LMFDB - Embedded newform 126.8.g.h.109.3

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			109.3
Root			$16.9812 + 29.4123i$ of defining polynomial
Character	$\chi$	$=$	126.109
Dual form			126.8.g.h.37.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.00000 - 6.92820i) q^{2} +(-32.0000 + 55.4256i) q^{4} +(99.3686 + 172.111i) q^{5} +(709.564 + 565.740i) q^{7} +512.000 q^{8} +(794.949 - 1376.89i) q^{10} +(-3946.05 + 6834.75i) q^{11} +10120.7 q^{13} +(1081.31 - 7178.96i) q^{14} +(-2048.00 - 3547.24i) q^{16} +(-4814.83 + 8339.53i) q^{17} +(-5120.94 - 8869.73i) q^{19} -12719.2 q^{20} +63136.8 q^{22} +(-23197.0 - 40178.4i) q^{23} +(19314.3 - 33453.3i) q^{25} +(-40482.9 - 70118.5i) q^{26} +(-54062.6 + 21224.3i) q^{28} -208906. q^{29} +(-118652. + 205512. i) q^{31} +(-16384.0 + 28377.9i) q^{32} +77037.3 q^{34} +(-26862.0 + 178341. i) q^{35} +(-162011. - 280611. i) q^{37} +(-40967.5 + 70957.9i) q^{38} +(50876.7 + 88121.0i) q^{40} +758284. q^{41} -558520. q^{43} +(-252547. - 437424. i) q^{44} +(-185576. + 321427. i) q^{46} +(134708. + 233321. i) q^{47} +(183419. + 802858. i) q^{49} -309028. q^{50} +(-323864. + 560948. i) q^{52} +(66909.5 - 115891. i) q^{53} -1.56845e6 q^{55} +(363297. + 289659. i) q^{56} +(835623. + 1.44734e6i) q^{58} +(-815863. + 1.41312e6i) q^{59} +(887949. + 1.53797e6i) q^{61} +1.89844e6 q^{62} +262144. q^{64} +(1.00568e6 + 1.74189e6i) q^{65} +(376991. - 652968. i) q^{67} +(-308149. - 533730. i) q^{68} +(1.34303e6 - 527258. i) q^{70} -1.44473e6 q^{71} +(-1.65487e6 + 2.86632e6i) q^{73} +(-1.29609e6 + 2.24489e6i) q^{74} +655481. q^{76} +(-6.66667e6 + 2.61726e6i) q^{77} +(3.31651e6 + 5.74437e6i) q^{79} +(407014. - 704968. i) q^{80} +(-3.03314e6 - 5.25354e6i) q^{82} -2.35482e6 q^{83} -1.91377e6 q^{85} +(2.23408e6 + 3.86954e6i) q^{86} +(-2.02038e6 + 3.49939e6i) q^{88} +(1.94917e6 + 3.37607e6i) q^{89} +(7.18131e6 + 5.72571e6i) q^{91} +2.96922e6 q^{92} +(1.07766e6 - 1.86657e6i) q^{94} +(1.01772e6 - 1.76275e6i) q^{95} -7.98505e6 q^{97} +(4.82869e6 - 4.48220e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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
$5$	99.3686	+	172.111i	0.355512	+	0.615764i	0.987205	−	0.159454i	$-0.0509733\pi$
$5$	99.3686	+	172.111i	0.355512	+	0.615764i	−0.631694	+	0.775218i	$0.717640\pi$
$6$		0			0
$7$	709.564	+	565.740i	0.781895	+	0.623410i
$7$	709.564	+	565.740i	0.781895	+	0.623410i
$8$	512.000			0.353553
$9$		0			0
$10$	794.949	−	1376.89i	0.251385	−	0.435411i
$11$	−3946.05	+	6834.75i	−0.893898	+	1.54828i	−0.0587350	+	0.998274i	$0.518707\pi$
$11$	−3946.05	+	6834.75i	−0.893898	+	1.54828i	−0.835163	+	0.550003i	$0.814627\pi$
$12$		0			0
$13$	10120.7			1.27765			0.638823	−	0.769354i	$-0.279422\pi$
$13$	10120.7			1.27765			0.638823	+	0.769354i	$0.279422\pi$
$14$	1081.31	−	7178.96i	0.105318	−	0.699220i
$15$		0			0
$16$	−2048.00	−	3547.24i	−0.125000	−	0.216506i
$17$	−4814.83	+	8339.53i	−0.237689	+	0.411690i	−0.960051	−	0.279826i	$-0.909723\pi$
$17$	−4814.83	+	8339.53i	−0.237689	+	0.411690i	0.722361	+	0.691516i	$0.243057\pi$
$18$		0			0
$19$	−5120.94	−	8869.73i	−0.171282	−	0.296670i	0.767586	−	0.640946i	$-0.221458\pi$
$19$	−5120.94	−	8869.73i	−0.171282	−	0.296670i	−0.938868	+	0.344276i	$0.888124\pi$
$20$	−12719.2			−0.355512
$21$		0			0
$22$	63136.8			1.26416
$23$	−23197.0	−	40178.4i	−0.397543	−	0.688565i	0.595879	−	0.803074i	$-0.296804\pi$
$23$	−23197.0	−	40178.4i	−0.397543	−	0.688565i	−0.993422	+	0.114509i	$0.963471\pi$
$24$		0			0
$25$	19314.3	−	33453.3i	0.247223	−	0.428202i
$26$	−40482.9	−	70118.5i	−0.451716	−	0.782395i
$27$		0			0
$28$	−54062.6	+	21224.3i	−0.465418	+	0.182718i
$29$	−208906.			−1.59059			−0.795293	−	0.606225i	$-0.792683\pi$
$29$	−208906.			−1.59059			−0.795293	+	0.606225i	$0.792683\pi$
$30$		0			0
$31$	−118652.	+	205512.i	−0.715337	+	1.23900i	0.247492	+	0.968890i	$0.420394\pi$
$31$	−118652.	+	205512.i	−0.715337	+	1.23900i	−0.962829	+	0.270111i	$0.912940\pi$
$32$	−16384.0	+	28377.9i	−0.0883883	+	0.153093i
$33$		0			0
$34$	77037.3			0.336144
$35$	−26862.0	+	178341.i	−0.105901	+	0.703093i
$36$		0			0
$37$	−162011.	−	280611.i	−0.525821	−	0.910748i	−0.999548	−	0.0300762i	$-0.990425\pi$
$37$	−162011.	−	280611.i	−0.525821	−	0.910748i	0.473727	−	0.880672i	$-0.342908\pi$
$38$	−40967.5	+	70957.9i	−0.121115	+	0.209777i
$39$		0			0
$40$	50876.7	+	88121.0i	0.125692	+	0.217706i
$41$	758284.			1.71826			0.859129	−	0.511759i	$-0.171006\pi$
$41$	758284.			1.71826			0.859129	+	0.511759i	$0.171006\pi$
$42$		0			0
$43$	−558520.			−1.07127			−0.535635	−	0.844450i	$-0.679928\pi$
$43$	−558520.			−1.07127			−0.535635	+	0.844450i	$0.679928\pi$
$44$	−252547.	−	437424.i	−0.446949	−	0.774138i
$45$		0			0
$46$	−185576.	+	321427.i	−0.281106	+	0.486889i
$47$	134708.	+	233321.i	0.189257	+	0.327802i	0.945003	−	0.327063i	$-0.106059\pi$
$47$	134708.	+	233321.i	0.189257	+	0.327802i	−0.755746	+	0.654865i	$0.772726\pi$
$48$		0			0
$49$	183419.	+	802858.i	0.222719	+	0.974883i
$50$	−309028.			−0.349626
$51$		0			0
$52$	−323864.	+	560948.i	−0.319411	+	0.553237i
$53$	66909.5	−	115891.i	0.0617337	−	0.106926i	−0.833507	−	0.552509i	$-0.813670\pi$
$53$	66909.5	−	115891.i	0.0617337	−	0.106926i	0.895240	+	0.445583i	$0.147004\pi$
$54$		0			0
$55$	−1.56845e6			−1.27116
$56$	363297.	+	289659.i	0.276442	+	0.220409i
$57$		0			0
$58$	835623.	+	1.44734e6i	0.562357	+	0.974032i
$59$	−815863.	+	1.41312e6i	−0.517172	+	0.895769i	0.482629	+	0.875825i	$0.339682\pi$
$59$	−815863.	+	1.41312e6i	−0.517172	+	0.895769i	−0.999801	+	0.0199439i	$0.993651\pi$
$60$		0			0
$61$	887949.	+	1.53797e6i	0.500880	+	0.867550i	0.999999	+	0.00101648i	$0.000323556\pi$
$61$	887949.	+	1.53797e6i	0.500880	+	0.867550i	−0.499119	+	0.866533i	$0.666343\pi$
$62$	1.89844e6			1.01164
$63$		0			0
$64$	262144.			0.125000
$65$	1.00568e6	+	1.74189e6i	0.454218	+	0.786729i
$66$		0			0
$67$	376991.	−	652968.i	0.153133	−	0.265235i	−0.779244	−	0.626720i	$-0.784397\pi$
$67$	376991.	−	652968.i	0.153133	−	0.265235i	0.932378	+	0.361485i	$0.117730\pi$
$68$	−308149.	−	533730.i	−0.118845	−	0.205845i
$69$		0			0
$70$	1.34303e6	−	527258.i	0.467996	−	0.183730i
$71$	−1.44473e6			−0.479053			−0.239526	−	0.970890i	$-0.576992\pi$
$71$	−1.44473e6			−0.479053			−0.239526	+	0.970890i	$0.576992\pi$
$72$		0			0
$73$	−1.65487e6	+	2.86632e6i	−0.497891	+	0.862373i	−0.999997	−	0.00243304i	$-0.999226\pi$
$73$	−1.65487e6	+	2.86632e6i	−0.497891	+	0.862373i	0.502106	+	0.864806i	$0.332559\pi$
$74$	−1.29609e6	+	2.24489e6i	−0.371811	+	0.643996i
$75$		0			0
$76$	655481.			0.171282
$77$	−6.66667e6	+	2.61726e6i	−1.66415	+	0.653324i
$78$		0			0
$79$	3.31651e6	+	5.74437e6i	0.756810	+	1.31083i	0.944469	+	0.328600i	$0.106577\pi$
$79$	3.31651e6	+	5.74437e6i	0.756810	+	1.31083i	−0.187659	+	0.982234i	$0.560090\pi$
$80$	407014.	−	704968.i	0.0888779	−	0.153941i
$81$		0			0
$82$	−3.03314e6	−	5.25354e6i	−0.607496	−	1.05221i
$83$	−2.35482e6			−0.452048			−0.226024	−	0.974122i	$-0.572573\pi$
$83$	−2.35482e6			−0.452048			−0.226024	+	0.974122i	$0.572573\pi$
$84$		0			0
$85$	−1.91377e6			−0.338006
$86$	2.23408e6	+	3.86954e6i	0.378751	+	0.656016i
$87$		0			0
$88$	−2.02038e6	+	3.49939e6i	−0.316041	+	0.547398i
$89$	1.94917e6	+	3.37607e6i	0.293079	+	0.507629i	0.974536	−	0.224230i	$-0.0719866\pi$
$89$	1.94917e6	+	3.37607e6i	0.293079	+	0.507629i	−0.681457	+	0.731858i	$0.738653\pi$
$90$		0			0
$91$	7.18131e6	+	5.72571e6i	0.998984	+	0.796497i
$92$	2.96922e6			0.397543
$93$		0			0
$94$	1.07766e6	−	1.86657e6i	0.133825	−	0.231791i
$95$	1.01772e6	−	1.76275e6i	0.121786	−	0.210939i
$96$		0			0
$97$	−7.98505e6			−0.888335			−0.444167	−	0.895944i	$-0.646500\pi$
$97$	−7.98505e6			−0.888335			−0.444167	+	0.895944i	$0.646500\pi$
$98$	4.82869e6	−	4.48220e6i	0.518248	−	0.481060i
$99$		0			0
$100$	1.23611e6	+	2.14101e6i	0.123611	+	0.214101i
$101$	4.86706e6	−	8.42999e6i	0.470047	−	0.814146i	−0.529366	−	0.848394i	$-0.677570\pi$
$101$	4.86706e6	−	8.42999e6i	0.470047	−	0.814146i	0.999413	+	0.0342476i	$0.0109035\pi$
$102$		0			0
$103$	−5.06333e6	−	8.76994e6i	−0.456568	−	0.790799i	0.542209	−	0.840244i	$-0.317588\pi$
$103$	−5.06333e6	−	8.76994e6i	−0.456568	−	0.790799i	−0.998777	+	0.0494445i	$0.984255\pi$
$104$	5.18182e6			0.451716
$105$		0			0
$106$	−1.07055e6			−0.0873047
$107$	−5.69879e6	−	9.87059e6i	−0.449717	−	0.778933i	0.548650	−	0.836052i	$-0.315142\pi$
$107$	−5.69879e6	−	9.87059e6i	−0.449717	−	0.778933i	−0.998367	+	0.0571192i	$0.981808\pi$
$108$		0			0
$109$	−9.70714e6	+	1.68133e7i	−0.717957	+	1.24354i	0.243851	+	0.969813i	$0.421589\pi$
$109$	−9.70714e6	+	1.68133e7i	−0.717957	+	1.24354i	−0.961808	+	0.273725i	$0.911744\pi$
$110$	6.27381e6	+	1.08666e7i	0.449425	+	0.778426i
$111$		0			0
$112$	553629.	−	3.67563e6i	0.0372354	−	0.247211i
$113$	−2.80072e7			−1.82598			−0.912988	−	0.407987i	$-0.866231\pi$
$113$	−2.80072e7			−1.82598			−0.912988	+	0.407987i	$0.866231\pi$
$114$		0			0
$115$	4.61011e6	−	7.98494e6i	0.282663	−	0.489586i
$116$	6.68498e6	−	1.15787e7i	0.397647	−	0.688744i
$117$		0			0
$118$	1.30538e7			0.731392
$119$	−8.13444e6	+	3.19349e6i	−0.442500	+	0.173720i
$120$		0			0
$121$	−2.13990e7	−	3.70641e7i	−1.09811	−	1.90198i
$122$	7.10359e6	−	1.23038e7i	0.354176	−	0.613450i
$123$		0			0
$124$	−7.59376e6	−	1.31528e7i	−0.357669	−	0.619500i
$125$	2.32033e7			1.06259
$126$		0			0
$127$	1.55135e7			0.672043			0.336021	−	0.941854i	$-0.390919\pi$
$127$	1.55135e7			0.672043			0.336021	+	0.941854i	$0.390919\pi$
$128$	−1.04858e6	−	1.81619e6i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	8.04546e6	−	1.39352e7i	0.321181	−	0.556301i
$131$	−9.19771e6	−	1.59309e7i	−0.357462	−	0.619143i	0.630074	−	0.776535i	$-0.283025\pi$
$131$	−9.19771e6	−	1.59309e7i	−0.357462	−	0.619143i	−0.987536	+	0.157392i	$0.949691\pi$
$132$		0			0
$133$	1.38433e6	−	9.19077e6i	0.0510221	−	0.338744i
$134$	−6.03186e6			−0.216563
$135$		0			0
$136$	−2.46519e6	+	4.26984e6i	−0.0840359	+	0.145554i
$137$	1.65808e7	−	2.87189e7i	0.550915	−	0.954213i	−0.447294	−	0.894387i	$-0.647612\pi$
$137$	1.65808e7	−	2.87189e7i	0.550915	−	0.954213i	0.998209	−	0.0598256i	$-0.0190544\pi$
$138$		0			0
$139$	3.41540e7			1.07867			0.539337	−	0.842090i	$-0.318675\pi$
$139$	3.41540e7			1.07867			0.539337	+	0.842090i	$0.318675\pi$
$140$	−9.02507e6	−	7.19575e6i	−0.277973	−	0.221630i
$141$		0			0
$142$	5.77893e6	+	1.00094e7i	0.169371	+	0.293359i
$143$	−3.99369e7	+	6.91727e7i	−1.14208	+	1.97815i
$144$		0			0
$145$	−2.07587e7	−	3.59551e7i	−0.565472	−	0.979427i
$146$	2.64780e7			0.704125
$147$		0			0
$148$	2.07374e7			0.525821
$149$	1.03906e7	+	1.79971e7i	0.257329	+	0.445707i	0.965526	−	0.260308i	$-0.0838242\pi$
$149$	1.03906e7	+	1.79971e7i	0.257329	+	0.445707i	−0.708196	+	0.706015i	$0.750491\pi$
$150$		0			0
$151$	−1.63037e7	+	2.82389e7i	−0.385361	+	0.667465i	−0.991819	−	0.127651i	$-0.959256\pi$
$151$	−1.63037e7	+	2.82389e7i	−0.385361	+	0.667465i	0.606458	+	0.795115i	$0.292590\pi$
$152$	−2.62192e6	−	4.54130e6i	−0.0605574	−	0.104889i
$153$		0			0
$154$	4.47996e7	+	3.57190e7i	0.988442	+	0.788092i
$155$	−4.71613e7			−1.01724
$156$		0			0
$157$	1.37310e7	−	2.37828e7i	0.283174	−	0.490471i	−0.688991	−	0.724770i	$-0.741946\pi$
$157$	1.37310e7	−	2.37828e7i	0.283174	−	0.490471i	0.972165	+	0.234299i	$0.0752793\pi$
$158$	2.65321e7	−	4.59550e7i	0.535146	−	0.926899i
$159$		0			0
$160$	−6.51222e6			−0.125692
$161$	6.27077e6	−	4.16326e7i	0.118421	−	0.786218i
$162$		0			0
$163$	−2.62267e7	−	4.54260e7i	−0.474337	−	0.821576i	0.525231	−	0.850959i	$-0.323979\pi$
$163$	−2.62267e7	−	4.54260e7i	−0.474337	−	0.821576i	−0.999568	+	0.0293839i	$0.990645\pi$
$164$	−2.42651e7	+	4.20284e7i	−0.429564	+	0.744027i
$165$		0			0
$166$	9.41929e6	+	1.63147e7i	0.159823	+	0.276822i
$167$	3.91024e7			0.649674			0.324837	−	0.945770i	$-0.394691\pi$
$167$	3.91024e7			0.649674			0.324837	+	0.945770i	$0.394691\pi$
$168$		0			0
$169$	3.96808e7			0.632378
$170$	7.65509e6	+	1.32590e7i	0.119503	+	0.206985i
$171$		0			0
$172$	1.78726e7	−	3.09563e7i	0.267817	−	0.463873i
$173$	1.12616e7	+	1.95057e7i	0.165363	+	0.286418i	0.936784	−	0.349907i	$-0.113787\pi$
$173$	1.12616e7	+	1.95057e7i	0.165363	+	0.286418i	−0.771421	+	0.636325i	$0.780454\pi$
$174$		0			0
$175$	3.26306e7	−	1.28104e7i	0.460248	−	0.180688i
$176$	3.23260e7			0.446949
$177$		0			0
$178$	1.55934e7	−	2.70085e7i	0.207238	−	0.358948i
$179$	−2.19056e7	+	3.79417e7i	−0.285476	+	0.494460i	−0.972725	−	0.231963i	$-0.925485\pi$
$179$	−2.19056e7	+	3.79417e7i	−0.285476	+	0.494460i	0.687248	+	0.726423i	$0.258819\pi$
$180$		0			0
$181$	−4.23221e7			−0.530508			−0.265254	−	0.964179i	$-0.585456\pi$
$181$	−4.23221e7			−0.530508			−0.265254	+	0.964179i	$0.585456\pi$
$182$	1.09436e7	−	7.26564e7i	0.134559	−	0.893355i
$183$		0			0
$184$	−1.18769e7	−	2.05713e7i	−0.140553	−	0.243445i
$185$	3.21975e7	−	5.57678e7i	0.373871	−	0.647563i
$186$		0			0
$187$	−3.79991e7	−	6.58164e7i	−0.424940	−	0.736018i
$188$	−1.72426e7			−0.189257
$189$		0			0
$190$	−1.62835e7			−0.172231
$191$	6.76367e7	+	1.17150e8i	0.702369	+	1.21654i	0.967633	+	0.252363i	$0.0812077\pi$
$191$	6.76367e7	+	1.17150e8i	0.702369	+	1.21654i	−0.265264	+	0.964176i	$0.585459\pi$
$192$		0			0
$193$	−8.46054e7	+	1.46541e8i	−0.847125	+	1.46726i	0.0366379	+	0.999329i	$0.488335\pi$
$193$	−8.46054e7	+	1.46541e8i	−0.847125	+	1.46726i	−0.883763	+	0.467935i	$0.844998\pi$
$194$	3.19402e7	+	5.53221e7i	0.314074	+	0.543992i
$195$		0			0
$196$	−5.03683e7	−	1.55253e7i	−0.477816	−	0.147280i
$197$	1.25987e7			0.117407			0.0587037	−	0.998275i	$-0.481303\pi$
$197$	1.25987e7			0.117407			0.0587037	+	0.998275i	$0.481303\pi$
$198$		0			0
$199$	−7.56030e7	+	1.30948e8i	−0.680069	+	1.17791i	0.294890	+	0.955531i	$0.404717\pi$
$199$	−7.56030e7	+	1.30948e8i	−0.680069	+	1.17791i	−0.974959	+	0.222383i	$0.928616\pi$
$200$	9.88891e6	−	1.71281e7i	0.0874064	−	0.151392i
$201$		0			0
$202$	−7.78729e7			−0.664747
$203$	−1.48232e8	−	1.18186e8i	−1.24367	−	0.991588i
$204$		0			0
$205$	7.53496e7	+	1.30509e8i	0.610861	+	1.05804i
$206$	−4.05066e7	+	7.01595e7i	−0.322843	+	0.559180i
$207$		0			0
$208$	−2.07273e7	−	3.59007e7i	−0.159706	−	0.276618i
$209$	8.08299e7			0.612435
$210$		0			0
$211$	1.55746e8			1.14137			0.570687	−	0.821168i	$-0.306677\pi$
$211$	1.55746e8			1.14137			0.570687	+	0.821168i	$0.306677\pi$
$212$	4.28221e6	+	7.41700e6i	0.0308669	+	0.0534630i
$213$		0			0
$214$	−4.55903e7	+	7.89647e7i	−0.317998	+	0.550789i
$215$	−5.54993e7	−	9.61276e7i	−0.380849	−	0.659650i
$216$		0			0
$217$	−2.00458e8	+	7.86975e7i	−1.33172	+	0.522820i
$218$	1.55314e8			1.01534
$219$		0			0
$220$	5.01905e7	−	8.69324e7i	0.317791	−	0.550431i
$221$	−4.87296e7	+	8.44022e7i	−0.303683	+	0.525994i
$222$		0			0
$223$	1.59012e8			0.960200			0.480100	−	0.877214i	$-0.340600\pi$
$223$	1.59012e8			0.960200			0.480100	+	0.877214i	$0.340600\pi$
$224$	−2.76800e7	+	1.08669e7i	−0.164550	+	0.0646005i
$225$		0			0
$226$	1.12029e8	+	1.94039e8i	0.645580	+	1.11818i
$227$	−1.95537e7	+	3.38680e7i	−0.110953	+	0.192176i	−0.916155	−	0.400825i	$-0.868724\pi$
$227$	−1.95537e7	+	3.38680e7i	−0.110953	+	0.192176i	0.805202	+	0.593001i	$0.202057\pi$
$228$		0			0
$229$	−5.31757e7	−	9.21030e7i	−0.292610	−	0.506815i	0.681816	−	0.731524i	$-0.261190\pi$
$229$	−5.31757e7	−	9.21030e7i	−0.292610	−	0.506815i	−0.974426	+	0.224708i	$0.927857\pi$
$230$	−7.37617e7			−0.399745
$231$		0			0
$232$	−1.06960e8			−0.562357
$233$	−4.09925e7	−	7.10011e7i	−0.212304	−	0.367722i	0.740131	−	0.672463i	$-0.234763\pi$
$233$	−4.09925e7	−	7.10011e7i	−0.212304	−	0.367722i	−0.952435	+	0.304741i	$0.901430\pi$
$234$		0			0
$235$	−2.67715e7	+	4.63696e7i	−0.134566	+	0.233075i
$236$	−5.22153e7	−	9.04395e7i	−0.258586	−	0.447885i
$237$		0			0
$238$	5.46629e7	+	4.35831e7i	0.262829	+	0.209555i
$239$	−2.35102e8			−1.11395			−0.556973	−	0.830531i	$-0.688037\pi$
$239$	−2.35102e8			−1.11395			−0.556973	+	0.830531i	$0.688037\pi$
$240$		0			0
$241$	−3.46303e7	+	5.99814e7i	−0.159366	+	0.276030i	−0.934640	−	0.355595i	$-0.884278\pi$
$241$	−3.46303e7	+	5.99814e7i	−0.159366	+	0.276030i	0.775274	+	0.631625i	$0.217612\pi$
$242$	−1.71192e8	+	2.96513e8i	−0.776479	+	1.34490i
$243$		0			0
$244$	−1.13658e8			−0.500880
$245$	−1.19955e8	+	1.11347e8i	−0.521119	+	0.483725i
$246$		0			0
$247$	−5.18277e7	−	8.97682e7i	−0.218838	−	0.379039i
$248$	−6.07501e7	+	1.05222e8i	−0.252910	+	0.438053i
$249$		0			0
$250$	−9.28131e7	−	1.60757e8i	−0.375681	−	0.650698i
$251$	1.52667e8			0.609379			0.304690	−	0.952452i	$-0.401447\pi$
$251$	1.52667e8			0.609379			0.304690	+	0.952452i	$0.401447\pi$
$252$		0			0
$253$	3.66146e8			1.42145
$254$	−6.20540e7	−	1.07481e8i	−0.237603	−	0.411540i
$255$		0			0
$256$	−8.38861e6	+	1.45295e7i	−0.0312500	+	0.0541266i
$257$	5.56435e7	+	9.63774e7i	0.204479	+	0.354168i	0.949967	−	0.312352i	$-0.101117\pi$
$257$	5.56435e7	+	9.63774e7i	0.204479	+	0.354168i	−0.745488	+	0.666519i	$0.767783\pi$
$258$		0			0
$259$	4.37958e7	−	2.90767e8i	0.156633	−	1.03991i
$260$	−1.28727e8			−0.454218
$261$		0			0
$262$	−7.35817e7	+	1.27447e8i	−0.252764	+	0.437800i
$263$	5.45137e7	−	9.44204e7i	0.184782	−	0.320052i	−0.758721	−	0.651416i	$-0.774175\pi$
$263$	5.45137e7	−	9.44204e7i	0.184782	−	0.320052i	0.943503	+	0.331364i	$0.107509\pi$
$264$		0			0
$265$	2.65948e7			0.0877883
$266$	−6.92128e7	+	2.71722e7i	−0.225476	+	0.0885194i
$267$		0			0
$268$	2.41275e7	+	4.17900e7i	0.0765667	+	0.132617i
$269$	2.10715e8	−	3.64970e8i	0.660030	−	1.14320i	−0.320578	−	0.947222i	$-0.603877\pi$
$269$	2.10715e8	−	3.64970e8i	0.660030	−	1.14320i	0.980607	−	0.195983i	$-0.0627896\pi$
$270$		0			0
$271$	2.52373e8	+	4.37123e8i	0.770283	+	1.33417i	0.937408	+	0.348233i	$0.113218\pi$
$271$	2.52373e8	+	4.37123e8i	0.770283	+	1.33417i	−0.167125	+	0.985936i	$0.553448\pi$
$272$	3.94431e7			0.118845
$273$		0			0
$274$	−2.65293e8			−0.779111
$275$	1.52430e8	+	2.64017e8i	0.441984	+	0.765538i
$276$		0			0
$277$	9.82407e7	−	1.70158e8i	0.277723	−	0.481031i	−0.693095	−	0.720846i	$-0.743754\pi$
$277$	9.82407e7	−	1.70158e8i	0.277723	−	0.481031i	0.970819	+	0.239815i	$0.0770868\pi$
$278$	−1.36616e8	−	2.36626e8i	−0.381369	−	0.660550i
$279$		0			0
$280$	−1.37533e7	+	9.13105e7i	−0.0374417	+	0.248581i
$281$	4.50497e8			1.21121			0.605605	−	0.795766i	$-0.292931\pi$
$281$	4.50497e8			1.21121			0.605605	+	0.795766i	$0.292931\pi$
$282$		0			0
$283$	−2.38684e8	+	4.13413e8i	−0.625995	+	1.08426i	0.362352	+	0.932041i	$0.381974\pi$
$283$	−2.38684e8	+	4.13413e8i	−0.625995	+	1.08426i	−0.988347	+	0.152215i	$0.951360\pi$
$284$	4.62314e7	−	8.00752e7i	0.119763	−	0.207436i
$285$		0			0
$286$	6.38990e8			1.61515
$287$	5.38051e8	+	4.28992e8i	1.34350	+	1.07118i
$288$		0			0
$289$	1.58804e8	+	2.75057e8i	0.387007	+	0.670317i
$290$	−1.66069e8	+	2.87640e8i	−0.399849	+	0.692559i
$291$		0			0
$292$	−1.05912e8	−	1.83445e8i	−0.248946	−	0.431187i
$293$	6.36994e8			1.47944			0.739722	−	0.672913i	$-0.234957\pi$
$293$	6.36994e8			1.47944			0.739722	+	0.672913i	$0.234957\pi$
$294$		0			0
$295$	−3.24285e8			−0.735444
$296$	−8.29495e7	−	1.43673e8i	−0.185906	−	0.321998i
$297$		0			0
$298$	8.31249e7	−	1.43976e8i	0.181959	−	0.315163i
$299$	−2.34771e8	−	4.06635e8i	−0.507919	−	0.879742i
$300$		0			0
$301$	−3.96305e8	−	3.15977e8i	−0.837620	−	0.667840i
$302$	2.60860e8			0.544982
$303$		0			0
$304$	−2.09754e7	+	3.63304e7i	−0.0428206	+	0.0741674i
$305$	−1.76468e8	+	3.05652e8i	−0.356138	+	0.616848i
$306$		0			0
$307$	−6.50187e8			−1.28249			−0.641245	−	0.767336i	$-0.721582\pi$
$307$	−6.50187e8			−1.28249			−0.641245	+	0.767336i	$0.721582\pi$
$308$	6.82702e7	−	4.53257e8i	0.133139	−	0.883927i
$309$		0			0
$310$	1.88645e8	+	3.26743e8i	0.359650	+	0.622932i
$311$	−3.75166e7	+	6.49807e7i	−0.0707232	+	0.122496i	−0.899218	−	0.437500i	$-0.855864\pi$
$311$	−3.75166e7	+	6.49807e7i	−0.0707232	+	0.122496i	0.828495	+	0.559996i	$0.189197\pi$
$312$		0			0
$313$	−4.24942e8	−	7.36021e8i	−0.783293	−	1.35670i	−0.930013	−	0.367526i	$-0.880205\pi$
$313$	−4.24942e8	−	7.36021e8i	−0.783293	−	1.35670i	0.146720	−	0.989178i	$-0.453128\pi$
$314$	−2.19696e8			−0.400468
$315$		0			0
$316$	−4.24514e8			−0.756810
$317$	4.71679e7	+	8.16971e7i	0.0831646	+	0.144045i	0.904608	−	0.426245i	$-0.140164\pi$
$317$	4.71679e7	+	8.16971e7i	0.0831646	+	0.144045i	−0.821443	+	0.570291i	$0.806831\pi$
$318$		0			0
$319$	8.24352e8	−	1.42782e9i	1.42182	−	2.46267i
$320$	2.60489e7	+	4.51180e7i	0.0444390	+	0.0769706i
$321$		0			0
$322$	−3.13522e8	+	1.23085e8i	−0.523327	+	0.205452i
$323$	9.86259e7			0.162848
$324$		0			0
$325$	1.95475e8	−	3.38572e8i	0.315863	−	0.547091i
$326$	−2.09814e8	+	3.63408e8i	−0.335407	+	0.580942i
$327$		0			0
$328$	3.88241e8			0.607496
$329$	−3.64152e7	+	2.41766e8i	−0.0563764	+	0.374291i
$330$		0			0
$331$	5.20721e7	+	9.01916e7i	0.0789237	+	0.136700i	0.902786	−	0.430090i	$-0.141518\pi$
$331$	5.20721e7	+	9.01916e7i	0.0789237	+	0.136700i	−0.823862	+	0.566790i	$0.808185\pi$
$332$	7.53543e7	−	1.30518e8i	0.113012	−	0.195743i
$333$		0			0
$334$	−1.56409e8	−	2.70909e8i	−0.229694	−	0.397842i
$335$	1.49844e8			0.217763
$336$		0			0
$337$	1.04307e9			1.48459			0.742296	−	0.670073i	$-0.233737\pi$
$337$	1.04307e9			1.48459			0.742296	+	0.670073i	$0.233737\pi$
$338$	−1.58723e8	−	2.74916e8i	−0.223579	−	0.387251i
$339$		0			0
$340$	6.12407e7	−	1.06072e8i	0.0845014	−	0.146361i
$341$	−9.36416e8	−	1.62192e9i	−1.27888	−	2.21508i
$342$		0			0
$343$	−3.24061e8	+	6.73446e8i	−0.433609	+	0.901101i
$344$	−2.85962e8			−0.378751
$345$		0			0
$346$	9.00929e7	−	1.56046e8i	0.116930	−	0.202528i
$347$	−2.01605e7	+	3.49190e7i	−0.0259029	+	0.0448651i	−0.878686	−	0.477400i	$-0.841579\pi$
$347$	−2.01605e7	+	3.49190e7i	−0.0259029	+	0.0448651i	0.852783	+	0.522265i	$0.174913\pi$
$348$		0			0
$349$	1.36569e9			1.71974			0.859871	−	0.510512i	$-0.170544\pi$
$349$	1.36569e9			1.71974			0.859871	+	0.510512i	$0.170544\pi$
$350$	−2.19275e8	−	1.74830e8i	−0.273371	−	0.217960i
$351$		0			0
$352$	−1.29304e8	−	2.23961e8i	−0.158020	−	0.273699i
$353$	6.58018e8	−	1.13972e9i	0.796207	−	1.37907i	−0.125863	−	0.992048i	$-0.540170\pi$
$353$	6.58018e8	−	1.13972e9i	0.796207	−	1.37907i	0.922070	−	0.387024i	$-0.126497\pi$
$354$		0			0
$355$	−1.43561e8	−	2.48655e8i	−0.170309	−	0.294984i
$356$	−2.49494e8			−0.293079
$357$		0			0
$358$	3.50490e8			0.403725
$359$	4.90745e8	+	8.49995e8i	0.559790	+	0.969585i	0.997514	+	0.0704751i	$0.0224515\pi$
$359$	4.90745e8	+	8.49995e8i	0.559790	+	0.969585i	−0.437724	+	0.899110i	$0.644215\pi$
$360$		0			0
$361$	3.94488e8	−	6.83273e8i	0.441325	−	0.764397i
$362$	1.69288e8	+	2.93216e8i	0.187563	+	0.324869i
$363$		0			0
$364$	−5.47153e8	+	2.14806e8i	−0.594640	+	0.233449i
$365$	−6.57769e8			−0.708025
$366$		0			0
$367$	−5.32019e8	+	9.21483e8i	−0.561818	+	0.973097i	0.435520	+	0.900179i	$0.356565\pi$
$367$	−5.32019e8	+	9.21483e8i	−0.561818	+	0.973097i	−0.997338	+	0.0729183i	$0.976769\pi$
$368$	−9.50149e7	+	1.64571e8i	−0.0993858	+	0.172141i
$369$		0			0
$370$	−5.15161e8			−0.528733
$371$	1.13041e8	−	4.43785e7i	0.114928	−	0.0451194i
$372$		0			0
$373$	−2.33167e8	−	4.03858e8i	−0.232641	−	0.402947i	0.725943	−	0.687755i	$-0.241403\pi$
$373$	−2.33167e8	−	4.03858e8i	−0.232641	−	0.402947i	−0.958585	+	0.284808i	$0.908070\pi$
$374$	−3.03993e8	+	5.26531e8i	−0.300478	+	0.520443i
$375$		0			0
$376$	6.89705e7	+	1.19460e8i	0.0669123	+	0.115896i
$377$	−2.11428e9			−2.03221
$378$		0			0
$379$	7.76974e8			0.733110			0.366555	−	0.930396i	$-0.380537\pi$
$379$	7.76974e8			0.733110			0.366555	+	0.930396i	$0.380537\pi$
$380$	6.51342e7	+	1.12816e8i	0.0608929	+	0.105470i
$381$		0			0
$382$	5.41093e8	−	9.37201e8i	0.496650	−	0.860223i
$383$	−5.50385e8	−	9.53295e8i	−0.500577	−	0.867025i	−1.00000		0.000666367i	$-0.999788\pi$
$383$	−5.50385e8	−	9.53295e8i	−0.500577	−	0.867025i	0.499423	−	0.866358i	$-0.333545\pi$
$384$		0			0
$385$	−1.11292e9	−	8.87336e8i	−0.993917	−	0.792457i
$386$	1.35369e9			1.19802
$387$		0			0
$388$	2.55522e8	−	4.42576e8i	0.222084	−	0.384660i
$389$	5.37920e8	−	9.31705e8i	0.463334	−	0.802518i	−0.535791	−	0.844351i	$-0.679986\pi$
$389$	5.37920e8	−	9.31705e8i	0.463334	−	0.802518i	0.999125	+	0.0418330i	$0.0133198\pi$
$390$		0			0
$391$	4.46759e8			0.377967
$392$	9.39105e7	+	4.11063e8i	0.0787432	+	0.344673i
$393$		0			0
$394$	−5.03949e7	−	8.72866e7i	−0.0415097	−	0.0718970i
$395$	−6.59114e8	+	1.14162e9i	−0.538110	+	0.932034i
$396$		0			0
$397$	3.42883e8	+	5.93891e8i	0.275030	+	0.476365i	0.970143	−	0.242535i	$-0.0779790\pi$
$397$	3.42883e8	+	5.93891e8i	0.275030	+	0.476365i	−0.695113	+	0.718900i	$0.744646\pi$
$398$	1.20965e9			0.961763
$399$		0			0
$400$	−1.58223e8			−0.123611
$401$	1.87277e8	+	3.24373e8i	0.145037	+	0.251211i	0.929387	−	0.369107i	$-0.120337\pi$
$401$	1.87277e8	+	3.24373e8i	0.145037	+	0.251211i	−0.784350	+	0.620319i	$0.787003\pi$
$402$		0			0
$403$	−1.20085e9	+	2.07993e9i	−0.913947	+	1.58300i
$404$	3.11492e8	+	5.39519e8i	0.235024	+	0.407073i
$405$		0			0
$406$	−2.25891e8	+	1.49973e9i	−0.167517	+	1.11217i
$407$	2.55721e9			1.88012
$408$		0			0
$409$	−4.41356e8	+	7.64451e8i	−0.318976	+	0.552482i	−0.980275	−	0.197640i	$-0.936672\pi$
$409$	−4.41356e8	+	7.64451e8i	−0.318976	+	0.552482i	0.661299	+	0.750122i	$0.270005\pi$
$410$	6.02797e8	−	1.04407e9i	0.431944	−	0.748149i
$411$		0			0
$412$	6.48106e8			0.456568
$413$	−1.37836e9	+	5.41130e8i	−0.962806	+	0.377987i
$414$		0			0
$415$	−2.33995e8	−	4.05292e8i	−0.160708	−	0.278355i
$416$	−1.65818e8	+	2.87205e8i	−0.112929	+	0.195599i
$417$		0			0
$418$	−3.23320e8	−	5.60006e8i	−0.216529	−	0.375039i
$419$	−2.03664e8			−0.135259			−0.0676294	−	0.997711i	$-0.521544\pi$
$419$	−2.03664e8			−0.135259			−0.0676294	+	0.997711i	$0.521544\pi$
$420$		0			0
$421$	1.72219e8			0.112485			0.0562423	−	0.998417i	$-0.482088\pi$
$421$	1.72219e8			0.112485			0.0562423	+	0.998417i	$0.482088\pi$
$422$	−6.22983e8	−	1.07904e9i	−0.403536	−	0.698946i
$423$		0			0
$424$	3.42577e7	−	5.93360e7i	0.0218262	−	0.0378040i
$425$	1.85990e8	+	3.22144e8i	0.117524	+	0.203558i
$426$		0			0
$427$	−2.40037e8	+	1.59364e9i	−0.149204	+	0.990586i
$428$	7.29445e8			0.449717
$429$		0			0
$430$	−4.43994e8	+	7.69021e8i	−0.269301	+	0.466443i
$431$	−1.21791e9	+	2.10948e9i	−0.732730	+	1.26913i	0.222982	+	0.974823i	$0.428421\pi$
$431$	−1.21791e9	+	2.10948e9i	−0.732730	+	1.26913i	−0.955712	+	0.294303i	$0.904912\pi$
$432$		0			0
$433$	−1.33927e9			−0.792792			−0.396396	−	0.918080i	$-0.629739\pi$
$433$	−1.33927e9			−0.792792			−0.396396	+	0.918080i	$0.629739\pi$
$434$	1.34706e9	+	1.07402e9i	0.790996	+	0.630666i
$435$		0			0
$436$	−6.21257e8	−	1.07605e9i	−0.358978	−	0.621769i
$437$	−2.37581e8	+	4.11503e8i	−0.136184	+	0.235878i
$438$		0			0
$439$	−1.34943e9	−	2.33729e9i	−0.761246	−	1.31852i	−0.942208	−	0.335027i	$-0.891254\pi$
$439$	−1.34943e9	−	2.33729e9i	−0.761246	−	1.31852i	0.180962	−	0.983490i	$-0.442079\pi$
$440$	−8.03048e8			−0.449425
$441$		0			0
$442$	7.79674e8			0.429472
$443$	3.54509e8	+	6.14028e8i	0.193738	+	0.335564i	0.946486	−	0.322745i	$-0.104606\pi$
$443$	3.54509e8	+	6.14028e8i	0.193738	+	0.335564i	−0.752748	+	0.658309i	$0.771272\pi$
$444$		0			0
$445$	−3.87373e8	+	6.70950e8i	−0.208386	+	0.360936i
$446$	−6.36046e8	−	1.10166e9i	−0.339482	−	0.588000i
$447$		0			0
$448$	1.86008e8	+	1.48305e8i	0.0977369	+	0.0779263i
$449$	−1.12477e9			−0.586408			−0.293204	−	0.956050i	$-0.594722\pi$
$449$	−1.12477e9			−0.586408			−0.293204	+	0.956050i	$0.594722\pi$
$450$		0			0
$451$	−2.99222e9	+	5.18268e9i	−1.53595	+	2.66034i
$452$	8.96230e8	−	1.55232e9i	0.456494	−	0.790671i
$453$		0			0
$454$	3.12859e8			0.156911
$455$	−2.71863e8	+	1.80494e9i	−0.135304	+	0.898303i
$456$		0			0
$457$	1.68026e9	+	2.91030e9i	0.823512	+	1.42637i	0.903051	+	0.429534i	$0.141322\pi$
$457$	1.68026e9	+	2.91030e9i	0.823512	+	1.42637i	−0.0795385	+	0.996832i	$0.525345\pi$
$458$	−4.25406e8	+	7.36824e8i	−0.206906	+	0.358372i
$459$		0			0
$460$	2.95047e8	+	5.11036e8i	0.141331	+	0.244793i
$461$	1.19222e9			0.566764			0.283382	−	0.959007i	$-0.408544\pi$
$461$	1.19222e9			0.566764			0.283382	+	0.959007i	$0.408544\pi$
$462$		0			0
$463$	1.89692e9			0.888210			0.444105	−	0.895975i	$-0.353522\pi$
$463$	1.89692e9			0.888210			0.444105	+	0.895975i	$0.353522\pi$
$464$	4.27839e8	+	7.41039e8i	0.198823	+	0.344372i
$465$		0			0
$466$	−3.27940e8	+	5.68008e8i	−0.150122	+	0.260018i
$467$	9.39761e8	+	1.62771e9i	0.426981	+	0.739553i	0.996603	−	0.0823540i	$-0.0262438\pi$
$467$	9.39761e8	+	1.62771e9i	0.426981	+	0.739553i	−0.569622	+	0.821907i	$0.692910\pi$
$468$		0			0
$469$	6.36910e8	−	2.50044e8i	0.285084	−	0.111921i
$470$	4.28344e8			0.190305
$471$		0			0
$472$	−4.17722e8	+	7.23516e8i	−0.182848	+	0.316702i
$473$	2.20394e9	−	3.81734e9i	0.957605	−	1.65862i
$474$		0			0
$475$	−3.95629e8			−0.169379
$476$	8.33010e7	−	5.53048e8i	0.0354018	−	0.235038i
$477$		0			0
$478$	9.40408e8	+	1.62884e9i	0.393839	+	0.682149i
$479$	−1.66902e9	+	2.89084e9i	−0.693887	+	1.20185i	0.276668	+	0.960966i	$0.410770\pi$
$479$	−1.66902e9	+	2.89084e9i	−0.693887	+	1.20185i	−0.970555	+	0.240881i	$0.922564\pi$
$480$		0			0
$481$	−1.63967e9	−	2.83999e9i	−0.671812	−	1.16361i
$482$	5.54084e8			0.225378
$483$		0			0
$484$	2.73907e9			1.09811
$485$	−7.93463e8	−	1.37432e9i	−0.315813	−	0.547005i
$486$		0			0
$487$	2.22852e9	−	3.85992e9i	0.874311	−	1.51435i	0.0168153	−	0.999859i	$-0.494647\pi$
$487$	2.22852e9	−	3.85992e9i	0.874311	−	1.51435i	0.857495	−	0.514492i	$-0.172019\pi$
$488$	4.54630e8	+	7.87442e8i	0.177088	+	0.306725i
$489$		0			0
$490$	1.25126e9	+	3.85683e8i	0.480463	+	0.148096i
$491$	−3.43015e9			−1.30776			−0.653880	−	0.756598i	$-0.726860\pi$
$491$	−3.43015e9			−1.30776			−0.653880	+	0.756598i	$0.726860\pi$
$492$		0			0
$493$	1.00585e9	−	1.74218e9i	0.378066	−	0.654829i
$494$	−4.14622e8	+	7.18146e8i	−0.154742	+	0.268021i
$495$		0			0
$496$	9.72001e8			0.357669
$497$	−1.02513e9	−	8.17343e8i	−0.374569	−	0.298646i
$498$		0			0
$499$	3.75424e8	+	6.50254e8i	0.135260	+	0.234278i	0.925697	−	0.378266i	$-0.123480\pi$
$499$	3.75424e8	+	6.50254e8i	0.135260	+	0.234278i	−0.790437	+	0.612544i	$0.790146\pi$
$500$	−7.42505e8	+	1.28606e9i	−0.265646	+	0.460113i
$501$		0			0
$502$	−6.10669e8	−	1.05771e9i	−0.215448	−	0.373167i
$503$	−2.79800e9			−0.980303			−0.490151	−	0.871637i	$-0.663058\pi$
$503$	−2.79800e9			−0.980303			−0.490151	+	0.871637i	$0.663058\pi$
$504$		0			0
$505$	1.93453e9			0.668430
$506$	−1.46458e9	−	2.53673e9i	−0.502559	−	0.870458i
$507$		0			0
$508$	−4.96432e8	+	8.59846e8i	−0.168011	+	0.291003i
$509$	2.07883e9	+	3.60064e9i	0.698725	+	1.21023i	0.968909	+	0.247419i	$0.0795823\pi$
$509$	2.07883e9	+	3.60064e9i	0.698725	+	1.21023i	−0.270184	+	0.962809i	$0.587084\pi$
$510$		0			0
$511$	−2.79583e9	+	1.09761e9i	−0.926911	+	0.363895i
$512$	1.34218e8			0.0441942
$513$		0			0
$514$	4.45148e8	−	7.71019e8i	0.144588	−	0.250435i
$515$	1.00627e9	−	1.74291e9i	0.324631	−	0.562277i
$516$		0			0
$517$	−2.12626e9			−0.676704
$518$	−2.18968e9	+	8.59642e8i	−0.692191	+	0.271746i
$519$		0			0
$520$	5.14910e8	+	8.91850e8i	0.160590	+	0.278151i
$521$	−7.53291e8	+	1.30474e9i	−0.233362	+	0.404196i	−0.958796	−	0.284097i	$-0.908306\pi$
$521$	−7.53291e8	+	1.30474e9i	−0.233362	+	0.404196i	0.725433	+	0.688293i	$0.241640\pi$
$522$		0			0
$523$	−1.35806e9	−	2.35223e9i	−0.415110	−	0.718992i	0.580330	−	0.814382i	$-0.302924\pi$
$523$	−1.35806e9	−	2.35223e9i	−0.415110	−	0.718992i	−0.995440	+	0.0953893i	$0.969590\pi$
$524$	1.17731e9			0.357462
$525$		0			0
$526$	−8.72219e8			−0.261322
$527$	−1.14258e9	−	1.97901e9i	−0.340056	−	0.588995i
$528$		0			0
$529$	6.26211e8	−	1.08463e9i	0.183919	−	0.318556i
$530$	−1.06379e8	−	1.84254e8i	−0.0310378	−	0.0537591i
$531$		0			0
$532$	4.65106e8	+	3.70832e8i	0.133925	+	0.106779i
$533$	7.67439e9			2.19532
$534$		0			0
$535$	1.13256e9	−	1.96165e9i	0.319759	−	0.553839i
$536$	1.93020e8	−	3.34320e8i	0.0541408	−	0.0937746i
$537$		0			0
$538$	−3.37145e9			−0.933423
$539$	−6.21112e9	−	1.91449e9i	−1.70848	−	0.526614i
$540$		0			0
$541$	−3.59033e8	−	6.21864e8i	−0.0974864	−	0.168851i	0.813157	−	0.582044i	$-0.197747\pi$
$541$	−3.59033e8	−	6.21864e8i	−0.0974864	−	0.168851i	−0.910644	+	0.413193i	$0.864414\pi$
$542$	2.01898e9	−	3.49698e9i	0.544672	−	0.943400i
$543$		0			0
$544$	−1.57772e8	−	2.73270e8i	−0.0420180	−	0.0727772i
$545$	−3.85834e9			−1.02097
$546$		0			0
$547$	5.09149e9			1.33011			0.665057	−	0.746792i	$-0.268407\pi$
$547$	5.09149e9			1.33011			0.665057	+	0.746792i	$0.268407\pi$
$548$	1.06117e9	+	1.83801e9i	0.275457	+	0.477106i
$549$		0			0
$550$	1.21944e9	−	2.11213e9i	0.312530	−	0.541317i
$551$	1.06979e9	+	1.85294e9i	0.272439	+	0.471879i
$552$		0			0
$553$	−8.96543e8	+	5.95228e9i	−0.225441	+	1.49674i
$554$	−1.57185e9			−0.392760
$555$		0			0
$556$	−1.09293e9	+	1.89301e9i	−0.269668	+	0.467079i
$557$	2.58456e9	−	4.47660e9i	0.633715	−	1.09763i	−0.353071	−	0.935597i	$-0.614862\pi$
$557$	2.58456e9	−	4.47660e9i	0.633715	−	1.09763i	0.986786	−	0.162030i	$-0.0518042\pi$
$558$		0			0
$559$	−5.65263e9			−1.36870
$560$	6.87631e8	−	2.69956e8i	0.165462	−	0.0649584i
$561$		0			0
$562$	−1.80199e9	−	3.12113e9i	−0.428227	−	0.741711i
$563$	3.69727e9	−	6.40386e9i	0.873177	−	1.51239i	0.0144840	−	0.999895i	$-0.495389\pi$
$563$	3.69727e9	−	6.40386e9i	0.873177	−	1.51239i	0.858693	−	0.512491i	$-0.171277\pi$
$564$		0			0
$565$	−2.78303e9	−	4.82036e9i	−0.649156	−	1.12437i
$566$	3.81895e9			0.885291
$567$		0			0
$568$	−7.39703e8			−0.169371
$569$	1.67602e9	+	2.90295e9i	0.381405	+	0.660612i	0.991263	−	0.131898i	$-0.0421071\pi$
$569$	1.67602e9	+	2.90295e9i	0.381405	+	0.660612i	−0.609859	+	0.792510i	$0.708774\pi$
$570$		0			0
$571$	−2.07567e9	+	3.59517e9i	−0.466586	+	0.808151i	−0.999272	−	0.0381621i	$-0.987850\pi$
$571$	−2.07567e9	+	3.59517e9i	−0.466586	+	0.808151i	0.532685	+	0.846313i	$0.321183\pi$
$572$	−2.55596e9	−	4.42706e9i	−0.571042	−	0.989074i
$573$		0			0
$574$	8.19938e8	−	5.44369e9i	0.180963	−	1.20144i
$575$	−1.79213e9			−0.393127
$576$		0			0
$577$	3.37611e9	−	5.84759e9i	0.731646	−	1.26725i	−0.224533	−	0.974467i	$-0.572086\pi$
$577$	3.37611e9	−	5.84759e9i	0.731646	−	1.26725i	0.956179	−	0.292782i	$-0.0945811\pi$
$578$	1.27043e9	−	2.20045e9i	0.273656	−	0.473985i
$579$		0			0
$580$	2.65711e9			0.565472
$581$	−1.67090e9	−	1.33222e9i	−0.353454	−	0.281812i
$582$		0			0
$583$	5.28056e8	+	9.14620e8i	0.110367	+	0.191162i
$584$	−8.47295e8	+	1.46756e9i	−0.176031	+	0.304895i
$585$		0			0
$586$	−2.54797e9	−	4.41322e9i	−0.523062	−	0.905971i
$587$	4.88293e9			0.996431			0.498216	−	0.867053i	$-0.333989\pi$
$587$	4.88293e9			0.996431			0.498216	+	0.867053i	$0.333989\pi$
$588$		0			0
$589$	2.43045e9			0.490098
$590$	1.29714e9	+	2.24671e9i	0.260019	+	0.450365i
$591$		0			0
$592$	−6.63596e8	+	1.14938e9i	−0.131455	+	0.227687i
$593$	−3.88570e9	−	6.73023e9i	−0.765205	−	1.32537i	−0.940138	−	0.340794i	$-0.889304\pi$
$593$	−3.88570e9	−	6.73023e9i	−0.765205	−	1.32537i	0.174933	−	0.984580i	$-0.444029\pi$
$594$		0			0
$595$	−1.35794e9	−	1.08270e9i	−0.264285	−	0.210716i
$596$	−1.33000e9			−0.257329
$597$		0			0
$598$	−1.87817e9	+	3.25308e9i	−0.359153	+	0.622072i
$599$	−4.57122e9	+	7.91759e9i	−0.869038	+	1.50522i	−0.00605623	+	0.999982i	$0.501928\pi$
$599$	−4.57122e9	+	7.91759e9i	−0.869038	+	1.50522i	−0.862981	+	0.505236i	$0.831406\pi$
$600$		0			0
$601$	6.52910e8			0.122685			0.0613427	−	0.998117i	$-0.480462\pi$
$601$	6.52910e8			0.122685			0.0613427	+	0.998117i	$0.480462\pi$
$602$	−6.03931e8	+	4.00959e9i	−0.112824	+	0.749053i
$603$		0			0
$604$	−1.04344e9	−	1.80729e9i	−0.192680	−	0.333732i
$605$	4.25277e9	−	7.36602e9i	0.780780	−	1.35235i
$606$		0			0
$607$	3.10668e9	+	5.38093e9i	0.563815	+	0.976556i	0.997159	+	0.0753272i	$0.0240001\pi$
$607$	3.10668e9	+	5.38093e9i	0.563815	+	0.976556i	−0.433344	+	0.901229i	$0.642667\pi$
$608$	3.35606e8			0.0605574
$609$		0			0
$610$	2.82350e9			0.503655
$611$	1.36334e9	+	2.36138e9i	0.241803	+	0.418815i
$612$		0			0
$613$	1.46039e9	−	2.52947e9i	0.256069	−	0.443525i	−0.709116	−	0.705092i	$-0.750906\pi$
$613$	1.46039e9	−	2.52947e9i	0.256069	−	0.443525i	0.965185	+	0.261567i	$0.0842392\pi$
$614$	2.60075e9	+	4.50463e9i	0.453429	+	0.785362i
$615$		0			0
$616$	−3.41333e9	+	1.34004e9i	−0.588364	+	0.230985i
$617$	6.40381e9			1.09759			0.548796	−	0.835957i	$-0.315087\pi$
$617$	6.40381e9			1.09759			0.548796	+	0.835957i	$0.315087\pi$
$618$		0			0
$619$	4.58054e9	−	7.93372e9i	0.776246	−	1.34450i	−0.157846	−	0.987464i	$-0.550455\pi$
$619$	4.58054e9	−	7.93372e9i	0.776246	−	1.34450i	0.934092	−	0.357033i	$-0.116212\pi$
$620$	1.50916e9	−	2.61394e9i	0.254311	−	0.440479i
$621$		0			0
$622$	6.00266e8			0.100018
$623$	−5.26914e8	+	3.49826e9i	−0.0873035	+	0.579621i
$624$		0			0
$625$	7.96747e8	+	1.38001e9i	0.130539	+	0.226100i
$626$	−3.39954e9	+	5.88817e9i	−0.553872	+	0.959334i
$627$		0			0
$628$	8.78783e8	+	1.52210e9i	0.141587	+	0.245236i
$629$	3.12022e9			0.499928
$630$		0			0
$631$	7.82656e9			1.24013			0.620066	−	0.784549i	$-0.287106\pi$
$631$	7.82656e9			1.24013			0.620066	+	0.784549i	$0.287106\pi$
$632$	1.69806e9	+	2.94112e9i	0.267573	+	0.463450i
$633$		0			0
$634$	3.77343e8	−	6.53577e8i	0.0588063	−	0.101855i
$635$	1.54155e9	+	2.67005e9i	0.238919	+	0.413820i
$636$		0			0
$637$	1.85634e9	+	8.12551e9i	0.284556	+	1.24555i
$638$	−1.31896e10			−2.01076
$639$		0			0
$640$	2.08391e8	−	3.60944e8i	0.0314231	−	0.0544264i
$641$	4.95682e9	−	8.58547e9i	0.743362	−	1.28754i	−0.207594	−	0.978215i	$-0.566563\pi$
$641$	4.95682e9	−	8.58547e9i	0.743362	−	1.28754i	0.950956	−	0.309326i	$-0.100103\pi$
$642$		0			0
$643$	1.11553e10			1.65480			0.827398	−	0.561616i	$-0.189820\pi$
$643$	1.11553e10			1.65480			0.827398	+	0.561616i	$0.189820\pi$
$644$	2.10685e9	+	1.67981e9i	0.310837	+	0.247833i
$645$		0			0
$646$	−3.94504e8	−	6.83300e8i	−0.0575754	−	0.0997236i
$647$	−5.74496e9	+	9.95056e9i	−0.833915	+	1.44438i	0.0609955	+	0.998138i	$0.480572\pi$
$647$	−5.74496e9	+	9.95056e9i	−0.833915	+	1.44438i	−0.894911	+	0.446245i	$0.852761\pi$
$648$		0			0
$649$	−6.43887e9	−	1.11525e10i	−0.924599	−	1.60145i
$650$	−3.12759e9			−0.446698
$651$		0			0
$652$	3.35702e9			0.474337
$653$	2.26085e8	+	3.91591e8i	0.0317743	+	0.0550347i	0.881475	−	0.472230i	$-0.156551\pi$
$653$	2.26085e8	+	3.91591e8i	0.0317743	+	0.0550347i	−0.849701	+	0.527265i	$0.823218\pi$
$654$		0			0
$655$	1.82793e9	−	3.16606e9i	0.254164	−	0.440225i
$656$	−1.55297e9	−	2.68981e9i	−0.214782	−	0.372014i
$657$		0			0
$658$	1.82066e9	−	7.14772e8i	0.249138	−	0.0978086i
$659$	1.13939e10			1.55086			0.775430	−	0.631434i	$-0.217533\pi$
$659$	1.13939e10			1.55086			0.775430	+	0.631434i	$0.217533\pi$
$660$		0			0
$661$	−3.02602e9	+	5.24121e9i	−0.407536	+	0.705873i	−0.994613	−	0.103658i	$-0.966945\pi$
$661$	−3.02602e9	+	5.24121e9i	−0.407536	+	0.705873i	0.587077	+	0.809531i	$0.300279\pi$
$662$	4.16577e8	−	7.21533e8i	0.0558075	−	0.0966614i
$663$		0			0
$664$	−1.20567e9			−0.159823
$665$	1.71939e9	−	6.75015e8i	0.226725	−	0.0890097i
$666$		0			0
$667$	4.84599e9	+	8.39350e9i	0.632327	+	1.09522i
$668$	−1.25128e9	+	2.16727e9i	−0.162418	+	0.281317i
$669$		0			0
$670$	−5.99378e8	−	1.03815e9i	−0.0769908	−	0.133352i
$671$	−1.40156e10			−1.79094
$672$		0			0
$673$	−1.20368e10			−1.52215			−0.761076	−	0.648663i	$-0.775328\pi$
$673$	−1.20368e10			−1.52215			−0.761076	+	0.648663i	$0.775328\pi$
$674$	−4.17226e9	−	7.22657e9i	−0.524882	−	0.909123i
$675$		0			0
$676$	−1.26978e9	+	2.19933e9i	−0.158094	+	0.273828i
$677$	−3.33947e9	−	5.78413e9i	−0.413635	−	0.716436i	0.581649	−	0.813440i	$-0.302408\pi$
$677$	−3.33947e9	−	5.78413e9i	−0.413635	−	0.716436i	−0.995284	+	0.0970033i	$0.969074\pi$
$678$		0			0
$679$	−5.66591e9	−	4.51747e9i	−0.694584	−	0.553797i
$680$	−9.79851e8			−0.119503
$681$		0			0
$682$	−7.49133e9	+	1.29754e10i	−0.904302	+	1.56630i
$683$	−2.78597e9	+	4.82545e9i	−0.334583	+	0.579516i	−0.983405	−	0.181425i	$-0.941929\pi$
$683$	−2.78597e9	+	4.82545e9i	−0.334583	+	0.579516i	0.648821	+	0.760941i	$0.275262\pi$
$684$		0			0
$685$	6.59046e9			0.783427
$686$	5.96202e9	−	4.48622e8i	0.705113	−	0.0530575i
$687$		0			0
$688$	1.14385e9	+	1.98120e9i	0.133909	+	0.231937i
$689$	6.77174e8	−	1.17290e9i	0.0788738	−	0.136613i
$690$		0			0
$691$	3.81749e9	+	6.61208e9i	0.440154	+	0.762369i	0.997701	−	0.0677769i	$-0.0215906\pi$
$691$	3.81749e9	+	6.61208e9i	0.440154	+	0.762369i	−0.557547	+	0.830146i	$0.688257\pi$
$692$	−1.44149e9			−0.165363
$693$		0			0
$694$	3.22568e8			0.0366322
$695$	3.39383e9	+	5.87829e9i	0.383481	+	0.664209i
$696$		0			0
$697$	−3.65101e9	+	6.32373e9i	−0.408412	+	0.707390i
$698$	−5.46276e9	−	9.46178e9i	−0.608020	−	1.05312i
$699$		0			0
$700$	−3.34155e8	+	2.21850e9i	−0.0368218	+	0.244465i
$701$	−1.19417e10			−1.30934			−0.654671	−	0.755914i	$-0.727193\pi$
$701$	−1.19417e10			−1.30934			−0.654671	+	0.755914i	$0.727193\pi$
$702$		0			0
$703$	−1.65929e9	+	2.87398e9i	−0.180127	+	0.311990i
$704$	−1.03443e9	+	1.79169e9i	−0.111737	+	0.193535i
$705$		0			0
$706$	−1.05283e10			−1.12601
$707$	8.22267e9	−	3.22813e9i	0.875075	−	0.343544i
$708$		0			0
$709$	−5.06814e9	−	8.77827e9i	−0.534055	−	0.925011i	−0.999208	−	0.0397809i	$-0.987334\pi$
$709$	−5.06814e9	−	8.77827e9i	−0.534055	−	0.925011i	0.465153	−	0.885230i	$-0.345999\pi$
$710$	−1.14849e9	+	1.98924e9i	−0.120427	+	0.208585i
$711$		0			0
$712$	9.97977e8	+	1.72855e9i	0.103619	+	0.179474i
$713$	1.10095e10			1.13751
$714$		0			0
$715$	−1.58739e10			−1.62410
$716$	−1.40196e9	−	2.42827e9i	−0.142738	−	0.247230i
$717$		0			0
$718$	3.92596e9	−	6.79996e9i	0.395831	−	0.685600i
$719$	3.20435e9	+	5.55010e9i	0.321506	+	0.556864i	0.980799	−	0.195022i	$-0.0624777\pi$
$719$	3.20435e9	+	5.55010e9i	0.321506	+	0.556864i	−0.659293	+	0.751886i	$0.729144\pi$
$720$		0			0
$721$	1.36875e9	−	9.08736e9i	0.136004	−	0.902951i
$722$	−6.31180e9			−0.624127
$723$		0			0
$724$	1.35431e9	−	2.34573e9i	0.132627	−	0.229717i
$725$	−4.03486e9	+	6.98859e9i	−0.393229	+	0.681093i
$726$		0			0
$727$	3.59040e8			0.0346555			0.0173278	−	0.999850i	$-0.494484\pi$
$727$	3.59040e8			0.0346555			0.0173278	+	0.999850i	$0.494484\pi$
$728$	3.67683e9	+	2.93156e9i	0.353194	+	0.281604i
$729$		0			0
$730$	2.63108e9	+	4.55716e9i	0.250325	+	0.433575i
$731$	2.68918e9	−	4.65779e9i	0.254629	−	0.441031i
$732$		0			0
$733$	3.53759e9	+	6.12729e9i	0.331775	+	0.574652i	0.982860	−	0.184353i	$-0.0590191\pi$
$733$	3.53759e9	+	6.12729e9i	0.331775	+	0.574652i	−0.651085	+	0.759005i	$0.725686\pi$
$734$	8.51230e9			0.794531
$735$		0			0
$736$	1.52024e9			0.140553
$737$	2.97525e9	+	5.15329e9i	0.273771	+	0.474185i
$738$		0			0
$739$	−4.55027e9	+	7.88130e9i	−0.414746	+	0.718361i	−0.995402	−	0.0957883i	$-0.969463\pi$
$739$	−4.55027e9	+	7.88130e9i	−0.414746	+	0.718361i	0.580656	+	0.814149i	$0.302796\pi$
$740$	2.06064e9	+	3.56914e9i	0.186935	+	0.323782i
$741$		0			0
$742$	−7.59625e8	−	6.05655e8i	−0.0682631	−	0.0544266i
$743$	2.11812e10			1.89448			0.947238	−	0.320532i	$-0.103862\pi$
$743$	2.11812e10			1.89448			0.947238	+	0.320532i	$0.103862\pi$
$744$		0			0
$745$	−2.06500e9	+	3.57668e9i	−0.182967	+	0.316908i
$746$	−1.86534e9	+	3.23086e9i	−0.164502	+	0.284926i
$747$		0			0
$748$	4.86389e9			0.424940
$749$	1.54054e9	−	1.02278e10i	0.133963	−	0.889402i
$750$		0			0
$751$	6.86477e8	+	1.18901e9i	0.0591407	+	0.102435i	0.894080	−	0.447907i	$-0.147831\pi$
$751$	6.86477e8	+	1.18901e9i	0.0591407	+	0.102435i	−0.834939	+	0.550342i	$0.814497\pi$
$752$	5.51764e8	−	9.55683e8i	0.0473141	−	0.0819505i
$753$		0			0
$754$	8.45712e9	+	1.46482e10i	0.718493	+	1.24447i
$755$	−6.48031e9			−0.548001
$756$		0			0
$757$	−1.24709e10			−1.04487			−0.522433	−	0.852680i	$-0.674976\pi$
$757$	−1.24709e10			−1.04487			−0.522433	+	0.852680i	$0.674976\pi$
$758$	−3.10789e9	−	5.38303e9i	−0.259193	−	0.448936i
$759$		0			0
$760$	5.21073e8	−	9.02526e8i	0.0430578	−	0.0745782i
$761$	3.70982e9	+	6.42560e9i	0.305145	+	0.528528i	0.977294	−	0.211889i	$-0.0679616\pi$
$761$	3.70982e9	+	6.42560e9i	0.305145	+	0.528528i	−0.672148	+	0.740417i	$0.734628\pi$
$762$		0			0
$763$	−1.63998e10	+	6.43836e9i	−1.33660	+	0.524734i
$764$	−8.65749e9			−0.702369
$765$		0			0
$766$	−4.40308e9	+	7.62636e9i	−0.353961	+	0.613079i
$767$	−8.25714e9	+	1.43018e10i	−0.660763	+	1.14448i
$768$		0			0
$769$	1.39749e10			1.10817			0.554085	−	0.832460i	$-0.313068\pi$
$769$	1.39749e10			1.10817			0.554085	+	0.832460i	$0.313068\pi$
$770$	−1.69598e9	+	1.12599e10i	−0.133876	+	0.888824i
$771$		0			0
$772$	−5.41475e9	−	9.37861e9i	−0.423563	−	0.733632i
$773$	−2.10460e9	+	3.64527e9i	−0.163886	+	0.283858i	−0.936259	−	0.351310i	$-0.885736\pi$
$773$	−2.10460e9	+	3.64527e9i	−0.163886	+	0.283858i	0.772373	+	0.635169i	$0.219069\pi$
$774$		0			0
$775$	4.58337e9	+	7.93864e9i	0.353695	+	0.612618i
$776$	−4.08835e9			−0.314074
$777$		0			0
$778$	−8.60672e9			−0.655253
$779$	−3.88313e9	−	6.72578e9i	−0.294307	−	0.509755i
$780$		0			0
$781$	5.70098e9	−	9.87439e9i	0.428224	−	0.741706i
$782$	−1.78703e9	−	3.09524e9i	−0.133632	−	0.231457i
$783$		0			0
$784$	2.47229e9	−	2.29488e9i	0.183228	−	0.170080i
$785$	5.45772e9			0.402686
$786$		0			0
$787$	7.38069e8	−	1.27837e9i	0.0539741	−	0.0934859i	−0.837776	−	0.546014i	$-0.816144\pi$
$787$	7.38069e8	−	1.27837e9i	0.0539741	−	0.0934859i	0.891750	+	0.452528i	$0.149478\pi$
$788$	−4.03159e8	+	6.98293e8i	−0.0293518	+	0.0508389i
$789$		0			0
$790$	1.05458e10			0.761002
$791$	−1.98729e10	−	1.58448e10i	−1.42772	−	1.13833i
$792$		0			0
$793$	8.98670e9	+	1.55654e10i	0.639947	+	1.10842i
$794$	2.74306e9	−	4.75113e9i	0.194475	−	0.336841i
$795$		0			0
$796$	−4.83859e9	−	8.38068e9i	−0.340035	−	0.588957i
$797$	−8.29050e8			−0.0580065			−0.0290033	−	0.999579i	$-0.509233\pi$
$797$	−8.29050e8			−0.0580065			−0.0290033	+	0.999579i	$0.509233\pi$
$798$		0			0
$799$	−2.59439e9			−0.179937
$800$	6.32890e8	+	1.09620e9i	0.0437032	+	0.0756962i
$801$		0			0
$802$	1.49821e9	−	2.59498e9i	0.102557	−	0.177633i
$803$	−1.30604e10	−	2.26213e10i	−0.890128	−	1.54175i
$804$		0			0
$805$	7.78857e9	−	3.05770e9i	0.526226	−	0.206590i
$806$	1.92136e10			1.29252
$807$		0			0
$808$	2.49193e9	−	4.31616e9i	0.166187	−	0.287844i
$809$	−1.18808e10	+	2.05781e10i	−0.788907	+	1.36643i	0.137730	+	0.990470i	$0.456019\pi$
$809$	−1.18808e10	+	2.05781e10i	−0.788907	+	1.36643i	−0.926637	+	0.375957i	$0.877314\pi$
$810$		0			0
$811$	−5.06935e9			−0.333718			−0.166859	−	0.985981i	$-0.553362\pi$
$811$	−5.06935e9			−0.333718			−0.166859	+	0.985981i	$0.553362\pi$
$812$	1.12940e10	−	4.43389e9i	0.740288	−	0.290629i
$813$		0			0
$814$	−1.02288e10	−	1.77168e10i	−0.664723	−	1.15133i
$815$	5.21222e9	−	9.02783e9i	0.337265	−	0.584160i
$816$		0			0
$817$	2.86015e9	+	4.95392e9i	0.183489	+	0.317813i
$818$	7.06170e9			0.451100
$819$		0			0
$820$	−9.64475e9			−0.610861
$821$	3.19979e8	+	5.54220e8i	0.0201800	+	0.0349527i	0.875939	−	0.482422i	$-0.160243\pi$
$821$	3.19979e8	+	5.54220e8i	0.0201800	+	0.0349527i	−0.855759	+	0.517375i	$0.826909\pi$
$822$		0			0
$823$	2.26480e9	−	3.92276e9i	0.141622	−	0.245297i	−0.786485	−	0.617609i	$-0.788102\pi$
$823$	2.26480e9	−	3.92276e9i	0.141622	−	0.245297i	0.928108	+	0.372312i	$0.121435\pi$
$824$	−2.59242e9	−	4.49021e9i	−0.161421	−	0.279590i
$825$		0			0
$826$	9.26252e9	+	7.38507e9i	0.571872	+	0.455957i
$827$	8.73001e9			0.536717			0.268359	−	0.963319i	$-0.413519\pi$
$827$	8.73001e9			0.536717			0.268359	+	0.963319i	$0.413519\pi$
$828$		0			0
$829$	7.79339e9	−	1.34985e10i	0.475100	−	0.822898i	−0.524493	−	0.851415i	$-0.675745\pi$
$829$	7.79339e9	−	1.34985e10i	0.475100	−	0.822898i	0.999593	+	0.0285169i	$0.00907844\pi$
$830$	−1.87196e9	+	3.24233e9i	−0.113638	+	0.196827i
$831$		0			0
$832$	2.65309e9			0.159706
$833$	−7.57859e9	−	2.33600e9i	−0.454288	−	0.140028i
$834$		0			0
$835$	3.88555e9	+	6.72996e9i	0.230967	+	0.400046i
$836$	−2.58656e9	+	4.48005e9i	−0.153109	+	0.265192i
$837$		0			0
$838$	8.14657e8	+	1.41103e9i	0.0478212	+	0.0828288i
$839$	−2.98612e9			−0.174558			−0.0872790	−	0.996184i	$-0.527817\pi$
$839$	−2.98612e9			−0.174558			−0.0872790	+	0.996184i	$0.527817\pi$
$840$		0			0
$841$	2.63917e10			1.52997
$842$	−6.88876e8	−	1.19317e9i	−0.0397693	−	0.0688825i
$843$		0			0
$844$	−4.98387e9	+	8.63231e9i	−0.285343	+	0.494229i
$845$	3.94302e9	+	6.82951e9i	0.224818	+	0.389396i
$846$		0			0
$847$	5.78472e9	−	3.84056e10i	0.327108	−	2.17172i
$848$	−5.48123e8			−0.0308669
$849$		0			0
$850$	1.48792e9	−	2.57715e9i	0.0831023	−	0.143937i
$851$	−7.51632e9	+	1.30187e10i	−0.418073	+	0.724124i
$852$		0			0
$853$	−3.07407e10			−1.69587			−0.847935	−	0.530100i	$-0.822154\pi$
$853$	−3.07407e10			−1.69587			−0.847935	+	0.530100i	$0.822154\pi$
$854$	1.20012e10	−	4.71153e9i	0.659359	−	0.258857i
$855$		0			0
$856$	−2.91778e9	−	5.05374e9i	−0.158999	−	0.275394i
$857$	2.31482e9	−	4.00938e9i	0.125627	−	0.217593i	−0.796351	−	0.604835i	$-0.793239\pi$
$857$	2.31482e9	−	4.00938e9i	0.125627	−	0.217593i	0.921978	+	0.387242i	$0.126572\pi$
$858$		0			0
$859$	1.16851e10	+	2.02392e10i	0.629009	+	1.08948i	0.987751	+	0.156039i	$0.0498725\pi$
$859$	1.16851e10	+	2.02392e10i	0.629009	+	1.08948i	−0.358742	+	0.933437i	$0.616794\pi$
$860$	7.10391e9			0.380849
$861$		0			0
$862$	1.94865e10			1.03624
$863$	2.53121e9	+	4.38419e9i	0.134058	+	0.232194i	0.925237	−	0.379390i	$-0.123866\pi$
$863$	2.53121e9	+	4.38419e9i	0.134058	+	0.232194i	−0.791180	+	0.611584i	$0.790533\pi$
$864$		0			0
$865$	−2.23810e9	+	3.87651e9i	−0.117577	+	0.203650i
$866$	5.35707e9	+	9.27871e9i	0.280294	+	0.485484i
$867$		0			0
$868$	2.05280e9	−	1.36288e10i	0.106543	−	0.707358i
$869$	−5.23485e10			−2.70604
$870$		0			0
$871$	3.81543e9	−	6.60852e9i	0.195650	−	0.338876i
$872$	−4.97005e9	+	8.60839e9i	−0.253836	+	0.439657i
$873$		0			0
$874$	3.80130e9			0.192594
$875$	1.64642e10	+	1.31270e10i	0.830831	+	0.662427i
$876$		0			0
$877$	3.59428e8	+	6.22548e8i	0.0179934	+	0.0311655i	0.874882	−	0.484336i	$-0.160939\pi$
$877$	3.59428e8	+	6.22548e8i	0.0179934	+	0.0311655i	−0.856888	+	0.515502i	$0.827606\pi$
$878$	−1.07955e10	+	1.86983e10i	−0.538282	+	0.932333i
$879$		0			0
$880$	3.21219e9	+	5.56368e9i	0.158896	+	0.275215i
$881$	3.21074e9			0.158194			0.0790968	−	0.996867i	$-0.474796\pi$
$881$	3.21074e9			0.158194			0.0790968	+	0.996867i	$0.474796\pi$
$882$		0			0
$883$	−3.00942e10			−1.47103			−0.735513	−	0.677511i	$-0.763059\pi$
$883$	−3.00942e10			−1.47103			−0.735513	+	0.677511i	$0.763059\pi$
$884$	−3.11870e9	−	5.40174e9i	−0.151841	−	0.262997i
$885$		0			0
$886$	2.83608e9	−	4.91223e9i	0.136993	−	0.237280i
$887$	5.65367e9	+	9.79245e9i	0.272018	+	0.471150i	0.969379	−	0.245571i	$-0.0789755\pi$
$887$	5.65367e9	+	9.79245e9i	0.272018	+	0.471150i	−0.697360	+	0.716721i	$0.745642\pi$
$888$		0			0
$889$	1.10078e10	+	8.77661e9i	0.525467	+	0.418958i
$890$	6.19797e9			0.294703
$891$		0			0
$892$	−5.08837e9	+	8.81331e9i	−0.240050	+	0.415779i
$893$	1.37966e9	−	2.38965e9i	0.0648326	−	0.112293i
$894$		0			0
$895$	−8.70693e9			−0.405961
$896$	2.83458e8	−	1.88192e9i	0.0131647	−	0.0874025i
$897$		0			0
$898$	4.49906e9	+	7.79261e9i	0.207327	+	0.359100i
$899$	2.47872e10	−	4.29327e10i	1.13781	−	1.97074i
$900$		0			0
$901$	6.44316e8	+	1.11599e9i	0.0293469	+	0.0508303i
$902$	4.78756e10			2.17216
$903$		0			0
$904$	−1.43397e10			−0.645580
$905$	−4.20549e9	−	7.28411e9i	−0.188602	−	0.326668i
$906$		0			0
$907$	1.27986e10	−	2.21679e10i	0.569558	−	0.986503i	−0.427052	−	0.904227i	$-0.640448\pi$
$907$	1.27986e10	−	2.21679e10i	0.569558	−	0.986503i	0.996610	−	0.0822756i	$-0.0262188\pi$
$908$	−1.25144e9	−	2.16755e9i	−0.0554764	−	0.0960879i
$909$		0			0
$910$	1.35924e10	−	5.33624e9i	0.597933	−	0.234742i
$911$	4.11144e9			0.180169			0.0900845	−	0.995934i	$-0.471286\pi$
$911$	4.11144e9			0.180169			0.0900845	+	0.995934i	$0.471286\pi$
$912$		0			0
$913$	9.29224e9	−	1.60946e10i	0.404085	−	0.699896i
$914$	1.34421e10	−	2.32824e10i	0.582311	−	1.00859i
$915$		0			0
$916$	6.80649e9			0.292610
$917$	2.48639e9	−	1.65075e10i	0.106482	−	0.706950i
$918$		0			0
$919$	−7.37403e9	−	1.27722e10i	−0.313401	−	0.542827i	0.665695	−	0.746224i	$-0.268135\pi$
$919$	−7.37403e9	−	1.27722e10i	−0.313401	−	0.542827i	−0.979096	+	0.203397i	$0.934802\pi$
$920$	2.36037e9	−	4.08829e9i	0.0999364	−	0.173095i
$921$		0			0
$922$	−4.76887e9	−	8.25993e9i	−0.200381	−	0.347071i
$923$	−1.46218e10			−0.612059
$924$		0			0
$925$	−1.25165e10			−0.519979
$926$	−7.58768e9	−	1.31423e10i	−0.314030	−	0.543915i
$927$		0			0
$928$	3.42271e9	−	5.92831e9i	0.140589	−	0.243508i
$929$	9.39242e9	+	1.62682e10i	0.384346	+	0.665707i	0.991678	−	0.128741i	$-0.0410936\pi$
$929$	9.39242e9	+	1.62682e10i	0.384346	+	0.665707i	−0.607332	+	0.794448i	$0.707760\pi$
$930$		0			0
$931$	6.18186e9	−	5.73827e9i	0.251070	−	0.233054i
$932$	5.24704e9			0.212304
$933$		0			0
$934$	7.51809e9	−	1.30217e10i	0.301921	−	0.522943i
$935$	7.55183e9	−	1.30802e10i	0.302142	−	0.523326i
$936$		0			0
$937$	−1.99897e9			−0.0793813			−0.0396906	−	0.999212i	$-0.512637\pi$
$937$	−1.99897e9			−0.0793813			−0.0396906	+	0.999212i	$0.512637\pi$
$938$	−4.27999e9	−	3.41247e9i	−0.169330	−	0.135008i
$939$		0			0
$940$	−1.71338e9	−	2.96765e9i	−0.0672829	−	0.116537i
$941$	−1.82073e9	+	3.15360e9i	−0.0712333	+	0.123380i	−0.899442	−	0.437040i	$-0.856027\pi$
$941$	−1.82073e9	+	3.15360e9i	−0.0712333	+	0.123380i	0.828209	+	0.560420i	$0.189360\pi$
$942$		0			0
$943$	−1.75899e10	−	3.04666e10i	−0.683082	−	1.18313i
$944$	6.68355e9			0.258586
$945$		0			0
$946$	−3.52631e10			−1.35426
$947$	5.25411e9	+	9.10039e9i	0.201036	+	0.348205i	0.948863	−	0.315689i	$-0.102236\pi$
$947$	5.25411e9	+	9.10039e9i	0.201036	+	0.348205i	−0.747826	+	0.663894i	$0.768902\pi$
$948$		0			0
$949$	−1.67485e10	+	2.90093e10i	−0.636129	+	1.10181i
$950$	1.58252e9	+	2.74100e9i	0.0598847	+	0.103723i
$951$		0			0
$952$	−4.16483e9	+	1.63507e9i	−0.156447	+	0.0614195i
$953$	7.06173e9			0.264293			0.132147	−	0.991230i	$-0.457813\pi$
$953$	7.06173e9			0.264293			0.132147	+	0.991230i	$0.457813\pi$
$954$		0			0
$955$	−1.34419e10	+	2.32821e10i	−0.499401	+	0.864988i
$956$	7.52327e9	−	1.30307e10i	0.278486	−	0.482352i
$957$		0			0
$958$	2.67044e10			0.981304
$959$	2.80126e10	−	1.09974e10i	1.02562	−	0.402648i
$960$		0			0
$961$	−1.44005e10	−	2.49424e10i	−0.523415	−	0.906581i
$962$	−1.31173e10	+	2.27199e10i	−0.475043	+	0.822799i
$963$		0			0
$964$	−2.21634e9	−	3.83881e9i	−0.0796831	−	0.138015i
$965$	−3.36285e10			−1.20465
$966$		0			0
$967$	1.66264e10			0.591296			0.295648	−	0.955297i	$-0.404464\pi$
$967$	1.66264e10			0.591296			0.295648	+	0.955297i	$0.404464\pi$
$968$	−1.09563e10	−	1.89768e10i	−0.388239	−	0.672450i
$969$		0			0
$970$	−6.34771e9	+	1.09945e10i	−0.223314	+	0.386791i
$971$	−1.29166e10	−	2.23722e10i	−0.452773	−	0.784226i	0.545784	−	0.837926i	$-0.316232\pi$
$971$	−1.29166e10	−	2.23722e10i	−0.452773	−	0.784226i	−0.998557	+	0.0536999i	$0.982899\pi$
$972$		0			0
$973$	2.42345e10	+	1.93223e10i	0.843409	+	0.672456i
$974$	−3.56564e10			−1.23646
$975$		0			0
$976$	3.63704e9	−	6.29954e9i	0.125220	−	0.216887i
$977$	7.20642e9	−	1.24819e10i	0.247223	−	0.428203i	−0.715531	−	0.698581i	$-0.753815\pi$
$977$	7.20642e9	−	1.24819e10i	0.247223	−	0.428203i	0.962754	+	0.270378i	$0.0871486\pi$
$978$		0			0
$979$	−3.07661e10			−1.04793
$980$	−2.33294e9	−	1.02117e10i	−0.0791794	−	0.346582i
$981$		0			0
$982$	1.37206e10	+	2.37648e10i	0.462363	+	0.800837i
$983$	−8.06293e9	+	1.39654e10i	−0.270742	+	0.468939i	−0.969052	−	0.246857i	$-0.920602\pi$
$983$	−8.06293e9	+	1.39654e10i	−0.270742	+	0.468939i	0.698310	+	0.715795i	$0.253936\pi$
$984$		0			0
$985$	1.25192e9	+	2.16839e9i	0.0417397	+	0.0722952i
$986$	−1.60935e10			−0.534666
$987$		0			0
$988$	6.63395e9			0.218838
$989$	1.29560e10	+	2.24404e10i	0.425876	+	0.737639i
$990$		0			0
$991$	−1.44468e10	+	2.50227e10i	−0.471536	+	0.816725i	−0.999470	−	0.0325611i	$-0.989634\pi$
$991$	−1.44468e10	+	2.50227e10i	−0.471536	+	0.816725i	0.527934	+	0.849286i	$0.322967\pi$
$992$	−3.88800e9	−	6.73422e9i	−0.126455	−	0.219026i
$993$		0			0
$994$	−1.56220e9	+	1.03717e10i	−0.0504527	+	0.334963i
$995$	−3.00502e10			−0.967090
$996$		0			0
$997$	2.45465e10	−	4.25157e10i	0.784433	−	1.35868i	−0.144904	−	0.989446i	$-0.546287\pi$
$997$	2.45465e10	−	4.25157e10i	0.784433	−	1.35868i	0.929337	−	0.369232i	$-0.120379\pi$
$998$	3.00339e9	−	5.20203e9i	0.0956435	−	0.165659i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.8.g.h.109.3		6
3.2	odd	2		42.8.e.e.25.1	✓	6
7.2	even	3	inner	126.8.g.h.37.3		6
21.2	odd	6		42.8.e.e.37.1	yes	6
21.5	even	6		294.8.e.ba.79.3		6
21.11	odd	6		294.8.a.v.1.3		3
21.17	even	6		294.8.a.w.1.1		3
21.20	even	2		294.8.e.ba.67.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.8.e.e.25.1	✓	6	3.2	odd	2
42.8.e.e.37.1	yes	6	21.2	odd	6
126.8.g.h.37.3		6	7.2	even	3	inner
126.8.g.h.109.3		6	1.1	even	1	trivial
294.8.a.v.1.3		3	21.11	odd	6
294.8.a.w.1.1		3	21.17	even	6
294.8.e.ba.67.3		6	21.20	even	2
294.8.e.ba.79.3		6	21.5	even	6

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)

\(f(q)\)	\(=\)	\(q+(-4.00000 - 6.92820i) q^{2} +(-32.0000 + 55.4256i) q^{4} +(99.3686 + 172.111i) q^{5} +(709.564 + 565.740i) q^{7} +512.000 q^{8} +(794.949 - 1376.89i) q^{10} +(-3946.05 + 6834.75i) q^{11} +10120.7 q^{13} +(1081.31 - 7178.96i) q^{14} +(-2048.00 - 3547.24i) q^{16} +(-4814.83 + 8339.53i) q^{17} +(-5120.94 - 8869.73i) q^{19} -12719.2 q^{20} +63136.8 q^{22} +(-23197.0 - 40178.4i) q^{23} +(19314.3 - 33453.3i) q^{25} +(-40482.9 - 70118.5i) q^{26} +(-54062.6 + 21224.3i) q^{28} -208906. q^{29} +(-118652. + 205512. i) q^{31} +(-16384.0 + 28377.9i) q^{32} +77037.3 q^{34} +(-26862.0 + 178341. i) q^{35} +(-162011. - 280611. i) q^{37} +(-40967.5 + 70957.9i) q^{38} +(50876.7 + 88121.0i) q^{40} +758284. q^{41} -558520. q^{43} +(-252547. - 437424. i) q^{44} +(-185576. + 321427. i) q^{46} +(134708. + 233321. i) q^{47} +(183419. + 802858. i) q^{49} -309028. q^{50} +(-323864. + 560948. i) q^{52} +(66909.5 - 115891. i) q^{53} -1.56845e6 q^{55} +(363297. + 289659. i) q^{56} +(835623. + 1.44734e6i) q^{58} +(-815863. + 1.41312e6i) q^{59} +(887949. + 1.53797e6i) q^{61} +1.89844e6 q^{62} +262144. q^{64} +(1.00568e6 + 1.74189e6i) q^{65} +(376991. - 652968. i) q^{67} +(-308149. - 533730. i) q^{68} +(1.34303e6 - 527258. i) q^{70} -1.44473e6 q^{71} +(-1.65487e6 + 2.86632e6i) q^{73} +(-1.29609e6 + 2.24489e6i) q^{74} +655481. q^{76} +(-6.66667e6 + 2.61726e6i) q^{77} +(3.31651e6 + 5.74437e6i) q^{79} +(407014. - 704968. i) q^{80} +(-3.03314e6 - 5.25354e6i) q^{82} -2.35482e6 q^{83} -1.91377e6 q^{85} +(2.23408e6 + 3.86954e6i) q^{86} +(-2.02038e6 + 3.49939e6i) q^{88} +(1.94917e6 + 3.37607e6i) q^{89} +(7.18131e6 + 5.72571e6i) q^{91} +2.96922e6 q^{92} +(1.07766e6 - 1.86657e6i) q^{94} +(1.01772e6 - 1.76275e6i) q^{95} -7.98505e6 q^{97} +(4.82869e6 - 4.48220e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 24 q^{2} - 192 q^{4} - 110 q^{5} + 635 q^{7} + 3072 q^{8} - 880 q^{10} + 548 q^{11} + 19898 q^{13} - 4568 q^{14} - 12288 q^{16} + 20972 q^{17} + 28383 q^{19} + 14080 q^{20} - 8768 q^{22} + 32732 q^{23}+ \cdots - 6110208 q^{98}+O(q^{100}) \) 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

Introduction

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