LMFDB - Embedded newform 5610.2.a.cg.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5610,2,Mod(1,5610)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5610, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5610.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5610.a (trivial)

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:	yes
Analytic conductor:	$44.7960755339$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.54764.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 9x^{2} + 3x + 2 $ x^4 - x^3 - 9x^2 + 3x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.36007$ of defining polynomial
Character	$\chi$	$=$	5610.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +0.487359 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +0.487359 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} +6.29009 q^{13} +0.487359 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +6.12492 q^{19} -1.00000 q^{20} -0.487359 q^{21} +1.00000 q^{22} +5.67781 q^{23} -1.00000 q^{24} +1.00000 q^{25} +6.29009 q^{26} -1.00000 q^{27} +0.487359 q^{28} -8.82801 q^{29} +1.00000 q^{30} -0.487359 q^{31} +1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} -0.487359 q^{35} +1.00000 q^{36} -5.31537 q^{37} +6.12492 q^{38} -6.29009 q^{39} -1.00000 q^{40} +0.165168 q^{41} -0.487359 q^{42} -8.77745 q^{43} +1.00000 q^{44} -1.00000 q^{45} +5.67781 q^{46} +12.2498 q^{47} -1.00000 q^{48} -6.76248 q^{49} +1.00000 q^{50} -1.00000 q^{51} +6.29009 q^{52} -0.165168 q^{53} -1.00000 q^{54} -1.00000 q^{55} +0.487359 q^{56} -6.12492 q^{57} -8.82801 q^{58} +9.22456 q^{59} +1.00000 q^{60} +1.31537 q^{61} -0.487359 q^{62} +0.487359 q^{63} +1.00000 q^{64} -6.29009 q^{65} -1.00000 q^{66} -6.12492 q^{67} +1.00000 q^{68} -5.67781 q^{69} -0.487359 q^{70} +4.97472 q^{71} +1.00000 q^{72} -14.5802 q^{73} -5.31537 q^{74} -1.00000 q^{75} +6.12492 q^{76} +0.487359 q^{77} -6.29009 q^{78} +9.19045 q^{79} -1.00000 q^{80} +1.00000 q^{81} +0.165168 q^{82} -5.26481 q^{83} -0.487359 q^{84} -1.00000 q^{85} -8.77745 q^{86} +8.82801 q^{87} +1.00000 q^{88} +17.6055 q^{89} -1.00000 q^{90} +3.06553 q^{91} +5.67781 q^{92} +0.487359 q^{93} +12.2498 q^{94} -6.12492 q^{95} -1.00000 q^{96} -0.652527 q^{97} -6.76248 q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} - 4 q^{10} + 4 q^{11} - 4 q^{12} - q^{13} + 4 q^{14} + 4 q^{15} + 4 q^{16} + 4 q^{17} + 4 q^{18} + 5 q^{19} - 4 q^{20} - 4 q^{21} + 4 q^{22} + 14 q^{23} - 4 q^{24} + 4 q^{25} - q^{26} - 4 q^{27} + 4 q^{28} - 3 q^{29} + 4 q^{30} - 4 q^{31} + 4 q^{32} - 4 q^{33} + 4 q^{34} - 4 q^{35} + 4 q^{36} + 9 q^{37} + 5 q^{38} + q^{39} - 4 q^{40} - 6 q^{41} - 4 q^{42} - 11 q^{43} + 4 q^{44} - 4 q^{45} + 14 q^{46} + 10 q^{47} - 4 q^{48} + 14 q^{49} + 4 q^{50} - 4 q^{51} - q^{52} + 6 q^{53} - 4 q^{54} - 4 q^{55} + 4 q^{56} - 5 q^{57} - 3 q^{58} + 2 q^{59} + 4 q^{60} - 25 q^{61} - 4 q^{62} + 4 q^{63} + 4 q^{64} + q^{65} - 4 q^{66} - 5 q^{67} + 4 q^{68} - 14 q^{69} - 4 q^{70} + 24 q^{71} + 4 q^{72} - 6 q^{73} + 9 q^{74} - 4 q^{75} + 5 q^{76} + 4 q^{77} + q^{78} + 26 q^{79} - 4 q^{80} + 4 q^{81} - 6 q^{82} + q^{83} - 4 q^{84} - 4 q^{85} - 11 q^{86} + 3 q^{87} + 4 q^{88} + 14 q^{89} - 4 q^{90} + 21 q^{91} + 14 q^{92} + 4 q^{93} + 10 q^{94} - 5 q^{95} - 4 q^{96} + 2 q^{97} + 14 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9 - 4 * q^10 + 4 * q^11 - 4 * q^12 - q^13 + 4 * q^14 + 4 * q^15 + 4 * q^16 + 4 * q^17 + 4 * q^18 + 5 * q^19 - 4 * q^20 - 4 * q^21 + 4 * q^22 + 14 * q^23 - 4 * q^24 + 4 * q^25 - q^26 - 4 * q^27 + 4 * q^28 - 3 * q^29 + 4 * q^30 - 4 * q^31 + 4 * q^32 - 4 * q^33 + 4 * q^34 - 4 * q^35 + 4 * q^36 + 9 * q^37 + 5 * q^38 + q^39 - 4 * q^40 - 6 * q^41 - 4 * q^42 - 11 * q^43 + 4 * q^44 - 4 * q^45 + 14 * q^46 + 10 * q^47 - 4 * q^48 + 14 * q^49 + 4 * q^50 - 4 * q^51 - q^52 + 6 * q^53 - 4 * q^54 - 4 * q^55 + 4 * q^56 - 5 * q^57 - 3 * q^58 + 2 * q^59 + 4 * q^60 - 25 * q^61 - 4 * q^62 + 4 * q^63 + 4 * q^64 + q^65 - 4 * q^66 - 5 * q^67 + 4 * q^68 - 14 * q^69 - 4 * q^70 + 24 * q^71 + 4 * q^72 - 6 * q^73 + 9 * q^74 - 4 * q^75 + 5 * q^76 + 4 * q^77 + q^78 + 26 * q^79 - 4 * q^80 + 4 * q^81 - 6 * q^82 + q^83 - 4 * q^84 - 4 * q^85 - 11 * q^86 + 3 * q^87 + 4 * q^88 + 14 * q^89 - 4 * q^90 + 21 * q^91 + 14 * q^92 + 4 * q^93 + 10 * q^94 - 5 * q^95 - 4 * q^96 + 2 * q^97 + 14 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.00000	−0.408248
$7$	0.487359	0.184204	0.0921022	−	0.995750i	$-0.470641\pi$
$7$	0.487359	0.184204	0.0921022	+	0.995750i	$0.470641\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.00000	−0.288675
$13$	6.29009	1.74456	0.872278	−	0.489010i	$-0.162642\pi$
$13$	6.29009	1.74456	0.872278	+	0.489010i	$0.162642\pi$
$14$	0.487359	0.130252
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	6.12492	1.40515	0.702577	−	0.711608i	$-0.252033\pi$
$19$	6.12492	1.40515	0.702577	+	0.711608i	$0.252033\pi$
$20$	−1.00000	−0.223607
$21$	−0.487359	−0.106350
$22$	1.00000	0.213201
$23$	5.67781	1.18391	0.591953	−	0.805973i	$-0.298357\pi$
$23$	5.67781	1.18391	0.591953	+	0.805973i	$0.298357\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	6.29009	1.23359
$27$	−1.00000	−0.192450
$28$	0.487359	0.0921022
$29$	−8.82801	−1.63932	−0.819660	−	0.572850i	$-0.805838\pi$
$29$	−8.82801	−1.63932	−0.819660	+	0.572850i	$0.805838\pi$
$30$	1.00000	0.182574
$31$	−0.487359	−0.0875322	−0.0437661	−	0.999042i	$-0.513936\pi$
$31$	−0.487359	−0.0875322	−0.0437661	+	0.999042i	$0.513936\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	1.00000	0.171499
$35$	−0.487359	−0.0823787
$36$	1.00000	0.166667
$37$	−5.31537	−0.873842	−0.436921	−	0.899500i	$-0.643931\pi$
$37$	−5.31537	−0.873842	−0.436921	+	0.899500i	$0.643931\pi$
$38$	6.12492	0.993593
$39$	−6.29009	−1.00722
$40$	−1.00000	−0.158114
$41$	0.165168	0.0257949	0.0128975	−	0.999917i	$-0.495894\pi$
$41$	0.165168	0.0257949	0.0128975	+	0.999917i	$0.495894\pi$
$42$	−0.487359	−0.0752011
$43$	−8.77745	−1.33855	−0.669274	−	0.743016i	$-0.733395\pi$
$43$	−8.77745	−1.33855	−0.669274	+	0.743016i	$0.733395\pi$
$44$	1.00000	0.150756
$45$	−1.00000	−0.149071
$46$	5.67781	0.837147
$47$	12.2498	1.78682	0.893411	−	0.449239i	$-0.148305\pi$
$47$	12.2498	1.78682	0.893411	+	0.449239i	$0.148305\pi$
$48$	−1.00000	−0.144338
$49$	−6.76248	−0.966069
$50$	1.00000	0.141421
$51$	−1.00000	−0.140028
$52$	6.29009	0.872278
$53$	−0.165168	−0.0226876	−0.0113438	−	0.999936i	$-0.503611\pi$
$53$	−0.165168	−0.0226876	−0.0113438	+	0.999936i	$0.503611\pi$
$54$	−1.00000	−0.136083
$55$	−1.00000	−0.134840
$56$	0.487359	0.0651261
$57$	−6.12492	−0.811265
$58$	−8.82801	−1.15917
$59$	9.22456	1.20094	0.600468	−	0.799649i	$-0.294981\pi$
$59$	9.22456	1.20094	0.600468	+	0.799649i	$0.294981\pi$
$60$	1.00000	0.129099
$61$	1.31537	0.168416	0.0842080	−	0.996448i	$-0.473164\pi$
$61$	1.31537	0.168416	0.0842080	+	0.996448i	$0.473164\pi$
$62$	−0.487359	−0.0618946
$63$	0.487359	0.0614014
$64$	1.00000	0.125000
$65$	−6.29009	−0.780189
$66$	−1.00000	−0.123091
$67$	−6.12492	−0.748278	−0.374139	−	0.927373i	$-0.622062\pi$
$67$	−6.12492	−0.748278	−0.374139	+	0.927373i	$0.622062\pi$
$68$	1.00000	0.121268
$69$	−5.67781	−0.683528
$70$	−0.487359	−0.0582505
$71$	4.97472	0.590390	0.295195	−	0.955437i	$-0.404615\pi$
$71$	4.97472	0.590390	0.295195	+	0.955437i	$0.404615\pi$
$72$	1.00000	0.117851
$73$	−14.5802	−1.70648	−0.853240	−	0.521518i	$-0.825366\pi$
$73$	−14.5802	−1.70648	−0.853240	+	0.521518i	$0.825366\pi$
$74$	−5.31537	−0.617899
$75$	−1.00000	−0.115470
$76$	6.12492	0.702577
$77$	0.487359	0.0555397
$78$	−6.29009	−0.712212
$79$	9.19045	1.03401	0.517003	−	0.855983i	$-0.327048\pi$
$79$	9.19045	1.03401	0.517003	+	0.855983i	$0.327048\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	0.165168	0.0182398
$83$	−5.26481	−0.577888	−0.288944	−	0.957346i	$-0.593304\pi$
$83$	−5.26481	−0.577888	−0.288944	+	0.957346i	$0.593304\pi$
$84$	−0.487359	−0.0531752
$85$	−1.00000	−0.108465
$86$	−8.77745	−0.946496
$87$	8.82801	0.946462
$88$	1.00000	0.106600
$89$	17.6055	1.86617	0.933087	−	0.359650i	$-0.117104\pi$
$89$	17.6055	1.86617	0.933087	+	0.359650i	$0.117104\pi$
$90$	−1.00000	−0.105409
$91$	3.06553	0.321355
$92$	5.67781	0.591953
$93$	0.487359	0.0505368
$94$	12.2498	1.26347
$95$	−6.12492	−0.628404
$96$	−1.00000	−0.102062
$97$	−0.652527	−0.0662541	−0.0331270	−	0.999451i	$-0.510547\pi$
$97$	−0.652527	−0.0662541	−0.0331270	+	0.999451i	$0.510547\pi$
$98$	−6.76248	−0.683114
$99$	1.00000	0.100504
$100$	1.00000	0.100000
$101$	15.4403	1.53637	0.768183	−	0.640230i	$-0.221161\pi$
$101$	15.4403	1.53637	0.768183	+	0.640230i	$0.221161\pi$
$102$	−1.00000	−0.0990148
$103$	−16.3427	−1.61029	−0.805145	−	0.593078i	$-0.797913\pi$
$103$	−16.3427	−1.61029	−0.805145	+	0.593078i	$0.797913\pi$
$104$	6.29009	0.616794
$105$	0.487359	0.0475614
$106$	−0.165168	−0.0160426
$107$	−7.80273	−0.754318	−0.377159	−	0.926148i	$-0.623099\pi$
$107$	−7.80273	−0.754318	−0.377159	+	0.926148i	$0.623099\pi$
$108$	−1.00000	−0.0962250
$109$	−18.5399	−1.77580	−0.887902	−	0.460034i	$-0.847837\pi$
$109$	−18.5399	−1.77580	−0.887902	+	0.460034i	$0.847837\pi$
$110$	−1.00000	−0.0953463
$111$	5.31537	0.504513
$112$	0.487359	0.0460511
$113$	19.4403	1.82879	0.914394	−	0.404825i	$-0.132667\pi$
$113$	19.4403	1.82879	0.914394	+	0.404825i	$0.132667\pi$
$114$	−6.12492	−0.573651
$115$	−5.67781	−0.529458
$116$	−8.82801	−0.819660
$117$	6.29009	0.581519
$118$	9.22456	0.849189
$119$	0.487359	0.0446761
$120$	1.00000	0.0912871
$121$	1.00000	0.0909091
$122$	1.31537	0.119088
$123$	−0.165168	−0.0148927
$124$	−0.487359	−0.0437661
$125$	−1.00000	−0.0894427
$126$	0.487359	0.0434174
$127$	11.2751	1.00051	0.500253	−	0.865879i	$-0.333240\pi$
$127$	11.2751	1.00051	0.500253	+	0.865879i	$0.333240\pi$
$128$	1.00000	0.0883883
$129$	8.77745	0.772811
$130$	−6.29009	−0.551677
$131$	5.26481	0.459988	0.229994	−	0.973192i	$-0.426129\pi$
$131$	5.26481	0.459988	0.229994	+	0.973192i	$0.426129\pi$
$132$	−1.00000	−0.0870388
$133$	2.98503	0.258835
$134$	−6.12492	−0.529113
$135$	1.00000	0.0860663
$136$	1.00000	0.0857493
$137$	14.4874	1.23774	0.618869	−	0.785494i	$-0.287591\pi$
$137$	14.4874	1.23774	0.618869	+	0.785494i	$0.287591\pi$
$138$	−5.67781	−0.483327
$139$	5.42183	0.459873	0.229937	−	0.973206i	$-0.426148\pi$
$139$	5.42183	0.459873	0.229937	+	0.973206i	$0.426148\pi$
$140$	−0.487359	−0.0411893
$141$	−12.2498	−1.03162
$142$	4.97472	0.417469
$143$	6.29009	0.526004
$144$	1.00000	0.0833333
$145$	8.82801	0.733126
$146$	−14.5802	−1.20666
$147$	6.76248	0.557760
$148$	−5.31537	−0.436921
$149$	7.23070	0.592362	0.296181	−	0.955132i	$-0.404287\pi$
$149$	7.23070	0.592362	0.296181	+	0.955132i	$0.404287\pi$
$150$	−1.00000	−0.0816497
$151$	7.31537	0.595316	0.297658	−	0.954673i	$-0.403794\pi$
$151$	7.31537	0.595316	0.297658	+	0.954673i	$0.403794\pi$
$152$	6.12492	0.496797
$153$	1.00000	0.0808452
$154$	0.487359	0.0392725
$155$	0.487359	0.0391456
$156$	−6.29009	−0.503610
$157$	11.1905	0.893095	0.446548	−	0.894760i	$-0.352653\pi$
$157$	11.1905	0.893095	0.446548	+	0.894760i	$0.352653\pi$
$158$	9.19045	0.731153
$159$	0.165168	0.0130987
$160$	−1.00000	−0.0790569
$161$	2.76713	0.218080
$162$	1.00000	0.0785674
$163$	16.3829	1.28321	0.641604	−	0.767036i	$-0.278269\pi$
$163$	16.3829	1.28321	0.641604	+	0.767036i	$0.278269\pi$
$164$	0.165168	0.0128975
$165$	1.00000	0.0778499
$166$	−5.26481	−0.408628
$167$	−13.5549	−1.04891	−0.524455	−	0.851438i	$-0.675731\pi$
$167$	−13.5549	−1.04891	−0.524455	+	0.851438i	$0.675731\pi$
$168$	−0.487359	−0.0376006
$169$	26.5652	2.04348
$170$	−1.00000	−0.0766965
$171$	6.12492	0.468384
$172$	−8.77745	−0.669274
$173$	21.5652	1.63957	0.819786	−	0.572670i	$-0.194092\pi$
$173$	21.5652	1.63957	0.819786	+	0.572670i	$0.194092\pi$
$174$	8.82801	0.669250
$175$	0.487359	0.0368409
$176$	1.00000	0.0753778
$177$	−9.22456	−0.693360
$178$	17.6055	1.31958
$179$	4.29009	0.320656	0.160328	−	0.987064i	$-0.448745\pi$
$179$	4.29009	0.320656	0.160328	+	0.987064i	$0.448745\pi$
$180$	−1.00000	−0.0745356
$181$	1.47239	0.109442	0.0547211	−	0.998502i	$-0.482573\pi$
$181$	1.47239	0.109442	0.0547211	+	0.998502i	$0.482573\pi$
$182$	3.06553	0.227232
$183$	−1.31537	−0.0972350
$184$	5.67781	0.418574
$185$	5.31537	0.390794
$186$	0.487359	0.0357349
$187$	1.00000	0.0731272
$188$	12.2498	0.893411
$189$	−0.487359	−0.0354501
$190$	−6.12492	−0.444348
$191$	−25.6075	−1.85289	−0.926446	−	0.376429i	$-0.877152\pi$
$191$	−25.6075	−1.85289	−0.926446	+	0.376429i	$0.877152\pi$
$192$	−1.00000	−0.0721688
$193$	18.5802	1.33743	0.668715	−	0.743519i	$-0.266845\pi$
$193$	18.5802	1.33743	0.668715	+	0.743519i	$0.266845\pi$
$194$	−0.652527	−0.0468487
$195$	6.29009	0.450443
$196$	−6.76248	−0.483034
$197$	13.9598	0.994591	0.497296	−	0.867581i	$-0.334326\pi$
$197$	13.9598	0.994591	0.497296	+	0.867581i	$0.334326\pi$
$198$	1.00000	0.0710669
$199$	−11.3154	−0.802125	−0.401063	−	0.916051i	$-0.631359\pi$
$199$	−11.3154	−0.802125	−0.401063	+	0.916051i	$0.631359\pi$
$200$	1.00000	0.0707107
$201$	6.12492	0.432019
$202$	15.4403	1.08638
$203$	−4.30241	−0.301970
$204$	−1.00000	−0.0700140
$205$	−0.165168	−0.0115358
$206$	−16.3427	−1.13865
$207$	5.67781	0.394635
$208$	6.29009	0.436139
$209$	6.12492	0.423670
$210$	0.487359	0.0336310
$211$	8.69695	0.598723	0.299361	−	0.954140i	$-0.403226\pi$
$211$	8.69695	0.598723	0.299361	+	0.954140i	$0.403226\pi$
$212$	−0.165168	−0.0113438
$213$	−4.97472	−0.340862
$214$	−7.80273	−0.533384
$215$	8.77745	0.598617
$216$	−1.00000	−0.0680414
$217$	−0.237519	−0.0161238
$218$	−18.5399	−1.25568
$219$	14.5802	0.985237
$220$	−1.00000	−0.0674200
$221$	6.29009	0.423117
$222$	5.31537	0.356744
$223$	−4.09282	−0.274075	−0.137038	−	0.990566i	$-0.543758\pi$
$223$	−4.09282	−0.274075	−0.137038	+	0.990566i	$0.543758\pi$
$224$	0.487359	0.0325630
$225$	1.00000	0.0666667
$226$	19.4403	1.29315
$227$	−18.1836	−1.20689	−0.603445	−	0.797405i	$-0.706206\pi$
$227$	−18.1836	−1.20689	−0.603445	+	0.797405i	$0.706206\pi$
$228$	−6.12492	−0.405633
$229$	−20.8197	−1.37580	−0.687902	−	0.725803i	$-0.741468\pi$
$229$	−20.8197	−1.37580	−0.687902	+	0.725803i	$0.741468\pi$
$230$	−5.67781	−0.374384
$231$	−0.487359	−0.0320659
$232$	−8.82801	−0.579587
$233$	18.4471	1.20851	0.604255	−	0.796791i	$-0.293471\pi$
$233$	18.4471	1.20851	0.604255	+	0.796791i	$0.293471\pi$
$234$	6.29009	0.411196
$235$	−12.2498	−0.799091
$236$	9.22456	0.600468
$237$	−9.19045	−0.596984
$238$	0.487359	0.0315908
$239$	−19.8553	−1.28433	−0.642166	−	0.766565i	$-0.721964\pi$
$239$	−19.8553	−1.28433	−0.642166	+	0.766565i	$0.721964\pi$
$240$	1.00000	0.0645497
$241$	−10.3728	−0.668168	−0.334084	−	0.942543i	$-0.608427\pi$
$241$	−10.3728	−0.668168	−0.334084	+	0.942543i	$0.608427\pi$
$242$	1.00000	0.0642824
$243$	−1.00000	−0.0641500
$244$	1.31537	0.0842080
$245$	6.76248	0.432039
$246$	−0.165168	−0.0105307
$247$	38.5263	2.45137
$248$	−0.487359	−0.0309473
$249$	5.26481	0.333644
$250$	−1.00000	−0.0632456
$251$	−14.9850	−0.945847	−0.472923	−	0.881103i	$-0.656801\pi$
$251$	−14.9850	−0.945847	−0.472923	+	0.881103i	$0.656801\pi$
$252$	0.487359	0.0307007
$253$	5.67781	0.356961
$254$	11.2751	0.707464
$255$	1.00000	0.0626224
$256$	1.00000	0.0625000
$257$	−6.05257	−0.377549	−0.188774	−	0.982020i	$-0.560452\pi$
$257$	−6.05257	−0.377549	−0.188774	+	0.982020i	$0.560452\pi$
$258$	8.77745	0.546460
$259$	−2.59049	−0.160965
$260$	−6.29009	−0.390095
$261$	−8.82801	−0.546440
$262$	5.26481	0.325261
$263$	−10.1434	−0.625468	−0.312734	−	0.949841i	$-0.601245\pi$
$263$	−10.1434	−0.625468	−0.312734	+	0.949841i	$0.601245\pi$
$264$	−1.00000	−0.0615457
$265$	0.165168	0.0101462
$266$	2.98503	0.183024
$267$	−17.6055	−1.07744
$268$	−6.12492	−0.374139
$269$	−2.93447	−0.178918	−0.0894589	−	0.995991i	$-0.528514\pi$
$269$	−2.93447	−0.178918	−0.0894589	+	0.995991i	$0.528514\pi$
$270$	1.00000	0.0608581
$271$	−3.22255	−0.195756	−0.0978781	−	0.995198i	$-0.531206\pi$
$271$	−3.22255	−0.195756	−0.0978781	+	0.995198i	$0.531206\pi$
$272$	1.00000	0.0606339
$273$	−3.06553	−0.185534
$274$	14.4874	0.875213
$275$	1.00000	0.0603023
$276$	−5.67781	−0.341764
$277$	−24.9611	−1.49977	−0.749883	−	0.661571i	$-0.769890\pi$
$277$	−24.9611	−1.49977	−0.749883	+	0.661571i	$0.769890\pi$
$278$	5.42183	0.325180
$279$	−0.487359	−0.0291774
$280$	−0.487359	−0.0291253
$281$	−10.3829	−0.619392	−0.309696	−	0.950836i	$-0.600227\pi$
$281$	−10.3829	−0.619392	−0.309696	+	0.950836i	$0.600227\pi$
$282$	−12.2498	−0.729467
$283$	17.8852	1.06317	0.531583	−	0.847006i	$-0.321597\pi$
$283$	17.8852	1.06317	0.531583	+	0.847006i	$0.321597\pi$
$284$	4.97472	0.295195
$285$	6.12492	0.362809
$286$	6.29009	0.371941
$287$	0.0804962	0.00475154
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	8.82801	0.518399
$291$	0.652527	0.0382518
$292$	−14.5802	−0.853240
$293$	32.5140	1.89949	0.949743	−	0.313030i	$-0.101344\pi$
$293$	32.5140	1.89949	0.949743	+	0.313030i	$0.101344\pi$
$294$	6.76248	0.394396
$295$	−9.22456	−0.537075
$296$	−5.31537	−0.308950
$297$	−1.00000	−0.0580259
$298$	7.23070	0.418863
$299$	35.7139	2.06539
$300$	−1.00000	−0.0577350
$301$	−4.27777	−0.246566
$302$	7.31537	0.420952
$303$	−15.4403	−0.887022
$304$	6.12492	0.351288
$305$	−1.31537	−0.0753179
$306$	1.00000	0.0571662
$307$	6.38090	0.364177	0.182089	−	0.983282i	$-0.441714\pi$
$307$	6.38090	0.364177	0.182089	+	0.983282i	$0.441714\pi$
$308$	0.487359	0.0277698
$309$	16.3427	0.929701
$310$	0.487359	0.0276801
$311$	8.24984	0.467806	0.233903	−	0.972260i	$-0.424850\pi$
$311$	8.24984	0.467806	0.233903	+	0.972260i	$0.424850\pi$
$312$	−6.29009	−0.356106
$313$	−8.17749	−0.462219	−0.231110	−	0.972928i	$-0.574236\pi$
$313$	−8.17749	−0.462219	−0.231110	+	0.972928i	$0.574236\pi$
$314$	11.1905	0.631514
$315$	−0.487359	−0.0274596
$316$	9.19045	0.517003
$317$	−8.39655	−0.471597	−0.235799	−	0.971802i	$-0.575771\pi$
$317$	−8.39655	−0.471597	−0.235799	+	0.971802i	$0.575771\pi$
$318$	0.165168	0.00926217
$319$	−8.82801	−0.494274
$320$	−1.00000	−0.0559017
$321$	7.80273	0.435506
$322$	2.76713	0.154206
$323$	6.12492	0.340800
$324$	1.00000	0.0555556
$325$	6.29009	0.348911
$326$	16.3829	0.907365
$327$	18.5399	1.02526
$328$	0.165168	0.00911989
$329$	5.97007	0.329141
$330$	1.00000	0.0550482
$331$	−11.1583	−0.613318	−0.306659	−	0.951819i	$-0.599211\pi$
$331$	−11.1583	−0.613318	−0.306659	+	0.951819i	$0.599211\pi$
$332$	−5.26481	−0.288944
$333$	−5.31537	−0.291281
$334$	−13.5549	−0.741691
$335$	6.12492	0.334640
$336$	−0.487359	−0.0265876
$337$	−7.36926	−0.401429	−0.200715	−	0.979650i	$-0.564326\pi$
$337$	−7.36926	−0.401429	−0.200715	+	0.979650i	$0.564326\pi$
$338$	26.5652	1.44496
$339$	−19.4403	−1.05585
$340$	−1.00000	−0.0542326
$341$	−0.487359	−0.0263920
$342$	6.12492	0.331198
$343$	−6.70727	−0.362158
$344$	−8.77745	−0.473248
$345$	5.67781	0.305683
$346$	21.5652	1.15935
$347$	−0.249840	−0.0134121	−0.00670606	−	0.999978i	$-0.502135\pi$
$347$	−0.249840	−0.0134121	−0.00670606	+	0.999978i	$0.502135\pi$
$348$	8.82801	0.473231
$349$	−17.4909	−0.936264	−0.468132	−	0.883659i	$-0.655073\pi$
$349$	−17.4909	−0.936264	−0.468132	+	0.883659i	$0.655073\pi$
$350$	0.487359	0.0260504
$351$	−6.29009	−0.335740
$352$	1.00000	0.0533002
$353$	21.1181	1.12400	0.562002	−	0.827136i	$-0.310032\pi$
$353$	21.1181	1.12400	0.562002	+	0.827136i	$0.310032\pi$
$354$	−9.22456	−0.490280
$355$	−4.97472	−0.264031
$356$	17.6055	0.933087
$357$	−0.487359	−0.0257938
$358$	4.29009	0.226738
$359$	−7.68596	−0.405649	−0.202825	−	0.979215i	$-0.565012\pi$
$359$	−7.68596	−0.405649	−0.202825	+	0.979215i	$0.565012\pi$
$360$	−1.00000	−0.0527046
$361$	18.5146	0.974455
$362$	1.47239	0.0773873
$363$	−1.00000	−0.0524864
$364$	3.06553	0.160677
$365$	14.5802	0.763161
$366$	−1.31537	−0.0687555
$367$	−24.7154	−1.29013	−0.645067	−	0.764126i	$-0.723171\pi$
$367$	−24.7154	−1.29013	−0.645067	+	0.764126i	$0.723171\pi$
$368$	5.67781	0.295976
$369$	0.165168	0.00859831
$370$	5.31537	0.276333
$371$	−0.0804962	−0.00417915
$372$	0.487359	0.0252684
$373$	30.4997	1.57921	0.789607	−	0.613613i	$-0.210285\pi$
$373$	30.4997	1.57921	0.789607	+	0.613613i	$0.210285\pi$
$374$	1.00000	0.0517088
$375$	1.00000	0.0516398
$376$	12.2498	0.631737
$377$	−55.5290	−2.85989
$378$	−0.487359	−0.0250670
$379$	−32.1454	−1.65120	−0.825599	−	0.564258i	$-0.809162\pi$
$379$	−32.1454	−1.65120	−0.825599	+	0.564258i	$0.809162\pi$
$380$	−6.12492	−0.314202
$381$	−11.2751	−0.577642
$382$	−25.6075	−1.31019
$383$	−1.80072	−0.0920127	−0.0460064	−	0.998941i	$-0.514649\pi$
$383$	−1.80072	−0.0920127	−0.0460064	+	0.998941i	$0.514649\pi$
$384$	−1.00000	−0.0510310
$385$	−0.487359	−0.0248381
$386$	18.5802	0.945706
$387$	−8.77745	−0.446183
$388$	−0.652527	−0.0331270
$389$	−27.0799	−1.37300	−0.686502	−	0.727128i	$-0.740855\pi$
$389$	−27.0799	−1.37300	−0.686502	+	0.727128i	$0.740855\pi$
$390$	6.29009	0.318511
$391$	5.67781	0.287139
$392$	−6.76248	−0.341557
$393$	−5.26481	−0.265574
$394$	13.9598	0.703282
$395$	−9.19045	−0.462422
$396$	1.00000	0.0502519
$397$	7.61910	0.382392	0.191196	−	0.981552i	$-0.438763\pi$
$397$	7.61910	0.382392	0.191196	+	0.981552i	$0.438763\pi$
$398$	−11.3154	−0.567188
$399$	−2.98503	−0.149439
$400$	1.00000	0.0500000
$401$	15.3816	0.768119	0.384060	−	0.923308i	$-0.374526\pi$
$401$	15.3816	0.768119	0.384060	+	0.923308i	$0.374526\pi$
$402$	6.12492	0.305483
$403$	−3.06553	−0.152705
$404$	15.4403	0.768183
$405$	−1.00000	−0.0496904
$406$	−4.30241	−0.213525
$407$	−5.31537	−0.263473
$408$	−1.00000	−0.0495074
$409$	7.22456	0.357231	0.178616	−	0.983919i	$-0.442838\pi$
$409$	7.22456	0.357231	0.178616	+	0.983919i	$0.442838\pi$
$410$	−0.165168	−0.00815708
$411$	−14.4874	−0.714609
$412$	−16.3427	−0.805145
$413$	4.49567	0.221217
$414$	5.67781	0.279049
$415$	5.26481	0.258439
$416$	6.29009	0.308397
$417$	−5.42183	−0.265508
$418$	6.12492	0.299580
$419$	3.15835	0.154295	0.0771477	−	0.997020i	$-0.475419\pi$
$419$	3.15835	0.154295	0.0771477	+	0.997020i	$0.475419\pi$
$420$	0.487359	0.0237807
$421$	−16.4894	−0.803642	−0.401821	−	0.915718i	$-0.631623\pi$
$421$	−16.4894	−0.803642	−0.401821	+	0.915718i	$0.631623\pi$
$422$	8.69695	0.423361
$423$	12.2498	0.595608
$424$	−0.165168	−0.00802128
$425$	1.00000	0.0485071
$426$	−4.97472	−0.241026
$427$	0.641058	0.0310229
$428$	−7.80273	−0.377159
$429$	−6.29009	−0.303688
$430$	8.77745	0.423286
$431$	−12.1672	−0.586072	−0.293036	−	0.956101i	$-0.594666\pi$
$431$	−12.1672	−0.586072	−0.293036	+	0.956101i	$0.594666\pi$
$432$	−1.00000	−0.0481125
$433$	21.9358	1.05417	0.527084	−	0.849813i	$-0.323285\pi$
$433$	21.9358	1.05417	0.527084	+	0.849813i	$0.323285\pi$
$434$	−0.237519	−0.0114013
$435$	−8.82801	−0.423271
$436$	−18.5399	−0.887902
$437$	34.7761	1.66357
$438$	14.5802	0.696668
$439$	25.2956	1.20729	0.603646	−	0.797252i	$-0.293714\pi$
$439$	25.2956	1.20729	0.603646	+	0.797252i	$0.293714\pi$
$440$	−1.00000	−0.0476731
$441$	−6.76248	−0.322023
$442$	6.29009	0.299189
$443$	7.25666	0.344774	0.172387	−	0.985029i	$-0.444852\pi$
$443$	7.25666	0.344774	0.172387	+	0.985029i	$0.444852\pi$
$444$	5.31537	0.252256
$445$	−17.6055	−0.834579
$446$	−4.09282	−0.193801
$447$	−7.23070	−0.342000
$448$	0.487359	0.0230255
$449$	−38.9228	−1.83688	−0.918441	−	0.395558i	$-0.870551\pi$
$449$	−38.9228	−1.83688	−0.918441	+	0.395558i	$0.870551\pi$
$450$	1.00000	0.0471405
$451$	0.165168	0.00777747
$452$	19.4403	0.914394
$453$	−7.31537	−0.343706
$454$	−18.1836	−0.853400
$455$	−3.06553	−0.143714
$456$	−6.12492	−0.286826
$457$	−3.01497	−0.141034	−0.0705171	−	0.997511i	$-0.522465\pi$
$457$	−3.01497	−0.141034	−0.0705171	+	0.997511i	$0.522465\pi$
$458$	−20.8197	−0.972841
$459$	−1.00000	−0.0466760
$460$	−5.67781	−0.264729
$461$	32.1010	1.49509	0.747545	−	0.664211i	$-0.231232\pi$
$461$	32.1010	1.49509	0.747545	+	0.664211i	$0.231232\pi$
$462$	−0.487359	−0.0226740
$463$	31.2349	1.45161	0.725804	−	0.687902i	$-0.241468\pi$
$463$	31.2349	1.45161	0.725804	+	0.687902i	$0.241468\pi$
$464$	−8.82801	−0.409830
$465$	−0.487359	−0.0226007
$466$	18.4471	0.854546
$467$	17.3392	0.802361	0.401180	−	0.915999i	$-0.368600\pi$
$467$	17.3392	0.802361	0.401180	+	0.915999i	$0.368600\pi$
$468$	6.29009	0.290759
$469$	−2.98503	−0.137836
$470$	−12.2498	−0.565043
$471$	−11.1905	−0.515629
$472$	9.22456	0.424595
$473$	−8.77745	−0.403587
$474$	−9.19045	−0.422131
$475$	6.12492	0.281031
$476$	0.487359	0.0223381
$477$	−0.165168	−0.00756253
$478$	−19.8553	−0.908160
$479$	35.4020	1.61756	0.808780	−	0.588111i	$-0.200128\pi$
$479$	35.4020	1.61756	0.808780	+	0.588111i	$0.200128\pi$
$480$	1.00000	0.0456435
$481$	−33.4342	−1.52447
$482$	−10.3728	−0.472466
$483$	−2.76713	−0.125909
$484$	1.00000	0.0454545
$485$	0.652527	0.0296297
$486$	−1.00000	−0.0453609
$487$	41.8758	1.89757	0.948786	−	0.315919i	$-0.102313\pi$
$487$	41.8758	1.89757	0.948786	+	0.315919i	$0.102313\pi$
$488$	1.31537	0.0595440
$489$	−16.3829	−0.740861
$490$	6.76248	0.305498
$491$	−19.1399	−0.863771	−0.431885	−	0.901928i	$-0.642152\pi$
$491$	−19.1399	−0.863771	−0.431885	+	0.901928i	$0.642152\pi$
$492$	−0.165168	−0.00744636
$493$	−8.82801	−0.397594
$494$	38.5263	1.73338
$495$	−1.00000	−0.0449467
$496$	−0.487359	−0.0218831
$497$	2.42447	0.108752
$498$	5.26481	0.235922
$499$	19.2109	0.859999	0.429999	−	0.902829i	$-0.358514\pi$
$499$	19.2109	0.859999	0.429999	+	0.902829i	$0.358514\pi$
$500$	−1.00000	−0.0447214
$501$	13.5549	0.605588
$502$	−14.9850	−0.668815
$503$	4.66067	0.207809	0.103905	−	0.994587i	$-0.466866\pi$
$503$	4.66067	0.207809	0.103905	+	0.994587i	$0.466866\pi$
$504$	0.487359	0.0217087
$505$	−15.4403	−0.687084
$506$	5.67781	0.252409
$507$	−26.5652	−1.17980
$508$	11.2751	0.500253
$509$	−4.44912	−0.197204	−0.0986018	−	0.995127i	$-0.531437\pi$
$509$	−4.44912	−0.197204	−0.0986018	+	0.995127i	$0.531437\pi$
$510$	1.00000	0.0442807
$511$	−7.10578	−0.314341
$512$	1.00000	0.0441942
$513$	−6.12492	−0.270422
$514$	−6.05257	−0.266967
$515$	16.3427	0.720144
$516$	8.77745	0.386406
$517$	12.2498	0.538747
$518$	−2.59049	−0.113820
$519$	−21.5652	−0.946608
$520$	−6.29009	−0.275839
$521$	−29.8955	−1.30975	−0.654874	−	0.755738i	$-0.727278\pi$
$521$	−29.8955	−1.30975	−0.654874	+	0.755738i	$0.727278\pi$
$522$	−8.82801	−0.386392
$523$	7.72223	0.337670	0.168835	−	0.985644i	$-0.446000\pi$
$523$	7.72223	0.337670	0.168835	+	0.985644i	$0.446000\pi$
$524$	5.26481	0.229994
$525$	−0.487359	−0.0212701
$526$	−10.1434	−0.442272
$527$	−0.487359	−0.0212297
$528$	−1.00000	−0.0435194
$529$	9.23752	0.401631
$530$	0.165168	0.00717445
$531$	9.22456	0.400312
$532$	2.98503	0.129418
$533$	1.03892	0.0450007
$534$	−17.6055	−0.761863
$535$	7.80273	0.337341
$536$	−6.12492	−0.264556
$537$	−4.29009	−0.185131
$538$	−2.93447	−0.126514
$539$	−6.76248	−0.291281
$540$	1.00000	0.0430331
$541$	13.2751	0.570742	0.285371	−	0.958417i	$-0.407883\pi$
$541$	13.2751	0.570742	0.285371	+	0.958417i	$0.407883\pi$
$542$	−3.22255	−0.138420
$543$	−1.47239	−0.0631864
$544$	1.00000	0.0428746
$545$	18.5399	0.794163
$546$	−3.06553	−0.131193
$547$	−14.0908	−0.602480	−0.301240	−	0.953548i	$-0.597400\pi$
$547$	−14.0908	−0.602480	−0.301240	+	0.953548i	$0.597400\pi$
$548$	14.4874	0.618869
$549$	1.31537	0.0561386
$550$	1.00000	0.0426401
$551$	−54.0709	−2.30350
$552$	−5.67781	−0.241664
$553$	4.47905	0.190468
$554$	−24.9611	−1.06049
$555$	−5.31537	−0.225625
$556$	5.42183	0.229937
$557$	38.2382	1.62020	0.810102	−	0.586288i	$-0.199411\pi$
$557$	38.2382	1.62020	0.810102	+	0.586288i	$0.199411\pi$
$558$	−0.487359	−0.0206315
$559$	−55.2109	−2.33517
$560$	−0.487359	−0.0205947
$561$	−1.00000	−0.0422200
$562$	−10.3829	−0.437976
$563$	−30.3447	−1.27888	−0.639438	−	0.768843i	$-0.720833\pi$
$563$	−30.3447	−1.27888	−0.639438	+	0.768843i	$0.720833\pi$
$564$	−12.2498	−0.515811
$565$	−19.4403	−0.817859
$566$	17.8852	0.751772
$567$	0.487359	0.0204671
$568$	4.97472	0.208735
$569$	25.3154	1.06128	0.530638	−	0.847599i	$-0.321952\pi$
$569$	25.3154	1.06128	0.530638	+	0.847599i	$0.321952\pi$
$570$	6.12492	0.256545
$571$	−24.7495	−1.03574	−0.517868	−	0.855461i	$-0.673274\pi$
$571$	−24.7495	−1.03574	−0.517868	+	0.855461i	$0.673274\pi$
$572$	6.29009	0.263002
$573$	25.6075	1.06977
$574$	0.0804962	0.00335985
$575$	5.67781	0.236781
$576$	1.00000	0.0416667
$577$	−10.3303	−0.430058	−0.215029	−	0.976608i	$-0.568985\pi$
$577$	−10.3303	−0.430058	−0.215029	+	0.976608i	$0.568985\pi$
$578$	1.00000	0.0415945
$579$	−18.5802	−0.772166
$580$	8.82801	0.366563
$581$	−2.56585	−0.106449
$582$	0.652527	0.0270481
$583$	−0.165168	−0.00684057
$584$	−14.5802	−0.603332
$585$	−6.29009	−0.260063
$586$	32.5140	1.34314
$587$	−42.7979	−1.76646	−0.883229	−	0.468941i	$-0.844636\pi$
$587$	−42.7979	−1.76646	−0.883229	+	0.468941i	$0.844636\pi$
$588$	6.76248	0.278880
$589$	−2.98503	−0.122996
$590$	−9.22456	−0.379769
$591$	−13.9598	−0.574227
$592$	−5.31537	−0.218460
$593$	12.4491	0.511224	0.255612	−	0.966779i	$-0.417723\pi$
$593$	12.4491	0.511224	0.255612	+	0.966779i	$0.417723\pi$
$594$	−1.00000	−0.0410305
$595$	−0.487359	−0.0199798
$596$	7.23070	0.296181
$597$	11.3154	0.463107
$598$	35.7139	1.46045
$599$	28.5925	1.16826	0.584129	−	0.811661i	$-0.301436\pi$
$599$	28.5925	1.16826	0.584129	+	0.811661i	$0.301436\pi$
$600$	−1.00000	−0.0408248
$601$	16.4553	0.671224	0.335612	−	0.942000i	$-0.391057\pi$
$601$	16.4553	0.671224	0.335612	+	0.942000i	$0.391057\pi$
$602$	−4.27777	−0.174349
$603$	−6.12492	−0.249426
$604$	7.31537	0.297658
$605$	−1.00000	−0.0406558
$606$	−15.4403	−0.627219
$607$	−37.6840	−1.52955	−0.764773	−	0.644300i	$-0.777149\pi$
$607$	−37.6840	−1.52955	−0.764773	+	0.644300i	$0.777149\pi$
$608$	6.12492	0.248398
$609$	4.30241	0.174342
$610$	−1.31537	−0.0532578
$611$	77.0526	3.11721
$612$	1.00000	0.0404226
$613$	6.66067	0.269022	0.134511	−	0.990912i	$-0.457054\pi$
$613$	6.66067	0.269022	0.134511	+	0.990912i	$0.457054\pi$
$614$	6.38090	0.257512
$615$	0.165168	0.00666022
$616$	0.487359	0.0196362
$617$	13.3897	0.539050	0.269525	−	0.962993i	$-0.413133\pi$
$617$	13.3897	0.539050	0.269525	+	0.962993i	$0.413133\pi$
$618$	16.3427	0.657398
$619$	2.48936	0.100056	0.0500280	−	0.998748i	$-0.484069\pi$
$619$	2.48936	0.100056	0.0500280	+	0.998748i	$0.484069\pi$
$620$	0.487359	0.0195728
$621$	−5.67781	−0.227843
$622$	8.24984	0.330788
$623$	8.58018	0.343758
$624$	−6.29009	−0.251805
$625$	1.00000	0.0400000
$626$	−8.17749	−0.326838
$627$	−6.12492	−0.244606
$628$	11.1905	0.446548
$629$	−5.31537	−0.211938
$630$	−0.487359	−0.0194168
$631$	−7.25449	−0.288797	−0.144398	−	0.989520i	$-0.546125\pi$
$631$	−7.25449	−0.288797	−0.144398	+	0.989520i	$0.546125\pi$
$632$	9.19045	0.365576
$633$	−8.69695	−0.345673
$634$	−8.39655	−0.333469
$635$	−11.2751	−0.447440
$636$	0.165168	0.00654934
$637$	−42.5366	−1.68536
$638$	−8.82801	−0.349504
$639$	4.97472	0.196797
$640$	−1.00000	−0.0395285
$641$	2.21356	0.0874304	0.0437152	−	0.999044i	$-0.486081\pi$
$641$	2.21356	0.0874304	0.0437152	+	0.999044i	$0.486081\pi$
$642$	7.80273	0.307949
$643$	−0.740523	−0.0292034	−0.0146017	−	0.999893i	$-0.504648\pi$
$643$	−0.740523	−0.0292034	−0.0146017	+	0.999893i	$0.504648\pi$
$644$	2.76713	0.109040
$645$	−8.77745	−0.345612
$646$	6.12492	0.240982
$647$	−15.6860	−0.616679	−0.308339	−	0.951276i	$-0.599773\pi$
$647$	−15.6860	−0.616679	−0.308339	+	0.951276i	$0.599773\pi$
$648$	1.00000	0.0392837
$649$	9.22456	0.362096
$650$	6.29009	0.246718
$651$	0.237519	0.00930909
$652$	16.3829	0.641604
$653$	45.5133	1.78107	0.890537	−	0.454911i	$-0.150329\pi$
$653$	45.5133	1.78107	0.890537	+	0.454911i	$0.150329\pi$
$654$	18.5399	0.724969
$655$	−5.26481	−0.205713
$656$	0.165168	0.00644873
$657$	−14.5802	−0.568827
$658$	5.97007	0.232737
$659$	−32.8116	−1.27816	−0.639078	−	0.769142i	$-0.720684\pi$
$659$	−32.8116	−1.27816	−0.639078	+	0.769142i	$0.720684\pi$
$660$	1.00000	0.0389249
$661$	−39.7808	−1.54729	−0.773646	−	0.633618i	$-0.781569\pi$
$661$	−39.7808	−1.54729	−0.773646	+	0.633618i	$0.781569\pi$
$662$	−11.1583	−0.433682
$663$	−6.29009	−0.244287
$664$	−5.26481	−0.204314
$665$	−2.98503	−0.115755
$666$	−5.31537	−0.205966
$667$	−50.1238	−1.94080
$668$	−13.5549	−0.524455
$669$	4.09282	0.158237
$670$	6.12492	0.236626
$671$	1.31537	0.0507793
$672$	−0.487359	−0.0188003
$673$	10.1856	0.392627	0.196314	−	0.980541i	$-0.437103\pi$
$673$	10.1856	0.392627	0.196314	+	0.980541i	$0.437103\pi$
$674$	−7.36926	−0.283853
$675$	−1.00000	−0.0384900
$676$	26.5652	1.02174
$677$	−14.0000	−0.538064	−0.269032	−	0.963131i	$-0.586704\pi$
$677$	−14.0000	−0.538064	−0.269032	+	0.963131i	$0.586704\pi$
$678$	−19.4403	−0.746600
$679$	−0.318015	−0.0122043
$680$	−1.00000	−0.0383482
$681$	18.1836	0.696798
$682$	−0.487359	−0.0186619
$683$	28.3270	1.08390	0.541952	−	0.840410i	$-0.317686\pi$
$683$	28.3270	1.08390	0.541952	+	0.840410i	$0.317686\pi$
$684$	6.12492	0.234192
$685$	−14.4874	−0.553534
$686$	−6.70727	−0.256085
$687$	20.8197	0.794321
$688$	−8.77745	−0.334637
$689$	−1.03892	−0.0395798
$690$	5.67781	0.216151
$691$	−23.1337	−0.880049	−0.440025	−	0.897986i	$-0.645030\pi$
$691$	−23.1337	−0.880049	−0.440025	+	0.897986i	$0.645030\pi$
$692$	21.5652	0.819786
$693$	0.487359	0.0185132
$694$	−0.249840	−0.00948380
$695$	−5.42183	−0.205662
$696$	8.82801	0.334625
$697$	0.165168	0.00625619
$698$	−17.4909	−0.662039
$699$	−18.4471	−0.697734
$700$	0.487359	0.0184204
$701$	−32.4313	−1.22491	−0.612457	−	0.790504i	$-0.709819\pi$
$701$	−32.4313	−1.22491	−0.612457	+	0.790504i	$0.709819\pi$
$702$	−6.29009	−0.237404
$703$	−32.5562	−1.22788
$704$	1.00000	0.0376889
$705$	12.2498	0.461356
$706$	21.1181	0.794790
$707$	7.52496	0.283005
$708$	−9.22456	−0.346680
$709$	36.8806	1.38508	0.692540	−	0.721380i	$-0.256492\pi$
$709$	36.8806	1.38508	0.692540	+	0.721380i	$0.256492\pi$
$710$	−4.97472	−0.186698
$711$	9.19045	0.344669
$712$	17.6055	0.659792
$713$	−2.76713	−0.103630
$714$	−0.487359	−0.0182389
$715$	−6.29009	−0.235236
$716$	4.29009	0.160328
$717$	19.8553	0.741510
$718$	−7.68596	−0.286837
$719$	3.45675	0.128915	0.0644575	−	0.997920i	$-0.479468\pi$
$719$	3.45675	0.128915	0.0644575	+	0.997920i	$0.479468\pi$
$720$	−1.00000	−0.0372678
$721$	−7.96474	−0.296622
$722$	18.5146	0.689044
$723$	10.3728	0.385767
$724$	1.47239	0.0547211
$725$	−8.82801	−0.327864
$726$	−1.00000	−0.0371135
$727$	−18.8280	−0.698292	−0.349146	−	0.937068i	$-0.613528\pi$
$727$	−18.8280	−0.698292	−0.349146	+	0.937068i	$0.613528\pi$
$728$	3.06553	0.113616
$729$	1.00000	0.0370370
$730$	14.5802	0.539637
$731$	−8.77745	−0.324646
$732$	−1.31537	−0.0486175
$733$	24.5905	0.908271	0.454135	−	0.890933i	$-0.349948\pi$
$733$	24.5905	0.908271	0.454135	+	0.890933i	$0.349948\pi$
$734$	−24.7154	−0.912263
$735$	−6.76248	−0.249438
$736$	5.67781	0.209287
$737$	−6.12492	−0.225614
$738$	0.165168	0.00607993
$739$	−4.57003	−0.168111	−0.0840556	−	0.996461i	$-0.526787\pi$
$739$	−4.57003	−0.168111	−0.0840556	+	0.996461i	$0.526787\pi$
$740$	5.31537	0.195397
$741$	−38.5263	−1.41530
$742$	−0.0804962	−0.00295511
$743$	−22.8806	−0.839407	−0.419704	−	0.907661i	$-0.637866\pi$
$743$	−22.8806	−0.839407	−0.419704	+	0.907661i	$0.637866\pi$
$744$	0.487359	0.0178674
$745$	−7.23070	−0.264912
$746$	30.4997	1.11667
$747$	−5.26481	−0.192629
$748$	1.00000	0.0365636
$749$	−3.80273	−0.138949
$750$	1.00000	0.0365148
$751$	22.8649	0.834353	0.417177	−	0.908825i	$-0.363020\pi$
$751$	22.8649	0.834353	0.417177	+	0.908825i	$0.363020\pi$
$752$	12.2498	0.446706
$753$	14.9850	0.546085
$754$	−55.5290	−2.02225
$755$	−7.31537	−0.266234
$756$	−0.487359	−0.0177251
$757$	22.1672	0.805680	0.402840	−	0.915271i	$-0.368023\pi$
$757$	22.1672	0.805680	0.402840	+	0.915271i	$0.368023\pi$
$758$	−32.1454	−1.16757
$759$	−5.67781	−0.206091
$760$	−6.12492	−0.222174
$761$	−36.6224	−1.32756	−0.663781	−	0.747927i	$-0.731049\pi$
$761$	−36.6224	−1.32756	−0.663781	+	0.747927i	$0.731049\pi$
$762$	−11.2751	−0.408455
$763$	−9.03560	−0.327111
$764$	−25.6075	−0.926446
$765$	−1.00000	−0.0361551
$766$	−1.80072	−0.0650628
$767$	58.0233	2.09510
$768$	−1.00000	−0.0360844
$769$	29.0293	1.04682	0.523412	−	0.852080i	$-0.324659\pi$
$769$	29.0293	1.04682	0.523412	+	0.852080i	$0.324659\pi$
$770$	−0.487359	−0.0175632
$771$	6.05257	0.217978
$772$	18.5802	0.668715
$773$	−33.9297	−1.22036	−0.610182	−	0.792261i	$-0.708904\pi$
$773$	−33.9297	−1.22036	−0.610182	+	0.792261i	$0.708904\pi$
$774$	−8.77745	−0.315499
$775$	−0.487359	−0.0175064
$776$	−0.652527	−0.0234244
$777$	2.59049	0.0929334
$778$	−27.0799	−0.970860
$779$	1.01164	0.0362458
$780$	6.29009	0.225221
$781$	4.97472	0.178009
$782$	5.67781	0.203038
$783$	8.82801	0.315487
$784$	−6.76248	−0.241517
$785$	−11.1905	−0.399404
$786$	−5.26481	−0.187789
$787$	−33.2854	−1.18650	−0.593249	−	0.805019i	$-0.702155\pi$
$787$	−33.2854	−1.18650	−0.593249	+	0.805019i	$0.702155\pi$
$788$	13.9598	0.497296
$789$	10.1434	0.361114
$790$	−9.19045	−0.326982
$791$	9.47440	0.336871
$792$	1.00000	0.0355335
$793$	8.27380	0.293811
$794$	7.61910	0.270392
$795$	−0.165168	−0.00585791
$796$	−11.3154	−0.401063
$797$	17.5993	0.623400	0.311700	−	0.950181i	$-0.399102\pi$
$797$	17.5993	0.623400	0.311700	+	0.950181i	$0.399102\pi$
$798$	−2.98503	−0.105669
$799$	12.2498	0.433368
$800$	1.00000	0.0353553
$801$	17.6055	0.622058
$802$	15.3816	0.543142
$803$	−14.5802	−0.514523
$804$	6.12492	0.216009
$805$	−2.76713	−0.0975285
$806$	−3.06553	−0.107979
$807$	2.93447	0.103298
$808$	15.4403	0.543188
$809$	−49.0321	−1.72388	−0.861939	−	0.507013i	$-0.830750\pi$
$809$	−49.0321	−1.72388	−0.861939	+	0.507013i	$0.830750\pi$
$810$	−1.00000	−0.0351364
$811$	−37.0799	−1.30205	−0.651025	−	0.759056i	$-0.725661\pi$
$811$	−37.0799	−1.30205	−0.651025	+	0.759056i	$0.725661\pi$
$812$	−4.30241	−0.150985
$813$	3.22255	0.113020
$814$	−5.31537	−0.186304
$815$	−16.3829	−0.573868
$816$	−1.00000	−0.0350070
$817$	−53.7612	−1.88086
$818$	7.22456	0.252601
$819$	3.06553	0.107118
$820$	−0.165168	−0.00576792
$821$	10.9468	0.382046	0.191023	−	0.981586i	$-0.438820\pi$
$821$	10.9468	0.382046	0.191023	+	0.981586i	$0.438820\pi$
$822$	−14.4874	−0.505305
$823$	28.8970	1.00729	0.503644	−	0.863911i	$-0.331992\pi$
$823$	28.8970	1.00729	0.503644	+	0.863911i	$0.331992\pi$
$824$	−16.3427	−0.569323
$825$	−1.00000	−0.0348155
$826$	4.49567	0.156424
$827$	18.6833	0.649682	0.324841	−	0.945769i	$-0.394689\pi$
$827$	18.6833	0.649682	0.324841	+	0.945769i	$0.394689\pi$
$828$	5.67781	0.197318
$829$	0.634065	0.0220220	0.0110110	−	0.999939i	$-0.496495\pi$
$829$	0.634065	0.0220220	0.0110110	+	0.999939i	$0.496495\pi$
$830$	5.26481	0.182744
$831$	24.9611	0.865890
$832$	6.29009	0.218070
$833$	−6.76248	−0.234306
$834$	−5.42183	−0.187743
$835$	13.5549	0.469086
$836$	6.12492	0.211835
$837$	0.487359	0.0168456
$838$	3.15835	0.109103
$839$	22.4860	0.776304	0.388152	−	0.921595i	$-0.373113\pi$
$839$	22.4860	0.776304	0.388152	+	0.921595i	$0.373113\pi$
$840$	0.487359	0.0168155
$841$	48.9338	1.68737
$842$	−16.4894	−0.568261
$843$	10.3829	0.357606
$844$	8.69695	0.299361
$845$	−26.5652	−0.913871
$846$	12.2498	0.421158
$847$	0.487359	0.0167458
$848$	−0.165168	−0.00567190
$849$	−17.8852	−0.613820
$850$	1.00000	0.0342997
$851$	−30.1797	−1.03455
$852$	−4.97472	−0.170431
$853$	4.67930	0.160216	0.0801081	−	0.996786i	$-0.474473\pi$
$853$	4.67930	0.160216	0.0801081	+	0.996786i	$0.474473\pi$
$854$	0.641058	0.0219365
$855$	−6.12492	−0.209468
$856$	−7.80273	−0.266692
$857$	35.8976	1.22624	0.613119	−	0.789991i	$-0.289915\pi$
$857$	35.8976	1.22624	0.613119	+	0.789991i	$0.289915\pi$
$858$	−6.29009	−0.214740
$859$	−0.740523	−0.0252663	−0.0126332	−	0.999920i	$-0.504021\pi$
$859$	−0.740523	−0.0252663	−0.0126332	+	0.999920i	$0.504021\pi$
$860$	8.77745	0.299308
$861$	−0.0804962	−0.00274330
$862$	−12.1672	−0.414416
$863$	24.4997	0.833979	0.416989	−	0.908911i	$-0.363085\pi$
$863$	24.4997	0.833979	0.416989	+	0.908911i	$0.363085\pi$
$864$	−1.00000	−0.0340207
$865$	−21.5652	−0.733239
$866$	21.9358	0.745409
$867$	−1.00000	−0.0339618
$868$	−0.237519	−0.00806191
$869$	9.19045	0.311765
$870$	−8.82801	−0.299298
$871$	−38.5263	−1.30541
$872$	−18.5399	−0.627841
$873$	−0.652527	−0.0220847
$874$	34.7761	1.17632
$875$	−0.487359	−0.0164757
$876$	14.5802	0.492619
$877$	0.578171	0.0195235	0.00976173	−	0.999952i	$-0.496893\pi$
$877$	0.578171	0.0195235	0.00976173	+	0.999952i	$0.496893\pi$
$878$	25.2956	0.853685
$879$	−32.5140	−1.09667
$880$	−1.00000	−0.0337100
$881$	−25.7222	−0.866604	−0.433302	−	0.901249i	$-0.642652\pi$
$881$	−25.7222	−0.866604	−0.433302	+	0.901249i	$0.642652\pi$
$882$	−6.76248	−0.227705
$883$	11.4909	0.386698	0.193349	−	0.981130i	$-0.438065\pi$
$883$	11.4909	0.386698	0.193349	+	0.981130i	$0.438065\pi$
$884$	6.29009	0.211559
$885$	9.22456	0.310080
$886$	7.25666	0.243792
$887$	−22.3809	−0.751477	−0.375739	−	0.926726i	$-0.622611\pi$
$887$	−22.3809	−0.751477	−0.375739	+	0.926726i	$0.622611\pi$
$888$	5.31537	0.178372
$889$	5.49503	0.184297
$890$	−17.6055	−0.590136
$891$	1.00000	0.0335013
$892$	−4.09282	−0.137038
$893$	75.0293	2.51076
$894$	−7.23070	−0.241831
$895$	−4.29009	−0.143402
$896$	0.487359	0.0162815
$897$	−35.7139	−1.19245
$898$	−38.9228	−1.29887
$899$	4.30241	0.143493
$900$	1.00000	0.0333333
$901$	−0.165168	−0.00550255
$902$	0.165168	0.00549950
$903$	4.27777	0.142355
$904$	19.4403	0.646574
$905$	−1.47239	−0.0489440
$906$	−7.31537	−0.243037
$907$	−30.0020	−0.996200	−0.498100	−	0.867120i	$-0.665969\pi$
$907$	−30.0020	−0.996200	−0.498100	+	0.867120i	$0.665969\pi$
$908$	−18.1836	−0.603445
$909$	15.4403	0.512122
$910$	−3.06553	−0.101621
$911$	−24.3986	−0.808360	−0.404180	−	0.914679i	$-0.632443\pi$
$911$	−24.3986	−0.808360	−0.404180	+	0.914679i	$0.632443\pi$
$912$	−6.12492	−0.202816
$913$	−5.26481	−0.174240
$914$	−3.01497	−0.0997262
$915$	1.31537	0.0434848
$916$	−20.8197	−0.687902
$917$	2.56585	0.0847318
$918$	−1.00000	−0.0330049
$919$	41.7488	1.37717	0.688584	−	0.725157i	$-0.258233\pi$
$919$	41.7488	1.37717	0.688584	+	0.725157i	$0.258233\pi$
$920$	−5.67781	−0.187192
$921$	−6.38090	−0.210258
$922$	32.1010	1.05719
$923$	31.2914	1.02997
$924$	−0.487359	−0.0160329
$925$	−5.31537	−0.174768
$926$	31.2349	1.02644
$927$	−16.3427	−0.536763
$928$	−8.82801	−0.289794
$929$	−24.6431	−0.808513	−0.404256	−	0.914646i	$-0.632470\pi$
$929$	−24.6431	−0.808513	−0.404256	+	0.914646i	$0.632470\pi$
$930$	−0.487359	−0.0159811
$931$	−41.4197	−1.35747
$932$	18.4471	0.604255
$933$	−8.24984	−0.270088
$934$	17.3392	0.567355
$935$	−1.00000	−0.0327035
$936$	6.29009	0.205598
$937$	−3.01497	−0.0984946	−0.0492473	−	0.998787i	$-0.515682\pi$
$937$	−3.01497	−0.0984946	−0.0492473	+	0.998787i	$0.515682\pi$
$938$	−2.98503	−0.0974648
$939$	8.17749	0.266862
$940$	−12.2498	−0.399546
$941$	−51.9099	−1.69221	−0.846107	−	0.533013i	$-0.821060\pi$
$941$	−51.9099	−1.69221	−0.846107	+	0.533013i	$0.821060\pi$
$942$	−11.1905	−0.364605
$943$	0.937794	0.0305388
$944$	9.22456	0.300234
$945$	0.487359	0.0158538
$946$	−8.77745	−0.285379
$947$	−17.6560	−0.573744	−0.286872	−	0.957969i	$-0.592615\pi$
$947$	−17.6560	−0.573744	−0.286872	+	0.957969i	$0.592615\pi$
$948$	−9.19045	−0.298492
$949$	−91.7106	−2.97705
$950$	6.12492	0.198719
$951$	8.39655	0.272277
$952$	0.487359	0.0157954
$953$	−33.8922	−1.09788	−0.548938	−	0.835863i	$-0.684968\pi$
$953$	−33.8922	−1.09788	−0.548938	+	0.835863i	$0.684968\pi$
$954$	−0.165168	−0.00534752
$955$	25.6075	0.828638
$956$	−19.8553	−0.642166
$957$	8.82801	0.285369
$958$	35.4020	1.14379
$959$	7.06054	0.227997
$960$	1.00000	0.0322749
$961$	−30.7625	−0.992338
$962$	−33.4342	−1.07796
$963$	−7.80273	−0.251439
$964$	−10.3728	−0.334084
$965$	−18.5802	−0.598117
$966$	−2.76713	−0.0890310
$967$	−15.6860	−0.504426	−0.252213	−	0.967672i	$-0.581158\pi$
$967$	−15.6860	−0.504426	−0.252213	+	0.967672i	$0.581158\pi$
$968$	1.00000	0.0321412
$969$	−6.12492	−0.196761
$970$	0.652527	0.0209514
$971$	2.09482	0.0672261	0.0336130	−	0.999435i	$-0.489299\pi$
$971$	2.09482	0.0672261	0.0336130	+	0.999435i	$0.489299\pi$
$972$	−1.00000	−0.0320750
$973$	2.64238	0.0847107
$974$	41.8758	1.34179
$975$	−6.29009	−0.201444
$976$	1.31537	0.0421040
$977$	40.4458	1.29398	0.646988	−	0.762500i	$-0.276028\pi$
$977$	40.4458	1.29398	0.646988	+	0.762500i	$0.276028\pi$
$978$	−16.3829	−0.523868
$979$	17.6055	0.562673
$980$	6.76248	0.216020
$981$	−18.5399	−0.591934
$982$	−19.1399	−0.610778
$983$	51.5434	1.64398	0.821990	−	0.569502i	$-0.192864\pi$
$983$	51.5434	1.64398	0.821990	+	0.569502i	$0.192864\pi$
$984$	−0.165168	−0.00526537
$985$	−13.9598	−0.444795
$986$	−8.82801	−0.281141
$987$	−5.97007	−0.190029
$988$	38.5263	1.22568
$989$	−49.8367	−1.58471
$990$	−1.00000	−0.0317821
$991$	33.4185	1.06157	0.530787	−	0.847505i	$-0.321896\pi$
$991$	33.4185	1.06157	0.530787	+	0.847505i	$0.321896\pi$
$992$	−0.487359	−0.0154737
$993$	11.1583	0.354099
$994$	2.42447	0.0768996
$995$	11.3154	0.358721
$996$	5.26481	0.166822
$997$	−34.5482	−1.09415	−0.547077	−	0.837082i	$-0.684259\pi$
$997$	−34.5482	−1.09415	−0.547077	+	0.837082i	$0.684259\pi$
$998$	19.2109	0.608111
$999$	5.31537	0.168171

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.cg.1.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.cg.1.2	✓	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5610.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +0.487359 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +0.487359 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +1.00000 q^{11} -1.00000 q^{12} +6.29009 q^{13} +0.487359 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +6.12492 q^{19} -1.00000 q^{20} -0.487359 q^{21} +1.00000 q^{22} +5.67781 q^{23} -1.00000 q^{24} +1.00000 q^{25} +6.29009 q^{26} -1.00000 q^{27} +0.487359 q^{28} -8.82801 q^{29} +1.00000 q^{30} -0.487359 q^{31} +1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} -0.487359 q^{35} +1.00000 q^{36} -5.31537 q^{37} +6.12492 q^{38} -6.29009 q^{39} -1.00000 q^{40} +0.165168 q^{41} -0.487359 q^{42} -8.77745 q^{43} +1.00000 q^{44} -1.00000 q^{45} +5.67781 q^{46} +12.2498 q^{47} -1.00000 q^{48} -6.76248 q^{49} +1.00000 q^{50} -1.00000 q^{51} +6.29009 q^{52} -0.165168 q^{53} -1.00000 q^{54} -1.00000 q^{55} +0.487359 q^{56} -6.12492 q^{57} -8.82801 q^{58} +9.22456 q^{59} +1.00000 q^{60} +1.31537 q^{61} -0.487359 q^{62} +0.487359 q^{63} +1.00000 q^{64} -6.29009 q^{65} -1.00000 q^{66} -6.12492 q^{67} +1.00000 q^{68} -5.67781 q^{69} -0.487359 q^{70} +4.97472 q^{71} +1.00000 q^{72} -14.5802 q^{73} -5.31537 q^{74} -1.00000 q^{75} +6.12492 q^{76} +0.487359 q^{77} -6.29009 q^{78} +9.19045 q^{79} -1.00000 q^{80} +1.00000 q^{81} +0.165168 q^{82} -5.26481 q^{83} -0.487359 q^{84} -1.00000 q^{85} -8.77745 q^{86} +8.82801 q^{87} +1.00000 q^{88} +17.6055 q^{89} -1.00000 q^{90} +3.06553 q^{91} +5.67781 q^{92} +0.487359 q^{93} +12.2498 q^{94} -6.12492 q^{95} -1.00000 q^{96} -0.652527 q^{97} -6.76248 q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 4 q^{5} - 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} - 4 q^{10} + 4 q^{11} - 4 q^{12} - q^{13} + 4 q^{14} + 4 q^{15} + 4 q^{16} + 4 q^{17} + 4 q^{18} + 5 q^{19} - 4 q^{20} - 4 q^{21} + 4 q^{22} + 14 q^{23} - 4 q^{24} + 4 q^{25} - q^{26} - 4 q^{27} + 4 q^{28} - 3 q^{29} + 4 q^{30} - 4 q^{31} + 4 q^{32} - 4 q^{33} + 4 q^{34} - 4 q^{35} + 4 q^{36} + 9 q^{37} + 5 q^{38} + q^{39} - 4 q^{40} - 6 q^{41} - 4 q^{42} - 11 q^{43} + 4 q^{44} - 4 q^{45} + 14 q^{46} + 10 q^{47} - 4 q^{48} + 14 q^{49} + 4 q^{50} - 4 q^{51} - q^{52} + 6 q^{53} - 4 q^{54} - 4 q^{55} + 4 q^{56} - 5 q^{57} - 3 q^{58} + 2 q^{59} + 4 q^{60} - 25 q^{61} - 4 q^{62} + 4 q^{63} + 4 q^{64} + q^{65} - 4 q^{66} - 5 q^{67} + 4 q^{68} - 14 q^{69} - 4 q^{70} + 24 q^{71} + 4 q^{72} - 6 q^{73} + 9 q^{74} - 4 q^{75} + 5 q^{76} + 4 q^{77} + q^{78} + 26 q^{79} - 4 q^{80} + 4 q^{81} - 6 q^{82} + q^{83} - 4 q^{84} - 4 q^{85} - 11 q^{86} + 3 q^{87} + 4 q^{88} + 14 q^{89} - 4 q^{90} + 21 q^{91} + 14 q^{92} + 4 q^{93} + 10 q^{94} - 5 q^{95} - 4 q^{96} + 2 q^{97} + 14 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 4 * q^5 - 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9 - 4 * q^10 + 4 * q^11 - 4 * q^12 - q^13 + 4 * q^14 + 4 * q^15 + 4 * q^16 + 4 * q^17 + 4 * q^18 + 5 * q^19 - 4 * q^20 - 4 * q^21 + 4 * q^22 + 14 * q^23 - 4 * q^24 + 4 * q^25 - q^26 - 4 * q^27 + 4 * q^28 - 3 * q^29 + 4 * q^30 - 4 * q^31 + 4 * q^32 - 4 * q^33 + 4 * q^34 - 4 * q^35 + 4 * q^36 + 9 * q^37 + 5 * q^38 + q^39 - 4 * q^40 - 6 * q^41 - 4 * q^42 - 11 * q^43 + 4 * q^44 - 4 * q^45 + 14 * q^46 + 10 * q^47 - 4 * q^48 + 14 * q^49 + 4 * q^50 - 4 * q^51 - q^52 + 6 * q^53 - 4 * q^54 - 4 * q^55 + 4 * q^56 - 5 * q^57 - 3 * q^58 + 2 * q^59 + 4 * q^60 - 25 * q^61 - 4 * q^62 + 4 * q^63 + 4 * q^64 + q^65 - 4 * q^66 - 5 * q^67 + 4 * q^68 - 14 * q^69 - 4 * q^70 + 24 * q^71 + 4 * q^72 - 6 * q^73 + 9 * q^74 - 4 * q^75 + 5 * q^76 + 4 * q^77 + q^78 + 26 * q^79 - 4 * q^80 + 4 * q^81 - 6 * q^82 + q^83 - 4 * q^84 - 4 * q^85 - 11 * q^86 + 3 * q^87 + 4 * q^88 + 14 * q^89 - 4 * q^90 + 21 * q^91 + 14 * q^92 + 4 * q^93 + 10 * q^94 - 5 * q^95 - 4 * q^96 + 2 * q^97 + 14 * q^98 + 4 * q^99

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