LMFDB - Embedded newform 54.21.d.a.35.9

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			35.9
Character	$\chi$	$=$	54.35
Dual form			54.21.d.a.17.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-627.069 - 362.039i) q^{2} +(262144. + 454047. i) q^{4} +(1.42842e7 - 8.24698e6i) q^{5} +(-5.08606e6 + 8.80931e6i) q^{7} -3.79625e8i q^{8} -1.19429e10 q^{10} +(-2.97586e10 - 1.71811e10i) q^{11} +(6.84602e10 + 1.18577e11i) q^{13} +(6.37862e9 - 3.68270e9i) q^{14} +(-1.37439e11 + 2.38051e11i) q^{16} +2.59494e12i q^{17} -1.15951e13 q^{19} +(7.48903e12 + 4.32379e12i) q^{20} +(1.24405e13 + 2.15475e13i) q^{22} +(2.77990e13 - 1.60498e13i) q^{23} +(8.83415e13 - 1.53012e14i) q^{25} -9.91409e13i q^{26} -5.33312e12 q^{28} +(5.44840e14 + 3.14564e14i) q^{29} +(-8.32813e12 - 1.44248e13i) q^{31} +(1.72368e14 - 9.95164e13i) q^{32} +(9.39469e14 - 1.62721e15i) q^{34} +1.67778e14i q^{35} +1.18057e15 q^{37} +(7.27094e15 + 4.19788e15i) q^{38} +(-3.13076e15 - 5.42263e15i) q^{40} +(5.47886e15 - 3.16322e15i) q^{41} +(1.57849e16 - 2.73402e16i) q^{43} -1.80157e16i q^{44} -2.32425e16 q^{46} +(-7.73213e15 - 4.46415e15i) q^{47} +(3.98444e16 + 6.90125e16i) q^{49} +(-1.10793e17 + 6.39661e16i) q^{50} +(-3.58928e16 + 6.21682e16i) q^{52} +3.42729e16i q^{53} -5.66769e17 q^{55} +(3.34424e15 + 1.93080e15i) q^{56} +(-2.27768e17 - 3.94507e17i) q^{58} +(5.59623e17 - 3.23098e17i) q^{59} +(-2.60145e17 + 4.50584e17i) q^{61} +1.20604e16i q^{62} -1.44115e17 q^{64} +(1.95580e18 + 1.12918e18i) q^{65} +(8.36439e17 + 1.44876e18i) q^{67} +(-1.17822e18 + 6.80248e17i) q^{68} +(6.07423e16 - 1.05209e17i) q^{70} +3.29004e18i q^{71} +6.31809e18 q^{73} +(-7.40297e17 - 4.27411e17i) q^{74} +(-3.03959e18 - 5.26472e18i) q^{76} +(3.02708e17 - 1.74768e17i) q^{77} +(-1.46957e18 + 2.54537e18i) q^{79} +4.53382e18i q^{80} -4.58083e18 q^{82} +(-1.69299e19 - 9.77449e18i) q^{83} +(2.14004e19 + 3.70666e19i) q^{85} +(-1.97964e19 + 1.14295e19i) q^{86} +(-6.52238e18 + 1.12971e19i) q^{88} -5.21129e19i q^{89} -1.39277e18 q^{91} +(1.45747e19 + 8.41469e18i) q^{92} +(3.23239e18 + 5.59866e18i) q^{94} +(-1.65627e20 + 9.56247e19i) q^{95} +(-4.99196e18 + 8.64633e18i) q^{97} -5.77009e19i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/54\mathbb{Z}\right)^\times$.

$n$	$29$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−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
$5$	1.42842e7	−	8.24698e6i	1.46270	−	0.844490i	0.463565	−	0.886063i	$-0.346570\pi$
$5$	1.42842e7	−	8.24698e6i	1.46270	−	0.844490i	0.999135	+	0.0415726i	$0.0132368\pi$
$6$		0			0
$7$	−5.08606e6	+	8.80931e6i	−0.0180053	+	0.0311861i	−0.874888	−	0.484326i	$-0.839065\pi$
$7$	−5.08606e6	+	8.80931e6i	−0.0180053	+	0.0311861i	0.856882	+	0.515512i	$0.172398\pi$
$8$		−	3.79625e8i		−	0.353553i
$9$		0			0
$10$	−1.19429e10			−1.19429
$11$	−2.97586e10	−	1.71811e10i	−1.14732	−	0.662406i	−0.199088	−	0.979982i	$-0.563798\pi$
$11$	−2.97586e10	−	1.71811e10i	−1.14732	−	0.662406i	−0.948233	+	0.317575i	$0.897131\pi$
$12$		0			0
$13$	6.84602e10	+	1.18577e11i	0.496597	+	0.860132i	0.999992	−	0.00392447i	$-0.00124920\pi$
$13$	6.84602e10	+	1.18577e11i	0.496597	+	0.860132i	−0.503395	+	0.864056i	$0.667916\pi$
$14$	6.37862e9	−	3.68270e9i	0.0220519	−	0.0127317i
$15$		0			0
$16$	−1.37439e11	+	2.38051e11i	−0.125000	+	0.216506i
$17$			2.59494e12i			1.28718i	0.765372	+	0.643588i	$0.222555\pi$
$17$			2.59494e12i			1.28718i	−0.765372	+	0.643588i	$0.777445\pi$
$18$		0			0
$19$	−1.15951e13			−1.89121			−0.945604	−	0.325321i	$-0.894528\pi$
$19$	−1.15951e13			−1.89121			−0.945604	+	0.325321i	$0.894528\pi$
$20$	7.48903e12	+	4.32379e12i	0.731350	+	0.422245i
$21$		0			0
$22$	1.24405e13	+	2.15475e13i	0.468392	+	0.811279i
$23$	2.77990e13	−	1.60498e13i	0.671043	−	0.387427i	−0.125428	−	0.992103i	$-0.540031\pi$
$23$	2.77990e13	−	1.60498e13i	0.671043	−	0.387427i	0.796472	+	0.604676i	$0.206697\pi$
$24$		0			0
$25$	8.83415e13	−	1.53012e14i	0.926328	−	1.60445i
$26$		−	9.91409e13i		−	0.702295i
$27$		0			0
$28$	−5.33312e12			−0.0180053
$29$	5.44840e14	+	3.14564e14i	1.29506	+	0.747702i	0.979546	−	0.201220i	$-0.0644905\pi$
$29$	5.44840e14	+	3.14564e14i	1.29506	+	0.747702i	0.315512	+	0.948922i	$0.397824\pi$
$30$		0			0
$31$	−8.32813e12	−	1.44248e13i	−0.0101609	−	0.0175991i	0.860900	−	0.508774i	$-0.169901\pi$
$31$	−8.32813e12	−	1.44248e13i	−0.0101609	−	0.0175991i	−0.871061	+	0.491175i	$0.836568\pi$
$32$	1.72368e14	−	9.95164e13i	0.153093	−	0.0883883i
$33$		0			0
$34$	9.39469e14	−	1.62721e15i	0.455086	−	0.788231i
$35$			1.67778e14i			0.0608213i
$36$		0			0
$37$	1.18057e15			0.245512			0.122756	−	0.992437i	$-0.460827\pi$
$37$	1.18057e15			0.245512			0.122756	+	0.992437i	$0.460827\pi$
$38$	7.27094e15	+	4.19788e15i	1.15812	+	0.668643i
$39$		0			0
$40$	−3.13076e15	−	5.42263e15i	−0.298572	−	0.517143i
$41$	5.47886e15	−	3.16322e15i	0.408180	−	0.235663i	−0.281828	−	0.959465i	$-0.590941\pi$
$41$	5.47886e15	−	3.16322e15i	0.408180	−	0.235663i	0.690007	+	0.723802i	$0.257607\pi$
$42$		0			0
$43$	1.57849e16	−	2.73402e16i	0.730393	−	1.26508i	−0.226323	−	0.974052i	$-0.572670\pi$
$43$	1.57849e16	−	2.73402e16i	0.730393	−	1.26508i	0.956716	−	0.291025i	$-0.0939962\pi$
$44$		−	1.80157e16i		−	0.662406i
$45$		0			0
$46$	−2.32425e16			−0.547905
$47$	−7.73213e15	−	4.46415e15i	−0.147001	−	0.0848711i	0.424695	−	0.905336i	$-0.360381\pi$
$47$	−7.73213e15	−	4.46415e15i	−0.147001	−	0.0848711i	−0.571696	+	0.820465i	$0.693715\pi$
$48$		0			0
$49$	3.98444e16	+	6.90125e16i	0.499352	+	0.864902i
$50$	−1.10793e17	+	6.39661e16i	−1.13452	+	0.655013i
$51$		0			0
$52$	−3.58928e16	+	6.21682e16i	−0.248299	+	0.430066i
$53$			3.42729e16i			0.195971i	0.995188	+	0.0979856i	$0.0312399\pi$
$53$			3.42729e16i			0.195971i	−0.995188	+	0.0979856i	$0.968760\pi$
$54$		0			0
$55$	−5.66769e17			−2.23758
$56$	3.34424e15	+	1.93080e15i	0.0110260	+	0.00636585i
$57$		0			0
$58$	−2.27768e17	−	3.94507e17i	−0.528705	−	0.915744i
$59$	5.59623e17	−	3.23098e17i	1.09490	−	0.632142i	0.160025	−	0.987113i	$-0.448843\pi$
$59$	5.59623e17	−	3.23098e17i	1.09490	−	0.632142i	0.934877	+	0.354971i	$0.115509\pi$
$60$		0			0
$61$	−2.60145e17	+	4.50584e17i	−0.364684	+	0.631651i	−0.988725	−	0.149740i	$-0.952156\pi$
$61$	−2.60145e17	+	4.50584e17i	−0.364684	+	0.631651i	0.624042	+	0.781391i	$0.285490\pi$
$62$			1.20604e16i			0.0143696i
$63$		0			0
$64$	−1.44115e17			−0.125000
$65$	1.95580e18	+	1.12918e18i	1.45275	+	0.838744i
$66$		0			0
$67$	8.36439e17	+	1.44876e18i	0.458867	+	0.794780i	0.998901	−	0.0468625i	$-0.0149222\pi$
$67$	8.36439e17	+	1.44876e18i	0.458867	+	0.794780i	−0.540035	+	0.841643i	$0.681589\pi$
$68$	−1.17822e18	+	6.80248e17i	−0.557364	+	0.321794i
$69$		0			0
$70$	6.07423e16	−	1.05209e17i	0.0215036	−	0.0372453i
$71$			3.29004e18i			1.01069i	0.862918	+	0.505345i	$0.168635\pi$
$71$			3.29004e18i			1.01069i	−0.862918	+	0.505345i	$0.831365\pi$
$72$		0			0
$73$	6.31809e18			1.47013			0.735067	−	0.677995i	$-0.237151\pi$
$73$	6.31809e18			1.47013			0.735067	+	0.677995i	$0.237151\pi$
$74$	−7.40297e17	−	4.27411e17i	−0.150345	−	0.0868017i
$75$		0			0
$76$	−3.03959e18	−	5.26472e18i	−0.472802	−	0.818917i
$77$	3.02708e17	−	1.74768e17i	0.0413158	−	0.0238537i
$78$		0			0
$79$	−1.46957e18	+	2.54537e18i	−0.155210	+	0.268831i	−0.933135	−	0.359525i	$-0.882939\pi$
$79$	−1.46957e18	+	2.54537e18i	−0.155210	+	0.268831i	0.777926	+	0.628356i	$0.216272\pi$
$80$			4.53382e18i			0.422245i
$81$		0			0
$82$	−4.58083e18			−0.333277
$83$	−1.69299e19	−	9.77449e18i	−1.09112	−	0.629960i	−0.157248	−	0.987559i	$-0.550262\pi$
$83$	−1.69299e19	−	9.77449e18i	−1.09112	−	0.629960i	−0.933875	+	0.357599i	$0.883596\pi$
$84$		0			0
$85$	2.14004e19	+	3.70666e19i	1.08701	+	1.88275i
$86$	−1.97964e19	+	1.14295e19i	−0.894545	+	0.516466i
$87$		0			0
$88$	−6.52238e18	+	1.12971e19i	−0.234196	+	0.405639i
$89$		−	5.21129e19i		−	1.67126i	−0.549289	−	0.835632i	$-0.685101\pi$
$89$		−	5.21129e19i		−	1.67126i	0.549289	−	0.835632i	$-0.314899\pi$
$90$		0			0
$91$	−1.39277e18			−0.0357656
$92$	1.45747e19	+	8.41469e18i	0.335522	+	0.193714i
$93$		0			0
$94$	3.23239e18	+	5.59866e18i	0.0600129	+	0.103945i
$95$	−1.65627e20	+	9.56247e19i	−2.76627	+	1.59711i
$96$		0			0
$97$	−4.99196e18	+	8.64633e18i	−0.0676946	+	0.117250i	−0.897886	−	0.440228i	$-0.854898\pi$
$97$	−4.99196e18	+	8.64633e18i	−0.0676946	+	0.117250i	0.830192	+	0.557478i	$0.188231\pi$
$98$		−	5.77009e19i		−	0.706190i
$99$		0			0
$100$	9.26328e19			0.926328
$101$	8.14501e19	+	4.70252e19i	0.737357	+	0.425713i	0.821107	−	0.570774i	$-0.193357\pi$
$101$	8.14501e19	+	4.70252e19i	0.737357	+	0.425713i	−0.0837507	+	0.996487i	$0.526690\pi$
$102$		0			0
$103$	2.36508e19	+	4.09644e19i	0.175984	+	0.304814i	0.940502	−	0.339790i	$-0.110356\pi$
$103$	2.36508e19	+	4.09644e19i	0.175984	+	0.304814i	−0.764517	+	0.644603i	$0.777023\pi$
$104$	4.50146e19	−	2.59892e19i	0.304103	−	0.175574i
$105$		0			0
$106$	1.24081e19	−	2.14915e19i	0.0692863	−	0.120007i
$107$		−	1.49808e20i		−	0.761546i	−0.924669	−	0.380773i	$-0.875658\pi$
$107$		−	1.49808e20i		−	0.761546i	0.924669	−	0.380773i	$-0.124342\pi$
$108$		0			0
$109$	−1.41604e19			−0.0598149			−0.0299074	−	0.999553i	$-0.509521\pi$
$109$	−1.41604e19			−0.0598149			−0.0299074	+	0.999553i	$0.509521\pi$
$110$	3.55403e20	+	2.05192e20i	1.37023	+	0.791105i
$111$		0			0
$112$	−1.39805e18	−	2.42149e18i	−0.00450133	−	0.00779654i
$113$	1.23139e20	−	7.10944e19i	0.362754	−	0.209436i	−0.307534	−	0.951537i	$-0.599504\pi$
$113$	1.23139e20	−	7.10944e19i	0.362754	−	0.209436i	0.670288	+	0.742101i	$0.266171\pi$
$114$		0			0
$115$	2.64724e20	−	4.58515e20i	0.654357	−	1.13338i
$116$			3.29844e20i			0.747702i
$117$		0			0
$118$	−4.67896e20			−0.893984
$119$	−2.28596e19	−	1.31980e19i	−0.0401421	−	0.0231760i
$120$		0			0
$121$	2.54006e20	+	4.39951e20i	0.377564	+	0.653960i
$122$	3.26257e20	−	1.88365e20i	0.446645	−	0.257870i
$123$		0			0
$124$	4.36634e18	−	7.56272e18i	0.00508043	−	0.00879957i
$125$		−	1.34122e21i		−	1.44012i
$126$		0			0
$127$	−6.25908e20			−0.573421			−0.286711	−	0.958017i	$-0.592562\pi$
$127$	−6.25908e20			−0.573421			−0.286711	+	0.958017i	$0.592562\pi$
$128$	9.03702e19	+	5.21753e19i	0.0765466	+	0.0441942i
$129$		0			0
$130$	−8.17613e20	−	1.41615e21i	−0.593081	−	1.02725i
$131$	6.15926e20	−	3.55605e20i	0.413824	−	0.238921i	−0.278608	−	0.960405i	$-0.589873\pi$
$131$	6.15926e20	−	3.55605e20i	0.413824	−	0.238921i	0.692431	+	0.721484i	$0.256540\pi$
$132$		0			0
$133$	5.89735e19	−	1.02145e20i	0.0340518	−	0.0589795i
$134$		−	1.21129e21i		−	0.648935i
$135$		0			0
$136$	9.85104e20			0.455086
$137$	−3.58323e20	−	2.06878e20i	−0.153840	−	0.0888194i	0.421104	−	0.907012i	$-0.361643\pi$
$137$	−3.58323e20	−	2.06878e20i	−0.153840	−	0.0888194i	−0.574944	+	0.818193i	$0.694976\pi$
$138$		0			0
$139$	2.76363e20	+	4.78674e20i	0.102644	+	0.177784i	0.912773	−	0.408467i	$-0.133937\pi$
$139$	2.76363e20	+	4.78674e20i	0.102644	+	0.177784i	−0.810129	+	0.586251i	$0.800603\pi$
$140$	−7.61793e19	+	4.39821e19i	−0.0263364	+	0.0152053i
$141$		0			0
$142$	1.19112e21	−	2.06308e21i	0.357333	−	0.618918i
$143$		−	4.70489e21i		−	1.31580i
$144$		0			0
$145$	1.03768e22			2.52571
$146$	−3.96188e21	−	2.28739e21i	−0.900270	−	0.519771i
$147$		0			0
$148$	3.09479e20	+	5.36033e20i	0.0613781	+	0.106310i
$149$	7.93211e21	−	4.57961e21i	1.47071	−	0.849113i	0.471248	−	0.882001i	$-0.343804\pi$
$149$	7.93211e21	−	4.57961e21i	1.47071	−	0.849113i	0.999459	+	0.0328878i	$0.0104704\pi$
$150$		0			0
$151$	5.11106e21	−	8.85262e21i	0.829357	−	1.43649i	−0.0691858	−	0.997604i	$-0.522040\pi$
$151$	5.11106e21	−	8.85262e21i	0.829357	−	1.43649i	0.898543	−	0.438885i	$-0.144627\pi$
$152$			4.40180e21i			0.668643i
$153$		0			0
$154$	−2.53092e20			−0.0337342
$155$	−2.37921e20	−	1.37364e20i	−0.0297246	−	0.0171615i
$156$		0			0
$157$	5.06508e21	+	8.77298e21i	0.556660	+	0.964163i	0.997772	+	0.0667115i	$0.0212507\pi$
$157$	5.06508e21	+	8.77298e21i	0.556660	+	0.964163i	−0.441112	+	0.897452i	$0.645416\pi$
$158$	1.84304e21	−	1.06408e21i	0.190092	−	0.109750i
$159$		0			0
$160$	1.64142e21	−	2.84302e21i	0.149286	−	0.258571i
$161$			3.26520e20i			0.0279030i
$162$		0			0
$163$	2.13313e21			0.161117			0.0805583	−	0.996750i	$-0.474330\pi$
$163$	2.13313e21			0.161117			0.0805583	+	0.996750i	$0.474330\pi$
$164$	2.87250e21	+	1.65844e21i	0.204090	+	0.117831i
$165$		0			0
$166$	7.07749e21	+	1.22586e22i	0.445449	+	0.771541i
$167$	1.07878e22	−	6.22833e21i	0.639392	−	0.369153i	−0.144988	−	0.989433i	$-0.546314\pi$
$167$	1.07878e22	−	6.22833e21i	0.639392	−	0.369153i	0.784380	+	0.620280i	$0.212981\pi$
$168$		0			0
$169$	1.28890e20	−	2.23245e20i	0.00678194	−	0.0117467i
$170$		−	3.09911e22i		−	1.53726i
$171$		0			0
$172$	1.65516e22			0.730393
$173$	−2.99802e22	−	1.73091e22i	−1.24845	−	0.720796i	−0.277654	−	0.960681i	$-0.589557\pi$
$173$	−2.99802e22	−	1.73091e22i	−1.24845	−	0.720796i	−0.970801	+	0.239885i	$0.922890\pi$
$174$		0			0
$175$	8.98621e20	+	1.55646e21i	0.0333577	+	0.0577772i
$176$	8.17997e21	−	4.72271e21i	0.286830	−	0.165602i
$177$		0			0
$178$	−1.88669e22	+	3.26784e22i	−0.590881	+	1.02344i
$179$			1.65998e22i			0.491556i	0.969326	+	0.245778i	$0.0790434\pi$
$179$			1.65998e22i			0.491556i	−0.969326	+	0.245778i	$0.920957\pi$
$180$		0			0
$181$	−3.19946e22			−0.847795			−0.423898	−	0.905710i	$-0.639338\pi$
$181$	−3.19946e22			−0.847795			−0.423898	+	0.905710i	$0.639338\pi$
$182$	8.73364e20	+	5.04237e20i	0.0219019	+	0.0126451i
$183$		0			0
$184$	−6.09289e21	−	1.05532e22i	−0.136976	−	0.237250i
$185$	1.68634e22	−	9.73611e21i	0.359111	−	0.207333i
$186$		0			0
$187$	4.45839e22	−	7.72217e22i	0.852634	−	1.47680i
$188$		−	4.68100e21i		−	0.0848711i
$189$		0			0
$190$	1.38479e23			2.25865
$191$	4.19498e22	+	2.42197e22i	0.649227	+	0.374831i	0.788160	−	0.615471i	$-0.211034\pi$
$191$	4.19498e22	+	2.42197e22i	0.649227	+	0.374831i	−0.138933	+	0.990302i	$0.544367\pi$
$192$		0			0
$193$	4.66854e21	+	8.08614e21i	0.0651040	+	0.112763i	0.896740	−	0.442558i	$-0.145929\pi$
$193$	4.66854e21	+	8.08614e21i	0.0651040	+	0.112763i	−0.831636	+	0.555321i	$0.812595\pi$
$194$	6.26061e21	−	3.61457e21i	0.0829086	−	0.0478673i
$195$		0			0
$196$	−2.08899e22	+	3.61824e22i	−0.249676	+	0.432451i
$197$		−	1.37214e23i		−	1.55861i	−0.626645	−	0.779305i	$-0.715572\pi$
$197$		−	1.37214e23i		−	1.55861i	0.626645	−	0.779305i	$-0.284428\pi$
$198$		0			0
$199$	1.43381e23			1.47218			0.736091	−	0.676882i	$-0.236669\pi$
$199$	1.43381e23			1.47218			0.736091	+	0.676882i	$0.236669\pi$
$200$	−5.80872e22	−	3.35367e22i	−0.567258	−	0.327506i
$201$		0			0
$202$	−3.40499e22	−	5.89761e22i	−0.301025	−	0.521390i
$203$	−5.54218e21	+	3.19978e21i	−0.0466359	+	0.0269252i
$204$		0			0
$205$	5.21740e22	−	9.03680e22i	0.398030	−	0.689408i
$206$		−	3.42501e22i		−	0.248880i
$207$		0			0
$208$	−3.76364e22			−0.248299
$209$	3.45054e23	+	1.99217e23i	2.16982	+	1.25275i
$210$		0			0
$211$	7.18868e22	+	1.24512e23i	0.410984	+	0.711845i	0.994998	−	0.0998987i	$-0.0318519\pi$
$211$	7.18868e22	+	1.24512e23i	0.410984	+	0.711845i	−0.584014	+	0.811744i	$0.698519\pi$
$212$	−1.55615e22	+	8.98444e21i	−0.0848580	+	0.0489928i
$213$		0			0
$214$	−5.42361e22	+	9.39397e22i	−0.269247	+	0.466350i
$215$		−	5.20710e23i		−	2.46724i
$216$		0			0
$217$	1.69430e20			0.000731799
$218$	8.87952e21	+	5.12659e21i	0.0366290	+	0.0211477i
$219$		0			0
$220$	−1.48575e23	−	2.57340e23i	−0.559396	−	0.968902i
$221$	−3.07699e23	+	1.77650e23i	−1.10714	+	0.639208i
$222$		0			0
$223$	−1.76076e22	+	3.04973e22i	−0.0578965	+	0.100280i	−0.893521	−	0.449021i	$-0.851773\pi$
$223$	−1.76076e22	+	3.04973e22i	−0.0578965	+	0.100280i	0.835624	+	0.549301i	$0.185106\pi$
$224$			2.02459e21i			0.00636585i
$225$		0			0
$226$	−1.02956e23			−0.296187
$227$	−4.82205e23	−	2.78401e23i	−1.32731	−	0.766324i	−0.342429	−	0.939544i	$-0.611250\pi$
$227$	−4.82205e23	−	2.78401e23i	−1.32731	−	0.766324i	−0.984883	+	0.173220i	$0.944583\pi$
$228$		0			0
$229$	2.55636e23	+	4.42775e23i	0.644567	+	1.11642i	0.984401	+	0.175937i	$0.0562956\pi$
$229$	2.55636e23	+	4.42775e23i	0.644567	+	1.11642i	−0.339835	+	0.940485i	$0.610371\pi$
$230$	−3.32000e23	+	1.91681e23i	−0.801420	+	0.462700i
$231$		0			0
$232$	1.19416e23	−	2.06835e23i	0.264353	−	0.457872i
$233$			3.15530e23i			0.669086i	0.942381	+	0.334543i	$0.108582\pi$
$233$			3.15530e23i			0.669086i	−0.942381	+	0.334543i	$0.891418\pi$
$234$		0			0
$235$	−1.47263e23			−0.286691
$236$	2.93404e23	+	1.69397e23i	0.547451	+	0.316071i
$237$		0			0
$238$	9.55639e21	+	1.65521e22i	0.0163879	+	0.0283847i
$239$	5.02829e23	−	2.90308e23i	0.826877	−	0.477398i	−0.0259049	−	0.999664i	$-0.508247\pi$
$239$	5.02829e23	−	2.90308e23i	0.826877	−	0.477398i	0.852782	+	0.522267i	$0.174913\pi$
$240$		0			0
$241$	1.82221e23	−	3.15617e23i	0.275695	−	0.477518i	−0.694615	−	0.719382i	$-0.744425\pi$
$241$	1.82221e23	−	3.15617e23i	0.275695	−	0.477518i	0.970310	+	0.241864i	$0.0777586\pi$
$242$		−	3.67840e23i		−	0.533956i
$243$		0			0
$244$	−2.72781e23			−0.364684
$245$	1.13829e24	+	6.57192e23i	1.46080	+	0.843395i
$246$		0			0
$247$	−7.93804e23	−	1.37491e24i	−0.939169	−	1.62669i
$248$	−5.47600e21	+	3.16157e21i	−0.00622223	+	0.00359241i
$249$		0			0
$250$	−4.85572e23	+	8.41036e23i	−0.509159	+	0.881890i
$251$			7.60101e23i			0.765833i	0.923783	+	0.382916i	$0.125080\pi$
$251$			7.60101e23i			0.765833i	−0.923783	+	0.382916i	$0.874920\pi$
$252$		0			0
$253$	−1.10301e24			−1.02654
$254$	3.92488e23	+	2.26603e23i	0.351147	+	0.202735i
$255$		0			0
$256$	−3.77789e22	−	6.54350e22i	−0.0312500	−	0.0541266i
$257$	−6.02580e23	+	3.47899e23i	−0.479384	+	0.276772i	−0.720160	−	0.693808i	$-0.755931\pi$
$257$	−6.02580e23	+	3.47899e23i	−0.479384	+	0.276772i	0.240776	+	0.970581i	$0.422598\pi$
$258$		0			0
$259$	−6.00443e21	+	1.04000e22i	−0.00442053	+	0.00765658i
$260$			1.18403e24i			0.838744i
$261$		0			0
$262$	−5.14971e23			−0.337886
$263$	−5.94105e23	−	3.43007e23i	−0.375237	−	0.216643i	0.300507	−	0.953780i	$-0.402844\pi$
$263$	−5.94105e23	−	3.43007e23i	−0.375237	−	0.216643i	−0.675744	+	0.737136i	$0.736178\pi$
$264$		0			0
$265$	2.82648e23	+	4.89560e23i	0.165496	+	0.286647i
$266$	−7.39609e22	+	4.27013e22i	−0.0417048	+	0.0240783i
$267$		0			0
$268$	−4.38535e23	+	7.59565e23i	−0.229433	+	0.397390i
$269$			2.19375e24i			1.10577i	0.833257	+	0.552886i	$0.186473\pi$
$269$			2.19375e24i			1.10577i	−0.833257	+	0.552886i	$0.813527\pi$
$270$		0			0
$271$	−6.09570e23			−0.285319			−0.142660	−	0.989772i	$-0.545565\pi$
$271$	−6.09570e23			−0.285319			−0.142660	+	0.989772i	$0.545565\pi$
$272$	−6.17729e23	−	3.56646e23i	−0.278682	−	0.160897i
$273$		0			0
$274$	1.49795e23	+	2.59453e23i	0.0628048	+	0.108781i
$275$	−5.25783e24	+	3.03561e24i	−2.12559	+	1.22721i
$276$		0			0
$277$	−2.47319e24	+	4.28369e24i	−0.929950	+	1.61072i	−0.146550	+	0.989203i	$0.546817\pi$
$277$	−2.47319e24	+	4.28369e24i	−0.929950	+	1.61072i	−0.783400	+	0.621518i	$0.786516\pi$
$278$		−	4.00216e23i		−	0.145160i
$279$		0			0
$280$	6.36929e22			0.0215036
$281$	2.08963e24	+	1.20645e24i	0.680780	+	0.393049i	0.800149	−	0.599801i	$-0.204754\pi$
$281$	2.08963e24	+	1.20645e24i	0.680780	+	0.393049i	−0.119369	+	0.992850i	$0.538087\pi$
$282$		0			0
$283$	6.33454e23	+	1.09717e24i	0.192243	+	0.332975i	0.945993	−	0.324186i	$-0.105090\pi$
$283$	6.33454e23	+	1.09717e24i	0.192243	+	0.332975i	−0.753750	+	0.657161i	$0.771757\pi$
$284$	−1.49383e24	+	8.62464e23i	−0.437641	+	0.252672i
$285$		0			0
$286$	−1.70335e24	+	2.95029e24i	−0.465204	+	0.805758i
$287$			6.43533e22i			0.0169727i
$288$		0			0
$289$	−2.66948e24			−0.656823
$290$	−6.50697e24	−	3.75680e24i	−1.54667	−	0.892973i
$291$		0			0
$292$	1.65625e24	+	2.86871e24i	0.367533	+	0.636587i
$293$	2.75361e24	−	1.58979e24i	0.590508	−	0.340930i	−0.174791	−	0.984606i	$-0.555925\pi$
$293$	2.75361e24	−	1.58979e24i	0.590508	−	0.340930i	0.765298	+	0.643676i	$0.222592\pi$
$294$		0			0
$295$	5.32917e24	−	9.23039e24i	1.06768	−	1.84927i
$296$		−	4.48173e23i		−	0.0868017i
$297$		0			0
$298$	−6.63198e24			−1.20083
$299$	3.80625e24	+	2.19754e24i	0.666477	+	0.384791i
$300$		0			0
$301$	1.60566e23	+	2.78108e23i	0.0263019	+	0.0455563i
$302$	−6.40998e24	+	3.70080e24i	−1.01575	+	0.586444i
$303$		0			0
$304$	1.59362e24	−	2.76023e24i	0.236401	−	0.409458i
$305$			8.58162e24i			1.23189i
$306$		0			0
$307$	9.57726e24			1.28783			0.643913	−	0.765099i	$-0.277310\pi$
$307$	9.57726e24			1.28783			0.643913	+	0.765099i	$0.277310\pi$
$308$	1.58706e23	+	9.16289e22i	0.0206579	+	0.0119268i
$309$		0			0
$310$	9.94620e22	+	1.72273e23i	0.0121350	+	0.0210185i
$311$	1.03734e25	−	5.98907e24i	1.22551	−	0.707547i	0.259421	−	0.965764i	$-0.416468\pi$
$311$	1.03734e25	−	5.98907e24i	1.22551	−	0.707547i	0.966087	+	0.258217i	$0.0831350\pi$
$312$		0			0
$313$	−2.01007e24	+	3.48155e24i	−0.222725	+	0.385771i	−0.955634	−	0.294555i	$-0.904828\pi$
$313$	−2.01007e24	+	3.48155e24i	−0.222725	+	0.385771i	0.732910	+	0.680326i	$0.238162\pi$
$314$		−	7.33502e24i		−	0.787236i
$315$		0			0
$316$	−1.54095e24			−0.155210
$317$	1.50505e25	+	8.68940e24i	1.46878	+	0.848002i	0.999388	−	0.0349858i	$-0.0111386\pi$
$317$	1.50505e25	+	8.68940e24i	1.46878	+	0.848002i	0.469395	+	0.882988i	$0.344472\pi$
$318$		0			0
$319$	−1.08091e25	−	1.87219e25i	−0.990565	−	1.71571i
$320$	−2.05857e24	+	1.18851e24i	−0.182838	+	0.105561i
$321$		0			0
$322$	1.18213e23	−	2.04751e23i	0.00986520	−	0.0170870i
$323$		−	3.00886e25i		−	2.43432i
$324$		0			0
$325$	2.41915e25			1.84005
$326$	−1.33762e24	−	7.72274e23i	−0.0986634	−	0.0569634i
$327$		0			0
$328$	−1.20084e24	−	2.07991e24i	−0.0833194	−	0.144313i
$329$	7.86521e22	−	4.54098e22i	0.00529360	−	0.00305626i
$330$		0			0
$331$	−2.50586e24	+	4.34028e24i	−0.158737	+	0.274940i	−0.934413	−	0.356191i	$-0.884075\pi$
$331$	−2.50586e24	+	4.34028e24i	−0.158737	+	0.274940i	0.775677	+	0.631130i	$0.217409\pi$
$332$		−	1.02493e25i		−	0.629960i
$333$		0			0
$334$	−9.01958e24			−0.522061
$335$	2.38957e25	+	1.37962e25i	1.34237	+	0.775017i
$336$		0			0
$337$	−1.57132e25	−	2.72161e25i	−0.831699	−	1.44055i	−0.896690	−	0.442660i	$-0.854035\pi$
$337$	−1.57132e25	−	2.72161e25i	−0.831699	−	1.44055i	0.0649903	−	0.997886i	$-0.479298\pi$
$338$	−1.61647e23	+	9.33267e22i	−0.00830614	+	0.00479555i
$339$		0			0
$340$	−1.12200e25	+	1.94336e25i	−0.543504	+	0.941377i
$341$			5.72346e23i			0.0269225i
$342$		0			0
$343$	−1.62226e24			−0.0719746
$344$	−1.03790e25	−	5.99233e24i	−0.447272	−	0.258233i
$345$		0			0
$346$	1.25331e25	+	2.17080e25i	0.509680	+	0.882791i
$347$	−2.17089e25	+	1.25336e25i	−0.857715	+	0.495202i	−0.863246	−	0.504783i	$-0.831573\pi$
$347$	−2.17089e25	+	1.25336e25i	−0.857715	+	0.495202i	0.00553154	+	0.999985i	$0.498239\pi$
$348$		0			0
$349$	1.04729e25	−	1.81396e25i	0.390674	−	0.676666i	−0.601865	−	0.798598i	$-0.705575\pi$
$349$	1.04729e25	−	1.81396e25i	0.390674	−	0.676666i	0.992539	+	0.121931i	$0.0389088\pi$
$350$		−	1.30134e24i		−	0.0471749i
$351$		0			0
$352$	−6.83921e24			−0.234196
$353$	−4.24608e25	−	2.45148e25i	−1.41332	−	0.815982i	−0.417623	−	0.908621i	$-0.637137\pi$
$353$	−4.24608e25	−	2.45148e25i	−1.41332	−	0.815982i	−0.995700	+	0.0926383i	$0.970470\pi$
$354$		0			0
$355$	2.71329e25	+	4.69955e25i	0.853517	+	1.47834i
$356$	2.36617e25	−	1.36611e25i	0.723679	−	0.417816i
$357$		0			0
$358$	6.00978e24	−	1.04092e25i	0.173791	−	0.301015i
$359$		−	2.99198e25i		−	0.841422i	−0.907195	−	0.420711i	$-0.861781\pi$
$359$		−	2.99198e25i		−	0.841422i	0.907195	−	0.420711i	$-0.138219\pi$
$360$		0			0
$361$	9.68567e25			2.57666
$362$	2.00628e25	+	1.15833e25i	0.519167	+	0.299741i
$363$		0			0
$364$	−3.65106e23	−	6.32383e23i	−0.00894140	−	0.0154870i
$365$	9.02487e25	−	5.21051e25i	2.15037	−	1.24151i
$366$		0			0
$367$	1.23715e25	−	2.14280e25i	0.279100	−	0.483416i	−0.692061	−	0.721839i	$-0.743297\pi$
$367$	1.23715e25	−	2.14280e25i	0.279100	−	0.483416i	0.971161	+	0.238423i	$0.0766304\pi$
$368$			8.82344e24i			0.193714i
$369$		0			0
$370$	−1.40994e25			−0.293213
$371$	−3.01921e23	−	1.74314e23i	−0.00611159	−	0.00352853i
$372$		0			0
$373$	−1.34753e25	−	2.33398e25i	−0.258493	−	0.447723i	0.707345	−	0.706868i	$-0.249893\pi$
$373$	−1.34753e25	−	2.33398e25i	−0.258493	−	0.447723i	−0.965838	+	0.259145i	$0.916559\pi$
$374$	−5.59144e25	+	3.22822e25i	−1.04426	+	0.602903i
$375$		0			0
$376$	−1.69470e24	+	2.93531e24i	−0.0300065	+	0.0519727i
$377$			8.61403e25i			1.48523i
$378$		0			0
$379$	9.18649e25			1.50230			0.751152	−	0.660130i	$-0.229499\pi$
$379$	9.18649e25			1.50230			0.751152	+	0.660130i	$0.229499\pi$
$380$	−8.68361e25	−	5.01349e25i	−1.38313	−	0.798553i
$381$		0			0
$382$	−1.75370e25	−	3.03749e25i	−0.265046	−	0.459073i
$383$	7.72606e25	−	4.46065e25i	1.13755	−	0.656765i	0.191727	−	0.981448i	$-0.438591\pi$
$383$	7.72606e25	−	4.46065e25i	1.13755	−	0.656765i	0.945823	+	0.324683i	$0.105258\pi$
$384$		0			0
$385$	2.88262e24	−	4.99284e24i	0.0402884	−	0.0697816i
$386$		−	6.76076e24i		−	0.0920710i
$387$		0			0
$388$	−5.23445e24			−0.0676946
$389$	−5.35622e25	−	3.09242e25i	−0.675091	−	0.389764i	0.122912	−	0.992418i	$-0.460777\pi$
$389$	−5.35622e25	−	3.09242e25i	−0.675091	−	0.389764i	−0.798003	+	0.602654i	$0.794110\pi$
$390$		0			0
$391$	4.16481e25	+	7.21367e25i	0.498687	+	0.863751i
$392$	2.61989e25	−	1.51259e25i	0.305789	−	0.176547i
$393$		0			0
$394$	−4.96769e25	+	8.60430e25i	−0.551052	+	0.954450i
$395$			4.84780e25i			0.524293i
$396$		0			0
$397$	3.61977e25			0.372200			0.186100	−	0.982531i	$-0.440415\pi$
$397$	3.61977e25			0.372200			0.186100	+	0.982531i	$0.440415\pi$
$398$	−8.99100e25	−	5.19096e25i	−0.901524	−	0.520495i
$399$		0			0
$400$	2.42831e25	+	4.20596e25i	0.231582	+	0.401112i
$401$	−6.25638e25	+	3.61212e25i	−0.581941	+	0.335984i	−0.761904	−	0.647689i	$-0.775735\pi$
$401$	−6.25638e25	+	3.61212e25i	−0.581941	+	0.335984i	0.179963	+	0.983673i	$0.442402\pi$
$402$		0			0
$403$	1.14029e24	−	1.97504e24i	0.0100917	−	0.0174794i
$404$			4.93095e25i			0.425713i
$405$		0			0
$406$	4.63378e24			0.0380780
$407$	−3.51320e25	−	2.02834e25i	−0.281682	−	0.162629i
$408$		0			0
$409$	−4.78708e25	−	8.29147e25i	−0.365458	−	0.632992i	0.623391	−	0.781910i	$-0.285754\pi$
$409$	−4.78708e25	−	8.29147e25i	−0.365458	−	0.632992i	−0.988850	+	0.148918i	$0.952421\pi$
$410$	−6.54335e25	+	3.77780e25i	−0.487485	+	0.281450i
$411$		0			0
$412$	−1.23998e25	+	2.14772e25i	−0.0879922	+	0.152407i
$413$			6.57319e24i			0.0455277i
$414$		0			0
$415$	−3.22440e26			−2.12798
$416$	2.36006e25	+	1.36258e25i	0.152051	+	0.0877869i
$417$		0			0
$418$	−1.44248e26	−	2.49846e26i	−0.885826	−	1.53430i
$419$	2.31795e26	−	1.33827e26i	1.38984	−	0.802423i	0.396541	−	0.918017i	$-0.370211\pi$
$419$	2.31795e26	−	1.33827e26i	1.38984	−	0.802423i	0.993296	+	0.115594i	$0.0368773\pi$
$420$		0			0
$421$	2.20291e25	−	3.81555e25i	0.125943	−	0.218140i	−0.796158	−	0.605089i	$-0.793138\pi$
$421$	2.20291e25	−	3.81555e25i	0.125943	−	0.218140i	0.922101	+	0.386949i	$0.126471\pi$
$422$		−	1.04103e26i		−	0.581219i
$423$		0			0
$424$	1.30109e25			0.0692863
$425$	3.97057e26	+	2.29241e26i	2.06521	+	1.19235i
$426$		0			0
$427$	−2.64622e24	−	4.58339e24i	−0.0131325	−	0.0227462i
$428$	6.80196e25	−	3.92712e25i	0.329759	−	0.190386i
$429$		0			0
$430$	−1.88517e26	+	3.26521e26i	−0.872300	+	1.51087i
$431$			2.84749e26i			1.28733i	0.765309	+	0.643663i	$0.222586\pi$
$431$			2.84749e26i			1.28733i	−0.765309	+	0.643663i	$0.777414\pi$
$432$		0			0
$433$	7.32156e25			0.316027			0.158014	−	0.987437i	$-0.449491\pi$
$433$	7.32156e25			0.316027			0.158014	+	0.987437i	$0.449491\pi$
$434$	−1.06244e23	−	6.13400e22i	−0.000448134	−	0.000258730i
$435$		0			0
$436$	−3.71205e24	−	6.42946e24i	−0.0149537	−	0.0259006i
$437$	−3.22332e26	+	1.86099e26i	−1.26908	+	0.732705i
$438$		0			0
$439$	−1.42450e26	+	2.46731e26i	−0.535819	+	0.928066i	0.463304	+	0.886199i	$0.346664\pi$
$439$	−1.42450e26	+	2.46731e26i	−0.535819	+	0.928066i	−0.999123	+	0.0418668i	$0.986669\pi$
$440$			2.15160e26i			0.791105i
$441$		0			0
$442$	2.57265e26			0.903977
$443$	1.55284e26	+	8.96533e25i	0.533445	+	0.307985i	0.742418	−	0.669937i	$-0.233679\pi$
$443$	1.55284e26	+	8.96533e25i	0.533445	+	0.307985i	−0.208973	+	0.977921i	$0.567012\pi$
$444$		0			0
$445$	−4.29774e26	−	7.44390e26i	−1.41137	−	2.44456i
$446$	2.20824e25	−	1.27493e25i	0.0709085	−	0.0409390i
$447$		0			0
$448$	7.32978e23	−	1.26956e24i	0.00225067	−	0.00389827i
$449$		−	1.46837e26i		−	0.440931i	−0.975395	−	0.220466i	$-0.929242\pi$
$449$		−	1.46837e26i		−	0.440931i	0.975395	−	0.220466i	$-0.0707577\pi$
$450$		0			0
$451$	−2.17391e26			−0.624418
$452$	6.45604e25	+	3.72740e25i	0.181377	+	0.104718i
$453$		0			0
$454$	2.01584e26	+	3.49154e26i	0.541873	+	0.938551i
$455$	−1.98946e25	+	1.14861e25i	−0.0523144	+	0.0302037i
$456$		0			0
$457$	3.57346e26	−	6.18941e26i	0.899345	−	1.55771i	0.0710124	−	0.997475i	$-0.477377\pi$
$457$	3.57346e26	−	6.18941e26i	0.899345	−	1.55771i	0.828333	−	0.560236i	$-0.189290\pi$
$458$		−	3.70201e26i		−	0.911555i
$459$		0			0
$460$	2.77583e26			0.654357
$461$	−6.08292e26	−	3.51197e26i	−1.40314	−	0.810106i	−0.408431	−	0.912789i	$-0.633924\pi$
$461$	−6.08292e26	−	3.51197e26i	−1.40314	−	0.810106i	−0.994714	+	0.102683i	$0.967257\pi$
$462$		0			0
$463$	1.10633e26	+	1.91623e26i	0.244386	+	0.423289i	0.961959	−	0.273195i	$-0.0880803\pi$
$463$	1.10633e26	+	1.91623e26i	0.244386	+	0.423289i	−0.717573	+	0.696483i	$0.754747\pi$
$464$	−1.49765e26	+	8.64666e25i	−0.323765	+	0.186926i
$465$		0			0
$466$	1.14234e26	−	1.97859e26i	0.236558	−	0.409730i
$467$			2.76662e26i			0.560766i	0.959888	+	0.280383i	$0.0904614\pi$
$467$			2.76662e26i			0.560766i	−0.959888	+	0.280383i	$0.909539\pi$
$468$		0			0
$469$	−1.70167e25			−0.0330482
$470$	9.23440e25	+	5.33148e25i	0.175562	+	0.101361i
$471$		0			0
$472$	−1.22656e26	−	2.12447e26i	−0.223496	−	0.387106i
$473$	−9.39470e26	+	5.42403e26i	−1.67599	+	0.967633i
$474$		0			0
$475$	−1.02433e27	+	1.77419e27i	−1.75188	+	3.03434i
$476$		−	1.38391e25i		−	0.0231760i
$477$		0			0
$478$	−4.20411e26			−0.675143
$479$	−3.01969e26	−	1.74342e26i	−0.474905	−	0.274186i	0.243386	−	0.969930i	$-0.421742\pi$
$479$	−3.01969e26	−	1.74342e26i	−0.474905	−	0.274186i	−0.718291	+	0.695743i	$0.755075\pi$
$480$		0			0
$481$	8.08218e25	+	1.39987e26i	0.121921	+	0.211173i
$482$	−2.28531e26	+	1.31942e26i	−0.337656	+	0.194946i
$483$		0			0
$484$	−1.33172e26	+	2.30661e26i	−0.188782	+	0.326980i
$485$			1.64674e26i			0.228670i
$486$		0			0
$487$	9.82619e26			1.30947			0.654735	−	0.755858i	$-0.272780\pi$
$487$	9.82619e26			1.30947			0.654735	+	0.755858i	$0.272780\pi$
$488$	1.71053e26	+	9.87574e25i	0.223322	+	0.128935i
$489$		0			0
$490$	−4.75858e26	−	8.24209e26i	−0.596371	−	1.03294i
$491$	1.10669e26	−	6.38949e25i	0.135898	−	0.0784606i	−0.430510	−	0.902586i	$-0.641666\pi$
$491$	1.10669e26	−	6.38949e25i	0.135898	−	0.0784606i	0.566407	+	0.824125i	$0.308333\pi$
$492$		0			0
$493$	−8.16274e26	+	1.41383e27i	−0.962424	+	1.66697i
$494$			1.14955e27i			1.32819i
$495$		0			0
$496$	4.57844e24			0.00508043
$497$	−2.89830e25	−	1.67333e25i	−0.0315195	−	0.0181978i
$498$		0			0
$499$	−4.51078e26	−	7.81290e26i	−0.471244	−	0.816219i	0.528215	−	0.849111i	$-0.322862\pi$
$499$	−4.51078e26	−	7.81290e26i	−0.471244	−	0.816219i	−0.999459	+	0.0328920i	$0.989528\pi$
$500$	6.08975e26	−	3.51592e26i	0.623590	−	0.360030i
$501$		0			0
$502$	2.75186e26	−	4.76636e26i	0.270763	−	0.468975i
$503$		−	1.47701e27i		−	1.42464i	−0.701857	−	0.712318i	$-0.747645\pi$
$503$		−	1.47701e27i		−	1.42464i	0.701857	−	0.712318i	$-0.252355\pi$
$504$		0			0
$505$	1.55126e27			1.43804
$506$	6.91664e26	+	3.99332e26i	0.628623	+	0.362935i
$507$		0			0
$508$	−1.64078e26	−	2.84192e26i	−0.143355	−	0.248299i
$509$	7.49057e26	−	4.32468e26i	0.641708	−	0.370490i	−0.143564	−	0.989641i	$-0.545856\pi$
$509$	7.49057e26	−	4.32468e26i	0.641708	−	0.370490i	0.785272	+	0.619151i	$0.212523\pi$
$510$		0			0
$511$	−3.21342e25	+	5.56580e25i	−0.0264702	+	0.0458478i
$512$			5.47097e25i			0.0441942i
$513$		0			0
$514$	5.03812e26			0.391415
$515$	6.75666e26	+	3.90096e26i	0.514825	+	0.297234i
$516$		0			0
$517$	1.53398e26	+	2.65693e26i	0.112438	+	0.194749i
$518$	7.53039e24	−	4.34767e24i	0.00541402	−	0.00312579i
$519$		0			0
$520$	4.28665e26	−	7.42469e26i	0.296541	−	0.513623i
$521$			4.90761e26i			0.333037i	0.986038	+	0.166519i	$0.0532526\pi$
$521$			4.90761e26i			0.333037i	−0.986038	+	0.166519i	$0.946747\pi$
$522$		0			0
$523$	1.78863e27			1.16816			0.584082	−	0.811695i	$-0.301455\pi$
$523$	1.78863e27			1.16816			0.584082	+	0.811695i	$0.301455\pi$
$524$	3.22922e26	+	1.86439e26i	0.206912	+	0.119461i
$525$		0			0
$526$	2.48363e26	+	4.30178e26i	0.153190	+	0.265333i
$527$	3.74314e25	−	2.16110e25i	0.0226532	−	0.0130788i
$528$		0			0
$529$	−3.42889e26	+	5.93901e26i	−0.199801	+	0.346065i
$530$		−	4.09318e26i		−	0.234046i
$531$		0			0
$532$	6.18382e25			0.0340518
$533$	7.50167e26	+	4.33109e26i	0.405402	+	0.234059i
$534$		0			0
$535$	−1.23546e27	−	2.13988e27i	−0.643118	−	1.11391i
$536$	5.49984e26	−	3.17533e26i	0.280997	−	0.162234i
$537$		0			0
$538$	7.94224e26	−	1.37564e27i	0.390949	−	0.677144i
$539$		−	2.73828e27i		−	1.32309i
$540$		0			0
$541$	−1.87369e27			−0.872421			−0.436211	−	0.899845i	$-0.643680\pi$
$541$	−1.87369e27			−0.872421			−0.436211	+	0.899845i	$0.643680\pi$
$542$	3.82243e26	+	2.20688e26i	0.174722	+	0.100876i
$543$		0			0
$544$	2.58239e26	+	4.47283e26i	0.113771	+	0.197058i
$545$	−2.02269e26	+	1.16780e26i	−0.0874912	+	0.0505131i
$546$		0			0
$547$	−1.41727e27	+	2.45479e27i	−0.590991	+	1.02363i	0.403109	+	0.915152i	$0.367930\pi$
$547$	−1.41727e27	+	2.45479e27i	−0.590991	+	1.02363i	−0.994099	+	0.108474i	$0.965404\pi$
$548$		−	2.16927e26i		−	0.0888194i
$549$		0			0
$550$	4.39603e27			1.73554
$551$	−6.31749e27	−	3.64740e27i	−2.44922	−	1.41406i
$552$		0			0
$553$	−1.49486e25	−	2.58918e25i	−0.00558921	−	0.00968079i
$554$	3.10172e27	−	1.79078e27i	1.13895	−	0.657574i
$555$		0			0
$556$	−1.44894e26	+	2.50963e26i	−0.0513218	+	0.0888919i
$557$		−	1.69901e27i		−	0.591078i	−0.955331	−	0.295539i	$-0.904501\pi$
$557$		−	1.69901e27i		−	0.591078i	0.955331	−	0.295539i	$-0.0954992\pi$
$558$		0			0
$559$	4.32254e27			1.45084
$560$	−3.99399e25	−	2.30593e25i	−0.0131682	−	0.00760266i
$561$		0			0
$562$	−8.73564e26	−	1.51306e27i	−0.277927	−	0.481384i
$563$	−1.43694e27	+	8.29616e26i	−0.449111	+	0.259294i	−0.707455	−	0.706759i	$-0.750157\pi$
$563$	−1.43694e27	+	8.29616e26i	−0.449111	+	0.259294i	0.258344	+	0.966053i	$0.416823\pi$
$564$		0			0
$565$	1.17263e27	−	2.03105e27i	0.353733	−	0.612684i
$566$		−	9.17340e26i		−	0.271873i
$567$		0			0
$568$	1.24898e27			0.357333
$569$	−3.13664e26	−	1.81094e26i	−0.0881743	−	0.0509075i	0.455265	−	0.890356i	$-0.349545\pi$
$569$	−3.13664e26	−	1.81094e26i	−0.0881743	−	0.0509075i	−0.543439	+	0.839449i	$0.682878\pi$
$570$		0			0
$571$	−1.96930e27	−	3.41093e27i	−0.534505	−	0.925790i	−0.999187	−	0.0403121i	$-0.987165\pi$
$571$	−1.96930e27	−	3.41093e27i	−0.534505	−	0.925790i	0.464682	−	0.885477i	$-0.346169\pi$
$572$	2.13624e27	−	1.23336e27i	0.569757	−	0.328949i
$573$		0			0
$574$	2.32984e25	−	4.03540e25i	0.00600077	−	0.0103936i
$575$		−	5.67144e27i		−	1.43554i
$576$		0			0
$577$	7.18896e26			0.175755			0.0878776	−	0.996131i	$-0.471992\pi$
$577$	7.18896e26			0.175755			0.0878776	+	0.996131i	$0.471992\pi$
$578$	1.67395e27	+	9.66455e26i	0.402220	+	0.232222i
$579$		0			0
$580$	2.72022e27	+	4.71155e27i	0.631427	+	1.09366i
$581$	1.72213e26	−	9.94273e25i	0.0392921	−	0.0226853i
$582$		0			0
$583$	5.88847e26	−	1.01991e27i	0.129813	−	0.224842i
$584$		−	2.39850e27i		−	0.519771i
$585$		0			0
$586$	−2.30227e27			−0.482147
$587$	6.27666e27	+	3.62383e27i	1.29225	+	0.746083i	0.979053	−	0.203604i	$-0.0652654\pi$
$587$	6.27666e27	+	3.62383e27i	1.29225	+	0.746083i	0.313201	+	0.949687i	$0.398599\pi$
$588$		0			0
$589$	9.65657e25	+	1.67257e26i	0.0192163	+	0.0332836i
$590$	−6.68352e27	+	3.85873e27i	−1.30763	+	0.754961i
$591$		0			0
$592$	−1.62256e26	+	2.81035e26i	−0.0306890	+	0.0531550i
$593$			6.43054e27i			1.19592i	0.801527	+	0.597958i	$0.204021\pi$
$593$			6.43054e27i			1.19592i	−0.801527	+	0.597958i	$0.795979\pi$
$594$		0			0
$595$	−4.35375e26			−0.0782878
$596$	4.15871e27	+	2.40103e27i	0.735353	+	0.424557i
$597$		0			0
$598$	−1.59119e27	−	2.75602e27i	−0.272088	−	0.471270i
$599$	−6.18517e26	+	3.57101e26i	−0.104012	+	0.0600513i	−0.551104	−	0.834437i	$-0.685793\pi$
$599$	−6.18517e26	+	3.57101e26i	−0.104012	+	0.0600513i	0.447092	+	0.894488i	$0.352460\pi$
$600$		0			0
$601$	−3.35334e27	+	5.80816e27i	−0.545423	+	0.944700i	0.453157	+	0.891431i	$0.350298\pi$
$601$	−3.35334e27	+	5.80816e27i	−0.545423	+	0.944700i	−0.998580	+	0.0532694i	$0.983036\pi$
$602$		−	2.32524e26i		−	0.0371965i
$603$		0			0
$604$	5.35934e27			0.829357
$605$	7.25654e27	+	4.18956e27i	1.10453	+	0.637698i
$606$		0			0
$607$	−1.56164e27	−	2.70484e27i	−0.229982	−	0.398341i	0.727820	−	0.685768i	$-0.240533\pi$
$607$	−1.56164e27	−	2.70484e27i	−0.229982	−	0.398341i	−0.957803	+	0.287427i	$0.907200\pi$
$608$	−1.99862e27	+	1.15390e27i	−0.289531	+	0.167161i
$609$		0			0
$610$	3.10688e27	−	5.38127e27i	0.435538	−	0.754374i
$611$		−	1.22246e27i		−	0.168587i
$612$		0			0
$613$	4.73153e27			0.631534			0.315767	−	0.948837i	$-0.397738\pi$
$613$	4.73153e27			0.631534			0.315767	+	0.948837i	$0.397738\pi$
$614$	−6.00560e27	−	3.46734e27i	−0.788629	−	0.455315i
$615$		0			0
$616$	−6.63464e25	−	1.14915e26i	−0.00843355	−	0.0146073i
$617$	−3.33324e27	+	1.92444e27i	−0.416883	+	0.240688i	−0.693743	−	0.720223i	$-0.744040\pi$
$617$	−3.33324e27	+	1.92444e27i	−0.416883	+	0.240688i	0.276860	+	0.960910i	$0.410706\pi$
$618$		0			0
$619$	−7.59616e27	+	1.31569e28i	−0.919788	+	1.59312i	−0.120053	+	0.992768i	$0.538306\pi$
$619$	−7.59616e27	+	1.31569e28i	−0.919788	+	1.59312i	−0.799736	+	0.600352i	$0.795027\pi$
$620$		−	1.44036e26i		−	0.0171615i
$621$		0			0
$622$	−8.67310e27			−1.00062
$623$	4.59079e26	+	2.65049e26i	0.0521203	+	0.0300917i
$624$		0			0
$625$	−2.63607e27	−	4.56581e27i	−0.289839	−	0.502017i
$626$	2.52091e27	−	1.45545e27i	0.272781	−	0.157490i
$627$		0			0
$628$	−2.65556e27	+	4.59957e27i	−0.278330	+	0.482082i
$629$			3.06350e27i			0.316018i
$630$		0			0
$631$	−4.43236e27			−0.442936			−0.221468	−	0.975168i	$-0.571085\pi$
$631$	−4.43236e27			−0.442936			−0.221468	+	0.975168i	$0.571085\pi$
$632$	9.66286e26	+	5.57885e26i	0.0950462	+	0.0548749i
$633$		0			0
$634$	−6.29180e27	−	1.08977e28i	−0.599628	−	1.03859i
$635$	−8.94059e27	+	5.16185e27i	−0.838743	+	0.484249i
$636$		0			0
$637$	−5.45551e27	+	9.44922e27i	−0.495953	+	0.859017i
$638$			1.56533e28i			1.40087i
$639$		0			0
$640$	1.72115e27			0.149286
$641$	−9.12912e27	−	5.27070e27i	−0.779559	−	0.450078i	0.0567153	−	0.998390i	$-0.481937\pi$
$641$	−9.12912e27	−	5.27070e27i	−0.779559	−	0.450078i	−0.836274	+	0.548312i	$0.815271\pi$
$642$		0			0
$643$	2.39714e26	+	4.15196e26i	0.0198419	+	0.0343672i	0.875776	−	0.482718i	$-0.160350\pi$
$643$	2.39714e26	+	4.15196e26i	0.0198419	+	0.0343672i	−0.855934	+	0.517085i	$0.827017\pi$
$644$	−1.48255e26	+	8.55953e25i	−0.0120824	+	0.00697575i
$645$		0			0
$646$	−1.08932e28	+	1.88677e28i	−0.860661	+	1.49071i
$647$			1.79252e28i			1.39451i	0.716823	+	0.697255i	$0.245595\pi$
$647$			1.79252e28i			1.39451i	−0.716823	+	0.697255i	$0.754405\pi$
$648$		0			0
$649$	−2.22048e28			−1.67494
$650$	−1.51698e28	−	8.75826e27i	−1.12680	−	0.650555i
$651$		0			0
$652$	5.59186e26	+	9.68539e26i	0.0402792	+	0.0697656i
$653$	2.20534e27	−	1.27326e27i	0.156439	−	0.0903199i	−0.419737	−	0.907646i	$-0.637878\pi$
$653$	2.20534e27	−	1.27326e27i	0.156439	−	0.0903199i	0.576176	+	0.817326i	$0.304544\pi$
$654$		0			0
$655$	5.86533e27	−	1.01590e28i	0.403533	−	0.698940i
$656$			1.73900e27i			0.117831i
$657$		0			0
$658$	−6.57605e25			−0.00432221
$659$	−6.74038e27	−	3.89156e27i	−0.436345	−	0.251924i	0.265701	−	0.964056i	$-0.414397\pi$
$659$	−6.74038e27	−	3.89156e27i	−0.436345	−	0.251924i	−0.702046	+	0.712131i	$0.747730\pi$
$660$		0			0
$661$	9.66007e27	+	1.67317e28i	0.606689	+	1.05082i	0.991782	+	0.127938i	$0.0408358\pi$
$661$	9.66007e27	+	1.67317e28i	0.606689	+	1.05082i	−0.385094	+	0.922878i	$0.625831\pi$
$662$	3.14270e27	−	1.81444e27i	0.194412	−	0.112244i
$663$		0			0
$664$	−3.71064e27	+	6.42702e27i	−0.222725	+	0.385770i
$665$		−	1.94541e27i		−	0.115026i
$666$		0			0
$667$	2.01947e28			1.15872
$668$	5.65590e27	+	3.26544e27i	0.319696	+	0.184577i
$669$		0			0
$670$	−9.98951e27	−	1.73023e28i	−0.548020	−	0.949198i
$671$	1.54831e28	−	8.93914e27i	0.836819	−	0.483137i
$672$		0			0
$673$	1.63888e28	−	2.83863e28i	0.859800	−	1.48922i	−0.0123185	−	0.999924i	$-0.503921\pi$
$673$	1.63888e28	−	2.83863e28i	0.859800	−	1.48922i	0.872119	−	0.489294i	$-0.162745\pi$
$674$			2.27552e28i			1.17620i
$675$		0			0
$676$	1.35151e26			0.00678194
$677$	−9.74252e27	−	5.62485e27i	−0.481709	−	0.278115i	0.239419	−	0.970916i	$-0.423043\pi$
$677$	−9.74252e27	−	5.62485e27i	−0.481709	−	0.278115i	−0.721128	+	0.692801i	$0.756376\pi$
$678$		0			0
$679$	−5.07788e25	−	8.79515e25i	−0.00243773	−	0.00422227i
$680$	1.40714e28	−	8.12413e27i	0.665654	−	0.384315i
$681$		0			0
$682$	2.07211e26	−	3.58901e26i	0.00951853	−	0.0164866i
$683$			3.22277e28i			1.45889i	0.684040	+	0.729445i	$0.260222\pi$
$683$			3.22277e28i			1.45889i	−0.684040	+	0.729445i	$0.739778\pi$
$684$		0			0
$685$	−6.82446e27			−0.300029
$686$	1.01727e27	+	5.87321e26i	0.0440753	+	0.0254469i
$687$		0			0
$688$	4.33891e27	+	7.51521e27i	0.182598	+	0.316269i
$689$	−4.06396e27	+	2.34633e27i	−0.168561	+	0.0973188i
$690$		0			0
$691$	1.49956e28	−	2.59732e28i	0.604204	−	1.04651i	−0.387973	−	0.921671i	$-0.626824\pi$
$691$	1.49956e28	−	2.59732e28i	0.604204	−	1.04651i	0.992177	−	0.124841i	$-0.0398422\pi$
$692$		−	1.81499e28i		−	0.720796i
$693$		0			0
$694$	1.81506e28			0.700321
$695$	7.89523e27	+	4.55831e27i	0.300273	+	0.173363i
$696$		0			0
$697$	8.20837e27	+	1.42173e28i	0.303340	+	0.525399i
$698$	−1.31345e28	+	7.58321e27i	−0.478475	+	0.276248i
$699$		0			0
$700$	−4.71136e26	+	8.16032e26i	−0.0166788	+	0.0288886i
$701$		−	3.44034e28i		−	1.20066i	−0.799751	−	0.600332i	$-0.795035\pi$
$701$		−	3.44034e28i		−	1.20066i	0.799751	−	0.600332i	$-0.204965\pi$
$702$		0			0
$703$	−1.36888e28			−0.464315
$704$	4.28866e27	+	2.47606e27i	0.143415	+	0.0828008i
$705$		0			0
$706$	1.77506e28	+	3.07449e28i	0.576987	+	0.999370i
$707$	−8.28520e26	+	4.78346e26i	−0.0265527	+	0.0153302i
$708$		0			0
$709$	−7.50851e27	+	1.30051e28i	−0.233933	+	0.405184i	−0.958962	−	0.283534i	$-0.908493\pi$
$709$	−7.50851e27	+	1.30051e28i	−0.233933	+	0.405184i	0.725029	+	0.688718i	$0.241826\pi$
$710$		−	3.92926e28i		−	1.20706i
$711$		0			0
$712$	−1.97834e28			−0.590881
$713$	−4.63027e26	−	2.67329e26i	−0.0136368	−	0.00787319i
$714$		0			0
$715$	−3.88011e28	−	6.72055e28i	−1.11118	−	1.92462i
$716$	−7.53709e27	+	4.35154e27i	−0.212850	+	0.122889i
$717$		0			0
$718$	−1.08321e28	+	1.87618e28i	−0.297488	+	0.515264i
$719$			5.73497e28i			1.55325i	0.629961	+	0.776627i	$0.283071\pi$
$719$			5.73497e28i			1.55325i	−0.629961	+	0.776627i	$0.716929\pi$
$720$		0			0
$721$	−4.81158e26			−0.0126746
$722$	−6.07359e28	−	3.50659e28i	−1.57788	−	0.910988i
$723$		0			0
$724$	−8.38720e27	−	1.45270e28i	−0.211949	−	0.367106i
$725$	9.62640e28	−	5.55781e28i	2.39930	−	1.38523i
$726$		0			0
$727$	−1.94524e28	+	3.36925e28i	−0.471659	+	0.816938i	−0.999474	−	0.0324216i	$-0.989678\pi$
$727$	−1.94524e28	+	3.36925e28i	−0.471659	+	0.816938i	0.527815	+	0.849359i	$0.323011\pi$
$728$			5.28730e26i			0.0126451i
$729$		0			0
$730$	−7.54563e28			−1.75577
$731$	7.09461e28	+	4.09608e28i	1.62838	+	0.940144i
$732$		0			0
$733$	1.43366e28	+	2.48318e28i	0.320190	+	0.554585i	0.980527	−	0.196384i	$-0.0629199\pi$
$733$	1.43366e28	+	2.48318e28i	0.320190	+	0.554585i	−0.660337	+	0.750969i	$0.729587\pi$
$734$	−1.55155e28	+	8.95790e27i	−0.341827	+	0.197354i
$735$		0			0
$736$	3.19443e27	−	5.53291e27i	0.0684881	−	0.118625i
$737$		−	5.74838e28i		−	1.21582i
$738$		0			0
$739$	5.53418e28			1.13922			0.569612	−	0.821914i	$-0.307094\pi$
$739$	5.53418e28			1.13922			0.569612	+	0.821914i	$0.307094\pi$
$740$	8.84130e27	+	5.10452e27i	0.179556	+	0.103666i
$741$		0			0
$742$	1.26217e26	+	2.18614e26i	0.00249504	+	0.00432154i
$743$	−9.71906e27	+	5.61130e27i	−0.189555	+	0.109440i	−0.591774	−	0.806104i	$-0.701572\pi$
$743$	−9.71906e27	+	5.61130e27i	−0.189555	+	0.109440i	0.402219	+	0.915543i	$0.368239\pi$
$744$		0			0
$745$	7.55358e28	−	1.30832e29i	1.43414	−	2.48400i
$746$			1.95143e28i			0.365564i
$747$		0			0
$748$	4.67497e28			0.852634
$749$	1.31970e27	+	7.61930e26i	0.0237497	+	0.0137119i
$750$		0			0
$751$	3.50210e28	+	6.06582e28i	0.613662	+	1.06289i	0.990618	+	0.136662i	$0.0436376\pi$
$751$	3.50210e28	+	6.06582e28i	0.613662	+	1.06289i	−0.376956	+	0.926231i	$0.623029\pi$
$752$	2.12539e27	−	1.22710e27i	0.0367503	−	0.0212178i
$753$		0			0
$754$	3.11861e28	−	5.40160e28i	0.525107	−	0.909513i
$755$		−	1.68603e29i		−	2.80154i
$756$		0			0
$757$	4.39619e28			0.711407			0.355703	−	0.934599i	$-0.384241\pi$
$757$	4.39619e28			0.711407			0.355703	+	0.934599i	$0.384241\pi$
$758$	−5.76057e28	−	3.32587e28i	−0.919969	−	0.531144i
$759$		0			0
$760$	3.63015e28	+	6.28761e28i	0.564662	+	0.978024i
$761$	−7.54570e28	+	4.35651e28i	−1.15838	+	0.668794i	−0.950916	−	0.309448i	$-0.899856\pi$
$761$	−7.54570e28	+	4.35651e28i	−1.15838	+	0.668794i	−0.207468	+	0.978242i	$0.566522\pi$
$762$		0			0
$763$	7.20204e25	−	1.24743e26i	0.00107699	−	0.00186539i
$764$			2.53962e28i			0.374831i
$765$		0			0
$766$	−6.45970e28			−0.928806
$767$	7.66238e28	+	4.42387e28i	1.08745	+	0.627840i
$768$		0			0
$769$	2.32555e28	+	4.02797e28i	0.321560	+	0.556958i	0.980810	−	0.194966i	$-0.0624595\pi$
$769$	2.32555e28	+	4.02797e28i	0.321560	+	0.556958i	−0.659250	+	0.751924i	$0.729126\pi$
$770$	−3.61521e27	+	2.08724e27i	−0.0493430	+	0.0284882i
$771$		0			0
$772$	−2.44766e27	+	4.23947e27i	−0.0325520	+	0.0563817i
$773$			5.82042e28i			0.764116i	0.924138	+	0.382058i	$0.124785\pi$
$773$			5.82042e28i			0.764116i	−0.924138	+	0.382058i	$0.875215\pi$
$774$		0			0
$775$	−2.94288e27			−0.0376492
$776$	3.28236e27	+	1.89507e27i	0.0414543	+	0.0239336i
$777$		0			0
$778$	2.23915e28	+	3.87832e28i	0.275605	+	0.477362i
$779$	−6.35280e28	+	3.66779e28i	−0.771953	+	0.445687i
$780$		0			0
$781$	5.65265e28	−	9.79068e28i	0.669487	−	1.15959i
$782$		−	6.03129e28i		−	0.705250i
$783$		0			0
$784$	−2.19047e28			−0.249676
$785$	1.44701e29	+	8.35432e28i	1.62845	+	0.940188i
$786$		0			0
$787$	4.67861e28	+	8.10358e28i	0.513297	+	0.889057i	0.999881	+	0.0154233i	$0.00490958\pi$
$787$	4.67861e28	+	8.10358e28i	0.513297	+	0.889057i	−0.486584	+	0.873634i	$0.661757\pi$
$788$	6.23018e28	−	3.59699e28i	0.674898	−	0.389653i
$789$		0			0
$790$	1.75509e28	−	3.03991e28i	0.185365	−	0.321062i
$791$			1.44636e27i			0.0150839i
$792$		0			0
$793$	−7.12382e28			−0.724404
$794$	−2.26985e28	−	1.31050e28i	−0.227925	−	0.131593i
$795$		0			0
$796$	3.75865e28	+	6.51018e28i	0.368046	+	0.637474i
$797$	−9.97801e27	+	5.76081e27i	−0.0964852	+	0.0557058i	−0.547466	−	0.836828i	$-0.684408\pi$
$797$	−9.97801e27	+	5.76081e27i	−0.0964852	+	0.0557058i	0.450981	+	0.892534i	$0.351074\pi$
$798$		0			0
$799$	1.15842e28	−	2.00644e28i	0.109244	−	0.189216i
$800$		−	3.51657e28i		−	0.327506i
$801$		0			0
$802$	5.23091e28			0.475153
$803$	−1.88017e29	−	1.08552e29i	−1.68672	−	0.973826i
$804$		0			0
$805$	2.69280e27	+	4.66407e27i	0.0235638	+	0.0408137i
$806$	−1.43008e27	+	8.25659e26i	−0.0123598	+	0.00713592i
$807$		0			0
$808$	1.78519e28	−	3.09205e28i	0.150512	−	0.260695i
$809$		−	9.08321e28i		−	0.756404i	−0.925723	−	0.378202i	$-0.876542\pi$
$809$		−	9.08321e28i		−	0.756404i	0.925723	−	0.378202i	$-0.123458\pi$
$810$		0			0
$811$	1.00676e28			0.0817932			0.0408966	−	0.999163i	$-0.486979\pi$
$811$	1.00676e28			0.0817932			0.0408966	+	0.999163i	$0.486979\pi$
$812$	−2.90570e27	−	1.67761e27i	−0.0233179	−	0.0134626i
$813$		0			0
$814$	1.46868e28	+	2.54383e28i	0.114996	+	0.199179i
$815$	3.04700e28	−	1.75918e28i	0.235665	−	0.136062i
$816$		0			0
$817$	−1.83027e29	+	3.17013e29i	−1.38132	+	2.39252i
$818$			6.93243e28i			0.516836i
$819$		0			0
$820$	5.47084e28			0.398030
$821$	−2.02346e29	−	1.16824e29i	−1.45433	−	0.839656i	−0.455604	−	0.890183i	$-0.650577\pi$
$821$	−2.02346e29	−	1.16824e29i	−1.45433	−	0.839656i	−0.998723	+	0.0505266i	$0.983910\pi$
$822$		0			0
$823$	−1.04115e29	−	1.80332e29i	−0.730320	−	1.26495i	−0.956746	−	0.290923i	$-0.906038\pi$
$823$	−1.04115e29	−	1.80332e29i	−0.730320	−	1.26495i	0.226427	−	0.974028i	$-0.427296\pi$
$824$	1.55511e28	−	8.97845e27i	0.107768	−	0.0622199i
$825$		0			0
$826$	2.37975e27	−	4.12185e27i	0.0160965	−	0.0278799i
$827$			1.53369e28i			0.102490i	0.998686	+	0.0512450i	$0.0163189\pi$
$827$			1.53369e28i			0.102490i	−0.998686	+	0.0512450i	$0.983681\pi$
$828$		0			0
$829$	−1.08449e29			−0.707426			−0.353713	−	0.935354i	$-0.615081\pi$
$829$	−1.08449e29			−0.707426			−0.353713	+	0.935354i	$0.615081\pi$
$830$	2.02192e29	+	1.16736e29i	1.30312	+	0.752355i
$831$		0			0
$832$	−9.86615e27	−	1.70887e28i	−0.0620747	−	0.107517i
$833$	−1.79083e29	+	1.03394e29i	−1.11328	+	0.642754i
$834$		0			0
$835$	1.02730e29	−	1.77933e29i	0.623493	−	1.07992i
$836$			2.08894e29i			1.25275i
$837$		0			0
$838$	−1.93802e29			−1.13480
$839$	7.78720e27	+	4.49594e27i	0.0450569	+	0.0260136i	0.522359	−	0.852726i	$-0.325052\pi$
$839$	7.78720e27	+	4.49594e27i	0.0450569	+	0.0260136i	−0.477302	+	0.878739i	$0.658385\pi$
$840$		0			0
$841$	1.09403e29	+	1.89492e29i	0.618117	+	1.07061i
$842$	−2.76275e28	+	1.59507e28i	−0.154248	+	0.0890554i
$843$		0			0
$844$	−3.76894e28	+	6.52800e28i	−0.205492	+	0.355923i
$845$		−	4.25183e27i		−	0.0229091i
$846$		0			0
$847$	−5.16756e27			−0.0271926
$848$	−8.15871e27	−	4.71043e27i	−0.0424290	−	0.0244964i
$849$		0			0
$850$	−1.65988e29	−	2.87500e29i	−0.843117	−	1.46032i
$851$	3.28186e28	−	1.89478e28i	0.164749	−	0.0951181i
$852$		0			0
$853$	1.41583e29	−	2.45230e29i	0.694259	−	1.20249i	−0.276170	−	0.961109i	$-0.589065\pi$
$853$	1.41583e29	−	2.45230e29i	0.694259	−	1.20249i	0.970430	−	0.241384i	$-0.0776013\pi$
$854$			3.83214e27i			0.0185722i
$855$		0			0
$856$	−5.68707e28			−0.269247
$857$	3.28323e29	+	1.89557e29i	1.53636	+	0.887017i	0.999048	+	0.0436324i	$0.0138930\pi$
$857$	3.28323e29	+	1.89557e29i	1.53636	+	0.887017i	0.537311	+	0.843384i	$0.319440\pi$
$858$		0			0
$859$	−4.85967e28	−	8.41719e28i	−0.222165	−	0.384800i	0.733300	−	0.679905i	$-0.237979\pi$
$859$	−4.85967e28	−	8.41719e28i	−0.222165	−	0.384800i	−0.955465	+	0.295104i	$0.904646\pi$
$860$	2.36427e29	−	1.36501e29i	1.06835	−	0.616810i
$861$		0			0
$862$	1.03090e29	−	1.78557e29i	0.455139	−	0.788323i
$863$		−	1.84519e28i		−	0.0805255i	−0.999189	−	0.0402627i	$-0.987181\pi$
$863$		−	1.84519e28i		−	0.0805255i	0.999189	−	0.0402627i	$-0.0128195\pi$
$864$		0			0
$865$	−5.70989e29			−2.43482
$866$	−4.59113e28	−	2.65069e28i	−0.193527	−	0.111733i
$867$		0			0
$868$	4.44149e25	+	7.69289e25i	0.000182950	+	0.000316878i
$869$	8.74645e28	−	5.04977e28i	0.356151	−	0.205624i
$870$		0			0
$871$	−1.14526e29	+	1.98364e29i	−0.455744	+	0.789372i
$872$			5.37562e27i			0.0211477i
$873$		0			0
$874$	2.69500e29			1.03620
$875$	1.18152e28	+	6.82151e27i	0.0449118	+	0.0259298i
$876$		0			0
$877$	7.63785e28	+	1.32291e29i	0.283776	+	0.491514i	0.972312	−	0.233688i	$-0.0750796\pi$
$877$	7.63785e28	+	1.32291e29i	0.283776	+	0.491514i	−0.688536	+	0.725202i	$0.741746\pi$
$878$	1.78653e29	−	1.03145e29i	0.656242	−	0.378881i
$879$		0			0
$880$	7.78961e28	−	1.34920e29i	0.279698	−	0.484451i
$881$			1.67615e29i			0.595050i	0.954714	+	0.297525i	$0.0961611\pi$
$881$			1.67615e29i			0.595050i	−0.954714	+	0.297525i	$0.903839\pi$
$882$		0			0
$883$	−2.47883e29			−0.860279			−0.430140	−	0.902762i	$-0.641536\pi$
$883$	−2.47883e29			−0.860279			−0.430140	+	0.902762i	$0.641536\pi$
$884$	−1.61323e29	−	9.31398e28i	−0.553571	−	0.319604i
$885$		0			0
$886$	−6.49159e28	−	1.12438e29i	−0.217778	−	0.377203i
$887$	−2.15678e29	+	1.24522e29i	−0.715433	+	0.413055i	−0.813069	−	0.582167i	$-0.802205\pi$
$887$	−2.15678e29	+	1.24522e29i	−0.715433	+	0.413055i	0.0976366	+	0.995222i	$0.468872\pi$
$888$		0			0
$889$	3.18341e27	−	5.51382e27i	0.0103246	−	0.0178828i
$890$			6.22379e29i			1.99597i
$891$		0			0
$892$	−1.84629e28			−0.0578965
$893$	8.96549e28	+	5.17623e28i	0.278009	+	0.160509i
$894$		0			0
$895$	1.36898e29	+	2.37115e29i	0.415114	+	0.718999i
$896$	−9.19257e26	+	5.30733e26i	−0.00275649	+	0.00159146i
$897$		0			0
$898$	−5.31605e28	+	9.20767e28i	−0.155893	+	0.270014i
$899$		−	1.04789e28i		−	0.0303892i
$900$		0			0
$901$	−8.89361e28			−0.252250
$902$	1.36319e29	+	7.87038e28i	0.382376	+	0.220765i
$903$		0			0
$904$	−2.69892e28	−	4.67467e28i	−0.0740468	−	0.128253i
$905$	−4.57017e29	+	2.63859e29i	−1.24007	+	0.715955i
$906$		0			0
$907$	−2.60794e29	+	4.51708e29i	−0.692188	+	1.19891i	0.278931	+	0.960311i	$0.410020\pi$
$907$	−2.60794e29	+	4.51708e29i	−0.692188	+	1.19891i	−0.971119	+	0.238594i	$0.923313\pi$
$908$		−	2.91925e29i		−	0.766324i
$909$		0			0
$910$	1.66337e28			0.0427145
$911$	−1.94996e29	−	1.12581e29i	−0.495269	−	0.285944i	0.231488	−	0.972838i	$-0.425640\pi$
$911$	−1.94996e29	−	1.12581e29i	−0.495269	−	0.285944i	−0.726758	+	0.686894i	$0.758974\pi$
$912$		0			0
$913$	3.35873e29	+	5.81749e29i	0.834579	+	1.44553i
$914$	−4.48161e29	+	2.58746e29i	−1.10147	+	0.635933i
$915$		0			0
$916$	−1.34027e29	+	2.32142e29i	−0.322283	+	0.558211i
$917$			7.23451e27i			0.0172074i
$918$		0			0
$919$	−6.75044e29			−1.57100			−0.785501	−	0.618860i	$-0.787595\pi$
$919$	−6.75044e29			−1.57100			−0.785501	+	0.618860i	$0.787595\pi$
$920$	−1.74064e29	−	1.00496e29i	−0.400710	−	0.231350i
$921$		0			0
$922$	2.54294e29	+	4.40450e29i	0.572832	+	0.992173i
$923$	−3.90121e29	+	2.25237e29i	−0.869326	+	0.501906i
$924$		0			0
$925$	1.04293e29	−	1.80641e29i	0.227425	−	0.393912i
$926$		−	1.60214e29i		−	0.345614i
$927$		0			0
$928$	1.25217e29			0.264353
$929$	1.51840e29	+	8.76649e28i	0.317124	+	0.183092i	0.650110	−	0.759840i	$-0.274723\pi$
$929$	1.51840e29	+	8.76649e28i	0.317124	+	0.183092i	−0.332986	+	0.942932i	$0.608056\pi$
$930$		0			0
$931$	−4.62000e29	−	8.00208e29i	−0.944377	−	1.63571i
$932$	−1.43266e29	+	8.27144e28i	−0.289723	+	0.167271i
$933$		0			0
$934$	1.00162e29	−	1.73487e29i	0.198261	−	0.343397i
$935$		−	1.47073e30i		−	2.88016i
$936$		0			0
$937$	3.25202e29			0.623387			0.311693	−	0.950183i	$-0.399104\pi$
$937$	3.25202e29			0.623387			0.311693	+	0.950183i	$0.399104\pi$
$938$	1.06707e28	+	6.16071e27i	0.0202378	+	0.0116843i
$939$		0			0
$940$	−3.86041e28	−	6.68642e28i	−0.0716728	−	0.124141i
$941$	−5.13514e29	+	2.96478e29i	−0.943314	+	0.544623i	−0.890998	−	0.454008i	$-0.849994\pi$
$941$	−5.13514e29	+	2.96478e29i	−0.943314	+	0.544623i	−0.0523164	+	0.998631i	$0.516660\pi$
$942$		0			0
$943$	1.01538e29	−	1.75869e29i	0.182604	−	0.316280i
$944$			1.77625e29i			0.316071i
$945$		0			0
$946$	7.85483e29			1.36844
$947$	−1.58974e29	−	9.17838e28i	−0.274048	−	0.158222i	0.356678	−	0.934227i	$-0.383909\pi$
$947$	−1.58974e29	−	9.17838e28i	−0.274048	−	0.158222i	−0.630726	+	0.776006i	$0.717243\pi$
$948$		0			0
$949$	4.32537e29	+	7.49176e29i	0.730065	+	1.26451i
$950$	1.28465e30	−	7.41694e29i	2.14560	−	1.23876i
$951$		0			0
$952$	−5.01030e27	+	8.67809e27i	−0.00819397	+	0.0141924i
$953$			1.07797e30i			1.74453i	0.489032	+	0.872266i	$0.337350\pi$
$953$			1.07797e30i			1.74453i	−0.489032	+	0.872266i	$0.662650\pi$
$954$		0			0
$955$	7.98958e29			1.26617
$956$	2.63627e29	+	1.52205e29i	0.413439	+	0.238699i
$957$		0			0
$958$	1.26237e29	+	2.18649e29i	0.193879	+	0.335808i
$959$	3.64490e27	−	2.10438e27i	0.00553987	−	0.00319845i
$960$		0			0
$961$	3.35757e29	−	5.81547e29i	0.499794	−	0.865668i
$962$		−	1.17042e29i		−	0.172422i
$963$		0			0
$964$	1.91073e29			0.275695
$965$	1.33372e29	+	7.70026e28i	0.190455	+	0.109959i
$966$		0			0
$967$	−2.72141e29	−	4.71362e29i	−0.380653	−	0.659311i	0.610503	−	0.792014i	$-0.290967\pi$
$967$	−2.72141e29	−	4.71362e29i	−0.380653	−	0.659311i	−0.991156	+	0.132704i	$0.957634\pi$
$968$	1.67017e29	−	9.64271e28i	0.231210	−	0.133489i
$969$		0			0
$970$	5.96185e28	−	1.03262e29i	0.0808469	−	0.140031i
$971$			1.22935e29i			0.164999i	0.996591	+	0.0824997i	$0.0262903\pi$
$971$			1.22935e29i			0.164999i	−0.996591	+	0.0824997i	$0.973710\pi$
$972$		0			0
$973$	−5.62239e27			−0.00739252
$974$	−6.16170e29	−	3.55746e29i	−0.801883	−	0.462968i
$975$		0			0
$976$	−7.15080e28	−	1.23855e29i	−0.0911709	−	0.157913i
$977$	2.66367e29	−	1.53787e29i	0.336151	−	0.194077i	−0.322418	−	0.946597i	$-0.604496\pi$
$977$	2.66367e29	−	1.53787e29i	0.336151	−	0.194077i	0.658569	+	0.752521i	$0.271162\pi$
$978$		0			0
$979$	−8.95358e29	+	1.55080e30i	−1.10706	+	1.91748i
$980$			6.89115e29i			0.843395i
$981$		0			0
$982$	−9.25297e28			−0.110960
$983$	−2.02787e29	−	1.17079e29i	−0.240716	−	0.138977i	0.374790	−	0.927110i	$-0.377715\pi$
$983$	−2.02787e29	−	1.17079e29i	−0.240716	−	0.138977i	−0.615506	+	0.788133i	$0.711048\pi$
$984$		0			0
$985$	−1.13160e30	−	1.96000e30i	−1.31623	−	2.27978i
$986$	1.02372e30	−	5.91045e29i	1.17872	−	0.680537i
$987$		0			0
$988$	4.16182e29	−	7.20848e29i	0.469584	−	0.813344i
$989$		−	1.01337e30i		−	1.13190i
$990$		0			0
$991$	1.59921e30			1.75053			0.875265	−	0.483644i	$-0.160687\pi$
$991$	1.59921e30			1.75053			0.875265	+	0.483644i	$0.160687\pi$
$992$	−2.87100e27	−	1.65757e27i	−0.00311112	−	0.00179620i
$993$		0			0
$994$	1.21162e28	+	2.09859e28i	0.0128678	+	0.0222877i
$995$	2.04808e30	−	1.18246e30i	2.15336	−	1.24324i
$996$		0			0
$997$	8.93236e29	−	1.54713e30i	0.920480	−	1.59432i	0.121807	−	0.992554i	$-0.461131\pi$
$997$	8.93236e29	−	1.54713e30i	0.920480	−	1.59432i	0.798674	−	0.601764i	$-0.205535\pi$
$998$			6.53230e29i			0.666440i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.21.d.a.35.9		40
3.2	odd	2		18.21.d.a.11.12	yes	40
9.4	even	3		18.21.d.a.5.12	✓	40
9.5	odd	6	inner	54.21.d.a.17.9		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.21.d.a.5.12	✓	40	9.4	even	3
18.21.d.a.11.12	yes	40	3.2	odd	2
54.21.d.a.17.9		40	9.5	odd	6	inner
54.21.d.a.35.9		40	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:	\( N \)	\(=\)	\( 54 = 2 \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 21 \)
Character orbit:	\([\chi]\)	\(=\)	54.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-627.069 - 362.039i) q^{2} +(262144. + 454047. i) q^{4} +(1.42842e7 - 8.24698e6i) q^{5} +(-5.08606e6 + 8.80931e6i) q^{7} -3.79625e8i q^{8} -1.19429e10 q^{10} +(-2.97586e10 - 1.71811e10i) q^{11} +(6.84602e10 + 1.18577e11i) q^{13} +(6.37862e9 - 3.68270e9i) q^{14} +(-1.37439e11 + 2.38051e11i) q^{16} +2.59494e12i q^{17} -1.15951e13 q^{19} +(7.48903e12 + 4.32379e12i) q^{20} +(1.24405e13 + 2.15475e13i) q^{22} +(2.77990e13 - 1.60498e13i) q^{23} +(8.83415e13 - 1.53012e14i) q^{25} -9.91409e13i q^{26} -5.33312e12 q^{28} +(5.44840e14 + 3.14564e14i) q^{29} +(-8.32813e12 - 1.44248e13i) q^{31} +(1.72368e14 - 9.95164e13i) q^{32} +(9.39469e14 - 1.62721e15i) q^{34} +1.67778e14i q^{35} +1.18057e15 q^{37} +(7.27094e15 + 4.19788e15i) q^{38} +(-3.13076e15 - 5.42263e15i) q^{40} +(5.47886e15 - 3.16322e15i) q^{41} +(1.57849e16 - 2.73402e16i) q^{43} -1.80157e16i q^{44} -2.32425e16 q^{46} +(-7.73213e15 - 4.46415e15i) q^{47} +(3.98444e16 + 6.90125e16i) q^{49} +(-1.10793e17 + 6.39661e16i) q^{50} +(-3.58928e16 + 6.21682e16i) q^{52} +3.42729e16i q^{53} -5.66769e17 q^{55} +(3.34424e15 + 1.93080e15i) q^{56} +(-2.27768e17 - 3.94507e17i) q^{58} +(5.59623e17 - 3.23098e17i) q^{59} +(-2.60145e17 + 4.50584e17i) q^{61} +1.20604e16i q^{62} -1.44115e17 q^{64} +(1.95580e18 + 1.12918e18i) q^{65} +(8.36439e17 + 1.44876e18i) q^{67} +(-1.17822e18 + 6.80248e17i) q^{68} +(6.07423e16 - 1.05209e17i) q^{70} +3.29004e18i q^{71} +6.31809e18 q^{73} +(-7.40297e17 - 4.27411e17i) q^{74} +(-3.03959e18 - 5.26472e18i) q^{76} +(3.02708e17 - 1.74768e17i) q^{77} +(-1.46957e18 + 2.54537e18i) q^{79} +4.53382e18i q^{80} -4.58083e18 q^{82} +(-1.69299e19 - 9.77449e18i) q^{83} +(2.14004e19 + 3.70666e19i) q^{85} +(-1.97964e19 + 1.14295e19i) q^{86} +(-6.52238e18 + 1.12971e19i) q^{88} -5.21129e19i q^{89} -1.39277e18 q^{91} +(1.45747e19 + 8.41469e18i) q^{92} +(3.23239e18 + 5.59866e18i) q^{94} +(-1.65627e20 + 9.56247e19i) q^{95} +(-4.99196e18 + 8.64633e18i) q^{97} -5.77009e19i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 10485760 q^{4} - 29763918 q^{5} + 133479866 q^{7} + 35793208728 q^{11} + 39827158550 q^{13} - 187564400640 q^{14} - 5497558138880 q^{16} - 10560819523540 q^{19} - 15604865040384 q^{20} + 10829007458304 q^{22}+ \cdots - 66\!\cdots\!16 q^{97}+O(q^{100}) \) 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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