LMFDB - Embedded newform 735.2.i.d.226.1

Newspace parameters

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.i (of order $3$, degree $2$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
Defining polynomial:	$x^{2} - x + 1$
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	735.226
Dual form			735.2.i.d.361.1

$q$-expansion

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(2.00000 + 3.46410i) q^{11} +(0.500000 - 0.866025i) q^{12} +2.00000 q^{13} -1.00000 q^{15} +(0.500000 - 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(0.500000 + 0.866025i) q^{18} +(2.00000 - 3.46410i) q^{19} +1.00000 q^{20} +4.00000 q^{22} +(-1.50000 - 2.59808i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.00000 - 1.73205i) q^{26} +1.00000 q^{27} -2.00000 q^{29} +(-0.500000 + 0.866025i) q^{30} +(2.50000 + 4.33013i) q^{32} +(2.00000 - 3.46410i) q^{33} +2.00000 q^{34} -1.00000 q^{36} +(5.00000 - 8.66025i) q^{37} +(-2.00000 - 3.46410i) q^{38} +(-1.00000 - 1.73205i) q^{39} +(1.50000 - 2.59808i) q^{40} -10.0000 q^{41} +4.00000 q^{43} +(-2.00000 + 3.46410i) q^{44} +(0.500000 + 0.866025i) q^{45} +(4.00000 - 6.92820i) q^{47} -1.00000 q^{48} -1.00000 q^{50} +(1.00000 - 1.73205i) q^{51} +(1.00000 + 1.73205i) q^{52} +(5.00000 + 8.66025i) q^{53} +(0.500000 - 0.866025i) q^{54} +4.00000 q^{55} -4.00000 q^{57} +(-1.00000 + 1.73205i) q^{58} +(-2.00000 - 3.46410i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(-1.00000 + 1.73205i) q^{61} +7.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(-2.00000 - 3.46410i) q^{66} +(-6.00000 - 10.3923i) q^{67} +(-1.00000 + 1.73205i) q^{68} -8.00000 q^{71} +(-1.50000 + 2.59808i) q^{72} +(5.00000 + 8.66025i) q^{73} +(-5.00000 - 8.66025i) q^{74} +(-0.500000 + 0.866025i) q^{75} +4.00000 q^{76} -2.00000 q^{78} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.00000 + 8.66025i) q^{82} -12.0000 q^{83} +2.00000 q^{85} +(2.00000 - 3.46410i) q^{86} +(1.00000 + 1.73205i) q^{87} +(6.00000 + 10.3923i) q^{88} +(-3.00000 + 5.19615i) q^{89} +1.00000 q^{90} +(-4.00000 - 6.92820i) q^{94} +(-2.00000 - 3.46410i) q^{95} +(2.50000 - 4.33013i) q^{96} -2.00000 q^{97} -4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2q + q^{2} - q^{3} + q^{4} + q^{5} - 2q^{6} + 6q^{8} - q^{9} + O(q^{10}) $	$ 2q + q^{2} - q^{3} + q^{4} + q^{5} - 2q^{6} + 6q^{8} - q^{9} - q^{10} + 4q^{11} + q^{12} + 4q^{13} - 2q^{15} + q^{16} + 2q^{17} + q^{18} + 4q^{19} + 2q^{20} + 8q^{22} - 3q^{24} - q^{25} + 2q^{26} + 2q^{27} - 4q^{29} - q^{30} + 5q^{32} + 4q^{33} + 4q^{34} - 2q^{36} + 10q^{37} - 4q^{38} - 2q^{39} + 3q^{40} - 20q^{41} + 8q^{43} - 4q^{44} + q^{45} + 8q^{47} - 2q^{48} - 2q^{50} + 2q^{51} + 2q^{52} + 10q^{53} + q^{54} + 8q^{55} - 8q^{57} - 2q^{58} - 4q^{59} - q^{60} - 2q^{61} + 14q^{64} + 2q^{65} - 4q^{66} - 12q^{67} - 2q^{68} - 16q^{71} - 3q^{72} + 10q^{73} - 10q^{74} - q^{75} + 8q^{76} - 4q^{78} - q^{80} - q^{81} - 10q^{82} - 24q^{83} + 4q^{85} + 4q^{86} + 2q^{87} + 12q^{88} - 6q^{89} + 2q^{90} - 8q^{94} - 4q^{95} + 5q^{96} - 4q^{97} - 8q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i	−0.633316	−	0.773893i	$-0.718307\pi$
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i	0.986869	+	0.161521i	$0.0516399\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−1.00000			−0.408248
$7$		0			0
$7$		0			0
$8$	3.00000			1.06066
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	0.992361	+	0.123371i	$0.0393705\pi$
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	−0.389338	+	0.921095i	$0.627296\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	−0.540068	−	0.841621i	$-0.681602\pi$
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	0.998899	+	0.0469020i	$0.0149348\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	4.00000			0.852803
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	−1.50000	−	2.59808i	−0.306186	−	0.530330i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.00000	−	1.73205i	0.196116	−	0.339683i
$27$	1.00000			0.192450
$28$		0			0
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$	2.50000	+	4.33013i	0.441942	+	0.765466i
$33$	2.00000	−	3.46410i	0.348155	−	0.603023i
$34$	2.00000			0.342997
$35$		0			0
$36$	−1.00000			−0.166667
$37$	5.00000	−	8.66025i	0.821995	−	1.42374i	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	5.00000	−	8.66025i	0.821995	−	1.42374i	0.904194	−	0.427121i	$-0.140472\pi$
$38$	−2.00000	−	3.46410i	−0.324443	−	0.561951i
$39$	−1.00000	−	1.73205i	−0.160128	−	0.277350i
$40$	1.50000	−	2.59808i	0.237171	−	0.410792i
$41$	−10.0000			−1.56174			−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000			−1.56174			−0.780869	+	0.624695i	$0.785223\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$	−2.00000	+	3.46410i	−0.301511	+	0.522233i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$		0			0
$47$	4.00000	−	6.92820i	0.583460	−	1.01058i	−0.411606	−	0.911362i	$-0.635032\pi$
$47$	4.00000	−	6.92820i	0.583460	−	1.01058i	0.995066	−	0.0992202i	$-0.0316348\pi$
$48$	−1.00000			−0.144338
$49$		0			0
$50$	−1.00000			−0.141421
$51$	1.00000	−	1.73205i	0.140028	−	0.242536i
$52$	1.00000	+	1.73205i	0.138675	+	0.240192i
$53$	5.00000	+	8.66025i	0.686803	+	1.18958i	0.972867	+	0.231367i	$0.0743197\pi$
$53$	5.00000	+	8.66025i	0.686803	+	1.18958i	−0.286064	+	0.958211i	$0.592347\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	4.00000			0.539360
$56$		0			0
$57$	−4.00000			−0.529813
$58$	−1.00000	+	1.73205i	−0.131306	+	0.227429i
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	0.705965	−	0.708247i	$-0.250514\pi$
$59$	−2.00000	−	3.46410i	−0.260378	−	0.450988i	−0.966342	+	0.257260i	$0.917180\pi$
$60$	−0.500000	−	0.866025i	−0.0645497	−	0.111803i
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	−0.922916	−	0.385002i	$-0.874201\pi$
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	0.794879	+	0.606768i	$0.207534\pi$
$62$		0			0
$63$		0			0
$64$	7.00000			0.875000
$65$	1.00000	−	1.73205i	0.124035	−	0.214834i
$66$	−2.00000	−	3.46410i	−0.246183	−	0.426401i
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	−0.955588	−	0.294706i	$-0.904778\pi$
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	0.222571	−	0.974916i	$-0.428555\pi$
$68$	−1.00000	+	1.73205i	−0.121268	+	0.210042i
$69$		0			0
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$	−1.50000	+	2.59808i	−0.176777	+	0.306186i
$73$	5.00000	+	8.66025i	0.585206	+	1.01361i	0.994850	+	0.101361i	$0.0323196\pi$
$73$	5.00000	+	8.66025i	0.585206	+	1.01361i	−0.409644	+	0.912245i	$0.634347\pi$
$74$	−5.00000	−	8.66025i	−0.581238	−	1.00673i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	4.00000			0.458831
$77$		0			0
$78$	−2.00000			−0.226455
$79$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$79$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−5.00000	+	8.66025i	−0.552158	+	0.956365i
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$		0			0
$85$	2.00000			0.216930
$86$	2.00000	−	3.46410i	0.215666	−	0.373544i
$87$	1.00000	+	1.73205i	0.107211	+	0.185695i
$88$	6.00000	+	10.3923i	0.639602	+	1.10782i
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$	1.00000			0.105409
$91$		0			0
$92$		0			0
$93$		0			0
$94$	−4.00000	−	6.92820i	−0.412568	−	0.714590i
$95$	−2.00000	−	3.46410i	−0.205196	−	0.355409i
$96$	2.50000	−	4.33013i	0.255155	−	0.441942i
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$		0			0
$99$	−4.00000			−0.402015
$100$	0.500000	−	0.866025i	0.0500000	−	0.0866025i
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	0.975796	−	0.218685i	$-0.0701767\pi$
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	−0.677284	+	0.735721i	$0.736843\pi$
$102$	−1.00000	−	1.73205i	−0.0990148	−	0.171499i
$103$	−8.00000	+	13.8564i	−0.788263	+	1.36531i	0.138767	+	0.990325i	$0.455686\pi$
$103$	−8.00000	+	13.8564i	−0.788263	+	1.36531i	−0.927030	+	0.374987i	$0.877647\pi$
$104$	6.00000			0.588348
$105$		0			0
$106$	10.0000			0.971286
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	−0.415432	−	0.909624i	$-0.636370\pi$
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	0.995474	−	0.0950377i	$-0.0302972\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	−0.977769	−	0.209687i	$-0.932756\pi$
$109$	−7.00000	−	12.1244i	−0.670478	−	1.16130i	0.307290	−	0.951616i	$-0.400578\pi$
$110$	2.00000	−	3.46410i	0.190693	−	0.330289i
$111$	−10.0000			−0.949158
$112$		0			0
$113$	2.00000			0.188144			0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000			0.188144			0.0940721	+	0.995565i	$0.470012\pi$
$114$	−2.00000	+	3.46410i	−0.187317	+	0.324443i
$115$		0			0
$116$	−1.00000	−	1.73205i	−0.0928477	−	0.160817i
$117$	−1.00000	+	1.73205i	−0.0924500	+	0.160128i
$118$	−4.00000			−0.368230
$119$		0			0
$120$	−3.00000			−0.273861
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$	1.00000	+	1.73205i	0.0905357	+	0.156813i
$123$	5.00000	+	8.66025i	0.450835	+	0.780869i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−8.00000			−0.709885			−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000			−0.709885			−0.354943	+	0.934888i	$0.615500\pi$
$128$	−1.50000	+	2.59808i	−0.132583	+	0.229640i
$129$	−2.00000	−	3.46410i	−0.176090	−	0.304997i
$130$	−1.00000	−	1.73205i	−0.0877058	−	0.151911i
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	0.475380	+	0.879781i	$0.342311\pi$
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	−0.999602	+	0.0281993i	$0.991023\pi$
$132$	4.00000			0.348155
$133$		0			0
$134$	−12.0000			−1.03664
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	3.00000	+	5.19615i	0.257248	+	0.445566i
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	0.965250	−	0.261329i	$-0.0841608\pi$
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	−0.708942	+	0.705266i	$0.750827\pi$
$138$		0			0
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	−8.00000			−0.673722
$142$	−4.00000	+	6.92820i	−0.335673	+	0.581402i
$143$	4.00000	+	6.92820i	0.334497	+	0.579365i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−1.00000	+	1.73205i	−0.0830455	+	0.143839i
$146$	10.0000			0.827606
$147$		0			0
$148$	10.0000			0.821995
$149$	−11.0000	+	19.0526i	−0.901155	+	1.56085i	−0.0751583	+	0.997172i	$0.523946\pi$
$149$	−11.0000	+	19.0526i	−0.901155	+	1.56085i	−0.825997	+	0.563675i	$0.809387\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	0.981617	−	0.190864i	$-0.0611289\pi$
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	−0.656101	+	0.754673i	$0.727796\pi$
$152$	6.00000	−	10.3923i	0.486664	−	0.842927i
$153$	−2.00000			−0.161690
$154$		0			0
$155$		0			0
$156$	1.00000	−	1.73205i	0.0800641	−	0.138675i
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	0.997609	+	0.0691164i	$0.0220180\pi$
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	−0.438948	+	0.898513i	$0.644649\pi$
$158$		0			0
$159$	5.00000	−	8.66025i	0.396526	−	0.686803i
$160$	5.00000			0.395285
$161$		0			0
$162$	−1.00000			−0.0785674
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	−0.777007	−	0.629492i	$-0.783263\pi$
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	0.933659	+	0.358162i	$0.116597\pi$
$164$	−5.00000	−	8.66025i	−0.390434	−	0.676252i
$165$	−2.00000	−	3.46410i	−0.155700	−	0.269680i
$166$	−6.00000	+	10.3923i	−0.465690	+	0.806599i
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$	1.00000	−	1.73205i	0.0766965	−	0.132842i
$171$	2.00000	+	3.46410i	0.152944	+	0.264906i
$172$	2.00000	+	3.46410i	0.152499	+	0.264135i
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	0.289412	+	0.957205i	$0.406540\pi$
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	−0.973670	+	0.227964i	$0.926793\pi$
$174$	2.00000			0.151620
$175$		0			0
$176$	4.00000			0.301511
$177$	−2.00000	+	3.46410i	−0.150329	+	0.260378i
$178$	3.00000	+	5.19615i	0.224860	+	0.389468i
$179$	−10.0000	−	17.3205i	−0.747435	−	1.29460i	−0.949048	−	0.315130i	$-0.897952\pi$
$179$	−10.0000	−	17.3205i	−0.747435	−	1.29460i	0.201613	−	0.979465i	$-0.435382\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	10.0000			0.743294			0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000			0.743294			0.371647	+	0.928374i	$0.378793\pi$
$182$		0			0
$183$	2.00000			0.147844
$184$		0			0
$185$	−5.00000	−	8.66025i	−0.367607	−	0.636715i
$186$		0			0
$187$	−4.00000	+	6.92820i	−0.292509	+	0.506640i
$188$	8.00000			0.583460
$189$		0			0
$190$	−4.00000			−0.290191
$191$	−8.00000	+	13.8564i	−0.578860	+	1.00261i	0.416751	+	0.909021i	$0.363169\pi$
$191$	−8.00000	+	13.8564i	−0.578860	+	1.00261i	−0.995610	+	0.0935936i	$0.970165\pi$
$192$	−3.50000	−	6.06218i	−0.252591	−	0.437500i
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	0.827788	−	0.561041i	$-0.189599\pi$
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	−0.899770	+	0.436365i	$0.856266\pi$
$194$	−1.00000	+	1.73205i	−0.0717958	+	0.124354i
$195$	−2.00000			−0.143223
$196$		0			0
$197$	6.00000			0.427482			0.213741	−	0.976890i	$-0.431435\pi$
$197$	6.00000			0.427482			0.213741	+	0.976890i	$0.431435\pi$
$198$	−2.00000	+	3.46410i	−0.142134	+	0.246183i
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	0.688705	−	0.725042i	$-0.258180\pi$
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	−0.972257	+	0.233915i	$0.924846\pi$
$200$	−1.50000	−	2.59808i	−0.106066	−	0.183712i
$201$	−6.00000	+	10.3923i	−0.423207	+	0.733017i
$202$	6.00000			0.422159
$203$		0			0
$204$	2.00000			0.140028
$205$	−5.00000	+	8.66025i	−0.349215	+	0.604858i
$206$	8.00000	+	13.8564i	0.557386	+	0.965422i
$207$		0			0
$208$	1.00000	−	1.73205i	0.0693375	−	0.120096i
$209$	16.0000			1.10674
$210$		0			0
$211$	20.0000			1.37686			0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000			1.37686			0.688428	+	0.725304i	$0.258301\pi$
$212$	−5.00000	+	8.66025i	−0.343401	+	0.594789i
$213$	4.00000	+	6.92820i	0.274075	+	0.474713i
$214$	−6.00000	−	10.3923i	−0.410152	−	0.710403i
$215$	2.00000	−	3.46410i	0.136399	−	0.236250i
$216$	3.00000			0.204124
$217$		0			0
$218$	−14.0000			−0.948200
$219$	5.00000	−	8.66025i	0.337869	−	0.585206i
$220$	2.00000	+	3.46410i	0.134840	+	0.233550i
$221$	2.00000	+	3.46410i	0.134535	+	0.233021i
$222$	−5.00000	+	8.66025i	−0.335578	+	0.581238i
$223$	−8.00000			−0.535720			−0.267860	−	0.963458i	$-0.586316\pi$
$223$	−8.00000			−0.535720			−0.267860	+	0.963458i	$0.586316\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$	1.00000	−	1.73205i	0.0665190	−	0.115214i
$227$	−10.0000	−	17.3205i	−0.663723	−	1.14960i	−0.979630	−	0.200812i	$-0.935642\pi$
$227$	−10.0000	−	17.3205i	−0.663723	−	1.14960i	0.315906	−	0.948790i	$-0.397691\pi$
$228$	−2.00000	−	3.46410i	−0.132453	−	0.229416i
$229$	3.00000	−	5.19615i	0.198246	−	0.343371i	−0.749714	−	0.661762i	$-0.769809\pi$
$229$	3.00000	−	5.19615i	0.198246	−	0.343371i	0.947960	+	0.318390i	$0.103142\pi$
$230$		0			0
$231$		0			0
$232$	−6.00000			−0.393919
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	−0.750867	−	0.660454i	$-0.770364\pi$
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	0.947403	+	0.320043i	$0.103697\pi$
$234$	1.00000	+	1.73205i	0.0653720	+	0.113228i
$235$	−4.00000	−	6.92820i	−0.260931	−	0.451946i
$236$	2.00000	−	3.46410i	0.130189	−	0.225494i
$237$		0			0
$238$		0			0
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$	−0.500000	+	0.866025i	−0.0322749	+	0.0559017i
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	0.547533	−	0.836784i	$-0.315567\pi$
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$	2.50000	+	4.33013i	0.160706	+	0.278351i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−2.00000			−0.128037
$245$		0			0
$246$	10.0000			0.637577
$247$	4.00000	−	6.92820i	0.254514	−	0.440831i
$248$		0			0
$249$	6.00000	+	10.3923i	0.380235	+	0.658586i
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$		0			0
$254$	−4.00000	+	6.92820i	−0.250982	+	0.434714i
$255$	−1.00000	−	1.73205i	−0.0626224	−	0.108465i
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	−0.435970	−	0.899961i	$-0.643595\pi$
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	0.997374	−	0.0724199i	$-0.0230722\pi$
$258$	−4.00000			−0.249029
$259$		0			0
$260$	2.00000			0.124035
$261$	1.00000	−	1.73205i	0.0618984	−	0.107211i
$262$	6.00000	+	10.3923i	0.370681	+	0.642039i
$263$	−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	$0.997543\pi$
$264$	6.00000	−	10.3923i	0.369274	−	0.639602i
$265$	10.0000			0.614295
$266$		0			0
$267$	6.00000			0.367194
$268$	6.00000	−	10.3923i	0.366508	−	0.634811i
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	0.996586	−	0.0825561i	$-0.0263084\pi$
$269$	7.00000	+	12.1244i	0.426798	+	0.739235i	−0.569789	+	0.821791i	$0.692975\pi$
$270$	−0.500000	−	0.866025i	−0.0304290	−	0.0527046i
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$	2.00000			0.121268
$273$		0			0
$274$	6.00000			0.362473
$275$	2.00000	−	3.46410i	0.120605	−	0.208893i
$276$		0			0
$277$	−3.00000	−	5.19615i	−0.180253	−	0.312207i	0.761714	−	0.647913i	$-0.224358\pi$
$277$	−3.00000	−	5.19615i	−0.180253	−	0.312207i	−0.941966	+	0.335707i	$0.891025\pi$
$278$	2.00000	−	3.46410i	0.119952	−	0.207763i
$279$		0			0
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$	−4.00000	+	6.92820i	−0.238197	+	0.412568i
$283$	−6.00000	−	10.3923i	−0.356663	−	0.617758i	0.630738	−	0.775996i	$-0.282752\pi$
$283$	−6.00000	−	10.3923i	−0.356663	−	0.617758i	−0.987401	+	0.158237i	$0.949419\pi$
$284$	−4.00000	−	6.92820i	−0.237356	−	0.411113i
$285$	−2.00000	+	3.46410i	−0.118470	+	0.205196i
$286$	8.00000			0.473050
$287$		0			0
$288$	−5.00000			−0.294628
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	1.00000	+	1.73205i	0.0587220	+	0.101710i
$291$	1.00000	+	1.73205i	0.0586210	+	0.101535i
$292$	−5.00000	+	8.66025i	−0.292603	+	0.506803i
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$		0			0
$295$	−4.00000			−0.232889
$296$	15.0000	−	25.9808i	0.871857	−	1.51010i
$297$	2.00000	+	3.46410i	0.116052	+	0.201008i
$298$	11.0000	+	19.0526i	0.637213	+	1.10369i
$299$		0			0
$300$	−1.00000			−0.0577350
$301$		0			0
$302$	8.00000			0.460348
$303$	3.00000	−	5.19615i	0.172345	−	0.298511i
$304$	−2.00000	−	3.46410i	−0.114708	−	0.198680i
$305$	1.00000	+	1.73205i	0.0572598	+	0.0991769i
$306$	−1.00000	+	1.73205i	−0.0571662	+	0.0990148i
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$		0			0
$309$	16.0000			0.910208
$310$		0			0
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	−0.974841	−	0.222900i	$-0.928448\pi$
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	0.294384	−	0.955687i	$-0.404886\pi$
$312$	−3.00000	−	5.19615i	−0.169842	−	0.294174i
$313$	13.0000	−	22.5167i	0.734803	−	1.27272i	−0.220006	−	0.975499i	$-0.570608\pi$
$313$	13.0000	−	22.5167i	0.734803	−	1.27272i	0.954810	−	0.297218i	$-0.0960589\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$		0			0
$317$	1.00000	−	1.73205i	0.0561656	−	0.0972817i	−0.836576	−	0.547852i	$-0.815446\pi$
$317$	1.00000	−	1.73205i	0.0561656	−	0.0972817i	0.892741	+	0.450570i	$0.148779\pi$
$318$	−5.00000	−	8.66025i	−0.280386	−	0.485643i
$319$	−4.00000	−	6.92820i	−0.223957	−	0.387905i
$320$	3.50000	−	6.06218i	0.195656	−	0.338886i
$321$	−12.0000			−0.669775
$322$		0			0
$323$	8.00000			0.445132
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	−1.00000	−	1.73205i	−0.0554700	−	0.0960769i
$326$	−2.00000	−	3.46410i	−0.110770	−	0.191859i
$327$	−7.00000	+	12.1244i	−0.387101	+	0.670478i
$328$	−30.0000			−1.65647
$329$		0			0
$330$	−4.00000			−0.220193
$331$	−6.00000	+	10.3923i	−0.329790	+	0.571213i	−0.982470	−	0.186421i	$-0.940311\pi$
$331$	−6.00000	+	10.3923i	−0.329790	+	0.571213i	0.652680	+	0.757634i	$0.273645\pi$
$332$	−6.00000	−	10.3923i	−0.329293	−	0.570352i
$333$	5.00000	+	8.66025i	0.273998	+	0.474579i
$334$		0			0
$335$	−12.0000			−0.655630
$336$		0			0
$337$	−14.0000			−0.762629			−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000			−0.762629			−0.381314	+	0.924445i	$0.624528\pi$
$338$	−4.50000	+	7.79423i	−0.244768	+	0.423950i
$339$	−1.00000	−	1.73205i	−0.0543125	−	0.0940721i
$340$	1.00000	+	1.73205i	0.0542326	+	0.0939336i
$341$		0			0
$342$	4.00000			0.216295
$343$		0			0
$344$	12.0000			0.646997
$345$		0			0
$346$	9.00000	+	15.5885i	0.483843	+	0.838041i
$347$	14.0000	+	24.2487i	0.751559	+	1.30174i	0.947067	+	0.321037i	$0.104031\pi$
$347$	14.0000	+	24.2487i	0.751559	+	1.30174i	−0.195507	+	0.980702i	$0.562635\pi$
$348$	−1.00000	+	1.73205i	−0.0536056	+	0.0928477i
$349$	2.00000			0.107058			0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000			0.107058			0.0535288	+	0.998566i	$0.482953\pi$
$350$		0			0
$351$	2.00000			0.106752
$352$	−10.0000	+	17.3205i	−0.533002	+	0.923186i
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	0.999711	−	0.0240566i	$-0.00765819\pi$
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	−0.520689	+	0.853746i	$0.674325\pi$
$354$	2.00000	+	3.46410i	0.106299	+	0.184115i
$355$	−4.00000	+	6.92820i	−0.212298	+	0.367711i
$356$	−6.00000			−0.317999
$357$		0			0
$358$	−20.0000			−1.05703
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	−0.353529	−	0.935423i	$-0.615019\pi$
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	0.986865	−	0.161546i	$-0.0516481\pi$
$360$	1.50000	+	2.59808i	0.0790569	+	0.136931i
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	5.00000	−	8.66025i	0.262794	−	0.455173i
$363$	5.00000			0.262432
$364$		0			0
$365$	10.0000			0.523424
$366$	1.00000	−	1.73205i	0.0522708	−	0.0905357i
$367$	−12.0000	−	20.7846i	−0.626395	−	1.08495i	−0.988269	−	0.152721i	$-0.951196\pi$
$367$	−12.0000	−	20.7846i	−0.626395	−	1.08495i	0.361874	−	0.932227i	$-0.382137\pi$
$368$		0			0
$369$	5.00000	−	8.66025i	0.260290	−	0.450835i
$370$	−10.0000			−0.519875
$371$		0			0
$372$		0			0
$373$	13.0000	−	22.5167i	0.673114	−	1.16587i	−0.303902	−	0.952703i	$-0.598289\pi$
$373$	13.0000	−	22.5167i	0.673114	−	1.16587i	0.977016	−	0.213165i	$-0.0683772\pi$
$374$	4.00000	+	6.92820i	0.206835	+	0.358249i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	12.0000	−	20.7846i	0.618853	−	1.07188i
$377$	−4.00000			−0.206010
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	2.00000	−	3.46410i	0.102598	−	0.177705i
$381$	4.00000	+	6.92820i	0.204926	+	0.354943i
$382$	8.00000	+	13.8564i	0.409316	+	0.708955i
$383$	−12.0000	+	20.7846i	−0.613171	+	1.06204i	0.377531	+	0.925997i	$0.376773\pi$
$383$	−12.0000	+	20.7846i	−0.613171	+	1.06204i	−0.990702	+	0.136047i	$0.956560\pi$
$384$	3.00000			0.153093
$385$		0			0
$386$	−2.00000			−0.101797
$387$	−2.00000	+	3.46410i	−0.101666	+	0.176090i
$388$	−1.00000	−	1.73205i	−0.0507673	−	0.0879316i
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	0.779895	−	0.625910i	$-0.215272\pi$
$389$	−3.00000	−	5.19615i	−0.152106	−	0.263455i	−0.932002	+	0.362454i	$0.881939\pi$
$390$	−1.00000	+	1.73205i	−0.0506370	+	0.0877058i
$391$		0			0
$392$		0			0
$393$	12.0000			0.605320
$394$	3.00000	−	5.19615i	0.151138	−	0.261778i
$395$		0			0
$396$	−2.00000	−	3.46410i	−0.100504	−	0.174078i
$397$	−1.00000	+	1.73205i	−0.0501886	+	0.0869291i	−0.890028	−	0.455905i	$-0.849316\pi$
$397$	−1.00000	+	1.73205i	−0.0501886	+	0.0869291i	0.839840	+	0.542834i	$0.182649\pi$
$398$	−8.00000			−0.401004
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	−0.998350	−	0.0574304i	$-0.981709\pi$
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	0.548911	+	0.835881i	$0.315043\pi$
$402$	6.00000	+	10.3923i	0.299253	+	0.518321i
$403$		0			0
$404$	−3.00000	+	5.19615i	−0.149256	+	0.258518i
$405$	−1.00000			−0.0496904
$406$		0			0
$407$	40.0000			1.98273
$408$	3.00000	−	5.19615i	0.148522	−	0.257248i
$409$	13.0000	+	22.5167i	0.642809	+	1.11338i	0.984803	+	0.173675i	$0.0555643\pi$
$409$	13.0000	+	22.5167i	0.642809	+	1.11338i	−0.341994	+	0.939702i	$0.611102\pi$
$410$	5.00000	+	8.66025i	0.246932	+	0.427699i
$411$	3.00000	−	5.19615i	0.147979	−	0.256307i
$412$	−16.0000			−0.788263
$413$		0			0
$414$		0			0
$415$	−6.00000	+	10.3923i	−0.294528	+	0.510138i
$416$	5.00000	+	8.66025i	0.245145	+	0.424604i
$417$	−2.00000	−	3.46410i	−0.0979404	−	0.169638i
$418$	8.00000	−	13.8564i	0.391293	−	0.677739i
$419$	−4.00000			−0.195413			−0.0977064	−	0.995215i	$-0.531151\pi$
$419$	−4.00000			−0.195413			−0.0977064	+	0.995215i	$0.531151\pi$
$420$		0			0
$421$	−26.0000			−1.26716			−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000			−1.26716			−0.633581	+	0.773676i	$0.718416\pi$
$422$	10.0000	−	17.3205i	0.486792	−	0.843149i
$423$	4.00000	+	6.92820i	0.194487	+	0.336861i
$424$	15.0000	+	25.9808i	0.728464	+	1.26174i
$425$	1.00000	−	1.73205i	0.0485071	−	0.0840168i
$426$	8.00000			0.387601
$427$		0			0
$428$	12.0000			0.580042
$429$	4.00000	−	6.92820i	0.193122	−	0.334497i
$430$	−2.00000	−	3.46410i	−0.0964486	−	0.167054i
$431$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$431$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$		0			0
$435$	2.00000			0.0958927
$436$	7.00000	−	12.1244i	0.335239	−	0.580651i
$437$		0			0
$438$	−5.00000	−	8.66025i	−0.238909	−	0.413803i
$439$	20.0000	−	34.6410i	0.954548	−	1.65333i	0.219149	−	0.975691i	$-0.429672\pi$
$439$	20.0000	−	34.6410i	0.954548	−	1.65333i	0.735399	−	0.677634i	$-0.236995\pi$
$440$	12.0000			0.572078
$441$		0			0
$442$	4.00000			0.190261
$443$	6.00000	−	10.3923i	0.285069	−	0.493753i	−0.687557	−	0.726130i	$-0.741317\pi$
$443$	6.00000	−	10.3923i	0.285069	−	0.493753i	0.972626	+	0.232377i	$0.0746503\pi$
$444$	−5.00000	−	8.66025i	−0.237289	−	0.410997i
$445$	3.00000	+	5.19615i	0.142214	+	0.246321i
$446$	−4.00000	+	6.92820i	−0.189405	+	0.328060i
$447$	22.0000			1.04056
$448$		0			0
$449$	2.00000			0.0943858			0.0471929	−	0.998886i	$-0.484972\pi$
$449$	2.00000			0.0943858			0.0471929	+	0.998886i	$0.484972\pi$
$450$	0.500000	−	0.866025i	0.0235702	−	0.0408248i
$451$	−20.0000	−	34.6410i	−0.941763	−	1.63118i
$452$	1.00000	+	1.73205i	0.0470360	+	0.0814688i
$453$	4.00000	−	6.92820i	0.187936	−	0.325515i
$454$	−20.0000			−0.938647
$455$		0			0
$456$	−12.0000			−0.561951
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	−0.958950	−	0.283577i	$-0.908479\pi$
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	0.725059	+	0.688686i	$0.241812\pi$
$458$	−3.00000	−	5.19615i	−0.140181	−	0.242800i
$459$	1.00000	+	1.73205i	0.0466760	+	0.0808452i
$460$		0			0
$461$	18.0000			0.838344			0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000			0.838344			0.419172	+	0.907907i	$0.362320\pi$
$462$		0			0
$463$	24.0000			1.11537			0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000			1.11537			0.557687	+	0.830051i	$0.311689\pi$
$464$	−1.00000	+	1.73205i	−0.0464238	+	0.0804084i
$465$		0			0
$466$	−3.00000	−	5.19615i	−0.138972	−	0.240707i
$467$	14.0000	−	24.2487i	0.647843	−	1.12210i	−0.335794	−	0.941935i	$-0.609005\pi$
$467$	14.0000	−	24.2487i	0.647843	−	1.12210i	0.983637	−	0.180161i	$-0.0576619\pi$
$468$	−2.00000			−0.0924500
$469$		0			0
$470$	−8.00000			−0.369012
$471$	7.00000	−	12.1244i	0.322543	−	0.558661i
$472$	−6.00000	−	10.3923i	−0.276172	−	0.478345i
$473$	8.00000	+	13.8564i	0.367840	+	0.637118i
$474$		0			0
$475$	−4.00000			−0.183533
$476$		0			0
$477$	−10.0000			−0.457869
$478$	−8.00000	+	13.8564i	−0.365911	+	0.633777i
$479$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$479$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$480$	−2.50000	−	4.33013i	−0.114109	−	0.197642i
$481$	10.0000	−	17.3205i	0.455961	−	0.789747i
$482$	−14.0000			−0.637683
$483$		0			0
$484$	−5.00000			−0.227273
$485$	−1.00000	+	1.73205i	−0.0454077	+	0.0786484i
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	−16.0000	−	27.7128i	−0.725029	−	1.25579i	−0.958962	−	0.283535i	$-0.908493\pi$
$487$	−16.0000	−	27.7128i	−0.725029	−	1.25579i	0.233933	−	0.972253i	$-0.424840\pi$
$488$	−3.00000	+	5.19615i	−0.135804	+	0.235219i
$489$	−4.00000			−0.180886
$490$		0			0
$491$	28.0000			1.26362			0.631811	−	0.775122i	$-0.282312\pi$
$491$	28.0000			1.26362			0.631811	+	0.775122i	$0.282312\pi$
$492$	−5.00000	+	8.66025i	−0.225417	+	0.390434i
$493$	−2.00000	−	3.46410i	−0.0900755	−	0.156015i
$494$	−4.00000	−	6.92820i	−0.179969	−	0.311715i
$495$	−2.00000	+	3.46410i	−0.0898933	+	0.155700i
$496$		0			0
$497$		0			0
$498$	12.0000			0.537733
$499$	−2.00000	+	3.46410i	−0.0895323	+	0.155074i	−0.907314	−	0.420455i	$-0.861871\pi$
$499$	−2.00000	+	3.46410i	−0.0895323	+	0.155074i	0.817781	+	0.575529i	$0.195204\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$		0			0
$502$	−6.00000	+	10.3923i	−0.267793	+	0.463831i
$503$	32.0000			1.42681			0.713405	−	0.700752i	$-0.247152\pi$
$503$	32.0000			1.42681			0.713405	+	0.700752i	$0.247152\pi$
$504$		0			0
$505$	6.00000			0.266996
$506$		0			0
$507$	4.50000	+	7.79423i	0.199852	+	0.346154i
$508$	−4.00000	−	6.92820i	−0.177471	−	0.307389i
$509$	−17.0000	+	29.4449i	−0.753512	+	1.30512i	0.192599	+	0.981278i	$0.438308\pi$
$509$	−17.0000	+	29.4449i	−0.753512	+	1.30512i	−0.946111	+	0.323843i	$0.895025\pi$
$510$	−2.00000			−0.0885615
$511$		0			0
$512$	11.0000			0.486136
$513$	2.00000	−	3.46410i	0.0883022	−	0.152944i
$514$	−9.00000	−	15.5885i	−0.396973	−	0.687577i
$515$	8.00000	+	13.8564i	0.352522	+	0.610586i
$516$	2.00000	−	3.46410i	0.0880451	−	0.152499i
$517$	32.0000			1.40736
$518$		0			0
$519$	18.0000			0.790112
$520$	3.00000	−	5.19615i	0.131559	−	0.227866i
$521$	5.00000	+	8.66025i	0.219054	+	0.379413i	0.954519	−	0.298150i	$-0.0963696\pi$
$521$	5.00000	+	8.66025i	0.219054	+	0.379413i	−0.735465	+	0.677563i	$0.763036\pi$
$522$	−1.00000	−	1.73205i	−0.0437688	−	0.0758098i
$523$	2.00000	−	3.46410i	0.0874539	−	0.151475i	−0.818980	−	0.573822i	$-0.805460\pi$
$523$	2.00000	−	3.46410i	0.0874539	−	0.151475i	0.906434	+	0.422347i	$0.138794\pi$
$524$	−12.0000			−0.524222
$525$		0			0
$526$	−16.0000			−0.697633
$527$		0			0
$528$	−2.00000	−	3.46410i	−0.0870388	−	0.150756i
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	5.00000	−	8.66025i	0.217186	−	0.376177i
$531$	4.00000			0.173585
$532$		0			0
$533$	−20.0000			−0.866296
$534$	3.00000	−	5.19615i	0.129823	−	0.224860i
$535$	−6.00000	−	10.3923i	−0.259403	−	0.449299i
$536$	−18.0000	−	31.1769i	−0.777482	−	1.34664i
$537$	−10.0000	+	17.3205i	−0.431532	+	0.747435i
$538$	14.0000			0.603583
$539$		0			0
$540$	1.00000			0.0430331
$541$	−15.0000	+	25.9808i	−0.644900	+	1.11700i	0.339424	+	0.940633i	$0.389768\pi$
$541$	−15.0000	+	25.9808i	−0.644900	+	1.11700i	−0.984325	+	0.176367i	$0.943566\pi$
$542$	−8.00000	−	13.8564i	−0.343629	−	0.595184i
$543$	−5.00000	−	8.66025i	−0.214571	−	0.371647i
$544$	−5.00000	+	8.66025i	−0.214373	+	0.371305i
$545$	−14.0000			−0.599694
$546$		0			0
$547$	−20.0000			−0.855138			−0.427569	−	0.903983i	$-0.640630\pi$
$547$	−20.0000			−0.855138			−0.427569	+	0.903983i	$0.640630\pi$
$548$	−3.00000	+	5.19615i	−0.128154	+	0.221969i
$549$	−1.00000	−	1.73205i	−0.0426790	−	0.0739221i
$550$	−2.00000	−	3.46410i	−0.0852803	−	0.147710i
$551$	−4.00000	+	6.92820i	−0.170406	+	0.295151i
$552$		0			0
$553$		0			0
$554$	−6.00000			−0.254916
$555$	−5.00000	+	8.66025i	−0.212238	+	0.367607i
$556$	2.00000	+	3.46410i	0.0848189	+	0.146911i
$557$	9.00000	+	15.5885i	0.381342	+	0.660504i	0.991254	−	0.131965i	$-0.0421286\pi$
$557$	9.00000	+	15.5885i	0.381342	+	0.660504i	−0.609912	+	0.792469i	$0.708795\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$		0			0
$561$	8.00000			0.337760
$562$	−3.00000	+	5.19615i	−0.126547	+	0.219186i
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	0.964315	−	0.264758i	$-0.0852922\pi$
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	−0.711445	+	0.702742i	$0.751959\pi$
$564$	−4.00000	−	6.92820i	−0.168430	−	0.291730i
$565$	1.00000	−	1.73205i	0.0420703	−	0.0728679i
$566$	−12.0000			−0.504398
$567$		0			0
$568$	−24.0000			−1.00702
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	−0.796266	−	0.604947i	$-0.793194\pi$
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	0.922032	+	0.387113i	$0.126528\pi$
$570$	2.00000	+	3.46410i	0.0837708	+	0.145095i
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	0.904835	−	0.425762i	$-0.139994\pi$
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	−0.821138	+	0.570730i	$0.806660\pi$
$572$	−4.00000	+	6.92820i	−0.167248	+	0.289683i
$573$	16.0000			0.668410
$574$		0			0
$575$		0			0
$576$	−3.50000	+	6.06218i	−0.145833	+	0.252591i
$577$	1.00000	+	1.73205i	0.0416305	+	0.0721062i	0.886090	−	0.463513i	$-0.153411\pi$
$577$	1.00000	+	1.73205i	0.0416305	+	0.0721062i	−0.844459	+	0.535620i	$0.820078\pi$
$578$	−6.50000	−	11.2583i	−0.270364	−	0.468285i
$579$	−1.00000	+	1.73205i	−0.0415586	+	0.0719816i
$580$	−2.00000			−0.0830455
$581$		0			0
$582$	2.00000			0.0829027
$583$	−20.0000	+	34.6410i	−0.828315	+	1.43468i
$584$	15.0000	+	25.9808i	0.620704	+	1.07509i
$585$	1.00000	+	1.73205i	0.0413449	+	0.0716115i
$586$	−3.00000	+	5.19615i	−0.123929	+	0.214651i
$587$	12.0000			0.495293			0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000			0.495293			0.247647	+	0.968850i	$0.420343\pi$
$588$		0			0
$589$		0			0
$590$	−2.00000	+	3.46410i	−0.0823387	+	0.142615i
$591$	−3.00000	−	5.19615i	−0.123404	−	0.213741i
$592$	−5.00000	−	8.66025i	−0.205499	−	0.355934i
$593$	17.0000	−	29.4449i	0.698106	−	1.20916i	−0.271016	−	0.962575i	$-0.587360\pi$
$593$	17.0000	−	29.4449i	0.698106	−	1.20916i	0.969122	−	0.246581i	$-0.0793071\pi$
$594$	4.00000			0.164122
$595$		0			0
$596$	−22.0000			−0.901155
$597$	−4.00000	+	6.92820i	−0.163709	+	0.283552i
$598$		0			0
$599$	4.00000	+	6.92820i	0.163436	+	0.283079i	0.936099	−	0.351738i	$-0.114409\pi$
$599$	4.00000	+	6.92820i	0.163436	+	0.283079i	−0.772663	+	0.634816i	$0.781076\pi$
$600$	−1.50000	+	2.59808i	−0.0612372	+	0.106066i
$601$	−26.0000			−1.06056			−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000			−1.06056			−0.530281	+	0.847822i	$0.677914\pi$
$602$		0			0
$603$	12.0000			0.488678
$604$	−4.00000	+	6.92820i	−0.162758	+	0.281905i
$605$	2.50000	+	4.33013i	0.101639	+	0.176045i
$606$	−3.00000	−	5.19615i	−0.121867	−	0.211079i
$607$	−4.00000	+	6.92820i	−0.162355	+	0.281207i	−0.935713	−	0.352763i	$-0.885242\pi$
$607$	−4.00000	+	6.92820i	−0.162355	+	0.281207i	0.773358	+	0.633970i	$0.218576\pi$
$608$	20.0000			0.811107
$609$		0			0
$610$	2.00000			0.0809776
$611$	8.00000	−	13.8564i	0.323645	−	0.560570i
$612$	−1.00000	−	1.73205i	−0.0404226	−	0.0700140i
$613$	−11.0000	−	19.0526i	−0.444286	−	0.769526i	0.553716	−	0.832705i	$-0.313209\pi$
$613$	−11.0000	−	19.0526i	−0.444286	−	0.769526i	−0.998002	+	0.0631797i	$0.979876\pi$
$614$	−14.0000	+	24.2487i	−0.564994	+	0.978598i
$615$	10.0000			0.403239
$616$		0			0
$617$	−6.00000			−0.241551			−0.120775	−	0.992680i	$-0.538538\pi$
$617$	−6.00000			−0.241551			−0.120775	+	0.992680i	$0.538538\pi$
$618$	8.00000	−	13.8564i	0.321807	−	0.557386i
$619$	−2.00000	−	3.46410i	−0.0803868	−	0.139234i	0.823029	−	0.567999i	$-0.192282\pi$
$619$	−2.00000	−	3.46410i	−0.0803868	−	0.139234i	−0.903416	+	0.428765i	$0.858949\pi$
$620$		0			0
$621$		0			0
$622$	−24.0000			−0.962312
$623$		0			0
$624$	−2.00000			−0.0800641
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−13.0000	−	22.5167i	−0.519584	−	0.899947i
$627$	−8.00000	−	13.8564i	−0.319489	−	0.553372i
$628$	−7.00000	+	12.1244i	−0.279330	+	0.483814i
$629$	20.0000			0.797452
$630$		0			0
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$		0			0
$633$	−10.0000	−	17.3205i	−0.397464	−	0.688428i
$634$	−1.00000	−	1.73205i	−0.0397151	−	0.0687885i
$635$	−4.00000	+	6.92820i	−0.158735	+	0.274937i
$636$	10.0000			0.396526
$637$		0			0
$638$	−8.00000			−0.316723
$639$	4.00000	−	6.92820i	0.158238	−	0.274075i
$640$	1.50000	+	2.59808i	0.0592927	+	0.102698i
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	0.993899	+	0.110291i	$0.0351782\pi$
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	−0.401435	+	0.915888i	$0.631488\pi$
$642$	−6.00000	+	10.3923i	−0.236801	+	0.410152i
$643$	36.0000			1.41970			0.709851	−	0.704352i	$-0.248762\pi$
$643$	36.0000			1.41970			0.709851	+	0.704352i	$0.248762\pi$
$644$		0			0
$645$	−4.00000			−0.157500
$646$	4.00000	−	6.92820i	0.157378	−	0.272587i
$647$	16.0000	+	27.7128i	0.629025	+	1.08950i	0.987748	+	0.156059i	$0.0498790\pi$
$647$	16.0000	+	27.7128i	0.629025	+	1.08950i	−0.358723	+	0.933444i	$0.616788\pi$
$648$	−1.50000	−	2.59808i	−0.0589256	−	0.102062i
$649$	8.00000	−	13.8564i	0.314027	−	0.543912i
$650$	−2.00000			−0.0784465
$651$		0			0
$652$	4.00000			0.156652
$653$	−23.0000	+	39.8372i	−0.900060	+	1.55895i	−0.0726446	+	0.997358i	$0.523144\pi$
$653$	−23.0000	+	39.8372i	−0.900060	+	1.55895i	−0.827415	+	0.561591i	$0.810189\pi$
$654$	7.00000	+	12.1244i	0.273722	+	0.474100i
$655$	6.00000	+	10.3923i	0.234439	+	0.406061i
$656$	−5.00000	+	8.66025i	−0.195217	+	0.338126i
$657$	−10.0000			−0.390137
$658$		0			0
$659$	20.0000			0.779089			0.389545	−	0.921008i	$-0.372632\pi$
$659$	20.0000			0.779089			0.389545	+	0.921008i	$0.372632\pi$
$660$	2.00000	−	3.46410i	0.0778499	−	0.134840i
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	0.996682	−	0.0813955i	$-0.0259377\pi$
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	−0.568831	+	0.822454i	$0.692604\pi$
$662$	6.00000	+	10.3923i	0.233197	+	0.403908i
$663$	2.00000	−	3.46410i	0.0776736	−	0.134535i
$664$	−36.0000			−1.39707
$665$		0			0
$666$	10.0000			0.387492
$667$		0			0
$668$		0			0
$669$	4.00000	+	6.92820i	0.154649	+	0.267860i
$670$	−6.00000	+	10.3923i	−0.231800	+	0.401490i
$671$	−8.00000			−0.308837
$672$		0			0
$673$	−30.0000			−1.15642			−0.578208	−	0.815890i	$-0.696248\pi$
$673$	−30.0000			−1.15642			−0.578208	+	0.815890i	$0.696248\pi$
$674$	−7.00000	+	12.1244i	−0.269630	+	0.467013i
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	−4.50000	−	7.79423i	−0.173077	−	0.299778i
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	−0.802600	−	0.596518i	$-0.796551\pi$
$677$	3.00000	−	5.19615i	0.115299	−	0.199704i	0.917899	+	0.396813i	$0.129884\pi$
$678$	−2.00000			−0.0768095
$679$		0			0
$680$	6.00000			0.230089
$681$	−10.0000	+	17.3205i	−0.383201	+	0.663723i
$682$		0			0
$683$	−18.0000	−	31.1769i	−0.688751	−	1.19295i	−0.972242	−	0.233977i	$-0.924826\pi$
$683$	−18.0000	−	31.1769i	−0.688751	−	1.19295i	0.283491	−	0.958975i	$-0.408507\pi$
$684$	−2.00000	+	3.46410i	−0.0764719	+	0.132453i
$685$	6.00000			0.229248
$686$		0			0
$687$	−6.00000			−0.228914
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	10.0000	+	17.3205i	0.380970	+	0.659859i
$690$		0			0
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	0.0555386	+	0.998457i	$0.482312\pi$
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	−0.892458	+	0.451130i	$0.851021\pi$
$692$	−18.0000			−0.684257
$693$		0			0
$694$	28.0000			1.06287
$695$	2.00000	−	3.46410i	0.0758643	−	0.131401i
$696$	3.00000	+	5.19615i	0.113715	+	0.196960i
$697$	−10.0000	−	17.3205i	−0.378777	−	0.656061i
$698$	1.00000	−	1.73205i	0.0378506	−	0.0655591i
$699$	−6.00000			−0.226941
$700$		0			0
$701$	−2.00000			−0.0755390			−0.0377695	−	0.999286i	$-0.512025\pi$
$701$	−2.00000			−0.0755390			−0.0377695	+	0.999286i	$0.512025\pi$
$702$	1.00000	−	1.73205i	0.0377426	−	0.0653720i
$703$	−20.0000	−	34.6410i	−0.754314	−	1.30651i
$704$	14.0000	+	24.2487i	0.527645	+	0.913908i
$705$	−4.00000	+	6.92820i	−0.150649	+	0.260931i
$706$	18.0000			0.677439
$707$		0			0
$708$	−4.00000			−0.150329
$709$	13.0000	−	22.5167i	0.488225	−	0.845631i	−0.511683	−	0.859174i	$-0.670978\pi$
$709$	13.0000	−	22.5167i	0.488225	−	0.845631i	0.999908	+	0.0135434i	$0.00431112\pi$
$710$	4.00000	+	6.92820i	0.150117	+	0.260011i
$711$		0			0
$712$	−9.00000	+	15.5885i	−0.337289	+	0.584202i
$713$		0			0
$714$		0			0
$715$	8.00000			0.299183
$716$	10.0000	−	17.3205i	0.373718	−	0.647298i
$717$	8.00000	+	13.8564i	0.298765	+	0.517477i
$718$	−12.0000	−	20.7846i	−0.447836	−	0.775675i
$719$	−24.0000	+	41.5692i	−0.895049	+	1.55027i	−0.0613050	+	0.998119i	$0.519526\pi$
$719$	−24.0000	+	41.5692i	−0.895049	+	1.55027i	−0.833744	+	0.552151i	$0.813807\pi$
$720$	1.00000			0.0372678
$721$		0			0
$722$	3.00000			0.111648
$723$	−7.00000	+	12.1244i	−0.260333	+	0.450910i
$724$	5.00000	+	8.66025i	0.185824	+	0.321856i
$725$	1.00000	+	1.73205i	0.0371391	+	0.0643268i
$726$	2.50000	−	4.33013i	0.0927837	−	0.160706i
$727$	16.0000			0.593407			0.296704	−	0.954970i	$-0.404113\pi$
$727$	16.0000			0.593407			0.296704	+	0.954970i	$0.404113\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	5.00000	−	8.66025i	0.185058	−	0.320530i
$731$	4.00000	+	6.92820i	0.147945	+	0.256249i
$732$	1.00000	+	1.73205i	0.0369611	+	0.0640184i
$733$	7.00000	−	12.1244i	0.258551	−	0.447823i	−0.707303	−	0.706910i	$-0.750088\pi$
$733$	7.00000	−	12.1244i	0.258551	−	0.447823i	0.965854	+	0.259087i	$0.0834217\pi$
$734$	−24.0000			−0.885856
$735$		0			0
$736$		0			0
$737$	24.0000	−	41.5692i	0.884051	−	1.53122i
$738$	−5.00000	−	8.66025i	−0.184053	−	0.318788i
$739$	22.0000	+	38.1051i	0.809283	+	1.40172i	0.913361	+	0.407150i	$0.133477\pi$
$739$	22.0000	+	38.1051i	0.809283	+	1.40172i	−0.104078	+	0.994569i	$0.533189\pi$
$740$	5.00000	−	8.66025i	0.183804	−	0.318357i
$741$	−8.00000			−0.293887
$742$		0			0
$743$	−16.0000			−0.586983			−0.293492	−	0.955962i	$-0.594817\pi$
$743$	−16.0000			−0.586983			−0.293492	+	0.955962i	$0.594817\pi$
$744$		0			0
$745$	11.0000	+	19.0526i	0.403009	+	0.698032i
$746$	−13.0000	−	22.5167i	−0.475964	−	0.824394i
$747$	6.00000	−	10.3923i	0.219529	−	0.380235i
$748$	−8.00000			−0.292509
$749$		0			0
$750$	1.00000			0.0365148
$751$	−8.00000	+	13.8564i	−0.291924	+	0.505627i	−0.974265	−	0.225407i	$-0.927629\pi$
$751$	−8.00000	+	13.8564i	−0.291924	+	0.505627i	0.682341	+	0.731034i	$0.260962\pi$
$752$	−4.00000	−	6.92820i	−0.145865	−	0.252646i
$753$	6.00000	+	10.3923i	0.218652	+	0.378717i
$754$	−2.00000	+	3.46410i	−0.0728357	+	0.126155i
$755$	8.00000			0.291150
$756$		0			0
$757$	−26.0000			−0.944986			−0.472493	−	0.881334i	$-0.656646\pi$
$757$	−26.0000			−0.944986			−0.472493	+	0.881334i	$0.656646\pi$
$758$	−10.0000	+	17.3205i	−0.363216	+	0.629109i
$759$		0			0
$760$	−6.00000	−	10.3923i	−0.217643	−	0.376969i
$761$	−3.00000	+	5.19615i	−0.108750	+	0.188360i	−0.915264	−	0.402854i	$-0.868018\pi$
$761$	−3.00000	+	5.19615i	−0.108750	+	0.188360i	0.806514	+	0.591215i	$0.201351\pi$
$762$	8.00000			0.289809
$763$		0			0
$764$	−16.0000			−0.578860
$765$	−1.00000	+	1.73205i	−0.0361551	+	0.0626224i
$766$	12.0000	+	20.7846i	0.433578	+	0.750978i
$767$	−4.00000	−	6.92820i	−0.144432	−	0.250163i
$768$	8.50000	−	14.7224i	0.306717	−	0.531250i
$769$	−2.00000			−0.0721218			−0.0360609	−	0.999350i	$-0.511481\pi$
$769$	−2.00000			−0.0721218			−0.0360609	+	0.999350i	$0.511481\pi$
$770$		0			0
$771$	−18.0000			−0.648254
$772$	1.00000	−	1.73205i	0.0359908	−	0.0623379i
$773$	3.00000	+	5.19615i	0.107903	+	0.186893i	0.914920	−	0.403634i	$-0.132253\pi$
$773$	3.00000	+	5.19615i	0.107903	+	0.186893i	−0.807018	+	0.590527i	$0.798920\pi$
$774$	2.00000	+	3.46410i	0.0718885	+	0.124515i
$775$		0			0
$776$	−6.00000			−0.215387
$777$		0			0
$778$	−6.00000			−0.215110
$779$	−20.0000	+	34.6410i	−0.716574	+	1.24114i
$780$	−1.00000	−	1.73205i	−0.0358057	−	0.0620174i
$781$	−16.0000	−	27.7128i	−0.572525	−	0.991642i
$782$		0			0
$783$	−2.00000			−0.0714742
$784$		0			0
$785$	14.0000			0.499681
$786$	6.00000	−	10.3923i

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:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(2.00000 + 3.46410i) q^{11} +(0.500000 - 0.866025i) q^{12} +2.00000 q^{13} -1.00000 q^{15} +(0.500000 - 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(0.500000 + 0.866025i) q^{18} +(2.00000 - 3.46410i) q^{19} +1.00000 q^{20} +4.00000 q^{22} +(-1.50000 - 2.59808i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(1.00000 - 1.73205i) q^{26} +1.00000 q^{27} -2.00000 q^{29} +(-0.500000 + 0.866025i) q^{30} +(2.50000 + 4.33013i) q^{32} +(2.00000 - 3.46410i) q^{33} +2.00000 q^{34} -1.00000 q^{36} +(5.00000 - 8.66025i) q^{37} +(-2.00000 - 3.46410i) q^{38} +(-1.00000 - 1.73205i) q^{39} +(1.50000 - 2.59808i) q^{40} -10.0000 q^{41} +4.00000 q^{43} +(-2.00000 + 3.46410i) q^{44} +(0.500000 + 0.866025i) q^{45} +(4.00000 - 6.92820i) q^{47} -1.00000 q^{48} -1.00000 q^{50} +(1.00000 - 1.73205i) q^{51} +(1.00000 + 1.73205i) q^{52} +(5.00000 + 8.66025i) q^{53} +(0.500000 - 0.866025i) q^{54} +4.00000 q^{55} -4.00000 q^{57} +(-1.00000 + 1.73205i) q^{58} +(-2.00000 - 3.46410i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(-1.00000 + 1.73205i) q^{61} +7.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(-2.00000 - 3.46410i) q^{66} +(-6.00000 - 10.3923i) q^{67} +(-1.00000 + 1.73205i) q^{68} -8.00000 q^{71} +(-1.50000 + 2.59808i) q^{72} +(5.00000 + 8.66025i) q^{73} +(-5.00000 - 8.66025i) q^{74} +(-0.500000 + 0.866025i) q^{75} +4.00000 q^{76} -2.00000 q^{78} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.00000 + 8.66025i) q^{82} -12.0000 q^{83} +2.00000 q^{85} +(2.00000 - 3.46410i) q^{86} +(1.00000 + 1.73205i) q^{87} +(6.00000 + 10.3923i) q^{88} +(-3.00000 + 5.19615i) q^{89} +1.00000 q^{90} +(-4.00000 - 6.92820i) q^{94} +(-2.00000 - 3.46410i) q^{95} +(2.50000 - 4.33013i) q^{96} -2.00000 q^{97} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2q + q^{2} - q^{3} + q^{4} + q^{5} - 2q^{6} + 6q^{8} - q^{9} + O(q^{10}) \)	\( 2q + q^{2} - q^{3} + q^{4} + q^{5} - 2q^{6} + 6q^{8} - q^{9} - q^{10} + 4q^{11} + q^{12} + 4q^{13} - 2q^{15} + q^{16} + 2q^{17} + q^{18} + 4q^{19} + 2q^{20} + 8q^{22} - 3q^{24} - q^{25} + 2q^{26} + 2q^{27} - 4q^{29} - q^{30} + 5q^{32} + 4q^{33} + 4q^{34} - 2q^{36} + 10q^{37} - 4q^{38} - 2q^{39} + 3q^{40} - 20q^{41} + 8q^{43} - 4q^{44} + q^{45} + 8q^{47} - 2q^{48} - 2q^{50} + 2q^{51} + 2q^{52} + 10q^{53} + q^{54} + 8q^{55} - 8q^{57} - 2q^{58} - 4q^{59} - q^{60} - 2q^{61} + 14q^{64} + 2q^{65} - 4q^{66} - 12q^{67} - 2q^{68} - 16q^{71} - 3q^{72} + 10q^{73} - 10q^{74} - q^{75} + 8q^{76} - 4q^{78} - q^{80} - q^{81} - 10q^{82} - 24q^{83} + 4q^{85} + 4q^{86} + 2q^{87} + 12q^{88} - 6q^{89} + 2q^{90} - 8q^{94} - 4q^{95} + 5q^{96} - 4q^{97} - 8q^{99} + O(q^{100}) \)

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