LMFDB - Embedded newform 1950.2.i.n.451.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(451,1950)]

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, 0, 4]))

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

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

chi := DirichletCharacter("1950.451");

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.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1950.451
Dual form			1950.2.i.n.601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{11} -1.00000 q^{12} +(-1.00000 + 3.46410i) q^{13} -2.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +1.00000 q^{18} +(-1.00000 - 1.73205i) q^{19} +2.00000 q^{21} +(1.50000 + 2.59808i) q^{22} +(1.50000 - 2.59808i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-2.50000 - 2.59808i) q^{26} -1.00000 q^{27} +(1.00000 - 1.73205i) q^{28} +(-1.50000 + 2.59808i) q^{29} +5.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{33} -6.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-3.50000 + 6.06218i) q^{37} +2.00000 q^{38} +(2.50000 + 2.59808i) q^{39} +(-3.00000 + 5.19615i) q^{41} +(-1.00000 + 1.73205i) q^{42} +(-0.500000 - 0.866025i) q^{43} -3.00000 q^{44} +(1.50000 + 2.59808i) q^{46} +3.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} +6.00000 q^{51} +(3.50000 - 0.866025i) q^{52} +6.00000 q^{53} +(0.500000 - 0.866025i) q^{54} +(1.00000 + 1.73205i) q^{56} -2.00000 q^{57} +(-1.50000 - 2.59808i) q^{58} +(4.50000 + 7.79423i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(-2.50000 + 4.33013i) q^{62} +(1.00000 - 1.73205i) q^{63} +1.00000 q^{64} +3.00000 q^{66} +(4.00000 - 6.92820i) q^{67} +(3.00000 - 5.19615i) q^{68} +(-1.50000 - 2.59808i) q^{69} +(6.00000 + 10.3923i) q^{71} +(-0.500000 - 0.866025i) q^{72} -14.0000 q^{73} +(-3.50000 - 6.06218i) q^{74} +(-1.00000 + 1.73205i) q^{76} +6.00000 q^{77} +(-3.50000 + 0.866025i) q^{78} +5.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-3.00000 - 5.19615i) q^{82} +6.00000 q^{83} +(-1.00000 - 1.73205i) q^{84} +1.00000 q^{86} +(1.50000 + 2.59808i) q^{87} +(1.50000 - 2.59808i) q^{88} +(9.00000 - 15.5885i) q^{89} +(-7.00000 + 1.73205i) q^{91} -3.00000 q^{92} +(2.50000 - 4.33013i) q^{93} +(-1.50000 + 2.59808i) q^{94} -1.00000 q^{96} +(7.00000 + 12.1244i) q^{97} +(1.50000 + 2.59808i) q^{98} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{3} - q^{4} + q^{6} + 2 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 + q^3 - q^4 + q^6 + 2 * q^7 + 2 * q^8 - q^9	$ 2 q - q^{2} + q^{3} - q^{4} + q^{6} + 2 q^{7} + 2 q^{8} - q^{9} + 3 q^{11} - 2 q^{12} - 2 q^{13} - 4 q^{14} - q^{16} + 6 q^{17} + 2 q^{18} - 2 q^{19} + 4 q^{21} + 3 q^{22} + 3 q^{23} + q^{24} - 5 q^{26} - 2 q^{27} + 2 q^{28} - 3 q^{29} + 10 q^{31} - q^{32} - 3 q^{33} - 12 q^{34} - q^{36} - 7 q^{37} + 4 q^{38} + 5 q^{39} - 6 q^{41} - 2 q^{42} - q^{43} - 6 q^{44} + 3 q^{46} + 6 q^{47} + q^{48} + 3 q^{49} + 12 q^{51} + 7 q^{52} + 12 q^{53} + q^{54} + 2 q^{56} - 4 q^{57} - 3 q^{58} + 9 q^{59} - 2 q^{61} - 5 q^{62} + 2 q^{63} + 2 q^{64} + 6 q^{66} + 8 q^{67} + 6 q^{68} - 3 q^{69} + 12 q^{71} - q^{72} - 28 q^{73} - 7 q^{74} - 2 q^{76} + 12 q^{77} - 7 q^{78} + 10 q^{79} - q^{81} - 6 q^{82} + 12 q^{83} - 2 q^{84} + 2 q^{86} + 3 q^{87} + 3 q^{88} + 18 q^{89} - 14 q^{91} - 6 q^{92} + 5 q^{93} - 3 q^{94} - 2 q^{96} + 14 q^{97} + 3 q^{98} - 6 q^{99}+O(q^{100}) $ 2 * q - q^2 + q^3 - q^4 + q^6 + 2 * q^7 + 2 * q^8 - q^9 + 3 * q^11 - 2 * q^12 - 2 * q^13 - 4 * q^14 - q^16 + 6 * q^17 + 2 * q^18 - 2 * q^19 + 4 * q^21 + 3 * q^22 + 3 * q^23 + q^24 - 5 * q^26 - 2 * q^27 + 2 * q^28 - 3 * q^29 + 10 * q^31 - q^32 - 3 * q^33 - 12 * q^34 - q^36 - 7 * q^37 + 4 * q^38 + 5 * q^39 - 6 * q^41 - 2 * q^42 - q^43 - 6 * q^44 + 3 * q^46 + 6 * q^47 + q^48 + 3 * q^49 + 12 * q^51 + 7 * q^52 + 12 * q^53 + q^54 + 2 * q^56 - 4 * q^57 - 3 * q^58 + 9 * q^59 - 2 * q^61 - 5 * q^62 + 2 * q^63 + 2 * q^64 + 6 * q^66 + 8 * q^67 + 6 * q^68 - 3 * q^69 + 12 * q^71 - q^72 - 28 * q^73 - 7 * q^74 - 2 * q^76 + 12 * q^77 - 7 * q^78 + 10 * q^79 - q^81 - 6 * q^82 + 12 * q^83 - 2 * q^84 + 2 * q^86 + 3 * q^87 + 3 * q^88 + 18 * q^89 - 14 * q^91 - 6 * q^92 + 5 * q^93 - 3 * q^94 - 2 * q^96 + 14 * q^97 + 3 * q^98 - 6 * 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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	0.990766	−	0.135583i	$-0.0432908\pi$
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	−0.612801	+	0.790237i	$0.709957\pi$
$8$	1.00000			0.353553
$9$	−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	$0.0172821\pi$
$12$	−1.00000			−0.288675
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$13$	−1.00000	+	3.46410i	−0.277350	+	0.960769i
$14$	−2.00000			−0.534522
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	0.957892	+	0.287129i	$0.0927008\pi$
$17$	3.00000	+	5.19615i	0.727607	+	1.26025i	−0.230285	+	0.973123i	$0.573966\pi$
$18$	1.00000			0.235702
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	0.728219	−	0.685344i	$-0.240348\pi$
$19$	−1.00000	−	1.73205i	−0.229416	−	0.397360i	−0.957635	+	0.287984i	$0.907015\pi$
$20$		0			0
$21$	2.00000			0.436436
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$		0			0
$26$	−2.50000	−	2.59808i	−0.490290	−	0.509525i
$27$	−1.00000			−0.192450
$28$	1.00000	−	1.73205i	0.188982	−	0.327327i
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	−0.971023	−	0.238987i	$-0.923185\pi$
$29$	−1.50000	+	2.59808i	−0.278543	+	0.482451i	0.692480	+	0.721437i	$0.256518\pi$
$30$		0			0
$31$	5.00000			0.898027			0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000			0.898027			0.449013	+	0.893525i	$0.351776\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.50000	−	2.59808i	−0.261116	−	0.452267i
$34$	−6.00000			−1.02899
$35$		0			0
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	0.420602	+	0.907245i	$0.361819\pi$
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	−0.995998	+	0.0893706i	$0.971514\pi$
$38$	2.00000			0.324443
$39$	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	$0.321880\pi$
$42$	−1.00000	+	1.73205i	−0.154303	+	0.267261i
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	0.825380	−	0.564578i	$-0.190961\pi$
$43$	−0.500000	−	0.866025i	−0.0762493	−	0.132068i	−0.901629	+	0.432511i	$0.857628\pi$
$44$	−3.00000			−0.452267
$45$		0			0
$46$	1.50000	+	2.59808i	0.221163	+	0.383065i
$47$	3.00000			0.437595			0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000			0.437595			0.218797	+	0.975770i	$0.429787\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$		0			0
$51$	6.00000			0.840168
$52$	3.50000	−	0.866025i	0.485363	−	0.120096i
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$		0			0
$56$	1.00000	+	1.73205i	0.133631	+	0.231455i
$57$	−2.00000			−0.264906
$58$	−1.50000	−	2.59808i	−0.196960	−	0.341144i
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	0.994769	+	0.102151i	$0.0325726\pi$
$59$	4.50000	+	7.79423i	0.585850	+	1.01472i	−0.408919	+	0.912571i	$0.634094\pi$
$60$		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	$0.874201\pi$
$62$	−2.50000	+	4.33013i	−0.317500	+	0.549927i
$63$	1.00000	−	1.73205i	0.125988	−	0.218218i
$64$	1.00000			0.125000
$65$		0			0
$66$	3.00000			0.369274
$67$	4.00000	−	6.92820i	0.488678	−	0.846415i	−0.511237	−	0.859440i	$-0.670813\pi$
$67$	4.00000	−	6.92820i	0.488678	−	0.846415i	0.999915	+	0.0130248i	$0.00414604\pi$
$68$	3.00000	−	5.19615i	0.363803	−	0.630126i
$69$	−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	$0.581092\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−14.0000			−1.63858			−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000			−1.63858			−0.819288	+	0.573382i	$0.805631\pi$
$74$	−3.50000	−	6.06218i	−0.406867	−	0.704714i
$75$		0			0
$76$	−1.00000	+	1.73205i	−0.114708	+	0.198680i
$77$	6.00000			0.683763
$78$	−3.50000	+	0.866025i	−0.396297	+	0.0980581i
$79$	5.00000			0.562544			0.281272	−	0.959628i	$-0.409244\pi$
$79$	5.00000			0.562544			0.281272	+	0.959628i	$0.409244\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.00000	−	5.19615i	−0.331295	−	0.573819i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	−1.00000	−	1.73205i	−0.109109	−	0.188982i
$85$		0			0
$86$	1.00000			0.107833
$87$	1.50000	+	2.59808i	0.160817	+	0.278543i
$88$	1.50000	−	2.59808i	0.159901	−	0.276956i
$89$	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
$91$	−7.00000	+	1.73205i	−0.733799	+	0.181568i
$92$	−3.00000			−0.312772
$93$	2.50000	−	4.33013i	0.259238	−	0.449013i
$94$	−1.50000	+	2.59808i	−0.154713	+	0.267971i
$95$		0			0
$96$	−1.00000			−0.102062
$97$	7.00000	+	12.1244i	0.710742	+	1.23104i	0.964579	+	0.263795i	$0.0849741\pi$
$97$	7.00000	+	12.1244i	0.710742	+	1.23104i	−0.253837	+	0.967247i	$0.581693\pi$
$98$	1.50000	+	2.59808i	0.151523	+	0.262445i
$99$	−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	$0.263157\pi$
$102$	−3.00000	+	5.19615i	−0.297044	+	0.514496i
$103$	−14.0000			−1.37946			−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000			−1.37946			−0.689730	+	0.724066i	$0.742271\pi$
$104$	−1.00000	+	3.46410i	−0.0980581	+	0.339683i
$105$		0			0
$106$	−3.00000	+	5.19615i	−0.291386	+	0.504695i
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	−0.973814	−	0.227345i	$-0.926996\pi$
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	0.683793	+	0.729676i	$0.260329\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	14.0000			1.34096			0.670478	−	0.741929i	$-0.266089\pi$
$109$	14.0000			1.34096			0.670478	+	0.741929i	$0.266089\pi$
$110$		0			0
$111$	3.50000	+	6.06218i	0.332205	+	0.575396i
$112$	−2.00000			−0.188982
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	0.966496	+	0.256681i	$0.0826291\pi$
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	−0.260955	+	0.965351i	$0.584038\pi$
$114$	1.00000	−	1.73205i	0.0936586	−	0.162221i
$115$		0			0
$116$	3.00000			0.278543
$117$	3.50000	−	0.866025i	0.323575	−	0.0800641i
$118$	−9.00000			−0.828517
$119$	−6.00000	+	10.3923i	−0.550019	+	0.952661i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	2.00000			0.181071
$123$	3.00000	+	5.19615i	0.270501	+	0.468521i
$124$	−2.50000	−	4.33013i	−0.224507	−	0.388857i
$125$		0			0
$126$	1.00000	+	1.73205i	0.0890871	+	0.154303i
$127$	7.00000	−	12.1244i	0.621150	−	1.07586i	−0.368122	−	0.929777i	$-0.619999\pi$
$127$	7.00000	−	12.1244i	0.621150	−	1.07586i	0.989272	−	0.146085i	$-0.0466674\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−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	$0.371379\pi$
$132$	−1.50000	+	2.59808i	−0.130558	+	0.226134i
$133$	2.00000	−	3.46410i	0.173422	−	0.300376i
$134$	4.00000	+	6.92820i	0.345547	+	0.598506i
$135$		0			0
$136$	3.00000	+	5.19615i	0.257248	+	0.445566i
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	0.991694	−	0.128618i	$-0.0410540\pi$
$137$	4.50000	+	7.79423i	0.384461	+	0.665906i	−0.607233	+	0.794524i	$0.707721\pi$
$138$	3.00000			0.255377
$139$	−7.00000	−	12.1244i	−0.593732	−	1.02837i	−0.993724	−	0.111856i	$-0.964321\pi$
$139$	−7.00000	−	12.1244i	−0.593732	−	1.02837i	0.399992	−	0.916519i	$-0.369013\pi$
$140$		0			0
$141$	1.50000	−	2.59808i	0.126323	−	0.218797i
$142$	−12.0000			−1.00702
$143$	7.50000	+	7.79423i	0.627182	+	0.651786i
$144$	1.00000			0.0833333
$145$		0			0
$146$	7.00000	−	12.1244i	0.579324	−	1.00342i
$147$	−1.50000	−	2.59808i	−0.123718	−	0.214286i
$148$	7.00000			0.575396
$149$	4.50000	+	7.79423i	0.368654	+	0.638528i	0.989355	−	0.145519i	$-0.0464853\pi$
$149$	4.50000	+	7.79423i	0.368654	+	0.638528i	−0.620701	+	0.784047i	$0.713152\pi$
$150$		0			0
$151$	8.00000			0.651031			0.325515	−	0.945537i	$-0.394462\pi$
$151$	8.00000			0.651031			0.325515	+	0.945537i	$0.394462\pi$
$152$	−1.00000	−	1.73205i	−0.0811107	−	0.140488i
$153$	3.00000	−	5.19615i	0.242536	−	0.420084i
$154$	−3.00000	+	5.19615i	−0.241747	+	0.418718i
$155$		0			0
$156$	1.00000	−	3.46410i	0.0800641	−	0.277350i
$157$	13.0000			1.03751			0.518756	−	0.854922i	$-0.326395\pi$
$157$	13.0000			1.03751			0.518756	+	0.854922i	$0.326395\pi$
$158$	−2.50000	+	4.33013i	−0.198889	+	0.344486i
$159$	3.00000	−	5.19615i	0.237915	−	0.412082i
$160$		0			0
$161$	6.00000			0.472866
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	−6.50000	−	11.2583i	−0.509119	−	0.881820i	−0.999944	−	0.0105623i	$-0.996638\pi$
$163$	−6.50000	−	11.2583i	−0.509119	−	0.881820i	0.490825	−	0.871258i	$-0.336695\pi$
$164$	6.00000			0.468521
$165$		0			0
$166$	−3.00000	+	5.19615i	−0.232845	+	0.403300i
$167$	−4.50000	+	7.79423i	−0.348220	+	0.603136i	−0.985933	−	0.167139i	$-0.946547\pi$
$167$	−4.50000	+	7.79423i	−0.348220	+	0.603136i	0.637713	+	0.770274i	$0.279881\pi$
$168$	2.00000			0.154303
$169$	−11.0000	−	6.92820i	−0.846154	−	0.532939i
$170$		0			0
$171$	−1.00000	+	1.73205i	−0.0764719	+	0.132453i
$172$	−0.500000	+	0.866025i	−0.0381246	+	0.0660338i
$173$	6.00000	+	10.3923i	0.456172	+	0.790112i	0.998755	−	0.0498898i	$-0.0158870\pi$
$173$	6.00000	+	10.3923i	0.456172	+	0.790112i	−0.542583	+	0.840002i	$0.682554\pi$
$174$	−3.00000			−0.227429
$175$		0			0
$176$	1.50000	+	2.59808i	0.113067	+	0.195837i
$177$	9.00000			0.676481
$178$	9.00000	+	15.5885i	0.674579	+	1.16840i
$179$	1.50000	−	2.59808i	0.112115	−	0.194189i	−0.804508	−	0.593942i	$-0.797571\pi$
$179$	1.50000	−	2.59808i	0.112115	−	0.194189i	0.916623	+	0.399753i	$0.130904\pi$
$180$		0			0
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$	2.00000	−	6.92820i	0.148250	−	0.513553i
$183$	−2.00000			−0.147844
$184$	1.50000	−	2.59808i	0.110581	−	0.191533i
$185$		0			0
$186$	2.50000	+	4.33013i	0.183309	+	0.317500i
$187$	18.0000			1.31629
$188$	−1.50000	−	2.59808i	−0.109399	−	0.189484i
$189$	−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	$0.690384\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	−0.928986	−	0.370116i	$-0.879318\pi$
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	0.785022	+	0.619467i	$0.212651\pi$
$194$	−14.0000			−1.00514
$195$		0			0
$196$	−3.00000			−0.214286
$197$	12.0000	−	20.7846i	0.854965	−	1.48084i	−0.0217133	−	0.999764i	$-0.506912\pi$
$197$	12.0000	−	20.7846i	0.854965	−	1.48084i	0.876678	−	0.481078i	$-0.159755\pi$
$198$	1.50000	−	2.59808i	0.106600	−	0.184637i
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	0.688705	−	0.725042i	$-0.258180\pi$
$199$	−4.00000	−	6.92820i	−0.283552	−	0.491127i	−0.972257	+	0.233915i	$0.924846\pi$
$200$		0			0
$201$	−4.00000	−	6.92820i	−0.282138	−	0.488678i
$202$	−3.00000	−	5.19615i	−0.211079	−	0.365600i
$203$	−6.00000			−0.421117
$204$	−3.00000	−	5.19615i	−0.210042	−	0.363803i
$205$		0			0
$206$	7.00000	−	12.1244i	0.487713	−	0.844744i
$207$	−3.00000			−0.208514
$208$	−2.50000	−	2.59808i	−0.173344	−	0.180144i
$209$	−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	$0.924968\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$	12.0000			0.822226
$214$	−3.00000	−	5.19615i	−0.205076	−	0.355202i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	5.00000	+	8.66025i	0.339422	+	0.587896i
$218$	−7.00000	+	12.1244i	−0.474100	+	0.821165i
$219$	−7.00000	+	12.1244i	−0.473016	+	0.819288i
$220$		0			0
$221$	−21.0000	+	5.19615i	−1.41261	+	0.349531i
$222$	−7.00000			−0.469809
$223$	−5.00000	+	8.66025i	−0.334825	+	0.579934i	−0.983451	−	0.181173i	$-0.942010\pi$
$223$	−5.00000	+	8.66025i	−0.334825	+	0.579934i	0.648626	+	0.761107i	$0.275344\pi$
$224$	1.00000	−	1.73205i	0.0668153	−	0.115728i
$225$		0			0
$226$	−15.0000			−0.997785
$227$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$227$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$228$	1.00000	+	1.73205i	0.0662266	+	0.114708i
$229$	14.0000			0.925146			0.462573	−	0.886581i	$-0.346926\pi$
$229$	14.0000			0.925146			0.462573	+	0.886581i	$0.346926\pi$
$230$		0			0
$231$	3.00000	−	5.19615i	0.197386	−	0.341882i
$232$	−1.50000	+	2.59808i	−0.0984798	+	0.170572i
$233$	−21.0000			−1.37576			−0.687878	−	0.725826i	$-0.741458\pi$
$233$	−21.0000			−1.37576			−0.687878	+	0.725826i	$0.741458\pi$
$234$	−1.00000	+	3.46410i	−0.0653720	+	0.226455i
$235$		0			0
$236$	4.50000	−	7.79423i	0.292925	−	0.507361i
$237$	2.50000	−	4.33013i	0.162392	−	0.281272i
$238$	−6.00000	−	10.3923i	−0.388922	−	0.673633i
$239$	24.0000			1.55243			0.776215	−	0.630468i	$-0.217137\pi$
$239$	24.0000			1.55243			0.776215	+	0.630468i	$0.217137\pi$
$240$		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	$-0.351100\pi$
$242$	−2.00000			−0.128565
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−1.00000	+	1.73205i	−0.0640184	+	0.110883i
$245$		0			0
$246$	−6.00000			−0.382546
$247$	7.00000	−	1.73205i	0.445399	−	0.110208i
$248$	5.00000			0.317500
$249$	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	$0.990305\pi$
$252$	−2.00000			−0.125988
$253$	−4.50000	−	7.79423i	−0.282913	−	0.490019i
$254$	7.00000	+	12.1244i	0.439219	+	0.760750i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.5000	+	18.1865i	−0.654972	+	1.13444i	0.326929	+	0.945049i	$0.393986\pi$
$257$	−10.5000	+	18.1865i	−0.654972	+	1.13444i	−0.981901	+	0.189396i	$0.939347\pi$
$258$	0.500000	−	0.866025i	0.0311286	−	0.0539164i
$259$	−14.0000			−0.869918
$260$		0			0
$261$	3.00000			0.185695
$262$	−4.50000	+	7.79423i	−0.278011	+	0.481529i
$263$	−7.50000	+	12.9904i	−0.462470	+	0.801021i	−0.999083	−	0.0428069i	$-0.986370\pi$
$263$	−7.50000	+	12.9904i	−0.462470	+	0.801021i	0.536614	+	0.843828i	$0.319703\pi$
$264$	−1.50000	−	2.59808i	−0.0923186	−	0.159901i
$265$		0			0
$266$	2.00000	+	3.46410i	0.122628	+	0.212398i
$267$	−9.00000	−	15.5885i	−0.550791	−	0.953998i
$268$	−8.00000			−0.488678
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	−0.998361	−	0.0572259i	$-0.981774\pi$
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	0.449622	−	0.893219i	$-0.351559\pi$
$270$		0			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	$0.275099\pi$
$272$	−6.00000			−0.363803
$273$	−2.00000	+	6.92820i	−0.121046	+	0.419314i
$274$	−9.00000			−0.543710
$275$		0			0
$276$	−1.50000	+	2.59808i	−0.0902894	+	0.156386i
$277$	−0.500000	−	0.866025i	−0.0300421	−	0.0520344i	0.850613	−	0.525792i	$-0.176231\pi$
$277$	−0.500000	−	0.866025i	−0.0300421	−	0.0520344i	−0.880656	+	0.473757i	$0.842897\pi$
$278$	14.0000			0.839664
$279$	−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	$0.319597\pi$
$282$	1.50000	+	2.59808i	0.0893237	+	0.154713i
$283$	−15.5000	+	26.8468i	−0.921379	+	1.59588i	−0.124096	+	0.992270i	$0.539603\pi$
$283$	−15.5000	+	26.8468i	−0.921379	+	1.59588i	−0.797283	+	0.603606i	$0.793730\pi$
$284$	6.00000	−	10.3923i	0.356034	−	0.616670i
$285$		0			0
$286$	−10.5000	+	2.59808i	−0.620878	+	0.153627i
$287$	−12.0000			−0.708338
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$	14.0000			0.820695
$292$	7.00000	+	12.1244i	0.409644	+	0.709524i
$293$	−15.0000	−	25.9808i	−0.876309	−	1.51781i	−0.855361	−	0.518032i	$-0.826665\pi$
$293$	−15.0000	−	25.9808i	−0.876309	−	1.51781i	−0.0209480	−	0.999781i	$-0.506668\pi$
$294$	3.00000			0.174964
$295$		0			0
$296$	−3.50000	+	6.06218i	−0.203433	+	0.352357i
$297$	−1.50000	+	2.59808i	−0.0870388	+	0.150756i
$298$	−9.00000			−0.521356
$299$	7.50000	+	7.79423i	0.433736	+	0.450752i
$300$		0			0
$301$	1.00000	−	1.73205i	0.0576390	−	0.0998337i
$302$	−4.00000	+	6.92820i	−0.230174	+	0.398673i
$303$	3.00000	+	5.19615i	0.172345	+	0.298511i
$304$	2.00000			0.114708
$305$		0			0
$306$	3.00000	+	5.19615i	0.171499	+	0.297044i
$307$	−8.00000			−0.456584			−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000			−0.456584			−0.228292	+	0.973593i	$0.573314\pi$
$308$	−3.00000	−	5.19615i	−0.170941	−	0.296078i
$309$	−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	$0.610505\pi$
$312$	2.50000	+	2.59808i	0.141535	+	0.147087i
$313$	−8.00000			−0.452187			−0.226093	−	0.974106i	$-0.572595\pi$
$313$	−8.00000			−0.452187			−0.226093	+	0.974106i	$0.572595\pi$
$314$	−6.50000	+	11.2583i	−0.366816	+	0.635344i
$315$		0			0
$316$	−2.50000	−	4.33013i	−0.140636	−	0.243589i
$317$	−12.0000			−0.673987			−0.336994	−	0.941507i	$-0.609410\pi$
$317$	−12.0000			−0.673987			−0.336994	+	0.941507i	$0.609410\pi$
$318$	3.00000	+	5.19615i	0.168232	+	0.291386i
$319$	4.50000	+	7.79423i	0.251952	+	0.436393i
$320$		0			0
$321$	3.00000	+	5.19615i	0.167444	+	0.290021i
$322$	−3.00000	+	5.19615i	−0.167183	+	0.289570i
$323$	6.00000	−	10.3923i	0.333849	−	0.578243i
$324$	1.00000			0.0555556
$325$		0			0
$326$	13.0000			0.720003
$327$	7.00000	−	12.1244i	0.387101	−	0.670478i
$328$	−3.00000	+	5.19615i	−0.165647	+	0.286910i
$329$	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	$-0.508749\pi$
$332$	−3.00000	−	5.19615i	−0.164646	−	0.285176i
$333$	7.00000			0.383598
$334$	−4.50000	−	7.79423i	−0.246229	−	0.426481i
$335$		0			0
$336$	−1.00000	+	1.73205i	−0.0545545	+	0.0944911i
$337$	−14.0000			−0.762629			−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000			−0.762629			−0.381314	+	0.924445i	$0.624528\pi$
$338$	11.5000	−	6.06218i	0.625518	−	0.329739i
$339$	15.0000			0.814688
$340$		0			0
$341$	7.50000	−	12.9904i	0.406148	−	0.703469i
$342$	−1.00000	−	1.73205i	−0.0540738	−	0.0936586i
$343$	20.0000			1.07990
$344$	−0.500000	−	0.866025i	−0.0269582	−	0.0466930i
$345$		0			0
$346$	−12.0000			−0.645124
$347$	−15.0000	−	25.9808i	−0.805242	−	1.39472i	−0.916127	−	0.400887i	$-0.868702\pi$
$347$	−15.0000	−	25.9808i	−0.805242	−	1.39472i	0.110885	−	0.993833i	$-0.464631\pi$
$348$	1.50000	−	2.59808i	0.0804084	−	0.139272i
$349$	−4.00000	+	6.92820i	−0.214115	+	0.370858i	−0.952998	−	0.302975i	$-0.902020\pi$
$349$	−4.00000	+	6.92820i	−0.214115	+	0.370858i	0.738883	+	0.673833i	$0.235353\pi$
$350$		0			0
$351$	1.00000	−	3.46410i	0.0533761	−	0.184900i
$352$	−3.00000			−0.159901
$353$	15.0000	−	25.9808i	0.798369	−	1.38282i	−0.122308	−	0.992492i	$-0.539030\pi$
$353$	15.0000	−	25.9808i	0.798369	−	1.38282i	0.920677	−	0.390324i	$-0.127637\pi$
$354$	−4.50000	+	7.79423i	−0.239172	+	0.414259i
$355$		0			0
$356$	−18.0000			−0.953998
$357$	6.00000	+	10.3923i	0.317554	+	0.550019i
$358$	1.50000	+	2.59808i	0.0792775	+	0.137313i
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	8.00000	−	13.8564i	0.420471	−	0.728277i
$363$	2.00000			0.104973
$364$	5.00000	+	5.19615i	0.262071	+	0.272352i
$365$		0			0
$366$	1.00000	−	1.73205i	0.0522708	−	0.0905357i
$367$	10.0000	−	17.3205i	0.521996	−	0.904123i	−0.477677	−	0.878536i	$-0.658521\pi$
$367$	10.0000	−	17.3205i	0.521996	−	0.904123i	0.999673	−	0.0255875i	$-0.00814566\pi$
$368$	1.50000	+	2.59808i	0.0781929	+	0.135434i
$369$	6.00000			0.312348
$370$		0			0
$371$	6.00000	+	10.3923i	0.311504	+	0.539542i
$372$	−5.00000			−0.259238
$373$	−12.5000	−	21.6506i	−0.647225	−	1.12103i	−0.983783	−	0.179364i	$-0.942596\pi$
$373$	−12.5000	−	21.6506i	−0.647225	−	1.12103i	0.336557	−	0.941663i	$-0.390737\pi$
$374$	−9.00000	+	15.5885i	−0.465379	+	0.806060i
$375$		0			0
$376$	3.00000			0.154713
$377$	−7.50000	−	7.79423i	−0.386270	−	0.401423i
$378$	2.00000			0.102869
$379$	−19.0000	+	32.9090i	−0.975964	+	1.69042i	−0.299249	+	0.954175i	$0.596736\pi$
$379$	−19.0000	+	32.9090i	−0.975964	+	1.69042i	−0.676715	+	0.736245i	$0.736597\pi$
$380$		0			0
$381$	−7.00000	−	12.1244i	−0.358621	−	0.621150i
$382$	−12.0000			−0.613973
$383$	−10.5000	−	18.1865i	−0.536525	−	0.929288i	−0.999088	−	0.0427020i	$-0.986403\pi$
$383$	−10.5000	−	18.1865i	−0.536525	−	0.929288i	0.462563	−	0.886586i	$-0.346930\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$		0			0
$386$	−2.00000	−	3.46410i	−0.101797	−	0.176318i
$387$	−0.500000	+	0.866025i	−0.0254164	+	0.0440225i
$388$	7.00000	−	12.1244i	0.355371	−	0.615521i
$389$	3.00000			0.152106			0.0760530	−	0.997104i	$-0.475768\pi$
$389$	3.00000			0.152106			0.0760530	+	0.997104i	$0.475768\pi$
$390$		0			0
$391$	18.0000			0.910299
$392$	1.50000	−	2.59808i	0.0757614	−	0.131223i
$393$	4.50000	−	7.79423i	0.226995	−	0.393167i
$394$	12.0000	+	20.7846i	0.604551	+	1.04711i
$395$		0			0
$396$	1.50000	+	2.59808i	0.0753778	+	0.130558i
$397$	−15.5000	−	26.8468i	−0.777923	−	1.34740i	−0.933137	−	0.359521i	$-0.882940\pi$
$397$	−15.5000	−	26.8468i	−0.777923	−	1.34740i	0.155214	−	0.987881i	$-0.450393\pi$
$398$	8.00000			0.401004
$399$	−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	$0.0698049\pi$
$402$	8.00000			0.399004
$403$	−5.00000	+	17.3205i	−0.249068	+	0.862796i
$404$	6.00000			0.298511
$405$		0			0
$406$	3.00000	−	5.19615i	0.148888	−	0.257881i
$407$	10.5000	+	18.1865i	0.520466	+	0.901473i
$408$	6.00000			0.297044
$409$	5.00000	+	8.66025i	0.247234	+	0.428222i	0.962757	−	0.270367i	$-0.0871450\pi$
$409$	5.00000	+	8.66025i	0.247234	+	0.428222i	−0.715523	+	0.698589i	$0.753812\pi$
$410$		0			0
$411$	9.00000			0.443937
$412$	7.00000	+	12.1244i	0.344865	+	0.597324i
$413$	−9.00000	+	15.5885i	−0.442861	+	0.767058i
$414$	1.50000	−	2.59808i	0.0737210	−	0.127688i
$415$		0			0
$416$	3.50000	−	0.866025i	0.171602	−	0.0424604i
$417$	−14.0000			−0.685583
$418$	3.00000	−	5.19615i	0.146735	−	0.254152i
$419$	6.00000	−	10.3923i	0.293119	−	0.507697i	−0.681426	−	0.731887i	$-0.738640\pi$
$419$	6.00000	−	10.3923i	0.293119	−	0.507697i	0.974546	+	0.224189i	$0.0719734\pi$
$420$		0			0
$421$	−16.0000			−0.779792			−0.389896	−	0.920859i	$-0.627489\pi$
$421$	−16.0000			−0.779792			−0.389896	+	0.920859i	$0.627489\pi$
$422$	−10.0000	−	17.3205i	−0.486792	−	0.843149i
$423$	−1.50000	−	2.59808i	−0.0729325	−	0.126323i
$424$	6.00000			0.291386
$425$		0			0
$426$	−6.00000	+	10.3923i	−0.290701	+	0.503509i
$427$	2.00000	−	3.46410i	0.0967868	−	0.167640i
$428$	6.00000			0.290021
$429$	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	$0.259993\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−20.0000	−	34.6410i	−0.961139	−	1.66474i	−0.719650	−	0.694337i	$-0.755698\pi$
$433$	−20.0000	−	34.6410i	−0.961139	−	1.66474i	−0.241489	−	0.970404i	$-0.577636\pi$
$434$	−10.0000			−0.480015
$435$		0			0
$436$	−7.00000	−	12.1244i	−0.335239	−	0.580651i
$437$	−6.00000			−0.287019
$438$	−7.00000	−	12.1244i	−0.334473	−	0.579324i
$439$	2.00000	−	3.46410i	0.0954548	−	0.165333i	−0.814344	−	0.580383i	$-0.802903\pi$
$439$	2.00000	−	3.46410i	0.0954548	−	0.165333i	0.909798	+	0.415051i	$0.136236\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$	6.00000	−	20.7846i	0.285391	−	0.988623i
$443$	36.0000			1.71041			0.855206	−	0.518289i	$-0.173431\pi$
$443$	36.0000			1.71041			0.855206	+	0.518289i	$0.173431\pi$
$444$	3.50000	−	6.06218i	0.166103	−	0.287698i
$445$		0			0
$446$	−5.00000	−	8.66025i	−0.236757	−	0.410075i
$447$	9.00000			0.425685
$448$	1.00000	+	1.73205i	0.0472456	+	0.0818317i
$449$	−18.0000	−	31.1769i	−0.849473	−	1.47133i	−0.881680	−	0.471848i	$-0.843587\pi$
$449$	−18.0000	−	31.1769i	−0.849473	−	1.47133i	0.0322072	−	0.999481i	$-0.489746\pi$
$450$		0			0
$451$	9.00000	+	15.5885i	0.423793	+	0.734032i
$452$	7.50000	−	12.9904i	0.352770	−	0.611016i
$453$	4.00000	−	6.92820i	0.187936	−	0.325515i
$454$		0			0
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	1.00000	−	1.73205i	0.0467780	−	0.0810219i	−0.841688	−	0.539964i	$-0.818438\pi$
$457$	1.00000	−	1.73205i	0.0467780	−	0.0810219i	0.888466	+	0.458942i	$0.151771\pi$
$458$	−7.00000	+	12.1244i	−0.327089	+	0.566534i
$459$	−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	$0.946917\pi$
$462$	3.00000	+	5.19615i	0.139573	+	0.241747i
$463$	34.0000			1.58011			0.790057	−	0.613033i	$-0.210051\pi$
$463$	34.0000			1.58011			0.790057	+	0.613033i	$0.210051\pi$
$464$	−1.50000	−	2.59808i	−0.0696358	−	0.120613i
$465$		0			0
$466$	10.5000	−	18.1865i	0.486403	−	0.842475i
$467$	−18.0000			−0.832941			−0.416470	−	0.909149i	$-0.636733\pi$
$467$	−18.0000			−0.832941			−0.416470	+	0.909149i	$0.636733\pi$
$468$	−2.50000	−	2.59808i	−0.115563	−	0.120096i
$469$	16.0000			0.738811
$470$		0			0
$471$	6.50000	−	11.2583i	0.299504	−	0.518756i
$472$	4.50000	+	7.79423i	0.207129	+	0.358758i
$473$	−3.00000			−0.137940
$474$	2.50000	+	4.33013i	0.114829	+	0.198889i
$475$		0			0
$476$	12.0000			0.550019
$477$	−3.00000	−	5.19615i	−0.137361	−	0.237915i
$478$	−12.0000	+	20.7846i	−0.548867	+	0.950666i
$479$		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
$482$	17.0000			0.774329
$483$	3.00000	−	5.19615i	0.136505	−	0.236433i
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$		0			0
$486$	−1.00000			−0.0453609
$487$	1.00000	+	1.73205i	0.0453143	+	0.0784867i	0.887793	−	0.460243i	$-0.152238\pi$
$487$	1.00000	+	1.73205i	0.0453143	+	0.0784867i	−0.842479	+	0.538730i	$0.818904\pi$
$488$	−1.00000	−	1.73205i	−0.0452679	−	0.0784063i
$489$	−13.0000			−0.587880
$490$		0			0
$491$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$491$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$492$	3.00000	−	5.19615i	0.135250	−	0.234261i
$493$	−18.0000			−0.810679
$494$	−2.00000	+	6.92820i	−0.0899843	+	0.311715i
$495$		0			0
$496$	−2.50000	+	4.33013i	−0.112253	+	0.194428i
$497$	−12.0000	+	20.7846i	−0.538274	+	0.932317i
$498$	3.00000	+	5.19615i	0.134433	+	0.232845i
$499$	32.0000			1.43252			0.716258	−	0.697835i	$-0.245853\pi$
$499$	32.0000			1.43252			0.716258	+	0.697835i	$0.245853\pi$
$500$		0			0
$501$	4.50000	+	7.79423i	0.201045	+	0.348220i
$502$	15.0000			0.669483
$503$	12.0000	+	20.7846i	0.535054	+	0.926740i	0.999161	+	0.0409609i	$0.0130419\pi$
$503$	12.0000	+	20.7846i	0.535054	+	0.926740i	−0.464107	+	0.885779i	$0.653625\pi$
$504$	1.00000	−	1.73205i	0.0445435	−	0.0771517i
$505$		0			0
$506$	9.00000			0.400099
$507$	−11.5000	+	6.06218i	−0.510733	+	0.269231i
$508$	−14.0000			−0.621150
$509$	−1.50000	+	2.59808i	−0.0664863	+	0.115158i	−0.897352	−	0.441315i	$-0.854512\pi$
$509$	−1.50000	+	2.59808i	−0.0664863	+	0.115158i	0.830866	+	0.556473i	$0.187846\pi$
$510$		0			0
$511$	−14.0000	−	24.2487i	−0.619324	−	1.07270i
$512$	1.00000			0.0441942
$513$	1.00000	+	1.73205i	0.0441511	+	0.0764719i
$514$	−10.5000	−	18.1865i	−0.463135	−	0.802174i
$515$		0			0
$516$	0.500000	+	0.866025i	0.0220113	+	0.0381246i
$517$	4.50000	−	7.79423i	0.197910	−	0.342790i
$518$	7.00000	−	12.1244i	0.307562	−	0.532714i
$519$	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	$0.728243\pi$
$522$	−1.50000	+	2.59808i	−0.0656532	+	0.113715i
$523$	5.50000	−	9.52628i	0.240498	−	0.416555i	−0.720358	−	0.693602i	$-0.756023\pi$
$523$	5.50000	−	9.52628i	0.240498	−	0.416555i	0.960856	+	0.277047i	$0.0893559\pi$
$524$	−4.50000	−	7.79423i	−0.196583	−	0.340492i
$525$		0			0
$526$	−7.50000	−	12.9904i	−0.327016	−	0.566408i
$527$	15.0000	+	25.9808i	0.653410	+	1.13174i
$528$	3.00000			0.130558
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$	4.50000	−	7.79423i	0.195283	−	0.338241i
$532$	−4.00000			−0.173422
$533$	−15.0000	−	15.5885i	−0.649722	−	0.675211i
$534$	18.0000			0.778936
$535$		0			0
$536$	4.00000	−	6.92820i	0.172774	−	0.299253i
$537$	−1.50000	−	2.59808i	−0.0647298	−	0.112115i
$538$	18.0000			0.776035
$539$	−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	$0.358537\pi$
$542$	−5.50000	−	9.52628i	−0.236245	−	0.409189i
$543$	−8.00000	+	13.8564i	−0.343313	+	0.594635i
$544$	3.00000	−	5.19615i	0.128624	−	0.222783i
$545$		0			0
$546$	−5.00000	−	5.19615i	−0.213980	−	0.222375i
$547$	−20.0000			−0.855138			−0.427569	−	0.903983i	$-0.640630\pi$
$547$	−20.0000			−0.855138			−0.427569	+	0.903983i	$0.640630\pi$
$548$	4.50000	−	7.79423i	0.192230	−	0.332953i
$549$	−1.00000	+	1.73205i	−0.0426790	+	0.0739221i
$550$		0			0
$551$	6.00000			0.255609
$552$	−1.50000	−	2.59808i	−0.0638442	−	0.110581i
$553$	5.00000	+	8.66025i	0.212622	+	0.368271i
$554$	1.00000			0.0424859
$555$		0			0
$556$	−7.00000	+	12.1244i	−0.296866	+	0.514187i
$557$	−3.00000	+	5.19615i	−0.127114	+	0.220168i	−0.922557	−	0.385860i	$-0.873905\pi$
$557$	−3.00000	+	5.19615i	−0.127114	+	0.220168i	0.795443	+	0.606028i	$0.207238\pi$
$558$	5.00000			0.211667
$559$	3.50000	−	0.866025i	0.148034	−	0.0366290i
$560$		0			0
$561$	9.00000	−	15.5885i	0.379980	−	0.658145i
$562$	−9.00000	+	15.5885i	−0.379642	+	0.657559i
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	0.943560	+	0.331202i	$0.107454\pi$
$563$	18.0000	+	31.1769i	0.758610	+	1.31395i	−0.184950	+	0.982748i	$0.559212\pi$
$564$	−3.00000			−0.126323
$565$		0			0
$566$	−15.5000	−	26.8468i	−0.651514	−	1.12845i
$567$	−2.00000			−0.0839921
$568$	6.00000	+	10.3923i	0.251754	+	0.436051i
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	−0.922032	−	0.387113i	$-0.873472\pi$
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	0.796266	+	0.604947i	$0.206806\pi$
$570$		0			0
$571$	−40.0000			−1.67395			−0.836974	−	0.547243i	$-0.815677\pi$
$571$	−40.0000			−1.67395			−0.836974	+	0.547243i	$0.815677\pi$
$572$	3.00000	−	10.3923i	0.125436	−	0.434524i
$573$	12.0000			0.501307
$574$	6.00000	−	10.3923i	0.250435	−	0.433766i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−2.00000			−0.0832611			−0.0416305	−	0.999133i	$-0.513255\pi$
$577$	−2.00000			−0.0832611			−0.0416305	+	0.999133i	$0.513255\pi$
$578$	−9.50000	−	16.4545i	−0.395148	−	0.684416i
$579$	2.00000	+	3.46410i	0.0831172	+	0.143963i
$580$		0			0
$581$	6.00000	+	10.3923i	0.248922	+	0.431145i
$582$	−7.00000	+	12.1244i	−0.290159	+	0.502571i
$583$	9.00000	−	15.5885i	0.372742	−	0.645608i
$584$	−14.0000			−0.579324
$585$		0			0
$586$	30.0000			1.23929
$587$	9.00000	−	15.5885i	0.371470	−	0.643404i	−0.618322	−	0.785925i	$-0.712187\pi$
$587$	9.00000	−	15.5885i	0.371470	−	0.643404i	0.989792	+	0.142520i	$0.0455206\pi$
$588$	−1.50000	+	2.59808i	−0.0618590	+	0.107143i
$589$	−5.00000	−	8.66025i	−0.206021	−	0.356840i
$590$		0			0
$591$	−12.0000	−	20.7846i	−0.493614	−	0.854965i
$592$	−3.50000	−	6.06218i	−0.143849	−	0.249154i
$593$	−27.0000			−1.10876			−0.554379	−	0.832265i	$-0.687044\pi$
$593$	−27.0000			−1.10876			−0.554379	+	0.832265i	$0.687044\pi$
$594$	−1.50000	−	2.59808i	−0.0615457	−	0.106600i
$595$		0			0
$596$	4.50000	−	7.79423i	0.184327	−	0.319264i
$597$	−8.00000			−0.327418
$598$	−10.5000	+	2.59808i	−0.429377	+	0.106243i
$599$	6.00000			0.245153			0.122577	−	0.992459i	$-0.460884\pi$
$599$	6.00000			0.245153			0.122577	+	0.992459i	$0.460884\pi$
$600$		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	$0.0400009\pi$
$602$	1.00000	+	1.73205i	0.0407570	+	0.0705931i
$603$	−8.00000			−0.325785
$604$	−4.00000	−	6.92820i	−0.162758	−	0.281905i
$605$		0			0
$606$	−6.00000			−0.243733
$607$	−11.0000	−	19.0526i	−0.446476	−	0.773320i	0.551678	−	0.834058i	$-0.313988\pi$
$607$	−11.0000	−	19.0526i	−0.446476	−	0.773320i	−0.998154	+	0.0607380i	$0.980655\pi$
$608$	−1.00000	+	1.73205i	−0.0405554	+	0.0702439i
$609$	−3.00000	+	5.19615i	−0.121566	+	0.210559i
$610$		0			0
$611$	−3.00000	+	10.3923i	−0.121367	+	0.420428i
$612$	−6.00000			−0.242536
$613$	−15.5000	+	26.8468i	−0.626039	+	1.08433i	0.362300	+	0.932062i	$0.381992\pi$
$613$	−15.5000	+	26.8468i	−0.626039	+	1.08433i	−0.988339	+	0.152270i	$0.951342\pi$
$614$	4.00000	−	6.92820i	0.161427	−	0.279600i
$615$		0			0
$616$	6.00000			0.241747
$617$	10.5000	+	18.1865i	0.422714	+	0.732162i	0.996204	−	0.0870504i	$-0.0277441\pi$
$617$	10.5000	+	18.1865i	0.422714	+	0.732162i	−0.573490	+	0.819213i	$0.694411\pi$
$618$	−7.00000	−	12.1244i	−0.281581	−	0.487713i
$619$	−46.0000			−1.84890			−0.924448	−	0.381308i	$-0.875474\pi$
$619$	−46.0000			−1.84890			−0.924448	+	0.381308i	$0.875474\pi$
$620$		0			0
$621$	−1.50000	+	2.59808i	−0.0601929	+	0.104257i
$622$	6.00000	−	10.3923i	0.240578	−	0.416693i
$623$	36.0000			1.44231
$624$	−3.50000	+	0.866025i	−0.140112	+	0.0346688i
$625$		0			0
$626$	4.00000	−	6.92820i	0.159872	−	0.276907i
$627$	−3.00000	+	5.19615i	−0.119808	+	0.207514i
$628$	−6.50000	−	11.2583i	−0.259378	−	0.449256i
$629$	−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	$0.730163\pi$
$632$	5.00000			0.198889
$633$	10.0000	+	17.3205i	0.397464	+	0.688428i
$634$	6.00000	−	10.3923i	0.238290	−	0.412731i
$635$		0			0
$636$	−6.00000			−0.237915
$637$	7.50000	+	7.79423i	0.297161	+	0.308819i
$638$	−9.00000			−0.356313
$639$	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	$0.871140\pi$
$642$	−6.00000			−0.236801
$643$	−8.00000	−	13.8564i	−0.315489	−	0.546443i	0.664052	−	0.747686i	$-0.268835\pi$
$643$	−8.00000	−	13.8564i	−0.315489	−	0.546443i	−0.979541	+	0.201243i	$0.935502\pi$
$644$	−3.00000	−	5.19615i	−0.118217	−	0.204757i
$645$		0			0
$646$	6.00000	+	10.3923i	0.236067	+	0.408880i
$647$	12.0000	−	20.7846i	0.471769	−	0.817127i	−0.527710	−	0.849425i	$-0.676949\pi$
$647$	12.0000	−	20.7846i	0.471769	−	0.817127i	0.999478	+	0.0322975i	$0.0102824\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	27.0000			1.05984
$650$		0			0
$651$	10.0000			0.391931
$652$	−6.50000	+	11.2583i	−0.254560	+	0.440910i
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	−0.801337	−	0.598213i	$-0.795878\pi$
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	0.918736	+	0.394872i	$0.129211\pi$
$654$	7.00000	+	12.1244i	0.273722	+	0.474100i
$655$		0			0
$656$	−3.00000	−	5.19615i	−0.117130	−	0.202876i
$657$	7.00000	+	12.1244i	0.273096	+	0.473016i
$658$	−6.00000			−0.233904
$659$	−7.50000	−	12.9904i	−0.292159	−	0.506033i	0.682161	−	0.731202i	$-0.261040\pi$
$659$	−7.50000	−	12.9904i	−0.292159	−	0.506033i	−0.974320	+	0.225168i	$0.927707\pi$
$660$		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	$0.952854\pi$
$662$	32.0000			1.24372
$663$	−6.00000	+	20.7846i	−0.233021	+	0.807207i
$664$	6.00000			0.232845
$665$		0			0
$666$	−3.50000	+	6.06218i	−0.135622	+	0.234905i
$667$	4.50000	+	7.79423i	0.174241	+	0.301794i
$668$	9.00000			0.348220
$669$	5.00000	+	8.66025i	0.193311	+	0.334825i
$670$		0			0
$671$	−6.00000			−0.231627
$672$	−1.00000	−	1.73205i	−0.0385758	−	0.0668153i
$673$	−2.00000	+	3.46410i	−0.0770943	+	0.133531i	−0.901995	−	0.431746i	$-0.857898\pi$
$673$	−2.00000	+	3.46410i	−0.0770943	+	0.133531i	0.824901	+	0.565278i	$0.191231\pi$
$674$	7.00000	−	12.1244i	0.269630	−	0.467013i
$675$		0			0
$676$	−0.500000	+	12.9904i	−0.0192308	+	0.499630i
$677$	36.0000			1.38359			0.691796	−	0.722093i	$-0.256820\pi$
$677$	36.0000			1.38359			0.691796	+	0.722093i	$0.256820\pi$
$678$	−7.50000	+	12.9904i	−0.288036	+	0.498893i
$679$	−14.0000	+	24.2487i	−0.537271	+	0.930580i
$680$		0			0
$681$		0			0
$682$	7.50000	+	12.9904i	0.287190	+	0.497427i
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	0.728101	−	0.685470i	$-0.240403\pi$
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	−0.957685	+	0.287819i	$0.907070\pi$
$684$	2.00000			0.0764719
$685$		0			0
$686$	−10.0000	+	17.3205i	−0.381802	+	0.661300i
$687$	7.00000	−	12.1244i	0.267067	−	0.462573i
$688$	1.00000			0.0381246
$689$	−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	$-0.172447\pi$
$692$	6.00000	−	10.3923i	0.228086	−	0.395056i
$693$	−3.00000	−	5.19615i	−0.113961	−	0.197386i
$694$	30.0000			1.13878
$695$		0			0
$696$	1.50000	+	2.59808i	0.0568574	+	0.0984798i
$697$	−36.0000			−1.36360
$698$	−4.00000	−	6.92820i	−0.151402	−	0.262236i
$699$	−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	$0.629803\pi$
$702$	2.50000	+	2.59808i	0.0943564	+	0.0980581i
$703$	14.0000			0.528020
$704$	1.50000	−	2.59808i	0.0565334	−	0.0979187i
$705$		0			0
$706$	15.0000	+	25.9808i	0.564532	+	0.977799i
$707$	−12.0000			−0.451306
$708$	−4.50000	−	7.79423i	−0.169120	−	0.292925i
$709$	−16.0000	−	27.7128i	−0.600893	−	1.04078i	−0.992686	−	0.120723i	$-0.961479\pi$
$709$	−16.0000	−	27.7128i	−0.600893	−	1.04078i	0.391794	−	0.920053i	$-0.371855\pi$
$710$		0			0
$711$	−2.50000	−	4.33013i	−0.0937573	−	0.162392i
$712$	9.00000	−	15.5885i	0.337289	−	0.584202i
$713$	7.50000	−	12.9904i	0.280877	−	0.486494i
$714$	−12.0000			−0.449089
$715$		0			0
$716$	−3.00000			−0.112115
$717$	12.0000	−	20.7846i	0.448148	−	0.776215i
$718$	−12.0000	+	20.7846i	−0.447836	+	0.775675i
$719$	−18.0000	−	31.1769i	−0.671287	−	1.16270i	−0.977539	−	0.210752i	$-0.932409\pi$
$719$	−18.0000	−	31.1769i	−0.671287	−	1.16270i	0.306253	−	0.951950i	$-0.400925\pi$
$720$		0			0
$721$	−14.0000	−	24.2487i	−0.521387	−	0.903069i
$722$	7.50000	+	12.9904i	0.279121	+	0.483452i
$723$	−17.0000			−0.632237
$724$	8.00000	+	13.8564i	0.297318	+	0.514969i
$725$		0			0
$726$	−1.00000	+	1.73205i	−0.0371135	+	0.0642824i
$727$	4.00000			0.148352			0.0741759	−	0.997245i	$-0.476367\pi$
$727$	4.00000			0.148352			0.0741759	+	0.997245i	$0.476367\pi$
$728$	−7.00000	+	1.73205i	−0.259437	+	0.0641941i
$729$	1.00000			0.0370370
$730$		0			0
$731$	3.00000	−	5.19615i	0.110959	−	0.192187i
$732$	1.00000	+	1.73205i	0.0369611	+	0.0640184i
$733$	22.0000			0.812589			0.406294	−	0.913742i	$-0.366821\pi$
$733$	22.0000			0.812589			0.406294	+	0.913742i	$0.366821\pi$
$734$	10.0000	+	17.3205i	0.369107	+	0.639312i
$735$		0			0
$736$	−3.00000			−0.110581
$737$	−12.0000	−	20.7846i	−0.442026	−	0.765611i
$738$	−3.00000	+	5.19615i	−0.110432	+	0.191273i
$739$	8.00000	−	13.8564i	0.294285	−	0.509716i	−0.680534	−	0.732717i	$-0.738252\pi$
$739$	8.00000	−	13.8564i	0.294285	−	0.509716i	0.974818	+	0.223001i	$0.0715853\pi$
$740$		0			0
$741$	2.00000	−	6.92820i	0.0734718	−	0.254514i
$742$	−12.0000			−0.440534
$743$	−4.50000	+	7.79423i	−0.165089	+	0.285943i	−0.936687	−	0.350168i	$-0.886124\pi$
$743$	−4.50000	+	7.79423i	−0.165089	+	0.285943i	0.771598	+	0.636111i	$0.219458\pi$
$744$	2.50000	−	4.33013i	0.0916544	−	0.158750i
$745$		0			0
$746$	25.0000			0.915315
$747$	−3.00000	−	5.19615i	−0.109764	−	0.190117i
$748$	−9.00000	−	15.5885i	−0.329073	−	0.569970i
$749$	−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	$0.897654\pi$
$752$	−1.50000	+	2.59808i	−0.0546994	+	0.0947421i
$753$	−15.0000			−0.546630
$754$	10.5000	−	2.59808i	0.382387	−	0.0946164i
$755$		0			0
$756$	−1.00000	+	1.73205i	−0.0363696	+	0.0629941i
$757$	19.0000	−	32.9090i	0.690567	−	1.19610i	−0.281086	−	0.959683i	$-0.590695\pi$
$757$	19.0000	−	32.9090i	0.690567	−	1.19610i	0.971652	−	0.236414i	$-0.0759722\pi$
$758$	−19.0000	−	32.9090i	−0.690111	−	1.19531i
$759$	−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	$0.763543\pi$
$762$	14.0000			0.507166
$763$	14.0000	+	24.2487i	0.506834	+	0.877862i
$764$	6.00000	−	10.3923i	0.217072	−	0.375980i
$765$		0			0
$766$	21.0000			0.758761
$767$	−31.5000	+	7.79423i	−1.13740	+	0.281433i
$768$	−1.00000			−0.0360844
$769$	6.50000	−	11.2583i	0.234396	−	0.405986i	−0.724701	−	0.689063i	$-0.758022\pi$
$769$	6.50000	−	11.2583i	0.234396	−	0.405986i	0.959097	+	0.283078i	$0.0913554\pi$
$770$		0			0
$771$	10.5000	+	18.1865i	0.378148	+	0.654972i
$772$	4.00000			0.143963
$773$	−24.0000	−	41.5692i	−0.863220	−	1.49514i	−0.868804	−	0.495156i	$-0.835111\pi$
$773$	−24.0000	−	41.5692i	−0.863220	−	1.49514i	0.00558380	−	0.999984i	$-0.498223\pi$
$774$	−0.500000	−	0.866025i	−0.0179721	−	0.0311286i
$775$		0			0
$776$	7.00000	+	12.1244i	0.251285	+	0.435239i
$777$	−7.00000	+	12.1244i	−0.251124	+	0.434959i
$778$	−1.50000	+	2.59808i	−0.0537776	+	0.0931455i
$779$	12.0000			0.429945
$780$		0			0
$781$	36.0000			1.28818
$782$	−9.00000	+	15.5885i	−0.321839	+	0.557442i
$783$	1.50000	−	2.59808i	0.0536056	−	0.0928477i
$784$	1.50000	+	2.59808i	0.0535714	+	0.0927884i
$785$		0			0
$786$	4.50000	+	7.79423i	0.160510	+	0.278011i
$787$	17.5000	+	30.3109i	0.623808	+	1.08047i	0.988770	+	0.149444i	$0.0477485\pi$
$787$	17.5000	+	30.3109i	0.623808	+	1.08047i	−0.364963	+	0.931022i	$0.618918\pi$
$788$	−24.0000			−0.854965
$789$	7.50000	+	12.9904i	0.267007	+	0.462470i
$790$		0			0
$791$	−15.0000	+	25.9808i	−0.533339	+	0.923770i
$792$	−3.00000			−0.106600
$793$	7.00000	−	1.73205i	0.248577	−	0.0615069i
$794$	31.0000			1.10015
$795$		0			0
$796$	−4.00000	+	6.92820i	−0.141776	+	0.245564i
$797$	−12.0000	−	20.7846i	−0.425062	−	0.736229i	0.571364	−	0.820696i	$-0.306414\pi$
$797$	−12.0000	−	20.7846i	−0.425062	−	0.736229i	−0.996426	+	0.0844678i	$0.973081\pi$
$798$	4.00000			0.141598
$799$	9.00000	+	15.5885i	0.318397	+	0.551480i
$800$		0			0
$801$	−18.0000			−0.635999
$802$	6.00000	+	10.3923i	0.211867	+	0.366965i
$803$	−21.0000	+	36.3731i	−0.741074	+	1.28358i
$804$	−4.00000	+	6.92820i	−0.141069	+	0.244339i
$805$		0			0
$806$	−12.5000	−	12.9904i	−0.440294	−	0.457567i
$807$	−18.0000			−0.633630
$808$	−3.00000	+	5.19615i	−0.105540	+	0.182800i
$809$	−15.0000	+	25.9808i	−0.527372	+	0.913435i	0.472119	+	0.881535i	$0.343489\pi$
$809$	−15.0000	+	25.9808i	−0.527372	+	0.913435i	−0.999491	+	0.0319002i	$0.989844\pi$
$810$		0			0
$811$	32.0000			1.12367			0.561836	−	0.827249i	$-0.310095\pi$
$811$	32.0000			1.12367			0.561836	+	0.827249i	$0.310095\pi$
$812$	3.00000	+	5.19615i	0.105279	+	0.182349i
$813$	5.50000	+	9.52628i	0.192893	+	0.334101i
$814$	−21.0000			−0.736050
$815$		0			0
$816$	−3.00000	+	5.19615i	−0.105021	+	0.181902i
$817$	−1.00000	+	1.73205i	−0.0349856	+	0.0605968i
$818$	−10.0000			−0.349642
$819$	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	$0.322829\pi$
$822$	−4.50000	+	7.79423i	−0.156956	+	0.271855i
$823$	7.00000	+	12.1244i	0.244005	+	0.422628i	0.961851	−	0.273573i	$-0.0882054\pi$
$823$	7.00000	+	12.1244i	0.244005	+	0.422628i	−0.717847	+	0.696201i	$0.754872\pi$
$824$	−14.0000			−0.487713
$825$		0			0
$826$	−9.00000	−	15.5885i	−0.313150	−	0.542392i
$827$	−6.00000			−0.208640			−0.104320	−	0.994544i	$-0.533267\pi$
$827$	−6.00000			−0.208640			−0.104320	+	0.994544i	$0.533267\pi$
$828$	1.50000	+	2.59808i	0.0521286	+	0.0902894i
$829$	−13.0000	+	22.5167i	−0.451509	+	0.782036i	−0.998480	−	0.0551154i	$-0.982447\pi$
$829$	−13.0000	+	22.5167i	−0.451509	+	0.782036i	0.546971	+	0.837151i	$0.315781\pi$
$830$		0			0
$831$	−1.00000			−0.0346896
$832$	−1.00000	+	3.46410i	−0.0346688	+	0.120096i
$833$	18.0000			0.623663
$834$	7.00000	−	12.1244i	0.242390	−	0.419832i
$835$		0			0
$836$	3.00000	+	5.19615i	0.103757	+	0.179713i
$837$	−5.00000			−0.172825
$838$	6.00000	+	10.3923i	0.207267	+	0.358996i
$839$	−21.0000	−	36.3731i	−0.725001	−	1.25574i	−0.958974	−	0.283495i	$-0.908506\pi$
$839$	−21.0000	−	36.3731i	−0.725001	−	1.25574i	0.233973	−	0.972243i	$-0.424827\pi$
$840$		0			0
$841$	10.0000	+	17.3205i	0.344828	+	0.597259i
$842$	8.00000	−	13.8564i	0.275698	−	0.477523i
$843$	9.00000	−	15.5885i	0.309976	−	0.536895i
$844$	20.0000			0.688428
$845$		0			0
$846$	3.00000			0.103142
$847$	−2.00000	+	3.46410i	−0.0687208	+	0.119028i
$848$	−3.00000	+	5.19615i	−0.103020	+	0.178437i
$849$	15.5000	+	26.8468i	0.531959	+	0.921379i
$850$		0			0
$851$	10.5000	+	18.1865i	0.359935	+	0.623426i
$852$	−6.00000	−	10.3923i	−0.205557	−	0.356034i
$853$	19.0000			0.650548			0.325274	−	0.945620i	$-0.394544\pi$
$853$	19.0000			0.650548			0.325274	+	0.945620i	$0.394544\pi$
$854$	2.00000	+	3.46410i	0.0684386	+	0.118539i
$855$		0			0
$856$	−3.00000	+	5.19615i	−0.102538	+	0.177601i
$857$	−3.00000			−0.102478			−0.0512390	−	0.998686i	$-0.516317\pi$
$857$	−3.00000			−0.102478			−0.0512390	+	0.998686i	$0.516317\pi$
$858$	−3.00000	+	10.3923i	−0.102418	+	0.354787i
$859$	−46.0000			−1.56950			−0.784750	−	0.619813i	$-0.787209\pi$
$859$	−46.0000			−1.56950			−0.784750	+	0.619813i	$0.787209\pi$
$860$		0			0
$861$	−6.00000	+	10.3923i	−0.204479	+	0.354169i
$862$	−6.00000	−	10.3923i	−0.204361	−	0.353963i
$863$	45.0000			1.53182			0.765909	−	0.642949i	$-0.222289\pi$
$863$	45.0000			1.53182			0.765909	+	0.642949i	$0.222289\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$		0			0
$866$	40.0000			1.35926
$867$	9.50000	+	16.4545i	0.322637	+	0.558824i
$868$	5.00000	−	8.66025i	0.169711	−	0.293948i
$869$	7.50000	−	12.9904i	0.254420	−	0.440668i
$870$		0			0
$871$	20.0000	+	20.7846i	0.677674	+	0.704260i
$872$	14.0000			0.474100
$873$	7.00000	−	12.1244i	0.236914	−	0.410347i
$874$	3.00000	−	5.19615i	0.101477	−	0.175762i
$875$		0			0
$876$	14.0000			0.473016
$877$	11.5000	+	19.9186i	0.388327	+	0.672603i	0.992225	−	0.124459i	$-0.0397196\pi$
$877$	11.5000	+	19.9186i	0.388327	+	0.672603i	−0.603897	+	0.797062i	$0.706386\pi$
$878$	2.00000	+	3.46410i	0.0674967	+	0.116908i
$879$	−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	$0.198894\pi$
$882$	1.50000	−	2.59808i	0.0505076	−	0.0874818i
$883$	19.0000			0.639401			0.319700	−	0.947519i	$-0.396418\pi$
$883$	19.0000			0.639401			0.319700	+	0.947519i	$0.396418\pi$
$884$	15.0000	+	15.5885i	0.504505	+	0.524297i
$885$		0			0
$886$	−18.0000	+	31.1769i	−0.604722	+	1.04741i
$887$	−28.5000	+	49.3634i	−0.956936	+	1.65746i	−0.227063	+	0.973880i	$0.572912\pi$
$887$	−28.5000	+	49.3634i	−0.956936	+	1.65746i	−0.729873	+	0.683582i	$0.760421\pi$
$888$	3.50000	+	6.06218i	0.117452	+	0.203433i
$889$	28.0000			0.939090
$890$		0			0
$891$	1.50000	+	2.59808i	0.0502519	+	0.0870388i
$892$	10.0000			0.334825
$893$	−3.00000	−	5.19615i	−0.100391	−	0.173883i
$894$	−4.50000	+	7.79423i	−0.150503	+	0.260678i
$895$		0			0
$896$	−2.00000			−0.0668153
$897$	10.5000	−	2.59808i	0.350585	−	0.0867472i
$898$	36.0000			1.20134
$899$	−7.50000	+	12.9904i	−0.250139	+	0.433253i
$900$		0			0
$901$	18.0000	+	31.1769i	0.599667	+	1.03865i
$902$	−18.0000			−0.599334
$903$	−1.00000	−	1.73205i	−0.0332779	−	0.0576390i
$904$	7.50000	+	12.9904i	0.249446	+	0.432054i
$905$		0			0
$906$	4.00000	+	6.92820i	0.132891	+	0.230174i
$907$	8.50000	−	14.7224i	0.282238	−	0.488850i	−0.689698	−	0.724097i	$-0.742257\pi$
$907$	8.50000	−	14.7224i	0.282238	−	0.488850i	0.971936	+	0.235247i	$0.0755899\pi$
$908$		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	$0.531691\pi$
$912$	1.00000	−	1.73205i	0.0331133	−	0.0573539i
$913$	9.00000	−	15.5885i	0.297857	−	0.515903i
$914$	1.00000	+	1.73205i	0.0330771	+	0.0572911i
$915$		0			0
$916$	−7.00000	−	12.1244i	−0.231287	−	0.400600i
$917$	9.00000	+	15.5885i	0.297206	+	0.514776i
$918$	6.00000			0.198030
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	0.967274	−	0.253735i	$-0.0816592\pi$
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	−0.703378	+	0.710816i	$0.748326\pi$
$920$		0			0
$921$	−4.00000	+	6.92820i	−0.131804	+	0.228292i
$922$	15.0000			0.493999
$923$	−42.0000	+	10.3923i	−1.38245	+	0.342067i
$924$	−6.00000			−0.197386
$925$		0			0
$926$	−17.0000	+	29.4449i	−0.558655	+	0.967618i
$927$	7.00000	+	12.1244i	0.229910	+	0.398216i
$928$	3.00000			0.0984798
$929$	6.00000	+	10.3923i	0.196854	+	0.340960i	0.947507	−	0.319736i	$-0.103594\pi$
$929$	6.00000	+	10.3923i	0.196854	+	0.340960i	−0.750653	+	0.660697i	$0.770261\pi$
$930$		0			0
$931$	−6.00000			−0.196642
$932$	10.5000	+	18.1865i	0.343939	+	0.595720i
$933$	−6.00000	+	10.3923i	−0.196431	+	0.340229i
$934$	9.00000	−	15.5885i	0.294489	−	0.510070i
$935$		0			0
$936$	3.50000	−	0.866025i	0.114401	−	0.0283069i
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$	−8.00000	+	13.8564i	−0.261209	+	0.452428i
$939$	−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	$0.259985\pi$
$942$	6.50000	+	11.2583i	0.211781	+	0.366816i
$943$	9.00000	+	15.5885i	0.293080	+	0.507630i
$944$	−9.00000			−0.292925
$945$		0			0
$946$	1.50000	−	2.59808i	0.0487692	−	0.0844707i
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	−0.946892	−	0.321552i	$-0.895796\pi$
$947$	−6.00000	+	10.3923i	−0.194974	+	0.337705i	0.751918	+	0.659256i	$0.229129\pi$
$948$	−5.00000			−0.162392
$949$	14.0000	−	48.4974i	0.454459	−	1.57429i
$950$		0			0
$951$	−6.00000	+	10.3923i	−0.194563	+	0.336994i
$952$	−6.00000	+	10.3923i	−0.194461	+	0.336817i
$953$	4.50000	+	7.79423i	0.145769	+	0.252480i	0.929660	−	0.368419i	$-0.120101\pi$
$953$	4.50000	+	7.79423i	0.145769	+	0.252480i	−0.783890	+	0.620899i	$0.786768\pi$
$954$	6.00000			0.194257
$955$		0			0
$956$	−12.0000	−	20.7846i	−0.388108	−	0.672222i
$957$	9.00000			0.290929
$958$		0			0
$959$	−9.00000	+	15.5885i	−0.290625	+	0.503378i
$960$		0			0
$961$	−6.00000			−0.193548
$962$	24.5000	−	6.06218i	0.789912	−	0.195452i
$963$	6.00000			0.193347
$964$	−8.50000	+	14.7224i	−0.273767	+	0.474178i
$965$		0			0
$966$	3.00000	+	5.19615i	0.0965234	+	0.167183i
$967$	−32.0000			−1.02905			−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000			−1.02905			−0.514525	+	0.857475i	$0.672032\pi$
$968$	1.00000	+	1.73205i	0.0321412	+	0.0556702i
$969$	−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	$0.553491\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	14.0000	−	24.2487i	0.448819	−	0.777378i
$974$	−2.00000			−0.0640841
$975$		0			0
$976$	2.00000			0.0640184
$977$	−28.5000	+	49.3634i	−0.911796	+	1.57928i	−0.100270	+	0.994960i	$0.531971\pi$
$977$	−28.5000	+	49.3634i	−0.911796	+	1.57928i	−0.811526	+	0.584316i	$0.801363\pi$
$978$	6.50000	−	11.2583i	0.207847	−	0.360002i
$979$	−27.0000	−	46.7654i	−0.862924	−	1.49463i
$980$		0			0
$981$	−7.00000	−	12.1244i	−0.223493	−	0.387101i
$982$		0			0
$983$	−9.00000			−0.287055			−0.143528	−	0.989646i	$-0.545845\pi$
$983$	−9.00000			−0.287055			−0.143528	+	0.989646i	$0.545845\pi$
$984$	3.00000	+	5.19615i	0.0956365	+	0.165647i
$985$		0			0
$986$	9.00000	−	15.5885i	0.286618	−	0.496438i
$987$	6.00000			0.190982
$988$	−5.00000	−	5.19615i	−0.159071	−	0.165312i
$989$	−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	$0.0366917\pi$
$992$	−2.50000	−	4.33013i	−0.0793751	−	0.137482i
$993$	−32.0000			−1.01549
$994$	−12.0000	−	20.7846i	−0.380617	−	0.659248i
$995$		0			0
$996$	−6.00000			−0.190117
$997$	−11.0000	−	19.0526i	−0.348373	−	0.603401i	0.637587	−	0.770378i	$-0.279933\pi$
$997$	−11.0000	−	19.0526i	−0.348373	−	0.603401i	−0.985961	+	0.166978i	$0.946599\pi$
$998$	−16.0000	+	27.7128i	−0.506471	+	0.877234i
$999$	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.i.n.451.1		2
5.2	odd	4		1950.2.z.k.1699.1		4
5.3	odd	4		1950.2.z.k.1699.2		4
5.4	even	2		390.2.i.c.61.1	✓	2
13.3	even	3	inner	1950.2.i.n.601.1		2
15.14	odd	2		1170.2.i.d.451.1		2
65.3	odd	12		1950.2.z.k.1849.1		4
65.4	even	6		5070.2.a.v.1.1		1
65.9	even	6		5070.2.a.j.1.1		1
65.19	odd	12		5070.2.b.j.1351.2		2
65.29	even	6		390.2.i.c.211.1	yes	2
65.42	odd	12		1950.2.z.k.1849.2		4
65.59	odd	12		5070.2.b.j.1351.1		2
195.29	odd	6		1170.2.i.d.991.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.i.c.61.1	✓	2	5.4	even	2
390.2.i.c.211.1	yes	2	65.29	even	6
1170.2.i.d.451.1		2	15.14	odd	2
1170.2.i.d.991.1		2	195.29	odd	6
1950.2.i.n.451.1		2	1.1	even	1	trivial
1950.2.i.n.601.1		2	13.3	even	3	inner
1950.2.z.k.1699.1		4	5.2	odd	4
1950.2.z.k.1699.2		4	5.3	odd	4
1950.2.z.k.1849.1		4	65.3	odd	12
1950.2.z.k.1849.2		4	65.42	odd	12
5070.2.a.j.1.1		1	65.9	even	6
5070.2.a.v.1.1		1	65.4	even	6
5070.2.b.j.1351.1		2	65.59	odd	12
5070.2.b.j.1351.2		2	65.19	odd	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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{11} -1.00000 q^{12} +(-1.00000 + 3.46410i) q^{13} -2.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.00000 + 5.19615i) q^{17} +1.00000 q^{18} +(-1.00000 - 1.73205i) q^{19} +2.00000 q^{21} +(1.50000 + 2.59808i) q^{22} +(1.50000 - 2.59808i) q^{23} +(0.500000 - 0.866025i) q^{24} +(-2.50000 - 2.59808i) q^{26} -1.00000 q^{27} +(1.00000 - 1.73205i) q^{28} +(-1.50000 + 2.59808i) q^{29} +5.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{33} -6.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-3.50000 + 6.06218i) q^{37} +2.00000 q^{38} +(2.50000 + 2.59808i) q^{39} +(-3.00000 + 5.19615i) q^{41} +(-1.00000 + 1.73205i) q^{42} +(-0.500000 - 0.866025i) q^{43} -3.00000 q^{44} +(1.50000 + 2.59808i) q^{46} +3.00000 q^{47} +(0.500000 + 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} +6.00000 q^{51} +(3.50000 - 0.866025i) q^{52} +6.00000 q^{53} +(0.500000 - 0.866025i) q^{54} +(1.00000 + 1.73205i) q^{56} -2.00000 q^{57} +(-1.50000 - 2.59808i) q^{58} +(4.50000 + 7.79423i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(-2.50000 + 4.33013i) q^{62} +(1.00000 - 1.73205i) q^{63} +1.00000 q^{64} +3.00000 q^{66} +(4.00000 - 6.92820i) q^{67} +(3.00000 - 5.19615i) q^{68} +(-1.50000 - 2.59808i) q^{69} +(6.00000 + 10.3923i) q^{71} +(-0.500000 - 0.866025i) q^{72} -14.0000 q^{73} +(-3.50000 - 6.06218i) q^{74} +(-1.00000 + 1.73205i) q^{76} +6.00000 q^{77} +(-3.50000 + 0.866025i) q^{78} +5.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-3.00000 - 5.19615i) q^{82} +6.00000 q^{83} +(-1.00000 - 1.73205i) q^{84} +1.00000 q^{86} +(1.50000 + 2.59808i) q^{87} +(1.50000 - 2.59808i) q^{88} +(9.00000 - 15.5885i) q^{89} +(-7.00000 + 1.73205i) q^{91} -3.00000 q^{92} +(2.50000 - 4.33013i) q^{93} +(-1.50000 + 2.59808i) q^{94} -1.00000 q^{96} +(7.00000 + 12.1244i) q^{97} +(1.50000 + 2.59808i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} + q^{6} + 2 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 + q^3 - q^4 + q^6 + 2 * q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} + q^{3} - q^{4} + q^{6} + 2 q^{7} + 2 q^{8} - q^{9} + 3 q^{11} - 2 q^{12} - 2 q^{13} - 4 q^{14} - q^{16} + 6 q^{17} + 2 q^{18} - 2 q^{19} + 4 q^{21} + 3 q^{22} + 3 q^{23} + q^{24} - 5 q^{26} - 2 q^{27} + 2 q^{28} - 3 q^{29} + 10 q^{31} - q^{32} - 3 q^{33} - 12 q^{34} - q^{36} - 7 q^{37} + 4 q^{38} + 5 q^{39} - 6 q^{41} - 2 q^{42} - q^{43} - 6 q^{44} + 3 q^{46} + 6 q^{47} + q^{48} + 3 q^{49} + 12 q^{51} + 7 q^{52} + 12 q^{53} + q^{54} + 2 q^{56} - 4 q^{57} - 3 q^{58} + 9 q^{59} - 2 q^{61} - 5 q^{62} + 2 q^{63} + 2 q^{64} + 6 q^{66} + 8 q^{67} + 6 q^{68} - 3 q^{69} + 12 q^{71} - q^{72} - 28 q^{73} - 7 q^{74} - 2 q^{76} + 12 q^{77} - 7 q^{78} + 10 q^{79} - q^{81} - 6 q^{82} + 12 q^{83} - 2 q^{84} + 2 q^{86} + 3 q^{87} + 3 q^{88} + 18 q^{89} - 14 q^{91} - 6 q^{92} + 5 q^{93} - 3 q^{94} - 2 q^{96} + 14 q^{97} + 3 q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 + q^6 + 2 * q^7 + 2 * q^8 - q^9 + 3 * q^11 - 2 * q^12 - 2 * q^13 - 4 * q^14 - q^16 + 6 * q^17 + 2 * q^18 - 2 * q^19 + 4 * q^21 + 3 * q^22 + 3 * q^23 + q^24 - 5 * q^26 - 2 * q^27 + 2 * q^28 - 3 * q^29 + 10 * q^31 - q^32 - 3 * q^33 - 12 * q^34 - q^36 - 7 * q^37 + 4 * q^38 + 5 * q^39 - 6 * q^41 - 2 * q^42 - q^43 - 6 * q^44 + 3 * q^46 + 6 * q^47 + q^48 + 3 * q^49 + 12 * q^51 + 7 * q^52 + 12 * q^53 + q^54 + 2 * q^56 - 4 * q^57 - 3 * q^58 + 9 * q^59 - 2 * q^61 - 5 * q^62 + 2 * q^63 + 2 * q^64 + 6 * q^66 + 8 * q^67 + 6 * q^68 - 3 * q^69 + 12 * q^71 - q^72 - 28 * q^73 - 7 * q^74 - 2 * q^76 + 12 * q^77 - 7 * q^78 + 10 * q^79 - q^81 - 6 * q^82 + 12 * q^83 - 2 * q^84 + 2 * q^86 + 3 * q^87 + 3 * q^88 + 18 * q^89 - 14 * q^91 - 6 * q^92 + 5 * q^93 - 3 * q^94 - 2 * q^96 + 14 * q^97 + 3 * q^98 - 6 * q^99

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