LMFDB - Embedded newform 169.3.d.a.70.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [169,3,Mod(70,169)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("169.70"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(169, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([3])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	169.d (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$4.60491646769$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			70.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	169.70
Dual form			169.3.d.a.99.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.366025 - 0.366025i) q^{2} -0.732051 q^{3} +3.73205i q^{4} +(-2.63397 + 2.63397i) q^{5} +(-0.267949 + 0.267949i) q^{6} +(-4.19615 - 4.19615i) q^{7} +(2.83013 + 2.83013i) q^{8} -8.46410 q^{9} +1.92820i q^{10} +(-11.4641 - 11.4641i) q^{11} -2.73205i q^{12} -3.07180 q^{14} +(1.92820 - 1.92820i) q^{15} -12.8564 q^{16} +18.4641i q^{17} +(-3.09808 + 3.09808i) q^{18} +(4.46410 - 4.46410i) q^{19} +(-9.83013 - 9.83013i) q^{20} +(3.07180 + 3.07180i) q^{21} -8.39230 q^{22} +20.1962i q^{23} +(-2.07180 - 2.07180i) q^{24} +11.1244i q^{25} +12.7846 q^{27} +(15.6603 - 15.6603i) q^{28} +9.39230 q^{29} -1.41154i q^{30} +(-11.9282 + 11.9282i) q^{31} +(-16.0263 + 16.0263i) q^{32} +(8.39230 + 8.39230i) q^{33} +(6.75833 + 6.75833i) q^{34} +22.1051 q^{35} -31.5885i q^{36} +(22.1699 + 22.1699i) q^{37} -3.26795i q^{38} -14.9090 q^{40} +(-32.8827 + 32.8827i) q^{41} +2.24871 q^{42} -51.9615i q^{43} +(42.7846 - 42.7846i) q^{44} +(22.2942 - 22.2942i) q^{45} +(7.39230 + 7.39230i) q^{46} +(-34.3205 - 34.3205i) q^{47} +9.41154 q^{48} -13.7846i q^{49} +(4.07180 + 4.07180i) q^{50} -13.5167i q^{51} -14.7654 q^{53} +(4.67949 - 4.67949i) q^{54} +60.3923 q^{55} -23.7513i q^{56} +(-3.26795 + 3.26795i) q^{57} +(3.43782 - 3.43782i) q^{58} +(68.0526 + 68.0526i) q^{59} +(7.19615 + 7.19615i) q^{60} +25.6269 q^{61} +8.73205i q^{62} +(35.5167 + 35.5167i) q^{63} -39.6936i q^{64} +6.14359 q^{66} +(-28.5692 + 28.5692i) q^{67} -68.9090 q^{68} -14.7846i q^{69} +(8.09103 - 8.09103i) q^{70} +(-32.7128 + 32.7128i) q^{71} +(-23.9545 - 23.9545i) q^{72} +(-19.2750 - 19.2750i) q^{73} +16.2295 q^{74} -8.14359i q^{75} +(16.6603 + 16.6603i) q^{76} +96.2102i q^{77} +62.7461 q^{79} +(33.8634 - 33.8634i) q^{80} +66.8179 q^{81} +24.0718i q^{82} +(-24.4833 + 24.4833i) q^{83} +(-11.4641 + 11.4641i) q^{84} +(-48.6340 - 48.6340i) q^{85} +(-19.0192 - 19.0192i) q^{86} -6.87564 q^{87} -64.8897i q^{88} +(-63.3013 - 63.3013i) q^{89} -16.3205i q^{90} -75.3731 q^{92} +(8.73205 - 8.73205i) q^{93} -25.1244 q^{94} +23.5167i q^{95} +(11.7321 - 11.7321i) q^{96} +(38.7654 - 38.7654i) q^{97} +(-5.04552 - 5.04552i) q^{98} +(97.0333 + 97.0333i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 4 q^{3} - 14 q^{5} - 8 q^{6} + 4 q^{7} - 6 q^{8} - 20 q^{9} - 32 q^{11} - 40 q^{14} - 20 q^{15} + 4 q^{16} - 2 q^{18} + 4 q^{19} - 22 q^{20} + 40 q^{21} + 8 q^{22} - 36 q^{24} - 32 q^{27}+ \cdots + 208 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 4 * q^3 - 14 * q^5 - 8 * q^6 + 4 * q^7 - 6 * q^8 - 20 * q^9 - 32 * q^11 - 40 * q^14 - 20 * q^15 + 4 * q^16 - 2 * q^18 + 4 * q^19 - 22 * q^20 + 40 * q^21 + 8 * q^22 - 36 * q^24 - 32 * q^27 + 28 * q^28 - 4 * q^29 - 20 * q^31 - 26 * q^32 - 8 * q^33 - 18 * q^34 - 64 * q^35 + 106 * q^37 + 72 * q^40 - 38 * q^41 - 88 * q^42 + 88 * q^44 + 58 * q^45 - 12 * q^46 - 68 * q^47 + 100 * q^48 + 44 * q^50 + 128 * q^53 + 88 * q^54 + 200 * q^55 - 20 * q^57 + 38 * q^58 + 196 * q^59 + 8 * q^60 + 248 * q^61 + 52 * q^63 + 80 * q^66 + 52 * q^67 - 144 * q^68 + 164 * q^70 - 20 * q^71 - 30 * q^72 + 58 * q^73 - 136 * q^74 + 32 * q^76 - 40 * q^79 - 62 * q^80 + 4 * q^81 - 188 * q^83 - 32 * q^84 - 198 * q^85 - 180 * q^86 - 76 * q^87 - 80 * q^89 - 156 * q^92 + 28 * q^93 - 52 * q^94 + 40 * q^96 - 32 * q^97 - 86 * q^98 + 208 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.366025	−	0.366025i	0.183013	−	0.183013i	−0.609655	−	0.792667i	$-0.708692\pi$
$2$	0.366025	−	0.366025i	0.183013	−	0.183013i	0.792667	+	0.609655i	$0.208692\pi$
$3$	−0.732051			−0.244017			−0.122008	−	0.992529i	$-0.538934\pi$
$3$	−0.732051			−0.244017			−0.122008	+	0.992529i	$0.538934\pi$
$4$			3.73205i			0.933013i
$5$	−2.63397	+	2.63397i	−0.526795	+	0.526795i	−0.919615	−	0.392820i	$-0.871499\pi$
$5$	−2.63397	+	2.63397i	−0.526795	+	0.526795i	0.392820	+	0.919615i	$0.371499\pi$
$6$	−0.267949	+	0.267949i	−0.0446582	+	0.0446582i
$7$	−4.19615	−	4.19615i	−0.599450	−	0.599450i	0.340716	−	0.940166i	$-0.389331\pi$
$7$	−4.19615	−	4.19615i	−0.599450	−	0.599450i	−0.940166	+	0.340716i	$0.889331\pi$
$8$	2.83013	+	2.83013i	0.353766	+	0.353766i
$9$	−8.46410			−0.940456
$10$			1.92820i			0.192820i
$11$	−11.4641	−	11.4641i	−1.04219	−	1.04219i	−0.999070	−	0.0431212i	$-0.986270\pi$
$11$	−11.4641	−	11.4641i	−1.04219	−	1.04219i	−0.0431212	−	0.999070i	$-0.513730\pi$
$12$		−	2.73205i		−	0.227671i
$13$		0			0
$13$		0			0
$14$	−3.07180			−0.219414
$15$	1.92820	−	1.92820i	0.128547	−	0.128547i
$16$	−12.8564			−0.803525
$17$			18.4641i			1.08612i	0.839693	+	0.543062i	$0.182735\pi$
$17$			18.4641i			1.08612i	−0.839693	+	0.543062i	$0.817265\pi$
$18$	−3.09808	+	3.09808i	−0.172115	+	0.172115i
$19$	4.46410	−	4.46410i	0.234953	−	0.234953i	−0.579804	−	0.814756i	$-0.696871\pi$
$19$	4.46410	−	4.46410i	0.234953	−	0.234953i	0.814756	+	0.579804i	$0.196871\pi$
$20$	−9.83013	−	9.83013i	−0.491506	−	0.491506i
$21$	3.07180	+	3.07180i	0.146276	+	0.146276i
$22$	−8.39230			−0.381468
$23$			20.1962i			0.878094i	0.898464	+	0.439047i	$0.144684\pi$
$23$			20.1962i			0.878094i	−0.898464	+	0.439047i	$0.855316\pi$
$24$	−2.07180	−	2.07180i	−0.0863249	−	0.0863249i
$25$			11.1244i			0.444974i
$26$		0			0
$27$	12.7846			0.473504
$28$	15.6603	−	15.6603i	0.559295	−	0.559295i
$29$	9.39230			0.323873			0.161936	−	0.986801i	$-0.448226\pi$
$29$	9.39230			0.323873			0.161936	+	0.986801i	$0.448226\pi$
$30$		−	1.41154i		−	0.0470514i
$31$	−11.9282	+	11.9282i	−0.384781	+	0.384781i	−0.872821	−	0.488040i	$-0.837712\pi$
$31$	−11.9282	+	11.9282i	−0.384781	+	0.384781i	0.488040	+	0.872821i	$0.337712\pi$
$32$	−16.0263	+	16.0263i	−0.500821	+	0.500821i
$33$	8.39230	+	8.39230i	0.254312	+	0.254312i
$34$	6.75833	+	6.75833i	0.198774	+	0.198774i
$35$	22.1051			0.631575
$36$		−	31.5885i		−	0.877457i
$37$	22.1699	+	22.1699i	0.599186	+	0.599186i	0.940096	−	0.340910i	$-0.110735\pi$
$37$	22.1699	+	22.1699i	0.599186	+	0.599186i	−0.340910	+	0.940096i	$0.610735\pi$
$38$		−	3.26795i		−	0.0859987i
$39$		0			0
$40$	−14.9090			−0.372724
$41$	−32.8827	+	32.8827i	−0.802017	+	0.802017i	−0.983411	−	0.181394i	$-0.941939\pi$
$41$	−32.8827	+	32.8827i	−0.802017	+	0.802017i	0.181394	+	0.983411i	$0.441939\pi$
$42$	2.24871			0.0535407
$43$		−	51.9615i		−	1.20841i	−0.796830	−	0.604204i	$-0.793491\pi$
$43$		−	51.9615i		−	1.20841i	0.796830	−	0.604204i	$-0.206509\pi$
$44$	42.7846	−	42.7846i	0.972377	−	0.972377i
$45$	22.2942	−	22.2942i	0.495427	−	0.495427i
$46$	7.39230	+	7.39230i	0.160702	+	0.160702i
$47$	−34.3205	−	34.3205i	−0.730224	−	0.730224i	0.240440	−	0.970664i	$-0.422708\pi$
$47$	−34.3205	−	34.3205i	−0.730224	−	0.730224i	−0.970664	+	0.240440i	$0.922708\pi$
$48$	9.41154			0.196074
$49$		−	13.7846i		−	0.281319i
$50$	4.07180	+	4.07180i	0.0814359	+	0.0814359i
$51$		−	13.5167i		−	0.265033i
$52$		0			0
$53$	−14.7654			−0.278592			−0.139296	−	0.990251i	$-0.544484\pi$
$53$	−14.7654			−0.278592			−0.139296	+	0.990251i	$0.544484\pi$
$54$	4.67949	−	4.67949i	0.0866573	−	0.0866573i
$55$	60.3923			1.09804
$56$		−	23.7513i		−	0.424130i
$57$	−3.26795	+	3.26795i	−0.0573324	+	0.0573324i
$58$	3.43782	−	3.43782i	0.0592728	−	0.0592728i
$59$	68.0526	+	68.0526i	1.15343	+	1.15343i	0.985860	+	0.167574i	$0.0535932\pi$
$59$	68.0526	+	68.0526i	1.15343	+	1.15343i	0.167574	+	0.985860i	$0.446407\pi$
$60$	7.19615	+	7.19615i	0.119936	+	0.119936i
$61$	25.6269			0.420114			0.210057	−	0.977689i	$-0.432635\pi$
$61$	25.6269			0.420114			0.210057	+	0.977689i	$0.432635\pi$
$62$			8.73205i			0.140840i
$63$	35.5167	+	35.5167i	0.563757	+	0.563757i
$64$		−	39.6936i		−	0.620212i
$65$		0			0
$66$	6.14359			0.0930848
$67$	−28.5692	+	28.5692i	−0.426406	+	0.426406i	−0.887402	−	0.460996i	$-0.847492\pi$
$67$	−28.5692	+	28.5692i	−0.426406	+	0.426406i	0.460996	+	0.887402i	$0.347492\pi$
$68$	−68.9090			−1.01337
$69$		−	14.7846i		−	0.214270i
$70$	8.09103	−	8.09103i	0.115586	−	0.115586i
$71$	−32.7128	+	32.7128i	−0.460744	+	0.460744i	−0.898899	−	0.438155i	$-0.855632\pi$
$71$	−32.7128	+	32.7128i	−0.460744	+	0.460744i	0.438155	+	0.898899i	$0.355632\pi$
$72$	−23.9545	−	23.9545i	−0.332701	−	0.332701i
$73$	−19.2750	−	19.2750i	−0.264041	−	0.264041i	0.562653	−	0.826693i	$-0.309781\pi$
$73$	−19.2750	−	19.2750i	−0.264041	−	0.264041i	−0.826693	+	0.562653i	$0.809781\pi$
$74$	16.2295			0.219317
$75$		−	8.14359i		−	0.108581i
$76$	16.6603	+	16.6603i	0.219214	+	0.219214i
$77$			96.2102i			1.24948i
$78$		0			0
$79$	62.7461			0.794255			0.397127	−	0.917763i	$-0.370007\pi$
$79$	62.7461			0.794255			0.397127	+	0.917763i	$0.370007\pi$
$80$	33.8634	−	33.8634i	0.423293	−	0.423293i
$81$	66.8179			0.824913
$82$			24.0718i			0.293558i
$83$	−24.4833	+	24.4833i	−0.294980	+	0.294980i	−0.839044	−	0.544064i	$-0.816885\pi$
$83$	−24.4833	+	24.4833i	−0.294980	+	0.294980i	0.544064	+	0.839044i	$0.316885\pi$
$84$	−11.4641	+	11.4641i	−0.136477	+	0.136477i
$85$	−48.6340	−	48.6340i	−0.572164	−	0.572164i
$86$	−19.0192	−	19.0192i	−0.221154	−	0.221154i
$87$	−6.87564			−0.0790304
$88$		−	64.8897i		−	0.737383i
$89$	−63.3013	−	63.3013i	−0.711250	−	0.711250i	0.255547	−	0.966797i	$-0.417745\pi$
$89$	−63.3013	−	63.3013i	−0.711250	−	0.711250i	−0.966797	+	0.255547i	$0.917745\pi$
$90$		−	16.3205i		−	0.181339i
$91$		0			0
$92$	−75.3731			−0.819272
$93$	8.73205	−	8.73205i	0.0938930	−	0.0938930i
$94$	−25.1244			−0.267280
$95$			23.5167i			0.247544i
$96$	11.7321	−	11.7321i	0.122209	−	0.122209i
$97$	38.7654	−	38.7654i	0.399643	−	0.399643i	−0.478464	−	0.878107i	$-0.658806\pi$
$97$	38.7654	−	38.7654i	0.399643	−	0.399643i	0.878107	+	0.478464i	$0.158806\pi$
$98$	−5.04552	−	5.04552i	−0.0514849	−	0.0514849i
$99$	97.0333	+	97.0333i	0.980135	+	0.980135i
$100$	−41.5167			−0.415167
$101$			159.995i			1.58411i	0.610451	+	0.792054i	$0.290988\pi$
$101$			159.995i			1.58411i	−0.610451	+	0.792054i	$0.709012\pi$
$102$	−4.94744	−	4.94744i	−0.0485043	−	0.0485043i
$103$		−	78.7705i		−	0.764762i	−0.924005	−	0.382381i	$-0.875104\pi$
$103$		−	78.7705i		−	0.764762i	0.924005	−	0.382381i	$-0.124896\pi$
$104$		0			0
$105$	−16.1821			−0.154115
$106$	−5.40450	+	5.40450i	−0.0509859	+	0.0509859i
$107$	−95.3346			−0.890977			−0.445489	−	0.895288i	$-0.646970\pi$
$107$	−95.3346			−0.890977			−0.445489	+	0.895288i	$0.646970\pi$
$108$			47.7128i			0.441785i
$109$	−51.9808	+	51.9808i	−0.476888	+	0.476888i	−0.904135	−	0.427247i	$-0.859483\pi$
$109$	−51.9808	+	51.9808i	−0.476888	+	0.476888i	0.427247	+	0.904135i	$0.359483\pi$
$110$	22.1051	−	22.1051i	0.200956	−	0.200956i
$111$	−16.2295	−	16.2295i	−0.146211	−	0.146211i
$112$	53.9474	+	53.9474i	0.481674	+	0.481674i
$113$	−143.981			−1.27417			−0.637083	−	0.770795i	$-0.719859\pi$
$113$	−143.981			−1.27417			−0.637083	+	0.770795i	$0.719859\pi$
$114$			2.39230i			0.0209851i
$115$	−53.1962	−	53.1962i	−0.462575	−	0.462575i
$116$			35.0526i			0.302177i
$117$		0			0
$118$	49.8179			0.422186
$119$	77.4782	−	77.4782i	0.651077	−	0.651077i
$120$	10.9141			0.0909510
$121$			141.851i			1.17232i
$122$	9.38011	−	9.38011i	0.0768861	−	0.0768861i
$123$	24.0718	−	24.0718i	0.195706	−	0.195706i
$124$	−44.5167	−	44.5167i	−0.359005	−	0.359005i
$125$	−95.1506	−	95.1506i	−0.761205	−	0.761205i
$126$	26.0000			0.206349
$127$		−	28.4833i		−	0.224278i	−0.993693	−	0.112139i	$-0.964230\pi$
$127$		−	28.4833i		−	0.224278i	0.993693	−	0.112139i	$-0.0357702\pi$
$128$	−78.6340	−	78.6340i	−0.614328	−	0.614328i
$129$			38.0385i			0.294872i
$130$		0			0
$131$	−2.98076			−0.0227539			−0.0113770	−	0.999935i	$-0.503621\pi$
$131$	−2.98076			−0.0227539			−0.0113770	+	0.999935i	$0.503621\pi$
$132$	−31.3205	+	31.3205i	−0.237277	+	0.237277i
$133$	−37.4641			−0.281685
$134$			20.9141i			0.156076i
$135$	−33.6743	+	33.6743i	−0.249440	+	0.249440i
$136$	−52.2558	+	52.2558i	−0.384233	+	0.384233i
$137$	−69.2558	−	69.2558i	−0.505516	−	0.505516i	0.407631	−	0.913147i	$-0.366355\pi$
$137$	−69.2558	−	69.2558i	−0.505516	−	0.505516i	−0.913147	+	0.407631i	$0.866355\pi$
$138$	−5.41154	−	5.41154i	−0.0392141	−	0.0392141i
$139$	32.4308			0.233315			0.116657	−	0.993172i	$-0.462782\pi$
$139$	32.4308			0.233315			0.116657	+	0.993172i	$0.462782\pi$
$140$			82.4974i			0.589267i
$141$	25.1244	+	25.1244i	0.178187	+	0.178187i
$142$			23.9474i			0.168644i
$143$		0			0
$144$	108.818			0.755680
$145$	−24.7391	+	24.7391i	−0.170614	+	0.170614i
$146$	−14.1103			−0.0966457
$147$			10.0910i			0.0686465i
$148$	−82.7391	+	82.7391i	−0.559048	+	0.559048i
$149$	−90.4045	+	90.4045i	−0.606742	+	0.606742i	−0.942093	−	0.335351i	$-0.891145\pi$
$149$	−90.4045	+	90.4045i	−0.606742	+	0.606742i	0.335351	+	0.942093i	$0.391145\pi$
$150$	−2.98076	−	2.98076i	−0.0198717	−	0.0198717i
$151$	127.995	+	127.995i	0.847648	+	0.847648i	0.989839	−	0.142191i	$-0.0454148\pi$
$151$	127.995	+	127.995i	0.847648	+	0.847648i	−0.142191	+	0.989839i	$0.545415\pi$
$152$	25.2679			0.166237
$153$		−	156.282i		−	1.02145i
$154$	35.2154	+	35.2154i	0.228671	+	0.228671i
$155$		−	62.8372i		−	0.405401i
$156$		0			0
$157$	−97.7461			−0.622587			−0.311293	−	0.950314i	$-0.600762\pi$
$157$	−97.7461			−0.622587			−0.311293	+	0.950314i	$0.600762\pi$
$158$	22.9667	−	22.9667i	0.145359	−	0.145359i
$159$	10.8090			0.0679811
$160$		−	84.4256i		−	0.527660i
$161$	84.7461	−	84.7461i	0.526374	−	0.526374i
$162$	24.4571	−	24.4571i	0.150970	−	0.150970i
$163$	89.5167	+	89.5167i	0.549182	+	0.549182i	0.926204	−	0.377022i	$-0.123052\pi$
$163$	89.5167	+	89.5167i	0.549182	+	0.549182i	−0.377022	+	0.926204i	$0.623052\pi$
$164$	−122.720	−	122.720i	−0.748292	−	0.748292i
$165$	−44.2102			−0.267941
$166$			17.9230i			0.107970i
$167$	−37.1384	−	37.1384i	−0.222386	−	0.222386i	0.587117	−	0.809502i	$-0.300263\pi$
$167$	−37.1384	−	37.1384i	−0.222386	−	0.222386i	−0.809502	+	0.587117i	$0.800263\pi$
$168$			17.3872i			0.103495i
$169$		0			0
$170$	−35.6025			−0.209427
$171$	−37.7846	+	37.7846i	−0.220963	+	0.220963i
$172$	193.923			1.12746
$173$		−	137.254i		−	0.793375i	−0.917954	−	0.396687i	$-0.870160\pi$
$173$		−	137.254i		−	0.793375i	0.917954	−	0.396687i	$-0.129840\pi$
$174$	−2.51666	+	2.51666i	−0.0144636	+	0.0144636i
$175$	46.6795	−	46.6795i	0.266740	−	0.266740i
$176$	147.387	+	147.387i	0.837427	+	0.837427i
$177$	−49.8179	−	49.8179i	−0.281457	−	0.281457i
$178$	−46.3397			−0.260336
$179$			1.04363i			0.00583034i	0.999996	+	0.00291517i	$0.000927928\pi$
$179$			1.04363i			0.00583034i	−0.999996	+	0.00291517i	$0.999072\pi$
$180$	83.2032	+	83.2032i	0.462240	+	0.462240i
$181$		−	23.0807i		−	0.127518i	−0.997965	−	0.0637589i	$-0.979691\pi$
$181$		−	23.0807i		−	0.127518i	0.997965	−	0.0637589i	$-0.0203089\pi$
$182$		0			0
$183$	−18.7602			−0.102515
$184$	−57.1577	+	57.1577i	−0.310640	+	0.310640i
$185$	−116.790			−0.631296
$186$		−	6.39230i		−	0.0343672i
$187$	211.674	−	211.674i	1.13195	−	1.13195i
$188$	128.086	−	128.086i	0.681308	−	0.681308i
$189$	−53.6462	−	53.6462i	−0.283842	−	0.283842i
$190$	8.60770	+	8.60770i	0.0453037	+	0.0453037i
$191$	294.004			1.53929			0.769643	−	0.638474i	$-0.220434\pi$
$191$	294.004			1.53929			0.769643	+	0.638474i	$0.220434\pi$
$192$			29.0577i			0.151342i
$193$	233.729	+	233.729i	1.21103	+	1.21103i	0.970688	+	0.240342i	$0.0772595\pi$
$193$	233.729	+	233.729i	1.21103	+	1.21103i	0.240342	+	0.970688i	$0.422741\pi$
$194$		−	28.3782i		−	0.146279i
$195$		0			0
$196$	51.4449			0.262474
$197$	−62.3064	+	62.3064i	−0.316276	+	0.316276i	−0.847335	−	0.531059i	$-0.821794\pi$
$197$	−62.3064	+	62.3064i	−0.316276	+	0.316276i	0.531059	+	0.847335i	$0.321794\pi$
$198$	71.0333			0.358754
$199$		−	201.440i		−	1.01226i	−0.862457	−	0.506130i	$-0.831076\pi$
$199$		−	201.440i		−	1.01226i	0.862457	−	0.506130i	$-0.168924\pi$
$200$	−31.4833	+	31.4833i	−0.157417	+	0.157417i
$201$	20.9141	−	20.9141i	0.104050	−	0.104050i
$202$	58.5622	+	58.5622i	0.289912	+	0.289912i
$203$	−39.4115	−	39.4115i	−0.194146	−	0.194146i
$204$	50.4449			0.247279
$205$		−	173.224i		−	0.844997i
$206$	−28.8320	−	28.8320i	−0.139961	−	0.139961i
$207$		−	170.942i		−	0.825808i
$208$		0			0
$209$	−102.354			−0.489731
$210$	−5.92305	+	5.92305i	−0.0282050	+	0.0282050i
$211$	73.2961			0.347375			0.173687	−	0.984801i	$-0.444432\pi$
$211$	73.2961			0.347375			0.173687	+	0.984801i	$0.444432\pi$
$212$		−	55.1051i		−	0.259930i
$213$	23.9474	−	23.9474i	0.112429	−	0.112429i
$214$	−34.8949	+	34.8949i	−0.163060	+	0.163060i
$215$	136.865	+	136.865i	0.636583	+	0.636583i
$216$	36.1821	+	36.1821i	0.167510	+	0.167510i
$217$	100.105			0.461314
$218$			38.0526i			0.174553i
$219$	14.1103	+	14.1103i	0.0644305	+	0.0644305i
$220$			225.387i			1.02449i
$221$		0			0
$222$	−11.8808			−0.0535171
$223$	269.053	−	269.053i	1.20651	−	1.20651i	0.234365	−	0.972149i	$-0.424699\pi$
$223$	269.053	−	269.053i	1.20651	−	1.20651i	0.972149	−	0.234365i	$-0.0753011\pi$
$224$	134.497			0.600435
$225$		−	94.1577i		−	0.418479i
$226$	−52.7006	+	52.7006i	−0.233189	+	0.233189i
$227$	−295.827	+	295.827i	−1.30320	+	1.30320i	−0.376981	+	0.926221i	$0.623038\pi$
$227$	−295.827	+	295.827i	−1.30320	+	1.30320i	−0.926221	+	0.376981i	$0.876962\pi$
$228$	−12.1962	−	12.1962i	−0.0534919	−	0.0534919i
$229$	−72.2679	−	72.2679i	−0.315581	−	0.315581i	0.531486	−	0.847067i	$-0.321634\pi$
$229$	−72.2679	−	72.2679i	−0.315581	−	0.315581i	−0.847067	+	0.531486i	$0.821634\pi$
$230$	−38.9423			−0.169314
$231$		−	70.4308i		−	0.304895i
$232$	26.5814	+	26.5814i	0.114575	+	0.114575i
$233$			256.592i			1.10125i	0.834751	+	0.550627i	$0.185611\pi$
$233$			256.592i			1.10125i	−0.834751	+	0.550627i	$0.814389\pi$
$234$		0			0
$235$	180.799			0.769356
$236$	−253.976	+	253.976i	−1.07617	+	1.07617i
$237$	−45.9334			−0.193812
$238$		−	56.7180i		−	0.238311i
$239$	39.3449	−	39.3449i	0.164623	−	0.164623i	−0.619988	−	0.784611i	$-0.712863\pi$
$239$	39.3449	−	39.3449i	0.164623	−	0.164623i	0.784611	+	0.619988i	$0.212863\pi$
$240$	−24.7898	+	24.7898i	−0.103291	+	0.103291i
$241$	−170.825	−	170.825i	−0.708817	−	0.708817i	0.257469	−	0.966287i	$-0.417111\pi$
$241$	−170.825	−	170.825i	−0.708817	−	0.708817i	−0.966287	+	0.257469i	$0.917111\pi$
$242$	51.9212	+	51.9212i	0.214550	+	0.214550i
$243$	−163.976			−0.674797
$244$			95.6410i			0.391971i
$245$	36.3083	+	36.3083i	0.148197	+	0.148197i
$246$		−	17.6218i		−	0.0716332i
$247$		0			0
$248$	−67.5167			−0.272245
$249$	17.9230	−	17.9230i	0.0719801	−	0.0719801i
$250$	−69.6551			−0.278620
$251$			255.622i			1.01841i	0.860644	+	0.509207i	$0.170061\pi$
$251$			255.622i			1.01841i	−0.860644	+	0.509207i	$0.829939\pi$
$252$	−132.550	+	132.550i	−0.525992	+	0.525992i
$253$	231.531	−	231.531i	0.915141	−	0.915141i
$254$	−10.4256	−	10.4256i	−0.0410458	−	0.0410458i
$255$	35.6025	+	35.6025i	0.139618	+	0.139618i
$256$	101.210			0.395352
$257$			99.0422i			0.385378i	0.981260	+	0.192689i	$0.0617209\pi$
$257$			99.0422i			0.385378i	−0.981260	+	0.192689i	$0.938279\pi$
$258$	13.9230	+	13.9230i	0.0539653	+	0.0539653i
$259$		−	186.056i		−	0.718364i
$260$		0			0
$261$	−79.4974			−0.304588
$262$	−1.09103	+	1.09103i	−0.00416425	+	0.00416425i
$263$	−255.338			−0.970868			−0.485434	−	0.874273i	$-0.661338\pi$
$263$	−255.338			−0.970868			−0.485434	+	0.874273i	$0.661338\pi$
$264$			47.5026i			0.179934i
$265$	38.8916	−	38.8916i	0.146761	−	0.146761i
$266$	−13.7128	+	13.7128i	−0.0515519	+	0.0515519i
$267$	46.3397	+	46.3397i	0.173557	+	0.173557i
$268$	−106.622	−	106.622i	−0.397842	−	0.397842i
$269$	−92.7077			−0.344638			−0.172319	−	0.985041i	$-0.555126\pi$
$269$	−92.7077			−0.344638			−0.172319	+	0.985041i	$0.555126\pi$
$270$			24.6513i			0.0913012i
$271$	−309.086	−	309.086i	−1.14054	−	1.14054i	−0.988352	−	0.152187i	$-0.951369\pi$
$271$	−309.086	−	309.086i	−1.14054	−	1.14054i	−0.152187	−	0.988352i	$-0.548631\pi$
$272$		−	237.382i		−	0.872728i
$273$		0			0
$274$	−50.6987			−0.185032
$275$	127.531	−	127.531i	0.463748	−	0.463748i
$276$	55.1769			0.199916
$277$			348.846i			1.25937i	0.776850	+	0.629686i	$0.216816\pi$
$277$			348.846i			1.25937i	−0.776850	+	0.629686i	$0.783184\pi$
$278$	11.8705	−	11.8705i	0.0426996	−	0.0426996i
$279$	100.962	−	100.962i	0.361869	−	0.361869i
$280$	62.5603	+	62.5603i	0.223430	+	0.223430i
$281$	91.9737	+	91.9737i	0.327309	+	0.327309i	0.851562	−	0.524254i	$-0.175656\pi$
$281$	91.9737	+	91.9737i	0.327309	+	0.327309i	−0.524254	+	0.851562i	$0.675656\pi$
$282$	18.3923			0.0652209
$283$		−	35.5692i		−	0.125686i	−0.998023	−	0.0628431i	$-0.979983\pi$
$283$		−	35.5692i		−	0.125686i	0.998023	−	0.0628431i	$-0.0200168\pi$
$284$	−122.086	−	122.086i	−0.429880	−	0.429880i
$285$		−	17.2154i		−	0.0604049i
$286$		0			0
$287$	275.962			0.961538
$288$	135.648	−	135.648i	0.471000	−	0.471000i
$289$	−51.9230			−0.179665
$290$			18.1103i			0.0624492i
$291$	−28.3782	+	28.3782i	−0.0975197	+	0.0975197i
$292$	71.9352	−	71.9352i	0.246354	−	0.246354i
$293$	−283.126	−	283.126i	−0.966301	−	0.966301i	0.0331492	−	0.999450i	$-0.489446\pi$
$293$	−283.126	−	283.126i	−0.966301	−	0.966301i	−0.999450	+	0.0331492i	$0.989446\pi$
$294$	3.69358	+	3.69358i	0.0125632	+	0.0125632i
$295$	−358.497			−1.21525
$296$			125.487i			0.423943i
$297$	−146.564	−	146.564i	−0.493482	−	0.493482i
$298$			66.1807i			0.222083i
$299$		0			0
$300$	30.3923			0.101308
$301$	−218.038	+	218.038i	−0.724380	+	0.724380i
$302$	93.6987			0.310261
$303$		−	117.124i		−	0.386549i
$304$	−57.3923	+	57.3923i	−0.188790	+	0.188790i
$305$	−67.5007	+	67.5007i	−0.221314	+	0.221314i
$306$	−57.2032	−	57.2032i	−0.186939	−	0.186939i
$307$	260.219	+	260.219i	0.847619	+	0.847619i	0.989836	−	0.142216i	$-0.0454228\pi$
$307$	260.219	+	260.219i	0.847619	+	0.847619i	−0.142216	+	0.989836i	$0.545423\pi$
$308$	−359.061			−1.16578
$309$			57.6640i			0.186615i
$310$	−23.0000	−	23.0000i	−0.0741935	−	0.0741935i
$311$		−	71.4782i		−	0.229833i	−0.993375	−	0.114917i	$-0.963340\pi$
$311$		−	71.4782i		−	0.229833i	0.993375	−	0.114917i	$-0.0366601\pi$
$312$		0			0
$313$	−394.315			−1.25979			−0.629897	−	0.776679i	$-0.716903\pi$
$313$	−394.315			−1.25979			−0.629897	+	0.776679i	$0.716903\pi$
$314$	−35.7776	+	35.7776i	−0.113941	+	0.113941i
$315$	−187.100			−0.593968
$316$			234.172i			0.741050i
$317$	−206.054	+	206.054i	−0.650014	+	0.650014i	−0.952996	−	0.302982i	$-0.902018\pi$
$317$	−206.054	+	206.054i	−0.650014	+	0.650014i	0.302982	+	0.952996i	$0.402018\pi$
$318$	3.95637	−	3.95637i	0.0124414	−	0.0124414i
$319$	−107.674	−	107.674i	−0.337537	−	0.337537i
$320$	104.552	+	104.552i	0.326725	+	0.326725i
$321$	69.7898			0.217414
$322$		−	62.0385i		−	0.192666i
$323$	82.4256	+	82.4256i	0.255188	+	0.255188i
$324$			249.368i			0.769654i
$325$		0			0
$326$	65.5307			0.201015
$327$	38.0526	−	38.0526i	0.116369	−	0.116369i
$328$	−186.124			−0.567452
$329$			288.028i			0.875466i
$330$	−16.1821	+	16.1821i	−0.0490366	+	0.0490366i
$331$	−326.200	+	326.200i	−0.985498	+	0.985498i	−0.999896	−	0.0143981i	$-0.995417\pi$
$331$	−326.200	+	326.200i	−0.985498	+	0.985498i	0.0143981	+	0.999896i	$0.495417\pi$
$332$	−91.3731	−	91.3731i	−0.275220	−	0.275220i
$333$	−187.648	−	187.648i	−0.563508	−	0.563508i
$334$	−27.1872			−0.0813989
$335$		−	150.501i		−	0.449257i
$336$	−39.4923	−	39.4923i	−0.117537	−	0.117537i
$337$			144.779i			0.429613i	0.976657	+	0.214806i	$0.0689120\pi$
$337$			144.779i			0.429613i	−0.976657	+	0.214806i	$0.931088\pi$
$338$		0			0
$339$	105.401			0.310918
$340$	181.504	−	181.504i	0.533837	−	0.533837i
$341$	273.492			0.802030
$342$			27.6603i			0.0808779i
$343$	−263.454	+	263.454i	−0.768087	+	0.768087i
$344$	147.058	−	147.058i	0.427493	−	0.427493i
$345$	38.9423	+	38.9423i	0.112876	+	0.112876i
$346$	−50.2384	−	50.2384i	−0.145198	−	0.145198i
$347$	487.181			1.40398			0.701989	−	0.712187i	$-0.252295\pi$
$347$	487.181			1.40398			0.701989	+	0.712187i	$0.252295\pi$
$348$		−	25.6603i		−	0.0737364i
$349$	−8.30642	−	8.30642i	−0.0238006	−	0.0238006i	0.695106	−	0.718907i	$-0.255357\pi$
$349$	−8.30642	−	8.30642i	−0.0238006	−	0.0238006i	−0.718907	+	0.695106i	$0.755357\pi$
$350$		−	34.1718i		−	0.0976336i
$351$		0			0
$352$	367.454			1.04390
$353$	202.170	−	202.170i	0.572719	−	0.572719i	−0.360168	−	0.932887i	$-0.617281\pi$
$353$	202.170	−	202.170i	0.572719	−	0.572719i	0.932887	+	0.360168i	$0.117281\pi$
$354$	−36.4693			−0.103020
$355$		−	172.329i		−	0.485435i
$356$	236.244	−	236.244i	0.663605	−	0.663605i
$357$	−56.7180	+	56.7180i	−0.158874	+	0.158874i
$358$	0.381995	+	0.381995i	0.00106703	+	0.00106703i
$359$	92.0770	+	92.0770i	0.256482	+	0.256482i	0.823622	−	0.567140i	$-0.191950\pi$
$359$	92.0770	+	92.0770i	0.256482	+	0.256482i	−0.567140	+	0.823622i	$0.691950\pi$
$360$	126.191			0.350531
$361$			321.144i			0.889594i
$362$	−8.44813	−	8.44813i	−0.0233374	−	0.0233374i
$363$		−	103.842i		−	0.286067i
$364$		0			0
$365$	101.540			0.278191
$366$	−6.86672	+	6.86672i	−0.0187615	+	0.0187615i
$367$	12.5500			0.0341961			0.0170981	−	0.999854i	$-0.494557\pi$
$367$	12.5500			0.0341961			0.0170981	+	0.999854i	$0.494557\pi$
$368$		−	259.650i		−	0.705571i
$369$	278.322	−	278.322i	0.754261	−	0.754261i
$370$	−42.7480	+	42.7480i	−0.115535	+	0.115535i
$371$	61.9578	+	61.9578i	0.167002	+	0.167002i
$372$	32.5885	+	32.5885i	0.0876034	+	0.0876034i
$373$	−311.277			−0.834522			−0.417261	−	0.908787i	$-0.637010\pi$
$373$	−311.277			−0.834522			−0.417261	+	0.908787i	$0.637010\pi$
$374$		−	154.956i		−	0.414322i
$375$	69.6551	+	69.6551i	0.185747	+	0.185747i
$376$		−	194.263i		−	0.516656i
$377$		0			0
$378$	−39.2717			−0.103893
$379$	−278.076	+	278.076i	−0.733709	+	0.733709i	−0.971352	−	0.237644i	$-0.923625\pi$
$379$	−278.076	+	278.076i	−0.733709	+	0.733709i	0.237644	+	0.971352i	$0.423625\pi$
$380$	−87.7654			−0.230962
$381$			20.8513i			0.0547277i
$382$	107.613	−	107.613i	0.281709	−	0.281709i
$383$	521.990	−	521.990i	1.36290	−	1.36290i	0.492696	−	0.870202i	$-0.336012\pi$
$383$	521.990	−	521.990i	1.36290	−	1.36290i	0.870202	−	0.492696i	$-0.163988\pi$
$384$	57.5641	+	57.5641i	0.149906	+	0.149906i
$385$	−253.415	−	253.415i	−0.658222	−	0.658222i
$386$	171.101			0.443268
$387$			439.808i			1.13645i
$388$	144.674	+	144.674i	0.372872	+	0.372872i
$389$			344.478i			0.885548i	0.896633	+	0.442774i	$0.146006\pi$
$389$			344.478i			0.885548i	−0.896633	+	0.442774i	$0.853994\pi$
$390$		0			0
$391$	−372.904			−0.953718
$392$	39.0122	−	39.0122i	0.0995209	−	0.0995209i
$393$	2.18207			0.00555234
$394$			45.6115i			0.115765i
$395$	−165.272	+	165.272i	−0.418409	+	0.418409i
$396$	−362.133	+	362.133i	−0.914478	+	0.914478i
$397$	496.640	+	496.640i	1.25098	+	1.25098i	0.955281	+	0.295701i	$0.0955532\pi$
$397$	496.640	+	496.640i	1.25098	+	1.25098i	0.295701	+	0.955281i	$0.404447\pi$
$398$	−73.7321	−	73.7321i	−0.185256	−	0.185256i
$399$	27.4256			0.0687359
$400$		−	143.019i		−	0.357548i
$401$	401.156	+	401.156i	1.00039	+	1.00039i	1.00000		0.000388579i	$0.000123689\pi$
$401$	401.156	+	401.156i	1.00039	+	1.00039i	0.000388579		1.00000i	$0.499876\pi$
$402$		−	15.3102i		−	0.0380851i
$403$		0			0
$404$	−597.109			−1.47799
$405$	−175.997	+	175.997i	−0.434560	+	0.434560i
$406$	−28.8513			−0.0710622
$407$		−	508.315i		−	1.24893i
$408$	38.2539	−	38.2539i	0.0937595	−	0.0937595i
$409$	71.9109	−	71.9109i	0.175821	−	0.175821i	−0.613710	−	0.789531i	$-0.710324\pi$
$409$	71.9109	−	71.9109i	0.175821	−	0.175821i	0.789531	+	0.613710i	$0.210324\pi$
$410$	−63.4045	−	63.4045i	−0.154645	−	0.154645i
$411$	50.6987	+	50.6987i	0.123355	+	0.123355i
$412$	293.976			0.713533
$413$		−	571.118i		−	1.38285i
$414$	−62.5692	−	62.5692i	−0.151133	−	0.151133i
$415$		−	128.977i		−	0.310788i
$416$		0			0
$417$	−23.7410			−0.0569328
$418$	−37.4641	+	37.4641i	−0.0896270	+	0.0896270i
$419$	644.558			1.53832			0.769162	−	0.639054i	$-0.220674\pi$
$419$	644.558			1.53832			0.769162	+	0.639054i	$0.220674\pi$
$420$		−	60.3923i		−	0.143791i
$421$	346.619	−	346.619i	0.823322	−	0.823322i	−0.163261	−	0.986583i	$-0.552201\pi$
$421$	346.619	−	346.619i	0.823322	−	0.823322i	0.986583	+	0.163261i	$0.0522013\pi$
$422$	26.8282	−	26.8282i	0.0635740	−	0.0635740i
$423$	290.492	+	290.492i	0.686743	+	0.686743i
$424$	−41.7879	−	41.7879i	−0.0985563	−	0.0985563i
$425$	−205.401			−0.483297
$426$		−	17.5307i		−	0.0411520i
$427$	−107.535	−	107.535i	−0.251837	−	0.251837i
$428$		−	355.794i		−	0.831293i
$429$		0			0
$430$	100.192			0.233006
$431$	−74.4486	+	74.4486i	−0.172735	+	0.172735i	−0.788180	−	0.615445i	$-0.788976\pi$
$431$	−74.4486	+	74.4486i	−0.172735	+	0.172735i	0.615445	+	0.788180i	$0.288976\pi$
$432$	−164.364			−0.380473
$433$		−	689.232i		−	1.59176i	−0.605455	−	0.795880i	$-0.707009\pi$
$433$		−	689.232i		−	1.59176i	0.605455	−	0.795880i	$-0.292991\pi$
$434$	36.6410	−	36.6410i	0.0844263	−	0.0844263i
$435$	18.1103	−	18.1103i	0.0416328	−	0.0416328i
$436$	−193.995	−	193.995i	−0.444942	−	0.444942i
$437$	90.1577	+	90.1577i	0.206310	+	0.206310i
$438$	10.3294			0.0235832
$439$			90.1333i			0.205315i	0.994717	+	0.102657i	$0.0327346\pi$
$439$			90.1333i			0.205315i	−0.994717	+	0.102657i	$0.967265\pi$
$440$	170.918	+	170.918i	0.388450	+	0.388450i
$441$			116.674i			0.264568i
$442$		0			0
$443$	642.277			1.44983			0.724917	−	0.688836i	$-0.241878\pi$
$443$	642.277			1.44983			0.724917	+	0.688836i	$0.241878\pi$
$444$	60.5692	−	60.5692i	0.136417	−	0.136417i
$445$	333.468			0.749366
$446$		−	196.960i		−	0.441615i
$447$	66.1807	−	66.1807i	0.148055	−	0.148055i
$448$	−166.560	+	166.560i	−0.371786	+	0.371786i
$449$	−16.5448	−	16.5448i	−0.0368482	−	0.0368482i	0.688443	−	0.725291i	$-0.258295\pi$
$449$	−16.5448	−	16.5448i	−0.0368482	−	0.0368482i	−0.725291	+	0.688443i	$0.758295\pi$
$450$	−34.4641	−	34.4641i	−0.0765869	−	0.0765869i
$451$	753.941			1.67171
$452$		−	537.344i		−	1.18881i
$453$	−93.6987	−	93.6987i	−0.206840	−	0.206840i
$454$			216.560i			0.477005i
$455$		0			0
$456$	−18.4974			−0.0405645
$457$	−167.419	+	167.419i	−0.366343	+	0.366343i	−0.866141	−	0.499799i	$-0.833407\pi$
$457$	−167.419	+	167.419i	−0.366343	+	0.366343i	0.499799	+	0.866141i	$0.333407\pi$
$458$	−52.9038			−0.115511
$459$			236.056i			0.514284i
$460$	198.531	−	198.531i	0.431589	−	0.431589i
$461$	−34.4327	+	34.4327i	−0.0746913	+	0.0746913i	−0.743466	−	0.668774i	$-0.766819\pi$
$461$	−34.4327	+	34.4327i	−0.0746913	+	0.0746913i	0.668774	+	0.743466i	$0.266819\pi$
$462$	−25.7795	−	25.7795i	−0.0557997	−	0.0557997i
$463$	−521.191	−	521.191i	−1.12568	−	1.12568i	−0.990871	−	0.134811i	$-0.956957\pi$
$463$	−521.191	−	521.191i	−1.12568	−	1.12568i	−0.134811	−	0.990871i	$-0.543043\pi$
$464$	−120.751			−0.260240
$465$			46.0000i			0.0989247i
$466$	93.9193	+	93.9193i	0.201544	+	0.201544i
$467$		−	141.415i		−	0.302817i	−0.988471	−	0.151408i	$-0.951619\pi$
$467$		−	141.415i		−	0.302817i	0.988471	−	0.151408i	$-0.0483808\pi$
$468$		0			0
$469$	239.762			0.511219
$470$	66.1769	−	66.1769i	0.140802	−	0.140802i
$471$	71.5551			0.151922
$472$			385.195i			0.816091i
$473$	−595.692	+	595.692i	−1.25939	+	1.25939i
$474$	−16.8128	+	16.8128i	−0.0354700	+	0.0354700i
$475$	49.6603	+	49.6603i	0.104548	+	0.104548i
$476$	289.153	+	289.153i	0.607463	+	0.607463i
$477$	124.976			0.262003
$478$		−	28.8025i		−	0.0602562i
$479$	529.424	+	529.424i	1.10527	+	1.10527i	0.993764	+	0.111506i	$0.0355675\pi$
$479$	529.424	+	529.424i	1.10527	+	1.10527i	0.111506	+	0.993764i	$0.464433\pi$
$480$			61.8038i			0.128758i
$481$		0			0
$482$	−125.053			−0.259445
$483$	−62.0385	+	62.0385i	−0.128444	+	0.128444i
$484$	−529.396			−1.09379
$485$			204.214i			0.421060i
$486$	−60.0192	+	60.0192i	−0.123496	+	0.123496i
$487$	−171.947	+	171.947i	−0.353075	+	0.353075i	−0.861252	−	0.508178i	$-0.830319\pi$
$487$	−171.947	+	171.947i	−0.353075	+	0.353075i	0.508178	+	0.861252i	$0.330319\pi$
$488$	72.5275	+	72.5275i	0.148622	+	0.148622i
$489$	−65.5307	−	65.5307i	−0.134010	−	0.134010i
$490$	26.5795			0.0542439
$491$		−	84.6616i		−	0.172427i	−0.996277	−	0.0862135i	$-0.972523\pi$
$491$		−	84.6616i		−	0.172427i	0.996277	−	0.0862135i	$-0.0274767\pi$
$492$	89.8372	+	89.8372i	0.182596	+	0.182596i
$493$			173.420i			0.351766i
$494$		0			0
$495$	−511.167			−1.03266
$496$	153.354	−	153.354i	0.309181	−	0.309181i
$497$	274.536			0.552386
$498$		−	13.1206i		−	0.0263466i
$499$	−134.397	+	134.397i	−0.269334	+	0.269334i	−0.828832	−	0.559498i	$-0.810994\pi$
$499$	−134.397	+	134.397i	−0.269334	+	0.269334i	0.559498	+	0.828832i	$0.310994\pi$
$500$	355.107	−	355.107i	0.710214	−	0.710214i
$501$	27.1872	+	27.1872i	0.0542659	+	0.0542659i
$502$	93.5641	+	93.5641i	0.186383	+	0.186383i
$503$	−796.400			−1.58330			−0.791650	−	0.610975i	$-0.790778\pi$
$503$	−796.400			−1.58330			−0.791650	+	0.610975i	$0.790778\pi$
$504$			201.033i			0.398876i
$505$	−421.422	−	421.422i	−0.834500	−	0.834500i
$506$		−	169.492i		−	0.334965i
$507$		0			0
$508$	106.301			0.209254
$509$	−58.2750	+	58.2750i	−0.114489	+	0.114489i	−0.762030	−	0.647541i	$-0.775797\pi$
$509$	−58.2750	+	58.2750i	−0.114489	+	0.114489i	0.647541	+	0.762030i	$0.275797\pi$
$510$	26.0629			0.0511037
$511$			161.762i			0.316559i
$512$	351.581	−	351.581i	0.686682	−	0.686682i
$513$	57.0718	−	57.0718i	0.111251	−	0.111251i
$514$	36.2520	+	36.2520i	0.0705291	+	0.0705291i
$515$	207.480	+	207.480i	0.402873	+	0.402873i
$516$	−141.962			−0.275119
$517$			786.908i			1.52206i
$518$	−68.1013	−	68.1013i	−0.131470	−	0.131470i
$519$			100.477i			0.193597i
$520$		0			0
$521$	677.011			1.29945			0.649723	−	0.760171i	$-0.274885\pi$
$521$	677.011			1.29945			0.649723	+	0.760171i	$0.274885\pi$
$522$	−29.0981	+	29.0981i	−0.0557434	+	0.0557434i
$523$	−183.654			−0.351154			−0.175577	−	0.984466i	$-0.556179\pi$
$523$	−183.654			−0.351154			−0.175577	+	0.984466i	$0.556179\pi$
$524$		−	11.1244i		−	0.0212297i
$525$	−34.1718	+	34.1718i	−0.0650891	+	0.0650891i
$526$	−93.4603	+	93.4603i	−0.177681	+	0.177681i
$527$	−220.244	−	220.244i	−0.417919	−	0.417919i
$528$	−107.895	−	107.895i	−0.204346	−	0.204346i
$529$	121.115			0.228952
$530$		−	28.4706i		−	0.0537182i
$531$	−576.004	−	576.004i	−1.08475	−	1.08475i
$532$		−	139.818i		−	0.262816i
$533$		0			0
$534$	33.9230			0.0635263
$535$	251.109	−	251.109i	0.469362	−	0.469362i
$536$	−161.709			−0.301696
$537$		−	0.763991i		−	0.00142270i
$538$	−33.9334	+	33.9334i	−0.0630732	+	0.0630732i
$539$	−158.028	+	158.028i	−0.293188	+	0.293188i
$540$	−125.674	−	125.674i	−0.232730	−	0.232730i
$541$	317.629	+	317.629i	0.587114	+	0.587114i	0.936849	−	0.349735i	$-0.113728\pi$
$541$	317.629	+	317.629i	0.587114	+	0.587114i	−0.349735	+	0.936849i	$0.613728\pi$
$542$	−226.267			−0.417466
$543$			16.8963i			0.0311165i
$544$	−295.911	−	295.911i	−0.543954	−	0.543954i
$545$		−	273.832i		−	0.502444i
$546$		0			0
$547$	−724.904			−1.32524			−0.662618	−	0.748958i	$-0.730555\pi$
$547$	−724.904			−1.32524			−0.662618	+	0.748958i	$0.730555\pi$
$548$	258.466	−	258.466i	0.471653	−	0.471653i
$549$	−216.909			−0.395098
$550$		−	93.3590i		−	0.169744i
$551$	41.9282	−	41.9282i	0.0760947	−	0.0760947i
$552$	41.8423	−	41.8423i	0.0758013	−	0.0758013i
$553$	−263.292	−	263.292i	−0.476116	−	0.476116i
$554$	127.687	+	127.687i	0.230481	+	0.230481i
$555$	85.4960			0.154047
$556$			121.033i			0.217686i
$557$	−84.8686	−	84.8686i	−0.152367	−	0.152367i	0.626807	−	0.779174i	$-0.284361\pi$
$557$	−84.8686	−	84.8686i	−0.152367	−	0.152367i	−0.779174	+	0.626807i	$0.784361\pi$
$558$		−	73.9090i		−	0.132453i
$559$		0			0
$560$	−284.192			−0.507486
$561$	−154.956	+	154.956i	−0.276215	+	0.276215i
$562$	67.3294			0.119803
$563$			617.636i			1.09704i	0.836136	+	0.548522i	$0.184809\pi$
$563$			617.636i			1.09704i	−0.836136	+	0.548522i	$0.815191\pi$
$564$	−93.7654	+	93.7654i	−0.166251	+	0.166251i
$565$	379.242	−	379.242i	0.671224	−	0.671224i
$566$	−13.0192	−	13.0192i	−0.0230022	−	0.0230022i
$567$	−280.378	−	280.378i	−0.494494	−	0.494494i
$568$	−185.163			−0.325991
$569$		−	440.305i		−	0.773823i	−0.922117	−	0.386911i	$-0.873542\pi$
$569$		−	440.305i		−	0.773823i	0.922117	−	0.386911i	$-0.126458\pi$
$570$	−6.30127	−	6.30127i	−0.0110549	−	0.0110549i
$571$			618.249i			1.08275i	0.840782	+	0.541374i	$0.182096\pi$
$571$			618.249i			1.08275i	−0.840782	+	0.541374i	$0.817904\pi$
$572$		0			0
$573$	−215.226			−0.375612
$574$	101.009	−	101.009i	0.175974	−	0.175974i
$575$	−224.669			−0.390729
$576$			335.970i			0.583282i
$577$	−266.237	+	266.237i	−0.461415	+	0.461415i	−0.899119	−	0.437704i	$-0.855792\pi$
$577$	−266.237	+	266.237i	−0.461415	+	0.461415i	0.437704	+	0.899119i	$0.355792\pi$
$578$	−19.0052	+	19.0052i	−0.0328809	+	0.0328809i
$579$	−171.101	−	171.101i	−0.295512	−	0.295512i
$580$	−92.3275	−	92.3275i	−0.159185	−	0.159185i
$581$	205.472			0.353652
$582$			20.7743i			0.0356947i
$583$	169.272	+	169.272i	0.290346	+	0.290346i
$584$		−	109.101i		−	0.186817i
$585$		0			0
$586$	−207.263			−0.353691
$587$	−340.494	+	340.494i	−0.580057	+	0.580057i	−0.934919	−	0.354862i	$-0.884528\pi$
$587$	−340.494	+	340.494i	−0.580057	+	0.580057i	0.354862	+	0.934919i	$0.384528\pi$
$588$	−37.6603			−0.0640481
$589$			106.497i			0.180811i
$590$	−131.219	+	131.219i	−0.222405	+	0.222405i
$591$	45.6115	−	45.6115i	0.0771768	−	0.0771768i
$592$	−285.025	−	285.025i	−0.481461	−	0.481461i
$593$	389.671	+	389.671i	0.657118	+	0.657118i	0.954697	−	0.297579i	$-0.0961792\pi$
$593$	389.671	+	389.671i	0.657118	+	0.657118i	−0.297579	+	0.954697i	$0.596179\pi$
$594$	−107.292			−0.180627
$595$			408.151i			0.685968i
$596$	−337.394	−	337.394i	−0.566098	−	0.566098i
$597$			147.464i			0.247009i
$598$		0			0
$599$	808.596			1.34991			0.674955	−	0.737859i	$-0.264163\pi$
$599$	808.596			1.34991			0.674955	+	0.737859i	$0.264163\pi$
$600$	23.0474	−	23.0474i	0.0384123	−	0.0384123i
$601$	−442.688			−0.736586			−0.368293	−	0.929710i	$-0.620058\pi$
$601$	−442.688			−0.736586			−0.368293	+	0.929710i	$0.620058\pi$
$602$			159.615i			0.265142i
$603$	241.813	−	241.813i	0.401016	−	0.401016i
$604$	−477.683	+	477.683i	−0.790866	+	0.790866i
$605$	−373.633	−	373.633i	−0.617575	−	0.617575i
$606$	−42.8705	−	42.8705i	−0.0707434	−	0.0707434i
$607$	−942.796			−1.55321			−0.776603	−	0.629990i	$-0.783059\pi$
$607$	−942.796			−1.55321			−0.776603	+	0.629990i	$0.783059\pi$
$608$			143.086i			0.235339i
$609$	28.8513	+	28.8513i	0.0473748	+	0.0473748i
$610$			49.4139i			0.0810065i
$611$		0			0
$612$	583.252			0.953027
$613$	712.403	−	712.403i	1.16216	−	1.16216i	0.178156	−	0.984002i	$-0.442987\pi$
$613$	712.403	−	712.403i	1.16216	−	1.16216i	0.984002	−	0.178156i	$-0.0570132\pi$
$614$	190.494			0.310250
$615$			126.809i			0.206193i
$616$	−272.287	+	272.287i	−0.442025	+	0.442025i
$617$	−196.466	+	196.466i	−0.318421	+	0.318421i	−0.848161	−	0.529739i	$-0.822290\pi$
$617$	−196.466	+	196.466i	−0.318421	+	0.318421i	0.529739	+	0.848161i	$0.322290\pi$
$618$	21.1065	+	21.1065i	0.0341529	+	0.0341529i
$619$	206.483	+	206.483i	0.333576	+	0.333576i	0.853943	−	0.520367i	$-0.174205\pi$
$619$	206.483	+	206.483i	0.333576	+	0.333576i	−0.520367	+	0.853943i	$0.674205\pi$
$620$	234.512			0.378244
$621$			258.200i			0.415781i
$622$	−26.1628	−	26.1628i	−0.0420624	−	0.0420624i
$623$			531.244i			0.852718i
$624$		0			0
$625$	223.140			0.357024
$626$	−144.329	+	144.329i	−0.230558	+	0.230558i
$627$	74.9282			0.119503
$628$		−	364.794i		−	0.580881i
$629$	−409.347	+	409.347i	−0.650790	+	0.650790i
$630$	−68.4833	+	68.4833i	−0.108704	+	0.108704i
$631$	313.913	+	313.913i	0.497485	+	0.497485i	0.910654	−	0.413170i	$-0.135578\pi$
$631$	313.913	+	313.913i	0.497485	+	0.497485i	−0.413170	+	0.910654i	$0.635578\pi$
$632$	177.580	+	177.580i	0.280980	+	0.280980i
$633$	−53.6565			−0.0847654
$634$			150.842i			0.237922i
$635$	75.0244	+	75.0244i	0.118149	+	0.118149i
$636$			40.3397i			0.0634273i
$637$		0			0
$638$	−78.8231			−0.123547
$639$	276.885	−	276.885i	0.433309	−	0.433309i
$640$	414.240			0.647250
$641$			544.692i			0.849754i	0.905251	+	0.424877i	$0.139683\pi$
$641$			544.692i			0.849754i	−0.905251	+	0.424877i	$0.860317\pi$
$642$	25.5448	−	25.5448i	0.0397894	−	0.0397894i
$643$	273.405	−	273.405i	0.425202	−	0.425202i	−0.461788	−	0.886990i	$-0.652792\pi$
$643$	273.405	−	273.405i	0.425202	−	0.425202i	0.886990	+	0.461788i	$0.152792\pi$
$644$	316.277	+	316.277i	0.491113	+	0.491113i
$645$	−100.192	−	100.192i	−0.155337	−	0.155337i
$646$	60.3397			0.0934052
$647$		−	503.514i		−	0.778229i	−0.921189	−	0.389114i	$-0.872781\pi$
$647$		−	503.514i		−	0.778229i	0.921189	−	0.389114i	$-0.127219\pi$
$648$	189.103	+	189.103i	0.291826	+	0.291826i
$649$		−	1560.32i		−	2.40420i
$650$		0			0
$651$	−73.2820			−0.112568
$652$	−334.081	+	334.081i	−0.512394	+	0.512394i
$653$	31.1384			0.0476852			0.0238426	−	0.999716i	$-0.492410\pi$
$653$	31.1384			0.0476852			0.0238426	+	0.999716i	$0.492410\pi$
$654$		−	27.8564i		−	0.0425939i
$655$	7.85125	−	7.85125i	0.0119866	−	0.0119866i
$656$	422.753	−	422.753i	0.644441	−	0.644441i
$657$	163.145	+	163.145i	0.248319	+	0.248319i
$658$	105.426	+	105.426i	0.160221	+	0.160221i
$659$	758.977			1.15171			0.575855	−	0.817552i	$-0.304669\pi$
$659$	758.977			1.15171			0.575855	+	0.817552i	$0.304669\pi$
$660$		−	164.995i		−	0.249992i
$661$	185.256	+	185.256i	0.280266	+	0.280266i	0.833215	−	0.552949i	$-0.186498\pi$
$661$	185.256	+	185.256i	0.280266	+	0.280266i	−0.552949	+	0.833215i	$0.686498\pi$
$662$			238.795i			0.360717i
$663$		0			0
$664$	−138.582			−0.208708
$665$	98.6795	−	98.6795i	0.148390	−	0.148390i
$666$	−137.368			−0.206258
$667$			189.688i			0.284390i
$668$	138.603	−	138.603i	0.207489	−	0.207489i
$669$	−196.960	+	196.960i	−0.294410	+	0.294410i
$670$	−55.0873	−	55.0873i	−0.0822198	−	0.0822198i
$671$	−293.790	−	293.790i	−0.437839	−	0.437839i
$672$	−98.4589			−0.146516
$673$		−	314.321i		−	0.467044i	−0.972352	−	0.233522i	$-0.924975\pi$
$673$		−	314.321i		−	0.467044i	0.972352	−	0.233522i	$-0.0750251\pi$
$674$	52.9930	+	52.9930i	0.0786246	+	0.0786246i
$675$			142.221i			0.210697i
$676$		0			0
$677$	−547.384			−0.808544			−0.404272	−	0.914639i	$-0.632475\pi$
$677$	−547.384			−0.808544			−0.404272	+	0.914639i	$0.632475\pi$
$678$	38.5795	−	38.5795i	0.0569020	−	0.0569020i
$679$	−325.331			−0.479132
$680$		−	275.281i		−	0.404824i
$681$	216.560	−	216.560i	0.318003	−	0.318003i
$682$	100.105	−	100.105i	0.146782	−	0.146782i
$683$	−185.176	−	185.176i	−0.271121	−	0.271121i	0.558430	−	0.829551i	$-0.311404\pi$
$683$	−185.176	−	185.176i	−0.271121	−	0.271121i	−0.829551	+	0.558430i	$0.811404\pi$
$684$	−141.014	−	141.014i	−0.206161	−	0.206161i
$685$	364.836			0.532607
$686$			192.862i			0.281139i
$687$	52.9038	+	52.9038i	0.0770070	+	0.0770070i
$688$			668.038i			0.970986i
$689$		0			0
$690$	28.5077			0.0413156
$691$	−777.990	+	777.990i	−1.12589	+	1.12589i	−0.135051	+	0.990839i	$0.543120\pi$
$691$	−777.990	+	777.990i	−1.12589	+	1.12589i	−0.990839	+	0.135051i	$0.956880\pi$
$692$	512.238			0.740229
$693$		−	814.333i		−	1.17508i
$694$	178.321	−	178.321i	0.256946	−	0.256946i
$695$	−85.4219	+	85.4219i	−0.122909	+	0.122909i
$696$	−19.4589	−	19.4589i	−0.0279583	−	0.0279583i
$697$	−607.149	−	607.149i	−0.871089	−	0.871089i
$698$	−6.08073			−0.00871164
$699$		−	187.839i		−	0.268725i
$700$	174.210	+	174.210i	0.248872	+	0.248872i
$701$		−	638.323i		−	0.910589i	−0.890341	−	0.455295i	$-0.849534\pi$
$701$		−	638.323i		−	0.910589i	0.890341	−	0.455295i	$-0.150466\pi$
$702$		0			0
$703$	197.937			0.281561
$704$	−455.051	+	455.051i	−0.646380	+	0.646380i
$705$	−132.354			−0.187736
$706$		−	147.999i		−	0.209630i
$707$	671.363	−	671.363i	0.949594	−	0.949594i
$708$	185.923	−	185.923i	0.262603	−	0.262603i
$709$	457.667	+	457.667i	0.645511	+	0.645511i	0.951905	−	0.306394i	$-0.0991224\pi$
$709$	457.667	+	457.667i	0.645511	+	0.645511i	−0.306394	+	0.951905i	$0.599122\pi$
$710$	−63.0770	−	63.0770i	−0.0888408	−	0.0888408i
$711$	−531.090			−0.746962
$712$		−	358.301i		−	0.503232i
$713$	−240.904	−	240.904i	−0.337874	−	0.337874i
$714$			41.5204i			0.0581519i
$715$		0			0
$716$	−3.89488			−0.00543978
$717$	−28.8025	+	28.8025i	−0.0401708	+	0.0401708i
$718$	67.4050			0.0938788
$719$		−	1222.11i		−	1.69974i	−0.526993	−	0.849870i	$-0.676681\pi$
$719$		−	1222.11i		−	1.69974i	0.526993	−	0.849870i	$-0.323319\pi$
$720$	−286.624	+	286.624i	−0.398088	+	0.398088i
$721$	−330.533	+	330.533i	−0.458437	+	0.458437i
$722$	117.547	+	117.547i	0.162807	+	0.162807i
$723$	125.053	+	125.053i	0.172963	+	0.172963i
$724$	86.1384			0.118976
$725$			104.483i			0.144115i
$726$	−38.0089	−	38.0089i	−0.0523539	−	0.0523539i
$727$			508.974i			0.700102i	0.936731	+	0.350051i	$0.113836\pi$
$727$			508.974i			0.700102i	−0.936731	+	0.350051i	$0.886164\pi$
$728$		0			0
$729$	−481.323			−0.660251
$730$	37.1661	−	37.1661i	0.0509125	−	0.0509125i
$731$	959.423			1.31248
$732$		−	70.0141i		−	0.0956477i
$733$	861.681	−	861.681i	1.17555	−	1.17555i	0.194689	−	0.980865i	$-0.437630\pi$
$733$	861.681	−	861.681i	1.17555	−	1.17555i	0.980865	−	0.194689i	$-0.0623699\pi$
$734$	4.59361	−	4.59361i	0.00625833	−	0.00625833i
$735$	−26.5795	−	26.5795i	−0.0361626	−	0.0361626i
$736$	−323.669	−	323.669i	−0.439768	−	0.439768i
$737$	655.041			0.888794
$738$		−	203.746i		−	0.276079i
$739$	110.441	+	110.441i	0.149447	+	0.149447i	0.777871	−	0.628424i	$-0.216300\pi$
$739$	110.441	+	110.441i	0.149447	+	0.149447i	−0.628424	+	0.777871i	$0.716300\pi$
$740$		−	435.865i		−	0.589007i
$741$		0			0
$742$	45.3562			0.0611270
$743$	270.312	−	270.312i	0.363811	−	0.363811i	−0.501403	−	0.865214i	$-0.667183\pi$
$743$	270.312	−	270.312i	0.363811	−	0.363811i	0.865214	+	0.501403i	$0.167183\pi$
$744$	49.4256			0.0664323
$745$		−	476.246i		−	0.639257i
$746$	−113.935	+	113.935i	−0.152728	+	0.152728i
$747$	207.229	−	207.229i	0.277416	−	0.277416i
$748$	789.979	+	789.979i	1.05612	+	1.05612i
$749$	400.038	+	400.038i	0.534097	+	0.534097i
$750$	50.9911			0.0679881
$751$		−	1046.64i		−	1.39366i	−0.717237	−	0.696830i	$-0.754593\pi$
$751$		−	1046.64i		−	1.39366i	0.717237	−	0.696830i	$-0.245407\pi$
$752$	441.238	+	441.238i	0.586753	+	0.586753i
$753$		−	187.128i		−	0.248510i
$754$		0			0
$755$	−674.270			−0.893073
$756$	200.210	−	200.210i	0.264828	−	0.264828i
$757$	−376.831			−0.497795			−0.248897	−	0.968530i	$-0.580068\pi$
$757$	−376.831			−0.497795			−0.248897	+	0.968530i	$0.580068\pi$
$758$			203.565i			0.268556i
$759$	−169.492	+	169.492i	−0.223310	+	0.223310i
$760$	−66.5551	+	66.5551i	−0.0875725	+	0.0875725i
$761$	543.214	+	543.214i	0.713816	+	0.713816i	0.967331	−	0.253515i	$-0.0815868\pi$
$761$	543.214	+	543.214i	0.713816	+	0.713816i	−0.253515	+	0.967331i	$0.581587\pi$
$762$	7.63209	+	7.63209i	0.0100159	+	0.0100159i
$763$	436.238			0.571741
$764$			1097.24i			1.43617i
$765$	411.643	+	411.643i	0.538095	+	0.538095i
$766$		−	382.123i		−	0.498855i
$767$		0			0
$768$	−74.0910			−0.0964727
$769$	48.0962	−	48.0962i	0.0625438	−	0.0625438i	−0.675143	−	0.737687i	$-0.735918\pi$
$769$	48.0962	−	48.0962i	0.0625438	−	0.0625438i	0.737687	+	0.675143i	$0.235918\pi$
$770$	−185.513			−0.240926
$771$		−	72.5040i		−	0.0940389i
$772$	−872.288	+	872.288i	−1.12991	+	1.12991i
$773$	−652.090	+	652.090i	−0.843583	+	0.843583i	−0.989323	−	0.145740i	$-0.953444\pi$
$773$	−652.090	+	652.090i	−0.843583	+	0.843583i	0.145740	+	0.989323i	$0.453444\pi$
$774$	160.981	+	160.981i	0.207985	+	0.207985i
$775$	−132.694	−	132.694i	−0.171218	−	0.171218i
$776$	219.422			0.282760
$777$			136.203i			0.175293i
$778$	126.088	+	126.088i	0.162067	+	0.162067i
$779$			293.583i			0.376872i
$780$		0			0
$781$	750.046			0.960366
$782$	−136.492	+	136.492i	−0.174543	+	0.174543i
$783$	120.077			0.153355
$784$			177.221i			0.226047i
$785$	257.461	−	257.461i	0.327976	−	0.327976i
$786$	0.798693	−	0.798693i	0.00101615	−	0.00101615i
$787$	−870.128	−	870.128i	−1.10563	−	1.10563i	−0.993719	−	0.111908i	$-0.964304\pi$
$787$	−870.128	−	870.128i	−1.10563	−	1.10563i	−0.111908	−	0.993719i	$-0.535696\pi$
$788$	−232.531	−	232.531i	−0.295090	−	0.295090i
$789$	186.921			0.236908
$790$			120.987i			0.153148i
$791$	604.165	+	604.165i	0.763799	+	0.763799i
$792$			549.233i			0.693476i
$793$		0			0
$794$	363.565			0.457891
$795$	−28.4706	+	28.4706i	−0.0358121	+	0.0358121i
$796$	751.783			0.944451
$797$			25.4744i			0.0319629i	0.999872	+	0.0159814i	$0.00508727\pi$
$797$			25.4744i			0.0319629i	−0.999872	+	0.0159814i	$0.994913\pi$
$798$	10.0385	−	10.0385i	0.0125795	−	0.0125795i
$799$	633.697	−	633.697i	0.793113	−	0.793113i
$800$	−178.282	−	178.282i	−0.222853	−	0.222853i
$801$	535.788	+	535.788i	0.668899	+	0.668899i
$802$	293.666			0.366168
$803$			441.941i			0.550362i
$804$	78.0526	+	78.0526i	0.0970803	+	0.0970803i
$805$			446.438i			0.554582i
$806$		0			0
$807$	67.8667			0.0840975
$808$	−452.806	+	452.806i	−0.560403	+	0.560403i
$809$	−702.927			−0.868884			−0.434442	−	0.900700i	$-0.643054\pi$
$809$	−702.927			−0.868884			−0.434442	+	0.900700i	$0.643054\pi$
$810$			128.839i			0.159060i
$811$	506.292	−	506.292i	0.624282	−	0.624282i	−0.322342	−	0.946623i	$-0.604470\pi$
$811$	506.292	−	506.292i	0.624282	−	0.624282i	0.946623	+	0.322342i	$0.104470\pi$
$812$	147.086	−	147.086i	0.181140	−	0.181140i
$813$	226.267	+	226.267i	0.278311	+	0.278311i
$814$	−186.056	−	186.056i	−0.228570	−	0.228570i
$815$	−471.569			−0.578613
$816$			173.776i			0.212960i
$817$	−231.962	−	231.962i	−0.283919	−	0.283919i
$818$		−	52.6424i		−	0.0643550i
$819$		0			0
$820$	646.482			0.788393
$821$	798.514	−	798.514i	0.972611	−	0.972611i	−0.0270235	−	0.999635i	$-0.508603\pi$
$821$	798.514	−	798.514i	0.972611	−	0.972611i	0.999635	+	0.0270235i	$0.00860289\pi$
$822$	37.1140			0.0451509
$823$			519.451i			0.631168i	0.948898	+	0.315584i	$0.102200\pi$
$823$			519.451i			0.631168i	−0.948898	+	0.315584i	$0.897800\pi$
$824$	222.931	−	222.931i	0.270547	−	0.270547i
$825$	−93.3590	+	93.3590i	−0.113162	+	0.113162i
$826$	−209.044	−	209.044i	−0.253079	−	0.253079i
$827$	−571.769	−	571.769i	−0.691377	−	0.691377i	0.271158	−	0.962535i	$-0.412594\pi$
$827$	−571.769	−	571.769i	−0.691377	−	0.691377i	−0.962535	+	0.271158i	$0.912594\pi$
$828$	637.965			0.770489
$829$		−	979.295i		−	1.18130i	−0.806929	−	0.590648i	$-0.798872\pi$
$829$		−	979.295i		−	1.18130i	0.806929	−	0.590648i	$-0.201128\pi$
$830$	−47.2089	−	47.2089i	−0.0568781	−	0.0568781i
$831$		−	255.373i		−	0.307308i
$832$		0			0
$833$	254.520			0.305547
$834$	−8.68980	+	8.68980i	−0.0104194	+	0.0104194i
$835$	195.643			0.234303
$836$		−	381.990i		−	0.456925i
$837$	−152.497	+	152.497i	−0.182195	+	0.182195i
$838$	235.924	−	235.924i	0.281533	−	0.281533i
$839$	−376.096	−	376.096i	−0.448267	−	0.448267i	0.446511	−	0.894778i	$-0.352666\pi$
$839$	−376.096	−	376.096i	−0.448267	−	0.448267i	−0.894778	+	0.446511i	$0.852666\pi$
$840$	−45.7973	−	45.7973i	−0.0545206	−	0.0545206i
$841$	−752.785			−0.895107
$842$		−	253.742i		−	0.301357i
$843$	−67.3294	−	67.3294i	−0.0798688	−	0.0798688i
$844$			273.545i			0.324105i
$845$		0			0
$846$	212.655			0.251365
$847$	595.229	−	595.229i	0.702750	−	0.702750i
$848$	189.830			0.223856
$849$			26.0385i			0.0306696i
$850$	−75.1821	+	75.1821i	−0.0884495	+	0.0884495i
$851$	−447.746	+	447.746i	−0.526141	+	0.526141i
$852$	89.3731	+	89.3731i	0.104898	+	0.104898i
$853$	713.043	+	713.043i	0.835924	+	0.835924i	0.988320	−	0.152396i	$-0.0486989\pi$
$853$	713.043	+	713.043i	0.835924	+	0.835924i	−0.152396	+	0.988320i	$0.548699\pi$
$854$	−78.7207			−0.0921788
$855$		−	199.047i		−	0.232804i
$856$	−269.809	−	269.809i	−0.315197	−	0.315197i
$857$			311.663i			0.363667i	0.983329	+	0.181834i	$0.0582032\pi$
$857$			311.663i			0.363667i	−0.983329	+	0.181834i	$0.941797\pi$
$858$		0			0
$859$	−1475.02			−1.71714			−0.858568	−	0.512700i	$-0.828645\pi$
$859$	−1475.02			−1.71714			−0.858568	+	0.512700i	$0.828645\pi$
$860$	−510.788	+	510.788i	−0.593940	+	0.593940i
$861$	−202.018			−0.234632
$862$			54.5002i			0.0632253i
$863$	−700.396	+	700.396i	−0.811583	+	0.811583i	−0.984871	−	0.173288i	$-0.944561\pi$
$863$	−700.396	+	700.396i	−0.811583	+	0.811583i	0.173288	+	0.984871i	$0.444561\pi$
$864$	−204.890	+	204.890i	−0.237141	+	0.237141i
$865$	361.523	+	361.523i	0.417946	+	0.417946i
$866$	−252.276	−	252.276i	−0.291312	−	0.291312i
$867$	38.0103			0.0438412
$868$			373.597i			0.430412i
$869$	−719.328	−	719.328i	−0.827765	−	0.827765i
$870$		−	13.2576i		−	0.0152387i
$871$		0			0
$872$	−294.224			−0.337413
$873$	−328.114	+	328.114i	−0.375847	+	0.375847i
$874$	66.0000			0.0755149
$875$			798.533i			0.912609i
$876$	−52.6603	+	52.6603i	−0.0601144	+	0.0601144i
$877$	−96.8507	+	96.8507i	−0.110434	+	0.110434i	−0.760165	−	0.649730i	$-0.774882\pi$
$877$	−96.8507	+	96.8507i	−0.110434	+	0.110434i	0.649730	+	0.760165i	$0.274882\pi$
$878$	32.9911	+	32.9911i	0.0375753	+	0.0375753i
$879$	207.263	+	207.263i	0.235794	+	0.235794i
$880$	−776.428			−0.882305
$881$			443.032i			0.502874i	0.967874	+	0.251437i	$0.0809031\pi$
$881$			443.032i			0.502874i	−0.967874	+	0.251437i	$0.919097\pi$
$882$	42.7058	+	42.7058i	0.0484192	+	0.0484192i
$883$		−	1305.20i		−	1.47814i	−0.673630	−	0.739069i	$-0.735266\pi$
$883$		−	1305.20i		−	1.47814i	0.673630	−	0.739069i	$-0.264734\pi$
$884$		0			0
$885$	262.438			0.296540
$886$	235.090	−	235.090i	0.265338	−	0.265338i
$887$	−1722.75			−1.94223			−0.971113	−	0.238622i	$-0.923304\pi$
$887$	−1722.75			−1.94223			−0.971113	+	0.238622i	$0.923304\pi$
$888$		−	91.8629i		−	0.103449i
$889$	−119.520	+	119.520i	−0.134444	+	0.134444i
$890$	122.058	−	122.058i	0.137143	−	0.137143i
$891$	−766.008	−	766.008i	−0.859717	−	0.859717i
$892$	1004.12	+	1004.12i	1.12569	+	1.12569i
$893$	−306.420			−0.343136
$894$		−	48.4476i		−	0.0541920i
$895$	−2.74890	−	2.74890i	−0.00307139	−	0.00307139i
$896$			659.920i			0.736518i
$897$		0			0
$898$	−12.1117			−0.0134874
$899$	−112.033	+	112.033i	−0.124620	+	0.124620i
$900$	351.401			0.390446
$901$		−	272.629i		−	0.302585i
$902$	275.962	−	275.962i	0.305944	−	0.305944i
$903$	159.615	−	159.615i	0.176761	−	0.176761i
$904$	−407.484	−	407.484i	−0.450756	−	0.450756i
$905$	60.7940	+	60.7940i	0.0671757	+	0.0671757i
$906$	−68.5922			−0.0757089
$907$			876.187i			0.966027i	0.875613	+	0.483014i	$0.160458\pi$
$907$			876.187i			0.966027i	−0.875613	+	0.483014i	$0.839542\pi$
$908$	−1104.04	−	1104.04i	−1.21590	−	1.21590i
$909$		−	1354.21i		−	1.48978i
$910$		0			0
$911$	−1103.35			−1.21114			−0.605569	−	0.795793i	$-0.707054\pi$
$911$	−1103.35			−1.21114			−0.605569	+	0.795793i	$0.707054\pi$
$912$	42.0141	−	42.0141i	0.0460681	−	0.0460681i
$913$	561.359			0.614851
$914$			122.559i			0.134091i
$915$	49.4139	−	49.4139i	0.0540043	−	0.0540043i
$916$	269.708	−	269.708i	0.294441	−	0.294441i
$917$	12.5077	+	12.5077i	0.0136398	+	0.0136398i
$918$	86.4026	+	86.4026i	0.0941205	+	0.0941205i
$919$	−656.319			−0.714167			−0.357083	−	0.934073i	$-0.616229\pi$
$919$	−656.319			−0.714167			−0.357083	+	0.934073i	$0.616229\pi$
$920$		−	301.104i		−	0.327287i
$921$	−190.494	−	190.494i	−0.206833	−	0.206833i
$922$			25.2065i			0.0273389i
$923$		0			0
$924$	262.851			0.284471
$925$	−246.626	+	246.626i	−0.266622	+	0.266622i
$926$	−381.538			−0.412028
$927$			666.722i			0.719225i
$928$	−150.524	+	150.524i	−0.162202	+	0.162202i
$929$	599.886	−	599.886i	0.645734	−	0.645734i	−0.306225	−	0.951959i	$-0.599066\pi$
$929$	599.886	−	599.886i	0.645734	−	0.645734i	0.951959	+	0.306225i	$0.0990661\pi$
$930$	16.8372	+	16.8372i	0.0181045	+	0.0181045i
$931$	−61.5359	−	61.5359i	−0.0660966	−	0.0660966i
$932$	−957.615			−1.02748
$933$			52.3257i			0.0560832i
$934$	−51.7616	−	51.7616i	−0.0554193	−	0.0554193i
$935$			1115.09i			1.19261i
$936$		0			0
$937$	842.615			0.899269			0.449635	−	0.893213i	$-0.351554\pi$
$937$	842.615			0.899269			0.449635	+	0.893213i	$0.351554\pi$
$938$	87.7588	−	87.7588i	0.0935595	−	0.0935595i
$939$	288.659			0.307411
$940$			674.750i			0.717819i
$941$	−471.659	+	471.659i	−0.501232	+	0.501232i	−0.911821	−	0.410589i	$-0.865323\pi$
$941$	−471.659	+	471.659i	−0.501232	+	0.501232i	0.410589	+	0.911821i	$0.365323\pi$
$942$	26.1910	−	26.1910i	0.0278036	−	0.0278036i
$943$	−664.104	−	664.104i	−0.704246	−	0.704246i
$944$	−874.911	−	874.911i	−0.926813	−	0.926813i
$945$	282.605			0.299053
$946$			436.077i			0.460969i
$947$	−358.199	−	358.199i	−0.378246	−	0.378246i	0.492223	−	0.870469i	$-0.336184\pi$
$947$	−358.199	−	358.199i	−0.378246	−	0.378246i	−0.870469	+	0.492223i	$0.836184\pi$
$948$		−	171.426i		−	0.180829i
$949$		0			0
$950$	36.3538			0.0382672
$951$	150.842	−	150.842i	0.158614	−	0.158614i
$952$	438.546			0.460658
$953$			889.226i			0.933080i	0.884500	+	0.466540i	$0.154500\pi$
$953$			889.226i			0.933080i	−0.884500	+	0.466540i	$0.845500\pi$
$954$	45.7442	−	45.7442i	0.0479499	−	0.0479499i
$955$	−774.398	+	774.398i	−0.810888	+	0.810888i
$956$	146.837	+	146.837i	0.153595	+	0.153595i
$957$	78.8231	+	78.8231i	0.0823648	+	0.0823648i
$958$	387.565			0.404557
$959$			581.215i			0.606064i
$960$	−76.5373	−	76.5373i	−0.0797263	−	0.0797263i
$961$			676.436i			0.703888i
$962$		0			0
$963$	806.922			0.837925
$964$	637.527	−	637.527i	0.661336	−	0.661336i
$965$	−1231.27			−1.27593
$966$			45.4153i			0.0470138i
$967$	−384.317	+	384.317i	−0.397432	+	0.397432i	−0.877326	−	0.479894i	$-0.840675\pi$
$967$	−384.317	+	384.317i	−0.397432	+	0.397432i	0.479894	+	0.877326i	$0.340675\pi$
$968$	−401.457	+	401.457i	−0.414728	+	0.414728i
$969$	−60.3397	−	60.3397i	−0.0622701	−	0.0622701i
$970$	74.7475	+	74.7475i	0.0770593	+	0.0770593i
$971$	−243.727			−0.251006			−0.125503	−	0.992093i	$-0.540054\pi$
$971$	−243.727			−0.251006			−0.125503	+	0.992093i	$0.540054\pi$
$972$		−	611.965i		−	0.629594i
$973$	−136.084	−	136.084i	−0.139861	−	0.139861i
$974$			125.874i			0.129234i
$975$		0			0
$976$	−329.470			−0.337572
$977$	812.582	−	812.582i	0.831712	−	0.831712i	−0.156039	−	0.987751i	$-0.549873\pi$
$977$	812.582	−	812.582i	0.831712	−	0.831712i	0.987751	+	0.156039i	$0.0498726\pi$
$978$	−47.9718			−0.0490510
$979$			1451.38i			1.48252i
$980$	−135.504	+	135.504i	−0.138270	+	0.138270i
$981$	439.970	−	439.970i	0.448492	−	0.448492i
$982$	−30.9883	−	30.9883i	−0.0315563	−	0.0315563i
$983$	−774.213	−	774.213i	−0.787602	−	0.787602i	0.193499	−	0.981101i	$-0.438016\pi$
$983$	−774.213	−	774.213i	−0.787602	−	0.787602i	−0.981101	+	0.193499i	$0.938016\pi$
$984$	136.252			0.138468
$985$		−	328.227i		−	0.333225i
$986$	63.4763	+	63.4763i	0.0643776	+	0.0643776i
$987$		−	210.851i		−	0.213628i
$988$		0			0
$989$	1049.42			1.06109
$990$	−187.100	+	187.100i	−0.188990	+	0.188990i
$991$	−783.465			−0.790580			−0.395290	−	0.918556i	$-0.629356\pi$
$991$	−783.465			−0.790580			−0.395290	+	0.918556i	$0.629356\pi$
$992$		−	382.329i		−	0.385413i
$993$	238.795	−	238.795i	0.240478	−	0.240478i
$994$	100.487	−	100.487i	0.101094	−	0.101094i
$995$	530.587	+	530.587i	0.533253	+	0.533253i
$996$	66.8897	+	66.8897i	0.0671584	+	0.0671584i
$997$	501.634			0.503144			0.251572	−	0.967839i	$-0.419052\pi$
$997$	501.634			0.503144			0.251572	+	0.967839i	$0.419052\pi$
$998$			98.3858i			0.0985829i
$999$	283.433	+	283.433i	0.283717	+	0.283717i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.3.d.a.70.2		4
13.2	odd	12		169.3.f.b.150.1		4
13.3	even	3		169.3.f.c.19.1		4
13.4	even	6		169.3.f.b.80.1		4
13.5	odd	4		169.3.d.c.99.1		4
13.6	odd	12		169.3.f.a.89.1		4
13.7	odd	12		169.3.f.c.89.1		4
13.8	odd	4	inner	169.3.d.a.99.2		4
13.9	even	3		13.3.f.a.2.1	✓	4
13.10	even	6		169.3.f.a.19.1		4
13.11	odd	12		13.3.f.a.7.1	yes	4
13.12	even	2		169.3.d.c.70.1		4
39.11	even	12		117.3.bd.b.46.1		4
39.35	odd	6		117.3.bd.b.28.1		4
52.11	even	12		208.3.bd.d.33.1		4
52.35	odd	6		208.3.bd.d.145.1		4
65.9	even	6		325.3.t.a.301.1		4
65.22	odd	12		325.3.w.b.249.1		4
65.24	odd	12		325.3.t.a.176.1		4
65.37	even	12		325.3.w.a.124.1		4
65.48	odd	12		325.3.w.a.249.1		4
65.63	even	12		325.3.w.b.124.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.3.f.a.2.1	✓	4	13.9	even	3
13.3.f.a.7.1	yes	4	13.11	odd	12
117.3.bd.b.28.1		4	39.35	odd	6
117.3.bd.b.46.1		4	39.11	even	12
169.3.d.a.70.2		4	1.1	even	1	trivial
169.3.d.a.99.2		4	13.8	odd	4	inner
169.3.d.c.70.1		4	13.12	even	2
169.3.d.c.99.1		4	13.5	odd	4
169.3.f.a.19.1		4	13.10	even	6
169.3.f.a.89.1		4	13.6	odd	12
169.3.f.b.80.1		4	13.4	even	6
169.3.f.b.150.1		4	13.2	odd	12
169.3.f.c.19.1		4	13.3	even	3
169.3.f.c.89.1		4	13.7	odd	12
208.3.bd.d.33.1		4	52.11	even	12
208.3.bd.d.145.1		4	52.35	odd	6
325.3.t.a.176.1		4	65.24	odd	12
325.3.t.a.301.1		4	65.9	even	6
325.3.w.a.124.1		4	65.37	even	12
325.3.w.a.249.1		4	65.48	odd	12
325.3.w.b.124.1		4	65.63	even	12
325.3.w.b.249.1		4	65.22	odd	12

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:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	169.d (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 - 0.366025i) q^{2} -0.732051 q^{3} +3.73205i q^{4} +(-2.63397 + 2.63397i) q^{5} +(-0.267949 + 0.267949i) q^{6} +(-4.19615 - 4.19615i) q^{7} +(2.83013 + 2.83013i) q^{8} -8.46410 q^{9} +1.92820i q^{10} +(-11.4641 - 11.4641i) q^{11} -2.73205i q^{12} -3.07180 q^{14} +(1.92820 - 1.92820i) q^{15} -12.8564 q^{16} +18.4641i q^{17} +(-3.09808 + 3.09808i) q^{18} +(4.46410 - 4.46410i) q^{19} +(-9.83013 - 9.83013i) q^{20} +(3.07180 + 3.07180i) q^{21} -8.39230 q^{22} +20.1962i q^{23} +(-2.07180 - 2.07180i) q^{24} +11.1244i q^{25} +12.7846 q^{27} +(15.6603 - 15.6603i) q^{28} +9.39230 q^{29} -1.41154i q^{30} +(-11.9282 + 11.9282i) q^{31} +(-16.0263 + 16.0263i) q^{32} +(8.39230 + 8.39230i) q^{33} +(6.75833 + 6.75833i) q^{34} +22.1051 q^{35} -31.5885i q^{36} +(22.1699 + 22.1699i) q^{37} -3.26795i q^{38} -14.9090 q^{40} +(-32.8827 + 32.8827i) q^{41} +2.24871 q^{42} -51.9615i q^{43} +(42.7846 - 42.7846i) q^{44} +(22.2942 - 22.2942i) q^{45} +(7.39230 + 7.39230i) q^{46} +(-34.3205 - 34.3205i) q^{47} +9.41154 q^{48} -13.7846i q^{49} +(4.07180 + 4.07180i) q^{50} -13.5167i q^{51} -14.7654 q^{53} +(4.67949 - 4.67949i) q^{54} +60.3923 q^{55} -23.7513i q^{56} +(-3.26795 + 3.26795i) q^{57} +(3.43782 - 3.43782i) q^{58} +(68.0526 + 68.0526i) q^{59} +(7.19615 + 7.19615i) q^{60} +25.6269 q^{61} +8.73205i q^{62} +(35.5167 + 35.5167i) q^{63} -39.6936i q^{64} +6.14359 q^{66} +(-28.5692 + 28.5692i) q^{67} -68.9090 q^{68} -14.7846i q^{69} +(8.09103 - 8.09103i) q^{70} +(-32.7128 + 32.7128i) q^{71} +(-23.9545 - 23.9545i) q^{72} +(-19.2750 - 19.2750i) q^{73} +16.2295 q^{74} -8.14359i q^{75} +(16.6603 + 16.6603i) q^{76} +96.2102i q^{77} +62.7461 q^{79} +(33.8634 - 33.8634i) q^{80} +66.8179 q^{81} +24.0718i q^{82} +(-24.4833 + 24.4833i) q^{83} +(-11.4641 + 11.4641i) q^{84} +(-48.6340 - 48.6340i) q^{85} +(-19.0192 - 19.0192i) q^{86} -6.87564 q^{87} -64.8897i q^{88} +(-63.3013 - 63.3013i) q^{89} -16.3205i q^{90} -75.3731 q^{92} +(8.73205 - 8.73205i) q^{93} -25.1244 q^{94} +23.5167i q^{95} +(11.7321 - 11.7321i) q^{96} +(38.7654 - 38.7654i) q^{97} +(-5.04552 - 5.04552i) q^{98} +(97.0333 + 97.0333i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 4 q^{3} - 14 q^{5} - 8 q^{6} + 4 q^{7} - 6 q^{8} - 20 q^{9} - 32 q^{11} - 40 q^{14} - 20 q^{15} + 4 q^{16} - 2 q^{18} + 4 q^{19} - 22 q^{20} + 40 q^{21} + 8 q^{22} - 36 q^{24} - 32 q^{27}+ \cdots + 208 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 4 * q^3 - 14 * q^5 - 8 * q^6 + 4 * q^7 - 6 * q^8 - 20 * q^9 - 32 * q^11 - 40 * q^14 - 20 * q^15 + 4 * q^16 - 2 * q^18 + 4 * q^19 - 22 * q^20 + 40 * q^21 + 8 * q^22 - 36 * q^24 - 32 * q^27 + 28 * q^28 - 4 * q^29 - 20 * q^31 - 26 * q^32 - 8 * q^33 - 18 * q^34 - 64 * q^35 + 106 * q^37 + 72 * q^40 - 38 * q^41 - 88 * q^42 + 88 * q^44 + 58 * q^45 - 12 * q^46 - 68 * q^47 + 100 * q^48 + 44 * q^50 + 128 * q^53 + 88 * q^54 + 200 * q^55 - 20 * q^57 + 38 * q^58 + 196 * q^59 + 8 * q^60 + 248 * q^61 + 52 * q^63 + 80 * q^66 + 52 * q^67 - 144 * q^68 + 164 * q^70 - 20 * q^71 - 30 * q^72 + 58 * q^73 - 136 * q^74 + 32 * q^76 - 40 * q^79 - 62 * q^80 + 4 * q^81 - 188 * q^83 - 32 * q^84 - 198 * q^85 - 180 * q^86 - 76 * q^87 - 80 * q^89 - 156 * q^92 + 28 * q^93 - 52 * q^94 + 40 * q^96 - 32 * q^97 - 86 * q^98 + 208 * q^99

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