LMFDB - Embedded newform 225.2.e.a.76.1

Newspace parameters

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.e (of order $3$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			76.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	225.76
Dual form			225.2.e.a.151.1

$q$-expansion

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.73205i q^{6} +(-1.50000 - 2.59808i) q^{7} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.73205i q^{6} +(-1.50000 - 2.59808i) q^{7} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(1.00000 + 1.73205i) q^{11} +(1.50000 - 0.866025i) q^{12} +(-1.00000 + 1.73205i) q^{13} +(1.50000 - 2.59808i) q^{14} +(0.500000 + 0.866025i) q^{16} -4.00000 q^{17} +(-1.50000 + 2.59808i) q^{18} -8.00000 q^{19} -5.19615i q^{21} +(-1.00000 + 1.73205i) q^{22} +(1.50000 - 2.59808i) q^{23} +(4.50000 + 2.59808i) q^{24} -2.00000 q^{26} +5.19615i q^{27} -3.00000 q^{28} +(0.500000 + 0.866025i) q^{29} +(2.50000 - 4.33013i) q^{32} +3.46410i q^{33} +(-2.00000 - 3.46410i) q^{34} +3.00000 q^{36} +4.00000 q^{37} +(-4.00000 - 6.92820i) q^{38} +(-3.00000 + 1.73205i) q^{39} +(-2.50000 + 4.33013i) q^{41} +(4.50000 - 2.59808i) q^{42} +(-4.00000 - 6.92820i) q^{43} +2.00000 q^{44} +3.00000 q^{46} +(3.50000 + 6.06218i) q^{47} +1.73205i q^{48} +(-1.00000 + 1.73205i) q^{49} +(-6.00000 - 3.46410i) q^{51} +(1.00000 + 1.73205i) q^{52} +2.00000 q^{53} +(-4.50000 + 2.59808i) q^{54} +(-4.50000 - 7.79423i) q^{56} +(-12.0000 - 6.92820i) q^{57} +(-0.500000 + 0.866025i) q^{58} +(7.00000 - 12.1244i) q^{59} +(-3.50000 - 6.06218i) q^{61} +(4.50000 - 7.79423i) q^{63} +7.00000 q^{64} +(-3.00000 + 1.73205i) q^{66} +(-1.50000 + 2.59808i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(4.50000 - 2.59808i) q^{69} +2.00000 q^{71} +(4.50000 + 7.79423i) q^{72} -4.00000 q^{73} +(2.00000 + 3.46410i) q^{74} +(-4.00000 + 6.92820i) q^{76} +(3.00000 - 5.19615i) q^{77} +(-3.00000 - 1.73205i) q^{78} +(3.00000 + 5.19615i) q^{79} +(-4.50000 + 7.79423i) q^{81} -5.00000 q^{82} +(4.50000 + 7.79423i) q^{83} +(-4.50000 - 2.59808i) q^{84} +(4.00000 - 6.92820i) q^{86} +1.73205i q^{87} +(3.00000 + 5.19615i) q^{88} -15.0000 q^{89} +6.00000 q^{91} +(-1.50000 - 2.59808i) q^{92} +(-3.50000 + 6.06218i) q^{94} +(7.50000 - 4.33013i) q^{96} +(1.00000 + 1.73205i) q^{97} -2.00000 q^{98} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 3 q^{3} + q^{4} - 3 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q + q^2 + 3 * q^3 + q^4 - 3 * q^7 + 6 * q^8 + 3 * q^9	$ 2 q + q^{2} + 3 q^{3} + q^{4} - 3 q^{7} + 6 q^{8} + 3 q^{9} + 2 q^{11} + 3 q^{12} - 2 q^{13} + 3 q^{14} + q^{16} - 8 q^{17} - 3 q^{18} - 16 q^{19} - 2 q^{22} + 3 q^{23} + 9 q^{24} - 4 q^{26} - 6 q^{28} + q^{29} + 5 q^{32} - 4 q^{34} + 6 q^{36} + 8 q^{37} - 8 q^{38} - 6 q^{39} - 5 q^{41} + 9 q^{42} - 8 q^{43} + 4 q^{44} + 6 q^{46} + 7 q^{47} - 2 q^{49} - 12 q^{51} + 2 q^{52} + 4 q^{53} - 9 q^{54} - 9 q^{56} - 24 q^{57} - q^{58} + 14 q^{59} - 7 q^{61} + 9 q^{63} + 14 q^{64} - 6 q^{66} - 3 q^{67} - 4 q^{68} + 9 q^{69} + 4 q^{71} + 9 q^{72} - 8 q^{73} + 4 q^{74} - 8 q^{76} + 6 q^{77} - 6 q^{78} + 6 q^{79} - 9 q^{81} - 10 q^{82} + 9 q^{83} - 9 q^{84} + 8 q^{86} + 6 q^{88} - 30 q^{89} + 12 q^{91} - 3 q^{92} - 7 q^{94} + 15 q^{96} + 2 q^{97} - 4 q^{98} - 6 q^{99}+O(q^{100}) $ 2 * q + q^2 + 3 * q^3 + q^4 - 3 * q^7 + 6 * q^8 + 3 * q^9 + 2 * q^11 + 3 * q^12 - 2 * q^13 + 3 * q^14 + q^16 - 8 * q^17 - 3 * q^18 - 16 * q^19 - 2 * q^22 + 3 * q^23 + 9 * q^24 - 4 * q^26 - 6 * q^28 + q^29 + 5 * q^32 - 4 * q^34 + 6 * q^36 + 8 * q^37 - 8 * q^38 - 6 * q^39 - 5 * q^41 + 9 * q^42 - 8 * q^43 + 4 * q^44 + 6 * q^46 + 7 * q^47 - 2 * q^49 - 12 * q^51 + 2 * q^52 + 4 * q^53 - 9 * q^54 - 9 * q^56 - 24 * q^57 - q^58 + 14 * q^59 - 7 * q^61 + 9 * q^63 + 14 * q^64 - 6 * q^66 - 3 * q^67 - 4 * q^68 + 9 * q^69 + 4 * q^71 + 9 * q^72 - 8 * q^73 + 4 * q^74 - 8 * q^76 + 6 * q^77 - 6 * q^78 + 6 * q^79 - 9 * q^81 - 10 * q^82 + 9 * q^83 - 9 * q^84 + 8 * q^86 + 6 * q^88 - 30 * q^89 + 12 * q^91 - 3 * q^92 - 7 * q^94 + 15 * q^96 + 2 * q^97 - 4 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	0.986869	−	0.161521i	$-0.0516399\pi$
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	−0.633316	+	0.773893i	$0.718307\pi$
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$			1.73205i			0.707107i
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	−0.996866	−	0.0791130i	$-0.974791\pi$
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	0.429919	−	0.902867i	$-0.358542\pi$
$8$	3.00000			1.06066
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$		0			0
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$	1.50000	−	0.866025i	0.433013	−	0.250000i
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	1.50000	−	2.59808i	0.400892	−	0.694365i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−4.00000			−0.970143			−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000			−0.970143			−0.485071	+	0.874475i	$0.661206\pi$
$18$	−1.50000	+	2.59808i	−0.353553	+	0.612372i
$19$	−8.00000			−1.83533			−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−8.00000			−1.83533			−0.917663	+	0.397360i	$0.869927\pi$
$20$		0			0
$21$		−	5.19615i		−	1.13389i
$22$	−1.00000	+	1.73205i	−0.213201	+	0.369274i
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$	4.50000	+	2.59808i	0.918559	+	0.530330i
$25$		0			0
$26$	−2.00000			−0.392232
$27$			5.19615i			1.00000i
$28$	−3.00000			−0.566947
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	0.908708	−	0.417432i	$-0.137070\pi$
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	−0.815861	+	0.578249i	$0.803736\pi$
$30$		0			0
$31$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$31$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$32$	2.50000	−	4.33013i	0.441942	−	0.765466i
$33$			3.46410i			0.603023i
$34$	−2.00000	−	3.46410i	−0.342997	−	0.594089i
$35$		0			0
$36$	3.00000			0.500000
$37$	4.00000			0.657596			0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000			0.657596			0.328798	+	0.944400i	$0.393356\pi$
$38$	−4.00000	−	6.92820i	−0.648886	−	1.12390i
$39$	−3.00000	+	1.73205i	−0.480384	+	0.277350i
$40$		0			0
$41$	−2.50000	+	4.33013i	−0.390434	+	0.676252i	−0.992507	−	0.122189i	$-0.961009\pi$
$41$	−2.50000	+	4.33013i	−0.390434	+	0.676252i	0.602072	+	0.798441i	$0.294342\pi$
$42$	4.50000	−	2.59808i	0.694365	−	0.400892i
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	0.381246	−	0.924473i	$-0.375495\pi$
$44$	2.00000			0.301511
$45$		0			0
$46$	3.00000			0.442326
$47$	3.50000	+	6.06218i	0.510527	+	0.884260i	0.999926	+	0.0121990i	$0.00388317\pi$
$47$	3.50000	+	6.06218i	0.510527	+	0.884260i	−0.489398	+	0.872060i	$0.662783\pi$
$48$			1.73205i			0.250000i
$49$	−1.00000	+	1.73205i	−0.142857	+	0.247436i
$50$		0			0
$51$	−6.00000	−	3.46410i	−0.840168	−	0.485071i
$52$	1.00000	+	1.73205i	0.138675	+	0.240192i
$53$	2.00000			0.274721			0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000			0.274721			0.137361	+	0.990521i	$0.456138\pi$
$54$	−4.50000	+	2.59808i	−0.612372	+	0.353553i
$55$		0			0
$56$	−4.50000	−	7.79423i	−0.601338	−	1.04155i
$57$	−12.0000	−	6.92820i	−1.58944	−	0.917663i
$58$	−0.500000	+	0.866025i	−0.0656532	+	0.113715i
$59$	7.00000	−	12.1244i	0.911322	−	1.57846i	0.0991242	−	0.995075i	$-0.468396\pi$
$59$	7.00000	−	12.1244i	0.911322	−	1.57846i	0.812198	−	0.583382i	$-0.198271\pi$
$60$		0			0
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	0.550135	−	0.835076i	$-0.314576\pi$
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	−0.998264	+	0.0588933i	$0.981243\pi$
$62$		0			0
$63$	4.50000	−	7.79423i	0.566947	−	0.981981i
$64$	7.00000			0.875000
$65$		0			0
$66$	−3.00000	+	1.73205i	−0.369274	+	0.213201i
$67$	−1.50000	+	2.59808i	−0.183254	+	0.317406i	−0.942987	−	0.332830i	$-0.891996\pi$
$67$	−1.50000	+	2.59808i	−0.183254	+	0.317406i	0.759733	+	0.650236i	$0.225330\pi$
$68$	−2.00000	+	3.46410i	−0.242536	+	0.420084i
$69$	4.50000	−	2.59808i	0.541736	−	0.312772i
$70$		0			0
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$	4.50000	+	7.79423i	0.530330	+	0.918559i
$73$	−4.00000			−0.468165			−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000			−0.468165			−0.234082	+	0.972217i	$0.575209\pi$
$74$	2.00000	+	3.46410i	0.232495	+	0.402694i
$75$		0			0
$76$	−4.00000	+	6.92820i	−0.458831	+	0.794719i
$77$	3.00000	−	5.19615i	0.341882	−	0.592157i
$78$	−3.00000	−	1.73205i	−0.339683	−	0.196116i
$79$	3.00000	+	5.19615i	0.337526	+	0.584613i	0.983967	−	0.178352i	$-0.0570765\pi$
$79$	3.00000	+	5.19615i	0.337526	+	0.584613i	−0.646440	+	0.762964i	$0.723743\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−5.00000			−0.552158
$83$	4.50000	+	7.79423i	0.493939	+	0.855528i	0.999976	−	0.00698436i	$-0.00222321\pi$
$83$	4.50000	+	7.79423i	0.493939	+	0.855528i	−0.506036	+	0.862512i	$0.668890\pi$
$84$	−4.50000	−	2.59808i	−0.490990	−	0.283473i
$85$		0			0
$86$	4.00000	−	6.92820i	0.431331	−	0.747087i
$87$			1.73205i			0.185695i
$88$	3.00000	+	5.19615i	0.319801	+	0.553912i
$89$	−15.0000			−1.59000			−0.794998	−	0.606612i	$-0.792528\pi$
$89$	−15.0000			−1.59000			−0.794998	+	0.606612i	$0.792528\pi$
$90$		0			0
$91$	6.00000			0.628971
$92$	−1.50000	−	2.59808i	−0.156386	−	0.270868i
$93$		0			0
$94$	−3.50000	+	6.06218i	−0.360997	+	0.625266i
$95$		0			0
$96$	7.50000	−	4.33013i	0.765466	−	0.441942i
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	0.912317	−	0.409484i	$-0.134291\pi$
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	−0.810782	+	0.585348i	$0.800958\pi$
$98$	−2.00000			−0.202031
$99$	−3.00000	+	5.19615i	−0.301511	+	0.522233i
$100$		0			0
$101$	9.00000	+	15.5885i	0.895533	+	1.55111i	0.833143	+	0.553058i	$0.186539\pi$
$101$	9.00000	+	15.5885i	0.895533	+	1.55111i	0.0623905	+	0.998052i	$0.480128\pi$
$102$		−	6.92820i		−	0.685994i
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	−0.598858	−	0.800855i	$-0.704379\pi$
$103$	4.00000	−	6.92820i	0.394132	−	0.682656i	0.992990	+	0.118199i	$0.0377120\pi$
$104$	−3.00000	+	5.19615i	−0.294174	+	0.509525i
$105$		0			0
$106$	1.00000	+	1.73205i	0.0971286	+	0.168232i
$107$	−3.00000			−0.290021			−0.145010	−	0.989430i	$-0.546322\pi$
$107$	−3.00000			−0.290021			−0.145010	+	0.989430i	$0.546322\pi$
$108$	4.50000	+	2.59808i	0.433013	+	0.250000i
$109$	5.00000			0.478913			0.239457	−	0.970907i	$-0.423031\pi$
$109$	5.00000			0.478913			0.239457	+	0.970907i	$0.423031\pi$
$110$		0			0
$111$	6.00000	+	3.46410i	0.569495	+	0.328798i
$112$	1.50000	−	2.59808i	0.141737	−	0.245495i
$113$	−4.00000	+	6.92820i	−0.376288	+	0.651751i	−0.990519	−	0.137376i	$-0.956133\pi$
$113$	−4.00000	+	6.92820i	−0.376288	+	0.651751i	0.614231	+	0.789127i	$0.289466\pi$
$114$		−	13.8564i		−	1.29777i
$115$		0			0
$116$	1.00000			0.0928477
$117$	−6.00000			−0.554700
$118$	14.0000			1.28880
$119$	6.00000	+	10.3923i	0.550019	+	0.952661i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	3.50000	−	6.06218i	0.316875	−	0.548844i
$123$	−7.50000	+	4.33013i	−0.676252	+	0.390434i
$124$		0			0
$125$		0			0
$126$	9.00000			0.801784
$127$	5.00000			0.443678			0.221839	−	0.975083i	$-0.428794\pi$
$127$	5.00000			0.443678			0.221839	+	0.975083i	$0.428794\pi$
$128$	−1.50000	−	2.59808i	−0.132583	−	0.229640i
$129$		−	13.8564i		−	1.21999i
$130$		0			0
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	−0.704692	−	0.709514i	$-0.748915\pi$
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	0.966803	+	0.255524i	$0.0822479\pi$
$132$	3.00000	+	1.73205i	0.261116	+	0.150756i
$133$	12.0000	+	20.7846i	1.04053	+	1.80225i
$134$	−3.00000			−0.259161
$135$		0			0
$136$	−12.0000			−1.02899
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	0.999893	+	0.0146279i	$0.00465636\pi$
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	−0.487278	+	0.873247i	$0.662010\pi$
$138$	4.50000	+	2.59808i	0.383065	+	0.221163i
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	−0.296866	−	0.954919i	$-0.595942\pi$
$139$	8.00000	−	13.8564i	0.678551	−	1.17529i	0.975417	−	0.220366i	$-0.0707252\pi$
$140$		0			0
$141$			12.1244i			1.02105i
$142$	1.00000	+	1.73205i	0.0839181	+	0.145350i
$143$	−4.00000			−0.334497
$144$	−1.50000	+	2.59808i	−0.125000	+	0.216506i
$145$		0			0
$146$	−2.00000	−	3.46410i	−0.165521	−	0.286691i
$147$	−3.00000	+	1.73205i	−0.247436	+	0.142857i
$148$	2.00000	−	3.46410i	0.164399	−	0.284747i
$149$	−8.50000	+	14.7224i	−0.696347	+	1.20611i	0.273377	+	0.961907i	$0.411859\pi$
$149$	−8.50000	+	14.7224i	−0.696347	+	1.20611i	−0.969724	+	0.244202i	$0.921474\pi$
$150$		0			0
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	0.903842	−	0.427865i	$-0.140734\pi$
$151$	1.00000	+	1.73205i	0.0813788	+	0.140952i	−0.822464	+	0.568818i	$0.807401\pi$
$152$	−24.0000			−1.94666
$153$	−6.00000	−	10.3923i	−0.485071	−	0.840168i
$154$	6.00000			0.483494
$155$		0			0
$156$			3.46410i			0.277350i
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	0.997609	−	0.0691164i	$-0.0220180\pi$
$158$	−3.00000	+	5.19615i	−0.238667	+	0.413384i
$159$	3.00000	+	1.73205i	0.237915	+	0.137361i
$160$		0			0
$161$	−9.00000			−0.709299
$162$	−9.00000			−0.707107
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$	2.50000	+	4.33013i	0.195217	+	0.338126i
$165$		0			0
$166$	−4.50000	+	7.79423i	−0.349268	+	0.604949i
$167$	−4.50000	+	7.79423i	−0.348220	+	0.603136i	−0.985933	−	0.167139i	$-0.946547\pi$
$167$	−4.50000	+	7.79423i	−0.348220	+	0.603136i	0.637713	+	0.770274i	$0.279881\pi$
$168$		−	15.5885i		−	1.20268i
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$		0			0
$171$	−12.0000	−	20.7846i	−0.917663	−	1.58944i
$172$	−8.00000			−0.609994
$173$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$173$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$174$	−1.50000	+	0.866025i	−0.113715	+	0.0656532i
$175$		0			0
$176$	−1.00000	+	1.73205i	−0.0753778	+	0.130558i
$177$	21.0000	−	12.1244i	1.57846	−	0.911322i
$178$	−7.50000	−	12.9904i	−0.562149	−	0.973670i
$179$	−2.00000			−0.149487			−0.0747435	−	0.997203i	$-0.523814\pi$
$179$	−2.00000			−0.149487			−0.0747435	+	0.997203i	$0.523814\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$	3.00000	+	5.19615i	0.222375	+	0.385164i
$183$		−	12.1244i		−	0.896258i
$184$	4.50000	−	7.79423i	0.331744	−	0.574598i
$185$		0			0
$186$		0			0
$187$	−4.00000	−	6.92820i	−0.292509	−	0.506640i
$188$	7.00000			0.510527
$189$	13.5000	−	7.79423i	0.981981	−	0.566947i
$190$		0			0
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	0.684244	−	0.729253i	$-0.260132\pi$
$191$	−4.00000	−	6.92820i	−0.289430	−	0.501307i	−0.973674	+	0.227946i	$0.926799\pi$
$192$	10.5000	+	6.06218i	0.757772	+	0.437500i
$193$	−5.00000	+	8.66025i	−0.359908	+	0.623379i	−0.987945	−	0.154805i	$-0.950525\pi$
$193$	−5.00000	+	8.66025i	−0.359908	+	0.623379i	0.628037	+	0.778183i	$0.283859\pi$
$194$	−1.00000	+	1.73205i	−0.0717958	+	0.124354i
$195$		0			0
$196$	1.00000	+	1.73205i	0.0714286	+	0.123718i
$197$	12.0000			0.854965			0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000			0.854965			0.427482	+	0.904024i	$0.359401\pi$
$198$	−6.00000			−0.426401
$199$	4.00000			0.283552			0.141776	−	0.989899i	$-0.454719\pi$
$199$	4.00000			0.283552			0.141776	+	0.989899i	$0.454719\pi$
$200$		0			0
$201$	−4.50000	+	2.59808i	−0.317406	+	0.183254i
$202$	−9.00000	+	15.5885i	−0.633238	+	1.09680i
$203$	1.50000	−	2.59808i	0.105279	−	0.182349i
$204$	−6.00000	+	3.46410i	−0.420084	+	0.242536i
$205$		0			0
$206$	8.00000			0.557386
$207$	9.00000			0.625543
$208$	−2.00000			−0.138675
$209$	−8.00000	−	13.8564i	−0.553372	−	0.958468i
$210$		0			0
$211$	11.0000	−	19.0526i	0.757271	−	1.31163i	−0.186966	−	0.982366i	$-0.559865\pi$
$211$	11.0000	−	19.0526i	0.757271	−	1.31163i	0.944237	−	0.329266i	$-0.106801\pi$
$212$	1.00000	−	1.73205i	0.0686803	−	0.118958i
$213$	3.00000	+	1.73205i	0.205557	+	0.118678i
$214$	−1.50000	−	2.59808i	−0.102538	−	0.177601i
$215$		0			0
$216$			15.5885i			1.06066i
$217$		0			0
$218$	2.50000	+	4.33013i	0.169321	+	0.293273i
$219$	−6.00000	−	3.46410i	−0.405442	−	0.234082i
$220$		0			0
$221$	4.00000	−	6.92820i	0.269069	−	0.466041i
$222$			6.92820i			0.464991i
$223$	−9.50000	−	16.4545i	−0.636167	−	1.10187i	−0.986267	−	0.165161i	$-0.947186\pi$
$223$	−9.50000	−	16.4545i	−0.636167	−	1.10187i	0.350100	−	0.936713i	$-0.386148\pi$
$224$	−15.0000			−1.00223
$225$		0			0
$226$	−8.00000			−0.532152
$227$	−2.00000	−	3.46410i	−0.132745	−	0.229920i	0.791989	−	0.610535i	$-0.209046\pi$
$227$	−2.00000	−	3.46410i	−0.132745	−	0.229920i	−0.924734	+	0.380615i	$0.875712\pi$
$228$	−12.0000	+	6.92820i	−0.794719	+	0.458831i
$229$	−7.50000	+	12.9904i	−0.495614	+	0.858429i	−0.999987	−	0.00505719i	$-0.998390\pi$
$229$	−7.50000	+	12.9904i	−0.495614	+	0.858429i	0.504373	+	0.863486i	$0.331724\pi$
$230$		0			0
$231$	9.00000	−	5.19615i	0.592157	−	0.341882i
$232$	1.50000	+	2.59808i	0.0984798	+	0.170572i
$233$	−24.0000			−1.57229			−0.786146	−	0.618041i	$-0.787927\pi$
$233$	−24.0000			−1.57229			−0.786146	+	0.618041i	$0.787927\pi$
$234$	−3.00000	−	5.19615i	−0.196116	−	0.339683i
$235$		0			0
$236$	−7.00000	−	12.1244i	−0.455661	−	0.789228i
$237$			10.3923i			0.675053i
$238$	−6.00000	+	10.3923i	−0.388922	+	0.673633i
$239$	4.00000	−	6.92820i	0.258738	−	0.448148i	−0.707166	−	0.707048i	$-0.750027\pi$
$239$	4.00000	−	6.92820i	0.258738	−	0.448148i	0.965904	+	0.258900i	$0.0833599\pi$
$240$		0			0
$241$	5.50000	+	9.52628i	0.354286	+	0.613642i	0.986996	−	0.160748i	$-0.0513906\pi$
$241$	5.50000	+	9.52628i	0.354286	+	0.613642i	−0.632709	+	0.774389i	$0.718057\pi$
$242$	7.00000			0.449977
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$	−7.00000			−0.448129
$245$		0			0
$246$	−7.50000	−	4.33013i	−0.478183	−	0.276079i
$247$	8.00000	−	13.8564i	0.509028	−	0.881662i
$248$		0			0
$249$			15.5885i			0.987878i
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$	−4.50000	−	7.79423i	−0.283473	−	0.490990i
$253$	6.00000			0.377217
$254$	2.50000	+	4.33013i	0.156864	+	0.271696i
$255$		0			0
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	−0.944294	−	0.329104i	$-0.893253\pi$
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	0.757159	+	0.653231i	$0.226587\pi$
$258$	12.0000	−	6.92820i	0.747087	−	0.431331i
$259$	−6.00000	−	10.3923i	−0.372822	−	0.645746i
$260$		0			0
$261$	−1.50000	+	2.59808i	−0.0928477	+	0.160817i
$262$	6.00000			0.370681
$263$	−8.00000	−	13.8564i	−0.493301	−	0.854423i	0.506669	−	0.862141i	$-0.330877\pi$
$263$	−8.00000	−	13.8564i	−0.493301	−	0.854423i	−0.999970	+	0.00771799i	$0.997543\pi$
$264$			10.3923i			0.639602i
$265$		0			0
$266$	−12.0000	+	20.7846i	−0.735767	+	1.27439i
$267$	−22.5000	−	12.9904i	−1.37698	−	0.794998i
$268$	1.50000	+	2.59808i	0.0916271	+	0.158703i
$269$	25.0000			1.52428			0.762138	−	0.647414i	$-0.224150\pi$
$269$	25.0000			1.52428			0.762138	+	0.647414i	$0.224150\pi$
$270$		0			0
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$	−2.00000	−	3.46410i	−0.121268	−	0.210042i
$273$	9.00000	+	5.19615i	0.544705	+	0.314485i
$274$	−6.00000	+	10.3923i	−0.362473	+	0.627822i
$275$		0			0
$276$		−	5.19615i		−	0.312772i
$277$	6.00000	+	10.3923i	0.360505	+	0.624413i	0.988044	−	0.154172i	$-0.0492710\pi$
$277$	6.00000	+	10.3923i	0.360505	+	0.624413i	−0.627539	+	0.778585i	$0.715938\pi$
$278$	16.0000			0.959616
$279$		0			0
$280$		0			0
$281$	7.50000	+	12.9904i	0.447412	+	0.774941i	0.998217	−	0.0596933i	$-0.0190123\pi$
$281$	7.50000	+	12.9904i	0.447412	+	0.774941i	−0.550804	+	0.834634i	$0.685679\pi$
$282$	−10.5000	+	6.06218i	−0.625266	+	0.360997i
$283$	10.5000	−	18.1865i	0.624160	−	1.08108i	−0.364542	−	0.931187i	$-0.618775\pi$
$283$	10.5000	−	18.1865i	0.624160	−	1.08108i	0.988703	−	0.149890i	$-0.0478921\pi$
$284$	1.00000	−	1.73205i	0.0593391	−	0.102778i
$285$		0			0
$286$	−2.00000	−	3.46410i	−0.118262	−	0.204837i
$287$	15.0000			0.885422
$288$	15.0000			0.883883
$289$	−1.00000			−0.0588235
$290$		0			0
$291$			3.46410i			0.203069i
$292$	−2.00000	+	3.46410i	−0.117041	+	0.202721i
$293$	6.00000	−	10.3923i	0.350524	−	0.607125i	−0.635818	−	0.771839i	$-0.719337\pi$
$293$	6.00000	−	10.3923i	0.350524	−	0.607125i	0.986341	+	0.164714i	$0.0526703\pi$
$294$	−3.00000	−	1.73205i	−0.174964	−	0.101015i
$295$		0			0
$296$	12.0000			0.697486
$297$	−9.00000	+	5.19615i	−0.522233	+	0.301511i
$298$	−17.0000			−0.984784
$299$	3.00000	+	5.19615i	0.173494	+	0.300501i
$300$		0			0
$301$	−12.0000	+	20.7846i	−0.691669	+	1.19800i
$302$	−1.00000	+	1.73205i	−0.0575435	+	0.0996683i
$303$			31.1769i			1.79107i
$304$	−4.00000	−	6.92820i	−0.229416	−	0.397360i
$305$		0			0
$306$	6.00000	−	10.3923i	0.342997	−	0.594089i
$307$	−7.00000			−0.399511			−0.199756	−	0.979846i	$-0.564015\pi$
$307$	−7.00000			−0.399511			−0.199756	+	0.979846i	$0.564015\pi$
$308$	−3.00000	−	5.19615i	−0.170941	−	0.296078i
$309$	12.0000	−	6.92820i	0.682656	−	0.394132i
$310$		0			0
$311$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$311$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$312$	−9.00000	+	5.19615i	−0.509525	+	0.294174i
$313$	7.00000	+	12.1244i	0.395663	+	0.685309i	0.993186	−	0.116543i	$-0.0371814\pi$
$313$	7.00000	+	12.1244i	0.395663	+	0.685309i	−0.597522	+	0.801852i	$0.703848\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$	6.00000			0.337526
$317$	−17.0000	−	29.4449i	−0.954815	−	1.65379i	−0.734791	−	0.678294i	$-0.762720\pi$
$317$	−17.0000	−	29.4449i	−0.954815	−	1.65379i	−0.220024	−	0.975494i	$-0.570614\pi$
$318$			3.46410i			0.194257i
$319$	−1.00000	+	1.73205i	−0.0559893	+	0.0969762i
$320$		0			0
$321$	−4.50000	−	2.59808i	−0.251166	−	0.145010i
$322$	−4.50000	−	7.79423i	−0.250775	−	0.434355i
$323$	32.0000			1.78053
$324$	4.50000	+	7.79423i	0.250000	+	0.433013i
$325$		0			0
$326$	2.00000	+	3.46410i	0.110770	+	0.191859i
$327$	7.50000	+	4.33013i	0.414751	+	0.239457i
$328$	−7.50000	+	12.9904i	−0.414118	+	0.717274i
$329$	10.5000	−	18.1865i	0.578884	−	1.00266i
$330$		0			0
$331$	3.00000	+	5.19615i	0.164895	+	0.285606i	0.936618	−	0.350352i	$-0.113938\pi$
$331$	3.00000	+	5.19615i	0.164895	+	0.285606i	−0.771723	+	0.635959i	$0.780605\pi$
$332$	9.00000			0.493939
$333$	6.00000	+	10.3923i	0.328798	+	0.569495i
$334$	−9.00000			−0.492458
$335$		0			0
$336$	4.50000	−	2.59808i	0.245495	−	0.141737i
$337$	−4.00000	+	6.92820i	−0.217894	+	0.377403i	−0.954164	−	0.299285i	$-0.903252\pi$
$337$	−4.00000	+	6.92820i	−0.217894	+	0.377403i	0.736270	+	0.676688i	$0.236585\pi$
$338$	−4.50000	+	7.79423i	−0.244768	+	0.423950i
$339$	−12.0000	+	6.92820i	−0.651751	+	0.376288i
$340$		0			0
$341$		0			0
$342$	12.0000	−	20.7846i	0.648886	−	1.12390i
$343$	−15.0000			−0.809924
$344$	−12.0000	−	20.7846i	−0.646997	−	1.12063i
$345$		0			0
$346$		0			0
$347$	2.00000	−	3.46410i	0.107366	−	0.185963i	−0.807337	−	0.590091i	$-0.799092\pi$
$347$	2.00000	−	3.46410i	0.107366	−	0.185963i	0.914702	+	0.404128i	$0.132425\pi$
$348$	1.50000	+	0.866025i	0.0804084	+	0.0464238i
$349$	2.50000	+	4.33013i	0.133822	+	0.231786i	0.925147	−	0.379610i	$-0.123942\pi$
$349$	2.50000	+	4.33013i	0.133822	+	0.231786i	−0.791325	+	0.611396i	$0.790608\pi$
$350$		0			0
$351$	−9.00000	−	5.19615i	−0.480384	−	0.277350i
$352$	10.0000			0.533002
$353$	12.0000	+	20.7846i	0.638696	+	1.10625i	0.985719	+	0.168397i	$0.0538590\pi$
$353$	12.0000	+	20.7846i	0.638696	+	1.10625i	−0.347024	+	0.937856i	$0.612808\pi$
$354$	21.0000	+	12.1244i	1.11614	+	0.644402i
$355$		0			0
$356$	−7.50000	+	12.9904i	−0.397499	+	0.688489i
$357$			20.7846i			1.10004i
$358$	−1.00000	−	1.73205i	−0.0528516	−	0.0915417i
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$		0			0
$361$	45.0000			2.36842
$362$	−3.50000	−	6.06218i	−0.183956	−	0.318621i
$363$	10.5000	−	6.06218i	0.551107	−	0.318182i
$364$	3.00000	−	5.19615i	0.157243	−	0.272352i
$365$		0			0
$366$	10.5000	−	6.06218i	0.548844	−	0.316875i
$367$	12.0000	+	20.7846i	0.626395	+	1.08495i	0.988269	+	0.152721i	$0.0488036\pi$
$367$	12.0000	+	20.7846i	0.626395	+	1.08495i	−0.361874	+	0.932227i	$0.617863\pi$
$368$	3.00000			0.156386
$369$	−15.0000			−0.780869
$370$		0			0
$371$	−3.00000	−	5.19615i	−0.155752	−	0.269771i
$372$		0			0
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	−0.707055	−	0.707159i	$-0.749977\pi$
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	0.965945	+	0.258748i	$0.0833099\pi$
$374$	4.00000	−	6.92820i	0.206835	−	0.358249i
$375$		0			0
$376$	10.5000	+	18.1865i	0.541496	+	0.937899i
$377$	−2.00000			−0.103005
$378$	13.5000	+	7.79423i	0.694365	+	0.400892i
$379$	−26.0000			−1.33553			−0.667765	−	0.744372i	$-0.732749\pi$
$379$	−26.0000			−1.33553			−0.667765	+	0.744372i	$0.732749\pi$
$380$		0			0
$381$	7.50000	+	4.33013i	0.384237	+	0.221839i
$382$	4.00000	−	6.92820i	0.204658	−	0.354478i
$383$	18.0000	−	31.1769i	0.919757	−	1.59307i	0.119974	−	0.992777i	$-0.461719\pi$
$383$	18.0000	−	31.1769i	0.919757	−	1.59307i	0.799783	−	0.600289i	$-0.204948\pi$
$384$		−	5.19615i		−	0.265165i
$385$		0			0
$386$	−10.0000			−0.508987
$387$	12.0000	−	20.7846i	0.609994	−	1.05654i
$388$	2.00000			0.101535
$389$	−16.5000	−	28.5788i	−0.836583	−	1.44900i	−0.892735	−	0.450582i	$-0.851216\pi$
$389$	−16.5000	−	28.5788i	−0.836583	−	1.44900i	0.0561516	−	0.998422i	$-0.482117\pi$
$390$		0			0
$391$	−6.00000	+	10.3923i	−0.303433	+	0.525561i
$392$	−3.00000	+	5.19615i	−0.151523	+	0.262445i
$393$	9.00000	−	5.19615i	0.453990	−	0.262111i
$394$	6.00000	+	10.3923i	0.302276	+	0.523557i
$395$		0			0
$396$	3.00000	+	5.19615i	0.150756	+	0.261116i
$397$	−34.0000			−1.70641			−0.853206	−	0.521575i	$-0.825345\pi$
$397$	−34.0000			−1.70641			−0.853206	+	0.521575i	$0.825345\pi$
$398$	2.00000	+	3.46410i	0.100251	+	0.173640i
$399$			41.5692i			2.08106i
$400$		0			0
$401$	9.00000	−	15.5885i	0.449439	−	0.778450i	−0.548911	−	0.835881i	$-0.684957\pi$
$401$	9.00000	−	15.5885i	0.449439	−	0.778450i	0.998350	+	0.0574304i	$0.0182907\pi$
$402$	−4.50000	−	2.59808i	−0.224440	−	0.129580i
$403$		0			0
$404$	18.0000			0.895533
$405$		0			0
$406$	3.00000			0.148888
$407$	4.00000	+	6.92820i	0.198273	+	0.343418i
$408$	−18.0000	−	10.3923i	−0.891133	−	0.514496i
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	−0.985558	−	0.169338i	$-0.945837\pi$
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	0.639430	+	0.768849i	$0.279170\pi$
$410$		0			0
$411$			20.7846i			1.02523i
$412$	−4.00000	−	6.92820i	−0.197066	−	0.341328i
$413$	−42.0000			−2.06668
$414$	4.50000	+	7.79423i	0.221163	+	0.383065i
$415$		0			0
$416$	5.00000	+	8.66025i	0.245145	+	0.424604i
$417$	24.0000	−	13.8564i	1.17529	−	0.678551i
$418$	8.00000	−	13.8564i	0.391293	−	0.677739i
$419$	−13.0000	+	22.5167i	−0.635092	+	1.10001i	0.351404	+	0.936224i	$0.385704\pi$
$419$	−13.0000	+	22.5167i	−0.635092	+	1.10001i	−0.986496	+	0.163787i	$0.947629\pi$
$420$		0			0
$421$	−17.0000	−	29.4449i	−0.828529	−	1.43505i	−0.899192	−	0.437555i	$-0.855845\pi$
$421$	−17.0000	−	29.4449i	−0.828529	−	1.43505i	0.0706626	−	0.997500i	$-0.477489\pi$
$422$	22.0000			1.07094
$423$	−10.5000	+	18.1865i	−0.510527	+	0.884260i
$424$	6.00000			0.291386
$425$		0			0
$426$			3.46410i			0.167836i
$427$	−10.5000	+	18.1865i	−0.508131	+	0.880108i
$428$	−1.50000	+	2.59808i	−0.0725052	+	0.125583i
$429$	−6.00000	−	3.46410i	−0.289683	−	0.167248i
$430$		0			0
$431$	−30.0000			−1.44505			−0.722525	−	0.691345i	$-0.757018\pi$
$431$	−30.0000			−1.44505			−0.722525	+	0.691345i	$0.757018\pi$
$432$	−4.50000	+	2.59808i	−0.216506	+	0.125000i
$433$	−28.0000			−1.34559			−0.672797	−	0.739827i	$-0.734907\pi$
$433$	−28.0000			−1.34559			−0.672797	+	0.739827i	$0.734907\pi$
$434$		0			0
$435$		0			0
$436$	2.50000	−	4.33013i	0.119728	−	0.207375i
$437$	−12.0000	+	20.7846i	−0.574038	+	0.994263i
$438$		−	6.92820i		−	0.331042i
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	−0.978412	−	0.206666i	$-0.933739\pi$
$439$	−14.0000	−	24.2487i	−0.668184	−	1.15733i	0.310228	−	0.950662i	$-0.399595\pi$
$440$		0			0
$441$	−6.00000			−0.285714
$442$	8.00000			0.380521
$443$	7.50000	+	12.9904i	0.356336	+	0.617192i	0.987346	−	0.158583i	$-0.0506926\pi$
$443$	7.50000	+	12.9904i	0.356336	+	0.617192i	−0.631010	+	0.775775i	$0.717359\pi$
$444$	6.00000	−	3.46410i	0.284747	−	0.164399i
$445$		0			0
$446$	9.50000	−	16.4545i	0.449838	−	0.779142i
$447$	−25.5000	+	14.7224i	−1.20611	+	0.696347i
$448$	−10.5000	−	18.1865i	−0.496078	−	0.859233i
$449$	−26.0000			−1.22702			−0.613508	−	0.789689i	$-0.710242\pi$
$449$	−26.0000			−1.22702			−0.613508	+	0.789689i	$0.710242\pi$
$450$		0			0
$451$	−10.0000			−0.470882
$452$	4.00000	+	6.92820i	0.188144	+	0.325875i
$453$			3.46410i			0.162758i
$454$	2.00000	−	3.46410i	0.0938647	−	0.162578i
$455$		0			0
$456$	−36.0000	−	20.7846i	−1.68585	−	0.973329i
$457$	−10.0000	−	17.3205i	−0.467780	−	0.810219i	0.531542	−	0.847032i	$-0.321613\pi$
$457$	−10.0000	−	17.3205i	−0.467780	−	0.810219i	−0.999322	+	0.0368128i	$0.988279\pi$
$458$	−15.0000			−0.700904
$459$		−	20.7846i		−	0.970143i
$460$		0			0
$461$	−4.50000	−	7.79423i	−0.209586	−	0.363013i	0.741998	−	0.670402i	$-0.233878\pi$
$461$	−4.50000	−	7.79423i	−0.209586	−	0.363013i	−0.951584	+	0.307388i	$0.900545\pi$
$462$	9.00000	+	5.19615i	0.418718	+	0.241747i
$463$	−18.0000	+	31.1769i	−0.836531	+	1.44891i	0.0562469	+	0.998417i	$0.482087\pi$
$463$	−18.0000	+	31.1769i	−0.836531	+	1.44891i	−0.892778	+	0.450497i	$0.851247\pi$
$464$	−0.500000	+	0.866025i	−0.0232119	+	0.0402042i
$465$		0			0
$466$	−12.0000	−	20.7846i	−0.555889	−	0.962828i
$467$	−20.0000			−0.925490			−0.462745	−	0.886492i	$-0.653135\pi$
$467$	−20.0000			−0.925490			−0.462745	+	0.886492i	$0.653135\pi$
$468$	−3.00000	+	5.19615i	−0.138675	+	0.240192i
$469$	9.00000			0.415581
$470$		0			0
$471$	21.0000	−	12.1244i	0.967629	−	0.558661i
$472$	21.0000	−	36.3731i	0.966603	−	1.67421i
$473$	8.00000	−	13.8564i	0.367840	−	0.637118i
$474$	−9.00000	+	5.19615i	−0.413384	+	0.238667i
$475$		0			0
$476$	12.0000			0.550019
$477$	3.00000	+	5.19615i	0.137361	+	0.237915i
$478$	8.00000			0.365911
$479$	9.00000	+	15.5885i	0.411220	+	0.712255i	0.995023	−	0.0996406i	$-0.0317693\pi$
$479$	9.00000	+	15.5885i	0.411220	+	0.712255i	−0.583803	+	0.811895i	$0.698436\pi$
$480$		0			0
$481$	−4.00000	+	6.92820i	−0.182384	+	0.315899i
$482$	−5.50000	+	9.52628i	−0.250518	+	0.433910i
$483$	−13.5000	−	7.79423i	−0.614271	−	0.354650i
$484$	−3.50000	−	6.06218i	−0.159091	−	0.275554i
$485$		0			0
$486$	−13.5000	−	7.79423i	−0.612372	−	0.353553i
$487$	16.0000			0.725029			0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000			0.725029			0.362515	+	0.931978i	$0.381918\pi$
$488$	−10.5000	−	18.1865i	−0.475313	−	0.823266i
$489$	6.00000	+	3.46410i	0.271329	+	0.156652i
$490$		0			0
$491$	−10.0000	+	17.3205i	−0.451294	+	0.781664i	−0.998467	−	0.0553560i	$-0.982371\pi$
$491$	−10.0000	+	17.3205i	−0.451294	+	0.781664i	0.547173	+	0.837020i	$0.315704\pi$
$492$			8.66025i			0.390434i
$493$	−2.00000	−	3.46410i	−0.0900755	−	0.156015i
$494$	16.0000			0.719874
$495$		0			0
$496$		0			0
$497$	−3.00000	−	5.19615i	−0.134568	−	0.233079i
$498$	−13.5000	+	7.79423i	−0.604949	+	0.349268i
$499$	16.0000	−	27.7128i	0.716258	−	1.24060i	−0.246214	−	0.969216i	$-0.579187\pi$
$499$	16.0000	−	27.7128i	0.716258	−	1.24060i	0.962472	−	0.271380i	$-0.0874801\pi$
$500$		0			0
$501$	−13.5000	+	7.79423i	−0.603136	+	0.348220i
$502$		0			0
$503$	7.00000			0.312115			0.156057	−	0.987748i	$-0.450122\pi$
$503$	7.00000			0.312115			0.156057	+	0.987748i	$0.450122\pi$
$504$	13.5000	−	23.3827i	0.601338	−	1.04155i
$505$		0			0
$506$	3.00000	+	5.19615i	0.133366	+	0.230997i
$507$			15.5885i			0.692308i
$508$	2.50000	−	4.33013i	0.110920	−	0.192118i
$509$	−21.5000	+	37.2391i	−0.952971	+	1.65059i	−0.214026	+	0.976828i	$0.568658\pi$
$509$	−21.5000	+	37.2391i	−0.952971	+	1.65059i	−0.738945	+	0.673766i	$0.764676\pi$
$510$		0			0
$511$	6.00000	+	10.3923i	0.265424	+	0.459728i
$512$	11.0000			0.486136
$513$		−	41.5692i		−	1.83533i
$514$	−6.00000			−0.264649
$515$		0			0
$516$	−12.0000	−	6.92820i	−0.528271	−	0.304997i
$517$	−7.00000	+	12.1244i	−0.307860	+	0.533229i
$518$	6.00000	−	10.3923i	0.263625	−	0.456612i
$519$		0			0
$520$		0			0
$521$	11.0000			0.481919			0.240959	−	0.970535i	$-0.422538\pi$
$521$	11.0000			0.481919			0.240959	+	0.970535i	$0.422538\pi$
$522$	−3.00000			−0.131306
$523$	29.0000			1.26808			0.634041	−	0.773300i	$-0.281395\pi$
$523$	29.0000			1.26808			0.634041	+	0.773300i	$0.281395\pi$
$524$	−3.00000	−	5.19615i	−0.131056	−	0.226995i
$525$		0			0
$526$	8.00000	−	13.8564i	0.348817	−	0.604168i
$527$		0			0
$528$	−3.00000	+	1.73205i	−0.130558	+	0.0753778i
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$	42.0000			1.82264
$532$	24.0000			1.04053
$533$	−5.00000	−	8.66025i	−0.216574	−	0.375117i
$534$		−	25.9808i		−	1.12430i
$535$		0			0
$536$	−4.50000	+	7.79423i	−0.194370	+	0.336659i
$537$	−3.00000	−	1.73205i	−0.129460	−	0.0747435i
$538$	12.5000	+	21.6506i	0.538913	+	0.933425i
$539$	−4.00000			−0.172292
$540$		0			0
$541$	−39.0000			−1.67674			−0.838370	−	0.545101i	$-0.816491\pi$
$541$	−39.0000			−1.67674			−0.838370	+	0.545101i	$0.816491\pi$
$542$	−4.00000	−	6.92820i	−0.171815	−	0.297592i
$543$	−10.5000	−	6.06218i	−0.450598	−	0.260153i
$544$	−10.0000	+	17.3205i	−0.428746	+	0.742611i
$545$		0			0
$546$			10.3923i			0.444750i
$547$	−14.5000	−	25.1147i	−0.619975	−	1.07383i	−0.989490	−	0.144604i	$-0.953809\pi$
$547$	−14.5000	−	25.1147i	−0.619975	−	1.07383i	0.369514	−	0.929225i	$-0.379524\pi$
$548$	12.0000			0.512615
$549$	10.5000	−	18.1865i	0.448129	−	0.776182i
$550$		0			0
$551$	−4.00000	−	6.92820i	−0.170406	−	0.295151i
$552$	13.5000	−	7.79423i	0.574598	−	0.331744i
$553$	9.00000	−	15.5885i	0.382719	−	0.662889i
$554$	−6.00000	+	10.3923i	−0.254916	+	0.441527i
$555$		0			0
$556$	−8.00000	−	13.8564i	−0.339276	−	0.587643i
$557$	30.0000			1.27114			0.635570	−	0.772043i	$-0.280765\pi$
$557$	30.0000			1.27114			0.635570	+	0.772043i	$0.280765\pi$
$558$		0			0
$559$	16.0000			0.676728
$560$		0			0
$561$		−	13.8564i		−	0.585018i
$562$	−7.50000	+	12.9904i	−0.316368	+	0.547966i
$563$	−10.5000	+	18.1865i	−0.442522	+	0.766471i	−0.997876	−	0.0651433i	$-0.979250\pi$
$563$	−10.5000	+	18.1865i	−0.442522	+	0.766471i	0.555354	+	0.831614i	$0.312583\pi$
$564$	10.5000	+	6.06218i	0.442130	+	0.255264i
$565$		0			0
$566$	21.0000			0.882696
$567$	27.0000			1.13389
$568$	6.00000			0.251754
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$		0			0
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	0.308443	+	0.951243i	$0.400192\pi$
$571$	−16.0000	+	27.7128i	−0.669579	+	1.15975i	−0.978022	+	0.208502i	$0.933141\pi$
$572$	−2.00000	+	3.46410i	−0.0836242	+	0.144841i
$573$		−	13.8564i		−	0.578860i
$574$	7.50000	+	12.9904i	0.313044	+	0.542208i
$575$		0			0
$576$	10.5000	+	18.1865i	0.437500	+	0.757772i
$577$	10.0000			0.416305			0.208153	−	0.978096i	$-0.433255\pi$
$577$	10.0000			0.416305			0.208153	+	0.978096i	$0.433255\pi$
$578$	−0.500000	−	0.866025i	−0.0207973	−	0.0360219i
$579$	−15.0000	+	8.66025i	−0.623379	+	0.359908i
$580$		0			0
$581$	13.5000	−	23.3827i	0.560074	−	0.970077i
$582$	−3.00000	+	1.73205i	−0.124354	+	0.0717958i
$583$	2.00000	+	3.46410i	0.0828315	+	0.143468i
$584$	−12.0000			−0.496564
$585$		0			0
$586$	12.0000			0.495715
$587$	−16.5000	−	28.5788i	−0.681028	−	1.17957i	−0.974668	−	0.223659i	$-0.928200\pi$
$587$	−16.5000	−	28.5788i	−0.681028	−	1.17957i	0.293640	−	0.955916i	$-0.405133\pi$
$588$			3.46410i			0.142857i
$589$		0			0
$590$		0			0
$591$	18.0000	+	10.3923i	0.740421	+	0.427482i
$592$	2.00000	+	3.46410i	0.0821995	+	0.142374i
$593$	−20.0000			−0.821302			−0.410651	−	0.911793i	$-0.634698\pi$
$593$	−20.0000			−0.821302			−0.410651	+	0.911793i	$0.634698\pi$
$594$	−9.00000	−	5.19615i	−0.369274	−	0.213201i
$595$		0			0
$596$	8.50000	+	14.7224i	0.348174	+	0.603054i
$597$	6.00000	+	3.46410i	0.245564	+	0.141776i
$598$	−3.00000	+	5.19615i	−0.122679	+	0.212486i
$599$	5.00000	−	8.66025i	0.204294	−	0.353848i	−0.745613	−	0.666379i	$-0.767843\pi$
$599$	5.00000	−	8.66025i	0.204294	−	0.353848i	0.949908	+	0.312531i	$0.101177\pi$
$600$		0			0
$601$	−1.00000	−	1.73205i	−0.0407909	−	0.0706518i	0.844909	−	0.534910i	$-0.179654\pi$
$601$	−1.00000	−	1.73205i	−0.0407909	−	0.0706518i	−0.885700	+	0.464258i	$0.846321\pi$
$602$	−24.0000			−0.978167
$603$	−9.00000			−0.366508
$604$	2.00000			0.0813788
$605$		0			0
$606$	−27.0000	+	15.5885i	−1.09680	+	0.633238i
$607$	−20.5000	+	35.5070i	−0.832069	+	1.44119i	0.0643251	+	0.997929i	$0.479511\pi$
$607$	−20.5000	+	35.5070i	−0.832069	+	1.44119i	−0.896394	+	0.443257i	$0.853823\pi$
$608$	−20.0000	+	34.6410i	−0.811107	+	1.40488i
$609$	4.50000	−	2.59808i	0.182349	−	0.105279i
$610$		0			0
$611$	−14.0000			−0.566379
$612$	−12.0000			−0.485071
$613$	44.0000			1.77714			0.888572	−	0.458738i	$-0.151698\pi$
$613$	44.0000			1.77714			0.888572	+	0.458738i	$0.151698\pi$
$614$	−3.50000	−	6.06218i	−0.141249	−	0.244650i
$615$		0			0
$616$	9.00000	−	15.5885i	0.362620	−	0.628077i
$617$	−18.0000	+	31.1769i	−0.724653	+	1.25514i	0.234464	+	0.972125i	$0.424666\pi$
$617$	−18.0000	+	31.1769i	−0.724653	+	1.25514i	−0.959117	+	0.283011i	$0.908667\pi$
$618$	12.0000	+	6.92820i	0.482711	+	0.278693i
$619$	2.00000	+	3.46410i	0.0803868	+	0.139234i	0.903416	−	0.428765i	$-0.141051\pi$
$619$	2.00000	+	3.46410i	0.0803868	+	0.139234i	−0.823029	+	0.567999i	$0.807718\pi$
$620$		0			0
$621$	13.5000	+	7.79423i	0.541736	+	0.312772i
$622$		0			0
$623$	22.5000	+	38.9711i	0.901443	+	1.56135i
$624$	−3.00000	−	1.73205i	−0.120096	−	0.0693375i
$625$		0			0
$626$	−7.00000	+	12.1244i	−0.279776	+	0.484587i
$627$		−	27.7128i		−	1.10674i
$628$	−7.00000	−	12.1244i	−0.279330	−	0.483814i
$629$	−16.0000			−0.637962
$630$		0			0
$631$	16.0000			0.636950			0.318475	−	0.947931i	$-0.396829\pi$
$631$	16.0000			0.636950			0.318475	+	0.947931i	$0.396829\pi$
$632$	9.00000	+	15.5885i	0.358001	+	0.620076i
$633$	33.0000	−	19.0526i	1.31163	−	0.757271i
$634$	17.0000	−	29.4449i	0.675156	−	1.16940i
$635$		0			0
$636$	3.00000	−	1.73205i	0.118958	−	0.0686803i
$637$	−2.00000	−	3.46410i	−0.0792429	−	0.137253i
$638$	−2.00000			−0.0791808
$639$	3.00000	+	5.19615i	0.118678	+	0.205557i
$640$		0			0
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	−0.982708	−	0.185164i	$-0.940718\pi$
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	0.330997	−	0.943632i	$-0.392615\pi$
$642$		−	5.19615i		−	0.205076i
$643$	−4.50000	+	7.79423i	−0.177463	+	0.307374i	−0.941011	−	0.338377i	$-0.890122\pi$
$643$	−4.50000	+	7.79423i	−0.177463	+	0.307374i	0.763548	+	0.645751i	$0.223456\pi$
$644$	−4.50000	+	7.79423i	−0.177325	+	0.307136i
$645$		0			0
$646$	16.0000	+	27.7128i	0.629512	+	1.09035i
$647$	17.0000			0.668339			0.334169	−	0.942513i	$-0.391544\pi$
$647$	17.0000			0.668339			0.334169	+	0.942513i	$0.391544\pi$
$648$	−13.5000	+	23.3827i	−0.530330	+	0.918559i
$649$	28.0000			1.09910
$650$		0			0
$651$		0			0
$652$	2.00000	−	3.46410i	0.0783260	−	0.135665i
$653$	−2.00000	+	3.46410i	−0.0782660	+	0.135561i	−0.902502	−	0.430686i	$-0.858272\pi$
$653$	−2.00000	+	3.46410i	−0.0782660	+	0.135561i	0.824236	+	0.566247i	$0.191605\pi$
$654$			8.66025i			0.338643i
$655$		0			0
$656$	−5.00000			−0.195217
$657$	−6.00000	−	10.3923i	−0.234082	−	0.405442i
$658$	21.0000			0.818665
$659$	4.00000	+	6.92820i	0.155818	+	0.269884i	0.933357	−	0.358951i	$-0.116865\pi$
$659$	4.00000	+	6.92820i	0.155818	+	0.269884i	−0.777539	+	0.628835i	$0.783532\pi$
$660$		0			0
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	−0.697174	−	0.716902i	$-0.745559\pi$
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	0.969442	+	0.245319i	$0.0788928\pi$
$662$	−3.00000	+	5.19615i	−0.116598	+	0.201954i
$663$	12.0000	−	6.92820i	0.466041	−	0.269069i
$664$	13.5000	+	23.3827i	0.523902	+	0.907424i
$665$		0			0
$666$	−6.00000	+	10.3923i	−0.232495	+	0.402694i
$667$	3.00000			0.116160
$668$	4.50000	+	7.79423i	0.174110	+	0.301568i
$669$		−	32.9090i		−	1.27233i
$670$		0			0
$671$	7.00000	−	12.1244i	0.270232	−	0.468056i
$672$	−22.5000	−	12.9904i	−0.867956	−	0.501115i
$673$	3.00000	+	5.19615i	0.115642	+	0.200297i	0.918036	−	0.396497i	$-0.129774\pi$
$673$	3.00000	+	5.19615i	0.115642	+	0.200297i	−0.802395	+	0.596794i	$0.796441\pi$
$674$	−8.00000			−0.308148
$675$		0			0
$676$	9.00000			0.346154
$677$	−21.0000	−	36.3731i	−0.807096	−	1.39793i	−0.914867	−	0.403755i	$-0.867705\pi$
$677$	−21.0000	−	36.3731i	−0.807096	−	1.39793i	0.107772	−	0.994176i	$-0.465628\pi$
$678$	−12.0000	−	6.92820i	−0.460857	−	0.266076i
$679$	3.00000	−	5.19615i	0.115129	−	0.199410i
$680$		0			0
$681$		−	6.92820i		−	0.265489i
$682$		0			0
$683$	−12.0000			−0.459167			−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000			−0.459167			−0.229584	+	0.973289i	$0.573736\pi$
$684$	−24.0000			−0.917663
$685$		0			0
$686$	−7.50000	−	12.9904i	−0.286351	−	0.495975i
$687$	−22.5000	+	12.9904i	−0.858429	+	0.495614i
$688$	4.00000	−	6.92820i	0.152499	−	0.264135i
$689$	−2.00000	+	3.46410i	−0.0761939	+	0.131972i
$690$		0			0
$691$	7.00000	+	12.1244i	0.266293	+	0.461232i	0.967901	−	0.251330i	$-0.0808679\pi$
$691$	7.00000	+	12.1244i	0.266293	+	0.461232i	−0.701609	+	0.712562i	$0.747535\pi$
$692$		0			0
$693$	18.0000			0.683763
$694$	4.00000			0.151838
$695$		0			0
$696$			5.19615i			0.196960i
$697$	10.0000	−	17.3205i	0.378777	−	0.656061i
$698$	−2.50000	+	4.33013i	−0.0946264	+	0.163898i
$699$	−36.0000	−	20.7846i	−1.36165	−	0.786146i
$700$		0			0
$701$	23.0000			0.868698			0.434349	−	0.900745i	$-0.356978\pi$
$701$	23.0000			0.868698			0.434349	+	0.900745i	$0.356978\pi$
$702$		−	10.3923i		−	0.392232i
$703$	−32.0000			−1.20690
$704$	7.00000	+	12.1244i	0.263822	+	0.456954i
$705$		0			0
$706$	−12.0000	+	20.7846i	−0.451626	+	0.782239i
$707$	27.0000	−	46.7654i	1.01544	−	1.75879i
$708$		−	24.2487i		−	0.911322i
$709$	20.5000	+	35.5070i	0.769894	+	1.33349i	0.937620	+	0.347661i	$0.113024\pi$
$709$	20.5000	+	35.5070i	0.769894	+	1.33349i	−0.167727	+	0.985834i	$0.553643\pi$
$710$		0			0
$711$	−9.00000	+	15.5885i	−0.337526	+	0.584613i
$712$	−45.0000			−1.68645
$713$		0			0
$714$	−18.0000	+	10.3923i	−0.673633	+	0.388922i
$715$		0			0
$716$	−1.00000	+	1.73205i	−0.0373718	+	0.0647298i
$717$	12.0000	−	6.92820i	0.448148	−	0.258738i
$718$	12.0000	+	20.7846i	0.447836	+	0.775675i
$719$	6.00000			0.223762			0.111881	−	0.993722i	$-0.464312\pi$
$719$	6.00000			0.223762			0.111881	+	0.993722i	$0.464312\pi$
$720$		0			0
$721$	−24.0000			−0.893807
$722$	22.5000	+	38.9711i	0.837363	+	1.45036i
$723$			19.0526i			0.708572i
$724$	−3.50000	+	6.06218i	−0.130076	+	0.225299i
$725$		0			0
$726$	10.5000	+	6.06218i	0.389692	+	0.224989i
$727$	11.5000	+	19.9186i	0.426511	+	0.738739i	0.996560	−	0.0828714i	$-0.0264091\pi$
$727$	11.5000	+	19.9186i	0.426511	+	0.738739i	−0.570049	+	0.821611i	$0.693076\pi$
$728$	18.0000			0.667124
$729$	−27.0000			−1.00000
$730$		0			0
$731$	16.0000	+	27.7128i	0.591781	+	1.02500i
$732$	−10.5000	−	6.06218i	−0.388091	−	0.224065i
$733$	−17.0000	+	29.4449i	−0.627909	+	1.08757i	0.360061	+	0.932929i	$0.382756\pi$
$733$	−17.0000	+	29.4449i	−0.627909	+	1.08757i	−0.987971	+	0.154642i	$0.950578\pi$
$734$	−12.0000	+	20.7846i	−0.442928	+	0.767174i
$735$		0			0
$736$	−7.50000	−	12.9904i	−0.276454	−	0.478832i
$737$	−6.00000			−0.221013
$738$	−7.50000	−	12.9904i	−0.276079	−	0.478183i
$739$	−2.00000			−0.0735712			−0.0367856	−	0.999323i	$-0.511712\pi$
$739$	−2.00000			−0.0735712			−0.0367856	+	0.999323i	$0.511712\pi$
$740$		0			0
$741$	24.0000	−	13.8564i	0.881662	−	0.509028i
$742$	3.00000	−	5.19615i	0.110133	−	0.190757i
$743$	−14.5000	+	25.1147i	−0.531953	+	0.921370i	0.467351	+	0.884072i	$0.345209\pi$
$743$	−14.5000	+	25.1147i	−0.531953	+	0.921370i	−0.999304	+	0.0372984i	$0.988125\pi$
$744$		0			0
$745$		0			0
$746$	10.0000			0.366126
$747$	−13.5000	+	23.3827i	−0.493939	+	0.855528i
$748$	−8.00000			−0.292509
$749$	4.50000	+	7.79423i	0.164426	+	0.284795i
$750$		0			0
$751$	−5.00000	+	8.66025i	−0.182453	+	0.316017i	−0.942715	−	0.333599i	$-0.891737\pi$
$751$	−5.00000	+	8.66025i	−0.182453	+	0.316017i	0.760263	+	0.649616i	$0.225070\pi$
$752$	−3.50000	+	6.06218i	−0.127632	+	0.221065i
$753$		0			0
$754$	−1.00000	−	1.73205i	−0.0364179	−	0.0630776i
$755$		0			0
$756$		−	15.5885i		−	0.566947i
$757$	26.0000			0.944986			0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000			0.944986			0.472493	+	0.881334i	$0.343354\pi$
$758$	−13.0000	−	22.5167i	−0.472181	−	0.817842i
$759$	9.00000	+	5.19615i	0.326679	+	0.188608i
$760$		0			0
$761$	−7.50000	+	12.9904i	−0.271875	+	0.470901i	−0.969342	−	0.245716i	$-0.920977\pi$
$761$	−7.50000	+	12.9904i	−0.271875	+	0.470901i	0.697467	+	0.716617i	$0.254310\pi$
$762$			8.66025i			0.313728i
$763$	−7.50000	−	12.9904i	−0.271518	−	0.470283i
$764$	−8.00000			−0.289430
$765$		0			0
$766$	36.0000			1.30073
$767$	14.0000	+	24.2487i	0.505511	+	0.875570i
$768$	25.5000	−	14.7224i	0.920152	−	0.531250i
$769$	−2.50000	+	4.33013i	−0.0901523	+	0.156148i	−0.907575	−	0.419890i	$-0.862069\pi$
$769$	−2.50000	+	4.33013i	−0.0901523	+	0.156148i	0.817423	+	0.576038i	$0.195402\pi$
$770$		0			0
$771$	−9.00000	+	5.19615i	−0.324127	+	0.187135i
$772$	5.00000	+	8.66025i	0.179954	+	0.311689i
$773$	24.0000			0.863220			0.431610	−	0.902060i	$-0.357946\pi$
$773$	24.0000			0.863220			0.431610	+	0.902060i	$0.357946\pi$
$774$	24.0000			0.862662
$775$		0			0
$776$	3.00000	+	5.19615i	0.107694	+	0.186531i
$777$		−	20.7846i		−	0.745644i
$778$	16.5000	−	28.5788i	0.591554	−	1.02460i
$779$	20.0000	−	34.6410i	0.716574	−	1.24114i
$780$		0			0
$781$	2.00000	+	3.46410i	0.0715656	+	0.123955i
$782$	−12.0000			−0.429119
$783$	−4.50000	+	2.59808i	−0.160817	+	0.0928477i
$784$	−2.00000

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.73205i q^{6} +(-1.50000 - 2.59808i) q^{7} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.50000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.73205i q^{6} +(-1.50000 - 2.59808i) q^{7} +3.00000 q^{8} +(1.50000 + 2.59808i) q^{9} +(1.00000 + 1.73205i) q^{11} +(1.50000 - 0.866025i) q^{12} +(-1.00000 + 1.73205i) q^{13} +(1.50000 - 2.59808i) q^{14} +(0.500000 + 0.866025i) q^{16} -4.00000 q^{17} +(-1.50000 + 2.59808i) q^{18} -8.00000 q^{19} -5.19615i q^{21} +(-1.00000 + 1.73205i) q^{22} +(1.50000 - 2.59808i) q^{23} +(4.50000 + 2.59808i) q^{24} -2.00000 q^{26} +5.19615i q^{27} -3.00000 q^{28} +(0.500000 + 0.866025i) q^{29} +(2.50000 - 4.33013i) q^{32} +3.46410i q^{33} +(-2.00000 - 3.46410i) q^{34} +3.00000 q^{36} +4.00000 q^{37} +(-4.00000 - 6.92820i) q^{38} +(-3.00000 + 1.73205i) q^{39} +(-2.50000 + 4.33013i) q^{41} +(4.50000 - 2.59808i) q^{42} +(-4.00000 - 6.92820i) q^{43} +2.00000 q^{44} +3.00000 q^{46} +(3.50000 + 6.06218i) q^{47} +1.73205i q^{48} +(-1.00000 + 1.73205i) q^{49} +(-6.00000 - 3.46410i) q^{51} +(1.00000 + 1.73205i) q^{52} +2.00000 q^{53} +(-4.50000 + 2.59808i) q^{54} +(-4.50000 - 7.79423i) q^{56} +(-12.0000 - 6.92820i) q^{57} +(-0.500000 + 0.866025i) q^{58} +(7.00000 - 12.1244i) q^{59} +(-3.50000 - 6.06218i) q^{61} +(4.50000 - 7.79423i) q^{63} +7.00000 q^{64} +(-3.00000 + 1.73205i) q^{66} +(-1.50000 + 2.59808i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(4.50000 - 2.59808i) q^{69} +2.00000 q^{71} +(4.50000 + 7.79423i) q^{72} -4.00000 q^{73} +(2.00000 + 3.46410i) q^{74} +(-4.00000 + 6.92820i) q^{76} +(3.00000 - 5.19615i) q^{77} +(-3.00000 - 1.73205i) q^{78} +(3.00000 + 5.19615i) q^{79} +(-4.50000 + 7.79423i) q^{81} -5.00000 q^{82} +(4.50000 + 7.79423i) q^{83} +(-4.50000 - 2.59808i) q^{84} +(4.00000 - 6.92820i) q^{86} +1.73205i q^{87} +(3.00000 + 5.19615i) q^{88} -15.0000 q^{89} +6.00000 q^{91} +(-1.50000 - 2.59808i) q^{92} +(-3.50000 + 6.06218i) q^{94} +(7.50000 - 4.33013i) q^{96} +(1.00000 + 1.73205i) q^{97} -2.00000 q^{98} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 3 q^{3} + q^{4} - 3 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q + q^2 + 3 * q^3 + q^4 - 3 * q^7 + 6 * q^8 + 3 * q^9	\( 2 q + q^{2} + 3 q^{3} + q^{4} - 3 q^{7} + 6 q^{8} + 3 q^{9} + 2 q^{11} + 3 q^{12} - 2 q^{13} + 3 q^{14} + q^{16} - 8 q^{17} - 3 q^{18} - 16 q^{19} - 2 q^{22} + 3 q^{23} + 9 q^{24} - 4 q^{26} - 6 q^{28} + q^{29} + 5 q^{32} - 4 q^{34} + 6 q^{36} + 8 q^{37} - 8 q^{38} - 6 q^{39} - 5 q^{41} + 9 q^{42} - 8 q^{43} + 4 q^{44} + 6 q^{46} + 7 q^{47} - 2 q^{49} - 12 q^{51} + 2 q^{52} + 4 q^{53} - 9 q^{54} - 9 q^{56} - 24 q^{57} - q^{58} + 14 q^{59} - 7 q^{61} + 9 q^{63} + 14 q^{64} - 6 q^{66} - 3 q^{67} - 4 q^{68} + 9 q^{69} + 4 q^{71} + 9 q^{72} - 8 q^{73} + 4 q^{74} - 8 q^{76} + 6 q^{77} - 6 q^{78} + 6 q^{79} - 9 q^{81} - 10 q^{82} + 9 q^{83} - 9 q^{84} + 8 q^{86} + 6 q^{88} - 30 q^{89} + 12 q^{91} - 3 q^{92} - 7 q^{94} + 15 q^{96} + 2 q^{97} - 4 q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q + q^2 + 3 * q^3 + q^4 - 3 * q^7 + 6 * q^8 + 3 * q^9 + 2 * q^11 + 3 * q^12 - 2 * q^13 + 3 * q^14 + q^16 - 8 * q^17 - 3 * q^18 - 16 * q^19 - 2 * q^22 + 3 * q^23 + 9 * q^24 - 4 * q^26 - 6 * q^28 + q^29 + 5 * q^32 - 4 * q^34 + 6 * q^36 + 8 * q^37 - 8 * q^38 - 6 * q^39 - 5 * q^41 + 9 * q^42 - 8 * q^43 + 4 * q^44 + 6 * q^46 + 7 * q^47 - 2 * q^49 - 12 * q^51 + 2 * q^52 + 4 * q^53 - 9 * q^54 - 9 * q^56 - 24 * q^57 - q^58 + 14 * q^59 - 7 * q^61 + 9 * q^63 + 14 * q^64 - 6 * q^66 - 3 * q^67 - 4 * q^68 + 9 * q^69 + 4 * q^71 + 9 * q^72 - 8 * q^73 + 4 * q^74 - 8 * q^76 + 6 * q^77 - 6 * q^78 + 6 * q^79 - 9 * q^81 - 10 * q^82 + 9 * q^83 - 9 * q^84 + 8 * q^86 + 6 * q^88 - 30 * q^89 + 12 * q^91 - 3 * q^92 - 7 * q^94 + 15 * q^96 + 2 * q^97 - 4 * q^98 - 6 * q^99

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