LMFDB - Embedded newform 5610.2.a.cd.1.1

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			1.1
Root			$-0.309984$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -3.79696 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -3.79696 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +5.79696 q^{13} -3.79696 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +0.203037 q^{19} -1.00000 q^{20} -3.79696 q^{21} -1.00000 q^{22} -7.79696 q^{23} +1.00000 q^{24} +1.00000 q^{25} +5.79696 q^{26} +1.00000 q^{27} -3.79696 q^{28} +2.00000 q^{29} -1.00000 q^{30} +5.17700 q^{31} +1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} +3.79696 q^{35} +1.00000 q^{36} -4.41693 q^{37} +0.203037 q^{38} +5.79696 q^{39} -1.00000 q^{40} -2.00000 q^{41} -3.79696 q^{42} +2.61997 q^{43} -1.00000 q^{44} -1.00000 q^{45} -7.79696 q^{46} +12.8339 q^{47} +1.00000 q^{48} +7.41693 q^{49} +1.00000 q^{50} +1.00000 q^{51} +5.79696 q^{52} +3.38003 q^{53} +1.00000 q^{54} +1.00000 q^{55} -3.79696 q^{56} +0.203037 q^{57} +2.00000 q^{58} +2.61997 q^{59} -1.00000 q^{60} +8.41693 q^{61} +5.17700 q^{62} -3.79696 q^{63} +1.00000 q^{64} -5.79696 q^{65} -1.00000 q^{66} +14.4169 q^{67} +1.00000 q^{68} -7.79696 q^{69} +3.79696 q^{70} +10.2139 q^{71} +1.00000 q^{72} +10.9740 q^{73} -4.41693 q^{74} +1.00000 q^{75} +0.203037 q^{76} +3.79696 q^{77} +5.79696 q^{78} -6.21389 q^{79} -1.00000 q^{80} +1.00000 q^{81} -2.00000 q^{82} -2.82300 q^{83} -3.79696 q^{84} -1.00000 q^{85} +2.61997 q^{86} +2.00000 q^{87} -1.00000 q^{88} -18.4278 q^{89} -1.00000 q^{90} -22.0109 q^{91} -7.79696 q^{92} +5.17700 q^{93} +12.8339 q^{94} -0.203037 q^{95} +1.00000 q^{96} +14.7709 q^{97} +7.41693 q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	−3.79696	−1.43512	−0.717559	−	0.696498i	$-0.754740\pi$
$7$	−3.79696	−1.43512	−0.717559	+	0.696498i	$0.754740\pi$
$8$	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
$13$	5.79696	1.60779	0.803894	−	0.594772i	$-0.202758\pi$
$13$	5.79696	1.60779	0.803894	+	0.594772i	$0.202758\pi$
$14$	−3.79696	−1.01478
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	0.203037	0.0465798	0.0232899	−	0.999729i	$-0.492586\pi$
$19$	0.203037	0.0465798	0.0232899	+	0.999729i	$0.492586\pi$
$20$	−1.00000	−0.223607
$21$	−3.79696	−0.828565
$22$	−1.00000	−0.213201
$23$	−7.79696	−1.62578	−0.812890	−	0.582418i	$-0.802107\pi$
$23$	−7.79696	−1.62578	−0.812890	+	0.582418i	$0.802107\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	5.79696	1.13688
$27$	1.00000	0.192450
$28$	−3.79696	−0.717559
$29$	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
$31$	5.17700	0.929816	0.464908	−	0.885359i	$-0.346087\pi$
$31$	5.17700	0.929816	0.464908	+	0.885359i	$0.346087\pi$
$32$	1.00000	0.176777
$33$	−1.00000	−0.174078
$34$	1.00000	0.171499
$35$	3.79696	0.641804
$36$	1.00000	0.166667
$37$	−4.41693	−0.726139	−0.363069	−	0.931762i	$-0.618271\pi$
$37$	−4.41693	−0.726139	−0.363069	+	0.931762i	$0.618271\pi$
$38$	0.203037	0.0329369
$39$	5.79696	0.928257
$40$	−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	$0.549916\pi$
$42$	−3.79696	−0.585884
$43$	2.61997	0.399541	0.199771	−	0.979843i	$-0.435980\pi$
$43$	2.61997	0.399541	0.199771	+	0.979843i	$0.435980\pi$
$44$	−1.00000	−0.150756
$45$	−1.00000	−0.149071
$46$	−7.79696	−1.14960
$47$	12.8339	1.87201	0.936006	−	0.351985i	$-0.114493\pi$
$47$	12.8339	1.87201	0.936006	+	0.351985i	$0.114493\pi$
$48$	1.00000	0.144338
$49$	7.41693	1.05956
$50$	1.00000	0.141421
$51$	1.00000	0.140028
$52$	5.79696	0.803894
$53$	3.38003	0.464283	0.232142	−	0.972682i	$-0.425427\pi$
$53$	3.38003	0.464283	0.232142	+	0.972682i	$0.425427\pi$
$54$	1.00000	0.136083
$55$	1.00000	0.134840
$56$	−3.79696	−0.507391
$57$	0.203037	0.0268929
$58$	2.00000	0.262613
$59$	2.61997	0.341091	0.170545	−	0.985350i	$-0.445447\pi$
$59$	2.61997	0.341091	0.170545	+	0.985350i	$0.445447\pi$
$60$	−1.00000	−0.129099
$61$	8.41693	1.07768	0.538839	−	0.842409i	$-0.318863\pi$
$61$	8.41693	1.07768	0.538839	+	0.842409i	$0.318863\pi$
$62$	5.17700	0.657479
$63$	−3.79696	−0.478372
$64$	1.00000	0.125000
$65$	−5.79696	−0.719025
$66$	−1.00000	−0.123091
$67$	14.4169	1.76131	0.880654	−	0.473760i	$-0.157103\pi$
$67$	14.4169	1.76131	0.880654	+	0.473760i	$0.157103\pi$
$68$	1.00000	0.121268
$69$	−7.79696	−0.938644
$70$	3.79696	0.453824
$71$	10.2139	1.21217	0.606083	−	0.795401i	$-0.292740\pi$
$71$	10.2139	1.21217	0.606083	+	0.795401i	$0.292740\pi$
$72$	1.00000	0.117851
$73$	10.9740	1.28440	0.642202	−	0.766535i	$-0.278021\pi$
$73$	10.9740	1.28440	0.642202	+	0.766535i	$0.278021\pi$
$74$	−4.41693	−0.513458
$75$	1.00000	0.115470
$76$	0.203037	0.0232899
$77$	3.79696	0.432704
$78$	5.79696	0.656377
$79$	−6.21389	−0.699118	−0.349559	−	0.936914i	$-0.613669\pi$
$79$	−6.21389	−0.699118	−0.349559	+	0.936914i	$0.613669\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−2.00000	−0.220863
$83$	−2.82300	−0.309865	−0.154932	−	0.987925i	$-0.549516\pi$
$83$	−2.82300	−0.309865	−0.154932	+	0.987925i	$0.549516\pi$
$84$	−3.79696	−0.414283
$85$	−1.00000	−0.108465
$86$	2.61997	0.282518
$87$	2.00000	0.214423
$88$	−1.00000	−0.106600
$89$	−18.4278	−1.95334	−0.976671	−	0.214742i	$-0.931109\pi$
$89$	−18.4278	−1.95334	−0.976671	+	0.214742i	$0.931109\pi$
$90$	−1.00000	−0.105409
$91$	−22.0109	−2.30736
$92$	−7.79696	−0.812890
$93$	5.17700	0.536829
$94$	12.8339	1.32371
$95$	−0.203037	−0.0208311
$96$	1.00000	0.102062
$97$	14.7709	1.49976	0.749880	−	0.661574i	$-0.230111\pi$
$97$	14.7709	1.49976	0.749880	+	0.661574i	$0.230111\pi$
$98$	7.41693	0.749223
$99$	−1.00000	−0.100504
$100$	1.00000	0.100000
$101$	17.1879	1.71026	0.855128	−	0.518417i	$-0.173479\pi$
$101$	17.1879	1.71026	0.855128	+	0.518417i	$0.173479\pi$
$102$	1.00000	0.0990148
$103$	−6.01086	−0.592267	−0.296134	−	0.955147i	$-0.595697\pi$
$103$	−6.01086	−0.592267	−0.296134	+	0.955147i	$0.595697\pi$
$104$	5.79696	0.568439
$105$	3.79696	0.370546
$106$	3.38003	0.328298
$107$	−16.8339	−1.62739	−0.813695	−	0.581292i	$-0.802548\pi$
$107$	−16.8339	−1.62739	−0.813695	+	0.581292i	$0.802548\pi$
$108$	1.00000	0.0962250
$109$	−7.17700	−0.687432	−0.343716	−	0.939074i	$-0.611686\pi$
$109$	−7.17700	−0.687432	−0.343716	+	0.939074i	$0.611686\pi$
$110$	1.00000	0.0953463
$111$	−4.41693	−0.419236
$112$	−3.79696	−0.358779
$113$	4.61997	0.434610	0.217305	−	0.976104i	$-0.430273\pi$
$113$	4.61997	0.434610	0.217305	+	0.976104i	$0.430273\pi$
$114$	0.203037	0.0190161
$115$	7.79696	0.727071
$116$	2.00000	0.185695
$117$	5.79696	0.535929
$118$	2.61997	0.241188
$119$	−3.79696	−0.348067
$120$	−1.00000	−0.0912871
$121$	1.00000	0.0909091
$122$	8.41693	0.762033
$123$	−2.00000	−0.180334
$124$	5.17700	0.464908
$125$	−1.00000	−0.0894427
$126$	−3.79696	−0.338260
$127$	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
$129$	2.61997	0.230675
$130$	−5.79696	−0.508427
$131$	13.1770	1.15128	0.575640	−	0.817703i	$-0.304753\pi$
$131$	13.1770	1.15128	0.575640	+	0.817703i	$0.304753\pi$
$132$	−1.00000	−0.0870388
$133$	−0.770923	−0.0668475
$134$	14.4169	1.24543
$135$	−1.00000	−0.0860663
$136$	1.00000	0.0857493
$137$	−12.0109	−1.02616	−0.513078	−	0.858342i	$-0.671495\pi$
$137$	−12.0109	−1.02616	−0.513078	+	0.858342i	$0.671495\pi$
$138$	−7.79696	−0.663722
$139$	3.59393	0.304833	0.152416	−	0.988316i	$-0.451295\pi$
$139$	3.59393	0.304833	0.152416	+	0.988316i	$0.451295\pi$
$140$	3.79696	0.320902
$141$	12.8339	1.08081
$142$	10.2139	0.857131
$143$	−5.79696	−0.484766
$144$	1.00000	0.0833333
$145$	−2.00000	−0.166091
$146$	10.9740	0.908211
$147$	7.41693	0.611738
$148$	−4.41693	−0.363069
$149$	−19.6048	−1.60609	−0.803043	−	0.595921i	$-0.796787\pi$
$149$	−19.6048	−1.60609	−0.803043	+	0.595921i	$0.796787\pi$
$150$	1.00000	0.0816497
$151$	−1.58307	−0.128828	−0.0644142	−	0.997923i	$-0.520518\pi$
$151$	−1.58307	−0.128828	−0.0644142	+	0.997923i	$0.520518\pi$
$152$	0.203037	0.0164684
$153$	1.00000	0.0808452
$154$	3.79696	0.305968
$155$	−5.17700	−0.415826
$156$	5.79696	0.464129
$157$	14.8339	1.18387	0.591935	−	0.805985i	$-0.298364\pi$
$157$	14.8339	1.18387	0.591935	+	0.805985i	$0.298364\pi$
$158$	−6.21389	−0.494351
$159$	3.38003	0.268054
$160$	−1.00000	−0.0790569
$161$	29.6048	2.33318
$162$	1.00000	0.0785674
$163$	−19.1879	−1.50291	−0.751454	−	0.659785i	$-0.770647\pi$
$163$	−19.1879	−1.50291	−0.751454	+	0.659785i	$0.770647\pi$
$164$	−2.00000	−0.156174
$165$	1.00000	0.0778499
$166$	−2.82300	−0.219108
$167$	−4.00000	−0.309529	−0.154765	−	0.987951i	$-0.549462\pi$
$167$	−4.00000	−0.309529	−0.154765	+	0.987951i	$0.549462\pi$
$168$	−3.79696	−0.292942
$169$	20.6048	1.58498
$170$	−1.00000	−0.0766965
$171$	0.203037	0.0155266
$172$	2.61997	0.199771
$173$	0.416930	0.0316986	0.0158493	−	0.999874i	$-0.494955\pi$
$173$	0.416930	0.0316986	0.0158493	+	0.999874i	$0.494955\pi$
$174$	2.00000	0.151620
$175$	−3.79696	−0.287023
$176$	−1.00000	−0.0753778
$177$	2.61997	0.196929
$178$	−18.4278	−1.38122
$179$	−1.44297	−0.107853	−0.0539264	−	0.998545i	$-0.517174\pi$
$179$	−1.44297	−0.107853	−0.0539264	+	0.998545i	$0.517174\pi$
$180$	−1.00000	−0.0745356
$181$	9.59393	0.713111	0.356555	−	0.934274i	$-0.383951\pi$
$181$	9.59393	0.713111	0.356555	+	0.934274i	$0.383951\pi$
$182$	−22.0109	−1.63155
$183$	8.41693	0.622197
$184$	−7.79696	−0.574800
$185$	4.41693	0.324739
$186$	5.17700	0.379596
$187$	−1.00000	−0.0731272
$188$	12.8339	0.936006
$189$	−3.79696	−0.276188
$190$	−0.203037	−0.0147298
$191$	5.23993	0.379148	0.189574	−	0.981866i	$-0.439289\pi$
$191$	5.23993	0.379148	0.189574	+	0.981866i	$0.439289\pi$
$192$	1.00000	0.0721688
$193$	−6.97396	−0.501997	−0.250998	−	0.967988i	$-0.580759\pi$
$193$	−6.97396	−0.501997	−0.250998	+	0.967988i	$0.580759\pi$
$194$	14.7709	1.06049
$195$	−5.79696	−0.415129
$196$	7.41693	0.529781
$197$	26.3648	1.87842	0.939209	−	0.343346i	$-0.111560\pi$
$197$	26.3648	1.87842	0.939209	+	0.343346i	$0.111560\pi$
$198$	−1.00000	−0.0710669
$199$	−25.1987	−1.78629	−0.893145	−	0.449770i	$-0.851506\pi$
$199$	−25.1987	−1.78629	−0.893145	+	0.449770i	$0.851506\pi$
$200$	1.00000	0.0707107
$201$	14.4169	1.01689
$202$	17.1879	1.20933
$203$	−7.59393	−0.532989
$204$	1.00000	0.0700140
$205$	2.00000	0.139686
$206$	−6.01086	−0.418796
$207$	−7.79696	−0.541926
$208$	5.79696	0.401947
$209$	−0.203037	−0.0140443
$210$	3.79696	0.262015
$211$	−11.5939	−0.798159	−0.399079	−	0.916916i	$-0.630670\pi$
$211$	−11.5939	−0.798159	−0.399079	+	0.916916i	$0.630670\pi$
$212$	3.38003	0.232142
$213$	10.2139	0.699844
$214$	−16.8339	−1.15074
$215$	−2.61997	−0.178680
$216$	1.00000	0.0680414
$217$	−19.6569	−1.33439
$218$	−7.17700	−0.486088
$219$	10.9740	0.741551
$220$	1.00000	0.0674200
$221$	5.79696	0.389946
$222$	−4.41693	−0.296445
$223$	14.0109	0.938236	0.469118	−	0.883135i	$-0.344572\pi$
$223$	14.0109	0.938236	0.469118	+	0.883135i	$0.344572\pi$
$224$	−3.79696	−0.253695
$225$	1.00000	0.0666667
$226$	4.61997	0.307316
$227$	8.83386	0.586324	0.293162	−	0.956063i	$-0.405292\pi$
$227$	8.83386	0.586324	0.293162	+	0.956063i	$0.405292\pi$
$228$	0.203037	0.0134464
$229$	20.4169	1.34919	0.674594	−	0.738189i	$-0.264319\pi$
$229$	20.4169	1.34919	0.674594	+	0.738189i	$0.264319\pi$
$230$	7.79696	0.514117
$231$	3.79696	0.249822
$232$	2.00000	0.131306
$233$	22.4278	1.46929	0.734647	−	0.678450i	$-0.237348\pi$
$233$	22.4278	1.46929	0.734647	+	0.678450i	$0.237348\pi$
$234$	5.79696	0.378959
$235$	−12.8339	−0.837189
$236$	2.61997	0.170545
$237$	−6.21389	−0.403636
$238$	−3.79696	−0.246121
$239$	4.83386	0.312676	0.156338	−	0.987704i	$-0.450031\pi$
$239$	4.83386	0.312676	0.156338	+	0.987704i	$0.450031\pi$
$240$	−1.00000	−0.0645497
$241$	−7.03690	−0.453286	−0.226643	−	0.973978i	$-0.572775\pi$
$241$	−7.03690	−0.453286	−0.226643	+	0.973978i	$0.572775\pi$
$242$	1.00000	0.0642824
$243$	1.00000	0.0641500
$244$	8.41693	0.538839
$245$	−7.41693	−0.473850
$246$	−2.00000	−0.127515
$247$	1.17700	0.0748905
$248$	5.17700	0.328740
$249$	−2.82300	−0.178901
$250$	−1.00000	−0.0632456
$251$	29.7449	1.87748	0.938740	−	0.344626i	$-0.111994\pi$
$251$	29.7449	1.87748	0.938740	+	0.344626i	$0.111994\pi$
$252$	−3.79696	−0.239186
$253$	7.79696	0.490191
$254$	16.0000	1.00393
$255$	−1.00000	−0.0626224
$256$	1.00000	0.0625000
$257$	1.18785	0.0740963	0.0370481	−	0.999313i	$-0.488205\pi$
$257$	1.18785	0.0740963	0.0370481	+	0.999313i	$0.488205\pi$
$258$	2.61997	0.163112
$259$	16.7709	1.04209
$260$	−5.79696	−0.359512
$261$	2.00000	0.123797
$262$	13.1770	0.814078
$263$	−22.0109	−1.35725	−0.678624	−	0.734486i	$-0.737423\pi$
$263$	−22.0109	−1.35725	−0.678624	+	0.734486i	$0.737423\pi$
$264$	−1.00000	−0.0615457
$265$	−3.38003	−0.207634
$266$	−0.770923	−0.0472683
$267$	−18.4278	−1.12776
$268$	14.4169	0.880654
$269$	20.8447	1.27092	0.635462	−	0.772132i	$-0.280809\pi$
$269$	20.8447	1.27092	0.635462	+	0.772132i	$0.280809\pi$
$270$	−1.00000	−0.0608581
$271$	−7.18785	−0.436631	−0.218315	−	0.975878i	$-0.570056\pi$
$271$	−7.18785	−0.436631	−0.218315	+	0.975878i	$0.570056\pi$
$272$	1.00000	0.0606339
$273$	−22.0109	−1.33216
$274$	−12.0109	−0.725602
$275$	−1.00000	−0.0603023
$276$	−7.79696	−0.469322
$277$	−3.64601	−0.219067	−0.109534	−	0.993983i	$-0.534936\pi$
$277$	−3.64601	−0.219067	−0.109534	+	0.993983i	$0.534936\pi$
$278$	3.59393	0.215549
$279$	5.17700	0.309939
$280$	3.79696	0.226912
$281$	11.9479	0.712753	0.356377	−	0.934342i	$-0.384012\pi$
$281$	11.9479	0.712753	0.356377	+	0.934342i	$0.384012\pi$
$282$	12.8339	0.764245
$283$	−6.76007	−0.401844	−0.200922	−	0.979607i	$-0.564394\pi$
$283$	−6.76007	−0.401844	−0.200922	+	0.979607i	$0.564394\pi$
$284$	10.2139	0.606083
$285$	−0.203037	−0.0120269
$286$	−5.79696	−0.342782
$287$	7.59393	0.448255
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−2.00000	−0.117444
$291$	14.7709	0.865887
$292$	10.9740	0.642202
$293$	24.3540	1.42278	0.711388	−	0.702800i	$-0.248067\pi$
$293$	24.3540	1.42278	0.711388	+	0.702800i	$0.248067\pi$
$294$	7.41693	0.432564
$295$	−2.61997	−0.152540
$296$	−4.41693	−0.256729
$297$	−1.00000	−0.0580259
$298$	−19.6048	−1.13567
$299$	−45.1987	−2.61391
$300$	1.00000	0.0577350
$301$	−9.94792	−0.573389
$302$	−1.58307	−0.0910954
$303$	17.1879	0.987416
$304$	0.203037	0.0116450
$305$	−8.41693	−0.481952
$306$	1.00000	0.0571662
$307$	−15.3280	−0.874812	−0.437406	−	0.899264i	$-0.644103\pi$
$307$	−15.3280	−0.874812	−0.437406	+	0.899264i	$0.644103\pi$
$308$	3.79696	0.216352
$309$	−6.01086	−0.341946
$310$	−5.17700	−0.294034
$311$	−20.1618	−1.14327	−0.571636	−	0.820508i	$-0.693691\pi$
$311$	−20.1618	−1.14327	−0.571636	+	0.820508i	$0.693691\pi$
$312$	5.79696	0.328188
$313$	34.7926	1.96660	0.983298	−	0.182003i	$-0.0582579\pi$
$313$	34.7926	1.96660	0.983298	+	0.182003i	$0.0582579\pi$
$314$	14.8339	0.837123
$315$	3.79696	0.213935
$316$	−6.21389	−0.349559
$317$	14.4278	0.810345	0.405173	−	0.914240i	$-0.367211\pi$
$317$	14.4278	0.810345	0.405173	+	0.914240i	$0.367211\pi$
$318$	3.38003	0.189543
$319$	−2.00000	−0.111979
$320$	−1.00000	−0.0559017
$321$	−16.8339	−0.939574
$322$	29.6048	1.64981
$323$	0.203037	0.0112973
$324$	1.00000	0.0555556
$325$	5.79696	0.321558
$326$	−19.1879	−1.06272
$327$	−7.17700	−0.396889
$328$	−2.00000	−0.110432
$329$	−48.7297	−2.68656
$330$	1.00000	0.0550482
$331$	−11.1879	−0.614940	−0.307470	−	0.951558i	$-0.599482\pi$
$331$	−11.1879	−0.614940	−0.307470	+	0.951558i	$0.599482\pi$
$332$	−2.82300	−0.154932
$333$	−4.41693	−0.242046
$334$	−4.00000	−0.218870
$335$	−14.4169	−0.787681
$336$	−3.79696	−0.207141
$337$	34.1618	1.86091	0.930456	−	0.366403i	$-0.119411\pi$
$337$	34.1618	1.86091	0.930456	+	0.366403i	$0.119411\pi$
$338$	20.6048	1.12075
$339$	4.61997	0.250922
$340$	−1.00000	−0.0542326
$341$	−5.17700	−0.280350
$342$	0.203037	0.0109790
$343$	−1.58307	−0.0854777
$344$	2.61997	0.141259
$345$	7.79696	0.419774
$346$	0.416930	0.0224143
$347$	−14.3540	−0.770563	−0.385281	−	0.922799i	$-0.625896\pi$
$347$	−14.3540	−0.770563	−0.385281	+	0.922799i	$0.625896\pi$
$348$	2.00000	0.107211
$349$	−4.61997	−0.247301	−0.123651	−	0.992326i	$-0.539460\pi$
$349$	−4.61997	−0.247301	−0.123651	+	0.992326i	$0.539460\pi$
$350$	−3.79696	−0.202956
$351$	5.79696	0.309419
$352$	−1.00000	−0.0533002
$353$	−17.6569	−0.939780	−0.469890	−	0.882725i	$-0.655706\pi$
$353$	−17.6569	−0.939780	−0.469890	+	0.882725i	$0.655706\pi$
$354$	2.61997	0.139250
$355$	−10.2139	−0.542097
$356$	−18.4278	−0.976671
$357$	−3.79696	−0.200957
$358$	−1.44297	−0.0762634
$359$	28.0217	1.47893	0.739465	−	0.673195i	$-0.235079\pi$
$359$	28.0217	1.47893	0.739465	+	0.673195i	$0.235079\pi$
$360$	−1.00000	−0.0527046
$361$	−18.9588	−0.997830
$362$	9.59393	0.504246
$363$	1.00000	0.0524864
$364$	−22.0109	−1.15368
$365$	−10.9740	−0.574403
$366$	8.41693	0.439960
$367$	−25.9479	−1.35447	−0.677235	−	0.735767i	$-0.736822\pi$
$367$	−25.9479	−1.35447	−0.677235	+	0.735767i	$0.736822\pi$
$368$	−7.79696	−0.406445
$369$	−2.00000	−0.104116
$370$	4.41693	0.229625
$371$	−12.8339	−0.666301
$372$	5.17700	0.268415
$373$	−29.0478	−1.50404	−0.752018	−	0.659143i	$-0.770919\pi$
$373$	−29.0478	−1.50404	−0.752018	+	0.659143i	$0.770919\pi$
$374$	−1.00000	−0.0517088
$375$	−1.00000	−0.0516398
$376$	12.8339	0.661856
$377$	11.5939	0.597118
$378$	−3.79696	−0.195295
$379$	22.8447	1.17345	0.586727	−	0.809785i	$-0.300416\pi$
$379$	22.8447	1.17345	0.586727	+	0.809785i	$0.300416\pi$
$380$	−0.203037	−0.0104156
$381$	16.0000	0.819705
$382$	5.23993	0.268098
$383$	−30.7818	−1.57288	−0.786438	−	0.617670i	$-0.788077\pi$
$383$	−30.7818	−1.57288	−0.786438	+	0.617670i	$0.788077\pi$
$384$	1.00000	0.0510310
$385$	−3.79696	−0.193511
$386$	−6.97396	−0.354965
$387$	2.61997	0.133180
$388$	14.7709	0.749880
$389$	−21.4538	−1.08775	−0.543876	−	0.839166i	$-0.683044\pi$
$389$	−21.4538	−1.08775	−0.543876	+	0.839166i	$0.683044\pi$
$390$	−5.79696	−0.293541
$391$	−7.79696	−0.394309
$392$	7.41693	0.374612
$393$	13.1770	0.664692
$394$	26.3648	1.32824
$395$	6.21389	0.312655
$396$	−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	$0.484018\pi$
$398$	−25.1987	−1.26310
$399$	−0.770923	−0.0385944
$400$	1.00000	0.0500000
$401$	−29.7970	−1.48799	−0.743995	−	0.668186i	$-0.767071\pi$
$401$	−29.7970	−1.48799	−0.743995	+	0.668186i	$0.767071\pi$
$402$	14.4169	0.719051
$403$	30.0109	1.49495
$404$	17.1879	0.855128
$405$	−1.00000	−0.0496904
$406$	−7.59393	−0.376880
$407$	4.41693	0.218939
$408$	1.00000	0.0495074
$409$	−16.7601	−0.828732	−0.414366	−	0.910110i	$-0.635997\pi$
$409$	−16.7601	−0.828732	−0.414366	+	0.910110i	$0.635997\pi$
$410$	2.00000	0.0987730
$411$	−12.0109	−0.592452
$412$	−6.01086	−0.296134
$413$	−9.94792	−0.489505
$414$	−7.79696	−0.383200
$415$	2.82300	0.138576
$416$	5.79696	0.284220
$417$	3.59393	0.175995
$418$	−0.203037	−0.00993085
$419$	−4.00000	−0.195413	−0.0977064	−	0.995215i	$-0.531151\pi$
$419$	−4.00000	−0.195413	−0.0977064	+	0.995215i	$0.531151\pi$
$420$	3.79696	0.185273
$421$	7.17700	0.349785	0.174893	−	0.984587i	$-0.444042\pi$
$421$	7.17700	0.349785	0.174893	+	0.984587i	$0.444042\pi$
$422$	−11.5939	−0.564384
$423$	12.8339	0.624004
$424$	3.38003	0.164149
$425$	1.00000	0.0485071
$426$	10.2139	0.494865
$427$	−31.9588	−1.54659
$428$	−16.8339	−0.813695
$429$	−5.79696	−0.279880
$430$	−2.61997	−0.126346
$431$	−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
$433$	−10.4278	−0.501127	−0.250564	−	0.968100i	$-0.580616\pi$
$433$	−10.4278	−0.501127	−0.250564	+	0.968100i	$0.580616\pi$
$434$	−19.6569	−0.943560
$435$	−2.00000	−0.0958927
$436$	−7.17700	−0.343716
$437$	−1.58307	−0.0757285
$438$	10.9740	0.524356
$439$	−7.02604	−0.335335	−0.167667	−	0.985844i	$-0.553623\pi$
$439$	−7.02604	−0.335335	−0.167667	+	0.985844i	$0.553623\pi$
$440$	1.00000	0.0476731
$441$	7.41693	0.353187
$442$	5.79696	0.275733
$443$	−27.4538	−1.30437	−0.652185	−	0.758060i	$-0.726148\pi$
$443$	−27.4538	−1.30437	−0.652185	+	0.758060i	$0.726148\pi$
$444$	−4.41693	−0.209618
$445$	18.4278	0.873561
$446$	14.0109	0.663433
$447$	−19.6048	−0.927274
$448$	−3.79696	−0.179390
$449$	−36.5787	−1.72626	−0.863129	−	0.504984i	$-0.831498\pi$
$449$	−36.5787	−1.72626	−0.863129	+	0.504984i	$0.831498\pi$
$450$	1.00000	0.0471405
$451$	2.00000	0.0941763
$452$	4.61997	0.217305
$453$	−1.58307	−0.0743791
$454$	8.83386	0.414594
$455$	22.0109	1.03188
$456$	0.203037	0.00950806
$457$	−27.6048	−1.29130	−0.645649	−	0.763635i	$-0.723413\pi$
$457$	−27.6048	−1.29130	−0.645649	+	0.763635i	$0.723413\pi$
$458$	20.4169	0.954021
$459$	1.00000	0.0466760
$460$	7.79696	0.363535
$461$	27.9479	1.30166	0.650832	−	0.759222i	$-0.274420\pi$
$461$	27.9479	1.30166	0.650832	+	0.759222i	$0.274420\pi$
$462$	3.79696	0.176651
$463$	4.34314	0.201843	0.100921	−	0.994894i	$-0.467821\pi$
$463$	4.34314	0.201843	0.100921	+	0.994894i	$0.467821\pi$
$464$	2.00000	0.0928477
$465$	−5.17700	−0.240077
$466$	22.4278	1.03895
$467$	−24.2877	−1.12390	−0.561950	−	0.827171i	$-0.689949\pi$
$467$	−24.2877	−1.12390	−0.561950	+	0.827171i	$0.689949\pi$
$468$	5.79696	0.267965
$469$	−54.7406	−2.52768
$470$	−12.8339	−0.591982
$471$	14.8339	0.683508
$472$	2.61997	0.120594
$473$	−2.61997	−0.120466
$474$	−6.21389	−0.285414
$475$	0.203037	0.00931596
$476$	−3.79696	−0.174034
$477$	3.38003	0.154761
$478$	4.83386	0.221096
$479$	−27.1249	−1.23937	−0.619685	−	0.784851i	$-0.712739\pi$
$479$	−27.1249	−1.23937	−0.619685	+	0.784851i	$0.712739\pi$
$480$	−1.00000	−0.0456435
$481$	−25.6048	−1.16748
$482$	−7.03690	−0.320522
$483$	29.6048	1.34706
$484$	1.00000	0.0454545
$485$	−14.7709	−0.670713
$486$	1.00000	0.0453609
$487$	25.9479	1.17581	0.587906	−	0.808929i	$-0.299952\pi$
$487$	25.9479	1.17581	0.587906	+	0.808929i	$0.299952\pi$
$488$	8.41693	0.381017
$489$	−19.1879	−0.867705
$490$	−7.41693	−0.335063
$491$	−28.0217	−1.26460	−0.632301	−	0.774723i	$-0.717889\pi$
$491$	−28.0217	−1.26460	−0.632301	+	0.774723i	$0.717889\pi$
$492$	−2.00000	−0.0901670
$493$	2.00000	0.0900755
$494$	1.17700	0.0529556
$495$	1.00000	0.0449467
$496$	5.17700	0.232454
$497$	−38.7818	−1.73960
$498$	−2.82300	−0.126502
$499$	1.52013	0.0680504	0.0340252	−	0.999421i	$-0.489167\pi$
$499$	1.52013	0.0680504	0.0340252	+	0.999421i	$0.489167\pi$
$500$	−1.00000	−0.0447214
$501$	−4.00000	−0.178707
$502$	29.7449	1.32758
$503$	39.6156	1.76637	0.883187	−	0.469021i	$-0.155393\pi$
$503$	39.6156	1.76637	0.883187	+	0.469021i	$0.155393\pi$
$504$	−3.79696	−0.169130
$505$	−17.1879	−0.764849
$506$	7.79696	0.346617
$507$	20.6048	0.915091
$508$	16.0000	0.709885
$509$	−0.619967	−0.0274796	−0.0137398	−	0.999906i	$-0.504374\pi$
$509$	−0.619967	−0.0274796	−0.0137398	+	0.999906i	$0.504374\pi$
$510$	−1.00000	−0.0442807
$511$	−41.6677	−1.84327
$512$	1.00000	0.0441942
$513$	0.203037	0.00896429
$514$	1.18785	0.0523940
$515$	6.01086	0.264870
$516$	2.61997	0.115338
$517$	−12.8339	−0.564433
$518$	16.7709	0.736872
$519$	0.416930	0.0183012
$520$	−5.79696	−0.254214
$521$	−36.1727	−1.58475	−0.792377	−	0.610032i	$-0.791157\pi$
$521$	−36.1727	−1.58475	−0.792377	+	0.610032i	$0.791157\pi$
$522$	2.00000	0.0875376
$523$	39.0478	1.70744	0.853720	−	0.520733i	$-0.174341\pi$
$523$	39.0478	1.70744	0.853720	+	0.520733i	$0.174341\pi$
$524$	13.1770	0.575640
$525$	−3.79696	−0.165713
$526$	−22.0109	−0.959719
$527$	5.17700	0.225513
$528$	−1.00000	−0.0435194
$529$	37.7926	1.64316
$530$	−3.38003	−0.146819
$531$	2.61997	0.113697
$532$	−0.770923	−0.0334237
$533$	−11.5939	−0.502189
$534$	−18.4278	−0.797448
$535$	16.8339	0.727791
$536$	14.4169	0.622717
$537$	−1.44297	−0.0622688
$538$	20.8447	0.898680
$539$	−7.41693	−0.319470
$540$	−1.00000	−0.0430331
$541$	29.6156	1.27328	0.636638	−	0.771163i	$-0.280325\pi$
$541$	29.6156	1.27328	0.636638	+	0.771163i	$0.280325\pi$
$542$	−7.18785	−0.308745
$543$	9.59393	0.411715
$544$	1.00000	0.0428746
$545$	7.17700	0.307429
$546$	−22.0109	−0.941978
$547$	−10.8230	−0.462758	−0.231379	−	0.972864i	$-0.574324\pi$
$547$	−10.8230	−0.462758	−0.231379	+	0.972864i	$0.574324\pi$
$548$	−12.0109	−0.513078
$549$	8.41693	0.359226
$550$	−1.00000	−0.0426401
$551$	0.406073	0.0172993
$552$	−7.79696	−0.331861
$553$	23.5939	1.00332
$554$	−3.64601	−0.154904
$555$	4.41693	0.187488
$556$	3.59393	0.152416
$557$	10.8339	0.459045	0.229523	−	0.973303i	$-0.426283\pi$
$557$	10.8339	0.459045	0.229523	+	0.973303i	$0.426283\pi$
$558$	5.17700	0.219160
$559$	15.1879	0.642378
$560$	3.79696	0.160451
$561$	−1.00000	−0.0422200
$562$	11.9479	0.503993
$563$	31.5310	1.32887	0.664436	−	0.747345i	$-0.268672\pi$
$563$	31.5310	1.32887	0.664436	+	0.747345i	$0.268672\pi$
$564$	12.8339	0.540403
$565$	−4.61997	−0.194363
$566$	−6.76007	−0.284147
$567$	−3.79696	−0.159457
$568$	10.2139	0.428565
$569$	−17.5310	−0.734937	−0.367469	−	0.930036i	$-0.619775\pi$
$569$	−17.5310	−0.734937	−0.367469	+	0.930036i	$0.619775\pi$
$570$	−0.203037	−0.00850427
$571$	−9.11406	−0.381411	−0.190706	−	0.981647i	$-0.561078\pi$
$571$	−9.11406	−0.381411	−0.190706	+	0.981647i	$0.561078\pi$
$572$	−5.79696	−0.242383
$573$	5.23993	0.218901
$574$	7.59393	0.316964
$575$	−7.79696	−0.325156
$576$	1.00000	0.0416667
$577$	13.6156	0.566827	0.283413	−	0.958998i	$-0.408533\pi$
$577$	13.6156	0.566827	0.283413	+	0.958998i	$0.408533\pi$
$578$	1.00000	0.0415945
$579$	−6.97396	−0.289828
$580$	−2.00000	−0.0830455
$581$	10.7188	0.444692
$582$	14.7709	0.612274
$583$	−3.38003	−0.139987
$584$	10.9740	0.454106
$585$	−5.79696	−0.239675
$586$	24.3540	1.00605
$587$	−17.7861	−0.734111	−0.367056	−	0.930199i	$-0.619634\pi$
$587$	−17.7861	−0.734111	−0.367056	+	0.930199i	$0.619634\pi$
$588$	7.41693	0.305869
$589$	1.05112	0.0433107
$590$	−2.61997	−0.107862
$591$	26.3648	1.08450
$592$	−4.41693	−0.181535
$593$	22.4278	0.920999	0.460499	−	0.887660i	$-0.347670\pi$
$593$	22.4278	0.920999	0.460499	+	0.887660i	$0.347670\pi$
$594$	−1.00000	−0.0410305
$595$	3.79696	0.155660
$596$	−19.6048	−0.803043
$597$	−25.1987	−1.03131
$598$	−45.1987	−1.84831
$599$	−29.6048	−1.20962	−0.604809	−	0.796370i	$-0.706751\pi$
$599$	−29.6048	−1.20962	−0.604809	+	0.796370i	$0.706751\pi$
$600$	1.00000	0.0408248
$601$	−25.7970	−1.05228	−0.526140	−	0.850398i	$-0.676361\pi$
$601$	−25.7970	−1.05228	−0.526140	+	0.850398i	$0.676361\pi$
$602$	−9.94792	−0.405447
$603$	14.4169	0.587103
$604$	−1.58307	−0.0644142
$605$	−1.00000	−0.0406558
$606$	17.1879	0.698209
$607$	6.68291	0.271251	0.135625	−	0.990760i	$-0.456696\pi$
$607$	6.68291	0.271251	0.135625	+	0.990760i	$0.456696\pi$
$608$	0.203037	0.00823422
$609$	−7.59393	−0.307721
$610$	−8.41693	−0.340792
$611$	74.3974	3.00980
$612$	1.00000	0.0404226
$613$	20.6200	0.832833	0.416416	−	0.909174i	$-0.363286\pi$
$613$	20.6200	0.832833	0.416416	+	0.909174i	$0.363286\pi$
$614$	−15.3280	−0.618586
$615$	2.00000	0.0806478
$616$	3.79696	0.152984
$617$	−22.1401	−0.891327	−0.445663	−	0.895201i	$-0.647032\pi$
$617$	−22.1401	−0.891327	−0.445663	+	0.895201i	$0.647032\pi$
$618$	−6.01086	−0.241792
$619$	2.01086	0.0808232	0.0404116	−	0.999183i	$-0.487133\pi$
$619$	2.01086	0.0808232	0.0404116	+	0.999183i	$0.487133\pi$
$620$	−5.17700	−0.207913
$621$	−7.79696	−0.312881
$622$	−20.1618	−0.808415
$623$	69.9696	2.80327
$624$	5.79696	0.232064
$625$	1.00000	0.0400000
$626$	34.7926	1.39059
$627$	−0.203037	−0.00810850
$628$	14.8339	0.591935
$629$	−4.41693	−0.176115
$630$	3.79696	0.151275
$631$	−3.16614	−0.126042	−0.0630210	−	0.998012i	$-0.520074\pi$
$631$	−3.16614	−0.126042	−0.0630210	+	0.998012i	$0.520074\pi$
$632$	−6.21389	−0.247175
$633$	−11.5939	−0.460817
$634$	14.4278	0.573001
$635$	−16.0000	−0.634941
$636$	3.38003	0.134027
$637$	42.9957	1.70355
$638$	−2.00000	−0.0791808
$639$	10.2139	0.404055
$640$	−1.00000	−0.0395285
$641$	−9.32795	−0.368432	−0.184216	−	0.982886i	$-0.558975\pi$
$641$	−9.32795	−0.368432	−0.184216	+	0.982886i	$0.558975\pi$
$642$	−16.8339	−0.664379
$643$	11.1879	0.441206	0.220603	−	0.975364i	$-0.429198\pi$
$643$	11.1879	0.441206	0.220603	+	0.975364i	$0.429198\pi$
$644$	29.6048	1.16659
$645$	−2.61997	−0.103161
$646$	0.203037	0.00798837
$647$	−44.0217	−1.73067	−0.865336	−	0.501192i	$-0.832895\pi$
$647$	−44.0217	−1.73067	−0.865336	+	0.501192i	$0.832895\pi$
$648$	1.00000	0.0392837
$649$	−2.61997	−0.102843
$650$	5.79696	0.227376
$651$	−19.6569	−0.770413
$652$	−19.1879	−0.751454
$653$	−16.3540	−0.639981	−0.319991	−	0.947421i	$-0.603680\pi$
$653$	−16.3540	−0.639981	−0.319991	+	0.947421i	$0.603680\pi$
$654$	−7.17700	−0.280643
$655$	−13.1770	−0.514868
$656$	−2.00000	−0.0780869
$657$	10.9740	0.428135
$658$	−48.7297	−1.89968
$659$	−34.3540	−1.33824	−0.669121	−	0.743154i	$-0.733329\pi$
$659$	−34.3540	−1.33824	−0.669121	+	0.743154i	$0.733329\pi$
$660$	1.00000	0.0389249
$661$	17.2508	0.670978	0.335489	−	0.942044i	$-0.391098\pi$
$661$	17.2508	0.670978	0.335489	+	0.942044i	$0.391098\pi$
$662$	−11.1879	−0.434828
$663$	5.79696	0.225135
$664$	−2.82300	−0.109554
$665$	0.770923	0.0298951
$666$	−4.41693	−0.171153
$667$	−15.5939	−0.603799
$668$	−4.00000	−0.154765
$669$	14.0109	0.541691
$670$	−14.4169	−0.556975
$671$	−8.41693	−0.324932
$672$	−3.79696	−0.146471
$673$	13.7340	0.529408	0.264704	−	0.964330i	$-0.414726\pi$
$673$	13.7340	0.529408	0.264704	+	0.964330i	$0.414726\pi$
$674$	34.1618	1.31586
$675$	1.00000	0.0384900
$676$	20.6048	0.792492
$677$	−49.8958	−1.91765	−0.958826	−	0.283993i	$-0.908341\pi$
$677$	−49.8958	−1.91765	−0.958826	+	0.283993i	$0.908341\pi$
$678$	4.61997	0.177429
$679$	−56.0847	−2.15233
$680$	−1.00000	−0.0383482
$681$	8.83386	0.338514
$682$	−5.17700	−0.198237
$683$	−44.3648	−1.69757	−0.848787	−	0.528735i	$-0.822666\pi$
$683$	−44.3648	−1.69757	−0.848787	+	0.528735i	$0.822666\pi$
$684$	0.203037	0.00776330
$685$	12.0109	0.458911
$686$	−1.58307	−0.0604419
$687$	20.4169	0.778954
$688$	2.61997	0.0998853
$689$	19.5939	0.746469
$690$	7.79696	0.296825
$691$	−27.5527	−1.04815	−0.524077	−	0.851671i	$-0.675590\pi$
$691$	−27.5527	−1.04815	−0.524077	+	0.851671i	$0.675590\pi$
$692$	0.416930	0.0158493
$693$	3.79696	0.144235
$694$	−14.3540	−0.544870
$695$	−3.59393	−0.136325
$696$	2.00000	0.0758098
$697$	−2.00000	−0.0757554
$698$	−4.61997	−0.174868
$699$	22.4278	0.848297
$700$	−3.79696	−0.143512
$701$	−7.94792	−0.300189	−0.150094	−	0.988672i	$-0.547958\pi$
$701$	−7.94792	−0.300189	−0.150094	+	0.988672i	$0.547958\pi$
$702$	5.79696	0.218792
$703$	−0.896799	−0.0338234
$704$	−1.00000	−0.0376889
$705$	−12.8339	−0.483351
$706$	−17.6569	−0.664525
$707$	−65.2616	−2.45442
$708$	2.61997	0.0984644
$709$	−47.6677	−1.79020	−0.895099	−	0.445867i	$-0.852896\pi$
$709$	−47.6677	−1.79020	−0.895099	+	0.445867i	$0.852896\pi$
$710$	−10.2139	−0.383321
$711$	−6.21389	−0.233039
$712$	−18.4278	−0.690611
$713$	−40.3648	−1.51168
$714$	−3.79696	−0.142098
$715$	5.79696	0.216794
$716$	−1.44297	−0.0539264
$717$	4.83386	0.180524
$718$	28.0217	1.04576
$719$	28.1618	1.05026	0.525129	−	0.851023i	$-0.324017\pi$
$719$	28.1618	1.05026	0.525129	+	0.851023i	$0.324017\pi$
$720$	−1.00000	−0.0372678
$721$	22.8230	0.849973
$722$	−18.9588	−0.705573
$723$	−7.03690	−0.261705
$724$	9.59393	0.356555
$725$	2.00000	0.0742781
$726$	1.00000	0.0371135
$727$	13.5201	0.501434	0.250717	−	0.968060i	$-0.419334\pi$
$727$	13.5201	0.501434	0.250717	+	0.968060i	$0.419334\pi$
$728$	−22.0109	−0.815777
$729$	1.00000	0.0370370
$730$	−10.9740	−0.406164
$731$	2.61997	0.0969030
$732$	8.41693	0.311099
$733$	36.8589	1.36142	0.680708	−	0.732555i	$-0.261672\pi$
$733$	36.8589	1.36142	0.680708	+	0.732555i	$0.261672\pi$
$734$	−25.9479	−0.957755
$735$	−7.41693	−0.273578
$736$	−7.79696	−0.287400
$737$	−14.4169	−0.531054
$738$	−2.00000	−0.0736210
$739$	−5.44297	−0.200223	−0.100111	−	0.994976i	$-0.531920\pi$
$739$	−5.44297	−0.200223	−0.100111	+	0.994976i	$0.531920\pi$
$740$	4.41693	0.162370
$741$	1.17700	0.0432380
$742$	−12.8339	−0.471146
$743$	−8.42779	−0.309186	−0.154593	−	0.987978i	$-0.549407\pi$
$743$	−8.42779	−0.309186	−0.154593	+	0.987978i	$0.549407\pi$
$744$	5.17700	0.189798
$745$	19.6048	0.718264
$746$	−29.0478	−1.06351
$747$	−2.82300	−0.103288
$748$	−1.00000	−0.0365636
$749$	63.9176	2.33550
$750$	−1.00000	−0.0365148
$751$	21.9479	0.800891	0.400445	−	0.916321i	$-0.368855\pi$
$751$	21.9479	0.800891	0.400445	+	0.916321i	$0.368855\pi$
$752$	12.8339	0.468003
$753$	29.7449	1.08396
$754$	11.5939	0.422226
$755$	1.58307	0.0576138
$756$	−3.79696	−0.138094
$757$	13.6156	0.494869	0.247434	−	0.968905i	$-0.420413\pi$
$757$	13.6156	0.494869	0.247434	+	0.968905i	$0.420413\pi$
$758$	22.8447	0.829758
$759$	7.79696	0.283012
$760$	−0.203037	−0.00736491
$761$	−17.2508	−0.625341	−0.312670	−	0.949862i	$-0.601224\pi$
$761$	−17.2508	−0.625341	−0.312670	+	0.949862i	$0.601224\pi$
$762$	16.0000	0.579619
$763$	27.2508	0.986545
$764$	5.23993	0.189574
$765$	−1.00000	−0.0361551
$766$	−30.7818	−1.11219
$767$	15.1879	0.548402
$768$	1.00000	0.0360844
$769$	30.8339	1.11190	0.555949	−	0.831217i	$-0.312355\pi$
$769$	30.8339	1.11190	0.555949	+	0.831217i	$0.312355\pi$
$770$	−3.79696	−0.136833
$771$	1.18785	0.0427795
$772$	−6.97396	−0.250998
$773$	7.44297	0.267705	0.133853	−	0.991001i	$-0.457265\pi$
$773$	7.44297	0.267705	0.133853	+	0.991001i	$0.457265\pi$
$774$	2.61997	0.0941728
$775$	5.17700	0.185963
$776$	14.7709	0.530245
$777$	16.7709	0.601654
$778$	−21.4538	−0.769157
$779$	−0.406073	−0.0145491
$780$	−5.79696	−0.207565
$781$	−10.2139	−0.365482
$782$	−7.79696	−0.278819
$783$	2.00000	0.0714742
$784$	7.41693	0.264890
$785$	−14.8339	−0.529443
$786$	13.1770	0.470008
$787$	26.0109	0.927187	0.463593	−	0.886048i	$-0.346560\pi$
$787$	26.0109	0.927187	0.463593	+	0.886048i	$0.346560\pi$
$788$	26.3648	0.939209
$789$	−22.0109	−0.783607
$790$	6.21389	0.221080
$791$	−17.5418	−0.623716
$792$	−1.00000	−0.0355335
$793$	48.7926	1.73268
$794$	2.00000	0.0709773
$795$	−3.38003	−0.119877
$796$	−25.1987	−0.893145
$797$	7.03690	0.249260	0.124630	−	0.992203i	$-0.460226\pi$
$797$	7.03690	0.249260	0.124630	+	0.992203i	$0.460226\pi$
$798$	−0.770923	−0.0272904
$799$	12.8339	0.454029
$800$	1.00000	0.0353553
$801$	−18.4278	−0.651114
$802$	−29.7970	−1.05217
$803$	−10.9740	−0.387263
$804$	14.4169	0.508446
$805$	−29.6048	−1.04343
$806$	30.0109	1.05709
$807$	20.8447	0.733769
$808$	17.1879	0.604667
$809$	−7.23993	−0.254543	−0.127271	−	0.991868i	$-0.540622\pi$
$809$	−7.23993	−0.254543	−0.127271	+	0.991868i	$0.540622\pi$
$810$	−1.00000	−0.0351364
$811$	21.5418	0.756437	0.378218	−	0.925716i	$-0.376537\pi$
$811$	21.5418	0.756437	0.378218	+	0.925716i	$0.376537\pi$
$812$	−7.59393	−0.266495
$813$	−7.18785	−0.252089
$814$	4.41693	0.154813
$815$	19.1879	0.672121
$816$	1.00000	0.0350070
$817$	0.531949	0.0186106
$818$	−16.7601	−0.586002
$819$	−22.0109	−0.769122
$820$	2.00000	0.0698430
$821$	35.1358	1.22625	0.613123	−	0.789987i	$-0.289913\pi$
$821$	35.1358	1.22625	0.613123	+	0.789987i	$0.289913\pi$
$822$	−12.0109	−0.418927
$823$	−52.0217	−1.81336	−0.906681	−	0.421816i	$-0.861393\pi$
$823$	−52.0217	−1.81336	−0.906681	+	0.421816i	$0.861393\pi$
$824$	−6.01086	−0.209398
$825$	−1.00000	−0.0348155
$826$	−9.94792	−0.346132
$827$	23.1661	0.805566	0.402783	−	0.915296i	$-0.368043\pi$
$827$	23.1661	0.805566	0.402783	+	0.915296i	$0.368043\pi$
$828$	−7.79696	−0.270963
$829$	54.4083	1.88968	0.944839	−	0.327536i	$-0.106218\pi$
$829$	54.4083	1.88968	0.944839	+	0.327536i	$0.106218\pi$
$830$	2.82300	0.0979879
$831$	−3.64601	−0.126479
$832$	5.79696	0.200974
$833$	7.41693	0.256981
$834$	3.59393	0.124448
$835$	4.00000	0.138426
$836$	−0.203037	−0.00702217
$837$	5.17700	0.178943
$838$	−4.00000	−0.138178
$839$	35.7557	1.23443	0.617213	−	0.786796i	$-0.288262\pi$
$839$	35.7557	1.23443	0.617213	+	0.786796i	$0.288262\pi$
$840$	3.79696	0.131008
$841$	−25.0000	−0.862069
$842$	7.17700	0.247336
$843$	11.9479	0.411508
$844$	−11.5939	−0.399079
$845$	−20.6048	−0.708826
$846$	12.8339	0.441237
$847$	−3.79696	−0.130465
$848$	3.38003	0.116071
$849$	−6.76007	−0.232005
$850$	1.00000	0.0342997
$851$	34.4386	1.18054
$852$	10.2139	0.349922
$853$	32.5016	1.11283	0.556416	−	0.830904i	$-0.312176\pi$
$853$	32.5016	1.11283	0.556416	+	0.830904i	$0.312176\pi$
$854$	−31.9588	−1.09361
$855$	−0.203037	−0.00694371
$856$	−16.8339	−0.575370
$857$	−22.4907	−0.768269	−0.384134	−	0.923277i	$-0.625500\pi$
$857$	−22.4907	−0.768269	−0.384134	+	0.923277i	$0.625500\pi$
$858$	−5.79696	−0.197905
$859$	−32.7080	−1.11598	−0.557991	−	0.829847i	$-0.688428\pi$
$859$	−32.7080	−1.11598	−0.557991	+	0.829847i	$0.688428\pi$
$860$	−2.61997	−0.0893401
$861$	7.59393	0.258800
$862$	−8.00000	−0.272481
$863$	−49.1358	−1.67260	−0.836301	−	0.548271i	$-0.815286\pi$
$863$	−49.1358	−1.67260	−0.836301	+	0.548271i	$0.815286\pi$
$864$	1.00000	0.0340207
$865$	−0.416930	−0.0141761
$866$	−10.4278	−0.354351
$867$	1.00000	0.0339618
$868$	−19.6569	−0.667197
$869$	6.21389	0.210792
$870$	−2.00000	−0.0678064
$871$	83.5744	2.83181
$872$	−7.17700	−0.243044
$873$	14.7709	0.499920
$874$	−1.58307	−0.0535481
$875$	3.79696	0.128361
$876$	10.9740	0.370776
$877$	−26.0217	−0.878691	−0.439345	−	0.898318i	$-0.644790\pi$
$877$	−26.0217	−0.878691	−0.439345	+	0.898318i	$0.644790\pi$
$878$	−7.02604	−0.237117
$879$	24.3540	0.821440
$880$	1.00000	0.0337100
$881$	−33.8599	−1.14077	−0.570385	−	0.821378i	$-0.693206\pi$
$881$	−33.8599	−1.14077	−0.570385	+	0.821378i	$0.693206\pi$
$882$	7.41693	0.249741
$883$	−33.6677	−1.13301	−0.566505	−	0.824059i	$-0.691705\pi$
$883$	−33.6677	−1.13301	−0.566505	+	0.824059i	$0.691705\pi$
$884$	5.79696	0.194973
$885$	−2.61997	−0.0880692
$886$	−27.4538	−0.922329
$887$	−45.6677	−1.53337	−0.766686	−	0.642022i	$-0.778096\pi$
$887$	−45.6677	−1.53337	−0.766686	+	0.642022i	$0.778096\pi$
$888$	−4.41693	−0.148222
$889$	−60.7514	−2.03754
$890$	18.4278	0.617701
$891$	−1.00000	−0.0335013
$892$	14.0109	0.469118
$893$	2.60574	0.0871979
$894$	−19.6048	−0.655682
$895$	1.44297	0.0482332
$896$	−3.79696	−0.126848
$897$	−45.1987	−1.50914
$898$	−36.5787	−1.22065
$899$	10.3540	0.345325
$900$	1.00000	0.0333333
$901$	3.38003	0.112605
$902$	2.00000	0.0665927
$903$	−9.94792	−0.331046
$904$	4.61997	0.153658
$905$	−9.59393	−0.318913
$906$	−1.58307	−0.0525940
$907$	5.66772	0.188194	0.0940968	−	0.995563i	$-0.470004\pi$
$907$	5.66772	0.188194	0.0940968	+	0.995563i	$0.470004\pi$
$908$	8.83386	0.293162
$909$	17.1879	0.570085
$910$	22.0109	0.729653
$911$	15.0478	0.498554	0.249277	−	0.968432i	$-0.419807\pi$
$911$	15.0478	0.498554	0.249277	+	0.968432i	$0.419807\pi$
$912$	0.203037	0.00672322
$913$	2.82300	0.0934278
$914$	−27.6048	−0.913085
$915$	−8.41693	−0.278255
$916$	20.4169	0.674594
$917$	−50.0326	−1.65222
$918$	1.00000	0.0330049
$919$	−2.39522	−0.0790109	−0.0395054	−	0.999219i	$-0.512578\pi$
$919$	−2.39522	−0.0790109	−0.0395054	+	0.999219i	$0.512578\pi$
$920$	7.79696	0.257058
$921$	−15.3280	−0.505073
$922$	27.9479	0.920416
$923$	59.2096	1.94891
$924$	3.79696	0.124911
$925$	−4.41693	−0.145228
$926$	4.34314	0.142724
$927$	−6.01086	−0.197422
$928$	2.00000	0.0656532
$929$	43.4647	1.42603	0.713015	−	0.701149i	$-0.247329\pi$
$929$	43.4647	1.42603	0.713015	+	0.701149i	$0.247329\pi$
$930$	−5.17700	−0.169760
$931$	1.50591	0.0493542
$932$	22.4278	0.734647
$933$	−20.1618	−0.660068
$934$	−24.2877	−0.794717
$935$	1.00000	0.0327035
$936$	5.79696	0.189480
$937$	13.2508	0.432884	0.216442	−	0.976295i	$-0.430555\pi$
$937$	13.2508	0.432884	0.216442	+	0.976295i	$0.430555\pi$
$938$	−54.7406	−1.78734
$939$	34.7926	1.13541
$940$	−12.8339	−0.418594
$941$	−35.9696	−1.17258	−0.586288	−	0.810103i	$-0.699411\pi$
$941$	−35.9696	−1.17258	−0.586288	+	0.810103i	$0.699411\pi$
$942$	14.8339	0.483313
$943$	15.5939	0.507808
$944$	2.61997	0.0852727
$945$	3.79696	0.123515
$946$	−2.61997	−0.0851825
$947$	23.6156	0.767405	0.383703	−	0.923457i	$-0.374649\pi$
$947$	23.6156	0.767405	0.383703	+	0.923457i	$0.374649\pi$
$948$	−6.21389	−0.201818
$949$	63.6156	2.06505
$950$	0.203037	0.00658738
$951$	14.4278	0.467853
$952$	−3.79696	−0.123060
$953$	−12.7818	−0.414042	−0.207021	−	0.978336i	$-0.566377\pi$
$953$	−12.7818	−0.414042	−0.207021	+	0.978336i	$0.566377\pi$
$954$	3.38003	0.109433
$955$	−5.23993	−0.169560
$956$	4.83386	0.156338
$957$	−2.00000	−0.0646508
$958$	−27.1249	−0.876366
$959$	45.6048	1.47266
$960$	−1.00000	−0.0322749
$961$	−4.19871	−0.135442
$962$	−25.6048	−0.825531
$963$	−16.8339	−0.542464
$964$	−7.03690	−0.226643
$965$	6.97396	0.224500
$966$	29.6048	0.952518
$967$	−4.02171	−0.129330	−0.0646648	−	0.997907i	$-0.520598\pi$
$967$	−4.02171	−0.129330	−0.0646648	+	0.997907i	$0.520598\pi$
$968$	1.00000	0.0321412
$969$	0.203037	0.00652248
$970$	−14.7709	−0.474266
$971$	41.4864	1.33136	0.665681	−	0.746236i	$-0.268141\pi$
$971$	41.4864	1.33136	0.665681	+	0.746236i	$0.268141\pi$
$972$	1.00000	0.0320750
$973$	−13.6460	−0.437471
$974$	25.9479	0.831425
$975$	5.79696	0.185651
$976$	8.41693	0.269419
$977$	13.5310	0.432895	0.216447	−	0.976294i	$-0.430553\pi$
$977$	13.5310	0.432895	0.216447	+	0.976294i	$0.430553\pi$
$978$	−19.1879	−0.613560
$979$	18.4278	0.588955
$980$	−7.41693	−0.236925
$981$	−7.17700	−0.229144
$982$	−28.0217	−0.894209
$983$	−24.2877	−0.774657	−0.387328	−	0.921942i	$-0.626602\pi$
$983$	−24.2877	−0.774657	−0.387328	+	0.921942i	$0.626602\pi$
$984$	−2.00000	−0.0637577
$985$	−26.3648	−0.840054
$986$	2.00000	0.0636930
$987$	−48.7297	−1.55108
$988$	1.17700	0.0374452
$989$	−20.4278	−0.649566
$990$	1.00000	0.0317821
$991$	−9.60478	−0.305106	−0.152553	−	0.988295i	$-0.548749\pi$
$991$	−9.60478	−0.305106	−0.152553	+	0.988295i	$0.548749\pi$
$992$	5.17700	0.164370
$993$	−11.1879	−0.355036
$994$	−38.7818	−1.23008
$995$	25.1987	0.798853
$996$	−2.82300	−0.0894503
$997$	20.7601	0.657478	0.328739	−	0.944421i	$-0.393376\pi$
$997$	20.7601	0.657478	0.328739	+	0.944421i	$0.393376\pi$
$998$	1.52013	0.0481189
$999$	−4.41693	−0.139745

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5610.2.a.cd.1.1	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -3.79696 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} -3.79696 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{11} +1.00000 q^{12} +5.79696 q^{13} -3.79696 q^{14} -1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} +0.203037 q^{19} -1.00000 q^{20} -3.79696 q^{21} -1.00000 q^{22} -7.79696 q^{23} +1.00000 q^{24} +1.00000 q^{25} +5.79696 q^{26} +1.00000 q^{27} -3.79696 q^{28} +2.00000 q^{29} -1.00000 q^{30} +5.17700 q^{31} +1.00000 q^{32} -1.00000 q^{33} +1.00000 q^{34} +3.79696 q^{35} +1.00000 q^{36} -4.41693 q^{37} +0.203037 q^{38} +5.79696 q^{39} -1.00000 q^{40} -2.00000 q^{41} -3.79696 q^{42} +2.61997 q^{43} -1.00000 q^{44} -1.00000 q^{45} -7.79696 q^{46} +12.8339 q^{47} +1.00000 q^{48} +7.41693 q^{49} +1.00000 q^{50} +1.00000 q^{51} +5.79696 q^{52} +3.38003 q^{53} +1.00000 q^{54} +1.00000 q^{55} -3.79696 q^{56} +0.203037 q^{57} +2.00000 q^{58} +2.61997 q^{59} -1.00000 q^{60} +8.41693 q^{61} +5.17700 q^{62} -3.79696 q^{63} +1.00000 q^{64} -5.79696 q^{65} -1.00000 q^{66} +14.4169 q^{67} +1.00000 q^{68} -7.79696 q^{69} +3.79696 q^{70} +10.2139 q^{71} +1.00000 q^{72} +10.9740 q^{73} -4.41693 q^{74} +1.00000 q^{75} +0.203037 q^{76} +3.79696 q^{77} +5.79696 q^{78} -6.21389 q^{79} -1.00000 q^{80} +1.00000 q^{81} -2.00000 q^{82} -2.82300 q^{83} -3.79696 q^{84} -1.00000 q^{85} +2.61997 q^{86} +2.00000 q^{87} -1.00000 q^{88} -18.4278 q^{89} -1.00000 q^{90} -22.0109 q^{91} -7.79696 q^{92} +5.17700 q^{93} +12.8339 q^{94} -0.203037 q^{95} +1.00000 q^{96} +14.7709 q^{97} +7.41693 q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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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