LMFDB - Embedded newform 126.8.g.h.37.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,8,Mod(37,126)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

N = Newforms(chi, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("126.37");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	126.g (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$39.3605132110$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 2119x^{4} - 65706x^{3} + 4519836x^{2} - 71825616x + 1150023744 $ x^6 - x^5 + 2119x^4 - 65706x^3 + 4519836x^2 - 71825616x + 1150023744
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3\cdot 7^{3} $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			37.1
Root			$-26.0602 + 45.1375i$ of defining polynomial
Character	$\chi$	$=$	126.37
Dual form			126.8.g.h.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.00000 + 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(-201.921 + 349.738i) q^{5} +(514.742 + 747.384i) q^{7} +512.000 q^{8} +(-1615.37 - 2797.90i) q^{10} +(3237.34 + 5607.24i) q^{11} +11611.3 q^{13} +(-7237.00 + 576.704i) q^{14} +(-2048.00 + 3547.24i) q^{16} +(10154.5 + 17588.1i) q^{17} +(23247.9 - 40266.5i) q^{19} +25845.9 q^{20} -51797.4 q^{22} +(-6578.39 + 11394.1i) q^{23} +(-42481.8 - 73580.6i) q^{25} +(-46445.2 + 80445.4i) q^{26} +(24952.5 - 52446.2i) q^{28} +87278.1 q^{29} +(125138. + 216746. i) q^{31} +(-16384.0 - 28377.9i) q^{32} -162472. q^{34} +(-365326. + 29112.2i) q^{35} +(-197166. + 341501. i) q^{37} +(185983. + 322132. i) q^{38} +(-103384. + 179066. i) q^{40} +233278. q^{41} +596690. q^{43} +(207190. - 358863. i) q^{44} +(-52627.1 - 91152.9i) q^{46} +(-104168. + 180424. i) q^{47} +(-293623. + 769421. i) q^{49} +679709. q^{50} +(-371561. - 643563. i) q^{52} +(-551131. - 954586. i) q^{53} -2.61475e6 q^{55} +(263548. + 382661. i) q^{56} +(-349113. + 604681. i) q^{58} +(-1.06718e6 - 1.84842e6i) q^{59} +(-1.32732e6 + 2.29899e6i) q^{61} -2.00222e6 q^{62} +262144. q^{64} +(-2.34456e6 + 4.06091e6i) q^{65} +(-38517.8 - 66714.7i) q^{67} +(649889. - 1.12564e6i) q^{68} +(1.25961e6 - 2.64750e6i) q^{70} -1.55255e6 q^{71} +(-2.33206e6 - 4.03924e6i) q^{73} +(-1.57733e6 - 2.73201e6i) q^{74} -2.97573e6 q^{76} +(-2.52436e6 + 5.30582e6i) q^{77} +(1.16745e6 - 2.02209e6i) q^{79} +(-827069. - 1.43253e6i) q^{80} +(-933113. + 1.61620e6i) q^{82} +5.17043e6 q^{83} -8.20165e6 q^{85} +(-2.38676e6 + 4.13399e6i) q^{86} +(1.65752e6 + 2.87090e6i) q^{88} +(896976. - 1.55361e6i) q^{89} +(5.97682e6 + 8.67810e6i) q^{91} +842034. q^{92} +(-833343. - 1.44339e6i) q^{94} +(9.38847e6 + 1.62613e7i) q^{95} +2.34436e6 q^{97} +(-4.15621e6 - 5.11197e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 24 q^{2} - 192 q^{4} - 110 q^{5} + 635 q^{7} + 3072 q^{8} - 880 q^{10} + 548 q^{11} + 19898 q^{13} - 4568 q^{14} - 12288 q^{16} + 20972 q^{17} + 28383 q^{19} + 14080 q^{20} - 8768 q^{22} + 32732 q^{23}+ \cdots - 6110208 q^{98}+O(q^{100}) $ 6 * q - 24 * q^2 - 192 * q^4 - 110 * q^5 + 635 * q^7 + 3072 * q^8 - 880 * q^10 + 548 * q^11 + 19898 * q^13 - 4568 * q^14 - 12288 * q^16 + 20972 * q^17 + 28383 * q^19 + 14080 * q^20 - 8768 * q^22 + 32732 * q^23 + 22745 * q^25 - 79592 * q^26 - 4096 * q^28 - 234176 * q^29 - 147865 * q^31 - 98304 * q^32 - 335552 * q^34 - 876430 * q^35 - 367503 * q^37 + 227064 * q^38 - 56320 * q^40 + 2875908 * q^41 + 1498794 * q^43 + 35072 * q^44 + 261856 * q^46 - 741486 * q^47 + 1421697 * q^49 - 363920 * q^50 - 636736 * q^52 - 1032432 * q^53 - 7992560 * q^55 + 325120 * q^56 + 936704 * q^58 - 2389238 * q^59 - 1238746 * q^61 + 2365840 * q^62 + 1572864 * q^64 - 3798390 * q^65 + 2462497 * q^67 + 1342208 * q^68 + 4561840 * q^70 + 1272524 * q^71 - 4609961 * q^73 - 2940024 * q^74 - 3633024 * q^76 - 20044196 * q^77 + 6152849 * q^79 - 450560 * q^80 - 11503632 * q^82 + 24059768 * q^83 - 18273080 * q^85 - 5995176 * q^86 + 280576 * q^88 + 10646976 * q^89 + 47686115 * q^91 - 4189696 * q^92 - 5931888 * q^94 + 21560930 * q^95 + 4562944 * q^97 - 6110208 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−4.00000	+	6.92820i	−0.353553	+	0.612372i
$2$	−4.00000	+	6.92820i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−32.0000	−	55.4256i	−0.250000	−	0.433013i
$5$	−201.921	+	349.738i	−0.722415	+	1.25126i	0.237614	+	0.971360i	$0.423635\pi$
$5$	−201.921	+	349.738i	−0.722415	+	1.25126i	−0.960029	+	0.279900i	$0.909699\pi$
$6$		0			0
$7$	514.742	+	747.384i	0.567214	+	0.823571i
$7$	514.742	+	747.384i	0.567214	+	0.823571i
$8$	512.000			0.353553
$9$		0			0
$10$	−1615.37	−	2797.90i	−0.510825	−	0.884774i
$11$	3237.34	+	5607.24i	0.733354	+	1.27021i	0.955442	+	0.295180i	$0.0953797\pi$
$11$	3237.34	+	5607.24i	0.733354	+	1.27021i	−0.222087	+	0.975027i	$0.571287\pi$
$12$		0			0
$13$	11611.3			1.46581			0.732907	−	0.680329i	$-0.238163\pi$
$13$	11611.3			1.46581			0.732907	+	0.680329i	$0.238163\pi$
$14$	−7237.00	+	576.704i	−0.704872	+	0.0561700i
$15$		0			0
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	10154.5	+	17588.1i	0.501289	+	0.868258i	0.999999	+	0.00148911i	$0.000473998\pi$
$17$	10154.5	+	17588.1i	0.501289	+	0.868258i	−0.498710	+	0.866769i	$0.666193\pi$
$18$		0			0
$19$	23247.9	−	40266.5i	0.777580	−	1.34681i	−0.155752	−	0.987796i	$-0.549780\pi$
$19$	23247.9	−	40266.5i	0.777580	−	1.34681i	0.933333	−	0.359012i	$-0.116886\pi$
$20$	25845.9			0.722415
$21$		0			0
$22$	−51797.4			−1.03712
$23$	−6578.39	+	11394.1i	−0.112739	+	0.195269i	−0.916873	−	0.399178i	$-0.869296\pi$
$23$	−6578.39	+	11394.1i	−0.112739	+	0.195269i	0.804135	+	0.594447i	$0.202629\pi$
$24$		0			0
$25$	−42481.8	−	73580.6i	−0.543767	−	0.941832i
$26$	−46445.2	+	80445.4i	−0.518243	+	0.897624i
$27$		0			0
$28$	24952.5	−	52446.2i	0.214813	−	0.451503i
$29$	87278.1			0.664527			0.332263	−	0.943187i	$-0.392188\pi$
$29$	87278.1			0.664527			0.332263	+	0.943187i	$0.392188\pi$
$30$		0			0
$31$	125138.	+	216746.i	0.754440	+	1.30673i	0.945652	+	0.325180i	$0.105425\pi$
$31$	125138.	+	216746.i	0.754440	+	1.30673i	−0.191212	+	0.981549i	$0.561242\pi$
$32$	−16384.0	−	28377.9i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−162472.			−0.708930
$35$	−365326.	+	29112.2i	−1.44026	+	0.114772i
$36$		0			0
$37$	−197166.	+	341501.i	−0.639920	+	1.10837i	0.345530	+	0.938408i	$0.387699\pi$
$37$	−197166.	+	341501.i	−0.639920	+	1.10837i	−0.985450	+	0.169966i	$0.945634\pi$
$38$	185983.	+	322132.i	0.549832	+	0.952338i
$39$		0			0
$40$	−103384.	+	179066.i	−0.255412	+	0.442387i
$41$	233278.			0.528604			0.264302	−	0.964440i	$-0.414858\pi$
$41$	233278.			0.528604			0.264302	+	0.964440i	$0.414858\pi$
$42$		0			0
$43$	596690.			1.14448			0.572242	−	0.820085i	$-0.306074\pi$
$43$	596690.			1.14448			0.572242	+	0.820085i	$0.306074\pi$
$44$	207190.	−	358863.i	0.366677	−	0.635103i
$45$		0			0
$46$	−52627.1	−	91152.9i	−0.0797182	−	0.138076i
$47$	−104168.	+	180424.i	−0.146350	+	0.253485i	−0.929876	−	0.367874i	$-0.880086\pi$
$47$	−104168.	+	180424.i	−0.146350	+	0.253485i	0.783526	+	0.621359i	$0.213419\pi$
$48$		0			0
$49$	−293623.	+	769421.i	−0.356537	+	0.934281i
$50$	679709.			0.769002
$51$		0			0
$52$	−371561.	−	643563.i	−0.366453	−	0.634716i
$53$	−551131.	−	954586.i	−0.508498	−	0.880744i	−0.999952	−	0.00984042i	$-0.996868\pi$
$53$	−551131.	−	954586.i	−0.508498	−	0.880744i	0.491454	−	0.870904i	$-0.336466\pi$
$54$		0			0
$55$	−2.61475e6			−2.11914
$56$	263548.	+	382661.i	0.200540	+	0.291176i
$57$		0			0
$58$	−349113.	+	604681.i	−0.234946	+	0.406938i
$59$	−1.06718e6	−	1.84842e6i	−0.676484	−	1.17170i	−0.976033	−	0.217623i	$-0.930170\pi$
$59$	−1.06718e6	−	1.84842e6i	−0.676484	−	1.17170i	0.299549	−	0.954081i	$-0.403164\pi$
$60$		0			0
$61$	−1.32732e6	+	2.29899e6i	−0.748725	+	1.29683i	0.199709	+	0.979855i	$0.436000\pi$
$61$	−1.32732e6	+	2.29899e6i	−0.748725	+	1.29683i	−0.948434	+	0.316975i	$0.897333\pi$
$62$	−2.00222e6			−1.06694
$63$		0			0
$64$	262144.			0.125000
$65$	−2.34456e6	+	4.06091e6i	−1.05893	+	1.83411i
$66$		0			0
$67$	−38517.8	−	66714.7i	−0.0156459	−	0.0270994i	0.858096	−	0.513489i	$-0.171647\pi$
$67$	−38517.8	−	66714.7i	−0.0156459	−	0.0270994i	−0.873742	+	0.486389i	$0.838314\pi$
$68$	649889.	−	1.12564e6i	0.250645	−	0.434129i
$69$		0			0
$70$	1.25961e6	−	2.64750e6i	0.438927	−	0.922556i
$71$	−1.55255e6			−0.514805			−0.257402	−	0.966304i	$-0.582867\pi$
$71$	−1.55255e6			−0.514805			−0.257402	+	0.966304i	$0.582867\pi$
$72$		0			0
$73$	−2.33206e6	−	4.03924e6i	−0.701631	−	1.21526i	−0.967894	−	0.251360i	$-0.919122\pi$
$73$	−2.33206e6	−	4.03924e6i	−0.701631	−	1.21526i	0.266262	−	0.963901i	$-0.414211\pi$
$74$	−1.57733e6	−	2.73201e6i	−0.452492	−	0.783739i
$75$		0			0
$76$	−2.97573e6			−0.777580
$77$	−2.52436e6	+	5.30582e6i	−0.630136	+	1.32445i
$78$		0			0
$79$	1.16745e6	−	2.02209e6i	0.266407	−	0.461430i	−0.701524	−	0.712645i	$-0.747497\pi$
$79$	1.16745e6	−	2.02209e6i	0.266407	−	0.461430i	0.967931	+	0.251215i	$0.0808302\pi$
$80$	−827069.	−	1.43253e6i	−0.180604	−	0.312815i
$81$		0			0
$82$	−933113.	+	1.61620e6i	−0.186890	+	0.323703i
$83$	5.17043e6			0.992552			0.496276	−	0.868165i	$-0.334700\pi$
$83$	5.17043e6			0.992552			0.496276	+	0.868165i	$0.334700\pi$
$84$		0			0
$85$	−8.20165e6			−1.44855
$86$	−2.38676e6	+	4.13399e6i	−0.404636	+	0.700850i
$87$		0			0
$88$	1.65752e6	+	2.87090e6i	0.259280	+	0.449086i
$89$	896976.	−	1.55361e6i	0.134870	−	0.233602i	−0.790678	−	0.612233i	$-0.790272\pi$
$89$	896976.	−	1.55361e6i	0.134870	−	0.233602i	0.925548	+	0.378631i	$0.123605\pi$
$90$		0			0
$91$	5.97682e6	+	8.67810e6i	0.831430	+	1.20720i
$92$	842034.			0.112739
$93$		0			0
$94$	−833343.	−	1.44339e6i	−0.103485	−	0.179241i
$95$	9.38847e6	+	1.62613e7i	1.12347	+	1.94591i
$96$		0			0
$97$	2.34436e6			0.260809			0.130404	−	0.991461i	$-0.458372\pi$
$97$	2.34436e6			0.260809			0.130404	+	0.991461i	$0.458372\pi$
$98$	−4.15621e6	−	5.11197e6i	−0.446073	−	0.548652i
$99$		0			0
$100$	−2.71883e6	+	4.70916e6i	−0.271883	+	0.470916i
$101$	−9.05793e6	−	1.56888e7i	−0.874790	−	1.51518i	−0.856986	−	0.515340i	$-0.827666\pi$
$101$	−9.05793e6	−	1.56888e7i	−0.874790	−	1.51518i	−0.0178045	−	0.999841i	$-0.505668\pi$
$102$		0			0
$103$	−2.92574e6	+	5.06753e6i	−0.263819	+	0.456948i	−0.967253	−	0.253812i	$-0.918315\pi$
$103$	−2.92574e6	+	5.06753e6i	−0.263819	+	0.456948i	0.703435	+	0.710760i	$0.251649\pi$
$104$	5.94498e6			0.518243
$105$		0			0
$106$	8.81809e6			0.719125
$107$	−1.41810e6	+	2.45621e6i	−0.111908	+	0.193831i	−0.916540	−	0.399944i	$-0.869030\pi$
$107$	−1.41810e6	+	2.45621e6i	−0.111908	+	0.193831i	0.804631	+	0.593775i	$0.202363\pi$
$108$		0			0
$109$	−4.07843e6	−	7.06405e6i	−0.301648	−	0.522469i	0.674862	−	0.737944i	$-0.264203\pi$
$109$	−4.07843e6	−	7.06405e6i	−0.301648	−	0.522469i	−0.976509	+	0.215475i	$0.930870\pi$
$110$	1.04590e7	−	1.81155e7i	0.749231	−	1.29771i
$111$		0			0
$112$	−3.70534e6	+	295272.i	−0.249210	+	0.0198591i
$113$	1.57932e7			1.02966			0.514831	−	0.857292i	$-0.327855\pi$
$113$	1.57932e7			1.02966			0.514831	+	0.857292i	$0.327855\pi$
$114$		0			0
$115$	−2.65663e6	−	4.60142e6i	−0.162888	−	0.282130i
$116$	−2.79290e6	−	4.83745e6i	−0.166132	−	0.287749i
$117$		0			0
$118$	1.70749e7			0.956692
$119$	−7.91814e6	+	1.66427e7i	−0.430734	+	0.905335i
$120$		0			0
$121$	−1.12171e7	+	1.94287e7i	−0.575617	+	0.996998i
$122$	−1.06186e7	−	1.83919e7i	−0.529429	−	0.916997i
$123$		0			0
$124$	8.00886e6	−	1.38718e7i	0.377220	−	0.653364i
$125$	2.76170e6			0.126471
$126$		0			0
$127$	3.88646e7			1.68361			0.841805	−	0.539782i	$-0.181493\pi$
$127$	3.88646e7			1.68361			0.841805	+	0.539782i	$0.181493\pi$
$128$	−1.04858e6	+	1.81619e6i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−1.87565e7	−	3.24872e7i	−0.748774	−	1.29691i
$131$	−1.51059e6	+	2.61642e6i	−0.0587080	+	0.101685i	−0.893886	−	0.448295i	$-0.852031\pi$
$131$	−1.51059e6	+	2.61642e6i	−0.0587080	+	0.101685i	0.835178	+	0.549980i	$0.185365\pi$
$132$		0			0
$133$	4.20612e7	−	3.35178e6i	1.55025	−	0.123536i
$134$	616284.			0.0221266
$135$		0			0
$136$	5.19911e6	+	9.00513e6i	0.177232	+	0.306976i
$137$	3.30885e6	+	5.73109e6i	0.109940	+	0.190421i	0.915746	−	0.401759i	$-0.131601\pi$
$137$	3.30885e6	+	5.73109e6i	0.109940	+	0.190421i	−0.805806	+	0.592180i	$0.798268\pi$
$138$		0			0
$139$	2.69156e6			0.0850065			0.0425032	−	0.999096i	$-0.486467\pi$
$139$	2.69156e6			0.0850065			0.0425032	+	0.999096i	$0.486467\pi$
$140$	1.33040e7	+	1.93168e7i	0.409764	+	0.594960i
$141$		0			0
$142$	6.21022e6	−	1.07564e7i	0.182011	−	0.315252i
$143$	3.75897e7	+	6.51073e7i	1.07496	+	1.86189i
$144$		0			0
$145$	−1.76233e7	+	3.05245e7i	−0.480064	+	0.831495i
$146$	3.73129e7			0.992256
$147$		0			0
$148$	2.52372e7			0.639920
$149$	2.43159e7	−	4.21164e7i	0.602196	−	1.04303i	−0.390291	−	0.920691i	$-0.627626\pi$
$149$	2.43159e7	−	4.21164e7i	0.602196	−	1.04303i	0.992488	−	0.122343i	$-0.0390410\pi$
$150$		0			0
$151$	−1.65734e7	−	2.87059e7i	−0.391734	−	0.678504i	0.600944	−	0.799291i	$-0.294791\pi$
$151$	−1.65734e7	−	2.87059e7i	−0.391734	−	0.678504i	−0.992678	+	0.120787i	$0.961458\pi$
$152$	1.19029e7	−	2.06164e7i	0.274916	−	0.476169i
$153$		0			0
$154$	−2.66623e7	−	3.87126e7i	−0.588269	−	0.854141i
$155$	−1.01072e8			−2.18008
$156$		0			0
$157$	1.15214e7	+	1.99557e7i	0.237606	+	0.411545i	0.960027	−	0.279908i	$-0.0903041\pi$
$157$	1.15214e7	+	1.99557e7i	0.237606	+	0.411545i	−0.722421	+	0.691453i	$0.756971\pi$
$158$	9.33964e6	+	1.61767e7i	0.188378	+	0.326280i
$159$		0			0
$160$	1.32331e7			0.255412
$161$	−1.19020e7	+	948446.i	−0.224765	+	0.0179111i
$162$		0			0
$163$	2.84447e7	−	4.92676e7i	0.514451	−	0.891055i	−0.485408	−	0.874288i	$-0.661329\pi$
$163$	2.84447e7	−	4.92676e7i	0.514451	−	0.891055i	0.999859	−	0.0167678i	$-0.00533759\pi$
$164$	−7.46490e6	−	1.29296e7i	−0.132151	−	0.228892i
$165$		0			0
$166$	−2.06817e7	+	3.58218e7i	−0.350920	+	0.607811i
$167$	−2.37567e6			−0.0394710			−0.0197355	−	0.999805i	$-0.506282\pi$
$167$	−2.37567e6			−0.0394710			−0.0197355	+	0.999805i	$0.506282\pi$
$168$		0			0
$169$	7.20736e7			1.14861
$170$	3.28066e7	−	5.68227e7i	0.512141	−	0.887055i
$171$		0			0
$172$	−1.90941e7	−	3.30719e7i	−0.286121	−	0.495576i
$173$	−1.42860e7	+	2.47440e7i	−0.209772	+	0.363336i	−0.951643	−	0.307207i	$-0.900606\pi$
$173$	−1.42860e7	+	2.47440e7i	−0.209772	+	0.363336i	0.741870	+	0.670543i	$0.233939\pi$
$174$		0			0
$175$	3.31258e7	−	6.96253e7i	0.467233	−	0.982050i
$176$	−2.65203e7			−0.366677
$177$		0			0
$178$	7.17581e6	+	1.24289e7i	0.0953676	+	0.165181i
$179$	2.11897e7	+	3.67016e7i	0.276146	+	0.478298i	0.970424	−	0.241409i	$-0.0776094\pi$
$179$	2.11897e7	+	3.67016e7i	0.276146	+	0.478298i	−0.694278	+	0.719707i	$0.744276\pi$
$180$		0			0
$181$	−5.11373e7			−0.641007			−0.320504	−	0.947247i	$-0.603852\pi$
$181$	−5.11373e7			−0.641007			−0.320504	+	0.947247i	$0.603852\pi$
$182$	−8.40309e7	+	6.69627e6i	−1.03321	+	0.0823348i
$183$		0			0
$184$	−3.36814e6	+	5.83378e6i	−0.0398591	+	0.0690380i
$185$	−7.96239e7	−	1.37913e8i	−0.924576	−	1.60141i
$186$		0			0
$187$	−6.57473e7	+	1.13878e8i	−0.735245	+	1.27348i
$188$	1.33335e7			0.146350
$189$		0			0
$190$	−1.50215e8			−1.58883
$191$	7.26137e7	−	1.25771e8i	0.754053	−	1.30606i	−0.191791	−	0.981436i	$-0.561430\pi$
$191$	7.26137e7	−	1.25771e8i	0.754053	−	1.30606i	0.945844	−	0.324622i	$-0.105237\pi$
$192$		0			0
$193$	1.53841e7	+	2.66461e7i	0.154036	+	0.266798i	0.932708	−	0.360633i	$-0.117439\pi$
$193$	1.53841e7	+	2.66461e7i	0.154036	+	0.266798i	−0.778672	+	0.627432i	$0.784106\pi$
$194$	−9.37742e6	+	1.62422e7i	−0.0922099	+	0.159712i
$195$		0			0
$196$	5.20416e7	−	8.34721e6i	0.493690	−	0.0791854i
$197$	−6.36237e7			−0.592908			−0.296454	−	0.955047i	$-0.595804\pi$
$197$	−6.36237e7			−0.592908			−0.296454	+	0.955047i	$0.595804\pi$
$198$		0			0
$199$	−1.57738e7	−	2.73210e7i	−0.141890	−	0.245760i	0.786319	−	0.617821i	$-0.211984\pi$
$199$	−1.57738e7	−	2.73210e7i	−0.141890	−	0.245760i	−0.928208	+	0.372061i	$0.878651\pi$
$200$	−2.17507e7	−	3.76733e7i	−0.192251	−	0.332988i
$201$		0			0
$202$	1.44927e8			1.23714
$203$	4.49258e7	+	6.52303e7i	0.376929	+	0.547285i
$204$		0			0
$205$	−4.71038e7	+	8.15862e7i	−0.381872	+	0.661421i
$206$	−2.34059e7	−	4.05403e7i	−0.186548	−	0.323111i
$207$		0			0
$208$	−2.37799e7	+	4.11880e7i	−0.183227	+	0.317358i
$209$	3.01045e8			2.28097
$210$		0			0
$211$	−1.20761e7			−0.0884987			−0.0442493	−	0.999021i	$-0.514090\pi$
$211$	−1.20761e7			−0.0884987			−0.0442493	+	0.999021i	$0.514090\pi$
$212$	−3.52724e7	+	6.10935e7i	−0.254249	+	0.440372i
$213$		0			0
$214$	−1.13448e7	−	1.96497e7i	−0.0791311	−	0.137059i
$215$	−1.20484e8	+	2.08685e8i	−0.826792	+	1.43205i
$216$		0			0
$217$	−9.75786e7	+	2.05095e8i	−0.648254	+	1.36253i
$218$	6.52549e7			0.426594
$219$		0			0
$220$	8.36720e7	+	1.44924e8i	0.529786	+	0.917616i
$221$	1.17907e8	+	2.04221e8i	0.734796	+	1.27270i
$222$		0			0
$223$	−2.80825e8			−1.69578			−0.847889	−	0.530173i	$-0.822127\pi$
$223$	−2.80825e8			−1.69578			−0.847889	+	0.530173i	$0.822127\pi$
$224$	1.27757e7	−	2.68525e7i	0.0759479	−	0.159631i
$225$		0			0
$226$	−6.31727e7	+	1.09418e8i	−0.364041	+	0.630537i
$227$	8.19821e7	+	1.41997e8i	0.465188	+	0.805729i	0.999210	−	0.0397413i	$-0.0126534\pi$
$227$	8.19821e7	+	1.41997e8i	0.465188	+	0.805729i	−0.534022	+	0.845471i	$0.679320\pi$
$228$		0			0
$229$	1.34697e7	−	2.33303e7i	0.0741200	−	0.128380i	−0.826583	−	0.562814i	$-0.809719\pi$
$229$	1.34697e7	−	2.33303e7i	0.0741200	−	0.128380i	0.900703	+	0.434435i	$0.143052\pi$
$230$	4.25061e7			0.230358
$231$		0			0
$232$	4.46864e7			0.234946
$233$	−3.37092e7	+	5.83860e7i	−0.174583	+	0.302387i	−0.940017	−	0.341128i	$-0.889191\pi$
$233$	−3.37092e7	+	5.83860e7i	−0.174583	+	0.302387i	0.765434	+	0.643515i	$0.222524\pi$
$234$		0			0
$235$	−4.20674e7	−	7.28629e7i	−0.211450	−	0.366243i
$236$	−6.82998e7	+	1.18299e8i	−0.338242	+	0.585852i
$237$		0			0
$238$	−8.36314e7	−	1.21429e8i	−0.402115	−	0.583854i
$239$	−3.87968e8			−1.83824			−0.919122	−	0.393973i	$-0.871100\pi$
$239$	−3.87968e8			−1.83824			−0.919122	+	0.393973i	$0.871100\pi$
$240$		0			0
$241$	−1.15643e8	−	2.00299e8i	−0.532180	−	0.921762i	−0.999294	−	0.0375653i	$-0.988040\pi$
$241$	−1.15643e8	−	2.00299e8i	−0.532180	−	0.921762i	0.467115	−	0.884197i	$-0.345294\pi$
$242$	−8.97372e7	−	1.55429e8i	−0.407023	−	0.704984i
$243$		0			0
$244$	1.69897e8			0.748725
$245$	−2.09807e8	−	2.58053e8i	−0.911461	−	1.12106i
$246$		0			0
$247$	2.69938e8	−	4.67546e8i	1.13979	−	1.97417i
$248$	6.40709e7	+	1.10974e8i	0.266735	+	0.461998i
$249$		0			0
$250$	−1.10468e7	+	1.91336e7i	−0.0447143	+	0.0774475i
$251$	−1.20208e8			−0.479817			−0.239909	−	0.970795i	$-0.577117\pi$
$251$	−1.20208e8			−0.479817			−0.239909	+	0.970795i	$0.577117\pi$
$252$		0			0
$253$	−8.51860e7			−0.330709
$254$	−1.55459e8	+	2.69262e8i	−0.595246	+	1.03100i
$255$		0			0
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	1.16118e8	−	2.01122e8i	0.426711	−	0.739084i	−0.569868	−	0.821736i	$-0.693006\pi$
$257$	1.16118e8	−	2.01122e8i	0.426711	−	0.739084i	0.996578	+	0.0826520i	$0.0263390\pi$
$258$		0			0
$259$	−3.56722e8	+	2.84266e7i	−1.27580	+	0.101666i
$260$	3.00104e8			1.05893
$261$		0			0
$262$	−1.20847e7	−	2.09314e7i	−0.0415128	−	0.0719024i
$263$	−2.66338e8	−	4.61311e8i	−0.902792	−	1.56368i	−0.823853	−	0.566803i	$-0.808180\pi$
$263$	−2.66338e8	−	4.61311e8i	−0.902792	−	1.56368i	−0.0789391	−	0.996879i	$-0.525153\pi$
$264$		0			0
$265$	4.45140e8			1.46939
$266$	−1.45023e8	+	3.04816e8i	−0.472445	+	0.993005i
$267$		0			0
$268$	−2.46514e6	+	4.26974e6i	−0.00782293	+	0.0135497i
$269$	1.49165e8	+	2.58362e8i	0.467234	+	0.809274i	0.999299	−	0.0374298i	$-0.0119171\pi$
$269$	1.49165e8	+	2.58362e8i	0.467234	+	0.809274i	−0.532065	+	0.846704i	$0.678584\pi$
$270$		0			0
$271$	−2.76166e8	+	4.78333e8i	−0.842903	+	1.45995i	0.0445269	+	0.999008i	$0.485822\pi$
$271$	−2.76166e8	+	4.78333e8i	−0.842903	+	1.45995i	−0.887430	+	0.460943i	$0.847511\pi$
$272$	−8.31858e7			−0.250645
$273$		0			0
$274$	−5.29416e7			−0.155478
$275$	2.75056e8	−	4.76411e8i	0.797547	−	1.38139i
$276$		0			0
$277$	1.00415e8	+	1.73924e8i	0.283871	+	0.491678i	0.972335	−	0.233592i	$-0.0750480\pi$
$277$	1.00415e8	+	1.73924e8i	0.283871	+	0.491678i	−0.688464	+	0.725271i	$0.741715\pi$
$278$	−1.07662e7	+	1.86477e7i	−0.0300543	+	0.0520556i
$279$		0			0
$280$	−1.87047e8	+	1.49054e7i	−0.509210	+	0.0405781i
$281$	3.14684e8			0.846063			0.423031	−	0.906115i	$-0.360966\pi$
$281$	3.14684e8			0.846063			0.423031	+	0.906115i	$0.360966\pi$
$282$		0			0
$283$	−1.94424e8	−	3.36752e8i	−0.509914	−	0.883196i	−0.999934	−	0.0114853i	$-0.996344\pi$
$283$	−1.94424e8	−	3.36752e8i	−0.509914	−	0.883196i	0.490020	−	0.871711i	$-0.336989\pi$
$284$	4.96817e7	+	8.60513e7i	0.128701	+	0.222917i
$285$		0			0
$286$	−6.01435e8			−1.52022
$287$	1.20078e8	+	1.74348e8i	0.299832	+	0.435343i
$288$		0			0
$289$	−1.05926e6	+	1.83469e6i	−0.00258143	+	0.00447116i
$290$	−1.40986e8	−	2.44196e8i	−0.339457	−	0.587956i
$291$		0			0
$292$	−1.49252e8	+	2.58511e8i	−0.350816	+	0.607630i
$293$	8.20380e7			0.190537			0.0952684	−	0.995452i	$-0.469629\pi$
$293$	8.20380e7			0.190537			0.0952684	+	0.995452i	$0.469629\pi$
$294$		0			0
$295$	8.61948e8			1.95481
$296$	−1.00949e8	+	1.74849e8i	−0.226246	+	0.391869i
$297$		0			0
$298$	1.94527e8	+	3.36931e8i	0.425817	+	0.737537i
$299$	−7.63836e7	+	1.32300e8i	−0.165254	+	0.286228i
$300$		0			0
$301$	3.07142e8	+	4.45957e8i	0.649167	+	0.942563i
$302$	2.65174e8			0.553996
$303$		0			0
$304$	9.52232e7	+	1.64931e8i	0.194395	+	0.336702i
$305$	−5.36030e8	−	9.28430e8i	−1.08178	−	1.87370i
$306$		0			0
$307$	1.58854e8			0.313338			0.156669	−	0.987651i	$-0.449924\pi$
$307$	1.58854e8			0.313338			0.156669	+	0.987651i	$0.449924\pi$
$308$	3.74858e8	−	2.98718e7i	0.731037	−	0.0582550i
$309$		0			0
$310$	4.04290e8	−	7.00250e8i	0.770773	−	1.33502i
$311$	−2.77610e8	−	4.80834e8i	−0.523327	−	0.906430i	−0.999631	−	0.0271491i	$-0.991357\pi$
$311$	−2.77610e8	−	4.80834e8i	−0.523327	−	0.906430i	0.476304	−	0.879281i	$-0.341976\pi$
$312$		0			0
$313$	4.26038e8	−	7.37920e8i	0.785314	−	1.36020i	−0.143497	−	0.989651i	$-0.545835\pi$
$313$	4.26038e8	−	7.37920e8i	0.785314	−	1.36020i	0.928811	−	0.370553i	$-0.120832\pi$
$314$	−1.84342e8			−0.336025
$315$		0			0
$316$	−1.49434e8			−0.266407
$317$	2.34377e8	−	4.05953e8i	0.413245	−	0.715761i	−0.581998	−	0.813191i	$-0.697729\pi$
$317$	2.34377e8	−	4.05953e8i	0.413245	−	0.715761i	0.995242	+	0.0974294i	$0.0310620\pi$
$318$		0			0
$319$	2.82549e8	+	4.89389e8i	0.487334	+	0.844086i
$320$	−5.29324e7	+	9.16816e7i	−0.0903019	+	0.156407i
$321$		0			0
$322$	4.10368e7	−	8.62530e7i	0.0684980	−	0.143972i
$323$	9.44283e8			1.55917
$324$		0			0
$325$	−4.93268e8	−	8.54366e8i	−0.797061	−	1.38055i
$326$	2.27557e8	+	3.94141e8i	0.363772	+	0.630071i
$327$		0			0
$328$	1.19438e8			0.186890
$329$	−1.88466e8	+	1.50185e7i	−0.291774	+	0.0232510i
$330$		0			0
$331$	−1.24427e8	+	2.15514e8i	−0.188589	+	0.326646i	−0.944780	−	0.327705i	$-0.893725\pi$
$331$	−1.24427e8	+	2.15514e8i	−0.188589	+	0.326646i	0.756191	+	0.654351i	$0.227058\pi$
$332$	−1.65454e8	−	2.86574e8i	−0.248138	−	0.429788i
$333$		0			0
$334$	9.50267e6	−	1.64591e7i	0.0139551	−	0.0241710i
$335$	3.11102e7			0.0452112
$336$		0			0
$337$	5.86823e8			0.835223			0.417612	−	0.908626i	$-0.362867\pi$
$337$	5.86823e8			0.835223			0.417612	+	0.908626i	$0.362867\pi$
$338$	−2.88294e8	+	4.99340e8i	−0.406095	+	0.703377i
$339$		0			0
$340$	2.62453e8	+	4.54582e8i	0.362139	+	0.627243i
$341$	−8.10231e8	+	1.40336e9i	−1.10654	+	1.91659i
$342$		0			0
$343$	−7.26193e8	+	1.76604e8i	−0.971679	+	0.236304i
$344$	3.05505e8			0.404636
$345$		0			0
$346$	−1.14288e8	−	1.97952e8i	−0.148331	−	0.256918i
$347$	−6.07535e7	−	1.05228e8i	−0.0780581	−	0.135201i	0.824354	−	0.566075i	$-0.191539\pi$
$347$	−6.07535e7	−	1.05228e8i	−0.0780581	−	0.135201i	−0.902412	+	0.430874i	$0.858205\pi$
$348$		0			0
$349$	9.16462e8			1.15405			0.577026	−	0.816725i	$-0.304213\pi$
$349$	9.16462e8			1.15405			0.577026	+	0.816725i	$0.304213\pi$
$350$	3.49875e8	+	5.08003e8i	0.436189	+	0.633328i
$351$		0			0
$352$	1.06081e8	−	1.83738e8i	0.129640	−	0.224543i
$353$	−8.02933e7	−	1.39072e8i	−0.0971556	−	0.168278i	0.813351	−	0.581774i	$-0.197641\pi$
$353$	−8.02933e7	−	1.39072e8i	−0.0971556	−	0.168278i	−0.910506	+	0.413495i	$0.864308\pi$
$354$		0			0
$355$	3.13494e8	−	5.42987e8i	0.371903	−	0.644154i
$356$	−1.14813e8			−0.134870
$357$		0			0
$358$	−3.39034e8			−0.390529
$359$	−4.29774e8	+	7.44391e8i	−0.490241	+	0.849123i	−0.999937	−	0.0112320i	$-0.996425\pi$
$359$	−4.29774e8	+	7.44391e8i	−0.490241	+	0.849123i	0.509696	+	0.860355i	$0.329758\pi$
$360$		0			0
$361$	−6.33990e8	−	1.09810e9i	−0.709262	−	1.22848i
$362$	2.04549e8	−	3.54290e8i	0.226630	−	0.392535i
$363$		0			0
$364$	2.89730e8	−	6.08968e8i	0.314876	−	0.661820i
$365$	1.88357e9			2.02748
$366$		0			0
$367$	1.88818e8	+	3.27042e8i	0.199394	+	0.345361i	0.948332	−	0.317279i	$-0.102769\pi$
$367$	1.88818e8	+	3.27042e8i	0.199394	+	0.345361i	−0.748938	+	0.662640i	$0.769436\pi$
$368$	−2.69451e7	−	4.66703e7i	−0.0281846	−	0.0488172i
$369$		0			0
$370$	1.27398e9			1.30755
$371$	4.29752e8	−	9.03273e8i	0.436928	−	0.918354i
$372$		0			0
$373$	−3.81849e8	+	6.61382e8i	−0.380988	+	0.659890i	−0.991204	−	0.132345i	$-0.957749\pi$
$373$	−3.81849e8	+	6.61382e8i	−0.380988	+	0.659890i	0.610216	+	0.792235i	$0.291083\pi$
$374$	−5.25978e8	−	9.11021e8i	−0.519897	−	0.900487i
$375$		0			0
$376$	−5.33340e7	+	9.23772e7i	−0.0517424	+	0.0896205i
$377$	1.01341e9			0.974072
$378$		0			0
$379$	7.65774e8			0.722543			0.361271	−	0.932461i	$-0.382343\pi$
$379$	7.65774e8			0.722543			0.361271	+	0.932461i	$0.382343\pi$
$380$	6.00862e8	−	1.04072e9i	0.561736	−	0.972955i
$381$		0			0
$382$	5.80910e8	+	1.00616e9i	0.533196	+	0.923522i
$383$	−5.47890e8	+	9.48974e8i	−0.498308	+	0.863095i	−0.999998	−	0.00195262i	$-0.999378\pi$
$383$	−5.47890e8	+	9.48974e8i	−0.498308	+	0.863095i	0.501690	+	0.865047i	$0.332712\pi$
$384$		0			0
$385$	−1.34592e9	−	1.95422e9i	−1.20201	−	1.74526i
$386$	−2.46146e8			−0.217840
$387$		0			0
$388$	−7.50194e7	−	1.29937e8i	−0.0652022	−	0.112934i
$389$	6.99641e8	+	1.21181e9i	0.602631	+	1.04379i	0.992421	+	0.122884i	$0.0392143\pi$
$389$	6.99641e8	+	1.21181e9i	0.602631	+	1.04379i	−0.389790	+	0.920904i	$0.627452\pi$
$390$		0			0
$391$	−2.67202e8			−0.226058
$392$	−1.50335e8	+	3.93943e8i	−0.126055	+	0.330318i
$393$		0			0
$394$	2.54495e8	−	4.40798e8i	0.209625	−	0.363081i
$395$	4.71468e8	+	8.16606e8i	0.384913	+	0.666688i
$396$		0			0
$397$	−7.97000e8	+	1.38044e9i	−0.639281	+	1.10727i	0.346310	+	0.938120i	$0.387434\pi$
$397$	−7.97000e8	+	1.38044e9i	−0.639281	+	1.10727i	−0.985591	+	0.169147i	$0.945899\pi$
$398$	2.52381e8			0.200662
$399$		0			0
$400$	3.48011e8			0.271883
$401$	−4.17660e8	+	7.23409e8i	−0.323458	+	0.560246i	−0.981199	−	0.192998i	$-0.938179\pi$
$401$	−4.17660e8	+	7.23409e8i	−0.323458	+	0.560246i	0.657741	+	0.753244i	$0.271512\pi$
$402$		0			0
$403$	1.45302e9	+	2.51670e9i	1.10587	+	1.91542i
$404$	−5.79707e8	+	1.00408e9i	−0.437395	+	0.757591i
$405$		0			0
$406$	−6.31632e8	+	5.03336e7i	−0.468407	+	0.0373265i
$407$	−2.55317e9			−1.87715
$408$		0			0
$409$	−1.12482e9	−	1.94825e9i	−0.812930	−	1.40804i	−0.910805	−	0.412837i	$-0.864538\pi$
$409$	−1.12482e9	−	1.94825e9i	−0.812930	−	1.40804i	0.0978752	−	0.995199i	$-0.468795\pi$
$410$	−3.76830e8	−	6.52689e8i	−0.270024	−	0.467695i
$411$		0			0
$412$	3.74495e8			0.263819
$413$	8.32153e8	−	1.74906e9i	0.581270	−	1.22174i
$414$		0			0
$415$	−1.04402e9	+	1.80829e9i	−0.717034	+	1.24194i
$416$	−1.90239e8	−	3.29504e8i	−0.129561	−	0.224406i
$417$		0			0
$418$	−1.20418e9	+	2.08570e9i	−0.806444	+	1.39680i
$419$	−1.75510e9			−1.16561			−0.582803	−	0.812613i	$-0.698044\pi$
$419$	−1.75510e9			−1.16561			−0.582803	+	0.812613i	$0.698044\pi$
$420$		0			0
$421$	1.57373e9			1.02788			0.513940	−	0.857826i	$-0.328185\pi$
$421$	1.57373e9			1.02788			0.513940	+	0.857826i	$0.328185\pi$
$422$	4.83043e7	−	8.36654e7i	0.0312890	−	0.0541942i
$423$		0			0
$424$	−2.82179e8	−	4.88748e8i	−0.179781	−	0.311390i
$425$	8.62764e8	−	1.49435e9i	0.545169	−	0.944260i
$426$		0			0
$427$	−2.40146e9	+	1.91368e8i	−1.49272	+	0.118952i
$428$	1.81516e8			0.111908
$429$		0			0
$430$	−9.63875e8	−	1.66948e9i	−0.584630	−	1.01261i
$431$	8.75479e8	+	1.51637e9i	0.526714	+	0.912296i	0.999515	+	0.0311269i	$0.00990959\pi$
$431$	8.75479e8	+	1.51637e9i	0.526714	+	0.912296i	−0.472801	+	0.881169i	$0.656757\pi$
$432$		0			0
$433$	8.68747e8			0.514263			0.257132	−	0.966376i	$-0.417223\pi$
$433$	8.68747e8			0.514263			0.257132	+	0.966376i	$0.417223\pi$
$434$	−1.03063e9	−	1.49642e9i	−0.605183	−	0.878700i
$435$		0			0
$436$	−2.61019e8	+	4.52099e8i	−0.150824	+	0.261235i
$437$	3.05867e8	+	5.29777e8i	0.175327	+	0.303674i
$438$		0			0
$439$	−6.19056e8	+	1.07224e9i	−0.349224	+	0.604874i	−0.986112	−	0.166083i	$-0.946888\pi$
$439$	−6.19056e8	+	1.07224e9i	−0.349224	+	0.604874i	0.636888	+	0.770956i	$0.280221\pi$
$440$	−1.33875e9			−0.749231
$441$		0			0
$442$	−1.88651e9			−1.03916
$443$	1.68758e9	−	2.92298e9i	0.922256	−	1.59739i	0.126340	−	0.991987i	$-0.459677\pi$
$443$	1.68758e9	−	2.92298e9i	0.922256	−	1.59739i	0.795916	−	0.605408i	$-0.206990\pi$
$444$		0			0
$445$	3.62237e8	+	6.27412e8i	0.194864	+	0.337515i
$446$	1.12330e9	−	1.94561e9i	0.599548	−	1.03845i
$447$		0			0
$448$	1.34937e8	+	1.95922e8i	0.0709017	+	0.102946i
$449$	−2.12595e9			−1.10838			−0.554192	−	0.832389i	$-0.686973\pi$
$449$	−2.12595e9			−1.10838			−0.554192	+	0.832389i	$0.686973\pi$
$450$		0			0
$451$	7.55201e8	+	1.30805e9i	0.387654	+	0.671437i
$452$	−5.05381e8	−	8.75346e8i	−0.257416	−	0.445857i
$453$		0			0
$454$	−1.31171e9			−0.657875
$455$	−4.24190e9	+	3.38030e8i	−2.11116	+	0.168235i
$456$		0			0
$457$	1.00336e9	−	1.73787e9i	0.491758	−	0.851749i	−0.508197	−	0.861241i	$-0.669688\pi$
$457$	1.00336e9	−	1.73787e9i	0.491758	−	0.851749i	0.999955	+	0.00949148i	$0.00302128\pi$
$458$	1.07758e8	+	1.86642e8i	0.0524107	+	0.0907780i
$459$		0			0
$460$	−1.70025e8	+	2.94491e8i	−0.0814440	+	0.141065i
$461$	−1.93015e9			−0.917567			−0.458783	−	0.888548i	$-0.651715\pi$
$461$	−1.93015e9			−0.917567			−0.458783	+	0.888548i	$0.651715\pi$
$462$		0			0
$463$	−2.08029e9			−0.974072			−0.487036	−	0.873382i	$-0.661922\pi$
$463$	−2.08029e9			−0.974072			−0.487036	+	0.873382i	$0.661922\pi$
$464$	−1.78746e8	+	3.09597e8i	−0.0830658	+	0.143874i
$465$		0			0
$466$	−2.69673e8	−	4.67088e8i	−0.123449	−	0.213820i
$467$	−1.62399e9	+	2.81283e9i	−0.737861	+	1.27801i	0.215596	+	0.976483i	$0.430831\pi$
$467$	−1.62399e9	+	2.81283e9i	−0.737861	+	1.27801i	−0.953457	+	0.301530i	$0.902503\pi$
$468$		0			0
$469$	3.00348e7	−	6.31285e7i	0.0134437	−	0.0282566i
$470$	6.73079e8			0.299036
$471$		0			0
$472$	−5.46398e8	−	9.46390e8i	−0.239173	−	0.414260i
$473$	1.93169e9	+	3.34578e9i	0.839312	+	1.45373i
$474$		0			0
$475$	−3.95044e9			−1.69129
$476$	1.17581e9	−	9.36984e7i	0.499705	−	0.0398206i
$477$		0			0
$478$	1.55187e9	−	2.68792e9i	0.649917	−	1.12569i
$479$	1.28705e8	+	2.22924e8i	0.0535083	+	0.0926791i	0.891539	−	0.452944i	$-0.149626\pi$
$479$	1.28705e8	+	2.22924e8i	0.0535083	+	0.0926791i	−0.838031	+	0.545623i	$0.816293\pi$
$480$		0			0
$481$	−2.28935e9	+	3.96527e9i	−0.938003	+	1.62467i
$482$	1.85028e9			0.752616
$483$		0			0
$484$	1.43579e9			0.575617
$485$	−4.73375e8	+	8.19909e8i	−0.188412	+	0.326340i
$486$		0			0
$487$	−1.57169e9	−	2.72226e9i	−0.616619	−	1.06802i	−0.990098	−	0.140377i	$-0.955169\pi$
$487$	−1.57169e9	−	2.72226e9i	−0.616619	−	1.06802i	0.373479	−	0.927639i	$-0.378165\pi$
$488$	−6.79590e8	+	1.17708e9i	−0.264714	+	0.458499i
$489$		0			0
$490$	2.62707e9	−	4.21369e8i	1.00876	−	0.161799i
$491$	2.17591e9			0.829575			0.414788	−	0.909918i	$-0.363856\pi$
$491$	2.17591e9			0.829575			0.414788	+	0.909918i	$0.363856\pi$
$492$		0			0
$493$	8.86268e8	+	1.53506e9i	0.333120	+	0.576981i
$494$	2.15950e9	+	3.74036e9i	0.805952	+	1.39595i
$495$		0			0
$496$	−1.02513e9			−0.377220
$497$	−7.99166e8	−	1.16035e9i	−0.292004	−	0.423978i
$498$		0			0
$499$	1.66910e9	−	2.89096e9i	0.601353	−	1.04157i	−0.391263	−	0.920279i	$-0.627962\pi$
$499$	1.66910e9	−	2.89096e9i	0.601353	−	1.04157i	0.992616	−	0.121296i	$-0.0387049\pi$
$500$	−8.83745e7	−	1.53069e8i	−0.0316178	−	0.0547637i
$501$		0			0
$502$	4.80832e8	−	8.32826e8i	0.169641	−	0.293827i
$503$	3.49207e8			0.122347			0.0611737	−	0.998127i	$-0.480516\pi$
$503$	3.49207e8			0.122347			0.0611737	+	0.998127i	$0.480516\pi$
$504$		0			0
$505$	7.31595e9			2.52785
$506$	3.40744e8	−	5.90186e8i	0.116923	−	0.202517i
$507$		0			0
$508$	−1.24367e9	−	2.15410e9i	−0.420903	−	0.729025i
$509$	1.05045e9	−	1.81942e9i	0.353070	−	0.611536i	−0.633715	−	0.773566i	$-0.718471\pi$
$509$	1.05045e9	−	1.81942e9i	0.353070	−	0.611536i	0.986786	+	0.162031i	$0.0518043\pi$
$510$		0			0
$511$	1.81846e9	−	3.82211e9i	0.602878	−	1.26716i
$512$	1.34218e8			0.0441942
$513$		0			0
$514$	9.28943e8	+	1.60898e9i	0.301730	+	0.522612i
$515$	−1.18154e9	−	2.04648e9i	−0.381173	−	0.660212i
$516$		0			0
$517$	−1.34891e9			−0.429304
$518$	1.22994e9	−	2.58515e9i	0.388804	−	0.817206i
$519$		0			0
$520$	−1.20042e9	+	2.07918e9i	−0.374387	+	0.648457i
$521$	1.49421e9	+	2.58805e9i	0.462892	+	0.801753i	0.999104	−	0.0423306i	$-0.0134783\pi$
$521$	1.49421e9	+	2.58805e9i	0.462892	+	0.801753i	−0.536211	+	0.844084i	$0.680145\pi$
$522$		0			0
$523$	−1.84772e9	+	3.20035e9i	−0.564782	+	0.978231i	0.432288	+	0.901736i	$0.357706\pi$
$523$	−1.84772e9	+	3.20035e9i	−0.564782	+	0.978231i	−0.997070	+	0.0764954i	$0.975627\pi$
$524$	1.93356e8			0.0587080
$525$		0			0
$526$	4.26141e9			1.27674
$527$	−2.54144e9	+	4.40191e9i	−0.756385	+	1.31010i
$528$		0			0
$529$	1.61586e9	+	2.79876e9i	0.474580	+	0.821997i
$530$	−1.78056e9	+	3.08402e9i	−0.519506	+	0.899811i
$531$		0			0
$532$	−1.53173e9	−	2.22401e9i	−0.441054	−	0.640392i
$533$	2.70866e9			0.774835
$534$		0			0
$535$	−5.72687e8	−	9.91923e8i	−0.161688	−	0.280053i
$536$	−1.97211e7	−	3.41579e7i	−0.00553165	−	0.00958109i
$537$		0			0
$538$	−2.38665e9			−0.660769
$539$	−5.26488e9	+	8.44461e8i	−1.44820	+	0.232284i
$540$		0			0
$541$	−7.30573e8	+	1.26539e9i	−0.198369	+	0.343585i	−0.948000	−	0.318271i	$-0.896898\pi$
$541$	−7.30573e8	+	1.26539e9i	−0.198369	+	0.343585i	0.749631	+	0.661856i	$0.230231\pi$
$542$	−2.20933e9	−	3.82667e9i	−0.596022	−	1.03234i
$543$		0			0
$544$	3.32743e8	−	5.76328e8i	0.0886162	−	0.153488i
$545$	3.29408e9			0.871659
$546$		0			0
$547$	−3.60184e9			−0.940954			−0.470477	−	0.882412i	$-0.655918\pi$
$547$	−3.60184e9			−0.940954			−0.470477	+	0.882412i	$0.655918\pi$
$548$	2.11766e8	−	3.66790e8i	0.0549699	−	0.0952106i
$549$		0			0
$550$	2.20045e9	+	3.81129e9i	0.563951	+	0.976792i
$551$	2.02903e9	−	3.51438e9i	0.516723	−	0.894990i
$552$		0			0
$553$	2.11222e9	−	1.68319e8i	0.531130	−	0.0423248i
$554$	−1.60664e9			−0.401454
$555$		0			0
$556$	−8.61299e7	−	1.49181e8i	−0.0212516	−	0.0368089i
$557$	1.46695e9	+	2.54083e9i	0.359684	+	0.622991i	0.987908	−	0.155042i	$-0.0495512\pi$
$557$	1.46695e9	+	2.54083e9i	0.359684	+	0.622991i	−0.628224	+	0.778033i	$0.716218\pi$
$558$		0			0
$559$	6.92835e9			1.67760
$560$	6.44919e8	−	1.35552e9i	0.155184	−	0.326173i
$561$		0			0
$562$	−1.25874e9	+	2.18020e9i	−0.299128	+	0.518106i
$563$	−1.22429e8	−	2.12053e8i	−0.0289138	−	0.0500802i	0.851206	−	0.524831i	$-0.175871\pi$
$563$	−1.22429e8	−	2.12053e8i	−0.0289138	−	0.0500802i	−0.880120	+	0.474751i	$0.842538\pi$
$564$		0			0
$565$	−3.18897e9	+	5.52347e9i	−0.743843	+	1.28837i
$566$	3.11078e9			0.721127
$567$		0			0
$568$	−7.94908e8			−0.182011
$569$	3.99420e9	−	6.91816e9i	0.908944	−	1.57434i	0.0934095	−	0.995628i	$-0.470223\pi$
$569$	3.99420e9	−	6.91816e9i	0.908944	−	1.57434i	0.815534	−	0.578709i	$-0.196443\pi$
$570$		0			0
$571$	1.07784e9	+	1.86688e9i	0.242286	+	0.419652i	0.961365	−	0.275276i	$-0.0887694\pi$
$571$	1.07784e9	+	1.86688e9i	0.242286	+	0.419652i	−0.719079	+	0.694928i	$0.755436\pi$
$572$	2.40574e9	−	4.16686e9i	0.537480	−	0.930943i
$573$		0			0
$574$	−1.68823e9	+	1.34532e8i	−0.372599	+	0.0296917i
$575$	1.11785e9			0.245214
$576$		0			0
$577$	−1.42136e9	−	2.46187e9i	−0.308028	−	0.533520i	0.669903	−	0.742449i	$-0.266336\pi$
$577$	−1.42136e9	−	2.46187e9i	−0.308028	−	0.533520i	−0.977931	+	0.208929i	$0.933002\pi$
$578$	−8.47407e6	−	1.46775e7i	−0.00182534	−	0.00316159i
$579$		0			0
$580$	2.25578e9			0.480064
$581$	2.66144e9	+	3.86430e9i	0.562989	+	0.817436i
$582$		0			0
$583$	3.56839e9	−	6.18064e9i	0.745818	−	1.29179i
$584$	−1.19401e9	−	2.06809e9i	−0.248064	−	0.429660i
$585$		0			0
$586$	−3.28152e8	+	5.68376e8i	−0.0673649	+	0.116679i
$587$	1.27323e9			0.259821			0.129910	−	0.991526i	$-0.458531\pi$
$587$	1.27323e9			0.259821			0.129910	+	0.991526i	$0.458531\pi$
$588$		0			0
$589$	1.16368e10			2.34655
$590$	−3.44779e9	+	5.97175e9i	−0.691129	+	1.19707i
$591$		0			0
$592$	−8.07591e8	−	1.39879e9i	−0.159980	−	0.277093i
$593$	5.02956e9	−	8.71146e9i	0.990464	−	1.71553i	0.375921	−	0.926652i	$-0.377326\pi$
$593$	5.02956e9	−	8.71146e9i	0.990464	−	1.71553i	0.614543	−	0.788883i	$-0.289340\pi$
$594$		0			0
$595$	−4.22174e9	−	6.12978e9i	−0.821640	−	1.19299i
$596$	−3.11243e9			−0.602196
$597$		0			0
$598$	−6.11069e8	−	1.05840e9i	−0.116852	−	0.202394i
$599$	6.72728e8	+	1.16520e9i	0.127893	+	0.221517i	0.922860	−	0.385136i	$-0.125845\pi$
$599$	6.72728e8	+	1.16520e9i	0.127893	+	0.221517i	−0.794967	+	0.606652i	$0.792512\pi$
$600$		0			0
$601$	−3.26475e9			−0.613465			−0.306732	−	0.951796i	$-0.599236\pi$
$601$	−3.26475e9			−0.613465			−0.306732	+	0.951796i	$0.599236\pi$
$602$	−4.31825e9	+	3.44114e8i	−0.806714	+	0.0642856i
$603$		0			0
$604$	−1.06070e9	+	1.83718e9i	−0.195867	+	0.339252i
$605$	−4.52996e9	−	7.84612e9i	−0.831669	−	1.44049i
$606$		0			0
$607$	1.22422e9	−	2.12041e9i	0.222177	−	0.384821i	−0.733292	−	0.679914i	$-0.762017\pi$
$607$	1.22422e9	−	2.12041e9i	0.222177	−	0.384821i	0.955469	+	0.295093i	$0.0953505\pi$
$608$	−1.52357e9			−0.274916
$609$		0			0
$610$	8.57647e9			1.52987
$611$	−1.20952e9	+	2.09496e9i	−0.214521	+	0.371562i
$612$		0			0
$613$	−2.84315e9	−	4.92449e9i	−0.498527	−	0.863474i	0.501471	−	0.865174i	$-0.332792\pi$
$613$	−2.84315e9	−	4.92449e9i	−0.498527	−	0.863474i	−0.999999	+	0.00169981i	$0.999459\pi$
$614$	−6.35415e8	+	1.10057e9i	−0.110782	+	0.191879i
$615$		0			0
$616$	−1.29247e9	+	2.71658e9i	−0.222787	+	0.468263i
$617$	1.09146e10			1.87072			0.935361	−	0.353695i	$-0.115075\pi$
$617$	1.09146e10			1.87072			0.935361	+	0.353695i	$0.115075\pi$
$618$		0			0
$619$	2.50230e8	+	4.33411e8i	0.0424055	+	0.0734485i	0.886449	−	0.462826i	$-0.153165\pi$
$619$	2.50230e8	+	4.33411e8i	0.0424055	+	0.0734485i	−0.844044	+	0.536274i	$0.819831\pi$
$620$	3.23432e9	+	5.60200e9i	0.545019	+	0.944001i
$621$		0			0
$622$	4.44176e9			0.740097
$623$	1.62285e9	−	1.29322e8i	0.268888	−	0.0214272i
$624$		0			0
$625$	2.76124e9	−	4.78261e9i	0.452402	−	0.783583i
$626$	3.40831e9	+	5.90336e9i	0.555301	+	0.961809i
$627$		0			0
$628$	7.37370e8	−	1.27716e9i	0.118803	−	0.205772i
$629$	−8.00850e9			−1.28314
$630$		0			0
$631$	4.24339e9			0.672373			0.336186	−	0.941795i	$-0.390863\pi$
$631$	4.24339e9			0.672373			0.336186	+	0.941795i	$0.390863\pi$
$632$	5.97737e8	−	1.03531e9i	0.0941890	−	0.163140i
$633$		0			0
$634$	1.87502e9	+	3.24762e9i	0.292208	+	0.506120i
$635$	−7.84759e9	+	1.35924e10i	−1.21627	+	2.10663i
$636$		0			0
$637$	−3.40935e9	+	8.93397e9i	−0.522616	+	1.36948i
$638$	−4.52078e9			−0.689194
$639$		0			0
$640$	−4.23459e8	−	7.33453e8i	−0.0638531	−	0.110597i
$641$	−2.91419e9	−	5.04753e9i	−0.437034	−	0.756965i	0.560425	−	0.828205i	$-0.310638\pi$
$641$	−2.91419e9	−	5.04753e9i	−0.437034	−	0.756965i	−0.997459	+	0.0712398i	$0.977304\pi$
$642$		0			0
$643$	−8.45573e9			−1.25433			−0.627166	−	0.778886i	$-0.715785\pi$
$643$	−8.45573e9			−1.25433			−0.627166	+	0.778886i	$0.715785\pi$
$644$	4.33431e8	+	6.29323e8i	0.0639469	+	0.0928481i
$645$		0			0
$646$	−3.77713e9	+	6.54219e9i	−0.551250	+	0.954793i
$647$	−9.59555e8	−	1.66200e9i	−0.139285	−	0.241249i	0.787941	−	0.615751i	$-0.211147\pi$
$647$	−9.59555e8	−	1.66200e9i	−0.139285	−	0.241249i	−0.927226	+	0.374502i	$0.877814\pi$
$648$		0			0
$649$	6.90967e9	−	1.19679e10i	0.992204	−	1.71855i
$650$	7.89229e9			1.12721
$651$		0			0
$652$	−3.64092e9			−0.514451
$653$	5.64974e9	−	9.78563e9i	0.794021	−	1.37529i	−0.129437	−	0.991588i	$-0.541317\pi$
$653$	5.64974e9	−	9.78563e9i	0.794021	−	1.37529i	0.923459	−	0.383698i	$-0.125350\pi$
$654$		0			0
$655$	−6.10041e8	−	1.05662e9i	−0.0848231	−	0.146918i
$656$	−4.77754e8	+	8.27494e8i	−0.0660755	+	0.114446i
$657$		0			0
$658$	6.49812e8	−	1.36580e9i	0.0889195	−	0.186895i
$659$	3.23836e9			0.440784			0.220392	−	0.975411i	$-0.429266\pi$
$659$	3.23836e9			0.440784			0.220392	+	0.975411i	$0.429266\pi$
$660$		0			0
$661$	−3.59578e9	−	6.22808e9i	−0.484271	−	0.838781i	0.515566	−	0.856850i	$-0.327582\pi$
$661$	−3.59578e9	−	6.22808e9i	−0.484271	−	0.838781i	−0.999837	+	0.0180684i	$0.994248\pi$
$662$	−9.95415e8	−	1.72411e9i	−0.133353	−	0.230973i
$663$		0			0
$664$	2.64726e9			0.350920
$665$	−7.32080e9	+	1.53872e10i	−0.965345	+	2.02900i
$666$		0			0
$667$	−5.74150e8	+	9.94457e8i	−0.0749178	+	0.129761i
$668$	7.60214e7	+	1.31673e8i	0.00986775	+	0.0170914i
$669$		0			0
$670$	−1.24441e8	+	2.15538e8i	−0.0159846	+	0.0276861i
$671$	−1.71880e10			−2.19632
$672$		0			0
$673$	−6.55028e9			−0.828337			−0.414168	−	0.910200i	$-0.635928\pi$
$673$	−6.55028e9			−0.828337			−0.414168	+	0.910200i	$0.635928\pi$
$674$	−2.34729e9	+	4.06563e9i	−0.295296	+	0.511468i
$675$		0			0
$676$	−2.30635e9	−	3.99472e9i	−0.287152	−	0.497363i
$677$	5.19191e9	−	8.99265e9i	0.643082	−	1.11385i	−0.341658	−	0.939824i	$-0.610989\pi$
$677$	5.19191e9	−	8.99265e9i	0.643082	−	1.11385i	0.984741	−	0.174027i	$-0.0556781\pi$
$678$		0			0
$679$	1.20674e9	+	1.75213e9i	0.147934	+	0.214794i
$680$	−4.19924e9			−0.512141
$681$		0			0
$682$	−6.48185e9	−	1.12269e10i	−0.782445	−	1.35523i
$683$	6.33681e8	+	1.09757e9i	0.0761024	+	0.131813i	0.901565	−	0.432643i	$-0.142419\pi$
$683$	6.33681e8	+	1.09757e9i	0.0761024	+	0.131813i	−0.825463	+	0.564457i	$0.809086\pi$
$684$		0			0
$685$	−2.67250e9			−0.317689
$686$	1.68122e9	−	5.73763e9i	0.198834	−	0.678576i
$687$		0			0
$688$	−1.22202e9	+	2.11660e9i	−0.143060	+	0.247788i
$689$	−6.39934e9	−	1.10840e10i	−0.745363	−	1.29101i
$690$		0			0
$691$	−7.47471e9	+	1.29466e10i	−0.861829	+	1.49273i	0.00833297	+	0.999965i	$0.497348\pi$
$691$	−7.47471e9	+	1.29466e10i	−0.861829	+	1.49273i	−0.870162	+	0.492766i	$0.835986\pi$
$692$	1.82860e9			0.209772
$693$		0			0
$694$	9.72056e8			0.110391
$695$	−5.43483e8	+	9.41339e8i	−0.0614100	+	0.106365i
$696$		0			0
$697$	2.36883e9	+	4.10293e9i	0.264984	+	0.458965i
$698$	−3.66585e9	+	6.34944e9i	−0.408019	+	0.706710i
$699$		0			0
$700$	−4.91905e9	+	3.91990e8i	−0.542048	+	0.0431949i
$701$	1.40054e10			1.53562			0.767808	−	0.640680i	$-0.221347\pi$
$701$	1.40054e10			1.53562			0.767808	+	0.640680i	$0.221347\pi$
$702$		0			0
$703$	9.16737e9	+	1.58783e10i	0.995178	+	1.72370i
$704$	8.48649e8	+	1.46990e9i	0.0916693	+	0.158776i
$705$		0			0
$706$	1.28469e9			0.137399
$707$	7.06305e9	−	1.48454e10i	0.751665	−	1.57988i
$708$		0			0
$709$	6.92117e9	−	1.19878e10i	0.729319	−	1.26322i	−0.227852	−	0.973696i	$-0.573170\pi$
$709$	6.92117e9	−	1.19878e10i	0.729319	−	1.26322i	0.957171	−	0.289522i	$-0.0934965\pi$
$710$	2.50795e9	+	4.34389e9i	0.262975	+	0.455486i
$711$		0			0
$712$	4.59252e8	−	7.95447e8i	0.0476838	−	0.0825907i
$713$	−3.29284e9			−0.340218
$714$		0			0
$715$	−3.03606e10			−3.10627
$716$	1.35614e9	−	2.34890e9i	0.138073	−	0.239149i
$717$		0			0
$718$	−3.43819e9	−	5.95513e9i	−0.346653	−	0.600420i
$719$	−7.38278e9	+	1.27874e10i	−0.740745	+	1.28301i	0.211411	+	0.977397i	$0.432194\pi$
$719$	−7.38278e9	+	1.27874e10i	−0.740745	+	1.28301i	−0.952156	+	0.305611i	$0.901139\pi$
$720$		0			0
$721$	−5.29340e9	+	4.21822e8i	−0.525970	+	0.0419136i
$722$	1.01438e10			1.00305
$723$		0			0
$724$	1.63639e9	+	2.83432e9i	0.160252	+	0.277564i
$725$	−3.70773e9	−	6.42198e9i	−0.361348	−	0.625872i
$726$		0			0
$727$	1.82026e10			1.75696			0.878481	−	0.477777i	$-0.158557\pi$
$727$	1.82026e10			1.75696			0.878481	+	0.477777i	$0.158557\pi$
$728$	3.06013e9	+	4.44318e9i	0.293955	+	0.426810i
$729$		0			0
$730$	−7.53426e9	+	1.30497e10i	−0.716821	+	1.24157i
$731$	6.05910e9	+	1.04947e10i	0.573717	+	0.993707i
$732$		0			0
$733$	−5.45758e9	+	9.45281e9i	−0.511843	+	0.886537i	0.488063	+	0.872808i	$0.337704\pi$
$733$	−5.45758e9	+	9.45281e9i	−0.511843	+	0.886537i	−0.999906	+	0.0137290i	$0.995630\pi$
$734$	−3.02109e9			−0.281986
$735$		0			0
$736$	4.31122e8			0.0398591
$737$	2.49390e8	−	4.31956e8i	0.0229479	−	0.0397469i
$738$		0			0
$739$	6.46952e9	+	1.12055e10i	0.589680	+	1.02136i	0.994274	+	0.106859i	$0.0340794\pi$
$739$	6.46952e9	+	1.12055e10i	0.589680	+	1.02136i	−0.404594	+	0.914496i	$0.632587\pi$
$740$	−5.09593e9	+	8.82641e9i	−0.462288	+	0.800706i
$741$		0			0
$742$	4.53905e9	+	6.59050e9i	0.407897	+	0.592250i
$743$	−8.91147e9			−0.797056			−0.398528	−	0.917156i	$-0.630479\pi$
$743$	−8.91147e9			−0.797056			−0.398528	+	0.917156i	$0.630479\pi$
$744$		0			0
$745$	9.81978e9	+	1.70084e10i	0.870072	+	1.50701i
$746$	−3.05479e9	−	5.29106e9i	−0.269399	−	0.466613i
$747$		0			0
$748$	8.41565e9			0.735245
$749$	−2.56569e9	+	2.04455e8i	−0.223109	+	0.0177792i
$750$		0			0
$751$	1.68792e9	−	2.92357e9i	0.145416	−	0.251868i	−0.784112	−	0.620619i	$-0.786881\pi$
$751$	1.68792e9	−	2.92357e9i	0.145416	−	0.251868i	0.929528	+	0.368751i	$0.120215\pi$
$752$	−4.26672e8	−	7.39017e8i	−0.0365874	−	0.0633712i
$753$		0			0
$754$	−4.05365e9	+	7.02112e9i	−0.344387	+	0.596495i
$755$	1.33861e10			1.13198
$756$		0			0
$757$	4.09781e9			0.343333			0.171667	−	0.985155i	$-0.445085\pi$
$757$	4.09781e9			0.343333			0.171667	+	0.985155i	$0.445085\pi$
$758$	−3.06310e9	+	5.30544e9i	−0.255457	+	0.442465i
$759$		0			0
$760$	4.80689e9	+	8.32579e9i	0.397207	+	0.687983i
$761$	−4.36321e9	+	7.55729e9i	−0.358888	+	0.621613i	−0.987775	−	0.155884i	$-0.950177\pi$
$761$	−4.36321e9	+	7.55729e9i	−0.358888	+	0.621613i	0.628887	+	0.777497i	$0.283511\pi$
$762$		0			0
$763$	3.18022e9	−	6.68432e9i	0.259191	−	0.544780i
$764$	−9.29455e9			−0.754053
$765$		0			0
$766$	−4.38312e9	−	7.59179e9i	−0.352357	−	0.610300i
$767$	−1.23914e10	−	2.14625e10i	−0.991599	−	1.71750i
$768$		0			0
$769$	−2.27000e10			−1.80005			−0.900024	−	0.435840i	$-0.856451\pi$
$769$	−2.27000e10			−1.80005			−0.900024	+	0.435840i	$0.856451\pi$
$770$	1.89229e10	−	1.50794e9i	1.49373	−	0.119032i
$771$		0			0
$772$	9.84585e8	−	1.70535e9i	0.0770180	−	0.133399i
$773$	9.51851e9	+	1.64865e10i	0.741209	+	1.28381i	0.951945	+	0.306269i	$0.0990807\pi$
$773$	9.51851e9	+	1.64865e10i	0.741209	+	1.28381i	−0.210736	+	0.977543i	$0.567586\pi$
$774$		0			0
$775$	1.06322e10	−	1.84155e10i	0.820479	−	1.42111i
$776$	1.20031e9			0.0922099
$777$		0			0
$778$	−1.11943e10			−0.852249
$779$	5.42322e9	−	9.39329e9i	0.411032	−	0.711929i
$780$		0			0
$781$	−5.02615e9	−	8.70554e9i	−0.377534	−	0.653909i
$782$	1.06881e9	−	1.85123e9i	0.0799237	−	0.138432i
$783$		0			0
$784$	−2.12798e9	−	2.61733e9i	−0.157711	−	0.193978i
$785$	−9.30566e9			−0.686599
$786$		0			0
$787$	−1.13547e10	−	1.96670e10i	−0.830357	−	1.43822i	−0.897755	−	0.440495i	$-0.854803\pi$
$787$	−1.13547e10	−	1.96670e10i	−0.830357	−	1.43822i	0.0673979	−	0.997726i	$-0.478530\pi$
$788$	2.03596e9	+	3.52639e9i	0.148227	+	0.256737i
$789$		0			0
$790$	−7.54348e9			−0.544348
$791$	8.12941e9	+	1.18036e10i	0.584039	+	0.847999i
$792$		0			0
$793$	−1.54119e10	+	2.66943e10i	−1.09749	+	1.90091i
$794$	−6.37600e9	−	1.10436e10i	−0.452040	−	0.782956i
$795$		0			0
$796$	−1.00952e9	+	1.74854e9i	−0.0709448	+	0.122880i
$797$	5.57990e9			0.390411			0.195206	−	0.980762i	$-0.437463\pi$
$797$	5.57990e9			0.390411			0.195206	+	0.980762i	$0.437463\pi$
$798$		0			0
$799$	−4.23110e9			−0.293454
$800$	−1.39204e9	+	2.41109e9i	−0.0961253	+	0.166494i
$801$		0			0
$802$	−3.34128e9	−	5.78727e9i	−0.228719	−	0.396154i
$803$	1.50993e10	−	2.61528e10i	1.02909	−	1.78243i
$804$		0			0
$805$	2.07155e9	−	4.35407e9i	0.139962	−	0.294178i
$806$	−2.32483e10			−1.56393
$807$		0			0
$808$	−4.63766e9	−	8.03266e9i	−0.309285	−	0.535698i
$809$	−4.83729e8	−	8.37842e8i	−0.0321205	−	0.0556343i	0.849518	−	0.527559i	$-0.176893\pi$
$809$	−4.83729e8	−	8.37842e8i	−0.0321205	−	0.0556343i	−0.881639	+	0.471925i	$0.843559\pi$
$810$		0			0
$811$	2.31593e10			1.52459			0.762295	−	0.647229i	$-0.224072\pi$
$811$	2.31593e10			1.52459			0.762295	+	0.647229i	$0.224072\pi$
$812$	2.17781e9	−	4.57741e9i	0.142749	−	0.300036i
$813$		0			0
$814$	1.02127e10	−	1.76889e10i	0.663674	−	1.14952i
$815$	1.14872e10	+	1.98963e10i	0.743294	+	1.28742i
$816$		0			0
$817$	1.38718e10	−	2.40266e10i	0.889928	−	1.54140i
$818$	1.79972e10			1.14966
$819$		0			0
$820$	6.02929e9			0.381872
$821$	−9.32624e9	+	1.61535e10i	−0.588174	+	1.01875i	0.406298	+	0.913741i	$0.366820\pi$
$821$	−9.32624e9	+	1.61535e10i	−0.588174	+	1.01875i	−0.994472	+	0.105006i	$0.966514\pi$
$822$		0			0
$823$	7.23446e9	+	1.25304e10i	0.452383	+	0.783551i	0.998534	−	0.0541365i	$-0.0172406\pi$
$823$	7.23446e9	+	1.25304e10i	0.452383	+	0.783551i	−0.546150	+	0.837687i	$0.683907\pi$
$824$	−1.49798e9	+	2.59458e9i	−0.0932740	+	0.161555i
$825$		0			0
$826$	8.78920e9	+	1.27615e10i	0.542649	+	0.787904i
$827$	−2.18964e10			−1.34618			−0.673092	−	0.739559i	$-0.735034\pi$
$827$	−2.18964e10			−1.34618			−0.673092	+	0.739559i	$0.735034\pi$
$828$		0			0
$829$	−2.96991e9	−	5.14404e9i	−0.181052	−	0.313591i	0.761187	−	0.648532i	$-0.224617\pi$
$829$	−2.96991e9	−	5.14404e9i	−0.181052	−	0.313591i	−0.942239	+	0.334941i	$0.891283\pi$
$830$	−8.35215e9	−	1.44663e10i	−0.507020	−	0.878184i
$831$		0			0
$832$	3.04383e9			0.183227
$833$	−1.65143e10	+	2.64881e9i	−0.989925	+	0.158779i
$834$		0			0
$835$	4.79698e8	−	8.30861e8i	0.0285144	−	0.0493885i
$836$	−9.63343e9	−	1.66856e10i	−0.570242	−	0.987688i
$837$		0			0
$838$	7.02038e9	−	1.21597e10i	0.412104	−	0.713785i
$839$	2.57848e9			0.150729			0.0753646	−	0.997156i	$-0.475988\pi$
$839$	2.57848e9			0.150729			0.0753646	+	0.997156i	$0.475988\pi$
$840$		0			0
$841$	−9.63240e9			−0.558404
$842$	−6.29492e9	+	1.09031e10i	−0.363411	+	0.629446i
$843$		0			0
$844$	3.86434e8	+	6.69323e8i	0.0221247	+	0.0383211i
$845$	−1.45532e10	+	2.52068e10i	−0.829773	+	1.43721i
$846$		0			0
$847$	−2.02946e10	+	1.61724e9i	−1.14760	+	0.0914499i
$848$	4.51486e9			0.254249
$849$		0			0
$850$	6.90211e9	+	1.19548e10i	0.385492	+	0.667693i
$851$	−2.59407e9	−	4.49306e9i	−0.144287	−	0.249913i
$852$		0			0
$853$	2.41906e10			1.33452			0.667259	−	0.744826i	$-0.267467\pi$
$853$	2.41906e10			1.33452			0.667259	+	0.744826i	$0.267467\pi$
$854$	8.28001e9	−	1.74033e10i	0.454913	−	0.956156i
$855$		0			0
$856$	−7.26065e8	+	1.25758e9i	−0.0395656	+	0.0685296i
$857$	2.97434e9	+	5.15170e9i	0.161420	+	0.279588i	0.935378	−	0.353649i	$-0.115059\pi$
$857$	2.97434e9	+	5.15170e9i	0.161420	+	0.279588i	−0.773958	+	0.633237i	$0.781726\pi$
$858$		0			0
$859$	−5.90660e9	+	1.02305e10i	−0.317952	+	0.550709i	−0.980061	−	0.198699i	$-0.936328\pi$
$859$	−5.90660e9	+	1.02305e10i	−0.317952	+	0.550709i	0.662109	+	0.749408i	$0.269662\pi$
$860$	1.54220e10			0.826792
$861$		0			0
$862$	−1.40077e10			−0.744887
$863$	−3.65692e8	+	6.33397e8i	−0.0193677	+	0.0335458i	−0.875547	−	0.483133i	$-0.839499\pi$
$863$	−3.65692e8	+	6.33397e8i	−0.0193677	+	0.0335458i	0.856179	+	0.516679i	$0.172832\pi$
$864$		0			0
$865$	−5.76928e9	−	9.99268e9i	−0.303085	−	0.524959i
$866$	−3.47499e9	+	6.01885e9i	−0.181820	+	0.314921i
$867$		0			0
$868$	1.44900e10	−	1.15468e9i	0.752056	−	0.0599300i
$869$	1.51178e10			0.781482
$870$		0			0
$871$	−4.47241e8	−	7.74644e8i	−0.0229339	−	0.0397227i
$872$	−2.08816e9	−	3.61679e9i	−0.106649	−	0.184721i
$873$		0			0
$874$	−4.89387e9			−0.247949
$875$	1.42157e9	+	2.06405e9i	0.0717363	+	0.104158i
$876$		0			0
$877$	1.58323e10	−	2.74224e10i	0.792587	−	1.37280i	−0.131774	−	0.991280i	$-0.542067\pi$
$877$	1.58323e10	−	2.74224e10i	0.792587	−	1.37280i	0.924360	−	0.381520i	$-0.124599\pi$
$878$	−4.95245e9	−	8.57789e9i	−0.246939	−	0.427710i
$879$		0			0
$880$	5.35501e9	−	9.27514e9i	0.264893	−	0.458808i
$881$	1.90621e10			0.939192			0.469596	−	0.882881i	$-0.344400\pi$
$881$	1.90621e10			0.939192			0.469596	+	0.882881i	$0.344400\pi$
$882$		0			0
$883$	−2.91186e10			−1.42334			−0.711670	−	0.702514i	$-0.752061\pi$
$883$	−2.91186e10			−1.42334			−0.711670	+	0.702514i	$0.752061\pi$
$884$	7.54605e9	−	1.30701e10i	0.367398	−	0.636352i
$885$		0			0
$886$	1.35006e10	+	2.33838e10i	0.652134	+	1.12953i
$887$	8.54207e8	−	1.47953e9i	0.0410989	−	0.0711854i	−0.844744	−	0.535170i	$-0.820247\pi$
$887$	8.54207e8	−	1.47953e9i	0.0410989	−	0.0711854i	0.885843	+	0.463985i	$0.153581\pi$
$888$		0			0
$889$	2.00053e10	+	2.90468e10i	0.954967	+	1.38657i
$890$	−5.79579e9			−0.275580
$891$		0			0
$892$	8.98641e9	+	1.55649e10i	0.423945	+	0.734294i
$893$	4.84336e9	+	8.38895e9i	0.227597	+	0.394210i
$894$		0			0
$895$	−1.71146e10			−0.797967
$896$	−1.89714e9	+	1.51179e8i	−0.0881090	+	0.00702125i
$897$		0			0
$898$	8.50379e9	−	1.47290e10i	0.391873	−	0.678744i
$899$	1.09219e10	+	1.89172e10i	0.501346	+	0.868356i
$900$		0			0
$901$	1.11929e10	−	1.93867e10i	0.509809	−	0.883015i
$902$	−1.20832e10			−0.548226
$903$		0			0
$904$	8.08610e9			0.364041
$905$	1.03257e10	−	1.78846e10i	0.463073	−	0.802066i
$906$		0			0
$907$	2.36944e9	+	4.10399e9i	0.105444	+	0.182634i	0.913919	−	0.405896i	$-0.133040\pi$
$907$	2.36944e9	+	4.10399e9i	0.105444	+	0.182634i	−0.808476	+	0.588529i	$0.799707\pi$
$908$	5.24685e9	−	9.08782e9i	0.232594	−	0.402865i
$909$		0			0
$910$	1.46257e10	−	3.07409e10i	0.643385	−	1.35230i
$911$	2.73789e10			1.19978			0.599891	−	0.800082i	$-0.295211\pi$
$911$	2.73789e10			1.19978			0.599891	+	0.800082i	$0.295211\pi$
$912$		0			0
$913$	1.67384e10	+	2.89918e10i	0.727892	+	1.26075i
$914$	8.02690e9	+	1.39030e10i	0.347725	+	0.602278i
$915$		0			0
$916$	−1.72413e9			−0.0741200
$917$	−2.73304e9	+	2.17791e8i	−0.117045	+	0.00932711i
$918$		0			0
$919$	−4.85860e8	+	8.41534e8i	−0.0206494	+	0.0357657i	−0.876165	−	0.482011i	$-0.839907\pi$
$919$	−4.85860e8	+	8.41534e8i	−0.0206494	+	0.0357657i	0.855516	+	0.517776i	$0.173240\pi$
$920$	−1.36020e9	−	2.35593e9i	−0.0575896	−	0.0997481i
$921$		0			0
$922$	7.72060e9	−	1.33725e10i	0.324409	−	0.561893i
$923$	−1.80272e10			−0.754608
$924$		0			0
$925$	3.35038e10			1.39187
$926$	8.32117e9	−	1.44127e10i	0.344386	−	0.596495i
$927$		0			0
$928$	−1.42997e9	−	2.47677e9i	−0.0587364	−	0.101734i
$929$	2.24929e9	−	3.89588e9i	0.0920429	−	0.159423i	−0.816328	−	0.577589i	$-0.803994\pi$
$929$	2.24929e9	−	3.89588e9i	0.0920429	−	0.159423i	0.908371	+	0.418166i	$0.137327\pi$
$930$		0			0
$931$	2.41557e10	+	2.97106e10i	0.981062	+	1.20667i
$932$	4.31477e9			0.174583
$933$		0			0
$934$	−1.29919e10	−	2.25027e10i	−0.521746	−	0.903691i
$935$	−2.65515e10	−	4.59886e10i	−1.06230	−	1.83996i
$936$		0			0
$937$	−2.77390e10			−1.10155			−0.550773	−	0.834655i	$-0.685667\pi$
$937$	−2.77390e10			−1.10155			−0.550773	+	0.834655i	$0.685667\pi$
$938$	3.17228e8	+	4.60601e8i	0.0125505	+	0.0182228i
$939$		0			0
$940$	−2.69231e9	+	4.66323e9i	−0.105725	+	0.183121i
$941$	1.93638e10	+	3.35392e10i	0.757579	+	1.31216i	0.944082	+	0.329711i	$0.106951\pi$
$941$	1.93638e10	+	3.35392e10i	0.757579	+	1.31216i	−0.186503	+	0.982454i	$0.559716\pi$
$942$		0			0
$943$	−1.53460e9	+	2.65800e9i	−0.0595941	+	0.103220i
$944$	8.74237e9			0.338242
$945$		0			0
$946$	−3.09070e10			−1.18697
$947$	2.04015e10	−	3.53364e10i	0.780615	−	1.35207i	−0.150969	−	0.988539i	$-0.548239\pi$
$947$	2.04015e10	−	3.53364e10i	0.780615	−	1.35207i	0.931584	−	0.363527i	$-0.118427\pi$
$948$		0			0
$949$	−2.70782e10	−	4.69008e10i	−1.02846	−	1.78135i
$950$	1.58018e10	−	2.73695e10i	0.597961	−	1.03570i
$951$		0			0
$952$	−4.05409e9	+	8.52106e9i	−0.152287	+	0.320084i
$953$	−3.64067e10			−1.36256			−0.681280	−	0.732023i	$-0.738577\pi$
$953$	−3.64067e10			−1.36256			−0.681280	+	0.732023i	$0.738577\pi$
$954$		0			0
$955$	2.93245e10	+	5.07915e10i	1.08948	+	1.88703i
$956$	1.24150e10	+	2.15034e10i	0.459561	+	0.795983i
$957$		0			0
$958$	−2.05928e9			−0.0756722
$959$	−2.58012e9	+	5.42302e9i	−0.0944660	+	0.198553i
$960$		0			0
$961$	−1.75630e10	+	3.04199e10i	−0.638360	+	1.10567i
$962$	−1.83148e10	−	3.17222e10i	−0.663269	−	1.14881i
$963$		0			0
$964$	−7.40113e9	+	1.28191e10i	−0.266090	+	0.460881i
$965$	−1.24255e10			−0.445112
$966$		0			0
$967$	1.98247e10			0.705039			0.352519	−	0.935804i	$-0.385325\pi$
$967$	1.98247e10			0.705039			0.352519	+	0.935804i	$0.385325\pi$
$968$	−5.74318e9	+	9.94748e9i	−0.203511	+	0.352492i
$969$		0			0
$970$	−3.78700e9	−	6.55927e9i	−0.133228	−	0.230757i
$971$	8.85983e9	−	1.53457e10i	0.310569	−	0.537921i	−0.667917	−	0.744236i	$-0.732814\pi$
$971$	8.85983e9	−	1.53457e10i	0.310569	−	0.537921i	0.978486	+	0.206315i	$0.0661471\pi$
$972$		0			0
$973$	1.38546e9	+	2.01163e9i	0.0482169	+	0.0700088i
$974$	2.51471e10			0.872031
$975$		0			0
$976$	−5.43672e9	−	9.41667e9i	−0.187181	−	0.324208i
$977$	1.05326e10	+	1.82429e10i	0.361329	+	0.625841i	0.988180	−	0.153299i	$-0.0489897\pi$
$977$	1.05326e10	+	1.82429e10i	0.361329	+	0.625841i	−0.626851	+	0.779139i	$0.715656\pi$
$978$		0			0
$979$	1.16153e10			0.395630
$980$	−7.58896e9	+	1.98864e10i	−0.257567	+	0.674939i
$981$		0			0
$982$	−8.70364e9	+	1.50752e10i	−0.293299	+	0.508009i
$983$	−1.25543e9	−	2.17447e9i	−0.0421556	−	0.0730156i	0.844178	−	0.536063i	$-0.180089\pi$
$983$	−1.25543e9	−	2.17447e9i	−0.0421556	−	0.0730156i	−0.886333	+	0.463048i	$0.846756\pi$
$984$		0			0
$985$	1.28470e10	−	2.22516e10i	0.428326	−	0.741882i
$986$	−1.41803e10			−0.471103
$987$		0			0
$988$	−3.45520e10			−1.13979
$989$	−3.92526e9	+	6.79876e9i	−0.129027	+	0.223482i
$990$		0			0
$991$	−1.98537e10	−	3.43876e10i	−0.648013	−	1.12239i	−0.983597	−	0.180381i	$-0.942267\pi$
$991$	−1.98537e10	−	3.43876e10i	−0.648013	−	1.12239i	0.335584	−	0.942010i	$-0.391066\pi$
$992$	4.10054e9	−	7.10234e9i	0.133367	−	0.230999i
$993$		0			0
$994$	1.12358e10	−	8.95364e8i	0.362872	−	0.0289166i
$995$	1.27403e10			0.410013
$996$		0			0
$997$	1.61458e9	+	2.79654e9i	0.0515973	+	0.0893692i	0.890670	−	0.454649i	$-0.150235\pi$
$997$	1.61458e9	+	2.79654e9i	0.0515973	+	0.0893692i	−0.839073	+	0.544019i	$0.816902\pi$
$998$	1.33528e10	+	2.31277e10i	0.425221	+	0.736504i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.8.g.h.37.1		6
3.2	odd	2		42.8.e.e.37.3	yes	6
7.4	even	3	inner	126.8.g.h.109.1		6
21.2	odd	6		294.8.a.v.1.1		3
21.5	even	6		294.8.a.w.1.3		3
21.11	odd	6		42.8.e.e.25.3	✓	6
21.17	even	6		294.8.e.ba.67.1		6
21.20	even	2		294.8.e.ba.79.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.8.e.e.25.3	✓	6	21.11	odd	6
42.8.e.e.37.3	yes	6	3.2	odd	2
126.8.g.h.37.1		6	1.1	even	1	trivial
126.8.g.h.109.1		6	7.4	even	3	inner
294.8.a.v.1.1		3	21.2	odd	6
294.8.a.w.1.3		3	21.5	even	6
294.8.e.ba.67.1		6	21.17	even	6
294.8.e.ba.79.1		6	21.20	even	2

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 + 6.92820i) q^{2} +(-32.0000 - 55.4256i) q^{4} +(-201.921 + 349.738i) q^{5} +(514.742 + 747.384i) q^{7} +512.000 q^{8} +(-1615.37 - 2797.90i) q^{10} +(3237.34 + 5607.24i) q^{11} +11611.3 q^{13} +(-7237.00 + 576.704i) q^{14} +(-2048.00 + 3547.24i) q^{16} +(10154.5 + 17588.1i) q^{17} +(23247.9 - 40266.5i) q^{19} +25845.9 q^{20} -51797.4 q^{22} +(-6578.39 + 11394.1i) q^{23} +(-42481.8 - 73580.6i) q^{25} +(-46445.2 + 80445.4i) q^{26} +(24952.5 - 52446.2i) q^{28} +87278.1 q^{29} +(125138. + 216746. i) q^{31} +(-16384.0 - 28377.9i) q^{32} -162472. q^{34} +(-365326. + 29112.2i) q^{35} +(-197166. + 341501. i) q^{37} +(185983. + 322132. i) q^{38} +(-103384. + 179066. i) q^{40} +233278. q^{41} +596690. q^{43} +(207190. - 358863. i) q^{44} +(-52627.1 - 91152.9i) q^{46} +(-104168. + 180424. i) q^{47} +(-293623. + 769421. i) q^{49} +679709. q^{50} +(-371561. - 643563. i) q^{52} +(-551131. - 954586. i) q^{53} -2.61475e6 q^{55} +(263548. + 382661. i) q^{56} +(-349113. + 604681. i) q^{58} +(-1.06718e6 - 1.84842e6i) q^{59} +(-1.32732e6 + 2.29899e6i) q^{61} -2.00222e6 q^{62} +262144. q^{64} +(-2.34456e6 + 4.06091e6i) q^{65} +(-38517.8 - 66714.7i) q^{67} +(649889. - 1.12564e6i) q^{68} +(1.25961e6 - 2.64750e6i) q^{70} -1.55255e6 q^{71} +(-2.33206e6 - 4.03924e6i) q^{73} +(-1.57733e6 - 2.73201e6i) q^{74} -2.97573e6 q^{76} +(-2.52436e6 + 5.30582e6i) q^{77} +(1.16745e6 - 2.02209e6i) q^{79} +(-827069. - 1.43253e6i) q^{80} +(-933113. + 1.61620e6i) q^{82} +5.17043e6 q^{83} -8.20165e6 q^{85} +(-2.38676e6 + 4.13399e6i) q^{86} +(1.65752e6 + 2.87090e6i) q^{88} +(896976. - 1.55361e6i) q^{89} +(5.97682e6 + 8.67810e6i) q^{91} +842034. q^{92} +(-833343. - 1.44339e6i) q^{94} +(9.38847e6 + 1.62613e7i) q^{95} +2.34436e6 q^{97} +(-4.15621e6 - 5.11197e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 24 q^{2} - 192 q^{4} - 110 q^{5} + 635 q^{7} + 3072 q^{8} - 880 q^{10} + 548 q^{11} + 19898 q^{13} - 4568 q^{14} - 12288 q^{16} + 20972 q^{17} + 28383 q^{19} + 14080 q^{20} - 8768 q^{22} + 32732 q^{23}+ \cdots - 6110208 q^{98}+O(q^{100}) \) 6 * q - 24 * q^2 - 192 * q^4 - 110 * q^5 + 635 * q^7 + 3072 * q^8 - 880 * q^10 + 548 * q^11 + 19898 * q^13 - 4568 * q^14 - 12288 * q^16 + 20972 * q^17 + 28383 * q^19 + 14080 * q^20 - 8768 * q^22 + 32732 * q^23 + 22745 * q^25 - 79592 * q^26 - 4096 * q^28 - 234176 * q^29 - 147865 * q^31 - 98304 * q^32 - 335552 * q^34 - 876430 * q^35 - 367503 * q^37 + 227064 * q^38 - 56320 * q^40 + 2875908 * q^41 + 1498794 * q^43 + 35072 * q^44 + 261856 * q^46 - 741486 * q^47 + 1421697 * q^49 - 363920 * q^50 - 636736 * q^52 - 1032432 * q^53 - 7992560 * q^55 + 325120 * q^56 + 936704 * q^58 - 2389238 * q^59 - 1238746 * q^61 + 2365840 * q^62 + 1572864 * q^64 - 3798390 * q^65 + 2462497 * q^67 + 1342208 * q^68 + 4561840 * q^70 + 1272524 * q^71 - 4609961 * q^73 - 2940024 * q^74 - 3633024 * q^76 - 20044196 * q^77 + 6152849 * q^79 - 450560 * q^80 - 11503632 * q^82 + 24059768 * q^83 - 18273080 * q^85 - 5995176 * q^86 + 280576 * q^88 + 10646976 * q^89 + 47686115 * q^91 - 4189696 * q^92 - 5931888 * q^94 + 21560930 * q^95 + 4562944 * q^97 - 6110208 * q^98

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