LMFDB - Embedded newform 168.2.t.a.115.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(19,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 0, 5]))

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

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

chi := DirichletCharacter("168.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.t (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:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			115.1
Character	$\chi$	$=$	168.115
Dual form			168.2.t.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41257 - 0.0681843i) q^{2} +(0.866025 + 0.500000i) q^{3} +(1.99070 + 0.192630i) q^{4} +(2.08776 + 3.61611i) q^{5} +(-1.18923 - 0.765334i) q^{6} +(-2.39694 - 1.12013i) q^{7} +(-2.79887 - 0.407838i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.70255 - 5.25036i) q^{10} +(-0.855485 + 1.48174i) q^{11} +(1.62768 + 1.16217i) q^{12} -1.54062 q^{13} +(3.30947 + 1.74569i) q^{14} +4.17553i q^{15} +(3.92579 + 0.766938i) q^{16} +(2.02094 + 1.16679i) q^{17} +(-0.647235 - 1.25741i) q^{18} +(6.09693 - 3.52006i) q^{19} +(3.45954 + 7.60077i) q^{20} +(-1.51575 - 2.16853i) q^{21} +(1.30946 - 2.03473i) q^{22} +(-0.406066 + 0.234442i) q^{23} +(-2.21997 - 1.75263i) q^{24} +(-6.21752 + 10.7691i) q^{25} +(2.17624 + 0.105046i) q^{26} +1.00000i q^{27} +(-4.55582 - 2.69156i) q^{28} -3.33885i q^{29} +(0.284706 - 5.89822i) q^{30} +(1.58126 - 2.73883i) q^{31} +(-5.49315 - 1.35103i) q^{32} +(-1.48174 + 0.855485i) q^{33} +(-2.77516 - 1.78596i) q^{34} +(-0.953738 - 11.0062i) q^{35} +(0.828528 + 1.82031i) q^{36} +(7.74648 - 4.47243i) q^{37} +(-8.85235 + 4.55662i) q^{38} +(-1.33422 - 0.770311i) q^{39} +(-4.36859 - 10.9725i) q^{40} -5.31411i q^{41} +(1.99324 + 3.16654i) q^{42} -3.42772 q^{43} +(-1.98844 + 2.78492i) q^{44} +(-2.08776 + 3.61611i) q^{45} +(0.589581 - 0.303478i) q^{46} +(-2.95047 - 5.11037i) q^{47} +(3.01636 + 2.62708i) q^{48} +(4.49063 + 5.36975i) q^{49} +(9.51696 - 14.7881i) q^{50} +(1.16679 + 2.02094i) q^{51} +(-3.06692 - 0.296770i) q^{52} +(-1.35437 - 0.781947i) q^{53} +(0.0681843 - 1.41257i) q^{54} -7.14421 q^{55} +(6.25189 + 4.11265i) q^{56} +7.04013 q^{57} +(-0.227657 + 4.71636i) q^{58} +(-5.26742 - 3.04114i) q^{59} +(-0.804332 + 8.31223i) q^{60} +(4.55959 + 7.89744i) q^{61} +(-2.42039 + 3.76097i) q^{62} +(-0.228411 - 2.63587i) q^{63} +(7.66734 + 2.28297i) q^{64} +(-3.21646 - 5.57107i) q^{65} +(2.15140 - 1.10740i) q^{66} +(3.73658 - 6.47195i) q^{67} +(3.79832 + 2.71202i) q^{68} -0.468884 q^{69} +(0.596773 + 15.6120i) q^{70} +3.49263i q^{71} +(-1.04624 - 2.62781i) q^{72} +(-12.5811 - 7.26372i) q^{73} +(-11.2474 + 5.78943i) q^{74} +(-10.7691 + 6.21752i) q^{75} +(12.8152 - 5.83295i) q^{76} +(3.71029 - 2.59340i) q^{77} +(1.83215 + 1.17909i) q^{78} +(-1.46108 + 0.843557i) q^{79} +(5.42278 + 15.7973i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.362339 + 7.50655i) q^{82} +2.72601i q^{83} +(-2.59968 - 4.60887i) q^{84} +9.74391i q^{85} +(4.84189 + 0.233717i) q^{86} +(1.66943 - 2.89153i) q^{87} +(2.99870 - 3.79831i) q^{88} +(1.83829 - 1.06134i) q^{89} +(3.19567 - 4.96566i) q^{90} +(3.69278 + 1.72569i) q^{91} +(-0.853516 + 0.388484i) q^{92} +(2.73883 - 1.58126i) q^{93} +(3.81930 + 7.41993i) q^{94} +(25.4579 + 14.6981i) q^{95} +(-4.08169 - 3.91660i) q^{96} -1.95202i q^{97} +(-5.97720 - 7.89133i) q^{98} -1.71097 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 16 q^{9} - 18 q^{10} + 8 q^{11} - 10 q^{14} + 6 q^{16} + 2 q^{18} - 20 q^{22} - 18 q^{24} - 16 q^{25} - 30 q^{26} - 14 q^{28} - 8 q^{30} - 12 q^{32} - 24 q^{35} - 4 q^{36}+ \cdots + 16 q^{99}+O(q^{100}) $ 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 16 * q^9 - 18 * q^10 + 8 * q^11 - 10 * q^14 + 6 * q^16 + 2 * q^18 - 20 * q^22 - 18 * q^24 - 16 * q^25 - 30 * q^26 - 14 * q^28 - 8 * q^30 - 12 * q^32 - 24 * q^35 - 4 * q^36 - 18 * q^38 - 30 * q^40 + 4 * q^42 - 16 * q^43 + 24 * q^44 + 8 * q^46 + 8 * q^49 + 76 * q^50 + 36 * q^52 + 16 * q^56 + 16 * q^57 - 6 * q^58 - 96 * q^59 - 2 * q^60 + 76 * q^64 - 36 * q^66 - 32 * q^67 + 96 * q^68 + 6 * q^70 + 8 * q^72 - 24 * q^73 - 34 * q^74 - 12 * q^78 + 36 * q^80 - 16 * q^81 - 36 * q^82 + 16 * q^84 + 50 * q^86 - 14 * q^88 + 56 * q^91 - 128 * q^92 + 36 * q^94 + 30 * q^96 + 60 * q^98 + 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$	$-1$

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 $

$2$	−1.41257	−	0.0681843i	−0.998837	−	0.0482136i
$2$	−1.41257	−	0.0681843i	−0.998837	−	0.0482136i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	1.99070	+	0.192630i	0.995351	+	0.0963150i
$5$	2.08776	+	3.61611i	0.933677	+	1.61718i	0.776977	+	0.629529i	$0.216752\pi$
$5$	2.08776	+	3.61611i	0.933677	+	1.61718i	0.156700	+	0.987646i	$0.449915\pi$
$6$	−1.18923	−	0.765334i	−0.485500	−	0.312446i
$7$	−2.39694	−	1.12013i	−0.905958	−	0.423368i
$7$	−2.39694	−	1.12013i	−0.905958	−	0.423368i
$8$	−2.79887	−	0.407838i	−0.989550	−	0.144192i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−2.70255	−	5.25036i	−0.854621	−	1.66031i
$11$	−0.855485	+	1.48174i	−0.257939	+	0.446763i	−0.965690	−	0.259699i	$-0.916377\pi$
$11$	−0.855485	+	1.48174i	−0.257939	+	0.446763i	0.707751	+	0.706462i	$0.249710\pi$
$12$	1.62768	+	1.16217i	0.469872	+	0.335491i
$13$	−1.54062			−0.427292			−0.213646	−	0.976911i	$-0.568534\pi$
$13$	−1.54062			−0.427292			−0.213646	+	0.976911i	$0.568534\pi$
$14$	3.30947	+	1.74569i	0.884492	+	0.466555i
$15$			4.17553i			1.07812i
$16$	3.92579	+	0.766938i	0.981447	+	0.191735i
$17$	2.02094	+	1.16679i	0.490149	+	0.282988i	0.724636	−	0.689132i	$-0.242008\pi$
$17$	2.02094	+	1.16679i	0.490149	+	0.282988i	−0.234487	+	0.972119i	$0.575341\pi$
$18$	−0.647235	−	1.25741i	−0.152555	−	0.296375i
$19$	6.09693	−	3.52006i	1.39873	−	0.807558i	0.404472	−	0.914551i	$-0.367455\pi$
$19$	6.09693	−	3.52006i	1.39873	−	0.807558i	0.994260	+	0.106992i	$0.0341221\pi$
$20$	3.45954	+	7.60077i	0.773578	+	1.69958i
$21$	−1.51575	−	2.16853i	−0.330763	−	0.473212i
$22$	1.30946	−	2.03473i	0.279179	−	0.433807i
$23$	−0.406066	+	0.234442i	−0.0846705	+	0.0488846i	−0.541737	−	0.840548i	$-0.682233\pi$
$23$	−0.406066	+	0.234442i	−0.0846705	+	0.0488846i	0.457067	+	0.889432i	$0.348900\pi$
$24$	−2.21997	−	1.75263i	−0.453150	−	0.357755i
$25$	−6.21752	+	10.7691i	−1.24350	+	2.15381i
$26$	2.17624	+	0.105046i	0.426795	+	0.0206013i
$27$			1.00000i			0.192450i
$28$	−4.55582	−	2.69156i	−0.860969	−	0.508657i
$29$		−	3.33885i		−	0.620009i	−0.950735	−	0.310005i	$-0.899669\pi$
$29$		−	3.33885i		−	0.620009i	0.950735	−	0.310005i	$-0.100331\pi$
$30$	0.284706	−	5.89822i	0.0519799	−	1.07686i
$31$	1.58126	−	2.73883i	0.284003	−	0.491908i	−0.688364	−	0.725366i	$-0.741671\pi$
$31$	1.58126	−	2.73883i	0.284003	−	0.491908i	0.972367	+	0.233458i	$0.0750040\pi$
$32$	−5.49315	−	1.35103i	−0.971061	−	0.238831i
$33$	−1.48174	+	0.855485i	−0.257939	+	0.148921i
$34$	−2.77516	−	1.78596i	−0.475935	−	0.306290i
$35$	−0.953738	−	11.0062i	−0.161211	−	1.86038i
$36$	0.828528	+	1.82031i	0.138088	+	0.303386i
$37$	7.74648	−	4.47243i	1.27351	−	0.735263i	0.297865	−	0.954608i	$-0.403725\pi$
$37$	7.74648	−	4.47243i	1.27351	−	0.735263i	0.975647	+	0.219345i	$0.0703920\pi$
$38$	−8.85235	+	4.55662i	−1.43604	+	0.739181i
$39$	−1.33422	−	0.770311i	−0.213646	−	0.123349i
$40$	−4.36859	−	10.9725i	−0.690735	−	1.73490i
$41$		−	5.31411i		−	0.829925i	−0.909838	−	0.414963i	$-0.863795\pi$
$41$		−	5.31411i		−	0.829925i	0.909838	−	0.414963i	$-0.136205\pi$
$42$	1.99324	+	3.16654i	0.307563	+	0.488608i
$43$	−3.42772			−0.522722			−0.261361	−	0.965241i	$-0.584171\pi$
$43$	−3.42772			−0.522722			−0.261361	+	0.965241i	$0.584171\pi$
$44$	−1.98844	+	2.78492i	−0.299769	+	0.419842i
$45$	−2.08776	+	3.61611i	−0.311226	+	0.539058i
$46$	0.589581	−	0.303478i	0.0869290	−	0.0447454i
$47$	−2.95047	−	5.11037i	−0.430371	−	0.745424i	0.566534	−	0.824038i	$-0.308284\pi$
$47$	−2.95047	−	5.11037i	−0.430371	−	0.745424i	−0.996905	+	0.0786139i	$0.974951\pi$
$48$	3.01636	+	2.62708i	0.435374	+	0.379187i
$49$	4.49063	+	5.36975i	0.641519	+	0.767107i
$50$	9.51696	−	14.7881i	1.34590	−	2.09135i
$51$	1.16679	+	2.02094i	0.163383	+	0.282988i
$52$	−3.06692	−	0.296770i	−0.425305	−	0.0411546i
$53$	−1.35437	−	0.781947i	−0.186037	−	0.107409i	0.404089	−	0.914720i	$-0.367589\pi$
$53$	−1.35437	−	0.781947i	−0.186037	−	0.107409i	−0.590126	+	0.807311i	$0.700922\pi$
$54$	0.0681843	−	1.41257i	0.00927871	−	0.192226i
$55$	−7.14421			−0.963325
$56$	6.25189	+	4.11265i	0.835444	+	0.549576i
$57$	7.04013			0.932488
$58$	−0.227657	+	4.71636i	−0.0298929	+	0.619288i
$59$	−5.26742	−	3.04114i	−0.685759	−	0.395923i	0.116262	−	0.993219i	$-0.462909\pi$
$59$	−5.26742	−	3.04114i	−0.685759	−	0.395923i	−0.802021	+	0.597295i	$0.796242\pi$
$60$	−0.804332	+	8.31223i	−0.103839	+	1.07310i
$61$	4.55959	+	7.89744i	0.583795	+	1.01116i	0.995024	+	0.0996311i	$0.0317663\pi$
$61$	4.55959	+	7.89744i	0.583795	+	1.01116i	−0.411229	+	0.911532i	$0.634900\pi$
$62$	−2.42039	+	3.76097i	−0.307390	+	0.477643i
$63$	−0.228411	−	2.63587i	−0.0287771	−	0.332089i
$64$	7.66734	+	2.28297i	0.958417	+	0.285371i
$65$	−3.21646	−	5.57107i	−0.398952	−	0.691006i
$66$	2.15140	−	1.10740i	0.264819	−	0.136312i
$67$	3.73658	−	6.47195i	0.456496	−	0.790675i	−0.542276	−	0.840200i	$-0.682437\pi$
$67$	3.73658	−	6.47195i	0.456496	−	0.790675i	0.998773	+	0.0495251i	$0.0157708\pi$
$68$	3.79832	+	2.71202i	0.460614	+	0.328881i
$69$	−0.468884			−0.0564470
$70$	0.596773	+	15.6120i	0.0713281	+	1.86599i
$71$			3.49263i			0.414499i	0.978288	+	0.207249i	$0.0664512\pi$
$71$			3.49263i			0.414499i	−0.978288	+	0.207249i	$0.933549\pi$
$72$	−1.04624	−	2.62781i	−0.123300	−	0.309690i
$73$	−12.5811	−	7.26372i	−1.47251	−	0.850154i	−0.472988	−	0.881069i	$-0.656824\pi$
$73$	−12.5811	−	7.26372i	−1.47251	−	0.850154i	−0.999522	+	0.0309152i	$0.990158\pi$
$74$	−11.2474	+	5.78943i	−1.30748	+	0.673007i
$75$	−10.7691	+	6.21752i	−1.24350	+	0.717937i
$76$	12.8152	−	5.83295i	1.47001	−	0.669085i
$77$	3.71029	−	2.59340i	0.422826	−	0.295545i
$78$	1.83215	+	1.17909i	0.207450	+	0.133506i
$79$	−1.46108	+	0.843557i	−0.164385	+	0.0949075i	−0.579935	−	0.814662i	$-0.696922\pi$
$79$	−1.46108	+	0.843557i	−0.164385	+	0.0949075i	0.415551	+	0.909570i	$0.363589\pi$
$80$	5.42278	+	15.7973i	0.606286	+	1.76619i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.362339	+	7.50655i	−0.0400137	+	0.828960i
$83$			2.72601i			0.299219i	0.988745	+	0.149609i	$0.0478016\pi$
$83$			2.72601i			0.299219i	−0.988745	+	0.149609i	$0.952198\pi$
$84$	−2.59968	−	4.60887i	−0.283648	−	0.502869i
$85$			9.74391i			1.05688i
$86$	4.84189	+	0.233717i	0.522114	+	0.0252023i
$87$	1.66943	−	2.89153i	0.178981	−	0.310005i
$88$	2.99870	−	3.79831i	0.319663	−	0.404901i
$89$	1.83829	−	1.06134i	0.194858	−	0.112501i	−0.399397	−	0.916778i	$-0.630780\pi$
$89$	1.83829	−	1.06134i	0.194858	−	0.112501i	0.594255	+	0.804277i	$0.297447\pi$
$90$	3.19567	−	4.96566i	0.336854	−	0.523426i
$91$	3.69278	+	1.72569i	0.387108	+	0.180902i
$92$	−0.853516	+	0.388484i	−0.0889852	+	0.0405022i
$93$	2.73883	−	1.58126i	0.284003	−	0.163969i
$94$	3.81930	+	7.41993i	0.393931	+	0.765307i
$95$	25.4579	+	14.6981i	2.61193	+	1.50800i
$96$	−4.08169	−	3.91660i	−0.416586	−	0.399737i
$97$		−	1.95202i		−	0.198198i	−0.995078	−	0.0990990i	$-0.968404\pi$
$97$		−	1.95202i		−	0.198198i	0.995078	−	0.0990990i	$-0.0315960\pi$
$98$	−5.97720	−	7.89133i	−0.603788	−	0.797145i
$99$	−1.71097			−0.171959
$100$	−14.4517	+	20.2403i	−1.44517	+	2.02403i
$101$	6.89045	−	11.9346i	0.685625	−	1.18754i	−0.287615	−	0.957746i	$-0.592862\pi$
$101$	6.89045	−	11.9346i	0.685625	−	1.18754i	0.973240	−	0.229792i	$-0.0738044\pi$
$102$	−1.51037	−	2.93427i	−0.149549	−	0.290536i
$103$	−3.84129	−	6.65331i	−0.378494	−	0.655570i	0.612350	−	0.790587i	$-0.290224\pi$
$103$	−3.84129	−	6.65331i	−0.378494	−	0.655570i	−0.990843	+	0.135017i	$0.956891\pi$
$104$	4.31200	+	0.628324i	0.422826	+	0.0616123i
$105$	4.67712	−	10.0085i	0.456440	−	0.976728i
$106$	1.85983	+	1.19690i	0.180642	+	0.116253i
$107$	7.20414	+	12.4779i	0.696450	+	1.20629i	0.969689	+	0.244341i	$0.0785715\pi$
$107$	7.20414	+	12.4779i	0.696450	+	1.20629i	−0.273239	+	0.961946i	$0.588095\pi$
$108$	−0.192630	+	1.99070i	−0.0185358	+	0.191555i
$109$	−2.92380	−	1.68806i	−0.280050	−	0.161687i	0.353396	−	0.935474i	$-0.385027\pi$
$109$	−2.92380	−	1.68806i	−0.280050	−	0.161687i	−0.633446	+	0.773787i	$0.718360\pi$
$110$	10.0917	+	0.487123i	0.962204	+	0.0464453i
$111$	8.94486			0.849009
$112$	−8.55080	−	6.23568i	−0.807975	−	0.589217i
$113$	−10.7090			−1.00742			−0.503710	−	0.863873i	$-0.668032\pi$
$113$	−10.7090			−1.00742			−0.503710	+	0.863873i	$0.668032\pi$
$114$	−9.94467	−	0.480026i	−0.931403	−	0.0449586i
$115$	−1.69554	−	0.978920i	−0.158110	−	0.0912847i
$116$	0.643163	−	6.64666i	0.0597162	−	0.617127i
$117$	−0.770311	−	1.33422i	−0.0712153	−	0.123349i
$118$	7.23323	+	4.65498i	0.665873	+	0.428526i
$119$	−3.53711	−	5.06042i	−0.324246	−	0.463888i
$120$	1.70294	−	11.6868i	0.155456	−	1.06685i
$121$	4.03629	+	6.99106i	0.366935	+	0.635551i
$122$	−5.90225	−	11.4666i	−0.534365	−	1.03813i
$123$	2.65706	−	4.60216i	0.239579	−	0.414963i
$124$	3.67540	−	5.14759i	0.330061	−	0.462267i
$125$	−31.0452			−2.77677
$126$	0.142922	+	3.73893i	0.0127325	+	0.333090i
$127$			9.49738i			0.842757i	0.906885	+	0.421378i	$0.138454\pi$
$127$			9.49738i			0.842757i	−0.906885	+	0.421378i	$0.861546\pi$
$128$	−10.6750	−	3.74764i	−0.943544	−	0.331248i
$129$	−2.96849	−	1.71386i	−0.261361	−	0.150897i
$130$	4.16361	+	8.08883i	0.365173	+	0.709437i
$131$	−11.8364	+	6.83375i	−1.03415	+	0.597068i	−0.918171	−	0.396184i	$-0.870334\pi$
$131$	−11.8364	+	6.83375i	−1.03415	+	0.597068i	−0.115981	+	0.993251i	$0.537001\pi$
$132$	−3.11450	+	1.41759i	−0.271083	+	0.123385i
$133$	−18.5569	+	1.60805i	−1.60909	+	0.139435i
$134$	−5.71947	+	8.88730i	−0.494087	+	0.767746i
$135$	−3.61611	+	2.08776i	−0.311226	+	0.179686i
$136$	−5.18048	−	4.08990i	−0.444222	−	0.350706i
$137$	5.99460	−	10.3829i	0.512153	−	0.887075i	−0.487748	−	0.872985i	$-0.662181\pi$
$137$	5.99460	−	10.3829i	0.512153	−	0.887075i	0.999901	−	0.0140902i	$-0.00448520\pi$
$138$	0.662331	+	0.0319706i	0.0563814	+	0.00272151i
$139$		−	6.64909i		−	0.563968i	−0.959419	−	0.281984i	$-0.909007\pi$
$139$		−	6.64909i		−	0.563968i	0.959419	−	0.281984i	$-0.0909925\pi$
$140$	0.221510	−	22.0937i	0.0187210	−	1.86726i
$141$		−	5.90095i		−	0.496950i
$142$	0.238143	−	4.93358i	0.0199845	−	0.414017i
$143$	1.31798	−	2.28281i	0.110215	−	0.190898i
$144$	1.29871	+	3.78330i	0.108225	+	0.315275i
$145$	12.0737	−	6.97073i	1.00266	−	0.578888i
$146$	17.2764	+	11.1183i	1.42981	+	0.920160i
$147$	1.20413	+	6.89566i	0.0993147	+	0.568744i
$148$	16.2824	−	7.41107i	1.33841	−	0.609186i
$149$	7.03123	−	4.05948i	0.576021	−	0.332566i	−0.183530	−	0.983014i	$-0.558752\pi$
$149$	7.03123	−	4.05948i	0.576021	−	0.332566i	0.759550	+	0.650448i	$0.225419\pi$
$150$	15.6360	−	8.04839i	1.27667	−	0.657149i
$151$	−1.07044	−	0.618020i	−0.0871113	−	0.0502937i	0.455812	−	0.890076i	$-0.349349\pi$
$151$	−1.07044	−	0.618020i	−0.0871113	−	0.0502937i	−0.542923	+	0.839783i	$0.682682\pi$
$152$	−18.5001	+	7.36564i	−1.50056	+	0.597432i
$153$			2.33358i			0.188658i
$154$	−5.41786	+	3.41037i	−0.436584	+	0.274815i
$155$	13.2052			1.06067
$156$	−2.50765	−	1.79047i	−0.200772	−	0.143352i
$157$	−4.80286	+	8.31880i	−0.383310	+	0.663913i	−0.991533	−	0.129854i	$-0.958549\pi$
$157$	−4.80286	+	8.31880i	−0.383310	+	0.663913i	0.608223	+	0.793766i	$0.291883\pi$
$158$	2.12140	−	1.09196i	0.168769	−	0.0868716i
$159$	−0.781947	−	1.35437i	−0.0620124	−	0.107409i
$160$	−6.58293	−	22.6845i	−0.520426	−	1.79337i
$161$	1.23592	−	0.107099i	0.0974041	−	0.00844055i
$162$	0.765334	−	1.18923i	0.0601303	−	0.0934346i
$163$	9.70461	+	16.8089i	0.760123	+	1.31657i	0.942787	+	0.333397i	$0.108195\pi$
$163$	9.70461	+	16.8089i	0.760123	+	1.31657i	−0.182663	+	0.983176i	$0.558472\pi$
$164$	1.02366	−	10.5788i	0.0799343	−	0.826067i
$165$	−6.18706	−	3.57210i	−0.481662	−	0.278088i
$166$	0.185871	−	3.85068i	0.0144264	−	0.298871i
$167$	−17.7482			−1.37340			−0.686699	−	0.726942i	$-0.740941\pi$
$167$	−17.7482			−1.37340			−0.686699	+	0.726942i	$0.740941\pi$
$168$	3.35797	+	6.68760i	0.259073	+	0.515960i
$169$	−10.6265			−0.817422
$170$	0.664382	−	13.7639i	0.0509558	−	1.05565i
$171$	6.09693	+	3.52006i	0.466244	+	0.269186i
$172$	−6.82356	−	0.660281i	−0.520292	−	0.0503460i
$173$	3.57075	+	6.18472i	0.271479	+	0.470216i	0.969241	−	0.246114i	$-0.0791539\pi$
$173$	3.57075	+	6.18472i	0.271479	+	0.470216i	−0.697762	+	0.716330i	$0.745821\pi$
$174$	−2.55534	+	3.97066i	−0.193719	+	0.301015i
$175$	26.9657	−	18.8484i	2.03842	−	1.42480i
$176$	−4.49486	+	5.16091i	−0.338813	+	0.389018i
$177$	−3.04114	−	5.26742i	−0.228586	−	0.395923i
$178$	−2.66907	+	1.37387i	−0.200055	+	0.102976i
$179$	−11.9581	+	20.7121i	−0.893791	+	1.54809i	−0.0584980	+	0.998288i	$0.518631\pi$
$179$	−11.9581	+	20.7121i	−0.893791	+	1.54809i	−0.835293	+	0.549805i	$0.814702\pi$
$180$	−4.85269	+	6.79644i	−0.361698	+	0.506577i
$181$	20.5572			1.52800			0.764002	−	0.645214i	$-0.223232\pi$
$181$	20.5572			1.52800			0.764002	+	0.645214i	$0.223232\pi$
$182$	−5.09864	−	2.68945i	−0.377936	−	0.199355i
$183$			9.11917i			0.674109i
$184$	1.23214	−	0.490564i	0.0908345	−	0.0361648i
$185$	32.3456	+	18.6748i	2.37810	+	1.37300i
$186$	−3.97660	+	2.04690i	−0.291579	+	0.150086i
$187$	−3.45776	+	1.99634i	−0.252857	+	0.145987i
$188$	−4.88910	−	10.7416i	−0.356575	−	0.783410i
$189$	1.12013	−	2.39694i	0.0814772	−	0.174352i
$190$	−34.9589	−	22.4979i	−2.53618	−	1.63217i
$191$	−1.74523	+	1.00761i	−0.126280	+	0.0729079i	−0.561809	−	0.827267i	$-0.689895\pi$
$191$	−1.74523	+	1.00761i	−0.126280	+	0.0729079i	0.435529	+	0.900175i	$0.356561\pi$
$192$	5.49862	+	5.81078i	0.396829	+	0.419357i
$193$	1.78535	−	3.09232i	0.128512	−	0.222590i	−0.794588	−	0.607149i	$-0.792313\pi$
$193$	1.78535	−	3.09232i	0.128512	−	0.222590i	0.923100	+	0.384559i	$0.125646\pi$
$194$	−0.133097	+	2.75737i	−0.00955584	+	0.197967i
$195$		−	6.43291i		−	0.460671i
$196$	7.90514	+	11.5546i	0.564653	+	0.825329i
$197$			17.5393i			1.24962i	0.780775	+	0.624812i	$0.214824\pi$
$197$			17.5393i			1.24962i	−0.780775	+	0.624812i	$0.785176\pi$
$198$	2.41686	+	0.116661i	0.171759	+	0.00829076i
$199$	−8.85336	+	15.3345i	−0.627598	+	1.08703i	0.360434	+	0.932785i	$0.382629\pi$
$199$	−8.85336	+	15.3345i	−0.627598	+	1.08703i	−0.988032	+	0.154247i	$0.950705\pi$
$200$	21.7941	−	27.6054i	1.54107	−	1.95200i
$201$	6.47195	−	3.73658i	0.456496	−	0.263558i
$202$	−10.5470	+	16.3886i	−0.742083	+	1.15310i
$203$	−3.73994	+	8.00302i	−0.262492	+	0.561702i
$204$	1.93343	+	4.24784i	0.135367	+	0.297408i
$205$	19.2164	−	11.0946i	1.34213	−	0.774882i
$206$	4.97244	+	9.66017i	0.346446	+	0.673056i
$207$	−0.406066	−	0.234442i	−0.0282235	−	0.0162949i
$208$	−6.04816	−	1.18156i	−0.419364	−	0.0819266i
$209$			12.0455i			0.833201i
$210$	−7.28918	+	13.8188i	−0.503001	+	0.953586i
$211$	−4.23050			−0.291240			−0.145620	−	0.989341i	$-0.546518\pi$
$211$	−4.23050			−0.291240			−0.145620	+	0.989341i	$0.546518\pi$
$212$	−2.54552	−	1.81752i	−0.174827	−	0.124827i
$213$	−1.74631	+	3.02471i	−0.119656	+	0.207249i
$214$	−9.32554	−	18.1171i	−0.637481	−	1.23846i
$215$	−7.15626	−	12.3950i	−0.488053	−	0.845333i
$216$	0.407838	−	2.79887i	0.0277499	−	0.190439i
$217$	−6.85803	+	4.79359i	−0.465553	+	0.325410i
$218$	4.01498	+	2.58386i	0.271928	+	0.175001i
$219$	−7.26372	−	12.5811i	−0.490837	−	0.850154i
$220$	−14.2220	−	1.37619i	−0.958846	−	0.0927827i
$221$	−3.11350	−	1.79758i	−0.209437	−	0.120918i
$222$	−12.6352	−	0.609899i	−0.848021	−	0.0409338i
$223$	−1.43532			−0.0961162			−0.0480581	−	0.998845i	$-0.515303\pi$
$223$	−1.43532			−0.0961162			−0.0480581	+	0.998845i	$0.515303\pi$
$224$	11.6534	+	9.39136i	0.778627	+	0.627487i
$225$	−12.4350			−0.829003
$226$	15.1272	+	0.730187i	1.00625	+	0.0485713i
$227$	13.8688	+	8.00718i	0.920508	+	0.531455i	0.883797	−	0.467871i	$-0.154979\pi$
$227$	13.8688	+	8.00718i	0.920508	+	0.531455i	0.0367106	+	0.999326i	$0.488312\pi$
$228$	14.0148	+	1.35614i	0.928152	+	0.0898126i
$229$	−8.12499	−	14.0729i	−0.536914	−	0.929963i	−0.999068	−	0.0431631i	$-0.986256\pi$
$229$	−8.12499	−	14.0729i	−0.536914	−	0.929963i	0.462154	−	0.886800i	$-0.347077\pi$
$230$	2.32832	+	1.49840i	0.153525	+	0.0988016i
$231$	4.50990	−	0.390805i	0.296730	−	0.0257131i
$232$	−1.36171	+	9.34501i	−0.0894006	+	0.613530i
$233$	−5.93054	−	10.2720i	−0.388522	−	0.672941i	0.603729	−	0.797190i	$-0.293681\pi$
$233$	−5.93054	−	10.2720i	−0.388522	−	0.672941i	−0.992251	+	0.124249i	$0.960348\pi$
$234$	0.997145	+	1.93720i	0.0651854	+	0.126639i
$235$	12.3198	−	21.3385i	0.803654	−	1.39197i
$236$	−9.90004	−	7.06867i	−0.644438	−	0.460131i
$237$	−1.68711			−0.109590
$238$	4.65137	+	7.38937i	0.301504	+	0.478982i
$239$			0.846585i			0.0547610i	0.999625	+	0.0273805i	$0.00871657\pi$
$239$			0.846585i			0.0547610i	−0.999625	+	0.0273805i	$0.991283\pi$
$240$	−3.20237	+	16.3922i	−0.206712	+	1.05811i
$241$	−0.761425	−	0.439609i	−0.0490477	−	0.0283177i	0.475276	−	0.879837i	$-0.342348\pi$
$241$	−0.761425	−	0.439609i	−0.0490477	−	0.0283177i	−0.524323	+	0.851519i	$0.675682\pi$
$242$	−5.22486	−	10.1506i	−0.335867	−	0.652503i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	7.55549	+	16.5998i	0.483691	+	1.06269i
$245$	−10.0422	+	27.4494i	−0.641575	+	1.75368i
$246$	−4.06707	+	6.31969i	−0.259307	+	0.402929i
$247$	−9.39307	+	5.42309i	−0.597667	+	0.345063i
$248$	−5.54275	+	7.02072i	−0.351965	+	0.445816i
$249$	−1.36301	+	2.36080i	−0.0863771	+	0.149609i
$250$	43.8535	+	2.11680i	2.77354	+	0.133878i
$251$		−	18.1441i		−	1.14524i	−0.819820	−	0.572622i	$-0.805926\pi$
$251$		−	18.1441i		−	1.14524i	0.819820	−	0.572622i	$-0.194074\pi$
$252$	0.0530495	−	5.29124i	0.00334180	−	0.333317i
$253$		−	0.802247i		−	0.0504368i
$254$	0.647573	−	13.4157i	0.0406323	−	0.841776i
$255$	−4.87196	+	8.43848i	−0.305094	+	0.528438i
$256$	14.8236	+	6.02167i	0.926476	+	0.376354i
$257$	15.8902	−	9.17421i	0.991203	−	0.572271i	0.0855695	−	0.996332i	$-0.472729\pi$
$257$	15.8902	−	9.17421i	0.991203	−	0.572271i	0.905634	+	0.424061i	$0.139396\pi$
$258$	4.07634	+	2.62335i	0.253782	+	0.163322i
$259$	−23.5775	+	2.04311i	−1.46504	+	0.126953i
$260$	−5.32985	−	11.7099i	−0.330543	−	0.726218i
$261$	2.89153	−	1.66943i	0.178981	−	0.103335i
$262$	17.1857	−	8.84609i	1.06174	−	0.546513i
$263$	−3.02044	−	1.74385i	−0.186248	−	0.107531i	0.403977	−	0.914769i	$-0.367628\pi$
$263$	−3.02044	−	1.74385i	−0.186248	−	0.107531i	−0.590225	+	0.807239i	$0.700961\pi$
$264$	4.49611	−	1.79008i	0.276716	−	0.110172i
$265$		−	6.53008i		−	0.401140i
$266$	26.3225	−	1.00619i	1.61394	−	0.0616933i
$267$	2.12267			0.129905
$268$	8.68512	−	12.1640i	0.530528	−	0.743032i
$269$	7.35605	−	12.7410i	0.448506	−	0.776835i	−0.549783	−	0.835308i	$-0.685290\pi$
$269$	7.35605	−	12.7410i	0.448506	−	0.776835i	0.998289	+	0.0584722i	$0.0186229\pi$
$270$	5.25036	−	2.70255i	0.319527	−	0.164472i
$271$	9.95139	+	17.2363i	0.604504	+	1.04703i	0.992130	+	0.125215i	$0.0399619\pi$
$271$	9.95139	+	17.2363i	0.604504	+	1.04703i	−0.387626	+	0.921817i	$0.626705\pi$
$272$	7.03891	+	6.13049i	0.426797	+	0.371716i
$273$	2.33519	+	3.34088i	0.141332	+	0.202199i
$274$	−9.17573	+	14.2579i	−0.554326	+	0.861350i
$275$	−10.6380	−	18.4255i	−0.641495	−	1.11110i
$276$	−0.933409	−	0.0903212i	−0.0561846	−	0.00543670i
$277$	−22.9034	−	13.2233i	−1.37613	−	0.794510i	−0.384440	−	0.923150i	$-0.625605\pi$
$277$	−22.9034	−	13.2233i	−1.37613	−	0.794510i	−0.991691	+	0.128640i	$0.958939\pi$
$278$	−0.453363	+	9.39229i	−0.0271909	+	0.563312i
$279$	3.16253			0.189336
$280$	−1.81934	+	31.1938i	−0.108726	+	1.86419i
$281$	−20.2837			−1.21003			−0.605013	−	0.796216i	$-0.706832\pi$
$281$	−20.2837			−1.21003			−0.605013	+	0.796216i	$0.706832\pi$
$282$	−0.402352	+	8.33550i	−0.0239597	+	0.496372i
$283$	5.70426	+	3.29336i	0.339083	+	0.195770i	0.659866	−	0.751383i	$-0.270613\pi$
$283$	5.70426	+	3.29336i	0.339083	+	0.195770i	−0.320783	+	0.947153i	$0.603946\pi$
$284$	−0.672785	+	6.95278i	−0.0399225	+	0.412572i
$285$	14.6981	+	25.4579i	0.870642	+	1.50800i
$286$	−2.01739	+	3.13476i	−0.119291	+	0.185362i
$287$	−5.95248	+	12.7376i	−0.351364	+	0.751877i
$288$	−1.57655	−	5.43272i	−0.0928991	−	0.320126i
$289$	−5.77721	−	10.0064i	−0.339836	−	0.588613i
$290$	−17.5302	+	9.02341i	−1.02941	+	0.529873i
$291$	0.976012	−	1.69050i	0.0572148	−	0.0990990i
$292$	−23.6461	−	16.8834i	−1.38378	−	0.988026i
$293$	12.9438			0.756187			0.378094	−	0.925767i	$-0.376580\pi$
$293$	12.9438			0.756187			0.378094	+	0.925767i	$0.376580\pi$
$294$	−1.23074	−	9.82269i	−0.0717780	−	0.572871i
$295$		−	25.3968i		−	1.47866i
$296$	−23.5054	+	9.35844i	−1.36622	+	0.543948i
$297$	−1.48174	−	0.855485i	−0.0859795	−	0.0496403i
$298$	−10.2089	+	5.25488i	−0.591385	+	0.304407i
$299$	0.625594	−	0.361187i	0.0361790	−	0.0208880i
$300$	−22.6357	+	10.3028i	−1.30687	+	0.594831i
$301$	8.21603	+	3.83948i	0.473564	+	0.221304i
$302$	1.46993	+	0.945983i	0.0845851	+	0.0544352i
$303$	11.9346	−	6.89045i	0.685625	−	0.395846i
$304$	26.6349	−	9.14305i	1.52762	−	0.524390i
$305$	−19.0387	+	32.9760i	−1.09015	+	1.88820i
$306$	0.159113	−	3.29634i	0.00909590	−	0.188439i
$307$		−	11.8773i		−	0.677871i	−0.940810	−	0.338936i	$-0.889933\pi$
$307$		−	11.8773i		−	0.677871i	0.940810	−	0.338936i	$-0.110067\pi$
$308$	7.88564	−	4.44797i	0.449326	−	0.253447i
$309$		−	7.68258i		−	0.437047i
$310$	−18.6533	−	0.900389i	−1.05944	−	0.0511386i
$311$	5.91849	−	10.2511i	0.335607	−	0.581288i	−0.647994	−	0.761645i	$-0.724392\pi$
$311$	5.91849	−	10.2511i	0.335607	−	0.581288i	0.983601	+	0.180357i	$0.0577253\pi$
$312$	3.42014	+	2.70015i	0.193627	+	0.152866i
$313$	−12.8383	+	7.41217i	−0.725661	+	0.418961i	−0.816833	−	0.576875i	$-0.804272\pi$
$313$	−12.8383	+	7.41217i	−0.725661	+	0.418961i	0.0911716	+	0.995835i	$0.470939\pi$
$314$	7.35159	−	11.4234i	0.414874	−	0.644660i
$315$	9.05475	−	6.32904i	0.510177	−	0.356601i
$316$	−3.07107	+	1.39782i	−0.172761	+	0.0786336i
$317$	−5.87478	+	3.39181i	−0.329961	+	0.190503i	−0.655824	−	0.754914i	$-0.727678\pi$
$317$	−5.87478	+	3.39181i	−0.329961	+	0.190503i	0.325863	+	0.945417i	$0.394345\pi$
$318$	1.01221	+	1.96646i	0.0567617	+	0.110274i
$319$	4.94732	+	2.85634i	0.276997	+	0.159924i
$320$	7.75211	+	32.4923i	0.433356	+	1.81637i
$321$			14.4083i			0.804191i
$322$	−1.75312	+	0.0670137i	−0.0976978	+	0.00373453i
$323$	16.4287			0.914116
$324$	−1.16217	+	1.62768i	−0.0645652	+	0.0904268i
$325$	9.57885	−	16.5911i	0.531339	−	0.920306i
$326$	−12.5623	−	24.4054i	−0.695763	−	1.35169i
$327$	−1.68806	−	2.92380i	−0.0933499	−	0.161687i
$328$	−2.16730	+	14.8735i	−0.119669	+	0.821252i
$329$	1.34784	+	15.5542i	0.0743090	+	0.857528i
$330$	8.49609	+	5.46770i	0.467695	+	0.300987i
$331$	2.37285	+	4.10989i	0.130424	+	0.225900i	0.923840	−	0.382779i	$-0.125033\pi$
$331$	2.37285	+	4.10989i	0.130424	+	0.225900i	−0.793416	+	0.608679i	$0.791700\pi$
$332$	−0.525112	+	5.42668i	−0.0288193	+	0.297828i
$333$	7.74648	+	4.47243i	0.424504	+	0.245088i
$334$	25.0706	+	1.21015i	1.37180	+	0.0662164i
$335$	31.2044			1.70488
$336$	−4.28737	−	9.67566i	−0.233895	−	0.527851i
$337$	16.5173			0.899754			0.449877	−	0.893090i	$-0.351468\pi$
$337$	16.5173			0.899754			0.449877	+	0.893090i	$0.351468\pi$
$338$	15.0106	+	0.724559i	0.816471	+	0.0394108i
$339$	−9.27429	−	5.35451i	−0.503710	−	0.290817i
$340$	−1.87697	+	19.3972i	−0.101793	+	1.05196i
$341$	2.70549	+	4.68605i	0.146511	+	0.253764i
$342$	−8.37232	−	5.38805i	−0.452723	−	0.291352i
$343$	−4.74897	−	17.9010i	−0.256420	−	0.966565i
$344$	9.59373	+	1.39795i	0.517259	+	0.0753726i
$345$	−0.978920	−	1.69554i	−0.0527033	−	0.0912847i
$346$	−4.62223	−	8.97981i	−0.248493	−	0.482758i
$347$	9.54986	−	16.5408i	0.512663	−	0.887959i	−0.487229	−	0.873274i	$-0.661992\pi$
$347$	9.54986	−	16.5408i	0.512663	−	0.887959i	0.999892	−	0.0146846i	$-0.00467441\pi$
$348$	3.88032	−	5.43459i	0.208007	−	0.291325i
$349$	−2.49767			−0.133697			−0.0668485	−	0.997763i	$-0.521294\pi$
$349$	−2.49767			−0.133697			−0.0668485	+	0.997763i	$0.521294\pi$
$350$	−39.3761	+	24.7860i	−2.10474	+	1.32487i
$351$		−	1.54062i		−	0.0822323i
$352$	6.70119	−	6.98366i	0.357175	−	0.372230i
$353$	−22.3071	−	12.8790i	−1.18729	−	0.685481i	−0.229599	−	0.973285i	$-0.573741\pi$
$353$	−22.3071	−	12.8790i	−1.18729	−	0.685481i	−0.957689	+	0.287805i	$0.907075\pi$
$354$	3.93667	+	7.64795i	0.209232	+	0.406484i
$355$	−12.6297	+	7.29179i	−0.670317	+	0.387008i
$356$	3.86393	−	1.75869i	0.204788	−	0.0932105i
$357$	−0.533015	−	6.15101i	−0.0282102	−	0.325546i
$358$	18.3039	−	28.4419i	0.967391	−	1.50320i
$359$	−28.7697	+	16.6102i	−1.51840	+	0.876651i	−0.518639	+	0.854993i	$0.673561\pi$
$359$	−28.7697	+	16.6102i	−1.51840	+	0.876651i	−0.999765	+	0.0216582i	$0.993105\pi$
$360$	7.31817	−	9.26956i	0.385701	−	0.488549i
$361$	15.2817	−	26.4687i	0.804300	−	1.39309i
$362$	−29.0384	−	1.40168i	−1.52623	−	0.0736705i
$363$			8.07258i			0.423701i
$364$	7.01880	+	4.14668i	0.367885	+	0.217345i
$365$		−	60.6597i		−	3.17507i
$366$	0.621785	−	12.8815i	0.0325012	−	0.673325i
$367$	−2.17584	+	3.76866i	−0.113578	+	0.196722i	−0.917210	−	0.398403i	$-0.869564\pi$
$367$	−2.17584	+	3.76866i	−0.113578	+	0.196722i	0.803633	+	0.595126i	$0.202898\pi$
$368$	−1.77393	+	0.608943i	−0.0924725	+	0.0317433i
$369$	4.60216	−	2.65706i	0.239579	−	0.138321i
$370$	−44.4171	−	28.5849i	−2.30914	−	1.48606i
$371$	2.37047	+	3.39135i	0.123068	+	0.176070i
$372$	5.75679	−	2.62024i	0.298476	−	0.135853i
$373$	−11.0943	+	6.40533i	−0.574444	+	0.331655i	−0.758922	−	0.651181i	$-0.774274\pi$
$373$	−11.0943	+	6.40533i	−0.574444	+	0.331655i	0.184479	+	0.982837i	$0.440940\pi$
$374$	5.02045	−	2.58420i	0.259601	−	0.133626i
$375$	−26.8859	−	15.5226i	−1.38838	−	0.801584i
$376$	6.17379	+	15.5066i	0.318389	+	0.799691i
$377$			5.14391i			0.264925i
$378$	−1.74569	+	3.30947i	−0.0897886	+	0.170221i
$379$	−24.0807			−1.23694			−0.618472	−	0.785807i	$-0.712248\pi$
$379$	−24.0807			−1.23694			−0.618472	+	0.785807i	$0.712248\pi$
$380$	47.8478	+	34.1635i	2.45454	+	1.75255i
$381$	−4.74869	+	8.22498i	−0.243283	+	0.421378i
$382$	2.53396	−	1.30432i	0.129648	−	0.0667347i
$383$	−8.78233	−	15.2114i	−0.448756	−	0.777268i	0.549549	−	0.835461i	$-0.314799\pi$
$383$	−8.78233	−	15.2114i	−0.448756	−	0.777268i	−0.998305	+	0.0581930i	$0.981466\pi$
$384$	−7.37098	−	8.58304i	−0.376149	−	0.438002i
$385$	17.1242	+	8.00242i	0.872731	+	0.407841i
$386$	−2.73278	+	4.24638i	−0.139095	+	0.216135i
$387$	−1.71386	−	2.96849i	−0.0871203	−	0.150897i
$388$	0.376018	−	3.88590i	0.0190894	−	0.197277i
$389$	23.9022	+	13.7999i	1.21189	+	0.699685i	0.963171	−	0.268890i	$-0.0866570\pi$
$389$	23.9022	+	13.7999i	1.21189	+	0.699685i	0.248719	+	0.968576i	$0.419990\pi$
$390$	−0.438624	+	9.08693i	−0.0222106	+	0.460135i
$391$	−1.09418			−0.0553349
$392$	−10.3787	−	16.8607i	−0.524204	−	0.851593i
$393$	−13.6675			−0.689435
$394$	1.19591	−	24.7755i	0.0602488	−	1.24817i
$395$	−6.10079	−	3.52229i	−0.306964	−	0.177226i
$396$	−3.40603	−	0.329584i	−0.171160	−	0.0165622i
$397$	8.65850	+	14.9970i	0.434558	+	0.752676i	0.997259	−	0.0739841i	$-0.0235714\pi$
$397$	8.65850	+	14.9970i	0.434558	+	0.752676i	−0.562702	+	0.826660i	$0.690238\pi$
$398$	13.5516	−	21.0573i	0.679278	−	1.05551i
$399$	−16.8748	−	7.88583i	−0.844794	−	0.394786i
$400$	−32.6679	+	37.5086i	−1.63339	+	1.87543i
$401$	−3.87616	−	6.71371i	−0.193566	−	0.335266i	0.752863	−	0.658177i	$-0.228672\pi$
$401$	−3.87616	−	6.71371i	−0.193566	−	0.335266i	−0.946430	+	0.322910i	$0.895339\pi$
$402$	−9.39686	+	4.83690i	−0.468673	+	0.241242i
$403$	−2.43613	+	4.21950i	−0.121352	+	0.210188i
$404$	16.0158	−	22.4309i	0.796815	−	1.11598i
$405$	−4.17553			−0.207484
$406$	5.82860	−	11.0498i	0.289268	−	0.548393i
$407$			15.3044i			0.758611i
$408$	−2.44147	−	6.13220i	−0.120871	−	0.303589i
$409$	−4.01694	−	2.31918i	−0.198625	−	0.114676i	0.397389	−	0.917650i	$-0.369916\pi$
$409$	−4.01694	−	2.31918i	−0.198625	−	0.114676i	−0.596014	+	0.802974i	$0.703250\pi$
$410$	−27.9010	+	14.3617i	−1.37793	+	0.709271i
$411$	10.3829	−	5.99460i	0.512153	−	0.295692i
$412$	−6.36524	−	13.9847i	−0.313593	−	0.688977i
$413$	9.21921	+	13.1896i	0.453648	+	0.649018i
$414$	0.557610	+	0.358853i	0.0274051	+	0.0176367i
$415$	−9.85758	+	5.69128i	−0.483889	+	0.279374i
$416$	8.46287	+	2.08143i	0.414927	+	0.102050i
$417$	3.32454	−	5.75828i	0.162804	−	0.281984i
$418$	0.821311	−	17.0150i	0.0401716	−	0.832232i
$419$		−	14.2419i		−	0.695760i	−0.937539	−	0.347880i	$-0.886902\pi$
$419$		−	14.2419i		−	0.695760i	0.937539	−	0.347880i	$-0.113098\pi$
$420$	11.2387	−	19.0230i	0.548392	−	0.928225i
$421$			20.0126i			0.975356i	0.873024	+	0.487678i	$0.162156\pi$
$421$			20.0126i			0.975356i	−0.873024	+	0.487678i	$0.837844\pi$
$422$	5.97587	+	0.288454i	0.290901	+	0.0140417i
$423$	2.95047	−	5.11037i	0.143457	−	0.248475i
$424$	3.47180	+	2.74093i	0.168606	+	0.133111i
$425$	−25.1304	+	14.5091i	−1.21900	+	0.703793i
$426$	2.67303	−	4.15353i	0.129509	−	0.201239i
$427$	−2.08292	−	24.0370i	−0.100800	−	1.16323i
$428$	11.9377	+	26.2276i	0.577029	+	1.26776i
$429$	2.28281	−	1.31798i	0.110215	−	0.0636327i
$430$	9.26357	+	17.9968i	0.446729	+	0.867881i
$431$	−12.1099	−	6.99165i	−0.583313	−	0.336776i	0.179136	−	0.983824i	$-0.442670\pi$
$431$	−12.1099	−	6.99165i	−0.583313	−	0.336776i	−0.762449	+	0.647049i	$0.776003\pi$
$432$	−0.766938	+	3.92579i	−0.0368993	+	0.188880i
$433$		−	0.984888i		−	0.0473307i	−0.999720	−	0.0236653i	$-0.992466\pi$
$433$		−	0.984888i		−	0.0473307i	0.999720	−	0.0236653i	$-0.00753362\pi$
$434$	10.0143	−	6.30367i	0.480701	−	0.302586i
$435$	13.9415			0.668442
$436$	−5.49525	−	3.92363i	−0.263175	−	0.187908i
$437$	−1.65050	+	2.85875i	−0.0789542	+	0.136753i
$438$	9.40267	+	18.2670i	0.449277	+	0.872830i
$439$	−3.43693	−	5.95294i	−0.164036	−	0.284118i	0.772277	−	0.635286i	$-0.219118\pi$
$439$	−3.43693	−	5.95294i	−0.164036	−	0.284118i	−0.936312	+	0.351168i	$0.885785\pi$
$440$	19.9957	+	2.91368i	0.953258	+	0.138904i
$441$	−2.40502	+	6.57388i	−0.114525	+	0.313042i
$442$	4.27547	+	2.75150i	0.203363	+	0.130875i
$443$	−1.70483	−	2.95285i	−0.0809989	−	0.140294i	0.822680	−	0.568504i	$-0.192478\pi$
$443$	−1.70483	−	2.95285i	−0.0809989	−	0.140294i	−0.903679	+	0.428210i	$0.859144\pi$
$444$	17.8065	+	1.72305i	0.845061	+	0.0817723i
$445$	7.67582	+	4.43164i	0.363869	+	0.210080i
$446$	2.02749	+	0.0978664i	0.0960044	+	0.00463411i
$447$	8.11897			0.384014
$448$	−15.8209	−	14.0605i	−0.747468	−	0.664297i
$449$	32.9924			1.55701			0.778503	−	0.627641i	$-0.215979\pi$
$449$	32.9924			1.55701			0.778503	+	0.627641i	$0.215979\pi$
$450$	17.5653	+	0.847875i	0.828039	+	0.0399692i
$451$	7.87416	+	4.54615i	0.370780	+	0.214070i
$452$	−21.3185	−	2.06288i	−1.00274	−	0.0970297i
$453$	−0.618020	−	1.07044i	−0.0290371	−	0.0502937i
$454$	−19.0447	−	12.2563i	−0.893814	−	0.575218i
$455$	1.46935	+	16.9563i	0.0688842	+	0.794926i
$456$	−19.7044	−	2.87123i	−0.922743	−	0.134458i
$457$	11.4224	+	19.7842i	0.534319	+	0.925467i	0.999196	+	0.0400919i	$0.0127651\pi$
$457$	11.4224	+	19.7842i	0.534319	+	0.925467i	−0.464877	+	0.885375i	$0.653902\pi$
$458$	10.5176	+	20.4329i	0.491453	+	0.954768i
$459$	−1.16679	+	2.02094i	−0.0544610	+	0.0943292i
$460$	−3.18674	−	2.27535i	−0.148583	−	0.106089i
$461$	−15.8743			−0.739338			−0.369669	−	0.929164i	$-0.620529\pi$
$461$	−15.8743			−0.739338			−0.369669	+	0.929164i	$0.620529\pi$
$462$	−6.39719	+	0.244535i	−0.297624	+	0.0113768i
$463$		−	2.72059i		−	0.126436i	−0.998000	−	0.0632182i	$-0.979864\pi$
$463$		−	2.72059i		−	0.126436i	0.998000	−	0.0632182i	$-0.0201364\pi$
$464$	2.56069	−	13.1076i	0.118877	−	0.608506i
$465$	11.4361	+	6.60261i	0.530334	+	0.306189i
$466$	7.67691	+	14.9143i	0.355626	+	0.690890i
$467$	20.7726	−	11.9931i	0.961240	−	0.554972i	0.0646858	−	0.997906i	$-0.479395\pi$
$467$	20.7726	−	11.9931i	0.961240	−	0.554972i	0.896555	+	0.442933i	$0.146062\pi$
$468$	−1.27645	−	2.80442i	−0.0590039	−	0.129634i
$469$	−16.2058	+	11.3274i	−0.748313	+	0.523052i
$470$	−18.8575	+	29.3021i	−0.869832	+	1.35160i
$471$	−8.31880	+	4.80286i	−0.383310	+	0.221304i
$472$	13.5025	+	10.6600i	0.621504	+	0.490667i
$473$	2.93236	−	5.07900i	0.134830	−	0.233533i
$474$	2.38316	+	0.115035i	0.109462	+	0.00528372i
$475$			87.5443i			4.01681i
$476$	−6.06654	−	10.7551i	−0.278060	−	0.492961i
$477$		−	1.56389i		−	0.0716058i
$478$	0.0577238	−	1.19586i	0.00264022	−	0.0546973i
$479$	9.87511	−	17.1042i	0.451205	−	0.781511i	−0.547256	−	0.836965i	$-0.684328\pi$
$479$	9.87511	−	17.1042i	0.451205	−	0.781511i	0.998461	+	0.0554547i	$0.0176608\pi$
$480$	5.64126	−	22.9368i	0.257487	−	1.04692i
$481$	−11.9344	+	6.89033i	−0.544162	+	0.314172i
$482$	1.04559	+	0.672895i	0.0476253	+	0.0306495i
$483$	1.12389	+	0.525210i	0.0511386	+	0.0238979i
$484$	6.68836	+	14.6946i	0.304016	+	0.667937i
$485$	7.05874	−	4.07536i	0.320521	−	0.185053i
$486$	1.25741	−	0.647235i	0.0570374	−	0.0293592i
$487$	32.1435	+	18.5581i	1.45656	+	0.840946i	0.998840	−	0.0481495i	$-0.0153324\pi$
$487$	32.1435	+	18.5581i	1.45656	+	0.840946i	0.457721	+	0.889096i	$0.348666\pi$
$488$	−9.54081	−	23.9635i	−0.431892	−	1.08478i
$489$			19.4092i			0.877715i
$490$	16.0570	−	38.0895i	0.725381	−	1.72071i
$491$	−20.5746			−0.928517			−0.464259	−	0.885700i	$-0.653679\pi$
$491$	−20.5746			−0.928517			−0.464259	+	0.885700i	$0.653679\pi$
$492$	6.17592	−	8.64969i	0.278432	−	0.389958i
$493$	3.89573	−	6.74761i	0.175455	−	0.303897i
$494$	13.6381	−	7.02003i	0.613608	−	0.315846i
$495$	−3.57210	−	6.18706i	−0.160554	−	0.278088i
$496$	8.30821	−	9.53933i	0.373050	−	0.428328i
$497$	3.91219	−	8.37162i	0.175486	−	0.375518i
$498$	2.08631	−	3.24185i	0.0934898	−	0.145271i
$499$	−0.517579	−	0.896473i	−0.0231700	−	0.0401316i	0.854208	−	0.519932i	$-0.174043\pi$
$499$	−0.517579	−	0.896473i	−0.0231700	−	0.0401316i	−0.877378	+	0.479800i	$0.840709\pi$
$500$	−61.8018	−	5.98024i	−2.76386	−	0.267445i
$501$	−15.3704	−	8.87410i	−0.686699	−	0.396466i
$502$	−1.23714	+	25.6297i	−0.0552163	+	1.14391i
$503$	19.7898			0.882382			0.441191	−	0.897413i	$-0.354556\pi$
$503$	19.7898			0.882382			0.441191	+	0.897413i	$0.354556\pi$
$504$	−0.435715	+	7.47062i	−0.0194083	+	0.332768i
$505$	57.5425			2.56061
$506$	−0.0547007	+	1.13323i	−0.00243174	+	0.0503782i
$507$	−9.20280	−	5.31324i	−0.408711	−	0.235969i
$508$	−1.82948	+	18.9065i	−0.0811701	+	0.838838i
$509$	−2.11849	−	3.66933i	−0.0939004	−	0.162640i	0.815249	−	0.579111i	$-0.196600\pi$
$509$	−2.11849	−	3.66933i	−0.0939004	−	0.162640i	−0.909149	+	0.416471i	$0.863267\pi$
$510$	7.45735	−	11.5877i	0.330217	−	0.513114i
$511$	22.0199	+	31.5031i	0.974104	+	1.39362i
$512$	−20.5288	−	9.51676i	−0.907253	−	0.420586i
$513$	3.52006	+	6.09693i	0.155415	+	0.269186i
$514$	−23.0715	+	11.8757i	−1.01764	+	0.523816i
$515$	16.0394	−	27.7811i	0.706781	−	1.22418i
$516$	−5.57924	−	3.98360i	−0.245612	−	0.175368i
$517$	10.0963			0.444037
$518$	33.4442	−	1.27841i	1.46945	−	0.0561703i
$519$			7.14150i			0.313477i
$520$	6.73035	+	16.9045i	0.295145	+	0.741310i
$521$	−33.6570	−	19.4319i	−1.47454	−	0.851326i	−0.474952	−	0.880012i	$-0.657535\pi$
$521$	−33.6570	−	19.4319i	−1.47454	−	0.851326i	−0.999588	+	0.0286855i	$0.990868\pi$
$522$	−4.19831	+	2.16102i	−0.183755	+	0.0945854i
$523$	14.8181	−	8.55526i	0.647952	−	0.374095i	−0.139719	−	0.990191i	$-0.544620\pi$
$523$	14.8181	−	8.55526i	0.647952	−	0.374095i	0.787671	+	0.616096i	$0.211287\pi$
$524$	−24.8791	+	11.3239i	−1.08685	+	0.494688i
$525$	32.7772	−	2.84030i	1.43051	−	0.123961i
$526$	4.14768	+	2.66926i	0.180847	+	0.116385i
$527$	6.39126	−	3.69000i	0.278408	−	0.160739i
$528$	−6.47312	+	2.22205i	−0.281706	+	0.0967022i
$529$	−11.3901	+	19.7282i	−0.495221	+	0.857747i
$530$	−0.445249	+	9.22419i	−0.0193404	+	0.400673i
$531$		−	6.08229i		−	0.263949i
$532$	−37.2510	−	0.373475i	−1.61503	−	0.0161922i
$533$			8.18704i			0.354620i
$534$	−2.99842	−	0.144733i	−0.129754	−	0.00626320i
$535$	−30.0811	+	52.1019i	−1.30052	+	2.25256i
$536$	−13.0977	+	16.5902i	−0.565735	+	0.716589i
$537$	−20.7121	+	11.9581i	−0.893791	+	0.516031i
$538$	−11.2597	+	17.4960i	−0.485439	+	0.754308i
$539$	−11.7983	+	2.06023i	−0.508187	+	0.0887402i
$540$	−7.60077	+	3.45954i	−0.327085	+	0.148875i
$541$	−37.6652	+	21.7460i	−1.61935	+	0.934935i	−0.632268	+	0.774750i	$0.717876\pi$
$541$	−37.6652	+	21.7460i	−1.61935	+	0.934935i	−0.987087	+	0.160185i	$0.948791\pi$
$542$	−12.8818	−	25.0260i	−0.553320	−	1.07496i
$543$	17.8030	+	10.2786i	0.764002	+	0.441097i
$544$	−9.52494	−	9.13969i	−0.408379	−	0.391861i
$545$		−	14.0971i		−	0.603852i
$546$	−3.07083	−	4.87845i	−0.131419	−	0.208778i
$547$	10.8290			0.463016			0.231508	−	0.972833i	$-0.425634\pi$
$547$	10.8290			0.463016			0.231508	+	0.972833i	$0.425634\pi$
$548$	13.9335	−	19.5146i	0.595210	−	0.833623i
$549$	−4.55959	+	7.89744i	−0.194598	+	0.337054i
$550$	13.7706	+	26.7527i	0.587179	+	1.14074i
$551$	−11.7530	−	20.3567i	−0.500693	−	0.867226i
$552$	1.31235	+	0.191229i	0.0558571	+	0.00813924i
$553$	4.44702	−	0.385356i	0.189106	−	0.0163870i
$554$	31.4510	+	20.2404i	1.33622	+	0.859934i
$555$	18.6748	+	32.3456i	0.792699	+	1.37300i
$556$	1.28081	−	13.2363i	0.0543186	−	0.561346i
$557$	7.04197	+	4.06568i	0.298378	+	0.172269i	0.641714	−	0.766944i	$-0.278224\pi$
$557$	7.04197	+	4.06568i	0.298378	+	0.172269i	−0.343336	+	0.939213i	$0.611557\pi$
$558$	−4.46729	−	0.215635i	−0.189115	−	0.00912854i
$559$	5.28082			0.223355
$560$	4.69687	−	43.9393i	0.198479	−	1.85678i
$561$	−3.99268			−0.168571
$562$	28.6522	+	1.38303i	1.20862	+	0.0583397i
$563$	19.6081	+	11.3207i	0.826381	+	0.477111i	0.852612	−	0.522545i	$-0.175017\pi$
$563$	19.6081	+	11.3207i	0.826381	+	0.477111i	−0.0262311	+	0.999656i	$0.508351\pi$
$564$	1.13670	−	11.7470i	0.0478637	−	0.494639i
$565$	−22.3579	−	38.7251i	−0.940605	−	1.62918i
$566$	−7.83310	−	5.04103i	−0.329250	−	0.211890i
$567$	2.16853	−	1.51575i	0.0910696	−	0.0636554i
$568$	1.42443	−	9.77541i	0.0597676	−	0.410167i
$569$	10.1485	+	17.5778i	0.425449	+	0.736900i	0.996462	−	0.0840413i	$-0.0267828\pi$
$569$	10.1485	+	17.5778i	0.425449	+	0.736900i	−0.571013	+	0.820941i	$0.693449\pi$
$570$	−19.0263	−	36.9632i	−0.796924	−	1.54822i
$571$	−18.3819	+	31.8383i	−0.769257	+	1.33239i	0.168710	+	0.985666i	$0.446040\pi$
$571$	−18.3819	+	31.8383i	−0.769257	+	1.33239i	−0.937967	+	0.346726i	$0.887293\pi$
$572$	3.06344	−	4.29051i	0.128089	−	0.179395i
$573$	−2.01521			−0.0841868
$574$	9.27679	−	17.5869i	0.387206	−	0.734062i
$575$		−	5.83059i		−	0.243153i
$576$	1.85656	+	7.78159i	0.0773566	+	0.324233i
$577$	1.39915	+	0.807801i	0.0582475	+	0.0336292i	0.528841	−	0.848721i	$-0.322627\pi$
$577$	1.39915	+	0.807801i	0.0582475	+	0.0336292i	−0.470593	+	0.882350i	$0.655960\pi$
$578$	7.47843	+	14.5287i	0.311062	+	0.604313i
$579$	3.09232	−	1.78535i	0.128512	−	0.0741967i
$580$	25.3778	−	11.5509i	1.05376	−	0.479625i
$581$	3.05348	−	6.53409i	0.126680	−	0.271080i
$582$	−1.49395	+	2.32140i	−0.0619262	+	0.0962252i
$583$	2.31729	−	1.33789i	0.0959723	−	0.0554097i
$584$	32.2505	+	25.4613i	1.33454	+	1.05359i
$585$	3.21646	−	5.57107i	0.132984	−	0.230335i
$586$	−18.2841	−	0.882567i	−0.755308	−	0.0364585i
$587$			3.68747i			0.152198i	0.997100	+	0.0760991i	$0.0242465\pi$
$587$			3.68747i			0.152198i	−0.997100	+	0.0760991i	$0.975753\pi$
$588$	1.06875	+	13.9591i	0.0440744	+	0.575666i
$589$		−	22.2646i		−	0.917396i
$590$	−1.73166	+	35.8747i	−0.0712914	+	1.47694i
$591$	−8.76965	+	15.1895i	−0.360735	+	0.624812i
$592$	33.8411	−	11.6167i	1.39086	−	0.477445i
$593$	32.3781	−	18.6935i	1.32961	−	0.767650i	0.344370	−	0.938834i	$-0.388092\pi$
$593$	32.3781	−	18.6935i	1.32961	−	0.767650i	0.985239	+	0.171184i	$0.0547591\pi$
$594$	2.03473	+	1.30946i	0.0834862	+	0.0537279i
$595$	10.9144	−	23.3556i	0.447447	−	0.957485i
$596$	14.7791	−	6.72679i	0.605374	−	0.275540i
$597$	−15.3345	+	8.85336i	−0.627598	+	0.362344i
$598$	−0.908322	+	0.467546i	−0.0371440	+	0.0191194i
$599$	−8.61435	−	4.97350i	−0.351973	−	0.203212i	0.313581	−	0.949561i	$-0.398471\pi$
$599$	−8.61435	−	4.97350i	−0.351973	−	0.203212i	−0.665554	+	0.746350i	$0.731805\pi$
$600$	32.6769	−	13.0100i	1.33403	−	0.531131i
$601$		−	35.9296i		−	1.46560i	−0.680445	−	0.732799i	$-0.738214\pi$
$601$		−	35.9296i		−	1.46560i	0.680445	−	0.732799i	$-0.261786\pi$
$602$	−11.3439	−	5.98373i	−0.462343	−	0.243879i
$603$	7.47317			0.304331
$604$	−2.01188	−	1.43649i	−0.0818622	−	0.0584500i
$605$	−16.8536	+	29.1914i	−0.685198	+	1.18680i
$606$	−17.3283	+	8.91948i	−0.703913	+	0.362329i
$607$	14.9355	+	25.8690i	0.606212	+	1.04999i	0.991859	+	0.127344i	$0.0406451\pi$
$607$	14.9355	+	25.8690i	0.606212	+	1.04999i	−0.385646	+	0.922647i	$0.626022\pi$
$608$	−38.2471	+	11.0991i	−1.55112	+	0.450128i
$609$	−7.24039	+	5.06085i	−0.293395	+	0.205076i
$610$	29.1419	−	45.2827i	1.17992	−	1.83344i
$611$	4.54557	+	7.87315i	0.183894	+	0.318514i
$612$	−0.449517	+	4.64545i	−0.0181706	+	0.187781i
$613$	−32.8160	−	18.9463i	−1.32542	−	0.765234i	−0.340836	−	0.940123i	$-0.610710\pi$
$613$	−32.8160	−	18.9463i	−1.32542	−	0.765234i	−0.984588	+	0.174889i	$0.944043\pi$
$614$	−0.809843	+	16.7775i	−0.0326826	+	0.677083i
$615$	22.1892			0.894756
$616$	−11.4423	+	5.74539i	−0.461023	+	0.231488i
$617$	39.0332			1.57142			0.785709	−	0.618597i	$-0.212298\pi$
$617$	39.0332			1.57142			0.785709	+	0.618597i	$0.212298\pi$
$618$	−0.523831	+	10.8522i	−0.0210716	+	0.436538i
$619$	−21.5338	−	12.4325i	−0.865517	−	0.499706i	0.000339137	−	1.00000i	$-0.499892\pi$
$619$	−21.5338	−	12.4325i	−0.865517	−	0.499706i	−0.865856	+	0.500294i	$0.833225\pi$
$620$	26.2877	+	2.54372i	1.05574	+	0.102158i
$621$	−0.234442	−	0.406066i	−0.00940784	−	0.0162949i
$622$	−9.05924	+	14.0769i	−0.363242	+	0.564431i
$623$	−5.59509	+	0.484842i	−0.224163	+	0.0194248i
$624$	−4.64708	−	4.04734i	−0.186032	−	0.162023i
$625$	−33.7275	−	58.4177i	−1.34910	−	2.33671i
$626$	18.6403	−	9.59483i	0.745017	−	0.383487i
$627$	−6.02273	+	10.4317i	−0.240525	+	0.416601i
$628$	−11.1635	+	15.6351i	−0.445473	+	0.623908i
$629$	20.8735			0.832281
$630$	−13.2220	+	8.32282i	−0.526777	+	0.331589i
$631$		−	43.3823i		−	1.72702i	−0.504330	−	0.863511i	$-0.668260\pi$
$631$		−	43.3823i		−	1.72702i	0.504330	−	0.863511i	$-0.331740\pi$
$632$	4.43341	−	1.76512i	0.176352	−	0.0702127i
$633$	−3.66372	−	2.11525i	−0.145620	−	0.0840736i
$634$	8.52980	−	4.39059i	0.338762	−	0.174373i
$635$	−34.3436	+	19.8283i	−1.36289	+	0.786862i
$636$	−1.29573	−	2.84678i	−0.0513790	−	0.112882i
$637$	−6.91837	−	8.27276i	−0.274116	−	0.327779i
$638$	−6.79368	−	4.37210i	−0.268964	−	0.173093i
$639$	−3.02471	+	1.74631i	−0.119656	+	0.0690831i
$640$	−8.73493	−	46.4261i	−0.345278	−	1.83515i
$641$	−3.32559	+	5.76010i	−0.131353	+	0.227510i	−0.924198	−	0.381913i	$-0.875265\pi$
$641$	−3.32559	+	5.76010i	−0.131353	+	0.227510i	0.792845	+	0.609423i	$0.208599\pi$
$642$	0.982418	−	20.3527i	0.0387729	−	0.803256i
$643$			18.1066i			0.714055i	0.934094	+	0.357027i	$0.116210\pi$
$643$			18.1066i			0.714055i	−0.934094	+	0.357027i	$0.883790\pi$
$644$	2.48098	+	0.0248741i	0.0977642	+	0.000980176i
$645$		−	14.3125i		−	0.563555i
$646$	−23.2066	−	1.12018i	−0.913053	−	0.0440728i
$647$	24.6421	−	42.6815i	0.968783	−	1.67798i	0.269694	−	0.962946i	$-0.413077\pi$
$647$	24.6421	−	42.6815i	0.968783	−	1.67798i	0.699089	−	0.715035i	$-0.253589\pi$
$648$	1.75263	−	2.21997i	0.0688499	−	0.0872088i
$649$	9.01239	−	5.20331i	0.353767	−	0.204248i
$650$	−14.6620	+	22.7829i	−0.575092	+	0.893618i
$651$	−8.33602	+	0.722357i	−0.326714	+	0.0283114i
$652$	16.0811	+	35.3308i	0.629784	+	1.38366i
$653$	−22.1087	+	12.7645i	−0.865181	+	0.499512i	−0.865744	−	0.500488i	$-0.833154\pi$
$653$	−22.1087	+	12.7645i	−0.865181	+	0.499512i	0.000563051		1.00000i	$0.499821\pi$
$654$	2.18514	+	4.24517i	0.0854458	+	0.165999i
$655$	−49.4233	−	28.5345i	−1.93113	−	1.11494i
$656$	4.07560	−	20.8621i	0.159125	−	0.814527i
$657$		−	14.5274i		−	0.566769i
$658$	−0.843373	−	22.0632i	−0.0328781	−	0.860114i
$659$	−12.0942			−0.471125			−0.235562	−	0.971859i	$-0.575693\pi$
$659$	−12.0942			−0.471125			−0.235562	+	0.971859i	$0.575693\pi$
$660$	−11.6285	−	8.30281i	−0.452639	−	0.323186i
$661$	−5.42541	+	9.39708i	−0.211024	+	0.365504i	−0.952035	−	0.305988i	$-0.901013\pi$
$661$	−5.42541	+	9.39708i	−0.211024	+	0.365504i	0.741011	+	0.671493i	$0.234346\pi$
$662$	−3.07158	−	5.96730i	−0.119380	−	0.231926i
$663$	−1.79758	−	3.11350i	−0.0698122	−	0.120918i
$664$	1.11177	−	7.62976i	0.0431451	−	0.296092i
$665$	−44.5573	−	63.7466i	−1.72786	−	2.47199i
$666$	−10.6375	−	6.84580i	−0.412194	−	0.265270i
$667$	0.782767	+	1.35579i	0.0303089	+	0.0524965i
$668$	−35.3314	−	3.41884i	−1.36701	−	0.132279i
$669$	−1.24302	−	0.717661i	−0.0480581	−	0.0277464i
$670$	−44.0784	−	2.12765i	−1.70290	−	0.0821984i
$671$	−15.6026			−0.602333
$672$	5.39648	+	13.9599i	0.208174	+	0.538514i
$673$	−48.1931			−1.85771			−0.928854	−	0.370446i	$-0.879205\pi$
$673$	−48.1931			−1.85771			−0.928854	+	0.370446i	$0.879205\pi$
$674$	−23.3318	−	1.12622i	−0.898708	−	0.0433804i
$675$	−10.7691	−	6.21752i	−0.414501	−	0.239312i
$676$	−21.1542	−	2.04698i	−0.813621	−	0.0787300i
$677$	2.56093	+	4.43567i	0.0984246	+	0.170476i	0.911033	−	0.412334i	$-0.135286\pi$
$677$	2.56093	+	4.43567i	0.0984246	+	0.170476i	−0.812608	+	0.582810i	$0.801953\pi$
$678$	12.7355	+	8.19598i	0.489103	+	0.314765i
$679$	−2.18651	+	4.67888i	−0.0839107	+	0.179559i
$680$	3.97394	−	27.2719i	0.152394	−	1.04583i
$681$	8.00718	+	13.8688i	0.306836	+	0.531455i
$682$	−3.50218	−	6.80385i	−0.134105	−	0.260533i
$683$	−11.7191	+	20.2980i	−0.448418	+	0.776682i	−0.998283	−	0.0585709i	$-0.981346\pi$
$683$	−11.7191	+	20.2980i	−0.448418	+	0.776682i	0.549866	+	0.835253i	$0.314679\pi$
$684$	11.4591	+	8.18185i	0.438150	+	0.312841i
$685$	50.0612			1.91274
$686$	5.48768	+	25.6103i	0.209521	+	0.977804i
$687$		−	16.2500i		−	0.619975i
$688$	−13.4565	−	2.62885i	−0.513024	−	0.100224i
$689$	2.08658	+	1.20468i	0.0794922	+	0.0458948i
$690$	1.26718	+	2.46181i	0.0482408	+	0.0937196i
$691$	11.9534	−	6.90129i	0.454728	−	0.262537i	−0.255097	−	0.966915i	$-0.582107\pi$
$691$	11.9534	−	6.90129i	0.454728	−	0.262537i	0.709825	+	0.704378i	$0.248774\pi$
$692$	5.91694	+	12.9998i	0.224928	+	0.494177i
$693$	4.10109	+	1.91650i	0.155788	+	0.0728020i
$694$	−14.6177	+	22.7139i	−0.554879	+	0.862209i
$695$	24.0439	−	13.8817i	0.912035	−	0.526564i
$696$	−5.85178	+	7.41216i	−0.221811	+	0.280957i
$697$	6.20044	−	10.7395i	0.234859	−	0.406787i
$698$	3.52813	+	0.170302i	0.133542	+	0.00644601i
$699$		−	11.8611i		−	0.448627i
$700$	57.3115	−	32.3271i	2.16617	−	1.22185i
$701$		−	11.8718i		−	0.448393i	−0.974544	−	0.224196i	$-0.928024\pi$
$701$		−	11.8718i		−	0.448393i	0.974544	−	0.224196i	$-0.0719757\pi$
$702$	−0.105046	+	2.17624i	−0.00396472	+	0.0821367i
$703$	31.4865	−	54.5362i	1.18754	−	2.05687i
$704$	−9.94207	+	9.40798i	−0.374706	+	0.354577i
$705$	21.3385	−	12.3198i	0.803654	−	0.463990i
$706$	30.6322	+	19.7135i	1.15286	+	0.741927i
$707$	−29.8843	+	20.8883i	−1.12391	+	0.785587i
$708$	−5.03935	−	11.0717i	−0.189390	−	0.416099i
$709$	27.1241	−	15.6601i	1.01867	−	0.588127i	0.104949	−	0.994478i	$-0.466532\pi$
$709$	27.1241	−	15.6601i	1.01867	−	0.588127i	0.913717	+	0.406350i	$0.133199\pi$
$710$	18.3376	−	9.43900i	0.688197	−	0.354239i
$711$	−1.46108	−	0.843557i	−0.0547949	−	0.0316358i
$712$	−5.57798	+	2.22082i	−0.209043	+	0.0832286i
$713$			1.48286i			0.0555335i
$714$	0.333519	+	8.72507i	0.0124816	+	0.326528i
$715$	11.0065			0.411621
$716$	−27.7948	+	38.9280i	−1.03874	+	1.45481i
$717$	−0.423292	+	0.733164i	−0.0158081	+	0.0273805i
$718$	41.7717	−	21.5014i	1.55891	−	0.802424i
$719$	12.6273	+	21.8712i	0.470920	+	0.815657i	0.999447	−	0.0332594i	$-0.0105888\pi$
$719$	12.6273	+	21.8712i	0.470920	+	0.815657i	−0.528527	+	0.848917i	$0.677255\pi$
$720$	−10.9695	+	12.5949i	−0.408807	+	0.469385i
$721$	1.75479	+	20.2503i	0.0653518	+	0.754161i
$722$	−23.3912	+	36.3469i	−0.870530	+	1.35269i
$723$	−0.439609	−	0.761425i	−0.0163492	−	0.0283177i
$724$	40.9232	+	3.95993i	1.52090	+	0.147170i
$725$	35.9563	+	20.7594i	1.33538	+	0.770984i
$726$	0.550423	−	11.4031i	0.0204281	−	0.423208i
$727$	17.9342			0.665144			0.332572	−	0.943078i	$-0.392084\pi$
$727$	17.9342			0.665144			0.332572	+	0.943078i	$0.392084\pi$
$728$	−9.63180	−	6.33604i	−0.356978	−	0.234829i
$729$	−1.00000			−0.0370370
$730$	−4.13604	+	85.6860i	−0.153082	+	3.17138i
$731$	−6.92720	−	3.99942i	−0.256212	−	0.147924i
$732$	−1.75663	+	18.1536i	−0.0649268	+	0.670975i
$733$	−6.16779	−	10.6829i	−0.227813	−	0.394583i	0.729347	−	0.684144i	$-0.239824\pi$
$733$	−6.16779	−	10.6829i	−0.227813	−	0.394583i	−0.957160	+	0.289561i	$0.906491\pi$
$734$	3.33048	−	5.17513i	0.122930	−	0.191018i
$735$	−22.4215	+	18.7508i	−0.827031	+	0.691632i
$736$	2.54732	−	0.739219i	0.0938954	−	0.0272480i
$737$	6.39319	+	11.0733i	0.235496	+	0.407891i
$738$	−6.68203	+	3.43948i	−0.245969	+	0.126609i
$739$	−21.7463	+	37.6656i	−0.799949	+	1.38555i	0.119699	+	0.992810i	$0.461807\pi$
$739$	−21.7463	+	37.6656i	−0.799949	+	1.38555i	−0.919648	+	0.392743i	$0.871526\pi$
$740$	60.7932	+	43.4066i	2.23480	+	1.59566i
$741$	−10.8462			−0.398444
$742$	−3.11721	−	4.95214i	−0.114436	−	0.181799i
$743$			32.8397i			1.20477i	0.798205	+	0.602386i	$0.205783\pi$
$743$			32.8397i			1.20477i	−0.798205	+	0.602386i	$0.794217\pi$
$744$	−8.31052	+	3.30875i	−0.304678	+	0.121305i
$745$	29.3591	+	16.9505i	1.07563	+	0.621018i
$746$	16.1083	−	8.29150i	0.589766	−	0.303574i
$747$	−2.36080	+	1.36301i	−0.0863771	+	0.0498698i
$748$	−7.26793	+	3.30805i	−0.265742	+	0.120954i
$749$	−3.29101	−	37.9784i	−0.120251	−	1.38770i
$750$	36.9199	+	23.7600i	1.34812	+	0.867591i
$751$	7.62670	−	4.40328i	0.278302	−	0.160678i	−0.354352	−	0.935112i	$-0.615299\pi$
$751$	7.62670	−	4.40328i	0.278302	−	0.160678i	0.632655	+	0.774434i	$0.281965\pi$
$752$	−7.66360	−	22.3251i	−0.279463	−	0.814111i
$753$	9.07203	−	15.7132i	0.330603	−	0.572622i
$754$	0.350734	−	7.26613i	0.0127730	−	0.264617i
$755$		−	5.16112i		−	0.187832i
$756$	2.69156	−	4.55582i	0.0978911	−	0.165694i
$757$			16.9328i			0.615433i	0.951478	+	0.307717i	$0.0995649\pi$
$757$			16.9328i			0.615433i	−0.951478	+	0.307717i	$0.900435\pi$
$758$	34.0157	+	1.64193i	1.23551	+	0.0596375i
$759$	0.401124	−	0.694766i	0.0145599	−	0.0252184i
$760$	−65.2589	−	51.5208i	−2.36719	−	1.86886i
$761$	10.9108	−	6.29937i	0.395517	−	0.228352i	−0.289031	−	0.957320i	$-0.593333\pi$
$761$	10.9108	−	6.29937i	0.395517	−	0.228352i	0.684548	+	0.728968i	$0.260000\pi$
$762$	7.26867	−	11.2946i	0.263316	−	0.409159i
$763$	5.11734	+	7.32121i	0.185260	+	0.265045i
$764$	−3.66832	+	1.66966i	−0.132715	+	0.0604063i
$765$	−8.43848	+	4.87196i	−0.305094	+	0.176146i
$766$	11.3685	+	22.0860i	0.410759	+	0.798000i
$767$	8.11510	+	4.68526i	0.293019	+	0.169175i
$768$	9.82679	+	12.6267i	0.354594	+	0.455628i
$769$			16.0445i			0.578581i	0.957241	+	0.289291i	$0.0934194\pi$
$769$			16.0445i			0.578581i	−0.957241	+	0.289291i	$0.906581\pi$
$770$	−23.6435	−	12.4716i	−0.852053	−	0.449444i
$771$	18.3484			0.660802
$772$	4.14978	−	5.81197i	0.149354	−	0.209177i
$773$	−9.15671	+	15.8599i	−0.329344	+	0.570440i	−0.982382	−	0.186885i	$-0.940161\pi$
$773$	−9.15671	+	15.8599i	−0.329344	+	0.570440i	0.653038	+	0.757325i	$0.273494\pi$
$774$	2.21854	+	4.31005i	0.0797437	+	0.154922i
$775$	19.6631	+	34.0574i	0.706318	+	1.22338i
$776$	−0.796109	+	5.46346i	−0.0285787	+	0.196127i
$777$	−21.4403	−	10.0194i	−0.769166	−	0.359443i
$778$	−32.8226	−	21.1231i	−1.17675	−	0.757301i
$779$	−18.7060	−	32.3998i	−0.670213	−	1.16084i
$780$	1.23917	−	12.8060i	0.0443695	−	0.458529i
$781$	−5.17518	−	2.98789i	−0.185183	−	0.106915i
$782$	1.54560	+	0.0746057i	0.0552706	+	0.00266789i
$783$	3.33885			0.119321
$784$	13.5110	+	24.5245i	0.482536	+	0.875876i
$785$	−40.1090			−1.43155
$786$	19.3063	+	0.931910i	0.688633	+	0.0332401i
$787$	3.88976	+	2.24576i	0.138655	+	0.0800526i	0.567723	−	0.823220i	$-0.307825\pi$
$787$	3.88976	+	2.24576i	0.138655	+	0.0800526i	−0.429068	+	0.903272i	$0.641158\pi$
$788$	−3.37860	+	34.9155i	−0.120358	+	1.24381i
$789$	−1.74385	−	3.02044i	−0.0620828	−	0.107531i
$790$	8.37763	+	5.39146i	0.298063	+	0.191820i
$791$	25.6689	+	11.9955i	0.912680	+	0.426510i
$792$	4.78878	+	0.697799i	0.170162	+	0.0247952i
$793$	−7.02460	−	12.1670i	−0.249451	−	0.432062i
$794$	−11.2082	−	21.7746i	−0.397763	−	0.772752i
$795$	3.26504	−	5.65522i	0.115799	−	0.200570i
$796$	−20.5783	+	28.8209i	−0.729378	+	1.02153i
$797$	−31.7698			−1.12534			−0.562672	−	0.826680i	$-0.690227\pi$
$797$	−31.7698			−1.12534			−0.562672	+	0.826680i	$0.690227\pi$
$798$	23.2991	+	12.2899i	0.824778	+	0.435057i
$799$		−	13.7703i		−	0.487159i
$800$	48.7031	−	50.7560i	1.72191	−	1.79450i
$801$	1.83829	+	1.06134i	0.0649527	+	0.0375004i
$802$	5.01757	+	9.74786i	0.177177	+	0.344209i
$803$	21.5259	−	12.4280i	0.759634	−	0.438575i
$804$	13.6035	−	6.19173i	0.479759	−	0.218366i
$805$	2.96759	+	4.24563i	0.104594	+	0.149639i
$806$	3.72890	−	5.79423i	0.131345	−	0.204093i
$807$	12.7410	−	7.35605i	0.448506	−	0.258945i
$808$	−24.1528	+	30.5932i	−0.849694	+	1.07627i
$809$	−12.5784	+	21.7864i	−0.442232	+	0.765969i	−0.997855	−	0.0654659i	$-0.979147\pi$
$809$	−12.5784	+	21.7864i	−0.442232	+	0.765969i	0.555623	+	0.831435i	$0.312480\pi$
$810$	5.89822	+	0.284706i	0.207242	+	0.0100035i
$811$		−	48.0042i		−	1.68565i	−0.538184	−	0.842827i	$-0.680890\pi$
$811$		−	48.0042i		−	1.68565i	0.538184	−	0.842827i	$-0.319110\pi$
$812$	−8.98672	+	15.2112i	−0.315372	+	0.533809i
$813$			19.9028i			0.698021i
$814$	1.04352	−	21.6185i	0.0365753	−	0.757728i
$815$	−40.5219	+	70.1859i	−1.41942	+	2.45851i
$816$	3.03063	+	8.82862i	0.106093	+	0.309064i
$817$	−20.8985	+	12.0658i	−0.731148	+	0.422128i
$818$	5.51607	+	3.54989i	0.192865	+	0.124119i
$819$	0.351896	+	4.06089i	0.0122962	+	0.141899i
$820$	40.3914	−	18.3844i	1.41053	−	0.642011i
$821$	−14.5854	+	8.42089i	−0.509034	+	0.293891i	−0.732437	−	0.680835i	$-0.761617\pi$
$821$	−14.5854	+	8.42089i	−0.509034	+	0.293891i	0.223402	+	0.974726i	$0.428284\pi$
$822$	−15.0754	+	7.75983i	−0.525814	+	0.270655i
$823$	17.1163	+	9.88209i	0.596636	+	0.344468i	0.767717	−	0.640789i	$-0.221393\pi$
$823$	17.1163	+	9.88209i	0.596636	+	0.344468i	−0.171081	+	0.985257i	$0.554726\pi$
$824$	8.03780	+	20.1884i	0.280010	+	0.703295i
$825$		−	21.2760i		−	0.740735i
$826$	−12.1234	−	19.2598i	−0.421829	−	0.670135i
$827$	49.1702			1.70981			0.854907	−	0.518781i	$-0.173614\pi$
$827$	49.1702			1.70981			0.854907	+	0.518781i	$0.173614\pi$
$828$	−0.763195	−	0.544925i	−0.0265229	−	0.0189374i
$829$	−7.96007	+	13.7872i	−0.276465	+	0.478851i	−0.970504	−	0.241087i	$-0.922496\pi$
$829$	−7.96007	+	13.7872i	−0.276465	+	0.478851i	0.694039	+	0.719937i	$0.255829\pi$
$830$	14.3126	−	7.36719i	0.496796	−	0.255719i
$831$	−13.2233	−	22.9034i	−0.458710	−	0.794510i
$832$	−11.8125	−	3.51719i	−0.409524	−	0.121937i
$833$	2.80992	+	16.0915i	0.0973580	+	0.557539i
$834$	−5.08877	+	7.90728i	−0.176210	+	0.273807i
$835$	−37.0541	−	64.1795i	−1.28231	−	2.22102i
$836$	−2.32032	+	23.9789i	−0.0802498	+	0.829328i
$837$	2.73883	+	1.58126i	0.0946678	+	0.0546565i
$838$	−0.971071	+	20.1176i	−0.0335451	+	0.694951i
$839$	−38.3305			−1.32332			−0.661658	−	0.749806i	$-0.730147\pi$
$839$	−38.3305			−1.32332			−0.661658	+	0.749806i	$0.730147\pi$
$840$	−17.1725	+	26.1049i	−0.592507	+	0.900706i
$841$	17.8521			0.615589
$842$	1.36455	−	28.2692i	0.0470254	−	0.974221i
$843$	−17.5662	−	10.1419i	−0.605013	−	0.349304i
$844$	−8.42166	−	0.814921i	−0.289886	−	0.0280507i
$845$	−22.1856	−	38.4266i	−0.763207	−	1.32191i
$846$	−4.51620	+	7.01758i	−0.155270	+	0.241269i
$847$	−1.84387	−	21.2783i	−0.0633561	−	0.731131i
$848$	−4.71727	−	4.10848i	−0.161992	−	0.141086i
$849$	3.29336	+	5.70426i	0.113028	+	0.195770i
$850$	36.4877	−	18.7815i	1.25152	−	0.644202i
$851$	−2.09705	+	3.63220i	−0.0718860	+	0.124510i
$852$	−4.05904	+	5.68489i	−0.139060	+	0.194761i
$853$	22.5158			0.770927			0.385463	−	0.922723i	$-0.374042\pi$
$853$	22.5158			0.770927			0.385463	+	0.922723i	$0.374042\pi$
$854$	1.30333	+	34.0959i	0.0445989	+	1.16674i
$855$			29.3963i			1.00533i
$856$	−15.0745	−	37.8622i	−0.515234	−	1.29410i
$857$	−11.1913	−	6.46129i	−0.382287	−	0.220713i	0.296526	−	0.955025i	$-0.404172\pi$
$857$	−11.1913	−	6.46129i	−0.382287	−	0.220713i	−0.678813	+	0.734311i	$0.737505\pi$
$858$	−3.31449	+	1.70609i	−0.113155	+	0.0582448i
$859$	20.1418	−	11.6289i	0.687229	−	0.396772i	−0.115344	−	0.993326i	$-0.536797\pi$
$859$	20.1418	−	11.6289i	0.687229	−	0.396772i	0.802573	+	0.596554i	$0.203464\pi$
$860$	−11.8583	−	26.0533i	−0.404366	−	0.888410i
$861$	−11.5238	+	8.05485i	−0.392730	+	0.274509i
$862$	16.6293	+	10.7019i	0.566397	+	0.364508i
$863$	7.69412	−	4.44220i	0.261911	−	0.151214i	−0.363295	−	0.931674i	$-0.618348\pi$
$863$	7.69412	−	4.44220i	0.261911	−	0.151214i	0.625206	+	0.780460i	$0.285015\pi$
$864$	1.35103	−	5.49315i	0.0459630	−	0.186881i
$865$	−14.9098	+	25.8245i	−0.506947	+	0.878059i
$866$	−0.0671539	+	1.39122i	−0.00228198	+	0.0472756i
$867$		−	11.5544i		−	0.392409i
$868$	−14.5757	+	8.22154i	−0.494731	+	0.279057i
$869$		−	2.88660i		−	0.0979212i
$870$	−19.6933	−	0.950589i	−0.667665	−	0.0322280i
$871$	−5.75667	+	9.97084i	−0.195057	+	0.337849i
$872$	7.49489	+	5.91709i	0.253809	+	0.200378i
$873$	1.69050	−	0.976012i	0.0572148	−	0.0330330i
$874$	2.52637	−	3.92565i	0.0854558	−	0.132787i
$875$	74.4135	+	34.7746i	2.51564	+	1.17560i
$876$	−12.0364	−	26.4445i	−0.406672	−	0.893476i
$877$	40.2134	−	23.2172i	1.35791	−	0.783990i	0.368569	−	0.929600i	$-0.379848\pi$
$877$	40.2134	−	23.2172i	1.35791	−	0.783990i	0.989342	+	0.145610i	$0.0465145\pi$
$878$	4.44901	+	8.64329i	0.150147	+	0.291697i
$879$	11.2097	+	6.47192i	0.378094	+	0.218292i
$880$	−28.0466	−	5.47916i	−0.945452	−	0.184703i
$881$			27.1901i			0.916058i	0.888937	+	0.458029i	$0.151444\pi$
$881$			27.1901i			0.916058i	−0.888937	+	0.458029i	$0.848556\pi$
$882$	3.84550	−	9.12207i	0.129485	−	0.307156i
$883$	−21.7975			−0.733543			−0.366772	−	0.930311i	$-0.619537\pi$
$883$	−21.7975			−0.733543			−0.366772	+	0.930311i	$0.619537\pi$
$884$	−5.85178	−	4.17820i	−0.196817	−	0.140528i
$885$	12.6984	−	21.9942i	0.426852	−	0.739329i
$886$	2.20685	+	4.28735i	0.0741406	+	0.144036i
$887$	21.1661	+	36.6607i	0.710688	+	1.23095i	0.964599	+	0.263720i	$0.0849495\pi$
$887$	21.1661	+	36.6607i	0.710688	+	1.23095i	−0.253911	+	0.967227i	$0.581717\pi$
$888$	−25.0355	−	3.64805i	−0.840136	−	0.122421i
$889$	10.6383	−	22.7646i	0.356796	−	0.763502i
$890$	−10.5405	−	6.78336i	−0.353317	−	0.227379i
$891$	−0.855485	−	1.48174i	−0.0286598	−	0.0496403i
$892$	−2.85730	−	0.276486i	−0.0956694	−	0.00925744i
$893$	−35.9777	−	20.7717i	−1.20395	−	0.695099i
$894$	−11.4686	−	0.553586i	−0.383567	−	0.0185147i
$895$	−99.8629			−3.33805
$896$	21.3894	+	20.9402i	0.714571	+	0.699563i
$897$	0.722374			0.0241194
$898$	−46.6040	−	2.24956i	−1.55520	−	0.0750689i
$899$	−9.14454	−	5.27960i	−0.304987	−	0.176085i
$900$	−24.7545	−	2.39536i	−0.825148	−	0.0798454i
$901$	−1.82473	−	3.16053i	−0.0607906	−	0.105292i
$902$	−10.8128	−	6.95864i	−0.360027	−	0.231697i
$903$	5.19555	+	7.43310i	0.172897	+	0.247358i
$904$	29.9732	+	4.36755i	0.996892	+	0.145262i
$905$	42.9186	+	74.3371i	1.42666	+	2.47105i
$906$	0.800008	+	1.55421i	0.0265785	+	0.0516352i
$907$	22.5605	−	39.0760i	0.749109	−	1.29750i	−0.199141	−	0.979971i	$-0.563815\pi$
$907$	22.5605	−	39.0760i	0.749109	−	1.29750i	0.948250	−	0.317525i	$-0.102852\pi$
$908$	26.0663	+	18.6115i	0.865041	+	0.617643i
$909$	13.7809			0.457083
$910$	−0.919403	−	24.0522i	−0.0304779	−	0.797322i
$911$		−	36.2714i		−	1.20173i	−0.799352	−	0.600863i	$-0.794824\pi$
$911$		−	36.2714i		−	1.20173i	0.799352	−	0.600863i	$-0.205176\pi$
$912$	27.6380	+	5.39934i	0.915187	+	0.178790i
$913$	−4.03926	−	2.33207i	−0.133680	−	0.0771801i
$914$	−14.7860	−	28.7254i	−0.489077	−	0.950152i
$915$	−32.9760	+	19.0387i	−1.09015	+	0.629400i
$916$	−13.4636	−	29.5801i	−0.444849	−	0.977352i
$917$	36.0258	−	3.12181i	1.18968	−	0.103091i
$918$	1.78596	−	2.77516i	0.0589456	−	0.0915938i
$919$	37.7905	−	21.8183i	1.24659	−	0.719721i	0.276164	−	0.961110i	$-0.410937\pi$
$919$	37.7905	−	21.8183i	1.24659	−	0.719721i	0.970428	+	0.241390i	$0.0776032\pi$
$920$	4.34635	+	3.43137i	0.143295	+	0.113129i
$921$	5.93863	−	10.2860i	0.195685	−	0.338936i
$922$	22.4235	+	1.08238i	0.738478	+	0.0356461i
$923$		−	5.38082i		−	0.177112i
$924$	9.05315	+	0.0907661i	0.297827	+	0.00298599i
$925$			111.230i			3.65721i
$926$	−0.185501	+	3.84302i	−0.00609595	+	0.126289i
$927$	3.84129	−	6.65331i	0.126165	−	0.218523i
$928$	−4.51089	+	18.3408i	−0.148077	+	0.602067i
$929$	10.2075	−	5.89332i	0.334898	−	0.193354i	−0.323115	−	0.946360i	$-0.604730\pi$
$929$	10.2075	−	5.89332i	0.334898	−	0.193354i	0.658014	+	0.753006i	$0.271397\pi$
$930$	−15.7040	−	10.1064i	−0.514955	−	0.331402i
$931$	46.2809	+	16.9317i	1.51680	+	0.554913i
$932$	−9.82724	−	21.5909i	−0.321902	−	0.707233i
$933$	10.2511	−	5.91849i	0.335607	−	0.193763i
$934$	−30.1604	+	15.5247i	−0.986880	+	0.507982i
$935$	−14.4380	−	8.33578i	−0.472173	−	0.272609i
$936$	1.61186	+	4.04846i	0.0526852	+	0.132328i
$937$			35.0529i			1.14513i	0.819860	+	0.572565i	$0.194051\pi$
$937$			35.0529i			1.14513i	−0.819860	+	0.572565i	$0.805949\pi$
$938$	23.6641	−	14.8958i	0.772661	−	0.486365i
$939$	−14.8243			−0.483774
$940$	28.6355	−	40.1054i	0.933986	−	1.30809i
$941$	14.2985	−	24.7658i	0.466119	−	0.807342i	−0.533132	−	0.846032i	$-0.678985\pi$
$941$	14.2985	−	24.7658i	0.466119	−	0.807342i	0.999251	+	0.0386903i	$0.0123186\pi$
$942$	12.0784	−	6.21716i	0.393534	−	0.202566i
$943$	1.24585	+	2.15788i	0.0405705	+	0.0702702i
$944$	−18.3464	−	15.9787i	−0.597124	−	0.520061i
$945$	11.0062	−	0.953738i	0.358031	−	0.0310251i
$946$	−4.48847	+	6.97449i	−0.145933	+	0.226760i
$947$	25.7444	+	44.5906i	0.836580	+	1.44900i	0.892738	+	0.450577i	$0.148782\pi$
$947$	25.7444	+	44.5906i	0.836580	+	1.44900i	−0.0561576	+	0.998422i	$0.517885\pi$
$948$	−3.35854	−	0.324989i	−0.109080	−	0.0105551i
$949$	19.3828	+	11.1906i	0.629191	+	0.363264i
$950$	5.96915	−	123.662i	0.193665	−	4.01213i
$951$	−6.78361			−0.219974
$952$	7.83608	+	15.6060i	0.253969	+	0.505794i
$953$	−11.8761			−0.384706			−0.192353	−	0.981326i	$-0.561612\pi$
$953$	−11.8761			−0.384706			−0.192353	+	0.981326i	$0.561612\pi$
$954$	−0.106633	+	2.20911i	−0.00345237	+	0.0715225i
$955$	−7.28724	−	4.20729i	−0.235810	−	0.136145i
$956$	−0.163078	+	1.68530i	−0.00527431	+	0.0545064i
$957$	2.85634	+	4.94732i	0.0923323	+	0.159924i
$958$	−15.1155	+	23.4875i	−0.488360	+	0.758848i
$959$	−25.9989	+	18.1726i	−0.839548	+	0.586823i
$960$	−9.53261	+	32.0152i	−0.307664	+	1.03329i
$961$	10.4992	+	18.1852i	0.338684	+	0.586618i
$962$	17.3280	−	8.91932i	0.558676	−	0.287571i
$963$	−7.20414	+	12.4779i	−0.232150	+	0.402096i
$964$	−1.43109	−	1.02180i	−0.0460922	−	0.0329101i
$965$	14.9096			0.479956
$966$	−1.55176	−	0.818526i	−0.0499270	−	0.0263357i
$967$		−	59.2193i		−	1.90437i	−0.305530	−	0.952183i	$-0.598833\pi$
$967$		−	59.2193i		−	1.90437i	0.305530	−	0.952183i	$-0.401167\pi$
$968$	−8.44583	−	21.2132i	−0.271459	−	0.681818i
$969$	14.2276	+	8.21434i	0.457058	+	0.263883i
$970$	−10.2488	+	5.27544i	−0.329070	+	0.169384i
$971$	−4.53638	+	2.61908i	−0.145579	+	0.0840503i	−0.571020	−	0.820936i	$-0.693452\pi$
$971$	−4.53638	+	2.61908i	−0.145579	+	0.0840503i	0.425441	+	0.904986i	$0.360119\pi$
$972$	−1.82031	+	0.828528i	−0.0583866	+	0.0265751i
$973$	−7.44782	+	15.9375i	−0.238766	+	0.510931i
$974$	−44.1396	−	28.4062i	−1.41432	−	0.910194i
$975$	16.5911	−	9.57885i	0.531339	−	0.306769i
$976$	11.8431	+	34.5006i	0.379089	+	1.10434i
$977$	26.6049	−	46.0810i	0.851165	−	1.47426i	−0.0289924	−	0.999580i	$-0.509230\pi$
$977$	26.6049	−	46.0810i	0.851165	−	1.47426i	0.880158	−	0.474682i	$-0.157437\pi$
$978$	1.32340	−	27.4168i	0.0423178	−	0.876694i
$979$			3.63183i			0.116074i
$980$	−25.2787	+	52.7092i	−0.807498	+	1.68373i
$981$		−	3.37612i		−	0.107791i
$982$	29.0630	+	1.40286i	0.927438	+	0.0447672i
$983$	13.9737	−	24.2032i	0.445693	−	0.771963i	−0.552407	−	0.833574i	$-0.686291\pi$
$983$	13.9737	−	24.2032i	0.445693	−	0.771963i	0.998100	+	0.0616113i	$0.0196239\pi$
$984$	−9.31369	+	11.7972i	−0.296910	+	0.376081i
$985$	−63.4241	+	36.6179i	−2.02086	+	1.16674i
$986$	−5.96307	+	9.26583i	−0.189903	+	0.295084i
$987$	−6.60981	+	14.1442i	−0.210393	+	0.450215i
$988$	−19.7434	+	8.98637i	−0.628123	+	0.285894i
$989$	1.39188	−	0.803601i	0.0442592	−	0.0255530i
$990$	4.62398	+	8.98322i	0.146960	+	0.285505i
$991$	−18.7980	−	10.8530i	−0.597139	−	0.344758i	0.170776	−	0.985310i	$-0.445372\pi$
$991$	−18.7980	−	10.8530i	−0.597139	−	0.344758i	−0.767915	+	0.640552i	$0.778706\pi$
$992$	−12.3864	+	12.9085i	−0.393267	+	0.409844i
$993$			4.74570i			0.150600i
$994$	−6.09705	+	11.5587i	−0.193387	+	0.366621i
$995$	−73.9349			−2.34389
$996$	−3.16810	+	4.43709i	−0.100385	+	0.140595i
$997$	16.8274	−	29.1458i	0.532928	−	0.923058i	−0.466333	−	0.884609i	$-0.654425\pi$
$997$	16.8274	−	29.1458i	0.532928	−	0.923058i	0.999261	−	0.0384485i	$-0.0122416\pi$
$998$	0.669990	+	1.30162i	0.0212082	+	0.0412021i
$999$	4.47243	+	7.74648i	0.141501	+	0.245088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.t.a.115.1	yes	32
3.2	odd	2		504.2.bk.c.451.16		32
4.3	odd	2		672.2.bb.a.367.8		32
7.3	odd	6		1176.2.p.a.979.17		32
7.4	even	3		1176.2.p.a.979.18		32
7.5	odd	6	inner	168.2.t.a.19.12	yes	32
8.3	odd	2	inner	168.2.t.a.115.12	yes	32
8.5	even	2		672.2.bb.a.367.1		32
12.11	even	2		2016.2.bs.c.1711.1		32
21.5	even	6		504.2.bk.c.19.5		32
24.5	odd	2		2016.2.bs.c.1711.16		32
24.11	even	2		504.2.bk.c.451.5		32
28.3	even	6		4704.2.p.a.3919.23		32
28.11	odd	6		4704.2.p.a.3919.6		32
28.19	even	6		672.2.bb.a.271.1		32
56.3	even	6		1176.2.p.a.979.20		32
56.5	odd	6		672.2.bb.a.271.8		32
56.11	odd	6		1176.2.p.a.979.19		32
56.19	even	6	inner	168.2.t.a.19.1	✓	32
56.45	odd	6		4704.2.p.a.3919.5		32
56.53	even	6		4704.2.p.a.3919.24		32
84.47	odd	6		2016.2.bs.c.271.16		32
168.5	even	6		2016.2.bs.c.271.1		32
168.131	odd	6		504.2.bk.c.19.16		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.t.a.19.1	✓	32	56.19	even	6	inner
168.2.t.a.19.12	yes	32	7.5	odd	6	inner
168.2.t.a.115.1	yes	32	1.1	even	1	trivial
168.2.t.a.115.12	yes	32	8.3	odd	2	inner
504.2.bk.c.19.5		32	21.5	even	6
504.2.bk.c.19.16		32	168.131	odd	6
504.2.bk.c.451.5		32	24.11	even	2
504.2.bk.c.451.16		32	3.2	odd	2
672.2.bb.a.271.1		32	28.19	even	6
672.2.bb.a.271.8		32	56.5	odd	6
672.2.bb.a.367.1		32	8.5	even	2
672.2.bb.a.367.8		32	4.3	odd	2
1176.2.p.a.979.17		32	7.3	odd	6
1176.2.p.a.979.18		32	7.4	even	3
1176.2.p.a.979.19		32	56.11	odd	6
1176.2.p.a.979.20		32	56.3	even	6
2016.2.bs.c.271.1		32	168.5	even	6
2016.2.bs.c.271.16		32	84.47	odd	6
2016.2.bs.c.1711.1		32	12.11	even	2
2016.2.bs.c.1711.16		32	24.5	odd	2
4704.2.p.a.3919.5		32	56.45	odd	6
4704.2.p.a.3919.6		32	28.11	odd	6
4704.2.p.a.3919.23		32	28.3	even	6
4704.2.p.a.3919.24		32	56.53	even	6

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41257 - 0.0681843i) q^{2} +(0.866025 + 0.500000i) q^{3} +(1.99070 + 0.192630i) q^{4} +(2.08776 + 3.61611i) q^{5} +(-1.18923 - 0.765334i) q^{6} +(-2.39694 - 1.12013i) q^{7} +(-2.79887 - 0.407838i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.70255 - 5.25036i) q^{10} +(-0.855485 + 1.48174i) q^{11} +(1.62768 + 1.16217i) q^{12} -1.54062 q^{13} +(3.30947 + 1.74569i) q^{14} +4.17553i q^{15} +(3.92579 + 0.766938i) q^{16} +(2.02094 + 1.16679i) q^{17} +(-0.647235 - 1.25741i) q^{18} +(6.09693 - 3.52006i) q^{19} +(3.45954 + 7.60077i) q^{20} +(-1.51575 - 2.16853i) q^{21} +(1.30946 - 2.03473i) q^{22} +(-0.406066 + 0.234442i) q^{23} +(-2.21997 - 1.75263i) q^{24} +(-6.21752 + 10.7691i) q^{25} +(2.17624 + 0.105046i) q^{26} +1.00000i q^{27} +(-4.55582 - 2.69156i) q^{28} -3.33885i q^{29} +(0.284706 - 5.89822i) q^{30} +(1.58126 - 2.73883i) q^{31} +(-5.49315 - 1.35103i) q^{32} +(-1.48174 + 0.855485i) q^{33} +(-2.77516 - 1.78596i) q^{34} +(-0.953738 - 11.0062i) q^{35} +(0.828528 + 1.82031i) q^{36} +(7.74648 - 4.47243i) q^{37} +(-8.85235 + 4.55662i) q^{38} +(-1.33422 - 0.770311i) q^{39} +(-4.36859 - 10.9725i) q^{40} -5.31411i q^{41} +(1.99324 + 3.16654i) q^{42} -3.42772 q^{43} +(-1.98844 + 2.78492i) q^{44} +(-2.08776 + 3.61611i) q^{45} +(0.589581 - 0.303478i) q^{46} +(-2.95047 - 5.11037i) q^{47} +(3.01636 + 2.62708i) q^{48} +(4.49063 + 5.36975i) q^{49} +(9.51696 - 14.7881i) q^{50} +(1.16679 + 2.02094i) q^{51} +(-3.06692 - 0.296770i) q^{52} +(-1.35437 - 0.781947i) q^{53} +(0.0681843 - 1.41257i) q^{54} -7.14421 q^{55} +(6.25189 + 4.11265i) q^{56} +7.04013 q^{57} +(-0.227657 + 4.71636i) q^{58} +(-5.26742 - 3.04114i) q^{59} +(-0.804332 + 8.31223i) q^{60} +(4.55959 + 7.89744i) q^{61} +(-2.42039 + 3.76097i) q^{62} +(-0.228411 - 2.63587i) q^{63} +(7.66734 + 2.28297i) q^{64} +(-3.21646 - 5.57107i) q^{65} +(2.15140 - 1.10740i) q^{66} +(3.73658 - 6.47195i) q^{67} +(3.79832 + 2.71202i) q^{68} -0.468884 q^{69} +(0.596773 + 15.6120i) q^{70} +3.49263i q^{71} +(-1.04624 - 2.62781i) q^{72} +(-12.5811 - 7.26372i) q^{73} +(-11.2474 + 5.78943i) q^{74} +(-10.7691 + 6.21752i) q^{75} +(12.8152 - 5.83295i) q^{76} +(3.71029 - 2.59340i) q^{77} +(1.83215 + 1.17909i) q^{78} +(-1.46108 + 0.843557i) q^{79} +(5.42278 + 15.7973i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.362339 + 7.50655i) q^{82} +2.72601i q^{83} +(-2.59968 - 4.60887i) q^{84} +9.74391i q^{85} +(4.84189 + 0.233717i) q^{86} +(1.66943 - 2.89153i) q^{87} +(2.99870 - 3.79831i) q^{88} +(1.83829 - 1.06134i) q^{89} +(3.19567 - 4.96566i) q^{90} +(3.69278 + 1.72569i) q^{91} +(-0.853516 + 0.388484i) q^{92} +(2.73883 - 1.58126i) q^{93} +(3.81930 + 7.41993i) q^{94} +(25.4579 + 14.6981i) q^{95} +(-4.08169 - 3.91660i) q^{96} -1.95202i q^{97} +(-5.97720 - 7.89133i) q^{98} -1.71097 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{2} - 2 q^{4} + 16 q^{8} + 16 q^{9} - 18 q^{10} + 8 q^{11} - 10 q^{14} + 6 q^{16} + 2 q^{18} - 20 q^{22} - 18 q^{24} - 16 q^{25} - 30 q^{26} - 14 q^{28} - 8 q^{30} - 12 q^{32} - 24 q^{35} - 4 q^{36}+ \cdots + 16 q^{99}+O(q^{100}) \) 32 * q - 2 * q^2 - 2 * q^4 + 16 * q^8 + 16 * q^9 - 18 * q^10 + 8 * q^11 - 10 * q^14 + 6 * q^16 + 2 * q^18 - 20 * q^22 - 18 * q^24 - 16 * q^25 - 30 * q^26 - 14 * q^28 - 8 * q^30 - 12 * q^32 - 24 * q^35 - 4 * q^36 - 18 * q^38 - 30 * q^40 + 4 * q^42 - 16 * q^43 + 24 * q^44 + 8 * q^46 + 8 * q^49 + 76 * q^50 + 36 * q^52 + 16 * q^56 + 16 * q^57 - 6 * q^58 - 96 * q^59 - 2 * q^60 + 76 * q^64 - 36 * q^66 - 32 * q^67 + 96 * q^68 + 6 * q^70 + 8 * q^72 - 24 * q^73 - 34 * q^74 - 12 * q^78 + 36 * q^80 - 16 * q^81 - 36 * q^82 + 16 * q^84 + 50 * q^86 - 14 * q^88 + 56 * q^91 - 128 * q^92 + 36 * q^94 + 30 * q^96 + 60 * q^98 + 16 * q^99

Introduction

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