LMFDB - Embedded newform 350.2.j.f.149.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(149,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("350.149");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.j (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:	$2.79476407074$
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 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			149.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	350.149
Dual form			350.2.j.f.249.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-2.59808 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.00000 q^{6} +(2.59808 + 0.500000i) q^{7} -1.00000i q^{8} +(3.00000 - 5.19615i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-2.59808 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.00000 q^{6} +(2.59808 + 0.500000i) q^{7} -1.00000i q^{8} +(3.00000 - 5.19615i) q^{9} +(1.00000 + 1.73205i) q^{11} +(-2.59808 - 1.50000i) q^{12} +(-2.00000 - 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.46410 + 2.00000i) q^{17} +(-5.19615 + 3.00000i) q^{18} +(-3.00000 + 5.19615i) q^{19} +(-7.50000 + 2.59808i) q^{21} -2.00000i q^{22} +(2.59808 + 1.50000i) q^{23} +(1.50000 + 2.59808i) q^{24} +9.00000i q^{27} +(0.866025 + 2.50000i) q^{28} -9.00000 q^{29} +(2.00000 + 3.46410i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-5.19615 - 3.00000i) q^{33} +4.00000 q^{34} +6.00000 q^{36} +(3.46410 + 2.00000i) q^{37} +(5.19615 - 3.00000i) q^{38} -7.00000 q^{41} +(7.79423 + 1.50000i) q^{42} +5.00000i q^{43} +(-1.00000 + 1.73205i) q^{44} +(-1.50000 - 2.59808i) q^{46} +(-6.92820 - 4.00000i) q^{47} -3.00000i q^{48} +(6.50000 + 2.59808i) q^{49} +(6.00000 - 10.3923i) q^{51} +(1.73205 - 1.00000i) q^{53} +(4.50000 - 7.79423i) q^{54} +(0.500000 - 2.59808i) q^{56} -18.0000i q^{57} +(7.79423 + 4.50000i) q^{58} +(5.00000 + 8.66025i) q^{59} +(-0.500000 + 0.866025i) q^{61} -4.00000i q^{62} +(10.3923 - 12.0000i) q^{63} -1.00000 q^{64} +(3.00000 + 5.19615i) q^{66} +(-7.79423 + 4.50000i) q^{67} +(-3.46410 - 2.00000i) q^{68} -9.00000 q^{69} +2.00000 q^{71} +(-5.19615 - 3.00000i) q^{72} +(3.46410 - 2.00000i) q^{73} +(-2.00000 - 3.46410i) q^{74} -6.00000 q^{76} +(1.73205 + 5.00000i) q^{77} +(5.00000 - 8.66025i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(6.06218 + 3.50000i) q^{82} +7.00000i q^{83} +(-6.00000 - 5.19615i) q^{84} +(2.50000 - 4.33013i) q^{86} +(23.3827 - 13.5000i) q^{87} +(1.73205 - 1.00000i) q^{88} +(0.500000 - 0.866025i) q^{89} +3.00000i q^{92} +(-10.3923 - 6.00000i) q^{93} +(4.00000 + 6.92820i) q^{94} +(-1.50000 + 2.59808i) q^{96} +14.0000i q^{97} +(-4.33013 - 5.50000i) q^{98} +12.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 12 q^{6} + 12 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 12 * q^6 + 12 * q^9	$ 4 q + 2 q^{4} + 12 q^{6} + 12 q^{9} + 4 q^{11} - 8 q^{14} - 2 q^{16} - 12 q^{19} - 30 q^{21} + 6 q^{24} - 36 q^{29} + 8 q^{31} + 16 q^{34} + 24 q^{36} - 28 q^{41} - 4 q^{44} - 6 q^{46} + 26 q^{49} + 24 q^{51} + 18 q^{54} + 2 q^{56} + 20 q^{59} - 2 q^{61} - 4 q^{64} + 12 q^{66} - 36 q^{69} + 8 q^{71} - 8 q^{74} - 24 q^{76} + 20 q^{79} - 18 q^{81} - 24 q^{84} + 10 q^{86} + 2 q^{89} + 16 q^{94} - 6 q^{96} + 48 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 + 12 * q^6 + 12 * q^9 + 4 * q^11 - 8 * q^14 - 2 * q^16 - 12 * q^19 - 30 * q^21 + 6 * q^24 - 36 * q^29 + 8 * q^31 + 16 * q^34 + 24 * q^36 - 28 * q^41 - 4 * q^44 - 6 * q^46 + 26 * q^49 + 24 * q^51 + 18 * q^54 + 2 * q^56 + 20 * q^59 - 2 * q^61 - 4 * q^64 + 12 * q^66 - 36 * q^69 + 8 * q^71 - 8 * q^74 - 24 * q^76 + 20 * q^79 - 18 * q^81 - 24 * q^84 + 10 * q^86 + 2 * q^89 + 16 * q^94 - 6 * q^96 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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
$3$	−2.59808	+	1.50000i	−1.50000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$3$	−2.59808	+	1.50000i	−1.50000	+	0.866025i	−1.00000			$\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	3.00000			1.22474
$7$	2.59808	+	0.500000i	0.981981	+	0.188982i
$7$	2.59808	+	0.500000i	0.981981	+	0.188982i
$8$		−	1.00000i		−	0.353553i
$9$	3.00000	−	5.19615i	1.00000	−	1.73205i
$10$		0			0
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$	−2.59808	−	1.50000i	−0.750000	−	0.433013i
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$	−2.00000	−	1.73205i	−0.534522	−	0.462910i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.46410	+	2.00000i	−0.840168	+	0.485071i	−0.857321	−	0.514782i	$-0.827873\pi$
$17$	−3.46410	+	2.00000i	−0.840168	+	0.485071i	0.0171533	+	0.999853i	$0.494540\pi$
$18$	−5.19615	+	3.00000i	−1.22474	+	0.707107i
$19$	−3.00000	+	5.19615i	−0.688247	+	1.19208i	0.284157	+	0.958778i	$0.408286\pi$
$19$	−3.00000	+	5.19615i	−0.688247	+	1.19208i	−0.972404	+	0.233301i	$0.925047\pi$
$20$		0			0
$21$	−7.50000	+	2.59808i	−1.63663	+	0.566947i
$22$		−	2.00000i		−	0.426401i
$23$	2.59808	+	1.50000i	0.541736	+	0.312772i	0.745782	−	0.666190i	$-0.232076\pi$
$23$	2.59808	+	1.50000i	0.541736	+	0.312772i	−0.204046	+	0.978961i	$0.565409\pi$
$24$	1.50000	+	2.59808i	0.306186	+	0.530330i
$25$		0			0
$26$		0			0
$27$			9.00000i			1.73205i
$28$	0.866025	+	2.50000i	0.163663	+	0.472456i
$29$	−9.00000			−1.67126			−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000			−1.67126			−0.835629	+	0.549294i	$0.814897\pi$
$30$		0			0
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−5.19615	−	3.00000i	−0.904534	−	0.522233i
$34$	4.00000			0.685994
$35$		0			0
$36$	6.00000			1.00000
$37$	3.46410	+	2.00000i	0.569495	+	0.328798i	0.756948	−	0.653476i	$-0.226690\pi$
$37$	3.46410	+	2.00000i	0.569495	+	0.328798i	−0.187453	+	0.982274i	$0.560023\pi$
$38$	5.19615	−	3.00000i	0.842927	−	0.486664i
$39$		0			0
$40$		0			0
$41$	−7.00000			−1.09322			−0.546608	−	0.837389i	$-0.684081\pi$
$41$	−7.00000			−1.09322			−0.546608	+	0.837389i	$0.684081\pi$
$42$	7.79423	+	1.50000i	1.20268	+	0.231455i
$43$			5.00000i			0.762493i	0.924473	+	0.381246i	$0.124505\pi$
$43$			5.00000i			0.762493i	−0.924473	+	0.381246i	$0.875495\pi$
$44$	−1.00000	+	1.73205i	−0.150756	+	0.261116i
$45$		0			0
$46$	−1.50000	−	2.59808i	−0.221163	−	0.383065i
$47$	−6.92820	−	4.00000i	−1.01058	−	0.583460i	−0.0992202	−	0.995066i	$-0.531635\pi$
$47$	−6.92820	−	4.00000i	−1.01058	−	0.583460i	−0.911362	+	0.411606i	$0.864968\pi$
$48$		−	3.00000i		−	0.433013i
$49$	6.50000	+	2.59808i	0.928571	+	0.371154i
$50$		0			0
$51$	6.00000	−	10.3923i	0.840168	−	1.45521i
$52$		0			0
$53$	1.73205	−	1.00000i	0.237915	−	0.137361i	−0.376303	−	0.926497i	$-0.622805\pi$
$53$	1.73205	−	1.00000i	0.237915	−	0.137361i	0.614218	+	0.789136i	$0.289471\pi$
$54$	4.50000	−	7.79423i	0.612372	−	1.06066i
$55$		0			0
$56$	0.500000	−	2.59808i	0.0668153	−	0.347183i
$57$		−	18.0000i		−	2.38416i
$58$	7.79423	+	4.50000i	1.02343	+	0.590879i
$59$	5.00000	+	8.66025i	0.650945	+	1.12747i	0.982894	+	0.184172i	$0.0589603\pi$
$59$	5.00000	+	8.66025i	0.650945	+	1.12747i	−0.331949	+	0.943297i	$0.607706\pi$
$60$		0			0
$61$	−0.500000	+	0.866025i	−0.0640184	+	0.110883i	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−0.500000	+	0.866025i	−0.0640184	+	0.110883i	0.832240	+	0.554416i	$0.187058\pi$
$62$		−	4.00000i		−	0.508001i
$63$	10.3923	−	12.0000i	1.30931	−	1.51186i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	3.00000	+	5.19615i	0.369274	+	0.639602i
$67$	−7.79423	+	4.50000i	−0.952217	+	0.549762i	−0.893769	−	0.448528i	$-0.851948\pi$
$67$	−7.79423	+	4.50000i	−0.952217	+	0.549762i	−0.0584478	+	0.998290i	$0.518615\pi$
$68$	−3.46410	−	2.00000i	−0.420084	−	0.242536i
$69$	−9.00000			−1.08347
$70$		0			0
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$	−5.19615	−	3.00000i	−0.612372	−	0.353553i
$73$	3.46410	−	2.00000i	0.405442	−	0.234082i	−0.283387	−	0.959006i	$-0.591458\pi$
$73$	3.46410	−	2.00000i	0.405442	−	0.234082i	0.688830	+	0.724923i	$0.258125\pi$
$74$	−2.00000	−	3.46410i	−0.232495	−	0.402694i
$75$		0			0
$76$	−6.00000			−0.688247
$77$	1.73205	+	5.00000i	0.197386	+	0.569803i
$78$		0			0
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	−0.434730	−	0.900561i	$-0.643156\pi$
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	0.997274	−	0.0737937i	$-0.0235106\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	6.06218	+	3.50000i	0.669456	+	0.386510i
$83$			7.00000i			0.768350i	0.923260	+	0.384175i	$0.125514\pi$
$83$			7.00000i			0.768350i	−0.923260	+	0.384175i	$0.874486\pi$
$84$	−6.00000	−	5.19615i	−0.654654	−	0.566947i
$85$		0			0
$86$	2.50000	−	4.33013i	0.269582	−	0.466930i
$87$	23.3827	−	13.5000i	2.50689	−	1.44735i
$88$	1.73205	−	1.00000i	0.184637	−	0.106600i
$89$	0.500000	−	0.866025i	0.0529999	−	0.0917985i	−0.838308	−	0.545197i	$-0.816455\pi$
$89$	0.500000	−	0.866025i	0.0529999	−	0.0917985i	0.891308	+	0.453398i	$0.149788\pi$
$90$		0			0
$91$		0			0
$92$			3.00000i			0.312772i
$93$	−10.3923	−	6.00000i	−1.07763	−	0.622171i
$94$	4.00000	+	6.92820i	0.412568	+	0.714590i
$95$		0			0
$96$	−1.50000	+	2.59808i	−0.153093	+	0.265165i
$97$			14.0000i			1.42148i	0.703452	+	0.710742i	$0.251641\pi$
$97$			14.0000i			1.42148i	−0.703452	+	0.710742i	$0.748359\pi$
$98$	−4.33013	−	5.50000i	−0.437409	−	0.555584i
$99$	12.0000			1.20605
$100$		0			0
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	0.781697	−	0.623658i	$-0.214354\pi$
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	−0.930953	+	0.365140i	$0.881021\pi$
$102$	−10.3923	+	6.00000i	−1.02899	+	0.594089i
$103$	0.866025	+	0.500000i	0.0853320	+	0.0492665i	0.542059	−	0.840341i	$-0.317645\pi$
$103$	0.866025	+	0.500000i	0.0853320	+	0.0492665i	−0.456727	+	0.889607i	$0.650978\pi$
$104$		0			0
$105$		0			0
$106$	−2.00000			−0.194257
$107$	−2.59808	−	1.50000i	−0.251166	−	0.145010i	0.369132	−	0.929377i	$-0.379655\pi$
$107$	−2.59808	−	1.50000i	−0.251166	−	0.145010i	−0.620298	+	0.784366i	$0.712988\pi$
$108$	−7.79423	+	4.50000i	−0.750000	+	0.433013i
$109$	−4.50000	−	7.79423i	−0.431022	−	0.746552i	0.565940	−	0.824447i	$-0.308513\pi$
$109$	−4.50000	−	7.79423i	−0.431022	−	0.746552i	−0.996962	+	0.0778949i	$0.975180\pi$
$110$		0			0
$111$	−12.0000			−1.13899
$112$	−1.73205	+	2.00000i	−0.163663	+	0.188982i
$113$		−	2.00000i		−	0.188144i	−0.995565	−	0.0940721i	$-0.970012\pi$
$113$		−	2.00000i		−	0.188144i	0.995565	−	0.0940721i	$-0.0299884\pi$
$114$	−9.00000	+	15.5885i	−0.842927	+	1.45999i
$115$		0			0
$116$	−4.50000	−	7.79423i	−0.417815	−	0.723676i
$117$		0			0
$118$		−	10.0000i		−	0.920575i
$119$	−10.0000	+	3.46410i	−0.916698	+	0.317554i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	0.866025	−	0.500000i	0.0784063	−	0.0452679i
$123$	18.1865	−	10.5000i	1.63982	−	0.946753i
$124$	−2.00000	+	3.46410i	−0.179605	+	0.311086i
$125$		0			0
$126$	−15.0000	+	5.19615i	−1.33631	+	0.462910i
$127$			16.0000i			1.41977i	0.704317	+	0.709885i	$0.251253\pi$
$127$			16.0000i			1.41977i	−0.704317	+	0.709885i	$0.748747\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−7.50000	−	12.9904i	−0.660338	−	1.14374i
$130$		0			0
$131$	−4.00000	+	6.92820i	−0.349482	+	0.605320i	−0.986157	−	0.165812i	$-0.946976\pi$
$131$	−4.00000	+	6.92820i	−0.349482	+	0.605320i	0.636676	+	0.771132i	$0.280309\pi$
$132$		−	6.00000i		−	0.522233i
$133$	−10.3923	+	12.0000i	−0.901127	+	1.04053i
$134$	9.00000			0.777482
$135$		0			0
$136$	2.00000	+	3.46410i	0.171499	+	0.297044i
$137$	10.3923	−	6.00000i	0.887875	−	0.512615i	0.0146279	−	0.999893i	$-0.495344\pi$
$137$	10.3923	−	6.00000i	0.887875	−	0.512615i	0.873247	+	0.487278i	$0.162010\pi$
$138$	7.79423	+	4.50000i	0.663489	+	0.383065i
$139$	14.0000			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$140$		0			0
$141$	24.0000			2.02116
$142$	−1.73205	−	1.00000i	−0.145350	−	0.0839181i
$143$		0			0
$144$	3.00000	+	5.19615i	0.250000	+	0.433013i
$145$		0			0
$146$	−4.00000			−0.331042
$147$	−20.7846	+	3.00000i	−1.71429	+	0.247436i
$148$			4.00000i			0.328798i
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	−0.798019	−	0.602632i	$-0.794119\pi$
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	0.920904	+	0.389789i	$0.127452\pi$
$150$		0			0
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	0.982873	+	0.184284i	$0.0589965\pi$
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	−0.331842	+	0.943335i	$0.607670\pi$
$152$	5.19615	+	3.00000i	0.421464	+	0.243332i
$153$			24.0000i			1.94029i
$154$	1.00000	−	5.19615i	0.0805823	−	0.418718i
$155$		0			0
$156$		0			0
$157$	8.66025	−	5.00000i	0.691164	−	0.399043i	−0.112884	−	0.993608i	$-0.536009\pi$
$157$	8.66025	−	5.00000i	0.691164	−	0.399043i	0.804048	+	0.594565i	$0.202676\pi$
$158$	−8.66025	+	5.00000i	−0.688973	+	0.397779i
$159$	−3.00000	+	5.19615i	−0.237915	+	0.412082i
$160$		0			0
$161$	6.00000	+	5.19615i	0.472866	+	0.409514i
$162$			9.00000i			0.707107i
$163$	−3.46410	−	2.00000i	−0.271329	−	0.156652i	0.358162	−	0.933659i	$-0.383403\pi$
$163$	−3.46410	−	2.00000i	−0.271329	−	0.156652i	−0.629492	+	0.777007i	$0.716737\pi$
$164$	−3.50000	−	6.06218i	−0.273304	−	0.473377i
$165$		0			0
$166$	3.50000	−	6.06218i	0.271653	−	0.470516i
$167$		−	21.0000i		−	1.62503i	−0.582941	−	0.812514i	$-0.698098\pi$
$167$		−	21.0000i		−	1.62503i	0.582941	−	0.812514i	$-0.301902\pi$
$168$	2.59808	+	7.50000i	0.200446	+	0.578638i
$169$	13.0000			1.00000
$170$		0			0
$171$	18.0000	+	31.1769i	1.37649	+	2.38416i
$172$	−4.33013	+	2.50000i	−0.330169	+	0.190623i
$173$	6.92820	+	4.00000i	0.526742	+	0.304114i	0.739689	−	0.672949i	$-0.234973\pi$
$173$	6.92820	+	4.00000i	0.526742	+	0.304114i	−0.212947	+	0.977064i	$0.568306\pi$
$174$	−27.0000			−2.04686
$175$		0			0
$176$	−2.00000			−0.150756
$177$	−25.9808	−	15.0000i	−1.95283	−	1.12747i
$178$	−0.866025	+	0.500000i	−0.0649113	+	0.0374766i
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	0.998286	−	0.0585225i	$-0.0186389\pi$
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	−0.549825	+	0.835280i	$0.685306\pi$
$180$		0			0
$181$	7.00000			0.520306			0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000			0.520306			0.260153	+	0.965567i	$0.416227\pi$
$182$		0			0
$183$		−	3.00000i		−	0.221766i
$184$	1.50000	−	2.59808i	0.110581	−	0.191533i
$185$		0			0
$186$	6.00000	+	10.3923i	0.439941	+	0.762001i
$187$	−6.92820	−	4.00000i	−0.506640	−	0.292509i
$188$		−	8.00000i		−	0.583460i
$189$	−4.50000	+	23.3827i	−0.327327	+	1.70084i
$190$		0			0
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	−0.331611	−	0.943416i	$-0.607592\pi$
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	0.982828	−	0.184525i	$-0.0590746\pi$
$192$	2.59808	−	1.50000i	0.187500	−	0.108253i
$193$	−22.5167	+	13.0000i	−1.62078	+	0.935760i	−0.634074	+	0.773272i	$0.718619\pi$
$193$	−22.5167	+	13.0000i	−1.62078	+	0.935760i	−0.986710	+	0.162488i	$0.948048\pi$
$194$	7.00000	−	12.1244i	0.502571	−	0.870478i
$195$		0			0
$196$	1.00000	+	6.92820i	0.0714286	+	0.494872i
$197$			2.00000i			0.142494i	0.997459	+	0.0712470i	$0.0226979\pi$
$197$			2.00000i			0.142494i	−0.997459	+	0.0712470i	$0.977302\pi$
$198$	−10.3923	−	6.00000i	−0.738549	−	0.426401i
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	0.786389	−	0.617731i	$-0.211948\pi$
$199$	−2.00000	−	3.46410i	−0.141776	−	0.245564i	−0.928166	+	0.372168i	$0.878615\pi$
$200$		0			0
$201$	13.5000	−	23.3827i	0.952217	−	1.64929i
$202$			3.00000i			0.211079i
$203$	−23.3827	−	4.50000i	−1.64114	−	0.315838i
$204$	12.0000			0.840168
$205$		0			0
$206$	−0.500000	−	0.866025i	−0.0348367	−	0.0603388i
$207$	15.5885	−	9.00000i	1.08347	−	0.625543i
$208$		0			0
$209$	−12.0000			−0.830057
$210$		0			0
$211$	−26.0000			−1.78991			−0.894957	−	0.446153i	$-0.852794\pi$
$211$	−26.0000			−1.78991			−0.894957	+	0.446153i	$0.852794\pi$
$212$	1.73205	+	1.00000i	0.118958	+	0.0686803i
$213$	−5.19615	+	3.00000i	−0.356034	+	0.205557i
$214$	1.50000	+	2.59808i	0.102538	+	0.177601i
$215$		0			0
$216$	9.00000			0.612372
$217$	3.46410	+	10.0000i	0.235159	+	0.678844i
$218$			9.00000i			0.609557i
$219$	−6.00000	+	10.3923i	−0.405442	+	0.702247i
$220$		0			0
$221$		0			0
$222$	10.3923	+	6.00000i	0.697486	+	0.402694i
$223$		−	28.0000i		−	1.87502i	−0.347960	−	0.937509i	$-0.613126\pi$
$223$		−	28.0000i		−	1.87502i	0.347960	−	0.937509i	$-0.386874\pi$
$224$	2.50000	−	0.866025i	0.167038	−	0.0578638i
$225$		0			0
$226$	−1.00000	+	1.73205i	−0.0665190	+	0.115214i
$227$	−3.46410	+	2.00000i	−0.229920	+	0.132745i	−0.610535	−	0.791989i	$-0.709046\pi$
$227$	−3.46410	+	2.00000i	−0.229920	+	0.132745i	0.380615	+	0.924734i	$0.375712\pi$
$228$	15.5885	−	9.00000i	1.03237	−	0.596040i
$229$	11.0000	−	19.0526i	0.726900	−	1.25903i	−0.231287	−	0.972886i	$-0.574293\pi$
$229$	11.0000	−	19.0526i	0.726900	−	1.25903i	0.958187	−	0.286143i	$-0.0923732\pi$
$230$		0			0
$231$	−12.0000	−	10.3923i	−0.789542	−	0.683763i
$232$			9.00000i			0.590879i
$233$	20.7846	+	12.0000i	1.36165	+	0.786146i	0.989843	−	0.142166i	$-0.0454066\pi$
$233$	20.7846	+	12.0000i	1.36165	+	0.786146i	0.371802	+	0.928312i	$0.378740\pi$
$234$		0			0
$235$		0			0
$236$	−5.00000	+	8.66025i	−0.325472	+	0.563735i
$237$			30.0000i			1.94871i
$238$	10.3923	+	2.00000i	0.673633	+	0.129641i
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$		0			0
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	0.658838	−	0.752285i	$-0.271048\pi$
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	−0.980917	+	0.194429i	$0.937715\pi$
$242$	−6.06218	+	3.50000i	−0.389692	+	0.224989i
$243$		0			0
$244$	−1.00000			−0.0640184
$245$		0			0
$246$	−21.0000			−1.33891
$247$		0			0
$248$	3.46410	−	2.00000i	0.219971	−	0.127000i
$249$	−10.5000	−	18.1865i	−0.665410	−	1.15252i
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$	15.5885	+	3.00000i	0.981981	+	0.188982i
$253$			6.00000i			0.377217i
$254$	8.00000	−	13.8564i	0.501965	−	0.869428i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.92820	−	4.00000i	−0.432169	−	0.249513i	0.268101	−	0.963391i	$-0.413604\pi$
$257$	−6.92820	−	4.00000i	−0.432169	−	0.249513i	−0.700270	+	0.713878i	$0.746937\pi$
$258$			15.0000i			0.933859i
$259$	8.00000	+	6.92820i	0.497096	+	0.430498i
$260$		0			0
$261$	−27.0000	+	46.7654i	−1.67126	+	2.89470i
$262$	6.92820	−	4.00000i	0.428026	−	0.247121i
$263$	−4.33013	+	2.50000i	−0.267007	+	0.154157i	−0.627527	−	0.778595i	$-0.715933\pi$
$263$	−4.33013	+	2.50000i	−0.267007	+	0.154157i	0.360520	+	0.932752i	$0.382599\pi$
$264$	−3.00000	+	5.19615i	−0.184637	+	0.319801i
$265$		0			0
$266$	15.0000	−	5.19615i	0.919709	−	0.318597i
$267$			3.00000i			0.183597i
$268$	−7.79423	−	4.50000i	−0.476108	−	0.274881i
$269$	1.50000	+	2.59808i	0.0914566	+	0.158408i	0.908124	−	0.418701i	$-0.137514\pi$
$269$	1.50000	+	2.59808i	0.0914566	+	0.158408i	−0.816668	+	0.577108i	$0.804181\pi$
$270$		0			0
$271$	3.00000	−	5.19615i	0.182237	−	0.315644i	−0.760405	−	0.649449i	$-0.775000\pi$
$271$	3.00000	−	5.19615i	0.182237	−	0.315644i	0.942642	+	0.333805i	$0.108333\pi$
$272$		−	4.00000i		−	0.242536i
$273$		0			0
$274$	−12.0000			−0.724947
$275$		0			0
$276$	−4.50000	−	7.79423i	−0.270868	−	0.469157i
$277$	10.3923	−	6.00000i	0.624413	−	0.360505i	−0.154172	−	0.988044i	$-0.549271\pi$
$277$	10.3923	−	6.00000i	0.624413	−	0.360505i	0.778585	+	0.627539i	$0.215938\pi$
$278$	−12.1244	−	7.00000i	−0.727171	−	0.419832i
$279$	24.0000			1.43684
$280$		0			0
$281$	2.00000			0.119310			0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000			0.119310			0.0596550	+	0.998219i	$0.481000\pi$
$282$	−20.7846	−	12.0000i	−1.23771	−	0.714590i
$283$	3.46410	−	2.00000i	0.205919	−	0.118888i	−0.393494	−	0.919327i	$-0.628734\pi$
$283$	3.46410	−	2.00000i	0.205919	−	0.118888i	0.599414	+	0.800439i	$0.295400\pi$
$284$	1.00000	+	1.73205i	0.0593391	+	0.102778i
$285$		0			0
$286$		0			0
$287$	−18.1865	−	3.50000i	−1.07352	−	0.206598i
$288$		−	6.00000i		−	0.353553i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$		0			0
$291$	−21.0000	−	36.3731i	−1.23104	−	2.13223i
$292$	3.46410	+	2.00000i	0.202721	+	0.117041i
$293$		−	28.0000i		−	1.63578i	−0.575376	−	0.817889i	$-0.695144\pi$
$293$		−	28.0000i		−	1.63578i	0.575376	−	0.817889i	$-0.304856\pi$
$294$	19.5000	+	7.79423i	1.13726	+	0.454569i
$295$		0			0
$296$	2.00000	−	3.46410i	0.116248	−	0.201347i
$297$	−15.5885	+	9.00000i	−0.904534	+	0.522233i
$298$	−2.59808	+	1.50000i	−0.150503	+	0.0868927i
$299$		0			0
$300$		0			0
$301$	−2.50000	+	12.9904i	−0.144098	+	0.748753i
$302$		−	16.0000i		−	0.920697i
$303$	7.79423	+	4.50000i	0.447767	+	0.258518i
$304$	−3.00000	−	5.19615i	−0.172062	−	0.298020i
$305$		0			0
$306$	12.0000	−	20.7846i	0.685994	−	1.18818i
$307$			7.00000i			0.399511i	0.979846	+	0.199756i	$0.0640148\pi$
$307$			7.00000i			0.399511i	−0.979846	+	0.199756i	$0.935985\pi$
$308$	−3.46410	+	4.00000i	−0.197386	+	0.227921i
$309$	−3.00000			−0.170664
$310$		0			0
$311$	9.00000	+	15.5885i	0.510343	+	0.883940i	0.999928	+	0.0119847i	$0.00381495\pi$
$311$	9.00000	+	15.5885i	0.510343	+	0.883940i	−0.489585	+	0.871956i	$0.662852\pi$
$312$		0			0
$313$	6.92820	+	4.00000i	0.391605	+	0.226093i	0.682855	−	0.730554i	$-0.260738\pi$
$313$	6.92820	+	4.00000i	0.391605	+	0.226093i	−0.291250	+	0.956647i	$0.594071\pi$
$314$	−10.0000			−0.564333
$315$		0			0
$316$	10.0000			0.562544
$317$	27.7128	+	16.0000i	1.55651	+	0.898650i	0.997587	+	0.0694277i	$0.0221173\pi$
$317$	27.7128	+	16.0000i	1.55651	+	0.898650i	0.558920	+	0.829222i	$0.311216\pi$
$318$	5.19615	−	3.00000i	0.291386	−	0.168232i
$319$	−9.00000	−	15.5885i	−0.503903	−	0.872786i
$320$		0			0
$321$	9.00000			0.502331
$322$	−2.59808	−	7.50000i	−0.144785	−	0.417959i
$323$		−	24.0000i		−	1.33540i
$324$	4.50000	−	7.79423i	0.250000	−	0.433013i
$325$		0			0
$326$	2.00000	+	3.46410i	0.110770	+	0.191859i
$327$	23.3827	+	13.5000i	1.29307	+	0.746552i
$328$			7.00000i			0.386510i
$329$	−16.0000	−	13.8564i	−0.882109	−	0.763928i
$330$		0			0
$331$	16.0000	−	27.7128i	0.879440	−	1.52323i	0.0274825	−	0.999622i	$-0.491251\pi$
$331$	16.0000	−	27.7128i	0.879440	−	1.52323i	0.851957	−	0.523612i	$-0.175416\pi$
$332$	−6.06218	+	3.50000i	−0.332705	+	0.192087i
$333$	20.7846	−	12.0000i	1.13899	−	0.657596i
$334$	−10.5000	+	18.1865i	−0.574534	+	0.995123i
$335$		0			0
$336$	1.50000	−	7.79423i	0.0818317	−	0.425210i
$337$		−	26.0000i		−	1.41631i	−0.706057	−	0.708155i	$-0.749528\pi$
$337$		−	26.0000i		−	1.41631i	0.706057	−	0.708155i	$-0.250472\pi$
$338$	−11.2583	−	6.50000i	−0.612372	−	0.353553i
$339$	3.00000	+	5.19615i	0.162938	+	0.282216i
$340$		0			0
$341$	−4.00000	+	6.92820i	−0.216612	+	0.375183i
$342$		−	36.0000i		−	1.94666i
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$	5.00000			0.269582
$345$		0			0
$346$	−4.00000	−	6.92820i	−0.215041	−	0.372463i
$347$	16.4545	−	9.50000i	0.883323	−	0.509987i	0.0115703	−	0.999933i	$-0.496317\pi$
$347$	16.4545	−	9.50000i	0.883323	−	0.509987i	0.871753	+	0.489946i	$0.162984\pi$
$348$	23.3827	+	13.5000i	1.25344	+	0.723676i
$349$	35.0000			1.87351			0.936754	−	0.349990i	$-0.113815\pi$
$349$	35.0000			1.87351			0.936754	+	0.349990i	$0.113815\pi$
$350$		0			0
$351$		0			0
$352$	1.73205	+	1.00000i	0.0923186	+	0.0533002i
$353$	15.5885	−	9.00000i	0.829690	−	0.479022i	−0.0240566	−	0.999711i	$-0.507658\pi$
$353$	15.5885	−	9.00000i	0.829690	−	0.479022i	0.853746	+	0.520689i	$0.174325\pi$
$354$	15.0000	+	25.9808i	0.797241	+	1.38086i
$355$		0			0
$356$	1.00000			0.0529999
$357$	20.7846	−	24.0000i	1.10004	−	1.27021i
$358$		−	12.0000i		−	0.634220i
$359$	−2.00000	+	3.46410i	−0.105556	+	0.182828i	−0.913965	−	0.405793i	$-0.866996\pi$
$359$	−2.00000	+	3.46410i	−0.105556	+	0.182828i	0.808409	+	0.588621i	$0.200329\pi$
$360$		0			0
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$	−6.06218	−	3.50000i	−0.318621	−	0.183956i
$363$			21.0000i			1.10221i
$364$		0			0
$365$		0			0
$366$	−1.50000	+	2.59808i	−0.0784063	+	0.135804i
$367$	−9.52628	+	5.50000i	−0.497268	+	0.287098i	−0.727585	−	0.686018i	$-0.759357\pi$
$367$	−9.52628	+	5.50000i	−0.497268	+	0.287098i	0.230317	+	0.973116i	$0.426024\pi$
$368$	−2.59808	+	1.50000i	−0.135434	+	0.0781929i
$369$	−21.0000	+	36.3731i	−1.09322	+	1.89351i
$370$		0			0
$371$	5.00000	−	1.73205i	0.259587	−	0.0899236i
$372$		−	12.0000i		−	0.622171i
$373$	−3.46410	−	2.00000i	−0.179364	−	0.103556i	0.407630	−	0.913147i	$-0.366355\pi$
$373$	−3.46410	−	2.00000i	−0.179364	−	0.103556i	−0.586994	+	0.809591i	$0.699689\pi$
$374$	4.00000	+	6.92820i	0.206835	+	0.358249i
$375$		0			0
$376$	−4.00000	+	6.92820i	−0.206284	+	0.357295i
$377$		0			0
$378$	15.5885	−	18.0000i	0.801784	−	0.925820i
$379$	−30.0000			−1.54100			−0.770498	−	0.637442i	$-0.779993\pi$
$379$	−30.0000			−1.54100			−0.770498	+	0.637442i	$0.779993\pi$
$380$		0			0
$381$	−24.0000	−	41.5692i	−1.22956	−	2.12966i
$382$	−15.5885	+	9.00000i	−0.797575	+	0.460480i
$383$	12.9904	+	7.50000i	0.663777	+	0.383232i	0.793715	−	0.608290i	$-0.208144\pi$
$383$	12.9904	+	7.50000i	0.663777	+	0.383232i	−0.129937	+	0.991522i	$0.541478\pi$
$384$	−3.00000			−0.153093
$385$		0			0
$386$	26.0000			1.32337
$387$	25.9808	+	15.0000i	1.32068	+	0.762493i
$388$	−12.1244	+	7.00000i	−0.615521	+	0.355371i
$389$	13.0000	+	22.5167i	0.659126	+	1.14164i	0.980842	+	0.194804i	$0.0624070\pi$
$389$	13.0000	+	22.5167i	0.659126	+	1.14164i	−0.321716	+	0.946836i	$0.604260\pi$
$390$		0			0
$391$	−12.0000			−0.606866
$392$	2.59808	−	6.50000i	0.131223	−	0.328300i
$393$		−	24.0000i		−	1.21064i
$394$	1.00000	−	1.73205i	0.0503793	−	0.0872595i
$395$		0			0
$396$	6.00000	+	10.3923i	0.301511	+	0.522233i
$397$	−19.0526	−	11.0000i	−0.956221	−	0.552074i	−0.0612128	−	0.998125i	$-0.519497\pi$
$397$	−19.0526	−	11.0000i	−0.956221	−	0.552074i	−0.895008	+	0.446051i	$0.852830\pi$
$398$			4.00000i			0.200502i
$399$	9.00000	−	46.7654i	0.450564	−	2.34120i
$400$		0			0
$401$	−15.5000	+	26.8468i	−0.774033	+	1.34066i	0.161303	+	0.986905i	$0.448430\pi$
$401$	−15.5000	+	26.8468i	−0.774033	+	1.34066i	−0.935336	+	0.353760i	$0.884903\pi$
$402$	−23.3827	+	13.5000i	−1.16622	+	0.673319i
$403$		0			0
$404$	1.50000	−	2.59808i	0.0746278	−	0.129259i
$405$		0			0
$406$	18.0000	+	15.5885i	0.893325	+	0.773642i
$407$			8.00000i			0.396545i
$408$	−10.3923	−	6.00000i	−0.514496	−	0.297044i
$409$	1.50000	+	2.59808i	0.0741702	+	0.128467i	0.900725	−	0.434389i	$-0.143036\pi$
$409$	1.50000	+	2.59808i	0.0741702	+	0.128467i	−0.826555	+	0.562856i	$0.809703\pi$
$410$		0			0
$411$	−18.0000	+	31.1769i	−0.887875	+	1.53784i
$412$			1.00000i			0.0492665i
$413$	8.66025	+	25.0000i	0.426143	+	1.23017i
$414$	−18.0000			−0.884652
$415$		0			0
$416$		0			0
$417$	−36.3731	+	21.0000i	−1.78120	+	1.02837i
$418$	10.3923	+	6.00000i	0.508304	+	0.293470i
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	−19.0000			−0.926003			−0.463002	−	0.886357i	$-0.653228\pi$
$421$	−19.0000			−0.926003			−0.463002	+	0.886357i	$0.653228\pi$
$422$	22.5167	+	13.0000i	1.09609	+	0.632830i
$423$	−41.5692	+	24.0000i	−2.02116	+	1.16692i
$424$	−1.00000	−	1.73205i	−0.0485643	−	0.0841158i
$425$		0			0
$426$	6.00000			0.290701
$427$	−1.73205	+	2.00000i	−0.0838198	+	0.0967868i
$428$		−	3.00000i		−	0.145010i
$429$		0			0
$430$		0			0
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	0.959985	+	0.280052i	$0.0903517\pi$
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	−0.237460	+	0.971397i	$0.576315\pi$
$432$	−7.79423	−	4.50000i	−0.375000	−	0.216506i
$433$		−	14.0000i		−	0.672797i	−0.941720	−	0.336399i	$-0.890791\pi$
$433$		−	14.0000i		−	0.672797i	0.941720	−	0.336399i	$-0.109209\pi$
$434$	2.00000	−	10.3923i	0.0960031	−	0.498847i
$435$		0			0
$436$	4.50000	−	7.79423i	0.215511	−	0.373276i
$437$	−15.5885	+	9.00000i	−0.745697	+	0.430528i
$438$	10.3923	−	6.00000i	0.496564	−	0.286691i
$439$	−10.0000	+	17.3205i	−0.477274	+	0.826663i	−0.999661	−	0.0260459i	$-0.991708\pi$
$439$	−10.0000	+	17.3205i	−0.477274	+	0.826663i	0.522387	+	0.852709i	$0.325042\pi$
$440$		0			0
$441$	33.0000	−	25.9808i	1.57143	−	1.23718i
$442$		0			0
$443$	26.8468	+	15.5000i	1.27553	+	0.736427i	0.976023	−	0.217667i	$-0.0698447\pi$
$443$	26.8468	+	15.5000i	1.27553	+	0.736427i	0.299506	+	0.954094i	$0.403178\pi$
$444$	−6.00000	−	10.3923i	−0.284747	−	0.493197i
$445$		0			0
$446$	−14.0000	+	24.2487i	−0.662919	+	1.14821i
$447$			9.00000i			0.425685i
$448$	−2.59808	−	0.500000i	−0.122748	−	0.0236228i
$449$	33.0000			1.55737			0.778683	−	0.627417i	$-0.215888\pi$
$449$	33.0000			1.55737			0.778683	+	0.627417i	$0.215888\pi$
$450$		0			0
$451$	−7.00000	−	12.1244i	−0.329617	−	0.570914i
$452$	1.73205	−	1.00000i	0.0814688	−	0.0470360i
$453$	−41.5692	−	24.0000i	−1.95309	−	1.12762i
$454$	4.00000			0.187729
$455$		0			0
$456$	−18.0000			−0.842927
$457$	27.7128	+	16.0000i	1.29635	+	0.748448i	0.979772	−	0.200118i	$-0.0641325\pi$
$457$	27.7128	+	16.0000i	1.29635	+	0.748448i	0.316579	+	0.948566i	$0.397466\pi$
$458$	−19.0526	+	11.0000i	−0.890268	+	0.513996i
$459$	−18.0000	−	31.1769i	−0.840168	−	1.45521i
$460$		0			0
$461$	−14.0000			−0.652045			−0.326023	−	0.945362i	$-0.605709\pi$
$461$	−14.0000			−0.652045			−0.326023	+	0.945362i	$0.605709\pi$
$462$	5.19615	+	15.0000i	0.241747	+	0.697863i
$463$			19.0000i			0.883005i	0.897260	+	0.441502i	$0.145554\pi$
$463$			19.0000i			0.883005i	−0.897260	+	0.441502i	$0.854446\pi$
$464$	4.50000	−	7.79423i	0.208907	−	0.361838i
$465$		0			0
$466$	−12.0000	−	20.7846i	−0.555889	−	0.962828i
$467$	11.2583	+	6.50000i	0.520973	+	0.300784i	0.737333	−	0.675530i	$-0.236085\pi$
$467$	11.2583	+	6.50000i	0.520973	+	0.300784i	−0.216359	+	0.976314i	$0.569418\pi$
$468$		0			0
$469$	−22.5000	+	7.79423i	−1.03895	+	0.359904i
$470$		0			0
$471$	−15.0000	+	25.9808i	−0.691164	+	1.19713i
$472$	8.66025	−	5.00000i	0.398621	−	0.230144i
$473$	−8.66025	+	5.00000i	−0.398199	+	0.229900i
$474$	15.0000	−	25.9808i	0.688973	−	1.19334i
$475$		0			0
$476$	−8.00000	−	6.92820i	−0.366679	−	0.317554i
$477$		−	12.0000i		−	0.549442i
$478$	13.8564	+	8.00000i	0.633777	+	0.365911i
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	0.998392	+	0.0566937i	$0.0180558\pi$
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	−0.450098	+	0.892979i	$0.648611\pi$
$480$		0			0
$481$		0			0
$482$			10.0000i			0.455488i
$483$	−23.3827	−	4.50000i	−1.06395	−	0.204757i
$484$	7.00000			0.318182
$485$		0			0
$486$		0			0
$487$	−13.8564	+	8.00000i	−0.627894	+	0.362515i	−0.779936	−	0.625859i	$-0.784748\pi$
$487$	−13.8564	+	8.00000i	−0.627894	+	0.362515i	0.152042	+	0.988374i	$0.451415\pi$
$488$	0.866025	+	0.500000i	0.0392031	+	0.0226339i
$489$	12.0000			0.542659
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$	18.1865	+	10.5000i	0.819912	+	0.473377i
$493$	31.1769	−	18.0000i	1.40414	−	0.810679i
$494$		0			0
$495$		0			0
$496$	−4.00000			−0.179605
$497$	5.19615	+	1.00000i	0.233079	+	0.0448561i
$498$			21.0000i			0.941033i
$499$	−9.00000	+	15.5885i	−0.402895	+	0.697835i	−0.994074	−	0.108705i	$-0.965329\pi$
$499$	−9.00000	+	15.5885i	−0.402895	+	0.697835i	0.591179	+	0.806541i	$0.298663\pi$
$500$		0			0
$501$	31.5000	+	54.5596i	1.40732	+	2.43754i
$502$		0			0
$503$			21.0000i			0.936344i	0.883637	+	0.468172i	$0.155087\pi$
$503$			21.0000i			0.936344i	−0.883637	+	0.468172i	$0.844913\pi$
$504$	−12.0000	−	10.3923i	−0.534522	−	0.462910i
$505$		0			0
$506$	3.00000	−	5.19615i	0.133366	−	0.230997i
$507$	−33.7750	+	19.5000i	−1.50000	+	0.866025i
$508$	−13.8564	+	8.00000i	−0.614779	+	0.354943i
$509$	0.500000	−	0.866025i	0.0221621	−	0.0383859i	−0.854732	−	0.519070i	$-0.826278\pi$
$509$	0.500000	−	0.866025i	0.0221621	−	0.0383859i	0.876894	+	0.480684i	$0.159612\pi$
$510$		0			0
$511$	10.0000	−	3.46410i	0.442374	−	0.153243i
$512$			1.00000i			0.0441942i
$513$	−46.7654	−	27.0000i	−2.06474	−	1.19208i
$514$	4.00000	+	6.92820i	0.176432	+	0.305590i
$515$		0			0
$516$	7.50000	−	12.9904i	0.330169	−	0.571870i
$517$		−	16.0000i		−	0.703679i
$518$	−3.46410	−	10.0000i	−0.152204	−	0.439375i
$519$	−24.0000			−1.05348
$520$		0			0
$521$	−19.0000	−	32.9090i	−0.832405	−	1.44177i	−0.896126	−	0.443800i	$-0.853630\pi$
$521$	−19.0000	−	32.9090i	−0.832405	−	1.44177i	0.0637207	−	0.997968i	$-0.479703\pi$
$522$	46.7654	−	27.0000i	2.04686	−	1.18176i
$523$	−17.3205	−	10.0000i	−0.757373	−	0.437269i	0.0709788	−	0.997478i	$-0.477388\pi$
$523$	−17.3205	−	10.0000i	−0.757373	−	0.437269i	−0.828352	+	0.560208i	$0.810721\pi$
$524$	−8.00000			−0.349482
$525$		0			0
$526$	5.00000			0.218010
$527$	−13.8564	−	8.00000i	−0.603595	−	0.348485i
$528$	5.19615	−	3.00000i	0.226134	−	0.130558i
$529$	−7.00000	−	12.1244i	−0.304348	−	0.527146i
$530$		0			0
$531$	60.0000			2.60378
$532$	−15.5885	−	3.00000i	−0.675845	−	0.130066i
$533$		0			0
$534$	1.50000	−	2.59808i	0.0649113	−	0.112430i
$535$		0			0
$536$	4.50000	+	7.79423i	0.194370	+	0.336659i
$537$	−31.1769	−	18.0000i	−1.34538	−	0.776757i
$538$		−	3.00000i		−	0.129339i
$539$	2.00000	+	13.8564i	0.0861461	+	0.596838i
$540$		0			0
$541$	−1.50000	+	2.59808i	−0.0644900	+	0.111700i	−0.896468	−	0.443109i	$-0.853875\pi$
$541$	−1.50000	+	2.59808i	−0.0644900	+	0.111700i	0.831978	+	0.554809i	$0.187209\pi$
$542$	−5.19615	+	3.00000i	−0.223194	+	0.128861i
$543$	−18.1865	+	10.5000i	−0.780459	+	0.450598i
$544$	−2.00000	+	3.46410i	−0.0857493	+	0.148522i
$545$		0			0
$546$		0			0
$547$		−	33.0000i		−	1.41098i	−0.708721	−	0.705489i	$-0.750727\pi$
$547$		−	33.0000i		−	1.41098i	0.708721	−	0.705489i	$-0.249273\pi$
$548$	10.3923	+	6.00000i	0.443937	+	0.256307i
$549$	3.00000	+	5.19615i	0.128037	+	0.221766i
$550$		0			0
$551$	27.0000	−	46.7654i	1.15024	−	1.99227i
$552$			9.00000i			0.383065i
$553$	17.3205	−	20.0000i	0.736543	−	0.850487i
$554$	−12.0000			−0.509831
$555$		0			0
$556$	7.00000	+	12.1244i	0.296866	+	0.514187i
$557$	−1.73205	+	1.00000i	−0.0733893	+	0.0423714i	−0.536246	−	0.844062i	$-0.680158\pi$
$557$	−1.73205	+	1.00000i	−0.0733893	+	0.0423714i	0.462856	+	0.886433i	$0.346825\pi$
$558$	−20.7846	−	12.0000i	−0.879883	−	0.508001i
$559$		0			0
$560$		0			0
$561$	24.0000			1.01328
$562$	−1.73205	−	1.00000i	−0.0730622	−	0.0421825i
$563$	−14.7224	+	8.50000i	−0.620477	+	0.358232i	−0.777055	−	0.629433i	$-0.783287\pi$
$563$	−14.7224	+	8.50000i	−0.620477	+	0.358232i	0.156578	+	0.987666i	$0.449954\pi$
$564$	12.0000	+	20.7846i	0.505291	+	0.875190i
$565$		0			0
$566$	−4.00000			−0.168133
$567$	−7.79423	−	22.5000i	−0.327327	−	0.944911i
$568$		−	2.00000i		−	0.0839181i
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	−0.990668	−	0.136295i	$-0.956481\pi$
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	0.613369	+	0.789797i	$0.289814\pi$
$570$		0			0
$571$	15.0000	+	25.9808i	0.627730	+	1.08726i	0.988006	+	0.154415i	$0.0493493\pi$
$571$	15.0000	+	25.9808i	0.627730	+	1.08726i	−0.360276	+	0.932846i	$0.617317\pi$
$572$		0			0
$573$			54.0000i			2.25588i
$574$	14.0000	+	12.1244i	0.584349	+	0.506061i
$575$		0			0
$576$	−3.00000	+	5.19615i	−0.125000	+	0.216506i
$577$	8.66025	−	5.00000i	0.360531	−	0.208153i	−0.308783	−	0.951133i	$-0.599922\pi$
$577$	8.66025	−	5.00000i	0.360531	−	0.208153i	0.669314	+	0.742980i	$0.266588\pi$
$578$	0.866025	−	0.500000i	0.0360219	−	0.0207973i
$579$	39.0000	−	67.5500i	1.62078	−	2.80728i
$580$		0			0
$581$	−3.50000	+	18.1865i	−0.145204	+	0.754505i
$582$			42.0000i			1.74096i
$583$	3.46410	+	2.00000i	0.143468	+	0.0828315i
$584$	−2.00000	−	3.46410i	−0.0827606	−	0.143346i
$585$		0			0
$586$	−14.0000	+	24.2487i	−0.578335	+	1.00171i
$587$		−	28.0000i		−	1.15568i	−0.816149	−	0.577842i	$-0.803895\pi$
$587$		−	28.0000i		−	1.15568i	0.816149	−	0.577842i	$-0.196105\pi$
$588$	−12.9904	−	16.5000i	−0.535714	−	0.680449i
$589$	−24.0000			−0.988903
$590$		0			0
$591$	−3.00000	−	5.19615i	−0.123404	−	0.213741i
$592$	−3.46410	+	2.00000i	−0.142374	+	0.0821995i
$593$	−5.19615	−	3.00000i	−0.213380	−	0.123195i	0.389501	−	0.921026i	$-0.372647\pi$
$593$	−5.19615	−	3.00000i	−0.213380	−	0.123195i	−0.602881	+	0.797831i	$0.705981\pi$
$594$	18.0000			0.738549
$595$		0			0
$596$	3.00000			0.122885
$597$	10.3923	+	6.00000i	0.425329	+	0.245564i
$598$		0			0
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	0.962175	−	0.272433i	$-0.0878284\pi$
$599$	6.00000	+	10.3923i	0.245153	+	0.424618i	−0.717021	+	0.697051i	$0.754495\pi$
$600$		0			0
$601$	42.0000			1.71322			0.856608	−	0.515968i	$-0.172568\pi$
$601$	42.0000			1.71322			0.856608	+	0.515968i	$0.172568\pi$
$602$	8.66025	−	10.0000i	0.352966	−	0.407570i
$603$			54.0000i			2.19905i
$604$	−8.00000	+	13.8564i	−0.325515	+	0.563809i
$605$		0			0
$606$	−4.50000	−	7.79423i	−0.182800	−	0.316619i
$607$	−0.866025	−	0.500000i	−0.0351509	−	0.0202944i	0.482322	−	0.875994i	$-0.339794\pi$
$607$	−0.866025	−	0.500000i	−0.0351509	−	0.0202944i	−0.517472	+	0.855700i	$0.673127\pi$
$608$			6.00000i			0.243332i
$609$	67.5000	−	23.3827i	2.73524	−	0.947514i
$610$		0			0
$611$		0			0
$612$	−20.7846	+	12.0000i	−0.840168	+	0.485071i
$613$	−10.3923	+	6.00000i	−0.419741	+	0.242338i	−0.694967	−	0.719042i	$-0.744581\pi$
$613$	−10.3923	+	6.00000i	−0.419741	+	0.242338i	0.275225	+	0.961380i	$0.411248\pi$
$614$	3.50000	−	6.06218i	0.141249	−	0.244650i
$615$		0			0
$616$	5.00000	−	1.73205i	0.201456	−	0.0697863i
$617$			44.0000i			1.77137i	0.464283	+	0.885687i	$0.346312\pi$
$617$			44.0000i			1.77137i	−0.464283	+	0.885687i	$0.653688\pi$
$618$	2.59808	+	1.50000i	0.104510	+	0.0603388i
$619$	−23.0000	−	39.8372i	−0.924448	−	1.60119i	−0.792446	−	0.609941i	$-0.791193\pi$
$619$	−23.0000	−	39.8372i	−0.924448	−	1.60119i	−0.132002	−	0.991250i	$-0.542140\pi$
$620$		0			0
$621$	−13.5000	+	23.3827i	−0.541736	+	0.938315i
$622$		−	18.0000i		−	0.721734i
$623$	1.73205	−	2.00000i	0.0693932	−	0.0801283i
$624$		0			0
$625$		0			0
$626$	−4.00000	−	6.92820i	−0.159872	−	0.276907i
$627$	31.1769	−	18.0000i	1.24509	−	0.718851i
$628$	8.66025	+	5.00000i	0.345582	+	0.199522i
$629$	−16.0000			−0.637962
$630$		0			0
$631$	2.00000			0.0796187			0.0398094	−	0.999207i	$-0.487325\pi$
$631$	2.00000			0.0796187			0.0398094	+	0.999207i	$0.487325\pi$
$632$	−8.66025	−	5.00000i	−0.344486	−	0.198889i
$633$	67.5500	−	39.0000i	2.68487	−	1.55011i
$634$	−16.0000	−	27.7128i	−0.635441	−	1.10062i
$635$		0			0
$636$	−6.00000			−0.237915
$637$		0			0
$638$			18.0000i			0.712627i
$639$	6.00000	−	10.3923i	0.237356	−	0.411113i
$640$		0			0
$641$	−2.50000	−	4.33013i	−0.0987441	−	0.171030i	0.812421	−	0.583071i	$-0.198149\pi$
$641$	−2.50000	−	4.33013i	−0.0987441	−	0.171030i	−0.911165	+	0.412042i	$0.864816\pi$
$642$	−7.79423	−	4.50000i	−0.307614	−	0.177601i
$643$		−	28.0000i		−	1.10421i	−0.833774	−	0.552106i	$-0.813824\pi$
$643$		−	28.0000i		−	1.10421i	0.833774	−	0.552106i	$-0.186176\pi$
$644$	−1.50000	+	7.79423i	−0.0591083	+	0.307136i
$645$		0			0
$646$	−12.0000	+	20.7846i	−0.472134	+	0.817760i
$647$	−9.52628	+	5.50000i	−0.374517	+	0.216227i	−0.675430	−	0.737424i	$-0.736042\pi$
$647$	−9.52628	+	5.50000i	−0.374517	+	0.216227i	0.300913	+	0.953652i	$0.402709\pi$
$648$	−7.79423	+	4.50000i	−0.306186	+	0.176777i
$649$	−10.0000	+	17.3205i	−0.392534	+	0.679889i
$650$		0			0
$651$	−24.0000	−	20.7846i	−0.940634	−	0.814613i
$652$		−	4.00000i		−	0.156652i
$653$	−3.46410	−	2.00000i	−0.135561	−	0.0782660i	0.430686	−	0.902502i	$-0.358272\pi$
$653$	−3.46410	−	2.00000i	−0.135561	−	0.0782660i	−0.566247	+	0.824236i	$0.691605\pi$
$654$	−13.5000	−	23.3827i	−0.527892	−	0.914335i
$655$		0			0
$656$	3.50000	−	6.06218i	0.136652	−	0.236688i
$657$		−	24.0000i		−	0.936329i
$658$	6.92820	+	20.0000i	0.270089	+	0.779681i
$659$	26.0000			1.01282			0.506408	−	0.862294i	$-0.330973\pi$
$659$	26.0000			1.01282			0.506408	+	0.862294i	$0.330973\pi$
$660$		0			0
$661$	5.50000	+	9.52628i	0.213925	+	0.370529i	0.952940	−	0.303160i	$-0.0980418\pi$
$661$	5.50000	+	9.52628i	0.213925	+	0.370529i	−0.739014	+	0.673690i	$0.764708\pi$
$662$	−27.7128	+	16.0000i	−1.07709	+	0.621858i
$663$		0			0
$664$	7.00000			0.271653
$665$		0			0
$666$	−24.0000			−0.929981
$667$	−23.3827	−	13.5000i	−0.905381	−	0.522722i
$668$	18.1865	−	10.5000i	0.703658	−	0.406257i
$669$	42.0000	+	72.7461i	1.62381	+	2.81253i
$670$		0			0
$671$	−2.00000			−0.0772091
$672$	−5.19615	+	6.00000i	−0.200446	+	0.231455i
$673$		−	16.0000i		−	0.616755i	−0.951264	−	0.308377i	$-0.900214\pi$
$673$		−	16.0000i		−	0.616755i	0.951264	−	0.308377i	$-0.0997859\pi$
$674$	−13.0000	+	22.5167i	−0.500741	+	0.867309i
$675$		0			0
$676$	6.50000	+	11.2583i	0.250000	+	0.433013i
$677$	41.5692	+	24.0000i	1.59763	+	0.922395i	0.991941	+	0.126697i	$0.0404375\pi$
$677$	41.5692	+	24.0000i	1.59763	+	0.922395i	0.605693	+	0.795698i	$0.292896\pi$
$678$		−	6.00000i		−	0.230429i
$679$	−7.00000	+	36.3731i	−0.268635	+	1.39587i
$680$		0			0
$681$	6.00000	−	10.3923i	0.229920	−	0.398234i
$682$	6.92820	−	4.00000i	0.265295	−	0.153168i
$683$	32.0429	−	18.5000i	1.22609	−	0.707883i	0.259880	−	0.965641i	$-0.416317\pi$
$683$	32.0429	−	18.5000i	1.22609	−	0.707883i	0.966209	+	0.257758i	$0.0829838\pi$
$684$	−18.0000	+	31.1769i	−0.688247	+	1.19208i
$685$		0			0
$686$	−8.50000	−	16.4545i	−0.324532	−	0.628235i
$687$			66.0000i			2.51806i
$688$	−4.33013	−	2.50000i	−0.165085	−	0.0953116i
$689$		0			0
$690$		0			0
$691$	−11.0000	+	19.0526i	−0.418460	+	0.724793i	−0.995785	−	0.0917209i	$-0.970763\pi$
$691$	−11.0000	+	19.0526i	−0.418460	+	0.724793i	0.577325	+	0.816514i	$0.304097\pi$
$692$			8.00000i			0.304114i
$693$	31.1769	+	6.00000i	1.18431	+	0.227921i
$694$	−19.0000			−0.721230
$695$		0			0
$696$	−13.5000	−	23.3827i	−0.511716	−	0.886318i
$697$	24.2487	−	14.0000i	0.918485	−	0.530288i
$698$	−30.3109	−	17.5000i	−1.14728	−	0.662385i
$699$	−72.0000			−2.72329
$700$		0			0
$701$	−47.0000			−1.77517			−0.887583	−	0.460648i	$-0.847617\pi$
$701$	−47.0000			−1.77517			−0.887583	+	0.460648i	$0.847617\pi$
$702$		0			0
$703$	−20.7846	+	12.0000i	−0.783906	+	0.452589i
$704$	−1.00000	−	1.73205i	−0.0376889	−	0.0652791i
$705$		0			0
$706$	−18.0000			−0.677439
$707$	−2.59808	−	7.50000i	−0.0977107	−	0.282067i
$708$		−	30.0000i		−	1.12747i
$709$	−5.50000	+	9.52628i	−0.206557	+	0.357767i	−0.950628	−	0.310334i	$-0.899559\pi$
$709$	−5.50000	+	9.52628i	−0.206557	+	0.357767i	0.744071	+	0.668101i	$0.232892\pi$
$710$		0			0
$711$	−30.0000	−	51.9615i	−1.12509	−	1.94871i
$712$	−0.866025	−	0.500000i	−0.0324557	−	0.0187383i
$713$			12.0000i			0.449404i
$714$	−30.0000	+	10.3923i	−1.12272	+	0.388922i
$715$		0			0
$716$	−6.00000	+	10.3923i	−0.224231	+	0.388379i
$717$	41.5692	−	24.0000i	1.55243	−	0.896296i
$718$	3.46410	−	2.00000i	0.129279	−	0.0746393i
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	−0.916529	−	0.399969i	$-0.869021\pi$
$719$	−3.00000	+	5.19615i	−0.111881	+	0.193784i	0.804648	+	0.593753i	$0.202354\pi$
$720$		0			0
$721$	2.00000	+	1.73205i	0.0744839	+	0.0645049i
$722$			17.0000i			0.632674i
$723$	25.9808	+	15.0000i	0.966235	+	0.557856i
$724$	3.50000	+	6.06218i	0.130076	+	0.225299i
$725$		0			0
$726$	10.5000	−	18.1865i	0.389692	−	0.674966i
$727$		−	21.0000i		−	0.778847i	−0.921059	−	0.389423i	$-0.872674\pi$
$727$		−	21.0000i		−	0.778847i	0.921059	−	0.389423i	$-0.127326\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$		0			0
$731$	−10.0000	−	17.3205i	−0.369863	−	0.640622i
$732$	2.59808	−	1.50000i	0.0960277	−	0.0554416i
$733$	19.0526	+	11.0000i	0.703722	+	0.406294i	0.808732	−	0.588177i	$-0.200154\pi$
$733$	19.0526	+	11.0000i	0.703722	+	0.406294i	−0.105010	+	0.994471i	$0.533487\pi$
$734$	11.0000			0.406017
$735$		0			0
$736$	3.00000			0.110581
$737$	−15.5885	−	9.00000i	−0.574208	−	0.331519i
$738$	36.3731	−	21.0000i	1.33891	−	0.773021i
$739$	−1.00000	−	1.73205i	−0.0367856	−	0.0637145i	0.847046	−	0.531519i	$-0.178379\pi$
$739$	−1.00000	−	1.73205i	−0.0367856	−	0.0637145i	−0.883832	+	0.467804i	$0.845045\pi$
$740$		0			0
$741$		0			0
$742$	−5.19615	−	1.00000i	−0.190757	−	0.0367112i
$743$		−	9.00000i		−	0.330178i	−0.986279	−	0.165089i	$-0.947209\pi$
$743$		−	9.00000i		−	0.330178i	0.986279	−	0.165089i	$-0.0527911\pi$
$744$	−6.00000	+	10.3923i	−0.219971	+	0.381000i
$745$		0			0
$746$	2.00000	+	3.46410i	0.0732252	+	0.126830i
$747$	36.3731	+	21.0000i	1.33082	+	0.768350i
$748$		−	8.00000i		−	0.292509i
$749$	−6.00000	−	5.19615i	−0.219235	−	0.189863i
$750$		0			0
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	−0.827225	−	0.561870i	$-0.810082\pi$
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	0.900207	+	0.435463i	$0.143415\pi$
$752$	6.92820	−	4.00000i	0.252646	−	0.145865i
$753$		0			0
$754$		0			0
$755$		0			0
$756$	−22.5000	+	7.79423i	−0.818317	+	0.283473i
$757$			16.0000i			0.581530i	0.956795	+	0.290765i	$0.0939098\pi$
$757$			16.0000i			0.581530i	−0.956795	+	0.290765i	$0.906090\pi$
$758$	25.9808	+	15.0000i	0.943664	+	0.544825i
$759$	−9.00000	−	15.5885i	−0.326679	−	0.565825i
$760$		0			0
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	−0.806514	−	0.591215i	$-0.798649\pi$
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	0.915264	+	0.402854i	$0.131982\pi$
$762$			48.0000i			1.73886i
$763$	−7.79423	−	22.5000i	−0.282170	−	0.814555i
$764$	18.0000			0.651217
$765$		0			0
$766$	−7.50000	−	12.9904i	−0.270986	−	0.469362i
$767$		0			0
$768$	2.59808	+	1.50000i	0.0937500	+	0.0541266i
$769$	14.0000			0.504853			0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000			0.504853			0.252426	+	0.967616i	$0.418771\pi$
$770$		0			0
$771$	24.0000			0.864339
$772$	−22.5167	−	13.0000i	−0.810392	−	0.467880i
$773$	−20.7846	+	12.0000i	−0.747570	+	0.431610i	−0.824815	−	0.565402i	$-0.808721\pi$
$773$	−20.7846	+	12.0000i	−0.747570	+	0.431610i	0.0772449	+	0.997012i	$0.475388\pi$
$774$	−15.0000	−	25.9808i	−0.539164	−	0.933859i
$775$		0			0
$776$	14.0000			0.502571
$777$	−31.1769	−	6.00000i	−1.11847	−	0.215249i
$778$		−	26.0000i		−	0.932145i
$779$	21.0000	−	36.3731i	0.752403	−	1.30320i
$780$		0			0
$781$	2.00000	+	3.46410i	0.0715656	+	0.123955i
$782$	10.3923	+	6.00000i	0.371628	+	0.214560i
$783$		−	81.0000i		−	2.89470i
$784$	−5.50000	+	4.33013i	−0.196429	+	0.154647i
$785$		0			0
$786$	−12.0000	+	20.7846i	−0.428026	+	0.741362i
$787$	26.8468	−	15.5000i	0.956985	−	0.552515i	0.0617409	−	0.998092i	$-0.480335\pi$
$787$	26.8468	−	15.5000i	0.956985	−	0.552515i	0.895244	+	0.445577i	$0.147001\pi$
$788$	−1.73205	+	1.00000i	−0.0617018	+	0.0356235i
$789$	7.50000	−	12.9904i	0.267007	−	0.462470i
$790$		0			0
$791$	1.00000	−	5.19615i	0.0355559	−	0.184754i
$792$		−	12.0000i		−	0.426401i
$793$		0			0
$794$	11.0000	+	19.0526i	0.390375	+	0.676150i
$795$		0			0
$796$	2.00000	−	3.46410i	0.0708881	−	0.122782i
$797$		0			0		1.00000			$0$
$797$		0			0		−1.00000			$\pi$
$798$	−31.1769	+	36.0000i	−1.10365	+	1.27439i
$799$	32.0000			1.13208
$800$		0			0
$801$	−3.00000	−	5.19615i	−0.106000	−	0.183597i
$802$	26.8468	−	15.5000i	0.947993	−	0.547324i
$803$	6.92820	+	4.00000i	0.244491	+	0.141157i
$804$	27.0000			0.952217
$805$		0			0
$806$		0			0
$807$	−7.79423	−	4.50000i	−0.274370	−	0.158408i
$808$	−2.59808	+	1.50000i	−0.0914000	+	0.0527698i
$809$	−25.5000	−	44.1673i	−0.896532	−	1.55284i	−0.831897	−	0.554930i	$-0.812745\pi$
$809$	−25.5000	−	44.1673i	−0.896532	−	1.55284i	−0.0646355	−	0.997909i	$-0.520588\pi$
$810$		0			0
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	−7.79423	−	22.5000i	−0.273524	−	0.789595i
$813$			18.0000i			0.631288i
$814$	4.00000	−	6.92820i	0.140200	−	0.242833i
$815$		0			0
$816$	6.00000	+	10.3923i	0.210042	+	0.363803i
$817$	−25.9808	−	15.0000i	−0.908952	−	0.524784i
$818$		−	3.00000i		−	0.104893i
$819$		0			0
$820$		0			0
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	−0.665144	−	0.746715i	$-0.731630\pi$
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	0.979246	+	0.202674i	$0.0649632\pi$
$822$	31.1769	−	18.0000i	1.08742	−	0.627822i
$823$	−16.4545	+	9.50000i	−0.573567	+	0.331149i	−0.758573	−	0.651588i	$-0.774103\pi$
$823$	−16.4545	+	9.50000i	−0.573567	+	0.331149i	0.185006	+	0.982737i	$0.440770\pi$
$824$	0.500000	−	0.866025i	0.0174183	−	0.0301694i
$825$		0			0
$826$	5.00000	−	25.9808i	0.173972	−	0.903986i
$827$		−	19.0000i		−	0.660695i	−0.943859	−	0.330347i	$-0.892834\pi$
$827$		−	19.0000i		−	0.660695i	0.943859	−	0.330347i	$-0.107166\pi$
$828$	15.5885	+	9.00000i	0.541736	+	0.312772i
$829$	−23.0000	−	39.8372i	−0.798823	−	1.38360i	−0.920383	−	0.391018i	$-0.872123\pi$
$829$	−23.0000	−	39.8372i	−0.798823	−	1.38360i	0.121560	−	0.992584i	$-0.461210\pi$
$830$		0			0
$831$	−18.0000	+	31.1769i	−0.624413	+	1.08152i
$832$		0			0
$833$	−27.7128	+	4.00000i	−0.960192	+	0.138592i
$834$	42.0000			1.45434
$835$		0			0
$836$	−6.00000	−	10.3923i	−0.207514	−	0.359425i
$837$	−31.1769	+	18.0000i	−1.07763	+	0.622171i
$838$		0			0
$839$	−14.0000			−0.483334			−0.241667	−	0.970359i	$-0.577694\pi$
$839$	−14.0000			−0.483334			−0.241667	+	0.970359i	$0.577694\pi$
$840$		0			0
$841$	52.0000			1.79310
$842$	16.4545	+	9.50000i	0.567059	+	0.327392i
$843$	−5.19615	+	3.00000i	−0.178965	+	0.103325i
$844$	−13.0000	−	22.5167i	−0.447478	−	0.775055i
$845$		0			0
$846$	48.0000			1.65027
$847$	12.1244	−	14.0000i	0.416598	−	0.481046i
$848$			2.00000i			0.0686803i
$849$	−6.00000	+	10.3923i	−0.205919	+	0.356663i
$850$		0			0
$851$	6.00000	+	10.3923i	0.205677	+	0.356244i
$852$	−5.19615	−	3.00000i	−0.178017	−	0.102778i
$853$		−	14.0000i		−	0.479351i	−0.970853	−	0.239675i	$-0.922959\pi$
$853$		−	14.0000i		−	0.479351i	0.970853	−	0.239675i	$-0.0770410\pi$
$854$	2.50000	−	0.866025i	0.0855482	−	0.0296348i
$855$		0			0
$856$	−1.50000	+	2.59808i	−0.0512689	+	0.0888004i
$857$	−15.5885	+	9.00000i	−0.532492	+	0.307434i	−0.742030	−	0.670366i	$-0.766137\pi$
$857$	−15.5885	+	9.00000i	−0.532492	+	0.307434i	0.209539	+	0.977800i	$0.432804\pi$
$858$		0			0
$859$	−24.0000	+	41.5692i	−0.818869	+	1.41832i	0.0876464	+	0.996152i	$0.472065\pi$
$859$	−24.0000	+	41.5692i	−0.818869	+	1.41832i	−0.906516	+	0.422172i	$0.861268\pi$
$860$		0			0
$861$	52.5000	−	18.1865i	1.78920	−	0.619795i
$862$		−	30.0000i		−	1.02180i
$863$	−9.52628	−	5.50000i	−0.324278	−	0.187222i	0.329020	−	0.944323i	$-0.393282\pi$
$863$	−9.52628	−	5.50000i	−0.324278	−	0.187222i	−0.653298	+	0.757101i	$0.726615\pi$
$864$	4.50000	+	7.79423i	0.153093	+	0.265165i
$865$		0			0
$866$	−7.00000	+	12.1244i	−0.237870	+	0.412002i
$867$		−	3.00000i		−	0.101885i
$868$	−6.92820	+	8.00000i	−0.235159	+	0.271538i
$869$	20.0000			0.678454
$870$		0			0
$871$		0			0
$872$	−7.79423	+	4.50000i	−0.263946	+	0.152389i
$873$	72.7461	+	42.0000i	2.46208	+	1.42148i
$874$	18.0000			0.608859
$875$		0			0
$876$	−12.0000			−0.405442
$877$	−32.9090	−	19.0000i	−1.11126	−	0.641584i	−0.172102	−	0.985079i	$-0.555056\pi$
$877$	−32.9090	−	19.0000i	−1.11126	−	0.641584i	−0.939155	+	0.343495i	$0.888389\pi$
$878$	17.3205	−	10.0000i	0.584539	−	0.337484i
$879$	42.0000	+	72.7461i	1.41662	+	2.45367i
$880$		0			0
$881$	−7.00000			−0.235836			−0.117918	−	0.993023i	$-0.537622\pi$
$881$	−7.00000			−0.235836			−0.117918	+	0.993023i	$0.537622\pi$
$882$	−41.5692	+	6.00000i	−1.39971	+	0.202031i
$883$			12.0000i			0.403832i	0.979403	+	0.201916i	$0.0647168\pi$
$883$			12.0000i			0.403832i	−0.979403	+	0.201916i	$0.935283\pi$
$884$		0			0
$885$		0			0
$886$	−15.5000	−	26.8468i	−0.520733	−	0.901935i
$887$	−25.1147	−	14.5000i	−0.843270	−	0.486862i	0.0151042	−	0.999886i	$-0.495192\pi$
$887$	−25.1147	−	14.5000i	−0.843270	−	0.486862i	−0.858375	+	0.513024i	$0.828525\pi$
$888$			12.0000i			0.402694i
$889$	−8.00000	+	41.5692i	−0.268311	+	1.39419i
$890$		0			0
$891$	9.00000	−	15.5885i	0.301511	−	0.522233i
$892$	24.2487	−	14.0000i	0.811907	−	0.468755i
$893$	41.5692	−	24.0000i	1.39106	−	0.803129i
$894$	4.50000	−	7.79423i	0.150503	−	0.260678i
$895$		0			0
$896$	2.00000	+	1.73205i	0.0668153	+	0.0578638i
$897$		0			0
$898$	−28.5788	−	16.5000i	−0.953688	−	0.550612i
$899$	−18.0000	−	31.1769i	−0.600334	−	1.03981i
$900$		0			0
$901$	−4.00000	+	6.92820i	−0.133259	+	0.230812i
$902$			14.0000i			0.466149i
$903$	−12.9904	−	37.5000i	−0.432293	−	1.24792i
$904$	−2.00000			−0.0665190
$905$		0			0
$906$	24.0000	+	41.5692i	0.797347	+	1.38104i
$907$	4.33013	−	2.50000i	0.143780	−	0.0830111i	−0.426385	−	0.904542i	$-0.640213\pi$
$907$	4.33013	−	2.50000i	0.143780	−	0.0830111i	0.570164	+	0.821531i	$0.306880\pi$
$908$	−3.46410	−	2.00000i	−0.114960	−	0.0663723i
$909$	−18.0000			−0.597022
$910$		0			0
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$	15.5885	+	9.00000i	0.516185	+	0.298020i
$913$	−12.1244	+	7.00000i	−0.401258	+	0.231666i
$914$	−16.0000	−	27.7128i	−0.529233	−	0.916658i
$915$		0			0
$916$	22.0000			0.726900
$917$	−13.8564	+	16.0000i	−0.457579	+	0.528367i
$918$			36.0000i			1.18818i
$919$	19.0000	−	32.9090i	0.626752	−	1.08557i	−0.361447	−	0.932393i	$-0.617717\pi$
$919$	19.0000	−	32.9090i	0.626752	−	1.08557i	0.988199	−	0.153174i	$-0.0489495\pi$
$920$		0			0
$921$	−10.5000	−	18.1865i	−0.345987	−	0.599267i
$922$	12.1244	+	7.00000i	0.399294	+	0.230533i
$923$		0			0
$924$	3.00000	−	15.5885i	0.0986928	−	0.512823i
$925$		0			0
$926$	9.50000	−	16.4545i	0.312189	−	0.540728i
$927$	5.19615	−	3.00000i	0.170664	−	0.0985329i
$928$	−7.79423	+	4.50000i	−0.255858	+	0.147720i
$929$	21.5000	−	37.2391i	0.705392	−	1.22177i	−0.261158	−	0.965296i	$-0.584104\pi$
$929$	21.5000	−	37.2391i	0.705392	−	1.22177i	0.966550	−	0.256479i	$-0.0825624\pi$
$930$		0			0
$931$	−33.0000	+	25.9808i	−1.08153	+	0.851485i
$932$			24.0000i			0.786146i
$933$	−46.7654	−	27.0000i	−1.53103	−	0.883940i
$934$	−6.50000	−	11.2583i	−0.212686	−	0.368384i
$935$		0			0
$936$		0			0
$937$		−	28.0000i		−	0.914720i	−0.889282	−	0.457360i	$-0.848795\pi$
$937$		−	28.0000i		−	0.914720i	0.889282	−	0.457360i	$-0.151205\pi$
$938$	23.3827	+	4.50000i	0.763472	+	0.146930i
$939$	−24.0000			−0.783210
$940$		0			0
$941$	23.0000	+	39.8372i	0.749779	+	1.29865i	0.947929	+	0.318483i	$0.103173\pi$
$941$	23.0000	+	39.8372i	0.749779	+	1.29865i	−0.198150	+	0.980172i	$0.563493\pi$
$942$	25.9808	−	15.0000i	0.846499	−	0.488726i
$943$	−18.1865	−	10.5000i	−0.592235	−	0.341927i
$944$	−10.0000			−0.325472
$945$		0			0
$946$	10.0000			0.325128
$947$	21.6506	+	12.5000i	0.703551	+	0.406195i	0.808669	−	0.588264i	$-0.200189\pi$
$947$	21.6506	+	12.5000i	0.703551	+	0.406195i	−0.105118	+	0.994460i	$0.533522\pi$
$948$	−25.9808	+	15.0000i	−0.843816	+	0.487177i
$949$		0			0
$950$		0			0
$951$	−96.0000			−3.11301
$952$	3.46410	+	10.0000i	0.112272	+	0.324102i
$953$			12.0000i			0.388718i	0.980930	+	0.194359i	$0.0622627\pi$
$953$			12.0000i			0.388718i	−0.980930	+	0.194359i	$0.937737\pi$
$954$	−6.00000	+	10.3923i	−0.194257	+	0.336463i
$955$		0			0
$956$	−8.00000	−	13.8564i	−0.258738	−	0.448148i
$957$	46.7654	+	27.0000i	1.51171	+	0.872786i
$958$		−	24.0000i		−	0.775405i
$959$	30.0000	−	10.3923i	0.968751	−	0.335585i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		0			0
$963$	−15.5885	+	9.00000i	−0.502331	+	0.290021i
$964$	5.00000	−	8.66025i	0.161039	−	0.278928i
$965$		0			0
$966$	18.0000	+	15.5885i	0.579141	+	0.501550i
$967$			37.0000i			1.18984i	0.803785	+	0.594920i	$0.202816\pi$
$967$			37.0000i			1.18984i	−0.803785	+	0.594920i	$0.797184\pi$
$968$	−6.06218	−	3.50000i	−0.194846	−	0.112494i
$969$	36.0000	+	62.3538i	1.15649	+	2.00309i
$970$		0			0
$971$	24.0000	−	41.5692i	0.770197	−	1.33402i	−0.167258	−	0.985913i	$-0.553491\pi$
$971$	24.0000	−	41.5692i	0.770197	−	1.33402i	0.937455	−	0.348107i	$-0.113175\pi$
$972$		0			0
$973$	36.3731	+	7.00000i	1.16607	+	0.224410i
$974$	16.0000			0.512673
$975$		0			0
$976$	−0.500000	−	0.866025i	−0.0160046	−	0.0277208i
$977$	−25.9808	+	15.0000i	−0.831198	+	0.479893i	−0.854263	−	0.519841i	$-0.825991\pi$
$977$	−25.9808	+	15.0000i	−0.831198	+	0.479893i	0.0230645	+	0.999734i	$0.492658\pi$
$978$	−10.3923	−	6.00000i	−0.332309	−	0.191859i
$979$	2.00000			0.0639203
$980$		0			0
$981$	−54.0000			−1.72409
$982$	10.3923	+	6.00000i	0.331632	+	0.191468i
$983$	−14.7224	+	8.50000i	−0.469573	+	0.271108i	−0.716061	−	0.698038i	$-0.754057\pi$
$983$	−14.7224	+	8.50000i	−0.469573	+	0.271108i	0.246488	+	0.969146i	$0.420723\pi$
$984$	−10.5000	−	18.1865i	−0.334728	−	0.579766i
$985$		0			0
$986$	−36.0000			−1.14647
$987$	62.3538	+	12.0000i	1.98474	+	0.381964i
$988$		0			0
$989$	−7.50000	+	12.9904i	−0.238486	+	0.413070i
$990$		0			0
$991$	−20.0000	−	34.6410i	−0.635321	−	1.10041i	−0.986447	−	0.164080i	$-0.947534\pi$
$991$	−20.0000	−	34.6410i	−0.635321	−	1.10041i	0.351126	−	0.936328i	$-0.385799\pi$
$992$	3.46410	+	2.00000i	0.109985	+	0.0635001i
$993$			96.0000i			3.04647i
$994$	−4.00000	−	3.46410i	−0.126872	−	0.109875i
$995$		0			0
$996$	10.5000	−	18.1865i	0.332705	−	0.576262i
$997$	−39.8372	+	23.0000i	−1.26166	+	0.728417i	−0.973395	−	0.229135i	$-0.926410\pi$
$997$	−39.8372	+	23.0000i	−1.26166	+	0.728417i	−0.288261	+	0.957552i	$0.593077\pi$
$998$	15.5885	−	9.00000i	0.493444	−	0.284890i
$999$	−18.0000	+	31.1769i	−0.569495	+	0.986394i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.j.f.149.1		4
5.2	odd	4		350.2.e.l.51.1		2
5.3	odd	4		70.2.e.a.51.1	yes	2
5.4	even	2	inner	350.2.j.f.149.2		4
7.2	even	3		2450.2.c.s.99.2		2
7.4	even	3	inner	350.2.j.f.249.2		4
7.5	odd	6		2450.2.c.a.99.2		2
15.8	even	4		630.2.k.f.541.1		2
20.3	even	4		560.2.q.i.401.1		2
35.2	odd	12		2450.2.a.b.1.1		1
35.3	even	12		490.2.e.f.361.1		2
35.4	even	6	inner	350.2.j.f.249.1		4
35.9	even	6		2450.2.c.s.99.1		2
35.12	even	12		2450.2.a.q.1.1		1
35.13	even	4		490.2.e.f.471.1		2
35.18	odd	12		70.2.e.a.11.1	✓	2
35.19	odd	6		2450.2.c.a.99.1		2
35.23	odd	12		490.2.a.k.1.1		1
35.32	odd	12		350.2.e.l.151.1		2
35.33	even	12		490.2.a.e.1.1		1
105.23	even	12		4410.2.a.r.1.1		1
105.53	even	12		630.2.k.f.361.1		2
105.68	odd	12		4410.2.a.h.1.1		1
140.23	even	12		3920.2.a.b.1.1		1
140.103	odd	12		3920.2.a.bk.1.1		1
140.123	even	12		560.2.q.i.81.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.e.a.11.1	✓	2	35.18	odd	12
70.2.e.a.51.1	yes	2	5.3	odd	4
350.2.e.l.51.1		2	5.2	odd	4
350.2.e.l.151.1		2	35.32	odd	12
350.2.j.f.149.1		4	1.1	even	1	trivial
350.2.j.f.149.2		4	5.4	even	2	inner
350.2.j.f.249.1		4	35.4	even	6	inner
350.2.j.f.249.2		4	7.4	even	3	inner
490.2.a.e.1.1		1	35.33	even	12
490.2.a.k.1.1		1	35.23	odd	12
490.2.e.f.361.1		2	35.3	even	12
490.2.e.f.471.1		2	35.13	even	4
560.2.q.i.81.1		2	140.123	even	12
560.2.q.i.401.1		2	20.3	even	4
630.2.k.f.361.1		2	105.53	even	12
630.2.k.f.541.1		2	15.8	even	4
2450.2.a.b.1.1		1	35.2	odd	12
2450.2.a.q.1.1		1	35.12	even	12
2450.2.c.a.99.1		2	35.19	odd	6
2450.2.c.a.99.2		2	7.5	odd	6
2450.2.c.s.99.1		2	35.9	even	6
2450.2.c.s.99.2		2	7.2	even	3
3920.2.a.b.1.1		1	140.23	even	12
3920.2.a.bk.1.1		1	140.103	odd	12
4410.2.a.h.1.1		1	105.68	odd	12
4410.2.a.r.1.1		1	105.23	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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-2.59808 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.00000 q^{6} +(2.59808 + 0.500000i) q^{7} -1.00000i q^{8} +(3.00000 - 5.19615i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-2.59808 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.00000 q^{6} +(2.59808 + 0.500000i) q^{7} -1.00000i q^{8} +(3.00000 - 5.19615i) q^{9} +(1.00000 + 1.73205i) q^{11} +(-2.59808 - 1.50000i) q^{12} +(-2.00000 - 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.46410 + 2.00000i) q^{17} +(-5.19615 + 3.00000i) q^{18} +(-3.00000 + 5.19615i) q^{19} +(-7.50000 + 2.59808i) q^{21} -2.00000i q^{22} +(2.59808 + 1.50000i) q^{23} +(1.50000 + 2.59808i) q^{24} +9.00000i q^{27} +(0.866025 + 2.50000i) q^{28} -9.00000 q^{29} +(2.00000 + 3.46410i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-5.19615 - 3.00000i) q^{33} +4.00000 q^{34} +6.00000 q^{36} +(3.46410 + 2.00000i) q^{37} +(5.19615 - 3.00000i) q^{38} -7.00000 q^{41} +(7.79423 + 1.50000i) q^{42} +5.00000i q^{43} +(-1.00000 + 1.73205i) q^{44} +(-1.50000 - 2.59808i) q^{46} +(-6.92820 - 4.00000i) q^{47} -3.00000i q^{48} +(6.50000 + 2.59808i) q^{49} +(6.00000 - 10.3923i) q^{51} +(1.73205 - 1.00000i) q^{53} +(4.50000 - 7.79423i) q^{54} +(0.500000 - 2.59808i) q^{56} -18.0000i q^{57} +(7.79423 + 4.50000i) q^{58} +(5.00000 + 8.66025i) q^{59} +(-0.500000 + 0.866025i) q^{61} -4.00000i q^{62} +(10.3923 - 12.0000i) q^{63} -1.00000 q^{64} +(3.00000 + 5.19615i) q^{66} +(-7.79423 + 4.50000i) q^{67} +(-3.46410 - 2.00000i) q^{68} -9.00000 q^{69} +2.00000 q^{71} +(-5.19615 - 3.00000i) q^{72} +(3.46410 - 2.00000i) q^{73} +(-2.00000 - 3.46410i) q^{74} -6.00000 q^{76} +(1.73205 + 5.00000i) q^{77} +(5.00000 - 8.66025i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(6.06218 + 3.50000i) q^{82} +7.00000i q^{83} +(-6.00000 - 5.19615i) q^{84} +(2.50000 - 4.33013i) q^{86} +(23.3827 - 13.5000i) q^{87} +(1.73205 - 1.00000i) q^{88} +(0.500000 - 0.866025i) q^{89} +3.00000i q^{92} +(-10.3923 - 6.00000i) q^{93} +(4.00000 + 6.92820i) q^{94} +(-1.50000 + 2.59808i) q^{96} +14.0000i q^{97} +(-4.33013 - 5.50000i) q^{98} +12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 12 q^{6} + 12 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 12 * q^6 + 12 * q^9	\( 4 q + 2 q^{4} + 12 q^{6} + 12 q^{9} + 4 q^{11} - 8 q^{14} - 2 q^{16} - 12 q^{19} - 30 q^{21} + 6 q^{24} - 36 q^{29} + 8 q^{31} + 16 q^{34} + 24 q^{36} - 28 q^{41} - 4 q^{44} - 6 q^{46} + 26 q^{49} + 24 q^{51} + 18 q^{54} + 2 q^{56} + 20 q^{59} - 2 q^{61} - 4 q^{64} + 12 q^{66} - 36 q^{69} + 8 q^{71} - 8 q^{74} - 24 q^{76} + 20 q^{79} - 18 q^{81} - 24 q^{84} + 10 q^{86} + 2 q^{89} + 16 q^{94} - 6 q^{96} + 48 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 + 12 * q^6 + 12 * q^9 + 4 * q^11 - 8 * q^14 - 2 * q^16 - 12 * q^19 - 30 * q^21 + 6 * q^24 - 36 * q^29 + 8 * q^31 + 16 * q^34 + 24 * q^36 - 28 * q^41 - 4 * q^44 - 6 * q^46 + 26 * q^49 + 24 * q^51 + 18 * q^54 + 2 * q^56 + 20 * q^59 - 2 * q^61 - 4 * q^64 + 12 * q^66 - 36 * q^69 + 8 * q^71 - 8 * q^74 - 24 * q^76 + 20 * q^79 - 18 * q^81 - 24 * q^84 + 10 * q^86 + 2 * q^89 + 16 * q^94 - 6 * q^96 + 48 * q^99

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