LMFDB - Embedded newform 1950.2.z.j.1849.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1950.1699");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1849.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1950.1849
Dual form			1950.2.z.j.1699.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(4.33013 + 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(4.33013 + 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.50000 + 2.59808i) q^{11} +1.00000i q^{12} +(-2.59808 + 2.50000i) q^{13} -5.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(6.92820 + 4.00000i) q^{17} +1.00000i q^{18} +(-2.50000 + 4.33013i) q^{19} -5.00000 q^{21} +(-2.59808 - 1.50000i) q^{22} +(3.46410 - 2.00000i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(1.00000 - 3.46410i) q^{26} +1.00000i q^{27} +(4.33013 - 2.50000i) q^{28} +(-2.00000 - 3.46410i) q^{29} -2.00000 q^{31} +(0.866025 + 0.500000i) q^{32} +(-2.59808 - 1.50000i) q^{33} -8.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-6.06218 + 3.50000i) q^{37} -5.00000i q^{38} +(1.00000 - 3.46410i) q^{39} +(-3.00000 - 5.19615i) q^{41} +(4.33013 - 2.50000i) q^{42} +(5.19615 + 3.00000i) q^{43} +3.00000 q^{44} +(-2.00000 + 3.46410i) q^{46} -3.00000i q^{47} +(0.866025 + 0.500000i) q^{48} +(9.00000 + 15.5885i) q^{49} -8.00000 q^{51} +(0.866025 + 3.50000i) q^{52} -1.00000i q^{53} +(-0.500000 - 0.866025i) q^{54} +(-2.50000 + 4.33013i) q^{56} -5.00000i q^{57} +(3.46410 + 2.00000i) q^{58} +(6.00000 - 10.3923i) q^{59} +(-1.00000 + 1.73205i) q^{61} +(1.73205 - 1.00000i) q^{62} +(4.33013 - 2.50000i) q^{63} -1.00000 q^{64} +3.00000 q^{66} +(6.92820 - 4.00000i) q^{67} +(6.92820 - 4.00000i) q^{68} +(-2.00000 + 3.46410i) q^{69} +(-1.00000 + 1.73205i) q^{71} +(0.866025 + 0.500000i) q^{72} +(3.50000 - 6.06218i) q^{74} +(2.50000 + 4.33013i) q^{76} +15.0000i q^{77} +(0.866025 + 3.50000i) q^{78} +2.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(5.19615 + 3.00000i) q^{82} -8.00000i q^{83} +(-2.50000 + 4.33013i) q^{84} -6.00000 q^{86} +(3.46410 + 2.00000i) q^{87} +(-2.59808 + 1.50000i) q^{88} +(-5.50000 - 9.52628i) q^{89} +(-17.5000 + 4.33013i) q^{91} -4.00000i q^{92} +(1.73205 - 1.00000i) q^{93} +(1.50000 + 2.59808i) q^{94} -1.00000 q^{96} +(-15.5885 - 9.00000i) q^{98} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 2 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 2 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} + 2 q^{6} + 2 q^{9} + 6 q^{11} - 20 q^{14} - 2 q^{16} - 10 q^{19} - 20 q^{21} - 2 q^{24} + 4 q^{26} - 8 q^{29} - 8 q^{31} - 32 q^{34} - 2 q^{36} + 4 q^{39} - 12 q^{41} + 12 q^{44} - 8 q^{46} + 36 q^{49} - 32 q^{51} - 2 q^{54} - 10 q^{56} + 24 q^{59} - 4 q^{61} - 4 q^{64} + 12 q^{66} - 8 q^{69} - 4 q^{71} + 14 q^{74} + 10 q^{76} + 8 q^{79} - 2 q^{81} - 10 q^{84} - 24 q^{86} - 22 q^{89} - 70 q^{91} + 6 q^{94} - 4 q^{96} + 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 + 2 * q^6 + 2 * q^9 + 6 * q^11 - 20 * q^14 - 2 * q^16 - 10 * q^19 - 20 * q^21 - 2 * q^24 + 4 * q^26 - 8 * q^29 - 8 * q^31 - 32 * q^34 - 2 * q^36 + 4 * q^39 - 12 * q^41 + 12 * q^44 - 8 * q^46 + 36 * q^49 - 32 * q^51 - 2 * q^54 - 10 * q^56 + 24 * q^59 - 4 * q^61 - 4 * q^64 + 12 * q^66 - 8 * q^69 - 4 * q^71 + 14 * q^74 + 10 * q^76 + 8 * q^79 - 2 * q^81 - 10 * q^84 - 24 * q^86 - 22 * q^89 - 70 * q^91 + 6 * q^94 - 4 * q^96 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$3$	−0.866025	+	0.500000i	−0.500000	+	0.288675i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	4.33013	+	2.50000i	1.63663	+	0.944911i	0.981981	+	0.188982i	$0.0605189\pi$
$7$	4.33013	+	2.50000i	1.63663	+	0.944911i	0.654654	+	0.755929i	$0.272814\pi$
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$			1.00000i			0.288675i
$13$	−2.59808	+	2.50000i	−0.720577	+	0.693375i
$13$	−2.59808	+	2.50000i	−0.720577	+	0.693375i
$14$	−5.00000			−1.33631
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	6.92820	+	4.00000i	1.68034	+	0.970143i	0.961436	+	0.275029i	$0.0886875\pi$
$17$	6.92820	+	4.00000i	1.68034	+	0.970143i	0.718900	+	0.695113i	$0.244646\pi$
$18$			1.00000i			0.235702i
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	0.422659	+	0.906289i	$0.361097\pi$
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	−0.996199	+	0.0871106i	$0.972237\pi$
$20$		0			0
$21$	−5.00000			−1.09109
$22$	−2.59808	−	1.50000i	−0.553912	−	0.319801i
$23$	3.46410	−	2.00000i	0.722315	−	0.417029i	−0.0932891	−	0.995639i	$-0.529738\pi$
$23$	3.46410	−	2.00000i	0.722315	−	0.417029i	0.815604	+	0.578610i	$0.196405\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$		0			0
$26$	1.00000	−	3.46410i	0.196116	−	0.679366i
$27$			1.00000i			0.192450i
$28$	4.33013	−	2.50000i	0.818317	−	0.472456i
$29$	−2.00000	−	3.46410i	−0.371391	−	0.643268i	0.618389	−	0.785872i	$-0.287786\pi$
$29$	−2.00000	−	3.46410i	−0.371391	−	0.643268i	−0.989780	+	0.142605i	$0.954452\pi$
$30$		0			0
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−2.59808	−	1.50000i	−0.452267	−	0.261116i
$34$	−8.00000			−1.37199
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−6.06218	+	3.50000i	−0.996616	+	0.575396i	−0.907245	−	0.420602i	$-0.861819\pi$
$37$	−6.06218	+	3.50000i	−0.996616	+	0.575396i	−0.0893706	+	0.995998i	$0.528486\pi$
$38$		−	5.00000i		−	0.811107i
$39$	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	$0.988546\pi$
$42$	4.33013	−	2.50000i	0.668153	−	0.385758i
$43$	5.19615	+	3.00000i	0.792406	+	0.457496i	0.840809	−	0.541332i	$-0.182080\pi$
$43$	5.19615	+	3.00000i	0.792406	+	0.457496i	−0.0484030	+	0.998828i	$0.515413\pi$
$44$	3.00000			0.452267
$45$		0			0
$46$	−2.00000	+	3.46410i	−0.294884	+	0.510754i
$47$		−	3.00000i		−	0.437595i	−0.975770	−	0.218797i	$-0.929787\pi$
$47$		−	3.00000i		−	0.437595i	0.975770	−	0.218797i	$-0.0702134\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	9.00000	+	15.5885i	1.28571	+	2.22692i
$50$		0			0
$51$	−8.00000			−1.12022
$52$	0.866025	+	3.50000i	0.120096	+	0.485363i
$53$		−	1.00000i		−	0.137361i	−0.997639	−	0.0686803i	$-0.978121\pi$
$53$		−	1.00000i		−	0.137361i	0.997639	−	0.0686803i	$-0.0218788\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$		0			0
$56$	−2.50000	+	4.33013i	−0.334077	+	0.578638i
$57$		−	5.00000i		−	0.662266i
$58$	3.46410	+	2.00000i	0.454859	+	0.262613i
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	−0.150148	−	0.988663i	$-0.547975\pi$
$59$	6.00000	−	10.3923i	0.781133	−	1.35296i	0.931282	−	0.364299i	$-0.118692\pi$
$60$		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	$0.207534\pi$
$62$	1.73205	−	1.00000i	0.219971	−	0.127000i
$63$	4.33013	−	2.50000i	0.545545	−	0.314970i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	3.00000			0.369274
$67$	6.92820	−	4.00000i	0.846415	−	0.488678i	−0.0130248	−	0.999915i	$-0.504146\pi$
$67$	6.92820	−	4.00000i	0.846415	−	0.488678i	0.859440	+	0.511237i	$0.170813\pi$
$68$	6.92820	−	4.00000i	0.840168	−	0.485071i
$69$	−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	$0.204532\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	3.50000	−	6.06218i	0.406867	−	0.704714i
$75$		0			0
$76$	2.50000	+	4.33013i	0.286770	+	0.496700i
$77$			15.0000i			1.70941i
$78$	0.866025	+	3.50000i	0.0980581	+	0.396297i
$79$	2.00000			0.225018			0.112509	−	0.993651i	$-0.464111\pi$
$79$	2.00000			0.225018			0.112509	+	0.993651i	$0.464111\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	5.19615	+	3.00000i	0.573819	+	0.331295i
$83$		−	8.00000i		−	0.878114i	−0.898459	−	0.439057i	$-0.855313\pi$
$83$		−	8.00000i		−	0.878114i	0.898459	−	0.439057i	$-0.144687\pi$
$84$	−2.50000	+	4.33013i	−0.272772	+	0.472456i
$85$		0			0
$86$	−6.00000			−0.646997
$87$	3.46410	+	2.00000i	0.371391	+	0.214423i
$88$	−2.59808	+	1.50000i	−0.276956	+	0.159901i
$89$	−5.50000	−	9.52628i	−0.582999	−	1.00978i	−0.995122	−	0.0986553i	$-0.968546\pi$
$89$	−5.50000	−	9.52628i	−0.582999	−	1.00978i	0.412123	−	0.911128i	$-0.364787\pi$
$90$		0			0
$91$	−17.5000	+	4.33013i	−1.83450	+	0.453921i
$92$		−	4.00000i		−	0.417029i
$93$	1.73205	−	1.00000i	0.179605	−	0.103695i
$94$	1.50000	+	2.59808i	0.154713	+	0.267971i
$95$		0			0
$96$	−1.00000			−0.102062
$97$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$97$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$98$	−15.5885	−	9.00000i	−1.57467	−	0.909137i
$99$	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	$0.703033\pi$
$102$	6.92820	−	4.00000i	0.685994	−	0.396059i
$103$			7.00000i			0.689730i	0.938652	+	0.344865i	$0.112075\pi$
$103$			7.00000i			0.689730i	−0.938652	+	0.344865i	$0.887925\pi$
$104$	−2.50000	−	2.59808i	−0.245145	−	0.254762i
$105$		0			0
$106$	0.500000	+	0.866025i	0.0485643	+	0.0841158i
$107$	−5.19615	+	3.00000i	−0.502331	+	0.290021i	−0.729676	−	0.683793i	$-0.760329\pi$
$107$	−5.19615	+	3.00000i	−0.502331	+	0.290021i	0.227345	+	0.973814i	$0.426996\pi$
$108$	0.866025	+	0.500000i	0.0833333	+	0.0481125i
$109$	−14.0000			−1.34096			−0.670478	−	0.741929i	$-0.733911\pi$
$109$	−14.0000			−1.34096			−0.670478	+	0.741929i	$0.733911\pi$
$110$		0			0
$111$	3.50000	−	6.06218i	0.332205	−	0.575396i
$112$		−	5.00000i		−	0.472456i
$113$	6.92820	+	4.00000i	0.651751	+	0.376288i	0.789127	−	0.614231i	$-0.210534\pi$
$113$	6.92820	+	4.00000i	0.651751	+	0.376288i	−0.137376	+	0.990519i	$0.543867\pi$
$114$	2.50000	+	4.33013i	0.234146	+	0.405554i
$115$		0			0
$116$	−4.00000			−0.371391
$117$	0.866025	+	3.50000i	0.0800641	+	0.323575i
$118$			12.0000i			1.10469i
$119$	20.0000	+	34.6410i	1.83340	+	3.17554i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$		−	2.00000i		−	0.181071i
$123$	5.19615	+	3.00000i	0.468521	+	0.270501i
$124$	−1.00000	+	1.73205i	−0.0898027	+	0.155543i
$125$		0			0
$126$	−2.50000	+	4.33013i	−0.222718	+	0.385758i
$127$	−18.1865	+	10.5000i	−1.61379	+	0.931724i	−0.625314	+	0.780373i	$0.715029\pi$
$127$	−18.1865	+	10.5000i	−1.61379	+	0.931724i	−0.988480	+	0.151351i	$0.951638\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−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	$0.811670\pi$
$132$	−2.59808	+	1.50000i	−0.226134	+	0.130558i
$133$	−21.6506	+	12.5000i	−1.87735	+	1.08389i
$134$	−4.00000	+	6.92820i	−0.345547	+	0.598506i
$135$		0			0
$136$	−4.00000	+	6.92820i	−0.342997	+	0.594089i
$137$	10.3923	+	6.00000i	0.887875	+	0.512615i	0.873247	−	0.487278i	$-0.162010\pi$
$137$	10.3923	+	6.00000i	0.887875	+	0.512615i	0.0146279	+	0.999893i	$0.495344\pi$
$138$		−	4.00000i		−	0.340503i
$139$	3.50000	−	6.06218i	0.296866	−	0.514187i	−0.678551	−	0.734553i	$-0.737392\pi$
$139$	3.50000	−	6.06218i	0.296866	−	0.514187i	0.975417	+	0.220366i	$0.0707252\pi$
$140$		0			0
$141$	1.50000	+	2.59808i	0.126323	+	0.218797i
$142$		−	2.00000i		−	0.167836i
$143$	−10.3923	−	3.00000i	−0.869048	−	0.250873i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$		0			0
$147$	−15.5885	−	9.00000i	−1.28571	−	0.742307i
$148$			7.00000i			0.575396i
$149$	−1.00000	+	1.73205i	−0.0819232	+	0.141895i	−0.904076	−	0.427372i	$-0.859440\pi$
$149$	−1.00000	+	1.73205i	−0.0819232	+	0.141895i	0.822153	+	0.569267i	$0.192773\pi$
$150$		0			0
$151$	22.0000			1.79033			0.895167	−	0.445730i	$-0.147056\pi$
$151$	22.0000			1.79033			0.895167	+	0.445730i	$0.147056\pi$
$152$	−4.33013	−	2.50000i	−0.351220	−	0.202777i
$153$	6.92820	−	4.00000i	0.560112	−	0.323381i
$154$	−7.50000	−	12.9904i	−0.604367	−	1.04679i
$155$		0			0
$156$	−2.50000	−	2.59808i	−0.200160	−	0.208013i
$157$			15.0000i			1.19713i	0.801074	+	0.598565i	$0.204262\pi$
$157$			15.0000i			1.19713i	−0.801074	+	0.598565i	$0.795738\pi$
$158$	−1.73205	+	1.00000i	−0.137795	+	0.0795557i
$159$	0.500000	+	0.866025i	0.0396526	+	0.0686803i
$160$		0			0
$161$	20.0000			1.57622
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	−17.3205	−	10.0000i	−1.35665	−	0.783260i	−0.367477	−	0.930033i	$-0.619778\pi$
$163$	−17.3205	−	10.0000i	−1.35665	−	0.783260i	−0.989170	+	0.146772i	$0.953112\pi$
$164$	−6.00000			−0.468521
$165$		0			0
$166$	4.00000	+	6.92820i	0.310460	+	0.537733i
$167$	−19.9186	+	11.5000i	−1.54135	+	0.889897i	−0.542592	+	0.839996i	$0.682557\pi$
$167$	−19.9186	+	11.5000i	−1.54135	+	0.889897i	−0.998754	+	0.0499004i	$0.984110\pi$
$168$		−	5.00000i		−	0.385758i
$169$	0.500000	−	12.9904i	0.0384615	−	0.999260i
$170$		0			0
$171$	2.50000	+	4.33013i	0.191180	+	0.331133i
$172$	5.19615	−	3.00000i	0.396203	−	0.228748i
$173$	4.33013	+	2.50000i	0.329213	+	0.190071i	0.655492	−	0.755202i	$-0.272461\pi$
$173$	4.33013	+	2.50000i	0.329213	+	0.190071i	−0.326278	+	0.945274i	$0.605795\pi$
$174$	−4.00000			−0.303239
$175$		0			0
$176$	1.50000	−	2.59808i	0.113067	−	0.195837i
$177$			12.0000i			0.901975i
$178$	9.52628	+	5.50000i	0.714025	+	0.412242i
$179$	2.00000	+	3.46410i	0.149487	+	0.258919i	0.931038	−	0.364922i	$-0.118904\pi$
$179$	2.00000	+	3.46410i	0.149487	+	0.258919i	−0.781551	+	0.623841i	$0.785571\pi$
$180$		0			0
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$	12.9904	−	12.5000i	0.962911	−	0.926562i
$183$		−	2.00000i		−	0.147844i
$184$	2.00000	+	3.46410i	0.147442	+	0.255377i
$185$		0			0
$186$	−1.00000	+	1.73205i	−0.0733236	+	0.127000i
$187$			24.0000i			1.75505i
$188$	−2.59808	−	1.50000i	−0.189484	−	0.109399i
$189$	−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	$0.189719\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	−20.7846	+	12.0000i	−1.49611	+	0.863779i	−0.999990	−	0.00447566i	$-0.998575\pi$
$193$	−20.7846	+	12.0000i	−1.49611	+	0.863779i	−0.496119	+	0.868255i	$0.665242\pi$
$194$		0			0
$195$		0			0
$196$	18.0000			1.28571
$197$	2.59808	−	1.50000i	0.185105	−	0.106871i	−0.404584	−	0.914501i	$-0.632584\pi$
$197$	2.59808	−	1.50000i	0.185105	−	0.106871i	0.589689	+	0.807630i	$0.299250\pi$
$198$	−2.59808	+	1.50000i	−0.184637	+	0.106600i
$199$	11.0000	−	19.0526i	0.779769	−	1.35060i	−0.152305	−	0.988334i	$-0.548670\pi$
$199$	11.0000	−	19.0526i	0.779769	−	1.35060i	0.932075	−	0.362267i	$-0.117997\pi$
$200$		0			0
$201$	−4.00000	+	6.92820i	−0.282138	+	0.488678i
$202$	−6.92820	−	4.00000i	−0.487467	−	0.281439i
$203$		−	20.0000i		−	1.40372i
$204$	−4.00000	+	6.92820i	−0.280056	+	0.485071i
$205$		0			0
$206$	−3.50000	−	6.06218i	−0.243857	−	0.422372i
$207$		−	4.00000i		−	0.278019i
$208$	3.46410	+	1.00000i	0.240192	+	0.0693375i
$209$	−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	$0.660634\pi$
$212$	−0.866025	−	0.500000i	−0.0594789	−	0.0343401i
$213$		−	2.00000i		−	0.137038i
$214$	3.00000	−	5.19615i	0.205076	−	0.355202i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	−8.66025	−	5.00000i	−0.587896	−	0.339422i
$218$	12.1244	−	7.00000i	0.821165	−	0.474100i
$219$		0			0
$220$		0			0
$221$	−28.0000	+	6.92820i	−1.88348	+	0.466041i
$222$			7.00000i			0.469809i
$223$	2.59808	−	1.50000i	0.173980	−	0.100447i	−0.410481	−	0.911869i	$-0.634639\pi$
$223$	2.59808	−	1.50000i	0.173980	−	0.100447i	0.584461	+	0.811422i	$0.301306\pi$
$224$	2.50000	+	4.33013i	0.167038	+	0.289319i
$225$		0			0
$226$	−8.00000			−0.532152
$227$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$227$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$228$	−4.33013	−	2.50000i	−0.286770	−	0.165567i
$229$	−14.0000			−0.925146			−0.462573	−	0.886581i	$-0.653074\pi$
$229$	−14.0000			−0.925146			−0.462573	+	0.886581i	$0.653074\pi$
$230$		0			0
$231$	−7.50000	−	12.9904i	−0.493464	−	0.854704i
$232$	3.46410	−	2.00000i	0.227429	−	0.131306i
$233$			14.0000i			0.917170i	0.888650	+	0.458585i	$0.151644\pi$
$233$			14.0000i			0.917170i	−0.888650	+	0.458585i	$0.848356\pi$
$234$	−2.50000	−	2.59808i	−0.163430	−	0.169842i
$235$		0			0
$236$	−6.00000	−	10.3923i	−0.390567	−	0.676481i
$237$	−1.73205	+	1.00000i	−0.112509	+	0.0649570i
$238$	−34.6410	−	20.0000i	−2.24544	−	1.29641i
$239$	18.0000			1.16432			0.582162	−	0.813073i	$-0.302207\pi$
$239$	18.0000			1.16432			0.582162	+	0.813073i	$0.302207\pi$
$240$		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	$-0.131273\pi$
$242$			2.00000i			0.128565i
$243$	0.866025	+	0.500000i	0.0555556	+	0.0320750i
$244$	1.00000	+	1.73205i	0.0640184	+	0.110883i
$245$		0			0
$246$	−6.00000			−0.382546
$247$	−4.33013	−	17.5000i	−0.275519	−	1.11350i
$248$		−	2.00000i		−	0.127000i
$249$	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	$0.323639\pi$
$252$		−	5.00000i		−	0.314970i
$253$	10.3923	+	6.00000i	0.653359	+	0.377217i
$254$	10.5000	−	18.1865i	0.658829	−	1.14112i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	24.2487	−	14.0000i	1.51259	−	0.873296i	0.512702	−	0.858567i	$-0.328645\pi$
$257$	24.2487	−	14.0000i	1.51259	−	0.873296i	0.999892	−	0.0147291i	$-0.00468859\pi$
$258$	5.19615	−	3.00000i	0.323498	−	0.186772i
$259$	−35.0000			−2.17479
$260$		0			0
$261$	−4.00000			−0.247594
$262$	16.4545	−	9.50000i	1.01656	−	0.586912i
$263$	12.9904	−	7.50000i	0.801021	−	0.462470i	−0.0428069	−	0.999083i	$-0.513630\pi$
$263$	12.9904	−	7.50000i	0.801021	−	0.462470i	0.843828	+	0.536614i	$0.180297\pi$
$264$	1.50000	−	2.59808i	0.0923186	−	0.159901i
$265$		0			0
$266$	12.5000	−	21.6506i	0.766424	−	1.32749i
$267$	9.52628	+	5.50000i	0.582999	+	0.336595i
$268$		−	8.00000i		−	0.488678i
$269$	2.00000	−	3.46410i	0.121942	−	0.211210i	−0.798591	−	0.601874i	$-0.794421\pi$
$269$	2.00000	−	3.46410i	0.121942	−	0.211210i	0.920534	+	0.390664i	$0.127754\pi$
$270$		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	$0.872101\pi$
$272$		−	8.00000i		−	0.485071i
$273$	12.9904	−	12.5000i	0.786214	−	0.756534i
$274$	−12.0000			−0.724947
$275$		0			0
$276$	2.00000	+	3.46410i	0.120386	+	0.208514i
$277$	12.9904	+	7.50000i	0.780516	+	0.450631i	0.836613	−	0.547794i	$-0.184532\pi$
$277$	12.9904	+	7.50000i	0.780516	+	0.450631i	−0.0560969	+	0.998425i	$0.517866\pi$
$278$			7.00000i			0.419832i
$279$	−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	$0.319597\pi$
$282$	−2.59808	−	1.50000i	−0.154713	−	0.0893237i
$283$	8.66025	−	5.00000i	0.514799	−	0.297219i	−0.220005	−	0.975499i	$-0.570607\pi$
$283$	8.66025	−	5.00000i	0.514799	−	0.297219i	0.734804	+	0.678280i	$0.237274\pi$
$284$	1.00000	+	1.73205i	0.0593391	+	0.102778i
$285$		0			0
$286$	10.5000	−	2.59808i	0.620878	−	0.153627i
$287$		−	30.0000i		−	1.77084i
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	23.5000	+	40.7032i	1.38235	+	2.39431i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−7.79423	−	4.50000i	−0.455344	−	0.262893i	0.254741	−	0.967009i	$-0.418010\pi$
$293$	−7.79423	−	4.50000i	−0.455344	−	0.262893i	−0.710084	+	0.704117i	$0.751343\pi$
$294$	18.0000			1.04978
$295$		0			0
$296$	−3.50000	−	6.06218i	−0.203433	−	0.352357i
$297$	−2.59808	+	1.50000i	−0.150756	+	0.0870388i
$298$		−	2.00000i		−	0.115857i
$299$	−4.00000	+	13.8564i	−0.231326	+	0.801337i
$300$		0			0
$301$	15.0000	+	25.9808i	0.864586	+	1.49751i
$302$	−19.0526	+	11.0000i	−1.09635	+	0.632979i
$303$	−6.92820	−	4.00000i	−0.398015	−	0.229794i
$304$	5.00000			0.286770
$305$		0			0
$306$	−4.00000	+	6.92820i	−0.228665	+	0.396059i
$307$		−	6.00000i		−	0.342438i	−0.985233	−	0.171219i	$-0.945229\pi$
$307$		−	6.00000i		−	0.342438i	0.985233	−	0.171219i	$-0.0547706\pi$
$308$	12.9904	+	7.50000i	0.740196	+	0.427352i
$309$	−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	$0.610505\pi$
$312$	3.46410	+	1.00000i	0.196116	+	0.0566139i
$313$			6.00000i			0.339140i	0.985518	+	0.169570i	$0.0542379\pi$
$313$			6.00000i			0.339140i	−0.985518	+	0.169570i	$0.945762\pi$
$314$	−7.50000	−	12.9904i	−0.423249	−	0.733090i
$315$		0			0
$316$	1.00000	−	1.73205i	0.0562544	−	0.0974355i
$317$		−	23.0000i		−	1.29181i	−0.763418	−	0.645904i	$-0.776480\pi$
$317$		−	23.0000i		−	1.29181i	0.763418	−	0.645904i	$-0.223520\pi$
$318$	−0.866025	−	0.500000i	−0.0485643	−	0.0280386i
$319$	6.00000	−	10.3923i	0.335936	−	0.581857i
$320$		0			0
$321$	3.00000	−	5.19615i	0.167444	−	0.290021i
$322$	−17.3205	+	10.0000i	−0.965234	+	0.557278i
$323$	−34.6410	+	20.0000i	−1.92748	+	1.11283i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	20.0000			1.10770
$327$	12.1244	−	7.00000i	0.670478	−	0.387101i
$328$	5.19615	−	3.00000i	0.286910	−	0.165647i
$329$	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	$0.201729\pi$
$332$	−6.92820	−	4.00000i	−0.380235	−	0.219529i
$333$			7.00000i			0.383598i
$334$	11.5000	−	19.9186i	0.629252	−	1.08990i
$335$		0			0
$336$	2.50000	+	4.33013i	0.136386	+	0.236228i
$337$			14.0000i			0.762629i	0.924445	+	0.381314i	$0.124528\pi$
$337$			14.0000i			0.762629i	−0.924445	+	0.381314i	$0.875472\pi$
$338$	6.06218	+	11.5000i	0.329739	+	0.625518i
$339$	−8.00000			−0.434500
$340$		0			0
$341$	−3.00000	−	5.19615i	−0.162459	−	0.281387i
$342$	−4.33013	−	2.50000i	−0.234146	−	0.135185i
$343$			55.0000i			2.96972i
$344$	−3.00000	+	5.19615i	−0.161749	+	0.280158i
$345$		0			0
$346$	−5.00000			−0.268802
$347$	13.8564	+	8.00000i	0.743851	+	0.429463i	0.823468	−	0.567363i	$-0.192036\pi$
$347$	13.8564	+	8.00000i	0.743851	+	0.429463i	−0.0796169	+	0.996826i	$0.525370\pi$
$348$	3.46410	−	2.00000i	0.185695	−	0.107211i
$349$	4.00000	+	6.92820i	0.214115	+	0.370858i	0.952998	−	0.302975i	$-0.0979799\pi$
$349$	4.00000	+	6.92820i	0.214115	+	0.370858i	−0.738883	+	0.673833i	$0.764647\pi$
$350$		0			0
$351$	−2.50000	−	2.59808i	−0.133440	−	0.138675i
$352$			3.00000i			0.159901i
$353$	−13.8564	+	8.00000i	−0.737502	+	0.425797i	−0.821160	−	0.570697i	$-0.806673\pi$
$353$	−13.8564	+	8.00000i	−0.737502	+	0.425797i	0.0836583	+	0.996495i	$0.473340\pi$
$354$	−6.00000	−	10.3923i	−0.318896	−	0.552345i
$355$		0			0
$356$	−11.0000			−0.582999
$357$	−34.6410	−	20.0000i	−1.83340	−	1.05851i
$358$	−3.46410	−	2.00000i	−0.183083	−	0.105703i
$359$	18.0000			0.950004			0.475002	−	0.879985i	$-0.342447\pi$
$359$	18.0000			0.950004			0.475002	+	0.879985i	$0.342447\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$	1.73205	−	1.00000i	0.0910346	−	0.0525588i
$363$			2.00000i			0.104973i
$364$	−5.00000	+	17.3205i	−0.262071	+	0.907841i
$365$		0			0
$366$	1.00000	+	1.73205i	0.0522708	+	0.0905357i
$367$	−6.92820	+	4.00000i	−0.361649	+	0.208798i	−0.669804	−	0.742538i	$-0.733622\pi$
$367$	−6.92820	+	4.00000i	−0.361649	+	0.208798i	0.308155	+	0.951336i	$0.400289\pi$
$368$	−3.46410	−	2.00000i	−0.180579	−	0.104257i
$369$	−6.00000			−0.312348
$370$		0			0
$371$	2.50000	−	4.33013i	0.129794	−	0.224809i
$372$		−	2.00000i		−	0.103695i
$373$	32.9090	+	19.0000i	1.70396	+	0.983783i	0.941663	+	0.336557i	$0.109263\pi$
$373$	32.9090	+	19.0000i	1.70396	+	0.983783i	0.762299	+	0.647225i	$0.224071\pi$
$374$	−12.0000	−	20.7846i	−0.620505	−	1.07475i
$375$		0			0
$376$	3.00000			0.154713
$377$	13.8564	+	4.00000i	0.713641	+	0.206010i
$378$		−	5.00000i		−	0.257172i
$379$	−12.5000	−	21.6506i	−0.642082	−	1.11212i	−0.984967	−	0.172741i	$-0.944738\pi$
$379$	−12.5000	−	21.6506i	−0.642082	−	1.11212i	0.342885	−	0.939377i	$-0.388596\pi$
$380$		0			0
$381$	10.5000	−	18.1865i	0.537931	−	0.931724i
$382$		−	2.00000i		−	0.102329i
$383$	−24.2487	−	14.0000i	−1.23905	−	0.715367i	−0.270151	−	0.962818i	$-0.587074\pi$
$383$	−24.2487	−	14.0000i	−1.23905	−	0.715367i	−0.968900	+	0.247451i	$0.920407\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$		0			0
$386$	12.0000	−	20.7846i	0.610784	−	1.05791i
$387$	5.19615	−	3.00000i	0.264135	−	0.152499i
$388$		0			0
$389$	32.0000			1.62246			0.811232	−	0.584724i	$-0.198797\pi$
$389$	32.0000			1.62246			0.811232	+	0.584724i	$0.198797\pi$
$390$		0			0
$391$	32.0000			1.61831
$392$	−15.5885	+	9.00000i	−0.787336	+	0.454569i
$393$	16.4545	−	9.50000i	0.830019	−	0.479212i
$394$	−1.50000	+	2.59808i	−0.0755689	+	0.130889i
$395$		0			0
$396$	1.50000	−	2.59808i	0.0753778	−	0.130558i
$397$	−21.6506	−	12.5000i	−1.08661	−	0.627357i	−0.153941	−	0.988080i	$-0.549197\pi$
$397$	−21.6506	−	12.5000i	−1.08661	−	0.627357i	−0.932673	+	0.360723i	$0.882530\pi$
$398$			22.0000i			1.10276i
$399$	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	$0.675996\pi$
$402$		−	8.00000i		−	0.399004i
$403$	5.19615	−	5.00000i	0.258839	−	0.249068i
$404$	8.00000			0.398015
$405$		0			0
$406$	10.0000	+	17.3205i	0.496292	+	0.859602i
$407$	−18.1865	−	10.5000i	−0.901473	−	0.520466i
$408$		−	8.00000i		−	0.396059i
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	−0.371750	−	0.928333i	$-0.621242\pi$
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	0.989835	−	0.142222i	$-0.0454247\pi$
$410$		0			0
$411$	−12.0000			−0.591916
$412$	6.06218	+	3.50000i	0.298662	+	0.172433i
$413$	51.9615	−	30.0000i	2.55686	−	1.47620i
$414$	2.00000	+	3.46410i	0.0982946	+	0.170251i
$415$		0			0
$416$	−3.50000	+	0.866025i	−0.171602	+	0.0424604i
$417$			7.00000i			0.342791i
$418$	12.9904	−	7.50000i	0.635380	−	0.366837i
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	0.681426	−	0.731887i	$-0.261360\pi$
$419$	−6.00000	−	10.3923i	−0.293119	−	0.507697i	−0.974546	+	0.224189i	$0.928027\pi$
$420$		0			0
$421$	12.0000			0.584844			0.292422	−	0.956289i	$-0.405539\pi$
$421$	12.0000			0.584844			0.292422	+	0.956289i	$0.405539\pi$
$422$	−12.9904	−	7.50000i	−0.632362	−	0.365094i
$423$	−2.59808	−	1.50000i	−0.126323	−	0.0729325i
$424$	1.00000			0.0485643
$425$		0			0
$426$	1.00000	+	1.73205i	0.0484502	+	0.0839181i
$427$	−8.66025	+	5.00000i	−0.419099	+	0.241967i
$428$			6.00000i			0.290021i
$429$	10.5000	−	2.59808i	0.506945	−	0.125436i
$430$		0			0
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	0.684564	−	0.728953i	$-0.259993\pi$
$431$	−6.00000	−	10.3923i	−0.289010	−	0.500580i	−0.973574	+	0.228373i	$0.926659\pi$
$432$	0.866025	−	0.500000i	0.0416667	−	0.0240563i
$433$	13.8564	+	8.00000i	0.665896	+	0.384455i	0.794520	−	0.607238i	$-0.207723\pi$
$433$	13.8564	+	8.00000i	0.665896	+	0.384455i	−0.128624	+	0.991693i	$0.541056\pi$
$434$	10.0000			0.480015
$435$		0			0
$436$	−7.00000	+	12.1244i	−0.335239	+	0.580651i
$437$			20.0000i			0.956730i
$438$		0			0
$439$	5.00000	+	8.66025i	0.238637	+	0.413331i	0.960323	−	0.278889i	$-0.0899661\pi$
$439$	5.00000	+	8.66025i	0.238637	+	0.413331i	−0.721686	+	0.692220i	$0.756633\pi$
$440$		0			0
$441$	18.0000			0.857143
$442$	20.7846	−	20.0000i	0.988623	−	0.951303i
$443$		−	6.00000i		−	0.285069i	−0.989790	−	0.142534i	$-0.954475\pi$
$443$		−	6.00000i		−	0.285069i	0.989790	−	0.142534i	$-0.0455251\pi$
$444$	−3.50000	−	6.06218i	−0.166103	−	0.287698i
$445$		0			0
$446$	−1.50000	+	2.59808i	−0.0710271	+	0.123022i
$447$		−	2.00000i		−	0.0945968i
$448$	−4.33013	−	2.50000i	−0.204579	−	0.118114i
$449$	−13.5000	+	23.3827i	−0.637104	+	1.10350i	0.348961	+	0.937137i	$0.386535\pi$
$449$	−13.5000	+	23.3827i	−0.637104	+	1.10350i	−0.986065	+	0.166360i	$0.946799\pi$
$450$		0			0
$451$	9.00000	−	15.5885i	0.423793	−	0.734032i
$452$	6.92820	−	4.00000i	0.325875	−	0.188144i
$453$	−19.0526	+	11.0000i	−0.895167	+	0.516825i
$454$		0			0
$455$		0			0
$456$	5.00000			0.234146
$457$	25.9808	−	15.0000i	1.21533	−	0.701670i	0.251414	−	0.967880i	$-0.419105\pi$
$457$	25.9808	−	15.0000i	1.21533	−	0.701670i	0.963915	+	0.266209i	$0.0857713\pi$
$458$	12.1244	−	7.00000i	0.566534	−	0.327089i
$459$	−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	$0.226316\pi$
$462$	12.9904	+	7.50000i	0.604367	+	0.348932i
$463$		−	8.00000i		−	0.371792i	−0.982569	−	0.185896i	$-0.940481\pi$
$463$		−	8.00000i		−	0.371792i	0.982569	−	0.185896i	$-0.0595187\pi$
$464$	−2.00000	+	3.46410i	−0.0928477	+	0.160817i
$465$		0			0
$466$	−7.00000	−	12.1244i	−0.324269	−	0.561650i
$467$		−	24.0000i		−	1.11059i	−0.831654	−	0.555294i	$-0.812606\pi$
$467$		−	24.0000i		−	1.11059i	0.831654	−	0.555294i	$-0.187394\pi$
$468$	3.46410	+	1.00000i	0.160128	+	0.0462250i
$469$	40.0000			1.84703
$470$		0			0
$471$	−7.50000	−	12.9904i	−0.345582	−	0.598565i
$472$	10.3923	+	6.00000i	0.478345	+	0.276172i
$473$			18.0000i			0.827641i
$474$	1.00000	−	1.73205i	0.0459315	−	0.0795557i
$475$		0			0
$476$	40.0000			1.83340
$477$	−0.866025	−	0.500000i	−0.0396526	−	0.0228934i
$478$	−15.5885	+	9.00000i	−0.712999	+	0.411650i
$479$	−14.0000	−	24.2487i	−0.639676	−	1.10795i	−0.985504	−	0.169654i	$-0.945735\pi$
$479$	−14.0000	−	24.2487i	−0.639676	−	1.10795i	0.345827	−	0.938298i	$-0.387598\pi$
$480$		0			0
$481$	7.00000	−	24.2487i	0.319173	−	1.10565i
$482$			25.0000i			1.13872i
$483$	−17.3205	+	10.0000i	−0.788110	+	0.455016i
$484$	−1.00000	−	1.73205i	−0.0454545	−	0.0787296i
$485$		0			0
$486$	−1.00000			−0.0453609
$487$	−32.0429	−	18.5000i	−1.45200	−	0.838315i	−0.453409	−	0.891303i	$-0.649792\pi$
$487$	−32.0429	−	18.5000i	−1.45200	−	0.838315i	−0.998595	+	0.0529875i	$0.983126\pi$
$488$	−1.73205	−	1.00000i	−0.0784063	−	0.0452679i
$489$	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	$0.990472\pi$
$492$	5.19615	−	3.00000i	0.234261	−	0.135250i
$493$		−	32.0000i		−	1.44121i
$494$	12.5000	+	12.9904i	0.562402	+	0.584465i
$495$		0			0
$496$	1.00000	+	1.73205i	0.0449013	+	0.0777714i
$497$	−8.66025	+	5.00000i	−0.388465	+	0.224281i
$498$	−6.92820	−	4.00000i	−0.310460	−	0.179244i
$499$	−4.00000			−0.179065			−0.0895323	−	0.995984i	$-0.528537\pi$
$499$	−4.00000			−0.179065			−0.0895323	+	0.995984i	$0.528537\pi$
$500$		0			0
$501$	11.5000	−	19.9186i	0.513782	−	0.889897i
$502$		−	15.0000i		−	0.669483i
$503$	−9.52628	−	5.50000i	−0.424756	−	0.245233i	0.272354	−	0.962197i	$-0.412198\pi$
$503$	−9.52628	−	5.50000i	−0.424756	−	0.245233i	−0.697110	+	0.716964i	$0.745531\pi$
$504$	2.50000	+	4.33013i	0.111359	+	0.192879i
$505$		0			0
$506$	−12.0000			−0.533465
$507$	6.06218	+	11.5000i	0.269231	+	0.510733i
$508$			21.0000i			0.931724i
$509$	5.00000	+	8.66025i	0.221621	+	0.383859i	0.955300	−	0.295637i	$-0.0955319\pi$
$509$	5.00000	+	8.66025i	0.221621	+	0.383859i	−0.733679	+	0.679496i	$0.762199\pi$
$510$		0			0
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−4.33013	−	2.50000i	−0.191180	−	0.110378i
$514$	−14.0000	+	24.2487i	−0.617514	+	1.06956i
$515$		0			0
$516$	−3.00000	+	5.19615i	−0.132068	+	0.228748i
$517$	7.79423	−	4.50000i	0.342790	−	0.197910i
$518$	30.3109	−	17.5000i	1.33178	−	0.768906i
$519$	−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	$0.465066\pi$
$522$	3.46410	−	2.00000i	0.151620	−	0.0875376i
$523$	8.66025	−	5.00000i	0.378686	−	0.218635i	−0.298560	−	0.954391i	$-0.596506\pi$
$523$	8.66025	−	5.00000i	0.378686	−	0.218635i	0.677247	+	0.735756i	$0.263173\pi$
$524$	−9.50000	+	16.4545i	−0.415009	+	0.718817i
$525$		0			0
$526$	−7.50000	+	12.9904i	−0.327016	+	0.566408i
$527$	−13.8564	−	8.00000i	−0.603595	−	0.348485i
$528$			3.00000i			0.130558i
$529$	−3.50000	+	6.06218i	−0.152174	+	0.263573i
$530$		0			0
$531$	−6.00000	−	10.3923i	−0.260378	−	0.450988i
$532$			25.0000i			1.08389i
$533$	20.7846	+	6.00000i	0.900281	+	0.259889i
$534$	−11.0000			−0.476017
$535$		0			0
$536$	4.00000	+	6.92820i	0.172774	+	0.299253i
$537$	−3.46410	−	2.00000i	−0.149487	−	0.0863064i
$538$			4.00000i			0.172452i
$539$	−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	$0.239107\pi$
$542$	3.46410	+	2.00000i	0.148796	+	0.0859074i
$543$	1.73205	−	1.00000i	0.0743294	−	0.0429141i
$544$	4.00000	+	6.92820i	0.171499	+	0.297044i
$545$		0			0
$546$	−5.00000	+	17.3205i	−0.213980	+	0.741249i
$547$			6.00000i			0.256541i	0.991739	+	0.128271i	$0.0409426\pi$
$547$			6.00000i			0.256541i	−0.991739	+	0.128271i	$0.959057\pi$
$548$	10.3923	−	6.00000i	0.443937	−	0.256307i
$549$	1.00000	+	1.73205i	0.0426790	+	0.0739221i
$550$		0			0
$551$	20.0000			0.852029
$552$	−3.46410	−	2.00000i	−0.147442	−	0.0851257i
$553$	8.66025	+	5.00000i	0.368271	+	0.212622i
$554$	−15.0000			−0.637289
$555$		0			0
$556$	−3.50000	−	6.06218i	−0.148433	−	0.257094i
$557$	12.9904	−	7.50000i	0.550420	−	0.317785i	−0.198871	−	0.980026i	$-0.563728\pi$
$557$	12.9904	−	7.50000i	0.550420	−	0.317785i	0.749291	+	0.662240i	$0.230394\pi$
$558$		−	2.00000i		−	0.0846668i
$559$	−21.0000	+	5.19615i	−0.888205	+	0.219774i
$560$		0			0
$561$	−12.0000	−	20.7846i	−0.506640	−	0.877527i
$562$	−15.5885	+	9.00000i	−0.657559	+	0.379642i
$563$	31.1769	+	18.0000i	1.31395	+	0.758610i	0.982748	−	0.184950i	$-0.0592124\pi$
$563$	31.1769	+	18.0000i	1.31395	+	0.758610i	0.331202	+	0.943560i	$0.392546\pi$
$564$	3.00000			0.126323
$565$		0			0
$566$	−5.00000	+	8.66025i	−0.210166	+	0.364018i
$567$		−	5.00000i		−	0.209980i
$568$	−1.73205	−	1.00000i	−0.0726752	−	0.0419591i
$569$	−7.50000	−	12.9904i	−0.314416	−	0.544585i	0.664897	−	0.746935i	$-0.268475\pi$
$569$	−7.50000	−	12.9904i	−0.314416	−	0.544585i	−0.979313	+	0.202350i	$0.935142\pi$
$570$		0			0
$571$	−33.0000			−1.38101			−0.690504	−	0.723329i	$-0.742611\pi$
$571$	−33.0000			−1.38101			−0.690504	+	0.723329i	$0.742611\pi$
$572$	−7.79423	+	7.50000i	−0.325893	+	0.313591i
$573$		−	2.00000i		−	0.0835512i
$574$	15.0000	+	25.9808i	0.626088	+	1.08442i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$			2.00000i			0.0832611i	0.999133	+	0.0416305i	$0.0132552\pi$
$577$			2.00000i			0.0832611i	−0.999133	+	0.0416305i	$0.986745\pi$
$578$	−40.7032	−	23.5000i	−1.69303	−	0.977471i
$579$	12.0000	−	20.7846i	0.498703	−	0.863779i
$580$		0			0
$581$	20.0000	−	34.6410i	0.829740	−	1.43715i
$582$		0			0
$583$	2.59808	−	1.50000i	0.107601	−	0.0621237i
$584$		0			0
$585$		0			0
$586$	9.00000			0.371787
$587$	15.5885	−	9.00000i	0.643404	−	0.371470i	−0.142520	−	0.989792i	$-0.545521\pi$
$587$	15.5885	−	9.00000i	0.643404	−	0.371470i	0.785925	+	0.618322i	$0.212187\pi$
$588$	−15.5885	+	9.00000i	−0.642857	+	0.371154i
$589$	5.00000	−	8.66025i	0.206021	−	0.356840i
$590$		0			0
$591$	−1.50000	+	2.59808i	−0.0617018	+	0.106871i
$592$	6.06218	+	3.50000i	0.249154	+	0.143849i
$593$		−	20.0000i		−	0.821302i	−0.911793	−	0.410651i	$-0.865302\pi$
$593$		−	20.0000i		−	0.821302i	0.911793	−	0.410651i	$-0.134698\pi$
$594$	1.50000	−	2.59808i	0.0615457	−	0.106600i
$595$		0			0
$596$	1.00000	+	1.73205i	0.0409616	+	0.0709476i
$597$			22.0000i			0.900400i
$598$	−3.46410	−	14.0000i	−0.141658	−	0.572503i
$599$	−34.0000			−1.38920			−0.694601	−	0.719395i	$-0.744419\pi$
$599$	−34.0000			−1.38920			−0.694601	+	0.719395i	$0.744419\pi$
$600$		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	$-0.438851\pi$
$602$	−25.9808	−	15.0000i	−1.05890	−	0.611354i
$603$		−	8.00000i		−	0.325785i
$604$	11.0000	−	19.0526i	0.447584	−	0.775238i
$605$		0			0
$606$	8.00000			0.324978
$607$	25.1147	+	14.5000i	1.01938	+	0.588537i	0.913923	−	0.405887i	$-0.133038\pi$
$607$	25.1147	+	14.5000i	1.01938	+	0.588537i	0.105453	+	0.994424i	$0.466371\pi$
$608$	−4.33013	+	2.50000i	−0.175610	+	0.101388i
$609$	10.0000	+	17.3205i	0.405220	+	0.701862i
$610$		0			0
$611$	7.50000	+	7.79423i	0.303418	+	0.315321i
$612$		−	8.00000i		−	0.323381i
$613$	−21.6506	+	12.5000i	−0.874461	+	0.504870i	−0.868828	−	0.495114i	$-0.835126\pi$
$613$	−21.6506	+	12.5000i	−0.874461	+	0.504870i	−0.00563283	+	0.999984i	$0.501793\pi$
$614$	3.00000	+	5.19615i	0.121070	+	0.209700i
$615$		0			0
$616$	−15.0000			−0.604367
$617$	12.1244	+	7.00000i	0.488108	+	0.281809i	0.723789	−	0.690021i	$-0.242399\pi$
$617$	12.1244	+	7.00000i	0.488108	+	0.281809i	−0.235681	+	0.971830i	$0.575732\pi$
$618$	6.06218	+	3.50000i	0.243857	+	0.140791i
$619$	−17.0000			−0.683288			−0.341644	−	0.939829i	$-0.610984\pi$
$619$	−17.0000			−0.683288			−0.341644	+	0.939829i	$0.610984\pi$
$620$		0			0
$621$	2.00000	+	3.46410i	0.0802572	+	0.139010i
$622$	10.3923	−	6.00000i	0.416693	−	0.240578i
$623$		−	55.0000i		−	2.20353i
$624$	−3.50000	+	0.866025i	−0.140112	+	0.0346688i
$625$		0			0
$626$	−3.00000	−	5.19615i	−0.119904	−	0.207680i
$627$	12.9904	−	7.50000i	0.518786	−	0.299521i
$628$	12.9904	+	7.50000i	0.518373	+	0.299283i
$629$	−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	$0.243439\pi$
$632$			2.00000i			0.0795557i
$633$	−12.9904	−	7.50000i	−0.516321	−	0.298098i
$634$	11.5000	+	19.9186i	0.456723	+	0.791068i
$635$		0			0
$636$	1.00000			0.0396526
$637$	−62.3538	−	18.0000i	−2.47055	−	0.713186i
$638$			12.0000i			0.475085i
$639$	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	$0.987649\pi$
$642$			6.00000i			0.236801i
$643$	−38.1051	−	22.0000i	−1.50272	−	0.867595i	−0.999995	−	0.00314839i	$-0.998998\pi$
$643$	−38.1051	−	22.0000i	−1.50272	−	0.867595i	−0.502724	−	0.864447i	$-0.667669\pi$
$644$	10.0000	−	17.3205i	0.394055	−	0.682524i
$645$		0			0
$646$	20.0000	−	34.6410i	0.786889	−	1.36293i
$647$	2.59808	−	1.50000i	0.102141	−	0.0589711i	−0.448059	−	0.894004i	$-0.647885\pi$
$647$	2.59808	−	1.50000i	0.102141	−	0.0589711i	0.550200	+	0.835033i	$0.314551\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	36.0000			1.41312
$650$		0			0
$651$	10.0000			0.391931
$652$	−17.3205	+	10.0000i	−0.678323	+	0.391630i
$653$	−23.3827	+	13.5000i	−0.915035	+	0.528296i	−0.882048	−	0.471160i	$-0.843835\pi$
$653$	−23.3827	+	13.5000i	−0.915035	+	0.528296i	−0.0329874	+	0.999456i	$0.510502\pi$
$654$	−7.00000	+	12.1244i	−0.273722	+	0.474100i
$655$		0			0
$656$	−3.00000	+	5.19615i	−0.117130	+	0.202876i
$657$		0			0
$658$			15.0000i			0.584761i
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	−0.266872	−	0.963732i	$-0.585990\pi$
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	0.968052	−	0.250748i	$-0.0806766\pi$
$660$		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	$0.771032\pi$
$662$		−	4.00000i		−	0.155464i
$663$	20.7846	−	20.0000i	0.807207	−	0.776736i
$664$	8.00000			0.310460
$665$		0			0
$666$	−3.50000	−	6.06218i	−0.135622	−	0.234905i
$667$	−13.8564	−	8.00000i	−0.536522	−	0.309761i
$668$			23.0000i			0.889897i
$669$	−1.50000	+	2.59808i	−0.0579934	+	0.100447i
$670$		0			0
$671$	−6.00000			−0.231627
$672$	−4.33013	−	2.50000i	−0.167038	−	0.0964396i
$673$	27.7128	−	16.0000i	1.06825	−	0.616755i	0.140548	−	0.990074i	$-0.455114\pi$
$673$	27.7128	−	16.0000i	1.06825	−	0.616755i	0.927703	+	0.373319i	$0.121780\pi$
$674$	−7.00000	−	12.1244i	−0.269630	−	0.467013i
$675$		0			0
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$		−	22.0000i		−	0.845529i	−0.906240	−	0.422764i	$-0.861060\pi$
$677$		−	22.0000i		−	0.845529i	0.906240	−	0.422764i	$-0.138940\pi$
$678$	6.92820	−	4.00000i	0.266076	−	0.153619i
$679$		0			0
$680$		0			0
$681$		0			0
$682$	5.19615	+	3.00000i	0.198971	+	0.114876i
$683$	25.9808	+	15.0000i	0.994126	+	0.573959i	0.906505	−	0.422195i	$-0.138740\pi$
$683$	25.9808	+	15.0000i	0.994126	+	0.573959i	0.0876211	+	0.996154i	$0.472074\pi$
$684$	5.00000			0.191180
$685$		0			0
$686$	−27.5000	−	47.6314i	−1.04995	−	1.81858i
$687$	12.1244	−	7.00000i	0.462573	−	0.267067i
$688$		−	6.00000i		−	0.228748i
$689$	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	$0.938144\pi$
$692$	4.33013	−	2.50000i	0.164607	−	0.0950357i
$693$	12.9904	+	7.50000i	0.493464	+	0.284901i
$694$	−16.0000			−0.607352
$695$		0			0
$696$	−2.00000	+	3.46410i	−0.0758098	+	0.131306i
$697$		−	48.0000i		−	1.81813i
$698$	−6.92820	−	4.00000i	−0.262236	−	0.151402i
$699$	−7.00000	−	12.1244i	−0.264764	−	0.458585i
$700$		0			0
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	3.46410	+	1.00000i	0.130744	+	0.0377426i
$703$		−	35.0000i		−	1.32005i
$704$	−1.50000	−	2.59808i	−0.0565334	−	0.0979187i
$705$		0			0
$706$	8.00000	−	13.8564i	0.301084	−	0.521493i
$707$			40.0000i			1.50435i
$708$	10.3923	+	6.00000i	0.390567	+	0.225494i
$709$	16.0000	−	27.7128i	0.600893	−	1.04078i	−0.391794	−	0.920053i	$-0.628145\pi$
$709$	16.0000	−	27.7128i	0.600893	−	1.04078i	0.992686	−	0.120723i	$-0.0385214\pi$
$710$		0			0
$711$	1.00000	−	1.73205i	0.0375029	−	0.0649570i
$712$	9.52628	−	5.50000i	0.357012	−	0.206121i
$713$	−6.92820	+	4.00000i	−0.259463	+	0.149801i
$714$	40.0000			1.49696
$715$		0			0
$716$	4.00000			0.149487
$717$	−15.5885	+	9.00000i	−0.582162	+	0.336111i
$718$	−15.5885	+	9.00000i	−0.581756	+	0.335877i
$719$	−10.0000	+	17.3205i	−0.372937	+	0.645946i	−0.990016	−	0.140955i	$-0.954983\pi$
$719$	−10.0000	+	17.3205i	−0.372937	+	0.645946i	0.617079	+	0.786901i	$0.288316\pi$
$720$		0			0
$721$	−17.5000	+	30.3109i	−0.651734	+	1.12884i
$722$	5.19615	+	3.00000i	0.193381	+	0.111648i
$723$			25.0000i			0.929760i
$724$	−1.00000	+	1.73205i	−0.0371647	+	0.0643712i
$725$		0			0
$726$	−1.00000	−	1.73205i	−0.0371135	−	0.0642824i
$727$		−	11.0000i		−	0.407967i	−0.978974	−	0.203984i	$-0.934611\pi$
$727$		−	11.0000i		−	0.407967i	0.978974	−	0.203984i	$-0.0653890\pi$
$728$	−4.33013	−	17.5000i	−0.160485	−	0.648593i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	24.0000	+	41.5692i	0.887672	+	1.53749i
$732$	−1.73205	−	1.00000i	−0.0640184	−	0.0369611i
$733$			43.0000i			1.58824i	0.607760	+	0.794121i	$0.292068\pi$
$733$			43.0000i			1.58824i	−0.607760	+	0.794121i	$0.707932\pi$
$734$	4.00000	−	6.92820i	0.147643	−	0.255725i
$735$		0			0
$736$	4.00000			0.147442
$737$	20.7846	+	12.0000i	0.765611	+	0.442026i
$738$	5.19615	−	3.00000i	0.191273	−	0.110432i
$739$	9.50000	+	16.4545i	0.349463	+	0.605288i	0.986154	−	0.165831i	$-0.0530307\pi$
$739$	9.50000	+	16.4545i	0.349463	+	0.605288i	−0.636691	+	0.771119i	$0.719697\pi$
$740$		0			0
$741$	12.5000	+	12.9904i	0.459199	+	0.477214i
$742$			5.00000i			0.183556i
$743$	13.8564	−	8.00000i	0.508342	−	0.293492i	−0.223810	−	0.974633i	$-0.571849\pi$
$743$	13.8564	−	8.00000i	0.508342	−	0.293492i	0.732152	+	0.681141i	$0.238516\pi$
$744$	1.00000	+	1.73205i	0.0366618	+	0.0635001i
$745$		0			0
$746$	−38.0000			−1.39128
$747$	−6.92820	−	4.00000i	−0.253490	−	0.146352i
$748$	20.7846	+	12.0000i	0.759961	+	0.438763i
$749$	−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	$0.786706\pi$
$752$	−2.59808	+	1.50000i	−0.0947421	+	0.0546994i
$753$		−	15.0000i		−	0.546630i
$754$	−14.0000	+	3.46410i	−0.509850	+	0.126155i
$755$		0			0
$756$	2.50000	+	4.33013i	0.0909241	+	0.157485i
$757$	14.7224	−	8.50000i	0.535096	−	0.308938i	−0.207993	−	0.978130i	$-0.566693\pi$
$757$	14.7224	−	8.50000i	0.535096	−	0.308938i	0.743089	+	0.669193i	$0.233360\pi$
$758$	21.6506	+	12.5000i	0.786386	+	0.454020i
$759$	−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	$0.218824\pi$
$762$			21.0000i			0.760750i
$763$	−60.6218	−	35.0000i	−2.19466	−	1.26709i
$764$	1.00000	+	1.73205i	0.0361787	+	0.0626634i
$765$		0			0
$766$	28.0000			1.01168
$767$	10.3923	+	42.0000i	0.375244	+	1.51653i
$768$		−	1.00000i		−	0.0360844i
$769$	−17.0000	−	29.4449i	−0.613036	−	1.06181i	−0.990726	−	0.135877i	$-0.956615\pi$
$769$	−17.0000	−	29.4449i	−0.613036	−	1.06181i	0.377690	−	0.925932i	$-0.376718\pi$
$770$		0			0
$771$	−14.0000	+	24.2487i	−0.504198	+	0.873296i
$772$			24.0000i			0.863779i
$773$	0.866025	+	0.500000i	0.0311488	+	0.0179838i	0.515494	−	0.856893i	$-0.327609\pi$
$773$	0.866025	+	0.500000i	0.0311488	+	0.0179838i	−0.484345	+	0.874877i	$0.660942\pi$
$774$	−3.00000	+	5.19615i	−0.107833	+	0.186772i
$775$		0			0
$776$		0			0
$777$	30.3109	−	17.5000i	1.08740	−	0.627809i
$778$	−27.7128	+	16.0000i	−0.993552	+	0.573628i
$779$	30.0000			1.07486
$780$		0			0
$781$	−6.00000			−0.214697
$782$	−27.7128	+	16.0000i	−0.991008	+	0.572159i
$783$	3.46410	−	2.00000i	0.123797	−	0.0714742i
$784$	9.00000	−	15.5885i	0.321429	−	0.556731i
$785$		0			0
$786$	−9.50000	+	16.4545i	−0.338854	+	0.586912i
$787$	24.2487	+	14.0000i	0.864373	+	0.499046i	0.865474	−	0.500953i	$-0.167017\pi$
$787$	24.2487	+	14.0000i	0.864373	+	0.499046i	−0.00110111	+	0.999999i	$0.500350\pi$
$788$		−	3.00000i		−	0.106871i
$789$	−7.50000	+	12.9904i	−0.267007	+	0.462470i
$790$		0			0
$791$	20.0000	+	34.6410i	0.711118	+	1.23169i
$792$			3.00000i			0.106600i
$793$	−1.73205	−	7.00000i	−0.0615069	−	0.248577i
$794$	25.0000			0.887217
$795$		0			0
$796$	−11.0000	−	19.0526i	−0.389885	−	0.675300i
$797$	8.66025	+	5.00000i	0.306762	+	0.177109i	0.645477	−	0.763780i	$-0.276659\pi$
$797$	8.66025	+	5.00000i	0.306762	+	0.177109i	−0.338715	+	0.940889i	$0.609992\pi$
$798$			25.0000i			0.884990i
$799$	12.0000	−	20.7846i	0.424529	−	0.735307i
$800$		0			0
$801$	−11.0000			−0.388666
$802$	−16.4545	−	9.50000i	−0.581028	−	0.335457i
$803$		0			0
$804$	4.00000	+	6.92820i	0.141069	+	0.244339i
$805$		0			0
$806$	−2.00000	+	6.92820i	−0.0704470	+	0.244036i
$807$			4.00000i			0.140807i
$808$	−6.92820	+	4.00000i	−0.243733	+	0.140720i
$809$	−13.0000	−	22.5167i	−0.457056	−	0.791644i	0.541748	−	0.840541i	$-0.317763\pi$
$809$	−13.0000	−	22.5167i	−0.457056	−	0.791644i	−0.998804	+	0.0488972i	$0.984429\pi$
$810$		0			0
$811$	25.0000			0.877869			0.438934	−	0.898519i	$-0.355356\pi$
$811$	25.0000			0.877869			0.438934	+	0.898519i	$0.355356\pi$
$812$	−17.3205	−	10.0000i	−0.607831	−	0.350931i
$813$	3.46410	+	2.00000i	0.121491	+	0.0701431i
$814$	21.0000			0.736050
$815$		0			0
$816$	4.00000	+	6.92820i	0.140028	+	0.242536i
$817$	−25.9808	+	15.0000i	−0.908952	+	0.524784i
$818$			25.0000i			0.874105i
$819$	−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	$0.707913\pi$
$822$	10.3923	−	6.00000i	0.362473	−	0.209274i
$823$	−30.3109	−	17.5000i	−1.05657	−	0.610012i	−0.132089	−	0.991238i	$-0.542169\pi$
$823$	−30.3109	−	17.5000i	−1.05657	−	0.610012i	−0.924482	+	0.381226i	$0.875502\pi$
$824$	−7.00000			−0.243857
$825$		0			0
$826$	−30.0000	+	51.9615i	−1.04383	+	1.80797i
$827$			6.00000i			0.208640i	0.994544	+	0.104320i	$0.0332667\pi$
$827$			6.00000i			0.208640i	−0.994544	+	0.104320i	$0.966733\pi$
$828$	−3.46410	−	2.00000i	−0.120386	−	0.0695048i
$829$	−8.00000	−	13.8564i	−0.277851	−	0.481253i	0.692999	−	0.720938i	$-0.256289\pi$
$829$	−8.00000	−	13.8564i	−0.277851	−	0.481253i	−0.970851	+	0.239686i	$0.922956\pi$
$830$		0			0
$831$	−15.0000			−0.520344
$832$	2.59808	−	2.50000i	0.0900721	−	0.0866719i
$833$			144.000i			4.98930i
$834$	−3.50000	−	6.06218i	−0.121195	−	0.209916i
$835$		0			0
$836$	−7.50000	+	12.9904i	−0.259393	+	0.449282i
$837$		−	2.00000i		−	0.0691301i
$838$	10.3923	+	6.00000i	0.358996	+	0.207267i
$839$	−7.00000	+	12.1244i	−0.241667	+	0.418579i	−0.961189	−	0.275890i	$-0.911027\pi$
$839$	−7.00000	+	12.1244i	−0.241667	+	0.418579i	0.719522	+	0.694469i	$0.244361\pi$
$840$		0			0
$841$	6.50000	−	11.2583i	0.224138	−	0.388218i
$842$	−10.3923	+	6.00000i	−0.358142	+	0.206774i
$843$	−15.5885	+	9.00000i	−0.536895	+	0.309976i
$844$	15.0000			0.516321
$845$		0			0
$846$	3.00000			0.103142
$847$	8.66025	−	5.00000i	0.297570	−	0.171802i
$848$	−0.866025	+	0.500000i	−0.0297394	+	0.0171701i
$849$	−5.00000	+	8.66025i	−0.171600	+	0.297219i
$850$		0			0
$851$	−14.0000	+	24.2487i	−0.479914	+	0.831235i
$852$	−1.73205	−	1.00000i	−0.0593391	−	0.0342594i
$853$			26.0000i			0.890223i	0.895475	+	0.445112i	$0.146836\pi$
$853$			26.0000i			0.890223i	−0.895475	+	0.445112i	$0.853164\pi$
$854$	5.00000	−	8.66025i	0.171096	−	0.296348i
$855$		0			0
$856$	−3.00000	−	5.19615i	−0.102538	−	0.177601i
$857$			38.0000i			1.29806i	0.760765	+	0.649028i	$0.224824\pi$
$857$			38.0000i			1.29806i	−0.760765	+	0.649028i	$0.775176\pi$
$858$	−7.79423	+	7.50000i	−0.266091	+	0.256046i
$859$	−3.00000			−0.102359			−0.0511793	−	0.998689i	$-0.516298\pi$
$859$	−3.00000			−0.102359			−0.0511793	+	0.998689i	$0.516298\pi$
$860$		0			0
$861$	15.0000	+	25.9808i	0.511199	+	0.885422i
$862$	10.3923	+	6.00000i	0.353963	+	0.204361i
$863$			24.0000i			0.816970i	0.912765	+	0.408485i	$0.133943\pi$
$863$			24.0000i			0.816970i	−0.912765	+	0.408485i	$0.866057\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$		0			0
$866$	−16.0000			−0.543702
$867$	−40.7032	−	23.5000i	−1.38235	−	0.798102i
$868$	−8.66025	+	5.00000i	−0.293948	+	0.169711i
$869$	3.00000	+	5.19615i	0.101768	+	0.176267i
$870$		0			0
$871$	−8.00000	+	27.7128i	−0.271070	+	0.939013i
$872$		−	14.0000i		−	0.474100i
$873$		0			0
$874$	−10.0000	−	17.3205i	−0.338255	−	0.585875i
$875$		0			0
$876$		0			0
$877$	46.7654	+	27.0000i	1.57915	+	0.911725i	0.994977	+	0.100099i	$0.0319159\pi$
$877$	46.7654	+	27.0000i	1.57915	+	0.911725i	0.584177	+	0.811626i	$0.301417\pi$
$878$	−8.66025	−	5.00000i	−0.292269	−	0.168742i
$879$	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	$0.752021\pi$
$882$	−15.5885	+	9.00000i	−0.524891	+	0.303046i
$883$		−	30.0000i		−	1.00958i	−0.863242	−	0.504790i	$-0.831570\pi$
$883$		−	30.0000i		−	1.00958i	0.863242	−	0.504790i	$-0.168430\pi$
$884$	−8.00000	+	27.7128i	−0.269069	+	0.932083i
$885$		0			0
$886$	3.00000	+	5.19615i	0.100787	+	0.174568i
$887$	35.5070	−	20.5000i	1.19221	−	0.688323i	0.233403	−	0.972380i	$-0.425014\pi$
$887$	35.5070	−	20.5000i	1.19221	−	0.688323i	0.958807	+	0.284058i	$0.0916807\pi$
$888$	6.06218	+	3.50000i	0.203433	+	0.117452i
$889$	−105.000			−3.52159
$890$		0			0
$891$	1.50000	−	2.59808i	0.0502519	−	0.0870388i
$892$		−	3.00000i		−	0.100447i
$893$	12.9904	+	7.50000i	0.434707	+	0.250978i
$894$	1.00000	+	1.73205i	0.0334450	+	0.0579284i
$895$		0			0
$896$	5.00000			0.167038
$897$	−3.46410	−	14.0000i	−0.115663	−	0.467446i
$898$		−	27.0000i		−	0.901002i
$899$	4.00000	+	6.92820i	0.133407	+	0.231069i
$900$		0			0
$901$	4.00000	−	6.92820i	0.133259	−	0.230812i
$902$			18.0000i			0.599334i
$903$	−25.9808	−	15.0000i	−0.864586	−	0.499169i
$904$	−4.00000	+	6.92820i	−0.133038	+	0.230429i
$905$		0			0
$906$	11.0000	−	19.0526i	0.365451	−	0.632979i
$907$	8.66025	−	5.00000i	0.287559	−	0.166022i	−0.349281	−	0.937018i	$-0.613574\pi$
$907$	8.66025	−	5.00000i	0.287559	−	0.166022i	0.636841	+	0.770996i	$0.280241\pi$
$908$		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	$0.607492\pi$
$912$	−4.33013	+	2.50000i	−0.143385	+	0.0827833i
$913$	20.7846	−	12.0000i	0.687870	−	0.397142i
$914$	−15.0000	+	25.9808i	−0.496156	+	0.859367i
$915$		0			0
$916$	−7.00000	+	12.1244i	−0.231287	+	0.400600i
$917$	−82.2724	−	47.5000i	−2.71687	−	1.56859i
$918$		−	8.00000i		−	0.264039i
$919$	−1.00000	+	1.73205i	−0.0329870	+	0.0571351i	−0.882048	−	0.471160i	$-0.843835\pi$
$919$	−1.00000	+	1.73205i	−0.0329870	+	0.0571351i	0.849061	+	0.528295i	$0.177169\pi$
$920$		0			0
$921$	3.00000	+	5.19615i	0.0988534	+	0.171219i
$922$		−	8.00000i		−	0.263466i
$923$	−1.73205	−	7.00000i	−0.0570111	−	0.230408i
$924$	−15.0000			−0.493464
$925$		0			0
$926$	4.00000	+	6.92820i	0.131448	+	0.227675i
$927$	6.06218	+	3.50000i	0.199108	+	0.114955i
$928$		−	4.00000i		−	0.131306i
$929$	1.00000	−	1.73205i	0.0328089	−	0.0568267i	−0.849155	−	0.528144i	$-0.822888\pi$
$929$	1.00000	−	1.73205i	0.0328089	−	0.0568267i	0.881964	+	0.471317i	$0.156221\pi$
$930$		0			0
$931$	−90.0000			−2.94963
$932$	12.1244	+	7.00000i	0.397146	+	0.229293i
$933$	10.3923	−	6.00000i	0.340229	−	0.196431i
$934$	12.0000	+	20.7846i	0.392652	+	0.680093i
$935$		0			0
$936$	−3.50000	+	0.866025i	−0.114401	+	0.0283069i
$937$			30.0000i			0.980057i	0.871706	+	0.490029i	$0.163014\pi$
$937$			30.0000i			0.980057i	−0.871706	+	0.490029i	$0.836986\pi$
$938$	−34.6410	+	20.0000i	−1.13107	+	0.653023i
$939$	−3.00000	−	5.19615i	−0.0979013	−	0.169570i
$940$		0			0
$941$		0			0			−	1.00000i	$-0.5\pi$
$941$		0			0				1.00000i	$0.5\pi$
$942$	12.9904	+	7.50000i	0.423249	+	0.244363i
$943$	−20.7846	−	12.0000i	−0.676840	−	0.390774i
$944$	−12.0000			−0.390567
$945$		0			0
$946$	−9.00000	−	15.5885i	−0.292615	−	0.506824i
$947$	50.2295	−	29.0000i	1.63224	−	0.942373i	0.648838	−	0.760927i	$-0.275255\pi$
$947$	50.2295	−	29.0000i	1.63224	−	0.942373i	0.983401	−	0.181447i	$-0.0580780\pi$
$948$			2.00000i			0.0649570i
$949$		0			0
$950$		0			0
$951$	11.5000	+	19.9186i	0.372913	+	0.645904i
$952$	−34.6410	+	20.0000i	−1.12272	+	0.648204i
$953$	−46.7654	−	27.0000i	−1.51488	−	0.874616i	−0.999848	−	0.0174443i	$-0.994447\pi$
$953$	−46.7654	−	27.0000i	−1.51488	−	0.874616i	−0.515031	−	0.857171i	$-0.672220\pi$
$954$	1.00000			0.0323762
$955$		0			0
$956$	9.00000	−	15.5885i	0.291081	−	0.504167i
$957$			12.0000i			0.387905i
$958$	24.2487	+	14.0000i	0.783440	+	0.452319i
$959$	30.0000	+	51.9615i	0.968751	+	1.67793i
$960$		0			0
$961$	−27.0000			−0.870968
$962$	6.06218	+	24.5000i	0.195452	+	0.789912i
$963$			6.00000i			0.193347i
$964$	−12.5000	−	21.6506i	−0.402598	−	0.697320i
$965$		0			0
$966$	10.0000	−	17.3205i	0.321745	−	0.557278i
$967$		−	31.0000i		−	0.996893i	−0.866921	−	0.498446i	$-0.833904\pi$
$967$		−	31.0000i		−	0.996893i	0.866921	−	0.498446i	$-0.166096\pi$
$968$	1.73205	+	1.00000i	0.0556702	+	0.0321412i
$969$	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	$0.244039\pi$
$972$	0.866025	−	0.500000i	0.0277778	−	0.0160375i
$973$	30.3109	−	17.5000i	0.971722	−	0.561024i
$974$	37.0000			1.18556
$975$		0			0
$976$	2.00000			0.0640184
$977$	17.3205	−	10.0000i	0.554132	−	0.319928i	−0.196655	−	0.980473i	$-0.563008\pi$
$977$	17.3205	−	10.0000i	0.554132	−	0.319928i	0.750787	+	0.660544i	$0.229674\pi$
$978$	−17.3205	+	10.0000i	−0.553849	+	0.319765i
$979$	16.5000	−	28.5788i	0.527342	−	0.913384i
$980$		0			0
$981$	−7.00000	+	12.1244i	−0.223493	+	0.387101i
$982$	18.1865	+	10.5000i	0.580356	+	0.335068i
$983$		−	23.0000i		−	0.733586i	−0.930303	−	0.366793i	$-0.880456\pi$
$983$		−	23.0000i		−	0.733586i	0.930303	−	0.366793i	$-0.119544\pi$
$984$	−3.00000	+	5.19615i	−0.0956365	+	0.165647i
$985$		0			0
$986$	16.0000	+	27.7128i	0.509544	+	0.882556i
$987$			15.0000i			0.477455i
$988$	−17.3205	−	5.00000i	−0.551039	−	0.159071i
$989$	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	$0.884106\pi$
$992$	−1.73205	−	1.00000i	−0.0549927	−	0.0317500i
$993$		−	4.00000i		−	0.126936i
$994$	5.00000	−	8.66025i	0.158590	−	0.274687i
$995$		0			0
$996$	8.00000			0.253490
$997$	0.866025	+	0.500000i	0.0274273	+	0.0158352i	0.513651	−	0.857999i	$-0.328293\pi$
$997$	0.866025	+	0.500000i	0.0274273	+	0.0158352i	−0.486224	+	0.873834i	$0.661626\pi$
$998$	3.46410	−	2.00000i	0.109654	−	0.0633089i
$999$	−3.50000	−	6.06218i	−0.110735	−	0.191799i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.z.j.1849.1		4
5.2	odd	4		1950.2.i.i.601.1		2
5.3	odd	4		390.2.i.d.211.1	yes	2
5.4	even	2	inner	1950.2.z.j.1849.2		4
13.9	even	3	inner	1950.2.z.j.1699.2		4
15.8	even	4		1170.2.i.g.991.1		2
65.3	odd	12		5070.2.a.i.1.1		1
65.9	even	6	inner	1950.2.z.j.1699.1		4
65.22	odd	12		1950.2.i.i.451.1		2
65.23	odd	12		5070.2.a.x.1.1		1
65.28	even	12		5070.2.b.l.1351.2		2
65.48	odd	12		390.2.i.d.61.1	✓	2
65.63	even	12		5070.2.b.l.1351.1		2
195.113	even	12		1170.2.i.g.451.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.i.d.61.1	✓	2	65.48	odd	12
390.2.i.d.211.1	yes	2	5.3	odd	4
1170.2.i.g.451.1		2	195.113	even	12
1170.2.i.g.991.1		2	15.8	even	4
1950.2.i.i.451.1		2	65.22	odd	12
1950.2.i.i.601.1		2	5.2	odd	4
1950.2.z.j.1699.1		4	65.9	even	6	inner
1950.2.z.j.1699.2		4	13.9	even	3	inner
1950.2.z.j.1849.1		4	1.1	even	1	trivial
1950.2.z.j.1849.2		4	5.4	even	2	inner
5070.2.a.i.1.1		1	65.3	odd	12
5070.2.a.x.1.1		1	65.23	odd	12
5070.2.b.l.1351.1		2	65.63	even	12
5070.2.b.l.1351.2		2	65.28	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(4.33013 + 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +(4.33013 + 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(1.50000 + 2.59808i) q^{11} +1.00000i q^{12} +(-2.59808 + 2.50000i) q^{13} -5.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(6.92820 + 4.00000i) q^{17} +1.00000i q^{18} +(-2.50000 + 4.33013i) q^{19} -5.00000 q^{21} +(-2.59808 - 1.50000i) q^{22} +(3.46410 - 2.00000i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(1.00000 - 3.46410i) q^{26} +1.00000i q^{27} +(4.33013 - 2.50000i) q^{28} +(-2.00000 - 3.46410i) q^{29} -2.00000 q^{31} +(0.866025 + 0.500000i) q^{32} +(-2.59808 - 1.50000i) q^{33} -8.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +(-6.06218 + 3.50000i) q^{37} -5.00000i q^{38} +(1.00000 - 3.46410i) q^{39} +(-3.00000 - 5.19615i) q^{41} +(4.33013 - 2.50000i) q^{42} +(5.19615 + 3.00000i) q^{43} +3.00000 q^{44} +(-2.00000 + 3.46410i) q^{46} -3.00000i q^{47} +(0.866025 + 0.500000i) q^{48} +(9.00000 + 15.5885i) q^{49} -8.00000 q^{51} +(0.866025 + 3.50000i) q^{52} -1.00000i q^{53} +(-0.500000 - 0.866025i) q^{54} +(-2.50000 + 4.33013i) q^{56} -5.00000i q^{57} +(3.46410 + 2.00000i) q^{58} +(6.00000 - 10.3923i) q^{59} +(-1.00000 + 1.73205i) q^{61} +(1.73205 - 1.00000i) q^{62} +(4.33013 - 2.50000i) q^{63} -1.00000 q^{64} +3.00000 q^{66} +(6.92820 - 4.00000i) q^{67} +(6.92820 - 4.00000i) q^{68} +(-2.00000 + 3.46410i) q^{69} +(-1.00000 + 1.73205i) q^{71} +(0.866025 + 0.500000i) q^{72} +(3.50000 - 6.06218i) q^{74} +(2.50000 + 4.33013i) q^{76} +15.0000i q^{77} +(0.866025 + 3.50000i) q^{78} +2.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(5.19615 + 3.00000i) q^{82} -8.00000i q^{83} +(-2.50000 + 4.33013i) q^{84} -6.00000 q^{86} +(3.46410 + 2.00000i) q^{87} +(-2.59808 + 1.50000i) q^{88} +(-5.50000 - 9.52628i) q^{89} +(-17.5000 + 4.33013i) q^{91} -4.00000i q^{92} +(1.73205 - 1.00000i) q^{93} +(1.50000 + 2.59808i) q^{94} -1.00000 q^{96} +(-15.5885 - 9.00000i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 2 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 2 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} + 2 q^{6} + 2 q^{9} + 6 q^{11} - 20 q^{14} - 2 q^{16} - 10 q^{19} - 20 q^{21} - 2 q^{24} + 4 q^{26} - 8 q^{29} - 8 q^{31} - 32 q^{34} - 2 q^{36} + 4 q^{39} - 12 q^{41} + 12 q^{44} - 8 q^{46} + 36 q^{49} - 32 q^{51} - 2 q^{54} - 10 q^{56} + 24 q^{59} - 4 q^{61} - 4 q^{64} + 12 q^{66} - 8 q^{69} - 4 q^{71} + 14 q^{74} + 10 q^{76} + 8 q^{79} - 2 q^{81} - 10 q^{84} - 24 q^{86} - 22 q^{89} - 70 q^{91} + 6 q^{94} - 4 q^{96} + 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 + 2 * q^6 + 2 * q^9 + 6 * q^11 - 20 * q^14 - 2 * q^16 - 10 * q^19 - 20 * q^21 - 2 * q^24 + 4 * q^26 - 8 * q^29 - 8 * q^31 - 32 * q^34 - 2 * q^36 + 4 * q^39 - 12 * q^41 + 12 * q^44 - 8 * q^46 + 36 * q^49 - 32 * q^51 - 2 * q^54 - 10 * q^56 + 24 * q^59 - 4 * q^61 - 4 * q^64 + 12 * q^66 - 8 * q^69 - 4 * q^71 + 14 * q^74 + 10 * q^76 + 8 * q^79 - 2 * q^81 - 10 * q^84 - 24 * q^86 - 22 * q^89 - 70 * q^91 + 6 * q^94 - 4 * q^96 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more