LMFDB - Embedded newform 189.2.be.a.20.4

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			20.4
Character	$\chi$	$=$	189.20
Dual form			189.2.be.a.104.4

$q$-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} +(2.51680 + 0.815925i) 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} +(-0.206962 - 5.81680i) 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} +(3.66829 + 2.74657i) 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} +(1.18747 - 8.48984i) 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} +(2.91777 - 9.64990i) 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} +(5.66853 + 4.10704i) 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} +(3.27276 + 3.62996i) 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} +(4.47463 + 6.55573i) 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} +(-18.4442 + 3.93313i) 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} +(-7.54658 - 4.00622i) 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} +(-12.9932 + 0.721122i) 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} +(5.83901 - 7.48374i) 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} +(4.22519 - 14.8086i) 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 $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$-1$

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	−0.856636	−	0.515921i	$-0.827450\pi$
$2$	−0.752422	−	2.06726i	−0.532042	−	1.46177i	0.324594	−	0.945854i	$-0.394772\pi$
$3$	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	−0.804605	−	0.593810i	$-0.797623\pi$
$5$	−0.562637	−	3.19087i	−0.251619	−	1.42700i	0.552986	−	0.833190i	$-0.313488\pi$
$6$	−0.0757386	−	3.80964i	−0.0309202	−	1.55528i
$7$	2.51680	+	0.815925i	0.951260	+	0.308391i
$7$	2.51680	+	0.815925i	0.951260	+	0.308391i
$8$	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	−0.327766	−	0.944759i	$-0.606296\pi$
$11$	−3.18028	−	0.560770i	−0.958891	−	0.169078i	−0.631126	+	0.775681i	$0.717407\pi$
$12$	−4.58754	+	1.77377i	−1.32431	+	0.512043i
$13$	1.22706	−	3.37132i	0.340325	−	0.935036i	−0.644975	−	0.764204i	$-0.723132\pi$
$13$	1.22706	−	3.37132i	0.340325	−	0.935036i	0.985300	−	0.170832i	$-0.0546456\pi$
$14$	−0.206962	−	5.81680i	−0.0553128	−	1.55460i
$15$	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	$-0.0488526\pi$
$17$	1.49145	+	2.58328i	0.361731	+	0.626536i	−0.626515	+	0.779409i	$0.715519\pi$
$18$	2.00899	−	6.28660i	0.473523	−	1.48177i
$19$	−3.49827	−	2.01973i	−0.802559	−	0.463358i	0.0418061	−	0.999126i	$-0.486689\pi$
$19$	−3.49827	−	2.01973i	−0.802559	−	0.463358i	−0.844365	+	0.535768i	$0.820022\pi$
$20$	7.04831	+	5.91424i	1.57605	+	1.32246i
$21$	3.66829	+	2.74657i	0.800487	+	0.599350i
$22$	1.23366	+	6.99641i	0.263016	+	1.49164i
$23$	−0.441437	−	0.526084i	−0.0920460	−	0.109696i	0.718055	−	0.695986i	$-0.245032\pi$
$23$	−0.441437	−	0.526084i	−0.0920460	−	0.109696i	−0.810101	+	0.586290i	$0.800588\pi$
$24$	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	0.710176	+	0.704024i	$0.248615\pi$
$29$	3.33174	+	9.15387i	0.618688	+	1.69983i	−0.0914880	+	0.995806i	$0.529162\pi$
$30$	−12.1135	+	2.38512i	−2.21161	+	0.435461i
$31$	−0.311578	−	0.371325i	−0.0559611	−	0.0666919i	0.737338	−	0.675524i	$-0.236083\pi$
$31$	−0.311578	−	0.371325i	−0.0559611	−	0.0666919i	−0.793299	+	0.608832i	$0.791638\pi$
$32$	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
$35$	1.18747	−	8.48984i	0.200719	−	1.43505i
$36$	−8.51239	+	0.338599i	−1.41873	+	0.0564332i
$37$	2.82040	+	4.88507i	0.463671	+	0.803101i	0.999140	−	0.0414533i	$-0.0131988\pi$
$37$	2.82040	+	4.88507i	0.463671	+	0.803101i	−0.535470	+	0.844554i	$0.679865\pi$
$38$	−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	$-0.339909\pi$
$41$	1.84441	+	0.671309i	0.288048	+	0.104841i	−0.193955	+	0.981010i	$0.562132\pi$
$42$	2.91777	−	9.64990i	0.450221	−	1.48901i
$43$	1.32012	−	7.48676i	0.201316	−	1.14172i	−0.701816	−	0.712358i	$-0.747627\pi$
$43$	1.32012	−	7.48676i	0.201316	−	1.14172i	0.903132	−	0.429362i	$-0.141262\pi$
$44$	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	$-0.0569216\pi$
$47$	6.71691	+	5.63616i	0.979762	+	0.822118i	−0.00429160	+	0.999991i	$0.501366\pi$
$48$	−1.35060	+	2.45055i	−0.194943	+	0.353706i
$49$	5.66853	+	4.10704i	0.809790	+	0.586719i
$50$	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	$0.0687084\pi$
$53$			3.11853i			0.428363i	−0.976794	+	0.214181i	$0.931292\pi$
$54$	6.81287	−	9.17916i	0.927114	−	1.24913i
$55$			10.4634i			1.41088i
$56$	3.27276	+	3.62996i	0.437342	+	0.485074i
$57$	−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	−0.796602	−	0.604504i	$-0.793372\pi$
$59$	−1.95711	−	11.0993i	−0.254793	−	1.44501i	0.541809	−	0.840502i	$-0.317740\pi$
$60$	8.24099	+	13.6403i	1.06391	+	1.76095i
$61$	−3.09075	+	3.68341i	−0.395730	+	0.471613i	−0.926713	−	0.375770i	$-0.877378\pi$
$61$	−3.09075	+	3.68341i	−0.395730	+	0.471613i	0.530983	+	0.847383i	$0.321823\pi$
$62$	−0.533187	+	0.923507i	−0.0677148	+	0.117285i
$63$	4.47463	+	6.55573i	0.563751	+	0.825945i
$64$	−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	−0.267360	−	0.963597i	$-0.586151\pi$
$67$	−8.93479	−	3.25200i	−1.09156	−	0.397295i	−0.824198	+	0.566302i	$0.808374\pi$
$68$	−7.95975	−	2.89711i	−0.965262	−	0.351327i
$69$	−0.428968	−	1.10945i	−0.0516417	−	0.133562i
$70$	−18.4442	+	3.93313i	−2.20450	+	0.470099i
$71$	−2.67528	+	1.54458i	−0.317498	+	0.183307i	−0.650277	−	0.759697i	$-0.725347\pi$
$71$	−2.67528	+	1.54458i	−0.317498	+	0.183307i	0.332779	+	0.943005i	$0.392014\pi$
$72$	2.10093	+	5.12823i	0.247597	+	0.604368i
$73$	9.91831	+	5.72634i	1.16085	+	0.670217i	0.951508	−	0.307625i	$-0.0995343\pi$
$73$	9.91831	+	5.72634i	1.16085	+	0.670217i	0.209342	+	0.977842i	$0.432868\pi$
$74$	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
$77$	−7.54658	−	4.00622i	−0.860012	−	0.456551i
$78$	−12.9365	−	4.41932i	−1.46477	−	0.500390i
$79$	6.20601	−	2.25880i	0.698231	−	0.254135i	0.0315757	−	0.999501i	$-0.489947\pi$
$79$	6.20601	−	2.25880i	0.698231	−	0.254135i	0.666655	+	0.745366i	$0.267725\pi$
$80$	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	−0.813385	+	0.581726i	$0.802378\pi$
$83$	−16.4935	+	6.00315i	−1.81040	+	0.658932i	−0.997015	+	0.0772059i	$0.975400\pi$
$84$	−12.9932	+	0.721122i	−1.41767	+	0.0786808i
$85$	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	$-0.953699\pi$
$89$	−3.48296	+	6.03267i	−0.369193	+	0.639462i	0.620246	+	0.784407i	$0.287033\pi$
$90$	−21.1901	−	2.87334i	−2.23363	−	0.302877i
$91$	5.83901	−	7.48374i	0.612094	−	0.784509i
$92$	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	$-0.485219\pi$
$97$	−2.47809	−	0.436955i	−0.251612	−	0.0443660i	−0.298032	+	0.954556i	$0.596330\pi$
$98$	4.22519	−	14.8086i	0.426809	−	1.49589i
$99$	−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	$-0.471795\pi$
$101$	−8.81458	−	7.39631i	−0.877083	−	0.735960i	−0.965577	+	0.260117i	$0.916239\pi$
$102$	9.72840	−	5.87757i	0.963255	−	0.581966i
$103$	−17.5678	+	3.09768i	−1.73101	+	0.305223i	−0.948349	−	0.317229i	$-0.897248\pi$
$103$	−17.5678	+	3.09768i	−1.73101	+	0.305223i	−0.782658	+	0.622452i	$0.786137\pi$
$104$	5.07698	−	4.26009i	0.497839	−	0.417737i
$105$	6.70002	−	13.2504i	0.653855	−	1.29310i
$106$	6.44681	−	2.34645i	0.626170	−	0.227907i
$107$			2.99079i			0.289131i	0.989495	+	0.144565i	$0.0461784\pi$
$107$			2.99079i			0.289131i	−0.989495	+	0.144565i	$0.953822\pi$
$108$	−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
$112$	−2.00411	+	3.77517i	−0.189370	+	0.356720i
$113$	3.48822	−	0.615067i	0.328144	−	0.0578607i	−0.00714917	−	0.999974i	$-0.502276\pi$
$113$	3.48822	−	0.615067i	0.328144	−	0.0578607i	0.335293	+	0.942114i	$0.391165\pi$
$114$	−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
$119$	1.64593	+	7.71850i	0.150882	+	0.707553i
$120$	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
$126$	10.1856	−	14.1829i	0.907406	−	1.26351i
$127$	−7.37491	+	12.7737i	−0.654418	+	1.13348i	0.327622	+	0.944809i	$0.393753\pi$
$127$	−7.37491	+	12.7737i	−0.654418	+	1.13348i	−0.982039	+	0.188676i	$0.939580\pi$
$128$	−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	$-0.591960\pi$
$131$	6.97748	−	5.85480i	0.609625	−	0.511536i	0.894523	+	0.447021i	$0.147515\pi$
$132$	15.5844	−	3.06853i	1.35644	−	0.267081i
$133$	−7.15650	−	7.93758i	−0.620547	−	0.688275i
$134$			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	−0.995601	−	0.0936959i	$-0.970132\pi$
$137$	−3.43127	−	9.42733i	−0.293153	−	0.805431i	0.702448	−	0.711735i	$-0.252090\pi$
$138$	−1.97076	+	1.72156i	−0.167762	+	0.146549i
$139$	2.61949	+	3.12178i	0.222182	+	0.264786i	0.865608	−	0.500722i	$-0.166932\pi$
$139$	2.61949	+	3.12178i	0.222182	+	0.264786i	−0.643426	+	0.765508i	$0.722488\pi$
$140$	12.9136	+	20.6358i	1.09140	+	1.74405i
$141$	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
$147$	6.99136	+	9.90560i	0.576637	+	0.817000i
$148$	−15.0522	−	5.47855i	−1.23728	−	0.450334i
$149$	3.33221	−	9.15518i	0.272985	−	0.750021i	−0.725127	−	0.688615i	$-0.758219\pi$
$149$	3.33221	−	9.15518i	0.272985	−	0.750021i	0.998113	−	0.0614066i	$-0.0195586\pi$
$150$	7.55535	+	19.5406i	0.616892	+	1.59548i
$151$	3.65868	−	20.7494i	0.297739	−	1.68856i	−0.358116	−	0.933677i	$-0.616581\pi$
$151$	3.65868	−	20.7494i	0.297739	−	1.68856i	0.655855	−	0.754887i	$-0.272308\pi$
$152$	−3.73105	−	6.46236i	−0.302628	−	0.524167i
$153$	−1.20243	+	8.86758i	−0.0972108	+	0.716901i
$154$	−2.60369	+	18.6151i	−0.209811	+	1.50005i
$155$	−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	$-0.688739\pi$
$157$	−10.0273	+	1.76809i	−0.800269	+	0.141109i	−0.241466	+	0.970409i	$0.577628\pi$
$158$	−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	−0.942564	−	0.334026i	$-0.891593\pi$
$167$	−2.21093	−	12.5388i	−0.171087	−	0.970284i	0.771477	−	0.636258i	$-0.219518\pi$
$168$	3.33170	+	7.78220i	0.257046	+	0.600410i
$169$	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	−0.899464	−	0.436995i	$-0.856043\pi$
$173$	1.25238	−	7.10260i	0.0952167	−	0.540001i	0.994681	−	0.103006i	$-0.0328461\pi$
$174$	34.6206	−	13.3860i	2.62458	−	1.01479i
$175$	−14.5377	+	0.517252i	−1.09895	+	0.0391006i
$176$	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	−0.252486	−	0.967601i	$-0.581248\pi$
$179$	6.14419	−	3.54735i	0.459238	−	0.265141i	0.711724	+	0.702459i	$0.247915\pi$
$180$	5.86981	+	26.9714i	0.437510	+	2.01033i
$181$	−4.46843	−	2.57985i	−0.332136	−	0.191759i	0.324653	−	0.945833i	$-0.394752\pi$
$181$	−4.46843	−	2.57985i	−0.332136	−	0.191759i	−0.656789	+	0.754074i	$0.728086\pi$
$182$	−19.8642	−	6.43983i	−1.47244	−	0.477352i
$183$	−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
$189$	3.66340	+	13.2506i	0.266473	+	0.963842i
$190$	28.7932			2.08888
$191$	1.36266	+	3.74387i	0.0985984	+	0.270897i	0.979179	−	0.203000i	$-0.0650691\pi$
$191$	1.36266	+	3.74387i	0.0985984	+	0.270897i	−0.880580	+	0.473897i	$0.842847\pi$
$192$	−4.25472	−	21.6088i	−0.307058	−	1.55948i
$193$	5.82741	−	4.88978i	0.419466	−	0.351974i	−0.408494	−	0.912761i	$-0.633946\pi$
$193$	5.82741	−	4.88978i	0.419466	−	0.351974i	0.827960	+	0.560787i	$0.189501\pi$
$194$	0.961271	+	5.45164i	0.0690152	+	0.391405i
$195$	−17.6333	−	9.71848i	−1.26275	−	0.695955i
$196$	−19.8277	+	1.41273i	−1.41626	+	0.100909i
$197$	−3.24083	−	1.87109i	−0.230899	−	0.133310i	0.380087	−	0.924951i	$-0.375894\pi$
$197$	−3.24083	−	1.87109i	−0.230899	−	0.133310i	−0.610987	+	0.791641i	$0.709227\pi$
$198$	−9.91448	+	18.8666i	−0.704591	+	1.34079i
$199$	−1.91984	+	1.10842i	−0.136094	+	0.0785736i	−0.566501	−	0.824061i	$-0.691703\pi$
$199$	−1.91984	+	1.10842i	−0.136094	+	0.0785736i	0.430407	+	0.902635i	$0.358370\pi$
$200$	−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
$203$	0.916430	+	25.7569i	0.0643207	+	1.80778i
$204$	−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
$210$	−32.4332	−	3.88083i	−2.23810	−	0.267803i
$211$	−0.591357	−	3.35375i	−0.0407107	−	0.230882i	0.957663	−	0.287892i	$-0.0929544\pi$
$211$	−0.591357	−	3.35375i	−0.0407107	−	0.230882i	−0.998374	+	0.0570100i	$0.981843\pi$
$212$	−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	$-0.829080\pi$
$223$	−3.08075	+	3.67150i	−0.206302	+	0.245862i	0.652965	+	0.757388i	$0.273525\pi$
$224$	18.9930	+	2.65653i	1.26902	+	0.177497i
$225$	−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	0.895618	+	0.444825i	$0.146734\pi$
$227$	−1.47843	+	8.38458i	−0.0981267	+	0.556504i	−0.993744	+	0.111679i	$0.964377\pi$
$228$	19.6310	+	3.06047i	1.30010	+	0.202685i
$229$	−7.67684	+	21.0920i	−0.507300	+	1.39380i	0.376712	+	0.926331i	$0.377055\pi$
$229$	−7.67684	+	21.0920i	−0.507300	+	1.39380i	−0.884012	+	0.467465i	$0.845167\pi$
$230$	4.59997	+	1.67425i	0.303313	+	0.110397i
$231$	−10.1260	−	10.7919i	−0.666243	−	0.710056i
$232$	−3.12483	+	17.7218i	−0.205155	+	1.16349i
$233$	−4.77720	+	2.75812i	−0.312965	+	0.180690i	−0.648252	−	0.761426i	$-0.724500\pi$
$233$	−4.77720	+	2.75812i	−0.312965	+	0.180690i	0.335288	+	0.942116i	$0.391167\pi$
$234$	−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
$238$	14.7177	−	9.21013i	0.954008	−	0.597004i
$239$	17.7886	+	21.1996i	1.15065	+	1.37129i	0.916961	+	0.398977i	$0.130635\pi$
$239$	17.7886	+	21.1996i	1.15065	+	1.37129i	0.233687	+	0.972312i	$0.424921\pi$
$240$	8.57927	+	2.93083i	0.553790	+	0.189184i
$241$	−0.237543	−	0.652643i	−0.0153015	−	0.0420404i	0.931807	−	0.362955i	$-0.118232\pi$
$241$	−0.237543	−	0.652643i	−0.0153015	−	0.0420404i	−0.947108	+	0.320914i	$0.896010\pi$
$242$			1.25692i			0.0807978i
$243$	−1.17025	+	15.5445i	−0.0750715	+	0.997178i
$244$		−	13.6543i		−	0.874128i
$245$	9.91570	−	20.3983i	0.633491	−	1.30320i
$246$	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	$-0.876538\pi$
$251$	−2.14378	+	3.71314i	−0.135314	+	0.234371i	0.790403	+	0.612587i	$0.209871\pi$
$252$	−21.7002	−	6.09329i	−1.36699	−	0.383841i
$253$	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	$-0.489029\pi$
$257$	−9.32291	−	3.39326i	−0.581547	−	0.211666i	−0.616007	+	0.787740i	$0.711251\pi$
$258$	−28.6219	−	4.46214i	−1.78192	−	0.277801i
$259$	3.11252	+	14.5960i	0.193402	+	0.906950i
$260$	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	−0.669682	−	0.742648i	$-0.733570\pi$
$263$	2.88623	−	3.43967i	0.177973	−	0.212099i	0.847655	+	0.530549i	$0.178014\pi$
$264$	−5.34318	−	8.84389i	−0.328850	−	0.544304i
$265$	9.95082	−	1.75460i	0.611274	−	0.107784i
$266$	−11.0243	+	20.7668i	−0.675946	+	1.27329i
$267$	−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	$-0.467853\pi$
$269$	3.30722			0.201645			0.100823	+	0.994904i	$0.467853\pi$
$270$	−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
$273$	13.7608	−	8.99679i	0.832840	−	0.544511i
$274$	−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	0.974243	−	0.225499i	$-0.0724013\pi$
$277$	15.3342	+	12.8670i	0.921346	+	0.773101i	−0.0528977	+	0.998600i	$0.516846\pi$
$278$	4.48259	−	7.76407i	0.268848	−	0.465658i
$279$	−0.0577979	−	1.45304i	−0.00346027	−	0.0869913i
$280$	9.74137	−	12.4853i	0.582158	−	0.746141i
$281$	22.5838	+	3.98212i	1.34723	+	0.237554i	0.800289	−	0.599615i	$-0.204680\pi$
$281$	22.5838	+	3.98212i	1.34723	+	0.237554i	0.546945	+	0.837169i	$0.315791\pi$
$282$	20.9630	−	26.0159i	1.24833	−	1.54922i
$283$	7.62218	−	20.9418i	0.453091	−	1.24486i	−0.477446	−	0.878661i	$-0.658437\pi$
$283$	7.62218	−	20.9418i	0.453091	−	1.24486i	0.930537	−	0.366197i	$-0.119340\pi$
$284$	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
$287$	4.09426	+	3.19444i	0.241676	+	0.188562i
$288$	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	$-0.589066\pi$
$293$	10.6534	−	8.93928i	0.622379	−	0.522238i	0.898550	+	0.438870i	$0.144621\pi$
$294$	15.2170	−	21.9061i	0.887474	−	1.27759i
$295$	−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
$301$	9.43110	−	17.7655i	0.543600	−	1.02399i
$302$	−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	$-0.623937\pi$
$307$	4.06170	−	2.34502i	0.231813	−	0.133837i	0.611408	+	0.791315i	$0.290603\pi$
$308$	23.7290	−	5.06010i	1.35209	−	0.288326i
$309$	−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	$-0.390286\pi$
$311$	−0.145456	−	0.0529415i	−0.00824803	−	0.00300204i	−0.346141	+	0.938183i	$0.612508\pi$
$312$	10.7068	−	4.13976i	0.606151	−	0.234368i
$313$	−23.8814	−	4.21093i	−1.34986	−	0.238016i	−0.548473	−	0.836168i	$-0.684791\pi$
$313$	−23.8814	−	4.21093i	−1.34986	−	0.238016i	−0.801383	+	0.598152i	$0.795902\pi$
$314$	11.1999	+	19.3988i	0.632047	+	1.09474i
$315$	18.4009	−	17.9665i	1.03677	−	1.01230i
$316$	−9.37714	+	16.2417i	−0.527505	+	0.913666i
$317$	−3.59159	+	4.28029i	−0.201724	+	0.240405i	−0.857417	−	0.514623i	$-0.827932\pi$
$317$	−3.59159	+	4.28029i	−0.201724	+	0.240405i	0.655693	+	0.755027i	$0.272376\pi$
$318$	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
$322$	−2.96877	+	2.67663i	−0.165443	+	0.149163i
$323$		−	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
$329$	12.3064	+	19.6656i	0.678475	+	1.08420i
$330$	39.8617	−	0.792482i	2.19432	−	0.0436247i
$331$	−6.72476	−	5.64274i	−0.369626	−	0.310153i	0.438987	−	0.898493i	$-0.355337\pi$
$331$	−6.72476	−	5.64274i	−0.369626	−	0.310153i	−0.808614	+	0.588340i	$0.799782\pi$
$332$	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
$336$	−5.39865	+	5.06553i	−0.294521	+	0.276348i
$337$	16.3526	+	5.95186i	0.890783	+	0.324218i	0.746553	−	0.665326i	$-0.231707\pi$
$337$	16.3526	+	5.95186i	0.890783	+	0.324218i	0.144230	+	0.989544i	$0.453930\pi$
$338$	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
$343$	10.9155	+	14.9617i	0.589382	+	0.807854i
$344$	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	0.812464	−	0.583011i	$-0.198126\pi$
$347$	1.81114	+	2.15843i	0.0972268	+	0.115870i	−0.715237	+	0.698882i	$0.753681\pi$
$348$	−31.5213	−	36.0840i	−1.68972	−	1.93431i
$349$	7.28167	+	20.0062i	0.389779	+	1.07091i	0.967101	+	0.254392i	$0.0818753\pi$
$349$	7.28167	+	20.0062i	0.389779	+	1.07091i	−0.577323	+	0.816516i	$0.695902\pi$
$350$	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	$-0.810624\pi$
$353$	−20.7113	+	7.53828i	−1.10235	+	0.401222i	−0.274167	+	0.961682i	$0.588402\pi$
$354$	−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
$357$	−1.62404	+	13.5726i	−0.0859534	+	0.718338i
$358$	−11.9563	−	10.0325i	−0.631911	−	0.530236i
$359$	−17.6192	−	10.1725i	−0.929908	−	0.536883i	−0.0431257	−	0.999070i	$-0.513732\pi$
$359$	−17.6192	−	10.1725i	−0.929908	−	0.536883i	−0.886783	+	0.462187i	$0.847065\pi$
$360$	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
$364$	0.958447	+	26.9378i	0.0502363	+	1.41192i
$365$	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	$-0.229483\pi$
$367$	23.5883	+	4.15925i	1.23130	+	0.217111i	0.480116	+	0.877205i	$0.340595\pi$
$368$	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
$371$	−2.54449	+	7.84870i	−0.132103	+	0.407484i
$372$	2.08802	+	1.15080i	0.108259	+	0.0596662i
$373$	3.20352	+	18.1680i	0.165872	+	0.940706i	0.948161	+	0.317790i	$0.102941\pi$
$373$	3.20352	+	18.1680i	0.165872	+	0.940706i	−0.782289	+	0.622915i	$0.785948\pi$
$374$	−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
$378$	24.6361	−	17.5433i	1.26714	−	0.902329i
$379$	−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	0.900846	+	0.434138i	$0.142947\pi$
$383$	3.96910	+	22.5099i	0.202812	+	1.15020i	−0.698035	+	0.716064i	$0.745942\pi$
$384$	−19.9778	+	12.0699i	−1.01949	+	0.615940i
$385$	−8.53733	+	26.3342i	−0.435103	+	1.34211i
$386$	−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	0.112242	−	0.993681i	$-0.464197\pi$
$389$	−2.40905	−	0.424780i	−0.122143	−	0.0215372i	−0.234386	+	0.972144i	$0.575308\pi$
$390$	−6.82296	+	43.7651i	−0.345494	+	2.21613i
$391$	0.700637	−	1.92499i	0.0354328	−	0.0973507i
$392$	5.27510	+	11.8062i	0.266433	+	0.596304i
$393$	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	$-0.222672\pi$
$397$	11.7575	+	6.78822i	0.590094	+	0.340691i	−0.175041	+	0.984561i	$0.556006\pi$
$398$	3.73591	+	3.13480i	0.187264	+	0.157134i
$399$	−7.28538	−	17.0172i	−0.364725	−	0.851926i
$400$	−1.54239	−	8.74730i	−0.0771193	−	0.437365i
$401$	−12.2624	−	14.6138i	−0.612356	−	0.729777i	0.367380	−	0.930071i	$-0.380255\pi$
$401$	−12.2624	−	14.6138i	−0.612356	−	0.729777i	−0.979736	+	0.200294i	$0.935810\pi$
$402$	−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	−0.969027	−	0.246955i	$-0.920570\pi$
$409$	−21.1128	−	25.1612i	−1.04396	−	1.24414i	−0.0749336	−	0.997189i	$-0.523874\pi$
$410$	−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
$413$	4.13056	−	29.5315i	0.203252	−	1.45315i
$414$	−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	$-0.604445\pi$
$419$	−24.1055	−	8.77369i	−1.17763	−	0.428623i	−0.855365	+	0.518026i	$0.826667\pi$
$420$	9.61144	+	41.0538i	0.468990	+	2.00322i
$421$	−2.00087	+	11.3475i	−0.0975165	+	0.553044i	0.896431	+	0.443184i	$0.146151\pi$
$421$	−2.00087	+	11.3475i	−0.0975165	+	0.553044i	−0.993947	+	0.109860i	$0.964960\pi$
$422$	−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
$427$	−10.7842	+	6.74858i	−0.521883	+	0.326587i
$428$	−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	$0.231339\pi$
$431$			27.5891i			1.32892i	−0.747323	+	0.664461i	$0.768661\pi$
$432$	−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	$0.991737\pi$
$434$	−2.09544	+	1.88924i	−0.100584	+	0.0906863i
$435$	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	$-0.757666\pi$
$439$	1.70073	−	2.02686i	0.0811716	−	0.0967365i	0.805102	+	0.593137i	$0.202111\pi$
$440$	−9.66450	+	16.7394i	−0.460737	+	0.798020i
$441$	5.91275	+	20.1504i	0.281560	+	0.959544i
$442$	−11.7716	−	20.3889i	−0.559916	−	0.969803i
$443$	−15.9507	−	2.81254i	−0.757840	−	0.133628i	−0.218640	−	0.975806i	$-0.570162\pi$
$443$	−15.9507	−	2.81254i	−0.757840	−	0.133628i	−0.539200	+	0.842178i	$0.681273\pi$
$444$	−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
$448$	−7.01616	−	32.9019i	−0.331482	−	1.55447i
$449$	16.4077	−	9.47299i	0.774327	−	0.447058i	−0.0600887	−	0.998193i	$-0.519138\pi$
$449$	16.4077	−	9.47299i	0.774327	−	0.447058i	0.834416	+	0.551135i	$0.185805\pi$
$450$	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
$455$	−27.1649	−	14.4209i	−1.27351	−	0.676062i
$456$	−2.49691	−	12.6812i	−0.116929	−	0.593854i
$457$	−27.2962	+	9.93500i	−1.27686	+	0.464740i	−0.889393	−	0.457143i	$-0.848873\pi$
$457$	−27.2962	+	9.93500i	−1.27686	+	0.464740i	−0.387468	+	0.921883i	$0.626650\pi$
$458$	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	0.880453	−	0.474134i	$-0.157239\pi$
$461$	39.9292	−	14.5330i	1.85969	−	0.676870i	0.979233	−	0.202737i	$-0.0649836\pi$
$462$	−14.6907	+	29.0532i	−0.683473	+	1.35168i
$463$	−10.3324	+	8.66991i	−0.480187	+	0.402925i	−0.850494	−	0.525985i	$-0.823697\pi$
$463$	−10.3324	+	8.66991i	−0.480187	+	0.402925i	0.370307	+	0.928909i	$0.379252\pi$
$464$	−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	−0.442471	−	0.896783i	$-0.645898\pi$
$467$	12.0023	−	20.7886i	0.555401	−	0.961983i	0.997872	−	0.0652000i	$-0.0207685\pi$
$468$	−9.30369	+	29.1135i	−0.430063	+	1.34577i
$469$	−19.8337	−	15.4747i	−0.915833	−	0.714557i
$470$	−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
$476$	−17.6692	−	13.7860i	−0.809869	−	0.631881i
$477$	−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	$-0.106630\pi$
$479$	17.1728	+	14.4097i	0.784647	+	0.658397i	−0.159767	+	0.987155i	$0.551074\pi$
$480$	−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
$483$	−0.174396	−	3.14227i	−0.00793529	−	0.142978i
$484$	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
$490$	−49.6294	−	5.15020i	−2.24203	−	0.232662i
$491$	−5.85169	+	1.03181i	−0.264083	+	0.0465650i	−0.304122	−	0.952633i	$-0.598363\pi$
$491$	−5.85169	+	1.03181i	−0.264083	+	0.0465650i	0.0400387	+	0.999198i	$0.487252\pi$
$492$	−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
$497$	−7.99340	+	1.70455i	−0.358553	+	0.0764596i
$498$	24.1191	+	62.3798i	1.08080	+	2.79531i
$499$	8.89086	+	3.23601i	0.398010	+	0.144864i	0.533267	−	0.845947i	$-0.320964\pi$
$499$	8.89086	+	3.23601i	0.398010	+	0.144864i	−0.135258	+	0.990810i	$0.543186\pi$
$500$	−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	$-0.283253\pi$
$503$	−8.03207	−	13.9120i	−0.358132	−	0.620303i	−0.987649	+	0.156684i	$0.949920\pi$
$504$	1.10335	+	14.6209i	0.0491473	+	0.651267i
$505$	−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	$-0.794602\pi$
$509$	−7.79226	+	6.53848i	−0.345386	+	0.289813i	0.453548	+	0.891232i	$0.350158\pi$
$510$	−24.2281	−	27.7351i	−1.07284	−	1.22813i
$511$	20.2901	+	22.5046i	0.897581	+	0.995546i
$512$			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
$518$	27.8318	−	17.4167i	1.22286	−	0.765246i
$519$	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	0.0751836	+	0.997170i	$0.476046\pi$
$521$	−18.8534	+	32.6550i	−0.825982	+	1.43064i	−0.901166	+	0.433474i	$0.857288\pi$
$522$	64.2401	−	2.55529i	2.81171	−	0.111842i
$523$	−1.29357	+	0.746842i	−0.0565638	+	0.0326571i	−0.528015	−	0.849235i	$-0.677064\pi$
$523$	−1.29357	+	0.746842i	−0.0565638	+	0.0326571i	0.471451	+	0.881892i	$0.343730\pi$
$524$	−4.49147	+	25.4724i	−0.196211	+	1.11277i
$525$	−24.1176	−	7.29227i	−1.05258	−	0.318261i
$526$	−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
$532$	30.0565	+	4.20399i	1.30312	+	0.182266i
$533$	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
$546$	−28.9526	−	21.6777i	−1.23906	−	0.927721i
$547$	28.1372	+	23.6099i	1.20306	+	1.00949i	0.999537	+	0.0304178i	$0.00968377\pi$
$547$	28.1372	+	23.6099i	1.20306	+	1.00949i	0.203523	+	0.979070i	$0.434761\pi$
$548$	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
$553$	17.4623	−	0.621308i	0.742572	−	0.0264207i
$554$	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	−0.448143	−	0.893962i	$-0.647914\pi$
$557$	2.40680	−	1.38957i	0.101979	−	0.0588778i	0.550122	+	0.835084i	$0.314581\pi$
$558$	−2.96033	+	1.21278i	−0.125321	+	0.0513412i
$559$	−23.6204	−	13.6372i	−0.999036	−	0.576794i
$560$	13.1737	+	4.27080i	0.556689	+	0.180474i
$561$	−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	$-0.472091\pi$
$563$	25.7160	−	21.5783i	1.08380	−	0.909415i	0.996231	+	0.0867435i	$0.0276461\pi$
$564$	−40.8113	−	13.9419i	−1.71847	−	0.587059i
$565$	−3.92520	−	10.7844i	−0.165134	−	0.453703i
$566$	−49.0272			−2.06077
$567$	−1.41490	+	23.7697i	−0.0594204	+	0.998233i
$568$	−5.70659			−0.239443
$569$	−12.7217	−	34.9527i	−0.533323	−	1.46529i	−0.855093	−	0.518474i	$-0.826500\pi$
$569$	−12.7217	−	34.9527i	−0.533323	−	1.46529i	0.321771	−	0.946818i	$-0.395722\pi$
$570$	47.1935	+	16.1221i	1.97672	+	0.675282i
$571$	−6.22425	+	5.22276i	−0.260477	+	0.218566i	−0.763668	−	0.645609i	$-0.776604\pi$
$571$	−6.22425	+	5.22276i	−0.260477	+	0.218566i	0.503191	+	0.864175i	$0.332159\pi$
$572$	−5.71311	−	32.4006i	−0.238877	−	1.35474i
$573$	0.137165	+	6.89938i	0.00573014	+	0.288226i
$574$	3.52314	−	10.8675i	0.147053	−	0.453599i
$575$	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	$-0.787373\pi$
$577$	−15.4017	+	8.89220i	−0.641183	+	0.370187i	0.143887	+	0.989594i	$0.454040\pi$
$578$	−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
$581$	−46.4090	+	1.65123i	−1.92537	+	0.0685046i
$582$	−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	$-0.145657\pi$
$587$	14.9687	+	12.5602i	0.617822	+	0.518415i	−0.279296	+	0.960205i	$0.590101\pi$
$588$	−33.2896	−	8.78654i	−1.37284	−	0.362351i
$589$	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	$-0.640870\pi$
$593$	−20.8572			−0.856502			−0.428251	+	0.903660i	$0.640870\pi$
$594$	−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	0.162421	−	0.986722i	$-0.448070\pi$
$599$	15.9702	−	2.81598i	0.652526	−	0.115058i	0.490105	+	0.871664i	$0.336959\pi$
$600$	−15.4071	−	8.49153i	−0.628993	−	0.346665i
$601$	22.4423	−	26.7456i	0.915439	−	1.09098i	−0.0801156	−	0.996786i	$-0.525529\pi$
$601$	22.4423	−	26.7456i	0.915439	−	1.09098i	0.995554	−	0.0941916i	$-0.0300266\pi$
$602$	−43.8222	−	6.12938i	−1.78606	−	0.249815i
$603$	−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	$-0.863892\pi$
$607$	1.32209	−	3.63240i	0.0536618	−	0.147435i	0.963628	+	0.267249i	$0.0861146\pi$
$608$	−27.5144	−	10.0144i	−1.11586	−	0.406138i
$609$	−12.9199	+	42.7299i	−0.523541	+	1.73150i
$610$	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	−0.896612	−	0.442818i	$-0.853979\pi$
$613$	−1.60472	+	2.77946i	−0.0648142	+	0.112261i	0.831797	+	0.555079i	$0.187312\pi$
$614$	−7.90388	−	6.63214i	−0.318975	−	0.267651i
$615$	5.31686	−	9.64696i	0.214396	−	0.389003i
$616$	−8.37274	−	13.3796i	−0.337347	−	0.539078i
$617$	−3.37702	−	4.02458i	−0.135954	−	0.162024i	0.693772	−	0.720195i	$-0.255948\pi$
$617$	−3.37702	−	4.02458i	−0.135954	−	0.162024i	−0.829726	+	0.558171i	$0.811503\pi$
$618$	13.1316	+	66.6925i	0.528231	+	2.68276i
$619$	−9.02167	−	24.7868i	−0.362611	−	0.996267i	−0.978103	−	0.208123i	$-0.933265\pi$
$619$	−9.02167	−	24.7868i	−0.362611	−	0.996267i	0.615491	−	0.788144i	$-0.288958\pi$
$620$		−	4.45996i		−	0.179116i
$621$	1.01847	−	3.42005i	0.0408698	−	0.137242i
$622$			0.340529i			0.0136540i
$623$	−13.6881	+	12.3412i	−0.548403	+	0.494438i
$624$	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
$630$	−50.9866	−	24.5211i	−2.03136	−	0.976945i
$631$	−21.3850	−	37.0399i	−0.851324	−	1.47454i	−0.880013	−	0.474949i	$-0.842467\pi$
$631$	−21.3850	−	37.0399i	−0.851324	−	1.47454i	0.0286891	−	0.999588i	$-0.490867\pi$
$632$	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
$637$	20.8018	−	14.0709i	0.824196	−	0.557508i
$638$	−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	−0.775912	−	0.630842i	$-0.782710\pi$
$641$	−0.504295	+	0.600995i	−0.0199185	+	0.0237379i	0.755993	+	0.654579i	$0.227154\pi$
$642$	11.3939	−	0.226519i	0.449680	−	0.00893997i
$643$	−10.7345	+	1.89279i	−0.423329	+	0.0746443i	−0.381254	−	0.924470i	$-0.624508\pi$
$643$	−10.7345	+	1.89279i	−0.423329	+	0.0746443i	−0.0420745	+	0.999114i	$0.513397\pi$
$644$	4.55733	+	2.41933i	0.179584	+	0.0953350i
$645$	−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	$-0.449468\pi$
$647$	8.04220			0.316172			0.158086	+	0.987425i	$0.449468\pi$
$648$	−4.42744	+	16.0253i	−0.173926	+	0.629535i
$649$			36.3964i			1.42868i
$650$	40.7785	−	14.8422i	1.59946	−	0.582158i
$651$	−0.123093	−	2.21790i	−0.00482441	−	0.0869263i
$652$	21.9778	−	18.4416i	0.860717	−	0.722228i
$653$	−10.0845	+	1.77817i	−0.394638	+	0.0695853i	−0.367446	−	0.930045i	$-0.619768\pi$
$653$	−10.0845	+	1.77817i	−0.394638	+	0.0695853i	−0.0271920	+	0.999630i	$0.508657\pi$
$654$	−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
$658$	31.3942	−	40.2374i	1.22387	−	1.56862i
$659$	20.5607	+	3.62540i	0.800930	+	0.141226i	0.559108	−	0.829095i	$-0.311144\pi$
$659$	20.5607	+	3.62540i	0.800930	+	0.141226i	0.241822	+	0.970321i	$0.422255\pi$
$660$	−18.5596	−	48.0012i	−0.722432	−	1.86844i
$661$	−1.62538	+	4.46570i	−0.0632200	+	0.173696i	−0.967281	−	0.253708i	$-0.918350\pi$
$661$	−1.62538	+	4.46570i	−0.0632200	+	0.173696i	0.904061	+	0.427404i	$0.140572\pi$
$662$	−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
$665$	−21.3013	+	27.3014i	−0.826028	+	1.05870i
$666$	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
$672$	29.6429	+	14.9889i	1.14350	+	0.578208i
$673$	30.7990	−	11.2099i	1.18721	−	0.432110i	0.328469	−	0.944515i	$-0.393467\pi$
$673$	30.7990	−	11.2099i	1.18721	−	0.432110i	0.858744	+	0.512404i	$0.171245\pi$
$674$		−	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	$-0.633004\pi$
$677$	−3.36060	+	1.22316i	−0.129158	+	0.0470098i	0.276632	+	0.960976i	$0.410782\pi$
$678$	−2.60738	−	13.2423i	−0.100136	−	0.508567i
$679$	−5.88033	−	3.12166i	−0.225666	−	0.119798i
$680$	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	0.362207	−	0.932098i	$-0.382023\pi$
$683$	−6.89711	−	3.98205i	−0.263910	−	0.152369i	−0.626117	+	0.779729i	$0.715357\pi$
$684$	30.4626	+	16.0082i	1.16476	+	0.612089i
$685$	−28.1508	+	16.2529i	−1.07559	+	0.620991i
$686$	22.7166	−	33.8227i	0.867325	−	1.29136i
$687$	−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	$-0.511722\pi$
$691$	−10.8617	−	1.91522i	−0.413200	−	0.0728583i	−0.376384	+	0.926464i	$0.622833\pi$
$692$	10.2402	+	17.7366i	0.389275	+	0.674244i
$693$	−10.5543	−	23.3583i	−0.400926	−	0.887309i
$694$	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
$700$	30.6803	−	27.6613i	1.15961	−	1.04550i
$701$		−	38.5950i		−	1.45771i	−0.684665	−	0.728857i	$-0.740052\pi$
$701$		−	38.5950i		−	1.45771i	0.684665	−	0.728857i	$-0.259948\pi$
$702$	−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
$707$	−16.1497	−	25.8070i	−0.607371	−	0.970573i
$708$	28.6659	+	47.4471i	1.07733	+	1.78317i
$709$	25.2492	+	21.1866i	0.948253	+	0.795679i	0.979002	−	0.203848i	$-0.0653450\pi$
$709$	25.2492	+	21.1866i	0.948253	+	0.795679i	−0.0307495	+	0.999527i	$0.509789\pi$
$710$	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
$714$	29.2801	−	6.85499i	1.09578	−	0.256542i
$715$	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	$-0.0559583\pi$
$719$	9.13910	+	15.8294i	0.340831	+	0.590336i	−0.643756	+	0.765231i	$0.722625\pi$
$720$	12.4208	+	9.60755i	0.462896	+	0.358052i
$721$	−46.7421	−	6.53779i	−1.74077	−	0.243480i
$722$	−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	0.907150	+	0.420808i	$0.138254\pi$
$727$	13.0156	+	35.7602i	0.482723	+	1.32627i	−0.424426	+	0.905462i	$0.639524\pi$
$728$	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	$-0.108186\pi$
$733$	12.2043	+	14.5445i	0.450776	+	0.537214i	−0.492020	+	0.870584i	$0.663741\pi$
$734$	−9.15008	−	51.8927i	−0.337736	−	1.91539i
$735$	27.6739	−	27.8818i	1.02077	−	1.02843i
$736$	−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	0.853360	−	0.521322i	$-0.174561\pi$
$739$	−0.674129	−	1.16763i	−0.0247982	−	0.0429518i	−0.878158	+	0.478370i	$0.841228\pi$
$740$	−9.01243	+	51.1120i	−0.331304	+	1.87892i
$741$	−23.4123	+	9.05234i	−0.860072	+	0.332546i
$742$	18.1398	−	0.645415i	0.665934	−	0.0236939i
$743$	−14.7521	+	40.5311i	−0.541203	+	1.48694i	0.304091	+	0.952643i	$0.401647\pi$
$743$	−14.7521	+	40.5311i	−0.541203	+	1.48694i	−0.845295	+	0.534301i	$0.820575\pi$
$744$	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
$749$	−2.44026	+	7.52722i	−0.0891653	+	0.275039i
$750$	5.26474	−	3.18077i	0.192241	−	0.116145i
$751$	−1.49167	−	8.45970i	−0.0544319	−	0.308699i	0.945421	−	0.325852i	$-0.105651\pi$
$751$	−1.49167	−	8.45970i	−0.0544319	−	0.308699i	−0.999853	+	0.0171527i	$0.994540\pi$
$752$	−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
$756$	−32.1559	−	22.1378i	−1.16950	−	0.805142i
$757$	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	0.766477	+	0.642271i	$0.222008\pi$
$761$	7.33501	+	41.5989i	0.265894	+	1.50796i	−0.500583	+	0.865688i	$0.666881\pi$
$762$	49.2219	+	27.1283i	1.78312	+	0.982756i
$763$	7.18287	+	2.32863i	0.260038	+	0.0843021i
$764$	−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	−0.744109	−	0.668059i	$-0.767126\pi$
$769$	7.08056	−	19.4537i	0.255331	−	0.701517i	0.999440	−	0.0334587i	$-0.0106522\pi$
$770$	60.8633	−	2.16552i	2.19336	−	0.0780398i
$771$	−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	$-0.226244\pi$
$773$	−5.17350	−	8.96077i	−0.186078	−	0.322296i	−0.943939	+	0.330119i	$0.892911\pi$
$774$	−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
$777$	−3.07113	+	25.6663i	−0.110176	+	0.920773i
$778$	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	0.999972	+	0.00745697i	$0.00237365\pi$
$787$	23.3874	+	27.8721i	0.833673	+	0.993532i	−0.166300	+	0.986075i	$0.553182\pi$
$788$	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
$791$	9.28099	+	1.29813i	0.329994	+	0.0461561i
$792$	−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	$-0.365113\pi$
$797$	3.95939	+	1.44110i	0.140249	+	0.0510464i	−0.270942	+	0.962596i	$0.587335\pi$
$798$	−29.6973	+	27.8649i	−1.05127	+	0.986406i
$799$	−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
$805$	−4.99057	+	3.12302i	−0.175894	+	0.110072i
$806$	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	$-0.742642\pi$
$809$		−	41.1433i		−	1.44652i	0.690574	−	0.723261i	$-0.257358\pi$
$810$	−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	$-0.149078\pi$
$812$	−49.0083	−	54.3572i	−1.71985	−	1.90756i
$813$	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
$819$	27.5921	−	7.04114i	0.964147	−	0.246037i
$820$	9.02967	+	15.6398i	0.315330	+	0.546167i
$821$	34.7029	+	6.11906i	1.21114	+	0.213557i	0.742508	−	0.669837i	$-0.233636\pi$
$821$	34.7029	+	6.11906i	1.21114	+	0.213557i	0.468632	+	0.883394i	$0.344747\pi$
$822$	−35.6549	+	13.7859i	−1.24361	+	0.480839i
$823$	−11.0749	−	4.03095i	−0.386048	−	0.140510i	0.141703	−	0.989909i	$-0.454742\pi$
$823$	−11.0749	−	4.03095i	−0.386048	−	0.140510i	−0.527751	+	0.849399i	$0.676964\pi$
$824$	−30.9663	−	11.2708i	−1.07876	−	0.392637i
$825$	30.3866	+	4.73726i	1.05793	+	0.164930i
$826$	−64.1573	+	13.6812i	−2.23232	+	0.476030i
$827$	4.77748	−	2.75828i	0.166129	−	0.0959148i	−0.414630	−	0.909990i	$-0.636089\pi$
$827$	4.77748	−	2.75828i	0.166129	−	0.0959148i	0.580759	+	0.814075i	$0.302756\pi$
$828$	3.93582	+	4.32877i	0.136779	+	0.150435i
$829$	33.5706	+	19.3820i	1.16595	+	0.673164i	0.952724	−	0.303837i	$-0.0982680\pi$
$829$	33.5706	+	19.3820i	1.16595	+	0.673164i	0.213231	+	0.977002i	$0.431601\pi$
$830$	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
$833$	−2.15525	+	20.7688i	−0.0746748	+	0.719598i
$834$	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	$-0.388456\pi$
$839$	35.0483	−	12.7566i	1.21000	−	0.440405i	0.866705	+	0.498821i	$0.166234\pi$
$840$	22.9575	−	15.0096i	0.792107	−	0.517880i
$841$	−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
$847$	−1.19180	−	0.929870i	−0.0409506	−	0.0319507i
$848$	−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	$-0.471242\pi$
$853$	−4.83719	−	0.852926i	−0.165622	−	0.0292036i	−0.255844	+	0.966718i	$0.582353\pi$
$854$	22.0653	+	17.2159i	0.755060	+	0.589118i
$855$	−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	$-0.209582\pi$
$857$	9.53580	+	8.00148i	0.325737	+	0.273325i	−0.465223	+	0.885193i	$0.654026\pi$
$858$	38.6634	+	21.3091i	1.31995	+	0.727480i
$859$	−48.9734	+	8.63533i	−1.67095	+	0.294634i	−0.927407	−	0.374054i	$-0.877968\pi$
$859$	−48.9734	+	8.63533i	−1.67095	+	0.294634i	−0.743544	+	0.668687i	$0.766856\pi$
$860$	53.5831	−	44.9615i	1.82717	−	1.53318i
$861$	4.92203	+	7.52834i	0.167742	+	0.256565i
$862$	57.0339	−	20.7587i	1.94258	−	0.707043i
$863$			7.82559i			0.266386i	0.991090	+	0.133193i	$0.0425230\pi$
$863$			7.82559i			0.266386i	−0.991090	+	0.133193i	$0.957477\pi$
$864$	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
$868$	3.21669	+	1.70763i	0.109182	+	0.0579607i
$869$	−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
$875$	0.890731	+	4.17703i	0.0301122	+	0.141209i
$876$	−55.6579	−	8.67704i	−1.88050	−	0.293170i
$877$	−38.6291	−	14.0598i	−1.30441	−	0.474767i	−0.405980	−	0.913882i	$-0.633070\pi$
$877$	−38.6291	−	14.0598i	−1.30441	−	0.474767i	−0.898431	+	0.439115i	$0.855292\pi$
$878$	−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	$-0.315893\pi$
$881$	−13.4109	−	23.2283i	−0.451824	−	0.782582i	−0.998499	+	0.0547623i	$0.982560\pi$
$882$	37.2073	−	27.3848i	1.25283	−	0.922095i
$883$	15.7111	−	27.2125i	0.528722	−	0.915773i	−0.470717	−	0.882284i	$-0.656005\pi$
$883$	15.7111	−	27.2125i	0.528722	−	0.915773i	0.999439	−	0.0334889i	$-0.0106618\pi$
$884$	−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	$-0.661796\pi$
$887$	8.61019	−	7.22481i	0.289102	−	0.242585i	0.775791	+	0.630990i	$0.217351\pi$
$888$	−5.83458	+	17.0793i	−0.195796	+	0.573143i
$889$	−28.9836	+	26.1315i	−0.972077	+	0.876422i
$890$		−	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
$896$	−30.2237	+	18.9135i	−1.00970	+	0.631856i
$897$	−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
$903$	25.4055	−	23.8378i	0.845441	−	0.793274i
$904$	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	−0.976442	−	0.215781i	$-0.930770\pi$
$907$	0.449186	−	2.54746i	0.0149150	−	0.0845870i	0.991357	+	0.131194i	$0.0418812\pi$
$908$	−12.0885	−	20.9379i	−0.401172	−	0.694850i
$909$	−7.34074	−	33.7303i	−0.243477	−	1.11876i
$910$	−9.37230	+	67.0075i	−0.310689	+	2.22128i
$911$	12.1000	−	14.4203i	0.400892	−	0.477765i	−0.527399	−	0.849617i	$-0.676833\pi$
$911$	12.1000	−	14.4203i	0.400892	−	0.477765i	0.928292	+	0.371852i	$0.121277\pi$
$912$	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
$924$	41.7264	+	4.99281i	1.37270	+	0.164251i
$925$	−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	−0.928446	−	0.371467i	$-0.878855\pi$
$929$	2.16578	−	12.2827i	0.0710569	−	0.402983i	0.999503	−	0.0315170i	$-0.0100338\pi$
$930$	4.65995	+	3.75488i	0.152806	+	0.123127i
$931$	−11.5350	−	25.8164i	−0.378044	−	0.846100i
$932$	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	$-0.0881662\pi$
$937$	36.9165	+	21.3137i	1.20601	+	0.696290i	0.244124	+	0.969744i	$0.421500\pi$
$938$	−17.0670	+	52.6449i	−0.557259	+	1.71892i
$939$	−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	−0.209503	+	0.977808i	$0.567185\pi$
$941$	−37.0819	+	31.1154i	−1.20884	+	1.01433i	−0.999333	+	0.0365255i	$0.988371\pi$
$942$	7.49526	+	38.0667i	0.244209	+	1.24028i
$943$	−0.461024	−	1.26665i	−0.0150130	−	0.0412479i
$944$	18.2073			0.592596
$945$	40.2199	−	19.1447i	1.30835	−	0.622779i
$946$	54.0090			1.75598
$947$	9.84660	+	27.0533i	0.319972	+	0.879115i	0.990535	+	0.137262i	$0.0438303\pi$
$947$	9.84660	+	27.0533i	0.319972	+	0.879115i	−0.670563	+	0.741852i	$0.733947\pi$
$948$	−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
$952$	−4.49602	+	13.8684i	−0.145717	+	0.449477i
$953$	29.6982	+	17.1463i	0.962020	+	0.555422i	0.896794	−	0.442448i	$-0.145890\pi$
$953$	29.6982	+	17.1463i	0.962020	+	0.555422i	0.0652258	+	0.997871i	$0.479223\pi$
$954$	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
$959$	−0.943807	−	26.5263i	−0.0304771	−	0.856580i
$960$	−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
$966$	−6.36467	+	2.72483i	−0.204780	+	0.0876701i
$967$	−8.18346	−	46.4107i	−0.263162	−	1.49247i	−0.774218	−	0.632919i	$-0.781856\pi$
$967$	−8.18346	−	46.4107i	−0.263162	−	1.49247i	0.511055	−	0.859548i	$-0.329255\pi$
$968$	−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	$-0.457213\pi$
$971$	8.35204			0.268030			0.134015	+	0.990979i	$0.457213\pi$
$972$	−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	0.805855	−	0.592113i	$-0.201706\pi$
$977$	55.1882	−	9.73116i	1.76563	−	0.311327i	0.959771	+	0.280785i	$0.0905948\pi$
$978$	0.765198	+	38.4894i	0.0244683	+	1.23076i
$979$	14.4597	−	17.2325i	0.462135	−	0.550752i
$980$	15.6636	+	62.4727i	0.500356	+	1.99562i
$981$	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	$-0.889345\pi$
$983$	1.87543	−	10.6361i	0.0598170	−	0.339239i	0.999999	+	0.00143367i	$0.000456353\pi$
$984$	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
$987$	9.15952	+	39.1235i	0.291551	+	1.24531i
$988$	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	−0.937371	−	0.348332i	$-0.886748\pi$
$991$	−5.25786	+	9.10688i	−0.167021	+	0.289290i	0.770350	+	0.637621i	$0.220082\pi$
$992$	−2.69156	−	2.25849i	−0.0854572	−	0.0717071i
$993$	−7.86268	−	13.0141i	−0.249515	−	0.412990i
$994$	9.53816	+	15.2419i	0.302532	+	0.483444i
$995$	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	−0.747146	−	0.664659i	$-0.768577\pi$
$997$	−19.0094	−	52.2279i	−0.602034	−	1.65407i	0.145113	−	0.989415i	$-0.453646\pi$
$998$		−	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.20.4	yes	132
3.2	odd	2		567.2.be.a.62.20		132
7.6	odd	2	inner	189.2.be.a.20.3	✓	132
21.20	even	2		567.2.be.a.62.19		132
27.4	even	9		567.2.be.a.503.19		132
27.23	odd	18	inner	189.2.be.a.104.3	yes	132
189.104	even	18	inner	189.2.be.a.104.4	yes	132
189.139	odd	18		567.2.be.a.503.20		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.3	✓	132	7.6	odd	2	inner
189.2.be.a.20.4	yes	132	1.1	even	1	trivial
189.2.be.a.104.3	yes	132	27.23	odd	18	inner
189.2.be.a.104.4	yes	132	189.104	even	18	inner
567.2.be.a.62.19		132	21.20	even	2
567.2.be.a.62.20		132	3.2	odd	2
567.2.be.a.503.19		132	27.4	even	9
567.2.be.a.503.20		132	189.139	odd	18

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} +(2.51680 + 0.815925i) 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} +(-0.206962 - 5.81680i) 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} +(3.66829 + 2.74657i) 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} +(1.18747 - 8.48984i) 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} +(2.91777 - 9.64990i) 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} +(5.66853 + 4.10704i) 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} +(3.27276 + 3.62996i) 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} +(4.47463 + 6.55573i) 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} +(-18.4442 + 3.93313i) 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} +(-7.54658 - 4.00622i) 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} +(-12.9932 + 0.721122i) 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} +(5.83901 - 7.48374i) 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} +(4.22519 - 14.8086i) 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

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Representations

Groups

Database

Properties

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