LMFDB - Embedded newform 756.2.bb.a.683.42

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			683.42
Character	$\chi$	$=$	756.683
Dual form			756.2.bb.a.611.42

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40608 + 0.151434i) q^{2} +(1.95414 + 0.425857i) q^{4} +(0.941391 + 0.543513i) q^{5} +(-2.38059 - 1.15446i) q^{7} +(2.68319 + 0.894712i) q^{8} +O(q^{10})$	\(q+(1.40608 + 0.151434i) q^{2} +(1.95414 + 0.425857i) q^{4} +(0.941391 + 0.543513i) q^{5} +(-2.38059 - 1.15446i) q^{7} +(2.68319 + 0.894712i) q^{8} +(1.24137 + 0.906782i) q^{10} +(0.751874 + 1.30228i) q^{11} +(1.59238 + 2.75809i) q^{13} +(-3.17249 - 1.98376i) q^{14} +(3.63729 + 1.66436i) q^{16} +(5.40337 + 3.11964i) q^{17} +(2.29977 - 1.32777i) q^{19} +(1.60815 + 1.46300i) q^{20} +(0.859987 + 1.94498i) q^{22} +(1.62579 - 2.81595i) q^{23} +(-1.90919 - 3.30681i) q^{25} +(1.82135 + 4.11924i) q^{26} +(-4.16037 - 3.26976i) q^{28} +(1.78455 + 1.03031i) q^{29} +0.818407i q^{31} +(4.86229 + 2.89104i) q^{32} +(7.12517 + 5.20472i) q^{34} +(-1.61361 - 2.38068i) q^{35} +(-4.35941 - 7.55073i) q^{37} +(3.43474 - 1.51870i) q^{38} +(2.03964 + 2.30062i) q^{40} +(-6.57171 + 3.79418i) q^{41} +(-3.95088 - 2.28104i) q^{43} +(0.914677 + 2.86503i) q^{44} +(2.71242 - 3.71325i) q^{46} -13.6215 q^{47} +(4.33446 + 5.49658i) q^{49} +(-2.18371 - 4.93876i) q^{50} +(1.93718 + 6.06780i) q^{52} +(-0.686610 - 0.396415i) q^{53} +1.63461i q^{55} +(-5.35467 - 5.22757i) q^{56} +(2.35320 + 1.71894i) q^{58} +2.39274 q^{59} +4.72586 q^{61} +(-0.123935 + 1.15075i) q^{62} +(6.39898 + 4.80136i) q^{64} +3.46192i q^{65} -9.19521i q^{67} +(9.23041 + 8.39726i) q^{68} +(-1.90835 - 3.59178i) q^{70} -12.1795 q^{71} +(-4.02960 + 6.97947i) q^{73} +(-4.98626 - 11.2771i) q^{74} +(5.05951 - 1.61528i) q^{76} +(-0.286478 - 3.96822i) q^{77} -14.4294i q^{79} +(2.51951 + 3.54373i) q^{80} +(-9.81494 + 4.33975i) q^{82} +(-2.40508 + 4.16573i) q^{83} +(3.39113 + 5.87360i) q^{85} +(-5.20984 - 3.80563i) q^{86} +(0.852249 + 4.16698i) q^{88} +(-5.90946 + 3.41183i) q^{89} +(-0.606727 - 8.40422i) q^{91} +(4.37620 - 4.81039i) q^{92} +(-19.1530 - 2.06276i) q^{94} +2.88665 q^{95} +(6.69603 - 11.5979i) q^{97} +(5.26224 + 8.38503i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$-1$

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	0.695506	−	0.718520i	$-0.255180\pi$
$5$	0.941391	+	0.543513i	0.421003	+	0.243066i	−0.274503	+	0.961586i	$0.588513\pi$
$6$		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
$10$	1.24137	+	0.906782i	0.392555	+	0.286750i
$11$	0.751874	+	1.30228i	0.226699	+	0.392653i	0.956828	−	0.290656i	$-0.0938734\pi$
$11$	0.751874	+	1.30228i	0.226699	+	0.392653i	−0.730129	+	0.683309i	$0.760540\pi$
$12$		0			0
$13$	1.59238	+	2.75809i	0.441647	+	0.764955i	0.997812	−	0.0661167i	$-0.0210610\pi$
$13$	1.59238	+	2.75809i	0.441647	+	0.764955i	−0.556165	+	0.831072i	$0.687728\pi$
$14$	−3.17249	−	1.98376i	−0.847883	−	0.530183i
$15$		0			0
$16$	3.63729	+	1.66436i	0.909323	+	0.416091i
$17$	5.40337	+	3.11964i	1.31051	+	0.756624i	0.982181	−	0.187939i	$-0.0601808\pi$
$17$	5.40337	+	3.11964i	1.31051	+	0.756624i	0.328330	+	0.944563i	$0.393514\pi$
$18$		0			0
$19$	2.29977	−	1.32777i	0.527604	−	0.304612i	−0.212436	−	0.977175i	$-0.568140\pi$
$19$	2.29977	−	1.32777i	0.527604	−	0.304612i	0.740040	+	0.672563i	$0.234806\pi$
$20$	1.60815	+	1.46300i	0.359593	+	0.327136i
$21$		0			0
$22$	0.859987	+	1.94498i	0.183350	+	0.414671i
$23$	1.62579	−	2.81595i	0.339000	−	0.587165i	−0.645245	−	0.763976i	$-0.723245\pi$
$23$	1.62579	−	2.81595i	0.339000	−	0.587165i	0.984245	+	0.176811i	$0.0565780\pi$
$24$		0			0
$25$	−1.90919	−	3.30681i	−0.381838	−	0.661362i
$26$	1.82135	+	4.11924i	0.357197	+	0.807849i
$27$		0			0
$28$	−4.16037	−	3.26976i	−0.786236	−	0.617926i
$29$	1.78455	+	1.03031i	0.331382	+	0.191324i	0.656455	−	0.754365i	$-0.272055\pi$
$29$	1.78455	+	1.03031i	0.331382	+	0.191324i	−0.325072	+	0.945689i	$0.605389\pi$
$30$		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
$34$	7.12517	+	5.20472i	1.22196	+	0.892603i
$35$	−1.61361	−	2.38068i	−0.272750	−	0.402408i
$36$		0			0
$37$	−4.35941	−	7.55073i	−0.716683	−	1.24133i	−0.962307	−	0.271967i	$-0.912326\pi$
$37$	−4.35941	−	7.55073i	−0.716683	−	1.24133i	0.245623	−	0.969365i	$-0.421007\pi$
$38$	3.43474	−	1.51870i	0.557188	−	0.246365i
$39$		0			0
$40$	2.03964	+	2.30062i	0.322496	+	0.363760i
$41$	−6.57171	+	3.79418i	−1.02633	+	0.592552i	−0.915931	−	0.401336i	$-0.868546\pi$
$41$	−6.57171	+	3.79418i	−1.02633	+	0.592552i	−0.110398	+	0.993887i	$0.535213\pi$
$42$		0			0
$43$	−3.95088	−	2.28104i	−0.602504	−	0.347856i	0.167522	−	0.985868i	$-0.446423\pi$
$43$	−3.95088	−	2.28104i	−0.602504	−	0.347856i	−0.770026	+	0.638012i	$0.779757\pi$
$44$	0.914677	+	2.86503i	0.137893	+	0.431920i
$45$		0			0
$46$	2.71242	−	3.71325i	0.399925	−	0.547489i
$47$	−13.6215			−1.98690			−0.993451	−	0.114259i	$-0.963551\pi$
$47$	−13.6215			−1.98690			−0.993451	+	0.114259i	$0.963551\pi$
$48$		0			0
$49$	4.33446	+	5.49658i	0.619209	+	0.785226i
$50$	−2.18371	−	4.93876i	−0.308824	−	0.698447i
$51$		0			0
$52$	1.93718	+	6.06780i	0.268638	+	0.841453i
$53$	−0.686610	−	0.396415i	−0.0943132	−	0.0544517i	0.452102	−	0.891966i	$-0.350674\pi$
$53$	−0.686610	−	0.396415i	−0.0943132	−	0.0544517i	−0.546415	+	0.837515i	$0.684008\pi$
$54$		0			0
$55$			1.63461i			0.220411i
$56$	−5.35467	−	5.22757i	−0.715548	−	0.698563i
$57$		0			0
$58$	2.35320	+	1.71894i	0.308990	+	0.225708i
$59$	2.39274			0.311508			0.155754	−	0.987796i	$-0.450219\pi$
$59$	2.39274			0.311508			0.155754	+	0.987796i	$0.450219\pi$
$60$		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	$-0.189847\pi$
$68$	9.23041	+	8.39726i	1.11935	+	1.01832i
$69$		0			0
$70$	−1.90835	−	3.59178i	−0.228092	−	0.429300i
$71$	−12.1795			−1.44545			−0.722723	−	0.691138i	$-0.757110\pi$
$71$	−12.1795			−1.44545			−0.722723	+	0.691138i	$0.757110\pi$
$72$		0			0
$73$	−4.02960	+	6.97947i	−0.471629	+	0.816886i	−0.999473	−	0.0324557i	$-0.989667\pi$
$73$	−4.02960	+	6.97947i	−0.471629	+	0.816886i	0.527844	+	0.849341i	$0.323001\pi$
$74$	−4.98626	−	11.2771i	−0.579641	−	1.31094i
$75$		0			0
$76$	5.05951	−	1.61528i	0.580365	−	0.185285i
$77$	−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	$-0.301467\pi$
$80$	2.51951	+	3.54373i	0.281690	+	0.396201i
$81$		0			0
$82$	−9.81494	+	4.33975i	−1.08388	+	0.479245i
$83$	−2.40508	+	4.16573i	−0.263992	+	0.457248i	−0.967299	−	0.253638i	$-0.918373\pi$
$83$	−2.40508	+	4.16573i	−0.263992	+	0.457248i	0.703307	+	0.710886i	$0.251706\pi$
$84$		0			0
$85$	3.39113	+	5.87360i	0.367819	+	0.637082i
$86$	−5.20984	−	3.80563i	−0.561791	−	0.410372i
$87$		0			0
$88$	0.852249	+	4.16698i	0.0908500	+	0.444202i
$89$	−5.90946	+	3.41183i	−0.626401	+	0.361653i	−0.779357	−	0.626580i	$-0.784454\pi$
$89$	−5.90946	+	3.41183i	−0.626401	+	0.361653i	0.152956	+	0.988233i	$0.451121\pi$
$90$		0			0
$91$	−0.606727	−	8.40422i	−0.0636023	−	0.881002i
$92$	4.37620	−	4.81039i	0.456250	−	0.501518i
$93$		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	−0.295139	−	0.955454i	$-0.595366\pi$
$97$	6.69603	−	11.5979i	0.679879	−	1.17758i	0.975017	−	0.222130i	$-0.0713008\pi$
$98$	5.26224	+	8.38503i	0.531567	+	0.847016i
$99$		0			0
$100$	−2.32258	−	7.27500i	−0.232258	−	0.727500i
$101$	1.78555	−	1.03089i	0.177669	−	0.102577i	−0.408528	−	0.912746i	$-0.633958\pi$
$101$	1.78555	−	1.03089i	0.177669	−	0.102577i	0.586197	+	0.810169i	$0.300624\pi$
$102$		0			0
$103$	2.53628	+	1.46432i	0.249907	+	0.144284i	0.619722	−	0.784822i	$-0.287245\pi$
$103$	2.53628	+	1.46432i	0.249907	+	0.144284i	−0.369814	+	0.929106i	$0.620579\pi$
$104$	1.80496	+	8.82518i	0.176991	+	0.865380i
$105$		0			0
$106$	−0.905400	−	0.661368i	−0.0879402	−	0.0642377i
$107$	5.47882	+	9.48960i	0.529658	+	0.917394i	0.999402	+	0.0345915i	$0.0110130\pi$
$107$	5.47882	+	9.48960i	0.529658	+	0.917394i	−0.469744	+	0.882803i	$0.655654\pi$
$108$		0			0
$109$	−7.27816	+	12.6061i	−0.697122	+	1.20745i	0.272339	+	0.962201i	$0.412203\pi$
$109$	−7.27816	+	12.6061i	−0.697122	+	1.20745i	−0.969460	+	0.245248i	$0.921130\pi$
$110$	−0.247536	+	2.29840i	−0.0236016	+	0.219144i
$111$		0			0
$112$	−6.73748	−	8.16127i	−0.636632	−	0.771168i
$113$	13.0910	−	7.55811i	1.23150	−	0.711008i	0.264158	−	0.964479i	$-0.414906\pi$
$113$	13.0910	−	7.55811i	1.23150	−	0.711008i	0.967343	+	0.253472i	$0.0815725\pi$
$114$		0			0
$115$	3.06100	−	1.76727i	0.285440	−	0.164799i
$116$	3.04849	+	2.77333i	0.283045	+	0.257497i
$117$		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	$-0.719106\pi$
$131$	4.01972	−	6.96236i	0.351204	−	0.608304i	0.986461	+	0.163997i	$0.0524389\pi$
$132$		0			0
$133$	−7.00768	+	0.505906i	−0.607643	+	0.0438676i
$134$	1.39247	−	12.9292i	0.120291	−	1.11691i
$135$		0			0
$136$	11.7071	+	13.2050i	1.00387	+	1.13232i
$137$	−14.1626	+	8.17679i	−1.20999	+	0.698590i	−0.962758	−	0.270365i	$-0.912856\pi$
$137$	−14.1626	+	8.17679i	−1.20999	+	0.698590i	−0.247236	+	0.968955i	$0.579522\pi$
$138$		0			0
$139$	−20.0549	+	11.5787i	−1.70104	+	0.982095i	−0.756325	+	0.654196i	$0.773007\pi$
$139$	−20.0549	+	11.5787i	−1.70104	+	0.982095i	−0.944713	+	0.327899i	$0.893659\pi$
$140$	−2.13938	−	5.33933i	−0.180811	−	0.451256i
$141$		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
$146$	−6.72288	+	9.20350i	−0.556389	+	0.761687i
$147$		0			0
$148$	−5.30336	−	16.6116i	−0.435933	−	1.36547i
$149$	−7.59709	−	4.38618i	−0.622378	−	0.359330i	0.155417	−	0.987849i	$-0.450328\pi$
$149$	−7.59709	−	4.38618i	−0.622378	−	0.359330i	−0.777794	+	0.628519i	$0.783661\pi$
$150$		0			0
$151$	−7.98995	+	4.61300i	−0.650213	+	0.375401i	−0.788538	−	0.614986i	$-0.789162\pi$
$151$	−7.98995	+	4.61300i	−0.650213	+	0.375401i	0.138325	+	0.990387i	$0.455828\pi$
$152$	7.35869	−	1.50503i	0.596869	−	0.122074i
$153$		0			0
$154$	0.198111	−	5.62302i	0.0159642	−	0.453116i
$155$	−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
$160$	3.00600	+	5.36432i	0.237645	+	0.424087i
$161$	−7.12123	+	4.82673i	−0.561231	+	0.380399i
$162$		0			0
$163$	−0.751164	+	0.433685i	−0.0588357	+	0.0339688i	−0.529129	−	0.848541i	$-0.677481\pi$
$163$	−0.751164	+	0.433685i	−0.0588357	+	0.0339688i	0.470294	+	0.882510i	$0.344148\pi$
$164$	−14.4578	+	4.61573i	−1.12896	+	0.360428i
$165$		0			0
$166$	−4.01258	+	5.49315i	−0.311437	+	0.426351i
$167$	2.24779	+	3.89329i	0.173939	+	0.301272i	0.939794	−	0.341742i	$-0.111017\pi$
$167$	2.24779	+	3.89329i	0.173939	+	0.301272i	−0.765854	+	0.643014i	$0.777684\pi$
$168$		0			0
$169$	1.42864	−	2.47448i	0.109895	−	0.190345i
$170$	3.87874	+	8.77230i	0.297486	+	0.672805i
$171$		0			0
$172$	−6.74916	−	6.13998i	−0.514619	−	0.468169i
$173$		−	19.8897i		−	1.51219i	−0.654464	−	0.756093i	$-0.727106\pi$
$173$		−	19.8897i		−	1.51219i	0.654464	−	0.756093i	$-0.272894\pi$
$174$		0			0
$175$	0.727436	+	10.0763i	0.0549890	+	0.761693i
$176$	0.567310	+	5.98818i	0.0427626	+	0.451376i
$177$		0			0
$178$	−8.82585	+	3.90242i	−0.661525	+	0.292499i
$179$	−1.85338	+	3.21014i	−0.138528	+	0.239937i	−0.926940	−	0.375211i	$-0.877570\pi$
$179$	−1.85338	+	3.21014i	−0.138528	+	0.239937i	0.788412	+	0.615148i	$0.210904\pi$
$180$		0			0
$181$	−20.5160			−1.52494			−0.762470	−	0.647024i	$-0.776013\pi$
$181$	−20.5160			−1.52494			−0.762470	+	0.647024i	$0.776013\pi$
$182$	0.419575	−	11.9089i	0.0311010	−	0.882747i
$183$		0			0
$184$	6.88175	−	6.10110i	0.507329	−	0.449779i
$185$		−	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	$-0.298520\pi$
$191$	16.3505			1.18308			0.591541	+	0.806275i	$0.298520\pi$
$192$		0			0
$193$	−11.5081			−0.828369			−0.414184	−	0.910193i	$-0.635933\pi$
$193$	−11.5081			−0.828369			−0.414184	+	0.910193i	$0.635933\pi$
$194$	11.1715	−	15.2935i	0.802065	−	1.09801i
$195$		0			0
$196$	6.12937	+	12.5869i	0.437812	+	0.899066i
$197$		−	11.6386i		−	0.829217i	−0.910000	−	0.414608i	$-0.863919\pi$
$197$		−	11.6386i		−	0.829217i	0.910000	−	0.414608i	$-0.136081\pi$
$198$		0			0
$199$	14.1464	+	8.16741i	1.00281	+	0.578972i	0.909078	−	0.416625i	$-0.136787\pi$
$199$	14.1464	+	8.16741i	1.00281	+	0.578972i	0.0937311	+	0.995598i	$0.470121\pi$
$200$	−2.16406	−	10.5810i	−0.153022	−	0.748187i
$201$		0			0
$202$	2.66674	−	1.17912i	0.187631	−	0.0829626i
$203$	−3.05884	−	4.51293i	−0.214688	−	0.316746i
$204$		0			0
$205$	−8.24874			−0.576117
$206$	3.34447	+	2.44304i	0.233021	+	0.170215i
$207$		0			0
$208$	1.20150	+	12.6823i	0.0833088	+	0.879357i
$209$	3.45828	+	1.99664i	0.239214	+	0.138110i
$210$		0			0
$211$	19.4336	−	11.2200i	1.33786	−	0.772416i	0.351373	−	0.936235i	$-0.385715\pi$
$211$	19.4336	−	11.2200i	1.33786	−	0.772416i	0.986490	+	0.163820i	$0.0523815\pi$
$212$	−1.17291	−	1.06705i	−0.0805560	−	0.0732850i
$213$		0			0
$214$	6.26663	+	14.1728i	0.428378	+	0.968835i
$215$	−2.47955	−	4.29471i	−0.169104	−	0.292897i
$216$		0			0
$217$	0.944815	−	1.94830i	0.0641382	−	0.132259i
$218$	−12.1427	+	16.6231i	−0.822407	+	1.12586i
$219$		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	$-0.130740\pi$
$223$	15.3730	+	8.87563i	1.02946	+	0.594356i	0.112627	+	0.993637i	$0.464074\pi$
$224$	−8.23756	−	12.4957i	−0.550395	−	0.834904i
$225$		0			0
$226$	19.5516	−	8.64491i	1.30056	−	0.575051i
$227$	6.69388	+	11.5941i	0.444288	+	0.769530i	0.998002	−	0.0631769i	$-0.0201232\pi$
$227$	6.69388	+	11.5941i	0.444288	+	0.769530i	−0.553714	+	0.832707i	$0.686790\pi$
$228$		0			0
$229$	6.53564	−	11.3201i	0.431887	−	0.748051i	−0.565149	−	0.824989i	$-0.691181\pi$
$229$	6.53564	−	11.3201i	0.431887	−	0.748051i	0.997036	+	0.0769385i	$0.0245145\pi$
$230$	4.57165	−	2.02139i	0.301446	−	0.133286i
$231$		0			0
$232$	3.86645	+	4.36117i	0.253845	+	0.286325i
$233$	5.07304	−	2.92892i	0.332346	−	0.191880i	−0.324536	−	0.945873i	$-0.605208\pi$
$233$	5.07304	−	2.92892i	0.332346	−	0.191880i	0.656882	+	0.753993i	$0.271875\pi$
$234$		0			0
$235$	−12.8232	−	7.40346i	−0.836492	−	0.482949i
$236$	4.67573	+	1.01896i	0.304364	+	0.0663288i
$237$		0			0
$238$	−10.9535	−	20.6160i	−0.710011	−	1.33634i
$239$	4.28685	+	7.42504i	0.277293	+	0.480286i	0.970711	−	0.240250i	$-0.0772293\pi$
$239$	4.28685	+	7.42504i	0.277293	+	0.480286i	−0.693418	+	0.720536i	$0.743896\pi$
$240$		0			0
$241$	−1.38778	−	2.40370i	−0.0893945	−	0.154836i	0.817861	−	0.575416i	$-0.195160\pi$
$241$	−1.38778	−	2.40370i	−0.0893945	−	0.154836i	−0.907255	+	0.420580i	$0.861827\pi$
$242$	7.28974	−	9.97952i	0.468602	−	0.641508i
$243$		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	$-0.446038\pi$
$251$	5.34591			0.337431			0.168716	+	0.985665i	$0.446038\pi$
$252$		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	0.558243	−	0.829678i	$-0.311476\pi$
$257$	1.90518	+	1.09996i	0.118842	+	0.0686135i	−0.439401	+	0.898291i	$0.644809\pi$
$258$		0			0
$259$	1.66102	+	23.0080i	0.103211	+	1.42965i
$260$	−1.47428	+	6.76506i	−0.0914311	+	0.419551i
$261$		0			0
$262$	6.70639	−	9.18093i	0.414322	−	0.567200i
$263$	−3.12661	−	5.41544i	−0.192795	−	0.333931i	0.753381	−	0.657585i	$-0.228422\pi$
$263$	−3.12661	−	5.41544i	−0.192795	−	0.333931i	−0.946175	+	0.323654i	$0.895089\pi$
$264$		0			0
$265$	−0.430913	−	0.746363i	−0.0264708	−	0.0458487i
$266$	−9.92999	−	0.349854i	−0.608847	−	0.0214509i
$267$		0			0
$268$	3.91584	−	17.9687i	0.239198	−	1.09761i
$269$	7.71725	+	4.45555i	0.470529	+	0.271660i	0.716461	−	0.697627i	$-0.245761\pi$
$269$	7.71725	+	4.45555i	0.470529	+	0.271660i	−0.245932	+	0.969287i	$0.579094\pi$
$270$		0			0
$271$	−2.17320	+	1.25470i	−0.132013	+	0.0762175i	−0.564552	−	0.825398i	$-0.690951\pi$
$271$	−2.17320	+	1.25470i	−0.132013	+	0.0762175i	0.432539	+	0.901615i	$0.357618\pi$
$272$	14.4614	+	20.3402i	0.876853	+	1.23331i
$273$		0			0
$274$	−21.1520	+	9.35254i	−1.27784	+	0.565008i
$275$	2.87094	−	4.97261i	0.173124	−	0.299860i
$276$		0			0
$277$	−14.7998	−	25.6340i	−0.889233	−	1.54020i	−0.840783	−	0.541372i	$-0.817905\pi$
$277$	−14.7998	−	25.6340i	−0.889233	−	1.54020i	−0.0484501	−	0.998826i	$-0.515428\pi$
$278$	−29.9523	+	13.2436i	−1.79642	+	0.794301i
$279$		0			0
$280$	−2.19959	−	7.83152i	−0.131451	−	0.468023i
$281$	21.1188	+	12.1929i	1.25984	+	0.727370i	0.973044	−	0.230621i	$-0.0740757\pi$
$281$	21.1188	+	12.1929i	1.25984	+	0.727370i	0.286798	+	0.957991i	$0.407409\pi$
$282$		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
$286$	−3.99499	+	5.46907i	−0.236229	+	0.323393i
$287$	20.0248	−	1.44565i	1.18203	−	0.0853342i
$288$		0			0
$289$	10.9643	+	18.9907i	0.644959	+	1.11710i
$290$	1.28101	+	2.89719i	0.0752238	+	0.170129i
$291$		0			0
$292$	−10.8466	+	11.9228i	−0.634752	+	0.697729i
$293$	−10.4046	+	6.00710i	−0.607843	+	0.350939i	−0.772121	−	0.635476i	$-0.780804\pi$
$293$	−10.4046	+	6.00710i	−0.607843	+	0.350939i	0.164278	+	0.986414i	$0.447471\pi$
$294$		0			0
$295$	2.25250	+	1.30048i	0.131146	+	0.0757170i
$296$	−4.94139	−	24.1604i	−0.287213	−	1.40430i
$297$		0			0
$298$	−10.0179	−	7.31779i	−0.580322	−	0.423908i
$299$	10.3555			0.598874
$300$		0			0
$301$	6.77209	+	9.99136i	0.390337	+	0.575892i
$302$	−11.9331	+	5.27631i	−0.686673	+	0.303618i
$303$		0			0
$304$	10.5748	−	1.00184i	0.606509	−	0.0574596i
$305$	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	$0.732990\pi$
$308$	1.13008	−	7.87643i	0.0643921	−	0.448801i
$309$		0			0
$310$	−0.742117	+	1.01594i	−0.0421494	+	0.0577017i
$311$	−5.17871			−0.293658			−0.146829	−	0.989162i	$-0.546907\pi$
$311$	−5.17871			−0.293658			−0.146829	+	0.989162i	$0.546907\pi$
$312$		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	$-0.770586\pi$
$317$		−	23.4995i		−	1.31986i	0.751326	−	0.659931i	$-0.229414\pi$
$318$		0			0
$319$			3.09865i			0.173491i
$320$	3.41434	+	7.99788i	0.190868	+	0.447095i
$321$		0			0
$322$	−10.7440	+	5.70838i	−0.598738	+	0.318116i
$323$	16.5687			0.921907
$324$		0			0
$325$	6.08031	−	10.5314i	0.337275	−	0.584178i
$326$	−1.12187	+	0.496045i	−0.0621348	+	0.0274734i
$327$		0			0
$328$	−21.0278	+	4.30070i	−1.16107	+	0.237467i
$329$	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	$-0.136667\pi$
$332$	−6.47387	+	7.11618i	−0.355300	+	0.390551i
$333$		0			0
$334$	2.57100	+	5.81468i	0.140679	+	0.318165i
$335$	4.99771	−	8.65629i	0.273054	−	0.472944i
$336$		0			0
$337$	13.2530	+	22.9549i	0.721938	+	1.25043i	0.960222	+	0.279238i	$0.0900817\pi$
$337$	13.2530	+	22.9549i	0.721938	+	1.25043i	−0.238284	+	0.971196i	$0.576585\pi$
$338$	2.38351	−	3.26298i	0.129646	−	0.177483i
$339$		0			0
$340$	4.12541	+	12.9220i	0.223732	+	0.700791i
$341$	−1.06580	+	0.615339i	−0.0577162	+	0.0333225i
$342$		0			0
$343$	−3.97304	−	18.0891i	−0.214524	−	0.976719i
$344$	−8.56008	−	9.65537i	−0.461528	−	0.520583i
$345$		0			0
$346$	3.01197	−	27.9666i	0.161925	−	1.50349i
$347$	−20.7082			−1.11168			−0.555839	−	0.831290i	$-0.687603\pi$
$347$	−20.7082			−1.11168			−0.555839	+	0.831290i	$0.687603\pi$
$348$		0			0
$349$	−2.18348	+	3.78189i	−0.116879	+	0.202440i	−0.918529	−	0.395353i	$-0.870622\pi$
$349$	−2.18348	+	3.78189i	−0.116879	+	0.202440i	0.801650	+	0.597793i	$0.203956\pi$
$350$	−0.503051	+	14.2782i	−0.0268892	+	0.763202i
$351$		0			0
$352$	−0.109128	+	8.50578i	−0.00581657	+	0.453360i
$353$	−3.12319	+	1.80317i	−0.166231	+	0.0959732i	−0.580807	−	0.814041i	$-0.697263\pi$
$353$	−3.12319	+	1.80317i	−0.166231	+	0.0959732i	0.414577	+	0.910014i	$0.363930\pi$
$354$		0			0
$355$	−11.4657	−	6.61973i	−0.608537	−	0.351339i
$356$	−13.0008	+	4.15059i	−0.689043	+	0.219981i
$357$		0			0
$358$	−3.09212	+	4.23306i	−0.163424	+	0.223724i
$359$	8.74493	+	15.1467i	0.461540	+	0.799410i	0.999038	−	0.0438545i	$-0.0139638\pi$
$359$	8.74493	+	15.1467i	0.461540	+	0.799410i	−0.537498	+	0.843265i	$0.680630\pi$
$360$		0			0
$361$	−5.97403	+	10.3473i	−0.314423	+	0.544596i
$362$	−28.8471	−	3.10681i	−1.51617	−	0.163290i
$363$		0			0
$364$	2.39337	−	16.6814i	0.125447	−	0.874341i
$365$	−7.58686	+	4.38028i	−0.397115	+	0.229274i
$366$		0			0
$367$	−1.07569	+	0.621050i	−0.0561506	+	0.0324185i	−0.527812	−	0.849361i	$-0.676988\pi$
$367$	−1.07569	+	0.621050i	−0.0561506	+	0.0324185i	0.471662	+	0.881779i	$0.343654\pi$
$368$	10.6002	−	7.53651i	0.552575	−	0.392868i
$369$		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	−0.886339	−	0.463036i	$-0.846760\pi$
$373$	−0.814411	+	1.41060i	−0.0421686	+	0.0730381i	0.844171	+	0.536074i	$0.180093\pi$
$374$	−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	0.294965	+	0.955508i	$0.404692\pi$
$383$	−13.3081	+	23.0503i	−0.680012	+	1.17781i	−0.974977	+	0.222307i	$0.928641\pi$
$384$		0			0
$385$	1.88709	−	3.89135i	0.0961749	−	0.198322i
$386$	−16.1813	−	1.74271i	−0.823606	−	0.0887016i
$387$		0			0
$388$	18.0240	−	19.8122i	0.915029	−	1.00581i
$389$	−24.8177	+	14.3285i	−1.25831	+	0.726483i	−0.972745	−	0.231877i	$-0.925513\pi$
$389$	−24.8177	+	14.3285i	−1.25831	+	0.726483i	−0.285561	+	0.958361i	$0.592180\pi$
$390$		0			0
$391$	17.5695	−	10.1437i	0.888526	−	0.512991i
$392$	6.71231	+	18.6265i	0.339023	+	0.940778i
$393$		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	−0.982446	−	0.186548i	$-0.940270\pi$
$397$	−13.0065	−	22.5280i	−0.652778	−	1.13065i	0.329667	−	0.944097i	$-0.393063\pi$
$398$	18.6541	+	13.6263i	0.935047	+	0.683024i
$399$		0			0
$400$	−1.44054	−	15.2054i	−0.0720268	−	0.760271i
$401$	−18.8023	−	10.8555i	−0.938942	−	0.542099i	−0.0493138	−	0.998783i	$-0.515703\pi$
$401$	−18.8023	−	10.8555i	−0.938942	−	0.542099i	−0.889629	+	0.456685i	$0.849037\pi$
$402$		0			0
$403$	−2.25724	+	1.30322i	−0.112441	+	0.0649178i
$404$	3.92821	−	1.25410i	0.195436	−	0.0623940i
$405$		0			0
$406$	−3.61757	−	6.80877i	−0.179537	−	0.337913i
$407$	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
$412$	4.33265	+	3.94158i	0.213454	+	0.194188i
$413$	−5.69613	−	2.76231i	−0.280288	−	0.135924i
$414$		0			0
$415$	−4.52825	+	2.61439i	−0.222283	+	0.128335i
$416$	−0.231121	+	18.0143i	−0.0113317	+	0.883222i
$417$		0			0
$418$	4.56027	+	3.33114i	0.223050	+	0.162931i
$419$	3.64856	+	6.31949i	0.178244	+	0.308727i	0.941279	−	0.337629i	$-0.109625\pi$
$419$	3.64856	+	6.31949i	0.178244	+	0.308727i	−0.763035	+	0.646357i	$0.776292\pi$
$420$		0			0
$421$	−6.81198	+	11.7987i	−0.331996	+	0.575034i	−0.982903	−	0.184124i	$-0.941055\pi$
$421$	−6.81198	+	11.7987i	−0.331996	+	0.575034i	0.650907	+	0.759157i	$0.274389\pi$
$422$	29.0243	−	12.8333i	1.41288	−	0.624717i
$423$		0			0
$424$	−1.48763	−	1.67797i	−0.0722455	−	0.0814896i
$425$		−	23.8239i		−	1.15563i
$426$		0			0
$427$	−11.2504	−	5.45580i	−0.544443	−	0.264025i
$428$	6.66515	+	20.8772i	0.322172	+	1.00914i
$429$		0			0
$430$	−2.83609	−	6.41420i	−0.136768	−	0.309320i
$431$	6.04210	−	10.4652i	0.291038	−	0.504092i	−0.683018	−	0.730402i	$-0.739333\pi$
$431$	6.04210	−	10.4652i	0.291038	−	0.504092i	0.974055	+	0.226310i	$0.0726661\pi$
$432$		0			0
$433$	22.6142			1.08677			0.543386	−	0.839483i	$-0.317142\pi$
$433$	22.6142			1.08677			0.543386	+	0.839483i	$0.317142\pi$
$434$	1.62353	−	2.59639i	0.0779317	−	0.124631i
$435$		0			0
$436$	−19.5909	+	21.5347i	−0.938235	+	1.03132i
$437$		−	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	$-0.386128\pi$
$443$	14.7400			0.700318			0.350159	+	0.936690i	$0.386128\pi$
$444$		0			0
$445$	−7.41748			−0.351622
$446$	20.2717	+	14.8079i	0.959893	+	0.701173i
$447$		0			0
$448$	−9.69042	−	18.8174i	−0.457829	−	0.889040i
$449$			36.4636i			1.72082i	0.509601	+	0.860411i	$0.329793\pi$
$449$			36.4636i			1.72082i	−0.509601	+	0.860411i	$0.670207\pi$
$450$		0			0
$451$	−9.88221	−	5.70549i	−0.465335	−	0.268661i
$452$	28.8003	−	9.19467i	1.35465	−	0.432481i
$453$		0			0
$454$	7.65640	+	17.3160i	0.359333	+	0.812680i
$455$	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	$0.374094\pi$
$458$	10.9039	−	14.9272i	0.509505	−	0.697503i
$459$		0			0
$460$	6.73422	−	2.14994i	0.313985	−	0.100241i
$461$	8.43340	+	4.86902i	0.392782	+	0.226773i	0.683365	−	0.730077i	$-0.260516\pi$
$461$	8.43340	+	4.86902i	0.392782	+	0.226773i	−0.290583	+	0.956850i	$0.593849\pi$
$462$		0			0
$463$	3.07391	−	1.77472i	0.142857	−	0.0824784i	−0.426868	−	0.904314i	$-0.640383\pi$
$463$	3.07391	−	1.77472i	0.142857	−	0.0824784i	0.569725	+	0.821836i	$0.307050\pi$
$464$	4.77611	+	6.71768i	0.221725	+	0.311860i
$465$		0			0
$466$	7.57665	−	3.35007i	0.350981	−	0.155189i
$467$	−4.49751	−	7.78991i	−0.208120	−	0.360474i	0.743002	−	0.669289i	$-0.233401\pi$
$467$	−4.49751	−	7.78991i	−0.208120	−	0.360474i	−0.951122	+	0.308815i	$0.900068\pi$
$468$		0			0
$469$	−10.6155	+	21.8901i	−0.490177	+	1.01079i
$470$	−16.9093	−	12.3517i	−0.779968	−	0.569743i
$471$		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
$476$	−12.2796	−	30.6466i	−0.562834	−	1.40468i
$477$		0			0
$478$	4.90326	+	11.0894i	0.224270	+	0.507217i
$479$	8.48898	+	14.7033i	0.387871	+	0.671813i	0.992163	−	0.124950i	$-0.0398772\pi$
$479$	8.48898	+	14.7033i	0.387871	+	0.671813i	−0.604292	+	0.796763i	$0.706544\pi$
$480$		0			0
$481$	13.8837	−	24.0473i	0.633042	−	1.09646i
$482$	−1.58733	−	3.58995i	−0.0723007	−	0.163518i
$483$		0			0
$484$	11.7612	−	12.9281i	0.534601	−	0.587642i
$485$	12.6072	−	7.27875i	0.572462	−	0.330511i
$486$		0			0
$487$	0.873051	+	0.504056i	0.0395617	+	0.0228410i	0.519650	−	0.854379i	$-0.326062\pi$
$487$	0.873051	+	0.504056i	0.0395617	+	0.0228410i	−0.480089	+	0.877220i	$0.659396\pi$
$488$	12.6804	+	4.22829i	0.574013	+	0.191405i
$489$		0			0
$490$	0.396459	+	10.7537i	0.0179102	+	0.485802i
$491$	−0.979328	−	1.69625i	−0.0441965	−	0.0765505i	0.843081	−	0.537787i	$-0.180739\pi$
$491$	−0.979328	−	1.69625i	−0.0441965	−	0.0765505i	−0.887277	+	0.461236i	$0.847406\pi$
$492$		0			0
$493$	6.42839	+	11.1343i	0.289520	+	0.501463i
$494$	9.65811	+	7.05496i	0.434539	+	0.317418i
$495$		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	$-0.122875\pi$
$499$	23.7580	+	13.7167i	1.06355	+	0.614043i	0.137141	+	0.990552i	$0.456209\pi$
$500$	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	$-0.688435\pi$
$503$	−25.0298			−1.11602			−0.558011	+	0.829834i	$0.688435\pi$
$504$		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	−0.0861990	−	0.996278i	$-0.527472\pi$
$509$	−22.3828	−	12.9227i	−0.992100	−	0.572789i	−0.905901	+	0.423488i	$0.860805\pi$
$510$		0			0
$511$	17.6503	−	11.9633i	0.780805	−	0.529225i
$512$	12.8738	+	18.6082i	0.568948	+	0.822374i
$513$		0			0
$514$	2.51227	+	1.83514i	0.110812	+	0.0809446i
$515$	1.59176	+	2.75700i	0.0701412	+	0.121488i
$516$		0			0
$517$	−10.2417	−	17.7391i	−0.450428	−	0.780164i
$518$	−1.14866	+	32.6026i	−0.0504692	+	1.43248i
$519$		0			0
$520$	−3.09742	+	9.28897i	−0.135831	+	0.407348i
$521$	−22.8154	−	13.1725i	−0.999562	−	0.577097i	−0.0914433	−	0.995810i	$-0.529148\pi$
$521$	−22.8154	−	13.1725i	−0.999562	−	0.577097i	−0.908119	+	0.418713i	$0.862481\pi$
$522$		0			0
$523$	15.0902	−	8.71233i	0.659848	−	0.380964i	−0.132371	−	0.991200i	$-0.542259\pi$
$523$	15.0902	−	8.71233i	0.659848	−	0.380964i	0.792219	+	0.610237i	$0.208926\pi$
$524$	10.8200	−	11.8936i	0.472676	−	0.519573i
$525$		0			0
$526$	−3.57619	−	8.08803i	−0.155929	−	0.352655i
$527$	−2.55313	+	4.42216i	−0.111216	+	0.192632i
$528$		0			0
$529$	6.21363	+	10.7623i	0.270158	+	0.467927i
$530$	−0.492874	−	1.11470i	−0.0214091	−	0.0484196i
$531$		0			0
$532$	−13.9094	−	1.99566i	−0.603049	−	0.0865228i
$533$	−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
$538$	10.1764	+	7.43353i	0.438734	+	0.320482i
$539$	−3.89914	+	9.77744i	−0.167948	+	0.421144i
$540$		0			0
$541$	−9.52540	−	16.4985i	−0.409529	−	0.709325i	0.585308	−	0.810811i	$-0.300974\pi$
$541$	−9.52540	−	16.4985i	−0.409529	−	0.709325i	−0.994837	+	0.101486i	$0.967640\pi$
$542$	−3.24571	+	1.43511i	−0.139415	+	0.0616434i
$543$		0			0
$544$	17.2538	+	30.7900i	0.739749	+	1.32011i
$545$	−13.7032	+	7.91154i	−0.586980	+	0.338893i
$546$		0			0
$547$	−4.36785	−	2.52178i	−0.186756	−	0.107824i	0.403707	−	0.914888i	$-0.367721\pi$
$547$	−4.36785	−	2.52178i	−0.186756	−	0.107824i	−0.590463	+	0.807065i	$0.701055\pi$
$548$	−31.1578	+	9.94731i	−1.33100	+	0.424928i
$549$		0			0
$550$	4.78980	−	6.55714i	0.204238	−	0.279598i
$551$	5.47207			0.233118
$552$		0			0
$553$	−16.6581	+	34.3505i	−0.708374	+	1.46073i
$554$	−16.9279	−	38.2847i	−0.719197	−	1.62656i
$555$		0			0
$556$	−44.1210	+	14.0859i	−1.87115	+	0.597374i
$557$	13.8266	+	7.98281i	0.585853	+	0.338242i	0.763456	−	0.645860i	$-0.223501\pi$
$557$	13.8266	+	7.98281i	0.585853	+	0.338242i	−0.177603	+	0.984102i	$0.556834\pi$
$558$		0			0
$559$		−	14.5292i		−	0.614518i
$560$	−1.90685	−	11.3449i	−0.0805793	−	0.479408i
$561$		0			0
$562$	27.8483	+	20.3424i	1.17471	+	0.858092i
$563$	−16.6909			−0.703436			−0.351718	−	0.936106i	$-0.614402\pi$
$563$	−16.6909			−0.703436			−0.351718	+	0.936106i	$0.614402\pi$
$564$		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	$0.252153\pi$
$569$			33.9617i			1.42375i	−0.702307	+	0.711874i	$0.747847\pi$
$570$		0			0
$571$			31.2885i			1.30938i	0.755895	+	0.654692i	$0.227202\pi$
$571$			31.2885i			1.30938i	−0.755895	+	0.654692i	$0.772798\pi$
$572$	−6.44549	+	7.08498i	−0.269499	+	0.296238i
$573$		0			0
$574$	28.3754	+	0.999726i	1.18437	+	0.0417278i
$575$	−12.4157			−0.517772
$576$		0			0
$577$	10.1541	−	17.5874i	0.422720	−	0.732172i	−0.573485	−	0.819216i	$-0.694409\pi$
$577$	10.1541	−	17.5874i	0.422720	−	0.732172i	0.996204	+	0.0870440i	$0.0277421\pi$
$578$	12.5409	+	28.3629i	0.521631	+	1.17974i
$579$		0			0
$580$	1.36248	+	4.26768i	0.0565739	+	0.177206i
$581$	10.5347	−	7.14035i	0.437052	−	0.296232i
$582$		0			0
$583$		−	1.19222i		−	0.0493765i
$584$	−17.0568	+	15.1219i	−0.705815	+	0.625748i
$585$		0			0
$586$	−15.5394	+	6.87087i	−0.641927	+	0.283833i
$587$	−4.77427	+	8.26929i	−0.197055	+	0.341310i	−0.947572	−	0.319541i	$-0.896471\pi$
$587$	−4.77427	+	8.26929i	−0.197055	+	0.341310i	0.750517	+	0.660851i	$0.229805\pi$
$588$		0			0
$589$	1.08666	+	1.88215i	0.0447750	+	0.0775526i
$590$	2.97026	+	2.16969i	0.122284	+	0.0893247i
$591$		0			0
$592$	−3.28930	−	34.7199i	−0.135189	−	1.42698i
$593$	−9.29829	+	5.36837i	−0.381835	+	0.220453i	−0.678616	−	0.734493i	$-0.737420\pi$
$593$	−9.29829	+	5.36837i	−0.381835	+	0.220453i	0.296781	+	0.954945i	$0.404087\pi$
$594$		0			0
$595$	−1.29208	−	17.8976i	−0.0529702	−	0.733729i
$596$	−12.9779	−	11.8065i	−0.531594	−	0.483612i
$597$		0			0
$598$	14.5607	+	1.56817i	0.595430	+	0.0641273i
$599$	29.7414			1.21520			0.607600	−	0.794243i	$-0.292132\pi$
$599$	29.7414			1.21520			0.607600	+	0.794243i	$0.292132\pi$
$600$		0			0
$601$	18.4639	−	31.9804i	0.753159	−	1.30451i	−0.193125	−	0.981174i	$-0.561862\pi$
$601$	18.4639	−	31.9804i	0.753159	−	1.30451i	0.946284	−	0.323336i	$-0.104804\pi$
$602$	8.00908	+	15.0742i	0.326426	+	0.614378i
$603$		0			0
$604$	−17.5779	+	5.61185i	−0.715236	+	0.228343i
$605$	8.22657	−	4.74962i	0.334458	−	0.193099i
$606$		0			0
$607$	−24.7329	−	14.2796i	−1.00388	−	0.579589i	−0.0944847	−	0.995526i	$-0.530120\pi$
$607$	−24.7329	−	14.2796i	−1.00388	−	0.579589i	−0.909393	+	0.415937i	$0.863454\pi$
$608$	15.0208	+	0.192716i	0.609174	+	0.00781565i
$609$		0			0
$610$	5.86653	+	4.28533i	0.237529	+	0.173508i
$611$	−21.6907	−	37.5693i	−0.877510	−	1.51989i
$612$		0			0
$613$	0.0951404	−	0.164788i	0.00384268	−	0.00665572i	−0.864098	−	0.503324i	$-0.832110\pi$
$613$	0.0951404	−	0.164788i	0.00384268	−	0.00665572i	0.867940	+	0.496668i	$0.165443\pi$
$614$	−3.94745	+	36.6525i	−0.159306	+	1.47918i
$615$		0			0
$616$	2.78174	−	10.9038i	0.112079	−	0.439326i
$617$	18.7268	−	10.8120i	0.753915	−	0.435273i	−0.0731920	−	0.997318i	$-0.523319\pi$
$617$	18.7268	−	10.8120i	0.753915	−	0.435273i	0.827107	+	0.562045i	$0.189985\pi$
$618$		0			0
$619$	−5.72420	+	3.30487i	−0.230075	+	0.132834i	−0.610607	−	0.791934i	$-0.709074\pi$
$619$	−5.72420	+	3.30487i	−0.230075	+	0.132834i	0.380532	+	0.924768i	$0.375741\pi$
$620$	−1.19733	+	1.31612i	−0.0480857	+	0.0528566i
$621$		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
$640$	3.58970	+	11.7627i	0.141895	+	0.464963i
$641$	−22.6874	+	13.0986i	−0.896097	+	0.517362i	−0.875932	−	0.482435i	$-0.839752\pi$
$641$	−22.6874	+	13.0986i	−0.896097	+	0.517362i	−0.0201649	+	0.999797i	$0.506419\pi$
$642$		0			0
$643$	19.2089	−	11.0902i	0.757524	−	0.437356i	−0.0708823	−	0.997485i	$-0.522581\pi$
$643$	19.2089	−	11.0902i	0.757524	−	0.437356i	0.828406	+	0.560128i	$0.189248\pi$
$644$	−15.9713	+	6.39945i	−0.629359	+	0.252174i
$645$		0			0
$646$	23.2970	+	2.50906i	0.916607	+	0.0987177i
$647$	−2.18326	+	3.78151i	−0.0858327	+	0.148667i	−0.905746	−	0.423822i	$-0.860688\pi$
$647$	−2.18326	+	3.78151i	−0.0858327	+	0.148667i	0.819913	+	0.572488i	$0.194022\pi$
$648$		0			0
$649$	1.79904	+	3.11602i	0.0706183	+	0.122315i
$650$	10.1442	−	13.8873i	0.397890	−	0.544703i
$651$		0			0
$652$	−1.65256	+	0.527590i	−0.0647194	+	0.0206620i
$653$	30.3258	+	17.5086i	1.18674	+	0.685166i	0.957565	−	0.288219i	$-0.0930631\pi$
$653$	30.3258	+	17.5086i	1.18674	+	0.685166i	0.229177	+	0.973385i	$0.426396\pi$
$654$		0			0
$655$	7.56826	−	4.36954i	0.295716	−	0.170732i
$656$	−30.2181	+	2.86282i	−1.17982	+	0.111774i
$657$		0			0
$658$	43.2141	+	27.0219i	1.68466	+	1.05342i
$659$	−13.6116	+	23.5760i	−0.530233	+	0.918390i	0.469145	+	0.883121i	$0.344562\pi$
$659$	−13.6116	+	23.5760i	−0.530233	+	0.918390i	−0.999378	+	0.0352689i	$0.988771\pi$
$660$		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
$664$	−10.1804	+	9.02557i	−0.395077	+	0.350260i
$665$	−6.87194	−	3.33251i	−0.266482	−	0.129229i
$666$		0			0
$667$	5.80259	−	3.35013i	0.224677	−	0.129717i
$668$	2.73451	+	8.56525i	0.105801	+	0.331400i
$669$		0			0
$670$	8.33805	−	11.4146i	0.322127	−	0.440986i
$671$	3.55325	+	6.15441i	0.137172	+	0.237589i
$672$		0			0
$673$	−6.84127	+	11.8494i	−0.263712	+	0.456762i	−0.967225	−	0.253920i	$-0.918280\pi$
$673$	−6.84127	+	11.8494i	−0.263712	+	0.456762i	0.703514	+	0.710682i	$0.251613\pi$
$674$	15.1587	+	34.2834i	0.583891	+	1.32055i
$675$		0			0
$676$	3.84553	−	4.22707i	0.147905	−	0.162580i
$677$		−	39.5753i		−	1.52100i	−0.649337	−	0.760500i	$-0.724954\pi$
$677$		−	39.5753i		−	1.52100i	0.649337	−	0.760500i	$-0.275046\pi$
$678$		0			0
$679$	−29.3297	+	19.8795i	−1.12557	+	0.762906i
$680$	3.84384	+	18.7941i	0.147405	+	0.720719i
$681$		0			0
$682$	−1.59178	+	0.703819i	−0.0609526	+	0.0269506i
$683$	11.3382	−	19.6384i	0.433846	−	0.751443i	−0.563355	−	0.826215i	$-0.690490\pi$
$683$	11.3382	−	19.6384i	0.433846	−	0.751443i	0.997201	+	0.0747721i	$0.0238229\pi$
$684$		0			0
$685$	−17.7768			−0.679215
$686$	−2.84712	−	26.0364i	−0.108703	−	0.994074i
$687$		0			0
$688$	−10.5740	−	14.8725i	−0.403131	−	0.567010i
$689$		−	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
$698$	−3.64286	+	4.98700i	−0.137884	+	0.188761i
$699$		0			0
$700$	−2.86953	+	20.0001i	−0.108458	+	0.755934i
$701$			20.6957i			0.781667i	0.920461	+	0.390833i	$0.127813\pi$
$701$			20.6957i			0.781667i	−0.920461	+	0.390833i	$0.872187\pi$
$702$		0			0
$703$	−20.0513	−	11.5766i	−0.756250	−	0.436621i
$704$	−1.44151	+	11.9433i	−0.0543289	+	0.450130i
$705$		0			0
$706$	−4.66452	+	2.06245i	−0.175552	+	0.0776215i
$707$	−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	$0.630333\pi$
$710$	−15.1193	−	11.0442i	−0.567417	−	0.414481i
$711$		0			0
$712$	−18.9088	+	3.86730i	−0.708636	+	0.144933i
$713$	2.30459	+	1.33056i	0.0863076	+	0.0498297i
$714$		0			0
$715$	−4.50840	+	2.60293i	−0.168605	+	0.0973439i
$716$	−4.98881	+	5.48378i	−0.186441	+	0.204938i
$717$		0			0
$718$	10.0024	+	22.6217i	0.373285	+	0.844236i
$719$	8.43001	+	14.6012i	0.314386	+	0.544533i	0.979307	−	0.202381i	$-0.0648680\pi$
$719$	8.43001	+	14.6012i	0.314386	+	0.544533i	−0.664921	+	0.746914i	$0.731535\pi$
$720$		0			0
$721$	−4.34736	−	6.41399i	−0.161904	−	0.238869i
$722$	−9.96692	+	13.6445i	−0.370930	+	0.507797i
$723$		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	$-0.379833\pi$
$727$	−6.79800	−	3.92483i	−0.252124	−	0.145564i	−0.620736	+	0.784019i	$0.713166\pi$
$728$	5.89140	−	23.0929i	0.218350	−	0.855881i
$729$		0			0
$730$	−11.3311	+	5.01012i	−0.419382	+	0.185433i
$731$	−14.2321	−	24.6507i	−0.526392	−	0.911738i
$732$		0			0
$733$	1.38987	−	2.40732i	0.0513360	−	0.0889165i	−0.839216	−	0.543799i	$-0.816985\pi$
$733$	1.38987	−	2.40732i	0.0513360	−	0.0889165i	0.890551	+	0.454882i	$0.150319\pi$
$734$	−1.60656	+	0.710351i	−0.0592991	+	0.0262195i
$735$		0			0
$736$	16.0461	−	8.99173i	0.591466	−	0.331440i
$737$	11.9748	−	6.91364i	0.441097	−	0.254667i
$738$		0			0
$739$	31.6800	+	18.2905i	1.16537	+	0.672826i	0.952585	−	0.304273i	$-0.0984135\pi$
$739$	31.6800	+	18.2905i	1.16537	+	0.672826i	0.212784	+	0.977099i	$0.431747\pi$
$740$	4.03610	−	18.5205i	0.148370	−	0.680827i
$741$		0			0
$742$	1.39187	+	2.61969i	0.0510972	+	0.0961720i
$743$	−11.7085	−	20.2798i	−0.429545	−	0.743993i	0.567288	−	0.823519i	$-0.307993\pi$
$743$	−11.7085	−	20.2798i	−0.429545	−	0.743993i	−0.996833	+	0.0795261i	$0.974659\pi$
$744$		0			0
$745$	−4.76789	−	8.25822i	−0.174682	−	0.302558i
$746$	−1.35874	+	1.86009i	−0.0497471	+	0.0681028i
$747$		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	$-0.446881\pi$
$751$	−16.5753	−	9.56973i	−0.604840	−	0.349205i	−0.770943	+	0.636904i	$0.780215\pi$
$752$	−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	0.790124	−	0.612947i	$-0.210016\pi$
$761$	18.0513	+	10.4219i	0.654358	+	0.377794i	−0.135766	+	0.990741i	$0.543349\pi$
$762$		0			0
$763$	31.8796	−	21.6078i	1.15412	−	0.782255i
$764$	31.9512	+	6.96299i	1.15595	+	0.251912i
$765$		0			0
$766$	−22.2029	+	30.3953i	−0.802222	+	1.09823i
$767$	3.81015	+	6.59937i	0.137576	+	0.238289i
$768$		0			0
$769$	−7.95585	−	13.7799i	−0.286895	−	0.496917i	0.686172	−	0.727440i	$-0.259290\pi$
$769$	−7.95585	−	13.7799i	−0.286895	−	0.496917i	−0.973067	+	0.230522i	$0.925957\pi$
$770$	3.24268	−	5.18579i	0.116858	−	0.186883i
$771$		0			0
$772$	−22.4883	−	4.90079i	−0.809372	−	0.176383i
$773$	−11.4250	−	6.59625i	−0.410930	−	0.237251i	0.280259	−	0.959924i	$-0.409580\pi$
$773$	−11.4250	−	6.59625i	−0.410930	−	0.237251i	−0.691189	+	0.722674i	$0.742913\pi$
$774$		0			0
$775$	2.70632	−	1.56249i	0.0972138	−	0.0561264i
$776$	28.3434	−	25.1282i	1.01747	−	0.902050i
$777$		0			0
$778$	−37.0655	+	16.3888i	−1.32886	+	0.587567i
$779$	−10.0756	+	17.4515i	−0.360997	+	0.625265i
$780$		0			0
$781$	−9.15748	−	15.8612i	−0.327680	−	0.567559i
$782$	26.2402	−	11.6023i	0.938349	−	0.414898i
$783$		0			0
$784$	6.61739	+	27.2068i	0.236335	+	0.971672i
$785$	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
$790$	13.0843	−	17.9122i	0.465519	−	0.637287i
$791$	−39.8900	+	2.87978i	−1.41832	+	0.102393i
$792$		0			0
$793$	7.52537	+	13.0343i	0.267234	+	0.462863i
$794$	−14.8767	−	33.6458i	−0.527956	−	1.19404i
$795$		0			0
$796$	24.1658	+	21.9846i	0.856533	+	0.779222i
$797$	−25.0813	+	14.4807i	−0.888424	+	0.512932i	−0.873427	−	0.486956i	$-0.838107\pi$
$797$	−25.0813	+	14.4807i	−0.888424	+	0.512932i	−0.0149975	+	0.999888i	$0.504774\pi$
$798$		0			0
$799$	−73.6021	−	42.4942i	−2.60386	−	1.50334i
$800$	0.277103	−	21.5982i	0.00979708	−	0.763612i
$801$		0			0
$802$	−24.7937	−	18.1111i	−0.875496	−	0.639524i
$803$	−12.1190			−0.427671
$804$		0			0
$805$	−9.32725	+	0.673363i	−0.328742	+	0.0237329i
$806$	−3.37121	+	1.49061i	−0.118746	+	0.0525044i
$807$		0			0
$808$	5.71331	−	1.16851i	0.200993	−	0.0411080i
$809$	−6.13234	−	3.54051i	−0.215601	−	0.124478i	0.388310	−	0.921529i	$-0.373059\pi$
$809$	−6.13234	−	3.54051i	−0.215601	−	0.124478i	−0.603912	+	0.797051i	$0.706392\pi$
$810$		0			0
$811$		−	50.7206i		−	1.78104i	−0.454943	−	0.890521i	$-0.650340\pi$
$811$		−	50.7206i		−	1.78104i	0.454943	−	0.890521i	$-0.349660\pi$
$812$	−4.05552	−	10.1215i	−0.142321	−	0.355195i
$813$		0			0
$814$	10.9370	−	14.9725i	0.383340	−	0.524786i
$815$	−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	$0.0738795\pi$
$821$			13.1816i			0.460042i	−0.973186	+	0.230021i	$0.926121\pi$
$822$		0			0
$823$		−	39.6894i		−	1.38349i	−0.722144	−	0.691743i	$-0.756843\pi$
$823$		−	39.6894i		−	1.38349i	0.722144	−	0.691743i	$-0.243157\pi$
$824$	5.49517	+	6.19830i	0.191433	+	0.215928i
$825$		0			0
$826$	−7.59093	−	4.74662i	−0.264122	−	0.165156i
$827$	23.2354			0.807973			0.403987	−	0.914765i	$-0.367624\pi$
$827$	23.2354			0.807973			0.403987	+	0.914765i	$0.367624\pi$
$828$		0			0
$829$	3.93228	−	6.81091i	0.136574	−	0.236553i	−0.789624	−	0.613591i	$-0.789724\pi$
$829$	3.93228	−	6.81091i	0.136574	−	0.236553i	0.926198	+	0.377039i	$0.123058\pi$
$830$	−6.76300	+	2.99031i	−0.234747	+	0.103795i
$831$		0			0
$832$	−3.05294	+	25.2945i	−0.105842	+	0.876930i
$833$	6.27337	+	43.2221i	0.217359	+	1.49756i
$834$		0			0
$835$			4.88681i			0.169115i
$836$	5.90766	+	5.37443i	0.204321	+	0.185879i
$837$		0			0
$838$	4.17319	+	9.43824i	0.144161	+	0.326039i
$839$	−25.5164	+	44.1957i	−0.880925	+	1.52581i	−0.0306106	+	0.999531i	$0.509745\pi$
$839$	−25.5164	+	44.1957i	−0.880925	+	1.52581i	−0.850314	+	0.526275i	$0.823588\pi$
$840$		0			0
$841$	−12.3769	−	21.4375i	−0.426790	−	0.739223i
$842$	−11.3649	+	15.5584i	−0.391661	+	0.536177i
$843$		0			0
$844$	42.7540	−	13.6494i	1.47165	−	0.469833i
$845$	2.68982	−	1.55297i	0.0925326	−	0.0534237i
$846$		0			0
$847$	−19.1386	+	12.9720i	−0.657610	+	0.445724i
$848$	−1.83762	−	2.58465i	−0.0631043	−	0.0887571i
$849$		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	0.0181661	+	0.999835i	$0.494217\pi$
$853$	−25.0238	+	43.3425i	−0.856799	+	1.48402i	−0.874966	+	0.484185i	$0.839116\pi$
$854$	−14.9927	−	9.37499i	−0.513041	−	0.320805i
$855$		0			0
$856$	6.21024	+	30.3643i	0.212262	+	1.03783i
$857$	34.6977	−	20.0327i	1.18525	−	0.684305i	0.228027	−	0.973655i	$-0.426772\pi$
$857$	34.6977	−	20.0327i	1.18525	−	0.684305i	0.957223	+	0.289350i	$0.0934392\pi$
$858$		0			0
$859$	−35.4399	−	20.4612i	−1.20919	−	0.698128i	−0.246610	−	0.969115i	$-0.579317\pi$
$859$	−35.4399	−	20.4612i	−1.20919	−	0.698128i	−0.962583	+	0.270987i	$0.912650\pi$
$860$	−3.01645	−	9.44838i	−0.102860	−	0.322187i
$861$		0			0
$862$	10.0805	−	13.8000i	0.343343	−	0.470030i
$863$	−15.2070	−	26.3392i	−0.517651	−	0.896598i	−0.999790	−	0.0205031i	$-0.993473\pi$
$863$	−15.2070	−	26.3392i	−0.517651	−	0.896598i	0.482139	−	0.876095i	$-0.339860\pi$
$864$		0			0
$865$	10.8103	−	18.7240i	0.367561	−	0.636635i
$866$	31.7975	+	3.42456i	1.08052	+	0.116371i
$867$		0			0
$868$	2.67599	−	3.40488i	0.0908291	−	0.115569i
$869$	18.7912	−	10.8491i	0.637447	−	0.368030i
$870$		0			0
$871$	25.3612	−	14.6423i	0.859331	−	0.496135i
$872$	−30.8075	+	27.3128i	−1.04328	+	0.924928i
$873$		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	−0.539472	−	0.842003i	$-0.681376\pi$
$877$	13.6065	−	23.5672i	0.459460	−	0.795808i	0.998932	+	0.0461951i	$0.0147096\pi$
$878$	−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	$0.103216\pi$
$881$			18.9137i			0.637219i	−0.947886	+	0.318610i	$0.896784\pi$
$882$		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	$-0.742057\pi$
$887$	8.42370	−	14.5903i	0.282840	−	0.489894i	0.972083	+	0.234637i	$0.0753900\pi$
$888$		0			0
$889$	1.07977	−	2.22658i	0.0362143	−	0.0746772i
$890$	−10.4296	−	1.12326i	−0.349601	−	0.0376517i
$891$		0			0
$892$	26.2613	+	23.8909i	0.879292	+	0.799927i
$893$	−31.3264	+	18.0863i	−1.04830	+	0.605235i
$894$		0			0
$895$	−3.48950	+	2.01467i	−0.116641	+	0.0673429i
$896$	−10.7759	−	27.9263i	−0.359999	−	0.932953i
$897$		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
$902$	−13.0312	−	9.51890i	−0.433891	−	0.316945i
$903$		0			0
$904$	41.8880	−	8.56712i	1.39318	−	0.284938i
$905$	−19.3136	−	11.1507i	−0.642004	−	0.370661i
$906$		0			0
$907$	−27.5335	+	15.8965i	−0.914234	+	0.527833i	−0.881791	−	0.471640i	$-0.843662\pi$
$907$	−27.5335	+	15.8965i	−0.914234	+	0.527833i	−0.0324433	+	0.999474i	$0.510329\pi$
$908$	8.14330	+	25.5072i	0.270245	+	0.846485i
$909$		0			0
$910$	6.86762	−	10.9829i	0.227659	−	0.364079i
$911$	16.0911	−	27.8705i	0.533121	−	0.923392i	−0.466131	−	0.884716i	$-0.654353\pi$
$911$	16.0911	−	27.8705i	0.533121	−	0.923392i	0.999252	−	0.0386763i	$-0.0123141\pi$
$912$		0			0
$913$	−7.23328			−0.239387
$914$	23.1638	+	2.49472i	0.766190	+	0.0825179i
$915$		0			0
$916$	17.5923	−	19.3377i	0.581264	−	0.638935i
$917$	−17.6071	+	11.9340i	−0.581436	+	0.394094i
$918$		0			0
$919$	−12.8002	+	7.39019i	−0.422239	+	0.243780i	−0.696035	−	0.718008i	$-0.745054\pi$
$919$	−12.8002	+	7.39019i	−0.422239	+	0.243780i	0.273796	+	0.961788i	$0.411721\pi$
$920$	9.79444	−	2.00320i	0.322913	−	0.0660436i
$921$		0			0
$922$	11.1207	+	8.12335i	0.366241	+	0.267528i
$923$	−19.3945	−	33.5922i	−0.638377	−	1.10570i
$924$		0			0
$925$	−16.6459	+	28.8315i	−0.547313	+	0.947975i
$926$	4.59093	−	2.02991i	0.150867	−	0.0667071i
$927$		0			0
$928$	5.69832	+	10.1689i	0.187057	+	0.333810i
$929$			50.5984i			1.66008i	0.557703	+	0.830041i	$0.311683\pi$
$929$			50.5984i			1.66008i	−0.557703	+	0.830041i	$0.688317\pi$
$930$		0			0
$931$	17.2665	+	6.88570i	0.565887	+	0.225670i
$932$	11.1607	−	3.56312i	0.365581	−	0.116714i
$933$		0			0
$934$	−5.14421	−	11.6343i	−0.168324	−	0.380687i
$935$	−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	$0.320459\pi$
$938$	−18.2411	+	29.1717i	−0.595594	+	0.952490i
$939$		0			0
$940$	−21.9054	−	19.9282i	−0.714476	−	0.649987i
$941$		−	8.32574i		−	0.271411i	−0.990749	−	0.135706i	$-0.956670\pi$
$941$		−	8.32574i		−	0.271411i	0.990749	−	0.135706i	$-0.0433302\pi$
$942$		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	$-0.817517\pi$
$947$	−51.7068			−1.68024			−0.840122	+	0.542397i	$0.817517\pi$
$948$		0			0
$949$	−25.6666			−0.833175
$950$	−11.5796	−	8.45855i	−0.375692	−	0.274432i
$951$		0			0
$952$	−12.6252	−	44.9512i	−0.409184	−	1.45688i
$953$		−	23.0749i		−	0.747468i	−0.927536	−	0.373734i	$-0.878077\pi$
$953$		−	23.0749i		−	0.747468i	0.927536	−	0.373734i	$-0.121923\pi$
$954$		0			0
$955$	15.3922	+	8.88672i	0.498081	+	0.287567i
$956$	5.21508	+	16.3351i	0.168668	+	0.528315i
$957$		0			0
$958$	9.70962	+	21.9596i	0.313704	+	0.709483i
$959$	43.1552	−	3.11551i	1.39355	−	0.100605i
$960$		0			0
$961$	30.3302			0.978394
$962$	23.1632	−	31.7100i	0.746812	−	1.02237i
$963$		0			0
$964$	−1.68827	−	5.28815i	−0.0543755	−	0.170320i
$965$	−10.8336	−	6.25478i	−0.348746	−	0.201348i
$966$		0			0
$967$	30.3476	−	17.5212i	0.975913	−	0.563444i	0.0748791	−	0.997193i	$-0.476143\pi$
$967$	30.3476	−	17.5212i	0.975913	−	0.563444i	0.901034	+	0.433749i	$0.142810\pi$
$968$	18.4950	−	16.3970i	0.594452	−	0.527018i
$969$		0			0
$970$	18.8290	−	8.32537i	0.604561	−	0.267311i
$971$	6.33039	+	10.9646i	0.203152	+	0.351869i	0.949542	−	0.313639i	$-0.101548\pi$
$971$	6.33039	+	10.9646i	0.203152	+	0.351869i	−0.746390	+	0.665508i	$0.768215\pi$
$972$		0			0
$973$	61.1098	−	4.41171i	1.95909	−	0.141433i
$974$	1.15125	+	0.840954i	0.0368885	+	0.0269459i
$975$		0			0
$976$	17.1893	+	7.86555i	0.550217	+	0.251770i
$977$		−	20.1911i		−	0.645970i	−0.946404	−	0.322985i	$-0.895314\pi$
$977$		−	20.1911i		−	0.645970i	0.946404	−	0.322985i	$-0.104686\pi$
$978$		0			0
$979$	−8.88634	−	5.13053i	−0.284009	−	0.163972i
$980$	−1.07102	+	15.1806i	−0.0342124	+	0.484927i
$981$		0			0
$982$	−1.12015	−	2.53337i	−0.0357453	−	0.0808430i
$983$	−21.9010	−	37.9337i	−0.698534	−	1.20990i	−0.968975	−	0.247159i	$-0.920503\pi$
$983$	−21.9010	−	37.9337i	−0.698534	−	1.20990i	0.270441	−	0.962736i	$-0.412830\pi$
$984$		0			0
$985$	6.32573	−	10.9565i	0.201554	−	0.349103i
$986$	7.35274	+	16.6292i	0.234159	+	0.529582i
$987$		0			0
$988$	12.5117	+	11.3824i	0.398051	+	0.362123i
$989$	−12.8466	+	7.41698i	−0.408498	+	0.235846i
$990$		0			0
$991$	24.9914	+	14.4288i	0.793878	+	0.458346i	0.841326	−	0.540528i	$-0.181776\pi$
$991$	24.9914	+	14.4288i	0.793878	+	0.458346i	−0.0474481	+	0.998874i	$0.515109\pi$
$992$	−2.36605	+	3.97933i	−0.0751221	+	0.126344i
$993$		0			0
$994$	38.6394	+	24.1613i	1.22557	+	0.766350i
$995$	8.87818	+	15.3775i	0.281457	+	0.487498i
$996$		0			0
$997$	11.8621	+	20.5457i	0.375676	+	0.650690i	0.990428	−	0.138031i	$-0.0440772\pi$
$997$	11.8621	+	20.5457i	0.375676	+	0.650690i	−0.614752	+	0.788720i	$0.710744\pi$
$998$	31.3285	+	22.8846i	0.991687	+	0.724398i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bb.a.683.42		88
3.2	odd	2		252.2.bb.a.11.3	yes	88
4.3	odd	2	inner	756.2.bb.a.683.3		88
7.2	even	3		756.2.o.a.359.17		88
9.4	even	3		252.2.o.a.95.14	✓	88
9.5	odd	6		756.2.o.a.179.31		88
12.11	even	2		252.2.bb.a.11.42	yes	88
21.2	odd	6		252.2.o.a.191.28	yes	88
28.23	odd	6		756.2.o.a.359.31		88
36.23	even	6		756.2.o.a.179.17		88
36.31	odd	6		252.2.o.a.95.28	yes	88
63.23	odd	6	inner	756.2.bb.a.611.3		88
63.58	even	3		252.2.bb.a.23.42	yes	88
84.23	even	6		252.2.o.a.191.14	yes	88
252.23	even	6	inner	756.2.bb.a.611.42		88
252.247	odd	6		252.2.bb.a.23.3	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.o.a.95.14	✓	88	9.4	even	3
252.2.o.a.95.28	yes	88	36.31	odd	6
252.2.o.a.191.14	yes	88	84.23	even	6
252.2.o.a.191.28	yes	88	21.2	odd	6
252.2.bb.a.11.3	yes	88	3.2	odd	2
252.2.bb.a.11.42	yes	88	12.11	even	2
252.2.bb.a.23.3	yes	88	252.247	odd	6
252.2.bb.a.23.42	yes	88	63.58	even	3
756.2.o.a.179.17		88	36.23	even	6
756.2.o.a.179.31		88	9.5	odd	6
756.2.o.a.359.17		88	7.2	even	3
756.2.o.a.359.31		88	28.23	odd	6
756.2.bb.a.611.3		88	63.23	odd	6	inner
756.2.bb.a.611.42		88	252.23	even	6	inner
756.2.bb.a.683.3		88	4.3	odd	2	inner
756.2.bb.a.683.42		88	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(1.40608 + 0.151434i) q^{2} +(1.95414 + 0.425857i) q^{4} +(0.941391 + 0.543513i) q^{5} +(-2.38059 - 1.15446i) q^{7} +(2.68319 + 0.894712i) q^{8} +O(q^{10})\)	\(q+(1.40608 + 0.151434i) q^{2} +(1.95414 + 0.425857i) q^{4} +(0.941391 + 0.543513i) q^{5} +(-2.38059 - 1.15446i) q^{7} +(2.68319 + 0.894712i) q^{8} +(1.24137 + 0.906782i) q^{10} +(0.751874 + 1.30228i) q^{11} +(1.59238 + 2.75809i) q^{13} +(-3.17249 - 1.98376i) q^{14} +(3.63729 + 1.66436i) q^{16} +(5.40337 + 3.11964i) q^{17} +(2.29977 - 1.32777i) q^{19} +(1.60815 + 1.46300i) q^{20} +(0.859987 + 1.94498i) q^{22} +(1.62579 - 2.81595i) q^{23} +(-1.90919 - 3.30681i) q^{25} +(1.82135 + 4.11924i) q^{26} +(-4.16037 - 3.26976i) q^{28} +(1.78455 + 1.03031i) q^{29} +0.818407i q^{31} +(4.86229 + 2.89104i) q^{32} +(7.12517 + 5.20472i) q^{34} +(-1.61361 - 2.38068i) q^{35} +(-4.35941 - 7.55073i) q^{37} +(3.43474 - 1.51870i) q^{38} +(2.03964 + 2.30062i) q^{40} +(-6.57171 + 3.79418i) q^{41} +(-3.95088 - 2.28104i) q^{43} +(0.914677 + 2.86503i) q^{44} +(2.71242 - 3.71325i) q^{46} -13.6215 q^{47} +(4.33446 + 5.49658i) q^{49} +(-2.18371 - 4.93876i) q^{50} +(1.93718 + 6.06780i) q^{52} +(-0.686610 - 0.396415i) q^{53} +1.63461i q^{55} +(-5.35467 - 5.22757i) q^{56} +(2.35320 + 1.71894i) q^{58} +2.39274 q^{59} +4.72586 q^{61} +(-0.123935 + 1.15075i) q^{62} +(6.39898 + 4.80136i) q^{64} +3.46192i q^{65} -9.19521i q^{67} +(9.23041 + 8.39726i) q^{68} +(-1.90835 - 3.59178i) q^{70} -12.1795 q^{71} +(-4.02960 + 6.97947i) q^{73} +(-4.98626 - 11.2771i) q^{74} +(5.05951 - 1.61528i) q^{76} +(-0.286478 - 3.96822i) q^{77} -14.4294i q^{79} +(2.51951 + 3.54373i) q^{80} +(-9.81494 + 4.33975i) q^{82} +(-2.40508 + 4.16573i) q^{83} +(3.39113 + 5.87360i) q^{85} +(-5.20984 - 3.80563i) q^{86} +(0.852249 + 4.16698i) q^{88} +(-5.90946 + 3.41183i) q^{89} +(-0.606727 - 8.40422i) q^{91} +(4.37620 - 4.81039i) q^{92} +(-19.1530 - 2.06276i) q^{94} +2.88665 q^{95} +(6.69603 - 11.5979i) q^{97} +(5.26224 + 8.38503i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q - 2 q^{4} + 6 q^{5}+O(q^{10}) \) 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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