LMFDB - Embedded newform 1386.2.bu.a.701.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(701,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 3]))

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

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

chi := DirichletCharacter("1386.701");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.bu (of order $10$, degree $4$, 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:	$11.0672657201$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			701.6
Character	$\chi$	$=$	1386.701
Dual form			1386.2.bu.a.953.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(0.0348544 - 0.0479729i) q^{5} +(0.951057 + 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(0.0348544 - 0.0479729i) q^{5} +(0.951057 + 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +0.0592978i q^{10} +(0.764896 + 3.22722i) q^{11} +(-2.76143 - 3.80078i) q^{13} +(-0.951057 + 0.309017i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(0.0206121 + 0.0149756i) q^{17} +(-5.33201 + 1.73247i) q^{19} +(-0.0348544 - 0.0479729i) q^{20} +(-2.51573 - 2.16128i) q^{22} +7.57543i q^{23} +(1.54400 + 4.75194i) q^{25} +(4.46808 + 1.45177i) q^{26} +(0.587785 - 0.809017i) q^{28} +(-1.03075 + 3.17232i) q^{29} +(3.61648 - 2.62752i) q^{31} +1.00000 q^{32} -0.0254779 q^{34} +(0.0479729 - 0.0348544i) q^{35} +(1.34532 - 4.14046i) q^{37} +(3.29536 - 4.53568i) q^{38} +(0.0563955 + 0.0183240i) q^{40} +(-0.884378 - 2.72184i) q^{41} +1.76335i q^{43} +(3.30563 + 0.269805i) q^{44} +(-4.45273 - 6.12865i) q^{46} +(-6.78589 + 2.20487i) q^{47} +(0.809017 + 0.587785i) q^{49} +(-4.04224 - 2.93686i) q^{50} +(-4.46808 + 1.45177i) q^{52} +(5.47359 + 7.53376i) q^{53} +(0.181479 + 0.0757883i) q^{55} +1.00000i q^{56} +(-1.03075 - 3.17232i) q^{58} +(2.52860 + 0.821591i) q^{59} +(1.10936 - 1.52690i) q^{61} +(-1.38137 + 4.25142i) q^{62} +(-0.809017 + 0.587785i) q^{64} -0.278582 q^{65} -6.35318 q^{67} +(0.0206121 - 0.0149756i) q^{68} +(-0.0183240 + 0.0563955i) q^{70} +(-8.20006 + 11.2864i) q^{71} +(0.975169 + 0.316852i) q^{73} +(1.34532 + 4.14046i) q^{74} +5.60640i q^{76} +(-0.269805 + 3.30563i) q^{77} +(7.60983 + 10.4740i) q^{79} +(-0.0563955 + 0.0183240i) q^{80} +(2.31533 + 1.68219i) q^{82} +(13.6996 + 9.95332i) q^{83} +(0.00143684 - 0.000466858i) q^{85} +(-1.03647 - 1.42658i) q^{86} +(-2.83290 + 1.72472i) q^{88} -1.58065i q^{89} +(-1.45177 - 4.46808i) q^{91} +(7.20466 + 2.34094i) q^{92} +(4.19391 - 5.77242i) q^{94} +(-0.102732 + 0.316176i) q^{95} +(-13.5147 + 9.81900i) q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8}+O(q^{10}) $ 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8	$ 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8} + 4 q^{11} - 12 q^{16} + 24 q^{17} + 4 q^{22} + 24 q^{25} + 40 q^{26} - 16 q^{29} + 40 q^{31} + 48 q^{32} - 16 q^{34} - 12 q^{35} + 16 q^{37} - 40 q^{38} + 24 q^{41} + 4 q^{44} - 40 q^{46} - 40 q^{47} + 12 q^{49} + 4 q^{50} - 40 q^{52} - 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} - 40 q^{62} - 12 q^{64} + 48 q^{67} + 24 q^{68} + 8 q^{70} + 40 q^{73} + 16 q^{74} + 32 q^{77} + 40 q^{79} - 16 q^{82} - 16 q^{83} - 20 q^{85} + 4 q^{88} - 20 q^{92} - 52 q^{95} - 8 q^{97} - 48 q^{98}+O(q^{100}) $ 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8 + 4 * q^11 - 12 * q^16 + 24 * q^17 + 4 * q^22 + 24 * q^25 + 40 * q^26 - 16 * q^29 + 40 * q^31 + 48 * q^32 - 16 * q^34 - 12 * q^35 + 16 * q^37 - 40 * q^38 + 24 * q^41 + 4 * q^44 - 40 * q^46 - 40 * q^47 + 12 * q^49 + 4 * q^50 - 40 * q^52 - 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 - 40 * q^62 - 12 * q^64 + 48 * q^67 + 24 * q^68 + 8 * q^70 + 40 * q^73 + 16 * q^74 + 32 * q^77 + 40 * q^79 - 16 * q^82 - 16 * q^83 - 20 * q^85 + 4 * q^88 - 20 * q^92 - 52 * q^95 - 8 * q^97 - 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$		0			0
$3$		0			0
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	0.0348544	−	0.0479729i	0.0155873	−	0.0214541i	−0.801152	−	0.598461i	$-0.795779\pi$
$5$	0.0348544	−	0.0479729i	0.0155873	−	0.0214541i	0.816740	+	0.577007i	$0.195779\pi$
$6$		0			0
$7$	0.951057	+	0.309017i	0.359466	+	0.116797i
$7$	0.951057	+	0.309017i	0.359466	+	0.116797i
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$		0			0
$10$			0.0592978i			0.0187516i
$11$	0.764896	+	3.22722i	0.230625	+	0.973043i
$11$	0.764896	+	3.22722i	0.230625	+	0.973043i
$12$		0			0
$13$	−2.76143	−	3.80078i	−0.765882	−	1.05415i	−0.996702	−	0.0811499i	$-0.974141\pi$
$13$	−2.76143	−	3.80078i	−0.765882	−	1.05415i	0.230820	−	0.972997i	$-0.425859\pi$
$14$	−0.951057	+	0.309017i	−0.254181	+	0.0825883i
$15$		0			0
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	0.0206121	+	0.0149756i	0.00499917	+	0.00363211i	0.590282	−	0.807197i	$-0.299017\pi$
$17$	0.0206121	+	0.0149756i	0.00499917	+	0.00363211i	−0.585283	+	0.810829i	$0.699017\pi$
$18$		0			0
$19$	−5.33201	+	1.73247i	−1.22325	+	0.397457i	−0.848263	−	0.529575i	$-0.822351\pi$
$19$	−5.33201	+	1.73247i	−1.22325	+	0.397457i	−0.374983	+	0.927032i	$0.622351\pi$
$20$	−0.0348544	−	0.0479729i	−0.00779367	−	0.0107271i
$21$		0			0
$22$	−2.51573	−	2.16128i	−0.536354	−	0.460786i
$23$			7.57543i			1.57959i	0.613373	+	0.789793i	$0.289812\pi$
$23$			7.57543i			1.57959i	−0.613373	+	0.789793i	$0.710188\pi$
$24$		0			0
$25$	1.54400	+	4.75194i	0.308800	+	0.950388i
$26$	4.46808	+	1.45177i	0.876263	+	0.284715i
$27$		0			0
$28$	0.587785	−	0.809017i	0.111081	−	0.152890i
$29$	−1.03075	+	3.17232i	−0.191405	+	0.589085i	0.808595	+	0.588366i	$0.200229\pi$
$29$	−1.03075	+	3.17232i	−0.191405	+	0.589085i	−1.00000		0.000718435i	$0.999771\pi$
$30$		0			0
$31$	3.61648	−	2.62752i	0.649538	−	0.471917i	−0.213576	−	0.976927i	$-0.568511\pi$
$31$	3.61648	−	2.62752i	0.649538	−	0.471917i	0.863114	+	0.505009i	$0.168511\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−0.0254779			−0.00436943
$35$	0.0479729	−	0.0348544i	0.00810890	−	0.00589146i
$36$		0			0
$37$	1.34532	−	4.14046i	0.221169	−	0.680688i	−0.777489	−	0.628897i	$-0.783507\pi$
$37$	1.34532	−	4.14046i	0.221169	−	0.680688i	0.998658	−	0.0517914i	$-0.0164931\pi$
$38$	3.29536	−	4.53568i	0.534578	−	0.735784i
$39$		0			0
$40$	0.0563955	+	0.0183240i	0.00891692	+	0.00289728i
$41$	−0.884378	−	2.72184i	−0.138117	−	0.425079i	0.857945	−	0.513741i	$-0.171741\pi$
$41$	−0.884378	−	2.72184i	−0.138117	−	0.425079i	−0.996062	+	0.0886621i	$0.971741\pi$
$42$		0			0
$43$			1.76335i			0.268908i	0.990920	+	0.134454i	$0.0429281\pi$
$43$			1.76335i			0.268908i	−0.990920	+	0.134454i	$0.957072\pi$
$44$	3.30563	+	0.269805i	0.498343	+	0.0406747i
$45$		0			0
$46$	−4.45273	−	6.12865i	−0.656519	−	0.903620i
$47$	−6.78589	+	2.20487i	−0.989824	+	0.321613i	−0.758792	−	0.651333i	$-0.774210\pi$
$47$	−6.78589	+	2.20487i	−0.989824	+	0.321613i	−0.231032	+	0.972946i	$0.574210\pi$
$48$		0			0
$49$	0.809017	+	0.587785i	0.115574	+	0.0839693i
$50$	−4.04224	−	2.93686i	−0.571659	−	0.415335i
$51$		0			0
$52$	−4.46808	+	1.45177i	−0.619612	+	0.201324i
$53$	5.47359	+	7.53376i	0.751856	+	1.03484i	0.997848	+	0.0655693i	$0.0208863\pi$
$53$	5.47359	+	7.53376i	0.751856	+	1.03484i	−0.245992	+	0.969272i	$0.579114\pi$
$54$		0			0
$55$	0.181479	+	0.0757883i	0.0244706	+	0.0102193i
$56$			1.00000i			0.133631i
$57$		0			0
$58$	−1.03075	−	3.17232i	−0.135344	−	0.416546i
$59$	2.52860	+	0.821591i	0.329195	+	0.106962i	0.468952	−	0.883224i	$-0.344632\pi$
$59$	2.52860	+	0.821591i	0.329195	+	0.106962i	−0.139756	+	0.990186i	$0.544632\pi$
$60$		0			0
$61$	1.10936	−	1.52690i	0.142038	−	0.195499i	−0.732071	−	0.681229i	$-0.761446\pi$
$61$	1.10936	−	1.52690i	0.142038	−	0.195499i	0.874109	+	0.485729i	$0.161446\pi$
$62$	−1.38137	+	4.25142i	−0.175434	+	0.539931i
$63$		0			0
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−0.278582			−0.0345539
$66$		0			0
$67$	−6.35318			−0.776164			−0.388082	−	0.921625i	$-0.626862\pi$
$67$	−6.35318			−0.776164			−0.388082	+	0.921625i	$0.626862\pi$
$68$	0.0206121	−	0.0149756i	0.00249958	−	0.00181605i
$69$		0			0
$70$	−0.0183240	+	0.0563955i	−0.00219014	+	0.00674056i
$71$	−8.20006	+	11.2864i	−0.973168	+	1.33945i	−0.0327385	+	0.999464i	$0.510423\pi$
$71$	−8.20006	+	11.2864i	−0.973168	+	1.33945i	−0.940430	+	0.339987i	$0.889577\pi$
$72$		0			0
$73$	0.975169	+	0.316852i	0.114135	+	0.0370847i	0.365528	−	0.930800i	$-0.380889\pi$
$73$	0.975169	+	0.316852i	0.114135	+	0.0370847i	−0.251393	+	0.967885i	$0.580889\pi$
$74$	1.34532	+	4.14046i	0.156390	+	0.481319i
$75$		0			0
$76$			5.60640i			0.643099i
$77$	−0.269805	+	3.30563i	−0.0307472	+	0.376712i
$78$		0			0
$79$	7.60983	+	10.4740i	0.856173	+	1.17842i	0.982469	+	0.186428i	$0.0596912\pi$
$79$	7.60983	+	10.4740i	0.856173	+	1.17842i	−0.126296	+	0.991993i	$0.540309\pi$
$80$	−0.0563955	+	0.0183240i	−0.00630521	+	0.00204869i
$81$		0			0
$82$	2.31533	+	1.68219i	0.255686	+	0.185766i
$83$	13.6996	+	9.95332i	1.50372	+	1.09252i	0.968869	+	0.247573i	$0.0796331\pi$
$83$	13.6996	+	9.95332i	1.50372	+	1.09252i	0.534853	+	0.844945i	$0.320367\pi$
$84$		0			0
$85$	0.00143684		0.000466858i	0.000155847		5.06379e-5i
$86$	−1.03647	−	1.42658i	−0.111766	−	0.153832i
$87$		0			0
$88$	−2.83290	+	1.72472i	−0.301988	+	0.183856i
$89$		−	1.58065i		−	0.167549i	−0.996485	−	0.0837744i	$-0.973303\pi$
$89$		−	1.58065i		−	0.167549i	0.996485	−	0.0837744i	$-0.0266975\pi$
$90$		0			0
$91$	−1.45177	−	4.46808i	−0.152187	−	0.468382i
$92$	7.20466	+	2.34094i	0.751138	+	0.244059i
$93$		0			0
$94$	4.19391	−	5.77242i	0.432569	−	0.595380i
$95$	−0.102732	+	0.316176i	−0.0105401	+	0.0324390i
$96$		0			0
$97$	−13.5147	+	9.81900i	−1.37221	+	0.996969i	−0.374649	+	0.927167i	$0.622237\pi$
$97$	−13.5147	+	9.81900i	−1.37221	+	0.996969i	−0.997561	+	0.0698022i	$0.977763\pi$
$98$	−1.00000			−0.101015
$99$		0			0
$100$	4.99648			0.499648
$101$	0.235879	−	0.171376i	0.0234708	−	0.0170525i	−0.575988	−	0.817458i	$-0.695383\pi$
$101$	0.235879	−	0.171376i	0.0234708	−	0.0170525i	0.599459	+	0.800406i	$0.295383\pi$
$102$		0			0
$103$	−2.89234	+	8.90170i	−0.284991	+	0.877111i	0.701411	+	0.712757i	$0.252554\pi$
$103$	−2.89234	+	8.90170i	−0.284991	+	0.877111i	−0.986401	+	0.164354i	$0.947446\pi$
$104$	2.76143	−	3.80078i	0.270780	−	0.372697i
$105$		0			0
$106$	−8.85646	−	2.87764i	−0.860216	−	0.279501i
$107$	−5.37919	−	16.5554i	−0.520026	−	1.60047i	−0.773948	−	0.633250i	$-0.781721\pi$
$107$	−5.37919	−	16.5554i	−0.520026	−	1.60047i	0.253922	−	0.967225i	$-0.418279\pi$
$108$		0			0
$109$		−	2.17414i		−	0.208245i	−0.994564	−	0.104123i	$-0.966797\pi$
$109$		−	2.17414i		−	0.208245i	0.994564	−	0.104123i	$-0.0332034\pi$
$110$	−0.191367	+	0.0453566i	−0.0182461	+	0.00432459i
$111$		0			0
$112$	−0.587785	−	0.809017i	−0.0555405	−	0.0764449i
$113$	−9.25879	+	3.00836i	−0.870994	+	0.283003i	−0.710213	−	0.703987i	$-0.751401\pi$
$113$	−9.25879	+	3.00836i	−0.870994	+	0.283003i	−0.160781	+	0.986990i	$0.551401\pi$
$114$		0			0
$115$	0.363415	+	0.264037i	0.0338887	+	0.0246216i
$116$	2.69854	+	1.96060i	0.250553	+	0.182037i
$117$		0			0
$118$	−2.52860	+	0.821591i	−0.232776	+	0.0756336i
$119$	0.0149756	+	0.0206121i	0.00137281	+	0.00188951i
$120$		0			0
$121$	−9.82987	+	4.93697i	−0.893624	+	0.448816i
$122$			1.88735i			0.170873i
$123$		0			0
$124$	−1.38137	−	4.25142i	−0.124051	−	0.381789i
$125$	0.563757	+	0.183176i	0.0504240	+	0.0163837i
$126$		0			0
$127$	−4.07030	+	5.60229i	−0.361181	+	0.497123i	−0.950477	−	0.310794i	$-0.899405\pi$
$127$	−4.07030	+	5.60229i	−0.361181	+	0.497123i	0.589297	+	0.807917i	$0.299405\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$		0			0
$130$	0.225378	−	0.163747i	0.0197669	−	0.0143615i
$131$	−10.9423			−0.956029			−0.478015	−	0.878352i	$-0.658643\pi$
$131$	−10.9423			−0.956029			−0.478015	+	0.878352i	$0.658643\pi$
$132$		0			0
$133$	−5.60640			−0.486137
$134$	5.13983	−	3.73430i	0.444013	−	0.322595i
$135$		0			0
$136$	−0.00787312	+	0.0242310i	−0.000675114	+	0.00207779i
$137$	−6.03633	+	8.30829i	−0.515718	+	0.709825i	−0.984870	−	0.173292i	$-0.944560\pi$
$137$	−6.03633	+	8.30829i	−0.515718	+	0.709825i	0.469152	+	0.883117i	$0.344560\pi$
$138$		0			0
$139$	2.09200	+	0.679732i	0.177441	+	0.0576541i	0.396390	−	0.918082i	$-0.370263\pi$
$139$	2.09200	+	0.679732i	0.177441	+	0.0576541i	−0.218949	+	0.975736i	$0.570263\pi$
$140$	−0.0183240	−	0.0563955i	−0.00154866	−	0.00476629i
$141$		0			0
$142$		−	13.9508i		−	1.17072i
$143$	10.1537	−	11.8189i	0.849098	−	0.988349i
$144$		0			0
$145$	0.116259	+	0.160017i	0.00965481	+	0.0132887i
$146$	−0.975169	+	0.316852i	−0.0807056	+	0.0262228i
$147$		0			0
$148$	−3.52209	−	2.55895i	−0.289514	−	0.210344i
$149$	1.40849	+	1.02333i	0.115388	+	0.0838343i	0.643983	−	0.765040i	$-0.277281\pi$
$149$	1.40849	+	1.02333i	0.115388	+	0.0838343i	−0.528595	+	0.848874i	$0.677281\pi$
$150$		0			0
$151$	8.22887	−	2.67372i	0.669656	−	0.217584i	0.0455950	−	0.998960i	$-0.485482\pi$
$151$	8.22887	−	2.67372i	0.669656	−	0.217584i	0.624061	+	0.781376i	$0.285482\pi$
$152$	−3.29536	−	4.53568i	−0.267289	−	0.367892i
$153$		0			0
$154$	−1.72472	−	2.83290i	−0.138982	−	0.228282i
$155$		−	0.265074i		−	0.0212912i
$156$		0			0
$157$	5.10246	+	15.7038i	0.407221	+	1.25330i	0.919027	+	0.394195i	$0.128977\pi$
$157$	5.10246	+	15.7038i	0.407221	+	1.25330i	−0.511806	+	0.859101i	$0.671023\pi$
$158$	−12.3130	−	4.00073i	−0.979567	−	0.318281i
$159$		0			0
$160$	0.0348544	−	0.0479729i	0.00275548	−	0.00379259i
$161$	−2.34094	+	7.20466i	−0.184492	+	0.567807i
$162$		0			0
$163$	14.8234	−	10.7698i	1.16106	−	0.843557i	0.171146	−	0.985246i	$-0.445253\pi$
$163$	14.8234	−	10.7698i	1.16106	−	0.843557i	0.989911	+	0.141688i	$0.0452530\pi$
$164$	−2.86191			−0.223477
$165$		0			0
$166$	−16.9336			−1.31430
$167$	−14.8716	+	10.8048i	−1.15080	+	0.836103i	−0.988587	−	0.150654i	$-0.951862\pi$
$167$	−14.8716	+	10.8048i	−1.15080	+	0.836103i	−0.162210	+	0.986756i	$0.551862\pi$
$168$		0			0
$169$	−2.80322	+	8.62742i	−0.215632	+	0.663648i
$170$	−0.000888017		0.00122225i	−6.81078e−5		9.37424e-5i
$171$		0			0
$172$	1.67705	+	0.544905i	0.127874	+	0.0415486i
$173$	−6.93754	−	21.3516i	−0.527451	−	1.62333i	−0.759417	−	0.650604i	$-0.774516\pi$
$173$	−6.93754	−	21.3516i	−0.527451	−	1.62333i	0.231965	−	0.972724i	$-0.425484\pi$
$174$		0			0
$175$			4.99648i			0.377699i
$176$	1.27810	−	3.06047i	0.0963402	−	0.230692i
$177$		0			0
$178$	0.929084	+	1.27877i	0.0696378	+	0.0958482i
$179$	−1.55614	+	0.505620i	−0.116311	+	0.0377918i	−0.366594	−	0.930381i	$-0.619476\pi$
$179$	−1.55614	+	0.505620i	−0.116311	+	0.0377918i	0.250283	+	0.968173i	$0.419476\pi$
$180$		0			0
$181$	12.9835	+	9.43308i	0.965058	+	0.701155i	0.954320	−	0.298787i	$-0.0965820\pi$
$181$	12.9835	+	9.43308i	0.965058	+	0.701155i	0.0107377	+	0.999942i	$0.496582\pi$
$182$	3.80078	+	2.76143i	0.281733	+	0.204691i
$183$		0			0
$184$	−7.20466	+	2.34094i	−0.531135	+	0.172576i
$185$	−0.151740	−	0.208852i	−0.0111561	−	0.0153551i
$186$		0			0
$187$	−0.0325633	+	0.0779745i	−0.00238126	+	0.00570206i
$188$			7.13511i			0.520381i
$189$		0			0
$190$	−0.102732	−	0.316176i	−0.00745295	−	0.0229378i
$191$	9.98802	+	3.24530i	0.722708	+	0.234822i	0.647197	−	0.762323i	$-0.275941\pi$
$191$	9.98802	+	3.24530i	0.722708	+	0.234822i	0.0755109	+	0.997145i	$0.475941\pi$
$192$		0			0
$193$	9.50113	−	13.0772i	0.683906	−	0.941316i	−0.316066	−	0.948737i	$-0.602362\pi$
$193$	9.50113	−	13.0772i	0.683906	−	0.941316i	0.999972	+	0.00742106i	$0.00236222\pi$
$194$	5.16216	−	15.8875i	0.370621	−	1.14065i
$195$		0			0
$196$	0.809017	−	0.587785i	0.0577869	−	0.0419847i
$197$	−4.82278			−0.343609			−0.171804	−	0.985131i	$-0.554960\pi$
$197$	−4.82278			−0.343609			−0.171804	+	0.985131i	$0.554960\pi$
$198$		0			0
$199$	20.7090			1.46802			0.734009	−	0.679139i	$-0.237647\pi$
$199$	20.7090			1.46802			0.734009	+	0.679139i	$0.237647\pi$
$200$	−4.04224	+	2.93686i	−0.285830	+	0.207667i
$201$		0			0
$202$	−0.0900976	+	0.277292i	−0.00633924	+	0.0195102i
$203$	−1.96060	+	2.69854i	−0.137607	+	0.189400i
$204$		0			0
$205$	−0.161399	−	0.0524416i	−0.0112726	−	0.00366268i
$206$	−2.89234	−	8.90170i	−0.201519	−	0.620211i
$207$		0			0
$208$			4.69802i			0.325749i
$209$	−9.66950	−	15.8824i	−0.668853	−	1.09861i
$210$		0			0
$211$	−9.45994	−	13.0205i	−0.651249	−	0.896368i	0.347903	−	0.937531i	$-0.386894\pi$
$211$	−9.45994	−	13.0205i	−0.651249	−	0.896368i	−0.999152	+	0.0411626i	$0.986894\pi$
$212$	8.85646	−	2.87764i	0.608264	−	0.197637i
$213$		0			0
$214$	14.0829	+	10.2318i	0.962687	+	0.699433i
$215$	0.0845930	+	0.0614604i	0.00576920	+	0.00419157i
$216$		0			0
$217$	4.25142	−	1.38137i	0.288605	−	0.0937736i
$218$	1.27793	+	1.75892i	0.0865523	+	0.119129i
$219$		0			0
$220$	0.128159	−	0.149177i	0.00864048	−	0.0100575i
$221$		−	0.119696i		−	0.00805162i
$222$		0			0
$223$	−6.18966	−	19.0498i	−0.414490	−	1.27567i	−0.912706	−	0.408617i	$-0.866011\pi$
$223$	−6.18966	−	19.0498i	−0.414490	−	1.27567i	0.498216	−	0.867053i	$-0.333989\pi$
$224$	0.951057	+	0.309017i	0.0635451	+	0.0206471i
$225$		0			0
$226$	5.72225	−	7.87600i	0.380638	−	0.523904i
$227$	3.89068	−	11.9743i	0.258234	−	0.794761i	−0.734942	−	0.678130i	$-0.762790\pi$
$227$	3.89068	−	11.9743i	0.258234	−	0.794761i	0.993175	−	0.116631i	$-0.0372095\pi$
$228$		0			0
$229$	−13.6628	+	9.92660i	−0.902863	+	0.655968i	−0.939200	−	0.343371i	$-0.888431\pi$
$229$	−13.6628	+	9.92660i	−0.902863	+	0.655968i	0.0363370	+	0.999340i	$0.488431\pi$
$230$	−0.449206			−0.0296198
$231$		0			0
$232$	−3.33557			−0.218991
$233$	0.573857	−	0.416932i	0.0375946	−	0.0273141i	−0.568829	−	0.822456i	$-0.692603\pi$
$233$	0.573857	−	0.416932i	0.0375946	−	0.0273141i	0.606424	+	0.795142i	$0.292603\pi$
$234$		0			0
$235$	−0.130744	+	0.402388i	−0.00852879	+	0.0262489i
$236$	1.56276	−	2.15095i	0.101727	−	0.140015i
$237$		0			0
$238$	−0.0242310	−	0.00787312i	−0.00157066	−	0.000510338i
$239$	0.999491	+	3.07612i	0.0646517	+	0.198978i	0.978164	−	0.207833i	$-0.0666410\pi$
$239$	0.999491	+	3.07612i	0.0646517	+	0.198978i	−0.913513	+	0.406810i	$0.866641\pi$
$240$		0			0
$241$			22.1903i			1.42940i	0.699431	+	0.714701i	$0.253437\pi$
$241$			22.1903i			1.42940i	−0.699431	+	0.714701i	$0.746563\pi$
$242$	5.05065	−	9.77195i	0.324668	−	0.628165i
$243$		0			0
$244$	−1.10936	−	1.52690i	−0.0710192	−	0.0977496i
$245$	0.0563955	−	0.0183240i	0.00360298	−	0.00117068i
$246$		0			0
$247$	21.3087	+	15.4817i	1.35584	+	0.985076i
$248$	3.61648	+	2.62752i	0.229647	+	0.166848i
$249$		0			0
$250$	−0.563757	+	0.183176i	−0.0356551	+	0.0115851i
$251$	11.2128	+	15.4331i	0.707746	+	0.974129i	0.999843	+	0.0177402i	$0.00564716\pi$
$251$	11.2128	+	15.4331i	0.707746	+	0.974129i	−0.292096	+	0.956389i	$0.594353\pi$
$252$		0			0
$253$	−24.4476	+	5.79442i	−1.53700	+	0.364292i
$254$		−	6.92481i		−	0.434501i
$255$		0			0
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−7.64780	−	2.48492i	−0.477057	−	0.155005i	0.0606119	−	0.998161i	$-0.480695\pi$
$257$	−7.64780	−	2.48492i	−0.477057	−	0.155005i	−0.537669	+	0.843156i	$0.680695\pi$
$258$		0			0
$259$	2.55895	−	3.52209i	0.159005	−	0.218852i
$260$	−0.0860866	+	0.264947i	−0.00533887	+	0.0164313i
$261$		0			0
$262$	8.85247	−	6.43169i	0.546907	−	0.397351i
$263$	1.41001			0.0869450			0.0434725	−	0.999055i	$-0.486158\pi$
$263$	1.41001			0.0869450			0.0434725	+	0.999055i	$0.486158\pi$
$264$		0			0
$265$	0.552195			0.0339211
$266$	4.53568	−	3.29536i	0.278100	−	0.202052i
$267$		0			0
$268$	−1.96324	+	6.04223i	−0.119924	+	0.369088i
$269$	12.0907	−	16.6414i	0.737183	−	1.01465i	−0.261592	−	0.965178i	$-0.584248\pi$
$269$	12.0907	−	16.6414i	0.737183	−	1.01465i	0.998776	−	0.0494673i	$-0.0157524\pi$
$270$		0			0
$271$	14.3324	+	4.65688i	0.870632	+	0.282886i	0.710062	−	0.704139i	$-0.248667\pi$
$271$	14.3324	+	4.65688i	0.870632	+	0.282886i	0.160570	+	0.987024i	$0.448667\pi$
$272$	−0.00787312	−	0.0242310i	−0.000477378	−	0.00146922i
$273$		0			0
$274$		−	10.2696i		−	0.620410i
$275$	−14.1545	+	8.61756i	−0.853551	+	0.519658i
$276$		0			0
$277$	−9.98405	−	13.7419i	−0.599884	−	0.825669i	0.395814	−	0.918331i	$-0.370462\pi$
$277$	−9.98405	−	13.7419i	−0.599884	−	0.825669i	−0.995698	+	0.0926618i	$0.970462\pi$
$278$	−2.09200	+	0.679732i	−0.125470	+	0.0407676i
$279$		0			0
$280$	0.0479729	+	0.0348544i	0.00286693	+	0.00208295i
$281$	−13.1621	−	9.56283i	−0.785186	−	0.570471i	0.121345	−	0.992610i	$-0.461279\pi$
$281$	−13.1621	−	9.56283i	−0.785186	−	0.570471i	−0.906531	+	0.422140i	$0.861279\pi$
$282$		0			0
$283$	30.3701	−	9.86783i	1.80531	−	0.586582i	0.805332	−	0.592823i	$-0.201987\pi$
$283$	30.3701	−	9.86783i	1.80531	−	0.586582i	0.999981	+	0.00624164i	$0.00198679\pi$
$284$	8.20006	+	11.2864i	0.486584	+	0.669726i
$285$		0			0
$286$	−1.26755	+	15.5299i	−0.0749519	+	0.918304i
$287$		−	2.86191i		−	0.168933i
$288$		0			0
$289$	−5.25309	−	16.1673i	−0.309005	−	0.951020i
$290$	−0.188111	−	0.0611211i	−0.0110463	−	0.00358916i
$291$		0			0
$292$	0.602688	−	0.829529i	0.0352696	−	0.0485445i
$293$	3.50715	−	10.7939i	0.204890	−	0.630586i	−0.794828	−	0.606835i	$-0.792439\pi$
$293$	3.50715	−	10.7939i	0.204890	−	0.630586i	0.999718	−	0.0237512i	$-0.00756096\pi$
$294$		0			0
$295$	0.127547	−	0.0926681i	0.00742606	−	0.00539535i
$296$	4.35354			0.253044
$297$		0			0
$298$	−1.74099			−0.100853
$299$	28.7925	−	20.9190i	1.66512	−	1.20978i
$300$		0			0
$301$	−0.544905	+	1.67705i	−0.0314078	+	0.0966633i
$302$	−5.08572	+	6.99990i	−0.292650	+	0.402799i
$303$		0			0
$304$	5.33201	+	1.73247i	0.305812	+	0.0993642i
$305$	−0.0345838	−	0.106438i	−0.00198026	−	0.00609462i
$306$		0			0
$307$		−	12.9610i		−	0.739722i	−0.929087	−	0.369861i	$-0.879405\pi$
$307$		−	12.9610i		−	0.739722i	0.929087	−	0.369861i	$-0.120595\pi$
$308$	3.06047	+	1.27810i	0.174386	+	0.0728263i
$309$		0			0
$310$	0.155806	+	0.214449i	0.00884921	+	0.0121799i
$311$	−3.36612	+	1.09372i	−0.190875	+	0.0620190i	−0.402895	−	0.915246i	$-0.631996\pi$
$311$	−3.36612	+	1.09372i	−0.190875	+	0.0620190i	0.212020	+	0.977265i	$0.431996\pi$
$312$		0			0
$313$	16.1759	+	11.7525i	0.914314	+	0.664288i	0.942102	−	0.335326i	$-0.108846\pi$
$313$	16.1759	+	11.7525i	0.914314	+	0.664288i	−0.0277884	+	0.999614i	$0.508846\pi$
$314$	−13.3584	−	9.70546i	−0.753859	−	0.547711i
$315$		0			0
$316$	12.3130	−	4.00073i	0.692659	−	0.225058i
$317$	−3.55156	−	4.88830i	−0.199475	−	0.274554i	0.697547	−	0.716539i	$-0.254275\pi$
$317$	−3.55156	−	4.88830i	−0.199475	−	0.274554i	−0.897023	+	0.441984i	$0.854275\pi$
$318$		0			0
$319$	−11.0262	−	0.899956i	−0.617347	−	0.0503879i
$320$			0.0592978i			0.00331485i
$321$		0			0
$322$	−2.34094	−	7.20466i	−0.130455	−	0.401500i
$323$	−0.135849	−	0.0441399i	−0.00755882	−	0.00245601i
$324$		0			0
$325$	13.7974	−	18.9905i	0.765344	−	1.05341i
$326$	−5.66203	+	17.4259i	−0.313591	+	0.965133i
$327$		0			0
$328$	2.31533	−	1.68219i	0.127843	−	0.0928832i
$329$	−7.13511			−0.393371
$330$		0			0
$331$	30.0698			1.65279			0.826394	−	0.563092i	$-0.190388\pi$
$331$	30.0698			1.65279			0.826394	+	0.563092i	$0.190388\pi$
$332$	13.6996	−	9.95332i	0.751861	−	0.546259i
$333$		0			0
$334$	5.68043	−	17.4826i	0.310819	−	0.956604i
$335$	−0.221436	+	0.304780i	−0.0120983	+	0.0166519i
$336$		0			0
$337$	−10.6134	−	3.44850i	−0.578149	−	0.187852i	0.00532227	−	0.999986i	$-0.498306\pi$
$337$	−10.6134	−	3.44850i	−0.578149	−	0.187852i	−0.583471	+	0.812134i	$0.698306\pi$
$338$	−2.80322	−	8.62742i	−0.152475	−	0.469270i
$339$		0			0
$340$		−	0.00151079i		−	8.19338e-5i
$341$	11.2458	+	9.66137i	0.608995	+	0.523193i
$342$		0			0
$343$	0.587785	+	0.809017i	0.0317374	+	0.0436828i
$344$	−1.67705	+	0.544905i	−0.0904202	+	0.0293793i
$345$		0			0
$346$	18.1627	+	13.1960i	0.976434	+	0.709421i
$347$	11.2020	+	8.13871i	0.601353	+	0.436909i	0.846359	−	0.532613i	$-0.178790\pi$
$347$	11.2020	+	8.13871i	0.601353	+	0.436909i	−0.245006	+	0.969522i	$0.578790\pi$
$348$		0			0
$349$	−23.1763	+	7.53044i	−1.24060	+	0.403095i	−0.854543	−	0.519380i	$-0.826163\pi$
$349$	−23.1763	+	7.53044i	−1.24060	+	0.403095i	−0.386056	+	0.922475i	$0.626163\pi$
$350$	−2.93686	−	4.04224i	−0.156982	−	0.216067i
$351$		0			0
$352$	0.764896	+	3.22722i	0.0407691	+	0.172011i
$353$		−	36.6956i		−	1.95311i	−0.215274	−	0.976554i	$-0.569064\pi$
$353$		−	36.6956i		−	1.95311i	0.215274	−	0.976554i	$-0.430936\pi$
$354$		0			0
$355$	0.255634	+	0.786762i	0.0135677	+	0.0417570i
$356$	−1.50329	−	0.488448i	−0.0796742	−	0.0258877i
$357$		0			0
$358$	0.961747	−	1.32373i	0.0508299	−	0.0699613i
$359$	6.26580	−	19.2841i	0.330696	−	1.01778i	−0.638107	−	0.769948i	$-0.720282\pi$
$359$	6.26580	−	19.2841i	0.330696	−	1.01778i	0.968803	−	0.247831i	$-0.0797177\pi$
$360$		0			0
$361$	10.0575	−	7.30720i	0.529342	−	0.384590i
$362$	−16.0485			−0.843491
$363$		0			0
$364$	−4.69802			−0.246243
$365$	0.0491892	−	0.0357380i	0.00257468	−	0.00187061i
$366$		0			0
$367$	2.47734	−	7.62446i	0.129316	−	0.397993i	−0.865347	−	0.501174i	$-0.832902\pi$
$367$	2.47734	−	7.62446i	0.129316	−	0.397993i	0.994663	+	0.103180i	$0.0329018\pi$
$368$	4.45273	−	6.12865i	0.232114	−	0.319478i
$369$		0			0
$370$	0.245520	+	0.0797744i	0.0127640	+	0.00414727i
$371$	2.87764	+	8.85646i	0.149400	+	0.459805i
$372$		0			0
$373$			21.5146i			1.11398i	0.830518	+	0.556992i	$0.188045\pi$
$373$			21.5146i			1.11398i	−0.830518	+	0.556992i	$0.811955\pi$
$374$	−0.0194880	−	0.0822229i	−0.00100770	−	0.00425164i
$375$		0			0
$376$	−4.19391	−	5.77242i	−0.216284	−	0.297690i
$377$	14.9036	−	4.84248i	0.767576	−	0.249400i
$378$		0			0
$379$	25.5690	+	18.5770i	1.31339	+	0.954234i	0.999989	+	0.00461312i	$0.00146841\pi$
$379$	25.5690	+	18.5770i	1.31339	+	0.954234i	0.313401	+	0.949621i	$0.398532\pi$
$380$	0.268955	+	0.195408i	0.0137971	+	0.0100242i
$381$		0			0
$382$	−9.98802	+	3.24530i	−0.511032	+	0.166044i
$383$	−5.05380	−	6.95596i	−0.258237	−	0.355433i	0.660138	−	0.751145i	$-0.270498\pi$
$383$	−5.05380	−	6.95596i	−0.258237	−	0.355433i	−0.918375	+	0.395712i	$0.870498\pi$
$384$		0			0
$385$	0.149177	+	0.128159i	0.00760276	+	0.00653159i
$386$			16.1643i			0.822740i
$387$		0			0
$388$	5.16216	+	15.8875i	0.262069	+	0.806565i
$389$	26.9778	+	8.76563i	1.36783	+	0.444435i	0.898649	−	0.438668i	$-0.144549\pi$
$389$	26.9778	+	8.76563i	1.36783	+	0.444435i	0.469180	+	0.883102i	$0.344549\pi$
$390$		0			0
$391$	−0.113446	+	0.156145i	−0.00573723	+	0.00789661i
$392$	−0.309017	+	0.951057i	−0.0156077	+	0.0480356i
$393$		0			0
$394$	3.90171	−	2.83476i	0.196565	−	0.142813i
$395$	0.767706			0.0386275
$396$		0			0
$397$	2.50209			0.125576			0.0627882	−	0.998027i	$-0.480001\pi$
$397$	2.50209			0.125576			0.0627882	+	0.998027i	$0.480001\pi$
$398$	−16.7539	+	12.1724i	−0.839797	+	0.610148i
$399$		0			0
$400$	1.54400	−	4.75194i	0.0771999	−	0.237597i
$401$	12.6065	−	17.3514i	0.629540	−	0.866487i	−0.368464	−	0.929642i	$-0.620116\pi$
$401$	12.6065	−	17.3514i	0.629540	−	0.866487i	0.998004	+	0.0631549i	$0.0201162\pi$
$402$		0			0
$403$	−19.9733	−	6.48971i	−0.994940	−	0.323276i
$404$	−0.0900976	−	0.277292i	−0.00448252	−	0.0137958i
$405$		0			0
$406$		−	3.33557i		−	0.165542i
$407$	14.3912	+	1.17461i	0.713346	+	0.0582232i
$408$		0			0
$409$	−16.4946	−	22.7029i	−0.815606	−	1.12259i	−0.990434	−	0.137987i	$-0.955937\pi$
$409$	−16.4946	−	22.7029i	−0.815606	−	1.12259i	0.174828	−	0.984599i	$-0.444063\pi$
$410$	0.161399	−	0.0524416i	0.00797092	−	0.00258991i
$411$		0			0
$412$	7.57224	+	5.50155i	0.373057	+	0.271042i
$413$	2.15095	+	1.56276i	0.105842	+	0.0768984i
$414$		0			0
$415$	0.954979	−	0.310291i	0.0468781	−	0.0152316i
$416$	−2.76143	−	3.80078i	−0.135390	−	0.186349i
$417$		0			0
$418$	17.1582	+	7.16553i	0.839236	+	0.350477i
$419$			14.1480i			0.691177i	0.938386	+	0.345589i	$0.112321\pi$
$419$			14.1480i			0.691177i	−0.938386	+	0.345589i	$0.887679\pi$
$420$		0			0
$421$	−1.20276	−	3.70173i	−0.0586192	−	0.180411i	0.917459	−	0.397829i	$-0.130236\pi$
$421$	−1.20276	−	3.70173i	−0.0586192	−	0.180411i	−0.976079	+	0.217418i	$0.930236\pi$
$422$	15.3065	+	4.97339i	0.745109	+	0.242101i
$423$		0			0
$424$	−5.47359	+	7.53376i	−0.265821	+	0.365872i
$425$	−0.0393379	+	0.121070i	−0.00190817	+	0.00587274i
$426$		0			0
$427$	1.52690	−	1.10936i	0.0738917	−	0.0536855i
$428$	−17.4074			−0.841419
$429$		0			0
$430$	−0.104563			−0.00504246
$431$	−23.3078	+	16.9341i	−1.12270	+	0.815688i	−0.984616	−	0.174733i	$-0.944094\pi$
$431$	−23.3078	+	16.9341i	−1.12270	+	0.815688i	−0.138082	+	0.990421i	$0.544094\pi$
$432$		0			0
$433$	12.6022	−	38.7855i	0.605622	−	1.86391i	0.113162	−	0.993577i	$-0.463902\pi$
$433$	12.6022	−	38.7855i	0.605622	−	1.86391i	0.492460	−	0.870335i	$-0.336098\pi$
$434$	−2.62752	+	3.61648i	−0.126125	+	0.173596i
$435$		0			0
$436$	−2.06773	−	0.671847i	−0.0990265	−	0.0321756i
$437$	−13.1242	−	40.3922i	−0.627817	−	1.93222i
$438$		0			0
$439$			36.3698i			1.73584i	0.496707	+	0.867918i	$0.334542\pi$
$439$			36.3698i			1.73584i	−0.496707	+	0.867918i	$0.665458\pi$
$440$	−0.0159989	+	0.196017i	−0.000762716	+	0.00934473i
$441$		0			0
$442$	0.0703555	+	0.0968360i	0.00334647	+	0.00460602i
$443$	−7.00952	+	2.27753i	−0.333032	+	0.108209i	−0.470760	−	0.882261i	$-0.656020\pi$
$443$	−7.00952	+	2.27753i	−0.333032	+	0.108209i	0.137727	+	0.990470i	$0.456020\pi$
$444$		0			0
$445$	−0.0758285	−	0.0550926i	−0.00359461	−	0.00261164i
$446$	16.2047	+	11.7734i	0.767317	+	0.557488i
$447$		0			0
$448$	−0.951057	+	0.309017i	−0.0449332	+	0.0145997i
$449$	16.4495	+	22.6409i	0.776302	+	1.06849i	0.995680	+	0.0928481i	$0.0295971\pi$
$449$	16.4495	+	22.6409i	0.776302	+	1.06849i	−0.219378	+	0.975640i	$0.570403\pi$
$450$		0			0
$451$	8.10750	−	4.93600i	0.381767	−	0.232427i
$452$			9.73527i			0.457909i
$453$		0			0
$454$	3.89068	+	11.9743i	0.182599	+	0.561981i
$455$	−0.264947	−	0.0860866i	−0.0124209	−	0.00403580i
$456$		0			0
$457$	6.16122	−	8.48019i	0.288210	−	0.396687i	−0.640222	−	0.768190i	$-0.721158\pi$
$457$	6.16122	−	8.48019i	0.288210	−	0.396687i	0.928432	+	0.371503i	$0.121158\pi$
$458$	5.21872	−	16.0616i	0.243855	−	0.750508i
$459$		0			0
$460$	0.363415	−	0.264037i	0.0169443	−	0.0123108i
$461$	2.20019			0.102473			0.0512366	−	0.998687i	$-0.483684\pi$
$461$	2.20019			0.102473			0.0512366	+	0.998687i	$0.483684\pi$
$462$		0			0
$463$	7.29634			0.339090			0.169545	−	0.985522i	$-0.445770\pi$
$463$	7.29634			0.339090			0.169545	+	0.985522i	$0.445770\pi$
$464$	2.69854	−	1.96060i	0.125276	−	0.0910186i
$465$		0			0
$466$	−0.219194	+	0.674610i	−0.0101540	+	0.0312507i
$467$	−12.9420	+	17.8131i	−0.598883	+	0.824291i	−0.995605	−	0.0936472i	$-0.970147\pi$
$467$	−12.9420	+	17.8131i	−0.598883	+	0.824291i	0.396723	+	0.917938i	$0.370147\pi$
$468$		0			0
$469$	−6.04223	−	1.96324i	−0.279004	−	0.0906540i
$470$	−0.130744	−	0.402388i	−0.00603076	−	0.0185608i
$471$		0			0
$472$			2.65872i			0.122378i
$473$	−5.69071	+	1.34878i	−0.261659	+	0.0620170i
$474$		0			0
$475$	−16.4652	−	22.6624i	−0.755476	−	1.03982i
$476$	0.0242310	−	0.00787312i	0.00111062	−	0.000360864i
$477$		0			0
$478$	−2.61670	−	1.90115i	−0.119685	−	0.0869564i
$479$	13.5703	+	9.85943i	0.620045	+	0.450489i	0.852937	−	0.522014i	$-0.174819\pi$
$479$	13.5703	+	9.85943i	0.620045	+	0.450489i	−0.232892	+	0.972503i	$0.574819\pi$
$480$		0			0
$481$	−19.4520	+	6.32033i	−0.886934	+	0.288182i
$482$	−13.0431	−	17.9523i	−0.594098	−	0.817705i
$483$		0			0
$484$	1.65775	+	10.8744i	0.0753520	+	0.494289i
$485$			0.990575i			0.0449797i
$486$		0			0
$487$	−8.75218	−	26.9364i	−0.396599	−	1.22061i	−0.927709	−	0.373304i	$-0.878225\pi$
$487$	−8.75218	−	26.9364i	−0.396599	−	1.22061i	0.531110	−	0.847303i	$-0.321775\pi$
$488$	1.79498	+	0.583223i	0.0812547	+	0.0264013i
$489$		0			0
$490$	−0.0348544	+	0.0479729i	−0.00157456	+	0.00216720i
$491$	2.00285	−	6.16413i	0.0903873	−	0.278183i	−0.895637	−	0.444786i	$-0.853280\pi$
$491$	2.00285	−	6.16413i	0.0903873	−	0.278183i	0.986024	+	0.166603i	$0.0532797\pi$
$492$		0			0
$493$	−0.0687531	+	0.0499521i	−0.00309649	+	0.00224973i
$494$	−26.3390			−1.18505
$495$		0			0
$496$	−4.47021			−0.200718
$497$	−11.2864	+	8.20006i	−0.506265	+	0.367823i
$498$		0			0
$499$	3.78897	−	11.6612i	0.169617	−	0.522029i	−0.829729	−	0.558166i	$-0.811505\pi$
$499$	3.78897	−	11.6612i	0.169617	−	0.522029i	0.999347	+	0.0361370i	$0.0115053\pi$
$500$	0.348421	−	0.479560i	0.0155819	−	0.0214466i
$501$		0			0
$502$	−18.1427	−	5.89492i	−0.809749	−	0.263103i
$503$	−8.92470	−	27.4674i	−0.397933	−	1.22471i	−0.926654	−	0.375915i	$-0.877328\pi$
$503$	−8.92470	−	27.4674i	−0.397933	−	1.22471i	0.528721	−	0.848795i	$-0.322672\pi$
$504$		0			0
$505$		−	0.0172890i		−	0.000769349i
$506$	16.3726	−	19.0577i	0.727852	−	0.847218i
$507$		0			0
$508$	4.07030	+	5.60229i	0.180590	+	0.248561i
$509$	−12.7731	+	4.15022i	−0.566157	+	0.183955i	−0.578089	−	0.815973i	$-0.696202\pi$
$509$	−12.7731	+	4.15022i	−0.566157	+	0.183955i	0.0119329	+	0.999929i	$0.496202\pi$
$510$		0			0
$511$	0.829529	+	0.602688i	0.0366962	+	0.0266613i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$		0			0
$514$	7.64780	−	2.48492i	0.337330	−	0.109605i
$515$	0.326230	+	0.449017i	0.0143754	+	0.0197860i
$516$		0			0
$517$	−12.3061	−	20.2130i	−0.541221	−	0.888969i
$518$			4.35354i			0.191284i
$519$		0			0
$520$	−0.0860866	−	0.264947i	−0.00377515	−	0.0116187i
$521$	−3.44303	−	1.11871i	−0.150842	−	0.0490114i	0.232623	−	0.972567i	$-0.425269\pi$
$521$	−3.44303	−	1.11871i	−0.150842	−	0.0490114i	−0.383465	+	0.923556i	$0.625269\pi$
$522$		0			0
$523$	18.9799	−	26.1236i	0.829935	−	1.14231i	−0.158001	−	0.987439i	$-0.550505\pi$
$523$	18.9799	−	26.1236i	0.829935	−	1.14231i	0.987935	−	0.154868i	$-0.0494952\pi$
$524$	−3.38134	+	10.4067i	−0.147715	+	0.454619i
$525$		0			0
$526$	−1.14072	+	0.828784i	−0.0497379	+	0.0361367i
$527$	0.113892			0.00496120
$528$		0			0
$529$	−34.3871			−1.49509
$530$	−0.446735	+	0.324572i	−0.0194049	+	0.0140985i
$531$		0			0
$532$	−1.73247	+	5.33201i	−0.0751123	+	0.231172i
$533$	−7.90295	+	10.8775i	−0.342315	+	0.471156i
$534$		0			0
$535$	−0.981701	−	0.318974i	−0.0424426	−	0.0137904i
$536$	−1.96324	−	6.04223i	−0.0847990	−	0.260985i
$537$		0			0
$538$			20.5699i			0.886833i
$539$	−1.27810	+	3.06047i	−0.0550515	+	0.131824i
$540$		0			0
$541$	24.9613	+	34.3563i	1.07317	+	1.47709i	0.866824	+	0.498613i	$0.166157\pi$
$541$	24.9613	+	34.3563i	1.07317	+	1.47709i	0.206346	+	0.978479i	$0.433843\pi$
$542$	−14.3324	+	4.65688i	−0.615630	+	0.200030i
$543$		0			0
$544$	0.0206121	+	0.0149756i	0.000883736	+	0.000642072i
$545$	−0.104300	−	0.0757784i	−0.00446772	−	0.00324599i
$546$		0			0
$547$	−36.5311	+	11.8697i	−1.56196	+	0.507511i	−0.957330	−	0.288996i	$-0.906679\pi$
$547$	−36.5311	+	11.8697i	−1.56196	+	0.507511i	−0.604629	+	0.796507i	$0.706679\pi$
$548$	6.03633	+	8.30829i	0.257859	+	0.354913i
$549$		0			0
$550$	6.38599	−	15.2916i	0.272300	−	0.652035i
$551$		−	18.7006i		−	0.796671i
$552$		0			0
$553$	4.00073	+	12.3130i	0.170128	+	0.523601i
$554$	16.1545	+	5.24893i	0.686340	+	0.223006i
$555$		0			0
$556$	1.29293	−	1.77956i	0.0548323	−	0.0754702i
$557$	1.70141	−	5.23641i	0.0720911	−	0.221874i	−0.908519	−	0.417844i	$-0.862786\pi$
$557$	1.70141	−	5.23641i	0.0720911	−	0.221874i	0.980610	+	0.195971i	$0.0627858\pi$
$558$		0			0
$559$	6.70210	−	4.86936i	0.283469	−	0.205952i
$560$	−0.0592978			−0.00250579
$561$		0			0
$562$	16.2693			0.686277
$563$	8.00272	−	5.81431i	0.337274	−	0.245044i	−0.406237	−	0.913768i	$-0.633159\pi$
$563$	8.00272	−	5.81431i	0.337274	−	0.245044i	0.743511	+	0.668724i	$0.233159\pi$
$564$		0			0
$565$	−0.178389	+	0.549026i	−0.00750489	+	0.0230977i
$566$	−18.7697	+	25.8343i	−0.788951	+	1.08590i
$567$		0			0
$568$	−13.2680	−	4.31103i	−0.556712	−	0.180887i
$569$	−0.518897	−	1.59700i	−0.0217533	−	0.0669497i	0.939591	−	0.342300i	$-0.111206\pi$
$569$	−0.518897	−	1.59700i	−0.0217533	−	0.0669497i	−0.961344	+	0.275351i	$0.911206\pi$
$570$		0			0
$571$			19.9762i			0.835977i	0.908452	+	0.417988i	$0.137265\pi$
$571$			19.9762i			0.835977i	−0.908452	+	0.417988i	$0.862735\pi$
$572$	−8.10279	−	13.3090i	−0.338795	−	0.556478i
$573$		0			0
$574$	1.68219	+	2.31533i	0.0702131	+	0.0966401i
$575$	−35.9980	+	11.6965i	−1.50122	+	0.487776i
$576$		0			0
$577$	2.39941	+	1.74327i	0.0998886	+	0.0725733i	0.636608	−	0.771187i	$-0.280337\pi$
$577$	2.39941	+	1.74327i	0.0998886	+	0.0725733i	−0.536720	+	0.843761i	$0.680337\pi$
$578$	13.7528	+	9.99197i	0.572040	+	0.415611i
$579$		0			0
$580$	0.188111	−	0.0611211i	0.00781090	−	0.00253792i
$581$	9.95332	+	13.6996i	0.412933	+	0.568354i
$582$		0			0
$583$	−20.1263	+	23.4270i	−0.833548	+	0.970248i
$584$			1.02535i			0.0424294i
$585$		0			0
$586$	3.50715	+	10.7939i	0.144879	+	0.445891i
$587$	18.3044	+	5.94746i	0.755504	+	0.245478i	0.661348	−	0.750079i	$-0.269985\pi$
$587$	18.3044	+	5.94746i	0.755504	+	0.245478i	0.0941559	+	0.995557i	$0.469985\pi$
$588$		0			0
$589$	−14.7310	+	20.2754i	−0.606979	+	0.835434i
$590$	−0.0487185	+	0.149940i	−0.00200571	+	0.00617294i
$591$		0			0
$592$	−3.52209	+	2.55895i	−0.144757	+	0.105172i
$593$	14.7732			0.606661			0.303331	−	0.952885i	$-0.401901\pi$
$593$	14.7732			0.606661			0.303331	+	0.952885i	$0.401901\pi$
$594$		0			0
$595$	0.00151079			6.19362e−5
$596$	1.40849	−	1.02333i	0.0576940	−	0.0419171i
$597$		0			0
$598$	−10.9978	+	33.8477i	−0.449732	+	1.38413i
$599$	−13.1218	+	18.0606i	−0.536142	+	0.737937i	−0.988051	−	0.154128i	$-0.950743\pi$
$599$	−13.1218	+	18.0606i	−0.536142	+	0.737937i	0.451909	+	0.892064i	$0.350743\pi$
$600$		0			0
$601$	−20.6863	−	6.72139i	−0.843812	−	0.274171i	−0.144960	−	0.989437i	$-0.546305\pi$
$601$	−20.6863	−	6.72139i	−0.843812	−	0.274171i	−0.698852	+	0.715266i	$0.746305\pi$
$602$	−0.544905	−	1.67705i	−0.0222087	−	0.0683513i
$603$		0			0
$604$		−	8.65235i		−	0.352059i
$605$	−0.105773	+	0.643642i	−0.00430027	+	0.0261678i
$606$		0			0
$607$	−16.2922	−	22.4244i	−0.661282	−	0.910176i	0.338241	−	0.941059i	$-0.390168\pi$
$607$	−16.2922	−	22.4244i	−0.661282	−	0.910176i	−0.999523	+	0.0308831i	$0.990168\pi$
$608$	−5.33201	+	1.73247i	−0.216241	+	0.0702611i
$609$		0			0
$610$	0.0905416	+	0.0657823i	0.00366592	+	0.00266345i
$611$	27.1190	+	19.7031i	1.09712	+	0.797101i
$612$		0			0
$613$	15.4827	−	5.03063i	0.625340	−	0.203185i	0.0208305	−	0.999783i	$-0.493369\pi$
$613$	15.4827	−	5.03063i	0.625340	−	0.203185i	0.604510	+	0.796598i	$0.293369\pi$
$614$	7.61827	+	10.4856i	0.307448	+	0.423166i
$615$		0			0
$616$	−3.22722	+	0.764896i	−0.130028	+	0.0308186i
$617$			29.5956i			1.19147i	0.803180	+	0.595737i	$0.203140\pi$
$617$			29.5956i			1.19147i	−0.803180	+	0.595737i	$0.796860\pi$
$618$		0			0
$619$	4.02271	+	12.3806i	0.161686	+	0.497619i	0.998777	−	0.0494452i	$-0.0157453\pi$
$619$	4.02271	+	12.3806i	0.161686	+	0.497619i	−0.837091	+	0.547064i	$0.815745\pi$
$620$	−0.252100	−	0.0819122i	−0.0101246	−	0.00328967i
$621$		0			0
$622$	2.08037	−	2.86339i	0.0834154	−	0.114811i
$623$	0.488448	−	1.50329i	0.0195693	−	0.0602280i
$624$		0			0
$625$	−20.1828	+	14.6636i	−0.807311	+	0.586545i
$626$	−19.9945			−0.799140
$627$		0			0
$628$	16.5119			0.658897
$629$	0.0897356	−	0.0651967i	0.00357799	−	0.00259956i
$630$		0			0
$631$	10.7968	−	33.2291i	0.429813	−	1.32283i	−0.468496	−	0.883465i	$-0.655204\pi$
$631$	10.7968	−	33.2291i	0.429813	−	1.32283i	0.898309	−	0.439363i	$-0.144796\pi$
$632$	−7.60983	+	10.4740i	−0.302703	+	0.416635i
$633$		0			0
$634$	5.74654	+	1.86716i	0.228224	+	0.0741546i
$635$	0.126890	+	0.390528i	0.00503549	+	0.0154976i
$636$		0			0
$637$		−	4.69802i		−	0.186142i
$638$	9.44935	−	5.75295i	0.374103	−	0.227761i
$639$		0			0
$640$	−0.0348544	−	0.0479729i	−0.00137774	−	0.00189630i
$641$	−9.27017	+	3.01206i	−0.366150	+	0.118969i	−0.486313	−	0.873785i	$-0.661658\pi$
$641$	−9.27017	+	3.01206i	−0.366150	+	0.118969i	0.120163	+	0.992754i	$0.461658\pi$
$642$		0			0
$643$	−14.5989	−	10.6067i	−0.575725	−	0.418289i	0.261456	−	0.965216i	$-0.415798\pi$
$643$	−14.5989	−	10.6067i	−0.575725	−	0.418289i	−0.837180	+	0.546927i	$0.815798\pi$
$644$	6.12865	+	4.45273i	0.241503	+	0.175462i
$645$		0			0
$646$	0.135849	−	0.0441399i	0.00534489	−	0.00173666i
$647$	20.2583	+	27.8832i	0.796436	+	1.09620i	0.993277	+	0.115765i	$0.0369318\pi$
$647$	20.2583	+	27.8832i	0.796436	+	1.09620i	−0.196841	+	0.980435i	$0.563068\pi$
$648$		0			0
$649$	−0.717338	+	8.78877i	−0.0281580	+	0.344989i
$650$			23.4736i			0.920710i
$651$		0			0
$652$	−5.66203	−	17.4259i	−0.221742	−	0.682452i
$653$	−36.1030	−	11.7306i	−1.41282	−	0.459053i	−0.499505	−	0.866311i	$-0.666485\pi$
$653$	−36.1030	−	11.7306i	−1.41282	−	0.459053i	−0.913313	+	0.407258i	$0.866485\pi$
$654$		0			0
$655$	−0.381385	+	0.524932i	−0.0149020	+	0.0205108i
$656$	−0.884378	+	2.72184i	−0.0345292	+	0.106270i
$657$		0			0
$658$	5.77242	−	4.19391i	0.225032	−	0.163496i
$659$	−2.14229			−0.0834518			−0.0417259	−	0.999129i	$-0.513286\pi$
$659$	−2.14229			−0.0834518			−0.0417259	+	0.999129i	$0.513286\pi$
$660$		0			0
$661$	−29.2506			−1.13772			−0.568859	−	0.822435i	$-0.692615\pi$
$661$	−29.2506			−1.13772			−0.568859	+	0.822435i	$0.692615\pi$
$662$	−24.3270	+	17.6746i	−0.945496	+	0.686943i
$663$		0			0
$664$	−5.23277	+	16.1048i	−0.203071	+	0.624988i
$665$	−0.195408	+	0.268955i	−0.00757758	+	0.0104296i
$666$		0			0
$667$	−24.0317	−	7.80836i	−0.930510	−	0.302341i
$668$	5.68043	+	17.4826i	0.219783	+	0.676421i
$669$		0			0
$670$		−	0.376729i		−	0.0145543i
$671$	5.77617	+	2.41221i	0.222987	+	0.0931225i
$672$		0			0
$673$	4.19248	+	5.77045i	0.161608	+	0.222435i	0.882140	−	0.470987i	$-0.156102\pi$
$673$	4.19248	+	5.77045i	0.161608	+	0.222435i	−0.720532	+	0.693422i	$0.756102\pi$
$674$	10.6134	−	3.44850i	0.408813	−	0.132831i
$675$		0			0
$676$	7.33892	+	5.33204i	0.282266	+	0.205078i
$677$	−14.7123	−	10.6891i	−0.565440	−	0.410816i	0.268006	−	0.963417i	$-0.413635\pi$
$677$	−14.7123	−	10.6891i	−0.565440	−	0.410816i	−0.833446	+	0.552601i	$0.813635\pi$
$678$		0			0
$679$	−15.8875	+	5.16216i	−0.609706	+	0.198105i
$680$	0.000888017		0.00122225i	3.40539e−5		4.68712e-5i
$681$		0			0
$682$	−14.7769	−	1.20609i	−0.565836	−	0.0461835i
$683$		−	4.95833i		−	0.189725i	−0.995490	−	0.0948626i	$-0.969759\pi$
$683$		−	4.95833i		−	0.189725i	0.995490	−	0.0948626i	$-0.0302412\pi$
$684$		0			0
$685$	0.188181	+	0.579160i	0.00719001	+	0.0221286i
$686$	−0.951057	−	0.309017i	−0.0363115	−	0.0117983i
$687$		0			0
$688$	1.03647	−	1.42658i	0.0395151	−	0.0543879i
$689$	13.5192	−	41.6079i	0.515041	−	1.58513i
$690$		0			0
$691$	3.47031	−	2.52132i	0.132017	−	0.0959157i	−0.519817	−	0.854278i	$-0.674000\pi$
$691$	3.47031	−	2.52132i	0.132017	−	0.0959157i	0.651834	+	0.758362i	$0.274000\pi$
$692$	−22.4504			−0.853434
$693$		0			0
$694$	−13.8464			−0.525602
$695$	0.105524	−	0.0766677i	0.00400276	−	0.00290817i
$696$		0			0
$697$	0.0225321	−	0.0693468i	0.000853465	−	0.00262670i
$698$	14.3237	−	19.7149i	0.542162	−	0.746222i
$699$		0			0
$700$	4.75194	+	1.54400i	0.179606	+	0.0583577i
$701$	−1.45406	−	4.47515i	−0.0549193	−	0.169024i	0.919835	−	0.392307i	$-0.128323\pi$
$701$	−1.45406	−	4.47515i	−0.0549193	−	0.169024i	−0.974754	+	0.223282i	$0.928323\pi$
$702$		0			0
$703$			24.4077i			0.920554i
$704$	−2.51573	−	2.16128i	−0.0948150	−	0.0814563i
$705$		0			0
$706$	21.5691	+	29.6873i	0.811764	+	1.11730i
$707$	0.277292	−	0.0900976i	0.0104286	−	0.00338847i
$708$		0			0
$709$	−8.50596	−	6.17994i	−0.319448	−	0.232093i	0.416492	−	0.909139i	$-0.363259\pi$
$709$	−8.50596	−	6.17994i	−0.319448	−	0.232093i	−0.735940	+	0.677047i	$0.763259\pi$
$710$	−0.669259	−	0.486245i	−0.0251169	−	0.0182485i
$711$		0			0
$712$	1.50329	−	0.488448i	0.0563381	−	0.0183054i
$713$	19.9046	+	27.3964i	0.745434	+	1.02600i
$714$		0			0
$715$	−0.213087	−	0.899045i	−0.00796898	−	0.0336224i
$716$			1.63622i			0.0611484i
$717$		0			0
$718$	6.26580	+	19.2841i	0.233838	+	0.719678i
$719$	34.0143	+	11.0519i	1.26852	+	0.412167i	0.864522	−	0.502594i	$-0.167621\pi$
$719$	34.0143	+	11.0519i	1.26852	+	0.412167i	0.403996	+	0.914761i	$0.367621\pi$
$720$		0			0
$721$	−5.50155	+	7.57224i	−0.204889	+	0.282005i
$722$	−3.84162	+	11.8233i	−0.142970	+	0.440018i
$723$		0			0
$724$	12.9835	−	9.43308i	0.482529	−	0.350578i
$725$	−16.6661			−0.618965
$726$		0			0
$727$	−40.3106			−1.49504			−0.747518	−	0.664242i	$-0.768755\pi$
$727$	−40.3106			−1.49504			−0.747518	+	0.664242i	$0.768755\pi$
$728$	3.80078	−	2.76143i	0.140866	−	0.102345i
$729$		0			0
$730$	−0.0187886	+	0.0578254i	−0.000695397	+	0.00214021i
$731$	−0.0264072	+	0.0363463i	−0.000976704	+	0.00134432i
$732$		0			0
$733$	−26.2632	−	8.53342i	−0.970052	−	0.315189i	−0.219215	−	0.975677i	$-0.570350\pi$
$733$	−26.2632	−	8.53342i	−0.970052	−	0.315189i	−0.750837	+	0.660488i	$0.770350\pi$
$734$	2.47734	+	7.62446i	0.0914401	+	0.281424i
$735$		0			0
$736$			7.57543i			0.279234i
$737$	−4.85952	−	20.5031i	−0.179003	−	0.755241i
$738$		0			0
$739$	5.75071	+	7.91517i	0.211543	+	0.291164i	0.901582	−	0.432608i	$-0.142407\pi$
$739$	5.75071	+	7.91517i	0.211543	+	0.291164i	−0.690039	+	0.723772i	$0.742407\pi$
$740$	−0.245520	+	0.0797744i	−0.00902550	+	0.00293256i
$741$		0			0
$742$	−7.53376	−	5.47359i	−0.276573	−	0.200942i
$743$	34.9528	+	25.3947i	1.28229	+	0.931641i	0.999620	−	0.0275754i	$-0.00877865\pi$
$743$	34.9528	+	25.3947i	1.28229	+	0.931641i	0.282674	+	0.959216i	$0.408779\pi$
$744$		0			0
$745$	0.0981840	−	0.0319019i	0.00359718	−	0.00116880i
$746$	−12.6460	−	17.4057i	−0.463002	−	0.637268i
$747$		0			0
$748$	0.0640955	+	0.0550650i	0.00234356	+	0.00201337i
$749$		−	17.4074i		−	0.636053i
$750$		0			0
$751$	0.243535	+	0.749523i	0.00888671	+	0.0273505i	0.955402	−	0.295310i	$-0.0954229\pi$
$751$	0.243535	+	0.749523i	0.00888671	+	0.0273505i	−0.946515	+	0.322660i	$0.895423\pi$
$752$	6.78589	+	2.20487i	0.247456	+	0.0804033i
$753$		0			0
$754$	−9.21094	+	12.6778i	−0.335443	+	0.461697i
$755$	0.158546	−	0.487954i	0.00577007	−	0.0177585i
$756$		0			0
$757$	−5.12551	+	3.72390i	−0.186290	+	0.135348i	−0.677021	−	0.735963i	$-0.736730\pi$
$757$	−5.12551	+	3.72390i	−0.186290	+	0.135348i	0.490732	+	0.871311i	$0.336730\pi$
$758$	−31.6050			−1.14795
$759$		0			0
$760$	−0.332447			−0.0120591
$761$	11.6297	−	8.44946i	0.421576	−	0.306293i	−0.356696	−	0.934221i	$-0.616097\pi$
$761$	11.6297	−	8.44946i	0.421576	−	0.306293i	0.778271	+	0.627928i	$0.216097\pi$
$762$		0			0
$763$	0.671847	−	2.06773i	0.0243225	−	0.0748570i
$764$	6.17294	−	8.49632i	0.223329	−	0.307386i
$765$		0			0
$766$	8.17722	+	2.65694i	0.295455	+	0.0959992i
$767$	−3.85985	−	11.8794i	−0.139371	−	0.428940i
$768$		0			0
$769$			15.6808i			0.565465i	0.959199	+	0.282733i	$0.0912409\pi$
$769$			15.6808i			0.565465i	−0.959199	+	0.282733i	$0.908759\pi$
$770$	−0.196017	−	0.0159989i	−0.00706395	−	0.000576559i
$771$		0			0
$772$	−9.50113	−	13.0772i	−0.341953	−	0.470658i
$773$	32.0856	−	10.4252i	1.15404	−	0.374970i	0.331376	−	0.943499i	$-0.392487\pi$
$773$	32.0856	−	10.4252i	1.15404	−	0.374970i	0.822663	+	0.568529i	$0.192487\pi$
$774$		0			0
$775$	18.0697	+	13.1284i	0.649082	+	0.471585i
$776$	−13.5147	−	9.81900i	−0.485149	−	0.352482i
$777$		0			0
$778$	−26.9778	+	8.76563i	−0.967202	+	0.314263i
$779$	9.43102	+	12.9807i	0.337901	+	0.465081i
$780$		0			0
$781$	−42.6959	−	17.8304i	−1.52778	−	0.638024i
$782$		−	0.193006i		−	0.00690189i
$783$		0			0
$784$	−0.309017	−	0.951057i	−0.0110363	−	0.0339663i
$785$	0.931198	+	0.302565i	0.0332359	+	0.0107990i
$786$		0			0
$787$	27.6886	−	38.1101i	0.986992	−	1.35848i	0.0540161	−	0.998540i	$-0.482798\pi$
$787$	27.6886	−	38.1101i	0.986992	−	1.35848i	0.932976	−	0.359938i	$-0.117202\pi$
$788$	−1.49032	+	4.58673i	−0.0530905	+	0.163396i
$789$		0			0
$790$	−0.621087	+	0.451246i	−0.0220973	+	0.0160546i
$791$	−9.73527			−0.346146
$792$		0			0
$793$	−8.86680			−0.314869
$794$	−2.02423	+	1.47069i	−0.0718374	+	0.0521929i
$795$		0			0
$796$	6.39942	−	19.6954i	0.226821	−	0.698084i
$797$	−24.0155	+	33.0545i	−0.850673	+	1.17085i	0.133042	+	0.991110i	$0.457526\pi$
$797$	−24.0155	+	33.0545i	−0.850673	+	1.17085i	−0.983714	+	0.179740i	$0.942474\pi$
$798$		0			0
$799$	−0.172890	−	0.0561755i	−0.00611643	−	0.00198735i
$800$	1.54400	+	4.75194i	0.0545886	+	0.168006i
$801$		0			0
$802$			21.4475i			0.757338i
$803$	−0.276646	+	3.38944i	−0.00976263	+	0.119611i
$804$		0			0
$805$	0.264037	+	0.363415i	0.00930607	+	0.0128087i
$806$	19.9733	−	6.48971i	0.703529	−	0.228590i
$807$		0			0
$808$	0.235879	+	0.171376i	0.00829818	+	0.00602898i
$809$	−15.6857	−	11.3963i	−0.551480	−	0.400674i	0.276851	−	0.960913i	$-0.410709\pi$
$809$	−15.6857	−	11.3963i	−0.551480	−	0.400674i	−0.828331	+	0.560239i	$0.810709\pi$
$810$		0			0
$811$	12.9056	−	4.19328i	0.453176	−	0.147246i	−0.0735304	−	0.997293i	$-0.523427\pi$
$811$	12.9056	−	4.19328i	0.453176	−	0.147246i	0.526707	+	0.850047i	$0.323427\pi$
$812$	1.96060	+	2.69854i	0.0688036	+	0.0947000i
$813$		0			0
$814$	−12.3331	+	7.50866i	−0.432277	+	0.263178i
$815$		−	1.08650i		−	0.0380583i
$816$		0			0
$817$	−3.05496	−	9.40219i	−0.106879	−	0.328941i
$818$	26.6889	+	8.67173i	0.933154	+	0.303200i
$819$		0			0
$820$	−0.0997499	+	0.137294i	−0.00348342	+	0.00479451i
$821$	5.32393	−	16.3854i	0.185806	−	0.571853i	−0.814155	−	0.580648i	$-0.802799\pi$
$821$	5.32393	−	16.3854i	0.185806	−	0.571853i	0.999961	+	0.00879430i	$0.00279935\pi$
$822$		0			0
$823$	18.7482	−	13.6214i	0.653521	−	0.474811i	−0.210948	−	0.977497i	$-0.567655\pi$
$823$	18.7482	−	13.6214i	0.653521	−	0.474811i	0.864469	+	0.502687i	$0.167655\pi$
$824$	−9.35980			−0.326064
$825$		0			0
$826$	−2.65872			−0.0925089
$827$	−28.7554	+	20.8920i	−0.999922	+	0.726486i	−0.962071	−	0.272798i	$-0.912051\pi$
$827$	−28.7554	+	20.8920i	−0.999922	+	0.726486i	−0.0378505	+	0.999283i	$0.512051\pi$
$828$		0			0
$829$	0.737731	−	2.27050i	0.0256224	−	0.0788578i	−0.937428	−	0.348180i	$-0.886800\pi$
$829$	0.737731	−	2.27050i	0.0256224	−	0.0788578i	0.963050	+	0.269322i	$0.0867997\pi$
$830$	−0.590209	+	0.812354i	−0.0204865	+	0.0281972i
$831$		0			0
$832$	4.46808	+	1.45177i	0.154903	+	0.0503310i
$833$	0.00787312	+	0.0242310i	0.000272787	+	0.000839553i
$834$		0			0
$835$			1.09003i			0.0377220i
$836$	−18.0931	+	4.28832i	−0.625762	+	0.148315i
$837$		0			0
$838$	−8.31601	−	11.4460i	−0.287272	−	0.395396i
$839$	−21.3649	+	6.94186i	−0.737597	+	0.239660i	−0.653636	−	0.756809i	$-0.726757\pi$
$839$	−21.3649	+	6.94186i	−0.737597	+	0.239660i	−0.0839610	+	0.996469i	$0.526757\pi$
$840$		0			0
$841$	14.4603	+	10.5060i	0.498632	+	0.362277i
$842$	3.14888	+	2.28779i	0.108518	+	0.0788426i
$843$		0			0
$844$	−15.3065	+	4.97339i	−0.526872	+	0.171191i
$845$	0.316178	+	0.435182i	0.0108769	+	0.0149707i
$846$		0			0
$847$	−10.8744	+	1.65775i	−0.373648	+	0.0569608i
$848$		−	9.31224i		−	0.319783i
$849$		0			0
$850$	−0.0393379	−	0.121070i	−0.00134928	−	0.00415265i
$851$	31.3658	+	10.1914i	1.07521	+	0.349355i
$852$		0			0
$853$	13.2918	−	18.2945i	0.455101	−	0.626393i	−0.518383	−	0.855149i	$-0.673466\pi$
$853$	13.2918	−	18.2945i	0.455101	−	0.626393i	0.973484	+	0.228756i	$0.0734658\pi$
$854$	−0.583223	+	1.79498i	−0.0199575	+	0.0614228i
$855$		0			0
$856$	14.0829	−	10.2318i	0.481343	−	0.349716i
$857$	−4.80954			−0.164291			−0.0821454	−	0.996620i	$-0.526177\pi$
$857$	−4.80954			−0.164291			−0.0821454	+	0.996620i	$0.526177\pi$
$858$		0			0
$859$	54.0627			1.84459			0.922297	−	0.386482i	$-0.126310\pi$
$859$	54.0627			1.84459			0.922297	+	0.386482i	$0.126310\pi$
$860$	0.0845930	−	0.0614604i	0.00288460	−	0.00209578i
$861$		0			0
$862$	8.90280	−	27.4000i	0.303230	−	0.933247i
$863$	−9.37952	+	12.9098i	−0.319282	+	0.439455i	−0.938248	−	0.345964i	$-0.887552\pi$
$863$	−9.37952	+	12.9098i	−0.319282	+	0.439455i	0.618965	+	0.785418i	$0.287552\pi$
$864$		0			0
$865$	−1.26610	−	0.411381i	−0.0430487	−	0.0139874i
$866$	12.6022	+	38.7855i	0.428239	+	1.31798i
$867$		0			0
$868$		−	4.47021i		−	0.151729i
$869$	−27.9813	+	32.5701i	−0.949199	+	1.10487i
$870$		0			0
$871$	17.5438	+	24.1470i	0.594450	+	0.818190i
$872$	2.06773	−	0.671847i	0.0700223	−	0.0227516i
$873$		0			0
$874$	34.3597	+	24.9638i	1.16223	+	0.844412i
$875$	0.479560	+	0.348421i	0.0162121	+	0.0117788i
$876$		0			0
$877$	2.22964	−	0.724456i	0.0752898	−	0.0244631i	−0.271130	−	0.962543i	$-0.587397\pi$
$877$	2.22964	−	0.724456i	0.0752898	−	0.0244631i	0.346420	+	0.938080i	$0.387397\pi$
$878$	−21.3776	−	29.4238i	−0.721461	−	0.993005i
$879$		0			0
$880$	−0.102272	−	0.167985i	−0.00344760	−	0.00566276i
$881$			17.8418i			0.601105i	0.953765	+	0.300553i	$0.0971711\pi$
$881$			17.8418i			0.601105i	−0.953765	+	0.300553i	$0.902829\pi$
$882$		0			0
$883$	−3.67747	−	11.3181i	−0.123757	−	0.380884i	0.869916	−	0.493200i	$-0.164173\pi$
$883$	−3.67747	−	11.3181i	−0.123757	−	0.380884i	−0.993672	+	0.112316i	$0.964173\pi$
$884$	−0.113838	−	0.0369881i	−0.00382877	−	0.00124404i
$885$		0			0
$886$	4.33212	−	5.96266i	0.145541	−	0.200319i
$887$	−7.69894	+	23.6949i	−0.258505	+	0.795597i	0.734614	+	0.678485i	$0.237363\pi$
$887$	−7.69894	+	23.6949i	−0.258505	+	0.795597i	−0.993119	+	0.117111i	$0.962637\pi$
$888$		0			0
$889$	−5.60229	+	4.07030i	−0.187895	+	0.136513i
$890$	0.0937291			0.00314181
$891$		0			0
$892$	−20.0302			−0.670659
$893$	32.3625	−	23.5127i	1.08297	−	0.786824i
$894$		0			0
$895$	−0.0299821	+	0.0922756i	−0.00100219	+	0.00308443i
$896$	0.587785	−	0.809017i	0.0196365	−	0.0270274i
$897$		0			0
$898$	−26.6159	−	8.64804i	−0.888185	−	0.288589i
$899$	4.60766	+	14.1809i	0.153674	+	0.472961i
$900$		0			0
$901$			0.237257i			0.00790416i
$902$	−3.65779	+	8.75878i	−0.121791	+	0.291635i
$903$		0			0
$904$	−5.72225	−	7.87600i	−0.190319	−	0.261952i
$905$	0.905065	−	0.294073i	0.0300854	−	0.00977533i
$906$		0			0
$907$	−31.6937	−	23.0268i	−1.05237	−	0.764592i	−0.0797087	−	0.996818i	$-0.525399\pi$
$907$	−31.6937	−	23.0268i	−1.05237	−	0.764592i	−0.972662	+	0.232226i	$0.925399\pi$
$908$	−10.1859	−	7.40052i	−0.338032	−	0.245595i
$909$		0			0
$910$	0.264947	−	0.0860866i	0.00878292	−	0.00285374i
$911$	0.738647	+	1.01666i	0.0244725	+	0.0336834i	0.821078	−	0.570816i	$-0.193373\pi$
$911$	0.738647	+	1.01666i	0.0244725	+	0.0336834i	−0.796605	+	0.604500i	$0.793373\pi$
$912$		0			0
$913$	−21.6428	+	51.8247i	−0.716271	+	1.71515i
$914$			10.4821i			0.346717i
$915$		0			0
$916$	5.21872	+	16.0616i	0.172431	+	0.530689i
$917$	−10.4067	−	3.38134i	−0.343660	−	0.111662i
$918$		0			0
$919$	−6.65654	+	9.16194i	−0.219579	+	0.302225i	−0.904568	−	0.426328i	$-0.859807\pi$
$919$	−6.65654	+	9.16194i	−0.219579	+	0.302225i	0.684989	+	0.728553i	$0.259807\pi$
$920$	−0.138812	+	0.427220i	−0.00457651	+	0.0140850i
$921$		0			0
$922$	−1.77999	+	1.29324i	−0.0586209	+	0.0425906i
$923$	65.5411			2.15731
$924$		0			0
$925$	21.7524			0.715214
$926$	−5.90287	+	4.28868i	−0.193980	+	0.140935i
$927$		0			0
$928$	−1.03075	+	3.17232i	−0.0338360	+	0.104136i
$929$	−4.83372	+	6.65305i	−0.158589	+	0.218280i	−0.880916	−	0.473272i	$-0.843073\pi$
$929$	−4.83372	+	6.65305i	−0.158589	+	0.218280i	0.722327	+	0.691552i	$0.243073\pi$
$930$		0			0
$931$	−5.33201	−	1.73247i	−0.174749	−	0.0567795i
$932$	−0.219194	−	0.674610i	−0.00717994	−	0.0220976i
$933$		0			0
$934$		−	22.0182i		−	0.720457i
$935$	0.00260569	+	0.00427990i	8.52151e−5	+	0.000139968i
$936$		0			0
$937$	−21.5371	−	29.6433i	−0.703586	−	0.968403i	−0.999911	−	0.0133162i	$-0.995761\pi$
$937$	−21.5371	−	29.6433i	−0.703586	−	0.968403i	0.296325	−	0.955087i	$-0.404239\pi$
$938$	6.04223	−	1.96324i	0.197286	−	0.0641020i
$939$		0			0
$940$	0.342292	+	0.248690i	0.0111643	+	0.00811136i
$941$	27.4572	+	19.9488i	0.895078	+	0.650312i	0.937197	−	0.348800i	$-0.113411\pi$
$941$	27.4572	+	19.9488i	0.895078	+	0.650312i	−0.0421190	+	0.999113i	$0.513411\pi$
$942$		0			0
$943$	20.6191	−	6.69954i	0.671449	−	0.218167i
$944$	−1.56276	−	2.15095i	−0.0508635	−	0.0700076i
$945$		0			0
$946$	3.81109	−	4.43610i	0.123909	−	0.144230i
$947$		−	41.0541i		−	1.33408i	−0.745022	−	0.667039i	$-0.767561\pi$
$947$		−	41.0541i		−	1.33408i	0.745022	−	0.667039i	$-0.232439\pi$
$948$		0			0
$949$	−1.48858	−	4.58137i	−0.0483212	−	0.148717i
$950$	26.6413	+	8.65628i	0.864357	+	0.280847i
$951$		0			0
$952$	−0.0149756	+	0.0206121i	−0.000485361	+	0.000668042i
$953$	−0.378588	+	1.16518i	−0.0122637	+	0.0377437i	−0.957001	−	0.290084i	$-0.906317\pi$
$953$	−0.378588	+	1.16518i	−0.0122637	+	0.0377437i	0.944737	+	0.327828i	$0.106317\pi$
$954$		0			0
$955$	0.503813	−	0.366041i	0.0163030	−	0.0118448i
$956$	3.23442			0.104609
$957$		0			0
$958$	−16.7739			−0.541939
$959$	−8.30829	+	6.03633i	−0.268289	+	0.194923i
$960$		0			0
$961$	−3.40451	+	10.4780i	−0.109823	+	0.338000i
$962$	12.0220	−	16.5468i	0.387604	−	0.533492i
$963$		0			0
$964$	21.1042	+	6.85717i	0.679721	+	0.220855i
$965$	−0.296195	−	0.911593i	−0.00953484	−	0.0293452i
$966$		0			0
$967$			25.9704i			0.835151i	0.908642	+	0.417576i	$0.137120\pi$
$967$			25.9704i			0.835151i	−0.908642	+	0.417576i	$0.862880\pi$
$968$	−7.73294	−	7.82315i	−0.248546	−	0.251446i
$969$		0			0
$970$	−0.582245	−	0.801392i	−0.0186948	−	0.0257311i
$971$	−33.1979	+	10.7866i	−1.06537	+	0.346160i	−0.788683	−	0.614800i	$-0.789237\pi$
$971$	−33.1979	+	10.7866i	−1.06537	+	0.346160i	−0.276688	+	0.960960i	$0.589237\pi$
$972$		0			0
$973$	1.77956	+	1.29293i	0.0570501	+	0.0414494i
$974$	22.9135	+	16.6476i	0.734196	+	0.533425i
$975$		0			0
$976$	−1.79498	+	0.583223i	−0.0574558	+	0.0186685i
$977$	19.6620	+	27.0624i	0.629042	+	0.865802i	0.997972	−	0.0636554i	$-0.0202759\pi$
$977$	19.6620	+	27.0624i	0.629042	+	0.865802i	−0.368930	+	0.929457i	$0.620276\pi$
$978$		0			0
$979$	5.10111	−	1.20903i	0.163032	−	0.0386409i
$980$		−	0.0592978i		−	0.00189420i
$981$		0			0
$982$	2.00285	+	6.16413i	0.0639135	+	0.196705i
$983$	−39.4269	−	12.8106i	−1.25752	−	0.408594i	−0.396912	−	0.917857i	$-0.629918\pi$
$983$	−39.4269	−	12.8106i	−1.25752	−	0.408594i	−0.860611	+	0.509263i	$0.829918\pi$
$984$		0			0
$985$	−0.168095	+	0.231363i	−0.00535595	+	0.00737183i
$986$	0.0262614	−	0.0808242i	0.000836332	−	0.00257397i
$987$		0			0
$988$	21.3087	−	15.4817i	0.677920	−	0.492538i
$989$	−13.3581			−0.424764
$990$		0			0
$991$	−14.6840			−0.466452			−0.233226	−	0.972423i	$-0.574928\pi$
$991$	−14.6840			−0.466452			−0.233226	+	0.972423i	$0.574928\pi$
$992$	3.61648	−	2.62752i	0.114823	−	0.0834240i
$993$		0			0
$994$	4.31103	−	13.2680i	0.136738	−	0.420835i
$995$	0.721797	−	0.993469i	0.0228825	−	0.0314951i
$996$		0			0
$997$	−26.8633	−	8.72841i	−0.850768	−	0.276431i	−0.149001	−	0.988837i	$-0.547606\pi$
$997$	−26.8633	−	8.72841i	−0.850768	−	0.276431i	−0.701768	+	0.712406i	$0.747606\pi$
$998$	3.78897	+	11.6612i	0.119938	+	0.369130i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.bu.a.701.6	✓	48
3.2	odd	2		1386.2.bu.b.701.7	yes	48
11.7	odd	10		1386.2.bu.b.953.7	yes	48
33.29	even	10	inner	1386.2.bu.a.953.6	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.bu.a.701.6	✓	48	1.1	even	1	trivial
1386.2.bu.a.953.6	yes	48	33.29	even	10	inner
1386.2.bu.b.701.7	yes	48	3.2	odd	2
1386.2.bu.b.953.7	yes	48	11.7	odd	10

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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.bu (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(0.0348544 - 0.0479729i) q^{5} +(0.951057 + 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(0.0348544 - 0.0479729i) q^{5} +(0.951057 + 0.309017i) q^{7} +(0.309017 + 0.951057i) q^{8} +0.0592978i q^{10} +(0.764896 + 3.22722i) q^{11} +(-2.76143 - 3.80078i) q^{13} +(-0.951057 + 0.309017i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(0.0206121 + 0.0149756i) q^{17} +(-5.33201 + 1.73247i) q^{19} +(-0.0348544 - 0.0479729i) q^{20} +(-2.51573 - 2.16128i) q^{22} +7.57543i q^{23} +(1.54400 + 4.75194i) q^{25} +(4.46808 + 1.45177i) q^{26} +(0.587785 - 0.809017i) q^{28} +(-1.03075 + 3.17232i) q^{29} +(3.61648 - 2.62752i) q^{31} +1.00000 q^{32} -0.0254779 q^{34} +(0.0479729 - 0.0348544i) q^{35} +(1.34532 - 4.14046i) q^{37} +(3.29536 - 4.53568i) q^{38} +(0.0563955 + 0.0183240i) q^{40} +(-0.884378 - 2.72184i) q^{41} +1.76335i q^{43} +(3.30563 + 0.269805i) q^{44} +(-4.45273 - 6.12865i) q^{46} +(-6.78589 + 2.20487i) q^{47} +(0.809017 + 0.587785i) q^{49} +(-4.04224 - 2.93686i) q^{50} +(-4.46808 + 1.45177i) q^{52} +(5.47359 + 7.53376i) q^{53} +(0.181479 + 0.0757883i) q^{55} +1.00000i q^{56} +(-1.03075 - 3.17232i) q^{58} +(2.52860 + 0.821591i) q^{59} +(1.10936 - 1.52690i) q^{61} +(-1.38137 + 4.25142i) q^{62} +(-0.809017 + 0.587785i) q^{64} -0.278582 q^{65} -6.35318 q^{67} +(0.0206121 - 0.0149756i) q^{68} +(-0.0183240 + 0.0563955i) q^{70} +(-8.20006 + 11.2864i) q^{71} +(0.975169 + 0.316852i) q^{73} +(1.34532 + 4.14046i) q^{74} +5.60640i q^{76} +(-0.269805 + 3.30563i) q^{77} +(7.60983 + 10.4740i) q^{79} +(-0.0563955 + 0.0183240i) q^{80} +(2.31533 + 1.68219i) q^{82} +(13.6996 + 9.95332i) q^{83} +(0.00143684 - 0.000466858i) q^{85} +(-1.03647 - 1.42658i) q^{86} +(-2.83290 + 1.72472i) q^{88} -1.58065i q^{89} +(-1.45177 - 4.46808i) q^{91} +(7.20466 + 2.34094i) q^{92} +(4.19391 - 5.77242i) q^{94} +(-0.102732 + 0.316176i) q^{95} +(-13.5147 + 9.81900i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8}+O(q^{10}) \) 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8	\( 48 q - 12 q^{2} - 12 q^{4} - 12 q^{8} + 4 q^{11} - 12 q^{16} + 24 q^{17} + 4 q^{22} + 24 q^{25} + 40 q^{26} - 16 q^{29} + 40 q^{31} + 48 q^{32} - 16 q^{34} - 12 q^{35} + 16 q^{37} - 40 q^{38} + 24 q^{41} + 4 q^{44} - 40 q^{46} - 40 q^{47} + 12 q^{49} + 4 q^{50} - 40 q^{52} - 40 q^{53} - 32 q^{55} - 16 q^{58} + 40 q^{61} - 40 q^{62} - 12 q^{64} + 48 q^{67} + 24 q^{68} + 8 q^{70} + 40 q^{73} + 16 q^{74} + 32 q^{77} + 40 q^{79} - 16 q^{82} - 16 q^{83} - 20 q^{85} + 4 q^{88} - 20 q^{92} - 52 q^{95} - 8 q^{97} - 48 q^{98}+O(q^{100}) \) 48 * q - 12 * q^2 - 12 * q^4 - 12 * q^8 + 4 * q^11 - 12 * q^16 + 24 * q^17 + 4 * q^22 + 24 * q^25 + 40 * q^26 - 16 * q^29 + 40 * q^31 + 48 * q^32 - 16 * q^34 - 12 * q^35 + 16 * q^37 - 40 * q^38 + 24 * q^41 + 4 * q^44 - 40 * q^46 - 40 * q^47 + 12 * q^49 + 4 * q^50 - 40 * q^52 - 40 * q^53 - 32 * q^55 - 16 * q^58 + 40 * q^61 - 40 * q^62 - 12 * q^64 + 48 * q^67 + 24 * q^68 + 8 * q^70 + 40 * q^73 + 16 * q^74 + 32 * q^77 + 40 * q^79 - 16 * q^82 - 16 * q^83 - 20 * q^85 + 4 * q^88 - 20 * q^92 - 52 * q^95 - 8 * q^97 - 48 * q^98

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