LMFDB - Embedded newform 1950.2.i.i.601.1

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			601.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1950.601
Dual form			1950.2.i.i.451.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-2.50000 + 4.33013i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(-2.50000 + 4.33013i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.50000 + 2.59808i) q^{11} -1.00000 q^{12} +(2.50000 + 2.59808i) q^{13} +5.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.00000 + 6.92820i) q^{17} +1.00000 q^{18} +(2.50000 - 4.33013i) q^{19} -5.00000 q^{21} +(1.50000 - 2.59808i) q^{22} +(-2.00000 - 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.00000 - 3.46410i) q^{26} -1.00000 q^{27} +(-2.50000 - 4.33013i) q^{28} +(2.00000 + 3.46410i) q^{29} -2.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +8.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-3.50000 - 6.06218i) q^{37} -5.00000 q^{38} +(-1.00000 + 3.46410i) q^{39} +(-3.00000 - 5.19615i) q^{41} +(2.50000 + 4.33013i) q^{42} +(3.00000 - 5.19615i) q^{43} -3.00000 q^{44} +(-2.00000 + 3.46410i) q^{46} +3.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-9.00000 - 15.5885i) q^{49} -8.00000 q^{51} +(-3.50000 + 0.866025i) q^{52} -1.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(-2.50000 + 4.33013i) q^{56} +5.00000 q^{57} +(2.00000 - 3.46410i) q^{58} +(-6.00000 + 10.3923i) q^{59} +(-1.00000 + 1.73205i) q^{61} +(1.00000 + 1.73205i) q^{62} +(-2.50000 - 4.33013i) q^{63} +1.00000 q^{64} +3.00000 q^{66} +(4.00000 + 6.92820i) q^{67} +(-4.00000 - 6.92820i) q^{68} +(2.00000 - 3.46410i) q^{69} +(-1.00000 + 1.73205i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-3.50000 + 6.06218i) q^{74} +(2.50000 + 4.33013i) q^{76} -15.0000 q^{77} +(3.50000 - 0.866025i) q^{78} -2.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-3.00000 + 5.19615i) q^{82} -8.00000 q^{83} +(2.50000 - 4.33013i) q^{84} -6.00000 q^{86} +(-2.00000 + 3.46410i) q^{87} +(1.50000 + 2.59808i) q^{88} +(5.50000 + 9.52628i) q^{89} +(-17.5000 + 4.33013i) q^{91} +4.00000 q^{92} +(-1.00000 - 1.73205i) q^{93} +(-1.50000 - 2.59808i) q^{94} -1.00000 q^{96} +(-9.00000 + 15.5885i) q^{98} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{3} - q^{4} + q^{6} - 5 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 + q^3 - q^4 + q^6 - 5 * q^7 + 2 * q^8 - q^9	$ 2 q - q^{2} + q^{3} - q^{4} + q^{6} - 5 q^{7} + 2 q^{8} - q^{9} + 3 q^{11} - 2 q^{12} + 5 q^{13} + 10 q^{14} - q^{16} - 8 q^{17} + 2 q^{18} + 5 q^{19} - 10 q^{21} + 3 q^{22} - 4 q^{23} + q^{24} + 2 q^{26} - 2 q^{27} - 5 q^{28} + 4 q^{29} - 4 q^{31} - q^{32} - 3 q^{33} + 16 q^{34} - q^{36} - 7 q^{37} - 10 q^{38} - 2 q^{39} - 6 q^{41} + 5 q^{42} + 6 q^{43} - 6 q^{44} - 4 q^{46} + 6 q^{47} + q^{48} - 18 q^{49} - 16 q^{51} - 7 q^{52} - 2 q^{53} + q^{54} - 5 q^{56} + 10 q^{57} + 4 q^{58} - 12 q^{59} - 2 q^{61} + 2 q^{62} - 5 q^{63} + 2 q^{64} + 6 q^{66} + 8 q^{67} - 8 q^{68} + 4 q^{69} - 2 q^{71} - q^{72} - 7 q^{74} + 5 q^{76} - 30 q^{77} + 7 q^{78} - 4 q^{79} - q^{81} - 6 q^{82} - 16 q^{83} + 5 q^{84} - 12 q^{86} - 4 q^{87} + 3 q^{88} + 11 q^{89} - 35 q^{91} + 8 q^{92} - 2 q^{93} - 3 q^{94} - 2 q^{96} - 18 q^{98} - 6 q^{99}+O(q^{100}) $ 2 * q - q^2 + q^3 - q^4 + q^6 - 5 * q^7 + 2 * q^8 - q^9 + 3 * q^11 - 2 * q^12 + 5 * q^13 + 10 * q^14 - q^16 - 8 * q^17 + 2 * q^18 + 5 * q^19 - 10 * q^21 + 3 * q^22 - 4 * q^23 + q^24 + 2 * q^26 - 2 * q^27 - 5 * q^28 + 4 * q^29 - 4 * q^31 - q^32 - 3 * q^33 + 16 * q^34 - q^36 - 7 * q^37 - 10 * q^38 - 2 * q^39 - 6 * q^41 + 5 * q^42 + 6 * q^43 - 6 * q^44 - 4 * q^46 + 6 * q^47 + q^48 - 18 * q^49 - 16 * q^51 - 7 * q^52 - 2 * q^53 + q^54 - 5 * q^56 + 10 * q^57 + 4 * q^58 - 12 * q^59 - 2 * q^61 + 2 * q^62 - 5 * q^63 + 2 * q^64 + 6 * q^66 + 8 * q^67 - 8 * q^68 + 4 * q^69 - 2 * q^71 - q^72 - 7 * q^74 + 5 * q^76 - 30 * q^77 + 7 * q^78 - 4 * q^79 - q^81 - 6 * q^82 - 16 * q^83 + 5 * q^84 - 12 * q^86 - 4 * q^87 + 3 * q^88 + 11 * q^89 - 35 * q^91 + 8 * q^92 - 2 * q^93 - 3 * q^94 - 2 * q^96 - 18 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$7$	−2.50000	+	4.33013i	−0.944911	+	1.63663i	−0.188982	+	0.981981i	$0.560519\pi$
$7$	−2.50000	+	4.33013i	−0.944911	+	1.63663i	−0.755929	+	0.654654i	$0.772814\pi$
$8$	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	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$	−1.00000			−0.288675
$13$	2.50000	+	2.59808i	0.693375	+	0.720577i
$13$	2.50000	+	2.59808i	0.693375	+	0.720577i
$14$	5.00000			1.33631
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−4.00000	+	6.92820i	−0.970143	+	1.68034i	−0.275029	+	0.961436i	$0.588688\pi$
$17$	−4.00000	+	6.92820i	−0.970143	+	1.68034i	−0.695113	+	0.718900i	$0.744646\pi$
$18$	1.00000			0.235702
$19$	2.50000	−	4.33013i	0.573539	−	0.993399i	−0.422659	−	0.906289i	$-0.638903\pi$
$19$	2.50000	−	4.33013i	0.573539	−	0.993399i	0.996199	−	0.0871106i	$-0.0277634\pi$
$20$		0			0
$21$	−5.00000			−1.09109
$22$	1.50000	−	2.59808i	0.319801	−	0.553912i
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$	1.00000	−	3.46410i	0.196116	−	0.679366i
$27$	−1.00000			−0.192450
$28$	−2.50000	−	4.33013i	−0.472456	−	0.818317i
$29$	2.00000	+	3.46410i	0.371391	+	0.643268i	0.989780	−	0.142605i	$-0.0455477\pi$
$29$	2.00000	+	3.46410i	0.371391	+	0.643268i	−0.618389	+	0.785872i	$0.712214\pi$
$30$		0			0
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−1.50000	+	2.59808i	−0.261116	+	0.452267i
$34$	8.00000			1.37199
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	−0.995998	−	0.0893706i	$-0.971514\pi$
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	0.420602	−	0.907245i	$-0.361819\pi$
$38$	−5.00000			−0.811107
$39$	−1.00000	+	3.46410i	−0.160128	+	0.554700i
$40$		0			0
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	0.530831	−	0.847477i	$-0.321880\pi$
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	−0.999353	+	0.0359748i	$0.988546\pi$
$42$	2.50000	+	4.33013i	0.385758	+	0.668153i
$43$	3.00000	−	5.19615i	0.457496	−	0.792406i	−0.541332	−	0.840809i	$-0.682080\pi$
$43$	3.00000	−	5.19615i	0.457496	−	0.792406i	0.998828	+	0.0484030i	$0.0154132\pi$
$44$	−3.00000			−0.452267
$45$		0			0
$46$	−2.00000	+	3.46410i	−0.294884	+	0.510754i
$47$	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
$49$	−9.00000	−	15.5885i	−1.28571	−	2.22692i
$50$		0			0
$51$	−8.00000			−1.12022
$52$	−3.50000	+	0.866025i	−0.485363	+	0.120096i
$53$	−1.00000			−0.137361			−0.0686803	−	0.997639i	$-0.521879\pi$
$53$	−1.00000			−0.137361			−0.0686803	+	0.997639i	$0.521879\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$		0			0
$56$	−2.50000	+	4.33013i	−0.334077	+	0.578638i
$57$	5.00000			0.662266
$58$	2.00000	−	3.46410i	0.262613	−	0.454859i
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	0.150148	+	0.988663i	$0.452025\pi$
$59$	−6.00000	+	10.3923i	−0.781133	+	1.35296i	−0.931282	+	0.364299i	$0.881308\pi$
$60$		0			0
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	−0.922916	−	0.385002i	$-0.874201\pi$
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	0.794879	+	0.606768i	$0.207534\pi$
$62$	1.00000	+	1.73205i	0.127000	+	0.219971i
$63$	−2.50000	−	4.33013i	−0.314970	−	0.545545i
$64$	1.00000			0.125000
$65$		0			0
$66$	3.00000			0.369274
$67$	4.00000	+	6.92820i	0.488678	+	0.846415i	0.999915	−	0.0130248i	$-0.00414604\pi$
$67$	4.00000	+	6.92820i	0.488678	+	0.846415i	−0.511237	+	0.859440i	$0.670813\pi$
$68$	−4.00000	−	6.92820i	−0.485071	−	0.840168i
$69$	2.00000	−	3.46410i	0.240772	−	0.417029i
$70$		0			0
$71$	−1.00000	+	1.73205i	−0.118678	+	0.205557i	−0.919244	−	0.393688i	$-0.871199\pi$
$71$	−1.00000	+	1.73205i	−0.118678	+	0.205557i	0.800566	+	0.599245i	$0.204532\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$		0			0			−	1.00000i	$-0.5\pi$
$73$		0			0				1.00000i	$0.5\pi$
$74$	−3.50000	+	6.06218i	−0.406867	+	0.704714i
$75$		0			0
$76$	2.50000	+	4.33013i	0.286770	+	0.496700i
$77$	−15.0000			−1.70941
$78$	3.50000	−	0.866025i	0.396297	−	0.0980581i
$79$	−2.00000			−0.225018			−0.112509	−	0.993651i	$-0.535889\pi$
$79$	−2.00000			−0.225018			−0.112509	+	0.993651i	$0.535889\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.00000	+	5.19615i	−0.331295	+	0.573819i
$83$	−8.00000			−0.878114			−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000			−0.878114			−0.439057	+	0.898459i	$0.644687\pi$
$84$	2.50000	−	4.33013i	0.272772	−	0.472456i
$85$		0			0
$86$	−6.00000			−0.646997
$87$	−2.00000	+	3.46410i	−0.214423	+	0.371391i
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	5.50000	+	9.52628i	0.582999	+	1.00978i	0.995122	+	0.0986553i	$0.0314541\pi$
$89$	5.50000	+	9.52628i	0.582999	+	1.00978i	−0.412123	+	0.911128i	$0.635213\pi$
$90$		0			0
$91$	−17.5000	+	4.33013i	−1.83450	+	0.453921i
$92$	4.00000			0.417029
$93$	−1.00000	−	1.73205i	−0.103695	−	0.179605i
$94$	−1.50000	−	2.59808i	−0.154713	−	0.267971i
$95$		0			0
$96$	−1.00000			−0.102062
$97$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$97$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$98$	−9.00000	+	15.5885i	−0.909137	+	1.57467i
$99$	−3.00000			−0.301511
$100$		0			0
$101$	4.00000	+	6.92820i	0.398015	+	0.689382i	0.993481	−	0.113998i	$-0.0363659\pi$
$101$	4.00000	+	6.92820i	0.398015	+	0.689382i	−0.595466	+	0.803380i	$0.703033\pi$
$102$	4.00000	+	6.92820i	0.396059	+	0.685994i
$103$	7.00000			0.689730			0.344865	−	0.938652i	$-0.387925\pi$
$103$	7.00000			0.689730			0.344865	+	0.938652i	$0.387925\pi$
$104$	2.50000	+	2.59808i	0.245145	+	0.254762i
$105$		0			0
$106$	0.500000	+	0.866025i	0.0485643	+	0.0841158i
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	0.683793	−	0.729676i	$-0.260329\pi$
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	−0.973814	+	0.227345i	$0.926996\pi$
$108$	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
$112$	5.00000			0.472456
$113$	4.00000	−	6.92820i	0.376288	−	0.651751i	−0.614231	−	0.789127i	$-0.710534\pi$
$113$	4.00000	−	6.92820i	0.376288	−	0.651751i	0.990519	+	0.137376i	$0.0438669\pi$
$114$	−2.50000	−	4.33013i	−0.234146	−	0.405554i
$115$		0			0
$116$	−4.00000			−0.371391
$117$	−3.50000	+	0.866025i	−0.323575	+	0.0800641i
$118$	12.0000			1.10469
$119$	−20.0000	−	34.6410i	−1.83340	−	3.17554i
$120$		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
$124$	1.00000	−	1.73205i	0.0898027	−	0.155543i
$125$		0			0
$126$	−2.50000	+	4.33013i	−0.222718	+	0.385758i
$127$	−10.5000	−	18.1865i	−0.931724	−	1.61379i	−0.780373	−	0.625314i	$-0.784971\pi$
$127$	−10.5000	−	18.1865i	−0.931724	−	1.61379i	−0.151351	−	0.988480i	$-0.548362\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	6.00000			0.528271
$130$		0			0
$131$	−19.0000			−1.66004			−0.830019	−	0.557735i	$-0.811670\pi$
$131$	−19.0000			−1.66004			−0.830019	+	0.557735i	$0.811670\pi$
$132$	−1.50000	−	2.59808i	−0.130558	−	0.226134i
$133$	12.5000	+	21.6506i	1.08389	+	1.87735i
$134$	4.00000	−	6.92820i	0.345547	−	0.598506i
$135$		0			0
$136$	−4.00000	+	6.92820i	−0.342997	+	0.594089i
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	0.487278	+	0.873247i	$0.337990\pi$
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	−0.999893	+	0.0146279i	$0.995344\pi$
$138$	−4.00000			−0.340503
$139$	−3.50000	+	6.06218i	−0.296866	+	0.514187i	−0.975417	−	0.220366i	$-0.929275\pi$
$139$	−3.50000	+	6.06218i	−0.296866	+	0.514187i	0.678551	+	0.734553i	$0.262608\pi$
$140$		0			0
$141$	1.50000	+	2.59808i	0.126323	+	0.218797i
$142$	2.00000			0.167836
$143$	−3.00000	+	10.3923i	−0.250873	+	0.869048i
$144$	1.00000			0.0833333
$145$		0			0
$146$		0			0
$147$	9.00000	−	15.5885i	0.742307	−	1.28571i
$148$	7.00000			0.575396
$149$	1.00000	−	1.73205i	0.0819232	−	0.141895i	−0.822153	−	0.569267i	$-0.807227\pi$
$149$	1.00000	−	1.73205i	0.0819232	−	0.141895i	0.904076	+	0.427372i	$0.140560\pi$
$150$		0			0
$151$	22.0000			1.79033			0.895167	−	0.445730i	$-0.147056\pi$
$151$	22.0000			1.79033			0.895167	+	0.445730i	$0.147056\pi$
$152$	2.50000	−	4.33013i	0.202777	−	0.351220i
$153$	−4.00000	−	6.92820i	−0.323381	−	0.560112i
$154$	7.50000	+	12.9904i	0.604367	+	1.04679i
$155$		0			0
$156$	−2.50000	−	2.59808i	−0.200160	−	0.208013i
$157$	−15.0000			−1.19713			−0.598565	−	0.801074i	$-0.704262\pi$
$157$	−15.0000			−1.19713			−0.598565	+	0.801074i	$0.704262\pi$
$158$	1.00000	+	1.73205i	0.0795557	+	0.137795i
$159$	−0.500000	−	0.866025i	−0.0396526	−	0.0686803i
$160$		0			0
$161$	20.0000			1.57622
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	0.146772	+	0.989170i	$0.453112\pi$
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	−0.930033	+	0.367477i	$0.880222\pi$
$164$	6.00000			0.468521
$165$		0			0
$166$	4.00000	+	6.92820i	0.310460	+	0.537733i
$167$	−11.5000	−	19.9186i	−0.889897	−	1.54135i	−0.839996	−	0.542592i	$-0.817443\pi$
$167$	−11.5000	−	19.9186i	−0.889897	−	1.54135i	−0.0499004	−	0.998754i	$-0.515890\pi$
$168$	−5.00000			−0.385758
$169$	−0.500000	+	12.9904i	−0.0384615	+	0.999260i
$170$		0			0
$171$	2.50000	+	4.33013i	0.191180	+	0.331133i
$172$	3.00000	+	5.19615i	0.228748	+	0.396203i
$173$	2.50000	−	4.33013i	0.190071	−	0.329213i	−0.755202	−	0.655492i	$-0.772461\pi$
$173$	2.50000	−	4.33013i	0.190071	−	0.329213i	0.945274	+	0.326278i	$0.105795\pi$
$174$	4.00000			0.303239
$175$		0			0
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$	−12.0000			−0.901975
$178$	5.50000	−	9.52628i	0.412242	−	0.714025i
$179$	−2.00000	−	3.46410i	−0.149487	−	0.258919i	0.781551	−	0.623841i	$-0.214429\pi$
$179$	−2.00000	−	3.46410i	−0.149487	−	0.258919i	−0.931038	+	0.364922i	$0.881096\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$	12.5000	+	12.9904i	0.926562	+	0.962911i
$183$	−2.00000			−0.147844
$184$	−2.00000	−	3.46410i	−0.147442	−	0.255377i
$185$		0			0
$186$	−1.00000	+	1.73205i	−0.0733236	+	0.127000i
$187$	−24.0000			−1.75505
$188$	−1.50000	+	2.59808i	−0.109399	+	0.189484i
$189$	2.50000	−	4.33013i	0.181848	−	0.314970i
$190$		0			0
$191$	−1.00000	+	1.73205i	−0.0723575	+	0.125327i	−0.899934	−	0.436026i	$-0.856386\pi$
$191$	−1.00000	+	1.73205i	−0.0723575	+	0.125327i	0.827577	+	0.561353i	$0.189719\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	12.0000	+	20.7846i	0.863779	+	1.49611i	0.868255	+	0.496119i	$0.165242\pi$
$193$	12.0000	+	20.7846i	0.863779	+	1.49611i	−0.00447566	+	0.999990i	$0.501425\pi$
$194$		0			0
$195$		0			0
$196$	18.0000			1.28571
$197$	1.50000	+	2.59808i	0.106871	+	0.185105i	0.914501	−	0.404584i	$-0.132584\pi$
$197$	1.50000	+	2.59808i	0.106871	+	0.185105i	−0.807630	+	0.589689i	$0.799250\pi$
$198$	1.50000	+	2.59808i	0.106600	+	0.184637i
$199$	−11.0000	+	19.0526i	−0.779769	+	1.35060i	0.152305	+	0.988334i	$0.451330\pi$
$199$	−11.0000	+	19.0526i	−0.779769	+	1.35060i	−0.932075	+	0.362267i	$0.882003\pi$
$200$		0			0
$201$	−4.00000	+	6.92820i	−0.282138	+	0.488678i
$202$	4.00000	−	6.92820i	0.281439	−	0.487467i
$203$	−20.0000			−1.40372
$204$	4.00000	−	6.92820i	0.280056	−	0.485071i
$205$		0			0
$206$	−3.50000	−	6.06218i	−0.243857	−	0.422372i
$207$	4.00000			0.278019
$208$	1.00000	−	3.46410i	0.0693375	−	0.240192i
$209$	15.0000			1.03757
$210$		0			0
$211$	7.50000	+	12.9904i	0.516321	+	0.894295i	0.999820	+	0.0189499i	$0.00603229\pi$
$211$	7.50000	+	12.9904i	0.516321	+	0.894295i	−0.483499	+	0.875345i	$0.660634\pi$
$212$	0.500000	−	0.866025i	0.0343401	−	0.0594789i
$213$	−2.00000			−0.137038
$214$	−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
$219$		0			0
$220$		0			0
$221$	−28.0000	+	6.92820i	−1.88348	+	0.466041i
$222$	−7.00000			−0.469809
$223$	−1.50000	−	2.59808i	−0.100447	−	0.173980i	0.811422	−	0.584461i	$-0.198694\pi$
$223$	−1.50000	−	2.59808i	−0.100447	−	0.173980i	−0.911869	+	0.410481i	$0.865361\pi$
$224$	−2.50000	−	4.33013i	−0.167038	−	0.289319i
$225$		0			0
$226$	−8.00000			−0.532152
$227$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$227$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$228$	−2.50000	+	4.33013i	−0.165567	+	0.286770i
$229$	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
$231$	−7.50000	−	12.9904i	−0.493464	−	0.854704i
$232$	2.00000	+	3.46410i	0.131306	+	0.227429i
$233$	14.0000			0.917170			0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000			0.917170			0.458585	+	0.888650i	$0.348356\pi$
$234$	2.50000	+	2.59808i	0.163430	+	0.169842i
$235$		0			0
$236$	−6.00000	−	10.3923i	−0.390567	−	0.676481i
$237$	−1.00000	−	1.73205i	−0.0649570	−	0.112509i
$238$	−20.0000	+	34.6410i	−1.29641	+	2.24544i
$239$	−18.0000			−1.16432			−0.582162	−	0.813073i	$-0.697793\pi$
$239$	−18.0000			−1.16432			−0.582162	+	0.813073i	$0.697793\pi$
$240$		0			0
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	−0.110963	−	0.993825i	$-0.535394\pi$
$241$	12.5000	−	21.6506i	0.805196	−	1.39464i	0.916159	−	0.400815i	$-0.131273\pi$
$242$	−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
$247$	17.5000	−	4.33013i	1.11350	−	0.275519i
$248$	−2.00000			−0.127000
$249$	−4.00000	−	6.92820i	−0.253490	−	0.439057i
$250$		0			0
$251$	−7.50000	+	12.9904i	−0.473396	+	0.819946i	−0.999536	−	0.0304521i	$-0.990305\pi$
$251$	−7.50000	+	12.9904i	−0.473396	+	0.819946i	0.526140	+	0.850398i	$0.323639\pi$
$252$	5.00000			0.314970
$253$	6.00000	−	10.3923i	0.377217	−	0.653359i
$254$	−10.5000	+	18.1865i	−0.658829	+	1.14112i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	14.0000	+	24.2487i	0.873296	+	1.51259i	0.858567	+	0.512702i	$0.171355\pi$
$257$	14.0000	+	24.2487i	0.873296	+	1.51259i	0.0147291	+	0.999892i	$0.495311\pi$
$258$	−3.00000	−	5.19615i	−0.186772	−	0.323498i
$259$	35.0000			2.17479
$260$		0			0
$261$	−4.00000			−0.247594
$262$	9.50000	+	16.4545i	0.586912	+	1.01656i
$263$	−7.50000	−	12.9904i	−0.462470	−	0.801021i	0.536614	−	0.843828i	$-0.319703\pi$
$263$	−7.50000	−	12.9904i	−0.462470	−	0.801021i	−0.999083	+	0.0428069i	$0.986370\pi$
$264$	−1.50000	+	2.59808i	−0.0923186	+	0.159901i
$265$		0			0
$266$	12.5000	−	21.6506i	0.766424	−	1.32749i
$267$	−5.50000	+	9.52628i	−0.336595	+	0.582999i
$268$	−8.00000			−0.488678
$269$	−2.00000	+	3.46410i	−0.121942	+	0.211210i	−0.920534	−	0.390664i	$-0.872246\pi$
$269$	−2.00000	+	3.46410i	−0.121942	+	0.211210i	0.798591	+	0.601874i	$0.205579\pi$
$270$		0			0
$271$	−2.00000	−	3.46410i	−0.121491	−	0.210429i	0.798865	−	0.601511i	$-0.205434\pi$
$271$	−2.00000	−	3.46410i	−0.121491	−	0.210429i	−0.920356	+	0.391082i	$0.872101\pi$
$272$	8.00000			0.485071
$273$	−12.5000	−	12.9904i	−0.756534	−	0.786214i
$274$	12.0000			0.724947
$275$		0			0
$276$	2.00000	+	3.46410i	0.120386	+	0.208514i
$277$	−7.50000	+	12.9904i	−0.450631	+	0.780516i	−0.998425	−	0.0560969i	$-0.982134\pi$
$277$	−7.50000	+	12.9904i	−0.450631	+	0.780516i	0.547794	+	0.836613i	$0.315468\pi$
$278$	7.00000			0.419832
$279$	1.00000	−	1.73205i	0.0598684	−	0.103695i
$280$		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
$283$	−5.00000	−	8.66025i	−0.297219	−	0.514799i	0.678280	−	0.734804i	$-0.262726\pi$
$283$	−5.00000	−	8.66025i	−0.297219	−	0.514799i	−0.975499	+	0.220005i	$0.929393\pi$
$284$	−1.00000	−	1.73205i	−0.0593391	−	0.102778i
$285$		0			0
$286$	10.5000	−	2.59808i	0.620878	−	0.153627i
$287$	30.0000			1.77084
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	−23.5000	−	40.7032i	−1.38235	−	2.39431i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−4.50000	+	7.79423i	−0.262893	+	0.455344i	−0.967009	−	0.254741i	$-0.918010\pi$
$293$	−4.50000	+	7.79423i	−0.262893	+	0.455344i	0.704117	+	0.710084i	$0.251343\pi$
$294$	−18.0000			−1.04978
$295$		0			0
$296$	−3.50000	−	6.06218i	−0.203433	−	0.352357i
$297$	−1.50000	−	2.59808i	−0.0870388	−	0.150756i
$298$	−2.00000			−0.115857
$299$	4.00000	−	13.8564i	0.231326	−	0.801337i
$300$		0			0
$301$	15.0000	+	25.9808i	0.864586	+	1.49751i
$302$	−11.0000	−	19.0526i	−0.632979	−	1.09635i
$303$	−4.00000	+	6.92820i	−0.229794	+	0.398015i
$304$	−5.00000			−0.286770
$305$		0			0
$306$	−4.00000	+	6.92820i	−0.228665	+	0.396059i
$307$	6.00000			0.342438			0.171219	−	0.985233i	$-0.445229\pi$
$307$	6.00000			0.342438			0.171219	+	0.985233i	$0.445229\pi$
$308$	7.50000	−	12.9904i	0.427352	−	0.740196i
$309$	3.50000	+	6.06218i	0.199108	+	0.344865i
$310$		0			0
$311$	−12.0000			−0.680458			−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000			−0.680458			−0.340229	+	0.940343i	$0.610505\pi$
$312$	−1.00000	+	3.46410i	−0.0566139	+	0.196116i
$313$	6.00000			0.339140			0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000			0.339140			0.169570	+	0.985518i	$0.445762\pi$
$314$	7.50000	+	12.9904i	0.423249	+	0.733090i
$315$		0			0
$316$	1.00000	−	1.73205i	0.0562544	−	0.0974355i
$317$	23.0000			1.29181			0.645904	−	0.763418i	$-0.276480\pi$
$317$	23.0000			1.29181			0.645904	+	0.763418i	$0.276480\pi$
$318$	−0.500000	+	0.866025i	−0.0280386	+	0.0485643i
$319$	−6.00000	+	10.3923i	−0.335936	+	0.581857i
$320$		0			0
$321$	3.00000	−	5.19615i	0.167444	−	0.290021i
$322$	−10.0000	−	17.3205i	−0.557278	−	0.965234i
$323$	20.0000	+	34.6410i	1.11283	+	1.92748i
$324$	1.00000			0.0555556
$325$		0			0
$326$	20.0000			1.10770
$327$	7.00000	+	12.1244i	0.387101	+	0.670478i
$328$	−3.00000	−	5.19615i	−0.165647	−	0.286910i
$329$	−7.50000	+	12.9904i	−0.413488	+	0.716183i
$330$		0			0
$331$	−2.00000	+	3.46410i	−0.109930	+	0.190404i	−0.915742	−	0.401768i	$-0.868396\pi$
$331$	−2.00000	+	3.46410i	−0.109930	+	0.190404i	0.805812	+	0.592172i	$0.201729\pi$
$332$	4.00000	−	6.92820i	0.219529	−	0.380235i
$333$	7.00000			0.383598
$334$	−11.5000	+	19.9186i	−0.629252	+	1.08990i
$335$		0			0
$336$	2.50000	+	4.33013i	0.136386	+	0.236228i
$337$	−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
$339$	8.00000			0.434500
$340$		0			0
$341$	−3.00000	−	5.19615i	−0.162459	−	0.281387i
$342$	2.50000	−	4.33013i	0.135185	−	0.234146i
$343$	55.0000			2.96972
$344$	3.00000	−	5.19615i	0.161749	−	0.280158i
$345$		0			0
$346$	−5.00000			−0.268802
$347$	−8.00000	+	13.8564i	−0.429463	+	0.743851i	−0.996826	−	0.0796169i	$-0.974630\pi$
$347$	−8.00000	+	13.8564i	−0.429463	+	0.743851i	0.567363	+	0.823468i	$0.307964\pi$
$348$	−2.00000	−	3.46410i	−0.107211	−	0.185695i
$349$	−4.00000	−	6.92820i	−0.214115	−	0.370858i	0.738883	−	0.673833i	$-0.235353\pi$
$349$	−4.00000	−	6.92820i	−0.214115	−	0.370858i	−0.952998	+	0.302975i	$0.902020\pi$
$350$		0			0
$351$	−2.50000	−	2.59808i	−0.133440	−	0.138675i
$352$	−3.00000			−0.159901
$353$	8.00000	+	13.8564i	0.425797	+	0.737502i	0.996495	−	0.0836583i	$-0.0266604\pi$
$353$	8.00000	+	13.8564i	0.425797	+	0.737502i	−0.570697	+	0.821160i	$0.693327\pi$
$354$	6.00000	+	10.3923i	0.318896	+	0.552345i
$355$		0			0
$356$	−11.0000			−0.582999
$357$	20.0000	−	34.6410i	1.05851	−	1.83340i
$358$	−2.00000	+	3.46410i	−0.105703	+	0.183083i
$359$	−18.0000			−0.950004			−0.475002	−	0.879985i	$-0.657553\pi$
$359$	−18.0000			−0.950004			−0.475002	+	0.879985i	$0.657553\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$	1.00000	+	1.73205i	0.0525588	+	0.0910346i
$363$	2.00000			0.104973
$364$	5.00000	−	17.3205i	0.262071	−	0.907841i
$365$		0			0
$366$	1.00000	+	1.73205i	0.0522708	+	0.0905357i
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	0.742538	−	0.669804i	$-0.233622\pi$
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	−0.951336	+	0.308155i	$0.900289\pi$
$368$	−2.00000	+	3.46410i	−0.104257	+	0.180579i
$369$	6.00000			0.312348
$370$		0			0
$371$	2.50000	−	4.33013i	0.129794	−	0.224809i
$372$	2.00000			0.103695
$373$	19.0000	−	32.9090i	0.983783	−	1.70396i	0.336557	−	0.941663i	$-0.390737\pi$
$373$	19.0000	−	32.9090i	0.983783	−	1.70396i	0.647225	−	0.762299i	$-0.275929\pi$
$374$	12.0000	+	20.7846i	0.620505	+	1.07475i
$375$		0			0
$376$	3.00000			0.154713
$377$	−4.00000	+	13.8564i	−0.206010	+	0.713641i
$378$	−5.00000			−0.257172
$379$	12.5000	+	21.6506i	0.642082	+	1.11212i	0.984967	+	0.172741i	$0.0552624\pi$
$379$	12.5000	+	21.6506i	0.642082	+	1.11212i	−0.342885	+	0.939377i	$0.611404\pi$
$380$		0			0
$381$	10.5000	−	18.1865i	0.537931	−	0.931724i
$382$	2.00000			0.102329
$383$	−14.0000	+	24.2487i	−0.715367	+	1.23905i	0.247451	+	0.968900i	$0.420407\pi$
$383$	−14.0000	+	24.2487i	−0.715367	+	1.23905i	−0.962818	+	0.270151i	$0.912926\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$		0			0
$386$	12.0000	−	20.7846i	0.610784	−	1.05791i
$387$	3.00000	+	5.19615i	0.152499	+	0.264135i
$388$		0			0
$389$	−32.0000			−1.62246			−0.811232	−	0.584724i	$-0.801203\pi$
$389$	−32.0000			−1.62246			−0.811232	+	0.584724i	$0.801203\pi$
$390$		0			0
$391$	32.0000			1.61831
$392$	−9.00000	−	15.5885i	−0.454569	−	0.787336i
$393$	−9.50000	−	16.4545i	−0.479212	−	0.830019i
$394$	1.50000	−	2.59808i	0.0755689	−	0.130889i
$395$		0			0
$396$	1.50000	−	2.59808i	0.0753778	−	0.130558i
$397$	12.5000	−	21.6506i	0.627357	−	1.08661i	−0.360723	−	0.932673i	$-0.617470\pi$
$397$	12.5000	−	21.6506i	0.627357	−	1.08661i	0.988080	−	0.153941i	$-0.0491966\pi$
$398$	22.0000			1.10276
$399$	−12.5000	+	21.6506i	−0.625783	+	1.08389i
$400$		0			0
$401$	9.50000	+	16.4545i	0.474407	+	0.821698i	0.999571	−	0.0293039i	$-0.00932905\pi$
$401$	9.50000	+	16.4545i	0.474407	+	0.821698i	−0.525163	+	0.851002i	$0.675996\pi$
$402$	8.00000			0.399004
$403$	−5.00000	−	5.19615i	−0.249068	−	0.258839i
$404$	−8.00000			−0.398015
$405$		0			0
$406$	10.0000	+	17.3205i	0.496292	+	0.859602i
$407$	10.5000	−	18.1865i	0.520466	−	0.901473i
$408$	−8.00000			−0.396059
$409$	−12.5000	+	21.6506i	−0.618085	+	1.07056i	0.371750	+	0.928333i	$0.378758\pi$
$409$	−12.5000	+	21.6506i	−0.618085	+	1.07056i	−0.989835	+	0.142222i	$0.954575\pi$
$410$		0			0
$411$	−12.0000			−0.591916
$412$	−3.50000	+	6.06218i	−0.172433	+	0.298662i
$413$	−30.0000	−	51.9615i	−1.47620	−	2.55686i
$414$	−2.00000	−	3.46410i	−0.0982946	−	0.170251i
$415$		0			0
$416$	−3.50000	+	0.866025i	−0.171602	+	0.0424604i
$417$	−7.00000			−0.342791
$418$	−7.50000	−	12.9904i	−0.366837	−	0.635380i
$419$	6.00000	+	10.3923i	0.293119	+	0.507697i	0.974546	−	0.224189i	$-0.0719734\pi$
$419$	6.00000	+	10.3923i	0.293119	+	0.507697i	−0.681426	+	0.731887i	$0.738640\pi$
$420$		0			0
$421$	12.0000			0.584844			0.292422	−	0.956289i	$-0.405539\pi$
$421$	12.0000			0.584844			0.292422	+	0.956289i	$0.405539\pi$
$422$	7.50000	−	12.9904i	0.365094	−	0.632362i
$423$	−1.50000	+	2.59808i	−0.0729325	+	0.126323i
$424$	−1.00000			−0.0485643
$425$		0			0
$426$	1.00000	+	1.73205i	0.0484502	+	0.0839181i
$427$	−5.00000	−	8.66025i	−0.241967	−	0.419099i
$428$	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	0.684564	−	0.728953i	$-0.259993\pi$
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	−0.973574	+	0.228373i	$0.926659\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	8.00000	−	13.8564i	0.384455	−	0.665896i	−0.607238	−	0.794520i	$-0.707723\pi$
$433$	8.00000	−	13.8564i	0.384455	−	0.665896i	0.991693	+	0.128624i	$0.0410559\pi$
$434$	−10.0000			−0.480015
$435$		0			0
$436$	−7.00000	+	12.1244i	−0.335239	+	0.580651i
$437$	−20.0000			−0.956730
$438$		0			0
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	0.721686	−	0.692220i	$-0.243367\pi$
$439$	−5.00000	−	8.66025i	−0.238637	−	0.413331i	−0.960323	+	0.278889i	$0.910034\pi$
$440$		0			0
$441$	18.0000			0.857143
$442$	20.0000	+	20.7846i	0.951303	+	0.988623i
$443$	−6.00000			−0.285069			−0.142534	−	0.989790i	$-0.545525\pi$
$443$	−6.00000			−0.285069			−0.142534	+	0.989790i	$0.545525\pi$
$444$	3.50000	+	6.06218i	0.166103	+	0.287698i
$445$		0			0
$446$	−1.50000	+	2.59808i	−0.0710271	+	0.123022i
$447$	2.00000			0.0945968
$448$	−2.50000	+	4.33013i	−0.118114	+	0.204579i
$449$	13.5000	−	23.3827i	0.637104	−	1.10350i	−0.348961	−	0.937137i	$-0.613465\pi$
$449$	13.5000	−	23.3827i	0.637104	−	1.10350i	0.986065	−	0.166360i	$-0.0532013\pi$
$450$		0			0
$451$	9.00000	−	15.5885i	0.423793	−	0.734032i
$452$	4.00000	+	6.92820i	0.188144	+	0.325875i
$453$	11.0000	+	19.0526i	0.516825	+	0.895167i
$454$		0			0
$455$		0			0
$456$	5.00000			0.234146
$457$	15.0000	+	25.9808i	0.701670	+	1.21533i	0.967880	+	0.251414i	$0.0808954\pi$
$457$	15.0000	+	25.9808i	0.701670	+	1.21533i	−0.266209	+	0.963915i	$0.585771\pi$
$458$	−7.00000	−	12.1244i	−0.327089	−	0.566534i
$459$	4.00000	−	6.92820i	0.186704	−	0.323381i
$460$		0			0
$461$	−4.00000	+	6.92820i	−0.186299	+	0.322679i	−0.944013	−	0.329907i	$-0.892983\pi$
$461$	−4.00000	+	6.92820i	−0.186299	+	0.322679i	0.757715	+	0.652586i	$0.226316\pi$
$462$	−7.50000	+	12.9904i	−0.348932	+	0.604367i
$463$	−8.00000			−0.371792			−0.185896	−	0.982569i	$-0.559519\pi$
$463$	−8.00000			−0.371792			−0.185896	+	0.982569i	$0.559519\pi$
$464$	2.00000	−	3.46410i	0.0928477	−	0.160817i
$465$		0			0
$466$	−7.00000	−	12.1244i	−0.324269	−	0.561650i
$467$	24.0000			1.11059			0.555294	−	0.831654i	$-0.312606\pi$
$467$	24.0000			1.11059			0.555294	+	0.831654i	$0.312606\pi$
$468$	1.00000	−	3.46410i	0.0462250	−	0.160128i
$469$	−40.0000			−1.84703
$470$		0			0
$471$	−7.50000	−	12.9904i	−0.345582	−	0.598565i
$472$	−6.00000	+	10.3923i	−0.276172	+	0.478345i
$473$	18.0000			0.827641
$474$	−1.00000	+	1.73205i	−0.0459315	+	0.0795557i
$475$		0			0
$476$	40.0000			1.83340
$477$	0.500000	−	0.866025i	0.0228934	−	0.0396526i
$478$	9.00000	+	15.5885i	0.411650	+	0.712999i
$479$	14.0000	+	24.2487i	0.639676	+	1.10795i	0.985504	+	0.169654i	$0.0542649\pi$
$479$	14.0000	+	24.2487i	0.639676	+	1.10795i	−0.345827	+	0.938298i	$0.612402\pi$
$480$		0			0
$481$	7.00000	−	24.2487i	0.319173	−	1.10565i
$482$	−25.0000			−1.13872
$483$	10.0000	+	17.3205i	0.455016	+	0.788110i
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$		0			0
$486$	−1.00000			−0.0453609
$487$	18.5000	−	32.0429i	0.838315	−	1.45200i	−0.0529875	−	0.998595i	$-0.516874\pi$
$487$	18.5000	−	32.0429i	0.838315	−	1.45200i	0.891303	−	0.453409i	$-0.149792\pi$
$488$	−1.00000	+	1.73205i	−0.0452679	+	0.0784063i
$489$	−20.0000			−0.904431
$490$		0			0
$491$	−10.5000	−	18.1865i	−0.473858	−	0.820747i	0.525694	−	0.850674i	$-0.323806\pi$
$491$	−10.5000	−	18.1865i	−0.473858	−	0.820747i	−0.999552	+	0.0299272i	$0.990472\pi$
$492$	3.00000	+	5.19615i	0.135250	+	0.234261i
$493$	−32.0000			−1.44121
$494$	−12.5000	−	12.9904i	−0.562402	−	0.584465i
$495$		0			0
$496$	1.00000	+	1.73205i	0.0449013	+	0.0777714i
$497$	−5.00000	−	8.66025i	−0.224281	−	0.388465i
$498$	−4.00000	+	6.92820i	−0.179244	+	0.310460i
$499$	4.00000			0.179065			0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000			0.179065			0.0895323	+	0.995984i	$0.471463\pi$
$500$		0			0
$501$	11.5000	−	19.9186i	0.513782	−	0.889897i
$502$	15.0000			0.669483
$503$	−5.50000	+	9.52628i	−0.245233	+	0.424756i	−0.962197	−	0.272354i	$-0.912198\pi$
$503$	−5.50000	+	9.52628i	−0.245233	+	0.424756i	0.716964	+	0.697110i	$0.245531\pi$
$504$	−2.50000	−	4.33013i	−0.111359	−	0.192879i
$505$		0			0
$506$	−12.0000			−0.533465
$507$	−11.5000	+	6.06218i	−0.510733	+	0.269231i
$508$	21.0000			0.931724
$509$	−5.00000	−	8.66025i	−0.221621	−	0.383859i	0.733679	−	0.679496i	$-0.237801\pi$
$509$	−5.00000	−	8.66025i	−0.221621	−	0.383859i	−0.955300	+	0.295637i	$0.904468\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$	−2.50000	+	4.33013i	−0.110378	+	0.191180i
$514$	14.0000	−	24.2487i	0.617514	−	1.06956i
$515$		0			0
$516$	−3.00000	+	5.19615i	−0.132068	+	0.228748i
$517$	4.50000	+	7.79423i	0.197910	+	0.342790i
$518$	−17.5000	−	30.3109i	−0.768906	−	1.33178i
$519$	5.00000			0.219476
$520$		0			0
$521$	5.00000			0.219054			0.109527	−	0.993984i	$-0.465066\pi$
$521$	5.00000			0.219054			0.109527	+	0.993984i	$0.465066\pi$
$522$	2.00000	+	3.46410i	0.0875376	+	0.151620i
$523$	−5.00000	−	8.66025i	−0.218635	−	0.378686i	0.735756	−	0.677247i	$-0.236827\pi$
$523$	−5.00000	−	8.66025i	−0.218635	−	0.378686i	−0.954391	+	0.298560i	$0.903494\pi$
$524$	9.50000	−	16.4545i	0.415009	−	0.718817i
$525$		0			0
$526$	−7.50000	+	12.9904i	−0.327016	+	0.566408i
$527$	8.00000	−	13.8564i	0.348485	−	0.603595i
$528$	3.00000			0.130558
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$		0			0
$531$	−6.00000	−	10.3923i	−0.260378	−	0.450988i
$532$	−25.0000			−1.08389
$533$	6.00000	−	20.7846i	0.259889	−	0.900281i
$534$	11.0000			0.476017
$535$		0			0
$536$	4.00000	+	6.92820i	0.172774	+	0.299253i
$537$	2.00000	−	3.46410i	0.0863064	−	0.149487i
$538$	4.00000			0.172452
$539$	27.0000	−	46.7654i	1.16297	−	2.01433i
$540$		0			0
$541$	34.0000			1.46177			0.730887	−	0.682498i	$-0.239107\pi$
$541$	34.0000			1.46177			0.730887	+	0.682498i	$0.239107\pi$
$542$	−2.00000	+	3.46410i	−0.0859074	+	0.148796i
$543$	−1.00000	−	1.73205i	−0.0429141	−	0.0743294i
$544$	−4.00000	−	6.92820i	−0.171499	−	0.297044i
$545$		0			0
$546$	−5.00000	+	17.3205i	−0.213980	+	0.741249i
$547$	−6.00000			−0.256541			−0.128271	−	0.991739i	$-0.540943\pi$
$547$	−6.00000			−0.256541			−0.128271	+	0.991739i	$0.540943\pi$
$548$	−6.00000	−	10.3923i	−0.256307	−	0.443937i
$549$	−1.00000	−	1.73205i	−0.0426790	−	0.0739221i
$550$		0			0
$551$	20.0000			0.852029
$552$	2.00000	−	3.46410i	0.0851257	−	0.147442i
$553$	5.00000	−	8.66025i	0.212622	−	0.368271i
$554$	15.0000			0.637289
$555$		0			0
$556$	−3.50000	−	6.06218i	−0.148433	−	0.257094i
$557$	7.50000	+	12.9904i	0.317785	+	0.550420i	0.980026	−	0.198871i	$-0.0637276\pi$
$557$	7.50000	+	12.9904i	0.317785	+	0.550420i	−0.662240	+	0.749291i	$0.730394\pi$
$558$	−2.00000			−0.0846668
$559$	21.0000	−	5.19615i	0.888205	−	0.219774i
$560$		0			0
$561$	−12.0000	−	20.7846i	−0.506640	−	0.877527i
$562$	−9.00000	−	15.5885i	−0.379642	−	0.657559i
$563$	18.0000	−	31.1769i	0.758610	−	1.31395i	−0.184950	−	0.982748i	$-0.559212\pi$
$563$	18.0000	−	31.1769i	0.758610	−	1.31395i	0.943560	−	0.331202i	$-0.107454\pi$
$564$	−3.00000			−0.126323
$565$		0			0
$566$	−5.00000	+	8.66025i	−0.210166	+	0.364018i
$567$	5.00000			0.209980
$568$	−1.00000	+	1.73205i	−0.0419591	+	0.0726752i
$569$	7.50000	+	12.9904i	0.314416	+	0.544585i	0.979313	−	0.202350i	$-0.0648579\pi$
$569$	7.50000	+	12.9904i	0.314416	+	0.544585i	−0.664897	+	0.746935i	$0.731525\pi$
$570$		0			0
$571$	−33.0000			−1.38101			−0.690504	−	0.723329i	$-0.742611\pi$
$571$	−33.0000			−1.38101			−0.690504	+	0.723329i	$0.742611\pi$
$572$	−7.50000	−	7.79423i	−0.313591	−	0.325893i
$573$	−2.00000			−0.0835512
$574$	−15.0000	−	25.9808i	−0.626088	−	1.08442i
$575$		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	$0.513255\pi$
$578$	−23.5000	+	40.7032i	−0.977471	+	1.69303i
$579$	−12.0000	+	20.7846i	−0.498703	+	0.863779i
$580$		0			0
$581$	20.0000	−	34.6410i	0.829740	−	1.43715i
$582$		0			0
$583$	−1.50000	−	2.59808i	−0.0621237	−	0.107601i
$584$		0			0
$585$		0			0
$586$	9.00000			0.371787
$587$	9.00000	+	15.5885i	0.371470	+	0.643404i	0.989792	−	0.142520i	$-0.0455206\pi$
$587$	9.00000	+	15.5885i	0.371470	+	0.643404i	−0.618322	+	0.785925i	$0.712187\pi$
$588$	9.00000	+	15.5885i	0.371154	+	0.642857i
$589$	−5.00000	+	8.66025i	−0.206021	+	0.356840i
$590$		0			0
$591$	−1.50000	+	2.59808i	−0.0617018	+	0.106871i
$592$	−3.50000	+	6.06218i	−0.143849	+	0.249154i
$593$	−20.0000			−0.821302			−0.410651	−	0.911793i	$-0.634698\pi$
$593$	−20.0000			−0.821302			−0.410651	+	0.911793i	$0.634698\pi$
$594$	−1.50000	+	2.59808i	−0.0615457	+	0.106600i
$595$		0			0
$596$	1.00000	+	1.73205i	0.0409616	+	0.0709476i
$597$	−22.0000			−0.900400
$598$	−14.0000	+	3.46410i	−0.572503	+	0.141658i
$599$	34.0000			1.38920			0.694601	−	0.719395i	$-0.255581\pi$
$599$	34.0000			1.38920			0.694601	+	0.719395i	$0.255581\pi$
$600$		0			0
$601$	−18.5000	−	32.0429i	−0.754631	−	1.30706i	−0.945558	−	0.325455i	$-0.894483\pi$
$601$	−18.5000	−	32.0429i	−0.754631	−	1.30706i	0.190927	−	0.981604i	$-0.438851\pi$
$602$	15.0000	−	25.9808i	0.611354	−	1.05890i
$603$	−8.00000			−0.325785
$604$	−11.0000	+	19.0526i	−0.447584	+	0.775238i
$605$		0			0
$606$	8.00000			0.324978
$607$	−14.5000	+	25.1147i	−0.588537	+	1.01938i	0.405887	+	0.913923i	$0.366962\pi$
$607$	−14.5000	+	25.1147i	−0.588537	+	1.01938i	−0.994424	+	0.105453i	$0.966371\pi$
$608$	2.50000	+	4.33013i	0.101388	+	0.175610i
$609$	−10.0000	−	17.3205i	−0.405220	−	0.701862i
$610$		0			0
$611$	7.50000	+	7.79423i	0.303418	+	0.315321i
$612$	8.00000			0.323381
$613$	12.5000	+	21.6506i	0.504870	+	0.874461i	0.999984	+	0.00563283i	$0.00179300\pi$
$613$	12.5000	+	21.6506i	0.504870	+	0.874461i	−0.495114	+	0.868828i	$0.664874\pi$
$614$	−3.00000	−	5.19615i	−0.121070	−	0.209700i
$615$		0			0
$616$	−15.0000			−0.604367
$617$	−7.00000	+	12.1244i	−0.281809	+	0.488108i	−0.971830	−	0.235681i	$-0.924268\pi$
$617$	−7.00000	+	12.1244i	−0.281809	+	0.488108i	0.690021	+	0.723789i	$0.257601\pi$
$618$	3.50000	−	6.06218i	0.140791	−	0.243857i
$619$	17.0000			0.683288			0.341644	−	0.939829i	$-0.389016\pi$
$619$	17.0000			0.683288			0.341644	+	0.939829i	$0.389016\pi$
$620$		0			0
$621$	2.00000	+	3.46410i	0.0802572	+	0.139010i
$622$	6.00000	+	10.3923i	0.240578	+	0.416693i
$623$	−55.0000			−2.20353
$624$	3.50000	−	0.866025i	0.140112	−	0.0346688i
$625$		0			0
$626$	−3.00000	−	5.19615i	−0.119904	−	0.207680i
$627$	7.50000	+	12.9904i	0.299521	+	0.518786i
$628$	7.50000	−	12.9904i	0.299283	−	0.518373i
$629$	56.0000			2.23287
$630$		0			0
$631$	−6.00000	+	10.3923i	−0.238856	+	0.413711i	−0.960386	−	0.278672i	$-0.910106\pi$
$631$	−6.00000	+	10.3923i	−0.238856	+	0.413711i	0.721530	+	0.692383i	$0.243439\pi$
$632$	−2.00000			−0.0795557
$633$	−7.50000	+	12.9904i	−0.298098	+	0.516321i
$634$	−11.5000	−	19.9186i	−0.456723	−	0.791068i
$635$		0			0
$636$	1.00000			0.0396526
$637$	18.0000	−	62.3538i	0.713186	−	2.47055i
$638$	12.0000			0.475085
$639$	−1.00000	−	1.73205i	−0.0395594	−	0.0685189i
$640$		0			0
$641$	−13.5000	+	23.3827i	−0.533218	+	0.923561i	0.466029	+	0.884769i	$0.345684\pi$
$641$	−13.5000	+	23.3827i	−0.533218	+	0.923561i	−0.999247	+	0.0387913i	$0.987649\pi$
$642$	−6.00000			−0.236801
$643$	−22.0000	+	38.1051i	−0.867595	+	1.50272i	−0.00314839	+	0.999995i	$0.501002\pi$
$643$	−22.0000	+	38.1051i	−0.867595	+	1.50272i	−0.864447	+	0.502724i	$0.832331\pi$
$644$	−10.0000	+	17.3205i	−0.394055	+	0.682524i
$645$		0			0
$646$	20.0000	−	34.6410i	0.786889	−	1.36293i
$647$	1.50000	+	2.59808i	0.0589711	+	0.102141i	0.894004	−	0.448059i	$-0.147885\pi$
$647$	1.50000	+	2.59808i	0.0589711	+	0.102141i	−0.835033	+	0.550200i	$0.814551\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−36.0000			−1.41312
$650$		0			0
$651$	10.0000			0.391931
$652$	−10.0000	−	17.3205i	−0.391630	−	0.678323i
$653$	13.5000	+	23.3827i	0.528296	+	0.915035i	0.999456	+	0.0329874i	$0.0105021\pi$
$653$	13.5000	+	23.3827i	0.528296	+	0.915035i	−0.471160	+	0.882048i	$0.656165\pi$
$654$	7.00000	−	12.1244i	0.273722	−	0.474100i
$655$		0			0
$656$	−3.00000	+	5.19615i	−0.117130	+	0.202876i
$657$		0			0
$658$	15.0000			0.584761
$659$	−18.0000	+	31.1769i	−0.701180	+	1.21448i	0.266872	+	0.963732i	$0.414010\pi$
$659$	−18.0000	+	31.1769i	−0.701180	+	1.21448i	−0.968052	+	0.250748i	$0.919323\pi$
$660$		0			0
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	0.946729	−	0.322031i	$-0.104366\pi$
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	−0.752252	+	0.658876i	$0.771032\pi$
$662$	4.00000			0.155464
$663$	−20.0000	−	20.7846i	−0.776736	−	0.807207i
$664$	−8.00000			−0.310460
$665$		0			0
$666$	−3.50000	−	6.06218i	−0.135622	−	0.234905i
$667$	8.00000	−	13.8564i	0.309761	−	0.536522i
$668$	23.0000			0.889897
$669$	1.50000	−	2.59808i	0.0579934	−	0.100447i
$670$		0			0
$671$	−6.00000			−0.231627
$672$	2.50000	−	4.33013i	0.0964396	−	0.167038i
$673$	−16.0000	−	27.7128i	−0.616755	−	1.06825i	−0.990074	−	0.140548i	$-0.955114\pi$
$673$	−16.0000	−	27.7128i	−0.616755	−	1.06825i	0.373319	−	0.927703i	$-0.378220\pi$
$674$	7.00000	+	12.1244i	0.269630	+	0.467013i
$675$		0			0
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$	22.0000			0.845529			0.422764	−	0.906240i	$-0.361060\pi$
$677$	22.0000			0.845529			0.422764	+	0.906240i	$0.361060\pi$
$678$	−4.00000	−	6.92820i	−0.153619	−	0.266076i
$679$		0			0
$680$		0			0
$681$		0			0
$682$	−3.00000	+	5.19615i	−0.114876	+	0.198971i
$683$	15.0000	−	25.9808i	0.573959	−	0.994126i	−0.422195	−	0.906505i	$-0.638740\pi$
$683$	15.0000	−	25.9808i	0.573959	−	0.994126i	0.996154	−	0.0876211i	$-0.0279265\pi$
$684$	−5.00000			−0.191180
$685$		0			0
$686$	−27.5000	−	47.6314i	−1.04995	−	1.81858i
$687$	7.00000	+	12.1244i	0.267067	+	0.462573i
$688$	−6.00000			−0.228748
$689$	−2.50000	−	2.59808i	−0.0952424	−	0.0989788i
$690$		0			0
$691$	−8.50000	−	14.7224i	−0.323355	−	0.560068i	0.657823	−	0.753173i	$-0.271478\pi$
$691$	−8.50000	−	14.7224i	−0.323355	−	0.560068i	−0.981178	+	0.193105i	$0.938144\pi$
$692$	2.50000	+	4.33013i	0.0950357	+	0.164607i
$693$	7.50000	−	12.9904i	0.284901	−	0.493464i
$694$	16.0000			0.607352
$695$		0			0
$696$	−2.00000	+	3.46410i	−0.0758098	+	0.131306i
$697$	48.0000			1.81813
$698$	−4.00000	+	6.92820i	−0.151402	+	0.262236i
$699$	7.00000	+	12.1244i	0.264764	+	0.458585i
$700$		0			0
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	−1.00000	+	3.46410i	−0.0377426	+	0.130744i
$703$	−35.0000			−1.32005
$704$	1.50000	+	2.59808i	0.0565334	+	0.0979187i
$705$		0			0
$706$	8.00000	−	13.8564i	0.301084	−	0.521493i
$707$	−40.0000			−1.50435
$708$	6.00000	−	10.3923i	0.225494	−	0.390567i
$709$	−16.0000	+	27.7128i	−0.600893	+	1.04078i	0.391794	+	0.920053i	$0.371855\pi$
$709$	−16.0000	+	27.7128i	−0.600893	+	1.04078i	−0.992686	+	0.120723i	$0.961479\pi$
$710$		0			0
$711$	1.00000	−	1.73205i	0.0375029	−	0.0649570i
$712$	5.50000	+	9.52628i	0.206121	+	0.357012i
$713$	4.00000	+	6.92820i	0.149801	+	0.259463i
$714$	−40.0000			−1.49696
$715$		0			0
$716$	4.00000			0.149487
$717$	−9.00000	−	15.5885i	−0.336111	−	0.582162i
$718$	9.00000	+	15.5885i	0.335877	+	0.581756i
$719$	10.0000	−	17.3205i	0.372937	−	0.645946i	−0.617079	−	0.786901i	$-0.711684\pi$
$719$	10.0000	−	17.3205i	0.372937	−	0.645946i	0.990016	+	0.140955i	$0.0450174\pi$
$720$		0			0
$721$	−17.5000	+	30.3109i	−0.651734	+	1.12884i
$722$	−3.00000	+	5.19615i	−0.111648	+	0.193381i
$723$	25.0000			0.929760
$724$	1.00000	−	1.73205i	0.0371647	−	0.0643712i
$725$		0			0
$726$	−1.00000	−	1.73205i	−0.0371135	−	0.0642824i
$727$	11.0000			0.407967			0.203984	−	0.978974i	$-0.434611\pi$
$727$	11.0000			0.407967			0.203984	+	0.978974i	$0.434611\pi$
$728$	−17.5000	+	4.33013i	−0.648593	+	0.160485i
$729$	1.00000			0.0370370
$730$		0			0
$731$	24.0000	+	41.5692i	0.887672	+	1.53749i
$732$	1.00000	−	1.73205i	0.0369611	−	0.0640184i
$733$	43.0000			1.58824			0.794121	−	0.607760i	$-0.207932\pi$
$733$	43.0000			1.58824			0.794121	+	0.607760i	$0.207932\pi$
$734$	−4.00000	+	6.92820i	−0.147643	+	0.255725i
$735$		0			0
$736$	4.00000			0.147442
$737$	−12.0000	+	20.7846i	−0.442026	+	0.765611i
$738$	−3.00000	−	5.19615i	−0.110432	−	0.191273i
$739$	−9.50000	−	16.4545i	−0.349463	−	0.605288i	0.636691	−	0.771119i	$-0.280303\pi$
$739$	−9.50000	−	16.4545i	−0.349463	−	0.605288i	−0.986154	+	0.165831i	$0.946969\pi$
$740$		0			0
$741$	12.5000	+	12.9904i	0.459199	+	0.477214i
$742$	−5.00000			−0.183556
$743$	−8.00000	−	13.8564i	−0.293492	−	0.508342i	0.681141	−	0.732152i	$-0.261484\pi$
$743$	−8.00000	−	13.8564i	−0.293492	−	0.508342i	−0.974633	+	0.223810i	$0.928151\pi$
$744$	−1.00000	−	1.73205i	−0.0366618	−	0.0635001i
$745$		0			0
$746$	−38.0000			−1.39128
$747$	4.00000	−	6.92820i	0.146352	−	0.253490i
$748$	12.0000	−	20.7846i	0.438763	−	0.759961i
$749$	30.0000			1.09618
$750$		0			0
$751$	4.00000	+	6.92820i	0.145962	+	0.252814i	0.929731	−	0.368238i	$-0.120039\pi$
$751$	4.00000	+	6.92820i	0.145962	+	0.252814i	−0.783769	+	0.621052i	$0.786706\pi$
$752$	−1.50000	−	2.59808i	−0.0546994	−	0.0947421i
$753$	−15.0000			−0.546630
$754$	14.0000	−	3.46410i	0.509850	−	0.126155i
$755$		0			0
$756$	2.50000	+	4.33013i	0.0909241	+	0.157485i
$757$	8.50000	+	14.7224i	0.308938	+	0.535096i	0.978130	−	0.207993i	$-0.0666932\pi$
$757$	8.50000	+	14.7224i	0.308938	+	0.535096i	−0.669193	+	0.743089i	$0.733360\pi$
$758$	12.5000	−	21.6506i	0.454020	−	0.786386i
$759$	12.0000			0.435572
$760$		0			0
$761$	−4.50000	+	7.79423i	−0.163125	+	0.282541i	−0.935988	−	0.352032i	$-0.885491\pi$
$761$	−4.50000	+	7.79423i	−0.163125	+	0.282541i	0.772863	+	0.634573i	$0.218824\pi$
$762$	−21.0000			−0.760750
$763$	−35.0000	+	60.6218i	−1.26709	+	2.19466i
$764$	−1.00000	−	1.73205i	−0.0361787	−	0.0626634i
$765$		0			0
$766$	28.0000			1.01168
$767$	−42.0000	+	10.3923i	−1.51653	+	0.375244i
$768$	−1.00000			−0.0360844
$769$	17.0000	+	29.4449i	0.613036	+	1.06181i	0.990726	+	0.135877i	$0.0433852\pi$
$769$	17.0000	+	29.4449i	0.613036	+	1.06181i	−0.377690	+	0.925932i	$0.623282\pi$
$770$		0			0
$771$	−14.0000	+	24.2487i	−0.504198	+	0.873296i
$772$	−24.0000			−0.863779
$773$	0.500000	−	0.866025i	0.0179838	−	0.0311488i	−0.856893	−	0.515494i	$-0.827609\pi$
$773$	0.500000	−	0.866025i	0.0179838	−	0.0311488i	0.874877	+	0.484345i	$0.160942\pi$
$774$	3.00000	−	5.19615i	0.107833	−	0.186772i
$775$		0			0
$776$		0			0
$777$	17.5000	+	30.3109i	0.627809	+	1.08740i
$778$	16.0000	+	27.7128i	0.573628	+	0.993552i
$779$	−30.0000			−1.07486
$780$		0			0
$781$	−6.00000			−0.214697
$782$	−16.0000	−	27.7128i	−0.572159	−	0.991008i
$783$	−2.00000	−	3.46410i	−0.0714742	−	0.123797i
$784$	−9.00000	+	15.5885i	−0.321429	+	0.556731i
$785$		0			0
$786$	−9.50000	+	16.4545i	−0.338854	+	0.586912i
$787$	−14.0000	+	24.2487i	−0.499046	+	0.864373i	−0.999999	−	0.00110111i	$-0.999650\pi$
$787$	−14.0000	+	24.2487i	−0.499046	+	0.864373i	0.500953	+	0.865474i	$0.332983\pi$
$788$	−3.00000			−0.106871
$789$	7.50000	−	12.9904i	0.267007	−	0.462470i
$790$		0			0
$791$	20.0000	+	34.6410i	0.711118	+	1.23169i
$792$	−3.00000			−0.106600
$793$	−7.00000	+	1.73205i	−0.248577	+	0.0615069i
$794$	−25.0000			−0.887217
$795$		0			0
$796$	−11.0000	−	19.0526i	−0.389885	−	0.675300i
$797$	−5.00000	+	8.66025i	−0.177109	+	0.306762i	−0.940889	−	0.338715i	$-0.890008\pi$
$797$	−5.00000	+	8.66025i	−0.177109	+	0.306762i	0.763780	+	0.645477i	$0.223341\pi$
$798$	25.0000			0.884990
$799$	−12.0000	+	20.7846i	−0.424529	+	0.735307i
$800$		0			0
$801$	−11.0000			−0.388666
$802$	9.50000	−	16.4545i	0.335457	−	0.581028i
$803$		0			0
$804$	−4.00000	−	6.92820i	−0.141069	−	0.244339i
$805$		0			0
$806$	−2.00000	+	6.92820i	−0.0704470	+	0.244036i
$807$	−4.00000			−0.140807
$808$	4.00000	+	6.92820i	0.140720	+	0.243733i
$809$	13.0000	+	22.5167i	0.457056	+	0.791644i	0.998804	−	0.0488972i	$-0.0155707\pi$
$809$	13.0000	+	22.5167i	0.457056	+	0.791644i	−0.541748	+	0.840541i	$0.682237\pi$
$810$		0			0
$811$	25.0000			0.877869			0.438934	−	0.898519i	$-0.355356\pi$
$811$	25.0000			0.877869			0.438934	+	0.898519i	$0.355356\pi$
$812$	10.0000	−	17.3205i	0.350931	−	0.607831i
$813$	2.00000	−	3.46410i	0.0701431	−	0.121491i
$814$	−21.0000			−0.736050
$815$		0			0
$816$	4.00000	+	6.92820i	0.140028	+	0.242536i
$817$	−15.0000	−	25.9808i	−0.524784	−	0.908952i
$818$	25.0000			0.874105
$819$	5.00000	−	17.3205i	0.174714	−	0.605228i
$820$		0			0
$821$	11.0000	+	19.0526i	0.383903	+	0.664939i	0.991616	−	0.129217i	$-0.0412465\pi$
$821$	11.0000	+	19.0526i	0.383903	+	0.664939i	−0.607714	+	0.794156i	$0.707913\pi$
$822$	6.00000	+	10.3923i	0.209274	+	0.362473i
$823$	−17.5000	+	30.3109i	−0.610012	+	1.05657i	0.381226	+	0.924482i	$0.375502\pi$
$823$	−17.5000	+	30.3109i	−0.610012	+	1.05657i	−0.991238	+	0.132089i	$0.957831\pi$
$824$	7.00000			0.243857
$825$		0			0
$826$	−30.0000	+	51.9615i	−1.04383	+	1.80797i
$827$	−6.00000			−0.208640			−0.104320	−	0.994544i	$-0.533267\pi$
$827$	−6.00000			−0.208640			−0.104320	+	0.994544i	$0.533267\pi$
$828$	−2.00000	+	3.46410i	−0.0695048	+	0.120386i
$829$	8.00000	+	13.8564i	0.277851	+	0.481253i	0.970851	−	0.239686i	$-0.0770444\pi$
$829$	8.00000	+	13.8564i	0.277851	+	0.481253i	−0.692999	+	0.720938i	$0.743711\pi$
$830$		0			0
$831$	−15.0000			−0.520344
$832$	2.50000	+	2.59808i	0.0866719	+	0.0900721i
$833$	144.000			4.98930
$834$	3.50000	+	6.06218i	0.121195	+	0.209916i
$835$		0			0
$836$	−7.50000	+	12.9904i	−0.259393	+	0.449282i
$837$	2.00000			0.0691301
$838$	6.00000	−	10.3923i	0.207267	−	0.358996i
$839$	7.00000	−	12.1244i	0.241667	−	0.418579i	−0.719522	−	0.694469i	$-0.755639\pi$
$839$	7.00000	−	12.1244i	0.241667	−	0.418579i	0.961189	+	0.275890i	$0.0889726\pi$
$840$		0			0
$841$	6.50000	−	11.2583i	0.224138	−	0.388218i
$842$	−6.00000	−	10.3923i	−0.206774	−	0.358142i
$843$	9.00000	+	15.5885i	0.309976	+	0.536895i
$844$	−15.0000			−0.516321
$845$		0			0
$846$	3.00000			0.103142
$847$	5.00000	+	8.66025i	0.171802	+	0.297570i
$848$	0.500000	+	0.866025i	0.0171701	+	0.0297394i
$849$	5.00000	−	8.66025i	0.171600	−	0.297219i
$850$		0			0
$851$	−14.0000	+	24.2487i	−0.479914	+	0.831235i
$852$	1.00000	−	1.73205i	0.0342594	−	0.0593391i
$853$	26.0000			0.890223			0.445112	−	0.895475i	$-0.353164\pi$
$853$	26.0000			0.890223			0.445112	+	0.895475i	$0.353164\pi$
$854$	−5.00000	+	8.66025i	−0.171096	+	0.296348i
$855$		0			0
$856$	−3.00000	−	5.19615i	−0.102538	−	0.177601i
$857$	−38.0000			−1.29806			−0.649028	−	0.760765i	$-0.724824\pi$
$857$	−38.0000			−1.29806			−0.649028	+	0.760765i	$0.724824\pi$
$858$	7.50000	+	7.79423i	0.256046	+	0.266091i
$859$	3.00000			0.102359			0.0511793	−	0.998689i	$-0.483702\pi$
$859$	3.00000			0.102359			0.0511793	+	0.998689i	$0.483702\pi$
$860$		0			0
$861$	15.0000	+	25.9808i	0.511199	+	0.885422i
$862$	−6.00000	+	10.3923i	−0.204361	+	0.353963i
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$		0			0
$866$	−16.0000			−0.543702
$867$	23.5000	−	40.7032i	0.798102	−	1.38235i
$868$	5.00000	+	8.66025i	0.169711	+	0.293948i
$869$	−3.00000	−	5.19615i	−0.101768	−	0.176267i
$870$		0			0
$871$	−8.00000	+	27.7128i	−0.271070	+	0.939013i
$872$	14.0000			0.474100
$873$		0			0
$874$	10.0000	+	17.3205i	0.338255	+	0.585875i
$875$		0			0
$876$		0			0
$877$	−27.0000	+	46.7654i	−0.911725	+	1.57915i	−0.100099	+	0.994977i	$0.531916\pi$
$877$	−27.0000	+	46.7654i	−0.911725	+	1.57915i	−0.811626	+	0.584177i	$0.801417\pi$
$878$	−5.00000	+	8.66025i	−0.168742	+	0.292269i
$879$	−9.00000			−0.303562
$880$		0			0
$881$	7.50000	+	12.9904i	0.252681	+	0.437657i	0.964263	−	0.264946i	$-0.0853542\pi$
$881$	7.50000	+	12.9904i	0.252681	+	0.437657i	−0.711582	+	0.702603i	$0.752021\pi$
$882$	−9.00000	−	15.5885i	−0.303046	−	0.524891i
$883$	−30.0000			−1.00958			−0.504790	−	0.863242i	$-0.668430\pi$
$883$	−30.0000			−1.00958			−0.504790	+	0.863242i	$0.668430\pi$
$884$	8.00000	−	27.7128i	0.269069	−	0.932083i
$885$		0			0
$886$	3.00000	+	5.19615i	0.100787	+	0.174568i
$887$	20.5000	+	35.5070i	0.688323	+	1.19221i	0.972380	+	0.233403i	$0.0749860\pi$
$887$	20.5000	+	35.5070i	0.688323	+	1.19221i	−0.284058	+	0.958807i	$0.591681\pi$
$888$	3.50000	−	6.06218i	0.117452	−	0.203433i
$889$	105.000			3.52159
$890$		0			0
$891$	1.50000	−	2.59808i	0.0502519	−	0.0870388i
$892$	3.00000			0.100447
$893$	7.50000	−	12.9904i	0.250978	−	0.434707i
$894$	−1.00000	−	1.73205i	−0.0334450	−	0.0579284i
$895$		0			0
$896$	5.00000			0.167038
$897$	14.0000	−	3.46410i	0.467446	−	0.115663i
$898$	−27.0000			−0.901002
$899$	−4.00000	−	6.92820i	−0.133407	−	0.231069i
$900$		0			0
$901$	4.00000	−	6.92820i	0.133259	−	0.230812i
$902$	−18.0000			−0.599334
$903$	−15.0000	+	25.9808i	−0.499169	+	0.864586i
$904$	4.00000	−	6.92820i	0.133038	−	0.230429i
$905$		0			0
$906$	11.0000	−	19.0526i	0.365451	−	0.632979i
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	0.937018	−	0.349281i	$-0.113574\pi$
$907$	5.00000	+	8.66025i	0.166022	+	0.287559i	−0.770996	+	0.636841i	$0.780241\pi$
$908$		0			0
$909$	−8.00000			−0.265343
$910$		0			0
$911$	−20.0000			−0.662630			−0.331315	−	0.943520i	$-0.607492\pi$
$911$	−20.0000			−0.662630			−0.331315	+	0.943520i	$0.607492\pi$
$912$	−2.50000	−	4.33013i	−0.0827833	−	0.143385i
$913$	−12.0000	−	20.7846i	−0.397142	−	0.687870i
$914$	15.0000	−	25.9808i	0.496156	−	0.859367i
$915$		0			0
$916$	−7.00000	+	12.1244i	−0.231287	+	0.400600i
$917$	47.5000	−	82.2724i	1.56859	−	2.71687i
$918$	−8.00000			−0.264039
$919$	1.00000	−	1.73205i	0.0329870	−	0.0571351i	−0.849061	−	0.528295i	$-0.822831\pi$
$919$	1.00000	−	1.73205i	0.0329870	−	0.0571351i	0.882048	+	0.471160i	$0.156165\pi$
$920$		0			0
$921$	3.00000	+	5.19615i	0.0988534	+	0.171219i
$922$	8.00000			0.263466
$923$	−7.00000	+	1.73205i	−0.230408	+	0.0570111i
$924$	15.0000			0.493464
$925$		0			0
$926$	4.00000	+	6.92820i	0.131448	+	0.227675i
$927$	−3.50000	+	6.06218i	−0.114955	+	0.199108i
$928$	−4.00000			−0.131306
$929$	−1.00000	+	1.73205i	−0.0328089	+	0.0568267i	−0.881964	−	0.471317i	$-0.843779\pi$
$929$	−1.00000	+	1.73205i	−0.0328089	+	0.0568267i	0.849155	+	0.528144i	$0.177112\pi$
$930$		0			0
$931$	−90.0000			−2.94963
$932$	−7.00000	+	12.1244i	−0.229293	+	0.397146i
$933$	−6.00000	−	10.3923i	−0.196431	−	0.340229i
$934$	−12.0000	−	20.7846i	−0.392652	−	0.680093i
$935$		0			0
$936$	−3.50000	+	0.866025i	−0.114401	+	0.0283069i
$937$	−30.0000			−0.980057			−0.490029	−	0.871706i	$-0.663014\pi$
$937$	−30.0000			−0.980057			−0.490029	+	0.871706i	$0.663014\pi$
$938$	20.0000	+	34.6410i	0.653023	+	1.13107i
$939$	3.00000	+	5.19615i	0.0979013	+	0.169570i
$940$		0			0
$941$		0			0			−	1.00000i	$-0.5\pi$
$941$		0			0				1.00000i	$0.5\pi$
$942$	−7.50000	+	12.9904i	−0.244363	+	0.423249i
$943$	−12.0000	+	20.7846i	−0.390774	+	0.676840i
$944$	12.0000			0.390567
$945$		0			0
$946$	−9.00000	−	15.5885i	−0.292615	−	0.506824i
$947$	29.0000	+	50.2295i	0.942373	+	1.63224i	0.760927	+	0.648838i	$0.224745\pi$
$947$	29.0000	+	50.2295i	0.942373	+	1.63224i	0.181447	+	0.983401i	$0.441922\pi$
$948$	2.00000			0.0649570
$949$		0			0
$950$		0			0
$951$	11.5000	+	19.9186i	0.372913	+	0.645904i
$952$	−20.0000	−	34.6410i	−0.648204	−	1.12272i
$953$	−27.0000	+	46.7654i	−0.874616	+	1.51488i	−0.0174443	+	0.999848i	$0.505553\pi$
$953$	−27.0000	+	46.7654i	−0.874616	+	1.51488i	−0.857171	+	0.515031i	$0.827780\pi$
$954$	−1.00000			−0.0323762
$955$		0			0
$956$	9.00000	−	15.5885i	0.291081	−	0.504167i
$957$	−12.0000			−0.387905
$958$	14.0000	−	24.2487i	0.452319	−	0.783440i
$959$	−30.0000	−	51.9615i	−0.968751	−	1.67793i
$960$		0			0
$961$	−27.0000			−0.870968
$962$	−24.5000	+	6.06218i	−0.789912	+	0.195452i
$963$	6.00000			0.193347
$964$	12.5000	+	21.6506i	0.402598	+	0.697320i
$965$		0			0
$966$	10.0000	−	17.3205i	0.321745	−	0.557278i
$967$	31.0000			0.996893			0.498446	−	0.866921i	$-0.333904\pi$
$967$	31.0000			0.996893			0.498446	+	0.866921i	$0.333904\pi$
$968$	1.00000	−	1.73205i	0.0321412	−	0.0556702i
$969$	−20.0000	+	34.6410i	−0.642493	+	1.11283i
$970$		0			0
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	−0.960910	−	0.276861i	$-0.910706\pi$
$971$	−7.50000	+	12.9904i	−0.240686	+	0.416881i	0.720224	+	0.693742i	$0.244039\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−17.5000	−	30.3109i	−0.561024	−	0.971722i
$974$	−37.0000			−1.18556
$975$		0			0
$976$	2.00000			0.0640184
$977$	10.0000	+	17.3205i	0.319928	+	0.554132i	0.980473	−	0.196655i	$-0.0630078\pi$
$977$	10.0000	+	17.3205i	0.319928	+	0.554132i	−0.660544	+	0.750787i	$0.729674\pi$
$978$	10.0000	+	17.3205i	0.319765	+	0.553849i
$979$	−16.5000	+	28.5788i	−0.527342	+	0.913384i
$980$		0			0
$981$	−7.00000	+	12.1244i	−0.223493	+	0.387101i
$982$	−10.5000	+	18.1865i	−0.335068	+	0.580356i
$983$	−23.0000			−0.733586			−0.366793	−	0.930303i	$-0.619544\pi$
$983$	−23.0000			−0.733586			−0.366793	+	0.930303i	$0.619544\pi$
$984$	3.00000	−	5.19615i	0.0956365	−	0.165647i
$985$		0			0
$986$	16.0000	+	27.7128i	0.509544	+	0.882556i
$987$	−15.0000			−0.477455
$988$	−5.00000	+	17.3205i	−0.159071	+	0.551039i
$989$	−24.0000			−0.763156
$990$		0			0
$991$	−5.00000	−	8.66025i	−0.158830	−	0.275102i	0.775617	−	0.631204i	$-0.217439\pi$
$991$	−5.00000	−	8.66025i	−0.158830	−	0.275102i	−0.934447	+	0.356102i	$0.884106\pi$
$992$	1.00000	−	1.73205i	0.0317500	−	0.0549927i
$993$	−4.00000			−0.126936
$994$	−5.00000	+	8.66025i	−0.158590	+	0.274687i
$995$		0			0
$996$	8.00000			0.253490
$997$	−0.500000	+	0.866025i	−0.0158352	+	0.0274273i	−0.873834	−	0.486224i	$-0.838374\pi$
$997$	−0.500000	+	0.866025i	−0.0158352	+	0.0274273i	0.857999	+	0.513651i	$0.171707\pi$
$998$	−2.00000	−	3.46410i	−0.0633089	−	0.109654i
$999$	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.i.601.1		2
5.2	odd	4		1950.2.z.j.1849.2		4
5.3	odd	4		1950.2.z.j.1849.1		4
5.4	even	2		390.2.i.d.211.1	yes	2
13.9	even	3	inner	1950.2.i.i.451.1		2
15.14	odd	2		1170.2.i.g.991.1		2
65.9	even	6		390.2.i.d.61.1	✓	2
65.22	odd	12		1950.2.z.j.1699.1		4
65.24	odd	12		5070.2.b.l.1351.1		2
65.29	even	6		5070.2.a.i.1.1		1
65.48	odd	12		1950.2.z.j.1699.2		4
65.49	even	6		5070.2.a.x.1.1		1
65.54	odd	12		5070.2.b.l.1351.2		2
195.74	odd	6		1170.2.i.g.451.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.i.d.61.1	✓	2	65.9	even	6
390.2.i.d.211.1	yes	2	5.4	even	2
1170.2.i.g.451.1		2	195.74	odd	6
1170.2.i.g.991.1		2	15.14	odd	2
1950.2.i.i.451.1		2	13.9	even	3	inner
1950.2.i.i.601.1		2	1.1	even	1	trivial
1950.2.z.j.1699.1		4	65.22	odd	12
1950.2.z.j.1699.2		4	65.48	odd	12
1950.2.z.j.1849.1		4	5.3	odd	4
1950.2.z.j.1849.2		4	5.2	odd	4
5070.2.a.i.1.1		1	65.29	even	6
5070.2.a.x.1.1		1	65.49	even	6
5070.2.b.l.1351.1		2	65.24	odd	12
5070.2.b.l.1351.2		2	65.54	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(-2.50000 + 4.33013i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(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} +(-2.50000 + 4.33013i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.50000 + 2.59808i) q^{11} -1.00000 q^{12} +(2.50000 + 2.59808i) q^{13} +5.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.00000 + 6.92820i) q^{17} +1.00000 q^{18} +(2.50000 - 4.33013i) q^{19} -5.00000 q^{21} +(1.50000 - 2.59808i) q^{22} +(-2.00000 - 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{24} +(1.00000 - 3.46410i) q^{26} -1.00000 q^{27} +(-2.50000 - 4.33013i) q^{28} +(2.00000 + 3.46410i) q^{29} -2.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +8.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-3.50000 - 6.06218i) q^{37} -5.00000 q^{38} +(-1.00000 + 3.46410i) q^{39} +(-3.00000 - 5.19615i) q^{41} +(2.50000 + 4.33013i) q^{42} +(3.00000 - 5.19615i) q^{43} -3.00000 q^{44} +(-2.00000 + 3.46410i) q^{46} +3.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-9.00000 - 15.5885i) q^{49} -8.00000 q^{51} +(-3.50000 + 0.866025i) q^{52} -1.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(-2.50000 + 4.33013i) q^{56} +5.00000 q^{57} +(2.00000 - 3.46410i) q^{58} +(-6.00000 + 10.3923i) q^{59} +(-1.00000 + 1.73205i) q^{61} +(1.00000 + 1.73205i) q^{62} +(-2.50000 - 4.33013i) q^{63} +1.00000 q^{64} +3.00000 q^{66} +(4.00000 + 6.92820i) q^{67} +(-4.00000 - 6.92820i) q^{68} +(2.00000 - 3.46410i) q^{69} +(-1.00000 + 1.73205i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-3.50000 + 6.06218i) q^{74} +(2.50000 + 4.33013i) q^{76} -15.0000 q^{77} +(3.50000 - 0.866025i) q^{78} -2.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-3.00000 + 5.19615i) q^{82} -8.00000 q^{83} +(2.50000 - 4.33013i) q^{84} -6.00000 q^{86} +(-2.00000 + 3.46410i) q^{87} +(1.50000 + 2.59808i) q^{88} +(5.50000 + 9.52628i) q^{89} +(-17.5000 + 4.33013i) q^{91} +4.00000 q^{92} +(-1.00000 - 1.73205i) q^{93} +(-1.50000 - 2.59808i) q^{94} -1.00000 q^{96} +(-9.00000 + 15.5885i) q^{98} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} + q^{6} - 5 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 + q^3 - q^4 + q^6 - 5 * q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} + q^{3} - q^{4} + q^{6} - 5 q^{7} + 2 q^{8} - q^{9} + 3 q^{11} - 2 q^{12} + 5 q^{13} + 10 q^{14} - q^{16} - 8 q^{17} + 2 q^{18} + 5 q^{19} - 10 q^{21} + 3 q^{22} - 4 q^{23} + q^{24} + 2 q^{26} - 2 q^{27} - 5 q^{28} + 4 q^{29} - 4 q^{31} - q^{32} - 3 q^{33} + 16 q^{34} - q^{36} - 7 q^{37} - 10 q^{38} - 2 q^{39} - 6 q^{41} + 5 q^{42} + 6 q^{43} - 6 q^{44} - 4 q^{46} + 6 q^{47} + q^{48} - 18 q^{49} - 16 q^{51} - 7 q^{52} - 2 q^{53} + q^{54} - 5 q^{56} + 10 q^{57} + 4 q^{58} - 12 q^{59} - 2 q^{61} + 2 q^{62} - 5 q^{63} + 2 q^{64} + 6 q^{66} + 8 q^{67} - 8 q^{68} + 4 q^{69} - 2 q^{71} - q^{72} - 7 q^{74} + 5 q^{76} - 30 q^{77} + 7 q^{78} - 4 q^{79} - q^{81} - 6 q^{82} - 16 q^{83} + 5 q^{84} - 12 q^{86} - 4 q^{87} + 3 q^{88} + 11 q^{89} - 35 q^{91} + 8 q^{92} - 2 q^{93} - 3 q^{94} - 2 q^{96} - 18 q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 + q^6 - 5 * q^7 + 2 * q^8 - q^9 + 3 * q^11 - 2 * q^12 + 5 * q^13 + 10 * q^14 - q^16 - 8 * q^17 + 2 * q^18 + 5 * q^19 - 10 * q^21 + 3 * q^22 - 4 * q^23 + q^24 + 2 * q^26 - 2 * q^27 - 5 * q^28 + 4 * q^29 - 4 * q^31 - q^32 - 3 * q^33 + 16 * q^34 - q^36 - 7 * q^37 - 10 * q^38 - 2 * q^39 - 6 * q^41 + 5 * q^42 + 6 * q^43 - 6 * q^44 - 4 * q^46 + 6 * q^47 + q^48 - 18 * q^49 - 16 * q^51 - 7 * q^52 - 2 * q^53 + q^54 - 5 * q^56 + 10 * q^57 + 4 * q^58 - 12 * q^59 - 2 * q^61 + 2 * q^62 - 5 * q^63 + 2 * q^64 + 6 * q^66 + 8 * q^67 - 8 * q^68 + 4 * q^69 - 2 * q^71 - q^72 - 7 * q^74 + 5 * q^76 - 30 * q^77 + 7 * q^78 - 4 * q^79 - q^81 - 6 * q^82 - 16 * q^83 + 5 * q^84 - 12 * q^86 - 4 * q^87 + 3 * q^88 + 11 * q^89 - 35 * q^91 + 8 * q^92 - 2 * q^93 - 3 * q^94 - 2 * q^96 - 18 * q^98 - 6 * q^99

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