LMFDB - Embedded newform 930.2.o.e.161.18

Newspace parameters

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.o (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			161.18
Character	$\chi$	$=$	930.161
Dual form			930.2.o.e.491.8

$q$-expansion

$f(q)$	$=$	$q+1.00000i q^{2} +(1.32888 - 1.11089i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.11089 + 1.32888i) q^{6} +(-0.581871 - 1.00783i) q^{7} -1.00000i q^{8} +(0.531863 - 2.95248i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(1.32888 - 1.11089i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.11089 + 1.32888i) q^{6} +(-0.581871 - 1.00783i) q^{7} -1.00000i q^{8} +(0.531863 - 2.95248i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-0.0889568 + 0.154078i) q^{11} +(-1.32888 + 1.11089i) q^{12} +(-4.88952 - 2.82297i) q^{13} +(1.00783 - 0.581871i) q^{14} +(-1.70629 + 0.297614i) q^{15} +1.00000 q^{16} +(1.93896 + 3.35837i) q^{17} +(2.95248 + 0.531863i) q^{18} +(-2.57689 - 4.46331i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-1.89282 - 0.692897i) q^{21} +(-0.154078 - 0.0889568i) q^{22} -5.70722 q^{23} +(-1.11089 - 1.32888i) q^{24} +(0.500000 + 0.866025i) q^{25} +(2.82297 - 4.88952i) q^{26} +(-2.57308 - 4.51434i) q^{27} +(0.581871 + 1.00783i) q^{28} -5.56575 q^{29} +(-0.297614 - 1.70629i) q^{30} +(5.12730 - 2.17043i) q^{31} +1.00000i q^{32} +(0.0529495 + 0.303572i) q^{33} +(-3.35837 + 1.93896i) q^{34} +1.16374i q^{35} +(-0.531863 + 2.95248i) q^{36} +(0.782503 - 0.451779i) q^{37} +(4.46331 - 2.57689i) q^{38} +(-9.63360 + 1.68031i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-2.48692 - 1.43582i) q^{41} +(0.692897 - 1.89282i) q^{42} +(0.735867 - 0.424853i) q^{43} +(0.0889568 - 0.154078i) q^{44} +(-1.93685 + 2.29099i) q^{45} -5.70722i q^{46} +4.11079i q^{47} +(1.32888 - 1.11089i) q^{48} +(2.82285 - 4.88932i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(6.30741 + 2.30892i) q^{51} +(4.88952 + 2.82297i) q^{52} +(6.25104 - 10.8271i) q^{53} +(4.51434 - 2.57308i) q^{54} +(0.154078 - 0.0889568i) q^{55} +(-1.00783 + 0.581871i) q^{56} +(-8.38261 - 3.06858i) q^{57} -5.56575i q^{58} +(4.27376 - 2.46746i) q^{59} +(1.70629 - 0.297614i) q^{60} -0.00227491i q^{61} +(2.17043 + 5.12730i) q^{62} +(-3.28507 + 1.18193i) q^{63} -1.00000 q^{64} +(2.82297 + 4.88952i) q^{65} +(-0.303572 + 0.0529495i) q^{66} +(-3.20296 + 5.54769i) q^{67} +(-1.93896 - 3.35837i) q^{68} +(-7.58423 + 6.34007i) q^{69} -1.16374 q^{70} +(-10.9712 - 6.33424i) q^{71} +(-2.95248 - 0.531863i) q^{72} +(9.32062 + 5.38127i) q^{73} +(0.451779 + 0.782503i) q^{74} +(1.62650 + 0.595404i) q^{75} +(2.57689 + 4.46331i) q^{76} +0.207046 q^{77} +(-1.68031 - 9.63360i) q^{78} +(-2.52627 + 1.45854i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(-8.43424 - 3.14063i) q^{81} +(1.43582 - 2.48692i) q^{82} +(7.95846 - 13.7845i) q^{83} +(1.89282 + 0.692897i) q^{84} -3.87791i q^{85} +(0.424853 + 0.735867i) q^{86} +(-7.39624 + 6.18292i) q^{87} +(0.154078 + 0.0889568i) q^{88} +5.20790 q^{89} +(-2.29099 - 1.93685i) q^{90} +6.57041i q^{91} +5.70722 q^{92} +(4.40248 - 8.58010i) q^{93} -4.11079 q^{94} +5.15378i q^{95} +(1.11089 + 1.32888i) q^{96} -13.7078 q^{97} +(4.88932 + 2.82285i) q^{98} +(0.407598 + 0.344591i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40q + 6q^{3} - 40q^{4} - 12q^{7} - 2q^{9} + O(q^{10}) $	$ 40q + 6q^{3} - 40q^{4} - 12q^{7} - 2q^{9} + 20q^{10} - 6q^{12} - 12q^{13} + 40q^{16} - 12q^{18} - 12q^{19} + 12q^{21} - 24q^{22} + 20q^{25} + 12q^{28} + 8q^{31} + 52q^{33} + 24q^{34} + 2q^{36} + 60q^{37} - 8q^{39} - 20q^{40} + 12q^{42} + 24q^{43} - 12q^{45} + 6q^{48} - 4q^{49} + 14q^{51} + 12q^{52} + 24q^{55} - 12q^{57} - 40q^{64} + 8q^{66} + 64q^{67} - 26q^{69} - 24q^{70} + 12q^{72} + 6q^{75} + 12q^{76} - 68q^{78} - 48q^{79} + 2q^{81} + 4q^{82} - 12q^{84} + 36q^{87} + 24q^{88} + 2q^{90} - 22q^{93} - 40q^{94} + 8q^{97} - 90q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	1.32888	−	1.11089i	0.767231	−	0.641370i
$3$	1.32888	−	1.11089i	0.767231	−	0.641370i
$4$	−1.00000			−0.500000
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$5$	−0.866025	−	0.500000i	−0.387298	−	0.223607i
$6$	1.11089	+	1.32888i	0.453517	+	0.542514i
$7$	−0.581871	−	1.00783i	−0.219927	−	0.380924i	0.734859	−	0.678220i	$-0.237248\pi$
$7$	−0.581871	−	1.00783i	−0.219927	−	0.380924i	−0.954785	+	0.297296i	$0.903915\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.531863	−	2.95248i	0.177288	−	0.984159i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−0.0889568	+	0.154078i	−0.0268215	+	0.0464562i	−0.879125	−	0.476592i	$-0.841872\pi$
$11$	−0.0889568	+	0.154078i	−0.0268215	+	0.0464562i	0.852303	+	0.523048i	$0.175205\pi$
$12$	−1.32888	+	1.11089i	−0.383616	+	0.320685i
$13$	−4.88952	−	2.82297i	−1.35611	−	0.782950i	−0.367012	−	0.930216i	$-0.619619\pi$
$13$	−4.88952	−	2.82297i	−1.35611	−	0.782950i	−0.989097	+	0.147266i	$0.952953\pi$
$14$	1.00783	−	0.581871i	0.269354	−	0.155512i
$15$	−1.70629	+	0.297614i	−0.440562	+	0.0768436i
$16$	1.00000			0.250000
$17$	1.93896	+	3.35837i	0.470266	+	0.814524i	0.999422	−	0.0340003i	$-0.0108247\pi$
$17$	1.93896	+	3.35837i	0.470266	+	0.814524i	−0.529156	+	0.848525i	$0.677491\pi$
$18$	2.95248	+	0.531863i	0.695906	+	0.125361i
$19$	−2.57689	−	4.46331i	−0.591179	−	1.02395i	−0.994074	−	0.108706i	$-0.965329\pi$
$19$	−2.57689	−	4.46331i	−0.591179	−	1.02395i	0.402895	−	0.915246i	$-0.368004\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$	−1.89282	−	0.692897i	−0.413048	−	0.151202i
$22$	−0.154078	−	0.0889568i	−0.0328495	−	0.0189656i
$23$	−5.70722			−1.19004			−0.595019	−	0.803712i	$-0.702855\pi$
$23$	−5.70722			−1.19004			−0.595019	+	0.803712i	$0.702855\pi$
$24$	−1.11089	−	1.32888i	−0.226759	−	0.271257i
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	2.82297	−	4.88952i	0.553629	−	0.958914i
$27$	−2.57308	−	4.51434i	−0.495190	−	0.868785i
$28$	0.581871	+	1.00783i	0.109963	+	0.190462i
$29$	−5.56575			−1.03353			−0.516767	−	0.856126i	$-0.672865\pi$
$29$	−5.56575			−1.03353			−0.516767	+	0.856126i	$0.672865\pi$
$30$	−0.297614	−	1.70629i	−0.0543366	−	0.311525i
$31$	5.12730	−	2.17043i	0.920891	−	0.389821i
$31$	5.12730	−	2.17043i	0.920891	−	0.389821i
$32$			1.00000i			0.176777i
$33$	0.0529495	+	0.303572i	0.00921733	+	0.0528451i
$34$	−3.35837	+	1.93896i	−0.575956	+	0.332528i
$35$			1.16374i			0.196708i
$36$	−0.531863	+	2.95248i	−0.0886439	+	0.492080i
$37$	0.782503	−	0.451779i	0.128643	−	0.0742719i	−0.434298	−	0.900769i	$-0.643003\pi$
$37$	0.782503	−	0.451779i	0.128643	−	0.0742719i	0.562940	+	0.826497i	$0.309670\pi$
$38$	4.46331	−	2.57689i	0.724044	−	0.418027i
$39$	−9.63360	+	1.68031i	−1.54261	+	0.269065i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−2.48692	−	1.43582i	−0.388391	−	0.224238i	0.293072	−	0.956091i	$-0.405323\pi$
$41$	−2.48692	−	1.43582i	−0.388391	−	0.224238i	−0.681463	+	0.731853i	$0.738656\pi$
$42$	0.692897	−	1.89282i	0.106916	−	0.292069i
$43$	0.735867	−	0.424853i	0.112219	−	0.0647895i	−0.442840	−	0.896601i	$-0.646029\pi$
$43$	0.735867	−	0.424853i	0.112219	−	0.0647895i	0.555059	+	0.831811i	$0.312696\pi$
$44$	0.0889568	−	0.154078i	0.0134107	−	0.0232281i
$45$	−1.93685	+	2.29099i	−0.288728	+	0.341520i
$46$		−	5.70722i		−	0.841484i
$47$			4.11079i			0.599620i	0.953999	+	0.299810i	$0.0969233\pi$
$47$			4.11079i			0.599620i	−0.953999	+	0.299810i	$0.903077\pi$
$48$	1.32888	−	1.11089i	0.191808	−	0.160343i
$49$	2.82285	−	4.88932i	0.403265	−	0.698475i
$50$	−0.866025	+	0.500000i	−0.122474	+	0.0707107i
$51$	6.30741	+	2.30892i	0.883214	+	0.323314i
$52$	4.88952	+	2.82297i	0.678055	+	0.391475i
$53$	6.25104	−	10.8271i	0.858646	−	1.48722i	−0.0145750	−	0.999894i	$-0.504640\pi$
$53$	6.25104	−	10.8271i	0.858646	−	1.48722i	0.873221	−	0.487325i	$-0.162027\pi$
$54$	4.51434	−	2.57308i	0.614324	−	0.350152i
$55$	0.154078	−	0.0889568i	0.0207758	−	0.0119949i
$56$	−1.00783	+	0.581871i	−0.134677	+	0.0777558i
$57$	−8.38261	−	3.06858i	−1.11030	−	0.406443i
$58$		−	5.56575i		−	0.730819i
$59$	4.27376	−	2.46746i	0.556396	−	0.321235i	−0.195302	−	0.980743i	$-0.562569\pi$
$59$	4.27376	−	2.46746i	0.556396	−	0.321235i	0.751698	+	0.659508i	$0.229235\pi$
$60$	1.70629	−	0.297614i	0.220281	−	0.0384218i
$61$		−	0.00227491i		−	0.000291272i	−1.00000		0.000145636i	$-0.999954\pi$
$61$		−	0.00227491i		−	0.000291272i	1.00000		0.000145636i	$-4.63574e-5\pi$
$62$	2.17043	+	5.12730i	0.275645	+	0.651168i
$63$	−3.28507	+	1.18193i	−0.413880	+	0.148910i
$64$	−1.00000			−0.125000
$65$	2.82297	+	4.88952i	0.350146	+	0.606471i
$66$	−0.303572	+	0.0529495i	−0.0373671	+	0.00651764i
$67$	−3.20296	+	5.54769i	−0.391304	+	0.677758i	−0.992622	−	0.121252i	$-0.961309\pi$
$67$	−3.20296	+	5.54769i	−0.391304	+	0.677758i	0.601318	+	0.799010i	$0.294642\pi$
$68$	−1.93896	−	3.35837i	−0.235133	−	0.407262i
$69$	−7.58423	+	6.34007i	−0.913034	+	0.763255i
$70$	−1.16374			−0.139094
$71$	−10.9712	−	6.33424i	−1.30204	−	0.751736i	−0.321290	−	0.946981i	$-0.604116\pi$
$71$	−10.9712	−	6.33424i	−1.30204	−	0.751736i	−0.980754	+	0.195245i	$0.937450\pi$
$72$	−2.95248	−	0.531863i	−0.347953	−	0.0626807i
$73$	9.32062	+	5.38127i	1.09090	+	0.629829i	0.933815	−	0.357756i	$-0.116458\pi$
$73$	9.32062	+	5.38127i	1.09090	+	0.629829i	0.157082	+	0.987586i	$0.449791\pi$
$74$	0.451779	+	0.782503i	0.0525182	+	0.0909642i
$75$	1.62650	+	0.595404i	0.187812	+	0.0687513i
$76$	2.57689	+	4.46331i	0.295590	+	0.511976i
$77$	0.207046			0.0235950
$78$	−1.68031	−	9.63360i	−0.190257	−	1.09079i
$79$	−2.52627	+	1.45854i	−0.284228	+	0.164099i	−0.635336	−	0.772236i	$-0.719138\pi$
$79$	−2.52627	+	1.45854i	−0.284228	+	0.164099i	0.351108	+	0.936335i	$0.385805\pi$
$80$	−0.866025	−	0.500000i	−0.0968246	−	0.0559017i
$81$	−8.43424	−	3.14063i	−0.937138	−	0.348959i
$82$	1.43582	−	2.48692i	0.158560	−	0.274634i
$83$	7.95846	−	13.7845i	0.873555	−	1.51304i	0.0152607	−	0.999884i	$-0.495142\pi$
$83$	7.95846	−	13.7845i	0.873555	−	1.51304i	0.858294	−	0.513158i	$-0.171524\pi$
$84$	1.89282	+	0.692897i	0.206524	+	0.0756012i
$85$		−	3.87791i		−	0.420618i
$86$	0.424853	+	0.735867i	0.0458131	+	0.0793506i
$87$	−7.39624	+	6.18292i	−0.792960	+	0.662878i
$88$	0.154078	+	0.0889568i	0.0164247	+	0.00948282i
$89$	5.20790			0.552036			0.276018	−	0.961152i	$-0.410985\pi$
$89$	5.20790			0.552036			0.276018	+	0.961152i	$0.410985\pi$
$90$	−2.29099	−	1.93685i	−0.241491	−	0.204161i
$91$			6.57041i			0.688766i
$92$	5.70722			0.595019
$93$	4.40248	−	8.58010i	0.456516	−	0.889715i
$94$	−4.11079			−0.423995
$95$			5.15378i			0.528767i
$96$	1.11089	+	1.32888i	0.113379	+	0.135629i
$97$	−13.7078			−1.39181			−0.695907	−	0.718132i	$-0.744997\pi$
$97$	−13.7078			−1.39181			−0.695907	+	0.718132i	$0.744997\pi$
$98$	4.88932	+	2.82285i	0.493896	+	0.285151i
$99$	0.407598	+	0.344591i	0.0409651	+	0.0346327i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$			2.34879i			0.233713i	0.993149	+	0.116856i	$0.0372817\pi$
$101$			2.34879i			0.233713i	−0.993149	+	0.116856i	$0.962718\pi$
$102$	−2.30892	+	6.30741i	−0.228617	+	0.624527i
$103$	−8.49332	+	14.7109i	−0.836872	+	1.44950i	0.0556251	+	0.998452i	$0.482285\pi$
$103$	−8.49332	+	14.7109i	−0.836872	+	1.44950i	−0.892497	+	0.451053i	$0.851048\pi$
$104$	−2.82297	+	4.88952i	−0.276815	+	0.479457i
$105$	1.29279	+	1.54648i	0.126163	+	0.150921i
$106$	10.8271	+	6.25104i	1.05162	+	0.607154i
$107$	4.00394	−	2.31167i	0.387075	−	0.223478i	−0.293817	−	0.955862i	$-0.594926\pi$
$107$	4.00394	−	2.31167i	0.387075	−	0.223478i	0.680892	+	0.732384i	$0.261592\pi$
$108$	2.57308	+	4.51434i	0.247595	+	0.434392i
$109$	18.3302			1.75571			0.877856	−	0.478925i	$-0.158973\pi$
$109$	18.3302			1.75571			0.877856	+	0.478925i	$0.158973\pi$
$110$	0.0889568	+	0.154078i	0.00848170	+	0.0146907i
$111$	0.537981	−	1.46963i	0.0510629	−	0.139491i
$112$	−0.581871	−	1.00783i	−0.0549817	−	0.0952310i
$113$	−0.376805	−	0.217548i	−0.0354468	−	0.0204652i	0.482172	−	0.876077i	$-0.339848\pi$
$113$	−0.376805	−	0.217548i	−0.0354468	−	0.0204652i	−0.517619	+	0.855611i	$0.673181\pi$
$114$	3.06858	−	8.38261i	0.287399	−	0.785104i
$115$	4.94260	+	2.85361i	0.460900	+	0.266101i
$116$	5.56575			0.516767
$117$	−10.9353	+	12.9348i	−1.01097	+	1.19582i
$118$	2.46746	+	4.27376i	0.227148	+	0.393431i
$119$	2.25644	−	3.90828i	0.206848	−	0.358271i
$120$	0.297614	+	1.70629i	0.0271683	+	0.155762i
$121$	5.48417	+	9.49887i	0.498561	+	0.863533i
$122$	0.00227491			0.000205960
$123$	−4.89986	+	0.854642i	−0.441806	+	0.0770604i
$124$	−5.12730	+	2.17043i	−0.460445	+	0.194911i
$125$		−	1.00000i		−	0.0894427i
$126$	−1.18193	−	3.28507i	−0.105295	−	0.292657i
$127$	10.9132	−	6.30073i	0.968388	−	0.559099i	0.0696438	−	0.997572i	$-0.477814\pi$
$127$	10.9132	−	6.30073i	0.968388	−	0.559099i	0.898745	+	0.438473i	$0.144480\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	0.505918	−	1.38204i	0.0445436	−	0.121682i
$130$	−4.88952	+	2.82297i	−0.428839	+	0.247591i
$131$	18.3335	−	10.5849i	1.60181	−	0.924803i	0.610679	−	0.791878i	$-0.290896\pi$
$131$	18.3335	−	10.5849i	1.60181	−	0.924803i	0.991126	−	0.132925i	$-0.0424369\pi$
$132$	−0.0529495	−	0.303572i	−0.00460867	−	0.0264226i
$133$	−2.99884	+	5.19414i	−0.260032	+	0.450389i
$134$	−5.54769	−	3.20296i	−0.479247	−	0.276693i
$135$	−0.0288151	+	5.19607i	−0.00248001	+	0.447207i
$136$	3.35837	−	1.93896i	0.287978	−	0.166264i
$137$	−6.42120	+	11.1218i	−0.548600	+	0.950203i	0.449771	+	0.893144i	$0.351506\pi$
$137$	−6.42120	+	11.1218i	−0.548600	+	0.950203i	−0.998371	+	0.0570592i	$0.981828\pi$
$138$	−6.34007	−	7.58423i	−0.539703	−	0.645613i
$139$			0.913499i			0.0774820i	0.999249	+	0.0387410i	$0.0123347\pi$
$139$			0.913499i			0.0774820i	−0.999249	+	0.0387410i	$0.987665\pi$
$140$		−	1.16374i		−	0.0983542i
$141$	4.56662	+	5.46276i	0.384579	+	0.460047i
$142$	6.33424	−	10.9712i	0.531557	−	0.920685i
$143$	0.869912	−	0.502244i	0.0727457	−	0.0419998i
$144$	0.531863	−	2.95248i	0.0443220	−	0.246040i
$145$	4.82008	+	2.78288i	0.400286	+	0.231105i
$146$	−5.38127	+	9.32062i	−0.445357	+	0.771380i
$147$	−1.68024	−	9.63321i	−0.138584	−	0.794534i
$148$	−0.782503	+	0.451779i	−0.0643214	+	0.0371360i
$149$	−3.97105	+	2.29269i	−0.325321	+	0.187824i	−0.653762	−	0.756700i	$-0.726810\pi$
$149$	−3.97105	+	2.29269i	−0.325321	+	0.187824i	0.328441	+	0.944525i	$0.393477\pi$
$150$	−0.595404	+	1.62650i	−0.0486145	+	0.132803i
$151$		−	18.0258i		−	1.46692i	−0.679734	−	0.733458i	$-0.737905\pi$
$151$		−	18.0258i		−	1.46692i	0.679734	−	0.733458i	$-0.262095\pi$
$152$	−4.46331	+	2.57689i	−0.362022	+	0.209013i
$153$	10.9468	−	3.93853i	0.884994	−	0.318411i
$154$			0.207046i			0.0166842i
$155$	−5.52559	−	0.684001i	−0.443826	−	0.0549403i
$156$	9.63360	−	1.68031i	0.771305	−	0.134532i
$157$	−9.03549			−0.721111			−0.360555	−	0.932738i	$-0.617413\pi$
$157$	−9.03549			−0.721111			−0.360555	+	0.932738i	$0.617413\pi$
$158$	−1.45854	−	2.52627i	−0.116036	−	0.200980i
$159$	−3.72079	−	21.3322i	−0.295078	−	1.69175i
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	3.32087	+	5.75191i	0.261721	+	0.453314i
$162$	3.14063	−	8.43424i	0.246751	−	0.662657i
$163$	17.0876			1.33840			0.669201	−	0.743082i	$-0.266637\pi$
$163$	17.0876			1.33840			0.669201	+	0.743082i	$0.266637\pi$
$164$	2.48692	+	1.43582i	0.194196	+	0.112119i
$165$	0.105930	−	0.289376i	0.00824667	−	0.0225279i
$166$	13.7845	+	7.95846i	1.06988	+	0.617697i
$167$	4.44098	+	7.69200i	0.343653	+	0.595225i	0.985108	−	0.171936i	$-0.0550021\pi$
$167$	4.44098	+	7.69200i	0.343653	+	0.595225i	−0.641455	+	0.767161i	$0.721669\pi$
$168$	−0.692897	+	1.89282i	−0.0534581	+	0.146035i
$169$	9.43828	+	16.3476i	0.726022	+	1.25751i
$170$	3.87791			0.297422
$171$	−14.5484	+	5.23434i	−1.11254	+	0.400280i
$172$	−0.735867	+	0.424853i	−0.0561093	+	0.0323947i
$173$	2.18205	+	1.25981i	0.165898	+	0.0957813i	0.580650	−	0.814153i	$-0.302798\pi$
$173$	2.18205	+	1.25981i	0.165898	+	0.0957813i	−0.414752	+	0.909934i	$0.636132\pi$
$174$	−6.18292	−	7.39624i	−0.468726	−	0.560707i
$175$	0.581871	−	1.00783i	0.0439853	−	0.0761848i
$176$	−0.0889568	+	0.154078i	−0.00670537	+	0.0116140i
$177$	2.93827	−	8.02662i	0.220854	−	0.603318i
$178$			5.20790i			0.390348i
$179$	−7.26572	−	12.5846i	−0.543065	−	0.940616i	−0.998726	−	0.0504628i	$-0.983930\pi$
$179$	−7.26572	−	12.5846i	−0.543065	−	0.940616i	0.455661	−	0.890153i	$-0.349403\pi$
$180$	1.93685	−	2.29099i	0.144364	−	0.170760i
$181$	−3.27223	−	1.88922i	−0.243223	−	0.140425i	0.373434	−	0.927657i	$-0.378180\pi$
$181$	−3.27223	−	1.88922i	−0.243223	−	0.140425i	−0.616657	+	0.787232i	$0.711513\pi$
$182$	−6.57041			−0.487031
$183$	−0.00252716	−	0.00302309i	−0.000186813	−	0.000223473i
$184$			5.70722i			0.420742i
$185$	−0.903557			−0.0664308
$186$	8.58010	+	4.40248i	0.629124	+	0.322806i
$187$	−0.689933			−0.0504529
$188$		−	4.11079i		−	0.299810i
$189$	−3.05249	+	5.21999i	−0.222036	+	0.379699i
$190$	−5.15378			−0.373895
$191$	−5.58732	−	3.22584i	−0.404284	−	0.233414i	0.284047	−	0.958810i	$-0.408323\pi$
$191$	−5.58732	−	3.22584i	−0.404284	−	0.233414i	−0.688331	+	0.725397i	$0.741656\pi$
$192$	−1.32888	+	1.11089i	−0.0959039	+	0.0801713i
$193$	−1.05136	−	1.82101i	−0.0756786	−	0.131079i	0.825703	−	0.564106i	$-0.190779\pi$
$193$	−1.05136	−	1.82101i	−0.0756786	−	0.131079i	−0.901381	+	0.433027i	$0.857446\pi$
$194$		−	13.7078i		−	0.984161i
$195$	9.18310	+	3.36161i	0.657615	+	0.240730i
$196$	−2.82285	+	4.88932i	−0.201632	+	0.349237i
$197$	−9.43359	+	16.3395i	−0.672115	+	1.16414i	0.305188	+	0.952292i	$0.401281\pi$
$197$	−9.43359	+	16.3395i	−0.672115	+	1.16414i	−0.977303	+	0.211846i	$0.932053\pi$
$198$	−0.344591	+	0.407598i	−0.0244890	+	0.0289667i
$199$	16.6694	+	9.62408i	1.18166	+	0.682233i	0.956398	−	0.292065i	$-0.0943425\pi$
$199$	16.6694	+	9.62408i	1.18166	+	0.682233i	0.225263	+	0.974298i	$0.427676\pi$
$200$	0.866025	−	0.500000i	0.0612372	−	0.0353553i
$201$	1.90649	+	10.9304i	0.134473	+	0.770967i
$202$	−2.34879			−0.165260
$203$	3.23855	+	5.60933i	0.227302	+	0.393698i
$204$	−6.30741	−	2.30892i	−0.441607	−	0.161657i
$205$	1.43582	+	2.48692i	0.100282	+	0.173694i
$206$	−14.7109	−	8.49332i	−1.02495	−	0.591758i
$207$	−3.03546	+	16.8504i	−0.210979	+	1.17119i
$208$	−4.88952	−	2.82297i	−0.339027	−	0.195738i
$209$	0.916927			0.0634252
$210$	−1.54648	+	1.29279i	−0.106717	+	0.0892107i
$211$	5.53532	+	9.58746i	0.381067	+	0.660028i	0.991215	−	0.132260i	$-0.0422233\pi$
$211$	5.53532	+	9.58746i	0.381067	+	0.660028i	−0.610148	+	0.792288i	$0.708890\pi$
$212$	−6.25104	+	10.8271i	−0.429323	+	0.743609i
$213$	−21.6161	+	3.77031i	−1.48111	+	0.258338i
$214$	2.31167	+	4.00394i	0.158023	+	0.273703i
$215$	−0.849706			−0.0579495
$216$	−4.51434	+	2.57308i	−0.307162	+	0.175076i
$217$	−5.17086	−	3.90454i	−0.351021	−	0.265057i
$218$			18.3302i			1.24148i
$219$	18.3640	−	3.20308i	1.24092	−	0.216444i
$220$	−0.154078	+	0.0889568i	−0.0103879	+	0.00599746i
$221$		−	21.8944i		−	1.47278i
$222$	1.46963	+	0.537981i	0.0986353	+	0.0361069i
$223$	−3.79542	+	2.19128i	−0.254160	+	0.146739i	−0.621668	−	0.783281i	$-0.713545\pi$
$223$	−3.79542	+	2.19128i	−0.254160	+	0.146739i	0.367508	+	0.930020i	$0.380211\pi$
$224$	1.00783	−	0.581871i	0.0673385	−	0.0388779i
$225$	2.82285	−	1.01563i	0.188190	−	0.0677088i
$226$	0.217548	−	0.376805i	0.0144711	−	0.0250647i
$227$	14.2337	+	8.21783i	0.944724	+	0.545436i	0.891438	−	0.453143i	$-0.149697\pi$
$227$	14.2337	+	8.21783i	0.944724	+	0.545436i	0.0532857	+	0.998579i	$0.483031\pi$
$228$	8.38261	+	3.06858i	0.555152	+	0.203222i
$229$	0.621599	−	0.358880i	0.0410764	−	0.0237155i	−0.479321	−	0.877640i	$-0.659117\pi$
$229$	0.621599	−	0.358880i	0.0410764	−	0.0237155i	0.520398	+	0.853924i	$0.325784\pi$
$230$	−2.85361	+	4.94260i	−0.188162	+	0.325905i
$231$	0.275139	−	0.230004i	0.0181028	−	0.0151332i
$232$			5.56575i			0.365410i
$233$			15.7057i			1.02891i	0.857517	+	0.514456i	$0.172006\pi$
$233$			15.7057i			1.02891i	−0.857517	+	0.514456i	$0.827994\pi$
$234$	−12.9348	−	10.9353i	−0.845572	−	0.714863i
$235$	2.05539	−	3.56005i	0.134079	−	0.232232i
$236$	−4.27376	+	2.46746i	−0.278198	+	0.160618i
$237$	−1.73685	+	4.74464i	−0.112820	+	0.308197i
$238$	3.90828	+	2.25644i	0.253336	+	0.146264i
$239$	2.90971	−	5.03976i	0.188213	−	0.325995i	−0.756441	−	0.654062i	$-0.773064\pi$
$239$	2.90971	−	5.03976i	0.188213	−	0.325995i	0.944655	+	0.328067i	$0.106397\pi$
$240$	−1.70629	+	0.297614i	−0.110141	+	0.0192109i
$241$	5.77410	−	3.33368i	0.371942	−	0.214741i	−0.302364	−	0.953192i	$-0.597776\pi$
$241$	5.77410	−	3.33368i	0.371942	−	0.214741i	0.674307	+	0.738451i	$0.264443\pi$
$242$	−9.49887	+	5.48417i	−0.610610	+	0.352536i
$243$	−14.6970	+	5.19595i	−0.942814	+	0.333321i
$244$			0.00227491i			0.000145636i
$245$	−4.88932	+	2.82285i	−0.312367	+	0.180345i
$246$	−0.854642	−	4.89986i	−0.0544900	−	0.312404i
$247$			29.0979i			1.85146i
$248$	−2.17043	−	5.12730i	−0.137823	−	0.325584i
$249$	−4.73710	−	27.1589i	−0.300201	−	1.72113i
$250$	1.00000			0.0632456
$251$	−4.15063	−	7.18911i	−0.261986	−	0.453773i	0.704784	−	0.709422i	$-0.251044\pi$
$251$	−4.15063	−	7.18911i	−0.261986	−	0.453773i	−0.966770	+	0.255650i	$0.917711\pi$
$252$	3.28507	−	1.18193i	0.206940	−	0.0744548i
$253$	0.507696	−	0.879355i	0.0319186	−	0.0552846i
$254$	6.30073	+	10.9132i	0.395343	+	0.684754i
$255$	−4.30792	−	5.15329i	−0.269772	−	0.322712i
$256$	1.00000			0.0625000
$257$	−20.8110	−	12.0152i	−1.29815	−	0.749490i	−0.318070	−	0.948067i	$-0.603035\pi$
$257$	−20.8110	−	12.0152i	−1.29815	−	0.749490i	−0.980085	+	0.198577i	$0.936368\pi$
$258$	1.38204	+	0.505918i	0.0860423	+	0.0314971i
$259$	−0.910632	−	0.525754i	−0.0565839	−	0.0326688i
$260$	−2.82297	−	4.88952i	−0.175073	−	0.303235i
$261$	−2.96022	+	16.4328i	−0.183233	+	1.01716i
$262$	10.5849	+	18.3335i	0.653934	+	1.13265i
$263$	−13.3178			−0.821209			−0.410605	−	0.911813i	$-0.634682\pi$
$263$	−13.3178			−0.821209			−0.410605	+	0.911813i	$0.634682\pi$
$264$	0.303572	−	0.0529495i	0.0186836	−	0.00325882i
$265$	−10.8271	+	6.25104i	−0.665104	+	0.383998i
$266$	−5.19414	−	2.99884i	−0.318473	−	0.183870i
$267$	6.92069	−	5.78538i	0.423539	−	0.354060i
$268$	3.20296	−	5.54769i	0.195652	−	0.338879i
$269$	−0.769900	+	1.33351i	−0.0469416	+	0.0813052i	−0.888542	−	0.458796i	$-0.848281\pi$
$269$	−0.769900	+	1.33351i	−0.0469416	+	0.0813052i	0.841600	+	0.540101i	$0.181614\pi$
$270$	−5.19607	−	0.0288151i	−0.316223	−	0.00175363i
$271$		−	8.84626i		−	0.537372i	−0.963228	−	0.268686i	$-0.913411\pi$
$271$		−	8.84626i		−	0.537372i	0.963228	−	0.268686i	$-0.0865894\pi$
$272$	1.93896	+	3.35837i	0.117566	+	0.203631i
$273$	7.29898	+	8.73131i	0.441754	+	0.528443i
$274$	−11.1218	−	6.42120i	−0.671895	−	0.387919i
$275$	−0.177914			−0.0107286
$276$	7.58423	−	6.34007i	0.456517	−	0.381628i
$277$		−	14.9715i		−	0.899552i	−0.893141	−	0.449776i	$-0.851504\pi$
$277$		−	14.9715i		−	0.899552i	0.893141	−	0.449776i	$-0.148496\pi$
$278$	−0.913499			−0.0547880
$279$	−3.68113	−	16.2926i	−0.220383	−	0.975413i
$280$	1.16374			0.0695469
$281$		−	7.32299i		−	0.436853i	−0.975853	−	0.218426i	$-0.929908\pi$
$281$		−	7.32299i		−	0.436853i	0.975853	−	0.218426i	$-0.0700924\pi$
$282$	−5.46276	+	4.56662i	−0.325303	+	0.271938i
$283$	−14.6211			−0.869133			−0.434567	−	0.900640i	$-0.643098\pi$
$283$	−14.6211			−0.869133			−0.434567	+	0.900640i	$0.643098\pi$
$284$	10.9712	+	6.33424i	0.651022	+	0.375868i
$285$	5.72526	+	6.84878i	0.339135	+	0.405686i
$286$	0.502244	+	0.869912i	0.0296983	+	0.0514390i
$287$			3.34186i			0.197263i
$288$	2.95248	+	0.531863i	0.173976	+	0.0313404i
$289$	0.980903	−	1.69897i	0.0577002	−	0.0999397i
$290$	−2.78288	+	4.82008i	−0.163416	+	0.283045i
$291$	−18.2160	+	15.2278i	−1.06784	+	0.892668i
$292$	−9.32062	−	5.38127i	−0.545448	−	0.314915i
$293$	−29.5457	+	17.0582i	−1.72608	+	0.996551i	−0.821545	+	0.570143i	$0.806888\pi$
$293$	−29.5457	+	17.0582i	−1.72608	+	0.996551i	−0.904531	+	0.426408i	$0.859779\pi$
$294$	9.63321	−	1.68024i	0.561820	−	0.0979936i
$295$	−4.93491			−0.287322
$296$	−0.451779	−	0.782503i	−0.0262591	−	0.0454821i
$297$	0.924452	+	0.00512660i	0.0536421	+	0.000297475i
$298$	−2.29269	−	3.97105i	−0.132812	−	0.230037i
$299$	27.9056	+	16.1113i	1.61382	+	0.931740i
$300$	−1.62650	−	0.595404i	−0.0939059	−	0.0343757i
$301$	−0.856359	−	0.494419i	−0.0493597	−	0.0284979i
$302$	18.0258			1.03727
$303$	2.60923	+	3.12126i	0.149897	+	0.179312i
$304$	−2.57689	−	4.46331i	−0.147795	−	0.255988i
$305$	−0.00113745	+	0.00197013i	−6.51304e−5	+	0.000112809i
$306$	3.93853	+	10.9468i	0.225151	+	0.625785i
$307$	8.94582	+	15.4946i	0.510565	+	0.884324i	0.999925	+	0.0122426i	$0.00389705\pi$
$307$	8.94582	+	15.4946i	0.510565	+	0.884324i	−0.489360	+	0.872082i	$0.662770\pi$
$308$	−0.207046			−0.0117975
$309$	5.05546	+	28.9841i	0.287595	+	1.64885i
$310$	0.684001	−	5.52559i	0.0388486	−	0.313832i
$311$		−	14.8875i		−	0.844194i	−0.906551	−	0.422097i	$-0.861294\pi$
$311$		−	14.8875i		−	0.844194i	0.906551	−	0.422097i	$-0.138706\pi$
$312$	1.68031	+	9.63360i	0.0951287	+	0.545395i
$313$	−6.65729	+	3.84359i	−0.376293	+	0.217253i	−0.676204	−	0.736714i	$-0.736376\pi$
$313$	−6.65729	+	3.84359i	−0.376293	+	0.217253i	0.299911	+	0.953967i	$0.403043\pi$
$314$		−	9.03549i		−	0.509902i
$315$	3.43592	+	0.618952i	0.193592	+	0.0348740i
$316$	2.52627	−	1.45854i	0.142114	−	0.0820495i
$317$	−4.78141	+	2.76055i	−0.268551	+	0.155048i	−0.628229	−	0.778029i	$-0.716220\pi$
$317$	−4.78141	+	2.76055i	−0.268551	+	0.155048i	0.359678	+	0.933076i	$0.382886\pi$
$318$	21.3322	−	3.72079i	1.19625	−	0.208652i
$319$	0.495111	−	0.857558i	0.0277209	−	0.0480140i
$320$	0.866025	+	0.500000i	0.0484123	+	0.0279508i
$321$	2.75276	−	7.51986i	0.153644	−	0.419718i
$322$	−5.75191	+	3.32087i	−0.320542	+	0.185065i
$323$	9.99295	−	17.3083i	0.556023	−	0.963060i
$324$	8.43424	+	3.14063i	0.468569	+	0.174479i
$325$		−	5.64593i		−	0.313180i
$326$			17.0876i			0.946392i
$327$	24.3587	−	20.3627i	1.34704	−	1.12606i
$328$	−1.43582	+	2.48692i	−0.0792800	+	0.137317i
$329$	4.14298	−	2.39195i	0.228410	−	0.131872i
$330$	0.289376	+	0.105930i	0.0159296	+	0.00583128i
$331$	−7.77002	−	4.48602i	−0.427079	−	0.246574i	0.271022	−	0.962573i	$-0.412638\pi$
$331$	−7.77002	−	4.48602i	−0.427079	−	0.246574i	−0.698101	+	0.715999i	$0.745972\pi$
$332$	−7.95846	+	13.7845i	−0.436777	+	0.756521i
$333$	−0.917681	−	2.55061i	−0.0502886	−	0.139772i
$334$	−7.69200	+	4.44098i	−0.420888	+	0.243000i
$335$	5.54769	−	3.20296i	0.303102	−	0.174996i
$336$	−1.89282	−	0.692897i	−0.103262	−	0.0378006i
$337$		−	2.44574i		−	0.133228i	−0.997779	−	0.0666141i	$-0.978780\pi$
$337$		−	2.44574i		−	0.133228i	0.997779	−	0.0666141i	$-0.0212196\pi$
$338$	−16.3476	+	9.43828i	−0.889191	+	0.513375i
$339$	−0.742401	+	0.129491i	−0.0403217	+	0.00703297i
$340$			3.87791i			0.210309i
$341$	−0.121693	+	0.983077i	−0.00659005	+	0.0532366i
$342$	−5.23434	−	14.5484i	−0.283041	−	0.786685i
$343$	−14.7163			−0.794608
$344$	−0.424853	−	0.735867i	−0.0229065	−	0.0396753i
$345$	9.73818	−	1.69855i	0.524286	−	0.0914468i
$346$	−1.25981	+	2.18205i	−0.0677276	+	0.117308i
$347$	8.43977	+	14.6181i	0.453071	+	0.784741i	0.998575	−	0.0533666i	$-0.0169952\pi$
$347$	8.43977	+	14.6181i	0.453071	+	0.784741i	−0.545504	+	0.838108i	$0.683662\pi$
$348$	7.39624	−	6.18292i	0.396480	−	0.331439i
$349$	32.6846			1.74957			0.874783	−	0.484515i	$-0.161004\pi$
$349$	32.6846			1.74957			0.874783	+	0.484515i	$0.161004\pi$
$350$	1.00783	+	0.581871i	0.0538708	+	0.0311023i
$351$	−0.162688	+	29.3367i	−0.00868365	+	1.56588i
$352$	−0.154078	−	0.0889568i	−0.00821237	−	0.00474141i
$353$	−5.87229	−	10.1711i	−0.312551	−	0.541353i	0.666363	−	0.745627i	$-0.267850\pi$
$353$	−5.87229	−	10.1711i	−0.312551	−	0.541353i	−0.978914	+	0.204274i	$0.934517\pi$
$354$	8.02662	+	2.93827i	0.426610	+	0.156167i
$355$	6.33424	+	10.9712i	0.336186	+	0.582292i
$356$	−5.20790			−0.276018
$357$	−1.34310	−	7.70030i	−0.0710843	−	0.407543i
$358$	12.5846	−	7.26572i	0.665116	−	0.384005i
$359$	9.22320	+	5.32502i	0.486782	+	0.281044i	0.723238	−	0.690598i	$-0.242653\pi$
$359$	9.22320	+	5.32502i	0.486782	+	0.281044i	−0.236457	+	0.971642i	$0.575986\pi$
$360$	2.29099	+	1.93685i	0.120746	+	0.102081i
$361$	−3.78073	+	6.54841i	−0.198986	+	0.344653i
$362$	1.88922	−	3.27223i	0.0992953	−	0.171984i
$363$	17.8400	+	6.53060i	0.936357	+	0.342767i
$364$		−	6.57041i		−	0.344383i
$365$	−5.38127	−	9.32062i	−0.281668	−	0.487864i
$366$	0.00302309	−	0.00252716i	0.000158019	−	0.000132097i
$367$	25.0136	+	14.4416i	1.30570	+	0.753847i	0.981376	−	0.192099i	$-0.0615294\pi$
$367$	25.0136	+	14.4416i	1.30570	+	0.753847i	0.324326	+	0.945946i	$0.394863\pi$
$368$	−5.70722			−0.297510
$369$	−5.56193	+	6.57891i	−0.289543	+	0.342484i
$370$		−	0.903557i		−	0.0469737i
$371$	−14.5492			−0.755356
$372$	−4.40248	+	8.58010i	−0.228258	+	0.444858i
$373$	−15.4070			−0.797744			−0.398872	−	0.917007i	$-0.630598\pi$
$373$	−15.4070			−0.797744			−0.398872	+	0.917007i	$0.630598\pi$
$374$		−	0.689933i		−	0.0356756i
$375$	−1.11089	−	1.32888i	−0.0573659	−	0.0686233i
$376$	4.11079			0.211998
$377$	27.2139	+	15.7119i	1.40159	+	0.809206i
$378$	−5.21999	−	3.05249i	−0.268487	−	0.157003i
$379$	−4.66494	−	8.07991i	−0.239622	−	0.415037i	0.720984	−	0.692952i	$-0.243690\pi$
$379$	−4.66494	−	8.07991i	−0.239622	−	0.415037i	−0.960606	+	0.277915i	$0.910357\pi$
$380$		−	5.15378i		−	0.264383i
$381$	7.50296	−	20.4962i	0.384388	−	1.05005i
$382$	3.22584	−	5.58732i	0.165048	−	0.285872i
$383$	11.7909	−	20.4225i	0.602488	−	1.04354i	−0.389955	−	0.920834i	$-0.627509\pi$
$383$	11.7909	−	20.4225i	0.602488	−	1.04354i	0.992443	−	0.122706i	$-0.0391574\pi$
$384$	−1.11089	−	1.32888i	−0.0566897	−	0.0678143i
$385$	−0.179307	−	0.103523i	−0.00913831	−	0.00527601i
$386$	1.82101	−	1.05136i	0.0926870	−	0.0535129i
$387$	−0.862988	−	2.39859i	−0.0438681	−	0.121927i
$388$	13.7078			0.695907
$389$	−17.1562	−	29.7153i	−0.869852	−	1.50663i	−0.862148	−	0.506657i	$-0.830881\pi$
$389$	−17.1562	−	29.7153i	−0.869852	−	1.50663i	−0.00770372	−	0.999970i	$-0.502452\pi$
$390$	−3.36161	+	9.18310i	−0.170222	+	0.465004i
$391$	−11.0660	−	19.1670i	−0.559634	−	0.969315i
$392$	−4.88932	−	2.82285i	−0.246948	−	0.142576i
$393$	12.6045	−	34.4325i	0.635814	−	1.73689i
$394$	−16.3395	−	9.43359i	−0.823170	−	0.475257i
$395$	2.91709			0.146775
$396$	−0.407598	−	0.344591i	−0.0204826	−	0.0173164i
$397$	−13.0551	−	22.6122i	−0.655218	−	1.13487i	−0.981839	−	0.189716i	$-0.939243\pi$
$397$	−13.0551	−	22.6122i	−0.655218	−	1.13487i	0.326621	−	0.945155i	$-0.394090\pi$
$398$	−9.62408	+	16.6694i	−0.482411	+	0.835561i
$399$	1.78499	+	10.2338i	0.0893613	+	0.512329i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	−1.81201			−0.0904873			−0.0452436	−	0.998976i	$-0.514406\pi$
$401$	−1.81201			−0.0904873			−0.0452436	+	0.998976i	$0.514406\pi$
$402$	−10.9304	+	1.90649i	−0.545156	+	0.0950871i
$403$	−31.1971	−	3.86182i	−1.55404	−	0.192371i
$404$		−	2.34879i		−	0.116856i
$405$	5.73395	+	6.93699i	0.284922	+	0.344702i
$406$	−5.60933	+	3.23855i	−0.278387	+	0.160727i
$407$			0.160755i			0.00796833i
$408$	2.30892	−	6.30741i	0.114309	−	0.312263i
$409$	−21.5022	+	12.4143i	−1.06322	+	0.613849i	−0.926320	−	0.376737i	$-0.877046\pi$
$409$	−21.5022	+	12.4143i	−1.06322	+	0.613849i	−0.136897	+	0.990585i	$0.543713\pi$
$410$	−2.48692	+	1.43582i	−0.122820	+	0.0709102i
$411$	3.82208	+	21.9129i	0.188529	+	1.08088i
$412$	8.49332	−	14.7109i	0.418436	−	0.724752i
$413$	−4.97356	−	2.87148i	−0.244733	−	0.141296i
$414$	−16.8504	−	3.03546i	−0.828154	−	0.149185i
$415$	−13.7845	+	7.95846i	−0.676653	+	0.390666i
$416$	2.82297	−	4.88952i	0.138407	−	0.239729i
$417$	1.01479	+	1.21393i	0.0496946	+	0.0594466i
$418$			0.916927i			0.0448484i
$419$		−	16.9548i		−	0.828295i	−0.910210	−	0.414148i	$-0.864080\pi$
$419$		−	16.9548i		−	0.828295i	0.910210	−	0.414148i	$-0.135920\pi$
$420$	−1.29279	−	1.54648i	−0.0630815	−	0.0754604i
$421$	14.5265	−	25.1607i	0.707980	−	1.22626i	−0.257625	−	0.966245i	$-0.582940\pi$
$421$	14.5265	−	25.1607i	0.707980	−	1.22626i	0.965605	−	0.260013i	$-0.0837267\pi$
$422$	−9.58746	+	5.53532i	−0.466710	+	0.269455i
$423$	12.1370	+	2.18638i	0.590121	+	0.106305i
$424$	−10.8271	−	6.25104i	−0.525811	−	0.303577i
$425$	−1.93896	+	3.35837i	−0.0940532	+	0.162905i
$426$	−3.77031	−	21.6161i	−0.182672	−	1.04730i
$427$	−0.00229272	+	0.00132370i	−0.000110953	+	6.40585e-5i
$428$	−4.00394	+	2.31167i	−0.193538	+	0.111739i
$429$	0.598076	−	1.63380i	0.0288754	−	0.0788805i
$430$		−	0.849706i		−	0.0409765i
$431$	18.8864	−	10.9041i	0.909726	−	0.525231i	0.0293833	−	0.999568i	$-0.490646\pi$
$431$	18.8864	−	10.9041i	0.909726	−	0.525231i	0.880343	+	0.474337i	$0.157312\pi$
$432$	−2.57308	−	4.51434i	−0.123797	−	0.217196i
$433$		−	22.8178i		−	1.09655i	−0.836297	−	0.548277i	$-0.815284\pi$
$433$		−	22.8178i		−	1.09655i	0.836297	−	0.548277i	$-0.184716\pi$
$434$	3.90454	−	5.17086i	0.187424	−	0.248209i
$435$	9.49679	−	1.65645i	0.455336	−	0.0794205i
$436$	−18.3302			−0.877856
$437$	14.7069	+	25.4731i	0.703526	+	1.21854i
$438$	3.20308	+	18.3640i	0.153049	+	0.877466i
$439$	11.9238	−	20.6527i	0.569094	−	0.985699i	−0.427562	−	0.903986i	$-0.640628\pi$
$439$	11.9238	−	20.6527i	0.569094	−	0.985699i	0.996656	−	0.0817131i	$-0.0260391\pi$
$440$	−0.0889568	−	0.154078i	−0.00424085	−	0.00734536i
$441$	−12.9342	−	10.9349i	−0.615916	−	0.520708i
$442$	21.8944			1.04141
$443$	18.1698	+	10.4904i	0.863275	+	0.498412i	0.865108	−	0.501586i	$-0.167250\pi$
$443$	18.1698	+	10.4904i	0.863275	+	0.498412i	−0.00183237	+	0.999998i	$0.500583\pi$
$444$	−0.537981	+	1.46963i	−0.0255315	+	0.0697457i
$445$	−4.51017	−	2.60395i	−0.213803	−	0.123439i
$446$	−2.19128	−	3.79542i	−0.103760	−	0.179718i
$447$	−2.73015	+	7.45810i	−0.129132	+	0.352756i
$448$	0.581871	+	1.00783i	0.0274908	+	0.0476155i
$449$	30.8958			1.45806			0.729032	−	0.684479i	$-0.239970\pi$
$449$	30.8958			1.45806			0.729032	+	0.684479i	$0.239970\pi$
$450$	1.01563	+	2.82285i	0.0478773	+	0.133071i
$451$	0.442456	−	0.255452i	0.0208345	−	0.0120288i
$452$	0.376805	+	0.217548i	0.0177234	+	0.0102326i
$453$	−20.0246	−	23.9542i	−0.940837	−	1.12546i
$454$	−8.21783	+	14.2337i	−0.385682	+	0.668020i
$455$	3.28521	−	5.69014i	0.154013	−	0.266758i
$456$	−3.06858	+	8.38261i	−0.143699	+	0.392552i
$457$		−	10.1581i		−	0.475177i	−0.971366	−	0.237589i	$-0.923643\pi$
$457$		−	10.1581i		−	0.475177i	0.971366	−	0.237589i	$-0.0763570\pi$
$458$	0.358880	+	0.621599i	0.0167694	+	0.0290454i
$459$	10.1717	−	17.3945i	0.474775	−	0.811904i
$460$	−4.94260	−	2.85361i	−0.230450	−	0.133050i
$461$	−19.8197			−0.923095			−0.461547	−	0.887116i	$-0.652706\pi$
$461$	−19.8197			−0.923095			−0.461547	+	0.887116i	$0.652706\pi$
$462$	0.230004	+	0.275139i	0.0107008	+	0.0128006i
$463$		−	10.9325i		−	0.508074i	−0.967194	−	0.254037i	$-0.918241\pi$
$463$		−	10.9325i		−	0.508074i	0.967194	−	0.254037i	$-0.0817586\pi$
$464$	−5.56575			−0.258384
$465$	−8.10271	+	5.22934i	−0.375754	+	0.242505i
$466$	−15.7057			−0.727551
$467$		−	11.3377i		−	0.524644i	−0.964980	−	0.262322i	$-0.915512\pi$
$467$		−	11.3377i		−	0.524644i	0.964980	−	0.262322i	$-0.0844883\pi$
$468$	10.9353	−	12.9348i	0.505485	−	0.597910i
$469$	7.45483			0.344232
$470$	3.56005	+	2.05539i	0.164213	+	0.0948083i
$471$	−12.0071	+	10.0374i	−0.553259	+	0.462499i
$472$	−2.46746	−	4.27376i	−0.113574	−	0.196716i
$473$			0.151174i			0.00695100i
$474$	−4.74464	−	1.73685i	−0.217928	−	0.0797760i
$475$	2.57689	−	4.46331i	0.118236	−	0.204790i
$476$	−2.25644	+	3.90828i	−0.103424	+	0.179136i
$477$	−28.6421	−	24.2146i	−1.31143	−	1.10871i
$478$	5.03976	+	2.90971i	0.230513	+	0.133087i
$479$	35.3823	−	20.4280i	1.61666	−	0.933377i	0.628880	−	0.777502i	$-0.283514\pi$
$479$	35.3823	−	20.4280i	1.61666	−	0.933377i	0.987777	−	0.155875i	$-0.0498198\pi$
$480$	−0.297614	−	1.70629i	−0.0135842	−	0.0778811i
$481$	−5.10142			−0.232605
$482$	3.33368	+	5.77410i	0.151845	+	0.263003i
$483$	10.8028	+	3.95452i	0.491543	+	0.179937i
$484$	−5.48417	−	9.49887i	−0.249281	−	0.431767i
$485$	11.8713	+	6.85389i	0.539047	+	0.311219i
$486$	−5.19595	−	14.6970i	−0.235693	−	0.666670i
$487$	−31.5249	−	18.2009i	−1.42853	−	0.824761i	−0.431524	−	0.902102i	$-0.642024\pi$
$487$	−31.5249	−	18.2009i	−1.42853	−	0.824761i	−0.997005	+	0.0773402i	$0.975357\pi$
$488$	−0.00227491			−0.000102980
$489$	22.7074	−	18.9823i	1.02686	−	0.858411i
$490$	−2.82285	−	4.88932i	−0.127523	−	0.220877i
$491$	16.2180	−	28.0904i	0.731908	−	1.26770i	−0.224159	−	0.974553i	$-0.571963\pi$
$491$	16.2180	−	28.0904i	0.731908	−	1.26770i	0.956067	−	0.293149i	$-0.0947032\pi$
$492$	4.89986	−	0.854642i	0.220903	−	0.0385302i
$493$	−10.7917	−	18.6919i	−0.486036	−	0.841839i
$494$	−29.0979			−1.30918
$495$	−0.180695	−	0.502224i	−0.00812162	−	0.0225733i
$496$	5.12730	−	2.17043i	0.230223	−	0.0974553i
$497$			14.7428i			0.661307i
$498$	27.1589	−	4.73710i	1.21702	−	0.212274i
$499$	36.8738	−	21.2891i	1.65070	−	0.953030i	0.673911	−	0.738812i	$-0.264613\pi$
$499$	36.8738	−	21.2891i	1.65070	−	0.953030i	0.976786	−	0.214218i	$-0.0687203\pi$
$500$			1.00000i			0.0447214i
$501$	14.4465	+	5.28835i	0.645421	+	0.236266i
$502$	7.18911	−	4.15063i	0.320866	−	0.185252i
$503$	32.1602	−	18.5677i	1.43395	−	0.827893i	0.436533	−	0.899688i	$-0.356206\pi$
$503$	32.1602	−	18.5677i	1.43395	−	0.827893i	0.997419	+	0.0717951i	$0.0228728\pi$
$504$	1.18193	+	3.28507i	0.0526475	+	0.146329i
$505$	1.17439	−	2.03411i	0.0522598	−	0.0905166i
$506$	0.879355	+	0.507696i	0.0390921	+	0.0225698i
$507$	30.7027	+	11.2392i	1.36355	+	0.499150i
$508$	−10.9132	+	6.30073i	−0.484194	+	0.279550i
$509$	−7.91070	+	13.7017i	−0.350636	+	0.607319i	−0.986361	−	0.164597i	$-0.947368\pi$
$509$	−7.91070	+	13.7017i	−0.350636	+	0.607319i	0.635725	+	0.771915i	$0.280701\pi$
$510$	5.15329	−	4.30792i	0.228192	−	0.190758i
$511$		−	12.5248i		−	0.554065i
$512$			1.00000i			0.0441942i
$513$	−13.5183	+	23.1174i	−0.596848	+	1.02066i
$514$	12.0152	−	20.8110i	0.529970	−	0.917934i
$515$	14.7109	−	8.49332i	0.648238	−	0.374261i
$516$	−0.505918	+	1.38204i	−0.0222718	+	0.0608411i
$517$	−0.633381	−	0.365682i	−0.0278560	−	0.0160827i
$518$	0.525754	−	0.910632i	0.0231003	−	0.0400109i
$519$	4.29919	−	0.749872i	0.188713	−	0.0329157i
$520$	4.88952	−	2.82297i	0.214420	−	0.123795i
$521$	−23.6227	+	13.6385i	−1.03493	+	0.597515i	−0.918392	−	0.395671i	$-0.870512\pi$
$521$	−23.6227	+	13.6385i	−1.03493	+	0.597515i	−0.116535	+	0.993187i	$0.537179\pi$
$522$	−16.4328	−	2.96022i	−0.719242	−	0.129565i
$523$			18.7630i			0.820447i	0.911985	+	0.410224i	$0.134549\pi$
$523$			18.7630i			0.820447i	−0.911985	+	0.410224i	$0.865451\pi$
$524$	−18.3335	+	10.5849i	−0.800903	+	0.462401i
$525$	−0.346346	−	1.98568i	−0.0151158	−	0.0866623i
$526$		−	13.3178i		−	0.580683i
$527$	17.2307	+	13.0110i	0.750582	+	0.566768i
$528$	0.0529495	+	0.303572i	0.00230433	+	0.0132113i
$529$	9.57238			0.416191
$530$	−6.25104	−	10.8271i	−0.271528	−	0.470300i
$531$	−5.01205	−	13.9305i	−0.217505	−	0.604533i
$532$	2.99884	−	5.19414i	0.130016	−	0.225194i
$533$	8.10656	+	14.0410i	0.351134	+	0.608182i
$534$	5.78538	+	6.92069i	0.250358	+	0.299488i
$535$	−4.62335			−0.199885
$536$	5.54769	+	3.20296i	0.239624	+	0.138347i
$537$	−23.6353	−	8.65207i	−1.01994	−	0.373364i
$538$	−1.33351	−	0.769900i	−0.0574915	−	0.0331927i
$539$	0.502224	+	0.869877i	0.0216323	+	0.0374682i
$540$	0.0288151	−	5.19607i	0.00124000	−	0.223603i
$541$	9.14009	+	15.8311i	0.392963	+	0.680632i	0.992839	−	0.119461i	$-0.0381167\pi$
$541$	9.14009	+	15.8311i	0.392963	+	0.680632i	−0.599876	+	0.800093i	$0.704783\pi$
$542$	8.84626			0.379979
$543$	−6.44712	+	1.12452i	−0.276672	+	0.0482576i
$544$	−3.35837	+	1.93896i	−0.143989	+	0.0831320i
$545$	−15.8744	−	9.16508i	−0.679984	−	0.392589i
$546$	−8.73131	+	7.29898i	−0.373666	+	0.312368i
$547$	4.88556	−	8.46204i	0.208891	−	0.361811i	−0.742474	−	0.669875i	$-0.766348\pi$
$547$	4.88556	−	8.46204i	0.208891	−	0.361811i	0.951366	+	0.308064i	$0.0996811\pi$
$548$	6.42120	−	11.1218i	0.274300	−	0.475102i
$549$	−0.00671661	−	0.00120994i	−0.000286658	−	5.16390e-5i
$550$		−	0.177914i		−	0.00758626i
$551$	14.3423	+	24.8417i	0.611004	+	1.05829i
$552$	6.34007	+	7.58423i	0.269851	+	0.322806i
$553$	2.93993	+	1.69737i	0.125019	+	0.0721795i
$554$	14.9715			0.636080
$555$	−1.20072	+	1.00375i	−0.0509678	+	0.0426068i
$556$		−	0.913499i		−	0.0387410i
$557$	−23.4375			−0.993081			−0.496540	−	0.868014i	$-0.665397\pi$
$557$	−23.4375			−0.993081			−0.496540	+	0.868014i	$0.665397\pi$
$558$	16.2926	−	3.68113i	0.689721	−	0.155835i
$559$	−4.79738			−0.202908
$560$			1.16374i			0.0491771i
$561$	−0.916841	+	0.766437i	−0.0387090	+	0.0323590i
$562$	7.32299			0.308902
$563$	3.55872	+	2.05463i	0.149982	+	0.0865923i	0.573113	−	0.819476i	$-0.305736\pi$
$563$	3.55872	+	2.05463i	0.149982	+	0.0865923i	−0.423131	+	0.906069i	$0.639069\pi$
$564$	−4.56662	−	5.46276i	−0.192289	−	0.230024i
$565$	0.217548	+	0.376805i	0.00915232	+	0.0158523i
$566$		−	14.6211i		−	0.614570i
$567$	1.74242	+	10.3277i	0.0731748	+	0.433724i
$568$	−6.33424	+	10.9712i	−0.265779	+	0.460342i
$569$	−20.3967	+	35.3280i	−0.855072	+	1.48103i	0.0215060	+	0.999769i	$0.493154\pi$
$569$	−20.3967	+	35.3280i	−0.855072	+	1.48103i	−0.876578	+	0.481260i	$0.840179\pi$
$570$	−6.84878	+	5.72526i	−0.286864	+	0.239805i
$571$	−22.6637	−	13.0849i	−0.948445	−	0.547585i	−0.0558476	−	0.998439i	$-0.517786\pi$
$571$	−22.6637	−	13.0849i	−0.948445	−	0.547585i	−0.892598	+	0.450854i	$0.851119\pi$
$572$	−0.869912	+	0.502244i	−0.0363729	+	0.0209999i
$573$	−11.0084	+	1.92011i	−0.459884	+	0.0802137i
$574$	−3.34186			−0.139486
$575$	−2.85361	−	4.94260i	−0.119004	−	0.206121i
$576$	−0.531863	+	2.95248i	−0.0221610	+	0.123020i
$577$	−10.2691	−	17.7866i	−0.427509	−	0.740467i	0.569142	−	0.822239i	$-0.307275\pi$
$577$	−10.2691	−	17.7866i	−0.427509	−	0.740467i	−0.996651	+	0.0817721i	$0.973942\pi$
$578$	1.69897	+	0.980903i	0.0706680	+	0.0408002i
$579$	−3.42007	−	1.25197i	−0.142133	−	0.0520301i
$580$	−4.82008	−	2.78288i	−0.200143	−	0.115553i
$581$	−18.5232			−0.768472
$582$	−15.2278	−	18.2160i	−0.631212	−	0.755079i
$583$	1.11214	+	1.92629i	0.0460603	+	0.0797788i
$584$	5.38127	−	9.32062i	0.222678	−	0.385690i
$585$	15.9376	−	5.73419i	0.658940	−	0.237079i
$586$	−17.0582	−	29.5457i	−0.704668	−	1.22052i
$587$	37.7684			1.55887			0.779433	−	0.626485i	$-0.215507\pi$
$587$	37.7684			1.55887			0.779433	+	0.626485i	$0.215507\pi$
$588$	1.68024	+	9.63321i	0.0692919	+	0.397267i
$589$	−22.8998	−	17.2917i	−0.943570	−	0.712494i
$590$		−	4.93491i		−	0.203167i
$591$	5.61513	+	32.1929i	0.230976	+	1.32424i
$592$	0.782503	−	0.451779i	0.0321607	−	0.0185680i
$593$			37.0997i			1.52350i	0.647870	+	0.761751i	$0.275660\pi$
$593$			37.0997i			1.52350i	−0.647870	+	0.761751i	$0.724340\pi$
$594$	−0.00512660	+	0.924452i	−0.000210347	+	0.0379307i
$595$	−3.90828	+	2.25644i	−0.160224	+	0.0925052i
$596$	3.97105	−	2.29269i	0.162661	−	0.0939121i
$597$	32.8429	−	5.72852i	1.34417	−	0.234453i
$598$	−16.1113	+	27.9056i	−0.658840	+	1.14114i
$599$	−17.6250	−	10.1758i	−0.720139	−	0.415773i	0.0946646	−	0.995509i	$-0.469822\pi$
$599$	−17.6250	−	10.1758i	−0.720139	−	0.415773i	−0.814804	+	0.579737i	$0.803155\pi$
$600$	0.595404	−	1.62650i	0.0243073	−	0.0664015i
$601$	−35.9489	+	20.7551i	−1.46639	+	0.846619i	−0.999293	−	0.0375894i	$-0.988032\pi$
$601$	−35.9489	+	20.7551i	−1.46639	+	0.846619i	−0.467093	+	0.884208i	$0.654699\pi$
$602$	0.494419	−	0.856359i	0.0201510	−	0.0349026i
$603$	14.6759	+	12.4073i	0.597648	+	0.505263i
$604$			18.0258i			0.733458i
$605$		−	10.9683i		−	0.445927i
$606$	−3.12126	+	2.60923i	−0.126793	+	0.105993i
$607$	−9.76384	+	16.9115i	−0.396302	+	0.686415i	−0.993266	−	0.115852i	$-0.963040\pi$
$607$	−9.76384	+	16.9115i	−0.396302	+	0.686415i	0.596964	+	0.802268i	$0.296373\pi$
$608$	4.46331	−	2.57689i	0.181011	−	0.104507i
$609$	10.5350	+	3.85649i	0.426899	+	0.156273i
$610$	−0.00197013	−	0.00113745i	−7.97681e−5	−	4.60541e-5i
$611$	11.6046	−	20.0998i	0.469473	−	0.813150i
$612$	−10.9468	+	3.93853i	−0.442497	+	0.159206i
$613$	−3.94704	+	2.27883i	−0.159420	+	0.0920409i	−0.577587	−	0.816329i	$-0.696006\pi$
$613$	−3.94704	+	2.27883i	−0.159420	+	0.0920409i	0.418168	+	0.908370i	$0.362672\pi$
$614$	−15.4946	+	8.94582i	−0.625312	+	0.361024i
$615$	4.67072	+	1.70979i	0.188342	+	0.0689453i
$616$		−	0.207046i		−	0.00834210i
$617$	17.5553	−	10.1355i	0.706749	−	0.408042i	−0.103107	−	0.994670i	$-0.532878\pi$
$617$	17.5553	−	10.1355i	0.706749	−	0.408042i	0.809856	+	0.586628i	$0.199545\pi$
$618$	−28.9841	+	5.05546i	−1.16591	+	0.203361i
$619$			13.7227i			0.551561i	0.961221	+	0.275781i	$0.0889363\pi$
$619$			13.7227i			0.551561i	−0.961221	+	0.275781i	$0.911064\pi$
$620$	5.52559	+	0.684001i	0.221913	+	0.0274701i
$621$	14.6851	+	25.7643i	0.589295	+	1.03389i
$622$	14.8875			0.596935
$623$	−3.03032	−	5.24868i	−0.121407	−	0.210284i
$624$	−9.63360	+	1.68031i	−0.385653	+	0.0672662i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−3.84359	−	6.65729i	−0.153621	−	0.266079i
$627$	1.21849	−	1.01860i	0.0486618	−	0.0406790i
$628$	9.03549			0.360555
$629$	3.03448	+	1.75196i	0.120993	+	0.0698551i
$630$	−0.618952	+	3.43592i	−0.0246596	+	0.136890i
$631$	9.02379	+	5.20989i	0.359231	+	0.207402i	0.668743	−	0.743493i	$-0.266832\pi$
$631$	9.02379	+	5.20989i	0.359231	+	0.207402i	−0.309512	+	0.950895i	$0.600166\pi$
$632$	1.45854	+	2.52627i	0.0580178	+	0.100490i
$633$	18.0064	+	6.59151i	0.715689	+	0.261989i
$634$	−2.76055	−	4.78141i	−0.109635	−	0.189894i
$635$	−12.6015			−0.500074
$636$	3.72079	+	21.3322i	0.147539	+	0.845875i
$637$	−27.6048	+	15.9376i	−1.09374	+	0.631472i
$638$	0.857558	+	0.495111i	0.0339510	+	0.0196016i
$639$	−24.5369	+	29.0233i	−0.970664	+	1.14815i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	10.4121	−	18.0343i	0.411254	−	0.712313i	−0.583773	−	0.811917i	$-0.698424\pi$
$641$	10.4121	−	18.0343i	0.411254	−	0.712313i	0.995027	+	0.0996039i	$0.0317576\pi$
$642$	7.51986	+	2.75276i	0.296785	+	0.108643i
$643$		−	45.6261i		−	1.79932i	−0.436595	−	0.899658i	$-0.643816\pi$
$643$		−	45.6261i		−	1.79932i	0.436595	−	0.899658i	$-0.356184\pi$
$644$	−3.32087	−	5.75191i	−0.130861	−	0.226657i
$645$	−1.12916	+	0.943927i	−0.0444606	+	0.0371671i
$646$	17.3083	+	9.99295i	0.680986	+	0.393167i
$647$	−29.3824			−1.15514			−0.577570	−	0.816341i	$-0.695999\pi$
$647$	−29.3824			−1.15514			−0.577570	+	0.816341i	$0.695999\pi$
$648$	−3.14063	+	8.43424i	−0.123376	+	0.331328i
$649$			0.877988i			0.0344640i
$650$	5.64593			0.221452
$651$	−11.2090	+	0.555557i	−0.439314	+	0.0217740i
$652$	−17.0876			−0.669201
$653$		−	36.5284i		−	1.42947i	−0.699397	−	0.714734i	$-0.746548\pi$
$653$		−	36.5284i		−	1.42947i	0.699397	−	0.714734i	$-0.253452\pi$
$654$	20.3627	+	24.3587i	0.796246	+	0.952499i
$655$	−21.1697			−0.827169
$656$	−2.48692	−	1.43582i	−0.0970978	−	0.0560595i
$657$	20.8454	−	24.6568i	0.813255	−	0.961955i
$658$	2.39195	+	4.14298i	0.0932479	+	0.161510i
$659$			18.6641i			0.727050i	0.931584	+	0.363525i	$0.118427\pi$
$659$			18.6641i			0.727050i	−0.931584	+	0.363525i	$0.881573\pi$
$660$	−0.105930	+	0.289376i	−0.00412334	+	0.0112639i
$661$	−16.6494	+	28.8377i	−0.647588	+	1.12166i	0.336109	+	0.941823i	$0.390889\pi$
$661$	−16.6494	+	28.8377i	−0.647588	+	1.12166i	−0.983697	+	0.179833i	$0.942444\pi$
$662$	4.48602	−	7.77002i	0.174354	−	0.301990i
$663$	−24.3222	−	29.0951i	−0.944597	−	1.12996i
$664$	−13.7845	−	7.95846i	−0.534941	−	0.308848i
$665$	5.19414	−	2.99884i	0.201420	−	0.116290i
$666$	2.55061	−	0.917681i	0.0988340	−	0.0355594i
$667$	31.7650			1.22995
$668$	−4.44098	−	7.69200i	−0.171827	−	0.297613i
$669$	−2.60940	+	7.12824i	−0.100885	+	0.275594i
$670$	3.20296	+	5.54769i	0.123741	+	0.214326i
$671$	0.000350512	0	0.000202368i	1.35314e−5	0	7.81234e-6i
$672$	0.692897	−	1.89282i	0.0267291	−	0.0730173i
$673$	28.5063	+	16.4581i	1.09884	+	0.634414i	0.935915	−	0.352225i	$-0.114575\pi$
$673$	28.5063	+	16.4581i	1.09884	+	0.634414i	0.162922	+	0.986639i	$0.447908\pi$
$674$	2.44574			0.0942066
$675$	2.62299	−	4.48552i	0.100959	−	0.172648i
$676$	−9.43828	−	16.3476i	−0.363011	−	0.628753i
$677$	3.71782	−	6.43945i	0.142887	−	0.247488i	−0.785695	−	0.618614i	$-0.787695\pi$
$677$	3.71782	−	6.43945i	0.142887	−	0.247488i	0.928583	+	0.371125i	$0.121028\pi$
$678$	−0.129491	−	0.742401i	−0.00497306	−	0.0285117i
$679$	7.97616	+	13.8151i	0.306097	+	0.530175i
$680$	−3.87791			−0.148711
$681$	28.0440	−	4.89148i	1.07465	−	0.187442i
$682$	−0.983077	−	0.121693i	−0.0376440	−	0.00465987i
$683$		−	27.8306i		−	1.06491i	−0.846459	−	0.532453i	$-0.821270\pi$
$683$		−	27.8306i		−	1.06491i	0.846459	−	0.532453i	$-0.178730\pi$
$684$	14.5484	−	5.23434i	0.556270	−	0.200140i
$685$	11.1218	−	6.42120i	0.424944	−	0.245341i
$686$		−	14.7163i		−	0.561872i
$687$	0.427357	−	1.16744i	0.0163047	−	0.0445405i
$688$	0.735867	−	0.424853i	0.0280547	−	0.0161974i
$689$	−61.1292	+	35.2929i	−2.32884	+	1.34455i
$690$	1.69855	+	9.73818i	0.0646626	+	0.370726i
$691$	−17.9160	+	31.0315i	−0.681558	+	1.18049i	0.292947	+	0.956129i	$0.405364\pi$
$691$	−17.9160	+	31.0315i	−0.681558	+	1.18049i	−0.974505	+	0.224365i	$0.927969\pi$
$692$	−2.18205	−	1.25981i	−0.0829490	−	0.0478906i
$693$	0.110120	−	0.611297i	0.00418311	−	0.0232213i
$694$	−14.6181	+	8.43977i	−0.554896	+	0.320369i
$695$	0.456749	−	0.791113i	0.0173255	−	0.0300086i
$696$	6.18292	+	7.39624i	0.234363	+	0.280354i
$697$		−	11.1360i		−	0.421806i
$698$			32.6846i			1.23713i
$699$	17.4472	+	20.8710i	0.659914	+	0.789414i
$700$	−0.581871	+	1.00783i	−0.0219927	+	0.0380924i
$701$	6.49145	−	3.74784i	0.245179	−	0.141554i	−0.372376	−	0.928082i	$-0.621457\pi$
$701$	6.49145	−	3.74784i	0.245179	−	0.141554i	0.617555	+	0.786528i	$0.288123\pi$
$702$	−29.3367	−	0.162688i	−1.10724	−	0.00614027i
$703$	−4.03285	−	2.32837i	−0.152102	−	0.0878160i
$704$	0.0889568	−	0.154078i	0.00335268	−	0.00580702i
$705$	−1.22343	−	7.01420i	−0.0460769	−	0.264170i
$706$	10.1711	−	5.87229i	0.382795	−	0.221007i
$707$	2.36718	−	1.36669i	0.0890269	−	0.0513997i
$708$	−2.93827	+	8.02662i	−0.110427	+	0.301659i
$709$		−	1.59160i		−	0.0597738i	−0.999553	−	0.0298869i	$-0.990485\pi$
$709$		−	1.59160i		−	0.0597738i	0.999553	−	0.0298869i	$-0.00951471\pi$
$710$	−10.9712	+	6.33424i	−0.411743	+	0.237720i
$711$	2.96269	+	8.23451i	0.111109	+	0.308818i
$712$		−	5.20790i		−	0.195174i
$713$	−29.2626	+	12.3871i	−1.09589	+	0.463902i
$714$	7.70030	−	1.34310i	0.288176	−	0.0502642i
$715$	−1.00449			−0.0375657
$716$	7.26572	+	12.5846i	0.271533	+	0.470308i
$717$	−1.73194	−	9.92961i	−0.0646804	−	0.370828i
$718$	−5.32502	+	9.22320i	−0.198728	+	0.344207i
$719$	1.12193	+	1.94324i	0.0418410	+	0.0724707i	0.886188	−	0.463327i	$-0.153344\pi$
$719$	1.12193	+	1.94324i	0.0418410	+	0.0724707i	−0.844347	+	0.535797i	$0.820011\pi$
$720$	−1.93685	+	2.29099i	−0.0721820	+	0.0853801i
$721$	19.7681			0.736202
$722$	−6.54841	−	3.78073i	−0.243707	−	0.140704i
$723$	3.96977	−	10.8444i	0.147637	−	0.403309i
$724$	3.27223	+	1.88922i	0.121611	+	0.0702124i
$725$	−2.78288	−	4.82008i	−0.103353	−	0.179013i
$726$	−6.53060	+	17.8400i	−0.242373	+	0.662104i
$727$	16.3097	+	28.2493i	0.604894	+	1.04771i	0.992068	+	0.125701i	$0.0401180\pi$
$727$	16.3097	+	28.2493i	0.604894	+	1.04771i	−0.387174	+	0.922007i	$0.626549\pi$
$728$	6.57041			0.243516
$729$	−13.7585	+	23.2315i	−0.509574	+	0.860427i
$730$	9.32062	−	5.38127i	0.344972	−	0.199170i
$731$	2.85363	+	1.64754i	0.105545	+	0.0609365i
$732$	0.00252716	+	0.00302309i	9.34066e−5	+	0.000111736i
$733$	−4.82676	+	8.36019i	−0.178280	+	0.308791i	−0.941292	−	0.337594i	$-0.890387\pi$
$733$	−4.82676	+	8.36019i	−0.178280	+	0.308791i	0.763011	+	0.646385i	$0.223720\pi$
$734$	−14.4416	+	25.0136i	−0.533050	+	0.923270i
$735$	−3.36147	+	9.18272i	−0.123990	+	0.338710i
$736$		−	5.70722i		−	0.210371i
$737$	−0.569850	−	0.987008i	−0.0209907	−	0.0363569i
$738$	−6.57891	−	5.56193i	−0.242173	−	0.204738i
$739$	20.5340	+	11.8553i	0.755355	+	0.436105i	0.827626	−	0.561281i	$-0.189691\pi$
$739$	20.5340	+	11.8553i	0.755355	+	0.436105i	−0.0722704	+	0.997385i	$0.523024\pi$
$740$	0.903557			0.0332154
$741$	32.3245	+	38.6677i	1.18747	+	1.42049i
$742$		−	14.5492i		−	0.534118i
$743$	−33.9392			−1.24511			−0.622555	−	0.782576i	$-0.713905\pi$
$743$	−33.9392			−1.24511			−0.622555	+	0.782576i	$0.713905\pi$
$744$	−8.58010	−	4.40248i	−0.314562	−	0.161403i
$745$	4.58537			0.167995
$746$		−	15.4070i		−	0.564090i
$747$	−36.4655	−	30.8286i	−1.33420	−	1.12796i
$748$	0.689933			0.0252264
$749$	−4.65955	−	2.69019i	−0.170256	−	0.0982975i
$750$	1.32888	−	1.11089i	0.0485240	−	0.0405638i
$751$	−3.61672	−	6.26434i	−0.131976	−	0.228589i	0.792462	−	0.609921i	$-0.208799\pi$
$751$	−3.61672	−	6.26434i	−0.131976	−	0.228589i	−0.924438	+	0.381332i	$0.875466\pi$
$752$			4.11079i			0.149905i
$753$	−13.5020	−	4.94261i	−0.492040	−	0.180119i
$754$	−15.7119	+	27.2139i	−0.572195	+	0.991071i
$755$	−9.01289	+	15.6108i	−0.328013	+	0.568134i
$756$	3.05249	−	5.21999i	0.111018	−	0.189849i
$757$	−0.672009	−	0.387984i	−0.0244246	−	0.0141015i	0.487738	−	0.872990i	$-0.337822\pi$
$757$	−0.672009	−	0.387984i	−0.0244246	−	0.0141015i	−0.512163	+	0.858889i	$0.671155\pi$
$758$	8.07991	−	4.66494i	0.293475	−	0.169438i
$759$	−0.302195	−	1.73255i	−0.0109690	−	0.0628877i
$760$	5.15378			0.186947
$761$	−3.20580	−	5.55261i	−0.116210	−	0.201282i	0.802053	−	0.597253i	$-0.203741\pi$
$761$	−3.20580	−	5.55261i	−0.116210	−	0.201282i	−0.918263	+	0.395971i	$0.870408\pi$
$762$	20.4962	+	7.50296i	0.742500	+	0.271803i
$763$	−10.6658	−	18.4737i	−0.386128	−	0.668793i
$764$	5.58732	+	3.22584i	0.202142	+	0.116707i
$765$	−11.4494	−	2.06252i	−0.413955	−	0.0745705i
$766$	20.4225	+	11.7909i	0.737895	+	0.426024i
$767$	−27.8622			−1.00605
$768$	1.32888	−	1.11089i	0.0479520	−	0.0400857i
$769$	9.17949	+	15.8993i	0.331021	+	0.573345i	0.982712	−	0.185139i	$-0.0592736\pi$
$769$	9.17949	+	15.8993i	0.331021	+	0.573345i	−0.651691	+	0.758484i	$0.725940\pi$
$770$	0.103523	−	0.179307i	0.00373070	−	0.00646176i
$771$	−41.0030	+	7.15180i	−1.47669	+	0.257566i
$772$	1.05136	+	1.82101i	0.0378393	+	0.0655396i
$773$	11.5363			0.414930			0.207465	−	0.978242i	$-0.433479\pi$
$773$	11.5363			0.414930			0.207465	+	0.978242i	$0.433479\pi$
$774$	2.39859	−	0.862988i	0.0862157	−	0.0310195i
$775$	4.44330	+	3.35516i	0.159608	+	0.120521i

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.o (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(1.32888 - 1.11089i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.11089 + 1.32888i) q^{6} +(-0.581871 - 1.00783i) q^{7} -1.00000i q^{8} +(0.531863 - 2.95248i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(1.32888 - 1.11089i) q^{3} -1.00000 q^{4} +(-0.866025 - 0.500000i) q^{5} +(1.11089 + 1.32888i) q^{6} +(-0.581871 - 1.00783i) q^{7} -1.00000i q^{8} +(0.531863 - 2.95248i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-0.0889568 + 0.154078i) q^{11} +(-1.32888 + 1.11089i) q^{12} +(-4.88952 - 2.82297i) q^{13} +(1.00783 - 0.581871i) q^{14} +(-1.70629 + 0.297614i) q^{15} +1.00000 q^{16} +(1.93896 + 3.35837i) q^{17} +(2.95248 + 0.531863i) q^{18} +(-2.57689 - 4.46331i) q^{19} +(0.866025 + 0.500000i) q^{20} +(-1.89282 - 0.692897i) q^{21} +(-0.154078 - 0.0889568i) q^{22} -5.70722 q^{23} +(-1.11089 - 1.32888i) q^{24} +(0.500000 + 0.866025i) q^{25} +(2.82297 - 4.88952i) q^{26} +(-2.57308 - 4.51434i) q^{27} +(0.581871 + 1.00783i) q^{28} -5.56575 q^{29} +(-0.297614 - 1.70629i) q^{30} +(5.12730 - 2.17043i) q^{31} +1.00000i q^{32} +(0.0529495 + 0.303572i) q^{33} +(-3.35837 + 1.93896i) q^{34} +1.16374i q^{35} +(-0.531863 + 2.95248i) q^{36} +(0.782503 - 0.451779i) q^{37} +(4.46331 - 2.57689i) q^{38} +(-9.63360 + 1.68031i) q^{39} +(-0.500000 + 0.866025i) q^{40} +(-2.48692 - 1.43582i) q^{41} +(0.692897 - 1.89282i) q^{42} +(0.735867 - 0.424853i) q^{43} +(0.0889568 - 0.154078i) q^{44} +(-1.93685 + 2.29099i) q^{45} -5.70722i q^{46} +4.11079i q^{47} +(1.32888 - 1.11089i) q^{48} +(2.82285 - 4.88932i) q^{49} +(-0.866025 + 0.500000i) q^{50} +(6.30741 + 2.30892i) q^{51} +(4.88952 + 2.82297i) q^{52} +(6.25104 - 10.8271i) q^{53} +(4.51434 - 2.57308i) q^{54} +(0.154078 - 0.0889568i) q^{55} +(-1.00783 + 0.581871i) q^{56} +(-8.38261 - 3.06858i) q^{57} -5.56575i q^{58} +(4.27376 - 2.46746i) q^{59} +(1.70629 - 0.297614i) q^{60} -0.00227491i q^{61} +(2.17043 + 5.12730i) q^{62} +(-3.28507 + 1.18193i) q^{63} -1.00000 q^{64} +(2.82297 + 4.88952i) q^{65} +(-0.303572 + 0.0529495i) q^{66} +(-3.20296 + 5.54769i) q^{67} +(-1.93896 - 3.35837i) q^{68} +(-7.58423 + 6.34007i) q^{69} -1.16374 q^{70} +(-10.9712 - 6.33424i) q^{71} +(-2.95248 - 0.531863i) q^{72} +(9.32062 + 5.38127i) q^{73} +(0.451779 + 0.782503i) q^{74} +(1.62650 + 0.595404i) q^{75} +(2.57689 + 4.46331i) q^{76} +0.207046 q^{77} +(-1.68031 - 9.63360i) q^{78} +(-2.52627 + 1.45854i) q^{79} +(-0.866025 - 0.500000i) q^{80} +(-8.43424 - 3.14063i) q^{81} +(1.43582 - 2.48692i) q^{82} +(7.95846 - 13.7845i) q^{83} +(1.89282 + 0.692897i) q^{84} -3.87791i q^{85} +(0.424853 + 0.735867i) q^{86} +(-7.39624 + 6.18292i) q^{87} +(0.154078 + 0.0889568i) q^{88} +5.20790 q^{89} +(-2.29099 - 1.93685i) q^{90} +6.57041i q^{91} +5.70722 q^{92} +(4.40248 - 8.58010i) q^{93} -4.11079 q^{94} +5.15378i q^{95} +(1.11089 + 1.32888i) q^{96} -13.7078 q^{97} +(4.88932 + 2.82285i) q^{98} +(0.407598 + 0.344591i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40q + 6q^{3} - 40q^{4} - 12q^{7} - 2q^{9} + O(q^{10}) \)	\( 40q + 6q^{3} - 40q^{4} - 12q^{7} - 2q^{9} + 20q^{10} - 6q^{12} - 12q^{13} + 40q^{16} - 12q^{18} - 12q^{19} + 12q^{21} - 24q^{22} + 20q^{25} + 12q^{28} + 8q^{31} + 52q^{33} + 24q^{34} + 2q^{36} + 60q^{37} - 8q^{39} - 20q^{40} + 12q^{42} + 24q^{43} - 12q^{45} + 6q^{48} - 4q^{49} + 14q^{51} + 12q^{52} + 24q^{55} - 12q^{57} - 40q^{64} + 8q^{66} + 64q^{67} - 26q^{69} - 24q^{70} + 12q^{72} + 6q^{75} + 12q^{76} - 68q^{78} - 48q^{79} + 2q^{81} + 4q^{82} - 12q^{84} + 36q^{87} + 24q^{88} + 2q^{90} - 22q^{93} - 40q^{94} + 8q^{97} - 90q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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