LMFDB - Embedded newform 1950.2.bc.i.901.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(751,1950)]

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, 5]))

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

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

chi := DirichletCharacter("1950.751");

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.bc (of order $6$, 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:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + \cdots + 2197 $ x^12 - 2x^11 - 8x^10 + 34x^9 + 8x^8 - 134x^7 + 98x^6 + 154x^5 + 104x^4 + 190x^3 - 1196x^2 - 338*x + 2197
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			901.4
Root			$-0.330925 + 1.46916i$ of defining polynomial
Character	$\chi$	$=$	1950.901
Dual form			1950.2.bc.i.751.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(-1.04466 + 0.603137i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(-1.04466 + 0.603137i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(4.46182 + 2.57603i) q^{11} -1.00000 q^{12} +(-2.82126 - 2.24511i) q^{13} -1.20627 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.36800 + 4.10150i) q^{17} -1.00000i q^{18} +(1.84474 - 1.06506i) q^{19} -1.20627i q^{21} +(2.57603 + 4.46182i) q^{22} +(-1.08711 + 1.88293i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-1.32073 - 3.35495i) q^{26} +1.00000 q^{27} +(-1.04466 - 0.603137i) q^{28} +(-2.38346 + 4.12828i) q^{29} +5.91046i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-4.46182 + 2.57603i) q^{33} +4.73601i q^{34} +(0.500000 - 0.866025i) q^{36} +(-3.81110 - 2.20034i) q^{37} +2.13012 q^{38} +(3.35495 - 1.32073i) q^{39} +(4.10150 + 2.36800i) q^{41} +(0.603137 - 1.04466i) q^{42} +(-0.986944 - 1.70944i) q^{43} +5.15206i q^{44} +(-1.88293 + 1.08711i) q^{46} +0.852296i q^{47} +(-0.500000 - 0.866025i) q^{48} +(-2.77245 + 4.80203i) q^{49} -4.73601 q^{51} +(0.533691 - 3.56583i) q^{52} -4.48042 q^{53} +(0.866025 + 0.500000i) q^{54} +(-0.603137 - 1.04466i) q^{56} +2.13012i q^{57} +(-4.12828 + 2.38346i) q^{58} +(-1.68133 + 0.970715i) q^{59} +(-1.53795 - 2.66381i) q^{61} +(-2.95523 + 5.11861i) q^{62} +(1.04466 + 0.603137i) q^{63} -1.00000 q^{64} -5.15206 q^{66} +(-12.1723 - 7.02765i) q^{67} +(-2.36800 + 4.10150i) q^{68} +(-1.08711 - 1.88293i) q^{69} +(-0.298707 + 0.172459i) q^{71} +(0.866025 - 0.500000i) q^{72} +15.7228i q^{73} +(-2.20034 - 3.81110i) q^{74} +(1.84474 + 1.06506i) q^{76} -6.21480 q^{77} +(3.56583 + 0.533691i) q^{78} +13.5863 q^{79} +(-0.500000 + 0.866025i) q^{81} +(2.36800 + 4.10150i) q^{82} +10.2045i q^{83} +(1.04466 - 0.603137i) q^{84} -1.97389i q^{86} +(-2.38346 - 4.12828i) q^{87} +(-2.57603 + 4.46182i) q^{88} +(-14.1941 - 8.19497i) q^{89} +(4.30137 + 0.643777i) q^{91} -2.17422 q^{92} +(-5.11861 - 2.95523i) q^{93} +(-0.426148 + 0.738110i) q^{94} -1.00000i q^{96} +(7.34631 - 4.24139i) q^{97} +(-4.80203 + 2.77245i) q^{98} -5.15206i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} + 6 q^{4} + 12 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 + 6 * q^4 + 12 * q^7 - 6 * q^9	$ 12 q - 6 q^{3} + 6 q^{4} + 12 q^{7} - 6 q^{9} + 6 q^{11} - 12 q^{12} - 4 q^{13} - 4 q^{14} - 6 q^{16} - 8 q^{17} + 6 q^{19} + 6 q^{22} - 16 q^{23} - 2 q^{26} + 12 q^{27} + 12 q^{28} - 14 q^{29} - 6 q^{33} + 6 q^{36} + 6 q^{37} + 8 q^{38} + 2 q^{39} - 18 q^{41} + 2 q^{42} - 10 q^{43} - 6 q^{46} - 6 q^{48} - 8 q^{49} + 16 q^{51} - 2 q^{52} - 2 q^{56} - 6 q^{58} + 36 q^{59} + 10 q^{61} - 16 q^{62} - 12 q^{63} - 12 q^{64} - 12 q^{66} - 24 q^{67} + 8 q^{68} - 16 q^{69} - 12 q^{71} + 12 q^{74} + 6 q^{76} - 24 q^{77} + 10 q^{78} - 4 q^{79} - 6 q^{81} - 8 q^{82} - 12 q^{84} - 14 q^{87} - 6 q^{88} - 18 q^{89} + 2 q^{91} - 32 q^{92} + 6 q^{93} + 8 q^{94} + 24 q^{97} - 24 q^{98}+O(q^{100}) $ 12 * q - 6 * q^3 + 6 * q^4 + 12 * q^7 - 6 * q^9 + 6 * q^11 - 12 * q^12 - 4 * q^13 - 4 * q^14 - 6 * q^16 - 8 * q^17 + 6 * q^19 + 6 * q^22 - 16 * q^23 - 2 * q^26 + 12 * q^27 + 12 * q^28 - 14 * q^29 - 6 * q^33 + 6 * q^36 + 6 * q^37 + 8 * q^38 + 2 * q^39 - 18 * q^41 + 2 * q^42 - 10 * q^43 - 6 * q^46 - 6 * q^48 - 8 * q^49 + 16 * q^51 - 2 * q^52 - 2 * q^56 - 6 * q^58 + 36 * q^59 + 10 * q^61 - 16 * q^62 - 12 * q^63 - 12 * q^64 - 12 * q^66 - 24 * q^67 + 8 * q^68 - 16 * q^69 - 12 * q^71 + 12 * q^74 + 6 * q^76 - 24 * q^77 + 10 * q^78 - 4 * q^79 - 6 * q^81 - 8 * q^82 - 12 * q^84 - 14 * q^87 - 6 * q^88 - 18 * q^89 + 2 * q^91 - 32 * q^92 + 6 * q^93 + 8 * q^94 + 24 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$1$

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
$3$	−0.500000	+	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
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	−1.04466	+	0.603137i	−0.394846	+	0.227964i	−0.684258	−	0.729240i	$-0.739874\pi$
$7$	−1.04466	+	0.603137i	−0.394846	+	0.227964i	0.289412	+	0.957205i	$0.406540\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	4.46182	+	2.57603i	1.34529	+	0.776703i	0.987578	−	0.157130i	$-0.0502240\pi$
$11$	4.46182	+	2.57603i	1.34529	+	0.776703i	0.357711	+	0.933832i	$0.383557\pi$
$12$	−1.00000			−0.288675
$13$	−2.82126	−	2.24511i	−0.782476	−	0.622681i
$13$	−2.82126	−	2.24511i	−0.782476	−	0.622681i
$14$	−1.20627			−0.322390
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.36800	+	4.10150i	0.574326	+	0.994761i	0.996115	+	0.0880670i	$0.0280689\pi$
$17$	2.36800	+	4.10150i	0.574326	+	0.994761i	−0.421789	+	0.906694i	$0.638598\pi$
$18$		−	1.00000i		−	0.235702i
$19$	1.84474	−	1.06506i	0.423212	−	0.244341i	−0.273239	−	0.961946i	$-0.588095\pi$
$19$	1.84474	−	1.06506i	0.423212	−	0.244341i	0.696450	+	0.717605i	$0.254762\pi$
$20$		0			0
$21$		−	1.20627i		−	0.263231i
$22$	2.57603	+	4.46182i	0.549212	+	0.951263i
$23$	−1.08711	+	1.88293i	−0.226678	+	0.392618i	−0.956822	−	0.290676i	$-0.906120\pi$
$23$	−1.08711	+	1.88293i	−0.226678	+	0.392618i	0.730144	+	0.683294i	$0.239453\pi$
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$		0			0
$26$	−1.32073	−	3.35495i	−0.259016	−	0.657960i
$27$	1.00000			0.192450
$28$	−1.04466	−	0.603137i	−0.197423	−	0.113982i
$29$	−2.38346	+	4.12828i	−0.442598	+	0.766602i	−0.997881	−	0.0650589i	$-0.979276\pi$
$29$	−2.38346	+	4.12828i	−0.442598	+	0.766602i	0.555283	+	0.831661i	$0.312610\pi$
$30$		0			0
$31$			5.91046i			1.06155i	0.847513	+	0.530775i	$0.178099\pi$
$31$			5.91046i			1.06155i	−0.847513	+	0.530775i	$0.821901\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−4.46182	+	2.57603i	−0.776703	+	0.448430i
$34$			4.73601i			0.812219i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−3.81110	−	2.20034i	−0.626541	−	0.361734i	0.152870	−	0.988246i	$-0.451148\pi$
$37$	−3.81110	−	2.20034i	−0.626541	−	0.361734i	−0.779411	+	0.626513i	$0.784482\pi$
$38$	2.13012			0.345551
$39$	3.35495	−	1.32073i	0.537222	−	0.211486i
$40$		0			0
$41$	4.10150	+	2.36800i	0.640547	+	0.369820i	0.784825	−	0.619717i	$-0.212753\pi$
$41$	4.10150	+	2.36800i	0.640547	+	0.369820i	−0.144278	+	0.989537i	$0.546086\pi$
$42$	0.603137	−	1.04466i	0.0930660	−	0.161195i
$43$	−0.986944	−	1.70944i	−0.150508	−	0.260687i	0.780907	−	0.624648i	$-0.214757\pi$
$43$	−0.986944	−	1.70944i	−0.150508	−	0.260687i	−0.931414	+	0.363961i	$0.881424\pi$
$44$			5.15206i			0.776703i
$45$		0			0
$46$	−1.88293	+	1.08711i	−0.277623	+	0.160285i
$47$			0.852296i			0.124320i	0.998066	+	0.0621600i	$0.0197989\pi$
$47$			0.852296i			0.124320i	−0.998066	+	0.0621600i	$0.980201\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	−2.77245	+	4.80203i	−0.396065	+	0.686004i
$50$		0			0
$51$	−4.73601			−0.663174
$52$	0.533691	−	3.56583i	0.0740096	−	0.494492i
$53$	−4.48042			−0.615433			−0.307716	−	0.951478i	$-0.599565\pi$
$53$	−4.48042			−0.615433			−0.307716	+	0.951478i	$0.599565\pi$
$54$	0.866025	+	0.500000i	0.117851	+	0.0680414i
$55$		0			0
$56$	−0.603137	−	1.04466i	−0.0805976	−	0.139599i
$57$			2.13012i			0.282141i
$58$	−4.12828	+	2.38346i	−0.542070	+	0.312964i
$59$	−1.68133	+	0.970715i	−0.218890	+	0.126376i	−0.605436	−	0.795894i	$-0.707001\pi$
$59$	−1.68133	+	0.970715i	−0.218890	+	0.126376i	0.386546	+	0.922270i	$0.373668\pi$
$60$		0			0
$61$	−1.53795	−	2.66381i	−0.196915	−	0.341066i	0.750612	−	0.660744i	$-0.229759\pi$
$61$	−1.53795	−	2.66381i	−0.196915	−	0.341066i	−0.947527	+	0.319677i	$0.896426\pi$
$62$	−2.95523	+	5.11861i	−0.375315	+	0.650064i
$63$	1.04466	+	0.603137i	0.131615	+	0.0759881i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−5.15206			−0.634175
$67$	−12.1723	−	7.02765i	−1.48708	−	0.858564i	−0.487186	−	0.873298i	$-0.661977\pi$
$67$	−12.1723	−	7.02765i	−1.48708	−	0.858564i	−0.999891	+	0.0147340i	$0.995310\pi$
$68$	−2.36800	+	4.10150i	−0.287163	+	0.497380i
$69$	−1.08711	−	1.88293i	−0.130873	−	0.226678i
$70$		0			0
$71$	−0.298707	+	0.172459i	−0.0354500	+	0.0204671i	−0.517620	−	0.855610i	$-0.673182\pi$
$71$	−0.298707	+	0.172459i	−0.0354500	+	0.0204671i	0.482170	+	0.876078i	$0.339849\pi$
$72$	0.866025	−	0.500000i	0.102062	−	0.0589256i
$73$			15.7228i			1.84022i	0.391662	+	0.920109i	$0.371900\pi$
$73$			15.7228i			1.84022i	−0.391662	+	0.920109i	$0.628100\pi$
$74$	−2.20034	−	3.81110i	−0.255784	−	0.443031i
$75$		0			0
$76$	1.84474	+	1.06506i	0.211606	+	0.122171i
$77$	−6.21480			−0.708242
$78$	3.56583	+	0.533691i	0.403751	+	0.0604286i
$79$	13.5863			1.52858			0.764290	−	0.644873i	$-0.223090\pi$
$79$	13.5863			1.52858			0.764290	+	0.644873i	$0.223090\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.36800	+	4.10150i	0.261502	+	0.452935i
$83$			10.2045i			1.12009i	0.828462	+	0.560046i	$0.189216\pi$
$83$			10.2045i			1.12009i	−0.828462	+	0.560046i	$0.810784\pi$
$84$	1.04466	−	0.603137i	0.113982	−	0.0658076i
$85$		0			0
$86$		−	1.97389i		−	0.212850i
$87$	−2.38346	−	4.12828i	−0.255534	−	0.442598i
$88$	−2.57603	+	4.46182i	−0.274606	+	0.475631i
$89$	−14.1941	−	8.19497i	−1.50457	−	0.868665i	−0.999986	−	0.00530346i	$-0.998312\pi$
$89$	−14.1941	−	8.19497i	−1.50457	−	0.868665i	−0.504586	−	0.863361i	$-0.668355\pi$
$90$		0			0
$91$	4.30137	+	0.643777i	0.450906	+	0.0674862i
$92$	−2.17422			−0.226678
$93$	−5.11861	−	2.95523i	−0.530775	−	0.306443i
$94$	−0.426148	+	0.738110i	−0.0439538	+	0.0761302i
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	7.34631	−	4.24139i	0.745904	−	0.430648i	−0.0783078	−	0.996929i	$-0.524952\pi$
$97$	7.34631	−	4.24139i	0.745904	−	0.430648i	0.824212	+	0.566281i	$0.191618\pi$
$98$	−4.80203	+	2.77245i	−0.485078	+	0.280060i
$99$		−	5.15206i		−	0.517802i
$100$		0			0
$101$	6.79121	−	11.7627i	0.675751	−	1.17044i	−0.300498	−	0.953783i	$-0.597153\pi$
$101$	6.79121	−	11.7627i	0.675751	−	1.17044i	0.976249	−	0.216653i	$-0.0695139\pi$
$102$	−4.10150	−	2.36800i	−0.406109	−	0.234467i
$103$	−2.15696			−0.212531			−0.106266	−	0.994338i	$-0.533889\pi$
$103$	−2.15696			−0.212531			−0.106266	+	0.994338i	$0.533889\pi$
$104$	2.24511	−	2.82126i	0.220151	−	0.276647i
$105$		0			0
$106$	−3.88016	−	2.24021i	−0.376874	−	0.217588i
$107$	4.04699	−	7.00959i	0.391237	−	0.677642i	−0.601376	−	0.798966i	$-0.705381\pi$
$107$	4.04699	−	7.00959i	0.391237	−	0.677642i	0.992613	+	0.121324i	$0.0387139\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$			16.8839i			1.61718i	0.588370	+	0.808592i	$0.299770\pi$
$109$			16.8839i			1.61718i	−0.588370	+	0.808592i	$0.700230\pi$
$110$		0			0
$111$	3.81110	−	2.20034i	0.361734	−	0.208847i
$112$		−	1.20627i		−	0.113982i
$113$	2.47551	+	4.28771i	0.232876	+	0.403354i	0.958653	−	0.284576i	$-0.0918530\pi$
$113$	2.47551	+	4.28771i	0.232876	+	0.403354i	−0.725777	+	0.687930i	$0.758520\pi$
$114$	−1.06506	+	1.84474i	−0.0997519	+	0.172775i
$115$		0			0
$116$	−4.76693			−0.442598
$117$	−0.533691	+	3.56583i	−0.0493397	+	0.329661i
$118$	−1.94143			−0.178723
$119$	−4.94754	−	2.85646i	−0.453540	−	0.261851i
$120$		0			0
$121$	7.77188	+	13.4613i	0.706535	+	1.22375i
$122$		−	3.07591i		−	0.278480i
$123$	−4.10150	+	2.36800i	−0.369820	+	0.213516i
$124$	−5.11861	+	2.95523i	−0.459665	+	0.265388i
$125$		0			0
$126$	0.603137	+	1.04466i	0.0537317	+	0.0930660i
$127$	−0.600957	+	1.04089i	−0.0533263	+	0.0923639i	−0.891456	−	0.453107i	$-0.850316\pi$
$127$	−0.600957	+	1.04089i	−0.0533263	+	0.0923639i	0.838130	+	0.545471i	$0.183649\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	1.97389			0.173791
$130$		0			0
$131$	−6.65149			−0.581143			−0.290572	−	0.956853i	$-0.593845\pi$
$131$	−6.65149			−0.581143			−0.290572	+	0.956853i	$0.593845\pi$
$132$	−4.46182	−	2.57603i	−0.388351	−	0.224215i
$133$	−1.28475	+	2.22526i	−0.111402	+	0.192954i
$134$	−7.02765	−	12.1723i	−0.607097	−	1.05152i
$135$		0			0
$136$	−4.10150	+	2.36800i	−0.351701	+	0.203055i
$137$	−12.7435	+	7.35746i	−1.08875	+	0.628590i	−0.933243	−	0.359245i	$-0.883034\pi$
$137$	−12.7435	+	7.35746i	−1.08875	+	0.628590i	−0.155507	+	0.987835i	$0.549701\pi$
$138$		−	2.17422i		−	0.185082i
$139$	7.82540	+	13.5540i	0.663742	+	1.14963i	0.979625	+	0.200837i	$0.0643660\pi$
$139$	7.82540	+	13.5540i	0.663742	+	1.14963i	−0.315883	+	0.948798i	$0.602301\pi$
$140$		0			0
$141$	−0.738110	−	0.426148i	−0.0621600	−	0.0358881i
$142$	−0.344918			−0.0289448
$143$	−6.80447	−	17.2849i	−0.569018	−	1.44544i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−7.86142	+	13.6164i	−0.650615	+	1.12690i
$147$	−2.77245	−	4.80203i	−0.228668	−	0.396065i
$148$		−	4.40068i		−	0.361734i
$149$	19.7555	−	11.4058i	1.61843	−	0.934401i	0.631103	−	0.775699i	$-0.282602\pi$
$149$	19.7555	−	11.4058i	1.61843	−	0.934401i	0.987327	−	0.158702i	$-0.0507309\pi$
$150$		0			0
$151$		−	19.8995i		−	1.61940i	−0.586845	−	0.809699i	$-0.699630\pi$
$151$		−	19.8995i		−	1.61940i	0.586845	−	0.809699i	$-0.300370\pi$
$152$	1.06506	+	1.84474i	0.0863877	+	0.149628i
$153$	2.36800	−	4.10150i	0.191442	−	0.331587i
$154$	−5.38217	−	3.10740i	−0.433708	−	0.250401i
$155$		0			0
$156$	2.82126	+	2.24511i	0.225881	+	0.179752i
$157$	−4.74392			−0.378606			−0.189303	−	0.981919i	$-0.560623\pi$
$157$	−4.74392			−0.378606			−0.189303	+	0.981919i	$0.560623\pi$
$158$	11.7661	+	6.79315i	0.936060	+	0.540434i
$159$	2.24021	−	3.88016i	0.177660	−	0.307716i
$160$		0			0
$161$		−	2.62270i		−	0.206698i
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$	−3.34855	+	1.93329i	−0.262279	+	0.151427i	−0.625374	−	0.780325i	$-0.715053\pi$
$163$	−3.34855	+	1.93329i	−0.262279	+	0.151427i	0.363095	+	0.931752i	$0.381720\pi$
$164$			4.73601i			0.369820i
$165$		0			0
$166$	−5.10226	+	8.83737i	−0.396012	+	0.685913i
$167$	19.6785	+	11.3614i	1.52277	+	0.879173i	0.999638	+	0.0269225i	$0.00857073\pi$
$167$	19.6785	+	11.3614i	1.52277	+	0.879173i	0.523134	+	0.852250i	$0.324763\pi$
$168$	1.20627			0.0930660
$169$	2.91899	+	12.6681i	0.224538	+	0.974465i
$170$		0			0
$171$	−1.84474	−	1.06506i	−0.141071	−	0.0814471i
$172$	0.986944	−	1.70944i	0.0752538	−	0.130343i
$173$	−2.34900	−	4.06859i	−0.178591	−	0.309329i	0.762807	−	0.646626i	$-0.223821\pi$
$173$	−2.34900	−	4.06859i	−0.178591	−	0.309329i	−0.941398	+	0.337297i	$0.890487\pi$
$174$		−	4.76693i		−	0.361380i
$175$		0			0
$176$	−4.46182	+	2.57603i	−0.336322	+	0.194176i
$177$		−	1.94143i		−	0.145927i
$178$	−8.19497	−	14.1941i	−0.614239	−	1.06389i
$179$	4.34913	−	7.53292i	0.325069	−	0.563037i	−0.656457	−	0.754363i	$-0.727946\pi$
$179$	4.34913	−	7.53292i	0.325069	−	0.563037i	0.981526	+	0.191327i	$0.0612790\pi$
$180$		0			0
$181$	9.75480			0.725069			0.362534	−	0.931970i	$-0.381912\pi$
$181$	9.75480			0.725069			0.362534	+	0.931970i	$0.381912\pi$
$182$	3.40321	+	2.70821i	0.252263	+	0.200746i
$183$	3.07591			0.227378
$184$	−1.88293	−	1.08711i	−0.138811	−	0.0801427i
$185$		0			0
$186$	−2.95523	−	5.11861i	−0.216688	−	0.375315i
$187$			24.4002i			1.78432i
$188$	−0.738110	+	0.426148i	−0.0538322	+	0.0310800i
$189$	−1.04466	+	0.603137i	−0.0759881	+	0.0438718i
$190$		0			0
$191$	−5.77729	−	10.0066i	−0.418030	−	0.724049i	0.577711	−	0.816241i	$-0.303946\pi$
$191$	−5.77729	−	10.0066i	−0.418030	−	0.724049i	−0.995741	+	0.0921920i	$0.970613\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	9.06130	+	5.23154i	0.652247	+	0.376575i	0.789316	−	0.613987i	$-0.210435\pi$
$193$	9.06130	+	5.23154i	0.652247	+	0.376575i	−0.137070	+	0.990561i	$0.543768\pi$
$194$	8.48278			0.609028
$195$		0			0
$196$	−5.54490			−0.396065
$197$	15.2329	+	8.79472i	1.08530	+	0.626598i	0.932321	−	0.361632i	$-0.117780\pi$
$197$	15.2329	+	8.79472i	1.08530	+	0.626598i	0.152978	+	0.988230i	$0.451113\pi$
$198$	2.57603	−	4.46182i	0.183071	−	0.317088i
$199$	−12.7858	−	22.1457i	−0.906362	−	1.56986i	−0.819079	−	0.573681i	$-0.805515\pi$
$199$	−12.7858	−	22.1457i	−0.906362	−	1.56986i	−0.0872828	−	0.996184i	$-0.527818\pi$
$200$		0			0
$201$	12.1723	−	7.02765i	0.858564	−	0.495692i
$202$	11.7627	−	6.79121i	0.827623	−	0.477828i
$203$		−	5.75022i		−	0.403586i
$204$	−2.36800	−	4.10150i	−0.165793	−	0.287163i
$205$		0			0
$206$	−1.86798	−	1.07848i	−0.130148	−	0.0751412i
$207$	2.17422			0.151119
$208$	3.35495	−	1.32073i	0.232624	−	0.0915760i
$209$	10.9745			0.759122
$210$		0			0
$211$	−6.45984	+	11.1888i	−0.444714	+	0.770267i	−0.998032	−	0.0627029i	$-0.980028\pi$
$211$	−6.45984	+	11.1888i	−0.444714	+	0.770267i	0.553318	+	0.832970i	$0.313361\pi$
$212$	−2.24021	−	3.88016i	−0.153858	−	0.266490i
$213$		−	0.344918i		−	0.0236334i
$214$	7.00959	−	4.04699i	0.479165	−	0.276646i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	−3.56482	−	6.17445i	−0.241996	−	0.419149i
$218$	−8.44195	+	14.6219i	−0.571761	+	0.990319i
$219$	−13.6164	−	7.86142i	−0.920109	−	0.531225i
$220$		0			0
$221$	2.52757	−	16.8878i	0.170022	−	1.13600i
$222$	4.40068			0.295354
$223$	−6.19518	−	3.57679i	−0.414860	−	0.239519i	0.278016	−	0.960576i	$-0.410323\pi$
$223$	−6.19518	−	3.57679i	−0.414860	−	0.239519i	−0.692876	+	0.721057i	$0.743657\pi$
$224$	0.603137	−	1.04466i	0.0402988	−	0.0697995i
$225$		0			0
$226$			4.95102i			0.329337i
$227$	22.3768	−	12.9192i	1.48520	−	0.857480i	0.485340	−	0.874325i	$-0.338696\pi$
$227$	22.3768	−	12.9192i	1.48520	−	0.857480i	0.999858	+	0.0168460i	$0.00536249\pi$
$228$	−1.84474	+	1.06506i	−0.122171	+	0.0705353i
$229$			8.95153i			0.591533i	0.955260	+	0.295767i	$0.0955751\pi$
$229$			8.95153i			0.591533i	−0.955260	+	0.295767i	$0.904425\pi$
$230$		0			0
$231$	3.10740	−	5.38217i	0.204452	−	0.354121i
$232$	−4.12828	−	2.38346i	−0.271035	−	0.156482i
$233$	−3.86657			−0.253308			−0.126654	−	0.991947i	$-0.540424\pi$
$233$	−3.86657			−0.253308			−0.126654	+	0.991947i	$0.540424\pi$
$234$	−2.24511	+	2.82126i	−0.146767	+	0.184431i
$235$		0			0
$236$	−1.68133	−	0.970715i	−0.109445	−	0.0631882i
$237$	−6.79315	+	11.7661i	−0.441263	+	0.764290i
$238$	−2.85646	−	4.94754i	−0.185157	−	0.320701i
$239$		−	15.4177i		−	0.997286i	−0.866807	−	0.498643i	$-0.833832\pi$
$239$		−	15.4177i		−	0.997286i	0.866807	−	0.498643i	$-0.166168\pi$
$240$		0			0
$241$	9.76603	−	5.63842i	0.629085	−	0.363203i	−0.151312	−	0.988486i	$-0.548350\pi$
$241$	9.76603	−	5.63842i	0.629085	−	0.363203i	0.780398	+	0.625283i	$0.215017\pi$
$242$			15.5438i			0.999191i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	1.53795	−	2.66381i	0.0984574	−	0.170533i
$245$		0			0
$246$	−4.73601			−0.301957
$247$	−7.59565	−	1.13682i	−0.483299	−	0.0723344i
$248$	−5.91046			−0.375315
$249$	−8.83737	−	5.10226i	−0.560046	−	0.323342i
$250$		0			0
$251$	6.15329	+	10.6578i	0.388392	+	0.672715i	0.992233	−	0.124390i	$-0.0396973\pi$
$251$	6.15329	+	10.6578i	0.388392	+	0.672715i	−0.603841	+	0.797104i	$0.706364\pi$
$252$			1.20627i			0.0759881i
$253$	−9.70096	+	5.60085i	−0.609894	+	0.352123i
$254$	−1.04089	+	0.600957i	−0.0653112	+	0.0377074i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−14.0434	+	24.3239i	−0.876004	+	1.51728i	−0.0203154	+	0.999794i	$0.506467\pi$
$257$	−14.0434	+	24.3239i	−0.876004	+	1.51728i	−0.855689	+	0.517490i	$0.826866\pi$
$258$	1.70944	+	0.986944i	0.106425	+	0.0614444i
$259$	5.30842			0.329849
$260$		0			0
$261$	4.76693			0.295065
$262$	−5.76036	−	3.32575i	−0.355876	−	0.205465i
$263$	3.79178	−	6.56756i	0.233811	−	0.404973i	−0.725115	−	0.688628i	$-0.758213\pi$
$263$	3.79178	−	6.56756i	0.233811	−	0.404973i	0.958927	+	0.283654i	$0.0915468\pi$
$264$	−2.57603	−	4.46182i	−0.158544	−	0.274606i
$265$		0			0
$266$	−2.22526	+	1.28475i	−0.136439	+	0.0787732i
$267$	14.1941	−	8.19497i	0.868665	−	0.501524i
$268$		−	14.0553i		−	0.858564i
$269$	12.2355	+	21.1924i	0.746010	+	1.29213i	0.949722	+	0.313096i	$0.101366\pi$
$269$	12.2355	+	21.1924i	0.746010	+	1.29213i	−0.203712	+	0.979031i	$0.565301\pi$
$270$		0			0
$271$	10.0199	+	5.78497i	0.608664	+	0.351412i	0.772442	−	0.635085i	$-0.219035\pi$
$271$	10.0199	+	5.78497i	0.608664	+	0.351412i	−0.163779	+	0.986497i	$0.552368\pi$
$272$	−4.73601			−0.287163
$273$	−2.70821	+	3.40321i	−0.163909	+	0.205972i
$274$	−14.7149			−0.888961
$275$		0			0
$276$	1.08711	−	1.88293i	0.0654363	−	0.113339i
$277$	−6.47271	−	11.2111i	−0.388908	−	0.673608i	0.603395	−	0.797442i	$-0.293814\pi$
$277$	−6.47271	−	11.2111i	−0.388908	−	0.673608i	−0.992303	+	0.123835i	$0.960481\pi$
$278$			15.6508i			0.938673i
$279$	5.11861	−	2.95523i	0.306443	−	0.176925i
$280$		0			0
$281$			2.57187i			0.153425i	0.997053	+	0.0767124i	$0.0244423\pi$
$281$			2.57187i			0.153425i	−0.997053	+	0.0767124i	$0.975558\pi$
$282$	−0.426148	−	0.738110i	−0.0253767	−	0.0439538i
$283$	−2.77427	+	4.80517i	−0.164913	+	0.285638i	−0.936624	−	0.350335i	$-0.886068\pi$
$283$	−2.77427	+	4.80517i	−0.164913	+	0.285638i	0.771711	+	0.635973i	$0.219401\pi$
$284$	−0.298707	−	0.172459i	−0.0177250	−	0.0102335i
$285$		0			0
$286$	2.74961	−	18.3714i	0.162588	−	1.08632i
$287$	−5.71292			−0.337223
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	−2.71489	+	4.70233i	−0.159700	+	0.276608i
$290$		0			0
$291$			8.48278i			0.497270i
$292$	−13.6164	+	7.86142i	−0.796838	+	0.460055i
$293$	20.8986	−	12.0658i	1.22091	−	0.704891i	0.255795	−	0.966731i	$-0.417663\pi$
$293$	20.8986	−	12.0658i	1.22091	−	0.704891i	0.965111	+	0.261840i	$0.0843293\pi$
$294$		−	5.54490i		−	0.323385i
$295$		0			0
$296$	2.20034	−	3.81110i	0.127892	−	0.221516i
$297$	4.46182	+	2.57603i	0.258901	+	0.149477i
$298$	22.8116			1.32144
$299$	7.29439	−	2.87155i	0.421845	−	0.166066i
$300$		0			0
$301$	2.06205	+	1.19052i	0.118855	+	0.0686207i
$302$	9.94975	−	17.2335i	0.572544	−	0.991675i
$303$	6.79121	+	11.7627i	0.390145	+	0.675751i
$304$			2.13012i			0.122171i
$305$		0			0
$306$	4.10150	−	2.36800i	0.234467	−	0.135370i
$307$			30.3243i			1.73070i	0.501171	+	0.865348i	$0.332903\pi$
$307$			30.3243i			1.73070i	−0.501171	+	0.865348i	$0.667097\pi$
$308$	−3.10740	−	5.38217i	−0.177061	−	0.306678i
$309$	1.07848	−	1.86798i	0.0613525	−	0.106266i
$310$		0			0
$311$	8.76406			0.496964			0.248482	−	0.968636i	$-0.420068\pi$
$311$	8.76406			0.496964			0.248482	+	0.968636i	$0.420068\pi$
$312$	1.32073	+	3.35495i	0.0747715	+	0.189937i
$313$	29.0155			1.64005			0.820026	−	0.572326i	$-0.193959\pi$
$313$	29.0155			1.64005			0.820026	+	0.572326i	$0.193959\pi$
$314$	−4.10836	−	2.37196i	−0.231848	−	0.133857i
$315$		0			0
$316$	6.79315	+	11.7661i	0.382145	+	0.661894i
$317$		−	25.9970i		−	1.46014i	−0.683375	−	0.730068i	$-0.739489\pi$
$317$		−	25.9970i		−	1.46014i	0.683375	−	0.730068i	$-0.260511\pi$
$318$	3.88016	−	2.24021i	0.217588	−	0.125625i
$319$	−21.2692	+	12.2798i	−1.19084	+	0.687534i
$320$		0			0
$321$	4.04699	+	7.00959i	0.225881	+	0.391237i
$322$	1.31135	−	2.27133i	0.0730787	−	0.126576i
$323$	8.73669	+	5.04413i	0.486122	+	0.280663i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−3.86657			−0.214150
$327$	−14.6219	−	8.44195i	−0.808592	−	0.466841i
$328$	−2.36800	+	4.10150i	−0.130751	+	0.226468i
$329$	−0.514051	−	0.890362i	−0.0283405	−	0.0490873i
$330$		0			0
$331$	−9.56025	+	5.51961i	−0.525479	+	0.303385i	−0.739173	−	0.673515i	$-0.764784\pi$
$331$	−9.56025	+	5.51961i	−0.525479	+	0.303385i	0.213694	+	0.976901i	$0.431450\pi$
$332$	−8.83737	+	5.10226i	−0.485014	+	0.280023i
$333$			4.40068i			0.241156i
$334$	11.3614	+	19.6785i	0.621669	+	1.07676i
$335$		0			0
$336$	1.04466	+	0.603137i	0.0569911	+	0.0329038i
$337$	17.7108			0.964769			0.482384	−	0.875960i	$-0.339771\pi$
$337$	17.7108			0.964769			0.482384	+	0.875960i	$0.339771\pi$
$338$	−3.80611	+	12.4303i	−0.207025	+	0.676122i
$339$	−4.95102			−0.268902
$340$		0			0
$341$	−15.2255	+	26.3714i	−0.824509	+	1.42809i
$342$	−1.06506	−	1.84474i	−0.0575918	−	0.0997519i
$343$		−	15.1326i		−	0.817083i
$344$	1.70944	−	0.986944i	0.0921667	−	0.0532124i
$345$		0			0
$346$		−	4.69800i		−	0.252566i
$347$	−17.3509	−	30.0526i	−0.931443	−	1.61331i	−0.780857	−	0.624710i	$-0.785217\pi$
$347$	−17.3509	−	30.0526i	−0.931443	−	1.61331i	−0.150587	−	0.988597i	$-0.548116\pi$
$348$	2.38346	−	4.12828i	0.127767	−	0.221299i
$349$	30.4563	+	17.5840i	1.63029	+	0.941249i	0.984002	+	0.178156i	$0.0570131\pi$
$349$	30.4563	+	17.5840i	1.63029	+	0.941249i	0.646288	+	0.763093i	$0.276320\pi$
$350$		0			0
$351$	−2.82126	−	2.24511i	−0.150588	−	0.119835i
$352$	−5.15206			−0.274606
$353$	−9.60495	−	5.54542i	−0.511220	−	0.295153i	0.222115	−	0.975020i	$-0.428704\pi$
$353$	−9.60495	−	5.54542i	−0.511220	−	0.295153i	−0.733335	+	0.679868i	$0.762037\pi$
$354$	0.970715	−	1.68133i	0.0515929	−	0.0893616i
$355$		0			0
$356$		−	16.3899i		−	0.868665i
$357$	4.94754	−	2.85646i	0.261851	−	0.151180i
$358$	7.53292	−	4.34913i	0.398127	−	0.229859i
$359$		−	26.1575i		−	1.38054i	−0.723552	−	0.690270i	$-0.757492\pi$
$359$		−	26.1575i		−	1.38054i	0.723552	−	0.690270i	$-0.242508\pi$
$360$		0			0
$361$	−7.23130	+	12.5250i	−0.380595	+	0.659209i
$362$	8.44791	+	4.87740i	0.444012	+	0.256351i
$363$	−15.5438			−0.815836
$364$	1.59316	+	4.04699i	0.0835042	+	0.212120i
$365$		0			0
$366$	2.66381	+	1.53795i	0.139240	+	0.0803901i
$367$	7.79352	−	13.4988i	0.406818	−	0.704630i	−0.587713	−	0.809070i	$-0.699972\pi$
$367$	7.79352	−	13.4988i	0.406818	−	0.704630i	0.994531	+	0.104440i	$0.0333049\pi$
$368$	−1.08711	−	1.88293i	−0.0566695	−	0.0981544i
$369$		−	4.73601i		−	0.246547i
$370$		0			0
$371$	4.68053	−	2.70231i	0.243001	−	0.140297i
$372$		−	5.91046i		−	0.306443i
$373$	0.496728	+	0.860358i	0.0257196	+	0.0445476i	0.878599	−	0.477561i	$-0.158479\pi$
$373$	0.496728	+	0.860358i	0.0257196	+	0.0445476i	−0.852879	+	0.522108i	$0.825146\pi$
$374$	−12.2001	+	21.1312i	−0.630853	+	1.09267i
$375$		0			0
$376$	−0.852296			−0.0439538
$377$	15.9928	−	6.29581i	0.823671	−	0.324251i
$378$	−1.20627			−0.0620440
$379$	−23.7856	−	13.7326i	−1.22178	−	0.705398i	−0.256486	−	0.966548i	$-0.582565\pi$
$379$	−23.7856	−	13.7326i	−1.22178	−	0.705398i	−0.965298	+	0.261150i	$0.915898\pi$
$380$		0			0
$381$	−0.600957	−	1.04089i	−0.0307880	−	0.0533263i
$382$		−	11.5546i		−	0.591184i
$383$	28.2067	−	16.2851i	1.44130	−	0.832132i	0.443359	−	0.896344i	$-0.353787\pi$
$383$	28.2067	−	16.2851i	1.44130	−	0.832132i	0.997936	+	0.0642122i	$0.0204534\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$		0			0
$386$	5.23154	+	9.06130i	0.266279	+	0.461208i
$387$	−0.986944	+	1.70944i	−0.0501692	+	0.0868956i
$388$	7.34631	+	4.24139i	0.372952	+	0.215324i
$389$	16.9110			0.857421			0.428710	−	0.903442i	$-0.358968\pi$
$389$	16.9110			0.857421			0.428710	+	0.903442i	$0.358968\pi$
$390$		0			0
$391$	−10.2971			−0.520747
$392$	−4.80203	−	2.77245i	−0.242539	−	0.140030i
$393$	3.32575	−	5.76036i	0.167762	−	0.290572i
$394$	8.79472	+	15.2329i	0.443072	+	0.767423i
$395$		0			0
$396$	4.46182	−	2.57603i	0.224215	−	0.129450i
$397$	27.9204	−	16.1198i	1.40128	−	0.809031i	0.406759	−	0.913536i	$-0.366659\pi$
$397$	27.9204	−	16.1198i	1.40128	−	0.809031i	0.994524	+	0.104504i	$0.0333256\pi$
$398$		−	25.5716i		−	1.28179i
$399$	−1.28475	−	2.22526i	−0.0643181	−	0.111402i
$400$		0			0
$401$	28.0082	+	16.1705i	1.39866	+	0.807518i	0.994253	−	0.107060i	$-0.0341437\pi$
$401$	28.0082	+	16.1705i	1.39866	+	0.807518i	0.404410	+	0.914578i	$0.367477\pi$
$402$	14.0553			0.701015
$403$	13.2696	−	16.6749i	0.661007	−	0.830638i
$404$	13.5824			0.675751
$405$		0			0
$406$	2.87511	−	4.97984i	0.142689	−	0.247145i
$407$	−11.3363	−	19.6350i	−0.561919	−	0.973272i
$408$		−	4.73601i		−	0.234467i
$409$	−1.00971	+	0.582957i	−0.0499270	+	0.0288254i	−0.524756	−	0.851253i	$-0.675843\pi$
$409$	−1.00971	+	0.582957i	−0.0499270	+	0.0288254i	0.474829	+	0.880078i	$0.342510\pi$
$410$		0			0
$411$		−	14.7149i		−	0.725833i
$412$	−1.07848	−	1.86798i	−0.0531328	−	0.0920288i
$413$	1.17095	−	2.02814i	0.0576186	−	0.0997984i
$414$	1.88293	+	1.08711i	0.0925408	+	0.0534285i
$415$		0			0
$416$	3.56583	+	0.533691i	0.174829	+	0.0261663i
$417$	−15.6508			−0.766423
$418$	9.50420	+	5.48725i	0.464866	+	0.268390i
$419$	−5.91396	+	10.2433i	−0.288916	+	0.500417i	−0.973551	−	0.228469i	$-0.926628\pi$
$419$	−5.91396	+	10.2433i	−0.288916	+	0.500417i	0.684635	+	0.728886i	$0.259961\pi$
$420$		0			0
$421$		−	23.9102i		−	1.16531i	−0.812719	−	0.582655i	$-0.802014\pi$
$421$		−	23.9102i		−	1.16531i	0.812719	−	0.582655i	$-0.197986\pi$
$422$	−11.1888	+	6.45984i	−0.544661	+	0.314460i
$423$	0.738110	−	0.426148i	0.0358881	−	0.0207200i
$424$		−	4.48042i		−	0.217588i
$425$		0			0
$426$	0.172459	−	0.298707i	0.00835566	−	0.0144724i
$427$	3.21329	+	1.85519i	0.155502	+	0.0897791i
$428$	8.09397			0.391237
$429$	18.3714	+	2.74961i	0.886980	+	0.132752i
$430$		0			0
$431$	−22.8082	−	13.1683i	−1.09863	−	0.634294i	−0.162769	−	0.986664i	$-0.552043\pi$
$431$	−22.8082	−	13.1683i	−1.09863	−	0.634294i	−0.935861	+	0.352370i	$0.885376\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	6.47972	+	11.2232i	0.311396	+	0.539353i	0.978665	−	0.205464i	$-0.0658702\pi$
$433$	6.47972	+	11.2232i	0.311396	+	0.539353i	−0.667269	+	0.744817i	$0.732537\pi$
$434$		−	7.12964i		−	0.342234i
$435$		0			0
$436$	−14.6219	+	8.44195i	−0.700261	+	0.404296i
$437$			4.63134i			0.221547i
$438$	−7.86142	−	13.6164i	−0.375633	−	0.650615i
$439$	−11.6234	+	20.1324i	−0.554756	+	0.960865i	0.443167	+	0.896439i	$0.353855\pi$
$439$	−11.6234	+	20.1324i	−0.554756	+	0.960865i	−0.997922	+	0.0644259i	$0.979478\pi$
$440$		0			0
$441$	5.54490			0.264043
$442$	10.6328	−	13.3615i	0.505753	−	0.635542i
$443$	23.3728			1.11047			0.555237	−	0.831692i	$-0.312627\pi$
$443$	23.3728			1.11047			0.555237	+	0.831692i	$0.312627\pi$
$444$	3.81110	+	2.20034i	0.180867	+	0.104423i
$445$		0			0
$446$	−3.57679	−	6.19518i	−0.169366	−	0.293350i
$447$			22.8116i			1.07895i
$448$	1.04466	−	0.603137i	0.0493557	−	0.0284955i
$449$	−1.20931	+	0.698196i	−0.0570709	+	0.0329499i	−0.528264	−	0.849080i	$-0.677157\pi$
$449$	−1.20931	+	0.698196i	−0.0570709	+	0.0329499i	0.471193	+	0.882030i	$0.343824\pi$
$450$		0			0
$451$	12.2001	+	21.1312i	0.574481	+	0.995030i
$452$	−2.47551	+	4.28771i	−0.116438	+	0.201677i
$453$	17.2335	+	9.94975i	0.809699	+	0.467480i
$454$	25.8385			1.21266
$455$		0			0
$456$	−2.13012			−0.0997519
$457$	−6.23699	−	3.60093i	−0.291754	−	0.168444i	0.346979	−	0.937873i	$-0.387208\pi$
$457$	−6.23699	−	3.60093i	−0.291754	−	0.168444i	−0.638733	+	0.769429i	$0.720541\pi$
$458$	−4.47576	+	7.75225i	−0.209139	+	0.362239i
$459$	2.36800	+	4.10150i	0.110529	+	0.191442i
$460$		0			0
$461$	−4.10920	+	2.37245i	−0.191384	+	0.110496i	−0.592630	−	0.805474i	$-0.701911\pi$
$461$	−4.10920	+	2.37245i	−0.191384	+	0.110496i	0.401246	+	0.915970i	$0.368577\pi$
$462$	5.38217	−	3.10740i	0.250401	−	0.144569i
$463$			15.7510i			0.732012i	0.930612	+	0.366006i	$0.119275\pi$
$463$			15.7510i			0.732012i	−0.930612	+	0.366006i	$0.880725\pi$
$464$	−2.38346	−	4.12828i	−0.110650	−	0.191651i
$465$		0			0
$466$	−3.34855	−	1.93329i	−0.155119	−	0.0895578i
$467$	17.9789			0.831962			0.415981	−	0.909373i	$-0.363438\pi$
$467$	17.9789			0.831962			0.415981	+	0.909373i	$0.363438\pi$
$468$	−3.35495	+	1.32073i	−0.155083	+	0.0610506i
$469$	16.9545			0.782888
$470$		0			0
$471$	2.37196	−	4.10836i	0.109294	−	0.189303i
$472$	−0.970715	−	1.68133i	−0.0446808	−	0.0773894i
$473$		−	10.1696i		−	0.467598i
$474$	−11.7661	+	6.79315i	−0.540434	+	0.312020i
$475$		0			0
$476$		−	5.71292i		−	0.261851i
$477$	2.24021	+	3.88016i	0.102572	+	0.177660i
$478$	7.70884	−	13.3521i	0.352594	−	0.610711i
$479$	−2.83964	−	1.63947i	−0.129747	−	0.0749093i	0.433722	−	0.901047i	$-0.357200\pi$
$479$	−2.83964	−	1.63947i	−0.129747	−	0.0749093i	−0.563468	+	0.826138i	$0.690533\pi$
$480$		0			0
$481$	5.81210	+	14.7640i	0.265009	+	0.673183i
$482$	11.2768			0.513646
$483$	2.27133	+	1.31135i	0.103349	+	0.0596685i
$484$	−7.77188	+	13.4613i	−0.353267	+	0.611877i
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	−8.64037	+	4.98852i	−0.391533	+	0.226052i	−0.682824	−	0.730583i	$-0.739248\pi$
$487$	−8.64037	+	4.98852i	−0.391533	+	0.226052i	0.291291	+	0.956634i	$0.405915\pi$
$488$	2.66381	−	1.53795i	0.120585	−	0.0696199i
$489$		−	3.86657i		−	0.174852i
$490$		0			0
$491$	10.0376	−	17.3857i	0.452992	−	0.784605i	−0.545578	−	0.838060i	$-0.683690\pi$
$491$	10.0376	−	17.3857i	0.452992	−	0.784605i	0.998570	+	0.0534548i	$0.0170233\pi$
$492$	−4.10150	−	2.36800i	−0.184910	−	0.106758i
$493$	−22.5762			−1.01678
$494$	−6.00961	−	4.78234i	−0.270385	−	0.215168i
$495$		0			0
$496$	−5.11861	−	2.95523i	−0.229832	−	0.132694i
$497$	0.208033	−	0.360323i	0.00933153	−	0.0161627i
$498$	−5.10226	−	8.83737i	−0.228638	−	0.396012i
$499$		−	23.9474i		−	1.07203i	−0.844208	−	0.536016i	$-0.819929\pi$
$499$		−	23.9474i		−	1.07203i	0.844208	−	0.536016i	$-0.180071\pi$
$500$		0			0
$501$	−19.6785	+	11.3614i	−0.879173	+	0.507591i
$502$			12.3066i			0.549269i
$503$	6.08395	+	10.5377i	0.271270	+	0.469853i	0.969187	−	0.246325i	$-0.0792231\pi$
$503$	6.08395	+	10.5377i	0.271270	+	0.469853i	−0.697917	+	0.716178i	$0.745890\pi$
$504$	−0.603137	+	1.04466i	−0.0268659	+	0.0465330i
$505$		0			0
$506$	−11.2017			−0.497977
$507$	−12.4303	−	3.80611i	−0.552051	−	0.169035i
$508$	−1.20191			−0.0533263
$509$	−34.9666	−	20.1880i	−1.54987	−	0.894817i	−0.998151	−	0.0607857i	$-0.980639\pi$
$509$	−34.9666	−	20.1880i	−1.54987	−	0.894817i	−0.551717	−	0.834031i	$-0.686027\pi$
$510$		0			0
$511$	−9.48302	−	16.4251i	−0.419504	−	0.726602i
$512$		−	1.00000i		−	0.0441942i
$513$	1.84474	−	1.06506i	0.0814471	−	0.0470235i
$514$	−24.3239	+	14.0434i	−1.07288	+	0.619429i
$515$		0			0
$516$	0.986944	+	1.70944i	0.0434478	+	0.0752538i
$517$	−2.19554	+	3.80279i	−0.0965598	+	0.167246i
$518$	4.59723	+	2.65421i	0.201991	+	0.116619i
$519$	4.69800			0.206219
$520$		0			0
$521$	−0.259356			−0.0113626			−0.00568129	−	0.999984i	$-0.501808\pi$
$521$	−0.259356			−0.0113626			−0.00568129	+	0.999984i	$0.501808\pi$
$522$	4.12828	+	2.38346i	0.180690	+	0.104321i
$523$	19.3139	−	33.4527i	0.844539	−	1.46278i	−0.0414825	−	0.999139i	$-0.513208\pi$
$523$	19.3139	−	33.4527i	0.844539	−	1.46278i	0.886021	−	0.463645i	$-0.153459\pi$
$524$	−3.32575	−	5.76036i	−0.145286	−	0.251642i
$525$		0			0
$526$	6.56756	−	3.79178i	0.286359	−	0.165330i
$527$	−24.2418	+	13.9960i	−1.05599	+	0.609676i
$528$		−	5.15206i		−	0.224215i
$529$	9.13639	+	15.8247i	0.397234	+	0.688030i
$530$		0			0
$531$	1.68133	+	0.970715i	0.0729634	+	0.0421255i
$532$	−2.56951			−0.111402
$533$	−6.25498	−	15.8891i	−0.270933	−	0.688232i
$534$	16.3899			0.709262
$535$		0			0
$536$	7.02765	−	12.1723i	0.303548	−	0.525761i
$537$	4.34913	+	7.53292i	0.187679	+	0.325069i
$538$			24.4709i			1.05502i
$539$	−24.7403	+	14.2838i	−1.06564	+	0.615249i
$540$		0			0
$541$			19.4443i			0.835975i	0.908453	+	0.417988i	$0.137264\pi$
$541$			19.4443i			0.835975i	−0.908453	+	0.417988i	$0.862736\pi$
$542$	5.78497	+	10.0199i	0.248486	+	0.430390i
$543$	−4.87740	+	8.44791i	−0.209309	+	0.362534i
$544$	−4.10150	−	2.36800i	−0.175851	−	0.101527i
$545$		0			0
$546$	−4.04699	+	1.59316i	−0.173195	+	0.0681809i
$547$	25.2121			1.07799			0.538997	−	0.842308i	$-0.318803\pi$
$547$	25.2121			1.07799			0.538997	+	0.842308i	$0.318803\pi$
$548$	−12.7435	−	7.35746i	−0.544375	−	0.314295i
$549$	−1.53795	+	2.66381i	−0.0656383	+	0.113689i
$550$		0			0
$551$			10.1541i			0.432580i
$552$	1.88293	−	1.08711i	0.0801427	−	0.0462704i
$553$	−14.1931	+	8.19440i	−0.603553	+	0.348462i
$554$		−	12.9454i		−	0.549998i
$555$		0			0
$556$	−7.82540	+	13.5540i	−0.331871	+	0.574817i
$557$	−9.75916	−	5.63445i	−0.413509	−	0.238739i	0.278787	−	0.960353i	$-0.410067\pi$
$557$	−9.75916	−	5.63445i	−0.413509	−	0.238739i	−0.692296	+	0.721613i	$0.743401\pi$
$558$	5.91046			0.250210
$559$	−1.05345	+	7.03856i	−0.0445560	+	0.297699i
$560$		0			0
$561$	−21.1312	−	12.2001i	−0.892160	−	0.515089i
$562$	−1.28593	+	2.22730i	−0.0542439	+	0.0939531i
$563$	−8.22694	−	14.2495i	−0.346724	−	0.600544i	0.638941	−	0.769256i	$-0.279373\pi$
$563$	−8.22694	−	14.2495i	−0.346724	−	0.600544i	−0.985665	+	0.168712i	$0.946039\pi$
$564$		−	0.852296i		−	0.0358881i
$565$		0			0
$566$	−4.80517	+	2.77427i	−0.201976	+	0.116611i
$567$		−	1.20627i		−	0.0506587i
$568$	−0.172459	−	0.298707i	−0.00723621	−	0.0125335i
$569$	−15.2444	+	26.4040i	−0.639077	+	1.10691i	0.346558	+	0.938028i	$0.387350\pi$
$569$	−15.2444	+	26.4040i	−0.639077	+	1.10691i	−0.985636	+	0.168886i	$0.945983\pi$
$570$		0			0
$571$	13.0909			0.547836			0.273918	−	0.961753i	$-0.411680\pi$
$571$	13.0909			0.547836			0.273918	+	0.961753i	$0.411680\pi$
$572$	11.5669	−	14.5353i	0.483638	−	0.607751i
$573$	11.5546			0.482699
$574$	−4.94754	−	2.85646i	−0.206506	−	0.119226i
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$		−	13.1315i		−	0.546670i	−0.961919	−	0.273335i	$-0.911873\pi$
$577$		−	13.1315i		−	0.546670i	0.961919	−	0.273335i	$-0.0881268\pi$
$578$	−4.70233	+	2.71489i	−0.195591	+	0.112925i
$579$	−9.06130	+	5.23154i	−0.376575	+	0.217416i
$580$		0			0
$581$	−6.15472	−	10.6603i	−0.255341	−	0.442263i
$582$	−4.24139	+	7.34631i	−0.175811	+	0.304514i
$583$	−19.9908	−	11.5417i	−0.827935	−	0.478009i
$584$	−15.7228			−0.650615
$585$		0			0
$586$	24.1316			0.996866
$587$	5.26171	+	3.03785i	0.217174	+	0.125386i	0.604641	−	0.796498i	$-0.293317\pi$
$587$	5.26171	+	3.03785i	0.217174	+	0.125386i	−0.387467	+	0.921884i	$0.626650\pi$
$588$	2.77245	−	4.80203i	0.114334	−	0.198032i
$589$	6.29499	+	10.9032i	0.259381	+	0.449260i
$590$		0			0
$591$	−15.2329	+	8.79472i	−0.626598	+	0.361767i
$592$	3.81110	−	2.20034i	0.156635	−	0.0904334i
$593$		−	18.3609i		−	0.753990i	−0.926215	−	0.376995i	$-0.876957\pi$
$593$		−	18.3609i		−	0.753990i	0.926215	−	0.376995i	$-0.123043\pi$
$594$	2.57603	+	4.46182i	0.105696	+	0.183071i
$595$		0			0
$596$	19.7555	+	11.4058i	0.809215	+	0.467200i
$597$	25.5716			1.04658
$598$	7.75290	+	1.16036i	0.317040	+	0.0474507i
$599$	−22.1098			−0.903382			−0.451691	−	0.892174i	$-0.649179\pi$
$599$	−22.1098			−0.903382			−0.451691	+	0.892174i	$0.649179\pi$
$600$		0			0
$601$	−5.90349	+	10.2251i	−0.240808	+	0.417092i	−0.960945	−	0.276740i	$-0.910746\pi$
$601$	−5.90349	+	10.2251i	−0.240808	+	0.417092i	0.720136	+	0.693832i	$0.244079\pi$
$602$	1.19052	+	2.06205i	0.0485222	+	0.0840428i
$603$			14.0553i			0.572376i
$604$	17.2335	−	9.94975i	0.701220	−	0.404850i
$605$		0			0
$606$			13.5824i			0.551748i
$607$	12.8818	+	22.3119i	0.522856	+	0.905612i	0.999646	+	0.0265955i	$0.00846661\pi$
$607$	12.8818	+	22.3119i	0.522856	+	0.905612i	−0.476791	+	0.879017i	$0.658200\pi$
$608$	−1.06506	+	1.84474i	−0.0431938	+	0.0748139i
$609$	4.97984	+	2.87511i	0.201793	+	0.116505i
$610$		0			0
$611$	1.91349	−	2.40455i	0.0774117	−	0.0972775i
$612$	4.73601			0.191442
$613$	−11.3307	−	6.54178i	−0.457642	−	0.264220i	0.253410	−	0.967359i	$-0.418448\pi$
$613$	−11.3307	−	6.54178i	−0.457642	−	0.264220i	−0.711052	+	0.703139i	$0.751781\pi$
$614$	−15.1621	+	26.2616i	−0.611894	+	1.05983i
$615$		0			0
$616$		−	6.21480i		−	0.250401i
$617$	3.82634	−	2.20914i	0.154043	−	0.0889366i	−0.420997	−	0.907062i	$-0.638320\pi$
$617$	3.82634	−	2.20914i	0.154043	−	0.0889366i	0.575040	+	0.818125i	$0.304986\pi$
$618$	1.86798	−	1.07848i	0.0751412	−	0.0433828i
$619$			1.12760i			0.0453220i	0.999743	+	0.0226610i	$0.00721383\pi$
$619$			1.12760i			0.0453220i	−0.999743	+	0.0226610i	$0.992786\pi$
$620$		0			0
$621$	−1.08711	+	1.88293i	−0.0436242	+	0.0755593i
$622$	7.58990	+	4.38203i	0.304327	+	0.175703i
$623$	19.7708			0.792099
$624$	−0.533691	+	3.56583i	−0.0213647	+	0.142748i
$625$		0			0
$626$	25.1282	+	14.5077i	1.00432	+	0.579846i
$627$	−5.48725	+	9.50420i	−0.219140	+	0.379561i
$628$	−2.37196	−	4.10836i	−0.0946515	−	0.163941i
$629$		−	20.8417i		−	0.831011i
$630$		0			0
$631$	−14.3916	+	8.30898i	−0.572920	+	0.330775i	−0.758315	−	0.651889i	$-0.773977\pi$
$631$	−14.3916	+	8.30898i	−0.572920	+	0.330775i	0.185395	+	0.982664i	$0.440644\pi$
$632$			13.5863i			0.540434i
$633$	−6.45984	−	11.1888i	−0.256756	−	0.444714i
$634$	12.9985	−	22.5140i	0.516236	−	0.894147i
$635$		0			0
$636$	4.48042			0.177660
$637$	18.6029	−	7.32331i	0.737072	−	0.290160i
$638$	−24.5595			−0.972320
$639$	0.298707	+	0.172459i	0.0118167	+	0.00682236i
$640$		0			0
$641$	5.05184	+	8.75005i	0.199536	+	0.345606i	0.948378	−	0.317142i	$-0.102723\pi$
$641$	5.05184	+	8.75005i	0.199536	+	0.345606i	−0.748842	+	0.662748i	$0.769390\pi$
$642$			8.09397i			0.319444i
$643$	−30.3469	+	17.5208i	−1.19676	+	0.690951i	−0.959832	−	0.280575i	$-0.909475\pi$
$643$	−30.3469	+	17.5208i	−1.19676	+	0.690951i	−0.236931	+	0.971526i	$0.576142\pi$
$644$	2.27133	−	1.31135i	0.0895028	−	0.0516745i
$645$		0			0
$646$	5.04413	+	8.73669i	0.198459	+	0.343740i
$647$	9.98031	−	17.2864i	0.392366	−	0.679598i	−0.600395	−	0.799704i	$-0.704990\pi$
$647$	9.98031	−	17.2864i	0.392366	−	0.679598i	0.992761	+	0.120105i	$0.0383232\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−10.0024			−0.392628
$650$		0			0
$651$	7.12964			0.279433
$652$	−3.34855	−	1.93329i	−0.131139	−	0.0757133i
$653$	2.60621	−	4.51410i	0.101989	−	0.176650i	−0.810515	−	0.585718i	$-0.800813\pi$
$653$	2.60621	−	4.51410i	0.101989	−	0.176650i	0.912504	+	0.409068i	$0.134146\pi$
$654$	−8.44195	−	14.6219i	−0.330106	−	0.571761i
$655$		0			0
$656$	−4.10150	+	2.36800i	−0.160137	+	0.0924551i
$657$	13.6164	−	7.86142i	0.531225	−	0.306703i
$658$		−	1.02810i		−	0.0400796i
$659$	−3.66183	−	6.34248i	−0.142645	−	0.247068i	0.785847	−	0.618421i	$-0.212227\pi$
$659$	−3.66183	−	6.34248i	−0.142645	−	0.247068i	−0.928492	+	0.371353i	$0.878894\pi$
$660$		0			0
$661$	−31.7189	−	18.3129i	−1.23372	−	0.712289i	−0.265917	−	0.963996i	$-0.585675\pi$
$661$	−31.7189	−	18.3129i	−1.23372	−	0.712289i	−0.967803	+	0.251707i	$0.919008\pi$
$662$	−11.0392			−0.429052
$663$	13.3615	+	10.6328i	0.518918	+	0.412946i
$664$	−10.2045			−0.396012
$665$		0			0
$666$	−2.20034	+	3.81110i	−0.0852614	+	0.147677i
$667$	−5.18217	−	8.97578i	−0.200654	−	0.347543i
$668$			22.7228i			0.879173i
$669$	6.19518	−	3.57679i	0.239519	−	0.138287i
$670$		0			0
$671$		−	15.8473i		−	0.611777i
$672$	0.603137	+	1.04466i	0.0232665	+	0.0402988i
$673$	16.9909	−	29.4292i	0.654952	−	1.13441i	−0.326953	−	0.945041i	$-0.606022\pi$
$673$	16.9909	−	29.4292i	0.654952	−	1.13441i	0.981906	−	0.189370i	$-0.0606447\pi$
$674$	15.3380	+	8.85540i	0.590798	+	0.341097i
$675$		0			0
$676$	−9.51136	+	8.86194i	−0.365822	+	0.340844i
$677$	−41.7902			−1.60613			−0.803063	−	0.595894i	$-0.796798\pi$
$677$	−41.7902			−1.60613			−0.803063	+	0.595894i	$0.796798\pi$
$678$	−4.28771	−	2.47551i	−0.164668	−	0.0950713i
$679$	−5.11628	+	8.86166i	−0.196345	+	0.340079i
$680$		0			0
$681$			25.8385i			0.990132i
$682$	−26.3714	+	15.2255i	−1.00981	+	0.583016i
$683$	41.9280	−	24.2071i	1.60433	−	0.926260i	0.613721	−	0.789523i	$-0.289672\pi$
$683$	41.9280	−	24.2071i	1.60433	−	0.926260i	0.990607	−	0.136737i	$-0.0436616\pi$
$684$		−	2.13012i		−	0.0814471i
$685$		0			0
$686$	7.56629	−	13.1052i	0.288882	−	0.500359i
$687$	−7.75225	−	4.47576i	−0.295767	−	0.170761i
$688$	1.97389			0.0752538
$689$	12.6404	+	10.0590i	0.481562	+	0.383218i
$690$		0			0
$691$	−23.8905	−	13.7932i	−0.908837	−	0.524717i	−0.0287804	−	0.999586i	$-0.509162\pi$
$691$	−23.8905	−	13.7932i	−0.908837	−	0.524717i	−0.880057	+	0.474868i	$0.842496\pi$
$692$	2.34900	−	4.06859i	0.0892955	−	0.154664i
$693$	3.10740	+	5.38217i	0.118040	+	0.204452i
$694$		−	34.7017i		−	1.31726i
$695$		0			0
$696$	4.12828	−	2.38346i	0.156482	−	0.0903449i
$697$			22.4298i			0.849589i
$698$	17.5840	+	30.4563i	0.665563	+	1.15279i
$699$	1.93329	−	3.34855i	0.0731236	−	0.126654i
$700$		0			0
$701$	−19.7883			−0.747392			−0.373696	−	0.927551i	$-0.621910\pi$
$701$	−19.7883			−0.747392			−0.373696	+	0.927551i	$0.621910\pi$
$702$	−1.32073	−	3.35495i	−0.0498476	−	0.126624i
$703$	−9.37396			−0.353546
$704$	−4.46182	−	2.57603i	−0.168161	−	0.0970879i
$705$		0			0
$706$	−5.54542	−	9.60495i	−0.208705	−	0.361487i
$707$			16.3841i			0.616189i
$708$	1.68133	−	0.970715i	0.0631882	−	0.0364817i
$709$	6.09389	−	3.51831i	0.228861	−	0.132133i	−0.381186	−	0.924499i	$-0.624484\pi$
$709$	6.09389	−	3.51831i	0.228861	−	0.132133i	0.610046	+	0.792366i	$0.291151\pi$
$710$		0			0
$711$	−6.79315	−	11.7661i	−0.254763	−	0.441263i
$712$	8.19497	−	14.1941i	0.307119	−	0.531946i
$713$	−11.1290	−	6.42532i	−0.416783	−	0.240630i
$714$	5.71292			0.213801
$715$		0			0
$716$	8.69827			0.325069
$717$	13.3521	+	7.70884i	0.498643	+	0.287892i
$718$	13.0788	−	22.6531i	0.488095	−	0.845405i
$719$	5.52118	+	9.56296i	0.205905	+	0.356638i	0.950421	−	0.310967i	$-0.100653\pi$
$719$	5.52118	+	9.56296i	0.205905	+	0.356638i	−0.744516	+	0.667605i	$0.767319\pi$
$720$		0			0
$721$	2.25330	−	1.30094i	0.0839171	−	0.0484496i
$722$	−12.5250	+	7.23130i	−0.466131	+	0.269121i
$723$			11.2768i			0.419390i
$724$	4.87740	+	8.44791i	0.181267	+	0.313964i
$725$		0			0
$726$	−13.4613	−	7.77188i	−0.499595	−	0.288442i
$727$	14.1056			0.523147			0.261573	−	0.965184i	$-0.415759\pi$
$727$	14.1056			0.523147			0.261573	+	0.965184i	$0.415759\pi$
$728$	−0.643777	+	4.30137i	−0.0238600	+	0.159419i
$729$	1.00000			0.0370370
$730$		0			0
$731$	4.67418	−	8.09591i	0.172881	−	0.299438i
$732$	1.53795	+	2.66381i	0.0568444	+	0.0984574i
$733$			11.3855i			0.420535i	0.977644	+	0.210267i	$0.0674334\pi$
$733$			11.3855i			0.420535i	−0.977644	+	0.210267i	$0.932567\pi$
$734$	13.4988	−	7.79352i	0.498249	−	0.287664i
$735$		0			0
$736$		−	2.17422i		−	0.0801427i
$737$	−36.2069	−	62.7122i	−1.33370	−	2.31003i
$738$	2.36800	−	4.10150i	0.0871675	−	0.150978i
$739$	7.93251	+	4.57983i	0.291802	+	0.168472i	0.638754	−	0.769411i	$-0.279450\pi$
$739$	7.93251	+	4.57983i	0.291802	+	0.168472i	−0.346952	+	0.937883i	$0.612783\pi$
$740$		0			0
$741$	4.78234	−	6.00961i	0.175684	−	0.220769i
$742$	5.40461			0.198410
$743$	−34.5658	−	19.9566i	−1.26809	−	0.732135i	−0.293468	−	0.955969i	$-0.594809\pi$
$743$	−34.5658	−	19.9566i	−1.26809	−	0.732135i	−0.974627	+	0.223834i	$0.928143\pi$
$744$	2.95523	−	5.11861i	0.108344	−	0.187657i
$745$		0			0
$746$			0.993455i			0.0363730i
$747$	8.83737	−	5.10226i	0.323342	−	0.186682i
$748$	−21.1312	+	12.2001i	−0.772634	+	0.446080i
$749$			9.76355i			0.356752i
$750$		0			0
$751$	8.79993	−	15.2419i	0.321114	−	0.556186i	−0.659604	−	0.751613i	$-0.729276\pi$
$751$	8.79993	−	15.2419i	0.321114	−	0.556186i	0.980718	+	0.195427i	$0.0626094\pi$
$752$	−0.738110	−	0.426148i	−0.0269161	−	0.0155400i
$753$	−12.3066			−0.448476
$754$	16.9981	+	2.54407i	0.619033	+	0.0926494i
$755$		0			0
$756$	−1.04466	−	0.603137i	−0.0379941	−	0.0219359i
$757$	−11.0331	+	19.1099i	−0.401004	+	0.694560i	−0.993847	−	0.110758i	$-0.964672\pi$
$757$	−11.0331	+	19.1099i	−0.401004	+	0.694560i	0.592843	+	0.805318i	$0.298005\pi$
$758$	−13.7326	−	23.7856i	−0.498791	−	0.863932i
$759$		−	11.2017i		−	0.406596i
$760$		0			0
$761$	−17.4454	+	10.0721i	−0.632394	+	0.365113i	−0.781678	−	0.623682i	$-0.785636\pi$
$761$	−17.4454	+	10.0721i	−0.632394	+	0.365113i	0.149285	+	0.988794i	$0.452303\pi$
$762$		−	1.20191i		−	0.0435408i
$763$	−10.1833	−	17.6380i	−0.368660	−	0.638538i
$764$	5.77729	−	10.0066i	0.209015	−	0.362025i
$765$		0			0
$766$	32.5703			1.17681
$767$	6.92282	+	1.03612i	0.249969	+	0.0374123i
$768$	1.00000			0.0360844
$769$	−26.9356	−	15.5513i	−0.971323	−	0.560794i	−0.0716840	−	0.997427i	$-0.522837\pi$
$769$	−26.9356	−	15.5513i	−0.971323	−	0.560794i	−0.899639	+	0.436634i	$0.856171\pi$
$770$		0			0
$771$	−14.0434	−	24.3239i	−0.505761	−	0.876004i
$772$			10.4631i			0.376575i
$773$	0.720739	−	0.416119i	0.0259232	−	0.0149668i	−0.486982	−	0.873412i	$-0.661902\pi$
$773$	0.720739	−	0.416119i	0.0259232	−	0.0149668i	0.512906	+	0.858445i	$0.328569\pi$
$774$	−1.70944	+	0.986944i	−0.0614444	+	0.0354750i
$775$		0			0
$776$	4.24139	+	7.34631i	0.152257	+	0.263717i
$777$	−2.65421	+	4.59723i	−0.0952193	+	0.164925i
$778$	14.6453	+	8.45549i	0.525061	+	0.303144i
$779$	10.0883			0.361449
$780$		0			0
$781$	−1.77704			−0.0635874
$782$	−8.91756	−	5.14856i	−0.318891	−	0.184112i
$783$	−2.38346	+	4.12828i	−0.0851780	+	0.147533i
$784$	−2.77245	−	4.80203i	−0.0990161	−	0.171501i
$785$		0			0
$786$	5.76036	−	3.32575i	0.205465	−	0.118625i
$787$	−21.4974	+	12.4115i	−0.766298	+	0.442422i	−0.831552	−	0.555446i	$-0.812547\pi$
$787$	−21.4974	+	12.4115i	−0.766298	+	0.442422i	0.0652545	+	0.997869i	$0.479214\pi$
$788$			17.5894i			0.626598i
$789$	3.79178	+	6.56756i	0.134991	+	0.233811i
$790$		0			0
$791$	−5.17215	−	2.98614i	−0.183900	−	0.106175i
$792$	5.15206			0.183071
$793$	−1.64158	+	10.9682i	−0.0582944	+	0.389491i
$794$	32.2397			1.14414
$795$		0			0
$796$	12.7858	−	22.1457i	0.453181	−	0.784932i
$797$	11.8636	+	20.5483i	0.420229	+	0.727858i	0.995962	−	0.0897802i	$-0.0286165\pi$
$797$	11.8636	+	20.5483i	0.420229	+	0.727858i	−0.575733	+	0.817638i	$0.695283\pi$
$798$		−	2.56951i		−	0.0909595i
$799$	−3.49569	+	2.01824i	−0.123669	+	0.0714002i
$800$		0			0
$801$			16.3899i			0.579110i
$802$	16.1705	+	28.0082i	0.571001	+	0.989003i
$803$	−40.5025	+	70.1524i	−1.42930	+	2.47562i
$804$	12.1723	+	7.02765i	0.429282	+	0.247846i
$805$		0			0
$806$	19.8293	−	7.80611i	0.698457	−	0.274959i
$807$	−24.4709			−0.861418
$808$	11.7627	+	6.79121i	0.413811	+	0.238914i
$809$	−18.7196	+	32.4233i	−0.658145	+	1.13994i	0.322950	+	0.946416i	$0.395325\pi$
$809$	−18.7196	+	32.4233i	−0.658145	+	1.13994i	−0.981095	+	0.193525i	$0.938008\pi$
$810$		0			0
$811$		−	40.2205i		−	1.41233i	−0.708046	−	0.706166i	$-0.750423\pi$
$811$		−	40.2205i		−	1.41233i	0.708046	−	0.706166i	$-0.249577\pi$
$812$	4.97984	−	2.87511i	0.174758	−	0.100897i
$813$	−10.0199	+	5.78497i	−0.351412	+	0.202888i
$814$		−	22.6726i		−	0.794673i
$815$		0			0
$816$	2.36800	−	4.10150i	0.0828967	−	0.143581i
$817$	−3.64130	−	2.10231i	−0.127393	−	0.0735504i
$818$	−1.16591			−0.0407652
$819$	−1.59316	−	4.04699i	−0.0556695	−	0.141413i
$820$		0			0
$821$	−24.5442	−	14.1706i	−0.856598	−	0.494557i	0.00627372	−	0.999980i	$-0.498003\pi$
$821$	−24.5442	−	14.1706i	−0.856598	−	0.494557i	−0.862872	+	0.505423i	$0.831336\pi$
$822$	7.35746	−	12.7435i	0.256621	−	0.444480i
$823$	23.6966	+	41.0437i	0.826011	+	1.43069i	0.901144	+	0.433520i	$0.142729\pi$
$823$	23.6966	+	41.0437i	0.826011	+	1.43069i	−0.0751325	+	0.997174i	$0.523938\pi$
$824$		−	2.15696i		−	0.0751412i
$825$		0			0
$826$	2.02814	−	1.17095i	0.0705681	−	0.0407425i
$827$		−	2.70177i		−	0.0939496i	−0.998896	−	0.0469748i	$-0.985042\pi$
$827$		−	2.70177i		−	0.0939496i	0.998896	−	0.0469748i	$-0.0149581\pi$
$828$	1.08711	+	1.88293i	0.0377796	+	0.0654363i
$829$	10.4285	−	18.0627i	0.362197	−	0.627343i	−0.626125	−	0.779722i	$-0.715360\pi$
$829$	10.4285	−	18.0627i	0.362197	−	0.627343i	0.988322	+	0.152379i	$0.0486935\pi$
$830$		0			0
$831$	12.9454			0.449072
$832$	2.82126	+	2.24511i	0.0978095	+	0.0778351i
$833$	−26.2607			−0.909880
$834$	−13.5540	−	7.82540i	−0.469336	−	0.270972i
$835$		0			0
$836$	5.48725	+	9.50420i	0.189781	+	0.328710i
$837$			5.91046i			0.204296i
$838$	−10.2433	+	5.91396i	−0.353848	+	0.204294i
$839$	−5.34438	+	3.08558i	−0.184508	+	0.106526i	−0.589409	−	0.807835i	$-0.700639\pi$
$839$	−5.34438	+	3.08558i	−0.184508	+	0.106526i	0.404901	+	0.914361i	$0.367306\pi$
$840$		0			0
$841$	3.13821	+	5.43553i	0.108214	+	0.187432i
$842$	11.9551	−	20.7068i	0.412000	−	0.713604i
$843$	−2.22730	−	1.28593i	−0.0767124	−	0.0442899i
$844$	−12.9197			−0.444714
$845$		0			0
$846$	0.852296			0.0293025
$847$	−16.2380	−	9.37502i	−0.557944	−	0.322129i
$848$	2.24021	−	3.88016i	0.0769291	−	0.133245i
$849$	−2.77427	−	4.80517i	−0.0952125	−	0.164913i
$850$		0			0
$851$	8.28616	−	4.78402i	0.284046	−	0.163994i
$852$	0.298707	−	0.172459i	0.0102335	−	0.00590834i
$853$			52.4997i			1.79756i	0.438405	+	0.898778i	$0.355544\pi$
$853$			52.4997i			1.79756i	−0.438405	+	0.898778i	$0.644456\pi$
$854$	1.85519	+	3.21329i	0.0634834	+	0.109956i
$855$		0			0
$856$	7.00959	+	4.04699i	0.239583	+	0.138323i
$857$	−23.9128			−0.816846			−0.408423	−	0.912793i	$-0.633921\pi$
$857$	−23.9128			−0.816846			−0.408423	+	0.912793i	$0.633921\pi$
$858$	14.5353	+	11.5669i	0.496227	+	0.394889i
$859$	35.2521			1.20279			0.601393	−	0.798953i	$-0.294613\pi$
$859$	35.2521			1.20279			0.601393	+	0.798953i	$0.294613\pi$
$860$		0			0
$861$	2.85646	−	4.94754i	0.0973480	−	0.168612i
$862$	−13.1683	−	22.8082i	−0.448514	−	0.776849i
$863$			7.68909i			0.261740i	0.991400	+	0.130870i	$0.0417770\pi$
$863$			7.68909i			0.261740i	−0.991400	+	0.130870i	$0.958223\pi$
$864$	−0.866025	+	0.500000i	−0.0294628	+	0.0170103i
$865$		0			0
$866$			12.9594i			0.440380i
$867$	−2.71489	−	4.70233i	−0.0922026	−	0.159700i
$868$	3.56482	−	6.17445i	0.120998	−	0.209574i
$869$	60.6196	+	34.9988i	2.05638	+	1.18725i
$870$		0			0
$871$	18.5632	+	47.1548i	0.628991	+	1.59778i
$872$	−16.8839			−0.571761
$873$	−7.34631	−	4.24139i	−0.248635	−	0.143549i
$874$	−2.31567	+	4.01086i	−0.0783287	+	0.135669i
$875$		0			0
$876$		−	15.7228i		−	0.531225i
$877$	−14.5959	+	8.42697i	−0.492870	+	0.284559i	−0.725764	−	0.687943i	$-0.758514\pi$
$877$	−14.5959	+	8.42697i	−0.492870	+	0.284559i	0.232894	+	0.972502i	$0.425180\pi$
$878$	−20.1324	+	11.6234i	−0.679434	+	0.392272i
$879$			24.1316i			0.813938i
$880$		0			0
$881$	−24.0475	+	41.6516i	−0.810182	+	1.40328i	0.102554	+	0.994727i	$0.467299\pi$
$881$	−24.0475	+	41.6516i	−0.810182	+	1.40328i	−0.912736	+	0.408550i	$0.866035\pi$
$882$	4.80203	+	2.77245i	0.161693	+	0.0933533i
$883$	38.3641			1.29105			0.645527	−	0.763737i	$-0.276638\pi$
$883$	38.3641			1.29105			0.645527	+	0.763737i	$0.276638\pi$
$884$	15.8891	−	6.25498i	0.534407	−	0.210378i
$885$		0			0
$886$	20.2414	+	11.6864i	0.680024	+	0.392612i
$887$	9.39331	−	16.2697i	0.315396	−	0.546283i	−0.664125	−	0.747621i	$-0.731196\pi$
$887$	9.39331	−	16.2697i	0.315396	−	0.546283i	0.979522	+	0.201339i	$0.0645292\pi$
$888$	2.20034	+	3.81110i	0.0738385	+	0.127892i
$889$		−	1.44984i		−	0.0486260i
$890$		0			0
$891$	−4.46182	+	2.57603i	−0.149477	+	0.0863003i
$892$		−	7.15357i		−	0.239519i
$893$	0.907745	+	1.57226i	0.0303765	+	0.0526137i
$894$	−11.4058	+	19.7555i	−0.381468	+	0.660721i
$895$		0			0
$896$	1.20627			0.0402988
$897$	−1.16036	+	7.75290i	−0.0387433	+	0.258862i
$898$	−1.39639			−0.0465982
$899$	−24.4000	−	14.0874i	−0.813787	−	0.469840i
$900$		0			0
$901$	−10.6097	−	18.3765i	−0.353459	−	0.612209i
$902$			24.4002i			0.812439i
$903$	−2.06205	+	1.19052i	−0.0686207	+	0.0396182i
$904$	−4.28771	+	2.47551i	−0.142607	+	0.0823342i
$905$		0			0
$906$	9.94975	+	17.2335i	0.330558	+	0.572544i
$907$	−10.5636	+	18.2967i	−0.350759	+	0.607532i	−0.986383	−	0.164467i	$-0.947410\pi$
$907$	−10.5636	+	18.2967i	−0.350759	+	0.607532i	0.635624	+	0.771999i	$0.280743\pi$
$908$	22.3768	+	12.9192i	0.742599	+	0.428740i
$909$	−13.5824			−0.450501
$910$		0			0
$911$	19.2766			0.638664			0.319332	−	0.947643i	$-0.396542\pi$
$911$	19.2766			0.638664			0.319332	+	0.947643i	$0.396542\pi$
$912$	−1.84474	−	1.06506i	−0.0610853	−	0.0352676i
$913$	−26.2872	+	45.5307i	−0.869978	+	1.50685i
$914$	−3.60093	−	6.23699i	−0.119108	−	0.206301i
$915$		0			0
$916$	−7.75225	+	4.47576i	−0.256142	+	0.147883i
$917$	6.94857	−	4.01176i	0.229462	−	0.132480i
$918$			4.73601i			0.156312i
$919$	−17.8995	−	31.0028i	−0.590450	−	1.02269i	−0.994172	−	0.107807i	$-0.965617\pi$
$919$	−17.8995	−	31.0028i	−0.590450	−	1.02269i	0.403722	−	0.914882i	$-0.367716\pi$
$920$		0			0
$921$	−26.2616	−	15.1621i	−0.865348	−	0.499609i
$922$	−4.74489			−0.156265
$923$	1.22992	+	0.184079i	0.0404833	+	0.00605905i
$924$	6.21480			0.204452
$925$		0			0
$926$	−7.87551	+	13.6408i	−0.258805	+	0.448264i
$927$	1.07848	+	1.86798i	0.0354219	+	0.0613525i
$928$		−	4.76693i		−	0.156482i
$929$	13.4933	−	7.79033i	0.442699	−	0.255593i	−0.262043	−	0.965056i	$-0.584396\pi$
$929$	13.4933	−	7.79033i	0.442699	−	0.255593i	0.704742	+	0.709464i	$0.251063\pi$
$930$		0			0
$931$			11.8113i			0.387100i
$932$	−1.93329	−	3.34855i	−0.0633269	−	0.109685i
$933$	−4.38203	+	7.58990i	−0.143461	+	0.248482i
$934$	15.5701	+	8.98943i	0.509471	+	0.294143i
$935$		0			0
$936$	−3.56583	−	0.533691i	−0.116553	−	0.0174442i
$937$	−27.4692			−0.897381			−0.448690	−	0.893687i	$-0.648109\pi$
$937$	−27.4692			−0.897381			−0.448690	+	0.893687i	$0.648109\pi$
$938$	14.6831	+	8.47727i	0.479419	+	0.276793i
$939$	−14.5077	+	25.1282i	−0.473442	+	0.820026i
$940$		0			0
$941$		−	5.01957i		−	0.163633i	−0.996647	−	0.0818167i	$-0.973928\pi$
$941$		−	5.01957i		−	0.163633i	0.996647	−	0.0818167i	$-0.0260722\pi$
$942$	4.10836	−	2.37196i	0.133857	−	0.0772826i
$943$	−8.91756	+	5.14856i	−0.290396	+	0.167660i
$944$		−	1.94143i		−	0.0631882i
$945$		0			0
$946$	5.08480	−	8.80713i	0.165321	−	0.286344i
$947$	34.7995	+	20.0915i	1.13083	+	0.652886i	0.944144	−	0.329534i	$-0.106891\pi$
$947$	34.7995	+	20.0915i	1.13083	+	0.652886i	0.186688	+	0.982419i	$0.440225\pi$
$948$	−13.5863			−0.441263
$949$	35.2994	−	44.3582i	1.14587	−	1.43993i
$950$		0			0
$951$	22.5140	+	12.9985i	0.730068	+	0.421505i
$952$	2.85646	−	4.94754i	0.0925785	−	0.160351i
$953$	5.44149	+	9.42493i	0.176267	+	0.305304i	0.940599	−	0.339519i	$-0.110264\pi$
$953$	5.44149	+	9.42493i	0.176267	+	0.305304i	−0.764332	+	0.644823i	$0.776931\pi$
$954$			4.48042i			0.145059i
$955$		0			0
$956$	13.3521	−	7.70884i	0.431838	−	0.249322i
$957$		−	24.5595i		−	0.793896i
$958$	−1.63947	−	2.83964i	−0.0529688	−	0.0917447i
$959$	8.87511	−	15.3721i	0.286592	−	0.496392i
$960$		0			0
$961$	−3.93359			−0.126890
$962$	−2.34860	+	15.6921i	−0.0757220	+	0.505933i
$963$	−8.09397			−0.260825
$964$	9.76603	+	5.63842i	0.314543	+	0.181601i
$965$		0			0
$966$	1.31135	+	2.27133i	0.0421920	+	0.0730787i
$967$		−	2.14376i		−	0.0689387i	−0.999406	−	0.0344693i	$-0.989026\pi$
$967$		−	2.14376i		−	0.0689387i	0.999406	−	0.0344693i	$-0.0109741\pi$
$968$	−13.4613	+	7.77188i	−0.432662	+	0.249798i
$969$	−8.73669	+	5.04413i	−0.280663	+	0.162041i
$970$		0			0
$971$	−4.57889	−	7.93087i	−0.146944	−	0.254514i	0.783153	−	0.621829i	$-0.213610\pi$
$971$	−4.57889	−	7.93087i	−0.146944	−	0.254514i	−0.930096	+	0.367316i	$0.880277\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−16.3498	−	9.43958i	−0.524151	−	0.302619i
$974$	−9.97704			−0.319685
$975$		0			0
$976$	3.07591			0.0984574
$977$	−12.4103	−	7.16508i	−0.397040	−	0.229231i	0.288166	−	0.957581i	$-0.406955\pi$
$977$	−12.4103	−	7.16508i	−0.397040	−	0.229231i	−0.685206	+	0.728349i	$0.740288\pi$
$978$	1.93329	−	3.34855i	0.0618197	−	0.107075i
$979$	−42.2210	−	73.1289i	−1.34939	−	2.33721i
$980$		0			0
$981$	14.6219	−	8.44195i	0.466841	−	0.269531i
$982$	17.3857	−	10.0376i	0.554800	−	0.320314i
$983$		−	21.6099i		−	0.689250i	−0.938740	−	0.344625i	$-0.888006\pi$
$983$		−	21.6099i		−	0.689250i	0.938740	−	0.344625i	$-0.111994\pi$
$984$	−2.36800	−	4.10150i	−0.0754892	−	0.130751i
$985$		0			0
$986$	−19.5516	−	11.2881i	−0.622649	−	0.359486i
$987$	1.02810			0.0327248
$988$	−2.81330	−	7.14644i	−0.0895031	−	0.227358i
$989$	4.29166			0.136467
$990$		0			0
$991$	−11.9222	+	20.6499i	−0.378722	+	0.655966i	−0.990877	−	0.134772i	$-0.956970\pi$
$991$	−11.9222	+	20.6499i	−0.378722	+	0.655966i	0.612154	+	0.790738i	$0.290303\pi$
$992$	−2.95523	−	5.11861i	−0.0938287	−	0.162516i
$993$		−	11.0392i		−	0.350319i
$994$	0.360323	−	0.208033i	0.0114287	−	0.00659839i
$995$		0			0
$996$		−	10.2045i		−	0.323342i
$997$	14.7670	+	25.5772i	0.467675	+	0.810037i	0.999318	−	0.0369315i	$-0.0117583\pi$
$997$	14.7670	+	25.5772i	0.467675	+	0.810037i	−0.531642	+	0.846969i	$0.678425\pi$
$998$	11.9737	−	20.7390i	0.379020	−	0.656482i
$999$	−3.81110	−	2.20034i	−0.120578	−	0.0696157i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.bc.i.901.4		12
5.2	odd	4		390.2.x.a.199.4	yes	12
5.3	odd	4		390.2.x.b.199.3	yes	12
5.4	even	2		1950.2.bc.j.901.3		12
13.10	even	6	inner	1950.2.bc.i.751.4		12
15.2	even	4		1170.2.bj.d.199.4		12
15.8	even	4		1170.2.bj.c.199.3		12
65.23	odd	12		390.2.x.a.49.4	✓	12
65.49	even	6		1950.2.bc.j.751.3		12
65.62	odd	12		390.2.x.b.49.3	yes	12
195.23	even	12		1170.2.bj.d.829.4		12
195.62	even	12		1170.2.bj.c.829.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.x.a.49.4	✓	12	65.23	odd	12
390.2.x.a.199.4	yes	12	5.2	odd	4
390.2.x.b.49.3	yes	12	65.62	odd	12
390.2.x.b.199.3	yes	12	5.3	odd	4
1170.2.bj.c.199.3		12	15.8	even	4
1170.2.bj.c.829.3		12	195.62	even	12
1170.2.bj.d.199.4		12	15.2	even	4
1170.2.bj.d.829.4		12	195.23	even	12
1950.2.bc.i.751.4		12	13.10	even	6	inner
1950.2.bc.i.901.4		12	1.1	even	1	trivial
1950.2.bc.j.751.3		12	65.49	even	6
1950.2.bc.j.901.3		12	5.4	even	2

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.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(-1.04466 + 0.603137i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(-1.04466 + 0.603137i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +(4.46182 + 2.57603i) q^{11} -1.00000 q^{12} +(-2.82126 - 2.24511i) q^{13} -1.20627 q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.36800 + 4.10150i) q^{17} -1.00000i q^{18} +(1.84474 - 1.06506i) q^{19} -1.20627i q^{21} +(2.57603 + 4.46182i) q^{22} +(-1.08711 + 1.88293i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-1.32073 - 3.35495i) q^{26} +1.00000 q^{27} +(-1.04466 - 0.603137i) q^{28} +(-2.38346 + 4.12828i) q^{29} +5.91046i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-4.46182 + 2.57603i) q^{33} +4.73601i q^{34} +(0.500000 - 0.866025i) q^{36} +(-3.81110 - 2.20034i) q^{37} +2.13012 q^{38} +(3.35495 - 1.32073i) q^{39} +(4.10150 + 2.36800i) q^{41} +(0.603137 - 1.04466i) q^{42} +(-0.986944 - 1.70944i) q^{43} +5.15206i q^{44} +(-1.88293 + 1.08711i) q^{46} +0.852296i q^{47} +(-0.500000 - 0.866025i) q^{48} +(-2.77245 + 4.80203i) q^{49} -4.73601 q^{51} +(0.533691 - 3.56583i) q^{52} -4.48042 q^{53} +(0.866025 + 0.500000i) q^{54} +(-0.603137 - 1.04466i) q^{56} +2.13012i q^{57} +(-4.12828 + 2.38346i) q^{58} +(-1.68133 + 0.970715i) q^{59} +(-1.53795 - 2.66381i) q^{61} +(-2.95523 + 5.11861i) q^{62} +(1.04466 + 0.603137i) q^{63} -1.00000 q^{64} -5.15206 q^{66} +(-12.1723 - 7.02765i) q^{67} +(-2.36800 + 4.10150i) q^{68} +(-1.08711 - 1.88293i) q^{69} +(-0.298707 + 0.172459i) q^{71} +(0.866025 - 0.500000i) q^{72} +15.7228i q^{73} +(-2.20034 - 3.81110i) q^{74} +(1.84474 + 1.06506i) q^{76} -6.21480 q^{77} +(3.56583 + 0.533691i) q^{78} +13.5863 q^{79} +(-0.500000 + 0.866025i) q^{81} +(2.36800 + 4.10150i) q^{82} +10.2045i q^{83} +(1.04466 - 0.603137i) q^{84} -1.97389i q^{86} +(-2.38346 - 4.12828i) q^{87} +(-2.57603 + 4.46182i) q^{88} +(-14.1941 - 8.19497i) q^{89} +(4.30137 + 0.643777i) q^{91} -2.17422 q^{92} +(-5.11861 - 2.95523i) q^{93} +(-0.426148 + 0.738110i) q^{94} -1.00000i q^{96} +(7.34631 - 4.24139i) q^{97} +(-4.80203 + 2.77245i) q^{98} -5.15206i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 6 q^{4} + 12 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 + 6 * q^4 + 12 * q^7 - 6 * q^9	\( 12 q - 6 q^{3} + 6 q^{4} + 12 q^{7} - 6 q^{9} + 6 q^{11} - 12 q^{12} - 4 q^{13} - 4 q^{14} - 6 q^{16} - 8 q^{17} + 6 q^{19} + 6 q^{22} - 16 q^{23} - 2 q^{26} + 12 q^{27} + 12 q^{28} - 14 q^{29} - 6 q^{33} + 6 q^{36} + 6 q^{37} + 8 q^{38} + 2 q^{39} - 18 q^{41} + 2 q^{42} - 10 q^{43} - 6 q^{46} - 6 q^{48} - 8 q^{49} + 16 q^{51} - 2 q^{52} - 2 q^{56} - 6 q^{58} + 36 q^{59} + 10 q^{61} - 16 q^{62} - 12 q^{63} - 12 q^{64} - 12 q^{66} - 24 q^{67} + 8 q^{68} - 16 q^{69} - 12 q^{71} + 12 q^{74} + 6 q^{76} - 24 q^{77} + 10 q^{78} - 4 q^{79} - 6 q^{81} - 8 q^{82} - 12 q^{84} - 14 q^{87} - 6 q^{88} - 18 q^{89} + 2 q^{91} - 32 q^{92} + 6 q^{93} + 8 q^{94} + 24 q^{97} - 24 q^{98}+O(q^{100}) \) 12 * q - 6 * q^3 + 6 * q^4 + 12 * q^7 - 6 * q^9 + 6 * q^11 - 12 * q^12 - 4 * q^13 - 4 * q^14 - 6 * q^16 - 8 * q^17 + 6 * q^19 + 6 * q^22 - 16 * q^23 - 2 * q^26 + 12 * q^27 + 12 * q^28 - 14 * q^29 - 6 * q^33 + 6 * q^36 + 6 * q^37 + 8 * q^38 + 2 * q^39 - 18 * q^41 + 2 * q^42 - 10 * q^43 - 6 * q^46 - 6 * q^48 - 8 * q^49 + 16 * q^51 - 2 * q^52 - 2 * q^56 - 6 * q^58 + 36 * q^59 + 10 * q^61 - 16 * q^62 - 12 * q^63 - 12 * q^64 - 12 * q^66 - 24 * q^67 + 8 * q^68 - 16 * q^69 - 12 * q^71 + 12 * q^74 + 6 * q^76 - 24 * q^77 + 10 * q^78 - 4 * q^79 - 6 * q^81 - 8 * q^82 - 12 * q^84 - 14 * q^87 - 6 * q^88 - 18 * q^89 + 2 * q^91 - 32 * q^92 + 6 * q^93 + 8 * q^94 + 24 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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