LMFDB - Embedded newform 177.3.b.a.119.20

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	177.b (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.82290067918$
Analytic rank:	$0$
Dimension:	$38$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			119.20
Character	$\chi$	$=$	177.119
Dual form			177.3.b.a.119.19

$q$-expansion

$f(q)$	$=$	$q+0.00789729i q^{2} +(2.45651 - 1.72208i) q^{3} +3.99994 q^{4} -4.78355i q^{5} +(0.0135997 + 0.0193998i) q^{6} +0.326558 q^{7} +0.0631778i q^{8} +(3.06891 - 8.46060i) q^{9} +O(q^{10})$	\(q+0.00789729i q^{2} +(2.45651 - 1.72208i) q^{3} +3.99994 q^{4} -4.78355i q^{5} +(0.0135997 + 0.0193998i) q^{6} +0.326558 q^{7} +0.0631778i q^{8} +(3.06891 - 8.46060i) q^{9} +0.0377771 q^{10} +7.17249i q^{11} +(9.82590 - 6.88819i) q^{12} -19.3728 q^{13} +0.00257892i q^{14} +(-8.23763 - 11.7509i) q^{15} +15.9993 q^{16} +10.2788i q^{17} +(0.0668158 + 0.0242361i) q^{18} -1.08623 q^{19} -19.1339i q^{20} +(0.802193 - 0.562357i) q^{21} -0.0566432 q^{22} +32.0040i q^{23} +(0.108797 + 0.155197i) q^{24} +2.11765 q^{25} -0.152993i q^{26} +(-7.03097 - 26.0685i) q^{27} +1.30621 q^{28} -29.7395i q^{29} +(0.0927999 - 0.0650550i) q^{30} +41.9784 q^{31} +0.379062i q^{32} +(12.3516 + 17.6193i) q^{33} -0.0811747 q^{34} -1.56211i q^{35} +(12.2755 - 33.8419i) q^{36} +15.1073 q^{37} -0.00857827i q^{38} +(-47.5895 + 33.3614i) q^{39} +0.302214 q^{40} -12.5253i q^{41} +(0.00444110 + 0.00633515i) q^{42} +1.19642 q^{43} +28.6895i q^{44} +(-40.4717 - 14.6803i) q^{45} -0.252745 q^{46} +75.4877i q^{47} +(39.3024 - 27.5519i) q^{48} -48.8934 q^{49} +0.0167237i q^{50} +(17.7009 + 25.2500i) q^{51} -77.4899 q^{52} +69.0255i q^{53} +(0.205870 - 0.0555256i) q^{54} +34.3100 q^{55} +0.0206312i q^{56} +(-2.66834 + 1.87057i) q^{57} +0.234861 q^{58} -7.68115i q^{59} +(-32.9500 - 47.0027i) q^{60} -87.2267 q^{61} +0.331516i q^{62} +(1.00218 - 2.76287i) q^{63} +63.9940 q^{64} +92.6707i q^{65} +(-0.139145 + 0.0975439i) q^{66} -37.6499 q^{67} +41.1146i q^{68} +(55.1133 + 78.6182i) q^{69} +0.0123364 q^{70} +36.3578i q^{71} +(0.534522 + 0.193887i) q^{72} +25.2915 q^{73} +0.119307i q^{74} +(5.20203 - 3.64675i) q^{75} -4.34485 q^{76} +2.34223i q^{77} +(-0.263465 - 0.375828i) q^{78} -103.938 q^{79} -76.5332i q^{80} +(-62.1635 - 51.9297i) q^{81} +0.0989162 q^{82} -72.1954i q^{83} +(3.20872 - 2.24939i) q^{84} +49.1692 q^{85} +0.00944845i q^{86} +(-51.2136 - 73.0554i) q^{87} -0.453142 q^{88} -143.843i q^{89} +(0.115935 - 0.319617i) q^{90} -6.32633 q^{91} +128.014i q^{92} +(103.120 - 72.2900i) q^{93} -0.596149 q^{94} +5.19603i q^{95} +(0.652773 + 0.931171i) q^{96} +57.9703 q^{97} -0.386125i q^{98} +(60.6836 + 22.0117i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38q - 76q^{4} - 8q^{6} - 12q^{7} + 20q^{9} + O(q^{10}) $	$ 38q - 76q^{4} - 8q^{6} - 12q^{7} + 20q^{9} + 36q^{10} - 4q^{13} - 17q^{15} + 100q^{16} - 2q^{18} - 28q^{19} - 11q^{21} + 84q^{22} - 6q^{24} - 166q^{25} + 3q^{27} + 12q^{28} + 102q^{30} - 40q^{31} - 46q^{33} - 148q^{34} - 96q^{36} + 112q^{37} + 62q^{39} - 56q^{40} + 14q^{42} + 164q^{43} + 55q^{45} - 4q^{46} - 124q^{48} + 242q^{49} + 52q^{51} + 8q^{52} + 18q^{54} - 228q^{55} - 147q^{57} - 80q^{58} + 128q^{60} + 12q^{61} + 86q^{63} + 48q^{64} - 24q^{66} + 124q^{67} - 240q^{69} + 148q^{70} + 166q^{72} - 192q^{73} - 78q^{75} - 304q^{76} + 244q^{78} + 64q^{79} - 156q^{81} - 180q^{82} + 300q^{84} - 52q^{85} - 83q^{87} - 96q^{88} - 376q^{90} - 332q^{91} + 454q^{93} + 768q^{94} - 722q^{96} + 416q^{97} + 494q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$1$	$-1$

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 $

$2$			0.00789729i			0.00394865i	0.999998	+	0.00197432i	$0.000628447\pi$
$2$			0.00789729i			0.00394865i	−0.999998	+	0.00197432i	$0.999372\pi$
$3$	2.45651	−	1.72208i	0.818838	−	0.574025i
$3$	2.45651	−	1.72208i	0.818838	−	0.574025i
$4$	3.99994			0.999984
$5$		−	4.78355i		−	0.956710i	−0.878167	−	0.478355i	$-0.841233\pi$
$5$		−	4.78355i		−	0.956710i	0.878167	−	0.478355i	$-0.158767\pi$
$6$	0.0135997	+	0.0193998i	0.00226662	+	0.00323330i
$7$	0.326558			0.0466511			0.0233255	−	0.999728i	$-0.492575\pi$
$7$	0.326558			0.0466511			0.0233255	+	0.999728i	$0.492575\pi$
$8$			0.0631778i			0.00789723i
$9$	3.06891	−	8.46060i	0.340990	−	0.940067i
$10$	0.0377771			0.00377771
$11$			7.17249i			0.652044i	0.945362	+	0.326022i	$0.105708\pi$
$11$			7.17249i			0.652044i	−0.945362	+	0.326022i	$0.894292\pi$
$12$	9.82590	−	6.88819i	0.818825	−	0.574016i
$13$	−19.3728			−1.49021			−0.745107	−	0.666945i	$-0.767602\pi$
$13$	−19.3728			−1.49021			−0.745107	+	0.666945i	$0.767602\pi$
$14$			0.00257892i			0.000184209i
$15$	−8.23763	−	11.7509i	−0.549176	−	0.783390i
$16$	15.9993			0.999953
$17$			10.2788i			0.604635i	0.953207	+	0.302318i	$0.0977603\pi$
$17$			10.2788i			0.604635i	−0.953207	+	0.302318i	$0.902240\pi$
$18$	0.0668158	+	0.0242361i	0.00371199	+	0.00134645i
$19$	−1.08623			−0.0571700			−0.0285850	−	0.999591i	$-0.509100\pi$
$19$	−1.08623			−0.0571700			−0.0285850	+	0.999591i	$0.509100\pi$
$20$		−	19.1339i		−	0.956695i
$21$	0.802193	−	0.562357i	0.0381997	−	0.0267789i
$22$	−0.0566432			−0.00257469
$23$			32.0040i			1.39148i	0.718295	+	0.695739i	$0.244923\pi$
$23$			32.0040i			1.39148i	−0.718295	+	0.695739i	$0.755077\pi$
$24$	0.108797	+	0.155197i	0.00453321	+	0.00646655i
$25$	2.11765			0.0847058
$26$		−	0.152993i		−	0.00588433i
$27$	−7.03097	−	26.0685i	−0.260406	−	0.965499i
$28$	1.30621			0.0466504
$29$		−	29.7395i		−	1.02550i	−0.858538	−	0.512750i	$-0.828627\pi$
$29$		−	29.7395i		−	1.02550i	0.858538	−	0.512750i	$-0.171373\pi$
$30$	0.0927999	−	0.0650550i	0.00309333	−	0.00216850i
$31$	41.9784			1.35414			0.677071	−	0.735918i	$-0.263249\pi$
$31$	41.9784			1.35414			0.677071	+	0.735918i	$0.263249\pi$
$32$			0.379062i			0.0118457i
$33$	12.3516	+	17.6193i	0.374290	+	0.533918i
$34$	−0.0811747			−0.00238749
$35$		−	1.56211i		−	0.0446316i
$36$	12.2755	−	33.8419i	0.340985	−	0.940052i
$37$	15.1073			0.408305			0.204153	−	0.978939i	$-0.434556\pi$
$37$	15.1073			0.408305			0.204153	+	0.978939i	$0.434556\pi$
$38$		−	0.00857827i		−	0.000225744i
$39$	−47.5895	+	33.3614i	−1.22024	+	0.855420i
$40$	0.302214			0.00755536
$41$		−	12.5253i		−	0.305496i	−0.988265	−	0.152748i	$-0.951188\pi$
$41$		−	12.5253i		−	0.305496i	0.988265	−	0.152748i	$-0.0488123\pi$
$42$	0.00444110	+	0.00633515i	0.000105740	+	0.000150837i
$43$	1.19642			0.0278236			0.0139118	−	0.999903i	$-0.495572\pi$
$43$	1.19642			0.0278236			0.0139118	+	0.999903i	$0.495572\pi$
$44$			28.6895i			0.652034i
$45$	−40.4717	−	14.6803i	−0.899371	−	0.326229i
$46$	−0.252745			−0.00549445
$47$			75.4877i			1.60612i	0.595897	+	0.803061i	$0.296797\pi$
$47$			75.4877i			1.60612i	−0.595897	+	0.803061i	$0.703203\pi$
$48$	39.3024	−	27.5519i	0.818799	−	0.573998i
$49$	−48.8934			−0.997824
$50$			0.0167237i			0.000334473i
$51$	17.7009	+	25.2500i	0.347076	+	0.495098i
$52$	−77.4899			−1.49019
$53$			69.0255i			1.30237i	0.758920	+	0.651184i	$0.225727\pi$
$53$			69.0255i			1.30237i	−0.758920	+	0.651184i	$0.774273\pi$
$54$	0.205870	−	0.0555256i	0.00381241	−	0.00102825i
$55$	34.3100			0.623817
$56$			0.0206312i			0.000368414i
$57$	−2.66834	+	1.87057i	−0.0468129	+	0.0328170i
$58$	0.234861			0.00404933
$59$		−	7.68115i		−	0.130189i
$59$		−	7.68115i		−	0.130189i
$60$	−32.9500	−	47.0027i	−0.549167	−	0.783378i
$61$	−87.2267			−1.42995			−0.714973	−	0.699152i	$-0.753561\pi$
$61$	−87.2267			−1.42995			−0.714973	+	0.699152i	$0.753561\pi$
$62$			0.331516i			0.00534703i
$63$	1.00218	−	2.76287i	0.0159076	−	0.0438551i
$64$	63.9940			0.999906
$65$			92.6707i			1.42570i
$66$	−0.139145	+	0.0975439i	−0.00210825	+	0.00147794i
$67$	−37.6499			−0.561938			−0.280969	−	0.959717i	$-0.590656\pi$
$67$	−37.6499			−0.561938			−0.280969	+	0.959717i	$0.590656\pi$
$68$			41.1146i			0.604626i
$69$	55.1133	+	78.6182i	0.798743	+	1.13939i
$70$	0.0123364			0.000176234
$71$			36.3578i			0.512081i	0.966666	+	0.256041i	$0.0824181\pi$
$71$			36.3578i			0.512081i	−0.966666	+	0.256041i	$0.917582\pi$
$72$	0.534522	+	0.193887i	0.00742392	+	0.00269288i
$73$	25.2915			0.346459			0.173230	−	0.984881i	$-0.444580\pi$
$73$	25.2915			0.346459			0.173230	+	0.984881i	$0.444580\pi$
$74$			0.119307i			0.00161225i
$75$	5.20203	−	3.64675i	0.0693603	−	0.0486233i
$76$	−4.34485			−0.0571691
$77$			2.34223i			0.0304186i
$78$	−0.263465	−	0.375828i	−0.00337775	−	0.00481831i
$79$	−103.938			−1.31567			−0.657836	−	0.753161i	$-0.728528\pi$
$79$	−103.938			−1.31567			−0.657836	+	0.753161i	$0.728528\pi$
$80$		−	76.5332i		−	0.956665i
$81$	−62.1635	−	51.9297i	−0.767451	−	0.641107i
$82$	0.0989162			0.00120630
$83$		−	72.1954i		−	0.869824i	−0.900473	−	0.434912i	$-0.856780\pi$
$83$		−	72.1954i		−	0.869824i	0.900473	−	0.434912i	$-0.143220\pi$
$84$	3.20872	−	2.24939i	0.0381991	−	0.0267785i
$85$	49.1692			0.578461
$86$			0.00944845i			0.000109866i
$87$	−51.2136	−	73.0554i	−0.588662	−	0.839718i
$88$	−0.453142			−0.00514934
$89$		−	143.843i		−	1.61622i	−0.589034	−	0.808108i	$-0.700491\pi$
$89$		−	143.843i		−	1.61622i	0.589034	−	0.808108i	$-0.299509\pi$
$90$	0.115935	−	0.319617i	0.00128816	−	0.00355130i
$91$	−6.32633			−0.0695201
$92$			128.014i			1.39146i
$93$	103.120	−	72.2900i	1.10882	−	0.777311i
$94$	−0.596149			−0.00634201
$95$			5.19603i			0.0546951i
$96$	0.652773	+	0.931171i	0.00679972	+	0.00969970i
$97$	57.9703			0.597632			0.298816	−	0.954311i	$-0.403408\pi$
$97$	57.9703			0.597632			0.298816	+	0.954311i	$0.403408\pi$
$98$		−	0.386125i		−	0.00394005i
$99$	60.6836	+	22.0117i	0.612965	+	0.222341i
$100$	8.47045			0.0847045
$101$			139.103i			1.37726i	0.725113	+	0.688629i	$0.241787\pi$
$101$			139.103i			1.37726i	−0.725113	+	0.688629i	$0.758213\pi$
$102$	−0.199407	+	0.139789i	−0.00195497	+	0.00137048i
$103$	24.0668			0.233658			0.116829	−	0.993152i	$-0.462727\pi$
$103$	24.0668			0.233658			0.116829	+	0.993152i	$0.462727\pi$
$104$		−	1.22393i		−	0.0117686i
$105$	−2.69006	−	3.83733i	−0.0256196	−	0.0365460i
$106$	−0.545114			−0.00514259
$107$		−	17.8500i		−	0.166822i	−0.996515	−	0.0834111i	$-0.973419\pi$
$107$		−	17.8500i		−	0.166822i	0.996515	−	0.0834111i	$-0.0265815\pi$
$108$	−28.1234	−	104.272i	−0.260402	−	0.965484i
$109$	27.7625			0.254702			0.127351	−	0.991858i	$-0.459353\pi$
$109$	27.7625			0.254702			0.127351	+	0.991858i	$0.459353\pi$
$110$			0.270956i			0.00246323i
$111$	37.1112	−	26.0159i	0.334336	−	0.234377i
$112$	5.22468			0.0466489
$113$			5.59084i			0.0494764i	0.999694	+	0.0247382i	$0.00787522\pi$
$113$			5.59084i			0.0494764i	−0.999694	+	0.0247382i	$0.992125\pi$
$114$	−0.0147724	−	0.0210726i	−0.000129583	−	0.000184848i
$115$	153.093			1.33124
$116$		−	118.956i		−	1.02548i
$117$	−59.4534	+	163.905i	−0.508149	+	1.40090i
$118$	0.0606602			0.000514070
$119$			3.35662i			0.0282069i
$120$	0.742393	−	0.520436i	0.00618661	−	0.00433697i
$121$	69.5554			0.574838
$122$		−	0.688855i		−	0.00564635i
$123$	−21.5696	−	30.7687i	−0.175362	−	0.250152i
$124$	167.911			1.35412
$125$		−	129.719i		−	1.03775i
$126$	0.0218192	+	0.00791448i	0.000173168	+	6.28134e-5i
$127$	−21.7333			−0.171128			−0.0855641	−	0.996333i	$-0.527269\pi$
$127$	−21.7333			−0.171128			−0.0855641	+	0.996333i	$0.527269\pi$
$128$			2.02163i			0.0157940i
$129$	2.93901	−	2.06032i	0.0227831	−	0.0159715i
$130$	−0.731847			−0.00562960
$131$		−	234.990i		−	1.79382i	−0.442216	−	0.896909i	$-0.645808\pi$
$131$		−	234.990i		−	1.79382i	0.442216	−	0.896909i	$-0.354192\pi$
$132$	49.4055	+	70.4761i	0.374284	+	0.533910i
$133$	−0.354717			−0.00266704
$134$		−	0.297332i		−	0.00221889i
$135$	−124.700	+	33.6330i	−0.923703	+	0.249133i
$136$	−0.649392			−0.00477494
$137$			21.1075i			0.154069i	0.997028	+	0.0770346i	$0.0245452\pi$
$137$			21.1075i			0.154069i	−0.997028	+	0.0770346i	$0.975455\pi$
$138$	−0.620871	+	0.435246i	−0.00449906	+	0.00315395i
$139$	−166.049			−1.19459			−0.597297	−	0.802020i	$-0.703759\pi$
$139$	−166.049			−1.19459			−0.597297	+	0.802020i	$0.703759\pi$
$140$		−	6.24832i		−	0.0446309i
$141$	129.996	+	185.437i	0.921954	+	1.31515i
$142$	−0.287128			−0.00202203
$143$		−	138.951i		−	0.971686i
$144$	49.1003	−	135.363i	0.340974	−	0.940023i
$145$	−142.260			−0.981106
$146$			0.199735i			0.00136804i
$147$	−120.107	+	84.1981i	−0.817056	+	0.572776i
$148$	60.4282			0.408299
$149$		−	131.101i		−	0.879874i	−0.898029	−	0.439937i	$-0.855001\pi$
$149$		−	131.101i		−	0.879874i	0.898029	−	0.439937i	$-0.144999\pi$
$150$	0.0287994	+	0.0410819i	0.000191996	+	0.000273879i
$151$	−143.720			−0.951790			−0.475895	−	0.879502i	$-0.657876\pi$
$151$	−143.720			−0.951790			−0.475895	+	0.879502i	$0.657876\pi$
$152$		−	0.0686256i		−	0.000451484i
$153$	86.9648	+	31.5447i	0.568398	+	0.206175i
$154$	−0.0184973			−0.000120112
$155$		−	200.806i		−	1.29552i
$156$	−190.355	+	133.444i	−1.22022	+	0.855407i
$157$	−116.809			−0.744006			−0.372003	−	0.928231i	$-0.621329\pi$
$157$	−116.809			−0.744006			−0.372003	+	0.928231i	$0.621329\pi$
$158$		−	0.820829i		−	0.00519512i
$159$	118.867	+	169.562i	0.747592	+	1.06643i
$160$	1.81326			0.0113329
$161$			10.4511i			0.0649140i
$162$	0.410104	−	0.490924i	0.00253151	−	0.00303039i
$163$	240.382			1.47474			0.737369	−	0.675491i	$-0.236068\pi$
$163$	240.382			1.47474			0.737369	+	0.675491i	$0.236068\pi$
$164$		−	50.1006i		−	0.305491i
$165$	84.2828	−	59.0843i	0.510805	−	0.358087i
$166$	0.570148			0.00343463
$167$		−	153.282i		−	0.917859i	−0.888473	−	0.458929i	$-0.848233\pi$
$167$		−	153.282i		−	0.917859i	0.888473	−	0.458929i	$-0.151767\pi$
$168$	0.0355285	+	0.0506808i	0.000211479	+	0.000301672i
$169$	206.305			1.22074
$170$			0.388303i			0.00228414i
$171$	−3.33354	+	9.19015i	−0.0194944	+	0.0537436i
$172$	4.78559			0.0278232
$173$			198.430i			1.14699i	0.819208	+	0.573497i	$0.194414\pi$
$173$			198.430i			1.14699i	−0.819208	+	0.573497i	$0.805586\pi$
$174$	0.576940	−	0.404449i	0.00331575	−	0.00232442i
$175$	0.691534			0.00395162
$176$			114.754i			0.652014i
$177$	−13.2275	−	18.8688i	−0.0747317	−	0.106604i
$178$	1.13597			0.00638187
$179$			84.3641i			0.471308i	0.971837	+	0.235654i	$0.0757232\pi$
$179$			84.3641i			0.471308i	−0.971837	+	0.235654i	$0.924277\pi$
$180$	−161.884	−	58.7203i	−0.899357	−	0.326224i
$181$	−300.804			−1.66190			−0.830950	−	0.556348i	$-0.812202\pi$
$181$	−300.804			−1.66190			−0.830950	+	0.556348i	$0.812202\pi$
$182$		−	0.0499609i		−	0.000274510i
$183$	−214.274	+	150.211i	−1.17089	+	0.820825i
$184$	−2.02194			−0.0109888
$185$		−	72.2665i		−	0.390630i
$186$	0.570895	+	0.814372i	0.00306933	+	0.00437835i
$187$	−73.7246			−0.394249
$188$			301.946i			1.60610i
$189$	−2.29602	−	8.51286i	−0.0121482	−	0.0450416i
$190$	−0.0410346			−0.000215971
$191$		−	62.9427i		−	0.329543i	−0.986332	−	0.164771i	$-0.947311\pi$
$191$		−	62.9427i		−	0.329543i	0.986332	−	0.164771i	$-0.0526886\pi$
$192$	157.202	−	110.203i	0.818761	−	0.573971i
$193$	−52.7589			−0.273362			−0.136681	−	0.990615i	$-0.543644\pi$
$193$	−52.7589			−0.273362			−0.136681	+	0.990615i	$0.543644\pi$
$194$			0.457808i			0.00235984i
$195$	159.586	+	227.647i	0.818389	+	1.16742i
$196$	−195.570			−0.997808
$197$			43.3687i			0.220146i	0.993924	+	0.110073i	$0.0351084\pi$
$197$			43.3687i			0.220146i	−0.993924	+	0.110073i	$0.964892\pi$
$198$	−0.173833	+	0.479236i	−0.000877945	+	0.00242038i
$199$	316.929			1.59261			0.796304	−	0.604896i	$-0.206785\pi$
$199$	316.929			1.59261			0.796304	+	0.604896i	$0.206785\pi$
$200$			0.133788i			0.000668941i
$201$	−92.4874	+	64.8359i	−0.460136	+	0.322567i
$202$	−1.09854			−0.00543831
$203$		−	9.71166i		−	0.0478407i
$204$	70.8024	+	100.998i	0.347070	+	0.495090i
$205$	−59.9156			−0.292271
$206$			0.190062i			0.000922633i
$207$	270.773	+	98.2175i	1.30808	+	0.474481i
$208$	−309.950			−1.49014
$209$		−	7.79097i		−	0.0372773i
$210$	0.0303045	−	0.0212442i	0.000144307	−	0.000101163i
$211$	−6.60578			−0.0313070			−0.0156535	−	0.999877i	$-0.504983\pi$
$211$	−6.60578			−0.0313070			−0.0156535	+	0.999877i	$0.504983\pi$
$212$			276.098i			1.30235i
$213$	62.6108	+	89.3134i	0.293948	+	0.419312i
$214$	0.140967			0.000658722
$215$		−	5.72312i		−	0.0266192i
$216$	1.64695	−	0.444201i	0.00762477	−	0.00205649i
$217$	13.7084			0.0631722
$218$			0.219249i			0.00100573i
$219$	62.1290	−	43.5539i	0.283694	−	0.198876i
$220$	137.238			0.623808
$221$		−	199.129i		−	0.901036i
$222$	0.205455	+	0.293078i	0.000925473	+	0.00132017i
$223$	136.161			0.610587			0.305294	−	0.952258i	$-0.401245\pi$
$223$	136.161			0.610587			0.305294	+	0.952258i	$0.401245\pi$
$224$			0.123786i			0.000552614i
$225$	6.49887	−	17.9166i	0.0288839	−	0.0796292i
$226$	−0.0441525			−0.000195365
$227$		−	405.806i		−	1.78769i	−0.448376	−	0.893845i	$-0.647997\pi$
$227$		−	405.806i		−	1.78769i	0.448376	−	0.893845i	$-0.352003\pi$
$228$	−10.6732	+	7.48216i	−0.0468122	+	0.0328165i
$229$	−347.346			−1.51680			−0.758398	−	0.651791i	$-0.774018\pi$
$229$	−347.346			−1.51680			−0.758398	+	0.651791i	$0.774018\pi$
$230$			1.20902i			0.00525660i
$231$	4.03350	+	5.75372i	0.0174610	+	0.0249079i
$232$	1.87888			0.00809860
$233$			461.344i			1.98002i	0.141009	+	0.990008i	$0.454965\pi$
$233$			461.344i			1.98002i	−0.141009	+	0.990008i	$0.545035\pi$
$234$	−1.29441	−	0.469521i	−0.00553166	−	0.00200650i
$235$	361.099			1.53659
$236$		−	30.7241i		−	0.130187i
$237$	−255.325	+	178.989i	−1.07732	+	0.755229i
$238$	−0.0265082			−0.000111379
$239$		−	438.371i		−	1.83419i	−0.398670	−	0.917094i	$-0.630528\pi$
$239$		−	438.371i		−	1.83419i	0.398670	−	0.917094i	$-0.369472\pi$
$240$	−131.796	−	188.005i	−0.549150	−	0.783354i
$241$	−136.775			−0.567530			−0.283765	−	0.958894i	$-0.591584\pi$
$241$	−136.775			−0.567530			−0.283765	+	0.958894i	$0.591584\pi$
$242$			0.549299i			0.00226983i
$243$	−242.132	−	20.5157i	−0.996430	−	0.0844266i
$244$	−348.901			−1.42992
$245$			233.884i			0.954628i
$246$	0.242989	−	0.170341i	0.000987760	−	0.000692444i
$247$	21.0433			0.0851955
$248$			2.65210i			0.0106940i
$249$	−124.326	−	177.349i	−0.499301	−	0.712245i
$250$	1.02443			0.00409770
$251$			106.863i			0.425749i	0.977080	+	0.212875i	$0.0682826\pi$
$251$			106.863i			0.425749i	−0.977080	+	0.212875i	$0.931717\pi$
$252$	4.00865	−	11.0513i	0.0159073	−	0.0438545i
$253$	−229.548			−0.907305
$254$		−	0.171634i		−	0.000675724i
$255$	120.785	−	84.6730i	0.473665	−	0.332051i
$256$	255.960			0.999844
$257$		−	113.716i		−	0.442474i	−0.975220	−	0.221237i	$-0.928991\pi$
$257$		−	113.716i		−	0.442474i	0.975220	−	0.221237i	$-0.0710094\pi$
$258$	0.0162709	+	0.0232102i	6.30657e−5	+	8.99622e-5i
$259$	4.93340			0.0190479
$260$			370.677i			1.42568i
$261$	−251.614	−	91.2679i	−0.964038	−	0.349685i
$262$	1.85578			0.00708315
$263$			75.6208i			0.287532i	0.989612	+	0.143766i	$0.0459212\pi$
$263$			75.6208i			0.287532i	−0.989612	+	0.143766i	$0.954079\pi$
$264$	−1.11315	+	0.780345i	−0.00421648	+	0.00295585i
$265$	330.187			1.24599
$266$		−	0.00280130i		−	1.05312e-5i
$267$	−247.709	−	353.353i	−0.927749	−	1.32342i
$268$	−150.597			−0.561929
$269$		−	154.580i		−	0.574648i	−0.957833	−	0.287324i	$-0.907234\pi$
$269$		−	154.580i		−	0.574648i	0.957833	−	0.287324i	$-0.0927657\pi$
$270$	−0.265609	−	0.984791i	−0.000983739	−	0.00364737i
$271$	355.108			1.31036			0.655181	−	0.755472i	$-0.272592\pi$
$271$	355.108			1.31036			0.655181	+	0.755472i	$0.272592\pi$
$272$			164.453i			0.604607i
$273$	−15.5407	+	10.8944i	−0.0569257	+	0.0399063i
$274$	−0.166692			−0.000608365
$275$			15.1888i			0.0552320i
$276$	220.450	+	314.468i	0.798731	+	1.13938i
$277$	226.249			0.816783			0.408391	−	0.912807i	$-0.366090\pi$
$277$	226.249			0.816783			0.408391	+	0.912807i	$0.366090\pi$
$278$		−	1.31133i		−	0.00471703i
$279$	128.828	−	355.162i	0.461749	−	1.27298i
$280$	0.0986904			0.000352466
$281$			516.299i			1.83736i	0.394999	+	0.918681i	$0.370745\pi$
$281$			516.299i			1.83736i	−0.394999	+	0.918681i	$0.629255\pi$
$282$	−1.46445	+	1.02661i	−0.00519307	+	0.00364047i
$283$	−127.805			−0.451609			−0.225805	−	0.974173i	$-0.572501\pi$
$283$	−127.805			−0.451609			−0.225805	+	0.974173i	$0.572501\pi$
$284$			145.429i			0.512073i
$285$	8.94796	+	12.7641i	0.0313963	+	0.0447864i
$286$	1.09734			0.00383684
$287$		−	4.09025i		−	0.0142517i
$288$	3.20709	+	1.16331i	0.0111357	+	0.00403927i
$289$	183.346			0.634416
$290$		−	1.12347i		−	0.00387404i
$291$	142.405	−	99.8292i	0.489363	−	0.343056i
$292$	101.165			0.346454
$293$		−	469.558i		−	1.60259i	−0.598272	−	0.801293i	$-0.704146\pi$
$293$		−	469.558i		−	1.60259i	0.598272	−	0.801293i	$-0.295854\pi$
$294$	−0.664936	−	0.948521i	−0.00226169	−	0.00322626i
$295$	−36.7431			−0.124553
$296$			0.954446i			0.00322448i
$297$	186.976	−	50.4295i	0.629548	−	0.169796i
$298$	1.03534			0.00347431
$299$		−	620.007i		−	2.07360i
$300$	20.8078	−	14.5868i	0.0693593	−	0.0486225i
$301$	0.390699			0.00129800
$302$		−	1.13500i		−	0.00375828i
$303$	239.546	+	341.709i	0.790581	+	1.12775i
$304$	−17.3789			−0.0571673
$305$			417.253i			1.36804i
$306$	−0.249118	+	0.686787i	−0.000814111	+	0.00224440i
$307$	−199.843			−0.650953			−0.325477	−	0.945550i	$-0.605525\pi$
$307$	−199.843			−0.650953			−0.325477	+	0.945550i	$0.605525\pi$
$308$			9.36878i			0.0304181i
$309$	59.1204	−	41.4448i	0.191328	−	0.134126i
$310$	1.58582			0.00511555
$311$		−	281.008i		−	0.903563i	−0.892129	−	0.451782i	$-0.850789\pi$
$311$		−	281.008i		−	0.903563i	0.892129	−	0.451782i	$-0.149211\pi$
$312$	−2.10770	−	3.00660i	−0.00675545	−	0.00963654i
$313$	35.5922			0.113713			0.0568566	−	0.998382i	$-0.481892\pi$
$313$	35.5922			0.113713			0.0568566	+	0.998382i	$0.481892\pi$
$314$		−	0.922475i		−	0.00293782i
$315$	−13.2163	−	4.79396i	−0.0419567	−	0.0152189i
$316$	−415.746			−1.31565
$317$		−	31.7840i		−	0.100265i	−0.998743	−	0.0501324i	$-0.984036\pi$
$317$		−	31.7840i		−	0.100265i	0.998743	−	0.0501324i	$-0.0159643\pi$
$318$	−1.33908	+	0.938728i	−0.00421095	+	0.00295198i
$319$	213.306			0.668671
$320$		−	306.119i		−	0.956621i
$321$	−30.7390	−	43.8487i	−0.0957602	−	0.136600i
$322$	−0.0825358			−0.000256322
$323$		−	11.1651i		−	0.0345670i
$324$	−248.650	−	207.716i	−0.767439	−	0.641097i
$325$	−41.0247			−0.126230
$326$			1.89837i			0.00582321i
$327$	68.1990	−	47.8091i	0.208560	−	0.146205i
$328$	0.791324			0.00241257
$329$			24.6511i			0.0749273i
$330$	0.466606	+	0.665606i	0.00141396	+	0.00201699i
$331$	383.342			1.15813			0.579066	−	0.815281i	$-0.303417\pi$
$331$	383.342			1.15813			0.579066	+	0.815281i	$0.303417\pi$
$332$		−	288.777i		−	0.869810i
$333$	46.3630	−	127.817i	0.139228	−	0.383834i
$334$	1.21052			0.00362430
$335$			180.100i			0.537612i
$336$	12.8345	−	8.99729i	0.0381979	−	0.0267776i
$337$	294.098			0.872693			0.436346	−	0.899779i	$-0.356272\pi$
$337$	294.098			0.872693			0.436346	+	0.899779i	$0.356272\pi$
$338$			1.62925i			0.00482026i
$339$	9.62784	+	13.7340i	0.0284007	+	0.0405132i
$340$	196.674			0.578452
$341$			301.089i			0.882960i
$342$	−0.0725773	−	0.0263260i	−0.000212214	−	7.69765e-5i
$343$	−31.9678			−0.0932007
$344$			0.0755870i			0.000219730i
$345$	376.074	−	263.637i	1.09007	−	0.764166i
$346$	−1.56706			−0.00452907
$347$		−	260.831i		−	0.751674i	−0.926686	−	0.375837i	$-0.877355\pi$
$347$		−	260.831i		−	0.751674i	0.926686	−	0.375837i	$-0.122645\pi$
$348$	−204.851	−	292.217i	−0.588653	−	0.839704i
$349$	65.8252			0.188611			0.0943054	−	0.995543i	$-0.469937\pi$
$349$	65.8252			0.188611			0.0943054	+	0.995543i	$0.469937\pi$
$350$			0.00546124i			1.56035e-5i
$351$	136.209	+	505.019i	0.388061	+	1.43880i
$352$	−2.71882			−0.00772391
$353$		−	204.142i		−	0.578306i	−0.957283	−	0.289153i	$-0.906626\pi$
$353$		−	204.142i		−	0.578306i	0.957283	−	0.289153i	$-0.0933736\pi$
$354$	0.149013	−	0.104461i	0.000420940	−	0.000295089i
$355$	173.919			0.489913
$356$		−	575.364i		−	1.61619i
$357$	5.78035	+	8.24558i	0.0161915	+	0.0230969i
$358$	−0.666248			−0.00186103
$359$		−	347.563i		−	0.968142i	−0.875029	−	0.484071i	$-0.839158\pi$
$359$		−	347.563i		−	0.968142i	0.875029	−	0.484071i	$-0.160842\pi$
$360$	0.927469	−	2.55691i	0.00257630	−	0.00710254i
$361$	−359.820			−0.996732
$362$		−	2.37553i		−	0.00656225i
$363$	170.864	−	119.780i	0.470699	−	0.329972i
$364$	−25.3049			−0.0695190
$365$		−	120.983i		−	0.331461i
$366$	−1.18626	−	1.69218i	−0.00324115	−	0.00462344i
$367$	−147.776			−0.402659			−0.201329	−	0.979524i	$-0.564526\pi$
$367$	−147.776			−0.402659			−0.201329	+	0.979524i	$0.564526\pi$
$368$			512.040i			1.39141i
$369$	−105.972	−	38.4392i	−0.287187	−	0.104171i
$370$	0.570709			0.00154246
$371$			22.5408i			0.0607569i
$372$	412.475	−	289.155i	1.10881	−	0.777299i
$373$	−384.525			−1.03090			−0.515450	−	0.856920i	$-0.672375\pi$
$373$	−384.525			−1.03090			−0.515450	+	0.856920i	$0.672375\pi$
$374$		−	0.582224i		−	0.00155675i
$375$	−223.385	−	318.655i	−0.595694	−	0.849748i
$376$	−4.76915			−0.0126839
$377$			576.137i			1.52821i
$378$	0.0672285	−	0.0181323i	0.000177853	−	4.79691e-5i
$379$	341.583			0.901276			0.450638	−	0.892707i	$-0.351197\pi$
$379$	341.583			0.901276			0.450638	+	0.892707i	$0.351197\pi$
$380$			20.7838i			0.0546942i
$381$	−53.3881	+	37.4263i	−0.140126	+	0.0982319i
$382$	0.497077			0.00130125
$383$			537.530i			1.40347i	0.712437	+	0.701736i	$0.247591\pi$
$383$			537.530i			1.40347i	−0.712437	+	0.701736i	$0.752409\pi$
$384$	3.48139	+	4.96615i	0.00906613	+	0.0129327i
$385$	11.2042			0.0291018
$386$		−	0.416652i		−	0.00107941i
$387$	3.67170	−	10.1224i	0.00948759	−	0.0261561i
$388$	231.877			0.597622
$389$			551.322i			1.41728i	0.705570	+	0.708641i	$0.250691\pi$
$389$			551.322i			1.41728i	−0.705570	+	0.708641i	$0.749309\pi$
$390$	−1.79779	+	1.26030i	−0.00460972	+	0.00323153i
$391$	−328.963			−0.841337
$392$		−	3.08898i		−	0.00788004i
$393$	−404.671	−	577.256i	−1.02970	−	1.46885i
$394$	−0.342495			−0.000869277
$395$			497.193i			1.25872i
$396$	242.730	+	88.0456i	0.612956	+	0.222337i
$397$	−535.112			−1.34789			−0.673945	−	0.738781i	$-0.735402\pi$
$397$	−535.112			−1.34789			−0.673945	+	0.738781i	$0.735402\pi$
$398$			2.50288i			0.00628865i
$399$	−0.871366	+	0.610849i	−0.00218387	+	0.00153095i
$400$	33.8808			0.0847019
$401$			270.808i			0.675331i	0.941266	+	0.337666i	$0.109637\pi$
$401$			270.808i			0.675331i	−0.941266	+	0.337666i	$0.890363\pi$
$402$	−0.512028	−	0.730400i	−0.00127370	−	0.00181691i
$403$	−813.238			−2.01796
$404$			556.404i			1.37724i
$405$	−248.408	+	297.362i	−0.613354	+	0.734228i
$406$	0.0766958			0.000188906
$407$			108.357i			0.266233i
$408$	−1.59524	+	1.11830i	−0.00390990	+	0.00274094i
$409$	714.539			1.74704			0.873520	−	0.486789i	$-0.161832\pi$
$409$	714.539			1.74704			0.873520	+	0.486789i	$0.161832\pi$
$410$		−	0.473171i		−	0.00115408i
$411$	36.3487	+	51.8508i	0.0884396	+	0.126158i
$412$	96.2657			0.233655
$413$		−	2.50834i		−	0.00607346i
$414$	−0.775652	+	2.13837i	−0.00187356	+	0.00516515i
$415$	−345.350			−0.832169
$416$		−	7.34349i		−	0.0176526i
$417$	−407.900	+	285.948i	−0.978178	+	0.685727i
$418$	0.0615275			0.000147195
$419$		−	136.316i		−	0.325337i	−0.986681	−	0.162668i	$-0.947990\pi$
$419$		−	136.316i		−	0.325337i	0.986681	−	0.162668i	$-0.0520100\pi$
$420$	−10.7601	−	15.3491i	−0.0256192	−	0.0365454i
$421$	−153.259			−0.364035			−0.182017	−	0.983295i	$-0.558263\pi$
$421$	−153.259			−0.364035			−0.182017	+	0.983295i	$0.558263\pi$
$422$		−	0.0521678i		−	0.000123620i
$423$	638.672	+	231.665i	1.50986	+	0.547672i
$424$	−4.36088			−0.0102851
$425$			21.7669i			0.0512161i
$426$	−0.705334	+	0.494456i	−0.00165571	+	0.00116069i
$427$	−28.4846			−0.0667086
$428$		−	71.3988i		−	0.166820i
$429$	−239.284	−	341.335i	−0.557772	−	0.795653i
$430$	0.0451971			0.000105110
$431$			324.323i			0.752488i	0.926521	+	0.376244i	$0.122785\pi$
$431$			324.323i			0.752488i	−0.926521	+	0.376244i	$0.877215\pi$
$432$	−112.490	−	417.076i	−0.260394	−	0.965454i
$433$	−443.293			−1.02377			−0.511885	−	0.859054i	$-0.671053\pi$
$433$	−443.293			−1.02377			−0.511885	+	0.859054i	$0.671053\pi$
$434$			0.108259i			0.000249445i
$435$	−349.464	+	244.983i	−0.803366	+	0.563179i
$436$	111.048			0.254698
$437$		−	34.7637i		−	0.0795507i
$438$	0.343958	+	0.490650i	0.000785292	+	0.00112021i
$439$	678.276			1.54505			0.772524	−	0.634986i	$-0.218994\pi$
$439$	678.276			1.54505			0.772524	+	0.634986i	$0.218994\pi$
$440$			2.16763i			0.00492643i
$441$	−150.049	+	413.667i	−0.340248	+	0.938021i
$442$	1.57258			0.00355787
$443$			353.521i			0.798015i	0.916948	+	0.399008i	$0.130645\pi$
$443$			353.521i			0.798015i	−0.916948	+	0.399008i	$0.869355\pi$
$444$	148.443	−	104.062i	0.334330	−	0.234374i
$445$	−688.082			−1.54625
$446$			1.07530i			0.00241099i
$447$	−225.766	−	322.052i	−0.505070	−	0.720474i
$448$	20.8977			0.0466467
$449$		−	648.304i		−	1.44388i	−0.691954	−	0.721942i	$-0.743250\pi$
$449$		−	648.304i		−	1.44388i	0.691954	−	0.721942i	$-0.256750\pi$
$450$	0.141492	+	0.0513235i	0.000314427	+	0.000114052i
$451$	89.8378			0.199197
$452$			22.3630i			0.0494756i
$453$	−353.051	+	247.497i	−0.779362	+	0.546352i
$454$	3.20477			0.00705895
$455$			30.2623i			0.0665106i
$456$	−0.118178	−	0.168580i	−0.000259163	−	0.000369692i
$457$	419.983			0.918999			0.459499	−	0.888178i	$-0.348029\pi$
$457$	419.983			0.918999			0.459499	+	0.888178i	$0.348029\pi$
$458$		−	2.74310i		−	0.00598929i
$459$	267.953	−	72.2699i	0.583775	−	0.157451i
$460$	612.361			1.33122
$461$			831.173i			1.80298i	0.432802	+	0.901489i	$0.357525\pi$
$461$			831.173i			1.80298i	−0.432802	+	0.901489i	$0.642475\pi$
$462$	−0.0454388	+	0.0318537i	−9.83524e−5	+	6.89474e-5i
$463$	−323.289			−0.698248			−0.349124	−	0.937076i	$-0.613521\pi$
$463$	−323.289			−0.698248			−0.349124	+	0.937076i	$0.613521\pi$
$464$		−	475.809i		−	1.02545i
$465$	−345.803	−	493.282i	−0.743662	−	1.06082i
$466$	−3.64337			−0.00781838
$467$			467.788i			1.00169i	0.865538	+	0.500844i	$0.166977\pi$
$467$			467.788i			1.00169i	−0.865538	+	0.500844i	$0.833023\pi$
$468$	−237.810	+	655.611i	−0.508141	+	1.40088i
$469$	−12.2949			−0.0262150
$470$			2.85171i			0.00606746i
$471$	−286.943	+	201.154i	−0.609220	+	0.427078i
$472$	0.485278			0.00102813
$473$			8.58128i			0.0181422i
$474$	−1.41353	−	2.01638i	−0.00298213	−	0.00425396i
$475$	−2.30025			−0.00484263
$476$			13.4263i			0.0282065i
$477$	583.997	+	211.833i	1.22431	+	0.444095i
$478$	3.46194			0.00724256
$479$		−	24.1346i		−	0.0503853i	−0.999683	−	0.0251927i	$-0.991980\pi$
$479$		−	24.1346i		−	0.0503853i	0.999683	−	0.0251927i	$-0.00801992\pi$
$480$	4.45430	−	3.12257i	0.00927980	−	0.00650536i
$481$	−292.670			−0.608462
$482$		−	1.08015i		−	0.00224098i
$483$	17.9977	+	25.6734i	0.0372622	+	0.0531540i
$484$	278.217			0.574829
$485$		−	277.304i		−	0.571760i
$486$	0.162018	−	1.91219i	0.000333371	−	0.00393455i
$487$	−800.518			−1.64377			−0.821887	−	0.569650i	$-0.807079\pi$
$487$	−800.518			−1.64377			−0.821887	+	0.569650i	$0.807079\pi$
$488$		−	5.51080i		−	0.0112926i
$489$	590.502	−	413.956i	1.20757	−	0.846536i
$490$	−1.84705			−0.00376949
$491$		−	119.978i		−	0.244355i	−0.992508	−	0.122177i	$-0.961012\pi$
$491$		−	119.978i		−	0.244355i	0.992508	−	0.122177i	$-0.0389877\pi$
$492$	−86.2770	−	123.073i	−0.175360	−	0.250148i
$493$	305.686			0.620053
$494$			0.166185i			0.000336407i
$495$	105.294	−	290.283i	0.212716	−	0.586430i
$496$	671.623			1.35408
$497$			11.8729i			0.0238892i
$498$	1.40058	−	0.981838i	0.00281240	−	0.00197156i
$499$	231.859			0.464647			0.232323	−	0.972639i	$-0.425367\pi$
$499$	231.859			0.464647			0.232323	+	0.972639i	$0.425367\pi$
$500$		−	518.866i		−	1.03773i
$501$	−263.964	−	376.540i	−0.526874	−	0.751577i
$502$	−0.843928			−0.00168113
$503$			688.560i			1.36891i	0.729056	+	0.684454i	$0.239959\pi$
$503$			688.560i			1.36891i	−0.729056	+	0.684454i	$0.760041\pi$
$504$	0.174552	+	0.0633154i	0.000346334	+	0.000125626i
$505$	665.407			1.31764
$506$		−	1.81281i		−	0.00358263i
$507$	506.791	−	355.272i	0.999587	−	0.700735i
$508$	−86.9317			−0.171125
$509$			142.587i			0.280131i	0.990142	+	0.140065i	$0.0447313\pi$
$509$			142.587i			0.280131i	−0.990142	+	0.140065i	$0.955269\pi$
$510$	0.668687	+	0.953872i	0.00131115	+	0.00187034i
$511$	8.25914			0.0161627
$512$			10.1079i			0.0197420i
$513$	7.63724	+	28.3163i	0.0148874	+	0.0551975i
$514$	0.898047			0.00174717
$515$		−	115.125i		−	0.223543i
$516$	11.7559	−	8.24115i	0.0227827	−	0.0159712i
$517$	−541.435			−1.04726
$518$			0.0389605i			7.52133e-5i
$519$	341.711	+	487.446i	0.658403	+	0.939202i
$520$	−5.85473			−0.0112591
$521$		−	617.668i		−	1.18554i	−0.805370	−	0.592772i	$-0.798034\pi$
$521$		−	617.668i		−	1.18554i	0.805370	−	0.592772i	$-0.201966\pi$
$522$	0.720769	−	1.98707i	0.00138078	−	0.00380664i
$523$	118.969			0.227473			0.113737	−	0.993511i	$-0.463718\pi$
$523$	118.969			0.227473			0.113737	+	0.993511i	$0.463718\pi$
$524$		−	939.945i		−	1.79379i
$525$	1.69876	−	1.19087i	0.00323574	−	0.00226833i
$526$	−0.597200			−0.00113536
$527$			431.488i			0.818762i
$528$	197.616	+	281.896i	0.374272	+	0.533893i
$529$	−495.256			−0.936211
$530$			2.60758i			0.00491997i
$531$	−64.9871	−	23.5728i	−0.122386	−	0.0443932i
$532$	−1.41884			−0.00266700
$533$			242.651i			0.455255i
$534$	2.79053	−	1.95623i	0.00522571	−	0.00366335i
$535$	−85.3863			−0.159601
$536$		−	2.37864i		−	0.00443775i
$537$	145.281	+	207.242i	0.270543	+	0.385925i
$538$	1.22077			0.00226908
$539$		−	350.687i		−	0.650625i
$540$	−498.792	+	134.530i	−0.923688	+	0.249129i
$541$	773.951			1.43059			0.715296	−	0.698821i	$-0.246292\pi$
$541$	773.951			1.43059			0.715296	+	0.698821i	$0.246292\pi$
$542$			2.80439i			0.00517416i
$543$	−738.928	+	518.007i	−1.36083	+	0.953972i
$544$	−3.89630			−0.00716232
$545$		−	132.803i		−	0.243676i
$546$	−0.0860364	−	0.122730i	−0.000157576	−	0.000224779i
$547$	−119.657			−0.218751			−0.109375	−	0.994001i	$-0.534885\pi$
$547$	−119.657			−0.218751			−0.109375	+	0.994001i	$0.534885\pi$
$548$			84.4286i			0.154067i
$549$	−267.691	+	737.991i	−0.487598	+	1.34425i
$550$	−0.119950			−0.000218091
$551$			32.3039i			0.0586278i
$552$	−4.96693	+	3.48194i	−0.00899806	+	0.00630786i
$553$	−33.9418			−0.0613775
$554$			1.78675i			0.00322518i
$555$	−124.448	−	177.524i	−0.224231	−	0.319862i
$556$	−664.184			−1.19457
$557$			885.523i			1.58981i	0.606735	+	0.794904i	$0.292479\pi$
$557$			885.523i			1.58981i	−0.606735	+	0.794904i	$0.707521\pi$
$558$	2.80482	+	1.01739i	0.00502656	+	0.00182328i
$559$	−23.1779			−0.0414632
$560$		−	24.9925i		−	0.0446295i
$561$	−181.105	+	126.959i	−0.322826	+	0.226309i
$562$	−4.07736			−0.00725509
$563$		−	849.508i		−	1.50889i	−0.656361	−	0.754447i	$-0.727905\pi$
$563$		−	849.508i		−	1.50889i	0.656361	−	0.754447i	$-0.272095\pi$
$564$	519.974	+	741.735i	0.921940	+	1.31513i
$565$	26.7440			0.0473346
$566$		−	1.00932i		−	0.00178325i
$567$	−20.3000	−	16.9580i	−0.0358024	−	0.0299084i
$568$	−2.29701			−0.00404402
$569$		−	659.670i		−	1.15935i	−0.814848	−	0.579675i	$-0.803180\pi$
$569$		−	659.670i		−	1.15935i	0.814848	−	0.579675i	$-0.196820\pi$
$570$	−0.100802	+	0.0706646i	−0.000176846	+	0.000123973i
$571$	528.453			0.925487			0.462744	−	0.886492i	$-0.346865\pi$
$571$	528.453			0.925487			0.462744	+	0.886492i	$0.346865\pi$
$572$		−	555.796i		−	0.971671i
$573$	−108.392	−	154.619i	−0.189166	−	0.269842i
$574$	0.0323019			5.62750e−5
$575$			67.7731i			0.117866i
$576$	196.392	−	541.428i	0.340958	−	0.939979i
$577$	133.967			0.232178			0.116089	−	0.993239i	$-0.462964\pi$
$577$	133.967			0.232178			0.116089	+	0.993239i	$0.462964\pi$
$578$			1.44794i			0.00250508i
$579$	−129.603	+	90.8548i	−0.223839	+	0.156917i
$580$	−569.032			−0.981090
$581$		−	23.5760i		−	0.0405782i
$582$	0.788380	+	1.12461i	0.00135460	+	0.00193232i
$583$	−495.084			−0.849202
$584$			1.59786i			0.00273607i
$585$	784.050	+	284.398i	1.34026	+	0.486151i
$586$	3.70823			0.00632804
$587$		−	771.291i		−	1.31395i	−0.753911	−	0.656977i	$-0.771835\pi$
$587$		−	771.291i		−	1.31395i	0.753911	−	0.656977i	$-0.228165\pi$
$588$	−480.421	+	336.787i	−0.817043	+	0.572767i
$589$	−45.5982			−0.0774162
$590$		−	0.290171i		−	0.000491816i
$591$	74.6842	+	106.536i	0.126369	+	0.180264i
$592$	241.705			0.408286
$593$			590.309i			0.995461i	0.867332	+	0.497731i	$0.165833\pi$
$593$			590.309i			0.995461i	−0.867332	+	0.497731i	$0.834167\pi$
$594$	0.398257	+	1.47660i	0.000670466	+	0.00248586i
$595$	16.0566			0.0269858
$596$		−	524.397i		−	0.879860i
$597$	778.541	−	545.776i	1.30409	−	0.914197i
$598$	4.89637			0.00818791
$599$		−	859.176i		−	1.43435i	−0.696893	−	0.717175i	$-0.745435\pi$
$599$		−	859.176i		−	1.43435i	0.696893	−	0.717175i	$-0.254565\pi$
$600$	0.230394	+	0.328653i	0.000383989	+	0.000547754i
$601$	−704.324			−1.17192			−0.585960	−	0.810340i	$-0.699283\pi$
$601$	−704.324			−1.17192			−0.585960	+	0.810340i	$0.699283\pi$
$602$			0.00308546i			5.12536e-6i
$603$	−115.544	+	318.540i	−0.191615	+	0.528259i
$604$	−574.872			−0.951776
$605$		−	332.722i		−	0.549954i
$606$	−2.69857	+	1.89176i	−0.00445309	+	0.00312172i
$607$	904.339			1.48985			0.744925	−	0.667148i	$-0.232485\pi$
$607$	904.339			1.48985			0.744925	+	0.667148i	$0.232485\pi$
$608$		−	0.411748i		−	0.000677218i
$609$	−16.7242	−	23.8568i	−0.0274617	−	0.0391737i
$610$	−3.29517			−0.00540192
$611$		−	1462.41i		−	2.39347i
$612$	347.854	+	126.177i	0.568389	+	0.206172i
$613$	612.747			0.999588			0.499794	−	0.866144i	$-0.333409\pi$
$613$	612.747			0.999588			0.499794	+	0.866144i	$0.333409\pi$
$614$		−	1.57821i		−	0.00257038i
$615$	−147.183	+	103.179i	−0.239323	+	0.167771i
$616$	−0.147977			−0.000240222
$617$			101.948i			0.165232i	0.996581	+	0.0826159i	$0.0263275\pi$
$617$			101.948i			0.165232i	−0.996581	+	0.0826159i	$0.973673\pi$
$618$	0.327302	+	0.466891i	0.000529615	+	0.000755487i
$619$	511.560			0.826430			0.413215	−	0.910633i	$-0.364406\pi$
$619$	511.560			0.826430			0.413215	+	0.910633i	$0.364406\pi$
$620$		−	803.211i		−	1.29550i
$621$	834.295	−	225.019i	1.34347	−	0.362350i
$622$	2.21920			0.00356785
$623$		−	46.9731i		−	0.0753983i
$624$	−761.396	+	533.757i	−1.22019	+	0.855380i
$625$	−567.574			−0.908119
$626$			0.281082i			0.000449013i
$627$	−13.4166	−	19.1386i	−0.0213981	−	0.0305241i
$628$	−467.229			−0.743995
$629$			155.285i			0.246876i
$630$	0.0378593	−	0.104373i	6.00942e−5	−	0.000165672i
$631$	−705.626			−1.11827			−0.559133	−	0.829078i	$-0.688866\pi$
$631$	−705.626			−1.11827			−0.559133	+	0.829078i	$0.688866\pi$
$632$		−	6.56658i		−	0.0103902i
$633$	−16.2272	+	11.3757i	−0.0256354	+	0.0179710i
$634$	0.251007			0.000395910
$635$			103.962i			0.163720i
$636$	475.461	+	678.238i	0.747580	+	1.06641i
$637$	947.201			1.48697
$638$			1.68454i			0.00264034i
$639$	307.609	+	111.579i	0.481391	+	0.174615i
$640$	9.67056			0.0151102
$641$			589.256i			0.919277i	0.888106	+	0.459638i	$0.152021\pi$
$641$			589.256i			0.919277i	−0.888106	+	0.459638i	$0.847979\pi$
$642$	0.346286	−	0.242755i	0.000539386	−	0.000378123i
$643$	−518.072			−0.805711			−0.402856	−	0.915264i	$-0.631982\pi$
$643$	−518.072			−0.805711			−0.402856	+	0.915264i	$0.631982\pi$
$644$			41.8039i			0.0649130i
$645$	−9.85564	−	14.0589i	−0.0152801	−	0.0217968i
$646$	0.0881743			0.000136493
$647$			696.737i			1.07687i	0.842666	+	0.538437i	$0.180985\pi$
$647$			696.737i			1.07687i	−0.842666	+	0.538437i	$0.819015\pi$
$648$	3.28081	−	3.92736i	0.00506297	−	0.00606074i
$649$	55.0929			0.0848889
$650$		−	0.323984i		−	0.000498437i
$651$	33.6748	−	23.6068i	0.0517278	−	0.0362624i
$652$	961.514			1.47471
$653$		−	628.404i		−	0.962334i	−0.876629	−	0.481167i	$-0.840213\pi$
$653$		−	628.404i		−	0.962334i	0.876629	−	0.481167i	$-0.159787\pi$
$654$	0.377563	+	0.538587i	0.000577313	+	0.000823528i
$655$	−1124.09			−1.71616
$656$		−	200.396i		−	0.305482i
$657$	77.6175	−	213.982i	0.118139	−	0.325695i
$658$	−0.194677			−0.000295861
$659$			89.8096i			0.136282i	0.997676	+	0.0681409i	$0.0217067\pi$
$659$			89.8096i			0.136282i	−0.997676	+	0.0681409i	$0.978293\pi$
$660$	337.126	−	236.334i	0.510797	−	0.358081i
$661$	1209.31			1.82952			0.914761	−	0.403996i	$-0.132379\pi$
$661$	1209.31			1.82952			0.914761	+	0.403996i	$0.132379\pi$
$662$			3.02736i			0.00457305i
$663$	−342.915	−	489.163i	−0.517217	−	0.737802i
$664$	4.56115			0.00686920
$665$			1.69680i			0.00255159i
$666$	1.00941	+	0.366142i	0.00151562	+	0.000549762i
$667$	951.782			1.42696
$668$		−	613.120i		−	0.917844i
$669$	334.481	−	234.479i	0.499972	−	0.350492i
$670$	−1.42230			−0.00212284
$671$		−	625.633i		−	0.932388i
$672$	0.213168	+	0.304081i	0.000317215	+	0.000452501i
$673$	1060.34			1.57554			0.787771	−	0.615968i	$-0.211235\pi$
$673$	1060.34			1.57554			0.787771	+	0.615968i	$0.211235\pi$
$674$			2.32257i			0.00344595i
$675$	−14.8891	−	55.2038i	−0.0220579	−	0.0817834i
$676$	825.206			1.22072
$677$		−	136.594i		−	0.201764i	−0.994898	−	0.100882i	$-0.967834\pi$
$677$		−	136.594i		−	0.201764i	0.994898	−	0.100882i	$-0.0321665\pi$
$678$	−0.108461	+	0.0760338i	−0.000159972	+	0.000112144i
$679$	18.9306			0.0278802
$680$			3.10640i			0.00456824i
$681$	−698.828	−	996.867i	−1.02618	−	1.46383i
$682$	−2.37779			−0.00348650
$683$			167.507i			0.245251i	0.992453	+	0.122626i	$0.0391315\pi$
$683$			167.507i			0.245251i	−0.992453	+	0.122626i	$0.960869\pi$
$684$	−13.3340	+	36.7600i	−0.0194941	+	0.0537427i
$685$	100.969			0.147400
$686$		−	0.252459i		−	0.000368016i
$687$	−853.261	+	598.157i	−1.24201	+	0.870679i
$688$	19.1418			0.0278223
$689$		−	1337.22i		−	1.94081i
$690$	2.08202	+	2.96997i	0.00301742	+	0.00430430i
$691$	512.344			0.741454			0.370727	−	0.928742i	$-0.379109\pi$
$691$	512.344			0.741454			0.370727	+	0.928742i	$0.379109\pi$
$692$			793.707i			1.14698i
$693$	19.8167	+	7.18810i	0.0285955	+	0.0103724i
$694$	2.05986			0.00296809
$695$			794.301i			1.14288i
$696$	4.61548	−	3.23557i	0.00663144	−	0.00464880i
$697$	128.745			0.184714
$698$			0.519841i			0.000744757i
$699$	794.469	+	1133.30i	1.13658	+	1.62131i
$700$	2.76609			0.00395156
$701$			810.841i			1.15669i	0.815792	+	0.578346i	$0.196302\pi$
$701$			810.841i			1.15669i	−0.815792	+	0.578346i	$0.803698\pi$
$702$	−3.98828	+	1.07569i	−0.00568131	+	0.00153232i
$703$	−16.4100			−0.0233428
$704$			458.996i			0.651983i
$705$	887.045	−	621.840i	1.25822	−	0.882043i
$706$	1.61217			0.00228352
$707$			45.4252i			0.0642506i
$708$	−52.9092	−	75.4742i	−0.0747305	−	0.106602i
$709$	466.935			0.658583			0.329291	−	0.944228i	$-0.393190\pi$
$709$	466.935			0.658583			0.329291	+	0.944228i	$0.393190\pi$
$710$			1.37349i			0.00193449i
$711$	−318.977	+	879.379i	−0.448631	+	1.23682i
$712$	9.08771			0.0127636
$713$			1343.48i			1.88426i
$714$	−0.0651178	+	0.0456491i	−9.12014e−5	+	6.39344e-5i
$715$	−664.679			−0.929621
$716$			337.451i			0.471300i
$717$	−754.908	−	1076.86i	−1.05287	−	1.50190i
$718$	2.74481			0.00382285
$719$		−	532.897i		−	0.741165i	−0.928800	−	0.370582i	$-0.879158\pi$
$719$		−	532.897i		−	0.741165i	0.928800	−	0.370582i	$-0.120842\pi$
$720$	−647.517	−	234.874i	−0.899329	−	0.326214i
$721$	7.85920			0.0109004
$722$		−	2.84160i		−	0.00393574i
$723$	−335.989	+	235.536i	−0.464715	+	0.325777i
$724$	−1203.20			−1.66187
$725$		−	62.9777i		−	0.0868658i
$726$	0.945935	+	1.34936i	0.00130294	+	0.00185862i
$727$	−1402.75			−1.92950			−0.964751	−	0.263164i	$-0.915234\pi$
$727$	−1402.75			−1.92950			−0.964751	+	0.263164i	$0.915234\pi$
$728$		−	0.399684i		−	0.000549016i
$729$	−630.131	+	366.573i	−0.864377	+	0.502844i
$730$	0.955440			0.00130882
$731$			12.2977i			0.0168232i
$732$	−857.081	+	600.835i	−1.17088	+	0.820812i
$733$	−323.758			−0.441688			−0.220844	−	0.975309i	$-0.570881\pi$
$733$	−323.758			−0.441688			−0.220844	+	0.975309i	$0.570881\pi$
$734$		−	1.16703i		−	0.00158996i
$735$	402.766	+	574.539i	0.547980	+	0.781685i
$736$	−12.1315			−0.0164830
$737$		−	270.043i		−	0.366409i
$738$	0.303565	−	0.836891i	0.000411335	−	0.00113400i
$739$	−815.403			−1.10339			−0.551694	−	0.834047i	$-0.686018\pi$
$739$	−815.403			−1.10339			−0.551694	+	0.834047i	$0.686018\pi$
$740$		−	289.061i		−	0.390623i
$741$	51.6931	−	36.2381i	0.0697613	−	0.0489044i
$742$	−0.178011			−0.000239907
$743$			681.903i			0.917769i	0.888496	+	0.458885i	$0.151751\pi$
$743$			681.903i			0.917769i	−0.888496	+	0.458885i	$0.848249\pi$
$744$	4.56712	+	6.51493i	0.00613861	+	0.00875662i
$745$	−627.129			−0.841784
$746$		−	3.03671i		−	0.00407065i
$747$	−610.816	−	221.561i	−0.817692	−	0.296602i
$748$	−294.894			−0.394243
$749$		−	5.82905i		−	0.00778244i
$750$	2.51651	−	1.76414i	0.00335535	−	0.00235218i
$751$	−761.193			−1.01357			−0.506786	−	0.862072i	$-0.669167\pi$
$751$	−761.193			−1.01357			−0.506786	+	0.862072i	$0.669167\pi$
$752$			1207.75i			1.60605i
$753$	184.026	+	262.510i	0.244391	+	0.348619i
$754$	−4.54992			−0.00603437
$755$			687.494i			0.910588i
$756$	−9.18392	−	34.0509i	−0.0121480	−	0.0450409i
$757$	−1302.94			−1.72119			−0.860594	−	0.509291i	$-0.829908\pi$
$757$	−1302.94			−1.72119			−0.860594	+	0.509291i	$0.829908\pi$
$758$			2.69758i			0.00355882i
$759$	−563.888	+	395.299i	−0.742936	+	0.520816i
$760$	−0.328274			−0.000431940
$761$			42.0468i			0.0552521i	0.999618	+	0.0276260i	$0.00879476\pi$
$761$			42.0468i			0.0552521i	−0.999618	+	0.0276260i	$0.991205\pi$
$762$	−0.295567	−	0.421621i	−0.000387883	−	0.000553309i
$763$	9.06606			0.0118821
$764$		−	251.767i		−	0.329538i
$765$	150.896	−	416.001i	0.197250	−	0.543792i
$766$	−4.24503			−0.00554181
$767$			148.805i			0.194009i
$768$	628.769	−	440.783i	0.818710	−	0.573936i
$769$	1230.19			1.59973			0.799863	−	0.600183i	$-0.204905\pi$
$769$	1230.19			1.59973			0.799863	+	0.600183i	$0.204905\pi$
$770$			0.0884826i			0.000114913i
$771$	−195.827	−	279.344i	−0.253991	−	0.362314i
$772$	−211.032			−0.273358
$773$		−	1097.05i		−	1.41921i	−0.704599	−	0.709606i	$-0.748873\pi$
$773$		−	1097.05i		−	1.41921i	0.704599	−	0.709606i	$-0.251127\pi$
$774$	0.0799396	+	0.0289965i	0.000103281	+	3.74631e-5i
$775$	88.8954			0.114704
$776$			3.66244i			0.00471963i
$777$	12.1190	−	8.49569i	0.0155971	−	0.0109340i
$778$	−4.35395			−0.00559634
$779$			13.6054i			0.0174652i
$780$	638.334	+	910.573i	0.818377	+	1.16740i
$781$	−260.776			−0.333900
$782$		−	2.59791i		−	0.00332214i
$783$	−775.263	+	209.097i	−0.990119	+	0.267046i
$784$	−782.257			−0.997777
$785$			558.762i			0.711798i

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	177.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.00789729i q^{2} +(2.45651 - 1.72208i) q^{3} +3.99994 q^{4} -4.78355i q^{5} +(0.0135997 + 0.0193998i) q^{6} +0.326558 q^{7} +0.0631778i q^{8} +(3.06891 - 8.46060i) q^{9} +O(q^{10})\)	\(q+0.00789729i q^{2} +(2.45651 - 1.72208i) q^{3} +3.99994 q^{4} -4.78355i q^{5} +(0.0135997 + 0.0193998i) q^{6} +0.326558 q^{7} +0.0631778i q^{8} +(3.06891 - 8.46060i) q^{9} +0.0377771 q^{10} +7.17249i q^{11} +(9.82590 - 6.88819i) q^{12} -19.3728 q^{13} +0.00257892i q^{14} +(-8.23763 - 11.7509i) q^{15} +15.9993 q^{16} +10.2788i q^{17} +(0.0668158 + 0.0242361i) q^{18} -1.08623 q^{19} -19.1339i q^{20} +(0.802193 - 0.562357i) q^{21} -0.0566432 q^{22} +32.0040i q^{23} +(0.108797 + 0.155197i) q^{24} +2.11765 q^{25} -0.152993i q^{26} +(-7.03097 - 26.0685i) q^{27} +1.30621 q^{28} -29.7395i q^{29} +(0.0927999 - 0.0650550i) q^{30} +41.9784 q^{31} +0.379062i q^{32} +(12.3516 + 17.6193i) q^{33} -0.0811747 q^{34} -1.56211i q^{35} +(12.2755 - 33.8419i) q^{36} +15.1073 q^{37} -0.00857827i q^{38} +(-47.5895 + 33.3614i) q^{39} +0.302214 q^{40} -12.5253i q^{41} +(0.00444110 + 0.00633515i) q^{42} +1.19642 q^{43} +28.6895i q^{44} +(-40.4717 - 14.6803i) q^{45} -0.252745 q^{46} +75.4877i q^{47} +(39.3024 - 27.5519i) q^{48} -48.8934 q^{49} +0.0167237i q^{50} +(17.7009 + 25.2500i) q^{51} -77.4899 q^{52} +69.0255i q^{53} +(0.205870 - 0.0555256i) q^{54} +34.3100 q^{55} +0.0206312i q^{56} +(-2.66834 + 1.87057i) q^{57} +0.234861 q^{58} -7.68115i q^{59} +(-32.9500 - 47.0027i) q^{60} -87.2267 q^{61} +0.331516i q^{62} +(1.00218 - 2.76287i) q^{63} +63.9940 q^{64} +92.6707i q^{65} +(-0.139145 + 0.0975439i) q^{66} -37.6499 q^{67} +41.1146i q^{68} +(55.1133 + 78.6182i) q^{69} +0.0123364 q^{70} +36.3578i q^{71} +(0.534522 + 0.193887i) q^{72} +25.2915 q^{73} +0.119307i q^{74} +(5.20203 - 3.64675i) q^{75} -4.34485 q^{76} +2.34223i q^{77} +(-0.263465 - 0.375828i) q^{78} -103.938 q^{79} -76.5332i q^{80} +(-62.1635 - 51.9297i) q^{81} +0.0989162 q^{82} -72.1954i q^{83} +(3.20872 - 2.24939i) q^{84} +49.1692 q^{85} +0.00944845i q^{86} +(-51.2136 - 73.0554i) q^{87} -0.453142 q^{88} -143.843i q^{89} +(0.115935 - 0.319617i) q^{90} -6.32633 q^{91} +128.014i q^{92} +(103.120 - 72.2900i) q^{93} -0.596149 q^{94} +5.19603i q^{95} +(0.652773 + 0.931171i) q^{96} +57.9703 q^{97} -0.386125i q^{98} +(60.6836 + 22.0117i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38q - 76q^{4} - 8q^{6} - 12q^{7} + 20q^{9} + O(q^{10}) \)	\( 38q - 76q^{4} - 8q^{6} - 12q^{7} + 20q^{9} + 36q^{10} - 4q^{13} - 17q^{15} + 100q^{16} - 2q^{18} - 28q^{19} - 11q^{21} + 84q^{22} - 6q^{24} - 166q^{25} + 3q^{27} + 12q^{28} + 102q^{30} - 40q^{31} - 46q^{33} - 148q^{34} - 96q^{36} + 112q^{37} + 62q^{39} - 56q^{40} + 14q^{42} + 164q^{43} + 55q^{45} - 4q^{46} - 124q^{48} + 242q^{49} + 52q^{51} + 8q^{52} + 18q^{54} - 228q^{55} - 147q^{57} - 80q^{58} + 128q^{60} + 12q^{61} + 86q^{63} + 48q^{64} - 24q^{66} + 124q^{67} - 240q^{69} + 148q^{70} + 166q^{72} - 192q^{73} - 78q^{75} - 304q^{76} + 244q^{78} + 64q^{79} - 156q^{81} - 180q^{82} + 300q^{84} - 52q^{85} - 83q^{87} - 96q^{88} - 376q^{90} - 332q^{91} + 454q^{93} + 768q^{94} - 722q^{96} + 416q^{97} + 494q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

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