LMFDB - Embedded newform 540.2.be.a.11.32

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [540,2,Mod(11,540)] 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("540.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(540, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 540 = 2^{2} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	540.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:	$4.31192170915$
Analytic rank:	$0$
Dimension:	$432$
Relative dimension:	$72$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.32
Character	$\chi$	$=$	540.11
Dual form			540.2.be.a.491.32

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.293022 - 1.38352i) q^{2} +(0.924312 - 1.46480i) q^{3} +(-1.82828 + 0.810806i) q^{4} +(-0.342020 + 0.939693i) q^{5} +(-2.29743 - 0.849589i) q^{6} +(-3.29465 - 0.580935i) q^{7} +(1.65749 + 2.29188i) q^{8} +(-1.29129 - 2.70787i) q^{9} +(1.40031 + 0.197842i) q^{10} +(-3.29684 + 1.19995i) q^{11} +(-0.502228 + 3.42750i) q^{12} +(-2.45658 + 2.06131i) q^{13} +(0.161666 + 4.72845i) q^{14} +(1.06033 + 1.36956i) q^{15} +(2.68519 - 2.96475i) q^{16} +(-1.99049 + 1.14921i) q^{17} +(-3.36803 + 2.58000i) q^{18} +(6.21007 + 3.58539i) q^{19} +(-0.136601 - 1.99533i) q^{20} +(-3.89624 + 4.28904i) q^{21} +(2.62620 + 4.20964i) q^{22} +(-1.19803 - 6.79437i) q^{23} +(4.88919 - 0.309489i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(3.57171 + 2.79472i) q^{26} +(-5.16005 - 0.611427i) q^{27} +(6.49455 - 1.60921i) q^{28} +(-3.26084 + 3.88612i) q^{29} +(1.58412 - 1.86830i) q^{30} +(-10.2081 + 1.79996i) q^{31} +(-4.88863 - 2.84628i) q^{32} +(-1.28962 + 5.93834i) q^{33} +(2.17322 + 2.41715i) q^{34} +(1.67274 - 2.89726i) q^{35} +(4.55640 + 3.90375i) q^{36} +(-1.43654 - 2.48815i) q^{37} +(3.14078 - 9.64238i) q^{38} +(0.748772 + 5.50370i) q^{39} +(-2.72056 + 0.773666i) q^{40} +(-1.45919 - 1.73899i) q^{41} +(7.07568 + 4.13376i) q^{42} +(4.01448 + 11.0297i) q^{43} +(5.05460 - 4.86693i) q^{44} +(2.98621 - 0.287273i) q^{45} +(-9.04913 + 3.64840i) q^{46} +(1.41945 - 8.05011i) q^{47} +(-1.86083 - 6.67363i) q^{48} +(3.93937 + 1.43381i) q^{49} +(-0.664844 + 1.24819i) q^{50} +(-0.156469 + 3.97791i) q^{51} +(2.81998 - 5.76045i) q^{52} -13.0945i q^{53} +(0.666085 + 7.31822i) q^{54} -3.50842i q^{55} +(-4.12943 - 8.51383i) q^{56} +(10.9919 - 5.78251i) q^{57} +(6.33204 + 3.37273i) q^{58} +(5.66375 + 2.06144i) q^{59} +(-3.04903 - 1.64421i) q^{60} +(0.987751 - 5.60182i) q^{61} +(5.48147 + 13.5957i) q^{62} +(2.68126 + 9.67164i) q^{63} +(-2.50543 + 7.59755i) q^{64} +(-1.09680 - 3.01344i) q^{65} +(8.59372 + 0.0441492i) q^{66} +(1.64134 + 1.95607i) q^{67} +(2.70738 - 3.71498i) q^{68} +(-11.0598 - 4.52524i) q^{69} +(-4.49858 - 1.46531i) q^{70} +(2.05687 + 3.56261i) q^{71} +(4.06580 - 7.44777i) q^{72} +(1.31500 - 2.27765i) q^{73} +(-3.02148 + 2.71656i) q^{74} +(-1.64962 + 0.527967i) q^{75} +(-14.2608 - 1.51992i) q^{76} +(11.5590 - 2.03816i) q^{77} +(7.39509 - 2.64865i) q^{78} +(-4.37177 + 5.21007i) q^{79} +(1.86757 + 3.53726i) q^{80} +(-5.66512 + 6.99331i) q^{81} +(-1.97836 + 2.52838i) q^{82} +(-11.3190 - 9.49778i) q^{83} +(3.64582 - 11.0006i) q^{84} +(-0.399117 - 2.26350i) q^{85} +(14.0835 - 8.78606i) q^{86} +(2.67836 + 8.36848i) q^{87} +(-8.21463 - 5.56704i) q^{88} +(-3.68021 - 2.12477i) q^{89} +(-1.27248 - 4.04732i) q^{90} +(9.29104 - 5.36419i) q^{91} +(7.69925 + 11.4506i) q^{92} +(-6.79885 + 16.6165i) q^{93} +(-11.5534 + 0.395014i) q^{94} +(-5.49313 + 4.60928i) q^{95} +(-8.68786 + 4.53002i) q^{96} +(5.16206 - 1.87884i) q^{97} +(0.829393 - 5.87035i) q^{98} +(7.50649 + 7.37792i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) $ 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	−0.293022	−	1.38352i	−0.207198	−	0.978299i
$2$	−0.293022	−	1.38352i	−0.207198	−	0.978299i
$3$	0.924312	−	1.46480i	0.533652	−	0.845704i
$3$	0.924312	−	1.46480i	0.533652	−	0.845704i
$4$	−1.82828	+	0.810806i	−0.914138	+	0.405403i
$5$	−0.342020	+	0.939693i	−0.152956	+	0.420243i
$5$	−0.342020	+	0.939693i	−0.152956	+	0.420243i
$6$	−2.29743	−	0.849589i	−0.937923	−	0.346843i
$7$	−3.29465	−	0.580935i	−1.24526	−	0.219573i	−0.488091	−	0.872793i	$-0.662307\pi$
$7$	−3.29465	−	0.580935i	−1.24526	−	0.219573i	−0.757168	+	0.653220i	$0.773418\pi$
$8$	1.65749	+	2.29188i	0.586013	+	0.810302i
$9$	−1.29129	−	2.70787i	−0.430431	−	0.902623i
$10$	1.40031	+	0.197842i	0.442816	+	0.0625633i
$11$	−3.29684	+	1.19995i	−0.994033	+	0.361799i	−0.787281	−	0.616595i	$-0.788512\pi$
$11$	−3.29684	+	1.19995i	−0.994033	+	0.361799i	−0.206753	+	0.978393i	$0.566290\pi$
$12$	−0.502228	+	3.42750i	−0.144981	+	0.989434i
$13$	−2.45658	+	2.06131i	−0.681332	+	0.571705i	−0.916395	−	0.400275i	$-0.868915\pi$
$13$	−2.45658	+	2.06131i	−0.681332	+	0.571705i	0.235063	+	0.971980i	$0.424470\pi$
$14$	0.161666	+	4.72845i	0.0432072	+	1.26373i
$15$	1.06033	+	1.36956i	0.273776	+	0.353619i
$16$	2.68519	−	2.96475i	0.671297	−	0.741188i
$17$	−1.99049	+	1.14921i	−0.482765	+	0.278725i	−0.721568	−	0.692344i	$-0.756578\pi$
$17$	−1.99049	+	1.14921i	−0.482765	+	0.278725i	0.238803	+	0.971068i	$0.423245\pi$
$18$	−3.36803	+	2.58000i	−0.793851	+	0.608112i
$19$	6.21007	+	3.58539i	1.42469	+	0.822544i	0.996695	−	0.0812381i	$-0.0258874\pi$
$19$	6.21007	+	3.58539i	1.42469	+	0.822544i	0.427993	+	0.903782i	$0.359221\pi$
$20$	−0.136601	−	1.99533i	−0.0305449	−	0.446169i
$21$	−3.89624	+	4.28904i	−0.850229	+	0.935946i
$22$	2.62620	+	4.20964i	0.559909	+	0.897498i
$23$	−1.19803	−	6.79437i	−0.249807	−	1.41672i	−0.809059	−	0.587727i	$-0.800023\pi$
$23$	−1.19803	−	6.79437i	−0.249807	−	1.41672i	0.559252	−	0.828997i	$-0.311088\pi$
$24$	4.88919	−	0.309489i	0.998003	−	0.0631742i
$25$	−0.766044	−	0.642788i	−0.153209	−	0.128558i
$26$	3.57171	+	2.79472i	0.700469	+	0.548090i
$27$	−5.16005	−	0.611427i	−0.993053	−	0.117669i
$28$	6.49455	−	1.60921i	1.22735	−	0.304112i
$29$	−3.26084	+	3.88612i	−0.605523	+	0.721634i	−0.978509	−	0.206203i	$-0.933889\pi$
$29$	−3.26084	+	3.88612i	−0.605523	+	0.721634i	0.372986	+	0.927837i	$0.378334\pi$
$30$	1.58412	−	1.86830i	0.289220	−	0.341104i
$31$	−10.2081	+	1.79996i	−1.83342	+	0.323282i	−0.980161	−	0.198204i	$-0.936489\pi$
$31$	−10.2081	+	1.79996i	−1.83342	+	0.323282i	−0.853260	+	0.521485i	$0.825378\pi$
$32$	−4.88863	−	2.84628i	−0.864195	−	0.503157i
$33$	−1.28962	+	5.93834i	−0.224493	+	1.03373i
$34$	2.17322	+	2.41715i	0.372704	+	0.414537i
$35$	1.67274	−	2.89726i	0.282744	−	0.489727i
$36$	4.55640	+	3.90375i	0.759400	+	0.650624i
$37$	−1.43654	−	2.48815i	−0.236165	−	0.409050i	0.723446	−	0.690381i	$-0.242557\pi$
$37$	−1.43654	−	2.48815i	−0.236165	−	0.409050i	−0.959611	+	0.281332i	$0.909224\pi$
$38$	3.14078	−	9.64238i	0.509502	−	1.56420i
$39$	0.748772	+	5.50370i	0.119899	+	0.881297i
$40$	−2.72056	+	0.773666i	−0.430158	+	0.122327i
$41$	−1.45919	−	1.73899i	−0.227887	−	0.271585i	0.639969	−	0.768400i	$-0.278947\pi$
$41$	−1.45919	−	1.73899i	−0.227887	−	0.271585i	−0.867856	+	0.496816i	$0.834503\pi$
$42$	7.07568	+	4.13376i	1.09180	+	0.637852i
$43$	4.01448	+	11.0297i	0.612202	+	1.68201i	0.725305	+	0.688427i	$0.241699\pi$
$43$	4.01448	+	11.0297i	0.612202	+	1.68201i	−0.113103	+	0.993583i	$0.536079\pi$
$44$	5.05460	−	4.86693i	0.762010	−	0.733718i
$45$	2.98621	−	0.287273i	0.445159	−	0.0428241i
$46$	−9.04913	+	3.64840i	−1.33422	+	0.537928i
$47$	1.41945	−	8.05011i	0.207048	−	1.17423i	−0.687136	−	0.726529i	$-0.741132\pi$
$47$	1.41945	−	8.05011i	0.207048	−	1.17423i	0.894184	−	0.447700i	$-0.147757\pi$
$48$	−1.86083	−	6.67363i	−0.268587	−	0.963255i
$49$	3.93937	+	1.43381i	0.562767	+	0.204831i
$50$	−0.664844	+	1.24819i	−0.0940232	+	0.176521i
$51$	−0.156469	+	3.97791i	−0.0219100	+	0.557018i
$52$	2.81998	−	5.76045i	0.391060	−	0.798831i
$53$		−	13.0945i		−	1.79866i	−0.437266	−	0.899332i	$-0.644053\pi$
$53$		−	13.0945i		−	1.79866i	0.437266	−	0.899332i	$-0.355947\pi$
$54$	0.666085	+	7.31822i	0.0906427	+	0.995883i
$55$		−	3.50842i		−	0.473075i
$56$	−4.12943	−	8.51383i	−0.551818	−	1.13771i
$57$	10.9919	−	5.78251i	1.45592	−	0.765912i
$58$	6.33204	+	3.37273i	0.831437	+	0.442862i
$59$	5.66375	+	2.06144i	0.737358	+	0.268376i	0.683276	−	0.730160i	$-0.260555\pi$
$59$	5.66375	+	2.06144i	0.737358	+	0.268376i	0.0540819	+	0.998537i	$0.482777\pi$
$60$	−3.04903	−	1.64421i	−0.393628	−	0.212267i
$61$	0.987751	−	5.60182i	0.126469	−	0.717239i	−0.853956	−	0.520345i	$-0.825803\pi$
$61$	0.987751	−	5.60182i	0.126469	−	0.717239i	0.980425	−	0.196894i	$-0.0630855\pi$
$62$	5.48147	+	13.5957i	0.696147	+	1.72665i
$63$	2.68126	+	9.67164i	0.337807	+	1.21851i
$64$	−2.50543	+	7.59755i	−0.313178	+	0.949694i
$65$	−1.09680	−	3.01344i	−0.136041	−	0.373771i
$66$	8.59372	+	0.0441492i	1.05781	+	0.00543439i
$67$	1.64134	+	1.95607i	0.200521	+	0.238972i	0.856929	−	0.515434i	$-0.172369\pi$
$67$	1.64134	+	1.95607i	0.200521	+	0.238972i	−0.656408	+	0.754406i	$0.727925\pi$
$68$	2.70738	−	3.71498i	0.328318	−	0.450507i
$69$	−11.0598	−	4.52524i	−1.33144	−	0.544775i
$70$	−4.49858	−	1.46531i	−0.537684	−	0.175138i
$71$	2.05687	+	3.56261i	0.244106	+	0.422804i	0.961880	−	0.273472i	$-0.0881722\pi$
$71$	2.05687	+	3.56261i	0.244106	+	0.422804i	−0.717774	+	0.696276i	$0.754839\pi$
$72$	4.06580	−	7.44777i	0.479159	−	0.877728i
$73$	1.31500	−	2.27765i	0.153909	−	0.266579i	−0.778752	−	0.627332i	$-0.784147\pi$
$73$	1.31500	−	2.27765i	0.153909	−	0.266579i	0.932661	+	0.360753i	$0.117480\pi$
$74$	−3.02148	+	2.71656i	−0.351240	+	0.315794i
$75$	−1.64962	+	0.527967i	−0.190482	+	0.0609644i
$76$	−14.2608	−	1.51992i	−1.63582	−	0.174346i
$77$	11.5590	−	2.03816i	1.31727	−	0.232270i
$78$	7.39509	−	2.64865i	0.837329	−	0.299900i
$79$	−4.37177	+	5.21007i	−0.491862	+	0.586179i	−0.953690	−	0.300791i	$-0.902749\pi$
$79$	−4.37177	+	5.21007i	−0.491862	+	0.586179i	0.461828	+	0.886970i	$0.347194\pi$
$80$	1.86757	+	3.53726i	0.208801	+	0.395477i
$81$	−5.66512	+	6.99331i	−0.629458	+	0.777035i
$82$	−1.97836	+	2.52838i	−0.218474	+	0.279213i
$83$	−11.3190	−	9.49778i	−1.24242	−	1.04252i	−0.997331	−	0.0730170i	$-0.976737\pi$
$83$	−11.3190	−	9.49778i	−1.24242	−	1.04252i	−0.245092	−	0.969500i	$-0.578818\pi$
$84$	3.64582	−	11.0006i	0.397792	−	1.20027i
$85$	−0.399117	−	2.26350i	−0.0432903	−	0.245511i
$86$	14.0835	−	8.78606i	1.51866	−	0.947425i
$87$	2.67836	+	8.36848i	0.287151	+	0.897195i
$88$	−8.21463	−	5.56704i	−0.875682	−	0.593449i
$89$	−3.68021	−	2.12477i	−0.390102	−	0.225225i	0.292102	−	0.956387i	$-0.405645\pi$
$89$	−3.68021	−	2.12477i	−0.390102	−	0.225225i	−0.682204	+	0.731162i	$0.738979\pi$
$90$	−1.27248	−	4.04732i	−0.134131	−	0.426625i
$91$	9.29104	−	5.36419i	0.973966	−	0.562319i
$92$	7.69925	+	11.4506i	0.802702	+	1.19381i
$93$	−6.79885	+	16.6165i	−0.705008	+	1.72305i
$94$	−11.5534	+	0.395014i	−1.19165	+	0.0407426i
$95$	−5.49313	+	4.60928i	−0.563583	+	0.472902i
$96$	−8.68786	+	4.53002i	−0.886701	+	0.462343i
$97$	5.16206	−	1.87884i	0.524128	−	0.190767i	−0.0663867	−	0.997794i	$-0.521147\pi$
$97$	5.16206	−	1.87884i	0.524128	−	0.190767i	0.590514	+	0.807027i	$0.298925\pi$
$98$	0.829393	−	5.87035i	0.0837814	−	0.592995i
$99$	7.50649	+	7.37792i	0.754431	+	0.741508i
$100$	1.92172	+	0.554080i	0.192172	+	0.0554080i
$101$	−19.5765	−	3.45187i	−1.94794	−	0.343474i	−0.999661	−	0.0260250i	$-0.991715\pi$
$101$	−19.5765	−	3.45187i	−1.94794	−	0.343474i	−0.948275	−	0.317449i	$-0.897174\pi$
$102$	5.54938	−	0.949136i	0.549470	−	0.0939785i
$103$	−0.567658	+	1.55963i	−0.0559331	+	0.153675i	−0.964512	−	0.264037i	$-0.914946\pi$
$103$	−0.567658	+	1.55963i	−0.0559331	+	0.153675i	0.908579	+	0.417712i	$0.137168\pi$
$104$	−8.79604	−	2.21356i	−0.862523	−	0.217058i
$105$	−2.69779	−	5.12821i	−0.263277	−	0.500462i
$106$	−18.1165	+	3.83697i	−1.75963	+	0.372679i
$107$	−7.95602			−0.769137			−0.384569	−	0.923096i	$-0.625650\pi$
$107$	−7.95602			−0.769137			−0.384569	+	0.923096i	$0.625650\pi$
$108$	9.92975	−	3.06594i	0.955491	−	0.295021i
$109$	8.28431			0.793493			0.396747	−	0.917928i	$-0.370139\pi$
$109$	8.28431			0.793493			0.396747	+	0.917928i	$0.370139\pi$
$110$	−4.85398	+	1.02804i	−0.462809	+	0.0980201i
$111$	−4.97246	−	0.195589i	−0.471965	−	0.0185645i
$112$	−10.5691	+	8.20790i	−0.998684	+	0.775574i
$113$	0.384656	−	1.05683i	0.0361854	−	0.0994187i	−0.920284	−	0.391251i	$-0.872043\pi$
$113$	0.384656	−	1.05683i	0.0361854	−	0.0994187i	0.956470	+	0.291832i	$0.0942648\pi$
$114$	−11.2211	−	13.5132i	−1.05095	−	1.26563i
$115$	6.79437	+	1.19803i	0.633578	+	0.111717i
$116$	2.81083	−	9.74881i	0.260979	−	0.905154i
$117$	8.75393	+	3.99033i	0.809301	+	0.368906i
$118$	1.19244	−	8.43998i	0.109773	−	0.776964i
$119$	7.22558	−	2.62990i	0.662368	−	0.241082i
$120$	−1.38138	+	4.70019i	−0.126102	+	0.429067i
$121$	1.00276	−	0.841413i	0.0911597	−	0.0764921i
$122$	−8.03968	+	0.274878i	−0.727878	+	0.0248863i
$123$	−3.89602	+	0.530050i	−0.351293	+	0.0477930i
$124$	17.2037	−	11.5676i	1.54494	−	1.03880i
$125$	0.866025	−	0.500000i	0.0774597	−	0.0447214i
$126$	12.5953	−	6.54359i	1.12208	−	0.582949i
$127$	−8.85407	−	5.11190i	−0.785672	−	0.453608i	0.0527647	−	0.998607i	$-0.483197\pi$
$127$	−8.85407	−	5.11190i	−0.785672	−	0.453608i	−0.838437	+	0.544999i	$0.816530\pi$
$128$	11.2455	+	1.24007i	0.993975	+	0.109607i
$129$	19.8669	+	4.31446i	1.74919	+	0.379867i
$130$	−3.84777	+	2.40045i	−0.337472	+	0.210534i
$131$	−0.916038	−	5.19511i	−0.0800346	−	0.453899i	−0.998318	−	0.0579751i	$-0.981536\pi$
$131$	−0.916038	−	5.19511i	−0.0800346	−	0.453899i	0.918283	−	0.395924i	$-0.129576\pi$
$132$	−2.45707	−	11.9026i	−0.213860	−	1.03598i
$133$	−18.3771	−	15.4202i	−1.59350	−	1.33710i
$134$	2.22532	−	2.84400i	0.192238	−	0.245684i
$135$	2.33940	−	4.63974i	0.201343	−	0.399326i
$136$	−5.93308	−	2.65716i	−0.508757	−	0.227849i
$137$	−0.188784	+	0.224983i	−0.0161289	+	0.0192216i	−0.774049	−	0.633126i	$-0.781771\pi$
$137$	−0.188784	+	0.224983i	−0.0161289	+	0.0192216i	0.757920	+	0.652348i	$0.226216\pi$
$138$	−3.02003	+	16.6275i	−0.257082	+	1.41542i
$139$	−0.720591	+	0.127060i	−0.0611198	+	0.0107771i	−0.204124	−	0.978945i	$-0.565435\pi$
$139$	−0.720591	+	0.127060i	−0.0611198	+	0.0107771i	0.143005	+	0.989722i	$0.454324\pi$
$140$	−0.709106	+	6.65326i	−0.0599304	+	0.562303i
$141$	−10.4798	−	9.52003i	−0.882559	−	0.801731i
$142$	4.32625	−	3.88966i	0.363050	−	0.326413i
$143$	5.62546	−	9.74358i	0.470424	−	0.814799i
$144$	−11.4955	−	3.44277i	−0.957961	−	0.286898i
$145$	−2.53648	−	4.39332i	−0.210644	−	0.364845i
$146$	−3.53651	−	1.15194i	−0.292684	−	0.0953349i
$147$	5.74146	−	4.44511i	0.473548	−	0.366626i
$148$	4.64379	+	3.38428i	0.381717	+	0.278186i
$149$	−1.27069	−	1.51435i	−0.104099	−	0.124061i	0.711479	−	0.702707i	$-0.248026\pi$
$149$	−1.27069	−	1.51435i	−0.104099	−	0.124061i	−0.815579	+	0.578646i	$0.803581\pi$
$150$	1.21383	+	2.12758i	0.0991089	+	0.173717i
$151$	5.01436	+	13.7768i	0.408062	+	1.12114i	0.958208	+	0.286073i	$0.0923501\pi$
$151$	5.01436	+	13.7768i	0.408062	+	1.12114i	−0.550145	+	0.835069i	$0.685428\pi$
$152$	2.07588	+	20.1755i	0.168376	+	1.63645i
$153$	5.68222	+	3.90602i	0.459380	+	0.315783i
$154$	−6.20689	−	15.3949i	−0.500166	−	1.24056i
$155$	1.79996	−	10.2081i	0.144576	−	0.819931i
$156$	−5.83139	−	9.45517i	−0.466885	−	0.757019i
$157$	−6.87422	−	2.50201i	−0.548622	−	0.199682i	0.0528119	−	0.998604i	$-0.483182\pi$
$157$	−6.87422	−	2.50201i	−0.548622	−	0.199682i	−0.601434	+	0.798922i	$0.705404\pi$
$158$	8.48928	+	4.52178i	0.675371	+	0.359734i
$159$	−19.1808	−	12.1034i	−1.52114	−	0.959861i
$160$	4.34664	−	3.62032i	0.343632	−	0.286211i
$161$			23.0810i			1.81904i
$162$	11.3354	+	5.78864i	0.890595	+	0.454798i
$163$			5.01110i			0.392500i	0.980554	+	0.196250i	$0.0628763\pi$
$163$			5.01110i			0.392500i	−0.980554	+	0.196250i	$0.937124\pi$
$164$	4.07778	+	1.99624i	0.318421	+	0.155880i
$165$	−5.13914	−	3.24288i	−0.400082	−	0.252457i
$166$	−9.82368	+	18.4432i	−0.762466	+	1.43147i
$167$	0.0590359	+	0.0214873i	0.00456833	+	0.00166274i	0.344303	−	0.938858i	$-0.388115\pi$
$167$	0.0590359	+	0.0214873i	0.00456833	+	0.00166274i	−0.339735	+	0.940521i	$0.610337\pi$
$168$	−16.2880	−	1.82065i	−1.25664	−	0.140466i
$169$	−0.471668	+	2.67496i	−0.0362821	+	0.205766i
$170$	−3.01466	+	1.21544i	−0.231214	+	0.0932203i
$171$	1.68973	−	21.4459i	0.129217	−	1.64001i
$172$	−16.2825	−	16.9103i	−1.24153	−	1.28940i
$173$	7.43436	+	20.4257i	0.565224	+	1.55294i	0.811873	+	0.583834i	$0.198448\pi$
$173$	7.43436	+	20.4257i	0.565224	+	1.55294i	−0.246649	+	0.969105i	$0.579330\pi$
$174$	10.7932	−	6.15773i	0.818228	−	0.466816i
$175$	2.15043	+	2.56278i	0.162557	+	0.193728i
$176$	−5.29507	+	12.9964i	−0.399131	+	0.979640i
$177$	8.25468	−	6.39087i	0.620459	−	0.480367i
$178$	−1.86129	+	5.71427i	−0.139510	+	0.428302i
$179$	0.858099	+	1.48627i	0.0641373	+	0.111089i	0.896311	−	0.443426i	$-0.146237\pi$
$179$	0.858099	+	1.48627i	0.0641373	+	0.111089i	−0.832174	+	0.554515i	$0.812904\pi$
$180$	−5.22670	+	2.94645i	−0.389575	+	0.219616i
$181$	2.23461	−	3.87045i	0.166097	−	0.287689i	−0.770947	−	0.636899i	$-0.780217\pi$
$181$	2.23461	−	3.87045i	0.166097	−	0.287689i	0.937044	+	0.349210i	$0.113550\pi$
$182$	−10.1440	−	11.2826i	−0.751920	−	0.836319i
$183$	−7.29257	−	6.62469i	−0.539082	−	0.489711i
$184$	13.5862	−	14.0074i	1.00158	−	1.03264i
$185$	2.82942	−	0.498904i	0.208023	−	0.0366801i
$186$	24.9815	+	4.53737i	1.83174	+	0.332696i
$187$	5.18333	−	6.17725i	0.379042	−	0.451725i
$188$	3.93192	+	15.8687i	0.286765	+	1.15735i
$189$	16.6454	+	5.01209i	1.21077	+	0.364576i
$190$	7.98666	+	6.24925i	0.579413	+	0.453369i
$191$	4.98368	+	4.18181i	0.360607	+	0.302585i	0.805033	−	0.593231i	$-0.202148\pi$
$191$	4.98368	+	4.18181i	0.360607	+	0.302585i	−0.444426	+	0.895816i	$0.646592\pi$
$192$	8.81312	+	10.6925i	0.636032	+	0.771662i
$193$	0.433360	+	2.45771i	0.0311939	+	0.176910i	0.996424	−	0.0844915i	$-0.0269266\pi$
$193$	0.433360	+	2.45771i	0.0311939	+	0.176910i	−0.965230	+	0.261401i	$0.915815\pi$
$194$	−4.11201	−	6.59129i	−0.295225	−	0.473227i
$195$	−5.42788	−	1.17876i	−0.388698	−	0.0844127i
$196$	−8.36480	+	0.572657i	−0.597486	+	0.0409041i
$197$	−0.904830	−	0.522404i	−0.0644664	−	0.0372197i	0.467420	−	0.884035i	$-0.345183\pi$
$197$	−0.904830	−	0.522404i	−0.0644664	−	0.0372197i	−0.531887	+	0.846815i	$0.678517\pi$
$198$	8.00795	−	12.5473i	0.569101	−	0.891698i
$199$	4.50825	−	2.60284i	0.319581	−	0.184510i	−0.331625	−	0.943411i	$-0.607597\pi$
$199$	4.50825	−	2.60284i	0.319581	−	0.184510i	0.651206	+	0.758901i	$0.274263\pi$
$200$	0.203478	−	2.82110i	0.0143881	−	0.199482i
$201$	4.38236	−	0.596216i	0.309108	−	0.0420538i
$202$	0.960608	+	28.0961i	0.0675881	+	1.97683i
$203$	13.0009	−	10.9091i	0.912485	−	0.765666i
$204$	−2.93924	−	7.39958i	−0.205788	−	0.518074i
$205$	2.13319	−	0.776417i	0.148988	−	0.0542273i
$206$	2.32412	+	0.328364i	0.161929	+	0.0228782i
$207$	−16.8513	+	12.0176i	−1.17124	+	0.835284i
$208$	−0.485086	+	12.8182i	−0.0336347	+	0.888779i
$209$	−24.7759	−	4.36865i	−1.71378	−	0.302186i
$210$	−6.30448	+	5.23513i	−0.435051	+	0.361259i
$211$	8.81073	−	24.2073i	0.606556	−	1.66650i	−0.131140	−	0.991364i	$-0.541864\pi$
$211$	8.81073	−	24.2073i	0.606556	−	1.66650i	0.737695	−	0.675134i	$-0.235914\pi$
$212$	10.6171	+	23.9403i	0.729184	+	1.64423i
$213$	7.11971	+	0.280050i	0.487835	+	0.0191887i
$214$	2.33129	+	11.0073i	0.159364	+	0.752446i
$215$	−11.7375			−0.800494
$216$	−7.15144	−	12.8397i	−0.486594	−	0.873628i
$217$	34.6776			2.35407
$218$	−2.42749	−	11.4615i	−0.164410	−	0.776274i
$219$	−2.12084	−	4.03148i	−0.143313	−	0.272422i
$220$	2.84465	+	6.41436i	0.191786	+	0.432456i
$221$	2.52091	−	6.92615i	0.169575	−	0.465903i
$222$	1.18644	+	6.93683i	0.0796285	+	0.465569i
$223$	22.2984	+	3.93181i	1.49321	+	0.263294i	0.859844	−	0.510557i	$-0.170561\pi$
$223$	22.2984	+	3.93181i	1.49321	+	0.263294i	0.633368	+	0.773851i	$0.281672\pi$
$224$	14.4528	+	12.2175i	0.965668	+	0.816315i
$225$	−0.751397	+	2.90438i	−0.0500931	+	0.193625i
$226$	−1.57487	−	0.222505i	−0.104759	−	0.0148008i
$227$	18.6663	−	6.79397i	1.23892	−	0.450932i	0.362280	−	0.932069i	$-0.381999\pi$
$227$	18.6663	−	6.79397i	1.23892	−	0.450932i	0.876645	+	0.481138i	$0.159776\pi$
$228$	−15.4078	+	19.4843i	−1.02041	+	1.29038i
$229$	−5.92513	+	4.97178i	−0.391544	+	0.328544i	−0.817214	−	0.576334i	$-0.804483\pi$
$229$	−5.92513	+	4.97178i	−0.391544	+	0.328544i	0.425670	+	0.904878i	$0.360038\pi$
$230$	−0.333396	−	9.75123i	−0.0219835	−	0.642977i
$231$	7.69862	−	18.8156i	0.506532	−	1.23797i
$232$	−14.3113	−	1.03224i	−0.939586	−	0.0677696i
$233$	5.62257	−	3.24619i	0.368347	−	0.212665i	−0.304389	−	0.952548i	$-0.598452\pi$
$233$	5.62257	−	3.24619i	0.368347	−	0.212665i	0.672736	+	0.739883i	$0.265119\pi$
$234$	2.95562	−	13.2805i	0.193215	−	0.868175i
$235$	7.07915	+	4.08715i	0.461793	+	0.266616i
$236$	−12.0263	+	0.823326i	−0.782848	+	0.0535940i
$237$	3.59085	+	11.2195i	0.233251	+	0.728786i
$238$	−5.75578	−	9.22615i	−0.373092	−	0.598043i
$239$	−1.62223	−	9.20012i	−0.104933	−	0.595106i	−0.991247	−	0.132021i	$-0.957853\pi$
$239$	−1.62223	−	9.20012i	−0.104933	−	0.595106i	0.886314	−	0.463086i	$-0.153258\pi$
$240$	6.90760	+	0.533910i	0.445884	+	0.0344638i
$241$	−14.1729	−	11.8925i	−0.912959	−	0.766064i	0.0597204	−	0.998215i	$-0.480979\pi$
$241$	−14.1729	−	11.8925i	−0.912959	−	0.766064i	−0.972680	+	0.232151i	$0.925424\pi$
$242$	−1.45794	−	1.14079i	−0.0937202	−	0.0733325i
$243$	5.00748	+	14.7623i	0.321230	+	0.947001i
$244$	2.73610	+	11.0425i	0.175161	+	0.706926i
$245$	−2.69469	+	3.21140i	−0.172157	+	0.205169i
$246$	1.87496	+	5.23492i	0.119543	+	0.333767i
$247$	−22.6461	+	3.99312i	−1.44094	+	0.254076i
$248$	−21.0451	−	20.4122i	−1.33636	−	1.29618i
$249$	−24.3747	+	7.80121i	−1.54468	+	0.494381i
$250$	−0.945526	−	1.05166i	−0.0598003	−	0.0665126i
$251$	−2.34514	+	4.06191i	−0.148024	+	0.256385i	−0.930497	−	0.366299i	$-0.880625\pi$
$251$	−2.34514	+	4.06191i	−0.148024	+	0.256385i	0.782473	+	0.622685i	$0.213958\pi$
$252$	−12.7439	−	15.5084i	−0.802790	−	0.976940i
$253$	12.1026	+	20.9624i	0.760885	+	1.31789i
$254$	−4.47800	+	13.7477i	−0.280975	+	0.862609i
$255$	−3.68449	−	1.50756i	−0.230732	−	0.0944069i
$256$	−1.57953	−	15.9218i	−0.0987206	−	0.995115i
$257$	−1.34330	−	1.60088i	−0.0837928	−	0.0998604i	0.722519	−	0.691351i	$-0.242984\pi$
$257$	−1.34330	−	1.60088i	−0.0837928	−	0.0998604i	−0.806312	+	0.591491i	$0.798540\pi$
$258$	0.147703	−	28.7506i	0.00919557	−	1.78993i
$259$	3.28742	+	9.03212i	0.204271	+	0.561229i
$260$	4.44857	+	4.62010i	0.275888	+	0.286527i
$261$	14.7338	+	3.81181i	0.912000	+	0.235945i
$262$	−6.91914	+	2.78964i	−0.427466	+	0.172345i
$263$	−1.56850	+	8.89543i	−0.0967181	+	0.548516i	0.897489	+	0.441036i	$0.145389\pi$
$263$	−1.56850	+	8.89543i	−0.0967181	+	0.548516i	−0.994207	+	0.107479i	$0.965722\pi$
$264$	−15.7475	+	6.88712i	−0.969191	+	0.423873i
$265$	12.3048	+	4.47857i	0.755877	+	0.275117i
$266$	−15.9494	+	29.9436i	−0.977918	+	1.83596i
$267$	−6.51404	+	3.42683i	−0.398653	+	0.209719i
$268$	−4.58681	−	2.24543i	−0.280184	−	0.137161i
$269$			8.69730i			0.530284i	0.964209	+	0.265142i	$0.0854188\pi$
$269$			8.69730i			0.530284i	−0.964209	+	0.265142i	$0.914581\pi$
$270$	−7.10469	−	1.87706i	−0.432378	−	0.114234i
$271$			19.7163i			1.19768i	0.800868	+	0.598841i	$0.204372\pi$
$271$			19.7163i			1.19768i	−0.800868	+	0.598841i	$0.795628\pi$
$272$	−1.93772	+	8.98716i	−0.117491	+	0.544927i
$273$	0.730351	−	18.5677i	0.0442028	−	1.12377i
$274$	0.366588	+	0.195261i	0.0221464	+	0.0117962i
$275$	3.29684	+	1.19995i	0.198807	+	0.0723597i
$276$	23.8894	−	0.693931i	1.43797	−	0.0417697i
$277$	0.122862	−	0.696782i	0.00738203	−	0.0418656i	−0.980894	−	0.194542i	$-0.937678\pi$
$277$	0.122862	−	0.696782i	0.00738203	−	0.0418656i	0.988276	+	0.152676i	$0.0487891\pi$
$278$	0.386939	+	0.959724i	0.0232071	+	0.0575604i
$279$	18.0556	+	25.3178i	1.08096	+	1.51574i
$280$	9.41273	−	0.968488i	0.562518	−	0.0578782i
$281$	9.36884	+	25.7407i	0.558898	+	1.53556i	0.821239	+	0.570585i	$0.193283\pi$
$281$	9.36884	+	25.7407i	0.558898	+	1.53556i	−0.262341	+	0.964975i	$0.584494\pi$
$282$	−10.1004	+	17.2886i	−0.601469	+	1.02952i
$283$	−3.74805	−	4.46675i	−0.222799	−	0.265521i	0.643053	−	0.765821i	$-0.277667\pi$
$283$	−3.74805	−	4.46675i	−0.222799	−	0.265521i	−0.865852	+	0.500300i	$0.833223\pi$
$284$	−6.64912	−	4.84571i	−0.394552	−	0.287540i
$285$	1.67432	+	12.3068i	0.0991783	+	0.728990i
$286$	−15.1289	−	4.92787i	−0.894588	−	0.291391i
$287$	3.79727	+	6.57706i	0.224145	+	0.388231i
$288$	−1.39471	+	16.9132i	−0.0821843	+	0.996617i
$289$	−5.85863	+	10.1474i	−0.344625	+	0.596908i
$290$	−5.33502	+	4.79663i	−0.313283	+	0.281668i
$291$	2.01923	−	9.29803i	0.118369	−	0.545060i
$292$	−0.557455	+	5.23039i	−0.0326226	+	0.306085i
$293$	19.0196	−	3.35367i	1.11114	−	0.195924i	0.412191	−	0.911097i	$-0.364764\pi$
$293$	19.0196	−	3.35367i	1.11114	−	0.195924i	0.698947	+	0.715174i	$0.253652\pi$
$294$	−7.83229	−	6.64094i	−0.456788	−	0.387307i
$295$	−3.87424	+	4.61713i	−0.225567	+	0.268820i
$296$	3.32150	−	7.41646i	0.193058	−	0.431073i
$297$	17.7455	−	4.17603i	1.02970	−	0.242318i
$298$	−1.72280	+	2.20178i	−0.0997994	+	0.127545i
$299$	16.9484	+	14.2214i	0.980150	+	0.822443i
$300$	2.58788	−	2.30279i	0.149412	−	0.132952i
$301$	−6.81875	−	38.6711i	−0.393026	−	2.22896i
$302$	17.5913	−	10.9744i	1.01226	−	0.631505i
$303$	−23.1511	+	25.4851i	−1.33000	+	1.46408i
$304$	27.3050	−	8.78389i	1.56605	−	0.503791i
$305$	4.92615	+	2.84412i	0.282071	+	0.162854i
$306$	3.73906	−	9.00604i	0.213748	−	0.514841i
$307$	4.60382	−	2.65802i	0.262754	−	0.151701i	−0.362836	−	0.931853i	$-0.618192\pi$
$307$	4.60382	−	2.65802i	0.262754	−	0.151701i	0.625590	+	0.780152i	$0.284858\pi$
$308$	−19.4805	+	13.0984i	−1.11000	+	0.746353i
$309$	1.75985	+	2.27309i	0.100115	+	0.129312i
$310$	−14.6505	+	0.500903i	−0.832093	+	0.0284494i
$311$	−5.65210	+	4.74268i	−0.320501	+	0.268933i	−0.788816	−	0.614629i	$-0.789306\pi$
$311$	−5.65210	+	4.74268i	−0.320501	+	0.268933i	0.468315	+	0.883562i	$0.344861\pi$
$312$	−11.3727	+	10.8384i	−0.643854	+	0.613606i
$313$	−18.4368	+	6.71044i	−1.04211	+	0.379296i	−0.805679	−	0.592353i	$-0.798199\pi$
$313$	−18.4368	+	6.71044i	−1.04211	+	0.379296i	−0.236429	+	0.971649i	$0.575977\pi$
$314$	−1.44729	+	10.2438i	−0.0816756	+	0.578090i
$315$	−10.0054	−	0.788334i	−0.563741	−	0.0444176i
$316$	3.76845	−	13.0701i	0.211992	−	0.735251i
$317$	−21.3647	−	3.76718i	−1.19996	−	0.211586i	−0.462280	−	0.886734i	$-0.652969\pi$
$317$	−21.3647	−	3.76718i	−1.19996	−	0.211586i	−0.737682	+	0.675148i	$0.764080\pi$
$318$	−11.1249	+	30.0837i	−0.623854	+	1.68701i
$319$	6.08731	−	16.7247i	0.340824	−	0.936406i
$320$	−6.28246	−	4.95285i	−0.351200	−	0.276873i
$321$	−7.35385	+	11.6540i	−0.410452	+	0.650463i
$322$	31.9332	−	6.76325i	1.77957	−	0.376901i
$323$	−16.4815			−0.917053
$324$	4.68719	−	17.3790i	0.260399	−	0.965501i
$325$	3.20683			0.177883
$326$	6.93297	−	1.46836i	0.383982	−	0.0813250i
$327$	7.65729	−	12.1349i	0.423449	−	0.671061i
$328$	1.56697	−	6.22665i	0.0865212	−	0.343809i
$329$	−9.35318	+	25.6977i	−0.515658	+	1.41676i
$330$	−2.98071	+	8.06036i	−0.164083	+	0.443708i
$331$	−2.81290	−	0.495990i	−0.154611	−	0.0272621i	0.0958069	−	0.995400i	$-0.469457\pi$
$331$	−2.81290	−	0.495990i	−0.154611	−	0.0272621i	−0.250418	+	0.968138i	$0.580568\pi$
$332$	28.3951	+	8.18704i	1.55839	+	0.449322i
$333$	−4.88260	+	7.10289i	−0.267565	+	0.389236i
$334$	0.0124294	−	0.0879738i	0.000680106	−	0.00481371i
$335$	−2.39947	+	0.873337i	−0.131097	+	0.0477155i
$336$	2.25382	+	23.0683i	0.122956	+	1.25848i
$337$	7.54649	−	6.33225i	0.411083	−	0.344940i	−0.413676	−	0.910424i	$-0.635755\pi$
$337$	7.54649	−	6.33225i	0.411083	−	0.344940i	0.824759	+	0.565485i	$0.191311\pi$
$338$	3.83908	−	0.131259i	0.208818	−	0.00713953i
$339$	−1.19251	−	1.54029i	−0.0647683	−	0.0836571i
$340$	2.56496	+	3.81470i	0.139104	+	0.206881i
$341$	31.4944	−	18.1833i	1.70552	−	0.984682i
$342$	−30.1660	+	3.94632i	−1.63119	+	0.213392i
$343$	8.13497	+	4.69673i	0.439247	+	0.253599i
$344$	−18.6247	+	27.4823i	−1.00418	+	1.48175i
$345$	8.03500	−	8.84506i	0.432590	−	0.476202i
$346$	26.0810	−	16.2708i	1.40213	−	0.874723i
$347$	−3.80102	−	21.5566i	−0.204049	−	1.15722i	−0.898929	−	0.438094i	$-0.855654\pi$
$347$	−3.80102	−	21.5566i	−0.204049	−	1.15722i	0.694880	−	0.719126i	$-0.255458\pi$
$348$	−11.6820	−	13.1283i	−0.626221	−	0.703748i
$349$	23.1742	+	19.4455i	1.24049	+	1.04089i	0.997486	+	0.0708662i	$0.0225763\pi$
$349$	23.1742	+	19.4455i	1.24049	+	1.04089i	0.243001	+	0.970026i	$0.421868\pi$
$350$	2.91555	−	3.72612i	0.155842	−	0.199170i
$351$	13.9364	−	9.13446i	0.743870	−	0.487562i
$352$	19.5324	+	3.51762i	1.04108	+	0.187490i
$353$	−9.39079	+	11.1915i	−0.499822	+	0.595664i	−0.955687	−	0.294385i	$-0.904885\pi$
$353$	−9.39079	+	11.1915i	−0.499822	+	0.595664i	0.455866	+	0.890049i	$0.349330\pi$
$354$	−11.2607	−	9.54788i	−0.598501	−	0.507464i
$355$	−4.05125	+	0.714345i	−0.215018	+	0.0379135i
$356$	8.45122	+	0.900732i	0.447914	+	0.0477387i
$357$	2.82642	−	13.0149i	0.149590	−	0.688822i
$358$	1.80485	−	1.62271i	0.0953893	−	0.0857629i
$359$	−1.97722	+	3.42464i	−0.104354	+	0.180746i	−0.913474	−	0.406897i	$-0.866611\pi$
$359$	−1.97722	+	3.42464i	−0.104354	+	0.180746i	0.809120	+	0.587643i	$0.199944\pi$
$360$	5.60803	+	6.36789i	0.295569	+	0.335617i
$361$	16.2100	+	28.0765i	0.853157	+	1.47771i
$362$	−6.00966	−	1.95751i	−0.315860	−	0.102884i
$363$	−0.305643	−	2.24657i	−0.0160421	−	0.117914i
$364$	−12.6373	+	17.3404i	−0.662373	+	0.908886i
$365$	1.69054	+	2.01470i	0.0884867	+	0.105454i
$366$	−7.02853	+	12.0306i	−0.367387	+	0.628850i
$367$	−13.0304	−	35.8008i	−0.680182	−	1.86879i	−0.439751	−	0.898120i	$-0.644933\pi$
$367$	−13.0304	−	35.8008i	−0.680182	−	1.86879i	−0.240431	−	0.970666i	$-0.577289\pi$
$368$	−23.3606	−	14.6923i	−1.21775	−	0.765889i
$369$	−2.82472	+	6.19684i	−0.147049	+	0.322594i
$370$	−1.51933	−	3.76838i	−0.0789861	−	0.195909i
$371$	−7.60704	+	43.1417i	−0.394938	+	2.23980i
$372$	−1.04258	−	35.8921i	−0.0540553	−	1.86092i
$373$	18.4754	+	6.72448i	0.956618	+	0.348181i	0.772707	−	0.634762i	$-0.218902\pi$
$373$	18.4754	+	6.72448i	0.956618	+	0.348181i	0.183911	+	0.982943i	$0.441124\pi$
$374$	−10.0652	−	5.36119i	−0.520459	−	0.277220i
$375$	0.0680766	−	1.73071i	0.00351546	−	0.0893736i
$376$	20.8026	−	10.0898i	1.07281	−	0.520341i
$377$		−	16.2682i		−	0.837853i
$378$	2.05690	−	24.4979i	0.105795	−	1.26004i
$379$		−	27.2900i		−	1.40179i	−0.713262	−	0.700897i	$-0.752783\pi$
$379$		−	27.2900i		−	1.40179i	0.713262	−	0.700897i	$-0.247217\pi$
$380$	6.30573	−	12.8809i	0.323477	−	0.660776i
$381$	−15.6719	+	8.24448i	−0.802893	+	0.422377i
$382$	4.32530	−	8.12041i	0.221302	−	0.415476i
$383$	−13.2067	−	4.80685i	−0.674832	−	0.245619i	−0.0182048	−	0.999834i	$-0.505795\pi$
$383$	−13.2067	−	4.80685i	−0.674832	−	0.245619i	−0.656627	+	0.754216i	$0.728017\pi$
$384$	12.2108	−	15.3263i	0.623132	−	0.782117i
$385$	−2.03816	+	11.5590i	−0.103874	+	0.589102i
$386$	3.27331	−	1.31973i	0.166607	−	0.0671723i
$387$	24.6831	−	25.1132i	1.25471	−	1.27658i
$388$	−7.91430	+	7.62046i	−0.401788	+	0.386870i
$389$	−7.86582	−	21.6112i	−0.398813	−	1.09573i	−0.962863	−	0.269990i	$-0.912980\pi$
$389$	−7.86582	−	21.6112i	−0.398813	−	1.09573i	0.564050	−	0.825741i	$-0.309242\pi$
$390$	−0.0403541	+	7.85500i	−0.00204341	+	0.397753i
$391$	10.1928	+	12.1473i	0.515474	+	0.614318i
$392$	3.24335	+	11.4051i	0.163814	+	0.576045i
$393$	−8.45651	−	3.46009i	−0.426575	−	0.174538i
$394$	−0.457623	+	1.40493i	−0.0230547	+	0.0707793i
$395$	−3.40063	−	5.89007i	−0.171104	−	0.296362i
$396$	−19.7060	−	7.40256i	−0.990264	−	0.371993i
$397$	−12.3689	+	21.4236i	−0.620779	+	1.07522i	0.368562	+	0.929603i	$0.379850\pi$
$397$	−12.3689	+	21.4236i	−0.620779	+	1.07522i	−0.989341	+	0.145618i	$0.953483\pi$
$398$	−4.92210	−	5.47458i	−0.246723	−	0.274416i
$399$	−39.5738	+	12.6657i	−1.98117	+	0.634080i
$400$	−3.96268	+	0.545127i	−0.198134	+	0.0272564i
$401$	6.23935	−	1.10017i	0.311579	−	0.0549397i	−0.0156724	−	0.999877i	$-0.504989\pi$
$401$	6.23935	−	1.10017i	0.311579	−	0.0549397i	0.327251	+	0.944937i	$0.393878\pi$
$402$	−2.10901	−	5.88840i	−0.105188	−	0.293687i
$403$	21.3666	−	25.4637i	1.06435	−	1.26844i
$404$	38.5901	−	9.56179i	1.91993	−	0.475717i
$405$	−4.63398	−	7.71533i	−0.230264	−	0.383378i
$406$	−18.9025	−	14.7905i	−0.938115	−	0.734039i
$407$	7.72168	+	6.47926i	0.382749	+	0.321165i
$408$	−9.37623	+	6.23475i	−0.464193	+	0.308666i
$409$	1.08096	+	6.13044i	0.0534502	+	0.303131i	0.999800	−	0.0200138i	$-0.00637103\pi$
$409$	1.08096	+	6.13044i	0.0534502	+	0.303131i	−0.946350	+	0.323145i	$0.895260\pi$
$410$	−1.69926	−	2.72381i	−0.0839206	−	0.134519i
$411$	0.155061	+	0.484486i	0.00764862	+	0.0238979i
$412$	−0.226719	−	3.31169i	−0.0111697	−	0.163155i
$413$	−17.4625	−	10.0820i	−0.859274	−	0.496102i
$414$	21.5645	+	19.7927i	1.05984	+	0.972758i
$415$	12.7963	−	7.38796i	0.628147	−	0.362661i
$416$	17.8764	−	3.08487i	0.876461	−	0.151248i
$417$	−0.479934	+	1.17297i	−0.0235025	+	0.0574404i
$418$	1.21574	+	35.5581i	0.0594636	+	1.73920i
$419$	2.94140	−	2.46813i	0.143697	−	0.120576i	−0.568106	−	0.822956i	$-0.692323\pi$
$419$	2.94140	−	2.46813i	0.143697	−	0.120576i	0.711803	+	0.702380i	$0.247879\pi$
$420$	9.09028	+	7.18839i	0.443560	+	0.350758i
$421$	−11.8996	+	4.33109i	−0.579950	+	0.211084i	−0.615303	−	0.788290i	$-0.710966\pi$
$421$	−11.8996	+	4.33109i	−0.579950	+	0.211084i	0.0353537	+	0.999375i	$0.488744\pi$
$422$	−36.0731	−	5.09659i	−1.75601	−	0.248098i
$423$	−23.6316	+	6.55136i	−1.14901	+	0.318538i
$424$	30.0110	−	21.7040i	1.45746	−	1.05404i
$425$	2.26350	+	0.399117i	0.109796	+	0.0193600i
$426$	−1.69878	−	9.93235i	−0.0823060	−	0.481224i
$427$	−6.50859	+	17.8822i	−0.314973	+	0.865380i
$428$	14.5458	−	6.45079i	0.703098	−	0.311810i
$429$	−9.07274	−	17.2463i	−0.438036	−	0.832659i
$430$	3.43936	+	16.2392i	0.165861	+	0.783122i
$431$	−6.22399			−0.299799			−0.149899	−	0.988701i	$-0.547895\pi$
$431$	−6.22399			−0.299799			−0.149899	+	0.988701i	$0.547895\pi$
$432$	−15.6684	+	13.6565i	−0.753848	+	0.657048i
$433$	−15.0813			−0.724760			−0.362380	−	0.932030i	$-0.618036\pi$
$433$	−15.0813			−0.724760			−0.362380	+	0.932030i	$0.618036\pi$
$434$	−10.1613	−	47.9773i	−0.487758	−	2.30298i
$435$	−8.77985	−	0.345350i	−0.420962	−	0.0165583i
$436$	−15.1460	+	6.71697i	−0.725362	+	0.321684i
$437$	16.9206	−	46.4889i	0.809422	−	2.22387i
$438$	−4.95620	+	4.11554i	−0.236816	+	0.196648i
$439$	−16.8683	−	2.97433i	−0.805078	−	0.141957i	−0.244060	−	0.969760i	$-0.578479\pi$
$439$	−16.8683	−	2.97433i	−0.805078	−	0.141957i	−0.561018	+	0.827803i	$0.689590\pi$
$440$	8.04088	−	5.81518i	0.383334	−	0.277228i
$441$	−1.20430	−	12.5188i	−0.0573478	−	0.596132i
$442$	−10.3212	−	1.45823i	−0.490928	−	0.0693608i
$443$	16.6015	−	6.04245i	0.788761	−	0.287086i	0.0839403	−	0.996471i	$-0.473250\pi$
$443$	16.6015	−	6.04245i	0.788761	−	0.287086i	0.704821	+	0.709385i	$0.251027\pi$
$444$	9.24961	−	3.67411i	0.438967	−	0.174365i
$445$	3.25534	−	2.73155i	0.154318	−	0.129488i
$446$	−1.09417	−	32.0025i	−0.0518104	−	1.51536i
$447$	−3.39275	+	0.461580i	−0.160472	+	0.0218320i
$448$	12.6682	−	23.5758i	0.598516	−	1.11385i
$449$	2.47053	−	1.42636i	0.116592	−	0.0673142i	−0.440570	−	0.897718i	$-0.645224\pi$
$449$	2.47053	−	1.42636i	0.116592	−	0.0673142i	0.557162	+	0.830404i	$0.311890\pi$
$450$	4.23845	+	0.188530i	0.199802	+	0.00888737i
$451$	6.89740	+	3.98222i	0.324786	+	0.187515i
$452$	0.153630	+	2.24407i	0.00722613	+	0.105552i
$453$	24.8152	+	5.38905i	1.16592	+	0.253200i
$454$	−14.8692	−	23.8345i	−0.697848	−	1.11861i
$455$	1.86296	+	10.5654i	0.0873370	+	0.495313i
$456$	31.4719	+	15.6077i	1.47381	+	0.730897i
$457$	−28.6557	−	24.0450i	−1.34046	−	1.12478i	−0.981508	−	0.191420i	$-0.938691\pi$
$457$	−28.6557	−	24.0450i	−1.34046	−	1.12478i	−0.358949	−	0.933357i	$-0.616865\pi$
$458$	8.61477	+	6.74072i	0.402542	+	0.314973i
$459$	10.9737	−	4.71295i	0.512208	−	0.219982i
$460$	−13.3934	+	3.31858i	−0.624469	+	0.154730i
$461$	5.34367	−	6.36834i	0.248879	−	0.296603i	−0.627112	−	0.778929i	$-0.715763\pi$
$461$	5.34367	−	6.36834i	0.248879	−	0.296603i	0.875992	+	0.482326i	$0.160208\pi$
$462$	−28.2876	−	5.13785i	−1.31606	−	0.239035i
$463$	13.0649	−	2.30369i	0.607177	−	0.107062i	0.138397	−	0.990377i	$-0.455805\pi$
$463$	13.0649	−	2.30369i	0.607177	−	0.107062i	0.468780	+	0.883315i	$0.344694\pi$
$464$	2.76541	+	20.1026i	0.128381	+	0.933238i
$465$	−13.2891	−	12.0720i	−0.616266	−	0.559826i
$466$	−6.13873	−	6.82776i	−0.284371	−	0.316290i
$467$	−10.6761	+	18.4916i	−0.494031	+	0.855687i	−0.999976	−	0.00687850i	$-0.997810\pi$
$467$	−10.6761	+	18.4916i	−0.494031	+	0.855687i	0.505945	+	0.862566i	$0.331144\pi$
$468$	−19.2400	−	0.197691i	−0.889368	−	0.00913829i
$469$	−4.27128	−	7.39807i	−0.197229	−	0.341611i
$470$	3.58032	−	10.9918i	0.165148	−	0.507013i
$471$	−10.0189	+	7.75673i	−0.461645	+	0.357411i
$472$	4.66307	+	16.3975i	0.214635	+	0.754754i
$473$	−26.4701	−	31.5459i	−1.21710	−	1.45048i
$474$	14.4703	−	8.25559i	0.664641	−	0.379192i
$475$	−2.45255	−	6.73832i	−0.112531	−	0.309175i
$476$	−11.0780	+	10.6667i	−0.507761	+	0.488909i
$477$	−35.4581	+	16.9088i	−1.62352	+	0.774201i
$478$	−12.2532	+	4.94023i	−0.560450	+	0.225961i
$479$	−4.22728	+	23.9741i	−0.193149	+	1.09540i	0.721880	+	0.692018i	$0.243278\pi$
$479$	−4.22728	+	23.9741i	−0.193149	+	1.09540i	−0.915030	+	0.403386i	$0.867833\pi$
$480$	−1.28540	−	9.71328i	−0.0586703	−	0.443348i
$481$	8.65782	+	3.15119i	0.394762	+	0.143682i
$482$	−12.3006	+	23.0934i	−0.560276	+	1.05187i
$483$	33.8092	+	21.3341i	1.53837	+	0.970735i
$484$	−1.15109	+	2.35138i	−0.0523225	+	0.106881i
$485$			5.49335i			0.249440i
$486$	18.9567	−	11.2536i	0.859892	−	0.510476i
$487$		−	4.18429i		−	0.189608i	−0.995496	−	0.0948041i	$-0.969778\pi$
$487$		−	4.18429i		−	0.189608i	0.995496	−	0.0948041i	$-0.0302225\pi$
$488$	14.4759	−	7.02117i	0.655292	−	0.317833i
$489$	7.34027	+	4.63182i	0.331938	+	0.209458i
$490$	5.23266	+	2.78715i	0.236387	+	0.125911i
$491$	8.76679	+	3.19085i	0.395640	+	0.144001i	0.532176	−	0.846634i	$-0.321375\pi$
$491$	8.76679	+	3.19085i	0.395640	+	0.144001i	−0.136536	+	0.990635i	$0.543597\pi$
$492$	6.69324	−	4.12800i	0.301754	−	0.186104i
$493$	2.02471	−	11.4827i	0.0911882	−	0.517154i
$494$	12.1604	+	30.1614i	0.547122	+	1.35702i
$495$	−9.50034	+	4.53040i	−0.427009	+	0.203626i
$496$	−22.0741	+	35.0976i	−0.991157	+	1.57593i
$497$	−4.70703	−	12.9325i	−0.211139	−	0.580100i
$498$	17.9355	+	31.4370i	0.803708	+	1.40873i
$499$	17.2143	+	20.5152i	0.770619	+	0.918388i	0.998469	−	0.0553079i	$-0.0176141\pi$
$499$	17.2143	+	20.5152i	0.770619	+	0.918388i	−0.227850	+	0.973696i	$0.573170\pi$
$500$	−1.17793	+	1.61632i	−0.0526787	+	0.0722839i
$501$	0.0860422	−	0.0666149i	0.00384408	−	0.00297614i
$502$	6.30693	+	2.05433i	0.281492	+	0.0916894i
$503$	0.270145	+	0.467904i	0.0120452	+	0.0208628i	0.871985	−	0.489532i	$-0.162832\pi$
$503$	0.270145	+	0.467904i	0.0120452	+	0.0208628i	−0.859940	+	0.510395i	$0.829499\pi$
$504$	−17.7221	+	22.1758i	−0.789403	+	0.987789i
$505$	9.93926	−	17.2153i	0.442291	−	0.766071i
$506$	25.4556	−	22.8867i	1.13164	−	1.01744i
$507$	3.48232	+	3.16340i	0.154655	+	0.140491i
$508$	20.3325	+	2.16703i	0.902107	+	0.0961466i
$509$	8.54203	−	1.50619i	0.378619	−	0.0667607i	0.0188998	−	0.999821i	$-0.493984\pi$
$509$	8.54203	−	1.50619i	0.378619	−	0.0667607i	0.359719	+	0.933061i	$0.382873\pi$
$510$	−1.00610	+	5.53933i	−0.0445510	+	0.245286i
$511$	−5.65564	+	6.74013i	−0.250191	+	0.298166i
$512$	−21.5654	+	6.85077i	−0.953066	+	0.302764i
$513$	−29.8521	−	22.2978i	−1.31800	−	0.984471i
$514$	−1.82124	+	2.32758i	−0.0803317	+	0.102665i
$515$	−1.27142	−	1.06685i	−0.0560255	−	0.0470110i
$516$	−39.8204	+	8.22021i	−1.75300	+	0.361875i
$517$	4.98003	+	28.2432i	0.219021	+	1.24213i
$518$	11.5329	−	7.19484i	0.506725	−	0.316123i
$519$	36.7913	+	7.98988i	1.61496	+	0.350717i
$520$	5.08849	−	7.50849i	0.223145	−	0.329269i
$521$	−32.7994	−	18.9367i	−1.43697	−	0.829634i	−0.439330	−	0.898326i	$-0.644784\pi$
$521$	−32.7994	−	18.9367i	−1.43697	−	0.829634i	−0.997638	+	0.0686916i	$0.978118\pi$
$522$	0.956405	−	21.5015i	0.0418607	−	0.941096i
$523$	−19.5110	+	11.2647i	−0.853155	+	0.492569i	−0.861714	−	0.507394i	$-0.830609\pi$
$523$	−19.5110	+	11.2647i	−0.853155	+	0.492569i	0.00855929	+	0.999963i	$0.497275\pi$
$524$	5.88699	+	8.75536i	0.257175	+	0.382480i
$525$	5.74164	−	0.781144i	0.250586	−	0.0340919i
$526$	12.7666	−	0.436493i	0.556652	−	0.0190320i
$527$	18.2505	−	15.3140i	0.795005	−	0.667088i
$528$	14.1429	+	19.7690i	0.615489	+	0.860334i
$529$	−23.1153	+	8.41328i	−1.00501	+	0.365795i
$530$	2.59064	−	18.3363i	0.112530	−	0.796477i
$531$	−1.73146	−	17.9986i	−0.0751391	−	0.781074i
$532$	46.1013	+	13.2922i	1.99874	+	0.576289i
$533$	7.16921	+	1.26412i	0.310533	+	0.0547553i
$534$	6.64986	+	8.00819i	0.287768	+	0.346548i
$535$	2.72112	−	7.47621i	0.117644	−	0.323225i
$536$	−1.76257	+	7.00392i	−0.0761314	+	0.302523i
$537$	2.97025	+	0.116833i	0.128176	+	0.00504171i
$538$	12.0329	−	2.54850i	0.518776	−	0.109874i
$539$	−14.7080			−0.633517
$540$	−0.515131	+	10.3795i	−0.0221677	+	0.446664i
$541$	24.3954			1.04884			0.524421	−	0.851459i	$-0.324282\pi$
$541$	24.3954			1.04884			0.524421	+	0.851459i	$0.324282\pi$
$542$	27.2780	−	5.77732i	1.17169	−	0.248157i
$543$	−3.60398	−	6.85077i	−0.154661	−	0.293995i
$544$	13.0017	+	0.0474413i	0.557445	+	0.00203403i
$545$	−2.83340	+	7.78471i	−0.121370	+	0.333460i
$546$	−25.9029	+	4.43029i	−1.10854	+	0.189599i
$547$	−24.8094	−	4.37457i	−1.06077	−	0.187043i	−0.384074	−	0.923302i	$-0.625479\pi$
$547$	−24.8094	−	4.37457i	−1.06077	−	0.187043i	−0.676700	+	0.736259i	$0.736590\pi$
$548$	0.162731	−	0.564399i	0.00695151	−	0.0241099i
$549$	−16.4445	+	4.55889i	−0.701833	+	0.194569i
$550$	0.694114	−	4.91286i	0.0295971	−	0.209485i
$551$	−34.1833	+	12.4417i	−1.45626	+	0.530034i
$552$	−7.96019	−	32.8482i	−0.338808	−	1.39811i
$553$	17.4302	−	14.6256i	0.741206	−	0.621945i
$554$	−1.00002	+	0.0341907i	−0.0424866	+	0.00145262i
$555$	1.88447	−	4.60569i	0.0799915	−	0.195501i
$556$	1.21442	−	0.816560i	0.0515029	−	0.0346298i
$557$	−3.79549	+	2.19132i	−0.160820	+	0.0928494i	−0.578250	−	0.815860i	$-0.696264\pi$
$557$	−3.79549	+	2.19132i	−0.160820	+	0.0928494i	0.417430	+	0.908709i	$0.362931\pi$
$558$	29.7371	−	32.3991i	1.25887	−	1.37156i
$559$	−32.5975	−	18.8202i	−1.37873	−	0.796008i
$560$	−4.09806	−	12.7390i	−0.173175	−	0.538319i
$561$	−4.25744	−	13.3023i	−0.179749	−	0.561622i
$562$	32.8676	−	20.5046i	1.38643	−	0.864934i
$563$	3.80378	+	21.5723i	0.160310	+	0.909164i	0.953769	+	0.300540i	$0.0971670\pi$
$563$	3.80378	+	21.5723i	0.160310	+	0.909164i	−0.793459	+	0.608624i	$0.791722\pi$
$564$	26.8789	+	8.90816i	1.13180	+	0.375101i
$565$	0.861540	+	0.722918i	0.0362452	+	0.0304134i
$566$	−5.08160	+	6.49437i	−0.213596	+	0.272979i
$567$	22.7272	−	19.7494i	0.954454	−	0.829398i
$568$	−4.75582	+	10.6191i	−0.199550	+	0.445568i
$569$	−7.22498	+	8.61040i	−0.302887	+	0.360967i	−0.895923	−	0.444209i	$-0.853485\pi$
$569$	−7.22498	+	8.61040i	−0.302887	+	0.360967i	0.593036	+	0.805176i	$0.297929\pi$
$570$	16.5361	−	5.92262i	0.692621	−	0.248071i
$571$	−27.8556	+	4.91170i	−1.16572	+	0.205548i	−0.722829	−	0.691026i	$-0.757159\pi$
$571$	−27.8556	+	4.91170i	−1.16572	+	0.205548i	−0.442893	+	0.896575i	$0.646048\pi$
$572$	−2.38474	+	22.3751i	−0.0997110	+	0.935550i
$573$	10.7320	−	3.43482i	0.448336	−	0.143492i
$574$	7.98683	−	7.18083i	0.333364	−	0.299722i
$575$	−3.44959	+	5.97487i	−0.143858	+	0.249169i
$576$	23.8084	−	3.02630i	0.992018	−	0.126096i
$577$	−0.731900	−	1.26769i	−0.0304694	−	0.0527745i	0.850389	−	0.526155i	$-0.176367\pi$
$577$	−0.731900	−	1.26769i	−0.0304694	−	0.0527745i	−0.880858	+	0.473381i	$0.843034\pi$
$578$	15.7559	+	5.13213i	0.655361	+	0.213468i
$579$	4.00061	+	1.63690i	0.166260	+	0.0680273i
$580$	8.19952	+	5.97561i	0.340467	+	0.248124i
$581$	31.7746	+	37.8675i	1.31823	+	1.57101i
$582$	−13.4557	−	0.0691272i	−0.557758	−	0.00286541i
$583$	15.7127	+	43.1703i	0.650754	+	1.78793i
$584$	7.39971	−	0.761366i	0.306202	−	0.0315055i
$585$	−6.74370	+	6.86123i	−0.278818	+	0.283677i
$586$	−10.2131	−	25.3314i	−0.421897	−	1.04643i
$587$	1.66130	−	9.42170i	0.0685692	−	0.388875i	−0.931138	−	0.364668i	$-0.881183\pi$
$587$	1.66130	−	9.42170i	0.0685692	−	0.388875i	0.999707	−	0.0242075i	$-0.00770625\pi$
$588$	−6.89286	+	12.7821i	−0.284257	+	0.527125i
$589$	−69.8463	−	25.4220i	−2.87797	−	1.04749i
$590$	7.52315	+	4.00718i	0.309723	+	0.164973i
$591$	−1.60156	+	0.842533i	−0.0658795	+	0.0346572i
$592$	−11.2341	−	2.42218i	−0.461720	−	0.0995511i
$593$		−	9.16389i		−	0.376316i	−0.982139	−	0.188158i	$-0.939748\pi$
$593$		−	9.16389i		−	0.376316i	0.982139	−	0.188158i	$-0.0602517\pi$
$594$	−10.9775	−	23.3277i	−0.450411	−	0.957147i
$595$			7.68931i			0.315231i
$596$	3.55103	+	1.73837i	0.145456	+	0.0712065i
$597$	0.354385	−	9.00953i	0.0145040	−	0.368735i
$598$	14.7094	−	27.6157i	0.601511	−	1.12929i
$599$	−30.5902	−	11.1339i	−1.24988	−	0.454920i	−0.369520	−	0.929223i	$-0.620478\pi$
$599$	−30.5902	−	11.1339i	−1.24988	−	0.454920i	−0.880362	+	0.474303i	$0.842700\pi$
$600$	−3.94428	−	2.90563i	−0.161024	−	0.118622i
$601$	5.89242	−	33.4176i	0.240357	−	1.36313i	−0.590676	−	0.806909i	$-0.701139\pi$
$601$	5.89242	−	33.4176i	0.240357	−	1.36313i	0.831033	−	0.556223i	$-0.187750\pi$
$602$	−51.5043	+	20.7654i	−2.09916	+	0.846334i
$603$	3.17733	−	6.97039i	0.129391	−	0.283856i
$604$	−20.3380	−	21.1222i	−0.827540	−	0.859449i
$605$	0.447707	+	1.23006i	0.0182019	+	0.0500092i
$606$	42.0431	+	24.5624i	1.70788	+	0.997780i
$607$	−20.5781	−	24.5241i	−0.835241	−	0.995402i	−0.999959	−	0.00906087i	$-0.997116\pi$
$607$	−20.5781	−	24.5241i	−0.835241	−	0.995402i	0.164718	−	0.986341i	$-0.447329\pi$
$608$	−20.1537	−	35.2032i	−0.817340	−	1.42768i
$609$	−3.96272	−	29.1271i	−0.160577	−	1.18029i
$610$	2.49143	−	7.64884i	0.100875	−	0.309693i
$611$	13.1068	+	22.7016i	0.530244	+	0.918410i
$612$	−13.5557	−	2.53411i	−0.547957	−	0.102435i
$613$	−9.67422	+	16.7562i	−0.390738	+	0.676778i	−0.992547	−	0.121862i	$-0.961114\pi$
$613$	−9.67422	+	16.7562i	−0.390738	+	0.676778i	0.601809	+	0.798640i	$0.294447\pi$
$614$	−5.02645	−	5.59064i	−0.202851	−	0.225620i
$615$	0.834434	−	3.84235i	0.0336476	−	0.154939i
$616$	23.8302	+	23.1136i	0.960147	+	0.931274i
$617$	−18.4821	+	3.25889i	−0.744062	+	0.131198i	−0.532812	−	0.846234i	$-0.678865\pi$
$617$	−18.4821	+	3.25889i	−0.744062	+	0.131198i	−0.211250	+	0.977432i	$0.567753\pi$
$618$	2.62920	−	3.10087i	0.105762	−	0.124735i
$619$	−18.3423	+	21.8595i	−0.737238	+	0.878606i	−0.996183	−	0.0872863i	$-0.972181\pi$
$619$	−18.3423	+	21.8595i	−0.737238	+	0.878606i	0.258946	+	0.965892i	$0.416625\pi$
$620$	4.98593	+	20.1226i	0.200240	+	0.808141i
$621$	2.02764	+	35.7918i	0.0813665	+	1.43628i
$622$	8.21780	+	6.43011i	0.329504	+	0.257824i
$623$	10.8907	+	9.13834i	0.436325	+	0.366120i
$624$	18.3277	+	12.5585i	0.733695	+	0.502744i
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	14.6864	+	23.5414i	0.586988	+	0.940904i
$627$	−29.2999	+	32.2538i	−1.17012	+	1.28809i
$628$	14.5966	−	0.999289i	0.582468	−	0.0398760i
$629$	5.71882	+	3.30176i	0.228024	+	0.131650i
$630$	1.84113	+	14.0737i	0.0733522	+	0.560711i
$631$	21.3908	−	12.3500i	0.851553	−	0.491645i	−0.00962134	−	0.999954i	$-0.503063\pi$
$631$	21.3908	−	12.3500i	0.851553	−	0.491645i	0.861175	+	0.508309i	$0.169729\pi$
$632$	−19.1870	−	1.38391i	−0.763219	−	0.0550488i
$633$	−27.3150	−	35.2811i	−1.08567	−	1.40230i
$634$	1.04835	+	30.6625i	0.0416355	+	1.21776i
$635$	7.83189	−	6.57173i	0.310799	−	0.260791i
$636$	44.8813	+	6.57641i	1.77966	+	0.260772i
$637$	−12.6329	+	4.59800i	−0.500534	+	0.182179i
$638$	−24.9228	−	3.52122i	−0.986703	−	0.139406i
$639$	6.99105	−	10.1701i	0.276562	−	0.402324i
$640$	−5.01148	+	10.1432i	−0.198096	+	0.400946i
$641$	34.0788	+	6.00902i	1.34603	+	0.237342i	0.799788	−	0.600283i	$-0.204945\pi$
$641$	34.0788	+	6.00902i	1.34603	+	0.237342i	0.546246	+	0.837625i	$0.316057\pi$
$642$	18.2784	+	6.75934i	0.721392	+	0.266770i
$643$	14.8492	−	40.7979i	0.585595	−	1.60891i	−0.192871	−	0.981224i	$-0.561780\pi$
$643$	14.8492	−	40.7979i	0.585595	−	1.60891i	0.778467	−	0.627686i	$-0.215998\pi$
$644$	−18.7142	−	42.1985i	−0.737444	−	1.66285i
$645$	−10.8492	+	17.1932i	−0.427185	+	0.676981i
$646$	4.82943	+	22.8025i	0.190011	+	0.897152i
$647$	−21.8300			−0.858227			−0.429114	−	0.903251i	$-0.641174\pi$
$647$	−21.8300			−0.858227			−0.429114	+	0.903251i	$0.641174\pi$
$648$	−25.4177	−	1.39241i	−0.998503	−	0.0546988i
$649$	−21.1461			−0.830057
$650$	−0.939672	−	4.43673i	−0.0368570	−	0.174023i
$651$	32.0529	−	50.7959i	1.25625	−	1.99085i
$652$	−4.06303	−	9.16167i	−0.159120	−	0.358799i
$653$	−8.08482	+	22.2129i	−0.316384	+	0.869257i	0.674947	+	0.737866i	$0.264166\pi$
$653$	−8.08482	+	22.2129i	−0.316384	+	0.869257i	−0.991331	+	0.131391i	$0.958056\pi$
$654$	−19.0327	−	7.03826i	−0.744236	−	0.275218i
$655$	5.19511	+	0.916038i	0.202990	+	0.0357926i
$656$	−9.07387	−	0.343389i	−0.354275	−	0.0134071i
$657$	−7.86564	−	0.619740i	−0.306868	−	0.0241783i
$658$	38.2940	+	5.41037i	1.49286	+	0.210918i
$659$	23.9853	−	8.72992i	0.934333	−	0.340069i	0.170407	−	0.985374i	$-0.445492\pi$
$659$	23.9853	−	8.72992i	0.934333	−	0.340069i	0.763926	+	0.645304i	$0.223269\pi$
$660$	12.0251	+	1.76203i	0.468077	+	0.0685868i
$661$	−4.15845	+	3.48935i	−0.161745	+	0.135720i	−0.720068	−	0.693904i	$-0.755889\pi$
$661$	−4.15845	+	3.48935i	−0.161745	+	0.135720i	0.558323	+	0.829624i	$0.311445\pi$
$662$	0.138027	+	4.03705i	0.00536458	+	0.156904i
$663$	−7.81533	−	10.0946i	−0.303522	−	0.392040i
$664$	3.00657	−	41.6843i	0.116678	−	1.61767i
$665$	20.7756	−	11.9948i	0.805644	−	0.465139i
$666$	11.2577	+	4.67390i	0.436228	+	0.181110i
$667$	30.3103	+	17.4997i	1.17362	+	0.677590i
$668$	−0.125356	+	0.00858190i	−0.00485017	+	0.000332044i
$669$	26.3700	−	29.0285i	1.01952	−	1.12231i
$670$	1.91138	+	3.06382i	0.0738431	+	0.118366i
$671$	3.46545	+	19.6535i	0.133782	+	0.758716i
$672$	31.2551	−	9.87773i	1.20569	−	0.381042i
$673$	31.3838	+	26.3342i	1.20976	+	1.01511i	0.999296	+	0.0375058i	$0.0119413\pi$
$673$	31.3838	+	26.3342i	1.20976	+	1.01511i	0.210462	+	0.977602i	$0.432503\pi$
$674$	−10.9721	−	8.58525i	−0.422630	−	0.330692i
$675$	3.55981	+	3.78520i	0.137017	+	0.145692i
$676$	−1.30653	−	5.27300i	−0.0502513	−	0.202808i
$677$	−8.96862	+	10.6884i	−0.344692	+	0.410788i	−0.910342	−	0.413858i	$-0.864181\pi$
$677$	−8.96862	+	10.6884i	−0.344692	+	0.410788i	0.565649	+	0.824646i	$0.308626\pi$
$678$	−1.78160	+	2.10121i	−0.0684218	+	0.0806964i
$679$	−18.0986	+	3.19128i	−0.694562	+	0.122470i
$680$	4.52614	−	4.66647i	0.173570	−	0.178951i
$681$	7.30165	−	33.6222i	0.279800	−	1.28840i
$682$	−34.3856	−	38.2452i	−1.31669	−	1.46448i
$683$	10.4379	−	18.0789i	0.399394	−	0.691771i	−0.594257	−	0.804275i	$-0.702554\pi$
$683$	10.4379	−	18.0789i	0.399394	−	0.691771i	0.993651	+	0.112504i	$0.0358871\pi$
$684$	14.2991	+	40.5790i	0.546740	+	1.55158i
$685$	−0.146848	−	0.254347i	−0.00561075	−	0.00971811i
$686$	4.11431	−	12.6312i	0.157085	−	0.482260i
$687$	1.80600	+	13.2746i	0.0689032	+	0.506459i
$688$	43.4799	+	17.7148i	1.65766	+	0.675372i
$689$	26.9918	+	32.1676i	1.02831	+	1.22549i
$690$	−14.5918	−	8.52482i	−0.555500	−	0.324534i
$691$	−4.04094	−	11.1024i	−0.153724	−	0.422354i	0.838794	−	0.544449i	$-0.183261\pi$
$691$	−4.04094	−	11.1024i	−0.153724	−	0.422354i	−0.992518	+	0.122094i	$0.961039\pi$
$692$	−30.1534	−	31.3160i	−1.14626	−	1.19046i
$693$	−20.4452	−	28.6684i	−0.776647	−	1.08902i
$694$	−28.7103	+	11.5754i	−1.08983	+	0.439395i
$695$	0.127060	−	0.720591i	0.00481965	−	0.0273336i
$696$	−14.7402	+	20.0092i	−0.558725	+	0.758446i
$697$	4.90297	+	1.78453i	0.185713	+	0.0675940i
$698$	20.1127	−	37.7600i	0.761278	−	1.42924i
$699$	0.441980	−	11.2365i	0.0167172	−	0.425002i
$700$	−6.00950	−	2.94189i	−0.227138	−	0.111193i
$701$			33.7134i			1.27334i	0.771137	+	0.636669i	$0.219688\pi$
$701$			33.7134i			1.27334i	−0.771137	+	0.636669i	$0.780312\pi$
$702$	−16.7214	−	16.6048i	−0.631109	−	0.626706i
$703$		−	20.6021i		−	0.777024i
$704$	−0.856707	−	28.0543i	−0.0322884	−	1.05734i
$705$	12.5302	−	6.59175i	0.471915	−	0.248260i
$706$	18.2354	+	9.71303i	0.686300	+	0.365555i
$707$	62.4924	+	22.7454i	2.35027	+	0.855428i
$708$	−9.91008	+	18.3772i	−0.372443	+	0.690658i
$709$	0.162738	−	0.922932i	0.00611175	−	0.0346614i	−0.981599	−	0.190952i	$-0.938843\pi$
$709$	0.162738	−	0.922932i	0.00611175	−	0.0346614i	0.987711	+	0.156291i	$0.0499536\pi$
$710$	2.17542	+	5.39568i	0.0816420	+	0.202496i
$711$	19.7534	+	5.11045i	0.740812	+	0.191657i
$712$	−1.23021	−	11.9564i	−0.0461040	−	0.448085i
$713$	24.4591	+	67.2009i	0.916002	+	2.51669i
$714$	−18.8346	−	0.0967606i	−0.704868	−	0.00362118i
$715$	7.23195	+	8.61870i	0.270459	+	0.322321i
$716$	−2.77392	−	2.02156i	−0.103666	−	0.0755493i
$717$	−14.9758	−	6.12754i	−0.559282	−	0.228837i
$718$	5.31744	+	1.73203i	0.198445	+	0.0646389i
$719$	11.5378	+	19.9841i	0.430289	+	0.745282i	0.996898	−	0.0787049i	$-0.0250785\pi$
$719$	11.5378	+	19.9841i	0.430289	+	0.745282i	−0.566609	+	0.823987i	$0.691745\pi$
$720$	7.16685	−	9.62477i	0.267093	−	0.358694i
$721$	2.77628	−	4.80866i	0.103394	−	0.179084i
$722$	34.0946	−	30.6539i	1.26887	−	1.14082i
$723$	−30.5204	+	9.76817i	−1.13507	+	0.363282i
$724$	−0.947294	+	8.88809i	−0.0352059	+	0.330323i
$725$	4.99590	−	0.880912i	0.185543	−	0.0327162i
$726$	−3.01862	+	1.08116i	−0.112032	+	0.0401256i
$727$	−28.5327	+	34.0040i	−1.05822	+	1.26114i	−0.0941300	+	0.995560i	$0.530007\pi$
$727$	−28.5327	+	34.0040i	−1.05822	+	1.26114i	−0.964090	+	0.265577i	$0.914437\pi$
$728$	27.6939	+	12.4028i	1.02640	+	0.459680i
$729$	26.2523	+	6.30999i	0.972308	+	0.233704i
$730$	2.29202	−	2.92925i	0.0848316	−	0.108416i
$731$	−20.6662	−	17.3410i	−0.764367	−	0.641380i
$732$	18.7042	+	6.19891i	0.691326	+	0.229118i
$733$	−7.35750	−	41.7265i	−0.271756	−	1.54120i	−0.749083	−	0.662477i	$-0.769505\pi$
$733$	−7.35750	−	41.7265i	−0.271756	−	1.54120i	0.477327	−	0.878726i	$-0.341606\pi$
$734$	−45.7130	+	28.5183i	−1.68730	+	1.05263i
$735$	2.21334	+	6.91553i	0.0816403	+	0.255083i
$736$	−13.4820	+	36.6251i	−0.496953	+	1.35002i
$737$	−7.75841	−	4.47932i	−0.285785	−	0.164998i
$738$	9.40118	+	2.09226i	0.346062	+	0.0770173i
$739$	−24.5287	+	14.1616i	−0.902301	+	0.520944i	−0.877946	−	0.478759i	$-0.841087\pi$
$739$	−24.5287	+	14.1616i	−0.902301	+	0.520944i	−0.0243552	+	0.999703i	$0.507753\pi$
$740$	−4.76845	+	3.20625i	−0.175292	+	0.117864i
$741$	−15.0829	+	36.8630i	−0.554086	+	1.35420i
$742$	61.9166	−	2.11694i	2.27303	−	0.0777152i
$743$	16.4461	−	13.7999i	0.603349	−	0.506270i	−0.289171	−	0.957277i	$-0.593380\pi$
$743$	16.4461	−	13.7999i	0.603349	−	0.506270i	0.892520	+	0.451007i	$0.148935\pi$
$744$	−49.3521	+	11.9596i	−1.80934	+	0.438461i
$745$	1.85763	−	0.676122i	0.0680583	−	0.0247712i
$746$	3.88979	−	27.5315i	0.142416	−	1.00800i
$747$	−11.1026	+	42.9148i	−0.406222	+	1.57017i
$748$	−4.46801	+	15.4964i	−0.163366	+	0.566604i
$749$	26.2123	+	4.62193i	0.957776	+	0.168882i
$750$	−2.41443	+	0.412951i	−0.0881625	+	0.0150788i
$751$	−13.7122	+	37.6740i	−0.500366	+	1.37474i	0.390553	+	0.920580i	$0.372284\pi$
$751$	−13.7122	+	37.6740i	−0.500366	+	1.37474i	−0.890919	+	0.454163i	$0.849938\pi$
$752$	−20.0551	−	25.8244i	−0.731334	−	0.941718i
$753$	3.78225	+	7.18965i	0.137833	+	0.262005i
$754$	−22.5074	+	4.76693i	−0.819671	+	0.173601i
$755$	−14.6610			−0.533568
$756$	−34.4962	+	4.33266i	−1.25461	+	0.157577i
$757$	−33.4950			−1.21739			−0.608697	−	0.793402i	$-0.708308\pi$
$757$	−33.4950			−1.21739			−0.608697	+	0.793402i	$0.708308\pi$
$758$	−37.7564	+	7.99658i	−1.37137	+	0.290449i
$759$	41.8923	+	1.64781i	1.52059	+	0.0598117i
$760$	−19.6688	−	4.94973i	−0.713461	−	0.179546i
$761$	9.33508	−	25.6479i	0.338396	−	0.929736i	−0.647453	−	0.762105i	$-0.724166\pi$
$761$	9.33508	−	25.6479i	0.338396	−	0.929736i	0.985850	−	0.167631i	$-0.0536118\pi$
$762$	15.9986	+	19.2666i	0.579569	+	0.697954i
$763$	−27.2939	−	4.81265i	−0.988105	−	0.174230i
$764$	−12.5022	−	3.60470i	−0.452313	−	0.130413i
$765$	−5.61390	+	4.00360i	−0.202971	+	0.144751i
$766$	−2.78054	+	19.6803i	−0.100465	+	0.711079i
$767$	−18.1627	+	6.61069i	−0.655817	+	0.238698i
$768$	−24.7823	−	12.4031i	−0.894256	−	0.447557i
$769$	6.92881	−	5.81397i	0.249859	−	0.209657i	−0.509252	−	0.860617i	$-0.670078\pi$
$769$	6.92881	−	5.81397i	0.249859	−	0.209657i	0.759112	+	0.650960i	$0.225634\pi$
$770$	16.5894	−	0.567193i	0.597840	−	0.0204402i
$771$	−3.58661	+	0.487954i	−0.129169	+	0.0175733i
$772$	−2.78502	−	4.14199i	−0.100235	−	0.149074i
$773$	−12.1103	+	6.99190i	−0.435578	+	0.251481i	−0.701720	−	0.712453i	$-0.747584\pi$
$773$	−12.1103	+	6.99190i	−0.435578	+	0.251481i	0.266142	+	0.963934i	$0.414251\pi$
$774$	−41.9774	−	26.7909i	−1.50885	−	0.962979i
$775$	8.97681	+	5.18277i	0.322457	+	0.186170i
$776$	12.8621	+	8.71666i	0.461724	+	0.312910i
$777$	16.2689	+	3.53307i	0.583643	+	0.126748i
$778$	−27.5947	+	17.2151i	−0.989319	+	0.617191i
$779$	−2.82670	−	16.0310i	−0.101277	−	0.574370i
$780$	10.8794	−	2.24586i	0.389545	−	0.0804146i
$781$	−11.0561	−	9.27719i	−0.395619	−	0.331964i
$782$	13.8194	−	17.6615i	0.494181	−	0.631573i
$783$	19.2022	−	18.0588i	0.686231	−	0.645370i
$784$	14.8289	−	7.82920i	0.529602	−	0.279614i
$785$	4.70224	−	5.60391i	0.167830	−	0.200012i
$786$	−2.30917	+	12.7137i	−0.0823654	+	0.453482i
$787$	−46.6396	+	8.22382i	−1.66252	+	0.293148i	−0.924373	−	0.381490i	$-0.875411\pi$
$787$	−46.6396	+	8.22382i	−1.66252	+	0.293148i	−0.738149	+	0.674637i	$0.764300\pi$
$788$	2.07785	+	0.221457i	0.0740202	+	0.00788908i
$789$	11.5803	+	10.5197i	0.412268	+	0.374511i
$790$	−7.15259	+	6.43078i	−0.254478	+	0.228797i
$791$	−1.88126	+	3.25844i	−0.0668899	+	0.115857i
$792$	−4.46733	+	29.4328i	−0.158740	+	1.04585i
$793$	9.12061	+	15.7974i	0.323882	+	0.560980i
$794$	33.2645	+	10.8351i	1.18051	+	0.384524i
$795$	17.9337	−	13.8845i	0.636042	−	0.492432i
$796$	−6.13193	+	8.41402i	−0.217340	+	0.298227i
$797$	20.3965	+	24.3076i	0.722480	+	0.861019i	0.994869	−	0.101169i	$-0.0322582\pi$
$797$	20.3965	+	24.3076i	0.722480	+	0.861019i	−0.272389	+	0.962187i	$0.587814\pi$
$798$	29.1193	+	51.0399i	1.03081	+	1.80679i
$799$	6.42586	+	17.6549i	0.227331	+	0.624586i
$800$	1.91535	+	5.32273i	0.0677178	+	0.188187i
$801$	−1.00137	+	12.7092i	−0.0353817	+	0.449059i
$802$	−3.35037	−	8.30992i	−0.118306	−	0.293434i
$803$	−1.60228	+	9.08698i	−0.0565432	+	0.320673i
$804$	−7.52876	+	4.64329i	−0.265519	+	0.163756i
$805$	−21.6891	−	7.89418i	−0.764440	−	0.278233i
$806$	−41.4905	−	22.0998i	−1.46144	−	0.778431i
$807$	12.7398	+	8.03902i	0.448463	+	0.282987i
$808$	−24.5367	−	50.5885i	−0.863198	−	1.77970i
$809$		−	50.8650i		−	1.78832i	−0.447749	−	0.894159i	$-0.647774\pi$
$809$		−	50.8650i		−	1.78832i	0.447749	−	0.894159i	$-0.352226\pi$
$810$	−9.31648	+	8.67198i	−0.327348	+	0.304702i
$811$		−	21.7980i		−	0.765433i	−0.923866	−	0.382716i	$-0.874989\pi$
$811$		−	21.7980i		−	0.765433i	0.923866	−	0.382716i	$-0.125011\pi$
$812$	−14.9241	+	30.4860i	−0.523734	+	1.06985i
$813$	28.8805	+	18.2240i	1.01288	+	0.639145i
$814$	6.70159	−	12.5817i	0.234891	−	0.440988i
$815$	−4.70889	−	1.71390i	−0.164945	−	0.0600352i
$816$	11.3734	+	11.1453i	0.398147	+	0.390164i
$817$	−14.6155	+	82.8885i	−0.511331	+	2.89990i
$818$	8.16487	−	3.29189i	0.285478	−	0.115098i
$819$	−26.5230	−	18.2322i	−0.926788	−	0.637085i
$820$	−3.27053	+	3.14911i	−0.114212	+	0.109972i
$821$	−4.77717	−	13.1252i	−0.166724	−	0.458072i	0.827991	−	0.560741i	$-0.189484\pi$
$821$	−4.77717	−	13.1252i	−0.166724	−	0.458072i	−0.994716	+	0.102670i	$0.967262\pi$
$822$	0.624861	−	0.356496i	0.0217945	−	0.0124342i
$823$	−11.9241	−	14.2106i	−0.415648	−	0.495350i	0.517077	−	0.855939i	$-0.327020\pi$
$823$	−11.9241	−	14.2106i	−0.415648	−	0.495350i	−0.932725	+	0.360589i	$0.882576\pi$
$824$	−4.51537	+	1.28407i	−0.157300	+	0.0447327i
$825$	4.80500	−	3.72009i	0.167288	−	0.129517i
$826$	−8.83177	+	27.1140i	−0.307297	+	0.943418i
$827$	−7.54660	−	13.0711i	−0.262421	−	0.454527i	0.704464	−	0.709740i	$-0.251188\pi$
$827$	−7.54660	−	13.0711i	−0.262421	−	0.454527i	−0.966885	+	0.255213i	$0.917854\pi$
$828$	21.0648	−	35.6347i	0.732052	−	1.23839i
$829$	15.5011	−	26.8486i	0.538374	−	0.932491i	−0.460618	−	0.887598i	$-0.652372\pi$
$829$	15.5011	−	26.8486i	0.538374	−	0.932491i	0.998992	−	0.0448923i	$-0.0142945\pi$
$830$	−13.9710	−	15.5392i	−0.484941	−	0.539373i
$831$	−0.907086	−	0.824012i	−0.0314665	−	0.0285847i
$832$	−9.50616	−	23.8284i	−0.329567	−	0.826102i
$833$	−9.48904	+	1.67317i	−0.328776	+	0.0579720i
$834$	1.76346	+	0.320295i	0.0610636	+	0.0110909i
$835$	−0.0403829	+	0.0481265i	−0.00139751	+	0.00166549i
$836$	48.8393	−	12.1013i	1.68914	−	0.418533i
$837$	53.7747	−	3.04639i	1.85872	−	0.105298i
$838$	−4.27662	−	3.34629i	−0.147733	−	0.115596i
$839$	−21.1753	−	17.7682i	−0.731052	−	0.613425i	0.199366	−	0.979925i	$-0.436112\pi$
$839$	−21.1753	−	17.7682i	−0.731052	−	0.613425i	−0.930418	+	0.366500i	$0.880556\pi$
$840$	7.28166	−	14.6830i	0.251241	−	0.506611i
$841$	0.566959	+	3.21538i	0.0195503	+	0.110875i
$842$	9.47900	+	15.1942i	0.326668	+	0.523628i
$843$	46.3647	+	10.0689i	1.59689	+	0.346792i
$844$	3.51895	+	51.4014i	0.121127	+	1.76931i
$845$	−2.35232	−	1.35811i	−0.0809223	−	0.0467205i
$846$	15.9885	+	30.7752i	0.549697	+	1.05807i
$847$	−3.79254	+	2.18962i	−0.130313	+	0.0752363i
$848$	−38.8219	−	35.1611i	−1.33315	−	1.20744i
$849$	−10.0073	+	1.36148i	−0.343449	+	0.0467259i
$850$	−0.111069	−	3.24856i	−0.00380963	−	0.111425i
$851$	−15.1844	+	12.7412i	−0.520515	+	0.436764i
$852$	−13.2439	+	5.26070i	−0.453727	+	0.180228i
$853$	−49.0082	+	17.8375i	−1.67801	+	0.610745i	−0.993034	−	0.117824i	$-0.962408\pi$
$853$	−49.0082	+	17.8375i	−1.67801	+	0.610745i	−0.684973	+	0.728569i	$0.740186\pi$
$854$	26.6476	+	3.76491i	0.911862	+	0.128833i
$855$	19.5746	+	8.92274i	0.669437	+	0.305151i
$856$	−13.1871	−	18.2342i	−0.450724	−	0.623233i
$857$	−15.4560	−	2.72531i	−0.527966	−	0.0930947i	−0.0966899	−	0.995315i	$-0.530826\pi$
$857$	−15.4560	−	2.72531i	−0.527966	−	0.0930947i	−0.431276	+	0.902220i	$0.641937\pi$
$858$	−21.2021	+	17.6059i	−0.723829	+	0.601055i
$859$	9.45006	−	25.9638i	0.322432	−	0.885874i	−0.667535	−	0.744578i	$-0.732651\pi$
$859$	9.45006	−	25.9638i	0.322432	−	0.885874i	0.989967	−	0.141296i	$-0.0451270\pi$
$860$	21.4595	−	9.51687i	0.731762	−	0.324522i
$861$	13.1439	+	0.517010i	0.447945	+	0.0176196i
$862$	1.82376	+	8.61103i	0.0621177	+	0.293293i
$863$	−25.0822			−0.853807			−0.426904	−	0.904297i	$-0.640396\pi$
$863$	−25.0822			−0.853807			−0.426904	+	0.904297i	$0.640396\pi$
$864$	23.4853	+	17.6760i	0.798985	+	0.601350i
$865$	−21.7366			−0.739067
$866$	4.41915	+	20.8653i	0.150169	+	0.709032i
$867$	9.44880	+	17.9611i	0.320898	+	0.609992i
$868$	−63.4002	+	28.1168i	−2.15194	+	0.954346i
$869$	8.16118	−	22.4227i	0.276849	−	0.760637i
$870$	2.09489	+	12.2483i	0.0710234	+	0.415257i
$871$	−8.06414	−	1.42193i	−0.273243	−	0.0481801i
$872$	13.7312	+	18.9866i	0.464997	+	0.642969i
$873$	−11.7534	−	11.5521i	−0.397792	−	0.390978i
$874$	−69.2767	−	9.78776i	−2.34332	−	0.331076i
$875$	−3.14372	+	1.14422i	−0.106277	+	0.0386817i
$876$	7.14622	+	5.65107i	0.241449	+	0.190932i
$877$	−18.9398	+	15.8924i	−0.639552	+	0.536648i	−0.903881	−	0.427785i	$-0.859294\pi$
$877$	−18.9398	+	15.8924i	−0.639552	+	0.536648i	0.264329	+	0.964433i	$0.414850\pi$
$878$	0.827715	+	24.2092i	0.0279340	+	0.817020i
$879$	12.6676	−	30.9598i	0.427267	−	1.04425i
$880$	−10.4016	−	9.42077i	−0.350638	−	0.317574i
$881$	−44.7128	+	25.8149i	−1.50641	+	0.869727i	−0.506439	+	0.862276i	$0.669038\pi$
$881$	−44.7128	+	25.8149i	−1.50641	+	0.869727i	−0.999972	+	0.00745086i	$0.997628\pi$
$882$	−16.9671	+	5.33446i	−0.571313	+	0.179621i
$883$	−17.5357	−	10.1242i	−0.590123	−	0.340708i	0.175023	−	0.984564i	$-0.444000\pi$
$883$	−17.5357	−	10.1242i	−0.590123	−	0.340708i	−0.765146	+	0.643857i	$0.777333\pi$
$884$	1.00684	+	14.7069i	0.0338636	+	0.494646i
$885$	3.18219	+	9.94266i	0.106968	+	0.334219i
$886$	−13.2245	−	21.1980i	−0.444285	−	0.712161i
$887$	2.55743	+	14.5039i	0.0858701	+	0.486994i	0.997165	+	0.0752402i	$0.0239724\pi$
$887$	2.55743	+	14.5039i	0.0858701	+	0.486994i	−0.911295	+	0.411753i	$0.864917\pi$
$888$	−7.79356	−	11.7205i	−0.261535	−	0.393313i
$889$	26.2014	+	21.9856i	0.878766	+	0.737372i
$890$	−4.73306	−	3.70343i	−0.158652	−	0.124139i
$891$	10.2854	−	29.8537i	0.344572	−	1.00014i
$892$	−43.9556	+	10.8912i	−1.47174	+	0.364666i
$893$	37.6776	−	44.9025i	1.26083	−	1.50260i
$894$	1.63276	+	4.55870i	0.0546076	+	0.152466i
$895$	−1.69013	+	0.298015i	−0.0564946	+	0.00996153i
$896$	−36.3297	−	10.6185i	−1.21369	−	0.354740i
$897$	36.4971	−	11.6810i	1.21860	−	0.390018i
$898$	−2.69733	−	3.00009i	−0.0900110	−	0.100114i
$899$	26.2920	−	45.5391i	0.876888	−	1.51881i
$900$	−0.981124	−	5.91924i	−0.0327041	−	0.197308i
$901$	15.0483	+	26.0644i	0.501332	+	0.868332i
$902$	3.48840	−	10.7096i	0.116151	−	0.356591i
$903$	−62.9481	−	25.7560i	−2.09478	−	0.857107i
$904$	3.05970	−	0.870111i	0.101764	−	0.0289395i
$905$	2.87276	+	3.42362i	0.0954937	+	0.113805i
$906$	0.184491	−	35.9115i	0.00612930	−	1.19308i
$907$	−10.9877	−	30.1885i	−0.364841	−	1.00239i	−0.977294	−	0.211886i	$-0.932040\pi$
$907$	−10.9877	−	30.1885i	−0.364841	−	1.00239i	0.612453	−	0.790507i	$-0.290183\pi$
$908$	−28.6185	+	27.5560i	−0.949739	+	0.914477i
$909$	15.9318	+	57.4681i	0.528425	+	1.90610i
$910$	14.0716	−	5.67334i	0.466468	−	0.188069i
$911$	−2.71224	+	15.3819i	−0.0898606	+	0.509625i	0.906341	+	0.422547i	$0.138864\pi$
$911$	−2.71224	+	15.3819i	−0.0898606	+	0.509625i	−0.996202	+	0.0870775i	$0.972247\pi$
$912$	12.3717	−	48.1155i	0.409667	−	1.59326i
$913$	48.7138	+	17.7304i	1.61219	+	0.586790i
$914$	−24.8701	+	46.6916i	−0.822629	+	1.54442i
$915$	8.71938	−	4.58699i	0.288254	−	0.151641i
$916$	6.80164	−	13.8939i	0.224732	−	0.459068i
$917$			17.6482i			0.582795i
$918$	−9.73601	−	13.8014i	−0.321336	−	0.455513i
$919$			8.98488i			0.296384i	0.988959	+	0.148192i	$0.0473454\pi$
$919$			8.98488i			0.296384i	−0.988959	+	0.148192i	$0.952655\pi$
$920$	8.51589	+	17.5576i	0.280761	+	0.578857i
$921$	0.361897	−	9.20053i	0.0119249	−	0.303168i
$922$	−10.3766	−	5.52703i	−0.341734	−	0.182023i
$923$	−12.3965	−	4.51196i	−0.408036	−	0.148513i
$924$	1.18056	+	40.6421i	0.0388375	+	1.33703i
$925$	−0.498904	+	2.82942i	−0.0164038	+	0.0930308i
$926$	−7.01551	−	17.4005i	−0.230544	−	0.571818i
$927$	4.95629	−	0.476793i	0.162786	−	0.0156600i
$928$	27.0020	−	9.71651i	0.886385	−	0.318960i
$929$	−12.3543	−	33.9433i	−0.405333	−	1.11364i	−0.959616	−	0.281314i	$-0.909230\pi$
$929$	−12.3543	−	33.9433i	−0.405333	−	1.11364i	0.554283	−	0.832328i	$-0.312993\pi$
$930$	−12.8079	+	21.9231i	−0.419988	+	0.718887i
$931$	19.3230	+	23.0282i	0.633285	+	0.754720i
$932$	−7.64759	+	10.4938i	−0.250505	+	0.343734i
$933$	1.72278	+	12.6629i	0.0564012	+	0.414566i
$934$	28.7118	+	9.35221i	0.939480	+	0.306014i
$935$	4.03191	+	6.98348i	0.131858	+	0.228384i
$936$	5.36423	+	26.6769i	0.175335	+	0.871962i
$937$	−9.20827	+	15.9492i	−0.300821	+	0.521038i	−0.976322	−	0.216321i	$-0.930594\pi$
$937$	−9.20827	+	15.9492i	−0.300821	+	0.521038i	0.675501	+	0.737359i	$0.263927\pi$
$938$	−8.98383	+	8.07721i	−0.293332	+	0.263730i
$939$	−7.21187	+	33.2088i	−0.235350	+	1.08373i
$940$	−16.2565	−	1.73262i	−0.530229	−	0.0565119i
$941$	32.9621	−	5.81211i	1.07453	−	0.189469i	0.391737	−	0.920077i	$-0.371874\pi$
$941$	32.9621	−	5.81211i	1.07453	−	0.189469i	0.682797	+	0.730608i	$0.260763\pi$
$942$	13.6674	+	11.5885i	0.445307	+	0.377572i
$943$	−10.0672	+	11.9976i	−0.327833	+	0.390696i
$944$	21.3199	−	11.2563i	0.693904	−	0.366361i
$945$	−10.4029	+	13.9273i	−0.338406	+	0.453055i
$946$	−35.8881	+	45.8657i	−1.16682	+	1.49122i
$947$	34.6344	+	29.0617i	1.12547	+	0.944378i	0.998868	−	0.0475763i	$-0.0151497\pi$
$947$	34.6344	+	29.0617i	1.12547	+	0.944378i	0.126598	+	0.991954i	$0.459594\pi$
$948$	−15.6619	−	17.6009i	−0.508675	−	0.571650i
$949$	1.46455	+	8.30586i	0.0475412	+	0.269620i
$950$	−8.60398	+	5.36764i	−0.279150	+	0.174149i
$951$	−25.2658	+	27.8131i	−0.819301	+	0.901900i
$952$	18.0038	+	12.2011i	0.583506	+	0.395441i
$953$	−29.7405	−	17.1707i	−0.963389	−	0.556213i	−0.0661748	−	0.997808i	$-0.521079\pi$
$953$	−29.7405	−	17.1707i	−0.963389	−	0.556213i	−0.897215	+	0.441595i	$0.854413\pi$
$954$	33.7838	+	44.1025i	1.09379	+	1.42787i
$955$	−5.63413	+	3.25287i	−0.182316	+	0.105260i
$956$	10.4254	+	15.5051i	0.337181	+	0.501469i
$957$	−18.8719	−	24.3756i	−0.610041	−	0.787951i
$958$	34.4074	−	1.17639i	1.11165	−	0.0380076i
$959$	0.752676	−	0.631570i	0.0243052	−	0.0203945i
$960$	−13.0619	+	4.62459i	−0.421571	+	0.149258i
$961$	71.8341	−	26.1455i	2.31723	−	0.843402i
$962$	1.82281	−	12.9017i	0.0587698	−	0.415966i
$963$	10.2736	+	21.5439i	0.331061	+	0.694241i
$964$	35.5546	+	10.2513i	1.14514	+	0.330172i
$965$	−2.45771	−	0.433360i	−0.0791164	−	0.0139503i
$966$	19.6094	−	53.0272i	0.630922	−	1.70612i
$967$	5.68196	−	15.6111i	0.182719	−	0.502018i	−0.814188	−	0.580601i	$-0.802818\pi$
$967$	5.68196	−	15.6111i	0.182719	−	0.502018i	0.996908	+	0.0785837i	$0.0250398\pi$
$968$	3.59048	+	0.903561i	0.115402	+	0.0290416i
$969$	−15.2340	+	24.1421i	−0.489387	+	0.775555i
$970$	7.60018	−	1.60967i	0.244027	−	0.0516834i
$971$	−47.3923			−1.52089			−0.760445	−	0.649402i	$-0.775019\pi$
$971$	−47.3923			−1.52089			−0.760445	+	0.649402i	$0.775019\pi$
$972$	−21.1244	−	22.9294i	−0.677566	−	0.735462i
$973$	2.44791			0.0784763
$974$	−5.78906	+	1.22609i	−0.185494	+	0.0392864i
$975$	2.96411	−	4.69738i	0.0949276	−	0.150436i
$976$	−13.9557	−	17.9704i	−0.446711	−	0.575218i
$977$	−10.2925	+	28.2785i	−0.329287	+	0.904708i	0.659006	+	0.752138i	$0.270977\pi$
$977$	−10.2925	+	28.2785i	−0.329287	+	0.904708i	−0.988293	+	0.152570i	$0.951245\pi$
$978$	4.25737	−	11.5127i	0.136136	−	0.368134i
$979$	14.6827	+	2.58895i	0.469260	+	0.0827433i
$980$	2.32281	−	8.05620i	0.0741994	−	0.257346i
$981$	−10.6975	−	22.4328i	−0.341544	−	0.716226i
$982$	1.84576	−	13.0641i	0.0589004	−	0.416891i
$983$	18.3494	−	6.67863i	0.585254	−	0.213015i	−0.0323866	−	0.999475i	$-0.510311\pi$
$983$	18.3494	−	6.67863i	0.585254	−	0.213015i	0.617641	+	0.786460i	$0.288089\pi$
$984$	−7.67245	−	8.05066i	−0.244589	−	0.256646i
$985$	0.800369	−	0.671589i	0.0255019	−	0.0213986i
$986$	−16.4798	+	0.563448i	−0.524825	+	0.0179438i
$987$	28.9967	+	37.4532i	0.922976	+	1.19215i
$988$	38.1657	−	25.6621i	1.21421	−	0.816421i
$989$	70.1303	−	40.4897i	2.23001	−	1.28750i
$990$	9.05173	+	11.8164i	0.287683	+	0.375551i
$991$	−23.2834	−	13.4427i	−0.739622	−	0.427021i	0.0823100	−	0.996607i	$-0.473770\pi$
$991$	−23.2834	−	13.4427i	−0.739622	−	0.427021i	−0.821932	+	0.569586i	$0.807104\pi$
$992$	55.0266	+	20.2557i	1.74709	+	0.643120i
$993$	−3.32652	+	3.66189i	−0.105564	+	0.116207i
$994$	−16.5131	+	10.3018i	−0.523764	+	0.326753i
$995$	0.903956	+	5.12659i	0.0286573	+	0.162524i
$996$	38.2384	−	34.0259i	1.21163	−	1.07815i
$997$	−18.9498	−	15.9008i	−0.600147	−	0.503583i	0.291346	−	0.956618i	$-0.405897\pi$
$997$	−18.9498	−	15.9008i	−0.600147	−	0.503583i	−0.891493	+	0.453035i	$0.850341\pi$
$998$	23.3391	−	29.8279i	0.738788	−	0.944184i
$999$	5.89128	+	13.7173i	0.186392	+	0.433997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.be.a.11.32	✓	432
4.3	odd	2	inner	540.2.be.a.11.71	yes	432
27.5	odd	18	inner	540.2.be.a.491.71	yes	432
108.59	even	18	inner	540.2.be.a.491.32	yes	432

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
540.2.be.a.11.32	✓	432	1.1	even	1	trivial
540.2.be.a.11.71	yes	432	4.3	odd	2	inner
540.2.be.a.491.32	yes	432	108.59	even	18	inner
540.2.be.a.491.71	yes	432	27.5	odd	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.293022 - 1.38352i) q^{2} +(0.924312 - 1.46480i) q^{3} +(-1.82828 + 0.810806i) q^{4} +(-0.342020 + 0.939693i) q^{5} +(-2.29743 - 0.849589i) q^{6} +(-3.29465 - 0.580935i) q^{7} +(1.65749 + 2.29188i) q^{8} +(-1.29129 - 2.70787i) q^{9} +(1.40031 + 0.197842i) q^{10} +(-3.29684 + 1.19995i) q^{11} +(-0.502228 + 3.42750i) q^{12} +(-2.45658 + 2.06131i) q^{13} +(0.161666 + 4.72845i) q^{14} +(1.06033 + 1.36956i) q^{15} +(2.68519 - 2.96475i) q^{16} +(-1.99049 + 1.14921i) q^{17} +(-3.36803 + 2.58000i) q^{18} +(6.21007 + 3.58539i) q^{19} +(-0.136601 - 1.99533i) q^{20} +(-3.89624 + 4.28904i) q^{21} +(2.62620 + 4.20964i) q^{22} +(-1.19803 - 6.79437i) q^{23} +(4.88919 - 0.309489i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(3.57171 + 2.79472i) q^{26} +(-5.16005 - 0.611427i) q^{27} +(6.49455 - 1.60921i) q^{28} +(-3.26084 + 3.88612i) q^{29} +(1.58412 - 1.86830i) q^{30} +(-10.2081 + 1.79996i) q^{31} +(-4.88863 - 2.84628i) q^{32} +(-1.28962 + 5.93834i) q^{33} +(2.17322 + 2.41715i) q^{34} +(1.67274 - 2.89726i) q^{35} +(4.55640 + 3.90375i) q^{36} +(-1.43654 - 2.48815i) q^{37} +(3.14078 - 9.64238i) q^{38} +(0.748772 + 5.50370i) q^{39} +(-2.72056 + 0.773666i) q^{40} +(-1.45919 - 1.73899i) q^{41} +(7.07568 + 4.13376i) q^{42} +(4.01448 + 11.0297i) q^{43} +(5.05460 - 4.86693i) q^{44} +(2.98621 - 0.287273i) q^{45} +(-9.04913 + 3.64840i) q^{46} +(1.41945 - 8.05011i) q^{47} +(-1.86083 - 6.67363i) q^{48} +(3.93937 + 1.43381i) q^{49} +(-0.664844 + 1.24819i) q^{50} +(-0.156469 + 3.97791i) q^{51} +(2.81998 - 5.76045i) q^{52} -13.0945i q^{53} +(0.666085 + 7.31822i) q^{54} -3.50842i q^{55} +(-4.12943 - 8.51383i) q^{56} +(10.9919 - 5.78251i) q^{57} +(6.33204 + 3.37273i) q^{58} +(5.66375 + 2.06144i) q^{59} +(-3.04903 - 1.64421i) q^{60} +(0.987751 - 5.60182i) q^{61} +(5.48147 + 13.5957i) q^{62} +(2.68126 + 9.67164i) q^{63} +(-2.50543 + 7.59755i) q^{64} +(-1.09680 - 3.01344i) q^{65} +(8.59372 + 0.0441492i) q^{66} +(1.64134 + 1.95607i) q^{67} +(2.70738 - 3.71498i) q^{68} +(-11.0598 - 4.52524i) q^{69} +(-4.49858 - 1.46531i) q^{70} +(2.05687 + 3.56261i) q^{71} +(4.06580 - 7.44777i) q^{72} +(1.31500 - 2.27765i) q^{73} +(-3.02148 + 2.71656i) q^{74} +(-1.64962 + 0.527967i) q^{75} +(-14.2608 - 1.51992i) q^{76} +(11.5590 - 2.03816i) q^{77} +(7.39509 - 2.64865i) q^{78} +(-4.37177 + 5.21007i) q^{79} +(1.86757 + 3.53726i) q^{80} +(-5.66512 + 6.99331i) q^{81} +(-1.97836 + 2.52838i) q^{82} +(-11.3190 - 9.49778i) q^{83} +(3.64582 - 11.0006i) q^{84} +(-0.399117 - 2.26350i) q^{85} +(14.0835 - 8.78606i) q^{86} +(2.67836 + 8.36848i) q^{87} +(-8.21463 - 5.56704i) q^{88} +(-3.68021 - 2.12477i) q^{89} +(-1.27248 - 4.04732i) q^{90} +(9.29104 - 5.36419i) q^{91} +(7.69925 + 11.4506i) q^{92} +(-6.79885 + 16.6165i) q^{93} +(-11.5534 + 0.395014i) q^{94} +(-5.49313 + 4.60928i) q^{95} +(-8.68786 + 4.53002i) q^{96} +(5.16206 - 1.87884i) q^{97} +(0.829393 - 5.87035i) q^{98} +(7.50649 + 7.37792i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) \) 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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