.405097i
$383$	−4.12689	−	7.14797i	−0.210874	−	0.365244i	0.741114	−	0.671379i	$-0.234298\pi$
$383$	−4.12689	−	7.14797i	−0.210874	−	0.365244i	−0.951988	+	0.306134i	$0.900964\pi$
$384$	−1.72278	+	0.178972i	−0.0879152	+	0.00913313i
$385$	5.14245	+	35.4667i	0.262083	+	1.80755i
$386$		−	23.3898i		−	1.19051i
$387$	9.30410	−	8.33692i	0.472954	−	0.423789i
$388$	−14.1904	−	8.19285i	−0.720410	−	0.415929i
$389$	10.0477	−	17.4032i	0.509441	−	0.882377i	−0.490500	−	0.871441i	$-0.663186\pi$
$389$	10.0477	−	17.4032i	0.509441	−	0.882377i	0.999940	−	0.0109355i	$-0.00348096\pi$
$390$	−11.9544	−	16.4956i	−0.605333	−	0.835285i
$391$	19.2993	−	14.5857i	0.976009	−	0.737631i
$392$	−1.98811	−	6.71174i	−0.100415	−	0.338994i
$393$	8.83678	−	0.918014i	0.445757	−	0.0463077i
$394$	−4.51672	−	7.82318i	−0.227549	−	0.394126i
$395$	−8.36518	−	4.82964i	−0.420898	−	0.243005i
$396$	4.11050	−	12.5478i	0.206560	−	0.630551i
$397$	9.96051	+	17.2521i	0.499903	+	0.865858i	1.00000		0.000111500i	$-3.54916e-5\pi$
$397$	9.96051	+	17.2521i	0.499903	+	0.865858i	−0.500097	+	0.865970i	$0.666702\pi$
$398$	−1.31192			−0.0657604
$399$	3.48130	+	13.7772i	0.174283	+	0.689723i
$400$	4.47144			0.223572
$401$	5.66903	+	9.81905i	0.283098	+	0.490340i	0.972146	−	0.234375i	$-0.0753045\pi$
$401$	5.66903	+	9.81905i	0.283098	+	0.490340i	−0.689048	+	0.724716i	$0.741971\pi$
$402$	5.42999	+	2.42543i	0.270823	+	0.120970i
$403$	18.7535	−	32.4820i	0.934178	−	1.61804i
$404$	12.1304	−	7.00352i	0.603512	−	0.348438i
$405$	25.3575	−	11.1437i	1.26003	−	0.553735i
$406$	−6.20758	+	4.89366i	−0.308077	+	0.242868i
$407$			4.68133i			0.232045i
$408$	−5.12682	−	7.07439i	−0.253816	−	0.350234i
$409$	6.27343	−	10.8659i	0.310201	−	0.537284i	−0.668205	−	0.743977i	$-0.732937\pi$
$409$	6.27343	−	10.8659i	0.310201	−	0.537284i	0.978406	+	0.206694i	$0.0662703\pi$
$410$	7.64067	−	13.2340i	0.377346	−	0.653582i
$411$	19.8585	−	14.3915i	0.979548	−	0.709881i
$412$			0.358733i			0.0176735i
$413$	9.91276	−	24.8466i	0.487775	−	1.22262i
$414$	−10.8489	−	9.44994i	−0.533194	−	0.464439i
$415$	−13.2971	−	23.0313i	−0.652731	−	1.13056i
$416$	3.30972	+	1.91087i	0.162273	+	0.0936881i
$417$	−5.58754	−	2.49581i	−0.273623	−	0.122220i
$418$	6.82406	+	11.8196i	0.333776	+	0.578117i
$419$	−25.2058			−1.23138			−0.615692	−	0.787987i	$-0.711123\pi$
$419$	−25.2058			−1.23138			−0.615692	+	0.787987i	$0.711123\pi$
$420$	3.84453	−	13.5691i	0.187594	−	0.662103i
$421$			23.5327i			1.14691i	0.819236	+	0.573456i	$0.194398\pi$
$421$			23.5327i			1.14691i	−0.819236	+	0.573456i	$0.805602\pi$
$422$	−9.63530	+	5.56294i	−0.469039	+	0.270800i
$423$	−32.2294	−	10.5580i	−1.56705	−	0.513345i
$424$	−4.49800	−	2.59692i	−0.218442	−	0.126118i
$425$	11.2774	+	19.5330i	0.547033	+	0.947488i
$426$	−1.70915	−	16.4522i	−0.0828087	−	0.797114i
$427$	−4.20997	−	5.34032i	−0.203735	−	0.258436i
$428$	5.15544			0.249198
$429$	−23.5907	+	17.0962i	−1.13897	+	0.825414i
$430$	6.40792	−	11.0988i	0.309017	−	0.535234i
$431$	−4.31684	+	7.47699i	−0.207935	+	0.360154i	−0.951064	−	0.308994i	$-0.900008\pi$
$431$	−4.31684	+	7.47699i	−0.207935	+	0.360154i	0.743129	+	0.669148i	$0.233341\pi$
$432$	−3.49085	+	3.84889i	−0.167953	+	0.185180i
$433$		−	23.0214i		−	1.10634i	−0.833069	−	0.553169i	$-0.813418\pi$
$433$		−	23.0214i		−	1.10634i	0.833069	−	0.553169i	$-0.186582\pi$
$434$	25.6970	−	3.72590i	1.23350	−	0.178849i
$435$	−15.8404	+	1.64559i	−0.759489	+	0.0788999i
$436$	8.92907	−	5.15520i	0.427625	−	0.246889i
$437$	14.7581	−	1.83315i	0.705976	−	0.0876914i
$438$	−7.61141	+	17.0402i	−0.363687	+	0.814212i
$439$	−19.1647	−	33.1942i	−0.914681	−	1.58427i	−0.807368	−	0.590049i	$-0.799109\pi$
$439$	−19.1647	−	33.1942i	−0.914681	−	1.58427i	−0.107313	−	0.994225i	$-0.534225\pi$
$440$		−	13.5453i		−	0.645748i
$441$	−17.8790	−	11.0156i	−0.851379	−	0.524552i
$442$			19.2775i			0.916939i
$443$	18.1008	−	10.4505i	0.859994	−	0.496518i	−0.00401647	−	0.999992i	$-0.501278\pi$
$443$	18.1008	−	10.4505i	0.859994	−	0.496518i	0.864010	+	0.503474i	$0.167945\pi$
$444$	0.751338	−	1.68207i	0.0356569	−	0.0798276i
$445$	0.540506	−	0.936185i	0.0256225	−	0.0443794i
$446$	−8.71279	+	5.03033i	−0.412563	+	0.238193i
$447$	−2.99542	−	28.8338i	−0.141678	−	1.36379i
$448$	0.379647	+	2.61837i	0.0179366	+	0.123706i
$449$		−	33.2299i		−	1.56821i	−0.620625	−	0.784107i	$-0.713121\pi$
$449$		−	33.2299i		−	1.56821i	0.620625	−	0.784107i	$-0.286879\pi$
$450$	9.99039	−	8.95186i	0.470951	−	0.421995i
$451$	−18.9263	−	10.9271i	−0.891205	−	0.514537i
$452$	−7.48150	+	12.9583i	−0.351900	+	0.609509i
$453$	−2.22591	+	1.61313i	−0.104583	+	0.0757913i
$454$			27.2766i			1.28015i
$455$	−24.4378	+	19.2653i	−1.14566	+	0.903169i
$456$	−0.554979	−	5.34221i	−0.0259893	−	0.250172i
$457$	24.8373	−	14.3398i	1.16184	−	0.670790i	0.210097	−	0.977681i	$-0.432622\pi$
$457$	24.8373	−	14.3398i	1.16184	−	0.670790i	0.951745	+	0.306891i	$0.0992887\pi$
$458$	0.855761	−	1.48222i	0.0399871	−	0.0692597i
$459$	−25.6177	−	5.54211i	−1.19573	−	0.258684i
$460$	−13.5943	−	5.74788i	−0.633837	−	0.267996i
$461$			19.0947i			0.889330i	0.895697	+	0.444665i	$0.146677\pi$
$461$			19.0947i			0.889330i	−0.895697	+	0.444665i	$0.853323\pi$
$462$	−19.4055	−	5.49815i	−0.902824	−	0.255797i
$463$	36.9549			1.71744			0.858719	−	0.512447i	$-0.171261\pi$
$463$	36.9549			1.71744			0.858719	+	0.512447i	$0.171261\pi$
$464$	2.58737	−	1.49382i	0.120116	−	0.0693489i
$465$	47.7657	+	21.3357i	2.21508	+	0.989419i
$466$	1.43108	−	2.47869i	0.0662933	−	0.114823i
$467$	−4.78953	−	8.29571i	−0.221633	−	0.383880i	0.733671	−	0.679505i	$-0.237805\pi$
$467$	−4.78953	−	8.29571i	−0.221633	−	0.383880i	−0.955304	+	0.295625i	$0.904472\pi$
$468$	11.2204	−	2.35671i	0.518663	−	0.108939i
$469$	3.36624	−	8.43756i	0.155439	−	0.389611i
$470$	−34.7916			−1.60482
$471$	20.7710	+	28.6614i	0.957075	+	1.32065i
$472$	−5.05546	+	8.75632i	−0.232696	+	0.403042i
$473$	−15.8727	−	9.16412i	−0.729829	−	0.421367i
$474$	4.40184	−	3.19003i	0.202183	−	0.146523i
$475$			13.8656i			0.636197i
$476$	−10.4806	+	8.26221i	−0.480376	+	0.378698i
$477$	−15.2488	+	3.20283i	−0.698195	+	0.146648i
$478$	10.1292	+	17.5443i	0.463300	+	0.802459i
$479$	21.4349	−	37.1263i	0.979385	−	1.69634i	0.314754	−	0.949173i	$-0.398078\pi$
$479$	21.4349	−	37.1263i	0.979385	−	1.69634i	0.664631	−	0.747172i	$-0.268589\pi$
$480$	−2.17398	+	4.86704i	−0.0992282	+	0.222149i
$481$	−3.52030	+	2.03244i	−0.160512	+	0.0926715i
$482$	−3.05723			−0.139253
$483$	−13.7526	+	17.1425i	−0.625766	+	0.780011i
$484$	−8.37150			−0.380523
$485$	−43.6720	+	25.2141i	−1.98305	+	1.14491i
$486$	−0.0939555	+	15.5882i	−0.00426191	+	0.707094i
$487$	6.75714	−	11.7037i	0.306195	−	0.530346i	−0.671332	−	0.741157i	$-0.734277\pi$
$487$	6.75714	−	11.7037i	0.306195	−	0.530346i	0.977527	+	0.210812i	$0.0676107\pi$
$488$	1.28512	+	2.22589i	0.0581746	+	0.100761i
$489$	−1.18304	−	11.3879i	−0.0534991	−	0.514981i
$490$	−20.9478	−	5.02909i	−0.946323	−	0.227191i
$491$			5.26234i			0.237486i	0.992925	+	0.118743i	$0.0378865\pi$
$491$			5.26234i			0.237486i	−0.992925	+	0.118743i	$0.962114\pi$
$492$	5.04674	+	6.96389i	0.227525	+	0.313956i
$493$	13.0512	+	7.53510i	0.587795	+	0.339364i
$494$	−5.92547	+	10.2632i	−0.266599	+	0.461764i
$495$	−27.1179	−	30.2639i	−1.21886	−	1.36026i
$496$	−9.81411			−0.440667
$497$	−25.0050	+	3.62557i	−1.12163	+	0.162629i
$498$	14.8871	−	1.54656i	0.667107	−	0.0693028i
$499$	15.3157	+	26.5276i	0.685625	+	1.18754i	0.973240	+	0.229792i	$0.0738045\pi$
$499$	15.3157	+	26.5276i	0.685625	+	1.18754i	−0.287614	+	0.957746i	$0.592862\pi$
$500$	−0.813346	+	1.40876i	−0.0363739	+	0.0630015i
$501$	13.9831	−	31.3050i	0.624720	−	1.39860i
$502$	20.8652	−	12.0465i	0.931261	−	0.537664i
$503$	−31.9103			−1.42281			−0.711405	−	0.702782i	$-0.751941\pi$
$503$	−31.9103			−1.42281			−0.711405	+	0.702782i	$0.751941\pi$
$504$	6.09024	+	5.09008i	0.271281	+	0.226730i
$505$		−	43.1076i		−	1.91826i
$506$	−8.22018	+	19.4415i	−0.365431	+	0.864282i
$507$	−2.53934	−	1.13426i	−0.112776	−	0.0503741i
$508$	−4.99343	+	8.64888i	−0.221548	+	0.383732i
$509$	0.444150	−	0.256430i	0.0196866	−	0.0113661i	−0.490124	−	0.871652i	$-0.663049\pi$
$509$	0.444150	−	0.256430i	0.0196866	−	0.0113661i	0.509811	+	0.860286i	$0.329715\pi$
$510$	−26.7441	+	2.77833i	−1.18425	+	0.123026i
$511$	26.4785	+	10.5638i	1.17134	+	0.467316i
$512$		−	1.00000i		−	0.0441942i
$513$	−11.9351	−	10.8249i	−0.526949	−	0.477929i
$514$	7.34781	−	12.7268i	0.324098	−	0.561354i
$515$	0.956115	+	0.552013i	0.0421315	+	0.0243246i
$516$	4.23250	+	5.84033i	0.186325	+	0.257106i
$517$			49.7563i			2.18828i
$518$	−2.61375	−	1.04278i	−0.114841	−	0.0458170i
$519$	−29.7008	+	3.08549i	−1.30372	+	0.135438i
$520$	10.1859	−	5.88084i	0.446682	−	0.257892i
$521$	2.27058	−	3.93275i	0.0994757	−	0.172297i	−0.811992	−	0.583668i	$-0.801617\pi$
$521$	2.27058	−	3.93275i	0.0994757	−	0.172297i	0.911468	+	0.411372i	$0.134950\pi$
$522$	2.79024	−	8.51754i	0.122125	−	0.372803i
$523$	−4.64025	+	2.67905i	−0.202904	+	0.117147i	−0.598009	−	0.801489i	$-0.704041\pi$
$523$	−4.64025	+	2.67905i	−0.202904	+	0.117147i	0.395105	+	0.918636i	$0.370708\pi$
$524$			5.12937i			0.224078i
$525$	−14.2805	−	14.6947i	−0.623253	−	0.641331i
$526$			11.4751i			0.500337i
$527$	−24.7521	−	42.8719i	−1.07822	−	1.86753i
$528$	6.96048	+	3.10906i	0.302916	+	0.135305i
$529$	16.0236	+	16.4998i	0.696680	+	0.717382i
$530$	−13.8429	+	7.99221i	−0.601298	+	0.347160i
$531$	6.23499	+	29.6850i	0.270575	+	1.28822i
$532$	−8.11938	+	1.17726i	−0.352020	+	0.0510406i
$533$		−	18.9764i		−	0.821961i
$534$	0.357010	+	0.492630i	0.0154493	+	0.0213182i
$535$	7.93312	−	13.7406i	0.342979	−	0.594056i
$536$	−1.71677	+	2.97353i	−0.0741530	+	0.128437i
$537$	−10.8301	−	14.9442i	−0.467355	−	0.644892i
$538$	−6.91948			−0.298320
$539$	−7.19222	+	29.9579i	−0.309791	+	1.29038i
$540$	4.88662	+	15.2266i	0.210287	+	0.655249i
$541$	22.9013	+	39.6662i	0.984604	+	1.70538i	0.643685	+	0.765291i	$0.277405\pi$
$541$	22.9013	+	39.6662i	0.984604	+	1.70538i	0.340919	+	0.940093i	$0.389262\pi$
$542$	−20.4355	−	11.7984i	−0.877779	−	0.506786i
$543$	18.2717	−	40.9061i	0.784114	−	1.75545i
$544$	4.36839	−	2.52209i	0.187293	−	0.108134i
$545$		−	31.7310i		−	1.35921i
$546$	−4.29053	−	16.9797i	−0.183618	−	0.726665i
$547$	35.9342			1.53644			0.768218	−	0.640189i	$-0.221144\pi$
$547$	35.9342			1.53644			0.768218	+	0.640189i	$0.221144\pi$
$548$	7.07976	+	12.2625i	0.302432	+	0.523828i
$549$	7.32756	+	2.40042i	0.312733	+	0.102447i
$550$	−17.0435	−	9.84008i	−0.726738	−	0.419582i
$551$	4.63223	+	8.02325i	0.197339	+	0.341802i
$552$	6.07394	−	5.66633i	0.258524	−	0.241175i
$553$	−5.14094	−	6.52124i	−0.218615	−	0.277311i
$554$			3.75840i			0.159679i
$555$	−3.32700	−	4.59085i	−0.141223	−	0.194871i
$556$	1.76658	−	3.05980i	0.0749196	−	0.129765i
$557$	−1.44330	+	2.49986i	−0.0611544	+	0.105923i	−0.894982	−	0.446103i	$-0.852812\pi$
$557$	−1.44330	+	2.49986i	−0.0611544	+	0.105923i	0.833827	+	0.552025i	$0.186145\pi$
$558$	−21.9274	+	19.6480i	−0.928259	+	0.831765i
$559$		−	15.9148i		−	0.673123i
$560$	7.56282	+	3.01725i	0.319587	+	0.127502i
$561$	3.97335	+	38.2474i	0.167755	+	1.61481i
$562$	9.36261	−	5.40551i	0.394938	−	0.228018i
$563$	2.29962	−	3.98306i	0.0969176	−	0.167866i	−0.813490	−	0.581579i	$-0.802435\pi$
$563$	2.29962	−	3.98306i	0.0969176	−	0.167866i	0.910407	+	0.413713i	$0.135768\pi$
$564$	7.98573	−	17.8782i	0.336260	−	0.752809i
$565$	23.0248	+	39.8802i	0.968662	+	1.67777i
$566$	10.0593			0.422823
$567$	23.7976	−	0.820121i	0.999407	−	0.0344418i
$568$	9.54983			0.400702
$569$	−16.4480	−	28.4888i	−0.689537	−	1.19431i	−0.971988	−	0.235031i	$-0.924481\pi$
$569$	−16.4480	−	28.4888i	−0.689537	−	1.19431i	0.282451	−	0.959282i	$-0.408853\pi$
$570$	−15.0923	−	6.74136i	−0.632149	−	0.282364i
$571$	−17.3244	−	10.0022i	−0.725002	−	0.418580i	0.0915886	−	0.995797i	$-0.470806\pi$
$571$	−17.3244	−	10.0022i	−0.725002	−	0.418580i	−0.816591	+	0.577217i	$0.804139\pi$
$572$	−8.41032	−	14.5671i	−0.351653	−	0.609081i
$573$	−2.83404	−	27.2804i	−0.118394	−	1.13965i
$574$	10.3169	−	8.13316i	0.430617	−	0.339472i
$575$	−17.1080	+	12.9296i	−0.713452	+	0.539200i
$576$	−2.00201	−	2.23427i	−0.0834171	−	0.0930945i
$577$	−6.71432	+	11.6295i	−0.279521	+	0.484144i	−0.971266	−	0.237998i	$-0.923509\pi$
$577$	−6.71432	+	11.6295i	−0.279521	+	0.484144i	0.691745	+	0.722142i	$0.256842\pi$
$578$	7.31251	+	4.22188i	0.304160	+	0.175607i
$579$	32.8039	−	23.7730i	1.36328	−	0.987974i
$580$		−	9.19467i		−	0.381788i
$581$	−3.28066	−	22.6262i	−0.136105	−	0.938693i
$582$	−2.93258	−	28.2289i	−0.121559	−	1.17013i
$583$	11.4299	+	19.7971i	0.473376	+	0.819912i
$584$	−9.33143	−	5.38750i	−0.386137	−	0.222936i
$585$	10.9845	−	33.5317i	0.454155	−	1.38636i
$586$	−17.6229	+	10.1746i	−0.727995	+	0.420308i
$587$			42.7016i			1.76249i	0.472664	+	0.881243i	$0.343293\pi$
$587$			42.7016i			1.76249i	−0.472664	+	0.881243i	$0.656707\pi$
$588$	7.39242	−	9.61000i	0.304858	−	0.396310i
$589$		−	30.4328i		−	1.25396i
$590$	15.5585	+	26.9482i	0.640535	+	1.10944i
$591$	6.38118	−	14.2860i	0.262487	−	0.587647i
$592$	0.921124	+	0.531811i	0.0378580	+	0.0218573i
$593$	1.94554	−	1.12326i	0.0798937	−	0.0461266i	−0.459521	−	0.888167i	$-0.651979\pi$
$593$	1.94554	−	1.12326i	0.0798937	−	0.0461266i	0.539415	+	0.842040i	$0.318646\pi$
$594$	21.7759	−	6.98847i	0.893478	−	0.286740i
$595$	5.89357	+	40.6471i	0.241613	+	1.66637i
$596$	16.7368			0.685566
$597$	−1.33341	−	1.83994i	−0.0545729	−	0.0753039i
$598$	−18.1886	+	2.25927i	−0.743789	+	0.0923883i
$599$	−9.63702	−	5.56394i	−0.393758	−	0.227336i	0.290029	−	0.957018i	$-0.406335\pi$
$599$	−9.63702	−	5.56394i	−0.393758	−	0.227336i	−0.683787	+	0.729681i	$0.739668\pi$
$600$	4.54470	+	6.27112i	0.185536	+	0.256017i
$601$	−18.9886			−0.774562			−0.387281	−	0.921962i	$-0.626586\pi$
$601$	−18.9886			−0.774562			−0.387281	+	0.921962i	$0.626586\pi$
$602$	8.65233	−	6.82095i	0.352643	−	0.278001i
$603$	2.11732	+	10.0806i	0.0862239	+	0.410515i
$604$	−0.793561	−	1.37449i	−0.0322895	−	0.0559271i
$605$	−12.8819	+	22.3122i	−0.523725	+	0.907119i
$606$	22.1515	+	9.89450i	0.899844	+	0.401937i
$607$	9.07549	+	15.7192i	0.368363	+	0.638023i	0.989310	−	0.145830i	$-0.0465851\pi$
$607$	9.07549	+	15.7192i	0.368363	+	0.638023i	−0.620947	+	0.783853i	$0.713252\pi$
$608$	3.10093			0.125759
$609$	−13.1726	−	3.73219i	−0.533779	−	0.151236i
$610$	7.91009			0.320270
$611$	−37.4161	+	21.6022i	−1.51369	+	0.873932i
$612$	4.71090	−	14.3806i	0.190427	−	0.581301i
$613$	13.2501	+	7.64992i	0.535165	+	0.308977i	0.743117	−	0.669162i	$-0.233347\pi$
$613$	13.2501	+	7.64992i	0.535165	+	0.308977i	−0.207952	+	0.978139i	$0.566680\pi$
$614$	21.4673	−	12.3941i	0.866349	−	0.500187i
$615$	26.3264	−	2.73493i	1.06158	−	0.110283i
$616$	4.31505	−	10.8158i	0.173858	−	0.435780i
$617$	−7.20949			−0.290243			−0.145122	−	0.989414i	$-0.546357\pi$
$617$	−7.20949			−0.290243			−0.145122	+	0.989414i	$0.546357\pi$
$618$	−0.503118	+	0.364611i	−0.0202384	+	0.0146668i
$619$	−33.3880	−	19.2765i	−1.34198	−	0.774790i	−0.354878	−	0.934913i	$-0.615478\pi$
$619$	−33.3880	−	19.2765i	−1.34198	−	0.774790i	−0.987097	+	0.160123i	$0.948811\pi$
$620$	−15.1018	+	26.1571i	−0.606503	+	1.05049i
$621$	2.22675	−	24.8202i	0.0893564	−	0.996000i
$622$	−12.8299			−0.514432
$623$	0.729822	−	0.575346i	0.0292397	−	0.0230507i
$624$	0.683984	+	6.58402i	0.0273813	+	0.263572i
$625$	13.6817	+	23.6974i	0.547269	+	0.947897i
$626$	1.03629	−	1.79490i	0.0414183	−	0.0717386i
$627$	−9.64097	+	21.5839i	−0.385023	+	0.861979i
$628$	−17.6982	+	10.2181i	−0.706236	+	0.407745i
$629$			5.36510i			0.213921i
$630$	22.9379	−	8.39949i	0.913869	−	0.334644i
$631$			35.2273i			1.40238i	0.712977	+	0.701188i	$0.247346\pi$
$631$			35.2273i			1.40238i	−0.712977	+	0.701188i	$0.752654\pi$
$632$	1.56930	+	2.71811i	0.0624235	+	0.108121i
$633$	−17.5951	−	7.85927i	−0.699342	−	0.312378i
$634$	3.88182	−	6.72351i	0.154167	−	0.267025i
$635$	15.3676	+	26.6175i	0.609846	+	1.05628i
$636$	−0.929553	−	8.94785i	−0.0368592	−	0.354805i
$637$	−25.6505	+	7.59806i	−1.01631	+	0.301046i
$638$	−13.1495			−0.520594
$639$	21.3369	−	19.1189i	0.844074	−	0.756331i
$640$	−2.66525	−	1.53878i	−0.105353	−	0.0608258i
$641$	17.7954	−	30.8226i	0.702877	−	1.21742i	−0.264575	−	0.964365i	$-0.585232\pi$
$641$	17.7954	−	30.8226i	0.702877	−	1.21742i	0.967452	−	0.253054i	$-0.0814349\pi$
$642$	5.23991	+	7.23043i	0.206803	+	0.285362i
$643$		−	24.6674i		−	0.972788i	−0.873740	−	0.486394i	$-0.838312\pi$
$643$		−	24.6674i		−	0.972788i	0.873740	−	0.486394i	$-0.161688\pi$
$644$	−9.02381	−	8.92025i	−0.355588	−	0.351507i
$645$	22.0789	−	2.29368i	0.869355	−	0.0903134i
$646$	7.82082	+	13.5460i	0.307706	+	0.532962i
$647$	9.80531	+	5.66110i	0.385487	+	0.222561i	0.680203	−	0.733024i	$-0.261892\pi$
$647$	9.80531	+	5.66110i	0.385487	+	0.222561i	−0.294716	+	0.955585i	$0.595225\pi$
$648$	−8.94606	−	0.983904i	−0.351434	−	0.0386514i
$649$	38.5392	−	22.2506i	1.51280	−	0.873414i
$650$		−	17.0887i		−	0.670273i
$651$	31.3435	+	32.2527i	1.22845	+	1.26408i
$652$	6.61022			0.258876
$653$	1.01696	−	0.587142i	0.0397967	−	0.0229766i	−0.479970	−	0.877285i	$-0.659352\pi$
$653$	1.01696	−	0.587142i	0.0397967	−	0.0229766i	0.519766	+	0.854308i	$0.326019\pi$
$654$	16.3055	+	7.28322i	0.637594	+	0.284796i
$655$	13.6711	+	7.89300i	0.534173	+	0.308405i
$656$	−4.30015	+	2.48270i	−0.167893	+	0.0969330i
$657$	−31.6347	+	6.64450i	−1.23419	+	0.259227i
$658$	−27.7807	−	11.0833i	−1.08300	−	0.432074i
$659$	−7.97006			−0.310469			−0.155235	−	0.987878i	$-0.549613\pi$
$659$	−7.97006			−0.310469			−0.155235	+	0.987878i	$0.549613\pi$
$660$	18.9971	−	13.7673i	0.739462	−	0.535890i
$661$	−3.42255	−	1.97601i	−0.133122	−	0.0768579i	0.431960	−	0.901893i	$-0.357822\pi$
$661$	−3.42255	−	1.97601i	−0.133122	−	0.0768579i	−0.565082	+	0.825035i	$0.691155\pi$
$662$	20.5166	+	11.8453i	0.797400	+	0.460379i
$663$	−27.0365	+	19.5934i	−1.05001	+	0.760944i
$664$			8.64133i			0.335349i
$665$	−9.35628	+	23.4517i	−0.362821	+	0.909420i
$666$	3.12273	−	0.655892i	0.121003	−	0.0254153i
$667$	−5.57992	+	13.1971i	−0.216055	+	0.510992i
$668$	17.1430	+	9.89751i	0.663283	+	0.382946i
$669$	−15.9105	−	7.10681i	−0.615136	−	0.274765i
$670$	5.28347	+	9.15124i	0.204118	+	0.353543i
$671$		−	11.3124i		−	0.436711i
$672$	−3.28636	+	3.19372i	−0.126774	+	0.123200i
$673$	−7.89987			−0.304518			−0.152259	−	0.988341i	$-0.548655\pi$
$673$	−7.89987			−0.304518			−0.152259	+	0.988341i	$0.548655\pi$
$674$	−7.84161	−	13.5821i	−0.302048	−	0.523162i
$675$	22.7089	+	4.91283i	0.874067	+	0.189095i
$676$	0.802849	−	1.39057i	0.0308788	−	0.0534836i
$677$	19.7207	+	34.1573i	0.757929	+	1.31277i	0.943905	+	0.330218i	$0.107122\pi$
$677$	19.7207	+	34.1573i	0.757929	+	1.31277i	−0.185976	+	0.982554i	$0.559545\pi$
$678$	−25.7779	+	2.67796i	−0.989996	+	0.102846i
$679$	−42.9038	+	6.22079i	−1.64650	+	0.238732i
$680$		−	15.5238i		−	0.595311i
$681$	−38.2550	+	27.7235i	−1.46593	+	1.06237i
$682$	37.4079	+	21.5975i	1.43242	+	0.827010i
$683$	37.9522	+	21.9117i	1.45220	+	0.838428i	0.998606	−	0.0527797i	$-0.0168081\pi$
$683$	37.9522	+	21.9117i	1.45220	+	0.838428i	0.453595	+	0.891208i	$0.350141\pi$
$684$	6.92830	−	6.20809i	0.264910	−	0.237372i
$685$	43.5769			1.66499
$686$	−15.1244	−	10.6889i	−0.577453	−	0.408102i
$687$	2.94858	−	0.306315i	0.112495	−	0.0116866i
$688$	−3.60637	+	2.08214i	−0.137491	+	0.0793807i
$689$	−9.92477	+	17.1902i	−0.378104	+	0.654895i
$690$	−5.75572	−	24.9078i	−0.219116	−	0.948226i
$691$	−1.93213	−	3.34655i	−0.0735017	−	0.127309i	0.826932	−	0.562302i	$-0.190084\pi$
$691$	−1.93213	−	3.34655i	−0.0735017	−	0.127309i	−0.900434	+	0.434993i	$0.856751\pi$
$692$		−	17.2400i		−	0.655368i
$693$	−12.0123	−	32.8041i	−0.456310	−	1.24612i
$694$	12.8977			0.489588
$695$	−5.43677	−	9.41676i	−0.206228	−	0.357198i
$696$	4.72482	+	2.11046i	0.179094	+	0.0799966i
$697$	−21.6908	−	12.5232i	−0.821596	−	0.474349i
$698$	−9.36805	+	5.40864i	−0.354586	+	0.204720i
$699$	4.93085	−	0.512245i	0.186502	−	0.0193749i
$700$	9.29054	−	7.32408i	0.351149	−	0.276824i
$701$	−3.41203			−0.128870			−0.0644352	−	0.997922i	$-0.520525\pi$
$701$	−3.41203			−0.128870			−0.0644352	+	0.997922i	$0.520525\pi$
$702$	14.7095	+	13.3411i	0.555173	+	0.503528i
$703$	−1.64911	+	2.85634i	−0.0621973	+	0.107729i
$704$	−2.20065	+	3.81164i	−0.0829402	+	0.143657i
$705$	−35.3617	−	48.7947i	−1.33180	−	1.83772i
$706$	21.3590			0.803857
$707$	13.7325	−	34.4209i	0.516464	−	1.29453i
$708$	−17.4189	+	1.80957i	−0.654642	+	0.0680079i
$709$	−9.46538	+	5.46484i	−0.355480	+	0.205236i	−0.667096	−	0.744972i	$-0.732463\pi$
$709$	−9.46538	+	5.46484i	−0.355480	+	0.205236i	0.311616	+	0.950208i	$0.399130\pi$
$710$	14.6951	−	25.4527i	0.551499	−	0.955223i
$711$	8.94793	+	2.93123i	0.335574	+	0.109930i
$712$	−0.304196	+	0.175628i	−0.0114002	+	0.00658192i
$713$	37.5494	−	28.3784i	1.40623	−	1.06278i
$714$	−22.2399	−	6.30124i	−0.832307	−	0.235818i
$715$	−51.7667			−1.93597
$716$	9.22798	−	5.32777i	0.344866	−	0.199108i
$717$	−14.3105	+	32.0378i	−0.534434	+	1.19648i
$718$	2.58402	+	1.49189i	0.0964349	+	0.0556767i
$719$	−37.8622	+	21.8598i	−1.41202	+	0.815232i	−0.995579	−	0.0939294i	$-0.970057\pi$
$719$	−37.8622	+	21.8598i	−1.41202	+	0.815232i	−0.416444	+	0.909161i	$0.636724\pi$
$720$	−9.03555	+	1.89781i	−0.336735	+	0.0707272i
$721$	0.587594	+	0.745359i	0.0218832	+	0.0277586i
$722$		−	9.38426i		−	0.349246i
$723$	−3.10732	−	4.28772i	−0.115563	−	0.159462i
$724$	22.4007	+	12.9331i	0.832516	+	0.480653i
$725$	−11.5693	−	6.67952i	−0.429672	−	0.248071i
$726$	−8.50866	−	11.7409i	−0.315786	−	0.435746i
$727$		−	30.3607i		−	1.12602i	−0.826451	−	0.563009i	$-0.809644\pi$
$727$		−	30.3607i		−	1.12602i	0.826451	−	0.563009i	$-0.190356\pi$
$728$	10.0067	−	1.45091i	0.370874	−	0.0537744i
$729$	−21.9577	+	15.7118i	−0.813247	+	0.581919i
$730$	−28.7181	+	16.5804i	−1.06291	+	0.613669i
$731$	−18.1912	−	10.5027i	−0.672824	−	0.388455i
$732$	−1.81560	+	4.06472i	−0.0671067	+	0.150236i
$733$	−29.6462	+	17.1162i	−1.09501	+	0.632203i	−0.934905	−	0.354898i	$-0.884516\pi$
$733$	−29.6462	+	17.1162i	−1.09501	+	0.632203i	−0.160102	+	0.987100i	$0.551182\pi$
$734$	−10.9169			−0.402949
$735$	−14.2378	−	34.4904i	−0.525167	−	1.27220i
$736$	2.89159	+	3.82606i	0.106585	+	0.141030i
$737$	13.0874	−	7.55602i	0.482081	−	0.278329i
$738$	−4.63731	+	14.1560i	−0.170702	+	0.521088i
$739$	−4.31095	+	7.46679i	−0.158581	+	0.274670i	−0.934357	−	0.356338i	$-0.884025\pi$
$739$	−4.31095	+	7.46679i	−0.158581	+	0.274670i	0.775776	+	0.631008i	$0.217359\pi$
$740$	2.83482	−	1.63669i	0.104210	−	0.0601658i
$741$	−20.4165	+	2.12099i	−0.750021	+	0.0779163i
$742$	−13.5994	+	1.97183i	−0.499250	+	0.0723882i
$743$	1.52278			0.0558656			0.0279328	−	0.999610i	$-0.491108\pi$
$743$	1.52278			0.0558656			0.0279328	+	0.999610i	$0.491108\pi$
$744$	−9.97491	−	13.7641i	−0.365698	−	0.504618i
$745$	25.7543	−	44.6078i	0.943566	−	1.63430i
$746$	13.1302	−	22.7421i	0.480729	−	0.832648i
$747$	17.3000	+	19.3070i	0.632975	+	0.706408i
$748$	−22.2010			−0.811748
$749$	10.7117	−	8.44446i	0.391398	−	0.308554i
$750$	−2.80243	+	0.291132i	−0.102330	+	0.0106306i
$751$	−23.4488	+	13.5382i	−0.855658	+	0.494014i	−0.862556	−	0.505962i	$-0.831138\pi$
$751$	−23.4488	+	13.5382i	−0.855658	+	0.494014i	0.00689806	+	0.999976i	$0.497804\pi$
$752$	9.79033	+	5.65245i	0.357017	+	0.206124i
$753$	38.1022	+	17.0192i	1.38852	+	0.620216i
$754$	−5.70899	−	9.88826i	−0.207909	−	0.360109i
$755$	−4.88448			−0.177764
$756$	−0.948741	+	13.7150i	−0.0345054	+	0.498808i
$757$		−	1.68399i		−	0.0612056i	−0.999532	−	0.0306028i	$-0.990257\pi$
$757$		−	1.68399i		−	0.0612056i	0.999532	−	0.0306028i	$-0.00974269\pi$
$758$	1.51419	+	2.62265i	0.0549979	+	0.0952591i
$759$	−35.6213	+	8.23139i	−1.29297	+	0.298781i
$760$	4.77166	−	8.26476i	0.173086	−	0.299794i
$761$	30.8598	−	17.8169i	1.11867	−	0.645862i	0.177606	−	0.984102i	$-0.443165\pi$
$761$	30.8598	−	17.8169i	1.11867	−	0.645862i	0.941060	+	0.338239i	$0.109831\pi$
$762$	−17.2052	+	1.78737i	−0.623277	+	0.0647495i
$763$	10.1083	−	25.3368i	0.365946	−	0.917253i
$764$	15.8351			0.572894
$765$	−31.0789	−	34.6844i	−1.12366	−	1.25402i
$766$	7.14797	+	4.12689i	0.258267	+	0.149110i
$767$	33.4644	+	19.3207i	1.20833	+	0.697629i
$768$	1.40248	−	1.01638i	0.0506078	−	0.0366756i
$769$			15.0497i			0.542705i	0.962480	+	0.271353i	$0.0874710\pi$
$769$			15.0497i			0.542705i	−0.962480	+	0.271353i	$0.912529\pi$
$770$	−22.1868	−	28.1438i	−0.799558	−	1.01423i
$771$	25.3173	−	2.63011i	0.911781	−	0.0947209i
$772$	11.6949	+	20.2562i	0.420909	+	0.729036i
$773$	−5.90858	+	10.2340i	−0.212517	+	0.368090i	−0.952502	−	0.304534i	$-0.901499\pi$
$773$	−5.90858	+	10.2340i	−0.212517	+	0.368090i	0.739985	+	0.672624i	$0.234833\pi$
$774$	−3.88913	+	11.8720i	−0.139792	+	0.426731i
$775$	21.9416	+	38.0040i	0.788165	+	1.36514i
$776$	16.3857			0.588212
$777$	−1.19409	−	4.72560i	−0.0428377	−	0.169530i
$778$			20.0955i			0.720458i
$779$	−7.69866	−	13.3345i	−0.275833	−	0.477757i
$780$	18.6006	+	8.30839i	0.666007	+	0.297488i
$781$	−36.4005	−	21.0159i	−1.30251	−	0.752007i
$782$	−9.42085	+	22.2812i	−0.336889	+	0.796776i
$783$	14.7817	−	4.74383i	0.528254	−	0.169531i
$784$	5.07763	+	4.81848i	0.181344	+	0.172088i
$785$			62.8936i			2.24477i
$786$	−7.19387	+	5.21341i	−0.256597	+	0.185956i
$787$	0.305804	+	0.176556i	0.0109007	+	0.00629355i	0.505440	−	0.862861i	$-0.331330\pi$
$787$	0.305804	+	0.176556i	0.0109007	+	0.00629355i	−0.494540	+	0.869155i	$0.664663\pi$
$788$	7.82318	+	4.51672i	0.278689	+	0.160901i
$789$	−16.0936	+	11.6631i	−0.572948	+	0.415217i
$790$	9.65927			0.343661
$791$	5.68066	+	39.1787i	0.201981	+	1.39303i
$792$	2.71410	+	12.9220i	0.0964415	+	0.459162i
$793$	8.50678	−	4.91139i	0.302085	−	0.174409i
$794$	−17.2521	−	9.96051i	−0.612254	−	0.353485i
$795$	−25.2787	−	11.2913i	−0.896543	−	0.400462i
$796$	1.13615	−	0.655958i	0.0402699	−	0.0232498i
$797$	−43.7396			−1.54934			−0.774669	−	0.632367i	$-0.782083\pi$
$797$	−43.7396			−1.54934			−0.774669	+	0.632367i	$0.782083\pi$
$798$	−9.90349	−	10.1908i	−0.350580	−	0.360749i
$799$			57.0240i			2.01736i
$800$	−3.87238	+	2.23572i	−0.136909	+	0.0790446i
$801$	−0.328047	+	1.00140i	−0.0115910	+	0.0353828i
$802$	−9.81905	−	5.66903i	−0.346723	−	0.200181i
$803$	23.7120	+	41.0705i	0.836780	+	1.44935i
$804$	−5.91522	+	0.614506i	−0.208614	+	0.0216720i
$805$	−37.6604	+	10.3244i	−1.32736	+	0.363887i
$806$			37.5070i			1.32113i
$807$	−7.03285	−	9.70447i	−0.247568	−	0.341613i
$808$	−7.00352	+	12.1304i	−0.246383	+	0.426748i
$809$	8.27549	+	4.77786i	0.290951	+	0.167980i	0.638371	−	0.769729i	$-0.279609\pi$
$809$	8.27549	+	4.77786i	0.290951	+	0.167980i	−0.347420	+	0.937710i	$0.612942\pi$
$810$	−16.3884	+	22.3295i	−0.575830	+	0.784578i
$811$	−19.8195			−0.695957			−0.347979	−	0.937502i	$-0.613132\pi$
$811$	−19.8195			−0.695957			−0.347979	+	0.937502i	$0.613132\pi$
$812$	2.92909	−	7.34183i	0.102791	−	0.257648i
$813$	−4.22318	−	40.6522i	−0.148113	−	1.42573i
$814$	−2.34066	−	4.05415i	−0.0820402	−	0.142098i
$815$	10.1717	−	17.6179i	0.356299	−	0.617128i
$816$	7.97715	+	3.56319i	0.279256	+	0.124736i
$817$	−6.45655	−	11.1831i	−0.225886	−	0.391246i
$818$			12.5469i			0.438690i
$819$	19.4530	−	23.2753i	0.679742	−	0.813306i
$820$			15.2813i			0.533647i
$821$	32.7609	−	18.9145i	1.14336	−	0.660121i	0.196102	−	0.980583i	$-0.437172\pi$
$821$	32.7609	−	18.9145i	1.14336	−	0.660121i	0.947261	+	0.320462i	$0.103838\pi$
$822$	−10.0022	+	22.3927i	−0.348867	+	0.781034i
$823$	−13.1505	+	22.7773i	−0.458397	+	0.793967i	−0.998876	−	0.0473904i	$-0.984910\pi$
$823$	−13.1505	+	22.7773i	−0.458397	+	0.793967i	0.540479	+	0.841357i	$0.318243\pi$
$824$	−0.179367	−	0.310672i	−0.00624853	−	0.0108228i
$825$	−3.52220	−	33.9046i	−0.122627	−	1.18041i
$826$	3.83858	+	26.4741i	0.133561	+	0.921153i
$827$	−6.65800			−0.231521			−0.115761	−	0.993277i	$-0.536931\pi$
$827$	−6.65800			−0.231521			−0.115761	+	0.993277i	$0.536931\pi$
$828$	14.1204	+	2.75944i	0.490718	+	0.0958972i
$829$	15.9243	−	27.5816i	0.553072	−	0.957949i	−0.444978	−	0.895541i	$-0.646789\pi$
$829$	15.9243	−	27.5816i	0.553072	−	0.957949i	0.998051	−	0.0624081i	$-0.0198780\pi$
$830$	23.0313	+	13.2971i	0.799429	+	0.461551i
$831$	−5.27110	+	3.81998i	−0.182853	+	0.132514i
$832$	−3.82174			−0.132495
$833$	−8.24274	+	34.3337i	−0.285594	+	1.18959i
$834$	6.08685	−	0.632336i	0.210770	−	0.0218960i
$835$	52.7588	−	30.4603i	1.82579	−	1.05412i
$836$	−11.8196	−	6.82406i	−0.408790	−	0.236015i
$837$	−49.8426	−	10.7829i	−1.72281	−	0.372712i
$838$	21.8289	−	12.6029i	0.754066	−	0.435360i
$839$	50.0728			1.72871			0.864353	−	0.502886i	$-0.167728\pi$
$839$	50.0728			1.72871			0.864353	+	0.502886i	$0.167728\pi$
$840$	3.45508	+	13.6734i	0.119211	+	0.471778i
$841$	20.0740			0.692207
$842$	−11.7663	−	20.3799i	−0.405495	−	0.702338i
$843$	17.0972	+	7.63685i	0.588857	+	0.263027i
$844$	5.56294	−	9.63530i	0.191484	−	0.331661i
$845$	−2.47082	−	4.27959i	−0.0849989	−	0.147222i
$846$	33.1905	−	6.97127i	1.14111	−	0.239677i
$847$	−17.3939	+	13.7123i	−0.597662	+	0.471159i
$848$	5.19385			0.178357
$849$	10.2241	+	14.1080i	0.350890	+	0.484185i
$850$	−19.5330	−	11.2774i	−0.669975	−	0.386810i
$851$	−5.06205	+	0.628773i	−0.173525	+	0.0215541i
$852$	9.70629	+	13.3935i	0.332532	+	0.458853i
$853$	2.11079			0.0722719			0.0361360	−	0.999347i	$-0.488495\pi$
$853$	2.11079			0.0722719			0.0361360	+	0.999347i	$0.488495\pi$
$854$	6.31610	+	2.51987i	0.216133	+	0.0862280i
$855$	−5.88497	−	28.0186i	−0.201262	−	0.958216i
$856$	−4.46475	+	2.57772i	−0.152602	+	0.0881047i
$857$	25.3079	+	14.6115i	0.864501	+	0.499120i	0.865517	−	0.500880i	$-0.166990\pi$
$857$	25.3079	+	14.6115i	0.864501	+	0.499120i	−0.00101594	+	0.999999i	$0.500323\pi$
$858$	11.8820	−	26.6011i	0.405646	−	0.908148i
$859$	25.6115	+	44.3604i	0.873854	+	1.51356i	0.857979	+	0.513685i	$0.171720\pi$
$859$	25.6115	+	44.3604i	0.873854	+	1.51356i	0.0158747	+	0.999874i	$0.494947\pi$
$860$			12.8158i			0.437017i
$861$	21.8925	+	6.20281i	0.746095	+	0.211391i
$862$		−	8.63368i		−	0.294064i
$863$	−4.22037	+	2.43663i	−0.143663	+	0.0829439i	−0.570109	−	0.821569i	$-0.693099\pi$
$863$	−4.22037	+	2.43663i	−0.143663	+	0.0829439i	0.426446	+	0.904513i	$0.359766\pi$
$864$	1.09871	−	5.07866i	0.0373790	−	0.172780i
$865$	−45.9491	−	26.5287i	−1.56232	−	0.902004i
$866$	11.5107	+	19.9371i	0.391150	+	0.677491i
$867$	1.51120	+	14.5467i	0.0513229	+	0.494033i
$868$	−20.3913	+	16.0752i	−0.692126	+	0.545629i
$869$		−	13.8140i		−	0.468606i
$870$	12.8954	−	9.34532i	0.437195	−	0.316836i
$871$	11.3640	+	6.56104i	0.385056	+	0.222312i
$872$	−5.15520	+	8.92907i	−0.174577	+	0.302376i
$873$	36.6100	−	32.8044i	1.23906	−	1.11026i
$874$	−11.8643	+	8.96661i	−0.401317	+	0.303300i
$875$	0.617569	+	4.25928i	0.0208776	+	0.143990i
$876$	−1.92842	−	18.5630i	−0.0651554	−	0.627184i
$877$	−2.38313	−	4.12771i	−0.0804727	−	0.139383i	0.822980	−	0.568070i	$-0.192310\pi$
$877$	−2.38313	−	4.12771i	−0.0804727	−	0.139383i	−0.903453	+	0.428687i	$0.858976\pi$
$878$	33.1942	+	19.1647i	1.12025	+	0.646777i
$879$	−32.1813	−	14.3745i	−1.08545	−	0.484841i
$880$	6.77266	+	11.7306i	0.228306	+	0.395438i
$881$	−9.15443			−0.308421			−0.154210	−	0.988038i	$-0.549283\pi$
$881$	−9.15443			−0.308421			−0.154210	+	0.988038i	$0.549283\pi$
$882$	20.9914	+	0.600302i	0.706818	+	0.0202132i
$883$	7.19339			0.242077			0.121038	−	0.992648i	$-0.461378\pi$
$883$	7.19339			0.242077			0.121038	+	0.992648i	$0.461378\pi$
$884$	−9.63877	−	16.6948i	−0.324187	−	0.561508i
$885$	−21.9810	+	49.2103i	−0.738882	+	1.65419i
$886$	−10.4505	+	18.1008i	−0.351091	+	0.608107i
$887$	−13.3350	+	7.69894i	−0.447744	+	0.258505i	−0.706877	−	0.707337i	$-0.749897\pi$
$887$	−13.3350	+	7.69894i	−0.447744	+	0.258505i	0.259133	+	0.965842i	$0.416563\pi$
$888$	0.190359	+	1.83239i	0.00638802	+	0.0614909i
$889$	3.79148	+	26.1493i	0.127162	+	0.877020i
$890$			1.08101i			0.0362356i
$891$	31.9339	+	23.4375i	1.06983	+	0.785184i
$892$	5.03033	−	8.71279i	0.168428	−	0.291726i
$893$	−17.5278	+	30.3591i	−0.586547	+	1.01593i
$894$	17.0110	+	23.4731i	0.568934	+	0.785058i
$895$		−	32.7932i		−	1.09616i
$896$	−1.63797	−	2.07775i	−0.0547207	−	0.0694128i
$897$	−21.6552	−	23.2130i	−0.723047	−	0.775060i
$898$	16.6149	+	28.7779i	0.554448	+	0.960331i
$899$	25.3928	+	14.6605i	0.846896	+	0.488956i
$900$	−4.17600	+	12.7477i	−0.139200	+	0.424925i
$901$	13.0994	+	22.6887i	0.436403	+	0.755872i
$902$	21.8542			0.727666
$903$	18.3604	+	5.20205i	0.610995	+	0.173113i
$904$		−	14.9630i		−	0.497662i
$905$	68.9397	−	39.8024i	2.29163	−	1.32308i
$906$	1.12114	−	2.50997i	0.0372472	−	0.0833880i
$907$	6.77884	+	3.91377i	0.225088	+	0.129954i	0.608304	−	0.793704i	$-0.291850\pi$
$907$	6.77884	+	3.91377i	0.225088	+	0.129954i	−0.383216	+	0.923659i	$0.625184\pi$
$908$	−13.6383	−	23.6222i	−0.452603	−	0.783931i
$909$	8.63756	+	41.1238i	0.286490	+	1.36399i
$910$	11.5312	−	28.9031i	0.382254	−	0.958129i
$911$	−34.4591			−1.14168			−0.570840	−	0.821061i	$-0.693382\pi$
$911$	−34.4591			−1.14168			−0.570840	+	0.821061i	$0.693382\pi$
$912$	3.15173	+	4.34900i	0.104364	+	0.144010i
$913$	19.0166	−	32.9377i	0.629357	−	1.09008i
$914$	−14.3398	+	24.8373i	−0.474320	+	0.821546i
$915$	8.03969	+	11.0938i	0.265784	+	0.366749i
$916$			1.71152i			0.0565503i
$917$	8.40176	+	10.6576i	0.277451	+	0.351944i
$918$	24.9566	−	8.00924i	0.823692	−	0.264344i
$919$	−42.7272	+	24.6686i	−1.40944	+	0.813741i	−0.995334	−	0.0964874i	$-0.969239\pi$
$919$	−42.7272	+	24.6686i	−1.40944	+	0.813741i	−0.414107	+	0.910228i	$0.635906\pi$
$920$	14.6469	−	1.81934i	0.482896	−	0.0599819i
$921$	39.2016	+	17.5103i	1.29174	+	0.576985i
$922$	−9.54737	−	16.5365i	−0.314426	−	0.544601i
$923$		−	36.4970i		−	1.20131i
$924$	19.5547	−	4.94119i	0.643302	−	0.162553i
$925$		−	4.75592i		−	0.156374i
$926$	−32.0038	+	18.4774i	−1.05171	+	0.607206i
$927$	−1.02272	−	0.335031i	−0.0335906	−	0.0110039i
$928$	−1.49382	+	2.58737i	−0.0490370	+	0.0849346i
$929$	18.5130	−	10.6885i	0.607392	−	0.350678i	−0.164552	−	0.986368i	$-0.552618\pi$
$929$	18.5130	−	10.6885i	0.607392	−	0.350678i	0.771944	+	0.635690i	$0.219284\pi$
$930$	−52.0342	+	5.40560i	−1.70627	+	0.177257i
$931$	−14.9417	+	15.7453i	−0.489696	+	0.516033i
$932$			2.86215i			0.0937528i
$933$	−13.0401	−	17.9938i	−0.426914	−	0.589089i
$934$	8.29571	+	4.78953i	0.271444	+	0.156718i
$935$	−34.1625	+	59.1713i	−1.11723	+	1.93511i
$936$	−8.53879	+	7.65117i	−0.279099	+	0.250086i
$937$			32.3195i			1.05583i	0.849297	+	0.527916i	$0.177026\pi$
$937$			32.3195i			1.05583i	−0.849297	+	0.527916i	$0.822974\pi$
$938$	1.30353	+	8.99027i	0.0425618	+	0.293543i
$939$	3.57058	−	0.370932i	0.116522	−	0.0121049i
$940$	30.1304	−	17.3958i	0.982746	−	0.567389i
$941$	−4.81736	+	8.34391i	−0.157041	+	0.272004i	−0.933800	−	0.357794i	$-0.883529\pi$
$941$	−4.81736	+	8.34391i	−0.157041	+	0.272004i	0.776759	+	0.629798i	$0.216862\pi$
$942$	−32.3189	−	14.4360i	−1.05301	−	0.470350i
$943$	9.27370	−	21.9332i	0.301993	−	0.714244i
$944$		−	10.1109i		−	0.329082i
$945$	35.0939	+	23.6330i	1.14161	+	0.768781i
$946$	18.3282			0.595903
$947$	−5.69781	+	3.28963i	−0.185154	+	0.106899i	−0.589712	−	0.807614i	$-0.700759\pi$
$947$	−5.69781	+	3.28963i	−0.185154	+	0.106899i	0.404558	+	0.914512i	$0.367425\pi$
$948$	−2.21710	+	4.96357i	−0.0720079	+	0.161209i
$949$	−20.5896	+	35.6623i	−0.668368	+	1.15765i
$950$	−6.93280	−	12.0080i	−0.224930	−	0.389590i
$951$	13.3750	−	1.38947i	0.433716	−	0.0450568i
$952$	4.94532	−	12.3956i	0.160279	−	0.401743i
$953$	52.4446			1.69885			0.849423	−	0.527713i	$-0.176950\pi$
$953$	52.4446			1.69885			0.849423	+	0.527713i	$0.176950\pi$
$954$	11.6044	−	10.3981i	0.375708	−	0.336652i
$955$	24.3668	−	42.2046i	0.788492	−	1.36571i
$956$	−17.5443	−	10.1292i	−0.567424	−	0.327602i
$957$	−13.3650	−	18.4420i	−0.432028	−	0.596145i
$958$			42.8698i			1.38506i
$959$	34.7956	+	13.8820i	1.12361	+	0.448273i
$960$	−0.550799	−	5.30197i	−0.0177770	−	0.171120i
$961$	−32.6584	−	56.5661i	−1.05350	−	1.82471i
$962$	2.03244	−	3.52030i	0.0655286	−	0.113499i
$963$	−4.81481	+	14.6978i	−0.155155	+	0.473630i
$964$	2.64764	−	1.52862i	0.0852747	−	0.0492334i
$965$	71.9838			2.31724
$966$	3.33886	−	21.7222i	0.107426	−	0.698899i
$967$	−7.47567			−0.240401			−0.120201	−	0.992750i	$-0.538354\pi$
$967$	−7.47567			−0.240401			−0.120201	+	0.992750i	$0.538354\pi$
$968$	7.24993	−	4.18575i	0.233022	−	0.134535i
$969$	−11.0492	+	24.7366i	−0.354951	+	0.794653i
$970$	25.2141	−	43.6720i	0.809575	−	1.40222i
$971$	21.2252	+	36.7631i	0.681148	+	1.17978i	0.974631	+	0.223819i	$0.0718524\pi$
$971$	21.2252	+	36.7631i	0.681148	+	1.17978i	−0.293483	+	0.955964i	$0.594814\pi$
$972$	−7.71272	−	13.5467i	−0.247386	−	0.434512i
$973$	−1.34135	−	9.25112i	−0.0430018	−	0.296577i
$974$			13.5143i			0.433025i
$975$	23.9666	−	17.3686i	0.767545	−	0.556242i
$976$	−2.22589	−	1.28512i	−0.0712491	−	0.0411357i
$977$	8.40337	−	14.5551i	0.268848	−	0.465658i	−0.699717	−	0.714420i	$-0.746690\pi$
$977$	8.40337	−	14.5551i	0.268848	−	0.465658i	0.968565	+	0.248762i	$0.0800238\pi$
$978$	6.71852	+	9.27073i	0.214835	+	0.296445i
$979$	1.54598			0.0494098
$980$	20.6558	−	6.11856i	0.659826	−	0.195450i
$981$	6.35800	+	30.2707i	0.202995	+	0.966469i
$982$	−2.63117	−	4.55732i	−0.0839640	−	0.145430i
$983$	−24.7168	+	42.8108i	−0.788344	+	1.36545i	0.138637	+	0.990343i	$0.455728\pi$
$983$	−24.7168	+	42.8108i	−0.788344	+	1.36545i	−0.926981	+	0.375109i	$0.877605\pi$
$984$	−7.85255	−	3.50753i	−0.250330	−	0.111816i
$985$	24.0764	−	13.9005i	0.767138	−	0.442907i
$986$	−15.0702			−0.479933
$987$	−12.6916	−	50.2269i	−0.403978	−	1.59874i
$988$		−	11.8509i		−	0.377028i
$989$	7.77748	−	18.3945i	0.247309	−	0.584911i
$990$	38.6167	+	12.6503i	1.22732	+	0.402054i
$991$	1.28196	−	2.22043i	0.0407230	−	0.0705342i	−0.844946	−	0.534852i	$-0.820367\pi$
$991$	1.28196	−	2.22043i	0.0407230	−	0.0705342i	0.885668	+	0.464318i	$0.153701\pi$
$992$	8.49927	−	4.90706i	0.269852	−	0.155799i
$993$	4.23994	+	40.8136i	0.134550	+	1.29518i
$994$	19.8422	−	15.6423i	0.629356	−	0.496145i
$995$		−	4.03751i		−	0.127998i
$996$	−12.1193	+	8.78291i	−0.384016	+	0.278297i
$997$	−2.31318	+	4.00654i	−0.0732590	+	0.126888i	−0.900328	−	0.435212i	$-0.856673\pi$
$997$	−2.31318	+	4.00654i	−0.0732590	+	0.126888i	0.827069	+	0.562101i	$0.190007\pi$
$998$	−26.5276	−	15.3157i	−0.839716	−	0.484810i
$999$	4.09377	+	3.71294i	0.129521	+	0.117472i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.j.a.137.5	✓	128
3.2	odd	2	inner	966.2.j.a.137.58	yes	128
7.2	even	3	inner	966.2.j.a.275.57	yes	128
21.2	odd	6	inner	966.2.j.a.275.6	yes	128
23.22	odd	2	inner	966.2.j.a.137.6	yes	128
69.68	even	2	inner	966.2.j.a.137.57	yes	128
161.114	odd	6	inner	966.2.j.a.275.58	yes	128
483.275	even	6	inner	966.2.j.a.275.5	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.j.a.137.5	✓	128	1.1	even	1	trivial
966.2.j.a.137.6	yes	128	23.22	odd	2	inner
966.2.j.a.137.57	yes	128	69.68	even	2	inner
966.2.j.a.137.58	yes	128	3.2	odd	2	inner
966.2.j.a.275.5	yes	128	483.275	even	6	inner
966.2.j.a.275.6	yes	128	21.2	odd	6	inner
966.2.j.a.275.57	yes	128	7.2	even	3	inner
966.2.j.a.275.58	yes	128	161.114	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.58146 - 0.706395i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.53878 - 2.66525i) q^{5} +(1.72278 - 0.178972i) q^{6} +(-0.379647 - 2.61837i) q^{7} +1.00000i q^{8} +(2.00201 + 2.23427i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.58146 - 0.706395i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.53878 - 2.66525i) q^{5} +(1.72278 - 0.178972i) q^{6} +(-0.379647 - 2.61837i) q^{7} +1.00000i q^{8} +(2.00201 + 2.23427i) q^{9} +(2.66525 + 1.53878i) q^{10} +(2.20065 - 3.81164i) q^{11} +(-1.40248 + 1.01638i) q^{12} +3.82174 q^{13} +(1.63797 + 2.07775i) q^{14} +(0.550799 + 5.30197i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.52209 - 4.36839i) q^{17} +(-2.85093 - 0.933927i) q^{18} +(2.68548 - 1.55046i) q^{19} -3.07757 q^{20} +(-1.24921 + 4.40902i) q^{21} +4.40131i q^{22} +(4.41722 + 1.86767i) q^{23} +(0.706395 - 1.58146i) q^{24} +(-2.23572 + 3.87238i) q^{25} +(-3.30972 + 1.91087i) q^{26} +(-1.58782 - 4.94761i) q^{27} +(-2.45740 - 0.980401i) q^{28} +2.98764i q^{29} +(-3.12799 - 4.31624i) q^{30} +(4.90706 - 8.49927i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-6.17277 + 4.47342i) q^{33} +5.04418i q^{34} +(-6.39443 + 5.04097i) q^{35} +(2.93594 - 0.616659i) q^{36} +(-0.921124 + 0.531811i) q^{37} +(-1.55046 + 2.68548i) q^{38} +(-6.04392 - 2.69966i) q^{39} +(2.66525 - 1.53878i) q^{40} -4.96539i q^{41} +(-1.12266 - 4.44293i) q^{42} -4.16427i q^{43} +(-2.20065 - 3.81164i) q^{44} +(2.87423 - 8.77392i) q^{45} +(-4.75926 + 0.591162i) q^{46} +(-9.79033 + 5.65245i) q^{47} +(0.178972 + 1.72278i) q^{48} +(-6.71174 + 1.98811i) q^{49} -4.47144i q^{50} +(-7.07439 + 5.12682i) q^{51} +(1.91087 - 3.30972i) q^{52} +(-2.59692 + 4.49800i) q^{53} +(3.84889 + 3.49085i) q^{54} -13.5453 q^{55} +(2.61837 - 0.379647i) q^{56} +(-5.34221 + 0.554979i) q^{57} +(-1.49382 - 2.58737i) q^{58} +(8.75632 + 5.05546i) q^{59} +(4.86704 + 2.17398i) q^{60} +(2.22589 - 1.28512i) q^{61} +9.81411i q^{62} +(5.09008 - 6.09024i) q^{63} -1.00000 q^{64} +(-5.88084 - 10.1859i) q^{65} +(3.10906 - 6.96048i) q^{66} +(2.97353 + 1.71677i) q^{67} +(-2.52209 - 4.36839i) q^{68} +(-5.66633 - 6.07394i) q^{69} +(3.01725 - 7.56282i) q^{70} -9.54983i q^{71} +(-2.23427 + 2.00201i) q^{72} +(-5.38750 + 9.33143i) q^{73} +(0.531811 - 0.921124i) q^{74} +(6.27112 - 4.54470i) q^{75} -3.10093i q^{76} +(-10.8158 - 4.31505i) q^{77} +(6.58402 - 0.683984i) q^{78} +(2.71811 - 1.56930i) q^{79} +(-1.53878 + 2.66525i) q^{80} +(-0.983904 + 8.94606i) q^{81} +(2.48270 + 4.30015i) q^{82} +8.64133 q^{83} +(3.19372 + 3.28636i) q^{84} -15.5238 q^{85} +(2.08214 + 3.60637i) q^{86} +(2.11046 - 4.72482i) q^{87} +(3.81164 + 2.20065i) q^{88} +(0.175628 + 0.304196i) q^{89} +(1.89781 + 9.03555i) q^{90} +(-1.45091 - 10.0067i) q^{91} +(3.82606 - 2.89159i) q^{92} +(-13.7641 + 9.97491i) q^{93} +(5.65245 - 9.79033i) q^{94} +(-8.26476 - 4.77166i) q^{95} +(-1.01638 - 1.40248i) q^{96} -16.3857i q^{97} +(4.81848 - 5.07763i) q^{98} +(12.9220 - 2.71410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9}+O(q^{10}) \) 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9	\( 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9} - 64 q^{16} + 4 q^{24} - 72 q^{25} + 24 q^{27} - 8 q^{36} + 4 q^{39} + 12 q^{46} + 72 q^{49} + 4 q^{54} - 96 q^{55} - 128 q^{64} - 56 q^{69} + 32 q^{70} - 40 q^{73} - 40 q^{75} - 16 q^{78} + 36 q^{81} - 32 q^{82} - 64 q^{85} - 24 q^{87} + 32 q^{93} - 8 q^{94} - 4 q^{96}+O(q^{100}) \) 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9 - 64 * q^16 + 4 * q^24 - 72 * q^25 + 24 * q^27 - 8 * q^36 + 4 * q^39 + 12 * q^46 + 72 * q^49 + 4 * q^54 - 96 * q^55 - 128 * q^64 - 56 * q^69 + 32 * q^70 - 40 * q^73 - 40 * q^75 - 16 * q^78 + 36 * q^81 - 32 * q^82 - 64 * q^85 - 24 * q^87 + 32 * q^93 - 8 * q^94 - 4 * q^96

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