LMFDB - Embedded newform 54.21.d.a.17.20

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			17.20
Character	$\chi$	$=$	54.17
Dual form			54.21.d.a.35.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(627.069 - 362.039i) q^{2} +(262144. - 454047. i) q^{4} +(-1.35661e7 - 7.83237e6i) q^{5} +(-1.44553e8 - 2.50374e8i) q^{7} -3.79625e8i q^{8} -1.13425e10 q^{10} +(-2.16289e8 + 1.24874e8i) q^{11} +(-1.02318e11 + 1.77219e11i) q^{13} +(-1.81290e11 - 1.04668e11i) q^{14} +(-1.37439e11 - 2.38051e11i) q^{16} +3.27084e12i q^{17} +6.83256e12 q^{19} +(-7.11253e12 + 4.10642e12i) q^{20} +(-9.04188e10 + 1.56610e11i) q^{22} +(1.99240e13 + 1.15031e13i) q^{23} +(7.50084e13 + 1.29918e14i) q^{25} +1.48172e14i q^{26} -1.51575e14 q^{28} +(4.37882e13 - 2.52811e13i) q^{29} +(-5.34721e13 + 9.26164e13i) q^{31} +(-1.72368e14 - 9.95164e13i) q^{32} +(1.18417e15 + 2.05104e15i) q^{34} +4.52878e15i q^{35} -6.08677e15 q^{37} +(4.28449e15 - 2.47365e15i) q^{38} +(-2.97336e15 + 5.15002e15i) q^{40} +(1.11337e16 + 6.42805e15i) q^{41} +(-1.04115e16 - 1.80333e16i) q^{43} +1.30940e14i q^{44} +1.66583e16 q^{46} +(3.71215e16 - 2.14321e16i) q^{47} +(-1.89519e15 + 3.28256e15i) q^{49} +(9.40709e16 + 5.43119e16i) q^{50} +(5.36439e16 + 9.29140e16i) q^{52} -2.87385e17i q^{53} +3.91225e15 q^{55} +(-9.50481e16 + 5.48761e16i) q^{56} +(1.83055e16 - 3.17061e16i) q^{58} +(-3.86495e17 - 2.23143e17i) q^{59} +(-4.61942e17 - 8.00108e17i) q^{61} +7.74359e16i q^{62} -1.44115e17 q^{64} +(2.77610e18 - 1.60278e18i) q^{65} +(-1.15505e18 + 2.00061e18i) q^{67} +(1.48511e18 + 8.57431e17i) q^{68} +(1.63959e18 + 2.83986e18i) q^{70} -4.08371e17i q^{71} -5.70990e18 q^{73} +(-3.81683e18 + 2.20365e18i) q^{74} +(1.79111e18 - 3.10230e18i) q^{76} +(6.25306e16 + 3.61020e16i) q^{77} +(7.17413e18 + 1.24260e19i) q^{79} +4.30589e18i q^{80} +9.30881e18 q^{82} +(1.76947e19 - 1.02160e19i) q^{83} +(2.56184e19 - 4.43724e19i) q^{85} +(-1.30575e19 - 7.53876e18i) q^{86} +(4.74055e16 + 8.21087e16i) q^{88} -8.44270e18i q^{89} +5.91614e19 q^{91} +(1.04459e19 - 6.03096e18i) q^{92} +(1.55185e19 - 2.68788e19i) q^{94} +(-9.26910e19 - 5.35152e19i) q^{95} +(9.95365e18 + 1.72402e19i) q^{97} +2.74453e18i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.35661e7	−	7.83237e6i	−1.38917	−	0.802035i	−0.395944	−	0.918275i	$-0.629583\pi$
$5$	−1.35661e7	−	7.83237e6i	−1.38917	−	0.802035i	−0.993221	+	0.116240i	$0.962916\pi$
$6$		0			0
$7$	−1.44553e8	−	2.50374e8i	−0.511738	−	0.886356i	−0.999907	−	0.0136073i	$-0.995669\pi$
$7$	−1.44553e8	−	2.50374e8i	−0.511738	−	0.886356i	0.488169	−	0.872749i	$-0.337665\pi$
$8$		−	3.79625e8i		−	0.353553i
$9$		0			0
$10$	−1.13425e10			−1.13425
$11$	−2.16289e8	+	1.24874e8i	−0.00833887	+	0.00481445i	−0.504164	−	0.863608i	$-0.668199\pi$
$11$	−2.16289e8	+	1.24874e8i	−0.00833887	+	0.00481445i	0.495825	+	0.868423i	$0.334866\pi$
$12$		0			0
$13$	−1.02318e11	+	1.77219e11i	−0.742193	+	1.28552i	0.209302	+	0.977851i	$0.432881\pi$
$13$	−1.02318e11	+	1.77219e11i	−0.742193	+	1.28552i	−0.951495	+	0.307665i	$0.900452\pi$
$14$	−1.81290e11	−	1.04668e11i	−0.626748	−	0.361853i
$15$		0			0
$16$	−1.37439e11	−	2.38051e11i	−0.125000	−	0.216506i
$17$			3.27084e12i			1.62245i	0.584737	+	0.811223i	$0.301198\pi$
$17$			3.27084e12i			1.62245i	−0.584737	+	0.811223i	$0.698802\pi$
$18$		0			0
$19$	6.83256e12			1.11442			0.557208	−	0.830373i	$-0.311873\pi$
$19$	6.83256e12			1.11442			0.557208	+	0.830373i	$0.311873\pi$
$20$	−7.11253e12	+	4.10642e12i	−0.694583	+	0.401017i
$21$		0			0
$22$	−9.04188e10	+	1.56610e11i	−0.00340433	+	0.00589647i
$23$	1.99240e13	+	1.15031e13i	0.480948	+	0.277676i	0.720812	−	0.693131i	$-0.243769\pi$
$23$	1.99240e13	+	1.15031e13i	0.480948	+	0.277676i	−0.239863	+	0.970807i	$0.577103\pi$
$24$		0			0
$25$	7.50084e13	+	1.29918e14i	0.786520	+	1.36229i
$26$			1.48172e14i			1.04962i
$27$		0			0
$28$	−1.51575e14			−0.511738
$29$	4.37882e13	−	2.52811e13i	0.104082	−	0.0600920i	−0.447055	−	0.894506i	$-0.647527\pi$
$29$	4.37882e13	−	2.52811e13i	0.104082	−	0.0600920i	0.551138	+	0.834414i	$0.314194\pi$
$30$		0			0
$31$	−5.34721e13	+	9.26164e13i	−0.0652394	+	0.112998i	−0.896800	−	0.442436i	$-0.854114\pi$
$31$	−5.34721e13	+	9.26164e13i	−0.0652394	+	0.112998i	0.831561	+	0.555434i	$0.187448\pi$
$32$	−1.72368e14	−	9.95164e13i	−0.153093	−	0.0883883i
$33$		0			0
$34$	1.18417e15	+	2.05104e15i	0.573621	+	0.993541i
$35$			4.52878e15i			1.64173i
$36$		0			0
$37$	−6.08677e15			−1.26581			−0.632906	−	0.774228i	$-0.718138\pi$
$37$	−6.08677e15			−1.26581			−0.632906	+	0.774228i	$0.718138\pi$
$38$	4.28449e15	−	2.47365e15i	0.682438	−	0.394006i
$39$		0			0
$40$	−2.97336e15	+	5.15002e15i	−0.283562	+	0.491144i
$41$	1.11337e16	+	6.42805e15i	0.829471	+	0.478896i	0.853672	−	0.520812i	$-0.174371\pi$
$41$	1.11337e16	+	6.42805e15i	0.829471	+	0.478896i	−0.0242002	+	0.999707i	$0.507704\pi$
$42$		0			0
$43$	−1.04115e16	−	1.80333e16i	−0.481760	−	0.834433i	0.518021	−	0.855368i	$-0.326669\pi$
$43$	−1.04115e16	−	1.80333e16i	−0.481760	−	0.834433i	−0.999781	+	0.0209353i	$0.993336\pi$
$44$			1.30940e14i			0.00481445i
$45$		0			0
$46$	1.66583e16			0.392693
$47$	3.71215e16	−	2.14321e16i	0.705744	−	0.407461i	−0.103740	−	0.994605i	$-0.533081\pi$
$47$	3.71215e16	−	2.14321e16i	0.705744	−	0.407461i	0.809483	+	0.587143i	$0.199747\pi$
$48$		0			0
$49$	−1.89519e15	+	3.28256e15i	−0.0237515	+	0.0411389i
$50$	9.40709e16	+	5.43119e16i	0.963286	+	0.556154i
$51$		0			0
$52$	5.36439e16	+	9.29140e16i	0.371097	+	0.642758i
$53$		−	2.87385e17i		−	1.64326i	−0.570024	−	0.821628i	$-0.693066\pi$
$53$		−	2.87385e17i		−	1.64326i	0.570024	−	0.821628i	$-0.306934\pi$
$54$		0			0
$55$	3.91225e15			0.0154454
$56$	−9.50481e16	+	5.48761e16i	−0.313374	+	0.180927i
$57$		0			0
$58$	1.83055e16	−	3.17061e16i	0.0424915	−	0.0735974i
$59$	−3.86495e17	−	2.23143e17i	−0.756177	−	0.436579i	0.0717445	−	0.997423i	$-0.477143\pi$
$59$	−3.86495e17	−	2.23143e17i	−0.756177	−	0.436579i	−0.827921	+	0.560844i	$0.810477\pi$
$60$		0			0
$61$	−4.61942e17	−	8.00108e17i	−0.647574	−	1.12163i	−0.983701	−	0.179814i	$-0.942450\pi$
$61$	−4.61942e17	−	8.00108e17i	−0.647574	−	1.12163i	0.336127	−	0.941817i	$-0.390883\pi$
$62$			7.74359e16i			0.0922625i
$63$		0			0
$64$	−1.44115e17			−0.125000
$65$	2.77610e18	−	1.60278e18i	2.06206	−	1.19053i
$66$		0			0
$67$	−1.15505e18	+	2.00061e18i	−0.633655	+	1.09752i	0.353143	+	0.935569i	$0.385113\pi$
$67$	−1.15505e18	+	2.00061e18i	−0.633655	+	1.09752i	−0.986798	+	0.161954i	$0.948220\pi$
$68$	1.48511e18	+	8.57431e17i	0.702540	+	0.405611i
$69$		0			0
$70$	1.63959e18	+	2.83986e18i	0.580438	+	1.00535i
$71$		−	4.08371e17i		−	0.125450i	−0.998031	−	0.0627250i	$-0.980021\pi$
$71$		−	4.08371e17i		−	0.125450i	0.998031	−	0.0627250i	$-0.0199791\pi$
$72$		0			0
$73$	−5.70990e18			−1.32862			−0.664309	−	0.747458i	$-0.731274\pi$
$73$	−5.70990e18			−1.32862			−0.664309	+	0.747458i	$0.731274\pi$
$74$	−3.81683e18	+	2.20365e18i	−0.775149	+	0.447532i
$75$		0			0
$76$	1.79111e18	−	3.10230e18i	0.278604	−	0.482556i
$77$	6.25306e16	+	3.61020e16i	0.00853464	+	0.00492748i
$78$		0			0
$79$	7.17413e18	+	1.24260e19i	0.757702	+	1.31238i	0.944020	+	0.329888i	$0.107011\pi$
$79$	7.17413e18	+	1.24260e19i	0.757702	+	1.31238i	−0.186319	+	0.982489i	$0.559656\pi$
$80$			4.30589e18i			0.401017i
$81$		0			0
$82$	9.30881e18			0.677261
$83$	1.76947e19	−	1.02160e19i	1.14041	−	0.658418i	0.193881	−	0.981025i	$-0.437893\pi$
$83$	1.76947e19	−	1.02160e19i	1.14041	−	0.658418i	0.946533	+	0.322607i	$0.104559\pi$
$84$		0			0
$85$	2.56184e19	−	4.43724e19i	1.30126	−	2.25385i
$86$	−1.30575e19	−	7.53876e18i	−0.590033	−	0.340656i
$87$		0			0
$88$	4.74055e16	+	8.21087e16i	0.00170217	+	0.00294824i
$89$		−	8.44270e18i		−	0.270758i	−0.990794	−	0.135379i	$-0.956775\pi$
$89$		−	8.44270e18i		−	0.270758i	0.990794	−	0.135379i	$-0.0432252\pi$
$90$		0			0
$91$	5.91614e19			1.51923
$92$	1.04459e19	−	6.03096e18i	0.240474	−	0.138838i
$93$		0			0
$94$	1.55185e19	−	2.68788e19i	0.288119	−	0.499036i
$95$	−9.26910e19	−	5.35152e19i	−1.54811	−	0.893801i
$96$		0			0
$97$	9.95365e18	+	1.72402e19i	0.134979	+	0.233790i	0.925589	−	0.378529i	$-0.123570\pi$
$97$	9.95365e18	+	1.72402e19i	0.134979	+	0.233790i	−0.790611	+	0.612319i	$0.790237\pi$
$98$			2.74453e18i			0.0335897i
$99$		0			0
$100$	7.86520e19			0.786520
$101$	1.55530e20	−	8.97954e19i	1.40799	−	0.812906i	0.412799	−	0.910822i	$-0.364551\pi$
$101$	1.55530e20	−	8.97954e19i	1.40799	−	0.812906i	0.995195	+	0.0979163i	$0.0312177\pi$
$102$		0			0
$103$	−1.27016e20	+	2.19998e20i	−0.945117	+	1.63699i	−0.189600	+	0.981861i	$0.560719\pi$
$103$	−1.27016e20	+	2.19998e20i	−0.945117	+	1.63699i	−0.755517	+	0.655129i	$0.772614\pi$
$104$	6.72769e19	+	3.88423e19i	0.454499	+	0.262405i
$105$		0			0
$106$	−1.04044e20	−	1.80210e20i	−0.580979	−	1.00628i
$107$			3.38566e20i			1.72110i	0.509368	+	0.860549i	$0.329879\pi$
$107$			3.38566e20i			1.72110i	−0.509368	+	0.860549i	$0.670121\pi$
$108$		0			0
$109$	5.36620e19			0.226674			0.113337	−	0.993557i	$-0.463846\pi$
$109$	5.36620e19			0.226674			0.113337	+	0.993557i	$0.463846\pi$
$110$	2.45325e18	−	1.41639e18i	0.00945836	−	0.00546078i
$111$		0			0
$112$	−3.97345e19	+	6.88222e19i	−0.127934	+	0.221589i
$113$	9.91388e19	+	5.72378e19i	0.292051	+	0.168616i	0.638867	−	0.769318i	$-0.279404\pi$
$113$	9.91388e19	+	5.72378e19i	0.292051	+	0.168616i	−0.346815	+	0.937933i	$0.612737\pi$
$114$		0			0
$115$	−1.80194e20	−	3.12105e20i	−0.445411	−	0.771475i
$116$		−	2.65092e19i		−	0.0600920i
$117$		0			0
$118$	−3.23145e20			−0.617416
$119$	8.18932e20	−	4.72811e20i	1.43806	−	0.830267i
$120$		0			0
$121$	−3.36344e20	+	5.82565e20i	−0.499954	+	0.865945i
$122$	−5.79340e20	−	3.34482e20i	−0.793113	−	0.457904i
$123$		0			0
$124$	2.80348e19	+	4.85577e19i	0.0326197	+	0.0564990i
$125$		−	8.56068e20i		−	0.919196i
$126$		0			0
$127$	−3.25700e20			−0.298387			−0.149194	−	0.988808i	$-0.547668\pi$
$127$	−3.25700e20			−0.298387			−0.149194	+	0.988808i	$0.547668\pi$
$128$	−9.03702e19	+	5.21753e19i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	1.16054e21	−	2.01011e21i	0.841832	−	1.45810i
$131$	1.16487e20	+	6.72538e19i	0.0782644	+	0.0451860i	0.538621	−	0.842548i	$-0.318945\pi$
$131$	1.16487e20	+	6.72538e19i	0.0782644	+	0.0451860i	−0.460357	+	0.887734i	$0.652279\pi$
$132$		0			0
$133$	−9.87669e20	−	1.71069e21i	−0.570289	−	0.987770i
$134$			1.67269e21i			0.896124i
$135$		0			0
$136$	1.24169e21			0.573621
$137$	6.80672e20	−	3.92986e20i	0.292235	−	0.168722i	−0.346714	−	0.937971i	$-0.612703\pi$
$137$	6.80672e20	−	3.92986e20i	0.292235	−	0.168722i	0.638949	+	0.769249i	$0.279369\pi$
$138$		0			0
$139$	1.24417e21	−	2.15497e21i	0.462095	−	0.800373i	−0.536970	−	0.843601i	$-0.680431\pi$
$139$	1.24417e21	−	2.15497e21i	0.462095	−	0.800373i	0.999065	+	0.0432287i	$0.0137644\pi$
$140$	2.05628e21	+	1.18719e21i	0.710889	+	0.410432i
$141$		0			0
$142$	−1.47846e20	−	2.56077e20i	−0.0443533	−	0.0768222i
$143$		−	5.11074e19i		−	0.0142930i
$144$		0			0
$145$	−7.92045e20			−0.192784
$146$	−3.58050e21	+	2.06720e21i	−0.813609	+	0.469737i
$147$		0			0
$148$	−1.59561e21	+	2.76368e21i	−0.316453	+	0.548113i
$149$	3.88733e21	+	2.24435e21i	0.720756	+	0.416129i	0.815031	−	0.579418i	$-0.196720\pi$
$149$	3.88733e21	+	2.24435e21i	0.720756	+	0.416129i	−0.0942750	+	0.995546i	$0.530053\pi$
$150$		0			0
$151$	−3.02147e21	−	5.23334e21i	−0.490285	−	0.849199i	0.509652	−	0.860380i	$-0.329774\pi$
$151$	−3.02147e21	−	5.23334e21i	−0.490285	−	0.849199i	−0.999937	+	0.0111818i	$0.996441\pi$
$152$		−	2.59381e21i		−	0.394006i
$153$		0			0
$154$	5.22813e19			0.00696850
$155$	1.45081e21	−	8.37627e20i	0.181257	−	0.104649i
$156$		0			0
$157$	3.24291e21	−	5.61689e21i	0.356401	−	0.617305i	−0.630956	−	0.775819i	$-0.717337\pi$
$157$	3.24291e21	−	5.61689e21i	0.356401	−	0.617305i	0.987357	+	0.158514i	$0.0506704\pi$
$158$	8.99735e21	+	5.19462e21i	0.927991	+	0.535776i
$159$		0			0
$160$	1.55890e21	+	2.70009e21i	0.141781	+	0.245572i
$161$		−	6.65127e21i		−	0.568389i
$162$		0			0
$163$	1.02093e22			0.771116			0.385558	−	0.922684i	$-0.374009\pi$
$163$	1.02093e22			0.771116			0.385558	+	0.922684i	$0.374009\pi$
$164$	5.83727e21	−	3.37015e21i	0.414736	−	0.239448i
$165$		0			0
$166$	7.39720e21	−	1.28123e22i	0.465572	−	0.806394i
$167$	−5.46994e21	−	3.15807e21i	−0.324203	−	0.187179i	0.329061	−	0.944309i	$-0.393268\pi$
$167$	−5.46994e21	−	3.15807e21i	−0.324203	−	0.187179i	−0.653265	+	0.757130i	$0.726601\pi$
$168$		0			0
$169$	−1.14353e22	−	1.98065e22i	−0.601701	−	1.04218i
$170$		−	3.70995e22i		−	1.84026i
$171$		0			0
$172$	−1.09173e22			−0.481760
$173$	3.93259e22	−	2.27048e22i	1.63764	−	0.945490i	0.655992	−	0.754768i	$-0.272250\pi$
$173$	3.93259e22	−	2.27048e22i	1.63764	−	0.945490i	0.981644	−	0.190722i	$-0.0610829\pi$
$174$		0			0
$175$	2.16854e22	−	3.75603e22i	0.804984	−	1.39427i
$176$	5.94530e19	+	3.43252e19i	0.00208472	+	0.00120361i
$177$		0			0
$178$	−3.05658e21	−	5.29416e21i	−0.0957274	−	0.165805i
$179$			2.01936e22i			0.597975i	0.954257	+	0.298987i	$0.0966489\pi$
$179$			2.01936e22i			0.597975i	−0.954257	+	0.298987i	$0.903351\pi$
$180$		0			0
$181$	6.08622e22			1.61273			0.806366	−	0.591417i	$-0.201431\pi$
$181$	6.08622e22			1.61273			0.806366	+	0.591417i	$0.201431\pi$
$182$	3.70983e22	−	2.14187e22i	0.930337	−	0.537130i
$183$		0			0
$184$	4.36688e21	−	7.56366e21i	0.0981732	−	0.170041i
$185$	8.25735e22	+	4.76738e22i	1.75842	+	1.01523i
$186$		0			0
$187$	−4.08444e20	−	7.07447e20i	−0.00781119	−	0.0135294i
$188$		−	2.24732e22i		−	0.407461i
$189$		0			0
$190$	−7.74982e22			−1.26403
$191$	5.88269e22	−	3.39637e22i	0.910420	−	0.525631i	0.0298540	−	0.999554i	$-0.490496\pi$
$191$	5.88269e22	−	3.39637e22i	0.910420	−	0.525631i	0.880566	+	0.473923i	$0.157162\pi$
$192$		0			0
$193$	−2.20472e22	+	3.81868e22i	−0.307454	+	0.532525i	−0.977805	−	0.209519i	$-0.932810\pi$
$193$	−2.20472e22	+	3.81868e22i	−0.307454	+	0.532525i	0.670351	+	0.742044i	$0.266144\pi$
$194$	1.24833e22	+	7.20721e21i	0.165314	+	0.0954443i
$195$		0			0
$196$	9.93625e20	+	1.72101e21i	0.0118758	+	0.0205694i
$197$		−	6.40286e22i		−	0.727297i	−0.931536	−	0.363648i	$-0.881531\pi$
$197$		−	6.40286e22i		−	0.727297i	0.931536	−	0.363648i	$-0.118469\pi$
$198$		0			0
$199$	−1.08194e20			−0.00111090			−0.000555448	−	1.00000i	$-0.500177\pi$
$199$	−1.08194e20			−0.00111090			−0.000555448		1.00000i	$0.500177\pi$
$200$	4.93203e22	−	2.84751e22i	0.481643	−	0.278077i
$201$		0			0
$202$	6.50188e22	−	1.12616e23i	0.574811	−	0.995602i
$203$	−1.26595e22	−	7.30895e21i	−0.106526	−	0.0615027i
$204$		0			0
$205$	−1.00694e23	−	1.74407e23i	−0.768182	−	1.33053i
$206$			1.83939e23i			1.33660i
$207$		0			0
$208$	5.62497e22			0.371097
$209$	−1.47781e21	+	8.53212e20i	−0.00929298	+	0.00536530i
$210$		0			0
$211$	5.46452e22	−	9.46482e22i	0.312412	−	0.541113i	−0.666472	−	0.745530i	$-0.732196\pi$
$211$	5.46452e22	−	9.46482e22i	0.312412	−	0.541113i	0.978884	+	0.204417i	$0.0655298\pi$
$212$	−1.30486e23	−	7.53362e22i	−0.711550	−	0.410814i
$213$		0			0
$214$	1.22574e23	+	2.12304e23i	0.608500	+	1.05395i
$215$			3.26188e23i			1.54555i
$216$		0			0
$217$	3.09183e22			0.133542
$218$	3.36498e22	−	1.94277e22i	0.138809	−	0.0801414i
$219$		0			0
$220$	1.02557e21	−	1.77635e21i	0.00386136	−	0.00668807i
$221$	−5.79656e23	−	3.34665e23i	−2.08568	−	1.20417i
$222$		0			0
$223$	−1.14885e23	−	1.98987e23i	−0.377759	−	0.654299i	0.612976	−	0.790101i	$-0.289972\pi$
$223$	−1.14885e23	−	1.98987e23i	−0.377759	−	0.654299i	−0.990736	+	0.135803i	$0.956639\pi$
$224$			5.75417e22i			0.180927i
$225$		0			0
$226$	8.28892e22			0.238459
$227$	1.67461e23	−	9.66839e22i	0.460952	−	0.266131i	−0.251492	−	0.967859i	$-0.580921\pi$
$227$	1.67461e23	−	9.66839e22i	0.460952	−	0.266131i	0.712445	+	0.701728i	$0.247588\pi$
$228$		0			0
$229$	−1.06364e23	+	1.84228e23i	−0.268188	+	0.464515i	−0.968394	−	0.249426i	$-0.919758\pi$
$229$	−1.06364e23	+	1.84228e23i	−0.268188	+	0.464515i	0.700206	+	0.713941i	$0.253091\pi$
$230$	−2.25988e23	−	1.30474e23i	−0.545515	−	0.314953i
$231$		0			0
$232$	−9.59736e21	−	1.66231e22i	−0.0212457	−	0.0367987i
$233$		−	2.12636e23i		−	0.450897i	−0.974255	−	0.225449i	$-0.927615\pi$
$233$		−	2.12636e23i		−	0.450897i	0.974255	−	0.225449i	$-0.0723848\pi$
$234$		0			0
$235$	−6.71457e23			−1.30719
$236$	−2.02635e23	+	1.16991e23i	−0.378088	+	0.218289i
$237$		0			0
$238$	3.42352e23	−	5.92970e23i	0.587087	−	1.01687i
$239$	8.24298e23	+	4.75909e23i	1.35552	+	0.782609i	0.989016	−	0.147809i	$-0.0472219\pi$
$239$	8.24298e23	+	4.75909e23i	1.35552	+	0.782609i	0.366502	+	0.930417i	$0.380555\pi$
$240$		0			0
$241$	4.02417e23	+	6.97006e23i	0.608843	+	1.05455i	0.991431	+	0.130628i	$0.0416995\pi$
$241$	4.02417e23	+	6.97006e23i	0.608843	+	1.05455i	−0.382588	+	0.923919i	$0.624967\pi$
$242$			4.87078e23i			0.707041i
$243$		0			0
$244$	−4.84382e23			−0.647574
$245$	5.14205e22	−	2.96876e22i	0.0659896	−	0.0380991i
$246$		0			0
$247$	−6.99091e23	+	1.21086e24i	−0.827112	+	1.43260i
$248$	3.51595e22	+	2.02993e22i	0.0399508	+	0.0230656i
$249$		0			0
$250$	−3.09930e23	−	5.36814e23i	−0.324985	−	0.562890i
$251$			1.16823e24i			1.17704i	0.808483	+	0.588519i	$0.200289\pi$
$251$			1.16823e24i			1.17704i	−0.808483	+	0.588519i	$0.799711\pi$
$252$		0			0
$253$	−5.74579e21			−0.00534742
$254$	−2.04236e23	+	1.17916e23i	−0.182724	+	0.105496i
$255$		0			0
$256$	−3.77789e22	+	6.54350e22i	−0.0312500	+	0.0541266i
$257$	−8.59422e23	−	4.96187e23i	−0.683715	−	0.394743i	0.117538	−	0.993068i	$-0.462500\pi$
$257$	−8.59422e23	−	4.96187e23i	−0.683715	−	0.394743i	−0.801253	+	0.598325i	$0.795833\pi$
$258$		0			0
$259$	8.79862e23	+	1.52397e24i	0.647764	+	1.12196i
$260$		−	1.68064e24i		−	1.19053i
$261$		0			0
$262$	9.73938e22			0.0639026
$263$	−6.48744e23	+	3.74553e23i	−0.409747	+	0.236568i	−0.690681	−	0.723159i	$-0.742689\pi$
$263$	−6.48744e23	+	3.74553e23i	−0.409747	+	0.236568i	0.280934	+	0.959727i	$0.409356\pi$
$264$		0			0
$265$	−2.25090e24	+	3.89868e24i	−1.31795	+	2.28275i
$266$	−1.23867e24	−	7.15149e23i	−0.698459	−	0.403255i
$267$		0			0
$268$	6.05579e23	+	1.04889e24i	0.316828	+	0.548762i
$269$			2.06928e24i			1.04303i	0.853242	+	0.521515i	$0.174633\pi$
$269$			2.06928e24i			1.04303i	−0.853242	+	0.521515i	$0.825367\pi$
$270$		0			0
$271$	3.76536e24			1.76244			0.881218	−	0.472710i	$-0.156724\pi$
$271$	3.76536e24			1.76244			0.881218	+	0.472710i	$0.156724\pi$
$272$	7.78628e23	−	4.49541e23i	0.351270	−	0.202806i
$273$		0			0
$274$	2.84552e23	−	4.92859e23i	0.119304	−	0.206641i
$275$	−3.24470e22	−	1.87333e22i	−0.0131174	−	0.00757332i
$276$		0			0
$277$	−1.02367e24	−	1.77305e24i	−0.384914	−	0.666690i	0.606843	−	0.794821i	$-0.292435\pi$
$277$	−1.02367e24	−	1.77305e24i	−0.384914	−	0.666690i	−0.991757	+	0.128131i	$0.959102\pi$
$278$		−	1.80175e24i		−	0.653502i
$279$		0			0
$280$	1.71924e24			0.580438
$281$	−2.63952e24	+	1.52393e24i	−0.859927	+	0.496479i	−0.863988	−	0.503513i	$-0.832041\pi$
$281$	−2.63952e24	+	1.52393e24i	−0.859927	+	0.496479i	0.00406093	+	0.999992i	$0.498707\pi$
$282$		0			0
$283$	2.82190e24	−	4.88768e24i	0.856402	−	1.48333i	−0.0189360	−	0.999821i	$-0.506028\pi$
$283$	2.82190e24	−	4.88768e24i	0.856402	−	1.48333i	0.875338	−	0.483511i	$-0.160639\pi$
$284$	−1.85419e23	−	1.07052e23i	−0.0543215	−	0.0313625i
$285$		0			0
$286$	−1.85029e22	−	3.20479e22i	−0.00505334	−	0.00875265i
$287$		−	3.71678e24i		−	0.980276i
$288$		0			0
$289$	−6.63417e24			−1.63233
$290$	−4.96667e23	+	2.86751e23i	−0.118055	+	0.0681593i
$291$		0			0
$292$	−1.49682e24	+	2.59256e24i	−0.332154	+	0.575308i
$293$	−4.60556e24	−	2.65902e24i	−0.987657	−	0.570224i	−0.0830836	−	0.996543i	$-0.526477\pi$
$293$	−4.60556e24	−	2.65902e24i	−0.987657	−	0.570224i	−0.904573	+	0.426319i	$0.859810\pi$
$294$		0			0
$295$	3.49548e24	+	6.05434e24i	0.700303	+	1.21296i
$296$			2.31069e24i			0.447532i
$297$		0			0
$298$	3.25016e24			0.588495
$299$	−4.07716e24	+	2.35395e24i	−0.713913	+	0.412178i
$300$		0			0
$301$	−3.01005e24	+	5.21355e24i	−0.493070	+	0.854022i
$302$	−3.78934e24	−	2.18778e24i	−0.600474	−	0.346684i
$303$		0			0
$304$	−9.39060e23	−	1.62650e24i	−0.139302	−	0.241278i
$305$			1.44724e25i			2.07751i
$306$		0			0
$307$	7.43201e23			0.0999362			0.0499681	−	0.998751i	$-0.484088\pi$
$307$	7.43201e23			0.0999362			0.0499681	+	0.998751i	$0.484088\pi$
$308$	3.27840e22	−	1.89279e22i	0.00426732	−	0.00246374i
$309$		0			0
$310$	6.06507e23	−	1.05050e24i	0.0739978	−	0.128168i
$311$	7.81079e24	+	4.50956e24i	0.922765	+	0.532759i	0.884516	−	0.466510i	$-0.154489\pi$
$311$	7.81079e24	+	4.50956e24i	0.922765	+	0.532759i	0.0382488	+	0.999268i	$0.487822\pi$
$312$		0			0
$313$	−3.26100e23	−	5.64821e23i	−0.0361332	−	0.0625846i	0.847393	−	0.530966i	$-0.178171\pi$
$313$	−3.26100e23	−	5.64821e23i	−0.0361332	−	0.0625846i	−0.883526	+	0.468381i	$0.844837\pi$
$314$		−	4.69624e24i		−	0.504027i
$315$		0			0
$316$	7.52262e24			0.757702
$317$	9.07358e24	−	5.23864e24i	0.885495	−	0.511241i	0.0130290	−	0.999915i	$-0.495853\pi$
$317$	9.07358e24	−	5.23864e24i	0.885495	−	0.511241i	0.872466	+	0.488674i	$0.162519\pi$
$318$		0			0
$319$	−6.31394e21	+	1.09361e22i	−0.000578620	+	0.00100220i
$320$	1.95508e24	+	1.12876e24i	0.173646	+	0.100254i
$321$		0			0
$322$	−2.40802e24	−	4.17080e24i	−0.200956	−	0.348066i
$323$			2.23482e25i			1.80808i
$324$		0			0
$325$	−3.06987e25			−2.33500
$326$	6.40194e24	−	3.69616e24i	0.472210	−	0.272631i
$327$		0			0
$328$	2.44025e24	−	4.22664e24i	0.169315	−	0.293262i
$329$	−1.07321e25	−	6.19616e24i	−0.722312	−	0.417027i
$330$		0			0
$331$	5.88449e24	+	1.01922e25i	0.372760	+	0.645639i	0.989989	−	0.141144i	$-0.0450782\pi$
$331$	5.88449e24	+	1.01922e25i	0.372760	+	0.645639i	−0.617229	+	0.786783i	$0.711745\pi$
$332$		−	1.07123e25i		−	0.658418i
$333$		0			0
$334$	−4.57337e24			−0.264711
$335$	3.13390e25	−	1.80936e25i	1.76050	−	1.01643i
$336$		0			0
$337$	1.35298e25	−	2.34343e25i	0.716132	−	1.24038i	−0.246390	−	0.969171i	$-0.579244\pi$
$337$	1.35298e25	−	2.34343e25i	0.716132	−	1.24038i	0.962521	−	0.271206i	$-0.0874223\pi$
$338$	−1.43415e25	−	8.28005e24i	−0.736931	−	0.425467i
$339$		0			0
$340$	−1.34314e25	−	2.32639e25i	−0.650629	−	1.12692i
$341$		−	2.67092e22i		−	0.00125637i
$342$		0			0
$343$	−2.19727e25			−0.974858
$344$	−6.84590e24	+	3.95248e24i	−0.295016	+	0.170328i
$345$		0			0
$346$	1.64400e25	−	2.84750e25i	0.668562	−	1.15798i
$347$	1.84040e25	+	1.06256e25i	0.727139	+	0.419814i	0.817375	−	0.576107i	$-0.195429\pi$
$347$	1.84040e25	+	1.06256e25i	0.727139	+	0.419814i	−0.0902356	+	0.995920i	$0.528762\pi$
$348$		0			0
$349$	3.86177e24	+	6.68878e24i	0.144056	+	0.249513i	0.929020	−	0.370028i	$-0.120652\pi$
$349$	3.86177e24	+	6.68878e24i	0.144056	+	0.249513i	−0.784964	+	0.619541i	$0.787319\pi$
$350$		−	3.14038e25i		−	1.13842i
$351$		0			0
$352$	4.97082e22			0.00170217
$353$	6.97163e23	−	4.02507e23i	0.0232053	−	0.0133976i	−0.488352	−	0.872646i	$-0.662402\pi$
$353$	6.97163e23	−	4.02507e23i	0.0232053	−	0.0133976i	0.511558	+	0.859249i	$0.329069\pi$
$354$		0			0
$355$	−3.19851e24	+	5.53998e24i	−0.100615	+	0.174271i
$356$	−3.83338e24	−	2.21320e24i	−0.117242	−	0.0676895i
$357$		0			0
$358$	7.31086e24	+	1.26628e25i	0.211416	+	0.366183i
$359$		−	2.40384e25i		−	0.676021i	−0.941142	−	0.338010i	$-0.890246\pi$
$359$		−	2.40384e25i		−	0.676021i	0.941142	−	0.338010i	$-0.109754\pi$
$360$		0			0
$361$	9.09391e24			0.241924
$362$	3.81648e25	−	2.20345e25i	0.987593	−	0.570187i
$363$		0			0
$364$	1.55088e25	−	2.68620e25i	0.379808	−	0.657848i
$365$	7.74609e25	+	4.47221e25i	1.84567	+	1.06560i
$366$		0			0
$367$	−1.21188e24	−	2.09903e24i	−0.0273399	−	0.0473541i	0.852032	−	0.523490i	$-0.175370\pi$
$367$	−1.21188e24	−	2.09903e24i	−0.0273399	−	0.0473541i	−0.879372	+	0.476136i	$0.842037\pi$
$368$		−	6.32392e24i		−	0.138838i
$369$		0			0
$370$	6.90391e25			1.43575
$371$	−7.19536e25	+	4.15424e25i	−1.45651	+	0.840916i
$372$		0			0
$373$	−1.39422e24	+	2.41485e24i	−0.0267449	+	0.0463236i	−0.879088	−	0.476659i	$-0.841848\pi$
$373$	−1.39422e24	+	2.41485e24i	−0.0267449	+	0.0463236i	0.852343	+	0.522983i	$0.175181\pi$
$374$	−5.12246e23	−	2.95745e23i	−0.00956671	−	0.00552334i
$375$		0			0
$376$	−8.13616e24	−	1.40923e25i	−0.144059	−	0.249518i
$377$			1.03468e25i			0.178400i
$378$		0			0
$379$	4.34516e25			0.710582			0.355291	−	0.934756i	$-0.384382\pi$
$379$	4.34516e25			0.710582			0.355291	+	0.934756i	$0.384382\pi$
$380$	−4.85968e25	+	2.80574e25i	−0.774054	+	0.446900i
$381$		0			0
$382$	2.45923e25	−	4.25952e25i	0.371678	−	0.643764i
$383$	4.18050e25	+	2.41361e25i	0.615518	+	0.355370i	0.775122	−	0.631812i	$-0.217688\pi$
$383$	4.18050e25	+	2.41361e25i	0.615518	+	0.355370i	−0.159604	+	0.987181i	$0.551022\pi$
$384$		0			0
$385$	−5.65529e23	−	9.79525e23i	−0.00790401	−	0.0136902i
$386$			3.19277e25i			0.434805i
$387$		0			0
$388$	1.04372e25			0.134979
$389$	7.59402e25	−	4.38441e25i	0.957141	−	0.552605i	0.0618489	−	0.998086i	$-0.480300\pi$
$389$	7.59402e25	−	4.38441e25i	0.957141	−	0.552605i	0.895292	+	0.445480i	$0.146967\pi$
$390$		0			0
$391$	−3.76249e25	+	6.51683e25i	−0.450514	+	0.780313i
$392$	1.24614e24	+	7.19461e23i	0.0145448	+	0.00839743i
$393$		0			0
$394$	−2.31808e25	−	4.01504e25i	−0.257138	−	0.445376i
$395$		−	2.24762e26i		−	2.43081i
$396$		0			0
$397$	−8.53397e24			−0.0877498			−0.0438749	−	0.999037i	$-0.513970\pi$
$397$	−8.53397e24			−0.0877498			−0.0438749	+	0.999037i	$0.513970\pi$
$398$	−6.78453e22	+	3.91705e22i	−0.000680282	+	0.000392761i
$399$		0			0
$400$	2.06181e25	−	3.57117e25i	0.196630	−	0.340573i
$401$	1.27396e26	+	7.35523e25i	1.18499	+	0.684152i	0.957163	−	0.289551i	$-0.0935059\pi$
$401$	1.27396e26	+	7.35523e25i	1.18499	+	0.684152i	0.227823	+	0.973703i	$0.426839\pi$
$402$		0			0
$403$	−1.09423e25	−	1.89526e25i	−0.0968405	−	0.167733i
$404$		−	9.41573e25i		−	0.812906i
$405$		0			0
$406$	−1.05845e25			−0.0869780
$407$	1.31650e24	−	7.60082e23i	0.0105555	−	0.00609419i
$408$		0			0
$409$	9.09184e25	−	1.57475e26i	0.694095	−	1.20221i	−0.276390	−	0.961046i	$-0.589138\pi$
$409$	9.09184e25	−	1.57475e26i	0.694095	−	1.20221i	0.970485	−	0.241162i	$-0.0775285\pi$
$410$	−1.26284e26	−	7.29101e25i	−0.940827	−	0.543187i
$411$		0			0
$412$	6.65929e25	+	1.15342e26i	0.472558	+	0.818495i
$413$			1.29024e26i			0.893656i
$414$		0			0
$415$	−3.20063e26			−2.11230
$416$	3.52725e25	−	2.03646e25i	0.227249	−	0.131202i
$417$		0			0
$418$	−6.17792e23	+	1.07005e24i	−0.00379384	+	0.00657113i
$419$	−1.20430e26	−	6.95301e25i	−0.722093	−	0.416901i	0.0934295	−	0.995626i	$-0.470217\pi$
$419$	−1.20430e26	−	6.95301e25i	−0.722093	−	0.416901i	−0.815523	+	0.578725i	$0.803550\pi$
$420$		0			0
$421$	6.94255e25	+	1.20249e26i	0.396916	+	0.687478i	0.993344	−	0.115189i	$-0.0367472\pi$
$421$	6.94255e25	+	1.20249e26i	0.396916	+	0.687478i	−0.596428	+	0.802667i	$0.703414\pi$
$422$		−	7.91347e25i		−	0.441817i
$423$		0			0
$424$	−1.09098e26			−0.580979
$425$	−4.24942e26	+	2.45340e26i	−2.21025	+	1.27609i
$426$		0			0
$427$	−1.33551e26	+	2.31316e26i	−0.662776	+	1.14796i
$428$	1.53725e26	+	8.87530e25i	0.745257	+	0.430274i
$429$		0			0
$430$	1.18093e26	+	2.04543e26i	0.546435	+	0.946454i
$431$			2.59226e26i			1.17194i	0.810332	+	0.585971i	$0.199287\pi$
$431$			2.59226e26i			1.17194i	−0.810332	+	0.585971i	$0.800713\pi$
$432$		0			0
$433$	−6.00398e25			−0.259155			−0.129578	−	0.991569i	$-0.541362\pi$
$433$	−6.00398e25			−0.259155			−0.129578	+	0.991569i	$0.541362\pi$
$434$	1.93879e25	−	1.11936e25i	0.0817774	−	0.0472142i
$435$		0			0
$436$	1.40672e25	−	2.43651e25i	0.0566686	−	0.0981528i
$437$	1.36132e26	+	7.85959e25i	0.535977	+	0.309446i
$438$		0			0
$439$	1.70308e26	+	2.94982e26i	0.640603	+	1.10956i	0.985298	+	0.170843i	$0.0546490\pi$
$439$	1.70308e26	+	2.94982e26i	0.640603	+	1.10956i	−0.344695	+	0.938715i	$0.612018\pi$
$440$		−	1.48519e24i		−	0.00546078i
$441$		0			0
$442$	−4.84646e26			−1.70295
$443$	−2.21589e26	+	1.27935e26i	−0.761222	+	0.439492i	−0.829734	−	0.558159i	$-0.811508\pi$
$443$	−2.21589e26	+	1.27935e26i	−0.761222	+	0.439492i	0.0685123	+	0.997650i	$0.478175\pi$
$444$		0			0
$445$	−6.61263e25	+	1.14534e26i	−0.217157	+	0.376127i
$446$	−1.44082e26	−	8.31857e25i	−0.462659	−	0.267116i
$447$		0			0
$448$	2.08323e25	+	3.60827e25i	0.0639672	+	0.110795i
$449$			3.39399e26i			1.01917i	0.860420	+	0.509586i	$0.170201\pi$
$449$			3.39399e26i			1.01917i	−0.860420	+	0.509586i	$0.829799\pi$
$450$		0			0
$451$	−3.21080e24			−0.00922248
$452$	5.19773e25	−	3.00091e25i	0.146026	−	0.0843080i
$453$		0			0
$454$	7.00066e25	−	1.21255e26i	0.188183	−	0.325943i
$455$	−8.02588e26	−	4.63374e26i	−2.11047	−	1.21848i
$456$		0			0
$457$	−1.29708e26	−	2.24661e26i	−0.326441	−	0.565413i	0.655362	−	0.755315i	$-0.272516\pi$
$457$	−1.29708e26	−	2.24661e26i	−0.326441	−	0.565413i	−0.981803	+	0.189902i	$0.939183\pi$
$458$			1.54031e26i			0.379275i
$459$		0			0
$460$	−1.88947e26			−0.445411
$461$	3.02090e26	−	1.74412e26i	0.696830	−	0.402315i	−0.109336	−	0.994005i	$-0.534872\pi$
$461$	3.02090e26	−	1.74412e26i	0.696830	−	0.402315i	0.806166	+	0.591690i	$0.201539\pi$
$462$		0			0
$463$	−4.60365e25	+	7.97376e25i	−0.101693	+	0.176138i	−0.912382	−	0.409339i	$-0.865759\pi$
$463$	−4.60365e25	+	7.97376e25i	−0.101693	+	0.176138i	0.810689	+	0.585477i	$0.199093\pi$
$464$	−1.20364e25	−	6.94923e24i	−0.0260206	−	0.0150230i
$465$		0			0
$466$	−7.69825e25	−	1.33338e26i	−0.159416	−	0.276117i
$467$			3.75500e26i			0.761100i	0.924760	+	0.380550i	$0.124265\pi$
$467$			3.75500e26i			0.761100i	−0.924760	+	0.380550i	$0.875735\pi$
$468$		0			0
$469$	6.67866e26			1.29706
$470$	−4.21050e26	+	2.43093e26i	−0.800489	+	0.462162i
$471$		0			0
$472$	−8.47106e25	+	1.46723e26i	−0.154354	+	0.267349i
$473$	4.50380e24	+	2.60027e24i	0.00803467	+	0.00463882i
$474$		0			0
$475$	5.12499e26	+	8.87675e26i	0.876511	+	1.51816i
$476$		−	4.95778e26i		−	0.830267i
$477$		0			0
$478$	6.89189e26			1.10678
$479$	1.81412e26	−	1.04738e26i	0.285306	−	0.164722i	−0.350517	−	0.936556i	$-0.613994\pi$
$479$	1.81412e26	−	1.04738e26i	0.285306	−	0.164722i	0.635823	+	0.771835i	$0.280661\pi$
$480$		0			0
$481$	6.22784e26	−	1.07869e27i	0.939478	−	1.62722i
$482$	5.04686e26	+	2.91381e26i	0.745678	+	0.430517i
$483$		0			0
$484$	1.76341e26	+	3.05432e26i	0.249977	+	0.432973i
$485$		−	3.11843e26i		−	0.433030i
$486$		0			0
$487$	−5.41217e26			−0.721243			−0.360622	−	0.932712i	$-0.617435\pi$
$487$	−5.41217e26			−0.721243			−0.360622	+	0.932712i	$0.617435\pi$
$488$	−3.03741e26	+	1.75365e26i	−0.396556	+	0.228952i
$489$		0			0
$490$	2.14962e25	−	3.72324e25i	0.0269401	−	0.0466617i
$491$	−9.29002e26	−	5.36359e26i	−1.14078	−	0.658629i	−0.194156	−	0.980971i	$-0.562197\pi$
$491$	−9.29002e26	−	5.36359e26i	−1.14078	−	0.658629i	−0.946623	+	0.322342i	$0.895530\pi$
$492$		0			0
$493$	8.26906e25	+	1.43224e26i	0.0974960	+	0.168868i
$494$			1.01239e27i			1.16971i
$495$		0			0
$496$	2.93966e25			0.0326197
$497$	−1.02245e26	+	5.90313e25i	−0.111193	+	0.0641976i
$498$		0			0
$499$	5.42966e26	−	9.40444e26i	0.567240	−	0.982488i	−0.429598	−	0.903020i	$-0.641345\pi$
$499$	5.42966e26	−	9.40444e26i	0.567240	−	0.982488i	0.996837	−	0.0794679i	$-0.0253221\pi$
$500$	−3.88695e26	−	2.24413e26i	−0.398024	−	0.229799i
$501$		0			0
$502$	4.22944e26	+	7.32561e26i	0.416146	+	0.720786i
$503$		−	1.85221e27i		−	1.78653i	−0.449534	−	0.893263i	$-0.648410\pi$
$503$		−	1.85221e27i		−	1.78653i	0.449534	−	0.893263i	$-0.351590\pi$
$504$		0			0
$505$	−2.81324e27			−2.60792
$506$	−3.60301e24	+	2.08020e24i	−0.00327462	+	0.00189060i
$507$		0			0
$508$	−8.53802e25	+	1.47883e26i	−0.0745968	+	0.129205i
$509$	1.90313e27	+	1.09877e27i	1.63039	+	0.941306i	0.983972	+	0.178322i	$0.0570669\pi$
$509$	1.90313e27	+	1.09877e27i	1.63039	+	0.941306i	0.646418	+	0.762984i	$0.276266\pi$
$510$		0			0
$511$	8.25385e26	+	1.42961e27i	0.679904	+	1.17763i
$512$			5.47097e25i			0.0441942i
$513$		0			0
$514$	−7.18556e26			−0.558251
$515$	3.44621e27	−	1.98967e27i	2.62585	−	1.51603i
$516$		0			0
$517$	−5.35265e24	+	9.27105e24i	−0.00392340	+	0.00679554i
$518$	1.10347e27	+	6.37088e26i	0.793346	+	0.458039i
$519$		0			0
$520$	−6.08455e26	−	1.05388e27i	−0.420916	−	0.729048i
$521$		−	1.95978e27i		−	1.32993i	−0.746873	−	0.664966i	$-0.768446\pi$
$521$		−	1.95978e27i		−	1.32993i	0.746873	−	0.664966i	$-0.231554\pi$
$522$		0			0
$523$	−1.44938e26			−0.0946599			−0.0473299	−	0.998879i	$-0.515071\pi$
$523$	−1.44938e26			−0.0946599			−0.0473299	+	0.998879i	$0.515071\pi$
$524$	6.10727e25	−	3.52603e25i	0.0391322	−	0.0225930i
$525$		0			0
$526$	−2.71205e26	+	4.69741e26i	−0.167279	+	0.289735i
$527$	−3.02933e26	−	1.74899e26i	−0.183333	−	0.105847i
$528$		0			0
$529$	−5.93434e26	−	1.02786e27i	−0.345792	−	0.598930i
$530$			3.25966e27i			1.86386i
$531$		0			0
$532$	−1.03565e27			−0.570289
$533$	−2.27835e27	+	1.31541e27i	−1.23126	+	0.710866i
$534$		0			0
$535$	2.65177e27	−	4.59301e27i	1.38038	−	2.39089i
$536$	7.59480e26	+	4.38486e26i	0.388033	+	0.224031i
$537$		0			0
$538$	7.49160e26	+	1.29758e27i	0.368767	+	0.638723i
$539$		−	9.46643e23i		−	0.000457402i
$540$		0			0
$541$	−1.84462e27			−0.858884			−0.429442	−	0.903095i	$-0.641290\pi$
$541$	−1.84462e27			−0.858884			−0.429442	+	0.903095i	$0.641290\pi$
$542$	2.36114e27	−	1.36321e27i	1.07927	−	0.623115i
$543$		0			0
$544$	3.25502e26	−	5.63787e26i	0.143405	−	0.248385i
$545$	−7.27983e26	−	4.20301e26i	−0.314888	−	0.181801i
$546$		0			0
$547$	5.95431e26	+	1.03132e27i	0.248289	+	0.430050i	0.963051	−	0.269318i	$-0.0867983\pi$
$547$	5.95431e26	+	1.03132e27i	0.248289	+	0.430050i	−0.714762	+	0.699368i	$0.753465\pi$
$548$		−	4.12076e26i		−	0.168722i
$549$		0			0
$550$	−2.71287e25			−0.0107103
$551$	2.99186e26	−	1.72735e26i	0.115991	−	0.0669675i
$552$		0			0
$553$	2.07409e27	−	3.59243e27i	0.775489	−	1.34319i
$554$	−1.28383e27	−	7.41218e26i	−0.471421	−	0.272175i
$555$		0			0
$556$	−6.52303e26	−	1.12982e27i	−0.231048	−	0.400186i
$557$			1.47553e27i			0.513331i	0.966500	+	0.256665i	$0.0826238\pi$
$557$			1.47553e27i			0.513331i	−0.966500	+	0.256665i	$0.917376\pi$
$558$		0			0
$559$	4.26114e27			1.43024
$560$	1.07808e27	−	6.22431e26i	0.355444	−	0.205216i
$561$		0			0
$562$	−1.10344e27	+	1.91122e27i	−0.351064	+	0.608060i
$563$	5.58880e26	+	3.22670e26i	0.174677	+	0.100850i	0.584789	−	0.811185i	$-0.301177\pi$
$563$	5.58880e26	+	3.22670e26i	0.174677	+	0.100850i	−0.410113	+	0.912035i	$0.634511\pi$
$564$		0			0
$565$	−8.96616e26	−	1.55298e27i	−0.270472	−	0.468471i
$566$		−	4.08655e27i		−	1.21114i
$567$		0			0
$568$	−1.55028e26			−0.0443533
$569$	4.20172e26	−	2.42586e26i	0.118115	−	0.0681936i	−0.439779	−	0.898106i	$-0.644943\pi$
$569$	4.20172e26	−	2.42586e26i	0.118115	−	0.0681936i	0.557893	+	0.829913i	$0.311610\pi$
$570$		0			0
$571$	2.03620e27	−	3.52680e27i	0.552662	−	0.957239i	−0.445419	−	0.895322i	$-0.646945\pi$
$571$	2.03620e27	−	3.52680e27i	0.552662	−	0.957239i	0.998081	−	0.0619166i	$-0.0197213\pi$
$572$	−2.32052e25	−	1.33975e25i	−0.00618906	−	0.00357325i
$573$		0			0
$574$	−1.34562e27	−	2.33068e27i	−0.346580	−	0.600294i
$575$			3.45133e27i			0.873590i
$576$		0			0
$577$	3.75159e27			0.917186			0.458593	−	0.888647i	$-0.348354\pi$
$577$	3.75159e27			0.917186			0.458593	+	0.888647i	$0.348354\pi$
$578$	−4.16008e27	+	2.40182e27i	−0.999594	+	0.577116i
$579$		0			0
$580$	−2.07630e26	+	3.59626e26i	−0.0481959	+	0.0834777i
$581$	−5.11566e27	−	2.95353e27i	−1.16719	−	0.673875i
$582$		0			0
$583$	3.58870e25	+	6.21581e25i	0.00791137	+	0.0137029i
$584$			2.16762e27i			0.469737i
$585$		0			0
$586$	−3.85067e27			−0.806418
$587$	7.02910e25	−	4.05825e25i	0.0144717	−	0.00835522i	−0.492747	−	0.870173i	$-0.664007\pi$
$587$	7.02910e25	−	4.05825e25i	0.0144717	−	0.00835522i	0.507218	+	0.861818i	$0.330674\pi$
$588$		0			0
$589$	−3.65351e26	+	6.32807e26i	−0.0727039	+	0.125927i
$590$	4.38381e27	+	2.53099e27i	0.857693	+	0.495189i
$591$		0			0
$592$	8.36559e26	+	1.44896e27i	0.158227	+	0.274056i
$593$		−	3.25998e26i		−	0.0606273i	−0.999540	−	0.0303137i	$-0.990349\pi$
$593$		−	3.25998e26i		−	0.0606273i	0.999540	−	0.0303137i	$-0.00965061\pi$
$594$		0			0
$595$	−1.48129e28			−2.66361
$596$	2.03808e27	−	1.17668e27i	0.360378	−	0.208064i
$597$		0			0
$598$	−1.70444e27	+	2.95218e27i	−0.291454	+	0.504813i
$599$	−1.41711e26	−	8.18170e25i	−0.0238307	−	0.0137586i	0.488037	−	0.872823i	$-0.337713\pi$
$599$	−1.41711e26	−	8.18170e25i	−0.0238307	−	0.0137586i	−0.511868	+	0.859064i	$0.671046\pi$
$600$		0			0
$601$	3.58359e27	+	6.20696e27i	0.582872	+	1.00956i	0.995137	+	0.0985002i	$0.0314045\pi$
$601$	3.58359e27	+	6.20696e27i	0.582872	+	1.00956i	−0.412265	+	0.911064i	$0.635262\pi$
$602$			4.35901e27i			0.697306i
$603$		0			0
$604$	−3.16824e27			−0.490285
$605$	9.12572e27	−	5.26874e27i	1.38904	−	0.801961i
$606$		0			0
$607$	4.96623e26	−	8.60177e26i	0.0731375	−	0.126678i	−0.827137	−	0.562000i	$-0.810032\pi$
$607$	4.96623e26	−	8.60177e26i	0.0731375	−	0.126678i	0.900275	+	0.435322i	$0.143365\pi$
$608$	−1.17771e27	−	6.79952e26i	−0.170609	−	0.0985014i
$609$		0			0
$610$	5.23957e27	+	9.07521e27i	0.734510	+	1.27221i
$611$			8.77153e27i			1.20966i
$612$		0			0
$613$	−1.25966e27			−0.168131			−0.0840657	−	0.996460i	$-0.526791\pi$
$613$	−1.25966e27			−0.168131			−0.0840657	+	0.996460i	$0.526791\pi$
$614$	4.66039e26	−	2.69068e26i	0.0611982	−	0.0353328i
$615$		0			0
$616$	1.37052e25	−	2.37382e25i	0.00174213	−	0.00301745i
$617$	−5.41799e27	−	3.12808e27i	−0.677620	−	0.391224i	0.121338	−	0.992611i	$-0.461282\pi$
$617$	−5.41799e27	−	3.12808e27i	−0.677620	−	0.391224i	−0.798958	+	0.601387i	$0.794615\pi$
$618$		0			0
$619$	1.54446e27	+	2.67508e27i	0.187012	+	0.323914i	0.944253	−	0.329222i	$-0.106786\pi$
$619$	1.54446e27	+	2.67508e27i	0.187012	+	0.323914i	−0.757241	+	0.653136i	$0.773453\pi$
$620$		−	8.78315e26i		−	0.104649i
$621$		0			0
$622$	6.53054e27			0.753434
$623$	−2.11383e27	+	1.22042e27i	−0.239988	+	0.138557i
$624$		0			0
$625$	4.48314e26	−	7.76502e26i	0.0492926	−	0.0853773i
$626$	−4.08974e26	−	2.36121e26i	−0.0442540	−	0.0255501i
$627$		0			0
$628$	−1.70022e27	−	2.94487e27i	−0.178200	−	0.308652i
$629$		−	1.99088e28i		−	2.05371i
$630$		0			0
$631$	7.63696e27			0.763180			0.381590	−	0.924332i	$-0.375377\pi$
$631$	7.63696e27			0.763180			0.381590	+	0.924332i	$0.375377\pi$
$632$	4.71720e27	−	2.72348e27i	0.463996	−	0.267888i
$633$		0			0
$634$	3.79318e27	−	6.56998e27i	0.361502	−	0.626140i
$635$	4.41846e27	+	2.55100e27i	0.414509	+	0.239317i
$636$		0			0
$637$	−3.87822e26	−	6.71728e26i	−0.0352565	−	0.0610660i
$638$			9.14356e24i			0.000818293i
$639$		0			0
$640$	1.63462e27			0.141781
$641$	−1.33512e28	+	7.70830e27i	−1.14009	+	0.658231i	−0.946453	−	0.322843i	$-0.895361\pi$
$641$	−1.33512e28	+	7.70830e27i	−1.14009	+	0.658231i	−0.193636	+	0.981073i	$0.562028\pi$
$642$		0			0
$643$	−7.08614e27	+	1.22736e28i	−0.586543	+	1.01592i	0.408138	+	0.912920i	$0.366178\pi$
$643$	−7.08614e27	+	1.22736e28i	−0.586543	+	1.01592i	−0.994681	+	0.103002i	$0.967155\pi$
$644$	−3.01999e27	−	1.74359e27i	−0.246120	−	0.142097i
$645$		0			0
$646$	8.09092e27	+	1.40139e28i	0.639253	+	1.10722i
$647$		−	1.51132e28i		−	1.17574i	−0.808954	−	0.587871i	$-0.799966\pi$
$647$		−	1.51132e28i		−	1.17574i	0.808954	−	0.587871i	$-0.200034\pi$
$648$		0			0
$649$	1.11459e26			0.00840755
$650$	−1.92502e28	+	1.11141e28i	−1.42989	+	0.825547i
$651$		0			0
$652$	2.67631e27	−	4.63550e27i	0.192779	−	0.333903i
$653$	−6.05384e25	−	3.49519e25i	−0.00429437	−	0.00247935i	0.497851	−	0.867262i	$-0.334123\pi$
$653$	−6.05384e25	−	3.49519e25i	−0.00429437	−	0.00247935i	−0.502146	+	0.864783i	$0.667456\pi$
$654$		0			0
$655$	−1.05351e27	−	1.82474e27i	−0.0724814	−	0.125542i
$656$		−	3.53386e27i		−	0.239448i
$657$		0			0
$658$	−8.97300e27			−0.589765
$659$	−6.74915e27	+	3.89662e27i	−0.436913	+	0.252252i	−0.702287	−	0.711894i	$-0.747838\pi$
$659$	−6.74915e27	+	3.89662e27i	−0.436913	+	0.252252i	0.265374	+	0.964145i	$0.414504\pi$
$660$		0			0
$661$	−1.12419e28	+	1.94715e28i	−0.706033	+	1.22288i	0.260285	+	0.965532i	$0.416184\pi$
$661$	−1.12419e28	+	1.94715e28i	−0.706033	+	1.22288i	−0.966318	+	0.257353i	$0.917150\pi$
$662$	7.37997e27	+	4.26083e27i	0.456536	+	0.263581i
$663$		0			0
$664$	−3.87827e27	−	6.71735e27i	−0.232786	−	0.403197i
$665$			3.09432e28i			1.82957i
$666$		0			0
$667$	1.16325e27			0.0667444
$668$	−2.86782e27	+	1.65574e27i	−0.162102	+	0.0935895i
$669$		0			0
$670$	1.31011e28	−	2.26919e28i	0.718723	−	1.24486i
$671$	1.99826e26	+	1.15370e26i	0.0108001	+	0.00623543i
$672$		0			0
$673$	1.42705e28	+	2.47173e28i	0.748669	+	1.29673i	0.948461	+	0.316894i	$0.102640\pi$
$673$	1.42705e28	+	2.47173e28i	0.748669	+	1.29673i	−0.199792	+	0.979838i	$0.564027\pi$
$674$		−	1.95933e28i		−	1.01276i
$675$		0			0
$676$	−1.19908e28			−0.601701
$677$	−8.68082e27	+	5.01188e27i	−0.429214	+	0.247807i	−0.699012	−	0.715110i	$-0.746377\pi$
$677$	−8.68082e27	+	5.01188e27i	−0.429214	+	0.247807i	0.269798	+	0.962917i	$0.413043\pi$
$678$		0			0
$679$	2.87767e27	−	4.98426e27i	0.138147	−	0.239278i
$680$	−1.68449e28	−	9.72540e27i	−0.796855	−	0.460064i
$681$		0			0
$682$	−9.66976e24	−	1.67485e25i	−0.000444193	−	0.000769365i
$683$			3.20778e28i			1.45210i	0.687639	+	0.726052i	$0.258647\pi$
$683$			3.20778e28i			1.45210i	−0.687639	+	0.726052i	$0.741353\pi$
$684$		0			0
$685$	−1.23121e28			−0.541283
$686$	−1.37784e28	+	7.95495e27i	−0.596976	+	0.344664i
$687$		0			0
$688$	−2.86190e27	+	4.95696e27i	−0.120440	+	0.208608i
$689$	5.09301e28	+	2.94045e28i	2.11243	+	1.21961i
$690$		0			0
$691$	1.03068e28	+	1.78519e28i	0.415283	+	0.719291i	0.995458	−	0.0952006i	$-0.0303492\pi$
$691$	1.03068e28	+	1.78519e28i	0.415283	+	0.719291i	−0.580175	+	0.814492i	$0.697016\pi$
$692$		−	2.38077e28i		−	0.945490i
$693$		0			0
$694$	1.53874e28			0.593706
$695$	−3.37570e28	+	1.94896e28i	−1.28385	+	0.741233i
$696$		0			0
$697$	−2.10251e28	+	3.64166e28i	−0.776982	+	1.34577i
$698$	4.84320e27	+	2.79622e27i	0.176432	+	0.101863i
$699$		0			0
$700$	−1.13694e28	−	1.96924e28i	−0.402492	−	0.697137i
$701$		−	1.65456e28i		−	0.577433i	−0.957415	−	0.288717i	$-0.906771\pi$
$701$		−	1.65456e28i		−	0.577433i	0.957415	−	0.288717i	$-0.0932286\pi$
$702$		0			0
$703$	−4.15882e28			−1.41064
$704$	3.11705e25	−	1.79963e25i	0.00104236	−	0.000601806i
$705$		0			0
$706$	2.91446e26	−	5.04800e26i	0.00947353	−	0.0164086i
$707$	−4.49648e28	−	2.59604e28i	−1.44105	−	0.831989i
$708$		0			0
$709$	−1.52468e28	−	2.64082e28i	−0.475024	−	0.822766i	0.524567	−	0.851369i	$-0.324227\pi$
$709$	−1.52468e28	−	2.64082e28i	−0.475024	−	0.822766i	−0.999591	+	0.0286034i	$0.990894\pi$
$710$			4.63194e27i			0.142292i
$711$		0			0
$712$	−3.20506e27			−0.0957274
$713$	−2.13076e27	+	1.23019e27i	−0.0627536	+	0.0362308i
$714$		0			0
$715$	−4.00292e26	+	6.93327e26i	−0.0114635	+	0.0198554i
$716$	9.16883e27	+	5.29363e27i	0.258931	+	0.149494i
$717$		0			0
$718$	−8.70281e27	−	1.50737e28i	−0.239010	−	0.413977i
$719$		−	2.10680e28i		−	0.570604i	−0.958438	−	0.285302i	$-0.907906\pi$
$719$		−	2.10680e28i		−	0.570604i	0.958438	−	0.285302i	$-0.0920939\pi$
$720$		0			0
$721$	7.34422e28			1.93461
$722$	5.70252e27	−	3.29235e27i	0.148148	−	0.0855330i
$723$		0			0
$724$	1.59547e28	−	2.76343e28i	0.403183	−	0.698333i
$725$	6.56897e27	+	3.79260e27i	0.163726	+	0.0945272i
$726$		0			0
$727$	−3.48941e28	−	6.04384e28i	−0.846074	−	1.46544i	−0.884685	−	0.466189i	$-0.845627\pi$
$727$	−3.48941e28	−	6.04384e28i	−0.846074	−	1.46544i	0.0386109	−	0.999254i	$-0.487707\pi$
$728$		−	2.24592e28i		−	0.537130i
$729$		0			0
$730$	6.47645e28			1.50698
$731$	5.89841e28	−	3.40545e28i	1.35382	−	0.781629i
$732$		0			0
$733$	1.90109e28	−	3.29278e28i	0.424583	−	0.735400i	−0.571798	−	0.820394i	$-0.693754\pi$
$733$	1.90109e28	−	3.29278e28i	0.424583	−	0.735400i	0.996381	+	0.0849946i	$0.0270873\pi$
$734$	−1.51986e27	−	8.77491e26i	−0.0334844	−	0.0193322i
$735$		0			0
$736$	−2.28950e27	−	3.96553e27i	−0.0490866	−	0.0850205i
$737$		−	5.76945e26i		−	0.0122028i
$738$		0			0
$739$	−3.19618e28			−0.657941			−0.328971	−	0.944340i	$-0.606702\pi$
$739$	−3.19618e28			−0.657941			−0.328971	+	0.944340i	$0.606702\pi$
$740$	4.32923e28	−	2.49948e28i	0.879212	−	0.507613i
$741$		0			0
$742$	−3.00799e28	+	5.21000e28i	−0.594618	+	1.02991i
$743$	5.55891e28	+	3.20944e28i	1.08418	+	0.625952i	0.932021	−	0.362404i	$-0.118044\pi$
$743$	5.55891e28	+	3.20944e28i	1.08418	+	0.625952i	0.152159	+	0.988356i	$0.451377\pi$
$744$		0			0
$745$	−3.51571e28	−	6.08940e28i	−0.667499	−	1.15614i
$746$			2.01904e27i			0.0378231i
$747$		0			0
$748$	−4.28285e26			−0.00781119
$749$	8.47680e28	−	4.89408e28i	1.52551	−	0.880751i
$750$		0			0
$751$	−2.13021e27	+	3.68964e27i	−0.0373270	+	0.0646523i	−0.884085	−	0.467325i	$-0.845218\pi$
$751$	−2.13021e27	+	3.68964e27i	−0.0373270	+	0.0646523i	0.846758	+	0.531978i	$0.178551\pi$
$752$	−1.02039e28	−	5.89121e27i	−0.176436	−	0.101865i
$753$		0			0
$754$	3.74595e27	+	6.48818e27i	0.0630738	+	0.109247i
$755$			9.46611e28i			1.57290i
$756$		0			0
$757$	5.13713e28			0.831308			0.415654	−	0.909523i	$-0.363553\pi$
$757$	5.13713e28			0.831308			0.415654	+	0.909523i	$0.363553\pi$
$758$	2.72472e28	−	1.57312e28i	0.435141	−	0.251229i
$759$		0			0
$760$	−2.03157e28	+	3.51878e28i	−0.316006	+	0.547339i
$761$	−5.22370e28	−	3.01591e28i	−0.801922	−	0.462990i	0.0422209	−	0.999108i	$-0.486557\pi$
$761$	−5.22370e28	−	3.01591e28i	−0.801922	−	0.462990i	−0.844143	+	0.536119i	$0.819890\pi$
$762$		0			0
$763$	−7.75703e27	−	1.34356e28i	−0.115998	−	0.200914i
$764$		−	3.56135e28i		−	0.525631i
$765$		0			0
$766$	3.49529e28			0.502568
$767$	7.90904e28	−	4.56629e28i	1.12246	−	0.648052i
$768$		0			0
$769$	−5.11668e28	+	8.86235e28i	−0.707498	+	1.22542i	0.258285	+	0.966069i	$0.416843\pi$
$769$	−5.11668e28	+	8.86235e28i	−0.707498	+	1.22542i	−0.965783	+	0.259353i	$0.916491\pi$
$770$	−7.09252e26	−	4.09487e26i	−0.00968040	−	0.00558898i
$771$		0			0
$772$	1.15591e28	+	2.00209e28i	0.153727	+	0.266263i
$773$			5.76585e28i			0.756953i	0.925611	+	0.378476i	$0.123552\pi$
$773$			5.76585e28i			0.756953i	−0.925611	+	0.378476i	$0.876448\pi$
$774$		0			0
$775$	−1.60434e28			−0.205249
$776$	6.54482e27	−	3.77865e27i	0.0826572	−	0.0477221i
$777$		0			0
$778$	3.17465e28	−	5.49866e28i	0.390751	−	0.676801i
$779$	7.60718e28	+	4.39201e28i	0.924377	+	0.533689i
$780$		0			0
$781$	5.09951e25	+	8.83260e25i	0.000603973	+	0.00104611i
$782$			5.44867e28i			0.637123i
$783$		0			0
$784$	1.04189e27			0.0118758
$785$	−8.79872e28	+	5.07994e28i	−0.990200	+	0.571692i
$786$		0			0
$787$	8.81592e28	−	1.52696e29i	0.967209	−	1.67526i	0.263650	−	0.964618i	$-0.415074\pi$
$787$	8.81592e28	−	1.52696e29i	0.967209	−	1.67526i	0.703559	−	0.710637i	$-0.251593\pi$
$788$	−2.90720e28	−	1.67847e28i	−0.314929	−	0.181824i
$789$		0			0
$790$	−8.13724e28	−	1.40941e29i	−0.859422	−	1.48856i
$791$		−	3.30957e28i		−	0.345149i
$792$		0			0
$793$	1.89059e29			1.92250
$794$	−5.35139e27	+	3.08963e27i	−0.0537356	+	0.0310242i
$795$		0			0
$796$	−2.83625e25	+	4.91253e25i	−0.000277724	+	0.000481032i
$797$	−5.65241e28	−	3.26342e28i	−0.546576	−	0.315566i	0.201164	−	0.979558i	$-0.435528\pi$
$797$	−5.65241e28	−	3.26342e28i	−0.546576	−	0.315566i	−0.747740	+	0.663992i	$0.768861\pi$
$798$		0			0
$799$	7.01010e28	+	1.21418e29i	0.661084	+	1.14503i
$800$		−	2.98583e28i		−	0.278077i
$801$		0			0
$802$	1.06515e29			0.967537
$803$	1.23499e27	−	7.13021e26i	0.0110792	−	0.00639656i
$804$		0			0
$805$	−5.20952e28	+	9.02315e28i	−0.455868	+	0.789586i
$806$	−1.37231e28	−	7.92305e27i	−0.118605	−	0.0684766i
$807$		0			0
$808$	−3.40886e28	−	5.90431e28i	−0.287406	−	0.497801i
$809$		−	1.62400e29i		−	1.35239i	−0.736724	−	0.676194i	$-0.763628\pi$
$809$		−	1.62400e29i		−	1.35239i	0.736724	−	0.676194i	$-0.236372\pi$
$810$		0			0
$811$	−1.45773e29			−1.18432			−0.592158	−	0.805822i	$-0.701724\pi$
$811$	−1.45773e29			−1.18432			−0.592158	+	0.805822i	$0.701724\pi$
$812$	−6.63721e27	+	3.83199e27i	−0.0532629	+	0.0307514i
$813$		0			0
$814$	5.50358e26	−	9.53248e26i	0.00430925	−	0.00746383i
$815$	−1.38500e29	−	7.99630e28i	−1.07121	−	0.618462i
$816$		0			0
$817$	−7.11375e28	−	1.23214e29i	−0.536881	−	0.929905i
$818$		−	1.31664e29i		−	0.981598i
$819$		0			0
$820$	−1.05585e29			−0.768182
$821$	1.00485e29	−	5.80151e28i	0.722221	−	0.416974i	−0.0933488	−	0.995633i	$-0.529757\pi$
$821$	1.00485e29	−	5.80151e28i	0.722221	−	0.416974i	0.815569	+	0.578659i	$0.196424\pi$
$822$		0			0
$823$	2.91619e28	−	5.05099e28i	0.204559	−	0.354306i	−0.745433	−	0.666580i	$-0.767757\pi$
$823$	2.91619e28	−	5.05099e28i	0.204559	−	0.354306i	0.949992	+	0.312274i	$0.101091\pi$
$824$	8.35167e28	+	4.82184e28i	0.578764	+	0.334149i
$825$		0			0
$826$	4.67117e28	+	8.09071e28i	0.315955	+	0.547250i
$827$			1.07464e29i			0.718138i	0.933311	+	0.359069i	$0.116906\pi$
$827$			1.07464e29i			0.718138i	−0.933311	+	0.359069i	$0.883094\pi$
$828$		0			0
$829$	1.36212e29			0.888526			0.444263	−	0.895896i	$-0.353466\pi$
$829$	1.36212e29			0.888526			0.444263	+	0.895896i	$0.353466\pi$
$830$	−2.00702e29	+	1.15875e29i	−1.29351	+	0.746810i
$831$		0			0
$832$	1.47455e28	−	2.55400e28i	0.0927741	−	0.160690i
$833$	−1.07367e28	−	6.19886e27i	−0.0667456	−	0.0385356i
$834$		0			0
$835$	4.94703e28	+	8.56852e28i	0.300248	+	0.520045i
$836$			8.94658e26i			0.00536530i
$837$		0			0
$838$	−1.00690e29			−0.589587
$839$	−8.80015e28	+	5.08077e28i	−0.509179	+	0.293975i	−0.732496	−	0.680771i	$-0.761645\pi$
$839$	−8.80015e28	+	5.08077e28i	−0.509179	+	0.293975i	0.223317	+	0.974746i	$0.428311\pi$
$840$		0			0
$841$	−8.72190e28	+	1.51068e29i	−0.492778	+	0.853516i
$842$	8.70692e28	+	5.02694e28i	0.486120	+	0.280662i
$843$		0			0
$844$	−2.86498e28	−	4.96229e28i	−0.156206	−	0.270556i
$845$			3.58263e29i			1.93034i
$846$		0			0
$847$	1.94478e29			1.02338
$848$	−6.84123e28	+	3.94979e28i	−0.355775	+	0.205407i
$849$		0			0
$850$	−1.77645e29	+	3.07691e29i	−0.902329	+	1.56288i
$851$	−1.21273e29	−	7.00169e28i	−0.608791	−	0.351485i
$852$		0			0
$853$	−2.70088e28	−	4.67807e28i	−0.132439	−	0.229391i	0.792177	−	0.610291i	$-0.208948\pi$
$853$	−2.70088e28	−	4.67807e28i	−0.132439	−	0.229391i	−0.924616	+	0.380900i	$0.875614\pi$
$854$			1.93402e29i			0.937307i
$855$		0			0
$856$	1.28528e29			0.608500
$857$	1.13643e29	−	6.56120e28i	0.531784	−	0.307026i	−0.209959	−	0.977710i	$-0.567333\pi$
$857$	1.13643e29	−	6.56120e28i	0.531784	−	0.307026i	0.741743	+	0.670685i	$0.234000\pi$
$858$		0			0
$859$	−1.52143e29	+	2.63519e29i	−0.695536	+	1.20470i	0.274464	+	0.961597i	$0.411500\pi$
$859$	−1.52143e29	+	2.63519e29i	−0.695536	+	1.20470i	−0.970000	+	0.243106i	$0.921834\pi$
$860$	1.48105e29	+	8.55083e28i	0.669244	+	0.386388i
$861$		0			0
$862$	9.38499e28	+	1.62553e29i	0.414344	+	0.717665i
$863$		−	7.66633e28i		−	0.334564i	−0.985909	−	0.167282i	$-0.946501\pi$
$863$		−	7.66633e28i		−	0.334564i	0.985909	−	0.167282i	$-0.0534991\pi$
$864$		0			0
$865$	−7.11330e29			−3.03326
$866$	−3.76491e28	+	2.17367e28i	−0.158700	+	0.0916252i
$867$		0			0
$868$	8.10504e27	−	1.40383e28i	0.0333855	−	0.0578254i
$869$	−3.10337e27	−	1.79173e27i	−0.0126368	−	0.00729583i
$870$		0			0
$871$	−2.36364e29	−	4.09395e29i	−0.940589	−	1.62915i
$872$		−	2.03715e28i		−	0.0801414i
$873$		0			0
$874$	1.13819e29			0.437623
$875$	−2.14337e29	+	1.23747e29i	−0.814735	+	0.470388i
$876$		0			0
$877$	−2.05590e29	+	3.56093e29i	−0.763848	+	1.32302i	0.177006	+	0.984210i	$0.443359\pi$
$877$	−2.05590e29	+	3.56093e29i	−0.763848	+	1.32302i	−0.940854	+	0.338813i	$0.889974\pi$
$878$	2.13589e29	+	1.23316e29i	0.784575	+	0.452975i
$879$		0			0
$880$	−5.37696e26	−	9.31317e26i	−0.00193068	−	0.00334403i
$881$		−	2.10665e29i		−	0.747882i	−0.927452	−	0.373941i	$-0.878006\pi$
$881$		−	2.10665e29i		−	0.747882i	0.927452	−	0.373941i	$-0.121994\pi$
$882$		0			0
$883$	1.99293e29			0.691648			0.345824	−	0.938299i	$-0.387599\pi$
$883$	1.99293e29			0.691648			0.345824	+	0.938299i	$0.387599\pi$
$884$	−3.03907e29	+	1.75461e29i	−1.04284	+	0.602084i
$885$		0			0
$886$	−9.26345e28	+	1.60448e29i	−0.310768	+	0.538265i
$887$	−2.34665e29	−	1.35484e29i	−0.778415	−	0.449418i	0.0574532	−	0.998348i	$-0.481702\pi$
$887$	−2.34665e29	−	1.35484e29i	−0.778415	−	0.449418i	−0.835868	+	0.548930i	$0.815035\pi$
$888$		0			0
$889$	4.70810e28	+	8.15466e28i	0.152696	+	0.264477i
$890$			9.57612e28i			0.307107i
$891$		0			0
$892$	−1.20466e29			−0.377759
$893$	2.53635e29	−	1.46436e29i	0.786492	−	0.454081i
$894$		0			0
$895$	1.58164e29	−	2.73947e29i	0.479597	−	0.830686i
$896$	2.61266e28	+	1.50842e28i	0.0783436	+	0.0452317i
$897$		0			0
$898$	1.22876e29	+	2.12827e29i	0.360332	+	0.624113i
$899$			5.40734e27i			0.0156815i
$900$		0			0
$901$	9.39990e29			2.66609
$902$	−2.01339e27	+	1.16243e27i	−0.00564759	+	0.00326064i
$903$		0			0
$904$	2.17289e28	−	3.76356e28i	0.0596147	−	0.103256i
$905$	−8.25661e29	−	4.76696e29i	−2.24035	−	1.29347i
$906$		0			0
$907$	1.86159e29	+	3.22436e29i	0.494094	+	0.855797i	0.999977	−	0.00680574i	$-0.00216635\pi$
$907$	1.86159e29	+	3.22436e29i	0.494094	+	0.855797i	−0.505882	+	0.862602i	$0.668833\pi$
$908$		−	1.01380e29i		−	0.266131i
$909$		0			0
$910$	−6.71038e29			−1.72319
$911$	1.73791e29	−	1.00338e29i	0.441412	−	0.254849i	−0.262784	−	0.964855i	$-0.584641\pi$
$911$	1.73791e29	−	1.00338e29i	0.441412	−	0.254849i	0.704196	+	0.710005i	$0.251307\pi$
$912$		0			0
$913$	−2.55145e27	+	4.41923e27i	−0.00633984	+	0.0109809i
$914$	−1.62672e29	−	9.39187e28i	−0.399807	−	0.230829i
$915$		0			0
$916$	5.57653e28	+	9.65883e28i	0.134094	+	0.232258i
$917$		−	3.88870e28i		−	0.0924935i
$918$		0			0
$919$	6.33863e29			1.47516			0.737582	−	0.675258i	$-0.235968\pi$
$919$	6.33863e29			1.47516			0.737582	+	0.675258i	$0.235968\pi$
$920$	−1.18483e29	+	6.84060e28i	−0.272758	+	0.157477i
$921$		0			0
$922$	1.26287e29	−	2.18736e29i	0.284480	−	0.492733i
$923$	7.23712e28	+	4.17835e28i	0.161268	+	0.0931082i
$924$		0			0
$925$	−4.56559e29	−	7.90783e29i	−0.995587	−	1.72441i
$926$			6.66680e28i			0.143816i
$927$		0			0
$928$	−1.00636e28			−0.0212457
$929$	−3.99049e29	+	2.30391e29i	−0.833429	+	0.481180i	−0.855025	−	0.518586i	$-0.826458\pi$
$929$	−3.99049e29	+	2.30391e29i	−0.833429	+	0.481180i	0.0215963	+	0.999767i	$0.493125\pi$
$930$		0			0
$931$	−1.29490e28	+	2.24283e28i	−0.0264691	+	0.0458458i
$932$	−9.65467e28	−	5.57413e28i	−0.195244	−	0.112724i
$933$		0			0
$934$	1.35946e29	+	2.35465e29i	0.269089	+	0.466076i
$935$			1.27964e28i			0.0250594i
$936$		0			0
$937$	6.28798e29			1.20536			0.602678	−	0.797984i	$-0.294100\pi$
$937$	6.28798e29			1.20536			0.602678	+	0.797984i	$0.294100\pi$
$938$	4.18798e29	−	2.41793e29i	0.794285	−	0.458581i
$939$		0			0
$940$	−1.76018e29	+	3.04873e29i	−0.326798	+	0.566031i
$941$	2.77198e29	+	1.60040e29i	0.509206	+	0.293990i	0.732507	−	0.680759i	$-0.238350\pi$
$941$	2.77198e29	+	1.60040e29i	0.509206	+	0.293990i	−0.223302	+	0.974749i	$0.571683\pi$
$942$		0			0
$943$	1.47885e29	+	2.56145e29i	0.265955	+	0.460648i
$944$			1.22674e29i			0.218289i
$945$		0			0
$946$	3.76560e27			0.00656028
$947$	2.94641e29	−	1.70111e29i	0.507918	−	0.293247i	−0.224059	−	0.974575i	$-0.571931\pi$
$947$	2.94641e29	−	1.70111e29i	0.507918	−	0.293247i	0.731977	+	0.681329i	$0.238598\pi$
$948$		0			0
$949$	5.84223e29	−	1.01190e30i	0.986091	−	1.70796i
$950$	6.42745e29	+	3.71089e29i	1.07350	+	0.619787i
$951$		0			0
$952$	−1.79491e29	−	3.10887e29i	−0.293544	−	0.508433i
$953$			8.83613e29i			1.42999i	0.699130	+	0.714995i	$0.253571\pi$
$953$			8.83613e29i			1.42999i	−0.699130	+	0.714995i	$0.746429\pi$
$954$		0			0
$955$	−1.06407e30			−1.68630
$956$	4.32170e29	−	2.49513e29i	0.677759	−	0.391304i
$957$		0			0
$958$	7.58386e28	−	1.31356e29i	0.116476	−	0.201742i
$959$	−1.96787e29	−	1.13615e29i	−0.299095	−	0.172683i
$960$		0			0
$961$	3.30177e29	+	5.71883e29i	0.491488	+	0.851282i
$962$		−	9.01887e29i		−	1.32862i
$963$		0			0
$964$	4.21964e29			0.608843
$965$	5.98187e29	−	3.45363e29i	0.854208	−	0.493177i
$966$		0			0
$967$	2.93257e29	−	5.07936e29i	0.410188	−	0.710467i	−0.584722	−	0.811234i	$-0.698796\pi$
$967$	2.93257e29	−	5.07936e29i	0.410188	−	0.710467i	0.994910	+	0.100767i	$0.0321296\pi$
$968$	2.21156e29	+	1.27685e29i	0.306158	+	0.176760i
$969$		0			0
$970$	−1.12899e29	−	1.95547e29i	−0.153099	−	0.265176i
$971$		−	3.69674e29i		−	0.496166i	−0.968739	−	0.248083i	$-0.920199\pi$
$971$		−	3.69674e29i		−	0.496166i	0.968739	−	0.248083i	$-0.0798005\pi$
$972$		0			0
$973$	−7.19395e29			−0.945887
$974$	−3.39381e29	+	1.95941e29i	−0.441670	+	0.254998i
$975$		0			0
$976$	−1.26978e29	+	2.19932e29i	−0.161894	+	0.280408i
$977$	1.27081e30	+	7.33700e29i	1.60374	+	0.925919i	0.990731	+	0.135841i	$0.0433737\pi$
$977$	1.27081e30	+	7.33700e29i	1.60374	+	0.925919i	0.613007	+	0.790077i	$0.289960\pi$
$978$		0			0
$979$	1.05428e27	+	1.82606e27i	0.00130355	+	0.00225782i
$980$		−	3.11298e28i		−	0.0380991i
$981$		0			0
$982$	−7.76731e29			−0.931442
$983$	−1.76471e29	+	1.01886e29i	−0.209478	+	0.120942i	−0.601069	−	0.799197i	$-0.705258\pi$
$983$	−1.76471e29	+	1.01886e29i	−0.209478	+	0.120942i	0.391591	+	0.920139i	$0.371925\pi$
$984$		0			0
$985$	−5.01496e29	+	8.68616e29i	−0.583317	+	1.01034i
$986$	1.03705e29	+	5.98744e28i	0.119408	+	0.0689401i
$987$		0			0
$988$	3.66525e29	+	6.34840e29i	0.413556	+	0.716300i
$989$		−	4.79062e29i		−	0.535092i
$990$		0			0
$991$	2.62344e29			0.287166			0.143583	−	0.989638i	$-0.454138\pi$
$991$	2.62344e29			0.287166			0.143583	+	0.989638i	$0.454138\pi$
$992$	1.84337e28	−	1.06427e28i	0.0199754	−	0.0115328i
$993$		0			0
$994$	−4.27432e28	+	7.40335e28i	−0.0453945	+	0.0786257i
$995$	1.46777e27	+	8.47418e26i	0.00154322	+	0.000890978i
$996$		0			0
$997$	−5.55867e29	−	9.62790e29i	−0.572822	−	0.992156i	−0.996275	−	0.0862380i	$-0.972515\pi$
$997$	−5.55867e29	−	9.62790e29i	−0.572822	−	0.992156i	0.423453	−	0.905918i	$-0.360818\pi$
$998$		−	7.86298e29i		−	0.802198i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.21.d.a.17.20		40
3.2	odd	2		18.21.d.a.5.1	✓	40
9.2	odd	6	inner	54.21.d.a.35.20		40
9.7	even	3		18.21.d.a.11.1	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.21.d.a.5.1	✓	40	3.2	odd	2
18.21.d.a.11.1	yes	40	9.7	even	3
54.21.d.a.17.20		40	1.1	even	1	trivial
54.21.d.a.35.20		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)

\(f(q)\)	\(=\)	\(q+(627.069 - 362.039i) q^{2} +(262144. - 454047. i) q^{4} +(-1.35661e7 - 7.83237e6i) q^{5} +(-1.44553e8 - 2.50374e8i) q^{7} -3.79625e8i q^{8} -1.13425e10 q^{10} +(-2.16289e8 + 1.24874e8i) q^{11} +(-1.02318e11 + 1.77219e11i) q^{13} +(-1.81290e11 - 1.04668e11i) q^{14} +(-1.37439e11 - 2.38051e11i) q^{16} +3.27084e12i q^{17} +6.83256e12 q^{19} +(-7.11253e12 + 4.10642e12i) q^{20} +(-9.04188e10 + 1.56610e11i) q^{22} +(1.99240e13 + 1.15031e13i) q^{23} +(7.50084e13 + 1.29918e14i) q^{25} +1.48172e14i q^{26} -1.51575e14 q^{28} +(4.37882e13 - 2.52811e13i) q^{29} +(-5.34721e13 + 9.26164e13i) q^{31} +(-1.72368e14 - 9.95164e13i) q^{32} +(1.18417e15 + 2.05104e15i) q^{34} +4.52878e15i q^{35} -6.08677e15 q^{37} +(4.28449e15 - 2.47365e15i) q^{38} +(-2.97336e15 + 5.15002e15i) q^{40} +(1.11337e16 + 6.42805e15i) q^{41} +(-1.04115e16 - 1.80333e16i) q^{43} +1.30940e14i q^{44} +1.66583e16 q^{46} +(3.71215e16 - 2.14321e16i) q^{47} +(-1.89519e15 + 3.28256e15i) q^{49} +(9.40709e16 + 5.43119e16i) q^{50} +(5.36439e16 + 9.29140e16i) q^{52} -2.87385e17i q^{53} +3.91225e15 q^{55} +(-9.50481e16 + 5.48761e16i) q^{56} +(1.83055e16 - 3.17061e16i) q^{58} +(-3.86495e17 - 2.23143e17i) q^{59} +(-4.61942e17 - 8.00108e17i) q^{61} +7.74359e16i q^{62} -1.44115e17 q^{64} +(2.77610e18 - 1.60278e18i) q^{65} +(-1.15505e18 + 2.00061e18i) q^{67} +(1.48511e18 + 8.57431e17i) q^{68} +(1.63959e18 + 2.83986e18i) q^{70} -4.08371e17i q^{71} -5.70990e18 q^{73} +(-3.81683e18 + 2.20365e18i) q^{74} +(1.79111e18 - 3.10230e18i) q^{76} +(6.25306e16 + 3.61020e16i) q^{77} +(7.17413e18 + 1.24260e19i) q^{79} +4.30589e18i q^{80} +9.30881e18 q^{82} +(1.76947e19 - 1.02160e19i) q^{83} +(2.56184e19 - 4.43724e19i) q^{85} +(-1.30575e19 - 7.53876e18i) q^{86} +(4.74055e16 + 8.21087e16i) q^{88} -8.44270e18i q^{89} +5.91614e19 q^{91} +(1.04459e19 - 6.03096e18i) q^{92} +(1.55185e19 - 2.68788e19i) q^{94} +(-9.26910e19 - 5.35152e19i) q^{95} +(9.95365e18 + 1.72402e19i) q^{97} +2.74453e18i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 10485760 q^{4} - 29763918 q^{5} + 133479866 q^{7} + 35793208728 q^{11} + 39827158550 q^{13} - 187564400640 q^{14} - 5497558138880 q^{16} - 10560819523540 q^{19} - 15604865040384 q^{20} + 10829007458304 q^{22}+ \cdots - 66\!\cdots\!16 q^{97}+O(q^{100}) \) 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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