LMFDB - Embedded newform 162.10.c.l.55.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [162,10,Mod(55,162)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(162, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("162.55"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	162.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-32,0,-512,-912] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$83.4358054585$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{3329})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 833x^{2} + 832x + 692224 $ x^4 - x^3 + 833x^2 + 832x + 692224
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{6} $
Twist minimal:	no (minimal twist has level 54)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			55.1
Root			$-14.1744 - 24.5507i$ of defining polynomial
Character	$\chi$	$=$	162.55
Dual form			162.10.c.l.109.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-8.00000 + 13.8564i) q^{2} +(-128.000 - 221.703i) q^{4} +(-1006.92 - 1744.03i) q^{5} +(2282.58 - 3953.55i) q^{7} +4096.00 q^{8} +32221.3 q^{10} +(-34938.1 + 60514.6i) q^{11} +(-22806.3 - 39501.7i) q^{13} +(36521.3 + 63256.7i) q^{14} +(-32768.0 + 56755.8i) q^{16} -142743. q^{17} -759286. q^{19} +(-257771. + 446472. i) q^{20} +(-559010. - 968234. i) q^{22} +(-936881. - 1.62273e6i) q^{23} +(-1.05120e6 + 1.82073e6i) q^{25} +729802. q^{26} -1.16868e6 q^{28} +(-398681. + 690537. i) q^{29} +(-4.46571e6 - 7.73483e6i) q^{31} +(-524288. - 908093. i) q^{32} +(1.14194e6 - 1.97791e6i) q^{34} -9.19347e6 q^{35} +1.97984e7 q^{37} +(6.07429e6 - 1.05210e7i) q^{38} +(-4.12433e6 - 7.14355e6i) q^{40} +(9.60381e6 + 1.66343e7i) q^{41} +(-6.91208e6 + 1.19721e7i) q^{43} +1.78883e7 q^{44} +2.99802e7 q^{46} +(-1.40905e7 + 2.44054e7i) q^{47} +(9.75646e6 + 1.68987e7i) q^{49} +(-1.68192e7 - 2.91316e7i) q^{50} +(-5.83842e6 + 1.01124e7i) q^{52} -6.10387e7 q^{53} +1.40719e8 q^{55} +(9.34945e6 - 1.61937e7i) q^{56} +(-6.37890e6 - 1.10486e7i) q^{58} +(4.08905e7 + 7.08244e7i) q^{59} +(7.14068e7 - 1.23680e8i) q^{61} +1.42903e8 q^{62} +1.67772e7 q^{64} +(-4.59281e7 + 7.95498e7i) q^{65} +(-8.44061e7 - 1.46196e8i) q^{67} +(1.82711e7 + 3.16465e7i) q^{68} +(7.35477e7 - 1.27388e8i) q^{70} +1.12191e8 q^{71} -3.08721e8 q^{73} +(-1.58387e8 + 2.74335e8i) q^{74} +(9.71886e7 + 1.68336e8i) q^{76} +(1.59498e8 + 2.76259e8i) q^{77} +(1.61758e8 - 2.80173e8i) q^{79} +1.31979e8 q^{80} -3.07322e8 q^{82} +(2.67054e8 - 4.62551e8i) q^{83} +(1.43730e8 + 2.48948e8i) q^{85} +(-1.10593e8 - 1.91553e8i) q^{86} +(-1.43107e8 + 2.47868e8i) q^{88} -7.97823e8 q^{89} -2.08229e8 q^{91} +(-2.39842e8 + 4.15418e8i) q^{92} +(-2.25447e8 - 3.90486e8i) q^{94} +(7.64537e8 + 1.32422e9i) q^{95} +(3.21944e8 - 5.57624e8i) q^{97} -3.12207e8 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 32 q^{2} - 512 q^{4} - 912 q^{5} - 6448 q^{7} + 16384 q^{8} + 29184 q^{10} - 15126 q^{11} - 28912 q^{13} - 103168 q^{14} - 131072 q^{16} + 799920 q^{17} + 16208 q^{19} - 233472 q^{20} - 242016 q^{22}+ \cdots + 1965542016 q^{98}+O(q^{100}) $ 4 * q - 32 * q^2 - 512 * q^4 - 912 * q^5 - 6448 * q^7 + 16384 * q^8 + 29184 * q^10 - 15126 * q^11 - 28912 * q^13 - 103168 * q^14 - 131072 * q^16 + 799920 * q^17 + 16208 * q^19 - 233472 * q^20 - 242016 * q^22 - 2563572 * q^23 - 1363304 * q^25 + 925184 * q^26 + 3301376 * q^28 - 3059088 * q^29 - 16787920 * q^31 - 2097152 * q^32 - 6399360 * q^34 - 42656244 * q^35 + 69597368 * q^37 - 129664 * q^38 - 3735552 * q^40 + 24238968 * q^41 - 12599680 * q^43 + 7744512 * q^44 + 82034304 * q^46 + 19535772 * q^47 - 61423188 * q^49 - 21812864 * q^50 - 7401472 * q^52 + 25069824 * q^53 + 402089472 * q^55 - 26411008 * q^56 - 48945408 * q^58 + 140256744 * q^59 + 169724624 * q^61 + 537213440 * q^62 + 67108864 * q^64 - 110257512 * q^65 + 72241232 * q^67 - 102389760 * q^68 + 341249952 * q^70 - 107692560 * q^71 - 407115388 * q^73 - 556778944 * q^74 - 2074624 * q^76 + 921970176 * q^77 + 877964864 * q^79 + 119537664 * q^80 - 775646976 * q^82 + 111456714 * q^83 + 885428280 * q^85 - 201594880 * q^86 - 61956096 * q^88 - 2468521728 * q^89 - 784311824 * q^91 - 656274432 * q^92 + 312572352 * q^94 + 2374608756 * q^95 + 165265682 * q^97 + 1965542016 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−8.00000	+	13.8564i	−0.353553	+	0.612372i
$2$	−8.00000	+	13.8564i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−128.000	−	221.703i	−0.250000	−	0.433013i
$5$	−1006.92	−	1744.03i	−0.720490	−	1.24793i	−0.960803	−	0.277231i	$-0.910583\pi$
$5$	−1006.92	−	1744.03i	−0.720490	−	1.24793i	0.240313	−	0.970695i	$-0.422750\pi$
$6$		0			0
$7$	2282.58	−	3953.55i	0.359323	−	0.622366i	−0.628525	−	0.777789i	$-0.716341\pi$
$7$	2282.58	−	3953.55i	0.359323	−	0.622366i	0.987848	+	0.155424i	$0.0496743\pi$
$8$	4096.00			0.353553
$9$		0			0
$10$	32221.3			1.01893
$11$	−34938.1	+	60514.6i	−0.719503	+	1.24622i	0.241694	+	0.970353i	$0.422297\pi$
$11$	−34938.1	+	60514.6i	−0.719503	+	1.24622i	−0.961197	+	0.275863i	$0.911036\pi$
$12$		0			0
$13$	−22806.3	−	39501.7i	−0.221468	−	0.383593i	0.733786	−	0.679380i	$-0.237751\pi$
$13$	−22806.3	−	39501.7i	−0.221468	−	0.383593i	−0.955254	+	0.295787i	$0.904418\pi$
$14$	36521.3	+	63256.7i	0.254080	+	0.440079i
$15$		0			0
$16$	−32768.0	+	56755.8i	−0.125000	+	0.216506i
$17$	−142743.			−0.414510			−0.207255	−	0.978287i	$-0.566453\pi$
$17$	−142743.			−0.414510			−0.207255	+	0.978287i	$0.566453\pi$
$18$		0			0
$19$	−759286.			−1.33664			−0.668319	−	0.743874i	$-0.732986\pi$
$19$	−759286.			−1.33664			−0.668319	+	0.743874i	$0.732986\pi$
$20$	−257771.	+	446472.i	−0.360245	+	0.623963i
$21$		0			0
$22$	−559010.	−	968234.i	−0.508766	−	0.881208i
$23$	−936881.	−	1.62273e6i	−0.698086	−	1.20912i	−0.969129	−	0.246554i	$-0.920702\pi$
$23$	−936881.	−	1.62273e6i	−0.698086	−	1.20912i	0.271043	−	0.962567i	$-0.412632\pi$
$24$		0			0
$25$	−1.05120e6	+	1.82073e6i	−0.538213	+	0.932212i
$26$	729802.			0.313202
$27$		0			0
$28$	−1.16868e6			−0.359323
$29$	−398681.	+	690537.i	−0.104673	+	0.181299i	−0.913605	−	0.406604i	$-0.866713\pi$
$29$	−398681.	+	690537.i	−0.104673	+	0.181299i	0.808932	+	0.587903i	$0.200046\pi$
$30$		0			0
$31$	−4.46571e6	−	7.73483e6i	−0.868485	−	1.50426i	−0.863544	−	0.504273i	$-0.831761\pi$
$31$	−4.46571e6	−	7.73483e6i	−0.868485	−	1.50426i	−0.00494109	−	0.999988i	$-0.501573\pi$
$32$	−524288.	−	908093.i	−0.0883883	−	0.153093i
$33$		0			0
$34$	1.14194e6	−	1.97791e6i	0.146551	−	0.253834i
$35$	−9.19347e6			−1.03555
$36$		0			0
$37$	1.97984e7			1.73669			0.868345	−	0.495960i	$-0.165184\pi$
$37$	1.97984e7			1.73669			0.868345	+	0.495960i	$0.165184\pi$
$38$	6.07429e6	−	1.05210e7i	0.472573	−	0.818521i
$39$		0			0
$40$	−4.12433e6	−	7.14355e6i	−0.254732	−	0.441209i
$41$	9.60381e6	+	1.66343e7i	0.530782	+	0.919341i	0.999355	+	0.0359165i	$0.0114350\pi$
$41$	9.60381e6	+	1.66343e7i	0.530782	+	0.919341i	−0.468573	+	0.883425i	$0.655232\pi$
$42$		0			0
$43$	−6.91208e6	+	1.19721e7i	−0.308320	+	0.534025i	−0.977995	−	0.208629i	$-0.933100\pi$
$43$	−6.91208e6	+	1.19721e7i	−0.308320	+	0.534025i	0.669675	+	0.742654i	$0.266433\pi$
$44$	1.78883e7			0.719503
$45$		0			0
$46$	2.99802e7			0.987243
$47$	−1.40905e7	+	2.44054e7i	−0.421196	+	0.729533i	−0.996057	−	0.0887180i	$-0.971723\pi$
$47$	−1.40905e7	+	2.44054e7i	−0.421196	+	0.729533i	0.574860	+	0.818251i	$0.305056\pi$
$48$		0			0
$49$	9.75646e6	+	1.68987e7i	0.241774	+	0.418765i
$50$	−1.68192e7	−	2.91316e7i	−0.380574	−	0.659174i
$51$		0			0
$52$	−5.83842e6	+	1.01124e7i	−0.110734	+	0.191797i
$53$	−6.10387e7			−1.06259			−0.531293	−	0.847188i	$-0.678293\pi$
$53$	−6.10387e7			−1.06259			−0.531293	+	0.847188i	$0.678293\pi$
$54$		0			0
$55$	1.40719e8			2.07358
$56$	9.34945e6	−	1.61937e7i	0.127040	−	0.220039i
$57$		0			0
$58$	−6.37890e6	−	1.10486e7i	−0.0740150	−	0.128198i
$59$	4.08905e7	+	7.08244e7i	0.439327	+	0.760937i	0.997638	−	0.0686950i	$-0.0218835\pi$
$59$	4.08905e7	+	7.08244e7i	0.439327	+	0.760937i	−0.558310	+	0.829632i	$0.688550\pi$
$60$		0			0
$61$	7.14068e7	−	1.23680e8i	0.660322	−	1.14371i	−0.320209	−	0.947347i	$-0.603753\pi$
$61$	7.14068e7	−	1.23680e8i	0.660322	−	1.14371i	0.980531	−	0.196364i	$-0.0629134\pi$
$62$	1.42903e8			1.22822
$63$		0			0
$64$	1.67772e7			0.125000
$65$	−4.59281e7	+	7.95498e7i	−0.319131	+	0.552750i
$66$		0			0
$67$	−8.44061e7	−	1.46196e8i	−0.511726	−	0.886335i	−0.999908	−	0.0135930i	$-0.995673\pi$
$67$	−8.44061e7	−	1.46196e8i	−0.511726	−	0.886335i	0.488182	−	0.872742i	$-0.337660\pi$
$68$	1.82711e7	+	3.16465e7i	0.103627	+	0.179488i
$69$		0			0
$70$	7.35477e7	−	1.27388e8i	0.366124	−	0.634145i
$71$	1.12191e8			0.523958			0.261979	−	0.965074i	$-0.415625\pi$
$71$	1.12191e8			0.523958			0.261979	+	0.965074i	$0.415625\pi$
$72$		0			0
$73$	−3.08721e8			−1.27237			−0.636185	−	0.771536i	$-0.719489\pi$
$73$	−3.08721e8			−1.27237			−0.636185	+	0.771536i	$0.719489\pi$
$74$	−1.58387e8	+	2.74335e8i	−0.614013	+	1.06350i
$75$		0			0
$76$	9.71886e7	+	1.68336e8i	0.334160	+	0.578782i
$77$	1.59498e8	+	2.76259e8i	0.517068	+	0.895588i
$78$		0			0
$79$	1.61758e8	−	2.80173e8i	0.467244	−	0.809290i	−0.532056	−	0.846709i	$-0.678580\pi$
$79$	1.61758e8	−	2.80173e8i	0.467244	−	0.809290i	0.999300	+	0.0374190i	$0.0119136\pi$
$80$	1.31979e8			0.360245
$81$		0			0
$82$	−3.07322e8			−0.750639
$83$	2.67054e8	−	4.62551e8i	0.617657	−	1.06981i	−0.372255	−	0.928130i	$-0.621415\pi$
$83$	2.67054e8	−	4.62551e8i	0.617657	−	1.06981i	0.989912	−	0.141683i	$-0.0452512\pi$
$84$		0			0
$85$	1.43730e8	+	2.48948e8i	0.298650	+	0.517278i
$86$	−1.10593e8	−	1.91553e8i	−0.218015	−	0.377613i
$87$		0			0
$88$	−1.43107e8	+	2.47868e8i	−0.254383	+	0.440604i
$89$	−7.97823e8			−1.34788			−0.673941	−	0.738785i	$-0.735400\pi$
$89$	−7.97823e8			−1.34788			−0.673941	+	0.738785i	$0.735400\pi$
$90$		0			0
$91$	−2.08229e8			−0.318313
$92$	−2.39842e8	+	4.15418e8i	−0.349043	+	0.604561i
$93$		0			0
$94$	−2.25447e8	−	3.90486e8i	−0.297831	−	0.515858i
$95$	7.64537e8	+	1.32422e9i	0.963036	+	1.66803i
$96$		0			0
$97$	3.21944e8	−	5.57624e8i	0.369239	−	0.639541i	−0.620207	−	0.784438i	$-0.712952\pi$
$97$	3.21944e8	−	5.57624e8i	0.369239	−	0.639541i	0.989447	+	0.144897i	$0.0462849\pi$
$98$	−3.12207e8			−0.341920
$99$		0			0
$100$	5.38213e8			0.538213
$101$	−6.90263e8	+	1.19557e9i	−0.660038	+	1.14322i	0.320568	+	0.947226i	$0.396126\pi$
$101$	−6.90263e8	+	1.19557e9i	−0.660038	+	1.14322i	−0.980605	+	0.195993i	$0.937207\pi$
$102$		0			0
$103$	8.31574e8	+	1.44033e9i	0.728003	+	1.26094i	0.957726	+	0.287683i	$0.0928848\pi$
$103$	8.31574e8	+	1.44033e9i	0.728003	+	1.26094i	−0.229722	+	0.973256i	$0.573782\pi$
$104$	−9.34147e7	−	1.61799e8i	−0.0783006	−	0.135621i
$105$		0			0
$106$	4.88309e8	−	8.45777e8i	0.375681	−	0.650698i
$107$	1.55743e9			1.14864			0.574318	−	0.818632i	$-0.305267\pi$
$107$	1.55743e9			1.14864			0.574318	+	0.818632i	$0.305267\pi$
$108$		0			0
$109$	1.76222e9			1.19575			0.597877	−	0.801588i	$-0.296011\pi$
$109$	1.76222e9			1.19575			0.597877	+	0.801588i	$0.296011\pi$
$110$	−1.12575e9	+	1.94986e9i	−0.733122	+	1.26980i
$111$		0			0
$112$	1.49591e8	+	2.59100e8i	0.0898307	+	0.155591i
$113$	9.14978e8	+	1.58479e9i	0.527907	+	0.914362i	0.999471	+	0.0325298i	$0.0103564\pi$
$113$	9.14978e8	+	1.58479e9i	0.527907	+	0.914362i	−0.471564	+	0.881832i	$0.656310\pi$
$114$		0			0
$115$	−1.88672e9	+	3.26790e9i	−1.00593	+	1.74232i
$116$	2.04125e8			0.104673
$117$		0			0
$118$	−1.30850e9			−0.621303
$119$	−3.25823e8	+	5.64341e8i	−0.148943	+	0.257977i
$120$		0			0
$121$	−1.26237e9	−	2.18650e9i	−0.535370	−	0.927288i
$122$	1.14251e9	+	1.97888e9i	0.466918	+	0.808726i
$123$		0			0
$124$	−1.14322e9	+	1.98012e9i	−0.434243	+	0.752130i
$125$	3.00605e8			0.110129
$126$		0			0
$127$	−1.41081e9			−0.481228			−0.240614	−	0.970621i	$-0.577349\pi$
$127$	−1.41081e9			−0.481228			−0.240614	+	0.970621i	$0.577349\pi$
$128$	−1.34218e8	+	2.32472e8i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−7.34850e8	−	1.27280e9i	−0.225659	−	0.390854i
$131$	1.43902e9	+	2.49246e9i	0.426920	+	0.739447i	0.996598	−	0.0824213i	$-0.0262653\pi$
$131$	1.43902e9	+	2.49246e9i	0.426920	+	0.739447i	−0.569678	+	0.821868i	$0.692932\pi$
$132$		0			0
$133$	−1.73313e9	+	3.00187e9i	−0.480285	+	0.831878i
$134$	2.70100e9			0.723689
$135$		0			0
$136$	−5.84676e8			−0.146551
$137$	−2.00235e9	+	3.46818e9i	−0.485622	+	0.841122i	−0.999863	−	0.0165235i	$-0.994740\pi$
$137$	−2.00235e9	+	3.46818e9i	−0.485622	+	0.841122i	0.514242	+	0.857645i	$0.328073\pi$
$138$		0			0
$139$	−9.28631e8	−	1.60844e9i	−0.210997	−	0.365458i	0.741030	−	0.671472i	$-0.234338\pi$
$139$	−9.28631e8	−	1.60844e9i	−0.210997	−	0.365458i	−0.952027	+	0.306014i	$0.901004\pi$
$140$	1.17676e9	+	2.03821e9i	0.258889	+	0.448408i
$141$		0			0
$142$	−8.97530e8	+	1.55457e9i	−0.185247	+	0.320857i
$143$	3.18724e9			0.637387
$144$		0			0
$145$	1.60576e9			0.301664
$146$	2.46977e9	−	4.27777e9i	0.449851	−	0.779165i
$147$		0			0
$148$	−2.53420e9	−	4.38936e9i	−0.434173	−	0.752009i
$149$	3.47194e9	+	6.01358e9i	0.577077	+	0.999527i	0.995813	+	0.0914189i	$0.0291402\pi$
$149$	3.47194e9	+	6.01358e9i	0.577077	+	0.999527i	−0.418735	+	0.908108i	$0.637526\pi$
$150$		0			0
$151$	2.51936e9	−	4.36366e9i	0.394361	−	0.683053i	−0.598659	−	0.801004i	$-0.704299\pi$
$151$	2.51936e9	−	4.36366e9i	0.394361	−	0.683053i	0.993019	+	0.117951i	$0.0376327\pi$
$152$	−3.11003e9			−0.472573
$153$		0			0
$154$	−5.10394e9			−0.731245
$155$	−8.99318e9	+	1.55766e10i	−1.25147	+	2.16761i
$156$		0			0
$157$	2.43125e9	+	4.21104e9i	0.319360	+	0.553147i	0.980355	−	0.197243i	$-0.0631988\pi$
$157$	2.43125e9	+	4.21104e9i	0.319360	+	0.553147i	−0.660995	+	0.750390i	$0.729865\pi$
$158$	2.58813e9	+	4.48277e9i	0.330391	+	0.572255i
$159$		0			0
$160$	−1.05583e9	+	1.82875e9i	−0.127366	+	0.220604i
$161$	−8.55403e9			−1.00335
$162$		0			0
$163$	−5.20600e9			−0.577644			−0.288822	−	0.957383i	$-0.593264\pi$
$163$	−5.20600e9			−0.577644			−0.288822	+	0.957383i	$0.593264\pi$
$164$	2.45858e9	−	4.25838e9i	0.265391	−	0.459671i
$165$		0			0
$166$	4.27286e9	+	7.40081e9i	0.436749	+	0.756472i
$167$	5.23759e9	+	9.07177e9i	0.521083	+	0.902543i	0.999699	+	0.0245187i	$0.00780532\pi$
$167$	5.23759e9	+	9.07177e9i	0.521083	+	0.902543i	−0.478616	+	0.878024i	$0.658861\pi$
$168$		0			0
$169$	4.26199e9	−	7.38199e9i	0.401904	−	0.696119i
$170$	−4.59937e9			−0.422355
$171$		0			0
$172$	3.53899e9			0.308320
$173$	−2.85883e9	+	4.95164e9i	−0.242650	+	0.420283i	−0.961468	−	0.274916i	$-0.911350\pi$
$173$	−2.85883e9	+	4.95164e9i	−0.242650	+	0.420283i	0.718818	+	0.695198i	$0.244683\pi$
$174$		0			0
$175$	4.79889e9	+	8.31191e9i	0.386785	+	0.669931i
$176$	−2.28971e9	−	3.96589e9i	−0.179876	−	0.311554i
$177$		0			0
$178$	6.38259e9	−	1.10550e10i	0.476548	−	0.825406i
$179$	1.76705e10			1.28650			0.643249	−	0.765657i	$-0.277586\pi$
$179$	1.76705e10			1.28650			0.643249	+	0.765657i	$0.277586\pi$
$180$		0			0
$181$	2.45903e10			1.70298			0.851492	−	0.524368i	$-0.175698\pi$
$181$	2.45903e10			1.70298			0.851492	+	0.524368i	$0.175698\pi$
$182$	1.66583e9	−	2.88531e9i	0.112541	−	0.194926i
$183$		0			0
$184$	−3.83747e9	−	6.64668e9i	−0.246811	−	0.427489i
$185$	−1.99353e10	−	3.45290e10i	−1.25127	−	2.16726i
$186$		0			0
$187$	4.98718e9	−	8.63805e9i	0.298241	−	0.516569i
$188$	7.21431e9			0.421196
$189$		0			0
$190$	−2.44652e10			−1.36194
$191$	1.23175e9	−	2.13346e9i	0.0669688	−	0.115993i	−0.830597	−	0.556874i	$-0.812001\pi$
$191$	1.23175e9	−	2.13346e9i	0.0669688	−	0.115993i	0.897566	+	0.440881i	$0.145334\pi$
$192$		0			0
$193$	1.69591e10	+	2.93740e10i	0.879821	+	1.52389i	0.851537	+	0.524295i	$0.175671\pi$
$193$	1.69591e10	+	2.93740e10i	0.879821	+	1.52389i	0.0282845	+	0.999600i	$0.490996\pi$
$194$	5.15111e9	+	8.92198e9i	0.261092	+	0.452224i
$195$		0			0
$196$	2.49765e9	−	4.32606e9i	0.120887	−	0.209383i
$197$	−4.87423e9			−0.230573			−0.115286	−	0.993332i	$-0.536779\pi$
$197$	−4.87423e9			−0.230573			−0.115286	+	0.993332i	$0.536779\pi$
$198$		0			0
$199$	3.53697e10			1.59879			0.799397	−	0.600804i	$-0.205153\pi$
$199$	3.53697e10			1.59879			0.799397	+	0.600804i	$0.205153\pi$
$200$	−4.30570e9	+	7.45770e9i	−0.190287	+	0.329587i
$201$		0			0
$202$	−1.10442e10	−	1.91291e10i	−0.466717	−	0.808378i
$203$	1.82004e9	+	3.15241e9i	0.0752229	+	0.130290i
$204$		0			0
$205$	1.93405e10	−	3.34987e10i	0.764847	−	1.32475i
$206$	−2.66104e10			−1.02955
$207$		0			0
$208$	2.98927e9			0.110734
$209$	2.65280e10	−	4.59479e10i	0.961716	−	1.66574i
$210$		0			0
$211$	−1.01964e9	−	1.76607e9i	−0.0354141	−	0.0613390i	0.847775	−	0.530356i	$-0.177942\pi$
$211$	−1.01964e9	−	1.76607e9i	−0.0354141	−	0.0613390i	−0.883189	+	0.469017i	$0.844608\pi$
$212$	7.81295e9	+	1.35324e10i	0.265646	+	0.460113i
$213$		0			0
$214$	−1.24595e10	+	2.15804e10i	−0.406104	+	0.703393i
$215$	2.78396e10			0.888565
$216$		0			0
$217$	−4.07733e10			−1.24827
$218$	−1.40978e10	+	2.44181e10i	−0.422763	+	0.732247i
$219$		0			0
$220$	−1.80120e10	−	3.11978e10i	−0.518395	−	0.897887i
$221$	3.25544e9	+	5.63860e9i	0.0918005	+	0.159003i
$222$		0			0
$223$	−3.17176e10	+	5.49365e10i	−0.858872	+	1.48761i	0.0141339	+	0.999900i	$0.495501\pi$
$223$	−3.17176e10	+	5.49365e10i	−0.858872	+	1.48761i	−0.873006	+	0.487710i	$0.837832\pi$
$224$	−4.78692e9			−0.127040
$225$		0			0
$226$	−2.92793e10			−0.746573
$227$	1.55854e10	−	2.69947e10i	0.389584	−	0.674779i	−0.602810	−	0.797885i	$-0.705952\pi$
$227$	1.55854e10	−	2.69947e10i	0.389584	−	0.674779i	0.992394	+	0.123106i	$0.0392855\pi$
$228$		0			0
$229$	−3.12529e10	−	5.41316e10i	−0.750983	−	1.30074i	−0.947346	−	0.320210i	$-0.896246\pi$
$229$	−3.12529e10	−	5.41316e10i	−0.750983	−	1.30074i	0.196363	−	0.980531i	$-0.437087\pi$
$230$	−3.01875e10	−	5.22864e10i	−0.711299	−	1.23201i
$231$		0			0
$232$	−1.63300e9	+	2.82844e9i	−0.0370075	+	0.0640989i
$233$	−6.62666e10			−1.47297			−0.736483	−	0.676456i	$-0.763515\pi$
$233$	−6.62666e10			−1.47297			−0.736483	+	0.676456i	$0.763515\pi$
$234$		0			0
$235$	5.67516e10			1.21387
$236$	1.04680e10	−	1.81310e10i	0.219664	−	0.380469i
$237$		0			0
$238$	−5.21316e9	−	9.02946e9i	−0.105319	−	0.182417i
$239$	−2.09479e10	−	3.62829e10i	−0.415289	−	0.719302i	0.580170	−	0.814496i	$-0.302986\pi$
$239$	−2.09479e10	−	3.62829e10i	−0.415289	−	0.719302i	−0.995459	+	0.0951940i	$0.969653\pi$
$240$		0			0
$241$	−2.41413e10	+	4.18139e10i	−0.460982	+	0.798443i	−0.999010	−	0.0444831i	$-0.985836\pi$
$241$	−2.41413e10	+	4.18139e10i	−0.460982	+	0.798443i	0.538029	+	0.842927i	$0.319169\pi$
$242$	4.03960e10			0.757127
$243$		0			0
$244$	−3.65603e10			−0.660322
$245$	1.96479e10	−	3.40311e10i	0.348392	−	0.603432i
$246$		0			0
$247$	1.73165e10	+	2.99931e10i	0.296022	+	0.512725i
$248$	−1.82915e10	−	3.16819e10i	−0.307056	−	0.531837i
$249$		0			0
$250$	−2.40484e9	+	4.16530e9i	−0.0389364	+	0.0674398i
$251$	3.68932e10			0.586699			0.293349	−	0.956005i	$-0.405230\pi$
$251$	3.68932e10			0.586699			0.293349	+	0.956005i	$0.405230\pi$
$252$		0			0
$253$	1.30932e11			2.00910
$254$	1.12864e10	−	1.95487e10i	0.170140	−	0.294691i
$255$		0			0
$256$	−2.14748e9	−	3.71955e9i	−0.0312500	−	0.0541266i
$257$	−1.04030e10	−	1.80186e10i	−0.148751	−	0.257645i	0.782015	−	0.623260i	$-0.214192\pi$
$257$	−1.04030e10	−	1.80186e10i	−0.148751	−	0.257645i	−0.930766	+	0.365615i	$0.880859\pi$
$258$		0			0
$259$	4.51914e10	−	7.82739e10i	0.624033	−	1.08086i
$260$	2.35152e10			0.319131
$261$		0			0
$262$	−4.60487e10			−0.603756
$263$	3.76669e10	−	6.52410e10i	0.485467	−	0.840853i	−0.514394	−	0.857554i	$-0.671983\pi$
$263$	3.76669e10	−	6.52410e10i	0.485467	−	0.840853i	0.999861	+	0.0167013i	$0.00531643\pi$
$264$		0			0
$265$	6.14608e10	+	1.06453e11i	0.765582	+	1.32603i
$266$	−2.77301e10	−	4.80299e10i	−0.339613	−	0.588226i
$267$		0			0
$268$	−2.16080e10	+	3.74261e10i	−0.255863	+	0.443167i
$269$	−1.50056e11			−1.74730			−0.873650	−	0.486554i	$-0.838254\pi$
$269$	−1.50056e11			−1.74730			−0.873650	+	0.486554i	$0.838254\pi$
$270$		0			0
$271$	−1.87348e10			−0.211003			−0.105501	−	0.994419i	$-0.533645\pi$
$271$	−1.87348e10			−0.211003			−0.105501	+	0.994419i	$0.533645\pi$
$272$	4.67740e9	−	8.10150e9i	0.0518137	−	0.0897440i
$273$		0			0
$274$	−3.20377e10	−	5.54909e10i	−0.343387	−	0.594763i
$275$	−7.34538e10	−	1.27226e11i	−0.774492	−	1.34146i
$276$		0			0
$277$	−6.64283e10	+	1.15057e11i	−0.677945	+	1.17423i	0.297654	+	0.954674i	$0.403796\pi$
$277$	−6.64283e10	+	1.15057e11i	−0.677945	+	1.17423i	−0.975599	+	0.219561i	$0.929538\pi$
$278$	2.97162e10			0.298395
$279$		0			0
$280$	−3.76564e10			−0.366124
$281$	2.58872e7	−	4.48380e7i	0.000247689	−	0.000429011i	−0.865902	−	0.500214i	$-0.833254\pi$
$281$	2.58872e7	−	4.48380e7i	0.000247689	−	0.000429011i	0.866149	+	0.499785i	$0.166588\pi$
$282$		0			0
$283$	6.12757e10	+	1.06133e11i	0.567870	+	0.983580i	0.996776	+	0.0802311i	$0.0255658\pi$
$283$	6.12757e10	+	1.06133e11i	0.567870	+	0.983580i	−0.428906	+	0.903349i	$0.641101\pi$
$284$	−1.43605e10	−	2.48731e10i	−0.130990	−	0.226880i
$285$		0			0
$286$	−2.54979e10	+	4.41637e10i	−0.225350	+	0.390318i
$287$	8.76859e10			0.762889
$288$		0			0
$289$	−9.82123e10			−0.828182
$290$	−1.28460e10	+	2.22500e10i	−0.106654	+	0.184731i
$291$		0			0
$292$	3.95163e10	+	6.84443e10i	0.318093	+	0.550953i
$293$	1.98069e10	+	3.43066e10i	0.157005	+	0.271940i	0.933787	−	0.357829i	$-0.116483\pi$
$293$	1.98069e10	+	3.43066e10i	0.157005	+	0.271940i	−0.776783	+	0.629769i	$0.783150\pi$
$294$		0			0
$295$	8.23466e10	−	1.42628e11i	0.633062	−	1.09650i
$296$	8.10943e10			0.614013
$297$		0			0
$298$	−1.11102e11			−0.816111
$299$	−4.27336e10	+	7.40168e10i	−0.309207	+	0.535562i
$300$		0			0
$301$	3.15548e10	+	5.46545e10i	0.221573	+	0.383775i
$302$	4.03097e10	+	6.98185e10i	0.278855	+	0.482991i
$303$		0			0
$304$	2.48803e10	−	4.30939e10i	0.167080	−	0.289391i
$305$	−2.87603e11			−1.90302
$306$		0			0
$307$	−3.98499e10			−0.256038			−0.128019	−	0.991772i	$-0.540862\pi$
$307$	−3.98499e10			−0.256038			−0.128019	+	0.991772i	$0.540862\pi$
$308$	4.08315e10	−	7.07223e10i	0.258534	−	0.447794i
$309$		0			0
$310$	−1.43891e11	−	2.49226e11i	−0.884924	−	1.53273i
$311$	2.19109e10	+	3.79507e10i	0.132812	+	0.230037i	0.924760	−	0.380552i	$-0.124266\pi$
$311$	2.19109e10	+	3.79507e10i	0.132812	+	0.230037i	−0.791947	+	0.610589i	$0.790933\pi$
$312$		0			0
$313$	4.72413e10	−	8.18244e10i	0.278210	−	0.481874i	−0.692730	−	0.721197i	$-0.743592\pi$
$313$	4.72413e10	−	8.18244e10i	0.278210	−	0.481874i	0.970940	+	0.239323i	$0.0769256\pi$
$314$	−7.77998e10			−0.451643
$315$		0			0
$316$	−8.28201e10			−0.467244
$317$	9.69797e10	−	1.67974e11i	0.539404	−	0.934275i	−0.459532	−	0.888161i	$-0.651983\pi$
$317$	9.69797e10	−	1.67974e11i	0.539404	−	0.934275i	0.998936	−	0.0461138i	$-0.0146837\pi$
$318$		0			0
$319$	−2.78584e10	−	4.82521e10i	−0.150625	−	0.260891i
$320$	−1.68932e10	−	2.92600e10i	−0.0900613	−	0.155991i
$321$		0			0
$322$	6.84322e10	−	1.18528e11i	0.354739	−	0.614426i
$323$	1.08383e11			0.554050
$324$		0			0
$325$	9.58958e10			0.476787
$326$	4.16480e10	−	7.21365e10i	0.204228	−	0.353733i
$327$		0			0
$328$	3.93372e10	+	6.81340e10i	0.187660	+	0.325036i
$329$	6.43252e10	+	1.11414e11i	0.302691	+	0.524276i
$330$		0			0
$331$	−2.99808e10	+	5.19283e10i	−0.137283	+	0.237782i	−0.926467	−	0.376375i	$-0.877170\pi$
$331$	−2.99808e10	+	5.19283e10i	−0.137283	+	0.237782i	0.789184	+	0.614157i	$0.210504\pi$
$332$	−1.36732e11			−0.617657
$333$		0			0
$334$	−1.67603e11			−0.736923
$335$	−1.69980e11	+	2.94414e11i	−0.737387	+	1.27719i
$336$		0			0
$337$	5.19827e10	+	9.00366e10i	0.219545	+	0.380264i	0.954669	−	0.297669i	$-0.0962093\pi$
$337$	5.19827e10	+	9.00366e10i	0.219545	+	0.380264i	−0.735124	+	0.677933i	$0.762876\pi$
$338$	6.81919e10	+	1.18112e11i	0.284189	+	0.492230i
$339$		0			0
$340$	3.67950e10	−	6.37307e10i	0.149325	−	0.258639i
$341$	6.24094e11			2.49951
$342$		0			0
$343$	2.73300e11			1.06615
$344$	−2.83119e10	+	4.90376e10i	−0.109007	+	0.188806i
$345$		0			0
$346$	−4.57413e10	−	7.92262e10i	−0.171580	−	0.297185i
$347$	−4.78480e10	−	8.28751e10i	−0.177166	−	0.306861i	0.763743	−	0.645521i	$-0.223360\pi$
$347$	−4.78480e10	−	8.28751e10i	−0.177166	−	0.306861i	−0.940909	+	0.338660i	$0.890026\pi$
$348$		0			0
$349$	−1.60443e10	+	2.77895e10i	−0.0578903	+	0.100269i	−0.893518	−	0.449027i	$-0.851771\pi$
$349$	−1.60443e10	+	2.77895e10i	−0.0578903	+	0.100269i	0.835628	+	0.549296i	$0.185104\pi$
$350$	−1.53564e11			−0.546996
$351$		0			0
$352$	7.32706e10			0.254383
$353$	−1.10681e11	+	1.91706e11i	−0.379392	+	0.657126i	−0.990974	−	0.134055i	$-0.957200\pi$
$353$	−1.10681e11	+	1.91706e11i	−0.379392	+	0.657126i	0.611582	+	0.791181i	$0.290533\pi$
$354$		0			0
$355$	−1.12967e11	−	1.95665e11i	−0.377507	−	0.653861i
$356$	1.02121e11	+	1.76879e11i	0.336970	+	0.583650i
$357$		0			0
$358$	−1.41364e11	+	2.44849e11i	−0.454846	+	0.787816i
$359$	2.52052e11			0.800874			0.400437	−	0.916324i	$-0.368858\pi$
$359$	2.52052e11			0.800874			0.400437	+	0.916324i	$0.368858\pi$
$360$		0			0
$361$	2.53827e11			0.786603
$362$	−1.96722e11	+	3.40733e11i	−0.602095	+	1.04286i
$363$		0			0
$364$	2.66533e10	+	4.61649e10i	0.0795784	+	0.137834i
$365$	3.10856e11	+	5.38419e11i	0.916731	+	1.58782i
$366$		0			0
$367$	−3.61273e10	+	6.25744e10i	−0.103953	+	0.180053i	−0.913310	−	0.407265i	$-0.866483\pi$
$367$	−3.61273e10	+	6.25744e10i	−0.103953	+	0.180053i	0.809357	+	0.587317i	$0.199816\pi$
$368$	1.22799e11			0.349043
$369$		0			0
$370$	6.37931e11			1.76956
$371$	−1.39326e11	+	2.41319e11i	−0.381811	+	0.661316i
$372$		0			0
$373$	−2.39177e10	−	4.14266e10i	−0.0639778	−	0.110813i	0.832262	−	0.554382i	$-0.187045\pi$
$373$	−2.39177e10	−	4.14266e10i	−0.0639778	−	0.110813i	−0.896240	+	0.443569i	$0.853712\pi$
$374$	7.97948e10	+	1.38209e11i	0.210888	+	0.365269i
$375$		0			0
$376$	−5.77145e10	+	9.99644e10i	−0.148915	+	0.257929i
$377$	3.63698e10			0.0927268
$378$		0			0
$379$	5.03865e11			1.25440			0.627202	−	0.778857i	$-0.284200\pi$
$379$	5.03865e11			1.25440			0.627202	+	0.778857i	$0.284200\pi$
$380$	1.95721e11	−	3.39000e11i	0.481518	−	0.834013i
$381$		0			0
$382$	1.97080e10	+	3.41353e10i	0.0473541	+	0.0820197i
$383$	−2.89438e11	−	5.01321e11i	−0.687322	−	1.19048i	−0.972701	−	0.232062i	$-0.925453\pi$
$383$	−2.89438e11	−	5.01321e11i	−0.687322	−	1.19048i	0.285379	−	0.958415i	$-0.407881\pi$
$384$		0			0
$385$	3.21203e11	−	5.56339e11i	0.745085	−	1.29053i
$386$	−5.42691e11			−1.24426
$387$		0			0
$388$	−1.64835e11			−0.369239
$389$	2.40990e11	−	4.17406e11i	0.533611	−	0.924242i	−0.465618	−	0.884986i	$-0.654168\pi$
$389$	2.40990e11	−	4.17406e11i	0.533611	−	0.924242i	0.999229	−	0.0392560i	$-0.0124988\pi$
$390$		0			0
$391$	1.33733e11	+	2.31633e11i	0.289364	+	0.501193i
$392$	3.99624e10	+	6.92170e10i	0.0854801	+	0.148056i
$393$		0			0
$394$	3.89938e10	−	6.75393e10i	0.0815197	−	0.141196i
$395$	−6.51507e11			−1.34658
$396$		0			0
$397$	5.02870e10			0.101601			0.0508006	−	0.998709i	$-0.483823\pi$
$397$	5.02870e10			0.101601			0.0508006	+	0.998709i	$0.483823\pi$
$398$	−2.82957e11	+	4.90097e11i	−0.565259	+	0.979057i
$399$		0			0
$400$	−6.88913e10	−	1.19323e11i	−0.134553	−	0.233053i
$401$	3.05197e11	+	5.28617e11i	0.589429	+	1.02092i	0.994307	+	0.106550i	$0.0339804\pi$
$401$	3.05197e11	+	5.28617e11i	0.589429	+	1.02092i	−0.404879	+	0.914370i	$0.632686\pi$
$402$		0			0
$403$	−2.03693e11	+	3.52806e11i	−0.384683	+	0.666290i
$404$	3.53415e11			0.660038
$405$		0			0
$406$	−5.82414e10			−0.106381
$407$	−6.91719e11	+	1.19809e12i	−1.24955	+	2.16429i
$408$		0			0
$409$	−3.72674e11	−	6.45491e11i	−0.658529	−	1.14061i	−0.980997	−	0.194025i	$-0.937846\pi$
$409$	−3.72674e11	−	6.45491e11i	−0.658529	−	1.14061i	0.322468	−	0.946580i	$-0.395488\pi$
$410$	3.09447e11	+	5.35979e11i	0.540828	+	0.936742i
$411$		0			0
$412$	2.12883e11	−	3.68724e11i	0.364002	−	0.630469i
$413$	3.73343e11			0.631441
$414$		0			0
$415$	−1.07560e12			−1.78006
$416$	−2.39142e10	+	4.14205e10i	−0.0391503	+	0.0678103i
$417$		0			0
$418$	4.24449e11	+	7.35166e11i	0.680036	+	1.17786i
$419$	1.48142e10	+	2.56590e10i	0.0234809	+	0.0406702i	0.877527	−	0.479527i	$-0.159192\pi$
$419$	1.48142e10	+	2.56590e10i	0.0234809	+	0.0406702i	−0.854046	+	0.520197i	$0.825858\pi$
$420$		0			0
$421$	−2.70046e11	+	4.67733e11i	−0.418955	+	0.725652i	−0.995835	−	0.0911777i	$-0.970937\pi$
$421$	−2.70046e11	+	4.67733e11i	−0.418955	+	0.725652i	0.576879	+	0.816829i	$0.304270\pi$
$422$	3.26285e10			0.0500831
$423$		0			0
$424$	−2.50014e11			−0.375681
$425$	1.50051e11	−	2.59896e11i	0.223095	−	0.386411i
$426$		0			0
$427$	−3.25984e11	−	5.64620e11i	−0.474537	−	0.821923i
$428$	−1.99351e11	−	3.45287e11i	−0.287159	−	0.497374i
$429$		0			0
$430$	−2.22716e11	+	3.85756e11i	−0.314155	+	0.544133i
$431$	−5.69766e11			−0.795333			−0.397666	−	0.917530i	$-0.630180\pi$
$431$	−5.69766e11			−0.795333			−0.397666	+	0.917530i	$0.630180\pi$
$432$		0			0
$433$	−1.15909e12			−1.58460			−0.792301	−	0.610131i	$-0.791117\pi$
$433$	−1.15909e12			−1.58460			−0.792301	+	0.610131i	$0.791117\pi$
$434$	3.26187e11	−	5.64972e11i	0.441329	−	0.764404i
$435$		0			0
$436$	−2.25565e11	−	3.90689e11i	−0.298938	−	0.517777i
$437$	7.11360e11	+	1.23211e12i	0.933089	+	1.61616i
$438$		0			0
$439$	−4.39268e10	+	7.60834e10i	−0.0564467	+	0.0977686i	−0.892868	−	0.450319i	$-0.851310\pi$
$439$	−4.39268e10	+	7.60834e10i	−0.0564467	+	0.0977686i	0.836421	+	0.548087i	$0.184644\pi$
$440$	5.76385e11			0.733122
$441$		0			0
$442$	−1.04174e11			−0.129826
$443$	−9.88616e9	+	1.71233e10i	−0.0121958	+	0.0211238i	−0.872059	−	0.489401i	$-0.837215\pi$
$443$	−9.88616e9	+	1.71233e10i	−0.0121958	+	0.0211238i	0.859863	+	0.510525i	$0.170549\pi$
$444$		0			0
$445$	8.03341e11	+	1.39143e12i	0.971136	+	1.68206i
$446$	−5.07482e11	−	8.78984e11i	−0.607314	−	1.05190i
$447$		0			0
$448$	3.82953e10	−	6.63295e10i	0.0449154	−	0.0777957i
$449$	−4.74948e11			−0.551490			−0.275745	−	0.961231i	$-0.588925\pi$
$449$	−4.74948e11			−0.551490			−0.275745	+	0.961231i	$0.588925\pi$
$450$		0			0
$451$	−1.34216e12			−1.52760
$452$	2.34234e11	−	4.05706e11i	0.263954	−	0.457181i
$453$		0			0
$454$	2.49366e11	+	4.31915e11i	0.275477	+	0.477141i
$455$	2.09669e11	+	3.63158e11i	0.229342	+	0.397232i
$456$		0			0
$457$	−4.13907e11	+	7.16908e11i	−0.443895	+	0.768848i	−0.997974	−	0.0636154i	$-0.979737\pi$
$457$	−4.13907e11	+	7.16908e11i	−0.443895	+	0.768848i	0.554080	+	0.832464i	$0.313070\pi$
$458$	1.00009e12			1.06205
$459$		0			0
$460$	9.66001e11			1.00593
$461$	−2.13021e11	+	3.68963e11i	−0.219669	+	0.380477i	−0.954707	−	0.297549i	$-0.903831\pi$
$461$	−2.13021e11	+	3.68963e11i	−0.219669	+	0.380477i	0.735038	+	0.678026i	$0.237164\pi$
$462$		0			0
$463$	−4.58672e10	−	7.94444e10i	−0.0463861	−	0.0803431i	0.841900	−	0.539633i	$-0.181437\pi$
$463$	−4.58672e10	−	7.94444e10i	−0.0463861	−	0.0803431i	−0.888286	+	0.459290i	$0.848104\pi$
$464$	−2.61280e10	−	4.52550e10i	−0.0261683	−	0.0453248i
$465$		0			0
$466$	5.30133e11	−	9.18217e11i	0.520772	−	0.902004i
$467$	1.26314e12			1.22892			0.614462	−	0.788947i	$-0.289373\pi$
$467$	1.26314e12			1.22892			0.614462	+	0.788947i	$0.289373\pi$
$468$		0			0
$469$	−7.70655e11			−0.735499
$470$	−4.54013e11	+	7.86373e11i	−0.429168	+	0.743342i
$471$		0			0
$472$	1.67487e11	+	2.90097e11i	0.155326	+	0.269032i
$473$	−4.82991e11	−	8.36565e11i	−0.443674	−	0.768465i
$474$		0			0
$475$	7.98159e11	−	1.38245e12i	0.719396	−	1.24603i
$476$	1.66821e11			0.148943
$477$		0			0
$478$	6.70333e11			0.587307
$479$	6.18800e11	−	1.07179e12i	0.537082	−	0.930253i	−0.461978	−	0.886892i	$-0.652860\pi$
$479$	6.18800e11	−	1.07179e12i	0.537082	−	0.930253i	0.999059	−	0.0433615i	$-0.0138067\pi$
$480$		0			0
$481$	−4.51529e11	−	7.82071e11i	−0.384621	−	0.666182i
$482$	−3.86260e11	−	6.69023e11i	−0.325963	−	0.564585i
$483$		0			0
$484$	−3.23168e11	+	5.59743e11i	−0.267685	+	0.463644i
$485$	−1.29668e12			−1.06413
$486$		0			0
$487$	4.32311e11			0.348270			0.174135	−	0.984722i	$-0.444287\pi$
$487$	4.32311e11			0.348270			0.174135	+	0.984722i	$0.444287\pi$
$488$	2.92482e11	−	5.06594e11i	0.233459	−	0.404363i
$489$		0			0
$490$	3.14366e11	+	5.44498e11i	0.246350	+	0.426691i
$491$	−8.15711e11	−	1.41285e12i	−0.633388	−	1.09706i	−0.986854	−	0.161613i	$-0.948330\pi$
$491$	−8.15711e11	−	1.41285e12i	−0.633388	−	1.09706i	0.353466	−	0.935447i	$-0.385003\pi$
$492$		0			0
$493$	5.69090e10	−	9.85693e10i	0.0433880	−	0.0751503i
$494$	−5.54128e11			−0.418639
$495$		0			0
$496$	5.85329e11			0.434243
$497$	2.56086e11	−	4.43553e11i	0.188270	−	0.326093i
$498$		0			0
$499$	3.59266e11	+	6.22267e11i	0.259396	+	0.449288i	0.966080	−	0.258242i	$-0.0831431\pi$
$499$	3.59266e11	+	6.22267e11i	0.259396	+	0.449288i	−0.706684	+	0.707529i	$0.749810\pi$
$500$	−3.84774e10	−	6.66448e10i	−0.0275322	−	0.0476871i
$501$		0			0
$502$	−2.95146e11	+	5.11208e11i	−0.207429	+	0.359278i
$503$	−5.17308e11			−0.360324			−0.180162	−	0.983637i	$-0.557662\pi$
$503$	−5.17308e11			−0.360324			−0.180162	+	0.983637i	$0.557662\pi$
$504$		0			0
$505$	2.78015e12			1.90220
$506$	−1.04745e12	+	1.81424e12i	−0.710325	+	1.23032i
$507$		0			0
$508$	1.80583e11	+	3.12779e11i	0.120307	+	0.208378i
$509$	−3.98945e11	−	6.90992e11i	−0.263441	−	0.456292i	0.703713	−	0.710484i	$-0.251524\pi$
$509$	−3.98945e11	−	6.90992e11i	−0.263441	−	0.456292i	−0.967154	+	0.254192i	$0.918191\pi$
$510$		0			0
$511$	−7.04681e11	+	1.22054e12i	−0.457192	+	0.791880i
$512$	6.87195e10			0.0441942
$513$		0			0
$514$	3.32897e11			0.210366
$515$	1.67465e12	−	2.90058e12i	1.04904	−	1.81699i
$516$		0			0
$517$	−9.84588e11	−	1.70536e12i	−0.606104	−	1.04980i
$518$	7.23063e11	+	1.25238e12i	0.441258	+	0.764281i
$519$		0			0
$520$	−1.88122e11	+	3.25836e11i	−0.112830	+	0.195427i
$521$	−8.24635e10			−0.0490334			−0.0245167	−	0.999699i	$-0.507805\pi$
$521$	−8.24635e10			−0.0490334			−0.0245167	+	0.999699i	$0.507805\pi$
$522$		0			0
$523$	−1.54815e12			−0.904805			−0.452402	−	0.891814i	$-0.649433\pi$
$523$	−1.54815e12			−0.904805			−0.452402	+	0.891814i	$0.649433\pi$
$524$	3.68389e11	−	6.38069e11i	0.213460	−	0.369723i
$525$		0			0
$526$	6.02671e11	+	1.04386e12i	0.343277	+	0.594573i
$527$	6.37449e11	+	1.10409e12i	0.359996	+	0.623531i
$528$		0			0
$529$	−8.54916e11	+	1.48076e12i	−0.474649	+	0.822117i
$530$	−1.96675e12			−1.08270
$531$		0			0
$532$	8.87363e11			0.480285
$533$	4.38055e11	−	7.58734e11i	0.235102	−	0.407209i
$534$		0			0
$535$	−1.56820e12	−	2.71621e12i	−0.827581	−	1.43341i
$536$	−3.45727e11	−	5.98817e11i	−0.180922	−	0.313367i
$537$		0			0
$538$	1.20045e12	−	2.07923e12i	0.617764	−	1.07000i
$539$	−1.36349e12			−0.695829
$540$		0			0
$541$	−6.21988e11			−0.312172			−0.156086	−	0.987743i	$-0.549888\pi$
$541$	−6.21988e11			−0.312172			−0.156086	+	0.987743i	$0.549888\pi$
$542$	1.49879e11	−	2.59597e11i	0.0746007	−	0.129212i
$543$		0			0
$544$	7.48385e10	+	1.29624e11i	0.0366378	+	0.0634586i
$545$	−1.77441e12	−	3.07337e12i	−0.861529	−	1.49221i
$546$		0			0
$547$	−2.08975e11	+	3.61956e11i	−0.0998050	+	0.172867i	−0.911604	−	0.411070i	$-0.865155\pi$
$547$	−2.08975e11	+	3.61956e11i	−0.0998050	+	0.172867i	0.811799	+	0.583937i	$0.198489\pi$
$548$	1.02521e12			0.485622
$549$		0			0
$550$	2.35052e12			1.09530
$551$	3.02713e11	−	5.24315e11i	0.139910	−	0.242331i
$552$		0			0
$553$	−7.38451e11	−	1.27903e12i	−0.335783	−	0.581593i
$554$	−1.06285e12	−	1.84092e12i	−0.479379	−	0.830309i
$555$		0			0
$556$	−2.37730e11	+	4.11760e11i	−0.105499	+	0.182729i
$557$	1.53061e12			0.673776			0.336888	−	0.941545i	$-0.390626\pi$
$557$	1.53061e12			0.673776			0.336888	+	0.941545i	$0.390626\pi$
$558$		0			0
$559$	6.30557e11			0.273131
$560$	3.01252e11	−	5.21783e11i	0.129444	−	0.224204i
$561$		0			0
$562$	4.14196e8	+	7.17408e8i	0.000175143	+	0.000303356i
$563$	−1.84506e12	−	3.19574e12i	−0.773969	−	1.34055i	−0.935372	−	0.353665i	$-0.884935\pi$
$563$	−1.84506e12	−	3.19574e12i	−0.773969	−	1.34055i	0.161403	−	0.986889i	$-0.448398\pi$
$564$		0			0
$565$	1.84261e12	−	3.19150e12i	0.760704	−	1.31758i
$566$	−1.96082e12			−0.803090
$567$		0			0
$568$	4.59535e11			0.185247
$569$	3.72714e11	−	6.45559e11i	0.149063	−	0.258185i	−0.781818	−	0.623506i	$-0.785708\pi$
$569$	3.72714e11	−	6.45559e11i	0.149063	−	0.258185i	0.930881	+	0.365321i	$0.119041\pi$
$570$		0			0
$571$	−1.74561e12	−	3.02348e12i	−0.687202	−	1.19027i	−0.972739	−	0.231901i	$-0.925505\pi$
$571$	−1.74561e12	−	3.02348e12i	−0.687202	−	1.19027i	0.285538	−	0.958368i	$-0.407828\pi$
$572$	−4.07967e11	−	7.06620e11i	−0.159347	−	0.275996i
$573$		0			0
$574$	−7.01487e11	+	1.21501e12i	−0.269722	+	0.467172i
$575$	3.93939e12			1.50288
$576$		0			0
$577$	−4.10159e12			−1.54050			−0.770249	−	0.637743i	$-0.779868\pi$
$577$	−4.10159e12			−1.54050			−0.770249	+	0.637743i	$0.779868\pi$
$578$	7.85698e11	−	1.36087e12i	0.292806	−	0.507156i
$579$		0			0
$580$	−2.05537e11	−	3.56000e11i	−0.0754160	−	0.130624i
$581$	−1.21914e12	−	2.11162e12i	−0.443876	−	0.768817i
$582$		0			0
$583$	2.13258e12	−	3.69373e12i	0.764533	−	1.32421i
$584$	−1.26452e12			−0.449851
$585$		0			0
$586$	−6.33821e11			−0.222038
$587$	2.24313e11	−	3.88522e11i	0.0779801	−	0.135066i	−0.824398	−	0.566010i	$-0.808486\pi$
$587$	2.24313e11	−	3.88522e11i	0.0779801	−	0.135066i	0.902378	+	0.430945i	$0.141820\pi$
$588$		0			0
$589$	3.39075e12	+	5.87295e12i	1.16085	+	2.01065i
$590$	1.31754e12	+	2.28205e12i	0.447643	+	0.775340i
$591$		0			0
$592$	−6.48754e11	+	1.12368e12i	−0.217086	+	0.376005i
$593$	−8.10869e11			−0.269280			−0.134640	−	0.990895i	$-0.542988\pi$
$593$	−8.10869e11			−0.269280			−0.134640	+	0.990895i	$0.542988\pi$
$594$		0			0
$595$	1.31230e12			0.429248
$596$	8.88817e11	−	1.53948e12i	0.288539	−	0.499764i
$597$		0			0
$598$	−6.83738e11	−	1.18427e12i	−0.218642	−	0.378700i
$599$	2.41691e12	+	4.18621e12i	0.767078	+	1.32862i	0.939141	+	0.343533i	$0.111624\pi$
$599$	2.41691e12	+	4.18621e12i	0.767078	+	1.32862i	−0.172062	+	0.985086i	$0.555043\pi$
$600$		0			0
$601$	−1.93313e12	+	3.34827e12i	−0.604401	+	1.04685i	0.387745	+	0.921767i	$0.373254\pi$
$601$	−1.93313e12	+	3.34827e12i	−0.604401	+	1.04685i	−0.992146	+	0.125086i	$0.960079\pi$
$602$	−1.00975e12			−0.313351
$603$		0			0
$604$	−1.28991e12			−0.394361
$605$	−2.54221e12	+	4.40324e12i	−0.771458	+	1.33620i
$606$		0			0
$607$	−1.45385e10	−	2.51814e10i	−0.00434681	−	0.00752890i	0.863844	−	0.503760i	$-0.168050\pi$
$607$	−1.45385e10	−	2.51814e10i	−0.00434681	−	0.00752890i	−0.868191	+	0.496231i	$0.834717\pi$
$608$	3.98084e11	+	6.89502e11i	0.118143	+	0.204630i
$609$		0			0
$610$	2.30082e12	−	3.98514e12i	0.672820	−	1.16536i
$611$	1.28541e12			0.373125
$612$		0			0
$613$	8.01432e11			0.229242			0.114621	−	0.993409i	$-0.463435\pi$
$613$	8.01432e11			0.229242			0.114621	+	0.993409i	$0.463435\pi$
$614$	3.18799e11	−	5.52177e11i	0.0905232	−	0.156791i
$615$		0			0
$616$	6.53305e11	+	1.13156e12i	0.182811	+	0.316638i
$617$	−9.79884e11	−	1.69721e12i	−0.272202	−	0.471468i	0.697223	−	0.716854i	$-0.254419\pi$
$617$	−9.79884e11	−	1.69721e12i	−0.272202	−	0.471468i	−0.969425	+	0.245386i	$0.921085\pi$
$618$		0			0
$619$	−9.61617e11	+	1.66557e12i	−0.263266	+	0.455990i	−0.967108	−	0.254367i	$-0.918133\pi$
$619$	−9.61617e11	+	1.66557e12i	−0.263266	+	0.455990i	0.703842	+	0.710356i	$0.251466\pi$
$620$	4.60451e12			1.25147
$621$		0			0
$622$	−7.01148e11			−0.187825
$623$	−1.82110e12	+	3.15423e12i	−0.484325	+	0.838875i
$624$		0			0
$625$	1.75044e12	+	3.03184e12i	0.458866	+	0.794780i
$626$	7.55861e11	+	1.30919e12i	0.196724	+	0.340736i
$627$		0			0
$628$	6.22399e11	−	1.07803e12i	0.159680	−	0.276574i
$629$	−2.82608e12			−0.719875
$630$		0			0
$631$	2.04866e12			0.514444			0.257222	−	0.966352i	$-0.417193\pi$
$631$	2.04866e12			0.514444			0.257222	+	0.966352i	$0.417193\pi$
$632$	6.62561e11	−	1.14759e12i	0.165196	−	0.286127i
$633$		0			0
$634$	1.55167e12	+	2.68758e12i	0.381416	+	0.660632i
$635$	1.42056e12	+	2.46049e12i	0.346720	+	0.600537i
$636$		0			0
$637$	4.45018e11	−	7.70793e11i	0.107090	−	0.185486i
$638$	8.91468e11			0.213016
$639$		0			0
$640$	5.40584e11			0.127366
$641$	−1.65327e12	+	2.86354e12i	−0.386796	+	0.669950i	−0.992017	−	0.126108i	$-0.959752\pi$
$641$	−1.65327e12	+	2.86354e12i	−0.386796	+	0.669950i	0.605221	+	0.796058i	$0.293085\pi$
$642$		0			0
$643$	1.90539e12	+	3.30024e12i	0.439577	+	0.761370i	0.997657	−	0.0684173i	$-0.0217949\pi$
$643$	1.90539e12	+	3.30024e12i	0.439577	+	0.761370i	−0.558080	+	0.829787i	$0.688462\pi$
$644$	1.09492e12	+	1.89645e12i	0.250838	+	0.434465i
$645$		0			0
$646$	−8.67062e11	+	1.50180e12i	−0.195886	+	0.339285i
$647$	−5.14649e12			−1.15463			−0.577314	−	0.816522i	$-0.695899\pi$
$647$	−5.14649e12			−1.15463			−0.577314	+	0.816522i	$0.695899\pi$
$648$		0			0
$649$	−5.71455e12			−1.26439
$650$	−7.67166e11	+	1.32877e12i	−0.168570	+	0.291971i
$651$		0			0
$652$	6.66368e11	+	1.15418e12i	0.144411	+	0.250127i
$653$	−1.62323e12	−	2.81151e12i	−0.349357	−	0.605105i	0.636778	−	0.771047i	$-0.280267\pi$
$653$	−1.62323e12	−	2.81151e12i	−0.349357	−	0.605105i	−0.986135	+	0.165942i	$0.946933\pi$
$654$		0			0
$655$	2.89795e12	−	5.01939e12i	0.615183	−	1.06553i
$656$	−1.25879e12			−0.265391
$657$		0			0
$658$	−2.05841e12			−0.428070
$659$	1.64322e12	−	2.84615e12i	0.339400	−	0.587859i	−0.644920	−	0.764250i	$-0.723109\pi$
$659$	1.64322e12	−	2.84615e12i	0.339400	−	0.587859i	0.984320	+	0.176392i	$0.0564425\pi$
$660$		0			0
$661$	3.10849e11	+	5.38406e11i	0.0633348	+	0.109699i	0.895954	−	0.444147i	$-0.146493\pi$
$661$	3.10849e11	+	5.38406e11i	0.0633348	+	0.109699i	−0.832619	+	0.553846i	$0.813160\pi$
$662$	−4.79693e11	−	8.30853e11i	−0.0970740	−	0.168137i
$663$		0			0
$664$	1.09385e12	−	1.89461e12i	0.218375	−	0.378236i
$665$	6.98047e12			1.38416
$666$		0			0
$667$	1.49407e12			0.292283
$668$	1.34082e12	−	2.32237e12i	0.260542	−	0.451272i
$669$		0			0
$670$	−2.71968e12	−	4.71062e12i	−0.521411	−	0.903111i
$671$	4.98964e12	+	8.64232e12i	0.950207	+	1.64581i
$672$		0			0
$673$	−4.73224e12	+	8.19648e12i	−0.889199	+	1.54014i	−0.0483757	+	0.998829i	$0.515404\pi$
$673$	−4.73224e12	+	8.19648e12i	−0.889199	+	1.54014i	−0.840824	+	0.541309i	$0.817929\pi$
$674$	−1.66345e12			−0.310484
$675$		0			0
$676$	−2.18214e12			−0.401904
$677$	1.86865e12	−	3.23660e12i	0.341884	−	0.592161i	−0.642899	−	0.765951i	$-0.722268\pi$
$677$	1.86865e12	−	3.23660e12i	0.341884	−	0.592161i	0.984783	+	0.173791i	$0.0556017\pi$
$678$		0			0
$679$	−1.46973e12	−	2.54564e12i	−0.265352	−	0.459604i
$680$	5.88719e11	+	1.01969e12i	0.105589	+	0.182885i
$681$		0			0
$682$	−4.99275e12	+	8.64770e12i	−0.883711	+	1.53063i
$683$	−1.24743e12			−0.219343			−0.109671	−	0.993968i	$-0.534980\pi$
$683$	−1.24743e12			−0.219343			−0.109671	+	0.993968i	$0.534980\pi$
$684$		0			0
$685$	8.06481e12			1.39954
$686$	−2.18640e12	+	3.78696e12i	−0.376939	+	0.652878i
$687$		0			0
$688$	−4.52990e11	−	7.84602e11i	−0.0770799	−	0.133506i
$689$	1.39207e12	+	2.41113e12i	0.235328	+	0.407600i
$690$		0			0
$691$	1.32898e12	−	2.30186e12i	0.221752	−	0.384086i	−0.733588	−	0.679594i	$-0.762156\pi$
$691$	1.32898e12	−	2.30186e12i	0.221752	−	0.384086i	0.955340	+	0.295509i	$0.0954891\pi$
$692$	1.46372e12			0.242650
$693$		0			0
$694$	1.53113e12			0.250551
$695$	−1.87011e12	+	3.23912e12i	−0.304043	+	0.526618i
$696$		0			0
$697$	−1.37088e12	−	2.37443e12i	−0.220014	−	0.381076i
$698$	−2.56709e11	−	4.44632e11i	−0.0409347	−	0.0709009i
$699$		0			0
$700$	1.22851e12	−	2.12785e12i	0.193392	−	0.334965i
$701$	−3.12836e12			−0.489311			−0.244656	−	0.969610i	$-0.578675\pi$
$701$	−3.12836e12			−0.489311			−0.244656	+	0.969610i	$0.578675\pi$
$702$		0			0
$703$	−1.50326e13			−2.32133
$704$	−5.86165e11	+	1.01527e12i	−0.0899379	+	0.155777i
$705$		0			0
$706$	−1.77090e12	−	3.06729e12i	−0.268271	−	0.464658i
$707$	3.15116e12	+	5.45798e12i	0.474333	+	0.821569i
$708$		0			0
$709$	−5.40799e12	+	9.36691e12i	−0.803763	+	1.39216i	0.113361	+	0.993554i	$0.463838\pi$
$709$	−5.40799e12	+	9.36691e12i	−0.803763	+	1.39216i	−0.917123	+	0.398604i	$0.869495\pi$
$710$	3.61495e12			0.533875
$711$		0			0
$712$	−3.26788e12			−0.476548
$713$	−8.36767e12	+	1.44932e13i	−1.21256	+	2.10021i
$714$		0			0
$715$	−3.20929e12	−	5.55865e12i	−0.459231	−	0.795411i
$716$	−2.26182e12	−	3.91759e12i	−0.321625	−	0.557070i
$717$		0			0
$718$	−2.01641e12	+	3.49253e12i	−0.283152	+	0.490433i
$719$	−5.06139e10			−0.00706300			−0.00353150	−	0.999994i	$-0.501124\pi$
$719$	−5.06139e10			−0.00706300			−0.00353150	+	0.999994i	$0.501124\pi$
$720$		0			0
$721$	7.59254e12			1.04635
$722$	−2.03062e12	+	3.51713e12i	−0.278106	+	0.481694i
$723$		0			0
$724$	−3.14756e12	−	5.45173e12i	−0.425746	−	0.737413i
$725$	−8.38186e11	−	1.45178e12i	−0.112673	−	0.195155i
$726$		0			0
$727$	−1.67169e12	+	2.89545e12i	−0.221948	+	0.384425i	−0.955399	−	0.295317i	$-0.904575\pi$
$727$	−1.67169e12	+	2.89545e12i	−0.221948	+	0.384425i	0.733452	+	0.679742i	$0.237908\pi$
$728$	−8.52906e11			−0.112541
$729$		0			0
$730$	−9.94741e12			−1.29645
$731$	9.86652e11	−	1.70893e12i	0.127801	−	0.221359i
$732$		0			0
$733$	2.08081e12	+	3.60406e12i	0.266234	+	0.461131i	0.967886	−	0.251389i	$-0.0808873\pi$
$733$	2.08081e12	+	3.60406e12i	0.266234	+	0.461131i	−0.701652	+	0.712520i	$0.747554\pi$
$734$	−5.78037e11	−	1.00119e12i	−0.0735061	−	0.127316i
$735$		0			0
$736$	−9.82391e11	+	1.70155e12i	−0.123405	+	0.213744i
$737$	1.17960e13			1.47275
$738$		0			0
$739$	9.32557e12			1.15020			0.575102	−	0.818081i	$-0.304962\pi$
$739$	9.32557e12			1.15020			0.575102	+	0.818081i	$0.304962\pi$
$740$	−5.10344e12	+	8.83943e12i	−0.625634	+	1.08363i
$741$		0			0
$742$	−2.22921e12	−	3.86111e12i	−0.269981	−	0.467621i
$743$	4.46909e12	+	7.74069e12i	0.537984	+	0.931815i	0.999012	+	0.0444301i	$0.0141472\pi$
$743$	4.46909e12	+	7.74069e12i	0.537984	+	0.931815i	−0.461029	+	0.887385i	$0.652519\pi$
$744$		0			0
$745$	6.99190e12	−	1.21103e13i	0.831557	−	1.44030i
$746$	7.65366e11			0.0904783
$747$		0			0
$748$	−2.55344e12			−0.298241
$749$	3.55497e12	−	6.15738e12i	0.412731	−	0.714871i
$750$		0			0
$751$	−1.80514e12	−	3.12659e12i	−0.207076	−	0.358666i	0.743716	−	0.668496i	$-0.233061\pi$
$751$	−1.80514e12	−	3.12659e12i	−0.207076	−	0.358666i	−0.950792	+	0.309829i	$0.899728\pi$
$752$	−9.23432e11	−	1.59943e12i	−0.105299	−	0.182383i
$753$		0			0
$754$	−2.90959e11	+	5.03955e11i	−0.0327839	+	0.0567833i
$755$	−1.01471e13			−1.13653
$756$		0			0
$757$	1.48103e13			1.63920			0.819599	−	0.572938i	$-0.194196\pi$
$757$	1.48103e13			1.63920			0.819599	+	0.572938i	$0.194196\pi$
$758$	−4.03092e12	+	6.98175e12i	−0.443499	+	0.768163i
$759$		0			0
$760$	3.13154e12	+	5.42399e12i	0.340484	+	0.589736i
$761$	8.50988e12	+	1.47396e13i	0.919798	+	1.59314i	0.799720	+	0.600373i	$0.204981\pi$
$761$	8.50988e12	+	1.47396e13i	0.919798	+	1.59314i	0.120079	+	0.992764i	$0.461685\pi$
$762$		0			0
$763$	4.02242e12	−	6.96703e12i	0.429662	−	0.744196i
$764$	−6.30656e11			−0.0669688
$765$		0			0
$766$	9.26200e12			0.972020
$767$	1.86512e12	−	3.23049e12i	0.194593	−	0.337046i
$768$		0			0
$769$	5.98957e12	+	1.03742e13i	0.617629	+	1.06976i	0.989917	+	0.141647i	$0.0452398\pi$
$769$	5.98957e12	+	1.03742e13i	0.617629	+	1.06976i	−0.372289	+	0.928117i	$0.621427\pi$
$770$	5.13924e12	+	8.90143e12i	0.526855	+	0.912539i
$771$		0			0
$772$	4.34152e12	−	7.51974e12i	0.439911	−	0.761947i
$773$	−7.00938e12			−0.706110			−0.353055	−	0.935603i	$-0.614857\pi$
$773$	−7.00938e12			−0.706110			−0.353055	+	0.935603i	$0.614857\pi$
$774$		0			0
$775$	1.87774e13			1.86972
$776$	1.31868e12	−	2.28403e12i	0.130546	−	0.226112i
$777$		0			0
$778$	3.85583e12	+	6.67850e12i	0.377320	+	0.653538i
$779$	−7.29204e12	−	1.26302e13i	−0.709464	−	1.22883i
$780$		0			0
$781$	−3.91975e12	+	6.78921e12i	−0.376989	+	0.652965i
$782$	−4.27947e12			−0.409222
$783$		0			0
$784$	−1.27880e12			−0.120887
$785$	4.89612e12	−	8.48033e12i	0.460191	−	0.797075i
$786$		0			0
$787$	3.95505e12	+	6.85035e12i	0.367507	+	0.636541i	0.989175	−	0.146740i	$-0.0468780\pi$
$787$	3.95505e12	+	6.85035e12i	0.367507	+	0.636541i	−0.621668	+	0.783281i	$0.713545\pi$
$788$	6.23901e11	+	1.08063e12i	0.0576432	+	0.0998409i
$789$		0			0
$790$	5.21205e12	−	9.02754e12i	0.476088	−	0.824608i
$791$	8.35404e12			0.758756
$792$		0			0
$793$	−6.51411e12			−0.584959
$794$	−4.02296e11	+	6.96798e11i	−0.0359214	+	0.0622178i
$795$		0			0
$796$	−4.52732e12	−	7.84155e12i	−0.399698	−	0.692298i
$797$	−3.58482e12	−	6.20910e12i	−0.314706	−	0.545087i	0.664669	−	0.747138i	$-0.268573\pi$
$797$	−3.58482e12	−	6.20910e12i	−0.314706	−	0.545087i	−0.979375	+	0.202051i	$0.935239\pi$
$798$		0			0
$799$	2.01131e12	−	3.48370e12i	0.174590	−	0.302399i
$800$	2.20452e12			0.190287
$801$		0			0
$802$	−9.76632e12			−0.833578
$803$	1.07861e13	−	1.86822e13i	0.915475	−	1.58565i
$804$		0			0
$805$	8.61319e12	+	1.49185e13i	0.722907	+	1.25211i
$806$	−3.25908e12	−	5.64490e12i	−0.272012	−	0.471138i
$807$		0			0
$808$	−2.82732e12	+	4.89706e12i	−0.233359	+	0.404189i
$809$	1.58279e13			1.29914			0.649568	−	0.760304i	$-0.274950\pi$
$809$	1.58279e13			1.29914			0.649568	+	0.760304i	$0.274950\pi$
$810$		0			0
$811$	−9.43072e11			−0.0765510			−0.0382755	−	0.999267i	$-0.512186\pi$
$811$	−9.43072e11			−0.0765510			−0.0382755	+	0.999267i	$0.512186\pi$
$812$	4.65931e11	−	8.07017e11i	0.0376114	−	0.0651449i
$813$		0			0
$814$	−1.10675e13	−	1.91695e13i	−0.883568	−	1.53039i
$815$	5.24201e12	+	9.07942e12i	0.416187	+	0.720857i
$816$		0			0
$817$	5.24825e12	−	9.09023e12i	0.412112	−	0.713799i
$818$	1.19256e13			0.931300
$819$		0			0
$820$	−9.90232e12			−0.764847
$821$	−9.58597e12	+	1.66034e13i	−0.736363	+	1.27542i	0.217760	+	0.976002i	$0.430125\pi$
$821$	−9.58597e12	+	1.66034e13i	−0.736363	+	1.27542i	−0.954123	+	0.299416i	$0.903208\pi$
$822$		0			0
$823$	4.66915e12	+	8.08721e12i	0.354763	+	0.614468i	0.987077	−	0.160244i	$-0.0512281\pi$
$823$	4.66915e12	+	8.08721e12i	0.354763	+	0.614468i	−0.632314	+	0.774712i	$0.717895\pi$
$824$	3.40613e12	+	5.89959e12i	0.257388	+	0.445809i
$825$		0			0
$826$	−2.98675e12	+	5.17320e12i	−0.223248	+	0.386677i
$827$	−1.08669e13			−0.807854			−0.403927	−	0.914791i	$-0.632355\pi$
$827$	−1.08669e13			−0.807854			−0.403927	+	0.914791i	$0.632355\pi$
$828$		0			0
$829$	−3.98687e12			−0.293181			−0.146591	−	0.989197i	$-0.546830\pi$
$829$	−3.98687e12			−0.293181			−0.146591	+	0.989197i	$0.546830\pi$
$830$	8.60482e12	−	1.49040e13i	0.629347	−	1.09006i
$831$		0			0
$832$	−3.82627e11	−	6.62729e11i	−0.0276834	−	0.0479491i
$833$	−1.39267e12	−	2.41217e12i	−0.100218	−	0.173582i
$834$		0			0
$835$	1.05476e13	−	1.82690e13i	0.750871	−	1.30055i
$836$	−1.35824e13			−0.961716
$837$		0			0
$838$	−4.74055e11			−0.0332071
$839$	−9.38444e12	+	1.62543e13i	−0.653852	+	1.13251i	0.328328	+	0.944564i	$0.393515\pi$
$839$	−9.38444e12	+	1.62543e13i	−0.653852	+	1.13251i	−0.982180	+	0.187941i	$0.939818\pi$
$840$		0			0
$841$	6.93568e12	+	1.20129e13i	0.478087	+	0.828071i
$842$	−4.32073e12	−	7.48372e12i	−0.296246	−	0.513113i
$843$		0			0
$844$	−2.61028e11	+	4.52114e11i	−0.0177070	+	0.0306695i
$845$	−1.71659e13			−1.15827
$846$		0			0
$847$	−1.15259e13			−0.769482
$848$	2.00012e12	−	3.46430e12i	0.132823	−	0.230056i
$849$		0			0
$850$	2.40082e12	+	4.15834e12i	0.157752	+	0.273234i
$851$	−1.85488e13	−	3.21274e13i	−1.21236	−	2.09987i
$852$		0			0
$853$	6.74068e11	−	1.16752e12i	0.0435947	−	0.0755082i	−0.843405	−	0.537279i	$-0.819452\pi$
$853$	6.74068e11	−	1.16752e12i	0.0435947	−	0.0755082i	0.886999	+	0.461771i	$0.152786\pi$
$854$	1.04315e13			0.671097
$855$		0			0
$856$	6.37924e12			0.406104
$857$	−2.53665e11	+	4.39361e11i	−0.0160637	+	0.0278232i	−0.873946	−	0.486024i	$-0.838447\pi$
$857$	−2.53665e11	+	4.39361e11i	−0.0160637	+	0.0278232i	0.857882	+	0.513847i	$0.171780\pi$
$858$		0			0
$859$	−1.43730e13	−	2.48947e13i	−0.900693	−	1.56005i	−0.826596	−	0.562795i	$-0.809726\pi$
$859$	−1.43730e13	−	2.48947e13i	−0.900693	−	1.56005i	−0.0740966	−	0.997251i	$-0.523607\pi$
$860$	−3.56346e12	−	6.17210e12i	−0.222141	−	0.384760i
$861$		0			0
$862$	4.55813e12	−	7.89491e12i	0.281193	−	0.487040i
$863$	−3.00660e11			−0.0184513			−0.00922566	−	0.999957i	$-0.502937\pi$
$863$	−3.00660e11			−0.0184513			−0.00922566	+	0.999957i	$0.502937\pi$
$864$		0			0
$865$	1.15144e13			0.699309
$866$	9.27268e12	−	1.60608e13i	0.560241	−	0.970366i
$867$		0			0
$868$	5.21899e12	+	9.03955e12i	0.312067	+	0.540515i
$869$	1.13030e13	+	1.95774e13i	0.672367	+	1.16457i
$870$		0			0
$871$	−3.84999e12	+	6.66837e12i	−0.226661	+	0.392589i
$872$	7.21807e12			0.422763
$873$		0			0
$874$	−2.27635e13			−1.31959
$875$	6.86154e11	−	1.18845e12i	0.0395718	−	0.0685403i
$876$		0			0
$877$	−4.54436e12	−	7.87107e12i	−0.259403	−	0.449299i	0.706679	−	0.707534i	$-0.250192\pi$
$877$	−4.54436e12	−	7.87107e12i	−0.259403	−	0.449299i	−0.966082	+	0.258235i	$0.916859\pi$
$878$	−7.02828e11	−	1.21733e12i	−0.0399139	−	0.0691328i
$879$		0			0
$880$	−4.61108e12	+	7.98663e12i	−0.259198	+	0.448943i
$881$	−1.67414e12			−0.0936266			−0.0468133	−	0.998904i	$-0.514907\pi$
$881$	−1.67414e12			−0.0936266			−0.0468133	+	0.998904i	$0.514907\pi$
$882$		0			0
$883$	−2.69670e13			−1.49283			−0.746413	−	0.665483i	$-0.768226\pi$
$883$	−2.69670e13			−1.49283			−0.746413	+	0.665483i	$0.768226\pi$
$884$	8.33394e11	−	1.44348e12i	0.0459003	−	0.0795016i
$885$		0			0
$886$	−1.58179e11	−	2.73973e11i	−0.00862375	−	0.0149368i
$887$	−1.65697e13	−	2.86996e13i	−0.898793	−	1.55676i	−0.829039	−	0.559191i	$-0.811112\pi$
$887$	−1.65697e13	−	2.86996e13i	−0.898793	−	1.55676i	−0.0697540	−	0.997564i	$-0.522221\pi$
$888$		0			0
$889$	−3.22028e12	+	5.57769e12i	−0.172916	+	0.299499i
$890$	−2.57069e13			−1.37339
$891$		0			0
$892$	1.62394e13			0.858872
$893$	1.06987e13	−	1.85307e13i	0.562987	−	0.975123i
$894$		0			0
$895$	−1.77927e13	−	3.08178e13i	−0.926910	−	1.60545i
$896$	6.12726e11	+	1.06127e12i	0.0317600	+	0.0550099i
$897$		0			0
$898$	3.79959e12	−	6.58108e12i	0.194981	−	0.337717i
$899$	7.12158e12			0.363628
$900$		0			0
$901$	8.71285e12			0.440452
$902$	1.07373e13	−	1.85975e13i	0.540087	−	0.935459i
$903$		0			0
$904$	3.74775e12	+	6.49129e12i	0.186643	+	0.323276i
$905$	−2.47604e13	−	4.28862e13i	−1.22698	−	2.12520i
$906$		0			0
$907$	−1.40098e13	+	2.42658e13i	−0.687386	+	1.19059i	0.285295	+	0.958440i	$0.407909\pi$
$907$	−1.40098e13	+	2.42658e13i	−0.687386	+	1.19059i	−0.972681	+	0.232147i	$0.925425\pi$
$908$	−7.97971e12			−0.389584
$909$		0			0
$910$	−6.70941e12			−0.324338
$911$	−1.22604e13	+	2.12357e13i	−0.589758	+	1.02149i	0.404506	+	0.914535i	$0.367443\pi$
$911$	−1.22604e13	+	2.12357e13i	−0.589758	+	1.02149i	−0.994264	+	0.106955i	$0.965890\pi$
$912$		0			0
$913$	1.86607e13	+	3.23213e13i	0.888812	+	1.53947i
$914$	−6.62251e12	−	1.14705e13i	−0.313881	−	0.543658i
$915$		0			0
$916$	−8.00074e12	+	1.38577e13i	−0.375492	+	0.650371i
$917$	1.31387e13			0.613608
$918$		0			0
$919$	2.79427e13			1.29226			0.646128	−	0.763229i	$-0.276387\pi$
$919$	2.79427e13			1.29226			0.646128	+	0.763229i	$0.276387\pi$
$920$	−7.72801e12	+	1.33853e13i	−0.355650	+	0.616003i
$921$		0			0
$922$	−3.40833e12	−	5.90341e12i	−0.155329	−	0.269038i
$923$	−2.55867e12	−	4.43175e12i	−0.116040	−	0.200987i
$924$		0			0
$925$	−2.08120e13	+	3.60475e13i	−0.934710	+	1.61896i
$926$	1.46775e12			0.0655999
$927$		0			0
$928$	8.36096e11			0.0370075
$929$	5.87646e11	−	1.01783e12i	0.0258848	−	0.0448338i	−0.852793	−	0.522249i	$-0.825093\pi$
$929$	5.87646e11	−	1.01783e12i	0.0258848	−	0.0448338i	0.878678	+	0.477416i	$0.158426\pi$
$930$		0			0
$931$	−7.40794e12	−	1.28309e13i	−0.323165	−	0.559738i
$932$	8.48212e12	+	1.46915e13i	0.368242	+	0.637813i
$933$		0			0
$934$	−1.01051e13	+	1.75026e13i	−0.434490	+	0.752559i
$935$	−2.00867e13			−0.859520
$936$		0			0
$937$	−3.99627e12			−0.169366			−0.0846830	−	0.996408i	$-0.526988\pi$
$937$	−3.99627e12			−0.169366			−0.0846830	+	0.996408i	$0.526988\pi$
$938$	6.16524e12	−	1.06785e13i	0.260038	−	0.450399i
$939$		0			0
$940$	−7.26421e12	−	1.25820e13i	−0.303468	−	0.525622i
$941$	3.54323e12	+	6.13706e12i	0.147315	+	0.255157i	0.930234	−	0.366966i	$-0.119604\pi$
$941$	3.54323e12	+	6.13706e12i	0.147315	+	0.255157i	−0.782919	+	0.622123i	$0.786270\pi$
$942$		0			0
$943$	1.79953e13	−	3.11687e13i	0.741064	−	1.28356i
$944$	−5.35960e12			−0.219664
$945$		0			0
$946$	1.54557e13			0.627449
$947$	2.14474e13	−	3.71481e13i	0.866564	−	1.50093i	0.00107803	−	0.999999i	$-0.499657\pi$
$947$	2.14474e13	−	3.71481e13i	0.866564	−	1.50093i	0.865486	−	0.500933i	$-0.167010\pi$
$948$		0			0
$949$	7.04080e12	+	1.21950e13i	0.281789	+	0.488073i
$950$	1.27705e13	+	2.21192e13i	0.508690	+	0.881077i
$951$		0			0
$952$	−1.33457e12	+	2.31154e12i	−0.0526593	+	0.0912085i
$953$	1.57454e13			0.618350			0.309175	−	0.951005i	$-0.399947\pi$
$953$	1.57454e13			0.618350			0.309175	+	0.951005i	$0.399947\pi$
$954$		0			0
$955$	−4.96108e12			−0.193002
$956$	−5.36267e12	+	9.28841e12i	−0.207644	+	0.359651i
$957$		0			0
$958$	9.90080e12	+	1.71487e13i	0.379774	+	0.657788i
$959$	9.14107e12	+	1.58328e13i	0.348990	+	0.604469i
$960$		0			0
$961$	−2.66652e13	+	4.61856e13i	−1.00853	+	1.74683i
$962$	1.44489e13			0.543936
$963$		0			0
$964$	1.23603e13			0.460982
$965$	3.41527e13	−	5.91543e13i	1.26781	−	2.19590i
$966$		0			0
$967$	−4.50810e12	−	7.80826e12i	−0.165796	−	0.287168i	0.771141	−	0.636664i	$-0.219686\pi$
$967$	−4.50810e12	−	7.80826e12i	−0.165796	−	0.287168i	−0.936938	+	0.349496i	$0.886353\pi$
$968$	−5.17068e12	−	8.95589e12i	−0.189282	−	0.327846i
$969$		0			0
$970$	1.03735e13	−	1.79674e13i	0.376228	−	0.651646i
$971$	−1.47845e13			−0.533730			−0.266865	−	0.963734i	$-0.585988\pi$
$971$	−1.47845e13			−0.533730			−0.266865	+	0.963734i	$0.585988\pi$
$972$		0			0
$973$	−8.47870e12			−0.303265
$974$	−3.45849e12	+	5.99028e12i	−0.123132	+	0.213271i
$975$		0			0
$976$	4.67972e12	+	8.10551e12i	0.165080	+	0.285928i
$977$	1.09991e13	+	1.90510e13i	0.386217	+	0.668948i	0.991937	−	0.126730i	$-0.0404481\pi$
$977$	1.09991e13	+	1.90510e13i	0.386217	+	0.668948i	−0.605720	+	0.795678i	$0.707115\pi$
$978$		0			0
$979$	2.78745e13	−	4.82800e13i	0.969805	−	1.67975i
$980$	−1.00597e13			−0.348392
$981$		0			0
$982$	2.61028e13			0.895746
$983$	−1.53163e13	+	2.65286e13i	−0.523194	+	0.906198i	0.476442	+	0.879206i	$0.341926\pi$
$983$	−1.53163e13	+	2.65286e13i	−0.523194	+	0.906198i	−0.999636	+	0.0269921i	$0.991407\pi$
$984$		0			0
$985$	4.90794e12	+	8.50080e12i	0.166125	+	0.287738i
$986$	9.10544e11	+	1.57711e12i	0.0306800	+	0.0531393i
$987$		0			0
$988$	4.43303e12	−	7.67823e12i	0.148011	−	0.256363i
$989$	2.59032e13			0.860935
$990$		0			0
$991$	−1.39052e13			−0.457978			−0.228989	−	0.973429i	$-0.573542\pi$
$991$	−1.39052e13			−0.457978			−0.228989	+	0.973429i	$0.573542\pi$
$992$	−4.68263e12	+	8.11056e12i	−0.153528	+	0.265918i
$993$		0			0
$994$	4.09737e12	+	7.09685e12i	0.133127	+	0.230583i
$995$	−3.56143e13	−	6.16858e13i	−1.15192	−	1.99518i
$996$		0			0
$997$	−6.13004e12	+	1.06175e13i	−0.196488	+	0.340326i	−0.947387	−	0.320090i	$-0.896287\pi$
$997$	−6.13004e12	+	1.06175e13i	−0.196488	+	0.340326i	0.750900	+	0.660416i	$0.229620\pi$
$998$	−1.14965e13			−0.366842
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.10.c.l.55.1		4
3.2	odd	2		162.10.c.o.55.2		4
9.2	odd	6		54.10.a.f.1.1	✓	2
9.4	even	3	inner	162.10.c.l.109.1		4
9.5	odd	6		162.10.c.o.109.2		4
9.7	even	3		54.10.a.g.1.2	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
54.10.a.f.1.1	✓	2	9.2	odd	6
54.10.a.g.1.2	yes	2	9.7	even	3
162.10.c.l.55.1		4	1.1	even	1	trivial
162.10.c.l.109.1		4	9.4	even	3	inner
162.10.c.o.55.2		4	3.2	odd	2
162.10.c.o.109.2		4	9.5	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	162.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-8.00000 + 13.8564i) q^{2} +(-128.000 - 221.703i) q^{4} +(-1006.92 - 1744.03i) q^{5} +(2282.58 - 3953.55i) q^{7} +4096.00 q^{8} +32221.3 q^{10} +(-34938.1 + 60514.6i) q^{11} +(-22806.3 - 39501.7i) q^{13} +(36521.3 + 63256.7i) q^{14} +(-32768.0 + 56755.8i) q^{16} -142743. q^{17} -759286. q^{19} +(-257771. + 446472. i) q^{20} +(-559010. - 968234. i) q^{22} +(-936881. - 1.62273e6i) q^{23} +(-1.05120e6 + 1.82073e6i) q^{25} +729802. q^{26} -1.16868e6 q^{28} +(-398681. + 690537. i) q^{29} +(-4.46571e6 - 7.73483e6i) q^{31} +(-524288. - 908093. i) q^{32} +(1.14194e6 - 1.97791e6i) q^{34} -9.19347e6 q^{35} +1.97984e7 q^{37} +(6.07429e6 - 1.05210e7i) q^{38} +(-4.12433e6 - 7.14355e6i) q^{40} +(9.60381e6 + 1.66343e7i) q^{41} +(-6.91208e6 + 1.19721e7i) q^{43} +1.78883e7 q^{44} +2.99802e7 q^{46} +(-1.40905e7 + 2.44054e7i) q^{47} +(9.75646e6 + 1.68987e7i) q^{49} +(-1.68192e7 - 2.91316e7i) q^{50} +(-5.83842e6 + 1.01124e7i) q^{52} -6.10387e7 q^{53} +1.40719e8 q^{55} +(9.34945e6 - 1.61937e7i) q^{56} +(-6.37890e6 - 1.10486e7i) q^{58} +(4.08905e7 + 7.08244e7i) q^{59} +(7.14068e7 - 1.23680e8i) q^{61} +1.42903e8 q^{62} +1.67772e7 q^{64} +(-4.59281e7 + 7.95498e7i) q^{65} +(-8.44061e7 - 1.46196e8i) q^{67} +(1.82711e7 + 3.16465e7i) q^{68} +(7.35477e7 - 1.27388e8i) q^{70} +1.12191e8 q^{71} -3.08721e8 q^{73} +(-1.58387e8 + 2.74335e8i) q^{74} +(9.71886e7 + 1.68336e8i) q^{76} +(1.59498e8 + 2.76259e8i) q^{77} +(1.61758e8 - 2.80173e8i) q^{79} +1.31979e8 q^{80} -3.07322e8 q^{82} +(2.67054e8 - 4.62551e8i) q^{83} +(1.43730e8 + 2.48948e8i) q^{85} +(-1.10593e8 - 1.91553e8i) q^{86} +(-1.43107e8 + 2.47868e8i) q^{88} -7.97823e8 q^{89} -2.08229e8 q^{91} +(-2.39842e8 + 4.15418e8i) q^{92} +(-2.25447e8 - 3.90486e8i) q^{94} +(7.64537e8 + 1.32422e9i) q^{95} +(3.21944e8 - 5.57624e8i) q^{97} -3.12207e8 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 32 q^{2} - 512 q^{4} - 912 q^{5} - 6448 q^{7} + 16384 q^{8} + 29184 q^{10} - 15126 q^{11} - 28912 q^{13} - 103168 q^{14} - 131072 q^{16} + 799920 q^{17} + 16208 q^{19} - 233472 q^{20} - 242016 q^{22}+ \cdots + 1965542016 q^{98}+O(q^{100}) \) 4 * q - 32 * q^2 - 512 * q^4 - 912 * q^5 - 6448 * q^7 + 16384 * q^8 + 29184 * q^10 - 15126 * q^11 - 28912 * q^13 - 103168 * q^14 - 131072 * q^16 + 799920 * q^17 + 16208 * q^19 - 233472 * q^20 - 242016 * q^22 - 2563572 * q^23 - 1363304 * q^25 + 925184 * q^26 + 3301376 * q^28 - 3059088 * q^29 - 16787920 * q^31 - 2097152 * q^32 - 6399360 * q^34 - 42656244 * q^35 + 69597368 * q^37 - 129664 * q^38 - 3735552 * q^40 + 24238968 * q^41 - 12599680 * q^43 + 7744512 * q^44 + 82034304 * q^46 + 19535772 * q^47 - 61423188 * q^49 - 21812864 * q^50 - 7401472 * q^52 + 25069824 * q^53 + 402089472 * q^55 - 26411008 * q^56 - 48945408 * q^58 + 140256744 * q^59 + 169724624 * q^61 + 537213440 * q^62 + 67108864 * q^64 - 110257512 * q^65 + 72241232 * q^67 - 102389760 * q^68 + 341249952 * q^70 - 107692560 * q^71 - 407115388 * q^73 - 556778944 * q^74 - 2074624 * q^76 + 921970176 * q^77 + 877964864 * q^79 + 119537664 * q^80 - 775646976 * q^82 + 111456714 * q^83 + 885428280 * q^85 - 201594880 * q^86 - 61956096 * q^88 - 2468521728 * q^89 - 784311824 * q^91 - 656274432 * q^92 + 312572352 * q^94 + 2374608756 * q^95 + 165265682 * q^97 + 1965542016 * q^98

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