LMFDB - Embedded newform 1950.2.z.g.1699.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(1699,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("1950.1699");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.z (of order $6$, 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:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1699.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1950.1699
Dual form			1950.2.z.g.1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(-1.73205 + 1.00000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(-1.73205 + 1.00000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-3.00000 + 5.19615i) q^{11} -1.00000i q^{12} +(0.866025 - 3.50000i) q^{13} +2.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.59808 - 1.50000i) q^{17} -1.00000i q^{18} +(1.00000 + 1.73205i) q^{19} +2.00000 q^{21} +(5.19615 - 3.00000i) q^{22} +(5.19615 + 3.00000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.50000 + 2.59808i) q^{26} -1.00000i q^{27} +(-1.73205 - 1.00000i) q^{28} +(1.50000 - 2.59808i) q^{29} -4.00000 q^{31} +(0.866025 - 0.500000i) q^{32} +(5.19615 - 3.00000i) q^{33} -3.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-6.06218 - 3.50000i) q^{37} -2.00000i q^{38} +(-2.50000 + 2.59808i) q^{39} +(1.50000 - 2.59808i) q^{41} +(-1.73205 - 1.00000i) q^{42} +(-8.66025 + 5.00000i) q^{43} -6.00000 q^{44} +(-3.00000 - 5.19615i) q^{46} -6.00000i q^{47} +(0.866025 - 0.500000i) q^{48} +(-1.50000 + 2.59808i) q^{49} -3.00000 q^{51} +(3.46410 - 1.00000i) q^{52} +3.00000i q^{53} +(-0.500000 + 0.866025i) q^{54} +(1.00000 + 1.73205i) q^{56} -2.00000i q^{57} +(-2.59808 + 1.50000i) q^{58} +(3.50000 + 6.06218i) q^{61} +(3.46410 + 2.00000i) q^{62} +(-1.73205 - 1.00000i) q^{63} -1.00000 q^{64} -6.00000 q^{66} +(-8.66025 - 5.00000i) q^{67} +(2.59808 + 1.50000i) q^{68} +(-3.00000 - 5.19615i) q^{69} +(-3.00000 - 5.19615i) q^{71} +(0.866025 - 0.500000i) q^{72} -13.0000i q^{73} +(3.50000 + 6.06218i) q^{74} +(-1.00000 + 1.73205i) q^{76} -12.0000i q^{77} +(3.46410 - 1.00000i) q^{78} +4.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-2.59808 + 1.50000i) q^{82} -6.00000i q^{83} +(1.00000 + 1.73205i) q^{84} +10.0000 q^{86} +(-2.59808 + 1.50000i) q^{87} +(5.19615 + 3.00000i) q^{88} +(9.00000 - 15.5885i) q^{89} +(2.00000 + 6.92820i) q^{91} +6.00000i q^{92} +(3.46410 + 2.00000i) q^{93} +(-3.00000 + 5.19615i) q^{94} -1.00000 q^{96} +(-12.1244 + 7.00000i) q^{97} +(2.59808 - 1.50000i) q^{98} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 2 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 2 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} + 2 q^{6} + 2 q^{9} - 12 q^{11} + 8 q^{14} - 2 q^{16} + 4 q^{19} + 8 q^{21} - 2 q^{24} - 10 q^{26} + 6 q^{29} - 16 q^{31} - 12 q^{34} - 2 q^{36} - 10 q^{39} + 6 q^{41} - 24 q^{44} - 12 q^{46} - 6 q^{49} - 12 q^{51} - 2 q^{54} + 4 q^{56} + 14 q^{61} - 4 q^{64} - 24 q^{66} - 12 q^{69} - 12 q^{71} + 14 q^{74} - 4 q^{76} + 16 q^{79} - 2 q^{81} + 4 q^{84} + 40 q^{86} + 36 q^{89} + 8 q^{91} - 12 q^{94} - 4 q^{96} - 24 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 + 2 * q^6 + 2 * q^9 - 12 * q^11 + 8 * q^14 - 2 * q^16 + 4 * q^19 + 8 * q^21 - 2 * q^24 - 10 * q^26 + 6 * q^29 - 16 * q^31 - 12 * q^34 - 2 * q^36 - 10 * q^39 + 6 * q^41 - 24 * q^44 - 12 * q^46 - 6 * q^49 - 12 * q^51 - 2 * q^54 + 4 * q^56 + 14 * q^61 - 4 * q^64 - 24 * q^66 - 12 * q^69 - 12 * q^71 + 14 * q^74 - 4 * q^76 + 16 * q^79 - 2 * q^81 + 4 * q^84 + 40 * q^86 + 36 * q^89 + 8 * q^91 - 12 * q^94 - 4 * q^96 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	−1.73205	+	1.00000i	−0.654654	+	0.377964i	−0.790237	−	0.612801i	$-0.790043\pi$
$7$	−1.73205	+	1.00000i	−0.654654	+	0.377964i	0.135583	+	0.990766i	$0.456709\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.0829925	+	0.996550i	$0.526448\pi$
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.821541	+	0.570149i	$0.806886\pi$
$12$		−	1.00000i		−	0.288675i
$13$	0.866025	−	3.50000i	0.240192	−	0.970725i
$13$	0.866025	−	3.50000i	0.240192	−	0.970725i
$14$	2.00000			0.534522
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.59808	−	1.50000i	0.630126	−	0.363803i	−0.150675	−	0.988583i	$-0.548145\pi$
$17$	2.59808	−	1.50000i	0.630126	−	0.363803i	0.780801	+	0.624780i	$0.214811\pi$
$18$		−	1.00000i		−	0.235702i
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$		0			0
$21$	2.00000			0.436436
$22$	5.19615	−	3.00000i	1.10782	−	0.639602i
$23$	5.19615	+	3.00000i	1.08347	+	0.625543i	0.931831	−	0.362892i	$-0.118211\pi$
$23$	5.19615	+	3.00000i	1.08347	+	0.625543i	0.151642	+	0.988436i	$0.451544\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$		0			0
$26$	−2.50000	+	2.59808i	−0.490290	+	0.509525i
$27$		−	1.00000i		−	0.192450i
$28$	−1.73205	−	1.00000i	−0.327327	−	0.188982i
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	−0.692480	−	0.721437i	$-0.743482\pi$
$29$	1.50000	−	2.59808i	0.278543	−	0.482451i	0.971023	+	0.238987i	$0.0768152\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	5.19615	−	3.00000i	0.904534	−	0.522233i
$34$	−3.00000			−0.514496
$35$		0			0
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−6.06218	−	3.50000i	−0.996616	−	0.575396i	−0.0893706	−	0.995998i	$-0.528486\pi$
$37$	−6.06218	−	3.50000i	−0.996616	−	0.575396i	−0.907245	+	0.420602i	$0.861819\pi$
$38$		−	2.00000i		−	0.324443i
$39$	−2.50000	+	2.59808i	−0.400320	+	0.416025i
$40$		0			0
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	−0.724797	−	0.688963i	$-0.758066\pi$
$41$	1.50000	−	2.59808i	0.234261	−	0.405751i	0.959058	+	0.283211i	$0.0913998\pi$
$42$	−1.73205	−	1.00000i	−0.267261	−	0.154303i
$43$	−8.66025	+	5.00000i	−1.32068	+	0.762493i	−0.983836	−	0.179069i	$-0.942691\pi$
$43$	−8.66025	+	5.00000i	−1.32068	+	0.762493i	−0.336840	+	0.941562i	$0.609358\pi$
$44$	−6.00000			−0.904534
$45$		0			0
$46$	−3.00000	−	5.19615i	−0.442326	−	0.766131i
$47$		−	6.00000i		−	0.875190i	−0.899172	−	0.437595i	$-0.855830\pi$
$47$		−	6.00000i		−	0.875190i	0.899172	−	0.437595i	$-0.144170\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	−1.50000	+	2.59808i	−0.214286	+	0.371154i
$50$		0			0
$51$	−3.00000			−0.420084
$52$	3.46410	−	1.00000i	0.480384	−	0.138675i
$53$			3.00000i			0.412082i	0.978543	+	0.206041i	$0.0660580\pi$
$53$			3.00000i			0.412082i	−0.978543	+	0.206041i	$0.933942\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$		0			0
$56$	1.00000	+	1.73205i	0.133631	+	0.231455i
$57$		−	2.00000i		−	0.264906i
$58$	−2.59808	+	1.50000i	−0.341144	+	0.196960i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	0.998264	−	0.0588933i	$-0.0187572\pi$
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	−0.550135	+	0.835076i	$0.685424\pi$
$62$	3.46410	+	2.00000i	0.439941	+	0.254000i
$63$	−1.73205	−	1.00000i	−0.218218	−	0.125988i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−6.00000			−0.738549
$67$	−8.66025	−	5.00000i	−1.05802	−	0.610847i	−0.133135	−	0.991098i	$-0.542504\pi$
$67$	−8.66025	−	5.00000i	−1.05802	−	0.610847i	−0.924883	+	0.380251i	$0.875838\pi$
$68$	2.59808	+	1.50000i	0.315063	+	0.181902i
$69$	−3.00000	−	5.19615i	−0.361158	−	0.625543i
$70$		0			0
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	0.631260	−	0.775571i	$-0.282538\pi$
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	−0.987294	+	0.158901i	$0.949205\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$		−	13.0000i		−	1.52153i	−0.649025	−	0.760767i	$-0.724823\pi$
$73$		−	13.0000i		−	1.52153i	0.649025	−	0.760767i	$-0.275177\pi$
$74$	3.50000	+	6.06218i	0.406867	+	0.704714i
$75$		0			0
$76$	−1.00000	+	1.73205i	−0.114708	+	0.198680i
$77$		−	12.0000i		−	1.36753i
$78$	3.46410	−	1.00000i	0.392232	−	0.113228i
$79$	4.00000			0.450035			0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000			0.450035			0.225018	+	0.974355i	$0.427756\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.59808	+	1.50000i	−0.286910	+	0.165647i
$83$		−	6.00000i		−	0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$		−	6.00000i		−	0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$	1.00000	+	1.73205i	0.109109	+	0.188982i
$85$		0			0
$86$	10.0000			1.07833
$87$	−2.59808	+	1.50000i	−0.278543	+	0.160817i
$88$	5.19615	+	3.00000i	0.553912	+	0.319801i
$89$	9.00000	−	15.5885i	0.953998	−	1.65237i	0.217354	−	0.976093i	$-0.430258\pi$
$89$	9.00000	−	15.5885i	0.953998	−	1.65237i	0.736644	−	0.676280i	$-0.236409\pi$
$90$		0			0
$91$	2.00000	+	6.92820i	0.209657	+	0.726273i
$92$			6.00000i			0.625543i
$93$	3.46410	+	2.00000i	0.359211	+	0.207390i
$94$	−3.00000	+	5.19615i	−0.309426	+	0.535942i
$95$		0			0
$96$	−1.00000			−0.102062
$97$	−12.1244	+	7.00000i	−1.23104	+	0.710742i	−0.967247	−	0.253837i	$-0.918307\pi$
$97$	−12.1244	+	7.00000i	−1.23104	+	0.710742i	−0.263795	+	0.964579i	$0.584974\pi$
$98$	2.59808	−	1.50000i	0.262445	−	0.151523i
$99$	−6.00000			−0.603023
$100$		0			0
$101$	−7.50000	+	12.9904i	−0.746278	+	1.29259i	0.203317	+	0.979113i	$0.434828\pi$
$101$	−7.50000	+	12.9904i	−0.746278	+	1.29259i	−0.949595	+	0.313478i	$0.898506\pi$
$102$	2.59808	+	1.50000i	0.257248	+	0.148522i
$103$			14.0000i			1.37946i	0.724066	+	0.689730i	$0.242271\pi$
$103$			14.0000i			1.37946i	−0.724066	+	0.689730i	$0.757729\pi$
$104$	−3.50000	−	0.866025i	−0.343203	−	0.0849208i
$105$		0			0
$106$	1.50000	−	2.59808i	0.145693	−	0.252347i
$107$	−5.19615	−	3.00000i	−0.502331	−	0.290021i	0.227345	−	0.973814i	$-0.426996\pi$
$107$	−5.19615	−	3.00000i	−0.502331	−	0.290021i	−0.729676	+	0.683793i	$0.760329\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	−14.0000			−1.34096			−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000			−1.34096			−0.670478	+	0.741929i	$0.733911\pi$
$110$		0			0
$111$	3.50000	+	6.06218i	0.332205	+	0.575396i
$112$		−	2.00000i		−	0.188982i
$113$	−2.59808	+	1.50000i	−0.244406	+	0.141108i	−0.617200	−	0.786806i	$-0.711733\pi$
$113$	−2.59808	+	1.50000i	−0.244406	+	0.141108i	0.372794	+	0.927914i	$0.378400\pi$
$114$	−1.00000	+	1.73205i	−0.0936586	+	0.162221i
$115$		0			0
$116$	3.00000			0.278543
$117$	3.46410	−	1.00000i	0.320256	−	0.0924500i
$118$		0			0
$119$	−3.00000	+	5.19615i	−0.275010	+	0.476331i
$120$		0			0
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$		−	7.00000i		−	0.633750i
$123$	−2.59808	+	1.50000i	−0.234261	+	0.135250i
$124$	−2.00000	−	3.46410i	−0.179605	−	0.311086i
$125$		0			0
$126$	1.00000	+	1.73205i	0.0890871	+	0.154303i
$127$	−3.46410	−	2.00000i	−0.307389	−	0.177471i	0.338368	−	0.941014i	$-0.390125\pi$
$127$	−3.46410	−	2.00000i	−0.307389	−	0.177471i	−0.645758	+	0.763542i	$0.723458\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	10.0000			0.880451
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	5.19615	+	3.00000i	0.452267	+	0.261116i
$133$	−3.46410	−	2.00000i	−0.300376	−	0.173422i
$134$	5.00000	+	8.66025i	0.431934	+	0.748132i
$135$		0			0
$136$	−1.50000	−	2.59808i	−0.128624	−	0.222783i
$137$	−7.79423	+	4.50000i	−0.665906	+	0.384461i	−0.794524	−	0.607233i	$-0.792279\pi$
$137$	−7.79423	+	4.50000i	−0.665906	+	0.384461i	0.128618	+	0.991694i	$0.458946\pi$
$138$			6.00000i			0.510754i
$139$	−2.00000	−	3.46410i	−0.169638	−	0.293821i	0.768655	−	0.639664i	$-0.220926\pi$
$139$	−2.00000	−	3.46410i	−0.169638	−	0.293821i	−0.938293	+	0.345843i	$0.887593\pi$
$140$		0			0
$141$	−3.00000	+	5.19615i	−0.252646	+	0.437595i
$142$			6.00000i			0.503509i
$143$	15.5885	+	15.0000i	1.30357	+	1.25436i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	−6.50000	+	11.2583i	−0.537944	+	0.931746i
$147$	2.59808	−	1.50000i	0.214286	−	0.123718i
$148$		−	7.00000i		−	0.575396i
$149$	−4.50000	−	7.79423i	−0.368654	−	0.638528i	0.620701	−	0.784047i	$-0.286848\pi$
$149$	−4.50000	−	7.79423i	−0.368654	−	0.638528i	−0.989355	+	0.145519i	$0.953515\pi$
$150$		0			0
$151$	−10.0000			−0.813788			−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000			−0.813788			−0.406894	+	0.913475i	$0.633388\pi$
$152$	1.73205	−	1.00000i	0.140488	−	0.0811107i
$153$	2.59808	+	1.50000i	0.210042	+	0.121268i
$154$	−6.00000	+	10.3923i	−0.483494	+	0.837436i
$155$		0			0
$156$	−3.50000	−	0.866025i	−0.280224	−	0.0693375i
$157$		−	5.00000i		−	0.399043i	−0.979893	−	0.199522i	$-0.936061\pi$
$157$		−	5.00000i		−	0.399043i	0.979893	−	0.199522i	$-0.0639388\pi$
$158$	−3.46410	−	2.00000i	−0.275589	−	0.159111i
$159$	1.50000	−	2.59808i	0.118958	−	0.206041i
$160$		0			0
$161$	−12.0000			−0.945732
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	−3.46410	+	2.00000i	−0.271329	+	0.156652i	−0.629492	−	0.777007i	$-0.716737\pi$
$163$	−3.46410	+	2.00000i	−0.271329	+	0.156652i	0.358162	+	0.933659i	$0.383403\pi$
$164$	3.00000			0.234261
$165$		0			0
$166$	−3.00000	+	5.19615i	−0.232845	+	0.403300i
$167$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$167$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$168$		−	2.00000i		−	0.154303i
$169$	−11.5000	−	6.06218i	−0.884615	−	0.466321i
$170$		0			0
$171$	−1.00000	+	1.73205i	−0.0764719	+	0.132453i
$172$	−8.66025	−	5.00000i	−0.660338	−	0.381246i
$173$	−5.19615	+	3.00000i	−0.395056	+	0.228086i	−0.684349	−	0.729155i	$-0.739913\pi$
$173$	−5.19615	+	3.00000i	−0.395056	+	0.228086i	0.289292	+	0.957241i	$0.406580\pi$
$174$	3.00000			0.227429
$175$		0			0
$176$	−3.00000	−	5.19615i	−0.226134	−	0.391675i
$177$		0			0
$178$	−15.5885	+	9.00000i	−1.16840	+	0.674579i
$179$	3.00000	−	5.19615i	0.224231	−	0.388379i	−0.731858	−	0.681457i	$-0.761346\pi$
$179$	3.00000	−	5.19615i	0.224231	−	0.388379i	0.956088	+	0.293079i	$0.0946798\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$	1.73205	−	7.00000i	0.128388	−	0.518875i
$183$		−	7.00000i		−	0.517455i
$184$	3.00000	−	5.19615i	0.221163	−	0.383065i
$185$		0			0
$186$	−2.00000	−	3.46410i	−0.146647	−	0.254000i
$187$			18.0000i			1.31629i
$188$	5.19615	−	3.00000i	0.378968	−	0.218797i
$189$	1.00000	+	1.73205i	0.0727393	+	0.125988i
$190$		0			0
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	0.997225	−	0.0744412i	$-0.0237173\pi$
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	−0.563081	+	0.826402i	$0.690384\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	−19.9186	−	11.5000i	−1.43377	−	0.827788i	−0.436365	−	0.899770i	$-0.643734\pi$
$193$	−19.9186	−	11.5000i	−1.43377	−	0.827788i	−0.997406	+	0.0719816i	$0.977068\pi$
$194$	14.0000			1.00514
$195$		0			0
$196$	−3.00000			−0.214286
$197$	5.19615	+	3.00000i	0.370211	+	0.213741i	0.673550	−	0.739141i	$-0.264768\pi$
$197$	5.19615	+	3.00000i	0.370211	+	0.213741i	−0.303340	+	0.952882i	$0.598102\pi$
$198$	5.19615	+	3.00000i	0.369274	+	0.213201i
$199$	−5.00000	−	8.66025i	−0.354441	−	0.613909i	0.632581	−	0.774494i	$-0.281995\pi$
$199$	−5.00000	−	8.66025i	−0.354441	−	0.613909i	−0.987022	+	0.160585i	$0.948662\pi$
$200$		0			0
$201$	5.00000	+	8.66025i	0.352673	+	0.610847i
$202$	12.9904	−	7.50000i	0.914000	−	0.527698i
$203$			6.00000i			0.421117i
$204$	−1.50000	−	2.59808i	−0.105021	−	0.181902i
$205$		0			0
$206$	7.00000	−	12.1244i	0.487713	−	0.844744i
$207$			6.00000i			0.417029i
$208$	2.59808	+	2.50000i	0.180144	+	0.173344i
$209$	−12.0000			−0.830057
$210$		0			0
$211$	8.00000	−	13.8564i	0.550743	−	0.953914i	−0.447478	−	0.894295i	$-0.647678\pi$
$211$	8.00000	−	13.8564i	0.550743	−	0.953914i	0.998221	−	0.0596196i	$-0.0189888\pi$
$212$	−2.59808	+	1.50000i	−0.178437	+	0.103020i
$213$			6.00000i			0.411113i
$214$	3.00000	+	5.19615i	0.205076	+	0.355202i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	6.92820	−	4.00000i	0.470317	−	0.271538i
$218$	12.1244	+	7.00000i	0.821165	+	0.474100i
$219$	−6.50000	+	11.2583i	−0.439229	+	0.760767i
$220$		0			0
$221$	−3.00000	−	10.3923i	−0.201802	−	0.699062i
$222$		−	7.00000i		−	0.469809i
$223$	−6.92820	−	4.00000i	−0.463947	−	0.267860i	0.249756	−	0.968309i	$-0.419650\pi$
$223$	−6.92820	−	4.00000i	−0.463947	−	0.267860i	−0.713702	+	0.700449i	$0.752983\pi$
$224$	−1.00000	+	1.73205i	−0.0668153	+	0.115728i
$225$		0			0
$226$	3.00000			0.199557
$227$	−15.5885	+	9.00000i	−1.03464	+	0.597351i	−0.918311	−	0.395860i	$-0.870447\pi$
$227$	−15.5885	+	9.00000i	−1.03464	+	0.597351i	−0.116331	+	0.993210i	$0.537113\pi$
$228$	1.73205	−	1.00000i	0.114708	−	0.0662266i
$229$	22.0000			1.45380			0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000			1.45380			0.726900	+	0.686743i	$0.240960\pi$
$230$		0			0
$231$	−6.00000	+	10.3923i	−0.394771	+	0.683763i
$232$	−2.59808	−	1.50000i	−0.170572	−	0.0984798i
$233$		−	6.00000i		−	0.393073i	−0.980497	−	0.196537i	$-0.937031\pi$
$233$		−	6.00000i		−	0.393073i	0.980497	−	0.196537i	$-0.0629694\pi$
$234$	−3.50000	−	0.866025i	−0.228802	−	0.0566139i
$235$		0			0
$236$		0			0
$237$	−3.46410	−	2.00000i	−0.225018	−	0.129914i
$238$	5.19615	−	3.00000i	0.336817	−	0.194461i
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$		0			0
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	0.881680	−	0.471848i	$-0.156413\pi$
$241$	0.500000	+	0.866025i	0.0322078	+	0.0557856i	−0.849472	+	0.527633i	$0.823079\pi$
$242$			25.0000i			1.60706i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−3.50000	+	6.06218i	−0.224065	+	0.388091i
$245$		0			0
$246$	3.00000			0.191273
$247$	6.92820	−	2.00000i	0.440831	−	0.127257i
$248$			4.00000i			0.254000i
$249$	−3.00000	+	5.19615i	−0.190117	+	0.329293i
$250$		0			0
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	0.990876	−	0.134778i	$-0.0430322\pi$
$251$	6.00000	+	10.3923i	0.378717	+	0.655956i	−0.612159	+	0.790735i	$0.709699\pi$
$252$		−	2.00000i		−	0.125988i
$253$	−31.1769	+	18.0000i	−1.96008	+	1.13165i
$254$	2.00000	+	3.46410i	0.125491	+	0.217357i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.59808	−	1.50000i	−0.162064	−	0.0935674i	0.416775	−	0.909010i	$-0.363160\pi$
$257$	−2.59808	−	1.50000i	−0.162064	−	0.0935674i	−0.578838	+	0.815442i	$0.696494\pi$
$258$	−8.66025	−	5.00000i	−0.539164	−	0.311286i
$259$	14.0000			0.869918
$260$		0			0
$261$	3.00000			0.185695
$262$		0			0
$263$	5.19615	+	3.00000i	0.320408	+	0.184988i	0.651575	−	0.758585i	$-0.274109\pi$
$263$	5.19615	+	3.00000i	0.320408	+	0.184988i	−0.331166	+	0.943572i	$0.607442\pi$
$264$	−3.00000	−	5.19615i	−0.184637	−	0.319801i
$265$		0			0
$266$	2.00000	+	3.46410i	0.122628	+	0.212398i
$267$	−15.5885	+	9.00000i	−0.953998	+	0.550791i
$268$		−	10.0000i		−	0.610847i
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	0.998361	+	0.0572259i	$0.0182255\pi$
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	−0.449622	+	0.893219i	$0.648441\pi$
$270$		0			0
$271$	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	$0.00513477\pi$
$272$			3.00000i			0.181902i
$273$	1.73205	−	7.00000i	0.104828	−	0.423659i
$274$	9.00000			0.543710
$275$		0			0
$276$	3.00000	−	5.19615i	0.180579	−	0.312772i
$277$	−14.7224	+	8.50000i	−0.884585	+	0.510716i	−0.872167	−	0.489207i	$-0.837286\pi$
$277$	−14.7224	+	8.50000i	−0.884585	+	0.510716i	−0.0124177	+	0.999923i	$0.503953\pi$
$278$			4.00000i			0.239904i
$279$	−2.00000	−	3.46410i	−0.119737	−	0.207390i
$280$		0			0
$281$	9.00000			0.536895			0.268447	−	0.963294i	$-0.413489\pi$
$281$	9.00000			0.536895			0.268447	+	0.963294i	$0.413489\pi$
$282$	5.19615	−	3.00000i	0.309426	−	0.178647i
$283$	−12.1244	−	7.00000i	−0.720718	−	0.416107i	0.0942988	−	0.995544i	$-0.469939\pi$
$283$	−12.1244	−	7.00000i	−0.720718	−	0.416107i	−0.815017	+	0.579437i	$0.803272\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$		0			0
$286$	−6.00000	−	20.7846i	−0.354787	−	1.22902i
$287$			6.00000i			0.354169i
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$		0			0
$291$	14.0000			0.820695
$292$	11.2583	−	6.50000i	0.658844	−	0.380384i
$293$	−18.1865	+	10.5000i	−1.06247	+	0.613417i	−0.926114	−	0.377244i	$-0.876872\pi$
$293$	−18.1865	+	10.5000i	−1.06247	+	0.613417i	−0.136355	+	0.990660i	$0.543539\pi$
$294$	−3.00000			−0.174964
$295$		0			0
$296$	−3.50000	+	6.06218i	−0.203433	+	0.352357i
$297$	5.19615	+	3.00000i	0.301511	+	0.174078i
$298$			9.00000i			0.521356i
$299$	15.0000	−	15.5885i	0.867472	−	0.901504i
$300$		0			0
$301$	10.0000	−	17.3205i	0.576390	−	0.998337i
$302$	8.66025	+	5.00000i	0.498342	+	0.287718i
$303$	12.9904	−	7.50000i	0.746278	−	0.430864i
$304$	−2.00000			−0.114708
$305$		0			0
$306$	−1.50000	−	2.59808i	−0.0857493	−	0.148522i
$307$			10.0000i			0.570730i	0.958419	+	0.285365i	$0.0921148\pi$
$307$			10.0000i			0.570730i	−0.958419	+	0.285365i	$0.907885\pi$
$308$	10.3923	−	6.00000i	0.592157	−	0.341882i
$309$	7.00000	−	12.1244i	0.398216	−	0.689730i
$310$		0			0
$311$	−30.0000			−1.70114			−0.850572	−	0.525859i	$-0.823744\pi$
$311$	−30.0000			−1.70114			−0.850572	+	0.525859i	$0.823744\pi$
$312$	2.59808	+	2.50000i	0.147087	+	0.141535i
$313$		−	10.0000i		−	0.565233i	−0.959233	−	0.282617i	$-0.908798\pi$
$313$		−	10.0000i		−	0.565233i	0.959233	−	0.282617i	$-0.0912024\pi$
$314$	−2.50000	+	4.33013i	−0.141083	+	0.244363i
$315$		0			0
$316$	2.00000	+	3.46410i	0.112509	+	0.194871i
$317$		−	3.00000i		−	0.168497i	−0.996445	−	0.0842484i	$-0.973151\pi$
$317$		−	3.00000i		−	0.168497i	0.996445	−	0.0842484i	$-0.0268489\pi$
$318$	−2.59808	+	1.50000i	−0.145693	+	0.0841158i
$319$	9.00000	+	15.5885i	0.503903	+	0.872786i
$320$		0			0
$321$	3.00000	+	5.19615i	0.167444	+	0.290021i
$322$	10.3923	+	6.00000i	0.579141	+	0.334367i
$323$	5.19615	+	3.00000i	0.289122	+	0.166924i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	4.00000			0.221540
$327$	12.1244	+	7.00000i	0.670478	+	0.387101i
$328$	−2.59808	−	1.50000i	−0.143455	−	0.0828236i
$329$	6.00000	+	10.3923i	0.330791	+	0.572946i
$330$		0			0
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	0.915742	−	0.401768i	$-0.131604\pi$
$331$	2.00000	+	3.46410i	0.109930	+	0.190404i	−0.805812	+	0.592172i	$0.798271\pi$
$332$	5.19615	−	3.00000i	0.285176	−	0.164646i
$333$		−	7.00000i		−	0.383598i
$334$		0			0
$335$		0			0
$336$	−1.00000	+	1.73205i	−0.0545545	+	0.0944911i
$337$		−	23.0000i		−	1.25289i	−0.779466	−	0.626445i	$-0.784509\pi$
$337$		−	23.0000i		−	1.25289i	0.779466	−	0.626445i	$-0.215491\pi$
$338$	6.92820	+	11.0000i	0.376845	+	0.598321i
$339$	3.00000			0.162938
$340$		0			0
$341$	12.0000	−	20.7846i	0.649836	−	1.12555i
$342$	1.73205	−	1.00000i	0.0936586	−	0.0540738i
$343$		−	20.0000i		−	1.07990i
$344$	5.00000	+	8.66025i	0.269582	+	0.466930i
$345$		0			0
$346$	6.00000			0.322562
$347$	25.9808	−	15.0000i	1.39472	−	0.805242i	0.400887	−	0.916127i	$-0.368702\pi$
$347$	25.9808	−	15.0000i	1.39472	−	0.805242i	0.993833	+	0.110885i	$0.0353686\pi$
$348$	−2.59808	−	1.50000i	−0.139272	−	0.0804084i
$349$	−5.00000	+	8.66025i	−0.267644	+	0.463573i	−0.968253	−	0.249973i	$-0.919578\pi$
$349$	−5.00000	+	8.66025i	−0.267644	+	0.463573i	0.700609	+	0.713545i	$0.252912\pi$
$350$		0			0
$351$	−3.50000	−	0.866025i	−0.186816	−	0.0462250i
$352$			6.00000i			0.319801i
$353$	12.9904	+	7.50000i	0.691408	+	0.399185i	0.804139	−	0.594441i	$-0.202627\pi$
$353$	12.9904	+	7.50000i	0.691408	+	0.399185i	−0.112731	+	0.993626i	$0.535960\pi$
$354$		0			0
$355$		0			0
$356$	18.0000			0.953998
$357$	5.19615	−	3.00000i	0.275010	−	0.158777i
$358$	−5.19615	+	3.00000i	−0.274625	+	0.158555i
$359$	−6.00000			−0.316668			−0.158334	−	0.987386i	$-0.550612\pi$
$359$	−6.00000			−0.316668			−0.158334	+	0.987386i	$0.550612\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	6.06218	+	3.50000i	0.318621	+	0.183956i
$363$			25.0000i			1.31216i
$364$	−5.00000	+	5.19615i	−0.262071	+	0.272352i
$365$		0			0
$366$	−3.50000	+	6.06218i	−0.182948	+	0.316875i
$367$	1.73205	+	1.00000i	0.0904123	+	0.0521996i	0.544524	−	0.838745i	$-0.316710\pi$
$367$	1.73205	+	1.00000i	0.0904123	+	0.0521996i	−0.454112	+	0.890945i	$0.650043\pi$
$368$	−5.19615	+	3.00000i	−0.270868	+	0.156386i
$369$	3.00000			0.156174
$370$		0			0
$371$	−3.00000	−	5.19615i	−0.155752	−	0.269771i
$372$			4.00000i			0.207390i
$373$	25.1147	−	14.5000i	1.30039	−	0.750782i	0.319921	−	0.947444i	$-0.396344\pi$
$373$	25.1147	−	14.5000i	1.30039	−	0.750782i	0.980471	+	0.196663i	$0.0630104\pi$
$374$	9.00000	−	15.5885i	0.465379	−	0.806060i
$375$		0			0
$376$	−6.00000			−0.309426
$377$	−7.79423	−	7.50000i	−0.401423	−	0.386270i
$378$		−	2.00000i		−	0.102869i
$379$	10.0000	−	17.3205i	0.513665	−	0.889695i	−0.486209	−	0.873843i	$-0.661621\pi$
$379$	10.0000	−	17.3205i	0.513665	−	0.889695i	0.999874	−	0.0158521i	$-0.00504609\pi$
$380$		0			0
$381$	2.00000	+	3.46410i	0.102463	+	0.177471i
$382$		−	12.0000i		−	0.613973i
$383$	20.7846	−	12.0000i	1.06204	−	0.613171i	0.136047	−	0.990702i	$-0.456560\pi$
$383$	20.7846	−	12.0000i	1.06204	−	0.613171i	0.925997	+	0.377531i	$0.123227\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$		0			0
$386$	11.5000	+	19.9186i	0.585335	+	1.01383i
$387$	−8.66025	−	5.00000i	−0.440225	−	0.254164i
$388$	−12.1244	−	7.00000i	−0.615521	−	0.355371i
$389$	−39.0000			−1.97738			−0.988689	−	0.149979i	$-0.952080\pi$
$389$	−39.0000			−1.97738			−0.988689	+	0.149979i	$0.952080\pi$
$390$		0			0
$391$	18.0000			0.910299
$392$	2.59808	+	1.50000i	0.131223	+	0.0757614i
$393$		0			0
$394$	−3.00000	−	5.19615i	−0.151138	−	0.261778i
$395$		0			0
$396$	−3.00000	−	5.19615i	−0.150756	−	0.261116i
$397$	−12.1244	+	7.00000i	−0.608504	+	0.351320i	−0.772380	−	0.635161i	$-0.780934\pi$
$397$	−12.1244	+	7.00000i	−0.608504	+	0.351320i	0.163876	+	0.986481i	$0.447600\pi$
$398$			10.0000i			0.501255i
$399$	2.00000	+	3.46410i	0.100125	+	0.173422i
$400$		0			0
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	−0.826139	−	0.563466i	$-0.809468\pi$
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	0.901046	+	0.433724i	$0.142801\pi$
$402$		−	10.0000i		−	0.498755i
$403$	−3.46410	+	14.0000i	−0.172559	+	0.697390i
$404$	−15.0000			−0.746278
$405$		0			0
$406$	3.00000	−	5.19615i	0.148888	−	0.257881i
$407$	36.3731	−	21.0000i	1.80295	−	1.04093i
$408$			3.00000i			0.148522i
$409$	−0.500000	−	0.866025i	−0.0247234	−	0.0428222i	0.853399	−	0.521258i	$-0.174537\pi$
$409$	−0.500000	−	0.866025i	−0.0247234	−	0.0428222i	−0.878122	+	0.478436i	$0.841204\pi$
$410$		0			0
$411$	9.00000			0.443937
$412$	−12.1244	+	7.00000i	−0.597324	+	0.344865i
$413$		0			0
$414$	3.00000	−	5.19615i	0.147442	−	0.255377i
$415$		0			0
$416$	−1.00000	−	3.46410i	−0.0490290	−	0.169842i
$417$			4.00000i			0.195881i
$418$	10.3923	+	6.00000i	0.508304	+	0.293470i
$419$	12.0000	−	20.7846i	0.586238	−	1.01539i	−0.408481	−	0.912767i	$-0.633942\pi$
$419$	12.0000	−	20.7846i	0.586238	−	1.01539i	0.994720	−	0.102628i	$-0.0327251\pi$
$420$		0			0
$421$	29.0000			1.41337			0.706687	−	0.707527i	$-0.250189\pi$
$421$	29.0000			1.41337			0.706687	+	0.707527i	$0.250189\pi$
$422$	−13.8564	+	8.00000i	−0.674519	+	0.389434i
$423$	5.19615	−	3.00000i	0.252646	−	0.145865i
$424$	3.00000			0.145693
$425$		0			0
$426$	3.00000	−	5.19615i	0.145350	−	0.251754i
$427$	−12.1244	−	7.00000i	−0.586739	−	0.338754i
$428$		−	6.00000i		−	0.290021i
$429$	−6.00000	−	20.7846i	−0.289683	−	1.00349i
$430$		0			0
$431$	3.00000	−	5.19615i	0.144505	−	0.250290i	−0.784683	−	0.619897i	$-0.787174\pi$
$431$	3.00000	−	5.19615i	0.144505	−	0.250290i	0.929188	+	0.369607i	$0.120508\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	−11.2583	+	6.50000i	−0.541041	+	0.312370i	−0.745501	−	0.666505i	$-0.767790\pi$
$433$	−11.2583	+	6.50000i	−0.541041	+	0.312370i	0.204460	+	0.978875i	$0.434456\pi$
$434$	−8.00000			−0.384012
$435$		0			0
$436$	−7.00000	−	12.1244i	−0.335239	−	0.580651i
$437$			12.0000i			0.574038i
$438$	11.2583	−	6.50000i	0.537944	−	0.310582i
$439$	7.00000	−	12.1244i	0.334092	−	0.578664i	−0.649218	−	0.760602i	$-0.724904\pi$
$439$	7.00000	−	12.1244i	0.334092	−	0.578664i	0.983310	+	0.181938i	$0.0582371\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$	−2.59808	+	10.5000i	−0.123578	+	0.499434i
$443$		−	36.0000i		−	1.71041i	−0.518289	−	0.855206i	$-0.673431\pi$
$443$		−	36.0000i		−	1.71041i	0.518289	−	0.855206i	$-0.326569\pi$
$444$	−3.50000	+	6.06218i	−0.166103	+	0.287698i
$445$		0			0
$446$	4.00000	+	6.92820i	0.189405	+	0.328060i
$447$			9.00000i			0.425685i
$448$	1.73205	−	1.00000i	0.0818317	−	0.0472456i
$449$	9.00000	+	15.5885i	0.424736	+	0.735665i	0.996396	−	0.0848262i	$-0.0270335\pi$
$449$	9.00000	+	15.5885i	0.424736	+	0.735665i	−0.571660	+	0.820491i	$0.693700\pi$
$450$		0			0
$451$	9.00000	+	15.5885i	0.423793	+	0.734032i
$452$	−2.59808	−	1.50000i	−0.122203	−	0.0705541i
$453$	8.66025	+	5.00000i	0.406894	+	0.234920i
$454$	18.0000			0.844782
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	9.52628	+	5.50000i	0.445621	+	0.257279i	0.705979	−	0.708233i	$-0.250507\pi$
$457$	9.52628	+	5.50000i	0.445621	+	0.257279i	−0.260358	+	0.965512i	$0.583841\pi$
$458$	−19.0526	−	11.0000i	−0.890268	−	0.513996i
$459$	−1.50000	−	2.59808i	−0.0700140	−	0.121268i
$460$		0			0
$461$	−7.50000	−	12.9904i	−0.349310	−	0.605022i	0.636817	−	0.771015i	$-0.280251\pi$
$461$	−7.50000	−	12.9904i	−0.349310	−	0.605022i	−0.986127	+	0.165992i	$0.946917\pi$
$462$	10.3923	−	6.00000i	0.483494	−	0.279145i
$463$			38.0000i			1.76601i	0.469364	+	0.883005i	$0.344483\pi$
$463$			38.0000i			1.76601i	−0.469364	+	0.883005i	$0.655517\pi$
$464$	1.50000	+	2.59808i	0.0696358	+	0.120613i
$465$		0			0
$466$	−3.00000	+	5.19615i	−0.138972	+	0.240707i
$467$			18.0000i			0.832941i	0.909149	+	0.416470i	$0.136733\pi$
$467$			18.0000i			0.832941i	−0.909149	+	0.416470i	$0.863267\pi$
$468$	2.59808	+	2.50000i	0.120096	+	0.115563i
$469$	20.0000			0.923514
$470$		0			0
$471$	−2.50000	+	4.33013i	−0.115194	+	0.199522i
$472$		0			0
$473$		−	60.0000i		−	2.75880i
$474$	2.00000	+	3.46410i	0.0918630	+	0.159111i
$475$		0			0
$476$	−6.00000			−0.275010
$477$	−2.59808	+	1.50000i	−0.118958	+	0.0686803i
$478$	5.19615	+	3.00000i	0.237666	+	0.137217i
$479$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$479$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$480$		0			0
$481$	−17.5000	+	18.1865i	−0.797931	+	0.829235i
$482$		−	1.00000i		−	0.0455488i
$483$	10.3923	+	6.00000i	0.472866	+	0.273009i
$484$	12.5000	−	21.6506i	0.568182	−	0.984120i
$485$		0			0
$486$	−1.00000			−0.0453609
$487$	−1.73205	+	1.00000i	−0.0784867	+	0.0453143i	−0.538730	−	0.842479i	$-0.681096\pi$
$487$	−1.73205	+	1.00000i	−0.0784867	+	0.0453143i	0.460243	+	0.887793i	$0.347762\pi$
$488$	6.06218	−	3.50000i	0.274422	−	0.158438i
$489$	4.00000			0.180886
$490$		0			0
$491$	9.00000	−	15.5885i	0.406164	−	0.703497i	−0.588292	−	0.808649i	$-0.700199\pi$
$491$	9.00000	−	15.5885i	0.406164	−	0.703497i	0.994456	+	0.105151i	$0.0335327\pi$
$492$	−2.59808	−	1.50000i	−0.117130	−	0.0676252i
$493$		−	9.00000i		−	0.405340i
$494$	−7.00000	−	1.73205i	−0.314945	−	0.0779287i
$495$		0			0
$496$	2.00000	−	3.46410i	0.0898027	−	0.155543i
$497$	10.3923	+	6.00000i	0.466159	+	0.269137i
$498$	5.19615	−	3.00000i	0.232845	−	0.134433i
$499$	−32.0000			−1.43252			−0.716258	−	0.697835i	$-0.754147\pi$
$499$	−32.0000			−1.43252			−0.716258	+	0.697835i	$0.754147\pi$
$500$		0			0
$501$		0			0
$502$		−	12.0000i		−	0.535586i
$503$	5.19615	−	3.00000i	0.231685	−	0.133763i	−0.379664	−	0.925124i	$-0.623960\pi$
$503$	5.19615	−	3.00000i	0.231685	−	0.133763i	0.611349	+	0.791361i	$0.290627\pi$
$504$	−1.00000	+	1.73205i	−0.0445435	+	0.0771517i
$505$		0			0
$506$	36.0000			1.60040
$507$	6.92820	+	11.0000i	0.307692	+	0.488527i
$508$		−	4.00000i		−	0.177471i
$509$	1.50000	−	2.59808i	0.0664863	−	0.115158i	−0.830866	−	0.556473i	$-0.812154\pi$
$509$	1.50000	−	2.59808i	0.0664863	−	0.115158i	0.897352	+	0.441315i	$0.145488\pi$
$510$		0			0
$511$	13.0000	+	22.5167i	0.575086	+	0.996078i
$512$			1.00000i			0.0441942i
$513$	1.73205	−	1.00000i	0.0764719	−	0.0441511i
$514$	1.50000	+	2.59808i	0.0661622	+	0.114596i
$515$		0			0
$516$	5.00000	+	8.66025i	0.220113	+	0.381246i
$517$	31.1769	+	18.0000i	1.37116	+	0.791639i
$518$	−12.1244	−	7.00000i	−0.532714	−	0.307562i
$519$	6.00000			0.263371
$520$		0			0
$521$	33.0000			1.44576			0.722878	−	0.690976i	$-0.242819\pi$
$521$	33.0000			1.44576			0.722878	+	0.690976i	$0.242819\pi$
$522$	−2.59808	−	1.50000i	−0.113715	−	0.0656532i
$523$	29.4449	+	17.0000i	1.28753	+	0.743358i	0.978214	−	0.207600i	$-0.0665652\pi$
$523$	29.4449	+	17.0000i	1.28753	+	0.743358i	0.309320	+	0.950958i	$0.399899\pi$
$524$		0			0
$525$		0			0
$526$	−3.00000	−	5.19615i	−0.130806	−	0.226563i
$527$	−10.3923	+	6.00000i	−0.452696	+	0.261364i
$528$			6.00000i			0.261116i
$529$	6.50000	+	11.2583i	0.282609	+	0.489493i
$530$		0			0
$531$		0			0
$532$		−	4.00000i		−	0.173422i
$533$	−7.79423	−	7.50000i	−0.337606	−	0.324861i
$534$	18.0000			0.778936
$535$		0			0
$536$	−5.00000	+	8.66025i	−0.215967	+	0.374066i
$537$	−5.19615	+	3.00000i	−0.224231	+	0.129460i
$538$		−	18.0000i		−	0.776035i
$539$	−9.00000	−	15.5885i	−0.387657	−	0.671442i
$540$		0			0
$541$	29.0000			1.24681			0.623404	−	0.781900i	$-0.285749\pi$
$541$	29.0000			1.24681			0.623404	+	0.781900i	$0.285749\pi$
$542$	−13.8564	+	8.00000i	−0.595184	+	0.343629i
$543$	6.06218	+	3.50000i	0.260153	+	0.150199i
$544$	1.50000	−	2.59808i	0.0643120	−	0.111392i
$545$		0			0
$546$	−5.00000	+	5.19615i	−0.213980	+	0.222375i
$547$			34.0000i			1.45374i	0.686778	+	0.726868i	$0.259025\pi$
$547$			34.0000i			1.45374i	−0.686778	+	0.726868i	$0.740975\pi$
$548$	−7.79423	−	4.50000i	−0.332953	−	0.192230i
$549$	−3.50000	+	6.06218i	−0.149376	+	0.258727i
$550$		0			0
$551$	6.00000			0.255609
$552$	−5.19615	+	3.00000i	−0.221163	+	0.127688i
$553$	−6.92820	+	4.00000i	−0.294617	+	0.170097i
$554$	17.0000			0.722261
$555$		0			0
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	2.59808	+	1.50000i	0.110084	+	0.0635570i	0.554031	−	0.832496i	$-0.313089\pi$
$557$	2.59808	+	1.50000i	0.110084	+	0.0635570i	−0.443947	+	0.896053i	$0.646422\pi$
$558$			4.00000i			0.169334i
$559$	10.0000	+	34.6410i	0.422955	+	1.46516i
$560$		0			0
$561$	9.00000	−	15.5885i	0.379980	−	0.658145i
$562$	−7.79423	−	4.50000i	−0.328780	−	0.189821i
$563$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$563$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$564$	−6.00000			−0.252646
$565$		0			0
$566$	7.00000	+	12.1244i	0.294232	+	0.509625i
$567$		−	2.00000i		−	0.0839921i
$568$	−5.19615	+	3.00000i	−0.218026	+	0.125877i
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	−0.796266	−	0.604947i	$-0.793194\pi$
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	0.922032	+	0.387113i	$0.126528\pi$
$570$		0			0
$571$	−22.0000			−0.920671			−0.460336	−	0.887745i	$-0.652271\pi$
$571$	−22.0000			−0.920671			−0.460336	+	0.887745i	$0.652271\pi$
$572$	−5.19615	+	21.0000i	−0.217262	+	0.878054i
$573$		−	12.0000i		−	0.501307i
$574$	3.00000	−	5.19615i	0.125218	−	0.216883i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$		−	11.0000i		−	0.457936i	−0.973434	−	0.228968i	$-0.926465\pi$
$577$		−	11.0000i		−	0.457936i	0.973434	−	0.228968i	$-0.0735351\pi$
$578$	6.92820	−	4.00000i	0.288175	−	0.166378i
$579$	11.5000	+	19.9186i	0.477924	+	0.827788i
$580$		0			0
$581$	6.00000	+	10.3923i	0.248922	+	0.431145i
$582$	−12.1244	−	7.00000i	−0.502571	−	0.290159i
$583$	−15.5885	−	9.00000i	−0.645608	−	0.372742i
$584$	−13.0000			−0.537944
$585$		0			0
$586$	21.0000			0.867502
$587$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$587$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$588$	2.59808	+	1.50000i	0.107143	+	0.0618590i
$589$	−4.00000	−	6.92820i	−0.164817	−	0.285472i
$590$		0			0
$591$	−3.00000	−	5.19615i	−0.123404	−	0.213741i
$592$	6.06218	−	3.50000i	0.249154	−	0.143849i
$593$			9.00000i			0.369586i	0.982777	+	0.184793i	$0.0591614\pi$
$593$			9.00000i			0.369586i	−0.982777	+	0.184793i	$0.940839\pi$
$594$	−3.00000	−	5.19615i	−0.123091	−	0.213201i
$595$		0			0
$596$	4.50000	−	7.79423i	0.184327	−	0.319264i
$597$			10.0000i			0.409273i
$598$	−20.7846	+	6.00000i	−0.849946	+	0.245358i
$599$	−24.0000			−0.980613			−0.490307	−	0.871550i	$-0.663115\pi$
$599$	−24.0000			−0.980613			−0.490307	+	0.871550i	$0.663115\pi$
$600$		0			0
$601$	18.5000	−	32.0429i	0.754631	−	1.30706i	−0.190927	−	0.981604i	$-0.561149\pi$
$601$	18.5000	−	32.0429i	0.754631	−	1.30706i	0.945558	−	0.325455i	$-0.105517\pi$
$602$	−17.3205	+	10.0000i	−0.705931	+	0.407570i
$603$		−	10.0000i		−	0.407231i
$604$	−5.00000	−	8.66025i	−0.203447	−	0.352381i
$605$		0			0
$606$	−15.0000			−0.609333
$607$	−27.7128	+	16.0000i	−1.12483	+	0.649420i	−0.942629	−	0.333842i	$-0.891655\pi$
$607$	−27.7128	+	16.0000i	−1.12483	+	0.649420i	−0.182199	+	0.983262i	$0.558322\pi$
$608$	1.73205	+	1.00000i	0.0702439	+	0.0405554i
$609$	3.00000	−	5.19615i	0.121566	−	0.210559i
$610$		0			0
$611$	−21.0000	−	5.19615i	−0.849569	−	0.210214i
$612$			3.00000i			0.121268i
$613$	26.8468	+	15.5000i	1.08433	+	0.626039i	0.932062	−	0.362300i	$-0.118008\pi$
$613$	26.8468	+	15.5000i	1.08433	+	0.626039i	0.152270	+	0.988339i	$0.451342\pi$
$614$	5.00000	−	8.66025i	0.201784	−	0.349499i
$615$		0			0
$616$	−12.0000			−0.483494
$617$	12.9904	−	7.50000i	0.522973	−	0.301939i	−0.215177	−	0.976575i	$-0.569033\pi$
$617$	12.9904	−	7.50000i	0.522973	−	0.301939i	0.738150	+	0.674636i	$0.235700\pi$
$618$	−12.1244	+	7.00000i	−0.487713	+	0.281581i
$619$	−8.00000			−0.321547			−0.160774	−	0.986991i	$-0.551399\pi$
$619$	−8.00000			−0.321547			−0.160774	+	0.986991i	$0.551399\pi$
$620$		0			0
$621$	3.00000	−	5.19615i	0.120386	−	0.208514i
$622$	25.9808	+	15.0000i	1.04173	+	0.601445i
$623$			36.0000i			1.44231i
$624$	−1.00000	−	3.46410i	−0.0400320	−	0.138675i
$625$		0			0
$626$	−5.00000	+	8.66025i	−0.199840	+	0.346133i
$627$	10.3923	+	6.00000i	0.415029	+	0.239617i
$628$	4.33013	−	2.50000i	0.172791	−	0.0997609i
$629$	−21.0000			−0.837325
$630$		0			0
$631$	−10.0000	−	17.3205i	−0.398094	−	0.689519i	0.595397	−	0.803432i	$-0.296995\pi$
$631$	−10.0000	−	17.3205i	−0.398094	−	0.689519i	−0.993491	+	0.113913i	$0.963661\pi$
$632$		−	4.00000i		−	0.159111i
$633$	−13.8564	+	8.00000i	−0.550743	+	0.317971i
$634$	−1.50000	+	2.59808i	−0.0595726	+	0.103183i
$635$		0			0
$636$	3.00000			0.118958
$637$	7.79423	+	7.50000i	0.308819	+	0.297161i
$638$		−	18.0000i		−	0.712627i
$639$	3.00000	−	5.19615i	0.118678	−	0.205557i
$640$		0			0
$641$	1.50000	+	2.59808i	0.0592464	+	0.102618i	0.894127	−	0.447813i	$-0.147797\pi$
$641$	1.50000	+	2.59808i	0.0592464	+	0.102618i	−0.834881	+	0.550431i	$0.814464\pi$
$642$		−	6.00000i		−	0.236801i
$643$	−13.8564	+	8.00000i	−0.546443	+	0.315489i	−0.747686	−	0.664052i	$-0.768835\pi$
$643$	−13.8564	+	8.00000i	−0.546443	+	0.315489i	0.201243	+	0.979541i	$0.435502\pi$
$644$	−6.00000	−	10.3923i	−0.236433	−	0.409514i
$645$		0			0
$646$	−3.00000	−	5.19615i	−0.118033	−	0.204440i
$647$	20.7846	+	12.0000i	0.817127	+	0.471769i	0.849425	−	0.527710i	$-0.176949\pi$
$647$	20.7846	+	12.0000i	0.817127	+	0.471769i	−0.0322975	+	0.999478i	$0.510282\pi$
$648$	0.866025	+	0.500000i	0.0340207	+	0.0196419i
$649$		0			0
$650$		0			0
$651$	−8.00000			−0.313545
$652$	−3.46410	−	2.00000i	−0.135665	−	0.0783260i
$653$	−36.3731	−	21.0000i	−1.42339	−	0.821794i	−0.426801	−	0.904345i	$-0.640360\pi$
$653$	−36.3731	−	21.0000i	−1.42339	−	0.821794i	−0.996587	+	0.0825519i	$0.973693\pi$
$654$	−7.00000	−	12.1244i	−0.273722	−	0.474100i
$655$		0			0
$656$	1.50000	+	2.59808i	0.0585652	+	0.101438i
$657$	11.2583	−	6.50000i	0.439229	−	0.253589i
$658$		−	12.0000i		−	0.467809i
$659$	12.0000	+	20.7846i	0.467454	+	0.809653i	0.999309	−	0.0371821i	$-0.0118382\pi$
$659$	12.0000	+	20.7846i	0.467454	+	0.809653i	−0.531855	+	0.846836i	$0.678505\pi$
$660$		0			0
$661$	−2.50000	+	4.33013i	−0.0972387	+	0.168422i	−0.910541	−	0.413419i	$-0.864334\pi$
$661$	−2.50000	+	4.33013i	−0.0972387	+	0.168422i	0.813302	+	0.581842i	$0.197668\pi$
$662$		−	4.00000i		−	0.155464i
$663$	−2.59808	+	10.5000i	−0.100901	+	0.407786i
$664$	−6.00000			−0.232845
$665$		0			0
$666$	−3.50000	+	6.06218i	−0.135622	+	0.234905i
$667$	15.5885	−	9.00000i	0.603587	−	0.348481i
$668$		0			0
$669$	4.00000	+	6.92820i	0.154649	+	0.267860i
$670$		0			0
$671$	−42.0000			−1.62139
$672$	1.73205	−	1.00000i	0.0668153	−	0.0385758i
$673$	11.2583	+	6.50000i	0.433977	+	0.250557i	0.701039	−	0.713123i	$-0.252720\pi$
$673$	11.2583	+	6.50000i	0.433977	+	0.250557i	−0.267063	+	0.963679i	$0.586053\pi$
$674$	−11.5000	+	19.9186i	−0.442963	+	0.767235i
$675$		0			0
$676$	−0.500000	−	12.9904i	−0.0192308	−	0.499630i
$677$		−	18.0000i		−	0.691796i	−0.938272	−	0.345898i	$-0.887574\pi$
$677$		−	18.0000i		−	0.691796i	0.938272	−	0.345898i	$-0.112426\pi$
$678$	−2.59808	−	1.50000i	−0.0997785	−	0.0576072i
$679$	14.0000	−	24.2487i	0.537271	−	0.930580i
$680$		0			0
$681$	18.0000			0.689761
$682$	−20.7846	+	12.0000i	−0.795884	+	0.459504i
$683$	−41.5692	+	24.0000i	−1.59060	+	0.918334i	−0.597398	+	0.801945i	$0.703799\pi$
$683$	−41.5692	+	24.0000i	−1.59060	+	0.918334i	−0.993204	+	0.116390i	$0.962868\pi$
$684$	−2.00000			−0.0764719
$685$		0			0
$686$	−10.0000	+	17.3205i	−0.381802	+	0.661300i
$687$	−19.0526	−	11.0000i	−0.726900	−	0.419676i
$688$		−	10.0000i		−	0.381246i
$689$	10.5000	+	2.59808i	0.400018	+	0.0989788i
$690$		0			0
$691$	−13.0000	+	22.5167i	−0.494543	+	0.856574i	−0.999980	−	0.00628943i	$-0.997998\pi$
$691$	−13.0000	+	22.5167i	−0.494543	+	0.856574i	0.505437	+	0.862864i	$0.331331\pi$
$692$	−5.19615	−	3.00000i	−0.197528	−	0.114043i
$693$	10.3923	−	6.00000i	0.394771	−	0.227921i
$694$	−30.0000			−1.13878
$695$		0			0
$696$	1.50000	+	2.59808i	0.0568574	+	0.0984798i
$697$		−	9.00000i		−	0.340899i
$698$	8.66025	−	5.00000i	0.327795	−	0.189253i
$699$	−3.00000	+	5.19615i	−0.113470	+	0.196537i
$700$		0			0
$701$	−30.0000			−1.13308			−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000			−1.13308			−0.566542	+	0.824033i	$0.691719\pi$
$702$	2.59808	+	2.50000i	0.0980581	+	0.0943564i
$703$		−	14.0000i		−	0.528020i
$704$	3.00000	−	5.19615i	0.113067	−	0.195837i
$705$		0			0
$706$	−7.50000	−	12.9904i	−0.282266	−	0.488899i
$707$		−	30.0000i		−	1.12827i
$708$		0			0
$709$	2.50000	+	4.33013i	0.0938895	+	0.162621i	0.909145	−	0.416481i	$-0.136737\pi$
$709$	2.50000	+	4.33013i	0.0938895	+	0.162621i	−0.815255	+	0.579102i	$0.803403\pi$
$710$		0			0
$711$	2.00000	+	3.46410i	0.0750059	+	0.129914i
$712$	−15.5885	−	9.00000i	−0.584202	−	0.337289i
$713$	−20.7846	−	12.0000i	−0.778390	−	0.449404i
$714$	−6.00000			−0.224544
$715$		0			0
$716$	6.00000			0.224231
$717$	5.19615	+	3.00000i	0.194054	+	0.112037i
$718$	5.19615	+	3.00000i	0.193919	+	0.111959i
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$		0			0
$721$	−14.0000	−	24.2487i	−0.521387	−	0.903069i
$722$	−12.9904	+	7.50000i	−0.483452	+	0.279121i
$723$		−	1.00000i		−	0.0371904i
$724$	−3.50000	−	6.06218i	−0.130076	−	0.225299i
$725$		0			0
$726$	12.5000	−	21.6506i	0.463919	−	0.803530i
$727$		−	14.0000i		−	0.519231i	−0.965712	−	0.259616i	$-0.916404\pi$
$727$		−	14.0000i		−	0.519231i	0.965712	−	0.259616i	$-0.0835959\pi$
$728$	6.92820	−	2.00000i	0.256776	−	0.0741249i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−15.0000	+	25.9808i	−0.554795	+	0.960933i
$732$	6.06218	−	3.50000i	0.224065	−	0.129364i
$733$		−	31.0000i		−	1.14501i	−0.819901	−	0.572506i	$-0.805971\pi$
$733$		−	31.0000i		−	1.14501i	0.819901	−	0.572506i	$-0.194029\pi$
$734$	−1.00000	−	1.73205i	−0.0369107	−	0.0639312i
$735$		0			0
$736$	6.00000			0.221163
$737$	51.9615	−	30.0000i	1.91403	−	1.10506i
$738$	−2.59808	−	1.50000i	−0.0956365	−	0.0552158i
$739$	−8.00000	+	13.8564i	−0.294285	+	0.509716i	−0.974818	−	0.223001i	$-0.928415\pi$
$739$	−8.00000	+	13.8564i	−0.294285	+	0.509716i	0.680534	+	0.732717i	$0.261748\pi$
$740$		0			0
$741$	−7.00000	−	1.73205i	−0.257151	−	0.0636285i
$742$			6.00000i			0.220267i
$743$	31.1769	+	18.0000i	1.14377	+	0.660356i	0.947361	−	0.320166i	$-0.103739\pi$
$743$	31.1769	+	18.0000i	1.14377	+	0.660356i	0.196409	+	0.980522i	$0.437072\pi$
$744$	2.00000	−	3.46410i	0.0733236	−	0.127000i
$745$		0			0
$746$	−29.0000			−1.06177
$747$	5.19615	−	3.00000i	0.190117	−	0.109764i
$748$	−15.5885	+	9.00000i	−0.569970	+	0.329073i
$749$	12.0000			0.438470
$750$		0			0
$751$	−7.00000	+	12.1244i	−0.255434	+	0.442424i	−0.965013	−	0.262201i	$-0.915552\pi$
$751$	−7.00000	+	12.1244i	−0.255434	+	0.442424i	0.709580	+	0.704625i	$0.248885\pi$
$752$	5.19615	+	3.00000i	0.189484	+	0.109399i
$753$		−	12.0000i		−	0.437304i
$754$	3.00000	+	10.3923i	0.109254	+	0.378465i
$755$		0			0
$756$	−1.00000	+	1.73205i	−0.0363696	+	0.0629941i
$757$	−29.4449	−	17.0000i	−1.07019	−	0.617876i	−0.141958	−	0.989873i	$-0.545340\pi$
$757$	−29.4449	−	17.0000i	−1.07019	−	0.617876i	−0.928234	+	0.371997i	$0.878673\pi$
$758$	−17.3205	+	10.0000i	−0.629109	+	0.363216i
$759$	36.0000			1.30672
$760$		0			0
$761$	15.0000	+	25.9808i	0.543750	+	0.941802i	0.998684	+	0.0512772i	$0.0163292\pi$
$761$	15.0000	+	25.9808i	0.543750	+	0.941802i	−0.454935	+	0.890525i	$0.650337\pi$
$762$		−	4.00000i		−	0.144905i
$763$	24.2487	−	14.0000i	0.877862	−	0.506834i
$764$	−6.00000	+	10.3923i	−0.217072	+	0.375980i
$765$		0			0
$766$	−24.0000			−0.867155
$767$		0			0
$768$			1.00000i			0.0360844i
$769$	7.00000	−	12.1244i	0.252426	−	0.437215i	−0.711767	−	0.702416i	$-0.752105\pi$
$769$	7.00000	−	12.1244i	0.252426	−	0.437215i	0.964193	+	0.265200i	$0.0854381\pi$
$770$		0			0
$771$	1.50000	+	2.59808i	0.0540212	+	0.0935674i
$772$		−	23.0000i		−	0.827788i
$773$	−25.9808	+	15.0000i	−0.934463	+	0.539513i	−0.888220	−	0.459418i	$-0.848058\pi$
$773$	−25.9808	+	15.0000i	−0.934463	+	0.539513i	−0.0462427	+	0.998930i	$0.514725\pi$
$774$	5.00000	+	8.66025i	0.179721	+	0.311286i
$775$		0			0
$776$	7.00000	+	12.1244i	0.251285	+	0.435239i
$777$	−12.1244	−	7.00000i	−0.434959	−	0.251124i
$778$	33.7750	+	19.5000i	1.21089	+	0.699109i
$779$	6.00000			0.214972
$780$		0			0
$781$	36.0000			1.28818
$782$	−15.5885	−	9.00000i	−0.557442	−	0.321839i
$783$	−2.59808	−	1.50000i	−0.0928477	−	0.0536056i
$784$	−1.50000	−	2.59808i	−0.0535714	−	0.0927884i
$785$		0			0
$786$		0			0
$787$	24.2487	−	14.0000i	0.864373	−	0.499046i	−0.00110111	−	0.999999i	$-0.500350\pi$
$787$	24.2487	−	14.0000i	0.864373	−	0.499046i	0.865474	+	0.500953i	$0.167017\pi$
$788$			6.00000i			0.213741i
$789$	−3.00000	−	5.19615i	−0.106803	−	0.184988i
$790$		0			0
$791$	3.00000	−	5.19615i	0.106668	−	0.184754i
$792$			6.00000i			0.213201i
$793$	24.2487	−	7.00000i	0.861097	−	0.248577i
$794$	14.0000			0.496841
$795$		0			0
$796$	5.00000	−	8.66025i	0.177220	−	0.306955i
$797$	−25.9808	+	15.0000i	−0.920286	+	0.531327i	−0.883726	−	0.468004i	$-0.844973\pi$
$797$	−25.9808	+	15.0000i	−0.920286	+	0.531327i	−0.0365596	+	0.999331i	$0.511640\pi$
$798$		−	4.00000i		−	0.141598i
$799$	−9.00000	−	15.5885i	−0.318397	−	0.551480i
$800$		0			0
$801$	18.0000			0.635999
$802$	−2.59808	+	1.50000i	−0.0917413	+	0.0529668i
$803$	67.5500	+	39.0000i	2.38379	+	1.37628i
$804$	−5.00000	+	8.66025i	−0.176336	+	0.305424i
$805$		0			0
$806$	10.0000	−	10.3923i	0.352235	−	0.366053i
$807$		−	18.0000i		−	0.633630i
$808$	12.9904	+	7.50000i	0.457000	+	0.263849i
$809$	−25.5000	+	44.1673i	−0.896532	+	1.55284i	−0.0646355	+	0.997909i	$0.520588\pi$
$809$	−25.5000	+	44.1673i	−0.896532	+	1.55284i	−0.831897	+	0.554930i	$0.812745\pi$
$810$		0			0
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$	−5.19615	+	3.00000i	−0.182349	+	0.105279i
$813$	−13.8564	+	8.00000i	−0.485965	+	0.280572i
$814$	−42.0000			−1.47210
$815$		0			0
$816$	1.50000	−	2.59808i	0.0525105	−	0.0909509i
$817$	−17.3205	−	10.0000i	−0.605968	−	0.349856i
$818$			1.00000i			0.0349642i
$819$	−5.00000	+	5.19615i	−0.174714	+	0.181568i
$820$		0			0
$821$	−9.00000	+	15.5885i	−0.314102	+	0.544041i	−0.979246	−	0.202674i	$-0.935037\pi$
$821$	−9.00000	+	15.5885i	−0.314102	+	0.544041i	0.665144	+	0.746715i	$0.268370\pi$
$822$	−7.79423	−	4.50000i	−0.271855	−	0.156956i
$823$	−34.6410	+	20.0000i	−1.20751	+	0.697156i	−0.962215	−	0.272292i	$-0.912218\pi$
$823$	−34.6410	+	20.0000i	−1.20751	+	0.697156i	−0.245295	+	0.969448i	$0.578885\pi$
$824$	14.0000			0.487713
$825$		0			0
$826$		0			0
$827$			48.0000i			1.66912i	0.550914	+	0.834562i	$0.314279\pi$
$827$			48.0000i			1.66912i	−0.550914	+	0.834562i	$0.685721\pi$
$828$	−5.19615	+	3.00000i	−0.180579	+	0.104257i
$829$	8.50000	−	14.7224i	0.295217	−	0.511331i	−0.679818	−	0.733381i	$-0.737941\pi$
$829$	8.50000	−	14.7224i	0.295217	−	0.511331i	0.975035	+	0.222049i	$0.0712747\pi$
$830$		0			0
$831$	17.0000			0.589723
$832$	−0.866025	+	3.50000i	−0.0300240	+	0.121341i
$833$			9.00000i			0.311832i
$834$	2.00000	−	3.46410i	0.0692543	−	0.119952i
$835$		0			0
$836$	−6.00000	−	10.3923i	−0.207514	−	0.359425i
$837$			4.00000i			0.138260i
$838$	−20.7846	+	12.0000i	−0.717992	+	0.414533i
$839$	−6.00000	−	10.3923i	−0.207143	−	0.358782i	0.743670	−	0.668546i	$-0.233083\pi$
$839$	−6.00000	−	10.3923i	−0.207143	−	0.358782i	−0.950813	+	0.309764i	$0.899750\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	−25.1147	−	14.5000i	−0.865511	−	0.499703i
$843$	−7.79423	−	4.50000i	−0.268447	−	0.154988i
$844$	16.0000			0.550743
$845$		0			0
$846$	−6.00000			−0.206284
$847$	43.3013	+	25.0000i	1.48785	+	0.859010i
$848$	−2.59808	−	1.50000i	−0.0892183	−	0.0515102i
$849$	7.00000	+	12.1244i	0.240239	+	0.416107i
$850$		0			0
$851$	−21.0000	−	36.3731i	−0.719871	−	1.24685i
$852$	−5.19615	+	3.00000i	−0.178017	+	0.102778i
$853$		−	19.0000i		−	0.650548i	−0.945620	−	0.325274i	$-0.894544\pi$
$853$		−	19.0000i		−	0.650548i	0.945620	−	0.325274i	$-0.105456\pi$
$854$	7.00000	+	12.1244i	0.239535	+	0.414887i
$855$		0			0
$856$	−3.00000	+	5.19615i	−0.102538	+	0.177601i
$857$		−	21.0000i		−	0.717346i	−0.933463	−	0.358673i	$-0.883229\pi$
$857$		−	21.0000i		−	0.717346i	0.933463	−	0.358673i	$-0.116771\pi$
$858$	−5.19615	+	21.0000i	−0.177394	+	0.716928i
$859$	−26.0000			−0.887109			−0.443554	−	0.896248i	$-0.646283\pi$
$859$	−26.0000			−0.887109			−0.443554	+	0.896248i	$0.646283\pi$
$860$		0			0
$861$	3.00000	−	5.19615i	0.102240	−	0.177084i
$862$	−5.19615	+	3.00000i	−0.176982	+	0.102180i
$863$			18.0000i			0.612727i	0.951915	+	0.306364i	$0.0991123\pi$
$863$			18.0000i			0.612727i	−0.951915	+	0.306364i	$0.900888\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$		0			0
$866$	13.0000			0.441758
$867$	6.92820	−	4.00000i	0.235294	−	0.135847i
$868$	6.92820	+	4.00000i	0.235159	+	0.135769i
$869$	−12.0000	+	20.7846i	−0.407072	+	0.705070i
$870$		0			0
$871$	−25.0000	+	25.9808i	−0.847093	+	0.880325i
$872$			14.0000i			0.474100i
$873$	−12.1244	−	7.00000i	−0.410347	−	0.236914i
$874$	6.00000	−	10.3923i	0.202953	−	0.351525i
$875$		0			0
$876$	−13.0000			−0.439229
$877$	−35.5070	+	20.5000i	−1.19899	+	0.692236i	−0.960329	−	0.278868i	$-0.910041\pi$
$877$	−35.5070	+	20.5000i	−1.19899	+	0.692236i	−0.238658	+	0.971104i	$0.576708\pi$
$878$	−12.1244	+	7.00000i	−0.409177	+	0.236239i
$879$	21.0000			0.708312
$880$		0			0
$881$	−16.5000	+	28.5788i	−0.555899	+	0.962846i	0.441934	+	0.897048i	$0.354293\pi$
$881$	−16.5000	+	28.5788i	−0.555899	+	0.962846i	−0.997833	+	0.0657979i	$0.979041\pi$
$882$	2.59808	+	1.50000i	0.0874818	+	0.0505076i
$883$			8.00000i			0.269221i	0.990899	+	0.134611i	$0.0429784\pi$
$883$			8.00000i			0.269221i	−0.990899	+	0.134611i	$0.957022\pi$
$884$	7.50000	−	7.79423i	0.252252	−	0.262148i
$885$		0			0
$886$	−18.0000	+	31.1769i	−0.604722	+	1.04741i
$887$	−41.5692	−	24.0000i	−1.39576	−	0.805841i	−0.401813	−	0.915722i	$-0.631620\pi$
$887$	−41.5692	−	24.0000i	−1.39576	−	0.805841i	−0.993945	+	0.109881i	$0.964953\pi$
$888$	6.06218	−	3.50000i	0.203433	−	0.117452i
$889$	8.00000			0.268311
$890$		0			0
$891$	−3.00000	−	5.19615i	−0.100504	−	0.174078i
$892$		−	8.00000i		−	0.267860i
$893$	10.3923	−	6.00000i	0.347765	−	0.200782i
$894$	4.50000	−	7.79423i	0.150503	−	0.260678i
$895$		0			0
$896$	−2.00000			−0.0668153
$897$	−20.7846	+	6.00000i	−0.693978	+	0.200334i
$898$		−	18.0000i		−	0.600668i
$899$	−6.00000	+	10.3923i	−0.200111	+	0.346603i
$900$		0			0
$901$	4.50000	+	7.79423i	0.149917	+	0.259663i
$902$		−	18.0000i		−	0.599334i
$903$	−17.3205	+	10.0000i	−0.576390	+	0.332779i
$904$	1.50000	+	2.59808i	0.0498893	+	0.0864107i
$905$		0			0
$906$	−5.00000	−	8.66025i	−0.166114	−	0.287718i
$907$	38.1051	+	22.0000i	1.26526	+	0.730498i	0.974087	−	0.226173i	$-0.0726213\pi$
$907$	38.1051	+	22.0000i	1.26526	+	0.730498i	0.291172	+	0.956671i	$0.405955\pi$
$908$	−15.5885	−	9.00000i	−0.517321	−	0.298675i
$909$	−15.0000			−0.497519
$910$		0			0
$911$	−24.0000			−0.795155			−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000			−0.795155			−0.397578	+	0.917568i	$0.630149\pi$
$912$	1.73205	+	1.00000i	0.0573539	+	0.0331133i
$913$	31.1769	+	18.0000i	1.03181	+	0.595713i
$914$	−5.50000	−	9.52628i	−0.181924	−	0.315101i
$915$		0			0
$916$	11.0000	+	19.0526i	0.363450	+	0.629514i
$917$		0			0
$918$			3.00000i			0.0990148i
$919$	−8.00000	−	13.8564i	−0.263896	−	0.457081i	0.703378	−	0.710816i	$-0.251674\pi$
$919$	−8.00000	−	13.8564i	−0.263896	−	0.457081i	−0.967274	+	0.253735i	$0.918341\pi$
$920$		0			0
$921$	5.00000	−	8.66025i	0.164756	−	0.285365i
$922$			15.0000i			0.493999i
$923$	−20.7846	+	6.00000i	−0.684134	+	0.197492i
$924$	−12.0000			−0.394771
$925$		0			0
$926$	19.0000	−	32.9090i	0.624379	−	1.08146i
$927$	−12.1244	+	7.00000i	−0.398216	+	0.229910i
$928$		−	3.00000i		−	0.0984798i
$929$	16.5000	+	28.5788i	0.541347	+	0.937641i	0.998827	+	0.0484211i	$0.0154190\pi$
$929$	16.5000	+	28.5788i	0.541347	+	0.937641i	−0.457480	+	0.889220i	$0.651248\pi$
$930$		0			0
$931$	−6.00000			−0.196642
$932$	5.19615	−	3.00000i	0.170206	−	0.0982683i
$933$	25.9808	+	15.0000i	0.850572	+	0.491078i
$934$	9.00000	−	15.5885i	0.294489	−	0.510070i
$935$		0			0
$936$	−1.00000	−	3.46410i	−0.0326860	−	0.113228i
$937$		−	47.0000i		−	1.53542i	−0.640796	−	0.767712i	$-0.721395\pi$
$937$		−	47.0000i		−	1.53542i	0.640796	−	0.767712i	$-0.278605\pi$
$938$	−17.3205	−	10.0000i	−0.565535	−	0.326512i
$939$	−5.00000	+	8.66025i	−0.163169	+	0.282617i
$940$		0			0
$941$	42.0000			1.36916			0.684580	−	0.728937i	$-0.259985\pi$
$941$	42.0000			1.36916			0.684580	+	0.728937i	$0.259985\pi$
$942$	4.33013	−	2.50000i	0.141083	−	0.0814544i
$943$	15.5885	−	9.00000i	0.507630	−	0.293080i
$944$		0			0
$945$		0			0
$946$	−30.0000	+	51.9615i	−0.975384	+	1.68941i
$947$	20.7846	+	12.0000i	0.675409	+	0.389948i	0.798123	−	0.602494i	$-0.205826\pi$
$947$	20.7846	+	12.0000i	0.675409	+	0.389948i	−0.122714	+	0.992442i	$0.539160\pi$
$948$		−	4.00000i		−	0.129914i
$949$	−45.5000	−	11.2583i	−1.47699	−	0.365461i
$950$		0			0
$951$	−1.50000	+	2.59808i	−0.0486408	+	0.0842484i
$952$	5.19615	+	3.00000i	0.168408	+	0.0972306i
$953$	46.7654	−	27.0000i	1.51488	−	0.874616i	0.515031	−	0.857171i	$-0.327780\pi$
$953$	46.7654	−	27.0000i	1.51488	−	0.874616i	0.999848	−	0.0174443i	$-0.00555298\pi$
$954$	3.00000			0.0971286
$955$		0			0
$956$	−3.00000	−	5.19615i	−0.0970269	−	0.168056i
$957$		−	18.0000i		−	0.581857i
$958$		0			0
$959$	9.00000	−	15.5885i	0.290625	−	0.503378i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	24.2487	−	7.00000i	0.781810	−	0.225689i
$963$		−	6.00000i		−	0.193347i
$964$	−0.500000	+	0.866025i	−0.0161039	+	0.0278928i
$965$		0			0
$966$	−6.00000	−	10.3923i	−0.193047	−	0.334367i
$967$			22.0000i			0.707472i	0.935345	+	0.353736i	$0.115089\pi$
$967$			22.0000i			0.707472i	−0.935345	+	0.353736i	$0.884911\pi$
$968$	−21.6506	+	12.5000i	−0.695878	+	0.401765i
$969$	−3.00000	−	5.19615i	−0.0963739	−	0.166924i
$970$		0			0
$971$	−30.0000	−	51.9615i	−0.962746	−	1.66752i	−0.715553	−	0.698558i	$-0.753825\pi$
$971$	−30.0000	−	51.9615i	−0.962746	−	1.66752i	−0.247193	−	0.968966i	$-0.579508\pi$
$972$	0.866025	+	0.500000i	0.0277778	+	0.0160375i
$973$	6.92820	+	4.00000i	0.222108	+	0.128234i
$974$	2.00000			0.0640841
$975$		0			0
$976$	−7.00000			−0.224065
$977$	−2.59808	−	1.50000i	−0.0831198	−	0.0479893i	0.457864	−	0.889022i	$-0.348615\pi$
$977$	−2.59808	−	1.50000i	−0.0831198	−	0.0479893i	−0.540984	+	0.841033i	$0.681948\pi$
$978$	−3.46410	−	2.00000i	−0.110770	−	0.0639529i
$979$	54.0000	+	93.5307i	1.72585	+	2.98926i
$980$		0			0
$981$	−7.00000	−	12.1244i	−0.223493	−	0.387101i
$982$	−15.5885	+	9.00000i	−0.497448	+	0.287202i
$983$		−	36.0000i		−	1.14822i	−0.818778	−	0.574111i	$-0.805348\pi$
$983$		−	36.0000i		−	1.14822i	0.818778	−	0.574111i	$-0.194652\pi$
$984$	1.50000	+	2.59808i	0.0478183	+	0.0828236i
$985$		0			0
$986$	−4.50000	+	7.79423i	−0.143309	+	0.248219i
$987$		−	12.0000i		−	0.381964i
$988$	5.19615	+	5.00000i	0.165312	+	0.159071i
$989$	−60.0000			−1.90789
$990$		0			0
$991$	−19.0000	+	32.9090i	−0.603555	+	1.04539i	0.388723	+	0.921355i	$0.372916\pi$
$991$	−19.0000	+	32.9090i	−0.603555	+	1.04539i	−0.992278	+	0.124033i	$0.960417\pi$
$992$	−3.46410	+	2.00000i	−0.109985	+	0.0635001i
$993$		−	4.00000i		−	0.126936i
$994$	−6.00000	−	10.3923i	−0.190308	−	0.329624i
$995$		0			0
$996$	−6.00000			−0.190117
$997$	−4.33013	+	2.50000i	−0.137136	+	0.0791758i	−0.566999	−	0.823719i	$-0.691896\pi$
$997$	−4.33013	+	2.50000i	−0.137136	+	0.0791758i	0.429862	+	0.902895i	$0.358562\pi$
$998$	27.7128	+	16.0000i	0.877234	+	0.506471i
$999$	−3.50000	+	6.06218i	−0.110735	+	0.191799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.z.g.1699.1		4
5.2	odd	4		78.2.e.a.61.1	yes	2
5.3	odd	4		1950.2.i.m.451.1		2
5.4	even	2	inner	1950.2.z.g.1699.2		4
13.3	even	3	inner	1950.2.z.g.1849.2		4
15.2	even	4		234.2.h.a.217.1		2
20.7	even	4		624.2.q.g.529.1		2
60.47	odd	4		1872.2.t.c.1153.1		2
65.2	even	12		1014.2.i.b.361.2		4
65.3	odd	12		1950.2.i.m.601.1		2
65.7	even	12		1014.2.b.c.337.1		2
65.12	odd	4		1014.2.e.a.529.1		2
65.17	odd	12		1014.2.a.f.1.1		1
65.22	odd	12		1014.2.a.c.1.1		1
65.29	even	6	inner	1950.2.z.g.1849.1		4
65.32	even	12		1014.2.b.c.337.2		2
65.37	even	12		1014.2.i.b.361.1		4
65.42	odd	12		78.2.e.a.55.1	✓	2
65.47	even	4		1014.2.i.b.823.2		4
65.57	even	4		1014.2.i.b.823.1		4
65.62	odd	12		1014.2.e.a.991.1		2
195.17	even	12		3042.2.a.h.1.1		1
195.32	odd	12		3042.2.b.h.1351.1		2
195.107	even	12		234.2.h.a.55.1		2
195.137	odd	12		3042.2.b.h.1351.2		2
195.152	even	12		3042.2.a.i.1.1		1
260.87	even	12		8112.2.a.m.1.1		1
260.107	even	12		624.2.q.g.289.1		2
260.147	even	12		8112.2.a.c.1.1		1
780.107	odd	12		1872.2.t.c.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.2.e.a.55.1	✓	2	65.42	odd	12
78.2.e.a.61.1	yes	2	5.2	odd	4
234.2.h.a.55.1		2	195.107	even	12
234.2.h.a.217.1		2	15.2	even	4
624.2.q.g.289.1		2	260.107	even	12
624.2.q.g.529.1		2	20.7	even	4
1014.2.a.c.1.1		1	65.22	odd	12
1014.2.a.f.1.1		1	65.17	odd	12
1014.2.b.c.337.1		2	65.7	even	12
1014.2.b.c.337.2		2	65.32	even	12
1014.2.e.a.529.1		2	65.12	odd	4
1014.2.e.a.991.1		2	65.62	odd	12
1014.2.i.b.361.1		4	65.37	even	12
1014.2.i.b.361.2		4	65.2	even	12
1014.2.i.b.823.1		4	65.57	even	4
1014.2.i.b.823.2		4	65.47	even	4
1872.2.t.c.289.1		2	780.107	odd	12
1872.2.t.c.1153.1		2	60.47	odd	4
1950.2.i.m.451.1		2	5.3	odd	4
1950.2.i.m.601.1		2	65.3	odd	12
1950.2.z.g.1699.1		4	1.1	even	1	trivial
1950.2.z.g.1699.2		4	5.4	even	2	inner
1950.2.z.g.1849.1		4	65.29	even	6	inner
1950.2.z.g.1849.2		4	13.3	even	3	inner
3042.2.a.h.1.1		1	195.17	even	12
3042.2.a.i.1.1		1	195.152	even	12
3042.2.b.h.1351.1		2	195.32	odd	12
3042.2.b.h.1351.2		2	195.137	odd	12
8112.2.a.c.1.1		1	260.147	even	12
8112.2.a.m.1.1		1	260.87	even	12

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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.z (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(-1.73205 + 1.00000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(-1.73205 + 1.00000i) q^{7} -1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(-3.00000 + 5.19615i) q^{11} -1.00000i q^{12} +(0.866025 - 3.50000i) q^{13} +2.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.59808 - 1.50000i) q^{17} -1.00000i q^{18} +(1.00000 + 1.73205i) q^{19} +2.00000 q^{21} +(5.19615 - 3.00000i) q^{22} +(5.19615 + 3.00000i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.50000 + 2.59808i) q^{26} -1.00000i q^{27} +(-1.73205 - 1.00000i) q^{28} +(1.50000 - 2.59808i) q^{29} -4.00000 q^{31} +(0.866025 - 0.500000i) q^{32} +(5.19615 - 3.00000i) q^{33} -3.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-6.06218 - 3.50000i) q^{37} -2.00000i q^{38} +(-2.50000 + 2.59808i) q^{39} +(1.50000 - 2.59808i) q^{41} +(-1.73205 - 1.00000i) q^{42} +(-8.66025 + 5.00000i) q^{43} -6.00000 q^{44} +(-3.00000 - 5.19615i) q^{46} -6.00000i q^{47} +(0.866025 - 0.500000i) q^{48} +(-1.50000 + 2.59808i) q^{49} -3.00000 q^{51} +(3.46410 - 1.00000i) q^{52} +3.00000i q^{53} +(-0.500000 + 0.866025i) q^{54} +(1.00000 + 1.73205i) q^{56} -2.00000i q^{57} +(-2.59808 + 1.50000i) q^{58} +(3.50000 + 6.06218i) q^{61} +(3.46410 + 2.00000i) q^{62} +(-1.73205 - 1.00000i) q^{63} -1.00000 q^{64} -6.00000 q^{66} +(-8.66025 - 5.00000i) q^{67} +(2.59808 + 1.50000i) q^{68} +(-3.00000 - 5.19615i) q^{69} +(-3.00000 - 5.19615i) q^{71} +(0.866025 - 0.500000i) q^{72} -13.0000i q^{73} +(3.50000 + 6.06218i) q^{74} +(-1.00000 + 1.73205i) q^{76} -12.0000i q^{77} +(3.46410 - 1.00000i) q^{78} +4.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-2.59808 + 1.50000i) q^{82} -6.00000i q^{83} +(1.00000 + 1.73205i) q^{84} +10.0000 q^{86} +(-2.59808 + 1.50000i) q^{87} +(5.19615 + 3.00000i) q^{88} +(9.00000 - 15.5885i) q^{89} +(2.00000 + 6.92820i) q^{91} +6.00000i q^{92} +(3.46410 + 2.00000i) q^{93} +(-3.00000 + 5.19615i) q^{94} -1.00000 q^{96} +(-12.1244 + 7.00000i) q^{97} +(2.59808 - 1.50000i) q^{98} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 2 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 2 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} + 2 q^{6} + 2 q^{9} - 12 q^{11} + 8 q^{14} - 2 q^{16} + 4 q^{19} + 8 q^{21} - 2 q^{24} - 10 q^{26} + 6 q^{29} - 16 q^{31} - 12 q^{34} - 2 q^{36} - 10 q^{39} + 6 q^{41} - 24 q^{44} - 12 q^{46} - 6 q^{49} - 12 q^{51} - 2 q^{54} + 4 q^{56} + 14 q^{61} - 4 q^{64} - 24 q^{66} - 12 q^{69} - 12 q^{71} + 14 q^{74} - 4 q^{76} + 16 q^{79} - 2 q^{81} + 4 q^{84} + 40 q^{86} + 36 q^{89} + 8 q^{91} - 12 q^{94} - 4 q^{96} - 24 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 + 2 * q^6 + 2 * q^9 - 12 * q^11 + 8 * q^14 - 2 * q^16 + 4 * q^19 + 8 * q^21 - 2 * q^24 - 10 * q^26 + 6 * q^29 - 16 * q^31 - 12 * q^34 - 2 * q^36 - 10 * q^39 + 6 * q^41 - 24 * q^44 - 12 * q^46 - 6 * q^49 - 12 * q^51 - 2 * q^54 + 4 * q^56 + 14 * q^61 - 4 * q^64 - 24 * q^66 - 12 * q^69 - 12 * q^71 + 14 * q^74 - 4 * q^76 + 16 * q^79 - 2 * q^81 + 4 * q^84 + 40 * q^86 + 36 * q^89 + 8 * q^91 - 12 * q^94 - 4 * q^96 - 24 * q^99

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