LMFDB - Embedded newform 7942.2.a.cb.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7942,2,Mod(1,7942)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7942, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("7942.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7942 = 2 \cdot 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7942.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:	$63.4171892853$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 3 x^{14} - 27 x^{13} + 83 x^{12} + 264 x^{11} - 828 x^{10} - 1171 x^{9} + 3624 x^{8} + 2634 x^{7} + \cdots - 8 $ x^15 - 3x^14 - 27x^13 + 83x^12 + 264x^11 - 828x^10 - 1171x^9 + 3624x^8 + 2634x^7 - 6798x^6 - 3621x^5 + 3936x^4 + 3195x^3 + 618x^2 - 12x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.19779$ of defining polynomial
Character	$\chi$	$=$	7942.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.19779 q^{3} +1.00000 q^{4} -0.357000 q^{5} -3.19779 q^{6} +4.43696 q^{7} +1.00000 q^{8} +7.22586 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.19779 q^{3} +1.00000 q^{4} -0.357000 q^{5} -3.19779 q^{6} +4.43696 q^{7} +1.00000 q^{8} +7.22586 q^{9} -0.357000 q^{10} +1.00000 q^{11} -3.19779 q^{12} -0.308524 q^{13} +4.43696 q^{14} +1.14161 q^{15} +1.00000 q^{16} +2.41338 q^{17} +7.22586 q^{18} -0.357000 q^{20} -14.1885 q^{21} +1.00000 q^{22} +1.48559 q^{23} -3.19779 q^{24} -4.87255 q^{25} -0.308524 q^{26} -13.5134 q^{27} +4.43696 q^{28} +3.81482 q^{29} +1.14161 q^{30} +9.99220 q^{31} +1.00000 q^{32} -3.19779 q^{33} +2.41338 q^{34} -1.58400 q^{35} +7.22586 q^{36} +6.92288 q^{37} +0.986596 q^{39} -0.357000 q^{40} +6.29205 q^{41} -14.1885 q^{42} +3.24536 q^{43} +1.00000 q^{44} -2.57963 q^{45} +1.48559 q^{46} +11.2995 q^{47} -3.19779 q^{48} +12.6866 q^{49} -4.87255 q^{50} -7.71746 q^{51} -0.308524 q^{52} -9.44121 q^{53} -13.5134 q^{54} -0.357000 q^{55} +4.43696 q^{56} +3.81482 q^{58} -11.8477 q^{59} +1.14161 q^{60} +3.86756 q^{61} +9.99220 q^{62} +32.0608 q^{63} +1.00000 q^{64} +0.110143 q^{65} -3.19779 q^{66} +1.56356 q^{67} +2.41338 q^{68} -4.75060 q^{69} -1.58400 q^{70} -5.02681 q^{71} +7.22586 q^{72} +3.27027 q^{73} +6.92288 q^{74} +15.5814 q^{75} +4.43696 q^{77} +0.986596 q^{78} -13.7070 q^{79} -0.357000 q^{80} +21.5354 q^{81} +6.29205 q^{82} +0.214235 q^{83} -14.1885 q^{84} -0.861576 q^{85} +3.24536 q^{86} -12.1990 q^{87} +1.00000 q^{88} +17.7537 q^{89} -2.57963 q^{90} -1.36891 q^{91} +1.48559 q^{92} -31.9530 q^{93} +11.2995 q^{94} -3.19779 q^{96} -6.87100 q^{97} +12.6866 q^{98} +7.22586 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 15 q^{2} + 3 q^{3} + 15 q^{4} + 9 q^{5} + 3 q^{6} + 12 q^{7} + 15 q^{8} + 18 q^{9}+O(q^{10}) $ 15 * q + 15 * q^2 + 3 * q^3 + 15 * q^4 + 9 * q^5 + 3 * q^6 + 12 * q^7 + 15 * q^8 + 18 * q^9	\( 15 q + 15 q^{2} + 3 q^{3} + 15 q^{4} + 9 q^{5} + 3 q^{6} + 12 q^{7} + 15 q^{8} + 18 q^{9} + 9 q^{10} + 15 q^{11} + 3 q^{12} + 12 q^{14} - 9 q^{15} + 15 q^{16} + 21 q^{17} + 18 q^{18} + 9 q^{20} - 27 q^{21} + 15 q^{22} + 21 q^{23} + 3 q^{24} + 36 q^{25} + 3 q^{27} + 12 q^{28} - 15 q^{29} - 9 q^{30} + 30 q^{31} + 15 q^{32} + 3 q^{33} + 21 q^{34} + 30 q^{35} + 18 q^{36} - 9 q^{37} + 9 q^{40} + 9 q^{41} - 27 q^{42} + 33 q^{43} + 15 q^{44} + 18 q^{45} + 21 q^{46} + 39 q^{47} + 3 q^{48} + 33 q^{49} + 36 q^{50} + 6 q^{51} - 6 q^{53} + 3 q^{54} + 9 q^{55} + 12 q^{56} - 15 q^{58} - 6 q^{59} - 9 q^{60} + 36 q^{61} + 30 q^{62} + 30 q^{63} + 15 q^{64} + 18 q^{65} + 3 q^{66} + 15 q^{67} + 21 q^{68} + 48 q^{69} + 30 q^{70} - 3 q^{71} + 18 q^{72} + 60 q^{73} - 9 q^{74} + 21 q^{75} + 12 q^{77} + 18 q^{79} + 9 q^{80} + 27 q^{81} + 9 q^{82} + 36 q^{83} - 27 q^{84} + 15 q^{85} + 33 q^{86} + 21 q^{87} + 15 q^{88} + 6 q^{89} + 18 q^{90} - 18 q^{91} + 21 q^{92} - 54 q^{93} + 39 q^{94} + 3 q^{96} + 33 q^{98} + 18 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 + 3 * q^3 + 15 * q^4 + 9 * q^5 + 3 * q^6 + 12 * q^7 + 15 * q^8 + 18 * q^9 + 9 * q^10 + 15 * q^11 + 3 * q^12 + 12 * q^14 - 9 * q^15 + 15 * q^16 + 21 * q^17 + 18 * q^18 + 9 * q^20 - 27 * q^21 + 15 * q^22 + 21 * q^23 + 3 * q^24 + 36 * q^25 + 3 * q^27 + 12 * q^28 - 15 * q^29 - 9 * q^30 + 30 * q^31 + 15 * q^32 + 3 * q^33 + 21 * q^34 + 30 * q^35 + 18 * q^36 - 9 * q^37 + 9 * q^40 + 9 * q^41 - 27 * q^42 + 33 * q^43 + 15 * q^44 + 18 * q^45 + 21 * q^46 + 39 * q^47 + 3 * q^48 + 33 * q^49 + 36 * q^50 + 6 * q^51 - 6 * q^53 + 3 * q^54 + 9 * q^55 + 12 * q^56 - 15 * q^58 - 6 * q^59 - 9 * q^60 + 36 * q^61 + 30 * q^62 + 30 * q^63 + 15 * q^64 + 18 * q^65 + 3 * q^66 + 15 * q^67 + 21 * q^68 + 48 * q^69 + 30 * q^70 - 3 * q^71 + 18 * q^72 + 60 * q^73 - 9 * q^74 + 21 * q^75 + 12 * q^77 + 18 * q^79 + 9 * q^80 + 27 * q^81 + 9 * q^82 + 36 * q^83 - 27 * q^84 + 15 * q^85 + 33 * q^86 + 21 * q^87 + 15 * q^88 + 6 * q^89 + 18 * q^90 - 18 * q^91 + 21 * q^92 - 54 * q^93 + 39 * q^94 + 3 * q^96 + 33 * q^98 + 18 * 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
$3$	−3.19779	−1.84624	−0.923122	−	0.384507i	$-0.874372\pi$
$3$	−3.19779	−1.84624	−0.923122	+	0.384507i	$0.874372\pi$
$4$	1.00000	0.500000
$5$	−0.357000	−0.159655	−0.0798277	−	0.996809i	$-0.525437\pi$
$5$	−0.357000	−0.159655	−0.0798277	+	0.996809i	$0.525437\pi$
$6$	−3.19779	−1.30549
$7$	4.43696	1.67701	0.838507	−	0.544892i	$-0.183429\pi$
$7$	4.43696	1.67701	0.838507	+	0.544892i	$0.183429\pi$
$8$	1.00000	0.353553
$9$	7.22586	2.40862
$10$	−0.357000	−0.112893
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−3.19779	−0.923122
$13$	−0.308524	−0.0855692	−0.0427846	−	0.999084i	$-0.513623\pi$
$13$	−0.308524	−0.0855692	−0.0427846	+	0.999084i	$0.513623\pi$
$14$	4.43696	1.18583
$15$	1.14161	0.294763
$16$	1.00000	0.250000
$17$	2.41338	0.585329	0.292665	−	0.956215i	$-0.405458\pi$
$17$	2.41338	0.585329	0.292665	+	0.956215i	$0.405458\pi$
$18$	7.22586	1.70315
$19$	0	0
$19$	0	0
$20$	−0.357000	−0.0798277
$21$	−14.1885	−3.09618
$22$	1.00000	0.213201
$23$	1.48559	0.309767	0.154884	−	0.987933i	$-0.450500\pi$
$23$	1.48559	0.309767	0.154884	+	0.987933i	$0.450500\pi$
$24$	−3.19779	−0.652746
$25$	−4.87255	−0.974510
$26$	−0.308524	−0.0605066
$27$	−13.5134	−2.60065
$28$	4.43696	0.838507
$29$	3.81482	0.708395	0.354197	−	0.935171i	$-0.384754\pi$
$29$	3.81482	0.708395	0.354197	+	0.935171i	$0.384754\pi$
$30$	1.14161	0.208429
$31$	9.99220	1.79465	0.897326	−	0.441368i	$-0.145506\pi$
$31$	9.99220	1.79465	0.897326	+	0.441368i	$0.145506\pi$
$32$	1.00000	0.176777
$33$	−3.19779	−0.556664
$34$	2.41338	0.413890
$35$	−1.58400	−0.267744
$36$	7.22586	1.20431
$37$	6.92288	1.13811	0.569057	−	0.822298i	$-0.307308\pi$
$37$	6.92288	1.13811	0.569057	+	0.822298i	$0.307308\pi$
$38$	0	0
$39$	0.986596	0.157982
$40$	−0.357000	−0.0564467
$41$	6.29205	0.982653	0.491326	−	0.870975i	$-0.336512\pi$
$41$	6.29205	0.982653	0.491326	+	0.870975i	$0.336512\pi$
$42$	−14.1885	−2.18933
$43$	3.24536	0.494912	0.247456	−	0.968899i	$-0.420405\pi$
$43$	3.24536	0.494912	0.247456	+	0.968899i	$0.420405\pi$
$44$	1.00000	0.150756
$45$	−2.57963	−0.384549
$46$	1.48559	0.219038
$47$	11.2995	1.64820	0.824102	−	0.566442i	$-0.191680\pi$
$47$	11.2995	1.64820	0.824102	+	0.566442i	$0.191680\pi$
$48$	−3.19779	−0.461561
$49$	12.6866	1.81237
$50$	−4.87255	−0.689083
$51$	−7.71746	−1.08066
$52$	−0.308524	−0.0427846
$53$	−9.44121	−1.29685	−0.648425	−	0.761279i	$-0.724572\pi$
$53$	−9.44121	−1.29685	−0.648425	+	0.761279i	$0.724572\pi$
$54$	−13.5134	−1.83894
$55$	−0.357000	−0.0481379
$56$	4.43696	0.592914
$57$	0	0
$58$	3.81482	0.500911
$59$	−11.8477	−1.54245	−0.771223	−	0.636565i	$-0.780354\pi$
$59$	−11.8477	−1.54245	−0.771223	+	0.636565i	$0.780354\pi$
$60$	1.14161	0.147381
$61$	3.86756	0.495190	0.247595	−	0.968864i	$-0.420360\pi$
$61$	3.86756	0.495190	0.247595	+	0.968864i	$0.420360\pi$
$62$	9.99220	1.26901
$63$	32.0608	4.03928
$64$	1.00000	0.125000
$65$	0.110143	0.0136616
$66$	−3.19779	−0.393621
$67$	1.56356	0.191020	0.0955098	−	0.995428i	$-0.469552\pi$
$67$	1.56356	0.191020	0.0955098	+	0.995428i	$0.469552\pi$
$68$	2.41338	0.292665
$69$	−4.75060	−0.571906
$70$	−1.58400	−0.189324
$71$	−5.02681	−0.596573	−0.298286	−	0.954476i	$-0.596415\pi$
$71$	−5.02681	−0.596573	−0.298286	+	0.954476i	$0.596415\pi$
$72$	7.22586	0.851575
$73$	3.27027	0.382756	0.191378	−	0.981516i	$-0.438704\pi$
$73$	3.27027	0.382756	0.191378	+	0.981516i	$0.438704\pi$
$74$	6.92288	0.804769
$75$	15.5814	1.79918
$76$	0	0
$77$	4.43696	0.505638
$78$	0.986596	0.111710
$79$	−13.7070	−1.54216	−0.771079	−	0.636739i	$-0.780283\pi$
$79$	−13.7070	−1.54216	−0.771079	+	0.636739i	$0.780283\pi$
$80$	−0.357000	−0.0399139
$81$	21.5354	2.39282
$82$	6.29205	0.694841
$83$	0.214235	0.0235154	0.0117577	−	0.999931i	$-0.496257\pi$
$83$	0.214235	0.0235154	0.0117577	+	0.999931i	$0.496257\pi$
$84$	−14.1885	−1.54809
$85$	−0.861576	−0.0934510
$86$	3.24536	0.349956
$87$	−12.1990	−1.30787
$88$	1.00000	0.106600
$89$	17.7537	1.88189	0.940946	−	0.338556i	$-0.109938\pi$
$89$	17.7537	1.88189	0.940946	+	0.338556i	$0.109938\pi$
$90$	−2.57963	−0.271917
$91$	−1.36891	−0.143501
$92$	1.48559	0.154884
$93$	−31.9530	−3.31337
$94$	11.2995	1.16546
$95$	0	0
$96$	−3.19779	−0.326373
$97$	−6.87100	−0.697644	−0.348822	−	0.937189i	$-0.613418\pi$
$97$	−6.87100	−0.697644	−0.348822	+	0.937189i	$0.613418\pi$
$98$	12.6866	1.28154
$99$	7.22586	0.726226
$100$	−4.87255	−0.487255
$101$	−1.71003	−0.170154	−0.0850771	−	0.996374i	$-0.527114\pi$
$101$	−1.71003	−0.170154	−0.0850771	+	0.996374i	$0.527114\pi$
$102$	−7.71746	−0.764143
$103$	−14.7792	−1.45624	−0.728120	−	0.685450i	$-0.759606\pi$
$103$	−14.7792	−1.45624	−0.728120	+	0.685450i	$0.759606\pi$
$104$	−0.308524	−0.0302533
$105$	5.06529	0.494321
$106$	−9.44121	−0.917011
$107$	−7.73728	−0.747991	−0.373996	−	0.927430i	$-0.622012\pi$
$107$	−7.73728	−0.747991	−0.373996	+	0.927430i	$0.622012\pi$
$108$	−13.5134	−1.30033
$109$	−17.2958	−1.65664	−0.828318	−	0.560259i	$-0.810702\pi$
$109$	−17.2958	−1.65664	−0.828318	+	0.560259i	$0.810702\pi$
$110$	−0.357000	−0.0340386
$111$	−22.1379	−2.10124
$112$	4.43696	0.419253
$113$	1.56875	0.147575	0.0737877	−	0.997274i	$-0.476491\pi$
$113$	1.56875	0.147575	0.0737877	+	0.997274i	$0.476491\pi$
$114$	0	0
$115$	−0.530356	−0.0494560
$116$	3.81482	0.354197
$117$	−2.22935	−0.206104
$118$	−11.8477	−1.09067
$119$	10.7080	0.981605
$120$	1.14161	0.104214
$121$	1.00000	0.0909091
$122$	3.86756	0.350152
$123$	−20.1206	−1.81422
$124$	9.99220	0.897326
$125$	3.52450	0.315241
$126$	32.0608	2.85621
$127$	12.8959	1.14432	0.572162	−	0.820141i	$-0.306105\pi$
$127$	12.8959	1.14432	0.572162	+	0.820141i	$0.306105\pi$
$128$	1.00000	0.0883883
$129$	−10.3780	−0.913729
$130$	0.110143	0.00966020
$131$	14.3292	1.25194	0.625972	−	0.779845i	$-0.284702\pi$
$131$	14.3292	1.25194	0.625972	+	0.779845i	$0.284702\pi$
$132$	−3.19779	−0.278332
$133$	0	0
$134$	1.56356	0.135071
$135$	4.82429	0.415208
$136$	2.41338	0.206945
$137$	−3.35560	−0.286689	−0.143344	−	0.989673i	$-0.545786\pi$
$137$	−3.35560	−0.286689	−0.143344	+	0.989673i	$0.545786\pi$
$138$	−4.75060	−0.404398
$139$	−14.0368	−1.19059	−0.595294	−	0.803508i	$-0.702964\pi$
$139$	−14.0368	−1.19059	−0.595294	+	0.803508i	$0.702964\pi$
$140$	−1.58400	−0.133872
$141$	−36.1335	−3.04299
$142$	−5.02681	−0.421840
$143$	−0.308524	−0.0258001
$144$	7.22586	0.602155
$145$	−1.36189	−0.113099
$146$	3.27027	0.270650
$147$	−40.5691	−3.34608
$148$	6.92288	0.569057
$149$	−2.28347	−0.187069	−0.0935344	−	0.995616i	$-0.529817\pi$
$149$	−2.28347	−0.187069	−0.0935344	+	0.995616i	$0.529817\pi$
$150$	15.5814	1.27222
$151$	9.06104	0.737377	0.368688	−	0.929553i	$-0.379807\pi$
$151$	9.06104	0.737377	0.368688	+	0.929553i	$0.379807\pi$
$152$	0	0
$153$	17.4387	1.40984
$154$	4.43696	0.357540
$155$	−3.56722	−0.286526
$156$	0.986596	0.0789909
$157$	−2.81789	−0.224892	−0.112446	−	0.993658i	$-0.535868\pi$
$157$	−2.81789	−0.224892	−0.112446	+	0.993658i	$0.535868\pi$
$158$	−13.7070	−1.09047
$159$	30.1910	2.39430
$160$	−0.357000	−0.0282234
$161$	6.59150	0.519483
$162$	21.5354	1.69198
$163$	−5.92293	−0.463920	−0.231960	−	0.972725i	$-0.574514\pi$
$163$	−5.92293	−0.463920	−0.231960	+	0.972725i	$0.574514\pi$
$164$	6.29205	0.491326
$165$	1.14161	0.0888744
$166$	0.214235	0.0166279
$167$	−3.00172	−0.232280	−0.116140	−	0.993233i	$-0.537052\pi$
$167$	−3.00172	−0.232280	−0.116140	+	0.993233i	$0.537052\pi$
$168$	−14.1885	−1.09466
$169$	−12.9048	−0.992678
$170$	−0.861576	−0.0660798
$171$	0	0
$172$	3.24536	0.247456
$173$	11.3901	0.865975	0.432988	−	0.901400i	$-0.357459\pi$
$173$	11.3901	0.865975	0.432988	+	0.901400i	$0.357459\pi$
$174$	−12.1990	−0.924804
$175$	−21.6193	−1.63427
$176$	1.00000	0.0753778
$177$	37.8866	2.84773
$178$	17.7537	1.33070
$179$	15.2856	1.14250	0.571250	−	0.820776i	$-0.306459\pi$
$179$	15.2856	1.14250	0.571250	+	0.820776i	$0.306459\pi$
$180$	−2.57963	−0.192274
$181$	4.95120	0.368020	0.184010	−	0.982924i	$-0.441092\pi$
$181$	4.95120	0.368020	0.184010	+	0.982924i	$0.441092\pi$
$182$	−1.36891	−0.101470
$183$	−12.3676	−0.914242
$184$	1.48559	0.109519
$185$	−2.47147	−0.181706
$186$	−31.9530	−2.34290
$187$	2.41338	0.176483
$188$	11.2995	0.824102
$189$	−59.9584	−4.36133
$190$	0	0
$191$	6.24996	0.452231	0.226116	−	0.974100i	$-0.427397\pi$
$191$	6.24996	0.452231	0.226116	+	0.974100i	$0.427397\pi$
$192$	−3.19779	−0.230781
$193$	2.32310	0.167220	0.0836102	−	0.996499i	$-0.473355\pi$
$193$	2.32310	0.167220	0.0836102	+	0.996499i	$0.473355\pi$
$194$	−6.87100	−0.493309
$195$	−0.352215	−0.0252226
$196$	12.6866	0.906186
$197$	−19.3912	−1.38157	−0.690784	−	0.723061i	$-0.742735\pi$
$197$	−19.3912	−1.38157	−0.690784	+	0.723061i	$0.742735\pi$
$198$	7.22586	0.513519
$199$	−15.5586	−1.10292	−0.551461	−	0.834201i	$-0.685929\pi$
$199$	−15.5586	−1.10292	−0.551461	+	0.834201i	$0.685929\pi$
$200$	−4.87255	−0.344541
$201$	−4.99995	−0.352669
$202$	−1.71003	−0.120317
$203$	16.9262	1.18799
$204$	−7.71746	−0.540331
$205$	−2.24626	−0.156886
$206$	−14.7792	−1.02972
$207$	10.7347	0.746111
$208$	−0.308524	−0.0213923
$209$	0	0
$210$	5.06529	0.349538
$211$	−12.1001	−0.833003	−0.416501	−	0.909135i	$-0.636744\pi$
$211$	−12.1001	−0.833003	−0.416501	+	0.909135i	$0.636744\pi$
$212$	−9.44121	−0.648425
$213$	16.0747	1.10142
$214$	−7.73728	−0.528910
$215$	−1.15859	−0.0790154
$216$	−13.5134	−0.919470
$217$	44.3350	3.00966
$218$	−17.2958	−1.17142
$219$	−10.4576	−0.706662
$220$	−0.357000	−0.0240690
$221$	−0.744585	−0.0500862
$222$	−22.1379	−1.48580
$223$	17.9644	1.20299	0.601494	−	0.798878i	$-0.294573\pi$
$223$	17.9644	1.20299	0.601494	+	0.798878i	$0.294573\pi$
$224$	4.43696	0.296457
$225$	−35.2083	−2.34722
$226$	1.56875	0.104352
$227$	7.82077	0.519083	0.259541	−	0.965732i	$-0.416429\pi$
$227$	7.82077	0.519083	0.259541	+	0.965732i	$0.416429\pi$
$228$	0	0
$229$	−26.9364	−1.78001	−0.890004	−	0.455952i	$-0.849299\pi$
$229$	−26.9364	−1.78001	−0.890004	+	0.455952i	$0.849299\pi$
$230$	−0.530356	−0.0349707
$231$	−14.1885	−0.933532
$232$	3.81482	0.250455
$233$	−8.55510	−0.560463	−0.280232	−	0.959932i	$-0.590411\pi$
$233$	−8.55510	−0.560463	−0.280232	+	0.959932i	$0.590411\pi$
$234$	−2.22935	−0.145737
$235$	−4.03393	−0.263145
$236$	−11.8477	−0.771223
$237$	43.8321	2.84720
$238$	10.7080	0.694100
$239$	15.9376	1.03092	0.515460	−	0.856913i	$-0.327621\pi$
$239$	15.9376	1.03092	0.515460	+	0.856913i	$0.327621\pi$
$240$	1.14161	0.0736907
$241$	−18.3272	−1.18056	−0.590280	−	0.807198i	$-0.700983\pi$
$241$	−18.3272	−1.18056	−0.590280	+	0.807198i	$0.700983\pi$
$242$	1.00000	0.0642824
$243$	−28.3255	−1.81708
$244$	3.86756	0.247595
$245$	−4.52912	−0.289355
$246$	−20.1206	−1.28285
$247$	0	0
$248$	9.99220	0.634506
$249$	−0.685079	−0.0434151
$250$	3.52450	0.222909
$251$	−3.90331	−0.246375	−0.123187	−	0.992383i	$-0.539312\pi$
$251$	−3.90331	−0.246375	−0.123187	+	0.992383i	$0.539312\pi$
$252$	32.0608	2.01964
$253$	1.48559	0.0933983
$254$	12.8959	0.809159
$255$	2.75514	0.172533
$256$	1.00000	0.0625000
$257$	28.4469	1.77447	0.887235	−	0.461317i	$-0.152623\pi$
$257$	28.4469	1.77447	0.887235	+	0.461317i	$0.152623\pi$
$258$	−10.3780	−0.646104
$259$	30.7165	1.90863
$260$	0.110143	0.00683080
$261$	27.5654	1.70625
$262$	14.3292	0.885258
$263$	10.3663	0.639212	0.319606	−	0.947550i	$-0.396449\pi$
$263$	10.3663	0.639212	0.319606	+	0.947550i	$0.396449\pi$
$264$	−3.19779	−0.196810
$265$	3.37051	0.207049
$266$	0	0
$267$	−56.7727	−3.47443
$268$	1.56356	0.0955098
$269$	−19.3899	−1.18222	−0.591112	−	0.806589i	$-0.701311\pi$
$269$	−19.3899	−1.18222	−0.591112	+	0.806589i	$0.701311\pi$
$270$	4.82429	0.293597
$271$	4.30985	0.261805	0.130902	−	0.991395i	$-0.458213\pi$
$271$	4.30985	0.261805	0.130902	+	0.991395i	$0.458213\pi$
$272$	2.41338	0.146332
$273$	4.37748	0.264937
$274$	−3.35560	−0.202719
$275$	−4.87255	−0.293826
$276$	−4.75060	−0.285953
$277$	4.76355	0.286214	0.143107	−	0.989707i	$-0.454291\pi$
$277$	4.76355	0.286214	0.143107	+	0.989707i	$0.454291\pi$
$278$	−14.0368	−0.841873
$279$	72.2022	4.32263
$280$	−1.58400	−0.0946619
$281$	−12.7133	−0.758409	−0.379205	−	0.925313i	$-0.623802\pi$
$281$	−12.7133	−0.758409	−0.379205	+	0.925313i	$0.623802\pi$
$282$	−36.1335	−2.15172
$283$	25.0106	1.48672	0.743362	−	0.668890i	$-0.233230\pi$
$283$	25.0106	1.48672	0.743362	+	0.668890i	$0.233230\pi$
$284$	−5.02681	−0.298286
$285$	0	0
$286$	−0.308524	−0.0182434
$287$	27.9176	1.64792
$288$	7.22586	0.425788
$289$	−11.1756	−0.657389
$290$	−1.36189	−0.0799731
$291$	21.9720	1.28802
$292$	3.27027	0.191378
$293$	−7.47018	−0.436412	−0.218206	−	0.975903i	$-0.570021\pi$
$293$	−7.47018	−0.436412	−0.218206	+	0.975903i	$0.570021\pi$
$294$	−40.5691	−2.36604
$295$	4.22965	0.246260
$296$	6.92288	0.402384
$297$	−13.5134	−0.784127
$298$	−2.28347	−0.132278
$299$	−0.458341	−0.0265065
$300$	15.5814	0.899592
$301$	14.3995	0.829974
$302$	9.06104	0.521404
$303$	5.46831	0.314146
$304$	0	0
$305$	−1.38072	−0.0790597
$306$	17.4387	0.996904
$307$	26.4411	1.50907	0.754535	−	0.656259i	$-0.227862\pi$
$307$	26.4411	1.50907	0.754535	+	0.656259i	$0.227862\pi$
$308$	4.43696	0.252819
$309$	47.2608	2.68857
$310$	−3.56722	−0.202604
$311$	−8.39448	−0.476007	−0.238004	−	0.971264i	$-0.576493\pi$
$311$	−8.39448	−0.476007	−0.238004	+	0.971264i	$0.576493\pi$
$312$	0.986596	0.0558550
$313$	−14.5344	−0.821530	−0.410765	−	0.911741i	$-0.634738\pi$
$313$	−14.5344	−0.821530	−0.410765	+	0.911741i	$0.634738\pi$
$314$	−2.81789	−0.159022
$315$	−11.4457	−0.644894
$316$	−13.7070	−0.771079
$317$	5.58001	0.313404	0.156702	−	0.987646i	$-0.449914\pi$
$317$	5.58001	0.313404	0.156702	+	0.987646i	$0.449914\pi$
$318$	30.1910	1.69303
$319$	3.81482	0.213589
$320$	−0.357000	−0.0199569
$321$	24.7422	1.38097
$322$	6.59150	0.367330
$323$	0	0
$324$	21.5354	1.19641
$325$	1.50330	0.0833881
$326$	−5.92293	−0.328041
$327$	55.3083	3.05855
$328$	6.29205	0.347420
$329$	50.1355	2.76406
$330$	1.14161	0.0628437
$331$	23.0985	1.26961	0.634805	−	0.772673i	$-0.281081\pi$
$331$	23.0985	1.26961	0.634805	+	0.772673i	$0.281081\pi$
$332$	0.214235	0.0117577
$333$	50.0237	2.74128
$334$	−3.00172	−0.164247
$335$	−0.558193	−0.0304973
$336$	−14.1885	−0.774044
$337$	6.68570	0.364193	0.182097	−	0.983281i	$-0.441712\pi$
$337$	6.68570	0.364193	0.182097	+	0.983281i	$0.441712\pi$
$338$	−12.9048	−0.701929
$339$	−5.01653	−0.272460
$340$	−0.861576	−0.0467255
$341$	9.99220	0.541108
$342$	0	0
$343$	25.2313	1.36236
$344$	3.24536	0.174978
$345$	1.69597	0.0913078
$346$	11.3901	0.612337
$347$	20.2656	1.08792	0.543958	−	0.839112i	$-0.316925\pi$
$347$	20.2656	1.08792	0.543958	+	0.839112i	$0.316925\pi$
$348$	−12.1990	−0.653935
$349$	14.0779	0.753575	0.376788	−	0.926300i	$-0.377029\pi$
$349$	14.0779	0.753575	0.376788	+	0.926300i	$0.377029\pi$
$350$	−21.6193	−1.15560
$351$	4.16921	0.222536
$352$	1.00000	0.0533002
$353$	−6.89023	−0.366730	−0.183365	−	0.983045i	$-0.558699\pi$
$353$	−6.89023	−0.366730	−0.183365	+	0.983045i	$0.558699\pi$
$354$	37.8866	2.01365
$355$	1.79457	0.0952460
$356$	17.7537	0.940946
$357$	−34.2421	−1.81228
$358$	15.2856	0.807869
$359$	24.2330	1.27897	0.639485	−	0.768803i	$-0.279148\pi$
$359$	24.2330	1.27897	0.639485	+	0.768803i	$0.279148\pi$
$360$	−2.57963	−0.135959
$361$	0	0
$362$	4.95120	0.260229
$363$	−3.19779	−0.167840
$364$	−1.36891	−0.0717504
$365$	−1.16749	−0.0611091
$366$	−12.3676	−0.646466
$367$	5.78070	0.301750	0.150875	−	0.988553i	$-0.451791\pi$
$367$	5.78070	0.301750	0.150875	+	0.988553i	$0.451791\pi$
$368$	1.48559	0.0774418
$369$	45.4654	2.36684
$370$	−2.47147	−0.128486
$371$	−41.8903	−2.17483
$372$	−31.9530	−1.65668
$373$	19.3978	1.00438	0.502189	−	0.864758i	$-0.332528\pi$
$373$	19.3978	1.00438	0.502189	+	0.864758i	$0.332528\pi$
$374$	2.41338	0.124793
$375$	−11.2706	−0.582012
$376$	11.2995	0.582728
$377$	−1.17697	−0.0606168
$378$	−59.9584	−3.08393
$379$	19.2308	0.987822	0.493911	−	0.869513i	$-0.335567\pi$
$379$	19.2308	0.987822	0.493911	+	0.869513i	$0.335567\pi$
$380$	0	0
$381$	−41.2383	−2.11270
$382$	6.24996	0.319776
$383$	−14.0822	−0.719568	−0.359784	−	0.933036i	$-0.617150\pi$
$383$	−14.0822	−0.719568	−0.359784	+	0.933036i	$0.617150\pi$
$384$	−3.19779	−0.163186
$385$	−1.58400	−0.0807279
$386$	2.32310	0.118243
$387$	23.4505	1.19205
$388$	−6.87100	−0.348822
$389$	21.9487	1.11284	0.556422	−	0.830900i	$-0.312174\pi$
$389$	21.9487	1.11284	0.556422	+	0.830900i	$0.312174\pi$
$390$	−0.352215	−0.0178351
$391$	3.58529	0.181316
$392$	12.6866	0.640771
$393$	−45.8216	−2.31140
$394$	−19.3912	−0.976916
$395$	4.89340	0.246214
$396$	7.22586	0.363113
$397$	12.5890	0.631822	0.315911	−	0.948789i	$-0.397690\pi$
$397$	12.5890	0.631822	0.315911	+	0.948789i	$0.397690\pi$
$398$	−15.5586	−0.779883
$399$	0	0
$400$	−4.87255	−0.243628
$401$	8.62903	0.430913	0.215457	−	0.976513i	$-0.430876\pi$
$401$	8.62903	0.430913	0.215457	+	0.976513i	$0.430876\pi$
$402$	−4.99995	−0.249375
$403$	−3.08284	−0.153567
$404$	−1.71003	−0.0850771
$405$	−7.68815	−0.382027
$406$	16.9262	0.840034
$407$	6.92288	0.343155
$408$	−7.71746	−0.382071
$409$	−33.5645	−1.65966	−0.829828	−	0.558019i	$-0.811562\pi$
$409$	−33.5645	−1.65966	−0.829828	+	0.558019i	$0.811562\pi$
$410$	−2.24626	−0.110935
$411$	10.7305	0.529297
$412$	−14.7792	−0.728120
$413$	−52.5680	−2.58670
$414$	10.7347	0.527580
$415$	−0.0764820	−0.00375436
$416$	−0.308524	−0.0151266
$417$	44.8868	2.19812
$418$	0	0
$419$	25.6178	1.25151	0.625756	−	0.780019i	$-0.284791\pi$
$419$	25.6178	1.25151	0.625756	+	0.780019i	$0.284791\pi$
$420$	5.06529	0.247161
$421$	21.3954	1.04275	0.521375	−	0.853328i	$-0.325419\pi$
$421$	21.3954	1.04275	0.521375	+	0.853328i	$0.325419\pi$
$422$	−12.1001	−0.589022
$423$	81.6487	3.96989
$424$	−9.44121	−0.458506
$425$	−11.7593	−0.570409
$426$	16.0747	0.778821
$427$	17.1602	0.830440
$428$	−7.73728	−0.373996
$429$	0.986596	0.0476333
$430$	−1.15859	−0.0558723
$431$	−32.4149	−1.56137	−0.780685	−	0.624925i	$-0.785130\pi$
$431$	−32.4149	−1.56137	−0.780685	+	0.624925i	$0.785130\pi$
$432$	−13.5134	−0.650163
$433$	7.22023	0.346982	0.173491	−	0.984835i	$-0.444495\pi$
$433$	7.22023	0.346982	0.173491	+	0.984835i	$0.444495\pi$
$434$	44.3350	2.12815
$435$	4.35505	0.208809
$436$	−17.2958	−0.828318
$437$	0	0
$438$	−10.4576	−0.499685
$439$	31.5914	1.50778	0.753888	−	0.657003i	$-0.228176\pi$
$439$	31.5914	1.50778	0.753888	+	0.657003i	$0.228176\pi$
$440$	−0.357000	−0.0170193
$441$	91.6716	4.36531
$442$	−0.744585	−0.0354163
$443$	−33.3320	−1.58365	−0.791825	−	0.610748i	$-0.790869\pi$
$443$	−33.3320	−1.58365	−0.791825	+	0.610748i	$0.790869\pi$
$444$	−22.1379	−1.05062
$445$	−6.33809	−0.300454
$446$	17.9644	0.850640
$447$	7.30204	0.345375
$448$	4.43696	0.209627
$449$	−4.83691	−0.228268	−0.114134	−	0.993465i	$-0.536409\pi$
$449$	−4.83691	−0.228268	−0.114134	+	0.993465i	$0.536409\pi$
$450$	−35.2083	−1.65974
$451$	6.29205	0.296281
$452$	1.56875	0.0737877
$453$	−28.9753	−1.36138
$454$	7.82077	0.367047
$455$	0.488701	0.0229107
$456$	0	0
$457$	−32.4861	−1.51964	−0.759818	−	0.650136i	$-0.774712\pi$
$457$	−32.4861	−1.51964	−0.759818	+	0.650136i	$0.774712\pi$
$458$	−26.9364	−1.25866
$459$	−32.6129	−1.52224
$460$	−0.530356	−0.0247280
$461$	−25.5267	−1.18890	−0.594448	−	0.804134i	$-0.702629\pi$
$461$	−25.5267	−1.18890	−0.594448	+	0.804134i	$0.702629\pi$
$462$	−14.1885	−0.660107
$463$	−25.0232	−1.16293	−0.581464	−	0.813572i	$-0.697520\pi$
$463$	−25.0232	−1.16293	−0.581464	+	0.813572i	$0.697520\pi$
$464$	3.81482	0.177099
$465$	11.4072	0.528997
$466$	−8.55510	−0.396307
$467$	23.3277	1.07948	0.539738	−	0.841833i	$-0.318523\pi$
$467$	23.3277	1.07948	0.539738	+	0.841833i	$0.318523\pi$
$468$	−2.22935	−0.103052
$469$	6.93747	0.320342
$470$	−4.03393	−0.186071
$471$	9.01100	0.415205
$472$	−11.8477	−0.545337
$473$	3.24536	0.149222
$474$	43.8321	2.01328
$475$	0	0
$476$	10.7080	0.490803
$477$	−68.2208	−3.12362
$478$	15.9376	0.728971
$479$	16.4785	0.752920	0.376460	−	0.926433i	$-0.377141\pi$
$479$	16.4785	0.752920	0.376460	+	0.926433i	$0.377141\pi$
$480$	1.14161	0.0521072
$481$	−2.13588	−0.0973876
$482$	−18.3272	−0.834782
$483$	−21.0782	−0.959093
$484$	1.00000	0.0454545
$485$	2.45295	0.111383
$486$	−28.3255	−1.28487
$487$	−16.1160	−0.730287	−0.365143	−	0.930951i	$-0.618980\pi$
$487$	−16.1160	−0.730287	−0.365143	+	0.930951i	$0.618980\pi$
$488$	3.86756	0.175076
$489$	18.9403	0.856509
$490$	−4.52912	−0.204605
$491$	31.1554	1.40602	0.703012	−	0.711178i	$-0.251838\pi$
$491$	31.1554	1.40602	0.703012	+	0.711178i	$0.251838\pi$
$492$	−20.1206	−0.907109
$493$	9.20660	0.414644
$494$	0	0
$495$	−2.57963	−0.115946
$496$	9.99220	0.448663
$497$	−22.3037	−1.00046
$498$	−0.685079	−0.0306991
$499$	−17.9493	−0.803522	−0.401761	−	0.915745i	$-0.631602\pi$
$499$	−17.9493	−0.803522	−0.401761	+	0.915745i	$0.631602\pi$
$500$	3.52450	0.157621
$501$	9.59887	0.428846
$502$	−3.90331	−0.174213
$503$	37.7277	1.68219	0.841097	−	0.540884i	$-0.181910\pi$
$503$	37.7277	1.68219	0.841097	+	0.540884i	$0.181910\pi$
$504$	32.0608	1.42810
$505$	0.610481	0.0271660
$506$	1.48559	0.0660425
$507$	41.2669	1.83273
$508$	12.8959	0.572162
$509$	36.8592	1.63376	0.816878	−	0.576811i	$-0.195703\pi$
$509$	36.8592	1.63376	0.816878	+	0.576811i	$0.195703\pi$
$510$	2.75514	0.122000
$511$	14.5101	0.641887
$512$	1.00000	0.0441942
$513$	0	0
$514$	28.4469	1.25474
$515$	5.27619	0.232496
$516$	−10.3780	−0.456864
$517$	11.2995	0.496952
$518$	30.7165	1.34961
$519$	−36.4232	−1.59880
$520$	0.110143	0.00483010
$521$	0.990963	0.0434149	0.0217074	−	0.999764i	$-0.493090\pi$
$521$	0.990963	0.0434149	0.0217074	+	0.999764i	$0.493090\pi$
$522$	27.5654	1.20650
$523$	−2.32008	−0.101450	−0.0507251	−	0.998713i	$-0.516153\pi$
$523$	−2.32008	−0.101450	−0.0507251	+	0.998713i	$0.516153\pi$
$524$	14.3292	0.625972
$525$	69.1340	3.01726
$526$	10.3663	0.451991
$527$	24.1149	1.05046
$528$	−3.19779	−0.139166
$529$	−20.7930	−0.904044
$530$	3.37051	0.146406
$531$	−85.6101	−3.71516
$532$	0	0
$533$	−1.94125	−0.0840849
$534$	−56.7727	−2.45680
$535$	2.76221	0.119421
$536$	1.56356	0.0675356
$537$	−48.8802	−2.10933
$538$	−19.3899	−0.835959
$539$	12.6866	0.546451
$540$	4.82429	0.207604
$541$	0.0363339	0.00156212	0.000781059	−	1.00000i	$-0.499751\pi$
$541$	0.0363339	0.00156212	0.000781059		1.00000i	$0.499751\pi$
$542$	4.30985	0.185124
$543$	−15.8329	−0.679454
$544$	2.41338	0.103473
$545$	6.17460	0.264491
$546$	4.37748	0.187339
$547$	2.49645	0.106740	0.0533702	−	0.998575i	$-0.483004\pi$
$547$	2.49645	0.106740	0.0533702	+	0.998575i	$0.483004\pi$
$548$	−3.35560	−0.143344
$549$	27.9464	1.19272
$550$	−4.87255	−0.207766
$551$	0	0
$552$	−4.75060	−0.202199
$553$	−60.8174	−2.58622
$554$	4.76355	0.202384
$555$	7.90324	0.335474
$556$	−14.0368	−0.595294
$557$	−28.9081	−1.22488	−0.612438	−	0.790518i	$-0.709811\pi$
$557$	−28.9081	−1.22488	−0.612438	+	0.790518i	$0.709811\pi$
$558$	72.2022	3.05656
$559$	−1.00127	−0.0423493
$560$	−1.58400	−0.0669361
$561$	−7.71746	−0.325832
$562$	−12.7133	−0.536276
$563$	−37.9891	−1.60105	−0.800526	−	0.599298i	$-0.795446\pi$
$563$	−37.9891	−1.60105	−0.800526	+	0.599298i	$0.795446\pi$
$564$	−36.1335	−1.52149
$565$	−0.560044	−0.0235612
$566$	25.0106	1.05127
$567$	95.5518	4.01280
$568$	−5.02681	−0.210920
$569$	−35.4109	−1.48450	−0.742250	−	0.670123i	$-0.766242\pi$
$569$	−35.4109	−1.48450	−0.742250	+	0.670123i	$0.766242\pi$
$570$	0	0
$571$	−34.6990	−1.45211	−0.726054	−	0.687637i	$-0.758648\pi$
$571$	−34.6990	−1.45211	−0.726054	+	0.687637i	$0.758648\pi$
$572$	−0.308524	−0.0129000
$573$	−19.9861	−0.834930
$574$	27.9176	1.16526
$575$	−7.23861	−0.301871
$576$	7.22586	0.301077
$577$	−27.6397	−1.15066	−0.575328	−	0.817923i	$-0.695126\pi$
$577$	−27.6397	−1.15066	−0.575328	+	0.817923i	$0.695126\pi$
$578$	−11.1756	−0.464845
$579$	−7.42879	−0.308730
$580$	−1.36189	−0.0565495
$581$	0.950553	0.0394356
$582$	21.9720	0.910769
$583$	−9.44121	−0.391015
$584$	3.27027	0.135325
$585$	0.795879	0.0329056
$586$	−7.47018	−0.308590
$587$	−10.5891	−0.437060	−0.218530	−	0.975830i	$-0.570126\pi$
$587$	−10.5891	−0.437060	−0.218530	+	0.975830i	$0.570126\pi$
$588$	−40.5691	−1.67304
$589$	0	0
$590$	4.22965	0.174132
$591$	62.0091	2.55071
$592$	6.92288	0.284529
$593$	22.2364	0.913138	0.456569	−	0.889688i	$-0.349078\pi$
$593$	22.2364	0.913138	0.456569	+	0.889688i	$0.349078\pi$
$594$	−13.5134	−0.554461
$595$	−3.82278	−0.156719
$596$	−2.28347	−0.0935344
$597$	49.7532	2.03626
$598$	−0.458341	−0.0187429
$599$	−16.2690	−0.664735	−0.332367	−	0.943150i	$-0.607847\pi$
$599$	−16.2690	−0.664735	−0.332367	+	0.943150i	$0.607847\pi$
$600$	15.5814	0.636108
$601$	30.7890	1.25591	0.627956	−	0.778249i	$-0.283892\pi$
$601$	30.7890	1.25591	0.627956	+	0.778249i	$0.283892\pi$
$602$	14.3995	0.586880
$603$	11.2981	0.460093
$604$	9.06104	0.368688
$605$	−0.357000	−0.0145141
$606$	5.46831	0.222135
$607$	24.6730	1.00145	0.500724	−	0.865607i	$-0.333067\pi$
$607$	24.6730	1.00145	0.500724	+	0.865607i	$0.333067\pi$
$608$	0	0
$609$	−54.1265	−2.19332
$610$	−1.38072	−0.0559037
$611$	−3.48618	−0.141036
$612$	17.4387	0.704918
$613$	−25.7851	−1.04145	−0.520724	−	0.853725i	$-0.674338\pi$
$613$	−25.7851	−1.04145	−0.520724	+	0.853725i	$0.674338\pi$
$614$	26.4411	1.06707
$615$	7.18308	0.289650
$616$	4.43696	0.178770
$617$	−45.7324	−1.84112	−0.920558	−	0.390605i	$-0.872266\pi$
$617$	−45.7324	−1.84112	−0.920558	+	0.390605i	$0.872266\pi$
$618$	47.2608	1.90111
$619$	13.7292	0.551824	0.275912	−	0.961183i	$-0.411020\pi$
$619$	13.7292	0.551824	0.275912	+	0.961183i	$0.411020\pi$
$620$	−3.56722	−0.143263
$621$	−20.0754	−0.805597
$622$	−8.39448	−0.336588
$623$	78.7726	3.15596
$624$	0.986596	0.0394954
$625$	23.1045	0.924180
$626$	−14.5344	−0.580910
$627$	0	0
$628$	−2.81789	−0.112446
$629$	16.7075	0.666172
$630$	−11.4457	−0.456009
$631$	−12.5170	−0.498292	−0.249146	−	0.968466i	$-0.580150\pi$
$631$	−12.5170	−0.498292	−0.249146	+	0.968466i	$0.580150\pi$
$632$	−13.7070	−0.545235
$633$	38.6935	1.53793
$634$	5.58001	0.221610
$635$	−4.60383	−0.182698
$636$	30.1910	1.19715
$637$	−3.91413	−0.155083
$638$	3.81482	0.151030
$639$	−36.3230	−1.43692
$640$	−0.357000	−0.0141117
$641$	15.2601	0.602736	0.301368	−	0.953508i	$-0.402557\pi$
$641$	15.2601	0.602736	0.301368	+	0.953508i	$0.402557\pi$
$642$	24.7422	0.976496
$643$	−24.4145	−0.962814	−0.481407	−	0.876497i	$-0.659874\pi$
$643$	−24.4145	−0.962814	−0.481407	+	0.876497i	$0.659874\pi$
$644$	6.59150	0.259742
$645$	3.70494	0.145882
$646$	0	0
$647$	38.9821	1.53255	0.766273	−	0.642515i	$-0.222109\pi$
$647$	38.9821	1.53255	0.766273	+	0.642515i	$0.222109\pi$
$648$	21.5354	0.845991
$649$	−11.8477	−0.465065
$650$	1.50330	0.0589643
$651$	−141.774	−5.55656
$652$	−5.92293	−0.231960
$653$	−2.38996	−0.0935262	−0.0467631	−	0.998906i	$-0.514891\pi$
$653$	−2.38996	−0.0935262	−0.0467631	+	0.998906i	$0.514891\pi$
$654$	55.3083	2.16272
$655$	−5.11551	−0.199880
$656$	6.29205	0.245663
$657$	23.6305	0.921914
$658$	50.1355	1.95449
$659$	46.9484	1.82885	0.914425	−	0.404755i	$-0.132643\pi$
$659$	46.9484	1.82885	0.914425	+	0.404755i	$0.132643\pi$
$660$	1.14161	0.0444372
$661$	15.6153	0.607367	0.303683	−	0.952773i	$-0.401784\pi$
$661$	15.6153	0.607367	0.303683	+	0.952773i	$0.401784\pi$
$662$	23.0985	0.897749
$663$	2.38103	0.0924714
$664$	0.214235	0.00831394
$665$	0	0
$666$	50.0237	1.93838
$667$	5.66726	0.219437
$668$	−3.00172	−0.116140
$669$	−57.4465	−2.22101
$670$	−0.558193	−0.0215649
$671$	3.86756	0.149305
$672$	−14.1885	−0.547332
$673$	30.2047	1.16431	0.582153	−	0.813079i	$-0.302210\pi$
$673$	30.2047	1.16431	0.582153	+	0.813079i	$0.302210\pi$
$674$	6.68570	0.257523
$675$	65.8447	2.53436
$676$	−12.9048	−0.496339
$677$	7.25055	0.278661	0.139331	−	0.990246i	$-0.455505\pi$
$677$	7.25055	0.278661	0.139331	+	0.990246i	$0.455505\pi$
$678$	−5.01653	−0.192659
$679$	−30.4864	−1.16996
$680$	−0.861576	−0.0330399
$681$	−25.0092	−0.958354
$682$	9.99220	0.382621
$683$	−4.56748	−0.174770	−0.0873848	−	0.996175i	$-0.527851\pi$
$683$	−4.56748	−0.174770	−0.0873848	+	0.996175i	$0.527851\pi$
$684$	0	0
$685$	1.19795	0.0457714
$686$	25.2313	0.963334
$687$	86.1370	3.28633
$688$	3.24536	0.123728
$689$	2.91284	0.110970
$690$	1.69597	0.0645644
$691$	−32.8921	−1.25128	−0.625638	−	0.780114i	$-0.715161\pi$
$691$	−32.8921	−1.25128	−0.625638	+	0.780114i	$0.715161\pi$
$692$	11.3901	0.432988
$693$	32.0608	1.21789
$694$	20.2656	0.769273
$695$	5.01115	0.190084
$696$	−12.1990	−0.462402
$697$	15.1851	0.575176
$698$	14.0779	0.532858
$699$	27.3574	1.03475
$700$	−21.6193	−0.817133
$701$	−24.8597	−0.938938	−0.469469	−	0.882949i	$-0.655555\pi$
$701$	−24.8597	−0.938938	−0.469469	+	0.882949i	$0.655555\pi$
$702$	4.16921	0.157357
$703$	0	0
$704$	1.00000	0.0376889
$705$	12.8997	0.485829
$706$	−6.89023	−0.259317
$707$	−7.58733	−0.285351
$708$	37.8866	1.42387
$709$	18.5658	0.697254	0.348627	−	0.937262i	$-0.386648\pi$
$709$	18.5658	0.697254	0.348627	+	0.937262i	$0.386648\pi$
$710$	1.79457	0.0673491
$711$	−99.0448	−3.71447
$712$	17.7537	0.665349
$713$	14.8443	0.555924
$714$	−34.2421	−1.28148
$715$	0.110143	0.00411912
$716$	15.2856	0.571250
$717$	−50.9652	−1.90333
$718$	24.2330	0.904369
$719$	8.99861	0.335591	0.167796	−	0.985822i	$-0.446335\pi$
$719$	8.99861	0.335591	0.167796	+	0.985822i	$0.446335\pi$
$720$	−2.57963	−0.0961372
$721$	−65.5748	−2.44213
$722$	0	0
$723$	58.6066	2.17960
$724$	4.95120	0.184010
$725$	−18.5879	−0.690338
$726$	−3.19779	−0.118681
$727$	37.9321	1.40682	0.703412	−	0.710782i	$-0.251659\pi$
$727$	37.9321	1.40682	0.703412	+	0.710782i	$0.251659\pi$
$728$	−1.36891	−0.0507352
$729$	25.9729	0.961958
$730$	−1.16749	−0.0432107
$731$	7.83226	0.289687
$732$	−12.3676	−0.457121
$733$	−48.0462	−1.77463	−0.887314	−	0.461166i	$-0.847431\pi$
$733$	−48.0462	−1.77463	−0.887314	+	0.461166i	$0.847431\pi$
$734$	5.78070	0.213370
$735$	14.4832	0.534220
$736$	1.48559	0.0547596
$737$	1.56356	0.0575946
$738$	45.4654	1.67361
$739$	31.9192	1.17416	0.587082	−	0.809527i	$-0.300276\pi$
$739$	31.9192	1.17416	0.587082	+	0.809527i	$0.300276\pi$
$740$	−2.47147	−0.0908531
$741$	0	0
$742$	−41.8903	−1.53784
$743$	−30.0105	−1.10098	−0.550489	−	0.834843i	$-0.685559\pi$
$743$	−30.0105	−1.10098	−0.550489	+	0.834843i	$0.685559\pi$
$744$	−31.9530	−1.17145
$745$	0.815198	0.0298666
$746$	19.3978	0.710203
$747$	1.54803	0.0566395
$748$	2.41338	0.0882417
$749$	−34.3300	−1.25439
$750$	−11.2706	−0.411545
$751$	−25.7340	−0.939045	−0.469523	−	0.882920i	$-0.655574\pi$
$751$	−25.7340	−0.939045	−0.469523	+	0.882920i	$0.655574\pi$
$752$	11.2995	0.412051
$753$	12.4820	0.454868
$754$	−1.17697	−0.0428626
$755$	−3.23479	−0.117726
$756$	−59.9584	−2.18067
$757$	22.6227	0.822236	0.411118	−	0.911582i	$-0.365138\pi$
$757$	22.6227	0.822236	0.411118	+	0.911582i	$0.365138\pi$
$758$	19.2308	0.698495
$759$	−4.75060	−0.172436
$760$	0	0
$761$	−9.25481	−0.335486	−0.167743	−	0.985831i	$-0.553648\pi$
$761$	−9.25481	−0.335486	−0.167743	+	0.985831i	$0.553648\pi$
$762$	−41.2383	−1.49391
$763$	−76.7407	−2.77820
$764$	6.24996	0.226116
$765$	−6.22562	−0.225088
$766$	−14.0822	−0.508811
$767$	3.65532	0.131986
$768$	−3.19779	−0.115390
$769$	21.0397	0.758710	0.379355	−	0.925251i	$-0.376146\pi$
$769$	21.0397	0.758710	0.379355	+	0.925251i	$0.376146\pi$
$770$	−1.58400	−0.0570833
$771$	−90.9673	−3.27611
$772$	2.32310	0.0836102
$773$	−1.61812	−0.0581997	−0.0290998	−	0.999577i	$-0.509264\pi$
$773$	−1.61812	−0.0581997	−0.0290998	+	0.999577i	$0.509264\pi$
$774$	23.4505	0.842910
$775$	−48.6875	−1.74891
$776$	−6.87100	−0.246655
$777$	−98.2250	−3.52380
$778$	21.9487	0.786900
$779$	0	0
$780$	−0.352215	−0.0126113
$781$	−5.02681	−0.179873
$782$	3.58529	0.128210
$783$	−51.5512	−1.84229
$784$	12.6866	0.453093
$785$	1.00599	0.0359052
$786$	−45.8216	−1.63440
$787$	−3.99780	−0.142506	−0.0712532	−	0.997458i	$-0.522700\pi$
$787$	−3.99780	−0.142506	−0.0712532	+	0.997458i	$0.522700\pi$
$788$	−19.3912	−0.690784
$789$	−33.1492	−1.18014
$790$	4.89340	0.174100
$791$	6.96048	0.247486
$792$	7.22586	0.256760
$793$	−1.19324	−0.0423730
$794$	12.5890	0.446766
$795$	−10.7782	−0.382263
$796$	−15.5586	−0.551461
$797$	49.7813	1.76334	0.881672	−	0.471863i	$-0.156418\pi$
$797$	49.7813	1.76334	0.881672	+	0.471863i	$0.156418\pi$
$798$	0	0
$799$	27.2700	0.964742
$800$	−4.87255	−0.172271
$801$	128.286	4.53276
$802$	8.62903	0.304702
$803$	3.27027	0.115405
$804$	−4.99995	−0.176334
$805$	−2.35317	−0.0829383
$806$	−3.08284	−0.108588
$807$	62.0049	2.18267
$808$	−1.71003	−0.0601586
$809$	15.8027	0.555592	0.277796	−	0.960640i	$-0.410396\pi$
$809$	15.8027	0.555592	0.277796	+	0.960640i	$0.410396\pi$
$810$	−7.68815	−0.270134
$811$	25.1934	0.884660	0.442330	−	0.896852i	$-0.354152\pi$
$811$	25.1934	0.884660	0.442330	+	0.896852i	$0.354152\pi$
$812$	16.9262	0.593994
$813$	−13.7820	−0.483356
$814$	6.92288	0.242647
$815$	2.11449	0.0740673
$816$	−7.71746	−0.270165
$817$	0	0
$818$	−33.5645	−1.17355
$819$	−9.89154	−0.345639
$820$	−2.24626	−0.0784429
$821$	−20.0868	−0.701034	−0.350517	−	0.936556i	$-0.613994\pi$
$821$	−20.0868	−0.701034	−0.350517	+	0.936556i	$0.613994\pi$
$822$	10.7305	0.374270
$823$	10.1273	0.353014	0.176507	−	0.984299i	$-0.443520\pi$
$823$	10.1273	0.353014	0.176507	+	0.984299i	$0.443520\pi$
$824$	−14.7792	−0.514858
$825$	15.5814	0.542474
$826$	−52.5680	−1.82907
$827$	14.3951	0.500568	0.250284	−	0.968172i	$-0.419476\pi$
$827$	14.3951	0.500568	0.250284	+	0.968172i	$0.419476\pi$
$828$	10.7347	0.373055
$829$	15.6207	0.542529	0.271265	−	0.962505i	$-0.412558\pi$
$829$	15.6207	0.542529	0.271265	+	0.962505i	$0.412558\pi$
$830$	−0.0764820	−0.00265473
$831$	−15.2328	−0.528421
$832$	−0.308524	−0.0106962
$833$	30.6175	1.06084
$834$	44.8868	1.55430
$835$	1.07161	0.0370848
$836$	0	0
$837$	−135.029	−4.66727
$838$	25.6178	0.884952
$839$	22.8273	0.788086	0.394043	−	0.919092i	$-0.371076\pi$
$839$	22.8273	0.788086	0.394043	+	0.919092i	$0.371076\pi$
$840$	5.06529	0.174769
$841$	−14.4471	−0.498177
$842$	21.3954	0.737335
$843$	40.6543	1.40021
$844$	−12.1001	−0.416501
$845$	4.60702	0.158486
$846$	81.6487	2.80714
$847$	4.43696	0.152456
$848$	−9.44121	−0.324212
$849$	−79.9785	−2.74486
$850$	−11.7593	−0.403340
$851$	10.2846	0.352550
$852$	16.0747	0.550709
$853$	9.71488	0.332631	0.166316	−	0.986073i	$-0.446813\pi$
$853$	9.71488	0.332631	0.166316	+	0.986073i	$0.446813\pi$
$854$	17.1602	0.587210
$855$	0	0
$856$	−7.73728	−0.264455
$857$	55.9738	1.91203	0.956015	−	0.293319i	$-0.0947598\pi$
$857$	55.9738	1.91203	0.956015	+	0.293319i	$0.0947598\pi$
$858$	0.986596	0.0336818
$859$	14.4721	0.493782	0.246891	−	0.969043i	$-0.420591\pi$
$859$	14.4721	0.493782	0.246891	+	0.969043i	$0.420591\pi$
$860$	−1.15859	−0.0395077
$861$	−89.2745	−3.04247
$862$	−32.4149	−1.10406
$863$	−3.98567	−0.135674	−0.0678369	−	0.997696i	$-0.521610\pi$
$863$	−3.98567	−0.135674	−0.0678369	+	0.997696i	$0.521610\pi$
$864$	−13.5134	−0.459735
$865$	−4.06628	−0.138258
$866$	7.22023	0.245353
$867$	35.7373	1.21370
$868$	44.3350	1.50483
$869$	−13.7070	−0.464978
$870$	4.35505	0.147650
$871$	−0.482397	−0.0163454
$872$	−17.2958	−0.585709
$873$	−49.6489	−1.68036
$874$	0	0
$875$	15.6381	0.528664
$876$	−10.4576	−0.353331
$877$	−8.99140	−0.303618	−0.151809	−	0.988410i	$-0.548510\pi$
$877$	−8.99140	−0.303618	−0.151809	+	0.988410i	$0.548510\pi$
$878$	31.5914	1.06616
$879$	23.8880	0.805724
$880$	−0.357000	−0.0120345
$881$	−46.1453	−1.55467	−0.777337	−	0.629084i	$-0.783430\pi$
$881$	−46.1453	−1.55467	−0.777337	+	0.629084i	$0.783430\pi$
$882$	91.6716	3.08674
$883$	−32.9371	−1.10842	−0.554211	−	0.832376i	$-0.686980\pi$
$883$	−32.9371	−1.10842	−0.554211	+	0.832376i	$0.686980\pi$
$884$	−0.744585	−0.0250431
$885$	−13.5255	−0.454656
$886$	−33.3320	−1.11981
$887$	17.0764	0.573368	0.286684	−	0.958025i	$-0.407447\pi$
$887$	17.0764	0.573368	0.286684	+	0.958025i	$0.407447\pi$
$888$	−22.1379	−0.742900
$889$	57.2185	1.91905
$890$	−6.33809	−0.212453
$891$	21.5354	0.721464
$892$	17.9644	0.601494
$893$	0	0
$894$	7.30204	0.244217
$895$	−5.45697	−0.182406
$896$	4.43696	0.148228
$897$	1.46568	0.0489375
$898$	−4.83691	−0.161410
$899$	38.1185	1.27132
$900$	−35.2083	−1.17361
$901$	−22.7852	−0.759084
$902$	6.29205	0.209502
$903$	−46.0466	−1.53233
$904$	1.56875	0.0521758
$905$	−1.76758	−0.0587563
$906$	−28.9753	−0.962640
$907$	−31.5606	−1.04795	−0.523977	−	0.851733i	$-0.675552\pi$
$907$	−31.5606	−1.04795	−0.523977	+	0.851733i	$0.675552\pi$
$908$	7.82077	0.259541
$909$	−12.3564	−0.409836
$910$	0.488701	0.0162003
$911$	9.70449	0.321524	0.160762	−	0.986993i	$-0.448605\pi$
$911$	9.70449	0.321524	0.160762	+	0.986993i	$0.448605\pi$
$912$	0	0
$913$	0.214235	0.00709015
$914$	−32.4861	−1.07455
$915$	4.41525	0.145964
$916$	−26.9364	−0.890004
$917$	63.5779	2.09953
$918$	−32.6129	−1.07639
$919$	34.7144	1.14512	0.572561	−	0.819862i	$-0.305950\pi$
$919$	34.7144	1.14512	0.572561	+	0.819862i	$0.305950\pi$
$920$	−0.530356	−0.0174853
$921$	−84.5529	−2.78611
$922$	−25.5267	−0.840676
$923$	1.55089	0.0510483
$924$	−14.1885	−0.466766
$925$	−33.7321	−1.10910
$926$	−25.0232	−0.822314
$927$	−106.792	−3.50753
$928$	3.81482	0.125228
$929$	16.8393	0.552480	0.276240	−	0.961089i	$-0.410911\pi$
$929$	16.8393	0.552480	0.276240	+	0.961089i	$0.410911\pi$
$930$	11.4072	0.374057
$931$	0	0
$932$	−8.55510	−0.280232
$933$	26.8438	0.878826
$934$	23.3277	0.763305
$935$	−0.861576	−0.0281765
$936$	−2.22935	−0.0728686
$937$	0.849855	0.0277636	0.0138818	−	0.999904i	$-0.495581\pi$
$937$	0.849855	0.0277636	0.0138818	+	0.999904i	$0.495581\pi$
$938$	6.93747	0.226516
$939$	46.4778	1.51675
$940$	−4.03393	−0.131572
$941$	−43.8513	−1.42951	−0.714756	−	0.699374i	$-0.753462\pi$
$941$	−43.8513	−1.42951	−0.714756	+	0.699374i	$0.753462\pi$
$942$	9.01100	0.293594
$943$	9.34741	0.304393
$944$	−11.8477	−0.385611
$945$	21.4052	0.696310
$946$	3.24536	0.105516
$947$	19.1096	0.620980	0.310490	−	0.950577i	$-0.399507\pi$
$947$	19.1096	0.620980	0.310490	+	0.950577i	$0.399507\pi$
$948$	43.8321	1.42360
$949$	−1.00896	−0.0327522
$950$	0	0
$951$	−17.8437	−0.578621
$952$	10.7080	0.347050
$953$	−34.9831	−1.13322	−0.566608	−	0.823988i	$-0.691744\pi$
$953$	−34.9831	−1.13322	−0.566608	+	0.823988i	$0.691744\pi$
$954$	−68.2208	−2.20873
$955$	−2.23124	−0.0722012
$956$	15.9376	0.515460
$957$	−12.1990	−0.394338
$958$	16.4785	0.532395
$959$	−14.8887	−0.480780
$960$	1.14161	0.0368454
$961$	68.8441	2.22078
$962$	−2.13588	−0.0688634
$963$	−55.9085	−1.80163
$964$	−18.3272	−0.590280
$965$	−0.829348	−0.0266977
$966$	−21.0782	−0.678181
$967$	−21.9543	−0.706002	−0.353001	−	0.935623i	$-0.614839\pi$
$967$	−21.9543	−0.706002	−0.353001	+	0.935623i	$0.614839\pi$
$968$	1.00000	0.0321412
$969$	0	0
$970$	2.45295	0.0787595
$971$	35.8886	1.15172	0.575859	−	0.817549i	$-0.304668\pi$
$971$	35.8886	1.15172	0.575859	+	0.817549i	$0.304668\pi$
$972$	−28.3255	−0.908542
$973$	−62.2808	−1.99663
$974$	−16.1160	−0.516391
$975$	−4.80724	−0.153955
$976$	3.86756	0.123797
$977$	−20.5305	−0.656830	−0.328415	−	0.944534i	$-0.606514\pi$
$977$	−20.5305	−0.656830	−0.328415	+	0.944534i	$0.606514\pi$
$978$	18.9403	0.605643
$979$	17.7537	0.567412
$980$	−4.52912	−0.144678
$981$	−124.977	−3.99020
$982$	31.1554	0.994208
$983$	34.8811	1.11253	0.556266	−	0.831004i	$-0.312233\pi$
$983$	34.8811	1.11253	0.556266	+	0.831004i	$0.312233\pi$
$984$	−20.1206	−0.641423
$985$	6.92268	0.220575
$986$	9.20660	0.293198
$987$	−160.323	−5.10313
$988$	0	0
$989$	4.82127	0.153307
$990$	−2.57963	−0.0819861
$991$	−9.61243	−0.305349	−0.152674	−	0.988277i	$-0.548789\pi$
$991$	−9.61243	−0.305349	−0.152674	+	0.988277i	$0.548789\pi$
$992$	9.99220	0.317253
$993$	−73.8642	−2.34401
$994$	−22.3037	−0.707432
$995$	5.55443	0.176087
$996$	−0.685079	−0.0217076
$997$	−35.6818	−1.13005	−0.565026	−	0.825073i	$-0.691134\pi$
$997$	−35.6818	−1.13005	−0.565026	+	0.825073i	$0.691134\pi$
$998$	−17.9493	−0.568176
$999$	−93.5516	−2.95984

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7942.2.a.cb.1.1		15
19.14	odd	18		418.2.j.c.177.1	yes	30
19.15	odd	18		418.2.j.c.111.1	✓	30
19.18	odd	2		7942.2.a.bz.1.15		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.j.c.111.1	✓	30	19.15	odd	18
418.2.j.c.177.1	yes	30	19.14	odd	18
7942.2.a.bz.1.15		15	19.18	odd	2
7942.2.a.cb.1.1		15	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:	\( N \)	\(=\)	\( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7942.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.19779 q^{3} +1.00000 q^{4} -0.357000 q^{5} -3.19779 q^{6} +4.43696 q^{7} +1.00000 q^{8} +7.22586 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.19779 q^{3} +1.00000 q^{4} -0.357000 q^{5} -3.19779 q^{6} +4.43696 q^{7} +1.00000 q^{8} +7.22586 q^{9} -0.357000 q^{10} +1.00000 q^{11} -3.19779 q^{12} -0.308524 q^{13} +4.43696 q^{14} +1.14161 q^{15} +1.00000 q^{16} +2.41338 q^{17} +7.22586 q^{18} -0.357000 q^{20} -14.1885 q^{21} +1.00000 q^{22} +1.48559 q^{23} -3.19779 q^{24} -4.87255 q^{25} -0.308524 q^{26} -13.5134 q^{27} +4.43696 q^{28} +3.81482 q^{29} +1.14161 q^{30} +9.99220 q^{31} +1.00000 q^{32} -3.19779 q^{33} +2.41338 q^{34} -1.58400 q^{35} +7.22586 q^{36} +6.92288 q^{37} +0.986596 q^{39} -0.357000 q^{40} +6.29205 q^{41} -14.1885 q^{42} +3.24536 q^{43} +1.00000 q^{44} -2.57963 q^{45} +1.48559 q^{46} +11.2995 q^{47} -3.19779 q^{48} +12.6866 q^{49} -4.87255 q^{50} -7.71746 q^{51} -0.308524 q^{52} -9.44121 q^{53} -13.5134 q^{54} -0.357000 q^{55} +4.43696 q^{56} +3.81482 q^{58} -11.8477 q^{59} +1.14161 q^{60} +3.86756 q^{61} +9.99220 q^{62} +32.0608 q^{63} +1.00000 q^{64} +0.110143 q^{65} -3.19779 q^{66} +1.56356 q^{67} +2.41338 q^{68} -4.75060 q^{69} -1.58400 q^{70} -5.02681 q^{71} +7.22586 q^{72} +3.27027 q^{73} +6.92288 q^{74} +15.5814 q^{75} +4.43696 q^{77} +0.986596 q^{78} -13.7070 q^{79} -0.357000 q^{80} +21.5354 q^{81} +6.29205 q^{82} +0.214235 q^{83} -14.1885 q^{84} -0.861576 q^{85} +3.24536 q^{86} -12.1990 q^{87} +1.00000 q^{88} +17.7537 q^{89} -2.57963 q^{90} -1.36891 q^{91} +1.48559 q^{92} -31.9530 q^{93} +11.2995 q^{94} -3.19779 q^{96} -6.87100 q^{97} +12.6866 q^{98} +7.22586 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 15 q^{2} + 3 q^{3} + 15 q^{4} + 9 q^{5} + 3 q^{6} + 12 q^{7} + 15 q^{8} + 18 q^{9}+O(q^{10}) \) 15 * q + 15 * q^2 + 3 * q^3 + 15 * q^4 + 9 * q^5 + 3 * q^6 + 12 * q^7 + 15 * q^8 + 18 * q^9	\( 15 q + 15 q^{2} + 3 q^{3} + 15 q^{4} + 9 q^{5} + 3 q^{6} + 12 q^{7} + 15 q^{8} + 18 q^{9} + 9 q^{10} + 15 q^{11} + 3 q^{12} + 12 q^{14} - 9 q^{15} + 15 q^{16} + 21 q^{17} + 18 q^{18} + 9 q^{20} - 27 q^{21} + 15 q^{22} + 21 q^{23} + 3 q^{24} + 36 q^{25} + 3 q^{27} + 12 q^{28} - 15 q^{29} - 9 q^{30} + 30 q^{31} + 15 q^{32} + 3 q^{33} + 21 q^{34} + 30 q^{35} + 18 q^{36} - 9 q^{37} + 9 q^{40} + 9 q^{41} - 27 q^{42} + 33 q^{43} + 15 q^{44} + 18 q^{45} + 21 q^{46} + 39 q^{47} + 3 q^{48} + 33 q^{49} + 36 q^{50} + 6 q^{51} - 6 q^{53} + 3 q^{54} + 9 q^{55} + 12 q^{56} - 15 q^{58} - 6 q^{59} - 9 q^{60} + 36 q^{61} + 30 q^{62} + 30 q^{63} + 15 q^{64} + 18 q^{65} + 3 q^{66} + 15 q^{67} + 21 q^{68} + 48 q^{69} + 30 q^{70} - 3 q^{71} + 18 q^{72} + 60 q^{73} - 9 q^{74} + 21 q^{75} + 12 q^{77} + 18 q^{79} + 9 q^{80} + 27 q^{81} + 9 q^{82} + 36 q^{83} - 27 q^{84} + 15 q^{85} + 33 q^{86} + 21 q^{87} + 15 q^{88} + 6 q^{89} + 18 q^{90} - 18 q^{91} + 21 q^{92} - 54 q^{93} + 39 q^{94} + 3 q^{96} + 33 q^{98} + 18 q^{99}+O(q^{100}) \) 15 * q + 15 * q^2 + 3 * q^3 + 15 * q^4 + 9 * q^5 + 3 * q^6 + 12 * q^7 + 15 * q^8 + 18 * q^9 + 9 * q^10 + 15 * q^11 + 3 * q^12 + 12 * q^14 - 9 * q^15 + 15 * q^16 + 21 * q^17 + 18 * q^18 + 9 * q^20 - 27 * q^21 + 15 * q^22 + 21 * q^23 + 3 * q^24 + 36 * q^25 + 3 * q^27 + 12 * q^28 - 15 * q^29 - 9 * q^30 + 30 * q^31 + 15 * q^32 + 3 * q^33 + 21 * q^34 + 30 * q^35 + 18 * q^36 - 9 * q^37 + 9 * q^40 + 9 * q^41 - 27 * q^42 + 33 * q^43 + 15 * q^44 + 18 * q^45 + 21 * q^46 + 39 * q^47 + 3 * q^48 + 33 * q^49 + 36 * q^50 + 6 * q^51 - 6 * q^53 + 3 * q^54 + 9 * q^55 + 12 * q^56 - 15 * q^58 - 6 * q^59 - 9 * q^60 + 36 * q^61 + 30 * q^62 + 30 * q^63 + 15 * q^64 + 18 * q^65 + 3 * q^66 + 15 * q^67 + 21 * q^68 + 48 * q^69 + 30 * q^70 - 3 * q^71 + 18 * q^72 + 60 * q^73 - 9 * q^74 + 21 * q^75 + 12 * q^77 + 18 * q^79 + 9 * q^80 + 27 * q^81 + 9 * q^82 + 36 * q^83 - 27 * q^84 + 15 * q^85 + 33 * q^86 + 21 * q^87 + 15 * q^88 + 6 * q^89 + 18 * q^90 - 18 * q^91 + 21 * q^92 - 54 * q^93 + 39 * q^94 + 3 * q^96 + 33 * q^98 + 18 * q^99

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