LMFDB - Embedded newform 54.21.d.a.35.7

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			35.7
Character	$\chi$	$=$	54.35
Dual form			54.21.d.a.17.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-627.069 - 362.039i) q^{2} +(262144. + 454047. i) q^{4} +(1.17375e7 - 6.77667e6i) q^{5} +(3.57156e7 - 6.18612e7i) q^{7} -3.79625e8i q^{8} -9.81366e9 q^{10} +(2.56780e10 + 1.48252e10i) q^{11} +(-1.57772e10 - 2.73268e10i) q^{13} +(-4.47923e10 + 2.58609e10i) q^{14} +(-1.37439e11 + 2.38051e11i) q^{16} -7.23153e11i q^{17} -8.01652e11 q^{19} +(6.15385e12 + 3.55293e12i) q^{20} +(-1.07346e13 - 1.85929e13i) q^{22} +(1.19655e13 - 6.90828e12i) q^{23} +(4.41627e13 - 7.64921e13i) q^{25} +2.28478e13i q^{26} +3.74505e13 q^{28} +(-6.91902e14 - 3.99470e14i) q^{29} +(-3.37835e14 - 5.85147e14i) q^{31} +(1.72368e14 - 9.95164e13i) q^{32} +(-2.61809e14 + 4.53467e14i) q^{34} -9.68131e14i q^{35} -5.05880e15 q^{37} +(5.02692e14 + 2.90229e14i) q^{38} +(-2.57259e15 - 4.45586e15i) q^{40} +(3.60872e15 - 2.08350e15i) q^{41} +(7.26248e15 - 1.25790e16i) q^{43} +1.55453e16i q^{44} -1.00043e16 q^{46} +(-5.75400e16 - 3.32207e16i) q^{47} +(3.73449e16 + 6.46833e16i) q^{49} +(-5.53862e16 + 3.19772e16i) q^{50} +(8.27178e15 - 1.43271e16i) q^{52} +1.90762e17i q^{53} +4.01862e17 q^{55} +(-2.34841e16 - 1.35585e16i) q^{56} +(2.89247e17 + 5.00990e17i) q^{58} +(-3.45568e17 + 1.99514e17i) q^{59} +(6.96650e17 - 1.20663e18i) q^{61} +4.89237e17i q^{62} -1.44115e17 q^{64} +(-3.70370e17 - 2.13833e17i) q^{65} +(-3.54139e17 - 6.13387e17i) q^{67} +(3.28345e17 - 1.89570e17i) q^{68} +(-3.50501e17 + 6.07085e17i) q^{70} -5.51361e18i q^{71} +3.91758e18 q^{73} +(3.17222e18 + 1.83148e18i) q^{74} +(-2.10148e17 - 3.63988e17i) q^{76} +(1.83421e18 - 1.05898e18i) q^{77} +(5.39686e17 - 9.34764e17i) q^{79} +3.72551e18i q^{80} -3.01722e18 q^{82} +(2.36693e19 + 1.36655e19i) q^{83} +(-4.90056e18 - 8.48803e18i) q^{85} +(-9.10816e18 + 5.25860e18i) q^{86} +(5.62802e18 - 9.74801e18i) q^{88} +3.04183e19i q^{89} -2.25396e18 q^{91} +(6.27337e18 + 3.62193e18i) q^{92} +(2.40544e19 + 4.16634e19i) q^{94} +(-9.40942e18 + 5.43253e18i) q^{95} +(1.89576e18 - 3.28356e18i) q^{97} -5.40812e19i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	1.17375e7	−	6.77667e6i	1.20192	−	0.693931i	0.240941	−	0.970540i	$-0.422544\pi$
$5$	1.17375e7	−	6.77667e6i	1.20192	−	0.693931i	0.960983	+	0.276609i	$0.0892107\pi$
$6$		0			0
$7$	3.57156e7	−	6.18612e7i	0.126438	−	0.218997i	−0.795856	−	0.605486i	$-0.792979\pi$
$7$	3.57156e7	−	6.18612e7i	0.126438	−	0.218997i	0.922294	+	0.386489i	$0.126312\pi$
$8$		−	3.79625e8i		−	0.353553i
$9$		0			0
$10$	−9.81366e9			−0.981366
$11$	2.56780e10	+	1.48252e10i	0.989998	+	0.571576i	0.905274	−	0.424829i	$-0.139666\pi$
$11$	2.56780e10	+	1.48252e10i	0.989998	+	0.571576i	0.0847243	+	0.996404i	$0.472999\pi$
$12$		0			0
$13$	−1.57772e10	−	2.73268e10i	−0.114445	−	0.198224i	0.803113	−	0.595827i	$-0.203176\pi$
$13$	−1.57772e10	−	2.73268e10i	−0.114445	−	0.198224i	−0.917558	+	0.397603i	$0.869842\pi$
$14$	−4.47923e10	+	2.58609e10i	−0.154854	+	0.0894052i
$15$		0			0
$16$	−1.37439e11	+	2.38051e11i	−0.125000	+	0.216506i
$17$		−	7.23153e11i		−	0.358708i	−0.983785	−	0.179354i	$-0.942599\pi$
$17$		−	7.23153e11i		−	0.358708i	0.983785	−	0.179354i	$-0.0574007\pi$
$18$		0			0
$19$	−8.01652e11			−0.130753			−0.0653763	−	0.997861i	$-0.520825\pi$
$19$	−8.01652e11			−0.130753			−0.0653763	+	0.997861i	$0.520825\pi$
$20$	6.15385e12	+	3.55293e12i	0.600962	+	0.346965i
$21$		0			0
$22$	−1.07346e13	−	1.85929e13i	−0.404165	−	0.700034i
$23$	1.19655e13	−	6.90828e12i	0.288837	−	0.166760i	−0.348580	−	0.937279i	$-0.613336\pi$
$23$	1.19655e13	−	6.90828e12i	0.288837	−	0.166760i	0.637417	+	0.770519i	$0.280003\pi$
$24$		0			0
$25$	4.41627e13	−	7.64921e13i	0.463080	−	0.802078i
$26$			2.28478e13i			0.161849i
$27$		0			0
$28$	3.74505e13			0.126438
$29$	−6.91902e14	−	3.99470e14i	−1.64462	−	0.949519i	−0.979162	−	0.203079i	$-0.934905\pi$
$29$	−6.91902e14	−	3.99470e14i	−1.64462	−	0.949519i	−0.665453	−	0.746440i	$-0.731762\pi$
$30$		0			0
$31$	−3.37835e14	−	5.85147e14i	−0.412181	−	0.713918i	0.582947	−	0.812510i	$-0.301899\pi$
$31$	−3.37835e14	−	5.85147e14i	−0.412181	−	0.713918i	−0.995128	+	0.0985921i	$0.968566\pi$
$32$	1.72368e14	−	9.95164e13i	0.153093	−	0.0883883i
$33$		0			0
$34$	−2.61809e14	+	4.53467e14i	−0.126822	+	0.219663i
$35$		−	9.68131e14i		−	0.350957i
$36$		0			0
$37$	−5.05880e15			−1.05204			−0.526018	−	0.850473i	$-0.676316\pi$
$37$	−5.05880e15			−1.05204			−0.526018	+	0.850473i	$0.676316\pi$
$38$	5.02692e14	+	2.90229e14i	0.0800692	+	0.0462280i
$39$		0			0
$40$	−2.57259e15	−	4.45586e15i	−0.245342	−	0.424944i
$41$	3.60872e15	−	2.08350e15i	0.268853	−	0.155222i	−0.359513	−	0.933140i	$-0.617057\pi$
$41$	3.60872e15	−	2.08350e15i	0.268853	−	0.155222i	0.628366	+	0.777918i	$0.283724\pi$
$42$		0			0
$43$	7.26248e15	−	1.25790e16i	0.336047	−	0.582051i	−0.647638	−	0.761948i	$-0.724243\pi$
$43$	7.26248e15	−	1.25790e16i	0.336047	−	0.582051i	0.983685	+	0.179897i	$0.0575765\pi$
$44$			1.55453e16i			0.571576i
$45$		0			0
$46$	−1.00043e16			−0.235834
$47$	−5.75400e16	−	3.32207e16i	−1.09393	−	0.631583i	−0.159313	−	0.987228i	$-0.550928\pi$
$47$	−5.75400e16	−	3.32207e16i	−1.09393	−	0.631583i	−0.934621	+	0.355645i	$0.884261\pi$
$48$		0			0
$49$	3.73449e16	+	6.46833e16i	0.468027	+	0.810646i
$50$	−5.53862e16	+	3.19772e16i	−0.567155	+	0.327447i
$51$		0			0
$52$	8.27178e15	−	1.43271e16i	0.0572223	−	0.0991119i
$53$			1.90762e17i			1.09077i	0.838186	+	0.545385i	$0.183617\pi$
$53$			1.90762e17i			1.09077i	−0.838186	+	0.545385i	$0.816383\pi$
$54$		0			0
$55$	4.01862e17			1.58654
$56$	−2.34841e16	−	1.35585e16i	−0.0774271	−	0.0447026i
$57$		0			0
$58$	2.89247e17	+	5.00990e17i	0.671411	+	1.16292i
$59$	−3.45568e17	+	1.99514e17i	−0.676104	+	0.390349i	−0.798385	−	0.602147i	$-0.794312\pi$
$59$	−3.45568e17	+	1.99514e17i	−0.676104	+	0.390349i	0.122282	+	0.992495i	$0.460979\pi$
$60$		0			0
$61$	6.96650e17	−	1.20663e18i	0.976599	−	1.69152i	0.302045	−	0.953294i	$-0.402331\pi$
$61$	6.96650e17	−	1.20663e18i	0.976599	−	1.69152i	0.674554	−	0.738225i	$-0.264336\pi$
$62$			4.89237e17i			0.582912i
$63$		0			0
$64$	−1.44115e17			−0.125000
$65$	−3.70370e17	−	2.13833e17i	−0.275107	−	0.158833i
$66$		0			0
$67$	−3.54139e17	−	6.13387e17i	−0.194279	−	0.336501i	0.752385	−	0.658724i	$-0.228903\pi$
$67$	−3.54139e17	−	6.13387e17i	−0.194279	−	0.336501i	−0.946664	+	0.322223i	$0.895570\pi$
$68$	3.28345e17	−	1.89570e17i	0.155325	−	0.0896769i
$69$		0			0
$70$	−3.50501e17	+	6.07085e17i	−0.124082	+	0.214916i
$71$		−	5.51361e18i		−	1.69376i	−0.531781	−	0.846882i	$-0.678477\pi$
$71$		−	5.51361e18i		−	1.69376i	0.531781	−	0.846882i	$-0.321523\pi$
$72$		0			0
$73$	3.91758e18			0.911568			0.455784	−	0.890091i	$-0.349359\pi$
$73$	3.91758e18			0.911568			0.455784	+	0.890091i	$0.349359\pi$
$74$	3.17222e18	+	1.83148e18i	0.644238	+	0.371951i
$75$		0			0
$76$	−2.10148e17	−	3.63988e17i	−0.0326881	−	0.0566175i
$77$	1.83421e18	−	1.05898e18i	0.250347	−	0.144538i
$78$		0			0
$79$	5.39686e17	−	9.34764e17i	0.0569994	−	0.0987258i	−0.836118	−	0.548550i	$-0.815180\pi$
$79$	5.39686e17	−	9.34764e17i	0.0569994	−	0.0987258i	0.893117	+	0.449824i	$0.148513\pi$
$80$			3.72551e18i			0.346965i
$81$		0			0
$82$	−3.01722e18			−0.219517
$83$	2.36693e19	+	1.36655e19i	1.52548	+	0.880734i	0.999544	+	0.0302074i	$0.00961679\pi$
$83$	2.36693e19	+	1.36655e19i	1.52548	+	0.880734i	0.525932	+	0.850526i	$0.323717\pi$
$84$		0			0
$85$	−4.90056e18	−	8.48803e18i	−0.248918	−	0.431139i
$86$	−9.10816e18	+	5.25860e18i	−0.411572	+	0.237621i
$87$		0			0
$88$	5.62802e18	−	9.74801e18i	0.202083	−	0.350017i
$89$			3.04183e19i			0.975517i	0.872979	+	0.487758i	$0.162185\pi$
$89$			3.04183e19i			0.975517i	−0.872979	+	0.487758i	$0.837815\pi$
$90$		0			0
$91$	−2.25396e18			−0.0578806
$92$	6.27337e18	+	3.62193e18i	0.144418	+	0.0833800i
$93$		0			0
$94$	2.40544e19	+	4.16634e19i	0.446597	+	0.773528i
$95$	−9.40942e18	+	5.43253e18i	−0.157155	+	0.0907332i
$96$		0			0
$97$	1.89576e18	−	3.28356e18i	0.0257079	−	0.0445274i	−0.852885	−	0.522098i	$-0.825149\pi$
$97$	1.89576e18	−	3.28356e18i	0.0257079	−	0.0445274i	0.878593	+	0.477571i	$0.158483\pi$
$98$		−	5.40812e19i		−	0.661890i
$99$		0			0
$100$	4.63080e19			0.463080
$101$	1.86158e20	+	1.07479e20i	1.68527	+	0.972989i	0.958059	+	0.286572i	$0.0925157\pi$
$101$	1.86158e20	+	1.07479e20i	1.68527	+	0.972989i	0.727208	+	0.686417i	$0.240818\pi$
$102$		0			0
$103$	−4.53235e19	−	7.85026e19i	−0.337250	−	0.584133i	0.646665	−	0.762774i	$-0.276163\pi$
$103$	−4.53235e19	−	7.85026e19i	−0.337250	−	0.584133i	−0.983914	+	0.178641i	$0.942830\pi$
$104$	−1.03740e19	+	5.98941e18i	−0.0700827	+	0.0404623i
$105$		0			0
$106$	6.90632e19	−	1.19621e20i	0.385646	−	0.667958i
$107$		−	1.83106e20i		−	0.930819i	−0.885095	−	0.465410i	$-0.845907\pi$
$107$		−	1.83106e20i		−	0.930819i	0.885095	−	0.465410i	$-0.154093\pi$
$108$		0			0
$109$	−2.69469e20			−1.13826			−0.569132	−	0.822246i	$-0.692721\pi$
$109$	−2.69469e20			−1.13826			−0.569132	+	0.822246i	$0.692721\pi$
$110$	−2.51995e20	−	1.45490e20i	−0.971551	−	0.560925i
$111$		0			0
$112$	9.81743e18	+	1.70043e19i	0.0316095	+	0.0547493i
$113$	−1.93171e20	+	1.11527e20i	−0.569059	+	0.328546i	−0.756773	−	0.653677i	$-0.773225\pi$
$113$	−1.93171e20	+	1.11527e20i	−0.569059	+	0.328546i	0.187715	+	0.982224i	$0.439892\pi$
$114$		0			0
$115$	9.36303e19	−	1.62172e20i	0.231440	−	0.400865i
$116$		−	4.18874e20i		−	0.949519i
$117$		0			0
$118$	2.88927e20			0.552036
$119$	−4.47351e19	−	2.58278e19i	−0.0785559	−	0.0453543i
$120$		0			0
$121$	1.03198e20	+	1.78744e20i	0.153397	+	0.265692i
$122$	−8.73696e20	+	5.04428e20i	−1.19608	+	0.690560i
$123$		0			0
$124$	1.77123e20	−	3.06786e20i	0.206090	−	0.356959i
$125$			9.54418e19i			0.102480i
$126$		0			0
$127$	4.60714e19			0.0422080			0.0211040	−	0.999777i	$-0.493282\pi$
$127$	4.60714e19			0.0422080			0.0211040	+	0.999777i	$0.493282\pi$
$128$	9.03702e19	+	5.21753e19i	0.0765466	+	0.0441942i
$129$		0			0
$130$	1.54832e20	+	2.68176e20i	0.112312	+	0.194530i
$131$	−1.81540e21	+	1.04812e21i	−1.21972	+	0.704205i	−0.964858	−	0.262772i	$-0.915363\pi$
$131$	−1.81540e21	+	1.04812e21i	−1.21972	+	0.704205i	−0.254861	+	0.966978i	$0.582030\pi$
$132$		0			0
$133$	−2.86315e19	+	4.95912e19i	−0.0165321	+	0.0286344i
$134$			5.12848e20i			0.274752i
$135$		0			0
$136$	−2.74527e20			−0.126822
$137$	−3.11573e21	−	1.79887e21i	−1.33769	−	0.772314i	−0.351223	−	0.936292i	$-0.614234\pi$
$137$	−3.11573e21	−	1.79887e21i	−1.33769	−	0.772314i	−0.986464	+	0.163978i	$0.947567\pi$
$138$		0			0
$139$	−2.35790e21	−	4.08401e21i	−0.875745	−	1.51684i	−0.855967	−	0.517031i	$-0.827037\pi$
$139$	−2.35790e21	−	4.08401e21i	−0.875745	−	1.51684i	−0.0197788	−	0.999804i	$-0.506296\pi$
$140$	4.39577e20	−	2.53790e20i	0.151969	−	0.0877392i
$141$		0			0
$142$	−1.99614e21	+	3.45742e21i	−0.598836	+	1.03721i
$143$		−	9.35598e20i		−	0.261655i
$144$		0			0
$145$	−1.08283e22			−2.63560
$146$	−2.45659e21	−	1.41831e21i	−0.558219	−	0.322288i
$147$		0			0
$148$	−1.32614e21	−	2.29693e21i	−0.263009	−	0.455545i
$149$	6.19507e21	−	3.57673e21i	1.14864	−	0.663167i	0.200084	−	0.979779i	$-0.435879\pi$
$149$	6.19507e21	−	3.57673e21i	1.14864	−	0.663167i	0.948555	+	0.316612i	$0.102545\pi$
$150$		0			0
$151$	5.52344e21	−	9.56687e21i	0.896272	−	1.55239i	0.0640500	−	0.997947i	$-0.479598\pi$
$151$	5.52344e21	−	9.56687e21i	0.896272	−	1.55239i	0.832222	−	0.554442i	$-0.187068\pi$
$152$			3.04327e20i			0.0462280i
$153$		0			0
$154$	−1.53357e21			−0.204407
$155$	−7.93070e21	−	4.57879e21i	−0.990819	−	0.572050i
$156$		0			0
$157$	1.52260e21	+	2.63722e21i	0.167336	+	0.289835i	0.937482	−	0.348033i	$-0.113150\pi$
$157$	1.52260e21	+	2.63722e21i	0.167336	+	0.289835i	−0.770146	+	0.637867i	$0.779817\pi$
$158$	−6.76841e20	+	3.90774e20i	−0.0698097	+	0.0403047i
$159$		0			0
$160$	1.34878e21	−	2.33615e21i	0.122671	−	0.212472i
$161$		−	9.86934e20i		−	0.0843392i
$162$		0			0
$163$	2.38113e20			0.0179848			0.00899242	−	0.999960i	$-0.497138\pi$
$163$	2.38113e20			0.0179848			0.00899242	+	0.999960i	$0.497138\pi$
$164$	1.89201e21	+	1.09235e21i	0.134426	+	0.0776111i
$165$		0			0
$166$	−9.89488e21	−	1.71384e22i	−0.622773	−	1.07867i
$167$	−2.21610e22	+	1.27947e22i	−1.31348	+	0.758340i	−0.982671	−	0.185357i	$-0.940656\pi$
$167$	−2.21610e22	+	1.27947e22i	−1.31348	+	0.758340i	−0.330811	+	0.943697i	$0.607322\pi$
$168$		0			0
$169$	9.00464e21	−	1.55965e22i	0.473805	−	0.820654i
$170$			7.09678e21i			0.352024i
$171$		0			0
$172$	7.61526e21			0.336047
$173$	−2.38592e22	−	1.37751e22i	−0.993563	−	0.573634i	−0.0872255	−	0.996189i	$-0.527800\pi$
$173$	−2.38592e22	−	1.37751e22i	−0.993563	−	0.573634i	−0.906337	+	0.422555i	$0.861133\pi$
$174$		0			0
$175$	−3.15460e21	−	5.46392e21i	−0.117102	−	0.202826i
$176$	−7.05831e21	+	4.07512e21i	−0.247500	+	0.142894i
$177$		0			0
$178$	1.10126e22	−	1.90744e22i	0.344897	−	0.597380i
$179$			3.23550e22i			0.958100i	0.877787	+	0.479050i	$0.159019\pi$
$179$			3.23550e22i			0.958100i	−0.877787	+	0.479050i	$0.840981\pi$
$180$		0			0
$181$	3.89570e22			1.03229			0.516143	−	0.856503i	$-0.327367\pi$
$181$	3.89570e22			1.03229			0.516143	+	0.856503i	$0.327367\pi$
$182$	1.41339e21	+	8.16022e20i	0.0354445	+	0.0204639i
$183$		0			0
$184$	−2.62256e21	−	4.54240e21i	−0.0589586	−	0.102119i
$185$	−5.93779e22	+	3.42818e22i	−1.26447	+	0.730040i
$186$		0			0
$187$	1.07209e22	−	1.85691e22i	0.205029	−	0.355120i
$188$		−	3.48344e22i		−	0.631583i
$189$		0			0
$190$	7.86715e21			0.128316
$191$	−2.25973e22	−	1.30465e22i	−0.349721	−	0.201912i	0.314841	−	0.949144i	$-0.398049\pi$
$191$	−2.25973e22	−	1.30465e22i	−0.349721	−	0.201912i	−0.664563	+	0.747233i	$0.731382\pi$
$192$		0			0
$193$	−5.38625e22	−	9.32926e22i	−0.751127	−	1.30099i	−0.947277	−	0.320416i	$-0.896177\pi$
$193$	−5.38625e22	−	9.32926e22i	−0.751127	−	1.30099i	0.196150	−	0.980574i	$-0.437156\pi$
$194$	−2.37755e21	+	1.37268e21i	−0.0314856	+	0.0181782i
$195$		0			0
$196$	−1.95795e22	+	3.39127e22i	−0.234013	+	0.405323i
$197$		−	1.12584e23i		−	1.27883i	−0.768860	−	0.639417i	$-0.779176\pi$
$197$		−	1.12584e23i		−	1.27883i	0.768860	−	0.639417i	$-0.220824\pi$
$198$		0			0
$199$	−1.09579e23			−1.12511			−0.562557	−	0.826759i	$-0.690182\pi$
$199$	−1.09579e23			−1.12511			−0.562557	+	0.826759i	$0.690182\pi$
$200$	−2.90383e22	−	1.67653e22i	−0.283577	−	0.163723i
$201$		0			0
$202$	−7.78228e22	−	1.34793e23i	−0.688007	−	1.19166i
$203$	−4.94234e22	+	2.85346e22i	−0.415884	+	0.240111i
$204$		0			0
$205$	2.82383e22	−	4.89102e22i	0.215427	−	0.373131i
$206$			6.56355e22i			0.476943i
$207$		0			0
$208$	8.67359e21			0.0572223
$209$	−2.05848e22	−	1.18847e22i	−0.129445	−	0.0747350i
$210$		0			0
$211$	−2.26674e22	−	3.92612e22i	−0.129592	−	0.224460i	0.793927	−	0.608014i	$-0.208033\pi$
$211$	−2.26674e22	−	3.92612e22i	−0.129592	−	0.224460i	−0.923519	+	0.383554i	$0.874700\pi$
$212$	−8.66149e22	+	5.00071e22i	−0.472317	+	0.272693i
$213$		0			0
$214$	−6.62915e22	+	1.14820e23i	−0.329094	+	0.570008i
$215$		−	1.96862e23i		−	0.932774i
$216$		0			0
$217$	−4.82639e22			−0.208461
$218$	1.68975e23	+	9.75580e22i	0.697042	+	0.402437i
$219$		0			0
$220$	1.05346e23	+	1.82464e23i	0.396634	+	0.686990i
$221$	−1.97615e22	+	1.14093e22i	−0.0711044	+	0.0410522i
$222$		0			0
$223$	1.67381e22	−	2.89912e22i	0.0550374	−	0.0953275i	−0.837194	−	0.546906i	$-0.815806\pi$
$223$	1.67381e22	−	2.89912e22i	0.0550374	−	0.0953275i	0.892231	+	0.451578i	$0.149139\pi$
$224$		−	1.42172e22i		−	0.0447026i
$225$		0			0
$226$	1.61509e23			0.464634
$227$	2.57354e23	+	1.48584e23i	0.708391	+	0.408990i	0.810465	−	0.585787i	$-0.199215\pi$
$227$	2.57354e23	+	1.48584e23i	0.708391	+	0.408990i	−0.102074	+	0.994777i	$0.532548\pi$
$228$		0			0
$229$	1.24038e23	+	2.14841e23i	0.312753	+	0.541703i	0.978957	−	0.204066i	$-0.0654156\pi$
$229$	1.24038e23	+	2.14841e23i	0.312753	+	0.541703i	−0.666205	+	0.745769i	$0.732082\pi$
$230$	−1.17425e23	+	6.77956e22i	−0.283455	+	0.163653i
$231$		0			0
$232$	−1.51649e23	+	2.62663e23i	−0.335706	+	0.581459i
$233$		−	6.33329e23i		−	1.34298i	−0.741013	−	0.671491i	$-0.765654\pi$
$233$		−	6.33329e23i		−	1.34298i	0.741013	−	0.671491i	$-0.234346\pi$
$234$		0			0
$235$	−9.00503e23			−1.75310
$236$	−1.81177e23	−	1.04603e23i	−0.338052	−	0.195174i
$237$		0			0
$238$	1.87013e22	+	3.23917e22i	0.0320703	+	0.0555474i
$239$	−4.10320e23	+	2.36898e23i	−0.674751	+	0.389567i	−0.797874	−	0.602824i	$-0.794042\pi$
$239$	−4.10320e23	+	2.36898e23i	−0.674751	+	0.389567i	0.123124	+	0.992391i	$0.460709\pi$
$240$		0			0
$241$	4.46115e22	−	7.72693e22i	0.0674957	−	0.116906i	−0.830303	−	0.557313i	$-0.811832\pi$
$241$	4.46115e22	−	7.72693e22i	0.0674957	−	0.116906i	0.897798	+	0.440407i	$0.145166\pi$
$242$		−	1.49447e23i		−	0.216937i
$243$		0			0
$244$	7.30490e23			0.976599
$245$	8.76675e23	+	5.06148e23i	1.12506	+	0.649557i
$246$		0			0
$247$	1.26478e22	+	2.19066e22i	0.0149639	+	0.0259183i
$248$	−2.22137e23	+	1.28251e23i	−0.252408	+	0.145728i
$249$		0			0
$250$	3.45536e22	−	5.98487e22i	0.0362321	−	0.0627559i
$251$			5.28845e23i			0.532833i	0.963858	+	0.266416i	$0.0858396\pi$
$251$			5.28845e23i			0.532833i	−0.963858	+	0.266416i	$0.914160\pi$
$252$		0			0
$253$	4.09667e23			0.381264
$254$	−2.88900e22	−	1.66796e22i	−0.0258470	−	0.0149228i
$255$		0			0
$256$	−3.77789e22	−	6.54350e22i	−0.0312500	−	0.0541266i
$257$	1.10861e24	−	6.40053e23i	0.881953	−	0.509196i	0.0106514	−	0.999943i	$-0.496610\pi$
$257$	1.10861e24	−	6.40053e23i	0.881953	−	0.509196i	0.871302	+	0.490747i	$0.163276\pi$
$258$		0			0
$259$	−1.80678e23	+	3.12944e23i	−0.133017	+	0.230393i
$260$		−	2.24220e23i		−	0.158833i
$261$		0			0
$262$	1.51784e24			0.995897
$263$	6.04040e23	+	3.48742e23i	0.381512	+	0.220266i	0.678476	−	0.734623i	$-0.262641\pi$
$263$	6.04040e23	+	3.48742e23i	0.381512	+	0.220266i	−0.296964	+	0.954889i	$0.595974\pi$
$264$		0			0
$265$	1.29273e24	+	2.23908e24i	0.756919	+	1.31102i
$266$	3.59079e22	−	2.07314e22i	0.0202476	−	0.0116900i
$267$		0			0
$268$	1.85671e23	−	3.21592e23i	0.0971395	−	0.168251i
$269$			3.02071e23i			0.152260i	0.997098	+	0.0761300i	$0.0242564\pi$
$269$			3.02071e23i			0.152260i	−0.997098	+	0.0761300i	$0.975744\pi$
$270$		0			0
$271$	7.70140e23			0.360476			0.180238	−	0.983623i	$-0.442313\pi$
$271$	7.70140e23			0.360476			0.180238	+	0.983623i	$0.442313\pi$
$272$	1.72147e23	+	9.93893e22i	0.0776625	+	0.0448385i
$273$		0			0
$274$	1.30252e24	+	2.25603e24i	0.546108	+	0.945887i
$275$	2.26802e24	−	1.30944e24i	0.916896	−	0.529370i
$276$		0			0
$277$	−2.31359e23	+	4.00726e23i	−0.0869940	+	0.150678i	−0.906239	−	0.422765i	$-0.861059\pi$
$277$	−2.31359e23	+	4.00726e23i	−0.0869940	+	0.150678i	0.819245	+	0.573443i	$0.194393\pi$
$278$			3.41461e24i			1.23849i
$279$		0			0
$280$	−3.67527e23			−0.124082
$281$	2.54661e24	+	1.47029e24i	0.829658	+	0.479003i	0.853736	−	0.520707i	$-0.174332\pi$
$281$	2.54661e24	+	1.47029e24i	0.829658	+	0.479003i	−0.0240776	+	0.999710i	$0.507665\pi$
$282$		0			0
$283$	−6.62782e23	−	1.14797e24i	−0.201144	−	0.348391i	0.747753	−	0.663976i	$-0.231132\pi$
$283$	−6.62782e23	−	1.14797e24i	−0.201144	−	0.348391i	−0.948897	+	0.315585i	$0.897799\pi$
$284$	2.50344e24	−	1.44536e24i	0.733421	−	0.423441i
$285$		0			0
$286$	−3.38723e23	+	5.86685e23i	−0.0925090	+	0.160230i
$287$		−	2.97653e23i		−	0.0785040i
$288$		0			0
$289$	3.54128e24			0.871329
$290$	6.79009e24	+	3.92026e24i	1.61397	+	0.931826i
$291$		0			0
$292$	1.02697e24	+	1.77876e24i	0.227892	+	0.394720i
$293$	4.64156e24	−	2.67981e24i	0.995378	−	0.574682i	0.0885007	−	0.996076i	$-0.471792\pi$
$293$	4.64156e24	−	2.67981e24i	0.995378	−	0.574682i	0.906878	+	0.421394i	$0.138459\pi$
$294$		0			0
$295$	−2.70408e24	+	4.68360e24i	−0.541750	+	0.938338i
$296$			1.92045e24i			0.371951i
$297$		0			0
$298$	−5.17965e24			−0.937860
$299$	−3.77563e23	−	2.17986e23i	−0.0661116	−	0.0381696i
$300$		0			0
$301$	−5.18768e23	−	8.98532e23i	−0.0849783	−	0.147187i
$302$	−6.92716e24	+	3.99940e24i	−1.09770	+	0.633760i
$303$		0			0
$304$	1.10178e23	−	1.90834e23i	0.0163441	−	0.0283088i
$305$		−	1.88839e25i		−	2.71077i
$306$		0			0
$307$	−5.00111e24			−0.672485			−0.336242	−	0.941775i	$-0.609156\pi$
$307$	−5.00111e24			−0.672485			−0.336242	+	0.941775i	$0.609156\pi$
$308$	9.61655e23	+	5.55212e23i	0.125173	+	0.0722689i
$309$		0			0
$310$	3.31540e24	+	5.74244e24i	0.404500	+	0.700615i
$311$	−1.21897e25	+	7.03775e24i	−1.44009	+	0.831438i	−0.997855	−	0.0654605i	$-0.979148\pi$
$311$	−1.21897e25	+	7.03775e24i	−1.44009	+	0.831438i	−0.442237	+	0.896898i	$0.645815\pi$
$312$		0			0
$313$	3.23512e24	−	5.60340e24i	0.358466	−	0.620881i	−0.629239	−	0.777212i	$-0.716633\pi$
$313$	3.23512e24	−	5.60340e24i	0.358466	−	0.620881i	0.987705	+	0.156331i	$0.0499667\pi$
$314$		−	2.20496e24i		−	0.236649i
$315$		0			0
$316$	5.65902e23			0.0569994
$317$	−7.21900e24	−	4.16789e24i	−0.704506	−	0.406746i	0.104518	−	0.994523i	$-0.466670\pi$
$317$	−7.21900e24	−	4.16789e24i	−0.704506	−	0.406746i	−0.809023	+	0.587777i	$0.800003\pi$
$318$		0			0
$319$	−1.18444e25	−	2.05152e25i	−1.08544	−	1.88004i
$320$	−1.69156e24	+	9.76621e23i	−0.150240	+	0.0867414i
$321$		0			0
$322$	−3.57308e23	+	6.18876e23i	−0.0298184	+	0.0516470i
$323$			5.79717e23i			0.0469019i
$324$		0			0
$325$	−2.78705e24			−0.211988
$326$	−1.49313e23	−	8.62061e22i	−0.0110134	−	0.00635860i
$327$		0			0
$328$	−7.90947e23	−	1.36996e24i	−0.0548794	−	0.0950538i
$329$	−4.11015e24	+	2.37300e24i	−0.276630	+	0.159712i
$330$		0			0
$331$	−5.88743e24	+	1.01973e25i	−0.372946	+	0.645961i	−0.990017	−	0.140946i	$-0.954986\pi$
$331$	−5.88743e24	+	1.01973e25i	−0.372946	+	0.645961i	0.617071	+	0.786907i	$0.288319\pi$
$332$			1.43293e25i			0.880734i
$333$		0			0
$334$	1.85286e25			1.07245
$335$	−8.31344e24	−	4.79977e24i	−0.467017	−	0.269632i
$336$		0			0
$337$	−7.37533e23	−	1.27744e24i	−0.0390375	−	0.0676150i	0.845847	−	0.533426i	$-0.179096\pi$
$337$	−7.37533e23	−	1.27744e24i	−0.0390375	−	0.0676150i	−0.884884	+	0.465811i	$0.845763\pi$
$338$	−1.12931e25	+	6.52006e24i	−0.580290	+	0.335031i
$339$		0			0
$340$	2.56931e24	−	4.45017e24i	0.124459	−	0.215570i
$341$		−	2.00339e25i		−	0.942370i
$342$		0			0
$343$	1.10348e25			0.489582
$344$	−4.77530e24	−	2.75702e24i	−0.205786	−	0.118811i
$345$		0			0
$346$	9.97426e24	+	1.72759e25i	0.405620	+	0.702555i
$347$	−1.38885e25	+	8.01853e24i	−0.548732	+	0.316811i	−0.748610	−	0.663010i	$-0.769279\pi$
$347$	−1.38885e25	+	8.01853e24i	−0.548732	+	0.316811i	0.199878	+	0.979821i	$0.435945\pi$
$348$		0			0
$349$	−1.12977e25	+	1.95683e25i	−0.421441	+	0.729958i	−0.996081	−	0.0884488i	$-0.971809\pi$
$349$	−1.12977e25	+	1.95683e25i	−0.421441	+	0.729958i	0.574639	+	0.818407i	$0.305142\pi$
$350$			4.56835e24i			0.165607i
$351$		0			0
$352$	5.90140e24			0.202083
$353$	−1.69679e25	−	9.79639e24i	−0.564781	−	0.326076i	0.190281	−	0.981730i	$-0.439060\pi$
$353$	−1.69679e25	−	9.79639e24i	−0.564781	−	0.326076i	−0.755062	+	0.655653i	$0.772393\pi$
$354$		0			0
$355$	−3.73639e25	−	6.47162e25i	−1.17535	−	2.03577i
$356$	−1.38113e25	+	7.97397e24i	−0.422411	+	0.243879i
$357$		0			0
$358$	1.17138e25	−	2.02888e25i	0.338740	−	0.586714i
$359$			2.41949e24i			0.0680423i	0.999421	+	0.0340211i	$0.0108314\pi$
$359$			2.41949e24i			0.0680423i	−0.999421	+	0.0340211i	$0.989169\pi$
$360$		0			0
$361$	−3.69473e25			−0.982904
$362$	−2.44287e25	−	1.41039e25i	−0.632143	−	0.364968i
$363$		0			0
$364$	−5.90863e23	−	1.02340e24i	−0.0144701	−	0.0250630i
$365$	4.59827e25	−	2.65481e25i	1.09563	−	0.632565i
$366$		0			0
$367$	2.58177e25	−	4.47175e25i	0.582447	−	1.00883i	−0.412741	−	0.910848i	$-0.635429\pi$
$367$	2.58177e25	−	4.47175e25i	0.582447	−	1.00883i	0.995188	−	0.0979799i	$-0.0312381\pi$
$368$			3.79787e24i			0.0833800i
$369$		0			0
$370$	4.96454e25			1.03243
$371$	1.18008e25	+	6.81318e24i	0.238875	+	0.137915i
$372$		0			0
$373$	−4.44983e25	−	7.70733e25i	−0.853601	−	1.47848i	−0.877936	−	0.478777i	$-0.841080\pi$
$373$	−4.44983e25	−	7.70733e25i	−0.853601	−	1.47848i	0.0243350	−	0.999704i	$-0.492253\pi$
$374$	−1.34455e25	+	7.76275e24i	−0.251108	+	0.144977i
$375$		0			0
$376$	−1.26114e25	+	2.18436e25i	−0.223298	+	0.386764i
$377$			2.52100e25i			0.434669i
$378$		0			0
$379$	−7.69536e25			−1.25845			−0.629226	−	0.777222i	$-0.716628\pi$
$379$	−7.69536e25			−1.25845			−0.629226	+	0.777222i	$0.716628\pi$
$380$	−4.93325e24	−	2.84821e24i	−0.0785773	−	0.0453666i
$381$		0			0
$382$	9.44670e24	+	1.63622e25i	0.142773	+	0.247290i
$383$	8.62530e25	−	4.97982e25i	1.26995	−	0.733205i	0.294971	−	0.955506i	$-0.404690\pi$
$383$	8.62530e25	−	4.97982e25i	1.26995	−	0.733205i	0.974978	+	0.222301i	$0.0713568\pi$
$384$		0			0
$385$	1.43527e25	−	2.48597e25i	0.200598	−	0.347447i
$386$			7.80012e25i			1.06225i
$387$		0			0
$388$	1.98785e24			0.0257079
$389$	−6.87204e25	−	3.96758e25i	−0.866143	−	0.500068i	−7.86158e−5	−	1.00000i	$-0.500025\pi$
$389$	−6.87204e25	−	3.96758e25i	−0.866143	−	0.500068i	−0.866065	+	0.499932i	$0.833358\pi$
$390$		0			0
$391$	−4.99574e24	−	8.65288e24i	−0.0598181	−	0.103608i
$392$	2.45554e25	−	1.41771e25i	0.286607	−	0.165472i
$393$		0			0
$394$	−4.07597e25	+	7.05979e25i	−0.452136	+	0.783123i
$395$		−	1.46291e25i		−	0.158215i
$396$		0			0
$397$	6.75249e24			0.0694319			0.0347159	−	0.999397i	$-0.488947\pi$
$397$	6.75249e24			0.0694319			0.0347159	+	0.999397i	$0.488947\pi$
$398$	6.87136e25	+	3.96718e25i	0.688988	+	0.397788i
$399$		0			0
$400$	1.21394e25	+	2.10260e25i	0.115770	+	0.200519i
$401$	−7.87531e25	+	4.54681e25i	−0.732527	+	0.422925i	−0.819346	−	0.573299i	$-0.805663\pi$
$401$	−7.87531e25	+	4.54681e25i	−0.732527	+	0.422925i	0.0868187	+	0.996224i	$0.472330\pi$
$402$		0			0
$403$	−1.06602e25	+	1.84639e25i	−0.0943437	+	0.163408i
$404$			1.12699e26i			0.972989i
$405$		0			0
$406$	4.13225e25			0.339568
$407$	−1.29900e26	−	7.49978e25i	−1.04151	−	0.601318i
$408$		0			0
$409$	4.39357e25	+	7.60988e25i	0.335416	+	0.580958i	0.983565	−	0.180556i	$-0.0577897\pi$
$409$	4.39357e25	+	7.60988e25i	0.335416	+	0.580958i	−0.648148	+	0.761514i	$0.724456\pi$
$410$	−3.54148e25	+	2.04467e25i	−0.263843	+	0.152330i
$411$		0			0
$412$	2.37626e25	−	4.11580e25i	0.168625	−	0.292067i
$413$			2.85030e25i			0.197420i
$414$		0			0
$415$	3.70426e26			2.44467
$416$	−5.43894e24	−	3.14017e24i	−0.0350414	−	0.0202311i
$417$		0			0
$418$	8.60541e24	+	1.49050e25i	0.0528456	+	0.0915313i
$419$	1.72756e26	−	9.97405e25i	1.03584	−	0.598041i	0.117186	−	0.993110i	$-0.462613\pi$
$419$	1.72756e26	−	9.97405e25i	1.03584	−	0.598041i	0.918652	+	0.395069i	$0.129279\pi$
$420$		0			0
$421$	−4.94483e25	+	8.56470e25i	−0.282703	+	0.489656i	−0.972050	−	0.234776i	$-0.924564\pi$
$421$	−4.94483e25	+	8.56470e25i	−0.282703	+	0.489656i	0.689346	+	0.724432i	$0.257898\pi$
$422$			3.28260e25i			0.183271i
$423$		0			0
$424$	7.24181e25			0.385646
$425$	−5.53155e25	−	3.19364e25i	−0.287712	−	0.166110i
$426$		0			0
$427$	−4.97625e25	−	8.61913e25i	−0.246958	−	0.427745i
$428$	8.31388e25	−	4.80002e25i	0.403057	−	0.232705i
$429$		0			0
$430$	−7.12715e25	+	1.23446e26i	−0.329786	+	0.571205i
$431$		−	4.19498e25i		−	0.189652i	−0.995494	−	0.0948259i	$-0.969771\pi$
$431$		−	4.19498e25i		−	0.189652i	0.995494	−	0.0948259i	$-0.0302294\pi$
$432$		0			0
$433$	−2.39593e26			−1.03418			−0.517089	−	0.855932i	$-0.672984\pi$
$433$	−2.39593e26			−1.03418			−0.517089	+	0.855932i	$0.672984\pi$
$434$	3.02648e25	+	1.74734e25i	0.127656	+	0.0737022i
$435$		0			0
$436$	−7.06396e25	−	1.22351e26i	−0.284566	−	0.492883i
$437$	−9.59217e24	+	5.53804e24i	−0.0377661	+	0.0218043i
$438$		0			0
$439$	−1.08478e26	+	1.87889e26i	−0.408034	+	0.706735i	−0.994669	−	0.103116i	$-0.967119\pi$
$439$	−1.08478e26	+	1.87889e26i	−0.408034	+	0.706735i	0.586636	+	0.809851i	$0.300452\pi$
$440$		−	1.52557e26i		−	0.560925i
$441$		0			0
$442$	1.65224e25			0.0580565
$443$	2.83375e26	+	1.63606e26i	0.973472	+	0.562035i	0.900293	−	0.435284i	$-0.143352\pi$
$443$	2.83375e26	+	1.63606e26i	0.973472	+	0.562035i	0.0731794	+	0.997319i	$0.476685\pi$
$444$		0			0
$445$	2.06135e26	+	3.57036e26i	0.676941	+	1.17250i
$446$	−2.09919e25	+	1.21197e25i	−0.0674067	+	0.0389173i
$447$		0			0
$448$	−5.14716e24	+	8.91514e24i	−0.0158048	+	0.0273746i
$449$		−	4.05735e26i		−	1.21837i	−0.793028	−	0.609185i	$-0.791497\pi$
$449$		−	4.05735e26i		−	1.21837i	0.793028	−	0.609185i	$-0.208503\pi$
$450$		0			0
$451$	1.23553e26			0.354885
$452$	−1.01277e26	−	5.84724e25i	−0.284529	−	0.164273i
$453$		0			0
$454$	−1.07586e26	−	1.86344e26i	−0.289199	−	0.500908i
$455$	−2.64560e25	+	1.52744e25i	−0.0695680	+	0.0401651i
$456$		0			0
$457$	−2.91178e26	+	5.04335e26i	−0.732819	+	1.26928i	0.222855	+	0.974852i	$0.428462\pi$
$457$	−2.91178e26	+	5.04335e26i	−0.732819	+	1.26928i	−0.955674	+	0.294428i	$0.904871\pi$
$458$		−	1.79627e26i		−	0.442299i
$459$		0			0
$460$	9.81785e25			0.231440
$461$	2.57481e26	+	1.48657e26i	0.593932	+	0.342907i	0.766651	−	0.642064i	$-0.221922\pi$
$461$	2.57481e26	+	1.48657e26i	0.593932	+	0.342907i	−0.172719	+	0.984971i	$0.555255\pi$
$462$		0			0
$463$	−1.24694e26	−	2.15976e26i	−0.275445	−	0.477085i	0.694802	−	0.719201i	$-0.255492\pi$
$463$	−1.24694e26	−	2.15976e26i	−0.275445	−	0.477085i	−0.970247	+	0.242116i	$0.922159\pi$
$464$	1.90188e26	−	1.09805e26i	0.411154	−	0.237380i
$465$		0			0
$466$	−2.29289e26	+	3.97141e26i	−0.474816	+	0.822405i
$467$			7.84889e26i			1.59089i	0.606027	+	0.795444i	$0.292762\pi$
$467$			7.84889e26i			1.59089i	−0.606027	+	0.795444i	$0.707238\pi$
$468$		0			0
$469$	−5.05932e25			−0.0982570
$470$	5.64678e26	+	3.26017e26i	1.07355	+	0.619814i
$471$		0			0
$472$	7.57404e25	+	1.31186e26i	0.138009	+	0.239039i
$473$	3.72972e26	−	2.15335e26i	0.665372	−	0.384153i
$474$		0			0
$475$	−3.54032e25	+	6.13201e25i	−0.0605489	+	0.104874i
$476$		−	2.70824e25i		−	0.0453543i
$477$		0			0
$478$	3.43065e26			0.550932
$479$	9.26128e26	+	5.34700e26i	1.45652	+	0.840921i	0.998838	−	0.0481961i	$-0.0153472\pi$
$479$	9.26128e26	+	5.34700e26i	1.45652	+	0.840921i	0.457680	+	0.889117i	$0.348681\pi$
$480$		0			0
$481$	7.98136e25	+	1.38241e26i	0.120400	+	0.208539i
$482$	−5.59490e25	+	3.23022e25i	−0.0826650	+	0.0477267i
$483$		0			0
$484$	−5.41055e25	+	9.37135e25i	−0.0766987	+	0.132846i
$485$		−	5.13879e25i		−	0.0713581i
$486$		0			0
$487$	1.07718e27			1.43548			0.717742	−	0.696310i	$-0.245176\pi$
$487$	1.07718e27			1.43548			0.717742	+	0.696310i	$0.245176\pi$
$488$	−4.58068e26	−	2.64466e26i	−0.598042	−	0.345280i
$489$		0			0
$490$	−3.66491e26	−	6.34780e26i	−0.459306	−	0.795541i
$491$	−6.73824e26	+	3.89032e26i	−0.827430	+	0.477717i	−0.852972	−	0.521957i	$-0.825202\pi$
$491$	−6.73824e26	+	3.89032e26i	−0.827430	+	0.477717i	0.0255418	+	0.999674i	$0.491869\pi$
$492$		0			0
$493$	−2.88877e26	+	5.00350e26i	−0.340600	+	0.589936i
$494$		−	1.83160e25i		−	0.0211622i
$495$		0			0
$496$	1.85727e26			0.206090
$497$	−3.41079e26	−	1.96922e26i	−0.370929	−	0.214156i
$498$		0			0
$499$	−4.57085e26	−	7.91695e26i	−0.477520	−	0.827089i	0.522148	−	0.852855i	$-0.325131\pi$
$499$	−4.57085e26	−	7.91695e26i	−0.477520	−	0.827089i	−0.999668	+	0.0257656i	$0.991798\pi$
$500$	−4.33351e25	+	2.50195e25i	−0.0443751	+	0.0256200i
$501$		0			0
$502$	1.91462e26	−	3.31622e26i	0.188385	−	0.326292i
$503$		−	2.27443e25i		−	0.0219378i	−0.999940	−	0.0109689i	$-0.996508\pi$
$503$		−	2.27443e25i		−	0.0219378i	0.999940	−	0.0109689i	$-0.00349158\pi$
$504$		0			0
$505$	2.91339e27			2.70075
$506$	−2.56889e26	−	1.48315e26i	−0.233475	−	0.134797i
$507$		0			0
$508$	1.20774e25	+	2.09186e25i	0.0105520	+	0.0182766i
$509$	3.10112e26	−	1.79043e26i	0.265669	−	0.153384i	−0.361249	−	0.932469i	$-0.617650\pi$
$509$	3.10112e26	−	1.79043e26i	0.265669	−	0.153384i	0.626918	+	0.779086i	$0.284316\pi$
$510$		0			0
$511$	1.39919e26	−	2.42346e26i	0.115257	−	0.199631i
$512$			5.47097e25i			0.0441942i
$513$		0			0
$514$	−9.26896e26			−0.720112
$515$	−1.06397e27	−	6.14285e26i	−0.810696	−	0.468056i
$516$		0			0
$517$	−9.85008e26	−	1.70608e27i	−0.721995	−	1.25053i
$518$	2.26596e26	−	1.30825e26i	0.162912	−	0.0940575i
$519$		0			0
$520$	−8.11764e25	+	1.40602e26i	−0.0561560	+	0.0972651i
$521$			3.50373e26i			0.237768i	0.992908	+	0.118884i	$0.0379317\pi$
$521$			3.50373e26i			0.237768i	−0.992908	+	0.118884i	$0.962068\pi$
$522$		0			0
$523$	−3.50734e24			−0.00229066			−0.00114533	−	0.999999i	$-0.500365\pi$
$523$	−3.50734e24			−0.00229066			−0.00114533	+	0.999999i	$0.500365\pi$
$524$	−9.51794e26	−	5.49518e26i	−0.609860	−	0.352103i
$525$		0			0
$526$	−2.52516e26	−	4.37371e26i	−0.155752	−	0.269770i
$527$	−4.23151e26	+	2.44306e26i	−0.256088	+	0.147852i
$528$		0			0
$529$	−7.62629e26	+	1.32091e27i	−0.444382	+	0.769693i
$530$		−	1.87207e27i		−	1.07045i
$531$		0			0
$532$	−3.00223e25			−0.0165321
$533$	−1.13871e26	−	6.57433e25i	−0.0615375	−	0.0355287i
$534$		0			0
$535$	−1.24085e27	−	2.14922e27i	−0.645924	−	1.11877i
$536$	−2.32857e26	+	1.34440e26i	−0.118971	+	0.0686880i
$537$		0			0
$538$	1.09361e26	−	1.89419e26i	0.0538320	−	0.0932398i
$539$			2.21458e27i			1.07005i
$540$		0			0
$541$	4.45186e26			0.207286			0.103643	−	0.994615i	$-0.466950\pi$
$541$	4.45186e26			0.207286			0.103643	+	0.994615i	$0.466950\pi$
$542$	−4.82931e26	−	2.78820e26i	−0.220746	−	0.127448i
$543$		0			0
$544$	−7.19656e25	−	1.24648e26i	−0.0317056	−	0.0549157i
$545$	−3.16290e27	+	1.82610e27i	−1.36811	+	0.789877i
$546$		0			0
$547$	−4.19622e26	+	7.26807e26i	−0.174979	+	0.303072i	−0.940154	−	0.340750i	$-0.889319\pi$
$547$	−4.19622e26	+	7.26807e26i	−0.174979	+	0.303072i	0.765175	+	0.643822i	$0.222652\pi$
$548$		−	1.88625e27i		−	0.772314i
$549$		0			0
$550$	−1.89628e27			−0.748643
$551$	5.54665e26	+	3.20236e26i	0.215038	+	0.124152i
$552$		0			0
$553$	−3.85504e25	−	6.67713e25i	−0.0144138	−	0.0249654i
$554$	2.90157e26	−	1.67522e26i	0.106545	−	0.0615141i
$555$		0			0
$556$	1.23622e27	−	2.14120e27i	0.437873	−	0.758418i
$557$		−	1.69008e27i		−	0.587971i	−0.955810	−	0.293986i	$-0.905018\pi$
$557$		−	1.69008e27i		−	0.587971i	0.955810	−	0.293986i	$-0.0949818\pi$
$558$		0			0
$559$	−4.58325e26			−0.153835
$560$	2.30465e26	+	1.33059e26i	0.0759844	+	0.0438696i
$561$		0			0
$562$	−1.06460e27	−	1.84394e27i	−0.338706	−	0.586657i
$563$	−5.46117e27	+	3.15301e27i	−1.70687	+	0.985464i	−0.768495	+	0.639855i	$0.778994\pi$
$563$	−5.46117e27	+	3.15301e27i	−1.70687	+	0.985464i	−0.938379	+	0.345609i	$0.887672\pi$
$564$		0			0
$565$	−1.51157e27	+	2.61811e27i	−0.455977	+	0.789775i
$566$			9.59811e26i			0.284460i
$567$		0			0
$568$	−2.09311e27			−0.598836
$569$	1.70330e26	+	9.83402e25i	0.0478816	+	0.0276445i	0.523750	−	0.851872i	$-0.324533\pi$
$569$	1.70330e26	+	9.83402e25i	0.0478816	+	0.0276445i	−0.475868	+	0.879517i	$0.657866\pi$
$570$		0			0
$571$	−1.22424e26	−	2.12045e26i	−0.0332281	−	0.0575527i	0.848933	−	0.528500i	$-0.177245\pi$
$571$	−1.22424e26	−	2.12045e26i	−0.0332281	−	0.0575527i	−0.882161	+	0.470948i	$0.843912\pi$
$572$	4.24805e26	−	2.45261e26i	0.113300	−	0.0654137i
$573$		0			0
$574$	−1.07762e26	+	1.86649e26i	−0.0277553	+	0.0480737i
$575$		−	1.22036e27i		−	0.308893i
$576$		0			0
$577$	4.91486e27			1.20158			0.600790	−	0.799407i	$-0.294853\pi$
$577$	4.91486e27			1.20158			0.600790	+	0.799407i	$0.294853\pi$
$578$	−2.22063e27	−	1.28208e27i	−0.533578	−	0.308061i
$579$		0			0
$580$	−2.83857e27	−	4.91655e27i	−0.658901	−	1.14125i
$581$	1.69073e27	−	9.76144e26i	0.385756	−	0.222716i
$582$		0			0
$583$	−2.82809e27	+	4.89839e27i	−0.623458	+	1.07986i
$584$		−	1.48721e27i		−	0.322288i
$585$		0			0
$586$	−3.88078e27			−0.812723
$587$	−7.39242e26	−	4.26802e26i	−0.152197	−	0.0878709i	0.421968	−	0.906611i	$-0.361340\pi$
$587$	−7.39242e26	−	4.26802e26i	−0.152197	−	0.0878709i	−0.574164	+	0.818740i	$0.694673\pi$
$588$		0			0
$589$	2.70826e26	+	4.69085e26i	0.0538937	+	0.0933466i
$590$	3.39129e27	−	1.95796e27i	0.663505	−	0.383075i
$591$		0			0
$592$	6.95277e26	−	1.20425e27i	0.131505	−	0.227772i
$593$		−	4.28762e27i		−	0.797388i	−0.917084	−	0.398694i	$-0.869464\pi$
$593$		−	4.28762e27i		−	0.797388i	0.917084	−	0.398694i	$-0.130536\pi$
$594$		0			0
$595$	−7.00107e26			−0.125891
$596$	3.24800e27	+	1.87523e27i	0.574320	+	0.331584i
$597$		0			0
$598$	1.57839e26	+	2.73385e26i	0.0269900	+	0.0467480i
$599$	2.31087e27	−	1.33418e27i	0.388604	−	0.224361i	−0.292951	−	0.956127i	$-0.594637\pi$
$599$	2.31087e27	−	1.33418e27i	0.388604	−	0.224361i	0.681555	+	0.731767i	$0.261304\pi$
$600$		0			0
$601$	2.01551e27	−	3.49096e27i	0.327823	−	0.567806i	−0.654257	−	0.756273i	$-0.727018\pi$
$601$	2.01551e27	−	3.49096e27i	0.327823	−	0.567806i	0.982080	+	0.188467i	$0.0603517\pi$
$602$			7.51256e26i			0.120177i
$603$		0			0
$604$	5.79174e27			0.896272
$605$	2.42258e27	+	1.39868e27i	0.368744	+	0.212894i
$606$		0			0
$607$	−3.15307e27	−	5.46128e27i	−0.464351	−	0.804280i	0.534821	−	0.844966i	$-0.320379\pi$
$607$	−3.15307e27	−	5.46128e27i	−0.464351	−	0.804280i	−0.999172	+	0.0406855i	$0.987046\pi$
$608$	−1.38179e26	+	7.97776e25i	−0.0200173	+	0.0115570i
$609$		0			0
$610$	−6.83669e27	+	1.18415e28i	−0.958401	+	1.66000i
$611$			2.09651e27i			0.289125i
$612$		0			0
$613$	8.02807e27			1.07153			0.535767	−	0.844366i	$-0.320022\pi$
$613$	8.02807e27			1.07153			0.535767	+	0.844366i	$0.320022\pi$
$614$	3.13604e27	+	1.81059e27i	0.411811	+	0.237759i
$615$		0			0
$616$	−4.02016e26	−	6.96312e26i	−0.0511018	−	0.0885109i
$617$	−1.62373e27	+	9.37459e26i	−0.203077	+	0.117247i	−0.598090	−	0.801429i	$-0.704073\pi$
$617$	−1.62373e27	+	9.37459e26i	−0.203077	+	0.117247i	0.395013	+	0.918676i	$0.370740\pi$
$618$		0			0
$619$	3.28392e27	−	5.68792e27i	0.397637	−	0.688727i	−0.595797	−	0.803135i	$-0.703164\pi$
$619$	3.28392e27	−	5.68792e27i	0.397637	−	0.688727i	0.993434	+	0.114408i	$0.0364970\pi$
$620$		−	4.80121e27i		−	0.572050i
$621$		0			0
$622$	1.01917e28			1.17583
$623$	1.88171e27	+	1.08641e27i	0.213635	+	0.123342i
$624$		0			0
$625$	4.85847e27	+	8.41511e27i	0.534194	+	0.925251i
$626$	−4.05730e27	+	2.34248e27i	−0.439029	+	0.253474i
$627$		0			0
$628$	−7.98281e26	+	1.38266e27i	−0.0836680	+	0.144917i
$629$			3.65829e27i			0.377373i
$630$		0			0
$631$	1.58647e28			1.58540			0.792700	−	0.609612i	$-0.208675\pi$
$631$	1.58647e28			1.58540			0.792700	+	0.609612i	$0.208675\pi$
$632$	−3.54860e26	−	2.04878e26i	−0.0349049	−	0.0201523i
$633$		0			0
$634$	3.01788e27	+	5.22711e27i	0.287613	+	0.498161i
$635$	5.40765e26	−	3.12211e26i	0.0507308	−	0.0292894i
$636$		0			0
$637$	1.17839e27	−	2.04104e27i	0.107126	−	0.185548i
$638$			1.71526e28i			1.53505i
$639$		0			0
$640$	1.41430e27			0.122671
$641$	2.49882e27	+	1.44269e27i	0.213380	+	0.123195i	0.602881	−	0.797831i	$-0.294019\pi$
$641$	2.49882e27	+	1.44269e27i	0.213380	+	0.123195i	−0.389501	+	0.921026i	$0.627353\pi$
$642$		0			0
$643$	7.51543e27	+	1.30171e28i	0.622077	+	1.07747i	0.989098	+	0.147256i	$0.0470441\pi$
$643$	7.51543e27	+	1.30171e28i	0.622077	+	1.07747i	−0.367022	+	0.930212i	$0.619623\pi$
$644$	4.48114e26	−	2.58719e26i	0.0365199	−	0.0210848i
$645$		0			0
$646$	2.09880e26	−	3.63523e26i	0.0165823	−	0.0287215i
$647$			1.11464e28i			0.867145i	0.901119	+	0.433572i	$0.142747\pi$
$647$			1.11464e28i			0.867145i	−0.901119	+	0.433572i	$0.857253\pi$
$648$		0			0
$649$	−1.18313e28			−0.892455
$650$	1.74767e27	+	1.00902e27i	0.129816	+	0.0749491i
$651$		0			0
$652$	6.24199e25	+	1.08114e26i	0.00449621	+	0.00778767i
$653$	1.35404e28	−	7.81754e27i	0.960503	−	0.554547i	0.0641753	−	0.997939i	$-0.479558\pi$
$653$	1.35404e28	−	7.81754e27i	0.960503	−	0.554547i	0.896328	+	0.443392i	$0.146225\pi$
$654$		0			0
$655$	−1.42056e28	+	2.46048e28i	−0.977339	+	1.69280i
$656$			1.14541e27i			0.0776111i
$657$		0			0
$658$	3.43647e27			0.225867
$659$	1.42753e28	+	8.24182e27i	0.924123	+	0.533543i	0.884948	−	0.465690i	$-0.154194\pi$
$659$	1.42753e28	+	8.24182e27i	0.924123	+	0.533543i	0.0391748	+	0.999232i	$0.487527\pi$
$660$		0			0
$661$	−8.69166e27	−	1.50544e28i	−0.545868	−	0.945472i	−0.998552	−	0.0538003i	$-0.982867\pi$
$661$	−8.69166e27	−	1.50544e28i	−0.545868	−	0.945472i	0.452683	−	0.891671i	$-0.350467\pi$
$662$	7.38366e27	−	4.26296e27i	0.456764	−	0.263713i
$663$		0			0
$664$	5.18777e27	−	8.98548e27i	0.311386	−	0.539337i
$665$			7.76105e26i			0.0458885i
$666$		0			0
$667$	−1.10386e28			−0.633367
$668$	−1.16187e28	−	6.70808e27i	−0.656741	−	0.379170i
$669$		0			0
$670$	3.47540e27	+	6.01958e27i	0.190659	+	0.330231i
$671$	3.57772e28	−	2.06559e28i	1.93366	−	1.11640i
$672$		0			0
$673$	2.54159e27	−	4.40216e27i	0.133338	−	0.230948i	−0.791623	−	0.611010i	$-0.790764\pi$
$673$	2.54159e27	−	4.40216e27i	0.133338	−	0.230948i	0.924961	+	0.380061i	$0.124097\pi$
$674$			1.06806e27i			0.0552074i
$675$		0			0
$676$	9.44205e27			0.473805
$677$	1.08522e28	+	6.26551e27i	0.536575	+	0.309792i	0.743690	−	0.668525i	$-0.233074\pi$
$677$	1.08522e28	+	6.26551e27i	0.536575	+	0.309792i	−0.207115	+	0.978317i	$0.566407\pi$
$678$		0			0
$679$	−1.35417e26	−	2.34549e26i	−0.00650092	−	0.0112599i
$680$	−3.22227e27	+	1.86038e27i	−0.152431	+	0.0880059i
$681$		0			0
$682$	−7.25304e27	+	1.25626e28i	−0.333178	+	0.577081i
$683$		−	2.48751e28i		−	1.12605i	−0.826440	−	0.563024i	$-0.809638\pi$
$683$		−	2.48751e28i		−	1.12605i	0.826440	−	0.563024i	$-0.190362\pi$
$684$		0			0
$685$	−4.87614e28			−2.14373
$686$	−6.91961e27	−	3.99504e27i	−0.299806	−	0.173093i
$687$		0			0
$688$	1.99630e27	+	3.45768e27i	0.0840118	+	0.145513i
$689$	5.21292e27	−	3.00968e27i	0.216217	−	0.124833i
$690$		0			0
$691$	−3.36724e27	+	5.83223e27i	−0.135673	+	0.234993i	−0.925854	−	0.377881i	$-0.876653\pi$
$691$	−3.36724e27	+	5.83223e27i	−0.135673	+	0.234993i	0.790181	+	0.612873i	$0.209986\pi$
$692$		−	1.44443e28i		−	0.573634i
$693$		0			0
$694$	1.16121e28			0.448038
$695$	−5.53519e28	−	3.19574e28i	−2.10516	−	1.21541i
$696$		0			0
$697$	−1.50669e27	−	2.60966e27i	−0.0556794	−	0.0964396i
$698$	1.41689e28	−	8.18044e27i	0.516158	−	0.298004i
$699$		0			0
$700$	1.65392e27	−	2.86467e27i	0.0585509	−	0.101413i
$701$			3.22847e28i			1.12672i	0.826211	+	0.563360i	$0.190492\pi$
$701$			3.22847e28i			1.12672i	−0.826211	+	0.563360i	$0.809508\pi$
$702$		0			0
$703$	4.05540e27			0.137556
$704$	−3.70059e27	−	2.13654e27i	−0.123750	−	0.0714470i
$705$		0			0
$706$	7.09335e27	+	1.22860e28i	0.230571	+	0.399360i
$707$	1.32975e28	−	7.67732e27i	0.426163	−	0.246046i
$708$		0			0
$709$	1.00274e26	−	1.73680e26i	0.00312412	−	0.00541113i	−0.864459	−	0.502703i	$-0.832339\pi$
$709$	1.00274e26	−	1.73680e26i	0.00312412	−	0.00541113i	0.867583	+	0.497292i	$0.165672\pi$
$710$			5.41087e28i			1.66220i
$711$		0			0
$712$	1.15475e28			0.344897
$713$	−8.08473e27	−	4.66772e27i	−0.238106	−	0.137471i
$714$		0			0
$715$	−6.34024e27	−	1.09816e28i	−0.181570	−	0.314489i
$716$	−1.46907e28	+	8.48167e27i	−0.414870	+	0.239525i
$717$		0			0
$718$	8.75948e26	−	1.51719e27i	0.0240566	−	0.0416672i
$719$		−	2.65068e28i		−	0.717908i	−0.933355	−	0.358954i	$-0.883134\pi$
$719$		−	2.65068e28i		−	0.717908i	0.933355	−	0.358954i	$-0.116866\pi$
$720$		0			0
$721$	−6.47503e27			−0.170565
$722$	2.31685e28	+	1.33764e28i	0.601903	+	0.347509i
$723$		0			0
$724$	1.02123e28	+	1.76883e28i	0.258071	+	0.446993i
$725$	−6.11125e28	+	3.52833e28i	−1.52318	+	0.879406i
$726$		0			0
$727$	2.06388e28	−	3.57474e28i	0.500426	−	0.866763i	−0.499574	−	0.866271i	$-0.666510\pi$
$727$	2.06388e28	−	3.57474e28i	0.500426	−	0.866763i	1.00000		0.000491981i	$-0.000156602\pi$
$728$			8.55661e26i			0.0204639i
$729$		0			0
$730$	−3.84458e28			−0.894582
$731$	−9.09652e27	−	5.25188e27i	−0.208786	−	0.120543i
$732$		0			0
$733$	−1.25526e27	−	2.17417e27i	−0.0280345	−	0.0485571i	0.851668	−	0.524082i	$-0.175591\pi$
$733$	−1.25526e27	−	2.17417e27i	−0.0280345	−	0.0485571i	−0.879702	+	0.475525i	$0.842258\pi$
$734$	−3.23790e28	+	1.86940e28i	−0.713349	+	0.411852i
$735$		0			0
$736$	1.37498e27	−	2.38153e27i	0.0294793	−	0.0510596i
$737$		−	2.10007e28i		−	0.444181i
$738$		0			0
$739$	5.78514e28			1.19088			0.595442	−	0.803398i	$-0.296977\pi$
$739$	5.78514e28			1.19088			0.595442	+	0.803398i	$0.296977\pi$
$740$	−3.11311e28	−	1.79736e28i	−0.632233	−	0.365020i
$741$		0			0
$742$	−4.93327e27	−	8.54468e27i	−0.0975205	−	0.168910i
$743$	−6.60601e28	+	3.81398e28i	−1.28840	+	0.743859i	−0.978369	−	0.206867i	$-0.933673\pi$
$743$	−6.60601e28	+	3.81398e28i	−1.28840	+	0.743859i	−0.310032	+	0.950726i	$0.600340\pi$
$744$		0			0
$745$	4.84766e28	−	8.39639e28i	0.920384	−	1.59415i
$746$			6.44404e28i			1.20717i
$747$		0			0
$748$	1.12417e28			0.205029
$749$	−1.13272e28	−	6.53975e27i	−0.203847	−	0.117691i
$750$		0			0
$751$	−1.12424e28	−	1.94725e28i	−0.196997	−	0.341210i	0.750556	−	0.660807i	$-0.229786\pi$
$751$	−1.12424e28	−	1.94725e28i	−0.196997	−	0.341210i	−0.947554	+	0.319597i	$0.896452\pi$
$752$	1.58165e28	−	9.13164e27i	0.273483	−	0.157896i
$753$		0			0
$754$	9.12699e27	−	1.58084e28i	0.153679	−	0.266180i
$755$		−	1.49722e29i		−	2.48780i
$756$		0			0
$757$	−1.06852e29			−1.72912			−0.864558	−	0.502533i	$-0.832401\pi$
$757$	−1.06852e29			−1.72912			−0.864558	+	0.502533i	$0.832401\pi$
$758$	4.82552e28	+	2.78602e28i	0.770642	+	0.444930i
$759$		0			0
$760$	2.06233e27	+	3.57205e27i	0.0320790	+	0.0555625i
$761$	−2.71508e28	+	1.56755e28i	−0.416808	+	0.240644i	−0.693710	−	0.720254i	$-0.744025\pi$
$761$	−2.71508e28	+	1.56755e28i	−0.416808	+	0.240644i	0.276903	+	0.960898i	$0.410692\pi$
$762$		0			0
$763$	−9.62423e27	+	1.66697e28i	−0.143920	+	0.249277i
$764$		−	1.36803e28i		−	0.201912i
$765$		0			0
$766$	−7.21154e28			−1.03691
$767$	1.09042e28	+	6.29552e27i	0.154753	+	0.0893466i
$768$		0			0
$769$	−7.64121e27	−	1.32350e28i	−0.105657	−	0.183003i	0.808349	−	0.588703i	$-0.200361\pi$
$769$	−7.64121e27	−	1.32350e28i	−0.105657	−	0.183003i	−0.914006	+	0.405700i	$0.867028\pi$
$770$	−1.80003e28	+	1.03925e28i	−0.245682	+	0.141844i
$771$		0			0
$772$	2.82395e28	−	4.89122e28i	0.375563	−	0.650495i
$773$		−	5.70947e28i		−	0.749551i	−0.927116	−	0.374775i	$-0.877720\pi$
$773$		−	5.70947e28i		−	0.749551i	0.927116	−	0.374775i	$-0.122280\pi$
$774$		0			0
$775$	−5.96789e28			−0.763491
$776$	−1.24652e27	−	7.19680e26i	−0.0157428	−	0.00908912i
$777$		0			0
$778$	2.87283e28	+	4.97589e28i	0.353602	+	0.612456i
$779$	−2.89294e27	+	1.67024e27i	−0.0351532	+	0.0202957i
$780$		0			0
$781$	8.17404e28	−	1.41579e29i	0.968114	−	1.67682i
$782$			7.23461e27i			0.0845956i
$783$		0			0
$784$	−2.05306e28			−0.234013
$785$	3.57432e28	+	2.06363e28i	0.402250	+	0.232239i
$786$		0			0
$787$	3.18285e28	+	5.51286e28i	0.349196	+	0.604825i	0.986107	−	0.166113i	$-0.0531215\pi$
$787$	3.18285e28	+	5.51286e28i	0.349196	+	0.604825i	−0.636911	+	0.770937i	$0.719788\pi$
$788$	5.11184e28	−	2.95132e28i	0.553751	−	0.319709i
$789$		0			0
$790$	−5.29630e27	+	9.17345e27i	−0.0559373	+	0.0968862i
$791$			1.59330e28i			0.166163i
$792$		0			0
$793$	−4.39646e28			−0.447066
$794$	−4.23428e27	−	2.44466e27i	−0.0425182	−	0.0245479i
$795$		0			0
$796$	−2.87255e28	−	4.97539e28i	−0.281278	−	0.487188i
$797$	−1.32308e27	+	7.63878e26i	−0.0127939	+	0.00738654i	−0.506383	−	0.862309i	$-0.669018\pi$
$797$	−1.32308e27	+	7.63878e26i	−0.0127939	+	0.00738654i	0.493589	+	0.869695i	$0.335685\pi$
$798$		0			0
$799$	−2.40236e28	+	4.16102e28i	−0.226554	+	0.392402i
$800$		−	1.75797e28i		−	0.163723i
$801$		0			0
$802$	6.58449e28			0.598106
$803$	1.00596e29	+	5.80788e28i	0.902450	+	0.521030i
$804$		0			0
$805$	−6.68813e27	−	1.15842e28i	−0.0585256	−	0.101369i
$806$	1.33693e28	−	7.71878e27i	0.115547	−	0.0667111i
$807$		0			0
$808$	4.08015e28	−	7.06703e28i	0.344004	−	0.595832i
$809$			1.79811e29i			1.49738i	0.662921	+	0.748690i	$0.269317\pi$
$809$			1.79811e29i			1.49738i	−0.662921	+	0.748690i	$0.730683\pi$
$810$		0			0
$811$	−3.60028e28			−0.292502			−0.146251	−	0.989248i	$-0.546721\pi$
$811$	−3.60028e28			−0.292502			−0.146251	+	0.989248i	$0.546721\pi$
$812$	−2.59121e28	−	1.49603e28i	−0.207942	−	0.120055i
$813$		0			0
$814$	5.43042e28	+	9.40576e28i	0.425196	+	0.736461i
$815$	2.79486e27	−	1.61361e27i	0.0216164	−	0.0124802i
$816$		0			0
$817$	−5.82198e27	+	1.00840e28i	−0.0439390	+	0.0761046i
$818$		−	6.36256e28i		−	0.474350i
$819$		0			0
$820$	2.96100e28			0.215427
$821$	2.44466e28	+	1.41143e28i	0.175706	+	0.101444i	0.585274	−	0.810836i	$-0.300987\pi$
$821$	2.44466e28	+	1.41143e28i	0.175706	+	0.101444i	−0.409567	+	0.912280i	$0.634320\pi$
$822$		0			0
$823$	−3.18755e28	−	5.52101e28i	−0.223594	−	0.387275i	0.732303	−	0.680979i	$-0.238445\pi$
$823$	−3.18755e28	−	5.52101e28i	−0.223594	−	0.387275i	−0.955897	+	0.293704i	$0.905112\pi$
$824$	−2.98016e28	+	1.72059e28i	−0.206522	+	0.119236i
$825$		0			0
$826$	1.03192e28	−	1.78734e28i	0.0697984	−	0.120894i
$827$			1.25713e29i			0.840085i	0.907504	+	0.420043i	$0.137985\pi$
$827$			1.25713e29i			0.840085i	−0.907504	+	0.420043i	$0.862015\pi$
$828$		0			0
$829$	9.00644e28			0.587500			0.293750	−	0.955882i	$-0.405097\pi$
$829$	9.00644e28			0.587500			0.293750	+	0.955882i	$0.405097\pi$
$830$	−2.32283e29	−	1.34109e29i	−1.49705	−	0.864323i
$831$		0			0
$832$	2.27373e27	+	3.93821e27i	0.0143056	+	0.0247780i
$833$	4.67759e28	−	2.70061e28i	0.290785	−	0.167885i
$834$		0			0
$835$	−1.73410e29	+	3.00355e29i	−1.05247	+	1.82293i
$836$		−	1.24620e28i		−	0.0747350i
$837$		0			0
$838$	−1.44440e29			−0.845758
$839$	1.49627e28	+	8.63873e27i	0.0865747	+	0.0499839i	0.542662	−	0.839951i	$-0.317416\pi$
$839$	1.49627e28	+	8.63873e27i	0.0865747	+	0.0499839i	−0.456088	+	0.889935i	$0.650750\pi$
$840$		0			0
$841$	2.30655e29	+	3.99505e29i	1.30317	+	2.25716i
$842$	6.20151e28	−	3.58044e28i	0.346239	−	0.199901i
$843$		0			0
$844$	1.18843e28	−	2.05842e28i	0.0647960	−	0.112230i
$845$		−	2.44086e29i		−	1.31515i
$846$		0			0
$847$	1.47431e28			0.0775810
$848$	−4.54111e28	−	2.62181e28i	−0.236159	−	0.136346i
$849$		0			0
$850$	2.31244e28	+	4.00527e28i	0.117458	+	0.203443i
$851$	−6.05311e28	+	3.49477e28i	−0.303867	+	0.175438i
$852$		0			0
$853$	1.40381e29	−	2.43147e29i	0.688365	−	1.19228i	−0.284002	−	0.958824i	$-0.591662\pi$
$853$	1.40381e29	−	2.43147e29i	0.688365	−	1.19228i	0.972367	−	0.233459i	$-0.0750046\pi$
$854$			7.20639e28i			0.349252i
$855$		0			0
$856$	−6.95117e28			−0.329094
$857$	1.60168e29	+	9.24731e28i	0.749494	+	0.432720i	0.825511	−	0.564386i	$-0.190887\pi$
$857$	1.60168e29	+	9.24731e28i	0.749494	+	0.432720i	−0.0760173	+	0.997106i	$0.524220\pi$
$858$		0			0
$859$	−8.41710e28	−	1.45788e29i	−0.384796	−	0.666486i	0.606945	−	0.794744i	$-0.292395\pi$
$859$	−8.41710e28	−	1.45788e29i	−0.384796	−	0.666486i	−0.991741	+	0.128258i	$0.959062\pi$
$860$	8.93844e28	−	5.16061e28i	0.403903	−	0.233194i
$861$		0			0
$862$	−1.51874e28	+	2.63054e28i	−0.0670520	+	0.116138i
$863$			5.33426e28i			0.232791i	0.993203	+	0.116395i	$0.0371340\pi$
$863$			5.33426e28i			0.232791i	−0.993203	+	0.116395i	$0.962866\pi$
$864$		0			0
$865$	−3.73398e29			−1.59225
$866$	1.50241e29	+	8.67419e28i	0.633302	+	0.365637i
$867$		0			0
$868$	−1.26521e28	−	2.19141e28i	−0.0521153	−	0.0902664i
$869$	2.77161e28	−	1.60019e28i	0.112859	−	0.0651589i
$870$		0			0
$871$	−1.11746e28	+	1.93550e28i	−0.0444684	+	0.0770215i
$872$			1.02297e29i			0.402437i
$873$		0			0
$874$	8.01994e27			0.0308359
$875$	5.90415e27	+	3.40876e27i	0.0224428	+	0.0129574i
$876$		0			0
$877$	1.32016e29	+	2.28659e29i	0.490491	+	0.849555i	0.999940	−	0.0109456i	$-0.00348417\pi$
$877$	1.32016e29	+	2.28659e29i	0.490491	+	0.849555i	−0.509449	+	0.860501i	$0.670151\pi$
$878$	1.36046e29	−	7.85464e28i	0.499737	−	0.288523i
$879$		0			0
$880$	−5.52315e28	+	9.56637e28i	−0.198317	+	0.343495i
$881$		−	4.57521e29i		−	1.62425i	−0.583485	−	0.812124i	$-0.698311\pi$
$881$		−	4.57521e29i		−	1.62425i	0.583485	−	0.812124i	$-0.301689\pi$
$882$		0			0
$883$	4.98043e29			1.72846			0.864230	−	0.503097i	$-0.167806\pi$
$883$	4.98043e29			1.72846			0.864230	+	0.503097i	$0.167806\pi$
$884$	−1.03607e28	−	5.98176e27i	−0.0355522	−	0.0205261i
$885$		0			0
$886$	−1.18464e29	−	2.05185e29i	−0.397418	−	0.688349i
$887$	−4.66934e29	+	2.69585e29i	−1.54889	+	0.894250i	−0.550659	+	0.834730i	$0.685624\pi$
$887$	−4.66934e29	+	2.69585e29i	−1.54889	+	0.894250i	−0.998227	+	0.0595196i	$0.981043\pi$
$888$		0			0
$889$	1.64547e27	−	2.85004e27i	0.00533669	−	0.00924342i
$890$		−	2.98515e29i		−	0.957339i
$891$		0			0
$892$	1.75512e28			0.0550374
$893$	4.61271e28	+	2.66315e28i	0.143035	+	0.0825811i
$894$		0			0
$895$	2.19259e29	+	3.79768e29i	0.664855	+	1.15156i
$896$	6.45525e27	−	3.72694e27i	0.0193568	−	0.0111756i
$897$		0			0
$898$	−1.46892e29	+	2.54424e29i	−0.430759	+	0.746097i
$899$			5.39819e29i			1.56549i
$900$		0			0
$901$	1.37950e29			0.391268
$902$	−7.74763e28	−	4.47309e28i	−0.217322	−	0.125471i
$903$		0			0
$904$	4.23385e28	+	7.33325e28i	0.116159	+	0.201193i
$905$	4.57259e29	−	2.63999e29i	1.24073	−	0.716335i
$906$		0			0
$907$	3.59428e29	−	6.22547e29i	0.953979	−	1.65234i	0.217291	−	0.976107i	$-0.430278\pi$
$907$	3.59428e29	−	6.22547e29i	0.953979	−	1.65234i	0.736688	−	0.676233i	$-0.236389\pi$
$908$			1.55801e29i			0.408990i
$909$		0			0
$910$	2.21196e28			0.0568021
$911$	5.22966e29	+	3.01935e29i	1.32828	+	0.766883i	0.985034	−	0.172363i	$-0.0551401\pi$
$911$	5.22966e29	+	3.01935e29i	1.32828	+	0.766883i	0.343246	+	0.939245i	$0.388473\pi$
$912$		0			0
$913$	4.05188e29	+	7.01806e29i	1.00681	+	1.74385i
$914$	3.65178e29	−	2.10835e29i	0.897516	−	0.518181i
$915$		0			0
$916$	−6.50318e28	+	1.12638e29i	−0.156376	+	0.270852i
$917$			1.49737e29i			0.356153i
$918$		0			0
$919$	−4.42787e29			−1.03048			−0.515240	−	0.857046i	$-0.672297\pi$
$919$	−4.42787e29			−1.03048			−0.515240	+	0.857046i	$0.672297\pi$
$920$	−6.15647e28	−	3.55444e28i	−0.141727	−	0.0818263i
$921$		0			0
$922$	−1.07639e29	−	1.86436e29i	−0.242472	−	0.419973i
$923$	−1.50670e29	+	8.69892e28i	−0.335744	+	0.193842i
$924$		0			0
$925$	−2.23411e29	+	3.86959e29i	−0.487177	+	0.843815i
$926$			1.80576e29i			0.389538i
$927$		0			0
$928$	−1.59015e29			−0.335706
$929$	7.15961e29	+	4.13360e29i	1.49531	+	0.863320i	0.999985	−	0.00538577i	$-0.00171435\pi$
$929$	7.15961e29	+	4.13360e29i	1.49531	+	0.863320i	0.495329	+	0.868706i	$0.335048\pi$
$930$		0			0
$931$	−2.99376e28	−	5.18535e28i	−0.0611957	−	0.105994i
$932$	2.87561e29	−	1.66023e29i	0.581528	−	0.335745i
$933$		0			0
$934$	2.84160e29	−	4.92180e29i	0.562464	−	0.974216i
$935$		−	2.90607e29i		−	0.569103i
$936$		0			0
$937$	4.83490e29			0.926812			0.463406	−	0.886146i	$-0.346627\pi$
$937$	4.83490e29			0.926812			0.463406	+	0.886146i	$0.346627\pi$
$938$	3.17254e28	+	1.83167e28i	0.0601699	+	0.0347391i
$939$		0			0
$940$	−2.36061e29	−	4.08870e29i	−0.438275	−	0.759114i
$941$	−4.57289e29	+	2.64016e29i	−0.840030	+	0.484992i	−0.857274	−	0.514860i	$-0.827844\pi$
$941$	−4.57289e29	+	2.64016e29i	−0.840030	+	0.484992i	0.0172444	+	0.999851i	$0.494511\pi$
$942$		0			0
$943$	2.87868e28	−	4.98601e28i	0.0517697	−	0.0896678i
$944$		−	1.09684e29i		−	0.195174i
$945$		0			0
$946$	−3.11839e29			−0.543274
$947$	−2.28379e29	−	1.31854e29i	−0.393691	−	0.227298i	0.290067	−	0.957006i	$-0.406322\pi$
$947$	−2.28379e29	−	1.31854e29i	−0.393691	−	0.227298i	−0.683758	+	0.729709i	$0.739656\pi$
$948$		0			0
$949$	−6.18082e28	−	1.07055e29i	−0.104324	−	0.180694i
$950$	4.44005e28	−	2.56346e28i	0.0741569	−	0.0428145i
$951$		0			0
$952$	−9.80489e27	+	1.69826e28i	−0.0160352	+	0.0277737i
$953$			1.52155e29i			0.246240i	0.992392	+	0.123120i	$0.0392900\pi$
$953$			1.52155e29i			0.246240i	−0.992392	+	0.123120i	$0.960710\pi$
$954$		0			0
$955$	−3.53648e29			−0.560451
$956$	−2.15126e29	−	1.24203e29i	−0.337375	−	0.194784i
$957$		0			0
$958$	−3.87164e29	−	6.70588e29i	−0.594621	−	1.02991i
$959$	−2.22561e29	+	1.28495e29i	−0.338269	+	0.195300i
$960$		0			0
$961$	1.07630e29	−	1.86421e29i	0.160214	−	0.277499i
$962$		−	1.15582e29i		−	0.170271i
$963$		0			0
$964$	4.67785e28			0.0674957
$965$	−1.26443e30	−	7.30016e29i	−1.80559	−	1.04246i
$966$		0			0
$967$	−2.52142e29	−	4.36722e29i	−0.352679	−	0.610858i	0.634039	−	0.773301i	$-0.281396\pi$
$967$	−2.52142e29	−	4.36722e29i	−0.352679	−	0.610858i	−0.986718	+	0.162443i	$0.948063\pi$
$968$	6.78558e28	−	3.91766e28i	0.0939363	−	0.0542342i
$969$		0			0
$970$	−1.86044e28	+	3.22238e28i	−0.0252289	+	0.0436977i
$971$		−	1.55921e29i		−	0.209272i	−0.994511	−	0.104636i	$-0.966632\pi$
$971$		−	1.55921e29i		−	0.209272i	0.994511	−	0.104636i	$-0.0333678\pi$
$972$		0			0
$973$	−3.36856e29			−0.442910
$974$	−6.75466e29	−	3.89980e29i	−0.879050	−	0.507520i
$975$		0			0
$976$	1.91494e29	+	3.31677e29i	0.244150	+	0.422880i
$977$	6.92264e28	−	3.99679e28i	0.0873628	−	0.0504389i	−0.455682	−	0.890143i	$-0.650605\pi$
$977$	6.92264e28	−	3.99679e28i	0.0873628	−	0.0504389i	0.543045	+	0.839704i	$0.317271\pi$
$978$		0			0
$979$	−4.50957e29	+	7.81081e29i	−0.557582	+	0.965760i
$980$			5.30735e29i			0.649557i
$981$		0			0
$982$	5.63379e29			0.675594
$983$	2.33336e28	+	1.34716e28i	0.0276979	+	0.0159914i	0.513785	−	0.857919i	$-0.328243\pi$
$983$	2.33336e28	+	1.34716e28i	0.0276979	+	0.0159914i	−0.486087	+	0.873910i	$0.661576\pi$
$984$		0			0
$985$	−7.62944e29	−	1.32146e30i	−0.887422	−	1.53706i
$986$	3.62292e29	−	2.09170e29i	0.417148	−	0.240840i
$987$		0			0
$988$	−6.63109e27	+	1.14854e28i	−0.00748196	+	0.0129591i
$989$		−	2.00685e29i		−	0.224157i
$990$		0			0
$991$	9.19922e29			1.00697			0.503483	−	0.864005i	$-0.332052\pi$
$991$	9.19922e29			1.00697			0.503483	+	0.864005i	$0.332052\pi$
$992$	−1.16464e29	−	6.72403e28i	−0.126204	−	0.0728639i
$993$		0			0
$994$	1.42587e29	+	2.46968e29i	0.151431	+	0.262287i
$995$	−1.28619e30	+	7.42580e29i	−1.35230	+	0.780751i
$996$		0			0
$997$	8.84459e29	−	1.53193e30i	0.911436	−	1.57865i	0.0993991	−	0.995048i	$-0.468308\pi$
$997$	8.84459e29	−	1.53193e30i	0.911436	−	1.57865i	0.812037	−	0.583606i	$-0.198359\pi$
$998$			6.61930e29i			0.675316i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	54.21.d.a.35.7		40
3.2	odd	2		18.21.d.a.11.14	yes	40
9.4	even	3		18.21.d.a.5.14	✓	40
9.5	odd	6	inner	54.21.d.a.17.7		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.21.d.a.5.14	✓	40	9.4	even	3
18.21.d.a.11.14	yes	40	3.2	odd	2
54.21.d.a.17.7		40	9.5	odd	6	inner
54.21.d.a.35.7		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)

\(f(q)\)	\(=\)	\(q+(-627.069 - 362.039i) q^{2} +(262144. + 454047. i) q^{4} +(1.17375e7 - 6.77667e6i) q^{5} +(3.57156e7 - 6.18612e7i) q^{7} -3.79625e8i q^{8} -9.81366e9 q^{10} +(2.56780e10 + 1.48252e10i) q^{11} +(-1.57772e10 - 2.73268e10i) q^{13} +(-4.47923e10 + 2.58609e10i) q^{14} +(-1.37439e11 + 2.38051e11i) q^{16} -7.23153e11i q^{17} -8.01652e11 q^{19} +(6.15385e12 + 3.55293e12i) q^{20} +(-1.07346e13 - 1.85929e13i) q^{22} +(1.19655e13 - 6.90828e12i) q^{23} +(4.41627e13 - 7.64921e13i) q^{25} +2.28478e13i q^{26} +3.74505e13 q^{28} +(-6.91902e14 - 3.99470e14i) q^{29} +(-3.37835e14 - 5.85147e14i) q^{31} +(1.72368e14 - 9.95164e13i) q^{32} +(-2.61809e14 + 4.53467e14i) q^{34} -9.68131e14i q^{35} -5.05880e15 q^{37} +(5.02692e14 + 2.90229e14i) q^{38} +(-2.57259e15 - 4.45586e15i) q^{40} +(3.60872e15 - 2.08350e15i) q^{41} +(7.26248e15 - 1.25790e16i) q^{43} +1.55453e16i q^{44} -1.00043e16 q^{46} +(-5.75400e16 - 3.32207e16i) q^{47} +(3.73449e16 + 6.46833e16i) q^{49} +(-5.53862e16 + 3.19772e16i) q^{50} +(8.27178e15 - 1.43271e16i) q^{52} +1.90762e17i q^{53} +4.01862e17 q^{55} +(-2.34841e16 - 1.35585e16i) q^{56} +(2.89247e17 + 5.00990e17i) q^{58} +(-3.45568e17 + 1.99514e17i) q^{59} +(6.96650e17 - 1.20663e18i) q^{61} +4.89237e17i q^{62} -1.44115e17 q^{64} +(-3.70370e17 - 2.13833e17i) q^{65} +(-3.54139e17 - 6.13387e17i) q^{67} +(3.28345e17 - 1.89570e17i) q^{68} +(-3.50501e17 + 6.07085e17i) q^{70} -5.51361e18i q^{71} +3.91758e18 q^{73} +(3.17222e18 + 1.83148e18i) q^{74} +(-2.10148e17 - 3.63988e17i) q^{76} +(1.83421e18 - 1.05898e18i) q^{77} +(5.39686e17 - 9.34764e17i) q^{79} +3.72551e18i q^{80} -3.01722e18 q^{82} +(2.36693e19 + 1.36655e19i) q^{83} +(-4.90056e18 - 8.48803e18i) q^{85} +(-9.10816e18 + 5.25860e18i) q^{86} +(5.62802e18 - 9.74801e18i) q^{88} +3.04183e19i q^{89} -2.25396e18 q^{91} +(6.27337e18 + 3.62193e18i) q^{92} +(2.40544e19 + 4.16634e19i) q^{94} +(-9.40942e18 + 5.43253e18i) q^{95} +(1.89576e18 - 3.28356e18i) q^{97} -5.40812e19i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 10485760 q^{4} - 29763918 q^{5} + 133479866 q^{7} + 35793208728 q^{11} + 39827158550 q^{13} - 187564400640 q^{14} - 5497558138880 q^{16} - 10560819523540 q^{19} - 15604865040384 q^{20} + 10829007458304 q^{22}+ \cdots - 66\!\cdots\!16 q^{97}+O(q^{100}) \) 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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