LMFDB - Embedded newform 432.9.q.c.305.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [432,9,Mod(17,432)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("432.17"); S:= CuspForms(chi, 9); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(432, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 5])) N = Newforms(chi, 9, names="a")

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	432.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,882] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$175.987559546$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 150208 x^{14} - 1927740 x^{13} + 8702363206 x^{12} + 239206241152 x^{11} + \cdots + 81\!\cdots\!61 $ x^16 - 4x^15 - 150208x^14 - 1927740x^13 + 8702363206x^12 + 239206241152x^11 - 241960304158448x^10 - 9458863275320348x^9 + 3259352971808015407x^8 + 150983052056025751536x^7 - 18744835998632687401792x^6 - 866018994869774202180460x^5 + 35643731791394373752805382x^4 + 1485002234815673954960734644x^3 + 16292568366453217677347743656x^2 + 62373298381917691066182105696*x + 81301302751102601946916438161
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{32}\cdot 3^{40} $
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			305.4
Root			$-2.97990 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	432.305
Dual form			432.9.q.c.17.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(69.6596 - 40.2180i) q^{5} +(-370.849 + 642.329i) q^{7} +(-19777.4 - 11418.5i) q^{11} +(-6499.12 - 11256.8i) q^{13} +105666. i q^{17} -118278. q^{19} +(-77410.8 + 44693.1i) q^{23} +(-192078. + 332688. i) q^{25} +(952037. + 549659. i) q^{29} +(-226348. - 392047. i) q^{31} +59659.1i q^{35} -2.12547e6 q^{37} +(1.45174e6 - 838161. i) q^{41} +(569118. - 985742. i) q^{43} +(-3.10681e6 - 1.79372e6i) q^{47} +(2.60734e6 + 4.51605e6i) q^{49} -1.16039e7i q^{53} -1.83692e6 q^{55} +(5.34715e6 - 3.08718e6i) q^{59} +(1.10379e7 - 1.91182e7i) q^{61} +(-905451. - 522763. i) q^{65} +(1.84669e7 + 3.19855e7i) q^{67} +1.51775e7i q^{71} -4.91641e7 q^{73} +(1.46689e7 - 8.46908e6i) q^{77} +(-3.15777e7 + 5.46942e7i) q^{79} +(4.45835e7 + 2.57403e7i) q^{83} +(4.24967e6 + 7.36064e6i) q^{85} -5.17343e7i q^{89} +9.64076e6 q^{91} +(-8.23923e6 + 4.75692e6i) q^{95} +(-4.54739e6 + 7.87630e6i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 882 q^{5} + 1846 q^{7} + 45756 q^{11} - 3370 q^{13} - 362180 q^{19} + 1311138 q^{23} + 963394 q^{25} + 2851290 q^{29} - 542438 q^{31} + 3343328 q^{37} - 9218592 q^{41} - 339512 q^{43} - 34980606 q^{47}+ \cdots - 89415484 q^{97}+O(q^{100}) $ 16 * q + 882 * q^5 + 1846 * q^7 + 45756 * q^11 - 3370 * q^13 - 362180 * q^19 + 1311138 * q^23 + 963394 * q^25 + 2851290 * q^29 - 542438 * q^31 + 3343328 * q^37 - 9218592 * q^41 - 339512 * q^43 - 34980606 * q^47 - 2364654 * q^49 + 4584276 * q^55 + 93924216 * q^59 - 841954 * q^61 + 126568134 * q^65 - 29946644 * q^67 - 7547764 * q^73 - 9309294 * q^77 - 33813002 * q^79 + 114200226 * q^83 - 125696772 * q^85 - 268578316 * q^91 - 143949240 * q^95 - 89415484 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	69.6596	−	40.2180i	0.111455	−	0.0643487i	−0.443236	−	0.896405i	$-0.646170\pi$
$5$	69.6596	−	40.2180i	0.111455	−	0.0643487i	0.554691	+	0.832056i	$0.312836\pi$
$6$		0			0
$7$	−370.849	+	642.329i	−0.154456	+	0.267526i	−0.932861	−	0.360237i	$-0.882696\pi$
$7$	−370.849	+	642.329i	−0.154456	+	0.267526i	0.778405	+	0.627763i	$0.216029\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−19777.4	−	11418.5i	−1.35083	−	0.779900i	−0.362461	−	0.931999i	$-0.618063\pi$
$11$	−19777.4	−	11418.5i	−1.35083	−	0.779900i	−0.988365	+	0.152099i	$0.951397\pi$
$12$		0			0
$13$	−6499.12	−	11256.8i	−0.227552	−	0.394132i	0.729530	−	0.683949i	$-0.239739\pi$
$13$	−6499.12	−	11256.8i	−0.227552	−	0.394132i	−0.957082	+	0.289817i	$0.906406\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$			105666.i			1.26514i	0.774502	+	0.632571i	$0.218000\pi$
$17$			105666.i			1.26514i	−0.774502	+	0.632571i	$0.782000\pi$
$18$		0			0
$19$	−118278.			−0.907594			−0.453797	−	0.891105i	$-0.649931\pi$
$19$	−118278.			−0.907594			−0.453797	+	0.891105i	$0.649931\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−77410.8	+	44693.1i	−0.276624	+	0.159709i	−0.631894	−	0.775055i	$-0.717722\pi$
$23$	−77410.8	+	44693.1i	−0.276624	+	0.159709i	0.355270	+	0.934764i	$0.384389\pi$
$24$		0			0
$25$	−192078.	+	332688.i	−0.491718	+	0.851681i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	952037.	+	549659.i	1.34605	+	0.777143i	0.987688	−	0.156439i	$-0.0500014\pi$
$29$	952037.	+	549659.i	1.34605	+	0.777143i	0.358364	+	0.933582i	$0.383335\pi$
$30$		0			0
$31$	−226348.	−	392047.i	−0.245093	−	0.424513i	0.717065	−	0.697007i	$-0.245485\pi$
$31$	−226348.	−	392047.i	−0.245093	−	0.424513i	−0.962158	+	0.272493i	$0.912152\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$			59659.1i			0.0397562i
$36$		0			0
$37$	−2.12547e6			−1.13409			−0.567046	−	0.823686i	$-0.691914\pi$
$37$	−2.12547e6			−1.13409			−0.567046	+	0.823686i	$0.691914\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	1.45174e6	−	838161.i	0.513751	−	0.296614i	−0.220623	−	0.975359i	$-0.570809\pi$
$41$	1.45174e6	−	838161.i	0.513751	−	0.296614i	0.734374	+	0.678745i	$0.237476\pi$
$42$		0			0
$43$	569118.	−	985742.i	0.166467	−	0.288330i	−0.770708	−	0.637188i	$-0.780097\pi$
$43$	569118.	−	985742.i	0.166467	−	0.288330i	0.937175	+	0.348859i	$0.113431\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−3.10681e6	−	1.79372e6i	−0.636683	−	0.367589i	0.146653	−	0.989188i	$-0.453150\pi$
$47$	−3.10681e6	−	1.79372e6i	−0.636683	−	0.367589i	−0.783336	+	0.621599i	$0.786483\pi$
$48$		0			0
$49$	2.60734e6	+	4.51605e6i	0.452287	+	0.783384i
$50$		0			0
$51$		0			0
$52$		0			0
$53$		−	1.16039e7i		−	1.47062i	−0.677730	−	0.735311i	$-0.737036\pi$
$53$		−	1.16039e7i		−	1.47062i	0.677730	−	0.735311i	$-0.262964\pi$
$54$		0			0
$55$	−1.83692e6			−0.200742
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.34715e6	−	3.08718e6i	0.441280	−	0.254773i	−0.262860	−	0.964834i	$-0.584666\pi$
$59$	5.34715e6	−	3.08718e6i	0.441280	−	0.254773i	0.704141	+	0.710061i	$0.251332\pi$
$60$		0			0
$61$	1.10379e7	−	1.91182e7i	0.797198	−	1.38079i	−0.124237	−	0.992253i	$-0.539648\pi$
$61$	1.10379e7	−	1.91182e7i	0.797198	−	1.38079i	0.921434	−	0.388534i	$-0.127018\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−905451.	−	522763.i	−0.0507238	−	0.0292854i
$66$		0			0
$67$	1.84669e7	+	3.19855e7i	0.916418	+	1.58728i	0.804811	+	0.593531i	$0.202267\pi$
$67$	1.84669e7	+	3.19855e7i	0.916418	+	1.58728i	0.111607	+	0.993752i	$0.464400\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$			1.51775e7i			0.597267i	0.954368	+	0.298633i	$0.0965307\pi$
$71$			1.51775e7i			0.597267i	−0.954368	+	0.298633i	$0.903469\pi$
$72$		0			0
$73$	−4.91641e7			−1.73124			−0.865618	−	0.500704i	$-0.833074\pi$
$73$	−4.91641e7			−1.73124			−0.865618	+	0.500704i	$0.833074\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	1.46689e7	−	8.46908e6i	0.417286	−	0.240920i
$78$		0			0
$79$	−3.15777e7	+	5.46942e7i	−0.810722	+	1.40421i	0.101637	+	0.994822i	$0.467592\pi$
$79$	−3.15777e7	+	5.46942e7i	−0.810722	+	1.40421i	−0.912359	+	0.409391i	$0.865741\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.45835e7	+	2.57403e7i	0.939425	+	0.542377i	0.889780	−	0.456390i	$-0.150858\pi$
$83$	4.45835e7	+	2.57403e7i	0.939425	+	0.542377i	0.0496450	+	0.998767i	$0.484191\pi$
$84$		0			0
$85$	4.24967e6	+	7.36064e6i	0.0814103	+	0.141007i
$86$		0			0
$87$		0			0
$88$		0			0
$89$		−	5.17343e7i		−	0.824553i	−0.911059	−	0.412277i	$-0.864734\pi$
$89$		−	5.17343e7i		−	0.824553i	0.911059	−	0.412277i	$-0.135266\pi$
$90$		0			0
$91$	9.64076e6			0.140587
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−8.23923e6	+	4.75692e6i	−0.101156	+	0.0584025i
$96$		0			0
$97$	−4.54739e6	+	7.87630e6i	−0.0513659	+	0.0889684i	−0.890565	−	0.454856i	$-0.849691\pi$
$97$	−4.54739e6	+	7.87630e6i	−0.0513659	+	0.0889684i	0.839199	+	0.543824i	$0.183024\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	9.46459e7	+	5.46438e7i	0.909528	+	0.525117i	0.880279	−	0.474456i	$-0.157355\pi$
$101$	9.46459e7	+	5.46438e7i	0.909528	+	0.525117i	0.0292491	+	0.999572i	$0.490688\pi$
$102$		0			0
$103$	−9.55744e7	−	1.65540e8i	−0.849166	−	1.47080i	−0.881954	−	0.471336i	$-0.843772\pi$
$103$	−9.55744e7	−	1.65540e8i	−0.849166	−	1.47080i	0.0327875	−	0.999462i	$-0.489562\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	1.73989e8i		−	1.32736i	−0.748019	−	0.663678i	$-0.768995\pi$
$107$		−	1.73989e8i		−	1.32736i	0.748019	−	0.663678i	$-0.231005\pi$
$108$		0			0
$109$	−1.00364e8			−0.711002			−0.355501	−	0.934676i	$-0.615690\pi$
$109$	−1.00364e8			−0.711002			−0.355501	+	0.934676i	$0.615690\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.26056e8	−	7.27784e7i	0.773124	−	0.446364i	−0.0608637	−	0.998146i	$-0.519386\pi$
$113$	1.26056e8	−	7.27784e7i	0.773124	−	0.446364i	0.833988	+	0.551783i	$0.186052\pi$
$114$		0			0
$115$	−3.59493e6	+	6.22661e6i	−0.0205542	+	0.0356008i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−6.78723e7	−	3.91861e7i	−0.338458	−	0.195409i
$120$		0			0
$121$	1.53585e8	+	2.66018e8i	0.716487	+	1.24099i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			6.23202e7i			0.255263i
$126$		0			0
$127$	1.57730e8			0.606315			0.303157	−	0.952941i	$-0.401959\pi$
$127$	1.57730e8			0.606315			0.303157	+	0.952941i	$0.401959\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	2.71215e8	−	1.56586e8i	0.920934	−	0.531701i	0.0370008	−	0.999315i	$-0.488220\pi$
$131$	2.71215e8	−	1.56586e8i	0.920934	−	0.531701i	0.883933	+	0.467614i	$0.154886\pi$
$132$		0			0
$133$	4.38634e7	−	7.59737e7i	0.140183	−	0.242804i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−8.44998e7	−	4.87860e7i	−0.239869	−	0.138488i	0.375248	−	0.926925i	$-0.377558\pi$
$137$	−8.44998e7	−	4.87860e7i	−0.239869	−	0.138488i	−0.615116	+	0.788436i	$0.710891\pi$
$138$		0			0
$139$	−4.51078e7	−	7.81290e7i	−0.120835	−	0.209292i	0.799262	−	0.600982i	$-0.205224\pi$
$139$	−4.51078e7	−	7.81290e7i	−0.120835	−	0.209292i	−0.920097	+	0.391690i	$0.871890\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			2.96841e8i			0.709872i
$144$		0			0
$145$	8.84246e7			0.200033
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−5.31181e8	+	3.06678e8i	−1.07770	+	0.622210i	−0.930275	−	0.366863i	$-0.880432\pi$
$149$	−5.31181e8	+	3.06678e8i	−1.07770	+	0.622210i	−0.147425	+	0.989073i	$0.547098\pi$
$150$		0			0
$151$	−7.34431e7	+	1.27207e8i	−0.141268	+	0.244683i	−0.927974	−	0.372644i	$-0.878451\pi$
$151$	−7.34431e7	+	1.27207e8i	−0.141268	+	0.244683i	0.786706	+	0.617327i	$0.211785\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−3.15347e7	−	1.82065e7i	−0.0546338	−	0.0315428i
$156$		0			0
$157$	−2.79253e8	−	4.83681e8i	−0.459621	−	0.796086i	0.539320	−	0.842101i	$-0.318681\pi$
$157$	−2.79253e8	−	4.83681e8i	−0.459621	−	0.796086i	−0.998941	+	0.0460145i	$0.985348\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	6.62976e7i		−	0.0986720i
$162$		0			0
$163$	2.70277e6			0.00382876			0.00191438	−	0.999998i	$-0.499391\pi$
$163$	2.70277e6			0.00382876			0.00191438	+	0.999998i	$0.499391\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	6.54080e8	−	3.77633e8i	0.840940	−	0.485517i	−0.0166436	−	0.999861i	$-0.505298\pi$
$167$	6.54080e8	−	3.77633e8i	0.840940	−	0.485517i	0.857584	+	0.514344i	$0.171965\pi$
$168$		0			0
$169$	3.23388e8	−	5.60125e8i	0.396440	−	0.686654i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	8.12759e8	+	4.69247e8i	0.907355	+	0.523862i	0.879579	−	0.475752i	$-0.157824\pi$
$173$	8.12759e8	+	4.69247e8i	0.907355	+	0.523862i	0.0277761	+	0.999614i	$0.491157\pi$
$174$		0			0
$175$	−1.42463e8	−	2.46754e8i	−0.151898	−	0.263095i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			9.19557e8i			0.895708i	0.894107	+	0.447854i	$0.147812\pi$
$179$			9.19557e8i			0.895708i	−0.894107	+	0.447854i	$0.852188\pi$
$180$		0			0
$181$	1.65808e9			1.54487			0.772435	−	0.635094i	$-0.219039\pi$
$181$	1.65808e9			1.54487			0.772435	+	0.635094i	$0.219039\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−1.48059e8	+	8.54821e7i	−0.126401	+	0.0729774i
$186$		0			0
$187$	1.20655e9	−	2.08980e9i	0.986684	−	1.70899i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	8.35643e8	+	4.82459e8i	0.627895	+	0.362516i	0.779937	−	0.625859i	$-0.215251\pi$
$191$	8.35643e8	+	4.82459e8i	0.627895	+	0.362516i	−0.152041	+	0.988374i	$0.548585\pi$
$192$		0			0
$193$	−3.96992e8	−	6.87610e8i	−0.286123	−	0.495579i	0.686758	−	0.726886i	$-0.259033\pi$
$193$	−3.96992e8	−	6.87610e8i	−0.286123	−	0.495579i	−0.972881	+	0.231307i	$0.925700\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$		−	1.07092e9i		−	0.711038i	−0.934669	−	0.355519i	$-0.884304\pi$
$197$		−	1.07092e9i		−	0.711038i	0.934669	−	0.355519i	$-0.115696\pi$
$198$		0			0
$199$	1.01385e9			0.646486			0.323243	−	0.946316i	$-0.395227\pi$
$199$	1.01385e9			0.646486			0.323243	+	0.946316i	$0.395227\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−7.06123e8	+	4.07680e8i	−0.415811	+	0.240069i
$204$		0			0
$205$	6.74183e7	−	1.16772e8i	0.0381735	−	0.0661185i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.33925e9	+	1.35056e9i	1.22600	+	0.707832i
$210$		0			0
$211$	3.50549e8	+	6.07168e8i	0.176856	+	0.306323i	0.940802	−	0.338957i	$-0.110074\pi$
$211$	3.50549e8	+	6.07168e8i	0.176856	+	0.306323i	−0.763946	+	0.645280i	$0.776741\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$		−	9.15551e7i		−	0.0428478i
$216$		0			0
$217$	3.35764e8			0.151424
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.18946e9	−	6.86736e8i	0.498633	−	0.287886i
$222$		0			0
$223$	1.37390e9	−	2.37966e9i	0.555566	−	0.962268i	−0.442293	−	0.896870i	$-0.645835\pi$
$223$	1.37390e9	−	2.37966e9i	0.555566	−	0.962268i	0.997859	−	0.0653978i	$-0.0208316\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.22472e9	−	1.28445e9i	−0.837862	−	0.483740i	0.0186746	−	0.999826i	$-0.494055\pi$
$227$	−2.22472e9	−	1.28445e9i	−0.837862	−	0.483740i	−0.856537	+	0.516085i	$0.827389\pi$
$228$		0			0
$229$	−1.26517e9	−	2.19134e9i	−0.460053	−	0.796835i	0.538910	−	0.842363i	$-0.318836\pi$
$229$	−1.26517e9	−	2.19134e9i	−0.460053	−	0.796835i	−0.998963	+	0.0455283i	$0.985503\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			1.19788e9i			0.406434i	0.979134	+	0.203217i	$0.0651397\pi$
$233$			1.19788e9i			0.406434i	−0.979134	+	0.203217i	$0.934860\pi$
$234$		0			0
$235$	−2.88559e8			−0.0946156
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.41385e9	−	8.16289e8i	0.433324	−	0.250180i	−0.267438	−	0.963575i	$-0.586177\pi$
$239$	1.41385e9	−	8.16289e8i	0.433324	−	0.250180i	0.700762	+	0.713395i	$0.252844\pi$
$240$		0			0
$241$	1.78726e9	−	3.09563e9i	0.529810	−	0.917659i	−0.469585	−	0.882887i	$-0.655596\pi$
$241$	1.78726e9	−	3.09563e9i	0.529810	−	0.917659i	0.999395	−	0.0347712i	$-0.0110702\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3.63253e8	+	2.09724e8i	0.100819	+	0.0582082i
$246$		0			0
$247$	7.68706e8	+	1.33144e9i	0.206525	+	0.357712i
$248$		0			0
$249$		0			0
$250$		0			0
$251$			2.65229e9i			0.668230i	0.942532	+	0.334115i	$0.108437\pi$
$251$			2.65229e9i			0.668230i	−0.942532	+	0.334115i	$0.891563\pi$
$252$		0			0
$253$	2.04132e9			0.498228
$254$		0			0
$255$		0			0
$256$		0			0
$257$	2.52067e9	−	1.45531e9i	0.577807	−	0.333597i	−0.182454	−	0.983214i	$-0.558404\pi$
$257$	2.52067e9	−	1.45531e9i	0.577807	−	0.333597i	0.760261	+	0.649617i	$0.225071\pi$
$258$		0			0
$259$	7.88228e8	−	1.36525e9i	0.175167	−	0.303399i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	7.19663e9	+	4.15498e9i	1.50420	+	0.868452i	0.999988	+	0.00487337i	$0.00155125\pi$
$263$	7.19663e9	+	4.15498e9i	1.50420	+	0.868452i	0.504215	+	0.863578i	$0.331782\pi$
$264$		0			0
$265$	−4.66686e8	−	8.08323e8i	−0.0946326	−	0.163909i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	3.91667e9i		−	0.748010i	−0.927427	−	0.374005i	$-0.877984\pi$
$269$		−	3.91667e9i		−	0.748010i	0.927427	−	0.374005i	$-0.122016\pi$
$270$		0			0
$271$	−4.26666e9			−0.791063			−0.395532	−	0.918452i	$-0.629440\pi$
$271$	−4.26666e9			−0.791063			−0.395532	+	0.918452i	$0.629440\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	7.59760e9	−	4.38648e9i	1.32845	−	0.766982i
$276$		0			0
$277$	6.34405e8	−	1.09882e9i	0.107758	−	0.186642i	−0.807104	−	0.590409i	$-0.798966\pi$
$277$	6.34405e8	−	1.09882e9i	0.107758	−	0.186642i	0.914861	+	0.403768i	$0.132300\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	5.43672e8	+	3.13889e8i	0.0871990	+	0.0503444i	0.542965	−	0.839755i	$-0.317301\pi$
$281$	5.43672e8	+	3.13889e8i	0.0871990	+	0.0503444i	−0.455766	+	0.890099i	$0.650635\pi$
$282$		0			0
$283$	7.75733e8	+	1.34361e9i	0.120939	+	0.209473i	0.920138	−	0.391594i	$-0.128076\pi$
$283$	7.75733e8	+	1.34361e9i	0.120939	+	0.209473i	−0.799199	+	0.601066i	$0.794743\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$			1.24332e9i			0.183255i
$288$		0			0
$289$	−4.18954e9			−0.600586
$290$		0			0
$291$		0			0
$292$		0			0
$293$	4.21204e9	−	2.43182e9i	0.571507	−	0.329960i	−0.186244	−	0.982504i	$-0.559631\pi$
$293$	4.21204e9	−	2.43182e9i	0.571507	−	0.329960i	0.757751	+	0.652544i	$0.226298\pi$
$294$		0			0
$295$	2.48320e8	−	4.30103e8i	0.0327887	−	0.0567917i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.00620e9	+	5.80932e8i	0.125893	+	0.0726843i
$300$		0			0
$301$	4.22114e8	+	7.31122e8i	0.0514237	+	0.0890685i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		−	1.77568e9i		−	0.205195i
$306$		0			0
$307$	1.51737e10			1.70820			0.854101	−	0.520108i	$-0.174108\pi$
$307$	1.51737e10			1.70820			0.854101	+	0.520108i	$0.174108\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1.31231e10	−	7.57662e9i	1.40280	−	0.809905i	0.408118	−	0.912929i	$-0.366185\pi$
$311$	1.31231e10	−	7.57662e9i	1.40280	−	0.809905i	0.994679	+	0.103024i	$0.0328518\pi$
$312$		0			0
$313$	5.67865e9	−	9.83571e9i	0.591654	−	1.02477i	−0.402356	−	0.915483i	$-0.631809\pi$
$313$	5.67865e9	−	9.83571e9i	0.591654	−	1.02477i	0.994010	−	0.109291i	$-0.0348581\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	1.44463e10	+	8.34059e9i	1.43061	+	0.825961i	0.997167	−	0.0752213i	$-0.0239663\pi$
$317$	1.44463e10	+	8.34059e9i	1.43061	+	0.825961i	0.433440	+	0.901183i	$0.357300\pi$
$318$		0			0
$319$	−1.25526e10	−	2.17417e10i	−1.21219	−	2.09957i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	1.24980e10i		−	1.14824i
$324$		0			0
$325$	4.99334e9			0.447566
$326$		0			0
$327$		0			0
$328$		0			0
$329$	2.30431e9	−	1.33040e9i	0.196679	−	0.113553i
$330$		0			0
$331$	1.60334e9	−	2.77707e9i	0.133571	−	0.231353i	−0.791479	−	0.611196i	$-0.790689\pi$
$331$	1.60334e9	−	2.77707e9i	0.133571	−	0.231353i	0.925051	+	0.379843i	$0.124022\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	2.57279e9	+	1.48540e9i	0.204279	+	0.117941i
$336$		0			0
$337$	8.82134e9	+	1.52790e10i	0.683935	+	1.18461i	0.973770	+	0.227534i	$0.0730662\pi$
$337$	8.82134e9	+	1.52790e10i	0.683935	+	1.18461i	−0.289835	+	0.957077i	$0.593600\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$			1.03383e10i			0.764592i
$342$		0			0
$343$	−8.14346e9			−0.588345
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−7.55287e9	+	4.36065e9i	−0.520948	+	0.300769i	−0.737322	−	0.675541i	$-0.763910\pi$
$347$	−7.55287e9	+	4.36065e9i	−0.520948	+	0.300769i	0.216375	+	0.976310i	$0.430577\pi$
$348$		0			0
$349$	−5.08867e9	+	8.81384e9i	−0.343007	+	0.594105i	−0.984990	−	0.172614i	$-0.944779\pi$
$349$	−5.08867e9	+	8.81384e9i	−0.343007	+	0.594105i	0.641983	+	0.766719i	$0.278112\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	1.37900e10	+	7.96168e9i	0.888109	+	0.512750i	0.873324	−	0.487141i	$-0.161960\pi$
$353$	1.37900e10	+	7.96168e9i	0.888109	+	0.512750i	0.0147858	+	0.999891i	$0.495293\pi$
$354$		0			0
$355$	6.10410e8	+	1.05726e9i	0.0384333	+	0.0665685i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	5.57548e9i		−	0.335664i	−0.985816	−	0.167832i	$-0.946323\pi$
$359$		−	5.57548e9i		−	0.335664i	0.985816	−	0.167832i	$-0.0536766\pi$
$360$		0			0
$361$	−2.99376e9			−0.176274
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−3.42475e9	+	1.97728e9i	−0.192955	+	0.111403i
$366$		0			0
$367$	−2.34540e9	+	4.06235e9i	−0.129286	+	0.223930i	−0.923400	−	0.383839i	$-0.874602\pi$
$367$	−2.34540e9	+	4.06235e9i	−0.129286	+	0.223930i	0.794114	+	0.607769i	$0.207935\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	7.45353e9	+	4.30330e9i	0.393429	+	0.227146i
$372$		0			0
$373$	−9.98911e9	−	1.73016e10i	−0.516049	−	0.893824i	−0.999826	−	0.0186325i	$-0.994069\pi$
$373$	−9.98911e9	−	1.73016e10i	−0.516049	−	0.893824i	0.483777	−	0.875191i	$-0.339265\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		−	1.42892e10i		−	0.707363i
$378$		0			0
$379$	3.40327e10			1.64945			0.824726	−	0.565532i	$-0.191329\pi$
$379$	3.40327e10			1.64945			0.824726	+	0.565532i	$0.191329\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−1.39611e10	+	8.06046e9i	−0.648822	+	0.374597i	−0.788005	−	0.615669i	$-0.788886\pi$
$383$	−1.39611e10	+	8.06046e9i	−0.648822	+	0.374597i	0.139183	+	0.990267i	$0.455552\pi$
$384$		0			0
$385$	6.81218e8	−	1.17990e9i	0.0310058	−	0.0537037i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−2.29807e10	−	1.32679e10i	−1.00361	−	0.579435i	−0.0942959	−	0.995544i	$-0.530060\pi$
$389$	−2.29807e10	−	1.32679e10i	−1.00361	−	0.579435i	−0.909315	+	0.416109i	$0.863393\pi$
$390$		0			0
$391$	−4.72254e9	−	8.17969e9i	−0.202055	−	0.349969i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			5.07996e9i			0.208676i
$396$		0			0
$397$	2.50944e10			1.01022			0.505108	−	0.863056i	$-0.331452\pi$
$397$	2.50944e10			1.01022			0.505108	+	0.863056i	$0.331452\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	6.71173e9	−	3.87502e9i	0.259572	−	0.149864i	−0.364567	−	0.931177i	$-0.618783\pi$
$401$	6.71173e9	−	3.87502e9i	0.259572	−	0.149864i	0.624139	+	0.781313i	$0.285450\pi$
$402$		0			0
$403$	−2.94213e9	+	5.09592e9i	−0.111543	+	0.193198i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.20364e10	+	2.42697e10i	1.53196	+	0.884478i
$408$		0			0
$409$	−1.37487e10	−	2.38135e10i	−0.491326	−	0.851001i	0.508624	−	0.860988i	$-0.330154\pi$
$409$	−1.37487e10	−	2.38135e10i	−0.491326	−	0.851001i	−0.999950	+	0.00998745i	$0.996821\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			4.57951e9i			0.157405i
$414$		0			0
$415$	4.14089e9			0.139605
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−3.00646e10	+	1.73578e10i	−0.975439	+	0.563170i	−0.900890	−	0.434048i	$-0.857085\pi$
$419$	−3.00646e10	+	1.73578e10i	−0.975439	+	0.563170i	−0.0745486	+	0.997217i	$0.523752\pi$
$420$		0			0
$421$	2.79802e10	−	4.84631e10i	0.890681	−	1.54271i	0.0516215	−	0.998667i	$-0.483561\pi$
$421$	2.79802e10	−	4.84631e10i	0.890681	−	1.54271i	0.839060	−	0.544039i	$-0.183106\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3.51538e10	−	2.02961e10i	−1.07750	−	0.622094i
$426$		0			0
$427$	8.18676e9	+	1.41799e10i	0.246264	+	0.426541i
$428$		0			0
$429$		0			0
$430$		0			0
$431$		−	1.05381e9i		−	0.0305390i	−0.999883	−	0.0152695i	$-0.995139\pi$
$431$		−	1.05381e9i		−	0.0305390i	0.999883	−	0.0152695i	$-0.00486062\pi$
$432$		0			0
$433$	−1.08239e10			−0.307916			−0.153958	−	0.988077i	$-0.549202\pi$
$433$	−1.08239e10			−0.307916			−0.153958	+	0.988077i	$0.549202\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	9.15603e9	−	5.28624e9i	0.251062	−	0.144951i
$438$		0			0
$439$	9.63567e9	−	1.66895e10i	0.259432	−	0.449350i	−0.706658	−	0.707556i	$-0.749798\pi$
$439$	9.63567e9	−	1.66895e10i	0.259432	−	0.449350i	0.966090	+	0.258206i	$0.0831312\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−3.47005e10	−	2.00344e10i	−0.900993	−	0.520189i	−0.0234707	−	0.999725i	$-0.507472\pi$
$443$	−3.47005e10	−	2.00344e10i	−0.900993	−	0.520189i	−0.877522	+	0.479536i	$0.840805\pi$
$444$		0			0
$445$	−2.08065e9	−	3.60379e9i	−0.0530590	−	0.0919008i
$446$		0			0
$447$		0			0
$448$		0			0
$449$			2.89578e10i			0.712493i	0.934392	+	0.356247i	$0.115944\pi$
$449$			2.89578e10i			0.712493i	−0.934392	+	0.356247i	$0.884056\pi$
$450$		0			0
$451$	−3.82822e10			−0.925318
$452$		0			0
$453$		0			0
$454$		0			0
$455$	6.71571e8	−	3.87732e8i	0.0156692	−	0.00904661i
$456$		0			0
$457$	−2.76429e9	+	4.78789e9i	−0.0633752	+	0.109769i	−0.895972	−	0.444110i	$-0.853520\pi$
$457$	−2.76429e9	+	4.78789e9i	−0.0633752	+	0.109769i	0.832597	+	0.553879i	$0.186853\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	4.96113e10	+	2.86431e10i	1.09844	+	0.634186i	0.935811	−	0.352501i	$-0.114669\pi$
$461$	4.96113e10	+	2.86431e10i	1.09844	+	0.634186i	0.162631	+	0.986687i	$0.448002\pi$
$462$		0			0
$463$	4.30725e10	+	7.46037e10i	0.937294	+	1.62344i	0.770492	+	0.637450i	$0.220011\pi$
$463$	4.30725e10	+	7.46037e10i	0.937294	+	1.62344i	0.166802	+	0.985990i	$0.446656\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$		−	1.73366e10i		−	0.364498i	−0.983252	−	0.182249i	$-0.941662\pi$
$467$		−	1.73366e10i		−	0.364498i	0.983252	−	0.182249i	$-0.0583377\pi$
$468$		0			0
$469$	−2.73936e10			−0.566185
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.25114e10	+	1.29970e10i	−0.449736	+	0.259655i
$474$		0			0
$475$	2.27186e10	−	3.93498e10i	0.446281	−	0.772981i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1.41007e10	+	8.14105e9i	0.267855	+	0.154646i	0.627912	−	0.778284i	$-0.283910\pi$
$479$	1.41007e10	+	8.14105e9i	0.267855	+	0.154646i	−0.360058	+	0.932930i	$0.617243\pi$
$480$		0			0
$481$	1.38137e10	+	2.39260e10i	0.258065	+	0.446982i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			7.31547e8i			0.0132213i
$486$		0			0
$487$	−8.59101e10			−1.52731			−0.763657	−	0.645622i	$-0.776598\pi$
$487$	−8.59101e10			−1.52731			−0.763657	+	0.645622i	$0.776598\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−9.42747e10	+	5.44295e10i	−1.62207	+	0.936502i	−0.635704	+	0.771933i	$0.719290\pi$
$491$	−9.42747e10	+	5.44295e10i	−1.62207	+	0.936502i	−0.986366	+	0.164569i	$0.947377\pi$
$492$		0			0
$493$	−5.80802e10	+	1.00598e11i	−0.983197	+	1.70295i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−9.74898e9	−	5.62857e9i	−0.159784	−	0.0922514i
$498$		0			0
$499$	−1.01210e10	−	1.75301e10i	−0.163238	−	0.282737i	0.772790	−	0.634662i	$-0.218861\pi$
$499$	−1.01210e10	−	1.75301e10i	−0.163238	−	0.282737i	−0.936028	+	0.351925i	$0.885527\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$			8.95990e9i			0.139969i	0.997548	+	0.0699844i	$0.0222949\pi$
$503$			8.95990e9i			0.139969i	−0.997548	+	0.0699844i	$0.977705\pi$
$504$		0			0
$505$	8.79066e9			0.135162
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−7.49283e10	+	4.32599e10i	−1.11628	+	0.644487i	−0.940450	−	0.339933i	$-0.889596\pi$
$509$	−7.49283e10	+	4.32599e10i	−1.11628	+	0.644487i	−0.175835	+	0.984420i	$0.556262\pi$
$510$		0			0
$511$	1.82324e10	−	3.15795e10i	0.267400	−	0.463150i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.33153e10	−	7.68761e9i	−0.189288	−	0.109286i
$516$		0			0
$517$	4.09632e10	+	7.09503e10i	0.573365	+	0.993098i
$518$		0			0
$519$		0			0
$520$		0			0
$521$		−	7.83590e10i		−	1.06350i	−0.846901	−	0.531750i	$-0.821534\pi$
$521$		−	7.83590e10i		−	1.06350i	0.846901	−	0.531750i	$-0.178466\pi$
$522$		0			0
$523$	9.36222e9			0.125133			0.0625665	−	0.998041i	$-0.480071\pi$
$523$	9.36222e9			0.125133			0.0625665	+	0.998041i	$0.480071\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4.14260e10	−	2.39173e10i	0.537070	−	0.310078i
$528$		0			0
$529$	−3.51605e10	+	6.08998e10i	−0.448986	+	0.777667i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−1.88700e10	−	1.08946e10i	−0.233810	−	0.134990i
$534$		0			0
$535$	−6.99749e9	−	1.21200e10i	−0.0854136	−	0.147941i
$536$		0			0
$537$		0			0
$538$		0			0
$539$		−	1.19088e11i		−	1.41095i
$540$		0			0
$541$	2.87519e10			0.335642			0.167821	−	0.985817i	$-0.446327\pi$
$541$	2.87519e10			0.335642			0.167821	+	0.985817i	$0.446327\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−6.99129e9	+	4.03642e9i	−0.0792449	+	0.0457521i
$546$		0			0
$547$	−7.14292e10	+	1.23719e11i	−0.797860	+	1.38193i	0.123147	+	0.992388i	$0.460701\pi$
$547$	−7.14292e10	+	1.23719e11i	−0.797860	+	1.38193i	−0.921007	+	0.389545i	$0.872632\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.12605e11	−	6.50128e10i	−1.22167	−	0.705330i
$552$		0			0
$553$	−2.34211e10	−	4.05665e10i	−0.250442	−	0.433778i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	1.20526e10i		−	0.125216i	−0.998038	−	0.0626080i	$-0.980058\pi$
$557$		−	1.20526e10i		−	0.125216i	0.998038	−	0.0626080i	$-0.0199418\pi$
$558$		0			0
$559$	−1.47951e10			−0.151520
$560$		0			0
$561$		0			0
$562$		0			0
$563$	7.41550e10	−	4.28134e10i	0.738086	−	0.426134i	−0.0832869	−	0.996526i	$-0.526542\pi$
$563$	7.41550e10	−	4.28134e10i	0.738086	−	0.426134i	0.821373	+	0.570391i	$0.193208\pi$
$564$		0			0
$565$	5.85400e9	−	1.01394e10i	0.0574459	−	0.0994992i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6.77244e10	−	3.91007e10i	−0.646095	−	0.373023i	0.140864	−	0.990029i	$-0.455012\pi$
$569$	−6.77244e10	−	3.91007e10i	−0.646095	−	0.373023i	−0.786958	+	0.617006i	$0.788345\pi$
$570$		0			0
$571$	1.68244e10	+	2.91408e10i	0.158269	+	0.274130i	0.934245	−	0.356633i	$-0.116075\pi$
$571$	1.68244e10	+	2.91408e10i	0.158269	+	0.274130i	−0.775975	+	0.630763i	$0.782742\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	3.43382e10i		−	0.314128i
$576$		0			0
$577$	−5.68149e10			−0.512577			−0.256288	−	0.966600i	$-0.582500\pi$
$577$	−5.68149e10			−0.512577			−0.256288	+	0.966600i	$0.582500\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−3.30675e10	+	1.90915e10i	−0.290200	+	0.167547i
$582$		0			0
$583$	−1.32499e11	+	2.29496e11i	−1.14694	+	1.98655i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.52093e11	+	8.78111e10i	1.28103	+	0.739600i	0.977036	−	0.213075i	$-0.0683478\pi$
$587$	1.52093e11	+	8.78111e10i	1.28103	+	0.739600i	0.303990	+	0.952675i	$0.401681\pi$
$588$		0			0
$589$	2.67722e10	+	4.63707e10i	0.222445	+	0.385286i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			1.42615e10i			0.115331i	0.998336	+	0.0576655i	$0.0183657\pi$
$593$			1.42615e10i			0.115331i	−0.998336	+	0.0576655i	$0.981634\pi$
$594$		0			0
$595$	−6.30394e9			−0.0502972
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−1.21666e11	+	7.02441e10i	−0.945068	+	0.545635i	−0.891545	−	0.452931i	$-0.850378\pi$
$599$	−1.21666e11	+	7.02441e10i	−0.945068	+	0.545635i	−0.0535228	+	0.998567i	$0.517045\pi$
$600$		0			0
$601$	−7.75136e10	+	1.34257e11i	−0.594128	+	1.02906i	0.399542	+	0.916715i	$0.369169\pi$
$601$	−7.75136e10	+	1.34257e11i	−0.594128	+	1.02906i	−0.993669	+	0.112344i	$0.964164\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2.13974e10	+	1.23538e10i	0.159713	+	0.0922101i
$606$		0			0
$607$	−5.96405e10	−	1.03300e11i	−0.439325	−	0.760934i	0.558312	−	0.829631i	$-0.311449\pi$
$607$	−5.96405e10	−	1.03300e11i	−0.439325	−	0.760934i	−0.997638	+	0.0686970i	$0.978116\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$			4.66303e10i			0.334583i
$612$		0			0
$613$	−1.07532e11			−0.761546			−0.380773	−	0.924669i	$-0.624342\pi$
$613$	−1.07532e11			−0.761546			−0.380773	+	0.924669i	$0.624342\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−1.08306e11	+	6.25304e10i	−0.747328	+	0.431470i	−0.824728	−	0.565530i	$-0.808672\pi$
$617$	−1.08306e11	+	6.25304e10i	−0.747328	+	0.431470i	0.0773997	+	0.997000i	$0.475338\pi$
$618$		0			0
$619$	−3.18581e10	+	5.51798e10i	−0.216998	+	0.375852i	−0.953889	−	0.300160i	$-0.902960\pi$
$619$	−3.18581e10	+	5.51798e10i	−0.216998	+	0.375852i	0.736890	+	0.676012i	$0.236293\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	3.32304e10	+	1.91856e10i	0.220589	+	0.127357i
$624$		0			0
$625$	−7.25239e10	−	1.25615e11i	−0.475293	−	0.823231i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	2.24590e11i		−	1.43479i
$630$		0			0
$631$	8.53724e10			0.538518			0.269259	−	0.963068i	$-0.413221\pi$
$631$	8.53724e10			0.538518			0.269259	+	0.963068i	$0.413221\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.09874e10	−	6.34356e9i	0.0675770	−	0.0390156i
$636$		0			0
$637$	3.38909e10	−	5.87007e10i	0.205838	−	0.356521i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	3.48018e10	+	2.00929e10i	0.206144	+	0.119017i	0.599518	−	0.800361i	$-0.295359\pi$
$641$	3.48018e10	+	2.00929e10i	0.206144	+	0.119017i	−0.393374	+	0.919378i	$0.628692\pi$
$642$		0			0
$643$	2.65057e10	+	4.59092e10i	0.155058	+	0.268569i	0.933080	−	0.359668i	$-0.117110\pi$
$643$	2.65057e10	+	4.59092e10i	0.155058	+	0.268569i	−0.778022	+	0.628237i	$0.783777\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		−	8.40520e10i		−	0.479657i	−0.970815	−	0.239829i	$-0.922909\pi$
$647$		−	8.40520e10i		−	0.479657i	0.970815	−	0.239829i	$-0.0770912\pi$
$648$		0			0
$649$	−1.41004e11			−0.794791
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−5.79412e10	+	3.34523e10i	−0.318665	+	0.183981i	−0.650797	−	0.759251i	$-0.725565\pi$
$653$	−5.79412e10	+	3.34523e10i	−0.318665	+	0.183981i	0.332132	+	0.943233i	$0.392232\pi$
$654$		0			0
$655$	1.25951e10	−	2.18154e10i	0.0684286	−	0.118522i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.98528e11	−	1.14620e11i	−1.05264	−	0.607741i	−0.129251	−	0.991612i	$-0.541257\pi$
$659$	−1.98528e11	−	1.14620e11i	−1.05264	−	0.607741i	−0.923387	+	0.383871i	$0.874591\pi$
$660$		0			0
$661$	1.62836e11	+	2.82040e11i	0.852989	+	1.47742i	0.878498	+	0.477746i	$0.158546\pi$
$661$	1.62836e11	+	2.82040e11i	0.852989	+	1.47742i	−0.0255089	+	0.999675i	$0.508121\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		−	7.05639e9i		−	0.0360825i
$666$		0			0
$667$	−9.82639e10			−0.496467
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−4.36602e11	+	2.52072e11i	−2.15375	+	1.24347i
$672$		0			0
$673$	−1.20089e10	+	2.08001e10i	−0.0585389	+	0.101392i	−0.893810	−	0.448446i	$-0.851977\pi$
$673$	−1.20089e10	+	2.08001e10i	−0.0585389	+	0.101392i	0.835271	+	0.549839i	$0.185311\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	2.50617e11	+	1.44694e11i	1.19304	+	0.688804i	0.958995	−	0.283421i	$-0.0914695\pi$
$677$	2.50617e11	+	1.44694e11i	1.19304	+	0.688804i	0.234048	+	0.972225i	$0.424803\pi$
$678$		0			0
$679$	−3.37279e9	−	5.84184e9i	−0.0158675	−	0.0274834i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			1.04015e11i			0.477982i	0.971022	+	0.238991i	$0.0768166\pi$
$683$			1.04015e11i			0.477982i	−0.971022	+	0.238991i	$0.923183\pi$
$684$		0			0
$685$	−7.84829e9			−0.0356462
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−1.30623e11	+	7.54152e10i	−0.579619	+	0.334643i
$690$		0			0
$691$	5.51122e10	−	9.54571e10i	0.241733	−	0.418694i	−0.719475	−	0.694518i	$-0.755618\pi$
$691$	5.51122e10	−	9.54571e10i	0.241733	−	0.418694i	0.961208	+	0.275825i	$0.0889509\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−6.28438e9	−	3.62829e9i	−0.0269354	−	0.0155511i
$696$		0			0
$697$	8.85651e10	+	1.53399e11i	0.375259	+	0.649968i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			7.57816e10i			0.313828i	0.987612	+	0.156914i	$0.0501546\pi$
$701$			7.57816e10i			0.313828i	−0.987612	+	0.156914i	$0.949845\pi$
$702$		0			0
$703$	2.51397e11			1.02929
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−7.01986e10	+	4.05292e10i	−0.280964	+	0.162215i
$708$		0			0
$709$	1.71004e11	−	2.96187e11i	0.676737	−	1.17214i	−0.299221	−	0.954184i	$-0.596727\pi$
$709$	1.71004e11	−	2.96187e11i	0.676737	−	1.17214i	0.975958	−	0.217959i	$-0.0699400\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	3.50436e10	+	2.02324e10i	0.135597	+	0.0782871i
$714$		0			0
$715$	1.19383e10	+	2.06778e10i	0.0456793	+	0.0791189i
$716$		0			0
$717$		0			0
$718$		0			0
$719$		−	8.86727e10i		−	0.331799i	−0.986143	−	0.165899i	$-0.946947\pi$
$719$		−	8.86727e10i		−	0.331799i	0.986143	−	0.165899i	$-0.0530527\pi$
$720$		0			0
$721$	1.41775e11			0.524635
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−3.65730e11	+	2.11154e11i	−1.32376	+	0.764271i
$726$		0			0
$727$	6.21757e10	−	1.07691e11i	0.222578	−	0.385517i	−0.733012	−	0.680216i	$-0.761886\pi$
$727$	6.21757e10	−	1.07691e11i	0.222578	−	0.385517i	0.955590	+	0.294699i	$0.0952193\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	1.04159e11	+	6.01364e10i	0.364778	+	0.210605i
$732$		0			0
$733$	−1.20019e11	−	2.07878e11i	−0.415750	−	0.720101i	0.579757	−	0.814790i	$-0.303148\pi$
$733$	−1.20019e11	−	2.07878e11i	−0.415750	−	0.720101i	−0.995507	+	0.0946891i	$0.969814\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	8.43456e11i		−	2.85886i
$738$		0			0
$739$	−9.80470e10			−0.328743			−0.164372	−	0.986398i	$-0.552560\pi$
$739$	−9.80470e10			−0.328743			−0.164372	+	0.986398i	$0.552560\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	3.60334e11	−	2.08039e11i	1.18236	−	0.682636i	0.225801	−	0.974173i	$-0.427500\pi$
$743$	3.60334e11	−	2.08039e11i	1.18236	−	0.682636i	0.956560	+	0.291537i	$0.0941666\pi$
$744$		0			0
$745$	−2.46679e10	+	4.27261e10i	−0.0800769	+	0.138697i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.11758e11	+	6.45237e10i	0.355101	+	0.205018i
$750$		0			0
$751$	1.91821e11	+	3.32243e11i	0.603025	+	1.04447i	0.992360	+	0.123374i	$0.0393715\pi$
$751$	1.91821e11	+	3.32243e11i	0.603025	+	1.04447i	−0.389335	+	0.921096i	$0.627295\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$			1.18149e10i			0.0363616i
$756$		0			0
$757$	2.00507e11			0.610584			0.305292	−	0.952259i	$-0.401246\pi$
$757$	2.00507e11			0.610584			0.305292	+	0.952259i	$0.401246\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	1.41971e11	−	8.19667e10i	0.423311	−	0.244399i	−0.273182	−	0.961962i	$-0.588076\pi$
$761$	1.41971e11	−	8.19667e10i	0.423311	−	0.244399i	0.696493	+	0.717564i	$0.254743\pi$
$762$		0			0
$763$	3.72198e10	−	6.44665e10i	0.109818	−	0.190211i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−6.95036e10	−	4.01279e10i	−0.200829	−	0.115948i
$768$		0			0
$769$	−3.02003e11	−	5.23085e11i	−0.863588	−	1.49578i	−0.868443	−	0.495789i	$-0.834879\pi$
$769$	−3.02003e11	−	5.23085e11i	−0.863588	−	1.49578i	0.00485515	−	0.999988i	$-0.498455\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$			5.78731e11i			1.62091i	0.585801	+	0.810455i	$0.300780\pi$
$773$			5.78731e11i			1.62091i	−0.585801	+	0.810455i	$0.699220\pi$
$774$		0			0
$775$	1.73906e11			0.482067
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−1.71709e11	+	9.91364e10i	−0.466277	+	0.269205i
$780$		0			0
$781$	1.73305e11	−	3.00173e11i	0.465808	−	0.806803i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−3.89053e10	−	2.24620e10i	−0.102454	−	0.0591520i
$786$		0			0
$787$	−1.88724e11	−	3.26880e11i	−0.491958	−	0.852096i	0.507999	−	0.861358i	$-0.330385\pi$
$787$	−1.88724e11	−	3.26880e11i	−0.491958	−	0.852096i	−0.999957	+	0.00926121i	$0.997052\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$			1.07959e11i			0.275774i
$792$		0			0
$793$	−2.86946e11			−0.725616
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−2.07081e11	+	1.19558e11i	−0.513224	+	0.296310i	−0.734158	−	0.678979i	$-0.762423\pi$
$797$	−2.07081e11	+	1.19558e11i	−0.513224	+	0.296310i	0.220934	+	0.975289i	$0.429090\pi$
$798$		0			0
$799$	1.89535e11	−	3.28284e11i	0.465053	−	0.805495i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	9.72340e11	+	5.61381e11i	2.33860	+	1.35019i
$804$		0			0
$805$	−2.66635e9	−	4.61826e9i	−0.00634942	−	0.0109975i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	2.09694e11i		−	0.489544i	−0.969581	−	0.244772i	$-0.921287\pi$
$809$		−	2.09694e11i		−	0.489544i	0.969581	−	0.244772i	$-0.0787131\pi$
$810$		0			0
$811$	−7.14392e11			−1.65140			−0.825702	−	0.564107i	$-0.809221\pi$
$811$	−7.14392e11			−1.65140			−0.825702	+	0.564107i	$0.809221\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.88273e8	−	1.08700e8i	0.000426735	−	0.000246376i
$816$		0			0
$817$	−6.73144e10	+	1.16592e11i	−0.151085	+	0.261686i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	5.95004e11	+	3.43526e11i	1.30963	+	0.756113i	0.982033	−	0.188707i	$-0.0604296\pi$
$821$	5.95004e11	+	3.43526e11i	1.30963	+	0.756113i	0.327592	+	0.944819i	$0.393763\pi$
$822$		0			0
$823$	4.54624e10	+	7.87432e10i	0.0990953	+	0.171638i	0.911310	−	0.411720i	$-0.135072\pi$
$823$	4.54624e10	+	7.87432e10i	0.0990953	+	0.171638i	−0.812215	+	0.583358i	$0.801738\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	3.03065e11i		−	0.647908i	−0.946073	−	0.323954i	$-0.894988\pi$
$827$		−	3.03065e11i		−	0.647908i	0.946073	−	0.323954i	$-0.105012\pi$
$828$		0			0
$829$	7.06427e11			1.49572			0.747858	−	0.663859i	$-0.231082\pi$
$829$	7.06427e11			1.49572			0.747858	+	0.663859i	$0.231082\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−4.77193e11	+	2.75507e11i	−0.991092	+	0.572207i
$834$		0			0
$835$	3.03753e10	−	5.26115e10i	0.0624848	−	0.108227i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	7.75197e10	+	4.47560e10i	0.156446	+	0.0903241i	0.576179	−	0.817323i	$-0.304543\pi$
$839$	7.75197e10	+	4.47560e10i	0.156446	+	0.0903241i	−0.419733	+	0.907648i	$0.637876\pi$
$840$		0			0
$841$	3.54126e11	+	6.13364e11i	0.707903	+	1.22612i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	5.20241e10i		−	0.102042i
$846$		0			0
$847$	−2.27828e11			−0.442663
$848$		0			0
$849$		0			0
$850$		0			0
$851$	1.64534e11	−	9.49940e10i	0.313717	−	0.181125i
$852$		0			0
$853$	−4.25979e11	+	7.37818e11i	−0.804623	+	1.39365i	0.111922	+	0.993717i	$0.464299\pi$
$853$	−4.25979e11	+	7.37818e11i	−0.804623	+	1.39365i	−0.916545	+	0.399931i	$0.869034\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	9.19638e10	+	5.30953e10i	0.170488	+	0.0984313i	0.582816	−	0.812604i	$-0.301951\pi$
$857$	9.19638e10	+	5.30953e10i	0.170488	+	0.0984313i	−0.412328	+	0.911035i	$0.635284\pi$
$858$		0			0
$859$	−1.80076e11	−	3.11901e11i	−0.330737	−	0.572854i	0.651919	−	0.758288i	$-0.273964\pi$
$859$	−1.80076e11	−	3.11901e11i	−0.330737	−	0.572854i	−0.982657	+	0.185435i	$0.940631\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	1.03087e12i		−	1.85849i	−0.369462	−	0.929246i	$-0.620458\pi$
$863$		−	1.03087e12i		−	1.85849i	0.369462	−	0.929246i	$-0.379542\pi$
$864$		0			0
$865$	7.54886e10			0.134839
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1.24905e12	−	7.21141e11i	2.19029	−	1.26456i
$870$		0			0
$871$	2.40037e11	−	4.15756e11i	0.417066	−	0.722380i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−4.00300e10	−	2.31113e10i	−0.0682895	−	0.0394269i
$876$		0			0
$877$	−1.55982e11	−	2.70169e11i	−0.263679	−	0.456706i	0.703537	−	0.710658i	$-0.251603\pi$
$877$	−1.55982e11	−	2.70169e11i	−0.263679	−	0.456706i	−0.967217	+	0.253952i	$0.918269\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			7.28854e10i			0.120987i	0.998169	+	0.0604933i	$0.0192674\pi$
$881$			7.28854e10i			0.120987i	−0.998169	+	0.0604933i	$0.980733\pi$
$882$		0			0
$883$	1.07132e12			1.76228			0.881142	−	0.472852i	$-0.156776\pi$
$883$	1.07132e12			1.76228			0.881142	+	0.472852i	$0.156776\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−3.56195e11	+	2.05649e11i	−0.575432	+	0.332226i	−0.759316	−	0.650722i	$-0.774466\pi$
$887$	−3.56195e11	+	2.05649e11i	−0.575432	+	0.332226i	0.183884	+	0.982948i	$0.441133\pi$
$888$		0			0
$889$	−5.84938e10	+	1.01314e11i	−0.0936489	+	0.162205i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	3.67469e11	+	2.12158e11i	0.577849	+	0.333621i
$894$		0			0
$895$	3.69827e10	+	6.40559e10i	0.0576377	+	0.0998314i
$896$		0			0
$897$		0			0
$898$		0			0
$899$		−	4.97658e11i		−	0.761889i
$900$		0			0
$901$	1.22614e12			1.86055
$902$		0			0
$903$		0			0
$904$		0			0
$905$	1.15501e11	−	6.66847e10i	0.172184	−	0.0994104i
$906$		0			0
$907$	7.64334e10	−	1.32387e11i	0.112942	−	0.195621i	−0.804013	−	0.594611i	$-0.797306\pi$
$907$	7.64334e10	−	1.32387e11i	0.112942	−	0.195621i	0.916955	+	0.398991i	$0.130639\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	7.19623e11	+	4.15475e11i	1.04480	+	0.603213i	0.921188	−	0.389118i	$-0.127220\pi$
$911$	7.19623e11	+	4.15475e11i	1.04480	+	0.603213i	0.123608	+	0.992331i	$0.460553\pi$
$912$		0			0
$913$	−5.87832e11	−	1.01816e12i	−0.846000	−	1.46531i
$914$		0			0
$915$		0			0
$916$		0			0
$917$			2.32279e11i			0.328498i
$918$		0			0
$919$	4.99778e11			0.700673			0.350336	−	0.936624i	$-0.386067\pi$
$919$	4.99778e11			0.700673			0.350336	+	0.936624i	$0.386067\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	1.70851e11	−	9.86407e10i	0.235402	−	0.135909i
$924$		0			0
$925$	4.08255e11	−	7.07119e11i	0.557654	−	0.965885i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	3.65549e11	+	2.11050e11i	0.490775	+	0.283349i	0.724896	−	0.688858i	$-0.241888\pi$
$929$	3.65549e11	+	2.11050e11i	0.490775	+	0.283349i	−0.234121	+	0.972207i	$0.575221\pi$
$930$		0			0
$931$	−3.08393e11	−	5.34152e11i	−0.410493	−	0.710994i
$932$		0			0
$933$		0			0
$934$		0			0
$935$		−	1.94100e11i		−	0.253968i
$936$		0			0
$937$	−1.46649e12			−1.90248			−0.951240	−	0.308452i	$-0.900189\pi$
$937$	−1.46649e12			−1.90248			−0.951240	+	0.308452i	$0.900189\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−1.80375e11	+	1.04140e11i	−0.230048	+	0.132818i	−0.610594	−	0.791944i	$-0.709069\pi$
$941$	−1.80375e11	+	1.04140e11i	−0.230048	+	0.132818i	0.380546	+	0.924762i	$0.375736\pi$
$942$		0			0
$943$	−7.49201e10	+	1.29765e11i	−0.0947440	+	0.164101i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	3.88417e11	+	2.24252e11i	0.482945	+	0.278828i	0.721643	−	0.692265i	$-0.243387\pi$
$947$	3.88417e11	+	2.24252e11i	0.482945	+	0.278828i	−0.238698	+	0.971094i	$0.576721\pi$
$948$		0			0
$949$	3.19523e11	+	5.53430e11i	0.393947	+	0.682336i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	1.57158e12i		−	1.90531i	−0.304053	−	0.952655i	$-0.598340\pi$
$953$		−	1.57158e12i		−	1.90531i	0.304053	−	0.952655i	$-0.401660\pi$
$954$		0			0
$955$	7.76140e10			0.0933097
$956$		0			0
$957$		0			0
$958$		0			0
$959$	6.26733e10	−	3.61844e10i	0.0740982	−	0.0427806i
$960$		0			0
$961$	3.23978e11	−	5.61147e11i	0.379859	−	0.657935i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−5.53086e10	−	3.19324e10i	−0.0637798	−	0.0368233i
$966$		0			0
$967$	4.92009e10	+	8.52185e10i	0.0562688	+	0.0974604i	0.892788	−	0.450478i	$-0.148746\pi$
$967$	4.92009e10	+	8.52185e10i	0.0562688	+	0.0974604i	−0.836519	+	0.547938i	$0.815413\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$		−	2.12176e11i		−	0.238682i	−0.992853	−	0.119341i	$-0.961922\pi$
$971$		−	2.12176e11i		−	0.238682i	0.992853	−	0.119341i	$-0.0380781\pi$
$972$		0			0
$973$	6.69127e10			0.0746547
$974$		0			0
$975$		0			0
$976$		0			0
$977$	9.53074e11	−	5.50257e11i	1.04604	−	0.603931i	0.124502	−	0.992219i	$-0.460267\pi$
$977$	9.53074e11	−	5.50257e11i	1.04604	−	0.603931i	0.921538	+	0.388288i	$0.126933\pi$
$978$		0			0
$979$	−5.90729e11	+	1.02317e12i	−0.643069	+	1.11383i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	6.07234e11	+	3.50586e11i	0.650342	+	0.375475i	0.788587	−	0.614923i	$-0.210813\pi$
$983$	6.07234e11	+	3.50586e11i	0.650342	+	0.375475i	−0.138245	+	0.990398i	$0.544146\pi$
$984$		0			0
$985$	−4.30703e10	−	7.45999e10i	−0.0457544	−	0.0792489i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			1.01743e11i			0.106345i
$990$		0			0
$991$	−1.38686e12			−1.43793			−0.718963	−	0.695048i	$-0.755383\pi$
$991$	−1.38686e12			−1.43793			−0.718963	+	0.695048i	$0.755383\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	7.06240e10	−	4.07748e10i	0.0720543	−	0.0416006i
$996$		0			0
$997$	3.17360e11	−	5.49684e11i	0.321197	−	0.556330i	−0.659538	−	0.751671i	$-0.729248\pi$
$997$	3.17360e11	−	5.49684e11i	0.321197	−	0.556330i	0.980735	+	0.195341i	$0.0625814\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.9.q.c.305.4		16
3.2	odd	2		144.9.q.b.65.6		16
4.3	odd	2		54.9.d.a.35.6		16
9.4	even	3		144.9.q.b.113.6		16
9.5	odd	6	inner	432.9.q.c.17.4		16
12.11	even	2		18.9.d.a.11.2	yes	16
36.7	odd	6		162.9.b.c.161.4		16
36.11	even	6		162.9.b.c.161.13		16
36.23	even	6		54.9.d.a.17.6		16
36.31	odd	6		18.9.d.a.5.2	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.9.d.a.5.2	✓	16	36.31	odd	6
18.9.d.a.11.2	yes	16	12.11	even	2
54.9.d.a.17.6		16	36.23	even	6
54.9.d.a.35.6		16	4.3	odd	2
144.9.q.b.65.6		16	3.2	odd	2
144.9.q.b.113.6		16	9.4	even	3
162.9.b.c.161.4		16	36.7	odd	6
162.9.b.c.161.13		16	36.11	even	6
432.9.q.c.17.4		16	9.5	odd	6	inner
432.9.q.c.305.4		16	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	432.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(69.6596 - 40.2180i) q^{5} +(-370.849 + 642.329i) q^{7} +(-19777.4 - 11418.5i) q^{11} +(-6499.12 - 11256.8i) q^{13} +105666. i q^{17} -118278. q^{19} +(-77410.8 + 44693.1i) q^{23} +(-192078. + 332688. i) q^{25} +(952037. + 549659. i) q^{29} +(-226348. - 392047. i) q^{31} +59659.1i q^{35} -2.12547e6 q^{37} +(1.45174e6 - 838161. i) q^{41} +(569118. - 985742. i) q^{43} +(-3.10681e6 - 1.79372e6i) q^{47} +(2.60734e6 + 4.51605e6i) q^{49} -1.16039e7i q^{53} -1.83692e6 q^{55} +(5.34715e6 - 3.08718e6i) q^{59} +(1.10379e7 - 1.91182e7i) q^{61} +(-905451. - 522763. i) q^{65} +(1.84669e7 + 3.19855e7i) q^{67} +1.51775e7i q^{71} -4.91641e7 q^{73} +(1.46689e7 - 8.46908e6i) q^{77} +(-3.15777e7 + 5.46942e7i) q^{79} +(4.45835e7 + 2.57403e7i) q^{83} +(4.24967e6 + 7.36064e6i) q^{85} -5.17343e7i q^{89} +9.64076e6 q^{91} +(-8.23923e6 + 4.75692e6i) q^{95} +(-4.54739e6 + 7.87630e6i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 882 q^{5} + 1846 q^{7} + 45756 q^{11} - 3370 q^{13} - 362180 q^{19} + 1311138 q^{23} + 963394 q^{25} + 2851290 q^{29} - 542438 q^{31} + 3343328 q^{37} - 9218592 q^{41} - 339512 q^{43} - 34980606 q^{47}+ \cdots - 89415484 q^{97}+O(q^{100}) \) 16 * q + 882 * q^5 + 1846 * q^7 + 45756 * q^11 - 3370 * q^13 - 362180 * q^19 + 1311138 * q^23 + 963394 * q^25 + 2851290 * q^29 - 542438 * q^31 + 3343328 * q^37 - 9218592 * q^41 - 339512 * q^43 - 34980606 * q^47 - 2364654 * q^49 + 4584276 * q^55 + 93924216 * q^59 - 841954 * q^61 + 126568134 * q^65 - 29946644 * q^67 - 7547764 * q^73 - 9309294 * q^77 - 33813002 * q^79 + 114200226 * q^83 - 125696772 * q^85 - 268578316 * q^91 - 143949240 * q^95 - 89415484 * q^97

Introduction

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