LMFDB - Embedded newform 490.2.e.f.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(361,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("490.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.e (of order $3$, 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:	$3.91266969904$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	490.361
Dual form			490.2.e.f.471.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -3.00000 q^{6} +1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -3.00000 q^{6} +1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(1.00000 - 1.73205i) q^{11} +(1.50000 + 2.59808i) q^{12} -3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(-3.00000 + 5.19615i) q^{18} +(-3.00000 - 5.19615i) q^{19} +1.00000 q^{20} -2.00000 q^{22} +(-1.50000 - 2.59808i) q^{23} +(1.50000 - 2.59808i) q^{24} +(-0.500000 + 0.866025i) q^{25} -9.00000 q^{27} +9.00000 q^{29} +(1.50000 + 2.59808i) q^{30} +(-2.00000 + 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{33} +4.00000 q^{34} +6.00000 q^{36} +(2.00000 + 3.46410i) q^{37} +(-3.00000 + 5.19615i) q^{38} +(-0.500000 - 0.866025i) q^{40} +7.00000 q^{41} -5.00000 q^{43} +(1.00000 + 1.73205i) q^{44} +(-3.00000 + 5.19615i) q^{45} +(-1.50000 + 2.59808i) q^{46} +(4.00000 + 6.92820i) q^{47} -3.00000 q^{48} +1.00000 q^{50} +(6.00000 + 10.3923i) q^{51} +(1.00000 - 1.73205i) q^{53} +(4.50000 + 7.79423i) q^{54} -2.00000 q^{55} -18.0000 q^{57} +(-4.50000 - 7.79423i) q^{58} +(5.00000 - 8.66025i) q^{59} +(1.50000 - 2.59808i) q^{60} +(0.500000 + 0.866025i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{66} +(4.50000 - 7.79423i) q^{67} +(-2.00000 - 3.46410i) q^{68} -9.00000 q^{69} +2.00000 q^{71} +(-3.00000 - 5.19615i) q^{72} +(-2.00000 + 3.46410i) q^{73} +(2.00000 - 3.46410i) q^{74} +(1.50000 + 2.59808i) q^{75} +6.00000 q^{76} +(-5.00000 - 8.66025i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-3.50000 - 6.06218i) q^{82} +7.00000 q^{83} +4.00000 q^{85} +(2.50000 + 4.33013i) q^{86} +(13.5000 - 23.3827i) q^{87} +(1.00000 - 1.73205i) q^{88} +(0.500000 + 0.866025i) q^{89} +6.00000 q^{90} +3.00000 q^{92} +(6.00000 + 10.3923i) q^{93} +(4.00000 - 6.92820i) q^{94} +(-3.00000 + 5.19615i) q^{95} +(1.50000 + 2.59808i) q^{96} -14.0000 q^{97} -12.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 3 q^{3} - q^{4} - q^{5} - 6 q^{6} + 2 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q - q^2 + 3 * q^3 - q^4 - q^5 - 6 * q^6 + 2 * q^8 - 6 * q^9	$ 2 q - q^{2} + 3 q^{3} - q^{4} - q^{5} - 6 q^{6} + 2 q^{8} - 6 q^{9} - q^{10} + 2 q^{11} + 3 q^{12} - 6 q^{15} - q^{16} - 4 q^{17} - 6 q^{18} - 6 q^{19} + 2 q^{20} - 4 q^{22} - 3 q^{23} + 3 q^{24} - q^{25} - 18 q^{27} + 18 q^{29} + 3 q^{30} - 4 q^{31} - q^{32} - 6 q^{33} + 8 q^{34} + 12 q^{36} + 4 q^{37} - 6 q^{38} - q^{40} + 14 q^{41} - 10 q^{43} + 2 q^{44} - 6 q^{45} - 3 q^{46} + 8 q^{47} - 6 q^{48} + 2 q^{50} + 12 q^{51} + 2 q^{53} + 9 q^{54} - 4 q^{55} - 36 q^{57} - 9 q^{58} + 10 q^{59} + 3 q^{60} + q^{61} + 8 q^{62} + 2 q^{64} - 6 q^{66} + 9 q^{67} - 4 q^{68} - 18 q^{69} + 4 q^{71} - 6 q^{72} - 4 q^{73} + 4 q^{74} + 3 q^{75} + 12 q^{76} - 10 q^{79} - q^{80} - 9 q^{81} - 7 q^{82} + 14 q^{83} + 8 q^{85} + 5 q^{86} + 27 q^{87} + 2 q^{88} + q^{89} + 12 q^{90} + 6 q^{92} + 12 q^{93} + 8 q^{94} - 6 q^{95} + 3 q^{96} - 28 q^{97} - 24 q^{99}+O(q^{100}) $ 2 * q - q^2 + 3 * q^3 - q^4 - q^5 - 6 * q^6 + 2 * q^8 - 6 * q^9 - q^10 + 2 * q^11 + 3 * q^12 - 6 * q^15 - q^16 - 4 * q^17 - 6 * q^18 - 6 * q^19 + 2 * q^20 - 4 * q^22 - 3 * q^23 + 3 * q^24 - q^25 - 18 * q^27 + 18 * q^29 + 3 * q^30 - 4 * q^31 - q^32 - 6 * q^33 + 8 * q^34 + 12 * q^36 + 4 * q^37 - 6 * q^38 - q^40 + 14 * q^41 - 10 * q^43 + 2 * q^44 - 6 * q^45 - 3 * q^46 + 8 * q^47 - 6 * q^48 + 2 * q^50 + 12 * q^51 + 2 * q^53 + 9 * q^54 - 4 * q^55 - 36 * q^57 - 9 * q^58 + 10 * q^59 + 3 * q^60 + q^61 + 8 * q^62 + 2 * q^64 - 6 * q^66 + 9 * q^67 - 4 * q^68 - 18 * q^69 + 4 * q^71 - 6 * q^72 - 4 * q^73 + 4 * q^74 + 3 * q^75 + 12 * q^76 - 10 * q^79 - q^80 - 9 * q^81 - 7 * q^82 + 14 * q^83 + 8 * q^85 + 5 * q^86 + 27 * q^87 + 2 * q^88 + q^89 + 12 * q^90 + 6 * q^92 + 12 * q^93 + 8 * q^94 - 6 * q^95 + 3 * q^96 - 28 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.50000	−	2.59808i	0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$3$	1.50000	−	2.59808i	0.866025	−	1.50000i	0.866025	−	0.500000i	$-0.166667\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−3.00000			−1.22474
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−3.00000	−	5.19615i	−1.00000	−	1.73205i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$	1.50000	+	2.59808i	0.433013	+	0.750000i
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$		0			0
$15$	−3.00000			−0.774597
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	−0.999853	−	0.0171533i	$-0.994540\pi$
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	0.514782	+	0.857321i	$0.327873\pi$
$18$	−3.00000	+	5.19615i	−0.707107	+	1.22474i
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	−0.972404	−	0.233301i	$-0.925047\pi$
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	0.284157	−	0.958778i	$-0.408286\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	−2.00000			−0.426401
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	0.666190	−	0.745782i	$-0.267924\pi$
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	−0.978961	+	0.204046i	$0.934591\pi$
$24$	1.50000	−	2.59808i	0.306186	−	0.530330i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−9.00000			−1.73205
$28$		0			0
$29$	9.00000			1.67126			0.835629	−	0.549294i	$-0.185103\pi$
$29$	9.00000			1.67126			0.835629	+	0.549294i	$0.185103\pi$
$30$	1.50000	+	2.59808i	0.273861	+	0.474342i
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−3.00000	−	5.19615i	−0.522233	−	0.904534i
$34$	4.00000			0.685994
$35$		0			0
$36$	6.00000			1.00000
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	0.982274	−	0.187453i	$-0.0600231\pi$
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	−0.653476	+	0.756948i	$0.726690\pi$
$38$	−3.00000	+	5.19615i	−0.486664	+	0.842927i
$39$		0			0
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	7.00000			1.09322			0.546608	−	0.837389i	$-0.315919\pi$
$41$	7.00000			1.09322			0.546608	+	0.837389i	$0.315919\pi$
$42$		0			0
$43$	−5.00000			−0.762493			−0.381246	−	0.924473i	$-0.624505\pi$
$43$	−5.00000			−0.762493			−0.381246	+	0.924473i	$0.624505\pi$
$44$	1.00000	+	1.73205i	0.150756	+	0.261116i
$45$	−3.00000	+	5.19615i	−0.447214	+	0.774597i
$46$	−1.50000	+	2.59808i	−0.221163	+	0.383065i
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	0.995066	+	0.0992202i	$0.0316348\pi$
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	−0.411606	+	0.911362i	$0.635032\pi$
$48$	−3.00000			−0.433013
$49$		0			0
$50$	1.00000			0.141421
$51$	6.00000	+	10.3923i	0.840168	+	1.45521i
$52$		0			0
$53$	1.00000	−	1.73205i	0.137361	−	0.237915i	−0.789136	−	0.614218i	$-0.789471\pi$
$53$	1.00000	−	1.73205i	0.137361	−	0.237915i	0.926497	+	0.376303i	$0.122805\pi$
$54$	4.50000	+	7.79423i	0.612372	+	1.06066i
$55$	−2.00000			−0.269680
$56$		0			0
$57$	−18.0000			−2.38416
$58$	−4.50000	−	7.79423i	−0.590879	−	1.02343i
$59$	5.00000	−	8.66025i	0.650945	−	1.12747i	−0.331949	−	0.943297i	$-0.607706\pi$
$59$	5.00000	−	8.66025i	0.650945	−	1.12747i	0.982894	−	0.184172i	$-0.0589603\pi$
$60$	1.50000	−	2.59808i	0.193649	−	0.335410i
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$	−3.00000	+	5.19615i	−0.369274	+	0.639602i
$67$	4.50000	−	7.79423i	0.549762	−	0.952217i	−0.448528	−	0.893769i	$-0.648052\pi$
$67$	4.50000	−	7.79423i	0.549762	−	0.952217i	0.998290	−	0.0584478i	$-0.0186151\pi$
$68$	−2.00000	−	3.46410i	−0.242536	−	0.420084i
$69$	−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	$0.462134\pi$
$72$	−3.00000	−	5.19615i	−0.353553	−	0.612372i
$73$	−2.00000	+	3.46410i	−0.234082	+	0.405442i	−0.959006	−	0.283387i	$-0.908542\pi$
$73$	−2.00000	+	3.46410i	−0.234082	+	0.405442i	0.724923	+	0.688830i	$0.241875\pi$
$74$	2.00000	−	3.46410i	0.232495	−	0.402694i
$75$	1.50000	+	2.59808i	0.173205	+	0.300000i
$76$	6.00000			0.688247
$77$		0			0
$78$		0			0
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	−0.997274	−	0.0737937i	$-0.976489\pi$
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	0.434730	−	0.900561i	$-0.356844\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−3.50000	−	6.06218i	−0.386510	−	0.669456i
$83$	7.00000			0.768350			0.384175	−	0.923260i	$-0.374486\pi$
$83$	7.00000			0.768350			0.384175	+	0.923260i	$0.374486\pi$
$84$		0			0
$85$	4.00000			0.433861
$86$	2.50000	+	4.33013i	0.269582	+	0.466930i
$87$	13.5000	−	23.3827i	1.44735	−	2.50689i
$88$	1.00000	−	1.73205i	0.106600	−	0.184637i
$89$	0.500000	+	0.866025i	0.0529999	+	0.0917985i	0.891308	−	0.453398i	$-0.149788\pi$
$89$	0.500000	+	0.866025i	0.0529999	+	0.0917985i	−0.838308	+	0.545197i	$0.816455\pi$
$90$	6.00000			0.632456
$91$		0			0
$92$	3.00000			0.312772
$93$	6.00000	+	10.3923i	0.622171	+	1.07763i
$94$	4.00000	−	6.92820i	0.412568	−	0.714590i
$95$	−3.00000	+	5.19615i	−0.307794	+	0.533114i
$96$	1.50000	+	2.59808i	0.153093	+	0.265165i
$97$	−14.0000			−1.42148			−0.710742	−	0.703452i	$-0.751641\pi$
$97$	−14.0000			−1.42148			−0.710742	+	0.703452i	$0.751641\pi$
$98$		0			0
$99$	−12.0000			−1.20605
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	−0.781697	−	0.623658i	$-0.785646\pi$
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	0.930953	+	0.365140i	$0.118979\pi$
$102$	6.00000	−	10.3923i	0.594089	−	1.02899i
$103$	0.500000	+	0.866025i	0.0492665	+	0.0853320i	0.889607	−	0.456727i	$-0.150978\pi$
$103$	0.500000	+	0.866025i	0.0492665	+	0.0853320i	−0.840341	+	0.542059i	$0.817645\pi$
$104$		0			0
$105$		0			0
$106$	−2.00000			−0.194257
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	0.784366	−	0.620298i	$-0.212988\pi$
$107$	−1.50000	−	2.59808i	−0.145010	−	0.251166i	−0.929377	+	0.369132i	$0.879655\pi$
$108$	4.50000	−	7.79423i	0.433013	−	0.750000i
$109$	4.50000	−	7.79423i	0.431022	−	0.746552i	−0.565940	−	0.824447i	$-0.691487\pi$
$109$	4.50000	−	7.79423i	0.431022	−	0.746552i	0.996962	+	0.0778949i	$0.0248199\pi$
$110$	1.00000	+	1.73205i	0.0953463	+	0.165145i
$111$	12.0000			1.13899
$112$		0			0
$113$	2.00000			0.188144			0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000			0.188144			0.0940721	+	0.995565i	$0.470012\pi$
$114$	9.00000	+	15.5885i	0.842927	+	1.45999i
$115$	−1.50000	+	2.59808i	−0.139876	+	0.242272i
$116$	−4.50000	+	7.79423i	−0.417815	+	0.723676i
$117$		0			0
$118$	−10.0000			−0.920575
$119$		0			0
$120$	−3.00000			−0.273861
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	0.500000	−	0.866025i	0.0452679	−	0.0784063i
$123$	10.5000	−	18.1865i	0.946753	−	1.63982i
$124$	−2.00000	−	3.46410i	−0.179605	−	0.311086i
$125$	1.00000			0.0894427
$126$		0			0
$127$	16.0000			1.41977			0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000			1.41977			0.709885	+	0.704317i	$0.248747\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−7.50000	+	12.9904i	−0.660338	+	1.14374i
$130$		0			0
$131$	4.00000	+	6.92820i	0.349482	+	0.605320i	0.986157	−	0.165812i	$-0.0530244\pi$
$131$	4.00000	+	6.92820i	0.349482	+	0.605320i	−0.636676	+	0.771132i	$0.719691\pi$
$132$	6.00000			0.522233
$133$		0			0
$134$	−9.00000			−0.777482
$135$	4.50000	+	7.79423i	0.387298	+	0.670820i
$136$	−2.00000	+	3.46410i	−0.171499	+	0.297044i
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	0.487278	+	0.873247i	$0.337990\pi$
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	−0.999893	+	0.0146279i	$0.995344\pi$
$138$	4.50000	+	7.79423i	0.383065	+	0.663489i
$139$	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
$142$	−1.00000	−	1.73205i	−0.0839181	−	0.145350i
$143$		0			0
$144$	−3.00000	+	5.19615i	−0.250000	+	0.433013i
$145$	−4.50000	−	7.79423i	−0.373705	−	0.647275i
$146$	4.00000			0.331042
$147$		0			0
$148$	−4.00000			−0.328798
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	0.798019	−	0.602632i	$-0.205881\pi$
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	−0.920904	+	0.389789i	$0.872548\pi$
$150$	1.50000	−	2.59808i	0.122474	−	0.212132i
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	−0.331842	−	0.943335i	$-0.607670\pi$
$151$	8.00000	−	13.8564i	0.651031	−	1.12762i	0.982873	−	0.184284i	$-0.0589965\pi$
$152$	−3.00000	−	5.19615i	−0.243332	−	0.421464i
$153$	24.0000			1.94029
$154$		0			0
$155$	4.00000			0.321288
$156$		0			0
$157$	5.00000	−	8.66025i	0.399043	−	0.691164i	−0.594565	−	0.804048i	$-0.702676\pi$
$157$	5.00000	−	8.66025i	0.399043	−	0.691164i	0.993608	+	0.112884i	$0.0360089\pi$
$158$	−5.00000	+	8.66025i	−0.397779	+	0.688973i
$159$	−3.00000	−	5.19615i	−0.237915	−	0.412082i
$160$	1.00000			0.0790569
$161$		0			0
$162$	9.00000			0.707107
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	0.933659	−	0.358162i	$-0.116597\pi$
$163$	2.00000	+	3.46410i	0.156652	+	0.271329i	−0.777007	+	0.629492i	$0.783263\pi$
$164$	−3.50000	+	6.06218i	−0.273304	+	0.473377i
$165$	−3.00000	+	5.19615i	−0.233550	+	0.404520i
$166$	−3.50000	−	6.06218i	−0.271653	−	0.470516i
$167$	21.0000			1.62503			0.812514	−	0.582941i	$-0.198098\pi$
$167$	21.0000			1.62503			0.812514	+	0.582941i	$0.198098\pi$
$168$		0			0
$169$	−13.0000			−1.00000
$170$	−2.00000	−	3.46410i	−0.153393	−	0.265684i
$171$	−18.0000	+	31.1769i	−1.37649	+	2.38416i
$172$	2.50000	−	4.33013i	0.190623	−	0.330169i
$173$	4.00000	+	6.92820i	0.304114	+	0.526742i	0.977064	−	0.212947i	$-0.0683062\pi$
$173$	4.00000	+	6.92820i	0.304114	+	0.526742i	−0.672949	+	0.739689i	$0.734973\pi$
$174$	−27.0000			−2.04686
$175$		0			0
$176$	−2.00000			−0.150756
$177$	−15.0000	−	25.9808i	−1.12747	−	1.95283i
$178$	0.500000	−	0.866025i	0.0374766	−	0.0649113i
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	−0.998286	−	0.0585225i	$-0.981361\pi$
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	0.549825	+	0.835280i	$0.314694\pi$
$180$	−3.00000	−	5.19615i	−0.223607	−	0.387298i
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$		0			0
$183$	3.00000			0.221766
$184$	−1.50000	−	2.59808i	−0.110581	−	0.191533i
$185$	2.00000	−	3.46410i	0.147043	−	0.254686i
$186$	6.00000	−	10.3923i	0.439941	−	0.762001i
$187$	4.00000	+	6.92820i	0.292509	+	0.506640i
$188$	−8.00000			−0.583460
$189$		0			0
$190$	6.00000			0.435286
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	0.982828	+	0.184525i	$0.0590746\pi$
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	−0.331611	+	0.943416i	$0.607592\pi$
$192$	1.50000	−	2.59808i	0.108253	−	0.187500i
$193$	−13.0000	+	22.5167i	−0.935760	+	1.62078i	−0.162488	+	0.986710i	$0.551952\pi$
$193$	−13.0000	+	22.5167i	−0.935760	+	1.62078i	−0.773272	+	0.634074i	$0.781381\pi$
$194$	7.00000	+	12.1244i	0.502571	+	0.870478i
$195$		0			0
$196$		0			0
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$	6.00000	+	10.3923i	0.426401	+	0.738549i
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	−0.928166	−	0.372168i	$-0.878615\pi$
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	0.786389	+	0.617731i	$0.211948\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	−13.5000	−	23.3827i	−0.952217	−	1.64929i
$202$	−3.00000			−0.211079
$203$		0			0
$204$	−12.0000			−0.840168
$205$	−3.50000	−	6.06218i	−0.244451	−	0.423401i
$206$	0.500000	−	0.866025i	0.0348367	−	0.0603388i
$207$	−9.00000	+	15.5885i	−0.625543	+	1.08347i
$208$		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	$0.852794\pi$
$212$	1.00000	+	1.73205i	0.0686803	+	0.118958i
$213$	3.00000	−	5.19615i	0.205557	−	0.356034i
$214$	−1.50000	+	2.59808i	−0.102538	+	0.177601i
$215$	2.50000	+	4.33013i	0.170499	+	0.295312i
$216$	−9.00000			−0.612372
$217$		0			0
$218$	−9.00000			−0.609557
$219$	6.00000	+	10.3923i	0.405442	+	0.702247i
$220$	1.00000	−	1.73205i	0.0674200	−	0.116775i
$221$		0			0
$222$	−6.00000	−	10.3923i	−0.402694	−	0.697486i
$223$	−28.0000			−1.87502			−0.937509	−	0.347960i	$-0.886874\pi$
$223$	−28.0000			−1.87502			−0.937509	+	0.347960i	$0.886874\pi$
$224$		0			0
$225$	6.00000			0.400000
$226$	−1.00000	−	1.73205i	−0.0665190	−	0.115214i
$227$	−2.00000	+	3.46410i	−0.132745	+	0.229920i	−0.924734	−	0.380615i	$-0.875712\pi$
$227$	−2.00000	+	3.46410i	−0.132745	+	0.229920i	0.791989	+	0.610535i	$0.209046\pi$
$228$	9.00000	−	15.5885i	0.596040	−	1.03237i
$229$	11.0000	+	19.0526i	0.726900	+	1.25903i	0.958187	+	0.286143i	$0.0923732\pi$
$229$	11.0000	+	19.0526i	0.726900	+	1.25903i	−0.231287	+	0.972886i	$0.574293\pi$
$230$	3.00000			0.197814
$231$		0			0
$232$	9.00000			0.590879
$233$	−12.0000	−	20.7846i	−0.786146	−	1.36165i	−0.928312	−	0.371802i	$-0.878740\pi$
$233$	−12.0000	−	20.7846i	−0.786146	−	1.36165i	0.142166	−	0.989843i	$-0.454593\pi$
$234$		0			0
$235$	4.00000	−	6.92820i	0.260931	−	0.451946i
$236$	5.00000	+	8.66025i	0.325472	+	0.563735i
$237$	−30.0000			−1.94871
$238$		0			0
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$	1.50000	+	2.59808i	0.0968246	+	0.167705i
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	−0.658838	−	0.752285i	$-0.728952\pi$
$241$	5.00000	−	8.66025i	0.322078	−	0.557856i	0.980917	+	0.194429i	$0.0622852\pi$
$242$	3.50000	−	6.06218i	0.224989	−	0.389692i
$243$		0			0
$244$	−1.00000			−0.0640184
$245$		0			0
$246$	−21.0000			−1.33891
$247$		0			0
$248$	−2.00000	+	3.46410i	−0.127000	+	0.219971i
$249$	10.5000	−	18.1865i	0.665410	−	1.15252i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$	−6.00000			−0.377217
$254$	−8.00000	−	13.8564i	−0.501965	−	0.869428i
$255$	6.00000	−	10.3923i	0.375735	−	0.650791i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.00000	+	6.92820i	0.249513	+	0.432169i	0.963391	−	0.268101i	$-0.0863961\pi$
$257$	4.00000	+	6.92820i	0.249513	+	0.432169i	−0.713878	+	0.700270i	$0.753063\pi$
$258$	15.0000			0.933859
$259$		0			0
$260$		0			0
$261$	−27.0000	−	46.7654i	−1.67126	−	2.89470i
$262$	4.00000	−	6.92820i	0.247121	−	0.428026i
$263$	−2.50000	+	4.33013i	−0.154157	+	0.267007i	−0.932752	−	0.360520i	$-0.882599\pi$
$263$	−2.50000	+	4.33013i	−0.154157	+	0.267007i	0.778595	+	0.627527i	$0.215933\pi$
$264$	−3.00000	−	5.19615i	−0.184637	−	0.319801i
$265$	−2.00000			−0.122859
$266$		0			0
$267$	3.00000			0.183597
$268$	4.50000	+	7.79423i	0.274881	+	0.476108i
$269$	1.50000	−	2.59808i	0.0914566	−	0.158408i	−0.816668	−	0.577108i	$-0.804181\pi$
$269$	1.50000	−	2.59808i	0.0914566	−	0.158408i	0.908124	+	0.418701i	$0.137514\pi$
$270$	4.50000	−	7.79423i	0.273861	−	0.474342i
$271$	−3.00000	−	5.19615i	−0.182237	−	0.315644i	0.760405	−	0.649449i	$-0.225000\pi$
$271$	−3.00000	−	5.19615i	−0.182237	−	0.315644i	−0.942642	+	0.333805i	$0.891667\pi$
$272$	4.00000			0.242536
$273$		0			0
$274$	12.0000			0.724947
$275$	1.00000	+	1.73205i	0.0603023	+	0.104447i
$276$	4.50000	−	7.79423i	0.270868	−	0.469157i
$277$	−6.00000	+	10.3923i	−0.360505	+	0.624413i	−0.988044	−	0.154172i	$-0.950729\pi$
$277$	−6.00000	+	10.3923i	−0.360505	+	0.624413i	0.627539	+	0.778585i	$0.284062\pi$
$278$	−7.00000	−	12.1244i	−0.419832	−	0.727171i
$279$	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	$0.481000\pi$
$282$	−12.0000	−	20.7846i	−0.714590	−	1.23771i
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	−0.919327	−	0.393494i	$-0.871266\pi$
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	0.800439	+	0.599414i	$0.204600\pi$
$284$	−1.00000	+	1.73205i	−0.0593391	+	0.102778i
$285$	9.00000	+	15.5885i	0.533114	+	0.923381i
$286$		0			0
$287$		0			0
$288$	6.00000			0.353553
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	−4.50000	+	7.79423i	−0.264249	+	0.457693i
$291$	−21.0000	+	36.3731i	−1.23104	+	2.13223i
$292$	−2.00000	−	3.46410i	−0.117041	−	0.202721i
$293$	−28.0000			−1.63578			−0.817889	−	0.575376i	$-0.804856\pi$
$293$	−28.0000			−1.63578			−0.817889	+	0.575376i	$0.804856\pi$
$294$		0			0
$295$	−10.0000			−0.582223
$296$	2.00000	+	3.46410i	0.116248	+	0.201347i
$297$	−9.00000	+	15.5885i	−0.522233	+	0.904534i
$298$	−1.50000	+	2.59808i	−0.0868927	+	0.150503i
$299$		0			0
$300$	−3.00000			−0.173205
$301$		0			0
$302$	−16.0000			−0.920697
$303$	−4.50000	−	7.79423i	−0.258518	−	0.447767i
$304$	−3.00000	+	5.19615i	−0.172062	+	0.298020i
$305$	0.500000	−	0.866025i	0.0286299	−	0.0495885i
$306$	−12.0000	−	20.7846i	−0.685994	−	1.18818i
$307$	−7.00000			−0.399511			−0.199756	−	0.979846i	$-0.564015\pi$
$307$	−7.00000			−0.399511			−0.199756	+	0.979846i	$0.564015\pi$
$308$		0			0
$309$	3.00000			0.170664
$310$	−2.00000	−	3.46410i	−0.113592	−	0.196748i
$311$	−9.00000	+	15.5885i	−0.510343	+	0.883940i	0.489585	+	0.871956i	$0.337148\pi$
$311$	−9.00000	+	15.5885i	−0.510343	+	0.883940i	−0.999928	+	0.0119847i	$0.996185\pi$
$312$		0			0
$313$	4.00000	+	6.92820i	0.226093	+	0.391605i	0.956647	−	0.291250i	$-0.0940712\pi$
$313$	4.00000	+	6.92820i	0.226093	+	0.391605i	−0.730554	+	0.682855i	$0.760738\pi$
$314$	−10.0000			−0.564333
$315$		0			0
$316$	10.0000			0.562544
$317$	16.0000	+	27.7128i	0.898650	+	1.55651i	0.829222	+	0.558920i	$0.188784\pi$
$317$	16.0000	+	27.7128i	0.898650	+	1.55651i	0.0694277	+	0.997587i	$0.477883\pi$
$318$	−3.00000	+	5.19615i	−0.168232	+	0.291386i
$319$	9.00000	−	15.5885i	0.503903	−	0.872786i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−9.00000			−0.502331
$322$		0			0
$323$	24.0000			1.33540
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$		0			0
$326$	2.00000	−	3.46410i	0.110770	−	0.191859i
$327$	−13.5000	−	23.3827i	−0.746552	−	1.29307i
$328$	7.00000			0.386510
$329$		0			0
$330$	6.00000			0.330289
$331$	16.0000	+	27.7128i	0.879440	+	1.52323i	0.851957	+	0.523612i	$0.175416\pi$
$331$	16.0000	+	27.7128i	0.879440	+	1.52323i	0.0274825	+	0.999622i	$0.491251\pi$
$332$	−3.50000	+	6.06218i	−0.192087	+	0.332705i
$333$	12.0000	−	20.7846i	0.657596	−	1.13899i
$334$	−10.5000	−	18.1865i	−0.574534	−	0.995123i
$335$	−9.00000			−0.491723
$336$		0			0
$337$	−26.0000			−1.41631			−0.708155	−	0.706057i	$-0.750472\pi$
$337$	−26.0000			−1.41631			−0.708155	+	0.706057i	$0.750472\pi$
$338$	6.50000	+	11.2583i	0.353553	+	0.612372i
$339$	3.00000	−	5.19615i	0.162938	−	0.282216i
$340$	−2.00000	+	3.46410i	−0.108465	+	0.187867i
$341$	4.00000	+	6.92820i	0.216612	+	0.375183i
$342$	36.0000			1.94666
$343$		0			0
$344$	−5.00000			−0.269582
$345$	4.50000	+	7.79423i	0.242272	+	0.419627i
$346$	4.00000	−	6.92820i	0.215041	−	0.372463i
$347$	−9.50000	+	16.4545i	−0.509987	+	0.883323i	0.489946	+	0.871753i	$0.337016\pi$
$347$	−9.50000	+	16.4545i	−0.509987	+	0.883323i	−0.999933	+	0.0115703i	$0.996317\pi$
$348$	13.5000	+	23.3827i	0.723676	+	1.25344i
$349$	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
$352$	1.00000	+	1.73205i	0.0533002	+	0.0923186i
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	−0.999711	−	0.0240566i	$-0.992342\pi$
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	0.520689	+	0.853746i	$0.325675\pi$
$354$	−15.0000	+	25.9808i	−0.797241	+	1.38086i
$355$	−1.00000	−	1.73205i	−0.0530745	−	0.0919277i
$356$	−1.00000			−0.0529999
$357$		0			0
$358$	12.0000			0.634220
$359$	2.00000	+	3.46410i	0.105556	+	0.182828i	0.913965	−	0.405793i	$-0.133004\pi$
$359$	2.00000	+	3.46410i	0.105556	+	0.182828i	−0.808409	+	0.588621i	$0.799671\pi$
$360$	−3.00000	+	5.19615i	−0.158114	+	0.273861i
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	3.50000	+	6.06218i	0.183956	+	0.318621i
$363$	21.0000			1.10221
$364$		0			0
$365$	4.00000			0.209370
$366$	−1.50000	−	2.59808i	−0.0784063	−	0.135804i
$367$	−5.50000	+	9.52628i	−0.287098	+	0.497268i	−0.973116	−	0.230317i	$-0.926024\pi$
$367$	−5.50000	+	9.52628i	−0.287098	+	0.497268i	0.686018	+	0.727585i	$0.259357\pi$
$368$	−1.50000	+	2.59808i	−0.0781929	+	0.135434i
$369$	−21.0000	−	36.3731i	−1.09322	−	1.89351i
$370$	−4.00000			−0.207950
$371$		0			0
$372$	−12.0000			−0.622171
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$	4.00000	−	6.92820i	0.206835	−	0.358249i
$375$	1.50000	−	2.59808i	0.0774597	−	0.134164i
$376$	4.00000	+	6.92820i	0.206284	+	0.357295i
$377$		0			0
$378$		0			0
$379$	30.0000			1.54100			0.770498	−	0.637442i	$-0.220007\pi$
$379$	30.0000			1.54100			0.770498	+	0.637442i	$0.220007\pi$
$380$	−3.00000	−	5.19615i	−0.153897	−	0.266557i
$381$	24.0000	−	41.5692i	1.22956	−	2.12966i
$382$	9.00000	−	15.5885i	0.460480	−	0.797575i
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	0.991522	−	0.129937i	$-0.0414776\pi$
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	−0.608290	+	0.793715i	$0.708144\pi$
$384$	−3.00000			−0.153093
$385$		0			0
$386$	26.0000			1.32337
$387$	15.0000	+	25.9808i	0.762493	+	1.32068i
$388$	7.00000	−	12.1244i	0.355371	−	0.615521i
$389$	−13.0000	+	22.5167i	−0.659126	+	1.14164i	0.321716	+	0.946836i	$0.395740\pi$
$389$	−13.0000	+	22.5167i	−0.659126	+	1.14164i	−0.980842	+	0.194804i	$0.937593\pi$
$390$		0			0
$391$	12.0000			0.606866
$392$		0			0
$393$	24.0000			1.21064
$394$	−1.00000	−	1.73205i	−0.0503793	−	0.0872595i
$395$	−5.00000	+	8.66025i	−0.251577	+	0.435745i
$396$	6.00000	−	10.3923i	0.301511	−	0.522233i
$397$	11.0000	+	19.0526i	0.552074	+	0.956221i	0.998125	+	0.0612128i	$0.0194968\pi$
$397$	11.0000	+	19.0526i	0.552074	+	0.956221i	−0.446051	+	0.895008i	$0.647170\pi$
$398$	4.00000			0.200502
$399$		0			0
$400$	1.00000			0.0500000
$401$	−15.5000	−	26.8468i	−0.774033	−	1.34066i	−0.935336	−	0.353760i	$-0.884903\pi$
$401$	−15.5000	−	26.8468i	−0.774033	−	1.34066i	0.161303	−	0.986905i	$-0.448430\pi$
$402$	−13.5000	+	23.3827i	−0.673319	+	1.16622i
$403$		0			0
$404$	1.50000	+	2.59808i	0.0746278	+	0.129259i
$405$	9.00000			0.447214
$406$		0			0
$407$	8.00000			0.396545
$408$	6.00000	+	10.3923i	0.297044	+	0.514496i
$409$	1.50000	−	2.59808i	0.0741702	−	0.128467i	−0.826555	−	0.562856i	$-0.809703\pi$
$409$	1.50000	−	2.59808i	0.0741702	−	0.128467i	0.900725	+	0.434389i	$0.143036\pi$
$410$	−3.50000	+	6.06218i	−0.172853	+	0.299390i
$411$	18.0000	+	31.1769i	0.887875	+	1.53784i
$412$	−1.00000			−0.0492665
$413$		0			0
$414$	18.0000			0.884652
$415$	−3.50000	−	6.06218i	−0.171808	−	0.297581i
$416$		0			0
$417$	21.0000	−	36.3731i	1.02837	−	1.78120i
$418$	6.00000	+	10.3923i	0.293470	+	0.508304i
$419$		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	$0.653228\pi$
$422$	13.0000	+	22.5167i	0.632830	+	1.09609i
$423$	24.0000	−	41.5692i	1.16692	−	2.02116i
$424$	1.00000	−	1.73205i	0.0485643	−	0.0841158i
$425$	−2.00000	−	3.46410i	−0.0970143	−	0.168034i
$426$	−6.00000			−0.290701
$427$		0			0
$428$	3.00000			0.145010
$429$		0			0
$430$	2.50000	−	4.33013i	0.120561	−	0.208817i
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	−0.237460	−	0.971397i	$-0.576315\pi$
$431$	15.0000	−	25.9808i	0.722525	−	1.25145i	0.959985	−	0.280052i	$-0.0903517\pi$
$432$	4.50000	+	7.79423i	0.216506	+	0.375000i
$433$	−14.0000			−0.672797			−0.336399	−	0.941720i	$-0.609209\pi$
$433$	−14.0000			−0.672797			−0.336399	+	0.941720i	$0.609209\pi$
$434$		0			0
$435$	−27.0000			−1.29455
$436$	4.50000	+	7.79423i	0.215511	+	0.373276i
$437$	−9.00000	+	15.5885i	−0.430528	+	0.745697i
$438$	6.00000	−	10.3923i	0.286691	−	0.496564i
$439$	−10.0000	−	17.3205i	−0.477274	−	0.826663i	0.522387	−	0.852709i	$-0.325042\pi$
$439$	−10.0000	−	17.3205i	−0.477274	−	0.826663i	−0.999661	+	0.0260459i	$0.991708\pi$
$440$	−2.00000			−0.0953463
$441$		0			0
$442$		0			0
$443$	−15.5000	−	26.8468i	−0.736427	−	1.27553i	−0.954094	−	0.299506i	$-0.903178\pi$
$443$	−15.5000	−	26.8468i	−0.736427	−	1.27553i	0.217667	−	0.976023i	$-0.430155\pi$
$444$	−6.00000	+	10.3923i	−0.284747	+	0.493197i
$445$	0.500000	−	0.866025i	0.0237023	−	0.0410535i
$446$	14.0000	+	24.2487i	0.662919	+	1.14821i
$447$	−9.00000			−0.425685
$448$		0			0
$449$	−33.0000			−1.55737			−0.778683	−	0.627417i	$-0.784112\pi$
$449$	−33.0000			−1.55737			−0.778683	+	0.627417i	$0.784112\pi$
$450$	−3.00000	−	5.19615i	−0.141421	−	0.244949i
$451$	7.00000	−	12.1244i	0.329617	−	0.570914i
$452$	−1.00000	+	1.73205i	−0.0470360	+	0.0814688i
$453$	−24.0000	−	41.5692i	−1.12762	−	1.95309i
$454$	4.00000			0.187729
$455$		0			0
$456$	−18.0000			−0.842927
$457$	16.0000	+	27.7128i	0.748448	+	1.29635i	0.948566	+	0.316579i	$0.102534\pi$
$457$	16.0000	+	27.7128i	0.748448	+	1.29635i	−0.200118	+	0.979772i	$0.564132\pi$
$458$	11.0000	−	19.0526i	0.513996	−	0.890268i
$459$	18.0000	−	31.1769i	0.840168	−	1.45521i
$460$	−1.50000	−	2.59808i	−0.0699379	−	0.121136i
$461$	14.0000			0.652045			0.326023	−	0.945362i	$-0.394291\pi$
$461$	14.0000			0.652045			0.326023	+	0.945362i	$0.394291\pi$
$462$		0			0
$463$	−19.0000			−0.883005			−0.441502	−	0.897260i	$-0.645554\pi$
$463$	−19.0000			−0.883005			−0.441502	+	0.897260i	$0.645554\pi$
$464$	−4.50000	−	7.79423i	−0.208907	−	0.361838i
$465$	6.00000	−	10.3923i	0.278243	−	0.481932i
$466$	−12.0000	+	20.7846i	−0.555889	+	0.962828i
$467$	−6.50000	−	11.2583i	−0.300784	−	0.520973i	0.675530	−	0.737333i	$-0.263915\pi$
$467$	−6.50000	−	11.2583i	−0.300784	−	0.520973i	−0.976314	+	0.216359i	$0.930582\pi$
$468$		0			0
$469$		0			0
$470$	−8.00000			−0.369012
$471$	−15.0000	−	25.9808i	−0.691164	−	1.19713i
$472$	5.00000	−	8.66025i	0.230144	−	0.398621i
$473$	−5.00000	+	8.66025i	−0.229900	+	0.398199i
$474$	15.0000	+	25.9808i	0.688973	+	1.19334i
$475$	6.00000			0.275299
$476$		0			0
$477$	−12.0000			−0.549442
$478$	−8.00000	−	13.8564i	−0.365911	−	0.633777i
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	−0.450098	−	0.892979i	$-0.648611\pi$
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	0.998392	−	0.0566937i	$-0.0180558\pi$
$480$	1.50000	−	2.59808i	0.0684653	−	0.118585i
$481$		0			0
$482$	−10.0000			−0.455488
$483$		0			0
$484$	−7.00000			−0.318182
$485$	7.00000	+	12.1244i	0.317854	+	0.550539i
$486$		0			0
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	−0.625859	−	0.779936i	$-0.715252\pi$
$487$	8.00000	−	13.8564i	0.362515	−	0.627894i	0.988374	+	0.152042i	$0.0485850\pi$
$488$	0.500000	+	0.866025i	0.0226339	+	0.0392031i
$489$	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	$0.587280\pi$
$492$	10.5000	+	18.1865i	0.473377	+	0.819912i
$493$	−18.0000	+	31.1769i	−0.810679	+	1.40414i
$494$		0			0
$495$	6.00000	+	10.3923i	0.269680	+	0.467099i
$496$	4.00000			0.179605
$497$		0			0
$498$	−21.0000			−0.941033
$499$	9.00000	+	15.5885i	0.402895	+	0.697835i	0.994074	−	0.108705i	$-0.0346705\pi$
$499$	9.00000	+	15.5885i	0.402895	+	0.697835i	−0.591179	+	0.806541i	$0.701337\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	31.5000	−	54.5596i	1.40732	−	2.43754i
$502$		0			0
$503$	21.0000			0.936344			0.468172	−	0.883637i	$-0.344913\pi$
$503$	21.0000			0.936344			0.468172	+	0.883637i	$0.344913\pi$
$504$		0			0
$505$	−3.00000			−0.133498
$506$	3.00000	+	5.19615i	0.133366	+	0.230997i
$507$	−19.5000	+	33.7750i	−0.866025	+	1.50000i
$508$	−8.00000	+	13.8564i	−0.354943	+	0.614779i
$509$	0.500000	+	0.866025i	0.0221621	+	0.0383859i	0.876894	−	0.480684i	$-0.159612\pi$
$509$	0.500000	+	0.866025i	0.0221621	+	0.0383859i	−0.854732	+	0.519070i	$0.826278\pi$
$510$	−12.0000			−0.531369
$511$		0			0
$512$	1.00000			0.0441942
$513$	27.0000	+	46.7654i	1.19208	+	2.06474i
$514$	4.00000	−	6.92820i	0.176432	−	0.305590i
$515$	0.500000	−	0.866025i	0.0220326	−	0.0381616i
$516$	−7.50000	−	12.9904i	−0.330169	−	0.571870i
$517$	16.0000			0.703679
$518$		0			0
$519$	24.0000			1.05348
$520$		0			0
$521$	19.0000	−	32.9090i	0.832405	−	1.44177i	−0.0637207	−	0.997968i	$-0.520297\pi$
$521$	19.0000	−	32.9090i	0.832405	−	1.44177i	0.896126	−	0.443800i	$-0.146370\pi$
$522$	−27.0000	+	46.7654i	−1.18176	+	2.04686i
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	0.560208	−	0.828352i	$-0.310721\pi$
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	−0.997478	+	0.0709788i	$0.977388\pi$
$524$	−8.00000			−0.349482
$525$		0			0
$526$	5.00000			0.218010
$527$	−8.00000	−	13.8564i	−0.348485	−	0.603595i
$528$	−3.00000	+	5.19615i	−0.130558	+	0.226134i
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	1.00000	+	1.73205i	0.0434372	+	0.0752355i
$531$	−60.0000			−2.60378
$532$		0			0
$533$		0			0
$534$	−1.50000	−	2.59808i	−0.0649113	−	0.112430i
$535$	−1.50000	+	2.59808i	−0.0648507	+	0.112325i
$536$	4.50000	−	7.79423i	0.194370	−	0.336659i
$537$	18.0000	+	31.1769i	0.776757	+	1.34538i
$538$	−3.00000			−0.129339
$539$		0			0
$540$	−9.00000			−0.387298
$541$	−1.50000	−	2.59808i	−0.0644900	−	0.111700i	0.831978	−	0.554809i	$-0.187209\pi$
$541$	−1.50000	−	2.59808i	−0.0644900	−	0.111700i	−0.896468	+	0.443109i	$0.853875\pi$
$542$	−3.00000	+	5.19615i	−0.128861	+	0.223194i
$543$	−10.5000	+	18.1865i	−0.450598	+	0.780459i
$544$	−2.00000	−	3.46410i	−0.0857493	−	0.148522i
$545$	−9.00000			−0.385518
$546$		0			0
$547$	−33.0000			−1.41098			−0.705489	−	0.708721i	$-0.749273\pi$
$547$	−33.0000			−1.41098			−0.705489	+	0.708721i	$0.749273\pi$
$548$	−6.00000	−	10.3923i	−0.256307	−	0.443937i
$549$	3.00000	−	5.19615i	0.128037	−	0.221766i
$550$	1.00000	−	1.73205i	0.0426401	−	0.0738549i
$551$	−27.0000	−	46.7654i	−1.15024	−	1.99227i
$552$	−9.00000			−0.383065
$553$		0			0
$554$	12.0000			0.509831
$555$	−6.00000	−	10.3923i	−0.254686	−	0.441129i
$556$	−7.00000	+	12.1244i	−0.296866	+	0.514187i
$557$	1.00000	−	1.73205i	0.0423714	−	0.0733893i	−0.844062	−	0.536246i	$-0.819842\pi$
$557$	1.00000	−	1.73205i	0.0423714	−	0.0733893i	0.886433	+	0.462856i	$0.153175\pi$
$558$	−12.0000	−	20.7846i	−0.508001	−	0.879883i
$559$		0			0
$560$		0			0
$561$	24.0000			1.01328
$562$	−1.00000	−	1.73205i	−0.0421825	−	0.0730622i
$563$	8.50000	−	14.7224i	0.358232	−	0.620477i	−0.629433	−	0.777055i	$-0.716713\pi$
$563$	8.50000	−	14.7224i	0.358232	−	0.620477i	0.987666	+	0.156578i	$0.0500463\pi$
$564$	−12.0000	+	20.7846i	−0.505291	+	0.875190i
$565$	−1.00000	−	1.73205i	−0.0420703	−	0.0728679i
$566$	4.00000			0.168133
$567$		0			0
$568$	2.00000			0.0839181
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	0.990668	−	0.136295i	$-0.0435194\pi$
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	−0.613369	+	0.789797i	$0.710186\pi$
$570$	9.00000	−	15.5885i	0.376969	−	0.652929i
$571$	15.0000	−	25.9808i	0.627730	−	1.08726i	−0.360276	−	0.932846i	$-0.617317\pi$
$571$	15.0000	−	25.9808i	0.627730	−	1.08726i	0.988006	−	0.154415i	$-0.0493493\pi$
$572$		0			0
$573$	54.0000			2.25588
$574$		0			0
$575$	3.00000			0.125109
$576$	−3.00000	−	5.19615i	−0.125000	−	0.216506i
$577$	5.00000	−	8.66025i	0.208153	−	0.360531i	−0.742980	−	0.669314i	$-0.766588\pi$
$577$	5.00000	−	8.66025i	0.208153	−	0.360531i	0.951133	+	0.308783i	$0.0999216\pi$
$578$	0.500000	−	0.866025i	0.0207973	−	0.0360219i
$579$	39.0000	+	67.5500i	1.62078	+	2.80728i
$580$	9.00000			0.373705
$581$		0			0
$582$	42.0000			1.74096
$583$	−2.00000	−	3.46410i	−0.0828315	−	0.143468i
$584$	−2.00000	+	3.46410i	−0.0827606	+	0.143346i
$585$		0			0
$586$	14.0000	+	24.2487i	0.578335	+	1.00171i
$587$	28.0000			1.15568			0.577842	−	0.816149i	$-0.303895\pi$
$587$	28.0000			1.15568			0.577842	+	0.816149i	$0.303895\pi$
$588$		0			0
$589$	24.0000			0.988903
$590$	5.00000	+	8.66025i	0.205847	+	0.356537i
$591$	3.00000	−	5.19615i	0.123404	−	0.213741i
$592$	2.00000	−	3.46410i	0.0821995	−	0.142374i
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	0.797831	−	0.602881i	$-0.205981\pi$
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	−0.921026	+	0.389501i	$0.872647\pi$
$594$	18.0000			0.738549
$595$		0			0
$596$	3.00000			0.122885
$597$	6.00000	+	10.3923i	0.245564	+	0.425329i
$598$		0			0
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	−0.962175	−	0.272433i	$-0.912172\pi$
$599$	−6.00000	+	10.3923i	−0.245153	+	0.424618i	0.717021	+	0.697051i	$0.245505\pi$
$600$	1.50000	+	2.59808i	0.0612372	+	0.106066i
$601$	−42.0000			−1.71322			−0.856608	−	0.515968i	$-0.827432\pi$
$601$	−42.0000			−1.71322			−0.856608	+	0.515968i	$0.827432\pi$
$602$		0			0
$603$	−54.0000			−2.19905
$604$	8.00000	+	13.8564i	0.325515	+	0.563809i
$605$	3.50000	−	6.06218i	0.142295	−	0.246463i
$606$	−4.50000	+	7.79423i	−0.182800	+	0.316619i
$607$	0.500000	+	0.866025i	0.0202944	+	0.0351509i	0.875994	−	0.482322i	$-0.160206\pi$
$607$	0.500000	+	0.866025i	0.0202944	+	0.0351509i	−0.855700	+	0.517472i	$0.826873\pi$
$608$	6.00000			0.243332
$609$		0			0
$610$	−1.00000			−0.0404888
$611$		0			0
$612$	−12.0000	+	20.7846i	−0.485071	+	0.840168i
$613$	−6.00000	+	10.3923i	−0.242338	+	0.419741i	−0.961380	−	0.275225i	$-0.911248\pi$
$613$	−6.00000	+	10.3923i	−0.242338	+	0.419741i	0.719042	+	0.694967i	$0.244581\pi$
$614$	3.50000	+	6.06218i	0.141249	+	0.244650i
$615$	−21.0000			−0.846802
$616$		0			0
$617$	44.0000			1.77137			0.885687	−	0.464283i	$-0.153688\pi$
$617$	44.0000			1.77137			0.885687	+	0.464283i	$0.153688\pi$
$618$	−1.50000	−	2.59808i	−0.0603388	−	0.104510i
$619$	−23.0000	+	39.8372i	−0.924448	+	1.60119i	−0.132002	+	0.991250i	$0.542140\pi$
$619$	−23.0000	+	39.8372i	−0.924448	+	1.60119i	−0.792446	+	0.609941i	$0.791193\pi$
$620$	−2.00000	+	3.46410i	−0.0803219	+	0.139122i
$621$	13.5000	+	23.3827i	0.541736	+	0.938315i
$622$	18.0000			0.721734
$623$		0			0
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	4.00000	−	6.92820i	0.159872	−	0.276907i
$627$	−18.0000	+	31.1769i	−0.718851	+	1.24509i
$628$	5.00000	+	8.66025i	0.199522	+	0.345582i
$629$	−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	$0.487325\pi$
$632$	−5.00000	−	8.66025i	−0.198889	−	0.344486i
$633$	−39.0000	+	67.5500i	−1.55011	+	2.68487i
$634$	16.0000	−	27.7128i	0.635441	−	1.10062i
$635$	−8.00000	−	13.8564i	−0.317470	−	0.549875i
$636$	6.00000			0.237915
$637$		0			0
$638$	−18.0000			−0.712627
$639$	−6.00000	−	10.3923i	−0.237356	−	0.411113i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−2.50000	+	4.33013i	−0.0987441	+	0.171030i	−0.911165	−	0.412042i	$-0.864816\pi$
$641$	−2.50000	+	4.33013i	−0.0987441	+	0.171030i	0.812421	+	0.583071i	$0.198149\pi$
$642$	4.50000	+	7.79423i	0.177601	+	0.307614i
$643$	−28.0000			−1.10421			−0.552106	−	0.833774i	$-0.686176\pi$
$643$	−28.0000			−1.10421			−0.552106	+	0.833774i	$0.686176\pi$
$644$		0			0
$645$	15.0000			0.590624
$646$	−12.0000	−	20.7846i	−0.472134	−	0.817760i
$647$	−5.50000	+	9.52628i	−0.216227	+	0.374517i	−0.953652	−	0.300913i	$-0.902709\pi$
$647$	−5.50000	+	9.52628i	−0.216227	+	0.374517i	0.737424	+	0.675430i	$0.236042\pi$
$648$	−4.50000	+	7.79423i	−0.176777	+	0.306186i
$649$	−10.0000	−	17.3205i	−0.392534	−	0.679889i
$650$		0			0
$651$		0			0
$652$	−4.00000			−0.156652
$653$	2.00000	+	3.46410i	0.0782660	+	0.135561i	0.902502	−	0.430686i	$-0.141728\pi$
$653$	2.00000	+	3.46410i	0.0782660	+	0.135561i	−0.824236	+	0.566247i	$0.808395\pi$
$654$	−13.5000	+	23.3827i	−0.527892	+	0.914335i
$655$	4.00000	−	6.92820i	0.156293	−	0.270707i
$656$	−3.50000	−	6.06218i	−0.136652	−	0.236688i
$657$	24.0000			0.936329
$658$		0			0
$659$	−26.0000			−1.01282			−0.506408	−	0.862294i	$-0.669027\pi$
$659$	−26.0000			−1.01282			−0.506408	+	0.862294i	$0.669027\pi$
$660$	−3.00000	−	5.19615i	−0.116775	−	0.202260i
$661$	−5.50000	+	9.52628i	−0.213925	+	0.370529i	−0.952940	−	0.303160i	$-0.901958\pi$
$661$	−5.50000	+	9.52628i	−0.213925	+	0.370529i	0.739014	+	0.673690i	$0.235292\pi$
$662$	16.0000	−	27.7128i	0.621858	−	1.07709i
$663$		0			0
$664$	7.00000			0.271653
$665$		0			0
$666$	−24.0000			−0.929981
$667$	−13.5000	−	23.3827i	−0.522722	−	0.905381i
$668$	−10.5000	+	18.1865i	−0.406257	+	0.703658i
$669$	−42.0000	+	72.7461i	−1.62381	+	2.81253i
$670$	4.50000	+	7.79423i	0.173850	+	0.301117i
$671$	2.00000			0.0772091
$672$		0			0
$673$	16.0000			0.616755			0.308377	−	0.951264i	$-0.400214\pi$
$673$	16.0000			0.616755			0.308377	+	0.951264i	$0.400214\pi$
$674$	13.0000	+	22.5167i	0.500741	+	0.867309i
$675$	4.50000	−	7.79423i	0.173205	−	0.300000i
$676$	6.50000	−	11.2583i	0.250000	−	0.433013i
$677$	−24.0000	−	41.5692i	−0.922395	−	1.59763i	−0.795698	−	0.605693i	$-0.792896\pi$
$677$	−24.0000	−	41.5692i	−0.922395	−	1.59763i	−0.126697	−	0.991941i	$-0.540438\pi$
$678$	−6.00000			−0.230429
$679$		0			0
$680$	4.00000			0.153393
$681$	6.00000	+	10.3923i	0.229920	+	0.398234i
$682$	4.00000	−	6.92820i	0.153168	−	0.265295i
$683$	18.5000	−	32.0429i	0.707883	−	1.22609i	−0.257758	−	0.966209i	$-0.582984\pi$
$683$	18.5000	−	32.0429i	0.707883	−	1.22609i	0.965641	−	0.259880i	$-0.0836829\pi$
$684$	−18.0000	−	31.1769i	−0.688247	−	1.19208i
$685$	12.0000			0.458496
$686$		0			0
$687$	66.0000			2.51806
$688$	2.50000	+	4.33013i	0.0953116	+	0.165085i
$689$		0			0
$690$	4.50000	−	7.79423i	0.171312	−	0.296721i
$691$	11.0000	+	19.0526i	0.418460	+	0.724793i	0.995785	−	0.0917209i	$-0.0292368\pi$
$691$	11.0000	+	19.0526i	0.418460	+	0.724793i	−0.577325	+	0.816514i	$0.695903\pi$
$692$	−8.00000			−0.304114
$693$		0			0
$694$	19.0000			0.721230
$695$	−7.00000	−	12.1244i	−0.265525	−	0.459903i
$696$	13.5000	−	23.3827i	0.511716	−	0.886318i
$697$	−14.0000	+	24.2487i	−0.530288	+	0.918485i
$698$	−17.5000	−	30.3109i	−0.662385	−	1.14728i
$699$	−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
$703$	12.0000	−	20.7846i	0.452589	−	0.783906i
$704$	1.00000	−	1.73205i	0.0376889	−	0.0652791i
$705$	−12.0000	−	20.7846i	−0.451946	−	0.782794i
$706$	18.0000			0.677439
$707$		0			0
$708$	30.0000			1.12747
$709$	5.50000	+	9.52628i	0.206557	+	0.357767i	0.950628	−	0.310334i	$-0.100441\pi$
$709$	5.50000	+	9.52628i	0.206557	+	0.357767i	−0.744071	+	0.668101i	$0.767108\pi$
$710$	−1.00000	+	1.73205i	−0.0375293	+	0.0650027i
$711$	−30.0000	+	51.9615i	−1.12509	+	1.94871i
$712$	0.500000	+	0.866025i	0.0187383	+	0.0324557i
$713$	12.0000			0.449404
$714$		0			0
$715$		0			0
$716$	−6.00000	−	10.3923i	−0.224231	−	0.388379i
$717$	24.0000	−	41.5692i	0.896296	−	1.55243i
$718$	2.00000	−	3.46410i	0.0746393	−	0.129279i
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	0.804648	−	0.593753i	$-0.202354\pi$
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	−0.916529	+	0.399969i	$0.869021\pi$
$720$	6.00000			0.223607
$721$		0			0
$722$	17.0000			0.632674
$723$	−15.0000	−	25.9808i	−0.557856	−	0.966235i
$724$	3.50000	−	6.06218i	0.130076	−	0.225299i
$725$	−4.50000	+	7.79423i	−0.167126	+	0.289470i
$726$	−10.5000	−	18.1865i	−0.389692	−	0.674966i
$727$	21.0000			0.778847			0.389423	−	0.921059i	$-0.372674\pi$
$727$	21.0000			0.778847			0.389423	+	0.921059i	$0.372674\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	−2.00000	−	3.46410i	−0.0740233	−	0.128212i
$731$	10.0000	−	17.3205i	0.369863	−	0.640622i
$732$	−1.50000	+	2.59808i	−0.0554416	+	0.0960277i
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	0.994471	−	0.105010i	$-0.0334875\pi$
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	−0.588177	+	0.808732i	$0.700154\pi$
$734$	11.0000			0.406017
$735$		0			0
$736$	3.00000			0.110581
$737$	−9.00000	−	15.5885i	−0.331519	−	0.574208i
$738$	−21.0000	+	36.3731i	−0.773021	+	1.33891i
$739$	1.00000	−	1.73205i	0.0367856	−	0.0637145i	−0.847046	−	0.531519i	$-0.821621\pi$
$739$	1.00000	−	1.73205i	0.0367856	−	0.0637145i	0.883832	+	0.467804i	$0.154955\pi$
$740$	2.00000	+	3.46410i	0.0735215	+	0.127343i
$741$		0			0
$742$		0			0
$743$	9.00000			0.330178			0.165089	−	0.986279i	$-0.447209\pi$
$743$	9.00000			0.330178			0.165089	+	0.986279i	$0.447209\pi$
$744$	6.00000	+	10.3923i	0.219971	+	0.381000i
$745$	−1.50000	+	2.59808i	−0.0549557	+	0.0951861i
$746$	2.00000	−	3.46410i	0.0732252	−	0.126830i
$747$	−21.0000	−	36.3731i	−0.768350	−	1.33082i
$748$	−8.00000			−0.292509
$749$		0			0
$750$	−3.00000			−0.109545
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	0.900207	−	0.435463i	$-0.143415\pi$
$751$	2.00000	+	3.46410i	0.0729810	+	0.126407i	−0.827225	+	0.561870i	$0.810082\pi$
$752$	4.00000	−	6.92820i	0.145865	−	0.252646i
$753$		0			0
$754$		0			0
$755$	−16.0000			−0.582300
$756$		0			0
$757$	16.0000			0.581530			0.290765	−	0.956795i	$-0.406090\pi$
$757$	16.0000			0.581530			0.290765	+	0.956795i	$0.406090\pi$
$758$	−15.0000	−	25.9808i	−0.544825	−	0.943664i
$759$	−9.00000	+	15.5885i	−0.326679	+	0.565825i
$760$	−3.00000	+	5.19615i	−0.108821	+	0.188484i
$761$	−3.00000	−	5.19615i	−0.108750	−	0.188360i	0.806514	−	0.591215i	$-0.201351\pi$
$761$	−3.00000	−	5.19615i	−0.108750	−	0.188360i	−0.915264	+	0.402854i	$0.868018\pi$
$762$	−48.0000			−1.73886
$763$		0			0
$764$	−18.0000			−0.651217
$765$	−12.0000	−	20.7846i	−0.433861	−	0.751469i
$766$	7.50000	−	12.9904i	0.270986	−	0.469362i
$767$		0			0
$768$	1.50000	+	2.59808i	0.0541266	+	0.0937500i
$769$	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
$772$	−13.0000	−	22.5167i	−0.467880	−	0.810392i
$773$	12.0000	−	20.7846i	0.431610	−	0.747570i	−0.565402	−	0.824815i	$-0.691279\pi$
$773$	12.0000	−	20.7846i	0.431610	−	0.747570i	0.997012	+	0.0772449i	$0.0246123\pi$
$774$	15.0000	−	25.9808i	0.539164	−	0.933859i
$775$	−2.00000	−	3.46410i	−0.0718421	−	0.124434i
$776$	−14.0000			−0.502571
$777$		0			0
$778$	26.0000			0.932145
$779$	−21.0000	−	36.3731i	−0.752403	−	1.30320i
$780$		0			0
$781$	2.00000	−	3.46410i	0.0715656	−	0.123955i
$782$	−6.00000	−	10.3923i	−0.214560	−	0.371628i
$783$	−81.0000			−2.89470
$784$		0			0
$785$	−10.0000			−0.356915
$786$	−12.0000	−	20.7846i	−0.428026	−	0.741362i
$787$	15.5000	−	26.8468i	0.552515	−	0.956985i	−0.445577	−	0.895244i	$-0.647001\pi$
$787$	15.5000	−	26.8468i	0.552515	−	0.956985i	0.998092	−	0.0617409i	$-0.0196653\pi$
$788$	−1.00000	+	1.73205i	−0.0356235	+	0.0617018i
$789$	7.50000	+	12.9904i	0.267007	+	0.462470i
$790$	10.0000			0.355784
$791$		0			0
$792$	−12.0000			−0.426401
$793$		0			0
$794$	11.0000	−	19.0526i	0.390375	−	0.676150i
$795$	−3.00000	+	5.19615i	−0.106399	+	0.184289i
$796$	−2.00000	−	3.46410i	−0.0708881	−	0.122782i
$797$		0			0			−	1.00000i	$-0.5\pi$
$797$		0			0				1.00000i	$0.5\pi$
$798$		0			0
$799$	−32.0000			−1.13208
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	3.00000	−	5.19615i	0.106000	−	0.183597i
$802$	−15.5000	+	26.8468i	−0.547324	+	0.947993i
$803$	4.00000	+	6.92820i	0.141157	+	0.244491i
$804$	27.0000			0.952217
$805$		0			0
$806$		0			0
$807$	−4.50000	−	7.79423i	−0.158408	−	0.274370i
$808$	1.50000	−	2.59808i	0.0527698	−	0.0914000i
$809$	25.5000	−	44.1673i	0.896532	−	1.55284i	0.0646355	−	0.997909i	$-0.479412\pi$
$809$	25.5000	−	44.1673i	0.896532	−	1.55284i	0.831897	−	0.554930i	$-0.187255\pi$
$810$	−4.50000	−	7.79423i	−0.158114	−	0.273861i
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$		0			0
$813$	−18.0000			−0.631288
$814$	−4.00000	−	6.92820i	−0.140200	−	0.242833i
$815$	2.00000	−	3.46410i	0.0700569	−	0.121342i
$816$	6.00000	−	10.3923i	0.210042	−	0.363803i
$817$	15.0000	+	25.9808i	0.524784	+	0.908952i
$818$	−3.00000			−0.104893
$819$		0			0
$820$	7.00000			0.244451
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	0.979246	−	0.202674i	$-0.0649632\pi$
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	−0.665144	+	0.746715i	$0.731630\pi$
$822$	18.0000	−	31.1769i	0.627822	−	1.08742i
$823$	−9.50000	+	16.4545i	−0.331149	+	0.573567i	−0.982737	−	0.185006i	$-0.940770\pi$
$823$	−9.50000	+	16.4545i	−0.331149	+	0.573567i	0.651588	+	0.758573i	$0.274103\pi$
$824$	0.500000	+	0.866025i	0.0174183	+	0.0301694i
$825$	6.00000			0.208893
$826$		0			0
$827$	−19.0000			−0.660695			−0.330347	−	0.943859i	$-0.607166\pi$
$827$	−19.0000			−0.660695			−0.330347	+	0.943859i	$0.607166\pi$
$828$	−9.00000	−	15.5885i	−0.312772	−	0.541736i
$829$	−23.0000	+	39.8372i	−0.798823	+	1.38360i	0.121560	+	0.992584i	$0.461210\pi$
$829$	−23.0000	+	39.8372i	−0.798823	+	1.38360i	−0.920383	+	0.391018i	$0.872123\pi$
$830$	−3.50000	+	6.06218i	−0.121487	+	0.210421i
$831$	18.0000	+	31.1769i	0.624413	+	1.08152i
$832$		0			0
$833$		0			0
$834$	−42.0000			−1.45434
$835$	−10.5000	−	18.1865i	−0.363367	−	0.629371i
$836$	6.00000	−	10.3923i	0.207514	−	0.359425i
$837$	18.0000	−	31.1769i	0.622171	−	1.07763i
$838$		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
$842$	9.50000	+	16.4545i	0.327392	+	0.567059i
$843$	3.00000	−	5.19615i	0.103325	−	0.178965i
$844$	13.0000	−	22.5167i	0.447478	−	0.775055i
$845$	6.50000	+	11.2583i	0.223607	+	0.387298i
$846$	−48.0000			−1.65027
$847$		0			0
$848$	−2.00000			−0.0686803
$849$	6.00000	+	10.3923i	0.205919	+	0.356663i
$850$	−2.00000	+	3.46410i	−0.0685994	+	0.118818i
$851$	6.00000	−	10.3923i	0.205677	−	0.356244i
$852$	3.00000	+	5.19615i	0.102778	+	0.178017i
$853$	−14.0000			−0.479351			−0.239675	−	0.970853i	$-0.577041\pi$
$853$	−14.0000			−0.479351			−0.239675	+	0.970853i	$0.577041\pi$
$854$		0			0
$855$	36.0000			1.23117
$856$	−1.50000	−	2.59808i	−0.0512689	−	0.0888004i
$857$	−9.00000	+	15.5885i	−0.307434	+	0.532492i	−0.977800	−	0.209539i	$-0.932804\pi$
$857$	−9.00000	+	15.5885i	−0.307434	+	0.532492i	0.670366	+	0.742030i	$0.266137\pi$
$858$		0			0
$859$	−24.0000	−	41.5692i	−0.818869	−	1.41832i	−0.906516	−	0.422172i	$-0.861268\pi$
$859$	−24.0000	−	41.5692i	−0.818869	−	1.41832i	0.0876464	−	0.996152i	$-0.472065\pi$
$860$	−5.00000			−0.170499
$861$		0			0
$862$	−30.0000			−1.02180
$863$	5.50000	+	9.52628i	0.187222	+	0.324278i	0.944323	−	0.329020i	$-0.106718\pi$
$863$	5.50000	+	9.52628i	0.187222	+	0.324278i	−0.757101	+	0.653298i	$0.773385\pi$
$864$	4.50000	−	7.79423i	0.153093	−	0.265165i
$865$	4.00000	−	6.92820i	0.136004	−	0.235566i
$866$	7.00000	+	12.1244i	0.237870	+	0.412002i
$867$	3.00000			0.101885
$868$		0			0
$869$	−20.0000			−0.678454
$870$	13.5000	+	23.3827i	0.457693	+	0.792747i
$871$		0			0
$872$	4.50000	−	7.79423i	0.152389	−	0.263946i
$873$	42.0000	+	72.7461i	1.42148	+	2.46208i
$874$	18.0000			0.608859
$875$		0			0
$876$	−12.0000			−0.405442
$877$	−19.0000	−	32.9090i	−0.641584	−	1.11126i	−0.985079	−	0.172102i	$-0.944944\pi$
$877$	−19.0000	−	32.9090i	−0.641584	−	1.11126i	0.343495	−	0.939155i	$-0.388389\pi$
$878$	−10.0000	+	17.3205i	−0.337484	+	0.584539i
$879$	−42.0000	+	72.7461i	−1.41662	+	2.45367i
$880$	1.00000	+	1.73205i	0.0337100	+	0.0583874i
$881$	7.00000			0.235836			0.117918	−	0.993023i	$-0.462378\pi$
$881$	7.00000			0.235836			0.117918	+	0.993023i	$0.462378\pi$
$882$		0			0
$883$	−12.0000			−0.403832			−0.201916	−	0.979403i	$-0.564717\pi$
$883$	−12.0000			−0.403832			−0.201916	+	0.979403i	$0.564717\pi$
$884$		0			0
$885$	−15.0000	+	25.9808i	−0.504219	+	0.873334i
$886$	−15.5000	+	26.8468i	−0.520733	+	0.901935i
$887$	14.5000	+	25.1147i	0.486862	+	0.843270i	0.999886	−	0.0151042i	$-0.00480800\pi$
$887$	14.5000	+	25.1147i	0.486862	+	0.843270i	−0.513024	+	0.858375i	$0.671475\pi$
$888$	12.0000			0.402694
$889$		0			0
$890$	−1.00000			−0.0335201
$891$	9.00000	+	15.5885i	0.301511	+	0.522233i
$892$	14.0000	−	24.2487i	0.468755	−	0.811907i
$893$	24.0000	−	41.5692i	0.803129	−	1.39106i
$894$	4.50000	+	7.79423i	0.150503	+	0.260678i
$895$	12.0000			0.401116
$896$		0			0
$897$		0			0
$898$	16.5000	+	28.5788i	0.550612	+	0.953688i
$899$	−18.0000	+	31.1769i	−0.600334	+	1.03981i
$900$	−3.00000	+	5.19615i	−0.100000	+	0.173205i
$901$	4.00000	+	6.92820i	0.133259	+	0.230812i
$902$	−14.0000			−0.466149
$903$		0			0
$904$	2.00000			0.0665190
$905$	3.50000	+	6.06218i	0.116344	+	0.201514i
$906$	−24.0000	+	41.5692i	−0.797347	+	1.38104i
$907$	−2.50000	+	4.33013i	−0.0830111	+	0.143780i	−0.904542	−	0.426385i	$-0.859787\pi$
$907$	−2.50000	+	4.33013i	−0.0830111	+	0.143780i	0.821531	+	0.570164i	$0.193120\pi$
$908$	−2.00000	−	3.46410i	−0.0663723	−	0.114960i
$909$	−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	$0.334445\pi$
$912$	9.00000	+	15.5885i	0.298020	+	0.516185i
$913$	7.00000	−	12.1244i	0.231666	−	0.401258i
$914$	16.0000	−	27.7128i	0.529233	−	0.916658i
$915$	−1.50000	−	2.59808i	−0.0495885	−	0.0858898i
$916$	−22.0000			−0.726900
$917$		0			0
$918$	−36.0000			−1.18818
$919$	−19.0000	−	32.9090i	−0.626752	−	1.08557i	−0.988199	−	0.153174i	$-0.951051\pi$
$919$	−19.0000	−	32.9090i	−0.626752	−	1.08557i	0.361447	−	0.932393i	$-0.382283\pi$
$920$	−1.50000	+	2.59808i	−0.0494535	+	0.0856560i
$921$	−10.5000	+	18.1865i	−0.345987	+	0.599267i
$922$	−7.00000	−	12.1244i	−0.230533	−	0.399294i
$923$		0			0
$924$		0			0
$925$	−4.00000			−0.131519
$926$	9.50000	+	16.4545i	0.312189	+	0.540728i
$927$	3.00000	−	5.19615i	0.0985329	−	0.170664i
$928$	−4.50000	+	7.79423i	−0.147720	+	0.255858i
$929$	21.5000	+	37.2391i	0.705392	+	1.22177i	0.966550	+	0.256479i	$0.0825624\pi$
$929$	21.5000	+	37.2391i	0.705392	+	1.22177i	−0.261158	+	0.965296i	$0.584104\pi$
$930$	−12.0000			−0.393496
$931$		0			0
$932$	24.0000			0.786146
$933$	27.0000	+	46.7654i	0.883940	+	1.53103i
$934$	−6.50000	+	11.2583i	−0.212686	+	0.368384i
$935$	4.00000	−	6.92820i	0.130814	−	0.226576i
$936$		0			0
$937$	28.0000			0.914720			0.457360	−	0.889282i	$-0.348795\pi$
$937$	28.0000			0.914720			0.457360	+	0.889282i	$0.348795\pi$
$938$		0			0
$939$	24.0000			0.783210
$940$	4.00000	+	6.92820i	0.130466	+	0.225973i
$941$	−23.0000	+	39.8372i	−0.749779	+	1.29865i	0.198150	+	0.980172i	$0.436507\pi$
$941$	−23.0000	+	39.8372i	−0.749779	+	1.29865i	−0.947929	+	0.318483i	$0.896827\pi$
$942$	−15.0000	+	25.9808i	−0.488726	+	0.846499i
$943$	−10.5000	−	18.1865i	−0.341927	−	0.592235i
$944$	−10.0000			−0.325472
$945$		0			0
$946$	10.0000			0.325128
$947$	12.5000	+	21.6506i	0.406195	+	0.703551i	0.994460	−	0.105118i	$-0.0335219\pi$
$947$	12.5000	+	21.6506i	0.406195	+	0.703551i	−0.588264	+	0.808669i	$0.700189\pi$
$948$	15.0000	−	25.9808i	0.487177	−	0.843816i
$949$		0			0
$950$	−3.00000	−	5.19615i	−0.0973329	−	0.168585i
$951$	96.0000			3.11301
$952$		0			0
$953$	−12.0000			−0.388718			−0.194359	−	0.980930i	$-0.562263\pi$
$953$	−12.0000			−0.388718			−0.194359	+	0.980930i	$0.562263\pi$
$954$	6.00000	+	10.3923i	0.194257	+	0.336463i
$955$	9.00000	−	15.5885i	0.291233	−	0.504431i
$956$	−8.00000	+	13.8564i	−0.258738	+	0.448148i
$957$	−27.0000	−	46.7654i	−0.872786	−	1.51171i
$958$	−24.0000			−0.775405
$959$		0			0
$960$	−3.00000			−0.0968246
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		0			0
$963$	−9.00000	+	15.5885i	−0.290021	+	0.502331i
$964$	5.00000	+	8.66025i	0.161039	+	0.278928i
$965$	26.0000			0.836970
$966$		0			0
$967$	37.0000			1.18984			0.594920	−	0.803785i	$-0.297184\pi$
$967$	37.0000			1.18984			0.594920	+	0.803785i	$0.297184\pi$
$968$	3.50000	+	6.06218i	0.112494	+	0.194846i
$969$	36.0000	−	62.3538i	1.15649	−	2.00309i
$970$	7.00000	−	12.1244i	0.224756	−	0.389290i
$971$	−24.0000	−	41.5692i	−0.770197	−	1.33402i	−0.937455	−	0.348107i	$-0.886825\pi$
$971$	−24.0000	−	41.5692i	−0.770197	−	1.33402i	0.167258	−	0.985913i	$-0.446509\pi$
$972$		0			0
$973$		0			0
$974$	−16.0000			−0.512673
$975$		0			0
$976$	0.500000	−	0.866025i	0.0160046	−	0.0277208i
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	−0.519841	−	0.854263i	$-0.674009\pi$
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	0.999734	+	0.0230645i	$0.00734232\pi$
$978$	−6.00000	−	10.3923i	−0.191859	−	0.332309i
$979$	2.00000			0.0639203
$980$		0			0
$981$	−54.0000			−1.72409
$982$	6.00000	+	10.3923i	0.191468	+	0.331632i
$983$	8.50000	−	14.7224i	0.271108	−	0.469573i	−0.698038	−	0.716061i	$-0.745943\pi$
$983$	8.50000	−	14.7224i	0.271108	−	0.469573i	0.969146	+	0.246488i	$0.0792766\pi$
$984$	10.5000	−	18.1865i	0.334728	−	0.579766i
$985$	−1.00000	−	1.73205i	−0.0318626	−	0.0551877i
$986$	36.0000			1.14647
$987$		0			0
$988$		0			0
$989$	7.50000	+	12.9904i	0.238486	+	0.413070i
$990$	6.00000	−	10.3923i	0.190693	−	0.330289i
$991$	−20.0000	+	34.6410i	−0.635321	+	1.10041i	0.351126	+	0.936328i	$0.385799\pi$
$991$	−20.0000	+	34.6410i	−0.635321	+	1.10041i	−0.986447	+	0.164080i	$0.947534\pi$
$992$	−2.00000	−	3.46410i	−0.0635001	−	0.109985i
$993$	96.0000			3.04647
$994$		0			0
$995$	4.00000			0.126809
$996$	10.5000	+	18.1865i	0.332705	+	0.576262i
$997$	−23.0000	+	39.8372i	−0.728417	+	1.26166i	0.229135	+	0.973395i	$0.426410\pi$
$997$	−23.0000	+	39.8372i	−0.728417	+	1.26166i	−0.957552	+	0.288261i	$0.906923\pi$
$998$	9.00000	−	15.5885i	0.284890	−	0.493444i
$999$	−18.0000	−	31.1769i	−0.569495	−	0.986394i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.e.f.361.1		2
7.2	even	3	inner	490.2.e.f.471.1		2
7.3	odd	6		490.2.a.k.1.1		1
7.4	even	3		490.2.a.e.1.1		1
7.5	odd	6		70.2.e.a.51.1	yes	2
7.6	odd	2		70.2.e.a.11.1	✓	2
21.5	even	6		630.2.k.f.541.1		2
21.11	odd	6		4410.2.a.h.1.1		1
21.17	even	6		4410.2.a.r.1.1		1
21.20	even	2		630.2.k.f.361.1		2
28.3	even	6		3920.2.a.b.1.1		1
28.11	odd	6		3920.2.a.bk.1.1		1
28.19	even	6		560.2.q.i.401.1		2
28.27	even	2		560.2.q.i.81.1		2
35.3	even	12		2450.2.c.s.99.1		2
35.4	even	6		2450.2.a.q.1.1		1
35.12	even	12		350.2.j.f.149.1		4
35.13	even	4		350.2.j.f.249.1		4
35.17	even	12		2450.2.c.s.99.2		2
35.18	odd	12		2450.2.c.a.99.1		2
35.19	odd	6		350.2.e.l.51.1		2
35.24	odd	6		2450.2.a.b.1.1		1
35.27	even	4		350.2.j.f.249.2		4
35.32	odd	12		2450.2.c.a.99.2		2
35.33	even	12		350.2.j.f.149.2		4
35.34	odd	2		350.2.e.l.151.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.e.a.11.1	✓	2	7.6	odd	2
70.2.e.a.51.1	yes	2	7.5	odd	6
350.2.e.l.51.1		2	35.19	odd	6
350.2.e.l.151.1		2	35.34	odd	2
350.2.j.f.149.1		4	35.12	even	12
350.2.j.f.149.2		4	35.33	even	12
350.2.j.f.249.1		4	35.13	even	4
350.2.j.f.249.2		4	35.27	even	4
490.2.a.e.1.1		1	7.4	even	3
490.2.a.k.1.1		1	7.3	odd	6
490.2.e.f.361.1		2	1.1	even	1	trivial
490.2.e.f.471.1		2	7.2	even	3	inner
560.2.q.i.81.1		2	28.27	even	2
560.2.q.i.401.1		2	28.19	even	6
630.2.k.f.361.1		2	21.20	even	2
630.2.k.f.541.1		2	21.5	even	6
2450.2.a.b.1.1		1	35.24	odd	6
2450.2.a.q.1.1		1	35.4	even	6
2450.2.c.a.99.1		2	35.18	odd	12
2450.2.c.a.99.2		2	35.32	odd	12
2450.2.c.s.99.1		2	35.3	even	12
2450.2.c.s.99.2		2	35.17	even	12
3920.2.a.b.1.1		1	28.3	even	6
3920.2.a.bk.1.1		1	28.11	odd	6
4410.2.a.h.1.1		1	21.11	odd	6
4410.2.a.r.1.1		1	21.17	even	6

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:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -3.00000 q^{6} +1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -3.00000 q^{6} +1.00000 q^{8} +(-3.00000 - 5.19615i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(1.00000 - 1.73205i) q^{11} +(1.50000 + 2.59808i) q^{12} -3.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(-3.00000 + 5.19615i) q^{18} +(-3.00000 - 5.19615i) q^{19} +1.00000 q^{20} -2.00000 q^{22} +(-1.50000 - 2.59808i) q^{23} +(1.50000 - 2.59808i) q^{24} +(-0.500000 + 0.866025i) q^{25} -9.00000 q^{27} +9.00000 q^{29} +(1.50000 + 2.59808i) q^{30} +(-2.00000 + 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{33} +4.00000 q^{34} +6.00000 q^{36} +(2.00000 + 3.46410i) q^{37} +(-3.00000 + 5.19615i) q^{38} +(-0.500000 - 0.866025i) q^{40} +7.00000 q^{41} -5.00000 q^{43} +(1.00000 + 1.73205i) q^{44} +(-3.00000 + 5.19615i) q^{45} +(-1.50000 + 2.59808i) q^{46} +(4.00000 + 6.92820i) q^{47} -3.00000 q^{48} +1.00000 q^{50} +(6.00000 + 10.3923i) q^{51} +(1.00000 - 1.73205i) q^{53} +(4.50000 + 7.79423i) q^{54} -2.00000 q^{55} -18.0000 q^{57} +(-4.50000 - 7.79423i) q^{58} +(5.00000 - 8.66025i) q^{59} +(1.50000 - 2.59808i) q^{60} +(0.500000 + 0.866025i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{66} +(4.50000 - 7.79423i) q^{67} +(-2.00000 - 3.46410i) q^{68} -9.00000 q^{69} +2.00000 q^{71} +(-3.00000 - 5.19615i) q^{72} +(-2.00000 + 3.46410i) q^{73} +(2.00000 - 3.46410i) q^{74} +(1.50000 + 2.59808i) q^{75} +6.00000 q^{76} +(-5.00000 - 8.66025i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(-3.50000 - 6.06218i) q^{82} +7.00000 q^{83} +4.00000 q^{85} +(2.50000 + 4.33013i) q^{86} +(13.5000 - 23.3827i) q^{87} +(1.00000 - 1.73205i) q^{88} +(0.500000 + 0.866025i) q^{89} +6.00000 q^{90} +3.00000 q^{92} +(6.00000 + 10.3923i) q^{93} +(4.00000 - 6.92820i) q^{94} +(-3.00000 + 5.19615i) q^{95} +(1.50000 + 2.59808i) q^{96} -14.0000 q^{97} -12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 3 q^{3} - q^{4} - q^{5} - 6 q^{6} + 2 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q - q^2 + 3 * q^3 - q^4 - q^5 - 6 * q^6 + 2 * q^8 - 6 * q^9	\( 2 q - q^{2} + 3 q^{3} - q^{4} - q^{5} - 6 q^{6} + 2 q^{8} - 6 q^{9} - q^{10} + 2 q^{11} + 3 q^{12} - 6 q^{15} - q^{16} - 4 q^{17} - 6 q^{18} - 6 q^{19} + 2 q^{20} - 4 q^{22} - 3 q^{23} + 3 q^{24} - q^{25} - 18 q^{27} + 18 q^{29} + 3 q^{30} - 4 q^{31} - q^{32} - 6 q^{33} + 8 q^{34} + 12 q^{36} + 4 q^{37} - 6 q^{38} - q^{40} + 14 q^{41} - 10 q^{43} + 2 q^{44} - 6 q^{45} - 3 q^{46} + 8 q^{47} - 6 q^{48} + 2 q^{50} + 12 q^{51} + 2 q^{53} + 9 q^{54} - 4 q^{55} - 36 q^{57} - 9 q^{58} + 10 q^{59} + 3 q^{60} + q^{61} + 8 q^{62} + 2 q^{64} - 6 q^{66} + 9 q^{67} - 4 q^{68} - 18 q^{69} + 4 q^{71} - 6 q^{72} - 4 q^{73} + 4 q^{74} + 3 q^{75} + 12 q^{76} - 10 q^{79} - q^{80} - 9 q^{81} - 7 q^{82} + 14 q^{83} + 8 q^{85} + 5 q^{86} + 27 q^{87} + 2 q^{88} + q^{89} + 12 q^{90} + 6 q^{92} + 12 q^{93} + 8 q^{94} - 6 q^{95} + 3 q^{96} - 28 q^{97} - 24 q^{99}+O(q^{100}) \) 2 * q - q^2 + 3 * q^3 - q^4 - q^5 - 6 * q^6 + 2 * q^8 - 6 * q^9 - q^10 + 2 * q^11 + 3 * q^12 - 6 * q^15 - q^16 - 4 * q^17 - 6 * q^18 - 6 * q^19 + 2 * q^20 - 4 * q^22 - 3 * q^23 + 3 * q^24 - q^25 - 18 * q^27 + 18 * q^29 + 3 * q^30 - 4 * q^31 - q^32 - 6 * q^33 + 8 * q^34 + 12 * q^36 + 4 * q^37 - 6 * q^38 - q^40 + 14 * q^41 - 10 * q^43 + 2 * q^44 - 6 * q^45 - 3 * q^46 + 8 * q^47 - 6 * q^48 + 2 * q^50 + 12 * q^51 + 2 * q^53 + 9 * q^54 - 4 * q^55 - 36 * q^57 - 9 * q^58 + 10 * q^59 + 3 * q^60 + q^61 + 8 * q^62 + 2 * q^64 - 6 * q^66 + 9 * q^67 - 4 * q^68 - 18 * q^69 + 4 * q^71 - 6 * q^72 - 4 * q^73 + 4 * q^74 + 3 * q^75 + 12 * q^76 - 10 * q^79 - q^80 - 9 * q^81 - 7 * q^82 + 14 * q^83 + 8 * q^85 + 5 * q^86 + 27 * q^87 + 2 * q^88 + q^89 + 12 * q^90 + 6 * q^92 + 12 * q^93 + 8 * q^94 - 6 * q^95 + 3 * q^96 - 28 * q^97 - 24 * q^99

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