LMFDB - Embedded newform 4641.2.a.w.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4641,2,Mod(1,4641)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4641, 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("4641.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4641 = 3 \cdot 7 \cdot 13 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4641.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:	$37.0585715781$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 22 x^{12} + 19 x^{11} + 187 x^{10} - 135 x^{9} - 776 x^{8} + 443 x^{7} + 1636 x^{6} + \cdots - 19 $ x^14 - x^13 - 22x^12 + 19x^11 + 187x^10 - 135x^9 - 776x^8 + 443x^7 + 1636x^6 - 648x^5 - 1635x^4 + 306x^3 + 604x^2 + 8x - 19
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.86457$ of defining polynomial
Character	$\chi$	$=$	4641.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.86457 q^{2} -1.00000 q^{3} +1.47663 q^{4} +3.72897 q^{5} +1.86457 q^{6} +1.00000 q^{7} +0.975863 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.86457 q^{2} -1.00000 q^{3} +1.47663 q^{4} +3.72897 q^{5} +1.86457 q^{6} +1.00000 q^{7} +0.975863 q^{8} +1.00000 q^{9} -6.95294 q^{10} +3.68206 q^{11} -1.47663 q^{12} +1.00000 q^{13} -1.86457 q^{14} -3.72897 q^{15} -4.77282 q^{16} +1.00000 q^{17} -1.86457 q^{18} +0.0317573 q^{19} +5.50631 q^{20} -1.00000 q^{21} -6.86546 q^{22} -0.593453 q^{23} -0.975863 q^{24} +8.90524 q^{25} -1.86457 q^{26} -1.00000 q^{27} +1.47663 q^{28} +1.98888 q^{29} +6.95294 q^{30} -2.22268 q^{31} +6.94755 q^{32} -3.68206 q^{33} -1.86457 q^{34} +3.72897 q^{35} +1.47663 q^{36} -0.430951 q^{37} -0.0592137 q^{38} -1.00000 q^{39} +3.63897 q^{40} -5.10754 q^{41} +1.86457 q^{42} -4.54395 q^{43} +5.43703 q^{44} +3.72897 q^{45} +1.10654 q^{46} +9.18727 q^{47} +4.77282 q^{48} +1.00000 q^{49} -16.6045 q^{50} -1.00000 q^{51} +1.47663 q^{52} +0.179536 q^{53} +1.86457 q^{54} +13.7303 q^{55} +0.975863 q^{56} -0.0317573 q^{57} -3.70842 q^{58} +8.15063 q^{59} -5.50631 q^{60} -1.32145 q^{61} +4.14434 q^{62} +1.00000 q^{63} -3.40856 q^{64} +3.72897 q^{65} +6.86546 q^{66} +2.06837 q^{67} +1.47663 q^{68} +0.593453 q^{69} -6.95294 q^{70} +12.8741 q^{71} +0.975863 q^{72} -5.61088 q^{73} +0.803539 q^{74} -8.90524 q^{75} +0.0468937 q^{76} +3.68206 q^{77} +1.86457 q^{78} +4.67937 q^{79} -17.7977 q^{80} +1.00000 q^{81} +9.52337 q^{82} +12.5843 q^{83} -1.47663 q^{84} +3.72897 q^{85} +8.47252 q^{86} -1.98888 q^{87} +3.59318 q^{88} +3.63953 q^{89} -6.95294 q^{90} +1.00000 q^{91} -0.876310 q^{92} +2.22268 q^{93} -17.1303 q^{94} +0.118422 q^{95} -6.94755 q^{96} +11.8594 q^{97} -1.86457 q^{98} +3.68206 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - q^{2} - 14 q^{3} + 17 q^{4} - q^{5} + q^{6} + 14 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) $ 14 * q - q^2 - 14 * q^3 + 17 * q^4 - q^5 + q^6 + 14 * q^7 - 6 * q^8 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 17 q^{4} - q^{5} + q^{6} + 14 q^{7} - 6 q^{8} + 14 q^{9} + 11 q^{10} - 4 q^{11} - 17 q^{12} + 14 q^{13} - q^{14} + q^{15} + 19 q^{16} + 14 q^{17} - q^{18} + 6 q^{19} + q^{20} - 14 q^{21} + 12 q^{22} + 7 q^{23} + 6 q^{24} + 19 q^{25} - q^{26} - 14 q^{27} + 17 q^{28} - 4 q^{29} - 11 q^{30} + 31 q^{31} - 18 q^{32} + 4 q^{33} - q^{34} - q^{35} + 17 q^{36} + 2 q^{37} + 9 q^{38} - 14 q^{39} + 50 q^{40} + 4 q^{41} + q^{42} + 14 q^{43} - 8 q^{44} - q^{45} - 17 q^{46} - q^{47} - 19 q^{48} + 14 q^{49} - 3 q^{50} - 14 q^{51} + 17 q^{52} - 43 q^{53} + q^{54} + 23 q^{55} - 6 q^{56} - 6 q^{57} - 10 q^{58} + 11 q^{59} - q^{60} + 25 q^{61} - 3 q^{62} + 14 q^{63} + 36 q^{64} - q^{65} - 12 q^{66} + 11 q^{67} + 17 q^{68} - 7 q^{69} + 11 q^{70} + 20 q^{71} - 6 q^{72} + 14 q^{73} - 24 q^{74} - 19 q^{75} + 9 q^{76} - 4 q^{77} + q^{78} + 42 q^{79} + 13 q^{80} + 14 q^{81} + 2 q^{82} + 15 q^{83} - 17 q^{84} - q^{85} - 11 q^{86} + 4 q^{87} + 63 q^{88} + 21 q^{89} + 11 q^{90} + 14 q^{91} + 30 q^{92} - 31 q^{93} - 29 q^{94} + 16 q^{95} + 18 q^{96} + 15 q^{97} - q^{98} - 4 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 17 * q^4 - q^5 + q^6 + 14 * q^7 - 6 * q^8 + 14 * q^9 + 11 * q^10 - 4 * q^11 - 17 * q^12 + 14 * q^13 - q^14 + q^15 + 19 * q^16 + 14 * q^17 - q^18 + 6 * q^19 + q^20 - 14 * q^21 + 12 * q^22 + 7 * q^23 + 6 * q^24 + 19 * q^25 - q^26 - 14 * q^27 + 17 * q^28 - 4 * q^29 - 11 * q^30 + 31 * q^31 - 18 * q^32 + 4 * q^33 - q^34 - q^35 + 17 * q^36 + 2 * q^37 + 9 * q^38 - 14 * q^39 + 50 * q^40 + 4 * q^41 + q^42 + 14 * q^43 - 8 * q^44 - q^45 - 17 * q^46 - q^47 - 19 * q^48 + 14 * q^49 - 3 * q^50 - 14 * q^51 + 17 * q^52 - 43 * q^53 + q^54 + 23 * q^55 - 6 * q^56 - 6 * q^57 - 10 * q^58 + 11 * q^59 - q^60 + 25 * q^61 - 3 * q^62 + 14 * q^63 + 36 * q^64 - q^65 - 12 * q^66 + 11 * q^67 + 17 * q^68 - 7 * q^69 + 11 * q^70 + 20 * q^71 - 6 * q^72 + 14 * q^73 - 24 * q^74 - 19 * q^75 + 9 * q^76 - 4 * q^77 + q^78 + 42 * q^79 + 13 * q^80 + 14 * q^81 + 2 * q^82 + 15 * q^83 - 17 * q^84 - q^85 - 11 * q^86 + 4 * q^87 + 63 * q^88 + 21 * q^89 + 11 * q^90 + 14 * q^91 + 30 * q^92 - 31 * q^93 - 29 * q^94 + 16 * q^95 + 18 * q^96 + 15 * q^97 - q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.86457	−1.31845	−0.659226	−	0.751945i	$-0.729116\pi$
$2$	−1.86457	−1.31845	−0.659226	+	0.751945i	$0.729116\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.47663	0.738315
$5$	3.72897	1.66765	0.833824	−	0.552031i	$-0.186147\pi$
$5$	3.72897	1.66765	0.833824	+	0.552031i	$0.186147\pi$
$6$	1.86457	0.761208
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.975863	0.345020
$9$	1.00000	0.333333
$10$	−6.95294	−2.19871
$11$	3.68206	1.11018	0.555091	−	0.831790i	$-0.312683\pi$
$11$	3.68206	1.11018	0.555091	+	0.831790i	$0.312683\pi$
$12$	−1.47663	−0.426266
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.86457	−0.498328
$15$	−3.72897	−0.962817
$16$	−4.77282	−1.19321
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.86457	−0.439484
$19$	0.0317573	0.00728562	0.00364281	−	0.999993i	$-0.498840\pi$
$19$	0.0317573	0.00728562	0.00364281	+	0.999993i	$0.498840\pi$
$20$	5.50631	1.23125
$21$	−1.00000	−0.218218
$22$	−6.86546	−1.46372
$23$	−0.593453	−0.123744	−0.0618718	−	0.998084i	$-0.519707\pi$
$23$	−0.593453	−0.123744	−0.0618718	+	0.998084i	$0.519707\pi$
$24$	−0.975863	−0.199197
$25$	8.90524	1.78105
$26$	−1.86457	−0.365673
$27$	−1.00000	−0.192450
$28$	1.47663	0.279057
$29$	1.98888	0.369326	0.184663	−	0.982802i	$-0.440881\pi$
$29$	1.98888	0.369326	0.184663	+	0.982802i	$0.440881\pi$
$30$	6.95294	1.26943
$31$	−2.22268	−0.399205	−0.199602	−	0.979877i	$-0.563965\pi$
$31$	−2.22268	−0.399205	−0.199602	+	0.979877i	$0.563965\pi$
$32$	6.94755	1.22816
$33$	−3.68206	−0.640964
$34$	−1.86457	−0.319771
$35$	3.72897	0.630312
$36$	1.47663	0.246105
$37$	−0.430951	−0.0708479	−0.0354240	−	0.999372i	$-0.511278\pi$
$37$	−0.430951	−0.0708479	−0.0354240	+	0.999372i	$0.511278\pi$
$38$	−0.0592137	−0.00960574
$39$	−1.00000	−0.160128
$40$	3.63897	0.575371
$41$	−5.10754	−0.797663	−0.398832	−	0.917024i	$-0.630584\pi$
$41$	−5.10754	−0.797663	−0.398832	+	0.917024i	$0.630584\pi$
$42$	1.86457	0.287710
$43$	−4.54395	−0.692946	−0.346473	−	0.938060i	$-0.612621\pi$
$43$	−4.54395	−0.692946	−0.346473	+	0.938060i	$0.612621\pi$
$44$	5.43703	0.819664
$45$	3.72897	0.555883
$46$	1.10654	0.163150
$47$	9.18727	1.34010	0.670051	−	0.742315i	$-0.266272\pi$
$47$	9.18727	1.34010	0.670051	+	0.742315i	$0.266272\pi$
$48$	4.77282	0.688898
$49$	1.00000	0.142857
$50$	−16.6045	−2.34823
$51$	−1.00000	−0.140028
$52$	1.47663	0.204772
$53$	0.179536	0.0246612	0.0123306	−	0.999924i	$-0.496075\pi$
$53$	0.179536	0.0246612	0.0123306	+	0.999924i	$0.496075\pi$
$54$	1.86457	0.253736
$55$	13.7303	1.85139
$56$	0.975863	0.130405
$57$	−0.0317573	−0.00420636
$58$	−3.70842	−0.486939
$59$	8.15063	1.06112	0.530561	−	0.847647i	$-0.321981\pi$
$59$	8.15063	1.06112	0.530561	+	0.847647i	$0.321981\pi$
$60$	−5.50631	−0.710862
$61$	−1.32145	−0.169195	−0.0845975	−	0.996415i	$-0.526960\pi$
$61$	−1.32145	−0.169195	−0.0845975	+	0.996415i	$0.526960\pi$
$62$	4.14434	0.526332
$63$	1.00000	0.125988
$64$	−3.40856	−0.426070
$65$	3.72897	0.462522
$66$	6.86546	0.845080
$67$	2.06837	0.252692	0.126346	−	0.991986i	$-0.459675\pi$
$67$	2.06837	0.252692	0.126346	+	0.991986i	$0.459675\pi$
$68$	1.47663	0.179068
$69$	0.593453	0.0714434
$70$	−6.95294	−0.831035
$71$	12.8741	1.52787	0.763936	−	0.645292i	$-0.223264\pi$
$71$	12.8741	1.52787	0.763936	+	0.645292i	$0.223264\pi$
$72$	0.975863	0.115007
$73$	−5.61088	−0.656704	−0.328352	−	0.944555i	$-0.606493\pi$
$73$	−5.61088	−0.656704	−0.328352	+	0.944555i	$0.606493\pi$
$74$	0.803539	0.0934096
$75$	−8.90524	−1.02829
$76$	0.0468937	0.00537908
$77$	3.68206	0.419609
$78$	1.86457	0.211121
$79$	4.67937	0.526471	0.263235	−	0.964732i	$-0.415210\pi$
$79$	4.67937	0.526471	0.263235	+	0.964732i	$0.415210\pi$
$80$	−17.7977	−1.98985
$81$	1.00000	0.111111
$82$	9.52337	1.05168
$83$	12.5843	1.38131	0.690655	−	0.723184i	$-0.257322\pi$
$83$	12.5843	1.38131	0.690655	+	0.723184i	$0.257322\pi$
$84$	−1.47663	−0.161113
$85$	3.72897	0.404464
$86$	8.47252	0.913616
$87$	−1.98888	−0.213231
$88$	3.59318	0.383035
$89$	3.63953	0.385789	0.192894	−	0.981220i	$-0.438212\pi$
$89$	3.63953	0.385789	0.192894	+	0.981220i	$0.438212\pi$
$90$	−6.95294	−0.732904
$91$	1.00000	0.104828
$92$	−0.876310	−0.0913616
$93$	2.22268	0.230481
$94$	−17.1303	−1.76686
$95$	0.118422	0.0121498
$96$	−6.94755	−0.709081
$97$	11.8594	1.20414	0.602072	−	0.798442i	$-0.294342\pi$
$97$	11.8594	1.20414	0.602072	+	0.798442i	$0.294342\pi$
$98$	−1.86457	−0.188350
$99$	3.68206	0.370061
$100$	13.1497	1.31497
$101$	−15.9760	−1.58967	−0.794836	−	0.606825i	$-0.792443\pi$
$101$	−15.9760	−1.58967	−0.794836	+	0.606825i	$0.792443\pi$
$102$	1.86457	0.184620
$103$	2.00129	0.197193	0.0985967	−	0.995127i	$-0.468565\pi$
$103$	2.00129	0.197193	0.0985967	+	0.995127i	$0.468565\pi$
$104$	0.975863	0.0956912
$105$	−3.72897	−0.363911
$106$	−0.334758	−0.0325146
$107$	3.22017	0.311305	0.155653	−	0.987812i	$-0.450252\pi$
$107$	3.22017	0.311305	0.155653	+	0.987812i	$0.450252\pi$
$108$	−1.47663	−0.142089
$109$	17.3573	1.66253	0.831265	−	0.555876i	$-0.187617\pi$
$109$	17.3573	1.66253	0.831265	+	0.555876i	$0.187617\pi$
$110$	−25.6011	−2.44097
$111$	0.430951	0.0409041
$112$	−4.77282	−0.450990
$113$	−8.82964	−0.830623	−0.415311	−	0.909679i	$-0.636327\pi$
$113$	−8.82964	−0.830623	−0.415311	+	0.909679i	$0.636327\pi$
$114$	0.0592137	0.00554588
$115$	−2.21297	−0.206361
$116$	2.93684	0.272679
$117$	1.00000	0.0924500
$118$	−15.1974	−1.39904
$119$	1.00000	0.0916698
$120$	−3.63897	−0.332191
$121$	2.55755	0.232505
$122$	2.46395	0.223075
$123$	5.10754	0.460531
$124$	−3.28207	−0.294739
$125$	14.5626	1.30251
$126$	−1.86457	−0.166109
$127$	−12.2156	−1.08396	−0.541980	−	0.840391i	$-0.682325\pi$
$127$	−12.2156	−1.08396	−0.541980	+	0.840391i	$0.682325\pi$
$128$	−7.53960	−0.666412
$129$	4.54395	0.400073
$130$	−6.95294	−0.609813
$131$	−8.45399	−0.738629	−0.369314	−	0.929305i	$-0.620407\pi$
$131$	−8.45399	−0.738629	−0.369314	+	0.929305i	$0.620407\pi$
$132$	−5.43703	−0.473233
$133$	0.0317573	0.00275371
$134$	−3.85663	−0.333162
$135$	−3.72897	−0.320939
$136$	0.975863	0.0836795
$137$	−13.4455	−1.14873	−0.574365	−	0.818599i	$-0.694751\pi$
$137$	−13.4455	−1.14873	−0.574365	+	0.818599i	$0.694751\pi$
$138$	−1.10654	−0.0941946
$139$	6.42635	0.545076	0.272538	−	0.962145i	$-0.412137\pi$
$139$	6.42635	0.545076	0.272538	+	0.962145i	$0.412137\pi$
$140$	5.50631	0.465368
$141$	−9.18727	−0.773708
$142$	−24.0047	−2.01443
$143$	3.68206	0.307909
$144$	−4.77282	−0.397735
$145$	7.41649	0.615906
$146$	10.4619	0.865832
$147$	−1.00000	−0.0824786
$148$	−0.636355	−0.0523081
$149$	−8.97612	−0.735352	−0.367676	−	0.929954i	$-0.619846\pi$
$149$	−8.97612	−0.735352	−0.367676	+	0.929954i	$0.619846\pi$
$150$	16.6045	1.35575
$151$	−2.91212	−0.236985	−0.118493	−	0.992955i	$-0.537806\pi$
$151$	−2.91212	−0.236985	−0.118493	+	0.992955i	$0.537806\pi$
$152$	0.0309908	0.00251368
$153$	1.00000	0.0808452
$154$	−6.86546	−0.553235
$155$	−8.28831	−0.665733
$156$	−1.47663	−0.118225
$157$	−0.120793	−0.00964029	−0.00482015	−	0.999988i	$-0.501534\pi$
$157$	−0.120793	−0.00964029	−0.00482015	+	0.999988i	$0.501534\pi$
$158$	−8.72503	−0.694126
$159$	−0.179536	−0.0142381
$160$	25.9072	2.04815
$161$	−0.593453	−0.0467707
$162$	−1.86457	−0.146495
$163$	9.23630	0.723443	0.361721	−	0.932286i	$-0.382189\pi$
$163$	9.23630	0.723443	0.361721	+	0.932286i	$0.382189\pi$
$164$	−7.54194	−0.588926
$165$	−13.7303	−1.06890
$166$	−23.4644	−1.82119
$167$	1.31275	0.101584	0.0507919	−	0.998709i	$-0.483825\pi$
$167$	1.31275	0.101584	0.0507919	+	0.998709i	$0.483825\pi$
$168$	−0.975863	−0.0752894
$169$	1.00000	0.0769231
$170$	−6.95294	−0.533266
$171$	0.0317573	0.00242854
$172$	−6.70973	−0.511612
$173$	−5.56872	−0.423382	−0.211691	−	0.977337i	$-0.567897\pi$
$173$	−5.56872	−0.423382	−0.211691	+	0.977337i	$0.567897\pi$
$174$	3.70842	0.281134
$175$	8.90524	0.673173
$176$	−17.5738	−1.32468
$177$	−8.15063	−0.612639
$178$	−6.78616	−0.508644
$179$	−19.1724	−1.43301	−0.716507	−	0.697579i	$-0.754260\pi$
$179$	−19.1724	−1.43301	−0.716507	+	0.697579i	$0.754260\pi$
$180$	5.50631	0.410416
$181$	9.13043	0.678660	0.339330	−	0.940667i	$-0.389800\pi$
$181$	9.13043	0.678660	0.339330	+	0.940667i	$0.389800\pi$
$182$	−1.86457	−0.138211
$183$	1.32145	0.0976847
$184$	−0.579129	−0.0426939
$185$	−1.60701	−0.118149
$186$	−4.14434	−0.303878
$187$	3.68206	0.269259
$188$	13.5662	0.989416
$189$	−1.00000	−0.0727393
$190$	−0.220807	−0.0160190
$191$	−8.87699	−0.642317	−0.321158	−	0.947026i	$-0.604072\pi$
$191$	−8.87699	−0.642317	−0.321158	+	0.947026i	$0.604072\pi$
$192$	3.40856	0.245992
$193$	19.9837	1.43846	0.719229	−	0.694773i	$-0.244495\pi$
$193$	19.9837	1.43846	0.719229	+	0.694773i	$0.244495\pi$
$194$	−22.1128	−1.58761
$195$	−3.72897	−0.267037
$196$	1.47663	0.105474
$197$	−15.2011	−1.08303	−0.541517	−	0.840690i	$-0.682150\pi$
$197$	−15.2011	−1.08303	−0.541517	+	0.840690i	$0.682150\pi$
$198$	−6.86546	−0.487907
$199$	4.99552	0.354123	0.177062	−	0.984200i	$-0.443341\pi$
$199$	4.99552	0.354123	0.177062	+	0.984200i	$0.443341\pi$
$200$	8.69030	0.614497
$201$	−2.06837	−0.145892
$202$	29.7884	2.09590
$203$	1.98888	0.139592
$204$	−1.47663	−0.103385
$205$	−19.0459	−1.33022
$206$	−3.73156	−0.259990
$207$	−0.593453	−0.0412478
$208$	−4.77282	−0.330936
$209$	0.116932	0.00808837
$210$	6.95294	0.479798
$211$	14.2604	0.981729	0.490864	−	0.871236i	$-0.336681\pi$
$211$	14.2604	0.981729	0.490864	+	0.871236i	$0.336681\pi$
$212$	0.265108	0.0182077
$213$	−12.8741	−0.882117
$214$	−6.00423	−0.410441
$215$	−16.9443	−1.15559
$216$	−0.975863	−0.0663990
$217$	−2.22268	−0.150885
$218$	−32.3640	−2.19197
$219$	5.61088	0.379148
$220$	20.2746	1.36691
$221$	1.00000	0.0672673
$222$	−0.803539	−0.0539300
$223$	7.10561	0.475827	0.237913	−	0.971286i	$-0.423537\pi$
$223$	7.10561	0.475827	0.237913	+	0.971286i	$0.423537\pi$
$224$	6.94755	0.464203
$225$	8.90524	0.593683
$226$	16.4635	1.09514
$227$	3.48338	0.231200	0.115600	−	0.993296i	$-0.463121\pi$
$227$	3.48338	0.231200	0.115600	+	0.993296i	$0.463121\pi$
$228$	−0.0468937	−0.00310561
$229$	−1.32918	−0.0878350	−0.0439175	−	0.999035i	$-0.513984\pi$
$229$	−1.32918	−0.0878350	−0.0439175	+	0.999035i	$0.513984\pi$
$230$	4.12624	0.272076
$231$	−3.68206	−0.242262
$232$	1.94088	0.127425
$233$	−28.8238	−1.88831	−0.944155	−	0.329502i	$-0.893119\pi$
$233$	−28.8238	−1.88831	−0.944155	+	0.329502i	$0.893119\pi$
$234$	−1.86457	−0.121891
$235$	34.2591	2.23482
$236$	12.0355	0.783442
$237$	−4.67937	−0.303958
$238$	−1.86457	−0.120862
$239$	26.4403	1.71028	0.855141	−	0.518395i	$-0.173470\pi$
$239$	26.4403	1.71028	0.855141	+	0.518395i	$0.173470\pi$
$240$	17.7977	1.14884
$241$	3.37995	0.217722	0.108861	−	0.994057i	$-0.465280\pi$
$241$	3.37995	0.217722	0.108861	+	0.994057i	$0.465280\pi$
$242$	−4.76874	−0.306546
$243$	−1.00000	−0.0641500
$244$	−1.95130	−0.124919
$245$	3.72897	0.238235
$246$	−9.52337	−0.607188
$247$	0.0317573	0.00202067
$248$	−2.16903	−0.137733
$249$	−12.5843	−0.797500
$250$	−27.1529	−1.71730
$251$	18.9831	1.19820	0.599102	−	0.800673i	$-0.295524\pi$
$251$	18.9831	1.19820	0.599102	+	0.800673i	$0.295524\pi$
$252$	1.47663	0.0930189
$253$	−2.18513	−0.137378
$254$	22.7769	1.42915
$255$	−3.72897	−0.233517
$256$	20.8752	1.30470
$257$	−21.7906	−1.35926	−0.679629	−	0.733556i	$-0.737859\pi$
$257$	−21.7906	−1.35926	−0.679629	+	0.733556i	$0.737859\pi$
$258$	−8.47252	−0.527476
$259$	−0.430951	−0.0267780
$260$	5.50631	0.341487
$261$	1.98888	0.123109
$262$	15.7631	0.973846
$263$	−8.01097	−0.493977	−0.246989	−	0.969018i	$-0.579441\pi$
$263$	−8.01097	−0.493977	−0.246989	+	0.969018i	$0.579441\pi$
$264$	−3.59318	−0.221145
$265$	0.669486	0.0411262
$266$	−0.0592137	−0.00363063
$267$	−3.63953	−0.222735
$268$	3.05422	0.186566
$269$	−21.6431	−1.31960	−0.659802	−	0.751440i	$-0.729360\pi$
$269$	−21.6431	−1.31960	−0.659802	+	0.751440i	$0.729360\pi$
$270$	6.95294	0.423142
$271$	−10.1049	−0.613831	−0.306916	−	0.951737i	$-0.599297\pi$
$271$	−10.1049	−0.613831	−0.306916	+	0.951737i	$0.599297\pi$
$272$	−4.77282	−0.289395
$273$	−1.00000	−0.0605228
$274$	25.0702	1.51454
$275$	32.7896	1.97729
$276$	0.876310	0.0527477
$277$	−4.41799	−0.265451	−0.132726	−	0.991153i	$-0.542373\pi$
$277$	−4.41799	−0.265451	−0.132726	+	0.991153i	$0.542373\pi$
$278$	−11.9824	−0.718656
$279$	−2.22268	−0.133068
$280$	3.63897	0.217470
$281$	27.8118	1.65911	0.829557	−	0.558422i	$-0.188593\pi$
$281$	27.8118	1.65911	0.829557	+	0.558422i	$0.188593\pi$
$282$	17.1303	1.02010
$283$	−13.3680	−0.794645	−0.397323	−	0.917679i	$-0.630061\pi$
$283$	−13.3680	−0.794645	−0.397323	+	0.917679i	$0.630061\pi$
$284$	19.0102	1.12805
$285$	−0.118422	−0.00701472
$286$	−6.86546	−0.405963
$287$	−5.10754	−0.301488
$288$	6.94755	0.409388
$289$	1.00000	0.0588235
$290$	−13.8286	−0.812043
$291$	−11.8594	−0.695213
$292$	−8.28519	−0.484854
$293$	5.41414	0.316298	0.158149	−	0.987415i	$-0.449447\pi$
$293$	5.41414	0.316298	0.158149	+	0.987415i	$0.449447\pi$
$294$	1.86457	0.108744
$295$	30.3935	1.76958
$296$	−0.420549	−0.0244439
$297$	−3.68206	−0.213655
$298$	16.7366	0.969526
$299$	−0.593453	−0.0343203
$300$	−13.1497	−0.759201
$301$	−4.54395	−0.261909
$302$	5.42986	0.312454
$303$	15.9760	0.917797
$304$	−0.151572	−0.00869325
$305$	−4.92767	−0.282158
$306$	−1.86457	−0.106590
$307$	−1.84362	−0.105221	−0.0526104	−	0.998615i	$-0.516754\pi$
$307$	−1.84362	−0.105221	−0.0526104	+	0.998615i	$0.516754\pi$
$308$	5.43703	0.309804
$309$	−2.00129	−0.113850
$310$	15.4541	0.877737
$311$	19.3946	1.09977	0.549883	−	0.835242i	$-0.314672\pi$
$311$	19.3946	1.09977	0.549883	+	0.835242i	$0.314672\pi$
$312$	−0.975863	−0.0552473
$313$	−2.52994	−0.143001	−0.0715005	−	0.997441i	$-0.522779\pi$
$313$	−2.52994	−0.143001	−0.0715005	+	0.997441i	$0.522779\pi$
$314$	0.225226	0.0127103
$315$	3.72897	0.210104
$316$	6.90970	0.388701
$317$	−24.1014	−1.35367	−0.676834	−	0.736135i	$-0.736649\pi$
$317$	−24.1014	−1.35367	−0.676834	+	0.736135i	$0.736649\pi$
$318$	0.334758	0.0187723
$319$	7.32318	0.410020
$320$	−12.7104	−0.710534
$321$	−3.22017	−0.179732
$322$	1.10654	0.0616648
$323$	0.0317573	0.00176702
$324$	1.47663	0.0820350
$325$	8.90524	0.493974
$326$	−17.2217	−0.953824
$327$	−17.3573	−0.959863
$328$	−4.98426	−0.275209
$329$	9.18727	0.506511
$330$	25.6011	1.40930
$331$	6.07853	0.334106	0.167053	−	0.985948i	$-0.446575\pi$
$331$	6.07853	0.334106	0.167053	+	0.985948i	$0.446575\pi$
$332$	18.5824	1.01984
$333$	−0.430951	−0.0236160
$334$	−2.44772	−0.133933
$335$	7.71291	0.421401
$336$	4.77282	0.260379
$337$	−21.7466	−1.18461	−0.592307	−	0.805713i	$-0.701783\pi$
$337$	−21.7466	−1.18461	−0.592307	+	0.805713i	$0.701783\pi$
$338$	−1.86457	−0.101419
$339$	8.82964	0.479560
$340$	5.50631	0.298622
$341$	−8.18403	−0.443190
$342$	−0.0592137	−0.00320191
$343$	1.00000	0.0539949
$344$	−4.43427	−0.239080
$345$	2.21297	0.119142
$346$	10.3833	0.558208
$347$	1.12414	0.0603472	0.0301736	−	0.999545i	$-0.490394\pi$
$347$	1.12414	0.0603472	0.0301736	+	0.999545i	$0.490394\pi$
$348$	−2.93684	−0.157431
$349$	−0.832249	−0.0445493	−0.0222746	−	0.999752i	$-0.507091\pi$
$349$	−0.832249	−0.0445493	−0.0222746	+	0.999752i	$0.507091\pi$
$350$	−16.6045	−0.887546
$351$	−1.00000	−0.0533761
$352$	25.5813	1.36349
$353$	22.7557	1.21116	0.605582	−	0.795783i	$-0.292940\pi$
$353$	22.7557	1.21116	0.605582	+	0.795783i	$0.292940\pi$
$354$	15.1974	0.807735
$355$	48.0071	2.54795
$356$	5.37423	0.284834
$357$	−1.00000	−0.0529256
$358$	35.7484	1.88936
$359$	6.72042	0.354690	0.177345	−	0.984149i	$-0.443249\pi$
$359$	6.72042	0.354690	0.177345	+	0.984149i	$0.443249\pi$
$360$	3.63897	0.191790
$361$	−18.9990	−0.999947
$362$	−17.0244	−0.894780
$363$	−2.55755	−0.134237
$364$	1.47663	0.0773964
$365$	−20.9228	−1.09515
$366$	−2.46395	−0.128793
$367$	−24.9606	−1.30293	−0.651465	−	0.758679i	$-0.725845\pi$
$367$	−24.9606	−1.30293	−0.651465	+	0.758679i	$0.725845\pi$
$368$	2.83245	0.147652
$369$	−5.10754	−0.265888
$370$	2.99638	0.155774
$371$	0.179536	0.00932105
$372$	3.28207	0.170167
$373$	26.4828	1.37123	0.685613	−	0.727967i	$-0.259534\pi$
$373$	26.4828	1.37123	0.685613	+	0.727967i	$0.259534\pi$
$374$	−6.86546	−0.355005
$375$	−14.5626	−0.752007
$376$	8.96552	0.462361
$377$	1.98888	0.102433
$378$	1.86457	0.0959032
$379$	−14.0898	−0.723743	−0.361872	−	0.932228i	$-0.617862\pi$
$379$	−14.0898	−0.723743	−0.361872	+	0.932228i	$0.617862\pi$
$380$	0.174865	0.00897041
$381$	12.2156	0.625825
$382$	16.5518	0.846863
$383$	13.9861	0.714657	0.357329	−	0.933979i	$-0.383688\pi$
$383$	13.9861	0.714657	0.357329	+	0.933979i	$0.383688\pi$
$384$	7.53960	0.384753
$385$	13.7303	0.699761
$386$	−37.2610	−1.89654
$387$	−4.54395	−0.230982
$388$	17.5120	0.889037
$389$	−27.8015	−1.40959	−0.704796	−	0.709410i	$-0.748961\pi$
$389$	−27.8015	−1.40959	−0.704796	+	0.709410i	$0.748961\pi$
$390$	6.95294	0.352076
$391$	−0.593453	−0.0300122
$392$	0.975863	0.0492885
$393$	8.45399	0.426447
$394$	28.3436	1.42793
$395$	17.4493	0.877968
$396$	5.43703	0.273221
$397$	22.1759	1.11298	0.556489	−	0.830855i	$-0.312148\pi$
$397$	22.1759	1.11298	0.556489	+	0.830855i	$0.312148\pi$
$398$	−9.31451	−0.466894
$399$	−0.0317573	−0.00158985
$400$	−42.5032	−2.12516
$401$	9.96051	0.497404	0.248702	−	0.968580i	$-0.419996\pi$
$401$	9.96051	0.497404	0.248702	+	0.968580i	$0.419996\pi$
$402$	3.85663	0.192351
$403$	−2.22268	−0.110719
$404$	−23.5906	−1.17368
$405$	3.72897	0.185294
$406$	−3.70842	−0.184046
$407$	−1.58679	−0.0786541
$408$	−0.975863	−0.0483124
$409$	−24.5293	−1.21290	−0.606449	−	0.795122i	$-0.707407\pi$
$409$	−24.5293	−1.21290	−0.606449	+	0.795122i	$0.707407\pi$
$410$	35.5124	1.75383
$411$	13.4455	0.663220
$412$	2.95517	0.145591
$413$	8.15063	0.401066
$414$	1.10654	0.0543833
$415$	46.9267	2.30354
$416$	6.94755	0.340632
$417$	−6.42635	−0.314700
$418$	−0.218028	−0.0106641
$419$	−8.30251	−0.405604	−0.202802	−	0.979220i	$-0.565005\pi$
$419$	−8.30251	−0.405604	−0.202802	+	0.979220i	$0.565005\pi$
$420$	−5.50631	−0.268680
$421$	40.6939	1.98330	0.991651	−	0.128952i	$-0.0411613\pi$
$421$	40.6939	1.98330	0.991651	+	0.128952i	$0.0411613\pi$
$422$	−26.5896	−1.29436
$423$	9.18727	0.446700
$424$	0.175203	0.00850859
$425$	8.90524	0.431968
$426$	24.0047	1.16303
$427$	−1.32145	−0.0639497
$428$	4.75499	0.229841
$429$	−3.68206	−0.177771
$430$	31.5938	1.52359
$431$	3.48199	0.167722	0.0838609	−	0.996477i	$-0.473275\pi$
$431$	3.48199	0.167722	0.0838609	+	0.996477i	$0.473275\pi$
$432$	4.77282	0.229633
$433$	14.9908	0.720414	0.360207	−	0.932872i	$-0.382706\pi$
$433$	14.9908	0.720414	0.360207	+	0.932872i	$0.382706\pi$
$434$	4.14434	0.198935
$435$	−7.41649	−0.355594
$436$	25.6303	1.22747
$437$	−0.0188465	−0.000901548 0
$438$	−10.4619	−0.499888
$439$	1.86048	0.0887960	0.0443980	−	0.999014i	$-0.485863\pi$
$439$	1.86048	0.0887960	0.0443980	+	0.999014i	$0.485863\pi$
$440$	13.3989	0.638767
$441$	1.00000	0.0476190
$442$	−1.86457	−0.0886887
$443$	−11.3192	−0.537789	−0.268895	−	0.963170i	$-0.586658\pi$
$443$	−11.3192	−0.537789	−0.268895	+	0.963170i	$0.586658\pi$
$444$	0.636355	0.0302001
$445$	13.5717	0.643360
$446$	−13.2489	−0.627355
$447$	8.97612	0.424556
$448$	−3.40856	−0.161039
$449$	20.9218	0.987359	0.493680	−	0.869644i	$-0.335652\pi$
$449$	20.9218	0.987359	0.493680	+	0.869644i	$0.335652\pi$
$450$	−16.6045	−0.782742
$451$	−18.8062	−0.885552
$452$	−13.0381	−0.613261
$453$	2.91212	0.136823
$454$	−6.49502	−0.304826
$455$	3.72897	0.174817
$456$	−0.0309908	−0.00145127
$457$	20.0212	0.936551	0.468275	−	0.883583i	$-0.344876\pi$
$457$	20.0212	0.936551	0.468275	+	0.883583i	$0.344876\pi$
$458$	2.47836	0.115806
$459$	−1.00000	−0.0466760
$460$	−3.26774	−0.152359
$461$	16.4263	0.765049	0.382524	−	0.923945i	$-0.375055\pi$
$461$	16.4263	0.765049	0.382524	+	0.923945i	$0.375055\pi$
$462$	6.86546	0.319410
$463$	1.63249	0.0758682	0.0379341	−	0.999280i	$-0.487922\pi$
$463$	1.63249	0.0758682	0.0379341	+	0.999280i	$0.487922\pi$
$464$	−9.49259	−0.440682
$465$	8.28831	0.384361
$466$	53.7440	2.48964
$467$	29.8000	1.37898	0.689490	−	0.724295i	$-0.257835\pi$
$467$	29.8000	1.37898	0.689490	+	0.724295i	$0.257835\pi$
$468$	1.47663	0.0682572
$469$	2.06837	0.0955086
$470$	−63.8785	−2.94650
$471$	0.120793	0.00556583
$472$	7.95390	0.366108
$473$	−16.7311	−0.769296
$474$	8.72503	0.400754
$475$	0.282806	0.0129760
$476$	1.47663	0.0676812
$477$	0.179536	0.00822039
$478$	−49.2999	−2.25492
$479$	−16.2631	−0.743080	−0.371540	−	0.928417i	$-0.621170\pi$
$479$	−16.2631	−0.743080	−0.371540	+	0.928417i	$0.621170\pi$
$480$	−25.9072	−1.18250
$481$	−0.430951	−0.0196497
$482$	−6.30216	−0.287055
$483$	0.593453	0.0270030
$484$	3.77656	0.171662
$485$	44.2236	2.00809
$486$	1.86457	0.0845787
$487$	−3.15497	−0.142965	−0.0714827	−	0.997442i	$-0.522773\pi$
$487$	−3.15497	−0.142965	−0.0714827	+	0.997442i	$0.522773\pi$
$488$	−1.28956	−0.0583756
$489$	−9.23630	−0.417680
$490$	−6.95294	−0.314102
$491$	20.0114	0.903102	0.451551	−	0.892245i	$-0.350871\pi$
$491$	20.0114	0.903102	0.451551	+	0.892245i	$0.350871\pi$
$492$	7.54194	0.340017
$493$	1.98888	0.0895748
$494$	−0.0592137	−0.00266415
$495$	13.7303	0.617131
$496$	10.6085	0.476334
$497$	12.8741	0.577481
$498$	23.4644	1.05147
$499$	18.6763	0.836065	0.418032	−	0.908432i	$-0.362720\pi$
$499$	18.6763	0.836065	0.418032	+	0.908432i	$0.362720\pi$
$500$	21.5035	0.961665
$501$	−1.31275	−0.0586495
$502$	−35.3954	−1.57977
$503$	12.0660	0.537996	0.268998	−	0.963141i	$-0.413307\pi$
$503$	12.0660	0.537996	0.268998	+	0.963141i	$0.413307\pi$
$504$	0.975863	0.0434684
$505$	−59.5741	−2.65101
$506$	4.07433	0.181126
$507$	−1.00000	−0.0444116
$508$	−18.0379	−0.800304
$509$	−15.3140	−0.678783	−0.339391	−	0.940645i	$-0.610221\pi$
$509$	−15.3140	−0.678783	−0.339391	+	0.940645i	$0.610221\pi$
$510$	6.95294	0.307881
$511$	−5.61088	−0.248211
$512$	−23.8442	−1.05377
$513$	−0.0317573	−0.00140212
$514$	40.6301	1.79212
$515$	7.46278	0.328849
$516$	6.70973	0.295379
$517$	33.8281	1.48776
$518$	0.803539	0.0353055
$519$	5.56872	0.244440
$520$	3.63897	0.159579
$521$	24.4029	1.06911	0.534555	−	0.845134i	$-0.320479\pi$
$521$	24.4029	1.06911	0.534555	+	0.845134i	$0.320479\pi$
$522$	−3.70842	−0.162313
$523$	21.4269	0.936934	0.468467	−	0.883481i	$-0.344806\pi$
$523$	21.4269	0.936934	0.468467	+	0.883481i	$0.344806\pi$
$524$	−12.4834	−0.545340
$525$	−8.90524	−0.388657
$526$	14.9370	0.651285
$527$	−2.22268	−0.0968214
$528$	17.5738	0.764802
$529$	−22.6478	−0.984688
$530$	−1.24830	−0.0542229
$531$	8.15063	0.353707
$532$	0.0468937	0.00203310
$533$	−5.10754	−0.221232
$534$	6.78616	0.293666
$535$	12.0079	0.519147
$536$	2.01845	0.0871837
$537$	19.1724	0.827352
$538$	40.3551	1.73983
$539$	3.68206	0.158597
$540$	−5.50631	−0.236954
$541$	−1.58226	−0.0680265	−0.0340132	−	0.999421i	$-0.510829\pi$
$541$	−1.58226	−0.0680265	−0.0340132	+	0.999421i	$0.510829\pi$
$542$	18.8414	0.809307
$543$	−9.13043	−0.391824
$544$	6.94755	0.297874
$545$	64.7250	2.77252
$546$	1.86457	0.0797963
$547$	12.5726	0.537564	0.268782	−	0.963201i	$-0.413379\pi$
$547$	12.5726	0.537564	0.268782	+	0.963201i	$0.413379\pi$
$548$	−19.8541	−0.848124
$549$	−1.32145	−0.0563983
$550$	−61.1386	−2.60696
$551$	0.0631615	0.00269077
$552$	0.579129	0.0246494
$553$	4.67937	0.198987
$554$	8.23766	0.349985
$555$	1.60701	0.0682136
$556$	9.48933	0.402437
$557$	−4.10273	−0.173838	−0.0869191	−	0.996215i	$-0.527702\pi$
$557$	−4.10273	−0.173838	−0.0869191	+	0.996215i	$0.527702\pi$
$558$	4.14434	0.175444
$559$	−4.54395	−0.192189
$560$	−17.7977	−0.752092
$561$	−3.68206	−0.155457
$562$	−51.8571	−2.18746
$563$	0.361669	0.0152425	0.00762127	−	0.999971i	$-0.497574\pi$
$563$	0.361669	0.0152425	0.00762127	+	0.999971i	$0.497574\pi$
$564$	−13.5662	−0.571240
$565$	−32.9255	−1.38519
$566$	24.9256	1.04770
$567$	1.00000	0.0419961
$568$	12.5633	0.527146
$569$	13.4730	0.564818	0.282409	−	0.959294i	$-0.408866\pi$
$569$	13.4730	0.564818	0.282409	+	0.959294i	$0.408866\pi$
$570$	0.220807	0.00924857
$571$	33.9874	1.42233	0.711164	−	0.703026i	$-0.248168\pi$
$571$	33.9874	1.42233	0.711164	+	0.703026i	$0.248168\pi$
$572$	5.43703	0.227334
$573$	8.87699	0.370842
$574$	9.52337	0.397498
$575$	−5.28484	−0.220393
$576$	−3.40856	−0.142023
$577$	−26.3013	−1.09494	−0.547470	−	0.836826i	$-0.684409\pi$
$577$	−26.3013	−1.09494	−0.547470	+	0.836826i	$0.684409\pi$
$578$	−1.86457	−0.0775560
$579$	−19.9837	−0.830494
$580$	10.9514	0.454733
$581$	12.5843	0.522086
$582$	22.1128	0.916605
$583$	0.661063	0.0273784
$584$	−5.47545	−0.226576
$585$	3.72897	0.154174
$586$	−10.0951	−0.417023
$587$	−6.41268	−0.264680	−0.132340	−	0.991204i	$-0.542249\pi$
$587$	−6.41268	−0.264680	−0.132340	+	0.991204i	$0.542249\pi$
$588$	−1.47663	−0.0608952
$589$	−0.0705862	−0.00290845
$590$	−56.6708	−2.33310
$591$	15.2011	0.625290
$592$	2.05685	0.0845362
$593$	−0.206684	−0.00848748	−0.00424374	−	0.999991i	$-0.501351\pi$
$593$	−0.206684	−0.00848748	−0.00424374	+	0.999991i	$0.501351\pi$
$594$	6.86546	0.281693
$595$	3.72897	0.152873
$596$	−13.2544	−0.542921
$597$	−4.99552	−0.204453
$598$	1.10654	0.0452496
$599$	16.8510	0.688514	0.344257	−	0.938875i	$-0.388131\pi$
$599$	16.8510	0.688514	0.344257	+	0.938875i	$0.388131\pi$
$600$	−8.69030	−0.354780
$601$	−2.37820	−0.0970090	−0.0485045	−	0.998823i	$-0.515446\pi$
$601$	−2.37820	−0.0970090	−0.0485045	+	0.998823i	$0.515446\pi$
$602$	8.47252	0.345314
$603$	2.06837	0.0842307
$604$	−4.30013	−0.174970
$605$	9.53705	0.387736
$606$	−29.7884	−1.21007
$607$	−39.3725	−1.59808	−0.799041	−	0.601277i	$-0.794659\pi$
$607$	−39.3725	−1.59808	−0.799041	+	0.601277i	$0.794659\pi$
$608$	0.220635	0.00894794
$609$	−1.98888	−0.0805936
$610$	9.18800	0.372011
$611$	9.18727	0.371677
$612$	1.47663	0.0596892
$613$	−11.9538	−0.482810	−0.241405	−	0.970424i	$-0.577608\pi$
$613$	−11.9538	−0.482810	−0.241405	+	0.970424i	$0.577608\pi$
$614$	3.43756	0.138729
$615$	19.0459	0.768004
$616$	3.59318	0.144773
$617$	−19.3307	−0.778223	−0.389112	−	0.921191i	$-0.627218\pi$
$617$	−19.3307	−0.778223	−0.389112	+	0.921191i	$0.627218\pi$
$618$	3.73156	0.150105
$619$	−24.1659	−0.971311	−0.485656	−	0.874150i	$-0.661419\pi$
$619$	−24.1659	−0.971311	−0.485656	+	0.874150i	$0.661419\pi$
$620$	−12.2388	−0.491520
$621$	0.593453	0.0238145
$622$	−36.1626	−1.44999
$623$	3.63953	0.145815
$624$	4.77282	0.191066
$625$	9.77716	0.391087
$626$	4.71726	0.188540
$627$	−0.116932	−0.00466982
$628$	−0.178366	−0.00711757
$629$	−0.430951	−0.0171831
$630$	−6.95294	−0.277012
$631$	25.7068	1.02337	0.511686	−	0.859173i	$-0.329021\pi$
$631$	25.7068	1.02337	0.511686	+	0.859173i	$0.329021\pi$
$632$	4.56643	0.181643
$633$	−14.2604	−0.566801
$634$	44.9388	1.78475
$635$	−45.5517	−1.80767
$636$	−0.265108	−0.0105122
$637$	1.00000	0.0396214
$638$	−13.6546	−0.540591
$639$	12.8741	0.509291
$640$	−28.1150	−1.11134
$641$	−23.8666	−0.942674	−0.471337	−	0.881953i	$-0.656228\pi$
$641$	−23.8666	−0.942674	−0.471337	+	0.881953i	$0.656228\pi$
$642$	6.00423	0.236968
$643$	−34.9364	−1.37776	−0.688878	−	0.724877i	$-0.741896\pi$
$643$	−34.9364	−1.37776	−0.688878	+	0.724877i	$0.741896\pi$
$644$	−0.876310	−0.0345315
$645$	16.9443	0.667180
$646$	−0.0592137	−0.00232973
$647$	−29.7808	−1.17080	−0.585402	−	0.810743i	$-0.699063\pi$
$647$	−29.7808	−1.17080	−0.585402	+	0.810743i	$0.699063\pi$
$648$	0.975863	0.0383355
$649$	30.0111	1.17804
$650$	−16.6045	−0.651281
$651$	2.22268	0.0871136
$652$	13.6386	0.534128
$653$	33.2616	1.30163	0.650813	−	0.759238i	$-0.274428\pi$
$653$	33.2616	1.30163	0.650813	+	0.759238i	$0.274428\pi$
$654$	32.3640	1.26553
$655$	−31.5247	−1.23177
$656$	24.3774	0.951777
$657$	−5.61088	−0.218901
$658$	−17.1303	−0.667810
$659$	11.4287	0.445199	0.222600	−	0.974910i	$-0.428546\pi$
$659$	11.4287	0.445199	0.222600	+	0.974910i	$0.428546\pi$
$660$	−20.2746	−0.789186
$661$	43.4009	1.68810	0.844049	−	0.536266i	$-0.180166\pi$
$661$	43.4009	1.68810	0.844049	+	0.536266i	$0.180166\pi$
$662$	−11.3339	−0.440503
$663$	−1.00000	−0.0388368
$664$	12.2806	0.476579
$665$	0.118422	0.00459221
$666$	0.803539	0.0311365
$667$	−1.18031	−0.0457017
$668$	1.93845	0.0750008
$669$	−7.10561	−0.274719
$670$	−14.3813	−0.555597
$671$	−4.86567	−0.187837
$672$	−6.94755	−0.268008
$673$	24.6909	0.951763	0.475881	−	0.879509i	$-0.342129\pi$
$673$	24.6909	0.951763	0.475881	+	0.879509i	$0.342129\pi$
$674$	40.5481	1.56186
$675$	−8.90524	−0.342763
$676$	1.47663	0.0567934
$677$	−8.09781	−0.311224	−0.155612	−	0.987818i	$-0.549735\pi$
$677$	−8.09781	−0.311224	−0.155612	+	0.987818i	$0.549735\pi$
$678$	−16.4635	−0.632277
$679$	11.8594	0.455124
$680$	3.63897	0.139548
$681$	−3.48338	−0.133484
$682$	15.2597	0.584325
$683$	−39.6310	−1.51644	−0.758219	−	0.652000i	$-0.773930\pi$
$683$	−39.6310	−1.51644	−0.758219	+	0.652000i	$0.773930\pi$
$684$	0.0468937	0.00179303
$685$	−50.1381	−1.91568
$686$	−1.86457	−0.0711897
$687$	1.32918	0.0507116
$688$	21.6875	0.826828
$689$	0.179536	0.00683978
$690$	−4.12624	−0.157083
$691$	−4.52008	−0.171952	−0.0859759	−	0.996297i	$-0.527401\pi$
$691$	−4.52008	−0.171952	−0.0859759	+	0.996297i	$0.527401\pi$
$692$	−8.22293	−0.312589
$693$	3.68206	0.139870
$694$	−2.09605	−0.0795648
$695$	23.9637	0.908994
$696$	−1.94088	−0.0735688
$697$	−5.10754	−0.193462
$698$	1.55179	0.0587361
$699$	28.8238	1.09022
$700$	13.1497	0.497014
$701$	−24.7350	−0.934229	−0.467115	−	0.884197i	$-0.654706\pi$
$701$	−24.7350	−0.934229	−0.467115	+	0.884197i	$0.654706\pi$
$702$	1.86457	0.0703737
$703$	−0.0136858	−0.000516171 0
$704$	−12.5505	−0.473015
$705$	−34.2591	−1.29027
$706$	−42.4297	−1.59686
$707$	−15.9760	−0.600839
$708$	−12.0355	−0.452320
$709$	24.8202	0.932143	0.466071	−	0.884747i	$-0.345669\pi$
$709$	24.8202	0.932143	0.466071	+	0.884747i	$0.345669\pi$
$710$	−89.5127	−3.35935
$711$	4.67937	0.175490
$712$	3.55168	0.133105
$713$	1.31906	0.0493990
$714$	1.86457	0.0697799
$715$	13.7303	0.513484
$716$	−28.3106	−1.05802
$717$	−26.4403	−0.987432
$718$	−12.5307	−0.467642
$719$	13.7268	0.511922	0.255961	−	0.966687i	$-0.417608\pi$
$719$	13.7268	0.511922	0.255961	+	0.966687i	$0.417608\pi$
$720$	−17.7977	−0.663283
$721$	2.00129	0.0745321
$722$	35.4250	1.31838
$723$	−3.37995	−0.125702
$724$	13.4823	0.501064
$725$	17.7115	0.657788
$726$	4.76874	0.176985
$727$	19.4894	0.722822	0.361411	−	0.932407i	$-0.382295\pi$
$727$	19.4894	0.722822	0.361411	+	0.932407i	$0.382295\pi$
$728$	0.975863	0.0361679
$729$	1.00000	0.0370370
$730$	39.0121	1.44390
$731$	−4.54395	−0.168064
$732$	1.95130	0.0721221
$733$	−18.6734	−0.689719	−0.344860	−	0.938654i	$-0.612073\pi$
$733$	−18.6734	−0.689719	−0.344860	+	0.938654i	$0.612073\pi$
$734$	46.5407	1.71785
$735$	−3.72897	−0.137545
$736$	−4.12305	−0.151977
$737$	7.61587	0.280534
$738$	9.52337	0.350560
$739$	−47.6257	−1.75194	−0.875970	−	0.482366i	$-0.839778\pi$
$739$	−47.6257	−1.75194	−0.875970	+	0.482366i	$0.839778\pi$
$740$	−2.37295	−0.0872314
$741$	−0.0317573	−0.00116663
$742$	−0.334758	−0.0122894
$743$	16.0872	0.590181	0.295090	−	0.955469i	$-0.404650\pi$
$743$	16.0872	0.590181	0.295090	+	0.955469i	$0.404650\pi$
$744$	2.16903	0.0795205
$745$	−33.4717	−1.22631
$746$	−49.3790	−1.80789
$747$	12.5843	0.460437
$748$	5.43703	0.198798
$749$	3.22017	0.117662
$750$	27.1529	0.991485
$751$	1.78983	0.0653118	0.0326559	−	0.999467i	$-0.489603\pi$
$751$	1.78983	0.0653118	0.0326559	+	0.999467i	$0.489603\pi$
$752$	−43.8492	−1.59902
$753$	−18.9831	−0.691783
$754$	−3.70842	−0.135053
$755$	−10.8592	−0.395208
$756$	−1.47663	−0.0537045
$757$	−49.3144	−1.79236	−0.896181	−	0.443688i	$-0.853670\pi$
$757$	−49.3144	−1.79236	−0.896181	+	0.443688i	$0.853670\pi$
$758$	26.2714	0.954220
$759$	2.18513	0.0793152
$760$	0.115564	0.00419194
$761$	26.9360	0.976428	0.488214	−	0.872724i	$-0.337649\pi$
$761$	26.9360	0.976428	0.488214	+	0.872724i	$0.337649\pi$
$762$	−22.7769	−0.825120
$763$	17.3573	0.628378
$764$	−13.1080	−0.474232
$765$	3.72897	0.134821
$766$	−26.0781	−0.942241
$767$	8.15063	0.294302
$768$	−20.8752	−0.753270
$769$	12.5282	0.451780	0.225890	−	0.974153i	$-0.427471\pi$
$769$	12.5282	0.451780	0.225890	+	0.974153i	$0.427471\pi$
$770$	−25.6011	−0.922601
$771$	21.7906	0.784768
$772$	29.5085	1.06203
$773$	−14.8428	−0.533859	−0.266929	−	0.963716i	$-0.586009\pi$
$773$	−14.8428	−0.533859	−0.266929	+	0.963716i	$0.586009\pi$
$774$	8.47252	0.304539
$775$	−19.7935	−0.711003
$776$	11.5732	0.415453
$777$	0.430951	0.0154603
$778$	51.8379	1.85848
$779$	−0.162202	−0.00581147
$780$	−5.50631	−0.197158
$781$	47.4031	1.69622
$782$	1.10654	0.0395696
$783$	−1.98888	−0.0710769
$784$	−4.77282	−0.170458
$785$	−0.450432	−0.0160766
$786$	−15.7631	−0.562250
$787$	−30.1087	−1.07326	−0.536630	−	0.843818i	$-0.680303\pi$
$787$	−30.1087	−1.07326	−0.536630	+	0.843818i	$0.680303\pi$
$788$	−22.4464	−0.799620
$789$	8.01097	0.285198
$790$	−32.5354	−1.15756
$791$	−8.82964	−0.313946
$792$	3.59318	0.127678
$793$	−1.32145	−0.0469262
$794$	−41.3486	−1.46741
$795$	−0.669486	−0.0237442
$796$	7.37653	0.261454
$797$	43.3311	1.53487	0.767434	−	0.641128i	$-0.221533\pi$
$797$	43.3311	1.53487	0.767434	+	0.641128i	$0.221533\pi$
$798$	0.0592137	0.00209614
$799$	9.18727	0.325022
$800$	61.8696	2.18742
$801$	3.63953	0.128596
$802$	−18.5721	−0.655803
$803$	−20.6596	−0.729061
$804$	−3.05422	−0.107714
$805$	−2.21297	−0.0779970
$806$	4.14434	0.145978
$807$	21.6431	0.761873
$808$	−15.5904	−0.548468
$809$	−31.3384	−1.10180	−0.550900	−	0.834571i	$-0.685715\pi$
$809$	−31.3384	−1.10180	−0.550900	+	0.834571i	$0.685715\pi$
$810$	−6.95294	−0.244301
$811$	−34.3095	−1.20477	−0.602385	−	0.798206i	$-0.705783\pi$
$811$	−34.3095	−1.20477	−0.602385	+	0.798206i	$0.705783\pi$
$812$	2.93684	0.103063
$813$	10.1049	0.354396
$814$	2.95868	0.103702
$815$	34.4419	1.20645
$816$	4.77282	0.167082
$817$	−0.144304	−0.00504854
$818$	45.7367	1.59915
$819$	1.00000	0.0349428
$820$	−28.1237	−0.982122
$821$	−20.0039	−0.698140	−0.349070	−	0.937097i	$-0.613502\pi$
$821$	−20.0039	−0.698140	−0.349070	+	0.937097i	$0.613502\pi$
$822$	−25.0702	−0.874423
$823$	12.0296	0.419327	0.209664	−	0.977774i	$-0.432763\pi$
$823$	12.0296	0.419327	0.209664	+	0.977774i	$0.432763\pi$
$824$	1.95299	0.0680356
$825$	−32.7896	−1.14159
$826$	−15.1974	−0.528787
$827$	3.90847	0.135911	0.0679554	−	0.997688i	$-0.478352\pi$
$827$	3.90847	0.135911	0.0679554	+	0.997688i	$0.478352\pi$
$828$	−0.876310	−0.0304539
$829$	35.7498	1.24164	0.620821	−	0.783953i	$-0.286799\pi$
$829$	35.7498	1.24164	0.620821	+	0.783953i	$0.286799\pi$
$830$	−87.4982	−3.03711
$831$	4.41799	0.153258
$832$	−3.40856	−0.118171
$833$	1.00000	0.0346479
$834$	11.9824	0.414916
$835$	4.89522	0.169406
$836$	0.172665	0.00597176
$837$	2.22268	0.0768270
$838$	15.4806	0.534769
$839$	4.37065	0.150892	0.0754458	−	0.997150i	$-0.475962\pi$
$839$	4.37065	0.150892	0.0754458	+	0.997150i	$0.475962\pi$
$840$	−3.63897	−0.125556
$841$	−25.0443	−0.863598
$842$	−75.8768	−2.61489
$843$	−27.8118	−0.957890
$844$	21.0574	0.724825
$845$	3.72897	0.128281
$846$	−17.1303	−0.588953
$847$	2.55755	0.0878786
$848$	−0.856894	−0.0294259
$849$	13.3680	0.458789
$850$	−16.6045	−0.569529
$851$	0.255749	0.00876697
$852$	−19.0102	−0.651280
$853$	−17.4942	−0.598991	−0.299496	−	0.954098i	$-0.596818\pi$
$853$	−17.4942	−0.598991	−0.299496	+	0.954098i	$0.596818\pi$
$854$	2.46395	0.0843146
$855$	0.118422	0.00404995
$856$	3.14244	0.107406
$857$	−47.6786	−1.62867	−0.814335	−	0.580395i	$-0.802898\pi$
$857$	−47.6786	−1.62867	−0.814335	+	0.580395i	$0.802898\pi$
$858$	6.86546	0.234383
$859$	48.8108	1.66540	0.832702	−	0.553721i	$-0.186793\pi$
$859$	48.8108	1.66540	0.832702	+	0.553721i	$0.186793\pi$
$860$	−25.0204	−0.853189
$861$	5.10754	0.174064
$862$	−6.49243	−0.221133
$863$	−34.3999	−1.17099	−0.585493	−	0.810678i	$-0.699099\pi$
$863$	−34.3999	−1.17099	−0.585493	+	0.810678i	$0.699099\pi$
$864$	−6.94755	−0.236360
$865$	−20.7656	−0.706052
$866$	−27.9515	−0.949830
$867$	−1.00000	−0.0339618
$868$	−3.28207	−0.111401
$869$	17.2297	0.584478
$870$	13.8286	0.468833
$871$	2.06837	0.0700842
$872$	16.9384	0.573606
$873$	11.8594	0.401381
$874$	0.0351406	0.00118865
$875$	14.5626	0.492304
$876$	8.28519	0.279931
$877$	−11.8590	−0.400451	−0.200226	−	0.979750i	$-0.564168\pi$
$877$	−11.8590	−0.400451	−0.200226	+	0.979750i	$0.564168\pi$
$878$	−3.46901	−0.117073
$879$	−5.41414	−0.182615
$880$	−65.5323	−2.20909
$881$	−53.0341	−1.78676	−0.893381	−	0.449299i	$-0.851674\pi$
$881$	−53.0341	−1.78676	−0.893381	+	0.449299i	$0.851674\pi$
$882$	−1.86457	−0.0627834
$883$	22.1160	0.744263	0.372132	−	0.928180i	$-0.378627\pi$
$883$	22.1160	0.744263	0.372132	+	0.928180i	$0.378627\pi$
$884$	1.47663	0.0496644
$885$	−30.3935	−1.02167
$886$	21.1054	0.709049
$887$	16.4106	0.551014	0.275507	−	0.961299i	$-0.411154\pi$
$887$	16.4106	0.551014	0.275507	+	0.961299i	$0.411154\pi$
$888$	0.420549	0.0141127
$889$	−12.2156	−0.409699
$890$	−25.3054	−0.848239
$891$	3.68206	0.123354
$892$	10.4924	0.351310
$893$	0.291763	0.00976347
$894$	−16.7366	−0.559756
$895$	−71.4935	−2.38976
$896$	−7.53960	−0.251880
$897$	0.593453	0.0198148
$898$	−39.0101	−1.30179
$899$	−4.42065	−0.147437
$900$	13.1497	0.438325
$901$	0.179536	0.00598122
$902$	35.0656	1.16756
$903$	4.54395	0.151213
$904$	−8.61652	−0.286581
$905$	34.0471	1.13177
$906$	−5.42986	−0.180395
$907$	34.2876	1.13850	0.569251	−	0.822164i	$-0.307233\pi$
$907$	34.2876	1.13850	0.569251	+	0.822164i	$0.307233\pi$
$908$	5.14366	0.170698
$909$	−15.9760	−0.529890
$910$	−6.95294	−0.230488
$911$	−9.49049	−0.314434	−0.157217	−	0.987564i	$-0.550252\pi$
$911$	−9.49049	−0.314434	−0.157217	+	0.987564i	$0.550252\pi$
$912$	0.151572	0.00501905
$913$	46.3363	1.53351
$914$	−37.3309	−1.23480
$915$	4.92767	0.162904
$916$	−1.96271	−0.0648499
$917$	−8.45399	−0.279175
$918$	1.86457	0.0615400
$919$	−44.3685	−1.46358	−0.731791	−	0.681529i	$-0.761315\pi$
$919$	−44.3685	−1.46358	−0.731791	+	0.681529i	$0.761315\pi$
$920$	−2.15956	−0.0711984
$921$	1.84362	0.0607493
$922$	−30.6280	−1.00868
$923$	12.8741	0.423756
$924$	−5.43703	−0.178865
$925$	−3.83773	−0.126184
$926$	−3.04389	−0.100029
$927$	2.00129	0.0657311
$928$	13.8179	0.453594
$929$	4.39784	0.144288	0.0721441	−	0.997394i	$-0.477016\pi$
$929$	4.39784	0.144288	0.0721441	+	0.997394i	$0.477016\pi$
$930$	−15.4541	−0.506761
$931$	0.0317573	0.00104080
$932$	−42.5621	−1.39417
$933$	−19.3946	−0.634951
$934$	−55.5643	−1.81812
$935$	13.7303	0.449029
$936$	0.975863	0.0318971
$937$	−49.7905	−1.62659	−0.813293	−	0.581855i	$-0.802327\pi$
$937$	−49.7905	−1.62659	−0.813293	+	0.581855i	$0.802327\pi$
$938$	−3.85663	−0.125923
$939$	2.52994	0.0825616
$940$	50.5880	1.65000
$941$	−38.7297	−1.26255	−0.631276	−	0.775558i	$-0.717468\pi$
$941$	−38.7297	−1.26255	−0.631276	+	0.775558i	$0.717468\pi$
$942$	−0.225226	−0.00733827
$943$	3.03108	0.0987057
$944$	−38.9015	−1.26614
$945$	−3.72897	−0.121304
$946$	31.1963	1.01428
$947$	−18.4113	−0.598287	−0.299144	−	0.954208i	$-0.596701\pi$
$947$	−18.4113	−0.598287	−0.299144	+	0.954208i	$0.596701\pi$
$948$	−6.90970	−0.224417
$949$	−5.61088	−0.182137
$950$	−0.527313	−0.0171083
$951$	24.1014	0.781541
$952$	0.975863	0.0316279
$953$	−33.3955	−1.08179	−0.540893	−	0.841091i	$-0.681914\pi$
$953$	−33.3955	−1.08179	−0.540893	+	0.841091i	$0.681914\pi$
$954$	−0.334758	−0.0108382
$955$	−33.1021	−1.07116
$956$	39.0425	1.26273
$957$	−7.32318	−0.236725
$958$	30.3237	0.979716
$959$	−13.4455	−0.434179
$960$	12.7104	0.410227
$961$	−26.0597	−0.840636
$962$	0.803539	0.0259072
$963$	3.22017	0.103768
$964$	4.99093	0.160747
$965$	74.5187	2.39884
$966$	−1.10654	−0.0356022
$967$	3.60324	0.115872	0.0579362	−	0.998320i	$-0.481548\pi$
$967$	3.60324	0.115872	0.0579362	+	0.998320i	$0.481548\pi$
$968$	2.49582	0.0802187
$969$	−0.0317573	−0.00102019
$970$	−82.4580	−2.64757
$971$	9.50775	0.305118	0.152559	−	0.988294i	$-0.451249\pi$
$971$	9.50775	0.305118	0.152559	+	0.988294i	$0.451249\pi$
$972$	−1.47663	−0.0473629
$973$	6.42635	0.206019
$974$	5.88267	0.188493
$975$	−8.90524	−0.285196
$976$	6.30707	0.201884
$977$	−11.2894	−0.361179	−0.180590	−	0.983559i	$-0.557801\pi$
$977$	−11.2894	−0.361179	−0.180590	+	0.983559i	$0.557801\pi$
$978$	17.2217	0.550691
$979$	13.4009	0.428296
$980$	5.50631	0.175893
$981$	17.3573	0.554177
$982$	−37.3127	−1.19070
$983$	−38.7457	−1.23580	−0.617898	−	0.786258i	$-0.712015\pi$
$983$	−38.7457	−1.23580	−0.617898	+	0.786258i	$0.712015\pi$
$984$	4.98426	0.158892
$985$	−56.6846	−1.80612
$986$	−3.70842	−0.118100
$987$	−9.18727	−0.292434
$988$	0.0468937	0.00149189
$989$	2.69662	0.0857476
$990$	−25.6011	−0.813657
$991$	18.6155	0.591341	0.295670	−	0.955290i	$-0.404457\pi$
$991$	18.6155	0.591341	0.295670	+	0.955290i	$0.404457\pi$
$992$	−15.4422	−0.490289
$993$	−6.07853	−0.192896
$994$	−24.0047	−0.761381
$995$	18.6282	0.590553
$996$	−18.5824	−0.588806
$997$	45.0131	1.42558	0.712790	−	0.701378i	$-0.247431\pi$
$997$	45.0131	1.42558	0.712790	+	0.701378i	$0.247431\pi$
$998$	−34.8233	−1.10231
$999$	0.430951	0.0136347

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4641.2.a.w.1.3	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4641.2.a.w.1.3	✓	14	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:	\( N \)	\(=\)	\( 4641 = 3 \cdot 7 \cdot 13 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4641.a (trivial)

\(f(q)\)	\(=\)	\(q-1.86457 q^{2} -1.00000 q^{3} +1.47663 q^{4} +3.72897 q^{5} +1.86457 q^{6} +1.00000 q^{7} +0.975863 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.86457 q^{2} -1.00000 q^{3} +1.47663 q^{4} +3.72897 q^{5} +1.86457 q^{6} +1.00000 q^{7} +0.975863 q^{8} +1.00000 q^{9} -6.95294 q^{10} +3.68206 q^{11} -1.47663 q^{12} +1.00000 q^{13} -1.86457 q^{14} -3.72897 q^{15} -4.77282 q^{16} +1.00000 q^{17} -1.86457 q^{18} +0.0317573 q^{19} +5.50631 q^{20} -1.00000 q^{21} -6.86546 q^{22} -0.593453 q^{23} -0.975863 q^{24} +8.90524 q^{25} -1.86457 q^{26} -1.00000 q^{27} +1.47663 q^{28} +1.98888 q^{29} +6.95294 q^{30} -2.22268 q^{31} +6.94755 q^{32} -3.68206 q^{33} -1.86457 q^{34} +3.72897 q^{35} +1.47663 q^{36} -0.430951 q^{37} -0.0592137 q^{38} -1.00000 q^{39} +3.63897 q^{40} -5.10754 q^{41} +1.86457 q^{42} -4.54395 q^{43} +5.43703 q^{44} +3.72897 q^{45} +1.10654 q^{46} +9.18727 q^{47} +4.77282 q^{48} +1.00000 q^{49} -16.6045 q^{50} -1.00000 q^{51} +1.47663 q^{52} +0.179536 q^{53} +1.86457 q^{54} +13.7303 q^{55} +0.975863 q^{56} -0.0317573 q^{57} -3.70842 q^{58} +8.15063 q^{59} -5.50631 q^{60} -1.32145 q^{61} +4.14434 q^{62} +1.00000 q^{63} -3.40856 q^{64} +3.72897 q^{65} +6.86546 q^{66} +2.06837 q^{67} +1.47663 q^{68} +0.593453 q^{69} -6.95294 q^{70} +12.8741 q^{71} +0.975863 q^{72} -5.61088 q^{73} +0.803539 q^{74} -8.90524 q^{75} +0.0468937 q^{76} +3.68206 q^{77} +1.86457 q^{78} +4.67937 q^{79} -17.7977 q^{80} +1.00000 q^{81} +9.52337 q^{82} +12.5843 q^{83} -1.47663 q^{84} +3.72897 q^{85} +8.47252 q^{86} -1.98888 q^{87} +3.59318 q^{88} +3.63953 q^{89} -6.95294 q^{90} +1.00000 q^{91} -0.876310 q^{92} +2.22268 q^{93} -17.1303 q^{94} +0.118422 q^{95} -6.94755 q^{96} +11.8594 q^{97} -1.86457 q^{98} +3.68206 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - q^{2} - 14 q^{3} + 17 q^{4} - q^{5} + q^{6} + 14 q^{7} - 6 q^{8} + 14 q^{9}+O(q^{10}) \) 14 * q - q^2 - 14 * q^3 + 17 * q^4 - q^5 + q^6 + 14 * q^7 - 6 * q^8 + 14 * q^9	\( 14 q - q^{2} - 14 q^{3} + 17 q^{4} - q^{5} + q^{6} + 14 q^{7} - 6 q^{8} + 14 q^{9} + 11 q^{10} - 4 q^{11} - 17 q^{12} + 14 q^{13} - q^{14} + q^{15} + 19 q^{16} + 14 q^{17} - q^{18} + 6 q^{19} + q^{20} - 14 q^{21} + 12 q^{22} + 7 q^{23} + 6 q^{24} + 19 q^{25} - q^{26} - 14 q^{27} + 17 q^{28} - 4 q^{29} - 11 q^{30} + 31 q^{31} - 18 q^{32} + 4 q^{33} - q^{34} - q^{35} + 17 q^{36} + 2 q^{37} + 9 q^{38} - 14 q^{39} + 50 q^{40} + 4 q^{41} + q^{42} + 14 q^{43} - 8 q^{44} - q^{45} - 17 q^{46} - q^{47} - 19 q^{48} + 14 q^{49} - 3 q^{50} - 14 q^{51} + 17 q^{52} - 43 q^{53} + q^{54} + 23 q^{55} - 6 q^{56} - 6 q^{57} - 10 q^{58} + 11 q^{59} - q^{60} + 25 q^{61} - 3 q^{62} + 14 q^{63} + 36 q^{64} - q^{65} - 12 q^{66} + 11 q^{67} + 17 q^{68} - 7 q^{69} + 11 q^{70} + 20 q^{71} - 6 q^{72} + 14 q^{73} - 24 q^{74} - 19 q^{75} + 9 q^{76} - 4 q^{77} + q^{78} + 42 q^{79} + 13 q^{80} + 14 q^{81} + 2 q^{82} + 15 q^{83} - 17 q^{84} - q^{85} - 11 q^{86} + 4 q^{87} + 63 q^{88} + 21 q^{89} + 11 q^{90} + 14 q^{91} + 30 q^{92} - 31 q^{93} - 29 q^{94} + 16 q^{95} + 18 q^{96} + 15 q^{97} - q^{98} - 4 q^{99}+O(q^{100}) \) 14 * q - q^2 - 14 * q^3 + 17 * q^4 - q^5 + q^6 + 14 * q^7 - 6 * q^8 + 14 * q^9 + 11 * q^10 - 4 * q^11 - 17 * q^12 + 14 * q^13 - q^14 + q^15 + 19 * q^16 + 14 * q^17 - q^18 + 6 * q^19 + q^20 - 14 * q^21 + 12 * q^22 + 7 * q^23 + 6 * q^24 + 19 * q^25 - q^26 - 14 * q^27 + 17 * q^28 - 4 * q^29 - 11 * q^30 + 31 * q^31 - 18 * q^32 + 4 * q^33 - q^34 - q^35 + 17 * q^36 + 2 * q^37 + 9 * q^38 - 14 * q^39 + 50 * q^40 + 4 * q^41 + q^42 + 14 * q^43 - 8 * q^44 - q^45 - 17 * q^46 - q^47 - 19 * q^48 + 14 * q^49 - 3 * q^50 - 14 * q^51 + 17 * q^52 - 43 * q^53 + q^54 + 23 * q^55 - 6 * q^56 - 6 * q^57 - 10 * q^58 + 11 * q^59 - q^60 + 25 * q^61 - 3 * q^62 + 14 * q^63 + 36 * q^64 - q^65 - 12 * q^66 + 11 * q^67 + 17 * q^68 - 7 * q^69 + 11 * q^70 + 20 * q^71 - 6 * q^72 + 14 * q^73 - 24 * q^74 - 19 * q^75 + 9 * q^76 - 4 * q^77 + q^78 + 42 * q^79 + 13 * q^80 + 14 * q^81 + 2 * q^82 + 15 * q^83 - 17 * q^84 - q^85 - 11 * q^86 + 4 * q^87 + 63 * q^88 + 21 * q^89 + 11 * q^90 + 14 * q^91 + 30 * q^92 - 31 * q^93 - 29 * q^94 + 16 * q^95 + 18 * q^96 + 15 * q^97 - q^98 - 4 * q^99

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