LMFDB - Embedded newform 756.2.cf.a.491.62

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(155,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 7, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.155"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.cf (of order $18$, degree $6$, 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$648$
Relative dimension:	$108$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			491.62
Character	$\chi$	$=$	756.491
Dual form			756.2.cf.a.659.62

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.277553 - 1.38671i) q^{2} +(-1.26614 - 1.18190i) q^{3} +(-1.84593 - 0.769771i) q^{4} +(-0.868390 - 2.38588i) q^{5} +(-1.99037 + 1.42773i) q^{6} +(-0.984808 + 0.173648i) q^{7} +(-1.57979 + 2.34612i) q^{8} +(0.206222 + 2.99290i) q^{9} +(-3.54955 + 0.541996i) q^{10} +(3.37805 + 1.22951i) q^{11} +(1.42741 + 3.15634i) q^{12} +(-4.51486 - 3.78842i) q^{13} +(-0.0325368 + 1.41384i) q^{14} +(-1.72037 + 4.04721i) q^{15} +(2.81490 + 2.84189i) q^{16} +(-3.47113 - 2.00406i) q^{17} +(4.20753 + 0.544719i) q^{18} +(-5.13278 + 2.96341i) q^{19} +(-0.233597 + 5.07263i) q^{20} +(1.45214 + 0.944082i) q^{21} +(2.64256 - 4.34312i) q^{22} +(-0.655097 + 3.71524i) q^{23} +(4.77311 - 1.10335i) q^{24} +(-1.10811 + 0.929818i) q^{25} +(-6.50655 + 5.20932i) q^{26} +(3.27621 - 4.03317i) q^{27} +(1.95155 + 0.437534i) q^{28} +(1.14149 + 1.36037i) q^{29} +(5.13482 + 3.50897i) q^{30} +(9.44906 + 1.66612i) q^{31} +(4.72216 - 3.11468i) q^{32} +(-2.82392 - 5.54924i) q^{33} +(-3.74247 + 4.25722i) q^{34} +(1.26950 + 2.19884i) q^{35} +(1.92318 - 5.68343i) q^{36} +(0.758455 - 1.31368i) q^{37} +(2.68477 + 7.94018i) q^{38} +(1.23891 + 10.1328i) q^{39} +(6.96943 + 1.73186i) q^{40} +(-3.88862 + 4.63428i) q^{41} +(1.71221 - 1.75166i) q^{42} +(2.65992 - 7.30807i) q^{43} +(-5.28919 - 4.86991i) q^{44} +(6.96164 - 3.09103i) q^{45} +(4.97014 + 1.93961i) q^{46} +(0.441166 + 2.50198i) q^{47} +(-0.205239 - 6.92516i) q^{48} +(0.939693 - 0.342020i) q^{49} +(0.981827 + 1.79471i) q^{50} +(2.02634 + 6.63995i) q^{51} +(5.41790 + 10.4686i) q^{52} -7.64032i q^{53} +(-4.68352 - 5.66257i) q^{54} -9.12732i q^{55} +(1.14839 - 2.58480i) q^{56} +(10.0013 + 2.31434i) q^{57} +(2.20327 - 1.20534i) q^{58} +(-6.58401 + 2.39638i) q^{59} +(6.29111 - 6.14657i) q^{60} +(-0.237449 - 1.34664i) q^{61} +(4.93304 - 12.6407i) q^{62} +(-0.722802 - 2.91162i) q^{63} +(-3.00851 - 7.41275i) q^{64} +(-5.11806 + 14.0618i) q^{65} +(-8.47898 + 2.37575i) q^{66} +(-7.87985 + 9.39084i) q^{67} +(4.86480 + 6.37133i) q^{68} +(5.22049 - 3.92976i) q^{69} +(3.40151 - 1.15014i) q^{70} +(-6.89650 + 11.9451i) q^{71} +(-7.34749 - 4.24434i) q^{72} +(-0.359794 - 0.623182i) q^{73} +(-1.61118 - 1.41637i) q^{74} +(2.50198 + 0.132400i) q^{75} +(11.7559 - 1.51918i) q^{76} +(-3.54023 - 0.624238i) q^{77} +(14.3951 + 1.09437i) q^{78} +(-8.79736 - 10.4843i) q^{79} +(4.33597 - 9.18390i) q^{80} +(-8.91494 + 1.23441i) q^{81} +(5.34710 + 6.67865i) q^{82} +(-3.06210 + 2.56941i) q^{83} +(-1.95382 - 2.86052i) q^{84} +(-1.76715 + 10.0220i) q^{85} +(-9.39590 - 5.71691i) q^{86} +(0.162541 - 3.07155i) q^{87} +(-8.22118 + 5.98292i) q^{88} +(-14.0823 + 8.13040i) q^{89} +(-2.35414 - 10.5117i) q^{90} +(5.10412 + 2.94687i) q^{91} +(4.06915 - 6.35379i) q^{92} +(-9.99464 - 13.2774i) q^{93} +(3.59196 + 0.0826620i) q^{94} +(11.5276 + 9.67282i) q^{95} +(-9.66016 - 1.63749i) q^{96} +(-11.5504 - 4.20399i) q^{97} +(-0.213468 - 1.39801i) q^{98} +(-2.98317 + 10.3637i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) $ 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$	$-1$

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 $

$2$	0.277553	−	1.38671i	0.196260	−	0.980552i
$2$	0.277553	−	1.38671i	0.196260	−	0.980552i
$3$	−1.26614	−	1.18190i	−0.731006	−	0.682371i
$3$	−1.26614	−	1.18190i	−0.731006	−	0.682371i
$4$	−1.84593	−	0.769771i	−0.922964	−	0.384886i
$5$	−0.868390	−	2.38588i	−0.388356	−	1.06700i	−0.967741	−	0.251946i	$-0.918930\pi$
$5$	−0.868390	−	2.38588i	−0.388356	−	1.06700i	0.579385	−	0.815054i	$-0.303293\pi$
$6$	−1.99037	+	1.42773i	−0.812567	+	0.582868i
$7$	−0.984808	+	0.173648i	−0.372222	+	0.0656328i
$7$	−0.984808	+	0.173648i	−0.372222	+	0.0656328i
$8$	−1.57979	+	2.34612i	−0.558541	+	0.829477i
$9$	0.206222	+	2.99290i	0.0687408	+	0.997635i
$10$	−3.54955	+	0.541996i	−1.12247	+	0.171394i
$11$	3.37805	+	1.22951i	1.01852	+	0.370711i	0.796699	−	0.604377i	$-0.206578\pi$
$11$	3.37805	+	1.22951i	1.01852	+	0.370711i	0.221821	+	0.975087i	$0.428800\pi$
$12$	1.42741	+	3.15634i	0.412058	+	0.911158i
$13$	−4.51486	−	3.78842i	−1.25220	−	1.05072i	−0.996468	−	0.0839696i	$-0.973240\pi$
$13$	−4.51486	−	3.78842i	−1.25220	−	1.05072i	−0.255729	−	0.966749i	$-0.582315\pi$
$14$	−0.0325368	+	1.41384i	−0.00869581	+	0.377864i
$15$	−1.72037	+	4.04721i	−0.444198	+	1.04499i
$16$	2.81490	+	2.84189i	0.703726	+	0.710471i
$17$	−3.47113	−	2.00406i	−0.841873	−	0.486056i	0.0160272	−	0.999872i	$-0.494898\pi$
$17$	−3.47113	−	2.00406i	−0.841873	−	0.486056i	−0.857901	+	0.513816i	$0.828231\pi$
$18$	4.20753	+	0.544719i	0.991724	+	0.128391i
$19$	−5.13278	+	2.96341i	−1.17754	+	0.679853i	−0.955444	−	0.295171i	$-0.904623\pi$
$19$	−5.13278	+	2.96341i	−1.17754	+	0.679853i	−0.222096	+	0.975025i	$0.571290\pi$
$20$	−0.233597	+	5.07263i	−0.0522339	+	1.13427i
$21$	1.45214	+	0.944082i	0.316883	+	0.206016i
$22$	2.64256	−	4.34312i	0.563395	−	0.925955i
$23$	−0.655097	+	3.71524i	−0.136597	+	0.774681i	0.837137	+	0.546993i	$0.184228\pi$
$23$	−0.655097	+	3.71524i	−0.136597	+	0.774681i	−0.973734	+	0.227688i	$0.926883\pi$
$24$	4.77311	−	1.10335i	0.974308	−	0.225221i
$25$	−1.10811	+	0.929818i	−0.221623	+	0.185964i
$26$	−6.50655	+	5.20932i	−1.27604	+	1.02163i
$27$	3.27621	−	4.03317i	0.630506	−	0.776184i
$28$	1.95155	+	0.437534i	0.368809	+	0.0826862i
$29$	1.14149	+	1.36037i	0.211969	+	0.252615i	0.861544	−	0.507683i	$-0.169498\pi$
$29$	1.14149	+	1.36037i	0.211969	+	0.252615i	−0.649575	+	0.760297i	$0.725053\pi$
$30$	5.13482	+	3.50897i	0.937485	+	0.640648i
$31$	9.44906	+	1.66612i	1.69710	+	0.299245i	0.936680	−	0.350186i	$-0.113882\pi$
$31$	9.44906	+	1.66612i	1.69710	+	0.299245i	0.760421	+	0.649431i	$0.224993\pi$
$32$	4.72216	−	3.11468i	0.834767	−	0.550603i
$33$	−2.82392	−	5.54924i	−0.491582	−	0.965999i
$34$	−3.74247	+	4.25722i	−0.641829	+	0.730107i
$35$	1.26950	+	2.19884i	0.214585	+	0.371672i
$36$	1.92318	−	5.68343i	0.320530	−	0.947238i
$37$	0.758455	−	1.31368i	0.124689	−	0.215968i	−0.796922	−	0.604082i	$-0.793540\pi$
$37$	0.758455	−	1.31368i	0.124689	−	0.215968i	0.921611	+	0.388114i	$0.126873\pi$
$38$	2.68477	+	7.94018i	0.435528	+	1.28807i
$39$	1.23891	+	10.1328i	0.198385	+	1.62254i
$40$	6.96943	+	1.73186i	1.10196	+	0.273830i
$41$	−3.88862	+	4.63428i	−0.607301	+	0.723753i	−0.978831	−	0.204668i	$-0.934389\pi$
$41$	−3.88862	+	4.63428i	−0.607301	+	0.723753i	0.371531	+	0.928421i	$0.378833\pi$
$42$	1.71221	−	1.75166i	0.264200	−	0.270288i
$43$	2.65992	−	7.30807i	0.405634	−	1.11447i	−0.553828	−	0.832631i	$-0.686833\pi$
$43$	2.65992	−	7.30807i	0.405634	−	1.11447i	0.959462	−	0.281839i	$-0.0909444\pi$
$44$	−5.28919	−	4.86991i	−0.797376	−	0.734166i
$45$	6.96164	−	3.09103i	1.03778	−	0.460784i
$46$	4.97014	+	1.93961i	0.732807	+	0.285979i
$47$	0.441166	+	2.50198i	0.0643507	+	0.364951i	0.999930	+	0.0118341i	$0.00376701\pi$
$47$	0.441166	+	2.50198i	0.0643507	+	0.364951i	−0.935579	+	0.353117i	$0.885122\pi$
$48$	−0.205239	−	6.92516i	−0.0296237	−	0.999561i
$49$	0.939693	−	0.342020i	0.134242	−	0.0488600i
$50$	0.981827	+	1.79471i	0.138851	+	0.253810i
$51$	2.02634	+	6.63995i	0.283745	+	0.929780i
$52$	5.41790	+	10.4686i	0.751327	+	1.45173i
$53$		−	7.64032i		−	1.04948i	−0.851263	−	0.524739i	$-0.824163\pi$
$53$		−	7.64032i		−	1.04948i	0.851263	−	0.524739i	$-0.175837\pi$
$54$	−4.68352	−	5.66257i	−0.637346	−	0.770578i
$55$		−	9.12732i		−	1.23073i
$56$	1.14839	−	2.58480i	0.153460	−	0.345408i
$57$	10.0013	+	2.31434i	1.32470	+	0.306542i
$58$	2.20327	−	1.20534i	0.289303	−	0.158269i
$59$	−6.58401	+	2.39638i	−0.857165	+	0.311983i	−0.732958	−	0.680274i	$-0.761861\pi$
$59$	−6.58401	+	2.39638i	−0.857165	+	0.311983i	−0.124207	+	0.992256i	$0.539639\pi$
$60$	6.29111	−	6.14657i	0.812179	−	0.793519i
$61$	−0.237449	−	1.34664i	−0.0304022	−	0.172420i	0.965826	−	0.259191i	$-0.0834560\pi$
$61$	−0.237449	−	1.34664i	−0.0304022	−	0.172420i	−0.996228	+	0.0867718i	$0.972345\pi$
$62$	4.93304	−	12.6407i	0.626497	−	1.60537i
$63$	−0.722802	−	2.91162i	−0.0910645	−	0.366830i
$64$	−3.00851	−	7.41275i	−0.376064	−	0.926594i
$65$	−5.11806	+	14.0618i	−0.634817	+	1.74415i
$66$	−8.47898	+	2.37575i	−1.04369	+	0.292435i
$67$	−7.87985	+	9.39084i	−0.962677	+	1.14727i	0.0263672	+	0.999652i	$0.491606\pi$
$67$	−7.87985	+	9.39084i	−0.962677	+	1.14727i	−0.989044	+	0.147621i	$0.952838\pi$
$68$	4.86480	+	6.37133i	0.589943	+	0.772637i
$69$	5.22049	−	3.92976i	0.628473	−	0.473087i
$70$	3.40151	−	1.15014i	0.406558	−	0.137467i
$71$	−6.89650	+	11.9451i	−0.818464	+	1.41762i	0.0883497	+	0.996090i	$0.471841\pi$
$71$	−6.89650	+	11.9451i	−0.818464	+	1.41762i	−0.906814	+	0.421532i	$0.861493\pi$
$72$	−7.34749	−	4.24434i	−0.865909	−	0.500201i
$73$	−0.359794	−	0.623182i	−0.0421107	−	0.0729379i	0.844202	−	0.536025i	$-0.180075\pi$
$73$	−0.359794	−	0.623182i	−0.0421107	−	0.0729379i	−0.886313	+	0.463088i	$0.846742\pi$
$74$	−1.61118	−	1.41637i	−0.187296	−	0.164650i
$75$	2.50198	+	0.132400i	0.288904	+	0.0152883i
$76$	11.7559	−	1.51918i	1.34849	−	0.174262i
$77$	−3.54023	−	0.624238i	−0.403446	−	0.0711385i
$78$	14.3951	+	1.09437i	1.62992	+	0.123913i
$79$	−8.79736	−	10.4843i	−0.989780	−	1.17957i	−0.983741	−	0.179593i	$-0.942522\pi$
$79$	−8.79736	−	10.4843i	−0.989780	−	1.17957i	−0.00603928	−	0.999982i	$-0.501922\pi$
$80$	4.33597	−	9.18390i	0.484776	−	1.02679i
$81$	−8.91494	+	1.23441i	−0.990549	+	0.137156i
$82$	5.34710	+	6.67865i	0.590488	+	0.737533i
$83$	−3.06210	+	2.56941i	−0.336110	+	0.282029i	−0.795184	−	0.606368i	$-0.792626\pi$
$83$	−3.06210	+	2.56941i	−0.336110	+	0.282029i	0.459074	+	0.888398i	$0.348181\pi$
$84$	−1.95382	−	2.86052i	−0.213179	−	0.312109i
$85$	−1.76715	+	10.0220i	−0.191675	+	1.08704i
$86$	−9.39590	−	5.71691i	−1.01319	−	0.616471i
$87$	0.162541	−	3.07155i	0.0174262	−	0.329304i
$88$	−8.22118	+	5.98292i	−0.876381	+	0.637781i
$89$	−14.0823	+	8.13040i	−1.49272	+	0.861821i	−0.999965	−	0.00834861i	$-0.997343\pi$
$89$	−14.0823	+	8.13040i	−1.49272	+	0.861821i	−0.492752	+	0.870170i	$0.664009\pi$
$90$	−2.35414	−	10.5117i	−0.248148	−	1.10803i
$91$	5.10412	+	2.94687i	0.535057	+	0.308916i
$92$	4.06915	−	6.35379i	0.424238	−	0.662429i
$93$	−9.99464	−	13.2774i	−1.03640	−	1.37680i
$94$	3.59196	+	0.0826620i	0.370483	+	0.00852594i
$95$	11.5276	+	9.67282i	1.18271	+	0.992410i
$96$	−9.66016	−	1.63749i	−0.985936	−	0.167126i
$97$	−11.5504	−	4.20399i	−1.17276	−	0.426851i	−0.319123	−	0.947713i	$-0.603388\pi$
$97$	−11.5504	−	4.20399i	−1.17276	−	0.426851i	−0.853641	+	0.520862i	$0.825610\pi$
$98$	−0.213468	−	1.39801i	−0.0215635	−	0.141220i
$99$	−2.98317	+	10.3637i	−0.299820	+	1.04159i
$100$	2.76125	−	0.863384i	0.276125	−	0.0863384i
$101$	15.4056	−	2.71643i	1.53292	−	0.270295i	0.657422	−	0.753522i	$-0.271647\pi$
$101$	15.4056	−	2.71643i	1.53292	−	0.270295i	0.875495	+	0.483228i	$0.160536\pi$
$102$	9.77011	−	0.967009i	0.967385	−	0.0957482i
$103$	3.80945	+	10.4664i	0.375356	+	1.03128i	0.973258	+	0.229714i	$0.0737790\pi$
$103$	3.80945	+	10.4664i	0.375356	+	1.03128i	−0.597902	+	0.801569i	$0.703999\pi$
$104$	16.0206	−	4.60747i	1.57095	−	0.451800i
$105$	0.991445	−	4.28447i	0.0967551	−	0.418121i
$106$	−10.5949	−	2.12059i	−1.02907	−	0.205970i
$107$	−13.6076			−1.31550			−0.657749	−	0.753238i	$-0.728491\pi$
$107$	−13.6076			−1.31550			−0.657749	+	0.753238i	$0.728491\pi$
$108$	−9.15226	+	4.92301i	−0.880677	+	0.473717i
$109$	−3.84314			−0.368106			−0.184053	−	0.982916i	$-0.558922\pi$
$109$	−3.84314			−0.368106			−0.184053	+	0.982916i	$0.558922\pi$
$110$	−12.6569	−	2.53331i	−1.20679	−	0.241542i
$111$	−2.51295	+	0.766888i	−0.238519	+	0.0727898i
$112$	−3.26563	−	2.30991i	−0.308573	−	0.218266i
$113$	4.03983	+	11.0993i	0.380035	+	1.04414i	0.971341	+	0.237691i	$0.0763904\pi$
$113$	4.03983	+	11.0993i	0.380035	+	1.04414i	−0.591306	+	0.806447i	$0.701387\pi$
$114$	5.98520	−	13.2265i	0.560566	−	1.23878i
$115$	9.43301	−	1.66329i	0.879633	−	0.155103i
$116$	−1.05993	−	3.38983i	−0.0984120	−	0.314738i
$117$	10.4073	−	14.2938i	0.962156	−	1.32146i
$118$	1.49568	+	9.79524i	0.137688	+	0.901725i
$119$	3.76640	+	1.37086i	0.345265	+	0.125666i
$120$	−6.77740	−	10.4299i	−0.618689	−	0.952120i
$121$	1.47302	+	1.23601i	0.133910	+	0.112364i
$122$	−1.93330	−	0.0444912i	−0.175033	−	0.00402804i
$123$	10.4008	−	1.27168i	0.937808	−	0.114664i
$124$	−16.1597	−	10.3492i	−1.45119	−	0.929382i
$125$	−7.81350	−	4.51112i	−0.698860	−	0.403487i
$126$	−4.23819	+	0.194186i	−0.377568	+	0.0172995i
$127$	3.87597	−	2.23779i	0.343937	−	0.198572i	−0.318075	−	0.948066i	$-0.603036\pi$
$127$	3.87597	−	2.23779i	0.343937	−	0.198572i	0.662012	+	0.749494i	$0.269703\pi$
$128$	−11.1144	+	2.11450i	−0.982379	+	0.186897i
$129$	−12.0052	+	6.10928i	−1.05700	+	0.537892i
$130$	18.0790	+	11.0001i	1.58564	+	0.964777i
$131$	0.924163	−	5.24119i	0.0807445	−	0.457925i	−0.917449	−	0.397852i	$-0.869756\pi$
$131$	0.924163	−	5.24119i	0.0807445	−	0.457925i	0.998194	−	0.0600727i	$-0.0191332\pi$
$132$	0.941114	+	12.4173i	0.0819134	+	1.08079i
$133$	4.54021	−	3.80969i	0.393686	−	0.330342i
$134$	10.8353	+	13.5335i	0.936027	+	1.16912i
$135$	−12.4677	−	4.31428i	−1.07305	−	0.371314i
$136$	10.1854	−	4.97768i	0.873393	−	0.426832i
$137$	−1.73249	−	2.06470i	−0.148016	−	0.176399i	0.686942	−	0.726712i	$-0.258953\pi$
$137$	−1.73249	−	2.06470i	−0.148016	−	0.176399i	−0.834958	+	0.550313i	$0.814508\pi$
$138$	−4.00047	−	8.33002i	−0.340542	−	0.709098i
$139$	−5.15369	−	0.908734i	−0.437130	−	0.0770778i	−0.0492474	−	0.998787i	$-0.515682\pi$
$139$	−5.15369	−	0.908734i	−0.437130	−	0.0770778i	−0.387883	+	0.921709i	$0.626793\pi$
$140$	−0.650805	−	5.03613i	−0.0550031	−	0.425631i
$141$	2.39851	−	3.68927i	0.201991	−	0.310692i
$142$	14.6502	+	12.8788i	1.22942	+	1.08077i
$143$	−10.5935	−	18.3485i	−0.885874	−	1.53438i
$144$	−7.92499	+	9.01080i	−0.660416	+	0.750900i
$145$	2.25443	−	3.90479i	0.187220	−	0.324275i
$146$	−0.964034	+	0.325964i	−0.0797840	+	0.0269770i
$147$	−1.59402	−	0.677578i	−0.131472	−	0.0558857i
$148$	−2.41129	+	1.84113i	−0.198207	+	0.151340i
$149$	0.699829	−	0.834023i	0.0573322	−	0.0683258i	−0.736616	−	0.676311i	$-0.763578\pi$
$149$	0.699829	−	0.834023i	0.0573322	−	0.0683258i	0.793948	+	0.607985i	$0.208022\pi$
$150$	0.878033	−	3.43277i	0.0716911	−	0.280285i
$151$	2.28134	−	6.26794i	0.185653	−	0.510078i	−0.811594	−	0.584221i	$-0.801400\pi$
$151$	2.28134	−	6.26794i	0.185653	−	0.510078i	0.997248	+	0.0741434i	$0.0236222\pi$
$152$	1.15622	−	16.7237i	0.0937819	−	1.35647i
$153$	5.28213	−	10.8020i	0.427035	−	0.873294i
$154$	−1.84824	+	4.73601i	−0.148935	+	0.381639i
$155$	−4.23029	−	23.9912i	−0.339785	−	1.92702i
$156$	5.51298	−	19.6581i	0.441392	−	1.57391i
$157$	14.1096	−	5.13547i	1.12607	−	0.409855i	0.289205	−	0.957267i	$-0.406609\pi$
$157$	14.1096	−	5.13547i	1.12607	−	0.409855i	0.836863	+	0.547412i	$0.184387\pi$
$158$	−16.9804	+	9.28944i	−1.35089	+	0.739028i
$159$	−9.03009	+	9.67371i	−0.716133	+	0.767175i
$160$	−11.5319	−	8.56175i	−0.911680	−	0.676866i
$161$		−	3.77255i		−	0.297319i
$162$	−0.762605	+	12.7051i	−0.0599159	+	0.998203i
$163$		−	2.88401i		−	0.225893i	−0.993601	−	0.112947i	$-0.963971\pi$
$163$		−	2.88401i		−	0.225893i	0.993601	−	0.112947i	$-0.0360289\pi$
$164$	10.7454	−	5.56120i	0.839079	−	0.434257i
$165$	−10.7876	+	11.5565i	−0.839812	+	0.899669i
$166$	2.71313	+	4.95940i	0.210580	+	0.384924i
$167$	−16.6516	+	6.06067i	−1.28854	+	0.468989i	−0.893247	−	0.449567i	$-0.851578\pi$
$167$	−16.6516	+	6.06067i	−1.28854	+	0.468989i	−0.395290	+	0.918556i	$0.629356\pi$
$168$	−4.50900	+	1.91543i	−0.347877	+	0.147779i
$169$	3.77443	+	21.4059i	0.290341	+	1.64660i
$170$	13.4072	+	5.23217i	1.02828	+	0.401289i
$171$	−9.92770	−	14.7508i	−0.759190	−	1.12802i
$172$	−10.5356	+	11.4426i	−0.803329	+	0.872493i
$173$	−7.44155	+	20.4455i	−0.565770	+	1.55444i	0.245272	+	0.969454i	$0.421123\pi$
$173$	−7.44155	+	20.4455i	−0.565770	+	1.55444i	−0.811043	+	0.584987i	$0.801100\pi$
$174$	−4.21423	−	1.07791i	−0.319480	−	0.0817165i
$175$	0.929818	−	1.10811i	0.0702876	−	0.0837655i
$176$	6.01476	+	13.0610i	0.453379	+	0.984507i
$177$	11.1686	+	4.74749i	0.839481	+	0.356843i
$178$	7.36593	+	21.7846i	0.552100	+	1.63283i
$179$	4.88178	−	8.45548i	0.364881	−	0.631993i	−0.623876	−	0.781523i	$-0.714443\pi$
$179$	4.88178	−	8.45548i	0.364881	−	0.631993i	0.988757	+	0.149531i	$0.0477763\pi$
$180$	−15.2301	+	0.346957i	−1.13518	+	0.0258606i
$181$	2.62851	+	4.55271i	0.195376	+	0.338401i	0.947024	−	0.321164i	$-0.104074\pi$
$181$	2.62851	+	4.55271i	0.195376	+	0.338401i	−0.751648	+	0.659565i	$0.770741\pi$
$182$	5.50311	−	6.26002i	0.407918	−	0.464024i
$183$	−1.29095	+	1.98568i	−0.0954298	+	0.146785i
$184$	−7.68146	−	7.40624i	−0.566285	−	0.545995i
$185$	−3.79293	−	0.668795i	−0.278862	−	0.0491708i
$186$	−21.1859	+	10.1745i	−1.55343	+	0.746029i
$187$	−9.26164	−	11.0376i	−0.677278	−	0.807149i
$188$	1.11159	−	4.95807i	0.0810709	−	0.361604i
$189$	−2.52608	+	4.54080i	−0.183745	+	0.330295i
$190$	16.6129	−	13.3007i	1.20523	−	0.964937i
$191$	−0.641745	+	0.538488i	−0.0464350	+	0.0389636i	−0.665710	−	0.746211i	$-0.731871\pi$
$191$	−0.641745	+	0.538488i	−0.0464350	+	0.0389636i	0.619275	+	0.785174i	$0.287427\pi$
$192$	−4.95193	+	12.9413i	−0.357375	+	0.933961i
$193$	3.20576	−	18.1808i	0.230756	−	1.30868i	−0.620614	−	0.784116i	$-0.713117\pi$
$193$	3.20576	−	18.1808i	0.230756	−	1.30868i	0.851370	−	0.524565i	$-0.175772\pi$
$194$	−9.03556	+	14.8502i	−0.648716	+	1.06618i
$195$	23.0998	−	11.7551i	1.65421	−	0.841801i
$196$	−1.99788	−	0.0920035i	−0.142706	−	0.00657168i
$197$	−11.2816	+	6.51345i	−0.803783	+	0.464064i	−0.844792	−	0.535095i	$-0.820276\pi$
$197$	−11.2816	+	6.51345i	−0.803783	+	0.464064i	0.0410094	+	0.999159i	$0.486943\pi$
$198$	13.5435	+	7.01327i	0.962493	+	0.498412i
$199$	9.30278	+	5.37096i	0.659457	+	0.380738i	0.792070	−	0.610430i	$-0.209003\pi$
$199$	9.30278	+	5.37096i	0.659457	+	0.380738i	−0.132613	+	0.991168i	$0.542337\pi$
$200$	−0.430870	−	4.06868i	−0.0304671	−	0.287699i
$201$	21.0760	−	2.57692i	1.48659	−	0.181762i
$202$	0.508982	−	22.1171i	0.0358118	−	1.55615i
$203$	−1.36037	−	1.14149i	−0.0954794	−	0.0801167i
$204$	1.37076	−	13.8167i	0.0959725	−	0.967363i
$205$	14.4337	+	5.25343i	1.00809	+	0.366916i
$206$	15.5712	−	2.37763i	1.08489	−	0.165657i
$207$	−11.2545	−	1.19448i	−0.782238	−	0.0830219i
$208$	−1.94265	−	23.4948i	−0.134699	−	1.62907i
$209$	−20.9823	+	3.69975i	−1.45138	+	0.255917i
$210$	−5.66613	−	2.56401i	−0.391000	−	0.176934i
$211$	−1.02558	−	2.81776i	−0.0706039	−	0.193983i	0.899372	−	0.437185i	$-0.144024\pi$
$211$	−1.02558	−	2.81776i	−0.0706039	−	0.193983i	−0.969976	+	0.243202i	$0.921802\pi$
$212$	−5.88129	+	14.1035i	−0.403929	+	0.968631i
$213$	22.8498	−	6.97318i	1.56565	−	0.477794i
$214$	−3.77683	+	18.8698i	−0.258179	+	1.28991i
$215$	−19.7460			−1.34667
$216$	4.28655	+	14.0579i	0.291663	+	0.956521i
$217$	−9.59482			−0.651339
$218$	−1.06668	+	5.32932i	−0.0722444	+	0.360947i
$219$	−0.280989	+	1.21428i	−0.0189875	+	0.0820532i
$220$	−7.02594	+	16.8484i	−0.473689	+	1.13592i
$221$	8.07947	+	22.1982i	0.543484	+	1.49321i
$222$	0.365974	+	3.69759i	0.0245625	+	0.248166i
$223$	−16.5729	+	2.92226i	−1.10981	+	0.195689i	−0.698361	−	0.715746i	$-0.746087\pi$
$223$	−16.5729	+	2.92226i	−1.10981	+	0.195689i	−0.411445	+	0.911434i	$0.634976\pi$
$224$	−4.10956	+	3.88736i	−0.274581	+	0.259735i
$225$	−3.01137	−	3.12473i	−0.200758	−	0.208315i
$226$	16.5128	−	2.52142i	1.09842	−	0.167722i
$227$	7.50645	+	2.73213i	0.498221	+	0.181338i	0.578894	−	0.815403i	$-0.303485\pi$
$227$	7.50645	+	2.73213i	0.498221	+	0.181338i	−0.0806727	+	0.996741i	$0.525707\pi$
$228$	−16.6801	−	11.9708i	−1.10467	−	0.792786i
$229$	−12.0105	−	10.0780i	−0.793673	−	0.665971i	0.152978	−	0.988230i	$-0.451114\pi$
$229$	−12.0105	−	10.0780i	−0.793673	−	0.665971i	−0.946652	+	0.322259i	$0.895558\pi$
$230$	0.311654	−	13.5425i	0.0205499	−	0.892966i
$231$	3.74464	+	4.97457i	0.246379	+	0.327303i
$232$	−4.99490	+	0.528956i	−0.327932	+	0.0347277i
$233$	−7.78858	−	4.49674i	−0.510247	−	0.294591i	0.222688	−	0.974890i	$-0.428517\pi$
$233$	−7.78858	−	4.49674i	−0.510247	−	0.294591i	−0.732935	+	0.680299i	$0.761850\pi$
$234$	−16.9328	−	18.3992i	−1.10693	−	1.20279i
$235$	5.58632	−	3.22526i	0.364411	−	0.210393i
$236$	13.9983	+	0.644628i	0.911210	+	0.0419617i
$237$	−1.25269	+	23.6722i	−0.0813710	+	1.53767i
$238$	2.94636	−	4.84242i	0.190984	−	0.313887i
$239$	0.811274	−	4.60097i	0.0524770	−	0.297612i	−0.947262	−	0.320460i	$-0.896162\pi$
$239$	0.811274	−	4.60097i	0.0524770	−	0.297612i	0.999739	+	0.0228485i	$0.00727354\pi$
$240$	−16.3444	+	6.50342i	−1.05503	+	0.419794i
$241$	−5.80991	+	4.87510i	−0.374249	+	0.314033i	−0.810440	−	0.585822i	$-0.800772\pi$
$241$	−5.80991	+	4.87510i	−0.374249	+	0.314033i	0.436190	+	0.899854i	$0.356327\pi$
$242$	2.12282	−	1.69959i	0.136460	−	0.109254i
$243$	12.7465	+	8.97364i	0.817689	+	0.575660i
$244$	−0.598291	+	2.66858i	−0.0383016	+	0.170838i
$245$	−1.63204	−	1.94499i	−0.104267	−	0.124261i
$246$	1.12332	−	14.7758i	0.0716201	−	0.942073i
$247$	34.4004	+	6.06573i	2.18885	+	0.385953i
$248$	−18.8365	+	19.5364i	−1.19612	+	1.24057i
$249$	6.91384	+	0.365868i	0.438147	+	0.0231860i
$250$	−8.42428	+	9.58298i	−0.532798	+	0.606081i
$251$	−0.888151	−	1.53832i	−0.0560596	−	0.0970980i	0.836634	−	0.547763i	$-0.184520\pi$
$251$	−0.888151	−	1.53832i	−0.0560596	−	0.0970980i	−0.892693	+	0.450665i	$0.851187\pi$
$252$	−0.907044	+	5.93104i	−0.0571384	+	0.373621i
$253$	−6.78087	+	11.7448i	−0.426309	+	0.738390i
$254$	−2.02738	−	5.99595i	−0.127209	−	0.376219i
$255$	14.0825	−	10.6007i	0.881880	−	0.663841i
$256$	−0.152622	+	15.9993i	−0.00953886	+	0.999955i
$257$	19.8898	−	23.7038i	1.24069	−	1.47860i	0.419700	−	0.907663i	$-0.362135\pi$
$257$	19.8898	−	23.7038i	1.24069	−	1.47860i	0.820993	−	0.570938i	$-0.193420\pi$
$258$	5.13971	+	18.3434i	0.319984	+	1.14201i
$259$	−0.518814	+	1.42543i	−0.0322375	+	0.0885718i
$260$	20.2719	−	22.0173i	1.25721	−	1.36545i
$261$	−3.83606	+	3.69690i	−0.237446	+	0.228833i
$262$	−7.01151	−	2.73626i	−0.433172	−	0.169046i
$263$	−2.94213	−	16.6856i	−0.181419	−	1.02888i	−0.930470	−	0.366368i	$-0.880601\pi$
$263$	−2.94213	−	16.6856i	−0.181419	−	1.02888i	0.749051	−	0.662513i	$-0.230510\pi$
$264$	17.4804	+	2.14140i	1.07584	+	0.131794i
$265$	−18.2289	+	6.63478i	−1.11979	+	0.407571i
$266$	−4.02278	−	7.35335i	−0.246653	−	0.450863i
$267$	27.4395	+	6.34961i	1.67927	+	0.388590i
$268$	21.7744	−	11.2691i	1.33009	−	0.688372i
$269$		−	2.16066i		−	0.131738i	−0.997828	−	0.0658688i	$-0.979018\pi$
$269$		−	2.16066i		−	0.131738i	0.997828	−	0.0658688i	$-0.0209819\pi$
$270$	−9.44311	+	16.0916i	−0.574689	+	0.979306i
$271$		−	19.7324i		−	1.19866i	−0.800503	−	0.599328i	$-0.795434\pi$
$271$		−	19.7324i		−	1.19866i	0.800503	−	0.599328i	$-0.204566\pi$
$272$	−4.07560	−	15.5058i	−0.247120	−	0.940177i
$273$	−2.97963	−	9.76371i	−0.180336	−	0.590927i
$274$	−3.34399	+	1.82939i	−0.202018	+	0.110518i
$275$	−4.88648	+	1.77853i	−0.294666	+	0.107250i
$276$	−12.6617	+	3.23547i	−0.762143	+	0.194752i
$277$	−2.21189	−	12.5443i	−0.132900	−	0.753712i	−0.976299	−	0.216425i	$-0.930560\pi$
$277$	−2.21189	−	12.5443i	−0.132900	−	0.753712i	0.843399	−	0.537287i	$-0.180551\pi$
$278$	−2.69057	+	6.89445i	−0.161370	+	0.413501i
$279$	−3.03794	+	28.6237i	−0.181877	+	1.71366i
$280$	−7.16429	−	0.495316i	−0.428148	−	0.0296008i
$281$	−4.55202	+	12.5066i	−0.271551	+	0.746080i	0.726700	+	0.686955i	$0.241053\pi$
$281$	−4.55202	+	12.5066i	−0.271551	+	0.746080i	−0.998251	+	0.0591249i	$0.981169\pi$
$282$	−4.45023	−	4.35000i	−0.265007	−	0.259039i
$283$	3.84661	−	4.58421i	0.228657	−	0.272503i	−0.639501	−	0.768790i	$-0.720859\pi$
$283$	3.84661	−	4.58421i	0.228657	−	0.272503i	0.868159	+	0.496287i	$0.165304\pi$
$284$	21.9254	−	16.7411i	1.30103	−	0.993399i
$285$	−3.16327	−	25.8716i	−0.187376	−	1.53250i
$286$	−28.3843	+	9.59745i	−1.67840	+	0.567509i
$287$	3.02481	−	5.23912i	0.178549	−	0.309256i
$288$	10.2958	+	13.4906i	0.606683	+	0.794944i
$289$	−0.467492	−	0.809719i	−0.0274995	−	0.0476305i
$290$	−4.78909	−	4.21003i	−0.281225	−	0.247221i
$291$	9.65570	+	18.9742i	0.566027	+	1.11229i
$292$	0.184447	+	1.42731i	0.0107939	+	0.0835269i
$293$	24.3108	+	4.28665i	1.42025	+	0.250429i	0.830439	−	0.557110i	$-0.188090\pi$
$293$	24.3108	+	4.28665i	1.42025	+	0.250429i	0.589814	+	0.807539i	$0.299201\pi$
$294$	−1.38203	+	2.02237i	−0.0806015	+	0.117947i
$295$	11.4350	+	13.6277i	0.665770	+	0.793434i
$296$	1.88385	+	3.85477i	0.109496	+	0.224054i
$297$	16.0260	−	9.59611i	0.929923	−	0.556823i
$298$	−0.962309	−	1.20194i	−0.0557450	−	0.0696268i
$299$	17.0326	−	14.2920i	0.985018	−	0.826528i
$300$	−4.51656	−	2.17035i	−0.260764	−	0.125305i
$301$	−1.35048	+	7.65893i	−0.0778402	+	0.441454i
$302$	−8.05862	−	4.90325i	−0.463722	−	0.282150i
$303$	−22.7162	−	14.7685i	−1.30501	−	0.848430i
$304$	−22.8700	−	6.24505i	−1.31168	−	0.358178i
$305$	−3.00673	+	1.73593i	−0.172165	+	0.0993993i
$306$	−13.5132	−	10.3229i	−0.772500	−	0.590122i
$307$	2.10864	+	1.21742i	0.120346	+	0.0694819i	0.558965	−	0.829191i	$-0.311199\pi$
$307$	2.10864	+	1.21742i	0.120346	+	0.0694819i	−0.438619	+	0.898673i	$0.644532\pi$
$308$	6.05449	+	3.87746i	0.344986	+	0.220939i
$309$	7.54692	−	17.7543i	0.429329	−	1.01001i
$310$	−34.4430	−	0.792637i	−1.95623	−	0.0450188i
$311$	−2.26962	−	1.90444i	−0.128698	−	0.107991i	0.576167	−	0.817332i	$-0.304548\pi$
$311$	−2.26962	−	1.90444i	−0.128698	−	0.107991i	−0.704865	+	0.709342i	$0.748992\pi$
$312$	−25.7299	−	13.1011i	−1.45667	−	0.741702i
$313$	−18.4995	−	6.73326i	−1.04565	−	0.380586i	−0.238632	−	0.971110i	$-0.576699\pi$
$313$	−18.4995	−	6.73326i	−1.04565	−	0.380586i	−0.807020	+	0.590524i	$0.798921\pi$
$314$	−3.20525	−	20.9913i	−0.180883	−	1.18461i
$315$	−6.31912	+	4.25295i	−0.356042	+	0.239626i
$316$	8.16880	+	26.1252i	0.459531	+	1.46966i
$317$	11.6815	−	2.05977i	0.656100	−	0.115688i	0.164319	−	0.986407i	$-0.447457\pi$
$317$	11.6815	−	2.05977i	0.656100	−	0.115688i	0.491781	+	0.870719i	$0.336346\pi$
$318$	10.9083	+	15.2071i	0.611707	+	0.852771i
$319$	2.18341	+	5.99887i	0.122247	+	0.335872i
$320$	−15.0734	+	13.6151i	−0.842628	+	0.761108i
$321$	17.2291	+	16.0828i	0.961637	+	0.897657i
$322$	−5.23144	−	1.04708i	−0.291537	−	0.0583517i
$323$	23.7554			1.32179
$324$	17.4066	+	4.58384i	0.967031	+	0.254658i
$325$	8.52552			0.472911
$326$	−3.99929	−	0.800466i	−0.221500	−	0.0443337i
$327$	4.86596	+	4.54221i	0.269088	+	0.251185i
$328$	−4.72934	−	16.4443i	−0.261134	−	0.907987i
$329$	−0.868927	−	2.38736i	−0.0479055	−	0.131619i
$330$	13.0313	+	18.1668i	0.717351	+	1.00005i
$331$	−21.6681	+	3.82067i	−1.19099	+	0.210003i	−0.733798	−	0.679368i	$-0.762254\pi$
$331$	−21.6681	+	3.82067i	−1.19099	+	0.210003i	−0.457187	+	0.889370i	$0.651143\pi$
$332$	7.63028	−	2.38583i	0.418766	−	0.130939i
$333$	4.08813	+	1.99907i	0.224028	+	0.109548i
$334$	3.78270	+	24.7731i	0.206980	+	1.35552i
$335$	29.2482	+	10.6455i	1.59800	+	0.581625i
$336$	1.40466	+	6.78431i	0.0766306	+	0.370115i
$337$	−13.9197	−	11.6801i	−0.758257	−	0.636253i	0.179415	−	0.983773i	$-0.442579\pi$
$337$	−13.9197	−	11.6801i	−0.758257	−	0.636253i	−0.937672	+	0.347520i	$0.887024\pi$
$338$	30.7313	+	0.707222i	1.67156	+	0.0384678i
$339$	8.00333	−	18.8280i	0.434681	−	1.02260i
$340$	10.9767	−	17.1396i	0.595295	−	0.929527i
$341$	29.8708	+	17.2459i	1.61760	+	0.933920i
$342$	−23.2105	+	9.67272i	−1.25508	+	0.523041i
$343$	−0.866025	+	0.500000i	−0.0467610	+	0.0269975i
$344$	12.9435	+	17.7857i	0.697864	+	0.958941i
$345$	−13.9094	−	9.04291i	−0.748855	−	0.486854i
$346$	26.2865	+	15.9940i	1.41317	+	0.859841i
$347$	−0.852066	+	4.83231i	−0.0457413	+	0.259412i	−0.999099	−	0.0424296i	$-0.986490\pi$
$347$	−0.852066	+	4.83231i	−0.0457413	+	0.259412i	0.953358	+	0.301841i	$0.0976013\pi$
$348$	−2.66443	+	5.54474i	−0.142828	+	0.297229i
$349$	22.5517	−	18.9232i	1.20717	−	1.01293i	0.207771	−	0.978177i	$-0.433379\pi$
$349$	22.5517	−	18.9232i	1.20717	−	1.01293i	0.999396	−	0.0347560i	$-0.0110654\pi$
$350$	−1.27856	−	1.59695i	−0.0683418	−	0.0853605i
$351$	−30.0710	+	5.79756i	−1.60507	+	0.309451i
$352$	19.7812	−	4.71561i	1.05434	−	0.251343i
$353$	4.66673	+	5.56159i	0.248385	+	0.296014i	0.875803	−	0.482669i	$-0.160333\pi$
$353$	4.66673	+	5.56159i	0.248385	+	0.296014i	−0.627418	+	0.778683i	$0.715888\pi$
$354$	9.68326	−	14.1699i	0.514659	−	0.753121i
$355$	34.4884	+	6.08124i	1.83046	+	0.322759i
$356$	32.2534	−	4.16802i	1.70943	−	0.220904i
$357$	−3.14857	−	6.18721i	−0.166640	−	0.327462i
$358$	−10.3704	−	9.11645i	−0.548090	−	0.481819i
$359$	−11.0505	−	19.1401i	−0.583226	−	1.01018i	−0.995094	−	0.0989331i	$-0.968457\pi$
$359$	−11.0505	−	19.1401i	−0.583226	−	1.01018i	0.411868	−	0.911243i	$-0.364876\pi$
$360$	−3.74602	+	21.2160i	−0.197433	+	1.11818i
$361$	8.06363	−	13.9666i	0.424402	−	0.735085i
$362$	7.04285	−	2.38136i	0.370164	−	0.125162i
$363$	−0.404207	−	3.30591i	−0.0212154	−	0.173516i
$364$	−7.15343	−	9.36871i	−0.374942	−	0.491054i
$365$	−1.17440	+	1.39959i	−0.0614707	+	0.0732580i
$366$	2.39525	+	2.34130i	0.125202	+	0.122382i
$367$	0.722335	−	1.98460i	0.0377056	−	0.103595i	−0.919411	−	0.393298i	$-0.871334\pi$
$367$	0.722335	−	1.98460i	0.0377056	−	0.103595i	0.957117	+	0.289703i	$0.0935564\pi$
$368$	−12.4023	+	8.59634i	−0.646516	+	0.448115i
$369$	−14.6719	−	10.6826i	−0.763787	−	0.556113i
$370$	−1.98016	+	5.07406i	−0.102944	+	0.263788i
$371$	1.32673	+	7.52424i	0.0688802	+	0.390639i
$372$	8.22884	+	32.2027i	0.426645	+	1.66963i
$373$	−27.2355	+	9.91290i	−1.41020	+	0.513271i	−0.931188	−	0.364538i	$-0.881227\pi$
$373$	−27.2355	+	9.91290i	−1.41020	+	0.513271i	−0.479011	+	0.877809i	$0.659005\pi$
$374$	−17.8765	+	9.77969i	−0.924373	+	0.505696i
$375$	4.56128	+	14.9465i	0.235544	+	0.771833i
$376$	−6.56687	−	2.91758i	−0.338661	−	0.150463i
$377$		−	10.4663i		−	0.539043i
$378$	5.59566	+	4.76326i	0.287810	+	0.244996i
$379$		−	20.2138i		−	1.03831i	−0.854679	−	0.519156i	$-0.826246\pi$
$379$		−	20.2138i		−	1.03831i	0.854679	−	0.519156i	$-0.173754\pi$
$380$	−13.8333	−	26.7290i	−0.709633	−	1.37117i
$381$	−7.55237	−	1.74765i	−0.386920	−	0.0895349i
$382$	0.568608	+	1.03937i	0.0290925	+	0.0531789i
$383$	1.39680	−	0.508393i	0.0713731	−	0.0259777i	−0.306087	−	0.952004i	$-0.599020\pi$
$383$	1.39680	−	0.508393i	0.0713731	−	0.0259777i	0.377460	+	0.926026i	$0.376798\pi$
$384$	16.5715	+	10.4588i	0.845659	+	0.533724i
$385$	1.58494	+	8.98865i	0.0807761	+	0.458104i
$386$	−24.3217	−	9.49159i	−1.23794	−	0.483109i
$387$	22.4209	+	6.45380i	1.13972	+	0.328065i
$388$	18.0851	+	16.6514i	0.918130	+	0.845348i
$389$	−2.01562	+	5.53787i	−0.102196	+	0.280781i	−0.980244	−	0.197791i	$-0.936623\pi$
$389$	−2.01562	+	5.53787i	−0.102196	+	0.280781i	0.878048	+	0.478572i	$0.158846\pi$
$390$	−9.88952	−	35.2954i	−0.500776	−	1.78725i
$391$	9.71949	−	11.5832i	0.491536	−	0.585790i
$392$	−0.682101	+	2.74495i	−0.0344513	+	0.138641i
$393$	−7.36469	+	5.54381i	−0.371499	+	0.279648i
$394$	5.90102	+	17.4522i	0.297289	+	0.879228i
$395$	−17.3747	+	30.0939i	−0.874218	+	1.51419i
$396$	13.4844	−	16.8343i	0.677617	−	0.845957i
$397$	−11.8332	−	20.4956i	−0.593890	−	1.02865i	−0.993703	−	0.112050i	$-0.964258\pi$
$397$	−11.8332	−	20.4956i	−0.593890	−	1.02865i	0.399813	−	0.916597i	$-0.369075\pi$
$398$	10.0300	−	11.4095i	0.502758	−	0.571908i
$399$	−10.2512	−	0.542477i	−0.513203	−	0.0271578i
$400$	−5.76167	−	0.531783i	−0.288084	−	0.0265892i
$401$	30.8265	+	5.43554i	1.53940	+	0.271438i	0.878024	−	0.478617i	$-0.158862\pi$
$401$	30.8265	+	5.43554i	1.53940	+	0.271438i	0.661376	+	0.750054i	$0.269973\pi$
$402$	2.27627	−	29.9416i	0.113530	−	1.49335i
$403$	−36.3492	−	43.3193i	−1.81068	−	2.15789i
$404$	−30.5287	−	6.84447i	−1.51886	−	0.340525i
$405$	10.6868	+	20.1981i	0.531032	+	1.00365i
$406$	−1.96049	+	1.56962i	−0.0972974	+	0.0778988i
$407$	4.17728	−	3.50515i	0.207060	−	0.173744i
$408$	−18.7793	−	5.73572i	−0.929714	−	0.283960i
$409$	3.64385	−	20.6653i	0.180177	−	1.02183i	−0.751820	−	0.659368i	$-0.770824\pi$
$409$	3.64385	−	20.6653i	0.180177	−	1.02183i	0.931997	−	0.362466i	$-0.118065\pi$
$410$	11.2911	−	18.5572i	0.557628	−	0.916476i
$411$	−0.246695	+	4.66182i	−0.0121686	+	0.229951i
$412$	1.02474	−	22.2526i	0.0504855	−	1.09631i
$413$	6.06786	−	3.50328i	0.298580	−	0.172385i
$414$	−4.78010	+	15.2751i	−0.234929	+	0.750732i
$415$	8.78942	+	5.07457i	0.431455	+	0.249101i
$416$	−33.1196	−	3.82714i	−1.62382	−	0.187641i
$417$	5.45126	+	7.24173i	0.266949	+	0.354629i
$418$	−0.693228	+	30.1233i	−0.0339069	+	1.47338i
$419$	−20.9009	−	17.5379i	−1.02107	−	0.856783i	−0.0313124	−	0.999510i	$-0.509969\pi$
$419$	−20.9009	−	17.5379i	−1.02107	−	0.856783i	−0.989762	+	0.142726i	$0.954413\pi$
$420$	−5.12820	+	7.14563i	−0.250230	+	0.348671i
$421$	29.3792	+	10.6932i	1.43186	+	0.521153i	0.937463	−	0.348085i	$-0.113168\pi$
$421$	29.3792	+	10.6932i	1.43186	+	0.521153i	0.494393	+	0.869238i	$0.335390\pi$
$422$	−4.19207	+	0.640105i	−0.204067	+	0.0311598i
$423$	−7.39720	+	1.83633i	−0.359664	+	0.0892855i
$424$	17.9251	+	12.0701i	0.870518	+	0.586177i
$425$	5.70982	−	1.00680i	0.276967	−	0.0488368i
$426$	−3.32774	−	33.6215i	−0.161229	−	1.62897i
$427$	0.467683	+	1.28495i	0.0226328	+	0.0621830i
$428$	25.1187	+	10.4747i	1.21416	+	0.506316i
$429$	−8.27323	+	35.7523i	−0.399436	+	1.72614i
$430$	−5.48058	+	27.3820i	−0.264297	+	1.32048i
$431$	10.4633			0.503998			0.251999	−	0.967728i	$-0.418912\pi$
$431$	10.4633			0.503998			0.251999	+	0.967728i	$0.418912\pi$
$432$	20.6840	−	2.04238i	0.995160	−	0.0982643i
$433$	−10.7272			−0.515514			−0.257757	−	0.966210i	$-0.582983\pi$
$433$	−10.7272			−0.515514			−0.257757	+	0.966210i	$0.582983\pi$
$434$	−2.66307	+	13.3052i	−0.127832	+	0.638672i
$435$	−7.46950	+	2.27950i	−0.358135	+	0.109294i
$436$	7.09417	+	2.95834i	0.339749	+	0.141679i
$437$	−7.64732	−	21.0108i	−0.365821	−	1.00508i
$438$	1.60586	+	0.726676i	0.0767309	+	0.0347219i
$439$	24.7427	−	4.36280i	1.18090	−	0.208225i	0.451476	−	0.892283i	$-0.350898\pi$
$439$	24.7427	−	4.36280i	1.18090	−	0.208225i	0.729427	+	0.684058i	$0.239787\pi$
$440$	21.4137	+	14.4193i	1.02086	+	0.687411i
$441$	1.21742	+	2.74188i	0.0579723	+	0.130566i
$442$	33.0249	−	5.04271i	1.57083	−	0.239857i
$443$	−0.410884	−	0.149550i	−0.0195217	−	0.00710531i	0.332241	−	0.943195i	$-0.392195\pi$
$443$	−0.410884	−	0.149550i	−0.0195217	−	0.00710531i	−0.351763	+	0.936089i	$0.614418\pi$
$444$	5.22906	+	0.518778i	0.248160	+	0.0246201i
$445$	31.6271	+	26.5383i	1.49927	+	1.25804i
$446$	−0.547548	+	23.7929i	−0.0259272	+	1.12663i
$447$	−1.87181	+	0.228863i	−0.0885338	+	0.0108248i
$448$	4.25002	+	6.77771i	0.200794	+	0.320217i
$449$	23.9927	+	13.8522i	1.13228	+	0.653725i	0.944508	−	0.328487i	$-0.106539\pi$
$449$	23.9927	+	13.8522i	1.13228	+	0.653725i	0.187776	+	0.982212i	$0.439872\pi$
$450$	−5.16891	+	3.30862i	−0.243665	+	0.155970i
$451$	−18.8338	+	10.8737i	−0.886850	+	0.512023i
$452$	1.08671	−	23.5983i	0.0511148	−	1.10997i
$453$	−10.2966	+	5.23977i	−0.483776	+	0.246186i
$454$	5.87211	−	9.65096i	0.275592	−	0.452942i
$455$	2.59851	−	14.7369i	0.121820	−	0.690875i
$456$	−21.2297	+	19.8080i	−0.994170	+	0.927593i
$457$	−27.7859	+	23.3152i	−1.29977	+	1.09064i	−0.309587	+	0.950871i	$0.600191\pi$
$457$	−27.7859	+	23.3152i	−1.29977	+	1.09064i	−0.990185	+	0.139766i	$0.955365\pi$
$458$	−17.3088	+	13.8578i	−0.808785	+	0.647535i
$459$	−19.4549	+	7.43395i	−0.908075	+	0.346987i
$460$	−18.6930	−	4.19094i	−0.871566	−	0.195403i
$461$	−14.7221	−	17.5451i	−0.685675	−	0.817156i	0.305150	−	0.952304i	$-0.401293\pi$
$461$	−14.7221	−	17.5451i	−0.685675	−	0.817156i	−0.990825	+	0.135148i	$0.956849\pi$
$462$	7.93762	−	3.81202i	0.369292	−	0.177351i
$463$	−5.05507	−	0.891345i	−0.234929	−	0.0414243i	0.0549441	−	0.998489i	$-0.482502\pi$
$463$	−5.05507	−	0.891345i	−0.234929	−	0.0414243i	−0.289873	+	0.957065i	$0.593613\pi$
$464$	−0.652842	+	7.07330i	−0.0303074	+	0.328370i
$465$	−22.9991	+	35.3760i	−1.06656	+	1.64052i
$466$	−8.39742	+	9.55242i	−0.389003	+	0.442507i
$467$	10.0386	+	17.3873i	0.464530	+	0.804589i	0.999180	−	0.0404842i	$-0.0128900\pi$
$467$	10.0386	+	17.3873i	0.464530	+	0.804589i	−0.534650	+	0.845073i	$0.679557\pi$
$468$	−30.2141	+	18.3741i	−1.39665	+	0.849343i
$469$	6.12943	−	10.6165i	0.283031	−	0.490224i
$470$	−2.92200	−	8.64178i	−0.134782	−	0.398616i
$471$	−23.9344	−	10.1739i	−1.10284	−	0.468789i
$472$	4.77918	−	19.2326i	0.219979	−	0.885254i
$473$	17.9707	−	21.4166i	0.826292	−	0.984736i
$474$	32.4788	+	8.30740i	1.49180	+	0.381572i
$475$	2.93227	−	8.05635i	0.134542	−	0.369651i
$476$	−5.89726	−	5.42977i	−0.270300	−	0.248873i
$477$	22.8667	−	1.57560i	1.04700	−	0.0721420i
$478$	−6.15503	−	2.40201i	−0.281525	−	0.109866i
$479$	6.50545	+	36.8942i	0.297241	+	1.68574i	0.657950	+	0.753061i	$0.271424\pi$
$479$	6.50545	+	36.8942i	0.297241	+	1.68574i	−0.360709	+	0.932678i	$0.617465\pi$
$480$	4.48192	+	24.4700i	0.204571	+	1.11690i
$481$	−8.40110	+	3.05775i	−0.383057	+	0.139421i
$482$	5.14778	+	9.40976i	0.234475	+	0.428603i
$483$	−4.45878	+	4.77658i	−0.202882	+	0.217342i
$484$	−1.76764	−	3.41546i	−0.0803472	−	0.155248i
$485$			31.2086i			1.41711i
$486$	15.9817	−	15.1851i	0.724944	−	0.688808i
$487$			14.2028i			0.643589i	0.946810	+	0.321794i	$0.104286\pi$
$487$			14.2028i			0.643589i	−0.946810	+	0.321794i	$0.895714\pi$
$488$	3.53449	+	1.57033i	0.159999	+	0.0710854i
$489$	−3.40861	+	3.65156i	−0.154143	+	0.165129i
$490$	−3.15011	+	1.72333i	−0.142308	+	0.0778520i
$491$	−14.8018	+	5.38741i	−0.667995	+	0.243130i	−0.653684	−	0.756767i	$-0.726778\pi$
$491$	−14.8018	+	5.38741i	−0.667995	+	0.243130i	−0.0143106	+	0.999898i	$0.504555\pi$
$492$	−20.1780	−	5.65880i	−0.909696	−	0.255118i
$493$	−1.23599	−	7.00964i	−0.0556661	−	0.315698i
$494$	17.9593	−	46.0199i	0.808029	−	2.07053i
$495$	27.3172	−	1.88226i	1.22782	−	0.0846012i
$496$	21.8633	+	31.5431i	0.981689	+	1.41633i
$497$	4.71748	−	12.9612i	0.211608	−	0.581388i
$498$	2.42631	−	9.48594i	0.108726	−	0.425075i
$499$	−25.8613	+	30.8202i	−1.15771	+	1.37970i	−0.245795	+	0.969322i	$0.579049\pi$
$499$	−25.8613	+	30.8202i	−1.15771	+	1.37970i	−0.911914	+	0.410382i	$0.865396\pi$
$500$	10.9506	+	14.3418i	0.489727	+	0.641386i
$501$	28.2463	+	12.0068i	1.26195	+	0.536426i
$502$	−2.37972	+	0.804641i	−0.106212	+	0.0359129i
$503$	−19.4218	+	33.6395i	−0.865973	+	1.49991i	0.000104606		1.00000i	$0.499967\pi$
$503$	−19.4218	+	33.6395i	−0.865973	+	1.49991i	−0.866078	+	0.499909i	$0.833367\pi$
$504$	7.97288	+	2.90399i	0.355140	+	0.129354i
$505$	−19.8592	−	34.3971i	−0.883722	−	1.53065i
$506$	14.4046	+	12.6629i	0.640362	+	0.562935i
$507$	20.5206	−	31.5638i	0.911354	−	1.40180i
$508$	−8.87735	+	1.14720i	−0.393869	+	0.0508985i
$509$	−12.4755	−	2.19976i	−0.552966	−	0.0975028i	−0.109819	−	0.993952i	$-0.535027\pi$
$509$	−12.4755	−	2.19976i	−0.552966	−	0.0975028i	−0.443147	+	0.896449i	$0.646138\pi$
$510$	−10.7914	−	22.4706i	−0.477853	−	0.995015i
$511$	0.462542	+	0.551236i	0.0204617	+	0.0243853i
$512$	22.1440	+	4.65229i	0.978635	+	0.205604i
$513$	−4.86411	+	30.4101i	−0.214756	+	1.34264i
$514$	−27.3498	−	34.1605i	−1.20635	−	1.50675i
$515$	21.6635	−	18.1778i	0.954606	−	0.801010i
$516$	26.8636	−	2.03601i	1.18260	−	0.0896302i
$517$	−1.58592	+	8.99421i	−0.0697487	+	0.395565i
$518$	1.83266	+	1.11508i	0.0805224	+	0.0489936i
$519$	33.5866	−	17.0917i	1.47429	−	0.750242i
$520$	−24.9050	−	34.2222i	−1.09216	−	1.50074i
$521$	−7.32281	+	4.22782i	−0.320818	+	0.185224i	−0.651757	−	0.758428i	$-0.725968\pi$
$521$	−7.32281	+	4.22782i	−0.320818	+	0.185224i	0.330939	+	0.943652i	$0.392635\pi$
$522$	4.06182	+	6.34559i	0.177781	+	0.277739i
$523$	5.13626	+	2.96542i	0.224593	+	0.129669i	0.608075	−	0.793879i	$-0.291942\pi$
$523$	5.13626	+	2.96542i	0.224593	+	0.129669i	−0.383482	+	0.923548i	$0.625275\pi$
$524$	−5.74046	+	8.96347i	−0.250773	+	0.391571i
$525$	−2.48696	+	0.304075i	−0.108540	+	0.0132709i
$526$	−23.9547	−	0.551272i	−1.04448	−	0.0240366i
$527$	−29.4599	−	24.7198i	−1.28329	−	1.07681i
$528$	7.82124	−	23.6459i	0.340376	−	1.02905i
$529$	8.23907	+	2.99878i	0.358221	+	0.130382i
$530$	4.14102	+	27.1197i	0.179875	+	1.17800i
$531$	−8.52992	−	19.2111i	−0.370167	−	0.833692i
$532$	−11.3135	+	3.53749i	−0.490502	+	0.153370i
$533$	35.1132	−	6.19140i	1.52092	−	0.268179i
$534$	16.4210	−	36.2882i	0.710605	−	1.57034i
$535$	11.8167	+	32.4662i	0.510881	+	1.40363i
$536$	−9.58346	−	33.3226i	−0.413943	−	1.43932i
$537$	−16.1746	+	4.93606i	−0.697984	+	0.213007i
$538$	−2.99620	−	0.599697i	−0.129175	−	0.0258548i
$539$	3.59484			0.154841
$540$	19.6935	+	17.5611i	0.847472	+	0.755711i
$541$	23.5098			1.01076			0.505382	−	0.862896i	$-0.331352\pi$
$541$	23.5098			1.01076			0.505382	+	0.862896i	$0.331352\pi$
$542$	−27.3631	−	5.47678i	−1.17535	−	0.235248i
$543$	2.05279	−	8.87101i	0.0880937	−	0.380692i
$544$	−22.6332	+	1.34800i	−0.970392	+	0.0577948i
$545$	3.33735	+	9.16929i	0.142956	+	0.392769i
$546$	−14.3664	+	1.42194i	−0.614827	+	0.0608533i
$547$	16.9279	−	2.98484i	0.723784	−	0.127623i	0.200393	−	0.979715i	$-0.435778\pi$
$547$	16.9279	−	2.98484i	0.723784	−	0.127623i	0.523391	+	0.852093i	$0.324667\pi$
$548$	1.60870	+	5.14490i	0.0687203	+	0.219779i
$549$	3.98139	−	0.988369i	0.169922	−	0.0421826i
$550$	1.11005	+	7.26977i	0.0473328	+	0.309984i
$551$	−9.89035	−	3.59979i	−0.421343	−	0.153356i
$552$	0.972370	+	18.4561i	0.0413868	+	0.785542i
$553$	10.4843	+	8.79736i	0.445837	+	0.374102i
$554$	−18.0092	−	0.414446i	−0.765137	−	0.0176081i
$555$	4.01193	+	5.32965i	0.170297	+	0.226231i
$556$	8.81382	+	5.64462i	0.373789	+	0.239385i
$557$	−17.6798	−	10.2074i	−0.749116	−	0.432502i	0.0762584	−	0.997088i	$-0.475703\pi$
$557$	−17.6798	−	10.2074i	−0.749116	−	0.432502i	−0.825374	+	0.564586i	$0.809036\pi$
$558$	38.8496	+	12.1573i	1.64463	+	0.514661i
$559$	−39.6952	+	22.9180i	−1.67893	+	0.969329i
$560$	−2.67533	+	9.79731i	−0.113053	+	0.414012i
$561$	−1.31880	+	24.9215i	−0.0556798	+	1.05219i
$562$	16.0796	+	9.78358i	0.678276	+	0.412695i
$563$	−3.58611	+	20.3378i	−0.151136	+	0.857137i	0.811097	+	0.584911i	$0.198871\pi$
$563$	−3.58611	+	20.3378i	−0.151136	+	0.857137i	−0.962234	+	0.272225i	$0.912240\pi$
$564$	−7.26737	+	4.96382i	−0.306011	+	0.209015i
$565$	22.9736	−	19.2771i	0.966506	−	0.810995i
$566$	−5.28933	−	6.60649i	−0.222327	−	0.277692i
$567$	8.56515	−	2.76372i	0.359703	−	0.116065i
$568$	−17.1295	−	35.0507i	−0.718738	−	1.47070i
$569$	−15.3298	−	18.2693i	−0.642657	−	0.765888i	0.342131	−	0.939652i	$-0.388851\pi$
$569$	−15.3298	−	18.2693i	−0.642657	−	0.765888i	−0.984787	+	0.173764i	$0.944407\pi$
$570$	−36.7544	−	2.79421i	−1.53947	−	0.117037i
$571$	−26.6373	−	4.69688i	−1.11474	−	0.196558i	−0.414208	−	0.910182i	$-0.635941\pi$
$571$	−26.6373	−	4.69688i	−1.11474	−	0.196558i	−0.700529	+	0.713624i	$0.747052\pi$
$572$	5.43072	+	42.0246i	0.227070	+	1.75714i
$573$	1.44898	+	0.0766774i	0.0605319	+	0.00320324i
$574$	−6.42560	−	5.64867i	−0.268199	−	0.235771i
$575$	−2.72857	−	4.72603i	−0.113789	−	0.197089i
$576$	21.5652	−	10.5329i	0.898551	−	0.438869i
$577$	1.48068	−	2.56462i	0.0616416	−	0.106766i	−0.833558	−	0.552432i	$-0.813700\pi$
$577$	1.48068	−	2.56462i	0.0616416	−	0.106766i	0.895199	+	0.445666i	$0.147033\pi$
$578$	−1.25260	+	0.423535i	−0.0521013	+	0.0176167i
$579$	−25.5468	+	19.2305i	−1.06169	+	0.799193i
$580$	−7.16732	+	5.47257i	−0.297607	+	0.227236i
$581$	2.56941	−	3.06210i	0.106597	−	0.127037i
$582$	28.9917	−	8.12329i	1.20175	−	0.336721i
$583$	9.39383	−	25.8093i	0.389053	−	1.06891i
$584$	2.03046	+	0.140379i	0.0840209	+	0.00580893i
$585$	−43.1409	−	12.4180i	−1.78366	−	0.513422i
$586$	12.6919	−	32.5223i	0.524297	−	1.34348i
$587$	6.23108	+	35.3382i	0.257184	+	1.45856i	0.790403	+	0.612587i	$0.209871\pi$
$587$	6.23108	+	35.3382i	0.257184	+	1.45856i	−0.533219	+	0.845977i	$0.679018\pi$
$588$	2.42086	+	2.47779i	0.0998346	+	0.102182i
$589$	−53.4374	+	19.4496i	−2.20185	+	0.801407i
$590$	22.0715	−	12.0746i	0.908668	−	0.497103i
$591$	21.9824	+	5.08682i	0.904234	+	0.209244i
$592$	5.86831	−	1.54245i	0.241186	−	0.0633943i
$593$		−	20.8685i		−	0.856966i	−0.903550	−	0.428483i	$-0.859048\pi$
$593$		−	20.8685i		−	0.856966i	0.903550	−	0.428483i	$-0.140952\pi$
$594$	−8.85896	−	24.8868i	−0.363487	−	1.02112i
$595$		−	10.1766i		−	0.417201i
$596$	−1.93384	+	1.00084i	−0.0792132	+	0.0409960i
$597$	−5.43068	−	17.7954i	−0.222263	−	0.728316i
$598$	−15.0914	−	27.5860i	−0.617135	−	1.12808i
$599$	11.1021	−	4.04083i	0.453619	−	0.165104i	−0.105099	−	0.994462i	$-0.533516\pi$
$599$	11.1021	−	4.04083i	0.453619	−	0.165104i	0.558718	+	0.829358i	$0.311294\pi$
$600$	−4.26324	+	5.66077i	−0.174046	+	0.231100i
$601$	−3.84395	−	21.8001i	−0.156798	−	0.889245i	−0.957124	−	0.289679i	$-0.906451\pi$
$601$	−3.84395	−	21.8001i	−0.156798	−	0.889245i	0.800326	−	0.599565i	$-0.204660\pi$
$602$	10.2459	+	3.99848i	0.417591	+	0.162966i
$603$	−29.7309	−	21.6470i	−1.21073	−	0.881535i
$604$	−9.03608	+	9.81406i	−0.367673	+	0.399328i
$605$	1.66981	−	4.58778i	0.0678876	−	0.186520i
$606$	−26.7846	+	27.4018i	−1.08805	+	1.11312i
$607$	18.5133	−	22.0633i	0.751431	−	0.895520i	−0.245843	−	0.969310i	$-0.579065\pi$
$607$	18.5133	−	22.0633i	0.751431	−	0.895520i	0.997274	+	0.0737892i	$0.0235092\pi$
$608$	−15.0077	+	29.9807i	−0.608643	+	1.21588i
$609$	0.373297	+	3.05311i	0.0151268	+	0.123718i
$610$	1.57271	+	4.65127i	0.0636772	+	0.188324i
$611$	7.48673	−	12.9674i	0.302881	−	0.524605i
$612$	−18.0655	+	15.8738i	−0.730256	+	0.641659i
$613$	−20.2599	−	35.0911i	−0.818289	−	1.41732i	−0.906942	−	0.421256i	$-0.861590\pi$
$613$	−20.2599	−	35.0911i	−0.818289	−	1.41732i	0.0886529	−	0.996063i	$-0.471744\pi$
$614$	2.27347	−	2.58617i	0.0917497	−	0.104369i
$615$	−12.0660	−	23.7108i	−0.486550	−	0.956110i
$616$	7.05736	−	7.31962i	0.284349	−	0.294916i
$617$	−2.76724	−	0.487939i	−0.111405	−	0.0196437i	0.117668	−	0.993053i	$-0.462458\pi$
$617$	−2.76724	−	0.487939i	−0.111405	−	0.0196437i	−0.229073	+	0.973409i	$0.573569\pi$
$618$	−22.5254	−	15.3931i	−0.906104	−	0.619203i
$619$	13.3331	+	15.8897i	0.535901	+	0.638663i	0.964264	−	0.264945i	$-0.0853537\pi$
$619$	13.3331	+	15.8897i	0.535901	+	0.638663i	−0.428362	+	0.903607i	$0.640909\pi$
$620$	−10.6589	+	47.5424i	−0.428072	+	1.90935i
$621$	12.8380	+	14.8140i	0.515170	+	0.594466i
$622$	−3.27084	+	2.61872i	−0.131149	+	0.105001i
$623$	12.4565	−	10.4522i	0.499059	−	0.418760i
$624$	−25.3088	+	32.0437i	−1.01316	+	1.28277i
$625$	−5.23379	+	29.6823i	−0.209352	+	1.18729i
$626$	−14.4717	+	23.7846i	−0.578404	+	0.950623i
$627$	30.9393	+	20.1146i	1.23560	+	0.803300i
$628$	−29.9985	−	1.38144i	−1.19707	−	0.0551256i
$629$	−5.26539	+	3.03998i	−0.209945	+	0.121212i
$630$	4.14371	+	9.94321i	0.165089	+	0.396147i
$631$	−26.1079	−	15.0734i	−1.03934	−	0.600063i	−0.119693	−	0.992811i	$-0.538191\pi$
$631$	−26.1079	−	15.0734i	−1.03934	−	0.600063i	−0.919646	+	0.392748i	$0.871524\pi$
$632$	38.4953	−	4.07663i	1.53126	−	0.162159i
$633$	−2.03178	+	4.77981i	−0.0807561	+	0.189980i
$634$	0.385942	−	16.7706i	0.0153277	−	0.666045i
$635$	−8.70497	−	7.30433i	−0.345446	−	0.289864i
$636$	24.1155	−	10.9059i	0.956240	−	0.432446i
$637$	−5.53830	−	2.01578i	−0.219435	−	0.0798679i
$638$	8.92470	−	1.36275i	0.353332	−	0.0539518i
$639$	−37.1727	−	18.1772i	−1.47053	−	0.719080i
$640$	14.6966	+	24.6813i	0.580932	+	0.975616i
$641$	−4.63305	+	0.816933i	−0.182995	+	0.0322669i	−0.264394	−	0.964415i	$-0.585172\pi$
$641$	−4.63305	+	0.816933i	−0.182995	+	0.0322669i	0.0813998	+	0.996682i	$0.474061\pi$
$642$	27.0842	−	19.4280i	1.06893	−	0.766761i
$643$	−6.94370	−	19.0777i	−0.273833	−	0.752350i	−0.998029	−	0.0627556i	$-0.980011\pi$
$643$	−6.94370	−	19.0777i	−0.273833	−	0.752350i	0.724196	−	0.689594i	$-0.242211\pi$
$644$	−2.90400	+	6.96386i	−0.114434	+	0.274415i
$645$	25.0013	+	23.3379i	0.984424	+	0.918927i
$646$	6.59339	−	32.9419i	0.259413	−	1.29608i
$647$	5.89746			0.231853			0.115927	−	0.993258i	$-0.463016\pi$
$647$	5.89746			0.231853			0.115927	+	0.993258i	$0.463016\pi$
$648$	11.1877	−	22.8656i	0.439494	−	0.898245i
$649$	−25.1875			−0.988694
$650$	2.36628	−	11.8224i	0.0928133	−	0.463714i
$651$	12.1484	+	11.3401i	0.476133	+	0.444455i
$652$	−2.22003	+	5.32368i	−0.0869430	+	0.208491i
$653$	−7.93336	−	21.7967i	−0.310456	−	0.852972i	−0.992564	−	0.121721i	$-0.961159\pi$
$653$	−7.93336	−	21.7967i	−0.310456	−	0.852972i	0.682108	−	0.731251i	$-0.261063\pi$
$654$	7.64929	−	5.48697i	0.299111	−	0.214557i
$655$	−13.3074	+	2.34645i	−0.519963	+	0.0916836i
$656$	−24.1162	+	1.99404i	−0.941579	+	0.0778541i
$657$	1.79092	−	1.20534i	0.0698706	−	0.0470249i
$658$	−3.55175	+	0.542331i	−0.138461	+	0.0211423i
$659$	9.49459	+	3.45575i	0.369857	+	0.134617i	0.520260	−	0.854008i	$-0.325835\pi$
$659$	9.49459	+	3.45575i	0.369857	+	0.134617i	−0.150403	+	0.988625i	$0.548057\pi$
$660$	28.8089	−	13.0284i	1.12139	−	0.507131i
$661$	21.8059	+	18.2973i	0.848152	+	0.711684i	0.959382	−	0.282111i	$-0.0910345\pi$
$661$	21.8059	+	18.2973i	0.848152	+	0.711684i	−0.111230	+	0.993795i	$0.535479\pi$
$662$	−0.715885	+	31.1078i	−0.0278237	+	1.20904i
$663$	16.0063	−	37.6551i	0.621632	−	1.46240i
$664$	−1.19064	−	11.2432i	−0.0462060	−	0.436320i
$665$	−13.0322	−	7.52412i	−0.505365	−	0.291773i
$666$	3.90681	−	5.11421i	0.151386	−	0.198172i
$667$	−5.80190	+	3.34973i	−0.224650	+	0.129702i
$668$	35.4029	+	1.63032i	1.36978	+	0.0630791i
$669$	24.4375	+	15.8876i	0.944808	+	0.614250i
$670$	22.8801	−	37.6041i	0.883937	−	1.45277i
$671$	0.853591	−	4.84096i	0.0329525	−	0.186883i
$672$	9.79774	−	0.0648526i	0.377956	−	0.00250174i
$673$	15.8518	−	13.3012i	0.611042	−	0.512725i	−0.283932	−	0.958845i	$-0.591639\pi$
$673$	15.8518	−	13.3012i	0.611042	−	0.512725i	0.894973	+	0.446120i	$0.147194\pi$
$674$	−20.0603	+	16.0608i	−0.772695	+	0.618640i
$675$	0.119703	+	7.51549i	0.00460736	+	0.289271i
$676$	9.51029	−	42.4191i	0.365780	−	1.63151i
$677$	26.2129	+	31.2394i	1.00745	+	1.20063i	0.979588	+	0.201015i	$0.0644239\pi$
$677$	26.2129	+	31.2394i	1.00745	+	1.20063i	0.0278571	+	0.999612i	$0.491132\pi$
$678$	−23.8876	−	16.3241i	−0.917399	−	0.626922i
$679$	12.1049	+	2.13442i	0.464544	+	0.0819117i
$680$	−20.7211	−	19.9787i	−0.794617	−	0.766147i
$681$	−6.27512	−	12.3311i	−0.240463	−	0.472530i
$682$	32.2058	−	36.6355i	1.23323	−	1.40285i
$683$	−2.42041	−	4.19228i	−0.0926145	−	0.160413i	0.815996	−	0.578058i	$-0.196189\pi$
$683$	−2.42041	−	4.19228i	−0.0926145	−	0.160413i	−0.908611	+	0.417644i	$0.862856\pi$
$684$	6.97109	+	34.8710i	0.266546	+	1.33333i
$685$	−3.42165	+	5.92647i	−0.130734	+	0.226439i
$686$	0.452987	+	1.33970i	0.0172951	+	0.0511501i
$687$	3.29577	+	26.9553i	0.125741	+	1.02841i
$688$	28.2561	−	13.0123i	1.07725	−	0.496091i
$689$	−28.9447	+	34.4950i	−1.10271	+	1.31415i
$690$	−16.4005	+	16.7784i	−0.624356	+	0.638741i
$691$	−11.8488	+	32.5543i	−0.450749	+	1.23842i	0.481449	+	0.876474i	$0.340111\pi$
$691$	−11.8488	+	32.5543i	−0.450749	+	1.23842i	−0.932198	+	0.361949i	$0.882111\pi$
$692$	29.4749	−	32.0126i	1.12047	−	1.21694i
$693$	1.13821	−	10.7243i	0.0432370	−	0.407382i
$694$	6.46451	+	2.52279i	0.245390	+	0.0957638i
$695$	2.30728	+	13.0852i	0.0875201	+	0.496351i
$696$	6.94942	+	5.23375i	0.263417	+	0.198385i
$697$	22.7853	−	8.29317i	0.863054	−	0.314126i
$698$	−19.9816	−	36.5249i	−0.756316	−	1.38249i
$699$	4.54674	+	14.8988i	0.171973	+	0.563525i
$700$	−2.56937	+	1.32975i	−0.0971131	+	0.0502599i
$701$			0.800827i			0.0302468i	0.999886	+	0.0151234i	$0.00481411\pi$
$701$			0.800827i			0.0302468i	−0.999886	+	0.0151234i	$0.995186\pi$
$702$	−0.306756	+	43.3088i	−0.0115777	+	1.63459i
$703$			8.99046i			0.339082i
$704$	−1.04886	−	28.7396i	−0.0395303	−	1.08316i
$705$	−10.8850	−	2.51884i	−0.409953	−	0.0948649i
$706$	9.00758	−	4.92776i	0.339005	−	0.185459i
$707$	−14.6999	+	5.35032i	−0.552846	+	0.201219i
$708$	−16.9619	−	17.3608i	−0.637467	−	0.652457i
$709$	−5.58549	−	31.6769i	−0.209768	−	1.18965i	−0.889759	−	0.456431i	$-0.849128\pi$
$709$	−5.58549	−	31.6769i	−0.209768	−	1.18965i	0.679991	−	0.733220i	$-0.261984\pi$
$710$	18.0053	−	46.1376i	0.675727	−	1.73151i
$711$	29.5642	−	28.4917i	1.10875	−	1.06852i
$712$	3.17220	−	45.8830i	0.118883	−	1.71954i
$713$	−12.3801	+	34.0140i	−0.463638	+	1.27384i
$714$	−9.45376	+	2.64888i	−0.353798	+	0.0991318i
$715$	−34.5781	+	41.2086i	−1.29315	+	1.54111i
$716$	−15.5202	+	11.8504i	−0.580017	+	0.442869i
$717$	−6.46507	+	4.86662i	−0.241443	+	0.181747i
$718$	−29.6089	+	10.0115i	−1.10499	+	0.373626i
$719$	−4.57215	+	7.91919i	−0.170512	+	0.295336i	−0.938599	−	0.345010i	$-0.887876\pi$
$719$	−4.57215	+	7.91919i	−0.170512	+	0.295336i	0.768087	+	0.640346i	$0.221209\pi$
$720$	28.3807	+	11.0832i	1.05769	+	0.413047i
$721$	−5.56904	−	9.64587i	−0.207402	−	0.359231i
$722$	−17.1296	−	15.0584i	−0.637496	−	0.560415i
$723$	13.1180	+	0.694184i	0.487865	+	0.0258170i
$724$	−1.34750	−	10.4273i	−0.0500793	−	0.387529i
$725$	−2.52980	−	0.446072i	−0.0939543	−	0.0165667i
$726$	−4.69653	−	0.357049i	−0.174305	−	0.0132513i
$727$	−0.526612	−	0.627591i	−0.0195309	−	0.0232761i	0.756191	−	0.654351i	$-0.227058\pi$
$727$	−0.526612	−	0.627591i	−0.0195309	−	0.0232761i	−0.775722	+	0.631075i	$0.782614\pi$
$728$	−14.9771	+	7.31942i	−0.555090	+	0.271276i
$729$	−5.53292	−	26.4270i	−0.204923	−	0.978778i
$730$	1.61487	+	2.01701i	0.0597690	+	0.0746528i
$731$	−23.8787	+	20.0366i	−0.883187	+	0.741082i
$732$	3.91152	−	2.67168i	0.144574	−	0.0987481i
$733$	4.60630	−	26.1236i	0.170138	−	0.964898i	−0.773470	−	0.633833i	$-0.781481\pi$
$733$	4.60630	−	26.1236i	0.170138	−	0.964898i	0.943608	−	0.331066i	$-0.107408\pi$
$734$	−2.55158	−	1.55250i	−0.0941805	−	0.0573039i
$735$	−0.232393	+	4.39154i	−0.00857193	+	0.161984i
$736$	8.47832	+	19.5844i	0.312515	+	0.721889i
$737$	−38.1646	+	22.0343i	−1.40581	+	0.811646i
$738$	−18.8859	+	17.3806i	−0.695198	+	0.639790i
$739$	−35.7992	−	20.6687i	−1.31690	−	0.760311i	−0.333668	−	0.942691i	$-0.608287\pi$
$739$	−35.7992	−	20.6687i	−1.31690	−	0.760311i	−0.983228	+	0.182380i	$0.941620\pi$
$740$	6.48665	+	4.15423i	0.238454	+	0.152713i
$741$	−36.3867	−	48.3380i	−1.33670	−	1.77574i
$742$	10.8022	+	0.248591i	0.396560	+	0.00912607i
$743$	16.0016	+	13.4269i	0.587041	+	0.492586i	0.887251	−	0.461287i	$-0.152612\pi$
$743$	16.0016	+	13.4269i	0.587041	+	0.492586i	−0.300210	+	0.953873i	$0.597057\pi$
$744$	46.9397	−	2.47305i	1.72089	−	0.0906665i
$745$	−2.59761	−	0.945451i	−0.0951689	−	0.0346387i
$746$	6.18703	+	40.5191i	0.226523	+	1.48351i
$747$	−8.32147	−	8.63471i	−0.304467	−	0.315928i
$748$	8.59990	+	27.5039i	0.314444	+	1.00564i
$749$	13.4009	−	2.36294i	0.489657	−	0.0863398i
$750$	21.9924	−	2.17673i	0.803051	−	0.0794830i
$751$	5.79734	+	15.9281i	0.211548	+	0.581224i	0.999400	−	0.0346414i	$-0.0110289\pi$
$751$	5.79734	+	15.9281i	0.211548	+	0.581224i	−0.787852	+	0.615865i	$0.788807\pi$
$752$	−5.86849	+	8.29657i	−0.214002	+	0.302545i
$753$	−0.693620	+	2.99744i	−0.0252769	+	0.109233i
$754$	−14.5138	−	2.90496i	−0.528560	−	0.105792i
$755$	−16.9357			−0.616352
$756$	8.15835	−	6.43750i	0.296716	−	0.234129i
$757$	−1.87362			−0.0680980			−0.0340490	−	0.999420i	$-0.510840\pi$
$757$	−1.87362			−0.0680980			−0.0340490	+	0.999420i	$0.510840\pi$
$758$	−28.0307	−	5.61040i	−1.01812	−	0.203779i
$759$	22.4667	−	6.85626i	0.815490	−	0.248867i
$760$	−40.9048	+	11.7641i	−1.48377	+	0.426728i
$761$	−4.64612	−	12.7651i	−0.168422	−	0.462735i	0.826553	−	0.562858i	$-0.190298\pi$
$761$	−4.64612	−	12.7651i	−0.168422	−	0.462735i	−0.994975	+	0.100124i	$0.968076\pi$
$762$	−4.51967	+	9.98788i	−0.163730	+	0.361823i
$763$	3.78476	−	0.667355i	0.137017	−	0.0241599i
$764$	1.59913	−	0.500013i	0.0578544	−	0.0180898i
$765$	−30.3594	−	3.22215i	−1.09765	−	0.116497i
$766$	−0.317308	−	2.07806i	−0.0114648	−	0.0750834i
$767$	38.8044	+	14.1236i	1.40115	+	0.509975i
$768$	19.1028	−	20.0769i	0.689312	−	0.724464i
$769$	30.3944	+	25.5040i	1.09605	+	0.919696i	0.997153	−	0.0754014i	$-0.0240238\pi$
$769$	30.3944	+	25.5040i	1.09605	+	0.919696i	0.0988980	+	0.995098i	$0.468468\pi$
$770$	12.9046	+	0.296973i	0.465048	+	0.0107022i
$771$	−53.1988	+	6.50451i	−1.91591	+	0.234254i
$772$	−19.9126	+	31.0927i	−0.716672	+	1.11905i
$773$	−22.2909	−	12.8697i	−0.801748	−	0.462889i	0.0423343	−	0.999104i	$-0.486521\pi$
$773$	−22.2909	−	12.8697i	−0.801748	−	0.462889i	−0.844082	+	0.536214i	$0.819854\pi$
$774$	15.1725	−	29.3000i	0.545365	−	1.05317i
$775$	−12.0198	+	6.93965i	−0.431765	+	0.249280i
$776$	28.1103	−	20.4571i	1.00910	−	0.734366i
$777$	2.34161	−	1.19161i	0.0840046	−	0.0427487i
$778$	7.11998	+	4.33214i	0.255264	+	0.155315i
$779$	6.22616	−	35.3103i	0.223075	−	1.26512i
$780$	−51.6893	+	3.91756i	−1.85077	+	0.140271i
$781$	−37.9833	+	31.8718i	−1.35915	+	1.14046i
$782$	−13.3649	−	16.6931i	−0.477928	−	0.596943i
$783$	9.22636	−	0.146953i	0.329723	−	0.00525166i
$784$	3.61713	+	1.70774i	0.129183	+	0.0609909i
$785$	−24.5053	−	29.2043i	−0.874631	−	1.04234i
$786$	5.64357	+	11.7514i	0.201299	+	0.419158i
$787$	7.39252	+	1.30350i	0.263515	+	0.0464648i	0.303844	−	0.952722i	$-0.401730\pi$
$787$	7.39252	+	1.30350i	0.263515	+	0.0464648i	−0.0403296	+	0.999186i	$0.512841\pi$
$788$	25.8389	−	3.33909i	0.920474	−	0.118950i
$789$	−15.9956	+	24.6037i	−0.569459	+	0.875914i
$790$	36.9091	+	32.4464i	1.31317	+	1.15439i
$791$	−5.90584	−	10.2292i	−0.209987	−	0.363709i
$792$	−19.6017	−	23.3714i	−0.696516	−	0.830466i
$793$	−4.02958	+	6.97945i	−0.143095	+	0.247847i
$794$	−31.7058	+	10.7205i	−1.12520	+	0.380458i
$795$	30.9220	+	13.1442i	1.09669	+	0.466176i
$796$	−13.0379	−	17.0754i	−0.462115	−	0.605223i
$797$	−2.21668	+	2.64173i	−0.0785187	+	0.0935750i	−0.803874	−	0.594800i	$-0.797231\pi$
$797$	−2.21668	+	2.64173i	−0.0785187	+	0.0935750i	0.725355	+	0.688375i	$0.241676\pi$
$798$	−3.59751	+	14.0649i	−0.127351	+	0.497892i
$799$	3.48276	−	9.56881i	0.123211	−	0.338520i
$800$	−2.33660	+	7.84217i	−0.0826112	+	0.277263i
$801$	−27.2376	−	40.4702i	−0.962393	−	1.42994i
$802$	16.0935	−	41.2387i	0.568281	−	1.45619i
$803$	−0.449194	−	2.54751i	−0.0158517	−	0.0898995i
$804$	−40.8885	−	11.4669i	−1.44203	−	0.404407i
$805$	−9.00087	+	3.27605i	−0.317239	+	0.115466i
$806$	−70.1601	+	38.3824i	−2.47129	+	1.35196i
$807$	−2.55368	+	2.73569i	−0.0898938	+	0.0963010i
$808$	−17.9646	+	40.4348i	−0.631994	+	1.42249i
$809$		−	51.7773i		−	1.82039i	−0.414176	−	0.910197i	$-0.635930\pi$
$809$		−	51.7773i		−	1.82039i	0.414176	−	0.910197i	$-0.364070\pi$
$810$	30.9750	−	9.21346i	1.08835	−	0.323728i
$811$		−	33.9227i		−	1.19119i	−0.803286	−	0.595594i	$-0.796917\pi$
$811$		−	33.9227i		−	1.19119i	0.803286	−	0.595594i	$-0.203083\pi$
$812$	1.63247	+	3.15428i	0.0572883	+	0.110694i
$813$	−23.3217	+	24.9840i	−0.817928	+	0.876226i
$814$	−3.70121	−	6.76554i	−0.129727	−	0.237132i
$815$	−6.88091	+	2.50445i	−0.241028	+	0.0877270i
$816$	−13.1660	+	24.4495i	−0.460903	+	0.855903i
$817$	8.00404	+	45.3932i	0.280026	+	1.58811i
$818$	−27.6454	−	10.7887i	−0.966600	−	0.377218i
$819$	−7.76710	+	15.8839i	−0.271405	+	0.555027i
$820$	−22.5996	−	20.8081i	−0.789213	−	0.726650i
$821$	5.29388	−	14.5448i	0.184758	−	0.507618i	−0.812388	−	0.583117i	$-0.801833\pi$
$821$	5.29388	−	14.5448i	0.184758	−	0.507618i	0.997146	+	0.0754994i	$0.0240551\pi$
$822$	6.39612	+	1.63600i	0.223090	+	0.0570619i
$823$	0.101128	−	0.120519i	0.00352509	−	0.00420104i	−0.764279	−	0.644886i	$-0.776905\pi$
$823$	0.101128	−	0.120519i	0.00352509	−	0.00420104i	0.767804	+	0.640685i	$0.221349\pi$
$824$	−30.5735	−	7.59730i	−1.06508	−	0.264664i
$825$	8.28902	+	3.52346i	0.288586	+	0.122671i
$826$	−3.17388	−	9.38670i	−0.110433	−	0.326605i
$827$	11.7269	−	20.3117i	0.407786	−	0.706306i	−0.586855	−	0.809692i	$-0.699634\pi$
$827$	11.7269	−	20.3117i	0.407786	−	0.706306i	0.994641	+	0.103386i	$0.0329676\pi$
$828$	19.8554	+	10.8683i	0.690024	+	0.377699i
$829$	−26.9598	−	46.6958i	−0.936353	−	1.62181i	−0.772204	−	0.635375i	$-0.780845\pi$
$829$	−26.9598	−	46.6958i	−0.936353	−	1.62181i	−0.164149	−	0.986436i	$-0.552488\pi$
$830$	9.47649	−	10.7799i	0.328934	−	0.374176i
$831$	−12.0255	+	18.4970i	−0.417160	+	0.641655i
$832$	−14.4996	+	44.8650i	−0.502683	+	1.55542i
$833$	−3.94723	−	0.696003i	−0.136763	−	0.0241151i
$834$	11.5552	−	5.54935i	0.400124	−	0.192158i
$835$	28.9201	+	34.4657i	1.00082	+	1.19273i
$836$	41.5798	+	9.32211i	1.43807	+	0.322412i
$837$	37.6768	−	32.6511i	1.30230	−	1.12859i
$838$	−30.1211	+	24.1157i	−1.04052	+	0.833065i
$839$	−1.09093	+	0.915398i	−0.0376630	+	0.0316030i	−0.661425	−	0.750011i	$-0.730048\pi$
$839$	−1.09093	+	0.915398i	−0.0376630	+	0.0316030i	0.623762	+	0.781614i	$0.285604\pi$
$840$	8.48558	+	9.09461i	0.292780	+	0.313794i
$841$	4.48818	−	25.4537i	0.154765	−	0.877715i
$842$	22.9826	−	37.7726i	0.792033	−	1.30173i
$843$	20.5450	−	10.4551i	0.707609	−	0.360091i
$844$	−0.275881	+	5.99084i	−0.00949623	+	0.206213i
$845$	47.7942	−	27.5940i	1.64417	−	0.949262i
$846$	0.493344	+	10.7674i	0.0169615	+	0.370192i
$847$	−1.66527	−	0.961442i	−0.0572193	−	0.0330355i
$848$	21.7129	−	21.5068i	0.745624	−	0.738545i
$849$	−10.2884	+	1.25794i	−0.353098	+	0.0431725i
$850$	0.188645	−	8.19730i	0.00647047	−	0.281165i
$851$	4.38378	+	3.67843i	0.150274	+	0.126095i
$852$	−47.5469	−	4.71716i	−1.62893	−	0.161607i
$853$	32.0853	+	11.6781i	1.09858	+	0.399851i	0.826793	−	0.562507i	$-0.190163\pi$
$853$	32.0853	+	11.6781i	1.09858	+	0.399851i	0.271788	+	0.962357i	$0.412385\pi$
$854$	1.91166	−	0.291899i	0.0654156	−	0.00998859i
$855$	−26.5726	+	36.4958i	−0.908762	+	1.24813i
$856$	21.4972	−	31.9250i	0.734759	−	1.09117i
$857$	42.5780	−	7.50765i	1.45444	−	0.256457i	0.610124	−	0.792306i	$-0.291120\pi$
$857$	42.5780	−	7.50765i	1.45444	−	0.256457i	0.844313	+	0.535850i	$0.180009\pi$
$858$	47.2818	+	21.3957i	1.61417	+	0.730438i
$859$	−5.54676	−	15.2396i	−0.189253	−	0.519969i	0.808385	−	0.588654i	$-0.200342\pi$
$859$	−5.54676	−	15.2396i	−0.189253	−	0.519969i	−0.997638	+	0.0686850i	$0.978120\pi$
$860$	36.4498	+	15.1999i	1.24293	+	0.518314i
$861$	−10.0220	+	3.05844i	−0.341547	+	0.104231i
$862$	2.90411	−	14.5095i	0.0989145	−	0.494196i
$863$	9.81183			0.333999			0.166999	−	0.985957i	$-0.446592\pi$
$863$	9.81183			0.333999			0.166999	+	0.985957i	$0.446592\pi$
$864$	2.90872	−	29.2496i	0.0989566	−	0.995092i
$865$	55.2427			1.87831
$866$	−2.97735	+	14.8754i	−0.101175	+	0.505488i
$867$	−0.365098	+	1.57775i	−0.0123994	+	0.0535831i
$868$	17.7114	+	7.38582i	0.601163	+	0.250691i
$869$	−16.8274	−	46.2328i	−0.570830	−	1.56834i
$870$	1.08782	+	10.9907i	0.0368806	+	0.372620i
$871$	71.1528	−	12.5462i	2.41092	−	0.425111i
$872$	6.07137	−	9.01645i	0.205602	−	0.305336i
$873$	10.2002	−	35.4361i	0.345225	−	1.19933i
$874$	−31.2585	+	4.77299i	−1.05733	+	0.161449i
$875$	8.47814	+	3.08579i	0.286613	+	0.104319i
$876$	1.45340	−	2.02517i	0.0491058	−	0.0684241i
$877$	18.2568	+	15.3192i	0.616487	+	0.517294i	0.896697	−	0.442645i	$-0.145960\pi$
$877$	18.2568	+	15.3192i	0.616487	+	0.517294i	−0.280210	+	0.959939i	$0.590404\pi$
$878$	0.817466	−	35.5218i	0.0275881	−	1.19880i
$879$	−25.7145	−	34.1605i	−0.867329	−	1.15220i
$880$	25.9388	−	25.6925i	0.874396	−	0.866095i
$881$	−1.98420	−	1.14558i	−0.0668493	−	0.0385955i	0.466203	−	0.884678i	$-0.345622\pi$
$881$	−1.98420	−	1.14558i	−0.0668493	−	0.0385955i	−0.533052	+	0.846082i	$0.678955\pi$
$882$	4.14009	−	0.927191i	0.139404	−	0.0312201i
$883$	−29.1285	+	16.8173i	−0.980252	+	0.565949i	−0.902346	−	0.431012i	$-0.858157\pi$
$883$	−29.1285	+	16.8173i	−0.980252	+	0.565949i	−0.0779056	+	0.996961i	$0.524823\pi$
$884$	2.17338	−	47.1955i	0.0730986	−	1.58736i
$885$	1.62827	−	30.7696i	0.0547338	−	1.03431i
$886$	−0.321424	+	0.528269i	−0.0107984	+	0.0177475i
$887$	1.22398	−	6.94151i	0.0410971	−	0.233073i	−0.957340	−	0.288965i	$-0.906689\pi$
$887$	1.22398	−	6.94151i	0.0410971	−	0.233073i	0.998437	+	0.0558916i	$0.0178001\pi$
$888$	2.17073	−	7.10720i	0.0728451	−	0.238502i
$889$	−3.42850	+	2.87685i	−0.114988	+	0.0964865i
$890$	45.5791	−	36.4918i	1.52781	−	1.22321i
$891$	−31.6328	−	6.79111i	−1.05974	−	0.227511i
$892$	32.8419	+	7.36310i	1.09963	+	0.246535i
$893$	−9.67880	−	11.5347i	−0.323889	−	0.385995i
$894$	−0.202161	+	2.65918i	−0.00676129	+	0.0889364i
$895$	−24.4131	−	4.30469i	−0.816039	−	0.143890i
$896$	10.5783	−	4.01237i	0.353397	−	0.134044i
$897$	−38.4573	−	2.03510i	−1.28405	−	0.0679498i
$898$	25.8682	−	29.4262i	0.863233	−	0.981964i
$899$	8.51944	+	14.7561i	0.284139	+	0.492143i
$900$	3.15345	+	8.08609i	0.105115	+	0.269536i
$901$	−15.3116	+	26.5206i	−0.510105	+	0.883528i
$902$	9.85130	+	29.1351i	0.328012	+	0.970092i
$903$	10.7620	−	8.10115i	0.358137	−	0.269590i
$904$	−32.4224	−	8.05675i	−1.07835	−	0.267963i
$905$	8.57967	−	10.2249i	0.285198	−	0.339886i
$906$	4.40820	+	15.7327i	0.146452	+	0.522684i
$907$	3.08021	−	8.46280i	0.102277	−	0.281003i	−0.877991	−	0.478677i	$-0.841117\pi$
$907$	3.08021	−	8.46280i	0.102277	−	0.281003i	0.980268	+	0.197674i	$0.0633388\pi$
$908$	−11.7533	−	10.8216i	−0.390046	−	0.359126i
$909$	11.3070	+	45.5474i	0.375029	+	1.51071i
$910$	−19.7145	−	7.69364i	−0.653531	−	0.255042i
$911$	−6.85555	−	38.8797i	−0.227134	−	1.28814i	−0.858562	−	0.512709i	$-0.828642\pi$
$911$	−6.85555	−	38.8797i	−0.227134	−	1.28814i	0.631428	−	0.775434i	$-0.282469\pi$
$912$	21.5756	+	34.9371i	0.714438	+	1.15688i
$913$	−13.5030	+	4.91470i	−0.446885	+	0.162653i
$914$	24.6193	+	45.0022i	0.814334	+	1.48854i
$915$	5.85864	+	1.35571i	0.193681	+	0.0448186i
$916$	14.4127	+	27.8485i	0.476209	+	0.920141i
$917$			5.32204i			0.175749i
$918$	4.90898	+	29.0416i	0.162021	+	0.958515i
$919$			54.0793i			1.78391i	0.452123	+	0.891956i	$0.350667\pi$
$919$			54.0793i			1.78391i	−0.452123	+	0.891956i	$0.649333\pi$
$920$	−10.9999	+	24.7586i	−0.362656	+	0.816266i
$921$	−1.23096	−	4.03362i	−0.0405614	−	0.132912i
$922$	−28.4161	+	15.5455i	−0.935834	+	0.511965i
$923$	76.3897	−	27.8036i	2.51440	−	0.915166i
$924$	−3.08305	−	12.0652i	−0.101425	−	0.396916i
$925$	0.381031	+	2.16093i	0.0125282	+	0.0710511i
$926$	−2.63909	+	6.76252i	−0.0867257	+	0.222230i
$927$	−30.5393	+	13.5597i	−1.00304	+	0.445360i
$928$	9.62741	+	2.86852i	0.316035	+	0.0941637i
$929$	−6.27955	+	17.2529i	−0.206025	+	0.566050i	−0.999070	−	0.0431132i	$-0.986272\pi$
$929$	−6.27955	+	17.2529i	−0.206025	+	0.566050i	0.793045	+	0.609163i	$0.208495\pi$
$930$	42.6728	+	41.7117i	1.39930	+	1.36778i
$931$	−3.80969	+	4.54021i	−0.124858	+	0.148799i
$932$	10.9157	+	14.2961i	0.357556	+	0.468284i
$933$	0.622802	+	5.09375i	0.0203896	+	0.166762i
$934$	26.8974	−	9.09469i	0.880110	−	0.297587i
$935$	−18.2917	+	31.6821i	−0.598202	+	1.03612i
$936$	17.0935	+	46.9980i	0.558719	+	1.53618i
$937$	5.47192	+	9.47764i	0.178760	+	0.309621i	0.941456	−	0.337136i	$-0.109458\pi$
$937$	5.47192	+	9.47764i	0.178760	+	0.309621i	−0.762696	+	0.646757i	$0.776125\pi$
$938$	−13.0208	−	11.4464i	−0.425143	−	0.373738i
$939$	15.4649	+	30.3898i	0.504678	+	0.991733i
$940$	−12.7947	+	1.65342i	−0.417316	+	0.0539285i
$941$	−8.34770	−	1.47192i	−0.272127	−	0.0479834i	0.0359192	−	0.999355i	$-0.488564\pi$
$941$	−8.34770	−	1.47192i	−0.272127	−	0.0479834i	−0.308046	+	0.951371i	$0.599675\pi$
$942$	−20.7513	+	30.3662i	−0.676114	+	0.989384i
$943$	−14.6700	−	17.4831i	−0.477722	−	0.569327i
$944$	−25.3436	−	11.9654i	−0.824864	−	0.389441i
$945$	13.0275	+	2.08375i	0.423783	+	0.0677842i
$946$	−24.7108	−	30.8643i	−0.803417	−	1.00349i
$947$	18.7513	−	15.7342i	0.609335	−	0.511293i	−0.285096	−	0.958499i	$-0.592025\pi$
$947$	18.7513	−	15.7342i	0.609335	−	0.511293i	0.894431	+	0.447206i	$0.147581\pi$
$948$	20.5345	−	42.7329i	0.666931	−	1.38790i
$949$	−0.736452	+	4.17663i	−0.0239063	+	0.135579i
$950$	−10.3580	−	6.30228i	−0.336057	−	0.204473i
$951$	−17.2249	−	11.1985i	−0.558556	−	0.363135i
$952$	−9.16632	+	6.67074i	−0.297082	+	0.216200i
$953$	11.0223	−	6.36373i	0.357047	−	0.206141i	−0.310737	−	0.950496i	$-0.600576\pi$
$953$	11.0223	−	6.36373i	0.357047	−	0.206141i	0.667785	+	0.744354i	$0.267243\pi$
$954$	4.16182	−	32.1468i	0.134744	−	1.04079i
$955$	1.84205	+	1.06351i	0.0596075	+	0.0344144i
$956$	−5.03925	+	7.86856i	−0.162981	+	0.254487i
$957$	4.32556	−	10.1760i	0.139826	−	0.328943i
$958$	52.9672	+	1.21894i	1.71129	+	0.0393821i
$959$	2.06470	+	1.73249i	0.0666725	+	0.0559449i
$960$	35.1767	+	0.576597i	1.13532	+	0.0186096i
$961$	57.3782	+	20.8840i	1.85091	+	0.673676i
$962$	1.90846	+	12.4986i	0.0615312	+	0.402970i
$963$	−2.80619	−	40.7263i	−0.0904283	−	1.31239i
$964$	14.4774	−	4.52678i	0.466285	−	0.145798i
$965$	−46.1611	+	8.13944i	−1.48598	+	0.262018i
$966$	5.38618	+	7.50879i	0.173298	+	0.241591i
$967$	−12.3247	−	33.8619i	−0.396336	−	1.08892i	−0.964055	−	0.265702i	$-0.914396\pi$
$967$	−12.3247	−	33.8619i	−0.396336	−	1.08892i	0.567719	−	0.823222i	$-0.307826\pi$
$968$	−5.22687	+	1.50323i	−0.167998	+	0.0483156i
$969$	−30.0777	−	28.0765i	−0.966235	−	0.901948i
$970$	43.2772	+	8.66203i	1.38955	+	0.278121i
$971$	−62.1195			−1.99351			−0.996754	−	0.0805047i	$-0.974347\pi$
$971$	−62.1195			−1.99351			−0.996754	+	0.0805047i	$0.974347\pi$
$972$	−16.6215	−	26.3766i	−0.533135	−	0.846030i
$973$	5.23319			0.167768
$974$	19.6951	+	3.94202i	0.631072	+	0.126311i
$975$	−10.7945	−	10.0763i	−0.345701	−	0.322700i
$976$	3.15860	−	4.46546i	0.101104	−	0.142936i
$977$	−3.44435	−	9.46326i	−0.110194	−	0.302757i	0.872322	−	0.488931i	$-0.162613\pi$
$977$	−3.44435	−	9.46326i	−0.110194	−	0.302757i	−0.982517	+	0.186175i	$0.940391\pi$
$978$	4.11759	+	5.74026i	0.131666	+	0.183553i
$979$	−57.5670	+	10.1506i	−1.83985	+	0.324415i
$980$	1.51543	+	4.84661i	0.0484087	+	0.154819i
$981$	−0.792542	−	11.5022i	−0.0253039	−	0.367236i
$982$	3.36249	+	22.0211i	0.107301	+	0.702720i
$983$	5.46885	+	1.99050i	0.174429	+	0.0634871i	0.427758	−	0.903893i	$-0.359303\pi$
$983$	5.46885	+	1.99050i	0.174429	+	0.0634871i	−0.253329	+	0.967380i	$0.581526\pi$
$984$	−13.4476	+	26.4105i	−0.428693	+	0.841935i
$985$	25.3372	+	21.2604i	0.807310	+	0.677414i
$986$	−10.0634	−	0.231589i	−0.320484	−	0.00737531i
$987$	−1.72144	+	4.04972i	−0.0547939	+	0.128904i
$988$	−58.8315	−	37.6774i	−1.87168	−	1.19868i
$989$	25.4087	+	14.6697i	0.807950	+	0.466470i
$990$	4.97182	−	38.4034i	0.158015	−	1.22054i
$991$	34.6904	−	20.0285i	1.10198	−	0.636227i	0.165238	−	0.986254i	$-0.447161\pi$
$991$	34.6904	−	20.0285i	1.10198	−	0.636227i	0.936740	+	0.350026i	$0.113827\pi$
$992$	49.8094	−	21.5631i	1.58145	−	0.684630i
$993$	31.9505	+	20.7720i	1.01392	+	0.659180i
$994$	−16.6640	−	10.1392i	−0.528551	−	0.321596i
$995$	4.73605	−	26.8594i	0.150143	−	0.851502i
$996$	−12.4808	−	5.99744i	−0.395470	−	0.190036i
$997$	7.74004	−	6.49467i	0.245130	−	0.205688i	−0.511942	−	0.859020i	$-0.671074\pi$
$997$	7.74004	−	6.49467i	0.245130	−	0.205688i	0.757072	+	0.653332i	$0.226629\pi$
$998$	35.5609	+	44.4163i	1.12566	+	1.40597i
$999$	−2.81345	−	7.36287i	−0.0890136	−	0.232951i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.cf.a.491.62	yes	648
4.3	odd	2	inner	756.2.cf.a.491.3	✓	648
27.11	odd	18	inner	756.2.cf.a.659.3	yes	648
108.11	even	18	inner	756.2.cf.a.659.62	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.cf.a.491.3	✓	648	4.3	odd	2	inner
756.2.cf.a.491.62	yes	648	1.1	even	1	trivial
756.2.cf.a.659.3	yes	648	27.11	odd	18	inner
756.2.cf.a.659.62	yes	648	108.11	even	18	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.cf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.277553 - 1.38671i) q^{2} +(-1.26614 - 1.18190i) q^{3} +(-1.84593 - 0.769771i) q^{4} +(-0.868390 - 2.38588i) q^{5} +(-1.99037 + 1.42773i) q^{6} +(-0.984808 + 0.173648i) q^{7} +(-1.57979 + 2.34612i) q^{8} +(0.206222 + 2.99290i) q^{9} +(-3.54955 + 0.541996i) q^{10} +(3.37805 + 1.22951i) q^{11} +(1.42741 + 3.15634i) q^{12} +(-4.51486 - 3.78842i) q^{13} +(-0.0325368 + 1.41384i) q^{14} +(-1.72037 + 4.04721i) q^{15} +(2.81490 + 2.84189i) q^{16} +(-3.47113 - 2.00406i) q^{17} +(4.20753 + 0.544719i) q^{18} +(-5.13278 + 2.96341i) q^{19} +(-0.233597 + 5.07263i) q^{20} +(1.45214 + 0.944082i) q^{21} +(2.64256 - 4.34312i) q^{22} +(-0.655097 + 3.71524i) q^{23} +(4.77311 - 1.10335i) q^{24} +(-1.10811 + 0.929818i) q^{25} +(-6.50655 + 5.20932i) q^{26} +(3.27621 - 4.03317i) q^{27} +(1.95155 + 0.437534i) q^{28} +(1.14149 + 1.36037i) q^{29} +(5.13482 + 3.50897i) q^{30} +(9.44906 + 1.66612i) q^{31} +(4.72216 - 3.11468i) q^{32} +(-2.82392 - 5.54924i) q^{33} +(-3.74247 + 4.25722i) q^{34} +(1.26950 + 2.19884i) q^{35} +(1.92318 - 5.68343i) q^{36} +(0.758455 - 1.31368i) q^{37} +(2.68477 + 7.94018i) q^{38} +(1.23891 + 10.1328i) q^{39} +(6.96943 + 1.73186i) q^{40} +(-3.88862 + 4.63428i) q^{41} +(1.71221 - 1.75166i) q^{42} +(2.65992 - 7.30807i) q^{43} +(-5.28919 - 4.86991i) q^{44} +(6.96164 - 3.09103i) q^{45} +(4.97014 + 1.93961i) q^{46} +(0.441166 + 2.50198i) q^{47} +(-0.205239 - 6.92516i) q^{48} +(0.939693 - 0.342020i) q^{49} +(0.981827 + 1.79471i) q^{50} +(2.02634 + 6.63995i) q^{51} +(5.41790 + 10.4686i) q^{52} -7.64032i q^{53} +(-4.68352 - 5.66257i) q^{54} -9.12732i q^{55} +(1.14839 - 2.58480i) q^{56} +(10.0013 + 2.31434i) q^{57} +(2.20327 - 1.20534i) q^{58} +(-6.58401 + 2.39638i) q^{59} +(6.29111 - 6.14657i) q^{60} +(-0.237449 - 1.34664i) q^{61} +(4.93304 - 12.6407i) q^{62} +(-0.722802 - 2.91162i) q^{63} +(-3.00851 - 7.41275i) q^{64} +(-5.11806 + 14.0618i) q^{65} +(-8.47898 + 2.37575i) q^{66} +(-7.87985 + 9.39084i) q^{67} +(4.86480 + 6.37133i) q^{68} +(5.22049 - 3.92976i) q^{69} +(3.40151 - 1.15014i) q^{70} +(-6.89650 + 11.9451i) q^{71} +(-7.34749 - 4.24434i) q^{72} +(-0.359794 - 0.623182i) q^{73} +(-1.61118 - 1.41637i) q^{74} +(2.50198 + 0.132400i) q^{75} +(11.7559 - 1.51918i) q^{76} +(-3.54023 - 0.624238i) q^{77} +(14.3951 + 1.09437i) q^{78} +(-8.79736 - 10.4843i) q^{79} +(4.33597 - 9.18390i) q^{80} +(-8.91494 + 1.23441i) q^{81} +(5.34710 + 6.67865i) q^{82} +(-3.06210 + 2.56941i) q^{83} +(-1.95382 - 2.86052i) q^{84} +(-1.76715 + 10.0220i) q^{85} +(-9.39590 - 5.71691i) q^{86} +(0.162541 - 3.07155i) q^{87} +(-8.22118 + 5.98292i) q^{88} +(-14.0823 + 8.13040i) q^{89} +(-2.35414 - 10.5117i) q^{90} +(5.10412 + 2.94687i) q^{91} +(4.06915 - 6.35379i) q^{92} +(-9.99464 - 13.2774i) q^{93} +(3.59196 + 0.0826620i) q^{94} +(11.5276 + 9.67282i) q^{95} +(-9.66016 - 1.63749i) q^{96} +(-11.5504 - 4.20399i) q^{97} +(-0.213468 - 1.39801i) q^{98} +(-2.98317 + 10.3637i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 648 q + 18 q^{12} + 42 q^{18} + 42 q^{20} - 48 q^{30} - 30 q^{32} + 60 q^{33} + 60 q^{41} - 30 q^{42} - 144 q^{44} - 18 q^{48} - 156 q^{50} + 54 q^{52} - 12 q^{57} + 54 q^{58} - 186 q^{60} - 24 q^{65} - 186 q^{66}+ \cdots + 36 q^{97}+O(q^{100}) \) 648 * q + 18 * q^12 + 42 * q^18 + 42 * q^20 - 48 * q^30 - 30 * q^32 + 60 * q^33 + 60 * q^41 - 30 * q^42 - 144 * q^44 - 18 * q^48 - 156 * q^50 + 54 * q^52 - 12 * q^57 + 54 * q^58 - 186 * q^60 - 24 * q^65 - 186 * q^66 - 78 * q^68 - 42 * q^72 - 24 * q^81 - 30 * q^86 - 36 * q^89 + 198 * q^90 + 114 * q^92 - 144 * q^93 - 54 * q^94 + 156 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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