LMFDB - Embedded newform 162.2.g.a.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(7,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("162.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.g (of order $27$, degree $18$, 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:	$1.29357651274$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$4$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			25.1
Character	$\chi$	$=$	162.25
Dual form			162.2.g.a.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.893633 + 0.448799i) q^{2} +(-1.71649 - 0.231626i) q^{3} +(0.597159 - 0.802123i) q^{4} +(-0.267154 + 0.892356i) q^{5} +(1.63787 - 0.563372i) q^{6} +(1.11188 - 2.57764i) q^{7} +(-0.173648 + 0.984808i) q^{8} +(2.89270 + 0.795169i) q^{9} +O(q^{10})$	\(q+(-0.893633 + 0.448799i) q^{2} +(-1.71649 - 0.231626i) q^{3} +(0.597159 - 0.802123i) q^{4} +(-0.267154 + 0.892356i) q^{5} +(1.63787 - 0.563372i) q^{6} +(1.11188 - 2.57764i) q^{7} +(-0.173648 + 0.984808i) q^{8} +(2.89270 + 0.795169i) q^{9} +(-0.161751 - 0.917337i) q^{10} +(4.46341 + 1.05785i) q^{11} +(-1.21081 + 1.23852i) q^{12} +(1.47403 - 0.969483i) q^{13} +(0.163226 + 2.80247i) q^{14} +(0.665260 - 1.46984i) q^{15} +(-0.286803 - 0.957990i) q^{16} +(1.42569 + 0.518907i) q^{17} +(-2.94188 + 0.587652i) q^{18} +(4.12421 - 1.50109i) q^{19} +(0.556246 + 0.747168i) q^{20} +(-2.50559 + 4.16696i) q^{21} +(-4.46341 + 1.05785i) q^{22} +(-2.92223 - 6.77448i) q^{23} +(0.526173 - 1.65019i) q^{24} +(3.45251 + 2.27075i) q^{25} +(-0.882135 + 1.52790i) q^{26} +(-4.78112 - 2.03493i) q^{27} +(-1.40361 - 2.43113i) q^{28} +(-0.418954 + 7.19315i) q^{29} +(0.0651659 + 1.61207i) q^{30} +(-6.24778 - 0.730261i) q^{31} +(0.686242 + 0.727374i) q^{32} +(-7.41639 - 2.84963i) q^{33} +(-1.50693 + 0.176134i) q^{34} +(2.00313 + 1.68082i) q^{35} +(2.36522 - 1.84546i) q^{36} +(-0.516723 + 0.433582i) q^{37} +(-3.01184 + 3.19236i) q^{38} +(-2.75471 + 1.32269i) q^{39} +(-0.832408 - 0.418051i) q^{40} +(-8.46317 - 4.25037i) q^{41} +(0.368950 - 4.84823i) q^{42} +(3.77539 - 4.00168i) q^{43} +(3.51389 - 2.94850i) q^{44} +(-1.48237 + 2.36888i) q^{45} +(5.65178 + 4.74241i) q^{46} +(5.01677 - 0.586377i) q^{47} +(0.270401 + 1.71081i) q^{48} +(-0.604237 - 0.640453i) q^{49} +(-4.10439 - 0.479734i) q^{50} +(-2.32699 - 1.22093i) q^{51} +(0.102583 - 1.76129i) q^{52} +(-1.33883 - 2.31892i) q^{53} +(5.18583 - 0.327285i) q^{54} +(-2.13639 + 3.70034i) q^{55} +(2.34540 + 1.54259i) q^{56} +(-7.42686 + 1.62134i) q^{57} +(-2.85389 - 6.61606i) q^{58} +(4.89941 - 1.16118i) q^{59} +(-0.781729 - 1.41135i) q^{60} +(3.14866 + 4.22938i) q^{61} +(5.91096 - 2.15141i) q^{62} +(5.26600 - 6.57219i) q^{63} +(-0.939693 - 0.342020i) q^{64} +(0.471331 + 1.57436i) q^{65} +(7.90644 - 0.781947i) q^{66} +(0.832311 + 14.2902i) q^{67} +(1.26759 - 0.833706i) q^{68} +(3.44684 + 12.3052i) q^{69} +(-2.54441 - 0.603036i) q^{70} +(-0.0492509 - 0.279316i) q^{71} +(-1.28540 + 2.71067i) q^{72} +(-2.01050 + 11.4021i) q^{73} +(0.267169 - 0.619368i) q^{74} +(-5.40025 - 4.69742i) q^{75} +(1.25875 - 4.20451i) q^{76} +(7.68955 - 10.3289i) q^{77} +(1.86808 - 2.41831i) q^{78} +(3.17920 - 1.59665i) q^{79} +0.931488 q^{80} +(7.73541 + 4.60037i) q^{81} +9.47053 q^{82} +(-9.56164 + 4.80204i) q^{83} +(1.84618 + 4.49813i) q^{84} +(-0.843927 + 1.13359i) q^{85} +(-1.57786 + 5.27043i) q^{86} +(2.38525 - 12.2500i) q^{87} +(-1.81684 + 4.21191i) q^{88} +(1.74720 - 9.90888i) q^{89} +(0.261540 - 2.78220i) q^{90} +(-0.860028 - 4.87746i) q^{91} +(-7.17900 - 1.70145i) q^{92} +(10.5551 + 2.70064i) q^{93} +(-4.21999 + 2.77553i) q^{94} +(0.237708 + 4.08128i) q^{95} +(-1.00945 - 1.40748i) q^{96} +(-4.96298 - 16.5775i) q^{97} +(0.827401 + 0.301149i) q^{98} +(12.0701 + 6.60920i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 9 q^{6}+O(q^{10}) $ 72 * q + 9 * q^6	$ 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) $ 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{23}{27}\right)$

Coefficient data

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

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

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

$2$	−0.893633	+	0.448799i	−0.631894	+	0.317349i
$2$	−0.893633	+	0.448799i	−0.631894	+	0.317349i
$3$	−1.71649	−	0.231626i	−0.991018	−	0.133729i
$3$	−1.71649	−	0.231626i	−0.991018	−	0.133729i
$4$	0.597159	−	0.802123i	0.298579	−	0.401062i
$5$	−0.267154	+	0.892356i	−0.119475	+	0.399074i	−0.996716	−	0.0809762i	$-0.974196\pi$
$5$	−0.267154	+	0.892356i	−0.119475	+	0.399074i	0.877241	+	0.480050i	$0.159381\pi$
$6$	1.63787	−	0.563372i	0.668657	−	0.229996i
$7$	1.11188	−	2.57764i	0.420253	−	0.974255i	−0.568223	−	0.822875i	$-0.692369\pi$
$7$	1.11188	−	2.57764i	0.420253	−	0.974255i	0.988476	−	0.151381i	$-0.0483719\pi$
$8$	−0.173648	+	0.984808i	−0.0613939	+	0.348182i
$9$	2.89270	+	0.795169i	0.964233	+	0.265056i
$10$	−0.161751	−	0.917337i	−0.0511502	−	0.290087i
$11$	4.46341	+	1.05785i	1.34577	+	0.318953i	0.839471	−	0.543405i	$-0.182865\pi$
$11$	4.46341	+	1.05785i	1.34577	+	0.318953i	0.506299	+	0.862358i	$0.331013\pi$
$12$	−1.21081	+	1.23852i	−0.349531	+	0.357530i
$13$	1.47403	−	0.969483i	0.408821	−	0.268886i	−0.328398	−	0.944539i	$-0.606509\pi$
$13$	1.47403	−	0.969483i	0.408821	−	0.268886i	0.737219	+	0.675653i	$0.236138\pi$
$14$	0.163226	+	2.80247i	0.0436239	+	0.748993i
$15$	0.665260	−	1.46984i	0.171769	−	0.379512i
$16$	−0.286803	−	0.957990i	−0.0717008	−	0.239497i
$17$	1.42569	+	0.518907i	0.345780	+	0.125854i	0.509071	−	0.860724i	$-0.329989\pi$
$17$	1.42569	+	0.518907i	0.345780	+	0.125854i	−0.163292	+	0.986578i	$0.552211\pi$
$18$	−2.94188	+	0.587652i	−0.693408	+	0.138511i
$19$	4.12421	−	1.50109i	0.946158	−	0.344373i	0.177563	−	0.984109i	$-0.443179\pi$
$19$	4.12421	−	1.50109i	0.946158	−	0.344373i	0.768595	+	0.639736i	$0.220956\pi$
$20$	0.556246	+	0.747168i	0.124380	+	0.167072i
$21$	−2.50559	+	4.16696i	−0.546764	+	0.909304i
$22$	−4.46341	+	1.05785i	−0.951603	+	0.225534i
$23$	−2.92223	−	6.77448i	−0.609326	−	1.41258i	−0.891415	−	0.453189i	$-0.850286\pi$
$23$	−2.92223	−	6.77448i	−0.609326	−	1.41258i	0.282088	−	0.959388i	$-0.408973\pi$
$24$	0.526173	−	1.65019i	0.107405	−	0.336845i
$25$	3.45251	+	2.27075i	0.690502	+	0.454151i
$26$	−0.882135	+	1.52790i	−0.173001	+	0.299646i
$27$	−4.78112	−	2.03493i	−0.920126	−	0.391622i
$28$	−1.40361	−	2.43113i	−0.265258	−	0.459440i
$29$	−0.418954	+	7.19315i	−0.0777977	+	1.33574i	0.703107	+	0.711085i	$0.251796\pi$
$29$	−0.418954	+	7.19315i	−0.0777977	+	1.33574i	−0.780904	+	0.624651i	$0.785241\pi$
$30$	0.0651659	+	1.61207i	0.0118976	+	0.294322i
$31$	−6.24778	−	0.730261i	−1.12213	−	0.131159i	−0.465271	−	0.885168i	$-0.654043\pi$
$31$	−6.24778	−	0.730261i	−1.12213	−	0.131159i	−0.656863	+	0.754010i	$0.728117\pi$
$32$	0.686242	+	0.727374i	0.121312	+	0.128583i
$33$	−7.41639	−	2.84963i	−1.29103	−	0.496057i
$34$	−1.50693	+	0.176134i	−0.258436	+	0.0302068i
$35$	2.00313	+	1.68082i	0.338590	+	0.284111i
$36$	2.36522	−	1.84546i	0.394204	−	0.307576i
$37$	−0.516723	+	0.433582i	−0.0849487	+	0.0712804i	−0.684273	−	0.729226i	$-0.739880\pi$
$37$	−0.516723	+	0.433582i	−0.0849487	+	0.0712804i	0.599324	+	0.800506i	$0.295436\pi$
$38$	−3.01184	+	3.19236i	−0.488585	+	0.517870i
$39$	−2.75471	+	1.32269i	−0.441107	+	0.211800i
$40$	−0.832408	−	0.418051i	−0.131615	−	0.0660997i
$41$	−8.46317	−	4.25037i	−1.32173	−	0.663796i	−0.358763	−	0.933429i	$-0.616801\pi$
$41$	−8.46317	−	4.25037i	−1.32173	−	0.663796i	−0.962963	+	0.269633i	$0.913098\pi$
$42$	0.368950	−	4.84823i	0.0569302	−	0.748099i
$43$	3.77539	−	4.00168i	0.575742	−	0.610251i	−0.372410	−	0.928068i	$-0.621468\pi$
$43$	3.77539	−	4.00168i	0.575742	−	0.610251i	0.948152	+	0.317817i	$0.102950\pi$
$44$	3.51389	−	2.94850i	0.529739	−	0.444504i
$45$	−1.48237	+	2.36888i	−0.220978	+	0.353132i
$46$	5.65178	+	4.74241i	0.833309	+	0.699230i
$47$	5.01677	−	0.586377i	0.731772	−	0.0855319i	0.257957	−	0.966156i	$-0.416951\pi$
$47$	5.01677	−	0.586377i	0.731772	−	0.0855319i	0.473815	+	0.880625i	$0.342877\pi$
$48$	0.270401	+	1.71081i	0.0390290	+	0.246935i
$49$	−0.604237	−	0.640453i	−0.0863195	−	0.0914934i
$50$	−4.10439	−	0.479734i	−0.580448	−	0.0678447i
$51$	−2.32699	−	1.22093i	−0.325844	−	0.170964i
$52$	0.102583	−	1.76129i	0.0142257	−	0.244246i
$53$	−1.33883	−	2.31892i	−0.183903	−	0.318529i	0.759304	−	0.650737i	$-0.225540\pi$
$53$	−1.33883	−	2.31892i	−0.183903	−	0.318529i	−0.943206	+	0.332208i	$0.892206\pi$
$54$	5.18583	−	0.327285i	0.705703	−	0.0445378i
$55$	−2.13639	+	3.70034i	−0.288071	+	0.498954i
$56$	2.34540	+	1.54259i	0.313417	+	0.206138i
$57$	−7.42686	+	1.62134i	−0.983712	+	0.214751i
$58$	−2.85389	−	6.61606i	−0.374734	−	0.868732i
$59$	4.89941	−	1.16118i	0.637849	−	0.151173i	0.101048	−	0.994882i	$-0.467781\pi$
$59$	4.89941	−	1.16118i	0.637849	−	0.151173i	0.536802	+	0.843708i	$0.319632\pi$
$60$	−0.781729	−	1.41135i	−0.100921	−	0.182205i
$61$	3.14866	+	4.22938i	0.403144	+	0.541517i	0.956616	−	0.291351i	$-0.0941048\pi$
$61$	3.14866	+	4.22938i	0.403144	+	0.541517i	−0.553472	+	0.832868i	$0.686697\pi$
$62$	5.91096	−	2.15141i	0.750693	−	0.273230i
$63$	5.26600	−	6.57219i	0.663454	−	0.828019i
$64$	−0.939693	−	0.342020i	−0.117462	−	0.0427525i
$65$	0.471331	+	1.57436i	0.0584615	+	0.195275i
$66$	7.90644	−	0.781947i	0.973216	−	0.0962511i
$67$	0.832311	+	14.2902i	0.101683	+	1.74583i	0.535237	+	0.844702i	$0.320222\pi$
$67$	0.832311	+	14.2902i	0.101683	+	1.74583i	−0.433554	+	0.901127i	$0.642741\pi$
$68$	1.26759	−	0.833706i	0.153718	−	0.101102i
$69$	3.44684	+	12.3052i	0.414950	+	1.48137i
$70$	−2.54441	−	0.603036i	−0.304115	−	0.0720766i
$71$	−0.0492509	−	0.279316i	−0.00584501	−	0.0331487i	0.981746	−	0.190198i	$-0.0609130\pi$
$71$	−0.0492509	−	0.279316i	−0.00584501	−	0.0331487i	−0.987591	+	0.157049i	$0.949802\pi$
$72$	−1.28540	+	2.71067i	−0.151486	+	0.319456i
$73$	−2.01050	+	11.4021i	−0.235312	+	1.33452i	0.606645	+	0.794973i	$0.292515\pi$
$73$	−2.01050	+	11.4021i	−0.235312	+	1.33452i	−0.841957	+	0.539545i	$0.818596\pi$
$74$	0.267169	−	0.619368i	0.0310578	−	0.0720000i
$75$	−5.40025	−	4.69742i	−0.623567	−	0.542412i
$76$	1.25875	−	4.20451i	0.144388	−	0.482290i
$77$	7.68955	−	10.3289i	0.876305	−	1.17708i
$78$	1.86808	−	2.41831i	0.211519	−	0.273820i
$79$	3.17920	−	1.59665i	0.357687	−	0.179637i	−0.260876	−	0.965372i	$-0.584011\pi$
$79$	3.17920	−	1.59665i	0.357687	−	0.179637i	0.618563	+	0.785735i	$0.287715\pi$
$80$	0.931488			0.104144
$81$	7.73541	+	4.60037i	0.859490	+	0.511152i
$82$	9.47053			1.04584
$83$	−9.56164	+	4.80204i	−1.04953	+	0.527092i	−0.888032	−	0.459782i	$-0.847928\pi$
$83$	−9.56164	+	4.80204i	−1.04953	+	0.527092i	−0.161494	+	0.986874i	$0.551631\pi$
$84$	1.84618	+	4.49813i	0.201435	+	0.490786i
$85$	−0.843927	+	1.13359i	−0.0915368	+	0.122955i
$86$	−1.57786	+	5.27043i	−0.170145	+	0.568325i
$87$	2.38525	−	12.2500i	0.255726	−	1.31333i
$88$	−1.81684	+	4.21191i	−0.193676	+	0.448991i
$89$	1.74720	−	9.90888i	0.185203	−	1.05034i	−0.740491	−	0.672066i	$-0.765407\pi$
$89$	1.74720	−	9.90888i	0.185203	−	1.05034i	0.925694	−	0.378273i	$-0.123482\pi$
$90$	0.261540	−	2.78220i	0.0275687	−	0.293269i
$91$	−0.860028	−	4.87746i	−0.0901554	−	0.511297i
$92$	−7.17900	−	1.70145i	−0.748463	−	0.177389i
$93$	10.5551	+	2.70064i	1.09452	+	0.280043i
$94$	−4.21999	+	2.77553i	−0.435259	+	0.286274i
$95$	0.237708	+	4.08128i	0.0243883	+	0.418731i
$96$	−1.00945	−	1.40748i	−0.103027	−	0.143651i
$97$	−4.96298	−	16.5775i	−0.503914	−	1.68319i	−0.709626	−	0.704579i	$-0.751136\pi$
$97$	−4.96298	−	16.5775i	−0.503914	−	1.68319i	0.205711	−	0.978613i	$-0.434049\pi$
$98$	0.827401	+	0.301149i	0.0835801	+	0.0304207i
$99$	12.0701	+	6.60920i	1.21309	+	0.664250i
$100$	3.88312	−	1.41334i	0.388312	−	0.141334i
$101$	−3.77928	−	5.07645i	−0.376052	−	0.505126i	0.573298	−	0.819347i	$-0.305664\pi$
$101$	−3.77928	−	5.07645i	−0.376052	−	0.505126i	−0.949350	+	0.314222i	$0.898257\pi$
$102$	2.62742	+	0.0467096i	0.260154	+	0.00462494i
$103$	−18.1237	+	4.29540i	−1.78578	+	0.423238i	−0.984548	−	0.175112i	$-0.943971\pi$
$103$	−18.1237	+	4.29540i	−1.78578	+	0.423238i	−0.801234	+	0.598350i	$0.795823\pi$
$104$	0.698792	+	1.61998i	0.0685222	+	0.158852i
$105$	−3.04903	−	3.34909i	−0.297555	−	0.326838i
$106$	2.23715	+	1.47140i	0.217292	+	0.142915i
$107$	−0.530621	+	0.919062i	−0.0512970	+	0.0888491i	−0.890534	−	0.454917i	$-0.849669\pi$
$107$	−0.530621	+	0.919062i	−0.0512970	+	0.0888491i	0.839237	+	0.543766i	$0.183002\pi$
$108$	−4.48735	+	2.61987i	−0.431795	+	0.252097i
$109$	6.12250	+	10.6045i	0.586429	+	1.01573i	0.994696	+	0.102863i	$0.0328002\pi$
$109$	6.12250	+	10.6045i	0.586429	+	1.01573i	−0.408266	+	0.912863i	$0.633866\pi$
$110$	0.248441	−	4.26556i	0.0236879	−	0.406705i
$111$	0.987380	−	0.624554i	0.0937179	−	0.0592800i
$112$	−2.78824	−	0.325899i	−0.263464	−	0.0307945i
$113$	−4.67396	−	4.95410i	−0.439689	−	0.466043i	0.469194	−	0.883095i	$-0.344545\pi$
$113$	−4.67396	−	4.95410i	−0.439689	−	0.466043i	−0.908882	+	0.417052i	$0.863063\pi$
$114$	5.90923	−	4.78205i	0.553450	−	0.447880i
$115$	6.82593	−	0.797837i	0.636521	−	0.0743987i
$116$	5.51961	+	4.63151i	0.512483	+	0.430025i
$117$	5.03482	−	1.63232i	0.465469	−	0.150908i
$118$	−3.85714	+	3.23652i	−0.355078	+	0.297946i
$119$	2.92275	−	3.09794i	0.267928	−	0.283987i
$120$	1.33199	+	0.910389i	0.121594	+	0.0831068i
$121$	8.97305	+	4.50643i	0.815732	+	0.409676i
$122$	−4.71189	−	2.36640i	−0.426594	−	0.214244i
$123$	13.5425	+	9.25601i	1.22108	+	0.834587i
$124$	−4.31667	+	4.57541i	−0.387649	+	0.410884i
$125$	−6.51648	+	5.46797i	−0.582851	+	0.489070i
$126$	−1.75628	+	8.23650i	−0.156462	+	0.733766i
$127$	−6.52630	−	5.47622i	−0.579116	−	0.485936i	0.305541	−	0.952179i	$-0.401163\pi$
$127$	−6.52630	−	5.47622i	−0.579116	−	0.485936i	−0.884657	+	0.466243i	$0.845607\pi$
$128$	0.993238	−	0.116093i	0.0877907	−	0.0102613i
$129$	−7.40733	+	5.99438i	−0.652179	+	0.527776i
$130$	−1.12777	−	1.19536i	−0.0989117	−	0.104840i
$131$	−15.8598	−	1.85375i	−1.38568	−	0.161963i	−0.609656	−	0.792666i	$-0.708692\pi$
$131$	−15.8598	−	1.85375i	−1.38568	−	0.161963i	−0.776024	+	0.630703i	$0.782766\pi$
$132$	−6.71452	+	4.24718i	−0.584424	+	0.369669i
$133$	0.716379	−	12.2997i	0.0621179	−	1.06652i
$134$	−7.15722	−	12.3967i	−0.618290	−	1.07091i
$135$	3.09317	−	3.72282i	0.266218	−	0.320409i
$136$	−0.758592	+	1.31392i	−0.0650487	+	0.112668i
$137$	8.99273	+	5.91461i	0.768301	+	0.505319i	0.872129	−	0.489276i	$-0.162739\pi$
$137$	8.99273	+	5.91461i	0.768301	+	0.505319i	−0.103828	+	0.994595i	$0.533109\pi$
$138$	−8.60278	−	9.44941i	−0.732317	−	0.804387i
$139$	2.55292	+	5.91833i	0.216536	+	0.501986i	0.991514	−	0.130002i	$-0.0414984\pi$
$139$	2.55292	+	5.91833i	0.216536	+	0.501986i	−0.774978	+	0.631988i	$0.782239\pi$
$140$	2.54441	−	0.603036i	0.215042	−	0.0509659i
$141$	−8.74708	−	0.155503i	−0.736637	−	0.0130957i
$142$	0.169369	+	0.227502i	0.0142131	+	0.0190916i
$143$	7.60475	−	2.76790i	0.635941	−	0.231464i
$144$	−0.0678720	−	2.99923i	−0.00565600	−	0.249936i
$145$	−6.30693	−	2.29553i	−0.523762	−	0.190634i
$146$	−3.32061	−	11.0916i	−0.274816	−	0.917949i
$147$	0.888823	+	1.23929i	0.0733089	+	0.102215i
$148$	0.0392206	+	0.673392i	0.00322392	+	0.0553525i
$149$	−0.0289210	+	0.0190217i	−0.00236930	+	0.00155831i	−0.550693	−	0.834708i	$-0.685637\pi$
$149$	−0.0289210	+	0.0190217i	−0.00236930	+	0.00155831i	0.548324	+	0.836266i	$0.315266\pi$
$150$	6.93404	+	1.77414i	0.566162	+	0.144858i
$151$	−22.1823	−	5.25731i	−1.80517	−	0.427834i	−0.816429	−	0.577446i	$-0.804049\pi$
$151$	−22.1823	−	5.25731i	−1.80517	−	0.427834i	−0.988745	+	0.149613i	$0.952197\pi$
$152$	0.762123	+	4.32221i	0.0618163	+	0.350578i
$153$	3.71146	+	2.63470i	0.300054	+	0.213003i
$154$	−2.23605	+	12.6813i	−0.180186	+	1.02189i
$155$	2.32077	−	5.38015i	0.186409	−	0.432144i
$156$	−0.584043	+	2.99947i	−0.0467609	+	0.240150i
$157$	2.53198	−	8.45740i	0.202074	−	0.674974i	−0.795538	−	0.605904i	$-0.792812\pi$
$157$	2.53198	−	8.45740i	0.202074	−	0.674974i	0.997612	−	0.0690700i	$-0.0220032\pi$
$158$	−2.12446	+	2.85364i	−0.169013	+	0.227023i
$159$	1.76097	+	4.29053i	0.139654	+	0.340261i
$160$	−0.832408	+	0.418051i	−0.0658076	+	0.0330498i
$161$	−20.7113			−1.63228
$162$	−8.97726	−	0.639391i	−0.705320	−	0.0502353i
$163$	−21.2225			−1.66227			−0.831137	−	0.556067i	$-0.812310\pi$
$163$	−21.2225			−1.66227			−0.831137	+	0.556067i	$0.812310\pi$
$164$	−8.46317	+	4.25037i	−0.660863	+	0.331898i
$165$	4.52420	−	5.85677i	0.352209	−	0.455949i
$166$	6.38944	−	8.58251i	0.495917	−	0.666132i
$167$	−4.59344	+	15.3431i	−0.355451	+	1.18729i	0.574159	+	0.818744i	$0.305329\pi$
$167$	−4.59344	+	15.3431i	−0.355451	+	1.18729i	−0.929610	+	0.368544i	$0.879856\pi$
$168$	−3.66856	−	3.19111i	−0.283036	−	0.246199i
$169$	−3.91618	+	9.07872i	−0.301245	+	0.698363i
$170$	0.245406	−	1.39177i	0.0188218	−	0.106744i
$171$	13.1237	−	1.06276i	1.00359	−	0.0812710i
$172$	−0.955334	−	5.41797i	−0.0728436	−	0.413116i
$173$	−10.9871	−	2.60399i	−0.835334	−	0.197978i	−0.209376	−	0.977835i	$-0.567143\pi$
$173$	−10.9871	−	2.60399i	−0.835334	−	0.197978i	−0.625957	+	0.779857i	$0.715292\pi$
$174$	3.36623	+	12.0175i	0.255194	+	0.911042i
$175$	9.69197	−	6.37451i	0.732644	−	0.481868i
$176$	−0.266714	−	4.57930i	−0.0201043	−	0.345177i
$177$	−8.67877	+	0.858331i	−0.652336	+	0.0645161i
$178$	2.88574	+	9.63905i	0.216295	+	0.722477i
$179$	18.7430	+	6.82191i	1.40092	+	0.509893i	0.928451	−	0.371454i	$-0.121141\pi$
$179$	18.7430	+	6.82191i	1.40092	+	0.509893i	0.472469	+	0.881347i	$0.343363\pi$
$180$	1.01493	+	2.60364i	0.0756482	+	0.194064i
$181$	19.9989	−	7.27900i	1.48651	−	0.541044i	0.533979	−	0.845498i	$-0.320696\pi$
$181$	19.9989	−	7.27900i	1.48651	−	0.541044i	0.952527	+	0.304454i	$0.0984739\pi$
$182$	2.95755	+	3.97268i	0.219228	+	0.294474i
$183$	−4.42502	−	7.98902i	−0.327107	−	0.590565i
$184$	7.17900	−	1.70145i	0.529243	−	0.125433i
$185$	−0.248865	−	0.576933i	−0.0182969	−	0.0424170i
$186$	−10.6444	+	2.32376i	−0.780489	+	0.170386i
$187$	5.81450	+	3.82426i	0.425198	+	0.279657i
$188$	2.52546	−	4.37423i	0.184188	−	0.319024i
$189$	−10.5613	+	10.0614i	−0.768225	+	0.731858i
$190$	−2.04410	−	3.54048i	−0.148294	−	0.256854i
$191$	−1.03657	+	17.7972i	−0.0750033	+	1.28776i	0.725414	+	0.688313i	$0.241649\pi$
$191$	−1.03657	+	17.7972i	−0.0750033	+	1.28776i	−0.800417	+	0.599444i	$0.795388\pi$
$192$	1.53376	+	0.804732i	0.110689	+	0.0580766i
$193$	22.1969	+	2.59445i	1.59777	+	0.186753i	0.867866	−	0.496798i	$-0.165491\pi$
$193$	22.1969	+	2.59445i	1.59777	+	0.186753i	0.729904	+	0.683550i	$0.239565\pi$
$194$	11.8751	+	12.5868i	0.852579	+	0.903681i
$195$	−0.444375	−	2.81155i	−0.0318224	−	0.201339i
$196$	−0.874548	+	0.102220i	−0.0624677	+	0.00730143i
$197$	−3.12785	−	2.62458i	−0.222850	−	0.186994i	0.524526	−	0.851394i	$-0.324242\pi$
$197$	−3.12785	−	2.62458i	−0.222850	−	0.186994i	−0.747377	+	0.664401i	$0.768687\pi$
$198$	−13.7525	−	0.489130i	−0.977346	−	0.0347610i
$199$	−0.620215	+	0.520423i	−0.0439659	+	0.0368918i	−0.664506	−	0.747283i	$-0.731358\pi$
$199$	−0.620215	+	0.520423i	−0.0439659	+	0.0368918i	0.620540	+	0.784175i	$0.286913\pi$
$200$	−2.83578	+	3.00575i	−0.200520	+	0.212538i
$201$	1.88133	−	24.7219i	0.132699	−	1.74375i
$202$	5.65559	+	2.84035i	0.397926	+	0.199846i
$203$	18.0755	+	9.07787i	1.26865	+	0.637141i
$204$	−2.36892	+	1.13744i	−0.165857	+	0.0796370i
$205$	6.05381	−	6.41666i	0.422816	−	0.448159i
$206$	14.2682	−	11.9724i	0.994111	−	0.834158i
$207$	−3.06626	−	21.9202i	−0.213120	−	1.52356i
$208$	−1.35151	−	1.13405i	−0.0937103	−	0.0786323i
$209$	19.9960	−	2.33719i	1.38315	−	0.161667i
$210$	4.22778	+	1.62446i	0.291745	+	0.112098i
$211$	−7.80319	−	8.27090i	−0.537194	−	0.569392i	0.400746	−	0.916189i	$-0.368751\pi$
$211$	−7.80319	−	8.27090i	−0.537194	−	0.569392i	−0.937940	+	0.346797i	$0.887269\pi$
$212$	−2.65956	−	0.310858i	−0.182659	−	0.0213498i
$213$	0.0198421	+	0.490852i	0.00135956	+	0.0336326i
$214$	0.0617057	−	1.05945i	0.00421811	−	0.0724222i
$215$	2.56231	+	4.43806i	0.174748	+	0.302673i
$216$	2.83424	−	4.35512i	0.192846	−	0.296328i
$217$	−8.82916	+	15.2925i	−0.599362	+	1.03813i
$218$	−10.2306	−	6.72874i	−0.692900	−	0.455728i
$219$	6.09204	−	19.1060i	0.411662	−	1.29106i
$220$	1.69236	+	3.92334i	0.114099	+	0.264512i
$221$	2.60457	−	0.617295i	0.175202	−	0.0415237i
$222$	−0.602055	+	1.00126i	−0.0404073	+	0.0672000i
$223$	10.6088	+	14.2500i	0.710415	+	0.954252i	0.999996	−	0.00290107i	$-0.000923440\pi$
$223$	10.6088	+	14.2500i	0.710415	+	0.954252i	−0.289581	+	0.957153i	$0.593516\pi$
$224$	2.63793	−	0.960127i	0.176254	−	0.0641512i
$225$	8.18144	+	9.31393i	0.545430	+	0.620929i
$226$	6.40020	+	2.32948i	0.425735	+	0.154955i
$227$	0.718661	+	2.40050i	0.0476992	+	0.159327i	0.978521	−	0.206147i	$-0.0660924\pi$
$227$	0.718661	+	2.40050i	0.0476992	+	0.159327i	−0.930822	+	0.365473i	$0.880907\pi$
$228$	−3.13451	+	6.92545i	−0.207588	+	0.458649i
$229$	−0.262629	−	4.50916i	−0.0173550	−	0.297974i	−0.995806	−	0.0914931i	$-0.970836\pi$
$229$	−0.262629	−	4.50916i	−0.0173550	−	0.297974i	0.978451	−	0.206480i	$-0.0662010\pi$
$230$	−5.74181	+	3.77645i	−0.378604	+	0.249011i
$231$	−15.5915	+	15.9483i	−1.02584	+	1.04932i
$232$	−7.01112	−	1.66167i	−0.460303	−	0.109094i
$233$	2.12497	+	12.0513i	0.139212	+	0.789508i	0.971834	+	0.235667i	$0.0757275\pi$
$233$	2.12497	+	12.0513i	0.139212	+	0.789508i	−0.832622	+	0.553841i	$0.813161\pi$
$234$	−3.76669	+	3.71832i	−0.246236	+	0.243074i
$235$	−0.816993	+	4.63340i	−0.0532948	+	0.302250i
$236$	1.99432	−	4.62334i	0.129819	−	0.300954i
$237$	−5.82689	+	2.00426i	−0.378497	+	0.130191i
$238$	−1.22152	+	4.08015i	−0.0791791	+	0.264477i
$239$	15.8275	−	21.2601i	1.02380	−	1.37520i	0.0988519	−	0.995102i	$-0.468483\pi$
$239$	15.8275	−	21.2601i	1.02380	−	1.37520i	0.924946	−	0.380098i	$-0.124110\pi$
$240$	−1.59889	−	0.215757i	−0.103208	−	0.0139270i
$241$	−4.87872	+	2.45019i	−0.314266	+	0.157830i	−0.598940	−	0.800794i	$-0.704411\pi$
$241$	−4.87872	+	2.45019i	−0.314266	+	0.157830i	0.284674	+	0.958625i	$0.408115\pi$
$242$	−10.0411			−0.645466
$243$	−12.2122	−	9.68822i	−0.783414	−	0.621500i
$244$	5.27273			0.337552
$245$	0.732936	−	0.368094i	0.0468256	−	0.0235167i
$246$	−16.2561	−	2.19362i	−1.03645	−	0.139860i
$247$	4.62391	−	6.21099i	0.294212	−	0.395196i
$248$	1.80408	−	6.02605i	0.114559	−	0.382655i
$249$	17.5248	−	6.02794i	1.11059	−	0.382005i
$250$	3.36931	−	7.81095i	0.213094	−	0.494008i
$251$	0.521714	−	2.95878i	0.0329303	−	0.186757i	−0.963906	−	0.266244i	$-0.914217\pi$
$251$	0.521714	−	2.95878i	0.0329303	−	0.186757i	0.996836	+	0.0794874i	$0.0253283\pi$
$252$	−2.12707	−	8.14862i	−0.133993	−	0.513315i
$253$	−5.87673	−	33.3286i	−0.369467	−	2.09535i
$254$	8.28984	+	1.96473i	0.520151	+	0.123278i
$255$	1.71116	−	1.75033i	0.107157	−	0.109610i
$256$	−0.835488	+	0.549509i	−0.0522180	+	0.0343443i
$257$	0.761444	+	13.0735i	0.0474975	+	0.815501i	0.934989	+	0.354677i	$0.115409\pi$
$257$	0.761444	+	13.0735i	0.0474975	+	0.815501i	−0.887491	+	0.460824i	$0.847554\pi$
$258$	3.92916	−	8.68118i	0.244619	−	0.540467i
$259$	0.543081	+	1.81402i	0.0337454	+	0.112717i
$260$	1.54429	+	0.562075i	0.0957727	+	0.0348584i
$261$	−6.93168	+	20.4745i	−0.429060	+	1.26734i
$262$	15.0048	−	5.46131i	0.927001	−	0.337401i
$263$	−1.87795	−	2.52252i	−0.115799	−	0.155545i	0.740444	−	0.672118i	$-0.234615\pi$
$263$	−1.87795	−	2.52252i	−0.115799	−	0.155545i	−0.856244	+	0.516572i	$0.827208\pi$
$264$	4.09418	−	6.80889i	0.251979	−	0.419058i
$265$	2.42698	−	0.575204i	0.149088	−	0.0353345i
$266$	4.87994	+	11.3130i	0.299208	+	0.693642i
$267$	−5.29422	+	16.6038i	−0.324001	+	1.01614i
$268$	11.9595	+	7.86592i	0.730545	+	0.480487i
$269$	−10.1021	+	17.4974i	−0.615938	+	1.06684i	0.374282	+	0.927315i	$0.377889\pi$
$269$	−10.1021	+	17.4974i	−0.615938	+	1.06684i	−0.990219	+	0.139520i	$0.955444\pi$
$270$	−1.09336	+	4.71504i	−0.0665398	+	0.286948i
$271$	−14.8899	−	25.7901i	−0.904500	−	1.56664i	−0.821587	−	0.570083i	$-0.806911\pi$
$271$	−14.8899	−	25.7901i	−0.904500	−	1.56664i	−0.0829129	−	0.996557i	$-0.526422\pi$
$272$	0.0882164	−	1.51462i	0.00534890	−	0.0918371i
$273$	0.346486	+	8.57133i	0.0209703	+	0.518760i
$274$	−10.6907	−	1.24956i	−0.645847	−	0.0754887i
$275$	13.0079	+	13.7875i	0.784404	+	0.831420i
$276$	11.9286	+	4.58338i	0.718018	+	0.275887i
$277$	−4.36989	+	0.510767i	−0.262561	+	0.0306890i	−0.246355	−	0.969180i	$-0.579233\pi$
$277$	−4.36989	+	0.510767i	−0.262561	+	0.0306890i	−0.0162063	+	0.999869i	$0.505159\pi$
$278$	−4.93751	−	4.14306i	−0.296132	−	0.248484i
$279$	−17.4923	−	7.08046i	−1.04723	−	0.423896i
$280$	−2.00313	+	1.68082i	−0.119710	+	0.100448i
$281$	19.4042	−	20.5672i	1.15755	−	1.22694i	0.187972	−	0.982174i	$-0.439809\pi$
$281$	19.4042	−	20.5672i	1.15755	−	1.22694i	0.969583	−	0.244762i	$-0.0787098\pi$
$282$	7.88647	−	3.78672i	0.469632	−	0.225496i
$283$	6.51124	+	3.27007i	0.387053	+	0.194385i	0.631675	−	0.775233i	$-0.282368\pi$
$283$	6.51124	+	3.27007i	0.387053	+	0.194385i	−0.244622	+	0.969618i	$0.578664\pi$
$284$	−0.253456	−	0.127291i	−0.0150399	−	0.00755331i
$285$	0.537307	−	7.06055i	0.0318273	−	0.418231i
$286$	−5.55362	+	5.88650i	−0.328393	+	0.348076i
$287$	−20.3660	+	17.0891i	−1.20217	+	1.00874i
$288$	1.40671	+	2.64975i	0.0828909	+	0.156138i
$289$	−11.2594	−	9.44779i	−0.662320	−	0.555752i
$290$	6.66631	−	0.779180i	0.391459	−	0.0457550i
$291$	4.67914	+	29.6047i	0.274296	+	1.73546i
$292$	7.94532	+	8.42155i	0.464965	+	0.492834i
$293$	−0.386477	−	0.0451727i	−0.0225782	−	0.00263902i	0.104796	−	0.994494i	$-0.466581\pi$
$293$	−0.386477	−	0.0451727i	−0.0225782	−	0.00263902i	−0.127375	+	0.991855i	$0.540655\pi$
$294$	−1.35047	−	0.708568i	−0.0787612	−	0.0413245i
$295$	−0.272709	+	4.68223i	−0.0158777	+	0.272610i
$296$	−0.337267	−	0.584163i	−0.0196032	−	0.0339538i
$297$	−19.1875	−	14.1404i	−1.11337	−	0.820510i
$298$	0.0173079	−	0.0299781i	0.00100262	−	0.00173658i
$299$	−10.8752	−	7.15272i	−0.628928	−	0.413652i
$300$	−6.99272	+	1.52656i	−0.403725	+	0.0881358i
$301$	−6.11709	−	14.1810i	−0.352583	−	0.817380i
$302$	22.1823	−	5.25731i	1.27645	−	0.302524i
$303$	5.31127	+	9.58907i	0.305124	+	0.550878i
$304$	−2.62086	−	3.52043i	−0.150317	−	0.201910i
$305$	−4.61529	+	1.67983i	−0.264271	+	0.0961866i
$306$	−4.49914	−	0.688756i	−0.257199	−	0.0393736i
$307$	15.8628	+	5.77360i	0.905340	+	0.329517i	0.752391	−	0.658717i	$-0.228901\pi$
$307$	15.8628	+	5.77360i	0.905340	+	0.329517i	0.152949	+	0.988234i	$0.451123\pi$
$308$	−3.69313	−	12.3359i	−0.210436	−	0.702905i
$309$	32.1042	−	3.17510i	1.82634	−	0.180625i
$310$	0.340691	+	5.84944i	0.0193499	+	0.332226i
$311$	−20.9613	+	13.7865i	−1.18861	+	0.781760i	−0.980533	−	0.196353i	$-0.937090\pi$
$311$	−20.9613	+	13.7865i	−1.18861	+	0.781760i	−0.208074	+	0.978113i	$0.566720\pi$
$312$	−0.824242	−	2.94255i	−0.0466635	−	0.166589i
$313$	9.15572	+	2.16994i	0.517512	+	0.122653i	0.481068	−	0.876683i	$-0.340249\pi$
$313$	9.15572	+	2.16994i	0.517512	+	0.122653i	0.0364435	+	0.999336i	$0.488397\pi$
$314$	1.53301	+	8.69416i	0.0865130	+	0.490640i
$315$	4.45790	+	6.45493i	0.251174	+	0.363694i
$316$	0.617772	−	3.50356i	0.0347524	−	0.197091i
$317$	−5.32798	+	12.3516i	−0.299249	+	0.693737i	−0.999803	−	0.0198626i	$-0.993677\pi$
$317$	−5.32798	+	12.3516i	−0.299249	+	0.693737i	0.700554	+	0.713600i	$0.252936\pi$
$318$	−3.49925	−	3.04383i	−0.196228	−	0.170690i
$319$	−9.47923	+	31.6628i	−0.530735	+	1.77278i
$320$	0.556246	−	0.747168i	0.0310951	−	0.0417680i
$321$	1.12369	−	1.45466i	0.0627180	−	0.0811911i
$322$	18.5083	−	9.29523i	1.03143	−	0.518003i
$323$	6.65875			0.370503
$324$	8.30933	−	3.45761i	0.461629	−	0.192089i
$325$	7.29055			0.404407
$326$	18.9651	−	9.52464i	1.05038	−	0.527521i
$327$	−8.05296	−	19.6207i	−0.445330	−	1.08503i
$328$	5.65541	−	7.59653i	0.312268	−	0.419448i
$329$	4.06661	−	13.5834i	0.224199	−	0.748878i
$330$	−1.41446	+	7.26426i	−0.0778635	+	0.399884i
$331$	−5.56619	+	12.9039i	−0.305946	+	0.709262i	−0.999943	−	0.0107163i	$-0.996589\pi$
$331$	−5.56619	+	12.9039i	−0.305946	+	0.709262i	0.693997	+	0.719978i	$0.255848\pi$
$332$	−1.85799	+	10.5372i	−0.101971	+	0.578303i
$333$	−1.83949	+	0.843340i	−0.100804	+	0.0462147i
$334$	−2.78115	−	15.7727i	−0.152178	−	0.863042i
$335$	−12.9743	−	3.07497i	−0.708863	−	0.168004i
$336$	4.71051	+	1.20523i	0.256979	+	0.0657508i
$337$	5.45623	−	3.58862i	0.297220	−	0.195485i	−0.392136	−	0.919907i	$-0.628264\pi$
$337$	5.45623	−	3.58862i	0.297220	−	0.195485i	0.689356	+	0.724423i	$0.257894\pi$
$338$	−0.574898	−	9.87062i	−0.0312703	−	0.536891i
$339$	6.87532	+	9.58630i	0.373416	+	0.520656i
$340$	0.405321	+	1.35387i	0.0219816	+	0.0734238i
$341$	−27.1139	−	9.86866i	−1.46830	−	0.534418i
$342$	−11.2508	+	6.83962i	−0.608374	+	0.369844i
$343$	16.1428	−	5.87549i	0.871629	−	0.317247i
$344$	3.28530	+	4.41292i	0.177131	+	0.237929i
$345$	−11.9015	−	0.211581i	−0.640753	−	0.0113911i
$346$	10.9871	−	2.60399i	0.590670	−	0.139991i
$347$	10.6690	+	24.7336i	0.572744	+	1.32777i	0.920705	+	0.390260i	$0.127615\pi$
$347$	10.6690	+	24.7336i	0.572744	+	1.32777i	−0.347961	+	0.937509i	$0.613126\pi$
$348$	−8.40160	−	9.22844i	−0.450373	−	0.494696i
$349$	−21.0859	−	13.8684i	−1.12870	−	0.742359i	−0.159153	−	0.987254i	$-0.550876\pi$
$349$	−21.0859	−	13.8684i	−1.12870	−	0.742359i	−0.969550	+	0.244895i	$0.921247\pi$
$350$	−5.80019	+	10.0462i	−0.310033	+	0.536993i
$351$	−9.02032	+	1.63567i	−0.481469	+	0.0873058i
$352$	2.29353	+	3.97251i	0.122245	+	0.211735i
$353$	−0.0557860	+	0.957808i	−0.00296919	+	0.0509790i	−0.999467	−	0.0326364i	$-0.989610\pi$
$353$	−0.0557860	+	0.957808i	−0.00296919	+	0.0509790i	0.996498	+	0.0836154i	$0.0266467\pi$
$354$	7.37042	−	4.66206i	0.391733	−	0.247786i
$355$	0.262407	+	0.0306710i	0.0139271	+	0.00162785i
$356$	−6.90479	−	7.31865i	−0.365953	−	0.387888i
$357$	−5.73445	+	4.64060i	−0.303499	+	0.245607i
$358$	−19.8111	+	2.31558i	−1.04705	+	0.122382i
$359$	−12.5985	−	10.5714i	−0.664925	−	0.557939i	0.246633	−	0.969109i	$-0.420676\pi$
$359$	−12.5985	−	10.5714i	−0.664925	−	0.557939i	−0.911559	+	0.411170i	$0.865120\pi$
$360$	−2.07548	−	1.87120i	−0.109388	−	0.0986209i
$361$	0.200968	−	0.168633i	0.0105773	−	0.00887540i
$362$	−14.6049	+	15.4802i	−0.767614	+	0.813623i
$363$	−14.3584	−	9.81365i	−0.753619	−	0.515083i
$364$	−4.42590	−	2.22277i	−0.231980	−	0.116505i
$365$	−9.63764	−	4.84020i	−0.504457	−	0.253348i
$366$	7.53980	+	5.15330i	0.394112	+	0.269367i
$367$	−1.16969	+	1.23980i	−0.0610575	+	0.0647172i	−0.757182	−	0.653204i	$-0.773425\pi$
$367$	−1.16969	+	1.23980i	−0.0610575	+	0.0647172i	0.696125	+	0.717921i	$0.254906\pi$
$368$	−5.65178	+	4.74241i	−0.294619	+	0.247215i
$369$	−21.1017	−	19.0247i	−1.09851	−	0.990385i
$370$	0.481321	+	0.403876i	0.0250227	+	0.0209965i
$371$	−7.46597	+	0.872647i	−0.387614	+	0.0453056i
$372$	8.46933	−	6.85380i	0.439114	−	0.355353i
$373$	−9.80490	−	10.3926i	−0.507678	−	0.538108i	0.421944	−	0.906622i	$-0.361348\pi$
$373$	−9.80490	−	10.3926i	−0.507678	−	0.538108i	−0.929622	+	0.368514i	$0.879866\pi$
$374$	−6.91235	−	0.807938i	−0.357429	−	0.0417775i
$375$	12.4520	−	7.87635i	0.643019	−	0.406733i
$376$	−0.293685	+	5.04238i	−0.0151457	+	0.260041i
$377$	6.35609	+	11.0091i	0.327355	+	0.566996i
$378$	4.92243	−	13.7311i	0.253182	−	0.706252i
$379$	−12.0604	+	20.8893i	−0.619504	+	1.07301i	0.370073	+	0.929003i	$0.379333\pi$
$379$	−12.0604	+	20.8893i	−0.619504	+	1.07301i	−0.989576	+	0.144009i	$0.954001\pi$
$380$	3.41564	+	2.24650i	0.175219	+	0.115243i
$381$	9.93392	+	10.9116i	0.508930	+	0.559016i
$382$	−7.06104	−	16.3693i	−0.361274	−	0.837528i
$383$	5.64393	−	1.33764i	0.288391	−	0.0683500i	−0.0838739	−	0.996476i	$-0.526729\pi$
$383$	5.64393	−	1.33764i	0.288391	−	0.0683500i	0.372265	+	0.928126i	$0.378581\pi$
$384$	−1.73178	−	0.0307871i	−0.0883744	−	0.00157110i
$385$	7.16272	+	9.62120i	0.365046	+	0.490342i
$386$	−21.0003	+	7.64348i	−1.06889	+	0.389043i
$387$	14.1031	−	8.57359i	0.716900	−	0.435820i
$388$	−16.2609	−	5.91848i	−0.825522	−	0.300465i
$389$	−5.89390	−	19.6870i	−0.298833	−	0.998170i	−0.967131	−	0.254277i	$-0.918162\pi$
$389$	−5.89390	−	19.6870i	−0.298833	−	0.998170i	0.668299	−	0.743893i	$-0.267023\pi$
$390$	1.65893	+	2.31305i	0.0840031	+	0.117126i
$391$	−0.650849	−	11.1747i	−0.0329149	−	0.565126i
$392$	0.735648	−	0.483843i	0.0371558	−	0.0244378i
$393$	26.7939	+	6.85550i	1.35157	+	0.345814i
$394$	3.97306	+	0.941633i	0.200160	+	0.0474388i
$395$	0.575447	+	3.26352i	0.0289539	+	0.164206i
$396$	12.5092	−	5.73500i	0.628610	−	0.288194i
$397$	−2.54727	+	14.4463i	−0.127844	+	0.725039i	0.851734	+	0.523974i	$0.175551\pi$
$397$	−2.54727	+	14.4463i	−0.127844	+	0.725039i	−0.979578	+	0.201065i	$0.935560\pi$
$398$	0.320680	−	0.743419i	0.0160742	−	0.0372642i
$399$	−4.07860	+	20.9465i	−0.204185	+	1.04864i
$400$	1.18517	−	3.95873i	0.0592583	−	0.197936i
$401$	15.9451	−	21.4180i	0.796262	−	1.06957i	−0.199706	−	0.979856i	$-0.563999\pi$
$401$	15.9451	−	21.4180i	0.796262	−	1.06957i	0.995968	−	0.0897093i	$-0.0285938\pi$
$402$	9.41393	+	22.9366i	0.469524	+	1.14397i
$403$	−9.91737	+	4.98069i	−0.494019	+	0.248106i
$404$	−6.32877			−0.314868
$405$	−6.17171	+	5.67373i	−0.306675	+	0.281930i
$406$	−20.2270			−1.00385
$407$	−2.76501	+	1.38864i	−0.137056	+	0.0688323i
$408$	1.60646	−	2.07962i	0.0795314	−	0.102957i
$409$	−5.81400	+	7.80956i	−0.287484	+	0.386158i	−0.922280	−	0.386521i	$-0.873677\pi$
$409$	−5.81400	+	7.80956i	−0.287484	+	0.386158i	0.634796	+	0.772679i	$0.281084\pi$
$410$	−2.53009	+	8.45108i	−0.124952	+	0.417369i
$411$	−14.0660	−	12.2353i	−0.693824	−	0.603525i
$412$	−7.37729	+	17.1025i	−0.363453	+	0.842579i
$413$	2.45447	−	13.9200i	0.120777	−	0.684959i
$414$	12.5779	+	18.2125i	0.618169	+	0.895094i
$415$	−1.73070	−	9.81527i	−0.0849565	−	0.481812i
$416$	1.71671	+	0.406869i	0.0841688	+	0.0199484i
$417$	−3.01123	−	10.7501i	−0.147460	−	0.526434i
$418$	−16.8201	+	11.0628i	−0.822698	+	0.541097i
$419$	0.515542	+	8.85151i	0.0251859	+	0.432425i	0.987206	+	0.159448i	$0.0509713\pi$
$419$	0.515542	+	8.85151i	0.0251859	+	0.432425i	−0.962021	+	0.272977i	$0.911992\pi$
$420$	−4.50714	+	0.445756i	−0.219926	+	0.0217507i
$421$	3.31057	+	11.0581i	0.161347	+	0.538938i	0.999983	−	0.00575434i	$-0.00183167\pi$
$421$	3.31057	+	11.0581i	0.161347	+	0.538938i	−0.838636	+	0.544692i	$0.816646\pi$
$422$	10.6852	+	3.88908i	0.520145	+	0.189317i
$423$	14.9783	+	2.29297i	0.728269	+	0.111488i
$424$	2.51618	−	0.915814i	0.122196	−	0.0444759i
$425$	3.74389	+	5.02891i	0.181605	+	0.243938i
$426$	−0.238025	−	0.429736i	−0.0115324	−	0.0208208i
$427$	14.4028	−	3.41352i	0.696998	−	0.165192i
$428$	0.420336	+	0.974449i	0.0203177	+	0.0471018i
$429$	−13.6946	+	2.98963i	−0.661183	+	0.144341i
$430$	−4.28156	−	2.81603i	−0.206475	−	0.135801i
$431$	13.5607	−	23.4878i	0.653196	−	1.13137i	−0.329147	−	0.944279i	$-0.606761\pi$
$431$	13.5607	−	23.4878i	0.653196	−	1.13137i	0.982343	−	0.187090i	$-0.0599056\pi$
$432$	−0.578198	+	5.16388i	−0.0278186	+	0.248447i
$433$	0.933229	+	1.61640i	0.0448481	+	0.0776792i	0.887578	−	0.460657i	$-0.152386\pi$
$433$	0.933229	+	1.61640i	0.0448481	+	0.0776792i	−0.842730	+	0.538337i	$0.819053\pi$
$434$	1.02674	−	17.6284i	0.0492851	−	0.846192i
$435$	10.2941	+	5.40112i	0.493564	+	0.258964i
$436$	12.1622	+	1.42156i	0.582464	+	0.0680803i
$437$	−22.2210	−	23.5528i	−1.06297	−	1.12669i
$438$	3.13070	+	19.8078i	0.149591	+	0.946455i
$439$	5.43863	−	0.635684i	0.259571	−	0.0303396i	0.0146882	−	0.999892i	$-0.495324\pi$
$439$	5.43863	−	0.635684i	0.259571	−	0.0303396i	0.244883	+	0.969553i	$0.421250\pi$
$440$	−3.27315	−	2.74650i	−0.156041	−	0.130934i
$441$	−1.23861	−	2.33311i	−0.0589812	−	0.111100i
$442$	−2.05049	+	1.72056i	−0.0975318	+	0.0818389i
$443$	7.84510	−	8.31532i	0.372732	−	0.395073i	−0.513671	−	0.857987i	$-0.671715\pi$
$443$	7.84510	−	8.31532i	0.372732	−	0.395073i	0.886403	+	0.462914i	$0.153196\pi$
$444$	0.0886532	−	1.16496i	0.00420729	−	0.0552865i
$445$	8.37548	+	4.20632i	0.397036	+	0.199399i
$446$	−15.8757	−	7.97309i	−0.751737	−	0.377537i
$447$	0.0540486	−	0.0259517i	0.00255641	−	0.00122747i
$448$	−1.92643	+	2.04190i	−0.0910154	+	0.0964707i
$449$	−0.447406	+	0.375418i	−0.0211144	+	0.0177171i	−0.653284	−	0.757113i	$-0.726609\pi$
$449$	−0.447406	+	0.375418i	−0.0211144	+	0.0177171i	0.632169	+	0.774830i	$0.282165\pi$
$450$	−11.4913	−	4.65141i	−0.541705	−	0.219270i
$451$	−33.2784	−	27.9239i	−1.56702	−	1.31488i
$452$	−6.76489	+	0.790703i	−0.318194	+	0.0371915i
$453$	36.8581	+	14.1621i	1.73175	+	0.665396i
$454$	−1.71956	−	1.82263i	−0.0807029	−	0.0855401i
$455$	4.58219	+	0.535581i	0.214816	+	0.0251084i
$456$	−0.307042	−	7.59558i	−0.0143786	−	0.355695i
$457$	−0.759073	+	13.0328i	−0.0355079	+	0.609648i	0.932878	+	0.360192i	$0.117289\pi$
$457$	−0.759073	+	13.0328i	−0.0355079	+	0.609648i	−0.968386	+	0.249456i	$0.919748\pi$
$458$	2.25840	+	3.91166i	0.105528	+	0.182780i
$459$	−5.76043	−	5.38212i	−0.268874	−	0.251216i
$460$	3.43620	−	5.95167i	0.160214	−	0.277498i
$461$	9.75285	+	6.41455i	0.454236	+	0.298756i	0.755934	−	0.654648i	$-0.227183\pi$
$461$	9.75285	+	6.41455i	0.454236	+	0.298756i	−0.301698	+	0.953403i	$0.597553\pi$
$462$	6.77547	−	21.2494i	0.315224	−	0.988611i
$463$	3.89577	+	9.03140i	0.181052	+	0.419725i	0.984438	−	0.175734i	$-0.0562297\pi$
$463$	3.89577	+	9.03140i	0.181052	+	0.419725i	−0.803386	+	0.595458i	$0.796970\pi$
$464$	7.01112	−	1.66167i	0.325483	−	0.0771409i
$465$	−5.22977	+	8.69744i	−0.242525	+	0.403334i
$466$	−7.30757	−	9.81577i	−0.338517	−	0.454707i
$467$	16.7575	−	6.09922i	0.775444	−	0.282238i	0.0761723	−	0.997095i	$-0.475730\pi$
$467$	16.7575	−	6.09922i	0.775444	−	0.282238i	0.699271	+	0.714856i	$0.253508\pi$
$468$	1.69726	−	5.01330i	0.0784559	−	0.231740i
$469$	37.7605	+	13.7437i	1.74362	+	0.634624i
$470$	−1.34937	−	4.50722i	−0.0622420	−	0.207903i
$471$	−6.30508	+	13.9306i	−0.290523	+	0.641888i
$472$	0.292767	+	5.02662i	0.0134757	+	0.231369i
$473$	21.0843	−	13.8674i	0.969458	−	0.637622i
$474$	4.30759	−	4.40618i	0.197854	−	0.202382i
$475$	17.6475	+	4.18253i	0.809722	+	0.191908i
$476$	−0.739580	−	4.19437i	−0.0338986	−	0.192249i
$477$	−2.02890	−	7.77254i	−0.0928969	−	0.355880i
$478$	−4.60250	+	26.1021i	−0.210513	+	1.19388i
$479$	14.2659	−	33.0722i	0.651827	−	1.51111i	−0.195873	−	0.980629i	$-0.562754\pi$
$479$	14.2659	−	33.0722i	0.651827	−	1.51111i	0.847700	−	0.530476i	$-0.177987\pi$
$480$	1.52565	−	0.524774i	0.0696363	−	0.0239526i
$481$	−0.341313	+	1.14006i	−0.0155625	+	0.0519825i
$482$	3.26014	−	4.37913i	0.148496	−	0.199464i
$483$	35.5509	+	4.79728i	1.61762	+	0.218284i
$484$	8.97305	−	4.50643i	0.407866	−	0.204838i
$485$	16.1189			0.731922
$486$	15.2613	+	3.17688i	0.692267	+	0.144106i
$487$	28.2800			1.28149			0.640744	−	0.767754i	$-0.278626\pi$
$487$	28.2800			1.28149			0.640744	+	0.767754i	$0.278626\pi$
$488$	−4.71189	+	2.36640i	−0.213297	+	0.107122i
$489$	36.4283	+	4.91568i	1.64734	+	0.222295i
$490$	−0.489775	+	0.657882i	−0.0221258	+	0.0297201i
$491$	−1.26149	+	4.21368i	−0.0569303	+	0.190161i	−0.981725	−	0.190307i	$-0.939052\pi$
$491$	−1.26149	+	4.21368i	−0.0569303	+	0.190161i	0.924794	+	0.380467i	$0.124237\pi$
$492$	15.5115	−	5.33543i	0.699311	−	0.240540i
$493$	−4.32988	+	10.0378i	−0.195008	+	0.452079i
$494$	−1.34459	+	7.62555i	−0.0604960	+	0.343090i
$495$	−9.12234	+	9.00518i	−0.410019	+	0.404753i
$496$	1.09230	+	6.19475i	0.0490458	+	0.278152i
$497$	−0.774737	−	0.183616i	−0.0347517	−	0.00823630i
$498$	−12.9554	+	13.2519i	−0.580544	+	0.593830i
$499$	−13.2375	+	8.70642i	−0.592590	+	0.389753i	−0.810088	−	0.586308i	$-0.800581\pi$
$499$	−13.2375	+	8.70642i	−0.592590	+	0.389753i	0.217498	+	0.976061i	$0.430210\pi$
$500$	0.494618	+	8.49226i	0.0221200	+	0.379786i
$501$	11.4385	−	25.2724i	0.511033	−	1.12909i
$502$	0.861680	+	2.87821i	0.0384587	+	0.128461i
$503$	−12.5996	−	4.58586i	−0.561786	−	0.204473i	0.0454892	−	0.998965i	$-0.485515\pi$
$503$	−12.5996	−	4.58586i	−0.561786	−	0.204473i	−0.607275	+	0.794491i	$0.707738\pi$
$504$	5.55791	+	6.32725i	0.247569	+	0.281838i
$505$	5.53965	−	2.01627i	0.246511	−	0.0897227i
$506$	20.2095	+	27.1460i	0.898421	+	1.20679i
$507$	8.82496	−	14.6765i	0.391930	−	0.651805i
$508$	−8.28984	+	1.96473i	−0.367802	+	0.0871707i
$509$	−5.98696	−	13.8793i	−0.265367	−	0.615191i	0.732479	−	0.680790i	$-0.238363\pi$
$509$	−5.98696	−	13.8793i	−0.265367	−	0.615191i	−0.997846	+	0.0655993i	$0.979104\pi$
$510$	−0.743608	+	2.33212i	−0.0329275	+	0.103268i
$511$	27.1551	+	17.8602i	1.20127	+	0.790088i
$512$	0.500000	−	0.866025i	0.0220971	−	0.0382733i
$513$	−22.7729	−	1.21558i	−1.00545	−	0.0536690i
$514$	−6.54782	−	11.3412i	−0.288812	−	0.500237i
$515$	1.00879	−	17.3203i	0.0444528	−	0.763225i
$516$	0.384883	+	9.52119i	0.0169435	+	0.419147i
$517$	23.0122	+	2.68974i	1.01208	+	0.118295i
$518$	−1.29944	−	1.37733i	−0.0570943	−	0.0605164i
$519$	18.2561	+	7.01463i	0.801355	+	0.307908i
$520$	−1.63228	+	0.190787i	−0.0715804	+	0.00836655i
$521$	1.94311	+	1.63047i	0.0851294	+	0.0714321i	0.684359	−	0.729145i	$-0.260082\pi$
$521$	1.94311	+	1.63047i	0.0851294	+	0.0714321i	−0.599230	+	0.800577i	$0.704526\pi$
$522$	−2.99456	−	21.4076i	−0.131068	−	0.936985i
$523$	−14.0884	+	11.8216i	−0.616042	+	0.516921i	−0.896557	−	0.442929i	$-0.853939\pi$
$523$	−14.0884	+	11.8216i	−0.616042	+	0.516921i	0.280514	+	0.959850i	$0.409495\pi$
$524$	−10.9578	+	11.6146i	−0.478692	+	0.507384i
$525$	−18.1127	+	8.69689i	−0.790503	+	0.379563i
$526$	2.81030	+	1.41139i	0.122535	+	0.0615394i
$527$	−8.52844	−	4.28314i	−0.371505	−	0.186577i
$528$	−0.602872	+	7.92211i	−0.0262366	+	0.344766i
$529$	−21.5707	+	22.8636i	−0.937854	+	0.994068i
$530$	−1.91068	+	1.60325i	−0.0829945	+	0.0696406i
$531$	15.0959	+	0.536910i	0.655105	+	0.0232999i
$532$	−9.43812	−	7.91952i	−0.409194	−	0.343355i
$533$	−16.5956	+	1.93975i	−0.718835	+	0.0840198i
$534$	−2.72070	−	17.2138i	−0.117736	−	0.744913i
$535$	−0.678373	−	0.719033i	−0.0293286	−	0.0310865i
$536$	−14.2177	−	1.66181i	−0.614109	−	0.0717791i
$537$	−30.5922	−	16.0511i	−1.32015	−	0.692658i
$538$	1.17477	−	20.1701i	0.0506481	−	0.869594i
$539$	−2.01945	−	3.49780i	−0.0869841	−	0.150661i
$540$	−1.13905	−	4.70422i	−0.0490167	−	0.202437i
$541$	−7.56562	+	13.1040i	−0.325271	+	0.563386i	−0.981567	−	0.191117i	$-0.938789\pi$
$541$	−7.56562	+	13.1040i	−0.325271	+	0.563386i	0.656296	+	0.754504i	$0.272122\pi$
$542$	24.8807	+	16.3643i	1.06872	+	0.702908i
$543$	−36.0140	+	7.86210i	−1.54551	+	0.337395i
$544$	0.600926	+	1.39310i	0.0257645	+	0.0597288i
$545$	−11.0986	+	2.63042i	−0.475413	+	0.112675i
$546$	−4.15644	−	7.50412i	−0.177879	−	0.321147i
$547$	−10.5461	−	14.1659i	−0.450920	−	0.605690i	0.517296	−	0.855806i	$-0.326939\pi$
$547$	−10.5461	−	14.1659i	−0.450920	−	0.605690i	−0.968216	+	0.250116i	$0.919531\pi$
$548$	10.1143	−	3.68132i	0.432063	−	0.157258i
$549$	5.74505	+	14.7380i	0.245193	+	0.629004i
$550$	−17.8121	−	6.48307i	−0.759510	−	0.276439i
$551$	9.06971	+	30.2949i	0.386383	+	1.29061i
$552$	−12.7168	+	1.25769i	−0.541263	+	0.0535310i
$553$	−0.580693	−	9.97011i	−0.0246936	−	0.423972i
$554$	3.67584	−	2.41764i	0.156172	−	0.102716i
$555$	0.293542	+	1.04795i	0.0124602	+	0.0444828i
$556$	6.27172	+	1.48643i	0.265980	+	0.0630385i
$557$	2.15648	+	12.2300i	0.0913731	+	0.518203i	0.995799	+	0.0915710i	$0.0291888\pi$
$557$	2.15648	+	12.2300i	0.0913731	+	0.518203i	−0.904425	+	0.426632i	$0.859700\pi$
$558$	18.8094	−	1.52318i	0.796264	−	0.0644814i
$559$	1.68547	−	9.55877i	0.0712877	−	0.404293i
$560$	1.03571	−	2.40104i	0.0437666	−	0.101462i
$561$	−9.09475	−	7.91110i	−0.383981	−	0.334007i
$562$	−8.10964	+	27.0881i	−0.342085	+	1.14264i
$563$	−15.6180	+	20.9785i	−0.658218	+	0.884140i	−0.998419	−	0.0562125i	$-0.982098\pi$
$563$	−15.6180	+	20.9785i	−0.658218	+	0.884140i	0.340201	+	0.940353i	$0.389505\pi$
$564$	−5.34813	+	6.92338i	−0.225197	+	0.291527i
$565$	5.66949	−	2.84732i	0.238517	−	0.119788i
$566$	−7.28626			−0.306264
$567$	20.4590	−	14.8240i	0.859196	−	0.622550i
$568$	0.283625			0.0119006
$569$	13.1704	−	6.61443i	0.552133	−	0.277291i	−0.150780	−	0.988567i	$-0.548179\pi$
$569$	13.1704	−	6.61443i	0.552133	−	0.277291i	0.702913	+	0.711276i	$0.251882\pi$
$570$	2.68861	+	6.55068i	0.112614	+	0.274378i
$571$	3.97285	−	5.33646i	0.166259	−	0.223324i	−0.711184	−	0.703006i	$-0.751841\pi$
$571$	3.97285	−	5.33646i	0.166259	−	0.223324i	0.877442	+	0.479682i	$0.159248\pi$
$572$	2.32104	−	7.75283i	0.0970477	−	0.324162i
$573$	5.90154	−	30.3086i	0.246540	−	1.26616i
$574$	10.5301	−	24.4116i	0.439519	−	1.01892i
$575$	5.29415	−	30.0246i	0.220781	−	1.25211i
$576$	−2.44628	−	1.73658i	−0.101929	−	0.0723573i
$577$	5.41335	+	30.7007i	0.225361	+	1.27809i	0.861994	+	0.506918i	$0.169215\pi$
$577$	5.41335	+	30.7007i	0.225361	+	1.27809i	−0.636633	+	0.771167i	$0.719673\pi$
$578$	14.3020	+	3.38963i	0.594883	+	0.140990i
$579$	−37.4999	−	9.59474i	−1.55844	−	0.398744i
$580$	−5.60754	+	3.68813i	−0.232840	+	0.153141i
$581$	1.74647	+	29.9858i	0.0724558	+	1.24402i
$582$	−17.4680	−	24.3558i	−0.724073	−	1.00958i
$583$	−3.52269	−	11.7666i	−0.145895	−	0.487322i
$584$	−10.8798	−	3.95992i	−0.450209	−	0.163863i
$585$	0.111541	+	4.92893i	0.00461164	+	0.203786i
$586$	0.365642	−	0.133083i	0.0151045	−	0.00549760i
$587$	−25.5016	−	34.2546i	−1.05256	−	1.41384i	−0.905316	−	0.424739i	$-0.860366\pi$
$587$	−25.5016	−	34.2546i	−1.05256	−	1.41384i	−0.147248	−	0.989100i	$-0.547042\pi$
$588$	1.52483	+	0.0271080i	0.0628830	+	0.00111792i
$589$	−26.8633	+	6.36672i	−1.10688	+	0.262336i
$590$	−1.85768	−	4.30659i	−0.0764795	−	0.177299i
$591$	4.76102	+	5.22957i	0.195842	+	0.215116i
$592$	0.563564	+	0.370662i	0.0231624	+	0.0152341i
$593$	6.95785	−	12.0513i	0.285725	−	0.494890i	−0.687060	−	0.726601i	$-0.741099\pi$
$593$	6.95785	−	12.0513i	0.285725	−	0.494890i	0.972785	+	0.231711i	$0.0744324\pi$
$594$	23.4927	+	4.02502i	0.963919	+	0.165149i
$595$	1.98364	+	3.43576i	0.0813212	+	0.140852i
$596$	−0.00201273	+	0.0345572i	−8.24445e−5	+	0.00141552i
$597$	1.18514	−	0.749644i	0.0485045	−	0.0306809i
$598$	12.9286	+	1.51113i	0.528688	+	0.0617947i
$599$	−4.87779	−	5.17016i	−0.199301	−	0.211247i	0.620013	−	0.784591i	$-0.287127\pi$
$599$	−4.87779	−	5.17016i	−0.199301	−	0.211247i	−0.819314	+	0.573344i	$0.805646\pi$
$600$	5.56380	−	4.50251i	0.227141	−	0.183814i
$601$	−22.4454	+	2.62349i	−0.915567	+	0.107014i	−0.560811	−	0.827944i	$-0.689510\pi$
$601$	−22.4454	+	2.62349i	−0.915567	+	0.107014i	−0.354757	+	0.934959i	$0.615436\pi$
$602$	11.8309	+	9.92726i	0.482190	+	0.404605i
$603$	−8.95552	+	41.9992i	−0.364697	+	1.71034i
$604$	−17.4634	+	14.6535i	−0.710575	+	0.596243i
$605$	−6.41852	+	6.80324i	−0.260950	+	0.276591i
$606$	−9.04989	−	6.18542i	−0.367627	−	0.251265i
$607$	−28.7677	−	14.4477i	−1.16765	−	0.586414i	−0.244043	−	0.969764i	$-0.578474\pi$
$607$	−28.7677	−	14.4477i	−1.16765	−	0.586414i	−0.923603	+	0.383350i	$0.874770\pi$
$608$	3.92205	+	1.96973i	0.159060	+	0.0798831i
$609$	−28.9238	−	19.7689i	−1.17205	−	0.801074i
$610$	3.37047	−	3.57249i	0.136466	−	0.144646i
$611$	6.82638	−	5.72801i	0.276166	−	0.231730i
$612$	4.32969	−	1.40371i	0.175017	−	0.0567418i
$613$	−17.0259	−	14.2864i	−0.687670	−	0.577024i	0.230566	−	0.973057i	$-0.425942\pi$
$613$	−17.0259	−	14.2864i	−0.687670	−	0.577024i	−0.918236	+	0.396033i	$0.870387\pi$
$614$	−16.7667	+	1.95975i	−0.676650	+	0.0790891i
$615$	−11.8776	+	9.61194i	−0.478950	+	0.387591i
$616$	8.83666	+	9.36631i	0.356039	+	0.377379i
$617$	33.2913	+	3.89120i	1.34026	+	0.156654i	0.755817	−	0.654783i	$-0.227240\pi$
$617$	33.2913	+	3.89120i	1.34026	+	0.156654i	0.584441	+	0.811437i	$0.301314\pi$
$618$	−27.2643	+	17.2457i	−1.09673	+	0.693724i
$619$	0.202006	−	3.46831i	0.00811931	−	0.139403i	−0.991812	−	0.127704i	$-0.959239\pi$
$619$	0.202006	−	3.46831i	0.00811931	−	0.139403i	0.999932	−	0.0116986i	$-0.00372387\pi$
$620$	−2.92968	−	5.07435i	−0.117659	−	0.203791i
$621$	0.185935	+	38.3361i	0.00746133	+	1.53838i
$622$	12.5444	−	21.7275i	0.502983	−	0.871192i
$623$	−23.5988	−	15.5212i	−0.945467	−	0.621843i
$624$	2.05718	+	2.25964i	0.0823532	+	0.0904578i
$625$	5.04519	+	11.6961i	0.201807	+	0.467842i
$626$	−9.15572	+	2.16994i	−0.365936	+	0.0867284i
$627$	−34.8643	−	0.619807i	−1.39235	−	0.0247527i
$628$	−5.27188	−	7.08137i	−0.210371	−	0.282577i
$629$	−0.961673	+	0.350020i	−0.0383444	+	0.0139562i
$630$	−6.88069	−	3.76764i	−0.274133	−	0.150106i
$631$	38.5574	+	14.0337i	1.53494	+	0.558674i	0.964826	−	0.262888i	$-0.0846751\pi$
$631$	38.5574	+	14.0337i	1.53494	+	0.558674i	0.570118	+	0.821563i	$0.306897\pi$
$632$	1.02033	+	3.40815i	0.0405867	+	0.135569i
$633$	11.4784	+	16.0044i	0.456224	+	0.636116i
$634$	−0.782151	−	13.4290i	−0.0310632	−	0.533334i
$635$	6.63026	−	4.36079i	0.263114	−	0.173053i
$636$	4.49311	+	1.14961i	0.178163	+	0.0455849i
$637$	−1.51157	−	0.358249i	−0.0598906	−	0.0141943i
$638$	−5.73930	−	32.5492i	−0.227221	−	1.28864i
$639$	0.0796352	−	0.847140i	0.00315032	−	0.0335123i
$640$	−0.161751	+	0.917337i	−0.00639378	+	0.0362609i
$641$	−9.47251	+	21.9598i	−0.374142	+	0.867358i	0.622277	+	0.782797i	$0.286208\pi$
$641$	−9.47251	+	21.9598i	−0.374142	+	0.867358i	−0.996418	+	0.0845606i	$0.973051\pi$
$642$	−0.351313	+	1.80424i	−0.0138652	+	0.0712076i
$643$	5.06218	−	16.9089i	0.199633	−	0.666821i	−0.798282	−	0.602284i	$-0.794258\pi$
$643$	5.06218	−	16.9089i	0.199633	−	0.666821i	0.997915	−	0.0645373i	$-0.0205572\pi$
$644$	−12.3680	+	16.6130i	−0.487366	+	0.654646i
$645$	−3.37023	−	8.21140i	−0.132703	−	0.323323i
$646$	−5.95048	+	2.98844i	−0.234118	+	0.117579i
$647$	28.7326			1.12959			0.564797	−	0.825230i	$-0.308954\pi$
$647$	28.7326			1.12959			0.564797	+	0.825230i	$0.308954\pi$
$648$	−5.87372	+	6.81905i	−0.230741	+	0.267878i
$649$	23.0965			0.906615
$650$	−6.51507	+	3.27199i	−0.255542	+	0.128338i
$651$	18.6973	−	24.2045i	0.732806	−	0.948649i
$652$	−12.6732	+	17.0231i	−0.496321	+	0.666675i
$653$	−5.44267	+	18.1798i	−0.212988	+	0.711430i	0.783006	+	0.622014i	$0.213685\pi$
$653$	−5.44267	+	18.1798i	−0.212988	+	0.711430i	−0.995994	+	0.0894161i	$0.971500\pi$
$654$	16.0021	+	13.9195i	0.625733	+	0.544296i
$655$	5.89122	−	13.6574i	0.230189	−	0.533638i
$656$	−1.64454	+	9.32665i	−0.0642085	+	0.364145i
$657$	−14.8824	+	31.3842i	−0.580618	+	1.22442i
$658$	2.46217	+	13.9637i	0.0959854	+	0.544360i
$659$	−28.0969	−	6.65909i	−1.09450	−	0.259401i	−0.356564	−	0.934271i	$-0.616052\pi$
$659$	−28.0969	−	6.65909i	−1.09450	−	0.259401i	−0.737937	+	0.674870i	$0.764200\pi$
$660$	−1.99619	−	7.12639i	−0.0777014	−	0.277394i
$661$	28.6512	−	18.8442i	1.11440	−	0.732955i	0.147746	−	0.989025i	$-0.452798\pi$
$661$	28.6512	−	18.8442i	1.11440	−	0.732955i	0.966658	+	0.256070i	$0.0824278\pi$
$662$	−0.817122	−	14.0294i	−0.0317583	−	0.545270i
$663$	−4.61371	+	0.456296i	−0.179182	+	0.0177211i
$664$	−3.06872	−	10.2502i	−0.119089	−	0.397787i
$665$	10.7844	+	3.92519i	0.418200	+	0.152212i
$666$	1.26534	−	1.57920i	0.0490310	−	0.0611927i
$667$	49.9542	−	18.1818i	1.93423	−	0.704003i
$668$	9.56408	+	12.8468i	0.370045	+	0.497057i
$669$	−14.9092	−	26.9173i	−0.576422	−	1.04068i
$670$	12.9743	−	3.07497i	0.501242	−	0.118796i
$671$	9.57971	+	22.2083i	0.369821	+	0.857341i
$672$	−4.75037	+	1.03704i	−0.183250	+	0.0400047i
$673$	−36.5808	−	24.0596i	−1.41009	−	0.927429i	−0.999881	−	0.0154368i	$-0.995086\pi$
$673$	−36.5808	−	24.0596i	−1.41009	−	0.927429i	−0.410207	−	0.911992i	$-0.634544\pi$
$674$	−3.26530	+	5.65566i	−0.125775	+	0.217848i
$675$	−11.8860	−	17.8823i	−0.457494	−	0.688292i
$676$	4.94367	+	8.56270i	0.190141	+	0.329334i
$677$	−2.24011	+	38.4612i	−0.0860945	+	1.47819i	0.628042	+	0.778179i	$0.283857\pi$
$677$	−2.24011	+	38.4612i	−0.0860945	+	1.47819i	−0.714137	+	0.700006i	$0.753181\pi$
$678$	−10.4463	−	5.48099i	−0.401189	−	0.210496i
$679$	−48.2491	−	5.63951i	−1.85163	−	0.216424i
$680$	−0.969823	−	1.02795i	−0.0371910	−	0.0394202i
$681$	−0.677560	−	4.28690i	−0.0259642	−	0.164274i
$682$	28.6589	−	3.34975i	1.09741	−	0.128268i
$683$	4.17850	+	3.50618i	0.159886	+	0.134160i	0.719221	−	0.694782i	$-0.244499\pi$
$683$	4.17850	+	3.50618i	0.159886	+	0.134160i	−0.559335	+	0.828942i	$0.688943\pi$
$684$	6.98447	−	11.1615i	0.267058	−	0.426769i
$685$	−7.68038	+	6.44460i	−0.293452	+	0.246236i
$686$	−11.7888	+	12.4954i	−0.450099	+	0.477077i
$687$	−0.593638	+	7.80077i	−0.0226487	+	0.297618i
$688$	−4.91637	−	2.46909i	−0.187435	−	0.0941332i
$689$	−4.22163	−	2.12018i	−0.160831	−	0.0807725i
$690$	10.7305	−	5.15229i	0.408503	−	0.196144i
$691$	17.2210	−	18.2532i	0.655117	−	0.694384i	−0.311605	−	0.950212i	$-0.600867\pi$
$691$	17.2210	−	18.2532i	0.655117	−	0.694384i	0.966722	+	0.255828i	$0.0823481\pi$
$692$	−8.64976	+	7.25801i	−0.328815	+	0.275908i
$693$	30.4567	−	23.7638i	1.15696	−	0.902711i
$694$	−20.6346	−	17.3145i	−0.783279	−	0.657250i
$695$	−5.96327	+	0.697007i	−0.226200	+	0.0264390i
$696$	11.6497	+	4.47620i	0.441579	+	0.169670i
$697$	−9.86028	−	10.4513i	−0.373485	−	0.395871i
$698$	25.0672	+	2.92993i	0.948807	+	0.110900i
$699$	−0.856104	−	21.1782i	−0.0323808	−	0.801033i
$700$	0.674502	−	11.5807i	0.0254938	−	0.437711i
$701$	−3.42730	−	5.93625i	−0.129447	−	0.224209i	0.794015	−	0.607898i	$-0.207987\pi$
$701$	−3.42730	−	5.93625i	−0.129447	−	0.224209i	−0.923463	+	0.383689i	$0.874654\pi$
$702$	7.32676	−	5.51000i	0.276531	−	0.207962i
$703$	−1.48023	+	2.56383i	−0.0558278	+	0.0966966i
$704$	−3.83243	−	2.52063i	−0.144440	−	0.0949998i
$705$	2.47558	−	7.76396i	0.0932357	−	0.292408i
$706$	−0.380011	−	0.880965i	−0.0143019	−	0.0331556i
$707$	−17.2874	+	4.09718i	−0.650158	+	0.154090i
$708$	−4.49412	+	7.47400i	−0.168899	+	0.280890i
$709$	−17.0943	−	22.9617i	−0.641991	−	0.862344i	0.355386	−	0.934720i	$-0.384349\pi$
$709$	−17.0943	−	22.9617i	−0.641991	−	0.862344i	−0.997377	+	0.0723754i	$0.976942\pi$
$710$	−0.248260	+	0.0903594i	−0.00931705	+	0.00339113i
$711$	10.4661	−	2.09064i	0.392508	−	0.0784050i
$712$	9.45495	+	3.44132i	0.354339	+	0.128969i
$713$	13.3103	+	44.4595i	0.498474	+	1.66502i
$714$	3.04179	−	6.72061i	0.113836	−	0.251513i
$715$	0.438316	+	7.52560i	0.0163921	+	0.281442i
$716$	16.6646	−	10.9605i	0.622785	−	0.409612i
$717$	−32.0922	+	32.8267i	−1.19851	+	1.22594i
$718$	16.0029	+	3.79276i	0.597223	+	0.141545i
$719$	−1.27419	−	7.22626i	−0.0475191	−	0.269494i	0.951786	−	0.306762i	$-0.0992456\pi$
$719$	−1.27419	−	7.22626i	−0.0475191	−	0.269494i	−0.999305	+	0.0372680i	$0.988134\pi$
$720$	2.69451	+	0.740690i	0.100419	+	0.0276039i
$721$	−9.07949	+	51.4924i	−0.338138	+	1.91768i
$722$	−0.103910	+	0.240890i	−0.00386712	+	0.00896500i
$723$	8.94182	−	3.07569i	0.332550	−	0.114386i
$724$	6.10386	−	20.3883i	0.226848	−	0.757725i
$725$	−17.7803	+	23.8831i	−0.660344	+	0.886996i
$726$	17.2355	+	2.32578i	0.639668	+	0.0863177i
$727$	13.3751	−	6.71724i	0.496056	−	0.249129i	−0.183138	−	0.983087i	$-0.558626\pi$
$727$	13.3751	−	6.71724i	0.496056	−	0.249129i	0.679194	+	0.733958i	$0.262329\pi$
$728$	4.95270			0.183559
$729$	18.7182	+	19.4584i	0.693265	+	0.720683i
$730$	10.7848			0.399163
$731$	7.45903	−	3.74607i	0.275882	−	0.138553i
$732$	−9.05061	−	1.22130i	−0.334520	−	0.0451406i
$733$	0.198111	−	0.266109i	0.00731738	−	0.00982895i	−0.798449	−	0.602062i	$-0.794346\pi$
$733$	0.198111	−	0.266109i	0.00731738	−	0.00982895i	0.805767	+	0.592233i	$0.201753\pi$
$734$	0.488854	−	1.63289i	0.0180439	−	0.0602709i
$735$	−1.34334	+	0.462065i	−0.0495499	+	0.0170435i
$736$	2.92223	−	6.77448i	0.107715	−	0.249711i
$737$	−11.4019	+	64.6636i	−0.419996	+	2.38192i
$738$	27.3954	+	7.53067i	1.00844	+	0.277208i
$739$	0.921946	+	5.22861i	0.0339143	+	0.192338i	0.997058	−	0.0766494i	$-0.0244222\pi$
$739$	0.921946	+	5.22861i	0.0339143	+	0.192338i	−0.963144	+	0.268987i	$0.913311\pi$
$740$	−0.611383	−	0.144901i	−0.0224749	−	0.00532665i
$741$	−9.37554	+	9.59011i	−0.344419	+	0.352301i
$742$	6.28019	−	4.13055i	0.230553	−	0.151637i
$743$	−1.43288	−	24.6016i	−0.0525673	−	0.902547i	−0.916773	−	0.399408i	$-0.869216\pi$
$743$	−1.43288	−	24.6016i	−0.0525673	−	0.902547i	0.864206	−	0.503138i	$-0.167821\pi$
$744$	−4.49249	+	9.92581i	−0.164703	+	0.363898i
$745$	−0.00924772	−	0.0308895i	−0.000338810	−	0.00113171i
$746$	13.4262	+	4.88672i	0.491567	+	0.178916i
$747$	−31.4774	+	6.28773i	−1.15170	+	0.230056i
$748$	6.53970	−	2.38026i	0.239115	−	0.0870308i
$749$	1.77902	+	2.38964i	0.0650040	+	0.0873155i
$750$	−7.59262	+	12.6270i	−0.277243	+	0.461074i
$751$	38.8862	−	9.21620i	1.41898	−	0.336304i	0.551665	−	0.834066i	$-0.313993\pi$
$751$	38.8862	−	9.21620i	1.41898	−	0.336304i	0.867314	+	0.497762i	$0.165845\pi$
$752$	−2.00057	−	4.63784i	−0.0729533	−	0.169125i
$753$	−1.58085	+	4.95789i	−0.0576093	+	0.180676i
$754$	−10.6209	−	6.98546i	−0.386789	−	0.254395i
$755$	10.6175	−	18.3900i	0.386410	−	0.669282i
$756$	1.76367	+	14.4797i	0.0641440	+	0.526623i
$757$	−1.35834	−	2.35271i	−0.0493695	−	0.0855105i	0.840285	−	0.542146i	$-0.182388\pi$
$757$	−1.35834	−	2.35271i	−0.0493695	−	0.0855105i	−0.889654	+	0.456635i	$0.849055\pi$
$758$	1.40251	−	24.0801i	0.0509413	−	0.874628i
$759$	2.36760	+	58.5695i	0.0859385	+	2.12594i
$760$	−4.06055	−	0.474611i	−0.147292	−	0.0172159i
$761$	−5.86783	−	6.21954i	−0.212709	−	0.225458i	0.612231	−	0.790679i	$-0.290272\pi$
$761$	−5.86783	−	6.21954i	−0.212709	−	0.225458i	−0.824939	+	0.565221i	$0.808791\pi$
$762$	−13.7744	−	5.29258i	−0.498993	−	0.191730i
$763$	34.1420	−	3.99063i	1.23602	−	0.144471i
$764$	13.6565	+	11.4592i	0.494075	+	0.414579i
$765$	−3.34262	+	2.60807i	−0.120853	+	0.0942951i
$766$	−4.44327	+	3.72835i	−0.160542	+	0.134711i
$767$	6.09612	−	6.46151i	0.220118	−	0.233312i
$768$	1.56139	−	0.749708i	0.0563418	−	0.0270528i
$769$	−11.2283	−	5.63904i	−0.404901	−	0.203349i	0.234680	−	0.972073i	$-0.424596\pi$
$769$	−11.2283	−	5.63904i	−0.404901	−	0.203349i	−0.639581	+	0.768724i	$0.720892\pi$
$770$	−10.7188	−	5.38320i	−0.386280	−	0.193997i
$771$	1.72114	−	22.6169i	0.0619855	−	0.814528i
$772$	15.3362	−	16.2554i	0.551960	−	0.585044i
$773$	39.4061	−	33.0656i	1.41734	−	1.18929i	0.464590	−	0.885526i	$-0.346202\pi$
$773$	39.4061	−	33.0656i	1.41734	−	1.18929i	0.952748	−	0.303761i	$-0.0982426\pi$
$774$	−8.75516	+	13.9911i	−0.314698	+	0.502900i
$775$	−19.9123	−	16.7084i	−0.715271	−	0.600183i
$776$	17.1875	−	2.00893i	0.616994	−	0.0721163i
$777$	−0.512021	−	3.23954i	−0.0183687	−	0.116218i
$778$	14.1025	+	14.9478i	0.505599	+	0.535903i
$779$	−41.2841	−	4.82541i	−1.47915	−	0.172888i
$780$	−2.52057	−	1.32249i	−0.0902508	−	0.0473529i
$781$	0.0756466	−	1.29880i	0.00270685	−	0.0464748i
$782$	5.59680	+	9.69393i	0.200141	+	0.346654i
$783$	16.6406	−	33.5388i	0.594687	−	1.19858i
$784$	−0.440251	+	0.762537i	−0.0157232	+	0.0272334i
$785$	6.87058	+	4.51885i	0.245221	+	0.161285i
$786$	−27.0207	+	5.89880i	−0.963795	+	0.210403i
$787$	1.22244	+	2.83392i	0.0435751	+	0.101018i	0.938613	−	0.344971i	$-0.112111\pi$
$787$	1.22244	+	2.83392i	0.0435751	+	0.101018i	−0.895038	+	0.445989i	$0.852852\pi$
$788$	−3.97306	+	0.941633i	−0.141534	+	0.0335443i
$789$	2.63920	+	4.76487i	0.0939581	+	0.169634i
$790$	−1.97891	−	2.65813i	−0.0704063	−	0.0945721i
$791$	−17.9668	+	6.53937i	−0.638825	+	0.232513i
$792$	−8.60475	+	10.7391i	−0.305757	+	0.381597i
$793$	8.74152	+	3.18165i	0.310420	+	0.112984i
$794$	−4.20716	−	14.0529i	−0.149307	−	0.498719i
$795$	−4.29912	+	0.425183i	−0.152474	+	0.0150797i
$796$	0.0470760	+	0.808264i	0.00166857	+	0.0286482i
$797$	−14.5827	+	9.59119i	−0.516546	+	0.339738i	−0.780867	−	0.624697i	$-0.785222\pi$
$797$	−14.5827	+	9.59119i	−0.516546	+	0.339738i	0.264321	+	0.964435i	$0.414852\pi$
$798$	−5.75600	−	20.5489i	−0.203760	−	0.727425i
$799$	7.45662	+	1.76725i	0.263796	+	0.0625209i
$800$	0.717572	+	4.06955i	0.0253700	+	0.143880i
$801$	12.9334	−	27.2741i	0.456978	−	0.963683i
$802$	−4.63670	+	26.2960i	−0.163727	+	0.928544i
$803$	−21.0354	+	48.7656i	−0.742324	+	1.72090i
$804$	−18.7065	−	16.2719i	−0.659728	−	0.573867i
$805$	5.53311	−	18.4819i	0.195017	−	0.651401i
$806$	6.62716	−	8.90181i	0.233432	−	0.313553i
$807$	21.3931	−	27.6943i	0.753072	−	0.974884i
$808$	5.65559	−	2.84035i	0.198963	−	0.0999230i
$809$	55.0128			1.93415			0.967074	−	0.254495i	$-0.0819092\pi$
$809$	55.0128			1.93415			0.967074	+	0.254495i	$0.0819092\pi$
$810$	2.96887	−	7.84009i	0.104316	−	0.275473i
$811$	−0.195906			−0.00687919			−0.00343960	−	0.999994i	$-0.501095\pi$
$811$	−0.195906			−0.00687919			−0.00343960	+	0.999994i	$0.501095\pi$
$812$	18.0755	−	9.07787i	0.634326	−	0.318571i
$813$	19.5848	+	47.7175i	0.686870	+	1.67353i
$814$	1.84768	−	2.48187i	0.0647612	−	0.0869894i
$815$	5.66967	−	18.9380i	0.198600	−	0.663370i
$816$	−0.502247	+	2.57940i	−0.0175822	+	0.0902969i
$817$	9.56362	−	22.1710i	0.334589	−	0.775664i
$818$	1.69066	−	9.58820i	0.0591125	−	0.335244i
$819$	1.39060	−	14.7929i	0.0485916	−	0.516905i
$820$	−1.53187	−	8.68766i	−0.0534952	−	0.303386i
$821$	8.41661	+	1.99477i	0.293742	+	0.0696181i	0.374845	−	0.927088i	$-0.377696\pi$
$821$	8.41661	+	1.99477i	0.293742	+	0.0696181i	−0.0811028	+	0.996706i	$0.525844\pi$
$822$	18.0610	+	4.62110i	0.629951	+	0.161179i
$823$	−29.5504	+	19.4356i	−1.03006	+	0.677482i	−0.947714	−	0.319122i	$-0.896612\pi$
$823$	−29.5504	+	19.4356i	−1.03006	+	0.677482i	−0.0823472	+	0.996604i	$0.526242\pi$
$824$	−1.08299	−	18.5943i	−0.0377278	−	0.647762i
$825$	−19.1344	−	26.6792i	−0.666173	−	0.928850i
$826$	4.05389	+	13.5409i	0.141053	+	0.471150i
$827$	17.2621	+	6.28287i	0.600261	+	0.218477i	0.624236	−	0.781236i	$-0.285410\pi$
$827$	17.2621	+	6.28287i	0.600261	+	0.218477i	−0.0239758	+	0.999713i	$0.507632\pi$
$828$	−19.4137	−	10.6303i	−0.674674	−	0.369429i
$829$	−25.5086	+	9.28437i	−0.885951	+	0.322460i	−0.744609	−	0.667501i	$-0.767364\pi$
$829$	−25.5086	+	9.28437i	−0.885951	+	0.322460i	−0.141342	+	0.989961i	$0.545142\pi$
$830$	5.95169	+	7.99451i	0.206586	+	0.277493i
$831$	7.61919	+	0.135452i	0.264307	+	0.00469877i
$832$	−1.71671	+	0.406869i	−0.0595164	+	0.0141056i
$833$	−0.529116	−	1.22663i	−0.0183328	−	0.0425002i
$834$	7.51556	+	8.25520i	0.260243	+	0.285854i
$835$	−12.4644	−	8.19796i	−0.431348	−	0.283702i
$836$	10.0660	−	17.4349i	0.348141	−	0.602998i
$837$	28.3853	+	16.2052i	0.981141	+	0.560135i
$838$	−4.43326	−	7.67862i	−0.153144	−	0.265254i
$839$	−0.691745	+	11.8768i	−0.0238817	+	0.410033i	0.965089	+	0.261922i	$0.0843563\pi$
$839$	−0.691745	+	11.8768i	−0.0238817	+	0.410033i	−0.988971	+	0.148111i	$0.952681\pi$
$840$	3.82767	−	2.42114i	0.132067	−	0.0835374i
$841$	−22.7620	−	2.66050i	−0.784898	−	0.0917414i
$842$	−7.92129	−	8.39608i	−0.272986	−	0.289348i
$843$	−38.0710	+	30.8090i	−1.31123	+	1.06112i
$844$	−11.2940	+	1.32008i	−0.388756	+	0.0454391i
$845$	−7.05523	−	5.92004i	−0.242707	−	0.203656i
$846$	−14.4142	+	4.67317i	−0.495569	+	0.160667i
$847$	21.5929	−	18.1186i	0.741942	−	0.622564i
$848$	−1.83752	+	1.94766i	−0.0631008	+	0.0668830i
$849$	−10.4191	−	7.12122i	−0.357582	−	0.244400i
$850$	−5.60263	−	2.81375i	−0.192169	−	0.0965108i
$851$	4.44727	+	2.23350i	0.152451	+	0.0765635i
$852$	0.405573	+	0.277201i	0.0138947	+	0.00949674i
$853$	20.9646	−	22.2211i	0.717813	−	0.760837i	−0.261056	−	0.965324i	$-0.584071\pi$
$853$	20.9646	−	22.2211i	0.717813	−	0.760837i	0.978869	+	0.204486i	$0.0655523\pi$
$854$	−11.3388	+	9.51437i	−0.388005	+	0.325575i
$855$	−2.55769	+	11.9949i	−0.0874712	+	0.410218i
$856$	−0.812958	−	0.682153i	−0.0277863	−	0.0233155i
$857$	−26.5253	+	3.10036i	−0.906087	+	0.105906i	−0.556356	−	0.830944i	$-0.687801\pi$
$857$	−26.5253	+	3.10036i	−0.906087	+	0.105906i	−0.349731	+	0.936850i	$0.613727\pi$
$858$	10.8962	−	8.81777i	0.371991	−	0.301034i
$859$	12.8776	+	13.6495i	0.439379	+	0.465715i	0.908783	−	0.417269i	$-0.137013\pi$
$859$	12.8776	+	13.6495i	0.439379	+	0.465715i	−0.469404	+	0.882984i	$0.655531\pi$
$860$	5.08998	+	0.594933i	0.173567	+	0.0202870i
$861$	38.9163	−	24.6160i	1.32626	−	0.838911i
$862$	−1.57697	+	27.0755i	−0.0537118	+	0.922196i
$863$	20.7662	+	35.9682i	0.706891	+	1.22437i	0.966005	+	0.258525i	$0.0832363\pi$
$863$	20.7662	+	35.9682i	0.706891	+	1.22437i	−0.259113	+	0.965847i	$0.583430\pi$
$864$	−1.80085	−	4.87411i	−0.0612662	−	0.165821i
$865$	5.25893	−	9.10873i	0.178809	−	0.309706i
$866$	−1.55940	−	1.02564i	−0.0529907	−	0.0348525i
$867$	17.1384	+	18.8250i	0.582051	+	0.639332i
$868$	6.99410	+	16.2141i	0.237395	+	0.550344i
$869$	15.8791	−	3.76341i	0.538661	−	0.127665i
$870$	−11.6232	−	0.206633i	−0.394062	−	0.00700552i
$871$	15.0810	+	20.2573i	0.510999	+	0.686391i
$872$	−11.5065	+	4.18804i	−0.389661	+	0.141825i
$873$	−1.17449	−	51.9002i	−0.0397505	−	1.75655i
$874$	30.4279	+	11.0748i	1.02924	+	0.374612i
$875$	6.84888	+	22.8769i	0.231535	+	0.773379i
$876$	−11.6874	−	16.2959i	−0.394882	−	0.550587i
$877$	−2.80398	−	48.1425i	−0.0946838	−	1.62566i	−0.626935	−	0.779072i	$-0.715691\pi$
$877$	−2.80398	−	48.1425i	−0.0946838	−	1.62566i	0.532251	−	0.846587i	$-0.321346\pi$
$878$	−4.57484	+	3.00892i	−0.154393	+	0.101546i
$879$	0.652922	+	0.167057i	0.0220225	+	0.00563468i
$880$	4.15761	+	0.985373i	0.140153	+	0.0332169i
$881$	−6.90826	−	39.1787i	−0.232745	−	1.31996i	−0.847310	−	0.531098i	$-0.821780\pi$
$881$	−6.90826	−	39.1787i	−0.232745	−	1.31996i	0.614565	−	0.788866i	$-0.289331\pi$
$882$	2.15396	+	1.52906i	0.0725275	+	0.0514860i
$883$	0.0528584	−	0.299775i	0.00177883	−	0.0100882i	−0.983905	−	0.178690i	$-0.942814\pi$
$883$	0.0528584	−	0.299775i	0.00177883	−	0.0100882i	0.985684	+	0.168602i	$0.0539252\pi$
$884$	1.06020	−	2.45781i	0.0356582	−	0.0826651i
$885$	1.55263	−	7.97386i	0.0521911	−	0.268038i
$886$	−3.27873	+	10.9517i	−0.110151	+	0.367930i
$887$	−12.3866	+	16.6381i	−0.415901	+	0.558652i	−0.959867	−	0.280455i	$-0.909515\pi$
$887$	−12.3866	+	16.6381i	−0.415901	+	0.558652i	0.543966	+	0.839107i	$0.316922\pi$
$888$	0.443609	+	1.08083i	0.0148865	+	0.0362703i
$889$	−21.3722	+	10.7335i	−0.716800	+	0.359991i
$890$	−9.37239			−0.314163
$891$	29.6598	+	28.7162i	0.993642	+	0.962030i
$892$	17.7654			0.594829
$893$	19.8100	−	9.94896i	0.662917	−	0.332929i
$894$	−0.0366525	+	0.0474483i	−0.00122584	+	0.00158691i
$895$	−11.0948	+	14.9030i	−0.370860	+	0.498151i
$896$	0.805121	−	2.68929i	0.0268972	−	0.0898429i
$897$	17.0104	+	14.7966i	0.567961	+	0.494043i
$898$	0.231329	−	0.536281i	0.00771956	−	0.0178959i
$899$	7.87041	−	44.6353i	0.262493	−	1.48867i
$900$	12.3565	−	1.00063i	0.411885	−	0.0333544i
$901$	−0.705447	−	4.00079i	−0.0235018	−	0.133286i
$902$	42.2709	+	10.0184i	1.40747	+	0.333576i
$903$	7.21525	+	25.7585i	0.240109	+	0.857188i
$904$	5.69046	−	3.74268i	0.189262	−	0.124480i
$905$	1.15268	+	19.7907i	0.0383164	+	0.657866i
$906$	−39.2936	+	3.88613i	−1.30544	+	0.129108i
$907$	−6.46164	−	21.5834i	−0.214555	−	0.716664i	−0.995727	−	0.0923479i	$-0.970563\pi$
$907$	−6.46164	−	21.5834i	−0.214555	−	0.716664i	0.781172	−	0.624316i	$-0.214622\pi$
$908$	2.35465	+	0.857022i	0.0781418	+	0.0284413i
$909$	−6.89568	−	17.6898i	−0.228715	−	0.586734i
$910$	−4.33516	+	1.57787i	−0.143709	+	0.0523059i
$911$	−10.4625	−	14.0536i	−0.346640	−	0.465618i	0.594275	−	0.804262i	$-0.297439\pi$
$911$	−10.4625	−	14.0536i	−0.346640	−	0.465618i	−0.940915	+	0.338644i	$0.890032\pi$
$912$	3.68327	+	6.64985i	0.121965	+	0.220199i
$913$	−47.7574	+	11.3187i	−1.58054	+	0.374594i
$914$	−5.17077	−	11.9872i	−0.171034	−	0.396501i
$915$	8.31120	−	1.81439i	0.274760	−	0.0599820i
$916$	−3.77373	−	2.48202i	−0.124688	−	0.0820083i
$917$	−22.4126	+	38.8197i	−0.740129	+	1.28194i
$918$	7.56320	+	2.22436i	0.249623	+	0.0734149i
$919$	6.84333	+	11.8530i	0.225741	+	0.390994i	0.956541	−	0.291597i	$-0.0941865\pi$
$919$	6.84333	+	11.8530i	0.225741	+	0.390994i	−0.730801	+	0.682591i	$0.760853\pi$
$920$	−0.399595	+	6.86077i	−0.0131742	+	0.226193i
$921$	−25.8911	−	13.5846i	−0.853142	−	0.447628i
$922$	−11.5943	−	1.35518i	−0.381838	−	0.0446305i
$923$	−0.343389	−	0.363971i	−0.0113028	−	0.0119803i
$924$	3.48192	+	22.0300i	0.114547	+	0.724733i
$925$	−2.76855	+	0.323597i	−0.0910293	+	0.0106398i
$926$	−7.53467	−	6.32234i	−0.247605	−	0.207765i
$927$	−55.8420	−	1.98612i	−1.83409	−	0.0652326i
$928$	−5.51961	+	4.63151i	−0.181190	+	0.152037i
$929$	24.0142	−	25.4536i	0.787880	−	0.835104i	−0.201646	−	0.979459i	$-0.564629\pi$
$929$	24.0142	−	25.4536i	0.787880	−	0.835104i	0.989526	+	0.144354i	$0.0461105\pi$
$930$	0.770088	−	10.1194i	0.0252522	−	0.331829i
$931$	−3.45337	−	1.73435i	−0.113180	−	0.0568410i
$932$	10.9356	+	5.49206i	0.358207	+	0.179898i
$933$	39.1733	−	18.8092i	1.28248	−	0.615786i
$934$	−12.2377	+	12.9712i	−0.400430	+	0.424431i
$935$	−4.96596	+	4.16694i	−0.162404	+	0.136273i
$936$	0.733236	+	5.24178i	0.0239666	+	0.171333i
$937$	16.4755	+	13.8246i	0.538230	+	0.451629i	0.870932	−	0.491403i	$-0.163516\pi$
$937$	16.4755	+	13.8246i	0.538230	+	0.451629i	−0.332702	+	0.943032i	$0.607960\pi$
$938$	−39.9121	+	4.66506i	−1.30318	+	0.152320i
$939$	−15.2131	−	5.84540i	−0.496461	−	0.190757i
$940$	3.22868	+	3.42220i	0.105308	+	0.111620i
$941$	3.44570	+	0.402744i	0.112326	+	0.0131291i	0.172070	−	0.985085i	$-0.444954\pi$
$941$	3.44570	+	0.402744i	0.112326	+	0.0131291i	−0.0597439	+	0.998214i	$0.519028\pi$
$942$	−0.617617	−	15.2785i	−0.0201230	−	0.497802i
$943$	−4.06272	+	69.7542i	−0.132300	+	2.27151i
$944$	−2.51757	−	4.36056i	−0.0819399	−	0.141924i
$945$	−6.15683	−	12.1124i	−0.200282	−	0.394017i
$946$	−12.6180	+	21.8550i	−0.410245	+	0.710566i
$947$	−43.1639	−	28.3894i	−1.40264	−	0.922530i	−0.999974	−	0.00718267i	$-0.997714\pi$
$947$	−43.1639	−	28.3894i	−1.40264	−	0.922530i	−0.402665	−	0.915348i	$-0.631916\pi$
$948$	−1.87192	+	5.87075i	−0.0607971	+	0.190673i
$949$	8.09063	+	18.7562i	0.262633	+	0.608852i
$950$	−17.6475	+	4.18253i	−0.572560	+	0.135699i
$951$	12.0064	−	19.9674i	0.389334	−	0.647487i
$952$	2.54334	+	3.41630i	0.0824302	+	0.110723i
$953$	−1.06059	+	0.386024i	−0.0343559	+	0.0125045i	−0.359141	−	0.933283i	$-0.616930\pi$
$953$	−1.06059	+	0.386024i	−0.0343559	+	0.0125045i	0.324785	+	0.945788i	$0.394708\pi$
$954$	5.30140	+	6.03523i	0.171639	+	0.195398i
$955$	−15.6045	−	5.67956i	−0.504949	−	0.183786i
$956$	−7.60165	−	25.3913i	−0.245855	−	0.821212i
$957$	23.6050	−	52.1534i	0.763040	−	1.68588i
$958$	2.09425	+	35.9569i	0.0676622	+	1.16171i
$959$	25.2446	−	16.6036i	0.815191	−	0.536159i
$960$	−1.12786	+	1.15367i	−0.0364014	+	0.0372345i
$961$	8.33709	+	1.97593i	0.268938	+	0.0637395i
$962$	−0.206652	−	1.17198i	−0.00666272	−	0.0377861i
$963$	−2.26574	+	2.23664i	−0.0730123	+	0.0720746i
$964$	−0.948020	+	5.37649i	−0.0305337	+	0.173165i
$965$	−8.24516	+	19.1144i	−0.265421	+	0.615316i
$966$	−33.9224	+	11.6682i	−1.09144	+	0.375418i
$967$	3.58456	−	11.9733i	0.115272	−	0.385035i	−0.880810	−	0.473470i	$-0.843001\pi$
$967$	3.58456	−	11.9733i	0.115272	−	0.385035i	0.996082	+	0.0884350i	$0.0281866\pi$
$968$	−5.99612	+	8.05419i	−0.192723	+	0.258872i
$969$	−11.4297	−	1.54234i	−0.367175	−	0.0495471i
$970$	−14.4044	+	7.23416i	−0.462497	+	0.232275i
$971$	13.7306			0.440635			0.220318	−	0.975428i	$-0.429291\pi$
$971$	13.7306			0.440635			0.220318	+	0.975428i	$0.429291\pi$
$972$	−15.0638	+	4.01030i	−0.483171	+	0.128630i
$973$	18.0939			0.580062
$974$	−25.2719	+	12.6920i	−0.809765	+	0.406679i
$975$	−12.5142	−	1.68868i	−0.400774	−	0.0540810i
$976$	3.14866	−	4.22938i	0.100786	−	0.135379i
$977$	1.36028	−	4.54365i	0.0435192	−	0.145364i	−0.933469	−	0.358659i	$-0.883234\pi$
$977$	1.36028	−	4.54365i	0.0435192	−	0.145364i	0.976988	+	0.213295i	$0.0684194\pi$
$978$	−34.7597	+	11.9562i	−1.11149	+	0.382316i
$979$	18.2806	−	42.3792i	0.584250	−	1.35444i
$980$	0.142422	−	0.807716i	0.00454951	−	0.0258015i
$981$	9.27820	+	35.5440i	0.296230	+	1.13483i
$982$	−0.763784	−	4.33163i	−0.0243733	−	0.138228i
$983$	25.3644	+	6.01148i	0.808999	+	0.191736i	0.614245	−	0.789116i	$-0.289461\pi$
$983$	25.3644	+	6.01148i	0.808999	+	0.191736i	0.194754	+	0.980852i	$0.437609\pi$
$984$	−11.4670	+	11.7295i	−0.365555	+	0.373921i
$985$	3.17768	−	2.08999i	0.101249	−	0.0665926i
$986$	−0.635629	−	10.9133i	−0.0202426	−	0.347551i
$987$	−10.1266	+	22.3739i	−0.322332	+	0.712169i
$988$	−2.22077	−	7.41789i	−0.0706521	−	0.235995i
$989$	−38.1419	−	13.8825i	−1.21284	−	0.441438i
$990$	4.11050	−	12.1414i	0.130640	−	0.385880i
$991$	−18.1061	+	6.59007i	−0.575158	+	0.209340i	−0.613189	−	0.789936i	$-0.710114\pi$
$991$	−18.1061	+	6.59007i	−0.575158	+	0.209340i	0.0380312	+	0.999277i	$0.487891\pi$
$992$	−3.75631	−	5.04561i	−0.119263	−	0.160198i
$993$	12.5432	−	20.8602i	0.398047	−	0.661977i
$994$	0.774737	−	0.183616i	0.0245732	−	0.00582395i
$995$	−0.298709	−	0.692486i	−0.00946972	−	0.0219533i
$996$	5.62992	−	17.6567i	0.178391	−	0.559473i
$997$	−20.9254	−	13.7628i	−0.662713	−	0.435873i	0.173088	−	0.984906i	$-0.444626\pi$
$997$	−20.9254	−	13.7628i	−0.662713	−	0.435873i	−0.835800	+	0.549033i	$0.814996\pi$
$998$	7.92200	−	13.7213i	0.250766	−	0.434340i
$999$	3.35282	−	1.02151i	0.106078	−	0.0323192i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.g.a.25.1	yes	72
3.2	odd	2		486.2.g.a.73.3		72
81.13	even	27	inner	162.2.g.a.13.1	✓	72
81.68	odd	54		486.2.g.a.253.3		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.g.a.13.1	✓	72	81.13	even	27	inner
162.2.g.a.25.1	yes	72	1.1	even	1	trivial
486.2.g.a.73.3		72	3.2	odd	2
486.2.g.a.253.3		72	81.68	odd	54

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:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.g (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.893633 + 0.448799i) q^{2} +(-1.71649 - 0.231626i) q^{3} +(0.597159 - 0.802123i) q^{4} +(-0.267154 + 0.892356i) q^{5} +(1.63787 - 0.563372i) q^{6} +(1.11188 - 2.57764i) q^{7} +(-0.173648 + 0.984808i) q^{8} +(2.89270 + 0.795169i) q^{9} +O(q^{10})\)	\(q+(-0.893633 + 0.448799i) q^{2} +(-1.71649 - 0.231626i) q^{3} +(0.597159 - 0.802123i) q^{4} +(-0.267154 + 0.892356i) q^{5} +(1.63787 - 0.563372i) q^{6} +(1.11188 - 2.57764i) q^{7} +(-0.173648 + 0.984808i) q^{8} +(2.89270 + 0.795169i) q^{9} +(-0.161751 - 0.917337i) q^{10} +(4.46341 + 1.05785i) q^{11} +(-1.21081 + 1.23852i) q^{12} +(1.47403 - 0.969483i) q^{13} +(0.163226 + 2.80247i) q^{14} +(0.665260 - 1.46984i) q^{15} +(-0.286803 - 0.957990i) q^{16} +(1.42569 + 0.518907i) q^{17} +(-2.94188 + 0.587652i) q^{18} +(4.12421 - 1.50109i) q^{19} +(0.556246 + 0.747168i) q^{20} +(-2.50559 + 4.16696i) q^{21} +(-4.46341 + 1.05785i) q^{22} +(-2.92223 - 6.77448i) q^{23} +(0.526173 - 1.65019i) q^{24} +(3.45251 + 2.27075i) q^{25} +(-0.882135 + 1.52790i) q^{26} +(-4.78112 - 2.03493i) q^{27} +(-1.40361 - 2.43113i) q^{28} +(-0.418954 + 7.19315i) q^{29} +(0.0651659 + 1.61207i) q^{30} +(-6.24778 - 0.730261i) q^{31} +(0.686242 + 0.727374i) q^{32} +(-7.41639 - 2.84963i) q^{33} +(-1.50693 + 0.176134i) q^{34} +(2.00313 + 1.68082i) q^{35} +(2.36522 - 1.84546i) q^{36} +(-0.516723 + 0.433582i) q^{37} +(-3.01184 + 3.19236i) q^{38} +(-2.75471 + 1.32269i) q^{39} +(-0.832408 - 0.418051i) q^{40} +(-8.46317 - 4.25037i) q^{41} +(0.368950 - 4.84823i) q^{42} +(3.77539 - 4.00168i) q^{43} +(3.51389 - 2.94850i) q^{44} +(-1.48237 + 2.36888i) q^{45} +(5.65178 + 4.74241i) q^{46} +(5.01677 - 0.586377i) q^{47} +(0.270401 + 1.71081i) q^{48} +(-0.604237 - 0.640453i) q^{49} +(-4.10439 - 0.479734i) q^{50} +(-2.32699 - 1.22093i) q^{51} +(0.102583 - 1.76129i) q^{52} +(-1.33883 - 2.31892i) q^{53} +(5.18583 - 0.327285i) q^{54} +(-2.13639 + 3.70034i) q^{55} +(2.34540 + 1.54259i) q^{56} +(-7.42686 + 1.62134i) q^{57} +(-2.85389 - 6.61606i) q^{58} +(4.89941 - 1.16118i) q^{59} +(-0.781729 - 1.41135i) q^{60} +(3.14866 + 4.22938i) q^{61} +(5.91096 - 2.15141i) q^{62} +(5.26600 - 6.57219i) q^{63} +(-0.939693 - 0.342020i) q^{64} +(0.471331 + 1.57436i) q^{65} +(7.90644 - 0.781947i) q^{66} +(0.832311 + 14.2902i) q^{67} +(1.26759 - 0.833706i) q^{68} +(3.44684 + 12.3052i) q^{69} +(-2.54441 - 0.603036i) q^{70} +(-0.0492509 - 0.279316i) q^{71} +(-1.28540 + 2.71067i) q^{72} +(-2.01050 + 11.4021i) q^{73} +(0.267169 - 0.619368i) q^{74} +(-5.40025 - 4.69742i) q^{75} +(1.25875 - 4.20451i) q^{76} +(7.68955 - 10.3289i) q^{77} +(1.86808 - 2.41831i) q^{78} +(3.17920 - 1.59665i) q^{79} +0.931488 q^{80} +(7.73541 + 4.60037i) q^{81} +9.47053 q^{82} +(-9.56164 + 4.80204i) q^{83} +(1.84618 + 4.49813i) q^{84} +(-0.843927 + 1.13359i) q^{85} +(-1.57786 + 5.27043i) q^{86} +(2.38525 - 12.2500i) q^{87} +(-1.81684 + 4.21191i) q^{88} +(1.74720 - 9.90888i) q^{89} +(0.261540 - 2.78220i) q^{90} +(-0.860028 - 4.87746i) q^{91} +(-7.17900 - 1.70145i) q^{92} +(10.5551 + 2.70064i) q^{93} +(-4.21999 + 2.77553i) q^{94} +(0.237708 + 4.08128i) q^{95} +(-1.00945 - 1.40748i) q^{96} +(-4.96298 - 16.5775i) q^{97} +(0.827401 + 0.301149i) q^{98} +(12.0701 + 6.60920i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 9 q^{6}+O(q^{10}) \) 72 * q + 9 * q^6	\( 72 q + 9 q^{6} + 18 q^{13} - 9 q^{20} - 81 q^{23} + 18 q^{25} - 27 q^{26} - 27 q^{27} + 18 q^{28} - 27 q^{29} - 63 q^{30} - 54 q^{31} + 9 q^{33} - 27 q^{35} - 9 q^{36} + 9 q^{38} - 9 q^{41} + 9 q^{42} + 36 q^{43} - 117 q^{45} - 18 q^{46} - 27 q^{47} + 9 q^{48} - 27 q^{51} - 36 q^{52} - 27 q^{53} + 54 q^{55} + 27 q^{57} + 9 q^{58} - 18 q^{59} + 9 q^{63} + 9 q^{65} + 36 q^{66} - 135 q^{67} - 18 q^{68} + 108 q^{69} + 18 q^{70} + 72 q^{71} + 54 q^{72} + 36 q^{73} + 99 q^{74} - 36 q^{75} - 9 q^{76} + 144 q^{77} + 90 q^{78} - 9 q^{79} + 18 q^{80} - 72 q^{82} + 99 q^{83} + 18 q^{84} + 9 q^{85} + 72 q^{86} + 207 q^{87} - 9 q^{88} + 126 q^{89} - 18 q^{90} + 63 q^{91} + 36 q^{92} + 81 q^{93} + 18 q^{94} + 45 q^{95} - 171 q^{97} + 36 q^{98} + 99 q^{99}+O(q^{100}) \) 72 * q + 9 * q^6 + 18 * q^13 - 9 * q^20 - 81 * q^23 + 18 * q^25 - 27 * q^26 - 27 * q^27 + 18 * q^28 - 27 * q^29 - 63 * q^30 - 54 * q^31 + 9 * q^33 - 27 * q^35 - 9 * q^36 + 9 * q^38 - 9 * q^41 + 9 * q^42 + 36 * q^43 - 117 * q^45 - 18 * q^46 - 27 * q^47 + 9 * q^48 - 27 * q^51 - 36 * q^52 - 27 * q^53 + 54 * q^55 + 27 * q^57 + 9 * q^58 - 18 * q^59 + 9 * q^63 + 9 * q^65 + 36 * q^66 - 135 * q^67 - 18 * q^68 + 108 * q^69 + 18 * q^70 + 72 * q^71 + 54 * q^72 + 36 * q^73 + 99 * q^74 - 36 * q^75 - 9 * q^76 + 144 * q^77 + 90 * q^78 - 9 * q^79 + 18 * q^80 - 72 * q^82 + 99 * q^83 + 18 * q^84 + 9 * q^85 + 72 * q^86 + 207 * q^87 - 9 * q^88 + 126 * q^89 - 18 * q^90 + 63 * q^91 + 36 * q^92 + 81 * q^93 + 18 * q^94 + 45 * q^95 - 171 * q^97 + 36 * q^98 + 99 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more