LMFDB - Embedded newform 336.2.bs.a.187.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,2,Mod(19,336)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("336.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(336, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 0, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bs (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			187.24
Character	$\chi$	$=$	336.187
Dual form			336.2.bs.a.115.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.03934 + 0.959049i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(0.160449 + 1.99355i) q^{4} +(0.627426 + 2.34159i) q^{5} +(-0.755704 - 1.19537i) q^{6} +(2.44702 - 1.00602i) q^{7} +(-1.74516 + 2.22586i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-1.59359 + 3.03543i) q^{10} +(-4.27235 - 1.14477i) q^{11} +(0.360988 - 1.96715i) q^{12} +(2.40484 + 2.40484i) q^{13} +(3.50811 + 1.30122i) q^{14} -2.42419i q^{15} +(-3.94851 + 0.639726i) q^{16} +(-2.17215 + 1.25409i) q^{17} +(0.420569 + 1.35023i) q^{18} +(1.39363 + 5.20109i) q^{19} +(-4.56741 + 1.62651i) q^{20} +(-2.62402 + 0.338402i) q^{21} +(-3.34253 - 5.28720i) q^{22} +(2.78900 - 4.83069i) q^{23} +(2.26178 - 1.69833i) q^{24} +(-0.759236 + 0.438345i) q^{25} +(0.193082 + 4.80581i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(2.39817 + 4.71686i) q^{28} +(0.962214 - 0.962214i) q^{29} +(2.32492 - 2.51955i) q^{30} +(0.220090 + 0.381207i) q^{31} +(-4.71737 - 3.12193i) q^{32} +(3.83049 + 2.21153i) q^{33} +(-3.46033 - 0.779773i) q^{34} +(3.89100 + 5.09872i) q^{35} +(-0.857824 + 1.80669i) q^{36} +(-2.22506 + 0.596202i) q^{37} +(-3.53965 + 6.74225i) q^{38} +(-1.70048 - 2.94532i) q^{39} +(-6.30699 - 2.68987i) q^{40} +1.45203 q^{41} +(-3.05179 - 2.16485i) q^{42} +(8.53016 - 8.53016i) q^{43} +(1.59667 - 8.70084i) q^{44} +(-0.627426 + 2.34159i) q^{45} +(7.53158 - 2.34593i) q^{46} +(3.59301 - 6.22327i) q^{47} +(3.97954 + 0.404023i) q^{48} +(4.97586 - 4.92350i) q^{49} +(-1.20950 - 0.272556i) q^{50} +(2.42272 - 0.649165i) q^{51} +(-4.40833 + 5.18004i) q^{52} +(-0.397428 + 1.48322i) q^{53} +(-0.0567729 - 1.41307i) q^{54} -10.7223i q^{55} +(-2.03119 + 7.20238i) q^{56} -5.38456i q^{57} +(1.92288 - 0.0772552i) q^{58} +(0.768265 - 2.86721i) q^{59} +(4.83275 - 0.388958i) q^{60} +(2.14675 - 0.575220i) q^{61} +(-0.136848 + 0.607280i) q^{62} +(2.62219 + 0.352275i) q^{63} +(-1.90886 - 7.76893i) q^{64} +(-4.12228 + 7.14001i) q^{65} +(1.86020 + 5.97216i) q^{66} +(3.40860 - 12.7211i) q^{67} +(-2.84861 - 4.12908i) q^{68} +(-3.94424 + 3.94424i) q^{69} +(-0.845851 + 9.03096i) q^{70} -9.28298 q^{71} +(-2.62428 + 1.05507i) q^{72} +(1.40733 + 2.43756i) q^{73} +(-2.88437 - 1.51428i) q^{74} +(0.846818 - 0.226904i) q^{75} +(-10.1450 + 3.61278i) q^{76} +(-11.6062 + 1.49677i) q^{77} +(1.05733 - 4.69203i) q^{78} +(5.93453 + 3.42630i) q^{79} +(-3.97537 - 8.84440i) q^{80} +(0.500000 + 0.866025i) q^{81} +(1.50915 + 1.39257i) q^{82} +(-10.7397 + 10.7397i) q^{83} +(-1.09564 - 5.17683i) q^{84} +(-4.29942 - 4.29942i) q^{85} +(17.0466 - 0.684878i) q^{86} +(-1.17847 + 0.680388i) q^{87} +(10.0040 - 7.51183i) q^{88} +(8.48740 - 14.7006i) q^{89} +(-2.89781 + 1.83197i) q^{90} +(8.30402 + 3.46539i) q^{91} +(10.0777 + 4.78494i) q^{92} +(-0.113927 - 0.425181i) q^{93} +(9.70277 - 3.02221i) q^{94} +(-11.3044 + 6.52659i) q^{95} +(3.74861 + 4.23649i) q^{96} +8.13728i q^{97} +(9.89348 - 0.345090i) q^{98} +(-3.12758 - 3.12758i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 4 q^{4} - 24 q^{8} + 36 q^{10} - 8 q^{11} - 32 q^{14} - 4 q^{16} + 4 q^{18} + 16 q^{22} + 16 q^{23} - 32 q^{28} + 32 q^{29} - 24 q^{35} - 16 q^{37} + 60 q^{40} - 20 q^{42} - 16 q^{43} - 12 q^{44}+ \cdots - 16 q^{99}+O(q^{100}) $ 128 * q + 4 * q^4 - 24 * q^8 + 36 * q^10 - 8 * q^11 - 32 * q^14 - 4 * q^16 + 4 * q^18 + 16 * q^22 + 16 * q^23 - 32 * q^28 + 32 * q^29 - 24 * q^35 - 16 * q^37 + 60 * q^40 - 20 * q^42 - 16 * q^43 - 12 * q^44 - 20 * q^46 - 32 * q^50 - 144 * q^52 - 16 * q^53 - 56 * q^56 - 40 * q^58 - 96 * q^59 - 24 * q^60 - 32 * q^64 - 72 * q^66 + 16 * q^67 - 60 * q^68 + 28 * q^70 + 128 * q^71 - 4 * q^72 - 72 * q^74 + 72 * q^78 - 36 * q^80 + 64 * q^81 - 60 * q^82 + 24 * q^84 - 44 * q^86 - 48 * q^88 - 8 * q^91 + 56 * q^92 + 36 * q^94 + 60 * q^96 + 148 * q^98 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.03934	+	0.959049i	0.734923	+	0.678150i
$2$	1.03934	+	0.959049i	0.734923	+	0.678150i
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$3$	−0.965926	−	0.258819i	−0.557678	−	0.149429i
$4$	0.160449	+	1.99355i	0.0802243	+	0.996777i
$5$	0.627426	+	2.34159i	0.280594	+	1.04719i	0.952000	+	0.306100i	$0.0990240\pi$
$5$	0.627426	+	2.34159i	0.280594	+	1.04719i	−0.671406	+	0.741090i	$0.734309\pi$
$6$	−0.755704	−	1.19537i	−0.308515	−	0.488008i
$7$	2.44702	−	1.00602i	0.924888	−	0.380239i
$7$	2.44702	−	1.00602i	0.924888	−	0.380239i
$8$	−1.74516	+	2.22586i	−0.617006	+	0.786959i
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$	−1.59359	+	3.03543i	−0.503937	+	0.959888i
$11$	−4.27235	−	1.14477i	−1.28816	−	0.345162i	−0.451200	−	0.892423i	$-0.649004\pi$
$11$	−4.27235	−	1.14477i	−1.28816	−	0.345162i	−0.836962	+	0.547261i	$0.815671\pi$
$12$	0.360988	−	1.96715i	0.104208	−	0.567868i
$13$	2.40484	+	2.40484i	0.666983	+	0.666983i	0.957017	−	0.290033i	$-0.0936664\pi$
$13$	2.40484	+	2.40484i	0.666983	+	0.666983i	−0.290033	+	0.957017i	$0.593666\pi$
$14$	3.50811	+	1.30122i	0.937581	+	0.347767i
$15$		−	2.42419i		−	0.625923i
$16$	−3.94851	+	0.639726i	−0.987128	+	0.159931i
$17$	−2.17215	+	1.25409i	−0.526823	+	0.304162i	−0.739722	−	0.672913i	$-0.765043\pi$
$17$	−2.17215	+	1.25409i	−0.526823	+	0.304162i	0.212899	+	0.977074i	$0.431710\pi$
$18$	0.420569	+	1.35023i	0.0991290	+	0.318252i
$19$	1.39363	+	5.20109i	0.319720	+	1.19321i	0.919514	+	0.393057i	$0.128582\pi$
$19$	1.39363	+	5.20109i	0.319720	+	1.19321i	−0.599794	+	0.800154i	$0.704751\pi$
$20$	−4.56741	+	1.62651i	−1.02130	+	0.363699i
$21$	−2.62402	+	0.338402i	−0.572608	+	0.0738454i
$22$	−3.34253	−	5.28720i	−0.712629	−	1.12724i
$23$	2.78900	−	4.83069i	0.581546	−	1.00727i	−0.413750	−	0.910391i	$-0.635781\pi$
$23$	2.78900	−	4.83069i	0.581546	−	1.00727i	0.995296	−	0.0968774i	$-0.0308855\pi$
$24$	2.26178	−	1.69833i	0.461685	−	0.346670i
$25$	−0.759236	+	0.438345i	−0.151847	+	0.0876690i
$26$	0.193082	+	4.80581i	0.0378666	+	0.942496i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	2.39817	+	4.71686i	0.453212	+	0.891403i
$29$	0.962214	−	0.962214i	0.178679	−	0.178679i	−0.612101	−	0.790780i	$-0.709675\pi$
$29$	0.962214	−	0.962214i	0.178679	−	0.178679i	0.790780	+	0.612101i	$0.209675\pi$
$30$	2.32492	−	2.51955i	0.424470	−	0.460005i
$31$	0.220090	+	0.381207i	0.0395293	+	0.0684668i	0.885113	−	0.465376i	$-0.154081\pi$
$31$	0.220090	+	0.381207i	0.0395293	+	0.0684668i	−0.845584	+	0.533843i	$0.820747\pi$
$32$	−4.71737	−	3.12193i	−0.833921	−	0.551884i
$33$	3.83049	+	2.21153i	0.666802	+	0.384978i
$34$	−3.46033	−	0.779773i	−0.593442	−	0.133730i
$35$	3.89100	+	5.09872i	0.657700	+	0.861840i
$36$	−0.857824	+	1.80669i	−0.142971	+	0.301115i
$37$	−2.22506	+	0.596202i	−0.365797	+	0.0980150i	−0.437035	−	0.899444i	$-0.643972\pi$
$37$	−2.22506	+	0.596202i	−0.365797	+	0.0980150i	0.0712385	+	0.997459i	$0.477305\pi$
$38$	−3.53965	+	6.74225i	−0.574207	+	1.09374i
$39$	−1.70048	−	2.94532i	−0.272295	−	0.471628i
$40$	−6.30699	−	2.68987i	−0.997222	−	0.425306i
$41$	1.45203			0.226769			0.113384	−	0.993551i	$-0.463831\pi$
$41$	1.45203			0.226769			0.113384	+	0.993551i	$0.463831\pi$
$42$	−3.05179	−	2.16485i	−0.470901	−	0.334044i
$43$	8.53016	−	8.53016i	1.30084	−	1.30084i	0.373009	−	0.927828i	$-0.378326\pi$
$43$	8.53016	−	8.53016i	1.30084	−	1.30084i	0.927828	−	0.373009i	$-0.121674\pi$
$44$	1.59667	−	8.70084i	0.240708	−	1.31170i
$45$	−0.627426	+	2.34159i	−0.0935312	+	0.349063i
$46$	7.53158	−	2.34593i	1.11047	−	0.345889i
$47$	3.59301	−	6.22327i	0.524094	−	0.907757i	−0.475513	−	0.879709i	$-0.657737\pi$
$47$	3.59301	−	6.22327i	0.524094	−	0.907757i	0.999607	−	0.0280482i	$-0.00892920\pi$
$48$	3.97954	+	0.404023i	0.574398	+	0.0583156i
$49$	4.97586	−	4.92350i	0.710837	−	0.703357i
$50$	−1.20950	−	0.272556i	−0.171049	−	0.0385452i
$51$	2.42272	−	0.649165i	0.339248	−	0.0909013i
$52$	−4.40833	+	5.18004i	−0.611325	+	0.718342i
$53$	−0.397428	+	1.48322i	−0.0545910	+	0.203736i	−0.987835	−	0.155508i	$-0.950299\pi$
$53$	−0.397428	+	1.48322i	−0.0545910	+	0.203736i	0.933244	+	0.359244i	$0.116965\pi$
$54$	−0.0567729	−	1.41307i	−0.00772582	−	0.192295i
$55$		−	10.7223i		−	1.44580i
$56$	−2.03119	+	7.20238i	−0.271429	+	0.962458i
$57$		−	5.38456i		−	0.713202i
$58$	1.92288	−	0.0772552i	0.252486	−	0.0101441i
$59$	0.768265	−	2.86721i	0.100020	−	0.373278i	−0.897713	−	0.440581i	$-0.854773\pi$
$59$	0.768265	−	2.86721i	0.100020	−	0.373278i	0.997733	+	0.0673024i	$0.0214392\pi$
$60$	4.83275	−	0.388958i	0.623905	−	0.0502142i
$61$	2.14675	−	0.575220i	0.274863	−	0.0736494i	−0.118754	−	0.992924i	$-0.537890\pi$
$61$	2.14675	−	0.575220i	0.274863	−	0.0736494i	0.393618	+	0.919274i	$0.371223\pi$
$62$	−0.136848	+	0.607280i	−0.0173798	+	0.0771247i
$63$	2.62219	+	0.352275i	0.330365	+	0.0443825i
$64$	−1.90886	−	7.76893i	−0.238608	−	0.971116i
$65$	−4.12228	+	7.14001i	−0.511306	+	0.885609i
$66$	1.86020	+	5.97216i	0.228975	+	0.735122i
$67$	3.40860	−	12.7211i	0.416426	−	1.55412i	−0.365535	−	0.930797i	$-0.619114\pi$
$67$	3.40860	−	12.7211i	0.416426	−	1.55412i	0.781962	−	0.623327i	$-0.214219\pi$
$68$	−2.84861	−	4.12908i	−0.345445	−	0.500724i
$69$	−3.94424	+	3.94424i	−0.474831	+	0.474831i
$70$	−0.845851	+	9.03096i	−0.101099	+	1.07941i
$71$	−9.28298			−1.10169			−0.550844	−	0.834608i	$-0.685694\pi$
$71$	−9.28298			−1.10169			−0.550844	+	0.834608i	$0.685694\pi$
$72$	−2.62428	+	1.05507i	−0.309274	+	0.124341i
$73$	1.40733	+	2.43756i	0.164715	+	0.285295i	0.936554	−	0.350523i	$-0.113996\pi$
$73$	1.40733	+	2.43756i	0.164715	+	0.285295i	−0.771839	+	0.635818i	$0.780663\pi$
$74$	−2.88437	−	1.51428i	−0.335302	−	0.176032i
$75$	0.846818	−	0.226904i	0.0977821	−	0.0262006i
$76$	−10.1450	+	3.61278i	−1.16372	+	0.414414i
$77$	−11.6062	+	1.49677i	−1.32265	+	0.170573i
$78$	1.05733	−	4.69203i	0.119719	−	0.531267i
$79$	5.93453	+	3.42630i	0.667687	+	0.385489i	0.795200	−	0.606348i	$-0.207366\pi$
$79$	5.93453	+	3.42630i	0.667687	+	0.385489i	−0.127513	+	0.991837i	$0.540699\pi$
$80$	−3.97537	−	8.84440i	−0.444460	−	0.988834i
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$	1.50915	+	1.39257i	0.166658	+	0.153783i
$83$	−10.7397	+	10.7397i	−1.17883	+	1.17883i	−0.198792	+	0.980042i	$0.563702\pi$
$83$	−10.7397	+	10.7397i	−1.17883	+	1.17883i	−0.980042	+	0.198792i	$0.936298\pi$
$84$	−1.09564	−	5.17683i	−0.119544	−	0.564838i
$85$	−4.29942	−	4.29942i	−0.466338	−	0.466338i
$86$	17.0466	−	0.684878i	1.83818	−	0.0738523i
$87$	−1.17847	+	0.680388i	−0.126345	+	0.0729453i
$88$	10.0040	−	7.51183i	1.06643	−	0.800764i
$89$	8.48740	−	14.7006i	0.899662	−	1.55826i	0.0717366	−	0.997424i	$-0.477146\pi$
$89$	8.48740	−	14.7006i	0.899662	−	1.55826i	0.827926	−	0.560838i	$-0.189521\pi$
$90$	−2.89781	+	1.83197i	−0.305455	+	0.193106i
$91$	8.30402	+	3.46539i	0.870498	+	0.363272i
$92$	10.0777	+	4.78494i	1.05068	+	0.498865i
$93$	−0.113927	−	0.425181i	−0.0118137	−	0.0440892i
$94$	9.70277	−	3.02221i	1.00076	−	0.311717i
$95$	−11.3044	+	6.52659i	−1.15981	+	0.669615i
$96$	3.74861	+	4.23649i	0.382591	+	0.432385i
$97$			8.13728i			0.826216i	0.910682	+	0.413108i	$0.135557\pi$
$97$			8.13728i			0.826216i	−0.910682	+	0.413108i	$0.864443\pi$
$98$	9.89348	−	0.345090i	0.999392	−	0.0348593i
$99$	−3.12758	−	3.12758i	−0.314333	−	0.314333i
$100$	−0.995683	−	1.44325i	−0.0995683	−	0.144325i
$101$	12.2255	+	3.27581i	1.21648	+	0.325955i	0.809301	−	0.587394i	$-0.199846\pi$
$101$	12.2255	+	3.27581i	1.21648	+	0.325955i	0.407179	+	0.913348i	$0.366513\pi$
$102$	3.14060	+	1.64880i	0.310966	+	0.163256i
$103$	−9.03340	−	5.21544i	−0.890087	−	0.513892i	−0.0161163	−	0.999870i	$-0.505130\pi$
$103$	−9.03340	−	5.21544i	−0.890087	−	0.513892i	−0.873971	+	0.485978i	$0.838464\pi$
$104$	−9.54965	+	1.15601i	−0.936421	+	0.113356i
$105$	−2.43878	−	5.93205i	−0.238000	−	0.578909i
$106$	−1.83555	+	1.16042i	−0.178284	+	0.112710i
$107$	4.99229	+	18.6315i	0.482623	+	1.80117i	0.590535	+	0.807012i	$0.298917\pi$
$107$	4.99229	+	18.6315i	0.482623	+	1.80117i	−0.107912	+	0.994160i	$0.534417\pi$
$108$	1.29620	−	1.52311i	0.124727	−	0.146561i
$109$	−14.1167	−	3.78255i	−1.35213	−	0.362303i	−0.491211	−	0.871040i	$-0.663446\pi$
$109$	−14.1167	−	3.78255i	−1.35213	−	0.362303i	−0.860922	+	0.508737i	$0.830112\pi$
$110$	10.2833	−	11.1441i	0.980470	−	1.06255i
$111$	2.30355			0.218643
$112$	−9.01853	+	5.53770i	−0.852171	+	0.523263i
$113$	−10.2795			−0.967017			−0.483508	−	0.875340i	$-0.660638\pi$
$113$	−10.2795			−0.967017			−0.483508	+	0.875340i	$0.660638\pi$
$114$	5.16406	−	5.59638i	0.483658	−	0.524149i
$115$	13.0614	+	3.49978i	1.21798	+	0.326356i
$116$	2.07261	+	1.76384i	0.192437	+	0.163768i
$117$	0.880233	+	3.28508i	0.0813776	+	0.303705i
$118$	3.54828	−	2.24319i	0.326646	−	0.206503i
$119$	−4.05366	+	5.25401i	−0.371599	+	0.481634i
$120$	5.39589	+	4.23059i	0.492575	+	0.386198i
$121$	7.41621	+	4.28175i	0.674201	+	0.389250i
$122$	2.78286	+	1.46099i	0.251949	+	0.132272i
$123$	−1.40255	−	0.375813i	−0.126464	−	0.0338859i
$124$	−0.724643	+	0.499925i	−0.0650749	+	0.0448946i
$125$	7.06801	+	7.06801i	0.632182	+	0.632182i
$126$	2.38750	+	2.88095i	0.212695	+	0.256655i
$127$			13.5296i			1.20056i	0.799789	+	0.600281i	$0.204945\pi$
$127$			13.5296i			1.20056i	−0.799789	+	0.600281i	$0.795055\pi$
$128$	5.46683	−	9.90524i	0.483204	−	0.875508i
$129$	−10.4473	+	6.03173i	−0.919831	+	0.531064i
$130$	−11.1321	+	3.46741i	−0.976347	+	0.304112i
$131$	3.16808	+	11.8234i	0.276796	+	1.03302i	0.954628	+	0.297800i	$0.0962530\pi$
$131$	3.16808	+	11.8234i	0.276796	+	1.03302i	−0.677832	+	0.735217i	$0.737080\pi$
$132$	−3.79421	+	7.99112i	−0.330244	+	0.695537i
$133$	8.64262	+	11.3252i	0.749410	+	0.982017i
$134$	15.7428	−	9.95247i	1.35997	−	0.859762i
$135$	1.21209	−	2.09941i	0.104320	−	0.180688i
$136$	0.999314	−	7.02347i	0.0856905	−	0.602258i
$137$	11.5639	−	6.67643i	0.987972	−	0.570406i	0.0833044	−	0.996524i	$-0.473453\pi$
$137$	11.5639	−	6.67643i	0.987972	−	0.570406i	0.904667	+	0.426118i	$0.140119\pi$
$138$	−7.88212	+	0.316679i	−0.670971	+	0.0269575i
$139$	−12.2683	−	12.2683i	−1.04058	−	1.04058i	−0.999141	−	0.0414400i	$-0.986805\pi$
$139$	−12.2683	−	12.2683i	−1.04058	−	1.04058i	−0.0414400	−	0.999141i	$-0.513195\pi$
$140$	−9.54026	+	8.57501i	−0.806299	+	0.724720i
$141$	−5.08128	+	5.08128i	−0.427921	+	0.427921i
$142$	−9.64816	−	8.90284i	−0.809656	−	0.747110i
$143$	−7.52133	−	13.0273i	−0.628966	−	1.08940i
$144$	−3.73938	−	1.42024i	−0.311615	−	0.118353i
$145$	2.85683	+	1.64939i	0.237246	+	0.136974i
$146$	−0.875053	+	3.88315i	−0.0724199	+	0.321371i
$147$	−6.08060	+	3.46789i	−0.501520	+	0.286027i
$148$	−1.54557	−	4.34011i	−0.127045	−	0.356755i
$149$	−3.16745	+	0.848717i	−0.259488	+	0.0695296i	−0.386218	−	0.922408i	$-0.626219\pi$
$149$	−3.16745	+	0.848717i	−0.259488	+	0.0695296i	0.126730	+	0.991937i	$0.459552\pi$
$150$	1.09774	+	0.576310i	0.0896303	+	0.0470555i
$151$	−12.0326	−	20.8411i	−0.979198	−	1.69602i	−0.665322	−	0.746557i	$-0.731706\pi$
$151$	−12.0326	−	20.8411i	−0.979198	−	1.69602i	−0.313876	−	0.949464i	$-0.601628\pi$
$152$	−14.0090	−	5.97470i	−1.13628	−	0.484612i
$153$	−2.50818			−0.202774
$154$	−13.4983	−	9.57528i	−1.08772	−	0.771598i
$155$	−0.754539	+	0.754539i	−0.0606060	+	0.0606060i
$156$	5.59881	−	3.86257i	0.448264	−	0.309253i
$157$	0.858593	−	3.20431i	0.0685232	−	0.255732i	−0.923164	−	0.384407i	$-0.874406\pi$
$157$	0.858593	−	3.20431i	0.0685232	−	0.255732i	0.991687	+	0.128675i	$0.0410725\pi$
$158$	2.88199	+	9.25259i	0.229279	+	0.736097i
$159$	0.767773	−	1.32982i	0.0608883	−	0.105462i
$160$	4.35046	−	13.0049i	0.343934	−	1.02813i
$161$	1.96499	−	14.6266i	0.154863	−	1.15274i
$162$	−0.310892	+	1.37962i	−0.0244260	+	0.108393i
$163$	−10.0418	+	2.69070i	−0.786538	+	0.210752i	−0.629665	−	0.776867i	$-0.716808\pi$
$163$	−10.0418	+	2.69070i	−0.786538	+	0.210752i	−0.156873	+	0.987619i	$0.550141\pi$
$164$	0.232976	+	2.89470i	0.0181924	+	0.226038i
$165$	−2.77515	+	10.3570i	−0.216045	+	0.806290i
$166$	−21.4621	+	0.862279i	−1.66578	+	0.0669258i
$167$		−	0.0908142i		−	0.00702741i	−0.999994	−	0.00351371i	$-0.998882\pi$
$167$		−	0.0908142i		−	0.00702741i	0.999994	−	0.00351371i	$-0.00111845\pi$
$168$	3.82609	−	6.43125i	0.295189	−	0.496182i
$169$		−	1.43347i		−	0.110267i
$170$	−0.345196	−	8.59191i	−0.0264754	−	0.658970i
$171$	−1.39363	+	5.20109i	−0.106573	+	0.397737i
$172$	18.3740	+	15.6367i	1.40100	+	1.19229i
$173$	−9.20529	+	2.46655i	−0.699865	+	0.187528i	−0.591170	−	0.806547i	$-0.701334\pi$
$173$	−9.20529	+	2.46655i	−0.699865	+	0.187528i	−0.108695	+	0.994075i	$0.534667\pi$
$174$	−1.87735	−	0.423054i	−0.142322	−	0.0320717i
$175$	−1.41689	+	1.83645i	−0.107107	+	0.138822i
$176$	17.6018	+	1.78702i	1.32678	+	0.134702i
$177$	−1.48417	+	2.57067i	−0.111557	+	0.193223i
$178$	22.9199	−	7.13907i	1.71792	−	0.535096i
$179$	0.741799	−	2.76843i	0.0554447	−	0.206922i	−0.932647	−	0.360791i	$-0.882507\pi$
$179$	0.741799	−	2.76843i	0.0554447	−	0.206922i	0.988091	+	0.153869i	$0.0491734\pi$
$180$	−4.76875	−	0.875103i	−0.355441	−	0.0652264i
$181$	−12.5911	+	12.5911i	−0.935890	+	0.935890i	−0.998065	−	0.0621753i	$-0.980196\pi$
$181$	−12.5911	+	12.5911i	−0.935890	+	0.935890i	0.0621753	+	0.998065i	$0.480196\pi$
$182$	5.30720	+	11.5657i	0.393396	+	0.857305i
$183$	−2.22248			−0.164290
$184$	5.88517	+	14.6382i	0.433861	+	1.07914i
$185$	−2.79212	−	4.83609i	−0.205280	−	0.355556i
$186$	0.289361	−	0.551169i	0.0212170	−	0.0404136i
$187$	10.7158	−	2.87130i	0.783619	−	0.209970i
$188$	12.9829	+	6.16434i	0.946876	+	0.449580i
$189$	−2.44167	−	1.01895i	−0.177605	−	0.0741174i
$190$	−18.0084	−	4.05813i	−1.30647	−	0.294408i
$191$	−4.18475	−	2.41607i	−0.302798	−	0.174820i	0.340901	−	0.940099i	$-0.389268\pi$
$191$	−4.18475	−	2.41607i	−0.302798	−	0.174820i	−0.643699	+	0.765279i	$0.722601\pi$
$192$	−0.166928	+	7.99826i	−0.0120470	+	0.577225i
$193$	10.1698	+	17.6147i	0.732040	+	1.26793i	0.956010	+	0.293335i	$0.0947650\pi$
$193$	10.1698	+	17.6147i	0.732040	+	1.26793i	−0.223970	+	0.974596i	$0.571902\pi$
$194$	−7.80405	+	8.45739i	−0.560298	+	0.607205i
$195$	5.82979	−	5.82979i	0.417480	−	0.417480i
$196$	10.6136	+	9.12967i	0.758116	+	0.652119i
$197$	−14.1651	−	14.1651i	−1.00922	−	1.00922i	−0.999957	−	0.00926226i	$-0.997052\pi$
$197$	−14.1651	−	14.1651i	−1.00922	−	1.00922i	−0.00926226	−	0.999957i	$-0.502948\pi$
$198$	−0.251110	−	6.25012i	−0.0178456	−	0.444176i
$199$	−20.9977	+	12.1230i	−1.48849	+	0.859378i	−0.999914	−	0.0131450i	$-0.995816\pi$
$199$	−20.9977	+	12.1230i	−1.48849	+	0.859378i	−0.488573	+	0.872523i	$0.662482\pi$
$200$	0.349293	−	2.45493i	0.0246987	−	0.173590i
$201$	−6.58490	+	11.4054i	−0.464463	+	0.804474i
$202$	9.56475	+	15.1295i	0.672973	+	1.06451i
$203$	1.38656	−	3.32257i	0.0973172	−	0.233198i
$204$	1.68287	+	4.72566i	0.117824	+	0.330862i
$205$	0.911041	+	3.40005i	0.0636299	+	0.237470i
$206$	−4.38690	−	14.0841i	−0.305650	−	0.981284i
$207$	4.83069	−	2.78900i	0.335756	−	0.193849i
$208$	−11.0340	−	7.95711i	−0.765069	−	0.551726i
$209$		−	23.8163i		−	1.64740i
$210$	3.15441	−	8.50431i	0.217675	−	0.586853i
$211$	12.7220	+	12.7220i	0.875821	+	0.875821i	0.993099	−	0.117278i	$-0.0374170\pi$
$211$	12.7220	+	12.7220i	0.875821	+	0.875821i	−0.117278	+	0.993099i	$0.537417\pi$
$212$	−3.02065	−	0.554314i	−0.207459	−	0.0380704i
$213$	8.96667	+	2.40261i	0.614386	+	0.164624i
$214$	−12.6798	+	24.1523i	−0.866775	+	1.65101i
$215$	25.3261	+	14.6221i	1.72723	+	0.997216i
$216$	2.80793	−	0.339906i	0.191055	−	0.0231276i
$217$	0.922066	+	0.711408i	0.0625939	+	0.0482935i
$218$	−11.0444	−	17.4700i	−0.748018	−	1.18321i
$219$	−0.728486	−	2.71875i	−0.0492265	−	0.183716i
$220$	21.3756	−	1.72038i	1.44114	−	0.115988i
$221$	−8.23956	−	2.20778i	−0.554253	−	0.148512i
$222$	2.39416	+	2.20922i	0.160686	+	0.148273i
$223$	1.89320			0.126778			0.0633891	−	0.997989i	$-0.479809\pi$
$223$	1.89320			0.126778			0.0633891	+	0.997989i	$0.479809\pi$
$224$	−14.6842	−	2.89367i	−0.981131	−	0.193342i
$225$	−0.876690			−0.0584460
$226$	−10.6839	−	9.85858i	−0.710683	−	0.655783i
$227$	−17.0276	−	4.56253i	−1.13016	−	0.302825i	−0.355172	−	0.934801i	$-0.615578\pi$
$227$	−17.0276	−	4.56253i	−1.13016	−	0.302825i	−0.774988	+	0.631976i	$0.782244\pi$
$228$	10.7344	−	0.863945i	0.710904	−	0.0572162i
$229$	−5.64795	−	21.0784i	−0.373227	−	1.39290i	−0.855918	−	0.517112i	$-0.827007\pi$
$229$	−5.64795	−	21.0784i	−0.373227	−	1.39290i	0.482691	−	0.875791i	$-0.339660\pi$
$230$	10.2187	+	16.1639i	0.673802	+	1.06582i
$231$	11.5981	+	1.55814i	0.763101	+	0.102518i
$232$	0.462535	+	3.82096i	0.0303669	+	0.250858i
$233$	9.33083	+	5.38716i	0.611283	+	0.352924i	0.773467	−	0.633836i	$-0.218521\pi$
$233$	9.33083	+	5.38716i	0.611283	+	0.352924i	−0.162184	+	0.986760i	$0.551854\pi$
$234$	−2.23569	+	4.25849i	−0.146152	+	0.278386i
$235$	16.8267	+	4.50869i	1.09765	+	0.294115i
$236$	5.83919	+	1.07154i	0.380099	+	0.0697512i
$237$	−4.84552	−	4.84552i	−0.314751	−	0.314751i
$238$	−9.25198	+	1.57303i	−0.599717	+	0.101964i
$239$			1.65026i			0.106746i	0.998575	+	0.0533732i	$0.0169973\pi$
$239$			1.65026i			0.106746i	−0.998575	+	0.0533732i	$0.983003\pi$
$240$	1.55082	+	9.57194i	0.100105	+	0.617866i
$241$	15.3990	−	8.89064i	0.991940	−	0.572697i	0.0860861	−	0.996288i	$-0.472564\pi$
$241$	15.3990	−	8.89064i	0.991940	−	0.572697i	0.905854	+	0.423591i	$0.139231\pi$
$242$	3.60154	+	11.5627i	0.231516	+	0.743278i
$243$	−0.258819	−	0.965926i	−0.0166032	−	0.0619642i
$244$	1.49118	+	4.18737i	0.0954627	+	0.268069i
$245$	14.6508	+	8.56227i	0.936004	+	0.547023i
$246$	−1.09730	−	1.73571i	−0.0699615	−	0.110665i
$247$	−9.15634	+	15.8592i	−0.582604	+	1.00910i
$248$	−1.23260	−	0.175377i	−0.0782704	−	0.0111365i
$249$	13.1534	−	7.59411i	0.833562	−	0.481257i
$250$	0.567484	+	14.1246i	0.0358908	+	0.893320i
$251$	−4.32903	−	4.32903i	−0.273246	−	0.273246i	0.557159	−	0.830406i	$-0.311891\pi$
$251$	−4.32903	−	4.32903i	−0.273246	−	0.273246i	−0.830406	+	0.557159i	$0.811891\pi$
$252$	−0.281552	+	5.28401i	−0.0177361	+	0.332861i
$253$	−17.4456	+	17.4456i	−1.09680	+	1.09680i
$254$	−12.9756	+	14.0619i	−0.814161	+	0.882321i
$255$	3.04015	+	5.26570i	0.190382	+	0.329751i
$256$	15.1815	−	5.05193i	0.948844	−	0.315746i
$257$	4.80107	+	2.77190i	0.299483	+	0.172906i	0.642210	−	0.766528i	$-0.278018\pi$
$257$	4.80107	+	2.77190i	0.299483	+	0.172906i	−0.342728	+	0.939435i	$0.611351\pi$
$258$	−16.6430	−	3.75043i	−1.03615	−	0.233492i
$259$	−4.84498	+	3.69737i	−0.301052	+	0.229743i
$260$	−14.8954	−	7.07239i	−0.923774	−	0.438611i
$261$	1.31441	−	0.352195i	0.0813599	−	0.0218003i
$262$	−8.04654	+	15.3269i	−0.497117	+	0.946898i
$263$	6.03539	+	10.4536i	0.372158	+	0.644596i	0.989897	−	0.141787i	$-0.0452847\pi$
$263$	6.03539	+	10.4536i	0.372158	+	0.644596i	−0.617739	+	0.786383i	$0.711951\pi$
$264$	−11.6073	+	4.66664i	−0.714383	+	0.287212i
$265$	−3.72245			−0.228668
$266$	−1.87879	+	20.0594i	−0.115196	+	1.22992i
$267$	−12.0030	+	12.0030i	−0.734571	+	0.734571i
$268$	25.9070	+	4.75414i	1.58252	+	0.290406i
$269$	8.40725	−	31.3763i	0.512599	−	1.91305i	0.121849	−	0.992549i	$-0.461118\pi$
$269$	8.40725	−	31.3763i	0.512599	−	1.91305i	0.390750	−	0.920497i	$-0.372216\pi$
$270$	3.27321	−	1.01954i	0.199201	−	0.0620471i
$271$	7.75611	−	13.4340i	0.471150	−	0.816056i	−0.528305	−	0.849055i	$-0.677172\pi$
$271$	7.75611	−	13.4340i	0.471150	−	0.816056i	0.999455	+	0.0329982i	$0.0105056\pi$
$272$	7.77448	−	6.34137i	0.471397	−	0.384502i
$273$	−7.12416	−	5.49655i	−0.431174	−	0.332666i
$274$	18.4218	+	4.15130i	1.11290	+	0.250789i
$275$	3.74553	−	1.00361i	0.225864	−	0.0605201i
$276$	−8.49590	−	7.23021i	−0.511393	−	0.435207i
$277$	6.34925	−	23.6957i	0.381490	−	1.42374i	−0.462137	−	0.886808i	$-0.652917\pi$
$277$	6.34925	−	23.6957i	0.381490	−	1.42374i	0.843627	−	0.536930i	$-0.180416\pi$
$278$	−0.985007	−	24.5168i	−0.0590768	−	1.47042i
$279$			0.440180i			0.0263529i
$280$	−18.1394	−	0.237245i	−1.08404	−	0.0141781i
$281$			4.94605i			0.295056i	0.989058	+	0.147528i	$0.0471317\pi$
$281$			4.94605i			0.295056i	−0.989058	+	0.147528i	$0.952868\pi$
$282$	−10.1544	+	0.407971i	−0.604684	+	0.0242943i
$283$	−3.46312	+	12.9245i	−0.205861	+	0.768285i	0.783324	+	0.621614i	$0.213523\pi$
$283$	−3.46312	+	12.9245i	−0.205861	+	0.768285i	−0.989185	+	0.146671i	$0.953144\pi$
$284$	−1.48944	−	18.5061i	−0.0883821	−	1.09814i
$285$	12.6084	−	3.37841i	0.746858	−	0.200120i
$286$	4.67664	−	20.7531i	0.276536	−	1.22716i
$287$	3.55315	−	1.46077i	0.209736	−	0.0862263i
$288$	−2.52440	−	5.06235i	−0.148752	−	0.298302i
$289$	−5.35452	+	9.27429i	−0.314972	+	0.545547i
$290$	1.38736	+	4.45411i	0.0814688	+	0.261554i
$291$	2.10608	−	7.86001i	0.123461	−	0.460762i
$292$	−4.63360	+	3.19668i	−0.271161	+	0.187072i
$293$	12.6321	−	12.6321i	0.737977	−	0.737977i	−0.234209	−	0.972186i	$-0.575250\pi$
$293$	12.6321	−	12.6321i	0.737977	−	0.737977i	0.972186	+	0.234209i	$0.0752500\pi$
$294$	−9.64568	−	2.22729i	−0.562548	−	0.129898i
$295$	7.19584			0.418958
$296$	2.55601	−	5.99312i	0.148565	−	0.348343i
$297$	2.21153	+	3.83049i	0.128326	+	0.222267i
$298$	−4.10602	−	2.15564i	−0.237855	−	0.124873i
$299$	18.3241	−	4.90994i	1.05971	−	0.283949i
$300$	0.588216	+	1.65177i	0.0339607	+	0.0953650i
$301$	12.2920	−	29.4550i	0.708500	−	1.69776i
$302$	7.48167	−	33.2007i	0.430522	−	1.91049i
$303$	−10.9611	−	6.32837i	−0.629696	−	0.363555i
$304$	−8.83002	−	19.6450i	−0.506436	−	1.12672i
$305$	2.69386	+	4.66589i	0.154250	+	0.267168i
$306$	−2.60685	−	2.40547i	−0.149024	−	0.137511i
$307$	−14.9745	+	14.9745i	−0.854642	+	0.854642i	−0.990701	−	0.136059i	$-0.956556\pi$
$307$	−14.9745	+	14.9745i	−0.854642	+	0.854642i	0.136059	+	0.990701i	$0.456556\pi$
$308$	−4.84610	−	22.8975i	−0.276132	−	1.30470i
$309$	7.37574	+	7.37574i	0.419591	+	0.419591i
$310$	−1.50786	+	0.0605812i	−0.0856408	+	0.00344078i
$311$	−14.3950	+	8.31098i	−0.816267	+	0.471272i	−0.849128	−	0.528188i	$-0.822872\pi$
$311$	−14.3950	+	8.31098i	−0.816267	+	0.471272i	0.0328602	+	0.999460i	$0.489538\pi$
$312$	9.52345	+	1.35502i	0.539159	+	0.0767127i
$313$	−15.8923	+	27.5263i	−0.898288	+	1.55588i	−0.0686069	+	0.997644i	$0.521855\pi$
$313$	−15.8923	+	27.5263i	−0.898288	+	1.55588i	−0.829681	+	0.558237i	$0.811478\pi$
$314$	3.96546	−	2.50693i	0.223784	−	0.141474i
$315$	0.820350	+	6.36112i	0.0462215	+	0.358409i
$316$	−5.87833	+	12.3805i	−0.330682	+	0.696460i
$317$	2.38892	+	8.91556i	0.134175	+	0.500748i	1.00000		0.000400866i	$0.000127600\pi$
$317$	2.38892	+	8.91556i	0.134175	+	0.500748i	−0.865825	+	0.500347i	$0.833206\pi$
$318$	2.07334	−	0.645803i	0.116267	−	0.0362148i
$319$	−5.21243	+	3.00940i	−0.291840	+	0.168494i
$320$	16.9939	−	9.34419i	0.949991	−	0.522356i
$321$		−	19.2887i		−	1.07659i
$322$	16.0699	−	13.3175i	0.895541	−	0.742153i
$323$	−9.54979	−	9.54979i	−0.531365	−	0.531365i
$324$	−1.64624	+	1.13573i	−0.0914580	+	0.0630961i
$325$	−2.87999	−	0.771692i	−0.159753	−	0.0428058i
$326$	−13.0174	−	6.83407i	−0.720967	−	0.378504i
$327$	12.6567	+	7.30733i	0.699916	+	0.404096i
$328$	−2.53402	+	3.23201i	−0.139918	+	0.178458i
$329$	2.53145	−	18.8431i	0.139564	−	1.03885i
$330$	−12.8172	+	8.10291i	−0.705562	+	0.446051i
$331$	3.90124	+	14.5596i	0.214432	+	0.800270i	0.986366	+	0.164568i	$0.0526229\pi$
$331$	3.90124	+	14.5596i	0.214432	+	0.800270i	−0.771934	+	0.635703i	$0.780710\pi$
$332$	−23.1333	−	19.6870i	−1.26961	−	1.08046i
$333$	−2.22506	−	0.596202i	−0.121932	−	0.0326717i
$334$	0.0870953	−	0.0943867i	0.00476564	−	0.00516461i
$335$	31.9261			1.74431
$336$	10.1445	−	3.01484i	0.553428	−	0.164473i
$337$	11.2973			0.615405			0.307703	−	0.951483i	$-0.400440\pi$
$337$	11.2973			0.615405			0.307703	+	0.951483i	$0.400440\pi$
$338$	1.37477	−	1.48986i	0.0747774	−	0.0810376i
$339$	9.92926	+	2.66054i	0.539284	+	0.144501i
$340$	7.88129	−	9.26097i	0.427423	−	0.502246i
$341$	−0.503906	−	1.88060i	−0.0272880	−	0.101840i
$342$	−6.43655	+	4.06913i	−0.348049	+	0.220033i
$343$	7.22292	−	17.0537i	0.390001	−	0.920815i
$344$	4.10044	+	33.8733i	0.221081	+	1.82633i
$345$	−11.7105	−	6.76106i	−0.630472	−	0.364003i
$346$	−11.9329	−	6.26474i	−0.641519	−	0.336795i
$347$	−24.2917	−	6.50895i	−1.30405	−	0.349419i	−0.461069	−	0.887364i	$-0.652534\pi$
$347$	−24.2917	−	6.50895i	−1.30405	−	0.349419i	−0.842980	+	0.537945i	$0.819201\pi$
$348$	−1.54547	−	2.24017i	−0.0828461	−	0.120086i
$349$	−5.41974	−	5.41974i	−0.290112	−	0.290112i	0.547012	−	0.837124i	$-0.315765\pi$
$349$	−5.41974	−	5.41974i	−0.290112	−	0.290112i	−0.837124	+	0.547012i	$0.815765\pi$
$350$	−3.23387	+	0.549825i	−0.172857	+	0.0293894i
$351$		−	3.40096i		−	0.181530i
$352$	16.5804	+	18.7383i	0.883736	+	0.998754i
$353$	14.8839	−	8.59323i	0.792191	−	0.457372i	−0.0485424	−	0.998821i	$-0.515458\pi$
$353$	14.8839	−	8.59323i	0.792191	−	0.457372i	0.840733	+	0.541450i	$0.182124\pi$
$354$	−4.00795	+	1.24839i	−0.213020	+	0.0663514i
$355$	−5.82439	−	21.7369i	−0.309126	−	1.15368i
$356$	30.6682	+	14.5614i	1.62541	+	0.771752i
$357$	5.27537	−	4.02582i	0.279202	−	0.213069i
$358$	3.42604	−	2.16592i	0.181072	−	0.114472i
$359$	12.2506	−	21.2187i	0.646562	−	1.11988i	−0.337376	−	0.941370i	$-0.609539\pi$
$359$	12.2506	−	21.2187i	0.646562	−	1.11988i	0.983938	−	0.178509i	$-0.0571274\pi$
$360$	−4.11708	−	5.48299i	−0.216989	−	0.288979i
$361$	−8.65462	+	4.99675i	−0.455506	+	0.262987i
$362$	−25.1619	+	1.01093i	−1.32248	+	0.0531332i
$363$	−6.05531	−	6.05531i	−0.317821	−	0.317821i
$364$	−5.57608	+	17.1105i	−0.292266	+	0.896835i
$365$	−4.82477	+	4.82477i	−0.252540	+	0.252540i
$366$	−2.30991	−	2.13147i	−0.120741	−	0.111414i
$367$	−2.72200	−	4.71465i	−0.142087	−	0.246103i	0.786195	−	0.617978i	$-0.212048\pi$
$367$	−2.72200	−	4.71465i	−0.142087	−	0.246103i	−0.928283	+	0.371876i	$0.878715\pi$
$368$	−7.92208	+	20.8582i	−0.412967	+	1.08731i
$369$	1.25749	+	0.726014i	0.0654625	+	0.0377948i
$370$	1.73609	−	7.70411i	0.0902552	−	0.400518i
$371$	0.519632	+	4.02930i	0.0269779	+	0.209191i
$372$	0.829342	−	0.295339i	0.0429994	−	0.0153126i
$373$	−2.83919	+	0.760760i	−0.147008	+	0.0393907i	−0.331573	−	0.943430i	$-0.607579\pi$
$373$	−2.83919	+	0.760760i	−0.147008	+	0.0393907i	0.184565	+	0.982820i	$0.440913\pi$
$374$	13.8911	+	7.29276i	0.718291	+	0.377100i
$375$	−4.99784	−	8.65651i	−0.258087	−	0.447020i
$376$	7.58174	+	18.8581i	0.390998	+	0.972531i
$377$	4.62795			0.238351
$378$	−1.56050	−	3.40071i	−0.0802635	−	0.174914i
$379$	20.0922	−	20.0922i	1.03207	−	1.03207i	0.0325965	−	0.999469i	$-0.489622\pi$
$379$	20.0922	−	20.0922i	1.03207	−	1.03207i	0.999469	−	0.0325965i	$-0.0103776\pi$
$380$	−14.8249	−	21.4887i	−0.760501	−	1.10235i
$381$	3.50173	−	13.0686i	0.179399	−	0.669526i
$382$	−2.03224	−	6.52449i	−0.103979	−	0.333822i
$383$	−15.8961	+	27.5329i	−0.812253	+	1.40686i	0.0990301	+	0.995084i	$0.468426\pi$
$383$	−15.8961	+	27.5329i	−0.812253	+	1.40686i	−0.911283	+	0.411780i	$0.864907\pi$
$384$	−7.84422	+	8.15280i	−0.400299	+	0.416046i
$385$	−10.7869	−	26.2378i	−0.549750	−	1.33720i
$386$	−6.32343	+	28.0610i	−0.321854	+	1.42827i
$387$	11.6524	−	3.12225i	0.592325	−	0.158713i
$388$	−16.2221	+	1.30562i	−0.823553	+	0.0662826i
$389$	0.453109	−	1.69103i	0.0229736	−	0.0857385i	−0.953487	−	0.301433i	$-0.902535\pi$
$389$	0.453109	−	1.69103i	0.0229736	−	0.0857385i	0.976461	+	0.215695i	$0.0692016\pi$
$390$	11.6502	−	0.468068i	0.589930	−	0.0237016i
$391$			13.9906i			0.707536i
$392$	2.27535	+	19.6678i	0.114923	+	0.993374i
$393$		−	12.2405i		−	0.617452i
$394$	−1.13730	−	28.3073i	−0.0572963	−	1.42610i
$395$	−4.29950	+	16.0460i	−0.216331	+	0.807360i
$396$	5.73318	−	6.73681i	0.288103	−	0.338538i
$397$	4.18870	−	1.12236i	0.210225	−	0.0563295i	−0.152170	−	0.988354i	$-0.548626\pi$
$397$	4.18870	−	1.12236i	0.210225	−	0.0563295i	0.362394	+	0.932025i	$0.381959\pi$
$398$	−33.4503	−	7.53790i	−1.67671	−	0.377841i
$399$	−5.41696	−	13.1762i	−0.271187	−	0.659633i
$400$	2.71743	−	2.21651i	0.135872	−	0.110826i
$401$	−5.46346	+	9.46299i	−0.272832	+	0.472559i	−0.969586	−	0.244751i	$-0.921294\pi$
$401$	−5.46346	+	9.46299i	−0.272832	+	0.472559i	0.696754	+	0.717310i	$0.254627\pi$
$402$	−17.7823	+	5.53881i	−0.886899	+	0.276251i
$403$	−0.387461	+	1.44602i	−0.0193008	+	0.0720316i
$404$	−4.56893	+	24.8977i	−0.227313	+	1.23871i
$405$	−1.71416	+	1.71416i	−0.0851773	+	0.0851773i
$406$	4.62761	−	2.12349i	0.229664	−	0.105387i
$407$	10.1887			0.505037
$408$	−2.78307	+	6.52551i	−0.137783	+	0.323061i
$409$	−3.73199	−	6.46400i	−0.184535	−	0.319624i	0.758885	−	0.651225i	$-0.225745\pi$
$409$	−3.73199	−	6.46400i	−0.184535	−	0.319624i	−0.943420	+	0.331601i	$0.892411\pi$
$410$	−2.31394	+	4.40754i	−0.114277	+	0.217673i
$411$	−12.8979	+	3.45597i	−0.636205	+	0.170471i
$412$	8.94786	−	18.8454i	0.440829	−	0.928445i
$413$	−1.00450	−	7.78901i	−0.0494280	−	0.383272i
$414$	7.69551	+	1.73415i	0.378213	+	0.0852290i
$415$	−31.8863	−	18.4095i	−1.56524	−	0.903689i
$416$	−3.83679	−	18.8523i	−0.188114	−	0.924309i
$417$	8.67498	+	15.0255i	0.424815	+	0.735802i
$418$	22.8410	−	24.7532i	1.11719	−	1.21072i
$419$	5.53586	−	5.53586i	0.270444	−	0.270444i	−0.558835	−	0.829279i	$-0.688751\pi$
$419$	5.53586	−	5.53586i	0.270444	−	0.270444i	0.829279	+	0.558835i	$0.188751\pi$
$420$	11.4346	−	5.81362i	0.557949	−	0.283676i
$421$	−8.26266	−	8.26266i	−0.402697	−	0.402697i	0.476485	−	0.879183i	$-0.341911\pi$
$421$	−8.26266	−	8.26266i	−0.402697	−	0.402697i	−0.879183	+	0.476485i	$0.841911\pi$
$422$	1.02144	+	25.4236i	0.0497229	+	1.23760i
$423$	6.22327	−	3.59301i	0.302586	−	0.174698i
$424$	−2.60787	−	3.47307i	−0.126649	−	0.168667i
$425$	1.09945	−	1.90430i	0.0533311	−	0.0923722i
$426$	7.01518	+	11.0966i	0.339887	+	0.537632i
$427$	4.67447	−	3.56725i	0.226213	−	0.172631i
$428$	−36.3418	+	12.9418i	−1.75665	+	0.625565i
$429$	3.89333	+	14.5301i	0.187972	+	0.701520i
$430$	12.2992	+	39.4863i	0.593118	+	1.90420i
$431$	−6.10326	+	3.52372i	−0.293983	+	0.169731i	−0.639737	−	0.768594i	$-0.720957\pi$
$431$	−6.10326	+	3.52372i	−0.293983	+	0.169731i	0.345753	+	0.938325i	$0.387623\pi$
$432$	3.24437	+	2.33967i	0.156095	+	0.112567i
$433$			3.39440i			0.163124i	0.996668	+	0.0815622i	$0.0259909\pi$
$433$			3.39440i			0.163124i	−0.996668	+	0.0815622i	$0.974009\pi$
$434$	0.276063	+	1.62370i	0.0132515	+	0.0779402i
$435$	−2.33259	−	2.33259i	−0.111839	−	0.111839i
$436$	5.27572	−	28.7493i	0.252661	−	1.37684i
$437$	29.0116	+	7.77365i	1.38782	+	0.371864i
$438$	1.85027	−	3.52435i	0.0884092	−	0.168400i
$439$	2.34179	+	1.35203i	0.111768	+	0.0645291i	0.554842	−	0.831956i	$-0.312779\pi$
$439$	2.34179	+	1.35203i	0.111768	+	0.0645291i	−0.443074	+	0.896485i	$0.646112\pi$
$440$	23.8664	+	18.7122i	1.13778	+	0.892067i
$441$	6.77097	−	1.77595i	0.322427	−	0.0845689i
$442$	−6.44632	−	10.1968i	−0.306620	−	0.485011i
$443$	−1.45116	−	5.41580i	−0.0689467	−	0.257312i	0.922846	−	0.385169i	$-0.125857\pi$
$443$	−1.45116	−	5.41580i	−0.0689467	−	0.257312i	−0.991793	+	0.127857i	$0.959190\pi$
$444$	0.369601	+	4.59224i	0.0175405	+	0.217938i
$445$	39.7480	+	10.6504i	1.88423	+	0.504879i
$446$	1.96768	+	1.81568i	0.0931723	+	0.0859747i
$447$	3.27919			0.155100
$448$	−12.4867	−	17.0904i	−0.589942	−	0.807446i
$449$	16.0880			0.759239			0.379620	−	0.925143i	$-0.376055\pi$
$449$	16.0880			0.759239			0.379620	+	0.925143i	$0.376055\pi$
$450$	−0.911178	−	0.840789i	−0.0429533	−	0.0396352i
$451$	−6.20358	−	1.66224i	−0.292115	−	0.0782720i
$452$	−1.64934	−	20.4928i	−0.0775782	−	0.963900i
$453$	6.22852	+	23.2452i	0.292642	+	1.09215i
$454$	−13.3217	−	21.0723i	−0.625220	−	0.988972i
$455$	−2.90436	+	21.6189i	−0.136158	+	1.01351i
$456$	11.9853	+	9.39690i	0.561261	+	0.440050i
$457$	−17.6712	−	10.2025i	−0.826624	−	0.477251i	0.0260715	−	0.999660i	$-0.491700\pi$
$457$	−17.6712	−	10.2025i	−0.826624	−	0.477251i	−0.852695	+	0.522409i	$0.825034\pi$
$458$	14.3451	−	27.3243i	0.670304	−	1.27678i
$459$	2.42272	+	0.649165i	0.113083	+	0.0303004i
$460$	−4.88132	+	26.6001i	−0.227593	+	1.24023i
$461$	24.2472	+	24.2472i	1.12931	+	1.12931i	0.990290	+	0.139015i	$0.0443936\pi$
$461$	24.2472	+	24.2472i	1.12931	+	1.12931i	0.139015	+	0.990290i	$0.455606\pi$
$462$	10.5601	+	12.7426i	0.491298	+	0.592840i
$463$			30.8810i			1.43516i	0.696475	+	0.717581i	$0.254751\pi$
$463$			30.8810i			1.43516i	−0.696475	+	0.717581i	$0.745249\pi$
$464$	−3.18376	+	4.41487i	−0.147802	+	0.204955i
$465$	0.924118	−	0.533540i	0.0428549	−	0.0247423i
$466$	4.53134	+	14.5478i	0.209910	+	0.673914i
$467$	6.35865	+	23.7308i	0.294243	+	1.09813i	0.941816	+	0.336128i	$0.109117\pi$
$467$	6.35865	+	23.7308i	0.294243	+	1.09813i	−0.647573	+	0.762004i	$0.724216\pi$
$468$	−6.40774	+	2.28188i	−0.296198	+	0.105480i
$469$	−4.45669	−	34.5578i	−0.205791	−	1.59573i
$470$	13.1645	+	20.8237i	0.607235	+	0.960524i
$471$	−1.65867	+	2.87291i	−0.0764277	+	0.132377i
$472$	5.04124	+	6.71377i	0.232042	+	0.309026i
$473$	−46.2089	+	26.6787i	−2.12469	+	1.22669i
$474$	−0.389042	−	9.68323i	−0.0178693	−	0.444766i
$475$	−3.33796	−	3.33796i	−0.153156	−	0.153156i
$476$	−11.1246	−	7.23819i	−0.509893	−	0.331762i
$477$	−1.08579	+	1.08579i	−0.0497151	+	0.0497151i
$478$	−1.58268	+	1.71518i	−0.0723901	+	0.0784505i
$479$	8.23156	+	14.2575i	0.376110	+	0.651441i	0.990492	−	0.137567i	$-0.0439282\pi$
$479$	8.23156	+	14.2575i	0.376110	+	0.651441i	−0.614383	+	0.789008i	$0.710595\pi$
$480$	−7.56814	+	11.4358i	−0.345437	+	0.521970i
$481$	−6.78468	−	3.91714i	−0.309355	−	0.178606i
$482$	24.5314	+	5.52806i	1.11737	+	0.251796i
$483$	−5.68368	+	13.6196i	−0.258616	+	0.619714i
$484$	−7.34598	+	15.4716i	−0.333908	+	0.703255i
$485$	−19.0541	+	5.10554i	−0.865204	+	0.231831i
$486$	0.657370	−	1.25214i	0.0298189	−	0.0567984i
$487$	5.37839	+	9.31565i	0.243718	+	0.422132i	0.961770	−	0.273857i	$-0.0882995\pi$
$487$	5.37839	+	9.31565i	0.243718	+	0.422132i	−0.718052	+	0.695989i	$0.754966\pi$
$488$	−2.46606	+	5.78220i	−0.111633	+	0.261748i
$489$	10.3961			0.470127
$490$	7.01548	+	22.9499i	0.316927	+	1.03677i
$491$	15.7656	−	15.7656i	0.711492	−	0.711492i	−0.255355	−	0.966847i	$-0.582192\pi$
$491$	15.7656	−	15.7656i	0.711492	−	0.711492i	0.966847	+	0.255355i	$0.0821925\pi$
$492$	0.524165	−	2.85636i	0.0236312	−	0.128775i
$493$	−0.883368	+	3.29677i	−0.0397849	+	0.148479i
$494$	−24.7263	+	7.70174i	−1.11249	+	0.346518i
$495$	5.36117	−	9.28582i	0.240967	−	0.417367i
$496$	−1.11290	−	1.36440i	−0.0499705	−	0.0612635i
$497$	−22.7157	+	9.33884i	−1.01894	+	0.418904i
$498$	20.9539	+	4.72189i	0.938968	+	0.211593i
$499$	15.2541	−	4.08733i	0.682868	−	0.182974i	0.0993235	−	0.995055i	$-0.468332\pi$
$499$	15.2541	−	4.08733i	0.682868	−	0.182974i	0.583544	+	0.812081i	$0.301665\pi$
$500$	−12.9564	+	15.2245i	−0.579428	+	0.680861i
$501$	−0.0235044	+	0.0877198i	−0.00105010	+	0.00391903i
$502$	−0.347574	−	8.65109i	−0.0155130	−	0.386117i
$503$			10.6906i			0.476669i	0.971183	+	0.238334i	$0.0766014\pi$
$503$			10.6906i			0.476669i	−0.971183	+	0.238334i	$0.923399\pi$
$504$	−5.36025	+	5.22185i	−0.238765	+	0.232600i
$505$			30.6823i			1.36535i
$506$	−34.8631	+	1.40069i	−1.54985	+	0.0622684i
$507$	−0.371009	+	1.38462i	−0.0164771	+	0.0614933i
$508$	−26.9721	+	2.17081i	−1.19669	+	0.0963142i
$509$	5.20253	−	1.39401i	0.230598	−	0.0617886i	−0.141669	−	0.989914i	$-0.545247\pi$
$509$	5.20253	−	1.39401i	0.230598	−	0.0617886i	0.372268	+	0.928125i	$0.378580\pi$
$510$	−1.89032	+	8.38849i	−0.0837046	+	0.371449i
$511$	5.89599	+	4.54898i	0.260823	+	0.201235i
$512$	20.6238	+	9.30914i	0.911450	+	0.411410i
$513$	2.69228	−	4.66317i	0.118867	−	0.205884i
$514$	2.33155	+	7.48540i	0.102840	+	0.330167i
$515$	6.54460	−	24.4248i	0.288390	−	1.07628i
$516$	−13.7008	−	19.8594i	−0.603145	−	0.874261i
$517$	−22.4748	+	22.4748i	−0.988441	+	0.988441i
$518$	−8.58153	−	0.803757i	−0.377051	−	0.0353150i
$519$	9.53001			0.418321
$520$	−8.69859	−	21.6360i	−0.381458	−	0.948803i
$521$	2.18217	+	3.77963i	0.0956027	+	0.165589i	0.909860	−	0.414915i	$-0.136189\pi$
$521$	2.18217	+	3.77963i	0.0956027	+	0.165589i	−0.814257	+	0.580504i	$0.802856\pi$
$522$	1.70389	+	0.894533i	0.0745771	+	0.0391527i
$523$	8.83993	−	2.36865i	0.386543	−	0.103574i	−0.0603136	−	0.998179i	$-0.519210\pi$
$523$	8.83993	−	2.36865i	0.386543	−	0.103574i	0.446857	+	0.894606i	$0.352543\pi$
$524$	−23.0623	+	8.21278i	−1.00748	+	0.358777i
$525$	1.84391	−	1.40715i	0.0804750	−	0.0614132i
$526$	−3.75271	+	16.6531i	−0.163626	+	0.726108i
$527$	−0.956136	−	0.552025i	−0.0416499	−	0.0240466i
$528$	−16.5395	−	6.28180i	−0.719789	−	0.273380i
$529$	−4.05703	−	7.02698i	−0.176392	−	0.305521i
$530$	−3.86889	−	3.57002i	−0.168054	−	0.155072i
$531$	2.09894	−	2.09894i	0.0910862	−	0.0910862i
$532$	−21.1906	+	19.0466i	−0.918731	+	0.825777i
$533$	3.49190	+	3.49190i	0.151251	+	0.151251i
$534$	−23.9866	+	0.963709i	−1.03800	+	0.0417038i
$535$	−40.4949	+	23.3797i	−1.75075	+	1.01079i
$536$	22.3667	+	29.7873i	0.966094	+	1.28661i
$537$	−1.43305	+	2.48211i	−0.0618405	+	0.107111i
$538$	38.8294	−	24.5476i	1.67405	−	1.05832i
$539$	−26.8949	+	15.3387i	−1.15845	+	0.660684i
$540$	4.37976	+	2.07953i	0.188475	+	0.0894886i
$541$	−1.46654	−	5.47321i	−0.0630515	−	0.235311i	0.927208	−	0.374548i	$-0.122202\pi$
$541$	−1.46654	−	5.47321i	−0.0630515	−	0.235311i	−0.990259	+	0.139236i	$0.955535\pi$
$542$	20.9451	−	6.52396i	0.899668	−	0.280228i
$543$	15.4209	−	8.90326i	0.661774	−	0.382075i
$544$	14.1620	+	0.865280i	0.607191	+	0.0370986i
$545$		−	35.4287i		−	1.51760i
$546$	−2.13295	−	12.5452i	−0.0912817	−	0.536885i
$547$	−0.185636	−	0.185636i	−0.00793721	−	0.00793721i	0.703127	−	0.711064i	$-0.251787\pi$
$547$	−0.185636	−	0.185636i	−0.00793721	−	0.00793721i	−0.711064	+	0.703127i	$0.751787\pi$
$548$	15.1652	+	21.9821i	0.647827	+	0.939027i
$549$	2.14675	+	0.575220i	0.0916211	+	0.0245498i
$550$	4.85539	+	2.54906i	0.207034	+	0.108692i
$551$	6.34553	+	3.66359i	0.270328	+	0.156074i
$552$	−1.89599	−	15.6626i	−0.0806988	−	0.666645i
$553$	17.9689	+	2.41400i	0.764114	+	0.102654i
$554$	29.3244	−	18.5386i	1.24587	−	0.787631i
$555$	1.44531	+	5.39395i	0.0613498	+	0.228961i
$556$	22.4890	−	26.4259i	0.953747	−	1.12071i
$557$	−1.19244	−	0.319513i	−0.0505252	−	0.0135382i	0.233468	−	0.972365i	$-0.424993\pi$
$557$	−1.19244	−	0.319513i	−0.0505252	−	0.0135382i	−0.283993	+	0.958826i	$0.591659\pi$
$558$	−0.422154	+	0.457496i	−0.0178712	+	0.0193673i
$559$	41.0274			1.73527
$560$	−18.6255	−	17.6432i	−0.787069	−	0.745560i
$561$	−11.0938			−0.468382
$562$	−4.74350	+	5.14061i	−0.200093	+	0.216844i
$563$	−26.4419	−	7.08508i	−1.11439	−	0.298601i	−0.345780	−	0.938315i	$-0.612386\pi$
$563$	−26.4419	−	7.08508i	−1.11439	−	0.298601i	−0.768612	+	0.639715i	$0.779052\pi$
$564$	−10.9451	−	9.31452i	−0.460871	−	0.392212i
$565$	−6.44965	−	24.0704i	−0.271339	−	1.01265i
$566$	−15.9946	+	10.1117i	−0.672305	+	0.425025i
$567$	2.09475	+	1.61618i	0.0879712	+	0.0678730i
$568$	16.2003	−	20.6626i	0.679747	−	0.866982i
$569$	3.97832	+	2.29689i	0.166780	+	0.0962905i	0.581067	−	0.813856i	$-0.302636\pi$
$569$	3.97832	+	2.29689i	0.166780	+	0.0962905i	−0.414287	+	0.910146i	$0.635969\pi$
$570$	16.3445	+	8.58078i	0.684595	+	0.359409i
$571$	−27.3547	−	7.32966i	−1.14476	−	0.306737i	−0.363895	−	0.931440i	$-0.618553\pi$
$571$	−27.3547	−	7.32966i	−1.14476	−	0.306737i	−0.780862	+	0.624703i	$0.785220\pi$
$572$	24.7639	−	17.0844i	1.03543	−	0.714335i
$573$	3.41683	+	3.41683i	0.142740	+	0.142740i
$574$	5.09387	+	1.88942i	0.212614	+	0.0788627i
$575$			4.89018i			0.203934i
$576$	2.23134	−	7.68252i	0.0929726	−	0.320105i
$577$	−21.8849	+	12.6352i	−0.911079	+	0.526012i	−0.880778	−	0.473529i	$-0.842980\pi$
$577$	−21.8849	+	12.6352i	−0.911079	+	0.526012i	−0.0303008	+	0.999541i	$0.509647\pi$
$578$	−14.4597	+	4.50388i	−0.601443	+	0.187337i
$579$	−5.26429	−	19.6466i	−0.218776	−	0.816485i
$580$	−2.82977	+	5.95988i	−0.117500	+	0.247470i
$581$	−15.4760	+	37.0846i	−0.642051	+	1.53853i
$582$	9.72707	−	6.14937i	0.403200	−	0.254900i
$583$	3.39591	−	5.88189i	0.140644	−	0.243603i
$584$	−7.88166	−	1.12142i	−0.326145	−	0.0464047i
$585$	−7.14001	+	4.12228i	−0.295203	+	0.170435i
$586$	25.2439	−	1.01422i	1.04282	−	0.0418971i
$587$	−7.69114	−	7.69114i	−0.317447	−	0.317447i	0.530339	−	0.847786i	$-0.322065\pi$
$587$	−7.69114	−	7.69114i	−0.317447	−	0.317447i	−0.847786	+	0.530339i	$0.822065\pi$
$588$	−7.88905	−	11.5656i	−0.325339	−	0.476957i
$589$	−1.67597	+	1.67597i	−0.0690570	+	0.0690570i
$590$	7.47891	+	6.90116i	0.307902	+	0.284116i
$591$	10.0162	+	17.3486i	0.412012	+	0.713626i
$592$	8.40425	−	3.77754i	0.345413	−	0.155256i
$593$	−21.9302	−	12.6614i	−0.900564	−	0.519941i	−0.0231811	−	0.999731i	$-0.507379\pi$
$593$	−21.9302	−	12.6614i	−0.900564	−	0.519941i	−0.877383	+	0.479790i	$0.840713\pi$
$594$	−1.37509	+	6.10214i	−0.0564208	+	0.250374i
$595$	−14.8461	−	6.19550i	−0.608630	−	0.253991i
$596$	−2.20018	−	6.17831i	−0.0901227	−	0.253074i
$597$	23.4199	−	6.27534i	0.958512	−	0.256832i
$598$	23.7539	+	12.4707i	0.971368	+	0.509964i
$599$	−19.1368	−	33.1459i	−0.781907	−	1.35430i	−0.930829	−	0.365455i	$-0.880914\pi$
$599$	−19.1368	−	33.1459i	−0.781907	−	1.35430i	0.148922	−	0.988849i	$-0.452420\pi$
$600$	−0.972773	+	2.28088i	−0.0397133	+	0.0931164i
$601$	−12.9002			−0.526211			−0.263105	−	0.964767i	$-0.584747\pi$
$601$	−12.9002			−0.526211			−0.263105	+	0.964767i	$0.584747\pi$
$602$	41.0244	−	18.8251i	1.67203	−	0.767252i
$603$	9.31246	−	9.31246i	0.379233	−	0.379233i
$604$	39.6171	−	27.3315i	1.61200	−	1.11210i
$605$	−5.37296	+	20.0522i	−0.218442	+	0.815237i
$606$	−5.32303	−	17.0895i	−0.216233	−	0.694214i
$607$	−14.1850	+	24.5692i	−0.575753	+	0.997233i	0.420207	+	0.907428i	$0.361957\pi$
$607$	−14.1850	+	24.5692i	−0.575753	+	0.997233i	−0.995959	+	0.0898043i	$0.971376\pi$
$608$	9.66316	−	28.8862i	0.391893	−	1.17149i
$609$	−2.19925	+	2.85048i	−0.0891183	+	0.115507i
$610$	−1.67500	+	7.43298i	−0.0678186	+	0.300953i
$611$	23.6066	−	6.32537i	0.955020	−	0.255897i
$612$	−0.402434	−	5.00019i	−0.0162674	−	0.202121i
$613$	−5.07704	+	18.9478i	−0.205060	+	0.765294i	0.784371	+	0.620291i	$0.212986\pi$
$613$	−5.07704	+	18.9478i	−0.205060	+	0.765294i	−0.989431	+	0.145002i	$0.953681\pi$
$614$	−29.9249	+	1.20229i	−1.20767	+	0.0485205i
$615$		−	3.51999i		−	0.141940i
$616$	16.9230	−	28.4458i	0.681849	−	1.14612i
$617$			8.08504i			0.325491i	0.986668	+	0.162746i	$0.0520350\pi$
$617$			8.08504i			0.325491i	−0.986668	+	0.162746i	$0.947965\pi$
$618$	0.592191	+	14.7396i	0.0238214	+	0.592913i
$619$	1.29605	−	4.83693i	0.0520927	−	0.194413i	−0.934976	−	0.354712i	$-0.884579\pi$
$619$	1.29605	−	4.83693i	0.0520927	−	0.194413i	0.987069	+	0.160299i	$0.0512458\pi$
$620$	−1.62528	−	1.38315i	−0.0652728	−	0.0555486i
$621$	−5.38793	+	1.44369i	−0.216210	+	0.0579334i
$622$	−22.9319	−	5.16763i	−0.919487	−	0.207203i
$623$	5.97980	−	44.5112i	0.239576	−	1.78330i
$624$	8.59856	+	10.5418i	0.344218	+	0.422009i
$625$	−14.3074	+	24.7812i	−0.572297	+	0.991248i
$626$	−42.9166	+	13.3676i	−1.71529	+	0.534279i
$627$	−6.16410	+	23.0047i	−0.246170	+	0.918721i
$628$	6.52573	+	1.19752i	0.260405	+	0.0477864i
$629$	4.08546	−	4.08546i	0.162898	−	0.162898i
$630$	−5.24801	+	7.39811i	−0.209086	+	0.294748i
$631$	10.1186			0.402814			0.201407	−	0.979508i	$-0.435449\pi$
$631$	10.1186			0.402814			0.201407	+	0.979508i	$0.435449\pi$
$632$	−17.9831	+	7.22997i	−0.715330	+	0.287593i
$633$	−8.99583	−	15.5812i	−0.357552	−	0.619299i
$634$	−6.06757	+	11.5574i	−0.240974	+	0.459002i
$635$	−31.6808	+	8.48885i	−1.25722	+	0.336870i
$636$	2.77426	+	1.31723i	0.110007	+	0.0522315i
$637$	23.8064	+	0.125911i	0.943244	+	0.00498877i
$638$	−8.30365	−	1.87120i	−0.328745	−	0.0740814i
$639$	−8.03930	−	4.64149i	−0.318030	−	0.183615i
$640$	26.6240	+	6.58626i	1.05241	+	0.260345i
$641$	16.8383	+	29.1648i	0.665073	+	1.15194i	0.979265	+	0.202581i	$0.0649331\pi$
$641$	16.8383	+	29.1648i	0.665073	+	1.15194i	−0.314192	+	0.949359i	$0.601734\pi$
$642$	18.4988	−	20.0475i	0.730091	−	0.791212i
$643$	−0.913474	+	0.913474i	−0.0360239	+	0.0360239i	−0.724889	−	0.688865i	$-0.758109\pi$
$643$	−0.913474	+	0.913474i	−0.0360239	+	0.0360239i	0.688865	+	0.724889i	$0.258109\pi$
$644$	29.4742	+	1.57050i	1.16145	+	0.0618863i
$645$	−20.6787	−	20.6787i	−0.814223	−	0.814223i
$646$	−0.766744	−	19.0842i	−0.0301671	−	0.750857i
$647$	14.2145	−	8.20676i	0.558831	−	0.322641i	−0.193845	−	0.981032i	$-0.562096\pi$
$647$	14.2145	−	8.20676i	0.558831	−	0.322641i	0.752676	+	0.658391i	$0.228763\pi$
$648$	−2.80022	−	0.398422i	−0.110003	−	0.0156515i
$649$	−6.56460	+	11.3702i	−0.257683	+	0.446320i
$650$	−2.25320	−	3.56411i	−0.0883777	−	0.139796i
$651$	−0.706522	−	0.925816i	−0.0276908	−	0.0362856i
$652$	−6.97526	−	19.5872i	−0.273172	−	0.767096i
$653$	−4.36057	−	16.2739i	−0.170642	−	0.636846i	−0.997253	−	0.0740717i	$-0.976401\pi$
$653$	−4.36057	−	16.2739i	−0.170642	−	0.636846i	0.826611	−	0.562774i	$-0.190266\pi$
$654$	6.14647	+	19.7332i	0.240346	+	0.771628i
$655$	−25.6978	+	14.8366i	−1.00410	+	0.579716i
$656$	−5.73335	+	0.928900i	−0.223850	+	0.0362675i
$657$			2.81465i			0.109810i
$658$	20.7025	−	17.1566i	0.807068	−	0.668833i
$659$	−10.3214	−	10.3214i	−0.402065	−	0.402065i	0.476895	−	0.878960i	$-0.341762\pi$
$659$	−10.3214	−	10.3214i	−0.402065	−	0.402065i	−0.878960	+	0.476895i	$0.841762\pi$
$660$	−21.0925	−	3.87064i	−0.821024	−	0.150664i
$661$	−23.1791	−	6.21082i	−0.901562	−	0.241573i	−0.221875	−	0.975075i	$-0.571218\pi$
$661$	−23.1791	−	6.21082i	−0.901562	−	0.241573i	−0.679687	+	0.733502i	$0.737884\pi$
$662$	−9.90870	+	18.8739i	−0.385113	+	0.733554i
$663$	7.38739	+	4.26511i	0.286902	+	0.165643i
$664$	−5.16256	−	42.6474i	−0.200346	−	1.65504i
$665$	−21.0963	+	27.3432i	−0.818078	+	1.06032i
$666$	−1.74080	−	2.75359i	−0.0674546	−	0.106700i
$667$	−1.96454	−	7.33177i	−0.0760674	−	0.283887i
$668$	0.181043	−	0.0145710i	0.00700476	−	0.000563769i
$669$	−1.82869	−	0.489997i	−0.0707014	−	0.0189444i
$670$	33.1820	+	30.6187i	1.28193	+	1.18290i
$671$	−9.83017			−0.379490
$672$	13.4349	+	6.59563i	0.518264	+	0.254432i
$673$	19.5621			0.754063			0.377031	−	0.926201i	$-0.376945\pi$
$673$	19.5621			0.754063			0.377031	+	0.926201i	$0.376945\pi$
$674$	11.7418	+	10.8347i	0.452275	+	0.417337i
$675$	0.846818	+	0.226904i	0.0325940	+	0.00873354i
$676$	2.85770	−	0.229998i	0.109911	−	0.00884607i
$677$	−5.58828	−	20.8557i	−0.214775	−	0.801551i	−0.986246	−	0.165286i	$-0.947145\pi$
$677$	−5.58828	−	20.8557i	−0.214775	−	0.801551i	0.771471	−	0.636265i	$-0.219521\pi$
$678$	7.76828	+	12.2879i	0.298339	+	0.471912i
$679$	8.18625	+	19.9121i	0.314159	+	0.764157i
$680$	17.0731	−	2.06673i	0.654722	−	0.0792554i
$681$	15.2665	+	8.81412i	0.585014	+	0.337758i
$682$	1.27986	−	2.43785i	0.0490085	−	0.0933503i
$683$	−15.6221	−	4.18594i	−0.597764	−	0.160170i	−0.0527649	−	0.998607i	$-0.516803\pi$
$683$	−15.6221	−	4.18594i	−0.597764	−	0.160170i	−0.544999	+	0.838437i	$0.683470\pi$
$684$	−10.5922	−	1.94376i	−0.405005	−	0.0743216i
$685$	22.8889	+	22.8889i	0.874541	+	0.874541i
$686$	23.8624	−	10.7975i	0.911071	−	0.412249i
$687$			21.8220i			0.832562i
$688$	−28.2245	+	39.1384i	−1.07605	+	1.49214i
$689$	−4.52267	+	2.61117i	−0.172300	+	0.0994775i
$690$	−5.68698	−	18.2580i	−0.216500	−	0.695069i
$691$	−6.69444	−	24.9840i	−0.254668	−	0.950435i	−0.968275	−	0.249888i	$-0.919606\pi$
$691$	−6.69444	−	24.9840i	−0.254668	−	0.950435i	0.713606	−	0.700547i	$-0.247061\pi$
$692$	−6.39417	−	17.9555i	−0.243070	−	0.682565i
$693$	−10.7997	−	4.50686i	−0.410245	−	0.171202i
$694$	−19.0049	−	30.0620i	−0.721417	−	1.14114i
$695$	21.0298	−	36.4246i	0.797705	−	1.38167i
$696$	0.542163	−	3.81048i	0.0205506	−	0.144436i
$697$	−3.15402	+	1.82097i	−0.119467	+	0.0689743i
$698$	−0.435146	−	10.8307i	−0.0164705	−	0.409950i
$699$	−7.61859	−	7.61859i	−0.288162	−	0.288162i
$700$	−3.88839	−	2.52998i	−0.146967	−	0.0956244i
$701$	−10.5374	+	10.5374i	−0.397991	+	0.397991i	−0.877524	−	0.479533i	$-0.840806\pi$
$701$	−10.5374	+	10.5374i	−0.397991	+	0.397991i	0.479533	+	0.877524i	$0.340806\pi$
$702$	3.26169	−	3.53475i	0.123105	−	0.133410i
$703$	−6.20179	−	10.7418i	−0.233905	−	0.405136i
$704$	−0.738335	+	35.3768i	−0.0278270	+	1.33331i
$705$	−15.0864	−	8.71012i	−0.568186	−	0.328042i
$706$	23.7108	+	5.34313i	0.892366	+	0.201091i
$707$	33.2116	−	4.28307i	1.24905	−	0.161081i
$708$	−5.36289	−	2.54632i	−0.201550	−	0.0956966i
$709$	35.6627	−	9.55579i	1.33934	−	0.358875i	0.483151	−	0.875537i	$-0.339492\pi$
$709$	35.6627	−	9.55579i	1.33934	−	0.358875i	0.856190	+	0.516661i	$0.172825\pi$
$710$	14.7933	−	28.1779i	0.555181	−	1.05750i
$711$	3.42630	+	5.93453i	0.128496	+	0.222562i
$712$	17.9096	+	44.5466i	0.671190	+	1.66945i
$713$	2.45532			0.0919525
$714$	9.34386	+	0.875158i	0.349685	+	0.0327520i
$715$	25.7855	−	25.7855i	0.964325	−	0.964325i
$716$	5.63804	+	1.03463i	0.210703	+	0.0386658i
$717$	0.427119	−	1.59403i	0.0159510	−	0.0595301i
$718$	33.0823	−	10.3044i	1.23462	−	0.384559i
$719$	14.9264	−	25.8532i	0.556659	−	0.964162i	−0.441113	−	0.897451i	$-0.645416\pi$
$719$	14.9264	−	25.8532i	0.556659	−	0.964162i	0.997772	−	0.0667105i	$-0.0212504\pi$
$720$	0.979427	−	9.64716i	0.0365011	−	0.359529i
$721$	−27.3518	−	3.67454i	−1.01863	−	0.136847i
$722$	−13.7872	−	3.10690i	−0.513107	−	0.115627i
$723$	−17.1754	+	4.60214i	−0.638760	+	0.171155i
$724$	−27.1213	−	23.0808i	−1.00795	−	0.857792i
$725$	−0.308766	+	1.15233i	−0.0114673	+	0.0427964i
$726$	−0.486175	−	12.1009i	−0.0180436	−	0.449105i
$727$		−	10.1945i		−	0.378092i	−0.981968	−	0.189046i	$-0.939460\pi$
$727$		−	10.1945i		−	0.378092i	0.981968	−	0.189046i	$-0.0605395\pi$
$728$	−22.2053	+	12.4359i	−0.822982	+	0.460905i
$729$			1.00000i			0.0370370i
$730$	−9.64175	+	0.387376i	−0.356857	+	0.0143374i
$731$	−7.83118	+	29.2263i	−0.289647	+	1.08098i
$732$	−0.356594	−	4.43063i	−0.0131801	−	0.163761i
$733$	−20.2914	+	5.43706i	−0.749480	+	0.200823i	−0.613287	−	0.789860i	$-0.710153\pi$
$733$	−20.2914	+	5.43706i	−0.749480	+	0.200823i	−0.136192	+	0.990682i	$0.543487\pi$
$734$	1.69250	−	7.51065i	0.0624712	−	0.277223i
$735$	−11.9355	−	12.0624i	−0.440247	−	0.444929i
$736$	−28.2378	+	14.0811i	−1.04086	+	0.519036i
$737$	−29.1254	+	50.4467i	−1.07285	+	1.85823i
$738$	0.610678	+	1.96057i	0.0224794	+	0.0721697i
$739$	12.4173	−	46.3419i	0.456777	−	1.70471i	−0.226034	−	0.974119i	$-0.572576\pi$
$739$	12.4173	−	46.3419i	0.456777	−	1.70471i	0.682811	−	0.730595i	$-0.260757\pi$
$740$	9.19301	−	6.34218i	0.337942	−	0.233143i
$741$	12.9490	−	12.9490i	0.475694	−	0.475694i
$742$	−3.32423	+	4.68616i	−0.122036	+	0.172034i
$743$	47.1641			1.73028			0.865141	−	0.501528i	$-0.167229\pi$
$743$	47.1641			1.73028			0.865141	+	0.501528i	$0.167229\pi$
$744$	1.14521	+	0.488423i	0.0419855	+	0.0179064i
$745$	−3.97469	−	6.88436i	−0.145621	−	0.252223i
$746$	−3.68049	−	1.93224i	−0.134752	−	0.0707444i
$747$	−14.6707	+	3.93100i	−0.536772	+	0.143828i
$748$	7.44343	+	20.9019i	0.272159	+	0.764249i
$749$	30.9598	+	40.5693i	1.13125	+	1.48237i
$750$	3.10758	−	13.7902i	0.113473	−	0.503548i
$751$	−28.9955	−	16.7406i	−1.05806	−	0.610872i	−0.133166	−	0.991094i	$-0.542514\pi$
$751$	−28.9955	−	16.7406i	−1.05806	−	0.610872i	−0.924896	+	0.380221i	$0.875848\pi$
$752$	−10.2058	+	26.8712i	−0.372169	+	0.979892i
$753$	3.06109	+	5.30196i	0.111552	+	0.193214i
$754$	4.81000	+	4.43843i	0.175170	+	0.161638i
$755$	41.2516	−	41.2516i	1.50130	−	1.50130i
$756$	1.63956	−	5.03109i	0.0596302	−	0.182979i
$757$	−24.0059	−	24.0059i	−0.872508	−	0.872508i	0.120237	−	0.992745i	$-0.461635\pi$
$757$	−24.0059	−	24.0059i	−0.872508	−	0.872508i	−0.992745	+	0.120237i	$0.961635\pi$
$758$	40.1519	−	1.61318i	1.45838	−	0.0585933i
$759$	21.3664	−	12.3359i	0.775553	−	0.447766i
$760$	5.20068	−	36.5519i	0.188648	−	1.32588i
$761$	17.2157	−	29.8186i	0.624070	−	1.08092i	−0.364649	−	0.931145i	$-0.618811\pi$
$761$	17.2157	−	29.8186i	0.624070	−	1.08092i	0.988720	−	0.149777i	$-0.0478555\pi$
$762$	16.1729	−	10.2244i	0.585884	−	0.370391i
$763$	−38.3492	+	4.94563i	−1.38833	+	0.179044i
$764$	4.14512	−	8.73017i	0.149965	−	0.315847i
$765$	−1.57370	−	5.87312i	−0.0568972	−	0.212343i
$766$	−42.9268	+	13.3708i	−1.55101	+	0.483107i
$767$	8.74273	−	5.04762i	0.315682	−	0.182259i
$768$	−15.9717	+	0.950529i	−0.576331	+	0.0342993i
$769$			24.5562i			0.885518i	0.896641	+	0.442759i	$0.146000\pi$
$769$			24.5562i			0.885518i	−0.896641	+	0.442759i	$0.854000\pi$
$770$	13.9522	−	37.6151i	0.502801	−	1.35555i
$771$	−3.92006	−	3.92006i	−0.141177	−	0.141177i
$772$	−33.4840	+	23.1003i	−1.20512	+	0.831400i
$773$	2.55607	+	0.684896i	0.0919354	+	0.0246340i	0.304493	−	0.952514i	$-0.401513\pi$
$773$	2.55607	+	0.684896i	0.0919354	+	0.0246340i	−0.212558	+	0.977148i	$0.568179\pi$
$774$	15.1052	+	7.93016i	0.542945	+	0.285044i
$775$	−0.334200	−	0.192951i	−0.0120048	−	0.00693099i
$776$	−18.1124	−	14.2008i	−0.650198	−	0.509780i
$777$	5.63684	−	2.31741i	0.202220	−	0.0831366i
$778$	2.09271	−	1.32299i	0.0750274	−	0.0474317i
$779$	2.02359	+	7.55213i	0.0725025	+	0.270583i
$780$	12.5574	+	10.6866i	0.449626	+	0.382642i
$781$	39.6602	+	10.6269i	1.41915	+	0.380261i
$782$	−13.4177	+	14.5410i	−0.479816	+	0.519985i
$783$	−1.36078			−0.0486302
$784$	−16.4975	+	22.6237i	−0.589198	+	0.807989i
$785$	8.04188			0.287027
$786$	11.7392	−	12.7220i	0.418725	−	0.453780i
$787$	−3.81281	−	1.02164i	−0.135912	−	0.0364175i	0.190222	−	0.981741i	$-0.439079\pi$
$787$	−3.81281	−	1.02164i	−0.135912	−	0.0364175i	−0.326134	+	0.945324i	$0.605746\pi$
$788$	25.9661	−	30.5116i	0.925003	−	1.08693i
$789$	−3.12415	−	11.6595i	−0.111223	−	0.415088i
$790$	−19.8575	+	12.5537i	−0.706498	+	0.446642i
$791$	−25.1543	+	10.3414i	−0.894382	+	0.367697i
$792$	12.4196	−	1.50342i	0.441313	−	0.0534218i
$793$	6.54591	+	3.77928i	0.232452	+	0.134206i
$794$	5.42987	+	2.85066i	0.192699	+	0.101166i
$795$	3.59561	+	0.963442i	0.127523	+	0.0341698i
$796$	−27.5369	−	39.9149i	−0.976021	−	1.41475i
$797$	−21.2467	−	21.2467i	−0.752597	−	0.752597i	0.222366	−	0.974963i	$-0.428622\pi$
$797$	−21.2467	−	21.2467i	−0.752597	−	0.752597i	−0.974963	+	0.222366i	$0.928622\pi$
$798$	7.00652	−	18.8896i	0.248028	−	0.668685i
$799$			18.0238i			0.637637i
$800$	4.95008	+	0.302443i	0.175012	+	0.0106930i
$801$	14.7006	−	8.48740i	0.519420	−	0.299887i
$802$	−14.7539	+	4.59552i	−0.520977	+	0.162274i
$803$	−3.22214	−	12.0252i	−0.113707	−	0.424360i
$804$	−23.7938	−	11.2974i	−0.839142	−	0.398428i
$805$	35.4823	−	4.57591i	1.25059	−	0.161280i
$806$	−1.78951	+	1.13131i	−0.0630329	+	0.0398488i
$807$	−16.2416	+	28.1312i	−0.571730	+	0.990265i
$808$	−28.6268	+	21.4953i	−1.00709	+	0.756203i
$809$	2.97214	−	1.71596i	0.104495	−	0.0603300i	−0.446842	−	0.894613i	$-0.647451\pi$
$809$	2.97214	−	1.71596i	0.104495	−	0.0603300i	0.551337	+	0.834283i	$0.314118\pi$
$810$	−3.42556	+	0.137628i	−0.120362	+	0.00483576i
$811$	3.81271	+	3.81271i	0.133882	+	0.133882i	0.770872	−	0.636990i	$-0.219821\pi$
$811$	3.81271	+	3.81271i	0.133882	+	0.133882i	−0.636990	+	0.770872i	$0.719821\pi$
$812$	6.84618	+	2.23107i	0.240254	+	0.0782954i
$813$	−10.9688	+	10.9688i	−0.384693	+	0.384693i
$814$	10.5895	+	9.77150i	0.371163	+	0.342491i
$815$	−12.6010	−	21.8256i	−0.441395	−	0.764519i
$816$	−9.15084	+	4.11311i	−0.320343	+	0.143988i
$817$	56.2539	+	32.4782i	1.96808	+	1.13627i
$818$	2.32049	−	10.2975i	0.0811342	−	0.360042i
$819$	5.45880	+	7.15313i	0.190746	+	0.249951i
$820$	−6.63201	+	2.36174i	−0.231600	+	0.0824756i
$821$	−34.7236	+	9.30415i	−1.21186	+	0.324717i	−0.807492	−	0.589879i	$-0.799176\pi$
$821$	−34.7236	+	9.30415i	−1.21186	+	0.324717i	−0.404369	+	0.914596i	$0.632509\pi$
$822$	−16.7197	−	8.77777i	−0.583167	−	0.306160i
$823$	−4.80101	−	8.31559i	−0.167353	−	0.289863i	0.770136	−	0.637880i	$-0.220189\pi$
$823$	−4.80101	−	8.31559i	−0.167353	−	0.289863i	−0.937488	+	0.348017i	$0.886855\pi$
$824$	27.3735	−	11.0053i	0.953601	−	0.383387i
$825$	−3.87766			−0.135003
$826$	6.42603	−	9.05878i	0.223590	−	0.315195i
$827$	−0.959658	+	0.959658i	−0.0333706	+	0.0333706i	−0.723595	−	0.690225i	$-0.757512\pi$
$827$	−0.959658	+	0.959658i	−0.0333706	+	0.0333706i	0.690225	+	0.723595i	$0.257512\pi$
$828$	6.33510	+	9.18274i	0.220160	+	0.319122i
$829$	−5.83081	+	21.7609i	−0.202512	+	0.755786i	0.787681	+	0.616083i	$0.211281\pi$
$829$	−5.83081	+	21.7609i	−0.202512	+	0.755786i	−0.990193	+	0.139703i	$0.955385\pi$
$830$	−15.4850	−	49.7143i	−0.537491	−	1.72561i
$831$	−12.2658	+	21.2450i	−0.425496	+	0.736981i
$832$	14.0925	−	23.2736i	0.488571	−	0.806865i
$833$	−4.63378	+	16.9347i	−0.160551	+	0.586754i
$834$	−5.39396	+	23.9363i	−0.186778	+	0.828847i
$835$	0.212649	−	0.0569792i	0.00735903	−	0.00197185i
$836$	47.4790	−	3.82129i	1.64210	−	0.132162i
$837$	0.113927	−	0.425181i	0.00393789	−	0.0146964i
$838$	11.0628	−	0.444469i	0.382158	−	0.0153539i
$839$			23.1481i			0.799162i	0.916698	+	0.399581i	$0.130844\pi$
$839$			23.1481i			0.799162i	−0.916698	+	0.399581i	$0.869156\pi$
$840$	17.4599	+	4.92399i	0.602425	+	0.169894i
$841$			27.1483i			0.936148i
$842$	−0.663401	−	16.5120i	−0.0228623	−	0.569041i
$843$	1.28013	−	4.77751i	0.0440900	−	0.164546i
$844$	−23.3208	+	27.4033i	−0.802736	+	0.943260i
$845$	3.35659	−	0.899395i	0.115470	−	0.0309401i
$846$	9.91395	+	2.23407i	0.340849	+	0.0768090i
$847$	22.4552	+	3.01671i	0.771568	+	0.103655i
$848$	0.620395	−	6.11077i	0.0213045	−	0.209845i
$849$	6.69024	−	11.5878i	0.229608	−	0.397693i
$850$	2.96902	−	0.924788i	0.101836	−	0.0317200i
$851$	−3.32561	+	12.4114i	−0.114001	+	0.425456i
$852$	−3.35105	+	18.2610i	−0.114805	+	0.625613i
$853$	−3.49507	+	3.49507i	−0.119669	+	0.119669i	−0.764405	−	0.644736i	$-0.776967\pi$
$853$	−3.49507	+	3.49507i	−0.119669	+	0.119669i	0.644736	+	0.764405i	$0.276967\pi$
$854$	8.27952	+	0.775471i	0.283319	+	0.0265361i
$855$	−13.0532			−0.446410
$856$	−50.1833	−	21.4027i	−1.71523	−	0.731530i
$857$	1.00286	+	1.73701i	0.0342571	+	0.0593351i	0.882646	−	0.470039i	$-0.155760\pi$
$857$	1.00286	+	1.73701i	0.0342571	+	0.0593351i	−0.848389	+	0.529374i	$0.822427\pi$
$858$	−9.88860	+	18.8356i	−0.337591	+	0.643036i
$859$	−31.0122	+	8.30968i	−1.05812	+	0.283523i	−0.745604	−	0.666389i	$-0.767839\pi$
$859$	−31.0122	+	8.30968i	−1.05812	+	0.283523i	−0.312517	+	0.949912i	$0.601172\pi$
$860$	−25.0863	+	52.8351i	−0.855436	+	1.80166i
$861$	−3.81015	+	0.491369i	−0.129850	+	0.0167458i
$862$	−9.72277	−	2.19099i	−0.331159	−	0.0746254i
$863$	−5.25318	−	3.03293i	−0.178820	−	0.103242i	0.407918	−	0.913019i	$-0.366255\pi$
$863$	−5.25318	−	3.03293i	−0.178820	−	0.103242i	−0.586738	+	0.809777i	$0.699588\pi$
$864$	1.12815	+	5.54322i	0.0383804	+	0.188584i
$865$	−11.5513	−	20.0074i	−0.392755	−	0.680272i
$866$	−3.25540	+	3.52793i	−0.110623	+	0.119884i
$867$	7.57243	−	7.57243i	0.257173	−	0.257173i
$868$	−1.27029	+	1.95233i	−0.0431163	+	0.0662665i
$869$	−21.4321	−	21.4321i	−0.727033	−	0.727033i
$870$	−0.187281	−	4.66142i	−0.00634943	−	0.158037i
$871$	38.7893	−	22.3950i	1.31432	−	0.758825i
$872$	33.0552	−	24.8205i	1.11939	−	0.840530i
$873$	−4.06864	+	7.04709i	−0.137703	+	0.238508i
$874$	22.6976	+	35.9030i	0.767758	+	1.21444i
$875$	24.4061	+	10.1851i	0.825078	+	0.344318i
$876$	5.30308	−	1.88849i	0.179174	−	0.0638063i
$877$	−10.4367	−	38.9504i	−0.352423	−	1.31526i	−0.883697	−	0.468060i	$-0.844953\pi$
$877$	−10.4367	−	38.9504i	−0.352423	−	1.31526i	0.531274	−	0.847200i	$-0.321714\pi$
$878$	1.13725	+	3.65112i	0.0383802	+	0.123219i
$879$	−15.4711	+	8.93227i	−0.521829	+	0.301278i
$880$	6.85936	+	42.3373i	0.231229	+	1.42719i
$881$			26.1054i			0.879514i	0.898117	+	0.439757i	$0.144935\pi$
$881$			26.1054i			0.879514i	−0.898117	+	0.439757i	$0.855065\pi$
$882$	8.74055	+	4.64788i	0.294310	+	0.156502i
$883$	14.7022	+	14.7022i	0.494768	+	0.494768i	0.909805	−	0.415037i	$-0.136231\pi$
$883$	14.7022	+	14.7022i	0.494768	+	0.494768i	−0.415037	+	0.909805i	$0.636231\pi$
$884$	3.07931	−	16.7802i	0.103568	−	0.564381i
$885$	−6.95065	−	1.86242i	−0.233643	−	0.0626046i
$886$	3.68577	−	7.02058i	0.123826	−	0.235861i
$887$	−30.3666	−	17.5322i	−1.01961	−	0.588673i	−0.105620	−	0.994407i	$-0.533683\pi$
$887$	−30.3666	−	17.5322i	−1.01961	−	0.588673i	−0.913991	+	0.405733i	$0.867016\pi$
$888$	−4.02005	+	5.12736i	−0.134904	+	0.172063i
$889$	13.6111	+	33.1074i	0.456500	+	1.11039i
$890$	31.0973	+	49.1897i	1.04238	+	1.64884i
$891$	−1.14477	−	4.27235i	−0.0383513	−	0.143129i
$892$	0.303762	+	3.77420i	0.0101707	+	0.126370i
$893$	37.3751	+	10.0146i	1.25071	+	0.335126i
$894$	3.40819	+	3.14491i	0.113987	+	0.105181i
$895$	6.94795			0.232244
$896$	3.41263	−	29.7381i	0.114008	−	0.993480i
$897$	−18.9705			−0.633408
$898$	16.7209	+	15.4292i	0.557983	+	0.514878i
$899$	0.578576	+	0.155029i	0.0192966	+	0.00517051i
$900$	−0.140664	−	1.74773i	−0.00468879	−	0.0582576i
$901$	−0.996822	−	3.72019i	−0.0332090	−	0.123938i
$902$	−4.85344	−	7.67717i	−0.161602	−	0.255622i
$903$	−19.4967	+	25.2699i	−0.648809	+	0.840931i
$904$	17.9394	−	22.8807i	0.596655	−	0.761002i
$905$	−37.3832	−	21.5832i	−1.24266	−	0.717449i
$906$	−15.8197	+	30.1331i	−0.525575	+	1.00110i
$907$	35.3577	+	9.47407i	1.17403	+	0.314581i	0.792557	−	0.609797i	$-0.208749\pi$
$907$	35.3577	+	9.47407i	1.17403	+	0.314581i	0.381476	+	0.924379i	$0.375416\pi$
$908$	6.36359	−	34.6774i	0.211183	−	1.15081i
$909$	8.94967	+	8.94967i	0.296842	+	0.296842i
$910$	−23.7522	+	19.6839i	−0.787377	+	0.652515i
$911$			28.8004i			0.954201i	0.878849	+	0.477100i	$0.158312\pi$
$911$			28.8004i			0.954201i	−0.878849	+	0.477100i	$0.841688\pi$
$912$	3.44464	+	21.2610i	0.114064	+	0.704022i
$913$	58.1782	−	33.5892i	1.92542	−	1.11164i
$914$	−8.58168	−	27.5514i	−0.283857	−	0.911318i
$915$	−1.39444	−	5.20413i	−0.0460988	−	0.172043i
$916$	41.1148	−	14.6415i	1.35847	−	0.483769i
$917$	19.6469	+	25.7451i	0.648799	+	0.850177i
$918$	1.89544	+	2.99821i	0.0625589	+	0.0989556i
$919$	7.39818	−	12.8140i	0.244043	−	0.422695i	−0.717819	−	0.696230i	$-0.754859\pi$
$919$	7.39818	−	12.8140i	0.244043	−	0.422695i	0.961862	+	0.273534i	$0.0881928\pi$
$920$	−30.5841	+	22.9650i	−1.00833	+	0.757135i
$921$	18.3400	−	10.5886i	0.604323	−	0.348906i
$922$	1.94678	+	48.4553i	0.0641139	+	1.59579i
$923$	−22.3241	−	22.3241i	−0.734807	−	0.734807i
$924$	−1.24532	+	23.3715i	−0.0409682	+	0.768866i
$925$	1.42800	−	1.42800i	0.0469524	−	0.0469524i
$926$	−29.6164	+	32.0958i	−0.973256	+	1.05473i
$927$	−5.21544	−	9.03340i	−0.171297	−	0.296696i
$928$	−7.54308	+	1.53516i	−0.247614	+	0.0503940i
$929$	15.3531	+	8.86413i	0.503720	+	0.290823i	0.730248	−	0.683182i	$-0.239404\pi$
$929$	15.3531	+	8.86413i	0.503720	+	0.290823i	−0.226529	+	0.974005i	$0.572738\pi$
$930$	1.47216	+	0.331746i	0.0482741	+	0.0108784i
$931$	32.5420	+	19.0183i	1.06652	+	0.623301i
$932$	−9.24247	+	19.4659i	−0.302747	+	0.637626i
$933$	16.0556	−	4.30208i	0.525636	−	0.140844i
$934$	−16.1502	+	30.7626i	−0.528452	+	1.00658i
$935$	13.4468	+	23.2905i	0.439757	+	0.761681i
$936$	−8.84825	−	3.77370i	−0.289214	−	0.123347i
$937$	12.3329			0.402899			0.201449	−	0.979499i	$-0.435435\pi$
$937$	12.3329			0.402899			0.201449	+	0.979499i	$0.435435\pi$
$938$	28.5107	−	40.1915i	0.930906	−	1.31230i
$939$	22.4752	−	22.4752i	0.733449	−	0.733449i
$940$	−6.28850	+	34.2683i	−0.205108	+	1.11771i
$941$	15.0511	−	56.1715i	0.490652	−	1.83114i	−0.0624819	−	0.998046i	$-0.519902\pi$
$941$	15.0511	−	56.1715i	0.490652	−	1.83114i	0.553134	−	0.833092i	$-0.313432\pi$
$942$	−4.47918	+	1.39517i	−0.145940	+	0.0454572i
$943$	4.04971	−	7.01430i	0.131877	−	0.228417i
$944$	−1.19928	+	11.8127i	−0.0390332	+	0.384470i
$945$	0.853982	−	6.35669i	0.0277800	−	0.206783i
$946$	−73.6129	−	16.5884i	−2.39336	−	0.539336i
$947$	41.3008	−	11.0665i	1.34210	−	0.359613i	0.484884	−	0.874579i	$-0.338862\pi$
$947$	41.3008	−	11.0665i	1.34210	−	0.359613i	0.857211	+	0.514965i	$0.172195\pi$
$948$	8.88235	−	10.4373i	0.288485	−	0.338987i
$949$	−2.47755	+	9.24635i	−0.0804247	+	0.300149i
$950$	−0.268002	−	6.67054i	−0.00869513	−	0.216421i
$951$		−	9.23007i		−	0.299306i
$952$	−4.62039	−	18.1919i	−0.149748	−	0.589604i
$953$			17.8131i			0.577024i	0.957476	+	0.288512i	$0.0931605\pi$
$953$			17.8131i			0.577024i	−0.957476	+	0.288512i	$0.906839\pi$
$954$	−2.16984	+	0.0871774i	−0.0702511	+	0.00282247i
$955$	3.03181	−	11.3149i	0.0981069	−	0.366140i
$956$	−3.28988	+	0.264782i	−0.106402	+	0.00856366i
$957$	5.81371	−	1.55778i	0.187931	−	0.0503559i
$958$	−5.11825	+	22.7128i	−0.165363	+	0.733818i
$959$	21.5806	−	27.9709i	0.696873	−	0.903227i
$960$	−18.8333	+	4.62744i	−0.607844	+	0.149350i
$961$	15.4031	−	26.6790i	0.496875	−	0.860613i
$962$	−3.29485	−	10.5781i	−0.106230	−	0.341051i
$963$	−4.99229	+	18.6315i	−0.160874	+	0.600391i
$964$	20.1947	+	29.2723i	0.650428	+	0.942798i
$965$	−34.8654	+	34.8654i	−1.12236	+	1.12236i
$966$	−18.9692	+	8.70447i	−0.610323	+	0.280062i
$967$	26.3868			0.848542			0.424271	−	0.905535i	$-0.360530\pi$
$967$	26.3868			0.848542			0.424271	+	0.905535i	$0.360530\pi$
$968$	−22.4730	+	9.03508i	−0.722309	+	0.290399i
$969$	6.75272	+	11.6961i	0.216929	+	0.375732i
$970$	−24.7002	−	12.9675i	−0.793075	−	0.416361i
$971$	38.9135	−	10.4268i	1.24879	−	0.334613i	0.426923	−	0.904288i	$-0.359598\pi$
$971$	38.9135	−	10.4268i	1.24879	−	0.334613i	0.821870	+	0.569675i	$0.192931\pi$
$972$	1.88410	−	0.670951i	0.0604325	−	0.0215208i
$973$	−42.3629	−	17.6787i	−1.35809	−	0.566752i
$974$	−3.34420	+	14.8403i	−0.107155	+	0.475512i
$975$	2.58213	+	1.49079i	0.0826944	+	0.0477436i
$976$	−8.10849	+	3.64460i	−0.259546	+	0.116661i
$977$	−0.647020	−	1.12067i	−0.0207000	−	0.0358535i	0.855490	−	0.517820i	$-0.173256\pi$
$977$	−0.647020	−	1.12067i	−0.0207000	−	0.0358535i	−0.876190	+	0.481966i	$0.839923\pi$
$978$	10.8051	+	9.97036i	0.345507	+	0.318817i
$979$	−53.0900	+	53.0900i	−1.69676	+	1.69676i
$980$	−14.7186	+	30.5809i	−0.470170	+	0.976872i
$981$	−10.3341	−	10.3341i	−0.329943	−	0.329943i
$982$	31.5058	−	1.26581i	1.00539	−	0.0403935i
$983$	14.3660	−	8.29419i	0.458203	−	0.264544i	−0.253085	−	0.967444i	$-0.581445\pi$
$983$	14.3660	−	8.29419i	0.458203	−	0.264544i	0.711288	+	0.702900i	$0.248112\pi$
$984$	3.28418	−	2.46603i	0.104696	−	0.0786140i
$985$	24.2812	−	42.0563i	0.773663	−	1.34002i
$986$	−4.07989	+	2.57927i	−0.129930	+	0.0821407i
$987$	−7.32216	+	17.5459i	−0.233067	+	0.558491i
$988$	−33.0854	−	15.7091i	−1.05259	−	0.499772i
$989$	−17.4159	−	64.9971i	−0.553794	−	2.06679i
$990$	14.4776	−	4.50948i	0.460129	−	0.143321i
$991$	−29.4044	+	16.9766i	−0.934062	+	0.539281i	−0.888094	−	0.459662i	$-0.847971\pi$
$991$	−29.4044	+	16.9766i	−0.934062	+	0.539281i	−0.0459679	+	0.998943i	$0.514637\pi$
$992$	0.151855	−	2.48540i	0.00482139	−	0.0789115i
$993$		−	15.0733i		−	0.478335i
$994$	−32.5657	−	12.0792i	−1.03292	−	0.383130i
$995$	−41.5616	−	41.5616i	−1.31759	−	1.31759i
$996$	17.2497	+	25.0035i	0.546578	+	0.792266i
$997$	25.5901	+	6.85685i	0.810447	+	0.217159i	0.640166	−	0.768237i	$-0.278866\pi$
$997$	25.5901	+	6.85685i	0.810447	+	0.217159i	0.170282	+	0.985395i	$0.445532\pi$
$998$	19.7741	+	10.3813i	0.625939	+	0.328615i
$999$	1.99493	+	1.15177i	0.0631168	+	0.0364405i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bs.a.187.24	yes	128
7.3	odd	6	inner	336.2.bs.a.283.3	yes	128
16.3	odd	4	inner	336.2.bs.a.19.3	✓	128
112.3	even	12	inner	336.2.bs.a.115.24	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.bs.a.19.3	✓	128	16.3	odd	4	inner
336.2.bs.a.115.24	yes	128	112.3	even	12	inner
336.2.bs.a.187.24	yes	128	1.1	even	1	trivial
336.2.bs.a.283.3	yes	128	7.3	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bs (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.03934 + 0.959049i) q^{2} +(-0.965926 - 0.258819i) q^{3} +(0.160449 + 1.99355i) q^{4} +(0.627426 + 2.34159i) q^{5} +(-0.755704 - 1.19537i) q^{6} +(2.44702 - 1.00602i) q^{7} +(-1.74516 + 2.22586i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-1.59359 + 3.03543i) q^{10} +(-4.27235 - 1.14477i) q^{11} +(0.360988 - 1.96715i) q^{12} +(2.40484 + 2.40484i) q^{13} +(3.50811 + 1.30122i) q^{14} -2.42419i q^{15} +(-3.94851 + 0.639726i) q^{16} +(-2.17215 + 1.25409i) q^{17} +(0.420569 + 1.35023i) q^{18} +(1.39363 + 5.20109i) q^{19} +(-4.56741 + 1.62651i) q^{20} +(-2.62402 + 0.338402i) q^{21} +(-3.34253 - 5.28720i) q^{22} +(2.78900 - 4.83069i) q^{23} +(2.26178 - 1.69833i) q^{24} +(-0.759236 + 0.438345i) q^{25} +(0.193082 + 4.80581i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(2.39817 + 4.71686i) q^{28} +(0.962214 - 0.962214i) q^{29} +(2.32492 - 2.51955i) q^{30} +(0.220090 + 0.381207i) q^{31} +(-4.71737 - 3.12193i) q^{32} +(3.83049 + 2.21153i) q^{33} +(-3.46033 - 0.779773i) q^{34} +(3.89100 + 5.09872i) q^{35} +(-0.857824 + 1.80669i) q^{36} +(-2.22506 + 0.596202i) q^{37} +(-3.53965 + 6.74225i) q^{38} +(-1.70048 - 2.94532i) q^{39} +(-6.30699 - 2.68987i) q^{40} +1.45203 q^{41} +(-3.05179 - 2.16485i) q^{42} +(8.53016 - 8.53016i) q^{43} +(1.59667 - 8.70084i) q^{44} +(-0.627426 + 2.34159i) q^{45} +(7.53158 - 2.34593i) q^{46} +(3.59301 - 6.22327i) q^{47} +(3.97954 + 0.404023i) q^{48} +(4.97586 - 4.92350i) q^{49} +(-1.20950 - 0.272556i) q^{50} +(2.42272 - 0.649165i) q^{51} +(-4.40833 + 5.18004i) q^{52} +(-0.397428 + 1.48322i) q^{53} +(-0.0567729 - 1.41307i) q^{54} -10.7223i q^{55} +(-2.03119 + 7.20238i) q^{56} -5.38456i q^{57} +(1.92288 - 0.0772552i) q^{58} +(0.768265 - 2.86721i) q^{59} +(4.83275 - 0.388958i) q^{60} +(2.14675 - 0.575220i) q^{61} +(-0.136848 + 0.607280i) q^{62} +(2.62219 + 0.352275i) q^{63} +(-1.90886 - 7.76893i) q^{64} +(-4.12228 + 7.14001i) q^{65} +(1.86020 + 5.97216i) q^{66} +(3.40860 - 12.7211i) q^{67} +(-2.84861 - 4.12908i) q^{68} +(-3.94424 + 3.94424i) q^{69} +(-0.845851 + 9.03096i) q^{70} -9.28298 q^{71} +(-2.62428 + 1.05507i) q^{72} +(1.40733 + 2.43756i) q^{73} +(-2.88437 - 1.51428i) q^{74} +(0.846818 - 0.226904i) q^{75} +(-10.1450 + 3.61278i) q^{76} +(-11.6062 + 1.49677i) q^{77} +(1.05733 - 4.69203i) q^{78} +(5.93453 + 3.42630i) q^{79} +(-3.97537 - 8.84440i) q^{80} +(0.500000 + 0.866025i) q^{81} +(1.50915 + 1.39257i) q^{82} +(-10.7397 + 10.7397i) q^{83} +(-1.09564 - 5.17683i) q^{84} +(-4.29942 - 4.29942i) q^{85} +(17.0466 - 0.684878i) q^{86} +(-1.17847 + 0.680388i) q^{87} +(10.0040 - 7.51183i) q^{88} +(8.48740 - 14.7006i) q^{89} +(-2.89781 + 1.83197i) q^{90} +(8.30402 + 3.46539i) q^{91} +(10.0777 + 4.78494i) q^{92} +(-0.113927 - 0.425181i) q^{93} +(9.70277 - 3.02221i) q^{94} +(-11.3044 + 6.52659i) q^{95} +(3.74861 + 4.23649i) q^{96} +8.13728i q^{97} +(9.89348 - 0.345090i) q^{98} +(-3.12758 - 3.12758i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 4 q^{4} - 24 q^{8} + 36 q^{10} - 8 q^{11} - 32 q^{14} - 4 q^{16} + 4 q^{18} + 16 q^{22} + 16 q^{23} - 32 q^{28} + 32 q^{29} - 24 q^{35} - 16 q^{37} + 60 q^{40} - 20 q^{42} - 16 q^{43} - 12 q^{44}+ \cdots - 16 q^{99}+O(q^{100}) \) 128 * q + 4 * q^4 - 24 * q^8 + 36 * q^10 - 8 * q^11 - 32 * q^14 - 4 * q^16 + 4 * q^18 + 16 * q^22 + 16 * q^23 - 32 * q^28 + 32 * q^29 - 24 * q^35 - 16 * q^37 + 60 * q^40 - 20 * q^42 - 16 * q^43 - 12 * q^44 - 20 * q^46 - 32 * q^50 - 144 * q^52 - 16 * q^53 - 56 * q^56 - 40 * q^58 - 96 * q^59 - 24 * q^60 - 32 * q^64 - 72 * q^66 + 16 * q^67 - 60 * q^68 + 28 * q^70 + 128 * q^71 - 4 * q^72 - 72 * q^74 + 72 * q^78 - 36 * q^80 + 64 * q^81 - 60 * q^82 + 24 * q^84 - 44 * q^86 - 48 * q^88 - 8 * q^91 + 56 * q^92 + 36 * q^94 + 60 * q^96 + 148 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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