LMFDB - Embedded newform 483.2.bf.a.10.5

Newspace parameters

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.bf (of order $66$, degree $20$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$32$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			10.5
Character	$\chi$	$=$	483.10
Dual form			483.2.bf.a.145.5

$q$-expansion

$f(q)$	$=$	$q+(-0.647644 + 1.87125i) q^{2} +(0.458227 + 0.888835i) q^{3} +(-1.51001 - 1.18748i) q^{4} +(-3.91898 + 0.374217i) q^{5} +(-1.96000 + 0.281805i) q^{6} +(-1.01941 - 2.44148i) q^{7} +(-0.131596 + 0.0845715i) q^{8} +(-0.580057 + 0.814576i) q^{9} +O(q^{10})$	\(q+(-0.647644 + 1.87125i) q^{2} +(0.458227 + 0.888835i) q^{3} +(-1.51001 - 1.18748i) q^{4} +(-3.91898 + 0.374217i) q^{5} +(-1.96000 + 0.281805i) q^{6} +(-1.01941 - 2.44148i) q^{7} +(-0.131596 + 0.0845715i) q^{8} +(-0.580057 + 0.814576i) q^{9} +(1.83785 - 7.57573i) q^{10} +(0.645660 - 0.223465i) q^{11} +(0.363552 - 1.88629i) q^{12} +(-0.0976592 - 0.332597i) q^{13} +(5.22881 - 0.326361i) q^{14} +(-2.12840 - 3.31185i) q^{15} +(-0.978813 - 4.03472i) q^{16} +(5.85483 + 2.34392i) q^{17} +(-1.14860 - 1.61298i) q^{18} +(1.61603 - 0.646960i) q^{19} +(6.36207 + 4.08865i) q^{20} +(1.70295 - 2.02484i) q^{21} +1.35291i q^{22} +(-4.15203 - 2.40013i) q^{23} +(-0.135471 - 0.0782141i) q^{24} +(10.3087 - 1.98684i) q^{25} +(0.685619 + 0.0326600i) q^{26} +(-0.989821 - 0.142315i) q^{27} +(-1.35989 + 4.89719i) q^{28} +(-0.951297 - 6.61641i) q^{29} +(7.57573 - 1.83785i) q^{30} +(-4.91106 + 0.233942i) q^{31} +(7.87244 + 0.751727i) q^{32} +(0.494482 + 0.471488i) q^{33} +(-8.17789 + 9.43779i) q^{34} +(4.90869 + 9.18661i) q^{35} +(1.84319 - 0.541209i) q^{36} +(-8.88359 - 6.32597i) q^{37} +(0.164009 + 3.44298i) q^{38} +(0.250874 - 0.239208i) q^{39} +(0.484073 - 0.380679i) q^{40} +(-10.0291 - 4.58013i) q^{41} +(2.68606 + 4.49801i) q^{42} +(2.14542 - 3.33833i) q^{43} +(-1.24031 - 0.429277i) q^{44} +(1.96840 - 3.40937i) q^{45} +(7.18027 - 6.21504i) q^{46} +(-6.49244 + 3.74841i) q^{47} +(3.13769 - 2.71882i) q^{48} +(-4.92160 + 4.97773i) q^{49} +(-2.95851 + 20.5769i) q^{50} +(0.599478 + 6.27802i) q^{51} +(-0.247487 + 0.618193i) q^{52} +(0.0565734 + 0.0593325i) q^{53} +(0.907358 - 1.76003i) q^{54} +(-2.44670 + 1.11737i) q^{55} +(0.340629 + 0.235075i) q^{56} +(1.31555 + 1.13993i) q^{57} +(12.9970 + 2.50497i) q^{58} +(-7.52852 - 1.82640i) q^{59} +(-0.718872 + 7.52836i) q^{60} +(6.51667 + 3.35958i) q^{61} +(2.74285 - 9.34130i) q^{62} +(2.58008 + 0.585807i) q^{63} +(-3.05580 + 6.69128i) q^{64} +(0.507188 + 1.26689i) q^{65} +(-1.20252 + 0.619941i) q^{66} +(-0.257243 - 1.33470i) q^{67} +(-6.05747 - 10.4919i) q^{68} +(0.230747 - 4.79028i) q^{69} +(-20.3695 + 3.23571i) q^{70} +(0.530127 + 0.611800i) q^{71} +(0.00744315 - 0.156251i) q^{72} +(-1.37288 + 1.74576i) q^{73} +(17.5909 - 12.5264i) q^{74} +(6.48970 + 8.25232i) q^{75} +(-3.20847 - 0.942092i) q^{76} +(-1.20378 - 1.34856i) q^{77} +(0.285139 + 0.624368i) q^{78} +(4.52434 - 4.74500i) q^{79} +(5.34581 + 15.4457i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(15.0658 - 15.8006i) q^{82} +(5.09021 + 11.1460i) q^{83} +(-4.97593 + 1.03530i) q^{84} +(-23.8221 - 6.99479i) q^{85} +(4.85737 + 6.17665i) q^{86} +(5.44499 - 3.87736i) q^{87} +(-0.0660673 + 0.0840115i) q^{88} +(0.122645 - 2.57464i) q^{89} +(5.10495 + 5.89142i) q^{90} +(-0.712472 + 0.577485i) q^{91} +(3.41950 + 8.55469i) q^{92} +(-2.45831 - 4.25792i) q^{93} +(-2.80941 - 14.5766i) q^{94} +(-6.09107 + 3.14016i) q^{95} +(2.93920 + 7.34177i) q^{96} +(-6.54959 + 14.3416i) q^{97} +(-6.12712 - 12.4333i) q^{98} +(-0.192490 + 0.655561i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640q - 4q^{2} + 36q^{4} + 24q^{8} - 32q^{9} + O(q^{10}) $	$ 640q - 4q^{2} + 36q^{4} + 24q^{8} - 32q^{9} + 4q^{18} - 28q^{23} + 56q^{25} - 84q^{26} - 176q^{28} - 24q^{29} + 12q^{31} + 36q^{32} - 76q^{35} + 28q^{36} + 44q^{37} - 110q^{42} - 88q^{43} + 154q^{44} + 8q^{46} + 12q^{47} - 8q^{49} - 212q^{50} + 44q^{51} + 108q^{52} - 110q^{56} - 88q^{57} + 2q^{58} - 36q^{59} - 168q^{64} - 48q^{70} + 16q^{71} + 12q^{72} - 48q^{73} - 22q^{74} + 48q^{75} + 32q^{78} - 44q^{79} - 594q^{80} + 32q^{81} + 24q^{82} + 352q^{85} - 36q^{87} - 330q^{88} + 244q^{92} - 24q^{93} - 486q^{94} - 154q^{95} - 60q^{96} - 24q^{98} - 44q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{22}\right)$

Coefficient data

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

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

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

$2$	−0.647644	+	1.87125i	−0.457954	+	1.32317i	0.445806	+	0.895130i	$0.352917\pi$
$2$	−0.647644	+	1.87125i	−0.457954	+	1.32317i	−0.903760	+	0.428041i	$0.859204\pi$
$3$	0.458227	+	0.888835i	0.264557	+	0.513169i
$3$	0.458227	+	0.888835i	0.264557	+	0.513169i
$4$	−1.51001	−	1.18748i	−0.755005	−	0.593742i
$5$	−3.91898	+	0.374217i	−1.75262	+	0.167355i	−0.921407	−	0.388599i	$-0.872959\pi$
$5$	−3.91898	+	0.374217i	−1.75262	+	0.167355i	−0.831213	+	0.555954i	$0.812353\pi$
$6$	−1.96000	+	0.281805i	−0.800165	+	0.115046i
$7$	−1.01941	−	2.44148i	−0.385301	−	0.922791i
$7$	−1.01941	−	2.44148i	−0.385301	−	0.922791i
$8$	−0.131596	+	0.0845715i	−0.0465261	+	0.0299005i
$9$	−0.580057	+	0.814576i	−0.193352	+	0.271525i
$10$	1.83785	−	7.57573i	0.581180	−	2.39566i
$11$	0.645660	−	0.223465i	0.194674	−	0.0673772i	−0.227991	−	0.973663i	$-0.573216\pi$
$11$	0.645660	−	0.223465i	0.194674	−	0.0673772i	0.422665	+	0.906286i	$0.361095\pi$
$12$	0.363552	−	1.88629i	0.104948	−	0.544524i
$13$	−0.0976592	−	0.332597i	−0.0270858	−	0.0922457i	0.944841	−	0.327530i	$-0.106216\pi$
$13$	−0.0976592	−	0.332597i	−0.0270858	−	0.0922457i	−0.971927	+	0.235284i	$0.924398\pi$
$14$	5.22881	−	0.326361i	1.39746	−	0.0872237i
$15$	−2.12840	−	3.31185i	−0.549550	−	0.855116i
$16$	−0.978813	−	4.03472i	−0.244703	−	1.00868i
$17$	5.85483	+	2.34392i	1.42000	+	0.568484i	0.949459	−	0.313892i	$-0.101633\pi$
$17$	5.85483	+	2.34392i	1.42000	+	0.568484i	0.470545	+	0.882376i	$0.344057\pi$
$18$	−1.14860	−	1.61298i	−0.270728	−	0.380184i
$19$	1.61603	−	0.646960i	0.370742	−	0.148423i	−0.178807	−	0.983884i	$-0.557224\pi$
$19$	1.61603	−	0.646960i	0.370742	−	0.148423i	0.549549	+	0.835461i	$0.314800\pi$
$20$	6.36207	+	4.08865i	1.42260	+	0.914251i
$21$	1.70295	−	2.02484i	0.371614	−	0.441856i
$22$			1.35291i			0.288442i
$23$	−4.15203	−	2.40013i	−0.865759	−	0.500461i
$23$	−4.15203	−	2.40013i	−0.865759	−	0.500461i
$24$	−0.135471	−	0.0782141i	−0.0276529	−	0.0159654i
$25$	10.3087	−	1.98684i	2.06174	−	0.397368i
$26$	0.685619	+	0.0326600i	0.134461	+	0.00640516i
$27$	−0.989821	−	0.142315i	−0.190491	−	0.0273885i
$28$	−1.35989	+	4.89719i	−0.256996	+	0.925481i
$29$	−0.951297	−	6.61641i	−0.176651	−	1.22864i	−0.864444	−	0.502730i	$-0.832329\pi$
$29$	−0.951297	−	6.61641i	−0.176651	−	1.22864i	0.687792	−	0.725908i	$-0.258580\pi$
$30$	7.57573	−	1.83785i	1.38313	−	0.335544i
$31$	−4.91106	+	0.233942i	−0.882052	+	0.0420173i	−0.483719	−	0.875224i	$-0.660714\pi$
$31$	−4.91106	+	0.233942i	−0.882052	+	0.0420173i	−0.398333	+	0.917241i	$0.630411\pi$
$32$	7.87244	+	0.751727i	1.39166	+	0.132888i
$33$	0.494482	+	0.471488i	0.0860783	+	0.0820755i
$34$	−8.17789	+	9.43779i	−1.40250	+	1.61857i
$35$	4.90869	+	9.18661i	0.829720	+	1.55282i
$36$	1.84319	−	0.541209i	0.307198	−	0.0902015i
$37$	−8.88359	−	6.32597i	−1.46045	−	1.03998i	−0.987276	−	0.159016i	$-0.949168\pi$
$37$	−8.88359	−	6.32597i	−1.46045	−	1.03998i	−0.473176	−	0.880968i	$-0.656893\pi$
$38$	0.164009	+	3.44298i	0.0266058	+	0.558525i
$39$	0.250874	−	0.239208i	0.0401720	−	0.0383039i
$40$	0.484073	−	0.380679i	0.0765386	−	0.0601906i
$41$	−10.0291	−	4.58013i	−1.56628	−	0.715295i	−0.571815	−	0.820382i	$-0.693761\pi$
$41$	−10.0291	−	4.58013i	−1.56628	−	0.715295i	−0.994463	+	0.105087i	$0.966488\pi$
$42$	2.68606	+	4.49801i	0.414469	+	0.694058i
$43$	2.14542	−	3.33833i	0.327173	−	0.509091i	−0.638233	−	0.769843i	$-0.720334\pi$
$43$	2.14542	−	3.33833i	0.327173	−	0.509091i	0.965406	+	0.260753i	$0.0839707\pi$
$44$	−1.24031	−	0.429277i	−0.186984	−	0.0647159i
$45$	1.96840	−	3.40937i	0.293432	−	0.508239i
$46$	7.18027	−	6.21504i	1.05867	−	0.916358i
$47$	−6.49244	+	3.74841i	−0.947020	+	0.546762i	−0.892154	−	0.451732i	$-0.850806\pi$
$47$	−6.49244	+	3.74841i	−0.947020	+	0.546762i	−0.0548659	+	0.998494i	$0.517473\pi$
$48$	3.13769	−	2.71882i	0.452886	−	0.392428i
$49$	−4.92160	+	4.97773i	−0.703086	+	0.711105i
$50$	−2.95851	+	20.5769i	−0.418396	+	2.91001i
$51$	0.599478	+	6.27802i	0.0839438	+	0.879099i
$52$	−0.247487	+	0.618193i	−0.0343203	+	0.0857280i
$53$	0.0565734	+	0.0593325i	0.00777096	+	0.00814994i	0.727608	−	0.685993i	$-0.240632\pi$
$53$	0.0565734	+	0.0593325i	0.00777096	+	0.00814994i	−0.719837	+	0.694143i	$0.755784\pi$
$54$	0.907358	−	1.76003i	0.123476	−	0.239510i
$55$	−2.44670	+	1.11737i	−0.329913	+	0.150666i
$56$	0.340629	+	0.235075i	0.0455185	+	0.0314132i
$57$	1.31555	+	1.13993i	0.174248	+	0.150987i
$58$	12.9970	+	2.50497i	1.70659	+	0.328919i
$59$	−7.52852	−	1.82640i	−0.980129	−	0.237777i	−0.286477	−	0.958087i	$-0.592484\pi$
$59$	−7.52852	−	1.82640i	−0.980129	−	0.237777i	−0.693652	+	0.720310i	$0.743999\pi$
$60$	−0.718872	+	7.52836i	−0.0928059	+	0.971908i
$61$	6.51667	+	3.35958i	0.834374	+	0.430150i	0.821803	−	0.569771i	$-0.192968\pi$
$61$	6.51667	+	3.35958i	0.834374	+	0.430150i	0.0125705	+	0.999921i	$0.495999\pi$
$62$	2.74285	−	9.34130i	0.348343	−	1.18635i
$63$	2.58008	+	0.585807i	0.325060	+	0.0738047i
$64$	−3.05580	+	6.69128i	−0.381976	+	0.836410i
$65$	0.507188	+	1.26689i	0.0629089	+	0.157139i
$66$	−1.20252	+	0.619941i	−0.148020	+	0.0763095i
$67$	−0.257243	−	1.33470i	−0.0314272	−	0.163060i	0.962824	−	0.270128i	$-0.0870659\pi$
$67$	−0.257243	−	1.33470i	−0.0314272	−	0.163060i	−0.994252	+	0.107068i	$0.965854\pi$
$68$	−6.05747	−	10.4919i	−0.734577	−	1.27232i
$69$	0.230747	−	4.79028i	0.0277787	−	0.576682i
$70$	−20.3695	+	3.23571i	−2.43462	+	0.386742i
$71$	0.530127	+	0.611800i	0.0629145	+	0.0726073i	0.786334	−	0.617801i	$-0.211976\pi$
$71$	0.530127	+	0.611800i	0.0629145	+	0.0726073i	−0.723420	+	0.690408i	$0.757431\pi$
$72$	0.00744315	−	0.156251i	0.000877184	−	0.0184144i
$73$	−1.37288	+	1.74576i	−0.160683	+	0.204325i	−0.859727	−	0.510753i	$-0.829367\pi$
$73$	−1.37288	+	1.74576i	−0.160683	+	0.204325i	0.699044	+	0.715079i	$0.253609\pi$
$74$	17.5909	−	12.5264i	2.04489	−	1.45616i
$75$	6.48970	+	8.25232i	0.749366	+	0.952896i
$76$	−3.20847	−	0.942092i	−0.368037	−	0.108065i
$77$	−1.20378	−	1.34856i	−0.137183	−	0.153683i
$78$	0.285139	+	0.624368i	0.0322857	+	0.0706957i
$79$	4.52434	−	4.74500i	0.509029	−	0.533854i	−0.418197	−	0.908356i	$-0.637338\pi$
$79$	4.52434	−	4.74500i	0.509029	−	0.533854i	0.927226	+	0.374502i	$0.122186\pi$
$80$	5.34581	+	15.4457i	0.597680	+	1.72688i
$81$	−0.327068	−	0.945001i	−0.0363409	−	0.105000i
$82$	15.0658	−	15.8006i	1.66374	−	1.74488i
$83$	5.09021	+	11.1460i	0.558723	+	1.22343i	0.952588	+	0.304265i	$0.0984107\pi$
$83$	5.09021	+	11.1460i	0.558723	+	1.22343i	−0.393864	+	0.919169i	$0.628862\pi$
$84$	−4.97593	+	1.03530i	−0.542919	+	0.112960i
$85$	−23.8221	−	6.99479i	−2.58387	−	0.758691i
$86$	4.85737	+	6.17665i	0.523784	+	0.666045i
$87$	5.44499	−	3.87736i	0.583765	−	0.415697i
$88$	−0.0660673	+	0.0840115i	−0.00704280	+	0.00895565i
$89$	0.122645	−	2.57464i	0.0130004	−	0.272912i	−0.983003	−	0.183592i	$-0.941228\pi$
$89$	0.122645	−	2.57464i	0.0130004	−	0.272912i	0.996003	−	0.0893200i	$-0.0284694\pi$
$90$	5.10495	+	5.89142i	0.538109	+	0.621011i
$91$	−0.712472	+	0.577485i	−0.0746873	+	0.0605369i
$92$	3.41950	+	8.55469i	0.356507	+	0.891888i
$93$	−2.45831	−	4.25792i	−0.254915	−	0.441526i
$94$	−2.80941	−	14.5766i	−0.289768	−	1.50346i
$95$	−6.09107	+	3.14016i	−0.624931	+	0.322174i
$96$	2.93920	+	7.34177i	0.299981	+	0.749316i
$97$	−6.54959	+	14.3416i	−0.665010	+	1.45617i	0.212768	+	0.977103i	$0.431752\pi$
$97$	−6.54959	+	14.3416i	−0.665010	+	1.45617i	−0.877778	+	0.479067i	$0.840975\pi$
$98$	−6.12712	−	12.4333i	−0.618932	−	1.25596i
$99$	−0.192490	+	0.655561i	−0.0193460	+	0.0658864i
$100$	−17.9256	−	9.24128i	−1.79256	−	0.924128i
$101$	1.06419	−	11.1447i	0.105891	−	1.10894i	−0.773810	−	0.633418i	$-0.781652\pi$
$101$	1.06419	−	11.1447i	0.105891	−	1.10894i	0.879701	−	0.475526i	$-0.157742\pi$
$102$	−12.1360	−	2.94415i	−1.20164	−	0.291515i
$103$	−4.09375	−	0.789005i	−0.403369	−	0.0777430i	−0.0164683	−	0.999864i	$-0.505242\pi$
$103$	−4.09375	−	0.789005i	−0.403369	−	0.0777430i	−0.386901	+	0.922121i	$0.626454\pi$
$104$	0.0409797	+	0.0355091i	0.00401839	+	0.00348196i
$105$	−5.91609	+	8.57257i	−0.577351	+	0.836597i
$106$	−0.147665	+	0.0674364i	−0.0143425	+	0.00655000i
$107$	4.51533	−	8.75852i	0.436514	−	0.846718i	−0.563277	−	0.826268i	$-0.690460\pi$
$107$	4.51533	−	8.75852i	0.436514	−	0.846718i	0.999791	−	0.0204504i	$-0.00651002\pi$
$108$	1.32564	+	1.39029i	0.127560	+	0.133781i
$109$	1.75536	−	4.38468i	0.168133	−	0.419976i	−0.820241	−	0.572018i	$-0.806161\pi$
$109$	1.75536	−	4.38468i	0.168133	−	0.419976i	0.988374	+	0.152042i	$0.0485849\pi$
$110$	−0.506283	−	5.30204i	−0.0482722	−	0.505530i
$111$	1.55205	−	10.7948i	0.147314	−	1.02459i
$112$	−8.85286	+	6.50279i	−0.836517	+	0.614456i
$113$	2.23340	−	1.93525i	0.210101	−	0.182053i	−0.543453	−	0.839440i	$-0.682883\pi$
$113$	2.23340	−	1.93525i	0.210101	−	0.182053i	0.753554	+	0.657386i	$0.228338\pi$
$114$	−2.98509	+	1.72344i	−0.279579	+	0.161415i
$115$	17.1699	+	7.85229i	1.60110	+	0.732230i
$116$	−6.42042	+	11.1205i	−0.596121	+	1.03251i
$117$	0.327573	+	0.113374i	0.0302842	+	0.0104814i
$118$	8.29344	−	12.9048i	0.763473	−	1.18799i
$119$	−0.245856	−	16.6838i	−0.0225376	−	1.52940i
$120$	0.560176	+	0.255824i	0.0511368	+	0.0233534i
$121$	−8.27964	+	6.51118i	−0.752695	+	0.591926i
$122$	−10.5071	+	10.0185i	−0.951266	+	0.907030i
$123$	−0.524611	−	11.0129i	−0.0473025	−	0.993003i
$124$	7.69355	+	5.47855i	0.690901	+	0.491988i
$125$	−20.7694	+	6.09845i	−1.85767	+	0.545462i
$126$	−2.76716	+	4.44857i	−0.246519	+	0.396311i
$127$	−12.7772	+	14.7457i	−1.13380	+	1.30847i	−0.188569	+	0.982060i	$0.560385\pi$
$127$	−12.7772	+	14.7457i	−1.13380	+	1.30847i	−0.945228	+	0.326411i	$0.894161\pi$
$128$	0.904993	+	0.862909i	0.0799908	+	0.0762711i
$129$	3.95031	+	0.377209i	0.347806	+	0.0332114i
$130$	−2.69915	+	0.128576i	−0.236731	+	0.0112769i
$131$	−16.9772	+	4.11863i	−1.48331	+	0.359847i	−0.894002	−	0.448063i	$-0.852114\pi$
$131$	−16.9772	+	4.11863i	−1.48331	+	0.359847i	−0.589306	+	0.807910i	$0.700599\pi$
$132$	−0.186788	−	1.29914i	−0.0162578	−	0.113076i
$133$	−3.22693	−	3.28597i	−0.279810	−	0.284930i
$134$	2.66416	+	0.383048i	0.230148	+	0.0330903i
$135$	3.93235	+	0.187321i	0.338442	+	0.0161220i
$136$	−0.968699	+	0.186701i	−0.0830652	+	0.0160095i
$137$	−7.43006	−	4.28975i	−0.634793	−	0.366498i	0.147813	−	0.989015i	$-0.452777\pi$
$137$	−7.43006	−	4.28975i	−0.634793	−	0.366498i	−0.782606	+	0.622518i	$0.786110\pi$
$138$	8.81434	+	3.53418i	0.750327	+	0.300849i
$139$		−	10.8970i		−	0.924271i	−0.886809	−	0.462135i	$-0.847083\pi$
$139$		−	10.8970i		−	0.924271i	0.886809	−	0.462135i	$-0.152917\pi$
$140$	3.49678	−	19.7009i	0.295532	−	1.66503i
$141$	−6.30673	−	4.05309i	−0.531122	−	0.341332i
$142$	−1.48816	+	0.595770i	−0.124884	+	0.0499959i
$143$	−0.137378	−	0.192921i	−0.0114882	−	0.0161329i
$144$	3.85436	+	1.54305i	0.321196	+	0.128588i
$145$	6.20409	+	25.5736i	0.515221	+	2.12377i
$146$	−2.37760	−	3.69962i	−0.196772	−	0.306183i
$147$	−6.67960	−	2.09356i	−0.550924	−	0.172674i
$148$	5.90230	+	20.1014i	0.485166	+	1.65232i
$149$	2.04320	−	10.6011i	0.167385	−	0.868478i	−0.797001	−	0.603978i	$-0.793581\pi$
$149$	2.04320	−	10.6011i	0.167385	−	0.868478i	0.964386	−	0.264499i	$-0.0852066\pi$
$150$	−19.6451	+	6.79925i	−1.60402	+	0.555156i
$151$	−1.21104	+	4.99197i	−0.0985530	+	0.406241i	−0.999624	−	0.0274312i	$-0.991267\pi$
$151$	−1.21104	+	4.99197i	−0.0985530	+	0.406241i	0.901071	+	0.433672i	$0.142782\pi$
$152$	−0.157948	+	0.221807i	−0.0128113	+	0.0179909i
$153$	−5.30543	+	3.40959i	−0.428919	+	0.275649i
$154$	3.30311	−	1.37918i	0.266172	−	0.111137i
$155$	19.1588	−	2.75462i	1.53887	−	0.221256i
$156$	−0.662877	+	0.0632971i	−0.0530726	+	0.00506782i
$157$	9.44552	+	7.42804i	0.753834	+	0.592822i	0.919376	−	0.393381i	$-0.128695\pi$
$157$	9.44552	+	7.42804i	0.753834	+	0.592822i	−0.165541	+	0.986203i	$0.552937\pi$
$158$	5.94889	+	11.5392i	0.473268	+	0.918012i
$159$	−0.0268134	+	0.0774722i	−0.00212644	+	0.00614394i
$160$	−31.1332			−2.46130
$161$	−1.62722	+	12.5838i	−0.128243	+	0.991743i
$162$	1.98015			0.155575
$163$	2.04588	−	5.91118i	0.160246	−	0.462999i	−0.836084	−	0.548602i	$-0.815160\pi$
$163$	2.04588	−	5.91118i	0.160246	−	0.462999i	0.996329	+	0.0856026i	$0.0272816\pi$
$164$	9.70517	+	18.8254i	0.757847	+	1.47002i
$165$	−2.11430	−	1.66271i	−0.164598	−	0.129442i
$166$	−24.1536	+	2.30639i	−1.87468	+	0.179010i
$167$	2.27287	−	0.326790i	0.175880	−	0.0252878i	−0.0538119	−	0.998551i	$-0.517137\pi$
$167$	2.27287	−	0.326790i	0.175880	−	0.0252878i	0.229692	+	0.973263i	$0.426228\pi$
$168$	−0.0528573	+	0.410481i	−0.00407803	+	0.0316693i
$169$	10.8352	−	6.96337i	0.833478	−	0.535644i
$170$	28.5172	−	40.0468i	2.18717	−	3.07145i
$171$	−0.410390	+	1.69165i	−0.0313833	+	0.129364i
$172$	−7.20381	+	2.49326i	−0.549286	+	0.190110i
$173$	−2.13087	+	11.0560i	−0.162007	+	0.840573i	0.806433	+	0.591326i	$0.201395\pi$
$173$	−2.13087	+	11.0560i	−0.162007	+	0.840573i	−0.968440	+	0.249247i	$0.919817\pi$
$174$	3.72908	+	12.7001i	0.282701	+	0.962790i
$175$	−15.3596	−	23.1430i	−1.16108	−	1.74945i
$176$	−1.53360	−	2.38633i	−0.115599	−	0.179876i
$177$	−1.82640	−	7.52852i	−0.137281	−	0.565878i
$178$	4.73836	+	1.89695i	0.355155	+	0.142183i
$179$	−11.2525	−	15.8020i	−0.841055	−	1.18110i	−0.981586	−	0.191020i	$-0.938820\pi$
$179$	−11.2525	−	15.8020i	−0.841055	−	1.18110i	0.140531	−	0.990076i	$-0.455119\pi$
$180$	−7.02088	+	2.81074i	−0.523306	+	0.209500i
$181$	8.18964	+	5.26316i	0.608731	+	0.391208i	0.808381	−	0.588659i	$-0.200344\pi$
$181$	8.18964	+	5.26316i	0.608731	+	0.391208i	−0.199650	+	0.979867i	$0.563980\pi$
$182$	−0.619189	−	1.70721i	−0.0458973	−	0.126547i
$183$			7.33169i			0.541974i
$184$	0.749372	−	0.0352969i	0.0552445	−	0.00260212i
$185$	37.1819	+	21.4670i	2.73367	+	1.57828i
$186$	9.55973	−	1.84249i	0.700953	−	0.135098i
$187$	4.30401	+	0.205025i	0.314740	+	0.0149929i
$188$	14.2548	+	2.04953i	1.03964	+	0.149478i
$189$	0.661577	+	2.56170i	0.0481226	+	0.186336i
$190$	−1.93117	−	13.4316i	−0.140102	−	0.974430i
$191$	−22.2566	+	5.39940i	−1.61043	+	0.390687i	−0.937213	−	0.348756i	$-0.886604\pi$
$191$	−22.2566	+	5.39940i	−1.61043	+	0.390687i	−0.673219	+	0.739443i	$0.735089\pi$
$192$	−7.34770	+	0.350014i	−0.530274	+	0.0252601i
$193$	9.25174	+	0.883435i	0.665955	+	0.0635910i	0.422558	−	0.906336i	$-0.361132\pi$
$193$	9.25174	+	0.883435i	0.665955	+	0.0635910i	0.243397	+	0.969927i	$0.421738\pi$
$194$	−22.5949	−	21.5442i	−1.62222	−	1.54678i
$195$	−0.893653	+	1.03133i	−0.0639958	+	0.0738551i
$196$	13.3426	−	1.67210i	0.953046	−	0.119436i
$197$	18.9796	−	5.57291i	1.35224	−	0.397053i	0.476218	−	0.879327i	$-0.342007\pi$
$197$	18.9796	−	5.57291i	1.35224	−	0.397053i	0.876021	+	0.482274i	$0.160189\pi$
$198$	−1.10205	−	0.784767i	−0.0783194	−	0.0557710i
$199$	−0.714604	−	15.0014i	−0.0506569	−	1.06342i	−0.870917	−	0.491429i	$-0.836475\pi$
$199$	−0.714604	−	15.0014i	−0.0506569	−	1.06342i	0.820261	−	0.571990i	$-0.193828\pi$
$200$	−1.18855	+	1.13328i	−0.0840433	+	0.0801352i
$201$	1.06846	−	0.840244i	0.0753631	−	0.0592662i
$202$	20.1653	+	9.20920i	1.41883	+	0.647957i
$203$	−15.1840	+	9.06741i	−1.06571	+	0.636408i
$204$	6.54984	−	10.1917i	0.458580	−	0.713565i
$205$	41.0177	+	14.1964i	2.86480	+	0.991517i
$206$	4.12771	−	7.14941i	0.287591	−	0.498123i
$207$	4.36350	−	1.98994i	0.303284	−	0.138310i
$208$	−1.24635	+	0.719578i	−0.0864185	+	0.0498938i
$209$	0.898831	−	0.778841i	0.0621734	−	0.0538736i
$210$	−12.2099	−	16.6224i	−0.842560	−	1.14706i
$211$	0.448120	−	3.11675i	0.0308499	−	0.214566i	−0.968565	−	0.248759i	$-0.919977\pi$
$211$	0.448120	−	3.11675i	0.0308499	−	0.214566i	0.999415	+	0.0341936i	$0.0108863\pi$
$212$	−0.0149700	−	0.156773i	−0.00102814	−	0.0107672i
$213$	−0.300871	+	0.751539i	−0.0206153	+	0.0514946i
$214$	13.4650	+	14.1217i	0.920450	+	0.965340i
$215$	−7.15857	+	13.8857i	−0.488211	+	0.946997i
$216$	0.142292	−	0.0649826i	0.00968175	−	0.00442151i
$217$	5.57755	+	11.7517i	0.378629	+	0.797760i
$218$	7.06796	+	6.12442i	0.478703	+	0.414798i
$219$	−2.18078	−	0.420311i	−0.147363	−	0.0284020i
$220$	5.02141	+	1.21818i	0.338543	+	0.0821297i
$221$	0.207802	−	2.17620i	0.0139783	−	0.146387i
$222$	19.1945	+	9.89545i	1.28825	+	0.664139i
$223$	−1.19969	+	4.08576i	−0.0803370	+	0.273603i	−0.989859	−	0.142053i	$-0.954630\pi$
$223$	−1.19969	+	4.08576i	−0.0803370	+	0.273603i	0.909522	+	0.415656i	$0.136448\pi$
$224$	−6.18993	−	19.9867i	−0.413582	−	1.33542i
$225$	−4.36120	+	9.54971i	−0.290747	+	0.636647i
$226$	2.17488	+	5.43260i	0.144671	+	0.361371i
$227$	13.2908	−	6.85190i	0.882144	−	0.454777i	0.0432453	−	0.999064i	$-0.486230\pi$
$227$	13.2908	−	6.85190i	0.882144	−	0.454777i	0.838899	+	0.544288i	$0.183200\pi$
$228$	−0.632842	−	3.28349i	−0.0419110	−	0.217455i
$229$	5.05876	+	8.76203i	0.334292	+	0.579011i	0.983349	−	0.181729i	$-0.0581694\pi$
$229$	5.05876	+	8.76203i	0.334292	+	0.579011i	−0.649056	+	0.760740i	$0.724836\pi$
$230$	−25.8135	+	27.0436i	−1.70209	+	1.78320i
$231$	0.647045	−	1.68791i	0.0425724	−	0.111056i
$232$	0.684746	+	0.790240i	0.0449558	+	0.0518818i
$233$	0.400392	−	8.40527i	0.0262306	−	0.550648i	−0.947058	−	0.321063i	$-0.895960\pi$
$233$	0.400392	−	8.40527i	0.0262306	−	0.550648i	0.973289	−	0.229585i	$-0.0737369\pi$
$234$	−0.424302	+	0.539544i	−0.0277375	+	0.0352711i
$235$	24.0410	−	17.1195i	1.56826	−	1.11675i
$236$	9.19931	+	11.6979i	0.598824	+	0.761467i
$237$	6.29070	+	1.84711i	0.408625	+	0.119983i
$238$	31.3788	+	10.3451i	2.03398	+	0.670575i
$239$	12.7567	+	27.9332i	0.825160	+	1.80685i	0.518672	+	0.854973i	$0.326427\pi$
$239$	12.7567	+	27.9332i	0.825160	+	1.80685i	0.306488	+	0.951875i	$0.400846\pi$
$240$	−11.2791	+	11.8292i	−0.728063	+	0.763570i
$241$	−0.966841	−	2.79350i	−0.0622797	−	0.179945i	0.909568	−	0.415555i	$-0.136413\pi$
$241$	−0.966841	−	2.79350i	−0.0622797	−	0.179945i	−0.971848	+	0.235609i	$0.924291\pi$
$242$	−6.82176	−	19.7102i	−0.438519	−	1.26702i
$243$	0.690079	−	0.723734i	0.0442686	−	0.0464276i
$244$	−5.85078	−	12.8114i	−0.374558	−	0.820168i
$245$	17.4249	−	21.3494i	1.11324	−	1.36396i
$246$	20.9477	+	6.15079i	1.33557	+	0.392160i
$247$	−0.372997	−	0.474304i	−0.0237332	−	0.0301792i
$248$	0.626489	−	0.446121i	0.0397821	−	0.0283287i
$249$	−7.57450	+	9.63176i	−0.480014	+	0.610388i
$250$	2.03950	−	42.8143i	0.128989	−	2.70781i
$251$	−1.16615	−	1.34580i	−0.0736065	−	0.0849464i	0.717752	−	0.696299i	$-0.245171\pi$
$251$	−1.16615	−	1.34580i	−0.0736065	−	0.0849464i	−0.791358	+	0.611353i	$0.790626\pi$
$252$	−3.20031	−	3.94838i	−0.201601	−	0.248725i
$253$	−3.21715	−	0.621832i	−0.202260	−	0.0390942i
$254$	−19.3178	−	33.4593i	−1.21210	−	2.09943i
$255$	−4.69869	−	24.3791i	−0.294243	−	1.52668i
$256$	−15.2774	+	7.87606i	−0.954839	+	0.492254i
$257$	2.65654	+	6.63571i	0.165710	+	0.413924i	0.987860	−	0.155347i	$-0.0496496\pi$
$257$	2.65654	+	6.63571i	0.165710	+	0.413924i	−0.822150	+	0.569271i	$0.807225\pi$
$258$	−3.26425	+	7.14771i	−0.203223	+	0.444997i
$259$	−6.38868	+	28.1378i	−0.396973	+	1.74840i
$260$	0.738558	−	2.51530i	0.0458035	−	0.155992i
$261$	5.94138	+	3.06299i	0.367762	+	0.189595i
$262$	3.28824	−	34.4360i	0.203148	−	2.12746i
$263$	6.47774	+	1.57148i	0.399435	+	0.0969018i	0.430444	−	0.902617i	$-0.358357\pi$
$263$	6.47774	+	1.57148i	0.399435	+	0.0969018i	−0.0310092	+	0.999519i	$0.509872\pi$
$264$	−0.104946	−	0.0202267i	−0.00645899	−	0.00124487i
$265$	−0.243913	−	0.211352i	−0.0149835	−	0.0129832i
$266$	8.23876	−	3.91024i	0.505151	−	0.239752i
$267$	2.34463	−	1.07076i	0.143489	−	0.0655293i
$268$	−1.19650	+	2.32089i	−0.0730879	+	0.141771i
$269$	−10.0200	−	10.5087i	−0.610933	−	0.640728i	0.343500	−	0.939153i	$-0.388387\pi$
$269$	−10.0200	−	10.5087i	−0.610933	−	0.640728i	−0.954433	+	0.298425i	$0.903539\pi$
$270$	−2.89728	+	7.23706i	−0.176323	+	0.440434i
$271$	−1.08935	−	11.4082i	−0.0661733	−	0.692999i	−0.966308	−	0.257387i	$-0.917138\pi$
$271$	−1.08935	−	11.4082i	−0.0661733	−	0.692999i	0.900135	−	0.435611i	$-0.143468\pi$
$272$	3.72628	−	25.9169i	0.225939	−	1.57144i
$273$	−0.839763	−	0.368651i	−0.0508248	−	0.0223118i
$274$	12.8392	−	11.1252i	0.775644	−	0.672100i
$275$	6.21193	−	3.58646i	0.374593	−	0.216272i
$276$	−6.03681	+	6.95936i	−0.363373	+	0.418904i
$277$	−15.3389	+	26.5678i	−0.921627	+	1.59630i	−0.124728	+	0.992191i	$0.539806\pi$
$277$	−15.3389	+	26.5678i	−0.921627	+	1.59630i	−0.796899	+	0.604113i	$0.793528\pi$
$278$	20.3909	+	7.05737i	1.22297	+	0.423273i
$279$	2.65813	−	4.13613i	0.159138	−	0.247624i
$280$	−1.42289	−	0.793783i	−0.0850338	−	0.0474376i
$281$	−23.5563	−	10.7578i	−1.40525	−	0.641755i	−0.438793	−	0.898588i	$-0.644594\pi$
$281$	−23.5563	−	10.7578i	−1.40525	−	0.641755i	−0.966456	+	0.256833i	$0.917321\pi$
$282$	11.6688	−	9.17648i	0.694869	−	0.546451i
$283$	4.16423	−	3.97059i	0.247538	−	0.236027i	−0.556144	−	0.831086i	$-0.687720\pi$
$283$	4.16423	−	3.97059i	0.247538	−	0.236027i	0.803682	+	0.595059i	$0.202871\pi$
$284$	−0.0739948	−	1.55334i	−0.00439078	−	0.0921738i
$285$	−5.58218	−	3.97505i	−0.330660	−	0.235462i
$286$	0.449975	−	0.132125i	0.0266076	−	0.00781269i
$287$	−0.958509	+	29.1548i	−0.0565790	+	1.72095i
$288$	−5.17880	+	5.97666i	−0.305164	+	0.352178i
$289$	16.4815	+	15.7151i	0.969503	+	0.924419i
$290$	−51.8725	−	4.95322i	−3.04606	−	0.290863i
$291$	−15.7485	+	0.750195i	−0.923195	+	0.0439772i
$292$	4.14612	−	1.00584i	0.242633	−	0.0588622i
$293$	4.00329	+	27.8435i	0.233875	+	1.62663i	0.681085	+	0.732205i	$0.261508\pi$
$293$	4.00329	+	27.8435i	0.233875	+	1.62663i	−0.447210	+	0.894429i	$0.647582\pi$
$294$	8.24357	−	11.1433i	0.480775	−	0.649889i
$295$	30.1876	+	4.34032i	1.75759	+	0.252703i
$296$	1.70404	+	0.0811734i	0.0990453	+	0.00471811i
$297$	−0.670890	+	0.129304i	−0.0389290	+	0.00750295i
$298$	18.5140	+	10.6891i	1.07249	+	0.619202i
$299$	−0.392791	+	1.61535i	−0.0227157	+	0.0934180i
$300$		−	20.1675i		−	1.16437i
$301$	−10.3375	−	1.83485i	−0.595844	−	0.105759i
$302$	−8.55688	−	5.49918i	−0.492393	−	0.316442i
$303$	10.3935	−	4.16093i	0.597090	−	0.239039i
$304$	−4.19209	−	5.88697i	−0.240433	−	0.337641i
$305$	−26.7959	−	10.7275i	−1.53433	−	0.614252i
$306$	−2.94415	−	12.1360i	−0.168306	−	0.693767i
$307$	−14.8331	−	23.0807i	−0.846569	−	1.31729i	−0.946635	−	0.322307i	$-0.895542\pi$
$307$	−14.8331	−	23.0807i	−0.846569	−	1.31729i	0.100066	−	0.994981i	$-0.468095\pi$
$308$	0.216321	+	3.46580i	0.0123261	+	0.197483i
$309$	−1.17457	−	4.00021i	−0.0668188	−	0.227564i
$310$	−7.25351	+	37.6348i	−0.411972	+	2.13751i
$311$	−30.7333	+	10.6369i	−1.74273	+	0.603163i	−0.997941	−	0.0641410i	$-0.979569\pi$
$311$	−30.7333	+	10.6369i	−1.74273	+	0.603163i	−0.744785	+	0.667304i	$0.767448\pi$
$312$	−0.0127838	+	0.0526955i	−0.000723739	+	0.00298329i
$313$	2.37115	−	3.32981i	0.134025	−	0.188212i	−0.742109	−	0.670279i	$-0.766174\pi$
$313$	2.37115	−	3.32981i	0.134025	−	0.188212i	0.876134	+	0.482067i	$0.160114\pi$
$314$	−20.0170	+	12.8642i	−1.12963	+	0.725966i
$315$	−10.3305	−	1.33025i	−0.582058	−	0.0749512i
$316$	−12.4664	+	1.79240i	−0.701291	+	0.100830i
$317$	5.89091	−	0.562514i	0.330867	−	0.0315939i	0.0716990	−	0.997426i	$-0.477158\pi$
$317$	5.89091	−	0.562514i	0.330867	−	0.0315939i	0.259167	+	0.965832i	$0.416552\pi$
$318$	−0.127604	−	0.100349i	−0.00715567	−	0.00562728i
$319$	−2.09275	−	4.05937i	−0.117172	−	0.227281i
$320$	9.47164	−	27.3665i	0.529481	−	1.52983i
$321$	9.85393			0.549993
$322$	−22.4935	−	11.1948i	−1.25352	−	0.623860i
$323$	10.9780			0.610831
$324$	−0.628298	+	1.81535i	−0.0349055	+	0.100853i
$325$	−1.66756	−	3.23461i	−0.0924994	−	0.179424i
$326$	9.73626	+	7.65668i	0.539242	+	0.424064i
$327$	4.70161	−	0.448949i	0.260000	−	0.0248270i
$328$	1.70713	−	0.245448i	0.0942606	−	0.0135526i
$329$	15.7701	+	12.0300i	0.869435	+	0.663233i
$330$	4.48065	−	2.87954i	0.246652	−	0.158513i
$331$	−10.5380	+	14.7985i	−0.579219	+	0.813399i	−0.995392	−	0.0958863i	$-0.969431\pi$
$331$	−10.5380	+	14.7985i	−0.579219	+	0.813399i	0.416174	+	0.909285i	$0.363371\pi$
$332$	5.54945	−	22.8751i	0.304565	−	1.25544i
$333$	10.3060	−	3.56693i	0.564764	−	0.195467i
$334$	−0.860510	+	4.46475i	−0.0470850	+	0.244300i
$335$	1.50760	+	5.13441i	0.0823689	+	0.280523i
$336$	−9.83653	−	4.88899i	−0.536627	−	0.266716i
$337$	2.33495	+	3.63325i	0.127193	+	0.197916i	0.899009	−	0.437930i	$-0.144288\pi$
$337$	2.33495	+	3.63325i	0.127193	+	0.197916i	−0.771817	+	0.635845i	$0.780652\pi$
$338$	6.01281	+	24.7851i	0.327054	+	1.34813i
$339$	2.74352	+	1.09834i	0.149008	+	0.0596537i
$340$	27.6653	+	38.8505i	1.50036	+	2.10697i
$341$	−3.11859	+	1.24850i	−0.168881	+	0.0676099i
$342$	−2.89971	−	1.86353i	−0.156798	−	0.100768i
$343$	17.1702	+	6.94161i	0.927101	+	0.374812i
$344$			0.620751i			0.0334687i
$345$	0.888311	+	18.8593i	0.0478250	+	1.01535i
$346$	−19.3085	−	11.1478i	−1.03803	−	0.599307i
$347$	8.69828	−	1.67646i	0.466948	−	0.0899969i	0.0496503	−	0.998767i	$-0.484189\pi$
$347$	8.69828	−	1.67646i	0.466948	−	0.0899969i	0.417298	+	0.908770i	$0.362977\pi$
$348$	−12.8263	−	0.610992i	−0.687562	−	0.0327526i
$349$	17.7108	+	2.54643i	0.948038	+	0.136307i	0.598953	−	0.800784i	$-0.295583\pi$
$349$	17.7108	+	2.54643i	0.948038	+	0.136307i	0.349085	+	0.937091i	$0.386493\pi$
$350$	53.2539	−	13.7532i	2.84654	−	0.735138i
$351$	0.0493317	+	0.343110i	0.00263313	+	0.0183138i
$352$	5.25090	−	1.27386i	0.279874	−	0.0678967i
$353$	−19.1518	+	0.912313i	−1.01935	+	0.0485575i	−0.550596	−	0.834772i	$-0.685599\pi$
$353$	−19.1518	+	0.912313i	−1.01935	+	0.0485575i	−0.468752	+	0.883330i	$0.655296\pi$
$354$	15.2706	+	1.45816i	0.811621	+	0.0775004i
$355$	−2.30650	−	2.19925i	−0.122416	−	0.116724i
$356$	−3.24255	+	3.74210i	−0.171855	+	0.198331i
$357$	14.7165	−	7.86350i	0.778881	−	0.416180i
$358$	36.8570	−	10.8222i	1.94796	−	0.571971i
$359$	−2.80852	−	1.99994i	−0.148228	−	0.105553i	0.503537	−	0.863974i	$-0.332032\pi$
$359$	−2.80852	−	1.99994i	−0.148228	−	0.105553i	−0.651765	+	0.758421i	$0.725971\pi$
$360$	0.0293022	+	0.615130i	0.00154436	+	0.0324202i
$361$	−11.5580	+	11.0205i	−0.608314	+	0.580026i
$362$	−15.1526	+	11.9162i	−0.796405	+	0.626300i
$363$	−9.58132	−	4.37564i	−0.502889	−	0.229662i
$364$	1.76159	−	0.0259592i	0.0923326	−	0.00136063i
$365$	4.72699	−	7.35534i	0.247422	−	0.384996i
$366$	−13.7194	−	4.74833i	−0.717124	−	0.248199i
$367$	1.96355	−	3.40097i	0.102496	−	0.177529i	−0.810216	−	0.586131i	$-0.800650\pi$
$367$	1.96355	−	3.40097i	0.102496	−	0.177529i	0.912713	+	0.408602i	$0.133984\pi$
$368$	−5.61979	+	19.1016i	−0.292952	+	0.995739i
$369$	9.54829	−	5.51271i	0.497064	−	0.286980i
$370$	−64.2506	+	55.6734i	−3.34023	+	2.89432i
$371$	0.0871872	−	0.198607i	0.00452653	−	0.0103112i
$372$	−1.34414	+	9.34871i	−0.0696905	+	0.484708i
$373$	0.0981561	+	1.02794i	0.00508233	+	0.0532246i	0.997657	−	0.0684098i	$-0.0217925\pi$
$373$	0.0981561	+	1.02794i	0.00508233	+	0.0532246i	−0.992575	+	0.121634i	$0.961186\pi$
$374$	−3.17112	+	7.92107i	−0.163975	+	0.409589i
$375$	−14.9376	−	15.6661i	−0.771375	−	0.808995i
$376$	0.537369	−	1.04235i	0.0277127	−	0.0537551i
$377$	−2.10770	+	0.962552i	−0.108552	+	0.0495740i
$378$	−5.22204	−	0.421099i	−0.268593	−	0.0216590i
$379$	−17.1517	−	14.8621i	−0.881026	−	0.763413i	0.0915986	−	0.995796i	$-0.470802\pi$
$379$	−17.1517	−	14.8621i	−0.881026	−	0.763413i	−0.972624	+	0.232383i	$0.925348\pi$
$380$	12.9265	+	2.49137i	0.663114	+	0.127805i
$381$	−18.9614	−	4.59998i	−0.971422	−	0.235664i
$382$	4.31078	−	45.1445i	0.220558	−	2.30979i
$383$	−32.1828	−	16.5914i	−1.64447	−	0.847781i	−0.996269	−	0.0863077i	$-0.972493\pi$
$383$	−32.1828	−	16.5914i	−1.64447	−	0.847781i	−0.648197	−	0.761473i	$-0.724477\pi$
$384$	−0.352292	+	1.19980i	−0.0179778	+	0.0612269i
$385$	5.22223	+	4.83450i	0.266150	+	0.246389i
$386$	−7.64496	+	16.7401i	−0.389118	+	0.852050i
$387$	1.47486	+	3.68403i	0.0749714	+	0.187270i
$388$	26.9204	−	13.8784i	1.36668	−	0.704570i
$389$	−2.45025	−	12.7131i	−0.124233	−	0.644580i	−0.989647	−	0.143523i	$-0.954157\pi$
$389$	−2.45025	−	12.7131i	−0.124233	−	0.644580i	0.865414	−	0.501057i	$-0.167055\pi$
$390$	−1.35110	−	2.34018i	−0.0684158	−	0.118500i
$391$	−18.6837	−	23.7844i	−0.944877	−	1.20283i
$392$	0.226688	−	1.07128i	0.0114495	−	0.0541076i
$393$	−11.4402	−	13.2027i	−0.577082	−	0.665988i
$394$	−1.86374	+	39.1247i	−0.0938938	+	1.97107i
$395$	−15.9551	+	20.2886i	−0.802791	+	1.02083i
$396$	1.06913	−	0.761325i	0.0537259	−	0.0382580i
$397$	8.99229	+	11.4346i	0.451310	+	0.573888i	0.957463	−	0.288556i	$-0.0931752\pi$
$397$	8.99229	+	11.4346i	0.451310	+	0.573888i	−0.506153	+	0.862444i	$0.668933\pi$
$398$	28.5341	+	8.37836i	1.43028	+	0.419969i
$399$	1.44202	−	4.37393i	0.0721914	−	0.218970i
$400$	−18.1067	−	39.6480i	−0.905333	−	1.98240i
$401$	5.56411	−	5.83547i	0.277858	−	0.291409i	−0.569986	−	0.821654i	$-0.693052\pi$
$401$	5.56411	−	5.83547i	0.277858	−	0.291409i	0.847845	+	0.530245i	$0.177900\pi$
$402$	0.880322	+	2.54352i	0.0439065	+	0.126859i
$403$	0.557419	+	1.61056i	0.0277670	+	0.0802275i
$404$	−14.8412	+	15.5650i	−0.738375	+	0.774386i
$405$	1.63541	+	3.58104i	0.0812641	+	0.177943i
$406$	−7.13349	−	34.2855i	−0.354029	−	1.70156i
$407$	−7.14941	−	2.09926i	−0.354383	−	0.104056i
$408$	−0.609830	−	0.775462i	−0.0301911	−	0.0383911i
$409$	7.01773	−	4.99730i	0.347004	−	0.247101i	−0.393244	−	0.919434i	$-0.628647\pi$
$409$	7.01773	−	4.99730i	0.347004	−	0.247101i	0.740248	+	0.672333i	$0.234708\pi$
$410$	−53.1297	+	67.5600i	−2.62389	+	3.33655i
$411$	0.408229	−	8.56977i	0.0201364	−	0.422716i
$412$	5.24467	+	6.05267i	0.258386	+	0.298194i
$413$	3.21555	+	20.2425i	0.158227	+	0.996070i
$414$	0.897661	+	9.45395i	0.0441176	+	0.464636i
$415$	−24.1195	−	41.7761i	−1.18398	−	2.05071i
$416$	−0.518795	−	2.69176i	−0.0254360	−	0.131974i
$417$	9.68563	−	4.99329i	0.474307	−	0.244522i
$418$	0.875280	+	2.18634i	0.0428114	+	0.106938i
$419$	11.7356	−	25.6973i	0.573321	−	1.25540i	−0.371689	−	0.928357i	$-0.621221\pi$
$419$	11.7356	−	25.6973i	0.573321	−	1.25540i	0.945010	−	0.327041i	$-0.106051\pi$
$420$	19.1131	−	5.91939i	0.932626	−	0.288837i
$421$	−2.53574	+	8.63593i	−0.123584	+	0.420889i	−0.997922	−	0.0644279i	$-0.979478\pi$
$421$	−2.53574	+	8.63593i	−0.123584	+	0.420889i	0.874338	+	0.485317i	$0.161296\pi$
$422$	5.54197	+	2.85709i	0.269779	+	0.139081i
$423$	0.712618	−	7.46288i	0.0346487	−	0.362858i
$424$	−0.0124627	−	0.00302341i	−0.000605240	−	0.000146830i
$425$	65.0127	+	12.5302i	3.15358	+	0.607802i
$426$	−1.21146	−	1.04973i	−0.0586952	−	0.0508597i
$427$	1.55916	−	19.3351i	0.0754528	−	0.935690i
$428$	−17.2188	+	7.86357i	−0.832302	+	0.380100i
$429$	0.108525	−	0.210508i	0.00523962	−	0.0101634i
$430$	−21.3473	−	22.3884i	−1.02946	−	1.07967i
$431$	4.23796	−	10.5859i	0.204135	−	0.509905i	−0.790606	−	0.612325i	$-0.790234\pi$
$431$	4.23796	−	10.5859i	0.204135	−	0.509905i	0.994741	+	0.102420i	$0.0326586\pi$
$432$	0.394649	+	4.13296i	0.0189876	+	0.198847i
$433$	−0.527864	+	3.67137i	−0.0253675	+	0.176435i	−0.998566	−	0.0535311i	$-0.982952\pi$
$433$	−0.527864	+	3.67137i	−0.0253675	+	0.176435i	0.973199	+	0.229966i	$0.0738615\pi$
$434$	−25.6027	+	2.82602i	−1.22897	+	0.135653i
$435$	−19.8878	+	17.2329i	−0.953549	+	0.826255i
$436$	−7.85735	+	4.53644i	−0.376299	+	0.217256i
$437$	−8.26258	−	1.19247i	−0.395253	−	0.0570438i
$438$	2.19888	−	3.80856i	0.105066	−	0.181980i
$439$	−24.7214	−	8.55616i	−1.17989	−	0.408363i	−0.334438	−	0.942418i	$-0.608547\pi$
$439$	−24.7214	−	8.55616i	−1.17989	−	0.408363i	−0.845450	+	0.534054i	$0.820668\pi$
$440$	0.227478	−	0.353963i	0.0108446	−	0.0168745i
$441$	−1.19993	−	6.89639i	−0.0571397	−	0.328399i
$442$	3.93762	+	1.79825i	0.187294	+	0.0855342i
$443$	21.4767	−	16.8895i	1.02039	−	0.802444i	0.0399385	−	0.999202i	$-0.487284\pi$
$443$	21.4767	−	16.8895i	1.02039	−	0.802444i	0.980452	+	0.196758i	$0.0630414\pi$
$444$	−15.1622	+	14.4572i	−0.719568	+	0.686107i
$445$	0.482831	+	10.1359i	0.0228884	+	0.480486i
$446$	−6.86849	−	4.89103i	−0.325232	−	0.231597i
$447$	10.3589	−	3.04165i	0.489959	−	0.143865i
$448$	19.4517	+	0.639506i	0.919007	+	0.0302138i
$449$	10.5763	−	12.2058i	0.499129	−	0.576025i	−0.449153	−	0.893455i	$-0.648274\pi$
$449$	10.5763	−	12.2058i	0.499129	−	0.576025i	0.948282	+	0.317430i	$0.102820\pi$
$450$	−15.0453	−	14.3457i	−0.709244	−	0.676263i
$451$	−7.49887	−	0.716055i	−0.353108	−	0.0337177i
$452$	−5.67054	+	0.270121i	−0.266720	+	0.0127054i
$453$	−4.99197	+	1.21104i	−0.234543	+	0.0568996i
$454$	4.21386	+	29.3080i	0.197766	+	1.37549i
$455$	2.57606	−	2.52977i	0.120767	−	0.118598i
$456$	−0.269526	−	0.0387520i	−0.0126217	−	0.00181473i
$457$	−21.2351	−	1.01155i	−0.993338	−	0.0473185i	−0.455386	−	0.890294i	$-0.650499\pi$
$457$	−21.2351	−	1.01155i	−0.993338	−	0.0473185i	−0.537952	+	0.842976i	$0.680802\pi$
$458$	−19.6722	+	3.79150i	−0.919221	+	0.177165i
$459$	−5.46166	−	3.15329i	−0.254928	−	0.147183i
$460$	−16.6022	−	32.2460i	−0.774083	−	1.50348i
$461$		−	21.7102i		−	1.01114i	−0.862785	−	0.505572i	$-0.831282\pi$
$461$		−	21.7102i		−	1.01114i	0.862785	−	0.505572i	$-0.168718\pi$
$462$	2.73943	+	2.30394i	0.127450	+	0.107189i
$463$	34.9354	+	22.4516i	1.62358	+	1.04341i	0.953617	+	0.301023i	$0.0973281\pi$
$463$	34.9354	+	22.4516i	1.62358	+	1.04341i	0.669967	+	0.742391i	$0.266308\pi$
$464$	−25.7643	+	10.3145i	−1.19608	+	0.478837i
$465$	11.2275	+	15.7668i	0.520661	+	0.731166i
$466$	15.4690	+	6.19286i	0.716588	+	0.286879i
$467$	6.62086	+	27.2916i	0.306377	+	1.26290i	0.891894	+	0.452244i	$0.149376\pi$
$467$	6.62086	+	27.2916i	0.306377	+	1.26290i	−0.585517	+	0.810660i	$0.699109\pi$
$468$	−0.360009	−	0.560184i	−0.0166414	−	0.0258945i
$469$	−2.99641	+	1.98866i	−0.138361	+	0.0918280i
$470$	16.4648	+	56.0740i	0.759465	+	2.58650i
$471$	−2.27412	+	11.7992i	−0.104786	+	0.543680i
$472$	1.14518	−	0.396351i	0.0527113	−	0.0182436i
$473$	0.639208	−	2.63485i	0.0293908	−	0.121151i
$474$	−7.53054	+	10.5752i	−0.345889	+	0.485733i
$475$	15.3737	−	9.88010i	0.705396	−	0.453330i
$476$	−19.4405	+	25.4847i	−0.891056	+	1.16809i
$477$	−0.0811466	+	0.0116671i	−0.00371545	+	0.000534201i
$478$	−60.5316	+	5.78007i	−2.76865	+	0.264374i
$479$	5.00769	+	3.93809i	0.228807	+	0.179936i	0.725980	−	0.687715i	$-0.241386\pi$
$479$	5.00769	+	3.93809i	0.228807	+	0.179936i	−0.497173	+	0.867651i	$0.665629\pi$
$480$	−14.2661	−	27.6723i	−0.651154	−	1.26306i
$481$	−1.23643	+	3.57244i	−0.0563765	+	0.162889i
$482$	5.85350			0.266620
$483$	−11.9306	+	4.31990i	−0.542860	+	0.196562i
$484$	20.2343			0.919740
$485$	20.3008	−	58.6554i	0.921813	−	2.66340i
$486$	0.907358	+	1.76003i	0.0411586	+	0.0798365i
$487$	−10.8320	−	8.51840i	−0.490846	−	0.386005i	0.341834	−	0.939760i	$-0.388952\pi$
$487$	−10.8320	−	8.51840i	−0.490846	−	0.386005i	−0.832680	+	0.553755i	$0.813194\pi$
$488$	−1.14169	+	0.109018i	−0.0516819	+	0.00493502i
$489$	6.19154	−	0.890209i	0.279991	−	0.0402566i
$490$	28.6648	+	46.4331i	1.29494	+	2.09763i
$491$	−0.716179	+	0.460260i	−0.0323207	+	0.0207712i	−0.556701	−	0.830713i	$-0.687933\pi$
$491$	−0.716179	+	0.460260i	−0.0323207	+	0.0207712i	0.524381	+	0.851484i	$0.324297\pi$
$492$	−12.2855	+	17.2526i	−0.553874	+	0.777807i
$493$	9.93866	−	40.9677i	0.447615	−	1.84509i
$494$	1.12911	−	0.390788i	0.0508010	−	0.0175824i
$495$	0.509043	−	2.64116i	0.0228798	−	0.118711i
$496$	5.75090	+	19.5858i	0.258223	+	0.879427i
$497$	0.953276	−	1.91797i	0.0427603	−	0.0860326i
$498$	−13.1178	−	20.4117i	−0.587823	−	0.914670i
$499$	−2.10247	−	8.66649i	−0.0941194	−	0.387965i	0.905195	−	0.424997i	$-0.139725\pi$
$499$	−2.10247	−	8.66649i	−0.0941194	−	0.387965i	−0.999314	+	0.0370317i	$0.988210\pi$
$500$	38.6038	+	15.4546i	1.72642	+	0.691152i
$501$	1.33195	+	1.87047i	0.0595073	+	0.0835663i
$502$	3.27358	−	1.31054i	0.146107	−	0.0584924i
$503$	7.77122	+	4.99426i	0.346501	+	0.222683i	0.702302	−	0.711879i	$-0.252156\pi$
$503$	7.77122	+	4.99426i	0.346501	+	0.222683i	−0.355801	+	0.934562i	$0.615792\pi$
$504$	−0.389071	+	0.141112i	−0.0173306	+	0.00628562i
$505$			44.0743i			1.96128i
$506$	3.24717	−	5.61734i	0.144354	−	0.249721i
$507$	11.1543	+	6.43992i	0.495379	+	0.286007i
$508$	36.8041	−	7.09340i	1.63292	−	0.314719i
$509$	20.8551	+	0.993449i	0.924384	+	0.0440338i	0.504374	−	0.863485i	$-0.331723\pi$
$509$	20.8551	+	0.993449i	0.924384	+	0.0440338i	0.420010	+	0.907519i	$0.362026\pi$
$510$	48.6623	+	6.99659i	2.15480	+	0.309814i
$511$	5.66175	+	1.57220i	0.250461	+	0.0695502i
$512$	−4.48779	−	31.2132i	−0.198334	−	1.37944i
$513$	−1.69165	+	0.410390i	−0.0746882	+	0.0181192i
$514$	−14.1375	+	0.673453i	−0.623580	+	0.0297048i
$515$	16.3386	+	1.56014i	0.719963	+	0.0687481i
$516$	−5.51708	−	5.26053i	−0.242876	−	0.231582i
$517$	−3.35427	+	3.87103i	−0.147521	+	0.170248i
$518$	−48.5152	−	30.1781i	−2.13163	−	1.32595i
$519$	−10.8034	+	3.17216i	−0.474217	+	0.139243i
$520$	−0.173887	−	0.123824i	−0.00762544	−	0.00543005i
$521$	1.51337	+	31.7696i	0.0663020	+	1.39185i	0.749687	+	0.661792i	$0.230204\pi$
$521$	1.51337	+	31.7696i	0.0663020	+	1.39185i	−0.683385	+	0.730058i	$0.739493\pi$
$522$	−9.57951	+	9.13405i	−0.419284	+	0.399786i
$523$	6.04343	−	4.75261i	0.264261	−	0.207817i	−0.477233	−	0.878777i	$-0.658360\pi$
$523$	6.04343	−	4.75261i	0.264261	−	0.207817i	0.741494	+	0.670960i	$0.234118\pi$
$524$	30.5266	+	13.9410i	1.33356	+	0.609017i
$525$	13.5322	−	24.2569i	0.590592	−	1.05866i
$526$	−7.13591	+	11.1037i	−0.311140	+	0.484144i
$527$	−29.3017	−	10.1414i	−1.27640	−	0.441767i
$528$	1.41832	−	2.45660i	0.0617243	−	0.106910i
$529$	11.4788	+	19.9308i	0.499077	+	0.866558i
$530$	0.553460	−	0.319540i	0.0240408	−	0.0138800i
$531$	5.85471	−	5.07313i	0.254073	−	0.220155i
$532$	0.970657	+	8.79378i	0.0420833	+	0.381259i
$533$	−0.543903	+	3.78293i	−0.0235591	+	0.163857i
$534$	0.485163	+	5.08086i	0.0209950	+	0.219870i
$535$	−14.4179	+	36.0142i	−0.623340	+	1.55703i
$536$	0.146730	+	0.153886i	0.00633777	+	0.00664686i
$537$	8.88915	−	17.2426i	0.383595	−	0.744071i
$538$	26.1538	−	11.9440i	1.12757	−	0.514944i
$539$	−2.06533	+	4.31373i	−0.0889601	+	0.185805i
$540$	−5.71544	−	4.95246i	−0.245953	−	0.213120i
$541$	−5.11159	−	0.985179i	−0.219765	−	0.0423562i	0.0781802	−	0.996939i	$-0.475089\pi$
$541$	−5.11159	−	0.985179i	−0.219765	−	0.0423562i	−0.297945	+	0.954583i	$0.596301\pi$
$542$	22.0530	+	5.35001i	0.947259	+	0.229803i
$543$	−0.925375	+	9.69097i	−0.0397116	+	0.415879i
$544$	44.3298	+	22.8536i	1.90062	+	0.979840i
$545$	−5.23840	+	17.8403i	−0.224388	+	0.764196i
$546$	1.23370	−	1.33265i	0.0527977	−	0.0570321i
$547$	−4.04007	+	8.84652i	−0.172741	+	0.378250i	−0.976124	−	0.217212i	$-0.930304\pi$
$547$	−4.04007	+	8.84652i	−0.172741	+	0.378250i	0.803384	+	0.595462i	$0.203031\pi$
$548$	6.12545	+	15.3006i	0.261666	+	0.653611i
$549$	−6.51667	+	3.35958i	−0.278125	+	0.143383i
$550$	2.68802	+	13.9468i	0.114618	+	0.594693i
$551$	−5.81787	−	10.0769i	−0.247850	−	0.429288i
$552$	0.374755	+	0.649895i	0.0159506	+	0.0276614i
$553$	−16.1970	−	6.20897i	−0.688765	−	0.264032i
$554$	−39.7807	−	45.9094i	−1.69012	−	1.95050i
$555$	−2.04288	+	42.8853i	−0.0867153	+	1.82038i
$556$	−12.9400	+	16.4546i	−0.548779	+	0.697829i
$557$	−18.7269	+	13.3354i	−0.793485	+	0.565038i	−0.903348	−	0.428908i	$-0.858898\pi$
$557$	−18.7269	+	13.3354i	−0.793485	+	0.565038i	0.109863	+	0.993947i	$0.464959\pi$
$558$	6.01819	+	7.65275i	0.254770	+	0.323967i
$559$	−1.31984	−	0.387539i	−0.0558232	−	0.0163912i
$560$	32.2607	−	28.7972i	1.36326	−	1.21690i
$561$	1.78998	+	3.91950i	0.0755729	+	0.165482i
$562$	35.3865	−	37.1123i	1.49269	−	1.56549i
$563$	−10.7315	−	31.0067i	−0.452280	−	1.30678i	−0.908862	−	0.417097i	$-0.863048\pi$
$563$	−10.7315	−	31.0067i	−0.452280	−	1.30678i	0.456582	−	0.889681i	$-0.349074\pi$
$564$	4.71024	+	13.6093i	0.198337	+	0.573057i
$565$	−8.02844	+	8.41999i	−0.337759	+	0.354232i
$566$	4.73300	+	10.3638i	0.198943	+	0.435624i
$567$	−1.97378	+	1.76187i	−0.0828909	+	0.0739917i
$568$	−0.121503	−	0.0356766i	−0.00509817	−	0.00149696i
$569$	22.4597	+	28.5599i	0.941560	+	1.19729i	0.980194	+	0.198038i	$0.0634569\pi$
$569$	22.4597	+	28.5599i	0.941560	+	1.19729i	−0.0386340	+	0.999253i	$0.512301\pi$
$570$	11.0536	−	7.87121i	0.462983	−	0.329689i
$571$	3.99753	−	5.08327i	0.167291	−	0.212728i	−0.695178	−	0.718838i	$-0.744674\pi$
$571$	3.99753	−	5.08327i	0.167291	−	0.212728i	0.862469	+	0.506110i	$0.168917\pi$
$572$	−0.0216480	+	0.454447i	−0.000905148	+	0.0190014i
$573$	−14.9977	−	17.3083i	−0.626540	−	0.723066i
$574$	−53.9350	−	20.6755i	−2.25120	−	0.862980i
$575$	−47.5708	−	16.4928i	−1.98384	−	0.687797i
$576$	−3.67801	−	6.37051i	−0.153251	−	0.265438i
$577$	5.18104	+	26.8818i	0.215690	+	1.11910i	0.914744	+	0.404035i	$0.132393\pi$
$577$	5.18104	+	26.8818i	0.215690	+	1.11910i	−0.699054	+	0.715069i	$0.746395\pi$
$578$	−40.0810	+	20.6632i	−1.66715	+	0.859476i
$579$	3.45417	+	8.62809i	0.143550	+	0.358571i
$580$	21.0000	−	45.9836i	0.871978	−	1.90937i
$581$	22.0237	−	23.7900i	0.913696	−	0.986975i
$582$	8.79564	−	29.9552i	0.364591	−	1.24168i
$583$	0.0497859	+	0.0256664i	0.00206192	+	0.00106299i
$584$	0.0330238	−	0.345841i	0.00136653	−	0.0143110i
$585$	−1.32618	−	0.321728i	−0.0548307	−	0.0133018i
$586$	−54.6947	−	10.5415i	−2.25942	−	0.435467i
$587$	−16.0523	−	13.9094i	−0.662549	−	0.574102i	0.257320	−	0.966326i	$-0.417160\pi$
$587$	−16.0523	−	13.9094i	−0.662549	−	0.574102i	−0.919870	+	0.392224i	$0.871706\pi$
$588$	7.60018	+	11.0932i	0.313426	+	0.457477i
$589$	−7.78505	+	3.55531i	−0.320777	+	0.146494i
$590$	−27.6726	+	53.6773i	−1.13926	+	2.20986i
$591$	13.6503	+	14.3161i	0.561500	+	0.588884i
$592$	−16.8282	+	42.0348i	−0.691634	+	1.72762i
$593$	1.72869	+	18.1037i	0.0709887	+	0.743428i	0.958962	+	0.283533i	$0.0915067\pi$
$593$	1.72869	+	18.1037i	0.0709887	+	0.743428i	−0.887974	+	0.459894i	$0.847887\pi$
$594$	0.192540	−	1.33914i	0.00790000	−	0.0549457i
$595$	7.20688	+	65.2915i	0.295453	+	2.67669i
$596$	−15.6739	+	13.5815i	−0.642029	+	0.556321i
$597$	13.0063	−	7.50919i	0.532313	−	0.307331i
$598$	−2.76832	−	1.78118i	−0.113205	−	0.0728378i
$599$	8.58738	−	14.8738i	0.350871	−	0.607726i	−0.635532	−	0.772075i	$-0.719219\pi$
$599$	8.58738	−	14.8738i	0.350871	−	0.607726i	0.986402	+	0.164349i	$0.0525523\pi$
$600$	−1.55193	−	0.537127i	−0.0633572	−	0.0219281i
$601$	−1.54443	+	2.40318i	−0.0629986	+	0.0980278i	−0.871324	−	0.490709i	$-0.836738\pi$
$601$	−1.54443	+	2.40318i	−0.0629986	+	0.0980278i	0.808325	+	0.588736i	$0.200374\pi$
$602$	10.1285	−	18.1557i	0.412806	−	0.739971i
$603$	1.23643	+	0.564660i	0.0503515	+	0.0229947i
$604$	7.75657	−	6.09984i	0.315611	−	0.248199i
$605$	30.0111	−	28.6156i	1.22013	−	1.16339i
$606$	1.05483	+	22.1436i	0.0428495	+	0.899521i
$607$	11.4523	+	8.15518i	0.464836	+	0.331008i	0.788363	−	0.615211i	$-0.210929\pi$
$607$	11.4523	+	8.15518i	0.464836	+	0.331008i	−0.323526	+	0.946219i	$0.604868\pi$
$608$	13.2084	−	3.87834i	0.535672	−	0.157287i
$609$	−15.0172	−	9.34119i	−0.608527	−	0.378524i
$610$	37.4279	−	43.1941i	1.51541	−	1.74888i
$611$	1.88076	+	1.79330i	0.0760873	+	0.0725491i
$612$	12.0601	+	1.15160i	0.487500	+	0.0465506i
$613$	−7.19873	+	0.342918i	−0.290754	+	0.0138503i	−0.192452	−	0.981306i	$-0.561644\pi$
$613$	−7.19873	+	0.342918i	−0.290754	+	0.0138503i	−0.0983016	+	0.995157i	$0.531341\pi$
$614$	52.7963	−	12.8082i	2.13069	−	0.516899i
$615$	6.17716	+	42.9631i	0.249087	+	1.73244i
$616$	0.272462	+	0.0756595i	0.0109778	+	0.00304841i
$617$	26.0764	+	3.74922i	1.04980	+	0.150938i	0.645554	−	0.763715i	$-0.276627\pi$
$617$	26.0764	+	3.74922i	1.04980	+	0.150938i	0.404241	+	0.914652i	$0.367536\pi$
$618$	8.24608	+	0.392809i	0.331706	+	0.0158011i
$619$	17.9485	−	3.45930i	0.721413	−	0.139041i	0.184687	−	0.982797i	$-0.440873\pi$
$619$	17.9485	−	3.45930i	0.721413	−	0.139041i	0.536726	+	0.843757i	$0.319661\pi$
$620$	−32.2010	−	18.5913i	−1.29322	−	0.746643i
$621$	3.76820	+	2.96659i	0.151213	+	0.119045i
$622$		−	64.3985i		−	2.58214i
$623$	−6.41095	+	2.32518i	−0.256849	+	0.0931566i
$624$	−1.21070	−	0.778067i	−0.0484666	−	0.0311476i
$625$	30.3807	−	12.1626i	1.21523	−	0.486504i
$626$	4.69523	+	6.59353i	0.187659	+	0.263530i
$627$	1.10413	+	0.442027i	0.0440947	+	0.0176529i
$628$	−5.44214	−	22.4328i	−0.217165	−	0.895167i
$629$	−37.1843	−	57.8599i	−1.48263	−	2.30702i
$630$	9.17972	−	18.4694i	0.365729	−	0.735838i
$631$	−1.80425	−	6.14470i	−0.0718259	−	0.244617i	0.915753	−	0.401743i	$-0.131595\pi$
$631$	−1.80425	−	6.14470i	−0.0718259	−	0.244617i	−0.987579	+	0.157126i	$0.949777\pi$
$632$	−0.194093	+	1.00705i	−0.00772062	+	0.0400584i
$633$	2.97561	−	1.02987i	0.118270	−	0.0409337i
$634$	−2.76261	+	11.3876i	−0.109717	+	0.452261i
$635$	44.5556	−	62.5696i	1.76814	−	2.48300i
$636$	0.132485	−	0.0851432i	0.00525339	−	0.00337615i
$637$	2.13622	+	1.15079i	0.0846400	+	0.0455958i
$638$	8.95144	−	1.28702i	0.354391	−	0.0509537i
$639$	−0.805861	+	0.0769504i	−0.0318794	+	0.00304411i
$640$	−3.86956	−	3.04306i	−0.152958	−	0.120287i
$641$	−1.73644	−	3.36823i	−0.0685854	−	0.133037i	0.852050	−	0.523460i	$-0.175359\pi$
$641$	−1.73644	−	3.36823i	−0.0685854	−	0.133037i	−0.920636	+	0.390423i	$0.872329\pi$
$642$	−6.38184	+	18.4391i	−0.251871	+	0.727734i
$643$	−18.5664			−0.732188			−0.366094	−	0.930578i	$-0.619305\pi$
$643$	−18.5664			−0.732188			−0.366094	+	0.930578i	$0.619305\pi$
$644$	17.4002	−	17.0694i	0.685664	−	0.672627i
$645$	−15.6223			−0.615129
$646$	−7.10982	+	20.5425i	−0.279732	+	0.808233i
$647$	3.31677	+	6.43364i	0.130396	+	0.252932i	0.944990	−	0.327098i	$-0.106071\pi$
$647$	3.31677	+	6.43364i	0.130396	+	0.252932i	−0.814595	+	0.580031i	$0.803041\pi$
$648$	0.122961	+	0.0966975i	0.00483036	+	0.00379864i
$649$	−5.26900	+	0.503128i	−0.206826	+	0.0197495i
$650$	7.13273	−	1.02553i	0.279769	−	0.0402247i
$651$	−7.88958	+	10.3425i	−0.309217	+	0.405354i
$652$	−10.1087	+	6.49648i	−0.395888	+	0.254422i
$653$	−7.06547	+	9.92207i	−0.276493	+	0.388281i	−0.929349	−	0.369201i	$-0.879631\pi$
$653$	−7.06547	+	9.92207i	−0.276493	+	0.388281i	0.652856	+	0.757482i	$0.273571\pi$
$654$	−2.20488	+	9.08862i	−0.0862175	+	0.355393i
$655$	64.9921	−	22.4940i	2.53945	−	0.878913i
$656$	−8.66295	+	44.9476i	−0.338231	+	1.75491i
$657$	−0.625704	−	2.13095i	−0.0244110	−	0.0831364i
$658$	−32.7244	+	21.7186i	−1.27573	+	0.846680i
$659$	−11.6481	−	18.1248i	−0.453746	−	0.706043i	0.536726	−	0.843757i	$-0.319661\pi$
$659$	−11.6481	−	18.1248i	−0.453746	−	0.706043i	−0.990472	+	0.137714i	$0.956025\pi$
$660$	1.21818	+	5.02141i	0.0474176	+	0.195458i
$661$	24.3255	+	9.73847i	0.946153	+	0.378783i	0.792864	−	0.609399i	$-0.208589\pi$
$661$	24.3255	+	9.73847i	0.946153	+	0.378783i	0.153289	+	0.988181i	$0.451013\pi$
$662$	−20.8668	−	29.3033i	−0.811010	−	1.13890i
$663$	2.02951	−	0.812491i	0.0788195	−	0.0315545i
$664$	−1.61248	−	1.03628i	−0.0625765	−	0.0402155i
$665$	13.8759	+	11.6701i	0.538086	+	0.452546i
$666$			21.5951i			0.836793i
$667$	−11.9304	+	29.7548i	−0.461948	+	1.15211i
$668$	−3.82012	−	2.20555i	−0.147805	−	0.0853352i
$669$	−4.18130	+	0.805879i	−0.161658	+	0.0311571i
$670$	−10.5841	−	0.504184i	−0.408901	−	0.0194783i
$671$	4.95830	+	0.712896i	0.191413	+	0.0275210i
$672$	14.9285	−	14.6603i	0.575879	−	0.565532i
$673$	−7.19786	−	50.0622i	−0.277457	−	1.92976i	−0.359538	−	0.933130i	$-0.617066\pi$
$673$	−7.19786	−	50.0622i	−0.277457	−	1.92976i	0.0820809	−	0.996626i	$-0.473843\pi$
$674$	−8.31091	+	2.01621i	−0.320124	+	0.0776613i
$675$	−10.4865	+	0.499535i	−0.403627	+	0.0192271i
$676$	−24.6302	−	2.35190i	−0.947314	−	0.0904575i
$677$	19.2366	+	18.3421i	0.739323	+	0.704943i	0.962935	−	0.269735i	$-0.0869362\pi$
$677$	19.2366	+	18.3421i	0.739323	+	0.704943i	−0.223611	+	0.974678i	$0.571785\pi$
$678$	−3.83209	+	4.42247i	−0.147171	+	0.169844i
$679$	41.6914	+	1.37067i	1.59997	+	0.0526015i
$680$	3.72644	−	1.09418i	0.142903	−	0.0419600i
$681$	12.1804	+	8.67365i	0.466755	+	0.332375i
$682$	−0.316504	−	6.64424i	−0.0121196	−	0.254421i
$683$	25.3397	−	24.1614i	0.969598	−	0.924510i	−0.0275770	−	0.999620i	$-0.508779\pi$
$683$	25.3397	−	24.1614i	0.969598	−	0.924510i	0.997175	+	0.0751096i	$0.0239307\pi$
$684$	2.62850	−	2.06708i	0.100503	−	0.0790366i
$685$	30.7235	+	14.0310i	1.17389	+	0.536096i
$686$	−24.1096	+	27.6339i	−0.920509	+	1.05507i
$687$	−5.46994	+	8.51140i	−0.208691	+	0.324730i
$688$	−15.5692	−	5.38855i	−0.593570	−	0.205437i
$689$	0.0142089	−	0.0246105i	0.000541315	−	0.000937585i
$690$	−35.8658	−	10.5519i	−1.36539	−	0.401704i
$691$	−16.9702	+	9.79773i	−0.645575	+	0.372723i	−0.786759	−	0.617260i	$-0.788243\pi$
$691$	−16.9702	+	9.79773i	−0.645575	+	0.372723i	0.141184	+	0.989983i	$0.454909\pi$
$692$	16.3465	−	14.1643i	0.621400	−	0.538446i
$693$	1.79676	−	0.198327i	0.0682534	−	0.00753381i
$694$	−2.49633	+	17.3624i	−0.0947594	+	0.659066i
$695$	4.07784	+	42.7051i	0.154681	+	1.61990i
$696$	−0.388624	+	0.970736i	−0.0147308	+	0.0367956i
$697$	−47.9830	−	50.3232i	−1.81749	−	1.90613i
$698$	−16.2353	+	31.4921i	−0.614515	+	1.19199i
$699$	7.65437	−	3.49564i	0.289515	−	0.132217i
$700$	−4.28882	+	53.1855i	−0.162102	+	2.01022i
$701$	−2.59274	−	2.24662i	−0.0979265	−	0.0848538i	0.604522	−	0.796589i	$-0.293364\pi$
$701$	−2.59274	−	2.24662i	−0.0979265	−	0.0848538i	−0.702448	+	0.711735i	$0.747910\pi$
$702$	−0.673992	−	0.129901i	−0.0254382	−	0.00490281i
$703$	−18.4488	−	4.47562i	−0.695808	−	0.168801i
$704$	−0.477743	+	5.00315i	−0.0180056	+	0.188563i
$705$	26.2327	+	13.5239i	0.987980	+	0.509339i
$706$	10.6964	−	36.4286i	0.402564	−	1.37101i
$707$	−28.2945	+	8.76288i	−1.06412	+	0.329562i
$708$	−6.18212	+	13.5370i	−0.232338	+	0.508750i
$709$	−8.94005	−	22.3312i	−0.335751	−	0.838665i	−0.996143	−	0.0877439i	$-0.972034\pi$
$709$	−8.94005	−	22.3312i	−0.335751	−	0.838665i	0.660392	−	0.750921i	$-0.270390\pi$
$710$	5.60912	−	2.89170i	0.210507	−	0.108524i
$711$	1.24078	+	6.43779i	0.0465330	+	0.241436i
$712$	0.201602	+	0.349184i	0.00755534	+	0.0130862i
$713$	20.9524	+	10.8158i	0.784672	+	0.405056i
$714$	5.18346	+	32.6310i	0.193986	+	1.22118i
$715$	0.610577	+	0.704644i	0.0228343	+	0.0263522i
$716$	−1.77317	+	37.2234i	−0.0662664	+	1.39110i
$717$	−18.9826	+	24.1383i	−0.708917	+	0.901461i
$718$	5.56130	−	3.96019i	0.207546	−	0.147793i
$719$	−9.06245	−	11.5238i	−0.337972	−	0.429767i	0.587125	−	0.809496i	$-0.300260\pi$
$719$	−9.06245	−	11.5238i	−0.337972	−	0.429767i	−0.925098	+	0.379729i	$0.876017\pi$
$720$	−15.6826	−	4.60482i	−0.584455	−	0.171611i
$721$	2.24688	+	10.7991i	0.0836780	+	0.402180i
$722$	−13.1366	−	28.7651i	−0.488894	−	1.07053i
$723$	2.03993	−	2.13942i	0.0758660	−	0.0795659i
$724$	−6.11651	−	17.6725i	−0.227318	−	0.656793i
$725$	−22.9524	−	66.3166i	−0.852431	−	2.46294i
$726$	14.3932	−	15.0951i	0.534181	−	0.560233i
$727$	−2.76238	−	6.04878i	−0.102451	−	0.224337i	0.851464	−	0.524413i	$-0.175715\pi$
$727$	−2.76238	−	6.04878i	−0.102451	−	0.224337i	−0.953915	+	0.300076i	$0.902988\pi$
$728$	0.0449195	−	0.136249i	0.00166483	−	0.00504974i
$729$	0.959493	+	0.281733i	0.0355368	+	0.0104345i
$730$	10.7022	+	13.6090i	0.396108	+	0.503692i
$731$	20.3858	−	14.5167i	0.753996	−	0.536918i
$732$	8.70627	−	11.0709i	0.321793	−	0.409193i
$733$	2.19750	−	46.1311i	0.0811664	−	1.70389i	−0.480880	−	0.876786i	$-0.659683\pi$
$733$	2.19750	−	46.1311i	0.0811664	−	1.70389i	0.562046	−	0.827106i	$-0.310014\pi$
$734$	5.09236	+	5.87690i	0.187962	+	0.216920i
$735$	26.9606	+	5.70501i	0.994458	+	0.210433i
$736$	−30.8824	−	22.0161i	−1.13834	−	0.811523i
$737$	−0.464351	−	0.804280i	−0.0171046	−	0.0296260i
$738$	4.13173	+	21.4375i	0.152091	+	0.789124i
$739$	−18.9456	+	9.76716i	−0.696927	+	0.359291i	−0.770007	−	0.638035i	$-0.779747\pi$
$739$	−18.9456	+	9.76716i	−0.696927	+	0.359291i	0.0730804	+	0.997326i	$0.476717\pi$
$740$	−30.6533	−	76.5682i	−1.12684	−	2.81470i
$741$	0.250661	−	0.548871i	0.00920826	−	0.0201633i
$742$	0.315176	+	0.291775i	0.0115705	+	0.0107114i
$743$	14.1348	−	48.1386i	0.518554	−	1.76603i	−0.116102	−	0.993237i	$-0.537040\pi$
$743$	14.1348	−	48.1386i	0.518554	−	1.76603i	0.634656	−	0.772795i	$-0.281142\pi$
$744$	0.683602	+	0.352422i	0.0250621	+	0.0129204i
$745$	−4.04013	+	42.3102i	−0.148019	+	1.55012i
$746$	−1.98709	−	0.482064i	−0.0727527	−	0.0176496i
$747$	−12.0319	−	2.31896i	−0.440224	−	0.0848461i
$748$	−6.25563	−	5.42054i	−0.228729	−	0.198194i
$749$	−25.9867	−	2.09553i	−0.949533	−	0.0765692i
$750$	38.9894	−	17.8059i	1.42369	−	0.650178i
$751$	1.18162	−	2.29202i	0.0431178	−	0.0836369i	−0.866292	−	0.499538i	$-0.833503\pi$
$751$	1.18162	−	2.29202i	0.0431178	−	0.0836369i	0.909410	+	0.415901i	$0.136534\pi$
$752$	21.4787	+	22.5262i	0.783247	+	0.821446i
$753$	0.661839	−	1.65319i	0.0241188	−	0.0602458i
$754$	−0.436134	−	4.56741i	−0.0158831	−	0.166335i
$755$	2.87796	−	20.0166i	0.104740	−	0.728480i
$756$	2.04299	−	4.65381i	0.0743030	−	0.169257i
$757$	2.69550	−	2.33567i	0.0979698	−	0.0848913i	−0.604499	−	0.796606i	$-0.706627\pi$
$757$	2.69550	−	2.33567i	0.0979698	−	0.0848913i	0.702469	+	0.711715i	$0.252081\pi$
$758$	38.9188	−	22.4698i	1.41359	−	0.816139i
$759$	−0.921475	−	3.14445i	−0.0334474	−	0.114136i
$760$	0.535991	−	0.928363i	0.0194424	−	0.0336753i
$761$	−34.4020	−	11.9066i	−1.24707	−	0.431615i	−0.377770	−	0.925899i	$-0.623309\pi$
$761$	−34.4020	−	11.9066i	−1.24707	−	0.431615i	−0.869301	+	0.494284i	$0.835430\pi$
$762$	20.8879	−	32.5023i	0.756690	−	1.17743i
$763$	−12.4945	+	0.184122i	−0.452332	+	0.00666566i
$764$	40.0194	+	18.2763i	1.44785	+	0.661212i
$765$	19.5159	−	15.3475i	0.705600	−	0.554890i
$766$	51.8896	−	49.4766i	1.87485	−	1.78766i
$767$	0.127775	+	2.68232i	0.00461368	+	0.0968531i
$768$	−14.0010	−	9.97010i	−0.505219	−	0.359765i
$769$	−39.7059	+	11.6587i	−1.43183	+	0.420423i	−0.903490	−	0.428609i	$-0.859004\pi$
$769$	−39.7059	+	11.6587i	−1.43183	+	0.420423i	−0.528341	+	0.849032i	$0.677186\pi$
$770$	−12.4287	+	6.64104i	−0.447899	+	0.239326i
$771$	−4.68076	+	5.40188i	−0.168573	+	0.194544i
$772$	−12.9212	−	12.3203i	−0.465043	−	0.443417i
$773$	27.1510	+	2.59261i

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.bf (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.647644 + 1.87125i) q^{2} +(0.458227 + 0.888835i) q^{3} +(-1.51001 - 1.18748i) q^{4} +(-3.91898 + 0.374217i) q^{5} +(-1.96000 + 0.281805i) q^{6} +(-1.01941 - 2.44148i) q^{7} +(-0.131596 + 0.0845715i) q^{8} +(-0.580057 + 0.814576i) q^{9} +O(q^{10})\)	\(q+(-0.647644 + 1.87125i) q^{2} +(0.458227 + 0.888835i) q^{3} +(-1.51001 - 1.18748i) q^{4} +(-3.91898 + 0.374217i) q^{5} +(-1.96000 + 0.281805i) q^{6} +(-1.01941 - 2.44148i) q^{7} +(-0.131596 + 0.0845715i) q^{8} +(-0.580057 + 0.814576i) q^{9} +(1.83785 - 7.57573i) q^{10} +(0.645660 - 0.223465i) q^{11} +(0.363552 - 1.88629i) q^{12} +(-0.0976592 - 0.332597i) q^{13} +(5.22881 - 0.326361i) q^{14} +(-2.12840 - 3.31185i) q^{15} +(-0.978813 - 4.03472i) q^{16} +(5.85483 + 2.34392i) q^{17} +(-1.14860 - 1.61298i) q^{18} +(1.61603 - 0.646960i) q^{19} +(6.36207 + 4.08865i) q^{20} +(1.70295 - 2.02484i) q^{21} +1.35291i q^{22} +(-4.15203 - 2.40013i) q^{23} +(-0.135471 - 0.0782141i) q^{24} +(10.3087 - 1.98684i) q^{25} +(0.685619 + 0.0326600i) q^{26} +(-0.989821 - 0.142315i) q^{27} +(-1.35989 + 4.89719i) q^{28} +(-0.951297 - 6.61641i) q^{29} +(7.57573 - 1.83785i) q^{30} +(-4.91106 + 0.233942i) q^{31} +(7.87244 + 0.751727i) q^{32} +(0.494482 + 0.471488i) q^{33} +(-8.17789 + 9.43779i) q^{34} +(4.90869 + 9.18661i) q^{35} +(1.84319 - 0.541209i) q^{36} +(-8.88359 - 6.32597i) q^{37} +(0.164009 + 3.44298i) q^{38} +(0.250874 - 0.239208i) q^{39} +(0.484073 - 0.380679i) q^{40} +(-10.0291 - 4.58013i) q^{41} +(2.68606 + 4.49801i) q^{42} +(2.14542 - 3.33833i) q^{43} +(-1.24031 - 0.429277i) q^{44} +(1.96840 - 3.40937i) q^{45} +(7.18027 - 6.21504i) q^{46} +(-6.49244 + 3.74841i) q^{47} +(3.13769 - 2.71882i) q^{48} +(-4.92160 + 4.97773i) q^{49} +(-2.95851 + 20.5769i) q^{50} +(0.599478 + 6.27802i) q^{51} +(-0.247487 + 0.618193i) q^{52} +(0.0565734 + 0.0593325i) q^{53} +(0.907358 - 1.76003i) q^{54} +(-2.44670 + 1.11737i) q^{55} +(0.340629 + 0.235075i) q^{56} +(1.31555 + 1.13993i) q^{57} +(12.9970 + 2.50497i) q^{58} +(-7.52852 - 1.82640i) q^{59} +(-0.718872 + 7.52836i) q^{60} +(6.51667 + 3.35958i) q^{61} +(2.74285 - 9.34130i) q^{62} +(2.58008 + 0.585807i) q^{63} +(-3.05580 + 6.69128i) q^{64} +(0.507188 + 1.26689i) q^{65} +(-1.20252 + 0.619941i) q^{66} +(-0.257243 - 1.33470i) q^{67} +(-6.05747 - 10.4919i) q^{68} +(0.230747 - 4.79028i) q^{69} +(-20.3695 + 3.23571i) q^{70} +(0.530127 + 0.611800i) q^{71} +(0.00744315 - 0.156251i) q^{72} +(-1.37288 + 1.74576i) q^{73} +(17.5909 - 12.5264i) q^{74} +(6.48970 + 8.25232i) q^{75} +(-3.20847 - 0.942092i) q^{76} +(-1.20378 - 1.34856i) q^{77} +(0.285139 + 0.624368i) q^{78} +(4.52434 - 4.74500i) q^{79} +(5.34581 + 15.4457i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(15.0658 - 15.8006i) q^{82} +(5.09021 + 11.1460i) q^{83} +(-4.97593 + 1.03530i) q^{84} +(-23.8221 - 6.99479i) q^{85} +(4.85737 + 6.17665i) q^{86} +(5.44499 - 3.87736i) q^{87} +(-0.0660673 + 0.0840115i) q^{88} +(0.122645 - 2.57464i) q^{89} +(5.10495 + 5.89142i) q^{90} +(-0.712472 + 0.577485i) q^{91} +(3.41950 + 8.55469i) q^{92} +(-2.45831 - 4.25792i) q^{93} +(-2.80941 - 14.5766i) q^{94} +(-6.09107 + 3.14016i) q^{95} +(2.93920 + 7.34177i) q^{96} +(-6.54959 + 14.3416i) q^{97} +(-6.12712 - 12.4333i) q^{98} +(-0.192490 + 0.655561i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640q - 4q^{2} + 36q^{4} + 24q^{8} - 32q^{9} + O(q^{10}) \)	\( 640q - 4q^{2} + 36q^{4} + 24q^{8} - 32q^{9} + 4q^{18} - 28q^{23} + 56q^{25} - 84q^{26} - 176q^{28} - 24q^{29} + 12q^{31} + 36q^{32} - 76q^{35} + 28q^{36} + 44q^{37} - 110q^{42} - 88q^{43} + 154q^{44} + 8q^{46} + 12q^{47} - 8q^{49} - 212q^{50} + 44q^{51} + 108q^{52} - 110q^{56} - 88q^{57} + 2q^{58} - 36q^{59} - 168q^{64} - 48q^{70} + 16q^{71} + 12q^{72} - 48q^{73} - 22q^{74} + 48q^{75} + 32q^{78} - 44q^{79} - 594q^{80} + 32q^{81} + 24q^{82} + 352q^{85} - 36q^{87} - 330q^{88} + 244q^{92} - 24q^{93} - 486q^{94} - 154q^{95} - 60q^{96} - 24q^{98} - 44q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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