LMFDB - Embedded newform 570.2.q.b.49.4

Newspace parameters

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.q (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
Defining polynomial:	$x^{12} - 2 x^{11} + 2 x^{10} - 8 x^{9} + 4 x^{8} + 16 x^{7} - 8 x^{6} + 20 x^{5} + 20 x^{4} - 24 x^{3} + 8 x^{2} - 8 x + 4$
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			49.4
Root			$-1.16746 + 0.312819i$ of defining polynomial
Character	$\chi$	$=$	570.49
Dual form			570.2.q.b.349.4

$q$-expansion

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.60976 - 1.55199i) q^{5} +(0.500000 + 0.866025i) q^{6} +3.53919i q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.60976 - 1.55199i) q^{5} +(0.500000 + 0.866025i) q^{6} +3.53919i q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.618092 - 2.14894i) q^{10} +3.34017 q^{11} +1.00000i q^{12} +(1.48028 - 0.854638i) q^{13} +(-1.76959 + 3.06503i) q^{14} +(-0.618092 - 2.14894i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.29175 + 1.90049i) q^{17} +1.00000i q^{18} +(1.30878 + 4.15777i) q^{19} +(0.539189 - 2.17009i) q^{20} +(-1.76959 + 3.06503i) q^{21} +(2.89267 + 1.67009i) q^{22} +(-7.33350 + 4.23400i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(0.182626 + 4.99666i) q^{25} +1.70928 q^{26} +1.00000i q^{27} +(-3.06503 + 1.76959i) q^{28} +(-3.97887 - 6.89160i) q^{29} +(0.539189 - 2.17009i) q^{30} +1.07838 q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.89267 + 1.67009i) q^{33} +(1.90049 + 3.29175i) q^{34} +(5.49280 - 5.69723i) q^{35} +(-0.500000 + 0.866025i) q^{36} -4.70928i q^{37} +(-0.945448 + 4.25513i) q^{38} +1.70928 q^{39} +(1.55199 - 1.60976i) q^{40} +(5.96441 - 10.3307i) q^{41} +(-3.06503 + 1.76959i) q^{42} +(4.39800 + 2.53919i) q^{43} +(1.67009 + 2.89267i) q^{44} +(0.539189 - 2.17009i) q^{45} -8.46800 q^{46} +(-4.73543 + 2.73400i) q^{47} +(-0.866025 + 0.500000i) q^{48} -5.52586 q^{49} +(-2.34017 + 4.41855i) q^{50} +(1.90049 + 3.29175i) q^{51} +(1.48028 + 0.854638i) q^{52} +(10.8342 - 6.25513i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-5.37686 - 5.18393i) q^{55} -3.53919 q^{56} +(-0.945448 + 4.25513i) q^{57} -7.95774i q^{58} +(2.93302 - 5.08013i) q^{59} +(1.55199 - 1.60976i) q^{60} +(-6.92522 - 11.9948i) q^{61} +(0.933903 + 0.539189i) q^{62} +(-3.06503 + 1.76959i) q^{63} -1.00000 q^{64} +(-3.70928 - 0.921622i) q^{65} +(1.67009 + 2.89267i) q^{66} +(-7.82551 + 4.51806i) q^{67} +3.80098i q^{68} -8.46800 q^{69} +(7.60552 - 2.18754i) q^{70} +(4.04585 - 7.00763i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(-5.11673 - 2.95415i) q^{73} +(2.35464 - 4.07835i) q^{74} +(-2.34017 + 4.41855i) q^{75} +(-2.94635 + 3.21233i) q^{76} +11.8215i q^{77} +(1.48028 + 0.854638i) q^{78} +(-3.53919 + 6.13005i) q^{79} +(2.14894 - 0.618092i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(10.3307 - 5.96441i) q^{82} -4.68035i q^{83} -3.53919 q^{84} +(-2.34936 - 8.16810i) q^{85} +(2.53919 + 4.39800i) q^{86} -7.95774i q^{87} +3.34017i q^{88} +(4.66229 + 8.07532i) q^{89} +(1.55199 - 1.60976i) q^{90} +(3.02472 + 5.23898i) q^{91} +(-7.33350 - 4.23400i) q^{92} +(0.933903 + 0.539189i) q^{93} -5.46800 q^{94} +(4.34602 - 8.72422i) q^{95} -1.00000 q^{96} +(-5.06662 - 2.92522i) q^{97} +(-4.78553 - 2.76293i) q^{98} +(1.67009 + 2.89267i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12q + 6q^{4} + 6q^{6} + 6q^{9} + O(q^{10}) $	$ 12q + 6q^{4} + 6q^{6} + 6q^{9} - 2q^{10} - 4q^{11} - 18q^{14} - 2q^{15} - 6q^{16} + 6q^{19} - 18q^{21} - 6q^{24} - 2q^{25} - 8q^{26} - 16q^{29} + 4q^{34} + 2q^{35} - 6q^{36} - 8q^{39} + 2q^{40} + 10q^{41} - 2q^{44} + 28q^{46} - 56q^{49} + 16q^{50} + 4q^{51} - 6q^{54} - 8q^{55} - 36q^{56} + 8q^{59} + 2q^{60} - 28q^{61} - 12q^{64} - 16q^{65} - 2q^{66} + 28q^{69} + 16q^{70} + 44q^{71} + 14q^{74} + 16q^{75} - 12q^{76} - 36q^{79} - 6q^{81} - 36q^{84} - 32q^{85} + 24q^{86} + 6q^{89} + 2q^{90} + 64q^{94} - 12q^{95} - 12q^{96} - 2q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.60976	−	1.55199i	−0.719905	−	0.694073i
$5$	−1.60976	−	1.55199i	−0.719905	−	0.694073i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$			3.53919i			1.33769i	0.743403	+	0.668844i	$0.233211\pi$
$7$			3.53919i			1.33769i	−0.743403	+	0.668844i	$0.766789\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−0.618092	−	2.14894i	−0.195458	−	0.679556i
$11$	3.34017			1.00710			0.503550	−	0.863966i	$-0.332027\pi$
$11$	3.34017			1.00710			0.503550	+	0.863966i	$0.332027\pi$
$12$			1.00000i			0.288675i
$13$	1.48028	−	0.854638i	0.410555	−	0.237034i	−0.280473	−	0.959862i	$-0.590491\pi$
$13$	1.48028	−	0.854638i	0.410555	−	0.237034i	0.691028	+	0.722828i	$0.257158\pi$
$14$	−1.76959	+	3.06503i	−0.472944	+	0.819163i
$15$	−0.618092	−	2.14894i	−0.159591	−	0.554855i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.29175	+	1.90049i	0.798366	+	0.460937i	0.842900	−	0.538071i	$-0.180847\pi$
$17$	3.29175	+	1.90049i	0.798366	+	0.460937i	−0.0445332	+	0.999008i	$0.514180\pi$
$18$			1.00000i			0.235702i
$19$	1.30878	+	4.15777i	0.300255	+	0.953859i
$19$	1.30878	+	4.15777i	0.300255	+	0.953859i
$20$	0.539189	−	2.17009i	0.120566	−	0.485246i
$21$	−1.76959	+	3.06503i	−0.386157	+	0.668844i
$22$	2.89267	+	1.67009i	0.616720	+	0.356064i
$23$	−7.33350	+	4.23400i	−1.52914	+	0.882850i	−0.529743	+	0.848158i	$0.677712\pi$
$23$	−7.33350	+	4.23400i	−1.52914	+	0.882850i	−0.999398	+	0.0346916i	$0.988955\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	0.182626	+	4.99666i	0.0365252	+	0.999333i
$26$	1.70928			0.335216
$27$			1.00000i			0.192450i
$28$	−3.06503	+	1.76959i	−0.579236	+	0.334422i
$29$	−3.97887	−	6.89160i	−0.738858	−	1.27974i	−0.953010	−	0.302939i	$-0.902032\pi$
$29$	−3.97887	−	6.89160i	−0.738858	−	1.27974i	0.214152	−	0.976800i	$-0.431301\pi$
$30$	0.539189	−	2.17009i	0.0984420	−	0.396202i
$31$	1.07838			0.193682			0.0968412	−	0.995300i	$-0.469126\pi$
$31$	1.07838			0.193682			0.0968412	+	0.995300i	$0.469126\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	2.89267	+	1.67009i	0.503550	+	0.290725i
$34$	1.90049	+	3.29175i	0.325932	+	0.564530i
$35$	5.49280	−	5.69723i	0.928453	−	0.963007i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$		−	4.70928i		−	0.774200i	−0.922038	−	0.387100i	$-0.873477\pi$
$37$		−	4.70928i		−	0.774200i	0.922038	−	0.387100i	$-0.126523\pi$
$38$	−0.945448	+	4.25513i	−0.153372	+	0.690273i
$39$	1.70928			0.273703
$40$	1.55199	−	1.60976i	0.245392	−	0.254525i
$41$	5.96441	−	10.3307i	0.931484	−	1.61338i	0.150696	−	0.988580i	$-0.451848\pi$
$41$	5.96441	−	10.3307i	0.931484	−	1.61338i	0.780787	−	0.624797i	$-0.214818\pi$
$42$	−3.06503	+	1.76959i	−0.472944	+	0.273054i
$43$	4.39800	+	2.53919i	0.670689	+	0.387223i	0.796338	−	0.604852i	$-0.206768\pi$
$43$	4.39800	+	2.53919i	0.670689	+	0.387223i	−0.125648	+	0.992075i	$0.540101\pi$
$44$	1.67009	+	2.89267i	0.251775	+	0.436087i
$45$	0.539189	−	2.17009i	0.0803775	−	0.323497i
$46$	−8.46800			−1.24854
$47$	−4.73543	+	2.73400i	−0.690733	+	0.398795i	−0.803887	−	0.594783i	$-0.797238\pi$
$47$	−4.73543	+	2.73400i	−0.690733	+	0.398795i	0.113154	+	0.993578i	$0.463905\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	−5.52586			−0.789408
$50$	−2.34017	+	4.41855i	−0.330950	+	0.624877i
$51$	1.90049	+	3.29175i	0.266122	+	0.460937i
$52$	1.48028	+	0.854638i	0.205277	+	0.118517i
$53$	10.8342	−	6.25513i	1.48819	−	0.859208i	0.488283	−	0.872685i	$-0.337623\pi$
$53$	10.8342	−	6.25513i	1.48819	−	0.859208i	0.999909	+	0.0134772i	$0.00429006\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−5.37686	−	5.18393i	−0.725016	−	0.699001i
$56$	−3.53919			−0.472944
$57$	−0.945448	+	4.25513i	−0.125228	+	0.563606i
$58$		−	7.95774i		−	1.04490i
$59$	2.93302	−	5.08013i	0.381846	−	0.661377i	−0.609480	−	0.792801i	$-0.708622\pi$
$59$	2.93302	−	5.08013i	0.381846	−	0.661377i	0.991326	+	0.131425i	$0.0419551\pi$
$60$	1.55199	−	1.60976i	0.200362	−	0.207819i
$61$	−6.92522	−	11.9948i	−0.886683	−	1.53578i	−0.843772	−	0.536701i	$-0.819670\pi$
$61$	−6.92522	−	11.9948i	−0.886683	−	1.53578i	−0.0429107	−	0.999079i	$-0.513663\pi$
$62$	0.933903	+	0.539189i	0.118606	+	0.0684771i
$63$	−3.06503	+	1.76959i	−0.386157	+	0.222948i
$64$	−1.00000			−0.125000
$65$	−3.70928	−	0.921622i	−0.460079	−	0.114313i
$66$	1.67009	+	2.89267i	0.205573	+	0.356064i
$67$	−7.82551	+	4.51806i	−0.956038	+	0.551969i	−0.894951	−	0.446164i	$-0.852790\pi$
$67$	−7.82551	+	4.51806i	−0.956038	+	0.551969i	−0.0610865	+	0.998132i	$0.519457\pi$
$68$			3.80098i			0.460937i
$69$	−8.46800			−1.01943
$70$	7.60552	−	2.18754i	0.909034	−	0.261462i
$71$	4.04585	−	7.00763i	0.480155	−	0.831652i	−0.519586	−	0.854418i	$-0.673914\pi$
$71$	4.04585	−	7.00763i	0.480155	−	0.831652i	0.999741	+	0.0227659i	$0.00724723\pi$
$72$	−0.866025	+	0.500000i	−0.102062	+	0.0589256i
$73$	−5.11673	−	2.95415i	−0.598868	−	0.345757i	0.169728	−	0.985491i	$-0.445711\pi$
$73$	−5.11673	−	2.95415i	−0.598868	−	0.345757i	−0.768596	+	0.639734i	$0.779044\pi$
$74$	2.35464	−	4.07835i	0.273721	−	0.474099i
$75$	−2.34017	+	4.41855i	−0.270220	+	0.510210i
$76$	−2.94635	+	3.21233i	−0.337969	+	0.368479i
$77$			11.8215i			1.34719i
$78$	1.48028	+	0.854638i	0.167608	+	0.0967687i
$79$	−3.53919	+	6.13005i	−0.398190	+	0.689685i	−0.993503	−	0.113809i	$-0.963695\pi$
$79$	−3.53919	+	6.13005i	−0.398190	+	0.689685i	0.595313	+	0.803494i	$0.297028\pi$
$80$	2.14894	−	0.618092i	0.240259	−	0.0691048i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	10.3307	−	5.96441i	1.14083	−	0.658658i
$83$		−	4.68035i		−	0.513735i	−0.966447	−	0.256867i	$-0.917310\pi$
$83$		−	4.68035i		−	0.513735i	0.966447	−	0.256867i	$-0.0826903\pi$
$84$	−3.53919			−0.386157
$85$	−2.34936	−	8.16810i	−0.254824	−	0.885955i
$86$	2.53919	+	4.39800i	0.273808	+	0.474249i
$87$		−	7.95774i		−	0.853159i
$88$			3.34017i			0.356064i
$89$	4.66229	+	8.07532i	0.494201	+	0.855982i	0.999978	−	0.00668268i	$-0.00212718\pi$
$89$	4.66229	+	8.07532i	0.494201	+	0.855982i	−0.505776	+	0.862665i	$0.668794\pi$
$90$	1.55199	−	1.60976i	0.163595	−	0.169683i
$91$	3.02472	+	5.23898i	0.317077	+	0.549194i
$92$	−7.33350	−	4.23400i	−0.764570	−	0.441425i
$93$	0.933903	+	0.539189i	0.0968412	+	0.0559113i
$94$	−5.46800			−0.563981
$95$	4.34602	−	8.72422i	0.445892	−	0.895087i
$96$	−1.00000			−0.102062
$97$	−5.06662	−	2.92522i	−0.514438	−	0.297011i	0.220218	−	0.975451i	$-0.429323\pi$
$97$	−5.06662	−	2.92522i	−0.514438	−	0.297011i	−0.734656	+	0.678440i	$0.762656\pi$
$98$	−4.78553	−	2.76293i	−0.483412	−	0.279098i
$99$	1.67009	+	2.89267i	0.167850	+	0.290725i
$100$	−4.23592	+	2.65649i	−0.423592	+	0.265649i
$101$	4.32684	+	7.49431i	0.430537	+	0.745712i	0.996920	−	0.0784306i	$-0.0249909\pi$
$101$	4.32684	+	7.49431i	0.430537	+	0.745712i	−0.566383	+	0.824142i	$0.691658\pi$
$102$			3.80098i			0.376354i
$103$		−	0.751536i		−	0.0740510i	−0.999314	−	0.0370255i	$-0.988212\pi$
$103$		−	0.751536i		−	0.0740510i	0.999314	−	0.0370255i	$-0.0117883\pi$
$104$	0.854638	+	1.48028i	0.0838041	+	0.145153i
$105$	7.60552	−	2.18754i	0.742223	−	0.213482i
$106$	12.5103			1.21510
$107$		−	9.82377i		−	0.949700i	−0.880067	−	0.474850i	$-0.842502\pi$
$107$		−	9.82377i		−	0.949700i	0.880067	−	0.474850i	$-0.157498\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	−3.92522	+	6.79867i	−0.375968	+	0.651195i	−0.990471	−	0.137719i	$-0.956023\pi$
$109$	−3.92522	+	6.79867i	−0.375968	+	0.651195i	0.614504	+	0.788914i	$0.289356\pi$
$110$	−2.06453	−	7.17785i	−0.196846	−	0.684381i
$111$	2.35464	−	4.07835i	0.223492	−	0.387100i
$112$	−3.06503	−	1.76959i	−0.289618	−	0.167211i
$113$		−	7.98440i		−	0.751109i	−0.926800	−	0.375555i	$-0.877452\pi$
$113$		−	7.98440i		−	0.751109i	0.926800	−	0.375555i	$-0.122548\pi$
$114$	−2.94635	+	3.21233i	−0.275951	+	0.300862i
$115$	18.3763	+	4.56585i	1.71360	+	0.425768i
$116$	3.97887	−	6.89160i	0.369429	−	0.639869i
$117$	1.48028	+	0.854638i	0.136852	+	0.0790113i
$118$	5.08013	−	2.93302i	0.467664	−	0.270006i
$119$	−6.72620	+	11.6501i	−0.616590	+	1.06796i
$120$	2.14894	−	0.618092i	0.196171	−	0.0564238i
$121$	0.156755			0.0142505
$122$		−	13.8504i		−	1.25396i
$123$	10.3307	−	5.96441i	0.931484	−	0.537792i
$124$	0.539189	+	0.933903i	0.0484206	+	0.0838669i
$125$	7.46081	−	8.32684i	0.667315	−	0.744775i
$126$	−3.53919			−0.315296
$127$	16.1160	−	9.30458i	1.43006	−	0.825648i	0.432939	−	0.901423i	$-0.357477\pi$
$127$	16.1160	−	9.30458i	1.43006	−	0.825648i	0.997125	+	0.0757754i	$0.0241432\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	2.53919	+	4.39800i	0.223563	+	0.387223i
$130$	−2.75152	−	2.65279i	−0.241324	−	0.232665i
$131$	3.79072	−	6.56573i	0.331197	−	0.573650i	−0.651550	−	0.758606i	$-0.725881\pi$
$131$	3.79072	−	6.56573i	0.331197	−	0.573650i	0.982747	+	0.184956i	$0.0592141\pi$
$132$			3.34017i			0.290725i
$133$	−14.7151	+	4.63203i	−1.27597	+	0.401648i
$134$	−9.03612			−0.780602
$135$	1.55199	−	1.60976i	0.133574	−	0.138546i
$136$	−1.90049	+	3.29175i	−0.162966	+	0.282265i
$137$	−9.88875	+	5.70928i	−0.844853	+	0.487776i	−0.858911	−	0.512125i	$-0.828858\pi$
$137$	−9.88875	+	5.70928i	−0.844853	+	0.487776i	0.0140576	+	0.999901i	$0.495525\pi$
$138$	−7.33350	−	4.23400i	−0.624269	−	0.360422i
$139$	1.80098	+	3.11940i	0.152757	+	0.264584i	0.932240	−	0.361840i	$-0.117851\pi$
$139$	1.80098	+	3.11940i	0.152757	+	0.264584i	−0.779483	+	0.626424i	$0.784518\pi$
$140$	7.68035	+	1.90829i	0.649108	+	0.161280i
$141$	−5.46800			−0.460489
$142$	7.00763	−	4.04585i	0.588067	−	0.339521i
$143$	4.94438	−	2.85464i	0.413470	−	0.238717i
$144$	−1.00000			−0.0833333
$145$	−4.29072	+	17.2690i	−0.356325	+	1.43411i
$146$	−2.95415	−	5.11673i	−0.244487	−	0.423464i
$147$	−4.78553	−	2.76293i	−0.394704	−	0.227883i
$148$	4.07835	−	2.35464i	0.335238	−	0.193550i
$149$	−5.14896	+	8.91825i	−0.421819	+	0.730612i	−0.996117	−	0.0880341i	$-0.971942\pi$
$149$	−5.14896	+	8.91825i	−0.421819	+	0.730612i	0.574299	+	0.818646i	$0.305275\pi$
$150$	−4.23592	+	2.65649i	−0.345862	+	0.216902i
$151$	−4.69594			−0.382151			−0.191075	−	0.981575i	$-0.561197\pi$
$151$	−4.69594			−0.382151			−0.191075	+	0.981575i	$0.561197\pi$
$152$	−4.15777	+	1.30878i	−0.337240	+	0.106156i
$153$			3.80098i			0.307291i
$154$	−5.91075	+	10.2377i	−0.476302	+	0.824979i
$155$	−1.73592	−	1.67364i	−0.139433	−	0.134430i
$156$	0.854638	+	1.48028i	0.0684258	+	0.118517i
$157$	9.10838	+	5.25872i	0.726928	+	0.419692i	0.817297	−	0.576216i	$-0.195471\pi$
$157$	9.10838	+	5.25872i	0.726928	+	0.419692i	−0.0903695	+	0.995908i	$0.528805\pi$
$158$	−6.13005	+	3.53919i	−0.487681	+	0.281563i
$159$	12.5103			0.992128
$160$	2.17009	+	0.539189i	0.171560	+	0.0426266i
$161$	−14.9849	−	25.9546i	−1.18098	−	2.04551i
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$		−	16.7792i		−	1.31425i	−0.753781	−	0.657126i	$-0.771772\pi$
$163$		−	16.7792i		−	1.31425i	0.753781	−	0.657126i	$-0.228228\pi$
$164$	11.9288			0.931484
$165$	−2.06453	−	7.17785i	−0.160724	−	0.558795i
$166$	2.34017	−	4.05330i	0.181633	−	0.314597i
$167$	−10.0496	+	5.80212i	−0.777659	+	0.448981i	−0.835600	−	0.549339i	$-0.814880\pi$
$167$	−10.0496	+	5.80212i	−0.777659	+	0.448981i	0.0579413	+	0.998320i	$0.481546\pi$
$168$	−3.06503	−	1.76959i	−0.236472	−	0.136527i
$169$	−5.03919	+	8.72813i	−0.387630	+	0.671395i
$170$	2.04945	−	8.24846i	0.157186	−	0.632628i
$171$	−2.94635	+	3.21233i	−0.225313	+	0.245653i
$172$			5.07838i			0.387223i
$173$	7.70752	+	4.44994i	0.585992	+	0.338323i	0.763511	−	0.645795i	$-0.223474\pi$
$173$	7.70752	+	4.44994i	0.585992	+	0.338323i	−0.177519	+	0.984117i	$0.556807\pi$
$174$	3.97887	−	6.89160i	0.301637	−	0.522451i
$175$	−17.6841	+	0.646348i	−1.33680	+	0.0488593i
$176$	−1.67009	+	2.89267i	−0.125888	+	0.218044i
$177$	5.08013	−	2.93302i	0.381846	−	0.220459i
$178$			9.32457i			0.698906i
$179$	−21.8599			−1.63388			−0.816942	−	0.576719i	$-0.804333\pi$
$179$	−21.8599			−1.63388			−0.816942	+	0.576719i	$0.804333\pi$
$180$	2.14894	−	0.618092i	0.160173	−	0.0460699i
$181$	2.66342	+	4.61318i	0.197971	+	0.342895i	0.947870	−	0.318656i	$-0.103232\pi$
$181$	2.66342	+	4.61318i	0.197971	+	0.342895i	−0.749900	+	0.661551i	$0.769898\pi$
$182$			6.04945i			0.448415i
$183$		−	13.8504i		−	1.02385i
$184$	−4.23400	−	7.33350i	−0.312135	−	0.540633i
$185$	−7.30877	+	7.58078i	−0.537351	+	0.557350i
$186$	0.539189	+	0.933903i	0.0395352	+	0.0684771i
$187$	10.9950	+	6.34797i	0.804035	+	0.464210i
$188$	−4.73543	−	2.73400i	−0.345366	−	0.199397i
$189$	−3.53919			−0.257438
$190$	8.12588	−	5.38239i	0.589513	−	0.390480i
$191$	8.99386			0.650773			0.325386	−	0.945581i	$-0.394506\pi$
$191$	8.99386			0.650773			0.325386	+	0.945581i	$0.394506\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	−2.02042	−	1.16649i	−0.145433	−	0.0839660i	0.425518	−	0.904950i	$-0.360092\pi$
$193$	−2.02042	−	1.16649i	−0.145433	−	0.0839660i	−0.570951	+	0.820984i	$0.693425\pi$
$194$	−2.92522	−	5.06662i	−0.210018	−	0.363762i
$195$	−2.75152	−	2.65279i	−0.197040	−	0.189970i
$196$	−2.76293	−	4.78553i	−0.197352	−	0.341824i
$197$		−	24.0856i		−	1.71603i	−0.513628	−	0.858013i	$-0.671699\pi$
$197$		−	24.0856i		−	1.71603i	0.513628	−	0.858013i	$-0.328301\pi$
$198$			3.34017i			0.237376i
$199$	0.652028	+	1.12935i	0.0462210	+	0.0800572i	0.888210	−	0.459437i	$-0.151949\pi$
$199$	0.652028	+	1.12935i	0.0462210	+	0.0800572i	−0.841989	+	0.539494i	$0.818615\pi$
$200$	−4.99666	+	0.182626i	−0.353317	+	0.0129136i
$201$	−9.03612			−0.637359
$202$			8.65368i			0.608871i
$203$	24.3907	−	14.0820i	1.71189	−	0.988361i
$204$	−1.90049	+	3.29175i	−0.133061	+	0.230469i
$205$	−25.6344	+	7.37310i	−1.79038	+	0.514960i
$206$	0.375768	−	0.650849i	0.0261810	−	0.0453468i
$207$	−7.33350	−	4.23400i	−0.509714	−	0.294283i
$208$			1.70928i			0.118517i
$209$	4.37156	+	13.8877i	0.302387	+	0.960631i
$210$	7.68035	+	1.90829i	0.529994	+	0.131685i
$211$	−3.49220	+	6.04867i	−0.240413	+	0.416408i	−0.960832	−	0.277132i	$-0.910616\pi$
$211$	−3.49220	+	6.04867i	−0.240413	+	0.416408i	0.720419	+	0.693539i	$0.243950\pi$
$212$	10.8342	+	6.25513i	0.744096	+	0.429604i
$213$	7.00763	−	4.04585i	0.480155	−	0.277217i
$214$	4.91189	−	8.50763i	0.335770	−	0.581570i
$215$	−3.13890	−	10.9132i	−0.214072	−	0.744271i
$216$	−1.00000			−0.0680414
$217$			3.81658i			0.259087i
$218$	−6.79867	+	3.92522i	−0.460464	+	0.265849i
$219$	−2.95415	−	5.11673i	−0.199623	−	0.345757i
$220$	1.80098	−	7.24846i	0.121422	−	0.488691i
$221$	6.49693			0.437031
$222$	4.07835	−	2.35464i	0.273721	−	0.158033i
$223$	8.67180	+	5.00667i	0.580707	+	0.335271i	0.761414	−	0.648266i	$-0.224505\pi$
$223$	8.67180	+	5.00667i	0.580707	+	0.335271i	−0.180708	+	0.983537i	$0.557839\pi$
$224$	−1.76959	−	3.06503i	−0.118236	−	0.204791i
$225$	−4.23592	+	2.65649i	−0.282395	+	0.177099i
$226$	3.99220	−	6.91469i	0.265557	−	0.459959i
$227$			14.2485i			0.945704i	0.881142	+	0.472852i	$0.156775\pi$
$227$			14.2485i			0.945704i	−0.881142	+	0.472852i	$0.843225\pi$
$228$	−4.15777	+	1.30878i	−0.275355	+	0.0866763i
$229$	15.8576			1.04790			0.523951	−	0.851749i	$-0.324458\pi$
$229$	15.8576			1.04790			0.523951	+	0.851749i	$0.324458\pi$
$230$	13.6314	+	13.1423i	0.898828	+	0.866577i
$231$	−5.91075	+	10.2377i	−0.388899	+	0.673593i
$232$	6.89160	−	3.97887i	0.452456	−	0.261226i
$233$	21.3006	+	12.2979i	1.39545	+	0.805663i	0.993912	−	0.110179i	$-0.0351426\pi$
$233$	21.3006	+	12.2979i	1.39545	+	0.805663i	0.401538	+	0.915843i	$0.368476\pi$
$234$	0.854638	+	1.48028i	0.0558694	+	0.0967687i
$235$	11.8660	+	2.94828i	0.774055	+	0.192325i
$236$	5.86603			0.381846
$237$	−6.13005	+	3.53919i	−0.398190	+	0.229895i
$238$	−11.6501	+	6.72620i	−0.755165	+	0.435995i
$239$	−0.156755			−0.0101397			−0.00506983	−	0.999987i	$-0.501614\pi$
$239$	−0.156755			−0.0101397			−0.00506983	+	0.999987i	$0.501614\pi$
$240$	2.17009	+	0.539189i	0.140078	+	0.0348045i
$241$	12.7968	+	22.1647i	0.824313	+	1.42775i	0.902443	+	0.430809i	$0.141772\pi$
$241$	12.7968	+	22.1647i	0.824313	+	1.42775i	−0.0781302	+	0.996943i	$0.524895\pi$
$242$	0.135754	+	0.0783777i	0.00872661	+	0.00503831i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	6.92522	−	11.9948i	0.443342	−	0.767890i
$245$	8.89528	+	8.57610i	0.568299	+	0.547907i
$246$	11.9288			0.760553
$247$	5.49075	+	5.03612i	0.349368	+	0.320440i
$248$			1.07838i			0.0684771i
$249$	2.34017	−	4.05330i	0.148302	−	0.256867i
$250$	10.6247	−	3.48085i	0.671963	−	0.220148i
$251$	5.32684	+	9.22636i	0.336227	+	0.582363i	0.983720	−	0.179709i	$-0.0575156\pi$
$251$	5.32684	+	9.22636i	0.336227	+	0.582363i	−0.647493	+	0.762072i	$0.724182\pi$
$252$	−3.06503	−	1.76959i	−0.193079	−	0.111474i
$253$	−24.4952	+	14.1423i	−1.54000	+	0.889118i
$254$	18.6092			1.16764
$255$	2.04945	−	8.24846i	0.128341	−	0.516539i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−16.7899	+	9.69368i	−1.04733	+	0.604675i	−0.921900	−	0.387428i	$-0.873364\pi$
$257$	−16.7899	+	9.69368i	−1.04733	+	0.604675i	−0.125428	+	0.992103i	$0.540030\pi$
$258$			5.07838i			0.316166i
$259$	16.6670			1.03564
$260$	−1.05649	−	3.67314i	−0.0655207	−	0.227798i
$261$	3.97887	−	6.89160i	0.246286	−	0.426580i
$262$	6.56573	−	3.79072i	0.405632	−	0.234192i
$263$	−26.5877	−	15.3504i	−1.63947	−	0.946548i	−0.981016	−	0.193927i	$-0.937878\pi$
$263$	−26.5877	−	15.3504i	−1.63947	−	0.946548i	−0.658454	−	0.752621i	$-0.728789\pi$
$264$	−1.67009	+	2.89267i	−0.102787	+	0.178032i
$265$	−27.1483	−	6.74539i	−1.66771	−	0.414366i
$266$	−15.0597	−	3.34612i	−0.923370	−	0.205164i
$267$			9.32457i			0.570655i
$268$	−7.82551	−	4.51806i	−0.478019	−	0.275984i
$269$	−14.1334	+	24.4797i	−0.861726	+	1.49255i	0.00853563	+	0.999964i	$0.497283\pi$
$269$	−14.1334	+	24.4797i	−0.861726	+	1.49255i	−0.870262	+	0.492590i	$0.836050\pi$
$270$	2.14894	−	0.618092i	0.130781	−	0.0376159i
$271$	5.80817	−	10.0600i	0.352821	−	0.611104i	−0.633921	−	0.773398i	$-0.718556\pi$
$271$	5.80817	−	10.0600i	0.352821	−	0.611104i	0.986743	+	0.162293i	$0.0518890\pi$
$272$	−3.29175	+	1.90049i	−0.199592	+	0.115234i
$273$			6.04945i			0.366129i
$274$	−11.4186			−0.689820
$275$	0.610003	+	16.6897i	0.0367846	+	1.00643i
$276$	−4.23400	−	7.33350i	−0.254857	−	0.441425i
$277$		−	26.1750i		−	1.57270i	−0.617779	−	0.786352i	$-0.711967\pi$
$277$		−	26.1750i		−	1.57270i	0.617779	−	0.786352i	$-0.288033\pi$
$278$			3.60197i			0.216032i
$279$	0.539189	+	0.933903i	0.0322804	+	0.0559113i
$280$	5.69723	+	5.49280i	0.340475	+	0.328258i
$281$	−12.0139	−	20.8086i	−0.716686	−	1.24134i	−0.962305	−	0.271971i	$-0.912325\pi$
$281$	−12.0139	−	20.8086i	−0.716686	−	1.24134i	0.245619	−	0.969366i	$-0.421009\pi$
$282$	−4.73543	−	2.73400i	−0.281991	−	0.162807i
$283$	17.5920	+	10.1568i	1.04574	+	0.603756i	0.921453	−	0.388490i	$-0.127003\pi$
$283$	17.5920	+	10.1568i	1.04574	+	0.603756i	0.124284	+	0.992247i	$0.460337\pi$
$284$	8.09171			0.480155
$285$	8.12588	−	5.38239i	0.481335	−	0.318825i
$286$	5.70928			0.337597
$287$	36.5621	+	21.1092i	2.15819	+	1.24603i
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	−1.27626	−	2.21055i	−0.0750741	−	0.130032i
$290$	−12.3504	+	12.8100i	−0.725239	+	0.752230i
$291$	−2.92522	−	5.06662i	−0.171479	−	0.297011i
$292$		−	5.90829i		−	0.345757i
$293$		−	5.32457i		−	0.311065i	−0.987831	−	0.155532i	$-0.950291\pi$
$293$		−	5.32457i		−	0.311065i	0.987831	−	0.155532i	$-0.0497093\pi$
$294$	−2.76293	−	4.78553i	−0.161137	−	0.279098i
$295$	−12.6058	+	3.62575i	−0.733937	+	0.211099i
$296$	4.70928			0.273721
$297$			3.34017i			0.193816i
$298$	−8.91825	+	5.14896i	−0.516621	+	0.298271i
$299$	−7.23707	+	12.5350i	−0.418531	+	0.724916i
$300$	−4.99666	+	0.182626i	−0.288483	+	0.0105439i
$301$	−8.98667	+	15.5654i	−0.517983	+	0.897173i
$302$	−4.06681	−	2.34797i	−0.234018	−	0.135111i
$303$			8.65368i			0.497141i
$304$	−4.25513	−	0.945448i	−0.244048	−	0.0542251i
$305$	−7.46800	+	30.0566i	−0.427616	+	1.72104i
$306$	−1.90049	+	3.29175i	−0.108644	+	0.188177i
$307$	3.18301	+	1.83771i	0.181664	+	0.104884i	0.588074	−	0.808807i	$-0.299886\pi$
$307$	3.18301	+	1.83771i	0.181664	+	0.104884i	−0.406410	+	0.913691i	$0.633220\pi$
$308$	−10.2377	+	5.91075i	−0.583348	+	0.336796i
$309$	0.375768	−	0.650849i	0.0213767	−	0.0370255i
$310$	−0.666537	−	2.31737i	−0.0378567	−	0.131618i
$311$	−13.7321			−0.778674			−0.389337	−	0.921095i	$-0.627296\pi$
$311$	−13.7321			−0.778674			−0.389337	+	0.921095i	$0.627296\pi$
$312$			1.70928i			0.0967687i
$313$	15.5384	−	8.97107i	0.878279	−	0.507075i	0.00818874	−	0.999966i	$-0.497393\pi$
$313$	15.5384	−	8.97107i	0.878279	−	0.507075i	0.870091	+	0.492892i	$0.164060\pi$
$314$	5.25872	+	9.10838i	0.296767	+	0.514015i
$315$	7.68035	+	1.90829i	0.432738	+	0.107520i
$316$	−7.07838			−0.398190
$317$	−6.35055	+	3.66649i	−0.356682	+	0.205931i	−0.667625	−	0.744498i	$-0.732689\pi$
$317$	−6.35055	+	3.66649i	−0.356682	+	0.205931i	0.310942	+	0.950429i	$0.399355\pi$
$318$	10.8342	+	6.25513i	0.607552	+	0.350770i
$319$	−13.2901	−	23.0192i	−0.744103	−	1.28883i
$320$	1.60976	+	1.55199i	0.0899881	+	0.0867591i
$321$	4.91189	−	8.50763i	0.274155	−	0.474850i
$322$		−	29.9698i		−	1.67015i
$323$	−3.59363	+	16.1737i	−0.199955	+	0.899928i
$324$	−1.00000			−0.0555556
$325$	4.54067	+	7.24036i	0.251871	+	0.401623i
$326$	8.38962	−	14.5313i	0.464658	−	0.804812i
$327$	−6.79867	+	3.92522i	−0.375968	+	0.217065i
$328$	10.3307	+	5.96441i	0.570415	+	0.329329i
$329$	−9.67614	−	16.7596i	−0.533463	−	0.923985i
$330$	1.80098	−	7.24846i	0.0991409	−	0.399015i
$331$	21.4813			1.18072			0.590360	−	0.807140i	$-0.298986\pi$
$331$	21.4813			1.18072			0.590360	+	0.807140i	$0.298986\pi$
$332$	4.05330	−	2.34017i	0.222454	−	0.128434i
$333$	4.07835	−	2.35464i	0.223492	−	0.129033i
$334$	−11.6042			−0.634956
$335$	19.6092	+	4.87217i	1.07136	+	0.266195i
$336$	−1.76959	−	3.06503i	−0.0965393	−	0.167211i
$337$	−17.6151	−	10.1701i	−0.959556	−	0.554000i	−0.0635196	−	0.997981i	$-0.520233\pi$
$337$	−17.6151	−	10.1701i	−0.959556	−	0.554000i	−0.896036	+	0.443981i	$0.853566\pi$
$338$	−8.72813	+	5.03919i	−0.474748	+	0.274096i
$339$	3.99220	−	6.91469i	0.216827	−	0.375555i
$340$	5.89911	−	6.11866i	0.319924	−	0.331831i
$341$	3.60197			0.195058
$342$	−4.15777	+	1.30878i	−0.224827	+	0.0707709i
$343$			5.21727i			0.281706i
$344$	−2.53919	+	4.39800i	−0.136904	+	0.237124i
$345$	13.6314	+	13.1423i	0.733890	+	0.707557i
$346$	4.44994	+	7.70752i	0.239230	+	0.414359i
$347$	−7.97084	−	4.60197i	−0.427897	−	0.247047i	0.270553	−	0.962705i	$-0.412793\pi$
$347$	−7.97084	−	4.60197i	−0.427897	−	0.247047i	−0.698450	+	0.715658i	$0.746127\pi$
$348$	6.89160	−	3.97887i	0.369429	−	0.213290i
$349$	−8.24846			−0.441530			−0.220765	−	0.975327i	$-0.570855\pi$
$349$	−8.24846			−0.441530			−0.220765	+	0.975327i	$0.570855\pi$
$350$	−15.6381	−	8.28231i	−0.835891	−	0.442708i
$351$	0.854638	+	1.48028i	0.0456172	+	0.0790113i
$352$	−2.89267	+	1.67009i	−0.154180	+	0.0890159i
$353$		−	6.24005i		−	0.332125i	−0.986115	−	0.166062i	$-0.946895\pi$
$353$		−	6.24005i		−	0.332125i	0.986115	−	0.166062i	$-0.0531053\pi$
$354$	5.86603			0.311776
$355$	−17.3886	+	5.00142i	−0.922893	+	0.265448i
$356$	−4.66229	+	8.07532i	−0.247101	+	0.427991i
$357$	−11.6501	+	6.72620i	−0.616590	+	0.355988i
$358$	−18.9312	−	10.9299i	−1.00055	−	0.577665i
$359$	0.401626	−	0.695636i	0.0211970	−	0.0367143i	−0.855232	−	0.518245i	$-0.826586\pi$
$359$	0.401626	−	0.695636i	0.0211970	−	0.0367143i	0.876429	+	0.481531i	$0.159919\pi$
$360$	2.17009	+	0.539189i	0.114374	+	0.0284177i
$361$	−15.5742	+	10.8833i	−0.819693	+	0.572803i
$362$			5.32684i			0.279973i
$363$	0.135754	+	0.0783777i	0.00712525	+	0.00411376i
$364$	−3.02472	+	5.23898i	−0.158539	+	0.274597i
$365$	3.65187	+	12.6966i	0.191147	+	0.664570i
$366$	6.92522	−	11.9948i	0.361987	−	0.626980i
$367$	−2.54265	+	1.46800i	−0.132725	+	0.0766289i	−0.564892	−	0.825165i	$-0.691082\pi$
$367$	−2.54265	+	1.46800i	−0.132725	+	0.0766289i	0.432167	+	0.901793i	$0.357749\pi$
$368$		−	8.46800i		−	0.441425i
$369$	11.9288			0.620989
$370$	−10.1200	+	2.91077i	−0.526112	+	0.151323i
$371$	22.1381	+	38.3443i	1.14935	+	1.99074i
$372$			1.07838i			0.0559113i
$373$			25.5152i			1.32113i	0.750771	+	0.660563i	$0.229682\pi$
$373$			25.5152i			1.32113i	−0.750771	+	0.660563i	$0.770318\pi$
$374$	6.34797	+	10.9950i	0.328246	+	0.568538i
$375$	10.6247	−	3.48085i	0.548656	−	0.179750i
$376$	−2.73400	−	4.73543i	−0.140995	−	0.244211i
$377$	−11.7797	−	6.80098i	−0.606683	−	0.350269i
$378$	−3.06503	−	1.76959i	−0.157648	−	0.0910181i
$379$	26.6537			1.36911			0.684554	−	0.728962i	$-0.259997\pi$
$379$	26.6537			1.36911			0.684554	+	0.728962i	$0.259997\pi$
$380$	9.72841	−	0.598347i	0.499057	−	0.0306946i
$381$	18.6092			0.953376
$382$	7.78891	+	4.49693i	0.398515	+	0.230083i
$383$	8.35837	+	4.82571i	0.427093	+	0.246582i	0.698107	−	0.715993i	$-0.254026\pi$
$383$	8.35837	+	4.82571i	0.427093	+	0.246582i	−0.271015	+	0.962575i	$0.587359\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	18.3469	−	19.0297i	0.935045	−	0.969845i
$386$	−1.16649	−	2.02042i	−0.0593729	−	0.102837i
$387$			5.07838i			0.258148i
$388$		−	5.85043i		−	0.297011i
$389$	−10.2407	−	17.7374i	−0.519222	−	0.899319i	−0.999750	−	0.0223401i	$-0.992888\pi$
$389$	−10.2407	−	17.7374i	−0.519222	−	0.899319i	0.480528	−	0.876979i	$-0.340445\pi$
$390$	−1.05649	−	3.67314i	−0.0534974	−	0.185997i
$391$	−32.1867			−1.62775
$392$		−	5.52586i		−	0.279098i
$393$	6.56573	−	3.79072i	0.331197	−	0.191217i
$394$	12.0428	−	20.8587i	0.606707	−	1.05085i
$395$	15.2110	−	4.37509i	0.765351	−	0.220135i
$396$	−1.67009	+	2.89267i	−0.0839250	+	0.145362i
$397$	0.296562	+	0.171220i	0.0148840	+	0.00859330i	0.507424	−	0.861697i	$-0.330598\pi$
$397$	0.296562	+	0.171220i	0.0148840	+	0.00859330i	−0.492540	+	0.870290i	$0.663931\pi$
$398$			1.30406i			0.0653664i
$399$	−15.0597	−	3.34612i	−0.753928	−	0.167515i
$400$	−4.41855	−	2.34017i	−0.220928	−	0.117009i
$401$	−4.06278	+	7.03694i	−0.202886	+	0.351408i	−0.949457	−	0.313897i	$-0.898365\pi$
$401$	−4.06278	+	7.03694i	−0.202886	+	0.351408i	0.746571	+	0.665305i	$0.231699\pi$
$402$	−7.82551	−	4.51806i	−0.390301	−	0.225340i
$403$	1.59630	−	0.921622i	0.0795172	−	0.0459093i
$404$	−4.32684	+	7.49431i	−0.215268	+	0.372856i
$405$	2.14894	−	0.618092i	0.106782	−	0.0307132i
$406$	28.1639			1.39775
$407$		−	15.7298i		−	0.779697i
$408$	−3.29175	+	1.90049i	−0.162966	+	0.0940884i
$409$	6.03725	+	10.4568i	0.298523	+	0.517057i	0.975798	−	0.218673i	$-0.0701728\pi$
$409$	6.03725	+	10.4568i	0.298523	+	0.517057i	−0.677275	+	0.735730i	$0.736839\pi$
$410$	−25.8865	−	6.43188i	−1.27845	−	0.317648i
$411$	−11.4186			−0.563236
$412$	0.650849	−	0.375768i	0.0320650	−	0.0185128i
$413$	17.9795	+	10.3805i	0.884716	+	0.510791i
$414$	−4.23400	−	7.33350i	−0.208090	−	0.360422i
$415$	−7.26387	+	7.53421i	−0.356569	+	0.369840i
$416$	−0.854638	+	1.48028i	−0.0419021	+	0.0725765i
$417$			3.60197i			0.176389i
$418$	−3.15796	+	14.2129i	−0.154461	+	0.695174i
$419$	15.2290			0.743985			0.371992	−	0.928236i	$-0.378675\pi$
$419$	15.2290			0.743985			0.371992	+	0.928236i	$0.378675\pi$
$420$	5.69723	+	5.49280i	0.277996	+	0.268021i
$421$	−4.80458	+	8.32177i	−0.234161	+	0.405578i	−0.959028	−	0.283310i	$-0.908568\pi$
$421$	−4.80458	+	8.32177i	−0.234161	+	0.405578i	0.724868	+	0.688888i	$0.241901\pi$
$422$	−6.04867	+	3.49220i	−0.294445	+	0.169998i
$423$	−4.73543	−	2.73400i	−0.230244	−	0.132932i
$424$	6.25513	+	10.8342i	0.303776	+	0.526155i
$425$	−8.89496	+	16.7948i	−0.431469	+	0.814669i
$426$	8.09171			0.392045
$427$	42.4520	−	24.5096i	2.05439	−	1.18611i
$428$	8.50763	−	4.91189i	0.411232	−	0.237425i
$429$	5.70928			0.275646
$430$	2.73820	−	11.0205i	0.132048	−	0.531457i
$431$	6.62730	+	11.4788i	0.319226	+	0.552916i	0.980327	−	0.197381i	$-0.0632438\pi$
$431$	6.62730	+	11.4788i	0.319226	+	0.552916i	−0.661101	+	0.750297i	$0.729910\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	13.2965	−	7.67675i	0.638990	−	0.368921i	−0.145235	−	0.989397i	$-0.546394\pi$
$433$	13.2965	−	7.67675i	0.638990	−	0.368921i	0.784225	+	0.620476i	$0.213061\pi$
$434$	−1.90829	+	3.30526i	−0.0916009	+	0.158657i
$435$	−12.3504	+	12.8100i	−0.592155	+	0.614193i
$436$	−7.85043			−0.375968
$437$	−27.2020	−	24.9497i	−1.30125	−	1.19350i
$438$		−	5.90829i		−	0.282309i
$439$	10.4263	−	18.0590i	0.497623	−	0.861908i	−0.502374	−	0.864651i	$-0.667540\pi$
$439$	10.4263	−	18.0590i	0.497623	−	0.861908i	0.999996	+	0.00274309i	$0.000873154\pi$
$440$	5.18393	−	5.37686i	0.247134	−	0.256332i
$441$	−2.76293	−	4.78553i	−0.131568	−	0.227883i
$442$	5.62651	+	3.24846i	0.267626	+	0.154514i
$443$	−22.0694	+	12.7418i	−1.04855	+	0.605381i	−0.922243	−	0.386610i	$-0.873646\pi$
$443$	−22.0694	+	12.7418i	−1.04855	+	0.605381i	−0.126308	+	0.991991i	$0.540313\pi$
$444$	4.70928			0.223492
$445$	5.02771	−	20.2351i	0.238336	−	0.959237i
$446$	5.00667	+	8.67180i	0.237072	+	0.410622i
$447$	−8.91825	+	5.14896i	−0.421819	+	0.243537i
$448$		−	3.53919i		−	0.167211i
$449$	19.1412			0.903327			0.451664	−	0.892188i	$-0.350831\pi$
$449$	19.1412			0.903327			0.451664	+	0.892188i	$0.350831\pi$
$450$	−4.99666	+	0.182626i	−0.235545	+	0.00860908i
$451$	19.9221	−	34.5062i	0.938097	−	1.62483i
$452$	6.91469	−	3.99220i	0.325240	−	0.187777i
$453$	−4.06681	−	2.34797i	−0.191075	−	0.110317i
$454$	−7.12423	+	12.3395i	−0.334357	+	0.579123i
$455$	3.26180	−	13.1278i	0.152915	−	0.615442i
$456$	−4.25513	−	0.945448i	−0.199265	−	0.0442746i
$457$		−	32.0216i		−	1.49791i	−0.662623	−	0.748953i	$-0.730557\pi$
$457$		−	32.0216i		−	1.49791i	0.662623	−	0.748953i	$-0.269443\pi$
$458$	13.7331	+	7.92881i	0.641706	+	0.370489i
$459$	−1.90049	+	3.29175i	−0.0887074	+	0.153646i
$460$	5.23400	+	18.1973i	0.244037	+	0.848452i
$461$	−20.6381	+	35.7462i	−0.961211	+	1.66487i	−0.241745	+	0.970340i	$0.577720\pi$
$461$	−20.6381	+	35.7462i	−0.961211	+	1.66487i	−0.719466	+	0.694527i	$0.755614\pi$
$462$	−10.2377	+	5.91075i	−0.476302	+	0.274993i
$463$			8.16168i			0.379305i	0.981851	+	0.189653i	$0.0607362\pi$
$463$			8.16168i			0.379305i	−0.981851	+	0.189653i	$0.939264\pi$
$464$	7.95774			0.369429
$465$	−0.666537	−	2.31737i	−0.0309099	−	0.107466i
$466$	12.2979	+	21.3006i	0.569690	+	0.986732i
$467$		−	17.8238i		−	0.824786i	−0.911006	−	0.412393i	$-0.864693\pi$
$467$		−	17.8238i		−	0.824786i	0.911006	−	0.412393i	$-0.135307\pi$
$468$			1.70928i			0.0790113i
$469$	−15.9903	−	27.6959i	−0.738362	−	1.27888i
$470$	8.80214	+	8.48630i	0.406013	+	0.391444i
$471$	5.25872	+	9.10838i	0.242309	+	0.419692i
$472$	5.08013	+	2.93302i	0.233832	+	0.135003i
$473$	14.6901	+	8.48133i	0.675451	+	0.389972i
$474$	−7.07838			−0.325121
$475$	−20.5360	+	7.29887i	−0.942255	+	0.334895i
$476$	−13.4524			−0.616590
$477$	10.8342	+	6.25513i	0.496064	+	0.286403i
$478$	−0.135754	−	0.0783777i	−0.00620925	−	0.00358491i
$479$	−11.5694	−	20.0389i	−0.528621	−	0.915599i	−0.999443	−	0.0333707i	$-0.989376\pi$
$479$	−11.5694	−	20.0389i	−0.528621	−	0.915599i	0.470822	−	0.882228i	$-0.343958\pi$
$480$	1.60976	+	1.55199i	0.0734750	+	0.0708385i
$481$	−4.02472	−	6.97103i	−0.183512	−	0.317851i
$482$			25.5936i			1.16575i
$483$		−	29.9698i		−	1.36368i
$484$	0.0783777	+	0.135754i	0.00356262	+	0.00617065i
$485$	3.61611	+	12.5723i	0.164199	+	0.570877i
$486$	−1.00000			−0.0453609
$487$		−	10.8855i		−	0.493269i	−0.969109	−	0.246635i	$-0.920675\pi$
$487$		−	10.8855i		−	0.493269i	0.969109	−	0.246635i	$-0.0793248\pi$
$488$	11.9948	−	6.92522i	0.542980	−	0.313490i
$489$	8.38962	−	14.5313i	0.379392	−	0.657126i
$490$	3.41549	+	11.8748i	0.154296	+	0.536447i
$491$	−15.3732	+	26.6272i	−0.693784	+	1.20167i	0.276805	+	0.960926i	$0.410724\pi$
$491$	−15.3732	+	26.6272i	−0.693784	+	1.20167i	−0.970589	+	0.240743i	$0.922609\pi$
$492$	10.3307	+	5.96441i	0.465742	+	0.268896i
$493$		−	30.2472i		−	1.36227i
$494$	2.23707	+	7.10678i	0.100651	+	0.319749i
$495$	1.80098	−	7.24846i	0.0809482	−	0.325794i
$496$	−0.539189	+	0.933903i	−0.0242103	+	0.0419335i
$497$	24.8013	+	14.3190i	1.11249	+	0.642297i
$498$	4.05330	−	2.34017i	0.181633	−	0.104866i
$499$	−3.29545	+	5.70789i	−0.147525	+	0.255520i	−0.930312	−	0.366769i	$-0.880464\pi$
$499$	−3.29545	+	5.70789i	−0.147525	+	0.255520i	0.782787	+	0.622289i	$0.213797\pi$
$500$	10.9417	+	2.29783i	0.489326	+	0.102762i
$501$	−11.6042			−0.518439
$502$			10.6537i			0.475497i
$503$	−11.1192	+	6.41968i	−0.495781	+	0.286240i	−0.726970	−	0.686669i	$-0.759072\pi$
$503$	−11.1192	+	6.41968i	−0.495781	+	0.286240i	0.231188	+	0.972909i	$0.425739\pi$
$504$	−1.76959	−	3.06503i	−0.0788240	−	0.136527i
$505$	4.66597	−	18.7792i	0.207633	−	0.835665i
$506$	−28.2846			−1.25740
$507$	−8.72813	+	5.03919i	−0.387630	+	0.223798i
$508$	16.1160	+	9.30458i	0.715032	+	0.412824i
$509$	−11.4319	−	19.8006i	−0.506709	−	0.877646i	−0.999970	−	0.00776458i	$-0.997528\pi$
$509$	−11.4319	−	19.8006i	−0.506709	−	0.877646i	0.493261	−	0.869882i	$-0.335805\pi$
$510$	5.89911	−	6.11866i	0.261217	−	0.270939i
$511$	10.4553	−	18.1091i	0.462514	−	0.801098i
$512$		−	1.00000i		−	0.0441942i
$513$	−4.15777	+	1.30878i	−0.183570	+	0.0577842i
$514$	−19.3874			−0.855140
$515$	−1.16638	+	1.20979i	−0.0513968	+	0.0533097i
$516$	−2.53919	+	4.39800i	−0.111782	+	0.193611i
$517$	−15.8171	+	9.13203i	−0.695637	+	0.401626i
$518$	14.4341	+	8.33351i	0.634196	+	0.366153i
$519$	4.44994	+	7.70752i	0.195331	+	0.338323i
$520$	0.921622	−	3.70928i	0.0404158	−	0.162662i
$521$	3.34632			0.146605			0.0733024	−	0.997310i	$-0.476646\pi$
$521$	3.34632			0.146605			0.0733024	+	0.997310i	$0.476646\pi$
$522$	6.89160	−	3.97887i	0.301637	−	0.174150i
$523$	−38.8290	+	22.4179i	−1.69787	+	0.980268i	−0.750101	+	0.661324i	$0.769995\pi$
$523$	−38.8290	+	22.4179i	−1.69787	+	0.980268i	−0.947773	+	0.318944i	$0.896672\pi$
$524$	7.58145			0.331197
$525$	−15.6381	−	8.28231i	−0.682502	−	0.361470i
$526$	−15.3504	−	26.5877i	−0.669311	−	1.15928i
$527$	3.54975	+	2.04945i	0.154629	+	0.0892754i
$528$	−2.89267	+	1.67009i	−0.125888	+	0.0726812i
$529$	24.3535	−	42.1815i	1.05885	−	1.83398i
$530$	−20.1385	−	19.4159i	−0.874759	−	0.843371i
$531$	5.86603			0.254564
$532$	−11.3690	−	10.4277i	−0.492910	−	0.452097i
$533$		−	20.3896i		−	0.883173i
$534$	−4.66229	+	8.07532i	−0.201757	+	0.349453i
$535$	−15.2464	+	15.8139i	−0.659161	+	0.683693i
$536$	−4.51806	−	7.82551i	−0.195150	−	0.338010i
$537$	−18.9312	−	10.9299i	−0.816942	−	0.471662i
$538$	−24.4797	+	14.1334i	−1.05539	+	0.609332i
$539$	−18.4573			−0.795013
$540$	2.17009	+	0.539189i	0.0933857	+	0.0232030i
$541$	3.98440	+	6.90119i	0.171303	+	0.296705i	0.938876	−	0.344257i	$-0.111869\pi$
$541$	3.98440	+	6.90119i	0.171303	+	0.296705i	−0.767573	+	0.640962i	$0.778536\pi$
$542$	10.0600	−	5.80817i	0.432116	−	0.249482i
$543$			5.32684i			0.228597i
$544$	−3.80098			−0.162966
$545$	16.8701	−	4.85229i	0.722638	−	0.207849i
$546$	−3.02472	+	5.23898i	−0.129446	+	0.224207i
$547$	17.2203	−	9.94214i	0.736287	−	0.425095i	−0.0844310	−	0.996429i	$-0.526907\pi$
$547$	17.2203	−	9.94214i	0.736287	−	0.425095i	0.820718	+	0.571334i	$0.193574\pi$
$548$	−9.88875	−	5.70928i	−0.422427	−	0.243888i
$549$	6.92522	−	11.9948i	0.295561	−	0.511927i
$550$	−7.81658	+	14.7587i	−0.333300	+	0.629314i
$551$	23.4463	−	25.5629i	0.998844	−	1.08901i
$552$		−	8.46800i		−	0.360422i
$553$	−21.6954	−	12.5259i	−0.922583	−	0.532654i
$554$	13.0875	−	22.6682i	0.556035	−	0.963080i
$555$	−10.1200	+	2.91077i	−0.429569	+	0.123555i
$556$	−1.80098	+	3.11940i	−0.0763787	+	0.132292i
$557$	−17.1356	+	9.89322i	−0.726057	+	0.419189i	−0.816978	−	0.576669i	$-0.804352\pi$
$557$	−17.1356	+	9.89322i	−0.726057	+	0.419189i	0.0909212	+	0.995858i	$0.471019\pi$
$558$			1.07838i			0.0456514i
$559$	8.68035			0.367140
$560$	2.18754	+	7.60552i	0.0924406	+	0.321392i
$561$	6.34797	+	10.9950i	0.268012	+	0.464210i
$562$		−	24.0277i		−	1.01355i
$563$		−	32.6681i		−	1.37679i	−0.725334	−	0.688397i	$-0.758315\pi$
$563$		−	32.6681i		−	1.37679i	0.725334	−	0.688397i	$-0.241685\pi$
$564$	−2.73400	−	4.73543i	−0.115122	−	0.199397i
$565$	−12.3917	+	12.8529i	−0.521325	+	0.540727i
$566$	10.1568	+	17.5920i	0.426920	+	0.739448i
$567$	−3.06503	−	1.76959i	−0.128719	−	0.0743160i
$568$	7.00763	+	4.04585i	0.294033	+	0.169760i
$569$	−11.0650			−0.463871			−0.231935	−	0.972731i	$-0.574506\pi$
$569$	−11.0650			−0.463871			−0.231935	+	0.972731i	$0.574506\pi$
$570$	9.72841	−	0.598347i	0.407478	−	0.0250620i
$571$	−30.4040			−1.27237			−0.636184	−	0.771538i	$-0.719488\pi$
$571$	−30.4040			−1.27237			−0.636184	+	0.771538i	$0.719488\pi$
$572$	4.94438	+	2.85464i	0.206735	+	0.119358i
$573$	7.78891	+	4.49693i	0.325386	+	0.187862i
$574$	21.1092	+	36.5621i	0.881079	+	1.52607i
$575$	−22.4952	−	35.8698i	−0.938113	−	1.49587i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$			15.0010i			0.624502i	0.950000	+	0.312251i	$0.101083\pi$
$577$			15.0010i			0.624502i	−0.950000	+	0.312251i	$0.898917\pi$
$578$		−	2.55252i		−	0.106171i
$579$	−1.16649	−	2.02042i	−0.0484778	−	0.0839660i
$580$	−17.1007	+	4.91862i	−0.710070	+	0.204234i
$581$	16.5646			0.687217
$582$		−	5.85043i		−	0.242508i
$583$	36.1881	−	20.8932i	1.49876	−	0.865309i
$584$	2.95415	−	5.11673i	0.122243	−	0.211732i
$585$	−1.05649	−	3.67314i	−0.0436805	−	0.151866i
$586$	2.66229	−	4.61122i	0.109978	−	0.190488i
$587$	−0.566107	−	0.326842i	−0.0233657	−	0.0134902i	0.488272	−	0.872692i	$-0.337628\pi$
$587$	−0.566107	−	0.326842i	−0.0233657	−	0.0134902i	−0.511637	+	0.859201i	$0.670961\pi$
$588$		−	5.52586i		−	0.227883i
$589$	1.41136	+	4.48365i	0.0581542	+	0.184746i
$590$	−12.7298	−	3.16290i	−0.524077	−	0.130214i
$591$	12.0428	−	20.8587i	0.495374	−	0.858013i
$592$	4.07835	+	2.35464i	0.167619	+	0.0967750i
$593$	36.3095	−	20.9633i	1.49105	−	0.860858i	0.491103	−	0.871102i	$-0.336594\pi$
$593$	36.3095	−	20.9633i	1.49105	−	0.860858i	0.999948	+	0.0102432i	$0.00326056\pi$
$594$	−1.67009	+	2.89267i	−0.0685245	+	0.118688i
$595$	28.9085	−	8.31482i	1.18513	−	0.340874i
$596$	−10.2979			−0.421819
$597$			1.30406i			0.0533714i
$598$	−12.5350	+	7.23707i	−0.512593	+	0.295946i
$599$	−8.45722	−	14.6483i	−0.345553	−	0.598515i	0.639901	−	0.768457i	$-0.278975\pi$
$599$	−8.45722	−	14.6483i	−0.345553	−	0.598515i	−0.985454	+	0.169942i	$0.945642\pi$
$600$	−4.41855	−	2.34017i	−0.180387	−	0.0955372i
$601$	−4.42243			−0.180395			−0.0901973	−	0.995924i	$-0.528750\pi$
$601$	−4.42243			−0.180395			−0.0901973	+	0.995924i	$0.528750\pi$
$602$	−15.5654	+	8.98667i	−0.634397	+	0.366269i
$603$	−7.82551	−	4.51806i	−0.318679	−	0.183990i
$604$	−2.34797	−	4.06681i	−0.0955376	−	0.165476i
$605$	−0.252338	−	0.243284i	−0.0102590	−	0.00989089i
$606$	−4.32684	+	7.49431i	−0.175766	+	0.304436i
$607$			15.6030i			0.633307i	0.948541	+	0.316653i	$0.102559\pi$
$607$			15.6030i			0.633307i	−0.948541	+	0.316653i	$0.897441\pi$
$608$	−3.21233	−	2.94635i	−0.130277	−	0.119490i
$609$	28.1639			1.14126
$610$	−21.4958	+	22.2958i	−0.870339	+	0.902731i
$611$	−4.67316	+	8.09415i	−0.189056	+	0.327454i
$612$	−3.29175	+	1.90049i	−0.133061	+	0.0768228i
$613$	3.51225	+	2.02780i	0.141858	+	0.0819019i	0.569249	−	0.822165i	$-0.307234\pi$
$613$	3.51225	+	2.02780i	0.141858	+	0.0819019i	−0.427391	+	0.904067i	$0.640567\pi$
$614$	1.83771	+	3.18301i	0.0741640	+	0.128456i
$615$	−25.8865	−	6.43188i	−1.04385	−	0.259359i
$616$	−11.8215			−0.476302
$617$	17.4062	−	10.0494i	0.700745	−	0.404576i	−0.106880	−	0.994272i	$-0.534086\pi$
$617$	17.4062	−	10.0494i	0.700745	−	0.404576i	0.807625	+	0.589696i	$0.200753\pi$
$618$	0.650849	−	0.375768i	0.0261810	−	0.0151156i
$619$	17.0917			0.686974			0.343487	−	0.939157i	$-0.388392\pi$
$619$	17.0917			0.686974			0.343487	+	0.939157i	$0.388392\pi$
$620$	0.581449	−	2.34017i	0.0233516	−	0.0939836i
$621$	−4.23400	−	7.33350i	−0.169905	−	0.294283i
$622$	−11.8923	−	6.86603i	−0.476838	−	0.275303i
$623$	−28.5801	+	16.5007i	−1.14504	+	0.661087i
$624$	−0.854638	+	1.48028i	−0.0342129	+	0.0592585i
$625$	−24.9333	+	1.82504i	−0.997332	+	0.0730017i
$626$	17.9421			0.717112
$627$	−3.15796	+	14.2129i	−0.126117	+	0.567607i
$628$			10.5174i			0.419692i
$629$	8.94994	−	15.5018i	0.356857	−	0.618095i
$630$	5.69723	+	5.49280i	0.226983	+	0.218838i
$631$	−5.80652	−	10.0572i	−0.231154	−	0.400370i	0.726994	−	0.686644i	$-0.240917\pi$
$631$	−5.80652	−	10.0572i	−0.231154	−	0.400370i	−0.958148	+	0.286274i	$0.907583\pi$
$632$	−6.13005	−	3.53919i	−0.243840	−	0.140781i
$633$	−6.04867	+	3.49220i	−0.240413	+	0.138803i
$634$	−7.33299			−0.291230
$635$	−40.3835	−	10.0338i	−1.60257	−	0.398181i
$636$	6.25513	+	10.8342i	0.248032	+	0.429604i
$637$	−8.17979	+	4.72261i	−0.324095	+	0.187116i
$638$		−	26.5802i		−	1.05232i
$639$	8.09171			0.320103
$640$	0.618092	+	2.14894i	0.0244322	+	0.0849445i
$641$	−3.14116	+	5.44064i	−0.124068	+	0.214893i	−0.921368	−	0.388691i	$-0.872928\pi$
$641$	−3.14116	+	5.44064i	−0.124068	+	0.214893i	0.797300	+	0.603583i	$0.206261\pi$
$642$	8.50763	−	4.91189i	0.335770	−	0.193857i
$643$	−11.3358	−	6.54472i	−0.447040	−	0.258099i	0.259539	−	0.965733i	$-0.416429\pi$
$643$	−11.3358	−	6.54472i	−0.447040	−	0.258099i	−0.706579	+	0.707634i	$0.749763\pi$
$644$	14.9849	−	25.9546i	0.590489	−	1.02276i
$645$	2.73820	−	11.0205i	0.107817	−	0.433933i
$646$	−11.1990	+	12.2100i	−0.440619	+	0.480396i
$647$			7.89496i			0.310383i	0.987884	+	0.155191i	$0.0495994\pi$
$647$			7.89496i			0.310383i	−0.987884	+	0.155191i	$0.950401\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	9.79678	−	16.9685i	0.384557	−	0.666073i
$650$	0.312158	+	8.54067i	0.0122439	+	0.334993i
$651$	−1.90829	+	3.30526i	−0.0747918	+	0.129543i
$652$	14.5313	−	8.38962i	0.569088	−	0.328563i
$653$			36.7620i			1.43861i	0.694695	+	0.719305i	$0.255540\pi$
$653$			36.7620i			1.43861i	−0.694695	+	0.719305i	$0.744460\pi$
$654$	−7.85043			−0.306976
$655$	−16.2921	+	4.68603i	−0.636586	+	0.183098i
$656$	5.96441	+	10.3307i	0.232871	+	0.403344i
$657$		−	5.90829i		−	0.230504i
$658$		−	19.3523i		−	0.754430i
$659$	−14.8805	−	25.7738i	−0.579662	−	1.00400i	−0.995518	−	0.0945733i	$-0.969851\pi$
$659$	−14.8805	−	25.7738i	−0.579662	−	1.00400i	0.415856	−	0.909430i	$-0.363482\pi$
$660$	5.18393	−	5.37686i	0.201784	−	0.209294i
$661$	−2.94441	−	5.09987i	−0.114524	−	0.198362i	0.803065	−	0.595891i	$-0.203201\pi$
$661$	−2.94441	−	5.09987i	−0.114524	−	0.198362i	−0.917589	+	0.397529i	$0.869868\pi$
$662$	18.6034	+	10.7407i	0.723041	+	0.417448i
$663$	5.62651	+	3.24846i	0.218515	+	0.126160i
$664$	4.68035			0.181633
$665$	30.8767	+	15.3814i	1.19735	+	0.596465i
$666$	4.70928			0.182481
$667$	58.3581	+	33.6931i	2.25963	+	1.30460i
$668$	−10.0496	−	5.80212i	−0.388829	−	0.224491i
$669$	5.00667	+	8.67180i	0.193569	+	0.335271i
$670$	14.5459	+	14.0240i	0.561959	+	0.541795i
$671$	−23.1314	−	40.0648i	−0.892979	−	1.54668i
$672$		−	3.53919i		−	0.136527i
$673$		−	8.96719i		−	0.345660i	−0.984952	−	0.172830i	$-0.944709\pi$
$673$		−	8.96719i		−	0.345660i	0.984952	−	0.172830i	$-0.0552911\pi$
$674$	−10.1701	−	17.6151i	−0.391737	−	0.678509i
$675$	−4.99666	+	0.182626i	−0.192322	+	0.00702928i
$676$	−10.0784			−0.387630
$677$			20.9721i			0.806024i	0.915195	+	0.403012i	$0.132037\pi$
$677$			20.9721i			0.806024i	−0.915195	+	0.403012i	$0.867963\pi$
$678$	6.91469	−	3.99220i	0.265557	−	0.153320i
$679$	10.3529	−	17.9317i	0.397308	−	0.688157i
$680$	8.16810	−	2.34936i	0.313232	−	0.0900938i
$681$	−7.12423	+	12.3395i	−0.273001	+	0.472852i
$682$	3.11940	+	1.80098i	0.119448	+	0.0689632i
$683$		−	7.46922i		−	0.285802i	−0.989737	−	0.142901i	$-0.954357\pi$
$683$		−	7.46922i		−	0.285802i	0.989737	−	0.142901i	$-0.0456430\pi$
$684$	−4.25513	−	0.945448i	−0.162699	−	0.0361501i
$685$	24.7792	+	6.15676i	0.946766	+	0.235238i
$686$	−2.60863	+	4.51829i	−0.0995981	+	0.172509i
$687$	13.7331	+	7.92881i	0.523951	+	0.302503i
$688$	−4.39800	+	2.53919i	−0.167672	+	0.0968057i
$689$	10.6917	−	18.5186i	0.407323	−	0.705504i
$690$	5.23400	+	18.1973i	0.199255	+	0.692758i
$691$	4.35804			0.165788			0.0828938	−	0.996558i	$-0.473584\pi$
$691$	4.35804			0.165788			0.0828938	+	0.996558i	$0.473584\pi$
$692$			8.89988i			0.338323i
$693$	−10.2377	+	5.91075i	−0.388899	+	0.224531i
$694$	−4.60197	−	7.97084i	−0.174688	−	0.302569i
$695$	1.94214	−	7.81658i	0.0736696	−	0.296500i
$696$	7.95774			0.301637
$697$	39.2666	−	22.6706i	1.48733	−	0.858711i
$698$	−7.14338	−	4.12423i	−0.270381	−	0.156104i
$699$	12.2979	+	21.3006i	0.465150	+	0.805663i
$700$	−9.40182	−	14.9917i	−0.355355	−	0.566634i
$701$	10.1990	−	17.6652i	0.385212	−	0.667206i	−0.606587	−	0.795017i	$-0.707462\pi$
$701$	10.1990	−	17.6652i	0.385212	−	0.667206i	0.991799	+	0.127811i	$0.0407952\pi$
$702$			1.70928i			0.0645124i
$703$	19.5801	−	6.16342i	0.738478	−	0.232458i
$704$	−3.34017			−0.125888
$705$	8.80214	+	8.48630i	0.331508	+	0.319613i
$706$	3.12003	−	5.40405i	0.117424	−	0.203384i
$707$	−26.5238	+	15.3135i	−0.997529	+	0.575924i
$708$	5.08013	+	2.93302i	0.190923	+	0.110229i
$709$	14.4377	+	25.0069i	0.542221	+	0.939154i	0.998776	+	0.0494590i	$0.0157497\pi$
$709$	14.4377	+	25.0069i	0.542221	+	0.939154i	−0.456555	+	0.889695i	$0.650917\pi$
$710$	−17.5597	−	4.36296i	−0.659004	−	0.163739i
$711$	−7.07838			−0.265460
$712$	−8.07532	+	4.66229i	−0.302635	+	0.174727i
$713$	−7.90829	+	4.56585i	−0.296168	+	0.170992i
$714$	−13.4524			−0.503443
$715$	−12.3896	−	3.07838i	−0.463346	−	0.115125i
$716$	−10.9299	−	18.9312i	−0.408471	−	0.707493i
$717$	−0.135754	−	0.0783777i	−0.00506983	−	0.00292707i
$718$	0.695636	−	0.401626i	0.0259609	−	0.0149885i
$719$	−18.1701	+	31.4715i	−0.677630	+	1.17369i	0.298063	+	0.954546i	$0.403660\pi$
$719$	−18.1701	+	31.4715i	−0.677630	+	1.17369i	−0.975693	+	0.219143i	$0.929674\pi$
$720$	1.60976	+	1.55199i	0.0599920	+	0.0578394i
$721$	2.65983			0.0990571
$722$	−18.9293	+	1.63809i	−0.704474	+	0.0609632i
$723$			25.5936i			0.951835i
$724$	−2.66342	+	4.61318i	−0.0989853	+	0.171448i
$725$	33.7084	−	21.1397i	1.25190	−	0.785107i
$726$	0.0783777	+	0.135754i	0.00290887	+	0.00503831i
$727$	25.7020	+	14.8390i	0.953233	+	0.550350i	0.894084	−	0.447900i	$-0.147828\pi$
$727$	25.7020	+	14.8390i	0.953233	+	0.550350i	0.0591495	+	0.998249i	$0.481161\pi$
$728$	−5.23898	+	3.02472i	−0.194169	+	0.112104i
$729$	−1.00000			−0.0370370
$730$	−3.18568	+	12.8215i	−0.117907	+	0.474545i
$731$	9.65142	+	16.7167i	0.356971	+	0.618291i
$732$	11.9948	−	6.92522i	0.443342	−	0.255963i
$733$			29.8248i			1.10160i	0.834636	+	0.550802i	$0.185678\pi$
$733$			29.8248i			1.10160i	−0.834636	+	0.550802i	$0.814322\pi$
$734$	−2.93600			−0.108370
$735$	3.41549	+	11.8748i	0.125982	+	0.438007i
$736$	4.23400	−	7.33350i	0.156067	−	0.270316i
$737$	−26.1385	+	15.0911i	−0.962826	+	0.555888i
$738$	10.3307	+	5.96441i	0.380277	+	0.219553i
$739$	−26.6737	+	46.2002i	−0.981207	+	1.69950i	−0.323498	+	0.946229i	$0.604859\pi$
$739$	−26.6737	+	46.2002i	−0.981207	+	1.69950i	−0.657709	+	0.753272i	$0.728474\pi$
$740$	−10.2195	−	2.53919i	−0.375678	−	0.0933424i
$741$	2.23707	+	7.10678i	0.0821809	+	0.261074i
$742$			44.2762i			1.62543i
$743$	−7.56947	−	4.37024i	−0.277697	−	0.160328i	0.354683	−	0.934986i	$-0.384589\pi$
$743$	−7.56947	−	4.37024i	−0.277697	−	0.160328i	−0.632380	+	0.774658i	$0.717922\pi$
$744$	−0.539189	+	0.933903i	−0.0197676	+	0.0342385i
$745$	22.1296	−	6.36506i	0.810767	−	0.233198i
$746$	−12.7576	+	22.0968i	−0.467089	+	0.809021i
$747$	4.05330	−	2.34017i	0.148302	−	0.0856225i
$748$			12.6959i			0.464210i
$749$	34.7682			1.27040
$750$	10.9417	+	2.29783i	0.399533	+	0.0839049i
$751$	−19.4101	−	33.6193i	−0.708286	−	1.22679i	−0.965492	−	0.260431i	$-0.916135\pi$
$751$	−19.4101	−	33.6193i	−0.708286	−	1.22679i	0.257206	−	0.966356i	$-0.417198\pi$
$752$		−	5.46800i		−	0.199397i
$753$			10.6537i			0.388242i
$754$	−6.80098	−	11.7797i	−0.247677	−	0.428990i
$755$	7.55932	+	7.28808i	0.275112	+	0.265240i
$756$	−1.76959	−	3.06503i	−0.0643595	−	0.111474i
$757$	−44.1922	−	25.5144i	−1.60619	−	0.927336i	−0.990212	−	0.139575i	$-0.955426\pi$
$757$	−44.1922	−	25.5144i	−1.60619	−	0.927336i	−0.615981	−	0.787761i	$-0.711240\pi$
$758$	23.0828	+	13.3268i	0.838404	+	0.484053i
$759$	−28.2846			−1.02667
$760$	8.72422	+	4.34602i	0.316461	+	0.157647i
$761$	−24.2546			−0.879229			−0.439614	−	0.898187i	$-0.644885\pi$
$761$	−24.2546			−0.879229			−0.439614	+	0.898187i	$0.644885\pi$
$762$	16.1160	+	9.30458i	0.583821	+	0.337069i
$763$	−24.0618	−	13.8921i	−0.871095	−	0.502927i
$764$	4.49693	+	7.78891i	0.162693	+	0.281793i
$765$	5.89911	−	6.11866i	0.213283	−	0.221220i
$766$	4.82571	+	8.35837i	0.174360	+	0.302000i
$767$		−	10.0267i		−	0.362042i
$768$		−	1.00000i		−	0.0360844i
$769$	8.02472	+	13.8992i	0.289379	+	0.501219i	0.973662	−	0.227998i	$-0.0732179\pi$
$769$	8.02472	+	13.8992i	0.289379	+	0.501219i	−0.684283	+	0.729217i	$0.739885\pi$
$770$	25.4038	−	7.30678i	0.915488	−	0.263318i
$771$	−19.3874			−0.698218
$772$		−	2.33299i		−	0.0839660i
$773$	6.20751	−	3.58391i	0.223269	−	0.128904i	−0.384194	−	0.923252i	$-0.625521\pi$
$773$	6.20751	−	3.58391i	0.223269	−	0.128904i	0.607463	+	0.794348i	$0.292187\pi$
$774$	−2.53919	+	4.39800i	−0.0912693	+	0.158083i
$775$	0.196940	+	5.38829i	0.00707429	+	0.193553i

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.60976 - 1.55199i) q^{5} +(0.500000 + 0.866025i) q^{6} +3.53919i q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.60976 - 1.55199i) q^{5} +(0.500000 + 0.866025i) q^{6} +3.53919i q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.618092 - 2.14894i) q^{10} +3.34017 q^{11} +1.00000i q^{12} +(1.48028 - 0.854638i) q^{13} +(-1.76959 + 3.06503i) q^{14} +(-0.618092 - 2.14894i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.29175 + 1.90049i) q^{17} +1.00000i q^{18} +(1.30878 + 4.15777i) q^{19} +(0.539189 - 2.17009i) q^{20} +(-1.76959 + 3.06503i) q^{21} +(2.89267 + 1.67009i) q^{22} +(-7.33350 + 4.23400i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(0.182626 + 4.99666i) q^{25} +1.70928 q^{26} +1.00000i q^{27} +(-3.06503 + 1.76959i) q^{28} +(-3.97887 - 6.89160i) q^{29} +(0.539189 - 2.17009i) q^{30} +1.07838 q^{31} +(-0.866025 + 0.500000i) q^{32} +(2.89267 + 1.67009i) q^{33} +(1.90049 + 3.29175i) q^{34} +(5.49280 - 5.69723i) q^{35} +(-0.500000 + 0.866025i) q^{36} -4.70928i q^{37} +(-0.945448 + 4.25513i) q^{38} +1.70928 q^{39} +(1.55199 - 1.60976i) q^{40} +(5.96441 - 10.3307i) q^{41} +(-3.06503 + 1.76959i) q^{42} +(4.39800 + 2.53919i) q^{43} +(1.67009 + 2.89267i) q^{44} +(0.539189 - 2.17009i) q^{45} -8.46800 q^{46} +(-4.73543 + 2.73400i) q^{47} +(-0.866025 + 0.500000i) q^{48} -5.52586 q^{49} +(-2.34017 + 4.41855i) q^{50} +(1.90049 + 3.29175i) q^{51} +(1.48028 + 0.854638i) q^{52} +(10.8342 - 6.25513i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-5.37686 - 5.18393i) q^{55} -3.53919 q^{56} +(-0.945448 + 4.25513i) q^{57} -7.95774i q^{58} +(2.93302 - 5.08013i) q^{59} +(1.55199 - 1.60976i) q^{60} +(-6.92522 - 11.9948i) q^{61} +(0.933903 + 0.539189i) q^{62} +(-3.06503 + 1.76959i) q^{63} -1.00000 q^{64} +(-3.70928 - 0.921622i) q^{65} +(1.67009 + 2.89267i) q^{66} +(-7.82551 + 4.51806i) q^{67} +3.80098i q^{68} -8.46800 q^{69} +(7.60552 - 2.18754i) q^{70} +(4.04585 - 7.00763i) q^{71} +(-0.866025 + 0.500000i) q^{72} +(-5.11673 - 2.95415i) q^{73} +(2.35464 - 4.07835i) q^{74} +(-2.34017 + 4.41855i) q^{75} +(-2.94635 + 3.21233i) q^{76} +11.8215i q^{77} +(1.48028 + 0.854638i) q^{78} +(-3.53919 + 6.13005i) q^{79} +(2.14894 - 0.618092i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(10.3307 - 5.96441i) q^{82} -4.68035i q^{83} -3.53919 q^{84} +(-2.34936 - 8.16810i) q^{85} +(2.53919 + 4.39800i) q^{86} -7.95774i q^{87} +3.34017i q^{88} +(4.66229 + 8.07532i) q^{89} +(1.55199 - 1.60976i) q^{90} +(3.02472 + 5.23898i) q^{91} +(-7.33350 - 4.23400i) q^{92} +(0.933903 + 0.539189i) q^{93} -5.46800 q^{94} +(4.34602 - 8.72422i) q^{95} -1.00000 q^{96} +(-5.06662 - 2.92522i) q^{97} +(-4.78553 - 2.76293i) q^{98} +(1.67009 + 2.89267i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12q + 6q^{4} + 6q^{6} + 6q^{9} + O(q^{10}) \)	\( 12q + 6q^{4} + 6q^{6} + 6q^{9} - 2q^{10} - 4q^{11} - 18q^{14} - 2q^{15} - 6q^{16} + 6q^{19} - 18q^{21} - 6q^{24} - 2q^{25} - 8q^{26} - 16q^{29} + 4q^{34} + 2q^{35} - 6q^{36} - 8q^{39} + 2q^{40} + 10q^{41} - 2q^{44} + 28q^{46} - 56q^{49} + 16q^{50} + 4q^{51} - 6q^{54} - 8q^{55} - 36q^{56} + 8q^{59} + 2q^{60} - 28q^{61} - 12q^{64} - 16q^{65} - 2q^{66} + 28q^{69} + 16q^{70} + 44q^{71} + 14q^{74} + 16q^{75} - 12q^{76} - 36q^{79} - 6q^{81} - 36q^{84} - 32q^{85} + 24q^{86} + 6q^{89} + 2q^{90} + 64q^{94} - 12q^{95} - 12q^{96} - 2q^{99} + O(q^{100}) \)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Properties

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