LMFDB - Embedded newform 735.2.i.d.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(226,735)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("735.226");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
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 15)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	735.361
Dual form			735.2.i.d.226.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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	0.986869	−	0.161521i	$-0.0516399\pi$
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i	−0.633316	+	0.773893i	$0.718307\pi$
$3$	−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	−0.389338	−	0.921095i	$-0.627296\pi$
$11$	2.00000	−	3.46410i	0.603023	−	1.04447i	0.992361	−	0.123371i	$-0.0393705\pi$
$12$	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	−0.718900	−	0.695113i	$-0.755354\pi$
$17$	1.00000	−	1.73205i	0.242536	−	0.420084i	0.961436	+	0.275029i	$0.0886875\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	0.998899	−	0.0469020i	$-0.0149348\pi$
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	−0.540068	+	0.841621i	$0.681602\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	4.00000			0.852803
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	−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	$-0.833333\pi$
$31$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$32$	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	0.904194	+	0.427121i	$0.140472\pi$
$37$	5.00000	+	8.66025i	0.821995	+	1.42374i	−0.0821995	+	0.996616i	$0.526194\pi$
$38$	−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	0.995066	+	0.0992202i	$0.0316348\pi$
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	−0.411606	+	0.911362i	$0.635032\pi$
$48$	−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	−0.286064	−	0.958211i	$-0.592347\pi$
$53$	5.00000	−	8.66025i	0.686803	−	1.18958i	0.972867	−	0.231367i	$-0.0743197\pi$
$54$	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	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$	−0.500000	+	0.866025i	−0.0645497	+	0.111803i
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$		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	0.222571	+	0.974916i	$0.428555\pi$
$67$	−6.00000	+	10.3923i	−0.733017	+	1.26962i	−0.955588	+	0.294706i	$0.904778\pi$
$68$	−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	−0.409644	−	0.912245i	$-0.634347\pi$
$73$	5.00000	−	8.66025i	0.585206	−	1.01361i	0.994850	−	0.101361i	$-0.0323196\pi$
$74$	−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	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	−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	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$	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	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$	−1.00000	+	1.73205i	−0.0990148	+	0.171499i
$103$	−8.00000	−	13.8564i	−0.788263	−	1.36531i	−0.927030	−	0.374987i	$-0.877647\pi$
$103$	−8.00000	−	13.8564i	−0.788263	−	1.36531i	0.138767	−	0.990325i	$-0.455686\pi$
$104$	6.00000			0.588348
$105$		0			0
$106$	10.0000			0.971286
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	0.995474	+	0.0950377i	$0.0302972\pi$
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	−0.415432	+	0.909624i	$0.636370\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	0.307290	+	0.951616i	$0.400578\pi$
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	−0.977769	+	0.209687i	$0.932756\pi$
$110$	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	−0.999602	−	0.0281993i	$-0.991023\pi$
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	0.475380	−	0.879781i	$-0.342311\pi$
$132$	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	−0.708942	−	0.705266i	$-0.750827\pi$
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	0.965250	+	0.261329i	$0.0841608\pi$
$138$		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	−0.825997	−	0.563675i	$-0.809387\pi$
$149$	−11.0000	−	19.0526i	−0.901155	−	1.56085i	−0.0751583	−	0.997172i	$-0.523946\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	−0.656101	−	0.754673i	$-0.727796\pi$
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	0.981617	+	0.190864i	$0.0611289\pi$
$152$	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	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	0.997609	−	0.0691164i	$-0.0220180\pi$
$158$		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	0.933659	−	0.358162i	$-0.116597\pi$
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	−0.777007	+	0.629492i	$0.783263\pi$
$164$	−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	−0.973670	−	0.227964i	$-0.926793\pi$
$173$	−9.00000	−	15.5885i	−0.684257	−	1.18517i	0.289412	−	0.957205i	$-0.406540\pi$
$174$	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	0.201613	+	0.979465i	$0.435382\pi$
$179$	−10.0000	+	17.3205i	−0.747435	+	1.29460i	−0.949048	+	0.315130i	$0.897952\pi$
$180$	−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	−0.995610	−	0.0935936i	$-0.970165\pi$
$191$	−8.00000	−	13.8564i	−0.578860	−	1.00261i	0.416751	−	0.909021i	$-0.363169\pi$
$192$	−3.50000	+	6.06218i	−0.252591	+	0.437500i
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	−0.899770	−	0.436365i	$-0.856266\pi$
$193$	−1.00000	+	1.73205i	−0.0719816	+	0.124676i	0.827788	+	0.561041i	$0.189599\pi$
$194$	−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	−0.972257	−	0.233915i	$-0.924846\pi$
$199$	−4.00000	+	6.92820i	−0.283552	+	0.491127i	0.688705	+	0.725042i	$0.258180\pi$
$200$	−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	0.315906	+	0.948790i	$0.397691\pi$
$227$	−10.0000	+	17.3205i	−0.663723	+	1.14960i	−0.979630	+	0.200812i	$0.935642\pi$
$228$	−2.00000	+	3.46410i	−0.132453	+	0.229416i
$229$	3.00000	+	5.19615i	0.198246	+	0.343371i	0.947960	−	0.318390i	$-0.103142\pi$
$229$	3.00000	+	5.19615i	0.198246	+	0.343371i	−0.749714	+	0.661762i	$0.769809\pi$
$230$		0			0
$231$		0			0
$232$	−6.00000			−0.393919
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$	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	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−7.00000	+	12.1244i	−0.450910	+	0.780998i	0.547533	+	0.836784i	$0.315567\pi$
$242$	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	0.997374	+	0.0724199i	$0.0230722\pi$
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	−0.435970	+	0.899961i	$0.643595\pi$
$258$	−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	−0.999970	−	0.00771799i	$-0.997543\pi$
$263$	−8.00000	+	13.8564i	−0.493301	+	0.854423i	0.506669	+	0.862141i	$0.330877\pi$
$264$	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	−0.569789	−	0.821791i	$-0.692975\pi$
$269$	7.00000	−	12.1244i	0.426798	−	0.739235i	0.996586	+	0.0825561i	$0.0263084\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	0.999870	−	0.0161307i	$-0.00513477\pi$
$271$	8.00000	+	13.8564i	0.485965	+	0.841717i	−0.513905	+	0.857847i	$0.671801\pi$
$272$	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	−0.941966	−	0.335707i	$-0.891025\pi$
$277$	−3.00000	+	5.19615i	−0.180253	+	0.312207i	0.761714	+	0.647913i	$0.224358\pi$
$278$	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	−0.987401	−	0.158237i	$-0.949419\pi$
$283$	−6.00000	+	10.3923i	−0.356663	+	0.617758i	0.630738	+	0.775996i	$0.282752\pi$
$284$	−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	0.294384	+	0.955687i	$0.404886\pi$
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	−0.974841	+	0.222900i	$0.928448\pi$
$312$	−3.00000	+	5.19615i	−0.169842	+	0.294174i
$313$	13.0000	+	22.5167i	0.734803	+	1.27272i	0.954810	+	0.297218i	$0.0960589\pi$
$313$	13.0000	+	22.5167i	0.734803	+	1.27272i	−0.220006	+	0.975499i	$0.570608\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$		0			0
$317$	1.00000	+	1.73205i	0.0561656	+	0.0972817i	0.892741	−	0.450570i	$-0.148779\pi$
$317$	1.00000	+	1.73205i	0.0561656	+	0.0972817i	−0.836576	+	0.547852i	$0.815446\pi$
$318$	−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	0.652680	−	0.757634i	$-0.273645\pi$
$331$	−6.00000	−	10.3923i	−0.329790	−	0.571213i	−0.982470	+	0.186421i	$0.940311\pi$
$332$	−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	−0.195507	−	0.980702i	$-0.562635\pi$
$347$	14.0000	−	24.2487i	0.751559	−	1.30174i	0.947067	−	0.321037i	$-0.104031\pi$
$348$	−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	−0.520689	−	0.853746i	$-0.674325\pi$
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	0.999711	+	0.0240566i	$0.00765819\pi$
$354$	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	0.986865	+	0.161546i	$0.0516481\pi$
$359$	12.0000	+	20.7846i	0.633336	+	1.09697i	−0.353529	+	0.935423i	$0.615019\pi$
$360$	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	0.361874	+	0.932227i	$0.382137\pi$
$367$	−12.0000	+	20.7846i	−0.626395	+	1.08495i	−0.988269	+	0.152721i	$0.951196\pi$
$368$		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	0.977016	+	0.213165i	$0.0683772\pi$
$373$	13.0000	+	22.5167i	0.673114	+	1.16587i	−0.303902	+	0.952703i	$0.598289\pi$
$374$	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	−0.990702	−	0.136047i	$-0.956560\pi$
$383$	−12.0000	−	20.7846i	−0.613171	−	1.06204i	0.377531	−	0.925997i	$-0.376773\pi$
$384$	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	−0.932002	−	0.362454i	$-0.881939\pi$
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	0.779895	+	0.625910i	$0.215272\pi$
$390$	−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	0.839840	−	0.542834i	$-0.182649\pi$
$397$	−1.00000	−	1.73205i	−0.0501886	−	0.0869291i	−0.890028	+	0.455905i	$0.849316\pi$
$398$	−8.00000			−0.401004
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	0.548911	−	0.835881i	$-0.315043\pi$
$401$	−9.00000	−	15.5885i	−0.449439	−	0.778450i	−0.998350	+	0.0574304i	$0.981709\pi$
$402$	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	−0.341994	−	0.939702i	$-0.611102\pi$
$409$	13.0000	−	22.5167i	0.642809	−	1.11338i	0.984803	−	0.173675i	$-0.0555643\pi$
$410$	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	$-0.833333\pi$
$431$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$432$	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	0.735399	+	0.677634i	$0.236995\pi$
$439$	20.0000	+	34.6410i	0.954548	+	1.65333i	0.219149	+	0.975691i	$0.429672\pi$
$440$	12.0000			0.572078
$441$		0			0
$442$	4.00000			0.190261
$443$	6.00000	+	10.3923i	0.285069	+	0.493753i	0.972626	−	0.232377i	$-0.0746503\pi$
$443$	6.00000	+	10.3923i	0.285069	+	0.493753i	−0.687557	+	0.726130i	$0.741317\pi$
$444$	−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	0.725059	−	0.688686i	$-0.241812\pi$
$457$	−5.00000	−	8.66025i	−0.233890	−	0.405110i	−0.958950	+	0.283577i	$0.908479\pi$
$458$	−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	0.983637	+	0.180161i	$0.0576619\pi$
$467$	14.0000	+	24.2487i	0.647843	+	1.12210i	−0.335794	+	0.941935i	$0.609005\pi$
$468$	−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	$-0.833333\pi$
$479$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$480$	−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	0.233933	+	0.972253i	$0.424840\pi$
$487$	−16.0000	+	27.7128i	−0.725029	+	1.25579i	−0.958962	+	0.283535i	$0.908493\pi$
$488$	−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	0.817781	−	0.575529i	$-0.195204\pi$
$499$	−2.00000	−	3.46410i	−0.0895323	−	0.155074i	−0.907314	+	0.420455i	$0.861871\pi$
$500$	−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	−0.946111	−	0.323843i	$-0.895025\pi$
$509$	−17.0000	−	29.4449i	−0.753512	−	1.30512i	0.192599	−	0.981278i	$-0.438308\pi$
$510$	−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	−0.735465	−	0.677563i	$-0.763036\pi$
$521$	5.00000	−	8.66025i	0.219054	−	0.379413i	0.954519	+	0.298150i	$0.0963696\pi$
$522$	−1.00000	+	1.73205i	−0.0437688	+	0.0758098i
$523$	2.00000	+	3.46410i	0.0874539	+	0.151475i	0.906434	−	0.422347i	$-0.138794\pi$
$523$	2.00000	+	3.46410i	0.0874539	+	0.151475i	−0.818980	+	0.573822i	$0.805460\pi$
$524$	−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	−0.984325	−	0.176367i	$-0.943566\pi$
$541$	−15.0000	−	25.9808i	−0.644900	−	1.11700i	0.339424	−	0.940633i	$-0.389768\pi$
$542$	−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	−0.609912	−	0.792469i	$-0.708795\pi$
$557$	9.00000	−	15.5885i	0.381342	−	0.660504i	0.991254	+	0.131965i	$0.0421286\pi$
$558$		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	−0.711445	−	0.702742i	$-0.751959\pi$
$563$	6.00000	−	10.3923i	0.252870	−	0.437983i	0.964315	+	0.264758i	$0.0852922\pi$
$564$	−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	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$	2.00000	−	3.46410i	0.0837708	−	0.145095i
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	−0.821138	−	0.570730i	$-0.806660\pi$
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	0.904835	+	0.425762i	$0.139994\pi$
$572$	−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	−0.844459	−	0.535620i	$-0.820078\pi$
$577$	1.00000	−	1.73205i	0.0416305	−	0.0721062i	0.886090	+	0.463513i	$0.153411\pi$
$578$	−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	0.969122	+	0.246581i	$0.0793071\pi$
$593$	17.0000	+	29.4449i	0.698106	+	1.20916i	−0.271016	+	0.962575i	$0.587360\pi$
$594$	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	−0.772663	−	0.634816i	$-0.781076\pi$
$599$	4.00000	−	6.92820i	0.163436	−	0.283079i	0.936099	+	0.351738i	$0.114409\pi$
$600$	−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	0.773358	−	0.633970i	$-0.218576\pi$
$607$	−4.00000	−	6.92820i	−0.162355	−	0.281207i	−0.935713	+	0.352763i	$0.885242\pi$
$608$	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	−0.998002	−	0.0631797i	$-0.979876\pi$
$613$	−11.0000	+	19.0526i	−0.444286	+	0.769526i	0.553716	+	0.832705i	$0.313209\pi$
$614$	−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	−0.903416	−	0.428765i	$-0.858949\pi$
$619$	−2.00000	+	3.46410i	−0.0803868	+	0.139234i	0.823029	+	0.567999i	$0.192282\pi$
$620$		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	−0.401435	−	0.915888i	$-0.631488\pi$
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	0.993899	−	0.110291i	$-0.0351782\pi$
$642$	−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	−0.358723	−	0.933444i	$-0.616788\pi$
$647$	16.0000	−	27.7128i	0.629025	−	1.08950i	0.987748	−	0.156059i	$-0.0498790\pi$
$648$	−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	−0.827415	−	0.561591i	$-0.810189\pi$
$653$	−23.0000	−	39.8372i	−0.900060	−	1.55895i	−0.0726446	−	0.997358i	$-0.523144\pi$
$654$	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	−0.568831	−	0.822454i	$-0.692604\pi$
$661$	11.0000	−	19.0526i	0.427850	−	0.741059i	0.996682	+	0.0813955i	$0.0259377\pi$
$662$	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	0.917899	−	0.396813i	$-0.129884\pi$
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	−0.802600	+	0.596518i	$0.796551\pi$
$678$	−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	0.283491	+	0.958975i	$0.408507\pi$
$683$	−18.0000	+	31.1769i	−0.688751	+	1.19295i	−0.972242	+	0.233977i	$0.924826\pi$
$684$	−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	−0.892458	−	0.451130i	$-0.851021\pi$
$691$	−22.0000	−	38.1051i	−0.836919	−	1.44959i	0.0555386	−	0.998457i	$-0.482312\pi$
$692$	−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	0.999908	−	0.0135434i	$-0.00431112\pi$
$709$	13.0000	+	22.5167i	0.488225	+	0.845631i	−0.511683	+	0.859174i	$0.670978\pi$
$710$	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	−0.833744	−	0.552151i	$-0.813807\pi$
$719$	−24.0000	−	41.5692i	−0.895049	−	1.55027i	−0.0613050	−	0.998119i	$-0.519526\pi$
$720$	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	0.965854	−	0.259087i	$-0.0834217\pi$
$733$	7.00000	+	12.1244i	0.258551	+	0.447823i	−0.707303	+	0.706910i	$0.750088\pi$
$734$	−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	−0.104078	−	0.994569i	$-0.533189\pi$
$739$	22.0000	−	38.1051i	0.809283	−	1.40172i	0.913361	−	0.407150i	$-0.133477\pi$
$740$	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	0.682341	−	0.731034i	$-0.260962\pi$
$751$	−8.00000	−	13.8564i	−0.291924	−	0.505627i	−0.974265	+	0.225407i	$0.927629\pi$
$752$	−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	0.806514	−	0.591215i	$-0.201351\pi$
$761$	−3.00000	−	5.19615i	−0.108750	−	0.188360i	−0.915264	+	0.402854i	$0.868018\pi$
$762$	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	−0.807018	−	0.590527i	$-0.798920\pi$
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	0.914920	+	0.403634i	$0.132253\pi$
$774$	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	0.214013	+	0.370681i
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	−0.500953	−	0.865474i	$-0.667017\pi$
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	0.999999	+	0.00110111i	$0.000350496\pi$
$788$	3.00000	−	5.19615i	0.106871	−	0.185105i
$789$	−8.00000	−	13.8564i	−0.284808	−	0.493301i
$790$		0			0
$791$		0			0
$792$	−12.0000			−0.426401
$793$	−2.00000	−	3.46410i	−0.0710221	−	0.123014i
$794$	1.00000	−	1.73205i	0.0354887	−	0.0614682i
$795$	−5.00000	+	8.66025i	−0.177332	+	0.307148i
$796$	4.00000	+	6.92820i	0.141776	+	0.245564i
$797$	2.00000			0.0708436			0.0354218	−	0.999372i	$-0.488723\pi$
$797$	2.00000			0.0708436			0.0354218	+	0.999372i	$0.488723\pi$
$798$		0			0
$799$	16.0000			0.566039
$800$	2.50000	+	4.33013i	0.0883883	+	0.153093i
$801$	−3.00000	+	5.19615i	−0.106000	+	0.183597i
$802$	9.00000	−	15.5885i	0.317801	−	0.550448i
$803$	−20.0000	−	34.6410i	−0.705785	−	1.22245i
$804$	−12.0000			−0.423207
$805$		0			0
$806$		0			0
$807$	7.00000	+	12.1244i	0.246412	+	0.426798i
$808$	9.00000	−	15.5885i	0.316619	−	0.548400i
$809$	−5.00000	+	8.66025i	−0.175791	+	0.304478i	−0.940435	−	0.339975i	$-0.889582\pi$
$809$	−5.00000	+	8.66025i	−0.175791	+	0.304478i	0.764644	+	0.644453i	$0.222915\pi$
$810$	−0.500000	−	0.866025i	−0.0175682	−	0.0304290i
$811$	−12.0000			−0.421377			−0.210688	−	0.977553i	$-0.567571\pi$
$811$	−12.0000			−0.421377			−0.210688	+	0.977553i	$0.567571\pi$
$812$		0			0
$813$	−16.0000			−0.561144
$814$	20.0000	+	34.6410i	0.701000	+	1.21417i
$815$	−2.00000	+	3.46410i	−0.0700569	+	0.121342i
$816$	−1.00000	+	1.73205i	−0.0350070	+	0.0606339i
$817$	8.00000	+	13.8564i	0.279885	+	0.484774i
$818$	26.0000			0.909069
$819$		0			0
$820$	−10.0000			−0.349215
$821$	−27.0000	−	46.7654i	−0.942306	−	1.63212i	−0.761056	−	0.648686i	$-0.775319\pi$
$821$	−27.0000	−	46.7654i	−0.942306	−	1.63212i	−0.181250	−	0.983437i	$-0.558014\pi$
$822$	−3.00000	+	5.19615i	−0.104637	+	0.181237i
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	0.439961	+	0.898017i	$0.354992\pi$
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	−0.997686	+	0.0679910i	$0.978341\pi$
$824$	−24.0000	−	41.5692i	−0.836080	−	1.44813i
$825$	−4.00000			−0.139262
$826$		0			0
$827$	−28.0000			−0.973655			−0.486828	−	0.873498i	$-0.661846\pi$
$827$	−28.0000			−0.973655			−0.486828	+	0.873498i	$0.661846\pi$
$828$		0			0
$829$	15.0000	−	25.9808i	0.520972	−	0.902349i	−0.478731	−	0.877962i	$-0.658903\pi$
$829$	15.0000	−	25.9808i	0.520972	−	0.902349i	0.999703	−	0.0243876i	$-0.00776357\pi$
$830$	6.00000	−	10.3923i	0.208263	−	0.360722i
$831$	−3.00000	−	5.19615i	−0.104069	−	0.180253i
$832$	14.0000			0.485363
$833$		0			0
$834$	−4.00000			−0.138509
$835$		0			0
$836$	8.00000	−	13.8564i	0.276686	−	0.479234i
$837$		0			0
$838$	−2.00000	−	3.46410i	−0.0690889	−	0.119665i
$839$	−40.0000			−1.38095			−0.690477	−	0.723355i	$-0.742599\pi$
$839$	−40.0000			−1.38095			−0.690477	+	0.723355i	$0.742599\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	−13.0000	−	22.5167i	−0.448010	−	0.775975i
$843$	3.00000	−	5.19615i	0.103325	−	0.178965i
$844$	10.0000	−	17.3205i	0.344214	−	0.596196i
$845$	−4.50000	−	7.79423i	−0.154805	−	0.268130i
$846$	8.00000			0.275046
$847$		0			0
$848$	10.0000			0.343401
$849$	−6.00000	−	10.3923i	−0.205919	−	0.356663i
$850$	−1.00000	+	1.73205i	−0.0342997	+	0.0594089i
$851$		0			0
$852$	−4.00000	−	6.92820i	−0.137038	−	0.237356i
$853$	−6.00000			−0.205436			−0.102718	−	0.994711i	$-0.532754\pi$
$853$	−6.00000			−0.205436			−0.102718	+	0.994711i	$0.532754\pi$
$854$		0			0
$855$	4.00000			0.136797
$856$	18.0000	+	31.1769i	0.615227	+	1.06561i
$857$	−11.0000	+	19.0526i	−0.375753	+	0.650823i	−0.990439	−	0.137948i	$-0.955949\pi$
$857$	−11.0000	+	19.0526i	−0.375753	+	0.650823i	0.614687	+	0.788771i	$0.289283\pi$
$858$	−4.00000	+	6.92820i	−0.136558	+	0.236525i
$859$	−10.0000	−	17.3205i	−0.341196	−	0.590968i	0.643459	−	0.765480i	$-0.277499\pi$
$859$	−10.0000	−	17.3205i	−0.341196	−	0.590968i	−0.984655	+	0.174512i	$0.944165\pi$
$860$	4.00000			0.136399
$861$		0			0
$862$		0			0
$863$	28.0000	+	48.4974i	0.953131	+	1.65087i	0.738588	+	0.674157i	$0.235493\pi$
$863$	28.0000	+	48.4974i	0.953131	+	1.65087i	0.214543	+	0.976715i	$0.431174\pi$
$864$	2.50000	−	4.33013i	0.0850517	−	0.147314i
$865$	9.00000	−	15.5885i	0.306009	−	0.530023i
$866$	7.00000	+	12.1244i	0.237870	+	0.412002i
$867$	−13.0000			−0.441503
$868$		0			0
$869$		0			0
$870$	1.00000	+	1.73205i	0.0339032	+	0.0587220i
$871$	−12.0000	+	20.7846i	−0.406604	+	0.704260i
$872$	−21.0000	+	36.3731i	−0.711150	+	1.23175i
$873$	1.00000	+	1.73205i	0.0338449	+	0.0586210i
$874$		0			0
$875$		0			0
$876$	10.0000			0.337869
$877$	−15.0000	−	25.9808i	−0.506514	−	0.877308i	−0.999972	−	0.00753813i	$-0.997601\pi$
$877$	−15.0000	−	25.9808i	−0.506514	−	0.877308i	0.493458	−	0.869770i	$-0.335733\pi$
$878$	−20.0000	+	34.6410i	−0.674967	+	1.16908i
$879$	3.00000	−	5.19615i	0.101187	−	0.175262i
$880$	2.00000	+	3.46410i	0.0674200	+	0.116775i
$881$	46.0000			1.54978			0.774890	−	0.632096i	$-0.217805\pi$
$881$	46.0000			1.54978			0.774890	+	0.632096i	$0.217805\pi$
$882$		0			0
$883$	44.0000			1.48072			0.740359	−	0.672212i	$-0.234656\pi$
$883$	44.0000			1.48072			0.740359	+	0.672212i	$0.234656\pi$
$884$	−2.00000	−	3.46410i	−0.0672673	−	0.116510i
$885$	2.00000	−	3.46410i	0.0672293	−	0.116445i
$886$	−6.00000	+	10.3923i	−0.201574	+	0.349136i
$887$	24.0000	+	41.5692i	0.805841	+	1.39576i	0.915722	+	0.401813i	$0.131620\pi$
$887$	24.0000	+	41.5692i	0.805841	+	1.39576i	−0.109881	+	0.993945i	$0.535047\pi$
$888$	−30.0000			−1.00673
$889$		0			0
$890$	6.00000			0.201120
$891$	2.00000	+	3.46410i	0.0670025	+	0.116052i
$892$	−4.00000	+	6.92820i	−0.133930	+	0.231973i
$893$	−16.0000	+	27.7128i	−0.535420	+	0.927374i
$894$	11.0000	+	19.0526i	0.367895	+	0.637213i
$895$	−20.0000			−0.668526
$896$		0			0
$897$		0			0
$898$	1.00000	+	1.73205i	0.0333704	+	0.0577993i
$899$		0			0
$900$	0.500000	−	0.866025i	0.0166667	−	0.0288675i
$901$	−10.0000	−	17.3205i	−0.333148	−	0.577030i
$902$	−40.0000			−1.33185
$903$		0			0
$904$	6.00000			0.199557
$905$	5.00000	+	8.66025i	0.166206	+	0.287877i
$906$	−4.00000	+	6.92820i	−0.132891	+	0.230174i
$907$	6.00000	−	10.3923i	0.199227	−	0.345071i	−0.749051	−	0.662512i	$-0.769490\pi$
$907$	6.00000	−	10.3923i	0.199227	−	0.345071i	0.948278	+	0.317441i	$0.102824\pi$
$908$	10.0000	+	17.3205i	0.331862	+	0.574801i
$909$	−6.00000			−0.199007
$910$		0			0
$911$	32.0000			1.06021			0.530104	−	0.847933i	$-0.322153\pi$
$911$	32.0000			1.06021			0.530104	+	0.847933i	$0.322153\pi$
$912$	−2.00000	−	3.46410i	−0.0662266	−	0.114708i
$913$	−24.0000	+	41.5692i	−0.794284	+	1.37574i
$914$	5.00000	−	8.66025i	0.165385	−	0.286456i
$915$	1.00000	+	1.73205i	0.0330590	+	0.0572598i
$916$	6.00000			0.198246
$917$		0			0
$918$	2.00000			0.0660098
$919$	−20.0000	−	34.6410i	−0.659739	−	1.14270i	−0.980683	−	0.195603i	$-0.937333\pi$
$919$	−20.0000	−	34.6410i	−0.659739	−	1.14270i	0.320944	−	0.947098i	$-0.396000\pi$
$920$		0			0
$921$	14.0000	−	24.2487i	0.461316	−	0.799022i
$922$	9.00000	+	15.5885i	0.296399	+	0.513378i
$923$	−16.0000			−0.526646
$924$		0			0
$925$	−10.0000			−0.328798
$926$	12.0000	+	20.7846i	0.394344	+	0.683025i
$927$	−8.00000	+	13.8564i	−0.262754	+	0.455104i
$928$	−5.00000	+	8.66025i	−0.164133	+	0.284287i
$929$	17.0000	+	29.4449i	0.557752	+	0.966055i	0.997684	+	0.0680235i	$0.0216693\pi$
$929$	17.0000	+	29.4449i	0.557752	+	0.966055i	−0.439932	+	0.898031i	$0.644997\pi$
$930$		0			0
$931$		0			0
$932$	6.00000			0.196537
$933$	−12.0000	−	20.7846i	−0.392862	−	0.680458i
$934$	−14.0000	+	24.2487i	−0.458094	+	0.793442i
$935$	4.00000	−	6.92820i	0.130814	−	0.226576i
$936$	−3.00000	−	5.19615i	−0.0980581	−	0.169842i
$937$	54.0000			1.76410			0.882052	−	0.471153i	$-0.156162\pi$
$937$	54.0000			1.76410			0.882052	+	0.471153i	$0.156162\pi$
$938$		0			0
$939$	−26.0000			−0.848478
$940$	4.00000	+	6.92820i	0.130466	+	0.225973i
$941$	−25.0000	+	43.3013i	−0.814977	+	1.41158i	0.0943679	+	0.995537i	$0.469917\pi$
$941$	−25.0000	+	43.3013i	−0.814977	+	1.41158i	−0.909345	+	0.416044i	$0.863416\pi$
$942$	−7.00000	+	12.1244i	−0.228072	+	0.395033i
$943$		0			0
$944$	−4.00000			−0.130189
$945$		0			0
$946$	16.0000			0.520205
$947$	18.0000	+	31.1769i	0.584921	+	1.01311i	0.994885	+	0.101012i	$0.0322080\pi$
$947$	18.0000	+	31.1769i	0.584921	+	1.01311i	−0.409964	+	0.912102i	$0.634459\pi$
$948$		0			0
$949$	10.0000	−	17.3205i	0.324614	−	0.562247i
$950$	−2.00000	−	3.46410i	−0.0648886	−	0.112390i
$951$	−2.00000			−0.0648544
$952$		0			0
$953$	−22.0000			−0.712650			−0.356325	−	0.934362i	$-0.615970\pi$
$953$	−22.0000			−0.712650			−0.356325	+	0.934362i	$0.615970\pi$
$954$	−5.00000	−	8.66025i	−0.161881	−	0.280386i
$955$	8.00000	−	13.8564i	0.258874	−	0.448383i
$956$	−8.00000	+	13.8564i	−0.258738	+	0.448148i
$957$	−4.00000	−	6.92820i	−0.129302	−	0.223957i
$958$		0			0
$959$		0			0
$960$	−7.00000			−0.225924
$961$	15.5000	+	26.8468i	0.500000	+	0.866025i
$962$	−10.0000	+	17.3205i	−0.322413	+	0.558436i
$963$	6.00000	−	10.3923i	0.193347	−	0.334887i
$964$	7.00000	+	12.1244i	0.225455	+	0.390499i
$965$	−2.00000			−0.0643823
$966$		0			0
$967$	32.0000			1.02905			0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000			1.02905			0.514525	+	0.857475i	$0.327968\pi$
$968$	−7.50000	−	12.9904i	−0.241059	−	0.417527i
$969$	−4.00000	+	6.92820i	−0.128499	+	0.222566i
$970$	1.00000	−	1.73205i	0.0321081	−	0.0556128i
$971$	30.0000	+	51.9615i	0.962746	+	1.66752i	0.715553	+	0.698558i	$0.246175\pi$
$971$	30.0000	+	51.9615i	0.962746	+	1.66752i	0.247193	+	0.968966i	$0.420492\pi$
$972$	−1.00000			−0.0320750
$973$		0			0
$974$	−32.0000			−1.02535
$975$	−1.00000	−	1.73205i	−0.0320256	−	0.0554700i
$976$	1.00000	−	1.73205i	0.0320092	−	0.0554416i
$977$	−1.00000	+	1.73205i	−0.0319928	+	0.0554132i	−0.881579	−	0.472037i	$-0.843519\pi$
$977$	−1.00000	+	1.73205i	−0.0319928	+	0.0554132i	0.849586	+	0.527451i	$0.176852\pi$
$978$	−2.00000	−	3.46410i	−0.0639529	−	0.110770i
$979$	−24.0000			−0.767043
$980$		0			0
$981$	14.0000			0.446986
$982$	14.0000	+	24.2487i	0.446758	+	0.773807i
$983$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$983$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$984$	15.0000	−	25.9808i	0.478183	−	0.828236i
$985$	3.00000	+	5.19615i	0.0955879	+	0.165563i
$986$	−4.00000			−0.127386
$987$		0			0
$988$	8.00000			0.254514
$989$		0			0
$990$	2.00000	−	3.46410i	0.0635642	−	0.110096i
$991$	−16.0000	+	27.7128i	−0.508257	+	0.880327i	0.491698	+	0.870766i	$0.336377\pi$
$991$	−16.0000	+	27.7128i	−0.508257	+	0.880327i	−0.999954	+	0.00956046i	$0.996957\pi$
$992$		0			0
$993$	12.0000			0.380808
$994$		0			0
$995$	−8.00000			−0.253617
$996$	−6.00000	−	10.3923i	−0.190117	−	0.329293i
$997$	27.0000	−	46.7654i	0.855099	−	1.48107i	−0.0214550	−	0.999770i	$-0.506830\pi$
$997$	27.0000	−	46.7654i	0.855099	−	1.48107i	0.876554	−	0.481304i	$-0.159837\pi$
$998$	2.00000	−	3.46410i	0.0633089	−	0.109654i
$999$	5.00000	+	8.66025i	0.158193	+	0.273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.i.d.361.1		2
7.2	even	3	inner	735.2.i.d.226.1		2
7.3	odd	6		15.2.a.a.1.1	✓	1
7.4	even	3		735.2.a.c.1.1		1
7.5	odd	6		735.2.i.e.226.1		2
7.6	odd	2		735.2.i.e.361.1		2
21.11	odd	6		2205.2.a.i.1.1		1
21.17	even	6		45.2.a.a.1.1		1
28.3	even	6		240.2.a.d.1.1		1
35.3	even	12		75.2.b.b.49.2		2
35.4	even	6		3675.2.a.j.1.1		1
35.17	even	12		75.2.b.b.49.1		2
35.24	odd	6		75.2.a.b.1.1		1
56.3	even	6		960.2.a.a.1.1		1
56.45	odd	6		960.2.a.l.1.1		1
63.31	odd	6		405.2.e.f.136.1		2
63.38	even	6		405.2.e.c.271.1		2
63.52	odd	6		405.2.e.f.271.1		2
63.59	even	6		405.2.e.c.136.1		2
77.10	even	6		1815.2.a.d.1.1		1
84.59	odd	6		720.2.a.c.1.1		1
91.38	odd	6		2535.2.a.j.1.1		1
105.17	odd	12		225.2.b.b.199.2		2
105.38	odd	12		225.2.b.b.199.1		2
105.59	even	6		225.2.a.b.1.1		1
112.3	even	12		3840.2.k.r.1921.2		2
112.45	odd	12		3840.2.k.m.1921.1		2
112.59	even	12		3840.2.k.r.1921.1		2
112.101	odd	12		3840.2.k.m.1921.2		2
119.101	odd	6		4335.2.a.c.1.1		1
133.94	even	6		5415.2.a.j.1.1		1
140.3	odd	12		1200.2.f.h.49.2		2
140.59	even	6		1200.2.a.e.1.1		1
140.87	odd	12		1200.2.f.h.49.1		2
161.45	even	6		7935.2.a.d.1.1		1
168.59	odd	6		2880.2.a.bc.1.1		1
168.101	even	6		2880.2.a.y.1.1		1
231.164	odd	6		5445.2.a.c.1.1		1
273.38	even	6		7605.2.a.g.1.1		1
280.3	odd	12		4800.2.f.c.3649.1		2
280.59	even	6		4800.2.a.bz.1.1		1
280.157	even	12		4800.2.f.bf.3649.1		2
280.213	even	12		4800.2.f.bf.3649.2		2
280.227	odd	12		4800.2.f.c.3649.2		2
280.269	odd	6		4800.2.a.t.1.1		1
385.164	even	6		9075.2.a.g.1.1		1
420.59	odd	6		3600.2.a.u.1.1		1
420.143	even	12		3600.2.f.e.2449.1		2
420.227	even	12		3600.2.f.e.2449.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.2.a.a.1.1	✓	1	7.3	odd	6
45.2.a.a.1.1		1	21.17	even	6
75.2.a.b.1.1		1	35.24	odd	6
75.2.b.b.49.1		2	35.17	even	12
75.2.b.b.49.2		2	35.3	even	12
225.2.a.b.1.1		1	105.59	even	6
225.2.b.b.199.1		2	105.38	odd	12
225.2.b.b.199.2		2	105.17	odd	12
240.2.a.d.1.1		1	28.3	even	6
405.2.e.c.136.1		2	63.59	even	6
405.2.e.c.271.1		2	63.38	even	6
405.2.e.f.136.1		2	63.31	odd	6
405.2.e.f.271.1		2	63.52	odd	6
720.2.a.c.1.1		1	84.59	odd	6
735.2.a.c.1.1		1	7.4	even	3
735.2.i.d.226.1		2	7.2	even	3	inner
735.2.i.d.361.1		2	1.1	even	1	trivial
735.2.i.e.226.1		2	7.5	odd	6
735.2.i.e.361.1		2	7.6	odd	2
960.2.a.a.1.1		1	56.3	even	6
960.2.a.l.1.1		1	56.45	odd	6
1200.2.a.e.1.1		1	140.59	even	6
1200.2.f.h.49.1		2	140.87	odd	12
1200.2.f.h.49.2		2	140.3	odd	12
1815.2.a.d.1.1		1	77.10	even	6
2205.2.a.i.1.1		1	21.11	odd	6
2535.2.a.j.1.1		1	91.38	odd	6
2880.2.a.y.1.1		1	168.101	even	6
2880.2.a.bc.1.1		1	168.59	odd	6
3600.2.a.u.1.1		1	420.59	odd	6
3600.2.f.e.2449.1		2	420.143	even	12
3600.2.f.e.2449.2		2	420.227	even	12
3675.2.a.j.1.1		1	35.4	even	6
3840.2.k.m.1921.1		2	112.45	odd	12
3840.2.k.m.1921.2		2	112.101	odd	12
3840.2.k.r.1921.1		2	112.59	even	12
3840.2.k.r.1921.2		2	112.3	even	12
4335.2.a.c.1.1		1	119.101	odd	6
4800.2.a.t.1.1		1	280.269	odd	6
4800.2.a.bz.1.1		1	280.59	even	6
4800.2.f.c.3649.1		2	280.3	odd	12
4800.2.f.c.3649.2		2	280.227	odd	12
4800.2.f.bf.3649.1		2	280.157	even	12
4800.2.f.bf.3649.2		2	280.213	even	12
5415.2.a.j.1.1		1	133.94	even	6
5445.2.a.c.1.1		1	231.164	odd	6
7605.2.a.g.1.1		1	273.38	even	6
7935.2.a.d.1.1		1	161.45	even	6
9075.2.a.g.1.1		1	385.164	even	6

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)

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

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