LMFDB - Embedded newform 54.21.d.a.17.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [54,21,Mod(17,54)] 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("54.17"); S:= CuspForms(chi, 21); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(54, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 21, names="a")

Level:	$ N $	$=$	$ 54 = 2 \cdot 3^{3} $
Weight:	$ k $	$=$	$ 21 $
Character orbit:	$[\chi]$	$=$	54.d (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:	$136.897433155$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 18)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.6
Character	$\chi$	$=$	54.17
Dual form			54.21.d.a.35.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-627.069 + 362.039i) q^{2} +(262144. - 454047. i) q^{4} +(6.58251e6 + 3.80041e6i) q^{5} +(7.46524e7 + 1.29302e8i) q^{7} +3.79625e8i q^{8} -5.50358e9 q^{10} +(-3.07406e10 + 1.77481e10i) q^{11} +(-1.12062e11 + 1.94097e11i) q^{13} +(-9.36245e10 - 5.40541e10i) q^{14} +(-1.37439e11 - 2.38051e11i) q^{16} +2.48192e12i q^{17} -7.60316e12 q^{19} +(3.45113e12 - 1.99251e12i) q^{20} +(1.28510e13 - 2.22586e13i) q^{22} +(-5.93735e12 - 3.42793e12i) q^{23} +(-1.87975e13 - 3.25581e13i) q^{25} -1.62283e14i q^{26} +7.82787e13 q^{28} +(-6.25109e14 + 3.60907e14i) q^{29} +(4.26088e14 - 7.38006e14i) q^{31} +(1.72368e14 + 9.95164e13i) q^{32} +(-8.98551e14 - 1.55634e15i) q^{34} +1.13484e15i q^{35} +5.72383e15 q^{37} +(4.76771e15 - 2.75264e15i) q^{38} +(-1.44273e15 + 2.49888e15i) q^{40} +(-3.48457e15 - 2.01182e15i) q^{41} +(-1.52227e16 - 2.63664e16i) q^{43} +1.86102e16i q^{44} +4.96417e15 q^{46} +(1.80696e16 - 1.04325e16i) q^{47} +(2.87502e16 - 4.97968e16i) q^{49} +(2.35746e16 + 1.36108e16i) q^{50} +(5.87527e16 + 1.01763e17i) q^{52} +2.64537e17i q^{53} -2.69800e17 q^{55} +(-4.90862e16 + 2.83399e16i) q^{56} +(2.61325e17 - 4.52628e17i) q^{58} +(1.59453e17 + 9.20605e16i) q^{59} +(-1.11733e17 - 1.93528e17i) q^{61} +6.17041e17i q^{62} -1.44115e17 q^{64} +(-1.47530e18 + 8.51763e17i) q^{65} +(2.13397e17 - 3.69615e17i) q^{67} +(1.12691e18 + 6.50620e17i) q^{68} +(-4.10856e17 - 7.11623e17i) q^{70} -5.24061e17i q^{71} -4.66174e18 q^{73} +(-3.58924e18 + 2.07225e18i) q^{74} +(-1.99312e18 + 3.45219e18i) q^{76} +(-4.58972e18 - 2.64987e18i) q^{77} +(1.90733e18 + 3.30360e18i) q^{79} -2.08930e18i q^{80} +2.91343e18 q^{82} +(1.63293e19 - 9.42772e18i) q^{83} +(-9.43231e18 + 1.63372e19i) q^{85} +(1.90913e19 + 1.10224e19i) q^{86} +(-6.73762e18 - 1.16699e19i) q^{88} +3.96851e19i q^{89} -3.34628e19 q^{91} +(-3.11288e18 + 1.79722e18i) q^{92} +(-7.55392e18 + 1.30838e19i) q^{94} +(-5.00478e19 - 2.88951e19i) q^{95} +(5.68257e19 + 9.84250e19i) q^{97} +4.16347e19i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 10485760 q^{4} - 29763918 q^{5} + 133479866 q^{7} + 35793208728 q^{11} + 39827158550 q^{13} - 187564400640 q^{14} - 5497558138880 q^{16} - 10560819523540 q^{19} - 15604865040384 q^{20} + 10829007458304 q^{22}+ \cdots - 66\!\cdots\!16 q^{97}+O(q^{100}) $ 40 * q + 10485760 * q^4 - 29763918 * q^5 + 133479866 * q^7 + 35793208728 * q^11 + 39827158550 * q^13 - 187564400640 * q^14 - 5497558138880 * q^16 - 10560819523540 * q^19 - 15604865040384 * q^20 + 10829007458304 * q^22 + 95164852839678 * q^23 + 485893942617694 * q^25 + 139963783970816 * q^28 - 487337329131246 * q^29 - 386065992062842 * q^31 - 810410730184704 * q^34 + 7650497672534432 * q^37 + 27431157167935488 * q^38 + 76546903885431012 * q^41 - 10868849409851092 * q^43 + 13732137981788160 * q^46 - 220882065588142506 * q^47 - 201918836583922386 * q^49 - 84434006357065728 * q^50 - 20880901301862400 * q^52 - 689556443803109316 * q^55 - 98337764482744320 * q^56 + 289875600503808000 * q^58 + 4671324023815652220 * q^59 - 608513692992272866 * q^61 - 5764607523034234880 * q^64 - 4959300225343873626 * q^65 - 2581864509390888904 * q^67 + 5171455594224156672 * q^68 - 584784912675889152 * q^70 + 15022099327729072004 * q^73 - 7089371473773993984 * q^74 - 2768455473178869760 * q^76 + 30865724759591472834 * q^77 + 18532232803602736754 * q^79 - 35601230743051272192 * q^82 - 54829678294093455594 * q^83 + 43688870161052471388 * q^85 - 47393791396458614784 * q^86 - 5677518662299287552 * q^88 - 35182774173576758996 * q^91 + 49893790365609099264 * q^92 + 19892618446780047360 * q^94 - 332020921293200455200 * q^95 - 66463398176406835216 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−627.069	+	362.039i	−0.612372	+	0.353553i
$2$	−627.069	+	362.039i	−0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	262144.	−	454047.i	0.250000	−	0.433013i
$5$	6.58251e6	+	3.80041e6i	0.674049	+	0.389162i	0.797609	−	0.603175i	$-0.206098\pi$
$5$	6.58251e6	+	3.80041e6i	0.674049	+	0.389162i	−0.123560	+	0.992337i	$0.539431\pi$
$6$		0			0
$7$	7.46524e7	+	1.29302e8i	0.264279	+	0.457745i	0.967375	−	0.253350i	$-0.0815326\pi$
$7$	7.46524e7	+	1.29302e8i	0.264279	+	0.457745i	−0.703095	+	0.711096i	$0.748199\pi$
$8$			3.79625e8i			0.353553i
$9$		0			0
$10$	−5.50358e9			−0.550358
$11$	−3.07406e10	+	1.77481e10i	−1.18518	+	0.684266i	−0.957208	−	0.289401i	$-0.906544\pi$
$11$	−3.07406e10	+	1.77481e10i	−1.18518	+	0.684266i	−0.227975	+	0.973667i	$0.573210\pi$
$12$		0			0
$13$	−1.12062e11	+	1.94097e11i	−0.812877	+	1.40794i	0.0979657	+	0.995190i	$0.468766\pi$
$13$	−1.12062e11	+	1.94097e11i	−0.812877	+	1.40794i	−0.910842	+	0.412754i	$0.864567\pi$
$14$	−9.36245e10	−	5.40541e10i	−0.323675	−	0.186874i
$15$		0			0
$16$	−1.37439e11	−	2.38051e11i	−0.125000	−	0.216506i
$17$			2.48192e12i			1.23111i	0.788092	+	0.615557i	$0.211069\pi$
$17$			2.48192e12i			1.23111i	−0.788092	+	0.615557i	$0.788931\pi$
$18$		0			0
$19$	−7.60316e12			−1.24010			−0.620052	−	0.784561i	$-0.712888\pi$
$19$	−7.60316e12			−1.24010			−0.620052	+	0.784561i	$0.712888\pi$
$20$	3.45113e12	−	1.99251e12i	0.337024	−	0.194581i
$21$		0			0
$22$	1.28510e13	−	2.22586e13i	0.483849	−	0.838051i
$23$	−5.93735e12	−	3.42793e12i	−0.143322	−	0.0827472i	0.426624	−	0.904429i	$-0.359703\pi$
$23$	−5.93735e12	−	3.42793e12i	−0.143322	−	0.0827472i	−0.569946	+	0.821682i	$0.693036\pi$
$24$		0			0
$25$	−1.87975e13	−	3.25581e13i	−0.197106	−	0.341397i
$26$		−	1.62283e14i		−	1.14958i
$27$		0			0
$28$	7.82787e13			0.264279
$29$	−6.25109e14	+	3.60907e14i	−1.48585	+	0.857858i	−0.999870	−	0.0161097i	$-0.994872\pi$
$29$	−6.25109e14	+	3.60907e14i	−1.48585	+	0.857858i	−0.485984	+	0.873968i	$0.661539\pi$
$30$		0			0
$31$	4.26088e14	−	7.38006e14i	0.519855	−	0.900415i	−0.479879	−	0.877335i	$-0.659319\pi$
$31$	4.26088e14	−	7.38006e14i	0.519855	−	0.900415i	0.999734	−	0.0230802i	$-0.00734730\pi$
$32$	1.72368e14	+	9.95164e13i	0.153093	+	0.0883883i
$33$		0			0
$34$	−8.98551e14	−	1.55634e15i	−0.435265	−	0.753900i
$35$			1.13484e15i			0.411390i
$36$		0			0
$37$	5.72383e15			1.19033			0.595167	−	0.803602i	$-0.297086\pi$
$37$	5.72383e15			1.19033			0.595167	+	0.803602i	$0.297086\pi$
$38$	4.76771e15	−	2.75264e15i	0.759405	−	0.438443i
$39$		0			0
$40$	−1.44273e15	+	2.49888e15i	−0.137590	+	0.238312i
$41$	−3.48457e15	−	2.01182e15i	−0.259604	−	0.149882i	0.364550	−	0.931184i	$-0.381223\pi$
$41$	−3.48457e15	−	2.01182e15i	−0.259604	−	0.149882i	−0.624154	+	0.781301i	$0.714556\pi$
$42$		0			0
$43$	−1.52227e16	−	2.63664e16i	−0.704379	−	1.22002i	−0.966915	−	0.255098i	$-0.917892\pi$
$43$	−1.52227e16	−	2.63664e16i	−0.704379	−	1.22002i	0.262537	−	0.964922i	$-0.415441\pi$
$44$			1.86102e16i			0.684266i
$45$		0			0
$46$	4.96417e15			0.117022
$47$	1.80696e16	−	1.04325e16i	0.343534	−	0.198339i	−0.318300	−	0.947990i	$-0.603112\pi$
$47$	1.80696e16	−	1.04325e16i	0.343534	−	0.198339i	0.661834	+	0.749651i	$0.269779\pi$
$48$		0			0
$49$	2.87502e16	−	4.97968e16i	0.360313	−	0.624080i
$50$	2.35746e16	+	1.36108e16i	0.241404	+	0.139375i
$51$		0			0
$52$	5.87527e16	+	1.01763e17i	0.406438	+	0.703972i
$53$			2.64537e17i			1.51261i	0.654219	+	0.756305i	$0.272998\pi$
$53$			2.64537e17i			1.51261i	−0.654219	+	0.756305i	$0.727002\pi$
$54$		0			0
$55$	−2.69800e17			−1.06516
$56$	−4.90862e16	+	2.83399e16i	−0.161837	+	0.0934369i
$57$		0			0
$58$	2.61325e17	−	4.52628e17i	0.606597	−	1.05066i
$59$	1.59453e17	+	9.20605e16i	0.311971	+	0.180116i	0.647808	−	0.761804i	$-0.275686\pi$
$59$	1.59453e17	+	9.20605e16i	0.311971	+	0.180116i	−0.335837	+	0.941920i	$0.609019\pi$
$60$		0			0
$61$	−1.11733e17	−	1.93528e17i	−0.156633	−	0.271297i	0.777019	−	0.629477i	$-0.216731\pi$
$61$	−1.11733e17	−	1.93528e17i	−0.156633	−	0.271297i	−0.933653	+	0.358180i	$0.883397\pi$
$62$			6.17041e17i			0.735186i
$63$		0			0
$64$	−1.44115e17			−0.125000
$65$	−1.47530e18	+	8.51763e17i	−1.09584	+	0.632682i
$66$		0			0
$67$	2.13397e17	−	3.69615e17i	0.117069	−	0.202769i	−0.801536	−	0.597946i	$-0.795984\pi$
$67$	2.13397e17	−	3.69615e17i	0.117069	−	0.202769i	0.918605	+	0.395177i	$0.129317\pi$
$68$	1.12691e18	+	6.50620e17i	0.533088	+	0.307779i
$69$		0			0
$70$	−4.10856e17	−	7.11623e17i	−0.145448	−	0.251924i
$71$		−	5.24061e17i		−	0.160990i	−0.996755	−	0.0804950i	$-0.974350\pi$
$71$		−	5.24061e17i		−	0.160990i	0.996755	−	0.0804950i	$-0.0256501\pi$
$72$		0			0
$73$	−4.66174e18			−1.08472			−0.542362	−	0.840145i	$-0.682470\pi$
$73$	−4.66174e18			−1.08472			−0.542362	+	0.840145i	$0.682470\pi$
$74$	−3.58924e18	+	2.07225e18i	−0.728928	+	0.420847i
$75$		0			0
$76$	−1.99312e18	+	3.45219e18i	−0.310026	+	0.536981i
$77$	−4.58972e18	−	2.64987e18i	−0.626439	−	0.361675i
$78$		0			0
$79$	1.90733e18	+	3.30360e18i	0.201444	+	0.348912i	0.948994	−	0.315294i	$-0.102103\pi$
$79$	1.90733e18	+	3.30360e18i	0.201444	+	0.348912i	−0.747550	+	0.664206i	$0.768770\pi$
$80$		−	2.08930e18i		−	0.194581i
$81$		0			0
$82$	2.91343e18			0.211966
$83$	1.63293e19	−	9.42772e18i	1.05241	−	0.607611i	0.129089	−	0.991633i	$-0.458795\pi$
$83$	1.63293e19	−	9.42772e18i	1.05241	−	0.607611i	0.923324	+	0.384022i	$0.125461\pi$
$84$		0			0
$85$	−9.43231e18	+	1.63372e19i	−0.479103	+	0.829831i
$86$	1.90913e19	+	1.10224e19i	0.862684	+	0.498071i
$87$		0			0
$88$	−6.73762e18	−	1.16699e19i	−0.241924	−	0.419025i
$89$			3.96851e19i			1.27270i	0.771399	+	0.636352i	$0.219558\pi$
$89$			3.96851e19i			1.27270i	−0.771399	+	0.636352i	$0.780442\pi$
$90$		0			0
$91$	−3.34628e19			−0.859306
$92$	−3.11288e18	+	1.79722e18i	−0.0716612	+	0.0413736i
$93$		0			0
$94$	−7.55392e18	+	1.30838e19i	−0.140247	+	0.242915i
$95$	−5.00478e19	−	2.88951e19i	−0.835890	−	0.482601i
$96$		0			0
$97$	5.68257e19	+	9.84250e19i	0.770597	+	1.33471i	0.937236	+	0.348695i	$0.113375\pi$
$97$	5.68257e19	+	9.84250e19i	0.770597	+	1.33471i	−0.166639	+	0.986018i	$0.553292\pi$
$98$			4.16347e19i			0.509559i
$99$		0			0
$100$	−1.97106e19			−0.197106
$101$	6.10749e19	−	3.52616e19i	0.552903	−	0.319219i	−0.197389	−	0.980325i	$-0.563246\pi$
$101$	6.10749e19	−	3.52616e19i	0.552903	−	0.319219i	0.750292	+	0.661106i	$0.229913\pi$
$102$		0			0
$103$	3.14589e19	−	5.44884e19i	0.234084	−	0.405445i	−0.724922	−	0.688831i	$-0.758124\pi$
$103$	3.14589e19	−	5.44884e19i	0.234084	−	0.405445i	0.959006	+	0.283386i	$0.0914577\pi$
$104$	−7.36841e19	−	4.25415e19i	−0.497783	−	0.287395i
$105$		0			0
$106$	−9.57725e19	−	1.65883e20i	−0.534789	−	0.926281i
$107$		−	3.83535e19i		−	0.194970i	−0.995237	−	0.0974848i	$-0.968920\pi$
$107$		−	3.83535e19i		−	0.194970i	0.995237	−	0.0974848i	$-0.0310797\pi$
$108$		0			0
$109$	−2.15650e20			−0.910928			−0.455464	−	0.890254i	$-0.650527\pi$
$109$	−2.15650e20			−0.910928			−0.455464	+	0.890254i	$0.650527\pi$
$110$	1.69183e20	−	9.76781e19i	0.652275	−	0.376591i
$111$		0			0
$112$	2.05203e19	−	3.55422e19i	0.0660698	−	0.114436i
$113$	−6.06526e19	−	3.50178e19i	−0.178675	−	0.103158i	0.407995	−	0.912984i	$-0.366228\pi$
$113$	−6.06526e19	−	3.50178e19i	−0.178675	−	0.103158i	−0.586670	+	0.809826i	$0.699561\pi$
$114$		0			0
$115$	−2.60551e19	−	4.51287e19i	−0.0644042	−	0.111551i
$116$			3.78439e20i			0.857858i
$117$		0			0
$118$	−1.33318e20			−0.254723
$119$	−3.20916e20	+	1.85281e20i	−0.563537	+	0.325358i
$120$		0			0
$121$	2.93614e20	−	5.08555e20i	0.436439	−	0.755934i
$122$	1.40129e20	+	8.09035e19i	0.191836	+	0.110756i
$123$		0			0
$124$	−2.23393e20	−	3.86927e20i	−0.259927	−	0.450207i
$125$		−	1.01062e21i		−	1.08515i
$126$		0			0
$127$	1.83140e21			1.67782			0.838909	−	0.544271i	$-0.183194\pi$
$127$	1.83140e21			1.67782			0.838909	+	0.544271i	$0.183194\pi$
$128$	9.03702e19	−	5.21753e19i	0.0765466	−	0.0441942i
$129$		0			0
$130$	6.16743e20	−	1.06823e21i	0.447374	−	0.774874i
$131$	7.80204e20	+	4.50451e20i	0.524198	+	0.302646i	0.738651	−	0.674089i	$-0.235463\pi$
$131$	7.80204e20	+	4.50451e20i	0.524198	+	0.302646i	−0.214452	+	0.976734i	$0.568797\pi$
$132$		0			0
$133$	−5.67594e20	−	9.83101e20i	−0.327734	−	0.567652i
$134$			3.09032e20i			0.165560i
$135$		0			0
$136$	−9.42199e20			−0.435265
$137$	3.41822e21	−	1.97351e21i	1.46756	−	0.847293i	0.468215	−	0.883614i	$-0.344897\pi$
$137$	3.41822e21	−	1.97351e21i	1.46756	−	0.847293i	0.999340	+	0.0363210i	$0.0115639\pi$
$138$		0			0
$139$	−1.81808e20	+	3.14901e20i	−0.0675252	+	0.116957i	−0.897811	−	0.440380i	$-0.854844\pi$
$139$	−1.81808e20	+	3.14901e20i	−0.0675252	+	0.116957i	0.830286	+	0.557337i	$0.188177\pi$
$140$	5.15270e20	+	2.97491e20i	0.178137	+	0.102848i
$141$		0			0
$142$	1.89731e20	+	3.28623e20i	0.0569185	+	0.0985858i
$143$		−	7.95554e21i		−	2.22489i
$144$		0			0
$145$	−5.48638e21			−1.33538
$146$	2.92323e21	−	1.68773e21i	0.664255	−	0.383508i
$147$		0			0
$148$	1.50047e21	−	2.59888e21i	0.297584	−	0.515430i
$149$	−5.60568e21	−	3.23644e21i	−1.03936	−	0.600074i	−0.119707	−	0.992809i	$-0.538196\pi$
$149$	−5.60568e21	−	3.23644e21i	−1.03936	−	0.600074i	−0.919652	+	0.392735i	$0.871529\pi$
$150$		0			0
$151$	2.43706e20	+	4.22110e20i	0.0395454	+	0.0684946i	0.885121	−	0.465362i	$-0.154076\pi$
$151$	2.43706e20	+	4.22110e20i	0.0395454	+	0.0684946i	−0.845575	+	0.533856i	$0.820742\pi$
$152$		−	2.88635e21i		−	0.438443i
$153$		0			0
$154$	3.83743e21			0.511485
$155$	5.60945e21	−	3.23862e21i	0.700815	−	0.404616i
$156$		0			0
$157$	7.80176e21	−	1.35130e22i	0.857424	−	1.48510i	−0.0169529	−	0.999856i	$-0.505397\pi$
$157$	7.80176e21	−	1.35130e22i	0.857424	−	1.48510i	0.874377	−	0.485246i	$-0.161270\pi$
$158$	−2.39206e21	−	1.38106e21i	−0.246718	−	0.142443i
$159$		0			0
$160$	7.56407e20	+	1.31014e21i	0.0687948	+	0.119156i
$161$		−	1.02361e21i		−	0.0874735i
$162$		0			0
$163$	−1.64606e22			−1.24328			−0.621642	−	0.783301i	$-0.713534\pi$
$163$	−1.64606e22			−1.24328			−0.621642	+	0.783301i	$0.713534\pi$
$164$	−1.82692e21	+	1.05477e21i	−0.129802	+	0.0749412i
$165$		0			0
$166$	−6.82640e21	+	1.18237e22i	−0.429646	+	0.744169i
$167$	1.96107e22	+	1.13222e22i	1.16233	+	0.671069i	0.951860	−	0.306532i	$-0.0991688\pi$
$167$	1.96107e22	+	1.13222e22i	1.16233	+	0.671069i	0.210465	+	0.977601i	$0.432502\pi$
$168$		0			0
$169$	−1.56133e22	−	2.70430e22i	−0.821537	−	1.42294i
$170$		−	1.36595e22i		−	0.677554i
$171$		0			0
$172$	−1.59621e22			−0.704379
$173$	1.12442e19	−	6.49185e18i	0.000468239	−	0.000270338i	−0.499766	−	0.866161i	$-0.666581\pi$
$173$	1.12442e19	−	6.49185e18i	0.000468239	−	0.000270338i	0.500234	+	0.865890i	$0.333247\pi$
$174$		0			0
$175$	2.80655e21	−	4.86109e21i	0.104182	−	0.180448i
$176$	8.44991e21	+	4.87856e21i	0.296296	+	0.171066i
$177$		0			0
$178$	−1.43675e22	−	2.48853e22i	−0.449969	−	0.779369i
$179$			7.50426e21i			0.222217i	0.993808	+	0.111109i	$0.0354402\pi$
$179$			7.50426e21i			0.222217i	−0.993808	+	0.111109i	$0.964560\pi$
$180$		0			0
$181$	1.29707e22			0.343698			0.171849	−	0.985123i	$-0.445026\pi$
$181$	1.29707e22			0.343698			0.171849	+	0.985123i	$0.445026\pi$
$182$	2.09835e22	−	1.21148e22i	0.526216	−	0.303811i
$183$		0			0
$184$	1.30133e21	−	2.25397e21i	0.0292556	−	0.0506721i
$185$	3.76771e22	+	2.17529e22i	0.802344	+	0.463233i
$186$		0			0
$187$	−4.40493e22	−	7.62956e22i	−0.842409	−	1.45910i
$188$		−	1.09392e22i		−	0.198339i
$189$		0			0
$190$	4.18446e22			0.682501
$191$	5.31082e22	−	3.06621e22i	0.821917	−	0.474534i	−0.0291598	−	0.999575i	$-0.509283\pi$
$191$	5.31082e22	−	3.06621e22i	0.821917	−	0.474534i	0.851077	+	0.525041i	$0.175950\pi$
$192$		0			0
$193$	3.02115e22	−	5.23278e22i	0.421307	−	0.729725i	−0.574760	−	0.818322i	$-0.694905\pi$
$193$	3.02115e22	−	5.23278e22i	0.421307	−	0.729725i	0.996068	+	0.0885963i	$0.0282381\pi$
$194$	−7.12673e22	−	4.11462e22i	−0.943785	−	0.544894i
$195$		0			0
$196$	−1.50734e22	−	2.61078e22i	−0.180156	−	0.312040i
$197$			1.14453e22i			0.130007i	0.997885	+	0.0650033i	$0.0207058\pi$
$197$			1.14453e22i			0.130007i	−0.997885	+	0.0650033i	$0.979294\pi$
$198$		0			0
$199$	−1.31665e23			−1.35189			−0.675944	−	0.736953i	$-0.736264\pi$
$199$	−1.31665e23			−1.35189			−0.675944	+	0.736953i	$0.736264\pi$
$200$	1.23599e22	−	7.13598e21i	0.120702	−	0.0696873i
$201$		0			0
$202$	−2.55321e22	+	4.42230e22i	−0.225722	+	0.390962i
$203$	−9.33318e22	−	5.38852e22i	−0.785361	−	0.453428i
$204$		0			0
$205$	−1.52915e22	−	2.64856e22i	−0.116657	−	0.202056i
$206$			4.55573e22i			0.331044i
$207$		0			0
$208$	6.16067e22			0.406438
$209$	2.33726e23	−	1.34941e23i	1.46975	−	0.848560i
$210$		0			0
$211$	9.04919e22	−	1.56737e23i	0.517351	−	0.896078i	−0.482446	−	0.875926i	$-0.660252\pi$
$211$	9.04919e22	−	1.56737e23i	0.517351	−	0.896078i	0.999797	−	0.0201520i	$-0.00641503\pi$
$212$	1.20112e23	+	6.93467e22i	0.654980	+	0.378153i
$213$		0			0
$214$	1.38854e22	+	2.40503e22i	0.0689322	+	0.119394i
$215$		−	2.31410e23i		−	1.09647i
$216$		0			0
$217$	1.27234e23			0.549548
$218$	1.35227e23	−	7.80736e22i	0.557827	−	0.322062i
$219$		0			0
$220$	−7.07265e22	+	1.22502e23i	−0.266290	+	0.461228i
$221$	−4.81733e23	−	2.78129e23i	−1.73334	−	1.00074i
$222$		0			0
$223$	1.43694e23	+	2.48886e23i	0.472489	+	0.818375i	0.999504	−	0.0314811i	$-0.0100224\pi$
$223$	1.43694e23	+	2.48886e23i	0.472489	+	0.818375i	−0.527016	+	0.849856i	$0.676689\pi$
$224$			2.97166e22i			0.0934369i
$225$		0			0
$226$	5.07112e22			0.145888
$227$	−1.30573e23	+	7.53864e22i	−0.359414	+	0.207508i	−0.668824	−	0.743421i	$-0.733202\pi$
$227$	−1.30573e23	+	7.53864e22i	−0.359414	+	0.207508i	0.309410	+	0.950929i	$0.399869\pi$
$228$		0			0
$229$	−3.18946e23	+	5.52431e23i	−0.804197	+	1.39291i	0.112635	+	0.993636i	$0.464071\pi$
$229$	−3.18946e23	+	5.52431e23i	−0.804197	+	1.39291i	−0.916832	+	0.399274i	$0.869262\pi$
$230$	3.26767e22	+	1.88659e22i	0.0788787	+	0.0455406i
$231$		0			0
$232$	−1.37009e23	−	2.37307e23i	−0.303299	−	0.525329i
$233$			6.25874e22i			0.132717i	0.997796	+	0.0663587i	$0.0211382\pi$
$233$			6.25874e22i			0.132717i	−0.997796	+	0.0663587i	$0.978862\pi$
$234$		0			0
$235$	1.58591e23			0.308745
$236$	8.35995e22	−	4.82662e22i	0.155985	−	0.0900582i
$237$		0			0
$238$	1.34158e23	−	2.32368e23i	0.230063	−	0.398481i
$239$	2.82126e23	+	1.62886e23i	0.463943	+	0.267857i	0.713701	−	0.700451i	$-0.247018\pi$
$239$	2.82126e23	+	1.62886e23i	0.463943	+	0.267857i	−0.249758	+	0.968308i	$0.580351\pi$
$240$		0			0
$241$	7.38294e22	+	1.27876e23i	0.111701	+	0.193473i	0.916456	−	0.400135i	$-0.131037\pi$
$241$	7.38294e22	+	1.27876e23i	0.111701	+	0.193473i	−0.804755	+	0.593607i	$0.797703\pi$
$242$			4.25199e23i			0.617217i
$243$		0			0
$244$	−1.17161e23			−0.156633
$245$	3.78496e23	−	2.18525e23i	0.485737	−	0.280440i
$246$		0			0
$247$	8.52025e23	−	1.47575e24i	1.00805	−	1.74600i
$248$	2.80165e23	+	1.61754e23i	0.318345	+	0.183796i
$249$		0			0
$250$	3.65885e23	+	6.33731e23i	0.383658	+	0.664515i
$251$			1.48369e24i			1.49488i	0.664331	+	0.747439i	$0.268717\pi$
$251$			1.48369e24i			1.49488i	−0.664331	+	0.747439i	$0.731283\pi$
$252$		0			0
$253$	2.43357e23			0.226484
$254$	−1.14841e24	+	6.63036e23i	−1.02745	+	0.593199i
$255$		0			0
$256$	−3.77789e22	+	6.54350e22i	−0.0312500	+	0.0541266i
$257$	−2.06910e24	−	1.19460e24i	−1.64608	−	0.950363i	−0.978610	−	0.205723i	$-0.934045\pi$
$257$	−2.06910e24	−	1.19460e24i	−1.64608	−	0.950363i	−0.667467	−	0.744640i	$-0.732621\pi$
$258$		0			0
$259$	4.27297e23	+	7.40101e23i	0.314581	+	0.544870i
$260$			8.93139e23i			0.632682i
$261$		0			0
$262$	−6.52323e23			−0.428006
$263$	−1.37083e24	+	7.91449e23i	−0.865816	+	0.499879i	−0.865956	−	0.500121i	$-0.833289\pi$
$263$	−1.37083e24	+	7.91449e23i	−0.865816	+	0.499879i	0.000139273		1.00000i	$0.499956\pi$
$264$		0			0
$265$	−1.00535e24	+	1.74131e24i	−0.588651	+	1.01957i
$266$	7.11841e23	+	4.10982e23i	0.401390	+	0.231743i
$267$		0			0
$268$	−1.11882e23	−	1.93785e23i	−0.0585343	−	0.101384i
$269$			2.82543e24i			1.42417i	0.702093	+	0.712085i	$0.252249\pi$
$269$			2.82543e24i			1.42417i	−0.702093	+	0.712085i	$0.747751\pi$
$270$		0			0
$271$	9.79278e23			0.458367			0.229183	−	0.973383i	$-0.426394\pi$
$271$	9.79278e23			0.458367			0.229183	+	0.973383i	$0.426394\pi$
$272$	5.90824e23	−	3.41112e23i	0.266544	−	0.153889i
$273$		0			0
$274$	−1.42897e24	+	2.47506e24i	−0.599127	+	1.03772i
$275$	1.15569e24	+	6.67238e23i	0.467212	+	0.269745i
$276$		0			0
$277$	1.42582e23	+	2.46958e23i	0.0536124	+	0.0928595i	0.891586	−	0.452851i	$-0.149593\pi$
$277$	1.42582e23	+	2.46958e23i	0.0536124	+	0.0928595i	−0.837974	+	0.545711i	$0.816260\pi$
$278$		−	2.63287e23i		−	0.0954950i
$279$		0			0
$280$	−4.30813e23			−0.145448
$281$	−3.45341e24	+	1.99383e24i	−1.12508	+	0.649568i	−0.942694	−	0.333658i	$-0.891717\pi$
$281$	−3.45341e24	+	1.99383e24i	−1.12508	+	0.649568i	−0.182391	+	0.983226i	$0.558384\pi$
$282$		0			0
$283$	−1.81450e24	+	3.14281e24i	−0.550672	+	0.953792i	0.447554	+	0.894257i	$0.352295\pi$
$283$	−1.81450e24	+	3.14281e24i	−0.550672	+	0.953792i	−0.998226	+	0.0595353i	$0.981038\pi$
$284$	−2.37948e23	−	1.37380e23i	−0.0697107	−	0.0402475i
$285$		0			0
$286$	2.88021e24	+	4.98868e24i	0.786619	+	1.36246i
$287$		−	6.00749e23i		−	0.158443i
$288$		0			0
$289$	−2.09569e24			−0.515642
$290$	3.44034e24	−	1.98628e24i	0.817752	−	0.472129i
$291$		0			0
$292$	−1.22205e24	+	2.11665e24i	−0.271181	+	0.469699i
$293$	−3.58144e24	−	2.06774e24i	−0.768036	−	0.443426i	0.0641378	−	0.997941i	$-0.479570\pi$
$293$	−3.58144e24	−	2.06774e24i	−0.768036	−	0.443426i	−0.832173	+	0.554516i	$0.812904\pi$
$294$		0			0
$295$	6.99735e23	+	1.21198e24i	0.140189	+	0.242814i
$296$			2.17291e24i			0.420847i
$297$		0			0
$298$	4.68686e24			0.848633
$299$	1.33070e24	−	7.68281e23i	0.233007	−	0.134527i
$300$		0			0
$301$	2.27282e24	−	3.93663e24i	0.372306	−	0.644852i
$302$	−3.05641e23	−	1.76462e23i	−0.0484330	−	0.0279628i
$303$		0			0
$304$	1.04497e24	+	1.80994e24i	0.155013	+	0.268490i
$305$		−	1.69853e24i		−	0.243823i
$306$		0			0
$307$	8.10863e23			0.109034			0.0545172	−	0.998513i	$-0.482638\pi$
$307$	8.10863e23			0.109034			0.0545172	+	0.998513i	$0.482638\pi$
$308$	−2.40633e24	+	1.38930e24i	−0.313219	+	0.180837i
$309$		0			0
$310$	−2.34501e24	+	4.06168e24i	−0.286106	+	0.495551i
$311$	−4.54701e24	−	2.62521e24i	−0.537182	−	0.310142i	0.206754	−	0.978393i	$-0.433710\pi$
$311$	−4.54701e24	−	2.62521e24i	−0.537182	−	0.310142i	−0.743936	+	0.668251i	$0.767043\pi$
$312$		0			0
$313$	−6.63668e24	−	1.14951e25i	−0.735373	−	1.27370i	−0.954560	−	0.298020i	$-0.903674\pi$
$313$	−6.63668e24	−	1.14951e25i	−0.735373	−	1.27370i	0.219187	−	0.975683i	$-0.429660\pi$
$314$			1.12982e25i			1.21258i
$315$		0			0
$316$	1.99998e24			0.201444
$317$	3.58125e24	−	2.06763e24i	0.349496	−	0.201781i	−0.314968	−	0.949102i	$-0.601994\pi$
$317$	3.58125e24	−	2.06763e24i	0.349496	−	0.201781i	0.664463	+	0.747321i	$0.268660\pi$
$318$		0			0
$319$	1.28108e25	−	2.21890e25i	1.17401	−	2.03344i
$320$	−9.48639e23	−	5.47697e23i	−0.0842561	−	0.0486453i
$321$		0			0
$322$	3.70587e23	+	6.41876e23i	0.0309266	+	0.0535664i
$323$		−	1.88704e25i		−	1.52671i
$324$		0			0
$325$	8.42592e24			0.640890
$326$	1.03220e25	−	5.95939e24i	0.761353	−	0.439568i
$327$		0			0
$328$	7.63737e23	−	1.32283e24i	0.0529914	−	0.0917838i
$329$	2.69788e24	+	1.55762e24i	0.181578	+	0.104834i
$330$		0			0
$331$	−7.88493e24	−	1.36571e25i	−0.499480	−	0.865125i	0.500520	−	0.865725i	$-0.333142\pi$
$331$	−7.88493e24	−	1.36571e25i	−0.499480	−	0.865125i	−1.00000		0.000600484i	$0.999809\pi$
$332$		−	9.88568e24i		−	0.607611i
$333$		0			0
$334$	−1.63963e25			−0.949035
$335$	2.80938e24	−	1.62199e24i	0.157820	−	0.0911174i
$336$		0			0
$337$	−9.06706e24	+	1.57046e25i	−0.479918	+	0.831243i	−0.999735	−	0.0230352i	$-0.992667\pi$
$337$	−9.06706e24	+	1.57046e25i	−0.479918	+	0.831243i	0.519816	+	0.854278i	$0.326000\pi$
$338$	1.95812e25	+	1.13052e25i	1.00617	+	0.580915i
$339$		0			0
$340$	4.94525e24	+	8.56542e24i	0.239552	+	0.414915i
$341$			3.02490e25i			1.42287i
$342$		0			0
$343$	2.04984e25			0.909452
$344$	1.00094e25	−	5.77891e24i	0.431342	−	0.249035i
$345$		0			0
$346$	−4.70060e21	+	8.14168e21i	−0.000191158	+	0.000331095i
$347$	−3.70313e25	−	2.13800e25i	−1.46310	−	0.844722i	−0.463947	−	0.885863i	$-0.653567\pi$
$347$	−3.70313e25	−	2.13800e25i	−1.46310	−	0.844722i	−0.999153	+	0.0411410i	$0.986901\pi$
$348$		0			0
$349$	−2.08032e25	−	3.60322e25i	−0.776026	−	1.34412i	−0.934216	−	0.356708i	$-0.883899\pi$
$349$	−2.08032e25	−	3.60322e25i	−0.776026	−	1.34412i	0.158190	−	0.987409i	$-0.449434\pi$
$350$			4.06432e24i			0.147335i
$351$		0			0
$352$	−7.06490e24			−0.241924
$353$	3.51532e25	−	2.02957e25i	1.17009	−	0.675550i	0.216387	−	0.976308i	$-0.430573\pi$
$353$	3.51532e25	−	2.02957e25i	1.17009	−	0.675550i	0.953701	+	0.300757i	$0.0972394\pi$
$354$		0			0
$355$	1.99165e24	−	3.44964e24i	0.0626512	−	0.108515i
$356$	1.80189e25	+	1.04032e25i	0.551097	+	0.318176i
$357$		0			0
$358$	−2.71683e24	−	4.70569e24i	−0.0785657	−	0.136080i
$359$		−	4.95875e25i		−	1.39453i	−0.716813	−	0.697265i	$-0.754400\pi$
$359$		−	4.95875e25i		−	1.39453i	0.716813	−	0.697265i	$-0.245600\pi$
$360$		0			0
$361$	2.02180e25			0.537857
$362$	−8.13351e24	+	4.69588e24i	−0.210471	+	0.121515i
$363$		0			0
$364$	−8.77207e24	+	1.51937e25i	−0.214827	+	0.372091i
$365$	−3.06859e25	−	1.77165e25i	−0.731157	−	0.422133i
$366$		0			0
$367$	−3.21235e25	−	5.56395e25i	−0.724706	−	1.25523i	−0.959095	−	0.283084i	$-0.908642\pi$
$367$	−3.21235e25	−	5.56395e25i	−0.724706	−	1.25523i	0.234389	−	0.972143i	$-0.424691\pi$
$368$			1.88452e24i			0.0413736i
$369$		0			0
$370$	−3.15016e25			−0.655111
$371$	−3.42051e25	+	1.97483e25i	−0.692391	+	0.399752i
$372$		0			0
$373$	−2.95448e23	+	5.11730e23i	−0.00566751	+	0.00981642i	−0.868845	−	0.495084i	$-0.835137\pi$
$373$	−2.95448e23	+	5.11730e23i	−0.00566751	+	0.00981642i	0.863178	+	0.504900i	$0.168471\pi$
$374$	5.52439e25	+	3.18951e25i	1.03174	+	0.595673i
$375$		0			0
$376$	3.96043e24	+	6.85967e24i	0.0701236	+	0.121458i
$377$		−	1.61776e26i		−	2.78933i
$378$		0			0
$379$	−2.73780e25			−0.447724			−0.223862	−	0.974621i	$-0.571866\pi$
$379$	−2.73780e25			−0.447724			−0.223862	+	0.974621i	$0.571866\pi$
$380$	−2.62395e25	+	1.51494e25i	−0.417945	+	0.241301i
$381$		0			0
$382$	−2.22017e25	+	3.84545e25i	−0.335546	+	0.581183i
$383$	8.05273e25	+	4.64925e25i	1.18565	+	0.684534i	0.957314	−	0.289049i	$-0.0933391\pi$
$383$	8.05273e25	+	4.64925e25i	1.18565	+	0.684534i	0.228333	+	0.973583i	$0.426672\pi$
$384$		0			0
$385$	−2.01412e25	−	3.48856e25i	−0.281500	−	0.487573i
$386$			4.37509e25i			0.595818i
$387$		0			0
$388$	5.95860e25			0.770597
$389$	−1.85413e25	+	1.07048e25i	−0.233692	+	0.134922i	−0.612274	−	0.790645i	$-0.709745\pi$
$389$	−1.85413e25	+	1.07048e25i	−0.233692	+	0.134922i	0.378582	+	0.925568i	$0.376412\pi$
$390$		0			0
$391$	8.50784e24	−	1.47360e25i	0.101871	−	0.176446i
$392$	1.89041e25	+	1.09143e25i	0.220646	+	0.127390i
$393$		0			0
$394$	−4.14364e24	−	7.17700e24i	−0.0459643	−	0.0796124i
$395$			2.89946e25i			0.313578i
$396$		0			0
$397$	−1.11602e26			−1.14754			−0.573768	−	0.819018i	$-0.694519\pi$
$397$	−1.11602e26			−1.14754			−0.573768	+	0.819018i	$0.694519\pi$
$398$	8.25633e25	−	4.76679e25i	0.827859	−	0.477964i
$399$		0			0
$400$	−5.16700e24	+	8.94951e24i	−0.0492764	+	0.0853492i
$401$	4.79054e25	+	2.76582e25i	0.445596	+	0.257265i	0.705968	−	0.708243i	$-0.250512\pi$
$401$	4.79054e25	+	2.76582e25i	0.445596	+	0.257265i	−0.260373	+	0.965508i	$0.583845\pi$
$402$		0			0
$403$	9.54965e25	+	1.65405e26i	0.845156	+	1.46385i
$404$		−	3.69745e25i		−	0.319219i
$405$		0			0
$406$	7.80340e25			0.641245
$407$	−1.75954e26	+	1.01587e26i	−1.41076	+	0.814505i
$408$		0			0
$409$	4.79100e25	−	8.29825e25i	0.365757	−	0.633510i	−0.623140	−	0.782110i	$-0.714143\pi$
$409$	4.79100e25	−	8.29825e25i	0.365757	−	0.633510i	0.988897	+	0.148600i	$0.0474767\pi$
$410$	1.91776e25	+	1.10722e25i	0.142875	+	0.0824890i
$411$		0			0
$412$	−1.64935e25	−	2.85676e25i	−0.117042	−	0.202722i
$413$			2.74901e25i			0.190404i
$414$		0			0
$415$	1.43317e26			0.945837
$416$	−3.86317e25	+	2.23040e25i	−0.248892	+	0.143698i
$417$		0			0
$418$	−9.77081e25	+	1.69235e26i	−0.600023	+	1.03927i
$419$	−1.42182e26	−	8.20890e25i	−0.852521	−	0.492203i	0.00897958	−	0.999960i	$-0.497142\pi$
$419$	−1.42182e26	−	8.20890e25i	−0.852521	−	0.492203i	−0.861501	+	0.507756i	$0.830475\pi$
$420$		0			0
$421$	−1.67320e26	−	2.89806e26i	−0.956590	−	1.65686i	−0.730687	−	0.682712i	$-0.760800\pi$
$421$	−1.67320e26	−	2.89806e26i	−0.956590	−	1.65686i	−0.225902	−	0.974150i	$-0.572533\pi$
$422$			1.31046e26i			0.731644i
$423$		0			0
$424$	−1.00425e26			−0.534789
$425$	8.08067e25	−	4.66538e25i	0.420299	−	0.242659i
$426$		0			0
$427$	1.66823e25	−	2.88946e25i	0.0827899	−	0.143396i
$428$	−1.74143e25	−	1.00541e25i	−0.0844243	−	0.0487424i
$429$		0			0
$430$	8.37792e25	+	1.45110e26i	0.387661	+	0.671448i
$431$			1.33586e26i			0.603933i	0.953318	+	0.301967i	$0.0976431\pi$
$431$			1.33586e26i			0.603933i	−0.953318	+	0.301967i	$0.902357\pi$
$432$		0			0
$433$	3.10651e26			1.34089			0.670446	−	0.741958i	$-0.266103\pi$
$433$	3.10651e26			1.34089			0.670446	+	0.741958i	$0.266103\pi$
$434$	−7.97845e25	+	4.60636e25i	−0.336528	+	0.194294i
$435$		0			0
$436$	−5.65313e25	+	9.79151e25i	−0.227732	+	0.394443i
$437$	4.51426e25	+	2.60631e25i	0.177735	+	0.102615i
$438$		0			0
$439$	−5.58564e25	−	9.67461e25i	−0.210101	−	0.363905i	0.741645	−	0.670793i	$-0.234046\pi$
$439$	−5.58564e25	−	9.67461e25i	−0.210101	−	0.363905i	−0.951746	+	0.306887i	$0.900713\pi$
$440$		−	1.02423e26i		−	0.376591i
$441$		0			0
$442$	4.02773e26			1.41527
$443$	−2.50501e26	+	1.44627e26i	−0.860542	+	0.496834i	−0.864194	−	0.503159i	$-0.832171\pi$
$443$	−2.50501e26	+	1.44627e26i	−0.860542	+	0.496834i	0.00365183	+	0.999993i	$0.498838\pi$
$444$		0			0
$445$	−1.50820e26	+	2.61228e26i	−0.495288	+	0.857865i
$446$	−1.80213e26	−	1.04046e26i	−0.578678	−	0.334100i
$447$		0			0
$448$	−1.07585e25	−	1.86343e25i	−0.0330349	−	0.0572182i
$449$			3.29826e26i			0.990426i	0.868772	+	0.495213i	$0.164910\pi$
$449$			3.29826e26i			0.990426i	−0.868772	+	0.495213i	$0.835090\pi$
$450$		0			0
$451$	1.42824e26			0.410237
$452$	−3.17994e25	+	1.83594e25i	−0.0893377	+	0.0515791i
$453$		0			0
$454$	5.45856e25	−	9.45450e25i	0.146730	−	0.254144i
$455$	−2.20269e26	−	1.27172e26i	−0.579214	−	0.334410i
$456$		0			0
$457$	3.15710e26	+	5.46825e26i	0.794559	+	1.37622i	0.923119	+	0.384515i	$0.125631\pi$
$457$	3.15710e26	+	5.46825e26i	0.794559	+	1.37622i	−0.128560	+	0.991702i	$0.541035\pi$
$458$		−	4.61883e26i		−	1.13731i
$459$		0			0
$460$	−2.73207e25			−0.0644042
$461$	1.34579e26	−	7.76995e25i	0.310434	−	0.179229i	−0.336687	−	0.941617i	$-0.609306\pi$
$461$	1.34579e26	−	7.76995e25i	0.310434	−	0.179229i	0.647121	+	0.762388i	$0.275973\pi$
$462$		0			0
$463$	−1.94143e26	+	3.36266e26i	−0.428857	+	0.742803i	−0.996772	−	0.0802848i	$-0.974417\pi$
$463$	−1.94143e26	+	3.36266e26i	−0.428857	+	0.742803i	0.567915	+	0.823087i	$0.307750\pi$
$464$	1.71829e26	+	9.92054e25i	0.371463	+	0.214465i
$465$		0			0
$466$	−2.26591e25	−	3.92466e25i	−0.0469227	−	0.0812725i
$467$		−	4.39240e26i		−	0.890293i	−0.895458	−	0.445147i	$-0.853152\pi$
$467$		−	4.39240e26i		−	0.890293i	0.895458	−	0.445147i	$-0.146848\pi$
$468$		0			0
$469$	6.37224e25			0.123755
$470$	−9.94475e25	+	5.74160e25i	−0.189067	+	0.109158i
$471$		0			0
$472$	−3.49485e25	+	6.05325e25i	−0.0636807	+	0.110298i
$473$	9.35907e26	+	5.40346e26i	1.66963	+	0.963964i
$474$		0			0
$475$	1.42920e26	+	2.47545e26i	0.244431	+	0.423367i
$476$			1.94281e26i			0.325358i
$477$		0			0
$478$	−2.35883e26			−0.378807
$479$	−1.71483e26	+	9.90056e25i	−0.269690	+	0.155706i	−0.628747	−	0.777610i	$-0.716432\pi$
$479$	−1.71483e26	+	9.90056e25i	−0.269690	+	0.155706i	0.359057	+	0.933316i	$0.383098\pi$
$480$		0			0
$481$	−6.41423e26	+	1.11098e27i	−0.967596	+	1.67592i
$482$	−9.25923e25	−	5.34582e25i	−0.136806	−	0.0789849i
$483$		0			0
$484$	−1.53938e26	−	2.66629e26i	−0.218219	−	0.377967i
$485$			8.63844e26i			1.19955i
$486$		0			0
$487$	1.08075e27			1.44025			0.720123	−	0.693847i	$-0.244086\pi$
$487$	1.08075e27			1.44025			0.720123	+	0.693847i	$0.244086\pi$
$488$	7.34679e25	−	4.24167e25i	0.0959179	−	0.0553782i
$489$		0			0
$490$	−1.58229e26	+	2.74061e26i	−0.198301	+	0.343468i
$491$	−1.14696e27	−	6.62200e26i	−1.40843	−	0.813157i	−0.413193	−	0.910644i	$-0.635586\pi$
$491$	−1.14696e27	−	6.62200e26i	−1.40843	−	0.813157i	−0.995237	+	0.0974864i	$0.968920\pi$
$492$		0			0
$493$	−8.95742e26	−	1.55147e27i	−1.05612	−	1.82926i
$494$			1.23386e27i			1.42560i
$495$		0			0
$496$	−2.34244e26			−0.259927
$497$	6.77621e25	−	3.91224e25i	0.0736924	−	0.0425463i
$498$		0			0
$499$	−6.50855e26	+	1.12731e27i	−0.679953	+	1.17771i	0.295041	+	0.955484i	$0.404667\pi$
$499$	−6.50855e26	+	1.12731e27i	−0.679953	+	1.17771i	−0.974995	+	0.222229i	$0.928667\pi$
$500$	−4.58870e26	−	2.64929e26i	−0.469883	−	0.271287i
$501$		0			0
$502$	−5.37153e26	−	9.30376e26i	−0.528519	−	0.915421i
$503$			1.23825e26i			0.119434i	0.998215	+	0.0597170i	$0.0190198\pi$
$503$			1.23825e26i			0.119434i	−0.998215	+	0.0597170i	$0.980980\pi$
$504$		0			0
$505$	5.36035e26			0.496912
$506$	−1.52602e26	+	8.81045e25i	−0.138693	+	0.0800743i
$507$		0			0
$508$	4.80089e26	−	8.31539e26i	0.419455	−	0.726517i
$509$	3.75697e26	+	2.16909e26i	0.321855	+	0.185823i	0.652219	−	0.758030i	$-0.273838\pi$
$509$	3.75697e26	+	2.16909e26i	0.321855	+	0.185823i	−0.330364	+	0.943854i	$0.607172\pi$
$510$		0			0
$511$	−3.48010e26	−	6.02771e26i	−0.286670	−	0.496527i
$512$		−	5.47097e25i		−	0.0441942i
$513$		0			0
$514$	1.72996e27			1.34402
$515$	4.14156e26	−	2.39113e26i	0.315567	−	0.182193i
$516$		0			0
$517$	−3.70313e26	+	6.41401e26i	−0.271434	+	0.470137i
$518$	−5.35890e26	−	3.09396e26i	−0.385281	−	0.222442i
$519$		0			0
$520$	−3.23351e26	−	5.60060e26i	−0.223687	−	0.387437i
$521$		−	1.03233e27i		−	0.700556i	−0.936646	−	0.350278i	$-0.886087\pi$
$521$		−	1.03233e27i		−	0.700556i	0.936646	−	0.350278i	$-0.113913\pi$
$522$		0			0
$523$	2.32816e26			0.152053			0.0760267	−	0.997106i	$-0.475777\pi$
$523$	2.32816e26			0.152053			0.0760267	+	0.997106i	$0.475777\pi$
$524$	4.09052e26	−	2.36166e26i	0.262099	−	0.151323i
$525$		0			0
$526$	5.73070e26	−	9.92586e26i	0.353468	−	0.612225i
$527$	1.83167e27	+	1.05752e27i	1.10851	+	0.640001i
$528$		0			0
$529$	−8.34577e26	−	1.44553e27i	−0.486306	−	0.842306i
$530$		−	1.45590e27i		−	0.832478i
$531$		0			0
$532$	−5.95165e26			−0.327734
$533$	7.80976e26	−	4.50897e26i	0.422052	−	0.243672i
$534$		0			0
$535$	1.45759e26	−	2.52462e26i	0.0758748	−	0.131419i
$536$	1.40315e26	+	8.10109e25i	0.0716896	+	0.0413900i
$537$		0			0
$538$	−1.02291e27	−	1.77174e27i	−0.503520	−	0.872122i
$539$			2.04104e27i			0.986199i
$540$		0			0
$541$	−2.89168e27			−1.34641			−0.673206	−	0.739455i	$-0.735083\pi$
$541$	−2.89168e27			−1.34641			−0.673206	+	0.739455i	$0.735083\pi$
$542$	−6.14075e26	+	3.54537e26i	−0.280691	+	0.162057i
$543$		0			0
$544$	−2.46992e26	+	4.27802e26i	−0.108816	+	0.188475i
$545$	−1.41952e27	−	8.19558e26i	−0.614010	−	0.354499i
$546$		0			0
$547$	5.87270e26	+	1.01718e27i	0.244887	+	0.424156i	0.962100	−	0.272698i	$-0.0879160\pi$
$547$	5.87270e26	+	1.01718e27i	0.244887	+	0.424156i	−0.717213	+	0.696854i	$0.754583\pi$
$548$		−	2.06938e27i		−	0.847293i
$549$		0			0
$550$	−9.66263e26			−0.381477
$551$	4.75281e27	−	2.74403e27i	1.84261	−	1.06383i
$552$		0			0
$553$	−2.84774e26	+	4.93243e26i	−0.106475	+	0.184421i
$554$	−1.78817e26	−	1.03240e26i	−0.0656615	−	0.0379097i
$555$		0			0
$556$	9.53199e25	+	1.65099e26i	0.0337626	+	0.0584785i
$557$		−	2.65590e27i		−	0.923975i	−0.886887	−	0.461987i	$-0.847137\pi$
$557$		−	2.65590e27i		−	0.923975i	0.886887	−	0.461987i	$-0.152863\pi$
$558$		0			0
$559$	6.82353e27			2.29029
$560$	2.70150e26	−	1.55971e26i	0.0890686	−	0.0514238i
$561$		0			0
$562$	1.44369e27	−	2.50054e27i	0.459314	−	0.795555i
$563$	9.29295e26	+	5.36529e26i	0.290449	+	0.167691i	0.638144	−	0.769917i	$-0.279702\pi$
$563$	9.29295e26	+	5.36529e26i	0.290449	+	0.167691i	−0.347695	+	0.937608i	$0.613036\pi$
$564$		0			0
$565$	−2.66164e26	−	4.61010e26i	−0.0802906	−	0.139067i
$566$		−	2.62768e27i		−	0.778768i
$567$		0			0
$568$	1.98947e26			0.0569185
$569$	2.86879e27	−	1.65630e27i	0.806447	−	0.465602i	−0.0392736	−	0.999228i	$-0.512504\pi$
$569$	2.86879e27	−	1.65630e27i	0.806447	−	0.465602i	0.845720	+	0.533626i	$0.179171\pi$
$570$		0			0
$571$	2.67320e26	−	4.63013e26i	0.0725556	−	0.125670i	−0.827465	−	0.561517i	$-0.810218\pi$
$571$	2.67320e26	−	4.63013e26i	0.0725556	−	0.125670i	0.900021	+	0.435847i	$0.143551\pi$
$572$	−3.61219e27	−	2.08550e27i	−0.963407	−	0.556224i
$573$		0			0
$574$	2.17494e26	+	3.76711e26i	0.0560182	+	0.0970263i
$575$			2.57745e26i			0.0652398i
$576$		0			0
$577$	1.90115e27			0.464791			0.232395	−	0.972621i	$-0.425344\pi$
$577$	1.90115e27			0.464791			0.232395	+	0.972621i	$0.425344\pi$
$578$	1.31414e27	−	7.58721e26i	0.315765	−	0.182307i
$579$		0			0
$580$	−1.43822e27	+	2.49107e27i	−0.333846	+	0.578238i
$581$	2.43804e27	+	1.40760e27i	0.556262	+	0.321158i
$582$		0			0
$583$	−4.69502e27	−	8.13201e27i	−1.03503	−	1.79272i
$584$		−	1.76971e27i		−	0.383508i
$585$		0			0
$586$	2.99441e27			0.627098
$587$	−3.13416e27	+	1.80951e27i	−0.645269	+	0.372546i	−0.786641	−	0.617410i	$-0.788182\pi$
$587$	−3.13416e27	+	1.80951e27i	−0.645269	+	0.372546i	0.141373	+	0.989956i	$0.454848\pi$
$588$		0			0
$589$	−3.23961e27	+	5.61117e27i	−0.644674	+	1.11661i
$590$	−8.77565e26	−	5.06663e26i	−0.171696	−	0.0991285i
$591$		0			0
$592$	−7.86677e26	−	1.36256e27i	−0.148792	−	0.257715i
$593$			5.02313e27i			0.934174i	0.884211	+	0.467087i	$0.154696\pi$
$593$			5.02313e27i			0.934174i	−0.884211	+	0.467087i	$0.845304\pi$
$594$		0			0
$595$	−2.81658e27			−0.506468
$596$	−2.93899e27	+	1.69683e27i	−0.519679	+	0.300037i
$597$		0			0
$598$	−5.56295e26	+	9.63531e26i	−0.0951247	+	0.164761i
$599$	−3.45144e27	−	1.99269e27i	−0.580406	−	0.335098i	0.180889	−	0.983504i	$-0.442103\pi$
$599$	−3.45144e27	−	1.99269e27i	−0.580406	−	0.335098i	−0.761295	+	0.648406i	$0.775436\pi$
$600$		0			0
$601$	2.97714e27	+	5.15656e27i	0.484233	+	0.838716i	0.999836	−	0.0181115i	$-0.00576538\pi$
$601$	2.97714e27	+	5.15656e27i	0.484233	+	0.838716i	−0.515603	+	0.856828i	$0.672432\pi$
$602$			3.29139e27i			0.526520i
$603$		0			0
$604$	2.55544e26			0.0395454
$605$	3.86543e27	−	2.23171e27i	0.588362	−	0.339691i
$606$		0			0
$607$	−3.31580e27	+	5.74313e27i	−0.488316	+	0.845788i	−0.999910	−	0.0134392i	$-0.995722\pi$
$607$	−3.31580e27	+	5.74313e27i	−0.488316	+	0.845788i	0.511594	+	0.859228i	$0.329055\pi$
$608$	−1.31054e27	−	7.56639e26i	−0.189851	−	0.109611i
$609$		0			0
$610$	6.14933e26	+	1.06510e27i	0.0862044	+	0.149310i
$611$			4.67634e27i			0.644902i
$612$		0			0
$613$	−4.20248e26			−0.0560920			−0.0280460	−	0.999607i	$-0.508928\pi$
$613$	−4.20248e26			−0.0560920			−0.0280460	+	0.999607i	$0.508928\pi$
$614$	−5.08467e26	+	2.93564e26i	−0.0667697	+	0.0385495i
$615$		0			0
$616$	1.00596e27	−	1.74237e27i	0.127871	−	0.221480i
$617$	−6.17174e27	−	3.56326e27i	−0.771891	−	0.445652i	0.0616577	−	0.998097i	$-0.480361\pi$
$617$	−6.17174e27	−	3.56326e27i	−0.771891	−	0.445652i	−0.833549	+	0.552446i	$0.813695\pi$
$618$		0			0
$619$	−5.18300e27	−	8.97721e27i	−0.627588	−	1.08701i	−0.988034	−	0.154234i	$-0.950709\pi$
$619$	−5.18300e27	−	8.97721e27i	−0.627588	−	1.08701i	0.360447	−	0.932780i	$-0.382624\pi$
$620$		−	3.39594e27i		−	0.404616i
$621$		0			0
$622$	3.80172e27			0.438607
$623$	−5.13135e27	+	2.96259e27i	−0.582575	+	0.336350i
$624$		0			0
$625$	2.04812e27	−	3.54745e27i	0.225193	−	0.390046i
$626$	8.32332e27	+	4.80547e27i	0.900644	+	0.519987i
$627$		0			0
$628$	−4.09037e27	−	7.08472e27i	−0.428712	−	0.742551i
$629$			1.42061e28i			1.46544i
$630$		0			0
$631$	1.08984e28			1.08910			0.544550	−	0.838728i	$-0.316700\pi$
$631$	1.08984e28			1.08910			0.544550	+	0.838728i	$0.316700\pi$
$632$	−1.25413e27	+	7.24071e26i	−0.123359	+	0.0712214i
$633$		0			0
$634$	−1.49713e27	+	2.59310e27i	−0.142681	+	0.247131i
$635$	1.20552e28	+	6.96006e27i	1.13093	+	0.652944i
$636$		0			0
$637$	6.44360e27	+	1.11606e28i	0.585780	+	1.01460i
$638$			1.85521e28i			1.66029i
$639$		0			0
$640$	7.93150e26			0.0687948
$641$	−1.93720e28	+	1.11844e28i	−1.65423	+	0.955068i	−0.678919	+	0.734213i	$0.737551\pi$
$641$	−1.93720e28	+	1.11844e28i	−1.65423	+	0.955068i	−0.975307	+	0.220855i	$0.929115\pi$
$642$		0			0
$643$	−1.08420e28	+	1.87789e28i	−0.897430	+	1.55439i	−0.0666624	+	0.997776i	$0.521235\pi$
$643$	−1.08420e28	+	1.87789e28i	−0.897430	+	1.55439i	−0.830768	+	0.556619i	$0.812098\pi$
$644$	−4.64768e26	−	2.68334e26i	−0.0378772	−	0.0218684i
$645$		0			0
$646$	6.83182e27	+	1.18331e28i	0.539773	+	0.934915i
$647$		−	1.59598e28i		−	1.24161i	−0.783966	−	0.620804i	$-0.786806\pi$
$647$		−	1.59598e28i		−	1.24161i	0.783966	−	0.620804i	$-0.213194\pi$
$648$		0			0
$649$	−6.53559e27			−0.492990
$650$	−5.28364e27	+	3.05051e27i	−0.392463	+	0.226589i
$651$		0			0
$652$	−4.31506e27	+	7.47390e27i	−0.310821	+	0.538358i
$653$	2.49877e27	+	1.44266e27i	0.177253	+	0.102337i	0.586001	−	0.810310i	$-0.300701\pi$
$653$	2.49877e27	+	1.44266e27i	0.177253	+	0.102337i	−0.408748	+	0.912647i	$0.634035\pi$
$654$		0			0
$655$	3.42380e27	+	5.93020e27i	0.235557	+	0.407996i
$656$			1.10601e27i			0.0749412i
$657$		0			0
$658$	−2.25567e27			−0.148258
$659$	−1.70060e28	+	9.81842e27i	−1.10090	+	0.635605i	−0.936457	−	0.350781i	$-0.885916\pi$
$659$	−1.70060e28	+	9.81842e27i	−1.10090	+	0.635605i	−0.164443	+	0.986387i	$0.552583\pi$
$660$		0			0
$661$	1.29251e28	−	2.23869e28i	0.811743	−	1.40598i	−0.0999008	−	0.994997i	$-0.531853\pi$
$661$	1.29251e28	−	2.23869e28i	0.811743	−	1.40598i	0.911643	−	0.410982i	$-0.134814\pi$
$662$	9.88880e27	+	5.70930e27i	0.611735	+	0.353186i
$663$		0			0
$664$	3.57900e27	+	6.19901e27i	0.214823	+	0.372084i
$665$		−	8.62836e27i		−	0.510166i
$666$		0			0
$667$	4.94866e27			0.283942
$668$	1.02816e28	−	5.93611e27i	0.581163	−	0.335534i
$669$		0			0
$670$	−1.17445e27	+	2.03421e27i	−0.0644297	+	0.111596i
$671$	6.86949e27	+	3.96610e27i	0.371278	+	0.214357i
$672$		0			0
$673$	2.02522e27	+	3.50778e27i	0.106248	+	0.184027i	0.914247	−	0.405156i	$-0.132783\pi$
$673$	2.02522e27	+	3.50778e27i	0.106248	+	0.184027i	−0.807999	+	0.589183i	$0.799450\pi$
$674$		−	1.31305e28i		−	0.678707i
$675$		0			0
$676$	−1.63717e28			−0.821537
$677$	1.06064e28	−	6.12359e27i	0.524421	−	0.302775i	−0.214321	−	0.976763i	$-0.568754\pi$
$677$	1.06064e28	−	6.12359e27i	0.524421	−	0.302775i	0.738742	+	0.673989i	$0.235420\pi$
$678$		0			0
$679$	−8.48434e27	+	1.46953e28i	−0.407306	+	0.705474i
$680$	−6.20203e27	−	3.58074e27i	−0.293390	−	0.169389i
$681$		0			0
$682$	−1.09513e28	−	1.89682e28i	−0.503062	−	0.871329i
$683$		−	3.28560e28i		−	1.48733i	−0.668552	−	0.743665i	$-0.733086\pi$
$683$		−	3.28560e28i		−	1.48733i	0.668552	−	0.743665i	$-0.266914\pi$
$684$		0			0
$685$	3.00006e28			1.31894
$686$	−1.28539e28	+	7.42123e27i	−0.556923	+	0.321540i
$687$		0			0
$688$	−4.18437e27	+	7.24755e27i	−0.176095	+	0.305005i
$689$	−5.13458e28	−	2.96445e28i	−2.12967	−	1.22957i
$690$		0			0
$691$	1.76374e28	+	3.05489e28i	0.710647	+	1.23088i	0.964615	+	0.263664i	$0.0849311\pi$
$691$	1.76374e28	+	3.05489e28i	0.710647	+	1.23088i	−0.253967	+	0.967213i	$0.581736\pi$
$692$		−	6.80719e24i		−	0.000270338i
$693$		0			0
$694$	3.09616e28			1.19462
$695$	−2.39351e27	+	1.38189e27i	−0.0910305	+	0.0525565i
$696$		0			0
$697$	4.99317e27	−	8.64843e27i	0.184522	−	0.319602i
$698$	2.60901e28	+	1.50631e28i	0.950434	+	0.548733i
$699$		0			0
$700$	−1.47144e27	−	2.54861e27i	−0.0520909	−	0.0902242i
$701$		−	7.70743e27i		−	0.268986i	−0.990915	−	0.134493i	$-0.957059\pi$
$701$		−	7.70743e27i		−	0.268986i	0.990915	−	0.134493i	$-0.0429406\pi$
$702$		0			0
$703$	−4.35191e28			−1.47614
$704$	4.43019e27	−	2.55777e27i	0.148148	−	0.0855332i
$705$		0			0
$706$	−1.46957e28	+	2.54537e28i	−0.477686	+	0.827377i
$707$	9.11877e27	+	5.26473e27i	0.292242	+	0.168726i
$708$		0			0
$709$	−9.62818e27	−	1.66765e28i	−0.299973	−	0.519568i	0.676157	−	0.736758i	$-0.263644\pi$
$709$	−9.62818e27	−	1.66765e28i	−0.299973	−	0.519568i	−0.976129	+	0.217190i	$0.930311\pi$
$710$			2.88422e27i			0.0886022i
$711$		0			0
$712$	−1.50655e28			−0.449969
$713$	−5.05966e27	+	2.92120e27i	−0.149014	+	0.0860331i
$714$		0			0
$715$	3.02343e28	−	5.23674e28i	0.865845	−	1.49969i
$716$	3.40729e27	+	1.96720e27i	0.0962229	+	0.0555543i
$717$		0			0
$718$	1.79526e28	+	3.10948e28i	0.493041	+	0.853972i
$719$			2.73891e28i			0.741804i	0.928672	+	0.370902i	$0.120951\pi$
$719$			2.73891e28i			0.741804i	−0.928672	+	0.370902i	$0.879049\pi$
$720$		0			0
$721$	9.39392e27			0.247454
$722$	−1.26781e28	+	7.31971e27i	−0.329369	+	0.190161i
$723$		0			0
$724$	3.40018e27	−	5.88929e27i	0.0859244	−	0.148825i
$725$	2.35009e28	+	1.35683e28i	0.585740	+	0.338177i
$726$		0			0
$727$	−3.18180e28	−	5.51104e28i	−0.771488	−	1.33626i	−0.936748	−	0.350006i	$-0.886180\pi$
$727$	−3.18180e28	−	5.51104e28i	−0.771488	−	1.33626i	0.165260	−	0.986250i	$-0.447154\pi$
$728$		−	1.27033e28i		−	0.303811i
$729$		0			0
$730$	2.56563e28			0.596987
$731$	6.54393e28	−	3.77814e28i	1.50198	−	0.867171i
$732$		0			0
$733$	2.90889e28	−	5.03834e28i	0.649661	−	1.12525i	−0.333543	−	0.942735i	$-0.608244\pi$
$733$	2.90889e28	−	5.03834e28i	0.649661	−	1.12525i	0.983204	−	0.182511i	$-0.0584226\pi$
$734$	4.02873e28	+	2.32599e28i	0.887580	+	0.512444i
$735$		0			0
$736$	−6.82270e26	−	1.18173e27i	−0.0146278	−	0.0253361i
$737$			1.51496e28i			0.320424i
$738$		0			0
$739$	−2.99816e28			−0.617178			−0.308589	−	0.951195i	$-0.599857\pi$
$739$	−2.99816e28			−0.617178			−0.308589	+	0.951195i	$0.599857\pi$
$740$	1.97537e28	−	1.14048e28i	0.401172	−	0.231617i
$741$		0			0
$742$	1.42993e28	−	2.47671e28i	0.282667	−	0.489594i
$743$	−4.07816e28	−	2.35453e28i	−0.795383	−	0.459215i	0.0464709	−	0.998920i	$-0.485203\pi$
$743$	−4.07816e28	−	2.35453e28i	−0.795383	−	0.459215i	−0.841854	+	0.539705i	$0.818536\pi$
$744$		0			0
$745$	−2.45996e28	−	4.26078e28i	−0.467052	−	0.808958i
$746$		−	4.27854e26i		−	0.00801507i
$747$		0			0
$748$	−4.61890e28			−0.842409
$749$	4.95917e27	−	2.86318e27i	0.0892464	−	0.0515265i
$750$		0			0
$751$	3.74640e28	−	6.48896e28i	0.656470	−	1.13704i	−0.325053	−	0.945696i	$-0.605382\pi$
$751$	3.74640e28	−	6.48896e28i	0.656470	−	1.13704i	0.981523	−	0.191344i	$-0.0612846\pi$
$752$	−4.96693e27	−	2.86766e27i	−0.0858835	−	0.0495849i
$753$		0			0
$754$	5.85691e28	+	1.01445e29i	0.986178	+	1.70811i
$755$			3.70473e27i			0.0615583i
$756$		0			0
$757$	−8.81836e28			−1.42702			−0.713508	−	0.700647i	$-0.752895\pi$
$757$	−8.81836e28			−1.42702			−0.713508	+	0.700647i	$0.752895\pi$
$758$	1.71679e28	−	9.91190e27i	0.274174	−	0.158294i
$759$		0			0
$760$	1.09693e28	−	1.89994e28i	0.170625	−	0.295532i
$761$	−4.68643e28	−	2.70571e28i	−0.719441	−	0.415370i	0.0951057	−	0.995467i	$-0.469681\pi$
$761$	−4.68643e28	−	2.70571e28i	−0.719441	−	0.415370i	−0.814547	+	0.580098i	$0.803014\pi$
$762$		0			0
$763$	−1.60988e28	−	2.78839e28i	−0.240739	−	0.416973i
$764$		−	3.21515e28i		−	0.474534i
$765$		0			0
$766$	−6.73283e28			−0.968077
$767$	−3.57373e28	+	2.06330e28i	−0.507187	+	0.292825i
$768$		0			0
$769$	−2.50794e28	+	4.34388e28i	−0.346779	+	0.600640i	−0.985675	−	0.168654i	$-0.946058\pi$
$769$	−2.50794e28	+	4.34388e28i	−0.346779	+	0.600640i	0.638896	+	0.769293i	$0.279391\pi$
$770$	2.52599e28	+	1.45838e28i	0.344766	+	0.199051i
$771$		0			0
$772$	−1.58395e28	−	2.74348e28i	−0.210654	−	0.364863i
$773$		−	3.86083e28i		−	0.506857i	−0.967354	−	0.253429i	$-0.918442\pi$
$773$		−	3.86083e28i		−	0.506857i	0.967354	−	0.253429i	$-0.0815583\pi$
$774$		0			0
$775$	−3.20375e28			−0.409865
$776$	−3.73646e28	+	2.15724e28i	−0.471892	+	0.272447i
$777$		0			0
$778$	7.75113e27	−	1.34253e28i	0.0954045	−	0.165245i
$779$	2.64938e28	+	1.52962e28i	0.321936	+	0.185870i
$780$		0			0
$781$	9.30109e27	+	1.61100e28i	0.110160	+	0.190802i
$782$			1.23207e28i			0.144068i
$783$		0			0
$784$	−1.58056e28			−0.180156
$785$	1.02710e29	−	5.92998e28i	1.15589	−	0.667354i
$786$		0			0
$787$	1.73290e28	−	3.00147e28i	0.190119	−	0.329296i	−0.755171	−	0.655528i	$-0.772446\pi$
$787$	1.73290e28	−	3.00147e28i	0.190119	−	0.329296i	0.945290	+	0.326233i	$0.105779\pi$
$788$	5.19670e27	+	3.00032e27i	0.0562945	+	0.0325016i
$789$		0			0
$790$	−1.04972e28	−	1.81816e28i	−0.110867	−	0.192027i
$791$		−	1.04566e28i		−	0.109050i
$792$		0			0
$793$	5.00842e28			0.509294
$794$	6.99821e28	−	4.04042e28i	0.702720	−	0.405715i
$795$		0			0
$796$	−3.45153e28	+	5.97822e28i	−0.337972	+	0.585384i
$797$	−3.24969e28	−	1.87621e28i	−0.314238	−	0.181426i	0.334583	−	0.942366i	$-0.391404\pi$
$797$	−3.24969e28	−	1.87621e28i	−0.314238	−	0.181426i	−0.648821	+	0.760941i	$0.724738\pi$
$798$		0			0
$799$	2.58926e28	+	4.48473e28i	0.244178	+	0.422930i
$800$		−	7.48262e27i		−	0.0696873i
$801$		0			0
$802$	−4.00534e28			−0.363827
$803$	1.43304e29	−	8.27369e28i	1.28560	−	0.742239i
$804$		0			0
$805$	3.89015e27	−	6.73793e27i	0.0340414	−	0.0589614i
$806$	−1.19766e29	−	6.91468e28i	−1.03510	−	0.597615i
$807$		0			0
$808$	1.33862e28	+	2.31856e28i	0.112861	+	0.195481i
$809$			1.20471e29i			1.00322i	0.865093	+	0.501611i	$0.167259\pi$
$809$			1.20471e29i			1.00322i	−0.865093	+	0.501611i	$0.832741\pi$
$810$		0			0
$811$	−9.11156e28			−0.740260			−0.370130	−	0.928980i	$-0.620687\pi$
$811$	−9.11156e28			−0.740260			−0.370130	+	0.928980i	$0.620687\pi$
$812$	−4.89328e28	+	2.82513e28i	−0.392681	+	0.226714i
$813$		0			0
$814$	7.35568e28	−	1.27404e29i	0.575942	−	0.997561i
$815$	−1.08352e29	−	6.25572e28i	−0.838034	−	0.483839i
$816$		0			0
$817$	1.15740e29	+	2.00468e29i	0.873502	+	1.51295i
$818$			6.93811e28i			0.517259i
$819$		0			0
$820$	−1.60343e28			−0.116657
$821$	−1.66645e29	+	9.62123e28i	−1.19773	+	0.691511i	−0.960049	−	0.279832i	$-0.909721\pi$
$821$	−1.66645e29	+	9.62123e28i	−1.19773	+	0.691511i	−0.237683	+	0.971343i	$0.576388\pi$
$822$		0			0
$823$	−7.38735e28	+	1.27953e29i	−0.518191	+	0.897534i	0.481585	+	0.876399i	$0.340061\pi$
$823$	−7.38735e28	+	1.27953e29i	−0.518191	+	0.897534i	−0.999777	+	0.0211346i	$0.993272\pi$
$824$	2.06851e28	+	1.19426e28i	0.143346	+	0.0827610i
$825$		0			0
$826$	−9.95249e27	−	1.72382e28i	−0.0673180	−	0.116598i
$827$			1.21783e29i			0.813829i	0.913466	+	0.406915i	$0.133395\pi$
$827$			1.21783e29i			0.813829i	−0.913466	+	0.406915i	$0.866605\pi$
$828$		0			0
$829$	−6.95492e28			−0.453677			−0.226839	−	0.973932i	$-0.572839\pi$
$829$	−6.95492e28			−0.453677			−0.226839	+	0.973932i	$0.572839\pi$
$830$	−8.98696e28	+	5.18863e28i	−0.579205	+	0.334404i
$831$		0			0
$832$	1.61498e28	−	2.79723e28i	0.101610	−	0.175993i
$833$	1.23592e29	+	7.13556e28i	0.768314	+	0.443586i
$834$		0			0
$835$	8.60583e28	+	1.49057e29i	0.522309	+	0.904666i
$836$		−	1.41496e29i		−	0.848560i
$837$		0			0
$838$	1.18878e29			0.696081
$839$	9.81035e28	−	5.66401e28i	0.567629	−	0.327721i	−0.188573	−	0.982059i	$-0.560386\pi$
$839$	9.81035e28	−	5.66401e28i	0.567629	−	0.327721i	0.756202	+	0.654338i	$0.227053\pi$
$840$		0			0
$841$	1.72011e29	−	2.97931e29i	0.971841	−	1.68328i
$842$	2.09842e29	+	1.21152e29i	1.17158	+	0.676411i
$843$		0			0
$844$	−4.74438e28	−	8.21751e28i	−0.258675	−	0.448039i
$845$		−	2.37348e29i		−	1.27885i
$846$		0			0
$847$	8.76760e28			0.461367
$848$	6.29733e28	−	3.63576e28i	0.327490	−	0.189076i
$849$		0			0
$850$	−3.37809e28	+	5.85103e28i	−0.171586	+	0.297196i
$851$	−3.39843e28	−	1.96209e28i	−0.170602	−	0.0984969i
$852$		0			0
$853$	4.37710e28	+	7.58137e28i	0.214633	+	0.371755i	0.953159	−	0.302470i	$-0.0978111\pi$
$853$	4.37710e28	+	7.58137e28i	0.214633	+	0.371755i	−0.738526	+	0.674225i	$0.764478\pi$
$854$			2.41586e28i			0.117083i
$855$		0			0
$856$	1.45599e28			0.0689322
$857$	−1.45693e29	+	8.41156e28i	−0.681756	+	0.393612i	−0.800516	−	0.599311i	$-0.795441\pi$
$857$	−1.45693e29	+	8.41156e28i	−0.681756	+	0.393612i	0.118760	+	0.992923i	$0.462108\pi$
$858$		0			0
$859$	−1.11663e27	+	1.93406e27i	−0.00510479	+	0.00884176i	−0.868567	−	0.495573i	$-0.834958\pi$
$859$	−1.11663e27	+	1.93406e27i	−0.00510479	+	0.00884176i	0.863462	+	0.504414i	$0.168292\pi$
$860$	−1.05071e29	−	6.06626e28i	−0.474786	−	0.274118i
$861$		0			0
$862$	−4.83634e28	−	8.37678e28i	−0.213523	−	0.369832i
$863$			2.63875e29i			1.15157i	0.817602	+	0.575784i	$0.195303\pi$
$863$			2.63875e29i			1.15157i	−0.817602	+	0.575784i	$0.804697\pi$
$864$		0			0
$865$	9.86868e25			0.000420821
$866$	−1.94800e29	+	1.12468e29i	−0.821126	+	0.474077i
$867$		0			0
$868$	3.33536e28	−	5.77701e28i	0.137387	−	0.237961i
$869$	−1.17265e29	−	6.77030e28i	−0.477497	−	0.275683i
$870$		0			0
$871$	4.78274e28	+	8.28395e28i	0.190325	+	0.329652i
$872$		−	8.18661e28i		−	0.322062i
$873$		0			0
$874$	−3.77434e28			−0.145120
$875$	1.30675e29	−	7.54454e28i	0.496722	−	0.286782i
$876$		0			0
$877$	−9.34026e28	+	1.61778e29i	−0.347027	+	0.601068i	−0.985720	−	0.168393i	$-0.946142\pi$
$877$	−9.34026e28	+	1.61778e29i	−0.347027	+	0.601068i	0.638693	+	0.769462i	$0.279475\pi$
$878$	7.00517e28	+	4.04444e28i	0.257320	+	0.148564i
$879$		0			0
$880$	3.70811e28	+	6.42263e28i	0.133145	+	0.230614i
$881$			3.16713e29i			1.12436i	0.827013	+	0.562182i	$0.190038\pi$
$881$			3.16713e29i			1.12436i	−0.827013	+	0.562182i	$0.809962\pi$
$882$		0			0
$883$	2.71760e29			0.943146			0.471573	−	0.881827i	$-0.343686\pi$
$883$	2.71760e29			0.943146			0.471573	+	0.881827i	$0.343686\pi$
$884$	−2.52567e29	+	1.45820e29i	−0.866670	+	0.500372i
$885$		0			0
$886$	1.04721e29	−	1.81382e29i	0.351315	−	0.608495i
$887$	−1.06647e29	−	6.15726e28i	−0.353762	−	0.204245i	0.312579	−	0.949892i	$-0.398807\pi$
$887$	−1.06647e29	−	6.15726e28i	−0.353762	−	0.204245i	−0.666341	+	0.745647i	$0.732141\pi$
$888$		0			0
$889$	1.36718e29	+	2.36803e29i	0.443413	+	0.768014i
$890$		−	2.18410e29i		−	0.700444i
$891$		0			0
$892$	1.50675e29			0.472489
$893$	−1.37386e29	+	7.93198e28i	−0.426018	+	0.245961i
$894$		0			0
$895$	−2.85193e28	+	4.93969e28i	−0.0864786	+	0.149785i
$896$	1.34927e28	+	7.79002e27i	0.0404594	+	0.0233592i
$897$		0			0
$898$	−1.19410e29	−	2.06824e29i	−0.350169	−	0.606510i
$899$			6.15112e29i			1.78385i
$900$		0			0
$901$	−6.56559e29			−1.86220
$902$	−8.95604e28	+	5.17077e28i	−0.251218	+	0.145041i
$903$		0			0
$904$	1.32936e28	−	2.30252e28i	0.0364720	−	0.0631713i
$905$	8.53795e28	+	4.92939e28i	0.231669	+	0.133754i
$906$		0			0
$907$	2.34821e29	+	4.06721e29i	0.623252	+	1.07950i	0.988876	+	0.148741i	$0.0475221\pi$
$907$	2.34821e29	+	4.06721e29i	0.623252	+	1.07950i	−0.365624	+	0.930762i	$0.619145\pi$
$908$			7.90484e28i			0.207508i
$909$		0			0
$910$	1.84165e29			0.472927
$911$	1.59507e29	−	9.20916e28i	0.405132	−	0.233903i	−0.283564	−	0.958953i	$-0.591517\pi$
$911$	1.59507e29	−	9.20916e28i	0.405132	−	0.233903i	0.688696	+	0.725050i	$0.258183\pi$
$912$		0			0
$913$	−3.34648e29	+	5.79627e29i	−0.831535	+	1.44026i
$914$	−3.95944e29	−	2.28598e29i	−0.973132	−	0.561838i
$915$		0			0
$916$	1.67220e29	+	2.89633e29i	0.402099	+	0.696455i
$917$			1.34509e29i			0.319932i
$918$		0			0
$919$	2.44861e29			0.569855			0.284928	−	0.958549i	$-0.408030\pi$
$919$	2.44861e29			0.569855			0.284928	+	0.958549i	$0.408030\pi$
$920$	1.71320e28	−	9.89116e27i	0.0394393	−	0.0227703i
$921$		0			0
$922$	−5.62604e28	+	9.74459e28i	−0.126734	+	0.219510i
$923$	1.01719e29	+	5.87274e28i	0.226665	+	0.130865i
$924$		0			0
$925$	−1.07593e29	−	1.86357e29i	−0.234622	−	0.406377i
$926$		−	2.81150e29i		−	0.606496i
$927$		0			0
$928$	−1.43665e29			−0.303299
$929$	5.42304e29	−	3.13099e29i	1.13262	−	0.653921i	0.188031	−	0.982163i	$-0.439790\pi$
$929$	5.42304e29	−	3.13099e29i	1.13262	−	0.653921i	0.944594	+	0.328242i	$0.106456\pi$
$930$		0			0
$931$	−2.18592e29	+	3.78613e29i	−0.446825	+	0.773924i
$932$	2.84176e28	+	1.64069e28i	0.0574683	+	0.0331793i
$933$		0			0
$934$	1.59022e29	+	2.75434e29i	0.314766	+	0.545191i
$935$		−	6.69622e29i		−	1.31134i
$936$		0			0
$937$	−9.05889e29			−1.73652			−0.868258	−	0.496112i	$-0.834760\pi$
$937$	−9.05889e29			−1.73652			−0.868258	+	0.496112i	$0.834760\pi$
$938$	−3.99584e28	+	2.30700e28i	−0.0757844	+	0.0437541i
$939$		0			0
$940$	4.15737e28	−	7.20077e28i	0.0771862	−	0.133690i
$941$	2.45478e29	+	1.41727e29i	0.450938	+	0.260349i	0.708226	−	0.705985i	$-0.249496\pi$
$941$	2.45478e29	+	1.41727e29i	0.450938	+	0.260349i	−0.257288	+	0.966335i	$0.582829\pi$
$942$		0			0
$943$	1.37927e28	+	2.38897e28i	0.0248047	+	0.0429630i
$944$		−	5.06108e28i		−	0.0900582i
$945$		0			0
$946$	−7.82505e29			−1.36325
$947$	−2.77884e29	+	1.60437e29i	−0.479032	+	0.276569i	−0.720013	−	0.693961i	$-0.755864\pi$
$947$	−2.77884e29	+	1.60437e29i	−0.479032	+	0.276569i	0.240981	+	0.970530i	$0.422531\pi$
$948$		0			0
$949$	5.22403e29	−	9.04829e29i	0.881747	−	1.52723i
$950$	−1.79241e29	−	1.03485e29i	−0.299366	−	0.172839i
$951$		0			0
$952$	−7.03374e28	−	1.21828e29i	−0.115031	−	0.199240i
$953$			5.97459e29i			0.966895i	0.875373	+	0.483447i	$0.160616\pi$
$953$			5.97459e29i			0.966895i	−0.875373	+	0.483447i	$0.839384\pi$
$954$		0			0
$955$	4.66114e29			0.738683
$956$	1.47915e29	−	8.53989e28i	0.231971	−	0.133929i
$957$		0			0
$958$	7.16877e28	−	1.24167e29i	0.110101	−	0.190700i
$959$	5.10357e29	+	2.94655e29i	0.775689	+	0.447844i
$960$		0			0
$961$	−2.72062e28	−	4.71225e28i	−0.0404981	−	0.0701447i
$962$		−	9.28880e29i		−	1.36839i
$963$		0			0
$964$	7.74157e28			0.111701
$965$	3.97734e29	−	2.29632e29i	0.567963	−	0.327914i
$966$		0			0
$967$	3.60948e29	−	6.25180e29i	0.504870	−	0.874461i	−0.495114	−	0.868828i	$-0.664874\pi$
$967$	3.60948e29	−	6.25180e29i	0.504870	−	0.874461i	0.999984	−	0.00563284i	$-0.00179300\pi$
$968$	1.93060e29	+	1.11463e29i	0.267263	+	0.154304i
$969$		0			0
$970$	−3.12745e29	−	5.41690e29i	−0.424105	−	0.734571i
$971$			1.69506e29i			0.227505i	0.993509	+	0.113753i	$0.0362872\pi$
$971$			1.69506e29i			0.227505i	−0.993509	+	0.113753i	$0.963713\pi$
$972$		0			0
$973$	−5.42897e28			−0.0713821
$974$	−6.77706e29	+	3.91274e29i	−0.881966	+	0.509204i
$975$		0			0
$976$	−3.07130e28	+	5.31965e28i	−0.0391583	+	0.0678242i
$977$	−1.87816e29	−	1.08436e29i	−0.237021	−	0.136844i	0.376786	−	0.926300i	$-0.377029\pi$
$977$	−1.87816e29	−	1.08436e29i	−0.237021	−	0.136844i	−0.613807	+	0.789456i	$0.710363\pi$
$978$		0			0
$979$	−7.04335e29	−	1.21994e30i	−0.870868	−	1.50839i
$980$		−	2.29140e29i		−	0.280440i
$981$		0			0
$982$	9.58969e29			1.14998
$983$	−7.33174e29	+	4.23298e29i	−0.870305	+	0.502471i	−0.867450	−	0.497525i	$-0.834242\pi$
$983$	−7.33174e29	+	4.23298e29i	−0.870305	+	0.502471i	−0.00285568	+	0.999996i	$0.500909\pi$
$984$		0			0
$985$	−4.34969e28	+	7.53388e28i	−0.0505936	+	0.0876307i
$986$	1.12339e30	+	6.48587e29i	1.29348	+	0.746791i
$987$		0			0
$988$	−4.46706e29	−	7.73718e29i	−0.504026	−	0.872998i
$989$			2.08729e29i			0.233142i
$990$		0			0
$991$	1.23295e30			1.34961			0.674805	−	0.737996i	$-0.264228\pi$
$991$	1.23295e30			1.34961			0.674805	+	0.737996i	$0.264228\pi$
$992$	1.46887e29	−	8.48055e28i	0.159172	−	0.0918982i
$993$		0			0
$994$	−2.83277e28	+	4.90650e28i	−0.0300848	+	0.0521084i
$995$	−8.66688e29	−	5.00382e29i	−0.911238	−	0.526103i
$996$		0			0
$997$	−2.36157e29	−	4.09036e29i	−0.243360	−	0.421512i	0.718309	−	0.695724i	$-0.244916\pi$
$997$	−2.36157e29	−	4.09036e29i	−0.243360	−	0.421512i	−0.961669	+	0.274212i	$0.911583\pi$
$998$		−	9.42539e29i		−	0.961599i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.21.d.a.17.6		40
3.2	odd	2		18.21.d.a.5.15	✓	40
9.2	odd	6	inner	54.21.d.a.35.6		40
9.7	even	3		18.21.d.a.11.15	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.21.d.a.5.15	✓	40	3.2	odd	2
18.21.d.a.11.15	yes	40	9.7	even	3
54.21.d.a.17.6		40	1.1	even	1	trivial
54.21.d.a.35.6		40	9.2	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	54.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-627.069 + 362.039i) q^{2} +(262144. - 454047. i) q^{4} +(6.58251e6 + 3.80041e6i) q^{5} +(7.46524e7 + 1.29302e8i) q^{7} +3.79625e8i q^{8} -5.50358e9 q^{10} +(-3.07406e10 + 1.77481e10i) q^{11} +(-1.12062e11 + 1.94097e11i) q^{13} +(-9.36245e10 - 5.40541e10i) q^{14} +(-1.37439e11 - 2.38051e11i) q^{16} +2.48192e12i q^{17} -7.60316e12 q^{19} +(3.45113e12 - 1.99251e12i) q^{20} +(1.28510e13 - 2.22586e13i) q^{22} +(-5.93735e12 - 3.42793e12i) q^{23} +(-1.87975e13 - 3.25581e13i) q^{25} -1.62283e14i q^{26} +7.82787e13 q^{28} +(-6.25109e14 + 3.60907e14i) q^{29} +(4.26088e14 - 7.38006e14i) q^{31} +(1.72368e14 + 9.95164e13i) q^{32} +(-8.98551e14 - 1.55634e15i) q^{34} +1.13484e15i q^{35} +5.72383e15 q^{37} +(4.76771e15 - 2.75264e15i) q^{38} +(-1.44273e15 + 2.49888e15i) q^{40} +(-3.48457e15 - 2.01182e15i) q^{41} +(-1.52227e16 - 2.63664e16i) q^{43} +1.86102e16i q^{44} +4.96417e15 q^{46} +(1.80696e16 - 1.04325e16i) q^{47} +(2.87502e16 - 4.97968e16i) q^{49} +(2.35746e16 + 1.36108e16i) q^{50} +(5.87527e16 + 1.01763e17i) q^{52} +2.64537e17i q^{53} -2.69800e17 q^{55} +(-4.90862e16 + 2.83399e16i) q^{56} +(2.61325e17 - 4.52628e17i) q^{58} +(1.59453e17 + 9.20605e16i) q^{59} +(-1.11733e17 - 1.93528e17i) q^{61} +6.17041e17i q^{62} -1.44115e17 q^{64} +(-1.47530e18 + 8.51763e17i) q^{65} +(2.13397e17 - 3.69615e17i) q^{67} +(1.12691e18 + 6.50620e17i) q^{68} +(-4.10856e17 - 7.11623e17i) q^{70} -5.24061e17i q^{71} -4.66174e18 q^{73} +(-3.58924e18 + 2.07225e18i) q^{74} +(-1.99312e18 + 3.45219e18i) q^{76} +(-4.58972e18 - 2.64987e18i) q^{77} +(1.90733e18 + 3.30360e18i) q^{79} -2.08930e18i q^{80} +2.91343e18 q^{82} +(1.63293e19 - 9.42772e18i) q^{83} +(-9.43231e18 + 1.63372e19i) q^{85} +(1.90913e19 + 1.10224e19i) q^{86} +(-6.73762e18 - 1.16699e19i) q^{88} +3.96851e19i q^{89} -3.34628e19 q^{91} +(-3.11288e18 + 1.79722e18i) q^{92} +(-7.55392e18 + 1.30838e19i) q^{94} +(-5.00478e19 - 2.88951e19i) q^{95} +(5.68257e19 + 9.84250e19i) q^{97} +4.16347e19i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 10485760 q^{4} - 29763918 q^{5} + 133479866 q^{7} + 35793208728 q^{11} + 39827158550 q^{13} - 187564400640 q^{14} - 5497558138880 q^{16} - 10560819523540 q^{19} - 15604865040384 q^{20} + 10829007458304 q^{22}+ \cdots - 66\!\cdots\!16 q^{97}+O(q^{100}) \) 40 * q + 10485760 * q^4 - 29763918 * q^5 + 133479866 * q^7 + 35793208728 * q^11 + 39827158550 * q^13 - 187564400640 * q^14 - 5497558138880 * q^16 - 10560819523540 * q^19 - 15604865040384 * q^20 + 10829007458304 * q^22 + 95164852839678 * q^23 + 485893942617694 * q^25 + 139963783970816 * q^28 - 487337329131246 * q^29 - 386065992062842 * q^31 - 810410730184704 * q^34 + 7650497672534432 * q^37 + 27431157167935488 * q^38 + 76546903885431012 * q^41 - 10868849409851092 * q^43 + 13732137981788160 * q^46 - 220882065588142506 * q^47 - 201918836583922386 * q^49 - 84434006357065728 * q^50 - 20880901301862400 * q^52 - 689556443803109316 * q^55 - 98337764482744320 * q^56 + 289875600503808000 * q^58 + 4671324023815652220 * q^59 - 608513692992272866 * q^61 - 5764607523034234880 * q^64 - 4959300225343873626 * q^65 - 2581864509390888904 * q^67 + 5171455594224156672 * q^68 - 584784912675889152 * q^70 + 15022099327729072004 * q^73 - 7089371473773993984 * q^74 - 2768455473178869760 * q^76 + 30865724759591472834 * q^77 + 18532232803602736754 * q^79 - 35601230743051272192 * q^82 - 54829678294093455594 * q^83 + 43688870161052471388 * q^85 - 47393791396458614784 * q^86 - 5677518662299287552 * q^88 - 35182774173576758996 * q^91 + 49893790365609099264 * q^92 + 19892618446780047360 * q^94 - 332020921293200455200 * q^95 - 66463398176406835216 * q^97

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