LMFDB - Embedded newform 1470.2.i.j.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1470,2,Mod(361,1470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1470, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("1470.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1470.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:	$11.7380090971$
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 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1470.961
Dual form			1470.2.i.j.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +1.00000 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} +(4.00000 - 6.92820i) q^{23} +(0.500000 + 0.866025i) 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} +(-0.500000 - 0.866025i) q^{32} +(-2.00000 + 3.46410i) q^{33} -2.00000 q^{34} +1.00000 q^{36} +(-3.00000 + 5.19615i) q^{37} +(2.00000 + 3.46410i) q^{38} +(1.00000 + 1.73205i) q^{39} +(0.500000 - 0.866025i) q^{40} +6.00000 q^{41} -4.00000 q^{43} +(2.00000 - 3.46410i) q^{44} +(0.500000 + 0.866025i) q^{45} +(4.00000 + 6.92820i) q^{46} -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} +(6.00000 + 10.3923i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(7.00000 - 12.1244i) q^{61} +1.00000 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^{69} -8.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(5.00000 + 8.66025i) q^{73} +(-3.00000 - 5.19615i) q^{74} +(0.500000 - 0.866025i) q^{75} -4.00000 q^{76} -2.00000 q^{78} +(-8.00000 + 13.8564i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.00000 + 5.19615i) q^{82} +12.0000 q^{83} +2.00000 q^{85} +(2.00000 - 3.46410i) q^{86} +(-1.00000 - 1.73205i) q^{87} +(2.00000 + 3.46410i) q^{88} +(5.00000 - 8.66025i) q^{89} -1.00000 q^{90} -8.00000 q^{92} +(-2.00000 - 3.46410i) q^{95} +(0.500000 - 0.866025i) 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} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 + q^3 - q^4 + q^5 - 2 * q^6 + 2 * q^8 - q^9	$ 2 q - q^{2} + q^{3} - q^{4} + q^{5} - 2 q^{6} + 2 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} + 8 q^{23} + q^{24} - q^{25} - 2 q^{26} - 2 q^{27} - 4 q^{29} - q^{30} - q^{32} - 4 q^{33} - 4 q^{34} + 2 q^{36} - 6 q^{37} + 4 q^{38} + 2 q^{39} + q^{40} + 12 q^{41} - 8 q^{43} + 4 q^{44} + q^{45} + 8 q^{46} - 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} + 12 q^{59} - q^{60} + 14 q^{61} + 2 q^{64} + 2 q^{65} - 4 q^{66} + 12 q^{67} + 2 q^{68} + 16 q^{69} - 16 q^{71} - q^{72} + 10 q^{73} - 6 q^{74} + q^{75} - 8 q^{76} - 4 q^{78} - 16 q^{79} + q^{80} - q^{81} - 6 q^{82} + 24 q^{83} + 4 q^{85} + 4 q^{86} - 2 q^{87} + 4 q^{88} + 10 q^{89} - 2 q^{90} - 16 q^{92} - 4 q^{95} + q^{96} - 4 q^{97} - 8 q^{99}+O(q^{100}) $ 2 * q - q^2 + q^3 - q^4 + q^5 - 2 * q^6 + 2 * 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 + 8 * q^23 + q^24 - q^25 - 2 * q^26 - 2 * q^27 - 4 * q^29 - q^30 - q^32 - 4 * q^33 - 4 * q^34 + 2 * q^36 - 6 * q^37 + 4 * q^38 + 2 * q^39 + q^40 + 12 * q^41 - 8 * q^43 + 4 * q^44 + q^45 + 8 * q^46 - 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 + 12 * q^59 - q^60 + 14 * q^61 + 2 * q^64 + 2 * q^65 - 4 * q^66 + 12 * q^67 + 2 * q^68 + 16 * q^69 - 16 * q^71 - q^72 + 10 * q^73 - 6 * q^74 + q^75 - 8 * q^76 - 4 * q^78 - 16 * q^79 + q^80 - q^81 - 6 * q^82 + 24 * q^83 + 4 * q^85 + 4 * q^86 - 2 * q^87 + 4 * q^88 + 10 * q^89 - 2 * q^90 - 16 * q^92 - 4 * q^95 + q^96 - 4 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times$.

$n$	$491$	$1081$	$1177$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	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
$8$	1.00000			0.353553
$9$	−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
$23$	4.00000	−	6.92820i	0.834058	−	1.44463i	−0.0607377	−	0.998154i	$-0.519345\pi$
$23$	4.00000	−	6.92820i	0.834058	−	1.44463i	0.894795	−	0.446476i	$-0.147321\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−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	$0.833333\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−2.00000	+	3.46410i	−0.348155	+	0.603023i
$34$	−2.00000			−0.342997
$35$		0			0
$36$	1.00000			0.166667
$37$	−3.00000	+	5.19615i	−0.493197	+	0.854242i	−0.999969	−	0.00783774i	$-0.997505\pi$
$37$	−3.00000	+	5.19615i	−0.493197	+	0.854242i	0.506772	+	0.862080i	$0.330838\pi$
$38$	2.00000	+	3.46410i	0.324443	+	0.561951i
$39$	1.00000	+	1.73205i	0.160128	+	0.277350i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$	−4.00000			−0.609994			−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000			−0.609994			−0.304997	+	0.952353i	$0.598656\pi$
$44$	2.00000	−	3.46410i	0.301511	−	0.522233i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	4.00000	+	6.92820i	0.589768	+	1.02151i
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$	−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
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	0.931282	+	0.364299i	$0.118692\pi$
$59$	6.00000	+	10.3923i	0.781133	+	1.35296i	−0.150148	+	0.988663i	$0.547975\pi$
$60$	−0.500000	−	0.866025i	−0.0645497	−	0.111803i
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.0640184	−	0.997949i	$-0.479608\pi$
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.832240	−	0.554416i	$-0.187058\pi$
$62$		0			0
$63$		0			0
$64$	1.00000			0.125000
$65$	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	$0.0952216\pi$
$67$	6.00000	+	10.3923i	0.733017	+	1.26962i	−0.222571	+	0.974916i	$0.571445\pi$
$68$	1.00000	−	1.73205i	0.121268	−	0.210042i
$69$	8.00000			0.963087
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	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	$0.634347\pi$
$74$	−3.00000	−	5.19615i	−0.348743	−	0.604040i
$75$	0.500000	−	0.866025i	0.0577350	−	0.100000i
$76$	−4.00000			−0.458831
$77$		0			0
$78$	−2.00000			−0.226455
$79$	−8.00000	+	13.8564i	−0.900070	+	1.55897i	−0.0726692	+	0.997356i	$0.523152\pi$
$79$	−8.00000	+	13.8564i	−0.900070	+	1.55897i	−0.827401	+	0.561611i	$0.810182\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.00000	+	5.19615i	−0.331295	+	0.573819i
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		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
$88$	2.00000	+	3.46410i	0.213201	+	0.369274i
$89$	5.00000	−	8.66025i	0.529999	−	0.917985i	−0.469389	−	0.882992i	$-0.655526\pi$
$89$	5.00000	−	8.66025i	0.529999	−	0.917985i	0.999388	−	0.0349934i	$-0.0111410\pi$
$90$	−1.00000			−0.105409
$91$		0			0
$92$	−8.00000			−0.834058
$93$		0			0
$94$		0			0
$95$	−2.00000	−	3.46410i	−0.205196	−	0.355409i
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	−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
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	−0.992990	−	0.118199i	$-0.962288\pi$
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	0.598858	+	0.800855i	$0.295621\pi$
$104$	2.00000			0.196116
$105$		0			0
$106$	−10.0000			−0.971286
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$	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
$111$	−6.00000			−0.569495
$112$		0			0
$113$	18.0000			1.69330			0.846649	−	0.532152i	$-0.178617\pi$
$113$	18.0000			1.69330			0.846649	+	0.532152i	$0.178617\pi$
$114$	−2.00000	+	3.46410i	−0.187317	+	0.324443i
$115$	−4.00000	−	6.92820i	−0.373002	−	0.646058i
$116$	1.00000	+	1.73205i	0.0928477	+	0.160817i
$117$	−1.00000	+	1.73205i	−0.0924500	+	0.160128i
$118$	−12.0000			−1.10469
$119$		0			0
$120$	1.00000			0.0912871
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$	7.00000	+	12.1244i	0.633750	+	1.09769i
$123$	3.00000	+	5.19615i	0.270501	+	0.468521i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−2.00000	−	3.46410i	−0.176090	−	0.304997i
$130$	1.00000	+	1.73205i	0.0877058	+	0.151911i
$131$	10.0000	−	17.3205i	0.873704	−	1.51330i	0.0155672	−	0.999879i	$-0.495045\pi$
$131$	10.0000	−	17.3205i	0.873704	−	1.51330i	0.858137	−	0.513421i	$-0.171622\pi$
$132$	4.00000			0.348155
$133$		0			0
$134$	−12.0000			−1.03664
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$	1.00000	+	1.73205i	0.0857493	+	0.148522i
$137$	−5.00000	−	8.66025i	−0.427179	−	0.739895i	0.569442	−	0.822031i	$-0.307159\pi$
$137$	−5.00000	−	8.66025i	−0.427179	−	0.739895i	−0.996621	+	0.0821359i	$0.973826\pi$
$138$	−4.00000	+	6.92820i	−0.340503	+	0.589768i
$139$	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
$141$		0			0
$142$	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
$148$	6.00000			0.493197
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	−0.585231	−	0.810867i	$-0.698996\pi$
$149$	5.00000	−	8.66025i	0.409616	−	0.709476i	0.994847	+	0.101391i	$0.0323294\pi$
$150$	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	$0.727796\pi$
$152$	2.00000	−	3.46410i	0.162221	−	0.280976i
$153$	−2.00000			−0.161690
$154$		0			0
$155$		0			0
$156$	1.00000	−	1.73205i	0.0800641	−	0.138675i
$157$	−9.00000	−	15.5885i	−0.718278	−	1.24409i	−0.961681	−	0.274169i	$-0.911597\pi$
$157$	−9.00000	−	15.5885i	−0.718278	−	1.24409i	0.243403	−	0.969925i	$-0.421736\pi$
$158$	−8.00000	−	13.8564i	−0.636446	−	1.10236i
$159$	−5.00000	+	8.66025i	−0.396526	+	0.686803i
$160$	−1.00000			−0.0790569
$161$		0			0
$162$	1.00000			0.0785674
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	0.146772	+	0.989170i	$0.453112\pi$
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	−0.930033	+	0.367477i	$0.880222\pi$
$164$	−3.00000	−	5.19615i	−0.234261	−	0.405751i
$165$	2.00000	+	3.46410i	0.155700	+	0.269680i
$166$	−6.00000	+	10.3923i	−0.465690	+	0.806599i
$167$	8.00000			0.619059			0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000			0.619059			0.309529	+	0.950890i	$0.399829\pi$
$168$		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
$177$	−6.00000	+	10.3923i	−0.450988	+	0.781133i
$178$	5.00000	+	8.66025i	0.374766	+	0.649113i
$179$	−2.00000	−	3.46410i	−0.149487	−	0.258919i	0.781551	−	0.623841i	$-0.214429\pi$
$179$	−2.00000	−	3.46410i	−0.149487	−	0.258919i	−0.931038	+	0.364922i	$0.881096\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	−6.00000			−0.445976			−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000			−0.445976			−0.222988	+	0.974821i	$0.571581\pi$
$182$		0			0
$183$	14.0000			1.03491
$184$	4.00000	−	6.92820i	0.294884	−	0.510754i
$185$	3.00000	+	5.19615i	0.220564	+	0.382029i
$186$		0			0
$187$	−4.00000	+	6.92820i	−0.292509	+	0.506640i
$188$		0			0
$189$		0			0
$190$	4.00000			0.290191
$191$	8.00000	−	13.8564i	0.578860	−	1.00261i	−0.416751	−	0.909021i	$-0.636831\pi$
$191$	8.00000	−	13.8564i	0.578860	−	1.00261i	0.995610	−	0.0935936i	$-0.0298354\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−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
$199$	−12.0000	−	20.7846i	−0.850657	−	1.47338i	−0.880616	−	0.473831i	$-0.842871\pi$
$199$	−12.0000	−	20.7846i	−0.850657	−	1.47338i	0.0299585	−	0.999551i	$-0.490462\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−6.00000	+	10.3923i	−0.423207	+	0.733017i
$202$	−6.00000			−0.422159
$203$		0			0
$204$	2.00000			0.140028
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$	−4.00000	−	6.92820i	−0.278693	−	0.482711i
$207$	4.00000	+	6.92820i	0.278019	+	0.481543i
$208$	−1.00000	+	1.73205i	−0.0693375	+	0.120096i
$209$	16.0000			1.10674
$210$		0			0
$211$	−12.0000			−0.826114			−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000			−0.826114			−0.413057	+	0.910705i	$0.635539\pi$
$212$	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
$216$	−1.00000			−0.0680414
$217$		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
$222$	3.00000	−	5.19615i	0.201347	−	0.348743i
$223$	16.0000			1.07144			0.535720	−	0.844396i	$-0.320040\pi$
$223$	16.0000			1.07144			0.535720	+	0.844396i	$0.320040\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$	−9.00000	+	15.5885i	−0.598671	+	1.03693i
$227$	2.00000	+	3.46410i	0.132745	+	0.229920i	0.924734	−	0.380615i	$-0.124288\pi$
$227$	2.00000	+	3.46410i	0.132745	+	0.229920i	−0.791989	+	0.610535i	$0.790954\pi$
$228$	−2.00000	−	3.46410i	−0.132453	−	0.229416i
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	−0.982592	−	0.185776i	$-0.940520\pi$
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	0.652183	+	0.758062i	$0.273853\pi$
$230$	8.00000			0.527504
$231$		0			0
$232$	−2.00000			−0.131306
$233$	11.0000	−	19.0526i	0.720634	−	1.24817i	−0.240112	−	0.970745i	$-0.577184\pi$
$233$	11.0000	−	19.0526i	0.720634	−	1.24817i	0.960746	−	0.277429i	$-0.0894825\pi$
$234$	−1.00000	−	1.73205i	−0.0653720	−	0.113228i
$235$		0			0
$236$	6.00000	−	10.3923i	0.390567	−	0.676481i
$237$	−16.0000			−1.03931
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$	−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
$244$	−14.0000			−0.896258
$245$		0			0
$246$	−6.00000			−0.382546
$247$	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
$253$	32.0000			2.01182
$254$	8.00000	−	13.8564i	0.501965	−	0.869428i
$255$	1.00000	+	1.73205i	0.0626224	+	0.108465i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.00000	+	12.1244i	−0.436648	+	0.756297i	−0.997429	−	0.0716680i	$-0.977168\pi$
$257$	−7.00000	+	12.1244i	−0.436648	+	0.756297i	0.560781	+	0.827964i	$0.310501\pi$
$258$	4.00000			0.249029
$259$		0			0
$260$	−2.00000			−0.124035
$261$	1.00000	−	1.73205i	0.0618984	−	0.107211i
$262$	10.0000	+	17.3205i	0.617802	+	1.07006i
$263$	−4.00000	−	6.92820i	−0.246651	−	0.427211i	0.715944	−	0.698158i	$-0.245997\pi$
$263$	−4.00000	−	6.92820i	−0.246651	−	0.427211i	−0.962594	+	0.270947i	$0.912663\pi$
$264$	−2.00000	+	3.46410i	−0.123091	+	0.213201i
$265$	10.0000			0.614295
$266$		0			0
$267$	10.0000			0.611990
$268$	6.00000	−	10.3923i	0.366508	−	0.634811i
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	−0.998361	−	0.0572259i	$-0.981774\pi$
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	0.449622	−	0.893219i	$-0.351559\pi$
$270$	−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
$274$	10.0000			0.604122
$275$	2.00000	−	3.46410i	0.120605	−	0.208893i
$276$	−4.00000	−	6.92820i	−0.240772	−	0.417029i
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	−0.980373	−	0.197153i	$-0.936830\pi$
$277$	−11.0000	−	19.0526i	−0.660926	−	1.14476i	0.319447	−	0.947604i	$-0.396503\pi$
$278$	−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	$0.557275\pi$
$282$		0			0
$283$	14.0000	+	24.2487i	0.832214	+	1.44144i	0.896279	+	0.443491i	$0.146260\pi$
$283$	14.0000	+	24.2487i	0.832214	+	1.44144i	−0.0640654	+	0.997946i	$0.520407\pi$
$284$	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
$288$	1.00000			0.0589256
$289$	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
$295$	12.0000			0.698667
$296$	−3.00000	+	5.19615i	−0.174371	+	0.302020i
$297$	−2.00000	−	3.46410i	−0.116052	−	0.201008i
$298$	5.00000	+	8.66025i	0.289642	+	0.501675i
$299$	8.00000	−	13.8564i	0.462652	−	0.801337i
$300$	−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
$305$	−7.00000	−	12.1244i	−0.400819	−	0.694239i
$306$	1.00000	−	1.73205i	0.0571662	−	0.0990148i
$307$	−20.0000			−1.14146			−0.570730	−	0.821138i	$-0.693340\pi$
$307$	−20.0000			−1.14146			−0.570730	+	0.821138i	$0.693340\pi$
$308$		0			0
$309$	−8.00000			−0.455104
$310$		0			0
$311$	−4.00000	−	6.92820i	−0.226819	−	0.392862i	0.730044	−	0.683400i	$-0.239499\pi$
$311$	−4.00000	−	6.92820i	−0.226819	−	0.392862i	−0.956864	+	0.290537i	$0.906166\pi$
$312$	1.00000	+	1.73205i	0.0566139	+	0.0980581i
$313$	−3.00000	+	5.19615i	−0.169570	+	0.293704i	−0.938269	−	0.345907i	$-0.887571\pi$
$313$	−3.00000	+	5.19615i	−0.169570	+	0.293704i	0.768699	+	0.639611i	$0.220905\pi$
$314$	18.0000			1.01580
$315$		0			0
$316$	16.0000			0.900070
$317$	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
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−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
$326$	−10.0000	−	17.3205i	−0.553849	−	0.959294i
$327$	7.00000	−	12.1244i	0.387101	−	0.670478i
$328$	6.00000			0.331295
$329$		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
$333$	−3.00000	−	5.19615i	−0.164399	−	0.284747i
$334$	−4.00000	+	6.92820i	−0.218870	+	0.379094i
$335$	12.0000			0.655630
$336$		0			0
$337$	18.0000			0.980522			0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000			0.980522			0.490261	+	0.871576i	$0.336901\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$	9.00000	+	15.5885i	0.488813	+	0.846649i
$340$	−1.00000	−	1.73205i	−0.0542326	−	0.0939336i
$341$		0			0
$342$	−4.00000			−0.216295
$343$		0			0
$344$	−4.00000			−0.215666
$345$	4.00000	−	6.92820i	0.215353	−	0.373002i
$346$	−9.00000	−	15.5885i	−0.483843	−	0.838041i
$347$	2.00000	+	3.46410i	0.107366	+	0.185963i	0.914702	−	0.404128i	$-0.132425\pi$
$347$	2.00000	+	3.46410i	0.107366	+	0.185963i	−0.807337	+	0.590091i	$0.799092\pi$
$348$	−1.00000	+	1.73205i	−0.0536056	+	0.0928477i
$349$	−14.0000			−0.749403			−0.374701	−	0.927146i	$-0.622255\pi$
$349$	−14.0000			−0.749403			−0.374701	+	0.927146i	$0.622255\pi$
$350$		0			0
$351$	−2.00000			−0.106752
$352$	2.00000	−	3.46410i	0.106600	−	0.184637i
$353$	−7.00000	−	12.1244i	−0.372572	−	0.645314i	0.617388	−	0.786659i	$-0.288191\pi$
$353$	−7.00000	−	12.1244i	−0.372572	−	0.645314i	−0.989960	+	0.141344i	$0.954858\pi$
$354$	−6.00000	−	10.3923i	−0.318896	−	0.552345i
$355$	−4.00000	+	6.92820i	−0.212298	+	0.367711i
$356$	−10.0000			−0.529999
$357$		0			0
$358$	4.00000			0.211407
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	0.353529	+	0.935423i	$0.384981\pi$
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	−0.986865	+	0.161546i	$0.948352\pi$
$360$	0.500000	+	0.866025i	0.0263523	+	0.0456435i
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	3.00000	−	5.19615i	0.157676	−	0.273104i
$363$	−5.00000			−0.262432
$364$		0			0
$365$	10.0000			0.523424
$366$	−7.00000	+	12.1244i	−0.365896	+	0.633750i
$367$	−16.0000	−	27.7128i	−0.835193	−	1.44660i	−0.893873	−	0.448320i	$-0.852022\pi$
$367$	−16.0000	−	27.7128i	−0.835193	−	1.44660i	0.0586798	−	0.998277i	$-0.481311\pi$
$368$	4.00000	+	6.92820i	0.208514	+	0.361158i
$369$	−3.00000	+	5.19615i	−0.156174	+	0.270501i
$370$	−6.00000			−0.311925
$371$		0			0
$372$		0			0
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	−0.707055	−	0.707159i	$-0.749977\pi$
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	0.965945	+	0.258748i	$0.0833099\pi$
$374$	−4.00000	−	6.92820i	−0.206835	−	0.358249i
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$		0			0
$377$	−4.00000			−0.206010
$378$		0			0
$379$	28.0000			1.43826			0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000			1.43826			0.719132	+	0.694874i	$0.244540\pi$
$380$	−2.00000	+	3.46410i	−0.102598	+	0.177705i
$381$	−8.00000	−	13.8564i	−0.409852	−	0.709885i
$382$	8.00000	+	13.8564i	0.409316	+	0.708955i
$383$	8.00000	−	13.8564i	0.408781	−	0.708029i	−0.585973	−	0.810331i	$-0.699287\pi$
$383$	8.00000	−	13.8564i	0.408781	−	0.708029i	0.994753	+	0.102302i	$0.0326207\pi$
$384$	−1.00000			−0.0510310
$385$		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
$389$	13.0000	+	22.5167i	0.659126	+	1.14164i	0.980842	+	0.194804i	$0.0624070\pi$
$389$	13.0000	+	22.5167i	0.659126	+	1.14164i	−0.321716	+	0.946836i	$0.604260\pi$
$390$	−1.00000	+	1.73205i	−0.0506370	+	0.0877058i
$391$	16.0000			0.809155
$392$		0			0
$393$	20.0000			1.00887
$394$	−3.00000	+	5.19615i	−0.151138	+	0.261778i
$395$	8.00000	+	13.8564i	0.402524	+	0.697191i
$396$	2.00000	+	3.46410i	0.100504	+	0.174078i
$397$	15.0000	−	25.9808i	0.752828	−	1.30394i	−0.193618	−	0.981077i	$-0.562022\pi$
$397$	15.0000	−	25.9808i	0.752828	−	1.30394i	0.946447	−	0.322860i	$-0.104644\pi$
$398$	24.0000			1.20301
$399$		0			0
$400$	1.00000			0.0500000
$401$	7.00000	−	12.1244i	0.349563	−	0.605461i	−0.636609	−	0.771187i	$-0.719663\pi$
$401$	7.00000	−	12.1244i	0.349563	−	0.605461i	0.986172	+	0.165726i	$0.0529966\pi$
$402$	−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
$407$	−24.0000			−1.18964
$408$	−1.00000	+	1.73205i	−0.0495074	+	0.0857493i
$409$	−19.0000	−	32.9090i	−0.939490	−	1.62724i	−0.766426	−	0.642333i	$-0.777967\pi$
$409$	−19.0000	−	32.9090i	−0.939490	−	1.62724i	−0.173064	−	0.984911i	$-0.555367\pi$
$410$	3.00000	+	5.19615i	0.148159	+	0.256620i
$411$	5.00000	−	8.66025i	0.246632	−	0.427179i
$412$	8.00000			0.394132
$413$		0			0
$414$	−8.00000			−0.393179
$415$	6.00000	−	10.3923i	0.294528	−	0.510138i
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$	2.00000	+	3.46410i	0.0979404	+	0.169638i
$418$	−8.00000	+	13.8564i	−0.391293	+	0.677739i
$419$	−20.0000			−0.977064			−0.488532	−	0.872546i	$-0.662467\pi$
$419$	−20.0000			−0.977064			−0.488532	+	0.872546i	$0.662467\pi$
$420$		0			0
$421$	−26.0000			−1.26716			−0.633581	−	0.773676i	$-0.718416\pi$
$421$	−26.0000			−1.26716			−0.633581	+	0.773676i	$0.718416\pi$
$422$	6.00000	−	10.3923i	0.292075	−	0.505889i
$423$		0			0
$424$	5.00000	+	8.66025i	0.242821	+	0.420579i
$425$	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
$437$	−16.0000	−	27.7128i	−0.765384	−	1.32568i
$438$	−5.00000	−	8.66025i	−0.238909	−	0.413803i
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	−0.945552	−	0.325471i	$-0.894477\pi$
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	0.754642	+	0.656136i	$0.227810\pi$
$440$	4.00000			0.190693
$441$		0			0
$442$	−4.00000			−0.190261
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	−0.0212481	−	0.999774i	$-0.506764\pi$
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	0.876454	−	0.481486i	$-0.159903\pi$
$444$	3.00000	+	5.19615i	0.142374	+	0.246598i
$445$	−5.00000	−	8.66025i	−0.237023	−	0.410535i
$446$	−8.00000	+	13.8564i	−0.378811	+	0.656120i
$447$	10.0000			0.472984
$448$		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
$451$	12.0000	+	20.7846i	0.565058	+	0.978709i
$452$	−9.00000	−	15.5885i	−0.423324	−	0.733219i
$453$	−4.00000	+	6.92820i	−0.187936	+	0.325515i
$454$	−4.00000			−0.187729
$455$		0			0
$456$	4.00000			0.187317
$457$	−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	$0.241812\pi$
$458$	−5.00000	−	8.66025i	−0.233635	−	0.404667i
$459$	−1.00000	−	1.73205i	−0.0466760	−	0.0808452i
$460$	−4.00000	+	6.92820i	−0.186501	+	0.323029i
$461$	−14.0000			−0.652045			−0.326023	−	0.945362i	$-0.605709\pi$
$461$	−14.0000			−0.652045			−0.326023	+	0.945362i	$0.605709\pi$
$462$		0			0
$463$		0			0			−	1.00000i	$-0.5\pi$
$463$		0			0				1.00000i	$0.5\pi$
$464$	1.00000	−	1.73205i	0.0464238	−	0.0804084i
$465$		0			0
$466$	11.0000	+	19.0526i	0.509565	+	0.882593i
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	−0.970799	−	0.239892i	$-0.922888\pi$
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	0.693153	+	0.720791i	$0.256221\pi$
$468$	2.00000			0.0924500
$469$		0			0
$470$		0			0
$471$	9.00000	−	15.5885i	0.414698	−	0.718278i
$472$	6.00000	+	10.3923i	0.276172	+	0.478345i
$473$	−8.00000	−	13.8564i	−0.367840	−	0.637118i
$474$	8.00000	−	13.8564i	0.367452	−	0.636446i
$475$	−4.00000			−0.183533
$476$		0			0
$477$	−10.0000			−0.457869
$478$		0			0
$479$	16.0000	+	27.7128i	0.731059	+	1.26623i	0.956431	+	0.291958i	$0.0943068\pi$
$479$	16.0000	+	27.7128i	0.731059	+	1.26623i	−0.225372	+	0.974273i	$0.572360\pi$
$480$	−0.500000	−	0.866025i	−0.0228218	−	0.0395285i
$481$	−6.00000	+	10.3923i	−0.273576	+	0.473848i
$482$	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
$487$	4.00000	+	6.92820i	0.181257	+	0.313947i	0.942309	−	0.334744i	$-0.108650\pi$
$487$	4.00000	+	6.92820i	0.181257	+	0.313947i	−0.761052	+	0.648691i	$0.775317\pi$
$488$	7.00000	−	12.1244i	0.316875	−	0.548844i
$489$	−20.0000			−0.904431
$490$		0			0
$491$	−36.0000			−1.62466			−0.812329	−	0.583200i	$-0.801800\pi$
$491$	−36.0000			−1.62466			−0.812329	+	0.583200i	$0.801800\pi$
$492$	3.00000	−	5.19615i	0.135250	−	0.234261i
$493$	−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
$499$	6.00000	−	10.3923i	0.268597	−	0.465223i	−0.699903	−	0.714238i	$-0.746773\pi$
$499$	6.00000	−	10.3923i	0.268597	−	0.465223i	0.968500	+	0.249015i	$0.0801067\pi$
$500$	0.500000	+	0.866025i	0.0223607	+	0.0387298i
$501$	4.00000	+	6.92820i	0.178707	+	0.309529i
$502$	6.00000	−	10.3923i	0.267793	−	0.463831i
$503$	−40.0000			−1.78351			−0.891756	−	0.452517i	$-0.850526\pi$
$503$	−40.0000			−1.78351			−0.891756	+	0.452517i	$0.850526\pi$
$504$		0			0
$505$	6.00000			0.266996
$506$	−16.0000	+	27.7128i	−0.711287	+	1.23198i
$507$	−4.50000	−	7.79423i	−0.199852	−	0.346154i
$508$	8.00000	+	13.8564i	0.354943	+	0.614779i
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	−0.314459	−	0.949271i	$-0.601823\pi$
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	0.979322	−	0.202306i	$-0.0648436\pi$
$510$	−2.00000			−0.0885615
$511$		0			0
$512$	1.00000			0.0441942
$513$	−2.00000	+	3.46410i	−0.0883022	+	0.152944i
$514$	−7.00000	−	12.1244i	−0.308757	−	0.534782i
$515$	4.00000	+	6.92820i	0.176261	+	0.305293i
$516$	−2.00000	+	3.46410i	−0.0880451	+	0.152499i
$517$		0			0
$518$		0			0
$519$	−18.0000			−0.790112
$520$	1.00000	−	1.73205i	0.0438529	−	0.0759555i
$521$	−3.00000	−	5.19615i	−0.131432	−	0.227648i	0.792797	−	0.609486i	$-0.208624\pi$
$521$	−3.00000	−	5.19615i	−0.131432	−	0.227648i	−0.924229	+	0.381839i	$0.875291\pi$
$522$	1.00000	+	1.73205i	0.0437688	+	0.0758098i
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	−0.997478	−	0.0709788i	$-0.977388\pi$
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	0.560208	+	0.828352i	$0.310721\pi$
$524$	−20.0000			−0.873704
$525$		0			0
$526$	8.00000			0.348817
$527$		0			0
$528$	−2.00000	−	3.46410i	−0.0870388	−	0.150756i
$529$	−20.5000	−	35.5070i	−0.891304	−	1.54378i
$530$	−5.00000	+	8.66025i	−0.217186	+	0.376177i
$531$	−12.0000			−0.520756
$532$		0			0
$533$	12.0000			0.519778
$534$	−5.00000	+	8.66025i	−0.216371	+	0.374766i
$535$	6.00000	+	10.3923i	0.259403	+	0.449299i
$536$	6.00000	+	10.3923i	0.259161	+	0.448879i
$537$	2.00000	−	3.46410i	0.0863064	−	0.149487i
$538$	18.0000			0.776035
$539$		0			0
$540$	1.00000			0.0430331
$541$	17.0000	−	29.4449i	0.730887	−	1.26593i	−0.225617	−	0.974216i	$-0.572440\pi$
$541$	17.0000	−	29.4449i	0.730887	−	1.26593i	0.956504	−	0.291718i	$-0.0942267\pi$
$542$	8.00000	+	13.8564i	0.343629	+	0.595184i
$543$	−3.00000	−	5.19615i	−0.128742	−	0.222988i
$544$	1.00000	−	1.73205i	0.0428746	−	0.0742611i
$545$	−14.0000			−0.599694
$546$		0			0
$547$	−12.0000			−0.513083			−0.256541	−	0.966533i	$-0.582583\pi$
$547$	−12.0000			−0.513083			−0.256541	+	0.966533i	$0.582583\pi$
$548$	−5.00000	+	8.66025i	−0.213589	+	0.369948i
$549$	7.00000	+	12.1244i	0.298753	+	0.517455i
$550$	2.00000	+	3.46410i	0.0852803	+	0.147710i
$551$	−4.00000	+	6.92820i	−0.170406	+	0.295151i
$552$	8.00000			0.340503
$553$		0			0
$554$	22.0000			0.934690
$555$	−3.00000	+	5.19615i	−0.127343	+	0.220564i
$556$	−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
$563$	10.0000	+	17.3205i	0.421450	+	0.729972i	0.996082	−	0.0884397i	$-0.0281881\pi$
$563$	10.0000	+	17.3205i	0.421450	+	0.729972i	−0.574632	+	0.818412i	$0.694855\pi$
$564$		0			0
$565$	9.00000	−	15.5885i	0.378633	−	0.655811i
$566$	−28.0000			−1.17693
$567$		0			0
$568$	−8.00000			−0.335673
$569$	−13.0000	+	22.5167i	−0.544988	+	0.943948i	0.453619	+	0.891196i	$0.350133\pi$
$569$	−13.0000	+	22.5167i	−0.544988	+	0.943948i	−0.998608	+	0.0527519i	$0.983201\pi$
$570$	2.00000	+	3.46410i	0.0837708	+	0.145095i
$571$	−14.0000	−	24.2487i	−0.585882	−	1.01478i	−0.994765	−	0.102190i	$-0.967415\pi$
$571$	−14.0000	−	24.2487i	−0.585882	−	1.01478i	0.408883	−	0.912587i	$-0.365918\pi$
$572$	4.00000	−	6.92820i	0.167248	−	0.289683i
$573$	16.0000			0.668410
$574$		0			0
$575$	−8.00000			−0.333623
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	17.0000	+	29.4449i	0.707719	+	1.22581i	0.965701	+	0.259656i	$0.0836092\pi$
$577$	17.0000	+	29.4449i	0.707719	+	1.22581i	−0.257982	+	0.966150i	$0.583058\pi$
$578$	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
$584$	5.00000	+	8.66025i	0.206901	+	0.358364i
$585$	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	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$		0			0
$589$		0			0
$590$	−6.00000	+	10.3923i	−0.247016	+	0.427844i
$591$	3.00000	+	5.19615i	0.123404	+	0.213741i
$592$	−3.00000	−	5.19615i	−0.123299	−	0.213561i
$593$	−15.0000	+	25.9808i	−0.615976	+	1.06690i	0.374236	+	0.927333i	$0.377905\pi$
$593$	−15.0000	+	25.9808i	−0.615976	+	1.06690i	−0.990212	+	0.139569i	$0.955428\pi$
$594$	4.00000			0.164122
$595$		0			0
$596$	−10.0000			−0.409616
$597$	12.0000	−	20.7846i	0.491127	−	0.850657i
$598$	8.00000	+	13.8564i	0.327144	+	0.566631i
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	0.999938	−	0.0111569i	$-0.00355143\pi$
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	−0.509631	+	0.860393i	$0.670218\pi$
$600$	0.500000	−	0.866025i	0.0204124	−	0.0353553i
$601$	38.0000			1.55005			0.775026	−	0.631929i	$-0.217737\pi$
$601$	38.0000			1.55005			0.775026	+	0.631929i	$0.217737\pi$
$602$		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
$607$	8.00000	−	13.8564i	0.324710	−	0.562414i	−0.656744	−	0.754114i	$-0.728067\pi$
$607$	8.00000	−	13.8564i	0.324710	−	0.562414i	0.981454	+	0.191700i	$0.0614000\pi$
$608$	−4.00000			−0.162221
$609$		0			0
$610$	14.0000			0.566843
$611$		0			0
$612$	1.00000	+	1.73205i	0.0404226	+	0.0700140i
$613$	−3.00000	−	5.19615i	−0.121169	−	0.209871i	0.799060	−	0.601251i	$-0.205331\pi$
$613$	−3.00000	−	5.19615i	−0.121169	−	0.209871i	−0.920229	+	0.391381i	$0.871998\pi$
$614$	10.0000	−	17.3205i	0.403567	−	0.698999i
$615$	6.00000			0.241943
$616$		0			0
$617$	−22.0000			−0.885687			−0.442843	−	0.896599i	$-0.646030\pi$
$617$	−22.0000			−0.885687			−0.442843	+	0.896599i	$0.646030\pi$
$618$	4.00000	−	6.92820i	0.160904	−	0.278693i
$619$	−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
$621$	−4.00000	+	6.92820i	−0.160514	+	0.278019i
$622$	8.00000			0.320771
$623$		0			0
$624$	−2.00000			−0.0800641
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−3.00000	−	5.19615i	−0.119904	−	0.207680i
$627$	8.00000	+	13.8564i	0.319489	+	0.553372i
$628$	−9.00000	+	15.5885i	−0.359139	+	0.622047i
$629$	−12.0000			−0.478471
$630$		0			0
$631$	−40.0000			−1.59237			−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000			−1.59237			−0.796187	+	0.605050i	$0.793153\pi$
$632$	−8.00000	+	13.8564i	−0.318223	+	0.551178i
$633$	−6.00000	−	10.3923i	−0.238479	−	0.413057i
$634$	1.00000	+	1.73205i	0.0397151	+	0.0687885i
$635$	−8.00000	+	13.8564i	−0.317470	+	0.549875i
$636$	10.0000			0.396526
$637$		0			0
$638$	8.00000			0.316723
$639$	4.00000	−	6.92820i	0.158238	−	0.274075i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−17.0000	−	29.4449i	−0.671460	−	1.16300i	−0.977490	−	0.210981i	$-0.932334\pi$
$641$	−17.0000	−	29.4449i	−0.671460	−	1.16300i	0.306031	−	0.952022i	$-0.400999\pi$
$642$	6.00000	−	10.3923i	0.236801	−	0.410152i
$643$	28.0000			1.10421			0.552106	−	0.833774i	$-0.313824\pi$
$643$	28.0000			1.10421			0.552106	+	0.833774i	$0.313824\pi$
$644$		0			0
$645$	−4.00000			−0.157500
$646$	−4.00000	+	6.92820i	−0.157378	+	0.272587i
$647$	12.0000	+	20.7846i	0.471769	+	0.817127i	0.999478	−	0.0322975i	$-0.0102824\pi$
$647$	12.0000	+	20.7846i	0.471769	+	0.817127i	−0.527710	+	0.849425i	$0.676949\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−24.0000	+	41.5692i	−0.942082	+	1.63173i
$650$	2.00000			0.0784465
$651$		0			0
$652$	20.0000			0.783260
$653$	−7.00000	+	12.1244i	−0.273931	+	0.474463i	−0.969865	−	0.243643i	$-0.921657\pi$
$653$	−7.00000	+	12.1244i	−0.273931	+	0.474463i	0.695934	+	0.718106i	$0.254991\pi$
$654$	7.00000	+	12.1244i	0.273722	+	0.474100i
$655$	−10.0000	−	17.3205i	−0.390732	−	0.676768i
$656$	−3.00000	+	5.19615i	−0.117130	+	0.202876i
$657$	−10.0000			−0.390137
$658$		0			0
$659$	36.0000			1.40236			0.701180	−	0.712984i	$-0.252657\pi$
$659$	36.0000			1.40236			0.701180	+	0.712984i	$0.252657\pi$
$660$	2.00000	−	3.46410i	0.0778499	−	0.134840i
$661$	19.0000	+	32.9090i	0.739014	+	1.28001i	0.952940	+	0.303160i	$0.0980418\pi$
$661$	19.0000	+	32.9090i	0.739014	+	1.28001i	−0.213925	+	0.976850i	$0.568625\pi$
$662$	−6.00000	−	10.3923i	−0.233197	−	0.403908i
$663$	−2.00000	+	3.46410i	−0.0776736	+	0.134535i
$664$	12.0000			0.465690
$665$		0			0
$666$	6.00000			0.232495
$667$	−8.00000	+	13.8564i	−0.309761	+	0.536522i
$668$	−4.00000	−	6.92820i	−0.154765	−	0.268060i
$669$	8.00000	+	13.8564i	0.309298	+	0.535720i
$670$	−6.00000	+	10.3923i	−0.231800	+	0.401490i
$671$	56.0000			2.16186
$672$		0			0
$673$	−30.0000			−1.15642			−0.578208	−	0.815890i	$-0.696248\pi$
$673$	−30.0000			−1.15642			−0.578208	+	0.815890i	$0.696248\pi$
$674$	−9.00000	+	15.5885i	−0.346667	+	0.600445i
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	−13.0000	+	22.5167i	−0.499631	+	0.865386i	−1.00000		0.000426509i	$-0.999864\pi$
$677$	−13.0000	+	22.5167i	−0.499631	+	0.865386i	0.500369	+	0.865812i	$0.333198\pi$
$678$	−18.0000			−0.691286
$679$		0			0
$680$	2.00000			0.0766965
$681$	−2.00000	+	3.46410i	−0.0766402	+	0.132745i
$682$		0			0
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	0.728101	−	0.685470i	$-0.240403\pi$
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	−0.957685	+	0.287819i	$0.907070\pi$
$684$	2.00000	−	3.46410i	0.0764719	−	0.132453i
$685$	−10.0000			−0.382080
$686$		0			0
$687$	−10.0000			−0.381524
$688$	2.00000	−	3.46410i	0.0762493	−	0.132068i
$689$	10.0000	+	17.3205i	0.380970	+	0.659859i
$690$	4.00000	+	6.92820i	0.152277	+	0.263752i
$691$	18.0000	−	31.1769i	0.684752	−	1.18603i	−0.288762	−	0.957401i	$-0.593244\pi$
$691$	18.0000	−	31.1769i	0.684752	−	1.18603i	0.973515	−	0.228625i	$-0.0734229\pi$
$692$	18.0000			0.684257
$693$		0			0
$694$	−4.00000			−0.151838
$695$	2.00000	−	3.46410i	0.0758643	−	0.131401i
$696$	−1.00000	−	1.73205i	−0.0379049	−	0.0656532i
$697$	6.00000	+	10.3923i	0.227266	+	0.393637i
$698$	7.00000	−	12.1244i	0.264954	−	0.458914i
$699$	22.0000			0.832116
$700$		0			0
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$	1.00000	−	1.73205i	0.0377426	−	0.0653720i
$703$	12.0000	+	20.7846i	0.452589	+	0.783906i
$704$	2.00000	+	3.46410i	0.0753778	+	0.130558i
$705$		0			0
$706$	14.0000			0.526897
$707$		0			0
$708$	12.0000			0.450988
$709$	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
$711$	−8.00000	−	13.8564i	−0.300023	−	0.519656i
$712$	5.00000	−	8.66025i	0.187383	−	0.324557i
$713$		0			0
$714$		0			0
$715$	8.00000			0.299183
$716$	−2.00000	+	3.46410i	−0.0747435	+	0.129460i
$717$		0			0
$718$	−12.0000	−	20.7846i	−0.447836	−	0.775675i
$719$	−8.00000	+	13.8564i	−0.298350	+	0.516757i	−0.975759	−	0.218850i	$-0.929769\pi$
$719$	−8.00000	+	13.8564i	−0.298350	+	0.516757i	0.677409	+	0.735607i	$0.263103\pi$
$720$	−1.00000			−0.0372678
$721$		0			0
$722$	−3.00000			−0.111648
$723$	7.00000	−	12.1244i	0.260333	−	0.450910i
$724$	3.00000	+	5.19615i	0.111494	+	0.193113i
$725$	1.00000	+	1.73205i	0.0371391	+	0.0643268i
$726$	2.50000	−	4.33013i	0.0927837	−	0.160706i
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$		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
$732$	−7.00000	−	12.1244i	−0.258727	−	0.448129i
$733$	23.0000	−	39.8372i	0.849524	−	1.47142i	−0.0321090	−	0.999484i	$-0.510222\pi$
$733$	23.0000	−	39.8372i	0.849524	−	1.47142i	0.881633	−	0.471935i	$-0.156444\pi$
$734$	32.0000			1.18114
$735$		0			0
$736$	−8.00000			−0.294884
$737$	−24.0000	+	41.5692i	−0.884051	+	1.53122i
$738$	−3.00000	−	5.19615i	−0.110432	−	0.191273i
$739$	14.0000	+	24.2487i	0.514998	+	0.892003i	0.999849	+	0.0174060i	$0.00554079\pi$
$739$	14.0000	+	24.2487i	0.514998	+	0.892003i	−0.484850	+	0.874597i	$0.661126\pi$
$740$	3.00000	−	5.19615i	0.110282	−	0.191014i
$741$	8.00000			0.293887
$742$		0			0
$743$	−24.0000			−0.880475			−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000			−0.880475			−0.440237	+	0.897881i	$0.645106\pi$
$744$		0			0
$745$	−5.00000	−	8.66025i	−0.183186	−	0.317287i
$746$	5.00000	+	8.66025i	0.183063	+	0.317074i
$747$	−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	$0.260962\pi$
$752$		0			0
$753$	−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
$757$	22.0000			0.799604			0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000			0.799604			0.399802	+	0.916602i	$0.369079\pi$
$758$	−14.0000	+	24.2487i	−0.508503	+	0.880753i
$759$	16.0000	+	27.7128i	0.580763	+	1.00591i
$760$	−2.00000	−	3.46410i	−0.0725476	−	0.125656i
$761$	5.00000	−	8.66025i	0.181250	−	0.313934i	−0.761057	−	0.648686i	$-0.775319\pi$
$761$	5.00000	−	8.66025i	0.181250	−	0.313934i	0.942306	+	0.334752i	$0.108652\pi$
$762$	16.0000			0.579619
$763$		0			0
$764$	−16.0000			−0.578860
$765$	−1.00000	+	1.73205i	−0.0361551	+	0.0626224i
$766$	8.00000	+	13.8564i	0.289052	+	0.500652i
$767$	12.0000	+	20.7846i	0.433295	+	0.750489i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−34.0000			−1.22607			−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000			−1.22607			−0.613036	+	0.790055i	$0.710052\pi$
$770$		0			0
$771$	−14.0000			−0.504198
$772$	−1.00000	+	1.73205i	−0.0359908	+	0.0623379i
$773$	−13.0000	−	22.5167i	−0.467578	−	0.809868i	0.531736	−	0.846910i	$-0.321540\pi$
$773$	−13.0000	−	22.5167i	−0.467578	−	0.809868i	−0.999314	+	0.0370420i	$0.988206\pi$
$774$	2.00000	+	3.46410i	0.0718885	+	0.124515i
$775$		0			0
$776$	−2.00000			−0.0717958
$777$		0			0
$778$	−26.0000			−0.932145
$779$	12.0000	−	20.7846i	0.429945	−	0.744686i
$780$	−1.00000	−	1.73205i	−0.0358057	−	0.0620174i
$781$	−16.0000	−	27.7128i	−0.572525	−	0.991642i
$782$	−8.00000	+	13.8564i	−0.286079	+	0.495504i
$783$	2.00000			0.0714742
$784$		0			0
$785$	−18.0000			−0.642448
$786$	−10.0000	+	17.3205i	−0.356688	+	0.617802i
$787$	10.0000	+	17.3205i	0.356462	+	0.617409i	0.987367	−	0.158450i	$-0.0506498\pi$
$787$	10.0000	+	17.3205i	0.356462	+	0.617409i	−0.630905	+	0.775860i	$0.717316\pi$
$788$	−3.00000	−	5.19615i	−0.106871	−	0.185105i
$789$	4.00000	−	6.92820i	0.142404	−	0.246651i
$790$	−16.0000			−0.569254
$791$		0			0
$792$	−4.00000			−0.142134
$793$	14.0000	−	24.2487i	0.497155	−	0.861097i
$794$	15.0000	+	25.9808i	0.532330	+	0.922023i
$795$	5.00000	+	8.66025i	0.177332	+	0.307148i
$796$	−12.0000	+	20.7846i	−0.425329	+	0.736691i
$797$	−30.0000			−1.06265			−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000			−1.06265			−0.531327	+	0.847167i	$0.678307\pi$
$798$		0			0
$799$		0			0
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	5.00000	+	8.66025i	0.176666	+	0.305995i
$802$	7.00000	+	12.1244i	0.247179	+	0.428126i
$803$	−20.0000	+	34.6410i	−0.705785	+	1.22245i
$804$	12.0000			0.423207
$805$		0			0
$806$		0			0
$807$	9.00000	−	15.5885i	0.316815	−	0.548740i
$808$	3.00000	+	5.19615i	0.105540	+	0.182800i
$809$	11.0000	+	19.0526i	0.386739	+	0.669852i	0.992009	−	0.126168i	$-0.0402680\pi$
$809$	11.0000	+	19.0526i	0.386739	+	0.669852i	−0.605269	+	0.796021i	$0.706935\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$		0			0
$813$	16.0000			0.561144
$814$	12.0000	−	20.7846i	0.420600	−	0.728500i
$815$	10.0000	+	17.3205i	0.350285	+	0.606711i
$816$	−1.00000	−	1.73205i	−0.0350070	−	0.0606339i
$817$	−8.00000	+	13.8564i	−0.279885	+	0.484774i
$818$	38.0000			1.32864
$819$		0			0
$820$	−6.00000			−0.209529
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	−0.991616	−	0.129217i	$-0.958754\pi$
$821$	−11.0000	+	19.0526i	−0.383903	+	0.664939i	0.607714	+	0.794156i	$0.292087\pi$
$822$	5.00000	+	8.66025i	0.174395	+	0.302061i
$823$	12.0000	+	20.7846i	0.418294	+	0.724506i	0.995768	−	0.0919029i	$-0.0292950\pi$
$823$	12.0000	+	20.7846i	0.418294	+	0.724506i	−0.577474	+	0.816409i	$0.695962\pi$
$824$	−4.00000	+	6.92820i	−0.139347	+	0.241355i
$825$	4.00000			0.139262
$826$		0			0
$827$	28.0000			0.973655			0.486828	−	0.873498i	$-0.338154\pi$
$827$	28.0000			0.973655			0.486828	+	0.873498i	$0.338154\pi$
$828$	4.00000	−	6.92820i	0.139010	−	0.240772i
$829$	−9.00000	−	15.5885i	−0.312583	−	0.541409i	0.666338	−	0.745650i	$-0.267861\pi$
$829$	−9.00000	−	15.5885i	−0.312583	−	0.541409i	−0.978921	+	0.204240i	$0.934528\pi$
$830$	6.00000	+	10.3923i	0.208263	+	0.360722i
$831$	11.0000	−	19.0526i	0.381586	−	0.660926i
$832$	2.00000			0.0693375
$833$		0			0
$834$	−4.00000			−0.138509
$835$	4.00000	−	6.92820i	0.138426	−	0.239760i
$836$	−8.00000	−	13.8564i	−0.276686	−	0.479234i
$837$		0			0
$838$	10.0000	−	17.3205i	0.345444	−	0.598327i
$839$	−8.00000			−0.276191			−0.138095	−	0.990419i	$-0.544098\pi$
$839$	−8.00000			−0.276191			−0.138095	+	0.990419i	$0.544098\pi$
$840$		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
$844$	6.00000	+	10.3923i	0.206529	+	0.357718i
$845$	−4.50000	+	7.79423i	−0.154805	+	0.268130i
$846$		0			0
$847$		0			0
$848$	−10.0000			−0.343401
$849$	−14.0000	+	24.2487i	−0.480479	+	0.832214i
$850$	1.00000	+	1.73205i	0.0342997	+	0.0594089i
$851$	24.0000	+	41.5692i	0.822709	+	1.42497i
$852$	−4.00000	+	6.92820i	−0.137038	+	0.237356i
$853$	26.0000			0.890223			0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000			0.890223			0.445112	+	0.895475i	$0.353164\pi$
$854$		0			0
$855$	4.00000			0.136797
$856$	−6.00000	+	10.3923i	−0.205076	+	0.355202i
$857$	−11.0000	−	19.0526i	−0.375753	−	0.650823i	0.614687	−	0.788771i	$-0.289283\pi$
$857$	−11.0000	−	19.0526i	−0.375753	−	0.650823i	−0.990439	+	0.137948i	$0.955949\pi$
$858$	−4.00000	−	6.92820i	−0.136558	−	0.236525i
$859$	−10.0000	+	17.3205i	−0.341196	+	0.590968i	−0.984655	−	0.174512i	$-0.944165\pi$
$859$	−10.0000	+	17.3205i	−0.341196	+	0.590968i	0.643459	+	0.765480i	$0.277499\pi$
$860$	4.00000			0.136399
$861$		0			0
$862$		0			0
$863$	−16.0000	+	27.7128i	−0.544646	+	0.943355i	0.453983	+	0.891010i	$0.350003\pi$
$863$	−16.0000	+	27.7128i	−0.544646	+	0.943355i	−0.998629	+	0.0523446i	$0.983331\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	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
$869$	−64.0000			−2.17105
$870$	1.00000	−	1.73205i	0.0339032	−	0.0587220i
$871$	12.0000	+	20.7846i	0.406604	+	0.704260i
$872$	−7.00000	−	12.1244i	−0.237050	−	0.410582i
$873$	1.00000	−	1.73205i	0.0338449	−	0.0586210i
$874$	32.0000			1.08242
$875$		0			0
$876$	10.0000			0.337869
$877$	−7.00000	+	12.1244i	−0.236373	+	0.409410i	−0.959671	−	0.281126i	$-0.909292\pi$
$877$	−7.00000	+	12.1244i	−0.236373	+	0.409410i	0.723298	+	0.690536i	$0.242625\pi$
$878$	−4.00000	−	6.92820i	−0.134993	−	0.233816i
$879$	−3.00000	−	5.19615i	−0.101187	−	0.175262i
$880$	−2.00000	+	3.46410i	−0.0674200	+	0.116775i
$881$	−2.00000			−0.0673817			−0.0336909	−	0.999432i	$-0.510726\pi$
$881$	−2.00000			−0.0673817			−0.0336909	+	0.999432i	$0.510726\pi$
$882$		0			0
$883$	−28.0000			−0.942275			−0.471138	−	0.882060i	$-0.656156\pi$
$883$	−28.0000			−0.942275			−0.471138	+	0.882060i	$0.656156\pi$
$884$	2.00000	−	3.46410i	0.0672673	−	0.116510i
$885$	6.00000	+	10.3923i	0.201688	+	0.349334i
$886$	18.0000	+	31.1769i	0.604722	+	1.04741i
$887$	4.00000	−	6.92820i	0.134307	−	0.232626i	−0.791026	−	0.611783i	$-0.790453\pi$
$887$	4.00000	−	6.92820i	0.134307	−	0.232626i	0.925332	+	0.379157i	$0.123786\pi$
$888$	−6.00000			−0.201347
$889$		0			0
$890$	10.0000			0.335201
$891$	2.00000	−	3.46410i	0.0670025	−	0.116052i
$892$	−8.00000	−	13.8564i	−0.267860	−	0.463947i
$893$		0			0
$894$	−5.00000	+	8.66025i	−0.167225	+	0.289642i
$895$	−4.00000			−0.133705
$896$		0			0
$897$	16.0000			0.534224
$898$	−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
$902$	−24.0000			−0.799113
$903$		0			0
$904$	18.0000			0.598671
$905$	−3.00000	+	5.19615i	−0.0997234	+	0.172726i
$906$	−4.00000	−	6.92820i	−0.132891	−	0.230174i
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	0.534333	−	0.845274i	$-0.320563\pi$
$907$	−14.0000	−	24.2487i	−0.464862	−	0.805165i	−0.999195	+	0.0401089i	$0.987230\pi$
$908$	2.00000	−	3.46410i	0.0663723	−	0.114960i
$909$	−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
$915$	7.00000	−	12.1244i	0.231413	−	0.400819i
$916$	10.0000			0.330409
$917$		0			0
$918$	2.00000			0.0660098
$919$	4.00000	−	6.92820i	0.131948	−	0.228540i	−0.792480	−	0.609898i	$-0.791210\pi$
$919$	4.00000	−	6.92820i	0.131948	−	0.228540i	0.924427	+	0.381358i	$0.124544\pi$
$920$	−4.00000	−	6.92820i	−0.131876	−	0.228416i
$921$	−10.0000	−	17.3205i	−0.329511	−	0.570730i
$922$	7.00000	−	12.1244i	0.230533	−	0.399294i
$923$	−16.0000			−0.526646
$924$		0			0
$925$	6.00000			0.197279
$926$		0			0
$927$	−4.00000	−	6.92820i	−0.131377	−	0.227552i
$928$	1.00000	+	1.73205i	0.0328266	+	0.0568574i
$929$	−7.00000	+	12.1244i	−0.229663	+	0.397787i	−0.957708	−	0.287742i	$-0.907096\pi$
$929$	−7.00000	+	12.1244i	−0.229663	+	0.397787i	0.728046	+	0.685529i	$0.240429\pi$
$930$		0			0
$931$		0			0
$932$	−22.0000			−0.720634
$933$	4.00000	−	6.92820i	0.130954	−	0.226819i
$934$	−6.00000	−	10.3923i	−0.196326	−	0.340047i
$935$	4.00000	+	6.92820i	0.130814	+	0.226576i
$936$	−1.00000	+	1.73205i	−0.0326860	+	0.0566139i
$937$	−10.0000			−0.326686			−0.163343	−	0.986569i	$-0.552228\pi$
$937$	−10.0000			−0.326686			−0.163343	+	0.986569i	$0.552228\pi$
$938$		0			0
$939$	−6.00000			−0.195803
$940$		0			0
$941$	−9.00000	−	15.5885i	−0.293392	−	0.508169i	0.681218	−	0.732081i	$-0.261451\pi$
$941$	−9.00000	−	15.5885i	−0.293392	−	0.508169i	−0.974609	+	0.223912i	$0.928117\pi$
$942$	9.00000	+	15.5885i	0.293236	+	0.507899i
$943$	24.0000	−	41.5692i	0.781548	−	1.35368i
$944$	−12.0000			−0.390567
$945$		0			0
$946$	16.0000			0.520205
$947$	−26.0000	+	45.0333i	−0.844886	+	1.46339i	0.0408333	+	0.999166i	$0.486999\pi$
$947$	−26.0000	+	45.0333i	−0.844886	+	1.46339i	−0.885720	+	0.464220i	$0.846335\pi$
$948$	8.00000	+	13.8564i	0.259828	+	0.450035i
$949$	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
$953$	26.0000			0.842223			0.421111	−	0.907009i	$-0.361640\pi$
$953$	26.0000			0.842223			0.421111	+	0.907009i	$0.361640\pi$
$954$	5.00000	−	8.66025i	0.161881	−	0.280386i
$955$	−8.00000	−	13.8564i	−0.258874	−	0.448383i
$956$		0			0
$957$	4.00000	−	6.92820i	0.129302	−	0.223957i
$958$	−32.0000			−1.03387
$959$		0			0
$960$	1.00000			0.0322749
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$	−6.00000	−	10.3923i	−0.193448	−	0.335061i
$963$	−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
$967$	−8.00000			−0.257263			−0.128631	−	0.991692i	$-0.541058\pi$
$967$	−8.00000			−0.257263			−0.128631	+	0.991692i	$0.541058\pi$
$968$	−2.50000	+	4.33013i	−0.0803530	+	0.139176i
$969$	4.00000	+	6.92820i	0.128499	+	0.222566i
$970$	−1.00000	−	1.73205i	−0.0321081	−	0.0556128i
$971$	14.0000	−	24.2487i	0.449281	−	0.778178i	−0.549058	−	0.835784i	$-0.685013\pi$
$971$	14.0000	−	24.2487i	0.449281	−	0.778178i	0.998339	+	0.0576061i	$0.0183467\pi$
$972$	−1.00000			−0.0320750
$973$		0			0
$974$	−8.00000			−0.256337
$975$	1.00000	−	1.73205i	0.0320256	−	0.0554700i
$976$	7.00000	+	12.1244i	0.224065	+	0.388091i
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	0.685381	−	0.728184i	$-0.259636\pi$
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	−0.973317	+	0.229465i	$0.926302\pi$
$978$	10.0000	−	17.3205i	0.319765	−	0.553849i
$979$	40.0000			1.27841
$980$		0			0
$981$	14.0000			0.446986
$982$	18.0000	−	31.1769i	0.574403	−	0.994895i
$983$	−12.0000	−	20.7846i	−0.382741	−	0.662926i	0.608712	−	0.793391i	$-0.291686\pi$
$983$	−12.0000	−	20.7846i	−0.382741	−	0.662926i	−0.991453	+	0.130465i	$0.958353\pi$
$984$	3.00000	+	5.19615i	0.0956365	+	0.165647i
$985$	3.00000	−	5.19615i	0.0955879	−	0.165563i
$986$	4.00000			0.127386
$987$		0			0
$988$	−8.00000			−0.254514
$989$	−16.0000	+	27.7128i	−0.508770	+	0.881216i
$990$	−2.00000	−	3.46410i	−0.0635642	−	0.110096i
$991$	16.0000	+	27.7128i	0.508257	+	0.880327i	0.999954	+	0.00956046i	$0.00304324\pi$
$991$	16.0000	+	27.7128i	0.508257	+	0.880327i	−0.491698	+	0.870766i	$0.663623\pi$
$992$		0			0
$993$	−12.0000			−0.380808
$994$		0			0
$995$	−24.0000			−0.760851
$996$	6.00000	−	10.3923i	0.190117	−	0.329293i
$997$	11.0000	+	19.0526i	0.348373	+	0.603401i	0.985961	−	0.166978i	$-0.0534008\pi$
$997$	11.0000	+	19.0526i	0.348373	+	0.603401i	−0.637587	+	0.770378i	$0.720067\pi$
$998$	6.00000	+	10.3923i	0.189927	+	0.328963i
$999$	3.00000	−	5.19615i	0.0949158	−	0.164399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1470.2.i.j.961.1		2
7.2	even	3		1470.2.a.j.1.1		1
7.3	odd	6		1470.2.i.a.361.1		2
7.4	even	3	inner	1470.2.i.j.361.1		2
7.5	odd	6		210.2.a.e.1.1	✓	1
7.6	odd	2		1470.2.i.a.961.1		2
21.2	odd	6		4410.2.a.t.1.1		1
21.5	even	6		630.2.a.a.1.1		1
28.19	even	6		1680.2.a.j.1.1		1
35.9	even	6		7350.2.a.w.1.1		1
35.12	even	12		1050.2.g.g.799.2		2
35.19	odd	6		1050.2.a.c.1.1		1
35.33	even	12		1050.2.g.g.799.1		2
56.5	odd	6		6720.2.a.j.1.1		1
56.19	even	6		6720.2.a.bq.1.1		1
84.47	odd	6		5040.2.a.k.1.1		1
105.47	odd	12		3150.2.g.q.2899.1		2
105.68	odd	12		3150.2.g.q.2899.2		2
105.89	even	6		3150.2.a.bp.1.1		1
140.19	even	6		8400.2.a.ce.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.a.e.1.1	✓	1	7.5	odd	6
630.2.a.a.1.1		1	21.5	even	6
1050.2.a.c.1.1		1	35.19	odd	6
1050.2.g.g.799.1		2	35.33	even	12
1050.2.g.g.799.2		2	35.12	even	12
1470.2.a.j.1.1		1	7.2	even	3
1470.2.i.a.361.1		2	7.3	odd	6
1470.2.i.a.961.1		2	7.6	odd	2
1470.2.i.j.361.1		2	7.4	even	3	inner
1470.2.i.j.961.1		2	1.1	even	1	trivial
1680.2.a.j.1.1		1	28.19	even	6
3150.2.a.bp.1.1		1	105.89	even	6
3150.2.g.q.2899.1		2	105.47	odd	12
3150.2.g.q.2899.2		2	105.68	odd	12
4410.2.a.t.1.1		1	21.2	odd	6
5040.2.a.k.1.1		1	84.47	odd	6
6720.2.a.j.1.1		1	56.5	odd	6
6720.2.a.bq.1.1		1	56.19	even	6
7350.2.a.w.1.1		1	35.9	even	6
8400.2.a.ce.1.1		1	140.19	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:	\( N \)	\(=\)	\( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1470.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(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} +1.00000 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} +(4.00000 - 6.92820i) q^{23} +(0.500000 + 0.866025i) 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} +(-0.500000 - 0.866025i) q^{32} +(-2.00000 + 3.46410i) q^{33} -2.00000 q^{34} +1.00000 q^{36} +(-3.00000 + 5.19615i) q^{37} +(2.00000 + 3.46410i) q^{38} +(1.00000 + 1.73205i) q^{39} +(0.500000 - 0.866025i) q^{40} +6.00000 q^{41} -4.00000 q^{43} +(2.00000 - 3.46410i) q^{44} +(0.500000 + 0.866025i) q^{45} +(4.00000 + 6.92820i) q^{46} -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} +(6.00000 + 10.3923i) q^{59} +(-0.500000 - 0.866025i) q^{60} +(7.00000 - 12.1244i) q^{61} +1.00000 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^{69} -8.00000 q^{71} +(-0.500000 + 0.866025i) q^{72} +(5.00000 + 8.66025i) q^{73} +(-3.00000 - 5.19615i) q^{74} +(0.500000 - 0.866025i) q^{75} -4.00000 q^{76} -2.00000 q^{78} +(-8.00000 + 13.8564i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.00000 + 5.19615i) q^{82} +12.0000 q^{83} +2.00000 q^{85} +(2.00000 - 3.46410i) q^{86} +(-1.00000 - 1.73205i) q^{87} +(2.00000 + 3.46410i) q^{88} +(5.00000 - 8.66025i) q^{89} -1.00000 q^{90} -8.00000 q^{92} +(-2.00000 - 3.46410i) q^{95} +(0.500000 - 0.866025i) q^{96} -2.00000 q^{97} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} + q^{5} - 2 q^{6} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 + q^3 - q^4 + q^5 - 2 * q^6 + 2 * q^8 - q^9	\( 2 q - q^{2} + q^{3} - q^{4} + q^{5} - 2 q^{6} + 2 q^{8} - q^{9} + q^{10} + 4 q^{11} + q^{12} + 4 q^{13} + 2 q^{15} - q^{16} + 2 q^{17} - q^{18} + 4 q^{19} - 2 q^{20} - 8 q^{22} + 8 q^{23} + q^{24} - q^{25} - 2 q^{26} - 2 q^{27} - 4 q^{29} - q^{30} - q^{32} - 4 q^{33} - 4 q^{34} + 2 q^{36} - 6 q^{37} + 4 q^{38} + 2 q^{39} + q^{40} + 12 q^{41} - 8 q^{43} + 4 q^{44} + q^{45} + 8 q^{46} - 2 q^{48} + 2 q^{50} - 2 q^{51} - 2 q^{52} + 10 q^{53} + q^{54} + 8 q^{55} + 8 q^{57} + 2 q^{58} + 12 q^{59} - q^{60} + 14 q^{61} + 2 q^{64} + 2 q^{65} - 4 q^{66} + 12 q^{67} + 2 q^{68} + 16 q^{69} - 16 q^{71} - q^{72} + 10 q^{73} - 6 q^{74} + q^{75} - 8 q^{76} - 4 q^{78} - 16 q^{79} + q^{80} - q^{81} - 6 q^{82} + 24 q^{83} + 4 q^{85} + 4 q^{86} - 2 q^{87} + 4 q^{88} + 10 q^{89} - 2 q^{90} - 16 q^{92} - 4 q^{95} + q^{96} - 4 q^{97} - 8 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 + q^5 - 2 * q^6 + 2 * 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 + 8 * q^23 + q^24 - q^25 - 2 * q^26 - 2 * q^27 - 4 * q^29 - q^30 - q^32 - 4 * q^33 - 4 * q^34 + 2 * q^36 - 6 * q^37 + 4 * q^38 + 2 * q^39 + q^40 + 12 * q^41 - 8 * q^43 + 4 * q^44 + q^45 + 8 * q^46 - 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 + 12 * q^59 - q^60 + 14 * q^61 + 2 * q^64 + 2 * q^65 - 4 * q^66 + 12 * q^67 + 2 * q^68 + 16 * q^69 - 16 * q^71 - q^72 + 10 * q^73 - 6 * q^74 + q^75 - 8 * q^76 - 4 * q^78 - 16 * q^79 + q^80 - q^81 - 6 * q^82 + 24 * q^83 + 4 * q^85 + 4 * q^86 - 2 * q^87 + 4 * q^88 + 10 * q^89 - 2 * q^90 - 16 * q^92 - 4 * q^95 + q^96 - 4 * q^97 - 8 * q^99

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