LMFDB - Embedded newform 5610.2.a.cd.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:	$3$
Coefficient field:	3.3.2089.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 13x - 4 $ x^3 - 13*x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.75054$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.15799 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.15799 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +0.842010 q^{13} +1.15799 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +5.15799 q^{19} -1.00000 q^{20} +1.15799 q^{21} -1.00000 q^{22} -2.84201 q^{23} +1.00000 q^{24} +1.00000 q^{25} +0.842010 q^{26} +1.00000 q^{27} +1.15799 q^{28} +2.00000 q^{29} -1.00000 q^{30} +8.34308 q^{31} +1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} -1.15799 q^{35} +1.00000 q^{36} +8.65906 q^{37} +5.15799 q^{38} +0.842010 q^{39} -1.00000 q^{40} -2.00000 q^{41} +1.15799 q^{42} -5.50107 q^{43} -1.00000 q^{44} -1.00000 q^{45} -2.84201 q^{46} -13.3181 q^{47} +1.00000 q^{48} -5.65906 q^{49} +1.00000 q^{50} +1.00000 q^{51} +0.842010 q^{52} +11.5011 q^{53} +1.00000 q^{54} +1.00000 q^{55} +1.15799 q^{56} +5.15799 q^{57} +2.00000 q^{58} -5.50107 q^{59} -1.00000 q^{60} -4.65906 q^{61} +8.34308 q^{62} +1.15799 q^{63} +1.00000 q^{64} -0.842010 q^{65} -1.00000 q^{66} +1.34094 q^{67} +1.00000 q^{68} -2.84201 q^{69} -1.15799 q^{70} -7.81705 q^{71} +1.00000 q^{72} +9.18509 q^{73} +8.65906 q^{74} +1.00000 q^{75} +5.15799 q^{76} -1.15799 q^{77} +0.842010 q^{78} +11.8170 q^{79} -1.00000 q^{80} +1.00000 q^{81} -2.00000 q^{82} +0.343081 q^{83} +1.15799 q^{84} -1.00000 q^{85} -5.50107 q^{86} +2.00000 q^{87} -1.00000 q^{88} +17.6341 q^{89} -1.00000 q^{90} +0.975039 q^{91} -2.84201 q^{92} +8.34308 q^{93} -13.3181 q^{94} -5.15799 q^{95} +1.00000 q^{96} +8.02710 q^{97} -5.65906 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 + q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{10} - 3 q^{11} + 3 q^{12} + 5 q^{13} + q^{14} - 3 q^{15} + 3 q^{16} + 3 q^{17} + 3 q^{18} + 13 q^{19} - 3 q^{20} + q^{21} - 3 q^{22} - 11 q^{23} + 3 q^{24} + 3 q^{25} + 5 q^{26} + 3 q^{27} + q^{28} + 6 q^{29} - 3 q^{30} + 5 q^{31} + 3 q^{32} - 3 q^{33} + 3 q^{34} - q^{35} + 3 q^{36} + q^{37} + 13 q^{38} + 5 q^{39} - 3 q^{40} - 6 q^{41} + q^{42} + 6 q^{43} - 3 q^{44} - 3 q^{45} - 11 q^{46} + 10 q^{47} + 3 q^{48} + 8 q^{49} + 3 q^{50} + 3 q^{51} + 5 q^{52} + 12 q^{53} + 3 q^{54} + 3 q^{55} + q^{56} + 13 q^{57} + 6 q^{58} + 6 q^{59} - 3 q^{60} + 11 q^{61} + 5 q^{62} + q^{63} + 3 q^{64} - 5 q^{65} - 3 q^{66} + 29 q^{67} + 3 q^{68} - 11 q^{69} - q^{70} + 4 q^{71} + 3 q^{72} + 10 q^{73} + q^{74} + 3 q^{75} + 13 q^{76} - q^{77} + 5 q^{78} + 8 q^{79} - 3 q^{80} + 3 q^{81} - 6 q^{82} - 19 q^{83} + q^{84} - 3 q^{85} + 6 q^{86} + 6 q^{87} - 3 q^{88} - 2 q^{89} - 3 q^{90} - 27 q^{91} - 11 q^{92} + 5 q^{93} + 10 q^{94} - 13 q^{95} + 3 q^{96} + 9 q^{97} + 8 q^{98} - 3 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 + q^7 + 3 * q^8 + 3 * q^9 - 3 * q^10 - 3 * q^11 + 3 * q^12 + 5 * q^13 + q^14 - 3 * q^15 + 3 * q^16 + 3 * q^17 + 3 * q^18 + 13 * q^19 - 3 * q^20 + q^21 - 3 * q^22 - 11 * q^23 + 3 * q^24 + 3 * q^25 + 5 * q^26 + 3 * q^27 + q^28 + 6 * q^29 - 3 * q^30 + 5 * q^31 + 3 * q^32 - 3 * q^33 + 3 * q^34 - q^35 + 3 * q^36 + q^37 + 13 * q^38 + 5 * q^39 - 3 * q^40 - 6 * q^41 + q^42 + 6 * q^43 - 3 * q^44 - 3 * q^45 - 11 * q^46 + 10 * q^47 + 3 * q^48 + 8 * q^49 + 3 * q^50 + 3 * q^51 + 5 * q^52 + 12 * q^53 + 3 * q^54 + 3 * q^55 + q^56 + 13 * q^57 + 6 * q^58 + 6 * q^59 - 3 * q^60 + 11 * q^61 + 5 * q^62 + q^63 + 3 * q^64 - 5 * q^65 - 3 * q^66 + 29 * q^67 + 3 * q^68 - 11 * q^69 - q^70 + 4 * q^71 + 3 * q^72 + 10 * q^73 + q^74 + 3 * q^75 + 13 * q^76 - q^77 + 5 * q^78 + 8 * q^79 - 3 * q^80 + 3 * q^81 - 6 * q^82 - 19 * q^83 + q^84 - 3 * q^85 + 6 * q^86 + 6 * q^87 - 3 * q^88 - 2 * q^89 - 3 * q^90 - 27 * q^91 - 11 * q^92 + 5 * q^93 + 10 * q^94 - 13 * q^95 + 3 * q^96 + 9 * q^97 + 8 * q^98 - 3 * 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
$7$	1.15799	0.437679	0.218839	−	0.975761i	$-0.429773\pi$
$7$	1.15799	0.437679	0.218839	+	0.975761i	$0.429773\pi$
$8$	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
$13$	0.842010	0.233532	0.116766	−	0.993159i	$-0.462747\pi$
$13$	0.842010	0.233532	0.116766	+	0.993159i	$0.462747\pi$
$14$	1.15799	0.309486
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	5.15799	1.18332	0.591662	−	0.806186i	$-0.298472\pi$
$19$	5.15799	1.18332	0.591662	+	0.806186i	$0.298472\pi$
$20$	−1.00000	−0.223607
$21$	1.15799	0.252694
$22$	−1.00000	−0.213201
$23$	−2.84201	−0.592600	−0.296300	−	0.955095i	$-0.595753\pi$
$23$	−2.84201	−0.592600	−0.296300	+	0.955095i	$0.595753\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	0.842010	0.165132
$27$	1.00000	0.192450
$28$	1.15799	0.218839
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	−1.00000	−0.182574
$31$	8.34308	1.49846	0.749231	−	0.662309i	$-0.230423\pi$
$31$	8.34308	1.49846	0.749231	+	0.662309i	$0.230423\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	1.00000	0.171499
$35$	−1.15799	−0.195736
$36$	1.00000	0.166667
$37$	8.65906	1.42354	0.711770	−	0.702412i	$-0.247894\pi$
$37$	8.65906	1.42354	0.711770	+	0.702412i	$0.247894\pi$
$38$	5.15799	0.836736
$39$	0.842010	0.134830
$40$	−1.00000	−0.158114
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	1.15799	0.178682
$43$	−5.50107	−0.838905	−0.419453	−	0.907777i	$-0.637778\pi$
$43$	−5.50107	−0.838905	−0.419453	+	0.907777i	$0.637778\pi$
$44$	−1.00000	−0.150756
$45$	−1.00000	−0.149071
$46$	−2.84201	−0.419032
$47$	−13.3181	−1.94265	−0.971324	−	0.237761i	$-0.923587\pi$
$47$	−13.3181	−1.94265	−0.971324	+	0.237761i	$0.923587\pi$
$48$	1.00000	0.144338
$49$	−5.65906	−0.808437
$50$	1.00000	0.141421
$51$	1.00000	0.140028
$52$	0.842010	0.116766
$53$	11.5011	1.57979	0.789897	−	0.613240i	$-0.210134\pi$
$53$	11.5011	1.57979	0.789897	+	0.613240i	$0.210134\pi$
$54$	1.00000	0.136083
$55$	1.00000	0.134840
$56$	1.15799	0.154743
$57$	5.15799	0.683192
$58$	2.00000	0.262613
$59$	−5.50107	−0.716178	−0.358089	−	0.933687i	$-0.616572\pi$
$59$	−5.50107	−0.716178	−0.358089	+	0.933687i	$0.616572\pi$
$60$	−1.00000	−0.129099
$61$	−4.65906	−0.596532	−0.298266	−	0.954483i	$-0.596408\pi$
$61$	−4.65906	−0.596532	−0.298266	+	0.954483i	$0.596408\pi$
$62$	8.34308	1.05957
$63$	1.15799	0.145893
$64$	1.00000	0.125000
$65$	−0.842010	−0.104439
$66$	−1.00000	−0.123091
$67$	1.34094	0.163822	0.0819109	−	0.996640i	$-0.473898\pi$
$67$	1.34094	0.163822	0.0819109	+	0.996640i	$0.473898\pi$
$68$	1.00000	0.121268
$69$	−2.84201	−0.342138
$70$	−1.15799	−0.138406
$71$	−7.81705	−0.927713	−0.463857	−	0.885910i	$-0.653535\pi$
$71$	−7.81705	−0.927713	−0.463857	+	0.885910i	$0.653535\pi$
$72$	1.00000	0.117851
$73$	9.18509	1.07503	0.537517	−	0.843253i	$-0.319362\pi$
$73$	9.18509	1.07503	0.537517	+	0.843253i	$0.319362\pi$
$74$	8.65906	1.00660
$75$	1.00000	0.115470
$76$	5.15799	0.591662
$77$	−1.15799	−0.131965
$78$	0.842010	0.0953389
$79$	11.8170	1.32952	0.664761	−	0.747056i	$-0.268533\pi$
$79$	11.8170	1.32952	0.664761	+	0.747056i	$0.268533\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−2.00000	−0.220863
$83$	0.343081	0.0376580	0.0188290	−	0.999823i	$-0.494006\pi$
$83$	0.343081	0.0376580	0.0188290	+	0.999823i	$0.494006\pi$
$84$	1.15799	0.126347
$85$	−1.00000	−0.108465
$86$	−5.50107	−0.593196
$87$	2.00000	0.214423
$88$	−1.00000	−0.106600
$89$	17.6341	1.86921	0.934605	−	0.355686i	$-0.115753\pi$
$89$	17.6341	1.86921	0.934605	+	0.355686i	$0.115753\pi$
$90$	−1.00000	−0.105409
$91$	0.975039	0.102212
$92$	−2.84201	−0.296300
$93$	8.34308	0.865137
$94$	−13.3181	−1.37366
$95$	−5.15799	−0.529199
$96$	1.00000	0.102062
$97$	8.02710	0.815029	0.407514	−	0.913199i	$-0.366396\pi$
$97$	8.02710	0.815029	0.407514	+	0.913199i	$0.366396\pi$
$98$	−5.65906	−0.571651
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	−2.63196	−0.261890	−0.130945	−	0.991390i	$-0.541801\pi$
$101$	−2.63196	−0.261890	−0.130945	+	0.991390i	$0.541801\pi$
$102$	1.00000	0.0990148
$103$	16.9750	1.67260	0.836300	−	0.548272i	$-0.184714\pi$
$103$	16.9750	1.67260	0.836300	+	0.548272i	$0.184714\pi$
$104$	0.842010	0.0825659
$105$	−1.15799	−0.113008
$106$	11.5011	1.11708
$107$	9.31812	0.900817	0.450408	−	0.892823i	$-0.351278\pi$
$107$	9.31812	0.900817	0.450408	+	0.892823i	$0.351278\pi$
$108$	1.00000	0.0962250
$109$	−10.3431	−0.990687	−0.495344	−	0.868697i	$-0.664958\pi$
$109$	−10.3431	−0.990687	−0.495344	+	0.868697i	$0.664958\pi$
$110$	1.00000	0.0953463
$111$	8.65906	0.821882
$112$	1.15799	0.109420
$113$	−3.50107	−0.329353	−0.164677	−	0.986348i	$-0.552658\pi$
$113$	−3.50107	−0.329353	−0.164677	+	0.986348i	$0.552658\pi$
$114$	5.15799	0.483090
$115$	2.84201	0.265019
$116$	2.00000	0.185695
$117$	0.842010	0.0778439
$118$	−5.50107	−0.506415
$119$	1.15799	0.106153
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	−4.65906	−0.421811
$123$	−2.00000	−0.180334
$124$	8.34308	0.749231
$125$	−1.00000	−0.0894427
$126$	1.15799	0.103162
$127$	16.0000	1.41977	0.709885	−	0.704317i	$-0.248747\pi$
$127$	16.0000	1.41977	0.709885	+	0.704317i	$0.248747\pi$
$128$	1.00000	0.0883883
$129$	−5.50107	−0.484342
$130$	−0.842010	−0.0738492
$131$	16.3431	1.42790	0.713951	−	0.700196i	$-0.246904\pi$
$131$	16.3431	1.42790	0.713951	+	0.700196i	$0.246904\pi$
$132$	−1.00000	−0.0870388
$133$	5.97290	0.517916
$134$	1.34094	0.115840
$135$	−1.00000	−0.0860663
$136$	1.00000	0.0857493
$137$	10.9750	0.937661	0.468830	−	0.883288i	$-0.344676\pi$
$137$	10.9750	0.937661	0.468830	+	0.883288i	$0.344676\pi$
$138$	−2.84201	−0.241928
$139$	−6.31598	−0.535714	−0.267857	−	0.963459i	$-0.586316\pi$
$139$	−6.31598	−0.535714	−0.267857	+	0.963459i	$0.586316\pi$
$140$	−1.15799	−0.0978680
$141$	−13.3181	−1.12159
$142$	−7.81705	−0.655992
$143$	−0.842010	−0.0704124
$144$	1.00000	0.0833333
$145$	−2.00000	−0.166091
$146$	9.18509	0.760164
$147$	−5.65906	−0.466751
$148$	8.65906	0.711770
$149$	13.2910	1.08884	0.544421	−	0.838812i	$-0.316749\pi$
$149$	13.2910	1.08884	0.544421	+	0.838812i	$0.316749\pi$
$150$	1.00000	0.0816497
$151$	−14.6591	−1.19294	−0.596469	−	0.802636i	$-0.703430\pi$
$151$	−14.6591	−1.19294	−0.596469	+	0.802636i	$0.703430\pi$
$152$	5.15799	0.418368
$153$	1.00000	0.0808452
$154$	−1.15799	−0.0933135
$155$	−8.34308	−0.670132
$156$	0.842010	0.0674148
$157$	−11.3181	−0.903284	−0.451642	−	0.892199i	$-0.649162\pi$
$157$	−11.3181	−0.903284	−0.451642	+	0.892199i	$0.649162\pi$
$158$	11.8170	0.940114
$159$	11.5011	0.912094
$160$	−1.00000	−0.0790569
$161$	−3.29102	−0.259369
$162$	1.00000	0.0785674
$163$	0.631958	0.0494988	0.0247494	−	0.999694i	$-0.492121\pi$
$163$	0.631958	0.0494988	0.0247494	+	0.999694i	$0.492121\pi$
$164$	−2.00000	−0.156174
$165$	1.00000	0.0778499
$166$	0.343081	0.0266282
$167$	−4.00000	−0.309529	−0.154765	−	0.987951i	$-0.549462\pi$
$167$	−4.00000	−0.309529	−0.154765	+	0.987951i	$0.549462\pi$
$168$	1.15799	0.0893408
$169$	−12.2910	−0.945463
$170$	−1.00000	−0.0766965
$171$	5.15799	0.394441
$172$	−5.50107	−0.419453
$173$	−12.6591	−0.962451	−0.481225	−	0.876597i	$-0.659808\pi$
$173$	−12.6591	−0.962451	−0.481225	+	0.876597i	$0.659808\pi$
$174$	2.00000	0.151620
$175$	1.15799	0.0875358
$176$	−1.00000	−0.0753778
$177$	−5.50107	−0.413486
$178$	17.6341	1.32173
$179$	9.84415	0.735786	0.367893	−	0.929868i	$-0.380079\pi$
$179$	9.84415	0.735786	0.367893	+	0.929868i	$0.380079\pi$
$180$	−1.00000	−0.0745356
$181$	−0.315979	−0.0234866	−0.0117433	−	0.999931i	$-0.503738\pi$
$181$	−0.315979	−0.0234866	−0.0117433	+	0.999931i	$0.503738\pi$
$182$	0.975039	0.0722747
$183$	−4.65906	−0.344408
$184$	−2.84201	−0.209516
$185$	−8.65906	−0.636627
$186$	8.34308	0.611744
$187$	−1.00000	−0.0731272
$188$	−13.3181	−0.971324
$189$	1.15799	0.0842314
$190$	−5.15799	−0.374200
$191$	−11.0021	−0.796087	−0.398043	−	0.917367i	$-0.630311\pi$
$191$	−11.0021	−0.796087	−0.398043	+	0.917367i	$0.630311\pi$
$192$	1.00000	0.0721688
$193$	−5.18509	−0.373231	−0.186616	−	0.982433i	$-0.559752\pi$
$193$	−5.18509	−0.373231	−0.186616	+	0.982433i	$0.559752\pi$
$194$	8.02710	0.576312
$195$	−0.842010	−0.0602976
$196$	−5.65906	−0.404219
$197$	9.71112	0.691889	0.345944	−	0.938255i	$-0.387559\pi$
$197$	9.71112	0.691889	0.345944	+	0.938255i	$0.387559\pi$
$198$	−1.00000	−0.0710669
$199$	17.6070	1.24813	0.624063	−	0.781374i	$-0.285481\pi$
$199$	17.6070	1.24813	0.624063	+	0.781374i	$0.285481\pi$
$200$	1.00000	0.0707107
$201$	1.34094	0.0945826
$202$	−2.63196	−0.185184
$203$	2.31598	0.162550
$204$	1.00000	0.0700140
$205$	2.00000	0.139686
$206$	16.9750	1.18271
$207$	−2.84201	−0.197533
$208$	0.842010	0.0583829
$209$	−5.15799	−0.356786
$210$	−1.15799	−0.0799089
$211$	−1.68402	−0.115933	−0.0579664	−	0.998319i	$-0.518462\pi$
$211$	−1.68402	−0.115933	−0.0579664	+	0.998319i	$0.518462\pi$
$212$	11.5011	0.789897
$213$	−7.81705	−0.535615
$214$	9.31812	0.636974
$215$	5.50107	0.375170
$216$	1.00000	0.0680414
$217$	9.66120	0.655845
$218$	−10.3431	−0.700522
$219$	9.18509	0.620671
$220$	1.00000	0.0674200
$221$	0.842010	0.0566397
$222$	8.65906	0.581158
$223$	−8.97504	−0.601013	−0.300507	−	0.953780i	$-0.597156\pi$
$223$	−8.97504	−0.601013	−0.300507	+	0.953780i	$0.597156\pi$
$224$	1.15799	0.0773714
$225$	1.00000	0.0666667
$226$	−3.50107	−0.232888
$227$	−17.3181	−1.14944	−0.574722	−	0.818349i	$-0.694890\pi$
$227$	−17.3181	−1.14944	−0.574722	+	0.818349i	$0.694890\pi$
$228$	5.15799	0.341596
$229$	7.34094	0.485103	0.242551	−	0.970139i	$-0.422016\pi$
$229$	7.34094	0.485103	0.242551	+	0.970139i	$0.422016\pi$
$230$	2.84201	0.187397
$231$	−1.15799	−0.0761901
$232$	2.00000	0.131306
$233$	−13.6341	−0.893200	−0.446600	−	0.894734i	$-0.647365\pi$
$233$	−13.6341	−0.893200	−0.446600	+	0.894734i	$0.647365\pi$
$234$	0.842010	0.0550439
$235$	13.3181	0.868778
$236$	−5.50107	−0.358089
$237$	11.8170	0.767600
$238$	1.15799	0.0750613
$239$	−21.3181	−1.37895	−0.689477	−	0.724307i	$-0.742160\pi$
$239$	−21.3181	−1.37895	−0.689477	+	0.724307i	$0.742160\pi$
$240$	−1.00000	−0.0645497
$241$	14.1601	0.912134	0.456067	−	0.889945i	$-0.349258\pi$
$241$	14.1601	0.912134	0.456067	+	0.889945i	$0.349258\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	−4.65906	−0.298266
$245$	5.65906	0.361544
$246$	−2.00000	−0.127515
$247$	4.34308	0.276344
$248$	8.34308	0.529786
$249$	0.343081	0.0217419
$250$	−1.00000	−0.0632456
$251$	21.2122	1.33890	0.669451	−	0.742856i	$-0.266529\pi$
$251$	21.2122	1.33890	0.669451	+	0.742856i	$0.266529\pi$
$252$	1.15799	0.0729465
$253$	2.84201	0.178676
$254$	16.0000	1.00393
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	−18.6320	−1.16223	−0.581115	−	0.813822i	$-0.697383\pi$
$257$	−18.6320	−1.16223	−0.581115	+	0.813822i	$0.697383\pi$
$258$	−5.50107	−0.342482
$259$	10.0271	0.623054
$260$	−0.842010	−0.0522193
$261$	2.00000	0.123797
$262$	16.3431	1.00968
$263$	0.975039	0.0601235	0.0300617	−	0.999548i	$-0.490430\pi$
$263$	0.975039	0.0601235	0.0300617	+	0.999548i	$0.490430\pi$
$264$	−1.00000	−0.0615457
$265$	−11.5011	−0.706505
$266$	5.97290	0.366222
$267$	17.6341	1.07919
$268$	1.34094	0.0819109
$269$	−28.2932	−1.72506	−0.862532	−	0.506002i	$-0.831123\pi$
$269$	−28.2932	−1.72506	−0.862532	+	0.506002i	$0.831123\pi$
$270$	−1.00000	−0.0608581
$271$	12.6320	0.767337	0.383668	−	0.923471i	$-0.374661\pi$
$271$	12.6320	0.767337	0.383668	+	0.923471i	$0.374661\pi$
$272$	1.00000	0.0606339
$273$	0.975039	0.0590121
$274$	10.9750	0.663026
$275$	−1.00000	−0.0603023
$276$	−2.84201	−0.171069
$277$	2.68616	0.161396	0.0806979	−	0.996739i	$-0.474285\pi$
$277$	2.68616	0.161396	0.0806979	+	0.996739i	$0.474285\pi$
$278$	−6.31598	−0.378807
$279$	8.34308	0.499487
$280$	−1.15799	−0.0692031
$281$	8.37018	0.499323	0.249662	−	0.968333i	$-0.419681\pi$
$281$	8.37018	0.499323	0.249662	+	0.968333i	$0.419681\pi$
$282$	−13.3181	−0.793083
$283$	−23.0021	−1.36734	−0.683668	−	0.729793i	$-0.739616\pi$
$283$	−23.0021	−1.36734	−0.683668	+	0.729793i	$0.739616\pi$
$284$	−7.81705	−0.463857
$285$	−5.15799	−0.305533
$286$	−0.842010	−0.0497891
$287$	−2.31598	−0.136708
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−2.00000	−0.117444
$291$	8.02710	0.470557
$292$	9.18509	0.537517
$293$	30.6862	1.79270	0.896352	−	0.443342i	$-0.146207\pi$
$293$	30.6862	1.79270	0.896352	+	0.443342i	$0.146207\pi$
$294$	−5.65906	−0.330043
$295$	5.50107	0.320285
$296$	8.65906	0.503298
$297$	−1.00000	−0.0580259
$298$	13.2910	0.769928
$299$	−2.39300	−0.138391
$300$	1.00000	0.0577350
$301$	−6.37018	−0.367171
$302$	−14.6591	−0.843534
$303$	−2.63196	−0.151202
$304$	5.15799	0.295831
$305$	4.65906	0.266777
$306$	1.00000	0.0571662
$307$	−19.8713	−1.13411	−0.567056	−	0.823679i	$-0.691918\pi$
$307$	−19.8713	−1.13411	−0.567056	+	0.823679i	$0.691918\pi$
$308$	−1.15799	−0.0659826
$309$	16.9750	0.965676
$310$	−8.34308	−0.473855
$311$	1.44687	0.0820443	0.0410222	−	0.999158i	$-0.486939\pi$
$311$	1.44687	0.0820443	0.0410222	+	0.999158i	$0.486939\pi$
$312$	0.842010	0.0476695
$313$	−17.9230	−1.01307	−0.506533	−	0.862220i	$-0.669073\pi$
$313$	−17.9230	−1.01307	−0.506533	+	0.862220i	$0.669073\pi$
$314$	−11.3181	−0.638718
$315$	−1.15799	−0.0652453
$316$	11.8170	0.664761
$317$	−21.6341	−1.21509	−0.607546	−	0.794284i	$-0.707846\pi$
$317$	−21.6341	−1.21509	−0.607546	+	0.794284i	$0.707846\pi$
$318$	11.5011	0.644948
$319$	−2.00000	−0.111979
$320$	−1.00000	−0.0559017
$321$	9.31812	0.520087
$322$	−3.29102	−0.183401
$323$	5.15799	0.286998
$324$	1.00000	0.0555556
$325$	0.842010	0.0467063
$326$	0.631958	0.0350009
$327$	−10.3431	−0.571974
$328$	−2.00000	−0.110432
$329$	−15.4222	−0.850256
$330$	1.00000	0.0550482
$331$	8.63196	0.474455	0.237228	−	0.971454i	$-0.423761\pi$
$331$	8.63196	0.474455	0.237228	+	0.971454i	$0.423761\pi$
$332$	0.343081	0.0188290
$333$	8.65906	0.474514
$334$	−4.00000	−0.218870
$335$	−1.34094	−0.0732634
$336$	1.15799	0.0631735
$337$	12.5531	0.683813	0.341906	−	0.939734i	$-0.388927\pi$
$337$	12.5531	0.683813	0.341906	+	0.939734i	$0.388927\pi$
$338$	−12.2910	−0.668543
$339$	−3.50107	−0.190152
$340$	−1.00000	−0.0542326
$341$	−8.34308	−0.451803
$342$	5.15799	0.278912
$343$	−14.6591	−0.791515
$344$	−5.50107	−0.296598
$345$	2.84201	0.153009
$346$	−12.6591	−0.680555
$347$	−20.6862	−1.11049	−0.555246	−	0.831686i	$-0.687376\pi$
$347$	−20.6862	−1.11049	−0.555246	+	0.831686i	$0.687376\pi$
$348$	2.00000	0.107211
$349$	3.50107	0.187408	0.0937040	−	0.995600i	$-0.470129\pi$
$349$	3.50107	0.187408	0.0937040	+	0.995600i	$0.470129\pi$
$350$	1.15799	0.0618971
$351$	0.842010	0.0449432
$352$	−1.00000	−0.0533002
$353$	11.6612	0.620663	0.310332	−	0.950628i	$-0.399560\pi$
$353$	11.6612	0.620663	0.310332	+	0.950628i	$0.399560\pi$
$354$	−5.50107	−0.292379
$355$	7.81705	0.414886
$356$	17.6341	0.934605
$357$	1.15799	0.0612873
$358$	9.84415	0.520280
$359$	−17.9501	−0.947369	−0.473684	−	0.880695i	$-0.657076\pi$
$359$	−17.9501	−0.947369	−0.473684	+	0.880695i	$0.657076\pi$
$360$	−1.00000	−0.0527046
$361$	7.60486	0.400256
$362$	−0.315979	−0.0166075
$363$	1.00000	0.0524864
$364$	0.975039	0.0511059
$365$	−9.18509	−0.480770
$366$	−4.65906	−0.243533
$367$	−22.3702	−1.16771	−0.583857	−	0.811857i	$-0.698457\pi$
$367$	−22.3702	−1.16771	−0.583857	+	0.811857i	$0.698457\pi$
$368$	−2.84201	−0.148150
$369$	−2.00000	−0.104116
$370$	−8.65906	−0.450163
$371$	13.3181	0.691442
$372$	8.34308	0.432569
$373$	15.1352	0.783669	0.391835	−	0.920036i	$-0.371841\pi$
$373$	15.1352	0.783669	0.391835	+	0.920036i	$0.371841\pi$
$374$	−1.00000	−0.0517088
$375$	−1.00000	−0.0516398
$376$	−13.3181	−0.686830
$377$	1.68402	0.0867315
$378$	1.15799	0.0595606
$379$	−26.2932	−1.35059	−0.675294	−	0.737548i	$-0.735983\pi$
$379$	−26.2932	−1.35059	−0.675294	+	0.737548i	$0.735983\pi$
$380$	−5.15799	−0.264599
$381$	16.0000	0.819705
$382$	−11.0021	−0.562918
$383$	−1.05206	−0.0537579	−0.0268789	−	0.999639i	$-0.508557\pi$
$383$	−1.05206	−0.0537579	−0.0268789	+	0.999639i	$0.508557\pi$
$384$	1.00000	0.0510310
$385$	1.15799	0.0590166
$386$	−5.18509	−0.263914
$387$	−5.50107	−0.279635
$388$	8.02710	0.407514
$389$	12.8192	0.649959	0.324979	−	0.945721i	$-0.394643\pi$
$389$	12.8192	0.649959	0.324979	+	0.945721i	$0.394643\pi$
$390$	−0.842010	−0.0426369
$391$	−2.84201	−0.143727
$392$	−5.65906	−0.285826
$393$	16.3431	0.824399
$394$	9.71112	0.489239
$395$	−11.8170	−0.594580
$396$	−1.00000	−0.0502519
$397$	2.00000	0.100377	0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000	0.100377	0.0501886	+	0.998740i	$0.484018\pi$
$398$	17.6070	0.882559
$399$	5.97290	0.299019
$400$	1.00000	0.0500000
$401$	−24.8420	−1.24055	−0.620275	−	0.784384i	$-0.712979\pi$
$401$	−24.8420	−1.24055	−0.620275	+	0.784384i	$0.712979\pi$
$402$	1.34094	0.0668800
$403$	7.02496	0.349938
$404$	−2.63196	−0.130945
$405$	−1.00000	−0.0496904
$406$	2.31598	0.114940
$407$	−8.65906	−0.429214
$408$	1.00000	0.0495074
$409$	−33.0021	−1.63185	−0.815925	−	0.578157i	$-0.803772\pi$
$409$	−33.0021	−1.63185	−0.815925	+	0.578157i	$0.803772\pi$
$410$	2.00000	0.0987730
$411$	10.9750	0.541359
$412$	16.9750	0.836300
$413$	−6.37018	−0.313456
$414$	−2.84201	−0.139677
$415$	−0.343081	−0.0168412
$416$	0.842010	0.0412830
$417$	−6.31598	−0.309295
$418$	−5.15799	−0.252286
$419$	−4.00000	−0.195413	−0.0977064	−	0.995215i	$-0.531151\pi$
$419$	−4.00000	−0.195413	−0.0977064	+	0.995215i	$0.531151\pi$
$420$	−1.15799	−0.0565041
$421$	10.3431	0.504091	0.252045	−	0.967715i	$-0.418897\pi$
$421$	10.3431	0.504091	0.252045	+	0.967715i	$0.418897\pi$
$422$	−1.68402	−0.0819768
$423$	−13.3181	−0.647549
$424$	11.5011	0.558541
$425$	1.00000	0.0485071
$426$	−7.81705	−0.378737
$427$	−5.39514	−0.261089
$428$	9.31812	0.450408
$429$	−0.842010	−0.0406526
$430$	5.50107	0.265285
$431$	−8.00000	−0.385346	−0.192673	−	0.981263i	$-0.561716\pi$
$431$	−8.00000	−0.385346	−0.192673	+	0.981263i	$0.561716\pi$
$432$	1.00000	0.0481125
$433$	25.6341	1.23190	0.615948	−	0.787787i	$-0.288773\pi$
$433$	25.6341	1.23190	0.615948	+	0.787787i	$0.288773\pi$
$434$	9.66120	0.463752
$435$	−2.00000	−0.0958927
$436$	−10.3431	−0.495344
$437$	−14.6591	−0.701238
$438$	9.18509	0.438881
$439$	−8.81491	−0.420713	−0.210356	−	0.977625i	$-0.567462\pi$
$439$	−8.81491	−0.420713	−0.210356	+	0.977625i	$0.567462\pi$
$440$	1.00000	0.0476731
$441$	−5.65906	−0.269479
$442$	0.842010	0.0400503
$443$	6.81919	0.323990	0.161995	−	0.986792i	$-0.448207\pi$
$443$	6.81919	0.323990	0.161995	+	0.986792i	$0.448207\pi$
$444$	8.65906	0.410941
$445$	−17.6341	−0.835936
$446$	−8.97504	−0.424980
$447$	13.2910	0.628644
$448$	1.15799	0.0547099
$449$	−1.89407	−0.0893868	−0.0446934	−	0.999001i	$-0.514231\pi$
$449$	−1.89407	−0.0893868	−0.0446934	+	0.999001i	$0.514231\pi$
$450$	1.00000	0.0471405
$451$	2.00000	0.0941763
$452$	−3.50107	−0.164677
$453$	−14.6591	−0.688743
$454$	−17.3181	−0.812780
$455$	−0.975039	−0.0457105
$456$	5.15799	0.241545
$457$	5.29102	0.247503	0.123752	−	0.992313i	$-0.460507\pi$
$457$	5.29102	0.247503	0.123752	+	0.992313i	$0.460507\pi$
$458$	7.34094	0.343020
$459$	1.00000	0.0466760
$460$	2.84201	0.132509
$461$	24.3702	1.13503	0.567516	−	0.823362i	$-0.307904\pi$
$461$	24.3702	1.13503	0.567516	+	0.823362i	$0.307904\pi$
$462$	−1.15799	−0.0538746
$463$	33.6612	1.56437	0.782184	−	0.623047i	$-0.214106\pi$
$463$	33.6612	1.56437	0.782184	+	0.623047i	$0.214106\pi$
$464$	2.00000	0.0928477
$465$	−8.34308	−0.386901
$466$	−13.6341	−0.631587
$467$	36.1373	1.67224	0.836118	−	0.548550i	$-0.184820\pi$
$467$	36.1373	1.67224	0.836118	+	0.548550i	$0.184820\pi$
$468$	0.842010	0.0389219
$469$	1.55279	0.0717014
$470$	13.3181	0.614319
$471$	−11.3181	−0.521511
$472$	−5.50107	−0.253207
$473$	5.50107	0.252939
$474$	11.8170	0.542775
$475$	5.15799	0.236665
$476$	1.15799	0.0530764
$477$	11.5011	0.526598
$478$	−21.3181	−0.975068
$479$	−26.7133	−1.22056	−0.610280	−	0.792186i	$-0.708943\pi$
$479$	−26.7133	−1.22056	−0.610280	+	0.792186i	$0.708943\pi$
$480$	−1.00000	−0.0456435
$481$	7.29102	0.332442
$482$	14.1601	0.644976
$483$	−3.29102	−0.149747
$484$	1.00000	0.0454545
$485$	−8.02710	−0.364492
$486$	1.00000	0.0453609
$487$	22.3702	1.01369	0.506845	−	0.862037i	$-0.330812\pi$
$487$	22.3702	1.01369	0.506845	+	0.862037i	$0.330812\pi$
$488$	−4.65906	−0.210906
$489$	0.631958	0.0285781
$490$	5.65906	0.255650
$491$	17.9501	0.810076	0.405038	−	0.914300i	$-0.367258\pi$
$491$	17.9501	0.810076	0.405038	+	0.914300i	$0.367258\pi$
$492$	−2.00000	−0.0901670
$493$	2.00000	0.0900755
$494$	4.34308	0.195404
$495$	1.00000	0.0449467
$496$	8.34308	0.374615
$497$	−9.05206	−0.406040
$498$	0.343081	0.0153738
$499$	34.0043	1.52224	0.761120	−	0.648611i	$-0.224650\pi$
$499$	34.0043	1.52224	0.761120	+	0.648611i	$0.224650\pi$
$500$	−1.00000	−0.0447214
$501$	−4.00000	−0.178707
$502$	21.2122	0.946746
$503$	−16.2661	−0.725268	−0.362634	−	0.931932i	$-0.618122\pi$
$503$	−16.2661	−0.725268	−0.362634	+	0.931932i	$0.618122\pi$
$504$	1.15799	0.0515810
$505$	2.63196	0.117121
$506$	2.84201	0.126343
$507$	−12.2910	−0.545863
$508$	16.0000	0.709885
$509$	7.50107	0.332479	0.166240	−	0.986085i	$-0.446837\pi$
$509$	7.50107	0.332479	0.166240	+	0.986085i	$0.446837\pi$
$510$	−1.00000	−0.0442807
$511$	10.6362	0.470520
$512$	1.00000	0.0441942
$513$	5.15799	0.227731
$514$	−18.6320	−0.821820
$515$	−16.9750	−0.748010
$516$	−5.50107	−0.242171
$517$	13.3181	0.585730
$518$	10.0271	0.440566
$519$	−12.6591	−0.555671
$520$	−0.842010	−0.0369246
$521$	8.42191	0.368970	0.184485	−	0.982835i	$-0.440938\pi$
$521$	8.42191	0.368970	0.184485	+	0.982835i	$0.440938\pi$
$522$	2.00000	0.0875376
$523$	−5.13517	−0.224545	−0.112273	−	0.993677i	$-0.535813\pi$
$523$	−5.13517	−0.224545	−0.112273	+	0.993677i	$0.535813\pi$
$524$	16.3431	0.713951
$525$	1.15799	0.0505388
$526$	0.975039	0.0425137
$527$	8.34308	0.363430
$528$	−1.00000	−0.0435194
$529$	−14.9230	−0.648825
$530$	−11.5011	−0.499575
$531$	−5.50107	−0.238726
$532$	5.97290	0.258958
$533$	−1.68402	−0.0729430
$534$	17.6341	0.763102
$535$	−9.31812	−0.402857
$536$	1.34094	0.0579198
$537$	9.84415	0.424806
$538$	−28.2932	−1.21980
$539$	5.65906	0.243753
$540$	−1.00000	−0.0430331
$541$	−26.2661	−1.12927	−0.564633	−	0.825342i	$-0.690982\pi$
$541$	−26.2661	−1.12927	−0.564633	+	0.825342i	$0.690982\pi$
$542$	12.6320	0.542589
$543$	−0.315979	−0.0135600
$544$	1.00000	0.0428746
$545$	10.3431	0.443049
$546$	0.975039	0.0417278
$547$	−7.65692	−0.327386	−0.163693	−	0.986511i	$-0.552341\pi$
$547$	−7.65692	−0.327386	−0.163693	+	0.986511i	$0.552341\pi$
$548$	10.9750	0.468830
$549$	−4.65906	−0.198844
$550$	−1.00000	−0.0426401
$551$	10.3160	0.439475
$552$	−2.84201	−0.120964
$553$	13.6840	0.581904
$554$	2.68616	0.114124
$555$	−8.65906	−0.367557
$556$	−6.31598	−0.267857
$557$	−15.3181	−0.649050	−0.324525	−	0.945877i	$-0.605204\pi$
$557$	−15.3181	−0.649050	−0.324525	+	0.945877i	$0.605204\pi$
$558$	8.34308	0.353191
$559$	−4.63196	−0.195911
$560$	−1.15799	−0.0489340
$561$	−1.00000	−0.0422200
$562$	8.37018	0.353075
$563$	41.0292	1.72918	0.864588	−	0.502481i	$-0.167579\pi$
$563$	41.0292	1.72918	0.864588	+	0.502481i	$0.167579\pi$
$564$	−13.3181	−0.560794
$565$	3.50107	0.147291
$566$	−23.0021	−0.966852
$567$	1.15799	0.0486310
$568$	−7.81705	−0.327996
$569$	−27.0292	−1.13312	−0.566562	−	0.824019i	$-0.691727\pi$
$569$	−27.0292	−1.13312	−0.566562	+	0.824019i	$0.691727\pi$
$570$	−5.15799	−0.216044
$571$	−31.6883	−1.32611	−0.663057	−	0.748569i	$-0.730741\pi$
$571$	−31.6883	−1.32611	−0.663057	+	0.748569i	$0.730741\pi$
$572$	−0.842010	−0.0352062
$573$	−11.0021	−0.459621
$574$	−2.31598	−0.0966671
$575$	−2.84201	−0.118520
$576$	1.00000	0.0416667
$577$	−42.2661	−1.75956	−0.879780	−	0.475382i	$-0.842310\pi$
$577$	−42.2661	−1.75956	−0.879780	+	0.475382i	$0.842310\pi$
$578$	1.00000	0.0415945
$579$	−5.18509	−0.215485
$580$	−2.00000	−0.0830455
$581$	0.397284	0.0164821
$582$	8.02710	0.332734
$583$	−11.5011	−0.476326
$584$	9.18509	0.380082
$585$	−0.842010	−0.0348128
$586$	30.6862	1.26763
$587$	−35.8170	−1.47833	−0.739164	−	0.673526i	$-0.764779\pi$
$587$	−35.8170	−1.47833	−0.739164	+	0.673526i	$0.764779\pi$
$588$	−5.65906	−0.233376
$589$	43.0335	1.77317
$590$	5.50107	0.226475
$591$	9.71112	0.399462
$592$	8.65906	0.355885
$593$	−13.6341	−0.559885	−0.279943	−	0.960017i	$-0.590315\pi$
$593$	−13.6341	−0.559885	−0.279943	+	0.960017i	$0.590315\pi$
$594$	−1.00000	−0.0410305
$595$	−1.15799	−0.0474729
$596$	13.2910	0.544421
$597$	17.6070	0.720606
$598$	−2.39300	−0.0978571
$599$	3.29102	0.134467	0.0672337	−	0.997737i	$-0.478583\pi$
$599$	3.29102	0.134467	0.0672337	+	0.997737i	$0.478583\pi$
$600$	1.00000	0.0408248
$601$	−20.8420	−0.850163	−0.425082	−	0.905155i	$-0.639755\pi$
$601$	−20.8420	−0.850163	−0.425082	+	0.905155i	$0.639755\pi$
$602$	−6.37018	−0.259629
$603$	1.34094	0.0546073
$604$	−14.6591	−0.596469
$605$	−1.00000	−0.0406558
$606$	−2.63196	−0.106916
$607$	−20.8463	−0.846125	−0.423062	−	0.906101i	$-0.639045\pi$
$607$	−20.8463	−0.846125	−0.423062	+	0.906101i	$0.639045\pi$
$608$	5.15799	0.209184
$609$	2.31598	0.0938482
$610$	4.65906	0.188640
$611$	−11.2140	−0.453670
$612$	1.00000	0.0404226
$613$	12.4989	0.504827	0.252414	−	0.967619i	$-0.418776\pi$
$613$	12.4989	0.504827	0.252414	+	0.967619i	$0.418776\pi$
$614$	−19.8713	−0.801939
$615$	2.00000	0.0806478
$616$	−1.15799	−0.0466567
$617$	−46.5032	−1.87215	−0.936074	−	0.351802i	$-0.885569\pi$
$617$	−46.5032	−1.87215	−0.936074	+	0.351802i	$0.885569\pi$
$618$	16.9750	0.682836
$619$	−20.9750	−0.843058	−0.421529	−	0.906815i	$-0.638506\pi$
$619$	−20.9750	−0.843058	−0.421529	+	0.906815i	$0.638506\pi$
$620$	−8.34308	−0.335066
$621$	−2.84201	−0.114046
$622$	1.44687	0.0580141
$623$	20.4201	0.818114
$624$	0.842010	0.0337074
$625$	1.00000	0.0400000
$626$	−17.9230	−0.716346
$627$	−5.15799	−0.205990
$628$	−11.3181	−0.451642
$629$	8.65906	0.345259
$630$	−1.15799	−0.0461354
$631$	−29.3181	−1.16714	−0.583568	−	0.812064i	$-0.698344\pi$
$631$	−29.3181	−1.16714	−0.583568	+	0.812064i	$0.698344\pi$
$632$	11.8170	0.470057
$633$	−1.68402	−0.0669338
$634$	−21.6341	−0.859200
$635$	−16.0000	−0.634941
$636$	11.5011	0.456047
$637$	−4.76499	−0.188796
$638$	−2.00000	−0.0791808
$639$	−7.81705	−0.309238
$640$	−1.00000	−0.0395285
$641$	−13.8713	−0.547882	−0.273941	−	0.961747i	$-0.588327\pi$
$641$	−13.8713	−0.547882	−0.273941	+	0.961747i	$0.588327\pi$
$642$	9.31812	0.367757
$643$	−8.63196	−0.340411	−0.170206	−	0.985409i	$-0.554443\pi$
$643$	−8.63196	−0.340411	−0.170206	+	0.985409i	$0.554443\pi$
$644$	−3.29102	−0.129684
$645$	5.50107	0.216604
$646$	5.15799	0.202938
$647$	1.95008	0.0766655	0.0383327	−	0.999265i	$-0.487795\pi$
$647$	1.95008	0.0766655	0.0383327	+	0.999265i	$0.487795\pi$
$648$	1.00000	0.0392837
$649$	5.50107	0.215936
$650$	0.842010	0.0330264
$651$	9.66120	0.378652
$652$	0.631958	0.0247494
$653$	−22.6862	−0.887778	−0.443889	−	0.896082i	$-0.646402\pi$
$653$	−22.6862	−0.887778	−0.443889	+	0.896082i	$0.646402\pi$
$654$	−10.3431	−0.404446
$655$	−16.3431	−0.638577
$656$	−2.00000	−0.0780869
$657$	9.18509	0.358345
$658$	−15.4222	−0.601222
$659$	−40.6862	−1.58491	−0.792454	−	0.609932i	$-0.791197\pi$
$659$	−40.6862	−1.58491	−0.792454	+	0.609932i	$0.791197\pi$
$660$	1.00000	0.0389249
$661$	−21.9772	−0.854813	−0.427407	−	0.904060i	$-0.640573\pi$
$661$	−21.9772	−0.854813	−0.427407	+	0.904060i	$0.640573\pi$
$662$	8.63196	0.335491
$663$	0.842010	0.0327010
$664$	0.343081	0.0133141
$665$	−5.97290	−0.231619
$666$	8.65906	0.335532
$667$	−5.68402	−0.220086
$668$	−4.00000	−0.154765
$669$	−8.97504	−0.346995
$670$	−1.34094	−0.0518050
$671$	4.65906	0.179861
$672$	1.15799	0.0446704
$673$	28.1872	1.08654	0.543269	−	0.839559i	$-0.317186\pi$
$673$	28.1872	1.08654	0.543269	+	0.839559i	$0.317186\pi$
$674$	12.5531	0.483529
$675$	1.00000	0.0384900
$676$	−12.2910	−0.472731
$677$	−42.7404	−1.64265	−0.821323	−	0.570464i	$-0.806764\pi$
$677$	−42.7404	−1.64265	−0.821323	+	0.570464i	$0.806764\pi$
$678$	−3.50107	−0.134458
$679$	9.29530	0.356721
$680$	−1.00000	−0.0383482
$681$	−17.3181	−0.663632
$682$	−8.34308	−0.319473
$683$	−27.7111	−1.06034	−0.530168	−	0.847892i	$-0.677871\pi$
$683$	−27.7111	−1.06034	−0.530168	+	0.847892i	$0.677871\pi$
$684$	5.15799	0.197221
$685$	−10.9750	−0.419335
$686$	−14.6591	−0.559686
$687$	7.34094	0.280074
$688$	−5.50107	−0.209726
$689$	9.68402	0.368932
$690$	2.84201	0.108193
$691$	8.92084	0.339365	0.169682	−	0.985499i	$-0.445726\pi$
$691$	8.92084	0.339365	0.169682	+	0.985499i	$0.445726\pi$
$692$	−12.6591	−0.481225
$693$	−1.15799	−0.0439884
$694$	−20.6862	−0.785236
$695$	6.31598	0.239579
$696$	2.00000	0.0758098
$697$	−2.00000	−0.0757554
$698$	3.50107	0.132517
$699$	−13.6341	−0.515689
$700$	1.15799	0.0437679
$701$	−4.37018	−0.165060	−0.0825298	−	0.996589i	$-0.526300\pi$
$701$	−4.37018	−0.165060	−0.0825298	+	0.996589i	$0.526300\pi$
$702$	0.842010	0.0317796
$703$	44.6633	1.68451
$704$	−1.00000	−0.0376889
$705$	13.3181	0.501589
$706$	11.6612	0.438875
$707$	−3.04778	−0.114624
$708$	−5.50107	−0.206743
$709$	4.63624	0.174118	0.0870588	−	0.996203i	$-0.472253\pi$
$709$	4.63624	0.174118	0.0870588	+	0.996203i	$0.472253\pi$
$710$	7.81705	0.293369
$711$	11.8170	0.443174
$712$	17.6341	0.660866
$713$	−23.7111	−0.887989
$714$	1.15799	0.0433367
$715$	0.842010	0.0314894
$716$	9.84415	0.367893
$717$	−21.3181	−0.796140
$718$	−17.9501	−0.669891
$719$	6.55313	0.244391	0.122195	−	0.992506i	$-0.461007\pi$
$719$	6.55313	0.244391	0.122195	+	0.992506i	$0.461007\pi$
$720$	−1.00000	−0.0372678
$721$	19.6569	0.732062
$722$	7.60486	0.283023
$723$	14.1601	0.526621
$724$	−0.315979	−0.0117433
$725$	2.00000	0.0742781
$726$	1.00000	0.0371135
$727$	46.0043	1.70620	0.853102	−	0.521744i	$-0.174718\pi$
$727$	46.0043	1.70620	0.853102	+	0.521744i	$0.174718\pi$
$728$	0.975039	0.0361374
$729$	1.00000	0.0370370
$730$	−9.18509	−0.339955
$731$	−5.50107	−0.203464
$732$	−4.65906	−0.172204
$733$	50.9005	1.88005	0.940026	−	0.341102i	$-0.110800\pi$
$733$	50.9005	1.88005	0.940026	+	0.341102i	$0.110800\pi$
$734$	−22.3702	−0.825699
$735$	5.65906	0.208738
$736$	−2.84201	−0.104758
$737$	−1.34094	−0.0493942
$738$	−2.00000	−0.0736210
$739$	5.84415	0.214981	0.107490	−	0.994206i	$-0.465719\pi$
$739$	5.84415	0.214981	0.107490	+	0.994206i	$0.465719\pi$
$740$	−8.65906	−0.318313
$741$	4.34308	0.159547
$742$	13.3181	0.488924
$743$	27.6341	1.01380	0.506898	−	0.862006i	$-0.330792\pi$
$743$	27.6341	1.01380	0.506898	+	0.862006i	$0.330792\pi$
$744$	8.34308	0.305872
$745$	−13.2910	−0.486945
$746$	15.1352	0.554138
$747$	0.343081	0.0125527
$748$	−1.00000	−0.0365636
$749$	10.7903	0.394268
$750$	−1.00000	−0.0365148
$751$	18.3702	0.670337	0.335169	−	0.942158i	$-0.391207\pi$
$751$	18.3702	0.670337	0.335169	+	0.942158i	$0.391207\pi$
$752$	−13.3181	−0.485662
$753$	21.2122	0.773015
$754$	1.68402	0.0613284
$755$	14.6591	0.533498
$756$	1.15799	0.0421157
$757$	−42.2661	−1.53619	−0.768093	−	0.640338i	$-0.778794\pi$
$757$	−42.2661	−1.53619	−0.768093	+	0.640338i	$0.778794\pi$
$758$	−26.2932	−0.955011
$759$	2.84201	0.103158
$760$	−5.15799	−0.187100
$761$	21.9772	0.796672	0.398336	−	0.917240i	$-0.369588\pi$
$761$	21.9772	0.796672	0.398336	+	0.917240i	$0.369588\pi$
$762$	16.0000	0.579619
$763$	−11.9772	−0.433603
$764$	−11.0021	−0.398043
$765$	−1.00000	−0.0361551
$766$	−1.05206	−0.0380126
$767$	−4.63196	−0.167250
$768$	1.00000	0.0360844
$769$	4.68188	0.168833	0.0844165	−	0.996431i	$-0.473097\pi$
$769$	4.68188	0.168833	0.0844165	+	0.996431i	$0.473097\pi$
$770$	1.15799	0.0417310
$771$	−18.6320	−0.671014
$772$	−5.18509	−0.186616
$773$	−3.84415	−0.138265	−0.0691323	−	0.997608i	$-0.522023\pi$
$773$	−3.84415	−0.138265	−0.0691323	+	0.997608i	$0.522023\pi$
$774$	−5.50107	−0.197732
$775$	8.34308	0.299692
$776$	8.02710	0.288156
$777$	10.0271	0.359720
$778$	12.8192	0.459590
$779$	−10.3160	−0.369608
$780$	−0.842010	−0.0301488
$781$	7.81705	0.279716
$782$	−2.84201	−0.101630
$783$	2.00000	0.0714742
$784$	−5.65906	−0.202109
$785$	11.3181	0.403961
$786$	16.3431	0.582938
$787$	3.02496	0.107828	0.0539141	−	0.998546i	$-0.482830\pi$
$787$	3.02496	0.107828	0.0539141	+	0.998546i	$0.482830\pi$
$788$	9.71112	0.345944
$789$	0.975039	0.0347123
$790$	−11.8170	−0.420432
$791$	−4.05420	−0.144151
$792$	−1.00000	−0.0355335
$793$	−3.92298	−0.139309
$794$	2.00000	0.0709773
$795$	−11.5011	−0.407901
$796$	17.6070	0.624063
$797$	−14.1601	−0.501578	−0.250789	−	0.968042i	$-0.580690\pi$
$797$	−14.1601	−0.501578	−0.250789	+	0.968042i	$0.580690\pi$
$798$	5.97290	0.211438
$799$	−13.3181	−0.471161
$800$	1.00000	0.0353553
$801$	17.6341	0.623070
$802$	−24.8420	−0.877202
$803$	−9.18509	−0.324135
$804$	1.34094	0.0472913
$805$	3.29102	0.115993
$806$	7.02496	0.247444
$807$	−28.2932	−0.995966
$808$	−2.63196	−0.0925920
$809$	9.00214	0.316498	0.158249	−	0.987399i	$-0.449415\pi$
$809$	9.00214	0.316498	0.158249	+	0.987399i	$0.449415\pi$
$810$	−1.00000	−0.0351364
$811$	8.05420	0.282821	0.141411	−	0.989951i	$-0.454836\pi$
$811$	8.05420	0.282821	0.141411	+	0.989951i	$0.454836\pi$
$812$	2.31598	0.0812749
$813$	12.6320	0.443022
$814$	−8.65906	−0.303500
$815$	−0.631958	−0.0221365
$816$	1.00000	0.0350070
$817$	−28.3745	−0.992697
$818$	−33.0021	−1.15389
$819$	0.975039	0.0340706
$820$	2.00000	0.0698430
$821$	11.7382	0.409667	0.204833	−	0.978797i	$-0.434335\pi$
$821$	11.7382	0.409667	0.204833	+	0.978797i	$0.434335\pi$
$822$	10.9750	0.382798
$823$	−6.04992	−0.210887	−0.105444	−	0.994425i	$-0.533626\pi$
$823$	−6.04992	−0.210887	−0.105444	+	0.994425i	$0.533626\pi$
$824$	16.9750	0.591354
$825$	−1.00000	−0.0348155
$826$	−6.37018	−0.221647
$827$	49.3181	1.71496	0.857480	−	0.514518i	$-0.172029\pi$
$827$	49.3181	1.71496	0.857480	+	0.514518i	$0.172029\pi$
$828$	−2.84201	−0.0987667
$829$	−54.1890	−1.88206	−0.941031	−	0.338319i	$-0.890142\pi$
$829$	−54.1890	−1.88206	−0.941031	+	0.338319i	$0.890142\pi$
$830$	−0.343081	−0.0119085
$831$	2.68616	0.0931819
$832$	0.842010	0.0291915
$833$	−5.65906	−0.196075
$834$	−6.31598	−0.218704
$835$	4.00000	0.138426
$836$	−5.15799	−0.178393
$837$	8.34308	0.288379
$838$	−4.00000	−0.138178
$839$	4.23715	0.146283	0.0731414	−	0.997322i	$-0.476698\pi$
$839$	4.23715	0.146283	0.0731414	+	0.997322i	$0.476698\pi$
$840$	−1.15799	−0.0399544
$841$	−25.0000	−0.862069
$842$	10.3431	0.356446
$843$	8.37018	0.288284
$844$	−1.68402	−0.0579664
$845$	12.2910	0.422824
$846$	−13.3181	−0.457886
$847$	1.15799	0.0397890
$848$	11.5011	0.394948
$849$	−23.0021	−0.789431
$850$	1.00000	0.0342997
$851$	−24.6091	−0.843590
$852$	−7.81705	−0.267808
$853$	−45.9544	−1.57345	−0.786724	−	0.617305i	$-0.788224\pi$
$853$	−45.9544	−1.57345	−0.786724	+	0.617305i	$0.788224\pi$
$854$	−5.39514	−0.184618
$855$	−5.15799	−0.176400
$856$	9.31812	0.318487
$857$	32.9793	1.12655	0.563276	−	0.826269i	$-0.309541\pi$
$857$	32.9793	1.12655	0.563276	+	0.826269i	$0.309541\pi$
$858$	−0.842010	−0.0287458
$859$	−45.3723	−1.54808	−0.774042	−	0.633134i	$-0.781768\pi$
$859$	−45.3723	−1.54808	−0.774042	+	0.633134i	$0.781768\pi$
$860$	5.50107	0.187585
$861$	−2.31598	−0.0789284
$862$	−8.00000	−0.272481
$863$	−25.7382	−0.876139	−0.438070	−	0.898941i	$-0.644338\pi$
$863$	−25.7382	−0.876139	−0.438070	+	0.898941i	$0.644338\pi$
$864$	1.00000	0.0340207
$865$	12.6591	0.430421
$866$	25.6341	0.871082
$867$	1.00000	0.0339618
$868$	9.66120	0.327923
$869$	−11.8170	−0.400866
$870$	−2.00000	−0.0678064
$871$	1.12909	0.0382576
$872$	−10.3431	−0.350261
$873$	8.02710	0.271676
$874$	−14.6591	−0.495850
$875$	−1.15799	−0.0391472
$876$	9.18509	0.310335
$877$	19.9501	0.673666	0.336833	−	0.941564i	$-0.390644\pi$
$877$	19.9501	0.673666	0.336833	+	0.941564i	$0.390644\pi$
$878$	−8.81491	−0.297489
$879$	30.6862	1.03502
$880$	1.00000	0.0337100
$881$	−9.49679	−0.319955	−0.159977	−	0.987121i	$-0.551142\pi$
$881$	−9.49679	−0.319955	−0.159977	+	0.987121i	$0.551142\pi$
$882$	−5.65906	−0.190550
$883$	18.6362	0.627159	0.313580	−	0.949562i	$-0.398472\pi$
$883$	18.6362	0.627159	0.313580	+	0.949562i	$0.398472\pi$
$884$	0.842010	0.0283199
$885$	5.50107	0.184916
$886$	6.81919	0.229095
$887$	6.63624	0.222823	0.111412	−	0.993774i	$-0.464463\pi$
$887$	6.63624	0.222823	0.111412	+	0.993774i	$0.464463\pi$
$888$	8.65906	0.290579
$889$	18.5278	0.621404
$890$	−17.6341	−0.591096
$891$	−1.00000	−0.0335013
$892$	−8.97504	−0.300507
$893$	−68.6947	−2.29878
$894$	13.2910	0.444518
$895$	−9.84415	−0.329054
$896$	1.15799	0.0386857
$897$	−2.39300	−0.0799000
$898$	−1.89407	−0.0632060
$899$	16.6862	0.556515
$900$	1.00000	0.0333333
$901$	11.5011	0.383156
$902$	2.00000	0.0665927
$903$	−6.37018	−0.211986
$904$	−3.50107	−0.116444
$905$	0.315979	0.0105035
$906$	−14.6591	−0.487015
$907$	−46.6362	−1.54853	−0.774265	−	0.632861i	$-0.781880\pi$
$907$	−46.6362	−1.54853	−0.774265	+	0.632861i	$0.781880\pi$
$908$	−17.3181	−0.574722
$909$	−2.63196	−0.0872966
$910$	−0.975039	−0.0323222
$911$	−29.1352	−0.965291	−0.482646	−	0.875816i	$-0.660324\pi$
$911$	−29.1352	−0.965291	−0.482646	+	0.875816i	$0.660324\pi$
$912$	5.15799	0.170798
$913$	−0.343081	−0.0113543
$914$	5.29102	0.175011
$915$	4.65906	0.154024
$916$	7.34094	0.242551
$917$	18.9251	0.624962
$918$	1.00000	0.0330049
$919$	−35.2910	−1.16414	−0.582072	−	0.813138i	$-0.697758\pi$
$919$	−35.2910	−1.16414	−0.582072	+	0.813138i	$0.697758\pi$
$920$	2.84201	0.0936983
$921$	−19.8713	−0.654780
$922$	24.3702	0.802589
$923$	−6.58204	−0.216650
$924$	−1.15799	−0.0380951
$925$	8.65906	0.284708
$926$	33.6612	1.10618
$927$	16.9750	0.557533
$928$	2.00000	0.0656532
$929$	−13.7942	−0.452574	−0.226287	−	0.974061i	$-0.572659\pi$
$929$	−13.7942	−0.452574	−0.226287	+	0.974061i	$0.572659\pi$
$930$	−8.34308	−0.273580
$931$	−29.1894	−0.956643
$932$	−13.6341	−0.446600
$933$	1.44687	0.0473683
$934$	36.1373	1.18245
$935$	1.00000	0.0327035
$936$	0.842010	0.0275220
$937$	−25.9772	−0.848637	−0.424319	−	0.905513i	$-0.639486\pi$
$937$	−25.9772	−0.848637	−0.424319	+	0.905513i	$0.639486\pi$
$938$	1.55279	0.0507005
$939$	−17.9230	−0.584894
$940$	13.3181	0.434389
$941$	13.5799	0.442692	0.221346	−	0.975195i	$-0.428955\pi$
$941$	13.5799	0.442692	0.221346	+	0.975195i	$0.428955\pi$
$942$	−11.3181	−0.368764
$943$	5.68402	0.185097
$944$	−5.50107	−0.179045
$945$	−1.15799	−0.0376694
$946$	5.50107	0.178855
$947$	−32.2661	−1.04851	−0.524253	−	0.851563i	$-0.675655\pi$
$947$	−32.2661	−1.04851	−0.524253	+	0.851563i	$0.675655\pi$
$948$	11.8170	0.383800
$949$	7.73394	0.251054
$950$	5.15799	0.167347
$951$	−21.6341	−0.701534
$952$	1.15799	0.0375307
$953$	16.9479	0.548998	0.274499	−	0.961587i	$-0.411488\pi$
$953$	16.9479	0.548998	0.274499	+	0.961587i	$0.411488\pi$
$954$	11.5011	0.372361
$955$	11.0021	0.356021
$956$	−21.3181	−0.689477
$957$	−2.00000	−0.0646508
$958$	−26.7133	−0.863066
$959$	12.7090	0.410394
$960$	−1.00000	−0.0322749
$961$	38.6070	1.24539
$962$	7.29102	0.235072
$963$	9.31812	0.300272
$964$	14.1601	0.456067
$965$	5.18509	0.166914
$966$	−3.29102	−0.105887
$967$	41.9501	1.34902	0.674512	−	0.738264i	$-0.264354\pi$
$967$	41.9501	1.34902	0.674512	+	0.738264i	$0.264354\pi$
$968$	1.00000	0.0321412
$969$	5.15799	0.165698
$970$	−8.02710	−0.257735
$971$	−61.7443	−1.98147	−0.990735	−	0.135812i	$-0.956636\pi$
$971$	−61.7443	−1.98147	−0.990735	+	0.135812i	$0.956636\pi$
$972$	1.00000	0.0320750
$973$	−7.31384	−0.234471
$974$	22.3702	0.716787
$975$	0.842010	0.0269659
$976$	−4.65906	−0.149133
$977$	23.0292	0.736771	0.368385	−	0.929673i	$-0.379911\pi$
$977$	23.0292	0.736771	0.368385	+	0.929673i	$0.379911\pi$
$978$	0.631958	0.0202078
$979$	−17.6341	−0.563588
$980$	5.65906	0.180772
$981$	−10.3431	−0.330229
$982$	17.9501	0.572810
$983$	36.1373	1.15260	0.576301	−	0.817238i	$-0.304496\pi$
$983$	36.1373	1.15260	0.576301	+	0.817238i	$0.304496\pi$
$984$	−2.00000	−0.0637577
$985$	−9.71112	−0.309422
$986$	2.00000	0.0636930
$987$	−15.4222	−0.490895
$988$	4.34308	0.138172
$989$	15.6341	0.497135
$990$	1.00000	0.0317821
$991$	23.2910	0.739864	0.369932	−	0.929059i	$-0.379381\pi$
$991$	23.2910	0.739864	0.369932	+	0.929059i	$0.379381\pi$
$992$	8.34308	0.264893
$993$	8.63196	0.273927
$994$	−9.05206	−0.287114
$995$	−17.6070	−0.558179
$996$	0.343081	0.0108709
$997$	37.0021	1.17187	0.585935	−	0.810358i	$-0.300727\pi$
$997$	37.0021	1.17187	0.585935	+	0.810358i	$0.300727\pi$
$998$	34.0043	1.07639
$999$	8.65906	0.273961

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5610.2.a.cd.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.cd.1.2	✓	3	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.15799 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +1.15799 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +0.842010 q^{13} +1.15799 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +5.15799 q^{19} -1.00000 q^{20} +1.15799 q^{21} -1.00000 q^{22} -2.84201 q^{23} +1.00000 q^{24} +1.00000 q^{25} +0.842010 q^{26} +1.00000 q^{27} +1.15799 q^{28} +2.00000 q^{29} -1.00000 q^{30} +8.34308 q^{31} +1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} -1.15799 q^{35} +1.00000 q^{36} +8.65906 q^{37} +5.15799 q^{38} +0.842010 q^{39} -1.00000 q^{40} -2.00000 q^{41} +1.15799 q^{42} -5.50107 q^{43} -1.00000 q^{44} -1.00000 q^{45} -2.84201 q^{46} -13.3181 q^{47} +1.00000 q^{48} -5.65906 q^{49} +1.00000 q^{50} +1.00000 q^{51} +0.842010 q^{52} +11.5011 q^{53} +1.00000 q^{54} +1.00000 q^{55} +1.15799 q^{56} +5.15799 q^{57} +2.00000 q^{58} -5.50107 q^{59} -1.00000 q^{60} -4.65906 q^{61} +8.34308 q^{62} +1.15799 q^{63} +1.00000 q^{64} -0.842010 q^{65} -1.00000 q^{66} +1.34094 q^{67} +1.00000 q^{68} -2.84201 q^{69} -1.15799 q^{70} -7.81705 q^{71} +1.00000 q^{72} +9.18509 q^{73} +8.65906 q^{74} +1.00000 q^{75} +5.15799 q^{76} -1.15799 q^{77} +0.842010 q^{78} +11.8170 q^{79} -1.00000 q^{80} +1.00000 q^{81} -2.00000 q^{82} +0.343081 q^{83} +1.15799 q^{84} -1.00000 q^{85} -5.50107 q^{86} +2.00000 q^{87} -1.00000 q^{88} +17.6341 q^{89} -1.00000 q^{90} +0.975039 q^{91} -2.84201 q^{92} +8.34308 q^{93} -13.3181 q^{94} -5.15799 q^{95} +1.00000 q^{96} +8.02710 q^{97} -5.65906 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 + q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{10} - 3 q^{11} + 3 q^{12} + 5 q^{13} + q^{14} - 3 q^{15} + 3 q^{16} + 3 q^{17} + 3 q^{18} + 13 q^{19} - 3 q^{20} + q^{21} - 3 q^{22} - 11 q^{23} + 3 q^{24} + 3 q^{25} + 5 q^{26} + 3 q^{27} + q^{28} + 6 q^{29} - 3 q^{30} + 5 q^{31} + 3 q^{32} - 3 q^{33} + 3 q^{34} - q^{35} + 3 q^{36} + q^{37} + 13 q^{38} + 5 q^{39} - 3 q^{40} - 6 q^{41} + q^{42} + 6 q^{43} - 3 q^{44} - 3 q^{45} - 11 q^{46} + 10 q^{47} + 3 q^{48} + 8 q^{49} + 3 q^{50} + 3 q^{51} + 5 q^{52} + 12 q^{53} + 3 q^{54} + 3 q^{55} + q^{56} + 13 q^{57} + 6 q^{58} + 6 q^{59} - 3 q^{60} + 11 q^{61} + 5 q^{62} + q^{63} + 3 q^{64} - 5 q^{65} - 3 q^{66} + 29 q^{67} + 3 q^{68} - 11 q^{69} - q^{70} + 4 q^{71} + 3 q^{72} + 10 q^{73} + q^{74} + 3 q^{75} + 13 q^{76} - q^{77} + 5 q^{78} + 8 q^{79} - 3 q^{80} + 3 q^{81} - 6 q^{82} - 19 q^{83} + q^{84} - 3 q^{85} + 6 q^{86} + 6 q^{87} - 3 q^{88} - 2 q^{89} - 3 q^{90} - 27 q^{91} - 11 q^{92} + 5 q^{93} + 10 q^{94} - 13 q^{95} + 3 q^{96} + 9 q^{97} + 8 q^{98} - 3 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 3 * q^6 + q^7 + 3 * q^8 + 3 * q^9 - 3 * q^10 - 3 * q^11 + 3 * q^12 + 5 * q^13 + q^14 - 3 * q^15 + 3 * q^16 + 3 * q^17 + 3 * q^18 + 13 * q^19 - 3 * q^20 + q^21 - 3 * q^22 - 11 * q^23 + 3 * q^24 + 3 * q^25 + 5 * q^26 + 3 * q^27 + q^28 + 6 * q^29 - 3 * q^30 + 5 * q^31 + 3 * q^32 - 3 * q^33 + 3 * q^34 - q^35 + 3 * q^36 + q^37 + 13 * q^38 + 5 * q^39 - 3 * q^40 - 6 * q^41 + q^42 + 6 * q^43 - 3 * q^44 - 3 * q^45 - 11 * q^46 + 10 * q^47 + 3 * q^48 + 8 * q^49 + 3 * q^50 + 3 * q^51 + 5 * q^52 + 12 * q^53 + 3 * q^54 + 3 * q^55 + q^56 + 13 * q^57 + 6 * q^58 + 6 * q^59 - 3 * q^60 + 11 * q^61 + 5 * q^62 + q^63 + 3 * q^64 - 5 * q^65 - 3 * q^66 + 29 * q^67 + 3 * q^68 - 11 * q^69 - q^70 + 4 * q^71 + 3 * q^72 + 10 * q^73 + q^74 + 3 * q^75 + 13 * q^76 - q^77 + 5 * q^78 + 8 * q^79 - 3 * q^80 + 3 * q^81 - 6 * q^82 - 19 * q^83 + q^84 - 3 * q^85 + 6 * q^86 + 6 * q^87 - 3 * q^88 - 2 * q^89 - 3 * q^90 - 27 * q^91 - 11 * q^92 + 5 * q^93 + 10 * q^94 - 13 * q^95 + 3 * q^96 + 9 * q^97 + 8 * q^98 - 3 * q^99

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