LMFDB - Embedded newform 585.2.i.d.196.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(196,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("585.196");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.i (of order $3$, degree $2$, 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:	$4.67124851824$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			196.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	585.196
Dual form			585.2.i.d.391.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.46410i q^{6} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.46410i q^{6} +(1.50000 - 2.59808i) q^{9} +2.00000 q^{10} +(-2.00000 + 3.46410i) q^{11} +(3.00000 + 1.73205i) q^{12} +(0.500000 + 0.866025i) q^{13} +(-1.50000 - 0.866025i) q^{15} +(2.00000 - 3.46410i) q^{16} +7.00000 q^{17} +(-3.00000 - 5.19615i) q^{18} +4.00000 q^{19} +(1.00000 - 1.73205i) q^{20} +(4.00000 + 6.92820i) q^{22} +(1.50000 + 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} +2.00000 q^{26} +5.19615i q^{27} +(5.00000 - 8.66025i) q^{29} +(-3.00000 + 1.73205i) q^{30} +(3.00000 + 5.19615i) q^{31} +(-4.00000 - 6.92820i) q^{32} -6.92820i q^{33} +(7.00000 - 12.1244i) q^{34} -6.00000 q^{36} -10.0000 q^{37} +(4.00000 - 6.92820i) q^{38} +(-1.50000 - 0.866025i) q^{39} +(-1.00000 - 1.73205i) q^{41} +(-0.500000 + 0.866025i) q^{43} +8.00000 q^{44} +3.00000 q^{45} +6.00000 q^{46} +(1.00000 - 1.73205i) q^{47} +6.92820i q^{48} +(3.50000 + 6.06218i) q^{49} +(1.00000 + 1.73205i) q^{50} +(-10.5000 + 6.06218i) q^{51} +(1.00000 - 1.73205i) q^{52} -5.00000 q^{53} +(9.00000 + 5.19615i) q^{54} -4.00000 q^{55} +(-6.00000 + 3.46410i) q^{57} +(-10.0000 - 17.3205i) q^{58} +(-5.00000 - 8.66025i) q^{59} +3.46410i q^{60} +(2.50000 - 4.33013i) q^{61} +12.0000 q^{62} -8.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(-12.0000 - 6.92820i) q^{66} +(6.00000 + 10.3923i) q^{67} +(-7.00000 - 12.1244i) q^{68} +(-4.50000 - 2.59808i) q^{69} +8.00000 q^{71} -14.0000 q^{73} +(-10.0000 + 17.3205i) q^{74} -1.73205i q^{75} +(-4.00000 - 6.92820i) q^{76} +(-3.00000 + 1.73205i) q^{78} +(-4.50000 + 7.79423i) q^{79} +4.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} -4.00000 q^{82} +(-3.00000 + 5.19615i) q^{83} +(3.50000 + 6.06218i) q^{85} +(1.00000 + 1.73205i) q^{86} +17.3205i q^{87} +12.0000 q^{89} +(3.00000 - 5.19615i) q^{90} +(3.00000 - 5.19615i) q^{92} +(-9.00000 - 5.19615i) q^{93} +(-2.00000 - 3.46410i) q^{94} +(2.00000 + 3.46410i) q^{95} +(12.0000 + 6.92820i) q^{96} +(-4.00000 + 6.92820i) q^{97} +14.0000 q^{98} +(6.00000 + 10.3923i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{5} + 3 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 + q^5 + 3 * q^9	$ 2 q + 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{5} + 3 q^{9} + 4 q^{10} - 4 q^{11} + 6 q^{12} + q^{13} - 3 q^{15} + 4 q^{16} + 14 q^{17} - 6 q^{18} + 8 q^{19} + 2 q^{20} + 8 q^{22} + 3 q^{23} - q^{25} + 4 q^{26} + 10 q^{29} - 6 q^{30} + 6 q^{31} - 8 q^{32} + 14 q^{34} - 12 q^{36} - 20 q^{37} + 8 q^{38} - 3 q^{39} - 2 q^{41} - q^{43} + 16 q^{44} + 6 q^{45} + 12 q^{46} + 2 q^{47} + 7 q^{49} + 2 q^{50} - 21 q^{51} + 2 q^{52} - 10 q^{53} + 18 q^{54} - 8 q^{55} - 12 q^{57} - 20 q^{58} - 10 q^{59} + 5 q^{61} + 24 q^{62} - 16 q^{64} - q^{65} - 24 q^{66} + 12 q^{67} - 14 q^{68} - 9 q^{69} + 16 q^{71} - 28 q^{73} - 20 q^{74} - 8 q^{76} - 6 q^{78} - 9 q^{79} + 8 q^{80} - 9 q^{81} - 8 q^{82} - 6 q^{83} + 7 q^{85} + 2 q^{86} + 24 q^{89} + 6 q^{90} + 6 q^{92} - 18 q^{93} - 4 q^{94} + 4 q^{95} + 24 q^{96} - 8 q^{97} + 28 q^{98} + 12 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 + q^5 + 3 * q^9 + 4 * q^10 - 4 * q^11 + 6 * q^12 + q^13 - 3 * q^15 + 4 * q^16 + 14 * q^17 - 6 * q^18 + 8 * q^19 + 2 * q^20 + 8 * q^22 + 3 * q^23 - q^25 + 4 * q^26 + 10 * q^29 - 6 * q^30 + 6 * q^31 - 8 * q^32 + 14 * q^34 - 12 * q^36 - 20 * q^37 + 8 * q^38 - 3 * q^39 - 2 * q^41 - q^43 + 16 * q^44 + 6 * q^45 + 12 * q^46 + 2 * q^47 + 7 * q^49 + 2 * q^50 - 21 * q^51 + 2 * q^52 - 10 * q^53 + 18 * q^54 - 8 * q^55 - 12 * q^57 - 20 * q^58 - 10 * q^59 + 5 * q^61 + 24 * q^62 - 16 * q^64 - q^65 - 24 * q^66 + 12 * q^67 - 14 * q^68 - 9 * q^69 + 16 * q^71 - 28 * q^73 - 20 * q^74 - 8 * q^76 - 6 * q^78 - 9 * q^79 + 8 * q^80 - 9 * q^81 - 8 * q^82 - 6 * q^83 + 7 * q^85 + 2 * q^86 + 24 * q^89 + 6 * q^90 + 6 * q^92 - 18 * q^93 - 4 * q^94 + 4 * q^95 + 24 * q^96 - 8 * q^97 + 28 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	1.00000	−	1.73205i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$2$	1.00000	−	1.73205i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$4$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$			3.46410i			1.41421i
$7$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$7$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	2.00000			0.632456
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	0.389338	+	0.921095i	$0.372704\pi$
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	−0.992361	+	0.123371i	$0.960630\pi$
$12$	3.00000	+	1.73205i	0.866025	+	0.500000i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$14$		0			0
$15$	−1.50000	−	0.866025i	−0.387298	−	0.223607i
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	7.00000			1.69775			0.848875	−	0.528594i	$-0.177281\pi$
$17$	7.00000			1.69775			0.848875	+	0.528594i	$0.177281\pi$
$18$	−3.00000	−	5.19615i	−0.707107	−	1.22474i
$19$	4.00000			0.917663			0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000			0.917663			0.458831	+	0.888523i	$0.348268\pi$
$20$	1.00000	−	1.73205i	0.223607	−	0.387298i
$21$		0			0
$22$	4.00000	+	6.92820i	0.852803	+	1.47710i
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	2.00000			0.392232
$27$			5.19615i			1.00000i
$28$		0			0
$29$	5.00000	−	8.66025i	0.928477	−	1.60817i	0.142605	−	0.989780i	$-0.454452\pi$
$29$	5.00000	−	8.66025i	0.928477	−	1.60817i	0.785872	−	0.618389i	$-0.212214\pi$
$30$	−3.00000	+	1.73205i	−0.547723	+	0.316228i
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	0.998968	+	0.0454165i	$0.0144615\pi$
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	−0.460152	+	0.887840i	$0.652205\pi$
$32$	−4.00000	−	6.92820i	−0.707107	−	1.22474i
$33$		−	6.92820i		−	1.20605i
$34$	7.00000	−	12.1244i	1.20049	−	2.07931i
$35$		0			0
$36$	−6.00000			−1.00000
$37$	−10.0000			−1.64399			−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000			−1.64399			−0.821995	+	0.569495i	$0.807139\pi$
$38$	4.00000	−	6.92820i	0.648886	−	1.12390i
$39$	−1.50000	−	0.866025i	−0.240192	−	0.138675i
$40$		0			0
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	0.777312	−	0.629115i	$-0.216583\pi$
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	−0.933486	+	0.358614i	$0.883249\pi$
$42$		0			0
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	−0.901629	−	0.432511i	$-0.857628\pi$
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	0.825380	+	0.564578i	$0.190961\pi$
$44$	8.00000			1.20605
$45$	3.00000			0.447214
$46$	6.00000			0.884652
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	−0.783830	−	0.620975i	$-0.786737\pi$
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	0.929695	+	0.368329i	$0.120070\pi$
$48$			6.92820i			1.00000i
$49$	3.50000	+	6.06218i	0.500000	+	0.866025i
$50$	1.00000	+	1.73205i	0.141421	+	0.244949i
$51$	−10.5000	+	6.06218i	−1.47029	+	0.848875i
$52$	1.00000	−	1.73205i	0.138675	−	0.240192i
$53$	−5.00000			−0.686803			−0.343401	−	0.939189i	$-0.611579\pi$
$53$	−5.00000			−0.686803			−0.343401	+	0.939189i	$0.611579\pi$
$54$	9.00000	+	5.19615i	1.22474	+	0.707107i
$55$	−4.00000			−0.539360
$56$		0			0
$57$	−6.00000	+	3.46410i	−0.794719	+	0.458831i
$58$	−10.0000	−	17.3205i	−1.31306	−	2.27429i
$59$	−5.00000	−	8.66025i	−0.650945	−	1.12747i	−0.982894	−	0.184172i	$-0.941040\pi$
$59$	−5.00000	−	8.66025i	−0.650945	−	1.12747i	0.331949	−	0.943297i	$-0.392294\pi$
$60$			3.46410i			0.447214i
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	−0.660415	−	0.750901i	$-0.729619\pi$
$61$	2.50000	−	4.33013i	0.320092	−	0.554416i	0.980507	+	0.196485i	$0.0629528\pi$
$62$	12.0000			1.52400
$63$		0			0
$64$	−8.00000			−1.00000
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$	−12.0000	−	6.92820i	−1.47710	−	0.852803i
$67$	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	$0.571445\pi$
$68$	−7.00000	−	12.1244i	−0.848875	−	1.47029i
$69$	−4.50000	−	2.59808i	−0.541736	−	0.312772i
$70$		0			0
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$		0			0
$73$	−14.0000			−1.63858			−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000			−1.63858			−0.819288	+	0.573382i	$0.805631\pi$
$74$	−10.0000	+	17.3205i	−1.16248	+	2.01347i
$75$		−	1.73205i		−	0.200000i
$76$	−4.00000	−	6.92820i	−0.458831	−	0.794719i
$77$		0			0
$78$	−3.00000	+	1.73205i	−0.339683	+	0.196116i
$79$	−4.50000	+	7.79423i	−0.506290	+	0.876919i	0.493684	+	0.869641i	$0.335650\pi$
$79$	−4.50000	+	7.79423i	−0.506290	+	0.876919i	−0.999974	+	0.00727784i	$0.997683\pi$
$80$	4.00000			0.447214
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−4.00000			−0.441726
$83$	−3.00000	+	5.19615i	−0.329293	+	0.570352i	−0.982372	−	0.186938i	$-0.940144\pi$
$83$	−3.00000	+	5.19615i	−0.329293	+	0.570352i	0.653079	+	0.757290i	$0.273477\pi$
$84$		0			0
$85$	3.50000	+	6.06218i	0.379628	+	0.657536i
$86$	1.00000	+	1.73205i	0.107833	+	0.186772i
$87$			17.3205i			1.85695i
$88$		0			0
$89$	12.0000			1.27200			0.635999	−	0.771690i	$-0.280588\pi$
$89$	12.0000			1.27200			0.635999	+	0.771690i	$0.280588\pi$
$90$	3.00000	−	5.19615i	0.316228	−	0.547723i
$91$		0			0
$92$	3.00000	−	5.19615i	0.312772	−	0.541736i
$93$	−9.00000	−	5.19615i	−0.933257	−	0.538816i
$94$	−2.00000	−	3.46410i	−0.206284	−	0.357295i
$95$	2.00000	+	3.46410i	0.205196	+	0.355409i
$96$	12.0000	+	6.92820i	1.22474	+	0.707107i
$97$	−4.00000	+	6.92820i	−0.406138	+	0.703452i	−0.994453	−	0.105180i	$-0.966458\pi$
$97$	−4.00000	+	6.92820i	−0.406138	+	0.703452i	0.588315	+	0.808632i	$0.299792\pi$
$98$	14.0000			1.41421
$99$	6.00000	+	10.3923i	0.603023	+	1.04447i
$100$	2.00000			0.200000
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	−0.781697	−	0.623658i	$-0.785646\pi$
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	0.930953	+	0.365140i	$0.118979\pi$
$102$			24.2487i			2.40098i
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$104$		0			0
$105$		0			0
$106$	−5.00000	+	8.66025i	−0.485643	+	0.841158i
$107$	−9.00000			−0.870063			−0.435031	−	0.900415i	$-0.643263\pi$
$107$	−9.00000			−0.870063			−0.435031	+	0.900415i	$0.643263\pi$
$108$	9.00000	−	5.19615i	0.866025	−	0.500000i
$109$	−16.0000			−1.53252			−0.766261	−	0.642529i	$-0.777885\pi$
$109$	−16.0000			−1.53252			−0.766261	+	0.642529i	$0.777885\pi$
$110$	−4.00000	+	6.92820i	−0.381385	+	0.660578i
$111$	15.0000	−	8.66025i	1.42374	−	0.821995i
$112$		0			0
$113$	5.50000	+	9.52628i	0.517396	+	0.896157i	0.999796	+	0.0202056i	$0.00643208\pi$
$113$	5.50000	+	9.52628i	0.517396	+	0.896157i	−0.482399	+	0.875951i	$0.660235\pi$
$114$			13.8564i			1.29777i
$115$	−1.50000	+	2.59808i	−0.139876	+	0.242272i
$116$	−20.0000			−1.85695
$117$	3.00000			0.277350
$118$	−20.0000			−1.84115
$119$		0			0
$120$		0			0
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$	−5.00000	−	8.66025i	−0.452679	−	0.784063i
$123$	3.00000	+	1.73205i	0.270501	+	0.156174i
$124$	6.00000	−	10.3923i	0.538816	−	0.933257i
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	4.00000			0.354943			0.177471	−	0.984126i	$-0.443208\pi$
$127$	4.00000			0.354943			0.177471	+	0.984126i	$0.443208\pi$
$128$		0			0
$129$		−	1.73205i		−	0.152499i
$130$	1.00000	+	1.73205i	0.0877058	+	0.151911i
$131$	−7.50000	−	12.9904i	−0.655278	−	1.13497i	−0.981824	−	0.189794i	$-0.939218\pi$
$131$	−7.50000	−	12.9904i	−0.655278	−	1.13497i	0.326546	−	0.945181i	$-0.394115\pi$
$132$	−12.0000	+	6.92820i	−1.04447	+	0.603023i
$133$		0			0
$134$	24.0000			2.07328
$135$	−4.50000	+	2.59808i	−0.387298	+	0.223607i
$136$		0			0
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	−0.487278	−	0.873247i	$-0.662010\pi$
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	0.999893	−	0.0146279i	$-0.00465636\pi$
$138$	−9.00000	+	5.19615i	−0.766131	+	0.442326i
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	0.740308	−	0.672268i	$-0.234680\pi$
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	−0.952355	+	0.304991i	$0.901346\pi$
$140$		0			0
$141$			3.46410i			0.291730i
$142$	8.00000	−	13.8564i	0.671345	−	1.16280i
$143$	−4.00000			−0.334497
$144$	−6.00000	−	10.3923i	−0.500000	−	0.866025i
$145$	10.0000			0.830455
$146$	−14.0000	+	24.2487i	−1.15865	+	2.00684i
$147$	−10.5000	−	6.06218i	−0.866025	−	0.500000i
$148$	10.0000	+	17.3205i	0.821995	+	1.42374i
$149$	−4.00000	−	6.92820i	−0.327693	−	0.567581i	0.654361	−	0.756182i	$-0.272938\pi$
$149$	−4.00000	−	6.92820i	−0.327693	−	0.567581i	−0.982054	+	0.188602i	$0.939604\pi$
$150$	−3.00000	−	1.73205i	−0.244949	−	0.141421i
$151$	7.00000	−	12.1244i	0.569652	−	0.986666i	−0.426948	−	0.904276i	$-0.640411\pi$
$151$	7.00000	−	12.1244i	0.569652	−	0.986666i	0.996600	−	0.0823900i	$-0.0262553\pi$
$152$		0			0
$153$	10.5000	−	18.1865i	0.848875	−	1.47029i
$154$		0			0
$155$	−3.00000	+	5.19615i	−0.240966	+	0.417365i
$156$			3.46410i			0.277350i
$157$	−8.50000	−	14.7224i	−0.678374	−	1.17498i	−0.975470	−	0.220131i	$-0.929352\pi$
$157$	−8.50000	−	14.7224i	−0.678374	−	1.17498i	0.297097	−	0.954847i	$-0.403982\pi$
$158$	9.00000	+	15.5885i	0.716002	+	1.24015i
$159$	7.50000	−	4.33013i	0.594789	−	0.343401i
$160$	4.00000	−	6.92820i	0.316228	−	0.547723i
$161$		0			0
$162$	−18.0000			−1.41421
$163$	−22.0000			−1.72317			−0.861586	−	0.507611i	$-0.830529\pi$
$163$	−22.0000			−1.72317			−0.861586	+	0.507611i	$0.830529\pi$
$164$	−2.00000	+	3.46410i	−0.156174	+	0.270501i
$165$	6.00000	−	3.46410i	0.467099	−	0.269680i
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$	3.00000	+	5.19615i	0.232147	+	0.402090i	0.958440	−	0.285295i	$-0.0920916\pi$
$167$	3.00000	+	5.19615i	0.232147	+	0.402090i	−0.726293	+	0.687386i	$0.758758\pi$
$168$		0			0
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	14.0000			1.07375
$171$	6.00000	−	10.3923i	0.458831	−	0.794719i
$172$	2.00000			0.152499
$173$	1.50000	−	2.59808i	0.114043	−	0.197528i	−0.803354	−	0.595502i	$-0.796953\pi$
$173$	1.50000	−	2.59808i	0.114043	−	0.197528i	0.917397	+	0.397974i	$0.130287\pi$
$174$	30.0000	+	17.3205i	2.27429	+	1.31306i
$175$		0			0
$176$	8.00000	+	13.8564i	0.603023	+	1.04447i
$177$	15.0000	+	8.66025i	1.12747	+	0.650945i
$178$	12.0000	−	20.7846i	0.899438	−	1.55787i
$179$	−11.0000			−0.822179			−0.411089	−	0.911595i	$-0.634852\pi$
$179$	−11.0000			−0.822179			−0.411089	+	0.911595i	$0.634852\pi$
$180$	−3.00000	−	5.19615i	−0.223607	−	0.387298i
$181$	23.0000			1.70958			0.854788	−	0.518977i	$-0.173687\pi$
$181$	23.0000			1.70958			0.854788	+	0.518977i	$0.173687\pi$
$182$		0			0
$183$			8.66025i			0.640184i
$184$		0			0
$185$	−5.00000	−	8.66025i	−0.367607	−	0.636715i
$186$	−18.0000	+	10.3923i	−1.31982	+	0.762001i
$187$	−14.0000	+	24.2487i	−1.02378	+	1.77324i
$188$	−4.00000			−0.291730
$189$		0			0
$190$	8.00000			0.580381
$191$	6.50000	−	11.2583i	0.470323	−	0.814624i	−0.529101	−	0.848559i	$-0.677471\pi$
$191$	6.50000	−	11.2583i	0.470323	−	0.814624i	0.999424	+	0.0339349i	$0.0108039\pi$
$192$	12.0000	−	6.92820i	0.866025	−	0.500000i
$193$	8.00000	+	13.8564i	0.575853	+	0.997406i	0.995948	+	0.0899262i	$0.0286631\pi$
$193$	8.00000	+	13.8564i	0.575853	+	0.997406i	−0.420096	+	0.907480i	$0.638004\pi$
$194$	8.00000	+	13.8564i	0.574367	+	0.994832i
$195$		−	1.73205i		−	0.124035i
$196$	7.00000	−	12.1244i	0.500000	−	0.866025i
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$	24.0000			1.70561
$199$	−11.0000			−0.779769			−0.389885	−	0.920864i	$-0.627485\pi$
$199$	−11.0000			−0.779769			−0.389885	+	0.920864i	$0.627485\pi$
$200$		0			0
$201$	−18.0000	−	10.3923i	−1.26962	−	0.733017i
$202$	−3.00000	−	5.19615i	−0.211079	−	0.365600i
$203$		0			0
$204$	21.0000	+	12.1244i	1.47029	+	0.848875i
$205$	1.00000	−	1.73205i	0.0698430	−	0.120972i
$206$	−16.0000			−1.11477
$207$	9.00000			0.625543
$208$	4.00000			0.277350
$209$	−8.00000	+	13.8564i	−0.553372	+	0.958468i
$210$		0			0
$211$	−8.50000	−	14.7224i	−0.585164	−	1.01353i	−0.994855	−	0.101310i	$-0.967697\pi$
$211$	−8.50000	−	14.7224i	−0.585164	−	1.01353i	0.409691	−	0.912224i	$-0.365637\pi$
$212$	5.00000	+	8.66025i	0.343401	+	0.594789i
$213$	−12.0000	+	6.92820i	−0.822226	+	0.474713i
$214$	−9.00000	+	15.5885i	−0.615227	+	1.06561i
$215$	−1.00000			−0.0681994
$216$		0			0
$217$		0			0
$218$	−16.0000	+	27.7128i	−1.08366	+	1.87695i
$219$	21.0000	−	12.1244i	1.41905	−	0.819288i
$220$	4.00000	+	6.92820i	0.269680	+	0.467099i
$221$	3.50000	+	6.06218i	0.235435	+	0.407786i
$222$		−	34.6410i		−	2.32495i
$223$	−4.00000	+	6.92820i	−0.267860	+	0.463947i	−0.968309	−	0.249756i	$-0.919650\pi$
$223$	−4.00000	+	6.92820i	−0.267860	+	0.463947i	0.700449	+	0.713702i	$0.252983\pi$
$224$		0			0
$225$	1.50000	+	2.59808i	0.100000	+	0.173205i
$226$	22.0000			1.46342
$227$	5.00000	−	8.66025i	0.331862	−	0.574801i	−0.651015	−	0.759065i	$-0.725657\pi$
$227$	5.00000	−	8.66025i	0.331862	−	0.574801i	0.982877	+	0.184263i	$0.0589899\pi$
$228$	12.0000	+	6.92820i	0.794719	+	0.458831i
$229$	−9.00000	−	15.5885i	−0.594737	−	1.03011i	−0.993584	−	0.113097i	$-0.963923\pi$
$229$	−9.00000	−	15.5885i	−0.594737	−	1.03011i	0.398847	−	0.917017i	$-0.369410\pi$
$230$	3.00000	+	5.19615i	0.197814	+	0.342624i
$231$		0			0
$232$		0			0
$233$	−27.0000			−1.76883			−0.884414	−	0.466702i	$-0.845442\pi$
$233$	−27.0000			−1.76883			−0.884414	+	0.466702i	$0.845442\pi$
$234$	3.00000	−	5.19615i	0.196116	−	0.339683i
$235$	2.00000			0.130466
$236$	−10.0000	+	17.3205i	−0.650945	+	1.12747i
$237$		−	15.5885i		−	1.01258i
$238$		0			0
$239$	10.0000	+	17.3205i	0.646846	+	1.12037i	0.983872	+	0.178875i	$0.0572458\pi$
$239$	10.0000	+	17.3205i	0.646846	+	1.12037i	−0.337026	+	0.941495i	$0.609421\pi$
$240$	−6.00000	+	3.46410i	−0.387298	+	0.223607i
$241$	4.00000	−	6.92820i	0.257663	−	0.446285i	−0.707953	−	0.706260i	$-0.750381\pi$
$241$	4.00000	−	6.92820i	0.257663	−	0.446285i	0.965615	+	0.259975i	$0.0837143\pi$
$242$	−10.0000			−0.642824
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$	−10.0000			−0.640184
$245$	−3.50000	+	6.06218i	−0.223607	+	0.387298i
$246$	6.00000	−	3.46410i	0.382546	−	0.220863i
$247$	2.00000	+	3.46410i	0.127257	+	0.220416i
$248$		0			0
$249$		−	10.3923i		−	0.658586i
$250$	−1.00000	+	1.73205i	−0.0632456	+	0.109545i
$251$	21.0000			1.32551			0.662754	−	0.748837i	$-0.269387\pi$
$251$	21.0000			1.32551			0.662754	+	0.748837i	$0.269387\pi$
$252$		0			0
$253$	−12.0000			−0.754434
$254$	4.00000	−	6.92820i	0.250982	−	0.434714i
$255$	−10.5000	−	6.06218i	−0.657536	−	0.379628i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−10.5000	−	18.1865i	−0.654972	−	1.13444i	−0.981901	−	0.189396i	$-0.939347\pi$
$257$	−10.5000	−	18.1865i	−0.654972	−	1.13444i	0.326929	−	0.945049i	$-0.393986\pi$
$258$	−3.00000	−	1.73205i	−0.186772	−	0.107833i
$259$		0			0
$260$	2.00000			0.124035
$261$	−15.0000	−	25.9808i	−0.928477	−	1.60817i
$262$	−30.0000			−1.85341
$263$	0.500000	−	0.866025i	0.0308313	−	0.0534014i	−0.850198	−	0.526463i	$-0.823518\pi$
$263$	0.500000	−	0.866025i	0.0308313	−	0.0534014i	0.881029	+	0.473062i	$0.156851\pi$
$264$		0			0
$265$	−2.50000	−	4.33013i	−0.153574	−	0.265998i
$266$		0			0
$267$	−18.0000	+	10.3923i	−1.10158	+	0.635999i
$268$	12.0000	−	20.7846i	0.733017	−	1.26962i
$269$	−2.00000			−0.121942			−0.0609711	−	0.998140i	$-0.519420\pi$
$269$	−2.00000			−0.121942			−0.0609711	+	0.998140i	$0.519420\pi$
$270$			10.3923i			0.632456i
$271$	−20.0000			−1.21491			−0.607457	−	0.794353i	$-0.707810\pi$
$271$	−20.0000			−1.21491			−0.607457	+	0.794353i	$0.707810\pi$
$272$	14.0000	−	24.2487i	0.848875	−	1.47029i
$273$		0			0
$274$	−12.0000	−	20.7846i	−0.724947	−	1.25564i
$275$	−2.00000	−	3.46410i	−0.120605	−	0.208893i
$276$			10.3923i			0.625543i
$277$	−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	$0.224358\pi$
$278$	−10.0000			−0.599760
$279$	18.0000			1.07763
$280$		0			0
$281$	−6.00000	+	10.3923i	−0.357930	+	0.619953i	−0.987615	−	0.156898i	$-0.949851\pi$
$281$	−6.00000	+	10.3923i	−0.357930	+	0.619953i	0.629685	+	0.776851i	$0.283184\pi$
$282$	6.00000	+	3.46410i	0.357295	+	0.206284i
$283$	7.50000	+	12.9904i	0.445829	+	0.772198i	0.998110	−	0.0614601i	$-0.0195757\pi$
$283$	7.50000	+	12.9904i	0.445829	+	0.772198i	−0.552281	+	0.833658i	$0.686242\pi$
$284$	−8.00000	−	13.8564i	−0.474713	−	0.822226i
$285$	−6.00000	−	3.46410i	−0.355409	−	0.205196i
$286$	−4.00000	+	6.92820i	−0.236525	+	0.409673i
$287$		0			0
$288$	−24.0000			−1.41421
$289$	32.0000			1.88235
$290$	10.0000	−	17.3205i	0.587220	−	1.01710i
$291$		−	13.8564i		−	0.812277i
$292$	14.0000	+	24.2487i	0.819288	+	1.41905i
$293$	−6.00000	−	10.3923i	−0.350524	−	0.607125i	0.635818	−	0.771839i	$-0.280663\pi$
$293$	−6.00000	−	10.3923i	−0.350524	−	0.607125i	−0.986341	+	0.164714i	$0.947330\pi$
$294$	−21.0000	+	12.1244i	−1.22474	+	0.707107i
$295$	5.00000	−	8.66025i	0.291111	−	0.504219i
$296$		0			0
$297$	−18.0000	−	10.3923i	−1.04447	−	0.603023i
$298$	−16.0000			−0.926855
$299$	−1.50000	+	2.59808i	−0.0867472	+	0.150251i
$300$	−3.00000	+	1.73205i	−0.173205	+	0.100000i
$301$		0			0
$302$	−14.0000	−	24.2487i	−0.805609	−	1.39536i
$303$			5.19615i			0.298511i
$304$	8.00000	−	13.8564i	0.458831	−	0.794719i
$305$	5.00000			0.286299
$306$	−21.0000	−	36.3731i	−1.20049	−	2.07931i
$307$	10.0000			0.570730			0.285365	−	0.958419i	$-0.407885\pi$
$307$	10.0000			0.570730			0.285365	+	0.958419i	$0.407885\pi$
$308$		0			0
$309$	12.0000	+	6.92820i	0.682656	+	0.394132i
$310$	6.00000	+	10.3923i	0.340777	+	0.590243i
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	0.984475	−	0.175525i	$-0.0561621\pi$
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	−0.644246	+	0.764818i	$0.722829\pi$
$312$		0			0
$313$	11.0000	−	19.0526i	0.621757	−	1.07691i	−0.367402	−	0.930062i	$-0.619753\pi$
$313$	11.0000	−	19.0526i	0.621757	−	1.07691i	0.989158	−	0.146852i	$-0.0469141\pi$
$314$	−34.0000			−1.91873
$315$		0			0
$316$	18.0000			1.01258
$317$	5.00000	−	8.66025i	0.280828	−	0.486408i	−0.690761	−	0.723083i	$-0.742724\pi$
$317$	5.00000	−	8.66025i	0.280828	−	0.486408i	0.971589	+	0.236675i	$0.0760576\pi$
$318$		−	17.3205i		−	0.971286i
$319$	20.0000	+	34.6410i	1.11979	+	1.93952i
$320$	−4.00000	−	6.92820i	−0.223607	−	0.387298i
$321$	13.5000	−	7.79423i	0.753497	−	0.435031i
$322$		0			0
$323$	28.0000			1.55796
$324$	−9.00000	+	15.5885i	−0.500000	+	0.866025i
$325$	−1.00000			−0.0554700
$326$	−22.0000	+	38.1051i	−1.21847	+	2.11045i
$327$	24.0000	−	13.8564i	1.32720	−	0.766261i
$328$		0			0
$329$		0			0
$330$		−	13.8564i		−	0.762770i
$331$	−9.00000	+	15.5885i	−0.494685	+	0.856819i	−0.999981	−	0.00612670i	$-0.998050\pi$
$331$	−9.00000	+	15.5885i	−0.494685	+	0.856819i	0.505296	+	0.862946i	$0.331383\pi$
$332$	12.0000			0.658586
$333$	−15.0000	+	25.9808i	−0.821995	+	1.42374i
$334$	12.0000			0.656611
$335$	−6.00000	+	10.3923i	−0.327815	+	0.567792i
$336$		0			0
$337$	8.50000	+	14.7224i	0.463025	+	0.801982i	0.999110	−	0.0421818i	$-0.0134309\pi$
$337$	8.50000	+	14.7224i	0.463025	+	0.801982i	−0.536085	+	0.844164i	$0.680098\pi$
$338$	1.00000	+	1.73205i	0.0543928	+	0.0942111i
$339$	−16.5000	−	9.52628i	−0.896157	−	0.517396i
$340$	7.00000	−	12.1244i	0.379628	−	0.657536i
$341$	−24.0000			−1.29967
$342$	−12.0000	−	20.7846i	−0.648886	−	1.12390i
$343$		0			0
$344$		0			0
$345$		−	5.19615i		−	0.279751i
$346$	−3.00000	−	5.19615i	−0.161281	−	0.279347i
$347$	−6.50000	−	11.2583i	−0.348938	−	0.604379i	0.637123	−	0.770762i	$-0.280124\pi$
$347$	−6.50000	−	11.2583i	−0.348938	−	0.604379i	−0.986061	+	0.166383i	$0.946791\pi$
$348$	30.0000	−	17.3205i	1.60817	−	0.928477i
$349$	1.00000	−	1.73205i	0.0535288	−	0.0927146i	−0.838019	−	0.545640i	$-0.816286\pi$
$349$	1.00000	−	1.73205i	0.0535288	−	0.0927146i	0.891548	+	0.452926i	$0.149620\pi$
$350$		0			0
$351$	−4.50000	+	2.59808i	−0.240192	+	0.138675i
$352$	32.0000			1.70561
$353$	18.0000	−	31.1769i	0.958043	−	1.65938i	0.230799	−	0.973002i	$-0.425866\pi$
$353$	18.0000	−	31.1769i	0.958043	−	1.65938i	0.727245	−	0.686378i	$-0.240800\pi$
$354$	30.0000	−	17.3205i	1.59448	−	0.920575i
$355$	4.00000	+	6.92820i	0.212298	+	0.367711i
$356$	−12.0000	−	20.7846i	−0.635999	−	1.10158i
$357$		0			0
$358$	−11.0000	+	19.0526i	−0.581368	+	1.00696i
$359$	−24.0000			−1.26667			−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000			−1.26667			−0.633336	+	0.773877i	$0.718315\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$	23.0000	−	39.8372i	1.20885	−	2.09380i
$363$	7.50000	+	4.33013i	0.393648	+	0.227273i
$364$		0			0
$365$	−7.00000	−	12.1244i	−0.366397	−	0.634618i
$366$	15.0000	+	8.66025i	0.784063	+	0.452679i
$367$	−1.50000	+	2.59808i	−0.0782994	+	0.135618i	−0.902516	−	0.430656i	$-0.858282\pi$
$367$	−1.50000	+	2.59808i	−0.0782994	+	0.135618i	0.824217	+	0.566274i	$0.191616\pi$
$368$	12.0000			0.625543
$369$	−6.00000			−0.312348
$370$	−20.0000			−1.03975
$371$		0			0
$372$			20.7846i			1.07763i
$373$	11.5000	+	19.9186i	0.595447	+	1.03135i	0.993484	+	0.113975i	$0.0363585\pi$
$373$	11.5000	+	19.9186i	0.595447	+	1.03135i	−0.398036	+	0.917370i	$0.630308\pi$
$374$	28.0000	+	48.4974i	1.44785	+	2.50774i
$375$	1.50000	−	0.866025i	0.0774597	−	0.0447214i
$376$		0			0
$377$	10.0000			0.515026
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	4.00000	−	6.92820i	0.205196	−	0.355409i
$381$	−6.00000	+	3.46410i	−0.307389	+	0.177471i
$382$	−13.0000	−	22.5167i	−0.665138	−	1.15205i
$383$	−3.00000	−	5.19615i	−0.153293	−	0.265511i	0.779143	−	0.626846i	$-0.215654\pi$
$383$	−3.00000	−	5.19615i	−0.153293	−	0.265511i	−0.932436	+	0.361335i	$0.882321\pi$
$384$		0			0
$385$		0			0
$386$	32.0000			1.62876
$387$	1.50000	+	2.59808i	0.0762493	+	0.132068i
$388$	16.0000			0.812277
$389$	−1.50000	+	2.59808i	−0.0760530	+	0.131728i	−0.901544	−	0.432688i	$-0.857565\pi$
$389$	−1.50000	+	2.59808i	−0.0760530	+	0.131728i	0.825491	+	0.564416i	$0.190898\pi$
$390$	−3.00000	−	1.73205i	−0.151911	−	0.0877058i
$391$	10.5000	+	18.1865i	0.531008	+	0.919733i
$392$		0			0
$393$	22.5000	+	12.9904i	1.13497	+	0.655278i
$394$	−6.00000	+	10.3923i	−0.302276	+	0.523557i
$395$	−9.00000			−0.452839
$396$	12.0000	−	20.7846i	0.603023	−	1.04447i
$397$	16.0000			0.803017			0.401508	−	0.915855i	$-0.368486\pi$
$397$	16.0000			0.803017			0.401508	+	0.915855i	$0.368486\pi$
$398$	−11.0000	+	19.0526i	−0.551380	+	0.955018i
$399$		0			0
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	6.00000	+	10.3923i	0.299626	+	0.518967i	0.976050	−	0.217545i	$-0.0698049\pi$
$401$	6.00000	+	10.3923i	0.299626	+	0.518967i	−0.676425	+	0.736512i	$0.736472\pi$
$402$	−36.0000	+	20.7846i	−1.79552	+	1.03664i
$403$	−3.00000	+	5.19615i	−0.149441	+	0.258839i
$404$	−6.00000			−0.298511
$405$	4.50000	−	7.79423i	0.223607	−	0.387298i
$406$		0			0
$407$	20.0000	−	34.6410i	0.991363	−	1.71709i
$408$		0			0
$409$	5.00000	+	8.66025i	0.247234	+	0.428222i	0.962757	−	0.270367i	$-0.0871450\pi$
$409$	5.00000	+	8.66025i	0.247234	+	0.428222i	−0.715523	+	0.698589i	$0.753812\pi$
$410$	−2.00000	−	3.46410i	−0.0987730	−	0.171080i
$411$			20.7846i			1.02523i
$412$	−8.00000	+	13.8564i	−0.394132	+	0.682656i
$413$		0			0
$414$	9.00000	−	15.5885i	0.442326	−	0.766131i
$415$	−6.00000			−0.294528
$416$	4.00000	−	6.92820i	0.196116	−	0.339683i
$417$	7.50000	+	4.33013i	0.367277	+	0.212047i
$418$	16.0000	+	27.7128i	0.782586	+	1.35548i
$419$	−5.50000	−	9.52628i	−0.268693	−	0.465389i	0.699832	−	0.714308i	$-0.253258\pi$
$419$	−5.50000	−	9.52628i	−0.268693	−	0.465389i	−0.968524	+	0.248918i	$0.919925\pi$
$420$		0			0
$421$	−5.00000	+	8.66025i	−0.243685	+	0.422075i	−0.961761	−	0.273890i	$-0.911690\pi$
$421$	−5.00000	+	8.66025i	−0.243685	+	0.422075i	0.718076	+	0.695965i	$0.245023\pi$
$422$	−34.0000			−1.65509
$423$	−3.00000	−	5.19615i	−0.145865	−	0.252646i
$424$		0			0
$425$	−3.50000	+	6.06218i	−0.169775	+	0.294059i
$426$			27.7128i			1.34269i
$427$		0			0
$428$	9.00000	+	15.5885i	0.435031	+	0.753497i
$429$	6.00000	−	3.46410i	0.289683	−	0.167248i
$430$	−1.00000	+	1.73205i	−0.0482243	+	0.0835269i
$431$	12.0000			0.578020			0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000			0.578020			0.289010	+	0.957326i	$0.406674\pi$
$432$	18.0000	+	10.3923i	0.866025	+	0.500000i
$433$	1.00000			0.0480569			0.0240285	−	0.999711i	$-0.492351\pi$
$433$	1.00000			0.0480569			0.0240285	+	0.999711i	$0.492351\pi$
$434$		0			0
$435$	−15.0000	+	8.66025i	−0.719195	+	0.415227i
$436$	16.0000	+	27.7128i	0.766261	+	1.32720i
$437$	6.00000	+	10.3923i	0.287019	+	0.497131i
$438$		−	48.4974i		−	2.31730i
$439$	−3.50000	+	6.06218i	−0.167046	+	0.289332i	−0.937380	−	0.348309i	$-0.886756\pi$
$439$	−3.50000	+	6.06218i	−0.167046	+	0.289332i	0.770334	+	0.637641i	$0.220089\pi$
$440$		0			0
$441$	21.0000			1.00000
$442$	14.0000			0.665912
$443$	−1.50000	+	2.59808i	−0.0712672	+	0.123438i	−0.899457	−	0.437009i	$-0.856038\pi$
$443$	−1.50000	+	2.59808i	−0.0712672	+	0.123438i	0.828190	+	0.560448i	$0.189371\pi$
$444$	−30.0000	−	17.3205i	−1.42374	−	0.821995i
$445$	6.00000	+	10.3923i	0.284427	+	0.492642i
$446$	8.00000	+	13.8564i	0.378811	+	0.656120i
$447$	12.0000	+	6.92820i	0.567581	+	0.327693i
$448$		0			0
$449$	34.0000			1.60456			0.802280	−	0.596948i	$-0.203620\pi$
$449$	34.0000			1.60456			0.802280	+	0.596948i	$0.203620\pi$
$450$	6.00000			0.282843
$451$	8.00000			0.376705
$452$	11.0000	−	19.0526i	0.517396	−	0.896157i
$453$			24.2487i			1.13930i
$454$	−10.0000	−	17.3205i	−0.469323	−	0.812892i
$455$		0			0
$456$		0			0
$457$	−11.0000	+	19.0526i	−0.514558	+	0.891241i	0.485299	+	0.874348i	$0.338711\pi$
$457$	−11.0000	+	19.0526i	−0.514558	+	0.891241i	−0.999857	+	0.0168929i	$0.994623\pi$
$458$	−36.0000			−1.68217
$459$			36.3731i			1.69775i
$460$	6.00000			0.279751
$461$	12.0000	−	20.7846i	0.558896	−	0.968036i	−0.438693	−	0.898637i	$-0.644559\pi$
$461$	12.0000	−	20.7846i	0.558896	−	0.968036i	0.997589	−	0.0693989i	$-0.0221081\pi$
$462$		0			0
$463$	−6.00000	−	10.3923i	−0.278844	−	0.482971i	0.692254	−	0.721654i	$-0.256618\pi$
$463$	−6.00000	−	10.3923i	−0.278844	−	0.482971i	−0.971098	+	0.238683i	$0.923284\pi$
$464$	−20.0000	−	34.6410i	−0.928477	−	1.60817i
$465$		−	10.3923i		−	0.481932i
$466$	−27.0000	+	46.7654i	−1.25075	+	2.16636i
$467$	35.0000			1.61961			0.809803	−	0.586701i	$-0.199574\pi$
$467$	35.0000			1.61961			0.809803	+	0.586701i	$0.199574\pi$
$468$	−3.00000	−	5.19615i	−0.138675	−	0.240192i
$469$		0			0
$470$	2.00000	−	3.46410i	0.0922531	−	0.159787i
$471$	25.5000	+	14.7224i	1.17498	+	0.678374i
$472$		0			0
$473$	−2.00000	−	3.46410i	−0.0919601	−	0.159280i
$474$	−27.0000	−	15.5885i	−1.24015	−	0.716002i
$475$	−2.00000	+	3.46410i	−0.0917663	+	0.158944i
$476$		0			0
$477$	−7.50000	+	12.9904i	−0.343401	+	0.594789i
$478$	40.0000			1.82956
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	−0.995023	−	0.0996406i	$-0.968231\pi$
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	0.583803	+	0.811895i	$0.301564\pi$
$480$			13.8564i			0.632456i
$481$	−5.00000	−	8.66025i	−0.227980	−	0.394874i
$482$	−8.00000	−	13.8564i	−0.364390	−	0.631142i
$483$		0			0
$484$	−5.00000	+	8.66025i	−0.227273	+	0.393648i
$485$	−8.00000			−0.363261
$486$	27.0000	−	15.5885i	1.22474	−	0.707107i
$487$	8.00000			0.362515			0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000			0.362515			0.181257	+	0.983436i	$0.441983\pi$
$488$		0			0
$489$	33.0000	−	19.0526i	1.49231	−	0.861586i
$490$	7.00000	+	12.1244i	0.316228	+	0.547723i
$491$	−10.0000	−	17.3205i	−0.451294	−	0.781664i	0.547173	−	0.837020i	$-0.315704\pi$
$491$	−10.0000	−	17.3205i	−0.451294	−	0.781664i	−0.998467	+	0.0553560i	$0.982371\pi$
$492$		−	6.92820i		−	0.312348i
$493$	35.0000	−	60.6218i	1.57632	−	2.73027i
$494$	8.00000			0.359937
$495$	−6.00000	+	10.3923i	−0.269680	+	0.467099i
$496$	24.0000			1.07763
$497$		0			0
$498$	−18.0000	−	10.3923i	−0.806599	−	0.465690i
$499$	16.0000	+	27.7128i	0.716258	+	1.24060i	0.962472	+	0.271380i	$0.0874801\pi$
$499$	16.0000	+	27.7128i	0.716258	+	1.24060i	−0.246214	+	0.969216i	$0.579187\pi$
$500$	1.00000	+	1.73205i	0.0447214	+	0.0774597i
$501$	−9.00000	−	5.19615i	−0.402090	−	0.232147i
$502$	21.0000	−	36.3731i	0.937276	−	1.62341i
$503$	−31.0000			−1.38222			−0.691111	−	0.722749i	$-0.742878\pi$
$503$	−31.0000			−1.38222			−0.691111	+	0.722749i	$0.742878\pi$
$504$		0			0
$505$	3.00000			0.133498
$506$	−12.0000	+	20.7846i	−0.533465	+	0.923989i
$507$		−	1.73205i		−	0.0769231i
$508$	−4.00000	−	6.92820i	−0.177471	−	0.307389i
$509$	10.0000	+	17.3205i	0.443242	+	0.767718i	0.997928	−	0.0643419i	$-0.0204948\pi$
$509$	10.0000	+	17.3205i	0.443242	+	0.767718i	−0.554686	+	0.832060i	$0.687161\pi$
$510$	−21.0000	+	12.1244i	−0.929896	+	0.536875i
$511$		0			0
$512$	−32.0000			−1.41421
$513$			20.7846i			0.917663i
$514$	−42.0000			−1.85254
$515$	4.00000	−	6.92820i	0.176261	−	0.305293i
$516$	−3.00000	+	1.73205i	−0.132068	+	0.0762493i
$517$	4.00000	+	6.92820i	0.175920	+	0.304702i
$518$		0			0
$519$			5.19615i			0.228086i
$520$		0			0
$521$	−10.0000			−0.438108			−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000			−0.438108			−0.219054	+	0.975713i	$0.570297\pi$
$522$	−60.0000			−2.62613
$523$	−8.00000			−0.349816			−0.174908	−	0.984585i	$-0.555963\pi$
$523$	−8.00000			−0.349816			−0.174908	+	0.984585i	$0.555963\pi$
$524$	−15.0000	+	25.9808i	−0.655278	+	1.13497i
$525$		0			0
$526$	−1.00000	−	1.73205i	−0.0436021	−	0.0755210i
$527$	21.0000	+	36.3731i	0.914774	+	1.58444i
$528$	−24.0000	−	13.8564i	−1.04447	−	0.603023i
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	−10.0000			−0.434372
$531$	−30.0000			−1.30189
$532$		0			0
$533$	1.00000	−	1.73205i	0.0433148	−	0.0750234i
$534$			41.5692i			1.79888i
$535$	−4.50000	−	7.79423i	−0.194552	−	0.336974i
$536$		0			0
$537$	16.5000	−	9.52628i	0.712028	−	0.411089i
$538$	−2.00000	+	3.46410i	−0.0862261	+	0.149348i
$539$	−28.0000			−1.20605
$540$	9.00000	+	5.19615i	0.387298	+	0.223607i
$541$		0			0			−	1.00000i	$-0.5\pi$
$541$		0			0				1.00000i	$0.5\pi$
$542$	−20.0000	+	34.6410i	−0.859074	+	1.48796i
$543$	−34.5000	+	19.9186i	−1.48054	+	0.854788i
$544$	−28.0000	−	48.4974i	−1.20049	−	2.07931i
$545$	−8.00000	−	13.8564i	−0.342682	−	0.593543i
$546$		0			0
$547$	−2.00000	+	3.46410i	−0.0855138	+	0.148114i	−0.905610	−	0.424111i	$-0.860587\pi$
$547$	−2.00000	+	3.46410i	−0.0855138	+	0.148114i	0.820096	+	0.572226i	$0.193920\pi$
$548$	−24.0000			−1.02523
$549$	−7.50000	−	12.9904i	−0.320092	−	0.554416i
$550$	−8.00000			−0.341121
$551$	20.0000	−	34.6410i	0.852029	−	1.47576i
$552$		0			0
$553$		0			0
$554$	6.00000	+	10.3923i	0.254916	+	0.441527i
$555$	15.0000	+	8.66025i	0.636715	+	0.367607i
$556$	−5.00000	+	8.66025i	−0.212047	+	0.367277i
$557$		0			0			−	1.00000i	$-0.5\pi$
$557$		0			0				1.00000i	$0.5\pi$
$558$	18.0000	−	31.1769i	0.762001	−	1.31982i
$559$	−1.00000			−0.0422955
$560$		0			0
$561$		−	48.4974i		−	2.04756i
$562$	12.0000	+	20.7846i	0.506189	+	0.876746i
$563$	10.5000	+	18.1865i	0.442522	+	0.766471i	0.997876	−	0.0651433i	$-0.0207504\pi$
$563$	10.5000	+	18.1865i	0.442522	+	0.766471i	−0.555354	+	0.831614i	$0.687417\pi$
$564$	6.00000	−	3.46410i	0.252646	−	0.145865i
$565$	−5.50000	+	9.52628i	−0.231387	+	0.400774i
$566$	30.0000			1.26099
$567$		0			0
$568$		0			0
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	−0.922032	−	0.387113i	$-0.873472\pi$
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	0.796266	+	0.604947i	$0.206806\pi$
$570$	−12.0000	+	6.92820i	−0.502625	+	0.290191i
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	0.904835	−	0.425762i	$-0.139994\pi$
$571$	2.00000	+	3.46410i	0.0836974	+	0.144968i	−0.821138	+	0.570730i	$0.806660\pi$
$572$	4.00000	+	6.92820i	0.167248	+	0.289683i
$573$			22.5167i			0.940647i
$574$		0			0
$575$	−3.00000			−0.125109
$576$	−12.0000	+	20.7846i	−0.500000	+	0.866025i
$577$	−22.0000			−0.915872			−0.457936	−	0.888985i	$-0.651411\pi$
$577$	−22.0000			−0.915872			−0.457936	+	0.888985i	$0.651411\pi$
$578$	32.0000	−	55.4256i	1.33102	−	2.30540i
$579$	−24.0000	−	13.8564i	−0.997406	−	0.575853i
$580$	−10.0000	−	17.3205i	−0.415227	−	0.719195i
$581$		0			0
$582$	−24.0000	−	13.8564i	−0.994832	−	0.574367i
$583$	10.0000	−	17.3205i	0.414158	−	0.717342i
$584$		0			0
$585$	1.50000	+	2.59808i	0.0620174	+	0.107417i
$586$	−24.0000			−0.991431
$587$	−9.00000	+	15.5885i	−0.371470	+	0.643404i	−0.989792	−	0.142520i	$-0.954479\pi$
$587$	−9.00000	+	15.5885i	−0.371470	+	0.643404i	0.618322	+	0.785925i	$0.287813\pi$
$588$			24.2487i			1.00000i
$589$	12.0000	+	20.7846i	0.494451	+	0.856415i
$590$	−10.0000	−	17.3205i	−0.411693	−	0.713074i
$591$	9.00000	−	5.19615i	0.370211	−	0.213741i
$592$	−20.0000	+	34.6410i	−0.821995	+	1.42374i
$593$	−40.0000			−1.64260			−0.821302	−	0.570494i	$-0.806752\pi$
$593$	−40.0000			−1.64260			−0.821302	+	0.570494i	$0.806752\pi$
$594$	−36.0000	+	20.7846i	−1.47710	+	0.852803i
$595$		0			0
$596$	−8.00000	+	13.8564i	−0.327693	+	0.567581i
$597$	16.5000	−	9.52628i	0.675300	−	0.389885i
$598$	3.00000	+	5.19615i	0.122679	+	0.212486i
$599$	−5.50000	−	9.52628i	−0.224724	−	0.389233i	0.731513	−	0.681828i	$-0.238815\pi$
$599$	−5.50000	−	9.52628i	−0.224724	−	0.389233i	−0.956237	+	0.292595i	$0.905481\pi$
$600$		0			0
$601$	−14.5000	+	25.1147i	−0.591467	+	1.02445i	0.402568	+	0.915390i	$0.368118\pi$
$601$	−14.5000	+	25.1147i	−0.591467	+	1.02445i	−0.994035	+	0.109061i	$0.965216\pi$
$602$		0			0
$603$	36.0000			1.46603
$604$	−28.0000			−1.13930
$605$	2.50000	−	4.33013i	0.101639	−	0.176045i
$606$	9.00000	+	5.19615i	0.365600	+	0.211079i
$607$	−3.50000	−	6.06218i	−0.142061	−	0.246056i	0.786212	−	0.617957i	$-0.212039\pi$
$607$	−3.50000	−	6.06218i	−0.142061	−	0.246056i	−0.928272	+	0.371901i	$0.878706\pi$
$608$	−16.0000	−	27.7128i	−0.648886	−	1.12390i
$609$		0			0
$610$	5.00000	−	8.66025i	0.202444	−	0.350643i
$611$	2.00000			0.0809113
$612$	−42.0000			−1.69775
$613$	−26.0000			−1.05013			−0.525065	−	0.851062i	$-0.675959\pi$
$613$	−26.0000			−1.05013			−0.525065	+	0.851062i	$0.675959\pi$
$614$	10.0000	−	17.3205i	0.403567	−	0.698999i
$615$			3.46410i			0.139686i
$616$		0			0
$617$	9.00000	+	15.5885i	0.362326	+	0.627568i	0.988343	−	0.152242i	$-0.0486493\pi$
$617$	9.00000	+	15.5885i	0.362326	+	0.627568i	−0.626017	+	0.779809i	$0.715316\pi$
$618$	24.0000	−	13.8564i	0.965422	−	0.557386i
$619$	−1.00000	+	1.73205i	−0.0401934	+	0.0696170i	−0.885422	−	0.464787i	$-0.846131\pi$
$619$	−1.00000	+	1.73205i	−0.0401934	+	0.0696170i	0.845229	+	0.534404i	$0.179464\pi$
$620$	12.0000			0.481932
$621$	−13.5000	+	7.79423i	−0.541736	+	0.312772i
$622$	24.0000			0.962312
$623$		0			0
$624$	−6.00000	+	3.46410i	−0.240192	+	0.138675i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−22.0000	−	38.1051i	−0.879297	−	1.52299i
$627$		−	27.7128i		−	1.10674i
$628$	−17.0000	+	29.4449i	−0.678374	+	1.17498i
$629$	−70.0000			−2.79108
$630$		0			0
$631$	−26.0000			−1.03504			−0.517522	−	0.855670i	$-0.673145\pi$
$631$	−26.0000			−1.03504			−0.517522	+	0.855670i	$0.673145\pi$
$632$		0			0
$633$	25.5000	+	14.7224i	1.01353	+	0.585164i
$634$	−10.0000	−	17.3205i	−0.397151	−	0.687885i
$635$	2.00000	+	3.46410i	0.0793676	+	0.137469i
$636$	−15.0000	−	8.66025i	−0.594789	−	0.343401i
$637$	−3.50000	+	6.06218i	−0.138675	+	0.240192i
$638$	80.0000			3.16723
$639$	12.0000	−	20.7846i	0.474713	−	0.822226i
$640$		0			0
$641$	−3.00000	+	5.19615i	−0.118493	+	0.205236i	−0.919171	−	0.393860i	$-0.871140\pi$
$641$	−3.00000	+	5.19615i	−0.118493	+	0.205236i	0.800678	+	0.599095i	$0.204473\pi$
$642$		−	31.1769i		−	1.23045i
$643$	−3.00000	−	5.19615i	−0.118308	−	0.204916i	0.800789	−	0.598947i	$-0.204414\pi$
$643$	−3.00000	−	5.19615i	−0.118308	−	0.204916i	−0.919097	+	0.394030i	$0.871080\pi$
$644$		0			0
$645$	1.50000	−	0.866025i	0.0590624	−	0.0340997i
$646$	28.0000	−	48.4974i	1.10165	−	1.90811i
$647$	−5.00000			−0.196570			−0.0982851	−	0.995158i	$-0.531336\pi$
$647$	−5.00000			−0.196570			−0.0982851	+	0.995158i	$0.531336\pi$
$648$		0			0
$649$	40.0000			1.57014
$650$	−1.00000	+	1.73205i	−0.0392232	+	0.0679366i
$651$		0			0
$652$	22.0000	+	38.1051i	0.861586	+	1.49231i
$653$	17.0000	+	29.4449i	0.665261	+	1.15227i	0.979214	+	0.202828i	$0.0650132\pi$
$653$	17.0000	+	29.4449i	0.665261	+	1.15227i	−0.313953	+	0.949439i	$0.601653\pi$
$654$		−	55.4256i		−	2.16731i
$655$	7.50000	−	12.9904i	0.293049	−	0.507576i
$656$	−8.00000			−0.312348
$657$	−21.0000	+	36.3731i	−0.819288	+	1.41905i
$658$		0			0
$659$	−14.0000	+	24.2487i	−0.545363	+	0.944596i	0.453221	+	0.891398i	$0.350275\pi$
$659$	−14.0000	+	24.2487i	−0.545363	+	0.944596i	−0.998584	+	0.0531977i	$0.983059\pi$
$660$	−12.0000	−	6.92820i	−0.467099	−	0.269680i
$661$	16.0000	+	27.7128i	0.622328	+	1.07790i	0.989051	+	0.147573i	$0.0471463\pi$
$661$	16.0000	+	27.7128i	0.622328	+	1.07790i	−0.366723	+	0.930330i	$0.619520\pi$
$662$	18.0000	+	31.1769i	0.699590	+	1.21173i
$663$	−10.5000	−	6.06218i	−0.407786	−	0.235435i
$664$		0			0
$665$		0			0
$666$	30.0000	+	51.9615i	1.16248	+	2.01347i
$667$	30.0000			1.16160
$668$	6.00000	−	10.3923i	0.232147	−	0.402090i
$669$		−	13.8564i		−	0.535720i
$670$	12.0000	+	20.7846i	0.463600	+	0.802980i
$671$	10.0000	+	17.3205i	0.386046	+	0.668651i
$672$		0			0
$673$	16.5000	−	28.5788i	0.636028	−	1.10163i	−0.350268	−	0.936650i	$-0.613909\pi$
$673$	16.5000	−	28.5788i	0.636028	−	1.10163i	0.986296	−	0.164984i	$-0.0527572\pi$
$674$	34.0000			1.30963
$675$	−4.50000	−	2.59808i	−0.173205	−	0.100000i
$676$	2.00000			0.0769231
$677$	−21.0000	+	36.3731i	−0.807096	+	1.39793i	0.107772	+	0.994176i	$0.465628\pi$
$677$	−21.0000	+	36.3731i	−0.807096	+	1.39793i	−0.914867	+	0.403755i	$0.867705\pi$
$678$	−33.0000	+	19.0526i	−1.26736	+	0.731709i
$679$		0			0
$680$		0			0
$681$			17.3205i			0.663723i
$682$	−24.0000	+	41.5692i	−0.919007	+	1.59177i
$683$	−36.0000			−1.37750			−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000			−1.37750			−0.688751	+	0.724998i	$0.741841\pi$
$684$	−24.0000			−0.917663
$685$	12.0000			0.458496
$686$		0			0
$687$	27.0000	+	15.5885i	1.03011	+	0.594737i
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	−2.50000	−	4.33013i	−0.0952424	−	0.164965i
$690$	−9.00000	−	5.19615i	−0.342624	−	0.197814i
$691$	19.0000	−	32.9090i	0.722794	−	1.25192i	−0.237082	−	0.971490i	$-0.576191\pi$
$691$	19.0000	−	32.9090i	0.722794	−	1.25192i	0.959876	−	0.280426i	$-0.0904758\pi$
$692$	−6.00000			−0.228086
$693$		0			0
$694$	−26.0000			−0.986947
$695$	2.50000	−	4.33013i	0.0948304	−	0.164251i
$696$		0			0
$697$	−7.00000	−	12.1244i	−0.265144	−	0.459243i
$698$	−2.00000	−	3.46410i	−0.0757011	−	0.131118i
$699$	40.5000	−	23.3827i	1.53185	−	0.884414i
$700$		0			0
$701$	−13.0000			−0.491003			−0.245502	−	0.969396i	$-0.578953\pi$
$701$	−13.0000			−0.491003			−0.245502	+	0.969396i	$0.578953\pi$
$702$			10.3923i			0.392232i
$703$	−40.0000			−1.50863
$704$	16.0000	−	27.7128i	0.603023	−	1.04447i
$705$	−3.00000	+	1.73205i	−0.112987	+	0.0652328i
$706$	−36.0000	−	62.3538i	−1.35488	−	2.34672i
$707$		0			0
$708$		−	34.6410i		−	1.30189i
$709$	10.0000	−	17.3205i	0.375558	−	0.650485i	−0.614852	−	0.788642i	$-0.710784\pi$
$709$	10.0000	−	17.3205i	0.375558	−	0.650485i	0.990410	+	0.138157i	$0.0441178\pi$
$710$	16.0000			0.600469
$711$	13.5000	+	23.3827i	0.506290	+	0.876919i
$712$		0			0
$713$	−9.00000	+	15.5885i	−0.337053	+	0.583792i
$714$		0			0
$715$	−2.00000	−	3.46410i	−0.0747958	−	0.129550i
$716$	11.0000	+	19.0526i	0.411089	+	0.712028i
$717$	−30.0000	−	17.3205i	−1.12037	−	0.646846i
$718$	−24.0000	+	41.5692i	−0.895672	+	1.55135i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$	6.00000	−	10.3923i	0.223607	−	0.387298i
$721$		0			0
$722$	−3.00000	+	5.19615i	−0.111648	+	0.193381i
$723$			13.8564i			0.515325i
$724$	−23.0000	−	39.8372i	−0.854788	−	1.48054i
$725$	5.00000	+	8.66025i	0.185695	+	0.321634i
$726$	15.0000	−	8.66025i	0.556702	−	0.321412i
$727$	6.50000	−	11.2583i	0.241072	−	0.417548i	−0.719948	−	0.694028i	$-0.755834\pi$
$727$	6.50000	−	11.2583i	0.241072	−	0.417548i	0.961020	+	0.276479i	$0.0891678\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	−28.0000			−1.03633
$731$	−3.50000	+	6.06218i	−0.129452	+	0.224218i
$732$	15.0000	−	8.66025i	0.554416	−	0.320092i
$733$	8.00000	+	13.8564i	0.295487	+	0.511798i	0.975098	−	0.221774i	$-0.0711849\pi$
$733$	8.00000	+	13.8564i	0.295487	+	0.511798i	−0.679611	+	0.733572i	$0.737852\pi$
$734$	3.00000	+	5.19615i	0.110732	+	0.191793i
$735$		−	12.1244i		−	0.447214i
$736$	12.0000	−	20.7846i	0.442326	−	0.766131i
$737$	−48.0000			−1.76810
$738$	−6.00000	+	10.3923i	−0.220863	+	0.382546i
$739$	−38.0000			−1.39785			−0.698926	−	0.715194i	$-0.746338\pi$
$739$	−38.0000			−1.39785			−0.698926	+	0.715194i	$0.746338\pi$
$740$	−10.0000	+	17.3205i	−0.367607	+	0.636715i
$741$	−6.00000	−	3.46410i	−0.220416	−	0.127257i
$742$		0			0
$743$	10.0000	+	17.3205i	0.366864	+	0.635428i	0.989073	−	0.147423i	$-0.0470980\pi$
$743$	10.0000	+	17.3205i	0.366864	+	0.635428i	−0.622209	+	0.782851i	$0.713765\pi$
$744$		0			0
$745$	4.00000	−	6.92820i	0.146549	−	0.253830i
$746$	46.0000			1.68418
$747$	9.00000	+	15.5885i	0.329293	+	0.570352i
$748$	56.0000			2.04756
$749$		0			0
$750$		−	3.46410i		−	0.126491i
$751$	−26.0000	−	45.0333i	−0.948753	−	1.64329i	−0.748056	−	0.663636i	$-0.769012\pi$
$751$	−26.0000	−	45.0333i	−0.948753	−	1.64329i	−0.200698	−	0.979653i	$-0.564321\pi$
$752$	−4.00000	−	6.92820i	−0.145865	−	0.252646i
$753$	−31.5000	+	18.1865i	−1.14792	+	0.662754i
$754$	10.0000	−	17.3205i	0.364179	−	0.630776i
$755$	14.0000			0.509512
$756$		0			0
$757$	19.0000			0.690567			0.345283	−	0.938498i	$-0.387783\pi$
$757$	19.0000			0.690567			0.345283	+	0.938498i	$0.387783\pi$
$758$	−20.0000	+	34.6410i	−0.726433	+	1.25822i
$759$	18.0000	−	10.3923i	0.653359	−	0.377217i
$760$		0			0
$761$	6.00000	+	10.3923i	0.217500	+	0.376721i	0.954043	−	0.299670i	$-0.0968765\pi$
$761$	6.00000	+	10.3923i	0.217500	+	0.376721i	−0.736543	+	0.676391i	$0.763543\pi$
$762$			13.8564i			0.501965i
$763$		0			0
$764$	−26.0000			−0.940647
$765$	21.0000			0.759257
$766$	−12.0000			−0.433578
$767$	5.00000	−	8.66025i	0.180540	−	0.312704i
$768$	24.0000	+	13.8564i	0.866025	+	0.500000i
$769$	−22.0000	−	38.1051i	−0.793340	−	1.37411i	−0.923888	−	0.382664i	$-0.875007\pi$
$769$	−22.0000	−	38.1051i	−0.793340	−	1.37411i	0.130547	−	0.991442i	$-0.458327\pi$
$770$		0			0
$771$	31.5000	+	18.1865i	1.13444	+	0.654972i
$772$	16.0000	−	27.7128i	0.575853	−	0.997406i
$773$	18.0000			0.647415			0.323708	−	0.946157i	$-0.395071\pi$
$773$	18.0000			0.647415			0.323708	+	0.946157i	$0.395071\pi$
$774$	6.00000			0.215666
$775$	−6.00000			−0.215526
$776$		0			0
$777$		0			0
$778$	3.00000	+	5.19615i	0.107555	+	0.186291i
$779$	−4.00000	−	6.92820i	−0.143315	−	0.248229i
$780$	−3.00000	+	1.73205i	−0.107417	+	0.0620174i
$781$	−16.0000	+	27.7128i	−0.572525	+	0.991642i
$782$	42.0000			1.50192
$783$	45.0000	+	25.9808i	1.60817	+	0.928477i
$784$	28.0000			1.00000
$785$	8.50000	−	14.7224i	0.303378	−	0.525466i
$786$	45.0000	−	25.9808i	1.60510	−	0.926703i
$787$	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	$0.717316\pi$
$788$	6.00000	+	10.3923i	0.213741	+	0.370211i
$789$			1.73205i			0.0616626i
$790$	−9.00000	+	15.5885i	−0.320206	+	0.554612i
$791$		0			0
$792$		0			0
$793$	5.00000			0.177555
$794$	16.0000	−	27.7128i	0.567819	−	0.983491i
$795$	7.50000	+	4.33013i	0.265998	+	0.153574i
$796$	11.0000	+	19.0526i	0.389885	+	0.675300i
$797$	23.0000	+	39.8372i	0.814702	+	1.41110i	0.909542	+	0.415612i	$0.136433\pi$
$797$	23.0000	+	39.8372i	0.814702	+	1.41110i	−0.0948400	+	0.995493i	$0.530234\pi$
$798$		0			0
$799$	7.00000	−	12.1244i	0.247642	−	0.428929i
$800$	8.00000			0.282843
$801$	18.0000	−	31.1769i	0.635999	−	1.10158i
$802$	24.0000			0.847469
$803$	28.0000	−	48.4974i	0.988099	−	1.71144i
$804$			41.5692i			1.46603i
$805$		0			0
$806$	6.00000	+	10.3923i	0.211341	+	0.366053i
$807$	3.00000	−	1.73205i	0.105605	−	0.0609711i
$808$		0			0
$809$	−19.0000			−0.668004			−0.334002	−	0.942572i	$-0.608399\pi$
$809$	−19.0000			−0.668004			−0.334002	+	0.942572i	$0.608399\pi$
$810$	−9.00000	−	15.5885i	−0.316228	−	0.547723i
$811$		0			0			−	1.00000i	$-0.5\pi$
$811$		0			0				1.00000i	$0.5\pi$
$812$		0			0
$813$	30.0000	−	17.3205i	1.05215	−	0.607457i
$814$	−40.0000	−	69.2820i	−1.40200	−	2.42833i
$815$	−11.0000	−	19.0526i	−0.385313	−	0.667382i
$816$			48.4974i			1.69775i
$817$	−2.00000	+	3.46410i	−0.0699711	+	0.121194i
$818$	20.0000			0.699284
$819$		0			0
$820$	−4.00000			−0.139686
$821$	24.0000	−	41.5692i	0.837606	−	1.45078i	−0.0542853	−	0.998525i	$-0.517288\pi$
$821$	24.0000	−	41.5692i	0.837606	−	1.45078i	0.891891	−	0.452250i	$-0.149379\pi$
$822$	36.0000	+	20.7846i	1.25564	+	0.724947i
$823$	6.50000	+	11.2583i	0.226576	+	0.392441i	0.956791	−	0.290776i	$-0.0939136\pi$
$823$	6.50000	+	11.2583i	0.226576	+	0.392441i	−0.730215	+	0.683217i	$0.760580\pi$
$824$		0			0
$825$	6.00000	+	3.46410i	0.208893	+	0.120605i
$826$		0			0
$827$	−8.00000			−0.278187			−0.139094	−	0.990279i	$-0.544419\pi$
$827$	−8.00000			−0.278187			−0.139094	+	0.990279i	$0.544419\pi$
$828$	−9.00000	−	15.5885i	−0.312772	−	0.541736i
$829$	6.00000			0.208389			0.104194	−	0.994557i	$-0.466774\pi$
$829$	6.00000			0.208389			0.104194	+	0.994557i	$0.466774\pi$
$830$	−6.00000	+	10.3923i	−0.208263	+	0.360722i
$831$		−	10.3923i		−	0.360505i
$832$	−4.00000	−	6.92820i	−0.138675	−	0.240192i
$833$	24.5000	+	42.4352i	0.848875	+	1.47029i
$834$	15.0000	−	8.66025i	0.519408	−	0.299880i
$835$	−3.00000	+	5.19615i	−0.103819	+	0.179820i
$836$	32.0000			1.10674
$837$	−27.0000	+	15.5885i	−0.933257	+	0.538816i
$838$	−22.0000			−0.759977
$839$	2.00000	−	3.46410i	0.0690477	−	0.119594i	−0.829435	−	0.558604i	$-0.811337\pi$
$839$	2.00000	−	3.46410i	0.0690477	−	0.119594i	0.898482	+	0.439010i	$0.144671\pi$
$840$		0			0
$841$	−35.5000	−	61.4878i	−1.22414	−	2.12027i
$842$	10.0000	+	17.3205i	0.344623	+	0.596904i
$843$		−	20.7846i		−	0.715860i
$844$	−17.0000	+	29.4449i	−0.585164	+	1.01353i
$845$	−1.00000			−0.0344010
$846$	−12.0000			−0.412568
$847$		0			0
$848$	−10.0000	+	17.3205i	−0.343401	+	0.594789i
$849$	−22.5000	−	12.9904i	−0.772198	−	0.445829i
$850$	7.00000	+	12.1244i	0.240098	+	0.415862i
$851$	−15.0000	−	25.9808i	−0.514193	−	0.890609i
$852$	24.0000	+	13.8564i	0.822226	+	0.474713i
$853$	21.0000	−	36.3731i	0.719026	−	1.24539i	−0.242360	−	0.970186i	$-0.577921\pi$
$853$	21.0000	−	36.3731i	0.719026	−	1.24539i	0.961386	−	0.275204i	$-0.0887453\pi$
$854$		0			0
$855$	12.0000			0.410391
$856$		0			0
$857$	7.00000	−	12.1244i	0.239115	−	0.414160i	−0.721345	−	0.692576i	$-0.756476\pi$
$857$	7.00000	−	12.1244i	0.239115	−	0.414160i	0.960461	+	0.278416i	$0.0898092\pi$
$858$		−	13.8564i		−	0.473050i
$859$	20.5000	+	35.5070i	0.699451	+	1.21148i	0.968657	+	0.248402i	$0.0799054\pi$
$859$	20.5000	+	35.5070i	0.699451	+	1.21148i	−0.269206	+	0.963083i	$0.586761\pi$
$860$	1.00000	+	1.73205i	0.0340997	+	0.0590624i
$861$		0			0
$862$	12.0000	−	20.7846i	0.408722	−	0.707927i
$863$	8.00000			0.272323			0.136162	−	0.990687i	$-0.456523\pi$
$863$	8.00000			0.272323			0.136162	+	0.990687i	$0.456523\pi$
$864$	36.0000	−	20.7846i	1.22474	−	0.707107i
$865$	3.00000			0.102003
$866$	1.00000	−	1.73205i	0.0339814	−	0.0588575i
$867$	−48.0000	+	27.7128i	−1.63017	+	0.941176i
$868$		0			0
$869$	−18.0000	−	31.1769i	−0.610608	−	1.05760i
$870$			34.6410i			1.17444i
$871$	−6.00000	+	10.3923i	−0.203302	+	0.352130i
$872$		0			0
$873$	12.0000	+	20.7846i	0.406138	+	0.703452i
$874$	24.0000			0.811812
$875$		0			0
$876$	−42.0000	−	24.2487i	−1.41905	−	0.819288i
$877$	6.00000	+	10.3923i	0.202606	+	0.350923i	0.949367	−	0.314169i	$-0.101726\pi$
$877$	6.00000	+	10.3923i	0.202606	+	0.350923i	−0.746762	+	0.665092i	$0.768392\pi$
$878$	7.00000	+	12.1244i	0.236239	+	0.409177i
$879$	18.0000	+	10.3923i	0.607125	+	0.350524i
$880$	−8.00000	+	13.8564i	−0.269680	+	0.467099i
$881$	25.0000			0.842271			0.421136	−	0.906998i	$-0.361632\pi$
$881$	25.0000			0.842271			0.421136	+	0.906998i	$0.361632\pi$
$882$	21.0000	−	36.3731i	0.707107	−	1.22474i
$883$	−28.0000			−0.942275			−0.471138	−	0.882060i	$-0.656156\pi$
$883$	−28.0000			−0.942275			−0.471138	+	0.882060i	$0.656156\pi$
$884$	7.00000	−	12.1244i	0.235435	−	0.407786i
$885$			17.3205i			0.582223i
$886$	3.00000	+	5.19615i	0.100787	+	0.174568i
$887$	1.50000	+	2.59808i	0.0503651	+	0.0872349i	0.890109	−	0.455748i	$-0.150628\pi$
$887$	1.50000	+	2.59808i	0.0503651	+	0.0872349i	−0.839744	+	0.542983i	$0.817295\pi$
$888$		0			0
$889$		0			0
$890$	24.0000			0.804482
$891$	36.0000			1.20605
$892$	16.0000			0.535720
$893$	4.00000	−	6.92820i	0.133855	−	0.231843i
$894$	24.0000	−	13.8564i	0.802680	−	0.463428i
$895$	−5.50000	−	9.52628i	−0.183845	−	0.318428i
$896$		0			0
$897$		−	5.19615i		−	0.173494i
$898$	34.0000	−	58.8897i	1.13459	−	1.96518i
$899$	60.0000			2.00111
$900$	3.00000	−	5.19615i	0.100000	−	0.173205i
$901$	−35.0000			−1.16602
$902$	8.00000	−	13.8564i	0.266371	−	0.461368i
$903$		0			0
$904$		0			0
$905$	11.5000	+	19.9186i	0.382273	+	0.662116i
$906$	42.0000	+	24.2487i	1.39536	+	0.805609i
$907$	25.5000	−	44.1673i	0.846714	−	1.46655i	−0.0374111	−	0.999300i	$-0.511911\pi$
$907$	25.5000	−	44.1673i	0.846714	−	1.46655i	0.884125	−	0.467251i	$-0.154756\pi$
$908$	−20.0000			−0.663723
$909$	−4.50000	−	7.79423i	−0.149256	−	0.258518i
$910$		0			0
$911$	8.50000	−	14.7224i	0.281618	−	0.487776i	−0.690166	−	0.723651i	$-0.742462\pi$
$911$	8.50000	−	14.7224i	0.281618	−	0.487776i	0.971783	+	0.235875i	$0.0757957\pi$
$912$			27.7128i			0.917663i
$913$	−12.0000	−	20.7846i	−0.397142	−	0.687870i
$914$	22.0000	+	38.1051i	0.727695	+	1.26041i
$915$	−7.50000	+	4.33013i	−0.247942	+	0.143150i
$916$	−18.0000	+	31.1769i	−0.594737	+	1.03011i
$917$		0			0
$918$	63.0000	+	36.3731i	2.07931	+	1.20049i
$919$	−29.0000			−0.956622			−0.478311	−	0.878191i	$-0.658751\pi$
$919$	−29.0000			−0.956622			−0.478311	+	0.878191i	$0.658751\pi$
$920$		0			0
$921$	−15.0000	+	8.66025i	−0.494267	+	0.285365i
$922$	−24.0000	−	41.5692i	−0.790398	−	1.36901i
$923$	4.00000	+	6.92820i	0.131662	+	0.228045i
$924$		0			0
$925$	5.00000	−	8.66025i	0.164399	−	0.284747i
$926$	−24.0000			−0.788689
$927$	−24.0000			−0.788263
$928$	−80.0000			−2.62613
$929$	−10.0000	+	17.3205i	−0.328089	+	0.568267i	−0.982133	−	0.188190i	$-0.939738\pi$
$929$	−10.0000	+	17.3205i	−0.328089	+	0.568267i	0.654043	+	0.756457i	$0.273071\pi$
$930$	−18.0000	−	10.3923i	−0.590243	−	0.340777i
$931$	14.0000	+	24.2487i	0.458831	+	0.794719i
$932$	27.0000	+	46.7654i	0.884414	+	1.53185i
$933$	−18.0000	−	10.3923i	−0.589294	−	0.340229i
$934$	35.0000	−	60.6218i	1.14523	−	1.98361i
$935$	−28.0000			−0.915698
$936$		0			0
$937$	3.00000			0.0980057			0.0490029	−	0.998799i	$-0.484396\pi$
$937$	3.00000			0.0980057			0.0490029	+	0.998799i	$0.484396\pi$
$938$		0			0
$939$			38.1051i			1.24351i
$940$	−2.00000	−	3.46410i	−0.0652328	−	0.112987i
$941$	11.0000	+	19.0526i	0.358590	+	0.621096i	0.987725	−	0.156200i	$-0.0499244\pi$
$941$	11.0000	+	19.0526i	0.358590	+	0.621096i	−0.629136	+	0.777295i	$0.716591\pi$
$942$	51.0000	−	29.4449i	1.66167	−	0.959366i
$943$	3.00000	−	5.19615i	0.0976934	−	0.169210i
$944$	−40.0000			−1.30189
$945$		0			0
$946$	−8.00000			−0.260102
$947$	−18.0000	+	31.1769i	−0.584921	+	1.01311i	0.409964	+	0.912102i	$0.365541\pi$
$947$	−18.0000	+	31.1769i	−0.584921	+	1.01311i	−0.994885	+	0.101012i	$0.967792\pi$
$948$	−27.0000	+	15.5885i	−0.876919	+	0.506290i
$949$	−7.00000	−	12.1244i	−0.227230	−	0.393573i
$950$	4.00000	+	6.92820i	0.129777	+	0.224781i
$951$			17.3205i			0.561656i
$952$		0			0
$953$	34.0000			1.10137			0.550684	−	0.834714i	$-0.314367\pi$
$953$	34.0000			1.10137			0.550684	+	0.834714i	$0.314367\pi$
$954$	15.0000	+	25.9808i	0.485643	+	0.841158i
$955$	13.0000			0.420670
$956$	20.0000	−	34.6410i	0.646846	−	1.12037i
$957$	−60.0000	−	34.6410i	−1.93952	−	1.11979i
$958$	18.0000	+	31.1769i	0.581554	+	1.00728i
$959$		0			0
$960$	12.0000	+	6.92820i	0.387298	+	0.223607i
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$	−20.0000			−0.644826
$963$	−13.5000	+	23.3827i	−0.435031	+	0.753497i
$964$	−16.0000			−0.515325
$965$	−8.00000	+	13.8564i	−0.257529	+	0.446054i
$966$		0			0
$967$	−1.00000	−	1.73205i	−0.0321578	−	0.0556990i	0.849499	−	0.527591i	$-0.176905\pi$
$967$	−1.00000	−	1.73205i	−0.0321578	−	0.0556990i	−0.881656	+	0.471892i	$0.843571\pi$
$968$		0			0
$969$	−42.0000	+	24.2487i	−1.34923	+	0.778981i
$970$	−8.00000	+	13.8564i	−0.256865	+	0.444902i
$971$	48.0000			1.54039			0.770197	−	0.637806i	$-0.220158\pi$
$971$	48.0000			1.54039			0.770197	+	0.637806i	$0.220158\pi$
$972$		−	31.1769i		−	1.00000i
$973$		0			0
$974$	8.00000	−	13.8564i	0.256337	−	0.443988i
$975$	1.50000	−	0.866025i	0.0480384	−	0.0277350i
$976$	−10.0000	−	17.3205i	−0.320092	−	0.554416i
$977$	−11.0000	−	19.0526i	−0.351921	−	0.609545i	0.634665	−	0.772787i	$-0.281138\pi$
$977$	−11.0000	−	19.0526i	−0.351921	−	0.609545i	−0.986586	+	0.163242i	$0.947805\pi$
$978$		−	76.2102i		−	2.43693i
$979$	−24.0000	+	41.5692i	−0.767043	+	1.32856i
$980$	14.0000			0.447214
$981$	−24.0000	+	41.5692i	−0.766261	+	1.32720i
$982$	−40.0000			−1.27645
$983$	15.0000	−	25.9808i	0.478426	−	0.828658i	−0.521268	−	0.853393i	$-0.674541\pi$
$983$	15.0000	−	25.9808i	0.478426	−	0.828658i	0.999694	+	0.0247352i	$0.00787426\pi$
$984$		0			0
$985$	−3.00000	−	5.19615i	−0.0955879	−	0.165563i
$986$	−70.0000	−	121.244i	−2.22925	−	3.86118i
$987$		0			0
$988$	4.00000	−	6.92820i	0.127257	−	0.220416i
$989$	−3.00000			−0.0953945
$990$	12.0000	+	20.7846i	0.381385	+	0.660578i
$991$	−31.0000			−0.984747			−0.492374	−	0.870384i	$-0.663871\pi$
$991$	−31.0000			−0.984747			−0.492374	+	0.870384i	$0.663871\pi$
$992$	24.0000	−	41.5692i	0.762001	−	1.31982i
$993$		−	31.1769i		−	0.989369i
$994$		0			0
$995$	−5.50000	−	9.52628i	−0.174362	−	0.302003i
$996$	−18.0000	+	10.3923i	−0.570352	+	0.329293i
$997$	−13.5000	+	23.3827i	−0.427549	+	0.740537i	−0.996655	−	0.0817275i	$-0.973956\pi$
$997$	−13.5000	+	23.3827i	−0.427549	+	0.740537i	0.569105	+	0.822265i	$0.307290\pi$
$998$	64.0000			2.02588
$999$		−	51.9615i		−	1.64399i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.i.d.196.1	✓	2
3.2	odd	2		1755.2.i.a.586.1		2
9.2	odd	6		5265.2.a.p.1.1		1
9.4	even	3	inner	585.2.i.d.391.1	yes	2
9.5	odd	6		1755.2.i.a.1171.1		2
9.7	even	3		5265.2.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.i.d.196.1	✓	2	1.1	even	1	trivial
585.2.i.d.391.1	yes	2	9.4	even	3	inner
1755.2.i.a.586.1		2	3.2	odd	2
1755.2.i.a.1171.1		2	9.5	odd	6
5265.2.a.a.1.1		1	9.7	even	3
5265.2.a.p.1.1		1	9.2	odd	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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.46410i q^{6} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +3.46410i q^{6} +(1.50000 - 2.59808i) q^{9} +2.00000 q^{10} +(-2.00000 + 3.46410i) q^{11} +(3.00000 + 1.73205i) q^{12} +(0.500000 + 0.866025i) q^{13} +(-1.50000 - 0.866025i) q^{15} +(2.00000 - 3.46410i) q^{16} +7.00000 q^{17} +(-3.00000 - 5.19615i) q^{18} +4.00000 q^{19} +(1.00000 - 1.73205i) q^{20} +(4.00000 + 6.92820i) q^{22} +(1.50000 + 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} +2.00000 q^{26} +5.19615i q^{27} +(5.00000 - 8.66025i) q^{29} +(-3.00000 + 1.73205i) q^{30} +(3.00000 + 5.19615i) q^{31} +(-4.00000 - 6.92820i) q^{32} -6.92820i q^{33} +(7.00000 - 12.1244i) q^{34} -6.00000 q^{36} -10.0000 q^{37} +(4.00000 - 6.92820i) q^{38} +(-1.50000 - 0.866025i) q^{39} +(-1.00000 - 1.73205i) q^{41} +(-0.500000 + 0.866025i) q^{43} +8.00000 q^{44} +3.00000 q^{45} +6.00000 q^{46} +(1.00000 - 1.73205i) q^{47} +6.92820i q^{48} +(3.50000 + 6.06218i) q^{49} +(1.00000 + 1.73205i) q^{50} +(-10.5000 + 6.06218i) q^{51} +(1.00000 - 1.73205i) q^{52} -5.00000 q^{53} +(9.00000 + 5.19615i) q^{54} -4.00000 q^{55} +(-6.00000 + 3.46410i) q^{57} +(-10.0000 - 17.3205i) q^{58} +(-5.00000 - 8.66025i) q^{59} +3.46410i q^{60} +(2.50000 - 4.33013i) q^{61} +12.0000 q^{62} -8.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(-12.0000 - 6.92820i) q^{66} +(6.00000 + 10.3923i) q^{67} +(-7.00000 - 12.1244i) q^{68} +(-4.50000 - 2.59808i) q^{69} +8.00000 q^{71} -14.0000 q^{73} +(-10.0000 + 17.3205i) q^{74} -1.73205i q^{75} +(-4.00000 - 6.92820i) q^{76} +(-3.00000 + 1.73205i) q^{78} +(-4.50000 + 7.79423i) q^{79} +4.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} -4.00000 q^{82} +(-3.00000 + 5.19615i) q^{83} +(3.50000 + 6.06218i) q^{85} +(1.00000 + 1.73205i) q^{86} +17.3205i q^{87} +12.0000 q^{89} +(3.00000 - 5.19615i) q^{90} +(3.00000 - 5.19615i) q^{92} +(-9.00000 - 5.19615i) q^{93} +(-2.00000 - 3.46410i) q^{94} +(2.00000 + 3.46410i) q^{95} +(12.0000 + 6.92820i) q^{96} +(-4.00000 + 6.92820i) q^{97} +14.0000 q^{98} +(6.00000 + 10.3923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{5} + 3 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 + q^5 + 3 * q^9	\( 2 q + 2 q^{2} - 3 q^{3} - 2 q^{4} + q^{5} + 3 q^{9} + 4 q^{10} - 4 q^{11} + 6 q^{12} + q^{13} - 3 q^{15} + 4 q^{16} + 14 q^{17} - 6 q^{18} + 8 q^{19} + 2 q^{20} + 8 q^{22} + 3 q^{23} - q^{25} + 4 q^{26} + 10 q^{29} - 6 q^{30} + 6 q^{31} - 8 q^{32} + 14 q^{34} - 12 q^{36} - 20 q^{37} + 8 q^{38} - 3 q^{39} - 2 q^{41} - q^{43} + 16 q^{44} + 6 q^{45} + 12 q^{46} + 2 q^{47} + 7 q^{49} + 2 q^{50} - 21 q^{51} + 2 q^{52} - 10 q^{53} + 18 q^{54} - 8 q^{55} - 12 q^{57} - 20 q^{58} - 10 q^{59} + 5 q^{61} + 24 q^{62} - 16 q^{64} - q^{65} - 24 q^{66} + 12 q^{67} - 14 q^{68} - 9 q^{69} + 16 q^{71} - 28 q^{73} - 20 q^{74} - 8 q^{76} - 6 q^{78} - 9 q^{79} + 8 q^{80} - 9 q^{81} - 8 q^{82} - 6 q^{83} + 7 q^{85} + 2 q^{86} + 24 q^{89} + 6 q^{90} + 6 q^{92} - 18 q^{93} - 4 q^{94} + 4 q^{95} + 24 q^{96} - 8 q^{97} + 28 q^{98} + 12 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 + q^5 + 3 * q^9 + 4 * q^10 - 4 * q^11 + 6 * q^12 + q^13 - 3 * q^15 + 4 * q^16 + 14 * q^17 - 6 * q^18 + 8 * q^19 + 2 * q^20 + 8 * q^22 + 3 * q^23 - q^25 + 4 * q^26 + 10 * q^29 - 6 * q^30 + 6 * q^31 - 8 * q^32 + 14 * q^34 - 12 * q^36 - 20 * q^37 + 8 * q^38 - 3 * q^39 - 2 * q^41 - q^43 + 16 * q^44 + 6 * q^45 + 12 * q^46 + 2 * q^47 + 7 * q^49 + 2 * q^50 - 21 * q^51 + 2 * q^52 - 10 * q^53 + 18 * q^54 - 8 * q^55 - 12 * q^57 - 20 * q^58 - 10 * q^59 + 5 * q^61 + 24 * q^62 - 16 * q^64 - q^65 - 24 * q^66 + 12 * q^67 - 14 * q^68 - 9 * q^69 + 16 * q^71 - 28 * q^73 - 20 * q^74 - 8 * q^76 - 6 * q^78 - 9 * q^79 + 8 * q^80 - 9 * q^81 - 8 * q^82 - 6 * q^83 + 7 * q^85 + 2 * q^86 + 24 * q^89 + 6 * q^90 + 6 * q^92 - 18 * q^93 - 4 * q^94 + 4 * q^95 + 24 * q^96 - 8 * q^97 + 28 * q^98 + 12 * q^99

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