LMFDB - Embedded newform 380.2.be.b.51.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(51,380)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("380.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.be (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			51.6
Character	$\chi$	$=$	380.51
Dual form			380.2.be.b.231.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.888043 + 1.10063i) q^{2} +(-2.01002 - 0.731586i) q^{3} +(-0.422760 - 1.95481i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(2.59019 - 1.56260i) q^{6} +(0.167166 + 0.0965133i) q^{7} +(2.52694 + 1.27065i) q^{8} +(1.20682 + 1.01264i) q^{9} +O(q^{10})$	\(q+(-0.888043 + 1.10063i) q^{2} +(-2.01002 - 0.731586i) q^{3} +(-0.422760 - 1.95481i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(2.59019 - 1.56260i) q^{6} +(0.167166 + 0.0965133i) q^{7} +(2.52694 + 1.27065i) q^{8} +(1.20682 + 1.01264i) q^{9} +(1.23811 + 0.683429i) q^{10} +(1.70813 - 0.986190i) q^{11} +(-0.580355 + 4.23848i) q^{12} +(0.184786 + 0.507695i) q^{13} +(-0.254676 + 0.0982794i) q^{14} +(-0.371436 + 2.10652i) q^{15} +(-3.64255 + 1.65283i) q^{16} +(-5.25273 + 4.40756i) q^{17} +(-2.18624 + 0.428988i) q^{18} +(-2.29593 - 3.70523i) q^{19} +(-1.85170 + 0.755786i) q^{20} +(-0.265399 - 0.316290i) q^{21} +(-0.431466 + 2.75579i) q^{22} +(-5.85438 - 1.03229i) q^{23} +(-4.14961 - 4.40271i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(-0.722881 - 0.247475i) q^{26} +(1.52363 + 2.63901i) q^{27} +(0.117994 - 0.367579i) q^{28} +(-2.24172 + 2.67158i) q^{29} +(-1.98864 - 2.27949i) q^{30} +(-0.473866 + 0.820760i) q^{31} +(1.41559 - 5.47687i) q^{32} +(-4.15486 + 0.732613i) q^{33} +(-0.186436 - 9.69540i) q^{34} +(0.0660190 - 0.181386i) q^{35} +(1.46932 - 2.78720i) q^{36} +1.95740i q^{37} +(6.11696 + 0.763442i) q^{38} -1.15566i q^{39} +(0.812548 - 2.70920i) q^{40} +(-2.27152 + 6.24094i) q^{41} +(0.583802 - 0.0112261i) q^{42} +(-7.09043 + 1.25023i) q^{43} +(-2.64994 - 2.92215i) q^{44} +(0.787694 - 1.36433i) q^{45} +(6.33510 - 5.52678i) q^{46} +(-2.76199 + 3.29161i) q^{47} +(8.53077 - 0.657379i) q^{48} +(-3.48137 - 6.02991i) q^{49} +(0.458051 - 1.33798i) q^{50} +(13.7826 - 5.01645i) q^{51} +(0.914327 - 0.575855i) q^{52} +(-0.276364 - 0.0487304i) q^{53} +(-4.25762 - 0.666602i) q^{54} +(-1.26782 - 1.51093i) q^{55} +(0.299784 + 0.456293i) q^{56} +(1.90416 + 9.12724i) q^{57} +(-0.949670 - 4.83978i) q^{58} +(0.263884 - 0.221425i) q^{59} +(4.27487 - 0.164466i) q^{60} +(1.11630 - 6.33087i) q^{61} +(-0.482537 - 1.25042i) q^{62} +(0.104005 + 0.285753i) q^{63} +(4.77089 + 6.42173i) q^{64} +(0.467895 - 0.270139i) q^{65} +(2.88336 - 5.22354i) q^{66} +(6.99246 + 5.86737i) q^{67} +(10.8366 + 8.40473i) q^{68} +(11.0122 + 6.35790i) q^{69} +(0.141010 + 0.233740i) q^{70} +(1.93531 + 10.9757i) q^{71} +(1.76285 + 4.09233i) q^{72} +(-7.82470 - 2.84796i) q^{73} +(-2.15437 - 1.73826i) q^{74} +2.13902 q^{75} +(-6.27238 + 6.05452i) q^{76} +0.380722 q^{77} +(1.27195 + 1.02628i) q^{78} +(-5.99067 - 2.18043i) q^{79} +(2.26024 + 3.30020i) q^{80} +(-1.95256 - 11.0735i) q^{81} +(-4.85174 - 8.04231i) q^{82} +(6.78214 + 3.91567i) q^{83} +(-0.506085 + 0.652518i) q^{84} +(5.25273 + 4.40756i) q^{85} +(4.92056 - 8.91418i) q^{86} +(6.46040 - 3.72991i) q^{87} +(5.56946 - 0.321607i) q^{88} +(4.02976 + 11.0717i) q^{89} +(0.802108 + 2.07854i) q^{90} +(-0.0181094 + 0.102704i) q^{91} +(0.457080 + 11.8806i) q^{92} +(1.55293 - 1.30307i) q^{93} +(-1.17007 - 5.96302i) q^{94} +(-3.25025 + 2.90445i) q^{95} +(-6.85216 + 9.97298i) q^{96} +(-6.50646 - 7.75410i) q^{97} +(9.72829 + 1.52313i) q^{98} +(3.06006 + 0.539571i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9}+O(q^{10}) $ 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9	$ 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9} + 3 q^{10} - 12 q^{13} - 18 q^{14} + 9 q^{16} + 48 q^{17} - 12 q^{21} - 18 q^{24} - 24 q^{26} + 69 q^{28} - 12 q^{30} - 27 q^{32} + 6 q^{33} - 18 q^{34} - 72 q^{36} - 48 q^{38} - 36 q^{41} - 27 q^{42} - 99 q^{44} + 60 q^{45} + 27 q^{46} - 63 q^{48} + 60 q^{49} + 33 q^{52} - 24 q^{53} + 21 q^{54} - 48 q^{57} + 6 q^{60} - 24 q^{61} + 54 q^{62} + 84 q^{64} - 18 q^{65} - 132 q^{66} + 66 q^{68} - 72 q^{69} + 36 q^{70} - 42 q^{72} + 66 q^{74} + 180 q^{76} + 60 q^{77} + 114 q^{78} + 27 q^{80} - 66 q^{81} + 33 q^{82} - 144 q^{84} - 48 q^{85} + 75 q^{86} + 9 q^{88} - 3 q^{90} - 42 q^{92} - 144 q^{93} + 78 q^{96} + 42 q^{97} - 87 q^{98}+O(q^{100}) $ 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9 + 3 * q^10 - 12 * q^13 - 18 * q^14 + 9 * q^16 + 48 * q^17 - 12 * q^21 - 18 * q^24 - 24 * q^26 + 69 * q^28 - 12 * q^30 - 27 * q^32 + 6 * q^33 - 18 * q^34 - 72 * q^36 - 48 * q^38 - 36 * q^41 - 27 * q^42 - 99 * q^44 + 60 * q^45 + 27 * q^46 - 63 * q^48 + 60 * q^49 + 33 * q^52 - 24 * q^53 + 21 * q^54 - 48 * q^57 + 6 * q^60 - 24 * q^61 + 54 * q^62 + 84 * q^64 - 18 * q^65 - 132 * q^66 + 66 * q^68 - 72 * q^69 + 36 * q^70 - 42 * q^72 + 66 * q^74 + 180 * q^76 + 60 * q^77 + 114 * q^78 + 27 * q^80 - 66 * q^81 + 33 * q^82 - 144 * q^84 - 48 * q^85 + 75 * q^86 + 9 * q^88 - 3 * q^90 - 42 * q^92 - 144 * q^93 + 78 * q^96 + 42 * q^97 - 87 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.888043	+	1.10063i	−0.627941	+	0.778261i
$2$	−0.888043	+	1.10063i	−0.627941	+	0.778261i
$3$	−2.01002	−	0.731586i	−1.16048	−	0.422382i	−0.311214	−	0.950340i	$-0.600736\pi$
$3$	−2.01002	−	0.731586i	−1.16048	−	0.422382i	−0.849270	+	0.527958i	$0.822958\pi$
$4$	−0.422760	−	1.95481i	−0.211380	−	0.977404i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$5$	−0.173648	−	0.984808i	−0.0776578	−	0.440419i
$6$	2.59019	−	1.56260i	1.05744	−	0.637929i
$7$	0.167166	+	0.0965133i	0.0631828	+	0.0364786i	0.531259	−	0.847210i	$-0.321719\pi$
$7$	0.167166	+	0.0965133i	0.0631828	+	0.0364786i	−0.468076	+	0.883688i	$0.655053\pi$
$8$	2.52694	+	1.27065i	0.893410	+	0.449243i
$9$	1.20682	+	1.01264i	0.402272	+	0.337547i
$10$	1.23811	+	0.683429i	0.391526	+	0.216119i
$11$	1.70813	−	0.986190i	0.515021	−	0.297348i	−0.219874	−	0.975528i	$-0.570565\pi$
$11$	1.70813	−	0.986190i	0.515021	−	0.297348i	0.734895	+	0.678181i	$0.237231\pi$
$12$	−0.580355	+	4.23848i	−0.167534	+	1.22354i
$13$	0.184786	+	0.507695i	0.0512504	+	0.140809i	0.962677	−	0.270654i	$-0.0872400\pi$
$13$	0.184786	+	0.507695i	0.0512504	+	0.140809i	−0.911426	+	0.411464i	$0.865018\pi$
$14$	−0.254676	+	0.0982794i	−0.0680649	+	0.0262663i
$15$	−0.371436	+	2.10652i	−0.0959044	+	0.543901i
$16$	−3.64255	+	1.65283i	−0.910637	+	0.413208i
$17$	−5.25273	+	4.40756i	−1.27397	+	1.06899i	−0.279929	+	0.960021i	$0.590311\pi$
$17$	−5.25273	+	4.40756i	−1.27397	+	1.06899i	−0.994045	+	0.108970i	$0.965245\pi$
$18$	−2.18624	+	0.428988i	−0.515303	+	0.101114i
$19$	−2.29593	−	3.70523i	−0.526722	−	0.850038i
$19$	−2.29593	−	3.70523i	−0.526722	−	0.850038i
$20$	−1.85170	+	0.755786i	−0.414052	+	0.168999i
$21$	−0.265399	−	0.316290i	−0.0579147	−	0.0690201i
$22$	−0.431466	+	2.75579i	−0.0919889	+	0.587537i
$23$	−5.85438	−	1.03229i	−1.22072	−	0.215246i	−0.474086	−	0.880478i	$-0.657221\pi$
$23$	−5.85438	−	1.03229i	−1.22072	−	0.215246i	−0.746637	+	0.665232i	$0.768333\pi$
$24$	−4.14961	−	4.40271i	−0.847035	−	0.898699i
$25$	−0.939693	+	0.342020i	−0.187939	+	0.0684040i
$26$	−0.722881	−	0.247475i	−0.141769	−	0.0485338i
$27$	1.52363	+	2.63901i	0.293223	+	0.507878i
$28$	0.117994	−	0.367579i	0.0222987	−	0.0694659i
$29$	−2.24172	+	2.67158i	−0.416278	+	0.496100i	−0.932911	−	0.360106i	$-0.882740\pi$
$29$	−2.24172	+	2.67158i	−0.416278	+	0.496100i	0.516634	+	0.856207i	$0.327185\pi$
$30$	−1.98864	−	2.27949i	−0.363075	−	0.416176i
$31$	−0.473866	+	0.820760i	−0.0851088	+	0.147413i	−0.905438	−	0.424479i	$-0.860457\pi$
$31$	−0.473866	+	0.820760i	−0.0851088	+	0.147413i	0.820329	+	0.571892i	$0.193790\pi$
$32$	1.41559	−	5.47687i	0.250243	−	0.968183i
$33$	−4.15486	+	0.732613i	−0.723268	+	0.127532i
$34$	−0.186436	−	9.69540i	−0.0319735	−	1.66275i
$35$	0.0660190	−	0.181386i	0.0111592	−	0.0306598i
$36$	1.46932	−	2.78720i	0.244887	−	0.464533i
$37$			1.95740i			0.321795i	0.986971	+	0.160898i	$0.0514389\pi$
$37$			1.95740i			0.321795i	−0.986971	+	0.160898i	$0.948561\pi$
$38$	6.11696	+	0.763442i	0.992301	+	0.123847i
$39$		−	1.15566i		−	0.185054i
$40$	0.812548	−	2.70920i	0.128475	−	0.428362i
$41$	−2.27152	+	6.24094i	−0.354751	+	0.974671i	0.626071	+	0.779766i	$0.284662\pi$
$41$	−2.27152	+	6.24094i	−0.354751	+	0.974671i	−0.980822	+	0.194905i	$0.937560\pi$
$42$	0.583802	−	0.0112261i	0.0900826	−	0.00173223i
$43$	−7.09043	+	1.25023i	−1.08128	+	0.190659i	−0.685781	−	0.727808i	$-0.740539\pi$
$43$	−7.09043	+	1.25023i	−1.08128	+	0.190659i	−0.395499	+	0.918467i	$0.629428\pi$
$44$	−2.64994	−	2.92215i	−0.399494	−	0.440530i
$45$	0.787694	−	1.36433i	0.117423	−	0.203382i
$46$	6.33510	−	5.52678i	0.934060	−	0.814879i
$47$	−2.76199	+	3.29161i	−0.402878	+	0.480131i	−0.928895	−	0.370343i	$-0.879240\pi$
$47$	−2.76199	+	3.29161i	−0.402878	+	0.480131i	0.526017	+	0.850474i	$0.323685\pi$
$48$	8.53077	−	0.657379i	1.23131	−	0.0948845i
$49$	−3.48137	−	6.02991i	−0.497339	−	0.861416i
$50$	0.458051	−	1.33798i	0.0647781	−	0.189219i
$51$	13.7826	−	5.01645i	1.92995	−	0.702444i
$52$	0.914327	−	0.575855i	0.126794	−	0.0798567i
$53$	−0.276364	−	0.0487304i	−0.0379615	−	0.00669363i	0.154635	−	0.987972i	$-0.450580\pi$
$53$	−0.276364	−	0.0487304i	−0.0379615	−	0.00669363i	−0.192597	+	0.981278i	$0.561691\pi$
$54$	−4.25762	−	0.666602i	−0.579388	−	0.0907130i
$55$	−1.26782	−	1.51093i	−0.170953	−	0.203734i
$56$	0.299784	+	0.456293i	0.0400603	+	0.0609747i
$57$	1.90416	+	9.12724i	0.252212	+	1.20893i
$58$	−0.949670	−	4.83978i	−0.124698	−	0.635494i
$59$	0.263884	−	0.221425i	0.0343547	−	0.0288270i	−0.625449	−	0.780265i	$-0.715084\pi$
$59$	0.263884	−	0.221425i	0.0343547	−	0.0288270i	0.659803	+	0.751438i	$0.270640\pi$
$60$	4.27487	−	0.164466i	0.551883	−	0.0212325i
$61$	1.11630	−	6.33087i	0.142928	−	0.810585i	−0.826079	−	0.563554i	$-0.809434\pi$
$61$	1.11630	−	6.33087i	0.142928	−	0.810585i	0.969007	−	0.247031i	$-0.0794551\pi$
$62$	−0.482537	−	1.25042i	−0.0612823	−	0.158803i
$63$	0.104005	+	0.285753i	0.0131035	+	0.0360015i
$64$	4.77089	+	6.42173i	0.596361	+	0.802716i
$65$	0.467895	−	0.270139i	0.0580352	−	0.0335066i
$66$	2.88336	−	5.22354i	0.354917	−	0.642973i
$67$	6.99246	+	5.86737i	0.854264	+	0.716813i	0.960724	−	0.277504i	$-0.0895072\pi$
$67$	6.99246	+	5.86737i	0.854264	+	0.716813i	−0.106460	+	0.994317i	$0.533952\pi$
$68$	10.8366	+	8.40473i	1.31413	+	1.01922i
$69$	11.0122	+	6.35790i	1.32571	+	0.765401i
$70$	0.141010	+	0.233740i	0.0168540	+	0.0279373i
$71$	1.93531	+	10.9757i	0.229679	+	1.30258i	0.853535	+	0.521036i	$0.174454\pi$
$71$	1.93531	+	10.9757i	0.229679	+	1.30258i	−0.623856	+	0.781540i	$0.714435\pi$
$72$	1.76285	+	4.09233i	0.207754	+	0.482286i
$73$	−7.82470	−	2.84796i	−0.915812	−	0.333328i	−0.159241	−	0.987240i	$-0.550905\pi$
$73$	−7.82470	−	2.84796i	−0.915812	−	0.333328i	−0.756571	+	0.653911i	$0.773127\pi$
$74$	−2.15437	−	1.73826i	−0.250441	−	0.202068i
$75$	2.13902			0.246992
$76$	−6.27238	+	6.05452i	−0.719492	+	0.694501i
$77$	0.380722			0.0433873
$78$	1.27195	+	1.02628i	0.144020	+	0.116203i
$79$	−5.99067	−	2.18043i	−0.674003	−	0.245317i	−0.0177327	−	0.999843i	$-0.505645\pi$
$79$	−5.99067	−	2.18043i	−0.674003	−	0.245317i	−0.656271	+	0.754526i	$0.727867\pi$
$80$	2.26024	+	3.30020i	0.252703	+	0.368973i
$81$	−1.95256	−	11.0735i	−0.216951	−	1.23039i
$82$	−4.85174	−	8.04231i	−0.535786	−	0.888125i
$83$	6.78214	+	3.91567i	0.744436	+	0.429800i	0.823680	−	0.567055i	$-0.191917\pi$
$83$	6.78214	+	3.91567i	0.744436	+	0.429800i	−0.0792438	+	0.996855i	$0.525251\pi$
$84$	−0.506085	+	0.652518i	−0.0552185	+	0.0711955i
$85$	5.25273	+	4.40756i	0.569738	+	0.478067i
$86$	4.92056	−	8.91418i	0.530598	−	0.961241i
$87$	6.46040	−	3.72991i	0.692627	−	0.399889i
$88$	5.56946	−	0.321607i	0.593706	−	0.0342835i
$89$	4.02976	+	11.0717i	0.427154	+	1.17360i	0.947532	+	0.319660i	$0.103569\pi$
$89$	4.02976	+	11.0717i	0.427154	+	1.17360i	−0.520378	+	0.853936i	$0.674209\pi$
$90$	0.802108	+	2.07854i	0.0845497	+	0.219097i
$91$	−0.0181094	+	0.102704i	−0.00189838	+	0.0107663i
$92$	0.457080	+	11.8806i	0.0476539	+	1.23864i
$93$	1.55293	−	1.30307i	0.161032	−	0.135122i
$94$	−1.17007	−	5.96302i	−0.120684	−	0.615038i
$95$	−3.25025	+	2.90445i	−0.333469	+	0.297991i
$96$	−6.85216	+	9.97298i	−0.699346	+	1.01786i
$97$	−6.50646	−	7.75410i	−0.660631	−	0.787310i	0.326845	−	0.945078i	$-0.394015\pi$
$97$	−6.50646	−	7.75410i	−0.660631	−	0.787310i	−0.987476	+	0.157768i	$0.949570\pi$
$98$	9.72829	+	1.52313i	0.982706	+	0.153859i
$99$	3.06006	+	0.539571i	0.307547	+	0.0542289i
$100$	1.06585	+	1.69233i	0.106585	+	0.169233i
$101$	−12.2577	+	4.46142i	−1.21968	+	0.443928i	−0.870052	−	0.492960i	$-0.835915\pi$
$101$	−12.2577	+	4.46142i	−1.21968	+	0.443928i	−0.349630	+	0.936888i	$0.613693\pi$
$102$	−6.71828	+	19.6243i	−0.665209	+	1.94310i
$103$	−8.98038	−	15.5545i	−0.884863	−	1.53263i	−0.845871	−	0.533388i	$-0.820919\pi$
$103$	−8.98038	−	15.5545i	−0.884863	−	1.53263i	−0.0389920	−	0.999240i	$-0.512415\pi$
$104$	−0.178160	+	1.51772i	−0.0174700	+	0.148824i
$105$	−0.265399	+	0.316290i	−0.0259002	+	0.0308667i
$106$	0.299057	−	0.260899i	0.0290469	−	0.0253407i
$107$	0.685314	−	1.18700i	0.0662519	−	0.114752i	−0.830997	−	0.556277i	$-0.812229\pi$
$107$	0.685314	−	1.18700i	0.0662519	−	0.114752i	0.897249	+	0.441526i	$0.145563\pi$
$108$	4.51463	−	4.09408i	0.434420	−	0.393953i
$109$	19.9304	−	3.51426i	1.90898	−	0.336605i	0.911736	−	0.410776i	$-0.134742\pi$
$109$	19.9304	−	3.51426i	1.90898	−	0.336605i	0.997246	+	0.0741705i	$0.0236309\pi$
$110$	2.78885	−	0.0536277i	0.265907	−	0.00511320i
$111$	1.43201	−	3.93441i	0.135920	−	0.373438i
$112$	−0.768430	−	0.0752573i	−0.0726098	−	0.00711115i
$113$		−	4.28150i		−	0.402770i	−0.979512	−	0.201385i	$-0.935456\pi$
$113$		−	4.28150i		−	0.402770i	0.979512	−	0.201385i	$-0.0645442\pi$
$114$	−11.7367	−	6.00961i	−1.09924	−	0.562852i
$115$			5.94469i			0.554346i
$116$	6.17014	+	3.25270i	0.572883	+	0.302006i
$117$	−0.291110	+	0.799817i	−0.0269131	+	0.0739431i
$118$	0.00936605	+	0.487072i	0.000862215	+	0.0448386i
$119$	−1.30347	+	0.229836i	−0.119488	+	0.0210690i
$120$	−3.61525	+	4.85109i	−0.330026	+	0.442842i
$121$	−3.55486	+	6.15720i	−0.323169	+	0.559745i
$122$	5.97660	+	6.85072i	0.541096	+	0.620235i
$123$	9.13157	−	10.8826i	0.823366	−	0.981250i
$124$	1.80476	+	0.579332i	0.162072	+	0.0520255i
$125$	0.500000	+	0.866025i	0.0447214	+	0.0774597i
$126$	−0.406869	−	0.139289i	−0.0362467	−	0.0124089i
$127$	2.72908	−	0.993303i	0.242166	−	0.0881414i	−0.218086	−	0.975930i	$-0.569981\pi$
$127$	2.72908	−	0.993303i	0.242166	−	0.0881414i	0.460252	+	0.887788i	$0.347759\pi$
$128$	−11.3047	−	0.451799i	−0.999202	−	0.0399338i
$129$	15.1665	+	2.67427i	1.33534	+	0.235456i
$130$	−0.118188	+	0.754872i	−0.0103658	+	0.0662067i
$131$	−9.09735	−	10.8418i	−0.794839	−	0.947252i	0.204662	−	0.978833i	$-0.434390\pi$
$131$	−9.09735	−	10.8418i	−0.794839	−	0.947252i	−0.999501	+	0.0315803i	$0.989946\pi$
$132$	3.18863	+	7.81223i	0.277534	+	0.679967i
$133$	−0.0261969	−	0.840975i	−0.00227156	−	0.0729218i
$134$	−12.6674	+	2.48561i	−1.09430	+	0.214724i
$135$	2.33434	−	1.95875i	0.200908	−	0.168582i
$136$	−18.8738	+	4.46328i	−1.61842	+	0.382723i
$137$	1.20410	−	6.82878i	0.102873	−	0.583422i	−0.889176	−	0.457566i	$-0.848721\pi$
$137$	1.20410	−	6.82878i	0.102873	−	0.583422i	0.992049	−	0.125856i	$-0.0401676\pi$
$138$	−16.7770	+	6.47424i	−1.42815	+	0.551124i
$139$	−0.636283	−	1.74817i	−0.0539688	−	0.148278i	0.909779	−	0.415093i	$-0.136251\pi$
$139$	−0.636283	−	1.74817i	−0.0539688	−	0.148278i	−0.963748	+	0.266815i	$0.914029\pi$
$140$	−0.382484	−	0.0523718i	−0.0323258	−	0.00442622i
$141$	7.95975	−	4.59557i	0.670332	−	0.387016i
$142$	−13.7988	−	7.61683i	−1.15797	−	0.639190i
$143$	0.816323	+	0.684976i	0.0682643	+	0.0572806i
$144$	−6.06961	−	1.69393i	−0.505801	−	0.141160i
$145$	3.02027	+	1.74375i	0.250819	+	0.144811i
$146$	10.0832	−	6.08297i	0.834493	−	0.503430i
$147$	2.58621	+	14.6671i	0.213307	+	1.20973i
$148$	3.82635	−	0.827512i	0.314524	−	0.0680211i
$149$	7.47722	+	2.72148i	0.612557	+	0.222953i	0.629622	−	0.776902i	$-0.283210\pi$
$149$	7.47722	+	2.72148i	0.612557	+	0.222953i	−0.0170644	+	0.999854i	$0.505432\pi$
$150$	−1.89954	+	2.35426i	−0.155097	+	0.192224i
$151$	−8.90533			−0.724706			−0.362353	−	0.932041i	$-0.618026\pi$
$151$	−8.90533			−0.724706			−0.362353	+	0.932041i	$0.618026\pi$
$152$	−1.09362	−	12.2802i	−0.0887046	−	0.996058i
$153$	−10.8024			−0.873319
$154$	−0.338097	+	0.419033i	−0.0272446	+	0.0337666i
$155$	0.890576	+	0.324143i	0.0715328	+	0.0260358i
$156$	−2.25910	+	0.488569i	−0.180873	+	0.0391168i
$157$	−3.50528	−	19.8794i	−0.279751	−	1.58655i	−0.723452	−	0.690374i	$-0.757446\pi$
$157$	−3.50528	−	19.8794i	−0.279751	−	1.58655i	0.443701	−	0.896175i	$-0.353665\pi$
$158$	7.71981	−	4.65718i	0.614155	−	0.370506i
$159$	0.519845	+	0.300133i	0.0412264	+	0.0238021i
$160$	−5.63948	−	0.443033i	−0.445840	−	0.0350249i
$161$	−0.879023	−	0.737588i	−0.0692768	−	0.0581301i
$162$	13.9217	+	7.68470i	1.09379	+	0.603767i
$163$	14.9980	−	8.65912i	1.17474	−	0.678234i	0.219945	−	0.975512i	$-0.429412\pi$
$163$	14.9980	−	8.65912i	1.17474	−	0.678234i	0.954791	+	0.297278i	$0.0960788\pi$
$164$	13.1601	+	1.80196i	1.02763	+	0.140709i
$165$	1.44297	+	3.96452i	0.112335	+	0.308637i
$166$	−10.3325	+	3.98732i	−0.801959	+	0.309476i
$167$	0.0700136	−	0.397067i	0.00541782	−	0.0307260i	−0.981979	−	0.188990i	$-0.939479\pi$
$167$	0.0700136	−	0.397067i	0.00541782	−	0.0307260i	0.987397	+	0.158264i	$0.0505897\pi$
$168$	−0.268753	−	1.13648i	−0.0207348	−	0.0876810i
$169$	9.73497	−	8.16861i	0.748844	−	0.628355i
$170$	−9.51573	+	1.86719i	−0.729823	+	0.143207i
$171$	0.981299	−	6.79648i	0.0750418	−	0.519740i
$172$	5.44152	+	13.3319i	0.414912	+	1.01655i
$173$	−16.5033	−	19.6679i	−1.25473	−	1.49532i	−0.794173	−	0.607692i	$-0.792096\pi$
$173$	−16.5033	−	19.6679i	−1.25473	−	1.49532i	−0.460553	−	0.887632i	$-0.652349\pi$
$174$	−1.63187	+	10.4228i	−0.123711	+	0.790151i
$175$	−0.190094	−	0.0335187i	−0.0143698	−	0.00253378i
$176$	−4.59194	+	6.41550i	−0.346131	+	0.483586i
$177$	−0.692402	+	0.252014i	−0.0520441	+	0.0189425i
$178$	−15.7644	−	5.39686i	−1.18159	−	0.404512i
$179$	−4.99102	−	8.64470i	−0.373046	−	0.646135i	0.616986	−	0.786974i	$-0.288353\pi$
$179$	−4.99102	−	8.64470i	−0.373046	−	0.646135i	−0.990033	+	0.140839i	$0.955020\pi$
$180$	−3.00000	−	0.963008i	−0.223607	−	0.0717784i
$181$	2.30358	−	2.74530i	0.171224	−	0.204057i	−0.673607	−	0.739089i	$-0.735256\pi$
$181$	2.30358	−	2.74530i	0.171224	−	0.204057i	0.844832	+	0.535032i	$0.179701\pi$
$182$	−0.0969565	−	0.111137i	−0.00718689	−	0.00823802i
$183$	−6.87537	+	11.9085i	−0.508242	+	0.880301i
$184$	−13.4820	−	10.0474i	−0.993907	−	0.740704i
$185$	1.92767	−	0.339900i	0.141725	−	0.0249899i
$186$	0.0551185	+	2.86638i	0.00404149	+	0.210173i
$187$	−4.62566	+	12.7089i	−0.338261	+	0.929366i
$188$	7.60213	+	4.00760i	0.554443	+	0.292284i
$189$			0.588203i			0.0427855i
$190$	−0.310355	−	6.15660i	−0.0225155	−	0.446646i
$191$		−	2.92503i		−	0.211648i	−0.994385	−	0.105824i	$-0.966252\pi$
$191$		−	2.92503i		−	0.211648i	0.994385	−	0.105824i	$-0.0337480\pi$
$192$	−4.89152	−	16.3981i	−0.353015	−	1.18343i
$193$	2.04507	−	5.61878i	0.147207	−	0.404449i	−0.844071	−	0.536231i	$-0.819848\pi$
$193$	2.04507	−	5.61878i	0.147207	−	0.404449i	0.991279	+	0.131782i	$0.0420699\pi$
$194$	14.3124	−	0.275217i	1.02757	−	0.0197595i
$195$	−1.13811	+	0.200679i	−0.0815015	+	0.0143709i
$196$	−10.3155	+	9.35462i	−0.736824	+	0.668187i
$197$	1.14911	−	1.99031i	0.0818706	−	0.141804i	−0.822183	−	0.569223i	$-0.807244\pi$
$197$	1.14911	−	1.99031i	0.0818706	−	0.141804i	0.904053	+	0.427420i	$0.140577\pi$
$198$	−3.31133	+	2.88882i	−0.235326	+	0.205300i
$199$	−13.8825	+	16.5446i	−0.984107	+	1.17281i	0.000847763		1.00000i	$0.499730\pi$
$199$	−13.8825	+	16.5446i	−0.984107	+	1.17281i	−0.984955	+	0.172813i	$0.944714\pi$
$200$	−2.80914	−	0.329756i	−0.198636	−	0.0233173i
$201$	−9.76247	−	16.9091i	−0.688592	−	1.19268i
$202$	5.97496	−	17.4530i	0.420397	−	1.22799i
$203$	−0.632583	+	0.230241i	−0.0443986	+	0.0161598i
$204$	−15.6329	−	24.8216i	−1.09452	−	1.73786i
$205$	6.54057	+	1.15328i	0.456813	+	0.0805485i
$206$	25.0946	+	3.92899i	1.74843	+	0.273745i
$207$	−6.01984	−	7.17416i	−0.418407	−	0.498639i
$208$	−1.51223	−	1.54388i	−0.104854	−	0.107049i
$209$	−7.57580	−	4.06480i	−0.524029	−	0.281168i
$210$	−0.112432	−	0.572984i	−0.00775853	−	0.0395396i
$211$	−17.0212	+	14.2825i	−1.17179	+	0.983245i	−0.999998	−	0.00188878i	$-0.999399\pi$
$211$	−17.0212	+	14.2825i	−1.17179	+	0.983245i	−0.171788	+	0.985134i	$0.554954\pi$
$212$	0.0215771	+	0.560839i	0.00148192	+	0.0385186i
$213$	4.13966	−	23.4772i	0.283645	−	1.60863i
$214$	0.697855	+	1.80838i	0.0477044	+	0.123618i
$215$	2.46248	+	6.76561i	0.167940	+	0.461411i
$216$	0.496874	+	8.60464i	0.0338080	+	0.585471i
$217$	−0.158428	+	0.0914687i	−0.0107548	+	0.00620930i
$218$	−13.8311	+	25.0567i	−0.936762	+	1.69705i
$219$	13.6443	+	11.4489i	0.921994	+	0.773645i
$220$	−2.41759	+	3.11711i	−0.162994	+	0.210155i
$221$	−3.20833	−	1.85233i	−0.215816	−	0.124601i
$222$	3.05864	+	5.07004i	0.205282	+	0.340279i
$223$	0.403155	+	2.28641i	0.0269972	+	0.153109i	0.995326	−	0.0965682i	$-0.0307866\pi$
$223$	0.403155	+	2.28641i	0.0269972	+	0.153109i	−0.968329	+	0.249677i	$0.919675\pi$
$224$	0.765229	−	0.778923i	0.0511290	−	0.0520440i
$225$	−1.48038	−	0.538815i	−0.0986920	−	0.0359210i
$226$	4.71233	+	3.80215i	0.313460	+	0.252916i
$227$	−4.72705			−0.313745			−0.156873	−	0.987619i	$-0.550141\pi$
$227$	−4.72705			−0.313745			−0.156873	+	0.987619i	$0.550141\pi$
$228$	17.0370	−	7.58090i	1.12830	−	0.502057i
$229$	8.51537			0.562711			0.281356	−	0.959604i	$-0.409216\pi$
$229$	8.51537			0.562711			0.281356	+	0.959604i	$0.409216\pi$
$230$	−6.54289	−	5.27914i	−0.431426	−	0.348096i
$231$	−0.765257	−	0.278531i	−0.0503502	−	0.0183260i
$232$	−9.05936	+	3.90249i	−0.594776	+	0.256211i
$233$	2.55928	+	14.5144i	0.167664	+	0.950868i	0.946275	+	0.323362i	$0.104813\pi$
$233$	2.55928	+	14.5144i	0.167664	+	0.950868i	−0.778612	+	0.627506i	$0.784076\pi$
$234$	−0.621783	−	1.03068i	−0.0406472	−	0.0673773i
$235$	3.72122	+	2.14845i	0.242746	+	0.140149i
$236$	−0.544402	−	0.422232i	−0.0354376	−	0.0274850i
$237$	10.4462	+	8.76539i	0.678553	+	0.569373i
$238$	0.904569	−	1.63873i	0.0586345	−	0.106223i
$239$	7.09105	−	4.09402i	0.458682	−	0.264820i	−0.252808	−	0.967516i	$-0.581354\pi$
$239$	7.09105	−	4.09402i	0.458682	−	0.264820i	0.711490	+	0.702696i	$0.248021\pi$
$240$	−2.12874	−	8.28702i	−0.137410	−	0.534925i
$241$	9.69900	+	26.6478i	0.624768	+	1.71654i	0.695005	+	0.719005i	$0.255402\pi$
$241$	9.69900	+	26.6478i	0.624768	+	1.71654i	−0.0702372	+	0.997530i	$0.522376\pi$
$242$	−3.61991	−	9.38043i	−0.232697	−	0.602997i
$243$	−2.58909	+	14.6835i	−0.166090	+	0.941944i
$244$	−12.8476	+	0.494282i	−0.822481	+	0.0316432i
$245$	−5.33377	+	4.47556i	−0.340762	+	0.285933i
$246$	3.86844	+	19.7147i	0.246643	+	1.25696i
$247$	1.45687	−	1.85031i	0.0926986	−	0.117732i
$248$	−2.24033	+	1.47190i	−0.142261	+	0.0934654i
$249$	−10.7676	−	12.8323i	−0.682367	−	0.813213i
$250$	−1.39719	−	0.218754i	−0.0883662	−	0.0138352i
$251$	18.2440	+	3.21692i	1.15155	+	0.203050i	0.716654	−	0.697429i	$-0.245673\pi$
$251$	18.2440	+	3.21692i	1.15155	+	0.203050i	0.434900	+	0.900479i	$0.356784\pi$
$252$	0.514622	−	0.324116i	0.0324182	−	0.0204174i
$253$	−11.0181	+	4.01025i	−0.692701	+	0.252122i
$254$	−1.33028	+	3.88579i	−0.0834692	+	0.243816i
$255$	−7.33356	−	12.7021i	−0.459246	−	0.795437i
$256$	10.5363	−	12.0410i	0.658519	−	0.752564i
$257$	−6.02921	+	7.18533i	−0.376092	+	0.448208i	−0.920577	−	0.390562i	$-0.872281\pi$
$257$	−6.02921	+	7.18533i	−0.376092	+	0.448208i	0.544485	+	0.838771i	$0.316725\pi$
$258$	−16.4119	+	14.3178i	−1.02176	+	0.891390i
$259$	−0.188915	+	0.327211i	−0.0117386	+	0.0203319i
$260$	−0.725877	−	0.800440i	−0.0450170	−	0.0496412i
$261$	−5.41070	+	0.954053i	−0.334914	+	0.0590544i
$262$	20.0116	−	0.384809i	1.23632	−	0.0237736i
$263$	−3.32054	+	9.12311i	−0.204753	+	0.562555i	−0.998984	−	0.0450610i	$-0.985652\pi$
$263$	−3.32054	+	9.12311i	−0.204753	+	0.562555i	0.794231	+	0.607616i	$0.207874\pi$
$264$	−11.4300	−	3.42810i	−0.703467	−	0.210985i
$265$			0.280627i			0.0172388i
$266$	0.948864	+	0.717989i	0.0581786	+	0.0440227i
$267$		−	25.2024i		−	1.54236i
$268$	8.51344	−	16.1494i	0.520041	−	0.986481i
$269$	−5.23916	+	14.3945i	−0.319437	+	0.877647i	0.671218	+	0.741260i	$0.265771\pi$
$269$	−5.23916	+	14.3945i	−0.319437	+	0.877647i	−0.990656	+	0.136387i	$0.956451\pi$
$270$	0.0828531	+	4.30869i	0.00504228	+	0.262219i
$271$	−20.1226	+	3.54817i	−1.22236	+	0.215536i	−0.747343	−	0.664439i	$-0.768671\pi$
$271$	−20.1226	+	3.54817i	−1.22236	+	0.215536i	−0.475021	+	0.879974i	$0.657560\pi$
$272$	11.8484	−	24.7366i	0.718412	−	1.49988i
$273$	0.111537	−	0.193187i	0.00675052	−	0.0116922i
$274$	6.44665	+	7.38951i	0.389456	+	0.446417i
$275$	−1.26782	+	1.51093i	−0.0764525	+	0.0911126i
$276$	7.77295	−	24.2146i	0.467876	−	1.45755i
$277$	0.966462	+	1.67396i	0.0580691	+	0.100579i	0.893599	−	0.448867i	$-0.148172\pi$
$277$	0.966462	+	1.67396i	0.0580691	+	0.100579i	−0.835530	+	0.549446i	$0.814839\pi$
$278$	2.48913	+	0.852142i	0.149288	+	0.0511081i
$279$	−1.40300	+	0.510651i	−0.0839956	+	0.0305719i
$280$	0.397304	−	0.374464i	0.0237435	−	0.0223785i
$281$	11.4506	+	2.01905i	0.683084	+	0.120446i	0.504413	−	0.863463i	$-0.331709\pi$
$281$	11.4506	+	2.01905i	0.683084	+	0.120446i	0.178671	+	0.983909i	$0.442820\pi$
$282$	−2.01060	+	12.8418i	−0.119729	+	0.764717i
$283$	−2.11856	−	2.52480i	−0.125935	−	0.150084i	0.699393	−	0.714738i	$-0.253454\pi$
$283$	−2.11856	−	2.52480i	−0.125935	−	0.150084i	−0.825328	+	0.564654i	$0.809010\pi$
$284$	20.6372	−	8.42325i	1.22459	−	0.499828i
$285$	8.65793	−	3.46016i	0.512851	−	0.204962i
$286$	−1.47883	+	0.290179i	−0.0874452	+	0.0171586i
$287$	−0.982054	+	0.824041i	−0.0579688	+	0.0486416i
$288$	7.25445	−	5.17610i	0.427473	−	0.305005i
$289$	5.21253	−	29.5617i	0.306620	−	1.73893i
$290$	−4.60135	+	1.77566i	−0.270200	+	0.104270i
$291$	7.40531	+	20.3459i	0.434107	+	1.19270i
$292$	−2.25924	+	16.4998i	−0.132212	+	0.965578i
$293$	−26.3980	+	15.2409i	−1.54219	+	0.890382i	−0.543487	+	0.839418i	$0.682896\pi$
$293$	−26.3980	+	15.2409i	−1.54219	+	0.890382i	−0.998700	+	0.0509645i	$0.983770\pi$
$294$	−18.4397	−	10.1786i	−1.07543	−	0.593628i
$295$	−0.263884	−	0.221425i	−0.0153639	−	0.0128918i
$296$	−2.48718	+	4.94625i	−0.144564	+	0.287495i
$297$	5.20513	+	3.00518i	0.302032	+	0.174378i
$298$	−9.63543	+	5.81283i	−0.558165	+	0.336728i
$299$	−0.557721	−	3.16299i	−0.0322538	−	0.182921i
$300$	−0.904291	−	4.18136i	−0.0522093	−	0.241411i
$301$	−1.30594	−	0.475324i	−0.0752732	−	0.0273972i
$302$	7.90831	−	9.80145i	0.455072	−	0.564010i
$303$	27.9020			1.60293
$304$	14.4871	+	9.70169i	0.830894	+	0.556430i
$305$	−6.42854			−0.368097
$306$	9.59296	−	11.8894i	0.548393	−	0.679670i
$307$	9.60038	+	3.49425i	0.547923	+	0.199428i	0.601123	−	0.799156i	$-0.294720\pi$
$307$	9.60038	+	3.49425i	0.547923	+	0.199428i	−0.0532006	+	0.998584i	$0.516942\pi$
$308$	−0.160954	−	0.744238i	−0.00917121	−	0.0424069i
$309$	6.67127	+	37.8347i	0.379516	+	2.15234i
$310$	−1.14763	+	0.692339i	−0.0651810	+	0.0393222i
$311$	−29.4883	−	17.0251i	−1.67213	−	0.965405i	−0.966443	−	0.256880i	$-0.917305\pi$
$311$	−29.4883	−	17.0251i	−1.67213	−	0.965405i	−0.705686	−	0.708524i	$-0.749361\pi$
$312$	1.46845	−	2.92030i	0.0831343	−	0.165329i
$313$	26.3157	+	22.0815i	1.48745	+	1.24812i	0.897752	+	0.440501i	$0.145199\pi$
$313$	26.3157	+	22.0815i	1.48745	+	1.24812i	0.589702	+	0.807621i	$0.299245\pi$
$314$	24.9926	+	13.7958i	1.41042	+	0.778540i
$315$	0.263351	−	0.152046i	0.0148382	−	0.00856681i
$316$	−1.72970	+	12.6324i	−0.0973030	+	0.710629i
$317$	−10.0857	−	27.7103i	−0.566470	−	1.55636i	−0.809975	−	0.586465i	$-0.800519\pi$
$317$	−10.0857	−	27.7103i	−0.566470	−	1.55636i	0.243505	−	0.969900i	$-0.421703\pi$
$318$	−0.791979	+	0.305625i	−0.0444120	+	0.0171386i
$319$	−1.19447	+	6.77418i	−0.0668775	+	0.379281i
$320$	5.49571	−	5.81353i	0.307220	−	0.324986i
$321$	−2.24589	+	1.88452i	−0.125353	+	0.105184i
$322$	1.59242	−	0.312467i	0.0887421	−	0.0174131i
$323$	28.3909	+	9.34312i	1.57971	+	0.519865i
$324$	−20.8211	+	8.49830i	−1.15673	+	0.472128i
$325$	−0.347284	−	0.413877i	−0.0192639	−	0.0229578i
$326$	−3.78843	+	24.1969i	−0.209822	+	1.34014i
$327$	−42.6313	−	7.51706i	−2.35752	−	0.415694i
$328$	−13.6701	+	12.8842i	−0.754802	+	0.711411i
$329$	−0.779395	+	0.283677i	−0.0429695	+	0.0156396i
$330$	−5.64487	−	1.93249i	−0.310740	−	0.106380i
$331$	−10.3553	−	17.9359i	−0.569177	−	0.985844i	−0.996648	−	0.0818145i	$-0.973928\pi$
$331$	−10.3553	−	17.9359i	−0.569177	−	0.985844i	0.427470	−	0.904029i	$-0.359405\pi$
$332$	4.78716	−	14.9132i	0.262730	−	0.818466i
$333$	−1.98215	+	2.36223i	−0.108621	+	0.129449i
$334$	0.374848	+	0.429671i	0.0205108	+	0.0235106i
$335$	4.56400	−	7.90508i	0.249358	−	0.431901i
$336$	1.48950	+	0.713441i	0.0812589	+	0.0389214i
$337$	31.0167	−	5.46908i	1.68959	−	0.297920i	0.755548	−	0.655093i	$-0.227370\pi$
$337$	31.0167	−	5.46908i	1.68959	−	0.297920i	0.934038	+	0.357173i	$0.116259\pi$
$338$	0.345525	+	17.9686i	0.0187941	+	0.977365i
$339$	−3.13229	+	8.60589i	−0.170122	+	0.467408i
$340$	6.39529	−	12.1314i	0.346833	−	0.657919i
$341$			1.86929i			0.101228i
$342$	6.60896	+	7.11561i	0.357371	+	0.384768i
$343$		−	2.69518i		−	0.145526i
$344$	−19.5057	−	5.85019i	−1.05168	−	0.315421i
$345$	4.34906	−	11.9489i	0.234145	−	0.643309i
$346$	36.3027	−	0.698076i	1.95165	−	0.0375288i
$347$	34.8766	−	6.14969i	1.87227	−	0.330133i	0.882222	−	0.470833i	$-0.156047\pi$
$347$	34.8766	−	6.14969i	1.87227	−	0.330133i	0.990052	+	0.140700i	$0.0449354\pi$
$348$	−10.0225	−	11.0520i	−0.537260	−	0.592448i
$349$	−12.0221	+	20.8229i	−0.643528	+	1.11462i	0.341111	+	0.940023i	$0.389197\pi$
$349$	−12.0221	+	20.8229i	−0.643528	+	1.11462i	−0.984639	+	0.174601i	$0.944137\pi$
$350$	0.205703	−	0.179457i	0.0109953	−	0.00959236i
$351$	−1.05827	+	1.26119i	−0.0564861	+	0.0673175i
$352$	−2.98323	−	10.7513i	−0.159006	−	0.573044i
$353$	2.64401	+	4.57955i	0.140726	+	0.243745i	0.927770	−	0.373152i	$-0.121723\pi$
$353$	2.64401	+	4.57955i	0.140726	+	0.243745i	−0.787044	+	0.616897i	$0.788390\pi$
$354$	0.337509	−	0.985875i	0.0179384	−	0.0523987i
$355$	10.4729	−	3.81182i	0.555843	−	0.202310i
$356$	19.9394	−	12.5581i	1.05679	−	0.665577i
$357$	2.78813	+	0.491623i	0.147564	+	0.0260195i
$358$	13.9468	+	2.18361i	0.737113	+	0.115407i
$359$	9.81114	+	11.6925i	0.517812	+	0.617105i	0.960062	−	0.279787i	$-0.0902640\pi$
$359$	9.81114	+	11.6925i	0.517812	+	0.617105i	−0.442250	+	0.896892i	$0.645820\pi$
$360$	3.72404	−	2.44669i	0.196274	−	0.128952i
$361$	−8.45744	+	17.0139i	−0.445128	+	0.895467i
$362$	0.975876	+	4.97334i	0.0512909	+	0.261393i
$363$	11.6498	−	9.77538i	0.611458	−	0.513075i
$364$	0.208422	−	0.00801858i	0.0109243	−	0.000420288i
$365$	−1.44595	+	8.20037i	−0.0756843	+	0.429227i
$366$	−7.00119	−	18.1425i	−0.365958	−	0.948322i
$367$	−10.1507	−	27.8889i	−0.529865	−	1.45579i	−0.859231	−	0.511589i	$-0.829057\pi$
$367$	−10.1507	−	27.8889i	−0.529865	−	1.45579i	0.329366	−	0.944202i	$-0.393165\pi$
$368$	23.0311	−	5.91615i	1.20058	−	0.308401i
$369$	−9.06113	+	5.23145i	−0.471704	+	0.272338i
$370$	−1.33775	+	2.42349i	−0.0695462	+	0.125991i
$371$	−0.0414954	−	0.0348188i	−0.00215434	−	0.00180770i
$372$	−3.20377	−	2.48480i	−0.166107	−	0.128831i
$373$	−16.4506	−	9.49776i	−0.851780	−	0.491776i	0.00947088	−	0.999955i	$-0.496985\pi$
$373$	−16.4506	−	9.49776i	−0.851780	−	0.491776i	−0.861251	+	0.508180i	$0.830319\pi$
$374$	−9.87996	−	16.3772i	−0.510881	−	0.846843i
$375$	−0.371436	−	2.10652i	−0.0191809	−	0.108780i
$376$	−11.1619	+	4.80820i	−0.575631	+	0.247964i
$377$	−1.77059	−	0.644442i	−0.0911900	−	0.0331904i
$378$	−0.647393	−	0.522350i	−0.0332983	−	0.0268668i
$379$	28.9106			1.48504			0.742519	−	0.669825i	$-0.233631\pi$
$379$	28.9106			1.48504			0.742519	+	0.669825i	$0.233631\pi$
$380$	7.05173	+	5.12574i	0.361746	+	0.262945i
$381$	−6.21218			−0.318260
$382$	3.21937	+	2.59756i	0.164717	+	0.132903i
$383$	1.32675	+	0.482897i	0.0677938	+	0.0246749i	0.375694	−	0.926744i	$-0.377404\pi$
$383$	1.32675	+	0.482897i	0.0677938	+	0.0246749i	−0.307901	+	0.951419i	$0.599626\pi$
$384$	22.3921	+	9.17848i	1.14269	+	0.468387i
$385$	−0.0661116	−	0.374938i	−0.00336936	−	0.0191086i
$386$	4.36808	+	7.24058i	0.222329	+	0.368536i
$387$	−9.82289	−	5.67125i	−0.499325	−	0.288286i
$388$	−12.4071	+	15.9970i	−0.629875	+	0.812125i
$389$	−5.25821	−	4.41216i	−0.266602	−	0.223705i	0.499680	−	0.866210i	$-0.333451\pi$
$389$	−5.25821	−	4.41216i	−0.266602	−	0.223705i	−0.766282	+	0.642505i	$0.777895\pi$
$390$	0.789814	−	1.43084i	0.0399938	−	0.0724535i
$391$	35.3013	−	20.3812i	1.78527	−	1.03072i
$392$	−1.13531	−	19.6609i	−0.0573420	−	0.993023i
$393$	10.3541	+	28.4477i	0.522296	+	1.43500i
$394$	1.17014	+	3.03222i	0.0589506	+	0.152761i
$395$	−1.10703	+	6.27829i	−0.0557008	+	0.315895i
$396$	−0.238914	−	6.20993i	−0.0120059	−	0.312061i
$397$	−27.8638	+	23.3805i	−1.39844	+	1.17343i	−0.436656	+	0.899629i	$0.643837\pi$
$397$	−27.8638	+	23.3805i	−1.39844	+	1.17343i	−0.961786	+	0.273803i	$0.911718\pi$
$398$	−5.88111	−	29.9718i	−0.294793	−	1.50235i
$399$	−0.562590	+	1.70954i	−0.0281647	+	0.0855840i
$400$	2.85757	−	2.79898i	0.142879	−	0.139949i
$401$	−10.2394	−	12.2028i	−0.511330	−	0.609379i	0.447178	−	0.894445i	$-0.352429\pi$
$401$	−10.2394	−	12.2028i	−0.511330	−	0.609379i	−0.958508	+	0.285066i	$0.907985\pi$
$402$	27.2801	+	4.27116i	1.36061	+	0.213026i
$403$	−0.504260	−	0.0889146i	−0.0251190	−	0.00442915i
$404$	13.9033	+	22.0752i	0.691714	+	1.09828i
$405$	−10.5662	+	3.84578i	−0.525039	+	0.191098i
$406$	0.308351	−	0.900702i	0.0153032	−	0.0447011i
$407$	1.93037	+	3.34350i	0.0956850	+	0.165731i
$408$	41.2020	+	4.83657i	2.03980	+	0.239446i
$409$	6.78361	−	8.08439i	0.335428	−	0.399747i	−0.571796	−	0.820396i	$-0.693753\pi$
$409$	6.78361	−	8.08439i	0.335428	−	0.399747i	0.907224	+	0.420649i	$0.138197\pi$
$410$	−7.07764	+	6.17457i	−0.349540	+	0.304940i
$411$	−7.41610	+	12.8451i	−0.365809	+	0.633600i
$412$	−26.6095	+	24.1307i	−1.31095	+	1.18884i
$413$	0.0654827	−	0.0115464i	0.00322219	−	0.000568160i
$414$	13.2419	−	0.254633i	0.650806	−	0.0125146i
$415$	2.67848	−	7.35905i	0.131481	−	0.361242i
$416$	3.04216	−	0.293362i	0.149154	−	0.0143832i
$417$			3.97936i			0.194870i
$418$	11.2015	−	4.72842i	0.547882	−	0.231275i
$419$		−	27.3089i		−	1.33412i	−0.745002	−	0.667062i	$-0.767551\pi$
$419$		−	27.3089i		−	1.33412i	0.745002	−	0.667062i	$-0.232449\pi$
$420$	0.730485	+	0.385088i	0.0356440	+	0.0187904i
$421$	−2.95524	+	8.11946i	−0.144030	+	0.395718i	−0.990641	−	0.136493i	$-0.956417\pi$
$421$	−2.95524	+	8.11946i	−0.144030	+	0.395718i	0.846611	+	0.532212i	$0.178639\pi$
$422$	−0.604135	−	31.4174i	−0.0294088	−	1.52938i
$423$	−6.66644	+	1.17547i	−0.324133	+	0.0571535i
$424$	−0.636436	−	0.474301i	−0.0309081	−	0.0230341i
$425$	3.42848	−	5.93829i	0.166305	−	0.288050i
$426$	22.1634	+	25.4050i	1.07382	+	1.23087i
$427$	0.797621	−	0.950568i	0.0385996	−	0.0460012i
$428$	−2.61008	−	0.837842i	−0.126163	−	0.0404986i
$429$	−1.13970	−	1.97402i	−0.0550254	−	0.0953068i
$430$	−9.63320	−	3.29788i	−0.464554	−	0.159038i
$431$	22.1203	−	8.05115i	1.06550	−	0.387810i	0.251008	−	0.967985i	$-0.419238\pi$
$431$	22.1203	−	8.05115i	1.06550	−	0.387810i	0.814492	+	0.580175i	$0.197016\pi$
$432$	−9.91174	−	7.09441i	−0.476879	−	0.341330i
$433$	2.97417	+	0.524426i	0.142929	+	0.0252023i	0.244655	−	0.969610i	$-0.421325\pi$
$433$	2.97417	+	0.524426i	0.142929	+	0.0252023i	−0.101726	+	0.994812i	$0.532436\pi$
$434$	0.0400183	−	0.255599i	0.00192094	−	0.0122691i
$435$	−4.79508	−	5.71456i	−0.229907	−	0.273992i
$436$	−15.2955	−	37.4743i	−0.732520	−	1.79469i
$437$	9.61638	+	24.0619i	0.460014	+	1.15104i
$438$	−24.7177	+	4.85014i	−1.18106	+	0.231749i
$439$	−10.3465	+	8.68177i	−0.493813	+	0.414358i	−0.855390	−	0.517984i	$-0.826683\pi$
$439$	−10.3465	+	8.68177i	−0.493813	+	0.414358i	0.361578	+	0.932342i	$0.382238\pi$
$440$	−1.28385	−	5.42900i	−0.0612050	−	0.258817i
$441$	1.90475	−	10.8024i	0.0907024	−	0.514399i
$442$	4.88786	−	1.88623i	0.232492	−	0.0897187i
$443$	−7.77799	−	21.3698i	−0.369543	−	1.01531i	−0.975536	−	0.219841i	$-0.929446\pi$
$443$	−7.77799	−	21.3698i	−0.369543	−	1.01531i	0.605992	−	0.795470i	$-0.292776\pi$
$444$	−8.29642	−	1.13599i	−0.393731	−	0.0539117i
$445$	10.2037	−	5.89112i	0.483703	−	0.279266i
$446$	−2.87450	−	1.58670i	−0.136111	−	0.0751325i
$447$	−13.0383	−	10.9405i	−0.616692	−	0.517466i
$448$	0.177748	+	1.53395i	0.00839780	+	0.0724722i
$449$	−10.9977	−	6.34953i	−0.519014	−	0.299653i	0.217517	−	0.976056i	$-0.430204\pi$
$449$	−10.9977	−	6.34953i	−0.519014	−	0.299653i	−0.736531	+	0.676404i	$0.763537\pi$
$450$	1.90768	−	1.15086i	0.0899287	−	0.0542519i
$451$	2.27470	+	12.9005i	0.107112	+	0.607460i
$452$	−8.36951	+	1.81005i	−0.393669	+	0.0851375i
$453$	17.8999	+	6.51502i	0.841009	+	0.306102i
$454$	4.19782	−	5.20271i	0.197013	−	0.244175i
$455$	0.104288			0.00488910
$456$	−6.78585	+	25.4835i	−0.317776	+	1.19338i
$457$	−8.61310			−0.402904			−0.201452	−	0.979498i	$-0.564566\pi$
$457$	−8.61310			−0.402904			−0.201452	+	0.979498i	$0.564566\pi$
$458$	−7.56201	+	9.37225i	−0.353350	+	0.437936i
$459$	−19.6348	−	7.14650i	−0.916476	−	0.333570i
$460$	11.6207	−	2.51318i	0.541820	−	0.117178i
$461$	−4.50173	−	25.5306i	−0.209667	−	1.18908i	−0.889925	−	0.456106i	$-0.849244\pi$
$461$	−4.50173	−	25.5306i	−0.209667	−	1.18908i	0.680259	−	0.732972i	$-0.261867\pi$
$462$	0.986140	−	0.594916i	0.0458794	−	0.0276780i
$463$	−7.57555	−	4.37375i	−0.352066	−	0.203265i	0.313529	−	0.949579i	$-0.398489\pi$
$463$	−7.57555	−	4.37375i	−0.352066	−	0.203265i	−0.665595	+	0.746313i	$0.731822\pi$
$464$	3.74991	−	13.4366i	0.174085	−	0.623776i
$465$	−1.55293	−	1.30307i	−0.0720156	−	0.0604283i
$466$	−18.2477	−	10.0726i	−0.845306	−	0.466603i
$467$	−2.55552	+	1.47543i	−0.118256	+	0.0682748i	−0.557961	−	0.829867i	$-0.688416\pi$
$467$	−2.55552	+	1.47543i	−0.118256	+	0.0682748i	0.439706	+	0.898142i	$0.355083\pi$
$468$	1.68656	+	0.230932i	0.0779612	+	0.0106749i
$469$	0.602621	+	1.65569i	0.0278265	+	0.0764526i
$470$	−5.66925	+	2.18776i	−0.261503	+	0.100914i
$471$	−7.49784	+	42.5224i	−0.345482	+	1.95933i
$472$	0.948172	−	0.224223i	0.0436432	−	0.0103207i
$473$	−10.8784	+	9.12807i	−0.500190	+	0.419709i
$474$	−18.9241	+	3.71331i	−0.869212	+	0.170558i
$475$	3.42473	+	2.69652i	0.157137	+	0.123725i
$476$	1.00034	+	2.45086i	0.0458505	+	0.112335i
$477$	−0.284174	−	0.338665i	−0.0130114	−	0.0155064i
$478$	−1.79117	+	11.4403i	−0.0819260	+	0.523265i
$479$	−28.3395	−	4.99701i	−1.29486	−	0.228319i	−0.516583	−	0.856237i	$-0.672796\pi$
$479$	−28.3395	−	4.99701i	−1.29486	−	0.228319i	−0.778280	+	0.627918i	$0.783907\pi$
$480$	11.0113	+	5.01627i	0.502596	+	0.228960i
$481$	−0.993765	+	0.361701i	−0.0453118	+	0.0164921i
$482$	−37.9424	−	12.9894i	−1.72823	−	0.591651i
$483$	1.22724	+	2.12565i	0.0558415	+	0.0967203i
$484$	13.5390	+	4.34605i	0.615408	+	0.197548i
$485$	−6.50646	+	7.75410i	−0.295443	+	0.352096i
$486$	−13.8618	−	15.8892i	−0.628783	−	0.720747i
$487$	−8.61370	+	14.9194i	−0.390324	+	0.676061i	−0.992492	−	0.122308i	$-0.960970\pi$
$487$	−8.61370	+	14.9194i	−0.390324	+	0.676061i	0.602168	+	0.798369i	$0.294304\pi$
$488$	10.8652	−	14.5793i	0.491843	−	0.659975i
$489$	−36.4812	+	6.43262i	−1.64974	+	0.290893i
$490$	−0.189312	−	9.84498i	−0.00855225	−	0.444751i
$491$	7.93076	−	21.7896i	0.357910	−	0.983351i	−0.621843	−	0.783142i	$-0.713616\pi$
$491$	7.93076	−	21.7896i	0.357910	−	0.983351i	0.979753	−	0.200209i	$-0.0641620\pi$
$492$	−25.1338	−	13.2497i	−1.13312	−	0.597345i
$493$		−	23.9136i		−	1.07702i
$494$	0.742732	+	3.24662i	0.0334171	+	0.146073i
$495$		−	3.10726i		−	0.139661i
$496$	0.369502	−	3.77288i	0.0165911	−	0.169407i
$497$	−0.735782	+	2.02154i	−0.0330043	+	0.0906787i
$498$	23.6856	−	0.455458i	1.06138	−	0.0204096i
$499$	37.9031	−	6.68333i	1.69677	−	0.299187i	0.760208	−	0.649679i	$-0.225097\pi$
$499$	37.9031	−	6.68333i	1.69677	−	0.299187i	0.936566	+	0.350492i	$0.113986\pi$
$500$	1.48153	−	1.34353i	0.0662562	−	0.0600843i
$501$	−0.431218	+	0.746891i	−0.0192654	+	0.0333686i
$502$	−19.7421	+	17.2231i	−0.881134	+	0.768706i
$503$	−14.9462	+	17.8121i	−0.666416	+	0.794204i	−0.988291	−	0.152578i	$-0.951242\pi$
$503$	−14.9462	+	17.8121i	−0.666416	+	0.794204i	0.321875	+	0.946782i	$0.395687\pi$
$504$	−0.100276	+	0.854236i	−0.00446665	+	0.0380507i
$505$	6.52216	+	11.2967i	0.290232	+	0.502697i
$506$	5.37073	−	15.6881i	0.238758	−	0.697420i
$507$	−25.5435	+	9.29707i	−1.13443	+	0.412898i
$508$	−3.09546	−	4.91489i	−0.137339	−	0.218063i
$509$	−13.5173	−	2.38346i	−0.599143	−	0.105645i	−0.134152	−	0.990961i	$-0.542831\pi$
$509$	−13.5173	−	2.38346i	−0.599143	−	0.105645i	−0.464991	+	0.885316i	$0.653942\pi$
$510$	20.4928	+	3.20849i	0.907436	+	0.142074i
$511$	−1.03316	−	1.23127i	−0.0457042	−	0.0544681i
$512$	3.89599	+	22.2895i	0.172180	+	0.985065i
$513$	6.27999	−	11.7044i	0.277268	−	0.516761i
$514$	−2.55417	−	13.0168i	−0.112660	−	0.574146i
$515$	−13.7587	+	11.5449i	−0.606282	+	0.508731i
$516$	−1.18413	−	30.7782i	−0.0521282	−	1.35494i
$517$	−1.47169	+	8.34636i	−0.0647248	+	0.367072i
$518$	−0.192372	−	0.498503i	−0.00845236	−	0.0219030i
$519$	18.7832	+	51.6065i	0.824492	+	2.26527i
$520$	1.52560	−	0.0880953i	0.0669018	−	0.00386324i
$521$	2.81243	−	1.62375i	0.123215	−	0.0711380i	−0.437126	−	0.899400i	$-0.644004\pi$
$521$	2.81243	−	1.62375i	0.123215	−	0.0711380i	0.560341	+	0.828262i	$0.310670\pi$
$522$	3.75488	−	6.80241i	0.164347	−	0.297733i
$523$	−17.6595	−	14.8181i	−0.772196	−	0.647949i	0.169074	−	0.985603i	$-0.445922\pi$
$523$	−17.6595	−	14.8181i	−0.772196	−	0.647949i	−0.941270	+	0.337654i	$0.890367\pi$
$524$	−17.3476	+	22.3671i	−0.757835	+	0.977109i
$525$	0.357570	+	0.206443i	0.0156057	+	0.00900993i
$526$	−7.09236	−	11.7564i	−0.309242	−	0.512603i
$527$	−1.12846	−	6.39982i	−0.0491565	−	0.278781i
$528$	13.9234	−	9.53585i	0.605937	−	0.414995i
$529$	11.5952	+	4.22032i	0.504140	+	0.183492i
$530$	−0.308866	−	0.249209i	−0.0134163	−	0.0108249i
$531$	0.542683			0.0235504
$532$	−1.63287	+	0.406741i	−0.0707939	+	0.0176345i
$533$	−3.58824			−0.155424
$534$	27.7385	+	22.3808i	1.20036	+	0.968512i
$535$	−1.28797	−	0.468783i	−0.0556838	−	0.0202672i
$536$	10.2142	+	23.7115i	0.441185	+	1.02418i
$537$	3.70769	+	21.0274i	0.159999	+	0.907397i
$538$	−11.1904	−	18.5493i	−0.482451	−	0.799716i
$539$	−11.8933	−	6.86659i	−0.512280	−	0.295765i
$540$	−4.81584	−	3.73511i	−0.207241	−	0.160734i
$541$	9.59637	+	8.05231i	0.412580	+	0.346196i	0.825332	−	0.564648i	$-0.190988\pi$
$541$	9.59637	+	8.05231i	0.412580	+	0.346196i	−0.412752	+	0.910843i	$0.635432\pi$
$542$	13.9646	−	25.2985i	0.599829	−	1.08666i
$543$	−6.63867	+	3.83284i	−0.284893	+	0.164483i
$544$	16.7040	+	35.0078i	0.716176	+	1.50095i
$545$	−6.92174	−	19.0173i	−0.296495	−	0.814613i
$546$	0.113578	+	0.294319i	0.00486069	+	0.0125957i
$547$	−3.51935	+	19.9592i	−0.150477	+	0.853395i	0.812329	+	0.583200i	$0.198199\pi$
$547$	−3.51935	+	19.9592i	−0.150477	+	0.853395i	−0.962805	+	0.270196i	$0.912912\pi$
$548$	−13.8580	+	0.533156i	−0.591984	+	0.0227753i
$549$	7.75807	−	6.50979i	0.331106	−	0.277831i
$550$	−0.537092	−	2.73717i	−0.0229017	−	0.116713i
$551$	15.0457	+	2.17234i	0.640967	+	0.0925449i
$552$	19.7485	+	30.0587i	0.840554	+	1.27938i
$553$	−0.790996	−	0.942672i	−0.0336366	−	0.0400865i
$554$	−2.70067	−	0.422835i	−0.114740	−	0.0179645i
$555$	−4.12331	−	0.727050i	−0.175025	−	0.0308616i
$556$	−3.14835	+	1.98287i	−0.133520	+	0.0840924i
$557$	−21.3353	+	7.76540i	−0.904004	+	0.329031i	−0.751856	−	0.659327i	$-0.770841\pi$
$557$	−21.3353	+	7.76540i	−0.904004	+	0.329031i	−0.152148	+	0.988358i	$0.548619\pi$
$558$	0.683890	−	1.99766i	0.0289514	−	0.0845679i
$559$	−1.94495	−	3.36875i	−0.0822626	−	0.142483i
$560$	0.0593224	+	0.769824i	0.00250683	+	0.0325310i
$561$	18.5953	−	22.1610i	0.785094	−	0.935639i
$562$	−12.3908	+	10.8098i	−0.522675	+	0.455985i
$563$	−17.7749	+	30.7870i	−0.749122	+	1.29752i	0.199122	+	0.979975i	$0.436191\pi$
$563$	−17.7749	+	30.7870i	−0.749122	+	1.29752i	−0.948244	+	0.317543i	$0.897142\pi$
$564$	−12.3485	−	13.6170i	−0.519966	−	0.573378i
$565$	−4.21645	+	0.743475i	−0.177388	+	0.0312782i
$566$	4.66023	−	0.0896129i	0.195884	−	0.00376671i
$567$	0.742338	−	2.03956i	0.0311753	−	0.0856534i
$568$	−9.05586	+	30.1941i	−0.379975	+	1.26691i
$569$			19.4217i			0.814200i	0.913384	+	0.407100i	$0.133460\pi$
$569$			19.4217i			0.814200i	−0.913384	+	0.407100i	$0.866540\pi$
$570$	−3.88026	+	12.6019i	−0.162526	+	0.527836i
$571$			17.2537i			0.722043i	0.932558	+	0.361021i	$0.117572\pi$
$571$			17.2537i			0.722043i	−0.932558	+	0.361021i	$0.882428\pi$
$572$	0.993888	−	1.88534i	0.0415565	−	0.0788298i
$573$	−2.13992	+	5.87937i	−0.0893963	+	0.245614i
$574$	−0.0348562	−	1.81266i	−0.00145487	−	0.0756589i
$575$	5.85438	−	1.03229i	0.244145	−	0.0430493i
$576$	−0.745307	+	12.5810i	−0.0310545	+	0.524210i
$577$	12.8809	−	22.3104i	0.536240	−	0.928795i	−0.462862	−	0.886430i	$-0.653177\pi$
$577$	12.8809	−	22.3104i	0.536240	−	0.928795i	0.999102	−	0.0423649i	$-0.0134892\pi$
$578$	27.9075	+	31.9891i	1.16080	+	1.33057i
$579$	−8.22125	+	9.79771i	−0.341664	+	0.407179i
$580$	2.13185	−	6.64123i	0.0885203	−	0.275762i
$581$	0.755828	+	1.30913i	0.0313570	+	0.0543120i
$582$	−28.9695	−	9.91756i	−1.20082	−	0.411096i
$583$	−0.520123	+	0.189309i	−0.0215413	+	0.00784038i
$584$	−16.1538	−	17.1391i	−0.668450	−	0.709221i
$585$	0.838217	+	0.147800i	0.0346560	+	0.00611079i
$586$	6.66801	−	42.5889i	0.275453	−	1.75933i
$587$	1.39515	+	1.66268i	0.0575841	+	0.0686261i	0.794068	−	0.607829i	$-0.207960\pi$
$587$	1.39515	+	1.66268i	0.0575841	+	0.0686261i	−0.736484	+	0.676455i	$0.763515\pi$
$588$	27.5781	−	11.2562i	1.13730	−	0.464199i
$589$	4.12906	−	0.128623i	0.170135	−	0.00529981i
$590$	0.478046	−	0.0938029i	0.0196808	−	0.00386180i
$591$	−3.76581	+	3.15989i	−0.154905	+	0.129981i
$592$	−3.23526	−	7.12994i	−0.132968	−	0.293039i
$593$	0.194272	−	1.10177i	0.00797778	−	0.0452442i	−0.980559	−	0.196224i	$-0.937132\pi$
$593$	0.194272	−	1.10177i	0.00797778	−	0.0452442i	0.988537	+	0.150980i	$0.0482430\pi$
$594$	−7.92997	+	3.06018i	−0.325371	+	0.125561i
$595$	0.452689	+	1.24375i	0.0185584	+	0.0509889i
$596$	2.15891	−	15.7671i	0.0884323	−	0.645844i
$597$	40.0079	−	23.0986i	1.63741	−	0.945362i
$598$	3.97656	+	2.19503i	0.162614	+	0.0897615i
$599$	11.1169	+	9.32817i	0.454223	+	0.381139i	0.841000	−	0.541035i	$-0.181967\pi$
$599$	11.1169	+	9.32817i	0.454223	+	0.381139i	−0.386777	+	0.922173i	$0.626412\pi$
$600$	5.40517	+	2.71794i	0.220665	+	0.110960i
$601$	31.4865	+	18.1787i	1.28436	+	0.741526i	0.977642	−	0.210274i	$-0.0674357\pi$
$601$	31.4865	+	18.1787i	1.28436	+	0.741526i	0.306718	+	0.951800i	$0.400769\pi$
$602$	1.68289	−	1.01525i	0.0685893	−	0.0413784i
$603$	2.49709	+	14.1617i	0.101689	+	0.576708i
$604$	3.76482	+	17.4082i	0.153188	+	0.708330i
$605$	6.68095	+	2.43167i	0.271619	+	0.0988613i
$606$	−24.7782	+	30.7097i	−1.00654	+	1.24750i
$607$	22.2559			0.903339			0.451669	−	0.892185i	$-0.350829\pi$
$607$	22.2559			0.903339			0.451669	+	0.892185i	$0.350829\pi$
$608$	−23.5431	+	7.32942i	−0.954801	+	0.297247i
$609$	1.43994			0.0583495
$610$	5.70881	−	7.07542i	0.231143	−	0.286475i
$611$	−2.18151	−	0.794006i	−0.0882546	−	0.0321221i
$612$	4.56681	+	21.1165i	0.184602	+	0.853585i
$613$	−1.23773	−	7.01951i	−0.0499914	−	0.283515i	0.949556	−	0.313597i	$-0.101534\pi$
$613$	−1.23773	−	7.01951i	−0.0499914	−	0.283515i	−0.999547	+	0.0300821i	$0.990423\pi$
$614$	−12.3714	+	7.46340i	−0.499270	+	0.301198i
$615$	−12.3029	−	7.10310i	−0.496102	−	0.286425i
$616$	0.962062	+	0.483765i	0.0387626	+	0.0194914i
$617$	−10.6382	−	8.92653i	−0.428279	−	0.359369i	0.403023	−	0.915190i	$-0.367959\pi$
$617$	−10.6382	−	8.92653i	−0.428279	−	0.359369i	−0.831302	+	0.555821i	$0.812404\pi$
$618$	−47.5662	−	26.2562i	−1.91339	−	1.05618i
$619$	4.95067	−	2.85827i	0.198984	−	0.114884i	−0.397197	−	0.917733i	$-0.630017\pi$
$619$	4.95067	−	2.85827i	0.198984	−	0.114884i	0.596182	+	0.802850i	$0.296684\pi$
$620$	0.257138	−	1.87794i	0.0103269	−	0.0754199i
$621$	−6.19572	−	17.0226i	−0.248626	−	0.683093i
$622$	44.9252	−	17.3366i	1.80134	−	0.695136i
$623$	−0.394926	+	2.23973i	−0.0158224	+	0.0897331i
$624$	1.91012	+	4.20956i	0.0764658	+	0.168517i
$625$	0.766044	−	0.642788i	0.0306418	−	0.0257115i
$626$	−47.6730	+	9.35448i	−1.90540	+	0.373880i
$627$	12.2537	+	13.7127i	0.489368	+	0.547631i
$628$	−37.3785	+	15.2564i	−1.49157	+	0.608795i
$629$	−8.62738	−	10.2817i	−0.343996	−	0.409959i
$630$	−0.0665213	+	0.424875i	−0.00265027	+	0.0169274i
$631$	0.996164	+	0.175651i	0.0396567	+	0.00699254i	0.193441	−	0.981112i	$-0.438035\pi$
$631$	0.996164	+	0.175651i	0.0396567	+	0.00699254i	−0.153785	+	0.988104i	$0.549146\pi$
$632$	−12.3675	−	13.1219i	−0.491954	−	0.521960i
$633$	44.6617	−	16.2555i	1.77514	−	0.646099i
$634$	39.4552	+	13.5073i	1.56697	+	0.536443i
$635$	−1.45211	−	2.51513i	−0.0576253	−	0.0998099i
$636$	0.366932	−	1.14308i	0.0145498	−	0.0453261i
$637$	2.41805	−	2.88172i	0.0958066	−	0.114178i
$638$	−6.39510	−	7.33043i	−0.253185	−	0.290214i
$639$	−8.77886	+	15.2054i	−0.347286	+	0.601518i
$640$	1.51810	+	11.2114i	0.0600083	+	0.443169i
$641$	−4.64245	+	0.818589i	−0.183366	+	0.0323323i	−0.264577	−	0.964365i	$-0.585232\pi$
$641$	−4.64245	+	0.818589i	−0.183366	+	0.0323323i	0.0812111	+	0.996697i	$0.474121\pi$
$642$	−0.0797136	−	4.14542i	−0.00314604	−	0.163607i
$643$	−2.14205	+	5.88523i	−0.0844742	+	0.232091i	−0.974737	−	0.223357i	$-0.928299\pi$
$643$	−2.14205	+	5.88523i	−0.0844742	+	0.232091i	0.890263	+	0.455448i	$0.150521\pi$
$644$	−1.07023	+	2.03015i	−0.0421729	+	0.0799989i
$645$		−	15.4005i		−	0.606394i
$646$	−35.4956	+	22.9507i	−1.39656	+	0.902984i
$647$		−	41.9548i		−	1.64941i	−0.565560	−	0.824707i	$-0.691340\pi$
$647$		−	41.9548i		−	1.64941i	0.565560	−	0.824707i	$-0.308660\pi$
$648$	9.13655	−	30.4631i	0.358918	−	1.19670i
$649$	0.232381	−	0.638462i	0.00912175	−	0.0250618i
$650$	0.763927	−	0.0146898i	0.0299637	−	0.000576181i
$651$	0.385361	−	0.0679495i	0.0151035	−	0.00266315i
$652$	−23.2675	−	25.6575i	−0.911225	−	1.00483i
$653$	8.21914	−	14.2360i	0.321640	−	0.557096i	−0.659187	−	0.751979i	$-0.729099\pi$
$653$	8.21914	−	14.2360i	0.321640	−	0.557096i	0.980827	+	0.194883i	$0.0624327\pi$
$654$	46.1319	−	40.2458i	1.80390	−	1.57373i
$655$	−9.09735	+	10.8418i	−0.355463	+	0.423624i
$656$	−2.04111	−	26.4874i	−0.0796919	−	1.03416i
$657$	−6.55903	−	11.3606i	−0.255892	−	0.443218i
$658$	0.379914	−	1.10974i	0.0148106	−	0.0432622i
$659$	−26.3521	+	9.59139i	−1.02653	+	0.373627i	−0.799760	−	0.600320i	$-0.795040\pi$
$659$	−26.3521	+	9.59139i	−1.02653	+	0.373627i	−0.226773	+	0.973948i	$0.572818\pi$
$660$	7.13984	−	4.49676i	0.277918	−	0.175036i
$661$	−18.7651	−	3.30880i	−0.729880	−	0.128697i	−0.203655	−	0.979043i	$-0.565282\pi$
$661$	−18.7651	−	3.30880i	−0.729880	−	0.128697i	−0.526225	+	0.850345i	$0.676393\pi$
$662$	28.9366	+	4.53051i	1.12465	+	0.176083i
$663$	5.09366	+	6.07039i	0.197821	+	0.235754i
$664$	12.1626	+	18.5124i	0.472002	+	0.718421i
$665$	−0.823650	+	0.171833i	−0.0319398	+	0.00666339i
$666$	−0.839703	−	4.27936i	−0.0325378	−	0.165822i
$667$	15.8817	−	13.3264i	0.614943	−	0.515999i
$668$	−0.805789	+	0.0310010i	−0.0311769	+	0.00119946i
$669$	0.862355	−	4.89066i	0.0333406	−	0.189084i
$670$	4.64752	+	12.0433i	0.179549	+	0.465274i
$671$	−4.33665	−	11.9148i	−0.167415	−	0.459968i
$672$	−2.10797	+	1.00582i	−0.0813168	+	0.0388003i
$673$	−13.5121	+	7.80124i	−0.520855	+	0.300716i	−0.737284	−	0.675583i	$-0.763892\pi$
$673$	−13.5121	+	7.80124i	−0.520855	+	0.300716i	0.216429	+	0.976298i	$0.430559\pi$
$674$	−21.5247	+	38.9946i	−0.829101	+	1.50202i
$675$	−2.33434	−	1.95875i	−0.0898489	−	0.0753921i
$676$	−20.0836	−	15.5766i	−0.772447	−	0.599101i
$677$	32.6825	+	18.8692i	1.25609	+	0.725204i	0.972312	−	0.233687i	$-0.0750790\pi$
$677$	32.6825	+	18.8692i	1.25609	+	0.725204i	0.283777	+	0.958890i	$0.408412\pi$
$678$	−6.69027	−	11.0899i	−0.256938	−	0.425904i
$679$	−0.339285	−	1.92418i	−0.0130206	−	0.0738433i
$680$	7.67287	+	17.8121i	0.294241	+	0.683061i
$681$	9.50144	+	3.45824i	0.364096	+	0.132520i
$682$	−2.05739	−	1.66001i	−0.0787815	−	0.0635649i
$683$	−35.3839			−1.35393			−0.676964	−	0.736016i	$-0.736705\pi$
$683$	−35.3839			−1.35393			−0.676964	+	0.736016i	$0.736705\pi$
$684$	−13.7007	+	0.955033i	−0.523858	+	0.0365166i
$685$	−6.93412			−0.264939
$686$	2.96639	+	2.39343i	0.113257	+	0.0913818i
$687$	−17.1160	−	6.22973i	−0.653018	−	0.237679i
$688$	23.7608	−	16.2733i	0.905872	−	0.620414i
$689$	−0.0263279	−	0.149313i	−0.00100301	−	0.00568838i
$690$	9.28918	+	15.3979i	0.353633	+	0.586186i
$691$	30.4681	+	17.5908i	1.15906	+	0.669185i	0.951079	−	0.308948i	$-0.0999768\pi$
$691$	30.4681	+	17.5908i	1.15906	+	0.669185i	0.207983	+	0.978132i	$0.433310\pi$
$692$	−31.4700	+	40.5757i	−1.19631	+	1.54246i
$693$	0.459462	+	0.385534i	0.0174535	+	0.0146452i
$694$	−24.2034	+	43.8473i	−0.918749	+	1.66442i
$695$	−1.61113	+	0.930184i	−0.0611135	+	0.0352839i
$696$	21.0645	−	1.21637i	0.798447	−	0.0461062i
$697$	−15.5757	−	42.7938i	−0.589971	−	1.62093i
$698$	−12.2421	−	31.7235i	−0.463370	−	1.20075i
$699$	5.47433	−	31.0465i	0.207058	−	1.17429i
$700$	0.0148416	+	0.385768i	0.000560959	+	0.0145806i
$701$	11.7002	−	9.81765i	0.441911	−	0.370808i	−0.394513	−	0.918890i	$-0.629087\pi$
$701$	11.7002	−	9.81765i	0.441911	−	0.370808i	0.836424	+	0.548083i	$0.184642\pi$
$702$	−0.448318	−	2.28475i	−0.0169207	−	0.0862324i
$703$	7.25263	−	4.49406i	0.273538	−	0.169497i
$704$	14.4824	+	6.26415i	0.545824	+	0.236089i
$705$	−5.90795	−	7.04081i	−0.222506	−	0.265172i
$706$	−7.38837	−	1.15677i	−0.278065	−	0.0435357i
$707$	−2.47965	−	0.437229i	−0.0932568	−	0.0164437i
$708$	0.785358	+	1.24697i	0.0295156	+	0.0468640i
$709$	4.21657	−	1.53471i	0.158357	−	0.0576371i	−0.261626	−	0.965169i	$-0.584259\pi$
$709$	4.21657	−	1.53471i	0.158357	−	0.0576371i	0.419982	+	0.907532i	$0.362036\pi$
$710$	−5.10498	+	14.9118i	−0.191586	+	0.559630i
$711$	−5.02166	−	8.69777i	−0.188327	−	0.326192i
$712$	−3.88527	+	33.0980i	−0.145607	+	1.24040i
$713$	3.62145	−	4.31587i	0.135624	−	0.161631i
$714$	−3.01707	+	2.63211i	−0.112911	+	0.0985043i
$715$	0.532817	−	0.922866i	0.0199262	−	0.0345132i
$716$	−14.7887	+	13.4111i	−0.552680	+	0.501197i
$717$	−17.2483	+	3.04133i	−0.644148	+	0.113581i
$718$	−21.5818	+	0.415002i	−0.805424	+	0.0154877i
$719$	4.39584	−	12.0775i	0.163937	−	0.450413i	−0.830339	−	0.557259i	$-0.811853\pi$
$719$	4.39584	−	12.0775i	0.163937	−	0.450413i	0.994276	+	0.106846i	$0.0340751\pi$
$720$	−0.614214	+	6.27155i	−0.0228904	+	0.233727i
$721$		−	3.46690i		−	0.129114i
$722$	−11.2154	−	24.4175i	−0.417392	−	0.908726i
$723$		−	60.6582i		−	2.25590i
$724$	−6.34041	−	3.34246i	−0.235639	−	0.124222i
$725$	1.19280	−	3.27718i	0.0442993	−	0.121711i
$726$	0.413490	+	21.5031i	0.0153460	+	0.798055i
$727$	44.4969	−	7.84600i	1.65030	−	0.290992i	0.730362	−	0.683060i	$-0.239351\pi$
$727$	44.4969	−	7.84600i	1.65030	−	0.290992i	0.919936	+	0.392068i	$0.128240\pi$
$728$	−0.176262	+	0.236516i	−0.00653270	+	0.00876585i
$729$	−0.920146	+	1.59374i	−0.0340795	+	0.0590274i
$730$	−7.74149	−	8.87373i	−0.286525	−	0.328431i
$731$	31.7336	−	37.8186i	1.17371	−	1.39877i
$732$	26.1854	+	8.40559i	0.967842	+	0.310680i
$733$	15.0809	+	26.1208i	0.557025	+	0.964795i	0.997743	+	0.0671495i	$0.0213904\pi$
$733$	15.0809	+	26.1208i	0.557025	+	0.964795i	−0.440718	+	0.897645i	$0.645276\pi$
$734$	39.7096	+	13.5944i	1.46571	+	0.501778i
$735$	13.9952	−	5.09385i	0.516222	−	0.187889i
$736$	−13.9411	+	30.6024i	−0.513875	+	1.12802i
$737$	17.7304	+	3.12634i	0.653107	+	0.115160i
$738$	2.28880	−	14.6187i	0.0842519	−	0.538121i
$739$	−10.6343	−	12.6735i	−0.391189	−	0.466200i	0.534124	−	0.845406i	$-0.320642\pi$
$739$	−10.6343	−	12.6735i	−0.391189	−	0.466200i	−0.925312	+	0.379206i	$0.876197\pi$
$740$	−1.47938	−	3.62452i	−0.0543831	−	0.133240i
$741$	−4.28200	+	2.65332i	−0.157303	+	0.0974721i
$742$	0.0751722	−	0.0147504i	0.00275966	−	0.000541505i
$743$	−14.5286	+	12.1910i	−0.533004	+	0.447244i	−0.869137	−	0.494571i	$-0.835325\pi$
$743$	−14.5286	+	12.1910i	−0.533004	+	0.447244i	0.336133	+	0.941815i	$0.390881\pi$
$744$	5.57992	−	1.31954i	0.204570	−	0.0483766i
$745$	1.38173	−	7.83620i	0.0506228	−	0.287096i
$746$	25.0623	−	9.67157i	0.917597	−	0.354101i
$747$	4.21964	+	11.5934i	0.154388	+	0.424179i
$748$	26.7990	+	3.66946i	0.979868	+	0.134169i
$749$	0.229122	−	0.132284i	0.00837195	−	0.00483355i
$750$	2.64834	+	1.46187i	0.0967038	+	0.0533798i
$751$	11.0180	+	9.24523i	0.402054	+	0.337363i	0.821287	−	0.570515i	$-0.193256\pi$
$751$	11.0180	+	9.24523i	0.402054	+	0.337363i	−0.419233	+	0.907879i	$0.637701\pi$
$752$	4.62021	−	16.5550i	0.168482	−	0.603698i
$753$	−34.3174	−	19.8132i	−1.25059	−	0.722031i
$754$	2.28165	−	1.37647i	0.0830927	−	0.0501280i
$755$	1.54639	+	8.77004i	0.0562791	+	0.319174i
$756$	1.14982	−	0.248669i	0.0418187	−	0.00904401i
$757$	−36.0191	−	13.1099i	−1.30914	−	0.476487i	−0.409176	−	0.912456i	$-0.634184\pi$
$757$	−36.0191	−	13.1099i	−1.30914	−	0.476487i	−0.899962	+	0.435969i	$0.856406\pi$
$758$	−25.6738	+	31.8198i	−0.932516	+	1.15575i
$759$	25.0804			0.910360
$760$	−11.9038	+	3.20945i	−0.431795	+	0.116419i
$761$	41.1701			1.49241			0.746207	−	0.665714i	$-0.231873\pi$
$761$	41.1701			1.49241			0.746207	+	0.665714i	$0.231873\pi$
$762$	5.51668	−	6.83729i	0.199848	−	0.247689i
$763$	3.67085	+	1.33608i	0.132894	+	0.0483693i
$764$	−5.71788	+	1.23659i	−0.206866	+	0.0447382i
$765$	1.87581	+	10.6382i	0.0678201	+	0.384627i
$766$	−1.70970	+	1.03142i	−0.0617740	+	0.0372668i
$767$	0.161178	+	0.0930563i	0.00581981	+	0.00336007i
$768$	−29.9872	+	16.4945i	−1.08207	+	0.595192i
$769$	−39.6911	−	33.3048i	−1.43130	−	1.20100i	−0.944941	−	0.327241i	$-0.893881\pi$
$769$	−39.6911	−	33.3048i	−1.43130	−	1.20100i	−0.486357	−	0.873760i	$-0.661674\pi$
$770$	0.471377	+	0.260196i	0.0169872	+	0.00937683i
$771$	17.3755	−	10.0317i	0.625763	−	0.361285i
$772$	−11.8482	−	1.62232i	−0.426427	−	0.0583886i
$773$	−9.55809	−	26.2606i	−0.343780	−	0.944529i	−0.984287	−	0.176576i	$-0.943498\pi$
$773$	−9.55809	−	26.2606i	−0.343780	−	0.944529i	0.640506	−	0.767953i	$-0.278724\pi$
$774$	14.9651	−	5.77503i	0.537908	−	0.207579i
$775$	0.164572	−	0.933333i	0.00591160	−	0.0335263i
$776$	−6.58871	−	27.8616i	−0.236521	−	1.00017i
$777$	0.619106	−	0.519492i	0.0222103	−	0.0186367i
$778$	9.52565	−	1.86914i	0.341511	−	0.0670119i
$779$	28.3393	−	5.91225i	1.01536	−	0.211828i
$780$	0.873435	+	2.13994i	0.0312740	+	0.0766221i
$781$	14.1299	+	16.8393i	0.505607	+	0.602559i
$782$	−8.91695	+	56.9530i	−0.318870	+	2.03664i
$783$	−10.4659	−	1.84542i	−0.374021	−	0.0659499i
$784$	22.6475	+	16.2101i	0.808838	+	0.578933i
$785$	−18.9687	+	6.90404i	−0.677022	+	0.246416i
$786$	−40.5052	−	13.8668i	−1.44477	−	0.494611i
$787$	5.31387	+	9.20390i	0.189419	+	0.328083i	0.945057	−	0.326906i	$-0.106006\pi$
$787$	5.31387	+	9.20390i	0.189419	+	0.328083i	−0.755638	+	0.654990i	$0.772673\pi$
$788$	−4.37648	−	1.40486i	−0.155906	−	0.0500461i
$789$	13.3487	−	15.9083i	0.475226	−	0.566352i
$790$	−5.92696	−	6.79382i	−0.210872	−	0.241713i
$791$	0.413222	−	0.715721i	0.0146925	−	0.0254481i
$792$	7.04699	+	5.25173i	0.250404	+	0.186612i
$793$	3.42043	−	0.603114i	0.121463	−	0.0214172i
$794$	−0.988972	−	51.4305i	−0.0350973	−	1.82520i
$795$	0.205303	−	0.564065i	0.00728134	−	0.0200053i
$796$	38.2104	+	20.1433i	1.35433	+	0.713961i
$797$			19.6945i			0.697616i	0.937194	+	0.348808i	$0.113414\pi$
$797$			19.6945i			0.697616i	−0.937194	+	0.348808i	$0.886586\pi$
$798$	−1.38196	−	2.13735i	−0.0489209	−	0.0756612i
$799$		−	29.4636i		−	1.04235i
$800$	0.542983	+	5.63073i	0.0191973	+	0.199077i
$801$	−6.34844	+	17.4422i	−0.224311	+	0.616290i
$802$	22.5237	−	0.433116i	0.795341	−	0.0152939i
$803$	−16.1743	+	2.85196i	−0.570777	+	0.100643i
$804$	−28.9268	+	26.2322i	−1.02017	+	0.925140i
$805$	−0.573742	+	0.993750i	−0.0202217	+	0.0350251i
$806$	0.545666	−	0.476042i	0.0192203	−	0.0167679i
$807$	21.0616	−	25.1003i	0.741404	−	0.883571i
$808$	−36.6433	−	4.30144i	−1.28911	−	0.151324i
$809$	−15.4015	−	26.6763i	−0.541490	−	0.937888i	−0.998819	−	0.0485901i	$-0.984527\pi$
$809$	−15.4015	−	26.6763i	−0.541490	−	0.937888i	0.457329	−	0.889297i	$-0.348806\pi$
$810$	5.15047	−	15.0447i	0.180969	−	0.528616i
$811$	11.7165	−	4.26447i	0.411423	−	0.149746i	−0.128013	−	0.991773i	$-0.540860\pi$
$811$	11.7165	−	4.26447i	0.411423	−	0.149746i	0.539436	+	0.842027i	$0.318638\pi$
$812$	0.717508	+	1.13924i	0.0251796	+	0.0399795i
$813$	43.0427	+	7.58958i	1.50957	+	0.266178i
$814$	−5.39420	−	0.844553i	−0.189067	−	0.0296016i
$815$	−11.1319	−	13.2665i	−0.389935	−	0.464707i
$816$	−41.9124	+	41.0529i	−1.46723	+	1.43714i
$817$	20.9115	+	23.4012i	0.731601	+	0.818705i
$818$	2.87377	+	14.6455i	0.100479	+	0.512068i
$819$	−0.125857	+	0.105606i	−0.00439778	+	0.00369018i
$820$	−0.510655	−	13.2731i	−0.0178328	−	0.463517i
$821$	−5.48080	+	31.0832i	−0.191281	+	1.08481i	0.726335	+	0.687341i	$0.241222\pi$
$821$	−5.48080	+	31.0832i	−0.191281	+	1.08481i	−0.917616	+	0.397469i	$0.869889\pi$
$822$	−7.55181	−	19.5693i	−0.263400	−	0.682559i
$823$	5.17756	+	14.2252i	0.180478	+	0.495860i	0.996635	−	0.0819708i	$-0.0261214\pi$
$823$	5.17756	+	14.2252i	0.180478	+	0.495860i	−0.816156	+	0.577831i	$0.803899\pi$
$824$	−2.92860	−	50.7162i	−0.102023	−	1.76678i
$825$	3.65372	−	2.10948i	0.127206	−	0.0734425i
$826$	−0.0454432	+	0.0823257i	−0.00158117	+	0.00286448i
$827$	37.0045	+	31.0504i	1.28677	+	1.07973i	0.992272	+	0.124078i	$0.0395972\pi$
$827$	37.0045	+	31.0504i	1.28677	+	1.07973i	0.294499	+	0.955652i	$0.404847\pi$
$828$	−11.4792	+	14.8006i	−0.398928	+	0.514355i
$829$	−44.2604	−	25.5537i	−1.53723	−	0.887518i	−0.999000	−	0.0447175i	$-0.985761\pi$
$829$	−44.2604	−	25.5537i	−1.53723	−	0.887518i	−0.538226	−	0.842800i	$-0.680905\pi$
$830$	5.72097	+	9.48315i	0.198578	+	0.329165i
$831$	−0.717958	−	4.07174i	−0.0249057	−	0.141247i
$832$	−2.37869	+	3.60880i	−0.0824662	+	0.125113i
$833$	44.8639	+	16.3291i	1.55444	+	0.565771i
$834$	−4.37979	−	3.53384i	−0.151660	−	0.122367i
$835$	−0.403193			−0.0139531
$836$	−4.74315	+	16.5277i	−0.164045	+	0.571622i
$837$	−2.88799			−0.0998236
$838$	30.0569	+	24.2514i	1.03830	+	0.837752i
$839$	−21.8994	−	7.97073i	−0.756052	−	0.275180i	−0.0649016	−	0.997892i	$-0.520673\pi$
$839$	−21.8994	−	7.97073i	−0.756052	−	0.275180i	−0.691150	+	0.722711i	$0.742896\pi$
$840$	−1.07254	+	0.462017i	−0.0370062	+	0.0159411i
$841$	2.92377	+	16.5815i	0.100820	+	0.571777i
$842$	−6.31212	−	10.4630i	−0.217530	−	0.360580i
$843$	−21.5388	−	12.4354i	−0.741834	−	0.428298i
$844$	35.1153	+	27.2351i	1.20872	+	0.937470i
$845$	−9.73497	−	8.16861i	−0.334893	−	0.281009i
$846$	4.62633	−	8.38114i	0.159056	−	0.288149i
$847$	−1.18850	+	0.686182i	−0.0408374	+	0.0235775i
$848$	1.08721	−	0.279279i	0.0373350	−	0.00959050i
$849$	2.41123	+	6.62479i	0.0827531	+	0.227362i
$850$	3.49121	+	9.04693i	0.119748	+	0.310307i
$851$	2.02060	−	11.4594i	0.0692652	−	0.392823i
$852$	−47.6435	+	1.83298i	−1.63224	+	0.0627968i
$853$	7.55124	−	6.33625i	0.258550	−	0.216949i	−0.504294	−	0.863532i	$-0.668247\pi$
$853$	7.55124	−	6.33625i	0.258550	−	0.216949i	0.762843	+	0.646583i	$0.223803\pi$
$854$	0.337899	+	1.72203i	0.0115627	+	0.0589266i
$855$	−6.86363	+	0.213806i	−0.234731	+	0.00731202i
$856$	3.24001	−	2.12869i	0.110741	−	0.0727570i
$857$	32.3465	+	38.5491i	1.10494	+	1.31681i	0.944037	+	0.329841i	$0.106995\pi$
$857$	32.3465	+	38.5491i	1.10494	+	1.31681i	0.160899	+	0.986971i	$0.448561\pi$
$858$	3.18477	+	0.498629i	0.108726	+	0.0170229i
$859$	−21.5607	−	3.80174i	−0.735643	−	0.129714i	−0.206740	−	0.978396i	$-0.566285\pi$
$859$	−21.5607	−	3.80174i	−0.735643	−	0.129714i	−0.528903	+	0.848682i	$0.677397\pi$
$860$	12.1844	−	7.67390i	0.415485	−	0.261678i
$861$	2.57680	−	0.937879i	0.0878172	−	0.0319628i
$862$	−10.7825	+	31.4960i	−0.367253	+	1.07276i
$863$	23.0438	+	39.9130i	0.784419	+	1.35865i	0.929346	+	0.369211i	$0.120372\pi$
$863$	23.0438	+	39.9130i	0.784419	+	1.35865i	−0.144927	+	0.989442i	$0.546295\pi$
$864$	16.6104	−	4.60899i	0.565096	−	0.156801i
$865$	−16.5033	+	19.6679i	−0.561130	+	0.668729i
$866$	−3.21838	+	2.80774i	−0.109365	+	0.0954107i
$867$	−32.1042	+	55.6062i	−1.09032	+	1.88848i
$868$	0.245781	+	0.271028i	0.00834235	+	0.00919928i
$869$	−12.3832	+	2.18349i	−0.420070	+	0.0740697i
$870$	10.5478	−	0.202828i	0.357605	−	0.00687650i
$871$	−1.68673	+	4.63424i	−0.0571526	+	0.157025i
$872$	54.8283	+	16.4442i	1.85672	+	0.556871i
$873$		−	15.9465i		−	0.539707i
$874$	−35.0229	−	10.7839i	−1.18467	−	0.364772i
$875$			0.193027i			0.00652549i
$876$	16.6121	−	31.5120i	0.561272	−	1.06469i
$877$	17.0557	−	46.8602i	0.575931	−	1.58236i	−0.219044	−	0.975715i	$-0.570294\pi$
$877$	17.0557	−	46.8602i	0.575931	−	1.58236i	0.794975	−	0.606642i	$-0.207484\pi$
$878$	−0.367231	−	19.0974i	−0.0123934	−	0.644508i
$879$	64.2105	−	11.3220i	2.16576	−	0.381883i
$880$	7.11541	+	3.40814i	0.239861	+	0.114888i
$881$	−21.2356	+	36.7812i	−0.715447	+	1.23919i	0.247340	+	0.968929i	$0.420444\pi$
$881$	−21.2356	+	36.7812i	−0.715447	+	1.23919i	−0.962787	+	0.270262i	$0.912890\pi$
$882$	10.1979	+	11.6894i	0.343381	+	0.393602i
$883$	12.4083	−	14.7876i	0.417572	−	0.497643i	−0.515722	−	0.856756i	$-0.672476\pi$
$883$	12.4083	−	14.7876i	0.417572	−	0.497643i	0.933294	+	0.359113i	$0.116921\pi$
$884$	−2.26459	+	7.05476i	−0.0761666	+	0.237277i
$885$	0.368419	+	0.638121i	0.0123843	+	0.0214502i
$886$	30.4274	+	10.4167i	1.02223	+	0.349955i
$887$	−9.33508	+	3.39769i	−0.313441	+	0.114083i	−0.493951	−	0.869490i	$-0.664448\pi$
$887$	−9.33508	+	3.39769i	−0.313441	+	0.114083i	0.180509	+	0.983573i	$0.442225\pi$
$888$	8.61788	−	8.12246i	0.289197	−	0.272572i
$889$	0.552075	+	0.0973458i	0.0185160	+	0.00326487i
$890$	−2.57741	+	16.4621i	−0.0863951	+	0.551810i
$891$	−14.2558	−	16.9894i	−0.477587	−	0.569166i
$892$	4.29904	−	1.75469i	0.143943	−	0.0587514i
$893$	18.5375	+	2.67651i	0.620334	+	0.0895659i
$894$	23.6200	−	4.63475i	0.789970	−	0.155009i
$895$	−7.64668	+	6.41633i	−0.255600	+	0.214474i
$896$	−1.84615	−	1.16658i	−0.0616756	−	0.0389726i
$897$	−1.19297	+	6.76569i	−0.0398322	+	0.225900i
$898$	16.7549	−	6.46572i	0.559118	−	0.215764i
$899$	−1.13045	−	3.10589i	−0.0377026	−	0.103587i
$900$	−0.427433	+	3.12165i	−0.0142478	+	0.104055i
$901$	1.66644	−	0.962122i	0.0555173	−	0.0320529i
$902$	−16.2187	−	8.95259i	−0.540023	−	0.298089i
$903$	2.27722	+	1.91082i	0.0757813	+	0.0635881i
$904$	5.44029	−	10.8191i	0.180941	−	0.359838i
$905$	−3.10361	−	1.79187i	−0.103168	−	0.0595638i
$906$	−23.0665	+	13.9155i	−0.766332	+	0.462310i
$907$	8.73222	+	49.5229i	0.289949	+	1.64438i	0.687053	+	0.726607i	$0.258904\pi$
$907$	8.73222	+	49.5229i	0.289949	+	1.64438i	−0.397105	+	0.917773i	$0.629985\pi$
$908$	1.99841	+	9.24047i	0.0663195	+	0.306656i
$909$	−19.3106	−	7.02847i	−0.640491	−	0.233120i
$910$	−0.0926122	+	0.114782i	−0.00307006	+	0.00380499i
$911$	−14.1006			−0.467174			−0.233587	−	0.972336i	$-0.575046\pi$
$911$	−14.1006			−0.467174			−0.233587	+	0.972336i	$0.575046\pi$
$912$	−22.0218	−	30.0992i	−0.729214	−	0.996683i
$913$	15.4464			0.511200
$914$	7.64880	−	9.47981i	0.253000	−	0.313564i
$915$	12.9215	+	4.70303i	0.427171	+	0.155477i
$916$	−3.59996	−	16.6459i	−0.118946	−	0.549996i
$917$	−0.474389	−	2.69039i	−0.0156657	−	0.0888446i
$918$	25.3022	−	15.2642i	0.835097	−	0.503795i
$919$	−0.795029	−	0.459010i	−0.0262256	−	0.0151414i	0.486830	−	0.873497i	$-0.338153\pi$
$919$	−0.795029	−	0.459010i	−0.0262256	−	0.0151414i	−0.513055	+	0.858355i	$0.671486\pi$
$920$	−7.55363	+	15.0219i	−0.249036	+	0.495258i
$921$	−16.7406	−	14.0470i	−0.551621	−	0.462865i
$922$	32.0974	+	17.7175i	1.05707	+	0.583496i
$923$	−5.21469	+	3.01070i	−0.171644	+	0.0990985i
$924$	−0.220954	+	1.61368i	−0.00726885	+	0.0530863i
$925$	−0.669471	−	1.83936i	−0.0220121	−	0.0604777i
$926$	11.5413	−	4.45378i	0.379270	−	0.146360i
$927$	4.91340	−	27.8653i	0.161377	−	0.915216i
$928$	11.4586	+	16.0595i	0.376145	+	0.527179i
$929$	24.4295	−	20.4988i	0.801506	−	0.672543i	−0.147059	−	0.989128i	$-0.546981\pi$
$929$	24.4295	−	20.4988i	0.801506	−	0.672543i	0.948564	+	0.316585i	$0.102536\pi$
$930$	2.81326	−	0.552023i	0.0922505	−	0.0181016i
$931$	−14.3492	+	26.7435i	−0.470277	+	0.876483i
$932$	27.2908	−	11.1390i	0.893941	−	0.364870i
$933$	46.8167	+	55.7940i	1.53271	+	1.82661i
$934$	0.645513	−	4.12292i	0.0211218	−	0.134906i
$935$	13.3190	+	2.34851i	0.435579	+	0.0768044i
$936$	−1.75191	+	1.65119i	−0.0572629	+	0.0539710i
$937$	−50.8227	+	18.4979i	−1.66030	+	0.604301i	−0.990410	−	0.138156i	$-0.955883\pi$
$937$	−50.8227	+	18.4979i	−1.66030	+	0.604301i	−0.669894	+	0.742457i	$0.733660\pi$
$938$	−2.35745	−	0.807061i	−0.0769734	−	0.0263515i
$939$	−36.7406	−	63.6365i	−1.19898	−	2.07670i
$940$	2.62662	−	8.18255i	0.0856709	−	0.266885i
$941$	31.3628	−	37.3767i	1.02240	−	1.21845i	0.0467947	−	0.998905i	$-0.485099\pi$
$941$	31.3628	−	37.3767i	1.02240	−	1.21845i	0.975603	−	0.219542i	$-0.0704562\pi$
$942$	−40.1429	−	46.0140i	−1.30793	−	1.49922i
$943$	19.7408	−	34.1920i	0.642847	−	1.11344i
$944$	−0.595231	+	1.24270i	−0.0193731	+	0.0404466i
$945$	0.579267	−	0.102140i	0.0188436	−	0.00332263i
$946$	−0.386109	−	20.0792i	−0.0125535	−	0.652831i
$947$	−11.9508	+	32.8345i	−0.388348	+	1.06698i	0.579396	+	0.815046i	$0.303288\pi$
$947$	−11.9508	+	32.8345i	−0.388348	+	1.06698i	−0.967745	+	0.251932i	$0.918934\pi$
$948$	12.7184	−	24.1259i	0.413075	−	0.783574i
$949$		−	4.49883i		−	0.146038i
$950$	−6.00917	+	1.37472i	−0.194963	+	0.0446019i
$951$			63.0767i			2.04540i
$952$	−3.58583	−	1.07547i	−0.116217	−	0.0348561i
$953$	−2.56483	+	7.04682i	−0.0830831	+	0.228269i	−0.974277	−	0.225353i	$-0.927646\pi$
$953$	−2.56483	+	7.04682i	−0.0830831	+	0.228269i	0.891194	+	0.453622i	$0.149869\pi$
$954$	0.625103	−	0.0120203i	0.0202385	−	0.000389172i
$955$	−2.88060	+	0.507927i	−0.0932139	+	0.0164361i
$956$	−11.0008	−	12.1308i	−0.355792	−	0.392340i
$957$	7.35680	−	12.7424i	0.237812	−	0.411902i
$958$	30.6665	−	26.7536i	0.990790	−	0.864370i
$959$	0.860352	−	1.02533i	0.0277822	−	0.0331095i
$960$	−15.2996	+	7.66471i	−0.493792	+	0.247377i
$961$	15.0509	+	26.0689i	0.485513	+	0.840933i
$962$	0.484408	−	1.41497i	0.0156179	−	0.0456205i
$963$	2.02905	−	0.738515i	0.0653853	−	0.0237983i
$964$	47.9910	−	30.2253i	1.54568	−	0.973492i
$965$	−5.88854	−	1.03831i	−0.189559	−	0.0334244i
$966$	−3.42939	−	0.536928i	−0.110339	−	0.0172754i
$967$	37.0904	+	44.2026i	1.19275	+	1.42146i	0.882183	+	0.470907i	$0.156073\pi$
$967$	37.0904	+	44.2026i	1.19275	+	1.42146i	0.310564	+	0.950553i	$0.399482\pi$
$968$	−16.8066	+	11.0419i	−0.540184	+	0.354900i
$969$	−50.2309	−	39.5502i	−1.61365	−	1.27054i
$970$	−2.75636	−	14.0472i	−0.0885013	−	0.451027i
$971$	−32.2590	+	27.0685i	−1.03524	+	0.868670i	−0.991465	−	0.130372i	$-0.958383\pi$
$971$	−32.2590	+	27.0685i	−1.03524	+	0.868670i	−0.0437750	+	0.999041i	$0.513938\pi$
$972$	29.7979	−	1.14641i	0.955768	−	0.0367711i
$973$	0.0623571	−	0.353645i	0.00199908	−	0.0113373i
$974$	−8.77132	−	22.7295i	−0.281051	−	0.728300i
$975$	0.395260	+	1.08597i	0.0126585	+	0.0347788i
$976$	6.39767	+	24.9056i	0.204784	+	0.797208i
$977$	22.6242	−	13.0621i	0.723812	−	0.417893i	−0.0923423	−	0.995727i	$-0.529435\pi$
$977$	22.6242	−	13.0621i	0.723812	−	0.417893i	0.816154	+	0.577834i	$0.196102\pi$
$978$	25.3169	−	45.8646i	0.809547	−	1.46659i
$979$	17.8022	+	14.9378i	0.568959	+	0.477414i
$980$	11.0038	+	8.53440i	0.351503	+	0.272621i
$981$	27.6110	+	15.9412i	0.881551	+	0.508964i
$982$	16.9394	+	28.0789i	0.540557	+	0.896034i
$983$	7.41212	+	42.0362i	0.236410	+	1.34075i	0.839624	+	0.543168i	$0.182775\pi$
$983$	7.41212	+	42.0362i	0.236410	+	1.34075i	−0.603214	+	0.797580i	$0.706113\pi$
$984$	36.9030	−	15.8966i	1.17642	−	0.506766i
$985$	−2.15962	−	0.786036i	−0.0688111	−	0.0250452i
$986$	26.3200	+	21.2363i	0.838199	+	0.676303i
$987$	1.77413			0.0564712
$988$	−4.23290	−	2.06567i	−0.134666	−	0.0657177i
$989$	42.8007			1.36098
$990$	3.41994	+	2.75938i	0.108693	+	0.0876990i
$991$	−30.4796	−	11.0937i	−0.968217	−	0.352402i	−0.190969	−	0.981596i	$-0.561163\pi$
$991$	−30.4796	−	11.0937i	−0.968217	−	0.352402i	−0.777248	+	0.629194i	$0.783385\pi$
$992$	3.82440	+	3.75716i	0.121425	+	0.119290i
$993$	7.69265	+	43.6272i	0.244119	+	1.38447i
$994$	−1.57156	−	2.60504i	−0.0498469	−	0.0826268i
$995$	18.7039	+	10.7987i	0.592953	+	0.342342i
$996$	−20.5325	+	26.4735i	−0.650599	+	0.838845i
$997$	−14.5294	−	12.1916i	−0.460149	−	0.386111i	0.383037	−	0.923733i	$-0.374878\pi$
$997$	−14.5294	−	12.1916i	−0.460149	−	0.386111i	−0.843186	+	0.537622i	$0.819323\pi$
$998$	−26.3037	+	47.6522i	−0.832628	+	1.50840i
$999$	−5.16561	+	2.98237i	−0.163433	+	0.0943579i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.be.b.51.6	✓	120
4.3	odd	2	inner	380.2.be.b.51.18	yes	120
19.3	odd	18	inner	380.2.be.b.231.18	yes	120
76.3	even	18	inner	380.2.be.b.231.6	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.be.b.51.6	✓	120	1.1	even	1	trivial
380.2.be.b.51.18	yes	120	4.3	odd	2	inner
380.2.be.b.231.6	yes	120	76.3	even	18	inner
380.2.be.b.231.18	yes	120	19.3	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.888043 + 1.10063i) q^{2} +(-2.01002 - 0.731586i) q^{3} +(-0.422760 - 1.95481i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(2.59019 - 1.56260i) q^{6} +(0.167166 + 0.0965133i) q^{7} +(2.52694 + 1.27065i) q^{8} +(1.20682 + 1.01264i) q^{9} +O(q^{10})\)	\(q+(-0.888043 + 1.10063i) q^{2} +(-2.01002 - 0.731586i) q^{3} +(-0.422760 - 1.95481i) q^{4} +(-0.173648 - 0.984808i) q^{5} +(2.59019 - 1.56260i) q^{6} +(0.167166 + 0.0965133i) q^{7} +(2.52694 + 1.27065i) q^{8} +(1.20682 + 1.01264i) q^{9} +(1.23811 + 0.683429i) q^{10} +(1.70813 - 0.986190i) q^{11} +(-0.580355 + 4.23848i) q^{12} +(0.184786 + 0.507695i) q^{13} +(-0.254676 + 0.0982794i) q^{14} +(-0.371436 + 2.10652i) q^{15} +(-3.64255 + 1.65283i) q^{16} +(-5.25273 + 4.40756i) q^{17} +(-2.18624 + 0.428988i) q^{18} +(-2.29593 - 3.70523i) q^{19} +(-1.85170 + 0.755786i) q^{20} +(-0.265399 - 0.316290i) q^{21} +(-0.431466 + 2.75579i) q^{22} +(-5.85438 - 1.03229i) q^{23} +(-4.14961 - 4.40271i) q^{24} +(-0.939693 + 0.342020i) q^{25} +(-0.722881 - 0.247475i) q^{26} +(1.52363 + 2.63901i) q^{27} +(0.117994 - 0.367579i) q^{28} +(-2.24172 + 2.67158i) q^{29} +(-1.98864 - 2.27949i) q^{30} +(-0.473866 + 0.820760i) q^{31} +(1.41559 - 5.47687i) q^{32} +(-4.15486 + 0.732613i) q^{33} +(-0.186436 - 9.69540i) q^{34} +(0.0660190 - 0.181386i) q^{35} +(1.46932 - 2.78720i) q^{36} +1.95740i q^{37} +(6.11696 + 0.763442i) q^{38} -1.15566i q^{39} +(0.812548 - 2.70920i) q^{40} +(-2.27152 + 6.24094i) q^{41} +(0.583802 - 0.0112261i) q^{42} +(-7.09043 + 1.25023i) q^{43} +(-2.64994 - 2.92215i) q^{44} +(0.787694 - 1.36433i) q^{45} +(6.33510 - 5.52678i) q^{46} +(-2.76199 + 3.29161i) q^{47} +(8.53077 - 0.657379i) q^{48} +(-3.48137 - 6.02991i) q^{49} +(0.458051 - 1.33798i) q^{50} +(13.7826 - 5.01645i) q^{51} +(0.914327 - 0.575855i) q^{52} +(-0.276364 - 0.0487304i) q^{53} +(-4.25762 - 0.666602i) q^{54} +(-1.26782 - 1.51093i) q^{55} +(0.299784 + 0.456293i) q^{56} +(1.90416 + 9.12724i) q^{57} +(-0.949670 - 4.83978i) q^{58} +(0.263884 - 0.221425i) q^{59} +(4.27487 - 0.164466i) q^{60} +(1.11630 - 6.33087i) q^{61} +(-0.482537 - 1.25042i) q^{62} +(0.104005 + 0.285753i) q^{63} +(4.77089 + 6.42173i) q^{64} +(0.467895 - 0.270139i) q^{65} +(2.88336 - 5.22354i) q^{66} +(6.99246 + 5.86737i) q^{67} +(10.8366 + 8.40473i) q^{68} +(11.0122 + 6.35790i) q^{69} +(0.141010 + 0.233740i) q^{70} +(1.93531 + 10.9757i) q^{71} +(1.76285 + 4.09233i) q^{72} +(-7.82470 - 2.84796i) q^{73} +(-2.15437 - 1.73826i) q^{74} +2.13902 q^{75} +(-6.27238 + 6.05452i) q^{76} +0.380722 q^{77} +(1.27195 + 1.02628i) q^{78} +(-5.99067 - 2.18043i) q^{79} +(2.26024 + 3.30020i) q^{80} +(-1.95256 - 11.0735i) q^{81} +(-4.85174 - 8.04231i) q^{82} +(6.78214 + 3.91567i) q^{83} +(-0.506085 + 0.652518i) q^{84} +(5.25273 + 4.40756i) q^{85} +(4.92056 - 8.91418i) q^{86} +(6.46040 - 3.72991i) q^{87} +(5.56946 - 0.321607i) q^{88} +(4.02976 + 11.0717i) q^{89} +(0.802108 + 2.07854i) q^{90} +(-0.0181094 + 0.102704i) q^{91} +(0.457080 + 11.8806i) q^{92} +(1.55293 - 1.30307i) q^{93} +(-1.17007 - 5.96302i) q^{94} +(-3.25025 + 2.90445i) q^{95} +(-6.85216 + 9.97298i) q^{96} +(-6.50646 - 7.75410i) q^{97} +(9.72829 + 1.52313i) q^{98} +(3.06006 + 0.539571i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9}+O(q^{10}) \) 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9	\( 120 q + 3 q^{2} - 3 q^{4} + 3 q^{6} - 36 q^{8} + 6 q^{9} + 3 q^{10} - 12 q^{13} - 18 q^{14} + 9 q^{16} + 48 q^{17} - 12 q^{21} - 18 q^{24} - 24 q^{26} + 69 q^{28} - 12 q^{30} - 27 q^{32} + 6 q^{33} - 18 q^{34} - 72 q^{36} - 48 q^{38} - 36 q^{41} - 27 q^{42} - 99 q^{44} + 60 q^{45} + 27 q^{46} - 63 q^{48} + 60 q^{49} + 33 q^{52} - 24 q^{53} + 21 q^{54} - 48 q^{57} + 6 q^{60} - 24 q^{61} + 54 q^{62} + 84 q^{64} - 18 q^{65} - 132 q^{66} + 66 q^{68} - 72 q^{69} + 36 q^{70} - 42 q^{72} + 66 q^{74} + 180 q^{76} + 60 q^{77} + 114 q^{78} + 27 q^{80} - 66 q^{81} + 33 q^{82} - 144 q^{84} - 48 q^{85} + 75 q^{86} + 9 q^{88} - 3 q^{90} - 42 q^{92} - 144 q^{93} + 78 q^{96} + 42 q^{97} - 87 q^{98}+O(q^{100}) \) 120 * q + 3 * q^2 - 3 * q^4 + 3 * q^6 - 36 * q^8 + 6 * q^9 + 3 * q^10 - 12 * q^13 - 18 * q^14 + 9 * q^16 + 48 * q^17 - 12 * q^21 - 18 * q^24 - 24 * q^26 + 69 * q^28 - 12 * q^30 - 27 * q^32 + 6 * q^33 - 18 * q^34 - 72 * q^36 - 48 * q^38 - 36 * q^41 - 27 * q^42 - 99 * q^44 + 60 * q^45 + 27 * q^46 - 63 * q^48 + 60 * q^49 + 33 * q^52 - 24 * q^53 + 21 * q^54 - 48 * q^57 + 6 * q^60 - 24 * q^61 + 54 * q^62 + 84 * q^64 - 18 * q^65 - 132 * q^66 + 66 * q^68 - 72 * q^69 + 36 * q^70 - 42 * q^72 + 66 * q^74 + 180 * q^76 + 60 * q^77 + 114 * q^78 + 27 * q^80 - 66 * q^81 + 33 * q^82 - 144 * q^84 - 48 * q^85 + 75 * q^86 + 9 * q^88 - 3 * q^90 - 42 * q^92 - 144 * q^93 + 78 * q^96 + 42 * q^97 - 87 * q^98

Introduction

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