LMFDB - Embedded newform 171.3.p.c.145.2

Newspace parameters

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	171.p (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.65941252056$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{6})$
Coefficient field:	6.0.92607408.1
Defining polynomial:	$ x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 94x^{2} - 77x + 43 $ x^6 - 3x^5 + 20x^4 - 35x^3 + 94x^2 - 77*x + 43
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 57)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.2
Root			$0.500000 + 0.630453i$ of defining polynomial
Character	$\chi$	$=$	171.145
Dual form			171.3.p.c.46.2

$q$-expansion

$f(q)$	$=$	$q+(-0.204011 + 0.117786i) q^{2} +(-1.97225 + 3.41604i) q^{4} +(-2.88028 - 4.98878i) q^{5} +1.94451 q^{7} -1.87150i q^{8} +O(q^{10})$	\(q+(-0.204011 + 0.117786i) q^{2} +(-1.97225 + 3.41604i) q^{4} +(-2.88028 - 4.98878i) q^{5} +1.94451 q^{7} -1.87150i q^{8} +(1.17522 + 0.678513i) q^{10} -8.46561 q^{11} +(-16.7415 - 9.66573i) q^{13} +(-0.396701 + 0.229036i) q^{14} +(-7.66857 - 13.2824i) q^{16} +(-12.5365 - 21.7138i) q^{17} +(17.8181 - 6.59651i) q^{19} +22.7225 q^{20} +(1.72708 - 0.997131i) q^{22} +(-15.6408 + 27.0907i) q^{23} +(-4.09198 + 7.08751i) q^{25} +4.55395 q^{26} +(-3.83506 + 6.64251i) q^{28} +(-13.7071 - 7.91383i) q^{29} -14.4237i q^{31} +(9.61203 + 5.54951i) q^{32} +(5.11517 + 2.95325i) q^{34} +(-5.60071 - 9.70072i) q^{35} +41.6423i q^{37} +(-2.85813 + 3.44449i) q^{38} +(-9.33653 + 5.39045i) q^{40} +(-1.53439 + 0.885881i) q^{41} +(14.4358 + 25.0035i) q^{43} +(16.6963 - 28.9189i) q^{44} -7.36909i q^{46} +(-1.70506 + 2.95325i) q^{47} -45.2189 q^{49} -1.92791i q^{50} +(66.0371 - 38.1265i) q^{52} +(80.0952 + 46.2430i) q^{53} +(24.3833 + 42.2331i) q^{55} -3.63915i q^{56} +3.72855 q^{58} +(-4.27292 + 2.46697i) q^{59} +(7.45989 - 12.9209i) q^{61} +(1.69891 + 2.94259i) q^{62} +58.7340 q^{64} +111.360i q^{65} +(-70.4113 - 40.6520i) q^{67} +98.9005 q^{68} +(2.28522 + 1.31937i) q^{70} +(-52.9948 + 30.5966i) q^{71} +(-38.8299 - 67.2553i) q^{73} +(-4.90489 - 8.49551i) q^{74} +(-12.6079 + 73.8775i) q^{76} -16.4614 q^{77} +(84.0207 - 48.5094i) q^{79} +(-44.1752 + 76.5137i) q^{80} +(0.208689 - 0.361460i) q^{82} +102.323 q^{83} +(-72.2171 + 125.084i) q^{85} +(-5.89012 - 3.40067i) q^{86} +15.8434i q^{88} +(-103.596 - 59.8111i) q^{89} +(-32.5540 - 18.7951i) q^{91} +(-61.6953 - 106.859i) q^{92} -0.803328i q^{94} +(-84.2297 - 69.8911i) q^{95} +(-42.1438 + 24.3318i) q^{97} +(9.22517 - 5.32616i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 5 q^{4} - 4 q^{5} - 22 q^{7}+O(q^{10}) $ 6 * q - 3 * q^2 + 5 * q^4 - 4 * q^5 - 22 * q^7	$ 6 q - 3 q^{2} + 5 q^{4} - 4 q^{5} - 22 q^{7} + 54 q^{10} + 36 q^{11} - 3 q^{13} + 57 q^{14} - 23 q^{16} - 38 q^{17} - 10 q^{19} - 32 q^{20} + 36 q^{22} - 54 q^{23} - 21 q^{25} - 118 q^{26} - 101 q^{28} + 102 q^{29} + 63 q^{32} - 150 q^{34} + 24 q^{35} - 119 q^{38} + 30 q^{40} - 96 q^{41} + 107 q^{43} + 94 q^{44} + 50 q^{47} - 48 q^{49} + 399 q^{52} + 90 q^{53} + 148 q^{55} - 116 q^{58} + 27 q^{61} + 121 q^{62} + 46 q^{64} - 39 q^{67} + 388 q^{68} - 354 q^{70} - 84 q^{71} - 77 q^{73} - 219 q^{74} + 215 q^{76} - 260 q^{77} + 9 q^{79} - 312 q^{80} - 4 q^{82} + 348 q^{83} + 68 q^{85} - 249 q^{86} + 72 q^{89} - 393 q^{91} + 118 q^{92} - 104 q^{95} - 228 q^{97} - 540 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 + 5 * q^4 - 4 * q^5 - 22 * q^7 + 54 * q^10 + 36 * q^11 - 3 * q^13 + 57 * q^14 - 23 * q^16 - 38 * q^17 - 10 * q^19 - 32 * q^20 + 36 * q^22 - 54 * q^23 - 21 * q^25 - 118 * q^26 - 101 * q^28 + 102 * q^29 + 63 * q^32 - 150 * q^34 + 24 * q^35 - 119 * q^38 + 30 * q^40 - 96 * q^41 + 107 * q^43 + 94 * q^44 + 50 * q^47 - 48 * q^49 + 399 * q^52 + 90 * q^53 + 148 * q^55 - 116 * q^58 + 27 * q^61 + 121 * q^62 + 46 * q^64 - 39 * q^67 + 388 * q^68 - 354 * q^70 - 84 * q^71 - 77 * q^73 - 219 * q^74 + 215 * q^76 - 260 * q^77 + 9 * q^79 - 312 * q^80 - 4 * q^82 + 348 * q^83 + 68 * q^85 - 249 * q^86 + 72 * q^89 - 393 * q^91 + 118 * q^92 - 104 * q^95 - 228 * q^97 - 540 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.204011	+	0.117786i	−0.102006	+	0.0588930i	−0.550135	−	0.835076i	$-0.685424\pi$
$2$	−0.204011	+	0.117786i	−0.102006	+	0.0588930i	0.448129	+	0.893969i	$0.352090\pi$
$3$		0			0
$3$		0			0
$4$	−1.97225	+	3.41604i	−0.493063	+	0.854011i
$5$	−2.88028	−	4.98878i	−0.576055	−	0.997757i	−0.995926	−	0.0901730i	$-0.971258\pi$
$5$	−2.88028	−	4.98878i	−0.576055	−	0.997757i	0.419871	−	0.907584i	$-0.362075\pi$
$6$		0			0
$7$	1.94451			0.277787			0.138893	−	0.990307i	$-0.455646\pi$
$7$	1.94451			0.277787			0.138893	+	0.990307i	$0.455646\pi$
$8$		−	1.87150i		−	0.233938i
$9$		0			0
$10$	1.17522	+	0.678513i	0.117522	+	0.0678513i
$11$	−8.46561			−0.769601			−0.384800	−	0.923000i	$-0.625730\pi$
$11$	−8.46561			−0.769601			−0.384800	+	0.923000i	$0.625730\pi$
$12$		0			0
$13$	−16.7415	−	9.66573i	−1.28781	−	0.743518i	−0.309547	−	0.950884i	$-0.600178\pi$
$13$	−16.7415	−	9.66573i	−1.28781	−	0.743518i	−0.978263	+	0.207366i	$0.933511\pi$
$14$	−0.396701	+	0.229036i	−0.0283358	+	0.0163597i
$15$		0			0
$16$	−7.66857	−	13.2824i	−0.479286	−	0.830148i
$17$	−12.5365	−	21.7138i	−0.737440	−	1.27728i	−0.953644	−	0.300936i	$-0.902701\pi$
$17$	−12.5365	−	21.7138i	−0.737440	−	1.27728i	0.216204	−	0.976348i	$-0.430632\pi$
$18$		0			0
$19$	17.8181	−	6.59651i	0.937797	−	0.347185i
$19$	17.8181	−	6.59651i	0.937797	−	0.347185i
$20$	22.7225			1.13613
$21$		0			0
$22$	1.72708	−	0.997131i	0.0785037	−	0.0453241i
$23$	−15.6408	+	27.0907i	−0.680036	+	1.17786i	0.294933	+	0.955518i	$0.404703\pi$
$23$	−15.6408	+	27.0907i	−0.680036	+	1.17786i	−0.974969	+	0.222339i	$0.928631\pi$
$24$		0			0
$25$	−4.09198	+	7.08751i	−0.163679	+	0.283500i
$26$	4.55395			0.175152
$27$		0			0
$28$	−3.83506	+	6.64251i	−0.136966	+	0.237233i
$29$	−13.7071	−	7.91383i	−0.472660	−	0.272891i	0.244692	−	0.969601i	$-0.421313\pi$
$29$	−13.7071	−	7.91383i	−0.472660	−	0.272891i	−0.717353	+	0.696710i	$0.754646\pi$
$30$		0			0
$31$		−	14.4237i		−	0.465280i	−0.972563	−	0.232640i	$-0.925264\pi$
$31$		−	14.4237i		−	0.465280i	0.972563	−	0.232640i	$-0.0747363\pi$
$32$	9.61203	+	5.54951i	0.300376	+	0.173422i
$33$		0			0
$34$	5.11517	+	2.95325i	0.150446	+	0.0868602i
$35$	−5.60071	−	9.70072i	−0.160020	−	0.277163i
$36$		0			0
$37$			41.6423i			1.12547i	0.826638	+	0.562734i	$0.190251\pi$
$37$			41.6423i			1.12547i	−0.826638	+	0.562734i	$0.809749\pi$
$38$	−2.85813	+	3.44449i	−0.0752139	+	0.0906445i
$39$		0			0
$40$	−9.33653	+	5.39045i	−0.233413	+	0.134761i
$41$	−1.53439	+	0.885881i	−0.0374242	+	0.0216069i	−0.518595	−	0.855020i	$-0.673545\pi$
$41$	−1.53439	+	0.885881i	−0.0374242	+	0.0216069i	0.481171	+	0.876627i	$0.340212\pi$
$42$		0			0
$43$	14.4358	+	25.0035i	0.335716	+	0.581476i	0.983622	−	0.180243i	$-0.0576886\pi$
$43$	14.4358	+	25.0035i	0.335716	+	0.581476i	−0.647906	+	0.761720i	$0.724355\pi$
$44$	16.6963	−	28.9189i	0.379462	−	0.657247i
$45$		0			0
$46$		−	7.36909i		−	0.160198i
$47$	−1.70506	+	2.95325i	−0.0362778	+	0.0628350i	−0.883594	−	0.468253i	$-0.844883\pi$
$47$	−1.70506	+	2.95325i	−0.0362778	+	0.0628350i	0.847316	+	0.531088i	$0.178217\pi$
$48$		0			0
$49$	−45.2189			−0.922835
$50$		−	1.92791i		−	0.0385582i
$51$		0			0
$52$	66.0371	−	38.1265i	1.26994	−	0.733203i
$53$	80.0952	+	46.2430i	1.51123	+	0.872510i	0.999914	+	0.0131174i	$0.00417552\pi$
$53$	80.0952	+	46.2430i	1.51123	+	0.872510i	0.511317	+	0.859392i	$0.329158\pi$
$54$		0			0
$55$	24.3833	+	42.2331i	0.443333	+	0.767874i
$56$		−	3.63915i		−	0.0649848i
$57$		0			0
$58$	3.72855			0.0642854
$59$	−4.27292	+	2.46697i	−0.0724224	+	0.0418131i	−0.535774	−	0.844361i	$-0.679980\pi$
$59$	−4.27292	+	2.46697i	−0.0724224	+	0.0418131i	0.463352	+	0.886175i	$0.346647\pi$
$60$		0			0
$61$	7.45989	−	12.9209i	0.122293	−	0.211818i	−0.798378	−	0.602156i	$-0.794309\pi$
$61$	7.45989	−	12.9209i	0.122293	−	0.211818i	0.920672	+	0.390338i	$0.127642\pi$
$62$	1.69891	+	2.94259i	0.0274017	+	0.0474612i
$63$		0			0
$64$	58.7340			0.917718
$65$			111.360i			1.71323i
$66$		0			0
$67$	−70.4113	−	40.6520i	−1.05091	−	0.606746i	−0.128009	−	0.991773i	$-0.540859\pi$
$67$	−70.4113	−	40.6520i	−1.05091	−	0.606746i	−0.922905	+	0.385027i	$0.874192\pi$
$68$	98.9005			1.45442
$69$		0			0
$70$	2.28522	+	1.31937i	0.0326460	+	0.0188482i
$71$	−52.9948	+	30.5966i	−0.746406	+	0.430938i	−0.824394	−	0.566017i	$-0.808484\pi$
$71$	−52.9948	+	30.5966i	−0.746406	+	0.430938i	0.0779878	+	0.996954i	$0.475150\pi$
$72$		0			0
$73$	−38.8299	−	67.2553i	−0.531916	−	0.921306i	−0.999306	−	0.0372545i	$-0.988139\pi$
$73$	−38.8299	−	67.2553i	−0.531916	−	0.921306i	0.467390	−	0.884051i	$-0.345195\pi$
$74$	−4.90489	−	8.49551i	−0.0662822	−	0.114804i
$75$		0			0
$76$	−12.6079	+	73.8775i	−0.165894	+	0.972072i
$77$	−16.4614			−0.213785
$78$		0			0
$79$	84.0207	−	48.5094i	1.06355	−	0.614043i	0.137140	−	0.990552i	$-0.456209\pi$
$79$	84.0207	−	48.5094i	1.06355	−	0.614043i	0.926413	+	0.376509i	$0.122875\pi$
$80$	−44.1752	+	76.5137i	−0.552190	+	0.956422i
$81$		0			0
$82$	0.208689	−	0.361460i	0.00254499	−	0.00440805i
$83$	102.323			1.23280			0.616401	−	0.787432i	$-0.288590\pi$
$83$	102.323			1.23280			0.616401	+	0.787432i	$0.288590\pi$
$84$		0			0
$85$	−72.2171	+	125.084i	−0.849612	+	1.47157i
$86$	−5.89012	−	3.40067i	−0.0684898	−	0.0395426i
$87$		0			0
$88$			15.8434i			0.180039i
$89$	−103.596	−	59.8111i	−1.16400	−	0.672034i	−0.211739	−	0.977326i	$-0.567913\pi$
$89$	−103.596	−	59.8111i	−1.16400	−	0.672034i	−0.952259	+	0.305292i	$0.901246\pi$
$90$		0			0
$91$	−32.5540	−	18.7951i	−0.357737	−	0.206539i
$92$	−61.6953	−	106.859i	−0.670601	−	1.16152i
$93$		0			0
$94$		−	0.803328i		−	0.00854604i
$95$	−84.2297	−	69.8911i	−0.886629	−	0.735695i
$96$		0			0
$97$	−42.1438	+	24.3318i	−0.434473	+	0.250843i	−0.701250	−	0.712915i	$-0.747374\pi$
$97$	−42.1438	+	24.3318i	−0.434473	+	0.250843i	0.266778	+	0.963758i	$0.414041\pi$
$98$	9.22517	−	5.32616i	0.0941344	−	0.0543485i
$99$		0			0
$100$	−16.1408	−	27.9567i	−0.161408	−	0.279567i
$101$	81.5540	−	141.256i	0.807465	−	1.39857i	−0.107149	−	0.994243i	$-0.534172\pi$
$101$	81.5540	−	141.256i	0.807465	−	1.39857i	0.914614	−	0.404327i	$-0.132494\pi$
$102$		0			0
$103$		−	18.2732i		−	0.177410i	−0.996058	−	0.0887050i	$-0.971727\pi$
$103$		−	18.2732i		−	0.177410i	0.996058	−	0.0887050i	$-0.0282728\pi$
$104$	−18.0895	+	31.3319i	−0.173937	+	0.301268i
$105$		0			0
$106$	−21.7871			−0.205539
$107$			55.4789i			0.518494i	0.965811	+	0.259247i	$0.0834744\pi$
$107$			55.4789i			0.518494i	−0.965811	+	0.259247i	$0.916526\pi$
$108$		0			0
$109$	96.4369	−	55.6779i	0.884743	−	0.510806i	0.0125234	−	0.999922i	$-0.496014\pi$
$109$	96.4369	−	55.6779i	0.884743	−	0.510806i	0.872219	+	0.489115i	$0.162680\pi$
$110$	−9.94894	−	5.74402i	−0.0904449	−	0.0522184i
$111$		0			0
$112$	−14.9116	−	25.8276i	−0.133139	−	0.230604i
$113$		−	110.968i		−	0.982019i	−0.871154	−	0.491010i	$-0.836628\pi$
$113$		−	110.968i		−	0.982019i	0.871154	−	0.491010i	$-0.163372\pi$
$114$		0			0
$115$	180.200			1.56695
$116$	54.0679	−	31.2161i	0.466103	−	0.269105i
$117$		0			0
$118$	0.581150	−	1.00658i	0.00492500	−	0.00853034i
$119$	−24.3773	−	42.2227i	−0.204851	−	0.354812i
$120$		0			0
$121$	−49.3335			−0.407715
$122$			3.51468i			0.0288089i
$123$		0			0
$124$	49.2719	+	28.4471i	0.397354	+	0.229412i
$125$	−96.8697			−0.774958
$126$		0			0
$127$	−209.627	−	121.028i	−1.65061	−	0.952979i	−0.976822	−	0.214052i	$-0.931334\pi$
$127$	−209.627	−	121.028i	−1.65061	−	0.952979i	−0.673785	−	0.738927i	$-0.735333\pi$
$128$	−50.4305	+	29.1161i	−0.393989	+	0.227469i
$129$		0			0
$130$	−13.1166	−	22.7187i	−0.100897	−	0.174759i
$131$	−78.7288	−	136.362i	−0.600983	−	1.04093i	−0.992672	−	0.120836i	$-0.961443\pi$
$131$	−78.7288	−	136.362i	−0.600983	−	1.04093i	0.391689	−	0.920098i	$-0.371891\pi$
$132$		0			0
$133$	34.6475	−	12.8270i	0.260507	−	0.0964433i
$134$	19.1529			0.142932
$135$		0			0
$136$	−40.6375	+	23.4621i	−0.298805	+	0.172515i
$137$	−121.173	+	209.877i	−0.884473	+	1.53195i	−0.0381558	+	0.999272i	$0.512148\pi$
$137$	−121.173	+	209.877i	−0.884473	+	1.53195i	−0.846317	+	0.532680i	$0.821185\pi$
$138$		0			0
$139$	−65.0431	+	112.658i	−0.467936	+	0.810489i	−0.999329	−	0.0366365i	$-0.988336\pi$
$139$	−65.0431	+	112.658i	−0.467936	+	0.810489i	0.531392	+	0.847126i	$0.321669\pi$
$140$	44.1841			0.315601
$141$		0			0
$142$	7.20770	−	12.4841i	0.0507585	−	0.0879162i
$143$	141.727	+	81.8263i	0.991100	+	0.572212i
$144$		0			0
$145$			91.1760i			0.628800i
$146$	15.8435	+	9.14724i	0.108517	+	0.0626523i
$147$		0			0
$148$	−142.252	−	82.1292i	−0.961162	−	0.554927i
$149$	102.368	+	177.306i	0.687030	+	1.18997i	0.972794	+	0.231672i	$0.0744195\pi$
$149$	102.368	+	177.306i	0.687030	+	1.18997i	−0.285764	+	0.958300i	$0.592247\pi$
$150$		0			0
$151$		−	234.305i		−	1.55169i	−0.630924	−	0.775845i	$-0.717324\pi$
$151$		−	234.305i		−	1.55169i	0.630924	−	0.775845i	$-0.282676\pi$
$152$	−12.3454	−	33.3467i	−0.0812197	−	0.219386i
$153$		0			0
$154$	3.35832	−	1.93893i	0.0218073	−	0.0125904i
$155$	−71.9566	+	41.5441i	−0.464236	+	0.268027i
$156$		0			0
$157$	44.2955	+	76.7220i	0.282137	+	0.488675i	0.971911	−	0.235349i	$-0.0756234\pi$
$157$	44.2955	+	76.7220i	0.282137	+	0.488675i	−0.689774	+	0.724025i	$0.742290\pi$
$158$	−11.4275	+	19.7929i	−0.0723257	+	0.125272i
$159$		0			0
$160$		−	63.9365i		−	0.399603i
$161$	−30.4137	+	52.6780i	−0.188905	+	0.327193i
$162$		0			0
$163$	115.918			0.711153			0.355576	−	0.934647i	$-0.384285\pi$
$163$	115.918			0.711153			0.355576	+	0.934647i	$0.384285\pi$
$164$		−	6.98873i		−	0.0426142i
$165$		0			0
$166$	−20.8750	+	12.0522i	−0.125753	+	0.0726035i
$167$	−78.0426	−	45.0579i	−0.467321	−	0.269808i	0.247797	−	0.968812i	$-0.420293\pi$
$167$	−78.0426	−	45.0579i	−0.467321	−	0.269808i	−0.715118	+	0.699004i	$0.753627\pi$
$168$		0			0
$169$	102.353	+	177.280i	0.605638	+	1.04900i
$170$		−	34.0247i		−	0.200145i
$171$		0			0
$172$	−113.884			−0.662116
$173$	38.5739	−	22.2707i	0.222971	−	0.128732i	−0.384354	−	0.923186i	$-0.625576\pi$
$173$	38.5739	−	22.2707i	0.222971	−	0.128732i	0.607325	+	0.794454i	$0.292243\pi$
$174$		0			0
$175$	−7.95687	+	13.7817i	−0.0454678	+	0.0787526i
$176$	64.9192	+	112.443i	0.368859	+	0.638882i
$177$		0			0
$178$	28.1796			0.158313
$179$		−	229.632i		−	1.28286i	−0.767181	−	0.641431i	$-0.778341\pi$
$179$		−	229.632i		−	1.28286i	0.767181	−	0.641431i	$-0.221659\pi$
$180$		0			0
$181$	157.070	+	90.6845i	0.867791	+	0.501019i	0.866613	−	0.498980i	$-0.166292\pi$
$181$	157.070	+	90.6845i	0.867791	+	0.501019i	0.00117734	+	0.999999i	$0.499625\pi$
$182$	8.85519			0.0486549
$183$		0			0
$184$	50.7004	+	29.2719i	0.275545	+	0.159086i
$185$	207.745	−	119.941i	1.12294	−	0.648332i
$186$		0			0
$187$	106.129	+	183.821i	0.567535	+	0.982999i
$188$	−6.72561	−	11.6491i	−0.0357745	−	0.0619633i
$189$		0			0
$190$	25.4160	+	4.33749i	0.133769	+	0.0228289i
$191$	278.704			1.45918			0.729592	−	0.683882i	$-0.239710\pi$
$191$	278.704			1.45918			0.729592	+	0.683882i	$0.239710\pi$
$192$		0			0
$193$	−167.512	+	96.7133i	−0.867939	+	0.501105i	−0.866663	−	0.498894i	$-0.833740\pi$
$193$	−167.512	+	96.7133i	−0.867939	+	0.501105i	−0.00127645	+	0.999999i	$0.500406\pi$
$194$	5.73188	−	9.92791i	0.0295458	−	0.0511748i
$195$		0			0
$196$	89.1831	−	154.470i	0.455016	−	0.788111i
$197$	96.9300			0.492030			0.246015	−	0.969266i	$-0.420879\pi$
$197$	96.9300			0.492030			0.246015	+	0.969266i	$0.420879\pi$
$198$		0			0
$199$	172.893	−	299.460i	0.868811	−	1.50482i	0.00559823	−	0.999984i	$-0.498218\pi$
$199$	172.893	−	299.460i	0.868811	−	1.50482i	0.863213	−	0.504840i	$-0.168449\pi$
$200$	13.2643	+	7.65815i	0.0663215	+	0.0382908i
$201$		0			0
$202$			38.4237i			0.190216i
$203$	−26.6536	−	15.3885i	−0.131299	−	0.0758053i
$204$		0			0
$205$	8.83894	+	5.10316i	0.0431168	+	0.0248935i
$206$	2.15233	+	3.72795i	0.0104482	+	0.0180968i
$207$		0			0
$208$			296.490i			1.42543i
$209$	−150.841	+	55.8435i	−0.721729	+	0.267194i
$210$		0			0
$211$	−11.1758	+	6.45233i	−0.0529657	+	0.0305798i	−0.526249	−	0.850330i	$-0.676402\pi$
$211$	−11.1758	+	6.45233i	−0.0529657	+	0.0305798i	0.473283	+	0.880910i	$0.343069\pi$
$212$	−315.936	+	182.406i	−1.49026	+	0.860405i
$213$		0			0
$214$	−6.53464	−	11.3183i	−0.0305357	−	0.0528894i
$215$	83.1580	−	144.034i	0.386781	−	0.669925i
$216$		0			0
$217$		−	28.0469i		−	0.129248i
$218$	−13.1162	+	22.7179i	−0.0601659	+	0.104210i
$219$		0			0
$220$	−192.360			−0.874364
$221$			484.697i			2.19320i
$222$		0			0
$223$	−80.3821	+	46.4086i	−0.360458	+	0.208110i	−0.669282	−	0.743009i	$-0.733398\pi$
$223$	−80.3821	+	46.4086i	−0.360458	+	0.208110i	0.308824	+	0.951119i	$0.400065\pi$
$224$	18.6907	+	10.7911i	0.0834404	+	0.0481744i
$225$		0			0
$226$	13.0705	+	22.6388i	0.0578341	+	0.100172i
$227$		−	280.870i		−	1.23731i	−0.785662	−	0.618656i	$-0.787677\pi$
$227$		−	280.870i		−	1.23731i	0.785662	−	0.618656i	$-0.212323\pi$
$228$		0			0
$229$	137.541			0.600615			0.300308	−	0.953842i	$-0.402911\pi$
$229$	137.541			0.600615			0.300308	+	0.953842i	$0.402911\pi$
$230$	−36.7628	+	21.2250i	−0.159838	+	0.0922826i
$231$		0			0
$232$	−14.8108	+	25.6530i	−0.0638395	+	0.110573i
$233$	183.683	+	318.148i	0.788339	+	1.36544i	0.926984	+	0.375101i	$0.122392\pi$
$233$	183.683	+	318.148i	0.788339	+	1.36544i	−0.138645	+	0.990342i	$0.544275\pi$
$234$		0			0
$235$	19.6441			0.0835921
$236$		−	19.4620i		−	0.0824659i
$237$		0			0
$238$	9.94648	+	5.74260i	0.0417919	+	0.0241286i
$239$	196.388			0.821707			0.410854	−	0.911701i	$-0.365231\pi$
$239$	196.388			0.821707			0.410854	+	0.911701i	$0.365231\pi$
$240$		0			0
$241$	−118.225	−	68.2572i	−0.490560	−	0.283225i	0.234247	−	0.972177i	$-0.424738\pi$
$241$	−118.225	−	68.2572i	−0.490560	−	0.283225i	−0.724807	+	0.688952i	$0.758071\pi$
$242$	10.0646	−	5.81079i	0.0415892	−	0.0240115i
$243$		0			0
$244$	29.4256	+	50.9666i	0.120597	+	0.208879i
$245$	130.243	+	225.587i	0.531604	+	0.920765i
$246$		0			0
$247$	−362.063	−	61.7896i	−1.46584	−	0.250160i
$248$	−26.9940			−0.108847
$249$		0			0
$250$	19.7625	−	11.4099i	0.0790501	−	0.0456396i
$251$	23.3322	−	40.4126i	0.0929571	−	0.161006i	−0.815797	−	0.578338i	$-0.803701\pi$
$251$	23.3322	−	40.4126i	0.0929571	−	0.161006i	0.908754	+	0.417332i	$0.137035\pi$
$252$		0			0
$253$	132.409	−	229.339i	0.523356	−	0.906480i
$254$	57.0218			0.224495
$255$		0			0
$256$	−110.609	+	191.580i	−0.432066	+	0.748361i
$257$	−4.73878	−	2.73593i	−0.0184388	−	0.0106457i	0.490752	−	0.871299i	$-0.336722\pi$
$257$	−4.73878	−	2.73593i	−0.0184388	−	0.0106457i	−0.509191	+	0.860653i	$0.670055\pi$
$258$		0			0
$259$			80.9737i			0.312640i
$260$	−380.410	−	219.630i	−1.46312	−	0.844730i
$261$		0			0
$262$	32.1232	+	18.5463i	0.122607	+	0.0707874i
$263$	−37.1071	−	64.2713i	−0.141091	−	0.244378i	0.786816	−	0.617187i	$-0.211728\pi$
$263$	−37.1071	−	64.2713i	−0.141091	−	0.244378i	−0.927908	+	0.372809i	$0.878394\pi$
$264$		0			0
$265$		−	532.770i		−	2.01045i
$266$	−5.55764	+	6.69784i	−0.0208934	+	0.0251798i
$267$		0			0
$268$	277.738	−	160.352i	1.03633	−	0.598328i
$269$	64.2197	−	37.0772i	0.238735	−	0.137834i	−0.375860	−	0.926676i	$-0.622653\pi$
$269$	64.2197	−	37.0772i	0.238735	−	0.137834i	0.614595	+	0.788843i	$0.289319\pi$
$270$		0			0
$271$	48.0380	+	83.2043i	0.177262	+	0.307027i	0.940942	−	0.338568i	$-0.109943\pi$
$271$	48.0380	+	83.2043i	0.177262	+	0.307027i	−0.763680	+	0.645595i	$0.776609\pi$
$272$	−192.274	+	333.028i	−0.706889	+	1.22437i
$273$		0			0
$274$		−	57.0898i		−	0.208357i
$275$	34.6411	−	60.0001i	0.125968	−	0.218182i
$276$		0			0
$277$	123.007			0.444068			0.222034	−	0.975039i	$-0.428730\pi$
$277$	123.007			0.444068			0.222034	+	0.975039i	$0.428730\pi$
$278$		−	30.6447i		−	0.110233i
$279$		0			0
$280$	−18.1549	+	10.4818i	−0.0648391	+	0.0374348i
$281$	−352.110	−	203.291i	−1.25306	−	0.723454i	−0.281344	−	0.959607i	$-0.590780\pi$
$281$	−352.110	−	203.291i	−1.25306	−	0.723454i	−0.971716	+	0.236153i	$0.924113\pi$
$282$		0			0
$283$	−92.7689	−	160.680i	−0.327805	−	0.567776i	0.654271	−	0.756260i	$-0.272976\pi$
$283$	−92.7689	−	160.680i	−0.327805	−	0.567776i	−0.982076	+	0.188485i	$0.939642\pi$
$284$		−	241.377i		−	0.849918i
$285$		0			0
$286$	−38.5520			−0.134797
$287$	−2.98363	+	1.72260i	−0.0103959	+	0.00600209i
$288$		0			0
$289$	−169.827	+	294.149i	−0.587636	+	1.01782i
$290$	−10.7393	−	18.6009i	−0.0370319	−	0.0641412i
$291$		0			0
$292$	306.329			1.04907
$293$		−	360.407i		−	1.23006i	−0.788505	−	0.615028i	$-0.789145\pi$
$293$		−	360.407i		−	1.23006i	0.788505	−	0.615028i	$-0.210855\pi$
$294$		0			0
$295$	24.6144	+	14.2111i	0.0834385	+	0.0481733i
$296$	77.9338			0.263290
$297$		0			0
$298$	−41.7683	−	24.1149i	−0.140162	−	0.0809226i
$299$	523.703	−	302.360i	1.75152	−	1.01124i
$300$		0			0
$301$	28.0704	+	48.6194i	0.0932573	+	0.161526i
$302$	27.5979	+	47.8009i	0.0913837	+	0.158281i
$303$		0			0
$304$	−224.257	−	186.081i	−0.737687	−	0.612109i
$305$	−85.9461			−0.281791
$306$		0			0
$307$	−233.152	+	134.610i	−0.759453	+	0.438470i	−0.829099	−	0.559101i	$-0.811146\pi$
$307$	−233.152	+	134.610i	−0.759453	+	0.438470i	0.0696463	+	0.997572i	$0.477813\pi$
$308$	32.4661	−	56.2329i	0.105409	−	0.182574i
$309$		0			0
$310$	9.78664	−	16.9510i	0.0315698	−	0.0546805i
$311$	−53.4530			−0.171874			−0.0859372	−	0.996301i	$-0.527388\pi$
$311$	−53.4530			−0.171874			−0.0859372	+	0.996301i	$0.527388\pi$
$312$		0			0
$313$	−119.760	+	207.430i	−0.382618	+	0.662715i	−0.991436	−	0.130596i	$-0.958311\pi$
$313$	−119.760	+	207.430i	−0.382618	+	0.662715i	0.608817	+	0.793310i	$0.291644\pi$
$314$	−18.0736	−	10.4348i	−0.0575592	−	0.0332318i
$315$		0			0
$316$			382.691i			1.21105i
$317$	−391.754	−	226.179i	−1.23582	−	0.713499i	−0.267580	−	0.963536i	$-0.586224\pi$
$317$	−391.754	−	226.179i	−1.23582	−	0.713499i	−0.968236	+	0.250036i	$0.919557\pi$
$318$		0			0
$319$	116.039	+	66.9954i	0.363760	+	0.210017i
$320$	−169.170	−	293.011i	−0.528656	−	0.915660i
$321$		0			0
$322$		−	14.3292i		−	0.0445007i
$323$	−366.612	−	304.203i	−1.13502	−	0.941805i
$324$		0			0
$325$	137.012	−	79.1039i	0.421575	−	0.243397i
$326$	−23.6486	+	13.6535i	−0.0725417	+	0.0418820i
$327$		0			0
$328$	1.65793	+	2.87162i	0.00505467	+	0.00875494i
$329$	−3.31549	+	5.74260i	−0.0100775	+	0.0174547i
$330$		0			0
$331$			95.4707i			0.288431i	0.989546	+	0.144216i	$0.0460659\pi$
$331$			95.4707i			0.288431i	−0.989546	+	0.144216i	$0.953934\pi$
$332$	−201.806	+	349.538i	−0.607850	+	1.05283i
$333$		0			0
$334$	21.2288			0.0635592
$335$			468.356i			1.39808i
$336$		0			0
$337$	−82.2367	+	47.4794i	−0.244026	+	0.140888i	−0.617026	−	0.786943i	$-0.711663\pi$
$337$	−82.2367	+	47.4794i	−0.244026	+	0.140888i	0.373000	+	0.927831i	$0.378329\pi$
$338$	−41.7623	−	24.1115i	−0.123557	−	0.0713357i
$339$		0			0
$340$	−284.861	−	493.393i	−0.837825	−	1.45116i
$341$			122.105i			0.358080i
$342$		0			0
$343$	−183.209			−0.534138
$344$	46.7941	−	27.0166i	0.136029	−	0.0785366i
$345$		0			0
$346$	−5.24635	+	9.08694i	−0.0151628	+	0.0262628i
$347$	−115.221	−	199.568i	−0.332048	−	0.575124i	0.650865	−	0.759193i	$-0.274406\pi$
$347$	−115.221	−	199.568i	−0.332048	−	0.575124i	−0.982913	+	0.184069i	$0.941073\pi$
$348$		0			0
$349$	−209.160			−0.599312			−0.299656	−	0.954047i	$-0.596872\pi$
$349$	−209.160			−0.599312			−0.299656	+	0.954047i	$0.596872\pi$
$350$		−	3.74884i		−	0.0107110i
$351$		0			0
$352$	−81.3717	−	46.9800i	−0.231170	−	0.133466i
$353$	−326.125			−0.923866			−0.461933	−	0.886915i	$-0.652844\pi$
$353$	−326.125			−0.923866			−0.461933	+	0.886915i	$0.652844\pi$
$354$		0			0
$355$	305.279	+	176.253i	0.859942	+	0.496488i
$356$	408.634	−	235.925i	1.14785	−	0.662711i
$357$		0			0
$358$	27.0475	+	46.8476i	0.0755516	+	0.130859i
$359$	268.735	+	465.463i	0.748566	+	1.29655i	0.948510	+	0.316747i	$0.102590\pi$
$359$	268.735	+	465.463i	0.748566	+	1.29655i	−0.199945	+	0.979807i	$0.564076\pi$
$360$		0			0
$361$	273.972	−	235.075i	0.758925	−	0.651178i
$362$	−42.7255			−0.118026
$363$		0			0
$364$	128.410	−	74.1373i	0.352773	−	0.203674i
$365$	−223.682	+	387.428i	−0.612826	+	1.06145i
$366$		0			0
$367$	−181.274	+	313.976i	−0.493935	+	0.855520i	−0.999976	−	0.00698970i	$-0.997775\pi$
$367$	−181.274	+	313.976i	−0.493935	+	0.855520i	0.506041	+	0.862509i	$0.331108\pi$
$368$	479.771			1.30373
$369$		0			0
$370$	−28.2548	+	48.9388i	−0.0763644	+	0.132267i
$371$	155.746	+	89.9198i	0.419800	+	0.242371i
$372$		0			0
$373$		−	336.486i		−	0.902108i	−0.892497	−	0.451054i	$-0.851048\pi$
$373$		−	336.486i		−	0.902108i	0.892497	−	0.451054i	$-0.148952\pi$
$374$	−43.3030	−	25.0010i	−0.115784	−	0.0668477i
$375$		0			0
$376$	5.52701	+	3.19102i	0.0146995	+	0.00848676i
$377$	152.986	+	264.979i	0.405798	+	0.702863i
$378$		0			0
$379$		−	336.744i		−	0.888507i	−0.895901	−	0.444253i	$-0.853469\pi$
$379$		−	336.744i		−	0.888507i	0.895901	−	0.444253i	$-0.146531\pi$
$380$	404.873	−	149.889i	1.06546	−	0.394446i
$381$		0			0
$382$	−56.8589	+	32.8275i	−0.148845	+	0.0859358i
$383$	193.755	−	111.865i	0.505888	−	0.292075i	−0.225254	−	0.974300i	$-0.572321\pi$
$383$	193.755	−	111.865i	0.505888	−	0.292075i	0.731142	+	0.682226i	$0.238988\pi$
$384$		0			0
$385$	47.4134	+	82.1225i	0.123152	+	0.213305i
$386$	22.7830	−	39.4612i	0.0590232	−	0.102231i
$387$		0			0
$388$		−	191.954i		−	0.494726i
$389$	−100.458	+	173.998i	−0.258246	+	0.447295i	−0.965772	−	0.259392i	$-0.916478\pi$
$389$	−100.458	+	173.998i	−0.258246	+	0.447295i	0.707526	+	0.706687i	$0.249811\pi$
$390$		0			0
$391$	784.324			2.00594
$392$			84.6274i			0.215886i
$393$		0			0
$394$	−19.7748	+	11.4170i	−0.0501899	+	0.0289772i
$395$	−484.006	−	279.441i	−1.22533	−	0.707445i
$396$		0			0
$397$	−53.1506	−	92.0595i	−0.133880	−	0.231888i	0.791289	−	0.611443i	$-0.209410\pi$
$397$	−53.1506	−	92.0595i	−0.133880	−	0.231888i	−0.925169	+	0.379555i	$0.876077\pi$
$398$			81.4577i			0.204668i
$399$		0			0
$400$	125.519			0.313796
$401$	−185.008	+	106.815i	−0.461368	+	0.266371i	−0.712619	−	0.701551i	$-0.752491\pi$
$401$	−185.008	+	106.815i	−0.461368	+	0.266371i	0.251252	+	0.967922i	$0.419158\pi$
$402$		0			0
$403$	−139.415	+	241.474i	−0.345944	+	0.599192i
$404$	321.690	+	557.184i	0.796262	+	1.37917i
$405$		0			0
$406$	7.25019			0.0178576
$407$		−	352.528i		−	0.866161i
$408$		0			0
$409$	−46.6112	−	26.9110i	−0.113964	−	0.0657970i	0.441935	−	0.897047i	$-0.354292\pi$
$409$	−46.6112	−	26.9110i	−0.113964	−	0.0657970i	−0.555898	+	0.831250i	$0.687626\pi$
$410$	−2.40433			−0.00586421
$411$		0			0
$412$	62.4221	+	36.0394i	0.151510	+	0.0874744i
$413$	−8.30872	+	4.79704i	−0.0201180	+	0.0116151i
$414$		0			0
$415$	−294.717	−	510.465i	−0.710162	−	1.23004i
$416$	−107.280	−	185.815i	−0.257885	−	0.446670i
$417$		0			0
$418$	24.1958	−	29.1597i	0.0578846	−	0.0697601i
$419$	808.890			1.93052			0.965262	−	0.261282i	$-0.0841454\pi$
$419$	808.890			1.93052			0.965262	+	0.261282i	$0.0841454\pi$
$420$		0			0
$421$	−309.086	+	178.451i	−0.734171	+	0.423874i	−0.819946	−	0.572441i	$-0.805997\pi$
$421$	−309.086	+	178.451i	−0.734171	+	0.423874i	0.0857753	+	0.996315i	$0.472663\pi$
$422$	1.51999	−	2.63270i	0.00360187	−	0.00623863i
$423$		0			0
$424$	86.5440	−	149.899i	0.204113	−	0.353534i
$425$	205.196			0.482814
$426$		0			0
$427$	14.5058	−	25.1248i	0.0339714	−	0.0588402i
$428$	−189.518	−	109.418i	−0.442800	−	0.255651i
$429$		0			0
$430$			39.1794i			0.0911149i
$431$	36.3673	+	20.9967i	0.0843789	+	0.0487162i	0.541596	−	0.840639i	$-0.317820\pi$
$431$	36.3673	+	20.9967i	0.0843789	+	0.0487162i	−0.457217	+	0.889355i	$0.651154\pi$
$432$		0			0
$433$	533.602	+	308.075i	1.23234	+	0.711491i	0.967517	−	0.252807i	$-0.0813538\pi$
$433$	533.602	+	308.075i	1.23234	+	0.711491i	0.264821	+	0.964298i	$0.414687\pi$
$434$	3.30353	+	5.72189i	0.00761183	+	0.0131841i
$435$		0			0
$436$			439.244i			1.00744i
$437$	−99.9862	+	585.881i	−0.228801	+	1.34069i
$438$		0			0
$439$	−408.012	+	235.566i	−0.929413	+	0.536597i	−0.886626	−	0.462487i	$-0.846957\pi$
$439$	−408.012	+	235.566i	−0.929413	+	0.536597i	−0.0427870	+	0.999084i	$0.513624\pi$
$440$	79.0394	−	45.6334i	0.179635	−	0.103712i
$441$		0			0
$442$	−57.0906	−	98.8838i	−0.129164	−	0.223719i
$443$	−52.2697	+	90.5338i	−0.117990	+	0.204365i	−0.918971	−	0.394325i	$-0.870979\pi$
$443$	−52.2697	+	90.5338i	−0.117990	+	0.204365i	0.800981	+	0.598690i	$0.204312\pi$
$444$		0			0
$445$			689.089i			1.54852i
$446$	10.9326	−	18.9358i	0.0245125	−	0.0424569i
$447$		0			0
$448$	114.209			0.254930
$449$		−	713.259i		−	1.58855i	−0.607559	−	0.794275i	$-0.707851\pi$
$449$		−	713.259i		−	1.58855i	0.607559	−	0.794275i	$-0.292149\pi$
$450$		0			0
$451$	12.9896	−	7.49952i	0.0288017	−	0.0166287i
$452$	379.072	+	218.857i	0.838655	+	0.484198i
$453$		0			0
$454$	33.0826	+	57.3007i	0.0728691	+	0.126213i
$455$			216.540i			0.475912i
$456$		0			0
$457$	−5.29457			−0.0115855			−0.00579275	−	0.999983i	$-0.501844\pi$
$457$	−5.29457			−0.0115855			−0.00579275	+	0.999983i	$0.501844\pi$
$458$	−28.0599	+	16.2004i	−0.0612662	+	0.0353721i
$459$		0			0
$460$	−355.399	+	615.569i	−0.772607	+	1.33819i
$461$	93.4120	+	161.794i	0.202629	+	0.350964i	0.949375	−	0.314146i	$-0.101718\pi$
$461$	93.4120	+	161.794i	0.202629	+	0.350964i	−0.746746	+	0.665110i	$0.768385\pi$
$462$		0			0
$463$	718.582			1.55201			0.776007	−	0.630725i	$-0.217242\pi$
$463$	718.582			1.55201			0.776007	+	0.630725i	$0.217242\pi$
$464$			242.751i			0.523170i
$465$		0			0
$466$	−74.9468	−	43.2706i	−0.160830	−	0.0928553i
$467$	−864.548			−1.85128			−0.925641	−	0.378404i	$-0.876473\pi$
$467$	−864.548			−1.85128			−0.925641	+	0.378404i	$0.876473\pi$
$468$		0			0
$469$	−136.915	−	79.0480i	−0.291930	−	0.168546i
$470$	−4.00763	+	2.31381i	−0.00852687	+	0.00492299i
$471$		0			0
$472$	4.61695	+	7.99679i	0.00978167	+	0.0169423i
$473$	−122.208	−	211.670i	−0.258367	−	0.447505i
$474$		0			0
$475$	−26.1585	+	153.279i	−0.0550706	+	0.322693i
$476$	192.313			0.404018
$477$		0			0
$478$	−40.0654	+	23.1318i	−0.0838189	+	0.0483928i
$479$	−63.1395	+	109.361i	−0.131815	+	0.228311i	−0.924376	−	0.381482i	$-0.875414\pi$
$479$	−63.1395	+	109.361i	−0.131815	+	0.228311i	0.792561	+	0.609793i	$0.208747\pi$
$480$		0			0
$481$	402.504	−	697.157i	0.836806	−	1.44939i
$482$	32.1590			0.0667199
$483$		0			0
$484$	97.2981	−	168.525i	0.201029	−	0.348193i
$485$	242.772	+	140.164i	0.500560	+	0.288999i
$486$		0			0
$487$			12.1199i			0.0248868i	0.999923	+	0.0124434i	$0.00396097\pi$
$487$			12.1199i			0.0248868i	−0.999923	+	0.0124434i	$0.996039\pi$
$488$	−24.1815	−	13.9612i	−0.0495523	−	0.0286090i
$489$		0			0
$490$	−53.1421	−	30.6816i	−0.108453	−	0.0626155i
$491$	−246.271	−	426.554i	−0.501570	−	0.868745i	−0.999998	−	0.00181372i	$-0.999423\pi$
$491$	−246.271	−	426.554i	−0.501570	−	0.868745i	0.498428	−	0.866931i	$-0.333911\pi$
$492$		0			0
$493$			396.846i			0.804962i
$494$	81.1430	−	30.0402i	0.164257	−	0.0608102i
$495$		0			0
$496$	−191.580	+	110.609i	−0.386251	+	0.223002i
$497$	−103.049	+	59.4952i	−0.207342	+	0.119709i
$498$		0			0
$499$	173.134	+	299.877i	0.346962	+	0.600956i	0.985708	−	0.168462i	$-0.0538800\pi$
$499$	173.134	+	299.877i	0.346962	+	0.600956i	−0.638746	+	0.769417i	$0.720547\pi$
$500$	191.052	−	330.911i	0.382103	−	0.661822i
$501$		0			0
$502$			10.9928i			0.0218981i
$503$	−166.249	+	287.952i	−0.330516	+	0.572470i	−0.982613	−	0.185665i	$-0.940556\pi$
$503$	−166.249	+	287.952i	−0.330516	+	0.572470i	0.652098	+	0.758135i	$0.273889\pi$
$504$		0			0
$505$	−939.592			−1.86058
$506$			62.3838i			0.123288i
$507$		0			0
$508$	826.876	−	477.397i	1.62771	−	0.939758i
$509$	461.493	+	266.443i	0.906666	+	0.523464i	0.879357	−	0.476163i	$-0.157973\pi$
$509$	461.493	+	266.443i	0.906666	+	0.523464i	0.0273090	+	0.999627i	$0.491306\pi$
$510$		0			0
$511$	−75.5049	−	130.778i	−0.147759	−	0.255926i
$512$		−	285.041i		−	0.556722i
$513$		0			0
$514$	1.28902			0.00250782
$515$	−91.1612	+	52.6319i	−0.177012	+	0.102198i
$516$		0			0
$517$	14.4343	−	25.0010i	0.0279194	−	0.0483579i
$518$	−9.53758	−	16.5196i	−0.0184123	−	0.0318911i
$519$		0			0
$520$	208.411			0.400789
$521$			74.3056i			0.142621i	0.997454	+	0.0713106i	$0.0227181\pi$
$521$			74.3056i			0.142621i	−0.997454	+	0.0713106i	$0.977282\pi$
$522$		0			0
$523$	25.3191	+	14.6180i	0.0484113	+	0.0279503i	0.524010	−	0.851712i	$-0.324435\pi$
$523$	25.3191	+	14.6180i	0.0484113	+	0.0279503i	−0.475599	+	0.879662i	$0.657769\pi$
$524$	621.092			1.18529
$525$		0			0
$526$	15.1405	+	8.74139i	0.0287843	+	0.0166186i
$527$	−313.193	+	180.822i	−0.594294	+	0.343116i
$528$		0			0
$529$	−224.771	−	389.315i	−0.424898	−	0.735945i
$530$	62.7529	+	108.691i	0.118402	+	0.205078i
$531$		0			0
$532$	−24.5162	+	143.655i	−0.0460830	+	0.270029i
$533$	34.2508			0.0642603
$534$		0			0
$535$	276.772	−	159.795i	0.517331	−	0.298681i
$536$	−76.0803	+	131.775i	−0.141941	+	0.245849i
$537$		0			0
$538$	−8.73436	+	15.1284i	−0.0162349	+	0.0281196i
$539$	382.805			0.710214
$540$		0			0
$541$	109.055	−	188.889i	0.201580	−	0.349147i	−0.747458	−	0.664310i	$-0.768726\pi$
$541$	109.055	−	188.889i	0.201580	−	0.349147i	0.949038	+	0.315163i	$0.102059\pi$
$542$	−19.6006	−	11.3164i	−0.0361635	−	0.0208790i
$543$		0			0
$544$		−	278.285i		−	0.511554i
$545$	−555.530	−	320.735i	−1.01932	−	0.588505i
$546$		0			0
$547$	−465.237	−	268.605i	−0.850525	−	0.491051i	0.0103027	−	0.999947i	$-0.496721\pi$
$547$	−465.237	−	268.605i	−0.850525	−	0.491051i	−0.860828	+	0.508896i	$0.830054\pi$
$548$	−477.967	−	827.863i	−0.872202	−	1.51070i
$549$		0			0
$550$			16.3209i			0.0296744i
$551$	−296.440	−	50.5903i	−0.538003	−	0.0918154i
$552$		0			0
$553$	163.379	−	94.3268i	0.295441	−	0.170573i
$554$	−25.0948	+	14.4885i	−0.0452975	+	0.0261525i
$555$		0			0
$556$	−256.563	−	444.380i	−0.461444	−	0.799245i
$557$	158.164	−	273.947i	0.283956	−	0.491826i	−0.688399	−	0.725332i	$-0.741686\pi$
$557$	158.164	−	273.947i	0.283956	−	0.491826i	0.972355	+	0.233505i	$0.0750197\pi$
$558$		0			0
$559$		−	558.129i		−	0.998442i
$560$	−85.8990	+	148.781i	−0.153391	+	0.265681i
$561$		0			0
$562$	95.7792			0.170426
$563$			595.272i			1.05732i	0.848833	+	0.528661i	$0.177306\pi$
$563$			595.272i			1.05732i	−0.848833	+	0.528661i	$0.822694\pi$
$564$		0			0
$565$	−553.596	+	319.619i	−0.979816	+	0.565697i
$566$	37.8518	+	21.8538i	0.0668760	+	0.0386109i
$567$		0			0
$568$	57.2616	+	99.1800i	0.100813	+	0.174613i
$569$		−	536.213i		−	0.942377i	−0.882032	−	0.471189i	$-0.843825\pi$
$569$		−	536.213i		−	0.942377i	0.882032	−	0.471189i	$-0.156175\pi$
$570$		0			0
$571$	−84.5912			−0.148146			−0.0740729	−	0.997253i	$-0.523600\pi$
$571$	−84.5912			−0.148146			−0.0740729	+	0.997253i	$0.523600\pi$
$572$	−559.044	+	322.764i	−0.977350	+	0.564273i
$573$		0			0
$574$	0.405797	−	0.702861i	0.000706963	−	0.00122450i
$575$	−128.004	−	221.709i	−0.222615	−	0.385581i
$576$		0			0
$577$	−850.008			−1.47315			−0.736575	−	0.676356i	$-0.763558\pi$
$577$	−850.008			−1.47315			−0.736575	+	0.676356i	$0.763558\pi$
$578$		−	80.0129i		−	0.138431i
$579$		0			0
$580$	−311.461	−	179.822i	−0.537002	−	0.310038i
$581$	198.967			0.342456
$582$		0			0
$583$	−678.055	−	391.475i	−1.16304	−	0.671484i
$584$	−125.869	+	72.6703i	−0.215528	+	0.124435i
$585$		0			0
$586$	42.4509	+	73.5271i	0.0724417	+	0.125473i
$587$	−229.370	−	397.281i	−0.390750	−	0.676798i	0.601799	−	0.798648i	$-0.294451\pi$
$587$	−229.370	−	397.281i	−0.390750	−	0.676798i	−0.992549	+	0.121849i	$0.961117\pi$
$588$		0			0
$589$	−95.1459	−	257.003i	−0.161538	−	0.436338i
$590$	−6.69548			−0.0113483
$591$		0			0
$592$	553.108	−	319.337i	0.934305	−	0.539421i
$593$	51.3293	−	88.9049i	0.0865586	−	0.149924i	−0.819496	−	0.573085i	$-0.805746\pi$
$593$	51.3293	−	88.9049i	0.0865586	−	0.149924i	0.906054	+	0.423161i	$0.139080\pi$
$594$		0			0
$595$	−140.426	+	243.226i	−0.236011	+	0.408783i
$596$	−807.579			−1.35500
$597$		0			0
$598$	−71.2276	+	123.370i	−0.119110	+	0.206304i
$599$	−322.250	−	186.051i	−0.537980	−	0.310603i	0.206280	−	0.978493i	$-0.433864\pi$
$599$	−322.250	−	186.051i	−0.537980	−	0.310603i	−0.744260	+	0.667890i	$0.767198\pi$
$600$		0			0
$601$			850.837i			1.41570i	0.706362	+	0.707851i	$0.250335\pi$
$601$			850.837i			1.41570i	−0.706362	+	0.707851i	$0.749665\pi$
$602$	−11.4534	−	6.61261i	−0.0190256	−	0.0109844i
$603$		0			0
$604$	800.396	+	462.109i	1.32516	+	0.765081i
$605$	142.094	+	246.114i	0.234866	+	0.406800i
$606$		0			0
$607$		−	314.498i		−	0.518119i	−0.965861	−	0.259060i	$-0.916587\pi$
$607$		−	314.498i		−	0.518119i	0.965861	−	0.259060i	$-0.0834126\pi$
$608$	207.876	+	35.4760i	0.341901	+	0.0583488i
$609$		0			0
$610$	17.5340	−	10.1233i	0.0287442	−	0.0165955i
$611$	57.0906	−	32.9613i	0.0934379	−	0.0539464i
$612$		0			0
$613$	146.198	+	253.222i	0.238495	+	0.413086i	0.960283	−	0.279029i	$-0.0900125\pi$
$613$	146.198	+	253.222i	0.238495	+	0.413086i	−0.721787	+	0.692115i	$0.756679\pi$
$614$	31.7105	−	54.9241i	0.0516457	−	0.0894530i
$615$		0			0
$616$			30.8076i			0.0500124i
$617$	438.183	−	758.955i	0.710183	−	1.23007i	−0.254605	−	0.967045i	$-0.581945\pi$
$617$	438.183	−	758.955i	0.710183	−	1.23007i	0.964788	−	0.263028i	$-0.0847212\pi$
$618$		0			0
$619$	−166.847			−0.269542			−0.134771	−	0.990877i	$-0.543030\pi$
$619$	−166.847			−0.269542			−0.134771	+	0.990877i	$0.543030\pi$
$620$		−	327.742i		−	0.528617i
$621$		0			0
$622$	10.9050	−	6.29601i	0.0175322	−	0.0101222i
$623$	−201.443	−	116.303i	−0.323343	−	0.186682i
$624$		0			0
$625$	381.311	+	660.450i	0.610097	+	1.05672i
$626$		−	56.4240i		−	0.0901342i
$627$		0			0
$628$	−349.448			−0.556445
$629$	904.214	−	522.048i	1.43754	−	0.829965i
$630$		0			0
$631$	464.592	−	804.698i	0.736280	−	1.27527i	−0.217880	−	0.975976i	$-0.569914\pi$
$631$	464.592	−	804.698i	0.736280	−	1.27527i	0.954160	−	0.299298i	$-0.0967525\pi$
$632$	−90.7855	−	157.245i	−0.143648	−	0.248806i
$633$		0			0
$634$	106.563			0.168080
$635$			1394.38i			2.19587i
$636$		0			0
$637$	757.034	+	437.074i	1.18844	+	0.686144i
$638$	−31.5645			−0.0494741
$639$		0			0
$640$	290.508	+	167.725i	0.453918	+	0.262070i
$641$	−425.692	+	245.773i	−0.664106	+	0.383422i	−0.793840	−	0.608127i	$-0.791921\pi$
$641$	−425.692	+	245.773i	−0.664106	+	0.383422i	0.129734	+	0.991549i	$0.458588\pi$
$642$		0			0
$643$	175.770	+	304.442i	0.273359	+	0.473472i	0.969720	−	0.244220i	$-0.0785319\pi$
$643$	175.770	+	304.442i	0.273359	+	0.473472i	−0.696361	+	0.717692i	$0.745199\pi$
$644$	−119.967	−	207.789i	−0.186284	−	0.322653i
$645$		0			0
$646$	110.624	+	18.8790i	0.171245	+	0.0292245i
$647$	−767.027			−1.18551			−0.592757	−	0.805381i	$-0.701961\pi$
$647$	−767.027			−1.18551			−0.592757	+	0.805381i	$0.701961\pi$
$648$		0			0
$649$	36.1729	−	20.8844i	0.0557363	−	0.0321794i
$650$	−18.6347	+	32.2762i	−0.0286687	+	0.0496557i
$651$		0			0
$652$	−228.619	+	395.981i	−0.350643	+	0.607332i
$653$	254.877			0.390317			0.195159	−	0.980772i	$-0.437478\pi$
$653$	254.877			0.390317			0.195159	+	0.980772i	$0.437478\pi$
$654$		0			0
$655$	−453.521	+	785.522i	−0.692399	+	1.19927i
$656$	23.5332	+	13.5869i	0.0358738	+	0.0207117i
$657$		0			0
$658$		−	1.56208i		−	0.00237398i
$659$	427.502	+	246.818i	0.648713	+	0.374535i	0.787963	−	0.615723i	$-0.211136\pi$
$659$	427.502	+	246.818i	0.648713	+	0.374535i	−0.139250	+	0.990257i	$0.544469\pi$
$660$		0			0
$661$	−1110.75	−	641.292i	−1.68041	−	0.970185i	−0.961388	−	0.275197i	$-0.911257\pi$
$661$	−1110.75	−	641.292i	−1.68041	−	0.970185i	−0.719021	−	0.694988i	$-0.755410\pi$
$662$	−11.2451	−	19.4771i	−0.0169866	−	0.0294216i
$663$		0			0
$664$		−	191.497i		−	0.288399i
$665$	−163.785	−	135.904i	−0.246294	−	0.204366i
$666$		0			0
$667$	428.782	−	247.558i	0.642852	−	0.371151i
$668$	307.839	−	177.731i	0.460837	−	0.266065i
$669$		0			0
$670$	−55.1658	−	95.5499i	−0.0823370	−	0.142612i
$671$	−63.1525	+	109.383i	−0.0941169	+	0.163015i
$672$		0			0
$673$		−	337.649i		−	0.501707i	−0.968025	−	0.250853i	$-0.919289\pi$
$673$		−	337.649i		−	0.501707i	0.968025	−	0.250853i	$-0.0807112\pi$
$674$	11.1848	−	19.3727i	0.0165947	−	0.0287428i
$675$		0			0
$676$	−807.462			−1.19447
$677$			394.197i			0.582270i	0.956682	+	0.291135i	$0.0940329\pi$
$677$			394.197i			0.582270i	−0.956682	+	0.291135i	$0.905967\pi$
$678$		0			0
$679$	−81.9489	+	47.3132i	−0.120691	+	0.0696808i
$680$	234.094	+	135.155i	0.344257	+	0.198757i
$681$		0			0
$682$	−14.3823	−	24.9108i	−0.0210884	−	0.0365262i
$683$			612.782i			0.897192i	0.893735	+	0.448596i	$0.148076\pi$
$683$			612.782i			0.897192i	−0.893735	+	0.448596i	$0.851924\pi$
$684$		0			0
$685$	1396.04			2.03802
$686$	37.3768	−	21.5795i	0.0544851	−	0.0314570i
$687$		0			0
$688$	221.404	−	383.482i	0.321807	−	0.557387i
$689$	−893.945	−	1548.36i	−1.29745	−	2.24725i
$690$		0			0
$691$	254.757			0.368678			0.184339	−	0.982863i	$-0.440986\pi$
$691$	254.757			0.368678			0.184339	+	0.982863i	$0.440986\pi$
$692$			175.693i			0.253892i
$693$		0			0
$694$	47.0127	+	27.1428i	0.0677417	+	0.0391107i
$695$	749.369			1.07823
$696$		0			0
$697$	38.4717	+	22.2117i	0.0551962	+	0.0318675i
$698$	42.6710	−	24.6361i	0.0611333	−	0.0352953i
$699$		0			0
$700$	−31.3859	−	54.3620i	−0.0448370	−	0.0776600i
$701$	3.62864	+	6.28499i	0.00517638	+	0.00896576i	0.868602	−	0.495510i	$-0.165019\pi$
$701$	3.62864	+	6.28499i	0.00517638	+	0.00896576i	−0.863426	+	0.504476i	$0.831686\pi$
$702$		0			0
$703$	274.694	+	741.989i	0.390746	+	1.05546i
$704$	−497.219			−0.706277
$705$		0			0
$706$	66.5332	−	38.4130i	0.0942396	−	0.0544093i
$707$	158.582	−	274.672i	0.224303	−	0.388504i
$708$		0			0
$709$	−522.280	+	904.615i	−0.736643	+	1.27590i	0.217356	+	0.976092i	$0.430257\pi$
$709$	−522.280	+	904.615i	−0.736643	+	1.27590i	−0.953999	+	0.299810i	$0.903077\pi$
$710$	−83.0407			−0.116959
$711$		0			0
$712$	−111.937	+	193.880i	−0.157214	+	0.272303i
$713$	390.747	+	225.598i	0.548033	+	0.316407i
$714$		0			0
$715$		−	942.729i		−	1.31850i
$716$	784.433	+	452.893i	1.09558	+	0.632532i
$717$		0			0
$718$	−109.650	−	63.3065i	−0.152716	−	0.0881706i
$719$	658.810	+	1141.09i	0.916286	+	1.58705i	0.805007	+	0.593265i	$0.202161\pi$
$719$	658.810	+	1141.09i	0.916286	+	1.58705i	0.111279	+	0.993789i	$0.464505\pi$
$720$		0			0
$721$		−	35.5324i		−	0.0492821i
$722$	−28.2049	+	80.2281i	−0.0390649	+	0.111119i
$723$		0			0
$724$	−619.564	+	357.705i	−0.855751	+	0.494068i
$725$	112.179	−	64.7664i	0.154729	−	0.0893330i
$726$		0			0
$727$	−88.8280	−	153.855i	−0.122184	−	0.211630i	0.798444	−	0.602068i	$-0.205657\pi$
$727$	−88.8280	−	153.855i	−0.122184	−	0.211630i	−0.920629	+	0.390439i	$0.872323\pi$
$728$	−35.1751	+	60.9250i	−0.0483174	+	0.0836882i
$729$		0			0
$730$		−	105.386i		−	0.144365i
$731$	361.948	−	626.912i	0.495140	−	0.857608i
$732$		0			0
$733$	321.795			0.439011			0.219505	−	0.975611i	$-0.429556\pi$
$733$	321.795			0.439011			0.219505	+	0.975611i	$0.429556\pi$
$734$		−	85.4062i		−	0.116357i
$735$		0			0
$736$	−300.680	+	173.598i	−0.408533	+	0.235867i
$737$	596.074	+	344.144i	0.808785	+	0.466952i
$738$		0			0
$739$	85.7034	+	148.443i	0.115972	+	0.200870i	0.918168	−	0.396191i	$-0.129668\pi$
$739$	85.7034	+	148.443i	0.115972	+	0.200870i	−0.802196	+	0.597061i	$0.796335\pi$
$740$			946.219i			1.27867i
$741$		0			0
$742$	−42.3652			−0.0570960
$743$	257.044	−	148.405i	0.345955	−	0.199737i	−0.316947	−	0.948443i	$-0.602658\pi$
$743$	257.044	−	148.405i	0.345955	−	0.199737i	0.662902	+	0.748706i	$0.269325\pi$
$744$		0			0
$745$	589.693	−	1021.38i	0.791535	−	1.37098i
$746$	39.6334	+	68.6471i	0.0531279	+	0.0920202i
$747$		0			0
$748$	−837.253			−1.11932
$749$			107.879i			0.144031i
$750$		0			0
$751$	−117.403	−	67.7829i	−0.156329	−	0.0902568i	0.419795	−	0.907619i	$-0.362102\pi$
$751$	−117.403	−	67.7829i	−0.156329	−	0.0902568i	−0.576124	+	0.817362i	$0.695435\pi$
$752$	52.3014			0.0695498
$753$		0			0
$754$	−62.4217	−	36.0392i	−0.0827874	−	0.0477974i
$755$	−1168.90	+	674.864i	−1.54821	+	0.893859i
$756$		0			0
$757$	4.71078	+	8.15931i	0.00622296	+	0.0107785i	0.869120	−	0.494601i	$-0.164686\pi$
$757$	4.71078	+	8.15931i	0.00622296	+	0.0107785i	−0.862897	+	0.505380i	$0.831352\pi$
$758$	39.6637	+	68.6996i	0.0523268	+	0.0906327i
$759$		0			0
$760$	−130.801	+	157.636i	−0.172107	+	0.207416i
$761$	501.946			0.659587			0.329794	−	0.944053i	$-0.393021\pi$
$761$	501.946			0.659587			0.329794	+	0.944053i	$0.393021\pi$
$762$		0			0
$763$	187.522	−	108.266i	0.245770	−	0.141895i
$764$	−549.675	+	952.066i	−0.719470	+	1.24616i
$765$		0			0
$766$	−26.3522	+	45.6433i	−0.0344023	+	0.0595866i
$767$	95.3803			0.124355
$768$		0			0
$769$	722.257	−	1250.99i	0.939216	−	1.62677i	0.172279	−	0.985048i	$-0.444887\pi$
$769$	722.257	−	1250.99i	0.939216	−	1.62677i	0.766937	−	0.641722i	$-0.221780\pi$
$770$	−19.3458	−	11.1693i	−0.0251244	−	0.0145056i
$771$		0			0
$772$		−	762.972i		−	0.988306i
$773$	572.771	+	330.690i	0.740972	+	0.427800i	0.822423	−	0.568877i	$-0.192622\pi$
$773$	572.771	+	330.690i	0.740972	+	0.427800i	−0.0814506	+	0.996677i	$0.525955\pi$
$774$		0			0
$775$	102.228	+	59.0213i	0.131907	+	0.0761565i
$776$	45.5370	+	78.8724i	0.0586817	+	0.101640i
$777$		0			0
$778$		−	47.3301i		−	0.0608356i
$779$	−21.4963	+	25.9064i	−0.0275947	+	0.0332559i
$780$		0			0
$781$	448.633	−	259.019i	0.574435	−	0.331650i
$782$	−160.011	+	92.3824i	−0.204618	+	0.118136i
$783$		0			0
$784$	346.764	+	600.614i	0.442302	+	0.766089i

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	171.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.204011 + 0.117786i) q^{2} +(-1.97225 + 3.41604i) q^{4} +(-2.88028 - 4.98878i) q^{5} +1.94451 q^{7} -1.87150i q^{8} +O(q^{10})\)	\(q+(-0.204011 + 0.117786i) q^{2} +(-1.97225 + 3.41604i) q^{4} +(-2.88028 - 4.98878i) q^{5} +1.94451 q^{7} -1.87150i q^{8} +(1.17522 + 0.678513i) q^{10} -8.46561 q^{11} +(-16.7415 - 9.66573i) q^{13} +(-0.396701 + 0.229036i) q^{14} +(-7.66857 - 13.2824i) q^{16} +(-12.5365 - 21.7138i) q^{17} +(17.8181 - 6.59651i) q^{19} +22.7225 q^{20} +(1.72708 - 0.997131i) q^{22} +(-15.6408 + 27.0907i) q^{23} +(-4.09198 + 7.08751i) q^{25} +4.55395 q^{26} +(-3.83506 + 6.64251i) q^{28} +(-13.7071 - 7.91383i) q^{29} -14.4237i q^{31} +(9.61203 + 5.54951i) q^{32} +(5.11517 + 2.95325i) q^{34} +(-5.60071 - 9.70072i) q^{35} +41.6423i q^{37} +(-2.85813 + 3.44449i) q^{38} +(-9.33653 + 5.39045i) q^{40} +(-1.53439 + 0.885881i) q^{41} +(14.4358 + 25.0035i) q^{43} +(16.6963 - 28.9189i) q^{44} -7.36909i q^{46} +(-1.70506 + 2.95325i) q^{47} -45.2189 q^{49} -1.92791i q^{50} +(66.0371 - 38.1265i) q^{52} +(80.0952 + 46.2430i) q^{53} +(24.3833 + 42.2331i) q^{55} -3.63915i q^{56} +3.72855 q^{58} +(-4.27292 + 2.46697i) q^{59} +(7.45989 - 12.9209i) q^{61} +(1.69891 + 2.94259i) q^{62} +58.7340 q^{64} +111.360i q^{65} +(-70.4113 - 40.6520i) q^{67} +98.9005 q^{68} +(2.28522 + 1.31937i) q^{70} +(-52.9948 + 30.5966i) q^{71} +(-38.8299 - 67.2553i) q^{73} +(-4.90489 - 8.49551i) q^{74} +(-12.6079 + 73.8775i) q^{76} -16.4614 q^{77} +(84.0207 - 48.5094i) q^{79} +(-44.1752 + 76.5137i) q^{80} +(0.208689 - 0.361460i) q^{82} +102.323 q^{83} +(-72.2171 + 125.084i) q^{85} +(-5.89012 - 3.40067i) q^{86} +15.8434i q^{88} +(-103.596 - 59.8111i) q^{89} +(-32.5540 - 18.7951i) q^{91} +(-61.6953 - 106.859i) q^{92} -0.803328i q^{94} +(-84.2297 - 69.8911i) q^{95} +(-42.1438 + 24.3318i) q^{97} +(9.22517 - 5.32616i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 5 q^{4} - 4 q^{5} - 22 q^{7}+O(q^{10}) \) 6 * q - 3 * q^2 + 5 * q^4 - 4 * q^5 - 22 * q^7	\( 6 q - 3 q^{2} + 5 q^{4} - 4 q^{5} - 22 q^{7} + 54 q^{10} + 36 q^{11} - 3 q^{13} + 57 q^{14} - 23 q^{16} - 38 q^{17} - 10 q^{19} - 32 q^{20} + 36 q^{22} - 54 q^{23} - 21 q^{25} - 118 q^{26} - 101 q^{28} + 102 q^{29} + 63 q^{32} - 150 q^{34} + 24 q^{35} - 119 q^{38} + 30 q^{40} - 96 q^{41} + 107 q^{43} + 94 q^{44} + 50 q^{47} - 48 q^{49} + 399 q^{52} + 90 q^{53} + 148 q^{55} - 116 q^{58} + 27 q^{61} + 121 q^{62} + 46 q^{64} - 39 q^{67} + 388 q^{68} - 354 q^{70} - 84 q^{71} - 77 q^{73} - 219 q^{74} + 215 q^{76} - 260 q^{77} + 9 q^{79} - 312 q^{80} - 4 q^{82} + 348 q^{83} + 68 q^{85} - 249 q^{86} + 72 q^{89} - 393 q^{91} + 118 q^{92} - 104 q^{95} - 228 q^{97} - 540 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 + 5 * q^4 - 4 * q^5 - 22 * q^7 + 54 * q^10 + 36 * q^11 - 3 * q^13 + 57 * q^14 - 23 * q^16 - 38 * q^17 - 10 * q^19 - 32 * q^20 + 36 * q^22 - 54 * q^23 - 21 * q^25 - 118 * q^26 - 101 * q^28 + 102 * q^29 + 63 * q^32 - 150 * q^34 + 24 * q^35 - 119 * q^38 + 30 * q^40 - 96 * q^41 + 107 * q^43 + 94 * q^44 + 50 * q^47 - 48 * q^49 + 399 * q^52 + 90 * q^53 + 148 * q^55 - 116 * q^58 + 27 * q^61 + 121 * q^62 + 46 * q^64 - 39 * q^67 + 388 * q^68 - 354 * q^70 - 84 * q^71 - 77 * q^73 - 219 * q^74 + 215 * q^76 - 260 * q^77 + 9 * q^79 - 312 * q^80 - 4 * q^82 + 348 * q^83 + 68 * q^85 - 249 * q^86 + 72 * q^89 - 393 * q^91 + 118 * q^92 - 104 * q^95 - 228 * q^97 - 540 * q^98

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