LMFDB - Embedded newform 378.2.bf.a.101.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(5,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 15]))

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

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

chi := DirichletCharacter("378.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.bf (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.01834519640$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$24$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.11
Character	$\chi$	$=$	378.101
Dual form			378.2.bf.a.131.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.642788 + 0.766044i) q^{2} +(1.60013 + 0.663016i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(1.58293 - 1.32824i) q^{5} +(-1.53644 + 0.799591i) q^{6} +(-1.15983 - 2.37798i) q^{7} +(0.866025 + 0.500000i) q^{8} +(2.12082 + 2.12182i) q^{9} +O(q^{10})$	\(q+(-0.642788 + 0.766044i) q^{2} +(1.60013 + 0.663016i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(1.58293 - 1.32824i) q^{5} +(-1.53644 + 0.799591i) q^{6} +(-1.15983 - 2.37798i) q^{7} +(0.866025 + 0.500000i) q^{8} +(2.12082 + 2.12182i) q^{9} +2.06637i q^{10} +(0.979112 - 1.16686i) q^{11} +(0.375084 - 1.69095i) q^{12} +(0.512757 - 1.40879i) q^{13} +(2.56716 + 0.640057i) q^{14} +(3.41353 - 1.07584i) q^{15} +(-0.939693 + 0.342020i) q^{16} +2.18170 q^{17} +(-2.98865 + 0.260763i) q^{18} +1.55746i q^{19} +(-1.58293 - 1.32824i) q^{20} +(-0.279235 - 4.57406i) q^{21} +(0.264506 + 1.50009i) q^{22} +(1.80546 - 4.96047i) q^{23} +(1.05424 + 1.37425i) q^{24} +(-0.126785 + 0.719036i) q^{25} +(0.749601 + 1.29835i) q^{26} +(1.98678 + 4.80132i) q^{27} +(-2.14045 + 1.55514i) q^{28} +(0.292152 + 0.802682i) q^{29} +(-1.37003 + 3.30645i) q^{30} +(-7.09072 + 1.25028i) q^{31} +(0.342020 - 0.939693i) q^{32} +(2.34035 - 1.21796i) q^{33} +(-1.40237 + 1.67128i) q^{34} +(-4.99444 - 2.22365i) q^{35} +(1.72131 - 2.45705i) q^{36} +(-4.94601 + 8.56674i) q^{37} +(-1.19308 - 1.00112i) q^{38} +(1.75453 - 1.91428i) q^{39} +(2.03497 - 0.358821i) q^{40} +(9.51907 + 3.46466i) q^{41} +(3.68342 + 2.72624i) q^{42} +(0.210646 - 1.19463i) q^{43} +(-1.31915 - 0.761614i) q^{44} +(6.17538 + 0.541742i) q^{45} +(2.63941 + 4.57159i) q^{46} +(-0.626980 + 3.55578i) q^{47} +(-1.73039 - 0.0757548i) q^{48} +(-4.30960 + 5.51610i) q^{49} +(-0.469317 - 0.559310i) q^{50} +(3.49099 + 1.44650i) q^{51} +(-1.47643 - 0.260334i) q^{52} +(-4.42176 - 2.55290i) q^{53} +(-4.95511 - 1.56426i) q^{54} -3.14755i q^{55} +(0.184550 - 2.63931i) q^{56} +(-1.03262 + 2.49213i) q^{57} +(-0.802682 - 0.292152i) q^{58} +(4.37913 + 1.59387i) q^{59} +(-1.65225 - 3.17485i) q^{60} +(-4.87597 - 0.859765i) q^{61} +(3.60005 - 6.23547i) q^{62} +(2.58586 - 7.50422i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-1.05954 - 2.91107i) q^{65} +(-0.571338 + 2.57570i) q^{66} +(4.69157 - 3.93670i) q^{67} +(-0.378848 - 2.14855i) q^{68} +(6.17784 - 6.74033i) q^{69} +(4.91378 - 2.39663i) q^{70} +(-4.04327 + 2.33438i) q^{71} +(0.775774 + 2.89796i) q^{72} +(-8.09329 + 4.67267i) q^{73} +(-3.38327 - 9.29546i) q^{74} +(-0.679605 + 1.06649i) q^{75} +(1.53380 - 0.270450i) q^{76} +(-3.91037 - 0.974952i) q^{77} +(0.338633 + 2.57452i) q^{78} +(-6.29944 - 5.28586i) q^{79} +(-1.03318 + 1.78953i) q^{80} +(-0.00424038 + 9.00000i) q^{81} +(-8.77283 + 5.06499i) q^{82} +(9.24414 - 3.36459i) q^{83} +(-4.45608 + 1.06927i) q^{84} +(3.45347 - 2.89781i) q^{85} +(0.779740 + 0.929258i) q^{86} +(-0.0647095 + 1.47810i) q^{87} +(1.43137 - 0.520974i) q^{88} -18.6147 q^{89} +(-4.38446 + 4.38239i) q^{90} +(-3.94478 + 0.414626i) q^{91} +(-5.19862 - 0.916657i) q^{92} +(-12.1750 - 2.70064i) q^{93} +(-2.32087 - 2.76590i) q^{94} +(2.06867 + 2.46535i) q^{95} +(1.17031 - 1.27686i) q^{96} +(6.71192 + 1.18349i) q^{97} +(-1.45543 - 6.84702i) q^{98} +(4.55239 - 0.397202i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q + 18 q^{6} - 12 q^{9}+O(q^{10}) $ 144 * q + 18 * q^6 - 12 * q^9	$ 144 q + 18 q^{6} - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 6 q^{21} - 6 q^{23} - 6 q^{29} - 18 q^{30} - 54 q^{35} + 6 q^{36} - 6 q^{39} + 24 q^{42} - 54 q^{47} + 18 q^{49} + 12 q^{50} + 18 q^{51} + 90 q^{53} - 54 q^{54} - 12 q^{56} - 6 q^{57} - 90 q^{59} - 36 q^{60} - 24 q^{63} + 72 q^{64} - 84 q^{65} - 36 q^{69} - 18 q^{70} - 72 q^{71} + 12 q^{72} + 18 q^{74} - 90 q^{75} - 78 q^{77} - 60 q^{78} + 36 q^{79} - 6 q^{84} - 72 q^{85} + 24 q^{86} + 90 q^{87} - 18 q^{91} - 42 q^{92} - 12 q^{93} + 78 q^{95} - 36 q^{98} - 108 q^{99}+O(q^{100}) $ 144 * q + 18 * q^6 - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 6 * q^21 - 6 * q^23 - 6 * q^29 - 18 * q^30 - 54 * q^35 + 6 * q^36 - 6 * q^39 + 24 * q^42 - 54 * q^47 + 18 * q^49 + 12 * q^50 + 18 * q^51 + 90 * q^53 - 54 * q^54 - 12 * q^56 - 6 * q^57 - 90 * q^59 - 36 * q^60 - 24 * q^63 + 72 * q^64 - 84 * q^65 - 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 + 18 * q^74 - 90 * q^75 - 78 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 90 * q^87 - 18 * q^91 - 42 * q^92 - 12 * q^93 + 78 * q^95 - 36 * q^98 - 108 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.642788	+	0.766044i	−0.454519	+	0.541675i
$2$	−0.642788	+	0.766044i	−0.454519	+	0.541675i
$3$	1.60013	+	0.663016i	0.923834	+	0.382792i
$3$	1.60013	+	0.663016i	0.923834	+	0.382792i
$4$	−0.173648	−	0.984808i	−0.0868241	−	0.492404i
$5$	1.58293	−	1.32824i	0.707907	−	0.594005i	−0.216104	−	0.976370i	$-0.569335\pi$
$5$	1.58293	−	1.32824i	0.707907	−	0.594005i	0.924011	+	0.382366i	$0.124891\pi$
$6$	−1.53644	+	0.799591i	−0.627250	+	0.326432i
$7$	−1.15983	−	2.37798i	−0.438374	−	0.898793i
$7$	−1.15983	−	2.37798i	−0.438374	−	0.898793i
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$	2.12082	+	2.12182i	0.706940	+	0.707273i
$10$			2.06637i			0.653443i
$11$	0.979112	−	1.16686i	0.295213	−	0.351821i	−0.597967	−	0.801521i	$-0.704024\pi$
$11$	0.979112	−	1.16686i	0.295213	−	0.351821i	0.893180	+	0.449700i	$0.148469\pi$
$12$	0.375084	−	1.69095i	0.108277	−	0.488135i
$13$	0.512757	−	1.40879i	0.142213	−	0.390728i	−0.848053	−	0.529911i	$-0.822225\pi$
$13$	0.512757	−	1.40879i	0.142213	−	0.390728i	0.990267	+	0.139183i	$0.0444477\pi$
$14$	2.56716	+	0.640057i	0.686103	+	0.171062i
$15$	3.41353	−	1.07584i	0.881370	−	0.277781i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	2.18170			0.529139			0.264570	−	0.964367i	$-0.414770\pi$
$17$	2.18170			0.529139			0.264570	+	0.964367i	$0.414770\pi$
$18$	−2.98865	+	0.260763i	−0.704431	+	0.0614625i
$19$			1.55746i			0.357306i	0.983912	+	0.178653i	$0.0571739\pi$
$19$			1.55746i			0.357306i	−0.983912	+	0.178653i	$0.942826\pi$
$20$	−1.58293	−	1.32824i	−0.353954	−	0.297002i
$21$	−0.279235	−	4.57406i	−0.0609341	−	0.998142i
$22$	0.264506	+	1.50009i	0.0563928	+	0.319819i
$23$	1.80546	−	4.96047i	0.376465	−	1.03433i	−0.596346	−	0.802728i	$-0.703381\pi$
$23$	1.80546	−	4.96047i	0.376465	−	1.03433i	0.972811	−	0.231601i	$-0.0743965\pi$
$24$	1.05424	+	1.37425i	0.215197	+	0.280518i
$25$	−0.126785	+	0.719036i	−0.0253571	+	0.143807i
$26$	0.749601	+	1.29835i	0.147009	+	0.254627i
$27$	1.98678	+	4.80132i	0.382357	+	0.924015i
$28$	−2.14045	+	1.55514i	−0.404508	+	0.293894i
$29$	0.292152	+	0.802682i	0.0542513	+	0.149054i	0.963858	−	0.266416i	$-0.0858394\pi$
$29$	0.292152	+	0.802682i	0.0542513	+	0.149054i	−0.909607	+	0.415470i	$0.863617\pi$
$30$	−1.37003	+	3.30645i	−0.250133	+	0.603673i
$31$	−7.09072	+	1.25028i	−1.27353	+	0.224558i	−0.769231	−	0.638971i	$-0.779360\pi$
$31$	−7.09072	+	1.25028i	−1.27353	+	0.224558i	−0.504299	+	0.863529i	$0.668249\pi$
$32$	0.342020	−	0.939693i	0.0604612	−	0.166116i
$33$	2.34035	−	1.21796i	0.407403	−	0.212019i
$34$	−1.40237	+	1.67128i	−0.240504	+	0.286622i
$35$	−4.99444	−	2.22365i	−0.844215	−	0.375866i
$36$	1.72131	−	2.45705i	0.286885	−	0.409508i
$37$	−4.94601	+	8.56674i	−0.813119	+	1.40836i	0.0975521	+	0.995230i	$0.468899\pi$
$37$	−4.94601	+	8.56674i	−0.813119	+	1.40836i	−0.910671	+	0.413133i	$0.864435\pi$
$38$	−1.19308	−	1.00112i	−0.193544	−	0.162402i
$39$	1.75453	−	1.91428i	0.280949	−	0.306530i
$40$	2.03497	−	0.358821i	0.321758	−	0.0567346i
$41$	9.51907	+	3.46466i	1.48663	+	0.541089i	0.952560	−	0.304352i	$-0.0984397\pi$
$41$	9.51907	+	3.46466i	1.48663	+	0.541089i	0.534070	+	0.845440i	$0.320662\pi$
$42$	3.68342	+	2.72624i	0.568364	+	0.420668i
$43$	0.210646	−	1.19463i	0.0321232	−	0.182179i	−0.964524	−	0.263994i	$-0.914960\pi$
$43$	0.210646	−	1.19463i	0.0321232	−	0.182179i	0.996648	+	0.0818140i	$0.0260714\pi$
$44$	−1.31915	−	0.761614i	−0.198870	−	0.114818i
$45$	6.17538	+	0.541742i	0.920572	+	0.0807581i
$46$	2.63941	+	4.57159i	0.389160	+	0.674044i
$47$	−0.626980	+	3.55578i	−0.0914544	+	0.518664i	0.904322	+	0.426851i	$0.140377\pi$
$47$	−0.626980	+	3.55578i	−0.0914544	+	0.518664i	−0.995776	+	0.0918125i	$0.970734\pi$
$48$	−1.73039	−	0.0757548i	−0.249761	−	0.0109343i
$49$	−4.30960	+	5.51610i	−0.615657	+	0.788015i
$50$	−0.469317	−	0.559310i	−0.0663715	−	0.0790984i
$51$	3.49099	+	1.44650i	0.488837	+	0.202550i
$52$	−1.47643	−	0.260334i	−0.204743	−	0.0361018i
$53$	−4.42176	−	2.55290i	−0.607375	−	0.350668i	0.164562	−	0.986367i	$-0.447379\pi$
$53$	−4.42176	−	2.55290i	−0.607375	−	0.350668i	−0.771937	+	0.635699i	$0.780712\pi$
$54$	−4.95511	−	1.56426i	−0.674305	−	0.212869i
$55$		−	3.14755i		−	0.424415i
$56$	0.184550	−	2.63931i	0.0246615	−	0.352692i
$57$	−1.03262	+	2.49213i	−0.136774	+	0.330091i
$58$	−0.802682	−	0.292152i	−0.105397	−	0.0383615i
$59$	4.37913	+	1.59387i	0.570115	+	0.207505i	0.610961	−	0.791661i	$-0.290783\pi$
$59$	4.37913	+	1.59387i	0.570115	+	0.207505i	−0.0408463	+	0.999165i	$0.513005\pi$
$60$	−1.65225	−	3.17485i	−0.213304	−	0.409872i
$61$	−4.87597	−	0.859765i	−0.624304	−	0.110082i	−0.147458	−	0.989068i	$-0.547109\pi$
$61$	−4.87597	−	0.859765i	−0.624304	−	0.110082i	−0.476846	+	0.878987i	$0.658220\pi$
$62$	3.60005	−	6.23547i	0.457207	−	0.791906i
$63$	2.58586	−	7.50422i	0.325788	−	0.945443i
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	−1.05954	−	2.91107i	−0.131420	−	0.361074i
$66$	−0.571338	+	2.57570i	−0.0703268	+	0.317047i
$67$	4.69157	−	3.93670i	0.573167	−	0.480944i	−0.309528	−	0.950890i	$-0.600171\pi$
$67$	4.69157	−	3.93670i	0.573167	−	0.480944i	0.882695	+	0.469946i	$0.155727\pi$
$68$	−0.378848	−	2.14855i	−0.0459420	−	0.260550i
$69$	6.17784	−	6.74033i	0.743724	−	0.811441i
$70$	4.91378	−	2.39663i	0.587309	−	0.286452i
$71$	−4.04327	+	2.33438i	−0.479848	+	0.277040i	−0.720353	−	0.693608i	$-0.756020\pi$
$71$	−4.04327	+	2.33438i	−0.479848	+	0.277040i	0.240505	+	0.970648i	$0.422687\pi$
$72$	0.775774	+	2.89796i	0.0914259	+	0.341528i
$73$	−8.09329	+	4.67267i	−0.947248	+	0.546894i	−0.892225	−	0.451591i	$-0.850857\pi$
$73$	−8.09329	+	4.67267i	−0.947248	+	0.546894i	−0.0550233	+	0.998485i	$0.517523\pi$
$74$	−3.38327	−	9.29546i	−0.393297	−	1.08057i
$75$	−0.679605	+	1.06649i	−0.0784740	+	0.123147i
$76$	1.53380	−	0.270450i	0.175939	−	0.0310227i
$77$	−3.91037	−	0.974952i	−0.445628	−	0.111106i
$78$	0.338633	+	2.57452i	0.0383427	+	0.291507i
$79$	−6.29944	−	5.28586i	−0.708742	−	0.594705i	0.215504	−	0.976503i	$-0.430861\pi$
$79$	−6.29944	−	5.28586i	−0.708742	−	0.594705i	−0.924246	+	0.381798i	$0.875305\pi$
$80$	−1.03318	+	1.78953i	−0.115513	+	0.200075i
$81$	−0.00424038	+	9.00000i	−0.000471153	+	1.00000i
$82$	−8.77283	+	5.06499i	−0.968797	+	0.559335i
$83$	9.24414	−	3.36459i	1.01468	−	0.369312i	0.219450	−	0.975624i	$-0.429574\pi$
$83$	9.24414	−	3.36459i	1.01468	−	0.369312i	0.795227	+	0.606312i	$0.207352\pi$
$84$	−4.45608	+	1.06927i	−0.486198	+	0.116667i
$85$	3.45347	−	2.89781i	0.374581	−	0.314311i
$86$	0.779740	+	0.929258i	0.0840815	+	0.100204i
$87$	−0.0647095	+	1.47810i	−0.00693759	+	0.158469i
$88$	1.43137	−	0.520974i	0.152584	−	0.0555361i
$89$	−18.6147			−1.97316			−0.986579	−	0.163282i	$-0.947792\pi$
$89$	−18.6147			−1.97316			−0.986579	+	0.163282i	$0.947792\pi$
$90$	−4.38446	+	4.38239i	−0.462163	+	0.461945i
$91$	−3.94478	+	0.414626i	−0.413526	+	0.0434646i
$92$	−5.19862	−	0.916657i	−0.541994	−	0.0955681i
$93$	−12.1750	−	2.70064i	−1.26249	−	0.280043i
$94$	−2.32087	−	2.76590i	−0.239379	−	0.285281i
$95$	2.06867	+	2.46535i	0.212241	+	0.252939i
$96$	1.17031	−	1.27686i	0.119444	−	0.130319i
$97$	6.71192	+	1.18349i	0.681492	+	0.120165i	0.503669	−	0.863897i	$-0.331983\pi$
$97$	6.71192	+	1.18349i	0.681492	+	0.120165i	0.177823	+	0.984062i	$0.443094\pi$
$98$	−1.45543	−	6.84702i	−0.147020	−	0.691654i
$99$	4.55239	−	0.397202i	0.457532	−	0.0399203i
$100$	0.730128			0.0730128
$101$	−2.44705	+	0.890652i	−0.243490	+	0.0886232i	−0.460883	−	0.887461i	$-0.652467\pi$
$101$	−2.44705	+	0.890652i	−0.243490	+	0.0886232i	0.217392	+	0.976084i	$0.430245\pi$
$102$	−3.35205	+	1.74446i	−0.331902	+	0.172728i
$103$	−10.3247	−	12.3045i	−1.01732	−	1.21240i	−0.977006	−	0.213211i	$-0.931608\pi$
$103$	−10.3247	−	12.3045i	−1.01732	−	1.21240i	−0.0403164	−	0.999187i	$-0.512837\pi$
$104$	1.14845	−	0.963668i	0.112615	−	0.0944954i
$105$	−6.51744	−	6.86952i	−0.636037	−	0.670397i
$106$	4.79789	−	1.74629i	0.466012	−	0.169614i
$107$	−11.1677	+	6.44765i	−1.07962	+	0.623318i	−0.930793	−	0.365546i	$-0.880882\pi$
$107$	−11.1677	+	6.44765i	−1.07962	+	0.623318i	−0.148825	+	0.988864i	$0.547549\pi$
$108$	4.38338	−	2.79034i	0.421791	−	0.268501i
$109$	6.87640	−	11.9103i	0.658640	−	1.14080i	−0.322328	−	0.946628i	$-0.604466\pi$
$109$	6.87640	−	11.9103i	0.658640	−	1.14080i	0.980968	−	0.194169i	$-0.0622011\pi$
$110$	2.41116	+	2.02320i	0.229895	+	0.192905i
$111$	−13.5941	+	10.4286i	−1.29030	+	0.989839i
$112$	1.90320	+	1.83789i	0.179835	+	0.173664i
$113$	11.3189	−	1.99582i	1.06479	−	0.187751i	0.386310	−	0.922369i	$-0.373750\pi$
$113$	11.3189	−	1.99582i	1.06479	−	0.187751i	0.678481	+	0.734618i	$0.262638\pi$
$114$	−1.24533	−	2.39295i	−0.116636	−	0.224120i
$115$	−3.73075	−	10.2501i	−0.347894	−	0.955831i
$116$	0.739756	−	0.427098i	0.0686846	−	0.0396551i
$117$	4.07666	−	1.89981i	0.376887	−	0.175637i
$118$	−4.03583	+	2.33009i	−0.371528	+	0.214502i
$119$	−2.53039	−	5.18803i	−0.231961	−	0.475586i
$120$	3.49412	+	0.775060i	0.318968	+	0.0707530i
$121$	1.50723	+	8.54791i	0.137021	+	0.777083i
$122$	3.79283	−	3.18256i	0.343387	−	0.288136i
$123$	12.9346	+	11.8552i	1.16627	+	1.06895i
$124$	2.46258	+	6.76588i	0.221146	+	0.607594i
$125$	5.92027	+	10.2542i	0.529525	+	0.917165i
$126$	4.08641	+	6.80450i	0.364046	+	0.606193i
$127$	4.45509	−	7.71645i	0.395326	−	0.684724i	−0.597817	−	0.801633i	$-0.703965\pi$
$127$	4.45509	−	7.71645i	0.395326	−	0.684724i	0.993143	+	0.116909i	$0.0372984\pi$
$128$	−0.984808	−	0.173648i	−0.0870455	−	0.0153485i
$129$	1.12912	−	1.77190i	0.0994134	−	0.156007i
$130$	2.91107	+	1.05954i	0.255318	+	0.0929282i
$131$	−20.8061	−	7.57280i	−1.81784	−	0.661639i	−0.995731	−	0.0923061i	$-0.970576\pi$
$131$	−20.8061	−	7.57280i	−1.81784	−	0.661639i	−0.822107	−	0.569333i	$-0.807202\pi$
$132$	−1.60585	−	2.09330i	−0.139772	−	0.182198i
$133$	3.70361	−	1.80639i	0.321144	−	0.156633i
$134$			6.12441i			0.529069i
$135$	9.52222	+	4.96123i	0.819542	+	0.426995i
$136$	1.88940	+	1.09085i	0.162015	+	0.0935395i
$137$	−0.792970	−	0.139822i	−0.0677480	−	0.0119458i	0.139671	−	0.990198i	$-0.455395\pi$
$137$	−0.792970	−	0.139822i	−0.0677480	−	0.0119458i	−0.207419	+	0.978252i	$0.566506\pi$
$138$	1.19236	+	9.06510i	0.101500	+	0.771673i
$139$	−12.0222	−	14.3276i	−1.01971	−	1.21525i	−0.976352	−	0.216188i	$-0.930638\pi$
$139$	−12.0222	−	14.3276i	−1.01971	−	1.21525i	−0.0433618	−	0.999059i	$-0.513807\pi$
$140$	−1.32259	+	5.30470i	−0.111779	+	0.448329i
$141$	−3.36078	+	5.27400i	−0.283029	+	0.444151i
$142$	0.810722	−	4.59783i	0.0680343	−	0.385842i
$143$	−1.14181	−	1.97768i	−0.0954831	−	0.165382i
$144$	−2.71862	−	1.26850i	−0.226552	−	0.105708i
$145$	1.52861	+	0.882542i	0.126944	+	0.0732911i
$146$	1.62280	−	9.20335i	0.134304	−	0.761675i
$147$	−10.5532	+	5.96914i	−0.870411	+	0.492327i
$148$	9.29546	+	3.38327i	0.764082	+	0.278103i
$149$	6.74419	−	1.18918i	0.552506	−	0.0974217i	0.109577	−	0.993978i	$-0.465050\pi$
$149$	6.74419	−	1.18918i	0.552506	−	0.0974217i	0.442929	+	0.896557i	$0.353939\pi$
$150$	−0.380136	−	1.20613i	−0.0310380	−	0.0984804i
$151$	14.7979	+	12.4169i	1.20423	+	1.01047i	0.999499	+	0.0316559i	$0.0100781\pi$
$151$	14.7979	+	12.4169i	1.20423	+	1.01047i	0.204736	+	0.978817i	$0.434366\pi$
$152$	−0.778730	+	1.34880i	−0.0631633	+	0.109402i
$153$	4.62699	+	4.62917i	0.374070	+	0.374246i
$154$	3.26040	−	2.36883i	0.262730	−	0.190886i
$155$	−9.56343	+	11.3972i	−0.768153	+	0.915449i
$156$	−2.18986	−	1.39546i	−0.175329	−	0.111726i
$157$	−4.34364	+	11.9341i	−0.346660	+	0.952441i	0.636754	+	0.771067i	$0.280277\pi$
$157$	−4.34364	+	11.9341i	−0.346660	+	0.952441i	−0.983414	+	0.181374i	$0.941946\pi$
$158$	8.09840	−	1.42797i	0.644274	−	0.113603i
$159$	−5.38276	−	7.01666i	−0.426881	−	0.556458i
$160$	−0.706739	−	1.94175i	−0.0558726	−	0.153509i
$161$	−13.8899	+	1.45993i	−1.09468	+	0.115059i
$162$	−6.89167	−	5.78834i	−0.541461	−	0.454775i
$163$	11.1277	+	19.2738i	0.871591	+	1.50964i	0.860350	+	0.509704i	$0.170245\pi$
$163$	11.1277	+	19.2738i	0.871591	+	1.50964i	0.0112415	+	0.999937i	$0.496422\pi$
$164$	1.75905	−	9.97609i	0.137359	−	0.779002i
$165$	2.08687	−	5.03648i	0.162463	−	0.392089i
$166$	−3.36459	+	9.24414i	−0.261143	+	0.717485i
$167$	0.774279	+	4.39115i	0.0599155	+	0.339798i	0.999999	−	0.00114562i	$-0.000364664\pi$
$167$	0.774279	+	4.39115i	0.0599155	+	0.339798i	−0.940084	+	0.340943i	$0.889254\pi$
$168$	2.04521	−	4.10087i	0.157791	−	0.316389i
$169$	8.23681	+	6.91151i	0.633601	+	0.531654i
$170$			4.50818i			0.345762i
$171$	−3.30465	+	3.30309i	−0.252713	+	0.252594i
$172$	−1.21306			−0.0924949
$173$	16.0609	−	5.84570i	1.22109	−	0.444440i	0.350553	−	0.936543i	$-0.385994\pi$
$173$	16.0609	−	5.84570i	1.22109	−	0.444440i	0.870537	+	0.492103i	$0.163772\pi$
$174$	−1.09069	−	0.999672i	−0.0826852	−	0.0757849i
$175$	1.85690	−	0.532465i	0.140369	−	0.0402505i
$176$	−0.520974	+	1.43137i	−0.0392699	+	0.107893i
$177$	5.95041	+	5.45384i	0.447260	+	0.409936i
$178$	11.9653	−	14.2597i	0.896839	−	1.06881i
$179$			0.626241i			0.0468075i	0.999726	+	0.0234037i	$0.00745032\pi$
$179$			0.626241i			0.0468075i	−0.999726	+	0.0234037i	$0.992550\pi$
$180$	−0.538832	−	6.17564i	−0.0401622	−	0.460305i
$181$	−6.06528	−	3.50179i	−0.450829	−	0.260286i	0.257351	−	0.966318i	$-0.417150\pi$
$181$	−6.06528	−	3.50179i	−0.450829	−	0.260286i	−0.708180	+	0.706032i	$0.750484\pi$
$182$	2.21804	−	3.28840i	0.164412	−	0.243752i
$183$	−7.23214	−	4.60858i	−0.534615	−	0.340676i
$184$	4.04381	−	3.39316i	0.298114	−	0.250147i
$185$	3.54946	+	20.1300i	0.260962	+	1.47999i
$186$	9.89476	−	7.59066i	0.725519	−	0.556574i
$187$	2.13612	−	2.54573i	0.156209	−	0.186162i
$188$	3.61063			0.263332
$189$	9.11312	−	10.2932i	0.662882	−	0.748724i
$190$	−3.21828			−0.233479
$191$	−3.06712	+	3.65526i	−0.221929	+	0.264485i	−0.865508	−	0.500895i	$-0.833004\pi$
$191$	−3.06712	+	3.65526i	−0.221929	+	0.264485i	0.643579	+	0.765380i	$0.277449\pi$
$192$	0.225876	+	1.71726i	0.0163012	+	0.123933i
$193$	−0.960224	−	5.44570i	−0.0691184	−	0.391990i	−0.999667	−	0.0258206i	$-0.991780\pi$
$193$	−0.960224	−	5.44570i	−0.0691184	−	0.391990i	0.930548	−	0.366170i	$-0.119331\pi$
$194$	−5.22094	+	4.38089i	−0.374842	+	0.314530i
$195$	0.234681	−	5.36059i	0.0168058	−	0.383880i
$196$	6.18065	+	3.28626i	0.441475	+	0.234733i
$197$	22.5436	+	13.0155i	1.60616	+	0.927318i	0.990218	+	0.139528i	$0.0445585\pi$
$197$	22.5436	+	13.0155i	1.60616	+	0.927318i	0.615944	+	0.787790i	$0.288775\pi$
$198$	−2.62194	+	3.74265i	−0.186333	+	0.265978i
$199$		−	0.907874i		−	0.0643575i	−0.999482	−	0.0321788i	$-0.989755\pi$
$199$		−	0.907874i		−	0.0643575i	0.999482	−	0.0321788i	$-0.0102446\pi$
$200$	−0.469317	+	0.559310i	−0.0331857	+	0.0395492i
$201$	10.1172	−	3.18863i	0.713613	−	0.224909i
$202$	0.890652	−	2.44705i	0.0626661	−	0.172174i
$203$	1.56992	−	1.62571i	0.110187	−	0.114102i
$204$	0.818318	−	3.68914i	0.0572938	−	0.258291i
$205$	19.6699	−	7.15926i	1.37381	−	0.500024i
$206$	16.0624			1.11912
$207$	14.3543	−	6.68940i	0.997692	−	0.464945i
$208$			1.49920i			0.103951i
$209$	1.81734	+	1.52493i	0.125708	+	0.105481i
$210$	9.45169	−	0.577002i	0.652228	−	0.0398169i
$211$	−4.10129	−	23.2596i	−0.282345	−	1.60126i	−0.714619	−	0.699514i	$-0.753400\pi$
$211$	−4.10129	−	23.2596i	−0.282345	−	1.60126i	0.432275	−	0.901742i	$-0.357711\pi$
$212$	−1.74629	+	4.79789i	−0.119936	+	0.329520i
$213$	−8.01748	+	1.05456i	−0.549349	+	0.0722573i
$214$	2.23924	−	12.6994i	0.153072	−	0.868112i
$215$	−1.25331	−	2.17080i	−0.0854753	−	0.148047i
$216$	−0.680054	+	5.15146i	−0.0462718	+	0.350512i
$217$	11.1972	+	15.4115i	0.760113	+	1.04620i
$218$	4.70373	+	12.9234i	0.318577	+	0.875283i
$219$	−16.0484	+	2.11088i	−1.08445	+	0.142640i
$220$	−3.09973	+	0.546566i	−0.208984	+	0.0368495i
$221$	1.11868	−	3.07355i	0.0752506	−	0.206749i
$222$	0.749368	−	17.1171i	0.0502943	−	1.14882i
$223$	−7.35904	+	8.77016i	−0.492798	+	0.587293i	−0.953927	−	0.300040i	$-0.903000\pi$
$223$	−7.35904	+	8.77016i	−0.492798	+	0.587293i	0.461129	+	0.887333i	$0.347445\pi$
$224$	−2.63126	+	0.276565i	−0.175808	+	0.0184788i
$225$	−1.79455	+	1.25593i	−0.119637	+	0.0837287i
$226$	−5.74675	+	9.95366i	−0.382268	+	0.662108i
$227$	−1.27226	−	1.06755i	−0.0844430	−	0.0708561i	0.599589	−	0.800308i	$-0.295331\pi$
$227$	−1.27226	−	1.06755i	−0.0844430	−	0.0708561i	−0.684032	+	0.729452i	$0.739775\pi$
$228$	2.63359	+	0.584177i	0.174413	+	0.0386881i
$229$	−0.821699	+	0.144888i	−0.0542994	+	0.00957445i	−0.200732	−	0.979646i	$-0.564332\pi$
$229$	−0.821699	+	0.144888i	−0.0542994	+	0.00957445i	0.146432	+	0.989221i	$0.453221\pi$
$230$	10.2501	+	3.73075i	0.675875	+	0.245998i
$231$	−5.61069	−	4.15269i	−0.369156	−	0.273227i
$232$	−0.148330	+	0.841219i	−0.00973832	+	0.0552288i
$233$	22.2848	+	12.8662i	1.45993	+	0.842890i	0.999007	−	0.0445515i	$-0.0141859\pi$
$233$	22.2848	+	12.8662i	1.45993	+	0.842890i	0.460921	+	0.887441i	$0.347519\pi$
$234$	−1.16509	+	4.34408i	−0.0761642	+	0.283981i
$235$	3.73045	+	6.46132i	0.243347	+	0.421490i
$236$	0.809231	−	4.58938i	0.0526765	−	0.298743i
$237$	−6.57530	−	12.6347i	−0.427112	−	0.820710i
$238$	5.60077	+	1.39641i	0.363044	+	0.0905158i
$239$	4.18171	+	4.98357i	0.270492	+	0.322360i	0.884142	−	0.467218i	$-0.154744\pi$
$239$	4.18171	+	4.98357i	0.270492	+	0.322360i	−0.613650	+	0.789578i	$0.710299\pi$
$240$	−2.83971	+	2.17845i	−0.183302	+	0.140619i
$241$	−4.38852	−	0.773814i	−0.282689	−	0.0498457i	0.0305058	−	0.999535i	$-0.490288\pi$
$241$	−4.38852	−	0.773814i	−0.282689	−	0.0498457i	−0.313195	+	0.949689i	$0.601399\pi$
$242$	−7.51691	−	4.33989i	−0.483205	−	0.278979i
$243$	−5.97393	+	14.3983i	−0.383227	+	0.923654i
$244$			4.95119i			0.316967i
$245$	0.504897	+	14.4558i	0.0322567	+	0.923544i
$246$	−17.3958	+	2.28812i	−1.10912	+	0.145885i
$247$	2.19413	+	0.798598i	0.139609	+	0.0508136i
$248$	−6.76588	−	2.46258i	−0.429634	−	0.156374i
$249$	17.0226	+	0.745231i	1.07876	+	0.0472271i
$250$	−11.6607	−	2.05609i	−0.737485	−	0.130039i
$251$	−8.30653	+	14.3873i	−0.524304	+	0.908121i	0.475296	+	0.879826i	$0.342341\pi$
$251$	−8.30653	+	14.3873i	−0.524304	+	0.908121i	−0.999600	+	0.0282947i	$0.990992\pi$
$252$	−7.83924	−	1.24348i	−0.493826	−	0.0783320i
$253$	−4.02042	−	6.96357i	−0.252762	−	0.437796i
$254$	3.04746	+	8.37284i	0.191215	+	0.525358i
$255$	7.44729	−	2.34716i	0.466367	−	0.146985i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−2.34692	−	13.3101i	−0.146397	−	0.830259i	−0.966235	−	0.257663i	$-0.917048\pi$
$257$	−2.34692	−	13.3101i	−0.146397	−	0.830259i	0.819838	−	0.572596i	$-0.194064\pi$
$258$	0.631571	+	2.00391i	0.0393199	+	0.124758i
$259$	26.1081	+	1.82557i	1.62228	+	0.113435i
$260$	−2.68286	+	1.54895i	−0.166384	+	0.0960618i
$261$	−1.08354	+	2.32224i	−0.0670697	+	0.143743i
$262$	19.1750	−	11.0707i	1.18464	−	0.683950i
$263$	−2.83665	−	7.79364i	−0.174916	−	0.480576i	0.820994	−	0.570937i	$-0.193420\pi$
$263$	−2.83665	−	7.79364i	−0.174916	−	0.480576i	−0.995909	+	0.0903610i	$0.971198\pi$
$264$	2.63578	+	0.115392i	0.162221	+	0.00710188i
$265$	−10.3902	+	1.83207i	−0.638264	+	0.112543i
$266$	−0.996863	+	3.99825i	−0.0611216	+	0.245149i
$267$	−29.7860	−	12.3419i	−1.82287	−	0.755310i
$268$	−4.69157	−	3.93670i	−0.286583	−	0.240472i
$269$	−9.86399	+	17.0849i	−0.601418	+	1.04169i	0.391188	+	0.920311i	$0.372064\pi$
$269$	−9.86399	+	17.0849i	−0.601418	+	1.04169i	−0.992607	+	0.121376i	$0.961269\pi$
$270$	−9.92129	+	4.10543i	−0.603791	+	0.249848i
$271$	−14.1601	+	8.17533i	−0.860164	+	0.496616i	−0.864067	−	0.503377i	$-0.832091\pi$
$271$	−14.1601	+	8.17533i	−0.860164	+	0.496616i	0.00390338	+	0.999992i	$0.498758\pi$
$272$	−2.05012	+	0.746184i	−0.124307	+	0.0452441i
$273$	−6.58706	−	1.95200i	−0.398667	−	0.118140i
$274$	0.616821	−	0.517574i	0.0372635	−	0.0312678i
$275$	0.714877	+	0.851957i	0.0431087	+	0.0513749i
$276$	−7.71070	−	4.91354i	−0.464130	−	0.295760i
$277$	−19.2573	+	7.00910i	−1.15706	+	0.421136i	−0.848047	−	0.529922i	$-0.822221\pi$
$277$	−19.2573	+	7.00910i	−1.15706	+	0.421136i	−0.309014	+	0.951057i	$0.599999\pi$
$278$	18.7033			1.12175
$279$	−17.6910	−	12.3936i	−1.05913	−	0.741985i
$280$	−3.21349	−	4.42296i	−0.192043	−	0.264322i
$281$	−9.38521	−	1.65487i	−0.559875	−	0.0987210i	−0.113452	−	0.993543i	$-0.536191\pi$
$281$	−9.38521	−	1.65487i	−0.559875	−	0.0987210i	−0.446422	+	0.894822i	$0.647302\pi$
$282$	−1.87985	−	5.96457i	−0.111943	−	0.355185i
$283$	−19.4712	−	23.2049i	−1.15744	−	1.37939i	−0.912108	−	0.409950i	$-0.865546\pi$
$283$	−19.4712	−	23.2049i	−1.15744	−	1.37939i	−0.245336	−	0.969438i	$-0.578898\pi$
$284$	3.00102	+	3.57648i	0.178078	+	0.212225i
$285$	1.67558	+	5.31643i	0.0992526	+	0.314918i
$286$	2.24893	+	0.396547i	0.132982	+	0.0234483i
$287$	−2.80160	−	26.6546i	−0.165373	−	1.57337i
$288$	2.71922	−	1.26721i	0.160232	−	0.0746713i
$289$	−12.2402			−0.720012
$290$	−1.65864	+	0.603694i	−0.0973985	+	0.0354501i
$291$	9.95525	+	6.34384i	0.583587	+	0.371883i
$292$	6.00706	+	7.15894i	0.351537	+	0.418945i
$293$	12.6400	−	10.6062i	0.738436	−	0.619621i	−0.193981	−	0.981005i	$-0.562140\pi$
$293$	12.6400	−	10.6062i	0.738436	−	0.619621i	0.932417	+	0.361384i	$0.117696\pi$
$294$	2.21082	−	11.9211i	0.128937	−	0.695252i
$295$	9.04890	−	3.29353i	0.526847	−	0.191757i
$296$	−8.56674	+	4.94601i	−0.497932	+	0.287481i
$297$	7.54775	+	2.38273i	0.437965	+	0.138260i
$298$	−3.42412	+	5.93074i	−0.198354	+	0.343559i
$299$	−6.06249	−	5.08703i	−0.350603	−	0.294191i
$300$	1.16830	+	0.484086i	0.0674517	+	0.0279487i
$301$	−3.08512	+	0.884655i	−0.177824	+	0.0509907i
$302$	−19.0238	+	3.35441i	−1.09470	+	0.193025i
$303$	−4.50610	−	0.197273i	−0.258869	−	0.0113330i
$304$	−0.532682	−	1.46353i	−0.0305514	−	0.0839394i
$305$	−8.86028	+	5.11549i	−0.507338	+	0.292912i
$306$	−6.52032	+	0.568906i	−0.372742	+	0.0325222i
$307$	15.6283	−	9.02300i	0.891953	−	0.514970i	0.0173725	−	0.999849i	$-0.494470\pi$
$307$	15.6283	−	9.02300i	0.891953	−	0.514970i	0.874581	+	0.484880i	$0.161137\pi$
$308$	−0.281112	+	4.02026i	−0.0160178	+	0.229076i
$309$	−8.36277	−	26.5342i	−0.475741	−	1.50948i
$310$	−2.58355	−	14.6520i	−0.146736	−	0.832179i
$311$	−14.8754	+	12.4820i	−0.843508	+	0.707788i	−0.958350	−	0.285596i	$-0.907808\pi$
$311$	−14.8754	+	12.4820i	−0.843508	+	0.707788i	0.114842	+	0.993384i	$0.463364\pi$
$312$	2.47660	−	0.780549i	0.140210	−	0.0441899i
$313$	7.37915	+	20.2741i	0.417094	+	1.14596i	0.953341	+	0.301896i	$0.0976195\pi$
$313$	7.37915	+	20.2741i	0.417094	+	1.14596i	−0.536247	+	0.844061i	$0.680158\pi$
$314$	−6.34998	−	10.9985i	−0.358350	−	0.620680i
$315$	−5.87413	−	15.3133i	−0.330970	−	0.862805i
$316$	−4.11167	+	7.12161i	−0.231299	+	0.400622i
$317$	8.75704	+	1.54410i	0.491844	+	0.0867254i	0.414069	−	0.910245i	$-0.364107\pi$
$317$	8.75704	+	1.54410i	0.491844	+	0.0867254i	0.0777754	+	0.996971i	$0.475218\pi$
$318$	8.83505	+	0.386789i	0.495445	+	0.0216901i
$319$	1.22267	+	0.445015i	0.0684562	+	0.0249160i
$320$	1.94175	+	0.706739i	0.108547	+	0.0395079i
$321$	−22.1446	+	2.91273i	−1.23599	+	0.162573i
$322$	7.80990	−	11.5787i	0.435229	−	0.645257i
$323$			3.39790i			0.189064i
$324$	8.86401	−	1.55866i	0.492445	−	0.0865921i
$325$	0.947959	+	0.547304i	0.0525833	+	0.0303590i
$326$	−21.9174	−	3.86462i	−1.21389	−	0.214042i
$327$	18.8998	−	14.4988i	1.04516	−	0.801786i
$328$	6.51143	+	7.76002i	0.359534	+	0.428475i
$329$	9.18277	−	2.63315i	0.506262	−	0.145170i
$330$	2.51675	+	4.83602i	0.138543	+	0.266214i
$331$	−3.08064	+	17.4712i	−0.169327	+	0.960303i	0.775162	+	0.631762i	$0.217668\pi$
$331$	−3.08064	+	17.4712i	−0.169327	+	0.960303i	−0.944490	+	0.328541i	$0.893443\pi$
$332$	−4.91871	−	8.51945i	−0.269949	−	0.467566i
$333$	−28.6667	+	7.67397i	−1.57092	+	0.420531i
$334$	−3.86152	−	2.22945i	−0.211293	−	0.121990i
$335$	2.19757	−	12.4630i	0.120066	−	0.680927i
$336$	1.82682	+	4.20271i	0.0996610	+	0.229276i
$337$	−2.04246	−	0.743395i	−0.111260	−	0.0404953i	0.285790	−	0.958292i	$-0.407744\pi$
$337$	−2.04246	−	0.743395i	−0.111260	−	0.0404953i	−0.397050	+	0.917797i	$0.629966\pi$
$338$	−10.5890	+	1.86713i	−0.575968	+	0.101559i
$339$	19.4349	+	4.31102i	1.05556	+	0.234143i
$340$	−3.45347	−	2.89781i	−0.187291	−	0.157156i
$341$	−5.48370	+	9.49804i	−0.296959	+	0.514348i
$342$	−0.406128	−	4.65469i	−0.0219609	−	0.251697i
$343$	18.1156	+	3.85041i	0.978150	+	0.207902i
$344$	0.779740	−	0.929258i	0.0420407	−	0.0501022i
$345$	0.826332	−	18.8751i	0.0444882	−	1.01620i
$346$	−5.84570	+	16.0609i	−0.314267	+	0.863441i
$347$	5.66838	−	0.999488i	0.304294	−	0.0536553i	−0.0194161	−	0.999811i	$-0.506181\pi$
$347$	5.66838	−	0.999488i	0.304294	−	0.0536553i	0.323710	+	0.946156i	$0.395070\pi$
$348$	1.46688	−	0.192942i	0.0786329	−	0.0103428i
$349$	−5.14675	−	14.1406i	−0.275499	−	0.756928i	−0.997858	−	0.0654099i	$-0.979165\pi$
$349$	−5.14675	−	14.1406i	−0.275499	−	0.756928i	0.722359	−	0.691518i	$-0.243058\pi$
$350$	−0.785703	+	1.76473i	−0.0419976	+	0.0943289i
$351$	7.78278	−	0.337048i	0.415414	−	0.0179903i
$352$	−0.761614	−	1.31915i	−0.0405941	−	0.0703111i
$353$	3.90074	−	22.1222i	0.207616	−	1.17745i	−0.685655	−	0.727927i	$-0.740484\pi$
$353$	3.90074	−	22.1222i	0.207616	−	1.17745i	0.893270	−	0.449520i	$-0.148405\pi$
$354$	−8.00273	+	1.05262i	−0.425341	+	0.0559462i
$355$	−3.29960	+	9.06557i	−0.175124	+	0.481150i
$356$	3.23242	+	18.3319i	0.171318	+	0.971591i
$357$	−0.609206	−	9.97921i	−0.0322426	−	0.528156i
$358$	−0.479729	−	0.402540i	−0.0253544	−	0.0212749i
$359$		−	19.4617i		−	1.02715i	−0.858044	−	0.513576i	$-0.828321\pi$
$359$		−	19.4617i		−	1.02715i	0.858044	−	0.513576i	$-0.171679\pi$
$360$	5.07717	+	3.55685i	0.267590	+	0.187463i
$361$	16.5743			0.872333
$362$	6.58122	−	2.39537i	0.345901	−	0.125898i
$363$	−3.25564	+	14.6771i	−0.170877	+	0.770347i
$364$	1.09333	+	3.81285i	0.0573061	+	0.199848i
$365$	−6.60471	+	18.1463i	−0.345706	+	0.949820i
$366$	8.17910	−	2.57780i	0.427529	−	0.134744i
$367$	3.59460	−	4.28388i	0.187637	−	0.223617i	−0.664023	−	0.747712i	$-0.731152\pi$
$367$	3.59460	−	4.28388i	0.187637	−	0.223617i	0.851659	+	0.524096i	$0.175597\pi$
$368$			5.27882i			0.275177i
$369$	12.8369	+	27.5457i	0.668260	+	1.43397i
$370$	−17.7020	−	10.2203i	−0.920284	−	0.531326i
$371$	−0.942276	+	13.4758i	−0.0489205	+	0.699628i
$372$	−0.545442	+	12.4590i	−0.0282799	+	0.645969i
$373$	20.7348	−	17.3985i	1.07361	−	0.900862i	0.0782308	−	0.996935i	$-0.475073\pi$
$373$	20.7348	−	17.3985i	1.07361	−	0.900862i	0.995374	+	0.0960737i	$0.0306284\pi$
$374$	0.577071	+	3.27273i	0.0298396	+	0.169229i
$375$	2.67449	+	20.3333i	0.138110	+	1.05001i
$376$	−2.32087	+	2.76590i	−0.119690	+	0.142641i
$377$	1.28061			0.0659549
$378$	2.02728	+	13.5974i	0.104272	+	0.699376i
$379$	9.89683			0.508366			0.254183	−	0.967156i	$-0.418193\pi$
$379$	9.89683			0.508366			0.254183	+	0.967156i	$0.418193\pi$
$380$	2.06867	−	2.46535i	0.106121	−	0.126470i
$381$	12.2448	−	9.39351i	0.627322	−	0.481244i
$382$	−0.828579	−	4.69911i	−0.0423938	−	0.240427i
$383$	18.3356	−	15.3854i	0.936906	−	0.786158i	−0.0401379	−	0.999194i	$-0.512780\pi$
$383$	18.3356	−	15.3854i	0.936906	−	0.786158i	0.977044	+	0.213036i	$0.0683353\pi$
$384$	−1.46069	−	0.930802i	−0.0745404	−	0.0474998i
$385$	−7.48481	+	3.65061i	−0.381461	+	0.186053i
$386$	4.78887	+	2.76485i	0.243747	+	0.140727i
$387$	2.98153	−	2.08665i	0.151560	−	0.106070i
$388$		−	6.81546i		−	0.346003i
$389$	−16.3119	+	19.4398i	−0.827048	+	0.985638i	0.172952	+	0.984930i	$0.444670\pi$
$389$	−16.3119	+	19.4398i	−0.827048	+	0.985638i	−1.00000		0.000707217i	$0.999775\pi$
$390$	3.95560	+	3.62549i	0.200299	+	0.183584i
$391$	3.93897	−	10.8222i	0.199202	−	0.547304i
$392$	−6.49027	+	2.62229i	−0.327808	+	0.132446i
$393$	−28.2715	−	25.9122i	−1.42611	−	1.30710i
$394$	−24.4612	+	8.90315i	−1.23234	+	0.448534i
$395$	−16.9924			−0.854982
$396$	−1.18168	−	4.41425i	−0.0593817	−	0.221825i
$397$		−	2.32814i		−	0.116846i	−0.998292	−	0.0584230i	$-0.981393\pi$
$397$		−	2.32814i		−	0.116846i	0.998292	−	0.0584230i	$-0.0186072\pi$
$398$	0.695472	+	0.583570i	0.0348609	+	0.0292517i
$399$	7.12391	−	0.434897i	0.356642	−	0.0217721i
$400$	−0.126785	−	0.719036i	−0.00633927	−	0.0359518i
$401$	12.3811	−	34.0167i	0.618280	−	1.69871i	−0.0928763	−	0.995678i	$-0.529606\pi$
$401$	12.3811	−	34.0167i	0.618280	−	1.69871i	0.711157	−	0.703034i	$-0.248172\pi$
$402$	−4.06058	+	9.79984i	−0.202523	+	0.488772i
$403$	−1.87443	+	10.6304i	−0.0933719	+	0.529538i
$404$	1.30205	+	2.25521i	0.0647792	+	0.112201i
$405$	11.9474	+	14.2520i	0.593671	+	0.708187i
$406$	0.236241	+	2.24761i	0.0117244	+	0.111547i
$407$	5.15349	+	14.1591i	0.255449	+	0.701840i
$408$	2.30004	+	2.99820i	0.113869	+	0.148433i
$409$	−2.08443	+	0.367541i	−0.103068	+	0.0181737i	−0.224944	−	0.974372i	$-0.572220\pi$
$409$	−2.08443	+	0.367541i	−0.103068	+	0.0181737i	0.121876	+	0.992545i	$0.461109\pi$
$410$	−7.15926	+	19.6699i	−0.353571	+	0.971427i
$411$	−1.17615	−	0.749485i	−0.0580152	−	0.0369694i
$412$	−10.3247	+	12.3045i	−0.508661	+	0.606199i
$413$	−1.28884	−	12.2621i	−0.0634197	−	0.603380i
$414$	−4.10238	+	15.2959i	−0.201621	+	0.751751i
$415$	10.1639	−	17.6043i	0.498924	−	0.864162i
$416$	−1.14845	−	0.963668i	−0.0563076	−	0.0472477i
$417$	−9.73774	−	30.8969i	−0.476859	−	1.51303i
$418$	−2.33632	+	0.411957i	−0.114273	+	0.0201495i
$419$	3.24458	+	1.18093i	0.158508	+	0.0576922i	0.420056	−	0.907498i	$-0.362011\pi$
$419$	3.24458	+	1.18093i	0.158508	+	0.0576922i	−0.261547	+	0.965191i	$0.584233\pi$
$420$	−5.63342	+	7.61130i	−0.274883	+	0.371394i
$421$	−4.93421	+	27.9833i	−0.240479	+	1.36382i	0.590285	+	0.807195i	$0.299016\pi$
$421$	−4.93421	+	27.9833i	−0.240479	+	1.36382i	−0.830763	+	0.556626i	$0.812096\pi$
$422$	20.4541	+	11.8092i	0.995692	+	0.574863i
$423$	−8.87443	+	6.21083i	−0.431490	+	0.301981i
$424$	−2.55290	−	4.42176i	−0.123980	−	0.214739i
$425$	−0.276607	+	1.56872i	−0.0134174	+	0.0760940i
$426$	4.34570	−	6.81960i	0.210550	−	0.330411i
$427$	3.61078	+	12.5921i	0.174738	+	0.609377i
$428$	8.28894	+	9.87837i	0.400661	+	0.477489i
$429$	−0.515815	−	3.92158i	−0.0249038	−	0.189335i
$430$	2.46855	+	0.435271i	0.119044	+	0.0209906i
$431$	8.15733	+	4.70964i	0.392925	+	0.226855i	0.683427	−	0.730019i	$-0.260489\pi$
$431$	8.15733	+	4.70964i	0.392925	+	0.226855i	−0.290502	+	0.956874i	$0.593822\pi$
$432$	−3.50912	−	3.83225i	−0.168832	−	0.184379i
$433$		−	21.6820i		−	1.04197i	−0.853565	−	0.520986i	$-0.825564\pi$
$433$		−	21.6820i		−	1.04197i	0.853565	−	0.520986i	$-0.174436\pi$
$434$	−19.0033	−	1.32878i	−0.912187	−	0.0637834i
$435$	1.86083	+	2.42567i	0.0892199	+	0.116302i
$436$	−12.9234	−	4.70373i	−0.618919	−	0.225268i
$437$	7.72573	+	2.81193i	0.369572	+	0.134513i
$438$	8.69865	−	13.6506i	0.415638	−	0.652251i
$439$	2.82222	+	0.497633i	0.134697	+	0.0237507i	0.240590	−	0.970627i	$-0.422659\pi$
$439$	2.82222	+	0.497633i	0.134697	+	0.0237507i	−0.105893	+	0.994378i	$0.533770\pi$
$440$	1.57377	−	2.72586i	0.0750267	−	0.129950i
$441$	−20.8441	+	2.55448i	−0.992574	+	0.121642i
$442$	1.63540	+	2.83260i	0.0777881	+	0.134733i
$443$	−4.63178	−	12.7257i	−0.220063	−	0.604617i	0.779706	−	0.626146i	$-0.215369\pi$
$443$	−4.63178	−	12.7257i	−0.220063	−	0.604617i	−0.999768	+	0.0215294i	$0.993146\pi$
$444$	12.6308	+	11.5767i	0.599429	+	0.549406i
$445$	−29.4658	+	24.7248i	−1.39681	+	1.17207i
$446$	−1.98803	−	11.2747i	−0.0941361	−	0.533873i
$447$	11.5800	+	2.56866i	0.547716	+	0.121493i
$448$	1.47948	−	2.19343i	0.0698988	−	0.103630i
$449$	22.6946	−	13.1028i	1.07103	−	0.618357i	0.142564	−	0.989786i	$-0.454465\pi$
$449$	22.6946	−	13.1028i	1.07103	−	0.618357i	0.928462	+	0.371429i	$0.121132\pi$
$450$	0.191419	−	2.18200i	0.00902356	−	0.102861i
$451$	13.3630	−	7.71514i	0.629239	−	0.363292i
$452$	−3.93101	−	10.8004i	−0.184899	−	0.508006i
$453$	15.4459	+	29.6799i	0.725712	+	1.39448i
$454$	1.63559	−	0.288398i	0.0767620	−	0.0135352i
$455$	−5.69359	+	5.89592i	−0.266920	+	0.276405i
$456$	−2.14034	+	1.64194i	−0.100231	+	0.0768910i
$457$	−31.5777	−	26.4969i	−1.47714	−	1.23947i	−0.909171	−	0.416424i	$-0.863283\pi$
$457$	−31.5777	−	26.4969i	−1.47714	−	1.23947i	−0.567973	−	0.823047i	$-0.692272\pi$
$458$	0.417188	−	0.722590i	0.0194939	−	0.0337644i
$459$	4.33456	+	10.4750i	0.202320	+	0.488932i
$460$	−9.44659	+	5.45399i	−0.440449	+	0.254294i
$461$	28.4767	−	10.3647i	1.32629	−	0.482731i	0.420823	−	0.907143i	$-0.361741\pi$
$461$	28.4767	−	10.3647i	1.32629	−	0.482731i	0.905469	+	0.424412i	$0.139519\pi$
$462$	6.78763	−	1.62874i	0.315789	−	0.0757759i
$463$	22.9852	−	19.2869i	1.06821	−	0.896338i	0.0733242	−	0.997308i	$-0.476639\pi$
$463$	22.9852	−	19.2869i	1.06821	−	0.896338i	0.994889	+	0.100971i	$0.0321948\pi$
$464$	−0.549067	−	0.654352i	−0.0254898	−	0.0303776i
$465$	−22.8593	+	11.8964i	−1.06007	+	0.551680i
$466$	−24.1805	+	8.80097i	−1.12014	+	0.407697i
$467$	−1.13401			−0.0524757			−0.0262379	−	0.999656i	$-0.508353\pi$
$467$	−1.13401			−0.0524757			−0.0262379	+	0.999656i	$0.508353\pi$
$468$	−2.57885	−	3.68483i	−0.119207	−	0.170331i
$469$	−14.8028	−	6.59058i	−0.683530	−	0.304325i
$470$	−7.34754	−	1.29557i	−0.338917	−	0.0597602i
$471$	−14.8628	+	16.2161i	−0.684844	+	0.747199i
$472$	2.99550	+	3.56990i	0.137879	+	0.164318i
$473$	−1.18772	−	1.41547i	−0.0546115	−	0.0650834i
$474$	13.9052	+	3.08444i	0.638689	+	0.141673i
$475$	−1.11987	−	0.197463i	−0.0513831	−	0.00906023i
$476$	−4.66982	+	3.39284i	−0.214041	+	0.155511i
$477$	−3.96095	−	14.7964i	−0.181360	−	0.677481i
$478$	−6.50559			−0.297559
$479$	20.8982	−	7.60633i	0.954863	−	0.347542i	0.182845	−	0.983142i	$-0.441469\pi$
$479$	20.8982	−	7.60633i	0.954863	−	0.347542i	0.772019	+	0.635600i	$0.219247\pi$
$480$	0.156537	−	3.57563i	0.00714491	−	0.163204i
$481$	9.53262	+	11.3605i	0.434650	+	0.517996i
$482$	3.41366	−	2.86440i	0.155488	−	0.130470i
$483$	−23.1936	−	6.87316i	−1.05535	−	0.312740i
$484$	8.15632	−	2.96866i	0.370742	−	0.134939i
$485$	12.1964	−	7.04162i	0.553812	−	0.319743i
$486$	−7.18980	−	13.8314i	−0.326136	−	0.627404i
$487$	15.9653	−	27.6527i	0.723458	−	1.25307i	−0.236148	−	0.971717i	$-0.575885\pi$
$487$	15.9653	−	27.6527i	0.723458	−	1.25307i	0.959606	−	0.281348i	$-0.0907817\pi$
$488$	−3.79283	−	3.18256i	−0.171693	−	0.144068i
$489$	5.02697	+	38.2184i	0.227327	+	1.72830i
$490$	−11.3983	−	8.90521i	−0.514922	−	0.402296i
$491$	−24.5278	+	4.32492i	−1.10692	+	0.195181i	−0.697093	−	0.716981i	$-0.745524\pi$
$491$	−24.5278	+	4.32492i	−1.10692	+	0.195181i	−0.409832	+	0.912161i	$0.634413\pi$
$492$	9.42901	−	14.7967i	0.425093	−	0.667089i
$493$	0.637388	+	1.75121i	0.0287065	+	0.0788705i
$494$	−2.02212	+	1.16747i	−0.0909795	+	0.0525271i
$495$	6.67853	−	6.67538i	0.300177	−	0.300036i
$496$	6.23547	−	3.60005i	0.279981	−	0.161647i
$497$	10.2406	+	6.90733i	0.459354	+	0.309836i
$498$	−11.5128	+	12.5610i	−0.515901	+	0.562874i
$499$	3.02198	+	17.1385i	0.135282	+	0.767225i	0.974663	+	0.223680i	$0.0718071\pi$
$499$	3.02198	+	17.1385i	0.135282	+	0.767225i	−0.839380	+	0.543545i	$0.817082\pi$
$500$	9.07038	−	7.61096i	0.405640	−	0.340372i
$501$	−1.67246	+	7.53977i	−0.0747199	+	0.336852i
$502$	−5.68200	−	15.6112i	−0.253600	−	0.696761i
$503$	−2.03960	−	3.53269i	−0.0909413	−	0.157515i	0.816966	−	0.576686i	$-0.195654\pi$
$503$	−2.03960	−	3.53269i	−0.0909413	−	0.157515i	−0.907907	+	0.419171i	$0.862321\pi$
$504$	5.99153	−	5.20591i	0.266884	−	0.231890i
$505$	−2.69051	+	4.66009i	−0.119726	+	0.207371i
$506$	7.91868	+	1.39628i	0.352028	+	0.0620721i
$507$	8.59752	+	16.5204i	0.381829	+	0.733698i
$508$	−8.37284	−	3.04746i	−0.371485	−	0.135209i
$509$	−4.98479	−	1.81431i	−0.220947	−	0.0804181i	0.229175	−	0.973385i	$-0.426397\pi$
$509$	−4.98479	−	1.81431i	−0.220947	−	0.0804181i	−0.450122	+	0.892967i	$0.648619\pi$
$510$	−2.98900	+	7.21367i	−0.132355	+	0.319427i
$511$	20.4983	+	13.8262i	0.906793	+	0.611636i
$512$			1.00000i			0.0441942i
$513$	−7.47786	+	3.09434i	−0.330156	+	0.136618i
$514$	11.7047	+	6.75769i	0.516271	+	0.298069i
$515$	−32.6865	−	5.76352i	−1.44034	−	0.253971i
$516$	−1.94105	−	0.804278i	−0.0854500	−	0.0354063i
$517$	3.53521	+	4.21310i	0.155478	+	0.185292i
$518$	−18.1804	+	18.8265i	−0.798801	+	0.827188i
$519$	29.5753	+	1.29478i	1.29821	+	0.0568344i
$520$	0.537945	−	3.05084i	0.0235904	−	0.133788i
$521$	−14.5236	−	25.1557i	−0.636292	−	1.10209i	−0.986240	−	0.165321i	$-0.947134\pi$
$521$	−14.5236	−	25.1557i	−0.636292	−	1.10209i	0.349948	−	0.936769i	$-0.386199\pi$
$522$	−1.08245	−	2.32275i	−0.0473775	−	0.101664i
$523$	0.409018	+	0.236146i	0.0178851	+	0.0103260i	0.508916	−	0.860816i	$-0.330046\pi$
$523$	0.409018	+	0.236146i	0.0178851	+	0.0103260i	−0.491031	+	0.871142i	$0.663380\pi$
$524$	−3.84481	+	21.8050i	−0.167961	+	0.952557i
$525$	3.32432	+	0.379144i	0.145085	+	0.0165472i
$526$	7.79364	+	2.83665i	0.339819	+	0.123684i
$527$	−15.4698	+	2.72774i	−0.673875	+	0.118822i
$528$	−1.78264	+	1.94495i	−0.0775796	+	0.0846433i
$529$	−3.72752	−	3.12776i	−0.162066	−	0.135990i
$530$	5.27523	−	9.13697i	0.229141	−	0.396885i
$531$	5.90544	+	12.6721i	0.256274	+	0.549920i
$532$	−2.42207	−	3.33367i	−0.105010	−	0.144533i
$533$	9.76194	−	11.6338i	0.422837	−	0.503917i
$534$	28.6005	−	14.8842i	1.23766	−	0.644102i
$535$	−9.11361	+	25.0394i	−0.394016	+	1.08255i
$536$	6.03137	−	1.06349i	0.260515	−	0.0459359i
$537$	−0.415208	+	1.00207i	−0.0179175	+	0.0432423i
$538$	−6.74737	−	18.5382i	−0.290900	−	0.799240i
$539$	2.21694	+	10.4296i	0.0954905	+	0.449234i
$540$	3.23234	−	10.2391i	0.139098	−	0.440619i
$541$	−3.82696	−	6.62850i	−0.164534	−	0.284981i	0.771956	−	0.635676i	$-0.219279\pi$
$541$	−3.82696	−	6.62850i	−0.164534	−	0.284981i	−0.936490	+	0.350695i	$0.885945\pi$
$542$	2.83926	−	16.1023i	0.121957	−	0.691651i
$543$	−7.38349	−	9.62470i	−0.316856	−	0.413035i
$544$	0.746184	−	2.05012i	0.0319924	−	0.0878983i
$545$	−4.93479	−	27.9866i	−0.211383	−	1.19881i
$546$	5.72940	−	3.79126i	0.245196	−	0.162251i
$547$	18.3618	+	15.4074i	0.785095	+	0.658773i	0.944526	−	0.328436i	$-0.106522\pi$
$547$	18.3618	+	15.4074i	0.785095	+	0.658773i	−0.159431	+	0.987209i	$0.550966\pi$
$548$			0.805203i			0.0343966i
$549$	−8.51679	−	12.1693i	−0.363488	−	0.519374i
$550$	−1.11215			−0.0474223
$551$	−1.25014	+	0.455015i	−0.0532580	+	0.0193843i
$552$	8.72033	−	2.74838i	0.371162	−	0.116979i
$553$	−5.26340	+	21.1106i	−0.223823	+	0.897716i
$554$	7.00910	−	19.2573i	0.297788	−	0.818166i
$555$	−7.66691	+	34.5639i	−0.325442	+	1.46716i
$556$	−12.0222	+	14.3276i	−0.509857	+	0.607624i
$557$			21.2198i			0.899112i	0.893252	+	0.449556i	$0.148418\pi$
$557$			21.2198i			0.899112i	−0.893252	+	0.449556i	$0.851582\pi$
$558$	20.8656	−	5.58565i	0.883312	−	0.236460i
$559$	−1.57497	−	0.909310i	−0.0666142	−	0.0384597i
$560$	5.45378	+	0.381348i	0.230464	+	0.0161149i
$561$	5.10593	−	2.65722i	0.215573	−	0.112188i
$562$	7.30040	−	6.12576i	0.307949	−	0.258400i
$563$	2.66283	+	15.1017i	0.112225	+	0.636460i	0.988087	+	0.153898i	$0.0491826\pi$
$563$	2.66283	+	15.1017i	0.112225	+	0.636460i	−0.875862	+	0.482562i	$0.839706\pi$
$564$	5.77747	+	2.39391i	0.243276	+	0.100802i
$565$	15.2661	−	18.1934i	0.642248	−	0.765402i
$566$	30.2918			1.27326
$567$	21.4068	−	10.4284i	0.898999	−	0.437950i
$568$	−4.66876			−0.195897
$569$	23.9194	−	28.5060i	1.00275	−	1.19503i	0.0220049	−	0.999758i	$-0.492995\pi$
$569$	23.9194	−	28.5060i	1.00275	−	1.19503i	0.980748	−	0.195277i	$-0.0625605\pi$
$570$	−5.14966	−	2.13377i	−0.215696	−	0.0893738i
$571$	7.37780	+	41.8416i	0.308751	+	1.75102i	0.605300	+	0.795998i	$0.293053\pi$
$571$	7.37780	+	41.8416i	0.308751	+	1.75102i	−0.296548	+	0.955018i	$0.595836\pi$
$572$	−1.74936	+	1.46789i	−0.0731443	+	0.0613754i
$573$	−7.33129	+	3.81533i	−0.306269	+	0.159388i
$574$	22.2194	+	14.9871i	0.927421	+	0.625549i
$575$	3.33785	+	1.92711i	0.139198	+	0.0803659i
$576$	−0.777140	+	2.89759i	−0.0323808	+	0.120733i
$577$			43.4989i			1.81088i	0.424469	+	0.905442i	$0.360461\pi$
$577$			43.4989i			1.81088i	−0.424469	+	0.905442i	$0.639539\pi$
$578$	7.86785	−	9.37654i	0.327259	−	0.390013i
$579$	2.07410	−	9.35046i	0.0861968	−	0.388592i
$580$	0.603694	−	1.65864i	0.0250670	−	0.0688711i
$581$	−18.7226	−	18.0801i	−0.776743	−	0.750087i
$582$	−11.2588	+	3.54842i	−0.466691	+	0.147087i
$583$	−7.30827	+	2.65999i	−0.302678	+	0.110166i
$584$	−9.34533			−0.386713
$585$	3.92967	−	8.42203i	0.162472	−	0.348208i
$586$			16.5003i			0.681622i
$587$	−8.27048	−	6.93976i	−0.341359	−	0.286435i	0.455950	−	0.890005i	$-0.349300\pi$
$587$	−8.27048	−	6.93976i	−0.341359	−	0.286435i	−0.797309	+	0.603571i	$0.793744\pi$
$588$	7.71100	+	9.35631i	0.317996	+	0.385848i
$589$	−1.94727	−	11.0435i	−0.0802357	−	0.455039i
$590$	−3.29353	+	9.04890i	−0.135592	+	0.372537i
$591$	27.4431	+	35.7732i	1.12886	+	1.47151i
$592$	1.71773	−	9.74174i	0.0705983	−	0.400383i
$593$	−15.0617	−	26.0876i	−0.618509	−	1.07129i	−0.989758	−	0.142756i	$-0.954404\pi$
$593$	−15.0617	−	26.0876i	−0.618509	−	1.07129i	0.371249	−	0.928534i	$-0.378930\pi$
$594$	−6.67688	+	4.25033i	−0.273956	+	0.174393i
$595$	−10.8964	−	4.85133i	−0.446707	−	0.198885i
$596$	−2.34223	−	6.43523i	−0.0959416	−	0.263597i
$597$	0.601935	−	1.45272i	0.0246356	−	0.0594557i
$598$	7.79378	−	1.37425i	0.318711	−	0.0561974i
$599$	8.60228	−	23.6346i	0.351480	−	0.965683i	−0.630415	−	0.776258i	$-0.717115\pi$
$599$	8.60228	−	23.6346i	0.351480	−	0.965683i	0.981895	−	0.189425i	$-0.0606623\pi$
$600$	−1.12180	+	0.583804i	−0.0457973	+	0.0238337i
$601$	−10.2540	+	12.2202i	−0.418267	+	0.498472i	−0.933499	−	0.358579i	$-0.883261\pi$
$601$	−10.2540	+	12.2202i	−0.418267	+	0.498472i	0.515232	+	0.857051i	$0.327706\pi$
$602$	1.30539	−	2.93199i	0.0532039	−	0.119499i
$603$	18.3029	+	1.60564i	0.745353	+	0.0653869i
$604$	9.65863	−	16.7292i	0.393004	−	0.680703i
$605$	13.7395	+	11.5288i	0.558589	+	0.468712i
$606$	3.04759	−	3.32507i	0.123800	−	0.135072i
$607$	26.1821	−	4.61661i	1.06270	−	0.187383i	0.385146	−	0.922856i	$-0.374151\pi$
$607$	26.1821	−	4.61661i	1.06270	−	0.187383i	0.677554	+	0.735473i	$0.263040\pi$
$608$	1.46353	+	0.532682i	0.0593541	+	0.0216031i
$609$	3.58994	−	1.56046i	0.145472	−	0.0632330i
$610$	1.77659	−	10.0755i	0.0719320	−	0.407947i
$611$	4.68785	+	2.70653i	0.189650	+	0.109495i
$612$	3.75537	−	5.36054i	0.151802	−	0.216687i
$613$	−17.0547	−	29.5395i	−0.688831	−	1.19309i	−0.972216	−	0.234085i	$-0.924791\pi$
$613$	−17.0547	−	29.5395i	−0.688831	−	1.19309i	0.283385	−	0.959006i	$-0.408543\pi$
$614$	−3.13365	+	17.7718i	−0.126464	+	0.717213i
$615$	36.2211	+	1.58572i	1.46057	+	0.0639424i
$616$	−2.89901	−	2.79952i	−0.116804	−	0.112796i
$617$	−24.7063	−	29.4438i	−0.994636	−	1.18536i	−0.982657	−	0.185433i	$-0.940631\pi$
$617$	−24.7063	−	29.4438i	−0.994636	−	1.18536i	−0.0119793	−	0.999928i	$-0.503813\pi$
$618$	25.7019	+	10.6496i	1.03388	+	0.428390i
$619$	−30.1001	−	5.30745i	−1.20982	−	0.213325i	−0.467883	−	0.883790i	$-0.654983\pi$
$619$	−30.1001	−	5.30745i	−1.20982	−	0.213325i	−0.741941	+	0.670466i	$0.766094\pi$
$620$	12.8848	+	7.43903i	0.517465	+	0.298758i
$621$	27.4039	−	1.18678i	1.09968	−	0.0476237i
$622$		−	19.4185i		−	0.778611i
$623$	21.5899	+	44.2655i	0.864982	+	1.77346i
$624$	−0.993994	+	2.39891i	−0.0397916	+	0.0960334i
$625$	19.5609	+	7.11958i	0.782436	+	0.284783i
$626$	−20.2741	−	7.37915i	−0.810314	−	0.294930i
$627$	1.89692	+	3.64500i	0.0757557	+	0.145567i
$628$	12.5070	+	2.20532i	0.499084	+	0.0880020i
$629$	−10.7907	+	18.6900i	−0.430253	+	0.745220i
$630$	15.5065	+	5.34334i	0.617793	+	0.212884i
$631$	0.406480	+	0.704043i	0.0161817	+	0.0280275i	0.874003	−	0.485921i	$-0.161516\pi$
$631$	0.406480	+	0.704043i	0.0161817	+	0.0280275i	−0.857821	+	0.513948i	$0.828182\pi$
$632$	−2.81255	−	7.72740i	−0.111877	−	0.307380i
$633$	8.85887	−	39.9375i	0.352109	−	1.58737i
$634$	−6.81177	+	5.71575i	−0.270530	+	0.227002i
$635$	−3.19716	−	18.1320i	−0.126875	−	0.719546i
$636$	−5.97536	+	6.51942i	−0.236938	+	0.258512i
$637$	5.56125	+	8.89973i	0.220345	+	0.352620i
$638$	−1.12682	+	0.650568i	−0.0446111	+	0.0257562i
$639$	−13.5282	−	3.62828i	−0.535167	−	0.143533i
$640$	−1.78953	+	1.03318i	−0.0707372	+	0.0408402i
$641$	−2.21167	−	6.07652i	−0.0873558	−	0.240008i	0.888321	−	0.459224i	$-0.151872\pi$
$641$	−2.21167	−	6.07652i	−0.0873558	−	0.240008i	−0.975676	+	0.219216i	$0.929650\pi$
$642$	12.0030	−	18.8360i	0.473719	−	0.743397i
$643$	−19.8720	+	3.50397i	−0.783675	+	0.138183i	−0.551149	−	0.834407i	$-0.685810\pi$
$643$	−19.8720	+	3.50397i	−0.783675	+	0.138183i	−0.232526	+	0.972590i	$0.574699\pi$
$644$	3.84972	+	13.4254i	0.151700	+	0.529035i
$645$	−0.566186	−	4.30453i	−0.0222936	−	0.169491i
$646$	−2.60294	−	2.18413i	−0.102411	−	0.0859334i
$647$	18.8501	−	32.6493i	0.741073	−	1.28358i	−0.210935	−	0.977500i	$-0.567651\pi$
$647$	18.8501	−	32.6493i	0.741073	−	1.28358i	0.952007	−	0.306075i	$-0.0990160\pi$
$648$	−4.50367	+	7.79211i	−0.176921	+	0.306103i
$649$	6.14749	−	3.54926i	0.241310	−	0.139320i
$650$	−1.02860	+	0.374378i	−0.0403448	+	0.0146843i
$651$	7.69885	+	32.0842i	0.301742	+	1.25748i
$652$	17.0487	−	14.3055i	0.667678	−	0.560248i
$653$	−21.7181	−	25.8826i	−0.849893	−	1.01286i	−0.999708	−	0.0241494i	$-0.992312\pi$
$653$	−21.7181	−	25.8826i	−0.849893	−	1.01286i	0.149815	−	0.988714i	$-0.452132\pi$
$654$	−1.04184	+	23.7978i	−0.0407392	+	0.930566i
$655$	−42.9930	+	15.6482i	−1.67988	+	0.611425i
$656$	−10.1300			−0.395510
$657$	−27.0790	−	7.26263i	−1.05645	−	0.283342i
$658$	−3.88546	+	8.72696i	−0.151471	+	0.340212i
$659$	−11.0919	−	1.95579i	−0.432078	−	0.0761869i	−0.0466205	−	0.998913i	$-0.514845\pi$
$659$	−11.0919	−	1.95579i	−0.432078	−	0.0761869i	−0.385457	+	0.922726i	$0.625956\pi$
$660$	−5.32234	−	1.18059i	−0.207172	−	0.0459545i
$661$	−11.9115	−	14.1956i	−0.463304	−	0.552144i	0.482917	−	0.875666i	$-0.339577\pi$
$661$	−11.9115	−	14.1956i	−0.463304	−	0.552144i	−0.946221	+	0.323522i	$0.895133\pi$
$662$	−11.4035	−	13.5902i	−0.443210	−	0.528197i
$663$	3.82784	−	4.17637i	0.148661	−	0.162197i
$664$	9.68796	+	1.70825i	0.375966	+	0.0662929i
$665$	3.46325	−	7.77864i	0.134299	−	0.301643i
$666$	12.5480	−	26.8927i	0.486224	−	1.04207i
$667$	4.50915			0.174595
$668$	4.18999	−	1.52503i	0.162116	−	0.0590053i
$669$	−17.5902	+	9.15422i	−0.680075	+	0.353923i
$670$	8.13466	+	9.69451i	0.314269	+	0.374532i
$671$	−5.77734	+	4.84777i	−0.223032	+	0.187146i
$672$	−4.39371	−	1.30203i	−0.169491	−	0.0502267i
$673$	2.14541	−	0.780864i	0.0826994	−	0.0301001i	−0.300339	−	0.953832i	$-0.597100\pi$
$673$	2.14541	−	0.780864i	0.0826994	−	0.0301001i	0.383039	+	0.923732i	$0.374878\pi$
$674$	1.88234	−	1.08677i	0.0725052	−	0.0418609i
$675$	−3.70422	+	0.819832i	−0.142575	+	0.0315553i
$676$	5.37620	−	9.31185i	0.206777	−	0.358148i
$677$	9.85604	+	8.27020i	0.378798	+	0.317850i	0.812230	−	0.583337i	$-0.198253\pi$
$677$	9.85604	+	8.27020i	0.378798	+	0.317850i	−0.433432	+	0.901186i	$0.642698\pi$
$678$	−15.7950	+	12.1169i	−0.606602	+	0.465349i
$679$	−4.97035	−	17.3335i	−0.190745	−	0.665197i
$680$	4.43970	−	0.782838i	0.170255	−	0.0300205i
$681$	−1.32798	−	2.55175i	−0.0508882	−	0.0977834i
$682$	−3.75107	−	10.3060i	−0.143636	−	0.394636i
$683$	27.3988	−	15.8187i	1.04839	−	0.605287i	0.126190	−	0.992006i	$-0.459725\pi$
$683$	27.3988	−	15.8187i	1.04839	−	0.605287i	0.922198	+	0.386719i	$0.126392\pi$
$684$	3.82676	+	2.68087i	0.146320	+	0.102506i
$685$	−1.44093	+	0.831922i	−0.0550552	+	0.0317861i
$686$	−14.5941	+	11.4023i	−0.557204	+	0.435344i
$687$	−1.41089	−	0.312960i	−0.0538287	−	0.0119402i
$688$	0.210646	+	1.19463i	0.00803079	+	0.0455449i
$689$	−5.86379	+	4.92030i	−0.223392	+	0.187449i
$690$	13.9280	+	12.7657i	0.530230	+	0.485981i
$691$	8.19908	+	22.5268i	0.311908	+	0.856960i	0.992272	+	0.124085i	$0.0395996\pi$
$691$	8.19908	+	22.5268i	0.311908	+	0.856960i	−0.680364	+	0.732875i	$0.738178\pi$
$692$	−8.54584	−	14.8018i	−0.324864	−	0.562681i
$693$	−6.22453	−	10.3648i	−0.236450	−	0.393726i
$694$	−2.87791	+	4.98469i	−0.109244	+	0.189216i
$695$	−38.0607	−	6.71113i	−1.44373	−	0.254568i
$696$	−0.795088	+	1.24771i	−0.0301377	+	0.0472945i
$697$	20.7677	+	7.55883i	0.786634	+	0.286311i
$698$	14.1406	+	5.14675i	0.535229	+	0.194807i
$699$	27.1281	+	35.3627i	1.02608	+	1.33754i
$700$	−0.846823	−	1.73623i	−0.0320069	−	0.0656234i
$701$		−	16.6939i		−	0.630521i	−0.949005	−	0.315260i	$-0.897908\pi$
$701$		−	16.6939i		−	0.630521i	0.949005	−	0.315260i	$-0.102092\pi$
$702$	−4.74448	+	6.17861i	−0.179069	+	0.233197i
$703$	−13.3423	−	7.70321i	−0.503216	−	0.290532i
$704$	1.50009	+	0.264506i	0.0565366	+	0.00996893i
$705$	1.68523	+	12.8123i	0.0634696	+	0.482539i
$706$	14.4393	+	17.2080i	0.543428	+	0.647633i
$707$	4.95611	+	4.78603i	0.186394	+	0.179997i
$708$	4.33770	−	6.80706i	0.163021	−	0.255825i
$709$	0.922933	−	5.23421i	0.0346615	−	0.196575i	−0.962560	−	0.271069i	$-0.912623\pi$
$709$	0.922933	−	5.23421i	0.0346615	−	0.196575i	0.997221	+	0.0744937i	$0.0237341\pi$
$710$	−4.82369	−	8.35487i	−0.181030	−	0.313553i
$711$	−2.14434	−	24.5766i	−0.0804191	−	0.921695i
$712$	−16.1208	−	9.30737i	−0.604154	−	0.348809i
$713$	−6.60003	+	37.4306i	−0.247173	+	1.40179i
$714$	8.03611	+	5.94783i	0.300744	+	0.222592i
$715$	−4.43423	−	1.61393i	−0.165831	−	0.0603574i
$716$	0.616727	−	0.108746i	0.0230482	−	0.00406401i
$717$	3.38709	+	10.7469i	0.126493	+	0.401350i
$718$	14.9086	+	12.5098i	0.556382	+	0.466860i
$719$	−4.34812	+	7.53116i	−0.162157	+	0.280865i	−0.935642	−	0.352950i	$-0.885179\pi$
$719$	−4.34812	+	7.53116i	−0.162157	+	0.280865i	0.773485	+	0.633815i	$0.218512\pi$
$720$	−5.98825	+	1.60303i	−0.223169	+	0.0597416i
$721$	−17.2850	+	38.8230i	−0.643727	+	1.44585i
$722$	−10.6538	+	12.6967i	−0.396492	+	0.472521i
$723$	−6.50914	−	4.14786i	−0.242077	−	0.154260i
$724$	−2.39537	+	6.58122i	−0.0890231	+	0.244589i
$725$	−0.614198	+	0.108300i	−0.0228107	+	0.00402215i
$726$	−9.15060	−	11.9282i	−0.339611	−	0.442697i
$727$	−6.28026	−	17.2549i	−0.232922	−	0.639948i	0.767077	−	0.641555i	$-0.221711\pi$
$727$	−6.28026	−	17.2549i	−0.232922	−	0.639948i	−0.999999	+	0.00160756i	$0.999488\pi$
$728$	−3.62360	−	1.61332i	−0.134299	−	0.0597934i
$729$	−19.1054	+	19.0784i	−0.707606	+	0.706607i
$730$	−9.65544	−	16.7237i	−0.357364	−	0.618972i
$731$	0.459565	−	2.60632i	0.0169976	−	0.0963983i
$732$	−3.28271	+	7.92253i	−0.121333	+	0.292825i
$733$	−6.69197	+	18.3860i	−0.247174	+	0.679104i	0.752613	+	0.658463i	$0.228793\pi$
$733$	−6.69197	+	18.3860i	−0.247174	+	0.679104i	−0.999787	+	0.0206414i	$0.993429\pi$
$734$	0.971077	+	5.50725i	0.0358431	+	0.203276i
$735$	−8.77649	+	23.4658i	−0.323726	+	0.865550i
$736$	−4.04381	−	3.39316i	−0.149057	−	0.125074i
$737$		−	9.32887i		−	0.343633i
$738$	−29.3526	−	7.87242i	−1.08048	−	0.289788i
$739$	9.78089			0.359796			0.179898	−	0.983685i	$-0.442423\pi$
$739$	9.78089			0.359796			0.179898	+	0.983685i	$0.442423\pi$
$740$	19.2078	−	6.99108i	0.706094	−	0.256997i
$741$	2.98141	+	2.73260i	0.109525	+	0.100385i
$742$	−9.71737	−	9.38389i	−0.356736	−	0.344494i
$743$	−9.27191	+	25.4744i	−0.340154	+	0.934564i	0.645196	+	0.764017i	$0.276776\pi$
$743$	−9.27191	+	25.4744i	−0.340154	+	0.934564i	−0.985350	+	0.170547i	$0.945447\pi$
$744$	−9.19355	−	8.42633i	−0.337052	−	0.308924i
$745$	9.09606	−	10.8403i	0.333254	−	0.397157i
$746$			27.0673i			0.991004i
$747$	26.7442	+	12.4787i	0.978520	+	0.456572i
$748$	−2.87799	−	1.66161i	−0.105230	−	0.0607545i
$749$	28.2850	+	19.0783i	1.03351	+	0.697106i
$750$	−17.2953	−	11.0212i	−0.631536	−	0.402438i
$751$	25.5633	−	21.4502i	0.932818	−	0.782728i	−0.0435029	−	0.999053i	$-0.513852\pi$
$751$	25.5633	−	21.4502i	0.932818	−	0.782728i	0.976321	+	0.216326i	$0.0694073\pi$
$752$	−0.626980	−	3.55578i	−0.0228636	−	0.129666i
$753$	−22.8305	+	17.5142i	−0.831991	+	0.638254i
$754$	−0.823162	+	0.981006i	−0.0299778	+	0.0357261i
$755$	39.9166			1.45271
$756$	−11.7193	−	7.18727i	−0.426229	−	0.261399i
$757$	−42.2491			−1.53557			−0.767785	−	0.640708i	$-0.778641\pi$
$757$	−42.2491			−1.53557			−0.767785	+	0.640708i	$0.778641\pi$
$758$	−6.36156	+	7.58141i	−0.231062	+	0.275369i
$759$	−1.81623	−	13.8082i	−0.0659250	−	0.501206i
$760$	0.558849	+	3.16939i	0.0202716	+	0.114966i
$761$	0.233475	−	0.195909i	0.00846346	−	0.00710169i	−0.638546	−	0.769584i	$-0.720464\pi$
$761$	0.233475	−	0.195909i	0.00846346	−	0.00710169i	0.647010	+	0.762482i	$0.276019\pi$
$762$	−0.674990	+	15.4181i	−0.0244523	+	0.558540i
$763$	−36.2979	−	2.53808i	−1.31407	−	0.0918846i
$764$	4.13233	+	2.38580i	0.149502	+	0.0863152i
$765$	13.4728	+	1.18192i	0.487111	+	0.0427323i
$766$			23.9354i			0.864823i
$767$	4.49086	−	5.35200i	0.162156	−	0.193250i
$768$	1.65195	−	0.520643i	0.0596095	−	0.0187871i
$769$	−4.69727	+	12.9056i	−0.169388	+	0.465390i	−0.995120	−	0.0986731i	$-0.968540\pi$
$769$	−4.69727	+	12.9056i	−0.169388	+	0.465390i	0.825732	+	0.564063i	$0.190762\pi$
$770$	2.01461	−	8.08027i	0.0726015	−	0.291193i
$771$	5.06940	−	22.8538i	0.182570	−	0.823061i
$772$	−5.19623	+	1.89127i	−0.187016	+	0.0680684i
$773$	−25.4968			−0.917055			−0.458528	−	0.888680i	$-0.651623\pi$
$773$	−25.4968			−0.917055			−0.458528	+	0.888680i	$0.651623\pi$
$774$	−0.318029	+	3.62526i	−0.0114313	+	0.130307i
$775$		−	5.25700i		−	0.188837i
$776$	5.22094	+	4.38089i	0.187421	+	0.157265i
$777$	40.5659	+	20.2312i	1.45529	+	0.725790i
$778$	−4.40665	−	24.9913i	−0.157986	−	0.895983i
$779$	−5.39607	+	14.8256i	−0.193334	+	0.531181i
$780$	−5.31990	+	0.699740i	−0.190483	+	0.0250547i
$781$	−1.23491	+	7.00355i	−0.0441887	+	0.250607i
$782$	5.75839	+	9.97383i	0.205920	+	0.356663i
$783$	−3.27349	+	2.99747i	−0.116985	+	0.107121i
$784$	2.16308	−	6.65741i	0.0772527	−	0.237765i
$785$	8.97555	+	24.6601i	0.320351	+	0.880158i
$786$	38.0225	−	5.00120i	1.35622	−	0.178387i
$787$	−11.5492	+	2.03643i	−0.411684	+	0.0725909i	−0.375654	−	0.926760i	$-0.622582\pi$
$787$	−11.5492	+	2.03643i	−0.411684	+	0.0725909i	−0.0360291	+	0.999351i	$0.511471\pi$
$788$	8.90315	−	24.4612i	0.317161	−	0.871394i
$789$	0.628297	−	14.3516i	0.0223680	−	0.510929i
$790$	10.9225	−	13.0169i	0.388606	−	0.463122i
$791$	−17.8740	−	24.6013i	−0.635526	−	0.874721i
$792$	4.14108	+	1.93221i	0.147147	+	0.0686580i
$793$	−3.71141	+	6.42836i	−0.131796	+	0.228278i
$794$	1.78346	+	1.49650i	0.0632926	+	0.0531088i
$795$	−17.8403	−	3.95731i	−0.632731	−	0.140351i
$796$	−0.894082	+	0.157651i	−0.0316899	+	0.00558778i
$797$	−16.8199	−	6.12195i	−0.595792	−	0.216851i	0.0264830	−	0.999649i	$-0.491569\pi$
$797$	−16.8199	−	6.12195i	−0.595792	−	0.216851i	−0.622275	+	0.782799i	$0.713791\pi$
$798$	−4.24601	+	5.73678i	−0.150307	+	0.203080i
$799$	−1.36788	+	7.75763i	−0.0483921	+	0.274445i
$800$	0.632309	+	0.365064i	0.0223555	+	0.0129070i
$801$	−39.4785	−	39.4971i	−1.39491	−	1.39556i
$802$	18.0999	+	31.3499i	0.639129	+	1.10700i
$803$	−2.47189	+	14.0188i	−0.0872312	+	0.494713i
$804$	−4.89702	−	9.40980i	−0.172705	−	0.331858i
$805$	−20.0476	+	20.7601i	−0.706586	+	0.731696i
$806$	−6.93851	−	8.26899i	−0.244399	−	0.291263i
$807$	−27.1112	+	20.7981i	−0.954360	+	0.732128i
$808$	−2.56453	−	0.452196i	−0.0902199	−	0.0159082i
$809$	−12.6776	−	7.31944i	−0.445722	−	0.257338i	0.260300	−	0.965528i	$-0.416179\pi$
$809$	−12.6776	−	7.31944i	−0.445722	−	0.257338i	−0.706022	+	0.708190i	$0.749512\pi$
$810$	−18.5973	−	0.00876217i	−0.653443	−	0.000307871i
$811$			9.30362i			0.326694i	0.986569	+	0.163347i	$0.0522290\pi$
$811$			9.30362i			0.326694i	−0.986569	+	0.163347i	$0.947771\pi$
$812$	−1.87362	−	1.26377i	−0.0657512	−	0.0443495i
$813$	−28.0783	+	3.69322i	−0.984750	+	0.129527i
$814$	−14.1591	−	5.15349i	−0.496276	−	0.180630i
$815$	43.2145	+	15.7288i	1.51374	+	0.550956i
$816$	−3.77519	−	0.165274i	−0.132158	−	0.00578575i
$817$	1.86059	+	0.328072i	0.0650937	+	0.0114778i
$818$	1.05829	−	1.83301i	0.0370023	−	0.0640899i
$819$	−9.24594	−	7.49077i	−0.323079	−	0.261749i
$820$	−10.4661	−	18.1279i	−0.365493	−	0.633053i
$821$	8.07358	+	22.1820i	0.281770	+	0.774156i	0.997152	+	0.0754226i	$0.0240306\pi$
$821$	8.07358	+	22.1820i	0.281770	+	0.774156i	−0.715382	+	0.698734i	$0.753747\pi$
$822$	1.33015	−	0.419223i	0.0463944	−	0.0146221i
$823$	7.73552	−	6.49088i	0.269643	−	0.226258i	−0.497932	−	0.867216i	$-0.665907\pi$
$823$	7.73552	−	6.49088i	0.269643	−	0.226258i	0.767576	+	0.640958i	$0.221463\pi$
$824$	−2.78920	−	15.8184i	−0.0971665	−	0.551058i
$825$	0.579034	+	1.83721i	0.0201594	+	0.0639636i
$826$	10.2218	+	6.89463i	0.355661	+	0.239895i
$827$	−12.2505	+	7.07283i	−0.425992	+	0.245946i	−0.697638	−	0.716451i	$-0.745765\pi$
$827$	−12.2505	+	7.07283i	−0.425992	+	0.245946i	0.271646	+	0.962397i	$0.412432\pi$
$828$	−9.08036	−	12.9746i	−0.315564	−	0.450899i
$829$	10.6445	−	6.14558i	0.369697	−	0.213445i	−0.303629	−	0.952790i	$-0.598198\pi$
$829$	10.6445	−	6.14558i	0.369697	−	0.213445i	0.673326	+	0.739346i	$0.264865\pi$
$830$	6.95248	+	19.1018i	0.241324	+	0.663033i
$831$	−35.4613	−	1.55246i	−1.23014	−	0.0538543i
$832$	1.47643	−	0.260334i	0.0511858	−	0.00902544i
$833$	−9.40223	+	12.0345i	−0.325768	+	0.416969i
$834$	29.9277	+	12.4006i	1.03631	+	0.429397i
$835$	7.05811	+	5.92246i	0.244256	+	0.204955i
$836$	1.18618	−	2.05453i	0.0410250	−	0.0710573i
$837$	−20.0907	−	31.5608i	−0.694438	−	1.09090i
$838$	−2.99022	+	1.72641i	−0.103296	+	0.0596377i
$839$	−37.5231	+	13.6573i	−1.29544	+	0.471502i	−0.895509	−	0.445042i	$-0.853189\pi$
$839$	−37.5231	+	13.6573i	−1.29544	+	0.471502i	−0.399932	+	0.916545i	$0.630966\pi$
$840$	−2.20950	−	9.20790i	−0.0762352	−	0.317703i
$841$	21.6563	−	18.1718i	0.746770	−	0.626615i
$842$	−18.2648	−	21.7671i	−0.629446	−	0.750145i
$843$	−13.9203	−	8.87054i	−0.479442	−	0.305518i
$844$	−22.1940	+	8.07797i	−0.763950	+	0.278055i
$845$	22.2184			0.764336
$846$	0.946604	−	10.7905i	0.0325449	−	0.370983i
$847$	18.5787	−	13.4983i	0.638370	−	0.463806i
$848$	5.02824	+	0.886614i	0.172670	+	0.0304464i
$849$	−15.7712	−	50.0405i	−0.541268	−	1.71739i
$850$	−1.02391	−	1.22025i	−0.0351197	−	0.0418541i
$851$	33.5652	+	40.0014i	1.15060	+	1.37123i
$852$	2.43076	+	7.71255i	0.0832765	+	0.264228i
$853$	−22.3568	−	3.94211i	−0.765483	−	0.134975i	−0.222744	−	0.974877i	$-0.571501\pi$
$853$	−22.3568	−	3.94211i	−0.765483	−	0.134975i	−0.542739	+	0.839902i	$0.682613\pi$
$854$	−11.9671	−	5.32805i	−0.409506	−	0.182322i
$855$	−0.843741	+	9.61791i	−0.0288553	+	0.328926i
$856$	−12.8953			−0.440752
$857$	34.5746	−	12.5841i	1.18105	−	0.429866i	0.324475	−	0.945894i	$-0.394812\pi$
$857$	34.5746	−	12.5841i	1.18105	−	0.429866i	0.856572	+	0.516028i	$0.172590\pi$
$858$	3.33566	+	2.12560i	0.113878	+	0.0725669i
$859$	−21.6846	−	25.8427i	−0.739869	−	0.881742i	0.256529	−	0.966537i	$-0.417421\pi$
$859$	−21.6846	−	25.8427i	−0.739869	−	0.881742i	−0.996398	+	0.0847945i	$0.972977\pi$
$860$	−1.92019	+	1.61123i	−0.0654778	+	0.0549424i
$861$	13.1895	−	44.5083i	0.449497	−	1.51684i
$862$	−8.85122	+	3.22158i	−0.301474	+	0.109728i
$863$	37.5219	−	21.6633i	1.27726	−	0.737427i	0.300917	−	0.953650i	$-0.402707\pi$
$863$	37.5219	−	21.6633i	1.27726	−	0.737427i	0.976344	+	0.216224i	$0.0693741\pi$
$864$	5.19129	−	0.224819i	0.176611	−	0.00764848i
$865$	17.6588	−	30.5860i	0.600419	−	1.03996i
$866$	16.6094	+	13.9369i	0.564410	+	0.473596i
$867$	−19.5859	−	8.11544i	−0.665172	−	0.275615i
$868$	13.2330	−	13.7032i	0.449156	−	0.465118i
$869$	−12.3357	+	2.17512i	−0.418460	+	0.0737858i
$870$	−3.05429	−	0.133714i	−0.103550	−	0.00453331i
$871$	−3.14034	−	8.62800i	−0.106406	−	0.292349i
$872$	11.9103	−	6.87640i	0.403333	−	0.232864i
$873$	11.7236	+	16.7515i	0.396784	+	0.566951i
$874$	−7.12007	+	4.11077i	−0.240840	+	0.139049i
$875$	17.5178	−	25.9714i	0.592211	−	0.877995i
$876$	4.86558	+	15.4380i	0.164393	+	0.521602i
$877$	6.78561	+	38.4831i	0.229134	+	1.29948i	0.854623	+	0.519249i	$0.173788\pi$
$877$	6.78561	+	38.4831i	0.229134	+	1.29948i	−0.625489	+	0.780233i	$0.715101\pi$
$878$	−2.19530	+	1.84207i	−0.0740877	+	0.0621669i
$879$	27.2577	−	8.59078i	0.919379	−	0.289760i
$880$	1.07652	+	2.95773i	0.0362896	+	0.0997049i
$881$	−9.62127	−	16.6645i	−0.324149	−	0.561442i	0.657191	−	0.753724i	$-0.271744\pi$
$881$	−9.62127	−	16.6645i	−0.324149	−	0.561442i	−0.981340	+	0.192282i	$0.938411\pi$
$882$	11.4415	−	17.6095i	0.385254	−	0.592941i
$883$	3.09420	−	5.35931i	0.104128	−	0.180355i	−0.809254	−	0.587460i	$-0.800128\pi$
$883$	3.09420	−	5.35931i	0.104128	−	0.180355i	0.913382	+	0.407104i	$0.133461\pi$
$884$	−3.22111	−	0.567969i	−0.108338	−	0.0191029i
$885$	16.6631	+	0.729491i	0.560123	+	0.0245216i
$886$	12.7257	+	4.63178i	0.427529	+	0.155608i
$887$	−39.0528	−	14.2141i	−1.31127	−	0.477262i	−0.410616	−	0.911808i	$-0.634686\pi$
$887$	−39.0528	−	14.2141i	−1.31127	−	0.477262i	−0.900649	+	0.434546i	$0.856909\pi$
$888$	−16.9872	+	2.23437i	−0.570052	+	0.0749804i
$889$	−23.5167	−	1.64437i	−0.788725	−	0.0551506i
$890$		−	38.4649i		−	1.28935i
$891$	10.4976	+	8.81695i	0.351682	+	0.295379i
$892$	9.91480	+	5.72432i	0.331972	+	0.191664i
$893$	−5.53798	−	0.976495i	−0.185321	−	0.0326772i
$894$	−9.41120	+	7.21971i	−0.314758	+	0.241463i
$895$	0.831795	+	0.991295i	0.0278039	+	0.0331353i
$896$	0.729276	+	2.54326i	0.0243634	+	0.0849643i
$897$	−6.32797	−	12.1594i	−0.211285	−	0.405991i
$898$	−4.55054	+	25.8074i	−0.151853	+	0.861203i
$899$	−3.07515	−	5.32632i	−0.102562	−	0.177643i
$900$	1.54847	+	1.54920i	0.0516157	+	0.0516400i
$901$	−9.64693	−	5.56966i	−0.321386	−	0.185552i
$902$	−2.67944	+	15.1959i	−0.0892156	+	0.505967i
$903$	−5.52313	−	0.629923i	−0.183798	−	0.0209625i
$904$	10.8004	+	3.93101i	0.359214	+	0.130743i
$905$	−14.2521	+	2.51303i	−0.473756	+	0.0835360i
$906$	−32.6645	−	7.24559i	−1.08521	−	0.240719i
$907$	−32.7713	−	27.4984i	−1.08815	−	0.913068i	−0.0915800	−	0.995798i	$-0.529192\pi$
$907$	−32.7713	−	27.4984i	−1.08815	−	0.913068i	−0.996572	+	0.0827297i	$0.973636\pi$
$908$	−0.830410	+	1.43831i	−0.0275581	+	0.0477321i
$909$	−7.07955	−	3.30328i	−0.234814	−	0.109563i
$910$	−0.856770	−	8.15137i	−0.0284016	−	0.270215i
$911$	−9.27325	+	11.0514i	−0.307237	+	0.366150i	−0.897465	−	0.441086i	$-0.854593\pi$
$911$	−9.27325	+	11.0514i	−0.307237	+	0.366150i	0.590228	+	0.807236i	$0.299038\pi$
$912$	0.117985	−	2.69502i	0.00390687	−	0.0892409i
$913$	5.12504	−	14.0809i	0.169614	−	0.466011i
$914$	40.5955	−	7.15809i	1.34278	−	0.236769i
$915$	−17.5692	+	2.31093i	−0.580821	+	0.0763969i
$916$	0.285373	+	0.784056i	0.00942899	+	0.0259059i
$917$	6.12353	+	58.2597i	0.202217	+	1.92390i
$918$	−10.8105	−	3.41275i	−0.356801	−	0.112638i
$919$	−27.4545	−	47.5525i	−0.905640	−	1.56861i	−0.820056	−	0.572283i	$-0.806058\pi$
$919$	−27.4545	−	47.5525i	−0.905640	−	1.56861i	−0.0855832	−	0.996331i	$-0.527275\pi$
$920$	1.89415	−	10.7423i	0.0624483	−	0.354162i
$921$	30.9896	−	4.07615i	1.02114	−	0.134314i
$922$	−10.3647	+	28.4767i	−0.341342	+	0.937831i
$923$	1.21544	+	6.89308i	0.0400066	+	0.226888i
$924$	−3.11531	+	6.24656i	−0.102486	+	0.205497i
$925$	−5.53271	−	4.64249i	−0.181914	−	0.152644i
$926$			30.0051i			0.986028i
$927$	4.21109	−	48.0028i	0.138310	−	1.57662i
$928$	0.854197			0.0280404
$929$	−31.2508	+	11.3744i	−1.02531	+	0.373181i	−0.799292	−	0.600943i	$-0.794792\pi$
$929$	−31.2508	+	11.3744i	−1.02531	+	0.373181i	−0.226015	+	0.974124i	$0.572570\pi$
$930$	5.58051	−	25.1580i	0.182992	−	0.824965i
$931$	−8.59110	−	6.71202i	−0.281562	−	0.219978i
$932$	8.80097	−	24.1805i	0.288285	−	0.792057i
$933$	−32.0783	+	10.1101i	−1.05020	+	0.330990i
$934$	0.728928	−	0.868702i	0.0238512	−	0.0284248i
$935$		−	6.86699i		−	0.224575i
$936$	4.48040	+	0.393048i	0.146446	+	0.0128472i
$937$	18.4852	+	10.6725i	0.603886	+	0.348654i	0.770569	−	0.637357i	$-0.219972\pi$
$937$	18.4852	+	10.6725i	0.603886	+	0.348654i	−0.166683	+	0.986011i	$0.553306\pi$
$938$	14.5637	−	7.10327i	0.475523	−	0.231930i
$939$	−1.63443	+	37.3336i	−0.0533374	+	1.21834i
$940$	5.71537	−	4.79577i	0.186415	−	0.156421i
$941$	−3.40613	−	19.3171i	−0.111037	−	0.629720i	−0.988636	−	0.150326i	$-0.951968\pi$
$941$	−3.40613	−	19.3171i	−0.111037	−	0.629720i	0.877600	−	0.479394i	$-0.159144\pi$
$942$	−2.86861	−	21.8091i	−0.0934644	−	0.710579i
$943$	34.3727	−	40.9637i	1.11933	−	1.33396i
$944$	−4.66018			−0.151676
$945$	0.753576	−	28.3979i	0.0245138	−	0.923782i
$946$	1.84777			0.0600760
$947$	−22.0236	+	26.2467i	−0.715671	+	0.852904i	−0.994203	−	0.107523i	$-0.965708\pi$
$947$	−22.0236	+	26.2467i	−0.715671	+	0.852904i	0.278531	+	0.960427i	$0.410152\pi$
$948$	−11.3009	+	8.66940i	−0.367037	+	0.281569i
$949$	2.43290	+	13.7977i	0.0789754	+	0.447892i
$950$	0.871103	−	0.730942i	0.0282623	−	0.0237149i
$951$	12.9886	+	8.27682i	0.421185	+	0.268394i
$952$	0.402632	−	5.75817i	0.0130494	−	0.186623i
$953$	48.1317	+	27.7888i	1.55914	+	0.900168i	0.997340	+	0.0728936i	$0.0232234\pi$
$953$	48.1317	+	27.7888i	1.55914	+	0.900168i	0.561798	+	0.827275i	$0.310110\pi$
$954$	13.8808	+	6.47669i	0.449406	+	0.209691i
$955$			9.85987i			0.319058i
$956$	4.18171	−	4.98357i	0.135246	−	0.161180i
$957$	1.66137	+	1.52273i	0.0537046	+	0.0492228i
$958$	−7.60633	+	20.8982i	−0.245749	+	0.675190i
$959$	0.587215	+	2.04784i	0.0189622	+	0.0661281i
$960$	2.63847	+	2.41828i	0.0851562	+	0.0780498i
$961$	19.5846	−	7.12820i	0.631760	−	0.229942i
$962$	−14.8301			−0.478142
$963$	−37.3653	−	10.0214i	−1.20408	−	0.322937i
$964$			4.45622i			0.143525i
$965$	−8.75314	−	7.34475i	−0.281773	−	0.236436i
$966$	20.1737	−	13.3494i	0.649079	−	0.429509i
$967$	5.35574	+	30.3739i	0.172229	+	0.976760i	0.941294	+	0.337589i	$0.109611\pi$
$967$	5.35574	+	30.3739i	0.172229	+	0.976760i	−0.769065	+	0.639171i	$0.779278\pi$
$968$	−2.96866	+	8.15632i	−0.0954163	+	0.262154i
$969$	−2.25286	+	5.43708i	−0.0723724	+	0.174664i
$970$	−2.44553	+	13.8693i	−0.0785212	+	0.445316i
$971$	−3.61850	−	6.26742i	−0.116123	−	0.201131i	0.802105	−	0.597183i	$-0.203713\pi$
$971$	−3.61850	−	6.26742i	−0.116123	−	0.201131i	−0.918228	+	0.396052i	$0.870380\pi$
$972$	15.2170	+	3.38292i	0.488084	+	0.108507i
$973$	−20.1269	+	45.2062i	−0.645239	+	1.44924i
$974$	10.9209	+	30.0050i	0.349929	+	0.961422i
$975$	1.15398	+	1.50427i	0.0369571	+	0.0481752i
$976$	4.87597	−	0.859765i	0.156076	−	0.0275204i
$977$	7.47289	−	20.5316i	0.239079	−	0.656864i	−0.760889	−	0.648882i	$-0.775237\pi$
$977$	7.47289	−	20.5316i	0.239079	−	0.656864i	0.999968	−	0.00798207i	$-0.00254080\pi$
$978$	−32.5083	−	20.7154i	−1.03950	−	0.662407i
$979$	−18.2259	+	21.7208i	−0.582503	+	0.694200i
$980$	14.1485	−	3.00744i	0.451956	−	0.0960692i
$981$	39.8551	−	10.6691i	1.27247	−	0.340637i
$982$	12.4531	−	21.5694i	0.397394	−	0.688307i
$983$	38.7523	+	32.5170i	1.23601	+	1.03713i	0.997826	+	0.0659106i	$0.0209952\pi$
$983$	38.7523	+	32.5170i	1.23601	+	1.03713i	0.238180	+	0.971221i	$0.423449\pi$
$984$	5.27411	+	16.7342i	0.168132	+	0.533467i
$985$	52.9725	−	9.34049i	1.68785	−	0.297613i
$986$	−1.75121	−	0.637388i	−0.0557698	−	0.0202986i
$987$	16.4394	+	1.87494i	0.523272	+	0.0596801i
$988$	0.405459	−	2.29947i	0.0128994	−	0.0731559i
$989$	−5.54561	−	3.20176i	−0.176340	−	0.101810i
$990$	0.820764	+	9.40690i	0.0260856	+	0.298971i
$991$	11.0201	+	19.0874i	0.350066	+	0.606332i	0.986261	−	0.165196i	$-0.0528258\pi$
$991$	11.0201	+	19.0874i	0.350066	+	0.606332i	−0.636195	+	0.771529i	$0.719492\pi$
$992$	−1.25028	+	7.09072i	−0.0396966	+	0.225130i
$993$	−16.5131	+	25.9136i	−0.524027	+	0.822344i
$994$	−11.8739	+	3.40482i	−0.376616	+	0.107994i
$995$	−1.20587	−	1.43710i	−0.0382287	−	0.0455591i
$996$	−2.22203	−	16.8934i	−0.0704078	−	0.535288i
$997$	−12.8771	−	2.27057i	−0.407821	−	0.0719098i	−0.0340254	−	0.999421i	$-0.510833\pi$
$997$	−12.8771	−	2.27057i	−0.407821	−	0.0719098i	−0.373795	+	0.927511i	$0.621944\pi$
$998$	−15.0713	−	8.70145i	−0.477075	−	0.275440i
$999$	−50.9583	−	6.72711i	−1.61225	−	0.212836i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.2.bf.a.101.11	yes	144
7.5	odd	6		378.2.ba.a.47.23	✓	144
27.23	odd	18		378.2.ba.a.185.23	yes	144
189.131	even	18	inner	378.2.bf.a.131.11	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.ba.a.47.23	✓	144	7.5	odd	6
378.2.ba.a.185.23	yes	144	27.23	odd	18
378.2.bf.a.101.11	yes	144	1.1	even	1	trivial
378.2.bf.a.131.11	yes	144	189.131	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	378.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.642788 + 0.766044i) q^{2} +(1.60013 + 0.663016i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(1.58293 - 1.32824i) q^{5} +(-1.53644 + 0.799591i) q^{6} +(-1.15983 - 2.37798i) q^{7} +(0.866025 + 0.500000i) q^{8} +(2.12082 + 2.12182i) q^{9} +O(q^{10})\)	\(q+(-0.642788 + 0.766044i) q^{2} +(1.60013 + 0.663016i) q^{3} +(-0.173648 - 0.984808i) q^{4} +(1.58293 - 1.32824i) q^{5} +(-1.53644 + 0.799591i) q^{6} +(-1.15983 - 2.37798i) q^{7} +(0.866025 + 0.500000i) q^{8} +(2.12082 + 2.12182i) q^{9} +2.06637i q^{10} +(0.979112 - 1.16686i) q^{11} +(0.375084 - 1.69095i) q^{12} +(0.512757 - 1.40879i) q^{13} +(2.56716 + 0.640057i) q^{14} +(3.41353 - 1.07584i) q^{15} +(-0.939693 + 0.342020i) q^{16} +2.18170 q^{17} +(-2.98865 + 0.260763i) q^{18} +1.55746i q^{19} +(-1.58293 - 1.32824i) q^{20} +(-0.279235 - 4.57406i) q^{21} +(0.264506 + 1.50009i) q^{22} +(1.80546 - 4.96047i) q^{23} +(1.05424 + 1.37425i) q^{24} +(-0.126785 + 0.719036i) q^{25} +(0.749601 + 1.29835i) q^{26} +(1.98678 + 4.80132i) q^{27} +(-2.14045 + 1.55514i) q^{28} +(0.292152 + 0.802682i) q^{29} +(-1.37003 + 3.30645i) q^{30} +(-7.09072 + 1.25028i) q^{31} +(0.342020 - 0.939693i) q^{32} +(2.34035 - 1.21796i) q^{33} +(-1.40237 + 1.67128i) q^{34} +(-4.99444 - 2.22365i) q^{35} +(1.72131 - 2.45705i) q^{36} +(-4.94601 + 8.56674i) q^{37} +(-1.19308 - 1.00112i) q^{38} +(1.75453 - 1.91428i) q^{39} +(2.03497 - 0.358821i) q^{40} +(9.51907 + 3.46466i) q^{41} +(3.68342 + 2.72624i) q^{42} +(0.210646 - 1.19463i) q^{43} +(-1.31915 - 0.761614i) q^{44} +(6.17538 + 0.541742i) q^{45} +(2.63941 + 4.57159i) q^{46} +(-0.626980 + 3.55578i) q^{47} +(-1.73039 - 0.0757548i) q^{48} +(-4.30960 + 5.51610i) q^{49} +(-0.469317 - 0.559310i) q^{50} +(3.49099 + 1.44650i) q^{51} +(-1.47643 - 0.260334i) q^{52} +(-4.42176 - 2.55290i) q^{53} +(-4.95511 - 1.56426i) q^{54} -3.14755i q^{55} +(0.184550 - 2.63931i) q^{56} +(-1.03262 + 2.49213i) q^{57} +(-0.802682 - 0.292152i) q^{58} +(4.37913 + 1.59387i) q^{59} +(-1.65225 - 3.17485i) q^{60} +(-4.87597 - 0.859765i) q^{61} +(3.60005 - 6.23547i) q^{62} +(2.58586 - 7.50422i) q^{63} +(0.500000 + 0.866025i) q^{64} +(-1.05954 - 2.91107i) q^{65} +(-0.571338 + 2.57570i) q^{66} +(4.69157 - 3.93670i) q^{67} +(-0.378848 - 2.14855i) q^{68} +(6.17784 - 6.74033i) q^{69} +(4.91378 - 2.39663i) q^{70} +(-4.04327 + 2.33438i) q^{71} +(0.775774 + 2.89796i) q^{72} +(-8.09329 + 4.67267i) q^{73} +(-3.38327 - 9.29546i) q^{74} +(-0.679605 + 1.06649i) q^{75} +(1.53380 - 0.270450i) q^{76} +(-3.91037 - 0.974952i) q^{77} +(0.338633 + 2.57452i) q^{78} +(-6.29944 - 5.28586i) q^{79} +(-1.03318 + 1.78953i) q^{80} +(-0.00424038 + 9.00000i) q^{81} +(-8.77283 + 5.06499i) q^{82} +(9.24414 - 3.36459i) q^{83} +(-4.45608 + 1.06927i) q^{84} +(3.45347 - 2.89781i) q^{85} +(0.779740 + 0.929258i) q^{86} +(-0.0647095 + 1.47810i) q^{87} +(1.43137 - 0.520974i) q^{88} -18.6147 q^{89} +(-4.38446 + 4.38239i) q^{90} +(-3.94478 + 0.414626i) q^{91} +(-5.19862 - 0.916657i) q^{92} +(-12.1750 - 2.70064i) q^{93} +(-2.32087 - 2.76590i) q^{94} +(2.06867 + 2.46535i) q^{95} +(1.17031 - 1.27686i) q^{96} +(6.71192 + 1.18349i) q^{97} +(-1.45543 - 6.84702i) q^{98} +(4.55239 - 0.397202i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q + 18 q^{6} - 12 q^{9}+O(q^{10}) \) 144 * q + 18 * q^6 - 12 * q^9	\( 144 q + 18 q^{6} - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 6 q^{21} - 6 q^{23} - 6 q^{29} - 18 q^{30} - 54 q^{35} + 6 q^{36} - 6 q^{39} + 24 q^{42} - 54 q^{47} + 18 q^{49} + 12 q^{50} + 18 q^{51} + 90 q^{53} - 54 q^{54} - 12 q^{56} - 6 q^{57} - 90 q^{59} - 36 q^{60} - 24 q^{63} + 72 q^{64} - 84 q^{65} - 36 q^{69} - 18 q^{70} - 72 q^{71} + 12 q^{72} + 18 q^{74} - 90 q^{75} - 78 q^{77} - 60 q^{78} + 36 q^{79} - 6 q^{84} - 72 q^{85} + 24 q^{86} + 90 q^{87} - 18 q^{91} - 42 q^{92} - 12 q^{93} + 78 q^{95} - 36 q^{98} - 108 q^{99}+O(q^{100}) \) 144 * q + 18 * q^6 - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 6 * q^21 - 6 * q^23 - 6 * q^29 - 18 * q^30 - 54 * q^35 + 6 * q^36 - 6 * q^39 + 24 * q^42 - 54 * q^47 + 18 * q^49 + 12 * q^50 + 18 * q^51 + 90 * q^53 - 54 * q^54 - 12 * q^56 - 6 * q^57 - 90 * q^59 - 36 * q^60 - 24 * q^63 + 72 * q^64 - 84 * q^65 - 36 * q^69 - 18 * q^70 - 72 * q^71 + 12 * q^72 + 18 * q^74 - 90 * q^75 - 78 * q^77 - 60 * q^78 + 36 * q^79 - 6 * q^84 - 72 * q^85 + 24 * q^86 + 90 * q^87 - 18 * q^91 - 42 * q^92 - 12 * q^93 + 78 * q^95 - 36 * q^98 - 108 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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