LMFDB - Embedded newform 1950.2.z.k.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 390)
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.k.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} +(1.50000 - 2.59808i) q^{11} -1.00000i q^{12} +(3.46410 + 1.00000i) q^{13} +2.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-5.19615 + 3.00000i) q^{17} -1.00000i q^{18} +(1.00000 + 1.73205i) q^{19} +2.00000 q^{21} +(-2.59808 + 1.50000i) q^{22} +(-2.59808 - 1.50000i) 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} +5.00000 q^{31} +(0.866025 - 0.500000i) q^{32} +(-2.59808 + 1.50000i) q^{33} +6.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-6.06218 - 3.50000i) q^{37} -2.00000i q^{38} +(-2.50000 - 2.59808i) q^{39} +(-3.00000 + 5.19615i) q^{41} +(-1.73205 - 1.00000i) q^{42} +(-0.866025 + 0.500000i) q^{43} +3.00000 q^{44} +(1.50000 + 2.59808i) q^{46} +3.00000i q^{47} +(0.866025 - 0.500000i) q^{48} +(-1.50000 + 2.59808i) q^{49} +6.00000 q^{51} +(0.866025 + 3.50000i) q^{52} -6.00000i q^{53} +(-0.500000 + 0.866025i) q^{54} +(1.00000 + 1.73205i) q^{56} -2.00000i q^{57} +(-2.59808 + 1.50000i) q^{58} +(-4.50000 - 7.79423i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(-4.33013 - 2.50000i) q^{62} +(-1.73205 - 1.00000i) q^{63} -1.00000 q^{64} +3.00000 q^{66} +(6.92820 + 4.00000i) q^{67} +(-5.19615 - 3.00000i) q^{68} +(1.50000 + 2.59808i) q^{69} +(6.00000 + 10.3923i) q^{71} +(0.866025 - 0.500000i) q^{72} +14.0000i q^{73} +(3.50000 + 6.06218i) q^{74} +(-1.00000 + 1.73205i) q^{76} +6.00000i q^{77} +(0.866025 + 3.50000i) q^{78} -5.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(5.19615 - 3.00000i) q^{82} -6.00000i q^{83} +(1.00000 + 1.73205i) q^{84} +1.00000 q^{86} +(-2.59808 + 1.50000i) q^{87} +(-2.59808 - 1.50000i) q^{88} +(-9.00000 + 15.5885i) q^{89} +(-7.00000 + 1.73205i) q^{91} -3.00000i q^{92} +(-4.33013 - 2.50000i) q^{93} +(1.50000 - 2.59808i) q^{94} -1.00000 q^{96} +(-12.1244 + 7.00000i) q^{97} +(2.59808 - 1.50000i) q^{98} +3.00000 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} + 6 q^{11} + 8 q^{14} - 2 q^{16} + 4 q^{19} + 8 q^{21} - 2 q^{24} - 10 q^{26} + 6 q^{29} + 20 q^{31} + 24 q^{34} - 2 q^{36} - 10 q^{39} - 12 q^{41} + 12 q^{44} + 6 q^{46} - 6 q^{49} + 24 q^{51} - 2 q^{54} + 4 q^{56} - 18 q^{59} - 4 q^{61} - 4 q^{64} + 12 q^{66} + 6 q^{69} + 24 q^{71} + 14 q^{74} - 4 q^{76} - 20 q^{79} - 2 q^{81} + 4 q^{84} + 4 q^{86} - 36 q^{89} - 28 q^{91} + 6 q^{94} - 4 q^{96} + 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 + 2 * q^6 + 2 * q^9 + 6 * q^11 + 8 * q^14 - 2 * q^16 + 4 * q^19 + 8 * q^21 - 2 * q^24 - 10 * q^26 + 6 * q^29 + 20 * q^31 + 24 * q^34 - 2 * q^36 - 10 * q^39 - 12 * q^41 + 12 * q^44 + 6 * q^46 - 6 * q^49 + 24 * q^51 - 2 * q^54 + 4 * q^56 - 18 * q^59 - 4 * q^61 - 4 * q^64 + 12 * q^66 + 6 * q^69 + 24 * q^71 + 14 * q^74 - 4 * q^76 - 20 * q^79 - 2 * q^81 + 4 * q^84 + 4 * q^86 - 36 * q^89 - 28 * q^91 + 6 * q^94 - 4 * q^96 + 12 * 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
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$		−	1.00000i		−	0.288675i
$13$	3.46410	+	1.00000i	0.960769	+	0.277350i
$13$	3.46410	+	1.00000i	0.960769	+	0.277350i
$14$	2.00000			0.534522
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−5.19615	+	3.00000i	−1.26025	+	0.727607i	−0.973123	−	0.230285i	$-0.926034\pi$
$17$	−5.19615	+	3.00000i	−1.26025	+	0.727607i	−0.287129	+	0.957892i	$0.592701\pi$
$18$		−	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
$22$	−2.59808	+	1.50000i	−0.553912	+	0.319801i
$23$	−2.59808	−	1.50000i	−0.541736	−	0.312772i	0.204046	−	0.978961i	$-0.434591\pi$
$23$	−2.59808	−	1.50000i	−0.541736	−	0.312772i	−0.745782	+	0.666190i	$0.767924\pi$
$24$	−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
$31$	5.00000			0.898027			0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000			0.898027			0.449013	+	0.893525i	$0.351776\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−2.59808	+	1.50000i	−0.452267	+	0.261116i
$34$	6.00000			1.02899
$35$		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
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	−0.999353	−	0.0359748i	$-0.988546\pi$
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	0.530831	+	0.847477i	$0.321880\pi$
$42$	−1.73205	−	1.00000i	−0.267261	−	0.154303i
$43$	−0.866025	+	0.500000i	−0.132068	+	0.0762493i	−0.564578	−	0.825380i	$-0.690961\pi$
$43$	−0.866025	+	0.500000i	−0.132068	+	0.0762493i	0.432511	+	0.901629i	$0.357628\pi$
$44$	3.00000			0.452267
$45$		0			0
$46$	1.50000	+	2.59808i	0.221163	+	0.383065i
$47$			3.00000i			0.437595i	0.975770	+	0.218797i	$0.0702134\pi$
$47$			3.00000i			0.437595i	−0.975770	+	0.218797i	$0.929787\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	−1.50000	+	2.59808i	−0.214286	+	0.371154i
$50$		0			0
$51$	6.00000			0.840168
$52$	0.866025	+	3.50000i	0.120096	+	0.485363i
$53$		−	6.00000i		−	0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$		−	6.00000i		−	0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$	−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
$59$	−4.50000	−	7.79423i	−0.585850	−	1.01472i	−0.994769	−	0.102151i	$-0.967427\pi$
$59$	−4.50000	−	7.79423i	−0.585850	−	1.01472i	0.408919	−	0.912571i	$-0.365906\pi$
$60$		0			0
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$	−4.33013	−	2.50000i	−0.549927	−	0.317500i
$63$	−1.73205	−	1.00000i	−0.218218	−	0.125988i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	3.00000			0.369274
$67$	6.92820	+	4.00000i	0.846415	+	0.488678i	0.859440	−	0.511237i	$-0.170813\pi$
$67$	6.92820	+	4.00000i	0.846415	+	0.488678i	−0.0130248	+	0.999915i	$0.504146\pi$
$68$	−5.19615	−	3.00000i	−0.630126	−	0.363803i
$69$	1.50000	+	2.59808i	0.180579	+	0.312772i
$70$		0			0
$71$	6.00000	+	10.3923i	0.712069	+	1.23334i	0.964079	+	0.265615i	$0.0855750\pi$
$71$	6.00000	+	10.3923i	0.712069	+	1.23334i	−0.252010	+	0.967725i	$0.581092\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$			14.0000i			1.63858i	0.573382	+	0.819288i	$0.305631\pi$
$73$			14.0000i			1.63858i	−0.573382	+	0.819288i	$0.694369\pi$
$74$	3.50000	+	6.06218i	0.406867	+	0.704714i
$75$		0			0
$76$	−1.00000	+	1.73205i	−0.114708	+	0.198680i
$77$			6.00000i			0.683763i
$78$	0.866025	+	3.50000i	0.0980581	+	0.396297i
$79$	−5.00000			−0.562544			−0.281272	−	0.959628i	$-0.590756\pi$
$79$	−5.00000			−0.562544			−0.281272	+	0.959628i	$0.590756\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	5.19615	−	3.00000i	0.573819	−	0.331295i
$83$		−	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
$86$	1.00000			0.107833
$87$	−2.59808	+	1.50000i	−0.278543	+	0.160817i
$88$	−2.59808	−	1.50000i	−0.276956	−	0.159901i
$89$	−9.00000	+	15.5885i	−0.953998	+	1.65237i	−0.217354	+	0.976093i	$0.569742\pi$
$89$	−9.00000	+	15.5885i	−0.953998	+	1.65237i	−0.736644	+	0.676280i	$0.763591\pi$
$90$		0			0
$91$	−7.00000	+	1.73205i	−0.733799	+	0.181568i
$92$		−	3.00000i		−	0.312772i
$93$	−4.33013	−	2.50000i	−0.449013	−	0.259238i
$94$	1.50000	−	2.59808i	0.154713	−	0.267971i
$95$		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
$99$	3.00000			0.301511
$100$		0			0
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	−0.975796	−	0.218685i	$-0.929823\pi$
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	0.677284	+	0.735721i	$0.263157\pi$
$102$	−5.19615	−	3.00000i	−0.514496	−	0.297044i
$103$			14.0000i			1.37946i	0.724066	+	0.689730i	$0.242271\pi$
$103$			14.0000i			1.37946i	−0.724066	+	0.689730i	$0.757729\pi$
$104$	1.00000	−	3.46410i	0.0980581	−	0.339683i
$105$		0			0
$106$	−3.00000	+	5.19615i	−0.291386	+	0.504695i
$107$	−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
$113$	12.9904	−	7.50000i	1.22203	−	0.705541i	0.256681	−	0.966496i	$-0.417371\pi$
$113$	12.9904	−	7.50000i	1.22203	−	0.705541i	0.965351	+	0.260955i	$0.0840376\pi$
$114$	−1.00000	+	1.73205i	−0.0936586	+	0.162221i
$115$		0			0
$116$	3.00000			0.278543
$117$	0.866025	+	3.50000i	0.0800641	+	0.323575i
$118$			9.00000i			0.828517i
$119$	6.00000	−	10.3923i	0.550019	−	0.952661i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$			2.00000i			0.181071i
$123$	5.19615	−	3.00000i	0.468521	−	0.270501i
$124$	2.50000	+	4.33013i	0.224507	+	0.388857i
$125$		0			0
$126$	1.00000	+	1.73205i	0.0890871	+	0.154303i
$127$	12.1244	+	7.00000i	1.07586	+	0.621150i	0.929777	−	0.368122i	$-0.119999\pi$
$127$	12.1244	+	7.00000i	1.07586	+	0.621150i	0.146085	+	0.989272i	$0.453333\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	1.00000			0.0880451
$130$		0			0
$131$	9.00000			0.786334			0.393167	−	0.919467i	$-0.371379\pi$
$131$	9.00000			0.786334			0.393167	+	0.919467i	$0.371379\pi$
$132$	−2.59808	−	1.50000i	−0.226134	−	0.130558i
$133$	−3.46410	−	2.00000i	−0.300376	−	0.173422i
$134$	−4.00000	−	6.92820i	−0.345547	−	0.598506i
$135$		0			0
$136$	3.00000	+	5.19615i	0.257248	+	0.445566i
$137$	−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	$0.458946\pi$
$138$		−	3.00000i		−	0.255377i
$139$	7.00000	+	12.1244i	0.593732	+	1.02837i	0.993724	+	0.111856i	$0.0356795\pi$
$139$	7.00000	+	12.1244i	0.593732	+	1.02837i	−0.399992	+	0.916519i	$0.630987\pi$
$140$		0			0
$141$	1.50000	−	2.59808i	0.126323	−	0.218797i
$142$		−	12.0000i		−	1.00702i
$143$	7.79423	−	7.50000i	0.651786	−	0.627182i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	7.00000	−	12.1244i	0.579324	−	1.00342i
$147$	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
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$	1.73205	−	1.00000i	0.140488	−	0.0811107i
$153$	−5.19615	−	3.00000i	−0.420084	−	0.242536i
$154$	3.00000	−	5.19615i	0.241747	−	0.418718i
$155$		0			0
$156$	1.00000	−	3.46410i	0.0800641	−	0.277350i
$157$			13.0000i			1.03751i	0.854922	+	0.518756i	$0.173605\pi$
$157$			13.0000i			1.03751i	−0.854922	+	0.518756i	$0.826395\pi$
$158$	4.33013	+	2.50000i	0.344486	+	0.198889i
$159$	−3.00000	+	5.19615i	−0.237915	+	0.412082i
$160$		0			0
$161$	6.00000			0.472866
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$	−11.2583	+	6.50000i	−0.881820	+	0.509119i	−0.871258	−	0.490825i	$-0.836695\pi$
$163$	−11.2583	+	6.50000i	−0.881820	+	0.509119i	−0.0105623	+	0.999944i	$0.503362\pi$
$164$	−6.00000			−0.468521
$165$		0			0
$166$	−3.00000	+	5.19615i	−0.232845	+	0.403300i
$167$	−7.79423	−	4.50000i	−0.603136	−	0.348220i	0.167139	−	0.985933i	$-0.446547\pi$
$167$	−7.79423	−	4.50000i	−0.603136	−	0.348220i	−0.770274	+	0.637713i	$0.779881\pi$
$168$		−	2.00000i		−	0.154303i
$169$	11.0000	+	6.92820i	0.846154	+	0.532939i
$170$		0			0
$171$	−1.00000	+	1.73205i	−0.0764719	+	0.132453i
$172$	−0.866025	−	0.500000i	−0.0660338	−	0.0381246i
$173$	10.3923	−	6.00000i	0.790112	−	0.456172i	−0.0498898	−	0.998755i	$-0.515887\pi$
$173$	10.3923	−	6.00000i	0.790112	−	0.456172i	0.840002	+	0.542583i	$0.182554\pi$
$174$	3.00000			0.227429
$175$		0			0
$176$	1.50000	+	2.59808i	0.113067	+	0.195837i
$177$			9.00000i			0.676481i
$178$	15.5885	−	9.00000i	1.16840	−	0.674579i
$179$	−1.50000	+	2.59808i	−0.112115	+	0.194189i	−0.916623	−	0.399753i	$-0.869096\pi$
$179$	−1.50000	+	2.59808i	−0.112115	+	0.194189i	0.804508	+	0.593942i	$0.202429\pi$
$180$		0			0
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$	6.92820	+	2.00000i	0.513553	+	0.148250i
$183$			2.00000i			0.147844i
$184$	−1.50000	+	2.59808i	−0.110581	+	0.191533i
$185$		0			0
$186$	2.50000	+	4.33013i	0.183309	+	0.317500i
$187$			18.0000i			1.31629i
$188$	−2.59808	+	1.50000i	−0.189484	+	0.109399i
$189$	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
$193$	3.46410	+	2.00000i	0.249351	+	0.143963i	0.619467	−	0.785022i	$-0.287349\pi$
$193$	3.46410	+	2.00000i	0.249351	+	0.143963i	−0.370116	+	0.928986i	$0.620682\pi$
$194$	14.0000			1.00514
$195$		0			0
$196$	−3.00000			−0.214286
$197$	20.7846	+	12.0000i	1.48084	+	0.854965i	0.999764	−	0.0217133i	$-0.00691209\pi$
$197$	20.7846	+	12.0000i	1.48084	+	0.854965i	0.481078	+	0.876678i	$0.340245\pi$
$198$	−2.59808	−	1.50000i	−0.184637	−	0.106600i
$199$	4.00000	+	6.92820i	0.283552	+	0.491127i	0.972257	−	0.233915i	$-0.0751537\pi$
$199$	4.00000	+	6.92820i	0.283552	+	0.491127i	−0.688705	+	0.725042i	$0.741820\pi$
$200$		0			0
$201$	−4.00000	−	6.92820i	−0.282138	−	0.488678i
$202$	5.19615	−	3.00000i	0.365600	−	0.211079i
$203$			6.00000i			0.421117i
$204$	3.00000	+	5.19615i	0.210042	+	0.363803i
$205$		0			0
$206$	7.00000	−	12.1244i	0.487713	−	0.844744i
$207$		−	3.00000i		−	0.208514i
$208$	−2.59808	+	2.50000i	−0.180144	+	0.173344i
$209$	6.00000			0.415029
$210$		0			0
$211$	−10.0000	+	17.3205i	−0.688428	+	1.19239i	0.283918	+	0.958849i	$0.408366\pi$
$211$	−10.0000	+	17.3205i	−0.688428	+	1.19239i	−0.972346	+	0.233544i	$0.924968\pi$
$212$	5.19615	−	3.00000i	0.356873	−	0.206041i
$213$		−	12.0000i		−	0.822226i
$214$	3.00000	+	5.19615i	0.205076	+	0.355202i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	−8.66025	+	5.00000i	−0.587896	+	0.339422i
$218$	12.1244	+	7.00000i	0.821165	+	0.474100i
$219$	7.00000	−	12.1244i	0.473016	−	0.819288i
$220$		0			0
$221$	−21.0000	+	5.19615i	−1.41261	+	0.349531i
$222$		−	7.00000i		−	0.469809i
$223$	8.66025	+	5.00000i	0.579934	+	0.334825i	0.761107	−	0.648626i	$-0.224656\pi$
$223$	8.66025	+	5.00000i	0.579934	+	0.334825i	−0.181173	+	0.983451i	$0.557990\pi$
$224$	−1.00000	+	1.73205i	−0.0668153	+	0.115728i
$225$		0			0
$226$	−15.0000			−0.997785
$227$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$227$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$228$	1.73205	−	1.00000i	0.114708	−	0.0662266i
$229$	−14.0000			−0.925146			−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000			−0.925146			−0.462573	+	0.886581i	$0.653074\pi$
$230$		0			0
$231$	3.00000	−	5.19615i	0.197386	−	0.341882i
$232$	−2.59808	−	1.50000i	−0.170572	−	0.0984798i
$233$			21.0000i			1.37576i	0.725826	+	0.687878i	$0.241458\pi$
$233$			21.0000i			1.37576i	−0.725826	+	0.687878i	$0.758542\pi$
$234$	1.00000	−	3.46410i	0.0653720	−	0.226455i
$235$		0			0
$236$	4.50000	−	7.79423i	0.292925	−	0.507361i
$237$	4.33013	+	2.50000i	0.281272	+	0.162392i
$238$	−10.3923	+	6.00000i	−0.673633	+	0.388922i
$239$	−24.0000			−1.55243			−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000			−1.55243			−0.776215	+	0.630468i	$0.782863\pi$
$240$		0			0
$241$	−8.50000	−	14.7224i	−0.547533	−	0.948355i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−8.50000	−	14.7224i	−0.547533	−	0.948355i	0.450910	−	0.892570i	$-0.351100\pi$
$242$		−	2.00000i		−	0.128565i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	1.00000	−	1.73205i	0.0640184	−	0.110883i
$245$		0			0
$246$	−6.00000			−0.382546
$247$	1.73205	+	7.00000i	0.110208	+	0.445399i
$248$		−	5.00000i		−	0.317500i
$249$	−3.00000	+	5.19615i	−0.190117	+	0.329293i
$250$		0			0
$251$	−7.50000	−	12.9904i	−0.473396	−	0.819946i	0.526140	−	0.850398i	$-0.323639\pi$
$251$	−7.50000	−	12.9904i	−0.473396	−	0.819946i	−0.999536	+	0.0304521i	$0.990305\pi$
$252$		−	2.00000i		−	0.125988i
$253$	−7.79423	+	4.50000i	−0.490019	+	0.282913i
$254$	−7.00000	−	12.1244i	−0.439219	−	0.760750i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−18.1865	−	10.5000i	−1.13444	−	0.654972i	−0.189396	−	0.981901i	$-0.560653\pi$
$257$	−18.1865	−	10.5000i	−1.13444	−	0.654972i	−0.945049	+	0.326929i	$0.893986\pi$
$258$	−0.866025	−	0.500000i	−0.0539164	−	0.0311286i
$259$	14.0000			0.869918
$260$		0			0
$261$	3.00000			0.185695
$262$	−7.79423	−	4.50000i	−0.481529	−	0.278011i
$263$	12.9904	+	7.50000i	0.801021	+	0.462470i	0.843828	−	0.536614i	$-0.180297\pi$
$263$	12.9904	+	7.50000i	0.801021	+	0.462470i	−0.0428069	+	0.999083i	$0.513630\pi$
$264$	1.50000	+	2.59808i	0.0923186	+	0.159901i
$265$		0			0
$266$	2.00000	+	3.46410i	0.122628	+	0.212398i
$267$	15.5885	−	9.00000i	0.953998	−	0.550791i
$268$			8.00000i			0.488678i
$269$	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
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	−0.983312	−	0.181928i	$-0.941766\pi$
$271$	−5.50000	+	9.52628i	−0.334101	+	0.578680i	0.649211	+	0.760609i	$0.275099\pi$
$272$		−	6.00000i		−	0.363803i
$273$	6.92820	+	2.00000i	0.419314	+	0.121046i
$274$	9.00000			0.543710
$275$		0			0
$276$	−1.50000	+	2.59808i	−0.0902894	+	0.156386i
$277$	0.866025	−	0.500000i	0.0520344	−	0.0300421i	−0.473757	−	0.880656i	$-0.657103\pi$
$277$	0.866025	−	0.500000i	0.0520344	−	0.0300421i	0.525792	+	0.850613i	$0.323769\pi$
$278$		−	14.0000i		−	0.839664i
$279$	2.50000	+	4.33013i	0.149671	+	0.259238i
$280$		0			0
$281$	18.0000			1.07379			0.536895	−	0.843649i	$-0.319597\pi$
$281$	18.0000			1.07379			0.536895	+	0.843649i	$0.319597\pi$
$282$	−2.59808	+	1.50000i	−0.154713	+	0.0893237i
$283$	26.8468	+	15.5000i	1.59588	+	0.921379i	0.992270	+	0.124096i	$0.0396032\pi$
$283$	26.8468	+	15.5000i	1.59588	+	0.921379i	0.603606	+	0.797283i	$0.293730\pi$
$284$	−6.00000	+	10.3923i	−0.356034	+	0.616670i
$285$		0			0
$286$	−10.5000	+	2.59808i	−0.620878	+	0.153627i
$287$		−	12.0000i		−	0.708338i
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	9.50000	−	16.4545i	0.558824	−	0.967911i
$290$		0			0
$291$	14.0000			0.820695
$292$	−12.1244	+	7.00000i	−0.709524	+	0.409644i
$293$	−25.9808	+	15.0000i	−1.51781	+	0.876309i	−0.518032	+	0.855361i	$0.673335\pi$
$293$	−25.9808	+	15.0000i	−1.51781	+	0.876309i	−0.999781	+	0.0209480i	$0.993332\pi$
$294$	−3.00000			−0.174964
$295$		0			0
$296$	−3.50000	+	6.06218i	−0.203433	+	0.352357i
$297$	−2.59808	−	1.50000i	−0.150756	−	0.0870388i
$298$			9.00000i			0.521356i
$299$	−7.50000	−	7.79423i	−0.433736	−	0.450752i
$300$		0			0
$301$	1.00000	−	1.73205i	0.0576390	−	0.0998337i
$302$	−6.92820	−	4.00000i	−0.398673	−	0.230174i
$303$	5.19615	−	3.00000i	0.298511	−	0.172345i
$304$	−2.00000			−0.114708
$305$		0			0
$306$	3.00000	+	5.19615i	0.171499	+	0.297044i
$307$		−	8.00000i		−	0.456584i	−0.973593	−	0.228292i	$-0.926686\pi$
$307$		−	8.00000i		−	0.456584i	0.973593	−	0.228292i	$-0.0733141\pi$
$308$	−5.19615	+	3.00000i	−0.296078	+	0.170941i
$309$	7.00000	−	12.1244i	0.398216	−	0.689730i
$310$		0			0
$311$	−12.0000			−0.680458			−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000			−0.680458			−0.340229	+	0.940343i	$0.610505\pi$
$312$	−2.59808	+	2.50000i	−0.147087	+	0.141535i
$313$			8.00000i			0.452187i	0.974106	+	0.226093i	$0.0725954\pi$
$313$			8.00000i			0.452187i	−0.974106	+	0.226093i	$0.927405\pi$
$314$	6.50000	−	11.2583i	0.366816	−	0.635344i
$315$		0			0
$316$	−2.50000	−	4.33013i	−0.140636	−	0.243589i
$317$		−	12.0000i		−	0.673987i	−0.941507	−	0.336994i	$-0.890590\pi$
$317$		−	12.0000i		−	0.673987i	0.941507	−	0.336994i	$-0.109410\pi$
$318$	5.19615	−	3.00000i	0.291386	−	0.168232i
$319$	−4.50000	−	7.79423i	−0.251952	−	0.436393i
$320$		0			0
$321$	3.00000	+	5.19615i	0.167444	+	0.290021i
$322$	−5.19615	−	3.00000i	−0.289570	−	0.167183i
$323$	−10.3923	−	6.00000i	−0.578243	−	0.333849i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	13.0000			0.720003
$327$	12.1244	+	7.00000i	0.670478	+	0.387101i
$328$	5.19615	+	3.00000i	0.286910	+	0.165647i
$329$	−3.00000	−	5.19615i	−0.165395	−	0.286473i
$330$		0			0
$331$	−16.0000	−	27.7128i	−0.879440	−	1.52323i	−0.851957	−	0.523612i	$-0.824584\pi$
$331$	−16.0000	−	27.7128i	−0.879440	−	1.52323i	−0.0274825	−	0.999622i	$-0.508749\pi$
$332$	5.19615	−	3.00000i	0.285176	−	0.164646i
$333$		−	7.00000i		−	0.383598i
$334$	4.50000	+	7.79423i	0.246229	+	0.426481i
$335$		0			0
$336$	−1.00000	+	1.73205i	−0.0545545	+	0.0944911i
$337$		−	14.0000i		−	0.762629i	−0.924445	−	0.381314i	$-0.875472\pi$
$337$		−	14.0000i		−	0.762629i	0.924445	−	0.381314i	$-0.124528\pi$
$338$	−6.06218	−	11.5000i	−0.329739	−	0.625518i
$339$	−15.0000			−0.814688
$340$		0			0
$341$	7.50000	−	12.9904i	0.406148	−	0.703469i
$342$	1.73205	−	1.00000i	0.0936586	−	0.0540738i
$343$		−	20.0000i		−	1.07990i
$344$	0.500000	+	0.866025i	0.0269582	+	0.0466930i
$345$		0			0
$346$	−12.0000			−0.645124
$347$	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
$349$	4.00000	−	6.92820i	0.214115	−	0.370858i	−0.738883	−	0.673833i	$-0.764647\pi$
$349$	4.00000	−	6.92820i	0.214115	−	0.370858i	0.952998	+	0.302975i	$0.0979799\pi$
$350$		0			0
$351$	1.00000	−	3.46410i	0.0533761	−	0.184900i
$352$		−	3.00000i		−	0.159901i
$353$	−25.9808	−	15.0000i	−1.38282	−	0.798369i	−0.390324	−	0.920677i	$-0.627637\pi$
$353$	−25.9808	−	15.0000i	−1.38282	−	0.798369i	−0.992492	+	0.122308i	$0.960970\pi$
$354$	4.50000	−	7.79423i	0.239172	−	0.414259i
$355$		0			0
$356$	−18.0000			−0.953998
$357$	−10.3923	+	6.00000i	−0.550019	+	0.317554i
$358$	2.59808	−	1.50000i	0.137313	−	0.0792775i
$359$	−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
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	13.8564	+	8.00000i	0.728277	+	0.420471i
$363$		−	2.00000i		−	0.104973i
$364$	−5.00000	−	5.19615i	−0.262071	−	0.272352i
$365$		0			0
$366$	1.00000	−	1.73205i	0.0522708	−	0.0905357i
$367$	17.3205	+	10.0000i	0.904123	+	0.521996i	0.878536	−	0.477677i	$-0.158521\pi$
$367$	17.3205	+	10.0000i	0.904123	+	0.521996i	0.0255875	+	0.999673i	$0.491854\pi$
$368$	2.59808	−	1.50000i	0.135434	−	0.0781929i
$369$	−6.00000			−0.312348
$370$		0			0
$371$	6.00000	+	10.3923i	0.311504	+	0.539542i
$372$		−	5.00000i		−	0.259238i
$373$	−21.6506	+	12.5000i	−1.12103	+	0.647225i	−0.941663	−	0.336557i	$-0.890737\pi$
$373$	−21.6506	+	12.5000i	−1.12103	+	0.647225i	−0.179364	+	0.983783i	$0.557404\pi$
$374$	9.00000	−	15.5885i	0.465379	−	0.806060i
$375$		0			0
$376$	3.00000			0.154713
$377$	7.79423	−	7.50000i	0.401423	−	0.386270i
$378$		−	2.00000i		−	0.102869i
$379$	19.0000	−	32.9090i	0.975964	−	1.69042i	0.299249	−	0.954175i	$-0.403264\pi$
$379$	19.0000	−	32.9090i	0.975964	−	1.69042i	0.676715	−	0.736245i	$-0.263403\pi$
$380$		0			0
$381$	−7.00000	−	12.1244i	−0.358621	−	0.621150i
$382$		−	12.0000i		−	0.613973i
$383$	−18.1865	+	10.5000i	−0.929288	+	0.536525i	−0.886586	−	0.462563i	$-0.846930\pi$
$383$	−18.1865	+	10.5000i	−0.929288	+	0.536525i	−0.0427020	+	0.999088i	$0.513597\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$		0			0
$386$	−2.00000	−	3.46410i	−0.101797	−	0.176318i
$387$	−0.866025	−	0.500000i	−0.0440225	−	0.0254164i
$388$	−12.1244	−	7.00000i	−0.615521	−	0.355371i
$389$	−3.00000			−0.152106			−0.0760530	−	0.997104i	$-0.524232\pi$
$389$	−3.00000			−0.152106			−0.0760530	+	0.997104i	$0.524232\pi$
$390$		0			0
$391$	18.0000			0.910299
$392$	2.59808	+	1.50000i	0.131223	+	0.0757614i
$393$	−7.79423	−	4.50000i	−0.393167	−	0.226995i
$394$	−12.0000	−	20.7846i	−0.604551	−	1.04711i
$395$		0			0
$396$	1.50000	+	2.59808i	0.0753778	+	0.130558i
$397$	26.8468	−	15.5000i	1.34740	−	0.777923i	0.359521	−	0.933137i	$-0.382940\pi$
$397$	26.8468	−	15.5000i	1.34740	−	0.777923i	0.987881	+	0.155214i	$0.0496068\pi$
$398$		−	8.00000i		−	0.401004i
$399$	2.00000	+	3.46410i	0.100125	+	0.173422i
$400$		0			0
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	−0.676425	−	0.736512i	$-0.736472\pi$
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	0.976050	+	0.217545i	$0.0698049\pi$
$402$			8.00000i			0.399004i
$403$	17.3205	+	5.00000i	0.862796	+	0.249068i
$404$	−6.00000			−0.298511
$405$		0			0
$406$	3.00000	−	5.19615i	0.148888	−	0.257881i
$407$	−18.1865	+	10.5000i	−0.901473	+	0.520466i
$408$		−	6.00000i		−	0.297044i
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	0.715523	−	0.698589i	$-0.246188\pi$
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	−0.962757	+	0.270367i	$0.912855\pi$
$410$		0			0
$411$	9.00000			0.443937
$412$	−12.1244	+	7.00000i	−0.597324	+	0.344865i
$413$	15.5885	+	9.00000i	0.767058	+	0.442861i
$414$	−1.50000	+	2.59808i	−0.0737210	+	0.127688i
$415$		0			0
$416$	3.50000	−	0.866025i	0.171602	−	0.0424604i
$417$		−	14.0000i		−	0.685583i
$418$	−5.19615	−	3.00000i	−0.254152	−	0.146735i
$419$	−6.00000	+	10.3923i	−0.293119	+	0.507697i	−0.974546	−	0.224189i	$-0.928027\pi$
$419$	−6.00000	+	10.3923i	−0.293119	+	0.507697i	0.681426	+	0.731887i	$0.261360\pi$
$420$		0			0
$421$	−16.0000			−0.779792			−0.389896	−	0.920859i	$-0.627489\pi$
$421$	−16.0000			−0.779792			−0.389896	+	0.920859i	$0.627489\pi$
$422$	17.3205	−	10.0000i	0.843149	−	0.486792i
$423$	−2.59808	+	1.50000i	−0.126323	+	0.0729325i
$424$	−6.00000			−0.291386
$425$		0			0
$426$	−6.00000	+	10.3923i	−0.290701	+	0.503509i
$427$	3.46410	+	2.00000i	0.167640	+	0.0967868i
$428$		−	6.00000i		−	0.290021i
$429$	−10.5000	+	2.59808i	−0.506945	+	0.125436i
$430$		0			0
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	−0.973574	−	0.228373i	$-0.926659\pi$
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	0.684564	+	0.728953i	$0.259993\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	−34.6410	+	20.0000i	−1.66474	+	0.961139i	−0.694337	+	0.719650i	$0.744302\pi$
$433$	−34.6410	+	20.0000i	−1.66474	+	0.961139i	−0.970404	+	0.241489i	$0.922364\pi$
$434$	10.0000			0.480015
$435$		0			0
$436$	−7.00000	−	12.1244i	−0.335239	−	0.580651i
$437$		−	6.00000i		−	0.287019i
$438$	−12.1244	+	7.00000i	−0.579324	+	0.334473i
$439$	−2.00000	+	3.46410i	−0.0954548	+	0.165333i	−0.909798	−	0.415051i	$-0.863764\pi$
$439$	−2.00000	+	3.46410i	−0.0954548	+	0.165333i	0.814344	+	0.580383i	$0.197097\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$	20.7846	+	6.00000i	0.988623	+	0.285391i
$443$		−	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
$446$	−5.00000	−	8.66025i	−0.236757	−	0.410075i
$447$			9.00000i			0.425685i
$448$	1.73205	−	1.00000i	0.0818317	−	0.0472456i
$449$	18.0000	+	31.1769i	0.849473	+	1.47133i	0.881680	+	0.471848i	$0.156413\pi$
$449$	18.0000	+	31.1769i	0.849473	+	1.47133i	−0.0322072	+	0.999481i	$0.510254\pi$
$450$		0			0
$451$	9.00000	+	15.5885i	0.423793	+	0.734032i
$452$	12.9904	+	7.50000i	0.611016	+	0.352770i
$453$	−6.92820	−	4.00000i	−0.325515	−	0.187936i
$454$		0			0
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	1.73205	+	1.00000i	0.0810219	+	0.0467780i	0.539964	−	0.841688i	$-0.318438\pi$
$457$	1.73205	+	1.00000i	0.0810219	+	0.0467780i	−0.458942	+	0.888466i	$0.651771\pi$
$458$	12.1244	+	7.00000i	0.566534	+	0.327089i
$459$	3.00000	+	5.19615i	0.140028	+	0.242536i
$460$		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	$0.946917\pi$
$462$	−5.19615	+	3.00000i	−0.241747	+	0.139573i
$463$		−	34.0000i		−	1.58011i	−0.613033	−	0.790057i	$-0.710051\pi$
$463$		−	34.0000i		−	1.58011i	0.613033	−	0.790057i	$-0.289949\pi$
$464$	1.50000	+	2.59808i	0.0696358	+	0.120613i
$465$		0			0
$466$	10.5000	−	18.1865i	0.486403	−	0.842475i
$467$		−	18.0000i		−	0.832941i	−0.909149	−	0.416470i	$-0.863267\pi$
$467$		−	18.0000i		−	0.832941i	0.909149	−	0.416470i	$-0.136733\pi$
$468$	−2.59808	+	2.50000i	−0.120096	+	0.115563i
$469$	−16.0000			−0.738811
$470$		0			0
$471$	6.50000	−	11.2583i	0.299504	−	0.518756i
$472$	−7.79423	+	4.50000i	−0.358758	+	0.207129i
$473$			3.00000i			0.137940i
$474$	−2.50000	−	4.33013i	−0.114829	−	0.198889i
$475$		0			0
$476$	12.0000			0.550019
$477$	5.19615	−	3.00000i	0.237915	−	0.137361i
$478$	20.7846	+	12.0000i	0.950666	+	0.548867i
$479$		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
$482$			17.0000i			0.774329i
$483$	−5.19615	−	3.00000i	−0.236433	−	0.136505i
$484$	−1.00000	+	1.73205i	−0.0454545	+	0.0787296i
$485$		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	$0.347762\pi$
$488$	−1.73205	+	1.00000i	−0.0784063	+	0.0452679i
$489$	13.0000			0.587880
$490$		0			0
$491$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$491$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$492$	5.19615	+	3.00000i	0.234261	+	0.135250i
$493$			18.0000i			0.810679i
$494$	2.00000	−	6.92820i	0.0899843	−	0.311715i
$495$		0			0
$496$	−2.50000	+	4.33013i	−0.112253	+	0.194428i
$497$	−20.7846	−	12.0000i	−0.932317	−	0.538274i
$498$	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
$501$	4.50000	+	7.79423i	0.201045	+	0.348220i
$502$			15.0000i			0.669483i
$503$	20.7846	−	12.0000i	0.926740	−	0.535054i	0.0409609	−	0.999161i	$-0.486958\pi$
$503$	20.7846	−	12.0000i	0.926740	−	0.535054i	0.885779	+	0.464107i	$0.153625\pi$
$504$	−1.00000	+	1.73205i	−0.0445435	+	0.0771517i
$505$		0			0
$506$	9.00000			0.400099
$507$	−6.06218	−	11.5000i	−0.269231	−	0.510733i
$508$			14.0000i			0.621150i
$509$	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
$511$	−14.0000	−	24.2487i	−0.619324	−	1.07270i
$512$			1.00000i			0.0441942i
$513$	1.73205	−	1.00000i	0.0764719	−	0.0441511i
$514$	10.5000	+	18.1865i	0.463135	+	0.802174i
$515$		0			0
$516$	0.500000	+	0.866025i	0.0220113	+	0.0381246i
$517$	7.79423	+	4.50000i	0.342790	+	0.197910i
$518$	−12.1244	−	7.00000i	−0.532714	−	0.307562i
$519$	−12.0000			−0.526742
$520$		0			0
$521$	−30.0000			−1.31432			−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000			−1.31432			−0.657162	+	0.753749i	$0.728243\pi$
$522$	−2.59808	−	1.50000i	−0.113715	−	0.0656532i
$523$	−9.52628	−	5.50000i	−0.416555	−	0.240498i	0.277047	−	0.960856i	$-0.410644\pi$
$523$	−9.52628	−	5.50000i	−0.416555	−	0.240498i	−0.693602	+	0.720358i	$0.743977\pi$
$524$	4.50000	+	7.79423i	0.196583	+	0.340492i
$525$		0			0
$526$	−7.50000	−	12.9904i	−0.327016	−	0.566408i
$527$	−25.9808	+	15.0000i	−1.13174	+	0.653410i
$528$		−	3.00000i		−	0.130558i
$529$	−7.00000	−	12.1244i	−0.304348	−	0.527146i
$530$		0			0
$531$	4.50000	−	7.79423i	0.195283	−	0.338241i
$532$		−	4.00000i		−	0.173422i
$533$	−15.5885	+	15.0000i	−0.675211	+	0.649722i
$534$	−18.0000			−0.778936
$535$		0			0
$536$	4.00000	−	6.92820i	0.172774	−	0.299253i
$537$	2.59808	−	1.50000i	0.112115	−	0.0647298i
$538$		−	18.0000i		−	0.776035i
$539$	4.50000	+	7.79423i	0.193829	+	0.335721i
$540$		0			0
$541$	20.0000			0.859867			0.429934	−	0.902861i	$-0.358537\pi$
$541$	20.0000			0.859867			0.429934	+	0.902861i	$0.358537\pi$
$542$	9.52628	−	5.50000i	0.409189	−	0.236245i
$543$	13.8564	+	8.00000i	0.594635	+	0.343313i
$544$	−3.00000	+	5.19615i	−0.128624	+	0.222783i
$545$		0			0
$546$	−5.00000	−	5.19615i	−0.213980	−	0.222375i
$547$		−	20.0000i		−	0.855138i	−0.903983	−	0.427569i	$-0.859370\pi$
$547$		−	20.0000i		−	0.855138i	0.903983	−	0.427569i	$-0.140630\pi$
$548$	−7.79423	−	4.50000i	−0.332953	−	0.192230i
$549$	1.00000	−	1.73205i	0.0426790	−	0.0739221i
$550$		0			0
$551$	6.00000			0.255609
$552$	2.59808	−	1.50000i	0.110581	−	0.0638442i
$553$	8.66025	−	5.00000i	0.368271	−	0.212622i
$554$	−1.00000			−0.0424859
$555$		0			0
$556$	−7.00000	+	12.1244i	−0.296866	+	0.514187i
$557$	−5.19615	−	3.00000i	−0.220168	−	0.127114i	0.385860	−	0.922557i	$-0.373905\pi$
$557$	−5.19615	−	3.00000i	−0.220168	−	0.127114i	−0.606028	+	0.795443i	$0.707238\pi$
$558$		−	5.00000i		−	0.211667i
$559$	−3.50000	+	0.866025i	−0.148034	+	0.0366290i
$560$		0			0
$561$	9.00000	−	15.5885i	0.379980	−	0.658145i
$562$	−15.5885	−	9.00000i	−0.657559	−	0.379642i
$563$	31.1769	−	18.0000i	1.31395	−	0.758610i	0.331202	−	0.943560i	$-0.392546\pi$
$563$	31.1769	−	18.0000i	1.31395	−	0.758610i	0.982748	+	0.184950i	$0.0592124\pi$
$564$	3.00000			0.126323
$565$		0			0
$566$	−15.5000	−	26.8468i	−0.651514	−	1.12845i
$567$		−	2.00000i		−	0.0839921i
$568$	10.3923	−	6.00000i	0.436051	−	0.251754i
$569$	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
$571$	−40.0000			−1.67395			−0.836974	−	0.547243i	$-0.815677\pi$
$571$	−40.0000			−1.67395			−0.836974	+	0.547243i	$0.815677\pi$
$572$	10.3923	+	3.00000i	0.434524	+	0.125436i
$573$		−	12.0000i		−	0.501307i
$574$	−6.00000	+	10.3923i	−0.250435	+	0.433766i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$		−	2.00000i		−	0.0832611i	−0.999133	−	0.0416305i	$-0.986745\pi$
$577$		−	2.00000i		−	0.0832611i	0.999133	−	0.0416305i	$-0.0132552\pi$
$578$	−16.4545	+	9.50000i	−0.684416	+	0.395148i
$579$	−2.00000	−	3.46410i	−0.0831172	−	0.143963i
$580$		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
$584$	14.0000			0.579324
$585$		0			0
$586$	30.0000			1.23929
$587$	15.5885	+	9.00000i	0.643404	+	0.371470i	0.785925	−	0.618322i	$-0.212187\pi$
$587$	15.5885	+	9.00000i	0.643404	+	0.371470i	−0.142520	+	0.989792i	$0.545521\pi$
$588$	2.59808	+	1.50000i	0.107143	+	0.0618590i
$589$	5.00000	+	8.66025i	0.206021	+	0.356840i
$590$		0			0
$591$	−12.0000	−	20.7846i	−0.493614	−	0.854965i
$592$	6.06218	−	3.50000i	0.249154	−	0.143849i
$593$			27.0000i			1.10876i	0.832265	+	0.554379i	$0.187044\pi$
$593$			27.0000i			1.10876i	−0.832265	+	0.554379i	$0.812956\pi$
$594$	1.50000	+	2.59808i	0.0615457	+	0.106600i
$595$		0			0
$596$	4.50000	−	7.79423i	0.184327	−	0.319264i
$597$		−	8.00000i		−	0.327418i
$598$	2.59808	+	10.5000i	0.106243	+	0.429377i
$599$	−6.00000			−0.245153			−0.122577	−	0.992459i	$-0.539116\pi$
$599$	−6.00000			−0.245153			−0.122577	+	0.992459i	$0.539116\pi$
$600$		0			0
$601$	9.50000	−	16.4545i	0.387513	−	0.671192i	−0.604601	−	0.796528i	$-0.706668\pi$
$601$	9.50000	−	16.4545i	0.387513	−	0.671192i	0.992114	+	0.125336i	$0.0400009\pi$
$602$	−1.73205	+	1.00000i	−0.0705931	+	0.0407570i
$603$			8.00000i			0.325785i
$604$	4.00000	+	6.92820i	0.162758	+	0.281905i
$605$		0			0
$606$	−6.00000			−0.243733
$607$	19.0526	−	11.0000i	0.773320	−	0.446476i	−0.0607380	−	0.998154i	$-0.519345\pi$
$607$	19.0526	−	11.0000i	0.773320	−	0.446476i	0.834058	+	0.551678i	$0.186012\pi$
$608$	1.73205	+	1.00000i	0.0702439	+	0.0405554i
$609$	3.00000	−	5.19615i	0.121566	−	0.210559i
$610$		0			0
$611$	−3.00000	+	10.3923i	−0.121367	+	0.420428i
$612$		−	6.00000i		−	0.242536i
$613$	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	$0.451342\pi$
$614$	−4.00000	+	6.92820i	−0.161427	+	0.279600i
$615$		0			0
$616$	6.00000			0.241747
$617$	−18.1865	+	10.5000i	−0.732162	+	0.422714i	−0.819213	−	0.573490i	$-0.805589\pi$
$617$	−18.1865	+	10.5000i	−0.732162	+	0.422714i	0.0870504	+	0.996204i	$0.472256\pi$
$618$	−12.1244	+	7.00000i	−0.487713	+	0.281581i
$619$	46.0000			1.84890			0.924448	−	0.381308i	$-0.124526\pi$
$619$	46.0000			1.84890			0.924448	+	0.381308i	$0.124526\pi$
$620$		0			0
$621$	−1.50000	+	2.59808i	−0.0601929	+	0.104257i
$622$	10.3923	+	6.00000i	0.416693	+	0.240578i
$623$		−	36.0000i		−	1.44231i
$624$	3.50000	−	0.866025i	0.140112	−	0.0346688i
$625$		0			0
$626$	4.00000	−	6.92820i	0.159872	−	0.276907i
$627$	−5.19615	−	3.00000i	−0.207514	−	0.119808i
$628$	−11.2583	+	6.50000i	−0.449256	+	0.259378i
$629$	42.0000			1.67465
$630$		0			0
$631$	8.00000	+	13.8564i	0.318475	+	0.551615i	0.980170	−	0.198158i	$-0.0634960\pi$
$631$	8.00000	+	13.8564i	0.318475	+	0.551615i	−0.661695	+	0.749773i	$0.730163\pi$
$632$			5.00000i			0.198889i
$633$	17.3205	−	10.0000i	0.688428	−	0.397464i
$634$	−6.00000	+	10.3923i	−0.238290	+	0.412731i
$635$		0			0
$636$	−6.00000			−0.237915
$637$	−7.79423	+	7.50000i	−0.308819	+	0.297161i
$638$			9.00000i			0.356313i
$639$	−6.00000	+	10.3923i	−0.237356	+	0.411113i
$640$		0			0
$641$	−3.00000	−	5.19615i	−0.118493	−	0.205236i	0.800678	−	0.599095i	$-0.204473\pi$
$641$	−3.00000	−	5.19615i	−0.118493	−	0.205236i	−0.919171	+	0.393860i	$0.871140\pi$
$642$		−	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	$0.435502\pi$
$644$	3.00000	+	5.19615i	0.118217	+	0.204757i
$645$		0			0
$646$	6.00000	+	10.3923i	0.236067	+	0.408880i
$647$	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
$649$	−27.0000			−1.05984
$650$		0			0
$651$	10.0000			0.391931
$652$	−11.2583	−	6.50000i	−0.440910	−	0.254560i
$653$	−5.19615	−	3.00000i	−0.203341	−	0.117399i	0.394872	−	0.918736i	$-0.370789\pi$
$653$	−5.19615	−	3.00000i	−0.203341	−	0.117399i	−0.598213	+	0.801337i	$0.704122\pi$
$654$	−7.00000	−	12.1244i	−0.273722	−	0.474100i
$655$		0			0
$656$	−3.00000	−	5.19615i	−0.117130	−	0.202876i
$657$	−12.1244	+	7.00000i	−0.473016	+	0.273096i
$658$			6.00000i			0.233904i
$659$	7.50000	+	12.9904i	0.292159	+	0.506033i	0.974320	−	0.225168i	$-0.0722932\pi$
$659$	7.50000	+	12.9904i	0.292159	+	0.506033i	−0.682161	+	0.731202i	$0.738960\pi$
$660$		0			0
$661$	−16.0000	+	27.7128i	−0.622328	+	1.07790i	0.366723	+	0.930330i	$0.380480\pi$
$661$	−16.0000	+	27.7128i	−0.622328	+	1.07790i	−0.989051	+	0.147573i	$0.952854\pi$
$662$			32.0000i			1.24372i
$663$	20.7846	+	6.00000i	0.807207	+	0.233021i
$664$	−6.00000			−0.232845
$665$		0			0
$666$	−3.50000	+	6.06218i	−0.135622	+	0.234905i
$667$	−7.79423	+	4.50000i	−0.301794	+	0.174241i
$668$		−	9.00000i		−	0.348220i
$669$	−5.00000	−	8.66025i	−0.193311	−	0.334825i
$670$		0			0
$671$	−6.00000			−0.231627
$672$	1.73205	−	1.00000i	0.0668153	−	0.0385758i
$673$	3.46410	+	2.00000i	0.133531	+	0.0770943i	0.565278	−	0.824901i	$-0.308769\pi$
$673$	3.46410	+	2.00000i	0.133531	+	0.0770943i	−0.431746	+	0.901995i	$0.642102\pi$
$674$	−7.00000	+	12.1244i	−0.269630	+	0.467013i
$675$		0			0
$676$	−0.500000	+	12.9904i	−0.0192308	+	0.499630i
$677$			36.0000i			1.38359i	0.722093	+	0.691796i	$0.243180\pi$
$677$			36.0000i			1.38359i	−0.722093	+	0.691796i	$0.756820\pi$
$678$	12.9904	+	7.50000i	0.498893	+	0.288036i
$679$	14.0000	−	24.2487i	0.537271	−	0.930580i
$680$		0			0
$681$		0			0
$682$	−12.9904	+	7.50000i	−0.497427	+	0.287190i
$683$	−10.3923	+	6.00000i	−0.397650	+	0.229584i	−0.685470	−	0.728101i	$-0.740403\pi$
$683$	−10.3923	+	6.00000i	−0.397650	+	0.229584i	0.287819	+	0.957685i	$0.407070\pi$
$684$	−2.00000			−0.0764719
$685$		0			0
$686$	−10.0000	+	17.3205i	−0.381802	+	0.661300i
$687$	12.1244	+	7.00000i	0.462573	+	0.267067i
$688$		−	1.00000i		−	0.0381246i
$689$	6.00000	−	20.7846i	0.228582	−	0.791831i
$690$		0			0
$691$	23.0000	−	39.8372i	0.874961	−	1.51548i	0.0181572	−	0.999835i	$-0.494220\pi$
$691$	23.0000	−	39.8372i	0.874961	−	1.51548i	0.856804	−	0.515642i	$-0.172447\pi$
$692$	10.3923	+	6.00000i	0.395056	+	0.228086i
$693$	−5.19615	+	3.00000i	−0.197386	+	0.113961i
$694$	−30.0000			−1.13878
$695$		0			0
$696$	1.50000	+	2.59808i	0.0568574	+	0.0984798i
$697$		−	36.0000i		−	1.36360i
$698$	−6.92820	+	4.00000i	−0.262236	+	0.151402i
$699$	10.5000	−	18.1865i	0.397146	−	0.687878i
$700$		0			0
$701$	−21.0000			−0.793159			−0.396580	−	0.918000i	$-0.629803\pi$
$701$	−21.0000			−0.793159			−0.396580	+	0.918000i	$0.629803\pi$
$702$	−2.59808	+	2.50000i	−0.0980581	+	0.0943564i
$703$		−	14.0000i		−	0.528020i
$704$	−1.50000	+	2.59808i	−0.0565334	+	0.0979187i
$705$		0			0
$706$	15.0000	+	25.9808i	0.564532	+	0.977799i
$707$		−	12.0000i		−	0.451306i
$708$	−7.79423	+	4.50000i	−0.292925	+	0.169120i
$709$	16.0000	+	27.7128i	0.600893	+	1.04078i	0.992686	+	0.120723i	$0.0385214\pi$
$709$	16.0000	+	27.7128i	0.600893	+	1.04078i	−0.391794	+	0.920053i	$0.628145\pi$
$710$		0			0
$711$	−2.50000	−	4.33013i	−0.0937573	−	0.162392i
$712$	15.5885	+	9.00000i	0.584202	+	0.337289i
$713$	−12.9904	−	7.50000i	−0.486494	−	0.280877i
$714$	12.0000			0.449089
$715$		0			0
$716$	−3.00000			−0.112115
$717$	20.7846	+	12.0000i	0.776215	+	0.448148i
$718$	20.7846	+	12.0000i	0.775675	+	0.447836i
$719$	18.0000	+	31.1769i	0.671287	+	1.16270i	0.977539	+	0.210752i	$0.0675914\pi$
$719$	18.0000	+	31.1769i	0.671287	+	1.16270i	−0.306253	+	0.951950i	$0.599075\pi$
$720$		0			0
$721$	−14.0000	−	24.2487i	−0.521387	−	0.903069i
$722$	−12.9904	+	7.50000i	−0.483452	+	0.279121i
$723$			17.0000i			0.632237i
$724$	−8.00000	−	13.8564i	−0.297318	−	0.514969i
$725$		0			0
$726$	−1.00000	+	1.73205i	−0.0371135	+	0.0642824i
$727$			4.00000i			0.148352i	0.997245	+	0.0741759i	$0.0236326\pi$
$727$			4.00000i			0.148352i	−0.997245	+	0.0741759i	$0.976367\pi$
$728$	1.73205	+	7.00000i	0.0641941	+	0.259437i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	3.00000	−	5.19615i	0.110959	−	0.192187i
$732$	−1.73205	+	1.00000i	−0.0640184	+	0.0369611i
$733$		−	22.0000i		−	0.812589i	−0.913742	−	0.406294i	$-0.866821\pi$
$733$		−	22.0000i		−	0.812589i	0.913742	−	0.406294i	$-0.133179\pi$
$734$	−10.0000	−	17.3205i	−0.369107	−	0.639312i
$735$		0			0
$736$	−3.00000			−0.110581
$737$	20.7846	−	12.0000i	0.765611	−	0.442026i
$738$	5.19615	+	3.00000i	0.191273	+	0.110432i
$739$	−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
$741$	2.00000	−	6.92820i	0.0734718	−	0.254514i
$742$		−	12.0000i		−	0.440534i
$743$	7.79423	+	4.50000i	0.285943	+	0.165089i	0.636111	−	0.771598i	$-0.280542\pi$
$743$	7.79423	+	4.50000i	0.285943	+	0.165089i	−0.350168	+	0.936687i	$0.613876\pi$
$744$	−2.50000	+	4.33013i	−0.0916544	+	0.158750i
$745$		0			0
$746$	25.0000			0.915315
$747$	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
$751$	−20.5000	+	35.5070i	−0.748056	+	1.29567i	0.200698	+	0.979653i	$0.435679\pi$
$751$	−20.5000	+	35.5070i	−0.748056	+	1.29567i	−0.948753	+	0.316017i	$0.897654\pi$
$752$	−2.59808	−	1.50000i	−0.0947421	−	0.0546994i
$753$			15.0000i			0.546630i
$754$	−10.5000	+	2.59808i	−0.382387	+	0.0946164i
$755$		0			0
$756$	−1.00000	+	1.73205i	−0.0363696	+	0.0629941i
$757$	32.9090	+	19.0000i	1.19610	+	0.690567i	0.959683	−	0.281086i	$-0.0906945\pi$
$757$	32.9090	+	19.0000i	1.19610	+	0.690567i	0.236414	+	0.971652i	$0.424028\pi$
$758$	−32.9090	+	19.0000i	−1.19531	+	0.690111i
$759$	9.00000			0.326679
$760$		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	$0.763543\pi$
$762$			14.0000i			0.507166i
$763$	24.2487	−	14.0000i	0.877862	−	0.506834i
$764$	−6.00000	+	10.3923i	−0.217072	+	0.375980i
$765$		0			0
$766$	21.0000			0.758761
$767$	−7.79423	−	31.5000i	−0.281433	−	1.13740i
$768$			1.00000i			0.0360844i
$769$	−6.50000	+	11.2583i	−0.234396	+	0.405986i	−0.959097	−	0.283078i	$-0.908645\pi$
$769$	−6.50000	+	11.2583i	−0.234396	+	0.405986i	0.724701	+	0.689063i	$0.241978\pi$
$770$		0			0
$771$	10.5000	+	18.1865i	0.378148	+	0.654972i
$772$			4.00000i			0.143963i
$773$	−41.5692	+	24.0000i	−1.49514	+	0.863220i	−0.999984	−	0.00558380i	$-0.998223\pi$
$773$	−41.5692	+	24.0000i	−1.49514	+	0.863220i	−0.495156	+	0.868804i	$0.664889\pi$
$774$	0.500000	+	0.866025i	0.0179721	+	0.0311286i
$775$		0			0
$776$	7.00000	+	12.1244i	0.251285	+	0.435239i
$777$	−12.1244	−	7.00000i	−0.434959	−	0.251124i
$778$	2.59808	+	1.50000i	0.0931455	+	0.0537776i
$779$	−12.0000			−0.429945
$780$		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
$786$	4.50000	+	7.79423i	0.160510	+	0.278011i
$787$	−30.3109	+	17.5000i	−1.08047	+	0.623808i	−0.931022	−	0.364963i	$-0.881082\pi$
$787$	−30.3109	+	17.5000i	−1.08047	+	0.623808i	−0.149444	+	0.988770i	$0.547748\pi$
$788$			24.0000i			0.854965i
$789$	−7.50000	−	12.9904i	−0.267007	−	0.462470i
$790$		0			0
$791$	−15.0000	+	25.9808i	−0.533339	+	0.923770i
$792$		−	3.00000i		−	0.106600i
$793$	−1.73205	−	7.00000i	−0.0615069	−	0.248577i
$794$	−31.0000			−1.10015
$795$		0			0
$796$	−4.00000	+	6.92820i	−0.141776	+	0.245564i
$797$	20.7846	−	12.0000i	0.736229	−	0.425062i	−0.0844678	−	0.996426i	$-0.526919\pi$
$797$	20.7846	−	12.0000i	0.736229	−	0.425062i	0.820696	+	0.571364i	$0.193586\pi$
$798$		−	4.00000i		−	0.141598i
$799$	−9.00000	−	15.5885i	−0.318397	−	0.551480i
$800$		0			0
$801$	−18.0000			−0.635999
$802$	−10.3923	+	6.00000i	−0.366965	+	0.211867i
$803$	36.3731	+	21.0000i	1.28358	+	0.741074i
$804$	4.00000	−	6.92820i	0.141069	−	0.244339i
$805$		0			0
$806$	−12.5000	−	12.9904i	−0.440294	−	0.457567i
$807$		−	18.0000i		−	0.633630i
$808$	5.19615	+	3.00000i	0.182800	+	0.105540i
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	−0.472119	−	0.881535i	$-0.656511\pi$
$809$	15.0000	−	25.9808i	0.527372	−	0.913435i	0.999491	−	0.0319002i	$-0.0101559\pi$
$810$		0			0
$811$	32.0000			1.12367			0.561836	−	0.827249i	$-0.310095\pi$
$811$	32.0000			1.12367			0.561836	+	0.827249i	$0.310095\pi$
$812$	−5.19615	+	3.00000i	−0.182349	+	0.105279i
$813$	9.52628	−	5.50000i	0.334101	−	0.192893i
$814$	21.0000			0.736050
$815$		0			0
$816$	−3.00000	+	5.19615i	−0.105021	+	0.181902i
$817$	−1.73205	−	1.00000i	−0.0605968	−	0.0349856i
$818$			10.0000i			0.349642i
$819$	−5.00000	−	5.19615i	−0.174714	−	0.181568i
$820$		0			0
$821$	−13.5000	+	23.3827i	−0.471153	+	0.816061i	−0.999456	−	0.0329950i	$-0.989495\pi$
$821$	−13.5000	+	23.3827i	−0.471153	+	0.816061i	0.528302	+	0.849056i	$0.322829\pi$
$822$	−7.79423	−	4.50000i	−0.271855	−	0.156956i
$823$	12.1244	−	7.00000i	0.422628	−	0.244005i	−0.273573	−	0.961851i	$-0.588205\pi$
$823$	12.1244	−	7.00000i	0.422628	−	0.244005i	0.696201	+	0.717847i	$0.254872\pi$
$824$	14.0000			0.487713
$825$		0			0
$826$	−9.00000	−	15.5885i	−0.313150	−	0.542392i
$827$		−	6.00000i		−	0.208640i	−0.994544	−	0.104320i	$-0.966733\pi$
$827$		−	6.00000i		−	0.208640i	0.994544	−	0.104320i	$-0.0332667\pi$
$828$	2.59808	−	1.50000i	0.0902894	−	0.0521286i
$829$	13.0000	−	22.5167i	0.451509	−	0.782036i	−0.546971	−	0.837151i	$-0.684219\pi$
$829$	13.0000	−	22.5167i	0.451509	−	0.782036i	0.998480	+	0.0551154i	$0.0175527\pi$
$830$		0			0
$831$	−1.00000			−0.0346896
$832$	−3.46410	−	1.00000i	−0.120096	−	0.0346688i
$833$		−	18.0000i		−	0.623663i
$834$	−7.00000	+	12.1244i	−0.242390	+	0.419832i
$835$		0			0
$836$	3.00000	+	5.19615i	0.103757	+	0.179713i
$837$		−	5.00000i		−	0.172825i
$838$	10.3923	−	6.00000i	0.358996	−	0.207267i
$839$	21.0000	+	36.3731i	0.725001	+	1.25574i	0.958974	+	0.283495i	$0.0914938\pi$
$839$	21.0000	+	36.3731i	0.725001	+	1.25574i	−0.233973	+	0.972243i	$0.575173\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	13.8564	+	8.00000i	0.477523	+	0.275698i
$843$	−15.5885	−	9.00000i	−0.536895	−	0.309976i
$844$	−20.0000			−0.688428
$845$		0			0
$846$	3.00000			0.103142
$847$	−3.46410	−	2.00000i	−0.119028	−	0.0687208i
$848$	5.19615	+	3.00000i	0.178437	+	0.103020i
$849$	−15.5000	−	26.8468i	−0.531959	−	0.921379i
$850$		0			0
$851$	10.5000	+	18.1865i	0.359935	+	0.623426i
$852$	10.3923	−	6.00000i	0.356034	−	0.205557i
$853$		−	19.0000i		−	0.650548i	−0.945620	−	0.325274i	$-0.894544\pi$
$853$		−	19.0000i		−	0.650548i	0.945620	−	0.325274i	$-0.105456\pi$
$854$	−2.00000	−	3.46410i	−0.0684386	−	0.118539i
$855$		0			0
$856$	−3.00000	+	5.19615i	−0.102538	+	0.177601i
$857$		−	3.00000i		−	0.102478i	−0.998686	−	0.0512390i	$-0.983683\pi$
$857$		−	3.00000i		−	0.102478i	0.998686	−	0.0512390i	$-0.0163170\pi$
$858$	10.3923	+	3.00000i	0.354787	+	0.102418i
$859$	46.0000			1.56950			0.784750	−	0.619813i	$-0.212791\pi$
$859$	46.0000			1.56950			0.784750	+	0.619813i	$0.212791\pi$
$860$		0			0
$861$	−6.00000	+	10.3923i	−0.204479	+	0.354169i
$862$	10.3923	−	6.00000i	0.353963	−	0.204361i
$863$		−	45.0000i		−	1.53182i	−0.642949	−	0.765909i	$-0.722289\pi$
$863$		−	45.0000i		−	1.53182i	0.642949	−	0.765909i	$-0.277711\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$		0			0
$866$	40.0000			1.35926
$867$	−16.4545	+	9.50000i	−0.558824	+	0.322637i
$868$	−8.66025	−	5.00000i	−0.293948	−	0.169711i
$869$	−7.50000	+	12.9904i	−0.254420	+	0.440668i
$870$		0			0
$871$	20.0000	+	20.7846i	0.677674	+	0.704260i
$872$			14.0000i			0.474100i
$873$	−12.1244	−	7.00000i	−0.410347	−	0.236914i
$874$	−3.00000	+	5.19615i	−0.101477	+	0.175762i
$875$		0			0
$876$	14.0000			0.473016
$877$	−19.9186	+	11.5000i	−0.672603	+	0.388327i	−0.797062	−	0.603897i	$-0.793614\pi$
$877$	−19.9186	+	11.5000i	−0.672603	+	0.388327i	0.124459	+	0.992225i	$0.460280\pi$
$878$	3.46410	−	2.00000i	0.116908	−	0.0674967i
$879$	30.0000			1.01187
$880$		0			0
$881$	−3.00000	+	5.19615i	−0.101073	+	0.175063i	−0.912127	−	0.409908i	$-0.865561\pi$
$881$	−3.00000	+	5.19615i	−0.101073	+	0.175063i	0.811054	+	0.584971i	$0.198894\pi$
$882$	2.59808	+	1.50000i	0.0874818	+	0.0505076i
$883$		−	19.0000i		−	0.639401i	−0.947519	−	0.319700i	$-0.896418\pi$
$883$		−	19.0000i		−	0.639401i	0.947519	−	0.319700i	$-0.103582\pi$
$884$	−15.0000	−	15.5885i	−0.504505	−	0.524297i
$885$		0			0
$886$	−18.0000	+	31.1769i	−0.604722	+	1.04741i
$887$	−49.3634	−	28.5000i	−1.65746	−	0.956936i	−0.973880	−	0.227063i	$-0.927088\pi$
$887$	−49.3634	−	28.5000i	−1.65746	−	0.956936i	−0.683582	−	0.729873i	$-0.739579\pi$
$888$	6.06218	−	3.50000i	0.203433	−	0.117452i
$889$	−28.0000			−0.939090
$890$		0			0
$891$	1.50000	+	2.59808i	0.0502519	+	0.0870388i
$892$			10.0000i			0.334825i
$893$	−5.19615	+	3.00000i	−0.173883	+	0.100391i
$894$	4.50000	−	7.79423i	0.150503	−	0.260678i
$895$		0			0
$896$	−2.00000			−0.0668153
$897$	2.59808	+	10.5000i	0.0867472	+	0.350585i
$898$		−	36.0000i		−	1.20134i
$899$	7.50000	−	12.9904i	0.250139	−	0.433253i
$900$		0			0
$901$	18.0000	+	31.1769i	0.599667	+	1.03865i
$902$		−	18.0000i		−	0.599334i
$903$	−1.73205	+	1.00000i	−0.0576390	+	0.0332779i
$904$	−7.50000	−	12.9904i	−0.249446	−	0.432054i
$905$		0			0
$906$	4.00000	+	6.92820i	0.132891	+	0.230174i
$907$	14.7224	+	8.50000i	0.488850	+	0.282238i	0.724097	−	0.689698i	$-0.242257\pi$
$907$	14.7224	+	8.50000i	0.488850	+	0.282238i	−0.235247	+	0.971936i	$0.575590\pi$
$908$		0			0
$909$	−6.00000			−0.199007
$910$		0			0
$911$	−6.00000			−0.198789			−0.0993944	−	0.995048i	$-0.531691\pi$
$911$	−6.00000			−0.198789			−0.0993944	+	0.995048i	$0.531691\pi$
$912$	1.73205	+	1.00000i	0.0573539	+	0.0331133i
$913$	−15.5885	−	9.00000i	−0.515903	−	0.297857i
$914$	−1.00000	−	1.73205i	−0.0330771	−	0.0572911i
$915$		0			0
$916$	−7.00000	−	12.1244i	−0.231287	−	0.400600i
$917$	−15.5885	+	9.00000i	−0.514776	+	0.297206i
$918$		−	6.00000i		−	0.198030i
$919$	−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
$921$	−4.00000	+	6.92820i	−0.131804	+	0.228292i
$922$			15.0000i			0.493999i
$923$	10.3923	+	42.0000i	0.342067	+	1.38245i
$924$	6.00000			0.197386
$925$		0			0
$926$	−17.0000	+	29.4449i	−0.558655	+	0.967618i
$927$	−12.1244	+	7.00000i	−0.398216	+	0.229910i
$928$		−	3.00000i		−	0.0984798i
$929$	−6.00000	−	10.3923i	−0.196854	−	0.340960i	0.750653	−	0.660697i	$-0.229739\pi$
$929$	−6.00000	−	10.3923i	−0.196854	−	0.340960i	−0.947507	+	0.319736i	$0.896406\pi$
$930$		0			0
$931$	−6.00000			−0.196642
$932$	−18.1865	+	10.5000i	−0.595720	+	0.343939i
$933$	10.3923	+	6.00000i	0.340229	+	0.196431i
$934$	−9.00000	+	15.5885i	−0.294489	+	0.510070i
$935$		0			0
$936$	3.50000	−	0.866025i	0.114401	−	0.0283069i
$937$		−	2.00000i		−	0.0653372i	−0.999466	−	0.0326686i	$-0.989599\pi$
$937$		−	2.00000i		−	0.0653372i	0.999466	−	0.0326686i	$-0.0104006\pi$
$938$	13.8564	+	8.00000i	0.452428	+	0.261209i
$939$	4.00000	−	6.92820i	0.130535	−	0.226093i
$940$		0			0
$941$	42.0000			1.36916			0.684580	−	0.728937i	$-0.259985\pi$
$941$	42.0000			1.36916			0.684580	+	0.728937i	$0.259985\pi$
$942$	−11.2583	+	6.50000i	−0.366816	+	0.211781i
$943$	15.5885	−	9.00000i	0.507630	−	0.293080i
$944$	9.00000			0.292925
$945$		0			0
$946$	1.50000	−	2.59808i	0.0487692	−	0.0844707i
$947$	−10.3923	−	6.00000i	−0.337705	−	0.194974i	0.321552	−	0.946892i	$-0.395796\pi$
$947$	−10.3923	−	6.00000i	−0.337705	−	0.194974i	−0.659256	+	0.751918i	$0.729129\pi$
$948$			5.00000i			0.162392i
$949$	−14.0000	+	48.4974i	−0.454459	+	1.57429i
$950$		0			0
$951$	−6.00000	+	10.3923i	−0.194563	+	0.336994i
$952$	−10.3923	−	6.00000i	−0.336817	−	0.194461i
$953$	7.79423	−	4.50000i	0.252480	−	0.145769i	−0.368419	−	0.929660i	$-0.620101\pi$
$953$	7.79423	−	4.50000i	0.252480	−	0.145769i	0.620899	+	0.783890i	$0.286768\pi$
$954$	−6.00000			−0.194257
$955$		0			0
$956$	−12.0000	−	20.7846i	−0.388108	−	0.672222i
$957$			9.00000i			0.290929i
$958$		0			0
$959$	9.00000	−	15.5885i	0.290625	−	0.503378i
$960$		0			0
$961$	−6.00000			−0.193548
$962$	6.06218	+	24.5000i	0.195452	+	0.789912i
$963$		−	6.00000i		−	0.193347i
$964$	8.50000	−	14.7224i	0.273767	−	0.474178i
$965$		0			0
$966$	3.00000	+	5.19615i	0.0965234	+	0.167183i
$967$		−	32.0000i		−	1.02905i	−0.857475	−	0.514525i	$-0.827968\pi$
$967$		−	32.0000i		−	1.02905i	0.857475	−	0.514525i	$-0.172032\pi$
$968$	1.73205	−	1.00000i	0.0556702	−	0.0321412i
$969$	6.00000	+	10.3923i	0.192748	+	0.333849i
$970$		0			0
$971$	24.0000	+	41.5692i	0.770197	+	1.33402i	0.937455	+	0.348107i	$0.113175\pi$
$971$	24.0000	+	41.5692i	0.770197	+	1.33402i	−0.167258	+	0.985913i	$0.553491\pi$
$972$	0.866025	+	0.500000i	0.0277778	+	0.0160375i
$973$	−24.2487	−	14.0000i	−0.777378	−	0.448819i
$974$	2.00000			0.0640841
$975$		0			0
$976$	2.00000			0.0640184
$977$	−49.3634	−	28.5000i	−1.57928	−	0.911796i	−0.994960	−	0.100270i	$-0.968029\pi$
$977$	−49.3634	−	28.5000i	−1.57928	−	0.911796i	−0.584316	−	0.811526i	$-0.698637\pi$
$978$	−11.2583	−	6.50000i	−0.360002	−	0.207847i
$979$	27.0000	+	46.7654i	0.862924	+	1.49463i
$980$		0			0
$981$	−7.00000	−	12.1244i	−0.223493	−	0.387101i
$982$		0			0
$983$			9.00000i			0.287055i	0.989646	+	0.143528i	$0.0458446\pi$
$983$			9.00000i			0.287055i	−0.989646	+	0.143528i	$0.954155\pi$
$984$	−3.00000	−	5.19615i	−0.0956365	−	0.165647i
$985$		0			0
$986$	9.00000	−	15.5885i	0.286618	−	0.496438i
$987$			6.00000i			0.190982i
$988$	−5.19615	+	5.00000i	−0.165312	+	0.159071i
$989$	3.00000			0.0953945
$990$		0			0
$991$	12.5000	−	21.6506i	0.397076	−	0.687755i	−0.596288	−	0.802771i	$-0.703358\pi$
$991$	12.5000	−	21.6506i	0.397076	−	0.687755i	0.993364	+	0.115015i	$0.0366917\pi$
$992$	4.33013	−	2.50000i	0.137482	−	0.0793751i
$993$			32.0000i			1.01549i
$994$	12.0000	+	20.7846i	0.380617	+	0.659248i
$995$		0			0
$996$	−6.00000			−0.190117
$997$	19.0526	−	11.0000i	0.603401	−	0.348373i	−0.166978	−	0.985961i	$-0.553401\pi$
$997$	19.0526	−	11.0000i	0.603401	−	0.348373i	0.770378	+	0.637587i	$0.220067\pi$
$998$	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.k.1699.1		4
5.2	odd	4		390.2.i.c.61.1	✓	2
5.3	odd	4		1950.2.i.n.451.1		2
5.4	even	2	inner	1950.2.z.k.1699.2		4
13.3	even	3	inner	1950.2.z.k.1849.2		4
15.2	even	4		1170.2.i.d.451.1		2
65.3	odd	12		1950.2.i.n.601.1		2
65.7	even	12		5070.2.b.j.1351.1		2
65.17	odd	12		5070.2.a.v.1.1		1
65.22	odd	12		5070.2.a.j.1.1		1
65.29	even	6	inner	1950.2.z.k.1849.1		4
65.32	even	12		5070.2.b.j.1351.2		2
65.42	odd	12		390.2.i.c.211.1	yes	2
195.107	even	12		1170.2.i.d.991.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.i.c.61.1	✓	2	5.2	odd	4
390.2.i.c.211.1	yes	2	65.42	odd	12
1170.2.i.d.451.1		2	15.2	even	4
1170.2.i.d.991.1		2	195.107	even	12
1950.2.i.n.451.1		2	5.3	odd	4
1950.2.i.n.601.1		2	65.3	odd	12
1950.2.z.k.1699.1		4	1.1	even	1	trivial
1950.2.z.k.1699.2		4	5.4	even	2	inner
1950.2.z.k.1849.1		4	65.29	even	6	inner
1950.2.z.k.1849.2		4	13.3	even	3	inner
5070.2.a.j.1.1		1	65.22	odd	12
5070.2.a.v.1.1		1	65.17	odd	12
5070.2.b.j.1351.1		2	65.7	even	12
5070.2.b.j.1351.2		2	65.32	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} +(1.50000 - 2.59808i) q^{11} -1.00000i q^{12} +(3.46410 + 1.00000i) q^{13} +2.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-5.19615 + 3.00000i) q^{17} -1.00000i q^{18} +(1.00000 + 1.73205i) q^{19} +2.00000 q^{21} +(-2.59808 + 1.50000i) q^{22} +(-2.59808 - 1.50000i) 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} +5.00000 q^{31} +(0.866025 - 0.500000i) q^{32} +(-2.59808 + 1.50000i) q^{33} +6.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-6.06218 - 3.50000i) q^{37} -2.00000i q^{38} +(-2.50000 - 2.59808i) q^{39} +(-3.00000 + 5.19615i) q^{41} +(-1.73205 - 1.00000i) q^{42} +(-0.866025 + 0.500000i) q^{43} +3.00000 q^{44} +(1.50000 + 2.59808i) q^{46} +3.00000i q^{47} +(0.866025 - 0.500000i) q^{48} +(-1.50000 + 2.59808i) q^{49} +6.00000 q^{51} +(0.866025 + 3.50000i) q^{52} -6.00000i q^{53} +(-0.500000 + 0.866025i) q^{54} +(1.00000 + 1.73205i) q^{56} -2.00000i q^{57} +(-2.59808 + 1.50000i) q^{58} +(-4.50000 - 7.79423i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(-4.33013 - 2.50000i) q^{62} +(-1.73205 - 1.00000i) q^{63} -1.00000 q^{64} +3.00000 q^{66} +(6.92820 + 4.00000i) q^{67} +(-5.19615 - 3.00000i) q^{68} +(1.50000 + 2.59808i) q^{69} +(6.00000 + 10.3923i) q^{71} +(0.866025 - 0.500000i) q^{72} +14.0000i q^{73} +(3.50000 + 6.06218i) q^{74} +(-1.00000 + 1.73205i) q^{76} +6.00000i q^{77} +(0.866025 + 3.50000i) q^{78} -5.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(5.19615 - 3.00000i) q^{82} -6.00000i q^{83} +(1.00000 + 1.73205i) q^{84} +1.00000 q^{86} +(-2.59808 + 1.50000i) q^{87} +(-2.59808 - 1.50000i) q^{88} +(-9.00000 + 15.5885i) q^{89} +(-7.00000 + 1.73205i) q^{91} -3.00000i q^{92} +(-4.33013 - 2.50000i) q^{93} +(1.50000 - 2.59808i) q^{94} -1.00000 q^{96} +(-12.1244 + 7.00000i) q^{97} +(2.59808 - 1.50000i) q^{98} +3.00000 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	\( 4 q + 2 q^{4} + 2 q^{6} + 2 q^{9} + 6 q^{11} + 8 q^{14} - 2 q^{16} + 4 q^{19} + 8 q^{21} - 2 q^{24} - 10 q^{26} + 6 q^{29} + 20 q^{31} + 24 q^{34} - 2 q^{36} - 10 q^{39} - 12 q^{41} + 12 q^{44} + 6 q^{46} - 6 q^{49} + 24 q^{51} - 2 q^{54} + 4 q^{56} - 18 q^{59} - 4 q^{61} - 4 q^{64} + 12 q^{66} + 6 q^{69} + 24 q^{71} + 14 q^{74} - 4 q^{76} - 20 q^{79} - 2 q^{81} + 4 q^{84} + 4 q^{86} - 36 q^{89} - 28 q^{91} + 6 q^{94} - 4 q^{96} + 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 + 2 * q^6 + 2 * q^9 + 6 * q^11 + 8 * q^14 - 2 * q^16 + 4 * q^19 + 8 * q^21 - 2 * q^24 - 10 * q^26 + 6 * q^29 + 20 * q^31 + 24 * q^34 - 2 * q^36 - 10 * q^39 - 12 * q^41 + 12 * q^44 + 6 * q^46 - 6 * q^49 + 24 * q^51 - 2 * q^54 + 4 * q^56 - 18 * q^59 - 4 * q^61 - 4 * q^64 + 12 * q^66 + 6 * q^69 + 24 * q^71 + 14 * q^74 - 4 * q^76 - 20 * q^79 - 2 * q^81 + 4 * q^84 + 4 * q^86 - 36 * q^89 - 28 * q^91 + 6 * q^94 - 4 * q^96 + 12 * q^99

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