LMFDB - Embedded newform 60.2.e.a.11.3

Newspace parameters

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	60.e (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$0.479102412128$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.342102016.5
Defining polynomial:	$x^{8} + x^{6} + 4 x^{4} + 4 x^{2} + 16$
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			11.3
Root			$-0.599676 + 1.28078i$ of defining polynomial
Character	$\chi$	$=$	60.11
Dual form			60.2.e.a.11.4

$q$-expansion

$f(q)$	$=$	$q+(-0.599676 - 1.28078i) q^{2} +(-0.468213 - 1.66757i) q^{3} +(-1.28078 + 1.53610i) q^{4} -1.00000i q^{5} +(-1.85500 + 1.59968i) q^{6} -0.936426i q^{7} +(2.73546 + 0.719224i) q^{8} +(-2.56155 + 1.56155i) q^{9} +O(q^{10})$	\(q+(-0.599676 - 1.28078i) q^{2} +(-0.468213 - 1.66757i) q^{3} +(-1.28078 + 1.53610i) q^{4} -1.00000i q^{5} +(-1.85500 + 1.59968i) q^{6} -0.936426i q^{7} +(2.73546 + 0.719224i) q^{8} +(-2.56155 + 1.56155i) q^{9} +(-1.28078 + 0.599676i) q^{10} +4.27156 q^{11} +(3.16123 + 1.41656i) q^{12} +3.12311 q^{13} +(-1.19935 + 0.561553i) q^{14} +(-1.66757 + 0.468213i) q^{15} +(-0.719224 - 3.93481i) q^{16} +2.00000i q^{17} +(3.53610 + 2.34435i) q^{18} +4.27156i q^{19} +(1.53610 + 1.28078i) q^{20} +(-1.56155 + 0.438447i) q^{21} +(-2.56155 - 5.47091i) q^{22} -7.60669 q^{23} +(-0.0814236 - 4.89830i) q^{24} -1.00000 q^{25} +(-1.87285 - 4.00000i) q^{26} +(3.80335 + 3.54042i) q^{27} +(1.43845 + 1.19935i) q^{28} -5.12311i q^{29} +(1.59968 + 1.85500i) q^{30} +2.39871i q^{31} +(-4.60831 + 3.28078i) q^{32} +(-2.00000 - 7.12311i) q^{33} +(2.56155 - 1.19935i) q^{34} -0.936426 q^{35} +(0.882071 - 5.93481i) q^{36} -3.12311 q^{37} +(5.47091 - 2.56155i) q^{38} +(-1.46228 - 5.20798i) q^{39} +(0.719224 - 2.73546i) q^{40} +7.12311i q^{41} +(1.49798 + 1.73707i) q^{42} -1.46228i q^{43} +(-5.47091 + 6.56155i) q^{44} +(1.56155 + 2.56155i) q^{45} +(4.56155 + 9.74247i) q^{46} +0.936426 q^{47} +(-6.22480 + 3.04168i) q^{48} +6.12311 q^{49} +(0.599676 + 1.28078i) q^{50} +(3.33513 - 0.936426i) q^{51} +(-4.00000 + 4.79741i) q^{52} +4.24621i q^{53} +(2.25371 - 6.99434i) q^{54} -4.27156i q^{55} +(0.673500 - 2.56155i) q^{56} +(7.12311 - 2.00000i) q^{57} +(-6.56155 + 3.07221i) q^{58} +7.19612 q^{59} +(1.41656 - 3.16123i) q^{60} -5.12311 q^{61} +(3.07221 - 1.43845i) q^{62} +(1.46228 + 2.39871i) q^{63} +(6.96543 + 3.93481i) q^{64} -3.12311i q^{65} +(-7.92375 + 6.83311i) q^{66} -5.20798i q^{67} +(-3.07221 - 2.56155i) q^{68} +(3.56155 + 12.6847i) q^{69} +(0.561553 + 1.19935i) q^{70} -6.67026 q^{71} +(-8.13012 + 2.42923i) q^{72} -8.24621 q^{73} +(1.87285 + 4.00000i) q^{74} +(0.468213 + 1.66757i) q^{75} +(-6.56155 - 5.47091i) q^{76} -4.00000i q^{77} +(-5.79337 + 4.99596i) q^{78} -9.06897i q^{79} +(-3.93481 + 0.719224i) q^{80} +(4.12311 - 8.00000i) q^{81} +(9.12311 - 4.27156i) q^{82} +4.68213 q^{83} +(1.32650 - 2.96026i) q^{84} +2.00000 q^{85} +(-1.87285 + 0.876894i) q^{86} +(-8.54312 + 2.39871i) q^{87} +(11.6847 + 3.07221i) q^{88} -6.24621i q^{89} +(2.34435 - 3.53610i) q^{90} -2.92456i q^{91} +(9.74247 - 11.6847i) q^{92} +(4.00000 - 1.12311i) q^{93} +(-0.561553 - 1.19935i) q^{94} +4.27156 q^{95} +(7.62858 + 6.14856i) q^{96} -6.00000 q^{97} +(-3.67188 - 7.84233i) q^{98} +(-10.9418 + 6.67026i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8q - 2q^{4} - 6q^{6} - 4q^{9} + O(q^{10}) $	$ 8q - 2q^{4} - 6q^{6} - 4q^{9} - 2q^{10} + 4q^{12} - 8q^{13} - 14q^{16} + 16q^{18} + 4q^{21} - 4q^{22} - 2q^{24} - 8q^{25} + 28q^{28} + 8q^{30} - 16q^{33} + 4q^{34} + 18q^{36} + 8q^{37} + 14q^{40} - 12q^{42} - 4q^{45} + 20q^{46} - 36q^{48} + 16q^{49} - 32q^{52} - 10q^{54} + 24q^{57} - 36q^{58} - 14q^{60} - 8q^{61} - 2q^{64} - 40q^{66} + 12q^{69} - 12q^{70} + 24q^{72} - 36q^{76} + 40q^{78} + 40q^{82} + 16q^{84} + 16q^{85} + 44q^{88} + 18q^{90} + 32q^{93} + 12q^{94} + 42q^{96} - 48q^{97} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−0.599676	−	1.28078i	−0.424035	−	0.905646i
$2$	−0.599676	−	1.28078i	−0.424035	−	0.905646i
$3$	−0.468213	−	1.66757i	−0.270323	−	0.962770i
$3$	−0.468213	−	1.66757i	−0.270323	−	0.962770i
$4$	−1.28078	+	1.53610i	−0.640388	+	0.768051i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−1.85500	+	1.59968i	−0.757302	+	0.653065i
$7$		−	0.936426i		−	0.353936i	−0.984217	−	0.176968i	$-0.943371\pi$
$7$		−	0.936426i		−	0.353936i	0.984217	−	0.176968i	$-0.0566289\pi$
$8$	2.73546	+	0.719224i	0.967130	+	0.254284i
$9$	−2.56155	+	1.56155i	−0.853851	+	0.520518i
$10$	−1.28078	+	0.599676i	−0.405017	+	0.189634i
$11$	4.27156			1.28792			0.643962	−	0.765058i	$-0.277290\pi$
$11$	4.27156			1.28792			0.643962	+	0.765058i	$0.277290\pi$
$12$	3.16123	+	1.41656i	0.912568	+	0.408924i
$13$	3.12311			0.866194			0.433097	−	0.901347i	$-0.357421\pi$
$13$	3.12311			0.866194			0.433097	+	0.901347i	$0.357421\pi$
$14$	−1.19935	+	0.561553i	−0.320541	+	0.150081i
$15$	−1.66757	+	0.468213i	−0.430564	+	0.120892i
$16$	−0.719224	−	3.93481i	−0.179806	−	0.983702i
$17$			2.00000i			0.485071i	0.970143	+	0.242536i	$0.0779791\pi$
$17$			2.00000i			0.485071i	−0.970143	+	0.242536i	$0.922021\pi$
$18$	3.53610	+	2.34435i	0.833467	+	0.552569i
$19$			4.27156i			0.979963i	0.871733	+	0.489981i	$0.162996\pi$
$19$			4.27156i			0.979963i	−0.871733	+	0.489981i	$0.837004\pi$
$20$	1.53610	+	1.28078i	0.343483	+	0.286390i
$21$	−1.56155	+	0.438447i	−0.340759	+	0.0956770i
$22$	−2.56155	−	5.47091i	−0.546125	−	1.16640i
$23$	−7.60669			−1.58610			−0.793052	−	0.609154i	$-0.791509\pi$
$23$	−7.60669			−1.58610			−0.793052	+	0.609154i	$0.791509\pi$
$24$	−0.0814236	−	4.89830i	−0.0166205	−	0.999862i
$25$	−1.00000			−0.200000
$26$	−1.87285	−	4.00000i	−0.367297	−	0.784465i
$27$	3.80335	+	3.54042i	0.731954	+	0.681354i
$28$	1.43845	+	1.19935i	0.271841	+	0.226656i
$29$		−	5.12311i		−	0.951337i	−0.879625	−	0.475668i	$-0.842206\pi$
$29$		−	5.12311i		−	0.951337i	0.879625	−	0.475668i	$-0.157794\pi$
$30$	1.59968	+	1.85500i	0.292060	+	0.338676i
$31$			2.39871i			0.430820i	0.976524	+	0.215410i	$0.0691088\pi$
$31$			2.39871i			0.430820i	−0.976524	+	0.215410i	$0.930891\pi$
$32$	−4.60831	+	3.28078i	−0.814642	+	0.579965i
$33$	−2.00000	−	7.12311i	−0.348155	−	1.23997i
$34$	2.56155	−	1.19935i	0.439303	−	0.205687i
$35$	−0.936426			−0.158285
$36$	0.882071	−	5.93481i	0.147012	−	0.989135i
$37$	−3.12311			−0.513435			−0.256718	−	0.966486i	$-0.582641\pi$
$37$	−3.12311			−0.513435			−0.256718	+	0.966486i	$0.582641\pi$
$38$	5.47091	−	2.56155i	0.887499	−	0.415539i
$39$	−1.46228	−	5.20798i	−0.234152	−	0.833945i
$40$	0.719224	−	2.73546i	0.113719	−	0.432514i
$41$			7.12311i			1.11244i	0.831034	+	0.556221i	$0.187749\pi$
$41$			7.12311i			1.11244i	−0.831034	+	0.556221i	$0.812251\pi$
$42$	1.49798	+	1.73707i	0.231143	+	0.268036i
$43$		−	1.46228i		−	0.222995i	−0.993765	−	0.111498i	$-0.964435\pi$
$43$		−	1.46228i		−	0.222995i	0.993765	−	0.111498i	$-0.0355648\pi$
$44$	−5.47091	+	6.56155i	−0.824771	+	0.989191i
$45$	1.56155	+	2.56155i	0.232783	+	0.381854i
$46$	4.56155	+	9.74247i	0.672564	+	1.43645i
$47$	0.936426			0.136592			0.0682959	−	0.997665i	$-0.478244\pi$
$47$	0.936426			0.136592			0.0682959	+	0.997665i	$0.478244\pi$
$48$	−6.22480	+	3.04168i	−0.898473	+	0.439029i
$49$	6.12311			0.874729
$50$	0.599676	+	1.28078i	0.0848071	+	0.181129i
$51$	3.33513	−	0.936426i	0.467012	−	0.131126i
$52$	−4.00000	+	4.79741i	−0.554700	+	0.665281i
$53$			4.24621i			0.583262i	0.956531	+	0.291631i	$0.0941979\pi$
$53$			4.24621i			0.583262i	−0.956531	+	0.291631i	$0.905802\pi$
$54$	2.25371	−	6.99434i	0.306691	−	0.951809i
$55$		−	4.27156i		−	0.575977i
$56$	0.673500	−	2.56155i	0.0900002	−	0.342302i
$57$	7.12311	−	2.00000i	0.943478	−	0.264906i
$58$	−6.56155	+	3.07221i	−0.861574	+	0.403400i
$59$	7.19612			0.936855			0.468427	−	0.883502i	$-0.344821\pi$
$59$	7.19612			0.936855			0.468427	+	0.883502i	$0.344821\pi$
$60$	1.41656	−	3.16123i	0.182877	−	0.408113i
$61$	−5.12311			−0.655946			−0.327973	−	0.944687i	$-0.606366\pi$
$61$	−5.12311			−0.655946			−0.327973	+	0.944687i	$0.606366\pi$
$62$	3.07221	−	1.43845i	0.390171	−	0.182683i
$63$	1.46228	+	2.39871i	0.184230	+	0.302209i
$64$	6.96543	+	3.93481i	0.870679	+	0.491851i
$65$		−	3.12311i		−	0.387374i
$66$	−7.92375	+	6.83311i	−0.975347	+	0.841098i
$67$		−	5.20798i		−	0.636257i	−0.948048	−	0.318128i	$-0.896946\pi$
$67$		−	5.20798i		−	0.636257i	0.948048	−	0.318128i	$-0.103054\pi$
$68$	−3.07221	−	2.56155i	−0.372560	−	0.310634i
$69$	3.56155	+	12.6847i	0.428761	+	1.52705i
$70$	0.561553	+	1.19935i	0.0671184	+	0.143350i
$71$	−6.67026			−0.791615			−0.395807	−	0.918334i	$-0.629535\pi$
$71$	−6.67026			−0.791615			−0.395807	+	0.918334i	$0.629535\pi$
$72$	−8.13012	+	2.42923i	−0.958144	+	0.286287i
$73$	−8.24621			−0.965146			−0.482573	−	0.875856i	$-0.660298\pi$
$73$	−8.24621			−0.965146			−0.482573	+	0.875856i	$0.660298\pi$
$74$	1.87285	+	4.00000i	0.217715	+	0.464991i
$75$	0.468213	+	1.66757i	0.0540646	+	0.192554i
$76$	−6.56155	−	5.47091i	−0.752662	−	0.627557i
$77$		−	4.00000i		−	0.455842i
$78$	−5.79337	+	4.99596i	−0.655970	+	0.565681i
$79$		−	9.06897i		−	1.02034i	−0.860074	−	0.510169i	$-0.829583\pi$
$79$		−	9.06897i		−	1.02034i	0.860074	−	0.510169i	$-0.170417\pi$
$80$	−3.93481	+	0.719224i	−0.439925	+	0.0804116i
$81$	4.12311	−	8.00000i	0.458123	−	0.888889i
$82$	9.12311	−	4.27156i	1.00748	−	0.471715i
$83$	4.68213			0.513931			0.256965	−	0.966421i	$-0.417277\pi$
$83$	4.68213			0.513931			0.256965	+	0.966421i	$0.417277\pi$
$84$	1.32650	−	2.96026i	0.144733	−	0.322991i
$85$	2.00000			0.216930
$86$	−1.87285	+	0.876894i	−0.201955	+	0.0945580i
$87$	−8.54312	+	2.39871i	−0.915918	+	0.257168i
$88$	11.6847	+	3.07221i	1.24559	+	0.327498i
$89$		−	6.24621i		−	0.662097i	−0.943614	−	0.331049i	$-0.892598\pi$
$89$		−	6.24621i		−	0.662097i	0.943614	−	0.331049i	$-0.107402\pi$
$90$	2.34435	−	3.53610i	0.247116	−	0.372738i
$91$		−	2.92456i		−	0.306577i
$92$	9.74247	−	11.6847i	1.01572	−	1.21821i
$93$	4.00000	−	1.12311i	0.414781	−	0.116461i
$94$	−0.561553	−	1.19935i	−0.0579198	−	0.123704i
$95$	4.27156			0.438253
$96$	7.62858	+	6.14856i	0.778589	+	0.627534i
$97$	−6.00000			−0.609208			−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000			−0.609208			−0.304604	+	0.952479i	$0.598524\pi$
$98$	−3.67188	−	7.84233i	−0.370916	−	0.792195i
$99$	−10.9418	+	6.67026i	−1.09969	+	0.670387i
$100$	1.28078	−	1.53610i	0.128078	−	0.153610i
$101$		−	9.12311i		−	0.907783i	−0.891057	−	0.453891i	$-0.850035\pi$
$101$		−	9.12311i		−	0.907783i	0.891057	−	0.453891i	$-0.149965\pi$
$102$	−3.19935	−	3.71001i	−0.316783	−	0.367345i
$103$			12.4041i			1.22221i	0.791549	+	0.611106i	$0.209275\pi$
$103$			12.4041i			1.22221i	−0.791549	+	0.611106i	$0.790725\pi$
$104$	8.54312	+	2.24621i	0.837722	+	0.220259i
$105$	0.438447	+	1.56155i	0.0427881	+	0.152392i
$106$	5.43845	−	2.54635i	0.528229	−	0.247324i
$107$	−0.936426			−0.0905278			−0.0452639	−	0.998975i	$-0.514413\pi$
$107$	−0.936426			−0.0905278			−0.0452639	+	0.998975i	$0.514413\pi$
$108$	−10.3097	+	1.30784i	−0.992050	+	0.125847i
$109$	−9.12311			−0.873835			−0.436918	−	0.899502i	$-0.643930\pi$
$109$	−9.12311			−0.873835			−0.436918	+	0.899502i	$0.643930\pi$
$110$	−5.47091	+	2.56155i	−0.521631	+	0.244234i
$111$	1.46228	+	5.20798i	0.138793	+	0.494320i
$112$	−3.68466	+	0.673500i	−0.348167	+	0.0636398i
$113$			14.0000i			1.31701i	0.752577	+	0.658505i	$0.228811\pi$
$113$			14.0000i			1.31701i	−0.752577	+	0.658505i	$0.771189\pi$
$114$	−6.83311	−	7.92375i	−0.639980	−	0.742127i
$115$			7.60669i			0.709328i
$116$	7.86962	+	6.56155i	0.730676	+	0.609225i
$117$	−8.00000	+	4.87689i	−0.739600	+	0.450869i
$118$	−4.31534	−	9.21662i	−0.397259	−	0.848458i
$119$	1.87285			0.171684
$120$	−4.89830	+	0.0814236i	−0.447152	+	0.00743292i
$121$	7.24621			0.658746
$122$	3.07221	+	6.56155i	0.278144	+	0.594055i
$123$	11.8782	−	3.33513i	1.07103	−	0.300719i
$124$	−3.68466	−	3.07221i	−0.330892	−	0.275892i
$125$			1.00000i			0.0894427i
$126$	2.19531	−	3.31130i	0.195574	−	0.294994i
$127$			4.68213i			0.415472i	0.978185	+	0.207736i	$0.0666095\pi$
$127$			4.68213i			0.415472i	−0.978185	+	0.207736i	$0.933391\pi$
$128$	0.862603	−	11.2808i	0.0762440	−	0.997089i
$129$	−2.43845	+	0.684658i	−0.214693	+	0.0602808i
$130$	−4.00000	+	1.87285i	−0.350823	+	0.164260i
$131$	−17.6121			−1.53878			−0.769388	−	0.638782i	$-0.779438\pi$
$131$	−17.6121			−1.53878			−0.769388	+	0.638782i	$0.779438\pi$
$132$	13.5034	+	6.05090i	1.17532	+	0.526663i
$133$	4.00000			0.346844
$134$	−6.67026	+	3.12311i	−0.576223	+	0.269795i
$135$	3.54042	−	3.80335i	0.304711	−	0.327340i
$136$	−1.43845	+	5.47091i	−0.123346	+	0.469127i
$137$			8.24621i			0.704521i	0.935902	+	0.352261i	$0.114587\pi$
$137$			8.24621i			0.704521i	−0.935902	+	0.352261i	$0.885413\pi$
$138$	14.1104	−	12.1682i	1.20116	−	1.03583i
$139$			13.8664i			1.17613i	0.808813	+	0.588066i	$0.200110\pi$
$139$			13.8664i			1.17613i	−0.808813	+	0.588066i	$0.799890\pi$
$140$	1.19935	−	1.43845i	0.101364	−	0.121571i
$141$	−0.438447	−	1.56155i	−0.0369239	−	0.131506i
$142$	4.00000	+	8.54312i	0.335673	+	0.716922i
$143$	13.3405			1.11559
$144$	7.98674	+	8.95611i	0.665562	+	0.746343i
$145$	−5.12311			−0.425451
$146$	4.94506	+	10.5616i	0.409256	+	0.874080i
$147$	−2.86692	−	10.2107i	−0.236459	−	0.842163i
$148$	4.00000	−	4.79741i	0.328798	−	0.394345i
$149$		−	14.0000i		−	1.14692i	−0.819232	−	0.573462i	$-0.805600\pi$
$149$		−	14.0000i		−	1.14692i	0.819232	−	0.573462i	$-0.194400\pi$
$150$	1.85500	−	1.59968i	0.151460	−	0.130613i
$151$		−	6.14441i		−	0.500025i	−0.968243	−	0.250013i	$-0.919565\pi$
$151$		−	6.14441i		−	0.500025i	0.968243	−	0.250013i	$-0.0804347\pi$
$152$	−3.07221	+	11.6847i	−0.249189	+	0.947751i
$153$	−3.12311	−	5.12311i	−0.252488	−	0.414179i
$154$	−5.12311	+	2.39871i	−0.412832	+	0.193293i
$155$	2.39871			0.192669
$156$	9.87285	+	4.42405i	0.790461	+	0.354208i
$157$	21.3693			1.70546			0.852729	−	0.522354i	$-0.174946\pi$
$157$	21.3693			1.70546			0.852729	+	0.522354i	$0.174946\pi$
$158$	−11.6153	+	5.43845i	−0.924065	+	0.432660i
$159$	7.08084	−	1.98813i	0.561547	−	0.157669i
$160$	3.28078	+	4.60831i	0.259368	+	0.364319i
$161$			7.12311i			0.561379i
$162$	−12.7187	−	0.483365i	−0.999279	−	0.0379768i
$163$		−	24.1671i		−	1.89291i	−0.322834	−	0.946456i	$-0.604636\pi$
$163$		−	24.1671i		−	1.89291i	0.322834	−	0.946456i	$-0.395364\pi$
$164$	−10.9418	−	9.12311i	−0.854413	−	0.712395i
$165$	−7.12311	+	2.00000i	−0.554533	+	0.155700i
$166$	−2.80776	−	5.99676i	−0.217925	−	0.465439i
$167$	−2.80928			−0.217389			−0.108694	−	0.994075i	$-0.534667\pi$
$167$	−2.80928			−0.217389			−0.108694	+	0.994075i	$0.534667\pi$
$168$	−4.58690	+	0.0762472i	−0.353887	+	0.00588260i
$169$	−3.24621			−0.249709
$170$	−1.19935	−	2.56155i	−0.0919862	−	0.196462i
$171$	−6.67026	−	10.9418i	−0.510088	−	0.836742i
$172$	2.24621	+	1.87285i	0.171272	+	0.142804i
$173$			2.00000i			0.152057i	0.997106	+	0.0760286i	$0.0242240\pi$
$173$			2.00000i			0.152057i	−0.997106	+	0.0760286i	$0.975776\pi$
$174$	8.19531	+	9.50338i	0.621285	+	0.720449i
$175$			0.936426i			0.0707872i
$176$	−3.07221	−	16.8078i	−0.231576	−	1.26693i
$177$	−3.36932	−	12.0000i	−0.253253	−	0.901975i
$178$	−8.00000	+	3.74571i	−0.599625	+	0.280752i
$179$	−14.6875			−1.09780			−0.548899	−	0.835889i	$-0.684953\pi$
$179$	−14.6875			−1.09780			−0.548899	+	0.835889i	$0.684953\pi$
$180$	−5.93481	−	0.882071i	−0.442355	−	0.0657457i
$181$	4.24621			0.315618			0.157809	−	0.987470i	$-0.449557\pi$
$181$	4.24621			0.315618			0.157809	+	0.987470i	$0.449557\pi$
$182$	−3.74571	+	1.75379i	−0.277650	+	0.129999i
$183$	2.39871	+	8.54312i	0.177317	+	0.631525i
$184$	−20.8078	−	5.47091i	−1.53397	−	0.403321i
$185$			3.12311i			0.229615i
$186$	−3.83715	−	4.44961i	−0.281354	−	0.326261i
$187$			8.54312i			0.624735i
$188$	−1.19935	+	1.43845i	−0.0874718	+	0.104910i
$189$	3.31534	−	3.56155i	0.241156	−	0.259065i
$190$	−2.56155	−	5.47091i	−0.185835	−	0.396902i
$191$	7.72197			0.558742			0.279371	−	0.960183i	$-0.409874\pi$
$191$	7.72197			0.558742			0.279371	+	0.960183i	$0.409874\pi$
$192$	3.30024	−	13.4577i	0.238175	−	0.971222i
$193$	16.2462			1.16943			0.584714	−	0.811240i	$-0.301207\pi$
$193$	16.2462			1.16943			0.584714	+	0.811240i	$0.301207\pi$
$194$	3.59806	+	7.68466i	0.258326	+	0.551726i
$195$	−5.20798	+	1.46228i	−0.372952	+	0.104716i
$196$	−7.84233	+	9.40572i	−0.560166	+	0.671837i
$197$		−	12.2462i		−	0.872506i	−0.899824	−	0.436253i	$-0.856305\pi$
$197$		−	12.2462i		−	0.872506i	0.899824	−	0.436253i	$-0.143695\pi$
$198$	15.1047	+	10.0140i	1.07344	+	0.711666i
$199$		−	17.6121i		−	1.24849i	−0.781230	−	0.624244i	$-0.785407\pi$
$199$		−	17.6121i		−	1.24849i	0.781230	−	0.624244i	$-0.214593\pi$
$200$	−2.73546	−	0.719224i	−0.193426	−	0.0508568i
$201$	−8.68466	+	2.43845i	−0.612569	+	0.171995i
$202$	−11.6847	+	5.47091i	−0.822130	+	0.384932i
$203$	−4.79741			−0.336712
$204$	−2.83311	+	6.32246i	−0.198357	+	0.442661i
$205$	7.12311			0.497499
$206$	15.8869	−	7.43845i	1.10689	−	0.518261i
$207$	19.4849	−	11.8782i	1.35430	−	0.825595i
$208$	−2.24621	−	12.2888i	−0.155747	−	0.852077i
$209$			18.2462i			1.26212i
$210$	1.73707	−	1.49798i	0.119869	−	0.103370i
$211$		−	1.34700i		−	0.0927313i	−0.998925	−	0.0463656i	$-0.985236\pi$
$211$		−	1.34700i		−	0.0927313i	0.998925	−	0.0463656i	$-0.0147639\pi$
$212$	−6.52262	−	5.43845i	−0.447975	−	0.373514i
$213$	3.12311	+	11.1231i	0.213992	+	0.762143i
$214$	0.561553	+	1.19935i	0.0383870	+	0.0819861i
$215$	−1.46228			−0.0997266
$216$	7.85753	+	12.4201i	0.534637	+	0.845082i
$217$	2.24621			0.152483
$218$	5.47091	+	11.6847i	0.370537	+	0.791385i
$219$	3.86098	+	13.7511i	0.260901	+	0.929213i
$220$	6.56155	+	5.47091i	0.442380	+	0.368849i
$221$			6.24621i			0.420166i
$222$	5.79337	−	4.99596i	0.388826	−	0.335307i
$223$			18.0227i			1.20689i	0.797406	+	0.603443i	$0.206205\pi$
$223$			18.0227i			1.20689i	−0.797406	+	0.603443i	$0.793795\pi$
$224$	3.07221	+	4.31534i	0.205270	+	0.288331i
$225$	2.56155	−	1.56155i	0.170770	−	0.104104i
$226$	17.9309	−	8.39547i	1.19274	−	0.558458i
$227$	−8.65840			−0.574678			−0.287339	−	0.957829i	$-0.592771\pi$
$227$	−8.65840			−0.574678			−0.287339	+	0.957829i	$0.592771\pi$
$228$	−6.05090	+	13.5034i	−0.400731	+	0.894283i
$229$	0.246211			0.0162701			0.00813505	−	0.999967i	$-0.497411\pi$
$229$	0.246211			0.0162701			0.00813505	+	0.999967i	$0.497411\pi$
$230$	9.74247	−	4.56155i	0.642399	−	0.300780i
$231$	−6.67026	+	1.87285i	−0.438871	+	0.123225i
$232$	3.68466	−	14.0140i	0.241910	−	0.920066i
$233$		−	10.0000i		−	0.655122i	−0.944830	−	0.327561i	$-0.893773\pi$
$233$		−	10.0000i		−	0.655122i	0.944830	−	0.327561i	$-0.106227\pi$
$234$	11.0436	+	7.32165i	0.721944	+	0.478631i
$235$		−	0.936426i		−	0.0610857i
$236$	−9.21662	+	11.0540i	−0.599951	+	0.719553i
$237$	−15.1231	+	4.24621i	−0.982351	+	0.275821i
$238$	−1.12311	−	2.39871i	−0.0728001	−	0.155485i
$239$	20.8319			1.34751			0.673753	−	0.738957i	$-0.264681\pi$
$239$	20.8319			1.34751			0.673753	+	0.738957i	$0.264681\pi$
$240$	3.04168	+	6.22480i	0.196340	+	0.401809i
$241$	−11.3693			−0.732362			−0.366181	−	0.930544i	$-0.619335\pi$
$241$	−11.3693			−0.732362			−0.366181	+	0.930544i	$0.619335\pi$
$242$	−4.34538	−	9.28078i	−0.279332	−	0.596591i
$243$	−15.2710	−	3.12985i	−0.979636	−	0.200780i
$244$	6.56155	−	7.86962i	0.420060	−	0.503801i
$245$		−	6.12311i		−	0.391191i
$246$	−11.3947	−	13.2134i	−0.726497	−	0.842454i
$247$			13.3405i			0.848837i
$248$	−1.72521	+	6.56155i	−0.109551	+	0.416659i
$249$	−2.19224	−	7.80776i	−0.138927	−	0.494797i
$250$	1.28078	−	0.599676i	0.0810034	−	0.0379269i
$251$	25.1035			1.58452			0.792259	−	0.610184i	$-0.208905\pi$
$251$	25.1035			1.58452			0.792259	+	0.610184i	$0.208905\pi$
$252$	−5.55751	−	0.825994i	−0.350090	−	0.0520328i
$253$	−32.4924			−2.04278
$254$	5.99676	−	2.80776i	0.376270	−	0.176175i
$255$	−0.936426	−	3.33513i	−0.0586413	−	0.208854i
$256$	−14.9654	+	5.66001i	−0.935340	+	0.353751i
$257$		−	2.49242i		−	0.155473i	−0.996974	−	0.0777365i	$-0.975231\pi$
$257$		−	2.49242i		−	0.155473i	0.996974	−	0.0777365i	$-0.0247693\pi$
$258$	2.33917	+	2.71253i	0.145631	+	0.168875i
$259$			2.92456i			0.181723i
$260$	4.79741	+	4.00000i	0.297523	+	0.248069i
$261$	8.00000	+	13.1231i	0.495188	+	0.812300i
$262$	10.5616	+	22.5571i	0.652495	+	1.39359i
$263$	−15.0981			−0.930989			−0.465494	−	0.885051i	$-0.654123\pi$
$263$	−15.0981			−0.930989			−0.465494	+	0.885051i	$0.654123\pi$
$264$	−0.347806	−	20.9234i	−0.0214060	−	1.28775i
$265$	4.24621			0.260843
$266$	−2.39871	−	5.12311i	−0.147074	−	0.314118i
$267$	−10.4160	+	2.92456i	−0.637447	+	0.178980i
$268$	8.00000	+	6.67026i	0.488678	+	0.407451i
$269$			14.0000i			0.853595i	0.904347	+	0.426798i	$0.140358\pi$
$269$			14.0000i			0.853595i	−0.904347	+	0.426798i	$0.859642\pi$
$270$	−6.99434	−	2.25371i	−0.425662	−	0.137156i
$271$			31.7738i			1.93012i	0.262032	+	0.965059i	$0.415608\pi$
$271$			31.7738i			1.93012i	−0.262032	+	0.965059i	$0.584392\pi$
$272$	7.86962	−	1.43845i	0.477166	−	0.0872187i
$273$	−4.87689	+	1.36932i	−0.295163	+	0.0828748i
$274$	10.5616	−	4.94506i	0.638047	−	0.298742i
$275$	−4.27156			−0.257585
$276$	−24.0465	−	10.7753i	−1.44743	−	0.648597i
$277$	−1.36932			−0.0822743			−0.0411371	−	0.999154i	$-0.513098\pi$
$277$	−1.36932			−0.0822743			−0.0411371	+	0.999154i	$0.513098\pi$
$278$	17.7597	−	8.31534i	1.06516	−	0.498721i
$279$	−3.74571	−	6.14441i	−0.224250	−	0.367856i
$280$	−2.56155	−	0.673500i	−0.153082	−	0.0402493i
$281$		−	27.6155i		−	1.64740i	−0.567023	−	0.823702i	$-0.691905\pi$
$281$		−	27.6155i		−	1.64740i	0.567023	−	0.823702i	$-0.308095\pi$
$282$	−1.73707	+	1.49798i	−0.103441	+	0.0892034i
$283$		−	4.38684i		−	0.260770i	−0.991463	−	0.130385i	$-0.958379\pi$
$283$		−	4.38684i		−	0.260770i	0.991463	−	0.130385i	$-0.0416214\pi$
$284$	8.54312	−	10.2462i	0.506941	−	0.608001i
$285$	−2.00000	−	7.12311i	−0.118470	−	0.421936i
$286$	−8.00000	−	17.0862i	−0.473050	−	1.01033i
$287$	6.67026			0.393733
$288$	6.68132	−	15.6000i	0.393701	−	0.919239i
$289$	13.0000			0.764706
$290$	3.07221	+	6.56155i	0.180406	+	0.385308i
$291$	2.80928	+	10.0054i	0.164683	+	0.586527i
$292$	10.5616	−	12.6670i	0.618068	−	0.741282i
$293$		−	30.4924i		−	1.78139i	−0.454605	−	0.890693i	$-0.650220\pi$
$293$		−	30.4924i		−	1.78139i	0.454605	−	0.890693i	$-0.349780\pi$
$294$	−11.3584	+	9.79499i	−0.662434	+	0.571255i
$295$		−	7.19612i		−	0.418974i
$296$	−8.54312	−	2.24621i	−0.496559	−	0.130558i
$297$	16.2462	+	15.1231i	0.942701	+	0.877532i
$298$	−17.9309	+	8.39547i	−1.03871	+	0.486337i
$299$	−23.7565			−1.37387
$300$	−3.16123	−	1.41656i	−0.182514	−	0.0817849i
$301$	−1.36932			−0.0789261
$302$	−7.86962	+	3.68466i	−0.452846	+	0.212028i
$303$	−15.2134	+	4.27156i	−0.873986	+	0.245395i
$304$	16.8078	−	3.07221i	0.963991	−	0.176203i
$305$			5.12311i			0.293348i
$306$	−4.68870	+	7.07221i	−0.268035	+	0.404291i
$307$		−	8.13254i		−	0.464149i	−0.972698	−	0.232074i	$-0.925449\pi$
$307$		−	8.13254i		−	0.464149i	0.972698	−	0.232074i	$-0.0745513\pi$
$308$	6.14441	+	5.12311i	0.350110	+	0.291916i
$309$	20.6847	−	5.80776i	1.17671	−	0.330392i
$310$	−1.43845	−	3.07221i	−0.0816983	−	0.174490i
$311$	14.1617			0.803035			0.401517	−	0.915851i	$-0.368483\pi$
$311$	14.1617			0.803035			0.401517	+	0.915851i	$0.368483\pi$
$312$	−0.254294	−	15.2979i	−0.0143966	−	0.866074i
$313$	10.4924			0.593067			0.296533	−	0.955022i	$-0.404169\pi$
$313$	10.4924			0.593067			0.296533	+	0.955022i	$0.404169\pi$
$314$	−12.8147	−	27.3693i	−0.723174	−	1.54454i
$315$	2.39871	−	1.46228i	0.135152	−	0.0823901i
$316$	13.9309	+	11.6153i	0.783673	+	0.653413i
$317$			32.7386i			1.83878i	0.393342	+	0.919392i	$0.371319\pi$
$317$			32.7386i			1.83878i	−0.393342	+	0.919392i	$0.628681\pi$
$318$	−6.79256	−	7.87673i	−0.380908	−	0.441705i
$319$		−	21.8836i		−	1.22525i
$320$	3.93481	−	6.96543i	0.219962	−	0.389380i
$321$	0.438447	+	1.56155i	0.0244717	+	0.0871574i
$322$	9.12311	−	4.27156i	0.508411	−	0.238045i
$323$	−8.54312			−0.475352
$324$	7.00805	+	16.5797i	0.389336	+	0.921096i
$325$	−3.12311			−0.173239
$326$	−30.9526	+	14.4924i	−1.71431	+	0.802661i
$327$	4.27156	+	15.2134i	0.236218	+	0.841302i
$328$	−5.12311	+	19.4849i	−0.282876	+	1.07588i
$329$		−	0.876894i		−	0.0483448i
$330$	6.83311	+	7.92375i	0.376150	+	0.436188i
$331$		−	28.0281i		−	1.54056i	−0.637705	−	0.770281i	$-0.720116\pi$
$331$		−	28.0281i		−	1.54056i	0.637705	−	0.770281i	$-0.279884\pi$
$332$	−5.99676	+	7.19224i	−0.329115	+	0.394725i
$333$	8.00000	−	4.87689i	0.438397	−	0.267252i
$334$	1.68466	+	3.59806i	0.0921804	+	0.196877i
$335$	−5.20798			−0.284543
$336$	2.84831	+	5.82907i	0.155388	+	0.318002i
$337$	−34.4924			−1.87892			−0.939461	−	0.342656i	$-0.888674\pi$
$337$	−34.4924			−1.87892			−0.939461	+	0.342656i	$0.888674\pi$
$338$	1.94668	+	4.15767i	0.105885	+	0.226147i
$339$	23.3459	−	6.55498i	1.26798	−	0.356018i
$340$	−2.56155	+	3.07221i	−0.138920	+	0.166614i
$341$			10.2462i			0.554863i
$342$	−10.0140	+	15.1047i	−0.541497	+	0.816767i
$343$		−	12.2888i		−	0.663534i
$344$	1.05171	−	4.00000i	0.0567042	−	0.215666i
$345$	12.6847	−	3.56155i	0.682919	−	0.191748i
$346$	2.56155	−	1.19935i	0.137710	−	0.0644776i
$347$	23.8718			1.28150			0.640752	−	0.767748i	$-0.278623\pi$
$347$	23.8718			1.28150			0.640752	+	0.767748i	$0.278623\pi$
$348$	7.25716	−	16.1953i	0.389025	−	0.868160i
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$	1.19935	−	0.561553i	0.0641081	−	0.0300163i
$351$	11.8782	+	11.0571i	0.634014	+	0.590184i
$352$	−19.6847	+	14.0140i	−1.04920	+	0.746950i
$353$		−	3.75379i		−	0.199794i	−0.994998	−	0.0998970i	$-0.968149\pi$
$353$		−	3.75379i		−	0.199794i	0.994998	−	0.0998970i	$-0.0318513\pi$
$354$	−13.3488	+	11.5115i	−0.709482	+	0.611827i
$355$			6.67026i			0.354021i
$356$	9.59482	+	8.00000i	0.508525	+	0.423999i
$357$	−0.876894	−	3.12311i	−0.0464102	−	0.165292i
$358$	8.80776	+	18.8114i	0.465505	+	0.994215i
$359$	−1.05171			−0.0555069			−0.0277535	−	0.999615i	$-0.508835\pi$
$359$	−1.05171			−0.0555069			−0.0277535	+	0.999615i	$0.508835\pi$
$360$	2.42923	+	8.13012i	0.128032	+	0.428495i
$361$	0.753789			0.0396731
$362$	−2.54635	−	5.43845i	−0.133833	−	0.285838i
$363$	−3.39277	−	12.0835i	−0.178074	−	0.634221i
$364$	4.49242	+	3.74571i	0.235467	+	0.196328i
$365$			8.24621i			0.431626i
$366$	9.50338	−	8.19531i	0.496749	−	0.428376i
$367$		−	26.5658i		−	1.38672i	−0.720590	−	0.693361i	$-0.756129\pi$
$367$		−	26.5658i		−	1.38672i	0.720590	−	0.693361i	$-0.243871\pi$
$368$	5.47091	+	29.9309i	0.285191	+	1.56025i
$369$	−11.1231	−	18.2462i	−0.579046	−	0.949860i
$370$	4.00000	−	1.87285i	0.207950	−	0.0973650i
$371$	3.97626			0.206437
$372$	−3.39790	+	7.58286i	−0.176173	+	0.393153i
$373$	−0.876894			−0.0454039			−0.0227019	−	0.999742i	$-0.507227\pi$
$373$	−0.876894			−0.0454039			−0.0227019	+	0.999742i	$0.507227\pi$
$374$	10.9418	−	5.12311i	0.565788	−	0.264909i
$375$	1.66757	−	0.468213i	0.0861127	−	0.0241784i
$376$	2.56155	+	0.673500i	0.132102	+	0.0347331i
$377$		−	16.0000i		−	0.824042i
$378$	−6.54968	−	2.11043i	−0.336879	−	0.108549i
$379$			25.1035i			1.28948i	0.764402	+	0.644740i	$0.223034\pi$
$379$			25.1035i			1.28948i	−0.764402	+	0.644740i	$0.776966\pi$
$380$	−5.47091	+	6.56155i	−0.280652	+	0.336601i
$381$	7.80776	−	2.19224i	0.400004	−	0.112312i
$382$	−4.63068	−	9.89012i	−0.236926	−	0.506022i
$383$	−4.68213			−0.239246			−0.119623	−	0.992819i	$-0.538169\pi$
$383$	−4.68213			−0.239246			−0.119623	+	0.992819i	$0.538169\pi$
$384$	−19.2153	+	3.84336i	−0.980578	+	0.196131i
$385$	−4.00000			−0.203859
$386$	−9.74247	−	20.8078i	−0.495879	−	1.05909i
$387$	2.28343	+	3.74571i	0.116073	+	0.190405i
$388$	7.68466	−	9.21662i	0.390129	−	0.467903i
$389$			28.7386i			1.45711i	0.684989	+	0.728553i	$0.259807\pi$
$389$			28.7386i			1.45711i	−0.684989	+	0.728553i	$0.740193\pi$
$390$	4.99596	+	5.79337i	0.252980	+	0.293359i
$391$		−	15.2134i		−	0.769374i
$392$	16.7495	+	4.40388i	0.845977	+	0.222430i
$393$	8.24621	+	29.3693i	0.415966	+	1.48149i
$394$	−15.6847	+	7.34376i	−0.790182	+	0.369973i
$395$	−9.06897			−0.456309
$396$	3.76782	−	25.3509i	0.189340	−	1.27393i
$397$	23.1231			1.16052			0.580258	−	0.814433i	$-0.302952\pi$
$397$	23.1231			1.16052			0.580258	+	0.814433i	$0.302952\pi$
$398$	−22.5571	+	10.5616i	−1.13069	+	0.529403i
$399$	−1.87285	−	6.67026i	−0.0937599	−	0.333931i
$400$	0.719224	+	3.93481i	0.0359612	+	0.196740i
$401$			24.0000i			1.19850i	0.800561	+	0.599251i	$0.204535\pi$
$401$			24.0000i			1.19850i	−0.800561	+	0.599251i	$0.795465\pi$
$402$	8.33109	+	9.66083i	0.415517	+	0.481838i
$403$			7.49141i			0.373174i
$404$	14.0140	+	11.6847i	0.697224	+	0.581333i
$405$	−8.00000	−	4.12311i	−0.397523	−	0.204879i
$406$	2.87689	+	6.14441i	0.142778	+	0.304942i
$407$	−13.3405			−0.661265
$408$	9.79661	−	0.162847i	0.485004	−	0.00806214i
$409$	0.630683			0.0311853			0.0155926	−	0.999878i	$-0.495037\pi$
$409$	0.630683			0.0311853			0.0155926	+	0.999878i	$0.495037\pi$
$410$	−4.27156	−	9.12311i	−0.210957	−	0.450558i
$411$	13.7511	−	3.86098i	0.678292	−	0.190448i
$412$	−19.0540	−	15.8869i	−0.938722	−	0.782690i
$413$		−	6.73863i		−	0.331586i
$414$	−26.8980	−	17.8327i	−1.32197	−	0.876432i
$415$		−	4.68213i		−	0.229837i
$416$	−14.3922	+	10.2462i	−0.705637	+	0.502362i
$417$	23.1231	−	6.49242i	1.13234	−	0.317935i
$418$	23.3693	−	10.9418i	1.14303	−	0.535182i
$419$	6.14441			0.300174			0.150087	−	0.988673i	$-0.452045\pi$
$419$	6.14441			0.300174			0.150087	+	0.988673i	$0.452045\pi$
$420$	−2.96026	−	1.32650i	−0.144446	−	0.0647266i
$421$	−0.630683			−0.0307376			−0.0153688	−	0.999882i	$-0.504892\pi$
$421$	−0.630683			−0.0307376			−0.0153688	+	0.999882i	$0.504892\pi$
$422$	−1.72521	+	0.807764i	−0.0839817	+	0.0393213i
$423$	−2.39871	+	1.46228i	−0.116629	+	0.0710985i
$424$	−3.05398	+	11.6153i	−0.148314	+	0.564090i
$425$		−	2.00000i		−	0.0970143i
$426$	12.3734	−	10.6703i	0.599491	−	0.516976i
$427$			4.79741i			0.232163i
$428$	1.19935	−	1.43845i	0.0579729	−	0.0695300i
$429$	−6.24621	−	22.2462i	−0.301570	−	1.07406i
$430$	0.876894	+	1.87285i	0.0422876	+	0.0903170i
$431$	−36.0453			−1.73624			−0.868121	−	0.496353i	$-0.834672\pi$
$431$	−36.0453			−1.73624			−0.868121	+	0.496353i	$0.834672\pi$
$432$	11.1954	−	17.5118i	0.538640	−	0.842536i
$433$	18.0000			0.865025			0.432512	−	0.901628i	$-0.357627\pi$
$433$	18.0000			0.865025			0.432512	+	0.901628i	$0.357627\pi$
$434$	−1.34700	−	2.87689i	−0.0646581	−	0.138095i
$435$	2.39871	+	8.54312i	0.115009	+	0.409611i
$436$	11.6847	−	14.0140i	0.559594	−	0.671150i
$437$		−	32.4924i		−	1.55432i
$438$	15.2967	−	13.1913i	0.730907	−	0.630303i
$439$			29.9009i			1.42709i	0.700608	+	0.713546i	$0.252912\pi$
$439$			29.9009i			1.42709i	−0.700608	+	0.713546i	$0.747088\pi$
$440$	3.07221	−	11.6847i	0.146462	−	0.557044i
$441$	−15.6847	+	9.56155i	−0.746888	+	0.455312i
$442$	8.00000	−	3.74571i	0.380521	−	0.178165i
$443$	25.7446			1.22316			0.611582	−	0.791181i	$-0.290533\pi$
$443$	25.7446			1.22316			0.611582	+	0.791181i	$0.290533\pi$
$444$	−9.87285	−	4.42405i	−0.468545	−	0.209956i
$445$	−6.24621			−0.296099
$446$	23.0830	−	10.8078i	1.09301	−	0.511762i
$447$	−23.3459	+	6.55498i	−1.10422	+	0.310040i
$448$	3.68466	−	6.52262i	0.174084	−	0.308165i
$449$		−	2.63068i		−	0.124150i	−0.998071	−	0.0620748i	$-0.980228\pi$
$449$		−	2.63068i		−	0.124150i	0.998071	−	0.0620748i	$-0.0197717\pi$
$450$	−3.53610	−	2.34435i	−0.166693	−	0.110514i
$451$			30.4268i			1.43274i
$452$	−21.5054	−	17.9309i	−1.01153	−	0.843397i
$453$	−10.2462	+	2.87689i	−0.481409	+	0.135168i
$454$	5.19224	+	11.0895i	0.243684	+	0.520455i
$455$	−2.92456			−0.137105
$456$	20.9234	−	0.347806i	0.979827	−	0.0162875i
$457$	−10.0000			−0.467780			−0.233890	−	0.972263i	$-0.575146\pi$
$457$	−10.0000			−0.467780			−0.233890	+	0.972263i	$0.575146\pi$
$458$	−0.147647	−	0.315342i	−0.00689909	−	0.0147349i
$459$	−7.08084	+	7.60669i	−0.330505	+	0.355050i
$460$	−11.6847	−	9.74247i	−0.544800	−	0.454245i
$461$		−	15.8617i		−	0.738755i	−0.929279	−	0.369377i	$-0.879571\pi$
$461$		−	15.8617i		−	0.738755i	0.929279	−	0.369377i	$-0.120429\pi$
$462$	6.39871	+	7.42001i	0.297695	+	0.345210i
$463$			0.936426i			0.0435194i	0.999763	+	0.0217597i	$0.00692688\pi$
$463$			0.936426i			0.0435194i	−0.999763	+	0.0217597i	$0.993073\pi$
$464$	−20.1584	+	3.68466i	−0.935832	+	0.171056i
$465$	−1.12311	−	4.00000i	−0.0520828	−	0.185496i
$466$	−12.8078	+	5.99676i	−0.593308	+	0.277795i
$467$	16.1498			0.747324			0.373662	−	0.927565i	$-0.378102\pi$
$467$	16.1498			0.747324			0.373662	+	0.927565i	$0.378102\pi$
$468$	2.75480	−	18.5350i	0.127341	−	0.856782i
$469$	−4.87689			−0.225194
$470$	−1.19935	+	0.561553i	−0.0553220	+	0.0259025i
$471$	−10.0054	−	35.6347i	−0.461024	−	1.64196i
$472$	19.6847	+	5.17562i	0.906060	+	0.238227i
$473$		−	6.24621i		−	0.287201i
$474$	14.5074	+	16.8230i	0.666348	+	0.772704i
$475$		−	4.27156i		−	0.195993i
$476$	−2.39871	+	2.87689i	−0.109944	+	0.131862i
$477$	−6.63068	−	10.8769i	−0.303598	−	0.498019i
$478$	−12.4924	−	26.6811i	−0.571390	−	1.22036i
$479$	−22.9354			−1.04794			−0.523971	−	0.851736i	$-0.675550\pi$
$479$	−22.9354			−1.04794			−0.523971	+	0.851736i	$0.675550\pi$
$480$	6.14856	−	7.62858i	0.280642	−	0.348196i
$481$	−9.75379			−0.444734
$482$	6.81791	+	14.5616i	0.310547	+	0.663261i
$483$	11.8782	−	3.33513i	0.540479	−	0.151754i
$484$	−9.28078	+	11.1309i	−0.421853	+	0.505951i
$485$			6.00000i			0.272446i
$486$	5.14904	+	21.4357i	0.233565	+	0.972341i
$487$			15.3287i			0.694608i	0.937753	+	0.347304i	$0.112903\pi$
$487$			15.3287i			0.694608i	−0.937753	+	0.347304i	$0.887097\pi$
$488$	−14.0140	−	3.68466i	−0.634385	−	0.166797i
$489$	−40.3002	+	11.3153i	−1.82244	+	0.511697i
$490$	−7.84233	+	3.67188i	−0.354280	+	0.165879i
$491$	−18.6638			−0.842285			−0.421143	−	0.906994i	$-0.638371\pi$
$491$	−18.6638			−0.842285			−0.421143	+	0.906994i	$0.638371\pi$
$492$	−10.0903	+	22.5178i	−0.454905	+	1.01518i
$493$	10.2462			0.461466
$494$	17.0862	−	8.00000i	0.768746	−	0.359937i
$495$	6.67026	+	10.9418i	0.299806	+	0.491798i
$496$	9.43845	−	1.72521i	0.423799	−	0.0774640i
$497$			6.24621i			0.280181i
$498$	−8.68537	+	7.48990i	−0.389201	+	0.335630i
$499$		−	1.57756i		−	0.0706212i	−0.999376	−	0.0353106i	$-0.988758\pi$
$499$		−	1.57756i		−	0.0706212i	0.999376	−	0.0353106i	$-0.0112421\pi$
$500$	−1.53610	−	1.28078i	−0.0686966	−	0.0572781i
$501$	1.31534	+	4.68466i	0.0587651	+	0.209295i
$502$	−15.0540	−	32.1520i	−0.671892	−	1.43501i
$503$	19.8955			0.887097			0.443549	−	0.896250i	$-0.353719\pi$
$503$	19.8955			0.887097			0.443549	+	0.896250i	$0.353719\pi$
$504$	2.27479	+	7.61326i	0.101327	+	0.339121i
$505$	−9.12311			−0.405973
$506$	19.4849	+	41.6155i	0.866211	+	1.85004i
$507$	1.51992	+	5.41327i	0.0675020	+	0.240412i
$508$	−7.19224	−	5.99676i	−0.319104	−	0.266063i
$509$			2.87689i			0.127516i	0.997965	+	0.0637581i	$0.0203086\pi$
$509$			2.87689i			0.127516i	−0.997965	+	0.0637581i	$0.979691\pi$
$510$	−3.71001	+	3.19935i	−0.164282	+	0.141670i
$511$			7.72197i			0.341600i
$512$	16.2236	+	15.7732i	0.716990	+	0.697083i
$513$	−15.1231	+	16.2462i	−0.667701	+	0.717288i
$514$	−3.19224	+	1.49465i	−0.140803	+	0.0659261i
$515$	12.4041			0.546590
$516$	2.07140	−	4.62260i	0.0911883	−	0.203499i
$517$	4.00000			0.175920
$518$	3.74571	−	1.75379i	0.164577	−	0.0770571i
$519$	3.33513	−	0.936426i	0.146396	−	0.0411046i
$520$	2.24621	−	8.54312i	0.0985029	−	0.374640i
$521$		−	21.7538i		−	0.953051i	−0.879161	−	0.476525i	$-0.841896\pi$
$521$		−	21.7538i		−	0.953051i	0.879161	−	0.476525i	$-0.158104\pi$
$522$	12.0104	−	18.1158i	0.525679	−	0.792908i
$523$			0.641132i			0.0280348i	0.999902	+	0.0140174i	$0.00446202\pi$
$523$			0.641132i			0.0280348i	−0.999902	+	0.0140174i	$0.995538\pi$
$524$	22.5571	−	27.0540i	0.985413	−	1.18186i
$525$	1.56155	−	0.438447i	0.0681518	−	0.0191354i
$526$	9.05398	+	19.3373i	0.394772	+	0.843146i
$527$	−4.79741			−0.208979
$528$	−26.5896	+	12.9927i	−1.15716	+	0.565436i
$529$	34.8617			1.51573
$530$	−2.54635	−	5.43845i	−0.110606	−	0.236231i
$531$	−18.4332	+	11.2371i	−0.799934	+	0.487649i
$532$	−5.12311	+	6.14441i	−0.222115	+	0.266394i
$533$			22.2462i			0.963590i
$534$	9.99192	+	11.5867i	0.432393	+	0.501407i
$535$			0.936426i			0.0404852i
$536$	3.74571	−	14.2462i	0.161790	−	0.615343i
$537$	6.87689	+	24.4924i	0.296760	+	1.05693i
$538$	17.9309	−	8.39547i	0.773055	−	0.361954i
$539$	26.1552			1.12658
$540$	1.30784	+	10.3097i	0.0562807	+	0.443658i
$541$	38.9848			1.67609			0.838045	−	0.545602i	$-0.183699\pi$
$541$	38.9848			1.67609			0.838045	+	0.545602i	$0.183699\pi$
$542$	40.6951	−	19.0540i	1.74800	−	0.818438i
$543$	−1.98813	−	7.08084i	−0.0853189	−	0.303868i
$544$	−6.56155	−	9.21662i	−0.281324	−	0.395159i
$545$			9.12311i			0.390791i
$546$	4.67835	+	5.42506i	0.200215	+	0.232171i
$547$		−	25.2188i		−	1.07828i	−0.842217	−	0.539139i	$-0.818750\pi$
$547$		−	25.2188i		−	1.07828i	0.842217	−	0.539139i	$-0.181250\pi$
$548$	−12.6670	−	10.5616i	−0.541109	−	0.451167i
$549$	13.1231	−	8.00000i	0.560080	−	0.341432i
$550$	2.56155	+	5.47091i	0.109225	+	0.233280i
$551$	21.8836			0.932275
$552$	0.619364	+	37.2599i	0.0263619	+	1.58589i
$553$	−8.49242			−0.361135
$554$	0.821147	+	1.75379i	0.0348872	+	0.0745113i
$555$	5.20798	−	1.46228i	0.221067	−	0.0620703i
$556$	−21.3002	−	17.7597i	−0.903329	−	0.753180i
$557$			19.7538i			0.836995i	0.908218	+	0.418497i	$0.137443\pi$
$557$			19.7538i			0.836995i	−0.908218	+	0.418497i	$0.862557\pi$
$558$	−5.62341	+	8.48207i	−0.238058	+	0.359075i
$559$		−	4.56685i		−	0.193157i
$560$	0.673500	+	3.68466i	0.0284606	+	0.155705i
$561$	14.2462	−	4.00000i	0.601476	−	0.168880i
$562$	−35.3693	+	16.5604i	−1.49196	+	0.698558i
$563$	36.1606			1.52399			0.761994	−	0.647584i	$-0.224221\pi$
$563$	36.1606			1.52399			0.761994	+	0.647584i	$0.224221\pi$
$564$	2.96026	+	1.32650i	0.124649	+	0.0558557i
$565$	14.0000			0.588984
$566$	−5.61856	+	2.63068i	−0.236166	+	0.110576i
$567$	−7.49141	−	3.86098i	−0.314610	−	0.162146i
$568$	−18.2462	−	4.79741i	−0.765594	−	0.201295i
$569$		−	4.87689i		−	0.204450i	−0.994761	−	0.102225i	$-0.967404\pi$
$569$		−	4.87689i		−	0.204450i	0.994761	−	0.102225i	$-0.0325962\pi$
$570$	−7.92375	+	6.83311i	−0.331889	+	0.286208i
$571$		−	16.7909i		−	0.702679i	−0.936248	−	0.351339i	$-0.885726\pi$
$571$		−	16.7909i		−	0.702679i	0.936248	−	0.351339i	$-0.114274\pi$
$572$	−17.0862	+	20.4924i	−0.714411	+	0.856831i
$573$	−3.61553	−	12.8769i	−0.151041	−	0.537940i
$574$	−4.00000	−	8.54312i	−0.166957	−	0.356583i
$575$	7.60669			0.317221
$576$	−23.9867	+	0.797675i	−0.999448	+	0.0332364i
$577$	−15.7538			−0.655839			−0.327919	−	0.944706i	$-0.606347\pi$
$577$	−15.7538			−0.655839			−0.327919	+	0.944706i	$0.606347\pi$
$578$	−7.79579	−	16.6501i	−0.324262	−	0.692553i
$579$	−7.60669	−	27.0916i	−0.316123	−	1.12589i
$580$	6.56155	−	7.86962i	0.272454	−	0.326768i
$581$		−	4.38447i		−	0.181899i
$582$	11.1300	−	9.59806i	0.461354	−	0.397852i
$583$			18.1379i			0.751197i
$584$	−22.5571	−	5.93087i	−0.933421	−	0.245421i
$585$	4.87689	+	8.00000i	0.201635	+	0.330759i
$586$	−39.0540	+	18.2856i	−1.61330	+	0.755371i
$587$	−38.0335			−1.56981			−0.784904	−	0.619617i	$-0.787288\pi$
$587$	−38.0335			−1.56981			−0.784904	+	0.619617i	$0.787288\pi$
$588$	19.3565	+	8.67372i	0.798250	+	0.357698i
$589$	−10.2462			−0.422188
$590$	−9.21662	+	4.31534i	−0.379442	+	0.177660i
$591$	−20.4214	+	5.73384i	−0.840023	+	0.235859i
$592$	2.24621	+	12.2888i	0.0923187	+	0.505067i
$593$		−	8.24621i		−	0.338631i	−0.985562	−	0.169316i	$-0.945844\pi$
$593$		−	8.24621i		−	0.338631i	0.985562	−	0.169316i	$-0.0541557\pi$
$594$	9.62685	−	29.8767i	0.394994	−	1.22586i
$595$		−	1.87285i		−	0.0767795i
$596$	21.5054	+	17.9309i	0.880897	+	0.734477i
$597$	−29.3693	+	8.24621i	−1.20201	+	0.337495i
$598$	14.2462	+	30.4268i	0.582571	+	1.24424i
$599$	−36.8665			−1.50632			−0.753162	−	0.657836i	$-0.771472\pi$
$599$	−36.8665			−1.50632			−0.753162	+	0.657836i	$0.771472\pi$
$600$	0.0814236	+	4.89830i	0.00332410	+	0.199972i
$601$	14.8769			0.606841			0.303421	−	0.952857i	$-0.401871\pi$
$601$	14.8769			0.606841			0.303421	+	0.952857i	$0.401871\pi$
$602$	0.821147	+	1.75379i	0.0334675	+	0.0714791i
$603$	8.13254	+	13.3405i	0.331183	+	0.543268i
$604$	9.43845	+	7.86962i	0.384045	+	0.320210i
$605$		−	7.24621i		−	0.294600i
$606$	14.5940	+	16.9234i	0.592841	+	0.687466i
$607$		−	29.4903i		−	1.19698i	−0.801132	−	0.598488i	$-0.795768\pi$
$607$		−	29.4903i		−	1.19698i	0.801132	−	0.598488i	$-0.204232\pi$
$608$	−14.0140	−	19.6847i	−0.568344	−	0.798318i
$609$	2.24621	+	8.00000i	0.0910211	+	0.324176i
$610$	6.56155	−	3.07221i	0.265670	−	0.124390i
$611$	2.92456			0.118315
$612$	11.8696	+	1.76414i	0.479801	+	0.0713112i
$613$	0.876894			0.0354174			0.0177087	−	0.999843i	$-0.494363\pi$
$613$	0.876894			0.0354174			0.0177087	+	0.999843i	$0.494363\pi$
$614$	−10.4160	+	4.87689i	−0.420354	+	0.196815i
$615$	−3.33513	−	11.8782i	−0.134486	−	0.478977i
$616$	2.87689	−	10.9418i	0.115913	−	0.440859i
$617$		−	14.0000i		−	0.563619i	−0.959470	−	0.281809i	$-0.909065\pi$
$617$		−	14.0000i		−	0.563619i	0.959470	−	0.281809i	$-0.0909346\pi$
$618$	−19.8425	−	23.0096i	−0.798184	−	0.925584i
$619$		−	20.3061i		−	0.816171i	−0.912944	−	0.408085i	$-0.866197\pi$
$619$		−	20.3061i		−	0.816171i	0.912944	−	0.408085i	$-0.133803\pi$
$620$	−3.07221	+	3.68466i	−0.123383	+	0.147979i
$621$	−28.9309	−	26.9309i	−1.16096	−	1.08070i
$622$	−8.49242	−	18.1379i	−0.340515	−	0.727265i
$623$	−5.84912			−0.234340
$624$	−19.4407	+	9.49949i	−0.778252	+	0.380284i
$625$	1.00000			0.0400000
$626$	−6.29206	−	13.4384i	−0.251481	−	0.537108i
$627$	30.4268	−	8.54312i	1.21513	−	0.341179i
$628$	−27.3693	+	32.8255i	−1.09215	+	1.30988i
$629$		−	6.24621i		−	0.249053i
$630$	−3.31130	−	2.19531i	−0.131925	−	0.0874633i
$631$		−	30.1315i		−	1.19951i	−0.800182	−	0.599757i	$-0.795264\pi$
$631$		−	30.1315i		−	1.19951i	0.800182	−	0.599757i	$-0.204736\pi$
$632$	6.52262	−	24.8078i	0.259456	−	0.986800i
$633$	−2.24621	+	0.630683i	−0.0892789	+	0.0250674i
$634$	41.9309	−	19.6326i	1.66529	−	0.779710i
$635$	4.68213			0.185805
$636$	−6.01499	+	13.4232i	−0.238510	+	0.532266i
$637$	19.1231			0.757685
$638$	−28.0281	+	13.1231i	−1.10964	+	0.519549i
$639$	17.0862	−	10.4160i	0.675921	−	0.412049i
$640$	−11.2808	−	0.862603i	−0.445912	−	0.0340974i
$641$		−	47.6155i		−	1.88070i	−0.340208	−	0.940350i	$-0.610498\pi$
$641$		−	47.6155i		−	1.88070i	0.340208	−	0.940350i	$-0.389502\pi$
$642$	1.73707	−	1.49798i	0.0685568	−	0.0591205i
$643$			20.4214i			0.805340i	0.915345	+	0.402670i	$0.131918\pi$
$643$			20.4214i			0.805340i	−0.915345	+	0.402670i	$0.868082\pi$
$644$	−10.9418	−	9.12311i	−0.431168	−	0.359501i
$645$	0.684658	+	2.43845i	0.0269584	+	0.0960138i
$646$	5.12311	+	10.9418i	0.201566	+	0.430500i
$647$	−3.63043			−0.142727			−0.0713634	−	0.997450i	$-0.522735\pi$
$647$	−3.63043			−0.142727			−0.0713634	+	0.997450i	$0.522735\pi$
$648$	17.0324	−	18.9182i	0.669094	−	0.743177i
$649$	30.7386			1.20660
$650$	1.87285	+	4.00000i	0.0734593	+	0.156893i
$651$	−1.05171	−	3.74571i	−0.0412196	−	0.146806i
$652$	37.1231	+	30.9526i	1.45385	+	1.21220i
$653$			26.9848i			1.05600i	0.849245	+	0.527999i	$0.177058\pi$
$653$			26.9848i			1.05600i	−0.849245	+	0.527999i	$0.822942\pi$
$654$	16.9234	−	14.5940i	0.661757	−	0.570671i
$655$			17.6121i			0.688161i
$656$	28.0281	−	5.12311i	1.09431	−	0.200024i
$657$	21.1231	−	12.8769i	0.824091	−	0.502375i
$658$	−1.12311	+	0.525853i	−0.0437832	+	0.0204999i
$659$	26.9764			1.05085			0.525425	−	0.850840i	$-0.323906\pi$
$659$	26.9764			1.05085			0.525425	+	0.850840i	$0.323906\pi$
$660$	6.05090	−	13.5034i	0.235531	−	0.525618i
$661$	−46.1080			−1.79339			−0.896696	−	0.442647i	$-0.854039\pi$
$661$	−46.1080			−1.79339			−0.896696	+	0.442647i	$0.854039\pi$
$662$	−35.8977	+	16.8078i	−1.39520	+	0.653252i
$663$	10.4160	−	2.92456i	0.404523	−	0.113580i
$664$	12.8078	+	3.36750i	0.497038	+	0.130684i
$665$		−	4.00000i		−	0.155113i
$666$	−11.0436	−	7.32165i	−0.427932	−	0.283708i
$667$			38.9699i			1.50892i
$668$	3.59806	−	4.31534i	0.139213	−	0.166966i
$669$	30.0540	−	8.43845i	1.16195	−	0.326249i
$670$	3.12311	+	6.67026i	0.120656	+	0.257695i
$671$	−21.8836			−0.844809
$672$	5.75767	−	7.14361i	0.222107	−	0.275571i
$673$	−10.4924			−0.404453			−0.202227	−	0.979339i	$-0.564818\pi$
$673$	−10.4924			−0.404453			−0.202227	+	0.979339i	$0.564818\pi$
$674$	20.6843	+	44.1771i	0.796729	+	1.70164i
$675$	−3.80335	−	3.54042i	−0.146391	−	0.136271i
$676$	4.15767	−	4.98651i	0.159910	−	0.191789i
$677$			34.4924i			1.32565i	0.748774	+	0.662826i	$0.230643\pi$
$677$			34.4924i			1.32565i	−0.748774	+	0.662826i	$0.769357\pi$
$678$	−22.3955	−	25.9700i	−0.860093	−	0.997373i
$679$			5.61856i			0.215620i
$680$	5.47091	+	1.43845i	0.209800	+	0.0551619i
$681$	4.05398	+	14.4384i	0.155349	+	0.553282i
$682$	13.1231	−	6.14441i	0.502510	−	0.235282i
$683$	−36.1606			−1.38365			−0.691823	−	0.722067i	$-0.743192\pi$
$683$	−36.1606			−1.38365			−0.691823	+	0.722067i	$0.743192\pi$
$684$	25.3509	+	3.76782i	0.969315	+	0.144066i
$685$	8.24621			0.315072
$686$	−15.7392	+	7.36932i	−0.600927	+	0.281362i
$687$	−0.115279	−	0.410574i	−0.00439818	−	0.0156644i
$688$	−5.75379	+	1.05171i	−0.219361	+	0.0400959i
$689$			13.2614i			0.505218i
$690$	−12.1682	−	14.1104i	−0.463237	−	0.537175i
$691$			29.0798i			1.10625i	0.833100	+	0.553123i	$0.186564\pi$
$691$			29.0798i			1.10625i	−0.833100	+	0.553123i	$0.813436\pi$
$692$	−3.07221	−	2.56155i	−0.116788	−	0.0973756i
$693$	6.24621	+	10.2462i	0.237274	+	0.389221i
$694$	−14.3153	−	30.5744i	−0.543403	−	1.16059i
$695$	13.8664			0.525982
$696$	−25.0945	+	0.417142i	−0.951205	+	0.0158117i
$697$	−14.2462			−0.539614
$698$	8.39547	+	17.9309i	0.317773	+	0.678693i
$699$	−16.6757	+	4.68213i	−0.630731	+	0.177094i
$700$	−1.43845	−	1.19935i	−0.0543682	−	0.0453313i
$701$			50.4924i			1.90707i	0.301278	+	0.953536i	$0.402587\pi$
$701$			50.4924i			1.90707i	−0.301278	+	0.953536i	$0.597413\pi$
$702$	7.03857	−	21.8441i	0.265654	−	0.824451i
$703$		−	13.3405i		−	0.503148i
$704$	29.7533	+	16.8078i	1.12137	+	0.633466i
$705$	−1.56155	+	0.438447i	−0.0588115	+	0.0165129i
$706$	−4.80776	+	2.25106i	−0.180943	+	0.0847197i
$707$	−8.54312			−0.321297
$708$	22.7486	+	10.1937i	0.854944	+	0.383103i
$709$	−26.4924			−0.994944			−0.497472	−	0.867480i	$-0.665738\pi$
$709$	−26.4924			−0.994944			−0.497472	+	0.867480i	$0.665738\pi$
$710$	8.54312	−	4.00000i	0.320617	−	0.150117i
$711$	14.1617	+	23.2306i	0.531104	+	0.871217i
$712$	4.49242	−	17.0862i	0.168361	−	0.640334i
$713$		−	18.2462i		−	0.683326i
$714$	−3.47415	+	2.99596i	−0.130017	+	0.112121i
$715$		−	13.3405i		−	0.498907i
$716$	18.8114	−	22.5616i	0.703016	−	0.843165i
$717$	−9.75379	−	34.7386i	−0.364262	−	1.29734i
$718$	0.630683	+	1.34700i	0.0235369	+	0.0502696i
$719$	5.84912			0.218135			0.109068	−	0.994034i	$-0.465213\pi$
$719$	5.84912			0.218135			0.109068	+	0.994034i	$0.465213\pi$
$720$	8.95611	−	7.98674i	0.333775	−	0.297648i
$721$	11.6155			0.432585
$722$	−0.452029	−	0.965435i	−0.0168228	−	0.0359298i
$723$	5.32326	+	18.9591i	0.197974	+	0.705096i
$724$	−5.43845	+	6.52262i	−0.202118	+	0.242411i
$725$			5.12311i			0.190267i
$726$	−13.4417	+	11.5916i	−0.498870	+	0.430204i
$727$			26.5658i			0.985270i	0.870236	+	0.492635i	$0.163966\pi$
$727$			26.5658i			0.985270i	−0.870236	+	0.492635i	$0.836034\pi$
$728$	2.10341	−	8.00000i	0.0779576	−	0.296500i
$729$	1.93087	+	26.9309i	0.0715137	+	0.997440i
$730$	10.5616	−	4.94506i	0.390901	−	0.183025i
$731$	2.92456			0.108169
$732$	−16.1953	−	7.25716i	−0.598596	−	0.268233i
$733$	−35.1231			−1.29730			−0.648651	−	0.761086i	$-0.724666\pi$
$733$	−35.1231			−1.29730			−0.648651	+	0.761086i	$0.724666\pi$
$734$	−34.0248	+	15.9309i	−1.25588	+	0.588019i
$735$	−10.2107	+	2.86692i	−0.376627	+	0.105748i
$736$	35.0540	−	24.9559i	1.29211	−	0.919885i
$737$		−	22.2462i		−	0.819450i
$738$	−16.6991	+	25.1880i	−0.614701	+	0.927184i
$739$		−	18.6638i		−	0.686559i	−0.939233	−	0.343279i	$-0.888462\pi$
$739$		−	18.6638i		−	0.686559i	0.939233	−	0.343279i	$-0.111538\pi$
$740$	−4.79741	−	4.00000i	−0.176356	−	0.147043i
$741$	22.2462	−	6.24621i	0.817235	−	0.229460i
$742$	−2.38447	−	5.09271i	−0.0875367	−	0.186959i
$743$	12.4041			0.455062			0.227531	−	0.973771i	$-0.426935\pi$
$743$	12.4041			0.455062			0.227531	+	0.973771i	$0.426935\pi$
$744$	11.7496	−	0.195311i	0.430761	−	0.00716046i
$745$	−14.0000			−0.512920
$746$	0.525853	+	1.12311i	0.0192528	+	0.0411198i
$747$	−11.9935	+	7.31140i	−0.438820	+	0.267510i
$748$	−13.1231	−	10.9418i	−0.479828	−	0.400073i
$749$			0.876894i			0.0320410i
$750$	−1.59968	−	1.85500i	−0.0584119	−	0.0677351i
$751$			15.7392i			0.574333i	0.957881	+	0.287166i	$0.0927133\pi$
$751$			15.7392i			0.574333i	−0.957881	+	0.287166i	$0.907287\pi$
$752$	−0.673500	−	3.68466i	−0.0245600	−	0.134366i
$753$	−11.7538	−	41.8617i	−0.428332	−	1.52553i
$754$	−20.4924	+	9.59482i	−0.746290	+	0.349423i
$755$	−6.14441			−0.223618
$756$	1.22470	+	9.65426i	0.0445419	+	0.351122i
$757$	19.1231			0.695041			0.347521	−	0.937672i	$-0.387024\pi$
$757$	19.1231			0.695041			0.347521	+	0.937672i	$0.387024\pi$
$758$	32.1520	−	15.0540i	1.16781	−	0.546785i
$759$	15.2134	+	54.1833i	0.552211	+	1.96673i
$760$	11.6847	+	3.07221i	0.423847	+	0.111441i
$761$			51.2311i			1.85712i	0.371177	+	0.928562i	$0.378954\pi$
$761$			51.2311i			1.85712i	−0.371177	+	0.928562i	$0.621046\pi$
$762$	−7.48990	−	8.68537i	−0.271330	−	0.314638i
$763$			8.54312i			0.309282i
$764$	−9.89012	+	11.8617i	−0.357812	+	0.429143i
$765$	−5.12311	+	3.12311i	−0.185226	+	0.112916i
$766$	2.80776	+	5.99676i	0.101449	+	0.216672i
$767$	22.4742			0.811498
$768$	16.4455	+	22.3058i	0.593424	+	0.804890i
$769$	−26.9848			−0.973098			−0.486549	−	0.873653i	$-0.661745\pi$
$769$	−26.9848			−0.973098			−0.486549	+	0.873653i	$0.661745\pi$
$770$	2.39871	+	5.12311i	0.0864434	+	0.184624i
$771$	−4.15628	+	1.16699i	−0.149685	+	0.0420279i
$772$	−20.8078	+	24.9559i	−0.748888	+	0.898181i
$773$			16.2462i			0.584336i	0.956367	+	0.292168i	$0.0943766\pi$
$773$			16.2462i			0.584336i	−0.956367	+	0.292168i	$0.905623\pi$
$774$	3.42809	−	5.17077i	0.123220	−	0.185859i
$775$		−	2.39871i		−	0.0861641i
$776$	−16.4127	−	4.31534i	−0.589183	−	0.154912i
$777$	4.87689	−	1.36932i	0.174958	−	0.0491240i
$778$	36.8078	−

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:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	60.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.599676 - 1.28078i) q^{2} +(-0.468213 - 1.66757i) q^{3} +(-1.28078 + 1.53610i) q^{4} -1.00000i q^{5} +(-1.85500 + 1.59968i) q^{6} -0.936426i q^{7} +(2.73546 + 0.719224i) q^{8} +(-2.56155 + 1.56155i) q^{9} +O(q^{10})\)	\(q+(-0.599676 - 1.28078i) q^{2} +(-0.468213 - 1.66757i) q^{3} +(-1.28078 + 1.53610i) q^{4} -1.00000i q^{5} +(-1.85500 + 1.59968i) q^{6} -0.936426i q^{7} +(2.73546 + 0.719224i) q^{8} +(-2.56155 + 1.56155i) q^{9} +(-1.28078 + 0.599676i) q^{10} +4.27156 q^{11} +(3.16123 + 1.41656i) q^{12} +3.12311 q^{13} +(-1.19935 + 0.561553i) q^{14} +(-1.66757 + 0.468213i) q^{15} +(-0.719224 - 3.93481i) q^{16} +2.00000i q^{17} +(3.53610 + 2.34435i) q^{18} +4.27156i q^{19} +(1.53610 + 1.28078i) q^{20} +(-1.56155 + 0.438447i) q^{21} +(-2.56155 - 5.47091i) q^{22} -7.60669 q^{23} +(-0.0814236 - 4.89830i) q^{24} -1.00000 q^{25} +(-1.87285 - 4.00000i) q^{26} +(3.80335 + 3.54042i) q^{27} +(1.43845 + 1.19935i) q^{28} -5.12311i q^{29} +(1.59968 + 1.85500i) q^{30} +2.39871i q^{31} +(-4.60831 + 3.28078i) q^{32} +(-2.00000 - 7.12311i) q^{33} +(2.56155 - 1.19935i) q^{34} -0.936426 q^{35} +(0.882071 - 5.93481i) q^{36} -3.12311 q^{37} +(5.47091 - 2.56155i) q^{38} +(-1.46228 - 5.20798i) q^{39} +(0.719224 - 2.73546i) q^{40} +7.12311i q^{41} +(1.49798 + 1.73707i) q^{42} -1.46228i q^{43} +(-5.47091 + 6.56155i) q^{44} +(1.56155 + 2.56155i) q^{45} +(4.56155 + 9.74247i) q^{46} +0.936426 q^{47} +(-6.22480 + 3.04168i) q^{48} +6.12311 q^{49} +(0.599676 + 1.28078i) q^{50} +(3.33513 - 0.936426i) q^{51} +(-4.00000 + 4.79741i) q^{52} +4.24621i q^{53} +(2.25371 - 6.99434i) q^{54} -4.27156i q^{55} +(0.673500 - 2.56155i) q^{56} +(7.12311 - 2.00000i) q^{57} +(-6.56155 + 3.07221i) q^{58} +7.19612 q^{59} +(1.41656 - 3.16123i) q^{60} -5.12311 q^{61} +(3.07221 - 1.43845i) q^{62} +(1.46228 + 2.39871i) q^{63} +(6.96543 + 3.93481i) q^{64} -3.12311i q^{65} +(-7.92375 + 6.83311i) q^{66} -5.20798i q^{67} +(-3.07221 - 2.56155i) q^{68} +(3.56155 + 12.6847i) q^{69} +(0.561553 + 1.19935i) q^{70} -6.67026 q^{71} +(-8.13012 + 2.42923i) q^{72} -8.24621 q^{73} +(1.87285 + 4.00000i) q^{74} +(0.468213 + 1.66757i) q^{75} +(-6.56155 - 5.47091i) q^{76} -4.00000i q^{77} +(-5.79337 + 4.99596i) q^{78} -9.06897i q^{79} +(-3.93481 + 0.719224i) q^{80} +(4.12311 - 8.00000i) q^{81} +(9.12311 - 4.27156i) q^{82} +4.68213 q^{83} +(1.32650 - 2.96026i) q^{84} +2.00000 q^{85} +(-1.87285 + 0.876894i) q^{86} +(-8.54312 + 2.39871i) q^{87} +(11.6847 + 3.07221i) q^{88} -6.24621i q^{89} +(2.34435 - 3.53610i) q^{90} -2.92456i q^{91} +(9.74247 - 11.6847i) q^{92} +(4.00000 - 1.12311i) q^{93} +(-0.561553 - 1.19935i) q^{94} +4.27156 q^{95} +(7.62858 + 6.14856i) q^{96} -6.00000 q^{97} +(-3.67188 - 7.84233i) q^{98} +(-10.9418 + 6.67026i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8q - 2q^{4} - 6q^{6} - 4q^{9} + O(q^{10}) \)	\( 8q - 2q^{4} - 6q^{6} - 4q^{9} - 2q^{10} + 4q^{12} - 8q^{13} - 14q^{16} + 16q^{18} + 4q^{21} - 4q^{22} - 2q^{24} - 8q^{25} + 28q^{28} + 8q^{30} - 16q^{33} + 4q^{34} + 18q^{36} + 8q^{37} + 14q^{40} - 12q^{42} - 4q^{45} + 20q^{46} - 36q^{48} + 16q^{49} - 32q^{52} - 10q^{54} + 24q^{57} - 36q^{58} - 14q^{60} - 8q^{61} - 2q^{64} - 40q^{66} + 12q^{69} - 12q^{70} + 24q^{72} - 36q^{76} + 40q^{78} + 40q^{82} + 16q^{84} + 16q^{85} + 44q^{88} + 18q^{90} + 32q^{93} + 12q^{94} + 42q^{96} - 48q^{97} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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