LMFDB - Embedded newform 1512.2.cx.a.89.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1512,2,Mod(17,1512)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1512, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1512.17"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.cx (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 504)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.20
Character	$\chi$	$=$	1512.89
Dual form			1512.2.cx.a.17.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+2.22094 q^{5} +(-2.45091 + 0.996507i) q^{7} +1.17296i q^{11} +(3.12404 - 1.80366i) q^{13} +(3.71178 + 6.42899i) q^{17} +(-3.05231 - 1.76225i) q^{19} -5.81246i q^{23} -0.0674336 q^{25} +(6.04430 + 3.48968i) q^{29} +(6.88517 + 3.97516i) q^{31} +(-5.44333 + 2.21318i) q^{35} +(-5.54350 + 9.60163i) q^{37} +(0.809022 + 1.40127i) q^{41} +(0.904302 - 1.56630i) q^{43} +(4.26476 + 7.38679i) q^{47} +(5.01395 - 4.88471i) q^{49} +(9.62611 - 5.55764i) q^{53} +2.60508i q^{55} +(2.00138 - 3.46649i) q^{59} +(-7.09004 + 4.09344i) q^{61} +(6.93830 - 4.00583i) q^{65} +(-4.96334 + 8.59676i) q^{67} -3.67194i q^{71} +(6.92803 - 3.99990i) q^{73} +(-1.16887 - 2.87483i) q^{77} +(2.25993 + 3.91432i) q^{79} +(0.390969 - 0.677179i) q^{83} +(8.24363 + 14.2784i) q^{85} +(-1.75440 + 3.03870i) q^{89} +(-5.85938 + 7.53375i) q^{91} +(-6.77900 - 3.91386i) q^{95} +(-3.49226 - 2.01626i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 48 q^{25} - 18 q^{29} + 18 q^{31} + 6 q^{41} - 6 q^{43} - 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} + 6 q^{79} + 18 q^{89} + 6 q^{91} + 54 q^{95}+O(q^{100}) $ 48 * q + 48 * q^25 - 18 * q^29 + 18 * q^31 + 6 * q^41 - 6 * q^43 - 18 * q^47 - 12 * q^49 + 12 * q^53 + 18 * q^61 + 36 * q^65 + 12 * q^77 + 6 * q^79 + 18 * q^89 + 6 * q^91 + 54 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	2.22094			0.993234			0.496617	−	0.867970i	$-0.334575\pi$
$5$	2.22094			0.993234			0.496617	+	0.867970i	$0.334575\pi$
$6$		0			0
$7$	−2.45091	+	0.996507i	−0.926358	+	0.376644i
$7$	−2.45091	+	0.996507i	−0.926358	+	0.376644i
$8$		0			0
$9$		0			0
$10$		0			0
$11$			1.17296i			0.353662i	0.984241	+	0.176831i	$0.0565846\pi$
$11$			1.17296i			0.353662i	−0.984241	+	0.176831i	$0.943415\pi$
$12$		0			0
$13$	3.12404	−	1.80366i	0.866453	−	0.500247i	0.000284763	−	1.00000i	$-0.499909\pi$
$13$	3.12404	−	1.80366i	0.866453	−	0.500247i	0.866168	+	0.499753i	$0.166576\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.71178	+	6.42899i	0.900238	+	1.55926i	0.827185	+	0.561930i	$0.189941\pi$
$17$	3.71178	+	6.42899i	0.900238	+	1.55926i	0.0730533	+	0.997328i	$0.476726\pi$
$18$		0			0
$19$	−3.05231	−	1.76225i	−0.700249	−	0.404289i	0.107191	−	0.994238i	$-0.465814\pi$
$19$	−3.05231	−	1.76225i	−0.700249	−	0.404289i	−0.807440	+	0.589950i	$0.799148\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	5.81246i		−	1.21198i	−0.795472	−	0.605991i	$-0.792777\pi$
$23$		−	5.81246i		−	1.21198i	0.795472	−	0.605991i	$-0.207223\pi$
$24$		0			0
$25$	−0.0674336			−0.0134867
$26$		0			0
$27$		0			0
$28$		0			0
$29$	6.04430	+	3.48968i	1.12240	+	0.648017i	0.942012	−	0.335579i	$-0.108932\pi$
$29$	6.04430	+	3.48968i	1.12240	+	0.648017i	0.180387	+	0.983596i	$0.442265\pi$
$30$		0			0
$31$	6.88517	+	3.97516i	1.23661	+	0.713959i	0.968400	−	0.249400i	$-0.0802335\pi$
$31$	6.88517	+	3.97516i	1.23661	+	0.713959i	0.268213	+	0.963360i	$0.413567\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−5.44333	+	2.21318i	−0.920090	+	0.374096i
$36$		0			0
$37$	−5.54350	+	9.60163i	−0.911346	+	1.57850i	−0.0991818	+	0.995069i	$0.531623\pi$
$37$	−5.54350	+	9.60163i	−0.911346	+	1.57850i	−0.812164	+	0.583429i	$0.801711\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	0.809022	+	1.40127i	0.126348	+	0.218841i	0.922259	−	0.386572i	$-0.126341\pi$
$41$	0.809022	+	1.40127i	0.126348	+	0.218841i	−0.795911	+	0.605414i	$0.793008\pi$
$42$		0			0
$43$	0.904302	−	1.56630i	0.137905	−	0.238858i	−0.788799	−	0.614652i	$-0.789297\pi$
$43$	0.904302	−	1.56630i	0.137905	−	0.238858i	0.926703	+	0.375794i	$0.122630\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.26476	+	7.38679i	0.622080	+	1.07747i	0.989098	+	0.147260i	$0.0470454\pi$
$47$	4.26476	+	7.38679i	0.622080	+	1.07747i	−0.367018	+	0.930214i	$0.619621\pi$
$48$		0			0
$49$	5.01395	−	4.88471i	0.716278	−	0.697815i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	9.62611	−	5.55764i	1.32225	−	0.763400i	0.338161	−	0.941088i	$-0.390195\pi$
$53$	9.62611	−	5.55764i	1.32225	−	0.763400i	0.984087	+	0.177688i	$0.0568617\pi$
$54$		0			0
$55$			2.60508i			0.351269i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	2.00138	−	3.46649i	0.260557	−	0.451298i	−0.705833	−	0.708378i	$-0.749427\pi$
$59$	2.00138	−	3.46649i	0.260557	−	0.451298i	0.966390	+	0.257080i	$0.0827604\pi$
$60$		0			0
$61$	−7.09004	+	4.09344i	−0.907787	+	0.524111i	−0.879718	−	0.475495i	$-0.842269\pi$
$61$	−7.09004	+	4.09344i	−0.907787	+	0.524111i	−0.0280684	+	0.999606i	$0.508936\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	6.93830	−	4.00583i	0.860590	−	0.496862i
$66$		0			0
$67$	−4.96334	+	8.59676i	−0.606369	+	1.05026i	0.385465	+	0.922723i	$0.374041\pi$
$67$	−4.96334	+	8.59676i	−0.606369	+	1.05026i	−0.991834	+	0.127539i	$0.959292\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	3.67194i		−	0.435779i	−0.975973	−	0.217890i	$-0.930083\pi$
$71$		−	3.67194i		−	0.435779i	0.975973	−	0.217890i	$-0.0699172\pi$
$72$		0			0
$73$	6.92803	−	3.99990i	0.810865	−	0.468153i	−0.0363913	−	0.999338i	$-0.511586\pi$
$73$	6.92803	−	3.99990i	0.810865	−	0.468153i	0.847256	+	0.531185i	$0.178253\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.16887	−	2.87483i	−0.133205	−	0.327618i
$78$		0			0
$79$	2.25993	+	3.91432i	0.254262	+	0.440395i	0.964695	−	0.263370i	$-0.0848340\pi$
$79$	2.25993	+	3.91432i	0.254262	+	0.440395i	−0.710433	+	0.703765i	$0.751501\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.390969	−	0.677179i	0.0429145	−	0.0743300i	−0.843770	−	0.536704i	$-0.819669\pi$
$83$	0.390969	−	0.677179i	0.0429145	−	0.0743300i	0.886685	+	0.462374i	$0.153002\pi$
$84$		0			0
$85$	8.24363	+	14.2784i	0.894147	+	1.54871i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.75440	+	3.03870i	−0.185966	+	0.322102i	−0.943901	−	0.330227i	$-0.892875\pi$
$89$	−1.75440	+	3.03870i	−0.185966	+	0.322102i	0.757936	+	0.652329i	$0.226208\pi$
$90$		0			0
$91$	−5.85938	+	7.53375i	−0.614230	+	0.789752i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−6.77900	−	3.91386i	−0.695511	−	0.401553i
$96$		0			0
$97$	−3.49226	−	2.01626i	−0.354585	−	0.204720i	0.312118	−	0.950043i	$-0.398962\pi$
$97$	−3.49226	−	2.01626i	−0.354585	−	0.204720i	−0.666703	+	0.745324i	$0.732295\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−2.27809			−0.226678			−0.113339	−	0.993556i	$-0.536155\pi$
$101$	−2.27809			−0.226678			−0.113339	+	0.993556i	$0.536155\pi$
$102$		0			0
$103$			8.87303i			0.874285i	0.899392	+	0.437143i	$0.144010\pi$
$103$			8.87303i			0.874285i	−0.899392	+	0.437143i	$0.855990\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	0.574764	+	0.331840i	0.0555646	+	0.0320802i	0.527525	−	0.849540i	$-0.323120\pi$
$107$	0.574764	+	0.331840i	0.0555646	+	0.0320802i	−0.471960	+	0.881620i	$0.656453\pi$
$108$		0			0
$109$	−8.03435	−	13.9159i	−0.769551	−	1.33290i	−0.937807	−	0.347158i	$-0.887147\pi$
$109$	−8.03435	−	13.9159i	−0.769551	−	1.33290i	0.168256	−	0.985743i	$-0.446187\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	4.86666	−	2.80977i	0.457817	−	0.264321i	−0.253309	−	0.967385i	$-0.581519\pi$
$113$	4.86666	−	2.80977i	0.457817	−	0.264321i	0.711126	+	0.703065i	$0.248186\pi$
$114$		0			0
$115$		−	12.9091i		−	1.20378i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−15.5038	−	12.0581i	−1.42123	−	1.10536i
$120$		0			0
$121$	9.62415			0.874923
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−11.2545			−1.00663
$126$		0			0
$127$	7.74425			0.687191			0.343595	−	0.939118i	$-0.388355\pi$
$127$	7.74425			0.687191			0.343595	+	0.939118i	$0.388355\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	15.6259			1.36524			0.682619	−	0.730774i	$-0.260841\pi$
$131$	15.6259			1.36524			0.682619	+	0.730774i	$0.260841\pi$
$132$		0			0
$133$	9.23705	+	1.27748i	0.800954	+	0.110771i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		−	1.07565i		−	0.0918991i	−0.998944	−	0.0459496i	$-0.985369\pi$
$137$		−	1.07565i		−	0.0918991i	0.998944	−	0.0459496i	$-0.0146313\pi$
$138$		0			0
$139$	5.81776	−	3.35889i	0.493456	−	0.284897i	−0.232551	−	0.972584i	$-0.574707\pi$
$139$	5.81776	−	3.35889i	0.493456	−	0.284897i	0.726007	+	0.687687i	$0.241374\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	2.11563	+	3.66439i	0.176918	+	0.306431i
$144$		0			0
$145$	13.4240	+	7.75036i	1.11480	+	0.643633i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			17.5635i			1.43886i	0.694565	+	0.719430i	$0.255597\pi$
$149$			17.5635i			1.43886i	−0.694565	+	0.719430i	$0.744403\pi$
$150$		0			0
$151$	1.69606			0.138023			0.0690115	−	0.997616i	$-0.478015\pi$
$151$	1.69606			0.138023			0.0690115	+	0.997616i	$0.478015\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	15.2915	+	8.82858i	1.22825	+	0.709128i
$156$		0			0
$157$	6.82630	+	3.94116i	0.544798	+	0.314539i	0.747021	−	0.664800i	$-0.231483\pi$
$157$	6.82630	+	3.94116i	0.544798	+	0.314539i	−0.202223	+	0.979339i	$0.564817\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	5.79216	+	14.2458i	0.456486	+	1.12273i
$162$		0			0
$163$	−5.69385	+	9.86204i	−0.445977	+	0.772455i	−0.998120	−	0.0612949i	$-0.980477\pi$
$163$	−5.69385	+	9.86204i	−0.445977	+	0.772455i	0.552143	+	0.833750i	$0.313810\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−8.05638	−	13.9541i	−0.623422	−	1.07980i	−0.988844	−	0.148956i	$-0.952409\pi$
$167$	−8.05638	−	13.9541i	−0.623422	−	1.07980i	0.365422	−	0.930842i	$-0.380925\pi$
$168$		0			0
$169$	0.00641296	−	0.0111076i	0.000493305	−	0.000854429i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.45182	−	5.97872i	−0.262437	−	0.454554i	0.704452	−	0.709752i	$-0.251193\pi$
$173$	−3.45182	−	5.97872i	−0.262437	−	0.454554i	−0.966889	+	0.255198i	$0.917859\pi$
$174$		0			0
$175$	0.165274	−	0.0671981i	0.0124935	−	0.00507970i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	5.28759	−	3.05279i	0.395213	−	0.228176i	−0.289203	−	0.957268i	$-0.593390\pi$
$179$	5.28759	−	3.05279i	0.395213	−	0.228176i	0.684416	+	0.729091i	$0.260057\pi$
$180$		0			0
$181$		−	5.46329i		−	0.406083i	−0.979170	−	0.203041i	$-0.934917\pi$
$181$		−	5.46329i		−	0.406083i	0.979170	−	0.203041i	$-0.0650826\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−12.3118	+	21.3246i	−0.905180	+	1.56782i
$186$		0			0
$187$	−7.54097	+	4.35378i	−0.551451	+	0.318380i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−5.21032	+	3.00818i	−0.377005	+	0.217664i	−0.676515	−	0.736429i	$-0.736510\pi$
$191$	−5.21032	+	3.00818i	−0.377005	+	0.217664i	0.299509	+	0.954093i	$0.403177\pi$
$192$		0			0
$193$	2.89017	−	5.00592i	0.208039	−	0.360334i	−0.743058	−	0.669227i	$-0.766625\pi$
$193$	2.89017	−	5.00592i	0.208039	−	0.360334i	0.951097	+	0.308893i	$0.0999586\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	7.95354i		−	0.566666i	−0.959022	−	0.283333i	$-0.908560\pi$
$197$		−	7.95354i		−	0.566666i	0.959022	−	0.283333i	$-0.0914402\pi$
$198$		0			0
$199$	−15.5229	+	8.96214i	−1.10039	+	0.635309i	−0.936323	−	0.351141i	$-0.885794\pi$
$199$	−15.5229	+	8.96214i	−1.10039	+	0.635309i	−0.164065	+	0.986450i	$0.552461\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−18.2915	−	2.52971i	−1.28382	−	0.177551i
$204$		0			0
$205$	1.79679	+	3.11213i	0.125493	+	0.217360i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.06706	−	3.58026i	0.142982	−	0.247651i
$210$		0			0
$211$	−4.00200	−	6.93166i	−0.275509	−	0.477195i	0.694755	−	0.719247i	$-0.255513\pi$
$211$	−4.00200	−	6.93166i	−0.275509	−	0.477195i	−0.970263	+	0.242052i	$0.922180\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	2.00840	−	3.47865i	0.136972	−	0.237242i
$216$		0			0
$217$	−20.8362	−	2.88164i	−1.41446	−	0.195618i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	23.1915	+	13.3896i	1.56003	+	0.900682i
$222$		0			0
$223$	−14.2405	−	8.22177i	−0.953616	−	0.550570i	−0.0594134	−	0.998233i	$-0.518923\pi$
$223$	−14.2405	−	8.22177i	−0.953616	−	0.550570i	−0.894202	+	0.447663i	$0.852256\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	15.9930			1.06149			0.530746	−	0.847531i	$-0.321912\pi$
$227$	15.9930			1.06149			0.530746	+	0.847531i	$0.321912\pi$
$228$		0			0
$229$		−	15.4612i		−	1.02170i	−0.859669	−	0.510851i	$-0.829330\pi$
$229$		−	15.4612i		−	1.02170i	0.859669	−	0.510851i	$-0.170670\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−16.5268	−	9.54175i	−1.08271	−	0.625101i	−0.151081	−	0.988521i	$-0.548275\pi$
$233$	−16.5268	−	9.54175i	−1.08271	−	0.625101i	−0.931625	+	0.363421i	$0.881609\pi$
$234$		0			0
$235$	9.47178	+	16.4056i	0.617871	+	1.07018i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−7.37626	+	4.25868i	−0.477130	+	0.275471i	−0.719220	−	0.694783i	$-0.755501\pi$
$239$	−7.37626	+	4.25868i	−0.477130	+	0.275471i	0.242089	+	0.970254i	$0.422167\pi$
$240$		0			0
$241$		−	22.6376i		−	1.45821i	−0.684400	−	0.729107i	$-0.739936\pi$
$241$		−	22.6376i		−	1.45821i	0.684400	−	0.729107i	$-0.260064\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	11.1357	−	10.8486i	0.711431	−	0.693093i
$246$		0			0
$247$	−12.7141			−0.808976
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−7.74235			−0.488693			−0.244346	−	0.969688i	$-0.578573\pi$
$251$	−7.74235			−0.488693			−0.244346	+	0.969688i	$0.578573\pi$
$252$		0			0
$253$	6.81781			0.428632
$254$		0			0
$255$		0			0
$256$		0			0
$257$	23.7890			1.48392			0.741958	−	0.670447i	$-0.233897\pi$
$257$	23.7890			1.48392			0.741958	+	0.670447i	$0.233897\pi$
$258$		0			0
$259$	4.01855	−	29.0569i	0.249700	−	1.80551i
$260$		0			0
$261$		0			0
$262$		0			0
$263$			20.5341i			1.26619i	0.774075	+	0.633094i	$0.218215\pi$
$263$			20.5341i			1.26619i	−0.774075	+	0.633094i	$0.781785\pi$
$264$		0			0
$265$	21.3790	−	12.3432i	1.31330	−	0.758235i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−6.17188	−	10.6900i	−0.376306	−	0.651782i	0.614215	−	0.789138i	$-0.289473\pi$
$269$	−6.17188	−	10.6900i	−0.376306	−	0.651782i	−0.990522	+	0.137357i	$0.956139\pi$
$270$		0			0
$271$	−25.3900	−	14.6589i	−1.54233	−	0.890467i	−0.998691	−	0.0511505i	$-0.983711\pi$
$271$	−25.3900	−	14.6589i	−1.54233	−	0.890467i	−0.543643	−	0.839317i	$-0.682955\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$		−	0.0790972i		−	0.00476974i
$276$		0			0
$277$	−2.48230			−0.149147			−0.0745735	−	0.997216i	$-0.523760\pi$
$277$	−2.48230			−0.149147			−0.0745735	+	0.997216i	$0.523760\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−20.0970	−	11.6030i	−1.19889	−	0.692178i	−0.238581	−	0.971123i	$-0.576682\pi$
$281$	−20.0970	−	11.6030i	−1.19889	−	0.692178i	−0.960307	+	0.278944i	$0.910015\pi$
$282$		0			0
$283$	−23.6425	−	13.6500i	−1.40540	−	0.811408i	−0.410460	−	0.911879i	$-0.634632\pi$
$283$	−23.6425	−	13.6500i	−1.40540	−	0.811408i	−0.994940	+	0.100471i	$0.967965\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.37922	−	2.62819i	−0.199469	−	0.155137i
$288$		0			0
$289$	−19.0546	+	33.0035i	−1.12086	+	1.94138i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.15628	−	7.19888i	−0.242812	−	0.420563i	0.718702	−	0.695318i	$-0.244737\pi$
$293$	−4.15628	−	7.19888i	−0.242812	−	0.420563i	−0.961514	+	0.274755i	$0.911403\pi$
$294$		0			0
$295$	4.44494	−	7.69886i	0.258794	−	0.448245i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−10.4837	−	18.1584i	−0.606290	−	1.05012i
$300$		0			0
$301$	−0.655539	+	4.74000i	−0.0377846	+	0.273209i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−15.7465	+	9.09127i	−0.901645	+	0.520565i
$306$		0			0
$307$		−	22.4908i		−	1.28362i	−0.766864	−	0.641810i	$-0.778184\pi$
$307$		−	22.4908i		−	1.28362i	0.766864	−	0.641810i	$-0.221816\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−4.83900	+	8.38139i	−0.274394	+	0.475265i	−0.969982	−	0.243176i	$-0.921811\pi$
$311$	−4.83900	+	8.38139i	−0.274394	+	0.475265i	0.695588	+	0.718441i	$0.255144\pi$
$312$		0			0
$313$	21.2150	−	12.2485i	1.19914	−	0.692324i	0.238776	−	0.971075i	$-0.423254\pi$
$313$	21.2150	−	12.2485i	1.19914	−	0.692324i	0.960363	+	0.278751i	$0.0899204\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.95548	+	4.59310i	−0.446824	+	0.257974i	−0.706488	−	0.707725i	$-0.749722\pi$
$317$	−7.95548	+	4.59310i	−0.446824	+	0.257974i	0.259664	+	0.965699i	$0.416388\pi$
$318$		0			0
$319$	−4.09327	+	7.08975i	−0.229179	+	0.396950i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	26.1644i		−	1.45582i
$324$		0			0
$325$	−0.210665	+	0.121628i	−0.0116856	+	0.00674668i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−17.8136	−	13.8545i	−0.982093	−	0.763823i
$330$		0			0
$331$	−12.8599	−	22.2739i	−0.706842	−	1.22429i	−0.966023	−	0.258457i	$-0.916786\pi$
$331$	−12.8599	−	22.2739i	−0.706842	−	1.22429i	0.259181	−	0.965829i	$-0.416547\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−11.0233	+	19.0929i	−0.602266	+	1.04316i
$336$		0			0
$337$	8.80657	+	15.2534i	0.479724	+	0.830907i	0.999730	−	0.0232560i	$-0.00740329\pi$
$337$	8.80657	+	15.2534i	0.479724	+	0.830907i	−0.520005	+	0.854163i	$0.674070\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−4.66272	+	8.07606i	−0.252500	+	0.437343i
$342$		0			0
$343$	−7.42110	+	16.9684i	−0.400702	+	0.916209i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.23389	−	4.17649i	−0.388335	−	0.224206i	0.293103	−	0.956081i	$-0.405312\pi$
$347$	−7.23389	−	4.17649i	−0.388335	−	0.224206i	−0.681439	+	0.731875i	$0.738645\pi$
$348$		0			0
$349$	−16.4062	−	9.47211i	−0.878203	−	0.507031i	−0.00813729	−	0.999967i	$-0.502590\pi$
$349$	−16.4062	−	9.47211i	−0.878203	−	0.507031i	−0.870065	+	0.492936i	$0.835924\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−25.4971			−1.35707			−0.678537	−	0.734566i	$-0.737386\pi$
$353$	−25.4971			−1.35707			−0.678537	+	0.734566i	$0.737386\pi$
$354$		0			0
$355$		−	8.15515i		−	0.432830i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	17.4128	+	10.0533i	0.919013	+	0.530592i	0.883320	−	0.468771i	$-0.155303\pi$
$359$	17.4128	+	10.0533i	0.919013	+	0.530592i	0.0356928	+	0.999363i	$0.488636\pi$
$360$		0			0
$361$	−3.28892	−	5.69658i	−0.173101	−	0.299820i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	15.3867	−	8.88353i	0.805378	−	0.464985i
$366$		0			0
$367$			23.2850i			1.21547i	0.794140	+	0.607735i	$0.207922\pi$
$367$			23.2850i			1.21547i	−0.794140	+	0.607735i	$0.792078\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−18.0545	+	23.2138i	−0.937345	+	1.20520i
$372$		0			0
$373$	−25.1249			−1.30092			−0.650460	−	0.759540i	$-0.725424\pi$
$373$	−25.1249			−1.30092			−0.650460	+	0.759540i	$0.725424\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	25.1768			1.29667
$378$		0			0
$379$	32.3000			1.65914			0.829569	−	0.558404i	$-0.188586\pi$
$379$	32.3000			1.65914			0.829569	+	0.558404i	$0.188586\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−9.54363			−0.487657			−0.243828	−	0.969818i	$-0.578403\pi$
$383$	−9.54363			−0.487657			−0.243828	+	0.969818i	$0.578403\pi$
$384$		0			0
$385$	−2.59598	−	6.38483i	−0.132304	−	0.325401i
$386$		0			0
$387$		0			0
$388$		0			0
$389$		−	13.6201i		−	0.690566i	−0.938499	−	0.345283i	$-0.887783\pi$
$389$		−	13.6201i		−	0.690566i	0.938499	−	0.345283i	$-0.112217\pi$
$390$		0			0
$391$	37.3682	−	21.5746i	1.88979	−	1.09107i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	5.01917	+	8.69346i	0.252542	+	0.437415i
$396$		0			0
$397$	2.59589	+	1.49874i	0.130284	+	0.0752196i	0.563726	−	0.825962i	$-0.309368\pi$
$397$	2.59589	+	1.49874i	0.130284	+	0.0752196i	−0.433441	+	0.901182i	$0.642701\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$			13.0336i			0.650869i	0.945565	+	0.325434i	$0.105511\pi$
$401$			13.0336i			0.650869i	−0.945565	+	0.325434i	$0.894489\pi$
$402$		0			0
$403$	28.6794			1.42862
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−11.2624	−	6.50233i	−0.558255	−	0.322309i
$408$		0			0
$409$	−28.4682	−	16.4361i	−1.40766	−	0.812714i	−0.412500	−	0.910958i	$-0.635344\pi$
$409$	−28.4682	−	16.4361i	−1.40766	−	0.812714i	−0.995162	+	0.0982431i	$0.968678\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−1.45082	+	10.4905i	−0.0713903	+	0.516201i
$414$		0			0
$415$	0.868319	−	1.50397i	0.0426241	−	0.0738271i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−11.0687	−	19.1716i	−0.540742	−	0.936593i	−0.998862	−	0.0477024i	$-0.984810\pi$
$419$	−11.0687	−	19.1716i	−0.540742	−	0.936593i	0.458119	−	0.888891i	$-0.348523\pi$
$420$		0			0
$421$	12.1963	−	21.1245i	0.594409	−	1.02955i	−0.399221	−	0.916855i	$-0.630719\pi$
$421$	12.1963	−	21.1245i	0.594409	−	1.02955i	0.993630	−	0.112692i	$-0.0359472\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.250298	−	0.433529i	−0.0121413	−	0.0210293i
$426$		0			0
$427$	13.2979	−	17.0979i	0.643532	−	0.827427i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	12.2611	−	7.07897i	0.590598	−	0.340982i	−0.174736	−	0.984615i	$-0.555907\pi$
$431$	12.2611	−	7.07897i	0.590598	−	0.340982i	0.765334	+	0.643634i	$0.222574\pi$
$432$		0			0
$433$			8.90220i			0.427813i	0.976854	+	0.213906i	$0.0686187\pi$
$433$			8.90220i			0.427813i	−0.976854	+	0.213906i	$0.931381\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−10.2430	+	17.7415i	−0.489991	+	0.848689i
$438$		0			0
$439$	−13.9971	+	8.08120i	−0.668043	+	0.385695i	−0.795335	−	0.606171i	$-0.792705\pi$
$439$	−13.9971	+	8.08120i	−0.668043	+	0.385695i	0.127292	+	0.991865i	$0.459372\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	15.1101	−	8.72383i	0.717903	−	0.414482i	−0.0960772	−	0.995374i	$-0.530630\pi$
$443$	15.1101	−	8.72383i	0.717903	−	0.414482i	0.813980	+	0.580892i	$0.197296\pi$
$444$		0			0
$445$	−3.89640	+	6.74877i	−0.184707	+	0.319922i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			9.14988i			0.431809i	0.976414	+	0.215905i	$0.0692700\pi$
$449$			9.14988i			0.431809i	−0.976414	+	0.215905i	$0.930730\pi$
$450$		0			0
$451$	−1.64364	+	0.948954i	−0.0773958	+	0.0446845i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−13.0133	+	16.7320i	−0.610074	+	0.784408i
$456$		0			0
$457$	−7.05757	−	12.2241i	−0.330139	−	0.571818i	0.652400	−	0.757875i	$-0.273762\pi$
$457$	−7.05757	−	12.2241i	−0.330139	−	0.571818i	−0.982539	+	0.186057i	$0.940429\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	17.5323	−	30.3668i	0.816561	−	1.41432i	−0.0916412	−	0.995792i	$-0.529211\pi$
$461$	17.5323	−	30.3668i	0.816561	−	1.41432i	0.908202	−	0.418532i	$-0.137455\pi$
$462$		0			0
$463$	15.9985	+	27.7103i	0.743515	+	1.28781i	0.950885	+	0.309543i	$0.100176\pi$
$463$	15.9985	+	27.7103i	0.743515	+	1.28781i	−0.207370	+	0.978263i	$0.566490\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	8.02671	−	13.9027i	0.371432	−	0.643339i	−0.618354	−	0.785899i	$-0.712200\pi$
$467$	8.02671	−	13.9027i	0.371432	−	0.643339i	0.989786	+	0.142561i	$0.0455337\pi$
$468$		0			0
$469$	3.59798	−	26.0159i	0.166139	−	1.20130i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.83721	+	1.06071i	0.0844751	+	0.0487717i
$474$		0			0
$475$	0.205828	+	0.118835i	0.00944406	+	0.00545253i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−31.4961			−1.43909			−0.719547	−	0.694443i	$-0.755651\pi$
$479$	−31.4961			−1.43909			−0.719547	+	0.694443i	$0.755651\pi$
$480$		0			0
$481$			39.9945i			1.82359i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−7.75609	−	4.47798i	−0.352186	−	0.203335i
$486$		0			0
$487$	10.7924	+	18.6930i	0.489052	+	0.847062i	0.999921	−	0.0125963i	$-0.00400964\pi$
$487$	10.7924	+	18.6930i	0.489052	+	0.847062i	−0.510869	+	0.859659i	$0.670676\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	28.9290	−	16.7022i	1.30555	−	0.753758i	0.324197	−	0.945990i	$-0.394906\pi$
$491$	28.9290	−	16.7022i	1.30555	−	0.753758i	0.981349	+	0.192232i	$0.0615726\pi$
$492$		0			0
$493$			51.8116i			2.33348i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.65911	+	8.99960i	0.164134	+	0.403687i
$498$		0			0
$499$	32.1443			1.43898			0.719489	−	0.694504i	$-0.244376\pi$
$499$	32.1443			1.43898			0.719489	+	0.694504i	$0.244376\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	21.7295			0.968872			0.484436	−	0.874827i	$-0.339025\pi$
$503$	21.7295			0.968872			0.484436	+	0.874827i	$0.339025\pi$
$504$		0			0
$505$	−5.05949			−0.225145
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−23.8864			−1.05875			−0.529373	−	0.848389i	$-0.677573\pi$
$509$	−23.8864			−1.05875			−0.529373	+	0.848389i	$0.677573\pi$
$510$		0			0
$511$	−12.9941	+	16.7072i	−0.574824	+	0.739085i
$512$		0			0
$513$		0			0
$514$		0			0
$515$			19.7064i			0.868370i
$516$		0			0
$517$	−8.66444	+	5.00242i	−0.381062	+	0.220006i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−13.5098	−	23.3996i	−0.591874	−	1.02516i	−0.993980	−	0.109562i	$-0.965055\pi$
$521$	−13.5098	−	23.3996i	−0.591874	−	1.02516i	0.402106	−	0.915593i	$-0.368278\pi$
$522$		0			0
$523$	27.2136	+	15.7118i	1.18997	+	0.687028i	0.958299	−	0.285766i	$-0.0922482\pi$
$523$	27.2136	+	15.7118i	1.18997	+	0.687028i	0.231669	+	0.972795i	$0.425582\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			59.0196i			2.57093i
$528$		0			0
$529$	−10.7847			−0.468899
$530$		0			0
$531$		0			0
$532$		0			0
$533$	5.05483	+	2.91841i	0.218949	+	0.126410i
$534$		0			0
$535$	1.27652	+	0.736997i	0.0551886	+	0.0318632i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	5.72959	+	5.88118i	0.246791	+	0.253320i
$540$		0			0
$541$	−0.0969057	+	0.167846i	−0.00416630	+	0.00721624i	−0.868101	−	0.496388i	$-0.834660\pi$
$541$	−0.0969057	+	0.167846i	−0.00416630	+	0.00721624i	0.863935	+	0.503604i	$0.167993\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−17.8438	−	30.9064i	−0.764344	−	1.32388i
$546$		0			0
$547$	0.987053	−	1.70963i	0.0422033	−	0.0730983i	−0.844152	−	0.536104i	$-0.819896\pi$
$547$	0.987053	−	1.70963i	0.0422033	−	0.0730983i	0.886355	+	0.463005i	$0.153229\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−12.2994	−	21.3032i	−0.523972	−	0.907547i
$552$		0			0
$553$	−9.43955	−	7.34161i	−0.401410	−	0.312197i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	18.3383	−	10.5876i	0.777018	−	0.448612i	−0.0583543	−	0.998296i	$-0.518585\pi$
$557$	18.3383	−	10.5876i	0.777018	−	0.448612i	0.835373	+	0.549684i	$0.185252\pi$
$558$		0			0
$559$		−	6.52423i		−	0.275946i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	17.0645	−	29.5565i	0.719182	−	1.24566i	−0.242142	−	0.970241i	$-0.577850\pi$
$563$	17.0645	−	29.5565i	0.719182	−	1.24566i	0.961324	−	0.275419i	$-0.0888165\pi$
$564$		0			0
$565$	10.8085	−	6.24032i	0.454719	−	0.262532i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9.55993	+	5.51943i	−0.400773	+	0.231387i	−0.686818	−	0.726830i	$-0.740993\pi$
$569$	−9.55993	+	5.51943i	−0.400773	+	0.231387i	0.286044	+	0.958216i	$0.407660\pi$
$570$		0			0
$571$	−20.6616	+	35.7870i	−0.864663	+	1.49764i	0.00271871	+	0.999996i	$0.499135\pi$
$571$	−20.6616	+	35.7870i	−0.864663	+	1.49764i	−0.867382	+	0.497644i	$0.834199\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			0.391955i			0.0163456i
$576$		0			0
$577$	12.5253	−	7.23151i	0.521437	−	0.301052i	−0.216085	−	0.976374i	$-0.569329\pi$
$577$	12.5253	−	7.23151i	0.521437	−	0.301052i	0.737522	+	0.675323i	$0.235996\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−0.283418	+	2.04931i	−0.0117582	+	0.0850197i
$582$		0			0
$583$	6.51891	+	11.2911i	0.269986	+	0.467629i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	0.248251	−	0.429983i	0.0102464	−	0.0177473i	−0.860857	−	0.508847i	$-0.830072\pi$
$587$	0.248251	−	0.429983i	0.0102464	−	0.0177473i	0.871103	+	0.491100i	$0.163405\pi$
$588$		0			0
$589$	−14.0105	−	24.2669i	−0.577292	−	0.999898i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−12.2302	+	21.1834i	−0.502236	+	0.869898i	0.497761	+	0.867314i	$0.334156\pi$
$593$	−12.2302	+	21.1834i	−0.502236	+	0.869898i	−0.999997	+	0.00258345i	$0.999178\pi$
$594$		0			0
$595$	−34.4329	−	26.7802i	−1.41161	−	1.09788i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−16.3114	−	9.41741i	−0.666467	−	0.384785i	0.128270	−	0.991739i	$-0.459058\pi$
$599$	−16.3114	−	9.41741i	−0.666467	−	0.384785i	−0.794737	+	0.606954i	$0.792391\pi$
$600$		0			0
$601$	−6.37572	−	3.68102i	−0.260071	−	0.150152i	0.364296	−	0.931283i	$-0.381310\pi$
$601$	−6.37572	−	3.68102i	−0.260071	−	0.150152i	−0.624367	+	0.781131i	$0.714643\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	21.3747			0.869003
$606$		0			0
$607$		−	28.9923i		−	1.17676i	−0.808584	−	0.588380i	$-0.799766\pi$
$607$		−	28.9923i		−	1.17676i	0.808584	−	0.588380i	$-0.200234\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	26.6466	+	15.3844i	1.07801	+	0.622387i
$612$		0			0
$613$	12.4334	+	21.5352i	0.502179	+	0.869799i	0.999997	+	0.00251771i	$0.000801413\pi$
$613$	12.4334	+	21.5352i	0.502179	+	0.869799i	−0.497818	+	0.867282i	$0.665865\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	37.4629	−	21.6292i	1.50820	−	0.870759i	0.508245	−	0.861213i	$-0.330294\pi$
$617$	37.4629	−	21.6292i	1.50820	−	0.870759i	0.999954	−	0.00954684i	$-0.00303890\pi$
$618$		0			0
$619$			7.45221i			0.299529i	0.988722	+	0.149765i	$0.0478516\pi$
$619$			7.45221i			0.299529i	−0.988722	+	0.149765i	$0.952148\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.27178	−	9.19586i	0.0509528	−	0.368424i
$624$		0			0
$625$	−24.6583			−0.986331
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−82.3050			−3.28171
$630$		0			0
$631$	−9.67068			−0.384984			−0.192492	−	0.981299i	$-0.561657\pi$
$631$	−9.67068			−0.384984			−0.192492	+	0.981299i	$0.561657\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	17.1995			0.682541
$636$		0			0
$637$	6.85339	−	24.3035i	0.271541	−	0.962939i
$638$		0			0
$639$		0			0
$640$		0			0
$641$			30.9590i			1.22281i	0.791318	+	0.611404i	$0.209395\pi$
$641$			30.9590i			1.22281i	−0.791318	+	0.611404i	$0.790605\pi$
$642$		0			0
$643$	6.99262	−	4.03719i	0.275762	−	0.159211i	−0.355741	−	0.934585i	$-0.615772\pi$
$643$	6.99262	−	4.03719i	0.275762	−	0.159211i	0.631503	+	0.775373i	$0.282438\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−4.54355	−	7.86966i	−0.178625	−	0.309388i	0.762785	−	0.646653i	$-0.223832\pi$
$647$	−4.54355	−	7.86966i	−0.178625	−	0.309388i	−0.941410	+	0.337265i	$0.890498\pi$
$648$		0			0
$649$	4.06607	+	2.34755i	0.159607	+	0.0921492i
$650$		0			0
$651$		0			0
$652$		0			0
$653$			20.5913i			0.805800i	0.915244	+	0.402900i	$0.131998\pi$
$653$			20.5913i			0.805800i	−0.915244	+	0.402900i	$0.868002\pi$
$654$		0			0
$655$	34.7041			1.35600
$656$		0			0
$657$		0			0
$658$		0			0
$659$	41.7687	+	24.1152i	1.62708	+	0.939395i	0.984959	+	0.172791i	$0.0552785\pi$
$659$	41.7687	+	24.1152i	1.62708	+	0.939395i	0.642121	+	0.766604i	$0.278055\pi$
$660$		0			0
$661$	−23.8342	−	13.7607i	−0.927042	−	0.535228i	−0.0411674	−	0.999152i	$-0.513108\pi$
$661$	−23.8342	−	13.7607i	−0.927042	−	0.535228i	−0.885875	+	0.463924i	$0.846441\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	20.5149	+	2.83720i	0.795535	+	0.110022i
$666$		0			0
$667$	20.2836	−	35.1323i	0.785385	−	1.36033i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−4.80146	−	8.31637i	−0.185358	−	0.321050i
$672$		0			0
$673$	−17.5734	+	30.4380i	−0.677404	+	1.17330i	0.298355	+	0.954455i	$0.403562\pi$
$673$	−17.5734	+	30.4380i	−0.677404	+	1.17330i	−0.975760	+	0.218844i	$0.929771\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	21.9428	+	38.0060i	0.843329	+	1.46069i	0.887064	+	0.461646i	$0.152741\pi$
$677$	21.9428	+	38.0060i	0.843329	+	1.46069i	−0.0437349	+	0.999043i	$0.513926\pi$
$678$		0			0
$679$	10.5684	+	1.46161i	0.405579	+	0.0560913i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−17.9331	+	10.3537i	−0.686190	+	0.396172i	−0.802183	−	0.597078i	$-0.796328\pi$
$683$	−17.9331	+	10.3537i	−0.686190	+	0.396172i	0.115993	+	0.993250i	$0.462995\pi$
$684$		0			0
$685$		−	2.38896i		−	0.0912773i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	20.0482	−	34.7246i	0.763777	−	1.32290i
$690$		0			0
$691$	−15.8678	+	9.16129i	−0.603640	+	0.348512i	−0.770472	−	0.637474i	$-0.779980\pi$
$691$	−15.8678	+	9.16129i	−0.603640	+	0.348512i	0.166832	+	0.985985i	$0.446646\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	12.9209	−	7.45988i	0.490117	−	0.282969i
$696$		0			0
$697$	−6.00582	+	10.4024i	−0.227487	+	0.394018i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	2.62840i		−	0.0992734i	−0.998767	−	0.0496367i	$-0.984194\pi$
$701$		−	2.62840i		−	0.0992734i	0.998767	−	0.0496367i	$-0.0158064\pi$
$702$		0			0
$703$	33.8410	−	19.5381i	1.27634	−	0.736894i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	5.58340	−	2.27013i	0.209985	−	0.0853771i
$708$		0			0
$709$	8.16634	+	14.1445i	0.306693	+	0.531208i	0.977637	−	0.210300i	$-0.0674441\pi$
$709$	8.16634	+	14.1445i	0.306693	+	0.531208i	−0.670944	+	0.741508i	$0.734111\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	23.1054	−	40.0198i	0.865305	−	1.49875i
$714$		0			0
$715$	4.69869	+	8.13838i	0.175721	+	0.304358i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−3.15485	+	5.46436i	−0.117656	+	0.203786i	−0.918838	−	0.394634i	$-0.870871\pi$
$719$	−3.15485	+	5.46436i	−0.117656	+	0.203786i	0.801182	+	0.598420i	$0.204205\pi$
$720$		0			0
$721$	−8.84204	−	21.7470i	−0.329295	−	0.809901i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−0.407589	−	0.235322i	−0.0151375	−	0.00873962i
$726$		0			0
$727$	14.3318	+	8.27447i	0.531537	+	0.306883i	0.741642	−	0.670796i	$-0.234047\pi$
$727$	14.3318	+	8.27447i	0.531537	+	0.306883i	−0.210105	+	0.977679i	$0.567381\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	13.4263			0.496589
$732$		0			0
$733$			19.9109i			0.735425i	0.929939	+	0.367713i	$0.119859\pi$
$733$			19.9109i			0.735425i	−0.929939	+	0.367713i	$0.880141\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−10.0837	−	5.82183i	−0.371438	−	0.214450i
$738$		0			0
$739$	−24.1545	−	41.8368i	−0.888536	−	1.53899i	−0.841606	−	0.540092i	$-0.818389\pi$
$739$	−24.1545	−	41.8368i	−0.888536	−	1.53899i	−0.0469307	−	0.998898i	$-0.514944\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	7.17819	−	4.14433i	0.263342	−	0.152041i	−0.362516	−	0.931978i	$-0.618082\pi$
$743$	7.17819	−	4.14433i	0.263342	−	0.152041i	0.625858	+	0.779937i	$0.284749\pi$
$744$		0			0
$745$			39.0075i			1.42912i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−1.73938	−	0.240555i	−0.0635555	−	0.00878968i
$750$		0			0
$751$	−25.0229			−0.913099			−0.456549	−	0.889698i	$-0.650915\pi$
$751$	−25.0229			−0.913099			−0.456549	+	0.889698i	$0.650915\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	3.76683			0.137089
$756$		0			0
$757$	−18.7744			−0.682368			−0.341184	−	0.939997i	$-0.610828\pi$
$757$	−18.7744			−0.682368			−0.341184	+	0.939997i	$0.610828\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−23.1927			−0.840733			−0.420367	−	0.907354i	$-0.638099\pi$
$761$	−23.1927			−0.840733			−0.420367	+	0.907354i	$0.638099\pi$
$762$		0			0
$763$	33.5588	+	26.1004i	1.21491	+	0.944897i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	14.4393i		−	0.521372i
$768$		0			0
$769$	27.8202	−	16.0620i	1.00322	−	0.579210i	0.0940211	−	0.995570i	$-0.470028\pi$
$769$	27.8202	−	16.0620i	1.00322	−	0.579210i	0.909200	+	0.416360i	$0.136695\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	8.14023	+	14.0993i	0.292784	+	0.507116i	0.974467	−	0.224531i	$-0.0720851\pi$
$773$	8.14023	+	14.0993i	0.292784	+	0.507116i	−0.681683	+	0.731647i	$0.738752\pi$
$774$		0			0
$775$	−0.464292	−	0.268059i	−0.0166779	−	0.00962896i
$776$		0			0
$777$		0			0
$778$		0			0
$779$		−	5.70281i		−	0.204324i
$780$		0			0
$781$	4.30705			0.154119
$782$		0			0
$783$		0			0
$784$		0			0
$785$	15.1608	+	8.75308i	0.541112	+	0.312411i
$786$		0			0
$787$	−0.799139	−	0.461383i	−0.0284862	−	0.0164465i	0.485689	−	0.874132i	$-0.338569\pi$
$787$	−0.799139	−	0.461383i	−0.0284862	−	0.0164465i	−0.514175	+	0.857685i	$0.671902\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−9.12780	+	11.7362i	−0.324547	+	0.417290i
$792$		0			0
$793$	−14.7664	+	25.5761i	−0.524369	+	0.908235i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	2.98084	+	5.16296i	0.105587	+	0.182881i	0.913978	−	0.405764i	$-0.132995\pi$
$797$	2.98084	+	5.16296i	0.105587	+	0.182881i	−0.808391	+	0.588646i	$0.799661\pi$
$798$		0			0
$799$	−31.6597	+	54.8362i	−1.12004	+	1.93997i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	4.69174	+	8.12634i	0.165568	+	0.286772i
$804$		0			0
$805$	12.8640	+	31.6391i	0.453397	+	1.11513i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	18.0267	−	10.4077i	0.633784	−	0.365916i	−0.148432	−	0.988923i	$-0.547423\pi$
$809$	18.0267	−	10.4077i	0.633784	−	0.365916i	0.782216	+	0.623007i	$0.214089\pi$
$810$		0			0
$811$			11.7101i			0.411198i	0.978636	+	0.205599i	$0.0659142\pi$
$811$			11.7101i			0.411198i	−0.978636	+	0.205599i	$0.934086\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−12.6457	+	21.9030i	−0.442959	+	0.767228i
$816$		0			0
$817$	−5.52043	+	3.18722i	−0.193135	+	0.111507i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−0.483490	+	0.279143i	−0.0168739	+	0.00974215i	−0.508413	−	0.861113i	$-0.669768\pi$
$821$	−0.483490	+	0.279143i	−0.0168739	+	0.00974215i	0.491539	+	0.870855i	$0.336434\pi$
$822$		0			0
$823$	−20.7043	+	35.8609i	−0.721707	+	1.25003i	0.238607	+	0.971116i	$0.423309\pi$
$823$	−20.7043	+	35.8609i	−0.721707	+	1.25003i	−0.960315	+	0.278918i	$0.910024\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			8.83309i			0.307157i	0.988136	+	0.153578i	$0.0490797\pi$
$827$			8.83309i			0.307157i	−0.988136	+	0.153578i	$0.950920\pi$
$828$		0			0
$829$	−7.60753	+	4.39221i	−0.264220	+	0.152548i	−0.626258	−	0.779616i	$-0.715414\pi$
$829$	−7.60753	+	4.39221i	−0.264220	+	0.152548i	0.362038	+	0.932163i	$0.382081\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	50.0143	+	14.1037i	1.73289	+	0.488663i
$834$		0			0
$835$	−17.8927	−	30.9911i	−0.619204	−	1.07249i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−11.6778	+	20.2265i	−0.403161	+	0.698295i	−0.994106	−	0.108417i	$-0.965422\pi$
$839$	−11.6778	+	20.2265i	−0.403161	+	0.698295i	0.590944	+	0.806712i	$0.298755\pi$
$840$		0			0
$841$	9.85573	+	17.0706i	0.339853	+	0.588642i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.0142428	−	0.0246693i	0.000489967	−	0.000848648i
$846$		0			0
$847$	−23.5880	+	9.59054i	−0.810492	+	0.329535i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	55.8091	+	32.2214i	1.91311	+	1.10453i
$852$		0			0
$853$	−13.8754	−	8.01099i	−0.475086	−	0.274291i	0.243280	−	0.969956i	$-0.421777\pi$
$853$	−13.8754	−	8.01099i	−0.475086	−	0.274291i	−0.718366	+	0.695665i	$0.755110\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	16.8241			0.574700			0.287350	−	0.957826i	$-0.407226\pi$
$857$	16.8241			0.574700			0.287350	+	0.957826i	$0.407226\pi$
$858$		0			0
$859$		−	47.5953i		−	1.62393i	−0.583705	−	0.811966i	$-0.698397\pi$
$859$		−	47.5953i		−	1.62393i	0.583705	−	0.811966i	$-0.301603\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	44.7300	+	25.8249i	1.52263	+	0.879089i	0.999642	+	0.0267477i	$0.00851508\pi$
$863$	44.7300	+	25.8249i	1.52263	+	0.879089i	0.522985	+	0.852342i	$0.324818\pi$
$864$		0			0
$865$	−7.66628	−	13.2784i	−0.260661	−	0.451478i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−4.59136	+	2.65082i	−0.155751	+	0.0899230i
$870$		0			0
$871$			35.8088i			1.21334i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	27.5837	−	11.2151i	0.932499	−	0.379141i
$876$		0			0
$877$	14.3056			0.483066			0.241533	−	0.970393i	$-0.422350\pi$
$877$	14.3056			0.483066			0.241533	+	0.970393i	$0.422350\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	10.4054			0.350566			0.175283	−	0.984518i	$-0.443916\pi$
$881$	10.4054			0.350566			0.175283	+	0.984518i	$0.443916\pi$
$882$		0			0
$883$	44.9042			1.51115			0.755574	−	0.655064i	$-0.227358\pi$
$883$	44.9042			1.51115			0.755574	+	0.655064i	$0.227358\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−0.948519			−0.0318482			−0.0159241	−	0.999873i	$-0.505069\pi$
$887$	−0.948519			−0.0318482			−0.0159241	+	0.999873i	$0.505069\pi$
$888$		0			0
$889$	−18.9805	+	7.71720i	−0.636585	+	0.258827i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	30.0624i		−	1.00600i
$894$		0			0
$895$	11.7434	−	6.78006i	0.392539	−	0.226632i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	27.7440	+	48.0541i	0.925316	+	1.60269i
$900$		0			0
$901$	71.4600	+	41.2574i	2.38068	+	1.37448i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	12.1336i		−	0.403335i
$906$		0			0
$907$	35.0550			1.16398			0.581990	−	0.813196i	$-0.302274\pi$
$907$	35.0550			1.16398			0.581990	+	0.813196i	$0.302274\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	42.8316	+	24.7288i	1.41907	+	0.819303i	0.996218	−	0.0868934i	$-0.0276940\pi$
$911$	42.8316	+	24.7288i	1.41907	+	0.819303i	0.422857	+	0.906196i	$0.361027\pi$
$912$		0			0
$913$	0.794307	+	0.458593i	0.0262877	+	0.0151772i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−38.2976	+	15.5713i	−1.26470	+	0.514209i
$918$		0			0
$919$	8.34526	−	14.4544i	0.275285	−	0.476807i	−0.694922	−	0.719085i	$-0.744561\pi$
$919$	8.34526	−	14.4544i	0.275285	−	0.476807i	0.970207	+	0.242278i	$0.0778945\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−6.62295	−	11.4713i	−0.217997	−	0.377582i
$924$		0			0
$925$	0.373818	−	0.647472i	0.0122911	−	0.0212888i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	5.31860	+	9.21208i	0.174498	+	0.302239i	0.939987	−	0.341209i	$-0.110837\pi$
$929$	5.31860	+	9.21208i	0.174498	+	0.302239i	−0.765490	+	0.643448i	$0.777503\pi$
$930$		0			0
$931$	−23.9122	+	6.07381i	−0.783692	+	0.199061i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−16.7480	+	9.66948i	−0.547719	+	0.316226i
$936$		0			0
$937$		−	26.7085i		−	0.872528i	−0.899819	−	0.436264i	$-0.856301\pi$
$937$		−	26.7085i		−	0.872528i	0.899819	−	0.436264i	$-0.143699\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−3.29534	+	5.70769i	−0.107425	+	0.186065i	−0.914726	−	0.404074i	$-0.867594\pi$
$941$	−3.29534	+	5.70769i	−0.107425	+	0.186065i	0.807301	+	0.590139i	$0.200927\pi$
$942$		0			0
$943$	8.14481	−	4.70241i	0.265232	−	0.153131i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−24.8907	+	14.3706i	−0.808838	+	0.466983i	−0.846552	−	0.532306i	$-0.821326\pi$
$947$	−24.8907	+	14.3706i	−0.808838	+	0.466983i	0.0377144	+	0.999289i	$0.487992\pi$
$948$		0			0
$949$	14.4290	−	24.9917i	0.468384	−	0.811265i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	18.2616i		−	0.591550i	−0.955258	−	0.295775i	$-0.904422\pi$
$953$		−	18.2616i		−	0.591550i	0.955258	−	0.295775i	$-0.0955778\pi$
$954$		0			0
$955$	−11.5718	+	6.68098i	−0.374455	+	0.216191i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	1.07189	+	2.63633i	0.0346133	+	0.0851315i
$960$		0			0
$961$	16.1037	+	27.8925i	0.519476	+	0.899758i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	6.41889	−	11.1178i	0.206631	−	0.357896i
$966$		0			0
$967$	12.5899	+	21.8064i	0.404865	+	0.701247i	0.994306	−	0.106565i	$-0.0339851\pi$
$967$	12.5899	+	21.8064i	0.404865	+	0.701247i	−0.589441	+	0.807812i	$0.700652\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	23.7214	−	41.0866i	0.761255	−	1.31853i	−0.180949	−	0.983492i	$-0.557917\pi$
$971$	23.7214	−	41.0866i	0.761255	−	1.31853i	0.942204	−	0.335040i	$-0.108750\pi$
$972$		0			0
$973$	−10.9117	+	14.0298i	−0.349812	+	0.449774i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−47.9278	−	27.6711i	−1.53334	−	0.885277i	−0.999204	−	0.0398814i	$-0.987302\pi$
$977$	−47.9278	−	27.6711i	−1.53334	−	0.885277i	−0.534141	−	0.845396i	$-0.679365\pi$
$978$		0			0
$979$	−3.56429	−	2.05784i	−0.113915	−	0.0657690i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	25.3499			0.808537			0.404268	−	0.914640i	$-0.367526\pi$
$983$	25.3499			0.808537			0.404268	+	0.914640i	$0.367526\pi$
$984$		0			0
$985$		−	17.6643i		−	0.562832i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−9.10404	−	5.25622i	−0.289492	−	0.167138i
$990$		0			0
$991$	−12.9683	−	22.4618i	−0.411953	−	0.713523i	0.583151	−	0.812364i	$-0.301820\pi$
$991$	−12.9683	−	22.4618i	−0.411953	−	0.713523i	−0.995103	+	0.0988413i	$0.968486\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−34.4753	+	19.9043i	−1.09294	+	0.631010i
$996$		0			0
$997$			15.9283i			0.504453i	0.967668	+	0.252227i	$0.0811629\pi$
$997$			15.9283i			0.504453i	−0.967668	+	0.252227i	$0.918837\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.cx.a.89.20		48
3.2	odd	2		504.2.cx.a.425.13	yes	48
4.3	odd	2		3024.2.df.e.1601.20		48
7.3	odd	6		1512.2.bs.a.521.20		48
9.4	even	3		504.2.bs.a.257.5	✓	48
9.5	odd	6		1512.2.bs.a.1097.20		48
12.11	even	2		1008.2.df.e.929.12		48
21.17	even	6		504.2.bs.a.353.5	yes	48
28.3	even	6		3024.2.ca.e.2033.20		48
36.23	even	6		3024.2.ca.e.2609.20		48
36.31	odd	6		1008.2.ca.e.257.20		48
63.31	odd	6		504.2.cx.a.185.13	yes	48
63.59	even	6	inner	1512.2.cx.a.17.20		48
84.59	odd	6		1008.2.ca.e.353.20		48
252.31	even	6		1008.2.df.e.689.12		48
252.59	odd	6		3024.2.df.e.17.20		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.bs.a.257.5	✓	48	9.4	even	3
504.2.bs.a.353.5	yes	48	21.17	even	6
504.2.cx.a.185.13	yes	48	63.31	odd	6
504.2.cx.a.425.13	yes	48	3.2	odd	2
1008.2.ca.e.257.20		48	36.31	odd	6
1008.2.ca.e.353.20		48	84.59	odd	6
1008.2.df.e.689.12		48	252.31	even	6
1008.2.df.e.929.12		48	12.11	even	2
1512.2.bs.a.521.20		48	7.3	odd	6
1512.2.bs.a.1097.20		48	9.5	odd	6
1512.2.cx.a.17.20		48	63.59	even	6	inner
1512.2.cx.a.89.20		48	1.1	even	1	trivial
3024.2.ca.e.2033.20		48	28.3	even	6
3024.2.ca.e.2609.20		48	36.23	even	6
3024.2.df.e.17.20		48	252.59	odd	6
3024.2.df.e.1601.20		48	4.3	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.cx (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+2.22094 q^{5} +(-2.45091 + 0.996507i) q^{7} +1.17296i q^{11} +(3.12404 - 1.80366i) q^{13} +(3.71178 + 6.42899i) q^{17} +(-3.05231 - 1.76225i) q^{19} -5.81246i q^{23} -0.0674336 q^{25} +(6.04430 + 3.48968i) q^{29} +(6.88517 + 3.97516i) q^{31} +(-5.44333 + 2.21318i) q^{35} +(-5.54350 + 9.60163i) q^{37} +(0.809022 + 1.40127i) q^{41} +(0.904302 - 1.56630i) q^{43} +(4.26476 + 7.38679i) q^{47} +(5.01395 - 4.88471i) q^{49} +(9.62611 - 5.55764i) q^{53} +2.60508i q^{55} +(2.00138 - 3.46649i) q^{59} +(-7.09004 + 4.09344i) q^{61} +(6.93830 - 4.00583i) q^{65} +(-4.96334 + 8.59676i) q^{67} -3.67194i q^{71} +(6.92803 - 3.99990i) q^{73} +(-1.16887 - 2.87483i) q^{77} +(2.25993 + 3.91432i) q^{79} +(0.390969 - 0.677179i) q^{83} +(8.24363 + 14.2784i) q^{85} +(-1.75440 + 3.03870i) q^{89} +(-5.85938 + 7.53375i) q^{91} +(-6.77900 - 3.91386i) q^{95} +(-3.49226 - 2.01626i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 48 q^{25} - 18 q^{29} + 18 q^{31} + 6 q^{41} - 6 q^{43} - 18 q^{47} - 12 q^{49} + 12 q^{53} + 18 q^{61} + 36 q^{65} + 12 q^{77} + 6 q^{79} + 18 q^{89} + 6 q^{91} + 54 q^{95}+O(q^{100}) \) 48 * q + 48 * q^25 - 18 * q^29 + 18 * q^31 + 6 * q^41 - 6 * q^43 - 18 * q^47 - 12 * q^49 + 12 * q^53 + 18 * q^61 + 36 * q^65 + 12 * q^77 + 6 * q^79 + 18 * q^89 + 6 * q^91 + 54 * q^95

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