LMFDB - Embedded newform 756.2.cf.a.659.62

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			659.62
Character	$\chi$	$=$	756.659
Dual form			756.2.cf.a.491.62

$q$-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 $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$1$	$-1$

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	0.579385	+	0.815054i	$0.303293\pi$
$5$	−0.868390	+	2.38588i	−0.388356	+	1.06700i	−0.967741	+	0.251946i	$0.918930\pi$
$6$	−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	0.221821	−	0.975087i	$-0.428800\pi$
$11$	3.37805	−	1.22951i	1.01852	−	0.370711i	0.796699	+	0.604377i	$0.206578\pi$
$12$	1.42741	−	3.15634i	0.412058	−	0.911158i
$13$	−4.51486	+	3.78842i	−1.25220	+	1.05072i	−0.255729	+	0.966749i	$0.582315\pi$
$13$	−4.51486	+	3.78842i	−1.25220	+	1.05072i	−0.996468	+	0.0839696i	$0.973240\pi$
$14$	−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	−0.857901	−	0.513816i	$-0.828231\pi$
$17$	−3.47113	+	2.00406i	−0.841873	+	0.486056i	0.0160272	+	0.999872i	$0.494898\pi$
$18$	4.20753	−	0.544719i	0.991724	−	0.128391i
$19$	−5.13278	−	2.96341i	−1.17754	−	0.679853i	−0.222096	−	0.975025i	$-0.571290\pi$
$19$	−5.13278	−	2.96341i	−1.17754	−	0.679853i	−0.955444	+	0.295171i	$0.904623\pi$
$20$	−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	−0.973734	−	0.227688i	$-0.926883\pi$
$23$	−0.655097	−	3.71524i	−0.136597	−	0.774681i	0.837137	−	0.546993i	$-0.184228\pi$
$24$	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	−0.649575	−	0.760297i	$-0.725053\pi$
$29$	1.14149	−	1.36037i	0.211969	−	0.252615i	0.861544	+	0.507683i	$0.169498\pi$
$30$	5.13482	−	3.50897i	0.937485	−	0.640648i
$31$	9.44906	−	1.66612i	1.69710	−	0.299245i	0.760421	−	0.649431i	$-0.224993\pi$
$31$	9.44906	−	1.66612i	1.69710	−	0.299245i	0.936680	+	0.350186i	$0.113882\pi$
$32$	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	0.921611	−	0.388114i	$-0.126873\pi$
$37$	0.758455	+	1.31368i	0.124689	+	0.215968i	−0.796922	+	0.604082i	$0.793540\pi$
$38$	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	0.371531	−	0.928421i	$-0.378833\pi$
$41$	−3.88862	−	4.63428i	−0.607301	−	0.723753i	−0.978831	+	0.204668i	$0.934389\pi$
$42$	1.71221	+	1.75166i	0.264200	+	0.270288i
$43$	2.65992	+	7.30807i	0.405634	+	1.11447i	0.959462	+	0.281839i	$0.0909444\pi$
$43$	2.65992	+	7.30807i	0.405634	+	1.11447i	−0.553828	+	0.832631i	$0.686833\pi$
$44$	−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	−0.935579	−	0.353117i	$-0.885122\pi$
$47$	0.441166	−	2.50198i	0.0643507	−	0.364951i	0.999930	−	0.0118341i	$-0.00376701\pi$
$48$	−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	$0.175837\pi$
$53$			7.64032i			1.04948i	−0.851263	+	0.524739i	$0.824163\pi$
$54$	−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	−0.124207	−	0.992256i	$-0.539639\pi$
$59$	−6.58401	−	2.39638i	−0.857165	−	0.311983i	−0.732958	+	0.680274i	$0.761861\pi$
$60$	6.29111	+	6.14657i	0.812179	+	0.793519i
$61$	−0.237449	+	1.34664i	−0.0304022	+	0.172420i	−0.996228	−	0.0867718i	$-0.972345\pi$
$61$	−0.237449	+	1.34664i	−0.0304022	+	0.172420i	0.965826	+	0.259191i	$0.0834560\pi$
$62$	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	−0.989044	−	0.147621i	$-0.952838\pi$
$67$	−7.87985	−	9.39084i	−0.962677	−	1.14727i	0.0263672	−	0.999652i	$-0.491606\pi$
$68$	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	−0.906814	−	0.421532i	$-0.861493\pi$
$71$	−6.89650	−	11.9451i	−0.818464	−	1.41762i	0.0883497	−	0.996090i	$-0.471841\pi$
$72$	−7.34749	+	4.24434i	−0.865909	+	0.500201i
$73$	−0.359794	+	0.623182i	−0.0421107	+	0.0729379i	−0.886313	−	0.463088i	$-0.846742\pi$
$73$	−0.359794	+	0.623182i	−0.0421107	+	0.0729379i	0.844202	+	0.536025i	$0.180075\pi$
$74$	−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	−0.00603928	+	0.999982i	$0.501922\pi$
$79$	−8.79736	+	10.4843i	−0.989780	+	1.17957i	−0.983741	+	0.179593i	$0.942522\pi$
$80$	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	0.459074	−	0.888398i	$-0.348181\pi$
$83$	−3.06210	−	2.56941i	−0.336110	−	0.282029i	−0.795184	+	0.606368i	$0.792626\pi$
$84$	−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	−0.492752	−	0.870170i	$-0.664009\pi$
$89$	−14.0823	−	8.13040i	−1.49272	−	0.861821i	−0.999965	+	0.00834861i	$0.997343\pi$
$90$	−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	−0.853641	−	0.520862i	$-0.825610\pi$
$97$	−11.5504	+	4.20399i	−1.17276	+	0.426851i	−0.319123	+	0.947713i	$0.603388\pi$
$98$	−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	0.875495	−	0.483228i	$-0.160536\pi$
$101$	15.4056	+	2.71643i	1.53292	+	0.270295i	0.657422	+	0.753522i	$0.271647\pi$
$102$	9.77011	+	0.967009i	0.967385	+	0.0957482i
$103$	3.80945	−	10.4664i	0.375356	−	1.03128i	−0.597902	−	0.801569i	$-0.703999\pi$
$103$	3.80945	−	10.4664i	0.375356	−	1.03128i	0.973258	−	0.229714i	$-0.0737790\pi$
$104$	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	−0.591306	−	0.806447i	$-0.701387\pi$
$113$	4.03983	−	11.0993i	0.380035	−	1.04414i	0.971341	−	0.237691i	$-0.0763904\pi$
$114$	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	0.662012	−	0.749494i	$-0.269703\pi$
$127$	3.87597	+	2.23779i	0.343937	+	0.198572i	−0.318075	+	0.948066i	$0.603036\pi$
$128$	−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	0.998194	+	0.0600727i	$0.0191332\pi$
$131$	0.924163	+	5.24119i	0.0807445	+	0.457925i	−0.917449	+	0.397852i	$0.869756\pi$
$132$	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	−0.834958	−	0.550313i	$-0.814508\pi$
$137$	−1.73249	+	2.06470i	−0.148016	+	0.176399i	0.686942	+	0.726712i	$0.258953\pi$
$138$	−4.00047	+	8.33002i	−0.340542	+	0.709098i
$139$	−5.15369	+	0.908734i	−0.437130	+	0.0770778i	−0.387883	−	0.921709i	$-0.626793\pi$
$139$	−5.15369	+	0.908734i	−0.437130	+	0.0770778i	−0.0492474	+	0.998787i	$0.515682\pi$
$140$	−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	0.793948	−	0.607985i	$-0.208022\pi$
$149$	0.699829	+	0.834023i	0.0573322	+	0.0683258i	−0.736616	+	0.676311i	$0.763578\pi$
$150$	0.878033	+	3.43277i	0.0716911	+	0.280285i
$151$	2.28134	+	6.26794i	0.185653	+	0.510078i	0.997248	−	0.0741434i	$-0.0236222\pi$
$151$	2.28134	+	6.26794i	0.185653	+	0.510078i	−0.811594	+	0.584221i	$0.801400\pi$
$152$	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	0.836863	−	0.547412i	$-0.184387\pi$
$157$	14.1096	+	5.13547i	1.12607	+	0.409855i	0.289205	+	0.957267i	$0.406609\pi$
$158$	−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	$0.0360289\pi$
$163$			2.88401i			0.225893i	−0.993601	+	0.112947i	$0.963971\pi$
$164$	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	−0.395290	−	0.918556i	$-0.629356\pi$
$167$	−16.6516	−	6.06067i	−1.28854	−	0.468989i	−0.893247	+	0.449567i	$0.851578\pi$
$168$	−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	−0.811043	−	0.584987i	$-0.801100\pi$
$173$	−7.44155	−	20.4455i	−0.565770	−	1.55444i	0.245272	−	0.969454i	$-0.421123\pi$
$174$	−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	0.988757	−	0.149531i	$-0.0477763\pi$
$179$	4.88178	+	8.45548i	0.364881	+	0.631993i	−0.623876	+	0.781523i	$0.714443\pi$
$180$	−15.2301	−	0.346957i	−1.13518	−	0.0258606i
$181$	2.62851	−	4.55271i	0.195376	−	0.338401i	−0.751648	−	0.659565i	$-0.770741\pi$
$181$	2.62851	−	4.55271i	0.195376	−	0.338401i	0.947024	+	0.321164i	$0.104074\pi$
$182$	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	0.619275	−	0.785174i	$-0.287427\pi$
$191$	−0.641745	−	0.538488i	−0.0464350	−	0.0389636i	−0.665710	+	0.746211i	$0.731871\pi$
$192$	−4.95193	−	12.9413i	−0.357375	−	0.933961i
$193$	3.20576	+	18.1808i	0.230756	+	1.30868i	0.851370	+	0.524565i	$0.175772\pi$
$193$	3.20576	+	18.1808i	0.230756	+	1.30868i	−0.620614	+	0.784116i	$0.713117\pi$
$194$	−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	0.0410094	−	0.999159i	$-0.486943\pi$
$197$	−11.2816	−	6.51345i	−0.803783	−	0.464064i	−0.844792	+	0.535095i	$0.820276\pi$
$198$	13.5435	−	7.01327i	0.962493	−	0.498412i
$199$	9.30278	−	5.37096i	0.659457	−	0.380738i	−0.132613	−	0.991168i	$-0.542337\pi$
$199$	9.30278	−	5.37096i	0.659457	−	0.380738i	0.792070	+	0.610430i	$0.209003\pi$
$200$	−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	−0.969976	−	0.243202i	$-0.921802\pi$
$211$	−1.02558	+	2.81776i	−0.0706039	+	0.193983i	0.899372	+	0.437185i	$0.144024\pi$
$212$	−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	−0.411445	−	0.911434i	$-0.634976\pi$
$223$	−16.5729	−	2.92226i	−1.10981	−	0.195689i	−0.698361	+	0.715746i	$0.746087\pi$
$224$	−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	−0.0806727	−	0.996741i	$-0.525707\pi$
$227$	7.50645	−	2.73213i	0.498221	−	0.181338i	0.578894	+	0.815403i	$0.303485\pi$
$228$	−16.6801	+	11.9708i	−1.10467	+	0.792786i
$229$	−12.0105	+	10.0780i	−0.793673	+	0.665971i	−0.946652	−	0.322259i	$-0.895558\pi$
$229$	−12.0105	+	10.0780i	−0.793673	+	0.665971i	0.152978	+	0.988230i	$0.451114\pi$
$230$	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	−0.732935	−	0.680299i	$-0.761850\pi$
$233$	−7.78858	+	4.49674i	−0.510247	+	0.294591i	0.222688	+	0.974890i	$0.428517\pi$
$234$	−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	0.999739	−	0.0228485i	$-0.00727354\pi$
$239$	0.811274	+	4.60097i	0.0524770	+	0.297612i	−0.947262	+	0.320460i	$0.896162\pi$
$240$	−16.3444	−	6.50342i	−1.05503	−	0.419794i
$241$	−5.80991	−	4.87510i	−0.374249	−	0.314033i	0.436190	−	0.899854i	$-0.356327\pi$
$241$	−5.80991	−	4.87510i	−0.374249	−	0.314033i	−0.810440	+	0.585822i	$0.800772\pi$
$242$	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	−0.892693	−	0.450665i	$-0.851187\pi$
$251$	−0.888151	+	1.53832i	−0.0560596	+	0.0970980i	0.836634	+	0.547763i	$0.184520\pi$
$252$	−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	0.820993	+	0.570938i	$0.193420\pi$
$257$	19.8898	+	23.7038i	1.24069	+	1.47860i	0.419700	+	0.907663i	$0.362135\pi$
$258$	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	0.749051	+	0.662513i	$0.230510\pi$
$263$	−2.94213	+	16.6856i	−0.181419	+	1.02888i	−0.930470	+	0.366368i	$0.880601\pi$
$264$	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	$0.0209819\pi$
$269$			2.16066i			0.131738i	−0.997828	+	0.0658688i	$0.979018\pi$
$270$	−9.44311	−	16.0916i	−0.574689	−	0.979306i
$271$			19.7324i			1.19866i	0.800503	+	0.599328i	$0.204566\pi$
$271$			19.7324i			1.19866i	−0.800503	+	0.599328i	$0.795434\pi$
$272$	−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	0.843399	+	0.537287i	$0.180551\pi$
$277$	−2.21189	+	12.5443i	−0.132900	+	0.753712i	−0.976299	+	0.216425i	$0.930560\pi$
$278$	−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	−0.998251	−	0.0591249i	$-0.981169\pi$
$281$	−4.55202	−	12.5066i	−0.271551	−	0.746080i	0.726700	−	0.686955i	$-0.241053\pi$
$282$	−4.45023	+	4.35000i	−0.265007	+	0.259039i
$283$	3.84661	+	4.58421i	0.228657	+	0.272503i	0.868159	−	0.496287i	$-0.165304\pi$
$283$	3.84661	+	4.58421i	0.228657	+	0.272503i	−0.639501	+	0.768790i	$0.720859\pi$
$284$	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	0.589814	−	0.807539i	$-0.299201\pi$
$293$	24.3108	−	4.28665i	1.42025	−	0.250429i	0.830439	+	0.557110i	$0.188090\pi$
$294$	−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	−0.438619	−	0.898673i	$-0.644532\pi$
$307$	2.10864	−	1.21742i	0.120346	−	0.0694819i	0.558965	+	0.829191i	$0.311199\pi$
$308$	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	−0.704865	−	0.709342i	$-0.748992\pi$
$311$	−2.26962	+	1.90444i	−0.128698	+	0.107991i	0.576167	+	0.817332i	$0.304548\pi$
$312$	−25.7299	+	13.1011i	−1.45667	+	0.741702i
$313$	−18.4995	+	6.73326i	−1.04565	+	0.380586i	−0.807020	−	0.590524i	$-0.798921\pi$
$313$	−18.4995	+	6.73326i	−1.04565	+	0.380586i	−0.238632	+	0.971110i	$0.576699\pi$
$314$	−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	0.491781	−	0.870719i	$-0.336346\pi$
$317$	11.6815	+	2.05977i	0.656100	+	0.115688i	0.164319	+	0.986407i	$0.447457\pi$
$318$	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	−0.457187	−	0.889370i	$-0.651143\pi$
$331$	−21.6681	−	3.82067i	−1.19099	−	0.210003i	−0.733798	+	0.679368i	$0.762254\pi$
$332$	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	−0.937672	−	0.347520i	$-0.887024\pi$
$337$	−13.9197	+	11.6801i	−0.758257	+	0.636253i	0.179415	+	0.983773i	$0.442579\pi$
$338$	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	0.953358	−	0.301841i	$-0.0976013\pi$
$347$	−0.852066	−	4.83231i	−0.0457413	−	0.259412i	−0.999099	+	0.0424296i	$0.986490\pi$
$348$	−2.66443	−	5.54474i	−0.142828	−	0.297229i
$349$	22.5517	+	18.9232i	1.20717	+	1.01293i	0.999396	+	0.0347560i	$0.0110654\pi$
$349$	22.5517	+	18.9232i	1.20717	+	1.01293i	0.207771	+	0.978177i	$0.433379\pi$
$350$	−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	−0.627418	−	0.778683i	$-0.715888\pi$
$353$	4.66673	−	5.56159i	0.248385	−	0.296014i	0.875803	+	0.482669i	$0.160333\pi$
$354$	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	0.411868	+	0.911243i	$0.364876\pi$
$359$	−11.0505	+	19.1401i	−0.583226	+	1.01018i	−0.995094	+	0.0989331i	$0.968457\pi$
$360$	−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	0.957117	−	0.289703i	$-0.0935564\pi$
$367$	0.722335	+	1.98460i	0.0377056	+	0.103595i	−0.919411	+	0.393298i	$0.871334\pi$
$368$	−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	−0.479011	−	0.877809i	$-0.659005\pi$
$373$	−27.2355	−	9.91290i	−1.41020	−	0.513271i	−0.931188	+	0.364538i	$0.881227\pi$
$374$	−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	$0.173754\pi$
$379$			20.2138i			1.03831i	−0.854679	+	0.519156i	$0.826246\pi$
$380$	−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	0.377460	−	0.926026i	$-0.376798\pi$
$383$	1.39680	+	0.508393i	0.0713731	+	0.0259777i	−0.306087	+	0.952004i	$0.599020\pi$
$384$	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	0.878048	−	0.478572i	$-0.158846\pi$
$389$	−2.01562	−	5.53787i	−0.102196	−	0.280781i	−0.980244	+	0.197791i	$0.936623\pi$
$390$	−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	0.399813	+	0.916597i	$0.369075\pi$
$397$	−11.8332	+	20.4956i	−0.593890	+	1.02865i	−0.993703	+	0.112050i	$0.964258\pi$
$398$	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	0.661376	−	0.750054i	$-0.269973\pi$
$401$	30.8265	−	5.43554i	1.53940	−	0.271438i	0.878024	+	0.478617i	$0.158862\pi$
$402$	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	0.931997	+	0.362466i	$0.118065\pi$
$409$	3.64385	+	20.6653i	0.180177	+	1.02183i	−0.751820	+	0.659368i	$0.770824\pi$
$410$	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	−0.989762	−	0.142726i	$-0.954413\pi$
$419$	−20.9009	+	17.5379i	−1.02107	+	0.856783i	−0.0313124	+	0.999510i	$0.509969\pi$
$420$	−5.12820	−	7.14563i	−0.250230	−	0.348671i
$421$	29.3792	−	10.6932i	1.43186	−	0.521153i	0.494393	−	0.869238i	$-0.335390\pi$
$421$	29.3792	−	10.6932i	1.43186	−	0.521153i	0.937463	+	0.348085i	$0.113168\pi$
$422$	−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	0.729427	−	0.684058i	$-0.239787\pi$
$439$	24.7427	+	4.36280i	1.18090	+	0.208225i	0.451476	+	0.892283i	$0.350898\pi$
$440$	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	−0.351763	−	0.936089i	$-0.614418\pi$
$443$	−0.410884	+	0.149550i	−0.0195217	+	0.00710531i	0.332241	+	0.943195i	$0.392195\pi$
$444$	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	0.187776	−	0.982212i	$-0.439872\pi$
$449$	23.9927	−	13.8522i	1.13228	−	0.653725i	0.944508	+	0.328487i	$0.106539\pi$
$450$	−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	−0.990185	−	0.139766i	$-0.955365\pi$
$457$	−27.7859	−	23.3152i	−1.29977	−	1.09064i	−0.309587	−	0.950871i	$-0.600191\pi$
$458$	−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	−0.990825	−	0.135148i	$-0.956849\pi$
$461$	−14.7221	+	17.5451i	−0.685675	+	0.817156i	0.305150	+	0.952304i	$0.401293\pi$
$462$	7.93762	+	3.81202i	0.369292	+	0.177351i
$463$	−5.05507	+	0.891345i	−0.234929	+	0.0414243i	−0.289873	−	0.957065i	$-0.593613\pi$
$463$	−5.05507	+	0.891345i	−0.234929	+	0.0414243i	0.0549441	+	0.998489i	$0.482502\pi$
$464$	−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	−0.534650	−	0.845073i	$-0.679557\pi$
$467$	10.0386	−	17.3873i	0.464530	−	0.804589i	0.999180	+	0.0404842i	$0.0128900\pi$
$468$	−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	−0.360709	−	0.932678i	$-0.617465\pi$
$479$	6.50545	−	36.8942i	0.297241	−	1.68574i	0.657950	−	0.753061i	$-0.271424\pi$
$480$	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	$-0.895714\pi$
$487$		−	14.2028i		−	0.643589i	0.946810	−	0.321794i	$-0.104286\pi$
$488$	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	−0.0143106	−	0.999898i	$-0.504555\pi$
$491$	−14.8018	−	5.38741i	−0.667995	−	0.243130i	−0.653684	+	0.756767i	$0.726778\pi$
$492$	−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	−0.911914	−	0.410382i	$-0.865396\pi$
$499$	−25.8613	−	30.8202i	−1.15771	−	1.37970i	−0.245795	−	0.969322i	$-0.579049\pi$
$500$	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	−0.866078	−	0.499909i	$-0.833367\pi$
$503$	−19.4218	−	33.6395i	−0.865973	−	1.49991i	0.000104606	−	1.00000i	$-0.499967\pi$
$504$	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	−0.443147	−	0.896449i	$-0.646138\pi$
$509$	−12.4755	+	2.19976i	−0.552966	+	0.0975028i	−0.109819	+	0.993952i	$0.535027\pi$
$510$	−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	0.330939	−	0.943652i	$-0.392635\pi$
$521$	−7.32281	−	4.22782i	−0.320818	−	0.185224i	−0.651757	+	0.758428i	$0.725968\pi$
$522$	4.06182	−	6.34559i	0.177781	−	0.277739i
$523$	5.13626	−	2.96542i	0.224593	−	0.129669i	−0.383482	−	0.923548i	$-0.625275\pi$
$523$	5.13626	−	2.96542i	0.224593	−	0.129669i	0.608075	+	0.793879i	$0.291942\pi$
$524$	−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	0.523391	−	0.852093i	$-0.324667\pi$
$547$	16.9279	+	2.98484i	0.723784	+	0.127623i	0.200393	+	0.979715i	$0.435778\pi$
$548$	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	−0.825374	−	0.564586i	$-0.809036\pi$
$557$	−17.6798	+	10.2074i	−0.749116	+	0.432502i	0.0762584	+	0.997088i	$0.475703\pi$
$558$	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	−0.962234	−	0.272225i	$-0.912240\pi$
$563$	−3.58611	−	20.3378i	−0.151136	−	0.857137i	0.811097	−	0.584911i	$-0.198871\pi$
$564$	−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	−0.984787	−	0.173764i	$-0.944407\pi$
$569$	−15.3298	+	18.2693i	−0.642657	+	0.765888i	0.342131	+	0.939652i	$0.388851\pi$
$570$	−36.7544	+	2.79421i	−1.53947	+	0.117037i
$571$	−26.6373	+	4.69688i	−1.11474	+	0.196558i	−0.700529	−	0.713624i	$-0.747052\pi$
$571$	−26.6373	+	4.69688i	−1.11474	+	0.196558i	−0.414208	+	0.910182i	$0.635941\pi$
$572$	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	0.895199	−	0.445666i	$-0.147033\pi$
$577$	1.48068	+	2.56462i	0.0616416	+	0.106766i	−0.833558	+	0.552432i	$0.813700\pi$
$578$	−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	−0.533219	−	0.845977i	$-0.679018\pi$
$587$	6.23108	−	35.3382i	0.257184	−	1.45856i	0.790403	−	0.612587i	$-0.209871\pi$
$588$	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	$0.140952\pi$
$593$			20.8685i			0.856966i	−0.903550	+	0.428483i	$0.859048\pi$
$594$	−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	0.558718	−	0.829358i	$-0.311294\pi$
$599$	11.1021	+	4.04083i	0.453619	+	0.165104i	−0.105099	+	0.994462i	$0.533516\pi$
$600$	−4.26324	−	5.66077i	−0.174046	−	0.231100i
$601$	−3.84395	+	21.8001i	−0.156798	+	0.889245i	0.800326	+	0.599565i	$0.204660\pi$
$601$	−3.84395	+	21.8001i	−0.156798	+	0.889245i	−0.957124	+	0.289679i	$0.906451\pi$
$602$	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	0.997274	−	0.0737892i	$-0.0235092\pi$
$607$	18.5133	+	22.0633i	0.751431	+	0.895520i	−0.245843	+	0.969310i	$0.579065\pi$
$608$	−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	0.0886529	+	0.996063i	$0.471744\pi$
$613$	−20.2599	+	35.0911i	−0.818289	+	1.41732i	−0.906942	+	0.421256i	$0.861590\pi$
$614$	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	−0.229073	−	0.973409i	$-0.573569\pi$
$617$	−2.76724	+	0.487939i	−0.111405	+	0.0196437i	0.117668	+	0.993053i	$0.462458\pi$
$618$	−22.5254	+	15.3931i	−0.906104	+	0.619203i
$619$	13.3331	−	15.8897i	0.535901	−	0.638663i	−0.428362	−	0.903607i	$-0.640909\pi$
$619$	13.3331	−	15.8897i	0.535901	−	0.638663i	0.964264	+	0.264945i	$0.0853537\pi$
$620$	−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	−0.919646	−	0.392748i	$-0.871524\pi$
$631$	−26.1079	+	15.0734i	−1.03934	+	0.600063i	−0.119693	+	0.992811i	$0.538191\pi$
$632$	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	0.0813998	−	0.996682i	$-0.474061\pi$
$641$	−4.63305	−	0.816933i	−0.182995	−	0.0322669i	−0.264394	+	0.964415i	$0.585172\pi$
$642$	27.0842	+	19.4280i	1.06893	+	0.766761i
$643$	−6.94370	+	19.0777i	−0.273833	+	0.752350i	0.724196	+	0.689594i	$0.242211\pi$
$643$	−6.94370	+	19.0777i	−0.273833	+	0.752350i	−0.998029	+	0.0627556i	$0.980011\pi$
$644$	−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	0.682108	+	0.731251i	$0.261063\pi$
$653$	−7.93336	+	21.7967i	−0.310456	+	0.852972i	−0.992564	+	0.121721i	$0.961159\pi$
$654$	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	−0.150403	−	0.988625i	$-0.548057\pi$
$659$	9.49459	−	3.45575i	0.369857	−	0.134617i	0.520260	+	0.854008i	$0.325835\pi$
$660$	28.8089	+	13.0284i	1.12139	+	0.507131i
$661$	21.8059	−	18.2973i	0.848152	−	0.711684i	−0.111230	−	0.993795i	$-0.535479\pi$
$661$	21.8059	−	18.2973i	0.848152	−	0.711684i	0.959382	+	0.282111i	$0.0910345\pi$
$662$	−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	0.894973	−	0.446120i	$-0.147194\pi$
$673$	15.8518	+	13.3012i	0.611042	+	0.512725i	−0.283932	+	0.958845i	$0.591639\pi$
$674$	−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	0.0278571	−	0.999612i	$-0.491132\pi$
$677$	26.2129	−	31.2394i	1.00745	−	1.20063i	0.979588	−	0.201015i	$-0.0644239\pi$
$678$	−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	−0.908611	−	0.417644i	$-0.862856\pi$
$683$	−2.42041	+	4.19228i	−0.0926145	+	0.160413i	0.815996	+	0.578058i	$0.196189\pi$
$684$	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	−0.932198	−	0.361949i	$-0.882111\pi$
$691$	−11.8488	−	32.5543i	−0.450749	−	1.23842i	0.481449	−	0.876474i	$-0.340111\pi$
$692$	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	$-0.995186\pi$
$701$		−	0.800827i		−	0.0302468i	0.999886	−	0.0151234i	$-0.00481411\pi$
$702$	−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	0.679991	+	0.733220i	$0.261984\pi$
$709$	−5.58549	+	31.6769i	−0.209768	+	1.18965i	−0.889759	+	0.456431i	$0.849128\pi$
$710$	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	0.768087	−	0.640346i	$-0.221209\pi$
$719$	−4.57215	−	7.91919i	−0.170512	−	0.295336i	−0.938599	+	0.345010i	$0.887876\pi$
$720$	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	−0.775722	−	0.631075i	$-0.782614\pi$
$727$	−0.526612	+	0.627591i	−0.0195309	+	0.0232761i	0.756191	+	0.654351i	$0.227058\pi$
$728$	−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	0.943608	+	0.331066i	$0.107408\pi$
$733$	4.60630	+	26.1236i	0.170138	+	0.964898i	−0.773470	+	0.633833i	$0.781481\pi$
$734$	−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	−0.983228	−	0.182380i	$-0.941620\pi$
$739$	−35.7992	+	20.6687i	−1.31690	+	0.760311i	−0.333668	+	0.942691i	$0.608287\pi$
$740$	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	−0.300210	−	0.953873i	$-0.597057\pi$
$743$	16.0016	−	13.4269i	0.587041	−	0.492586i	0.887251	+	0.461287i	$0.152612\pi$
$744$	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	−0.787852	−	0.615865i	$-0.788807\pi$
$751$	5.79734	−	15.9281i	0.211548	−	0.581224i	0.999400	+	0.0346414i	$0.0110289\pi$
$752$	−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	−0.994975	−	0.100124i	$-0.968076\pi$
$761$	−4.64612	+	12.7651i	−0.168422	+	0.462735i	0.826553	+	0.562858i	$0.190298\pi$
$762$	−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	0.0988980	−	0.995098i	$-0.468468\pi$
$769$	30.3944	−	25.5040i	1.09605	−	0.919696i	0.997153	+	0.0754014i	$0.0240238\pi$
$770$	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	−0.844082	−	0.536214i	$-0.819854\pi$
$773$	−22.2909	+	12.8697i	−0.801748	+	0.462889i	0.0423343	+	0.999104i	$0.486521\pi$
$774$	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	−0.0403296	−	0.999186i	$-0.512841\pi$
$787$	7.39252	−	1.30350i	0.263515	−	0.0464648i	0.303844	+	0.952722i	$0.401730\pi$
$788$	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	0.725355	−	0.688375i	$-0.241676\pi$
$797$	−2.21668	−	2.64173i	−0.0785187	−	0.0935750i	−0.803874	+	0.594800i	$0.797231\pi$
$798$	−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	$0.364070\pi$
$809$			51.7773i			1.82039i	−0.414176	+	0.910197i	$0.635930\pi$
$810$	30.9750	+	9.21346i	1.08835	+	0.323728i
$811$			33.9227i			1.19119i	0.803286	+	0.595594i	$0.203083\pi$
$811$			33.9227i			1.19119i	−0.803286	+	0.595594i	$0.796917\pi$
$812$	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	0.997146	−	0.0754994i	$-0.0240551\pi$
$821$	5.29388	+	14.5448i	0.184758	+	0.507618i	−0.812388	+	0.583117i	$0.801833\pi$
$822$	6.39612	−	1.63600i	0.223090	−	0.0570619i
$823$	0.101128	+	0.120519i	0.00352509	+	0.00420104i	0.767804	−	0.640685i	$-0.221349\pi$
$823$	0.101128	+	0.120519i	0.00352509	+	0.00420104i	−0.764279	+	0.644886i	$0.776905\pi$
$824$	−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	0.994641	−	0.103386i	$-0.0329676\pi$
$827$	11.7269	+	20.3117i	0.407786	+	0.706306i	−0.586855	+	0.809692i	$0.699634\pi$
$828$	19.8554	−	10.8683i	0.690024	−	0.377699i
$829$	−26.9598	+	46.6958i	−0.936353	+	1.62181i	−0.164149	+	0.986436i	$0.552488\pi$
$829$	−26.9598	+	46.6958i	−0.936353	+	1.62181i	−0.772204	+	0.635375i	$0.780845\pi$
$830$	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	0.623762	−	0.781614i	$-0.285604\pi$
$839$	−1.09093	−	0.915398i	−0.0376630	−	0.0316030i	−0.661425	+	0.750011i	$0.730048\pi$
$840$	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	0.271788	−	0.962357i	$-0.412385\pi$
$853$	32.0853	−	11.6781i	1.09858	−	0.399851i	0.826793	+	0.562507i	$0.190163\pi$
$854$	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	0.844313	−	0.535850i	$-0.180009\pi$
$857$	42.5780	+	7.50765i	1.45444	+	0.256457i	0.610124	+	0.792306i	$0.291120\pi$
$858$	47.2818	−	21.3957i	1.61417	−	0.730438i
$859$	−5.54676	+	15.2396i	−0.189253	+	0.519969i	−0.997638	−	0.0686850i	$-0.978120\pi$
$859$	−5.54676	+	15.2396i	−0.189253	+	0.519969i	0.808385	+	0.588654i	$0.200342\pi$
$860$	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	−0.280210	−	0.959939i	$-0.590404\pi$
$877$	18.2568	−	15.3192i	0.616487	−	0.517294i	0.896697	+	0.442645i	$0.145960\pi$
$878$	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	−0.533052	−	0.846082i	$-0.678955\pi$
$881$	−1.98420	+	1.14558i	−0.0668493	+	0.0385955i	0.466203	+	0.884678i	$0.345622\pi$
$882$	4.14009	+	0.927191i	0.139404	+	0.0312201i
$883$	−29.1285	−	16.8173i	−0.980252	−	0.565949i	−0.0779056	−	0.996961i	$-0.524823\pi$
$883$	−29.1285	−	16.8173i	−0.980252	−	0.565949i	−0.902346	+	0.431012i	$0.858157\pi$
$884$	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	0.998437	−	0.0558916i	$-0.0178001\pi$
$887$	1.22398	+	6.94151i	0.0410971	+	0.233073i	−0.957340	+	0.288965i	$0.906689\pi$
$888$	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	0.980268	−	0.197674i	$-0.0633388\pi$
$907$	3.08021	+	8.46280i	0.102277	+	0.281003i	−0.877991	+	0.478677i	$0.841117\pi$
$908$	−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	0.631428	+	0.775434i	$0.282469\pi$
$911$	−6.85555	+	38.8797i	−0.227134	+	1.28814i	−0.858562	+	0.512709i	$0.828642\pi$
$912$	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	$-0.649333\pi$
$919$		−	54.0793i		−	1.78391i	0.452123	−	0.891956i	$-0.350667\pi$
$920$	−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	0.793045	−	0.609163i	$-0.208495\pi$
$929$	−6.27955	−	17.2529i	−0.206025	−	0.566050i	−0.999070	+	0.0431132i	$0.986272\pi$
$930$	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	−0.762696	−	0.646757i	$-0.776125\pi$
$937$	5.47192	−	9.47764i	0.178760	−	0.309621i	0.941456	+	0.337136i	$0.109458\pi$
$938$	−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	−0.308046	−	0.951371i	$-0.599675\pi$
$941$	−8.34770	+	1.47192i	−0.272127	+	0.0479834i	0.0359192	+	0.999355i	$0.488564\pi$
$942$	−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	0.894431	−	0.447206i	$-0.147581\pi$
$947$	18.7513	+	15.7342i	0.609335	+	0.511293i	−0.285096	+	0.958499i	$0.592025\pi$
$948$	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	0.667785	−	0.744354i	$-0.267243\pi$
$953$	11.0223	+	6.36373i	0.357047	+	0.206141i	−0.310737	+	0.950496i	$0.600576\pi$
$954$	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	0.567719	+	0.823222i	$0.307826\pi$
$967$	−12.3247	+	33.8619i	−0.396336	+	1.08892i	−0.964055	+	0.265702i	$0.914396\pi$
$968$	−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	−0.982517	−	0.186175i	$-0.940391\pi$
$977$	−3.44435	+	9.46326i	−0.110194	+	0.302757i	0.872322	+	0.488931i	$0.162613\pi$
$978$	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	−0.253329	−	0.967380i	$-0.581526\pi$
$983$	5.46885	−	1.99050i	0.174429	−	0.0634871i	0.427758	+	0.903893i	$0.359303\pi$
$984$	−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	0.936740	−	0.350026i	$-0.113827\pi$
$991$	34.6904	+	20.0285i	1.10198	+	0.636227i	0.165238	+	0.986254i	$0.447161\pi$
$992$	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	0.757072	−	0.653332i	$-0.226629\pi$
$997$	7.74004	+	6.49467i	0.245130	+	0.205688i	−0.511942	+	0.859020i	$0.671074\pi$
$998$	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.659.62	yes	648
4.3	odd	2	inner	756.2.cf.a.659.3	yes	648
27.5	odd	18	inner	756.2.cf.a.491.3	✓	648
108.59	even	18	inner	756.2.cf.a.491.62	yes	648

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
756.2.cf.a.491.3	✓	648	27.5	odd	18	inner
756.2.cf.a.491.62	yes	648	108.59	even	18	inner
756.2.cf.a.659.3	yes	648	4.3	odd	2	inner
756.2.cf.a.659.62	yes	648	1.1	even	1	trivial

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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