LMFDB - Embedded newform 378.2.z.a.41.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,2,Mod(41,378)]

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([17, 9]))

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

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

chi := DirichletCharacter("378.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	378.z (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			41.13
Character	$\chi$	$=$	378.41
Dual form			378.2.z.a.83.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.984808 - 0.173648i) q^{2} +(-1.64560 - 0.540384i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.881233 + 0.739442i) q^{5} +(-1.71443 - 0.246420i) q^{6} +(-0.336437 + 2.62427i) q^{7} +(0.866025 - 0.500000i) q^{8} +(2.41597 + 1.77851i) q^{9} +O(q^{10})$	\(q+(0.984808 - 0.173648i) q^{2} +(-1.64560 - 0.540384i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.881233 + 0.739442i) q^{5} +(-1.71443 - 0.246420i) q^{6} +(-0.336437 + 2.62427i) q^{7} +(0.866025 - 0.500000i) q^{8} +(2.41597 + 1.77851i) q^{9} +(0.996248 + 0.575184i) q^{10} +(0.595719 + 0.709951i) q^{11} +(-1.73118 + 0.0550316i) q^{12} +(4.25218 + 0.749775i) q^{13} +(0.124375 + 2.64283i) q^{14} +(-1.05057 - 1.69303i) q^{15} +(0.766044 - 0.642788i) q^{16} +(2.28111 - 3.95100i) q^{17} +(2.68810 + 1.33196i) q^{18} +(-0.687760 + 0.397079i) q^{19} +(1.08099 + 0.393449i) q^{20} +(1.97176 - 4.13669i) q^{21} +(0.709951 + 0.595719i) q^{22} +(1.46197 + 4.01673i) q^{23} +(-1.69532 + 0.354811i) q^{24} +(-0.638444 - 3.62080i) q^{25} +4.31778 q^{26} +(-3.01463 - 4.23226i) q^{27} +(0.581407 + 2.58108i) q^{28} +(1.10897 - 0.195541i) q^{29} +(-1.32860 - 1.48488i) q^{30} +(1.11895 + 3.07428i) q^{31} +(0.642788 - 0.766044i) q^{32} +(-0.596667 - 1.49021i) q^{33} +(1.56037 - 4.28708i) q^{34} +(-2.23698 + 2.06382i) q^{35} +(2.87855 + 0.844941i) q^{36} +(-5.27314 + 9.13334i) q^{37} +(-0.608360 + 0.510474i) q^{38} +(-6.59221 - 3.53164i) q^{39} +(1.13289 + 0.199759i) q^{40} +(1.15671 - 6.56003i) q^{41} +(1.22347 - 4.41623i) q^{42} +(-2.26242 + 1.89840i) q^{43} +(0.802610 + 0.463387i) q^{44} +(0.813928 + 3.35375i) q^{45} +(2.13726 + 3.70184i) q^{46} +(1.43434 + 0.522056i) q^{47} +(-1.60795 + 0.643810i) q^{48} +(-6.77362 - 1.76580i) q^{49} +(-1.25749 - 3.45492i) q^{50} +(-5.88884 + 5.26906i) q^{51} +(4.25218 - 0.749775i) q^{52} -6.12939i q^{53} +(-3.70376 - 3.64447i) q^{54} +1.06613i q^{55} +(1.02077 + 2.44091i) q^{56} +(1.34635 - 0.281776i) q^{57} +(1.05816 - 0.385140i) q^{58} +(0.539986 + 0.453102i) q^{59} +(-1.56626 - 1.23161i) q^{60} +(-2.12248 + 5.83147i) q^{61} +(1.63579 + 2.83327i) q^{62} +(-5.48011 + 5.74181i) q^{63} +(0.500000 - 0.866025i) q^{64} +(3.19275 + 3.80497i) q^{65} +(-0.846374 - 1.36396i) q^{66} +(0.0261392 - 0.148242i) q^{67} +(0.792221 - 4.49291i) q^{68} +(-0.235233 - 7.39994i) q^{69} +(-1.84461 + 2.42091i) q^{70} +(-13.9539 - 8.05630i) q^{71} +(2.98155 + 0.332249i) q^{72} +(-5.65711 + 3.26614i) q^{73} +(-3.60704 + 9.91026i) q^{74} +(-0.906001 + 6.30337i) q^{75} +(-0.510474 + 0.608360i) q^{76} +(-2.06353 + 1.32448i) q^{77} +(-7.10532 - 2.33326i) q^{78} +(-2.17885 - 12.3569i) q^{79} +1.15037 q^{80} +(2.67382 + 8.59364i) q^{81} -6.66123i q^{82} +(-2.26883 - 12.8672i) q^{83} +(0.438013 - 4.56159i) q^{84} +(4.93172 - 1.79500i) q^{85} +(-1.89840 + 2.26242i) q^{86} +(-1.93058 - 0.277487i) q^{87} +(0.870883 + 0.316976i) q^{88} +(-6.04165 - 10.4644i) q^{89} +(1.38394 + 3.16146i) q^{90} +(-3.39821 + 10.9066i) q^{91} +(2.74761 + 3.27447i) q^{92} +(-0.180040 - 5.66368i) q^{93} +(1.50320 + 0.265055i) q^{94} +(-0.899694 - 0.158640i) q^{95} +(-1.47173 + 0.913247i) q^{96} +(3.91366 + 4.66412i) q^{97} +(-6.97734 - 0.562750i) q^{98} +(0.176587 + 2.77471i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 12 q^{9}+O(q^{10}) $ 144 * q - 12 * q^9	$ 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) $ 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.984808	−	0.173648i	0.696364	−	0.122788i
$2$	0.984808	−	0.173648i	0.696364	−	0.122788i
$3$	−1.64560	−	0.540384i	−0.950085	−	0.311991i
$3$	−1.64560	−	0.540384i	−0.950085	−	0.311991i
$4$	0.939693	−	0.342020i	0.469846	−	0.171010i
$5$	0.881233	+	0.739442i	0.394099	+	0.330689i	0.818208	−	0.574923i	$-0.194968\pi$
$5$	0.881233	+	0.739442i	0.394099	+	0.330689i	−0.424108	+	0.905612i	$0.639412\pi$
$6$	−1.71443	−	0.246420i	−0.699914	−	0.100601i
$7$	−0.336437	+	2.62427i	−0.127161	+	0.991882i
$7$	−0.336437	+	2.62427i	−0.127161	+	0.991882i
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	2.41597	+	1.77851i	0.805323	+	0.592836i
$10$	0.996248	+	0.575184i	0.315041	+	0.181889i
$11$	0.595719	+	0.709951i	0.179616	+	0.214058i	0.848339	−	0.529454i	$-0.177603\pi$
$11$	0.595719	+	0.709951i	0.179616	+	0.214058i	−0.668723	+	0.743512i	$0.733159\pi$
$12$	−1.73118	+	0.0550316i	−0.499748	+	0.0158863i
$13$	4.25218	+	0.749775i	1.17934	+	0.207950i	0.728751	−	0.684779i	$-0.240101\pi$
$13$	4.25218	+	0.749775i	1.17934	+	0.207950i	0.450593	+	0.892729i	$0.351212\pi$
$14$	0.124375	+	2.64283i	0.0332406	+	0.706325i
$15$	−1.05057	−	1.69303i	−0.271256	−	0.437138i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	2.28111	−	3.95100i	0.553250	−	0.958257i	−0.444787	−	0.895636i	$-0.646721\pi$
$17$	2.28111	−	3.95100i	0.553250	−	0.958257i	0.998037	−	0.0626209i	$-0.0199459\pi$
$18$	2.68810	+	1.33196i	0.633591	+	0.313946i
$19$	−0.687760	+	0.397079i	−0.157783	+	0.0910961i	−0.576813	−	0.816877i	$-0.695704\pi$
$19$	−0.687760	+	0.397079i	−0.157783	+	0.0910961i	0.419030	+	0.907973i	$0.362370\pi$
$20$	1.08099	+	0.393449i	0.241717	+	0.0879779i
$21$	1.97176	−	4.13669i	0.430272	−	0.902699i
$22$	0.709951	+	0.595719i	0.151362	+	0.127008i
$23$	1.46197	+	4.01673i	0.304842	+	0.837546i	0.993641	+	0.112594i	$0.0359160\pi$
$23$	1.46197	+	4.01673i	0.304842	+	0.837546i	−0.688799	+	0.724952i	$0.741862\pi$
$24$	−1.69532	+	0.354811i	−0.346056	+	0.0724255i
$25$	−0.638444	−	3.62080i	−0.127689	−	0.724159i
$26$	4.31778			0.846787
$27$	−3.01463	−	4.23226i	−0.580166	−	0.814498i
$28$	0.581407	+	2.58108i	0.109876	+	0.487778i
$29$	1.10897	−	0.195541i	0.205930	−	0.0363110i	−0.0697315	−	0.997566i	$-0.522214\pi$
$29$	1.10897	−	0.195541i	0.205930	−	0.0363110i	0.275661	+	0.961255i	$0.411103\pi$
$30$	−1.32860	−	1.48488i	−0.242568	−	0.271100i
$31$	1.11895	+	3.07428i	0.200969	+	0.552157i	0.998706	−	0.0508475i	$-0.0161923\pi$
$31$	1.11895	+	3.07428i	0.200969	+	0.552157i	−0.797738	+	0.603005i	$0.793970\pi$
$32$	0.642788	−	0.766044i	0.113630	−	0.135419i
$33$	−0.596667	−	1.49021i	−0.103866	−	0.259412i
$34$	1.56037	−	4.28708i	0.267601	−	0.735228i
$35$	−2.23698	+	2.06382i	−0.378118	+	0.348849i
$36$	2.87855	+	0.844941i	0.479759	+	0.140823i
$37$	−5.27314	+	9.13334i	−0.866899	+	1.50151i	−0.00174896	+	0.999998i	$0.500557\pi$
$37$	−5.27314	+	9.13334i	−0.866899	+	1.50151i	−0.865150	+	0.501514i	$0.832777\pi$
$38$	−0.608360	+	0.510474i	−0.0986890	+	0.0828099i
$39$	−6.59221	−	3.53164i	−1.05560	−	0.565515i
$40$	1.13289	+	0.199759i	0.179126	+	0.0315847i
$41$	1.15671	−	6.56003i	0.180648	−	1.02450i	−0.750773	−	0.660560i	$-0.770319\pi$
$41$	1.15671	−	6.56003i	0.180648	−	1.02450i	0.931421	−	0.363944i	$-0.118570\pi$
$42$	1.22347	−	4.41623i	0.188786	−	0.681440i
$43$	−2.26242	+	1.89840i	−0.345016	+	0.289503i	−0.798785	−	0.601616i	$-0.794524\pi$
$43$	−2.26242	+	1.89840i	−0.345016	+	0.289503i	0.453769	+	0.891119i	$0.350079\pi$
$44$	0.802610	+	0.463387i	0.120998	+	0.0698583i
$45$	0.813928	+	3.35375i	0.121333	+	0.499948i
$46$	2.13726	+	3.70184i	0.315122	+	0.545807i
$47$	1.43434	+	0.522056i	0.209220	+	0.0761497i	0.444504	−	0.895777i	$-0.353380\pi$
$47$	1.43434	+	0.522056i	0.209220	+	0.0761497i	−0.235284	+	0.971927i	$0.575602\pi$
$48$	−1.60795	+	0.643810i	−0.232088	+	0.0929260i
$49$	−6.77362	−	1.76580i	−0.967660	−	0.252258i
$50$	−1.25749	−	3.45492i	−0.177836	−	0.488600i
$51$	−5.88884	+	5.26906i	−0.824602	+	0.737817i
$52$	4.25218	−	0.749775i	0.589672	−	0.103975i
$53$		−	6.12939i		−	0.841936i	−0.907075	−	0.420968i	$-0.861690\pi$
$53$		−	6.12939i		−	0.841936i	0.907075	−	0.420968i	$-0.138310\pi$
$54$	−3.70376	−	3.64447i	−0.504017	−	0.495950i
$55$			1.06613i			0.143757i
$56$	1.02077	+	2.44091i	0.136407	+	0.326180i
$57$	1.34635	−	0.281776i	0.178328	−	0.0373221i
$58$	1.05816	−	0.385140i	0.138944	−	0.0505714i
$59$	0.539986	+	0.453102i	0.0703002	+	0.0589889i	0.677261	−	0.735743i	$-0.263167\pi$
$59$	0.539986	+	0.453102i	0.0703002	+	0.0589889i	−0.606960	+	0.794732i	$0.707611\pi$
$60$	−1.56626	−	1.23161i	−0.202204	−	0.159000i
$61$	−2.12248	+	5.83147i	−0.271756	+	0.746644i	0.726475	+	0.687193i	$0.241157\pi$
$61$	−2.12248	+	5.83147i	−0.271756	+	0.746644i	−0.998231	+	0.0594509i	$0.981065\pi$
$62$	1.63579	+	2.83327i	0.207746	+	0.359826i
$63$	−5.48011	+	5.74181i	−0.690429	+	0.723400i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	3.19275	+	3.80497i	0.396012	+	0.471949i
$66$	−0.846374	−	1.36396i	−0.104181	−	0.167892i
$67$	0.0261392	−	0.148242i	0.00319341	−	0.0181107i	−0.983169	−	0.182696i	$-0.941518\pi$
$67$	0.0261392	−	0.148242i	0.00319341	−	0.0181107i	0.986363	+	0.164585i	$0.0526286\pi$
$68$	0.792221	−	4.49291i	0.0960709	−	0.544845i
$69$	−0.235233	−	7.39994i	−0.0283188	−	0.890848i
$70$	−1.84461	+	2.42091i	−0.220474	+	0.289355i
$71$	−13.9539	−	8.05630i	−1.65603	−	0.956107i	−0.974522	−	0.224292i	$-0.927993\pi$
$71$	−13.9539	−	8.05630i	−1.65603	−	0.956107i	−0.681504	−	0.731815i	$-0.738674\pi$
$72$	2.98155	+	0.332249i	0.351378	+	0.0391559i
$73$	−5.65711	+	3.26614i	−0.662115	+	0.382272i	−0.793082	−	0.609114i	$-0.791525\pi$
$73$	−5.65711	+	3.26614i	−0.662115	+	0.382272i	0.130967	+	0.991387i	$0.458192\pi$
$74$	−3.60704	+	9.91026i	−0.419310	+	1.15204i
$75$	−0.906001	+	6.30337i	−0.104616	+	0.727851i
$76$	−0.510474	+	0.608360i	−0.0585554	+	0.0697837i
$77$	−2.06353	+	1.32448i	−0.235161	+	0.150938i
$78$	−7.10532	−	2.33326i	−0.804519	−	0.264190i
$79$	−2.17885	−	12.3569i	−0.245140	−	1.39026i	−0.820168	−	0.572122i	$-0.806120\pi$
$79$	−2.17885	−	12.3569i	−0.245140	−	1.39026i	0.575029	−	0.818133i	$-0.304991\pi$
$80$	1.15037			0.128615
$81$	2.67382	+	8.59364i	0.297091	+	0.954849i
$82$		−	6.66123i		−	0.735609i
$83$	−2.26883	−	12.8672i	−0.249036	−	1.41236i	−0.810928	−	0.585145i	$-0.801037\pi$
$83$	−2.26883	−	12.8672i	−0.249036	−	1.41236i	0.561892	−	0.827211i	$-0.310074\pi$
$84$	0.438013	−	4.56159i	0.0477912	−	0.497711i
$85$	4.93172	−	1.79500i	0.534920	−	0.194695i
$86$	−1.89840	+	2.26242i	−0.204710	+	0.243963i
$87$	−1.93058	−	0.277487i	−0.206980	−	0.0297498i
$88$	0.870883	+	0.316976i	0.0928365	+	0.0337897i
$89$	−6.04165	−	10.4644i	−0.640413	−	1.10923i	−0.985341	−	0.170599i	$-0.945430\pi$
$89$	−6.04165	−	10.4644i	−0.640413	−	1.10923i	0.344927	−	0.938629i	$-0.387904\pi$
$90$	1.38394	+	3.16146i	0.145880	+	0.333247i
$91$	−3.39821	+	10.9066i	−0.356229	+	1.14333i
$92$	2.74761	+	3.27447i	0.286458	+	0.341387i
$93$	−0.180040	−	5.66368i	−0.0186693	−	0.587297i
$94$	1.50320	+	0.265055i	0.155043	+	0.0273383i
$95$	−0.899694	−	0.158640i	−0.0923067	−	0.0162762i
$96$	−1.47173	+	0.913247i	−0.150207	+	0.0932079i
$97$	3.91366	+	4.66412i	0.397372	+	0.473570i	0.927217	−	0.374525i	$-0.122194\pi$
$97$	3.91366	+	4.66412i	0.397372	+	0.473570i	−0.529844	+	0.848095i	$0.677750\pi$
$98$	−6.97734	−	0.562750i	−0.704818	−	0.0568464i
$99$	0.176587	+	2.77471i	0.0177476	+	0.278869i
$100$	−1.83833	−	3.18408i	−0.183833	−	0.318408i
$101$	5.99302	+	2.18128i	0.596327	+	0.217045i	0.622510	−	0.782612i	$-0.286113\pi$
$101$	5.99302	+	2.18128i	0.596327	+	0.217045i	−0.0261827	+	0.999657i	$0.508335\pi$
$102$	−4.88441	+	6.21160i	−0.483629	+	0.615040i
$103$	−5.43804	+	6.48081i	−0.535826	+	0.638573i	−0.964247	−	0.265007i	$-0.914626\pi$
$103$	−5.43804	+	6.48081i	−0.535826	+	0.638573i	0.428420	+	0.903580i	$0.359070\pi$
$104$	4.05739	−	1.47677i	0.397860	−	0.144809i
$105$	4.79642	−	2.18739i	0.468082	−	0.213467i
$106$	−1.06436	−	6.03627i	−0.103380	−	0.586294i
$107$			3.96659i			0.383465i	0.981447	+	0.191733i	$0.0614106\pi$
$107$			3.96659i			0.383465i	−0.981447	+	0.191733i	$0.938589\pi$
$108$	−4.28034	−	2.94596i	−0.411876	−	0.283475i
$109$	−3.76598			−0.360715			−0.180358	−	0.983601i	$-0.557725\pi$
$109$	−3.76598			−0.360715			−0.180358	+	0.983601i	$0.557725\pi$
$110$	0.185132	+	1.04993i	0.0176516	+	0.100107i
$111$	13.6130	−	12.1803i	1.29209	−	1.15610i
$112$	1.42912	+	2.22657i	0.135040	+	0.210391i
$113$	7.44407	−	8.87149i	0.700279	−	0.834560i	−0.292279	−	0.956333i	$-0.594414\pi$
$113$	7.44407	−	8.87149i	0.700279	−	0.834560i	0.992558	+	0.121773i	$0.0388580\pi$
$114$	1.27697	−	0.511286i	0.119599	−	0.0478864i
$115$	−1.68180	+	4.62072i	−0.156829	+	0.430884i
$116$	0.975209	−	0.563037i	0.0905459	−	0.0522767i
$117$	8.93967	+	9.37398i	0.826473	+	0.866625i
$118$	0.610463	+	0.352451i	0.0561977	+	0.0324457i
$119$	9.60104	+	7.31551i	0.880126	+	0.670612i
$120$	−1.75633	−	0.940920i	−0.160331	−	0.0858938i
$121$	1.76098	−	9.98702i	0.160089	−	0.907911i
$122$	−1.07761	+	6.11145i	−0.0975625	+	0.553304i
$123$	−5.44841	+	10.1701i	−0.491267	+	0.917006i
$124$	2.10293	+	2.50618i	0.188849	+	0.225061i
$125$	4.99067	−	8.64410i	0.446379	−	0.773152i
$126$	−4.39980	+	6.60619i	−0.391966	+	0.588526i
$127$	9.65635	+	16.7253i	0.856862	+	1.48413i	0.874906	+	0.484292i	$0.160923\pi$
$127$	9.65635	+	16.7253i	0.856862	+	1.48413i	−0.0180439	+	0.999837i	$0.505744\pi$
$128$	0.342020	−	0.939693i	0.0302306	−	0.0830579i
$129$	4.74890	−	1.90142i	0.418117	−	0.167411i
$130$	3.80497	+	3.19275i	0.333718	+	0.280023i
$131$	9.91874	−	3.61013i	0.866605	−	0.315418i	0.129813	−	0.991538i	$-0.458562\pi$
$131$	9.91874	−	3.61013i	0.866605	−	0.315418i	0.736791	+	0.676120i	$0.236340\pi$
$132$	−1.07036	−	1.19627i	−0.0931633	−	0.104122i
$133$	−0.810655	−	1.93846i	−0.0702927	−	0.168086i
$134$		−	0.150529i		−	0.0130038i
$135$	0.472918	−	5.95875i	0.0407023	−	0.512848i
$136$		−	4.56222i		−	0.391207i
$137$	10.4376	−	1.84042i	0.891740	−	0.157238i	0.291039	−	0.956711i	$-0.405999\pi$
$137$	10.4376	−	1.84042i	0.891740	−	0.157238i	0.600702	+	0.799473i	$0.294888\pi$
$138$	−1.51665	−	7.24667i	−0.129105	−	0.616878i
$139$	−7.04355	−	19.3520i	−0.597426	−	1.64141i	−0.756383	−	0.654129i	$-0.773036\pi$
$139$	−7.04355	−	19.3520i	−0.597426	−	1.64141i	0.158958	−	0.987285i	$-0.449187\pi$
$140$	−1.39620	+	2.70445i	−0.118001	+	0.228568i
$141$	−2.07823	−	1.63419i	−0.175018	−	0.137623i
$142$	−15.1409	−	5.51083i	−1.27060	−	0.462459i
$143$	2.00081	+	3.46550i	0.167316	+	0.289799i
$144$	2.99394	−	0.190539i	0.249495	−	0.0158782i
$145$	1.12185	+	0.647700i	0.0931645	+	0.0537885i
$146$	−5.00401	+	4.19886i	−0.414135	+	0.347500i
$147$	10.1924	+	6.56616i	0.840657	+	0.541568i
$148$	−1.83134	+	10.3861i	−0.150535	+	0.853728i
$149$	18.9694	+	3.34481i	1.55403	+	0.274018i	0.883703	−	0.468048i	$-0.155042\pi$
$149$	18.9694	+	3.34481i	1.55403	+	0.274018i	0.670328	+	0.742065i	$0.266154\pi$
$150$	0.202332	+	6.36494i	0.0165203	+	0.519695i
$151$	9.84852	−	8.26389i	0.801461	−	0.672506i	−0.147092	−	0.989123i	$-0.546991\pi$
$151$	9.84852	−	8.26389i	0.801461	−	0.672506i	0.948553	+	0.316617i	$0.102547\pi$
$152$	−0.397079	+	0.687760i	−0.0322073	+	0.0557847i
$153$	12.5380	−	5.48851i	1.01363	−	0.443720i
$154$	−1.80218	+	1.66268i	−0.145224	+	0.133983i
$155$	−1.28720	+	3.53655i	−0.103390	+	0.284063i
$156$	−7.40254	−	1.06399i	−0.592678	−	0.0851872i
$157$	−11.9587	+	14.2518i	−0.954406	+	1.13742i	0.0360175	+	0.999351i	$0.488533\pi$
$157$	−11.9587	+	14.2518i	−0.954406	+	1.13742i	−0.990423	+	0.138065i	$0.955912\pi$
$158$	−4.29149	−	11.7908i	−0.341413	−	0.938024i
$159$	−3.31223	+	10.0865i	−0.262677	+	0.799911i
$160$	1.13289	−	0.199759i	0.0895629	−	0.0157924i
$161$	−11.0329	+	2.48523i	−0.869511	+	0.195864i
$162$	4.12547	+	7.99878i	0.324127	+	0.628444i
$163$	−12.3894			−0.970410			−0.485205	−	0.874401i	$-0.661255\pi$
$163$	−12.3894			−0.970410			−0.485205	+	0.874401i	$0.661255\pi$
$164$	−1.15671	−	6.56003i	−0.0903239	−	0.512252i
$165$	0.576121	−	1.75442i	0.0448510	−	0.136582i
$166$	−4.46872	−	12.2777i	−0.346840	−	0.952935i
$167$	−2.95227	−	2.47725i	−0.228454	−	0.191695i	0.521375	−	0.853328i	$-0.325419\pi$
$167$	−2.95227	−	2.47725i	−0.228454	−	0.191695i	−0.749828	+	0.661633i	$0.769864\pi$
$168$	−0.360754	−	4.56835i	−0.0278327	−	0.352456i
$169$	5.30291	+	1.93010i	0.407916	+	0.148469i
$170$	4.54510	−	2.62411i	0.348593	−	0.201260i
$171$	−2.36782	−	0.263858i	−0.181071	−	0.0201777i
$172$	−1.47669	+	2.55771i	−0.112597	+	0.195023i
$173$	−14.1145	+	11.8435i	−1.07311	+	0.900443i	−0.995330	−	0.0965278i	$-0.969226\pi$
$173$	−14.1145	+	11.8435i	−1.07311	+	0.900443i	−0.0777759	+	0.996971i	$0.524782\pi$
$174$	−1.94943	+	0.0619697i	−0.147786	+	0.00469791i
$175$	9.71676	−	0.457283i	0.734518	−	0.0345673i
$176$	0.912695	+	0.160933i	0.0687970	+	0.0121308i
$177$	−0.643749	−	1.03742i	−0.0483872	−	0.0779775i
$178$	−7.76699	−	9.25634i	−0.582161	−	0.693792i
$179$	−18.3066	−	10.5693i	−1.36830	−	0.789989i	−0.377590	−	0.925973i	$-0.623247\pi$
$179$	−18.3066	−	10.5693i	−1.36830	−	0.789989i	−0.990711	+	0.135984i	$0.956580\pi$
$180$	1.91189	+	2.87311i	0.142504	+	0.214149i
$181$	−10.6192	+	6.13100i	−0.789319	+	0.455713i	−0.839723	−	0.543016i	$-0.817282\pi$
$181$	−10.6192	+	6.13100i	−0.789319	+	0.455713i	0.0504039	+	0.998729i	$0.483949\pi$
$182$	−1.45266	+	11.3310i	−0.107678	+	0.839913i
$183$	6.64399	−	8.44929i	0.491138	−	0.624589i
$184$	3.27447	+	2.74761i	0.241397	+	0.202556i
$185$	−11.4004	+	4.14942i	−0.838177	+	0.305072i
$186$	−1.16079	−	5.54638i	−0.0851135	−	0.406680i
$187$	4.16391	−	0.734210i	0.304495	−	0.0536907i
$188$	1.52639			0.111323
$189$	12.1208	−	6.48733i	0.881661	−	0.471884i
$190$	−0.913573			−0.0662776
$191$	6.03024	−	1.06329i	0.436333	−	0.0769372i	0.0488327	−	0.998807i	$-0.484450\pi$
$191$	6.03024	−	1.06329i	0.436333	−	0.0769372i	0.387500	+	0.921870i	$0.373339\pi$
$192$	−1.29078	+	1.15494i	−0.0931543	+	0.0833503i
$193$	22.4646	−	8.17645i	1.61704	−	0.588554i	0.634224	−	0.773149i	$-0.281320\pi$
$193$	22.4646	−	8.17645i	1.61704	−	0.588554i	0.982815	+	0.184595i	$0.0590974\pi$
$194$	4.66412	+	3.91366i	0.334865	+	0.280985i
$195$	−3.19783	−	7.98676i	−0.229001	−	0.571944i
$196$	−6.96906	+	0.657402i	−0.497790	+	0.0469573i
$197$	−18.6694	+	10.7788i	−1.33014	+	0.767956i	−0.985321	−	0.170713i	$-0.945393\pi$
$197$	−18.6694	+	10.7788i	−1.33014	+	0.767956i	−0.344818	+	0.938669i	$0.612059\pi$
$198$	0.655727	+	2.70189i	0.0466005	+	0.192015i
$199$	−4.91316	−	2.83662i	−0.348285	−	0.201082i	0.315645	−	0.948877i	$-0.397779\pi$
$199$	−4.91316	−	2.83662i	−0.348285	−	0.201082i	−0.663930	+	0.747795i	$0.731113\pi$
$200$	−2.36331	−	2.81648i	−0.167111	−	0.199155i
$201$	−0.123122	+	0.229822i	−0.00868438	+	0.0162104i
$202$	6.28074	+	1.10746i	0.441912	+	0.0779210i
$203$	0.140055	+	2.97602i	0.00982995	+	0.208876i
$204$	−3.73157	+	6.96540i	−0.261262	+	0.487676i
$205$	5.87009	−	4.92559i	0.409985	−	0.344018i
$206$	−4.23005	+	7.32666i	−0.294721	+	0.510472i
$207$	−3.61171	+	12.3044i	−0.251031	+	0.855217i
$208$	3.73931	−	2.15889i	0.259274	−	0.149692i
$209$	−0.691618	−	0.251728i	−0.0478402	−	0.0174124i
$210$	4.34371	−	2.98704i	0.299745	−	0.206126i
$211$	8.52289	+	7.15155i	0.586740	+	0.492333i	0.887153	−	0.461476i	$-0.152680\pi$
$211$	8.52289	+	7.15155i	0.586740	+	0.492333i	−0.300413	+	0.953809i	$0.597124\pi$
$212$	−2.09637	−	5.75974i	−0.143980	−	0.395581i
$213$	18.6090	+	20.7979i	1.27507	+	1.42505i
$214$	0.688792	+	3.90633i	0.0470848	+	0.267031i
$215$	−3.39748			−0.231706
$216$	−4.72688	−	2.15793i	−0.321623	−	0.146828i
$217$	−8.44421	+	1.90212i	−0.573230	+	0.129124i
$218$	−3.70876	+	0.653955i	−0.251189	+	0.0442914i
$219$	11.0743	−	2.31772i	0.748331	−	0.156617i
$220$	0.364639	+	1.00184i	0.0245839	+	0.0675438i
$221$	12.6621	−	15.0900i	0.851742	−	1.01507i
$222$	11.2911	−	14.3591i	0.757807	−	0.963719i
$223$	10.0557	−	27.6279i	0.673381	−	1.85010i	0.171444	−	0.985194i	$-0.445157\pi$
$223$	10.0557	−	27.6279i	0.673381	−	1.85010i	0.501937	−	0.864904i	$-0.332621\pi$
$224$	1.79405	+	1.94458i	0.119870	+	0.129927i
$225$	4.89716	−	9.88321i	0.326477	−	0.658881i
$226$	5.79046	−	10.0294i	0.385175	−	0.667143i
$227$	−13.3769	+	11.2245i	−0.887854	+	0.744998i	−0.967778	−	0.251803i	$-0.918976\pi$
$227$	−13.3769	+	11.2245i	−0.887854	+	0.744998i	0.0799249	+	0.996801i	$0.474532\pi$
$228$	1.16878	−	0.725262i	0.0774045	−	0.0480316i
$229$	0.315348	+	0.0556043i	0.0208388	+	0.00367444i	0.184058	−	0.982915i	$-0.441077\pi$
$229$	0.315348	+	0.0556043i	0.0208388	+	0.00367444i	−0.163219	+	0.986590i	$0.552188\pi$
$230$	−0.853874	+	4.84256i	−0.0563028	+	0.319309i
$231$	4.11146	−	1.06446i	0.270514	−	0.0700360i
$232$	0.862623	−	0.723827i	0.0566340	−	0.0475215i
$233$	1.42597	+	0.823285i	0.0934185	+	0.0539352i	0.545981	−	0.837797i	$-0.316157\pi$
$233$	1.42597	+	0.823285i	0.0934185	+	0.0539352i	−0.452563	+	0.891732i	$0.649490\pi$
$234$	10.4316	+	7.67921i	0.681937	+	0.502006i
$235$	0.877955	+	1.52066i	0.0572715	+	0.0991971i
$236$	0.662391	+	0.241091i	0.0431180	+	0.0156937i
$237$	−3.09195	+	21.5118i	−0.200844	+	1.39734i
$238$	10.7255	+	5.53717i	0.695231	+	0.358921i
$239$	1.13449	+	3.11699i	0.0733842	+	0.201621i	0.970962	−	0.239236i	$-0.0768968\pi$
$239$	1.13449	+	3.11699i	0.0733842	+	0.201621i	−0.897577	+	0.440857i	$0.854675\pi$
$240$	−1.89304	−	0.621641i	−0.122195	−	0.0401268i
$241$	2.28746	−	0.403341i	0.147348	−	0.0259814i	−0.0994875	−	0.995039i	$-0.531720\pi$
$241$	2.28746	−	0.403341i	0.147348	−	0.0259814i	0.246836	+	0.969057i	$0.420609\pi$
$242$		−	10.1411i		−	0.651894i
$243$	0.243850	−	15.5865i	0.0156430	−	0.999878i
$244$			6.20572i			0.397281i
$245$	−4.66343	−	6.56479i	−0.297936	−	0.419409i
$246$	−3.59962	+	10.9617i	−0.229504	+	0.698892i
$247$	−3.22220	+	1.17279i	−0.205024	+	0.0746226i
$248$	2.50618	+	2.10293i	0.159142	+	0.133536i
$249$	−3.21964	+	22.4002i	−0.204037	+	1.41956i
$250$	3.41382	−	9.37940i	0.215909	−	0.593205i
$251$	13.5744	+	23.5116i	0.856811	+	1.48404i	0.874954	+	0.484205i	$0.160891\pi$
$251$	13.5744	+	23.5116i	0.856811	+	1.48404i	−0.0181430	+	0.999835i	$0.505775\pi$
$252$	−3.18581	+	7.26984i	−0.200687	+	0.457957i
$253$	−1.98076	+	3.43077i	−0.124529	+	0.215691i
$254$	12.4140	+	14.7944i	0.778921	+	0.928282i
$255$	−9.08561	+	0.288818i	−0.568963	+	0.0180865i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	−1.33671	+	7.58084i	−0.0833814	+	0.472880i	0.914313	+	0.405009i	$0.132732\pi$
$257$	−1.33671	+	7.58084i	−0.0833814	+	0.472880i	−0.997694	+	0.0678706i	$0.978380\pi$
$258$	4.34658	−	2.69717i	0.270606	−	0.167918i
$259$	−22.1943	−	16.9109i	−1.37909	−	1.05080i
$260$	4.30158	+	2.48352i	0.266773	+	0.154021i
$261$	3.02700	+	1.49989i	0.187367	+	0.0928406i
$262$	9.14116	−	5.27765i	0.564743	−	0.326055i
$263$	4.38593	−	12.0503i	0.270448	−	0.743051i	−0.727905	−	0.685678i	$-0.759506\pi$
$263$	4.38593	−	12.0503i	0.270448	−	0.743051i	0.998353	−	0.0573722i	$-0.0182722\pi$
$264$	−1.26183	−	0.992225i	−0.0776605	−	0.0610672i
$265$	4.53233	−	5.40142i	0.278419	−	0.331807i
$266$	−1.13495	−	1.76824i	−0.0695882	−	0.108418i
$267$	4.28729	+	20.4850i	0.262378	+	1.25366i
$268$	−0.0261392	−	0.148242i	−0.00159670	−	0.00905535i
$269$	−4.85008			−0.295715			−0.147857	−	0.989009i	$-0.547238\pi$
$269$	−4.85008			−0.295715			−0.147857	+	0.989009i	$0.547238\pi$
$270$	−0.568992	−	5.95035i	−0.0346278	−	0.362126i
$271$		−	19.5627i		−	1.18835i	−0.804335	−	0.594176i	$-0.797478\pi$
$271$		−	19.5627i		−	1.18835i	0.804335	−	0.594176i	$-0.202522\pi$
$272$	−0.792221	−	4.49291i	−0.0480354	−	0.272422i
$273$	11.4859	−	16.1116i	0.695155	−	0.975118i
$274$	9.95940	−	3.62492i	0.601669	−	0.218990i
$275$	2.19025	−	2.61024i	0.132077	−	0.157404i
$276$	−2.75198	−	6.87322i	−0.165650	−	0.413719i
$277$	12.0567	+	4.38828i	0.724417	+	0.263666i	0.677800	−	0.735246i	$-0.262934\pi$
$277$	12.0567	+	4.38828i	0.724417	+	0.263666i	0.0466176	+	0.998913i	$0.485156\pi$
$278$	−10.2970	−	17.8349i	−0.617572	−	1.06967i
$279$	−2.76429	+	9.41742i	−0.165494	+	0.563806i
$280$	−0.905369	+	2.90581i	−0.0541062	+	0.173655i
$281$	−17.3811	−	20.7140i	−1.03687	−	1.23569i	−0.971303	−	0.237843i	$-0.923559\pi$
$281$	−17.3811	−	20.7140i	−1.03687	−	1.23569i	−0.0655650	−	0.997848i	$-0.520885\pi$
$282$	−2.33043	−	1.24848i	−0.138775	−	0.0743458i
$283$	25.3283	+	4.46607i	1.50561	+	0.265480i	0.864760	−	0.502185i	$-0.167470\pi$
$283$	25.3283	+	4.46607i	1.50561	+	0.265480i	0.640852	+	0.767665i	$0.278581\pi$
$284$	−15.8678	−	2.79792i	−0.941581	−	0.166026i
$285$	1.39481	+	0.747238i	0.0826212	+	0.0442626i
$286$	2.57219	+	3.06541i	0.152097	+	0.181262i
$287$	16.8261	+	5.24256i	0.993216	+	0.309458i
$288$	2.91537	−	0.707537i	0.171790	−	0.0416920i
$289$	−1.90691	−	3.30286i	−0.112171	−	0.194286i
$290$	1.21728	+	0.443053i	0.0714810	+	0.0260170i
$291$	−3.91989	−	9.79014i	−0.229788	−	0.573908i
$292$	−4.19886	+	5.00401i	−0.245720	+	0.292838i
$293$	−11.7001	+	4.25851i	−0.683530	+	0.248785i	−0.660362	−	0.750947i	$-0.729597\pi$
$293$	−11.7001	+	4.25851i	−0.683530	+	0.248785i	−0.0231675	+	0.999732i	$0.507375\pi$
$294$	11.1778	+	4.69651i	0.651902	+	0.273906i
$295$	0.140811	+	0.798577i	0.00819832	+	0.0464950i
$296$			10.5463i			0.612990i
$297$	1.20882	−	4.66148i	0.0701429	−	0.270486i
$298$	19.2620			1.11582
$299$	3.20493	+	18.1760i	0.185346	+	1.05115i
$300$	1.30452	+	6.23310i	0.0753164	+	0.359868i
$301$	−4.22076	−	6.57591i	−0.243280	−	0.379029i
$302$	8.26389	−	9.84852i	0.475533	−	0.566719i
$303$	−8.68335	−	6.82804i	−0.498846	−	0.392260i
$304$	−0.271618	+	0.746264i	−0.0155783	+	0.0428012i
$305$	−6.18244	+	3.56943i	−0.354005	+	0.204385i
$306$	11.3944	−	7.58233i	0.651375	−	0.433453i
$307$	−11.6597	−	6.73172i	−0.665453	−	0.384200i	0.128898	−	0.991658i	$-0.458856\pi$
$307$	−11.6597	−	6.73172i	−0.665453	−	0.384200i	−0.794352	+	0.607458i	$0.792189\pi$
$308$	−1.48608	+	1.95037i	−0.0846774	+	0.111133i
$309$	12.4510	−	7.72616i	0.708310	−	0.439526i
$310$	−0.653529	+	3.70635i	−0.0371179	+	0.210506i
$311$	−3.88220	+	22.0171i	−0.220140	+	1.24847i	0.651622	+	0.758543i	$0.274089\pi$
$311$	−3.88220	+	22.0171i	−0.220140	+	1.24847i	−0.871762	+	0.489930i	$0.837022\pi$
$312$	−7.47484	+	0.237614i	−0.423180	+	0.0134523i
$313$	13.4246	+	15.9988i	0.758803	+	0.904306i	0.997772	−	0.0667214i	$-0.0212539\pi$
$313$	13.4246	+	15.9988i	0.758803	+	0.904306i	−0.238969	+	0.971027i	$0.576809\pi$
$314$	−9.30219	+	16.1119i	−0.524953	+	0.909245i
$315$	−9.07499	+	1.00764i	−0.511318	+	0.0567743i
$316$	−6.27374	−	10.8664i	−0.352926	−	0.611285i
$317$	−8.35787	+	22.9631i	−0.469425	+	1.28973i	0.448785	+	0.893640i	$0.351857\pi$
$317$	−8.35787	+	22.9631i	−0.469425	+	1.28973i	−0.918210	+	0.396094i	$0.870365\pi$
$318$	−1.51040	+	10.5084i	−0.0846993	+	0.589283i
$319$	0.799457	+	0.670824i	0.0447610	+	0.0375589i
$320$	1.08099	−	0.393449i	0.0604293	−	0.0219945i
$321$	2.14348	−	6.52741i	0.119638	−	0.364324i
$322$	−10.4337	+	4.36331i	−0.581447	+	0.243158i
$323$			3.62312i			0.201596i
$324$	5.45176	+	7.16088i	0.302876	+	0.397827i
$325$		−	15.8750i		−	0.880586i
$326$	−12.2011	+	2.15139i	−0.675759	+	0.119154i
$327$	6.19728	+	2.03508i	0.342710	+	0.112540i
$328$	−2.27827	−	6.25951i	−0.125797	−	0.345623i
$329$	−1.85258	+	3.58845i	−0.102136	+	0.197838i
$330$	0.262716	−	1.82781i	0.0144621	−	0.100618i
$331$	−24.0446	−	8.75152i	−1.32161	−	0.481027i	−0.417636	−	0.908614i	$-0.637141\pi$
$331$	−24.0446	−	8.75152i	−1.32161	−	0.481027i	−0.903974	+	0.427587i	$0.859364\pi$
$332$	−6.53284	−	11.3152i	−0.358536	−	0.621002i
$333$	−28.9835	+	12.6876i	−1.58828	+	0.695274i
$334$	−3.33759	−	1.92696i	−0.182625	−	0.105438i
$335$	0.132651	−	0.111308i	0.00724752	−	0.00608139i
$336$	−1.14856	−	4.43631i	−0.0626590	−	0.242020i
$337$	−1.10784	+	6.28289i	−0.0603480	+	0.342251i	0.939652	+	0.342132i	$0.111149\pi$
$337$	−1.10784	+	6.28289i	−0.0603480	+	0.342251i	−1.00000		0.000118853i	$0.999962\pi$
$338$	5.55751	+	0.979938i	0.302288	+	0.0533016i
$339$	−17.0439	+	10.5762i	−0.925700	+	0.574422i
$340$	4.02038	−	3.37350i	0.218035	−	0.182953i
$341$	−1.51601	+	2.62580i	−0.0820965	+	0.142195i
$342$	−2.37766	+	0.151318i	−0.128569	+	0.00818233i
$343$	6.91285	−	17.1818i	0.373259	−	0.927727i
$344$	−1.01012	+	2.77527i	−0.0544619	+	0.149633i
$345$	5.26453	−	6.69501i	0.283433	−	0.360447i
$346$	−11.8435	+	14.1145i	−0.636709	+	0.758801i
$347$	2.07632	+	5.70464i	0.111463	+	0.306241i	0.982865	−	0.184328i	$-0.0590110\pi$
$347$	2.07632	+	5.70464i	0.111463	+	0.306241i	−0.871402	+	0.490570i	$0.836789\pi$
$348$	−1.90906	+	0.399544i	−0.102336	+	0.0214178i
$349$	−10.4569	+	1.84383i	−0.559743	+	0.0986978i	−0.446360	−	0.894854i	$-0.647280\pi$
$349$	−10.4569	+	1.84383i	−0.559743	+	0.0986978i	−0.113383	+	0.993551i	$0.536169\pi$
$350$	9.48973	−	2.13763i	0.507247	−	0.114261i
$351$	−9.64553	−	20.2566i	−0.514840	−	1.08122i
$352$	0.926775			0.0493973
$353$	−2.36199	−	13.3955i	−0.125716	−	0.712972i	−0.980880	−	0.194614i	$-0.937655\pi$
$353$	−2.36199	−	13.3955i	−0.125716	−	0.712972i	0.855164	−	0.518358i	$-0.173457\pi$
$354$	−0.814116	−	0.909876i	−0.0432698	−	0.0483594i
$355$	−6.33949	−	17.4176i	−0.336465	−	0.924430i
$356$	−9.25634	−	7.76699i	−0.490585	−	0.411650i
$357$	−11.8462	−	17.2266i	−0.626970	−	0.911730i
$358$	−19.8638	−	7.22985i	−1.04984	−	0.382109i
$359$	−15.8836	+	9.17041i	−0.838305	+	0.483996i	−0.856688	−	0.515835i	$-0.827482\pi$
$359$	−15.8836	+	9.17041i	−0.838305	+	0.483996i	0.0183825	+	0.999831i	$0.494148\pi$
$360$	2.38176	+	2.49747i	0.125530	+	0.131628i
$361$	−9.18466	+	15.9083i	−0.483403	+	0.837279i
$362$	−9.39323	+	7.88186i	−0.493697	+	0.414261i
$363$	−8.29469	+	15.4830i	−0.435359	+	0.812646i
$364$	0.537023	+	11.4111i	0.0281477	+	0.598107i
$365$	−7.40035	−	1.30488i	−0.387352	−	0.0683006i
$366$	5.07584	−	9.47464i	0.265319	−	0.495247i
$367$	2.37679	+	2.83255i	0.124067	+	0.147858i	0.824502	−	0.565858i	$-0.191455\pi$
$367$	2.37679	+	2.83255i	0.124067	+	0.147858i	−0.700435	+	0.713716i	$0.747011\pi$
$368$	3.70184	+	2.13726i	0.192972	+	0.111412i
$369$	14.4616	−	13.7916i	0.752843	−	0.717962i
$370$	−10.5067	+	6.06605i	−0.546218	+	0.315359i
$371$	16.0852	+	2.06215i	0.835102	+	0.107062i
$372$	−2.10628	−	5.26054i	−0.109205	−	0.272747i
$373$	−14.6959	−	12.3313i	−0.760922	−	0.638490i	0.177444	−	0.984131i	$-0.443217\pi$
$373$	−14.6959	−	12.3313i	−0.760922	−	0.638490i	−0.938367	+	0.345641i	$0.887661\pi$
$374$	3.97316	−	1.44611i	0.205447	−	0.0747766i
$375$	−12.8838	+	11.5278i	−0.665315	+	0.595293i
$376$	1.50320	−	0.265055i	0.0775216	−	0.0136692i
$377$	4.86214			0.250413
$378$	10.8102	−	8.49353i	0.556016	−	0.436860i
$379$	−3.29187			−0.169092			−0.0845461	−	0.996420i	$-0.526944\pi$
$379$	−3.29187			−0.169092			−0.0845461	+	0.996420i	$0.526944\pi$
$380$	−0.899694	+	0.158640i	−0.0461533	+	0.00813808i
$381$	−6.85236	−	32.7412i	−0.351057	−	1.67738i
$382$	5.75398	−	2.09428i	0.294399	−	0.107153i
$383$	9.42456	+	7.90814i	0.481572	+	0.404087i	0.850995	−	0.525174i	$-0.176000\pi$
$383$	9.42456	+	7.90814i	0.481572	+	0.404087i	−0.369422	+	0.929262i	$0.620444\pi$
$384$	−1.07062	+	1.36153i	−0.0546350	+	0.0694804i
$385$	−2.79782	−	0.358686i	−0.142590	−	0.0182803i
$386$	20.7035	−	11.9532i	1.05378	−	0.608401i
$387$	−8.84227	+	0.562734i	−0.449478	+	0.0286054i
$388$	5.27287	+	3.04429i	0.267689	+	0.154550i
$389$	−13.0307	−	15.5293i	−0.660681	−	0.787369i	0.326802	−	0.945093i	$-0.394029\pi$
$389$	−13.0307	−	15.5293i	−0.660681	−	0.787369i	−0.987483	+	0.157724i	$0.949584\pi$
$390$	−4.53613	−	7.31012i	−0.229696	−	0.370163i
$391$	19.2050	+	3.38636i	0.971239	+	0.171256i
$392$	−6.74903	+	1.85758i	−0.340877	+	0.0938219i
$393$	−18.2731	+	0.580875i	−0.921756	+	0.0293013i
$394$	−16.5140	+	13.8569i	−0.831966	+	0.698102i
$395$	7.21711	−	12.5004i	0.363132	−	0.628964i
$396$	1.11494	+	2.54698i	0.0560280	+	0.127990i
$397$	17.5042	−	10.1061i	0.878510	−	0.507208i	0.00834342	−	0.999965i	$-0.497344\pi$
$397$	17.5042	−	10.1061i	0.878510	−	0.507208i	0.870167	+	0.492757i	$0.164011\pi$
$398$	−5.33109	−	1.94036i	−0.267224	−	0.0972614i
$399$	0.286495	+	3.62799i	0.0143427	+	0.181627i
$400$	−2.81648	−	2.36331i	−0.140824	−	0.118165i
$401$	−0.374606	−	1.02922i	−0.0187069	−	0.0513969i	0.929988	−	0.367591i	$-0.119817\pi$
$401$	−0.374606	−	1.02922i	−0.0187069	−	0.0513969i	−0.948695	+	0.316194i	$0.897595\pi$
$402$	−0.0813437	+	0.247710i	−0.00405706	+	0.0123547i
$403$	2.45295	+	13.9114i	0.122190	+	0.692975i
$404$	6.37764			0.317299
$405$	−3.99825	+	9.55014i	−0.198675	+	0.474550i
$406$	0.654708	+	2.90649i	0.0324926	+	0.144246i
$407$	−9.62553	+	1.69724i	−0.477120	+	0.0841291i
$408$	−2.46535	+	7.50756i	−0.122053	+	0.371680i
$409$	−5.67973	−	15.6049i	−0.280845	−	0.771614i	−0.997262	−	0.0739429i	$-0.976442\pi$
$409$	−5.67973	−	15.6049i	−0.280845	−	0.771614i	0.716418	−	0.697672i	$-0.245780\pi$
$410$	4.92559	−	5.87009i	0.243258	−	0.289903i
$411$	−18.1705	−	2.61170i	−0.896286	−	0.128826i
$412$	−2.89352	+	7.94989i	−0.142554	+	0.391663i
$413$	−1.37074	+	1.26463i	−0.0674495	+	0.0622284i
$414$	−1.42020	+	12.7447i	−0.0697991	+	0.626366i
$415$	7.51517	−	13.0166i	0.368905	−	0.638962i
$416$	3.30761	−	2.77542i	0.162169	−	0.136076i
$417$	1.13332	+	35.6518i	0.0554988	+	1.74587i
$418$	−0.724823	−	0.127806i	−0.0354523	−	0.00625119i
$419$	3.12027	−	17.6960i	0.152435	−	0.864504i	−0.808658	−	0.588279i	$-0.799806\pi$
$419$	3.12027	−	17.6960i	0.152435	−	0.864504i	0.961093	−	0.276225i	$-0.0890833\pi$
$420$	3.75903	−	3.69594i	0.183422	−	0.180344i
$421$	−4.60854	+	3.86703i	−0.224607	+	0.188467i	−0.748146	−	0.663534i	$-0.769056\pi$
$421$	−4.60854	+	3.86703i	−0.224607	+	0.188467i	0.523539	+	0.852001i	$0.324611\pi$
$422$	9.63526	+	5.56292i	0.469037	+	0.270799i
$423$	2.53683	+	3.81225i	0.123345	+	0.185358i
$424$	−3.06469	−	5.30821i	−0.148835	−	0.257789i
$425$	−15.7621	−	5.73694i	−0.764575	−	0.278282i
$426$	21.9378	+	17.2505i	1.06289	+	0.835790i
$427$	−14.5893	−	7.53190i	−0.706026	−	0.364494i
$428$	1.35665	+	3.72738i	0.0655764	+	0.180170i
$429$	−1.41982	−	6.78401i	−0.0685494	−	0.327535i
$430$	−3.34586	+	0.589966i	−0.161352	+	0.0284507i
$431$		−	15.0976i		−	0.727225i	−0.931550	−	0.363613i	$-0.881543\pi$
$431$		−	15.0976i		−	0.727225i	0.931550	−	0.363613i	$-0.118457\pi$
$432$	−5.02978	−	1.30433i	−0.241996	−	0.0627546i
$433$			33.6460i			1.61692i	0.588550	+	0.808461i	$0.299699\pi$
$433$			33.6460i			1.61692i	−0.588550	+	0.808461i	$0.700301\pi$
$434$	−7.98562	+	3.33954i	−0.383322	+	0.160303i
$435$	−1.49610	−	1.67208i	−0.0717326	−	0.0801702i
$436$	−3.53886	+	1.28804i	−0.169481	+	0.0616859i
$437$	−2.60044	−	2.18203i	−0.124396	−	0.104381i
$438$	10.5036	−	4.20554i	0.501880	−	0.200949i
$439$	−4.30033	+	11.8150i	−0.205243	+	0.563902i	−0.999018	−	0.0443108i	$-0.985891\pi$
$439$	−4.30033	+	11.8150i	−0.205243	+	0.563902i	0.793774	+	0.608212i	$0.208113\pi$
$440$	0.533066	+	0.923297i	0.0254129	+	0.0440165i
$441$	−13.2244	−	16.3131i	−0.629732	−	0.776813i
$442$	9.84933	−	17.0595i	0.468485	−	0.811439i
$443$	0.885913	+	1.05579i	0.0420910	+	0.0501621i	0.786679	−	0.617362i	$-0.211799\pi$
$443$	0.885913	+	1.05579i	0.0420910	+	0.0501621i	−0.744588	+	0.667524i	$0.767354\pi$
$444$	8.62611	−	16.1016i	0.409377	−	0.764149i
$445$	2.41375	−	13.6891i	0.114423	−	0.648924i
$446$	5.10542	−	28.9543i	0.241749	−	1.37103i
$447$	−29.4084	−	15.7550i	−1.39097	−	0.745184i
$448$	2.10447	+	1.60350i	0.0994268	+	0.0757582i
$449$	5.55245	+	3.20571i	0.262036	+	0.151287i	0.625263	−	0.780414i	$-0.284992\pi$
$449$	5.55245	+	3.20571i	0.262036	+	0.151287i	−0.363227	+	0.931701i	$0.618325\pi$
$450$	3.10655	−	10.5834i	0.146444	−	0.498908i
$451$	5.34637	−	3.08673i	0.251751	−	0.145348i
$452$	3.96091	−	10.8825i	0.186305	−	0.511870i
$453$	−20.6724	+	8.27703i	−0.971272	+	0.388889i
$454$	−11.2245	+	13.3769i	−0.526793	+	0.627807i
$455$	−11.0594	+	7.09852i	−0.518475	+	0.332784i
$456$	1.02509	−	0.917200i	0.0480040	−	0.0429518i
$457$	6.87694	+	39.0011i	0.321690	+	1.82439i	0.531984	+	0.846754i	$0.321447\pi$
$457$	6.87694	+	39.0011i	0.321690	+	1.82439i	−0.210294	+	0.977638i	$0.567442\pi$
$458$	0.320213			0.0149626
$459$	−23.5983	+	2.25655i	−1.10148	+	0.105327i
$460$			4.91727i			0.229269i
$461$	−0.422916	−	2.39847i	−0.0196971	−	0.111708i	0.973374	−	0.229223i	$-0.0736184\pi$
$461$	−0.422916	−	2.39847i	−0.0196971	−	0.111708i	−0.993071	+	0.117515i	$0.962507\pi$
$462$	3.86415	−	1.76223i	0.179777	−	0.0819864i
$463$	2.04849	−	0.745590i	0.0952015	−	0.0346505i	−0.293980	−	0.955811i	$-0.594980\pi$
$463$	2.04849	−	0.745590i	0.0952015	−	0.0346505i	0.389182	+	0.921161i	$0.372758\pi$
$464$	0.723827	−	0.862623i	0.0336028	−	0.0400463i
$465$	4.02931	−	5.12415i	0.186855	−	0.237627i
$466$	1.54727	+	0.563160i	0.0716759	+	0.0260879i
$467$	2.83421	+	4.90900i	0.131152	+	0.227162i	0.924121	−	0.382100i	$-0.124799\pi$
$467$	2.83421	+	4.90900i	0.131152	+	0.227162i	−0.792969	+	0.609262i	$0.791466\pi$
$468$	11.6066	+	5.75111i	0.536517	+	0.265845i
$469$	0.380235	+	0.118470i	0.0175576	+	0.00547046i
$470$	1.12868	+	1.34510i	0.0520620	+	0.0620451i
$471$	27.3806	−	16.9904i	1.26163	−	0.782876i
$472$	0.694193	+	0.122405i	0.0319528	+	0.00563414i
$473$	−2.69554	−	0.475296i	−0.123941	−	0.0218541i
$474$	0.690508	+	21.7219i	0.0317161	+	0.997720i
$475$	1.87684	+	2.23673i	0.0861152	+	0.102628i
$476$	11.5241	+	3.59058i	0.528205	+	0.164574i
$477$	10.9012	−	14.8084i	0.499130	−	0.678031i
$478$	1.65852	+	2.87264i	0.0758588	+	0.131391i
$479$	39.1469	+	14.2483i	1.78867	+	0.651021i	0.999312	+	0.0370820i	$0.0118063\pi$
$479$	39.1469	+	14.2483i	1.78867	+	0.651021i	0.789353	+	0.613939i	$0.210416\pi$
$480$	−1.97223	−	0.283474i	−0.0900195	−	0.0129387i
$481$	−29.2703	+	34.8830i	−1.33461	+	1.59053i
$482$	2.18267	−	0.794426i	0.0994178	−	0.0361851i
$483$	19.4986	+	1.87230i	0.887218	+	0.0851924i
$484$	−1.76098	−	9.98702i	−0.0800446	−	0.453956i
$485$			7.00411i			0.318040i
$486$	−2.46643	−	15.3921i	−0.111880	−	0.698200i
$487$	42.5292			1.92718			0.963591	−	0.267379i	$-0.0861577\pi$
$487$	42.5292			1.92718			0.963591	+	0.267379i	$0.0861577\pi$
$488$	1.07761	+	6.11145i	0.0487812	+	0.276652i
$489$	20.3879	+	6.69502i	0.921972	+	0.302759i
$490$	−5.73254	−	5.65526i	−0.258970	−	0.255478i
$491$	−22.6956	+	27.0475i	−1.02424	+	1.22064i	−0.0491542	+	0.998791i	$0.515653\pi$
$491$	−22.6956	+	27.0475i	−1.02424	+	1.22064i	−0.975082	+	0.221846i	$0.928792\pi$
$492$	−1.64146	+	11.4202i	−0.0740027	+	0.514863i
$493$	1.75709	−	4.82757i	0.0791355	−	0.217423i
$494$	−2.96960	+	1.71450i	−0.133609	+	0.0771390i
$495$	−1.89612	+	2.57574i	−0.0852245	+	0.115771i
$496$	2.83327	+	1.63579i	0.127218	+	0.0734492i
$497$	25.8365	−	33.9085i	1.15893	−	1.52100i
$498$	0.719025	+	22.6190i	0.0322203	+	1.01358i
$499$	−4.32518	+	24.5293i	−0.193622	+	1.09808i	0.720747	+	0.693199i	$0.243799\pi$
$499$	−4.32518	+	24.5293i	−0.193622	+	1.09808i	−0.914368	+	0.404884i	$0.867312\pi$
$500$	1.73324	−	9.82971i	0.0775130	−	0.439598i
$501$	3.51958	+	5.67191i	0.157243	+	0.253402i
$502$	17.4510	+	20.7973i	0.778875	+	0.928227i
$503$	−6.72929	+	11.6555i	−0.300044	+	0.519692i	−0.976146	−	0.217117i	$-0.930335\pi$
$503$	−6.72929	+	11.6555i	−0.300044	+	0.519692i	0.676101	+	0.736809i	$0.263668\pi$
$504$	−1.87501	+	7.71261i	−0.0835197	+	0.343547i
$505$	3.66831	+	6.35371i	0.163238	+	0.282736i
$506$	−1.35492	+	3.72260i	−0.0602334	+	0.165490i
$507$	−7.68345	−	6.04178i	−0.341234	−	0.268325i
$508$	14.7944	+	12.4140i	0.656395	+	0.550781i
$509$	38.0354	−	13.8437i	1.68589	−	0.613613i	0.691791	−	0.722098i	$-0.256822\pi$
$509$	38.0354	−	13.8437i	1.68589	−	0.613613i	0.994098	+	0.108485i	$0.0345999\pi$
$510$	−8.89742	+	1.86213i	−0.393985	+	0.0824565i
$511$	−6.66797	−	15.9447i	−0.294974	−	0.705350i
$512$		−	1.00000i		−	0.0441942i
$513$	3.75388	+	1.71373i	0.165738	+	0.0756632i
$514$			7.69778i			0.339535i
$515$	−9.58437	+	1.68998i	−0.422338	+	0.0744695i
$516$	3.81218	−	3.41097i	0.167822	−	0.150160i
$517$	0.483828	+	1.32931i	0.0212787	+	0.0584628i
$518$	−24.7937	−	12.8000i	−1.08937	−	0.562401i
$519$	29.6268	−	11.8623i	1.30047	−	0.520698i
$520$	4.66749	+	1.69883i	0.204683	+	0.0744985i
$521$	−9.92445	−	17.1896i	−0.434798	−	0.753092i	0.562481	−	0.826810i	$-0.309847\pi$
$521$	−9.92445	−	17.1896i	−0.434798	−	0.753092i	−0.997279	+	0.0737180i	$0.976514\pi$
$522$	3.24147	+	0.951466i	0.141875	+	0.0416445i
$523$	14.7980	+	8.54363i	0.647071	+	0.373587i	0.787333	−	0.616528i	$-0.211461\pi$
$523$	14.7980	+	8.54363i	0.647071	+	0.373587i	−0.140262	+	0.990114i	$0.544795\pi$
$524$	8.08583	−	6.78482i	0.353231	−	0.296396i
$525$	−16.2370	−	4.49828i	−0.708639	−	0.196321i
$526$	2.22680	−	12.6288i	0.0970930	−	0.550642i
$527$	14.6989	+	2.59181i	0.640294	+	0.112901i
$528$	−1.41496	−	0.758036i	−0.0615783	−	0.0329893i
$529$	3.62225	−	3.03943i	0.157489	−	0.132149i
$530$	3.52553	−	6.10639i	0.153139	−	0.265245i
$531$	0.498744	+	2.05505i	0.0216436	+	0.0891816i
$532$	−1.42476	−	1.54430i	−0.0617712	−	0.0669539i
$533$	9.83709	−	27.0272i	0.426092	−	1.17068i
$534$	7.77935	+	19.4294i	0.336645	+	0.840790i
$535$	−2.93307	+	3.49549i	−0.126808	+	0.151123i
$536$	−0.0514841	−	0.141451i	−0.00222377	−	0.00610977i
$537$	24.4138	+	27.2855i	1.05353	+	1.17745i
$538$	−4.77640	+	0.842208i	−0.205925	+	0.0363102i
$539$	−2.78154	−	5.86086i	−0.119810	−	0.252445i
$540$	−1.59361	−	5.76114i	−0.0685783	−	0.247920i
$541$	−16.3856			−0.704471			−0.352236	−	0.935911i	$-0.614578\pi$
$541$	−16.3856			−0.704471			−0.352236	+	0.935911i	$0.614578\pi$
$542$	−3.39703	−	19.2655i	−0.145915	−	0.827526i
$543$	20.7880	−	4.35069i	0.892098	−	0.186706i
$544$	−1.56037	−	4.28708i	−0.0669003	−	0.183807i
$545$	−3.31870	−	2.78472i	−0.142158	−	0.119284i
$546$	8.51361	−	17.8613i	0.364349	−	0.764394i
$547$	28.2884	+	10.2961i	1.20952	+	0.440231i	0.866539	−	0.499110i	$-0.166340\pi$
$547$	28.2884	+	10.2961i	1.20952	+	0.440231i	0.342985	+	0.939341i	$0.388562\pi$
$548$	9.17863	−	5.29928i	0.392092	−	0.226374i
$549$	−15.4992	+	10.3138i	−0.661489	+	0.440183i
$550$	1.70371	−	2.95092i	0.0726466	−	0.125828i
$551$	−0.685058	+	0.574832i	−0.0291845	+	0.0244887i
$552$	−3.90369	−	6.29092i	−0.166152	−	0.267759i
$553$	33.1608	−	1.56059i	1.41014	−	0.0663631i
$554$	12.6356	+	2.22799i	0.536833	+	0.0946582i
$555$	21.0028	−	0.667649i	0.891519	−	0.0283401i
$556$	−13.2375	−	15.7759i	−0.561397	−	0.669046i
$557$	30.5051	+	17.6121i	1.29254	+	0.746250i	0.979104	−	0.203358i	$-0.0651857\pi$
$557$	30.5051	+	17.6121i	1.29254	+	0.746250i	0.313439	+	0.949608i	$0.398519\pi$
$558$	−1.08698	+	9.75437i	−0.0460155	+	0.412935i
$559$	−11.0436	+	6.37604i	−0.467095	+	0.269678i
$560$	−0.387026	+	3.01888i	−0.0163548	+	0.127571i
$561$	−7.24887	−	1.04190i	−0.306047	−	0.0439891i
$562$	−20.7140	−	17.3811i	−0.873766	−	0.733177i
$563$	8.65753	−	3.15108i	0.364871	−	0.132802i	−0.153077	−	0.988214i	$-0.548918\pi$
$563$	8.65753	−	3.15108i	0.364871	−	0.132802i	0.517948	+	0.855412i	$0.326696\pi$
$564$	−2.51182	−	0.824837i	−0.105767	−	0.0347319i
$565$	13.1199	−	2.31340i	0.551959	−	0.0973253i
$566$	25.7190			1.08105
$567$	−23.4516	+	4.12561i	−0.984876	+	0.173259i
$568$	−16.1126			−0.676070
$569$	−2.13966	+	0.377280i	−0.0896992	+	0.0158164i	−0.218318	−	0.975878i	$-0.570057\pi$
$569$	−2.13966	+	0.377280i	−0.0896992	+	0.0158164i	0.128618	+	0.991694i	$0.458946\pi$
$570$	1.50337	+	0.493681i	0.0629693	+	0.0206780i
$571$	−4.32364	+	1.57368i	−0.180939	+	0.0658564i	−0.430901	−	0.902399i	$-0.641804\pi$
$571$	−4.32364	+	1.57368i	−0.180939	+	0.0658564i	0.249962	+	0.968256i	$0.419582\pi$
$572$	3.06541	+	2.57219i	0.128171	+	0.107548i
$573$	−10.4979	−	1.50889i	−0.438557	−	0.0630350i
$574$	17.4809	+	2.24108i	0.729638	+	0.0935409i
$575$	13.6104	−	7.85796i	0.567592	−	0.327699i
$576$	2.74822	−	1.20304i	0.114509	−	0.0501265i
$577$	−14.5135	−	8.37937i	−0.604204	−	0.348838i	0.166489	−	0.986043i	$-0.446757\pi$
$577$	−14.5135	−	8.37937i	−0.604204	−	0.348838i	−0.770694	+	0.637206i	$0.780090\pi$
$578$	−2.45147	−	2.92155i	−0.101968	−	0.121521i
$579$	−41.3861	+	1.31560i	−1.71995	+	0.0546747i
$580$	1.27572	+	0.224944i	0.0529714	+	0.00934028i
$581$	34.5303	−	1.62504i	1.43256	−	0.0674180i
$582$	−5.56038	−	8.96073i	−0.230485	−	0.371434i
$583$	4.35156	−	3.65140i	0.180223	−	0.151225i
$584$	−3.26614	+	5.65711i	−0.135154	+	0.234093i
$585$	0.946414	+	14.8710i	0.0391294	+	0.614841i
$586$	−10.7829	+	6.22552i	−0.445438	+	0.257174i
$587$	−8.89249	−	3.23660i	−0.367032	−	0.133589i	0.151918	−	0.988393i	$-0.451455\pi$
$587$	−8.89249	−	3.23660i	−0.367032	−	0.133589i	−0.518951	+	0.854804i	$0.673677\pi$
$588$	11.8235	+	2.68415i	0.487593	+	0.110693i
$589$	−1.99030	−	1.67006i	−0.0820088	−	0.0688136i
$590$	0.277343	+	0.761993i	0.0114180	+	0.0313708i
$591$	36.5470	−	7.64886i	1.50334	−	0.314632i
$592$	1.83134	+	10.3861i	0.0752677	+	0.426864i
$593$	−47.5778			−1.95379			−0.976893	−	0.213727i	$-0.931440\pi$
$593$	−47.5778			−1.95379			−0.976893	+	0.213727i	$0.931440\pi$
$594$	0.380999	−	4.80057i	0.0156326	−	0.196970i
$595$	3.05136	+	13.5461i	0.125093	+	0.555335i
$596$	18.9694	−	3.34481i	0.777016	−	0.137009i
$597$	6.55222	+	7.32292i	0.268164	+	0.299707i
$598$	6.31247	+	17.3434i	0.258136	+	0.709223i
$599$	2.64821	−	3.15602i	0.108203	−	0.128951i	−0.709225	−	0.704982i	$-0.750955\pi$
$599$	2.64821	−	3.15602i	0.108203	−	0.128951i	0.817428	+	0.576031i	$0.195399\pi$
$600$	2.36707	+	5.91188i	0.0966351	+	0.241352i
$601$	−12.0190	+	33.0219i	−0.490265	+	1.34699i	0.410174	+	0.912008i	$0.365468\pi$
$601$	−12.0190	+	33.0219i	−0.490265	+	1.34699i	−0.900438	+	0.434984i	$0.856754\pi$
$602$	−5.29853	−	5.74308i	−0.215952	−	0.234071i
$603$	0.326802	−	0.311661i	0.0133084	−	0.0126918i
$604$	6.42816	−	11.1339i	0.261558	−	0.453032i
$605$	8.93666	−	7.49875i	0.363327	−	0.304868i
$606$	−9.73711	−	5.21646i	−0.395543	−	0.211904i
$607$	−22.8117	−	4.02232i	−0.925899	−	0.163261i	−0.309685	−	0.950839i	$-0.600223\pi$
$607$	−22.8117	−	4.02232i	−0.925899	−	0.163261i	−0.616215	+	0.787578i	$0.711335\pi$
$608$	−0.137904	+	0.782092i	−0.00559274	+	0.0317180i
$609$	1.37772	−	4.97301i	0.0558280	−	0.201516i
$610$	−5.46869	+	4.58878i	−0.221421	+	0.185794i
$611$	5.70764	+	3.29531i	0.230906	+	0.133314i
$612$	9.90465	−	9.44575i	0.400372	−	0.381822i
$613$	−9.08034	−	15.7276i	−0.366752	−	0.635232i	0.622304	−	0.782776i	$-0.286197\pi$
$613$	−9.08034	−	15.7276i	−0.366752	−	0.635232i	−0.989056	+	0.147543i	$0.952863\pi$
$614$	−12.6515	−	4.60477i	−0.510573	−	0.185833i
$615$	−12.3215	+	4.93343i	−0.496851	+	0.198935i
$616$	−1.12483	+	2.17879i	−0.0453206	+	0.0877861i
$617$	0.206906	+	0.568468i	0.00832971	+	0.0228857i	0.943788	−	0.330552i	$-0.107235\pi$
$617$	0.206906	+	0.568468i	0.00832971	+	0.0228857i	−0.935458	+	0.353438i	$0.885013\pi$
$618$	10.9202	−	9.77086i	0.439273	−	0.393042i
$619$	2.71439	−	0.478620i	0.109100	−	0.0192373i	−0.118831	−	0.992914i	$-0.537915\pi$
$619$	2.71439	−	0.478620i	0.109100	−	0.0192373i	0.227932	+	0.973677i	$0.426804\pi$
$620$			3.76352i			0.151147i
$621$	12.5925	−	18.2964i	0.505321	−	0.734209i
$622$			22.3567i			0.896423i
$623$	29.4942	−	12.3343i	1.18166	−	0.494164i
$624$	−7.32002	+	1.53200i	−0.293035	+	0.0613290i
$625$	−6.48486	+	2.36030i	−0.259394	+	0.0944119i
$626$	15.9988	+	13.4246i	0.639441	+	0.536555i
$627$	1.00209	+	0.787983i	0.0400198	+	0.0314690i
$628$	−6.36307	+	17.4824i	−0.253914	+	0.697624i
$629$	24.0572	+	41.6683i	0.959223	+	1.66142i
$630$	−8.76215	+	2.56819i	−0.349092	+	0.102319i
$631$	15.0925	−	26.1410i	0.600824	−	1.04066i	−0.391872	−	0.920020i	$-0.628172\pi$
$631$	15.0925	−	26.1410i	0.600824	−	1.04066i	0.992696	−	0.120639i	$-0.0384942\pi$
$632$	−8.06537	−	9.61193i	−0.320823	−	0.382342i
$633$	−10.1606	−	16.3742i	−0.403849	−	0.650816i
$634$	−4.24340	+	24.0655i	−0.168527	+	0.955764i
$635$	−3.85789	+	21.8792i	−0.153096	+	0.868249i
$636$	0.337310	+	10.6111i	0.0133752	+	0.420756i
$637$	−27.4787	−	12.5872i	−1.08875	−	0.498724i
$638$	0.903799	+	0.521808i	0.0357817	+	0.0206586i
$639$	−19.3840	−	44.2809i	−0.766821	−	1.75173i
$640$	0.996248	−	0.575184i	0.0393802	−	0.0227361i
$641$	6.85418	−	18.8317i	0.270724	−	0.743807i	−0.727604	−	0.685997i	$-0.759366\pi$
$641$	6.85418	−	18.8317i	0.270724	−	0.743807i	0.998328	−	0.0578097i	$-0.0184117\pi$
$642$	0.977448	−	6.80045i	0.0385768	−	0.268393i
$643$	13.3245	−	15.8795i	0.525466	−	0.626226i	−0.436398	−	0.899754i	$-0.643746\pi$
$643$	13.3245	−	15.8795i	0.525466	−	0.626226i	0.961864	+	0.273528i	$0.0881905\pi$
$644$	−9.51750	+	6.10882i	−0.375042	+	0.240721i
$645$	5.59088	+	1.83595i	0.220141	+	0.0722903i
$646$	0.629148	+	3.56807i	0.0247535	+	0.140384i
$647$	5.97287			0.234818			0.117409	−	0.993084i	$-0.462541\pi$
$647$	5.97287			0.234818			0.117409	+	0.993084i	$0.462541\pi$
$648$	6.61241	+	6.10541i	0.259760	+	0.239843i
$649$			0.653285i			0.0256437i
$650$	−2.75666	−	15.6338i	−0.108125	−	0.613208i
$651$	14.9236	+	1.43300i	0.584903	+	0.0561635i
$652$	−11.6422	+	4.23741i	−0.455943	+	0.165950i
$653$	−31.6331	+	37.6988i	−1.23790	+	1.47527i	−0.412264	+	0.911065i	$0.635262\pi$
$653$	−31.6331	+	37.6988i	−1.23790	+	1.47527i	−0.825635	+	0.564205i	$0.809183\pi$
$654$	6.45651	+	0.928012i	0.252470	+	0.0362882i
$655$	11.4102	+	4.15298i	0.445834	+	0.162270i
$656$	−3.33061	−	5.76879i	−0.130039	−	0.225233i
$657$	−19.4763	−	2.17034i	−0.759841	−	0.0846730i
$658$	−1.20131	+	3.85563i	−0.0468318	+	0.150308i
$659$	13.3461	+	15.9053i	0.519892	+	0.619583i	0.960555	−	0.278089i	$-0.0897011\pi$
$659$	13.3461	+	15.9053i	0.519892	+	0.619583i	−0.440663	+	0.897673i	$0.645257\pi$
$660$	−0.0586709	−	1.84566i	−0.00228376	−	0.0718423i
$661$	18.2615	+	3.21999i	0.710289	+	0.125243i	0.517108	−	0.855920i	$-0.327008\pi$
$661$	18.2615	+	3.21999i	0.710289	+	0.125243i	0.193181	+	0.981163i	$0.438120\pi$
$662$	−25.1990	−	4.44326i	−0.979386	−	0.172692i
$663$	−28.9910	+	17.9897i	−1.12592	+	0.698663i
$664$	−8.39845	−	10.0089i	−0.325923	−	0.388420i
$665$	0.719006	−	2.30767i	0.0278818	−	0.0894876i
$666$	−26.3400	+	17.5277i	−1.02065	+	0.679186i
$667$	2.40671	+	4.16855i	0.0931882	+	0.161407i
$668$	−3.62150	−	1.31812i	−0.140120	−	0.0509995i
$669$	−31.4773	+	40.0303i	−1.21698	+	1.54766i
$670$	0.111308	−	0.132651i	0.00430020	−	0.00512477i
$671$	−5.40446	+	1.96706i	−0.208637	+	0.0759376i
$672$	−1.90147	−	4.16946i	−0.0733507	−	0.160841i
$673$	2.06397	+	11.7053i	0.0795601	+	0.451208i	0.998398	+	0.0565737i	$0.0180176\pi$
$673$	2.06397	+	11.7053i	0.0795601	+	0.451208i	−0.918838	+	0.394634i	$0.870871\pi$
$674$			6.37981i			0.245741i
$675$	−13.3995	+	13.6174i	−0.515746	+	0.524135i
$676$	5.64324			0.217048
$677$	2.23220	+	12.6594i	0.0857904	+	0.486541i	0.997183	+	0.0750039i	$0.0238969\pi$
$677$	2.23220	+	12.6594i	0.0857904	+	0.486541i	−0.911393	+	0.411537i	$0.864992\pi$
$678$	−14.9485	+	13.3752i	−0.574092	+	0.513672i
$679$	−13.5566	+	8.70134i	−0.520256	+	0.333927i
$680$	3.37350	−	4.02038i	0.129368	−	0.154174i
$681$	28.0785	−	11.2424i	1.07597	−	0.430809i
$682$	−1.03701	+	2.84917i	−0.0397092	+	0.109100i
$683$	18.6286	−	10.7552i	0.712804	−	0.411538i	−0.0992942	−	0.995058i	$-0.531659\pi$
$683$	18.6286	−	10.7552i	0.712804	−	0.411538i	0.812098	+	0.583520i	$0.198325\pi$
$684$	−2.31526	+	0.561896i	−0.0885263	+	0.0214846i
$685$	10.5588	+	6.09613i	0.403431	+	0.232921i
$686$	3.82425	−	18.1211i	0.146010	−	0.691868i
$687$	−0.488887	−	0.261911i	−0.0186522	−	0.00999254i
$688$	−0.512850	+	2.90852i	−0.0195522	+	0.110886i
$689$	4.59566	−	26.0633i	0.175081	−	0.992933i
$690$	4.02198	−	7.50748i	0.153114	−	0.285805i
$691$	13.6930	+	16.3187i	0.520908	+	0.620794i	0.960795	−	0.277259i	$-0.0894260\pi$
$691$	13.6930	+	16.3187i	0.520908	+	0.620794i	−0.439887	+	0.898053i	$0.644982\pi$
$692$	−9.21259	+	15.9567i	−0.350210	+	0.606582i
$693$	−7.34101	−	0.470103i	−0.278862	−	0.0178577i
$694$	3.03538	+	5.25743i	0.115221	+	0.199569i
$695$	8.10267	−	22.2619i	0.307352	−	0.844442i
$696$	−1.81067	+	0.724978i	−0.0686334	+	0.0274802i
$697$	−23.2801	−	19.5343i	−0.881795	−	0.739914i
$698$	−9.97782	+	3.63163i	−0.377666	+	0.137459i
$699$	−1.90168	−	2.12537i	−0.0719282	−	0.0803888i
$700$	8.97436	−	3.75303i	0.339199	−	0.141851i
$701$			27.0367i			1.02116i	0.859829	+	0.510582i	$0.170570\pi$
$701$			27.0367i			1.02116i	−0.859829	+	0.510582i	$0.829430\pi$
$702$	−13.0165	−	18.2740i	−0.491277	−	0.689706i
$703$		−	8.37540i		−	0.315884i
$704$	0.912695	−	0.160933i	0.0343985	−	0.00606538i
$705$	−0.623016	−	2.97683i	−0.0234642	−	0.112114i
$706$	−4.65222	−	12.7819i	−0.175089	−	0.481052i
$707$	−7.74055	+	14.9935i	−0.291113	+	0.563887i
$708$	−0.959746	−	0.754683i	−0.0360695	−	0.0283627i
$709$	31.8767	+	11.6022i	1.19715	+	0.435728i	0.862230	−	0.506517i	$-0.169067\pi$
$709$	31.8767	+	11.6022i	1.19715	+	0.435728i	0.334924	+	0.942245i	$0.391289\pi$
$710$	−9.26771	−	16.0521i	−0.347811	−	0.602426i
$711$	16.7127	−	33.7289i	0.626777	−	1.26493i
$712$	−10.4644	−	6.04165i	−0.392171	−	0.226420i
$713$	−10.7127	+	8.98902i	−0.401194	+	0.336641i
$714$	−14.6576	−	14.9078i	−0.548549	−	0.557912i
$715$	−0.799359	+	4.53339i	−0.0298943	+	0.169539i
$716$	−20.8175	−	3.67069i	−0.777987	−	0.137180i
$717$	−0.182542	−	5.74237i	−0.00681714	−	0.214453i
$718$	−14.0499	+	11.7893i	−0.524337	+	0.439971i
$719$	25.2093	−	43.6637i	0.940147	−	1.62838i	0.174959	−	0.984576i	$-0.444021\pi$
$719$	25.2093	−	43.6637i	0.940147	−	1.62838i	0.765188	−	0.643807i	$-0.222646\pi$
$720$	2.77925	+	2.04594i	0.103577	+	0.0762476i
$721$	−15.1779	−	16.4513i	−0.565253	−	0.612678i
$722$	−6.28268	+	17.2615i	−0.233817	+	0.642407i
$723$	−3.98219	−	0.572371i	−0.148099	−	0.0212867i
$724$	−7.88186	+	9.39323i	−0.292927	+	0.349097i
$725$	−1.41603	−	3.89050i	−0.0525899	−	0.144490i
$726$	−5.48009	+	16.6881i	−0.203385	+	0.619355i
$727$	11.6409	−	2.05260i	0.431736	−	0.0761267i	0.0464430	−	0.998921i	$-0.485211\pi$
$727$	11.6409	−	2.05260i	0.431736	−	0.0761267i	0.385293	+	0.922794i	$0.374100\pi$
$728$	2.51039	+	11.1445i	0.0930412	+	0.413044i
$729$	−8.82401	+	25.5174i	−0.326815	+	0.945088i
$730$	−7.51452			−0.278125
$731$	2.33973	+	13.2693i	0.0865381	+	0.490782i
$732$	3.35348	−	10.2121i	0.123948	−	0.377451i
$733$	−5.59468	−	15.3712i	−0.206644	−	0.567750i	0.792467	−	0.609915i	$-0.208797\pi$
$733$	−5.59468	−	15.3712i	−0.206644	−	0.567750i	−0.999111	+	0.0421654i	$0.986574\pi$
$734$	2.83255	+	2.37679i	0.104551	+	0.0877288i
$735$	4.12661	+	13.3230i	0.152212	+	0.491427i
$736$	4.01673	+	1.46197i	0.148059	+	0.0538890i
$737$	0.120816	−	0.0697534i	0.00445033	−	0.00256940i
$738$	11.8470	−	16.0933i	0.436096	−	0.592403i
$739$	14.3118	−	24.7888i	0.526469	−	0.911872i	−0.473055	−	0.881033i	$-0.656849\pi$
$739$	14.3118	−	24.7888i	0.526469	−	0.911872i	0.999524	−	0.0308387i	$-0.00981783\pi$
$740$	−9.29373	+	7.79836i	−0.341644	+	0.286674i
$741$	5.93620	−	0.188703i	0.218072	−	0.00693219i
$742$	16.1989	−	0.762342i	0.594681	−	0.0279864i
$743$	−35.8446	−	6.32038i	−1.31501	−	0.231872i	−0.528229	−	0.849102i	$-0.677144\pi$
$743$	−35.8446	−	6.32038i	−1.31501	−	0.231872i	−0.786783	+	0.617230i	$0.788255\pi$
$744$	−2.98776	−	4.81487i	−0.109537	−	0.176522i
$745$	14.2431	+	16.9743i	0.521828	+	0.621891i
$746$	−16.6139	−	9.59204i	−0.608278	−	0.351189i
$747$	17.4030	−	35.1218i	0.636741	−	1.28504i
$748$	3.66168	−	2.11407i	0.133884	−	0.0772982i
$749$	−10.4094	−	1.33451i	−0.380352	−	0.0487618i
$750$	−10.6862	+	13.5899i	−0.390207	+	0.496234i
$751$	0.933392	+	0.783209i	0.0340600	+	0.0285797i	0.659659	−	0.751565i	$-0.270701\pi$
$751$	0.933392	+	0.783209i	0.0340600	+	0.0285797i	−0.625599	+	0.780145i	$0.715145\pi$
$752$	1.43434	−	0.522056i	0.0523049	−	0.0190374i
$753$	−9.63273	−	46.0260i	−0.351036	−	1.67728i
$754$	4.78828	−	0.844302i	0.174379	−	0.0307477i
$755$	14.7895			0.538245
$756$	9.17106	−	10.2417i	0.333548	−	0.372486i
$757$	−21.1015			−0.766946			−0.383473	−	0.923552i	$-0.625272\pi$
$757$	−21.1015			−0.766946			−0.383473	+	0.923552i	$0.625272\pi$
$758$	−3.24186	+	0.571628i	−0.117750	+	0.0207625i
$759$	5.11346	−	4.57529i	0.185607	−	0.166073i
$760$	−0.858478	+	0.312460i	−0.0311403	+	0.0113341i
$761$	26.9443	+	22.6090i	0.976730	+	0.819574i	0.983593	−	0.180402i	$-0.0577400\pi$
$761$	26.9443	+	22.6090i	0.976730	+	0.819574i	−0.00686247	+	0.999976i	$0.502184\pi$
$762$	−12.4337	−	31.0539i	−0.450426	−	1.12496i
$763$	1.26701	−	9.88295i	0.0458689	−	0.357787i
$764$	5.30290	−	3.06163i	0.191852	−	0.110766i
$765$	15.1073	+	4.43444i	0.546206	+	0.160328i
$766$	10.6546	+	6.15144i	0.384967	+	0.222261i
$767$	1.95640	+	2.33154i	0.0706414	+	0.0841871i
$768$	−0.817929	+	1.52676i	−0.0295145	+	0.0550922i
$769$	26.3550	+	4.64710i	0.950386	+	0.167579i	0.627289	−	0.778787i	$-0.284165\pi$
$769$	26.3550	+	4.64710i	0.950386	+	0.167579i	0.323098	+	0.946366i	$0.395276\pi$

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.z (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.984808 - 0.173648i) q^{2} +(-1.64560 - 0.540384i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.881233 + 0.739442i) q^{5} +(-1.71443 - 0.246420i) q^{6} +(-0.336437 + 2.62427i) q^{7} +(0.866025 - 0.500000i) q^{8} +(2.41597 + 1.77851i) q^{9} +O(q^{10})\)	\(q+(0.984808 - 0.173648i) q^{2} +(-1.64560 - 0.540384i) q^{3} +(0.939693 - 0.342020i) q^{4} +(0.881233 + 0.739442i) q^{5} +(-1.71443 - 0.246420i) q^{6} +(-0.336437 + 2.62427i) q^{7} +(0.866025 - 0.500000i) q^{8} +(2.41597 + 1.77851i) q^{9} +(0.996248 + 0.575184i) q^{10} +(0.595719 + 0.709951i) q^{11} +(-1.73118 + 0.0550316i) q^{12} +(4.25218 + 0.749775i) q^{13} +(0.124375 + 2.64283i) q^{14} +(-1.05057 - 1.69303i) q^{15} +(0.766044 - 0.642788i) q^{16} +(2.28111 - 3.95100i) q^{17} +(2.68810 + 1.33196i) q^{18} +(-0.687760 + 0.397079i) q^{19} +(1.08099 + 0.393449i) q^{20} +(1.97176 - 4.13669i) q^{21} +(0.709951 + 0.595719i) q^{22} +(1.46197 + 4.01673i) q^{23} +(-1.69532 + 0.354811i) q^{24} +(-0.638444 - 3.62080i) q^{25} +4.31778 q^{26} +(-3.01463 - 4.23226i) q^{27} +(0.581407 + 2.58108i) q^{28} +(1.10897 - 0.195541i) q^{29} +(-1.32860 - 1.48488i) q^{30} +(1.11895 + 3.07428i) q^{31} +(0.642788 - 0.766044i) q^{32} +(-0.596667 - 1.49021i) q^{33} +(1.56037 - 4.28708i) q^{34} +(-2.23698 + 2.06382i) q^{35} +(2.87855 + 0.844941i) q^{36} +(-5.27314 + 9.13334i) q^{37} +(-0.608360 + 0.510474i) q^{38} +(-6.59221 - 3.53164i) q^{39} +(1.13289 + 0.199759i) q^{40} +(1.15671 - 6.56003i) q^{41} +(1.22347 - 4.41623i) q^{42} +(-2.26242 + 1.89840i) q^{43} +(0.802610 + 0.463387i) q^{44} +(0.813928 + 3.35375i) q^{45} +(2.13726 + 3.70184i) q^{46} +(1.43434 + 0.522056i) q^{47} +(-1.60795 + 0.643810i) q^{48} +(-6.77362 - 1.76580i) q^{49} +(-1.25749 - 3.45492i) q^{50} +(-5.88884 + 5.26906i) q^{51} +(4.25218 - 0.749775i) q^{52} -6.12939i q^{53} +(-3.70376 - 3.64447i) q^{54} +1.06613i q^{55} +(1.02077 + 2.44091i) q^{56} +(1.34635 - 0.281776i) q^{57} +(1.05816 - 0.385140i) q^{58} +(0.539986 + 0.453102i) q^{59} +(-1.56626 - 1.23161i) q^{60} +(-2.12248 + 5.83147i) q^{61} +(1.63579 + 2.83327i) q^{62} +(-5.48011 + 5.74181i) q^{63} +(0.500000 - 0.866025i) q^{64} +(3.19275 + 3.80497i) q^{65} +(-0.846374 - 1.36396i) q^{66} +(0.0261392 - 0.148242i) q^{67} +(0.792221 - 4.49291i) q^{68} +(-0.235233 - 7.39994i) q^{69} +(-1.84461 + 2.42091i) q^{70} +(-13.9539 - 8.05630i) q^{71} +(2.98155 + 0.332249i) q^{72} +(-5.65711 + 3.26614i) q^{73} +(-3.60704 + 9.91026i) q^{74} +(-0.906001 + 6.30337i) q^{75} +(-0.510474 + 0.608360i) q^{76} +(-2.06353 + 1.32448i) q^{77} +(-7.10532 - 2.33326i) q^{78} +(-2.17885 - 12.3569i) q^{79} +1.15037 q^{80} +(2.67382 + 8.59364i) q^{81} -6.66123i q^{82} +(-2.26883 - 12.8672i) q^{83} +(0.438013 - 4.56159i) q^{84} +(4.93172 - 1.79500i) q^{85} +(-1.89840 + 2.26242i) q^{86} +(-1.93058 - 0.277487i) q^{87} +(0.870883 + 0.316976i) q^{88} +(-6.04165 - 10.4644i) q^{89} +(1.38394 + 3.16146i) q^{90} +(-3.39821 + 10.9066i) q^{91} +(2.74761 + 3.27447i) q^{92} +(-0.180040 - 5.66368i) q^{93} +(1.50320 + 0.265055i) q^{94} +(-0.899694 - 0.158640i) q^{95} +(-1.47173 + 0.913247i) q^{96} +(3.91366 + 4.66412i) q^{97} +(-6.97734 - 0.562750i) q^{98} +(0.176587 + 2.77471i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 12 q^{9}+O(q^{10}) \) 144 * q - 12 * q^9	\( 144 q - 12 q^{9} + 12 q^{11} + 6 q^{14} + 12 q^{15} + 24 q^{21} - 60 q^{23} + 12 q^{29} - 72 q^{30} + 54 q^{35} - 12 q^{36} + 48 q^{39} + 24 q^{42} + 18 q^{49} - 60 q^{50} - 36 q^{51} + 6 q^{56} - 60 q^{57} - 36 q^{60} - 78 q^{63} + 72 q^{64} - 120 q^{65} + 36 q^{70} - 72 q^{71} - 24 q^{72} - 36 q^{74} + 66 q^{77} - 60 q^{78} - 72 q^{79} + 12 q^{84} - 72 q^{85} - 48 q^{86} - 18 q^{91} + 12 q^{92} + 24 q^{93} - 120 q^{95} + 36 q^{98} + 144 q^{99}+O(q^{100}) \) 144 * q - 12 * q^9 + 12 * q^11 + 6 * q^14 + 12 * q^15 + 24 * q^21 - 60 * q^23 + 12 * q^29 - 72 * q^30 + 54 * q^35 - 12 * q^36 + 48 * q^39 + 24 * q^42 + 18 * q^49 - 60 * q^50 - 36 * q^51 + 6 * q^56 - 60 * q^57 - 36 * q^60 - 78 * q^63 + 72 * q^64 - 120 * q^65 + 36 * q^70 - 72 * q^71 - 24 * q^72 - 36 * q^74 + 66 * q^77 - 60 * q^78 - 72 * q^79 + 12 * q^84 - 72 * q^85 - 48 * q^86 - 18 * q^91 + 12 * q^92 + 24 * q^93 - 120 * q^95 + 36 * q^98 + 144 * q^99

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