LMFDB - Embedded newform 756.2.bb.a.611.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(611,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 2]))

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

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

chi := DirichletCharacter("756.611");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bb (of order $6$, degree $2$, not 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$44$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			611.3
Character	$\chi$	$=$	756.611
Dual form			756.2.bb.a.683.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40608 - 0.151434i) q^{2} +(1.95414 + 0.425857i) q^{4} +(0.941391 - 0.543513i) q^{5} +(2.38059 - 1.15446i) q^{7} +(-2.68319 - 0.894712i) q^{8} +O(q^{10})$	\(q+(-1.40608 - 0.151434i) q^{2} +(1.95414 + 0.425857i) q^{4} +(0.941391 - 0.543513i) q^{5} +(2.38059 - 1.15446i) q^{7} +(-2.68319 - 0.894712i) q^{8} +(-1.40598 + 0.621665i) q^{10} +(-0.751874 + 1.30228i) q^{11} +(1.59238 - 2.75809i) q^{13} +(-3.52214 + 1.26276i) q^{14} +(3.63729 + 1.66436i) q^{16} +(5.40337 - 3.11964i) q^{17} +(-2.29977 - 1.32777i) q^{19} +(2.07106 - 0.661199i) q^{20} +(1.25441 - 1.71726i) q^{22} +(-1.62579 - 2.81595i) q^{23} +(-1.90919 + 3.30681i) q^{25} +(-2.65669 + 3.63696i) q^{26} +(5.14364 - 1.24217i) q^{28} +(1.78455 - 1.03031i) q^{29} +0.818407i q^{31} +(-4.86229 - 2.89104i) q^{32} +(-8.07001 + 3.56822i) q^{34} +(1.61361 - 2.38068i) q^{35} +(-4.35941 + 7.55073i) q^{37} +(3.03260 + 2.21522i) q^{38} +(-3.01222 + 0.616071i) q^{40} +(-6.57171 - 3.79418i) q^{41} +(3.95088 - 2.28104i) q^{43} +(-2.02385 + 2.22465i) q^{44} +(1.85956 + 4.20565i) q^{46} +13.6215 q^{47} +(4.33446 - 5.49658i) q^{49} +(3.18524 - 4.36053i) q^{50} +(4.28628 - 4.71155i) q^{52} +(-0.686610 + 0.396415i) q^{53} +1.63461i q^{55} +(-7.42049 + 0.967673i) q^{56} +(-2.66525 + 1.17846i) q^{58} -2.39274 q^{59} +4.72586 q^{61} +(0.123935 - 1.15075i) q^{62} +(6.39898 + 4.80136i) q^{64} -3.46192i q^{65} -9.19521i q^{67} +(11.8874 - 3.79513i) q^{68} +(-2.62938 + 3.10307i) q^{70} +12.1795 q^{71} +(-4.02960 - 6.97947i) q^{73} +(7.27313 - 9.95678i) q^{74} +(-3.92862 - 3.57402i) q^{76} +(-0.286478 + 3.96822i) q^{77} -14.4294i q^{79} +(4.32872 - 0.410095i) q^{80} +(8.66581 + 6.33011i) q^{82} +(2.40508 + 4.16573i) q^{83} +(3.39113 - 5.87360i) q^{85} +(-5.90069 + 2.60904i) q^{86} +(3.18259 - 2.82156i) q^{88} +(-5.90946 - 3.41183i) q^{89} +(0.606727 - 8.40422i) q^{91} +(-1.97782 - 6.19509i) q^{92} +(-19.1530 - 2.06276i) q^{94} -2.88665 q^{95} +(6.69603 + 11.5979i) q^{97} +(-6.92698 + 7.07227i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) $ 88 * q - 2 * q^4 + 6 * q^5	$ 88 q - 2 q^{4} + 6 q^{5} + 2 q^{10} - 4 q^{13} + 18 q^{14} - 2 q^{16} + 6 q^{20} - 6 q^{22} + 30 q^{25} - 6 q^{26} + 24 q^{29} - 4 q^{34} - 4 q^{37} + 45 q^{38} - 4 q^{40} + 12 q^{41} - 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} - 7 q^{52} + 24 q^{56} + 5 q^{58} - 4 q^{61} - 8 q^{64} + 12 q^{68} - 27 q^{70} - 4 q^{73} - 51 q^{74} - 6 q^{76} + 30 q^{77} + 87 q^{80} - 4 q^{82} - 14 q^{85} - 81 q^{86} + 9 q^{88} + 60 q^{89} - 24 q^{92} - 18 q^{94} - 4 q^{97} - 57 q^{98}+O(q^{100}) $ 88 * q - 2 * q^4 + 6 * q^5 + 2 * q^10 - 4 * q^13 + 18 * q^14 - 2 * q^16 + 6 * q^20 - 6 * q^22 + 30 * q^25 - 6 * q^26 + 24 * q^29 - 4 * q^34 - 4 * q^37 + 45 * q^38 - 4 * q^40 + 12 * q^41 - 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 - 7 * q^52 + 24 * q^56 + 5 * q^58 - 4 * q^61 - 8 * q^64 + 12 * q^68 - 27 * q^70 - 4 * q^73 - 51 * q^74 - 6 * q^76 + 30 * q^77 + 87 * q^80 - 4 * q^82 - 14 * q^85 - 81 * q^86 + 9 * q^88 + 60 * q^89 - 24 * q^92 - 18 * q^94 - 4 * q^97 - 57 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−1.40608	−	0.151434i	−0.994250	−	0.107080i
$2$	−1.40608	−	0.151434i	−0.994250	−	0.107080i
$3$		0			0
$3$		0			0
$4$	1.95414	+	0.425857i	0.977068	+	0.212928i
$5$	0.941391	−	0.543513i	0.421003	−	0.243066i	−0.274503	−	0.961586i	$-0.588513\pi$
$5$	0.941391	−	0.543513i	0.421003	−	0.243066i	0.695506	+	0.718520i	$0.255180\pi$
$6$		0			0
$7$	2.38059	−	1.15446i	0.899780	−	0.436343i
$7$	2.38059	−	1.15446i	0.899780	−	0.436343i
$8$	−2.68319	−	0.894712i	−0.948650	−	0.316329i
$9$		0			0
$10$	−1.40598	+	0.621665i	−0.444610	+	0.196588i
$11$	−0.751874	+	1.30228i	−0.226699	+	0.392653i	−0.956828	−	0.290656i	$-0.906127\pi$
$11$	−0.751874	+	1.30228i	−0.226699	+	0.392653i	0.730129	+	0.683309i	$0.239460\pi$
$12$		0			0
$13$	1.59238	−	2.75809i	0.441647	−	0.764955i	−0.556165	−	0.831072i	$-0.687728\pi$
$13$	1.59238	−	2.75809i	0.441647	−	0.764955i	0.997812	+	0.0661167i	$0.0210610\pi$
$14$	−3.52214	+	1.26276i	−0.941330	+	0.337486i
$15$		0			0
$16$	3.63729	+	1.66436i	0.909323	+	0.416091i
$17$	5.40337	−	3.11964i	1.31051	−	0.756624i	0.328330	−	0.944563i	$-0.393514\pi$
$17$	5.40337	−	3.11964i	1.31051	−	0.756624i	0.982181	+	0.187939i	$0.0601808\pi$
$18$		0			0
$19$	−2.29977	−	1.32777i	−0.527604	−	0.304612i	0.212436	−	0.977175i	$-0.431860\pi$
$19$	−2.29977	−	1.32777i	−0.527604	−	0.304612i	−0.740040	+	0.672563i	$0.765194\pi$
$20$	2.07106	−	0.661199i	0.463104	−	0.147849i
$21$		0			0
$22$	1.25441	−	1.71726i	0.267440	−	0.366121i
$23$	−1.62579	−	2.81595i	−0.339000	−	0.587165i	0.645245	−	0.763976i	$-0.276755\pi$
$23$	−1.62579	−	2.81595i	−0.339000	−	0.587165i	−0.984245	+	0.176811i	$0.943422\pi$
$24$		0			0
$25$	−1.90919	+	3.30681i	−0.381838	+	0.661362i
$26$	−2.65669	+	3.63696i	−0.521019	+	0.713266i
$27$		0			0
$28$	5.14364	−	1.24217i	0.972056	−	0.234748i
$29$	1.78455	−	1.03031i	0.331382	−	0.191324i	−0.325072	−	0.945689i	$-0.605389\pi$
$29$	1.78455	−	1.03031i	0.331382	−	0.191324i	0.656455	+	0.754365i	$0.272055\pi$
$30$		0			0
$31$			0.818407i			0.146990i	0.997296	+	0.0734951i	$0.0234153\pi$
$31$			0.818407i			0.146990i	−0.997296	+	0.0734951i	$0.976585\pi$
$32$	−4.86229	−	2.89104i	−0.859540	−	0.511069i
$33$		0			0
$34$	−8.07001	+	3.56822i	−1.38400	+	0.611944i
$35$	1.61361	−	2.38068i	0.272750	−	0.402408i
$36$		0			0
$37$	−4.35941	+	7.55073i	−0.716683	+	1.24133i	0.245623	+	0.969365i	$0.421007\pi$
$37$	−4.35941	+	7.55073i	−0.716683	+	1.24133i	−0.962307	+	0.271967i	$0.912326\pi$
$38$	3.03260	+	2.21522i	0.491952	+	0.359357i
$39$		0			0
$40$	−3.01222	+	0.616071i	−0.476273	+	0.0974094i
$41$	−6.57171	−	3.79418i	−1.02633	−	0.592552i	−0.110398	−	0.993887i	$-0.535213\pi$
$41$	−6.57171	−	3.79418i	−1.02633	−	0.592552i	−0.915931	+	0.401336i	$0.868546\pi$
$42$		0			0
$43$	3.95088	−	2.28104i	0.602504	−	0.347856i	−0.167522	−	0.985868i	$-0.553577\pi$
$43$	3.95088	−	2.28104i	0.602504	−	0.347856i	0.770026	+	0.638012i	$0.220243\pi$
$44$	−2.02385	+	2.22465i	−0.305107	+	0.335378i
$45$		0			0
$46$	1.85956	+	4.20565i	0.274177	+	0.620089i
$47$	13.6215			1.98690			0.993451	−	0.114259i	$-0.0364492\pi$
$47$	13.6215			1.98690			0.993451	+	0.114259i	$0.0364492\pi$
$48$		0			0
$49$	4.33446	−	5.49658i	0.619209	−	0.785226i
$50$	3.18524	−	4.36053i	0.450461	−	0.616673i
$51$		0			0
$52$	4.28628	−	4.71155i	0.594400	−	0.653374i
$53$	−0.686610	+	0.396415i	−0.0943132	+	0.0544517i	−0.546415	−	0.837515i	$-0.684008\pi$
$53$	−0.686610	+	0.396415i	−0.0943132	+	0.0544517i	0.452102	+	0.891966i	$0.350674\pi$
$54$		0			0
$55$			1.63461i			0.220411i
$56$	−7.42049	+	0.967673i	−0.991604	+	0.129311i
$57$		0			0
$58$	−2.66525	+	1.17846i	−0.349964	+	0.154739i
$59$	−2.39274			−0.311508			−0.155754	−	0.987796i	$-0.549781\pi$
$59$	−2.39274			−0.311508			−0.155754	+	0.987796i	$0.549781\pi$
$60$		0			0
$61$	4.72586			0.605084			0.302542	−	0.953136i	$-0.402165\pi$
$61$	4.72586			0.605084			0.302542	+	0.953136i	$0.402165\pi$
$62$	0.123935	−	1.15075i	0.0157397	−	0.146145i
$63$		0			0
$64$	6.39898	+	4.80136i	0.799872	+	0.600170i
$65$		−	3.46192i		−	0.429398i
$66$		0			0
$67$		−	9.19521i		−	1.12337i	−0.827350	−	0.561687i	$-0.810153\pi$
$67$		−	9.19521i		−	1.12337i	0.827350	−	0.561687i	$-0.189847\pi$
$68$	11.8874	−	3.79513i	1.44156	−	0.460228i
$69$		0			0
$70$	−2.62938	+	3.10307i	−0.314271	+	0.370888i
$71$	12.1795			1.44545			0.722723	−	0.691138i	$-0.242890\pi$
$71$	12.1795			1.44545			0.722723	+	0.691138i	$0.242890\pi$
$72$		0			0
$73$	−4.02960	−	6.97947i	−0.471629	−	0.816886i	0.527844	−	0.849341i	$-0.323001\pi$
$73$	−4.02960	−	6.97947i	−0.471629	−	0.816886i	−0.999473	+	0.0324557i	$0.989667\pi$
$74$	7.27313	−	9.95678i	0.845484	−	1.15745i
$75$		0			0
$76$	−3.92862	−	3.57402i	−0.450644	−	0.409969i
$77$	−0.286478	+	3.96822i	−0.0326472	+	0.452220i
$78$		0			0
$79$		−	14.4294i		−	1.62343i	−0.584051	−	0.811717i	$-0.698533\pi$
$79$		−	14.4294i		−	1.62343i	0.584051	−	0.811717i	$-0.301467\pi$
$80$	4.32872	−	0.410095i	0.483965	−	0.0458501i
$81$		0			0
$82$	8.66581	+	6.33011i	0.956978	+	0.699044i
$83$	2.40508	+	4.16573i	0.263992	+	0.457248i	0.967299	−	0.253638i	$-0.0816273\pi$
$83$	2.40508	+	4.16573i	0.263992	+	0.457248i	−0.703307	+	0.710886i	$0.748294\pi$
$84$		0			0
$85$	3.39113	−	5.87360i	0.367819	−	0.637082i
$86$	−5.90069	+	2.60904i	−0.636288	+	0.281340i
$87$		0			0
$88$	3.18259	−	2.82156i	0.339265	−	0.300779i
$89$	−5.90946	−	3.41183i	−0.626401	−	0.361653i	0.152956	−	0.988233i	$-0.451121\pi$
$89$	−5.90946	−	3.41183i	−0.626401	−	0.361653i	−0.779357	+	0.626580i	$0.784454\pi$
$90$		0			0
$91$	0.606727	−	8.40422i	0.0636023	−	0.881002i
$92$	−1.97782	−	6.19509i	−0.206202	−	0.645883i
$93$		0			0
$94$	−19.1530	−	2.06276i	−1.97548	−	0.212757i
$95$	−2.88665			−0.296164
$96$		0			0
$97$	6.69603	+	11.5979i	0.679879	+	1.17758i	0.975017	+	0.222130i	$0.0713008\pi$
$97$	6.69603	+	11.5979i	0.679879	+	1.17758i	−0.295139	+	0.955454i	$0.595366\pi$
$98$	−6.92698	+	7.07227i	−0.699731	+	0.714407i
$99$		0			0
$100$	−5.13904	+	5.64892i	−0.513904	+	0.564892i
$101$	1.78555	+	1.03089i	0.177669	+	0.102577i	0.586197	−	0.810169i	$-0.300624\pi$
$101$	1.78555	+	1.03089i	0.177669	+	0.102577i	−0.408528	+	0.912746i	$0.633958\pi$
$102$		0			0
$103$	−2.53628	+	1.46432i	−0.249907	+	0.144284i	−0.619722	−	0.784822i	$-0.712755\pi$
$103$	−2.53628	+	1.46432i	−0.249907	+	0.144284i	0.369814	+	0.929106i	$0.379421\pi$
$104$	−6.74035	+	5.97574i	−0.660946	+	0.585969i
$105$		0			0
$106$	1.02546	−	0.453416i	0.0996016	−	0.0440396i
$107$	−5.47882	+	9.48960i	−0.529658	+	0.917394i	0.469744	+	0.882803i	$0.344346\pi$
$107$	−5.47882	+	9.48960i	−0.529658	+	0.917394i	−0.999402	+	0.0345915i	$0.988987\pi$
$108$		0			0
$109$	−7.27816	−	12.6061i	−0.697122	−	1.20745i	−0.969460	−	0.245248i	$-0.921130\pi$
$109$	−7.27816	−	12.6061i	−0.697122	−	1.20745i	0.272339	−	0.962201i	$-0.412203\pi$
$110$	0.247536	−	2.29840i	0.0236016	−	0.219144i
$111$		0			0
$112$	10.5804	−	0.236916i	0.999749	−	0.0223864i
$113$	13.0910	+	7.55811i	1.23150	+	0.711008i	0.967343	−	0.253472i	$-0.0815725\pi$
$113$	13.0910	+	7.55811i	1.23150	+	0.711008i	0.264158	+	0.964479i	$0.414906\pi$
$114$		0			0
$115$	−3.06100	−	1.76727i	−0.285440	−	0.164799i
$116$	3.92601	−	1.25340i	0.364521	−	0.116375i
$117$		0			0
$118$	3.36438	+	0.362341i	0.309717	+	0.0333562i
$119$	9.26176	−	13.6646i	0.849024	−	1.25263i
$120$		0			0
$121$	4.36937	+	7.56797i	0.397216	+	0.687997i
$122$	−6.64495	−	0.715655i	−0.601605	−	0.0647924i
$123$		0			0
$124$	−0.348524	+	1.59928i	−0.0312984	+	0.143619i
$125$			9.58580i			0.857380i
$126$		0			0
$127$			0.935305i			0.0829949i	0.999139	+	0.0414975i	$0.0132128\pi$
$127$			0.935305i			0.0829949i	−0.999139	+	0.0414975i	$0.986787\pi$
$128$	−8.27040	−	7.72013i	−0.731007	−	0.682370i
$129$		0			0
$130$	−0.524251	+	4.86774i	−0.0459799	+	0.426929i
$131$	−4.01972	−	6.96236i	−0.351204	−	0.608304i	0.635256	−	0.772301i	$-0.280894\pi$
$131$	−4.01972	−	6.96236i	−0.351204	−	0.608304i	−0.986461	+	0.163997i	$0.947561\pi$
$132$		0			0
$133$	−7.00768	−	0.505906i	−0.607643	−	0.0438676i
$134$	−1.39247	+	12.9292i	−0.120291	+	1.11691i
$135$		0			0
$136$	−17.2894	+	3.53611i	−1.48256	+	0.303219i
$137$	−14.1626	−	8.17679i	−1.20999	−	0.698590i	−0.247236	−	0.968955i	$-0.579522\pi$
$137$	−14.1626	−	8.17679i	−1.20999	−	0.698590i	−0.962758	+	0.270365i	$0.912856\pi$
$138$		0			0
$139$	20.0549	+	11.5787i	1.70104	+	0.982095i	0.944713	+	0.327899i	$0.106341\pi$
$139$	20.0549	+	11.5787i	1.70104	+	0.982095i	0.756325	+	0.654196i	$0.226993\pi$
$140$	4.16704	−	3.96500i	0.352179	−	0.335104i
$141$		0			0
$142$	−17.1254	−	1.84439i	−1.43713	−	0.154778i
$143$	2.39454	+	4.14747i	0.200242	+	0.346829i
$144$		0			0
$145$	1.11997	−	1.93985i	0.0930086	−	0.161096i
$146$	4.60902	+	10.4239i	0.381445	+	0.862691i
$147$		0			0
$148$	−11.7344	+	12.8987i	−0.964563	+	1.06026i
$149$	−7.59709	+	4.38618i	−0.622378	+	0.359330i	−0.777794	−	0.628519i	$-0.783661\pi$
$149$	−7.59709	+	4.38618i	−0.622378	+	0.359330i	0.155417	+	0.987849i	$0.450328\pi$
$150$		0			0
$151$	7.98995	+	4.61300i	0.650213	+	0.375401i	0.788538	−	0.614986i	$-0.210838\pi$
$151$	7.98995	+	4.61300i	0.650213	+	0.375401i	−0.138325	+	0.990387i	$0.544172\pi$
$152$	4.98274	+	5.62030i	0.404154	+	0.455866i
$153$		0			0
$154$	1.00373	−	5.53626i	0.0808832	−	0.446124i
$155$	0.444814	+	0.770441i	0.0357284	+	0.0618833i
$156$		0			0
$157$	4.54529			0.362753			0.181377	−	0.983414i	$-0.441945\pi$
$157$	4.54529			0.362753			0.181377	+	0.983414i	$0.441945\pi$
$158$	−2.18510	+	20.2889i	−0.173837	+	1.61410i
$159$		0			0
$160$	−6.14864	−	0.0788865i	−0.486092	−	0.00623652i
$161$	−7.12123	−	4.82673i	−0.561231	−	0.380399i
$162$		0			0
$163$	0.751164	+	0.433685i	0.0588357	+	0.0339688i	0.529129	−	0.848541i	$-0.322519\pi$
$163$	0.751164	+	0.433685i	0.0588357	+	0.0339688i	−0.470294	+	0.882510i	$0.655852\pi$
$164$	−11.2262	−	10.2130i	−0.876622	−	0.797498i
$165$		0			0
$166$	−2.75091	−	6.22157i	−0.213512	−	0.482887i
$167$	−2.24779	+	3.89329i	−0.173939	+	0.301272i	−0.939794	−	0.341742i	$-0.888983\pi$
$167$	−2.24779	+	3.89329i	−0.173939	+	0.301272i	0.765854	+	0.643014i	$0.222316\pi$
$168$		0			0
$169$	1.42864	+	2.47448i	0.109895	+	0.190345i
$170$	−5.65767	+	7.74524i	−0.433923	+	0.594033i
$171$		0			0
$172$	8.69196	−	2.77496i	0.662756	−	0.211588i
$173$			19.8897i			1.51219i	0.654464	+	0.756093i	$0.272894\pi$
$173$			19.8897i			1.51219i	−0.654464	+	0.756093i	$0.727106\pi$
$174$		0			0
$175$	−0.727436	+	10.0763i	−0.0549890	+	0.761693i
$176$	−4.90226	+	3.48540i	−0.369522	+	0.262722i
$177$		0			0
$178$	7.79252	+	5.69220i	0.584074	+	0.426649i
$179$	1.85338	+	3.21014i	0.138528	+	0.239937i	0.926940	−	0.375211i	$-0.122430\pi$
$179$	1.85338	+	3.21014i	0.138528	+	0.239937i	−0.788412	+	0.615148i	$0.789096\pi$
$180$		0			0
$181$	−20.5160			−1.52494			−0.762470	−	0.647024i	$-0.776013\pi$
$181$	−20.5160			−1.52494			−0.762470	+	0.647024i	$0.776013\pi$
$182$	−2.12579	+	11.7251i	−0.157574	+	0.869126i
$183$		0			0
$184$	1.84283	+	9.01032i	0.135855	+	0.664250i
$185$			9.47759i			0.696806i
$186$		0			0
$187$			9.38231i			0.686102i
$188$	26.6183	+	5.80082i	1.94134	+	0.423068i
$189$		0			0
$190$	4.05886	+	0.437136i	0.294461	+	0.0317132i
$191$	−16.3505			−1.18308			−0.591541	−	0.806275i	$-0.701480\pi$
$191$	−16.3505			−1.18308			−0.591541	+	0.806275i	$0.701480\pi$
$192$		0			0
$193$	−11.5081			−0.828369			−0.414184	−	0.910193i	$-0.635933\pi$
$193$	−11.5081			−0.828369			−0.414184	+	0.910193i	$0.635933\pi$
$194$	−7.65886	−	17.3216i	−0.549874	−	1.24361i
$195$		0			0
$196$	10.8109	−	8.89521i	0.772206	−	0.635372i
$197$			11.6386i			0.829217i	0.910000	+	0.414608i	$0.136081\pi$
$197$			11.6386i			0.829217i	−0.910000	+	0.414608i	$0.863919\pi$
$198$		0			0
$199$	−14.1464	+	8.16741i	−1.00281	+	0.578972i	−0.909078	−	0.416625i	$-0.863213\pi$
$199$	−14.1464	+	8.16741i	−1.00281	+	0.578972i	−0.0937311	+	0.995598i	$0.529879\pi$
$200$	8.08135	−	7.16462i	0.571438	−	0.506615i
$201$		0			0
$202$	−2.35452	−	1.71990i	−0.165663	−	0.121012i
$203$	3.05884	−	4.51293i	0.214688	−	0.316746i
$204$		0			0
$205$	−8.24874			−0.576117
$206$	3.78797	−	1.67488i	0.263920	−	0.116694i
$207$		0			0
$208$	10.3824	−	7.38166i	0.719891	−	0.511826i
$209$	3.45828	−	1.99664i	0.239214	−	0.138110i
$210$		0			0
$211$	−19.4336	−	11.2200i	−1.33786	−	0.772416i	−0.351373	−	0.936235i	$-0.614285\pi$
$211$	−19.4336	−	11.2200i	−1.33786	−	0.772416i	−0.986490	+	0.163820i	$0.947619\pi$
$212$	−1.51055	+	0.482250i	−0.103745	+	0.0331211i
$213$		0			0
$214$	9.14072	−	12.5135i	0.624847	−	0.855404i
$215$	2.47955	−	4.29471i	0.169104	−	0.292897i
$216$		0			0
$217$	0.944815	+	1.94830i	0.0641382	+	0.132259i
$218$	8.32470	+	18.8274i	0.563820	+	1.27516i
$219$		0			0
$220$	−0.696111	+	3.19425i	−0.0469318	+	0.215357i
$221$		−	19.8706i		−	1.33664i
$222$		0			0
$223$	−15.3730	+	8.87563i	−1.02946	+	0.594356i	−0.916829	−	0.399281i	$-0.869260\pi$
$223$	−15.3730	+	8.87563i	−1.02946	+	0.594356i	−0.112627	+	0.993637i	$0.535926\pi$
$224$	−14.9127	−	1.26910i	−0.996398	−	0.0847953i
$225$		0			0
$226$	−17.2625	−	12.6098i	−1.14829	−	0.838789i
$227$	−6.69388	+	11.5941i	−0.444288	+	0.769530i	−0.998002	−	0.0631769i	$-0.979877\pi$
$227$	−6.69388	+	11.5941i	−0.444288	+	0.769530i	0.553714	+	0.832707i	$0.313210\pi$
$228$		0			0
$229$	6.53564	+	11.3201i	0.431887	+	0.748051i	0.997036	−	0.0769385i	$-0.0245145\pi$
$229$	6.53564	+	11.3201i	0.431887	+	0.748051i	−0.565149	+	0.824989i	$0.691181\pi$
$230$	4.03640	+	2.94847i	0.266152	+	0.194416i
$231$		0			0
$232$	−5.71011	+	1.16786i	−0.374887	+	0.0766735i
$233$	5.07304	+	2.92892i	0.332346	+	0.191880i	0.656882	−	0.753993i	$-0.271875\pi$
$233$	5.07304	+	2.92892i	0.332346	+	0.191880i	−0.324536	+	0.945873i	$0.605208\pi$
$234$		0			0
$235$	12.8232	−	7.40346i	0.836492	−	0.482949i
$236$	−4.67573	−	1.01896i	−0.304364	−	0.0663288i
$237$		0			0
$238$	−15.0921	+	17.8109i	−0.978274	+	1.15451i
$239$	−4.28685	+	7.42504i	−0.277293	+	0.480286i	−0.970711	−	0.240250i	$-0.922771\pi$
$239$	−4.28685	+	7.42504i	−0.277293	+	0.480286i	0.693418	+	0.720536i	$0.256104\pi$
$240$		0			0
$241$	−1.38778	+	2.40370i	−0.0893945	+	0.154836i	−0.907255	−	0.420580i	$-0.861827\pi$
$241$	−1.38778	+	2.40370i	−0.0893945	+	0.154836i	0.817861	+	0.575416i	$0.195160\pi$
$242$	−4.99765	−	11.3029i	−0.321261	−	0.726576i
$243$		0			0
$244$	9.23497	+	2.01254i	0.591209	+	0.128840i
$245$	1.09296	−	7.53027i	0.0698269	−	0.481091i
$246$		0			0
$247$	−7.32423	+	4.22865i	−0.466030	+	0.269062i
$248$	0.732239	−	2.19594i	0.0464972	−	0.139442i
$249$		0			0
$250$	1.45161	−	13.4784i	0.0918081	−	0.852450i
$251$	−5.34591			−0.337431			−0.168716	−	0.985665i	$-0.553962\pi$
$251$	−5.34591			−0.337431			−0.168716	+	0.985665i	$0.553962\pi$
$252$		0			0
$253$	4.88955			0.307403
$254$	0.141637	−	1.31512i	0.00888709	−	0.0825178i
$255$		0			0
$256$	10.4598	+	12.1076i	0.653736	+	0.756722i
$257$	1.90518	−	1.09996i	0.118842	−	0.0686135i	−0.439401	−	0.898291i	$-0.644809\pi$
$257$	1.90518	−	1.09996i	0.118842	−	0.0686135i	0.558243	+	0.829678i	$0.311476\pi$
$258$		0			0
$259$	−1.66102	+	23.0080i	−0.103211	+	1.42965i
$260$	1.47428	−	6.76506i	0.0914311	−	0.419551i
$261$		0			0
$262$	4.59772	+	10.3984i	0.284048	+	0.642413i
$263$	3.12661	−	5.41544i	0.192795	−	0.333931i	−0.753381	−	0.657585i	$-0.771578\pi$
$263$	3.12661	−	5.41544i	0.192795	−	0.333931i	0.946175	+	0.323654i	$0.104911\pi$
$264$		0			0
$265$	−0.430913	+	0.746363i	−0.0264708	+	0.0458487i
$266$	9.77677	+	1.77255i	0.599452	+	0.108682i
$267$		0			0
$268$	3.91584	−	17.9687i	0.239198	−	1.09761i
$269$	7.71725	−	4.45555i	0.470529	−	0.271660i	−0.245932	−	0.969287i	$-0.579094\pi$
$269$	7.71725	−	4.45555i	0.470529	−	0.271660i	0.716461	+	0.697627i	$0.245761\pi$
$270$		0			0
$271$	2.17320	+	1.25470i	0.132013	+	0.0762175i	0.564552	−	0.825398i	$-0.309049\pi$
$271$	2.17320	+	1.25470i	0.132013	+	0.0762175i	−0.432539	+	0.901615i	$0.642382\pi$
$272$	24.8459	−	2.35386i	1.50650	−	0.142723i
$273$		0			0
$274$	18.6756	+	13.6419i	1.12823	+	0.824140i
$275$	−2.87094	−	4.97261i	−0.173124	−	0.299860i
$276$		0			0
$277$	−14.7998	+	25.6340i	−0.889233	+	1.54020i	−0.0484501	+	0.998826i	$0.515428\pi$
$277$	−14.7998	+	25.6340i	−0.889233	+	1.54020i	−0.840783	+	0.541372i	$0.817905\pi$
$278$	−26.4455	−	19.3176i	−1.58610	−	1.15860i
$279$		0			0
$280$	−6.45964	+	4.94409i	−0.386037	+	0.295466i
$281$	21.1188	−	12.1929i	1.25984	−	0.727370i	0.286798	−	0.957991i	$-0.407409\pi$
$281$	21.1188	−	12.1929i	1.25984	−	0.727370i	0.973044	+	0.230621i	$0.0740757\pi$
$282$		0			0
$283$		−	15.2575i		−	0.906965i	−0.891265	−	0.453482i	$-0.850182\pi$
$283$		−	15.2575i		−	0.906965i	0.891265	−	0.453482i	$-0.149818\pi$
$284$	23.8005	+	5.18674i	1.41230	+	0.307776i
$285$		0			0
$286$	−2.73886	−	6.19430i	−0.161952	−	0.366276i
$287$	−20.0248	−	1.44565i	−1.18203	−	0.0853342i
$288$		0			0
$289$	10.9643	−	18.9907i	0.644959	−	1.11710i
$290$	−1.86853	+	2.55799i	−0.109724	+	0.150210i
$291$		0			0
$292$	−4.90213	−	15.3549i	−0.286875	−	0.898576i
$293$	−10.4046	−	6.00710i	−0.607843	−	0.350939i	0.164278	−	0.986414i	$-0.447471\pi$
$293$	−10.4046	−	6.00710i	−0.607843	−	0.350939i	−0.772121	+	0.635476i	$0.780804\pi$
$294$		0			0
$295$	−2.25250	+	1.30048i	−0.131146	+	0.0757170i
$296$	18.4529	−	16.3596i	1.07255	−	0.950882i
$297$		0			0
$298$	11.3463	−	5.01687i	0.657276	−	0.290620i
$299$	−10.3555			−0.598874
$300$		0			0
$301$	6.77209	−	9.99136i	0.390337	−	0.575892i
$302$	−10.5360	−	7.69621i	−0.606277	−	0.442867i
$303$		0			0
$304$	−6.15504	−	8.65716i	−0.353016	−	0.496522i
$305$	4.44888	−	2.56856i	0.254742	−	0.147076i
$306$		0			0
$307$			26.0671i			1.48773i	0.668330	+	0.743865i	$0.267010\pi$
$307$			26.0671i			1.48773i	−0.668330	+	0.743865i	$0.732990\pi$
$308$	−2.24971	+	7.63243i	−0.128189	+	0.434898i
$309$		0			0
$310$	−0.508775	−	1.15066i	−0.0288965	−	0.0653533i
$311$	5.17871			0.293658			0.146829	−	0.989162i	$-0.453093\pi$
$311$	5.17871			0.293658			0.146829	+	0.989162i	$0.453093\pi$
$312$		0			0
$313$	11.5696			0.653955			0.326977	−	0.945032i	$-0.393970\pi$
$313$	11.5696			0.653955			0.326977	+	0.945032i	$0.393970\pi$
$314$	−6.39105	−	0.688310i	−0.360668	−	0.0388436i
$315$		0			0
$316$	6.14486	−	28.1970i	0.345675	−	1.58620i
$317$			23.4995i			1.31986i	0.751326	+	0.659931i	$0.229414\pi$
$317$			23.4995i			1.31986i	−0.751326	+	0.659931i	$0.770586\pi$
$318$		0			0
$319$			3.09865i			0.173491i
$320$	8.63354	+	1.04203i	0.482630	+	0.0582514i
$321$		0			0
$322$	9.28210	+	7.86517i	0.517271	+	0.438309i
$323$	−16.5687			−0.921907
$324$		0			0
$325$	6.08031	+	10.5314i	0.337275	+	0.584178i
$326$	−0.990524	−	0.723548i	−0.0548601	−	0.0400736i
$327$		0			0
$328$	14.2384	+	16.0603i	0.786186	+	0.886781i
$329$	32.4273	−	15.7254i	1.78778	−	0.866971i
$330$		0			0
$331$		−	15.1472i		−	0.832565i	−0.909235	−	0.416283i	$-0.863333\pi$
$331$		−	15.1472i		−	0.832565i	0.909235	−	0.416283i	$-0.136667\pi$
$332$	2.92586	+	9.16462i	0.160577	+	0.502974i
$333$		0			0
$334$	3.75016	−	5.13389i	0.205199	−	0.280914i
$335$	−4.99771	−	8.65629i	−0.273054	−	0.472944i
$336$		0			0
$337$	13.2530	−	22.9549i	0.721938	−	1.25043i	−0.238284	−	0.971196i	$-0.576585\pi$
$337$	13.2530	−	22.9549i	0.721938	−	1.25043i	0.960222	−	0.279238i	$-0.0900817\pi$
$338$	−1.63407	−	3.69567i	−0.0888815	−	0.201018i
$339$		0			0
$340$	9.12803	−	10.0337i	0.495037	−	0.544153i
$341$	−1.06580	−	0.615339i	−0.0577162	−	0.0333225i
$342$		0			0
$343$	3.97304	−	18.0891i	0.214524	−	0.976719i
$344$	−12.6418	+	2.58556i	−0.681602	+	0.139404i
$345$		0			0
$346$	3.01197	−	27.9666i	0.161925	−	1.50349i
$347$	20.7082			1.11168			0.555839	−	0.831290i	$-0.312397\pi$
$347$	20.7082			1.11168			0.555839	+	0.831290i	$0.312397\pi$
$348$		0			0
$349$	−2.18348	−	3.78189i	−0.116879	−	0.202440i	0.801650	−	0.597793i	$-0.203956\pi$
$349$	−2.18348	−	3.78189i	−0.116879	−	0.202440i	−0.918529	+	0.395353i	$0.870622\pi$
$350$	2.54872	−	14.0579i	0.136235	−	0.751425i
$351$		0			0
$352$	7.42079	−	4.15838i	0.395529	−	0.221643i
$353$	−3.12319	−	1.80317i	−0.166231	−	0.0959732i	0.414577	−	0.910014i	$-0.363930\pi$
$353$	−3.12319	−	1.80317i	−0.166231	−	0.0959732i	−0.580807	+	0.814041i	$0.697263\pi$
$354$		0			0
$355$	11.4657	−	6.61973i	0.608537	−	0.351339i
$356$	−10.0949	−	9.18376i	−0.535030	−	0.486738i
$357$		0			0
$358$	−2.11988	−	4.79439i	−0.112039	−	0.253391i
$359$	−8.74493	+	15.1467i	−0.461540	+	0.799410i	−0.999038	−	0.0438545i	$-0.986036\pi$
$359$	−8.74493	+	15.1467i	−0.461540	+	0.799410i	0.537498	+	0.843265i	$0.319370\pi$
$360$		0			0
$361$	−5.97403	−	10.3473i	−0.314423	−	0.544596i
$362$	28.8471	+	3.10681i	1.51617	+	0.163290i
$363$		0			0
$364$	4.76462	−	16.1646i	0.249734	−	0.847256i
$365$	−7.58686	−	4.38028i	−0.397115	−	0.229274i
$366$		0			0
$367$	1.07569	+	0.621050i	0.0561506	+	0.0324185i	0.527812	−	0.849361i	$-0.323012\pi$
$367$	1.07569	+	0.621050i	0.0561506	+	0.0324185i	−0.471662	+	0.881779i	$0.656346\pi$
$368$	−1.22670	−	12.9483i	−0.0639463	−	0.674978i
$369$		0			0
$370$	1.43523	−	13.3263i	0.0746139	−	0.692800i
$371$	−1.17690	+	1.73636i	−0.0611015	+	0.0901475i
$372$		0			0
$373$	−0.814411	−	1.41060i	−0.0421686	−	0.0730381i	0.844171	−	0.536074i	$-0.180093\pi$
$373$	−0.814411	−	1.41060i	−0.0421686	−	0.0730381i	−0.886339	+	0.463036i	$0.846760\pi$
$374$	1.42080	−	13.1923i	0.0734677	−	0.682157i
$375$		0			0
$376$	−36.5491	−	12.1873i	−1.88487	−	0.628514i
$377$		−	6.56258i		−	0.337990i
$378$		0			0
$379$			30.3716i			1.56008i	0.625727	+	0.780042i	$0.284802\pi$
$379$			30.3716i			1.56008i	−0.625727	+	0.780042i	$0.715198\pi$
$380$	−5.64090	−	1.22930i	−0.289372	−	0.0630617i
$381$		0			0
$382$	22.9902	+	2.47602i	1.17628	+	0.126684i
$383$	13.3081	+	23.0503i	0.680012	+	1.17781i	0.974977	+	0.222307i	$0.0713586\pi$
$383$	13.3081	+	23.0503i	0.680012	+	1.17781i	−0.294965	+	0.955508i	$0.595308\pi$
$384$		0			0
$385$	1.88709	+	3.89135i	0.0961749	+	0.198322i
$386$	16.1813	+	1.74271i	0.823606	+	0.0887016i
$387$		0			0
$388$	8.14592	+	25.5153i	0.413546	+	1.29534i
$389$	−24.8177	−	14.3285i	−1.25831	−	0.726483i	−0.285561	−	0.958361i	$-0.592180\pi$
$389$	−24.8177	−	14.3285i	−1.25831	−	0.726483i	−0.972745	+	0.231877i	$0.925513\pi$
$390$		0			0
$391$	−17.5695	−	10.1437i	−0.888526	−	0.512991i
$392$	−16.5480	+	10.8703i	−0.835802	+	0.549031i
$393$		0			0
$394$	1.76248	−	16.3648i	0.0887924	−	0.824449i
$395$	−7.84256	−	13.5837i	−0.394602	−	0.683470i
$396$		0			0
$397$	−13.0065	+	22.5280i	−0.652778	+	1.13065i	0.329667	+	0.944097i	$0.393063\pi$
$397$	−13.0065	+	22.5280i	−0.652778	+	1.13065i	−0.982446	+	0.186548i	$0.940270\pi$
$398$	21.1278	−	9.34181i	1.05904	−	0.468263i
$399$		0			0
$400$	−12.4480	+	8.85025i	−0.622401	+	0.442513i
$401$	−18.8023	+	10.8555i	−0.938942	+	0.542099i	−0.889629	−	0.456685i	$-0.849037\pi$
$401$	−18.8023	+	10.8555i	−0.938942	+	0.542099i	−0.0493138	+	0.998783i	$0.515703\pi$
$402$		0			0
$403$	2.25724	+	1.30322i	0.112441	+	0.0649178i
$404$	3.05019	+	2.77488i	0.151753	+	0.138056i
$405$		0			0
$406$	−4.98439	+	5.88234i	−0.247371	+	0.291936i
$407$	−6.55546	−	11.3544i	−0.324942	−	0.562816i
$408$		0			0
$409$	25.5894			1.26531			0.632657	−	0.774432i	$-0.281964\pi$
$409$	25.5894			1.26531			0.632657	+	0.774432i	$0.281964\pi$
$410$	11.5984	+	1.24914i	0.572805	+	0.0616906i
$411$		0			0
$412$	−5.57983	+	1.78139i	−0.274899	+	0.0877629i
$413$	−5.69613	+	2.76231i	−0.280288	+	0.135924i
$414$		0			0
$415$	4.52825	+	2.61439i	0.222283	+	0.128335i
$416$	−15.7164	+	8.80697i	−0.770558	+	0.431797i
$417$		0			0
$418$	−5.16498	+	2.28374i	−0.252628	+	0.111701i
$419$	−3.64856	+	6.31949i	−0.178244	+	0.308727i	−0.941279	−	0.337629i	$-0.890375\pi$
$419$	−3.64856	+	6.31949i	−0.178244	+	0.308727i	0.763035	+	0.646357i	$0.223708\pi$
$420$		0			0
$421$	−6.81198	−	11.7987i	−0.331996	−	0.575034i	0.650907	−	0.759157i	$-0.274389\pi$
$421$	−6.81198	−	11.7987i	−0.331996	−	0.575034i	−0.982903	+	0.184124i	$0.941055\pi$
$422$	25.6261	+	18.7191i	1.24746	+	0.911233i
$423$		0			0
$424$	2.19698	−	0.449336i	0.106695	−	0.0218217i
$425$			23.8239i			1.15563i
$426$		0			0
$427$	11.2504	−	5.45580i	0.544443	−	0.264025i
$428$	−14.7476	+	16.2108i	−0.712851	+	0.783577i
$429$		0			0
$430$	−4.13682	+	5.66323i	−0.199495	+	0.273105i
$431$	−6.04210	−	10.4652i	−0.291038	−	0.504092i	0.683018	−	0.730402i	$-0.260667\pi$
$431$	−6.04210	−	10.4652i	−0.291038	−	0.504092i	−0.974055	+	0.226310i	$0.927334\pi$
$432$		0			0
$433$	22.6142			1.08677			0.543386	−	0.839483i	$-0.317142\pi$
$433$	22.6142			1.08677			0.543386	+	0.839483i	$0.317142\pi$
$434$	−1.03345	−	2.88254i	−0.0496072	−	0.138366i
$435$		0			0
$436$	−8.85410	−	27.7336i	−0.424035	−	1.32820i
$437$			8.63471i			0.413054i
$438$		0			0
$439$			25.0718i			1.19661i	0.801267	+	0.598307i	$0.204159\pi$
$439$			25.0718i			1.19661i	−0.801267	+	0.598307i	$0.795841\pi$
$440$	1.46251	−	4.38597i	0.0697223	−	0.209093i
$441$		0			0
$442$	−3.00909	+	27.9397i	−0.143128	+	1.32896i
$443$	−14.7400			−0.700318			−0.350159	−	0.936690i	$-0.613872\pi$
$443$	−14.7400			−0.700318			−0.350159	+	0.936690i	$0.613872\pi$
$444$		0			0
$445$	−7.41748			−0.351622
$446$	22.9598	−	10.1519i	1.08718	−	0.480705i
$447$		0			0
$448$	20.7763	+	4.04275i	0.981590	+	0.191002i
$449$		−	36.4636i		−	1.72082i	−0.509601	−	0.860411i	$-0.670207\pi$
$449$		−	36.4636i		−	1.72082i	0.509601	−	0.860411i	$-0.329793\pi$
$450$		0			0
$451$	9.88221	−	5.70549i	0.465335	−	0.268661i
$452$	22.3630	+	20.3445i	1.05187	+	0.956924i
$453$		0			0
$454$	11.1679	−	15.2886i	0.524135	−	0.717531i
$455$	−3.99663	−	8.24142i	−0.187365	−	0.386364i
$456$		0			0
$457$	16.4740			0.770620			0.385310	−	0.922787i	$-0.374094\pi$
$457$	16.4740			0.770620			0.385310	+	0.922787i	$0.374094\pi$
$458$	−7.47541	−	16.9067i	−0.349303	−	0.789996i
$459$		0			0
$460$	−5.22901	−	4.75704i	−0.243804	−	0.221798i
$461$	8.43340	−	4.86902i	0.392782	−	0.226773i	−0.290583	−	0.956850i	$-0.593849\pi$
$461$	8.43340	−	4.86902i	0.392782	−	0.226773i	0.683365	+	0.730077i	$0.260516\pi$
$462$		0			0
$463$	−3.07391	−	1.77472i	−0.142857	−	0.0824784i	0.426868	−	0.904314i	$-0.359617\pi$
$463$	−3.07391	−	1.77472i	−0.142857	−	0.0824784i	−0.569725	+	0.821836i	$0.692950\pi$
$464$	8.20573	−	0.777397i	0.380942	−	0.0360898i
$465$		0			0
$466$	−6.68957	−	4.88653i	−0.309889	−	0.226364i
$467$	4.49751	−	7.78991i	0.208120	−	0.360474i	−0.743002	−	0.669289i	$-0.766599\pi$
$467$	4.49751	−	7.78991i	0.208120	−	0.360474i	0.951122	+	0.308815i	$0.0999322\pi$
$468$		0			0
$469$	−10.6155	−	21.8901i	−0.490177	−	1.01079i
$470$	−19.1516	+	8.46802i	−0.883396	+	0.390601i
$471$		0			0
$472$	6.42015	+	2.14081i	0.295512	+	0.0985387i
$473$			6.86023i			0.315434i
$474$		0			0
$475$	8.78139	−	5.06994i	0.402918	−	0.232625i
$476$	23.9179	−	22.7582i	1.09627	−	1.04312i
$477$		0			0
$478$	7.15206	−	9.79104i	0.327128	−	0.447832i
$479$	−8.48898	+	14.7033i	−0.387871	+	0.671813i	−0.992163	−	0.124950i	$-0.960123\pi$
$479$	−8.48898	+	14.7033i	−0.387871	+	0.671813i	0.604292	+	0.796763i	$0.293456\pi$
$480$		0			0
$481$	13.8837	+	24.0473i	0.633042	+	1.09646i
$482$	2.31533	−	3.16964i	0.105460	−	0.144373i
$483$		0			0
$484$	5.31547	+	16.6496i	0.241612	+	0.756799i
$485$	12.6072	+	7.27875i	0.572462	+	0.330511i
$486$		0			0
$487$	−0.873051	+	0.504056i	−0.0395617	+	0.0228410i	−0.519650	−	0.854379i	$-0.673938\pi$
$487$	−0.873051	+	0.504056i	−0.0395617	+	0.0228410i	0.480089	+	0.877220i	$0.340604\pi$
$488$	−12.6804	−	4.22829i	−0.574013	−	0.191405i
$489$		0			0
$490$	−2.67714	+	10.4227i	−0.120941	+	0.470848i
$491$	0.979328	−	1.69625i	0.0441965	−	0.0765505i	−0.843081	−	0.537787i	$-0.819261\pi$
$491$	0.979328	−	1.69625i	0.0441965	−	0.0765505i	0.887277	+	0.461236i	$0.152594\pi$
$492$		0			0
$493$	6.42839	−	11.1343i	0.289520	−	0.501463i
$494$	10.9388	−	4.83669i	0.492161	−	0.217613i
$495$		0			0
$496$	−1.36213	+	2.97679i	−0.0611613	+	0.133662i
$497$	28.9945	−	14.0607i	1.30058	−	0.630710i
$498$		0			0
$499$	−23.7580	+	13.7167i	−1.06355	+	0.614043i	−0.926413	−	0.376508i	$-0.877125\pi$
$499$	−23.7580	+	13.7167i	−1.06355	+	0.614043i	−0.137141	+	0.990552i	$0.543791\pi$
$500$	−4.08218	+	18.7319i	−0.182561	+	0.837718i
$501$		0			0
$502$	7.51680	+	0.809552i	0.335491	+	0.0361321i
$503$	25.0298			1.11602			0.558011	−	0.829834i	$-0.311565\pi$
$503$	25.0298			1.11602			0.558011	+	0.829834i	$0.311565\pi$
$504$		0			0
$505$	2.24120			0.0997321
$506$	−6.87511	−	0.740443i	−0.305636	−	0.0329167i
$507$		0			0
$508$	−0.398306	+	1.82771i	−0.0176720	+	0.0810917i
$509$	−22.3828	+	12.9227i	−0.992100	+	0.572789i	−0.905901	−	0.423488i	$-0.860805\pi$
$509$	−22.3828	+	12.9227i	−0.992100	+	0.572789i	−0.0861990	+	0.996278i	$0.527472\pi$
$510$		0			0
$511$	−17.6503	−	11.9633i	−0.780805	−	0.529225i
$512$	−12.8738	−	18.6082i	−0.568948	−	0.822374i
$513$		0			0
$514$	−2.84542	+	1.25812i	−0.125506	+	0.0554934i
$515$	−1.59176	+	2.75700i	−0.0701412	+	0.121488i
$516$		0			0
$517$	−10.2417	+	17.7391i	−0.450428	+	0.780164i
$518$	5.81971	−	32.0996i	0.255704	−	1.41037i
$519$		0			0
$520$	−3.09742	+	9.28897i	−0.135831	+	0.407348i
$521$	−22.8154	+	13.1725i	−0.999562	+	0.577097i	−0.908119	−	0.418713i	$-0.862481\pi$
$521$	−22.8154	+	13.1725i	−0.999562	+	0.577097i	−0.0914433	+	0.995810i	$0.529148\pi$
$522$		0			0
$523$	−15.0902	−	8.71233i	−0.659848	−	0.380964i	0.132371	−	0.991200i	$-0.457741\pi$
$523$	−15.0902	−	8.71233i	−0.659848	−	0.380964i	−0.792219	+	0.610237i	$0.791074\pi$
$524$	−4.89011	−	15.3172i	−0.213625	−	0.669136i
$525$		0			0
$526$	−5.21635	+	7.14109i	−0.227444	+	0.311366i
$527$	2.55313	+	4.42216i	0.111216	+	0.192632i
$528$		0			0
$529$	6.21363	−	10.7623i	0.270158	−	0.467927i
$530$	0.718923	−	0.984193i	0.0312280	−	0.0427506i
$531$		0			0
$532$	−13.4785	−	3.97288i	−0.584368	−	0.172246i
$533$	−20.9294	+	12.0836i	−0.906551	+	0.523398i
$534$		0			0
$535$			11.9112i			0.514968i
$536$	−8.22707	+	24.6725i	−0.355355	+	1.06569i
$537$		0			0
$538$	−11.5258	+	5.09622i	−0.496913	+	0.219714i
$539$	3.89914	+	9.77744i	0.167948	+	0.421144i
$540$		0			0
$541$	−9.52540	+	16.4985i	−0.409529	+	0.709325i	−0.994837	−	0.101486i	$-0.967640\pi$
$541$	−9.52540	+	16.4985i	−0.409529	+	0.709325i	0.585308	+	0.810811i	$0.300974\pi$
$542$	−2.86570	−	2.09331i	−0.123092	−	0.0899152i
$543$		0			0
$544$	−35.2918	−	0.452791i	−1.51312	−	0.0194132i
$545$	−13.7032	−	7.91154i	−0.586980	−	0.338893i
$546$		0			0
$547$	4.36785	−	2.52178i	0.186756	−	0.107824i	−0.403707	−	0.914888i	$-0.632279\pi$
$547$	4.36785	−	2.52178i	0.186756	−	0.107824i	0.590463	+	0.807065i	$0.298945\pi$
$548$	−24.1935	−	22.0098i	−1.03350	−	0.940212i
$549$		0			0
$550$	3.28375	+	7.42666i	0.140020	+	0.316674i
$551$	−5.47207			−0.233118
$552$		0			0
$553$	−16.6581	−	34.3505i	−0.708374	−	1.46073i
$554$	24.6916	−	33.8023i	1.04904	−	1.43612i
$555$		0			0
$556$	34.2592	+	31.1669i	1.45291	+	1.32177i
$557$	13.8266	−	7.98281i	0.585853	−	0.338242i	−0.177603	−	0.984102i	$-0.556834\pi$
$557$	13.8266	−	7.98281i	0.585853	−	0.338242i	0.763456	+	0.645860i	$0.223501\pi$
$558$		0			0
$559$		−	14.5292i		−	0.614518i
$560$	9.83149	−	5.97358i	0.415456	−	0.252430i
$561$		0			0
$562$	−31.5412	+	13.9462i	−1.33049	+	0.588284i
$563$	16.6909			0.703436			0.351718	−	0.936106i	$-0.385598\pi$
$563$	16.6909			0.703436			0.351718	+	0.936106i	$0.385598\pi$
$564$		0			0
$565$	16.4317			0.691288
$566$	−2.31050	+	21.4533i	−0.0971177	+	0.901750i
$567$		0			0
$568$	−32.6800	−	10.8972i	−1.37122	−	0.457236i
$569$		−	33.9617i		−	1.42375i	−0.702307	−	0.711874i	$-0.747847\pi$
$569$		−	33.9617i		−	1.42375i	0.702307	−	0.711874i	$-0.252153\pi$
$570$		0			0
$571$			31.2885i			1.30938i	0.755895	+	0.654692i	$0.227202\pi$
$571$			31.2885i			1.30938i	−0.755895	+	0.654692i	$0.772798\pi$
$572$	2.91303	+	9.12445i	0.121800	+	0.381512i
$573$		0			0
$574$	27.9376	+	5.06514i	1.16609	+	0.211415i
$575$	12.4157			0.517772
$576$		0			0
$577$	10.1541	+	17.5874i	0.422720	+	0.732172i	0.996204	−	0.0870440i	$-0.0277421\pi$
$577$	10.1541	+	17.5874i	0.422720	+	0.732172i	−0.573485	+	0.819216i	$0.694409\pi$
$578$	−18.2925	+	25.0422i	−0.760870	+	1.04162i
$579$		0			0
$580$	3.01468	−	3.31378i	0.125178	−	0.137597i
$581$	10.5347	+	7.14035i	0.437052	+	0.296232i
$582$		0			0
$583$		−	1.19222i		−	0.0493765i
$584$	4.56755	+	22.3326i	0.189007	+	0.924128i
$585$		0			0
$586$	13.7201	+	10.0221i	0.566770	+	0.414009i
$587$	4.77427	+	8.26929i	0.197055	+	0.341310i	0.947572	−	0.319541i	$-0.103529\pi$
$587$	4.77427	+	8.26929i	0.197055	+	0.341310i	−0.750517	+	0.660851i	$0.770195\pi$
$588$		0			0
$589$	1.08666	−	1.88215i	0.0447750	−	0.0775526i
$590$	3.36414	−	1.48748i	0.138499	−	0.0612386i
$591$		0			0
$592$	−28.4236	+	20.2085i	−1.16820	+	0.830566i
$593$	−9.29829	−	5.36837i	−0.381835	−	0.220453i	0.296781	−	0.954945i	$-0.404087\pi$
$593$	−9.29829	−	5.36837i	−0.381835	−	0.220453i	−0.678616	+	0.734493i	$0.737420\pi$
$594$		0			0
$595$	1.29208	−	17.8976i	0.0529702	−	0.733729i
$596$	−16.7136	+	5.33592i	−0.684617	+	0.218568i
$597$		0			0
$598$	14.5607	+	1.56817i	0.595430	+	0.0641273i
$599$	−29.7414			−1.21520			−0.607600	−	0.794243i	$-0.707868\pi$
$599$	−29.7414			−1.21520			−0.607600	+	0.794243i	$0.707868\pi$
$600$		0			0
$601$	18.4639	+	31.9804i	0.753159	+	1.30451i	0.946284	+	0.323336i	$0.104804\pi$
$601$	18.4639	+	31.9804i	0.753159	+	1.30451i	−0.193125	+	0.981174i	$0.561862\pi$
$602$	−11.0351	+	13.0232i	−0.449759	+	0.530784i
$603$		0			0
$604$	13.6490	+	12.4170i	0.555369	+	0.505241i
$605$	8.22657	+	4.74962i	0.334458	+	0.193099i
$606$		0			0
$607$	24.7329	−	14.2796i	1.00388	−	0.579589i	0.0944847	−	0.995526i	$-0.469880\pi$
$607$	24.7329	−	14.2796i	1.00388	−	0.579589i	0.909393	+	0.415937i	$0.136546\pi$
$608$	7.34351	+	13.1048i	0.297819	+	0.531468i
$609$		0			0
$610$	−6.64447	+	2.93790i	−0.269027	+	0.118952i
$611$	21.6907	−	37.5693i	0.877510	−	1.51989i
$612$		0			0
$613$	0.0951404	+	0.164788i	0.00384268	+	0.00665572i	0.867940	−	0.496668i	$-0.165443\pi$
$613$	0.0951404	+	0.164788i	0.00384268	+	0.00665572i	−0.864098	+	0.503324i	$0.832110\pi$
$614$	3.94745	−	36.6525i	0.159306	−	1.47918i
$615$		0			0
$616$	4.31909	−	10.3912i	0.174021	−	0.418671i
$617$	18.7268	+	10.8120i	0.753915	+	0.435273i	0.827107	−	0.562045i	$-0.189985\pi$
$617$	18.7268	+	10.8120i	0.753915	+	0.435273i	−0.0731920	+	0.997318i	$0.523319\pi$
$618$		0			0
$619$	5.72420	+	3.30487i	0.230075	+	0.132834i	0.610607	−	0.791934i	$-0.290926\pi$
$619$	5.72420	+	3.30487i	0.230075	+	0.132834i	−0.380532	+	0.924768i	$0.624259\pi$
$620$	0.541130	+	1.69497i	0.0217323	+	0.0680718i
$621$		0			0
$622$	−7.28169	−	0.784232i	−0.291969	−	0.0314448i
$623$	−18.0068	−	1.29997i	−0.721428	−	0.0520822i
$624$		0			0
$625$	−4.33594	−	7.51007i	−0.173438	−	0.300403i
$626$	−16.2679	−	1.75203i	−0.650195	−	0.0700254i
$627$		0			0
$628$	8.88211	+	1.93564i	0.354435	+	0.0772405i
$629$			54.3992i			2.16904i
$630$		0			0
$631$			10.8732i			0.432854i	0.976299	+	0.216427i	$0.0694403\pi$
$631$			10.8732i			0.432854i	−0.976299	+	0.216427i	$0.930560\pi$
$632$	−12.9102	+	38.7168i	−0.513538	+	1.54007i
$633$		0			0
$634$	3.55861	−	33.0422i	0.141331	−	1.31227i
$635$	0.508350	+	0.880488i	0.0201733	+	0.0349411i
$636$		0			0
$637$	−8.25793	−	20.7075i	−0.327191	−	0.820460i
$638$	0.469241	−	4.35696i	0.0185774	−	0.172494i
$639$		0			0
$640$	−11.9817	−	2.77259i	−0.473617	−	0.109596i
$641$	−22.6874	−	13.0986i	−0.896097	−	0.517362i	−0.0201649	−	0.999797i	$-0.506419\pi$
$641$	−22.6874	−	13.0986i	−0.896097	−	0.517362i	−0.875932	+	0.482435i	$0.839752\pi$
$642$		0			0
$643$	−19.2089	−	11.0902i	−0.757524	−	0.437356i	0.0708823	−	0.997485i	$-0.477419\pi$
$643$	−19.2089	−	11.0902i	−0.757524	−	0.437356i	−0.828406	+	0.560128i	$0.810752\pi$
$644$	−11.8603	−	12.4647i	−0.467363	−	0.491178i
$645$		0			0
$646$	23.2970	+	2.50906i	0.916607	+	0.0987177i
$647$	2.18326	+	3.78151i	0.0858327	+	0.148667i	0.905746	−	0.423822i	$-0.139312\pi$
$647$	2.18326	+	3.78151i	0.0858327	+	0.148667i	−0.819913	+	0.572488i	$0.805978\pi$
$648$		0			0
$649$	1.79904	−	3.11602i	0.0706183	−	0.122315i
$650$	−6.95461	−	15.7288i	−0.272782	−	0.616934i
$651$		0			0
$652$	1.28319	+	1.16737i	0.0502536	+	0.0457176i
$653$	30.3258	−	17.5086i	1.18674	−	0.685166i	0.229177	−	0.973385i	$-0.426396\pi$
$653$	30.3258	−	17.5086i	1.18674	−	0.685166i	0.957565	+	0.288219i	$0.0930631\pi$
$654$		0			0
$655$	−7.56826	−	4.36954i	−0.295716	−	0.170732i
$656$	−17.5883	−	24.7383i	−0.686709	−	0.965867i
$657$		0			0
$658$	−47.9768	+	17.2007i	−1.87033	+	0.670552i
$659$	13.6116	+	23.5760i	0.530233	+	0.918390i	0.999378	+	0.0352689i	$0.0112288\pi$
$659$	13.6116	+	23.5760i	0.530233	+	0.918390i	−0.469145	+	0.883121i	$0.655438\pi$
$660$		0			0
$661$	−15.2386			−0.592714			−0.296357	−	0.955077i	$-0.595772\pi$
$661$	−15.2386			−0.592714			−0.296357	+	0.955077i	$0.595772\pi$
$662$	−2.29380	+	21.2982i	−0.0891510	+	0.827778i
$663$		0			0
$664$	−2.72616	−	13.3293i	−0.105796	−	0.517277i
$665$	−6.87194	+	3.33251i	−0.266482	+	0.129229i
$666$		0			0
$667$	−5.80259	−	3.35013i	−0.224677	−	0.129717i
$668$	−6.05047	+	6.65078i	−0.234100	+	0.257326i
$669$		0			0
$670$	5.71634	+	12.9283i	0.220841	+	0.499463i
$671$	−3.55325	+	6.15441i	−0.137172	+	0.237589i
$672$		0			0
$673$	−6.84127	−	11.8494i	−0.263712	−	0.456762i	0.703514	−	0.710682i	$-0.251613\pi$
$673$	−6.84127	−	11.8494i	−0.263712	−	0.456762i	−0.967225	+	0.253920i	$0.918280\pi$
$674$	−22.1110	+	30.2695i	−0.851683	+	1.16594i
$675$		0			0
$676$	1.73798	+	5.44386i	0.0668456	+	0.209379i
$677$			39.5753i			1.52100i	0.649337	+	0.760500i	$0.275046\pi$
$677$			39.5753i			1.52100i	−0.649337	+	0.760500i	$0.724954\pi$
$678$		0			0
$679$	29.3297	+	19.8795i	1.12557	+	0.762906i
$680$	−14.3542	+	12.7259i	−0.550459	+	0.488016i
$681$		0			0
$682$	1.40542	+	1.02662i	0.0538162	+	0.0393111i
$683$	−11.3382	−	19.6384i	−0.433846	−	0.751443i	0.563355	−	0.826215i	$-0.309510\pi$
$683$	−11.3382	−	19.6384i	−0.433846	−	0.751443i	−0.997201	+	0.0747721i	$0.976177\pi$
$684$		0			0
$685$	−17.7768			−0.679215
$686$	−8.32572	+	24.8331i	−0.317877	+	0.948132i
$687$		0			0
$688$	18.1670	−	1.72111i	0.692610	−	0.0656167i
$689$			2.52497i			0.0961938i
$690$		0			0
$691$		−	21.0689i		−	0.801497i	−0.916188	−	0.400749i	$-0.868750\pi$
$691$		−	21.0689i		−	0.801497i	0.916188	−	0.400749i	$-0.131250\pi$
$692$	−8.47017	+	38.8672i	−0.321987	+	1.47751i
$693$		0			0
$694$	−29.1175	−	3.13593i	−1.10529	−	0.119038i
$695$	25.1727			0.954856
$696$		0			0
$697$	−47.3459			−1.79335
$698$	2.49744	+	5.64831i	0.0945296	+	0.213792i
$699$		0			0
$700$	−5.71255	+	19.3806i	−0.215914	+	0.732517i
$701$		−	20.6957i		−	0.781667i	−0.920461	−	0.390833i	$-0.872187\pi$
$701$		−	20.6957i		−	0.781667i	0.920461	−	0.390833i	$-0.127813\pi$
$702$		0			0
$703$	20.0513	−	11.5766i	0.756250	−	0.436621i
$704$	−11.0640	+	4.72327i	−0.416989	+	0.178015i
$705$		0			0
$706$	4.11840	+	3.00837i	0.154998	+	0.113221i
$707$	5.44078	+	0.392787i	0.204622	+	0.0147723i
$708$		0			0
$709$	−21.2009			−0.796216			−0.398108	−	0.917339i	$-0.630333\pi$
$709$	−21.2009			−0.796216			−0.398108	+	0.917339i	$0.630333\pi$
$710$	−17.1242	+	7.57159i	−0.642659	+	0.284157i
$711$		0			0
$712$	12.8036	+	14.4418i	0.479834	+	0.541230i
$713$	2.30459	−	1.33056i	0.0863076	−	0.0498297i
$714$		0			0
$715$	4.50840	+	2.60293i	0.168605	+	0.0973439i
$716$	2.25469	+	7.06233i	0.0842616	+	0.263932i
$717$		0			0
$718$	14.5898	−	19.9732i	0.544487	−	0.745393i
$719$	−8.43001	+	14.6012i	−0.314386	+	0.544533i	−0.979307	−	0.202381i	$-0.935132\pi$
$719$	−8.43001	+	14.6012i	−0.314386	+	0.544533i	0.664921	+	0.746914i	$0.268465\pi$
$720$		0			0
$721$	−4.34736	+	6.41399i	−0.161904	+	0.238869i
$722$	6.83305	+	15.4539i	0.254300	+	0.575133i
$723$		0			0
$724$	−40.0910	−	8.73687i	−1.48997	−	0.324703i
$725$			7.86822i			0.292218i
$726$		0			0
$727$	6.79800	−	3.92483i	0.252124	−	0.145564i	−0.368613	−	0.929583i	$-0.620167\pi$
$727$	6.79800	−	3.92483i	0.252124	−	0.145564i	0.620736	+	0.784019i	$0.286834\pi$
$728$	−9.14732	+	22.0072i	−0.339022	+	0.815643i
$729$		0			0
$730$	10.0044	+	7.30794i	0.370281	+	0.270479i
$731$	14.2321	−	24.6507i	0.526392	−	0.911738i
$732$		0			0
$733$	1.38987	+	2.40732i	0.0513360	+	0.0889165i	0.890551	−	0.454882i	$-0.150319\pi$
$733$	1.38987	+	2.40732i	0.0513360	+	0.0889165i	−0.839216	+	0.543799i	$0.816985\pi$
$734$	−1.41846	−	1.03614i	−0.0523563	−	0.0382447i
$735$		0			0
$736$	−0.235970	+	18.3922i	−0.00869797	+	0.677944i
$737$	11.9748	+	6.91364i	0.441097	+	0.254667i
$738$		0			0
$739$	−31.6800	+	18.2905i	−1.16537	+	0.672826i	−0.952585	−	0.304273i	$-0.901587\pi$
$739$	−31.6800	+	18.2905i	−1.16537	+	0.672826i	−0.212784	+	0.977099i	$0.568253\pi$
$740$	−4.03610	+	18.5205i	−0.148370	+	0.680827i
$741$		0			0
$742$	1.91776	−	2.26325i	0.0704032	−	0.0830865i
$743$	11.7085	−	20.2798i	0.429545	−	0.743993i	−0.567288	−	0.823519i	$-0.692007\pi$
$743$	11.7085	−	20.2798i	0.429545	−	0.743993i	0.996833	+	0.0795261i	$0.0253407\pi$
$744$		0			0
$745$	−4.76789	+	8.25822i	−0.174682	+	0.302558i
$746$	0.931516	+	2.10675i	0.0341052	+	0.0771336i
$747$		0			0
$748$	−3.99552	+	18.3343i	−0.146091	+	0.670368i
$749$	−2.08753	+	28.9160i	−0.0762768	+	1.05657i
$750$		0			0
$751$	16.5753	−	9.56973i	0.604840	−	0.349205i	−0.166103	−	0.986108i	$-0.553119\pi$
$751$	16.5753	−	9.56973i	0.604840	−	0.349205i	0.770943	+	0.636904i	$0.219785\pi$
$752$	49.5454	+	22.6712i	1.80674	+	0.826732i
$753$		0			0
$754$	−0.993797	+	9.22753i	−0.0361920	+	0.336047i
$755$	10.0289			0.364989
$756$		0			0
$757$	−18.7437			−0.681252			−0.340626	−	0.940199i	$-0.610639\pi$
$757$	−18.7437			−0.681252			−0.340626	+	0.940199i	$0.610639\pi$
$758$	4.59929	−	42.7050i	0.167054	−	1.55111i
$759$		0			0
$760$	7.74541	+	2.58272i	0.280956	+	0.0936850i
$761$	18.0513	−	10.4219i	0.654358	−	0.377794i	−0.135766	−	0.990741i	$-0.543349\pi$
$761$	18.0513	−	10.4219i	0.654358	−	0.377794i	0.790124	+	0.612947i	$0.210016\pi$
$762$		0			0
$763$	−31.8796	−	21.6078i	−1.15412	−	0.782255i
$764$	−31.9512	−	6.96299i	−1.15595	−	0.251912i
$765$		0			0
$766$	−15.2217	−	34.4259i	−0.549982	−	1.24386i
$767$	−3.81015	+	6.59937i	−0.137576	+	0.238289i
$768$		0			0
$769$	−7.95585	+	13.7799i	−0.286895	+	0.496917i	−0.973067	−	0.230522i	$-0.925957\pi$
$769$	−7.95585	+	13.7799i	−0.286895	+	0.496917i	0.686172	+	0.727440i	$0.259290\pi$
$770$	−2.06412	−	5.75733i	−0.0743857	−	0.207480i
$771$		0			0
$772$	−22.4883	−	4.90079i	−0.809372	−	0.176383i
$773$	−11.4250	+	6.59625i	−0.410930	+	0.237251i	−0.691189	−	0.722674i	$-0.742913\pi$
$773$	−11.4250	+	6.59625i	−0.410930	+	0.237251i	0.280259	+	0.959924i	$0.409580\pi$
$774$		0			0
$775$	−2.70632	−	1.56249i	−0.0972138	−	0.0561264i
$776$	−7.58994	−	37.1102i	−0.272463	−	1.33218i
$777$		0			0
$778$	32.7259	+	23.9053i	1.17328	+	0.857045i
$779$	10.0756	+	17.4515i	0.360997	+	0.625265i
$780$		0			0
$781$	−9.15748	+	15.8612i	−0.327680	+	0.567559i
$782$	23.1680	+	16.9235i	0.828487	+	0.605185i
$783$		0			0
$784$	24.9140	−	12.7786i	0.889787	−	0.456377i
$785$	4.27889	−	2.47042i	0.152720	−	0.0881731i
$786$		0			0
$787$			22.5200i			0.802750i	0.915914	+	0.401375i	$0.131468\pi$
$787$			22.5200i			0.802750i	−0.915914	+	0.401375i	$0.868532\pi$
$788$	−4.95638	+	22.7434i	−0.176564	+	0.810201i
$789$		0			0
$790$	8.97025	+	20.2874i	0.319147	+	0.721795i
$791$	39.8900	+	2.87978i	1.41832	+	0.102393i
$792$		0			0
$793$	7.52537	−	13.0343i	0.267234	−	0.462863i
$794$	21.6997	−	29.7065i	0.770095	−	1.05425i
$795$		0			0
$796$	−31.1221	+	9.93590i	−1.10309	+	0.352168i
$797$	−25.0813	−	14.4807i	−0.888424	−	0.512932i	−0.0149975	−	0.999888i	$-0.504774\pi$
$797$	−25.0813	−	14.4807i	−0.888424	−	0.512932i	−0.873427	+	0.486956i	$0.838107\pi$
$798$		0			0
$799$	73.6021	−	42.4942i	2.60386	−	1.50334i
$800$	18.8432	−	10.5591i	0.666206	−	0.373322i
$801$		0			0
$802$	28.0815	−	12.4164i	0.991592	−	0.438440i
$803$	12.1190			0.427671
$804$		0			0
$805$	−9.32725	−	0.673363i	−0.328742	−	0.0237329i
$806$	−2.97651	−	2.17425i	−0.104843	−	0.0765847i
$807$		0			0
$808$	−3.86861	−	4.36361i	−0.136097	−	0.153511i
$809$	−6.13234	+	3.54051i	−0.215601	+	0.124478i	−0.603912	−	0.797051i	$-0.706392\pi$
$809$	−6.13234	+	3.54051i	−0.215601	+	0.124478i	0.388310	+	0.921529i	$0.373059\pi$
$810$		0			0
$811$		−	50.7206i		−	1.78104i	−0.454943	−	0.890521i	$-0.650340\pi$
$811$		−	50.7206i		−	1.78104i	0.454943	−	0.890521i	$-0.349660\pi$
$812$	7.89925	−	7.51625i	0.277209	−	0.263769i
$813$		0			0
$814$	7.49808	+	16.9579i	0.262808	+	0.594375i
$815$	0.942853			0.0330267
$816$		0			0
$817$	−12.1148			−0.423845
$818$	−35.9808	−	3.87510i	−1.25804	−	0.135490i
$819$		0			0
$820$	−16.1192	−	3.51278i	−0.562905	−	0.122672i
$821$		−	13.1816i		−	0.460042i	−0.973186	−	0.230021i	$-0.926121\pi$
$821$		−	13.1816i		−	0.460042i	0.973186	−	0.230021i	$-0.0738795\pi$
$822$		0			0
$823$		−	39.6894i		−	1.38349i	−0.722144	−	0.691743i	$-0.756843\pi$
$823$		−	39.6894i		−	1.38349i	0.722144	−	0.691743i	$-0.243157\pi$
$824$	8.11547	−	1.65981i	0.282716	−	0.0578222i
$825$		0			0
$826$	8.42754	−	3.02144i	0.293232	−	0.105129i
$827$	−23.2354			−0.807973			−0.403987	−	0.914765i	$-0.632376\pi$
$827$	−23.2354			−0.807973			−0.403987	+	0.914765i	$0.632376\pi$
$828$		0			0
$829$	3.93228	+	6.81091i	0.136574	+	0.236553i	0.926198	−	0.377039i	$-0.123058\pi$
$829$	3.93228	+	6.81091i	0.136574	+	0.236553i	−0.789624	+	0.613591i	$0.789724\pi$
$830$	−5.97119	−	4.36177i	−0.207263	−	0.151399i
$831$		0			0
$832$	23.4322	−	10.0033i	0.812365	−	0.346803i
$833$	6.27337	−	43.2221i	0.217359	−	1.49756i
$834$		0			0
$835$			4.88681i			0.169115i
$836$	7.60823	−	2.42897i	0.263136	−	0.0840076i
$837$		0			0
$838$	6.08716	−	8.33321i	0.210278	−	0.287866i
$839$	25.5164	+	44.1957i	0.880925	+	1.52581i	0.850314	+	0.526275i	$0.176412\pi$
$839$	25.5164	+	44.1957i	0.880925	+	1.52581i	0.0306106	+	0.999531i	$0.490255\pi$
$840$		0			0
$841$	−12.3769	+	21.4375i	−0.426790	+	0.739223i
$842$	7.79149	+	17.6215i	0.268512	+	0.607277i
$843$		0			0
$844$	−33.1978	−	30.2013i	−1.14271	−	1.03957i
$845$	2.68982	+	1.55297i	0.0925326	+	0.0534237i
$846$		0			0
$847$	19.1386	+	12.9720i	0.657610	+	0.445724i
$848$	−3.15718	+	0.299106i	−0.108418	+	0.0102713i
$849$		0			0
$850$	3.60775	−	33.4984i	0.123745	−	1.14899i
$851$	28.3499			0.971823
$852$		0			0
$853$	−25.0238	−	43.3425i	−0.856799	−	1.48402i	−0.874966	−	0.484185i	$-0.839116\pi$
$853$	−25.0238	−	43.3425i	−0.856799	−	1.48402i	0.0181661	−	0.999835i	$-0.494217\pi$
$854$	−16.6451	+	5.96762i	−0.569584	+	0.204208i
$855$		0			0
$856$	23.1912	−	20.5604i	0.792658	−	0.702740i
$857$	34.6977	+	20.0327i	1.18525	+	0.684305i	0.957223	−	0.289350i	$-0.0934392\pi$
$857$	34.6977	+	20.0327i	1.18525	+	0.684305i	0.228027	+	0.973655i	$0.426772\pi$
$858$		0			0
$859$	35.4399	−	20.4612i	1.20919	−	0.698128i	0.246610	−	0.969115i	$-0.420683\pi$
$859$	35.4399	−	20.4612i	1.20919	−	0.698128i	0.962583	+	0.270987i	$0.0873501\pi$
$860$	6.67431	−	7.33651i	0.227592	−	0.250173i
$861$		0			0
$862$	6.91090	+	15.6299i	0.235386	+	0.532358i
$863$	15.2070	−	26.3392i	0.517651	−	0.896598i	−0.482139	−	0.876095i	$-0.660140\pi$
$863$	15.2070	−	26.3392i	0.517651	−	0.896598i	0.999790	−	0.0205031i	$-0.00652679\pi$
$864$		0			0
$865$	10.8103	+	18.7240i	0.367561	+	0.636635i
$866$	−31.7975	−	3.42456i	−1.08052	−	0.116371i
$867$		0			0
$868$	1.01660	+	4.20959i	0.0345057	+	0.142883i
$869$	18.7912	+	10.8491i	0.637447	+	0.368030i
$870$		0			0
$871$	−25.3612	−	14.6423i	−0.859331	−	0.496135i
$872$	8.24979	+	40.3365i	0.279373	+	1.36597i
$873$		0			0
$874$	1.30759	−	12.1411i	0.0442298	−	0.410679i
$875$	11.0664	+	22.8199i	0.374112	+	0.771453i
$876$		0			0
$877$	13.6065	+	23.5672i	0.459460	+	0.795808i	0.998932	−	0.0461951i	$-0.0147096\pi$
$877$	13.6065	+	23.5672i	0.459460	+	0.795808i	−0.539472	+	0.842003i	$0.681376\pi$
$878$	3.79672	−	35.2531i	0.128133	−	1.18973i
$879$		0			0
$880$	−2.72059	+	5.94556i	−0.0917111	+	0.200425i
$881$		−	18.9137i		−	0.637219i	−0.947886	−	0.318610i	$-0.896784\pi$
$881$		−	18.9137i		−	0.637219i	0.947886	−	0.318610i	$-0.103216\pi$
$882$		0			0
$883$		−	4.60566i		−	0.154993i	−0.996993	−	0.0774964i	$-0.975307\pi$
$883$		−	4.60566i		−	0.154993i	0.996993	−	0.0774964i	$-0.0246926\pi$
$884$	8.46204	−	38.8299i	0.284609	−	1.30599i
$885$		0			0
$886$	20.7256	+	2.23213i	0.696291	+	0.0749900i
$887$	−8.42370	−	14.5903i	−0.282840	−	0.489894i	0.689243	−	0.724530i	$-0.257943\pi$
$887$	−8.42370	−	14.5903i	−0.282840	−	0.489894i	−0.972083	+	0.234637i	$0.924610\pi$
$888$		0			0
$889$	1.07977	+	2.22658i	0.0362143	+	0.0746772i
$890$	10.4296	+	1.12326i	0.349601	+	0.0376517i
$891$		0			0
$892$	−33.8208	+	10.7975i	−1.13240	+	0.361526i
$893$	−31.3264	−	18.0863i	−1.04830	−	0.605235i
$894$		0			0
$895$	3.48950	+	2.01467i	0.116641	+	0.0673429i
$896$	−28.6010	−	8.83068i	−0.955493	−	0.295012i
$897$		0			0
$898$	−5.52182	+	51.2708i	−0.184265	+	1.71093i
$899$	0.843213	+	1.46049i	0.0281227	+	0.0487100i
$900$		0			0
$901$	−2.47334	+	4.28395i	−0.0823990	+	0.142719i
$902$	−14.7592	+	6.52589i	−0.491428	+	0.217289i
$903$		0			0
$904$	−28.3634	−	31.9925i	−0.943351	−	1.06406i
$905$	−19.3136	+	11.1507i	−0.642004	+	0.370661i
$906$		0			0
$907$	27.5335	+	15.8965i	0.914234	+	0.527833i	0.881791	−	0.471640i	$-0.156338\pi$
$907$	27.5335	+	15.8965i	0.914234	+	0.527833i	0.0324433	+	0.999474i	$0.489671\pi$
$908$	−18.0182	+	19.8059i	−0.597955	+	0.657281i
$909$		0			0
$910$	4.37156	+	12.1933i	0.144916	+	0.404205i
$911$	−16.0911	−	27.8705i	−0.533121	−	0.923392i	−0.999252	−	0.0386763i	$-0.987686\pi$
$911$	−16.0911	−	27.8705i	−0.533121	−	0.923392i	0.466131	−	0.884716i	$-0.345647\pi$
$912$		0			0
$913$	−7.23328			−0.239387
$914$	−23.1638	−	2.49472i	−0.766190	−	0.0825179i
$915$		0			0
$916$	7.95080	+	24.9042i	0.262702	+	0.822857i
$917$	−17.6071	−	11.9340i	−0.581436	−	0.394094i
$918$		0			0
$919$	12.8002	+	7.39019i	0.422239	+	0.243780i	0.696035	−	0.718008i	$-0.254946\pi$
$919$	12.8002	+	7.39019i	0.422239	+	0.243780i	−0.273796	+	0.961788i	$0.588279\pi$
$920$	6.63204	+	7.48064i	0.218652	+	0.246629i
$921$		0			0
$922$	−12.5954	+	5.56915i	−0.414807	+	0.183410i
$923$	19.3945	−	33.5922i	0.638377	−	1.10570i
$924$		0			0
$925$	−16.6459	−	28.8315i	−0.547313	−	0.947975i
$926$	4.05342	+	2.96090i	0.133204	+	0.0973013i
$927$		0			0
$928$	−11.6557	−	0.149541i	−0.382616	−	0.00490893i
$929$		−	50.5984i		−	1.66008i	−0.557703	−	0.830041i	$-0.688317\pi$
$929$		−	50.5984i		−	1.66008i	0.557703	−	0.830041i	$-0.311683\pi$
$930$		0			0
$931$	−17.2665	+	6.88570i	−0.565887	+	0.225670i
$932$	8.66611	+	7.88390i	0.283868	+	0.258246i
$933$		0			0
$934$	−7.50353	+	10.2722i	−0.245523	+	0.336116i
$935$	5.09940	+	8.83242i	0.166768	+	0.288851i
$936$		0			0
$937$	32.7292			1.06922			0.534608	−	0.845100i	$-0.320459\pi$
$937$	32.7292			1.06922			0.534608	+	0.845100i	$0.320459\pi$
$938$	11.6113	+	32.3868i	0.379123	+	1.05747i
$939$		0			0
$940$	28.2110	−	9.00653i	0.920143	−	0.293761i
$941$			8.32574i			0.271411i	0.990749	+	0.135706i	$0.0433302\pi$
$941$			8.32574i			0.271411i	−0.990749	+	0.135706i	$0.956670\pi$
$942$		0			0
$943$			24.6741i			0.803500i
$944$	−8.70308	−	3.98238i	−0.283261	−	0.129616i
$945$		0			0
$946$	1.03887	−	9.64605i	0.0337766	−	0.313620i
$947$	51.7068			1.68024			0.840122	−	0.542397i	$-0.182483\pi$
$947$	51.7068			1.68024			0.840122	+	0.542397i	$0.182483\pi$
$948$		0			0
$949$	−25.6666			−0.833175
$950$	−13.1151	+	5.79895i	−0.425511	+	0.188143i
$951$		0			0
$952$	−37.0769	+	28.3779i	−1.20167	+	0.919734i
$953$			23.0749i			0.747468i	0.927536	+	0.373734i	$0.121923\pi$
$953$			23.0749i			0.747468i	−0.927536	+	0.373734i	$0.878077\pi$
$954$		0			0
$955$	−15.3922	+	8.88672i	−0.498081	+	0.287567i
$956$	−11.5391	+	12.6839i	−0.373201	+	0.410228i
$957$		0			0
$958$	14.1628	−	19.3886i	0.457579	−	0.626417i
$959$	−43.1552	−	3.11551i	−1.39355	−	0.100605i
$960$		0			0
$961$	30.3302			0.978394
$962$	−15.8801	−	35.9149i	−0.511994	−	1.15794i
$963$		0			0
$964$	−3.73553	+	4.10616i	−0.120313	+	0.132250i
$965$	−10.8336	+	6.25478i	−0.348746	+	0.201348i
$966$		0			0
$967$	−30.3476	−	17.5212i	−0.975913	−	0.563444i	−0.0748791	−	0.997193i	$-0.523857\pi$
$967$	−30.3476	−	17.5212i	−0.975913	−	0.563444i	−0.901034	+	0.433749i	$0.857190\pi$
$968$	−4.95268	−	24.2156i	−0.159185	−	0.778319i
$969$		0			0
$970$	−16.6245	−	12.1437i	−0.533779	−	0.389910i
$971$	−6.33039	+	10.9646i	−0.203152	+	0.351869i	−0.949542	−	0.313639i	$-0.898452\pi$
$971$	−6.33039	+	10.9646i	−0.203152	+	0.351869i	0.746390	+	0.665508i	$0.231785\pi$
$972$		0			0
$973$	61.1098	+	4.41171i	1.95909	+	0.141433i
$974$	1.30391	−	0.576535i	0.0417801	−	0.0184734i
$975$		0			0
$976$	17.1893	+	7.86555i	0.550217	+	0.251770i
$977$			20.1911i			0.645970i	0.946404	+	0.322985i	$0.104686\pi$
$977$			20.1911i			0.645970i	−0.946404	+	0.322985i	$0.895314\pi$
$978$		0			0
$979$	8.88634	−	5.13053i	0.284009	−	0.163972i
$980$	5.34262	−	14.2497i	0.170664	−	0.455191i
$981$		0			0
$982$	−1.63389	+	2.23676i	−0.0521394	+	0.0713779i
$983$	21.9010	−	37.9337i	0.698534	−	1.20990i	−0.270441	−	0.962736i	$-0.587170\pi$
$983$	21.9010	−	37.9337i	0.698534	−	1.20990i	0.968975	−	0.247159i	$-0.0794971\pi$
$984$		0			0
$985$	6.32573	+	10.9565i	0.201554	+	0.349103i
$986$	−10.7250	+	14.6823i	−0.341552	+	0.467578i
$987$		0			0
$988$	−16.1133	+	5.14427i	−0.512633	+	0.163661i
$989$	−12.8466	−	7.41698i	−0.408498	−	0.235846i
$990$		0			0
$991$	−24.9914	+	14.4288i	−0.793878	+	0.458346i	−0.841326	−	0.540528i	$-0.818224\pi$
$991$	−24.9914	+	14.4288i	−0.793878	+	0.458346i	0.0474481	+	0.998874i	$0.484891\pi$
$992$	2.36605	−	3.97933i	0.0751221	−	0.126344i
$993$		0			0
$994$	−42.8980	+	15.3798i	−1.36064	+	0.487818i
$995$	−8.87818	+	15.3775i	−0.281457	+	0.487498i
$996$		0			0
$997$	11.8621	−	20.5457i	0.375676	−	0.650690i	−0.614752	−	0.788720i	$-0.710744\pi$
$997$	11.8621	−	20.5457i	0.375676	−	0.650690i	0.990428	+	0.138031i	$0.0440772\pi$
$998$	35.4829	−	15.6890i	1.12319	−	0.496628i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bb.a.611.3		88
3.2	odd	2		252.2.bb.a.23.42	yes	88
4.3	odd	2	inner	756.2.bb.a.611.42		88
7.4	even	3		756.2.o.a.179.31		88
9.2	odd	6		756.2.o.a.359.17		88
9.7	even	3		252.2.o.a.191.28	yes	88
12.11	even	2		252.2.bb.a.23.3	yes	88
21.11	odd	6		252.2.o.a.95.14	✓	88
28.11	odd	6		756.2.o.a.179.17		88
36.7	odd	6		252.2.o.a.191.14	yes	88
36.11	even	6		756.2.o.a.359.31		88
63.11	odd	6	inner	756.2.bb.a.683.42		88
63.25	even	3		252.2.bb.a.11.3	yes	88
84.11	even	6		252.2.o.a.95.28	yes	88
252.11	even	6	inner	756.2.bb.a.683.3		88
252.151	odd	6		252.2.bb.a.11.42	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.o.a.95.14	✓	88	21.11	odd	6
252.2.o.a.95.28	yes	88	84.11	even	6
252.2.o.a.191.14	yes	88	36.7	odd	6
252.2.o.a.191.28	yes	88	9.7	even	3
252.2.bb.a.11.3	yes	88	63.25	even	3
252.2.bb.a.11.42	yes	88	252.151	odd	6
252.2.bb.a.23.3	yes	88	12.11	even	2
252.2.bb.a.23.42	yes	88	3.2	odd	2
756.2.o.a.179.17		88	28.11	odd	6
756.2.o.a.179.31		88	7.4	even	3
756.2.o.a.359.17		88	9.2	odd	6
756.2.o.a.359.31		88	36.11	even	6
756.2.bb.a.611.3		88	1.1	even	1	trivial
756.2.bb.a.611.42		88	4.3	odd	2	inner
756.2.bb.a.683.3		88	252.11	even	6	inner
756.2.bb.a.683.42		88	63.11	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bb (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.40608 - 0.151434i) q^{2} +(1.95414 + 0.425857i) q^{4} +(0.941391 - 0.543513i) q^{5} +(2.38059 - 1.15446i) q^{7} +(-2.68319 - 0.894712i) q^{8} +O(q^{10})\)	\(q+(-1.40608 - 0.151434i) q^{2} +(1.95414 + 0.425857i) q^{4} +(0.941391 - 0.543513i) q^{5} +(2.38059 - 1.15446i) q^{7} +(-2.68319 - 0.894712i) q^{8} +(-1.40598 + 0.621665i) q^{10} +(-0.751874 + 1.30228i) q^{11} +(1.59238 - 2.75809i) q^{13} +(-3.52214 + 1.26276i) q^{14} +(3.63729 + 1.66436i) q^{16} +(5.40337 - 3.11964i) q^{17} +(-2.29977 - 1.32777i) q^{19} +(2.07106 - 0.661199i) q^{20} +(1.25441 - 1.71726i) q^{22} +(-1.62579 - 2.81595i) q^{23} +(-1.90919 + 3.30681i) q^{25} +(-2.65669 + 3.63696i) q^{26} +(5.14364 - 1.24217i) q^{28} +(1.78455 - 1.03031i) q^{29} +0.818407i q^{31} +(-4.86229 - 2.89104i) q^{32} +(-8.07001 + 3.56822i) q^{34} +(1.61361 - 2.38068i) q^{35} +(-4.35941 + 7.55073i) q^{37} +(3.03260 + 2.21522i) q^{38} +(-3.01222 + 0.616071i) q^{40} +(-6.57171 - 3.79418i) q^{41} +(3.95088 - 2.28104i) q^{43} +(-2.02385 + 2.22465i) q^{44} +(1.85956 + 4.20565i) q^{46} +13.6215 q^{47} +(4.33446 - 5.49658i) q^{49} +(3.18524 - 4.36053i) q^{50} +(4.28628 - 4.71155i) q^{52} +(-0.686610 + 0.396415i) q^{53} +1.63461i q^{55} +(-7.42049 + 0.967673i) q^{56} +(-2.66525 + 1.17846i) q^{58} -2.39274 q^{59} +4.72586 q^{61} +(0.123935 - 1.15075i) q^{62} +(6.39898 + 4.80136i) q^{64} -3.46192i q^{65} -9.19521i q^{67} +(11.8874 - 3.79513i) q^{68} +(-2.62938 + 3.10307i) q^{70} +12.1795 q^{71} +(-4.02960 - 6.97947i) q^{73} +(7.27313 - 9.95678i) q^{74} +(-3.92862 - 3.57402i) q^{76} +(-0.286478 + 3.96822i) q^{77} -14.4294i q^{79} +(4.32872 - 0.410095i) q^{80} +(8.66581 + 6.33011i) q^{82} +(2.40508 + 4.16573i) q^{83} +(3.39113 - 5.87360i) q^{85} +(-5.90069 + 2.60904i) q^{86} +(3.18259 - 2.82156i) q^{88} +(-5.90946 - 3.41183i) q^{89} +(0.606727 - 8.40422i) q^{91} +(-1.97782 - 6.19509i) q^{92} +(-19.1530 - 2.06276i) q^{94} -2.88665 q^{95} +(6.69603 + 11.5979i) q^{97} +(-6.92698 + 7.07227i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) \) 88 * q - 2 * q^4 + 6 * q^5	\( 88 q - 2 q^{4} + 6 q^{5} + 2 q^{10} - 4 q^{13} + 18 q^{14} - 2 q^{16} + 6 q^{20} - 6 q^{22} + 30 q^{25} - 6 q^{26} + 24 q^{29} - 4 q^{34} - 4 q^{37} + 45 q^{38} - 4 q^{40} + 12 q^{41} - 57 q^{44} - 6 q^{46} - 2 q^{49} - 9 q^{50} - 7 q^{52} + 24 q^{56} + 5 q^{58} - 4 q^{61} - 8 q^{64} + 12 q^{68} - 27 q^{70} - 4 q^{73} - 51 q^{74} - 6 q^{76} + 30 q^{77} + 87 q^{80} - 4 q^{82} - 14 q^{85} - 81 q^{86} + 9 q^{88} + 60 q^{89} - 24 q^{92} - 18 q^{94} - 4 q^{97} - 57 q^{98}+O(q^{100}) \) 88 * q - 2 * q^4 + 6 * q^5 + 2 * q^10 - 4 * q^13 + 18 * q^14 - 2 * q^16 + 6 * q^20 - 6 * q^22 + 30 * q^25 - 6 * q^26 + 24 * q^29 - 4 * q^34 - 4 * q^37 + 45 * q^38 - 4 * q^40 + 12 * q^41 - 57 * q^44 - 6 * q^46 - 2 * q^49 - 9 * q^50 - 7 * q^52 + 24 * q^56 + 5 * q^58 - 4 * q^61 - 8 * q^64 + 12 * q^68 - 27 * q^70 - 4 * q^73 - 51 * q^74 - 6 * q^76 + 30 * q^77 + 87 * q^80 - 4 * q^82 - 14 * q^85 - 81 * q^86 + 9 * q^88 + 60 * q^89 - 24 * q^92 - 18 * q^94 - 4 * q^97 - 57 * q^98

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