LMFDB - Embedded newform 171.3.p.c.145.3

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			145.3
Root			$0.500000 + 2.93068i$ of defining polynomial
Character	$\chi$	$=$	171.145
Dual form			171.3.p.c.46.3

$q$-expansion

$f(q)$	$=$	$q+(1.78805 - 1.03233i) q^{2} +(0.131406 - 0.227602i) q^{4} +(3.20750 + 5.55555i) q^{5} -2.26281 q^{7} +7.71601i q^{8} +O(q^{10})$	\(q+(1.78805 - 1.03233i) q^{2} +(0.131406 - 0.227602i) q^{4} +(3.20750 + 5.55555i) q^{5} -2.26281 q^{7} +7.71601i q^{8} +(11.4703 + 6.62239i) q^{10} +20.0928 q^{11} +(-0.135471 - 0.0782143i) q^{13} +(-4.04601 + 2.33597i) q^{14} +(8.49109 + 14.7070i) q^{16} +(-12.3133 - 21.3272i) q^{17} +(-18.9317 - 1.60945i) q^{19} +1.68594 q^{20} +(35.9269 - 20.7424i) q^{22} +(2.62250 - 4.54230i) q^{23} +(-8.07609 + 13.9882i) q^{25} -0.322972 q^{26} +(-0.297347 + 0.515021i) q^{28} +(31.4573 + 18.1619i) q^{29} -17.1105i q^{31} +(3.63586 + 2.09917i) q^{32} +(-44.0334 - 25.4227i) q^{34} +(-7.25797 - 12.5712i) q^{35} -42.7124i q^{37} +(-35.5123 + 16.6660i) q^{38} +(-42.8667 + 24.7491i) q^{40} +(-30.0928 + 17.3741i) q^{41} +(12.5553 + 21.7464i) q^{43} +(2.64032 - 4.57316i) q^{44} -10.8291i q^{46} +(14.6778 - 25.4227i) q^{47} -43.8797 q^{49} +33.3487i q^{50} +(-0.0356035 + 0.0205557i) q^{52} +(-48.4176 - 27.9539i) q^{53} +(64.4476 + 111.627i) q^{55} -17.4599i q^{56} +74.9962 q^{58} +(29.9269 - 17.2783i) q^{59} +(27.3805 - 47.4244i) q^{61} +(-17.6637 - 30.5944i) q^{62} -59.2606 q^{64} -1.00349i q^{65} +(66.0698 + 38.1454i) q^{67} -6.47216 q^{68} +(-25.9552 - 14.9852i) q^{70} +(-63.6080 + 36.7241i) q^{71} +(-45.9053 - 79.5103i) q^{73} +(-44.0932 - 76.3717i) q^{74} +(-2.85406 + 4.09740i) q^{76} -45.4662 q^{77} +(-53.1300 + 30.6746i) q^{79} +(-54.4703 + 94.3453i) q^{80} +(-35.8716 + 62.1313i) q^{82} +148.793 q^{83} +(78.9897 - 136.814i) q^{85} +(44.8990 + 25.9224i) q^{86} +155.036i q^{88} +(62.7829 + 36.2477i) q^{89} +(0.306546 + 0.176984i) q^{91} +(-0.689224 - 1.19377i) q^{92} -60.6093i q^{94} +(-51.7820 - 110.338i) q^{95} +(-70.0326 + 40.4334i) q^{97} +(-78.4589 + 45.2983i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.78805	−	1.03233i	0.894023	−	0.516164i	0.0187668	−	0.999824i	$-0.494026\pi$
$2$	1.78805	−	1.03233i	0.894023	−	0.516164i	0.875256	+	0.483659i	$0.160693\pi$
$3$		0			0
$3$		0			0
$4$	0.131406	−	0.227602i	0.0328515	−	0.0569005i
$5$	3.20750	+	5.55555i	0.641500	+	1.11111i	0.985098	+	0.171993i	$0.0550208\pi$
$5$	3.20750	+	5.55555i	0.641500	+	1.11111i	−0.343598	+	0.939117i	$0.611646\pi$
$6$		0			0
$7$	−2.26281			−0.323259			−0.161629	−	0.986852i	$-0.551675\pi$
$7$	−2.26281			−0.323259			−0.161629	+	0.986852i	$0.551675\pi$
$8$			7.71601i			0.964502i
$9$		0			0
$10$	11.4703	+	6.62239i	1.14703	+	0.662239i
$11$	20.0928			1.82662			0.913309	−	0.407267i	$-0.133518\pi$
$11$	20.0928			1.82662			0.913309	+	0.407267i	$0.133518\pi$
$12$		0			0
$13$	−0.135471	−	0.0782143i	−0.0104209	−	0.00601649i	0.494781	−	0.869018i	$-0.335248\pi$
$13$	−0.135471	−	0.0782143i	−0.0104209	−	0.00601649i	−0.505201	+	0.863001i	$0.668582\pi$
$14$	−4.04601	+	2.33597i	−0.289001	+	0.166855i
$15$		0			0
$16$	8.49109	+	14.7070i	0.530693	+	0.919187i
$17$	−12.3133	−	21.3272i	−0.724311	−	1.25454i	−0.959257	−	0.282534i	$-0.908825\pi$
$17$	−12.3133	−	21.3272i	−0.724311	−	1.25454i	0.234947	−	0.972008i	$-0.424508\pi$
$18$		0			0
$19$	−18.9317	−	1.60945i	−0.996406	−	0.0847081i
$19$	−18.9317	−	1.60945i	−0.996406	−	0.0847081i
$20$	1.68594			0.0842970
$21$		0			0
$22$	35.9269	−	20.7424i	1.63304	−	0.942836i
$23$	2.62250	−	4.54230i	0.114022	−	0.197491i	−0.803367	−	0.595485i	$-0.796960\pi$
$23$	2.62250	−	4.54230i	0.114022	−	0.197491i	0.917388	+	0.397994i	$0.130293\pi$
$24$		0			0
$25$	−8.07609	+	13.9882i	−0.323044	+	0.559528i
$26$	−0.322972			−0.0124220
$27$		0			0
$28$	−0.297347	+	0.515021i	−0.0106195	+	0.0183936i
$29$	31.4573	+	18.1619i	1.08474	+	0.626272i	0.932170	−	0.362021i	$-0.117913\pi$
$29$	31.4573	+	18.1619i	1.08474	+	0.626272i	0.152566	+	0.988293i	$0.451246\pi$
$30$		0			0
$31$		−	17.1105i		−	0.551952i	−0.961165	−	0.275976i	$-0.910999\pi$
$31$		−	17.1105i		−	0.551952i	0.961165	−	0.275976i	$-0.0890010\pi$
$32$	3.63586	+	2.09917i	0.113621	+	0.0655989i
$33$		0			0
$34$	−44.0334	−	25.4227i	−1.29510	−	0.747727i
$35$	−7.25797	−	12.5712i	−0.207370	−	0.359176i
$36$		0			0
$37$		−	42.7124i		−	1.15439i	−0.816607	−	0.577194i	$-0.804148\pi$
$37$		−	42.7124i		−	1.15439i	0.816607	−	0.577194i	$-0.195852\pi$
$38$	−35.5123	+	16.6660i	−0.934533	+	0.438578i
$39$		0			0
$40$	−42.8667	+	24.7491i	−1.07167	+	0.618728i
$41$	−30.0928	+	17.3741i	−0.733971	+	0.423758i	−0.819873	−	0.572545i	$-0.805956\pi$
$41$	−30.0928	+	17.3741i	−0.733971	+	0.423758i	0.0859022	+	0.996304i	$0.472623\pi$
$42$		0			0
$43$	12.5553	+	21.7464i	0.291984	+	0.505731i	0.974279	−	0.225346i	$-0.0723512\pi$
$43$	12.5553	+	21.7464i	0.291984	+	0.505731i	−0.682295	+	0.731077i	$0.739018\pi$
$44$	2.64032	−	4.57316i	0.0600072	−	0.103936i
$45$		0			0
$46$		−	10.8291i		−	0.235415i
$47$	14.6778	−	25.4227i	0.312294	−	0.540909i	−0.666565	−	0.745447i	$-0.732236\pi$
$47$	14.6778	−	25.4227i	0.312294	−	0.540909i	0.978859	+	0.204538i	$0.0655693\pi$
$48$		0			0
$49$	−43.8797			−0.895504
$50$			33.3487i			0.666975i
$51$		0			0
$52$	−0.0356035	+	0.0205557i	−0.000684682	+	0.000395301i
$53$	−48.4176	−	27.9539i	−0.913540	−	0.527433i	−0.0319716	−	0.999489i	$-0.510179\pi$
$53$	−48.4176	−	27.9539i	−0.913540	−	0.527433i	−0.881568	+	0.472056i	$0.843512\pi$
$54$		0			0
$55$	64.4476	+	111.627i	1.17178	+	2.02957i
$56$		−	17.4599i		−	0.311784i
$57$		0			0
$58$	74.9962			1.29304
$59$	29.9269	−	17.2783i	0.507235	−	0.292852i	−0.224461	−	0.974483i	$-0.572062\pi$
$59$	29.9269	−	17.2783i	0.507235	−	0.292852i	0.731696	+	0.681631i	$0.238729\pi$
$60$		0			0
$61$	27.3805	−	47.4244i	0.448860	−	0.777448i	−0.549452	−	0.835525i	$-0.685164\pi$
$61$	27.3805	−	47.4244i	0.448860	−	0.777448i	0.998312	+	0.0580769i	$0.0184968\pi$
$62$	−17.6637	−	30.5944i	−0.284898	−	0.493457i
$63$		0			0
$64$	−59.2606			−0.925947
$65$		−	1.00349i		−	0.0154383i
$66$		0			0
$67$	66.0698	+	38.1454i	0.986117	+	0.569335i	0.904111	−	0.427297i	$-0.140534\pi$
$67$	66.0698	+	38.1454i	0.986117	+	0.569335i	0.0820054	+	0.996632i	$0.473868\pi$
$68$	−6.47216			−0.0951788
$69$		0			0
$70$	−25.9552	−	14.9852i	−0.370788	−	0.214075i
$71$	−63.6080	+	36.7241i	−0.895887	+	0.517240i	−0.875863	−	0.482559i	$-0.839707\pi$
$71$	−63.6080	+	36.7241i	−0.895887	+	0.517240i	−0.0200233	+	0.999800i	$0.506374\pi$
$72$		0			0
$73$	−45.9053	−	79.5103i	−0.628840	−	1.08918i	−0.987785	−	0.155824i	$-0.950197\pi$
$73$	−45.9053	−	79.5103i	−0.628840	−	1.08918i	0.358945	−	0.933359i	$-0.383137\pi$
$74$	−44.0932	−	76.3717i	−0.595854	−	1.03205i
$75$		0			0
$76$	−2.85406	+	4.09740i	−0.0375534	+	0.0539132i
$77$	−45.4662			−0.590471
$78$		0			0
$79$	−53.1300	+	30.6746i	−0.672531	+	0.388286i	−0.797035	−	0.603933i	$-0.793599\pi$
$79$	−53.1300	+	30.6746i	−0.672531	+	0.388286i	0.124504	+	0.992219i	$0.460266\pi$
$80$	−54.4703	+	94.3453i	−0.680879	+	1.17932i
$81$		0			0
$82$	−35.8716	+	62.1313i	−0.437458	+	0.757699i
$83$	148.793			1.79268			0.896342	−	0.443363i	$-0.146215\pi$
$83$	148.793			1.79268			0.896342	+	0.443363i	$0.146215\pi$
$84$		0			0
$85$	78.9897	−	136.814i	0.929290	−	1.60958i
$86$	44.8990	+	25.9224i	0.522081	+	0.301424i
$87$		0			0
$88$			155.036i			1.76178i
$89$	62.7829	+	36.2477i	0.705426	+	0.407278i	0.809365	−	0.587306i	$-0.199811\pi$
$89$	62.7829	+	36.2477i	0.705426	+	0.407278i	−0.103939	+	0.994584i	$0.533145\pi$
$90$		0			0
$91$	0.306546	+	0.176984i	0.00336864	+	0.00194488i
$92$	−0.689224	−	1.19377i	−0.00749156	−	0.0129758i
$93$		0			0
$94$		−	60.6093i		−	0.644780i
$95$	−51.7820	−	110.338i	−0.545074	−	1.16146i
$96$		0			0
$97$	−70.0326	+	40.4334i	−0.721986	+	0.416839i	−0.815483	−	0.578781i	$-0.803529\pi$
$97$	−70.0326	+	40.4334i	−0.721986	+	0.416839i	0.0934972	+	0.995620i	$0.470195\pi$
$98$	−78.4589	+	45.2983i	−0.800601	+	0.462227i
$99$		0			0
$100$	2.12250	+	3.67627i	0.0212250	+	0.0367627i
$101$	76.6770	−	132.809i	0.759178	−	1.31494i	−0.184092	−	0.982909i	$-0.558934\pi$
$101$	76.6770	−	132.809i	0.759178	−	1.31494i	0.943270	−	0.332027i	$-0.107732\pi$
$102$		0			0
$103$		−	168.948i		−	1.64027i	−0.572169	−	0.820136i	$-0.693898\pi$
$103$		−	168.948i		−	1.64027i	0.572169	−	0.820136i	$-0.306102\pi$
$104$	0.603503	−	1.04530i	0.00580291	−	0.0100509i
$105$		0			0
$106$	−115.431			−1.08897
$107$			139.060i			1.29963i	0.760093	+	0.649815i	$0.225154\pi$
$107$			139.060i			1.29963i	−0.760093	+	0.649815i	$0.774846\pi$
$108$		0			0
$109$	−9.15888	+	5.28788i	−0.0840264	+	0.0485127i	−0.541424	−	0.840749i	$-0.682115\pi$
$109$	−9.15888	+	5.28788i	−0.0840264	+	0.0485127i	0.457398	+	0.889262i	$0.348781\pi$
$110$	230.471	+	133.062i	2.09519	+	1.20966i
$111$		0			0
$112$	−19.2137	−	33.2792i	−0.171551	−	0.297135i
$113$		−	69.1581i		−	0.612018i	−0.952029	−	0.306009i	$-0.901006\pi$
$113$		−	69.1581i		−	0.612018i	0.952029	−	0.306009i	$-0.0989938\pi$
$114$		0			0
$115$	33.6466			0.292579
$116$	8.26737	−	4.77317i	0.0712704	−	0.0411480i
$117$		0			0
$118$	35.6737	−	61.7887i	0.302320	−	0.523633i
$119$	27.8626	+	48.2595i	0.234140	+	0.405542i
$120$		0			0
$121$	282.721			2.33654
$122$		−	113.063i		−	0.926742i
$123$		0			0
$124$	−3.89438	−	2.24842i	−0.0314063	−	0.0181324i
$125$	56.7587			0.454070
$126$		0			0
$127$	−25.6547	−	14.8118i	−0.202006	−	0.116628i	0.395585	−	0.918429i	$-0.370542\pi$
$127$	−25.6547	−	14.8118i	−0.202006	−	0.116628i	−0.597591	+	0.801801i	$0.703875\pi$
$128$	−120.504	+	69.5731i	−0.941438	+	0.543540i
$129$		0			0
$130$	−1.03593	−	1.79428i	−0.00796870	−	0.0138022i
$131$	28.6526	+	49.6278i	0.218722	+	0.378838i	0.954418	−	0.298474i	$-0.0964777\pi$
$131$	28.6526	+	49.6278i	0.218722	+	0.378838i	−0.735695	+	0.677313i	$0.763144\pi$
$132$		0			0
$133$	42.8389	+	3.64189i	0.322097	+	0.0273826i
$134$	157.514			1.17548
$135$		0			0
$136$	164.561	−	95.0094i	1.21001	−	0.698599i
$137$	−47.4499	+	82.1856i	−0.346349	+	0.599895i	−0.985598	−	0.169105i	$-0.945912\pi$
$137$	−47.4499	+	82.1856i	−0.346349	+	0.599895i	0.639249	+	0.769000i	$0.279245\pi$
$138$		0			0
$139$	−91.2747	+	158.092i	−0.656652	+	1.13736i	0.324824	+	0.945774i	$0.394695\pi$
$139$	−91.2747	+	158.092i	−0.656652	+	1.13736i	−0.981477	+	0.191581i	$0.938639\pi$
$140$	−3.81496			−0.0272497
$141$		0			0
$142$	−75.8226	+	131.329i	−0.533962	+	0.924850i
$143$	−2.72200	−	1.57155i	−0.0190349	−	0.0109898i
$144$		0			0
$145$			233.017i			1.60701i
$146$	−164.162	−	94.7788i	−1.12439	−	0.649170i
$147$		0			0
$148$	−9.72142	−	5.61266i	−0.0656852	−	0.0379234i
$149$	5.50439	+	9.53389i	0.0369422	+	0.0639858i	0.883905	−	0.467666i	$-0.154905\pi$
$149$	5.50439	+	9.53389i	0.0369422	+	0.0639858i	−0.846963	+	0.531652i	$0.821572\pi$
$150$		0			0
$151$			238.846i			1.58176i	0.611968	+	0.790882i	$0.290378\pi$
$151$			238.846i			1.58176i	−0.611968	+	0.790882i	$0.709622\pi$
$152$	12.4186	−	146.077i	0.0817011	−	0.961035i
$153$		0			0
$154$	−81.2957	+	46.9361i	−0.527894	+	0.304780i
$155$	95.0582	−	54.8819i	0.613279	−	0.354077i
$156$		0			0
$157$	22.8125	+	39.5124i	0.145303	+	0.251671i	0.929486	−	0.368858i	$-0.120251\pi$
$157$	22.8125	+	39.5124i	0.145303	+	0.251671i	−0.784183	+	0.620529i	$0.786918\pi$
$158$	−63.3326	+	109.695i	−0.400839	+	0.694273i
$159$		0			0
$160$			26.9323i			0.168327i
$161$	−5.93421	+	10.2784i	−0.0368585	+	0.0638407i
$162$		0			0
$163$	5.89159			0.0361447			0.0180724	−	0.999837i	$-0.494247\pi$
$163$	5.89159			0.0361447			0.0180724	+	0.999837i	$0.494247\pi$
$164$			9.13224i			0.0556844i
$165$		0			0
$166$	266.048	−	153.603i	1.60270	−	0.925320i
$167$	−142.140	−	82.0646i	−0.851138	−	0.491405i	0.00989689	−	0.999951i	$-0.496850\pi$
$167$	−142.140	−	82.0646i	−0.851138	−	0.491405i	−0.861035	+	0.508546i	$0.830183\pi$
$168$		0			0
$169$	−84.4878	−	146.337i	−0.499928	−	0.865900i
$170$		−	326.173i		−	1.91867i
$171$		0			0
$172$	6.59938			0.0383685
$173$	−234.355	+	135.305i	−1.35465	+	0.782109i	−0.988897	−	0.148603i	$-0.952522\pi$
$173$	−234.355	+	135.305i	−1.35465	+	0.782109i	−0.365755	+	0.930711i	$0.619189\pi$
$174$		0			0
$175$	18.2747	−	31.6527i	0.104427	−	0.180872i
$176$	170.610	+	295.505i	0.969374	+	1.67900i
$177$		0			0
$178$	149.678			0.840890
$179$			186.439i			1.04156i	0.853691	+	0.520779i	$0.174359\pi$
$179$			186.439i			1.04156i	−0.853691	+	0.520779i	$0.825641\pi$
$180$		0			0
$181$	−40.1939	−	23.2059i	−0.222066	−	0.128210i	0.384841	−	0.922983i	$-0.374256\pi$
$181$	−40.1939	−	23.2059i	−0.222066	−	0.128210i	−0.606906	+	0.794773i	$0.707590\pi$
$182$	0.730824			0.00401552
$183$		0			0
$184$	35.0484	+	20.2352i	0.190481	+	0.109974i
$185$	237.291	−	137.000i	1.28265	−	0.740539i
$186$		0			0
$187$	−247.408	−	428.524i	−1.32304	−	2.29157i
$188$	−3.85751	−	6.68140i	−0.0205187	−	0.0355393i
$189$		0			0
$190$	−206.494	−	143.834i	−1.08681	−	0.757021i
$191$	36.7222			0.192263			0.0961315	−	0.995369i	$-0.469353\pi$
$191$	36.7222			0.192263			0.0961315	+	0.995369i	$0.469353\pi$
$192$		0			0
$193$	−173.472	+	100.154i	−0.898817	+	0.518932i	−0.876816	−	0.480826i	$-0.840337\pi$
$193$	−173.472	+	100.154i	−0.898817	+	0.518932i	−0.0220009	+	0.999758i	$0.507004\pi$
$194$	−83.4811	+	144.593i	−0.430315	+	0.745327i
$195$		0			0
$196$	−5.76606	+	9.98710i	−0.0294187	+	0.0509546i
$197$	171.512			0.870620			0.435310	−	0.900281i	$-0.356639\pi$
$197$	171.512			0.870620			0.435310	+	0.900281i	$0.356639\pi$
$198$		0			0
$199$	−43.7500	+	75.7772i	−0.219849	+	0.380790i	−0.954762	−	0.297372i	$-0.903890\pi$
$199$	−43.7500	+	75.7772i	−0.219849	+	0.380790i	0.734913	+	0.678162i	$0.237223\pi$
$200$	−107.933	−	62.3152i	−0.539666	−	0.311576i
$201$		0			0
$202$		−	316.624i		−	1.56744i
$203$	−71.1820	−	41.0970i	−0.350650	−	0.202448i
$204$		0			0
$205$	−193.045	−	111.455i	−0.941684	−	0.543682i
$206$	−174.410	−	302.087i	−0.846650	−	1.46644i
$207$		0			0
$208$		−	2.65650i		−	0.0127716i
$209$	−380.391	−	32.3384i	−1.82005	−	0.154729i
$210$		0			0
$211$	16.3950	−	9.46566i	0.0777014	−	0.0448609i	−0.460646	−	0.887584i	$-0.652382\pi$
$211$	16.3950	−	9.46566i	0.0777014	−	0.0448609i	0.538347	+	0.842723i	$0.319049\pi$
$212$	−12.7247	+	7.34663i	−0.0600224	+	0.0346539i
$213$		0			0
$214$	143.556	+	248.646i	0.670823	+	1.16190i
$215$	−80.5423	+	139.503i	−0.374615	+	0.648853i
$216$		0			0
$217$			38.7178i			0.178423i
$218$	−10.9177	+	18.9100i	−0.0500810	+	0.0867429i
$219$		0			0
$220$	33.8752			0.153978
$221$			3.85230i			0.0174312i
$222$		0			0
$223$	−224.162	+	129.420i	−1.00521	+	0.580358i	−0.909786	−	0.415078i	$-0.863754\pi$
$223$	−224.162	+	129.420i	−1.00521	+	0.580358i	−0.0954244	+	0.995437i	$0.530421\pi$
$224$	−8.22727	−	4.75002i	−0.0367289	−	0.0212054i
$225$		0			0
$226$	−71.3939	−	123.658i	−0.315902	−	0.547159i
$227$			129.054i			0.568522i	0.958747	+	0.284261i	$0.0917482\pi$
$227$			129.054i			0.568522i	−0.958747	+	0.284261i	$0.908252\pi$
$228$		0			0
$229$	−98.8946			−0.431854			−0.215927	−	0.976409i	$-0.569277\pi$
$229$	−98.8946			−0.431854			−0.215927	+	0.976409i	$0.569277\pi$
$230$	60.1617	−	34.7344i	0.261572	−	0.151019i
$231$		0			0
$232$	−140.137	+	242.725i	−0.604041	+	1.04623i
$233$	−174.731	−	302.644i	−0.749920	−	1.29890i	−0.947861	−	0.318685i	$-0.896759\pi$
$233$	−174.731	−	302.644i	−0.749920	−	1.29890i	0.197941	−	0.980214i	$-0.436575\pi$
$234$		0			0
$235$	188.316			0.801346
$236$		−	9.08189i		−	0.0384826i
$237$		0			0
$238$	99.6394	+	57.5268i	0.418653	+	0.241709i
$239$	−301.091			−1.25979			−0.629897	−	0.776679i	$-0.716903\pi$
$239$	−301.091			−1.25979			−0.629897	+	0.776679i	$0.716903\pi$
$240$		0			0
$241$	110.242	+	63.6485i	0.457438	+	0.264102i	0.710966	−	0.703226i	$-0.248258\pi$
$241$	110.242	+	63.6485i	0.457438	+	0.264102i	−0.253529	+	0.967328i	$0.581591\pi$
$242$	505.518	−	291.861i	2.08892	−	1.20604i
$243$		0			0
$244$	−7.19592	−	12.4637i	−0.0294915	−	0.0510807i
$245$	−140.744	−	243.776i	−0.574465	−	0.995003i
$246$		0			0
$247$	2.43882	+	1.69877i	0.00987376	+	0.00687759i
$248$	132.025			0.532358
$249$		0			0
$250$	101.487	−	58.5937i	0.405949	−	0.234375i
$251$	−177.023	+	306.613i	−0.705271	+	1.22157i	0.261322	+	0.965252i	$0.415841\pi$
$251$	−177.023	+	306.613i	−0.705271	+	1.22157i	−0.966594	+	0.256314i	$0.917492\pi$
$252$		0			0
$253$	52.6933	−	91.2675i	0.208274	−	0.360741i
$254$	−61.1625			−0.240797
$255$		0			0
$256$	−25.1234	+	43.5151i	−0.0981384	+	0.169981i
$257$	236.669	+	136.641i	0.920889	+	0.531676i	0.883919	−	0.467641i	$-0.154896\pi$
$257$	236.669	+	136.641i	0.920889	+	0.531676i	0.0369706	+	0.999316i	$0.488229\pi$
$258$		0			0
$259$			96.6500i			0.373166i
$260$	−0.228396	−	0.131865i	−0.000878447	−	0.000507171i
$261$		0			0
$262$	102.464	+	59.1579i	0.391086	+	0.225793i
$263$	75.5642	+	130.881i	0.287316	+	0.497646i	0.973168	−	0.230095i	$-0.0739036\pi$
$263$	75.5642	+	130.881i	0.287316	+	0.497646i	−0.685852	+	0.727741i	$0.740570\pi$
$264$		0			0
$265$		−	358.649i		−	1.35339i
$266$	80.3576	−	37.7120i	0.302096	−	0.141774i
$267$		0			0
$268$	17.3639	−	10.0251i	0.0647909	−	0.0374070i
$269$	−58.9364	+	34.0269i	−0.219094	+	0.126494i	−0.605531	−	0.795822i	$-0.707039\pi$
$269$	−58.9364	+	34.0269i	−0.219094	+	0.126494i	0.386437	+	0.922316i	$0.373706\pi$
$270$		0			0
$271$	56.8991	+	98.5521i	0.209960	+	0.363661i	0.951702	−	0.307025i	$-0.0993334\pi$
$271$	56.8991	+	98.5521i	0.209960	+	0.363661i	−0.741742	+	0.670685i	$0.766000\pi$
$272$	209.106	−	362.183i	0.768773	−	1.33155i
$273$		0			0
$274$			195.935i			0.715093i
$275$	−162.271	+	281.062i	−0.590078	+	1.02204i
$276$		0			0
$277$	440.910			1.59173			0.795867	−	0.605472i	$-0.207016\pi$
$277$	440.910			1.59173			0.795867	+	0.605472i	$0.207016\pi$
$278$			376.902i			1.35576i
$279$		0			0
$280$	96.9993	−	56.0026i	0.346426	−	0.200009i
$281$	−78.0928	−	45.0869i	−0.277910	−	0.160452i	0.354567	−	0.935031i	$-0.384628\pi$
$281$	−78.0928	−	45.0869i	−0.277910	−	0.160452i	−0.632477	+	0.774579i	$0.717962\pi$
$282$		0			0
$283$	34.5331	+	59.8131i	0.122025	+	0.211354i	0.920566	−	0.390587i	$-0.127728\pi$
$283$	34.5331	+	59.8131i	0.122025	+	0.211354i	−0.798541	+	0.601940i	$0.794394\pi$
$284$			19.3031i			0.0679685i
$285$		0			0
$286$	−6.48941			−0.0226902
$287$	68.0944	−	39.3143i	0.237263	−	0.136984i
$288$		0			0
$289$	−158.734	+	274.935i	−0.549252	+	0.951332i
$290$	240.550	+	416.645i	0.829484	+	1.43671i
$291$		0			0
$292$	−24.1289			−0.0826334
$293$		−	410.238i		−	1.40013i	−0.714079	−	0.700065i	$-0.753154\pi$
$293$		−	410.238i		−	1.40013i	0.714079	−	0.700065i	$-0.246846\pi$
$294$		0			0
$295$	191.981	+	110.840i	0.650782	+	0.375729i
$296$	329.569			1.11341
$297$		0			0
$298$	19.6842	+	11.3647i	0.0660544	+	0.0381365i
$299$	−0.710545	+	0.410233i	−0.00237640	+	0.00137202i
$300$		0			0
$301$	−28.4103	−	49.2081i	−0.0943864	−	0.163482i
$302$	246.568	+	427.068i	0.816451	+	1.41413i
$303$		0			0
$304$	−137.081	−	292.095i	−0.450923	−	0.960838i
$305$	351.291			1.15177
$306$		0			0
$307$	−201.882	+	116.556i	−0.657595	+	0.379663i	−0.791360	−	0.611350i	$-0.790627\pi$
$307$	−201.882	+	116.556i	−0.657595	+	0.379663i	0.133765	+	0.991013i	$0.457293\pi$
$308$	−5.97454	+	10.3482i	−0.0193979	+	0.0335981i
$309$		0			0
$310$	113.312	−	196.263i	0.365524	−	0.633106i
$311$	441.280			1.41891			0.709454	−	0.704752i	$-0.248942\pi$
$311$	441.280			1.41891			0.709454	+	0.704752i	$0.248942\pi$
$312$		0			0
$313$	−60.6339	+	105.021i	−0.193719	+	0.335530i	−0.946480	−	0.322763i	$-0.895388\pi$
$313$	−60.6339	+	105.021i	−0.193719	+	0.335530i	0.752761	+	0.658294i	$0.228722\pi$
$314$	81.5796	+	47.1000i	0.259808	+	0.150000i
$315$		0			0
$316$			16.1233i			0.0510232i
$317$	−286.409	−	165.358i	−0.903499	−	0.521635i	−0.0251649	−	0.999683i	$-0.508011\pi$
$317$	−286.409	−	165.358i	−0.903499	−	0.521635i	−0.878334	+	0.478048i	$0.841344\pi$
$318$		0			0
$319$	632.066	+	364.924i	1.98140	+	1.14396i
$320$	−190.078	−	329.225i	−0.593995	−	1.02883i
$321$		0			0
$322$			24.5042i			0.0761001i
$323$	198.786	+	423.579i	0.615437	+	1.31139i
$324$		0			0
$325$	2.18816	−	1.26333i	0.00673279	−	0.00388718i
$326$	10.5344	−	6.08206i	0.0323142	−	0.0186566i
$327$		0			0
$328$	−134.059	−	232.197i	−0.408716	−	0.707916i
$329$	−33.2131	+	57.5268i	−0.100952	+	0.174854i
$330$		0			0
$331$		−	436.308i		−	1.31815i	−0.752077	−	0.659075i	$-0.770948\pi$
$331$		−	436.308i		−	1.31815i	0.752077	−	0.659075i	$-0.229052\pi$
$332$	19.5523	−	33.8655i	0.0588924	−	0.102005i
$333$		0			0
$334$	−338.870			−1.01458
$335$			489.406i			1.46091i
$336$		0			0
$337$	−217.027	+	125.301i	−0.643997	+	0.371812i	−0.786153	−	0.618033i	$-0.787930\pi$
$337$	−217.027	+	125.301i	−0.643997	+	0.371812i	0.142156	+	0.989844i	$0.454597\pi$
$338$	−302.136	−	174.438i	−0.893894	−	0.516090i
$339$		0			0
$340$	−20.7594	−	35.9564i	−0.0610572	−	0.105754i
$341$		−	343.798i		−	1.00821i
$342$		0			0
$343$	210.169			0.612738
$344$	−167.796	+	96.8770i	−0.487779	+	0.281619i
$345$		0			0
$346$	−279.358	+	483.862i	−0.807393	+	1.39845i
$347$	83.6670	+	144.915i	0.241115	+	0.417624i	0.961032	−	0.276436i	$-0.0891535\pi$
$347$	83.6670	+	144.915i	0.241115	+	0.417624i	−0.719917	+	0.694060i	$0.755820\pi$
$348$		0			0
$349$	−486.776			−1.39477			−0.697387	−	0.716695i	$-0.745654\pi$
$349$	−486.776			−1.39477			−0.697387	+	0.716695i	$0.745654\pi$
$350$		−	75.4619i		−	0.215605i
$351$		0			0
$352$	73.0547	+	42.1781i	0.207542	+	0.119824i
$353$	−30.1507			−0.0854128			−0.0427064	−	0.999088i	$-0.513598\pi$
$353$	−30.1507			−0.0854128			−0.0427064	+	0.999088i	$0.513598\pi$
$354$		0			0
$355$	−408.045	−	235.585i	−1.14942	−	0.663619i
$356$	16.5001	−	9.52635i	0.0463486	−	0.0267594i
$357$		0			0
$358$	192.466	+	333.361i	0.537615	+	0.931177i
$359$	75.0088	+	129.919i	0.208938	+	0.361891i	0.951380	−	0.308019i	$-0.0996659\pi$
$359$	75.0088	+	129.919i	0.208938	+	0.361891i	−0.742442	+	0.669910i	$0.766333\pi$
$360$		0			0
$361$	355.819	+	60.9394i	0.985649	+	0.168807i
$362$	−95.8247			−0.264709
$363$		0			0
$364$	0.0805640	−	0.0465136i	0.000221330	−	0.000127785i
$365$	294.482	−	510.058i	0.806801	−	1.39742i
$366$		0			0
$367$	248.090	−	429.704i	0.675994	−	1.17086i	−0.300183	−	0.953882i	$-0.597048\pi$
$367$	248.090	−	429.704i	0.675994	−	1.17086i	0.976177	−	0.216975i	$-0.0696189\pi$
$368$	89.0714			0.242042
$369$		0			0
$370$	282.858	−	489.924i	0.764480	−	1.32412i
$371$	109.560	+	63.2545i	0.295310	+	0.170497i
$372$		0			0
$373$			449.613i			1.20540i	0.797969	+	0.602698i	$0.205908\pi$
$373$			449.613i			1.20540i	−0.797969	+	0.602698i	$0.794092\pi$
$374$	−884.755	−	510.814i	−2.36566	−	1.36581i
$375$		0			0
$376$	196.162	+	113.254i	0.521707	+	0.301208i
$377$	−2.84104	−	4.92083i	−0.00753592	−	0.0130526i
$378$		0			0
$379$		−	471.336i		−	1.24363i	−0.783163	−	0.621816i	$-0.786395\pi$
$379$		−	471.336i		−	1.24363i	0.783163	−	0.621816i	$-0.213605\pi$
$380$	−31.9177	−	2.71344i	−0.0839940	−	0.00714064i
$381$		0			0
$382$	65.6611	−	37.9094i	0.171888	−	0.0992393i
$383$	23.4258	−	13.5249i	0.0611641	−	0.0353131i	−0.469106	−	0.883142i	$-0.655424\pi$
$383$	23.4258	−	13.5249i	0.0611641	−	0.0353131i	0.530270	+	0.847829i	$0.322090\pi$
$384$		0			0
$385$	−145.833	−	252.590i	−0.378787	−	0.656078i
$386$	−206.784	+	358.160i	−0.535709	+	0.927875i
$387$		0			0
$388$			21.2528i			0.0547752i
$389$	−177.144	+	306.822i	−0.455382	+	0.788745i	−0.998710	−	0.0507758i	$-0.983831\pi$
$389$	−177.144	+	306.822i	−0.455382	+	0.788745i	0.543328	+	0.839520i	$0.317164\pi$
$390$		0			0
$391$	−129.166			−0.330348
$392$		−	338.576i		−	0.863715i
$393$		0			0
$394$	306.672	−	177.057i	0.778354	−	0.449383i
$395$	−340.829	−	196.777i	−0.862857	−	0.498171i
$396$		0			0
$397$	−79.5105	−	137.716i	−0.200278	−	0.346892i	0.748340	−	0.663316i	$-0.230851\pi$
$397$	−79.5105	−	137.716i	−0.200278	−	0.346892i	−0.948618	+	0.316423i	$0.897518\pi$
$398$			180.657i			0.453913i
$399$		0			0
$400$	−274.299			−0.685748
$401$	277.534	−	160.234i	0.692105	−	0.399587i	−0.112295	−	0.993675i	$-0.535820\pi$
$401$	277.534	−	160.234i	0.692105	−	0.399587i	0.804400	+	0.594088i	$0.202487\pi$
$402$		0			0
$403$	−1.33829	+	2.31798i	−0.00332081	+	0.00575181i
$404$	−20.1517	−	34.9037i	−0.0498803	−	0.0863953i
$405$		0			0
$406$	−169.702			−0.417986
$407$		−	858.211i		−	2.10863i
$408$		0			0
$409$	−251.776	−	145.363i	−0.615590	−	0.355411i	0.159560	−	0.987188i	$-0.448992\pi$
$409$	−251.776	−	145.363i	−0.615590	−	0.355411i	−0.775150	+	0.631777i	$0.782326\pi$
$410$	−460.232			−1.12252
$411$		0			0
$412$	−38.4529	−	22.2008i	−0.0933323	−	0.0538854i
$413$	−67.7189	+	39.0975i	−0.163968	+	0.0946671i
$414$		0			0
$415$	477.253	+	826.626i	1.15001	+	1.99187i
$416$	−0.328370	−	0.568753i	−0.000789350	−	0.00136719i
$417$		0			0
$418$	−713.541	+	334.866i	−1.70704	+	0.801115i
$419$	141.846			0.338535			0.169267	−	0.985570i	$-0.445860\pi$
$419$	141.846			0.338535			0.169267	+	0.985570i	$0.445860\pi$
$420$		0			0
$421$	98.6666	−	56.9652i	0.234362	−	0.135309i	−0.378220	−	0.925716i	$-0.623464\pi$
$421$	98.6666	−	56.9652i	0.234362	−	0.135309i	0.612583	+	0.790406i	$0.290131\pi$
$422$	19.5433	−	33.8501i	0.0463112	−	0.0802134i
$423$		0			0
$424$	215.693	−	373.591i	0.508710	−	0.881111i
$425$	397.773			0.935936
$426$		0			0
$427$	−61.9568	+	107.312i	−0.145098	+	0.251317i
$428$	31.6504	+	18.2734i	0.0739496	+	0.0426948i
$429$		0			0
$430$			332.585i			0.773453i
$431$	−229.263	−	132.365i	−0.531932	−	0.307111i	0.209871	−	0.977729i	$-0.432696\pi$
$431$	−229.263	−	132.365i	−0.531932	−	0.307111i	−0.741803	+	0.670618i	$0.766029\pi$
$432$		0			0
$433$	−631.333	−	364.500i	−1.45804	−	0.841802i	−0.459129	−	0.888369i	$-0.651839\pi$
$433$	−631.333	−	364.500i	−1.45804	−	0.841802i	−0.998915	+	0.0465669i	$0.985172\pi$
$434$	39.9695	+	69.2293i	0.0920957	+	0.159514i
$435$		0			0
$436$			2.77944i			0.00637486i
$437$	−56.9589	+	81.7726i	−0.130341	+	0.187123i
$438$		0			0
$439$	319.591	−	184.516i	0.727998	−	0.420310i	−0.0896911	−	0.995970i	$-0.528588\pi$
$439$	319.591	−	184.516i	0.727998	−	0.420310i	0.817689	+	0.575660i	$0.195255\pi$
$440$	−861.312	+	497.279i	−1.95753	+	1.13018i
$441$		0			0
$442$	3.97684	+	6.88809i	0.00899738	+	0.0155839i
$443$	291.547	−	504.975i	0.658120	−	1.13990i	−0.322982	−	0.946405i	$-0.604685\pi$
$443$	291.547	−	504.975i	0.658120	−	1.13990i	0.981102	−	0.193492i	$-0.0619815\pi$
$444$		0			0
$445$			465.058i			1.04507i
$446$	−267.208	+	462.818i	−0.599121	+	1.03771i
$447$		0			0
$448$	134.096			0.299321
$449$			314.423i			0.700273i	0.936699	+	0.350137i	$0.113865\pi$
$449$			314.423i			0.700273i	−0.936699	+	0.350137i	$0.886135\pi$
$450$		0			0
$451$	−604.649	+	349.094i	−1.34068	+	0.774045i
$452$	−15.7405	−	9.08779i	−0.0348242	−	0.0201057i
$453$		0			0
$454$	133.227	+	230.755i	0.293451	+	0.508272i
$455$			2.27071i			0.00499057i
$456$		0			0
$457$	505.253			1.10559			0.552793	−	0.833319i	$-0.313562\pi$
$457$	505.253			1.10559			0.552793	+	0.833319i	$0.313562\pi$
$458$	−176.828	+	102.092i	−0.386088	+	0.222908i
$459$		0			0
$460$	4.42137	−	7.65803i	0.00961167	−	0.0166479i
$461$	−136.902	−	237.122i	−0.296968	−	0.514364i	0.678473	−	0.734626i	$-0.262642\pi$
$461$	−136.902	−	237.122i	−0.296968	−	0.514364i	−0.975441	+	0.220262i	$0.929309\pi$
$462$		0			0
$463$	319.780			0.690669			0.345334	−	0.938480i	$-0.387765\pi$
$463$	319.780			0.690669			0.345334	+	0.938480i	$0.387765\pi$
$464$			616.857i			1.32943i
$465$		0			0
$466$	−624.855	−	360.760i	−1.34089	−	0.774164i
$467$	295.510			0.632785			0.316392	−	0.948628i	$-0.397528\pi$
$467$	295.510			0.632785			0.316392	+	0.948628i	$0.397528\pi$
$468$		0			0
$469$	−149.504	−	86.3159i	−0.318771	−	0.184042i
$470$	336.718	−	194.404i	0.716421	−	0.413626i
$471$		0			0
$472$	133.319	+	230.916i	0.282457	+	0.489229i
$473$	252.271	+	436.947i	0.533344	+	0.923778i
$474$		0			0
$475$	175.408	−	251.822i	0.369279	−	0.530153i
$476$	14.6453			0.0307674
$477$		0			0
$478$	−538.364	+	310.825i	−1.12629	+	0.650261i
$479$	−204.559	+	354.306i	−0.427054	+	0.739679i	−0.996610	−	0.0822735i	$-0.973782\pi$
$479$	−204.559	+	354.306i	−0.427054	+	0.739679i	0.569556	+	0.821953i	$0.307115\pi$
$480$		0			0
$481$	−3.34072	+	5.78629i	−0.00694536	+	0.0120297i
$482$	262.825			0.545280
$483$		0			0
$484$	37.1512	−	64.3478i	0.0767588	−	0.132950i
$485$	−449.259	−	259.380i	−0.926308	−	0.534804i
$486$		0			0
$487$		−	638.208i		−	1.31049i	−0.755417	−	0.655244i	$-0.772566\pi$
$487$		−	638.208i		−	1.31049i	0.755417	−	0.655244i	$-0.227434\pi$
$488$	365.927	+	211.268i	0.749850	+	0.432926i
$489$		0			0
$490$	−503.314	−	290.588i	−1.02717	−	0.593037i
$491$	173.278	+	300.126i	0.352908	+	0.611255i	0.986758	−	0.162202i	$-0.0518595\pi$
$491$	173.278	+	300.126i	0.352908	+	0.611255i	−0.633850	+	0.773456i	$0.718526\pi$
$492$		0			0
$493$		−	894.530i		−	1.81446i
$494$	6.11440	+	0.519808i	0.0123773	+	0.00105224i
$495$		0			0
$496$	251.644	−	145.287i	0.507347	−	0.292917i
$497$	143.933	−	83.0997i	0.289603	−	0.167203i
$498$		0			0
$499$	−40.3510	−	69.8900i	−0.0808638	−	0.140060i	0.822757	−	0.568393i	$-0.192435\pi$
$499$	−40.3510	−	69.8900i	−0.0808638	−	0.140060i	−0.903621	+	0.428333i	$0.859101\pi$
$500$	7.45844	−	12.9184i	0.0149169	−	0.0258368i
$501$		0			0
$502$			730.984i			1.45614i
$503$	247.050	−	427.903i	0.491153	−	0.850701i	−0.508796	−	0.860887i	$-0.669909\pi$
$503$	247.050	−	427.903i	0.491153	−	0.850701i	0.999948	+	0.0101862i	$0.00324242\pi$
$504$		0			0
$505$	983.766			1.94805
$506$		−	217.587i		−	0.430014i
$507$		0			0
$508$	−6.74237	+	3.89271i	−0.0132724	+	0.00766282i
$509$	−63.9084	−	36.8975i	−0.125557	−	0.0724902i	0.435906	−	0.899992i	$-0.356428\pi$
$509$	−63.9084	−	36.8975i	−0.125557	−	0.0724902i	−0.561463	+	0.827502i	$0.689761\pi$
$510$		0			0
$511$	103.875	+	179.917i	0.203278	+	0.352088i
$512$		−	452.842i		−	0.884457i
$513$		0			0
$514$	564.232			1.09773
$515$	938.599	−	541.900i	1.82252	−	1.05223i
$516$		0			0
$517$	294.918	−	510.814i	0.570442	−	0.988034i
$518$	99.7746	+	172.815i	0.192615	+	0.333619i
$519$		0			0
$520$	7.74294			0.0148903
$521$			357.582i			0.686337i	0.939274	+	0.343169i	$0.111500\pi$
$521$			357.582i			0.686337i	−0.939274	+	0.343169i	$0.888500\pi$
$522$		0			0
$523$	382.935	+	221.088i	0.732190	+	0.422730i	0.819223	−	0.573475i	$-0.194405\pi$
$523$	382.935	+	221.088i	0.732190	+	0.422730i	−0.0870328	+	0.996205i	$0.527739\pi$
$524$	15.0605			0.0287415
$525$		0			0
$526$	270.225	+	156.014i	0.513735	+	0.296605i
$527$	−364.919	+	210.686i	−0.692447	+	0.399784i
$528$		0			0
$529$	250.745	+	434.303i	0.473998	+	0.820989i
$530$	−370.243	−	641.281i	−0.698573	−	1.20996i
$531$		0			0
$532$	6.45819	−	9.27165i	0.0121395	−	0.0174279i
$533$	5.43561			0.0101981
$534$		0			0
$535$	−772.557	+	446.036i	−1.44403	+	0.833712i
$536$	−294.331	+	509.796i	−0.549124	+	0.951111i
$537$		0			0
$538$	−70.2539	+	121.683i	−0.130584	+	0.226177i
$539$	−881.666			−1.63574
$540$		0			0
$541$	−487.737	+	844.785i	−0.901547	+	1.56152i	−0.0760596	+	0.997103i	$0.524234\pi$
$541$	−487.737	+	844.785i	−0.901547	+	1.56152i	−0.825487	+	0.564421i	$0.809099\pi$
$542$	203.476	+	117.477i	0.375418	+	0.216747i
$543$		0			0
$544$		−	103.390i		−	0.190056i
$545$	−58.7542	−	33.9217i	−0.107806	−	0.0622417i
$546$		0			0
$547$	350.050	+	202.102i	0.639945	+	0.369473i	0.784594	−	0.620010i	$-0.212872\pi$
$547$	350.050	+	202.102i	0.639945	+	0.369473i	−0.144648	+	0.989483i	$0.546205\pi$
$548$	12.4704	+	21.5994i	0.0227562	+	0.0394149i
$549$		0			0
$550$			670.070i			1.21831i
$551$	−566.310	−	394.465i	−1.02779	−	0.715907i
$552$		0			0
$553$	120.223	−	69.4109i	0.217402	−	0.125517i
$554$	788.368	−	455.164i	1.42305	−	0.821596i
$555$		0			0
$556$	23.9881	+	41.5486i	0.0431441	+	0.0747277i
$557$	29.9352	−	51.8492i	0.0537435	−	0.0930866i	−0.837902	−	0.545821i	$-0.816218\pi$
$557$	29.9352	−	51.8492i	0.0537435	−	0.0930866i	0.891646	+	0.452734i	$0.149551\pi$
$558$		0			0
$559$		−	3.92802i		−	0.00702687i
$560$	123.256	−	213.486i	0.220100	−	0.381225i
$561$		0			0
$562$	−186.178			−0.331278
$563$		−	247.579i		−	0.439749i	−0.975528	−	0.219874i	$-0.929435\pi$
$563$		−	247.579i		−	0.439749i	0.975528	−	0.219874i	$-0.0705648\pi$
$564$		0			0
$565$	384.211	−	221.824i	0.680020	−	0.392610i
$566$	123.494	+	71.2990i	0.218186	+	0.125970i
$567$		0			0
$568$	−283.363	−	490.800i	−0.498879	−	0.864084i
$569$			76.4991i			0.134445i	0.997738	+	0.0672224i	$0.0214137\pi$
$569$			76.4991i			0.134445i	−0.997738	+	0.0672224i	$0.978586\pi$
$570$		0			0
$571$	−624.523			−1.09373			−0.546867	−	0.837219i	$-0.684180\pi$
$571$	−624.523			−1.09373			−0.546867	+	0.837219i	$0.684180\pi$
$572$	−0.715374	+	0.413021i	−0.00125065	+	0.000722065i
$573$		0			0
$574$	81.1706	−	140.592i	0.141412	−	0.244933i
$575$	42.3590	+	73.3680i	0.0736679	+	0.127597i
$576$		0			0
$577$	185.550			0.321577			0.160789	−	0.986989i	$-0.448596\pi$
$577$	185.550			0.321577			0.160789	+	0.986989i	$0.448596\pi$
$578$			655.462i			1.13402i
$579$		0			0
$580$	53.0352	+	30.6199i	0.0914399	+	0.0527929i
$581$	−336.690			−0.579501
$582$		0			0
$583$	−972.846	−	561.673i	−1.66869	−	0.963418i
$584$	613.503	−	354.206i	1.05052	−	0.606517i
$585$		0			0
$586$	−423.501	−	733.525i	−0.722698	−	1.25175i
$587$	130.891	+	226.710i	0.222983	+	0.386218i	0.955712	−	0.294302i	$-0.0950872\pi$
$587$	130.891	+	226.710i	0.222983	+	0.386218i	−0.732729	+	0.680520i	$0.761754\pi$
$588$		0			0
$589$	−27.5386	+	323.931i	−0.0467548	+	0.549968i
$590$	457.694			0.775752
$591$		0			0
$592$	628.170	−	362.674i	1.06110	−	0.612626i
$593$	124.254	−	215.215i	0.209535	−	0.362925i	−0.742033	−	0.670363i	$-0.766138\pi$
$593$	124.254	−	215.215i	0.209535	−	0.362925i	0.951568	+	0.307438i	$0.0994717\pi$
$594$		0			0
$595$	−178.739	+	309.585i	−0.300401	+	0.520310i
$596$	2.89324			0.00485443
$597$		0			0
$598$	−0.846992	+	1.46703i	−0.00141637	+	0.00245323i
$599$	167.646	+	96.7905i	0.279877	+	0.161587i	0.633368	−	0.773851i	$-0.281672\pi$
$599$	167.646	+	96.7905i	0.279877	+	0.161587i	−0.353491	+	0.935438i	$0.615005\pi$
$600$		0			0
$601$		−	675.975i		−	1.12475i	−0.826882	−	0.562375i	$-0.809888\pi$
$601$		−	675.975i		−	1.12475i	0.826882	−	0.562375i	$-0.190112\pi$
$602$	−101.598	−	58.6576i	−0.168767	−	0.0974378i
$603$		0			0
$604$	54.3619	+	31.3859i	0.0900032	+	0.0519634i
$605$	906.827	+	1570.67i	1.49889	+	2.59615i
$606$		0			0
$607$			383.052i			0.631057i	0.948916	+	0.315528i	$0.102182\pi$
$607$			383.052i			0.631057i	−0.948916	+	0.315528i	$0.897818\pi$
$608$	−65.4546	−	45.5925i	−0.107656	−	0.0749877i
$609$		0			0
$610$	628.125	−	362.648i	1.02971	−	0.594505i
$611$	−3.97684	+	2.29603i	−0.00650874	+	0.00375782i
$612$		0			0
$613$	−27.5410	−	47.7025i	−0.0449283	−	0.0778180i	0.842687	−	0.538404i	$-0.180973\pi$
$613$	−27.5410	−	47.7025i	−0.0449283	−	0.0778180i	−0.887615	+	0.460586i	$0.847639\pi$
$614$	−240.649	+	416.817i	−0.391937	+	0.678854i
$615$		0			0
$616$		−	350.818i		−	0.569510i
$617$	51.7851	−	89.6944i	0.0839305	−	0.145372i	−0.821004	−	0.570922i	$-0.806586\pi$
$617$	51.7851	−	89.6944i	0.0839305	−	0.145372i	0.904935	+	0.425550i	$0.139919\pi$
$618$		0			0
$619$	−263.102			−0.425043			−0.212521	−	0.977156i	$-0.568168\pi$
$619$	−263.102			−0.425043			−0.212521	+	0.977156i	$0.568168\pi$
$620$		−	28.8473i		−	0.0465278i
$621$		0			0
$622$	789.030	−	455.547i	1.26854	−	0.732390i
$623$	−142.066	−	82.0218i	−0.228035	−	0.131656i
$624$		0			0
$625$	383.956	+	665.031i	0.614329	+	1.06405i
$626$			250.377i			0.399963i
$627$		0			0
$628$	11.9908			0.0190936
$629$	−910.936	+	525.929i	−1.44823	+	0.836135i
$630$		0			0
$631$	72.5474	−	125.656i	0.114972	−	0.199137i	−0.802797	−	0.596253i	$-0.796655\pi$
$631$	72.5474	−	125.656i	0.114972	−	0.199137i	0.917769	+	0.397116i	$0.129989\pi$
$632$	−236.686	−	409.952i	−0.374503	−	0.648658i
$633$		0			0
$634$	−682.817			−1.07700
$635$		−	190.035i		−	0.299267i
$636$		0			0
$637$	5.94443	+	3.43202i	0.00933192	+	0.00538779i
$638$	1506.88			2.36189
$639$		0			0
$640$	−773.034	−	446.311i	−1.20787	−	0.697361i
$641$	583.796	−	337.055i	0.910758	−	0.525826i	0.0300832	−	0.999547i	$-0.490423\pi$
$641$	583.796	−	337.055i	0.910758	−	0.525826i	0.880675	+	0.473721i	$0.157089\pi$
$642$		0			0
$643$	0.719856	+	1.24683i	0.00111953	+	0.00193908i	0.866585	−	0.499030i	$-0.166310\pi$
$643$	0.719856	+	1.24683i	0.00111953	+	0.00193908i	−0.865465	+	0.500969i	$0.832977\pi$
$644$	1.55958	+	2.70128i	0.00242171	+	0.00419453i
$645$		0			0
$646$	792.711	+	552.165i	1.22711	+	0.854745i
$647$	614.044			0.949063			0.474532	−	0.880239i	$-0.342617\pi$
$647$	614.044			0.949063			0.474532	+	0.880239i	$0.342617\pi$
$648$		0			0
$649$	601.315	−	347.169i	0.926525	−	0.534929i
$650$	2.60835	−	4.51779i	0.00401284	−	0.00695045i
$651$		0			0
$652$	0.774191	−	1.34094i	0.00118741	−	0.00205665i
$653$	−822.374			−1.25938			−0.629689	−	0.776847i	$-0.716818\pi$
$653$	−822.374			−1.25938			−0.629689	+	0.776847i	$0.716818\pi$
$654$		0			0
$655$	−183.807	+	318.362i	−0.280621	+	0.486049i
$656$	−511.041	−	295.050i	−0.779027	−	0.449771i
$657$		0			0
$658$			137.147i			0.208431i
$659$	549.386	+	317.188i	0.833666	+	0.481317i	0.855106	−	0.518453i	$-0.173492\pi$
$659$	549.386	+	317.188i	0.833666	+	0.481317i	−0.0214404	+	0.999770i	$0.506825\pi$
$660$		0			0
$661$	−818.470	−	472.544i	−1.23823	−	0.714893i	−0.269498	−	0.963001i	$-0.586858\pi$
$661$	−818.470	−	472.544i	−1.23823	−	0.714893i	−0.968732	+	0.248108i	$0.920191\pi$
$662$	−450.413	−	780.138i	−0.680382	−	1.17846i
$663$		0			0
$664$			1148.09i			1.72905i
$665$	117.173	+	249.675i	0.176200	+	0.375451i
$666$		0			0
$667$	164.993	−	95.2590i	0.247366	−	0.142817i
$668$	−37.3561	+	21.5676i	−0.0559223	+	0.0322868i
$669$		0			0
$670$	505.228	+	875.080i	0.754071	+	1.30609i
$671$	550.150	−	952.888i	0.819896	−	1.42010i
$672$		0			0
$673$		−	570.803i		−	0.848147i	−0.905628	−	0.424074i	$-0.860600\pi$
$673$		−	570.803i		−	0.848147i	0.905628	−	0.424074i	$-0.139400\pi$
$674$	−258.703	+	448.086i	−0.383832	+	0.664817i
$675$		0			0
$676$	−44.4088			−0.0656935
$677$			275.976i			0.407646i	0.979008	+	0.203823i	$0.0653367\pi$
$677$			275.976i			0.407646i	−0.979008	+	0.203823i	$0.934663\pi$
$678$		0			0
$679$	158.471	−	91.4931i	0.233388	−	0.134747i
$680$	1055.66	+	609.485i	1.55244	+	0.896302i
$681$		0			0
$682$	−354.913	−	614.727i	−0.520400	−	0.901359i
$683$		−	106.224i		−	0.155525i	−0.996972	−	0.0777627i	$-0.975222\pi$
$683$		−	106.224i		−	0.155525i	0.996972	−	0.0777627i	$-0.0247776\pi$
$684$		0			0
$685$	−608.781			−0.888732
$686$	375.792	−	216.964i	0.547802	−	0.316274i
$687$		0			0
$688$	−213.217	+	369.302i	−0.309908	+	0.536776i
$689$	4.37279	+	7.57390i	0.00634658	+	0.0109926i
$690$		0			0
$691$	244.177			0.353367			0.176684	−	0.984268i	$-0.443463\pi$
$691$	244.177			0.353367			0.176684	+	0.984268i	$0.443463\pi$
$692$			71.1195i			0.102774i
$693$		0			0
$694$	299.201	+	172.744i	0.431125	+	0.248910i
$695$	−1171.05			−1.68497
$696$		0			0
$697$	741.082	+	427.864i	1.06325	+	0.613865i
$698$	−870.378	+	502.513i	−1.24696	+	0.719932i
$699$		0			0
$700$	−4.80281	−	8.31871i	−0.00686115	−	0.0118839i
$701$	−143.276	−	248.161i	−0.204388	−	0.354010i	0.745550	−	0.666450i	$-0.232187\pi$
$701$	−143.276	−	248.161i	−0.204388	−	0.354010i	−0.949938	+	0.312440i	$0.898854\pi$
$702$		0			0
$703$	−68.7436	+	808.618i	−0.0977860	+	1.15024i
$704$	−1190.71			−1.69135
$705$		0			0
$706$	−53.9108	+	31.1254i	−0.0763610	+	0.0440870i
$707$	−173.506	+	300.521i	−0.245411	+	0.425065i
$708$		0			0
$709$	−5.70585	+	9.88282i	−0.00804774	+	0.0139391i	−0.870021	−	0.493014i	$-0.835895\pi$
$709$	−5.70585	+	9.88282i	−0.00804774	+	0.0139391i	0.861973	+	0.506953i	$0.169228\pi$
$710$	−972.804			−1.37015
$711$		0			0
$712$	−279.688	+	484.434i	−0.392820	+	0.680385i
$713$	−77.7209	−	44.8722i	−0.109006	−	0.0629344i
$714$		0			0
$715$		−	20.1629i		−	0.0281999i
$716$	42.4339	+	24.4992i	0.0592652	+	0.0342168i
$717$		0			0
$718$	268.238	+	154.867i	0.373591	+	0.215693i
$719$	−438.491	−	759.488i	−0.609862	−	1.05631i	−0.991263	−	0.131902i	$-0.957892\pi$
$719$	−438.491	−	759.488i	−0.609862	−	1.05631i	0.381401	−	0.924410i	$-0.375442\pi$
$720$		0			0
$721$			382.298i			0.530232i
$722$	699.131	−	258.360i	0.968325	−	0.357839i
$723$		0			0
$724$	−10.5634	+	6.09880i	−0.0145904	+	0.00842376i
$725$	−508.105	+	293.354i	−0.700834	+	0.404627i
$726$		0			0
$727$	−360.167	−	623.827i	−0.495415	−	0.858084i	0.504571	−	0.863370i	$-0.331651\pi$
$727$	−360.167	−	623.827i	−0.495415	−	0.858084i	−0.999986	+	0.00528653i	$0.998317\pi$
$728$	−1.36561	+	2.36531i	−0.00187584	+	0.00324905i
$729$		0			0
$730$		−	1216.01i		−	1.66577i
$731$	309.194	−	535.540i	0.422974	−	0.732613i
$732$		0			0
$733$	−170.651			−0.232812			−0.116406	−	0.993202i	$-0.537137\pi$
$733$	−170.651			−0.232812			−0.116406	+	0.993202i	$0.537137\pi$
$734$		−	1024.44i		−	1.39570i
$735$		0			0
$736$	19.0701	−	11.0101i	0.0259104	−	0.0149594i
$737$	1327.53	+	766.449i	1.80126	+	1.03996i
$738$		0			0
$739$	530.334	+	918.566i	0.717637	+	1.24298i	0.961933	+	0.273284i	$0.0881098\pi$
$739$	530.334	+	918.566i	0.717637	+	1.24298i	−0.244296	+	0.969701i	$0.578557\pi$
$740$		−	72.0104i		−	0.0973114i
$741$		0			0
$742$	261.198			0.352019
$743$	−290.537	+	167.742i	−0.391033	+	0.225763i	−0.682607	−	0.730785i	$-0.739154\pi$
$743$	−290.537	+	167.742i	−0.391033	+	0.225763i	0.291575	+	0.956548i	$0.405821\pi$
$744$		0			0
$745$	−35.3107	+	61.1599i	−0.0473969	+	0.0820938i
$746$	464.148	+	803.928i	0.622182	+	1.07765i
$747$		0			0
$748$	−130.044			−0.173855
$749$		−	314.668i		−	0.420117i
$750$		0			0
$751$	−1128.41	−	651.490i	−1.50255	−	0.867497i	−0.999996	−	0.00295120i	$-0.999061\pi$
$751$	−1128.41	−	651.490i	−1.50255	−	0.867497i	−0.502554	−	0.864546i	$-0.667606\pi$
$752$	498.522			0.662929
$753$		0			0
$754$	−10.1598	−	5.86578i	−0.0134746	−	0.00777955i
$755$	−1326.92	+	766.100i	−1.75751	+	1.01470i
$756$		0			0
$757$	−60.1511	−	104.185i	−0.0794598	−	0.137628i	0.823557	−	0.567233i	$-0.191986\pi$
$757$	−60.1511	−	104.185i	−0.0794598	−	0.137628i	−0.903017	+	0.429605i	$0.858653\pi$
$758$	−486.574	−	842.771i	−0.641919	−	1.11184i
$759$		0			0
$760$	851.373	−	399.551i	1.12023	−	0.525725i
$761$	−1346.45			−1.76932			−0.884658	−	0.466240i	$-0.845608\pi$
$761$	−1346.45			−1.76932			−0.884658	+	0.466240i	$0.845608\pi$
$762$		0			0
$763$	20.7248	−	11.9655i	0.0271623	−	0.0156822i
$764$	4.82553	−	8.35805i	0.00631613	−	0.0109399i
$765$		0			0
$766$	27.9243	−	48.3663i	0.0364547	−	0.0631414i
$767$	−5.40564			−0.00704777
$768$		0			0
$769$	109.016	−	188.821i	0.141763	−	0.245541i	−0.786398	−	0.617721i	$-0.788056\pi$
$769$	109.016	−	188.821i	0.141763	−	0.245541i	0.928161	+	0.372180i	$0.121390\pi$
$770$	−521.512	−	301.095i	−0.677288	−	0.391033i
$771$		0			0
$772$			52.6433i			0.0681909i
$773$	48.6422	+	28.0836i	0.0629266	+	0.0363307i	0.531133	−	0.847288i	$-0.321766\pi$
$773$	48.6422	+	28.0836i	0.0629266	+	0.0363307i	−0.468207	+	0.883619i	$0.655100\pi$
$774$		0			0
$775$	239.345	+	138.186i	0.308832	+	0.178304i
$776$	−311.984	−	540.373i	−0.402042	−	0.696357i
$777$		0			0
$778$			731.482i			0.940208i
$779$	597.671	−	280.488i	0.767229	−	0.360062i
$780$		0			0
$781$	−1278.06	+	737.890i	−1.63644	+	0.944801i
$782$	−230.955	+	133.342i	−0.295339	+	0.170514i
$783$		0			0
$784$	−372.586	−	645.338i	−0.475238	−	0.823136i

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)

\(f(q)\)	\(=\)	\(q+(1.78805 - 1.03233i) q^{2} +(0.131406 - 0.227602i) q^{4} +(3.20750 + 5.55555i) q^{5} -2.26281 q^{7} +7.71601i q^{8} +O(q^{10})\)	\(q+(1.78805 - 1.03233i) q^{2} +(0.131406 - 0.227602i) q^{4} +(3.20750 + 5.55555i) q^{5} -2.26281 q^{7} +7.71601i q^{8} +(11.4703 + 6.62239i) q^{10} +20.0928 q^{11} +(-0.135471 - 0.0782143i) q^{13} +(-4.04601 + 2.33597i) q^{14} +(8.49109 + 14.7070i) q^{16} +(-12.3133 - 21.3272i) q^{17} +(-18.9317 - 1.60945i) q^{19} +1.68594 q^{20} +(35.9269 - 20.7424i) q^{22} +(2.62250 - 4.54230i) q^{23} +(-8.07609 + 13.9882i) q^{25} -0.322972 q^{26} +(-0.297347 + 0.515021i) q^{28} +(31.4573 + 18.1619i) q^{29} -17.1105i q^{31} +(3.63586 + 2.09917i) q^{32} +(-44.0334 - 25.4227i) q^{34} +(-7.25797 - 12.5712i) q^{35} -42.7124i q^{37} +(-35.5123 + 16.6660i) q^{38} +(-42.8667 + 24.7491i) q^{40} +(-30.0928 + 17.3741i) q^{41} +(12.5553 + 21.7464i) q^{43} +(2.64032 - 4.57316i) q^{44} -10.8291i q^{46} +(14.6778 - 25.4227i) q^{47} -43.8797 q^{49} +33.3487i q^{50} +(-0.0356035 + 0.0205557i) q^{52} +(-48.4176 - 27.9539i) q^{53} +(64.4476 + 111.627i) q^{55} -17.4599i q^{56} +74.9962 q^{58} +(29.9269 - 17.2783i) q^{59} +(27.3805 - 47.4244i) q^{61} +(-17.6637 - 30.5944i) q^{62} -59.2606 q^{64} -1.00349i q^{65} +(66.0698 + 38.1454i) q^{67} -6.47216 q^{68} +(-25.9552 - 14.9852i) q^{70} +(-63.6080 + 36.7241i) q^{71} +(-45.9053 - 79.5103i) q^{73} +(-44.0932 - 76.3717i) q^{74} +(-2.85406 + 4.09740i) q^{76} -45.4662 q^{77} +(-53.1300 + 30.6746i) q^{79} +(-54.4703 + 94.3453i) q^{80} +(-35.8716 + 62.1313i) q^{82} +148.793 q^{83} +(78.9897 - 136.814i) q^{85} +(44.8990 + 25.9224i) q^{86} +155.036i q^{88} +(62.7829 + 36.2477i) q^{89} +(0.306546 + 0.176984i) q^{91} +(-0.689224 - 1.19377i) q^{92} -60.6093i q^{94} +(-51.7820 - 110.338i) q^{95} +(-70.0326 + 40.4334i) q^{97} +(-78.4589 + 45.2983i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 5 q^{4} - 4 q^{5} - 22 q^{7}+O(q^{10}) \) 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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