LMFDB - Embedded newform 33.6.d.b.32.9

Newspace parameters

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	33.d (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$5.29266605383$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
Defining polynomial:	$x^{16} - 6 x^{15} - 195 x^{14} - 642 x^{13} + 89670 x^{12} + 53946 x^{11} + 91115757 x^{10} - 2121785838 x^{9} + 37710373995 x^{8} - 835758339660 x^{7} + 12972600642204 x^{6} - 129499271268696 x^{5} + 2168293345395660 x^{4} - 17336133272224368 x^{3} + 169639595563975056 x^{2} - 1075523563426213440 x + 9241272870780234240$
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{11}\cdot 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			32.9
Root			$0.456001 + 15.5879i$ of defining polynomial
Character	$\chi$	$=$	33.32
Dual form			33.6.d.b.32.10

$q$-expansion

$f(q)$	$=$	$q+3.58998 q^{2} +(0.133977 - 15.5879i) q^{3} -19.1121 q^{4} -11.8803i q^{5} +(0.480974 - 55.9601i) q^{6} -150.804i q^{7} -183.491 q^{8} +(-242.964 - 4.17684i) q^{9} +O(q^{10})$	\(q+3.58998 q^{2} +(0.133977 - 15.5879i) q^{3} -19.1121 q^{4} -11.8803i q^{5} +(0.480974 - 55.9601i) q^{6} -150.804i q^{7} -183.491 q^{8} +(-242.964 - 4.17684i) q^{9} -42.6500i q^{10} +(352.626 + 191.588i) q^{11} +(-2.56058 + 297.917i) q^{12} -778.957i q^{13} -541.384i q^{14} +(-185.188 - 1.59169i) q^{15} -47.1432 q^{16} +1255.02 q^{17} +(-872.236 - 14.9947i) q^{18} +1214.37i q^{19} +227.057i q^{20} +(-2350.72 - 20.2043i) q^{21} +(1265.92 + 687.798i) q^{22} -880.210i q^{23} +(-24.5836 + 2860.24i) q^{24} +2983.86 q^{25} -2796.44i q^{26} +(-97.6596 + 3786.74i) q^{27} +2882.18i q^{28} +3201.27 q^{29} +(-664.823 - 5.71411i) q^{30} -6446.10 q^{31} +5702.47 q^{32} +(3033.70 - 5471.02i) q^{33} +4505.50 q^{34} -1791.60 q^{35} +(4643.54 + 79.8279i) q^{36} -9311.53 q^{37} +4359.58i q^{38} +(-12142.3 - 104.362i) q^{39} +2179.93i q^{40} +5398.38 q^{41} +(-8439.03 - 72.5330i) q^{42} -20867.6i q^{43} +(-6739.40 - 3661.65i) q^{44} +(-49.6220 + 2886.48i) q^{45} -3159.93i q^{46} -11289.4i q^{47} +(-6.31611 + 734.863i) q^{48} -5934.91 q^{49} +10712.0 q^{50} +(168.144 - 19563.1i) q^{51} +14887.5i q^{52} -23978.4i q^{53} +(-350.596 + 13594.3i) q^{54} +(2276.12 - 4189.29i) q^{55} +27671.2i q^{56} +(18929.5 + 162.698i) q^{57} +11492.5 q^{58} +22954.8i q^{59} +(3539.33 + 30.4204i) q^{60} +27244.5i q^{61} -23141.4 q^{62} +(-629.884 + 36640.0i) q^{63} +21980.3 q^{64} -9254.23 q^{65} +(10890.9 - 19640.8i) q^{66} +20257.5 q^{67} -23986.0 q^{68} +(-13720.6 - 117.928i) q^{69} -6431.79 q^{70} +56465.7i q^{71} +(44581.8 + 766.412i) q^{72} +12025.4i q^{73} -33428.2 q^{74} +(399.768 - 46512.0i) q^{75} -23209.2i q^{76} +(28892.3 - 53177.5i) q^{77} +(-43590.5 - 374.658i) q^{78} +11065.5i q^{79} +560.075i q^{80} +(59014.1 + 2029.64i) q^{81} +19380.1 q^{82} -51574.3 q^{83} +(44927.1 + 386.146i) q^{84} -14910.0i q^{85} -74914.4i q^{86} +(428.897 - 49901.1i) q^{87} +(-64703.7 - 35154.8i) q^{88} +84147.7i q^{89} +(-178.142 + 10362.4i) q^{90} -117470. q^{91} +16822.6i q^{92} +(-863.629 + 100481. i) q^{93} -40528.8i q^{94} +14427.1 q^{95} +(764.000 - 88889.5i) q^{96} +99342.9 q^{97} -21306.2 q^{98} +(-84875.2 - 48021.9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16q - 54q^{3} + 316q^{4} - 222q^{9} + O(q^{10}) $	$ 16q - 54q^{3} + 316q^{4} - 222q^{9} - 552q^{12} - 1674q^{15} + 1684q^{16} + 7932q^{22} - 1356q^{25} - 3240q^{27} - 11980q^{31} - 5106q^{33} - 34032q^{34} + 14016q^{36} + 9356q^{37} + 45912q^{42} + 77430q^{45} - 78012q^{48} - 1136q^{49} + 117308q^{55} + 31848q^{58} - 220548q^{60} + 5860q^{64} - 164796q^{66} - 364132q^{67} + 113790q^{69} + 231144q^{70} + 320364q^{75} + 296088q^{78} - 251334q^{81} + 4824q^{82} + 586836q^{88} - 209184q^{91} - 521046q^{93} + 119852q^{97} - 243894q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/33\mathbb{Z}\right)^\times$.

$n$	$13$	$23$
$\chi(n)$	$-1$	$-1$

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 $

$2$	3.58998			0.634624			0.317312	−	0.948321i	$-0.397220\pi$
$2$	3.58998			0.634624			0.317312	+	0.948321i	$0.397220\pi$
$3$	0.133977	−	15.5879i	0.00859463	−	0.999963i
$3$	0.133977	−	15.5879i	0.00859463	−	0.999963i
$4$	−19.1121			−0.597252
$5$		−	11.8803i		−	0.212521i	−0.994338	−	0.106261i	$-0.966112\pi$
$5$		−	11.8803i		−	0.212521i	0.994338	−	0.106261i	$-0.0338877\pi$
$6$	0.480974	−	55.9601i	0.00545436	−	0.634601i
$7$		−	150.804i		−	1.16324i	−0.813461	−	0.581619i	$-0.802420\pi$
$7$		−	150.804i		−	1.16324i	0.813461	−	0.581619i	$-0.197580\pi$
$8$	−183.491			−1.01365
$9$	−242.964	−	4.17684i	−0.999852	−	0.0171886i
$10$		−	42.6500i		−	0.134871i
$11$	352.626	+	191.588i	0.878683	+	0.477405i
$11$	352.626	+	191.588i	0.878683	+	0.477405i
$12$	−2.56058	+	297.917i	−0.00513316	+	0.597230i
$13$		−	778.957i		−	1.27837i	−0.769055	−	0.639183i	$-0.779273\pi$
$13$		−	778.957i		−	1.27837i	0.769055	−	0.639183i	$-0.220727\pi$
$14$		−	541.384i		−	0.738219i
$15$	−185.188	−	1.59169i	−0.212513	−	0.00182654i
$16$	−47.1432			−0.0460383
$17$	1255.02			1.05324			0.526622	−	0.850100i	$-0.323458\pi$
$17$	1255.02			1.05324			0.526622	+	0.850100i	$0.323458\pi$
$18$	−872.236	−	14.9947i	−0.634531	−	0.0109083i
$19$			1214.37i			0.771736i	0.922554	+	0.385868i	$0.126098\pi$
$19$			1214.37i			0.771736i	−0.922554	+	0.385868i	$0.873902\pi$
$20$			227.057i			0.126929i
$21$	−2350.72	−	20.2043i	−1.16319	−	0.00999759i
$22$	1265.92	+	687.798i	0.557634	+	0.302973i
$23$		−	880.210i		−	0.346950i	−0.984838	−	0.173475i	$-0.944500\pi$
$23$		−	880.210i		−	0.346950i	0.984838	−	0.173475i	$-0.0554996\pi$
$24$	−24.5836	+	2860.24i	−0.00871199	+	1.01362i
$25$	2983.86			0.954835
$26$		−	2796.44i		−	0.811282i
$27$	−97.6596	+	3786.74i	−0.0257813	+	0.999668i
$28$			2882.18i			0.694746i
$29$	3201.27			0.706851			0.353425	−	0.935463i	$-0.385017\pi$
$29$	3201.27			0.706851			0.353425	+	0.935463i	$0.385017\pi$
$30$	−664.823	−	5.71411i	−0.134866	−	0.00115917i
$31$	−6446.10			−1.20474			−0.602369	−	0.798218i	$-0.705777\pi$
$31$	−6446.10			−1.20474			−0.602369	+	0.798218i	$0.705777\pi$
$32$	5702.47			0.984438
$33$	3033.70	−	5471.02i	0.484940	−	0.874548i
$34$	4505.50			0.668414
$35$	−1791.60			−0.247212
$36$	4643.54	+	79.8279i	0.597164	+	0.0102659i
$37$	−9311.53			−1.11819			−0.559096	−	0.829103i	$-0.688852\pi$
$37$	−9311.53			−1.11819			−0.559096	+	0.829103i	$0.688852\pi$
$38$			4359.58i			0.489762i
$39$	−12142.3	−	104.362i	−1.27832	−	0.0109871i
$40$			2179.93i			0.215423i
$41$	5398.38			0.501538			0.250769	−	0.968047i	$-0.419317\pi$
$41$	5398.38			0.501538			0.250769	+	0.968047i	$0.419317\pi$
$42$	−8439.03	−	72.5330i	−0.738192	−	0.00634472i
$43$		−	20867.6i		−	1.72108i	−0.509379	−	0.860542i	$-0.670125\pi$
$43$		−	20867.6i		−	1.72108i	0.509379	−	0.860542i	$-0.329875\pi$
$44$	−6739.40	−	3661.65i	−0.524795	−	0.285131i
$45$	−49.6220	+	2886.48i	−0.00365294	+	0.212490i
$46$		−	3159.93i		−	0.220183i
$47$		−	11289.4i		−	0.745465i	−0.927939	−	0.372732i	$-0.878421\pi$
$47$		−	11289.4i		−	0.745465i	0.927939	−	0.372732i	$-0.121579\pi$
$48$	−6.31611	+	734.863i	−0.000395682	+	0.0460366i
$49$	−5934.91			−0.353122
$50$	10712.0			0.605961
$51$	168.144	−	19563.1i	0.00905223	−	1.05320i
$52$			14887.5i			0.763506i
$53$		−	23978.4i		−	1.17255i	−0.810113	−	0.586274i	$-0.800594\pi$
$53$		−	23978.4i		−	1.17255i	0.810113	−	0.586274i	$-0.199406\pi$
$54$	−350.596	+	13594.3i	−0.0163615	+	0.634413i
$55$	2276.12	−	4189.29i	0.101459	−	0.186739i
$56$			27671.2i			1.17912i
$57$	18929.5	+	162.698i	0.771707	+	0.00663278i
$58$	11492.5			0.448585
$59$			22954.8i			0.858507i	0.903184	+	0.429254i	$0.141223\pi$
$59$			22954.8i			0.858507i	−0.903184	+	0.429254i	$0.858777\pi$
$60$	3539.33	+	30.4204i	0.126924	+	0.00109090i
$61$			27244.5i			0.937462i	0.883341	+	0.468731i	$0.155289\pi$
$61$			27244.5i			0.937462i	−0.883341	+	0.468731i	$0.844711\pi$
$62$	−23141.4			−0.764557
$63$	−629.884	+	36640.0i	−0.0199945	+	1.16307i
$64$	21980.3			0.670787
$65$	−9254.23			−0.271680
$66$	10890.9	−	19640.8i	0.307755	−	0.555009i
$67$	20257.5			0.551312			0.275656	−	0.961256i	$-0.411105\pi$
$67$	20257.5			0.551312			0.275656	+	0.961256i	$0.411105\pi$
$68$	−23986.0			−0.629051
$69$	−13720.6	−	117.928i	−0.346937	−	0.00298191i
$70$	−6431.79			−0.156887
$71$			56465.7i			1.32935i	0.747133	+	0.664674i	$0.231430\pi$
$71$			56465.7i			1.32935i	−0.747133	+	0.664674i	$0.768570\pi$
$72$	44581.8	+	766.412i	1.01351	+	0.0174233i
$73$			12025.4i			0.264116i	0.991242	+	0.132058i	$0.0421585\pi$
$73$			12025.4i			0.264116i	−0.991242	+	0.132058i	$0.957842\pi$
$74$	−33428.2			−0.709632
$75$	399.768	−	46512.0i	0.00820645	−	0.954800i
$76$		−	23209.2i		−	0.460921i
$77$	28892.3	−	53177.5i	0.555336	−	1.02212i
$78$	−43590.5	−	374.658i	−0.811252	−	0.00697267i
$79$			11065.5i			0.199481i	0.995013	+	0.0997407i	$0.0318013\pi$
$79$			11065.5i			0.199481i	−0.995013	+	0.0997407i	$0.968199\pi$
$80$			560.075i			0.00978411i
$81$	59014.1	+	2029.64i	0.999409	+	0.0343722i
$82$	19380.1			0.318288
$83$	−51574.3			−0.821747			−0.410873	−	0.911692i	$-0.634776\pi$
$83$	−51574.3			−0.821747			−0.410873	+	0.911692i	$0.634776\pi$
$84$	44927.1	+	386.146i	0.694720	+	0.00597108i
$85$		−	14910.0i		−	0.223836i
$86$		−	74914.4i		−	1.09224i
$87$	428.897	−	49901.1i	0.00607512	−	0.706825i
$88$	−64703.7	−	35154.8i	−0.890682	−	0.483924i
$89$			84147.7i			1.12608i	0.826431	+	0.563038i	$0.190367\pi$
$89$			84147.7i			1.12608i	−0.826431	+	0.563038i	$0.809633\pi$
$90$	−178.142	+	10362.4i	−0.00231825	+	0.134851i
$91$	−117470.			−1.48704
$92$			16822.6i			0.207216i
$93$	−863.629	+	100481.i	−0.0103543	+	1.20469i
$94$		−	40528.8i		−	0.473090i
$95$	14427.1			0.164010
$96$	764.000	−	88889.5i	0.00846088	−	0.984402i
$97$	99342.9			1.07203			0.536016	−	0.844208i	$-0.319929\pi$
$97$	99342.9			1.07203			0.536016	+	0.844208i	$0.319929\pi$
$98$	−21306.2			−0.224100
$99$	−84875.2	−	48021.9i	−0.870347	−	0.492438i
$100$	−57027.7			−0.570277
$101$	−8413.56			−0.0820685			−0.0410343	−	0.999158i	$-0.513065\pi$
$101$	−8413.56			−0.0820685			−0.0410343	+	0.999158i	$0.513065\pi$
$102$	603.633	−	70231.1i	0.00574477	−	0.668389i
$103$	11603.9			0.107773			0.0538864	−	0.998547i	$-0.482839\pi$
$103$	11603.9			0.107773			0.0538864	+	0.998547i	$0.482839\pi$
$104$			142932.i			1.29582i
$105$	−240.033	+	27927.2i	−0.00212470	+	0.247203i
$106$		−	86082.0i		−	0.744128i
$107$	181478.			1.53238			0.766188	−	0.642616i	$-0.222151\pi$
$107$	181478.			1.53238			0.766188	+	0.642616i	$0.222151\pi$
$108$	1866.48	−	72372.3i	0.0153980	−	0.597053i
$109$			153350.i			1.23628i	0.786067	+	0.618141i	$0.212114\pi$
$109$			153350.i			1.23628i	−0.786067	+	0.618141i	$0.787886\pi$
$110$	8171.23	−	15039.5i	0.0643881	−	0.118509i
$111$	−1247.53	+	145147.i	−0.00961045	+	1.11815i
$112$			7109.40i			0.0535535i
$113$		−	209395.i		−	1.54266i	−0.636435	−	0.771330i	$-0.719592\pi$
$113$		−	209395.i		−	1.54266i	0.636435	−	0.771330i	$-0.280408\pi$
$114$	67956.6	+	584.083i	0.489744	+	0.00420933i
$115$	−10457.1			−0.0737341
$116$	−61182.9			−0.422168
$117$	−3253.57	+	189259.i	−0.0219733	+	1.27818i
$118$			82407.3i			0.544830i
$119$		−	189262.i		−	1.22517i
$120$	33980.5	+	292.060i	0.215415	+	0.00185148i
$121$	87638.8	+	135118.i	0.544168	+	0.838976i
$122$			97807.0i			0.594936i
$123$	723.259	−	84149.3i	0.00431053	−	0.501519i
$124$	123198.			0.719532
$125$		−	72575.0i		−	0.415443i
$126$	−2261.27	+	131537.i	−0.0126890	+	0.738110i
$127$		−	117065.i		−	0.644046i	−0.946732	−	0.322023i	$-0.895637\pi$
$127$		−	117065.i		−	0.644046i	0.946732	−	0.322023i	$-0.104363\pi$
$128$	−103570.			−0.558740
$129$	−325282.	−	2795.78i	−1.72102	−	0.0147921i
$130$	−33222.5			−0.172414
$131$	176896.			0.900614			0.450307	−	0.892874i	$-0.351314\pi$
$131$	176896.			0.900614			0.450307	+	0.892874i	$0.351314\pi$
$132$	−57980.3	+	104562.i	−0.289631	+	0.522325i
$133$	183133.			0.897712
$134$	72723.8			0.349876
$135$	44987.5	+	1160.22i	0.212450	+	0.00547908i
$136$	−230285.			−1.06763
$137$			347712.i			1.58277i	0.611318	+	0.791385i	$0.290640\pi$
$137$			347712.i			1.58277i	−0.611318	+	0.791385i	$0.709360\pi$
$138$	−49256.7	−	423.359i	−0.220175	−	0.00189239i
$139$		−	8720.60i		−	0.0382833i	−0.999817	−	0.0191417i	$-0.993907\pi$
$139$		−	8720.60i		−	0.0382833i	0.999817	−	0.0191417i	$-0.00609335\pi$
$140$	34241.1			0.147648
$141$	−175978.	−	1512.52i	−0.745437	−	0.00640699i
$142$			202711.i			0.843637i
$143$	149239.	−	274680.i	0.610299	−	1.12328i
$144$	11454.1	+	196.909i	0.0460315	+	0.000791335i
$145$		−	38032.0i		−	0.150221i
$146$			43171.1i			0.167614i
$147$	−795.142	+	92512.7i	−0.00303495	+	0.353109i
$148$	177962.			0.667843
$149$	354108.			1.30668			0.653342	−	0.757063i	$-0.273366\pi$
$149$	354108.			1.30668			0.653342	+	0.757063i	$0.273366\pi$
$150$	1435.16	−	166977.i	0.00520801	−	0.605939i
$151$		−	493279.i		−	1.76056i	−0.474457	−	0.880278i	$-0.657356\pi$
$151$		−	493279.i		−	1.76056i	0.474457	−	0.880278i	$-0.342644\pi$
$152$		−	222827.i		−	0.782274i
$153$	−304925.	−	5242.02i	−1.05309	−	0.0181038i
$154$	103723.	−	190906.i	0.352430	−	0.648661i
$155$			76581.5i			0.256032i
$156$	232064.	+	1994.58i	0.763478	+	0.00656205i
$157$	−94457.3			−0.305834			−0.152917	−	0.988239i	$-0.548867\pi$
$157$	−94457.3			−0.305834			−0.152917	+	0.988239i	$0.548867\pi$
$158$			39724.8i			0.126596i
$159$	−373773.	−	3212.56i	−1.17251	−	0.0100776i
$160$		−	67747.0i		−	0.209214i
$161$	−132739.			−0.403585
$162$	211859.	+	7286.37i	0.634249	+	0.0218134i
$163$	−296304.			−0.873510			−0.436755	−	0.899580i	$-0.643872\pi$
$163$	−296304.			−0.873510			−0.436755	+	0.899580i	$0.643872\pi$
$164$	−103174.			−0.299544
$165$	−64997.3	−	36041.2i	−0.185860	−	0.103060i
$166$	−185151.			−0.521501
$167$	−571023.			−1.58439			−0.792196	−	0.610267i	$-0.791062\pi$
$167$	−571023.			−1.58439			−0.792196	+	0.610267i	$0.791062\pi$
$168$	431336.	+	3707.31i	1.17908	+	0.0101341i
$169$	−235481.			−0.634219
$170$		−	53526.6i		−	0.142052i
$171$	5072.24	−	295049.i	0.0132651	−	0.771622i
$172$			398824.i			1.02792i
$173$	−12657.7			−0.0321545			−0.0160772	−	0.999871i	$-0.505118\pi$
$173$	−12657.7			−0.0321545			−0.0160772	+	0.999871i	$0.505118\pi$
$174$	1539.73	−	179144.i	0.00385542	−	0.448568i
$175$		−	449979.i		−	1.11070i
$176$	−16623.9	−	9032.09i	−0.0404531	−	0.0219789i
$177$	357817.	+	3075.42i	0.858476	+	0.00737855i
$178$			302089.i			0.714635i
$179$			46770.9i			0.109105i	0.998511	+	0.0545523i	$0.0173732\pi$
$179$			46770.9i			0.109105i	−0.998511	+	0.0545523i	$0.982627\pi$
$180$	948.379	−	55166.6i	0.00218173	−	0.126910i
$181$	118107.			0.267965			0.133983	−	0.990984i	$-0.457223\pi$
$181$	118107.			0.267965			0.133983	+	0.990984i	$0.457223\pi$
$182$	−421715.			−0.943714
$183$	424683.	+	3650.13i	0.937427	+	0.00805714i
$184$			161511.i			0.351688i
$185$			110624.i			0.237639i
$186$	−3100.41	+	360725.i	−0.00657108	+	0.764528i
$187$	442553.	+	240447.i	0.925467	+	0.502824i
$188$			215764.i			0.445230i
$189$	571056.	+	14727.5i	1.16285	+	0.0299898i
$190$	51793.0			0.104085
$191$			540991.i			1.07302i	0.843895	+	0.536509i	$0.180257\pi$
$191$			540991.i			1.07302i	−0.843895	+	0.536509i	$0.819743\pi$
$192$	2944.86	−	342627.i	0.00576516	−	0.670762i
$193$			610969.i			1.18066i	0.807161	+	0.590331i	$0.201003\pi$
$193$			610969.i			1.18066i	−0.807161	+	0.590331i	$0.798997\pi$
$194$	356639.			0.680337
$195$	−1239.85	+	144254.i	−0.00233498	+	0.271670i
$196$	113428.			0.210903
$197$	365903.			0.671739			0.335869	−	0.941909i	$-0.390970\pi$
$197$	365903.			0.671739			0.335869	+	0.941909i	$0.390970\pi$
$198$	−304700.	−	172398.i	−0.552344	−	0.312513i
$199$	−218381.			−0.390915			−0.195457	−	0.980712i	$-0.562619\pi$
$199$	−218381.			−0.390915			−0.195457	+	0.980712i	$0.562619\pi$
$200$	−547512.			−0.967873
$201$	2714.03	−	315771.i	0.00473833	−	0.551292i
$202$	−30204.5			−0.0520827
$203$		−	482765.i		−	0.822235i
$204$	−3213.58	+	373891.i	−0.00540646	+	0.629028i
$205$		−	64134.3i		−	0.106587i
$206$	41657.6			0.0683953
$207$	−3676.49	+	213859.i	−0.00596359	+	0.346899i
$208$			36722.5i			0.0588538i
$209$	−232660.	+	428220.i	−0.368431	+	0.678111i
$210$	−861.713	+	100258.i	−0.00134839	+	0.156881i
$211$		−	697135.i		−	1.07798i	−0.842312	−	0.538990i	$-0.818806\pi$
$211$		−	697135.i		−	1.07798i	0.842312	−	0.538990i	$-0.181194\pi$
$212$			458277.i			0.700307i
$213$	880181.	+	7565.11i	1.32930	+	0.0114253i
$214$	651503.			0.972483
$215$	−247914.			−0.365767
$216$	17919.7	−	694833.i	0.0261334	−	1.01332i
$217$			972099.i			1.40140i
$218$			550523.i			0.784575i
$219$	187451.	+	1611.13i	0.264106	+	0.00226998i
$220$	−43501.4	+	80066.1i	−0.0605964	+	0.111530i
$221$		−	977607.i		−	1.34643i
$222$	−4478.61	+	521075.i	−0.00609903	+	0.709606i
$223$	−1.13148e6			−1.52365			−0.761826	−	0.647781i	$-0.775697\pi$
$223$	−1.13148e6			−1.52365			−0.761826	+	0.647781i	$0.775697\pi$
$224$		−	859957.i		−	1.14514i
$225$	−724971.	−	12463.1i	−0.954694	−	0.0164123i
$226$		−	751724.i		−	0.979010i
$227$	−1.33675e6			−1.72181			−0.860904	−	0.508767i	$-0.830101\pi$
$227$	−1.33675e6			−1.72181			−0.860904	+	0.508767i	$0.830101\pi$
$228$	−361782.	−	3109.50i	−0.460904	−	0.00396144i
$229$	936509.			1.18011			0.590056	−	0.807362i	$-0.299106\pi$
$229$	936509.			1.18011			0.590056	+	0.807362i	$0.299106\pi$
$230$	−37540.9			−0.0467935
$231$	−825053.	−	457495.i	−1.01731	−	0.564100i
$232$	−587405.			−0.716503
$233$	675682.			0.815366			0.407683	−	0.913124i	$-0.366337\pi$
$233$	675682.			0.815366			0.407683	+	0.913124i	$0.366337\pi$
$234$	−11680.3	+	679434.i	−0.0139448	+	0.811162i
$235$	−134122.			−0.158427
$236$		−	438714.i		−	0.512745i
$237$	172487.	+	1482.52i	0.199474	+	0.00171447i
$238$		−	679448.i		−	0.777524i
$239$	596353.			0.675319			0.337659	−	0.941268i	$-0.390365\pi$
$239$	596353.			0.675319			0.337659	+	0.941268i	$0.390365\pi$
$240$	8730.38	+	75.0372i	0.00978374	+	8.40908e-5i
$241$		−	1.24321e6i		−	1.37880i	−0.724381	−	0.689400i	$-0.757874\pi$
$241$		−	1.24321e6i		−	1.37880i	0.724381	−	0.689400i	$-0.242126\pi$
$242$	314621.	+	485070.i	0.345342	+	0.532435i
$243$	39544.4	−	919633.i	0.0429604	−	0.999077i
$244$		−	520698.i		−	0.559901i
$245$			70508.5i			0.0750458i
$246$	2596.48	−	302094.i	0.00273557	−	0.318276i
$247$	945945.			0.986560
$248$	1.18280e6			1.22119
$249$	−6909.77	+	803934.i	−0.00706261	+	0.821716i
$250$		−	260543.i		−	0.263651i
$251$			1.76567e6i			1.76899i	0.466551	+	0.884494i	$0.345496\pi$
$251$			1.76567e6i			1.76899i	−0.466551	+	0.884494i	$0.654504\pi$
$252$	12038.4	−	700266.i	0.0119417	−	0.694643i
$253$	168638.	−	310385.i	0.165636	−	0.304859i
$254$		−	420260.i		−	0.408727i
$255$	−232415.	−	1997.60i	−0.223828	−	0.00192379i
$256$	−1.07519e6			−1.02538
$257$		−	347788.i		−	0.328459i	−0.986422	−	0.164230i	$-0.947486\pi$
$257$		−	347788.i		−	0.328459i	0.986422	−	0.164230i	$-0.0525138\pi$
$258$	−1.16776e6	−	10036.8i	−1.09220	−	0.00938742i
$259$			1.40422e6i			1.30072i
$260$	176867.			0.162261
$261$	−777794.	−	13371.2i	−0.706746	−	0.0121498i
$262$	635051.			0.571552
$263$	−985521.			−0.878570			−0.439285	−	0.898348i	$-0.644768\pi$
$263$	−985521.			−0.878570			−0.439285	+	0.898348i	$0.644768\pi$
$264$	−556657.	+	1.00388e6i	−0.491562	+	0.886490i
$265$	−284871.			−0.249191
$266$	657443.			0.569710
$267$	1.31169e6	+	11273.9i	1.12603	+	0.00967820i
$268$	−387162.			−0.329272
$269$		−	1.36787e6i		−	1.15257i	−0.817250	−	0.576283i	$-0.804503\pi$
$269$		−	1.36787e6i		−	1.15257i	0.817250	−	0.576283i	$-0.195497\pi$
$270$	161504.	+	4165.18i	0.134826	+	0.00347716i
$271$			346976.i			0.286996i	0.989651	+	0.143498i	$0.0458351\pi$
$271$			346976.i			0.286996i	−0.989651	+	0.143498i	$0.954165\pi$
$272$	−59165.7			−0.0484895
$273$	−15738.3	+	1.83111e6i	−0.0127806	+	1.48699i
$274$			1.24828e6i			1.00446i
$275$	1.05219e6	+	571672.i	0.838997	+	0.455843i
$276$	262229.	+	2253.85i	0.207209	+	0.00178095i
$277$			1.92307e6i			1.50590i	0.658079	+	0.752949i	$0.271369\pi$
$277$			1.92307e6i			1.50590i	−0.658079	+	0.752949i	$0.728631\pi$
$278$		−	31306.8i		−	0.0242955i
$279$	1.56617e6	+	26924.3i	1.20456	+	0.0207078i
$280$	328742.			0.250588
$281$	−1.51815e6			−1.14696			−0.573482	−	0.819218i	$-0.694408\pi$
$281$	−1.51815e6			−1.14696			−0.573482	+	0.819218i	$0.694408\pi$
$282$	−631758.	−	5429.93i	−0.473073	−	0.00406603i
$283$			195988.i			0.145466i	0.997351	+	0.0727332i	$0.0231721\pi$
$283$			195988.i			0.145466i	−0.997351	+	0.0727332i	$0.976828\pi$
$284$		−	1.07918e6i		−	0.793956i
$285$	1932.90	−	224888.i	0.00140961	−	0.164004i
$286$	535765.	−	986096.i	0.387310	−	0.712860i
$287$		−	814098.i		−	0.583408i
$288$	−1.38550e6	−	23818.3i	−0.984293	−	0.0169211i
$289$	155220.			0.109321
$290$		−	136534.i		−	0.0953337i
$291$	13309.7	−	1.54855e6i	0.00921371	−	1.07199i
$292$		−	229831.i		−	0.157744i
$293$	2.75485e6			1.87469			0.937345	−	0.348403i	$-0.113276\pi$
$293$	2.75485e6			1.87469			0.937345	+	0.348403i	$0.113276\pi$
$294$	−2854.54	+	332119.i	−0.00192605	+	0.224091i
$295$	272710.			0.182451
$296$	1.70858e6			1.13346
$297$	−759932.	+	1.31659e6i	−0.499900	+	0.866083i
$298$	1.27124e6			0.829254
$299$	−685646.			−0.443529
$300$	−7640.40	+	888941.i	−0.00490132	+	0.570256i
$301$	−3.14693e6			−2.00203
$302$		−	1.77086e6i		−	1.11729i
$303$	−1127.22	+	131150.i	−0.000705348	+	0.0820655i
$304$		−	57249.5i		−	0.0355294i
$305$	323672.			0.199230
$306$	−1.09467e6	−	18818.7i	−0.668315	−	0.0114891i
$307$			684538.i			0.414526i	0.978285	+	0.207263i	$0.0664556\pi$
$307$			684538.i			0.414526i	−0.978285	+	0.207263i	$0.933544\pi$
$308$	−552192.	+	1.01633e6i	−0.331675	+	0.610461i
$309$	1554.65	−	180880.i	0.000926268	−	0.107769i
$310$			274926.i			0.162484i
$311$		−	414984.i		−	0.243294i	−0.992573	−	0.121647i	$-0.961182\pi$
$311$		−	414984.i		−	0.243294i	0.992573	−	0.121647i	$-0.0388175\pi$
$312$	2.22800e6	+	19149.6i	1.29577	+	0.0111371i
$313$	1.28268e6			0.740043			0.370022	−	0.929023i	$-0.379350\pi$
$313$	1.28268e6			0.740043			0.370022	+	0.929023i	$0.379350\pi$
$314$	−339099.			−0.194090
$315$	435294.	+	7483.21i	0.247176	+	0.00424924i
$316$		−	211484.i		−	0.119141i
$317$			2.70836e6i			1.51376i	0.653553	+	0.756881i	$0.273278\pi$
$317$			2.70836e6i			1.51376i	−0.653553	+	0.756881i	$0.726722\pi$
$318$	−1.34184e6	−	11533.0i	−0.744101	−	0.00639550i
$319$	1.12885e6	+	613326.i	0.621098	+	0.337454i
$320$		−	261133.i		−	0.142556i
$321$	24313.9	−	2.82886e6i	0.0131702	−	1.53232i
$322$	−476532.			−0.256125
$323$			1.52407e6i			0.812825i
$324$	−1.12788e6	−	38790.6i	−0.596899	−	0.0205288i
$325$		−	2.32430e6i		−	1.22063i
$326$	−1.06372e6			−0.554351
$327$	2.39040e6	+	20545.4i	1.23624	+	0.0106254i
$328$	−990555.			−0.508386
$329$	−1.70249e6			−0.867153
$330$	−233339.	−	129387.i	−0.117951	−	0.0654043i
$331$	−1.10525e6			−0.554486			−0.277243	−	0.960800i	$-0.589421\pi$
$331$	−1.10525e6			−0.554486			−0.277243	+	0.960800i	$0.589421\pi$
$332$	985691.			0.490790
$333$	2.26237e6	+	38892.7i	1.11803	+	0.0192202i
$334$	−2.04996e6			−1.00549
$335$		−	240664.i		−	0.117165i
$336$	110820.	+	952.496i	0.0535515	+	0.000460272i
$337$		−	1.20295e6i		−	0.576996i	−0.957480	−	0.288498i	$-0.906844\pi$
$337$		−	1.20295e6i		−	0.576996i	0.957480	−	0.288498i	$-0.0931559\pi$
$338$	−845371.			−0.402491
$339$	−3.26403e6	−	28054.1i	−1.54260	−	0.0132586i
$340$			284961.i			0.133687i
$341$	−2.27306e6	−	1.23500e6i	−1.05858	−	0.575149i
$342$	18209.2	−	1.05922e6i	0.00841834	−	0.489690i
$343$		−	1.63956e6i		−	0.752473i
$344$			3.82903e6i			1.74459i
$345$	−1401.02	+	163005.i	−0.000633718	+	0.0737314i
$346$	−45441.0			−0.0204060
$347$	1.61441e6			0.719765			0.359882	−	0.932998i	$-0.382817\pi$
$347$	1.61441e6			0.719765			0.359882	+	0.932998i	$0.382817\pi$
$348$	−8197.10	+	953712.i	−0.00362838	+	0.422152i
$349$		−	3.17188e6i		−	1.39397i	−0.717085	−	0.696986i	$-0.754524\pi$
$349$		−	3.17188e6i		−	1.39397i	0.717085	−	0.696986i	$-0.245476\pi$
$350$		−	1.61541e6i		−	0.704877i
$351$	2.94970e6	+	76072.6i	1.27794	+	0.0329580i
$352$	2.01084e6	+	1.09253e6i	0.865009	+	0.469976i
$353$		−	675430.i		−	0.288499i	−0.989541	−	0.144249i	$-0.953923\pi$
$353$		−	675430.i		−	0.288499i	0.989541	−	0.144249i	$-0.0460767\pi$
$354$	1.28456e6	+	11040.7i	0.544810	+	0.00468261i
$355$	670829.			0.282515
$356$		−	1.60824e6i		−	0.672551i
$357$	−2.95020e6	−	25356.8i	−1.22513	−	0.0105299i
$358$			167906.i			0.0692404i
$359$	−2.48053e6			−1.01580			−0.507900	−	0.861416i	$-0.669578\pi$
$359$	−2.48053e6			−1.01580			−0.507900	+	0.861416i	$0.669578\pi$
$360$	9105.20	−	529644.i	0.00370282	−	0.215391i
$361$	1.00139e6			0.404424
$362$	424001.			0.170057
$363$	2.11794e6	−	1.34800e6i	0.843622	−	0.536937i
$364$	2.24509e6			0.888139
$365$	142866.			0.0561301
$366$	1.52460e6	+	13103.9i	0.594914	+	0.00511326i
$367$	−2.46844e6			−0.956659			−0.478329	−	0.878181i	$-0.658757\pi$
$367$	−2.46844e6			−0.956659			−0.478329	+	0.878181i	$0.658757\pi$
$368$			41495.9i			0.0159730i
$369$	−1.31161e6	−	22548.1i	−0.501464	−	0.00862075i
$370$			397136.i			0.150812i
$371$	−3.61605e6			−1.36395
$372$	16505.7	−	1.92040e6i	0.00618411	−	0.719506i
$373$			2.16792e6i			0.806809i	0.915022	+	0.403405i	$0.132173\pi$
$373$			2.16792e6i			0.806809i	−0.915022	+	0.403405i	$0.867827\pi$
$374$	1.58875e6	+	863201.i	0.587324	+	0.319104i
$375$	−1.13129e6	−	9723.38i	−0.415428	−	0.00357058i
$376$			2.07151e6i			0.755644i
$377$		−	2.49365e6i		−	0.903614i
$378$	2.05008e6	+	52871.3i	0.737974	+	0.0190323i
$379$	3.73283e6			1.33487			0.667437	−	0.744666i	$-0.267391\pi$
$379$	3.73283e6			1.33487			0.667437	+	0.744666i	$0.267391\pi$
$380$	−275732.			−0.0979553
$381$	−1.82479e6	−	15684.0i	−0.644022	−	0.00553534i
$382$			1.94215e6i			0.680963i
$383$			2.18000e6i			0.759382i	0.925113	+	0.379691i	$0.123970\pi$
$383$			2.18000e6i			0.759382i	−0.925113	+	0.379691i	$0.876030\pi$
$384$	−13876.0	+	1.61444e6i	−0.00480217	+	0.558720i
$385$	−631763.	−	343249.i	−0.217221	−	0.118021i
$386$			2.19336e6i			0.749277i
$387$	−87160.7	+	5.07009e6i	−0.0295831	+	1.72083i
$388$	−1.89865e6			−0.640273
$389$			2.48481e6i			0.832567i	0.909235	+	0.416284i	$0.136668\pi$
$389$			2.48481e6i			0.832567i	−0.909235	+	0.416284i	$0.863332\pi$
$390$	−4451.05	+	517868.i	−0.00148184	+	0.172408i
$391$		−	1.10468e6i		−	0.365423i
$392$	1.08900e6			0.357943
$393$	23699.9	−	2.75743e6i	0.00774045	−	0.900581i
$394$	1.31358e6			0.426302
$395$	131461.			0.0423940
$396$	1.62214e6	+	917798.i	0.519817	+	0.294110i
$397$	−54162.3			−0.0172473			−0.00862364	−	0.999963i	$-0.502745\pi$
$397$	−54162.3			−0.0172473			−0.00862364	+	0.999963i	$0.502745\pi$
$398$	−783983.			−0.248084
$399$	24535.6	−	2.85465e6i	0.00771550	−	0.897679i
$400$	−140669.			−0.0439590
$401$			3.15932e6i			0.981144i	0.871401	+	0.490572i	$0.163212\pi$
$401$			3.15932e6i			0.981144i	−0.871401	+	0.490572i	$0.836788\pi$
$402$	9743.32	−	1.13361e6i	0.00300706	−	0.349863i
$403$			5.02123e6i			1.54010i
$404$	160801.			0.0490156
$405$	24112.7	−	701105.i	0.00730481	−	0.212395i
$406$		−	1.73312e6i		−	0.521811i
$407$	−3.28348e6	−	1.78398e6i	−0.982537	−	0.533831i
$408$	−30852.9	+	3.58966e6i	−0.00917584	+	1.06759i
$409$		−	3.24246e6i		−	0.958444i	−0.877694	−	0.479222i	$-0.840919\pi$
$409$		−	3.24246e6i		−	0.958444i	0.877694	−	0.479222i	$-0.159081\pi$
$410$		−	230241.i		−	0.0676429i
$411$	5.42009e6	+	46585.4i	1.58271	+	0.0136033i
$412$	−221774.			−0.0643675
$413$	3.46168e6			0.998648
$414$	−13198.5	+	767751.i	−0.00378464	+	0.220150i
$415$			612717.i			0.174638i
$416$		−	4.44198e6i		−	1.25847i
$417$	−135936.	−	1168.36i	−0.0382819	−	0.000329031i
$418$	−835244.	+	1.53730e6i	−0.233815	+	0.430346i
$419$			540226.i			0.150328i	0.997171	+	0.0751642i	$0.0239481\pi$
$419$			540226.i			0.150328i	−0.997171	+	0.0751642i	$0.976052\pi$
$420$	4587.52	−	533746.i	0.00126898	−	0.147643i
$421$	−3.05118e6			−0.839003			−0.419501	−	0.907755i	$-0.637795\pi$
$421$	−3.05118e6			−0.839003			−0.419501	+	0.907755i	$0.637795\pi$
$422$		−	2.50270e6i		−	0.684112i
$423$	−47154.1	+	2.74293e6i	−0.0128135	+	0.745355i
$424$			4.39983e6i			1.18856i
$425$	3.74480e6			1.00567
$426$	3.15983e6	+	27158.6i	0.843606	+	0.00725075i
$427$	4.10858e6			1.09049
$428$	−3.46843e6			−0.915215
$429$	−4.26169e6	−	2.36312e6i	−1.11799	−	0.619930i
$430$	−890004.			−0.232124
$431$	2.10023e6			0.544596			0.272298	−	0.962213i	$-0.412216\pi$
$431$	2.10023e6			0.544596			0.272298	+	0.962213i	$0.412216\pi$
$432$	4603.99	−	178519.i	0.00118693	−	0.0460230i
$433$	−3.92143e6			−1.00514			−0.502568	−	0.864538i	$-0.667611\pi$
$433$	−3.92143e6			−1.00514			−0.502568	+	0.864538i	$0.667611\pi$
$434$			3.48981e6i			0.889361i
$435$	−592839.	−	5095.42i	−0.150215	−	0.00129109i
$436$		−	2.93084e6i		−	0.738372i
$437$	1.06890e6			0.267754
$438$	672946.	+	5783.93i	0.167608	+	0.00144058i
$439$		−	1.31281e6i		−	0.325118i	−0.986699	−	0.162559i	$-0.948025\pi$
$439$		−	1.31281e6i		−	0.325118i	0.986699	−	0.162559i	$-0.0519748\pi$
$440$	−417649.	+	768699.i	−0.102844	+	0.189289i
$441$	1.44197e6	+	24789.2i	0.353069	+	0.00606967i
$442$		−	3.50959e6i		−	0.854477i
$443$		−	6.39479e6i		−	1.54816i	−0.633086	−	0.774082i	$-0.718212\pi$
$443$		−	6.39479e6i		−	1.54816i	0.633086	−	0.774082i	$-0.281788\pi$
$444$	23842.9	−	2.77406e6i	0.00573986	−	0.667818i
$445$	999699.			0.239315
$446$	−4.06200e6			−0.966947
$447$	47442.4	−	5.51980e6i	0.0112305	−	1.30664i
$448$		−	3.31473e6i		−	0.780284i
$449$		−	4.54884e6i		−	1.06484i	−0.846480	−	0.532420i	$-0.821283\pi$
$449$		−	4.54884e6i		−	1.06484i	0.846480	−	0.532420i	$-0.178717\pi$
$450$	−2.60263e6	−	44742.2i	−0.605872	−	0.0104156i
$451$	1.90361e6	+	1.03427e6i	0.440693	+	0.239437i
$452$			4.00197e6i			0.921357i
$453$	−7.68917e6	−	66088.0i	−1.76049	−	0.0151313i
$454$	−4.79889e6			−1.09270
$455$			1.39558e6i			0.316028i
$456$	−3.47340e6	−	29853.7i	−0.782245	−	0.00672335i
$457$		−	2.25014e6i		−	0.503987i	−0.967729	−	0.251993i	$-0.918914\pi$
$457$		−	2.25014e6i		−	0.503987i	0.967729	−	0.251993i	$-0.0810861\pi$
$458$	3.36205e6			0.748928
$459$	−122565.	+	4.75243e6i	−0.0271540	+	1.05289i
$460$	199858.			0.0440379
$461$	3.13541e6			0.687136			0.343568	−	0.939128i	$-0.388364\pi$
$461$	3.13541e6			0.687136			0.343568	+	0.939128i	$0.388364\pi$
$462$	−2.96192e6	−	1.64240e6i	−0.645608	−	0.357992i
$463$	−5.47459e6			−1.18686			−0.593429	−	0.804886i	$-0.702226\pi$
$463$	−5.47459e6			−1.18686			−0.593429	+	0.804886i	$0.702226\pi$
$464$	−150918.			−0.0325422
$465$	1.19374e6	+	10260.2i	0.256023	+	0.00220050i
$466$	2.42568e6			0.517451
$467$			8.52104e6i			1.80801i	0.427524	+	0.904004i	$0.359386\pi$
$467$			8.52104e6i			1.80801i	−0.427524	+	0.904004i	$0.640614\pi$
$468$	62182.5	−	3.61712e6i	0.0131236	−	0.763393i
$469$		−	3.05491e6i		−	0.641307i
$470$	−481494.			−0.100542
$471$	−12655.1	+	1.47239e6i	−0.00262853	+	0.305823i
$472$		−	4.21201e6i		−	0.870230i
$473$	3.99800e6	−	7.35847e6i	0.821655	−	1.51229i
$474$	619226.	+	5322.21i	0.126591	+	0.00108804i
$475$			3.62352e6i			0.736880i
$476$			3.61720e6i			0.731736i
$477$	−100154.	+	5.82590e6i	−0.0201545	+	1.17238i
$478$	2.14089e6			0.428574
$479$	8568.59			0.00170636			0.000853180	−	1.00000i	$-0.499728\pi$
$479$	8568.59			0.00170636			0.000853180		1.00000i	$0.499728\pi$
$480$	−1.05603e6	−	9076.54i	−0.209206	−	0.00179811i
$481$			7.25328e6i			1.42946i
$482$		−	4.46309e6i		−	0.875020i
$483$	−17784.0	+	2.06913e6i	−0.00346866	+	0.403570i
$484$	−1.67496e6	−	2.58238e6i	−0.325006	−	0.501080i
$485$		−	1.18022e6i		−	0.227829i
$486$	141963.	−	3.30146e6i	0.0272637	−	0.634038i
$487$	440964.			0.0842520			0.0421260	−	0.999112i	$-0.486587\pi$
$487$	440964.			0.0842520			0.0421260	+	0.999112i	$0.486587\pi$
$488$		−	4.99912e6i		−	0.950263i
$489$	−39697.9	+	4.61875e6i	−0.00750750	+	0.873478i
$490$			253124.i			0.0476259i
$491$	−179754.			−0.0336493			−0.0168246	−	0.999858i	$-0.505356\pi$
$491$	−179754.			−0.0336493			−0.0168246	+	0.999858i	$0.505356\pi$
$492$	−13823.0	+	1.60827e6i	−0.00257447	+	0.299533i
$493$	4.01766e6			0.744486
$494$	3.39592e6			0.626095
$495$	−570514.	+	1.00834e6i	−0.104653	+	0.184967i
$496$	303890.			0.0554641
$497$	8.51527e6			1.54635
$498$	−24805.9	+	2.88610e6i	−0.00448210	+	0.521481i
$499$	4.77108e6			0.857759			0.428879	−	0.903362i	$-0.358908\pi$
$499$	4.77108e6			0.857759			0.428879	+	0.903362i	$0.358908\pi$
$500$			1.38706e6i			0.248124i
$501$	−76504.0	+	8.90105e6i	−0.0136173	+	1.58433i
$502$			6.33871e6i			1.12264i
$503$	270590.			0.0476860			0.0238430	−	0.999716i	$-0.492410\pi$
$503$	270590.			0.0476860			0.0238430	+	0.999716i	$0.492410\pi$
$504$	115578.	−	6.72312e6i	0.0202675	−	1.17895i
$505$			99955.6i			0.0174413i
$506$	605407.	−	1.11427e6i	0.105116	−	0.193471i
$507$	−31549.0	+	3.67065e6i	−0.00545087	+	0.634195i
$508$			2.23735e6i			0.384658i
$509$		−	3.74567e6i		−	0.640819i	−0.947279	−	0.320410i	$-0.896179\pi$
$509$		−	3.74567e6i		−	0.640819i	0.947279	−	0.320410i	$-0.103821\pi$
$510$	−834366.	−	7171.33i	−0.142047	−	0.00122088i
$511$	1.81349e6			0.307229
$512$	−545645.			−0.0919888
$513$	−4.59852e6	−	118595.i	−0.771479	−	0.0198964i
$514$		−	1.24855e6i		−	0.208448i
$515$		−	137857.i		−	0.0229040i
$516$	6.21682e6	+	53433.2i	1.02788	+	0.00883460i
$517$	2.16292e6	−	3.98094e6i	0.355889	−	0.655027i
$518$			5.04111e6i			0.825471i
$519$	−1695.85	+	197307.i	−0.000276356	+	0.0321533i
$520$	1.69807e6			0.275389
$521$			6.27808e6i			1.01329i	0.862156	+	0.506644i	$0.169114\pi$
$521$			6.27808e6i			1.01329i	−0.862156	+	0.506644i	$0.830886\pi$
$522$	−2.79226e6	−	48002.3i	−0.448518	−	0.00771055i
$523$			5.76389e6i			0.921428i	0.887549	+	0.460714i	$0.152407\pi$
$523$			5.76389e6i			0.921428i	−0.887549	+	0.460714i	$0.847593\pi$
$524$	−3.38084e6			−0.537894
$525$	−7.01421e6	−	60286.8i	−1.11066	−	0.00954605i
$526$	−3.53800e6			−0.557562
$527$	−8.08999e6			−1.26888
$528$	−143018.	+	257921.i	−0.0223258	+	0.0402627i
$529$	5.66157e6			0.879626
$530$	−1.02268e6			−0.158143
$531$	95878.5	−	5.57720e6i	0.0147566	−	0.858380i
$532$	−3.50005e6			−0.536160
$533$		−	4.20510e6i		−	0.641149i
$534$	4.70892e6	+	40472.9i	0.714609	+	0.00614202i
$535$		−	2.15601e6i		−	0.325662i
$536$	−3.71706e6			−0.558841
$537$	729059.	+	6266.22i	0.109101	+	0.000937713i
$538$		−	4.91064e6i		−	0.731446i
$539$	−2.09280e6	−	1.13706e6i	−0.310282	−	0.168582i
$540$	−859804.	−	22174.3i	−0.126886	−	0.00327239i
$541$			7.90557e6i			1.16129i	0.814157	+	0.580644i	$0.197199\pi$
$541$			7.90557e6i			1.16129i	−0.814157	+	0.580644i	$0.802801\pi$
$542$			1.24564e6i			0.182135i
$543$	15823.6	−	1.84104e6i	0.00230306	−	0.267955i
$544$	7.15672e6			1.03685
$545$	1.82184e6			0.262736
$546$	−56500.1	+	6.57364e6i	−0.00811087	+	0.943679i
$547$		−	721261.i		−	0.103068i	−0.998671	−	0.0515341i	$-0.983589\pi$
$547$		−	721261.i		−	0.103068i	0.998671	−	0.0515341i	$-0.0164111\pi$
$548$		−	6.64549e6i		−	0.945312i
$549$	113796.	−	6.61943e6i	0.0161137	−	0.937323i
$550$	3.77732e6	+	2.05229e6i	0.532448	+	0.289289i
$551$			3.88754e6i			0.545502i
$552$	2.51761e6	+	21638.7i	0.351675	+	0.00302262i
$553$	1.66872e6			0.232044
$554$			6.90377e6i			0.955679i
$555$	1.72439e6	+	14821.0i	0.237631	+	0.00204242i
$556$			166669.i			0.0228648i
$557$	−8.49710e6			−1.16047			−0.580233	−	0.814450i	$-0.697039\pi$
$557$	−8.49710e6			−1.16047			−0.580233	+	0.814450i	$0.697039\pi$
$558$	5.62252e6	+	96657.6i	0.764444	+	0.0131417i
$559$	−1.62550e7			−2.20018
$560$	84461.7			0.0113812
$561$	3.80736e6	−	6.86624e6i	0.510759	−	0.921111i
$562$	−5.45013e6			−0.727891
$563$	−1.78249e6			−0.237005			−0.118502	−	0.992954i	$-0.537809\pi$
$563$	−1.78249e6			−0.237005			−0.118502	+	0.992954i	$0.537809\pi$
$564$	3.36331e6	+	28907.4i	0.445214	+	0.00382659i
$565$	−2.48767e6			−0.327848
$566$			703591.i			0.0923165i
$567$	306079.	−	8.89958e6i	0.0399830	−	1.16255i
$568$		−	1.03610e7i		−	1.34750i
$569$	1.16476e7			1.50819			0.754094	−	0.656767i	$-0.228076\pi$
$569$	1.16476e7			1.50819			0.754094	+	0.656767i	$0.228076\pi$
$570$	6939.07	−	807344.i	0.000894570	−	0.104081i
$571$			7.50760e6i			0.963632i	0.876272	+	0.481816i	$0.160023\pi$
$571$			7.50760e6i			0.963632i	−0.876272	+	0.481816i	$0.839977\pi$
$572$	−2.85227e6	+	5.24971e6i	−0.364502	+	0.670880i
$573$	8.43291e6	+	72480.4i	1.07298	+	0.00922219i
$574$		−	2.92260e6i		−	0.370245i
$575$		−	2.62642e6i		−	0.331280i
$576$	−5.34043e6	−	91808.2i	−0.670688	−	0.0115299i
$577$	−1.53192e7			−1.91557			−0.957784	−	0.287488i	$-0.907180\pi$
$577$	−1.53192e7			−1.91557			−0.957784	+	0.287488i	$0.907180\pi$
$578$	557237.			0.0693778
$579$	9.52371e6	+	81855.7i	1.18062	+	0.0101474i
$580$			726871.i			0.0897196i
$581$			7.77762e6i			0.955887i
$582$	47781.4	−	5.55924e6i	0.00584725	−	0.680312i
$583$	4.59399e6	−	8.45541e6i	0.559781	−	1.03030i
$584$		−	2.20656e6i		−	0.267722i
$585$	2.24845e6	+	38653.4i	0.271639	+	0.00466980i
$586$	9.88986e6			1.18972
$587$		−	2.66999e6i		−	0.319826i	−0.987131	−	0.159913i	$-0.948879\pi$
$587$		−	2.66999e6i		−	0.319826i	0.987131	−	0.159913i	$-0.0511214\pi$
$588$	15196.8	−	1.76811e6i	0.00181263	−	0.210895i
$589$		−	7.82798e6i		−	0.929740i
$590$	979022.			0.115788
$591$	49022.6	−	5.70365e6i	0.00577334	−	0.671714i
$592$	438975.			0.0514797
$593$	−814291.			−0.0950918			−0.0475459	−	0.998869i	$-0.515140\pi$
$593$	−814291.			−0.0950918			−0.0475459	+	0.998869i	$0.515140\pi$
$594$	−2.72814e6	+	4.72653e6i	−0.317249	+	0.549637i
$595$	−2.24849e6			−0.260375
$596$	−6.76774e6			−0.780419
$597$	−29258.0	+	3.40410e6i	−0.00335977	+	0.390900i
$598$	−2.46145e6			−0.281474
$599$		−	1.21744e6i		−	0.138637i	−0.997595	−	0.0693187i	$-0.977917\pi$
$599$		−	1.21744e6i		−	0.138637i	0.997595	−	0.0693187i	$-0.0220825\pi$
$600$	−73354.0	+	8.53455e6i	−0.00831851	+	0.967837i
$601$		−	3.13293e6i		−	0.353806i	−0.984228	−	0.176903i	$-0.943392\pi$
$601$		−	3.13293e6i		−	0.353806i	0.984228	−	0.176903i	$-0.0566078\pi$
$602$	−1.12974e7			−1.27054
$603$	−4.92183e6	−	84612.0i	−0.551231	−	0.00947630i
$604$			9.42757e6i			1.05150i
$605$	1.60524e6	−	1.04117e6i	0.178300	−	0.115647i
$606$	−4046.71	+	470824.i	−0.000447631	+	0.0520808i
$607$		−	1.32997e7i		−	1.46511i	−0.680707	−	0.732556i	$-0.738327\pi$
$607$		−	1.32997e7i		−	1.46511i	0.680707	−	0.732556i	$-0.261673\pi$
$608$			6.92494e6i			0.759726i
$609$	−7.52529e6	−	64679.5i	−0.822205	−	0.00706681i
$610$	1.16198e6			0.126436
$611$	−8.79398e6			−0.952977
$612$	5.82775e6	+	100186.i	0.628959	+	0.0108125i
$613$			2.10731e6i			0.226504i	0.993566	+	0.113252i	$0.0361268\pi$
$613$			2.10731e6i			0.226504i	−0.993566	+	0.113252i	$0.963873\pi$
$614$			2.45748e6i			0.263068i
$615$	−999718.	−	8592.52i	−0.106583	−	0.000916079i
$616$	−5.30149e6	+	9.75759e6i	−0.562919	+	1.03607i
$617$		−	4.13947e6i		−	0.437756i	−0.975752	−	0.218878i	$-0.929760\pi$
$617$		−	4.13947e6i		−	0.437756i	0.975752	−	0.218878i	$-0.0702397\pi$
$618$	5581.16	−	649354.i	0.000587832	−	0.0683928i
$619$	−5.30546e6			−0.556540			−0.278270	−	0.960503i	$-0.589761\pi$
$619$	−5.30546e6			−0.556540			−0.278270	+	0.960503i	$0.589761\pi$
$620$		−	1.46363e6i		−	0.152916i
$621$	3.33312e6	+	85961.0i	0.346835	+	0.00894484i
$622$		−	1.48978e6i		−	0.154400i
$623$	1.26898e7			1.30989
$624$	572426.	+	4919.97i	0.0588516	+	0.000505826i
$625$	8.46235e6			0.866544
$626$	4.60479e6			0.469649
$627$	6.64387e6	+	3.68405e6i	0.674920	+	0.374245i
$628$	1.80527e6			0.182660
$629$	−1.16862e7			−1.17773
$630$	1.56270e6	+	26864.5i	0.156864	+	0.00269667i
$631$	8.10190e6			0.810053			0.405027	−	0.914305i	$-0.367262\pi$
$631$	8.10190e6			0.810053			0.405027	+	0.914305i	$0.367262\pi$
$632$		−	2.03042e6i		−	0.202205i
$633$	−1.08669e7	−	93400.0i	−1.07794	−	0.00926483i
$634$			9.72293e6i			0.960670i
$635$	−1.39076e6			−0.136873
$636$	7.14357e6	+	61398.6i	0.700281	+	0.00601888i
$637$			4.62304e6i			0.451418i
$638$	4.05255e6	+	2.20183e6i	0.394164	+	0.214157i
$639$	235848.	−	1.37191e7i	0.0228497	−	1.32915i
$640$			1.23044e6i			0.118744i
$641$			1.82583e6i			0.175515i	0.996142	+	0.0877576i	$0.0279701\pi$
$641$			1.82583e6i			0.175515i	−0.996142	+	0.0877576i	$0.972030\pi$
$642$	87286.5	−	1.01556e7i	0.00835813	−	0.972447i
$643$	−3.69890e6			−0.352813			−0.176407	−	0.984317i	$-0.556447\pi$
$643$	−3.69890e6			−0.352813			−0.176407	+	0.984317i	$0.556447\pi$
$644$	2.53692e6			0.241042
$645$	−33214.7	+	3.86445e6i	−0.00314363	+	0.365753i
$646$			5.47136e6i			0.515839i
$647$			1.07732e7i			1.01178i	0.862599	+	0.505888i	$0.168835\pi$
$647$			1.07732e7i			1.01178i	−0.862599	+	0.505888i	$0.831165\pi$
$648$	−1.08286e7	−	372421.i	−1.01306	−	0.0348415i
$649$	−4.39788e6	+	8.09446e6i	−0.409856	+	0.754356i
$650$		−	8.34418e6i		−	0.774640i
$651$	1.51530e7	+	130239.i	1.40135	+	0.0120445i
$652$	5.66297e6			0.521706
$653$		−	1.06326e7i		−	0.975791i	−0.872902	−	0.487896i	$-0.837765\pi$
$653$		−	1.06326e7i		−	0.975791i	0.872902	−	0.487896i	$-0.162235\pi$
$654$	8.58149e6	+	73757.4i	0.784546	+	0.00674313i
$655$		−	2.10157e6i		−	0.191400i
$656$	−254497.			−0.0230899
$657$	50228.3	−	2.92175e6i	0.00453978	−	0.264077i
$658$	−6.11191e6			−0.550316
$659$	6.09424e6			0.546645			0.273323	−	0.961922i	$-0.411877\pi$
$659$	6.09424e6			0.546645			0.273323	+	0.961922i	$0.411877\pi$
$660$	1.24223e6	+	688822.i	0.111005	+	0.0615527i
$661$	1.01212e7			0.901004			0.450502	−	0.892775i	$-0.351245\pi$
$661$	1.01212e7			0.901004			0.450502	+	0.892775i	$0.351245\pi$
$662$	−3.96782e6			−0.351890
$663$	−1.52388e7	−	130977.i	−1.34638	−	0.0115721i
$664$	9.46342e6			0.832968
$665$		−	2.17567e6i		−	0.190783i
$666$	8.12185e6	+	139624.i	0.709528	+	0.0121976i
$667$		−	2.81779e6i		−	0.245242i
$668$	1.09134e7			0.946281
$669$	−151593.	+	1.76374e7i	−0.0130952	+	1.52360i
$670$		−	863980.i		−	0.0743561i
$671$	−5.21972e6	+	9.60710e6i	−0.447549	+	0.823732i
$672$	−1.34049e7	−	115214.i	−1.14509	−	0.00984201i
$673$			1.28100e7i			1.09022i	0.838366	+	0.545108i	$0.183511\pi$
$673$			1.28100e7i			1.09022i	−0.838366	+	0.545108i	$0.816489\pi$
$674$		−	4.31857e6i		−	0.366176i
$675$	−291403.	+	1.12991e7i	−0.0246169	+	0.954517i
$676$	4.50053e6			0.378788
$677$	1.11938e7			0.938656			0.469328	−	0.883024i	$-0.344496\pi$
$677$	1.11938e7			0.938656			0.469328	+	0.883024i	$0.344496\pi$
$678$	−1.17178e7	−	100714.i	−0.978974	−	0.00841423i
$679$		−	1.49813e7i		−	1.24703i
$680$			2.73585e6i			0.226893i
$681$	−179093.	+	2.08371e7i	−0.0147983	+	1.72174i
$682$	−8.16024e6	−	4.43361e6i	−0.671803	−	0.365003i
$683$			577600.i			0.0473779i	0.999719	+	0.0236889i	$0.00754113\pi$
$683$			577600.i			0.0473779i	−0.999719	+	0.0236889i	$0.992459\pi$
$684$	−96941.0	+	5.63900e6i	−0.00792259	+	0.460853i
$685$	4.13091e6			0.336372
$686$		−	5.88597e6i		−	0.477538i
$687$	125471.	−	1.45982e7i	0.0101426	−	1.18007i
$688$			983768.i			0.0792358i
$689$	−1.86782e7			−1.49895
$690$	−5029.62	+	585184.i	−0.000402173	+	0.0467918i
$691$	7.05063e6			0.561737			0.280868	−	0.959746i	$-0.409378\pi$
$691$	7.05063e6			0.561737			0.280868	+	0.959746i	$0.409378\pi$
$692$	241916.			0.0192043
$693$	−7.24191e6	+	1.27995e7i	−0.572823	+	1.01242i
$694$	5.79570e6			0.456780
$695$	−103603.			−0.00813601
$696$	−78698.8	+	9.15640e6i	−0.00615808	+	0.716476i
$697$	6.77508e6			0.528241
$698$		−	1.13870e7i		−	0.884648i
$699$	90525.8	−	1.05324e7i	0.00700777	−	0.815336i
$700$			8.60002e6i			0.663367i
$701$	5.52192e6			0.424419			0.212209	−	0.977224i	$-0.431934\pi$
$701$	5.52192e6			0.424419			0.212209	+	0.977224i	$0.431934\pi$
$702$	1.05894e7	+	273099.i	0.811012	+	0.0209159i
$703$		−	1.13077e7i		−	0.862949i
$704$	7.75083e6	+	4.21118e6i	0.589409	+	0.320237i
$705$	−17969.2	+	2.09067e6i	−0.00136162	+	0.158421i
$706$		−	2.42478e6i		−	0.183088i
$707$			1.26880e6i			0.0954652i
$708$	−6.83862e6	−	58777.6i	−0.512726	−	0.00440685i
$709$	−9.02213e6			−0.674052			−0.337026	−	0.941495i	$-0.609421\pi$
$709$	−9.02213e6			−0.674052			−0.337026	+	0.941495i	$0.609421\pi$
$710$	2.40826e6			0.179291
$711$	46218.7	−	2.68851e6i	0.00342881	−	0.199452i
$712$		−	1.54404e7i		−	1.14145i
$713$			5.67392e6i			0.417984i
$714$	−1.05912e7	−	91030.4i	−0.777495	−	0.00668253i
$715$	−3.26328e6	−	1.77300e6i	−0.238720	−	0.129701i
$716$		−	893888.i		−	0.0651629i
$717$	79897.6	−	9.29588e6i	0.00580411	−	0.675294i
$718$	−8.90505e6			−0.644652
$719$			1.01462e7i			0.731949i	0.930625	+	0.365974i	$0.119264\pi$
$719$			1.01462e7i			0.731949i	−0.930625	+	0.365974i	$0.880736\pi$
$720$	2339.34	−	136078.i	0.000168175	−	0.00978266i
$721$		−	1.74991e6i		−	0.125365i
$722$	3.59498e6			0.256657
$723$	−1.93790e7	−	166561.i	−1.37875	−	0.0118503i
$724$	−2.25726e6			−0.160043
$725$	9.55215e6			0.674926
$726$	7.60337e6	−	4.83929e6i	0.535383	−	0.340754i
$727$	−1.92374e7			−1.34993			−0.674965	−	0.737850i	$-0.735841\pi$
$727$	−1.92374e7			−1.34993			−0.674965	+	0.737850i	$0.735841\pi$
$728$	2.15547e7			1.50735
$729$	−1.43298e7	−	739622.i	−0.998671	−	0.0515456i
$730$	512885.			0.0356215
$731$		−	2.61893e7i		−	1.81272i
$732$	−8.11658e6	−	69761.5i	−0.559880	−	0.00481214i
$733$			1.22590e7i			0.842743i	0.906888	+	0.421371i	$0.138451\pi$
$733$			1.22590e7i			0.842743i	−0.906888	+	0.421371i	$0.861549\pi$
$734$	−8.86164e6			−0.607119
$735$	1.09908e6	+	9446.52i	0.0750430	+	0.000644990i
$736$		−	5.01938e6i		−	0.341551i
$737$	7.14330e6	+	3.88109e6i	0.484429	+	0.263200i
$738$	−4.70866e6	−	80947.3i	−0.318241	−	0.00547094i
$739$		−	1.89627e6i		−	0.127729i	−0.997959	−	0.0638645i	$-0.979657\pi$
$739$		−	1.89627e6i		−	0.127729i	0.997959	−	0.0638645i	$-0.0203425\pi$
$740$		−	2.11425e6i		−	0.141931i
$741$	126735.	−	1.47453e7i	0.00847912	−	0.986524i
$742$	−1.29815e7			−0.865598
$743$	6.60277e6			0.438787			0.219394	−	0.975636i	$-0.429592\pi$
$743$	6.60277e6			0.438787			0.219394	+	0.975636i	$0.429592\pi$
$744$	158468.	−	1.84374e7i	0.0104957	−	1.22114i
$745$		−	4.20691e6i		−	0.277698i
$746$			7.78278e6i			0.512021i
$747$	1.25307e7	+	215417.i	0.821625	+	0.0141247i
$748$	−8.45809e6	−	4.59544e6i	−0.552737	−	0.300313i
$749$		−	2.73677e7i		−	1.78252i
$750$	−4.06131e6	−	34906.7i	−0.263641	−	0.00226598i
$751$	3.98388e6			0.257754			0.128877	−	0.991661i	$-0.458863\pi$
$751$	3.98388e6			0.257754			0.128877	+	0.991661i	$0.458863\pi$
$752$			532220.i			0.0343199i
$753$	2.75230e7	+	236559.i	1.76892	+	0.0152038i
$754$		−	8.95216e6i		−	0.573455i
$755$	−5.86029e6			−0.374155
$756$	−1.09141e7	−	281473.i	−0.694515	−	0.0179115i
$757$	1.21560e7			0.770994			0.385497	−	0.922709i	$-0.374030\pi$
$757$	1.21560e7			0.770994			0.385497	+	0.922709i	$0.374030\pi$
$758$	1.34008e7			0.847143
$759$	−4.81565e6	−	2.67029e6i	−0.303424	−	0.168250i
$760$	−2.64725e6			−0.166250
$761$	−1.46323e7			−0.915904			−0.457952	−	0.888977i	$-0.651417\pi$
$761$	−1.46323e7			−0.915904			−0.457952	+	0.888977i	$0.651417\pi$
$762$	−6.55096e6	−	56305.2i	−0.408712	−	0.00351286i
$763$	2.31258e7			1.43809
$764$		−	1.03395e7i		−	0.640862i
$765$	−62276.6	+	3.62260e6i	−0.00384744	+	0.223803i
$766$			7.82616e6i			0.481922i
$767$	1.78808e7			1.09749
$768$	−144050.	+	1.67599e7i	−0.00881273	+	1.02534i
$769$		−	6.23273e6i		−	0.380069i	−0.981777	−	0.190034i	$-0.939140\pi$
$769$		−	6.23273e6i		−	0.380069i	0.981777	−	0.190034i	$-0.0608600\pi$
$770$	−2.26802e6	−	1.23226e6i	−0.137854	−	0.0748987i
$771$	−5.42128e6	−	46595.6i	−0.328447	−	0.00282299i
$772$		−	1.16769e7i		−	0.705153i
$773$			2.38906e7i			1.43806i	0.694978	+	0.719031i	$0.255414\pi$
$773$			2.38906e7i			1.43806i	−0.694978	+	0.719031i	$0.744586\pi$
$774$	−312905.	+	1.82015e7i	−0.0187741	+	1.09208i
$775$	−1.92343e7

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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	33.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+3.58998 q^{2} +(0.133977 - 15.5879i) q^{3} -19.1121 q^{4} -11.8803i q^{5} +(0.480974 - 55.9601i) q^{6} -150.804i q^{7} -183.491 q^{8} +(-242.964 - 4.17684i) q^{9} +O(q^{10})\)	\(q+3.58998 q^{2} +(0.133977 - 15.5879i) q^{3} -19.1121 q^{4} -11.8803i q^{5} +(0.480974 - 55.9601i) q^{6} -150.804i q^{7} -183.491 q^{8} +(-242.964 - 4.17684i) q^{9} -42.6500i q^{10} +(352.626 + 191.588i) q^{11} +(-2.56058 + 297.917i) q^{12} -778.957i q^{13} -541.384i q^{14} +(-185.188 - 1.59169i) q^{15} -47.1432 q^{16} +1255.02 q^{17} +(-872.236 - 14.9947i) q^{18} +1214.37i q^{19} +227.057i q^{20} +(-2350.72 - 20.2043i) q^{21} +(1265.92 + 687.798i) q^{22} -880.210i q^{23} +(-24.5836 + 2860.24i) q^{24} +2983.86 q^{25} -2796.44i q^{26} +(-97.6596 + 3786.74i) q^{27} +2882.18i q^{28} +3201.27 q^{29} +(-664.823 - 5.71411i) q^{30} -6446.10 q^{31} +5702.47 q^{32} +(3033.70 - 5471.02i) q^{33} +4505.50 q^{34} -1791.60 q^{35} +(4643.54 + 79.8279i) q^{36} -9311.53 q^{37} +4359.58i q^{38} +(-12142.3 - 104.362i) q^{39} +2179.93i q^{40} +5398.38 q^{41} +(-8439.03 - 72.5330i) q^{42} -20867.6i q^{43} +(-6739.40 - 3661.65i) q^{44} +(-49.6220 + 2886.48i) q^{45} -3159.93i q^{46} -11289.4i q^{47} +(-6.31611 + 734.863i) q^{48} -5934.91 q^{49} +10712.0 q^{50} +(168.144 - 19563.1i) q^{51} +14887.5i q^{52} -23978.4i q^{53} +(-350.596 + 13594.3i) q^{54} +(2276.12 - 4189.29i) q^{55} +27671.2i q^{56} +(18929.5 + 162.698i) q^{57} +11492.5 q^{58} +22954.8i q^{59} +(3539.33 + 30.4204i) q^{60} +27244.5i q^{61} -23141.4 q^{62} +(-629.884 + 36640.0i) q^{63} +21980.3 q^{64} -9254.23 q^{65} +(10890.9 - 19640.8i) q^{66} +20257.5 q^{67} -23986.0 q^{68} +(-13720.6 - 117.928i) q^{69} -6431.79 q^{70} +56465.7i q^{71} +(44581.8 + 766.412i) q^{72} +12025.4i q^{73} -33428.2 q^{74} +(399.768 - 46512.0i) q^{75} -23209.2i q^{76} +(28892.3 - 53177.5i) q^{77} +(-43590.5 - 374.658i) q^{78} +11065.5i q^{79} +560.075i q^{80} +(59014.1 + 2029.64i) q^{81} +19380.1 q^{82} -51574.3 q^{83} +(44927.1 + 386.146i) q^{84} -14910.0i q^{85} -74914.4i q^{86} +(428.897 - 49901.1i) q^{87} +(-64703.7 - 35154.8i) q^{88} +84147.7i q^{89} +(-178.142 + 10362.4i) q^{90} -117470. q^{91} +16822.6i q^{92} +(-863.629 + 100481. i) q^{93} -40528.8i q^{94} +14427.1 q^{95} +(764.000 - 88889.5i) q^{96} +99342.9 q^{97} -21306.2 q^{98} +(-84875.2 - 48021.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16q - 54q^{3} + 316q^{4} - 222q^{9} + O(q^{10}) \)	\( 16q - 54q^{3} + 316q^{4} - 222q^{9} - 552q^{12} - 1674q^{15} + 1684q^{16} + 7932q^{22} - 1356q^{25} - 3240q^{27} - 11980q^{31} - 5106q^{33} - 34032q^{34} + 14016q^{36} + 9356q^{37} + 45912q^{42} + 77430q^{45} - 78012q^{48} - 1136q^{49} + 117308q^{55} + 31848q^{58} - 220548q^{60} + 5860q^{64} - 164796q^{66} - 364132q^{67} + 113790q^{69} + 231144q^{70} + 320364q^{75} + 296088q^{78} - 251334q^{81} + 4824q^{82} + 586836q^{88} - 209184q^{91} - 521046q^{93} + 119852q^{97} - 243894q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

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Fields

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Groups

Properties

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