LMFDB - Embedded newform 216.2.t.a.13.31

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [216,2,Mod(13,216)] 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("216.13"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(216, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.t (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$204$
Relative dimension:	$34$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			13.31
Character	$\chi$	$=$	216.13
Dual form			216.2.t.a.133.31

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.24359 + 0.673416i) q^{2} +(0.0518114 - 1.73128i) q^{3} +(1.09302 + 1.67490i) q^{4} +(1.55117 - 1.84861i) q^{5} +(1.23030 - 2.11810i) q^{6} +(-1.49685 - 0.544810i) q^{7} +(0.231362 + 2.81895i) q^{8} +(-2.99463 - 0.179400i) q^{9} +(3.17390 - 1.25433i) q^{10} +(-0.102391 - 0.122025i) q^{11} +(2.95635 - 1.80554i) q^{12} +(3.39140 + 0.597995i) q^{13} +(-1.49458 - 1.68552i) q^{14} +(-3.12009 - 2.78128i) q^{15} +(-1.61061 + 3.66141i) q^{16} +(-1.43581 + 2.48690i) q^{17} +(-3.60328 - 2.23973i) q^{18} +(-3.75621 + 2.16865i) q^{19} +(4.79171 + 0.577486i) q^{20} +(-1.02077 + 2.56324i) q^{21} +(-0.0451590 - 0.220701i) q^{22} +(2.14748 - 0.781619i) q^{23} +(4.89236 - 0.254498i) q^{24} +(-0.142997 - 0.810974i) q^{25} +(3.81480 + 3.02748i) q^{26} +(-0.465746 + 5.17524i) q^{27} +(-0.723589 - 3.10257i) q^{28} +(8.60509 - 1.51731i) q^{29} +(-2.00714 - 5.55988i) q^{30} +(-6.69129 + 2.43543i) q^{31} +(-4.46858 + 3.46868i) q^{32} +(-0.216565 + 0.170946i) q^{33} +(-3.46028 + 2.12578i) q^{34} +(-3.32901 + 1.92201i) q^{35} +(-2.97272 - 5.21181i) q^{36} +(-5.14590 - 2.97099i) q^{37} +(-6.13158 + 0.167414i) q^{38} +(1.21101 - 5.84046i) q^{39} +(5.57002 + 3.94497i) q^{40} +(-1.74706 + 9.90807i) q^{41} +(-2.99554 + 2.50021i) q^{42} +(-7.59829 - 9.05529i) q^{43} +(0.0924647 - 0.304872i) q^{44} +(-4.97682 + 5.25763i) q^{45} +(3.19694 + 0.474136i) q^{46} +(3.66367 + 1.33347i) q^{47} +(6.25547 + 2.97810i) q^{48} +(-3.41856 - 2.86851i) q^{49} +(0.368294 - 1.10481i) q^{50} +(4.23112 + 2.61464i) q^{51} +(2.70529 + 6.33388i) q^{52} -9.80805i q^{53} +(-4.06428 + 6.12222i) q^{54} -0.384404 q^{55} +(1.18948 - 4.34560i) q^{56} +(3.55991 + 6.61539i) q^{57} +(11.7230 + 3.90790i) q^{58} +(1.72220 - 2.05244i) q^{59} +(1.24805 - 8.26584i) q^{60} +(-0.492702 + 1.35369i) q^{61} +(-9.96127 - 1.47735i) q^{62} +(4.38478 + 1.90004i) q^{63} +(-7.89294 + 1.30440i) q^{64} +(6.36609 - 5.34178i) q^{65} +(-0.384435 + 0.0667478i) q^{66} +(0.225321 + 0.0397302i) q^{67} +(-5.73470 + 0.313390i) q^{68} +(-1.24193 - 3.75838i) q^{69} +(-5.43423 + 0.148374i) q^{70} +(2.82317 - 4.88987i) q^{71} +(-0.187127 - 8.48322i) q^{72} +(7.14574 + 12.3768i) q^{73} +(-4.39867 - 7.16002i) q^{74} +(-1.41143 + 0.205549i) q^{75} +(-7.73789 - 3.92091i) q^{76} +(0.0867843 + 0.238438i) q^{77} +(5.43905 - 6.44761i) q^{78} +(-2.18269 - 12.3786i) q^{79} +(4.27021 + 8.65685i) q^{80} +(8.93563 + 1.07447i) q^{81} +(-8.84487 + 11.1451i) q^{82} +(11.1079 - 1.95862i) q^{83} +(-5.40890 + 1.09198i) q^{84} +(2.37013 + 6.51187i) q^{85} +(-3.35117 - 16.3779i) q^{86} +(-2.18104 - 14.9764i) q^{87} +(0.320294 - 0.316868i) q^{88} +(-3.73417 - 6.46777i) q^{89} +(-9.72968 + 3.18686i) q^{90} +(-4.75063 - 2.74278i) q^{91} +(3.65638 + 2.74250i) q^{92} +(3.86972 + 11.7107i) q^{93} +(3.65812 + 4.12546i) q^{94} +(-1.81753 + 10.3077i) q^{95} +(5.77372 + 7.91607i) q^{96} +(5.17680 - 4.34385i) q^{97} +(-2.31958 - 5.86936i) q^{98} +(0.284733 + 0.383790i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26}+ \cdots + 54 q^{98}+O(q^{100}) $ 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$-1$	$e\left(\frac{4}{9}\right)$

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 $

$2$	1.24359	+	0.673416i	0.879349	+	0.476177i
$2$	1.24359	+	0.673416i	0.879349	+	0.476177i
$3$	0.0518114	−	1.73128i	0.0299133	−	0.999552i
$3$	0.0518114	−	1.73128i	0.0299133	−	0.999552i
$4$	1.09302	+	1.67490i	0.546511	+	0.837452i
$5$	1.55117	−	1.84861i	0.693704	−	0.826724i	−0.298095	−	0.954536i	$-0.596351\pi$
$5$	1.55117	−	1.84861i	0.693704	−	0.826724i	0.991798	+	0.127812i	$0.0407956\pi$
$6$	1.23030	−	2.11810i	0.502268	−	0.864712i
$7$	−1.49685	−	0.544810i	−0.565757	−	0.205919i	0.0432765	−	0.999063i	$-0.486220\pi$
$7$	−1.49685	−	0.544810i	−0.565757	−	0.205919i	−0.609034	+	0.793144i	$0.708443\pi$
$8$	0.231362	+	2.81895i	0.0817989	+	0.996649i
$9$	−2.99463	−	0.179400i	−0.998210	−	0.0597999i
$10$	3.17390	−	1.25433i	1.00367	−	0.396653i
$11$	−0.102391	−	0.122025i	−0.0308722	−	0.0367920i	0.750387	−	0.660998i	$-0.229867\pi$
$11$	−0.102391	−	0.122025i	−0.0308722	−	0.0367920i	−0.781260	+	0.624206i	$0.785423\pi$
$12$	2.95635	−	1.80554i	0.853425	−	0.521216i
$13$	3.39140	+	0.597995i	0.940604	+	0.165854i	0.622869	−	0.782326i	$-0.285967\pi$
$13$	3.39140	+	0.597995i	0.940604	+	0.165854i	0.317735	+	0.948180i	$0.397078\pi$
$14$	−1.49458	−	1.68552i	−0.399445	−	0.450475i
$15$	−3.12009	−	2.78128i	−0.805603	−	0.718123i
$16$	−1.61061	+	3.66141i	−0.402651	+	0.915353i
$17$	−1.43581	+	2.48690i	−0.348236	+	0.603163i	−0.985936	−	0.167122i	$-0.946553\pi$
$17$	−1.43581	+	2.48690i	−0.348236	+	0.603163i	0.637700	+	0.770285i	$0.279886\pi$
$18$	−3.60328	−	2.23973i	−0.849300	−	0.527910i
$19$	−3.75621	+	2.16865i	−0.861733	+	0.497522i	−0.864592	−	0.502474i	$-0.832423\pi$
$19$	−3.75621	+	2.16865i	−0.861733	+	0.497522i	0.00285908	+	0.999996i	$0.499090\pi$
$20$	4.79171	+	0.577486i	1.07146	+	0.129130i
$21$	−1.02077	+	2.56324i	−0.222750	+	0.559344i
$22$	−0.0451590	−	0.220701i	−0.00962792	−	0.0470537i
$23$	2.14748	−	0.781619i	0.447781	−	0.162979i	−0.108280	−	0.994120i	$-0.534534\pi$
$23$	2.14748	−	0.781619i	0.447781	−	0.162979i	0.556061	+	0.831142i	$0.312312\pi$
$24$	4.89236	−	0.254498i	0.998650	−	0.0519493i
$25$	−0.142997	−	0.810974i	−0.0285993	−	0.162195i
$26$	3.81480	+	3.02748i	0.748144	+	0.593737i
$27$	−0.465746	+	5.17524i	−0.0896329	+	0.995975i
$28$	−0.723589	−	3.10257i	−0.136746	−	0.586331i
$29$	8.60509	−	1.51731i	1.59793	−	0.281757i	0.697440	−	0.716643i	$-0.254322\pi$
$29$	8.60509	−	1.51731i	1.59793	−	0.281757i	0.900486	+	0.434886i	$0.143211\pi$
$30$	−2.00714	−	5.55988i	−0.366453	−	1.01509i
$31$	−6.69129	+	2.43543i	−1.20179	+	0.437416i	−0.863849	−	0.503751i	$-0.831953\pi$
$31$	−6.69129	+	2.43543i	−1.20179	+	0.437416i	−0.337942	+	0.941167i	$0.609731\pi$
$32$	−4.46858	+	3.46868i	−0.789941	+	0.613182i
$33$	−0.216565	+	0.170946i	−0.0376991	+	0.0297578i
$34$	−3.46028	+	2.12578i	−0.593433	+	0.364569i
$35$	−3.32901	+	1.92201i	−0.562706	+	0.324878i
$36$	−2.97272	−	5.21181i	−0.495454	−	0.868634i
$37$	−5.14590	−	2.97099i	−0.845981	−	0.488427i	0.0133118	−	0.999911i	$-0.495763\pi$
$37$	−5.14590	−	2.97099i	−0.845981	−	0.488427i	−0.859293	+	0.511484i	$0.829096\pi$
$38$	−6.13158	+	0.167414i	−0.994673	+	0.0271582i
$39$	1.21101	−	5.84046i	0.193916	−	0.935222i
$40$	5.57002	+	3.94497i	0.880698	+	0.623754i
$41$	−1.74706	+	9.90807i	−0.272845	+	1.54738i	0.472880	+	0.881127i	$0.343214\pi$
$41$	−1.74706	+	9.90807i	−0.272845	+	1.54738i	−0.745725	+	0.666254i	$0.767897\pi$
$42$	−2.99554	+	2.50021i	−0.462222	+	0.385791i
$43$	−7.59829	−	9.05529i	−1.15873	−	1.38092i	−0.911162	−	0.412048i	$-0.864813\pi$
$43$	−7.59829	−	9.05529i	−1.15873	−	1.38092i	−0.247567	−	0.968871i	$-0.579631\pi$
$44$	0.0924647	−	0.304872i	0.0139396	−	0.0459612i
$45$	−4.97682	+	5.25763i	−0.741900	+	0.783761i
$46$	3.19694	+	0.474136i	0.471363	+	0.0699075i
$47$	3.66367	+	1.33347i	0.534402	+	0.194506i	0.595103	−	0.803650i	$-0.297111\pi$
$47$	3.66367	+	1.33347i	0.534402	+	0.194506i	−0.0607009	+	0.998156i	$0.519334\pi$
$48$	6.25547	+	2.97810i	0.902899	+	0.429852i
$49$	−3.41856	−	2.86851i	−0.488366	−	0.409788i
$50$	0.368294	−	1.10481i	0.0520846	−	0.156244i
$51$	4.23112	+	2.61464i	0.592476	+	0.366123i
$52$	2.70529	+	6.33388i	0.375156	+	0.878352i
$53$		−	9.80805i		−	1.34724i	−0.739078	−	0.673620i	$-0.764738\pi$
$53$		−	9.80805i		−	1.34724i	0.739078	−	0.673620i	$-0.235262\pi$
$54$	−4.06428	+	6.12222i	−0.553079	+	0.833129i
$55$	−0.384404			−0.0518330
$56$	1.18948	−	4.34560i	0.158950	−	0.580705i
$57$	3.55991	+	6.61539i	0.471522	+	0.876230i
$58$	11.7230	+	3.90790i	1.53930	+	0.513132i
$59$	1.72220	−	2.05244i	0.224212	−	0.267205i	−0.642198	−	0.766539i	$-0.721977\pi$
$59$	1.72220	−	2.05244i	0.224212	−	0.267205i	0.866410	+	0.499334i	$0.166422\pi$
$60$	1.24805	−	8.26584i	0.161123	−	1.06712i
$61$	−0.492702	+	1.35369i	−0.0630841	+	0.173322i	−0.967230	−	0.253902i	$-0.918286\pi$
$61$	−0.492702	+	1.35369i	−0.0630841	+	0.173322i	0.904146	+	0.427224i	$0.140508\pi$
$62$	−9.96127	−	1.47735i	−1.26508	−	0.187624i
$63$	4.38478	+	1.90004i	0.552431	+	0.239382i
$64$	−7.89294	+	1.30440i	−0.986618	+	0.163050i
$65$	6.36609	−	5.34178i	0.789616	−	0.662566i
$66$	−0.384435	+	0.0667478i	−0.0473206	+	0.00821608i
$67$	0.225321	+	0.0397302i	0.0275273	+	0.00485381i	0.187395	−	0.982285i	$-0.439996\pi$
$67$	0.225321	+	0.0397302i	0.0275273	+	0.00485381i	−0.159868	+	0.987138i	$0.551107\pi$
$68$	−5.73470	+	0.313390i	−0.695435	+	0.0380041i
$69$	−1.24193	−	3.75838i	−0.149511	−	0.452456i
$70$	−5.43423	+	0.148374i	−0.649515	+	0.0177341i
$71$	2.82317	−	4.88987i	0.335048	−	0.580320i	−0.648446	−	0.761261i	$-0.724581\pi$
$71$	2.82317	−	4.88987i	0.335048	−	0.580320i	0.983494	+	0.180940i	$0.0579141\pi$
$72$	−0.187127	−	8.48322i	−0.0220531	−	0.999757i
$73$	7.14574	+	12.3768i	0.836346	+	1.44859i	0.892930	+	0.450196i	$0.148646\pi$
$73$	7.14574	+	12.3768i	0.836346	+	1.44859i	−0.0565836	+	0.998398i	$0.518021\pi$
$74$	−4.39867	−	7.16002i	−0.511335	−	0.832335i
$75$	−1.41143	+	0.205549i	−0.162978	+	0.0237347i
$76$	−7.73789	−	3.92091i	−0.887597	−	0.449759i
$77$	0.0867843	+	0.238438i	0.00988999	+	0.0271725i
$78$	5.43905	−	6.44761i	0.615851	−	0.730048i
$79$	−2.18269	−	12.3786i	−0.245572	−	1.39271i	−0.819161	−	0.573563i	$-0.805561\pi$
$79$	−2.18269	−	12.3786i	−0.245572	−	1.39271i	0.573590	−	0.819143i	$-0.305550\pi$
$80$	4.27021	+	8.65685i	0.477424	+	0.967865i
$81$	8.93563	+	1.07447i	0.992848	+	0.119386i
$82$	−8.84487	+	11.1451i	−0.976753	+	1.23077i
$83$	11.1079	−	1.95862i	1.21925	−	0.214987i	0.473248	−	0.880929i	$-0.343081\pi$
$83$	11.1079	−	1.95862i	1.21925	−	0.214987i	0.746003	+	0.665942i	$0.231970\pi$
$84$	−5.40890	+	1.09198i	−0.590160	+	0.119145i
$85$	2.37013	+	6.51187i	0.257076	+	0.706311i
$86$	−3.35117	−	16.3779i	−0.361366	−	1.76607i
$87$	−2.18104	−	14.9764i	−0.233832	−	1.60564i
$88$	0.320294	−	0.316868i	0.0341434	−	0.0337783i
$89$	−3.73417	−	6.46777i	−0.395821	−	0.685582i	0.597385	−	0.801955i	$-0.296207\pi$
$89$	−3.73417	−	6.46777i	−0.395821	−	0.685582i	−0.993206	+	0.116373i	$0.962873\pi$
$90$	−9.72968	+	3.18686i	−1.02560	+	0.335924i
$91$	−4.75063	−	2.74278i	−0.498001	−	0.287521i
$92$	3.65638	+	2.74250i	0.381204	+	0.285925i
$93$	3.86972	+	11.7107i	0.401271	+	1.21434i
$94$	3.65812	+	4.12546i	0.377307	+	0.425509i
$95$	−1.81753	+	10.3077i	−0.186474	+	1.05755i
$96$	5.77372	+	7.91607i	0.589278	+	0.807930i
$97$	5.17680	−	4.34385i	0.525624	−	0.441051i	−0.340963	−	0.940077i	$-0.610753\pi$
$97$	5.17680	−	4.34385i	0.525624	−	0.441051i	0.866587	+	0.499026i	$0.166309\pi$
$98$	−2.31958	−	5.86936i	−0.234313	−	0.592895i
$99$	0.284733	+	0.383790i	0.0286168	+	0.0385724i
$100$	1.20201	−	1.12592i	0.120201	−	0.112592i
$101$	0.582767	−	1.60114i	0.0579875	−	0.159319i	−0.907316	−	0.420449i	$-0.861873\pi$
$101$	0.582767	−	1.60114i	0.0579875	−	0.159319i	0.965304	+	0.261129i	$0.0840949\pi$
$102$	3.50103	+	6.10084i	0.346654	+	0.604073i
$103$	9.82235	+	8.24193i	0.967825	+	0.812102i	0.982208	−	0.187795i	$-0.0601340\pi$
$103$	9.82235	+	8.24193i	0.967825	+	0.812102i	−0.0143832	+	0.999897i	$0.504578\pi$
$104$	−0.901075	+	9.69852i	−0.0883576	+	0.951019i
$105$	3.15504	+	5.86302i	0.307901	+	0.572172i
$106$	6.60490	−	12.1972i	0.641525	−	1.18469i
$107$			15.7558i			1.52317i	0.648065	+	0.761585i	$0.275579\pi$
$107$			15.7558i			1.52317i	−0.648065	+	0.761585i	$0.724421\pi$
$108$	−9.17710	+	4.87657i	−0.883066	+	0.469248i
$109$			4.23854i			0.405978i	0.979181	+	0.202989i	$0.0650656\pi$
$109$			4.23854i			0.405978i	−0.979181	+	0.202989i	$0.934934\pi$
$110$	−0.478040	−	0.258864i	−0.0455793	−	0.0246817i
$111$	−5.41021	+	8.75504i	−0.513515	+	0.830992i
$112$	4.40561	−	4.60312i	0.416291	−	0.434954i
$113$	−5.72871	−	4.80696i	−0.538912	−	0.452201i	0.332254	−	0.943190i	$-0.392191\pi$
$113$	−5.72871	−	4.80696i	−0.538912	−	0.452201i	−0.871166	+	0.490989i	$0.836635\pi$
$114$	−0.0278455	+	10.6241i	−0.00260797	+	0.995040i
$115$	1.88620	−	5.18228i	0.175889	−	0.483250i
$116$	11.9469	+	12.7542i	1.10924	+	1.18420i
$117$	−10.0487	−	2.39919i	−0.929003	−	0.221805i
$118$	3.52386	−	1.39263i	0.324397	−	0.128202i
$119$	3.50409	−	2.94028i	0.321220	−	0.269535i
$120$	7.11841	−	9.43885i	0.649819	−	0.861645i
$121$	1.90572	−	10.8079i	0.173248	−	0.982536i
$122$	−1.52431	+	1.35164i	−0.138005	+	0.122371i
$123$	17.0631	+	3.53799i	1.53853	+	0.319010i
$124$	−11.3928	−	8.54529i	−1.02311	−	0.767390i
$125$	8.72843	+	5.03936i	0.780695	+	0.450734i
$126$	4.17335	+	5.31565i	0.371791	+	0.473556i
$127$	6.92735	+	11.9985i	0.614703	+	1.06470i	0.990437	+	0.137969i	$0.0440574\pi$
$127$	6.92735	+	11.9985i	0.614703	+	1.06470i	−0.375734	+	0.926728i	$0.622609\pi$
$128$	−10.6940	−	3.69310i	−0.945222	−	0.326427i
$129$	−16.0709	+	12.6856i	−1.41496	+	1.11690i
$130$	11.5140	−	2.35595i	1.00985	−	0.206631i
$131$	−1.76657	−	4.85361i	−0.154346	−	0.424061i	0.838286	−	0.545231i	$-0.183558\pi$
$131$	−1.76657	−	4.85361i	−0.154346	−	0.424061i	−0.992632	+	0.121169i	$0.961336\pi$
$132$	−0.523027	−	0.175878i	−0.0455237	−	0.0153082i
$133$	6.80399	−	1.19973i	0.589981	−	0.104030i
$134$	0.253452	+	0.201143i	0.0218949	+	0.0173761i
$135$	8.84455	+	8.88865i	0.761217	+	0.765013i
$136$	−7.34265	−	3.47211i	−0.629627	−	0.297731i
$137$	−3.27446	−	18.5704i	−0.279756	−	1.58658i	−0.723436	−	0.690391i	$-0.757438\pi$
$137$	−3.27446	−	18.5704i	−0.279756	−	1.58658i	0.443680	−	0.896185i	$-0.353673\pi$
$138$	0.986497	−	5.51021i	0.0839762	−	0.469060i
$139$	−5.53623	−	15.2107i	−0.469577	−	1.29015i	−0.918089	−	0.396375i	$-0.870268\pi$
$139$	−5.53623	−	15.2107i	−0.469577	−	1.29015i	0.448512	−	0.893777i	$-0.351954\pi$
$140$	−6.85786	−	3.47498i	−0.579595	−	0.293689i
$141$	2.49842	−	6.27374i	0.210405	−	0.528344i
$142$	6.80377	−	4.17981i	0.570959	−	0.350762i
$143$	−0.274279	−	0.475066i	−0.0229364	−	0.0397270i
$144$	5.48002	−	10.6756i	0.456669	−	0.889637i
$145$	10.5430	−	18.2611i	0.875551	−	1.51650i
$146$	0.551633	+	20.2037i	0.0456535	+	1.67207i
$147$	−5.14331	+	5.76985i	−0.424213	+	0.475889i
$148$	−0.648466	−	11.8662i	−0.0533036	−	0.975399i
$149$	−12.7731	−	2.25224i	−1.04641	−	0.184511i	−0.376092	−	0.926582i	$-0.622732\pi$
$149$	−12.7731	−	2.25224i	−1.04641	−	0.184511i	−0.670321	+	0.742071i	$0.733843\pi$
$150$	−1.89366	−	0.694861i	−0.154616	−	0.0567351i
$151$	2.57721	−	2.16253i	0.209730	−	0.175985i	−0.531871	−	0.846825i	$-0.678511\pi$
$151$	2.57721	−	2.16253i	0.209730	−	0.175985i	0.741602	+	0.670841i	$0.234067\pi$
$152$	−6.98235	−	10.0868i	−0.566344	−	0.818149i
$153$	4.74588	−	7.18977i	0.383682	−	0.581259i
$154$	−0.0526440	+	0.354961i	−0.00424217	+	0.0286035i
$155$	−5.87716	+	16.1474i	−0.472065	+	1.29699i
$156$	11.1059	−	4.35543i	0.889181	−	0.348714i
$157$	−0.320529	+	0.381992i	−0.0255810	+	0.0304863i	−0.778683	−	0.627417i	$-0.784112\pi$
$157$	−0.320529	+	0.381992i	−0.0255810	+	0.0304863i	0.753102	+	0.657903i	$0.228557\pi$
$158$	5.62161	−	16.8638i	0.447231	−	1.34161i
$159$	−16.9804	−	0.508169i	−1.34664	−	0.0403004i
$160$	−0.519282	+	13.6412i	−0.0410528	+	1.07843i
$161$	−3.64030			−0.286896
$162$	10.3887	+	7.35360i	0.816212	+	0.577753i
$163$			11.3041i			0.885405i	0.896669	+	0.442703i	$0.145980\pi$
$163$			11.3041i			0.885405i	−0.896669	+	0.442703i	$0.854020\pi$
$164$	−18.5046	+	7.90358i	−1.44497	+	0.617166i
$165$	−0.0199165	+	0.665509i	−0.00155050	+	0.0518098i
$166$	15.1326	+	5.04452i	1.17452	+	0.391531i
$167$	10.0898	+	8.46632i	0.780770	+	0.655144i	0.943442	−	0.331536i	$-0.107567\pi$
$167$	10.0898	+	8.46632i	0.780770	+	0.655144i	−0.162673	+	0.986680i	$0.552011\pi$
$168$	−7.46180	−	2.28446i	−0.575691	−	0.176250i
$169$	−1.07204	−	0.390189i	−0.0824644	−	0.0300146i
$170$	−1.43773	+	9.69416i	−0.110269	+	0.743508i
$171$	11.6375	−	5.82044i	0.889943	−	0.445100i
$172$	6.86164	−	22.6240i	0.523195	−	1.72507i
$173$	−10.5281	−	12.5470i	−0.800440	−	0.953928i	0.199221	−	0.979955i	$-0.436159\pi$
$173$	−10.5281	−	12.5470i	−0.800440	−	0.953928i	−0.999661	+	0.0260269i	$0.991714\pi$
$174$	7.37303	−	20.0932i	0.558948	−	1.52326i
$175$	−0.227782	+	1.29182i	−0.0172187	+	0.0976521i
$176$	0.611698	−	0.178363i	0.0461085	−	0.0134446i
$177$	−3.46411	−	3.08795i	−0.260379	−	0.232104i
$178$	−0.288268	−	10.5579i	−0.0216066	−	0.791347i
$179$	−5.13398	−	2.96410i	−0.383731	−	0.221547i	0.295709	−	0.955278i	$-0.404444\pi$
$179$	−5.13398	−	2.96410i	−0.383731	−	0.221547i	−0.679441	+	0.733731i	$0.737777\pi$
$180$	−14.2458	−	2.58899i	−1.06182	−	0.192972i
$181$	1.50802	−	0.870656i	0.112090	−	0.0647154i	−0.442907	−	0.896568i	$-0.646053\pi$
$181$	1.50802	−	0.870656i	0.112090	−	0.0647154i	0.554997	+	0.831852i	$0.312719\pi$
$182$	−4.06079	−	6.61003i	−0.301006	−	0.489968i
$183$	2.31808	+	0.923140i	0.171357	+	0.0682405i
$184$	2.70019	+	5.87280i	0.199061	+	0.432949i
$185$	−13.4744	+	4.90427i	−0.990655	+	0.360569i
$186$	−3.07381	+	17.1692i	−0.225382	+	1.25890i
$187$	0.450481	−	0.0794319i	0.0329424	−	0.00580863i
$188$	1.77105	+	7.59381i	0.129167	+	0.553836i
$189$	3.51667	−	7.49283i	0.255800	−	0.545023i
$190$	−9.20163	+	11.5946i	−0.667556	+	0.841160i
$191$	1.88621	+	10.6972i	0.136481	+	0.774023i	0.973817	+	0.227334i	$0.0730008\pi$
$191$	1.88621	+	10.6972i	0.136481	+	0.774023i	−0.837336	+	0.546689i	$0.815888\pi$
$192$	1.84933	+	13.7324i	0.133464	+	0.991054i
$193$	−13.6021	+	4.95075i	−0.979100	+	0.356363i	−0.781490	−	0.623918i	$-0.785540\pi$
$193$	−13.6021	+	4.95075i	−0.979100	+	0.356363i	−0.197609	+	0.980281i	$0.563318\pi$
$194$	9.36302	−	1.91582i	0.672226	−	0.137548i
$195$	−8.91826	−	11.2982i	−0.638650	−	0.809082i
$196$	1.06792	−	8.86111i	0.0762800	−	0.632936i
$197$	7.36911	−	4.25456i	0.525027	−	0.303125i	−0.213962	−	0.976842i	$-0.568637\pi$
$197$	7.36911	−	4.25456i	0.525027	−	0.303125i	0.738989	+	0.673717i	$0.235303\pi$
$198$	0.0956407	+	0.669021i	0.00679689	+	0.0475452i
$199$	−6.17939	+	10.7030i	−0.438045	+	0.758716i	−0.997539	−	0.0701183i	$-0.977662\pi$
$199$	−6.17939	+	10.7030i	−0.438045	+	0.758716i	0.559494	+	0.828835i	$0.310996\pi$
$200$	2.25301	−	0.590729i	0.159312	−	0.0417709i
$201$	0.0804581	−	0.388034i	0.00567508	−	0.0273698i
$202$	1.80296	−	1.59871i	0.126855	−	0.112485i
$203$	−13.7072	−	2.41695i	−0.962057	−	0.169637i
$204$	0.245441	+	9.94458i	0.0171843	+	0.696260i
$205$	15.6062	+	18.5987i	1.08998	+	1.29899i
$206$	6.66471	+	16.8641i	0.464352	+	1.17498i
$207$	−6.57114	+	1.95540i	−0.456726	+	0.135910i
$208$	−7.65171	+	11.4542i	−0.530550	+	0.794204i
$209$	0.649234	+	0.236302i	0.0449084	+	0.0163453i
$210$	−0.0246786	+	9.41584i	−0.00170299	+	0.649754i
$211$	1.13641	−	1.35433i	0.0782339	−	0.0932356i	−0.725508	−	0.688214i	$-0.758395\pi$
$211$	1.13641	−	1.35433i	0.0782339	−	0.0932356i	0.803742	+	0.594978i	$0.202839\pi$
$212$	16.4275	−	10.7204i	1.12825	−	0.736281i
$213$	−8.31943	−	5.14103i	−0.570038	−	0.352257i
$214$	−10.6102	+	19.5937i	−0.725299	+	1.33940i
$215$	−28.5259			−1.94545
$216$	−14.6965	−	0.115559i	−0.999969	−	0.00786280i
$217$	11.3427			0.769994
$218$	−2.85430	+	5.27100i	−0.193318	+	0.356997i
$219$	21.7979	−	11.7300i	1.47296	−	0.792640i
$220$	−0.420162	−	0.643840i	−0.0283273	−	0.0434077i
$221$	−6.35657	+	7.57546i	−0.427589	+	0.509581i
$222$	−12.6239	+	7.24434i	−0.847258	+	0.486208i
$223$	−2.82725	−	1.02903i	−0.189327	−	0.0689092i	0.245617	−	0.969367i	$-0.421009\pi$
$223$	−2.82725	−	1.02903i	−0.189327	−	0.0689092i	−0.434944	+	0.900458i	$0.643232\pi$
$224$	8.57859	−	2.75758i	0.573181	−	0.184249i
$225$	0.282734	+	2.45422i	0.0188489	+	0.163615i
$226$	−3.88707	−	9.83568i	−0.258564	−	0.654260i
$227$	3.65533	+	4.35626i	0.242613	+	0.289135i	0.873586	−	0.486670i	$-0.161789\pi$
$227$	3.65533	+	4.35626i	0.242613	+	0.289135i	−0.630973	+	0.775805i	$0.717344\pi$
$228$	−7.18908	+	13.1933i	−0.476109	+	0.873746i
$229$	−21.4459	−	3.78149i	−1.41718	−	0.249888i	−0.587998	−	0.808862i	$-0.700084\pi$
$229$	−21.4459	−	3.78149i	−1.41718	−	0.249888i	−0.829185	+	0.558974i	$0.811195\pi$
$230$	5.83548	−	5.17443i	0.384780	−	0.341192i
$231$	0.417298	−	0.137894i	0.0274562	−	0.00907275i
$232$	6.26811	+	23.9063i	0.411522	+	1.56952i
$233$	−11.7482	+	20.3485i	−0.769650	+	1.33307i	0.168103	+	0.985769i	$0.446236\pi$
$233$	−11.7482	+	20.3485i	−0.769650	+	1.33307i	−0.937753	+	0.347303i	$0.887097\pi$
$234$	−10.8808	−	9.75056i	−0.711300	−	0.637414i
$235$	8.14804	−	4.70427i	0.531520	−	0.306873i
$236$	5.32005	+	0.641160i	0.346306	+	0.0417360i
$237$	−21.5439	+	3.13748i	−1.39943	+	0.203801i
$238$	6.33768	−	1.29679i	0.410811	−	0.0840583i
$239$	21.9880	−	8.00297i	1.42228	−	0.517669i	0.487574	−	0.873082i	$-0.337882\pi$
$239$	21.9880	−	8.00297i	1.42228	−	0.517669i	0.934710	+	0.355413i	$0.115660\pi$
$240$	15.2086	−	6.94438i	0.981714	−	0.448258i
$241$	0.682320	+	3.86963i	0.0439521	+	0.249265i	0.998866	−	0.0476196i	$-0.0151635\pi$
$241$	0.682320	+	3.86963i	0.0439521	+	0.249265i	−0.954913	+	0.296884i	$0.904052\pi$
$242$	9.64814	−	12.1572i	0.620206	−	0.781496i
$243$	2.32317	−	15.4144i	0.149032	−	0.988832i
$244$	−2.80583	+	0.654382i	−0.179625	+	0.0418925i
$245$	−10.6055	+	1.87004i	−0.677562	+	0.119472i
$246$	18.8369	+	15.8904i	1.20100	+	1.01313i
$247$	−14.0356	+	5.10855i	−0.893066	+	0.325049i
$248$	−8.41347	−	18.2989i	−0.534256	−	1.16198i
$249$	−2.81540	−	19.3323i	−0.178419	−	1.22514i
$250$	7.46099	+	12.1448i	0.471874	+	0.768102i
$251$	0.431970	−	0.249398i	0.0272657	−	0.0157419i	−0.486305	−	0.873789i	$-0.661656\pi$
$251$	0.431970	−	0.249398i	0.0272657	−	0.0157419i	0.513571	+	0.858047i	$0.328322\pi$
$252$	1.61028	+	9.42088i	0.101438	+	0.593459i
$253$	−0.315261	−	0.182016i	−0.0198203	−	0.0114433i
$254$	0.534774	+	19.5862i	0.0335547	+	1.22895i
$255$	11.3966	−	3.76595i	0.713685	−	0.235833i
$256$	−10.8119	−	11.7942i	−0.675744	−	0.737137i
$257$	0.156179	−	0.885735i	0.00974218	−	0.0552506i	−0.979549	−	0.201205i	$-0.935514\pi$
$257$	0.156179	−	0.885735i	0.00974218	−	0.0552506i	0.989291	+	0.145955i	$0.0466253\pi$
$258$	−28.5282	+	4.95324i	−1.77609	+	0.308375i
$259$	6.08403	+	7.25067i	0.378043	+	0.450535i
$260$	15.9052	+	4.82390i	0.986401	+	0.299165i
$261$	−26.0413	+	3.00003i	−1.61191	+	0.185697i
$262$	1.07161	−	7.22552i	0.0662044	−	0.446394i
$263$	−9.42004	−	3.42861i	−0.580864	−	0.211417i	0.0348423	−	0.999393i	$-0.488907\pi$
$263$	−9.42004	−	3.42861i	−0.580864	−	0.211417i	−0.615707	+	0.787976i	$0.711129\pi$
$264$	−0.531992	−	0.570934i	−0.0327418	−	0.0351386i
$265$	−18.1313	−	15.2139i	−1.11380	−	0.934585i
$266$	9.26928	+	3.08995i	0.568336	+	0.189457i
$267$	−11.3910	+	6.12977i	−0.697115	+	0.375136i
$268$	0.179737	+	0.420817i	0.0109792	+	0.0257055i
$269$			1.04059i			0.0634460i	0.999497	+	0.0317230i	$0.0100994\pi$
$269$			1.04059i			0.0634460i	−0.999497	+	0.0317230i	$0.989901\pi$
$270$	5.01322	+	17.0099i	0.305095	+	1.03519i
$271$	−30.0408			−1.82485			−0.912423	−	0.409248i	$-0.865791\pi$
$271$	−30.0408			−1.82485			−0.912423	+	0.409248i	$0.865791\pi$
$272$	−6.79305	−	9.26253i	−0.411889	−	0.561623i
$273$	−4.99464	+	8.08254i	−0.302289	+	0.489178i
$274$	8.43352	−	25.2990i	0.509488	−	1.52837i
$275$	−0.0843178	+	0.100486i	−0.00508456	+	0.00605954i
$276$	4.93746	−	6.18811i	0.297200	−	0.372481i
$277$	6.71914	−	18.4607i	0.403714	−	1.10920i	−0.556723	−	0.830698i	$-0.687941\pi$
$277$	6.71914	−	18.4607i	0.403714	−	1.10920i	0.960437	−	0.278497i	$-0.0898363\pi$
$278$	3.35832	−	22.6440i	0.201418	−	1.35810i
$279$	20.4749	−	6.09280i	1.22580	−	0.364767i
$280$	−6.18825	−	8.93964i	−0.369818	−	0.534245i
$281$	21.2698	−	17.8475i	1.26885	−	1.06469i	0.274167	−	0.961682i	$-0.411598\pi$
$281$	21.2698	−	17.8475i	1.26885	−	1.06469i	0.994681	−	0.103008i	$-0.0328467\pi$
$282$	7.33184	−	6.11947i	0.436605	−	0.364409i
$283$	24.5768	+	4.33356i	1.46094	+	0.257603i	0.846934	−	0.531698i	$-0.178446\pi$
$283$	24.5768	+	4.33356i	1.46094	+	0.257603i	0.614007	+	0.789301i	$0.289557\pi$
$284$	11.2758	−	0.616201i	0.669098	−	0.0365648i
$285$	17.7513	+	3.68070i	1.05150	+	0.218026i
$286$	−0.0211737	−	0.775490i	−0.00125203	−	0.0458557i
$287$	8.01310	−	13.8791i	0.472999	−	0.819258i
$288$	14.0040	−	9.58576i	0.825196	−	0.564847i
$289$	4.37687	+	7.58097i	0.257463	+	0.445939i
$290$	25.4085	−	15.6094i	1.49204	−	0.916615i
$291$	−7.25219	−	9.18753i	−0.425131	−	0.538582i
$292$	−12.9195	+	25.4965i	−0.756055	+	1.49207i
$293$	2.79279	+	7.67312i	0.163156	+	0.448268i	0.994149	−	0.108015i	$-0.0344493\pi$
$293$	2.79279	+	7.67312i	0.163156	+	0.448268i	−0.830993	+	0.556283i	$0.812227\pi$
$294$	−10.2817	+	3.71173i	−0.599639	+	0.216472i
$295$	−1.12274	−	6.36736i	−0.0653683	−	0.370722i
$296$	7.18449	−	15.1934i	0.417590	−	0.883099i
$297$	0.679199	−	0.473067i	0.0394111	−	0.0274501i
$298$	−14.3678	−	11.4025i	−0.832303	−	0.660527i
$299$	7.75036	−	1.36660i	0.448215	−	0.0790324i
$300$	−1.88700	−	2.13934i	−0.108946	−	0.123515i
$301$	6.44011	+	17.6941i	0.371202	+	1.01987i
$302$	4.66127	−	0.953769i	0.268226	−	0.0548832i
$303$	−2.74182	−	1.09189i	−0.157513	−	0.0627273i
$304$	−1.89055	−	17.2459i	−0.108430	−	0.989118i
$305$	1.73818	+	3.01061i	0.0995278	+	0.172387i
$306$	10.7436	−	5.74516i	0.614173	−	0.328429i
$307$	16.1236	+	9.30896i	0.920222	+	0.531290i	0.883706	−	0.468043i	$-0.155041\pi$
$307$	16.1236	+	9.30896i	0.920222	+	0.531290i	0.0365160	+	0.999333i	$0.488374\pi$
$308$	−0.304503	+	0.405973i	−0.0173507	+	0.0231325i
$309$	14.7780	−	16.5782i	0.840689	−	0.943099i
$310$	−18.1826	+	16.1229i	−1.03271	+	0.915718i
$311$	−0.851609	+	4.82971i	−0.0482903	+	0.273868i	−0.999386	−	0.0350274i	$-0.988848\pi$
$311$	−0.851609	+	4.82971i	−0.0482903	+	0.273868i	0.951096	+	0.308895i	$0.0999593\pi$
$312$	16.7441	+	2.06250i	0.947950	+	0.116766i
$313$	−7.88890	+	6.61958i	−0.445907	+	0.374161i	−0.837914	−	0.545802i	$-0.816225\pi$
$313$	−7.88890	+	6.61958i	−0.445907	+	0.374161i	0.392007	+	0.919962i	$0.371781\pi$
$314$	−0.655845	+	0.259191i	−0.0370115	+	0.0146270i
$315$	10.3140	−	5.15848i	0.581126	−	0.290647i
$316$	18.3473	−	17.1859i	1.03212	−	0.966783i
$317$	−7.72259	+	21.2177i	−0.433744	+	1.19170i	0.509753	+	0.860321i	$0.329737\pi$
$317$	−7.72259	+	21.2177i	−0.433744	+	1.19170i	−0.943497	+	0.331381i	$0.892485\pi$
$318$	−20.7745	−	12.0669i	−1.16497	−	0.676676i
$319$	−1.06624	−	0.894680i	−0.0596979	−	0.0500925i
$320$	−9.83196	+	16.6143i	−0.549623	+	0.928769i
$321$	27.2776	+	0.816330i	1.52249	+	0.0455631i
$322$	−4.52703	−	2.45143i	−0.252282	−	0.136613i
$323$		−	12.4551i		−	0.693020i
$324$	7.96721	+	16.1407i	0.442623	+	0.896708i
$325$		−	2.83585i		−	0.157304i
$326$	−7.61236	+	14.0576i	−0.421609	+	0.778581i
$327$	7.33808	+	0.219605i	0.405797	+	0.0121442i
$328$	−28.3345	−	2.63252i	−1.56451	−	0.145356i
$329$	−4.75749	−	3.99201i	−0.262289	−	0.220087i
$330$	−0.472932	+	0.814207i	−0.0260341	+	0.0448206i
$331$	−8.06296	+	22.1528i	−0.443180	+	1.21763i	0.494209	+	0.869343i	$0.335458\pi$
$331$	−8.06296	+	22.1528i	−0.443180	+	1.21763i	−0.937389	+	0.348284i	$0.886764\pi$
$332$	15.4217	+	16.4639i	0.846375	+	0.903572i
$333$	14.8771	+	9.82018i	0.815259	+	0.538143i
$334$	6.84616	+	17.3232i	0.374605	+	0.947885i
$335$	0.422957	−	0.354903i	0.0231086	−	0.0193904i
$336$	−7.74102	−	7.86583i	−0.422307	−	0.429116i
$337$	−5.70981	+	32.3820i	−0.311033	+	1.76396i	0.282615	+	0.959233i	$0.408798\pi$
$337$	−5.70981	+	32.3820i	−0.311033	+	1.76396i	−0.593649	+	0.804724i	$0.702313\pi$
$338$	−1.07041	−	1.20716i	−0.0582227	−	0.0656609i
$339$	−8.61898	+	9.66892i	−0.468119	+	0.525144i
$340$	−8.31615	+	11.0873i	−0.451007	+	0.601296i
$341$	0.982316	+	0.567140i	0.0531954	+	0.0307124i
$342$	18.3918	+	0.598659i	0.994517	+	0.0323718i
$343$	9.12950	+	15.8128i	0.492947	+	0.853809i
$344$	23.7684	−	23.5143i	1.28151	−	1.26780i
$345$	−8.87423	−	3.53403i	−0.477772	−	0.190266i
$346$	−4.64336	−	22.6931i	−0.249628	−	1.21999i
$347$	0.288638	+	0.793027i	0.0154949	+	0.0425719i	0.947199	−	0.320646i	$-0.103900\pi$
$347$	0.288638	+	0.793027i	0.0154949	+	0.0425719i	−0.931704	+	0.363218i	$0.881678\pi$
$348$	22.7001	−	20.0226i	1.21685	−	1.07332i
$349$	13.8072	−	2.43459i	0.739085	−	0.130321i	0.208583	−	0.978005i	$-0.433115\pi$
$349$	13.8072	−	2.43459i	0.739085	−	0.130321i	0.530501	+	0.847684i	$0.322004\pi$
$350$	−1.15320	+	1.45309i	−0.0616409	+	0.0776711i
$351$	−4.67429	+	17.2728i	−0.249495	+	0.921952i
$352$	0.880812	+	0.190117i	0.0469475	+	0.0101333i
$353$	4.09441	+	23.2205i	0.217923	+	1.23590i	0.875761	+	0.482744i	$0.160360\pi$
$353$	4.09441	+	23.2205i	0.217923	+	1.23590i	−0.657838	+	0.753159i	$0.728529\pi$
$354$	−2.22846	−	6.17292i	−0.118441	−	0.328087i
$355$	−4.66025	−	12.8039i	−0.247341	−	0.679562i
$356$	6.75136	−	13.3238i	0.357821	−	0.706159i
$357$	−4.90889	−	6.21889i	−0.259806	−	0.329139i
$358$	−4.38848	−	7.14342i	−0.231938	−	0.377542i
$359$	−13.4957	−	23.3753i	−0.712277	−	1.23370i	−0.964001	−	0.265900i	$-0.914331\pi$
$359$	−13.4957	−	23.3753i	−0.712277	−	1.23370i	0.251724	−	0.967799i	$-0.419003\pi$
$360$	−15.9724	−	12.8130i	−0.841821	−	0.675303i
$361$	−0.0939335	+	0.162698i	−0.00494387	+	0.00856303i
$362$	2.46167	−	0.0672125i	0.129383	−	0.00353261i
$363$	−18.6127	−	3.85931i	−0.976914	−	0.202561i
$364$	−0.598655	−	10.9548i	−0.0313780	−	0.574185i
$365$	33.9641	+	5.98879i	1.77776	+	0.313468i
$366$	2.26108	+	2.70904i	0.118189	+	0.141604i
$367$	22.3181	−	18.7271i	1.16500	−	0.977547i	0.165033	−	0.986288i	$-0.447227\pi$
$367$	22.3181	−	18.7271i	1.16500	−	0.977547i	0.999962	+	0.00874090i	$0.00278235\pi$
$368$	−0.596913	+	9.12170i	−0.0311163	+	0.475501i
$369$	7.00930	−	29.3576i	0.364890	−	1.52829i
$370$	−20.0592	−	2.97496i	−1.04283	−	0.154661i
$371$	−5.34353	+	14.6812i	−0.277422	+	0.762211i
$372$	−15.3845	+	19.2814i	−0.797651	+	0.999694i
$373$	−0.738799	+	0.880467i	−0.0382536	+	0.0455888i	−0.784832	−	0.619709i	$-0.787251\pi$
$373$	−0.738799	+	0.880467i	−0.0382536	+	0.0455888i	0.746578	+	0.665297i	$0.231695\pi$
$374$	0.613703	+	0.204580i	0.0317338	+	0.0105786i
$375$	9.17676	−	14.8502i	0.473886	−	0.766862i
$376$	−2.91134	+	10.6362i	−0.150141	+	0.548521i
$377$	30.0906			1.54975
$378$	9.41908	−	6.94980i	0.484465	−	0.357459i
$379$			16.9124i			0.868731i	0.900737	+	0.434365i	$0.143027\pi$
$379$			16.9124i			0.868731i	−0.900737	+	0.434365i	$0.856973\pi$
$380$	−19.2510	+	8.22237i	−0.987556	+	0.421799i
$381$	21.1317	−	11.3715i	1.08261	−	0.582579i
$382$	−4.85801	+	14.5731i	−0.248557	+	0.745626i
$383$	15.4572	+	12.9701i	0.789826	+	0.662743i	0.945702	−	0.325034i	$-0.105376\pi$
$383$	15.4572	+	12.9701i	0.789826	+	0.662743i	−0.155876	+	0.987777i	$0.549820\pi$
$384$	−6.94784	+	18.3229i	−0.354556	+	0.935035i
$385$	0.575396	+	0.209427i	0.0293249	+	0.0106734i
$386$	−20.2493	−	3.00316i	−1.03066	−	0.152857i
$387$	21.1296	+	28.4804i	1.07408	+	1.44774i
$388$	12.9339	+	3.92272i	0.656619	+	0.199146i
$389$	−18.7454	−	22.3399i	−0.950428	−	1.13268i	−0.991049	−	0.133502i	$-0.957378\pi$
$389$	−18.7454	−	22.3399i	−0.950428	−	1.13268i	0.0406204	−	0.999175i	$-0.487067\pi$
$390$	−3.48224	−	20.0560i	−0.176330	−	1.01558i
$391$	−1.13957	+	6.46284i	−0.0576307	+	0.326840i
$392$	7.29526	−	10.3004i	0.368466	−	0.520249i
$393$	−8.49446	+	2.80694i	−0.428489	+	0.141592i
$394$	12.0292	−	0.328441i	0.606023	−	0.0165466i
$395$	−26.2690	−	15.1664i	−1.32174	−	0.763105i
$396$	−0.331592	+	0.896392i	−0.0166631	+	0.0450454i
$397$	10.3158	−	5.95584i	0.517736	−	0.298915i	−0.218272	−	0.975888i	$-0.570042\pi$
$397$	10.3158	−	5.95584i	0.517736	−	0.298915i	0.736008	+	0.676973i	$0.236709\pi$
$398$	−14.8922	+	9.14884i	−0.746478	+	0.458590i
$399$	−1.72453	−	11.8417i	−0.0863347	−	0.592829i
$400$	3.19962	+	0.782590i	0.159981	+	0.0391295i
$401$	2.23681	−	0.814132i	0.111701	−	0.0406558i	−0.285565	−	0.958359i	$-0.592181\pi$
$401$	2.23681	−	0.814132i	0.111701	−	0.0406558i	0.397266	+	0.917704i	$0.369959\pi$
$402$	0.361365	−	0.428373i	0.0180233	−	0.0213653i
$403$	−24.1492	+	4.25815i	−1.20296	+	0.212114i
$404$	3.31873	−	0.774002i	0.165113	−	0.0385080i
$405$	15.8469	−	14.8518i	0.787441	−	0.737993i
$406$	−15.4185	−	12.2363i	−0.765207	−	0.607279i
$407$	0.164360	+	0.932134i	0.00814705	+	0.0462042i
$408$	−6.39161	+	12.5322i	−0.316432	+	0.620439i
$409$	12.0885	−	4.39986i	0.597739	−	0.217559i	−0.0253911	−	0.999678i	$-0.508083\pi$
$409$	12.0885	−	4.39986i	0.597739	−	0.217559i	0.623130	+	0.782119i	$0.285861\pi$
$410$	6.88298	+	33.6386i	0.339926	+	1.66129i
$411$	−32.3201	+	4.70684i	−1.59424	+	0.232171i
$412$	−3.06840	+	25.4601i	−0.151169	+	1.25433i
$413$	−3.69607	+	2.13393i	−0.181872	+	0.105004i
$414$	−9.48859	−	1.99339i	−0.466339	−	0.0979698i
$415$	13.6095	−	23.5724i	0.668064	−	1.15712i
$416$	−17.2290	+	9.09149i	−0.844721	+	0.445747i
$417$	−26.6207	+	8.79666i	−1.30362	+	0.430774i
$418$	0.648250	+	0.731066i	0.0317069	+	0.0357576i
$419$	7.38244	+	1.30172i	0.360656	+	0.0635933i	0.351040	−	0.936360i	$-0.385828\pi$
$419$	7.38244	+	1.30172i	0.360656	+	0.0635933i	0.00961568	+	0.999954i	$0.496939\pi$
$420$	−6.37146	+	11.6928i	−0.310896	+	0.570550i
$421$	−5.15270	−	6.14075i	−0.251127	−	0.299282i	0.625723	−	0.780045i	$-0.284804\pi$
$421$	−5.15270	−	6.14075i	−0.251127	−	0.299282i	−0.876850	+	0.480763i	$0.840360\pi$
$422$	2.32525	−	0.918943i	0.113192	−	0.0447335i
$423$	−10.7321	−	4.65051i	−0.521814	−	0.226115i
$424$	27.6484	−	2.26921i	1.34273	−	0.110203i
$425$	2.22213	+	0.808790i	0.107789	+	0.0392321i
$426$	−6.88390	−	11.9958i	−0.333526	−	0.581196i
$427$	1.47501	−	1.75784i	0.0713805	−	0.0850680i
$428$	−26.3894	+	17.2214i	−1.27558	+	0.832429i
$429$	−0.836681	+	0.450240i	−0.0403953	+	0.0217378i
$430$	−35.4745	−	19.2098i	−1.71073	−	0.926380i
$431$	−4.63698			−0.223356			−0.111678	−	0.993744i	$-0.535622\pi$
$431$	−4.63698			−0.223356			−0.111678	+	0.993744i	$0.535622\pi$
$432$	−18.1986	−	10.0406i	−0.875578	−	0.483076i
$433$	−0.0678381			−0.00326009			−0.00163005	−	0.999999i	$-0.500519\pi$
$433$	−0.0678381			−0.00326009			−0.00163005	+	0.999999i	$0.500519\pi$
$434$	14.1057	+	7.63837i	0.677094	+	0.366654i
$435$	−31.0687	−	19.1990i	−1.48963	−	0.920523i
$436$	−7.09914	+	4.63282i	−0.339987	+	0.221872i
$437$	−6.37133	+	7.59305i	−0.304782	+	0.363225i
$438$	35.0067	+	0.0917515i	1.67269	+	0.00438406i
$439$	12.9530	+	4.71449i	0.618211	+	0.225010i	0.632092	−	0.774893i	$-0.282196\pi$
$439$	12.9530	+	4.71449i	0.618211	+	0.225010i	−0.0138813	+	0.999904i	$0.504419\pi$
$440$	−0.0889366	−	1.08361i	−0.00423989	−	0.0516593i
$441$	9.72272	+	9.20343i	0.462987	+	0.438258i
$442$	−13.0064	+	5.14014i	−0.618651	+	0.244492i
$443$	−8.58044	−	10.2258i	−0.407669	−	0.485841i	0.522673	−	0.852533i	$-0.324935\pi$
$443$	−8.58044	−	10.2258i	−0.407669	−	0.485841i	−0.930342	+	0.366692i	$0.880490\pi$
$444$	−20.5773	+	0.507866i	−0.976557	+	0.0241023i
$445$	−17.7487	−	3.12957i	−0.841369	−	0.148356i
$446$	−2.82296	−	3.18361i	−0.133671	−	0.150748i
$447$	−4.56104	+	21.9971i	−0.215730	+	1.04043i
$448$	12.5252	+	2.34766i	0.591761	+	0.110917i
$449$	6.26480	−	10.8509i	0.295654	−	0.512088i	−0.679483	−	0.733692i	$-0.737796\pi$
$449$	6.26480	−	10.8509i	0.295654	−	0.512088i	0.975137	+	0.221604i	$0.0711291\pi$
$450$	−1.30111	+	3.24244i	−0.0613348	+	0.152850i
$451$	1.38792	−	0.801316i	0.0653546	−	0.0377325i
$452$	1.78959	−	14.8491i	0.0841751	−	0.698445i
$453$	−3.61041	−	4.57390i	−0.169632	−	0.214901i
$454$	1.61216	+	7.87895i	0.0756622	+	0.369777i
$455$	−12.4393	+	4.52755i	−0.583166	+	0.212255i
$456$	−17.8248	+	11.5658i	−0.834724	+	0.541617i
$457$	3.14504	+	17.8364i	0.147119	+	0.834352i	0.965642	+	0.259878i	$0.0836822\pi$
$457$	3.14504	+	17.8364i	0.147119	+	0.834352i	−0.818523	+	0.574474i	$0.805207\pi$
$458$	−24.1233	−	19.1446i	−1.12721	−	0.894569i
$459$	−12.2016	−	8.58894i	−0.569521	−	0.400898i
$460$	10.7415	−	2.50515i	0.500824	−	0.116803i
$461$	6.87340	−	1.21197i	0.320126	−	0.0564469i	−0.0112760	−	0.999936i	$-0.503589\pi$
$461$	6.87340	−	1.21197i	0.320126	−	0.0564469i	0.331402	+	0.943490i	$0.392478\pi$
$462$	0.611807	+	0.109532i	0.0284638	+	0.00509590i
$463$	26.8210	−	9.76206i	1.24648	−	0.453681i	0.367269	−	0.930115i	$-0.380293\pi$
$463$	26.8210	−	9.76206i	1.24648	−	0.453681i	0.879210	+	0.476434i	$0.158071\pi$
$464$	−8.30391	+	33.9506i	−0.385499	+	1.57612i
$465$	27.6510	+	11.0116i	1.28229	+	0.510651i
$466$	−28.3129	+	17.3937i	−1.31157	+	0.805747i
$467$	0.471619	−	0.272289i	0.0218239	−	0.0126000i	−0.489048	−	0.872257i	$-0.662656\pi$
$467$	0.471619	−	0.272289i	0.0218239	−	0.0126000i	0.510872	+	0.859657i	$0.329323\pi$
$468$	−6.96504	−	19.4530i	−0.321959	−	0.899214i
$469$	−0.315627	−	0.182227i	−0.0145743	−	0.00841448i
$470$	13.3007	−	0.363158i	0.613517	−	0.0167512i
$471$	0.644726	+	0.574716i	0.0297074	+	0.0264815i
$472$	6.18418	+	4.37994i	0.284650	+	0.201603i
$473$	−0.326975	+	1.85437i	−0.0150343	+	0.0852640i
$474$	−28.9046	−	10.6063i	−1.32763	−	0.487163i
$475$	2.29584	+	2.73608i	0.105340	+	0.125540i
$476$	8.75474	+	2.65522i	0.401273	+	0.121702i
$477$	−1.75956	+	29.3715i	−0.0805647	+	1.34483i
$478$	32.7333	+	4.85466i	1.49719	+	0.222047i
$479$	7.93244	+	2.88717i	0.362442	+	0.131918i	0.516821	−	0.856094i	$-0.327115\pi$
$479$	7.93244	+	2.88717i	0.362442	+	0.131918i	−0.154379	+	0.988012i	$0.549338\pi$
$480$	23.5897	+	1.60579i	1.07672	+	0.0732939i
$481$	−15.6752	−	13.1530i	−0.714725	−	0.599726i
$482$	−1.75735	+	5.27171i	−0.0800449	+	0.240120i
$483$	−0.188609	+	6.30236i	−0.00858200	+	0.286767i
$484$	20.1852	−	8.62137i	0.917508	−	0.391880i
$485$		−	16.3079i		−	0.740505i
$486$	13.2694	−	17.6047i	0.601910	−	0.798564i
$487$	−15.0013			−0.679775			−0.339888	−	0.940466i	$-0.610389\pi$
$487$	−15.0013			−0.679775			−0.339888	+	0.940466i	$0.610389\pi$
$488$	−3.92997	−	1.07571i	−0.177901	−	0.0486951i
$489$	19.5705	+	0.585681i	0.885009	+	0.0264854i
$490$	−14.4482	−	4.81637i	−0.652704	−	0.217581i
$491$	9.43399	−	11.2430i	0.425750	−	0.507389i	−0.509941	−	0.860209i	$-0.670333\pi$
$491$	9.43399	−	11.2430i	0.425750	−	0.507389i	0.935691	+	0.352820i	$0.114777\pi$
$492$	12.7245	+	32.4461i	0.573666	+	1.46278i
$493$	−8.58191	+	23.5786i	−0.386510	+	1.06193i
$494$	−20.8947	−	3.09888i	−0.940098	−	0.139425i
$495$	1.15115	+	0.0689619i	0.0517402	+	0.00309961i
$496$	1.85991	−	28.4221i	0.0835124	−	1.27619i
$497$	−6.88991	+	5.78132i	−0.309055	+	0.259328i
$498$	9.51750	−	25.9374i	0.426489	−	1.16228i
$499$	17.0588	+	3.00792i	0.763655	+	0.134653i	0.541892	−	0.840448i	$-0.317708\pi$
$499$	17.0588	+	3.00792i	0.763655	+	0.134653i	0.221762	+	0.975101i	$0.428819\pi$
$500$	1.09992	+	20.1274i	0.0491900	+	0.900125i
$501$	15.1803	−	17.0295i	0.678206	−	0.760823i
$502$	0.705142	−	0.0192529i	0.0314720	−	0.000859300i
$503$	−2.40445	+	4.16463i	−0.107209	+	0.185692i	−0.914639	−	0.404272i	$-0.867525\pi$
$503$	−2.40445	+	4.16463i	−0.107209	+	0.185692i	0.807429	+	0.589964i	$0.200858\pi$
$504$	−4.34164	+	12.8001i	−0.193392	+	0.570161i
$505$	−2.05591	−	3.56095i	−0.0914870	−	0.158460i
$506$	−0.269482	−	0.438655i	−0.0119800	−	0.0195006i
$507$	−0.731069	+	1.83577i	−0.0324679	+	0.0815296i
$508$	−12.5246	+	24.7173i	−0.555690	+	1.09665i
$509$	10.1785	+	27.9653i	0.451155	+	1.23954i	0.931912	+	0.362685i	$0.118140\pi$
$509$	10.1785	+	27.9653i	0.451155	+	1.23954i	−0.480757	+	0.876854i	$0.659638\pi$
$510$	16.7088	+	2.99138i	0.739877	+	0.132461i
$511$	−3.95313	−	22.4193i	−0.174876	−	0.991772i
$512$	−5.50316	−	21.9480i	−0.243208	−	0.969974i
$513$	−9.47383	−	20.4493i	−0.418280	−	0.902859i
$514$	0.790690	−	0.996316i	0.0348759	−	0.0439456i
$515$	30.4722	−	5.37308i	1.34277	−	0.236766i
$516$	−38.8129	−	13.0516i	−1.70864	−	0.574564i
$517$	−0.212412	−	0.583597i	−0.00934187	−	0.0256666i
$518$	2.68332	+	13.1139i	0.117898	+	0.576193i
$519$	−22.2677	+	17.5771i	−0.977445	+	0.771547i
$520$	16.5311	+	16.7098i	0.724936	+	0.732772i
$521$	15.3931	+	26.6615i	0.674382	+	1.16806i	0.976649	+	0.214840i	$0.0689231\pi$
$521$	15.3931	+	26.6615i	0.674382	+	1.16806i	−0.302267	+	0.953223i	$0.597744\pi$
$522$	−34.4049	−	13.8058i	−1.50586	−	0.604264i
$523$	−20.1716	−	11.6461i	−0.882042	−	0.509247i	−0.0107111	−	0.999943i	$-0.503410\pi$
$523$	−20.1716	−	11.6461i	−0.882042	−	0.509247i	−0.871331	+	0.490695i	$0.836743\pi$
$524$	6.19842	−	8.26393i	0.270779	−	0.361011i
$525$	2.22469	+	0.461284i	0.0970933	+	0.0201321i
$526$	−9.40576	−	10.6074i	−0.410111	−	0.462504i
$527$	3.55077	−	20.1374i	0.154674	−	0.877200i
$528$	−0.277102	−	1.06826i	−0.0120593	−	0.0464900i
$529$	−13.6183	+	11.4271i	−0.592099	+	0.496830i
$530$	−12.3025	−	31.1298i	−0.534387	−	1.35219i
$531$	−5.52557	+	5.83734i	−0.239789	+	0.253319i
$532$	9.44634	+	10.0847i	0.409551	+	0.437227i
$533$	−11.8499	+	32.5574i	−0.513278	+	1.41022i
$534$	−18.2935	−	0.0479468i	−0.791639	−	0.00207486i
$535$	29.1263	+	24.4399i	1.25924	+	1.05663i
$536$	−0.0598665	+	0.644361i	−0.00258584	+	0.0278321i
$537$	−5.39768	+	8.73475i	−0.232927	+	0.376932i
$538$	−0.700751	+	1.29407i	−0.0302115	+	0.0557912i
$539$			0.710862i			0.0306190i
$540$	−5.22034	+	24.5293i	−0.224648	+	1.05557i
$541$		−	29.0030i		−	1.24694i	−0.781848	−	0.623469i	$-0.785723\pi$
$541$		−	29.0030i		−	1.24694i	0.781848	−	0.623469i	$-0.214277\pi$
$542$	−37.3583	−	20.2299i	−1.60468	−	0.868950i
$543$	−1.42921	−	2.65591i	−0.0613334	−	0.113976i
$544$	−2.21022	−	16.0933i	−0.0947625	−	0.689995i
$545$	7.83541	+	6.57469i	0.335632	+	0.281629i
$546$	−11.6542	+	6.68788i	−0.498753	+	0.286215i
$547$	3.84045	−	10.5516i	0.164206	−	0.451152i	−0.830113	−	0.557596i	$-0.811724\pi$
$547$	3.84045	−	10.5516i	0.164206	−	0.451152i	0.994319	+	0.106443i	$0.0339463\pi$
$548$	27.5246	−	25.7823i	1.17579	−	1.10136i
$549$	1.71831	−	3.96541i	0.0733358	−	0.169239i
$550$	−0.172526	+	0.0681823i	−0.00735651	+	0.00290730i
$551$	−29.0320	+	24.3607i	−1.23681	+	1.03780i
$552$	10.3073	−	4.37050i	0.438710	−	0.186021i
$553$	−3.47684	+	19.7182i	−0.147850	+	0.838501i
$554$	20.7876	−	18.4327i	0.883179	−	0.783131i
$555$	7.79251	+	23.5819i	0.330774	+	1.00100i
$556$	19.4252	−	25.8983i	0.823811	−	1.09833i
$557$	2.53413	+	1.46308i	0.107374	+	0.0619927i	0.552726	−	0.833363i	$-0.313588\pi$
$557$	2.53413	+	1.46308i	0.107374	+	0.0619927i	−0.445351	+	0.895356i	$0.646921\pi$
$558$	29.5653	+	6.21116i	1.25160	+	0.262940i
$559$	−20.3538	−	35.2538i	−0.860874	−	1.49108i
$560$	−1.67553	−	15.2845i	−0.0708043	−	0.645887i
$561$	−0.114178	−	0.784021i	−0.00482062	−	0.0331014i
$562$	38.4696	−	7.87148i	1.62274	−	0.332038i
$563$	−2.96778	−	8.15390i	−0.125077	−	0.343646i	0.861312	−	0.508077i	$-0.169643\pi$
$563$	−2.96778	−	8.15390i	−0.125077	−	0.343646i	−0.986389	+	0.164431i	$0.947421\pi$
$564$	13.2387	−	2.67272i	0.557452	−	0.112542i
$565$	−17.7724	+	3.13375i	−0.747690	+	0.131838i
$566$	27.6452	+	21.9396i	1.16201	+	0.922190i
$567$	−12.7899	−	6.47655i	−0.537127	−	0.271989i
$568$	14.4375	+	6.82703i	0.605782	+	0.286456i
$569$	−1.80356	−	10.2285i	−0.0756093	−	0.428802i	−0.998991	−	0.0449179i	$-0.985697\pi$
$569$	−1.80356	−	10.2285i	−0.0756093	−	0.428802i	0.923381	−	0.383884i	$-0.125414\pi$
$570$	19.5967	+	16.5313i	0.820814	+	0.692419i
$571$	1.71537	+	4.71295i	0.0717862	+	0.197231i	0.970397	−	0.241516i	$-0.0776447\pi$
$571$	1.71537	+	4.71295i	0.0717862	+	0.197231i	−0.898611	+	0.438747i	$0.855422\pi$
$572$	0.495896	−	0.978649i	0.0207345	−	0.0409194i
$573$	18.6175	−	2.71131i	0.777759	−	0.113266i
$574$	19.3114	−	11.8637i	0.806043	−	0.495183i
$575$	−0.940956	−	1.62978i	−0.0392406	−	0.0679667i
$576$	23.8705	−	2.49020i	0.994603	−	0.103758i
$577$	4.43057	−	7.67398i	0.184447	−	0.319472i	−0.758943	−	0.651157i	$-0.774284\pi$
$577$	4.43057	−	7.67398i	0.184447	−	0.319472i	0.943390	+	0.331685i	$0.107617\pi$
$578$	0.337884	+	12.3751i	0.0140541	+	0.514735i
$579$	7.86638	+	23.8055i	0.326915	+	0.989321i
$580$	42.1093	−	2.30119i	1.74849	−	0.0955515i
$581$	−17.6940	−	3.11993i	−0.734070	−	0.129436i
$582$	−2.83170	−	16.3092i	−0.117378	−	0.676040i
$583$	−1.19683	+	1.00426i	−0.0495677	+	0.0415922i
$584$	−33.2363	+	23.0070i	−1.37533	+	0.952037i
$585$	−20.0224	+	14.8546i	−0.827824	+	0.614162i
$586$	−1.69412	+	11.4229i	−0.0699836	+	0.471876i
$587$	−0.553940	+	1.52194i	−0.0228636	+	0.0628171i	−0.950599	−	0.310420i	$-0.899530\pi$
$587$	−0.553940	+	1.52194i	−0.0228636	+	0.0628171i	0.927736	+	0.373238i	$0.121752\pi$
$588$	−15.2857	−	2.30797i	−0.630371	−	0.0951791i
$589$	19.8523	−	23.6590i	0.817999	−	0.974854i
$590$	2.89166	−	8.67445i	0.119048	−	0.357121i
$591$	−6.98401	−	12.9784i	−0.287284	−	0.533860i
$592$	19.1660	−	14.0562i	0.787719	−	0.577706i
$593$	−16.7535			−0.687984			−0.343992	−	0.938973i	$-0.611779\pi$
$593$	−16.7535			−0.687984			−0.343992	+	0.938973i	$0.611779\pi$
$594$	1.16321	−	0.130918i	0.0477273	−	0.00537161i
$595$		−	11.0386i		−	0.452538i
$596$	−10.1890	−	23.8555i	−0.417357	−	0.977158i
$597$	18.2097	+	11.2528i	0.745273	+	0.460545i
$598$	10.5585	+	3.51973i	0.431771	+	0.143933i
$599$	−31.3875	−	26.3372i	−1.28246	−	1.07611i	−0.992900	−	0.118949i	$-0.962048\pi$
$599$	−31.3875	−	26.3372i	−1.28246	−	1.07611i	−0.289557	−	0.957161i	$-0.593508\pi$
$600$	−0.905983	−	3.93119i	−0.0369866	−	0.160490i
$601$	−8.03176	−	2.92332i	−0.327622	−	0.119245i	0.172972	−	0.984927i	$-0.444663\pi$
$601$	−8.03176	−	2.92332i	−0.327622	−	0.119245i	−0.500594	+	0.865682i	$0.666885\pi$
$602$	−3.90662	+	26.3410i	−0.159222	+	1.07358i
$603$	−0.667626	−	0.159400i	−0.0271878	−	0.00649126i
$604$	6.43898	+	1.95288i	0.261998	+	0.0794614i
$605$	−17.0235	−	20.2878i	−0.692103	−	0.824817i
$606$	−2.67440	−	3.20424i	−0.108640	−	0.130164i
$607$	4.22098	−	23.9383i	0.171324	−	0.971627i	−0.770978	−	0.636862i	$-0.780232\pi$
$607$	4.22098	−	23.9383i	0.171324	−	0.971627i	0.942302	−	0.334765i	$-0.108657\pi$
$608$	9.26258	−	22.7199i	0.375647	−	0.921413i
$609$	−4.89460	+	23.6057i	−0.198339	+	0.956552i
$610$	0.134183	+	4.91448i	0.00543291	+	0.198981i
$611$	11.6276	+	6.71318i	0.470401	+	0.271586i
$612$	17.2295	+	0.0903167i	0.696463	+	0.00365084i
$613$	14.3628	−	8.29237i	0.580108	−	0.334926i	−0.181068	−	0.983471i	$-0.557955\pi$
$613$	14.3628	−	8.29237i	0.580108	−	0.334926i	0.761176	+	0.648545i	$0.224622\pi$
$614$	13.7823	+	22.4344i	0.556208	+	0.905378i
$615$	33.0081	−	26.0550i	1.33101	−	1.05064i
$616$	−0.652066	+	0.299806i	−0.0262725	+	0.0120795i
$617$	−17.6023	+	6.40672i	−0.708642	+	0.257925i	−0.671096	−	0.741370i	$-0.734176\pi$
$617$	−17.6023	+	6.40672i	−0.708642	+	0.257925i	−0.0375461	+	0.999295i	$0.511954\pi$
$618$	29.5417	−	10.6647i	1.18834	−	0.428997i
$619$	−4.87939	+	0.860368i	−0.196119	+	0.0345811i	−0.270845	−	0.962623i	$-0.587303\pi$
$619$	−4.87939	+	0.860368i	−0.196119	+	0.0345811i	0.0747256	+	0.997204i	$0.476192\pi$
$620$	−33.4691	+	7.80575i	−1.34415	+	0.313486i
$621$	3.04488	+	11.4778i	0.122187	+	0.460587i
$622$	−4.31146	+	5.43269i	−0.172874	+	0.217831i
$623$	2.06579	+	11.7157i	0.0827643	+	0.469380i
$624$	19.4339	+	13.8407i	0.777978	+	0.554070i
$625$	26.7242	−	9.72681i	1.06897	−	0.389072i
$626$	−14.2683	+	2.91951i	−0.570275	+	0.116687i
$627$	0.442741	−	1.11176i	0.0176814	−	0.0443994i
$628$	−0.990145	−	0.119330i	−0.0395111	−	0.00476179i
$629$	14.7771	−	8.53157i	0.589202	−	0.340176i
$630$	16.3001	+	0.530573i	0.649413	+	0.0211385i
$631$	−2.46788	+	4.27449i	−0.0982447	+	0.170165i	−0.910958	−	0.412499i	$-0.864656\pi$
$631$	−2.46788	+	4.27449i	−0.0982447	+	0.170165i	0.812713	+	0.582664i	$0.197989\pi$
$632$	34.3898	−	9.01684i	1.36795	−	0.358670i
$633$	−2.28583	−	2.03761i	−0.0908536	−	0.0809879i
$634$	−23.8920	+	21.1855i	−0.948874	+	0.841384i
$635$	32.9261	+	5.80576i	1.30663	+	0.230394i
$636$	−17.7089	−	28.9961i	−0.702202	−	1.14977i
$637$	−9.87834	−	11.7725i	−0.391394	−	0.466445i
$638$	−0.723469	−	1.83064i	−0.0286424	−	0.0724755i
$639$	−9.33158	+	14.1369i	−0.369152	+	0.559246i
$640$	−23.4153	+	14.0404i	−0.925569	+	0.554994i
$641$	1.74409	+	0.634798i	0.0688875	+	0.0250730i	0.376234	−	0.926525i	$-0.377219\pi$
$641$	1.74409	+	0.634798i	0.0688875	+	0.0250730i	−0.307347	+	0.951598i	$0.599441\pi$
$642$	33.3724	+	19.3844i	1.31710	+	0.765040i
$643$	−21.2761	+	25.3559i	−0.839048	+	0.999938i	0.160868	+	0.986976i	$0.448571\pi$
$643$	−21.2761	+	25.3559i	−0.839048	+	0.999938i	−0.999916	+	0.0129623i	$0.995874\pi$
$644$	−3.97893	−	6.09715i	−0.156792	−	0.240261i
$645$	−1.47797	+	49.3863i	−0.0581949	+	1.94458i
$646$	8.38746	−	15.4890i	0.330000	−	0.609407i
$647$	8.85391			0.348083			0.174042	−	0.984738i	$-0.444317\pi$
$647$	8.85391			0.348083			0.174042	+	0.984738i	$0.444317\pi$
$648$	−0.961510	+	25.4377i	−0.0377717	+	0.999286i
$649$	−0.426789			−0.0167529
$650$	1.90970	−	3.52662i	0.0749047	−	0.138326i
$651$	0.587682	−	19.6374i	0.0230331	−	0.769650i
$652$	−18.9333	+	12.3556i	−0.741484	+	0.483884i
$653$	−6.38975	+	7.61501i	−0.250050	+	0.297998i	−0.876439	−	0.481512i	$-0.840088\pi$
$653$	−6.38975	+	7.61501i	−0.250050	+	0.297998i	0.626389	+	0.779511i	$0.284532\pi$
$654$	8.97766	+	5.21468i	0.351054	+	0.203910i
$655$	−11.7127	−	4.26306i	−0.457652	−	0.166572i
$656$	−33.4637	−	22.3547i	−1.30654	−	0.872804i
$657$	−19.1785	−	38.3459i	−0.748224	−	1.49601i
$658$	−3.22808	−	8.16819i	−0.125844	−	0.318429i
$659$	−27.1973	−	32.4125i	−1.05946	−	1.26261i	−0.963637	−	0.267213i	$-0.913897\pi$
$659$	−27.1973	−	32.4125i	−1.05946	−	1.26261i	−0.0958197	−	0.995399i	$-0.530547\pi$
$660$	−1.13643	+	0.694058i	−0.0442356	+	0.0270162i
$661$	−49.7307	−	8.76886i	−1.93430	−	0.341069i	−0.934414	−	0.356189i	$-0.884076\pi$
$661$	−49.7307	−	8.76886i	−1.93430	−	0.341069i	−0.999886	+	0.0151198i	$0.995187\pi$
$662$	−24.9450	+	22.1192i	−0.969516	+	0.859688i
$663$	12.7859	+	11.3975i	0.496562	+	0.442641i
$664$	8.09121	+	30.8595i	0.314000	+	1.19758i
$665$	8.33631	−	14.4389i	0.323268	−	0.559917i
$666$	11.8879	+	22.2307i	0.460646	+	0.861423i
$667$	17.2933	−	9.98430i	0.669600	−	0.386594i
$668$	−3.15193	+	26.1533i	−0.121952	+	1.01190i
$669$	−1.92803	+	4.84143i	−0.0745418	+	0.187181i
$670$	0.764981	−	0.156527i	0.0295538	−	0.00604717i
$671$	0.215633	−	0.0784840i	0.00832442	−	0.00302984i
$672$	−4.32966	−	14.9948i	−0.167020	−	0.578436i
$673$	2.52619	+	14.3267i	0.0973775	+	0.552255i	0.993993	+	0.109445i	$0.0349074\pi$
$673$	2.52619	+	14.3267i	0.0973775	+	0.552255i	−0.896615	+	0.442810i	$0.853981\pi$
$674$	−28.9072	+	36.4247i	−1.11346	+	1.40303i
$675$	4.26358	−	0.362334i	0.164105	−	0.0139462i
$676$	−0.518230	−	2.22204i	−0.0199319	−	0.0854632i
$677$	39.3485	−	6.93820i	1.51229	−	0.266657i	0.644890	−	0.764276i	$-0.276903\pi$
$677$	39.3485	−	6.93820i	1.51229	−	0.266657i	0.867396	+	0.497619i	$0.165792\pi$
$678$	−17.2297	+	6.21999i	−0.661701	+	0.238877i
$679$	−10.1155	+	3.68173i	−0.388197	+	0.141292i
$680$	−17.8083	+	8.18786i	−0.682916	+	0.313990i
$681$	7.73127	−	6.10268i	0.296263	−	0.233855i
$682$	0.839675	+	1.36680i	0.0321528	+	0.0523373i
$683$	16.3031	−	9.41260i	0.623821	−	0.360163i	−0.154534	−	0.987987i	$-0.549388\pi$
$683$	16.3031	−	9.41260i	0.623821	−	0.360163i	0.778355	+	0.627824i	$0.216054\pi$
$684$	22.4687	+	13.1298i	0.859113	+	0.502032i
$685$	−39.4087	−	22.7526i	−1.50573	−	0.869333i
$686$	0.704774	+	25.8125i	0.0269084	+	0.985526i
$687$	−7.65794	+	36.9328i	−0.292168	+	1.40907i
$688$	45.3930	−	13.2360i	1.73059	−	0.504617i
$689$	5.86516	−	33.2630i	0.223445	−	1.26722i
$690$	−8.65601	−	10.3709i	−0.329529	−	0.394814i
$691$	−7.33473	−	8.74119i	−0.279026	−	0.332531i	0.608270	−	0.793730i	$-0.291864\pi$
$691$	−7.33473	−	8.74119i	−0.279026	−	0.332531i	−0.887297	+	0.461199i	$0.847419\pi$
$692$	9.50745	−	31.3477i	0.361419	−	1.19166i
$693$	−0.217111	−	0.729603i	−0.00824738	−	0.0277153i
$694$	−0.175090	+	1.18057i	−0.00664632	+	0.0448139i
$695$	−36.7062	−	13.3600i	−1.39235	−	0.506773i
$696$	41.7131	−	9.61322i	1.58113	−	0.364388i
$697$	−22.1320	−	18.5709i	−0.838307	−	0.703423i
$698$	18.8100	+	6.27039i	0.711969	+	0.237338i
$699$	34.6201	+	21.3937i	1.30945	+	0.809182i
$700$	−2.41264	+	1.03047i	−0.0911891	+	0.0389481i
$701$			29.8398i			1.12704i	0.826104	+	0.563518i	$0.190552\pi$
$701$			29.8398i			1.12704i	−0.826104	+	0.563518i	$0.809448\pi$
$702$	−17.4446	+	18.3325i	−0.658406	+	0.691914i
$703$	25.7721			0.972013
$704$	0.967340	+	0.829580i	0.0364580	+	0.0312660i
$705$	−7.72223	−	14.3502i	−0.290836	−	0.540461i
$706$	−10.5453	+	31.6340i	−0.396878	+	1.19056i
$707$	−1.74463	+	2.07917i	−0.0656137	+	0.0781954i
$708$	1.38566	−	9.17725i	0.0520764	−	0.344902i
$709$	−0.897749	+	2.46655i	−0.0337157	+	0.0926331i	−0.955408	−	0.295288i	$-0.904584\pi$
$709$	−0.897749	+	2.46655i	−0.0337157	+	0.0926331i	0.921693	+	0.387921i	$0.126807\pi$
$710$	2.82694	−	19.0611i	0.106093	−	0.715351i
$711$	4.31562	+	37.4610i	0.161849	+	1.40490i
$712$	17.3684	−	12.0228i	0.650907	−	0.450574i
$713$	−12.4658	+	10.4601i	−0.466849	+	0.391733i
$714$	−1.91673	−	11.0395i	−0.0717320	−	0.413141i
$715$	−1.30367	−	0.229871i	−0.0487543	−	0.00859670i
$716$	−0.646963	−	11.8387i	−0.0241781	−	0.442435i
$717$	−12.7161	−	38.4819i	−0.474892	−	1.43713i
$718$	−1.04184	−	38.1574i	−0.0388809	−	1.42402i
$719$	−6.54404	+	11.3346i	−0.244051	+	0.422709i	−0.961864	−	0.273526i	$-0.911810\pi$
$719$	−6.54404	+	11.3346i	−0.244051	+	0.422709i	0.717813	+	0.696236i	$0.245143\pi$
$720$	−11.2347	−	26.6902i	−0.418691	−	0.994683i
$721$	−10.2123	−	17.6883i	−0.380327	−	0.658746i
$722$	−0.226378	+	0.139072i	−0.00842491	+	0.00517574i
$723$	6.73475	−	0.980794i	0.250468	−	0.0364761i
$724$	3.10657	+	1.57414i	0.115455	+	0.0585026i
$725$	−2.46100	−	6.76154i	−0.0913992	−	0.251117i
$726$	−20.5476	−	17.3335i	−0.762594	−	0.643306i
$727$	6.97054	+	39.5319i	0.258523	+	1.46616i	0.786865	+	0.617125i	$0.211703\pi$
$727$	6.97054	+	39.5319i	0.258523	+	1.46616i	−0.528342	+	0.849031i	$0.677186\pi$
$728$	6.63263	−	14.0263i	0.245822	−	0.519851i
$729$	−26.5662	−	4.82069i	−0.983932	−	0.178544i
$730$	38.2044	+	30.3196i	1.41401	+	1.12218i
$731$	33.4294	−	5.89450i	1.23643	−	0.218016i
$732$	0.987542	+	4.89157i	0.0365006	+	0.180798i
$733$	0.696450	+	1.91348i	0.0257240	+	0.0706760i	0.951890	−	0.306440i	$-0.0991380\pi$
$733$	0.696450	+	1.91348i	0.0257240	+	0.0706760i	−0.926166	+	0.377116i	$0.876916\pi$
$734$	40.3657	−	8.25944i	1.48992	−	0.304862i
$735$	2.68807	+	18.4580i	0.0991509	+	0.680833i
$736$	−6.88501	+	10.9417i	−0.253785	+	0.403315i
$737$	−0.0182229	−	0.0315629i	−0.000671248	−	0.00116264i
$738$	28.4865	−	31.7886i	1.04860	−	1.17015i
$739$	30.6990	+	17.7241i	1.12928	+	0.651990i	0.943754	−	0.330649i	$-0.107268\pi$
$739$	30.6990	+	17.7241i	1.12928	+	0.651990i	0.185526	+	0.982639i	$0.440601\pi$
$740$	−22.9419	−	17.2078i	−0.843363	−	0.632571i
$741$	8.11710	+	24.5642i	0.298189	+	0.902389i
$742$	−16.5317	+	14.6590i	−0.606898	+	0.538148i
$743$	9.22773	−	52.3330i	0.338532	−	1.91991i	−0.0505739	−	0.998720i	$-0.516105\pi$
$743$	9.22773	−	52.3330i	0.338532	−	1.91991i	0.389106	−	0.921193i	$-0.372784\pi$
$744$	−32.1164	+	13.6179i	−1.17745	+	0.499258i
$745$	−23.9767	+	20.1189i	−0.878440	+	0.737099i
$746$	−1.51168	+	0.597419i	−0.0553466	+	0.0218731i
$747$	−33.6155	+	3.87260i	−1.22993	+	0.141691i
$748$	0.625426	+	0.667691i	0.0228678	+	0.0244132i
$749$	8.58392	−	23.5841i	0.313649	−	0.861745i
$750$	21.4125	−	12.2878i	0.781873	−	0.448687i
$751$	6.58894	+	5.52878i	0.240434	+	0.201748i	0.755040	−	0.655679i	$-0.227617\pi$
$751$	6.58894	+	5.52878i	0.240434	+	0.201748i	−0.514606	+	0.857427i	$0.672062\pi$
$752$	−10.7831	+	11.2665i	−0.393220	+	0.410848i
$753$	−0.409396	−	0.760782i	−0.0149192	−	0.0277244i
$754$	37.4203	+	20.2635i	1.36277	+	0.737953i
$755$		−	8.11871i		−	0.295470i
$756$	16.3936	−	2.29973i	0.596228	−	0.0836405i
$757$		−	21.7216i		−	0.789484i	−0.918792	−	0.394742i	$-0.870834\pi$
$757$		−	21.7216i		−	0.789484i	0.918792	−	0.394742i	$-0.129166\pi$
$758$	−11.3891	+	21.0320i	−0.413670	+	0.763918i
$759$	−0.331454	+	0.536373i	−0.0120310	+	0.0194691i
$760$	−29.4774	−	2.73870i	−1.06926	−	0.0993430i
$761$	−0.341041	−	0.286168i	−0.0123627	−	0.0103736i	0.636585	−	0.771206i	$-0.280346\pi$
$761$	−0.341041	−	0.286168i	−0.0123627	−	0.0103736i	−0.648948	+	0.760833i	$0.724791\pi$
$762$	33.9368	+	0.0889473i	1.22940	+	0.00322222i
$763$	2.30920	−	6.34447i	0.0835986	−	0.229685i
$764$	−15.8551	+	14.8515i	−0.573618	+	0.537308i
$765$	−5.92943	−	19.9258i	−0.214379	−	0.720420i
$766$	10.4881	+	26.5386i	0.378951	+	0.958880i
$767$	7.06802	−	5.93077i	0.255211	−	0.214148i
$768$	−20.9792	+	18.1073i	−0.757020	+	0.653391i
$769$	3.22004	−	18.2618i	0.116118	−	0.658536i	−0.870073	−	0.492923i	$-0.835928\pi$
$769$	3.22004	−	18.2618i	0.116118	−	0.658536i	0.986191	−	0.165614i	$-0.0529604\pi$
$770$	0.574524	+	0.647922i	0.0207044	+	0.0233495i
$771$	−1.52536	−	0.316280i	−0.0549345	−	0.0113905i
$772$	−23.1594	−	17.3709i	−0.833526	−	0.625192i
$773$	1.50501	+	0.868919i	0.0541315	+	0.0312528i	0.526822	−	0.849976i	$-0.323384\pi$
$773$	1.50501	+	0.868919i	0.0541315	+	0.0312528i	−0.472690	+	0.881229i	$0.656717\pi$
$774$	7.09733	+	49.6469i	0.255108	+	1.78452i
$775$	2.93190	+	5.07821i	0.105317	+	0.182415i
$776$	13.4428	+	13.5881i	0.482569	+	0.487785i
$777$	12.8681	−	10.1575i	0.461642	−	0.364397i
$778$	−8.26750	−	40.4050i	−0.296404	−	1.44859i
$779$	−14.9248	−	41.0055i	−0.534736	−	1.46918i
$780$	9.17557	−	27.2864i	0.328538	−	0.977011i
$781$	−0.885756	+	0.156183i	−0.0316948	+	0.00558865i
$782$	−5.76934	+	7.26970i	−0.206311	+	0.259964i
$783$	3.84465	+	45.2401i	0.137397	+	1.61675i
$784$	16.0088	−	7.89672i	0.571742	−	0.282026i
$785$	0.208959	+	1.18507i	0.00745808	+	0.0422969i
$786$	−12.4538	−	2.22962i	−0.444214	−	0.0795279i
$787$	−12.6576	−	34.7764i	−0.451193	−	1.23964i	−0.931885	−	0.362754i	$-0.881837\pi$
$787$	−12.6576	−	34.7764i	−0.451193	−	1.23964i	0.480692	−	0.876890i	$-0.340386\pi$
$788$	15.1806	+	7.69222i	0.540785	+	0.274024i
$789$	−6.42394	+	16.1310i	−0.228698	+	0.574280i
$790$	−22.4545	−	36.5507i	−0.798896	−	1.30042i
$791$	5.95616	+	10.3164i	0.211777	+	0.366808i
$792$	−1.01601	+	0.891443i	−0.0361023	+	0.0316761i
$793$	−2.48045	+	4.29626i	−0.0880833	+	0.152565i
$794$	16.8394	−	0.459776i	0.597608	−	0.0163168i
$795$	−27.2789	+	30.6020i	−0.967484	+	1.08534i
$796$	−24.6807	+	1.34875i	−0.874785	+	0.0478052i
$797$	11.7114	+	2.06503i	0.414837	+	0.0731470i	0.377172	−	0.926143i	$-0.376897\pi$
$797$	11.7114	+	2.06503i	0.414837	+	0.0731470i	0.0376658	+	0.999290i	$0.488008\pi$
$798$	5.82981	−	15.8876i	0.206373	−	0.562414i
$799$	−8.57656	+	7.19659i	−0.303417	+	0.254597i
$800$	3.45201	+	3.12790i	0.122047	+	0.110588i
$801$	10.0221	+	20.0385i	0.354115	+	0.708025i
$802$	3.32992	+	0.493858i	0.117584	+	0.0174387i
$803$	0.778620	−	2.13924i	0.0274769	−	0.0754922i
$804$	0.737863	−	0.289371i	0.0260224	−	0.0102053i
$805$	−5.64671	+	6.72949i	−0.199021	+	0.237183i
$806$	−32.8992	−	10.9671i	−1.15882	−	0.386298i
$807$	1.80155	+	0.0539145i	0.0634176	+	0.00189788i
$808$	4.64836	+	1.27235i	0.163529	+	0.0447610i
$809$	13.6067			0.478385			0.239192	−	0.970972i	$-0.423117\pi$
$809$	13.6067			0.478385			0.239192	+	0.970972i	$0.423117\pi$
$810$	29.7085	−	7.79796i	1.04385	−	0.273992i
$811$			23.1998i			0.814656i	0.913282	+	0.407328i	$0.133539\pi$
$811$			23.1998i			0.814656i	−0.913282	+	0.407328i	$0.866461\pi$
$812$	−10.9341	−	25.6000i	−0.383712	−	0.898385i
$813$	−1.55645	+	52.0088i	−0.0545872	+	1.82403i
$814$	−0.423317	+	1.26987i	−0.0148373	+	0.0445091i
$815$	20.8969	+	17.5346i	0.731985	+	0.614209i
$816$	−16.3879	+	11.2807i	−0.573693	+	0.394905i
$817$	48.1785	+	17.5355i	1.68555	+	0.613491i
$818$	17.9961	+	2.66899i	0.629218	+	0.0933189i
$819$	13.7343	+	9.06586i	0.479916	+	0.316787i
$820$	−14.0932	+	46.4676i	−0.492155	+	1.62272i
$821$	18.9516	+	22.5856i	0.661414	+	0.788243i	0.987588	−	0.157067i	$-0.0502039\pi$
$821$	18.9516	+	22.5856i	0.661414	+	0.788243i	−0.326174	+	0.945310i	$0.605759\pi$
$822$	−43.3626	−	15.9115i	−1.51244	−	0.554978i
$823$	2.95142	−	16.7383i	0.102880	−	0.583462i	−0.889166	−	0.457585i	$-0.848715\pi$
$823$	2.95142	−	16.7383i	0.102880	−	0.583462i	0.992046	−	0.125877i	$-0.0401744\pi$
$824$	−20.9611	+	29.5956i	−0.730213	+	1.03101i
$825$	0.169600	+	0.151184i	0.00590473	+	0.00526354i
$826$	−6.03342	+	0.164734i	−0.209929	+	0.00573183i
$827$	44.0488	+	25.4316i	1.53173	+	0.884343i	0.999282	+	0.0378772i	$0.0120596\pi$
$827$	44.0488	+	25.4316i	1.53173	+	0.884343i	0.532444	+	0.846465i	$0.321274\pi$
$828$	−10.4575	−	8.86872i	−0.363424	−	0.308209i
$829$	−41.8595	+	24.1676i	−1.45384	+	0.839374i	−0.998696	−	0.0510440i	$-0.983745\pi$
$829$	−41.8595	+	24.1676i	−1.45384	+	0.839374i	−0.455143	+	0.890418i	$0.650412\pi$
$830$	32.7986	−	20.1494i	1.13846	−	0.699397i
$831$	−31.6124	−	12.5892i	−1.09662	−	0.436713i
$832$	−27.5481	−	0.296210i	−0.955059	−	0.0102692i
$833$	12.0421	−	4.38298i	0.417235	−	0.151861i
$834$	−39.0290	−	6.98739i	−1.35146	−	0.241953i
$835$	31.3019	−	5.51936i	1.08325	−	0.191005i
$836$	0.313844	+	1.34569i	0.0108545	+	0.0465416i
$837$	−9.48749	−	35.7633i	−0.327936	−	1.23616i
$838$	8.30411	+	6.59026i	0.286861	+	0.227657i
$839$	4.93028	+	27.9610i	0.170212	+	0.965321i	0.943526	+	0.331298i	$0.107486\pi$
$839$	4.93028	+	27.9610i	0.170212	+	0.965321i	−0.773314	+	0.634023i	$0.781402\pi$
$840$	−15.7976	+	10.2504i	−0.545069	+	0.353672i
$841$	44.4943	−	16.1946i	1.53429	−	0.558434i
$842$	−2.27256	−	11.1065i	−0.0783176	−	0.382754i
$843$	−29.7968	−	37.7485i	−1.02626	−	1.30013i
$844$	3.51049	+	0.423076i	0.120836	+	0.0145629i
$845$	−2.38422	+	1.37653i	−0.0820196	+	0.0473540i
$846$	−10.2146	−	13.0105i	−0.351186	−	0.447310i
$847$	−8.74084	+	15.1396i	−0.300339	+	0.520202i
$848$	35.9113	+	15.7969i	1.23320	+	0.542468i
$849$	8.77594	−	42.3247i	0.301190	−	1.45258i
$850$	2.21876	+	2.50222i	0.0761030	+	0.0858254i
$851$	−13.3729	−	2.35800i	−0.458417	−	0.0808313i
$852$	−0.482597	−	19.5535i	−0.0165335	−	0.669892i
$853$	−17.3921	−	20.7271i	−0.595495	−	0.709684i	0.381157	−	0.924510i	$-0.375526\pi$
$853$	−17.3921	−	20.7271i	−0.595495	−	0.709684i	−0.976652	+	0.214827i	$0.931081\pi$
$854$	3.01806	−	1.19274i	0.103276	−	0.0408147i
$855$	7.29202	−	30.5417i	0.249382	−	1.04450i
$856$	−44.4148	+	3.64530i	−1.51807	+	0.124594i
$857$	1.73329	+	0.630867i	0.0592082	+	0.0215500i	0.371454	−	0.928451i	$-0.378859\pi$
$857$	1.73329	+	0.630867i	0.0592082	+	0.0215500i	−0.312246	+	0.950001i	$0.601081\pi$
$858$	−1.34368	−	0.00352175i	−0.0458726	−	0.000120231i
$859$	−11.6792	+	13.9187i	−0.398489	+	0.474901i	−0.927559	−	0.373678i	$-0.878097\pi$
$859$	−11.6792	+	13.9187i	−0.398489	+	0.474901i	0.529070	+	0.848578i	$0.322541\pi$
$860$	−31.1795	−	47.7782i	−1.06321	−	1.62922i
$861$	−23.6134	−	14.5920i	−0.804742	−	0.497294i
$862$	−5.76650	−	3.12262i	−0.196408	−	0.106357i
$863$	49.6695			1.69077			0.845385	−	0.534157i	$-0.179371\pi$
$863$	49.6695			1.69077			0.845385	+	0.534157i	$0.179371\pi$
$864$	−15.8700	−	24.7415i	−0.539909	−	0.841723i
$865$	−39.5254			−1.34390
$866$	−0.0843627	−	0.0456833i	−0.00286676	−	0.00155238i
$867$	13.3515	−	7.18480i	0.453441	−	0.244008i
$868$	12.3979	+	18.9980i	0.420810	+	0.644833i
$869$	−1.28702	+	1.53381i	−0.0436592	+	0.0520310i
$870$	−25.7077	−	44.7978i	−0.871573	−	1.51879i
$871$	0.740394	+	0.269482i	0.0250873	+	0.00913103i
$872$	−11.9482	+	0.980638i	−0.404618	+	0.0332086i
$873$	−16.2819	+	12.0795i	−0.551059	+	0.408830i
$874$	−13.0366	+	5.15208i	−0.440969	+	0.174272i
$875$	−10.3197	−	12.2985i	−0.348869	−	0.415766i
$876$	43.4722	+	23.6882i	1.46879	+	0.800350i
$877$	22.9919	+	4.05410i	0.776382	+	0.136897i	0.547779	−	0.836623i	$-0.315473\pi$
$877$	22.9919	+	4.05410i	0.776382	+	0.136897i	0.228603	+	0.973520i	$0.426584\pi$
$878$	12.9333	+	14.5856i	0.436479	+	0.492240i
$879$	13.4290	−	4.43753i	0.452948	−	0.149674i
$880$	0.619123	−	1.40746i	0.0208706	−	0.0474455i
$881$	−15.9640	+	27.6505i	−0.537842	+	0.931569i	0.461178	+	0.887307i	$0.347427\pi$
$881$	−15.9640	+	27.6505i	−0.537842	+	0.931569i	−0.999020	+	0.0442614i	$0.985907\pi$
$882$	5.89332	+	17.9927i	0.198438	+	0.605846i
$883$	−40.1101	+	23.1576i	−1.34981	+	0.779315i	−0.988223	−	0.153023i	$-0.951099\pi$
$883$	−40.1101	+	23.1576i	−1.34981	+	0.779315i	−0.361590	+	0.932337i	$0.617766\pi$
$884$	−19.6360	−	2.36649i	−0.660432	−	0.0795937i
$885$	−11.0818	+	1.61387i	−0.372512	+	0.0542496i
$886$	−3.78434	−	18.4949i	−0.127137	−	0.621347i
$887$	−32.0649	+	11.6707i	−1.07663	+	0.391863i	−0.818654	−	0.574288i	$-0.805279\pi$
$887$	−32.0649	+	11.6707i	−1.07663	+	0.391863i	−0.257980	+	0.966150i	$0.583057\pi$
$888$	−25.9317	−	13.2255i	−0.870212	−	0.443820i
$889$	−3.83231	−	21.7341i	−0.128532	−	0.728939i
$890$	−19.9646	−	15.8442i	−0.669214	−	0.531097i
$891$	−0.783820	−	1.20039i	−0.0262589	−	0.0402146i
$892$	−1.36671	−	5.86013i	−0.0457609	−	0.196212i
$893$	−16.6533	+	2.93643i	−0.557283	+	0.0982640i
$894$	−20.4852	+	24.2838i	−0.685129	+	0.812172i
$895$	−13.4431	+	4.89290i	−0.449354	+	0.163552i
$896$	13.9953	+	11.3542i	0.467549	+	0.379318i
$897$	−1.96440	−	13.4888i	−0.0655894	−	0.450379i
$898$	15.0980	−	9.27530i	0.503828	−	0.309521i
$899$	−53.8839	+	31.1099i	−1.79713	+	1.03757i
$900$	−3.80155	+	3.15607i	−0.126718	+	0.105202i
$901$	24.3917	+	14.0825i	0.812605	+	0.469158i
$902$	2.26562	−	0.0618596i	0.0754369	−	0.00205970i
$903$	30.9670	−	10.2329i	1.03052	−	0.340528i
$904$	12.2252	−	17.2611i	0.406603	−	0.574095i
$905$	0.729690	−	4.13828i	0.0242557	−	0.137561i
$906$	−1.40973	−	8.11936i	−0.0468351	−	0.269748i
$907$	0.685743	+	0.817237i	0.0227697	+	0.0271359i	0.777309	−	0.629119i	$-0.216584\pi$
$907$	0.685743	+	0.817237i	0.0227697	+	0.0271359i	−0.754539	+	0.656255i	$0.772140\pi$
$908$	−3.30095	+	10.8838i	−0.109546	+	0.361192i
$909$	−2.03242	+	4.69028i	−0.0674110	+	0.155567i
$910$	−18.5183	−	2.74644i	−0.613877	−	0.0910438i
$911$	2.39685	+	0.872383i	0.0794113	+	0.0289033i	0.381420	−	0.924402i	$-0.375435\pi$
$911$	2.39685	+	0.872383i	0.0794113	+	0.0289033i	−0.302009	+	0.953305i	$0.597657\pi$
$912$	−29.9553	+	2.37953i	−0.991919	+	0.0787940i
$913$	−1.37636	−	1.15490i	−0.0455508	−	0.0382216i
$914$	−8.10018	+	24.2991i	−0.267930	+	0.803741i
$915$	5.30226	−	2.85328i	0.175287	−	0.0943266i
$916$	−17.1072	−	40.0530i	−0.565237	−	1.32339i
$917$			8.22758i			0.271699i
$918$	−9.38982	−	18.8979i	−0.309910	−	0.623722i
$919$	3.85703			0.127232			0.0636159	−	0.997974i	$-0.479737\pi$
$919$	3.85703			0.127232			0.0636159	+	0.997974i	$0.479737\pi$
$920$	15.0450	+	4.11810i	0.496018	+	0.135770i
$921$	16.9518	−	27.4321i	0.558579	−	0.903917i
$922$	9.36384	+	3.12147i	0.308382	+	0.102800i
$923$	12.4986	−	14.8952i	0.411396	−	0.490283i
$924$	0.687075	+	0.548214i	0.0226031	+	0.0180349i
$925$	−1.67355	+	4.59804i	−0.0550259	+	0.151182i
$926$	39.9282	+	5.92173i	1.31212	+	0.194600i
$927$	−27.9357	−	26.4437i	−0.917530	−	0.868524i
$928$	−33.1895	+	36.6286i	−1.08950	+	1.20239i
$929$	23.6191	−	19.8188i	0.774919	−	0.650234i	−0.167045	−	0.985949i	$-0.553422\pi$
$929$	23.6191	−	19.8188i	0.774919	−	0.650234i	0.941964	+	0.335715i	$0.108978\pi$
$930$	26.9711	+	32.3145i	0.884417	+	1.05964i
$931$	19.0616	+	3.36108i	0.624719	+	0.110155i
$932$	−46.9228	+	2.56423i	−1.53701	+	0.0839942i
$933$	8.31744	+	1.72460i	0.272301	+	0.0564610i
$934$	0.769863	−	0.0210200i	0.0251907	−	0.000687797i
$935$	0.551933	−	0.955975i	0.0180501	−	0.0312637i
$936$	4.43830	−	28.8818i	0.145070	−	0.944033i
$937$	3.69048	+	6.39210i	0.120563	+	0.208821i	0.919990	−	0.391942i	$-0.128197\pi$
$937$	3.69048	+	6.39210i	0.120563	+	0.208821i	−0.799427	+	0.600763i	$0.794863\pi$
$938$	−0.269795	−	0.439164i	−0.00880913	−	0.0143392i
$939$	11.0516	+	14.0008i	0.360655	+	0.456900i
$940$	16.7852	+	8.50531i	0.547473	+	0.277413i
$941$	−13.1119	−	36.0246i	−0.427435	−	1.17437i	−0.947364	−	0.320158i	$-0.896264\pi$
$941$	−13.1119	−	36.0246i	−0.427435	−	1.17437i	0.519929	−	0.854209i	$-0.325958\pi$
$942$	0.414751	+	1.14888i	0.0135133	+	0.0374325i
$943$	3.99256	+	22.6429i	0.130016	+	0.737355i
$944$	4.74105	+	9.61137i	0.154308	+	0.312823i
$945$	−8.39636	−	18.1236i	−0.273134	−	0.589561i
$946$	−1.65538	+	2.08588i	−0.0538212	+	0.0678178i
$947$	−21.8272	+	3.84873i	−0.709289	+	0.125067i	−0.516642	−	0.856201i	$-0.672818\pi$
$947$	−21.8272	+	3.84873i	−0.709289	+	0.125067i	−0.192647	+	0.981268i	$0.561707\pi$
$948$	−28.8030	−	32.6547i	−0.935477	−	1.06057i
$949$	16.8328	+	46.2477i	0.546416	+	1.50126i
$950$	1.01256	+	4.94861i	0.0328519	+	0.160554i
$951$	36.3335	+	14.4693i	1.17819	+	0.469198i
$952$	9.09922	+	9.19759i	0.294907	+	0.298095i
$953$	22.3908	+	38.7819i	0.725308	+	1.25627i	0.958847	+	0.283922i	$0.0916358\pi$
$953$	22.3908	+	38.7819i	0.725308	+	1.25627i	−0.233540	+	0.972347i	$0.575031\pi$
$954$	−21.9674	+	35.3411i	−0.711221	+	1.14421i
$955$	22.7008	+	13.1063i	0.734580	+	0.424110i
$956$	37.4375	+	28.0803i	1.21082	+	0.908182i
$957$	−1.60418	+	1.79960i	−0.0518558	+	0.0581727i
$958$	7.92042	+	8.93228i	0.255897	+	0.288589i
$959$	−5.21595	+	29.5811i	−0.168432	+	0.955224i
$960$	28.2546	+	17.8826i	0.911912	+	0.577160i
$961$	15.0947	−	12.6659i	0.486925	−	0.408579i
$962$	−10.6360	−	26.9128i	−0.342918	−	0.867704i
$963$	2.82658	−	47.1828i	0.0910854	−	1.52044i
$964$	−5.73547	+	5.37241i	−0.184727	+	0.173034i
$965$	−11.9471	+	32.8244i	−0.384591	+	1.05666i
$966$	−4.47866	+	7.71053i	−0.144099	+	0.248082i
$967$	32.4852	+	27.2583i	1.04465	+	0.876567i	0.992521	−	0.122073i	$-0.0389542\pi$
$967$	32.4852	+	27.2583i	1.04465	+	0.876567i	0.0521310	+	0.998640i	$0.483399\pi$
$968$	30.9078	+	2.87160i	0.993415	+	0.0922966i
$969$	−21.5632	−	0.645316i	−0.692710	−	0.0207305i
$970$	10.9820	−	20.2803i	0.352611	−	0.651163i
$971$			9.33492i			0.299572i	0.988718	+	0.149786i	$0.0478584\pi$
$971$			9.33492i			0.299572i	−0.988718	+	0.149786i	$0.952142\pi$
$972$	28.3569	−	12.9572i	0.909547	−	0.415601i
$973$			25.7843i			0.826608i
$974$	−18.6555	−	10.1021i	−0.597760	−	0.323693i
$975$	−4.90963	−	0.146929i	−0.157234	−	0.00470550i
$976$	−4.16286	−	3.98424i	−0.133250	−	0.127533i
$977$	0.274142	+	0.230032i	0.00877057	+	0.00735938i	0.647162	−	0.762352i	$-0.275956\pi$
$977$	0.274142	+	0.230032i	0.00877057	+	0.00735938i	−0.638392	+	0.769712i	$0.720400\pi$
$978$	23.9432	+	13.9074i	0.765620	+	0.444711i
$979$	−0.406885	+	1.11791i	−0.0130041	+	0.0357285i
$980$	−14.7242	−	15.7192i	−0.470348	−	0.502133i
$981$	0.760392	−	12.6929i	0.0242774	−	0.405252i
$982$	19.3032	−	7.62865i	0.615990	−	0.243440i
$983$	−6.53130	+	5.48041i	−0.208316	+	0.174798i	−0.740976	−	0.671531i	$-0.765637\pi$
$983$	−6.53130	+	5.48041i	−0.208316	+	0.174798i	0.532660	+	0.846329i	$0.321192\pi$
$984$	−6.02567	+	48.9185i	−0.192091	+	1.55946i
$985$	3.56571	−	20.2221i	0.113613	−	0.644331i
$986$	−26.5506	+	23.5429i	−0.845542	+	0.749758i
$987$	−7.15777	+	8.02970i	−0.227834	+	0.255588i
$988$	−23.8976	−	17.9246i	−0.760283	−	0.570256i
$989$	−23.3950	−	13.5071i	−0.743917	−	0.429501i
$990$	1.38511	+	0.860961i	0.0440218	+	0.0273631i
$991$	−25.9790	−	44.9969i	−0.825249	−	1.42937i	−0.901729	−	0.432302i	$-0.857701\pi$
$991$	−25.9790	−	44.9969i	−0.825249	−	1.42937i	0.0764798	−	0.997071i	$-0.475632\pi$
$992$	21.4529	−	34.0929i	0.681129	−	1.08245i
$993$	37.9348	+	15.1070i	1.20383	+	0.479405i
$994$	−12.4614	+	2.54981i	−0.395253	+	0.0808750i
$995$	10.2004	+	28.0255i	0.323375	+	0.888467i
$996$	29.3025	−	25.8462i	0.928485	−	0.818968i
$997$	44.7921	−	7.89805i	1.41858	−	0.250134i	0.588824	−	0.808262i	$-0.299591\pi$
$997$	44.7921	−	7.89805i	1.41858	−	0.250134i	0.829755	+	0.558128i	$0.188480\pi$
$998$	19.1885	+	15.2282i	0.607401	+	0.482042i
$999$	17.7722	−	25.2475i	0.562289	−	0.798797i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.t.a.13.31	yes	204
3.2	odd	2		648.2.t.a.253.4		204
4.3	odd	2		864.2.bf.a.337.17		204
8.3	odd	2		864.2.bf.a.337.18		204
8.5	even	2	inner	216.2.t.a.13.9	✓	204
24.5	odd	2		648.2.t.a.253.26		204
27.2	odd	18		648.2.t.a.397.26		204
27.25	even	9	inner	216.2.t.a.133.9	yes	204
108.79	odd	18		864.2.bf.a.241.18		204
216.29	odd	18		648.2.t.a.397.4		204
216.133	even	18	inner	216.2.t.a.133.31	yes	204
216.187	odd	18		864.2.bf.a.241.17		204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.t.a.13.9	✓	204	8.5	even	2	inner
216.2.t.a.13.31	yes	204	1.1	even	1	trivial
216.2.t.a.133.9	yes	204	27.25	even	9	inner
216.2.t.a.133.31	yes	204	216.133	even	18	inner
648.2.t.a.253.4		204	3.2	odd	2
648.2.t.a.253.26		204	24.5	odd	2
648.2.t.a.397.4		204	216.29	odd	18
648.2.t.a.397.26		204	27.2	odd	18
864.2.bf.a.241.17		204	216.187	odd	18
864.2.bf.a.241.18		204	108.79	odd	18
864.2.bf.a.337.17		204	4.3	odd	2
864.2.bf.a.337.18		204	8.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.24359 + 0.673416i) q^{2} +(0.0518114 - 1.73128i) q^{3} +(1.09302 + 1.67490i) q^{4} +(1.55117 - 1.84861i) q^{5} +(1.23030 - 2.11810i) q^{6} +(-1.49685 - 0.544810i) q^{7} +(0.231362 + 2.81895i) q^{8} +(-2.99463 - 0.179400i) q^{9} +(3.17390 - 1.25433i) q^{10} +(-0.102391 - 0.122025i) q^{11} +(2.95635 - 1.80554i) q^{12} +(3.39140 + 0.597995i) q^{13} +(-1.49458 - 1.68552i) q^{14} +(-3.12009 - 2.78128i) q^{15} +(-1.61061 + 3.66141i) q^{16} +(-1.43581 + 2.48690i) q^{17} +(-3.60328 - 2.23973i) q^{18} +(-3.75621 + 2.16865i) q^{19} +(4.79171 + 0.577486i) q^{20} +(-1.02077 + 2.56324i) q^{21} +(-0.0451590 - 0.220701i) q^{22} +(2.14748 - 0.781619i) q^{23} +(4.89236 - 0.254498i) q^{24} +(-0.142997 - 0.810974i) q^{25} +(3.81480 + 3.02748i) q^{26} +(-0.465746 + 5.17524i) q^{27} +(-0.723589 - 3.10257i) q^{28} +(8.60509 - 1.51731i) q^{29} +(-2.00714 - 5.55988i) q^{30} +(-6.69129 + 2.43543i) q^{31} +(-4.46858 + 3.46868i) q^{32} +(-0.216565 + 0.170946i) q^{33} +(-3.46028 + 2.12578i) q^{34} +(-3.32901 + 1.92201i) q^{35} +(-2.97272 - 5.21181i) q^{36} +(-5.14590 - 2.97099i) q^{37} +(-6.13158 + 0.167414i) q^{38} +(1.21101 - 5.84046i) q^{39} +(5.57002 + 3.94497i) q^{40} +(-1.74706 + 9.90807i) q^{41} +(-2.99554 + 2.50021i) q^{42} +(-7.59829 - 9.05529i) q^{43} +(0.0924647 - 0.304872i) q^{44} +(-4.97682 + 5.25763i) q^{45} +(3.19694 + 0.474136i) q^{46} +(3.66367 + 1.33347i) q^{47} +(6.25547 + 2.97810i) q^{48} +(-3.41856 - 2.86851i) q^{49} +(0.368294 - 1.10481i) q^{50} +(4.23112 + 2.61464i) q^{51} +(2.70529 + 6.33388i) q^{52} -9.80805i q^{53} +(-4.06428 + 6.12222i) q^{54} -0.384404 q^{55} +(1.18948 - 4.34560i) q^{56} +(3.55991 + 6.61539i) q^{57} +(11.7230 + 3.90790i) q^{58} +(1.72220 - 2.05244i) q^{59} +(1.24805 - 8.26584i) q^{60} +(-0.492702 + 1.35369i) q^{61} +(-9.96127 - 1.47735i) q^{62} +(4.38478 + 1.90004i) q^{63} +(-7.89294 + 1.30440i) q^{64} +(6.36609 - 5.34178i) q^{65} +(-0.384435 + 0.0667478i) q^{66} +(0.225321 + 0.0397302i) q^{67} +(-5.73470 + 0.313390i) q^{68} +(-1.24193 - 3.75838i) q^{69} +(-5.43423 + 0.148374i) q^{70} +(2.82317 - 4.88987i) q^{71} +(-0.187127 - 8.48322i) q^{72} +(7.14574 + 12.3768i) q^{73} +(-4.39867 - 7.16002i) q^{74} +(-1.41143 + 0.205549i) q^{75} +(-7.73789 - 3.92091i) q^{76} +(0.0867843 + 0.238438i) q^{77} +(5.43905 - 6.44761i) q^{78} +(-2.18269 - 12.3786i) q^{79} +(4.27021 + 8.65685i) q^{80} +(8.93563 + 1.07447i) q^{81} +(-8.84487 + 11.1451i) q^{82} +(11.1079 - 1.95862i) q^{83} +(-5.40890 + 1.09198i) q^{84} +(2.37013 + 6.51187i) q^{85} +(-3.35117 - 16.3779i) q^{86} +(-2.18104 - 14.9764i) q^{87} +(0.320294 - 0.316868i) q^{88} +(-3.73417 - 6.46777i) q^{89} +(-9.72968 + 3.18686i) q^{90} +(-4.75063 - 2.74278i) q^{91} +(3.65638 + 2.74250i) q^{92} +(3.86972 + 11.7107i) q^{93} +(3.65812 + 4.12546i) q^{94} +(-1.81753 + 10.3077i) q^{95} +(5.77372 + 7.91607i) q^{96} +(5.17680 - 4.34385i) q^{97} +(-2.31958 - 5.86936i) q^{98} +(0.284733 + 0.383790i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - 6 q^{2} - 6 q^{4} - 6 q^{6} - 12 q^{7} - 3 q^{8} - 12 q^{9} - 3 q^{10} + 3 q^{12} - 21 q^{14} - 12 q^{15} - 6 q^{16} - 6 q^{17} - 27 q^{18} + 15 q^{20} - 6 q^{22} - 12 q^{23} - 12 q^{25} - 30 q^{26}+ \cdots + 54 q^{98}+O(q^{100}) \) 204 * q - 6 * q^2 - 6 * q^4 - 6 * q^6 - 12 * q^7 - 3 * q^8 - 12 * q^9 - 3 * q^10 + 3 * q^12 - 21 * q^14 - 12 * q^15 - 6 * q^16 - 6 * q^17 - 27 * q^18 + 15 * q^20 - 6 * q^22 - 12 * q^23 - 12 * q^25 - 30 * q^26 - 12 * q^28 - 39 * q^30 - 12 * q^31 - 36 * q^32 - 36 * q^36 - 42 * q^38 - 12 * q^39 - 21 * q^40 - 24 * q^41 - 66 * q^42 + 21 * q^44 - 3 * q^46 - 12 * q^47 + 51 * q^48 - 12 * q^49 - 99 * q^50 - 33 * q^52 - 90 * q^54 - 24 * q^55 + 99 * q^56 - 30 * q^57 + 21 * q^58 + 102 * q^60 - 36 * q^62 - 72 * q^63 - 3 * q^64 - 12 * q^65 - 9 * q^66 + 75 * q^68 + 9 * q^70 - 90 * q^71 + 60 * q^72 - 6 * q^73 + 9 * q^74 - 18 * q^76 + 12 * q^78 - 12 * q^79 + 78 * q^80 - 12 * q^81 - 12 * q^82 + 102 * q^84 - 30 * q^86 - 48 * q^87 - 30 * q^88 - 6 * q^89 + 6 * q^90 + 111 * q^92 - 33 * q^94 - 42 * q^95 + 126 * q^96 - 12 * q^97 + 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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