LMFDB - Embedded newform 189.2.be.a.104.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [189,2,Mod(20,189)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("189.20"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(189, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([7, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.be (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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			104.3
Character	$\chi$	$=$	189.104
Dual form			189.2.be.a.20.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.752422 + 2.06726i) q^{2} +(-1.63905 + 0.559928i) q^{3} +(-2.17534 - 1.82533i) q^{4} +(0.562637 - 3.19087i) q^{5} +(0.0757386 - 3.80964i) q^{6} +(1.24057 - 2.33688i) q^{7} +(1.59981 - 0.923650i) q^{8} +(2.37296 - 1.83550i) q^{9} +(6.17302 + 3.56400i) q^{10} +(-3.18028 + 0.560770i) q^{11} +(4.58754 + 1.77377i) q^{12} +(-1.22706 - 3.37132i) q^{13} +(3.89751 + 4.32289i) q^{14} +(0.864468 + 5.54503i) q^{15} +(-0.280525 - 1.59093i) q^{16} +(-1.49145 + 2.58328i) q^{17} +(2.00899 + 6.28660i) q^{18} +(3.49827 - 2.01973i) q^{19} +(-7.04831 + 5.91424i) q^{20} +(-0.724867 + 4.52488i) q^{21} +(1.23366 - 6.99641i) q^{22} +(-0.441437 + 0.526084i) q^{23} +(-2.10499 + 2.40968i) q^{24} +(-5.16663 - 1.88050i) q^{25} +7.89267 q^{26} +(-2.86165 + 4.33716i) q^{27} +(-6.96423 + 2.81906i) q^{28} +(3.33174 - 9.15387i) q^{29} +(-12.1135 - 2.38512i) q^{30} +(0.311578 - 0.371325i) q^{31} +(7.13842 + 1.25870i) q^{32} +(4.89865 - 2.69986i) q^{33} +(-4.21810 - 5.02694i) q^{34} +(-6.75868 - 5.27330i) q^{35} +(-8.51239 - 0.338599i) q^{36} +(2.82040 - 4.88507i) q^{37} +(1.54313 + 8.75153i) q^{38} +(3.89891 + 4.83869i) q^{39} +(-2.04714 - 5.62446i) q^{40} +(-1.84441 + 0.671309i) q^{41} +(-8.80871 - 4.90311i) q^{42} +(1.32012 + 7.48676i) q^{43} +(7.94179 + 4.58519i) q^{44} +(-4.52172 - 8.60453i) q^{45} +(-0.755407 - 1.30840i) q^{46} +(-6.71691 + 5.63616i) q^{47} +(1.35060 + 2.45055i) q^{48} +(-3.92199 - 5.79810i) q^{49} +(7.77497 - 9.26585i) q^{50} +(0.998119 - 5.06922i) q^{51} +(-3.48449 + 9.57356i) q^{52} -3.11853i q^{53} +(-6.81287 - 9.17916i) q^{54} +10.4634i q^{55} +(-0.173787 - 4.88441i) q^{56} +(-4.60294 + 5.26922i) q^{57} +(16.4166 + 13.7751i) q^{58} +(1.95711 - 11.0993i) q^{59} +(8.24099 - 13.6403i) q^{60} +(3.09075 + 3.68341i) q^{61} +(0.533187 + 0.923507i) q^{62} +(-1.34552 - 7.82238i) q^{63} +(-6.35768 + 11.0118i) q^{64} +(-11.4478 + 2.01856i) q^{65} +(1.89546 + 12.1582i) q^{66} +(-8.93479 + 3.25200i) q^{67} +(7.95975 - 2.89711i) q^{68} +(0.428968 - 1.10945i) q^{69} +(15.9867 - 10.0042i) q^{70} +(-2.67528 - 1.54458i) q^{71} +(2.10093 - 5.12823i) q^{72} +(-9.91831 + 5.72634i) q^{73} +(7.97659 + 9.50613i) q^{74} +(9.52131 + 0.189291i) q^{75} +(-11.2966 - 1.99190i) q^{76} +(-2.63490 + 8.12760i) q^{77} +(-12.9365 + 4.41932i) q^{78} +(6.20601 + 2.25880i) q^{79} -5.23430 q^{80} +(2.26189 - 8.71113i) q^{81} -4.31797i q^{82} +(16.4935 + 6.00315i) q^{83} +(9.83623 - 8.52005i) q^{84} +(7.40375 + 6.21249i) q^{85} +(-16.4704 - 2.90417i) q^{86} +(-0.335372 + 16.8692i) q^{87} +(-4.56989 + 3.83459i) q^{88} +(3.48296 + 6.03267i) q^{89} +(21.1901 - 2.87334i) q^{90} +(-9.40061 - 1.31486i) q^{91} +(1.92055 - 0.338646i) q^{92} +(-0.302777 + 0.783081i) q^{93} +(-6.59746 - 18.1264i) q^{94} +(-4.47644 - 12.2989i) q^{95} +(-12.4050 + 1.93394i) q^{96} +(2.47809 - 0.436955i) q^{97} +(14.9372 - 3.74516i) q^{98} +(-6.51740 + 7.16809i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30}+ \cdots - 192 q^{99}+O(q^{100}) $ 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.752422	+	2.06726i	−0.532042	+	1.46177i	0.324594	+	0.945854i	$0.394772\pi$
$2$	−0.752422	+	2.06726i	−0.532042	+	1.46177i	−0.856636	+	0.515921i	$0.827450\pi$
$3$	−1.63905	+	0.559928i	−0.946305	+	0.323274i
$3$	−1.63905	+	0.559928i	−0.946305	+	0.323274i
$4$	−2.17534	−	1.82533i	−1.08767	−	0.912664i
$5$	0.562637	−	3.19087i	0.251619	−	1.42700i	−0.552986	−	0.833190i	$-0.686512\pi$
$5$	0.562637	−	3.19087i	0.251619	−	1.42700i	0.804605	−	0.593810i	$-0.202377\pi$
$6$	0.0757386	−	3.80964i	0.0309202	−	1.55528i
$7$	1.24057	−	2.33688i	0.468890	−	0.883257i
$7$	1.24057	−	2.33688i	0.468890	−	0.883257i
$8$	1.59981	−	0.923650i	0.565618	−	0.326560i
$9$	2.37296	−	1.83550i	0.790987	−	0.611833i
$10$	6.17302	+	3.56400i	1.95208	+	1.12703i
$11$	−3.18028	+	0.560770i	−0.958891	+	0.169078i	−0.631126	−	0.775681i	$-0.717407\pi$
$11$	−3.18028	+	0.560770i	−0.958891	+	0.169078i	−0.327766	+	0.944759i	$0.606296\pi$
$12$	4.58754	+	1.77377i	1.32431	+	0.512043i
$13$	−1.22706	−	3.37132i	−0.340325	−	0.935036i	−0.985300	−	0.170832i	$-0.945354\pi$
$13$	−1.22706	−	3.37132i	−0.340325	−	0.935036i	0.644975	−	0.764204i	$-0.276868\pi$
$14$	3.89751	+	4.32289i	1.04165	+	1.15534i
$15$	0.864468	+	5.54503i	0.223205	+	1.43172i
$16$	−0.280525	−	1.59093i	−0.0701312	−	0.397734i
$17$	−1.49145	+	2.58328i	−0.361731	+	0.626536i	−0.988246	−	0.152873i	$-0.951147\pi$
$17$	−1.49145	+	2.58328i	−0.361731	+	0.626536i	0.626515	+	0.779409i	$0.284481\pi$
$18$	2.00899	+	6.28660i	0.473523	+	1.48177i
$19$	3.49827	−	2.01973i	0.802559	−	0.463358i	−0.0418061	−	0.999126i	$-0.513311\pi$
$19$	3.49827	−	2.01973i	0.802559	−	0.463358i	0.844365	+	0.535768i	$0.179978\pi$
$20$	−7.04831	+	5.91424i	−1.57605	+	1.32246i
$21$	−0.724867	+	4.52488i	−0.158179	+	0.987410i
$22$	1.23366	−	6.99641i	0.263016	−	1.49164i
$23$	−0.441437	+	0.526084i	−0.0920460	+	0.109696i	−0.810101	−	0.586290i	$-0.800588\pi$
$23$	−0.441437	+	0.526084i	−0.0920460	+	0.109696i	0.718055	+	0.695986i	$0.245032\pi$
$24$	−2.10499	+	2.40968i	−0.429679	+	0.491875i
$25$	−5.16663	−	1.88050i	−1.03333	−	0.376100i
$26$	7.89267			1.54788
$27$	−2.86165	+	4.33716i	−0.550726	+	0.834686i
$28$	−6.96423	+	2.81906i	−1.31611	+	0.532753i
$29$	3.33174	−	9.15387i	0.618688	−	1.69983i	−0.0914880	−	0.995806i	$-0.529162\pi$
$29$	3.33174	−	9.15387i	0.618688	−	1.69983i	0.710176	−	0.704024i	$-0.248615\pi$
$30$	−12.1135	−	2.38512i	−2.21161	−	0.435461i
$31$	0.311578	−	0.371325i	0.0559611	−	0.0666919i	−0.737338	−	0.675524i	$-0.763917\pi$
$31$	0.311578	−	0.371325i	0.0559611	−	0.0666919i	0.793299	+	0.608832i	$0.208362\pi$
$32$	7.13842	+	1.25870i	1.26191	+	0.222508i
$33$	4.89865	−	2.69986i	0.852745	−	0.469985i
$34$	−4.21810	−	5.02694i	−0.723399	−	0.862113i
$35$	−6.75868	−	5.27330i	−1.14243	−	0.891350i
$36$	−8.51239	−	0.338599i	−1.41873	−	0.0564332i
$37$	2.82040	−	4.88507i	0.463671	−	0.803101i	−0.535470	−	0.844554i	$-0.679865\pi$
$37$	2.82040	−	4.88507i	0.463671	−	0.803101i	0.999140	+	0.0414533i	$0.0131988\pi$
$38$	1.54313	+	8.75153i	0.250329	+	1.41969i
$39$	3.89891	+	4.83869i	0.624325	+	0.774811i
$40$	−2.04714	−	5.62446i	−0.323681	−	0.889306i
$41$	−1.84441	+	0.671309i	−0.288048	+	0.104841i	−0.482003	−	0.876170i	$-0.660091\pi$
$41$	−1.84441	+	0.671309i	−0.288048	+	0.104841i	0.193955	+	0.981010i	$0.437868\pi$
$42$	−8.80871	−	4.90311i	−1.35921	−	0.756566i
$43$	1.32012	+	7.48676i	0.201316	+	1.14172i	0.903132	+	0.429362i	$0.141262\pi$
$43$	1.32012	+	7.48676i	0.201316	+	1.14172i	−0.701816	+	0.712358i	$0.747627\pi$
$44$	7.94179	+	4.58519i	1.19727	+	0.691244i
$45$	−4.52172	−	8.60453i	−0.674058	−	1.28269i
$46$	−0.755407	−	1.30840i	−0.111379	−	0.192914i
$47$	−6.71691	+	5.63616i	−0.979762	+	0.822118i	−0.984053	−	0.177873i	$-0.943078\pi$
$47$	−6.71691	+	5.63616i	−0.979762	+	0.822118i	0.00429160	+	0.999991i	$0.498634\pi$
$48$	1.35060	+	2.45055i	0.194943	+	0.353706i
$49$	−3.92199	−	5.79810i	−0.560284	−	0.828300i
$50$	7.77497	−	9.26585i	1.09955	−	1.31039i
$51$	0.998119	−	5.06922i	0.139765	−	0.709833i
$52$	−3.48449	+	9.57356i	−0.483212	+	1.32761i
$53$		−	3.11853i		−	0.428363i	−0.976794	−	0.214181i	$-0.931292\pi$
$53$		−	3.11853i		−	0.428363i	0.976794	−	0.214181i	$-0.0687084\pi$
$54$	−6.81287	−	9.17916i	−0.927114	−	1.24913i
$55$			10.4634i			1.41088i
$56$	−0.173787	−	4.88441i	−0.0232233	−	0.652706i
$57$	−4.60294	+	5.26922i	−0.609674	+	0.697925i
$58$	16.4166	+	13.7751i	2.15560	+	1.80876i
$59$	1.95711	−	11.0993i	0.254793	−	1.44501i	−0.541809	−	0.840502i	$-0.682260\pi$
$59$	1.95711	−	11.0993i	0.254793	−	1.44501i	0.796602	−	0.604504i	$-0.206628\pi$
$60$	8.24099	−	13.6403i	1.06391	−	1.76095i
$61$	3.09075	+	3.68341i	0.395730	+	0.471613i	0.926713	−	0.375770i	$-0.122622\pi$
$61$	3.09075	+	3.68341i	0.395730	+	0.471613i	−0.530983	+	0.847383i	$0.678177\pi$
$62$	0.533187	+	0.923507i	0.0677148	+	0.117285i
$63$	−1.34552	−	7.82238i	−0.169519	−	0.985527i
$64$	−6.35768	+	11.0118i	−0.794710	+	1.37648i
$65$	−11.4478	+	2.01856i	−1.41993	+	0.250372i
$66$	1.89546	+	12.1582i	0.233315	+	1.49657i
$67$	−8.93479	+	3.25200i	−1.09156	+	0.397295i	−0.824198	−	0.566302i	$-0.808374\pi$
$67$	−8.93479	+	3.25200i	−1.09156	+	0.397295i	−0.267360	+	0.963597i	$0.586151\pi$
$68$	7.95975	−	2.89711i	0.965262	−	0.351327i
$69$	0.428968	−	1.10945i	0.0516417	−	0.133562i
$70$	15.9867	−	10.0042i	1.91077	−	1.19573i
$71$	−2.67528	−	1.54458i	−0.317498	−	0.183307i	0.332779	−	0.943005i	$-0.392014\pi$
$71$	−2.67528	−	1.54458i	−0.317498	−	0.183307i	−0.650277	+	0.759697i	$0.725347\pi$
$72$	2.10093	−	5.12823i	0.247597	−	0.604368i
$73$	−9.91831	+	5.72634i	−1.16085	+	0.670217i	−0.951508	−	0.307625i	$-0.900466\pi$
$73$	−9.91831	+	5.72634i	−1.16085	+	0.670217i	−0.209342	+	0.977842i	$0.567132\pi$
$74$	7.97659	+	9.50613i	0.927260	+	1.10507i
$75$	9.52131	+	0.189291i	1.09943	+	0.0218574i
$76$	−11.2966	−	1.99190i	−1.29581	−	0.228486i
$77$	−2.63490	+	8.12760i	−0.300275	+	0.926226i
$78$	−12.9365	+	4.41932i	−1.46477	+	0.500390i
$79$	6.20601	+	2.25880i	0.698231	+	0.254135i	0.666655	−	0.745366i	$-0.267725\pi$
$79$	6.20601	+	2.25880i	0.698231	+	0.254135i	0.0315757	+	0.999501i	$0.489947\pi$
$80$	−5.23430			−0.585212
$81$	2.26189	−	8.71113i	0.251322	−	0.967904i
$82$		−	4.31797i		−	0.476841i
$83$	16.4935	+	6.00315i	1.81040	+	0.658932i	0.997015	+	0.0772059i	$0.0245999\pi$
$83$	16.4935	+	6.00315i	1.81040	+	0.658932i	0.813385	+	0.581726i	$0.197622\pi$
$84$	9.83623	−	8.52005i	1.07322	−	0.929613i
$85$	7.40375	+	6.21249i	0.803050	+	0.673839i
$86$	−16.4704	−	2.90417i	−1.77605	−	0.313165i
$87$	−0.335372	+	16.8692i	−0.0359556	+	1.80856i
$88$	−4.56989	+	3.83459i	−0.487152	+	0.408769i
$89$	3.48296	+	6.03267i	0.369193	+	0.639462i	0.989440	−	0.144945i	$-0.0463006\pi$
$89$	3.48296	+	6.03267i	0.369193	+	0.639462i	−0.620246	+	0.784407i	$0.712967\pi$
$90$	21.1901	−	2.87334i	2.23363	−	0.302877i
$91$	−9.40061	−	1.31486i	−0.985452	−	0.137835i
$92$	1.92055	−	0.338646i	0.200232	−	0.0353062i
$93$	−0.302777	+	0.783081i	−0.0313965	+	0.0812017i
$94$	−6.59746	−	18.1264i	−0.680476	−	1.86959i
$95$	−4.47644	−	12.2989i	−0.459273	−	1.26184i
$96$	−12.4050	+	1.93394i	−1.26608	+	0.197381i
$97$	2.47809	−	0.436955i	0.251612	−	0.0443660i	−0.0464193	−	0.998922i	$-0.514781\pi$
$97$	2.47809	−	0.436955i	0.251612	−	0.0443660i	0.298032	+	0.954556i	$0.403670\pi$
$98$	14.9372	−	3.74516i	1.50888	−	0.378318i
$99$	−6.51740	+	7.16809i	−0.655023	+	0.720420i
$100$	7.80666	+	13.5215i	0.780666	+	1.35215i
$101$	8.81458	−	7.39631i	0.877083	−	0.735960i	−0.0884942	−	0.996077i	$-0.528205\pi$
$101$	8.81458	−	7.39631i	0.877083	−	0.735960i	0.965577	+	0.260117i	$0.0837610\pi$
$102$	9.72840	+	5.87757i	0.963255	+	0.581966i
$103$	17.5678	+	3.09768i	1.73101	+	0.305223i	0.948349	−	0.317229i	$-0.102752\pi$
$103$	17.5678	+	3.09768i	1.73101	+	0.305223i	0.782658	+	0.622452i	$0.213863\pi$
$104$	−5.07698	−	4.26009i	−0.497839	−	0.417737i
$105$	14.0305	+	4.85882i	1.36923	+	0.474172i
$106$	6.44681	+	2.34645i	0.626170	+	0.227907i
$107$		−	2.99079i		−	0.289131i	−0.989495	−	0.144565i	$-0.953822\pi$
$107$		−	2.99079i		−	0.289131i	0.989495	−	0.144565i	$-0.0461784\pi$
$108$	14.1418	−	4.21134i	1.36080	−	0.405237i
$109$	2.85397			0.273361			0.136681	−	0.990615i	$-0.456357\pi$
$109$	2.85397			0.273361			0.136681	+	0.990615i	$0.456357\pi$
$110$	−21.6305	−	7.87287i	−2.06239	−	0.750649i
$111$	−1.88748	+	9.58609i	−0.179152	+	0.909872i
$112$	−4.06583	−	1.31811i	−0.384185	−	0.124550i
$113$	3.48822	+	0.615067i	0.328144	+	0.0578607i	0.335293	−	0.942114i	$-0.391165\pi$
$113$	3.48822	+	0.615067i	0.328144	+	0.0578607i	−0.00714917	+	0.999974i	$0.502276\pi$
$114$	−7.42949	−	13.4801i	−0.695836	−	1.26253i
$115$	1.43030	+	1.70456i	0.133376	+	0.158951i
$116$	−23.9565	+	13.8313i	−2.22430	+	1.28420i
$117$	−9.09982	−	5.74775i	−0.841279	−	0.531379i
$118$	21.4726	+	12.3972i	1.97671	+	1.14125i
$119$	4.18655	+	6.69007i	0.383780	+	0.613278i
$120$	6.50465	+	8.07252i	0.593791	+	0.736917i
$121$	−0.536887	+	0.195411i	−0.0488080	+	0.0177646i
$122$	−9.94013	+	3.61791i	−0.899937	+	0.327550i
$123$	2.64719	−	2.13304i	0.238689	−	0.192330i
$124$	−1.35558	+	0.239025i	−0.121735	+	0.0214651i
$125$	−0.807133	+	1.39800i	−0.0721922	+	0.125041i
$126$	17.1833	+	3.10419i	1.53081	+	0.276543i
$127$	−7.37491	−	12.7737i	−0.654418	−	1.13348i	−0.982039	−	0.188676i	$-0.939580\pi$
$127$	−7.37491	−	12.7737i	−0.654418	−	1.13348i	0.327622	−	0.944809i	$-0.393753\pi$
$128$	−8.66211	−	10.3231i	−0.765630	−	0.912442i
$129$	−6.35578	−	11.5320i	−0.559595	−	1.01534i
$130$	4.44070	−	25.1845i	0.389475	−	2.20883i
$131$	−6.97748	−	5.85480i	−0.609625	−	0.511536i	0.284898	−	0.958558i	$-0.408040\pi$
$131$	−6.97748	−	5.85480i	−0.609625	−	0.511536i	−0.894523	+	0.447021i	$0.852485\pi$
$132$	−15.5844	−	3.06853i	−1.35644	−	0.267081i
$133$	−0.380017	−	10.6806i	−0.0329517	−	0.926129i
$134$		−	20.9174i		−	1.80699i
$135$	12.2292	+	11.5714i	1.05253	+	0.995908i
$136$			5.51033i			0.472507i
$137$	−3.43127	+	9.42733i	−0.293153	+	0.805431i	0.702448	+	0.711735i	$0.252090\pi$
$137$	−3.43127	+	9.42733i	−0.293153	+	0.805431i	−0.995601	+	0.0936959i	$0.970132\pi$
$138$	1.97076	+	1.72156i	0.167762	+	0.146549i
$139$	−2.61949	+	3.12178i	−0.222182	+	0.264786i	−0.865608	−	0.500722i	$-0.833068\pi$
$139$	−2.61949	+	3.12178i	−0.222182	+	0.264786i	0.643426	+	0.765508i	$0.277512\pi$
$140$	5.07694	+	23.8081i	0.429080	+	2.01215i
$141$	7.85350	−	12.9989i	0.661384	−	1.09471i
$142$	5.20598	−	4.36834i	0.436876	−	0.366583i
$143$	5.79293	+	10.0337i	0.484429	+	0.839056i
$144$	−3.58583	−	3.26032i	−0.298819	−	0.271694i
$145$	−27.3343	−	15.7814i	−2.26999	−	1.31058i
$146$	−4.37509	−	24.8123i	−0.362085	−	2.05348i
$147$	9.67485	+	7.30734i	0.797968	+	0.602700i
$148$	−15.0522	+	5.47855i	−1.23728	+	0.450334i
$149$	3.33221	+	9.15518i	0.272985	+	0.750021i	0.998113	+	0.0614066i	$0.0195586\pi$
$149$	3.33221	+	9.15518i	0.272985	+	0.750021i	−0.725127	+	0.688615i	$0.758219\pi$
$150$	−7.55535	+	19.5406i	−0.616892	+	1.59548i
$151$	3.65868	+	20.7494i	0.297739	+	1.68856i	0.655855	+	0.754887i	$0.272308\pi$
$151$	3.65868	+	20.7494i	0.297739	+	1.68856i	−0.358116	+	0.933677i	$0.616581\pi$
$152$	3.73105	−	6.46236i	0.302628	−	0.524167i
$153$	1.20243	+	8.86758i	0.0972108	+	0.716901i
$154$	−14.8193	−	11.5624i	−1.19417	−	0.931726i
$155$	−1.00954	−	1.20313i	−0.0810885	−	0.0966375i
$156$	0.350748	−	17.6426i	0.0280823	−	1.41254i
$157$	10.0273	+	1.76809i	0.800269	+	0.141109i	0.558803	−	0.829300i	$-0.311261\pi$
$157$	10.0273	+	1.76809i	0.800269	+	0.141109i	0.241466	+	0.970409i	$0.422372\pi$
$158$	−9.33908	+	11.1299i	−0.742977	+	0.885446i
$159$	1.74615	+	5.11142i	0.138479	+	0.405362i
$160$	8.03267	−	22.0696i	0.635039	−	1.74475i
$161$	0.681762	+	1.68423i	0.0537304	+	0.132736i
$162$	16.3063	+	11.2304i	1.28114	+	0.882341i
$163$	−10.1031			−0.791340			−0.395670	−	0.918393i	$-0.629488\pi$
$163$	−10.1031			−0.791340			−0.395670	+	0.918393i	$0.629488\pi$
$164$	5.23757	+	1.90632i	0.408986	+	0.148859i
$165$	−5.85874	−	17.1500i	−0.456102	−	1.33512i
$166$	−24.8202	+	29.5795i	−1.92642	+	2.29582i
$167$	2.21093	−	12.5388i	0.171087	−	0.970284i	−0.771477	−	0.636258i	$-0.780482\pi$
$167$	2.21093	−	12.5388i	0.171087	−	0.970284i	0.942564	−	0.334026i	$-0.108407\pi$
$168$	3.01976	+	7.90847i	0.232980	+	0.610152i
$169$	0.0984525	−	0.0826114i	0.00757327	−	0.00635473i
$170$	−18.4136	+	10.6311i	−1.41226	+	0.815367i
$171$	4.59406	−	11.2138i	0.351317	−	0.857542i
$172$	10.7941	−	18.6959i	0.823042	−	1.42555i
$173$	−1.25238	−	7.10260i	−0.0952167	−	0.540001i	−0.994681	−	0.103006i	$-0.967154\pi$
$173$	−1.25238	−	7.10260i	−0.0952167	−	0.540001i	0.899464	−	0.436995i	$-0.143957\pi$
$174$	−34.6206	−	13.3860i	−2.62458	−	1.01479i
$175$	−10.8041	+	9.74090i	−0.816709	+	0.736343i
$176$	1.78430	+	4.90231i	0.134496	+	0.369526i
$177$	3.00701	+	19.2881i	0.226021	+	1.44978i
$178$	−15.0918	+	2.66109i	−1.13118	+	0.199457i
$179$	6.14419	+	3.54735i	0.459238	+	0.265141i	0.711724	−	0.702459i	$-0.247915\pi$
$179$	6.14419	+	3.54735i	0.459238	+	0.265141i	−0.252486	+	0.967601i	$0.581248\pi$
$180$	−5.86981	+	26.9714i	−0.437510	+	2.01033i
$181$	4.46843	−	2.57985i	0.332136	−	0.191759i	−0.324653	−	0.945833i	$-0.605248\pi$
$181$	4.46843	−	2.57985i	0.332136	−	0.191759i	0.656789	+	0.754074i	$0.271914\pi$
$182$	9.79138	−	18.4442i	0.725785	−	1.36717i
$183$	−7.12834	−	4.30670i	−0.526942	−	0.318360i
$184$	−0.220297	+	1.24937i	−0.0162405	+	0.0921046i
$185$	−14.0008	−	11.7480i	−1.02936	−	0.863734i
$186$	−1.39102	−	1.21513i	−0.101994	−	0.0890974i
$187$	3.29462	−	9.05191i	0.240927	−	0.661941i
$188$	24.8994			1.81598
$189$	6.58533	+	12.0679i	0.479012	+	0.877808i
$190$	28.7932			2.08888
$191$	1.36266	−	3.74387i	0.0985984	−	0.270897i	−0.880580	−	0.473897i	$-0.842847\pi$
$191$	1.36266	−	3.74387i	0.0985984	−	0.270897i	0.979179	+	0.203000i	$0.0650691\pi$
$192$	4.25472	−	21.6088i	0.307058	−	1.55948i
$193$	5.82741	+	4.88978i	0.419466	+	0.351974i	0.827960	−	0.560787i	$-0.189501\pi$
$193$	5.82741	+	4.88978i	0.419466	+	0.351974i	−0.408494	+	0.912761i	$0.633946\pi$
$194$	−0.961271	+	5.45164i	−0.0690152	+	0.391405i
$195$	17.6333	−	9.71848i	1.26275	−	0.695955i
$196$	−2.05178	+	19.7718i	−0.146556	+	1.41227i
$197$	−3.24083	+	1.87109i	−0.230899	+	0.133310i	−0.610987	−	0.791641i	$-0.709227\pi$
$197$	−3.24083	+	1.87109i	−0.230899	+	0.133310i	0.380087	+	0.924951i	$0.375894\pi$
$198$	−9.91448	−	18.8666i	−0.704591	−	1.34079i
$199$	1.91984	+	1.10842i	0.136094	+	0.0785736i	0.566501	−	0.824061i	$-0.308297\pi$
$199$	1.91984	+	1.10842i	0.136094	+	0.0785736i	−0.430407	+	0.902635i	$0.641630\pi$
$200$	−10.0025	+	1.76372i	−0.707287	+	0.124714i
$201$	12.8237	−	10.3330i	0.904512	−	0.728835i
$202$	8.65782	+	23.7872i	0.609162	+	1.67366i
$203$	−17.2582	−	19.1418i	−1.21129	−	1.34349i
$204$	−11.4242	+	9.20539i	−0.799857	+	0.644507i
$205$	1.10433	+	6.26296i	0.0771297	+	0.437424i
$206$	−19.6221	+	33.9865i	−1.36714	+	2.36795i
$207$	−0.0818868	+	2.05864i	−0.00569153	+	0.143085i
$208$	−5.01933	+	2.89791i	−0.348028	+	0.200934i
$209$	−9.99289	+	8.38503i	−0.691223	+	0.580005i
$210$	−20.6013	+	25.3488i	−1.42162	+	1.74923i
$211$	−0.591357	+	3.35375i	−0.0407107	+	0.230882i	−0.998374	−	0.0570100i	$-0.981843\pi$
$211$	−0.591357	+	3.35375i	−0.0407107	+	0.230882i	0.957663	+	0.287892i	$0.0929544\pi$
$212$	−5.69234	+	6.78386i	−0.390951	+	0.465918i
$213$	5.24977	+	1.03367i	0.359708	+	0.0708259i
$214$	6.18275	+	2.25034i	0.422644	+	0.153830i
$215$	24.6320			1.67989
$216$	−0.572083	+	9.58179i	−0.0389253	+	0.651958i
$217$	−0.481206	−	1.18877i	−0.0326664	−	0.0806992i
$218$	−2.14739	+	5.89991i	−0.145440	+	0.399592i
$219$	13.0503	−	14.9393i	0.881854	−	1.00950i
$220$	19.0991	−	22.7614i	1.28766	−	1.53458i
$221$	10.5392	+	1.85834i	0.708940	+	0.125005i
$222$	−18.3968	−	11.1147i	−1.23471	−	0.745970i
$223$	3.08075	+	3.67150i	0.206302	+	0.245862i	0.859268	−	0.511526i	$-0.170920\pi$
$223$	3.08075	+	3.67150i	0.206302	+	0.245862i	−0.652965	+	0.757388i	$0.726475\pi$
$224$	11.7971	−	15.1201i	0.788227	−	1.01026i
$225$	−15.7119	+	5.02099i	−1.04746	+	0.334733i
$226$	−3.89612	+	6.74827i	−0.259166	+	0.448888i
$227$	1.47843	+	8.38458i	0.0981267	+	0.556504i	0.993744	+	0.111679i	$0.0356229\pi$
$227$	1.47843	+	8.38458i	0.0981267	+	0.556504i	−0.895618	+	0.444825i	$0.853266\pi$
$228$	19.6310	−	3.06047i	1.30010	−	0.202685i
$229$	7.67684	+	21.0920i	0.507300	+	1.39380i	0.884012	+	0.467465i	$0.154833\pi$
$229$	7.67684	+	21.0920i	0.507300	+	1.39380i	−0.376712	+	0.926331i	$0.622945\pi$
$230$	−4.59997	+	1.67425i	−0.303313	+	0.110397i
$231$	−0.232136	−	14.7969i	−0.0152734	−	0.973564i
$232$	−3.12483	−	17.7218i	−0.205155	−	1.16349i
$233$	−4.77720	−	2.75812i	−0.312965	−	0.180690i	0.335288	−	0.942116i	$-0.391167\pi$
$233$	−4.77720	−	2.75812i	−0.312965	−	0.180690i	−0.648252	+	0.761426i	$0.724500\pi$
$234$	18.7290	−	14.4870i	1.22435	−	0.947043i
$235$	14.2051	+	24.6039i	0.926636	+	1.60498i
$236$	−24.5172	+	20.5724i	−1.59594	+	1.33915i
$237$	−11.4367	−	0.227371i	−0.742895	−	0.0147693i
$238$	−16.9802	+	3.62093i	−1.10066	+	0.234710i
$239$	17.7886	−	21.1996i	1.15065	−	1.37129i	0.233687	−	0.972312i	$-0.424921\pi$
$239$	17.7886	−	21.1996i	1.15065	−	1.37129i	0.916961	−	0.398977i	$-0.130635\pi$
$240$	8.57927	−	2.93083i	0.553790	−	0.189184i
$241$	0.237543	−	0.652643i	0.0153015	−	0.0420404i	−0.931807	−	0.362955i	$-0.881768\pi$
$241$	0.237543	−	0.652643i	0.0153015	−	0.0420404i	0.947108	+	0.320914i	$0.103990\pi$
$242$		−	1.25692i		−	0.0807978i
$243$	1.17025	+	15.5445i	0.0750715	+	0.997178i
$244$		−	13.6543i		−	0.874128i
$245$	−20.7077	+	9.25233i	−1.32296	+	0.591110i
$246$	2.41775	+	7.07737i	0.154150	+	0.451237i
$247$	−11.1017	−	9.31547i	−0.706387	−	0.592729i
$248$	0.155492	−	0.881838i	0.00987374	−	0.0559968i
$249$	−30.3950	−	0.604276i	−1.92621	−	0.0382945i
$250$	−2.28272	−	2.72044i	−0.144372	−	0.172056i
$251$	2.14378	+	3.71314i	0.135314	+	0.234371i	0.925717	−	0.378216i	$-0.123462\pi$
$251$	2.14378	+	3.71314i	0.135314	+	0.234371i	−0.790403	+	0.612587i	$0.790129\pi$
$252$	−11.3515	+	19.4724i	−0.715074	+	1.22664i
$253$	1.10888	−	1.92064i	0.0697149	−	0.120750i
$254$	31.9557	−	5.63465i	2.00508	−	0.353549i
$255$	−15.6137	−	6.03700i	−0.977765	−	0.378052i
$256$	3.96106	−	1.44171i	0.247566	−	0.0901067i
$257$	9.32291	−	3.39326i	0.581547	−	0.211666i	−0.0344606	−	0.999406i	$-0.510971\pi$
$257$	9.32291	−	3.39326i	0.581547	−	0.211666i	0.616007	+	0.787740i	$0.288749\pi$
$258$	28.6219	−	4.46214i	1.78192	−	0.277801i
$259$	−7.91692	−	12.6512i	−0.491934	−	0.786106i
$260$	28.5875	+	16.5050i	1.77292	+	1.02360i
$261$	−8.89582	−	27.8372i	−0.550638	−	1.72308i
$262$	17.3534	−	10.0190i	1.07210	−	0.618976i
$263$	2.88623	+	3.43967i	0.177973	+	0.212099i	0.847655	−	0.530549i	$-0.178014\pi$
$263$	2.88623	+	3.43967i	0.177973	+	0.212099i	−0.669682	+	0.742648i	$0.733570\pi$
$264$	5.34318	−	8.84389i	0.328850	−	0.544304i
$265$	−9.95082	−	1.75460i	−0.611274	−	0.107784i
$266$	22.3656	+	7.25075i	1.37132	+	0.444572i
$267$	−9.08661	−	7.93763i	−0.556091	−	0.485775i
$268$	25.3722	+	9.23472i	1.54985	+	0.564100i
$269$	−3.30722			−0.201645			−0.100823	−	0.994904i	$-0.532147\pi$
$269$	−3.30722			−0.201645			−0.100823	+	0.994904i	$0.532147\pi$
$270$	−33.1227	+	16.5745i	−2.01578	+	1.00869i
$271$		−	27.4022i		−	1.66457i	−0.554351	−	0.832283i	$-0.687034\pi$
$271$		−	27.4022i		−	1.66457i	0.554351	−	0.832283i	$-0.312966\pi$
$272$	4.52821	+	1.64813i	0.274563	+	0.0999328i
$273$	16.1443	−	3.10855i	0.977097	−	0.188138i
$274$	−16.9070	−	14.1866i	−1.02139	−	0.857047i
$275$	17.4859	+	3.08323i	1.05444	+	0.185926i
$276$	−2.95826	+	1.63043i	−0.178067	+	0.0981402i
$277$	15.3342	−	12.8670i	0.921346	−	0.773101i	−0.0528977	−	0.998600i	$-0.516846\pi$
$277$	15.3342	−	12.8670i	0.921346	−	0.773101i	0.974243	+	0.225499i	$0.0724013\pi$
$278$	−4.48259	−	7.76407i	−0.268848	−	0.465658i
$279$	0.0577979	−	1.45304i	0.00346027	−	0.0869913i
$280$	−15.6833	−	2.19361i	−0.937256	−	0.131093i
$281$	22.5838	−	3.98212i	1.34723	−	0.237554i	0.546945	−	0.837169i	$-0.315791\pi$
$281$	22.5838	−	3.98212i	1.34723	−	0.237554i	0.800289	+	0.599615i	$0.204680\pi$
$282$	20.9630	+	26.0159i	1.24833	+	1.54922i
$283$	−7.62218	−	20.9418i	−0.453091	−	1.24486i	−0.930537	−	0.366197i	$-0.880660\pi$
$283$	−7.62218	−	20.9418i	−0.453091	−	1.24486i	0.477446	−	0.878661i	$-0.341563\pi$
$284$	3.00030	+	8.24325i	0.178035	+	0.489147i
$285$	14.2236	+	17.6520i	0.842534	+	1.04562i
$286$	−25.1009	+	4.42597i	−1.48425	+	0.261713i
$287$	−0.719342	+	5.14295i	−0.0424614	+	0.303579i
$288$	19.2495	−	10.1157i	1.13429	−	0.596074i
$289$	4.05112	+	7.01675i	0.238301	+	0.412750i
$290$	53.1912	−	44.6327i	3.12350	−	2.62093i
$291$	−3.81705	+	2.10374i	−0.223760	+	0.123324i
$292$	32.0282	+	5.64743i	1.87431	+	0.330491i
$293$	−10.6534	−	8.93928i	−0.622379	−	0.522238i	0.276171	−	0.961108i	$-0.410934\pi$
$293$	−10.6534	−	8.93928i	−0.622379	−	0.522238i	−0.898550	+	0.438870i	$0.855379\pi$
$294$	−22.3858	+	14.5022i	−1.30556	+	0.845788i
$295$	−34.3153	−	12.4897i	−1.99791	−	0.727181i
$296$		−	10.4202i		−	0.605664i
$297$	6.66872	−	15.3981i	0.386958	−	0.893489i
$298$	−21.4334			−1.24160
$299$	2.31527	+	0.842689i	0.133895	+	0.0487340i
$300$	−20.3666	−	17.7913i	−1.17587	−	1.02718i
$301$	19.1333	+	6.20287i	1.10283	+	0.357528i
$302$	−45.6474	−	8.04886i	−2.62671	−	0.463160i
$303$	−10.3061	+	17.0584i	−0.592071	+	0.979981i
$304$	−4.19461	−	4.99894i	−0.240577	−	0.286709i
$305$	13.4923	−	7.78977i	0.772565	−	0.446041i
$306$	−19.2363	−	4.18642i	−1.09967	−	0.239321i
$307$	−4.06170	−	2.34502i	−0.231813	−	0.133837i	0.379595	−	0.925153i	$-0.376063\pi$
$307$	−4.06170	−	2.34502i	−0.231813	−	0.133837i	−0.611408	+	0.791315i	$0.709397\pi$
$308$	20.5674	−	12.8707i	1.17193	−	0.733379i
$309$	−30.5290	+	4.75946i	−1.73673	+	0.270756i
$310$	3.24678	−	1.18173i	0.184405	−	0.0671178i
$311$	0.145456	−	0.0529415i	0.00824803	−	0.00300204i	−0.337893	−	0.941185i	$-0.609714\pi$
$311$	0.145456	−	0.0529415i	0.00824803	−	0.00300204i	0.346141	+	0.938183i	$0.387492\pi$
$312$	10.7068	+	4.13976i	0.606151	+	0.234368i
$313$	23.8814	−	4.21093i	1.34986	−	0.238016i	0.548473	−	0.836168i	$-0.315209\pi$
$313$	23.8814	−	4.21093i	1.34986	−	0.238016i	0.801383	+	0.598152i	$0.204098\pi$
$314$	−11.1999	+	19.3988i	−0.632047	+	1.09474i
$315$	−25.7172	−	0.107789i	−1.44900	−	0.00607321i
$316$	−9.37714	−	16.2417i	−0.527505	−	0.913666i
$317$	−3.59159	−	4.28029i	−0.201724	−	0.240405i	0.655693	−	0.755027i	$-0.272376\pi$
$317$	−3.59159	−	4.28029i	−0.201724	−	0.240405i	−0.857417	+	0.514623i	$0.827932\pi$
$318$	−11.8805	−	0.236193i	−0.666224	−	0.0132450i
$319$	−5.46265	+	30.9802i	−0.305850	+	1.73456i
$320$	31.5602	+	26.4822i	1.76427	+	1.48040i
$321$	1.67463	+	4.90206i	0.0934687	+	0.273606i
$322$	−3.99471	+	0.142132i	−0.222617	+	0.00792070i
$323$			12.0493i			0.670443i
$324$	−20.8211	+	14.8210i	−1.15673	+	0.823388i
$325$			19.7259i			1.09419i
$326$	7.60183	−	20.8858i	0.421026	−	1.15676i
$327$	−4.67780	+	1.59802i	−0.258683	+	0.0883707i
$328$	−2.33064	+	2.77755i	−0.128688	+	0.153365i
$329$	4.83823	+	22.6886i	0.266740	+	1.25086i
$330$	39.8617	+	0.792482i	2.19432	+	0.0436247i
$331$	−6.72476	+	5.64274i	−0.369626	+	0.310153i	−0.808614	−	0.588340i	$-0.799782\pi$
$331$	−6.72476	+	5.64274i	−0.369626	+	0.310153i	0.438987	+	0.898493i	$0.355337\pi$
$332$	−24.9213	−	43.1650i	−1.36774	−	2.36899i
$333$	−2.27384	−	16.7689i	−0.124606	−	0.918932i
$334$	24.2575	+	14.0051i	1.32731	+	0.766323i
$335$	5.34966	+	30.3394i	0.292283	+	1.65762i
$336$	7.40214	−	0.116126i	0.403820	−	0.00633518i
$337$	16.3526	−	5.95186i	0.890783	−	0.324218i	0.144230	−	0.989544i	$-0.453930\pi$
$337$	16.3526	−	5.95186i	0.890783	−	0.324218i	0.746553	+	0.665326i	$0.231707\pi$
$338$	0.0967017	+	0.265686i	0.00525988	+	0.0144514i
$339$	−6.06176	+	0.945026i	−0.329229	+	0.0513268i
$340$	−4.76586	−	27.0286i	−0.258465	−	1.46583i
$341$	−0.782680	+	1.35564i	−0.0423845	+	0.0734121i
$342$	19.7252	+	17.9346i	1.06662	+	0.969794i
$343$	−18.4149	+	1.97227i	−0.994313	+	0.106493i
$344$	9.02708	+	10.7581i	0.486708	+	0.580036i
$345$	−3.29876	−	1.99300i	−0.177599	−	0.107299i
$346$	15.6252	+	2.75515i	0.840018	+	0.148118i
$347$	1.81114	−	2.15843i	0.0972268	−	0.115870i	−0.715237	−	0.698882i	$-0.753681\pi$
$347$	1.81114	−	2.15843i	0.0972268	−	0.115870i	0.812464	+	0.583011i	$0.198126\pi$
$348$	31.5213	−	36.0840i	1.68972	−	1.93431i
$349$	−7.28167	+	20.0062i	−0.389779	+	1.07091i	0.577323	+	0.816516i	$0.304098\pi$
$349$	−7.28167	+	20.0062i	−0.389779	+	1.07091i	−0.967101	+	0.254392i	$0.918125\pi$
$350$	−12.0078	−	29.6641i	−0.641843	−	1.58561i
$351$	18.1334	+	4.32560i	0.967888	+	0.230883i
$352$	−23.4080			−1.24765
$353$	20.7113	+	7.53828i	1.10235	+	0.401222i	0.828182	−	0.560460i	$-0.189376\pi$
$353$	20.7113	+	7.53828i	1.10235	+	0.401222i	0.274167	+	0.961682i	$0.411598\pi$
$354$	−42.1361	−	8.29652i	−2.23951	−	0.440955i
$355$	−6.43375	+	7.66745i	−0.341468	+	0.406946i
$356$	3.43497	−	19.4807i	0.182053	−	1.03247i
$357$	−10.6079	−	8.62119i	−0.561430	−	0.456282i
$358$	−11.9563	+	10.0325i	−0.631911	+	0.530236i
$359$	−17.6192	+	10.1725i	−0.929908	+	0.536883i	−0.886783	−	0.462187i	$-0.847065\pi$
$359$	−17.6192	+	10.1725i	−0.929908	+	0.536883i	−0.0431257	+	0.999070i	$0.513732\pi$
$360$	−15.1815	−	9.58912i	−0.800134	−	0.505391i
$361$	−1.34139	+	2.32335i	−0.0705993	+	0.122282i
$362$	1.97108	+	11.1786i	0.103598	+	0.587532i
$363$	0.770569	−	0.620906i	0.0404444	−	0.0325891i
$364$	18.0495	+	20.0195i	0.946051	+	1.04931i
$365$	12.6916	+	34.8699i	0.664309	+	1.82517i
$366$	14.2666	−	11.4957i	0.745726	−	0.600889i
$367$	−23.5883	+	4.15925i	−1.23130	+	0.217111i	−0.751183	−	0.660094i	$-0.770517\pi$
$367$	−23.5883	+	4.15925i	−1.23130	+	0.217111i	−0.480116	+	0.877205i	$0.659405\pi$
$368$	0.960800	+	0.554718i	0.0500852	+	0.0289167i
$369$	−3.14452	+	4.97839i	−0.163697	+	0.259165i
$370$	34.8208	−	20.1038i	1.81025	−	1.04515i
$371$	−7.28762	−	3.86874i	−0.378354	−	0.200855i
$372$	2.08802	−	1.15080i	0.108259	−	0.0596662i
$373$	3.20352	−	18.1680i	0.165872	−	0.940706i	−0.782289	−	0.622915i	$-0.785948\pi$
$373$	3.20352	−	18.1680i	0.165872	−	0.940706i	0.948161	−	0.317790i	$-0.102941\pi$
$374$	16.2337	+	13.6217i	0.839425	+	0.704361i
$375$	0.540154	−	2.74332i	0.0278934	−	0.141664i
$376$	−5.53993	+	15.2208i	−0.285700	+	0.784955i
$377$	−34.9489			−1.79996
$378$	−29.9024	+	4.53348i	−1.53801	+	0.233177i
$379$	−14.2916			−0.734112			−0.367056	−	0.930199i	$-0.619634\pi$
$379$	−14.2916			−0.734112			−0.367056	+	0.930199i	$0.619634\pi$
$380$	−12.7118	+	34.9253i	−0.652100	+	1.79163i
$381$	19.2402	+	16.8073i	0.985706	+	0.861066i
$382$	6.71427	+	5.63394i	0.343532	+	0.288257i
$383$	−3.96910	+	22.5099i	−0.202812	+	1.15020i	0.698035	+	0.716064i	$0.254058\pi$
$383$	−3.96910	+	22.5099i	−0.202812	+	1.15020i	−0.900846	+	0.434138i	$0.857053\pi$
$384$	19.9778	+	12.0699i	1.01949	+	0.615940i
$385$	24.4516	+	12.9805i	1.24617	+	0.661548i
$386$	−14.4931	+	8.36760i	−0.737680	+	0.425900i
$387$	16.8745	+	15.3427i	0.857780	+	0.779914i
$388$	−6.18829	−	3.57281i	−0.314163	−	0.181382i
$389$	−2.40905	+	0.424780i	−0.122143	+	0.0215372i	−0.234386	−	0.972144i	$-0.575308\pi$
$389$	−2.40905	+	0.424780i	−0.122143	+	0.0215372i	0.112242	+	0.993681i	$0.464197\pi$
$390$	6.82296	+	43.7651i	0.345494	+	2.21613i
$391$	−0.700637	−	1.92499i	−0.0354328	−	0.0973507i
$392$	−11.6299	−	5.65331i	−0.587396	−	0.285535i
$393$	14.7147	+	5.68942i	0.742258	+	0.286993i
$394$	−1.42957	−	8.10749i	−0.0720207	−	0.408449i
$395$	10.6993	−	18.5317i	0.538339	−	0.932431i
$396$	27.2617	−	3.69665i	1.36995	−	0.185764i
$397$	−11.7575	+	6.78822i	−0.590094	+	0.340691i	−0.765135	−	0.643870i	$-0.777328\pi$
$397$	−11.7575	+	6.78822i	−0.590094	+	0.340691i	0.175041	+	0.984561i	$0.443994\pi$
$398$	−3.73591	+	3.13480i	−0.187264	+	0.157134i
$399$	6.60326	+	17.2933i	0.330576	+	0.865749i
$400$	−1.54239	+	8.74730i	−0.0771193	+	0.437365i
$401$	−12.2624	+	14.6138i	−0.612356	+	0.729777i	−0.979736	−	0.200294i	$-0.935810\pi$
$401$	−12.2624	+	14.6138i	−0.612356	+	0.729777i	0.367380	+	0.930071i	$0.380255\pi$
$402$	11.7122	+	34.2847i	0.584153	+	1.70996i
$403$	−1.63418	−	0.594793i	−0.0814043	−	0.0296287i
$404$	−32.6754			−1.62566
$405$	−26.5235	−	12.1186i	−1.31796	−	0.602179i
$406$	52.5566	−	21.2745i	2.60834	−	1.05584i
$407$	−6.23026	+	17.1175i	−0.308823	+	0.848483i
$408$	−3.08539	−	9.03170i	−0.152749	−	0.447136i
$409$	21.1128	−	25.1612i	1.04396	−	1.24414i	0.0749336	−	0.997189i	$-0.476126\pi$
$409$	21.1128	−	25.1612i	1.04396	−	1.24414i	0.969027	−	0.246955i	$-0.0794300\pi$
$410$	−13.7781	−	2.42945i	−0.680452	−	0.119982i
$411$	0.345391	−	17.3731i	0.0170369	−	0.856952i
$412$	−32.5617	−	38.8055i	−1.60420	−	1.91181i
$413$	−23.5098	−	18.3429i	−1.15684	−	0.902597i
$414$	−4.19412	−	1.71824i	−0.206130	−	0.0844470i
$415$	28.4352	−	49.2511i	1.39583	−	2.41764i
$416$	−4.51580	−	25.6104i	−0.221406	−	1.25565i
$417$	2.54550	−	6.58348i	0.124653	−	0.322395i
$418$	−9.81519	−	26.9670i	−0.480076	−	1.31900i
$419$	24.1055	−	8.77369i	1.17763	−	0.428623i	0.322267	−	0.946649i	$-0.395555\pi$
$419$	24.1055	−	8.77369i	1.17763	−	0.428623i	0.855365	+	0.518026i	$0.173333\pi$
$420$	−21.6521	−	36.1798i	−1.05652	−	1.76540i
$421$	−2.00087	−	11.3475i	−0.0975165	−	0.553044i	−0.993947	−	0.109860i	$-0.964960\pi$
$421$	−2.00087	−	11.3475i	−0.0975165	−	0.553044i	0.896431	−	0.443184i	$-0.146151\pi$
$422$	−6.48814	−	3.74593i	−0.315838	−	0.182349i
$423$	−5.59382	+	25.7033i	−0.271981	+	1.24973i
$424$	−2.88043	−	4.98905i	−0.139886	−	0.242290i
$425$	12.5637	−	10.5422i	0.609427	−	0.511370i
$426$	−6.08691	+	10.0749i	−0.294912	+	0.488130i
$427$	12.4420	−	2.65319i	0.602109	−	0.128397i
$428$	−5.45918	+	6.50600i	−0.263880	+	0.314479i
$429$	−15.1130	−	13.2020i	−0.729663	−	0.637400i
$430$	−18.5337	+	50.9208i	−0.893773	+	2.45562i
$431$		−	27.5891i		−	1.32892i	−0.747323	−	0.664461i	$-0.768661\pi$
$431$		−	27.5891i		−	1.32892i	0.747323	−	0.664461i	$-0.231339\pi$
$432$	7.70290	+	3.33602i	0.370606	+	0.160505i
$433$			1.08018i			0.0519102i	0.999663	+	0.0259551i	$0.00826269\pi$
$433$			1.08018i			0.0519102i	−0.999663	+	0.0259551i	$0.991737\pi$
$434$	2.81958	−	0.100320i	0.135344	−	0.00481554i
$435$	53.6386	+	10.5613i	2.57178	+	0.506377i
$436$	−6.20837	−	5.20944i	−0.297327	−	0.249487i
$437$	−0.481720	+	2.73197i	−0.0230438	+	0.130688i
$438$	21.0641	+	38.2189i	1.00648	+	1.82617i
$439$	−1.70073	−	2.02686i	−0.0811716	−	0.0967365i	0.723930	−	0.689873i	$-0.242334\pi$
$439$	−1.70073	−	2.02686i	−0.0811716	−	0.0967365i	−0.805102	+	0.593137i	$0.797889\pi$
$440$	9.66450	+	16.7394i	0.460737	+	0.798020i
$441$	−19.9491	−	6.55988i	−0.949959	−	0.312375i
$442$	−11.7716	+	20.3889i	−0.559916	+	0.969803i
$443$	−15.9507	+	2.81254i	−0.757840	+	0.133628i	−0.539200	−	0.842178i	$-0.681273\pi$
$443$	−15.9507	+	2.81254i	−0.757840	+	0.133628i	−0.218640	+	0.975806i	$0.570162\pi$
$444$	21.6037	−	17.4078i	1.02527	−	0.826135i
$445$	21.2091	−	7.71949i	1.00541	−	0.365939i
$446$	−9.90797	+	3.60621i	−0.469156	+	0.170759i
$447$	−10.5879	−	13.1400i	−0.500790	−	0.621500i
$448$	17.8462	+	28.5180i	0.843151	+	1.34735i
$449$	16.4077	+	9.47299i	0.774327	+	0.447058i	0.834416	−	0.551135i	$-0.185805\pi$
$449$	16.4077	+	9.47299i	0.774327	+	0.447058i	−0.0600887	+	0.998193i	$0.519138\pi$
$450$	1.44226	−	36.2585i	0.0679888	−	1.70924i
$451$	5.48928	−	3.16924i	0.258480	−	0.149234i
$452$	−6.46537	−	7.70513i	−0.304106	−	0.362419i
$453$	−17.6149	−	31.9607i	−0.827622	−	1.50165i
$454$	−18.4455	−	3.25244i	−0.865691	−	0.152645i
$455$	−9.48467	+	29.2563i	−0.444648	+	1.37156i
$456$	−2.49691	+	12.6812i	−0.116929	+	0.593854i
$457$	−27.2962	−	9.93500i	−1.27686	−	0.464740i	−0.387468	−	0.921883i	$-0.626650\pi$
$457$	−27.2962	−	9.93500i	−1.27686	−	0.464740i	−0.889393	+	0.457143i	$0.848873\pi$
$458$	−49.3788			−2.30732
$459$	−6.93605	−	13.8611i	−0.323747	−	0.646981i
$460$		−	6.31877i		−	0.294614i
$461$	−39.9292	−	14.5330i	−1.85969	−	0.676870i	−0.979233	−	0.202737i	$-0.935016\pi$
$461$	−39.9292	−	14.5330i	−1.85969	−	0.676870i	−0.880453	−	0.474134i	$-0.842761\pi$
$462$	30.7637	+	10.6536i	1.43126	+	0.495651i
$463$	−10.3324	−	8.66991i	−0.480187	−	0.402925i	0.370307	−	0.928909i	$-0.379252\pi$
$463$	−10.3324	−	8.66991i	−0.480187	−	0.402925i	−0.850494	+	0.525985i	$0.823697\pi$
$464$	−15.4978	−	2.73269i	−0.719469	−	0.126862i
$465$	2.32836	+	1.40671i	0.107975	+	0.0652347i
$466$	9.29622	−	7.80045i	0.430639	−	0.361349i
$467$	−12.0023	−	20.7886i	−0.555401	−	0.961983i	−0.997872	−	0.0652000i	$-0.979231\pi$
$467$	−12.0023	−	20.7886i	−0.555401	−	0.961983i	0.442471	−	0.896783i	$-0.354102\pi$
$468$	9.30369	+	29.1135i	0.430063	+	1.34577i
$469$	−3.48468	+	24.9138i	−0.160908	+	1.15041i
$470$	−61.5509	+	10.8531i	−2.83913	+	0.500615i
$471$	−17.4253	+	2.71660i	−0.802916	+	0.125174i
$472$	−7.12087	−	19.5644i	−0.327765	−	0.900526i
$473$	−8.39669	−	23.0697i	−0.386080	−	1.06075i
$474$	9.07527	−	23.4716i	0.416841	−	1.07809i
$475$	−21.8724	+	3.85669i	−1.00357	+	0.176957i
$476$	3.10441	−	22.1950i	0.142290	−	1.01731i
$477$	−5.72405	−	7.40015i	−0.262086	−	0.338829i
$478$	30.4406	+	52.7247i	1.39232	+	2.41157i
$479$	−17.1728	+	14.4097i	−0.784647	+	0.658397i	−0.944414	−	0.328758i	$-0.893370\pi$
$479$	−17.1728	+	14.4097i	−0.784647	+	0.658397i	0.159767	+	0.987155i	$0.448926\pi$
$480$	−0.808567	+	40.6709i	−0.0369059	+	1.85636i
$481$	−19.9299	−	3.51419i	−0.908727	−	0.160233i
$482$	1.17045	+	0.982126i	0.0533126	+	0.0447346i
$483$	−2.06049	−	2.37879i	−0.0937554	−	0.108239i
$484$	1.52460	+	0.554910i	0.0693002	+	0.0252232i
$485$		−	8.15312i		−	0.370214i
$486$	−33.0150	−	9.27678i	−1.49759	−	0.420803i
$487$	6.87495			0.311534			0.155767	−	0.987794i	$-0.450215\pi$
$487$	6.87495			0.311534			0.155767	+	0.987794i	$0.450215\pi$
$488$	8.34680	+	3.03799i	0.377842	+	0.137523i
$489$	16.5596	−	5.65703i	0.748849	−	0.255820i
$490$	−3.54611	−	49.7698i	−0.160197	−	2.24837i
$491$	−5.85169	−	1.03181i	−0.264083	−	0.0465650i	0.0400387	−	0.999198i	$-0.487252\pi$
$491$	−5.85169	−	1.03181i	−0.264083	−	0.0465650i	−0.304122	+	0.952633i	$0.598363\pi$
$492$	−9.65204	−	0.191890i	−0.435147	−	0.00865106i
$493$	18.6778	+	22.2594i	0.841207	+	1.00251i
$494$	27.6107	−	15.9411i	1.24226	−	0.717222i
$495$	19.2055	+	24.8292i	0.863223	+	1.11599i
$496$	−0.678159	−	0.391535i	−0.0304502	−	0.0175804i
$497$	−6.92835	+	4.33566i	−0.310779	+	0.194481i
$498$	24.1191	−	62.3798i	1.08080	−	2.79531i
$499$	8.89086	−	3.23601i	0.398010	−	0.144864i	−0.135258	−	0.990810i	$-0.543186\pi$
$499$	8.89086	−	3.23601i	0.398010	−	0.144864i	0.533267	+	0.845947i	$0.320964\pi$
$500$	4.30759	−	1.56784i	0.192641	−	0.0701158i
$501$	3.39701	+	21.7897i	0.151767	+	0.973493i
$502$	−9.28905	+	1.63791i	−0.414590	+	0.0731035i
$503$	8.03207	−	13.9120i	0.358132	−	0.620303i	−0.629517	−	0.776987i	$-0.716747\pi$
$503$	8.03207	−	13.9120i	0.358132	−	0.620303i	0.987649	+	0.156684i	$0.0500804\pi$
$504$	−9.37771	−	11.2715i	−0.417716	−	0.502074i
$505$	−18.6413	−	32.2876i	−0.829525	−	1.43678i
$506$	3.13612	+	3.73748i	0.139418	+	0.166151i
$507$	−0.115112	+	0.190530i	−0.00511230	+	0.00846175i
$508$	−7.27329	+	41.2489i	−0.322700	+	1.83012i
$509$	7.79226	+	6.53848i	0.345386	+	0.289813i	0.798934	−	0.601419i	$-0.205398\pi$
$509$	7.79226	+	6.53848i	0.345386	+	0.289813i	−0.453548	+	0.891232i	$0.649842\pi$
$510$	24.2281	−	27.7351i	1.07284	−	1.22813i
$511$	1.07743	+	30.2818i	0.0476625	+	1.33959i
$512$		−	17.6784i		−	0.781282i
$513$	−1.25096	+	20.9523i	−0.0552314	+	0.925068i
$514$			21.8260i			0.962705i
$515$	19.7686	−	54.3137i	0.871108	−	2.39335i
$516$	−7.22368	+	36.6874i	−0.318005	+	1.61507i
$517$	18.2011	−	21.6912i	0.800483	−	0.953978i
$518$	32.1102	−	6.84733i	1.41084	−	0.300854i
$519$	6.02965	+	10.9403i	0.264672	+	0.480224i
$520$	−16.4499	+	13.8031i	−0.721376	+	0.605306i
$521$	18.8534	+	32.6550i	0.825982	+	1.43064i	0.901166	+	0.433474i	$0.142712\pi$
$521$	18.8534	+	32.6550i	0.825982	+	1.43064i	−0.0751836	+	0.997170i	$0.523954\pi$
$522$	64.2401	+	2.55529i	2.81171	+	0.111842i
$523$	1.29357	+	0.746842i	0.0565638	+	0.0326571i	0.528015	−	0.849235i	$-0.322936\pi$
$523$	1.29357	+	0.746842i	0.0565638	+	0.0326571i	−0.471451	+	0.881892i	$0.656270\pi$
$524$	4.49147	+	25.4724i	0.196211	+	1.11277i
$525$	12.2542	−	22.0153i	0.534816	−	0.960826i
$526$	−9.28237	+	3.37851i	−0.404730	+	0.147310i
$527$	0.494529	+	1.35871i	0.0215420	+	0.0591862i
$528$	−5.66949	−	7.03605i	−0.246733	−	0.306205i
$529$	3.91201	+	22.1861i	0.170087	+	0.964614i
$530$	11.1144	−	19.2507i	0.482780	−	0.836199i
$531$	−15.7286	−	29.9305i	−0.682563	−	1.29887i
$532$	−18.6690	+	23.9277i	−0.809405	+	1.03740i
$533$	4.52639	+	5.39435i	0.196060	+	0.233655i
$534$	23.2461	−	12.8119i	1.00596	−	0.554427i
$535$	−9.54324	−	1.68273i	−0.412590	−	0.0727508i
$536$	−11.2902	+	13.4552i	−0.487664	+	0.581176i
$537$	−12.0569	−	2.37398i	−0.520293	−	0.102445i
$538$	2.48843	−	6.83690i	0.107284	−	0.294760i
$539$	15.7244	+	16.2403i	0.677299	+	0.699518i
$540$	−5.48115	−	47.4942i	−0.235871	−	2.04382i
$541$	3.68188			0.158297			0.0791483	−	0.996863i	$-0.474780\pi$
$541$	3.68188			0.158297			0.0791483	+	0.996863i	$0.474780\pi$
$542$	56.6475	+	20.6180i	2.43322	+	0.885620i
$543$	−5.87945	+	6.73050i	−0.252311	+	0.288834i
$544$	−13.8982	+	16.5632i	−0.595880	+	0.710142i
$545$	1.60575	−	9.10666i	0.0687828	−	0.390087i
$546$	−5.72113	+	35.7134i	−0.244842	+	1.52839i
$547$	28.1372	−	23.6099i	1.20306	−	1.00949i	0.203523	−	0.979070i	$-0.434761\pi$
$547$	28.1372	−	23.6099i	1.20306	−	1.00949i	0.999537	−	0.0304178i	$-0.00968377\pi$
$548$	24.6722	−	14.2445i	1.05394	−	0.608494i
$549$	14.0951	+	3.06753i	0.601566	+	0.130919i
$550$	−19.5306	+	33.8280i	−0.832787	+	1.44243i
$551$	−6.83301	−	38.7519i	−0.291096	−	1.65089i
$552$	−0.338478	−	2.17113i	−0.0144066	−	0.0924093i
$553$	12.9775	−	11.7005i	0.551860	−	0.497556i
$554$	15.0616	+	41.3813i	0.639904	+	1.75812i
$555$	29.5260	+	11.4162i	1.25331	+	0.484591i
$556$	11.3966	−	2.00952i	0.483322	−	0.0852227i
$557$	2.40680	+	1.38957i	0.101979	+	0.0588778i	0.550122	−	0.835084i	$-0.314581\pi$
$557$	2.40680	+	1.38957i	0.101979	+	0.0588778i	−0.448143	+	0.893962i	$0.647914\pi$
$558$	2.96033	+	1.21278i	0.125321	+	0.0513412i
$559$	23.6204	−	13.6372i	0.999036	−	0.576794i
$560$	−6.49350	+	12.2319i	−0.274400	+	0.516893i
$561$	−0.331636	+	16.6813i	−0.0140017	+	0.704284i
$562$	−8.76041	+	49.6827i	−0.369536	+	2.09574i
$563$	−25.7160	−	21.5783i	−1.08380	−	0.909415i	−0.0875679	−	0.996159i	$-0.527909\pi$
$563$	−25.7160	−	21.5783i	−1.08380	−	0.909415i	−0.996231	+	0.0867435i	$0.972354\pi$
$564$	−40.8113	+	13.9419i	−1.71847	+	0.587059i
$565$	3.92520	−	10.7844i	0.165134	−	0.453703i
$566$	49.0272			2.06077
$567$	−17.5508	−	16.0925i	−0.737065	−	0.675822i
$568$	−5.70659			−0.239443
$569$	−12.7217	+	34.9527i	−0.533323	+	1.46529i	0.321771	+	0.946818i	$0.395722\pi$
$569$	−12.7217	+	34.9527i	−0.533323	+	1.46529i	−0.855093	+	0.518474i	$0.826500\pi$
$570$	−47.1935	+	16.1221i	−1.97672	+	0.675282i
$571$	−6.22425	−	5.22276i	−0.260477	−	0.218566i	0.503191	−	0.864175i	$-0.332159\pi$
$571$	−6.22425	−	5.22276i	−0.260477	−	0.218566i	−0.763668	+	0.645609i	$0.776604\pi$
$572$	5.71311	−	32.4006i	0.238877	−	1.35474i
$573$	−0.137165	+	6.89938i	−0.00573014	+	0.288226i
$574$	−10.0906	−	5.35674i	−0.421173	−	0.223586i
$575$	3.27005	−	1.88796i	0.136370	−	0.0787335i
$576$	5.12565	+	37.8001i	0.213569	+	1.57501i
$577$	15.4017	+	8.89220i	0.641183	+	0.370187i	0.785070	−	0.619407i	$-0.212627\pi$
$577$	15.4017	+	8.89220i	0.641183	+	0.370187i	−0.143887	+	0.989594i	$0.545960\pi$
$578$	−17.5536	+	3.09518i	−0.730134	+	0.128742i
$579$	−12.2893	−	4.75165i	−0.510727	−	0.197472i
$580$	30.6550	+	84.2240i	1.27288	+	3.49721i
$581$	34.4900	−	31.0960i	1.43088	−	1.29008i
$582$	−1.47695	−	9.47375i	−0.0612217	−	0.392699i
$583$	1.74878	+	9.91780i	0.0724269	+	0.410753i
$584$	−10.5783	+	18.3221i	−0.437732	+	0.758173i
$585$	−23.4602	+	25.8025i	−0.969960	+	1.06680i
$586$	26.4957	−	15.2973i	1.09453	−	0.631925i
$587$	−14.9687	+	12.5602i	−0.617822	+	0.518415i	−0.897118	−	0.441791i	$-0.854343\pi$
$587$	−14.9687	+	12.5602i	−0.617822	+	0.518415i	0.279296	+	0.960205i	$0.409899\pi$
$588$	−7.70780	−	33.5558i	−0.317864	−	1.38382i
$589$	0.340011	−	1.92830i	0.0140099	−	0.0794542i
$590$	51.6391	−	61.5411i	2.12595	−	2.53361i
$591$	4.26420	−	4.88144i	0.175406	−	0.200796i
$592$	−8.56302	−	3.11669i	−0.351938	−	0.128095i
$593$	20.8572			0.856502			0.428251	−	0.903660i	$-0.359130\pi$
$593$	20.8572			0.856502			0.428251	+	0.903660i	$0.359130\pi$
$594$	26.8142	+	25.3719i	1.10020	+	1.04102i
$595$	23.7027	−	9.59466i	0.971714	−	0.393343i
$596$	9.46251	−	25.9980i	0.387599	−	1.06492i
$597$	−3.76734	−	0.741781i	−0.154187	−	0.0303591i
$598$	−3.48412	+	4.15221i	−0.142476	+	0.169796i
$599$	15.9702	+	2.81598i	0.652526	+	0.115058i	0.490105	−	0.871664i	$-0.336959\pi$
$599$	15.9702	+	2.81598i	0.652526	+	0.115058i	0.162421	+	0.986722i	$0.448070\pi$
$600$	15.4071	−	8.49153i	0.628993	−	0.346665i
$601$	−22.4423	−	26.7456i	−0.915439	−	1.09098i	−0.995554	−	0.0941916i	$-0.969973\pi$
$601$	−22.4423	−	26.7456i	−0.915439	−	1.09098i	0.0801156	−	0.996786i	$-0.474471\pi$
$602$	−27.2193	+	34.8864i	−1.10938	+	1.42186i
$603$	−15.2329	+	24.1166i	−0.620331	+	0.982106i
$604$	29.9156	−	51.8154i	1.21725	−	2.10834i
$605$	0.321459	+	1.82308i	0.0130692	+	0.0741189i
$606$	−27.5097	−	34.1406i	−1.11750	−	1.38687i
$607$	−1.32209	−	3.63240i	−0.0536618	−	0.147435i	0.909966	−	0.414683i	$-0.136108\pi$
$607$	−1.32209	−	3.63240i	−0.0536618	−	0.147435i	−0.963628	+	0.267249i	$0.913885\pi$
$608$	27.5144	−	10.0144i	1.11586	−	0.406138i
$609$	39.0051	+	21.7110i	1.58057	+	0.879776i
$610$	5.95161	+	33.7532i	0.240973	+	1.36663i
$611$	27.2433	+	15.7289i	1.10215	+	0.636325i
$612$	13.5705	−	21.4848i	0.548557	−	0.868473i
$613$	−1.60472	−	2.77946i	−0.0648142	−	0.112261i	0.831797	−	0.555079i	$-0.187312\pi$
$613$	−1.60472	−	2.77946i	−0.0648142	−	0.112261i	−0.896612	+	0.442818i	$0.853979\pi$
$614$	7.90388	−	6.63214i	0.318975	−	0.267651i
$615$	−5.31686	−	9.64696i	−0.214396	−	0.389003i
$616$	3.29172	+	15.4363i	0.132627	+	0.621948i
$617$	−3.37702	+	4.02458i	−0.135954	+	0.162024i	−0.829726	−	0.558171i	$-0.811503\pi$
$617$	−3.37702	+	4.02458i	−0.135954	+	0.162024i	0.693772	+	0.720195i	$0.255948\pi$
$618$	13.1316	−	66.6925i	0.528231	−	2.68276i
$619$	9.02167	−	24.7868i	0.362611	−	0.996267i	−0.615491	−	0.788144i	$-0.711042\pi$
$619$	9.02167	−	24.7868i	0.362611	−	0.996267i	0.978103	−	0.208123i	$-0.0667355\pi$
$620$			4.45996i			0.179116i
$621$	−1.01847	−	3.42005i	−0.0408698	−	0.137242i
$622$			0.340529i			0.0136540i
$623$	18.4185	−	0.655329i	0.737920	−	0.0262552i
$624$	6.60430	−	7.56028i	0.264384	−	0.302653i
$625$	−17.0527	−	14.3089i	−0.682107	−	0.572356i
$626$	−9.26377	+	52.5375i	−0.370255	+	2.09982i
$627$	11.6838	−	19.3388i	0.466607	−	0.772316i
$628$	−18.5856	−	22.1494i	−0.741645	−	0.883858i
$629$	8.41299	+	14.5717i	0.335448	+	0.581013i
$630$	19.5730	−	53.0831i	0.779808	−	2.11488i
$631$	−21.3850	+	37.0399i	−0.851324	+	1.47454i	0.0286891	+	0.999588i	$0.490867\pi$
$631$	−21.3850	+	37.0399i	−0.851324	+	1.47454i	−0.880013	+	0.474949i	$0.842467\pi$
$632$	12.0148	−	2.11853i	0.477922	−	0.0842706i
$633$	−0.908597	−	5.82808i	−0.0361135	−	0.231646i
$634$	11.5509	−	4.20417i	0.458743	−	0.166969i
$635$	−44.9087	+	16.3454i	−1.78215	+	0.648649i
$636$	5.53154	−	14.3064i	0.219340	−	0.567285i
$637$	−14.7347	+	20.3369i	−0.583812	+	0.805777i
$638$	−59.9340	−	34.6029i	−2.37281	−	1.36994i
$639$	−9.18341	+	1.24526i	−0.363290	+	0.0492617i
$640$	−37.8133	+	21.8315i	−1.49470	+	0.862967i
$641$	−0.504295	−	0.600995i	−0.0199185	−	0.0237379i	0.755993	−	0.654579i	$-0.227154\pi$
$641$	−0.504295	−	0.600995i	−0.0199185	−	0.0237379i	−0.775912	+	0.630842i	$0.782710\pi$
$642$	−11.3939	−	0.226519i	−0.449680	−	0.00893997i
$643$	10.7345	+	1.89279i	0.423329	+	0.0746443i	0.381254	−	0.924470i	$-0.375492\pi$
$643$	10.7345	+	1.89279i	0.423329	+	0.0746443i	0.0420745	+	0.999114i	$0.486603\pi$
$644$	1.59120	−	4.90821i	0.0627022	−	0.193411i
$645$	−40.3731	+	13.7922i	−1.58969	+	0.543066i
$646$	−24.9091	−	9.06618i	−0.980037	−	0.356704i
$647$	−8.04220			−0.316172			−0.158086	−	0.987425i	$-0.550532\pi$
$647$	−8.04220			−0.316172			−0.158086	+	0.987425i	$0.550532\pi$
$648$	−4.42744	−	16.0253i	−0.173926	−	0.629535i
$649$			36.3964i			1.42868i
$650$	−40.7785	−	14.8422i	−1.59946	−	0.582158i
$651$	1.45435	+	1.67902i	0.0570004	+	0.0658059i
$652$	21.9778	+	18.4416i	0.860717	+	0.722228i
$653$	−10.0845	−	1.77817i	−0.394638	−	0.0695853i	−0.0271920	−	0.999630i	$-0.508657\pi$
$653$	−10.0845	−	1.77817i	−0.394638	−	0.0695853i	−0.367446	+	0.930045i	$0.619768\pi$
$654$	0.216156	−	10.8726i	0.00845237	−	0.425153i
$655$	−22.6077	+	18.9701i	−0.883356	+	0.741224i
$656$	1.58541	+	2.74601i	0.0618998	+	0.107214i
$657$	−13.0251	+	31.7934i	−0.508157	+	1.24038i
$658$	−50.5437	−	7.06952i	−1.97040	−	0.275599i
$659$	20.5607	−	3.62540i	0.800930	−	0.141226i	0.241822	−	0.970321i	$-0.422255\pi$
$659$	20.5607	−	3.62540i	0.800930	−	0.141226i	0.559108	+	0.829095i	$0.311144\pi$
$660$	−18.5596	+	48.0012i	−0.722432	+	1.86844i
$661$	1.62538	+	4.46570i	0.0632200	+	0.173696i	0.967281	−	0.253708i	$-0.0816504\pi$
$661$	1.62538	+	4.46570i	0.0632200	+	0.173696i	−0.904061	+	0.427404i	$0.859428\pi$
$662$	−6.60517	−	18.1476i	−0.256717	−	0.705325i
$663$	−18.3147	+	2.85526i	−0.711285	+	0.110889i
$664$	31.9313	−	5.63035i	1.23918	−	0.218500i
$665$	−34.2944	−	4.79674i	−1.32988	−	0.186009i
$666$	36.3766	+	7.91667i	1.40957	+	0.306765i
$667$	3.34496	+	5.79363i	0.129517	+	0.224330i
$668$	−27.6970	+	23.2406i	−1.07163	+	0.899204i
$669$	−7.10528	−	4.29277i	−0.274706	−	0.165968i
$670$	−66.7448	−	11.7689i	−2.57857	−	0.454672i
$671$	−11.8950	−	9.98110i	−0.459202	−	0.385316i
$672$	−10.8699	+	31.3881i	−0.419314	+	1.21082i
$673$	30.7990	+	11.2099i	1.18721	+	0.432110i	0.858744	−	0.512404i	$-0.171245\pi$
$673$	30.7990	+	11.2099i	1.18721	+	0.432110i	0.328469	+	0.944515i	$0.393467\pi$
$674$			38.2834i			1.47462i
$675$	22.9411	−	17.0272i	0.883005	−	0.655376i
$676$	−0.364961			−0.0140370
$677$	3.36060	+	1.22316i	0.129158	+	0.0470098i	0.405791	−	0.913966i	$-0.366996\pi$
$677$	3.36060	+	1.22316i	0.129158	+	0.0470098i	−0.276632	+	0.960976i	$0.589218\pi$
$678$	2.60738	−	13.2423i	0.100136	−	0.508567i
$679$	2.05313	−	6.33307i	0.0787919	−	0.243041i
$680$	17.5827	+	3.10031i	0.674268	+	0.118892i
$681$	−7.11797	−	12.9149i	−0.272761	−	0.494901i
$682$	−2.21356	−	2.63802i	−0.0847615	−	0.101015i
$683$	−6.89711	+	3.98205i	−0.263910	+	0.152369i	−0.626117	−	0.779729i	$-0.715357\pi$
$683$	−6.89711	+	3.98205i	−0.263910	+	0.152369i	0.362207	+	0.932098i	$0.382023\pi$
$684$	−30.4626	+	16.0082i	−1.16476	+	0.612089i
$685$	28.1508	+	16.2529i	1.07559	+	0.620991i
$686$	9.77860	−	39.5525i	0.373349	−	1.51012i
$687$	−24.3927	−	30.2723i	−0.930639	−	1.15496i
$688$	11.5406	−	4.20044i	0.439982	−	0.160140i
$689$	−10.5136	+	3.82662i	−0.400535	+	0.145783i
$690$	6.60211	−	5.31983i	0.251338	−	0.202522i
$691$	10.8617	−	1.91522i	0.413200	−	0.0728583i	0.0368159	−	0.999322i	$-0.488278\pi$
$691$	10.8617	−	1.91522i	0.413200	−	0.0728583i	0.376384	+	0.926464i	$0.377167\pi$
$692$	−10.2402	+	17.7366i	−0.389275	+	0.674244i
$693$	8.66567	+	24.1228i	0.329182	+	0.916351i
$694$	3.09929	+	5.36814i	0.117648	+	0.203772i
$695$	8.48739	+	10.1149i	0.321945	+	0.383679i
$696$	15.0447	+	27.2972i	0.570267	+	1.03470i
$697$	1.01667	−	5.76583i	0.0385092	−	0.218397i
$698$	−35.8792	−	30.1062i	−1.35805	−	1.13954i
$699$	9.37441	+	1.84580i	0.354573	+	0.0698147i
$700$	41.2828	−	1.46884i	1.56035	−	0.0555171i
$701$			38.5950i			1.45771i	0.684665	+	0.728857i	$0.259948\pi$
$701$			38.5950i			1.45771i	−0.684665	+	0.728857i	$0.740052\pi$
$702$	−22.5861	+	34.2317i	−0.852457	+	1.29199i
$703$		−	22.7858i		−	0.859381i
$704$	14.0441	−	38.5859i	0.529308	−	1.45426i
$705$	−37.0592	−	32.3732i	−1.39573	−	1.21924i
$706$	−31.1672	+	37.1436i	−1.17299	+	1.39792i
$707$	−6.34919	−	29.7742i	−0.238786	−	1.11977i
$708$	28.6659	−	47.4471i	1.07733	−	1.78317i
$709$	25.2492	−	21.1866i	0.948253	−	0.795679i	−0.0307495	−	0.999527i	$-0.509789\pi$
$709$	25.2492	−	21.1866i	0.948253	−	0.795679i	0.979002	+	0.203848i	$0.0653450\pi$
$710$	−11.0097	−	19.0694i	−0.413188	−	0.715662i
$711$	18.8727	−	6.03107i	0.707780	−	0.226183i
$712$	11.1442	+	6.43408i	0.417645	+	0.241127i
$713$	0.0578058	+	0.327833i	0.00216484	+	0.0122774i
$714$	25.8039	−	15.4426i	0.965686	−	0.577923i
$715$	35.2754	−	12.8392i	1.31923	−	0.480159i
$716$	−6.89064	−	18.9319i	−0.257515	−	0.707517i
$717$	−17.2861	+	44.7075i	−0.645562	+	1.66963i
$718$	−7.77207	−	44.0776i	−0.290051	−	1.64496i
$719$	−9.13910	+	15.8294i	−0.340831	+	0.590336i	−0.984587	−	0.174894i	$-0.944042\pi$
$719$	−9.13910	+	15.8294i	−0.340831	+	0.590336i	0.643756	+	0.765231i	$0.277375\pi$
$720$	−12.4208	+	9.60755i	−0.462896	+	0.358052i
$721$	29.0329	−	37.2109i	1.08124	−	1.38581i
$722$	−3.79368	−	4.52114i	−0.141186	−	0.168259i
$723$	−0.0239110	+	1.20272i	−0.000889260	+	0.0447297i
$724$	−14.4294	−	2.54430i	−0.536266	−	0.0945582i
$725$	−34.4277	+	41.0293i	−1.27861	+	1.52379i
$726$	0.703783	+	2.06015i	0.0261199	+	0.0764593i
$727$	−13.0156	+	35.7602i	−0.482723	+	1.32627i	0.424426	+	0.905462i	$0.360476\pi$
$727$	−13.0156	+	35.7602i	−0.482723	+	1.32627i	−0.907150	+	0.420808i	$0.861746\pi$
$728$	−16.2537	+	6.57935i	−0.602400	+	0.243847i
$729$	−10.6219	−	24.8229i	−0.393403	−	0.919366i
$730$	−81.6346			−3.02143
$731$	−21.3093	−	7.75594i	−0.788151	−	0.286864i
$732$	7.64544	+	22.3801i	0.282583	+	0.827192i
$733$	−12.2043	+	14.5445i	−0.450776	+	0.537214i	−0.942796	−	0.333370i	$-0.891814\pi$
$733$	−12.2043	+	14.5445i	−0.450776	+	0.537214i	0.492020	+	0.870584i	$0.336259\pi$
$734$	9.15008	−	51.8927i	0.337736	−	1.91539i
$735$	28.7602	−	26.7598i	1.06084	−	0.987051i
$736$	−3.81335	+	3.19978i	−0.140562	+	0.117945i
$737$	26.5915	−	15.3526i	0.979511	−	0.565521i
$738$	−7.92563	−	10.2464i	−0.291747	−	0.377175i
$739$	−0.674129	+	1.16763i	−0.0247982	+	0.0429518i	−0.878158	−	0.478370i	$-0.841228\pi$
$739$	−0.674129	+	1.16763i	−0.0247982	+	0.0429518i	0.853360	+	0.521322i	$0.174561\pi$
$740$	9.01243	+	51.1120i	0.331304	+	1.87892i
$741$	23.4123	+	9.05234i	0.860072	+	0.332546i
$742$	13.4811	−	12.1545i	0.494905	−	0.446205i
$743$	−14.7521	−	40.5311i	−0.541203	−	1.48694i	−0.845295	−	0.534301i	$-0.820575\pi$
$743$	−14.7521	−	40.5311i	−0.541203	−	1.48694i	0.304091	−	0.952643i	$-0.401647\pi$
$744$	0.238907	+	1.53244i	0.00875875	+	0.0561820i
$745$	31.0878	−	5.48162i	1.13897	−	0.200831i
$746$	35.1477	+	20.2925i	1.28685	+	0.742962i
$747$	50.1573	−	16.0286i	1.83516	−	0.586455i
$748$	−23.6896	+	13.6772i	−0.866179	+	0.500089i
$749$	−6.98912	−	3.71028i	−0.255377	−	0.135571i
$750$	5.26474	+	3.18077i	0.192241	+	0.116145i
$751$	−1.49167	+	8.45970i	−0.0544319	+	0.308699i	−0.999853	−	0.0171527i	$-0.994540\pi$
$751$	−1.49167	+	8.45970i	−0.0544319	+	0.308699i	0.945421	+	0.325852i	$0.105651\pi$
$752$	10.8510	+	9.10508i	0.395696	+	0.332028i
$753$	−5.59285	−	4.88565i	−0.203815	−	0.178043i
$754$	26.2963	−	72.2484i	0.957654	−	2.63113i
$755$	68.2672			2.48450
$756$	7.70247	−	38.2721i	0.280136	−	1.39194i
$757$	42.8160			1.55618			0.778088	−	0.628156i	$-0.216190\pi$
$757$	42.8160			1.55618			0.778088	+	0.628156i	$0.216190\pi$
$758$	10.7533	−	29.5446i	0.390579	−	1.07311i
$759$	−0.742093	+	3.76892i	−0.0269363	+	0.136803i
$760$	−18.5213	−	15.5412i	−0.671840	−	0.563740i
$761$	−7.33501	+	41.5989i	−0.265894	+	1.50796i	0.500583	+	0.865688i	$0.333119\pi$
$761$	−7.33501	+	41.5989i	−0.265894	+	1.50796i	−0.766477	+	0.642271i	$0.777992\pi$
$762$	−49.2219	+	27.1283i	−1.78312	+	0.982756i
$763$	3.54055	−	6.66939i	0.128176	−	0.241448i
$764$	−9.79804	+	5.65690i	−0.354481	+	0.204659i
$765$	28.9718	+	1.15242i	1.04748	+	0.0416658i
$766$	−43.5474	−	25.1421i	−1.57343	−	0.908421i
$767$	−39.8208	+	7.02148i	−1.43784	+	0.253531i
$768$	−5.68511	+	4.58093i	−0.205144	+	0.165300i
$769$	−7.08056	−	19.4537i	−0.255331	−	0.701517i	−0.999440	−	0.0334587i	$-0.989348\pi$
$769$	−7.08056	−	19.4537i	−0.255331	−	0.701517i	0.744109	−	0.668059i	$-0.232874\pi$
$770$	−45.2321	+	40.7811i	−1.63005	+	1.46965i
$771$	−13.3807	+	10.7819i	−0.481895	+	0.388300i
$772$	−3.75116	−	21.2739i	−0.135007	−	0.765663i
$773$	5.17350	−	8.96077i	0.186078	−	0.322296i	−0.757861	−	0.652416i	$-0.773756\pi$
$773$	5.17350	−	8.96077i	0.186078	−	0.322296i	0.943939	+	0.330119i	$0.107089\pi$
$774$	−44.4142	+	23.3398i	−1.59643	+	0.838933i
$775$	−2.30809	+	1.33257i	−0.0829089	+	0.0478675i
$776$	3.56088	−	2.98793i	0.127828	−	0.107261i
$777$	20.0600	+	16.3030i	0.719648	+	0.584867i
$778$	0.934487	−	5.29974i	0.0335030	−	0.190005i
$779$	−5.09637	+	6.07362i	−0.182597	+	0.217610i
$780$	−56.0979	−	11.0456i	−2.00863	−	0.395495i
$781$	9.37431	+	3.41197i	0.335439	+	0.122090i
$782$	4.50662			0.161156
$783$	30.1675	+	40.6455i	1.07810	+	1.45255i
$784$	−8.12419	+	7.86614i	−0.290150	+	0.280933i
$785$	11.2835	−	31.0012i	0.402726	−	1.10648i
$786$	−22.8332	+	26.1383i	−0.814432	+	0.932322i
$787$	−23.3874	+	27.8721i	−0.833673	+	0.993532i	0.166300	+	0.986075i	$0.446818\pi$
$787$	−23.3874	+	27.8721i	−0.833673	+	0.993532i	−0.999972	+	0.00745697i	$0.997626\pi$
$788$	10.4653	+	1.84531i	0.372810	+	0.0657364i
$789$	−6.65664	−	4.02171i	−0.236983	−	0.143177i
$790$	30.2595	+	36.0619i	1.07658	+	1.28302i
$791$	5.76471	−	7.38851i	0.204969	−	0.262705i
$792$	−3.80579	+	17.4874i	−0.135233	+	0.621386i
$793$	8.62543	−	14.9397i	0.306298	−	0.530524i
$794$	−5.18640	−	29.4135i	−0.184058	−	1.04385i
$795$	17.2923	−	2.69587i	0.613296	−	0.0956126i
$796$	−2.15307	−	5.91552i	−0.0763136	−	0.209670i
$797$	−3.95939	+	1.44110i	−0.140249	+	0.0510464i	−0.411191	−	0.911549i	$-0.634887\pi$
$797$	−3.95939	+	1.44110i	−0.140249	+	0.0510464i	0.270942	+	0.962596i	$0.412665\pi$
$798$	−40.7182	+	0.638794i	−1.44141	+	0.0226130i
$799$	−4.54178	−	25.7577i	−0.160677	−	0.911242i
$800$	−34.5146	−	19.9270i	−1.22028	−	0.704527i
$801$	19.3379	+	7.92232i	0.683271	+	0.279922i
$802$	−20.9840	−	36.3453i	−0.740970	−	1.28340i
$803$	28.3319	−	23.7733i	0.999810	−	0.838940i
$804$	−46.7570	−	0.929565i	−1.64899	−	0.0327832i
$805$	5.75774	−	1.22781i	0.202934	−	0.0432745i
$806$	2.45918	−	2.93074i	0.0866211	−	0.103231i
$807$	5.42070	−	1.85181i	0.190818	−	0.0651867i
$808$	7.27004	−	19.9743i	0.255759	−	0.702692i
$809$			41.1433i			1.44652i	0.690574	+	0.723261i	$0.257358\pi$
$809$			41.1433i			1.44652i	−0.690574	+	0.723261i	$0.742642\pi$
$810$	45.0092	−	45.7126i	1.58146	−	1.60618i
$811$		−	25.7104i		−	0.902815i	−0.892318	−	0.451407i	$-0.850922\pi$
$811$		−	25.7104i		−	0.902815i	0.892318	−	0.451407i	$-0.149078\pi$
$812$	2.60239	+	73.1420i	0.0913260	+	2.56678i
$813$	15.3433	+	44.9136i	0.538112	+	1.57519i
$814$	−30.6986	−	25.7592i	−1.07598	−	0.902858i
$815$	−5.68440	+	32.2378i	−0.199116	+	1.12924i
$816$	−8.34480	−	0.165901i	−0.292126	−	0.00580769i
$817$	19.7394	+	23.5245i	0.690593	+	0.823016i
$818$	36.1292	+	62.5775i	1.26323	+	2.18797i
$819$	−24.7207	+	14.1347i	−0.863812	+	0.493906i
$820$	9.02967	−	15.6398i	0.315330	−	0.546167i
$821$	34.7029	−	6.11906i	1.21114	−	0.213557i	0.468632	−	0.883394i	$-0.344747\pi$
$821$	34.7029	−	6.11906i	1.21114	−	0.213557i	0.742508	+	0.669837i	$0.233636\pi$
$822$	35.6549	+	13.7859i	1.24361	+	0.480839i
$823$	−11.0749	+	4.03095i	−0.386048	+	0.140510i	−0.527751	−	0.849399i	$-0.676964\pi$
$823$	−11.0749	+	4.03095i	−0.386048	+	0.140510i	0.141703	+	0.989909i	$0.454742\pi$
$824$	30.9663	−	11.2708i	1.07876	−	0.392637i
$825$	−30.3866	+	4.73726i	−1.05793	+	0.164930i
$826$	55.6089	−	34.7992i	1.93488	−	1.21082i
$827$	4.77748	+	2.75828i	0.166129	+	0.0959148i	0.580759	−	0.814075i	$-0.302756\pi$
$827$	4.77748	+	2.75828i	0.166129	+	0.0959148i	−0.414630	+	0.909990i	$0.636089\pi$
$828$	3.93582	−	4.32877i	0.136779	−	0.150435i
$829$	−33.5706	+	19.3820i	−1.16595	+	0.673164i	−0.952724	−	0.303837i	$-0.901732\pi$
$829$	−33.5706	+	19.3820i	−1.16595	+	0.673164i	−0.213231	+	0.977002i	$0.568399\pi$
$830$	80.4197	+	95.8405i	2.79141	+	3.32667i
$831$	−17.9290	+	29.6757i	−0.621951	+	1.02944i
$832$	44.9256	+	7.92160i	1.55752	+	0.274632i
$833$	20.8276	−	1.48397i	0.721632	−	0.0514165i
$834$	11.6945	+	10.2158i	0.404947	+	0.353743i
$835$	−38.7658	−	14.1096i	−1.34155	−	0.488283i
$836$	37.0434			1.28117
$837$	0.718864	+	2.41397i	0.0248476	+	0.0834389i
$838$			56.4339i			1.94948i
$839$	−35.0483	−	12.7566i	−1.21000	−	0.440405i	−0.343298	−	0.939226i	$-0.611544\pi$
$839$	−35.0483	−	12.7566i	−1.21000	−	0.440405i	−0.866705	+	0.498821i	$0.833766\pi$
$840$	26.9339	−	5.18607i	0.929309	−	0.178936i
$841$	−50.4775	−	42.3557i	−1.74061	−	1.46054i
$842$	24.9638	+	4.40178i	0.860308	+	0.151696i
$843$	−34.7862	+	19.1722i	−1.19810	+	0.660324i
$844$	7.40811	−	6.21614i	0.254998	−	0.213968i
$845$	−0.208209	−	0.360629i	−0.00716262	−	0.0124060i
$846$	−48.9264	−	30.9036i	−1.68213	−	1.06249i
$847$	−0.209393	+	1.49706i	−0.00719483	+	0.0514396i
$848$	−4.96137	+	0.874824i	−0.170374	+	0.0300416i
$849$	24.2190	+	30.0567i	0.831194	+	1.03154i
$850$	12.3402	+	33.9045i	0.423266	+	1.16291i
$851$	1.32493	+	3.64022i	0.0454181	+	0.124785i
$852$	−9.53326	−	11.8311i	−0.326604	−	0.405328i
$853$	4.83719	−	0.852926i	0.165622	−	0.0292036i	−0.0902221	−	0.995922i	$-0.528758\pi$
$853$	4.83719	−	0.852926i	0.165622	−	0.0292036i	0.255844	+	0.966718i	$0.417647\pi$
$854$	−3.87678	+	27.7171i	−0.132661	+	0.948460i
$855$	−33.1970	−	20.9684i	−1.13532	−	0.717103i
$856$	−2.76245	−	4.78470i	−0.0944185	−	0.163538i
$857$	−9.53580	+	8.00148i	−0.325737	+	0.273325i	−0.790960	−	0.611868i	$-0.790418\pi$
$857$	−9.53580	+	8.00148i	−0.325737	+	0.273325i	0.465223	+	0.885193i	$0.345974\pi$
$858$	38.6634	−	21.3091i	1.31995	−	0.727480i
$859$	48.9734	+	8.63533i	1.67095	+	0.294634i	0.927407	−	0.374054i	$-0.122032\pi$
$859$	48.9734	+	8.63533i	1.67095	+	0.294634i	0.743544	+	0.668687i	$0.233144\pi$
$860$	−53.5831	−	44.9615i	−1.82717	−	1.53318i
$861$	−1.70064	−	8.83233i	−0.0579578	−	0.301005i
$862$	57.0339	+	20.7587i	1.94258	+	0.707043i
$863$		−	7.82559i		−	0.266386i	−0.991090	−	0.133193i	$-0.957477\pi$
$863$		−	7.82559i		−	0.266386i	0.991090	−	0.133193i	$-0.0425230\pi$
$864$	−25.8869	+	27.3585i	−0.880689	+	0.930755i
$865$	−23.3681			−0.794540
$866$	−2.23301	−	0.812751i	−0.0758809	−	0.0276184i
$867$	−10.5689	−	9.23246i	−0.358938	−	0.313551i
$868$	−1.12311	+	3.46435i	−0.0381210	+	0.117588i
$869$	−21.0035	−	3.70349i	−0.712496	−	0.125632i
$870$	−62.1919	+	102.939i	−2.10850	+	3.48994i
$871$	21.9270	+	26.1316i	0.742970	+	0.885437i
$872$	4.56581	−	2.63607i	0.154618	−	0.0892687i
$873$	5.07839	−	5.58541i	0.171877	−	0.189038i
$874$	−5.28524	−	3.05144i	−0.178776	−	0.103216i
$875$	2.26564	+	3.62048i	0.0765927	+	0.122395i
$876$	−55.6579	+	8.67704i	−1.88050	+	0.293170i
$877$	−38.6291	+	14.0598i	−1.30441	+	0.474767i	−0.898431	−	0.439115i	$-0.855292\pi$
$877$	−38.6291	+	14.0598i	−1.30441	+	0.474767i	−0.405980	+	0.913882i	$0.633070\pi$
$878$	5.46971	−	1.99081i	0.184594	−	0.0671866i
$879$	22.4668	+	8.68677i	0.757787	+	0.292997i
$880$	16.6465	−	2.93524i	0.561155	−	0.0989468i
$881$	13.4109	−	23.2283i	0.451824	−	0.782582i	−0.546675	−	0.837345i	$-0.684107\pi$
$881$	13.4109	−	23.2283i	0.451824	−	0.782582i	0.998499	+	0.0547623i	$0.0174401\pi$
$882$	28.5711	−	36.3043i	0.962040	−	1.22243i
$883$	15.7111	+	27.2125i	0.528722	+	0.915773i	0.999439	+	0.0334889i	$0.0106618\pi$
$883$	15.7111	+	27.2125i	0.528722	+	0.915773i	−0.470717	+	0.882284i	$0.656005\pi$
$884$	−19.5342	−	23.2799i	−0.657006	−	0.782989i
$885$	63.2378	+	1.25721i	2.12571	+	0.0422608i
$886$	6.18739	−	35.0905i	0.207870	−	1.17889i
$887$	−8.61019	−	7.22481i	−0.289102	−	0.242585i	0.486689	−	0.873575i	$-0.338204\pi$
$887$	−8.61019	−	7.22481i	−0.289102	−	0.242585i	−0.775791	+	0.630990i	$0.782649\pi$
$888$	5.83458	+	17.0793i	0.195796	+	0.573143i
$889$	−38.9997	+	1.38761i	−1.30801	+	0.0465389i
$890$			49.6531i			1.66438i
$891$	−2.30853	+	28.9723i	−0.0773385	+	0.970607i
$892$		−	13.6102i		−	0.455702i
$893$	−12.1141	+	33.2832i	−0.405382	+	1.11378i
$894$	35.1303	−	12.0011i	1.17493	−	0.401378i
$895$	14.7761	−	17.6094i	0.493910	−	0.588619i
$896$	−34.8698	+	7.43579i	−1.16492	+	0.248412i
$897$	−4.26668	−	0.0848249i	−0.142460	−	0.00283222i
$898$	−31.9287	+	26.7913i	−1.06547	+	0.894038i
$899$	−2.36096	−	4.08930i	−0.0787424	−	0.136386i
$900$	43.3437	+	17.7570i	1.44479	+	0.591899i
$901$	8.05602	+	4.65114i	0.268385	+	0.154952i
$902$	2.42139	+	13.7324i	0.0806234	+	0.457238i
$903$	−34.8336	+	0.546475i	−1.15919	+	0.0181855i
$904$	6.14859	−	2.23791i	0.204499	−	0.0744316i
$905$	−5.71787	−	15.7097i	−0.190068	−	0.522209i
$906$	79.3250	−	12.3667i	2.63540	−	0.410858i
$907$	0.449186	+	2.54746i	0.0149150	+	0.0845870i	0.991357	−	0.131194i	$-0.0418812\pi$
$907$	0.449186	+	2.54746i	0.0149150	+	0.0845870i	−0.976442	+	0.215781i	$0.930770\pi$
$908$	12.0885	−	20.9379i	0.401172	−	0.694850i
$909$	7.34074	−	33.7303i	0.243477	−	1.11876i
$910$	−53.3440	−	41.6204i	−1.76834	−	1.37970i
$911$	12.1000	+	14.4203i	0.400892	+	0.477765i	0.928292	−	0.371852i	$-0.121277\pi$
$911$	12.1000	+	14.4203i	0.400892	+	0.477765i	−0.527399	+	0.849617i	$0.676833\pi$
$912$	9.67421	+	5.84483i	0.320345	+	0.193542i
$913$	−55.8205	−	9.84265i	−1.84739	−	0.325744i
$914$	41.0765	−	48.9530i	1.35869	−	1.61922i
$915$	−17.7528	+	20.3225i	−0.586889	+	0.671841i
$916$	21.8000	−	59.8950i	0.720292	−	1.97899i
$917$	−22.3380	+	9.04224i	−0.737665	+	0.298601i
$918$	33.8734	−	3.90922i	1.11799	−	0.129023i
$919$	−28.9423			−0.954719			−0.477359	−	0.878708i	$-0.658406\pi$
$919$	−28.9423			−0.954719			−0.477359	+	0.878708i	$0.658406\pi$
$920$	3.86262	+	1.40588i	0.127347	+	0.0463505i
$921$	7.97036	+	1.56935i	0.262632	+	0.0517118i
$922$	60.0871	−	71.6090i	1.97886	−	2.35832i
$923$	−1.92453	+	10.9145i	−0.0633465	+	0.359256i
$924$	−26.5042	+	32.6120i	−0.871924	+	1.07286i
$925$	−23.7583	+	19.9356i	−0.781170	+	0.655479i
$926$	25.6973	−	14.8363i	0.844465	−	0.487552i
$927$	47.3735	−	24.8950i	1.55595	−	0.817659i
$928$	35.3053	−	61.1505i	1.15895	−	2.00736i
$929$	−2.16578	−	12.2827i	−0.0710569	−	0.402983i	−0.999503	−	0.0315170i	$-0.989966\pi$
$929$	−2.16578	−	12.2827i	−0.0710569	−	0.402983i	0.928446	−	0.371467i	$-0.121145\pi$
$930$	−4.65995	+	3.75488i	−0.152806	+	0.123127i
$931$	−25.4308	−	12.3620i	−0.833460	−	0.405148i
$932$	5.35757	+	14.7198i	0.175493	+	0.482163i
$933$	−0.208765	+	0.168218i	−0.00683467	+	0.00550722i
$934$	52.0063	−	9.17012i	1.70170	−	0.300055i
$935$	−27.0298	−	15.6057i	−0.883969	−	0.510360i
$936$	−19.8669	−	0.790250i	−0.649369	−	0.0258301i
$937$	−36.9165	+	21.3137i	−1.20601	+	0.696290i	−0.961885	−	0.273454i	$-0.911834\pi$
$937$	−36.9165	+	21.3137i	−1.20601	+	0.696290i	−0.244124	+	0.969744i	$0.578500\pi$
$938$	−48.8814	−	25.9494i	−1.59603	−	0.847279i
$939$	−36.7849	+	20.2738i	−1.20043	+	0.661610i
$940$	14.0093	−	79.4508i	0.456934	−	2.59140i
$941$	37.0819	+	31.1154i	1.20884	+	1.01433i	0.999333	+	0.0365255i	$0.0116290\pi$
$941$	37.0819	+	31.1154i	1.20884	+	1.01433i	0.209503	+	0.977808i	$0.432815\pi$
$942$	7.49526	−	38.0667i	0.244209	−	1.24028i
$943$	0.461024	−	1.26665i	0.0150130	−	0.0412479i
$944$	−18.2073			−0.592596
$945$	42.2122	−	14.2231i	1.37316	−	0.462678i
$946$	54.0090			1.75598
$947$	9.84660	−	27.0533i	0.319972	−	0.879115i	−0.670563	−	0.741852i	$-0.733947\pi$
$947$	9.84660	−	27.0533i	0.319972	−	0.879115i	0.990535	−	0.137262i	$-0.0438303\pi$
$948$	24.4638	+	21.3704i	0.794546	+	0.694078i
$949$	31.4757	+	26.4112i	1.02174	+	0.857345i
$950$	8.48447	−	48.1178i	0.275273	−	1.56115i
$951$	8.28344	+	5.00457i	0.268609	+	0.162284i
$952$	12.8770	+	6.83593i	0.417345	+	0.221554i
$953$	29.6982	−	17.1463i	0.962020	−	0.555422i	0.0652258	−	0.997871i	$-0.479223\pi$
$953$	29.6982	−	17.1463i	0.962020	−	0.555422i	0.896794	+	0.442448i	$0.145890\pi$
$954$	19.6049	−	6.26508i	0.634733	−	0.202839i
$955$	−11.1795	−	6.45450i	−0.361761	−	0.208863i
$956$	−77.3925	+	13.6464i	−2.50305	+	0.441356i
$957$	−8.39314	−	53.8368i	−0.271312	−	1.74030i
$958$	−16.8674	−	46.3429i	−0.544962	−	1.49727i
$959$	17.7738	+	19.7137i	0.573946	+	0.636588i
$960$	−66.5569	−	25.7341i	−2.14811	−	0.830566i
$961$	5.34229	+	30.2976i	0.172332	+	0.977343i
$962$	22.2605	−	38.5563i	0.717706	−	1.24310i
$963$	−5.48960	−	7.09704i	−0.176900	−	0.228699i
$964$	−1.70802	+	0.986129i	−0.0550118	+	0.0317611i
$965$	18.8814	−	15.8433i	0.607812	−	0.510015i
$966$	6.46794	−	2.46971i	0.208103	−	0.0794616i
$967$	−8.18346	+	46.4107i	−0.263162	+	1.49247i	0.511055	+	0.859548i	$0.329255\pi$
$967$	−8.18346	+	46.4107i	−0.263162	+	1.49247i	−0.774218	+	0.632919i	$0.781856\pi$
$968$	−0.678426	+	0.808517i	−0.0218054	+	0.0259867i
$969$	−6.74676	−	19.7495i	−0.216737	−	0.634444i
$970$	16.8546	+	6.13458i	0.541170	+	0.196970i
$971$	−8.35204			−0.268030			−0.134015	−	0.990979i	$-0.542787\pi$
$971$	−8.35204			−0.268030			−0.134015	+	0.990979i	$0.542787\pi$
$972$	25.8281	−	35.9506i	0.828436	−	1.15312i
$973$	4.04558	+	9.99421i	0.129695	+	0.320400i
$974$	−5.17286	+	14.2123i	−0.165749	+	0.455392i
$975$	−11.0451	−	32.3317i	−0.353725	−	1.03544i
$976$	4.99304	−	5.95047i	0.159823	−	0.190470i
$977$	55.1882	+	9.73116i	1.76563	+	0.311327i	0.959771	−	0.280785i	$-0.0905948\pi$
$977$	55.1882	+	9.73116i	1.76563	+	0.311327i	0.805855	+	0.592113i	$0.201706\pi$
$978$	−0.765198	+	38.4894i	−0.0244683	+	1.23076i
$979$	−14.4597	−	17.2325i	−0.462135	−	0.550752i
$980$	61.9348	+	17.6713i	1.97843	+	0.564488i
$981$	6.77237	−	5.23846i	0.216225	−	0.167251i
$982$	6.53596	−	11.3206i	0.208571	−	0.361255i
$983$	−1.87543	−	10.6361i	−0.0598170	−	0.339239i	0.940182	−	0.340673i	$-0.110655\pi$
$983$	−1.87543	−	10.6361i	−0.0598170	−	0.339239i	−0.999999	+	0.00143367i	$0.999544\pi$
$984$	2.26481	−	5.85753i	0.0721994	−	0.186731i
$985$	4.14701	+	11.3938i	0.132135	+	0.363037i
$986$	−60.0695	+	21.8635i	−1.91300	+	0.696276i
$987$	−20.6341	−	34.4787i	−0.656790	−	1.09747i
$988$	7.14630	+	40.5287i	0.227354	+	1.28939i
$989$	−4.52142	−	2.61044i	−0.143773	−	0.0830072i
$990$	−65.7791	+	21.0208i	−2.09060	+	0.668084i
$991$	−5.25786	−	9.10688i	−0.167021	−	0.289290i	0.770350	−	0.637621i	$-0.220082\pi$
$991$	−5.25786	−	9.10688i	−0.167021	−	0.289290i	−0.937371	+	0.348332i	$0.886748\pi$
$992$	2.69156	−	2.25849i	0.0854572	−	0.0717071i
$993$	7.86268	−	13.0141i	0.249515	−	0.412990i
$994$	−3.74990	−	17.5850i	−0.118940	−	0.557761i
$995$	4.61699	−	5.50231i	0.146368	−	0.174435i
$996$	65.0166	+	56.7954i	2.06013	+	1.79963i
$997$	19.0094	−	52.2279i	0.602034	−	1.65407i	−0.145113	−	0.989415i	$-0.546354\pi$
$997$	19.0094	−	52.2279i	0.602034	−	1.65407i	0.747146	−	0.664659i	$-0.231423\pi$
$998$			20.8146i			0.658874i
$999$	13.1163	+	26.2119i	0.414982	+	0.829308i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.be.a.104.3	yes	132
3.2	odd	2		567.2.be.a.503.19		132
7.6	odd	2	inner	189.2.be.a.104.4	yes	132
21.20	even	2		567.2.be.a.503.20		132
27.7	even	9		567.2.be.a.62.20		132
27.20	odd	18	inner	189.2.be.a.20.4	yes	132
189.20	even	18	inner	189.2.be.a.20.3	✓	132
189.34	odd	18		567.2.be.a.62.19		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.3	✓	132	189.20	even	18	inner
189.2.be.a.20.4	yes	132	27.20	odd	18	inner
189.2.be.a.104.3	yes	132	1.1	even	1	trivial
189.2.be.a.104.4	yes	132	7.6	odd	2	inner
567.2.be.a.62.19		132	189.34	odd	18
567.2.be.a.62.20		132	27.7	even	9
567.2.be.a.503.19		132	3.2	odd	2
567.2.be.a.503.20		132	21.20	even	2

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.752422 + 2.06726i) q^{2} +(-1.63905 + 0.559928i) q^{3} +(-2.17534 - 1.82533i) q^{4} +(0.562637 - 3.19087i) q^{5} +(0.0757386 - 3.80964i) q^{6} +(1.24057 - 2.33688i) q^{7} +(1.59981 - 0.923650i) q^{8} +(2.37296 - 1.83550i) q^{9} +(6.17302 + 3.56400i) q^{10} +(-3.18028 + 0.560770i) q^{11} +(4.58754 + 1.77377i) q^{12} +(-1.22706 - 3.37132i) q^{13} +(3.89751 + 4.32289i) q^{14} +(0.864468 + 5.54503i) q^{15} +(-0.280525 - 1.59093i) q^{16} +(-1.49145 + 2.58328i) q^{17} +(2.00899 + 6.28660i) q^{18} +(3.49827 - 2.01973i) q^{19} +(-7.04831 + 5.91424i) q^{20} +(-0.724867 + 4.52488i) q^{21} +(1.23366 - 6.99641i) q^{22} +(-0.441437 + 0.526084i) q^{23} +(-2.10499 + 2.40968i) q^{24} +(-5.16663 - 1.88050i) q^{25} +7.89267 q^{26} +(-2.86165 + 4.33716i) q^{27} +(-6.96423 + 2.81906i) q^{28} +(3.33174 - 9.15387i) q^{29} +(-12.1135 - 2.38512i) q^{30} +(0.311578 - 0.371325i) q^{31} +(7.13842 + 1.25870i) q^{32} +(4.89865 - 2.69986i) q^{33} +(-4.21810 - 5.02694i) q^{34} +(-6.75868 - 5.27330i) q^{35} +(-8.51239 - 0.338599i) q^{36} +(2.82040 - 4.88507i) q^{37} +(1.54313 + 8.75153i) q^{38} +(3.89891 + 4.83869i) q^{39} +(-2.04714 - 5.62446i) q^{40} +(-1.84441 + 0.671309i) q^{41} +(-8.80871 - 4.90311i) q^{42} +(1.32012 + 7.48676i) q^{43} +(7.94179 + 4.58519i) q^{44} +(-4.52172 - 8.60453i) q^{45} +(-0.755407 - 1.30840i) q^{46} +(-6.71691 + 5.63616i) q^{47} +(1.35060 + 2.45055i) q^{48} +(-3.92199 - 5.79810i) q^{49} +(7.77497 - 9.26585i) q^{50} +(0.998119 - 5.06922i) q^{51} +(-3.48449 + 9.57356i) q^{52} -3.11853i q^{53} +(-6.81287 - 9.17916i) q^{54} +10.4634i q^{55} +(-0.173787 - 4.88441i) q^{56} +(-4.60294 + 5.26922i) q^{57} +(16.4166 + 13.7751i) q^{58} +(1.95711 - 11.0993i) q^{59} +(8.24099 - 13.6403i) q^{60} +(3.09075 + 3.68341i) q^{61} +(0.533187 + 0.923507i) q^{62} +(-1.34552 - 7.82238i) q^{63} +(-6.35768 + 11.0118i) q^{64} +(-11.4478 + 2.01856i) q^{65} +(1.89546 + 12.1582i) q^{66} +(-8.93479 + 3.25200i) q^{67} +(7.95975 - 2.89711i) q^{68} +(0.428968 - 1.10945i) q^{69} +(15.9867 - 10.0042i) q^{70} +(-2.67528 - 1.54458i) q^{71} +(2.10093 - 5.12823i) q^{72} +(-9.91831 + 5.72634i) q^{73} +(7.97659 + 9.50613i) q^{74} +(9.52131 + 0.189291i) q^{75} +(-11.2966 - 1.99190i) q^{76} +(-2.63490 + 8.12760i) q^{77} +(-12.9365 + 4.41932i) q^{78} +(6.20601 + 2.25880i) q^{79} -5.23430 q^{80} +(2.26189 - 8.71113i) q^{81} -4.31797i q^{82} +(16.4935 + 6.00315i) q^{83} +(9.83623 - 8.52005i) q^{84} +(7.40375 + 6.21249i) q^{85} +(-16.4704 - 2.90417i) q^{86} +(-0.335372 + 16.8692i) q^{87} +(-4.56989 + 3.83459i) q^{88} +(3.48296 + 6.03267i) q^{89} +(21.1901 - 2.87334i) q^{90} +(-9.40061 - 1.31486i) q^{91} +(1.92055 - 0.338646i) q^{92} +(-0.302777 + 0.783081i) q^{93} +(-6.59746 - 18.1264i) q^{94} +(-4.47644 - 12.2989i) q^{95} +(-12.4050 + 1.93394i) q^{96} +(2.47809 - 0.436955i) q^{97} +(14.9372 - 3.74516i) q^{98} +(-6.51740 + 7.16809i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30}+ \cdots - 192 q^{99}+O(q^{100}) \) 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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