LMFDB - Embedded newform 2842.2.a.z.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2842,2,Mod(1,2842)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2842, 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("2842.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2842 = 2 \cdot 7^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2842.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:	$22.6934842544$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.1019601.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 10x^{3} - x^{2} + 24x + 7 $ x^5 - 10x^3 - x^2 + 24x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 406)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.37936$ of defining polynomial
Character	$\chi$	$=$	2842.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +3.23497 q^{3} +1.00000 q^{4} +1.14439 q^{5} +3.23497 q^{6} +1.00000 q^{8} +7.46501 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.23497 q^{3} +1.00000 q^{4} +1.14439 q^{5} +3.23497 q^{6} +1.00000 q^{8} +7.46501 q^{9} +1.14439 q^{10} -0.850683 q^{11} +3.23497 q^{12} +3.66136 q^{13} +3.70208 q^{15} +1.00000 q^{16} +0.194248 q^{17} +7.46501 q^{18} -6.99369 q^{19} +1.14439 q^{20} -0.850683 q^{22} -3.46219 q^{23} +3.23497 q^{24} -3.69036 q^{25} +3.66136 q^{26} +14.4442 q^{27} -1.00000 q^{29} +3.70208 q^{30} -3.97423 q^{31} +1.00000 q^{32} -2.75193 q^{33} +0.194248 q^{34} +7.46501 q^{36} +7.20919 q^{37} -6.99369 q^{38} +11.8444 q^{39} +1.14439 q^{40} +4.04493 q^{41} +9.77788 q^{43} -0.850683 q^{44} +8.54291 q^{45} -3.46219 q^{46} +0.0538211 q^{47} +3.23497 q^{48} -3.69036 q^{50} +0.628386 q^{51} +3.66136 q^{52} -2.67097 q^{53} +14.4442 q^{54} -0.973516 q^{55} -22.6244 q^{57} -1.00000 q^{58} -8.04354 q^{59} +3.70208 q^{60} -5.08144 q^{61} -3.97423 q^{62} +1.00000 q^{64} +4.19004 q^{65} -2.75193 q^{66} -11.6003 q^{67} +0.194248 q^{68} -11.2001 q^{69} -11.2825 q^{71} +7.46501 q^{72} -7.31077 q^{73} +7.20919 q^{74} -11.9382 q^{75} -6.99369 q^{76} +11.8444 q^{78} -13.3564 q^{79} +1.14439 q^{80} +24.3314 q^{81} +4.04493 q^{82} +9.04564 q^{83} +0.222296 q^{85} +9.77788 q^{86} -3.23497 q^{87} -0.850683 q^{88} +14.2305 q^{89} +8.54291 q^{90} -3.46219 q^{92} -12.8565 q^{93} +0.0538211 q^{94} -8.00353 q^{95} +3.23497 q^{96} +18.7779 q^{97} -6.35036 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 5 q^{2} + 3 q^{3} + 5 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{8} + 8 q^{9}+O(q^{10}) $ 5 * q + 5 * q^2 + 3 * q^3 + 5 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^8 + 8 * q^9	$ 5 q + 5 q^{2} + 3 q^{3} + 5 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{8} + 8 q^{9} + 7 q^{10} + 3 q^{12} + 10 q^{13} - 10 q^{15} + 5 q^{16} + 8 q^{17} + 8 q^{18} + 2 q^{19} + 7 q^{20} + q^{23} + 3 q^{24} + 12 q^{25} + 10 q^{26} + 15 q^{27} - 5 q^{29} - 10 q^{30} + 11 q^{31} + 5 q^{32} + 9 q^{33} + 8 q^{34} + 8 q^{36} - 8 q^{37} + 2 q^{38} + 18 q^{39} + 7 q^{40} + 23 q^{41} - 3 q^{43} + 4 q^{45} + q^{46} + 16 q^{47} + 3 q^{48} + 12 q^{50} + 7 q^{51} + 10 q^{52} + 7 q^{53} + 15 q^{54} + 6 q^{55} - 34 q^{57} - 5 q^{58} - 9 q^{59} - 10 q^{60} + 15 q^{61} + 11 q^{62} + 5 q^{64} + 5 q^{65} + 9 q^{66} - 4 q^{67} + 8 q^{68} + 14 q^{69} - 22 q^{71} + 8 q^{72} - 8 q^{74} - 34 q^{75} + 2 q^{76} + 18 q^{78} - 13 q^{79} + 7 q^{80} + 17 q^{81} + 23 q^{82} + 28 q^{83} - 7 q^{85} - 3 q^{86} - 3 q^{87} + 17 q^{89} + 4 q^{90} + q^{92} + 17 q^{93} + 16 q^{94} - 9 q^{95} + 3 q^{96} + 42 q^{97} - 42 q^{99}+O(q^{100}) $ 5 * q + 5 * q^2 + 3 * q^3 + 5 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^8 + 8 * q^9 + 7 * q^10 + 3 * q^12 + 10 * q^13 - 10 * q^15 + 5 * q^16 + 8 * q^17 + 8 * q^18 + 2 * q^19 + 7 * q^20 + q^23 + 3 * q^24 + 12 * q^25 + 10 * q^26 + 15 * q^27 - 5 * q^29 - 10 * q^30 + 11 * q^31 + 5 * q^32 + 9 * q^33 + 8 * q^34 + 8 * q^36 - 8 * q^37 + 2 * q^38 + 18 * q^39 + 7 * q^40 + 23 * q^41 - 3 * q^43 + 4 * q^45 + q^46 + 16 * q^47 + 3 * q^48 + 12 * q^50 + 7 * q^51 + 10 * q^52 + 7 * q^53 + 15 * q^54 + 6 * q^55 - 34 * q^57 - 5 * q^58 - 9 * q^59 - 10 * q^60 + 15 * q^61 + 11 * q^62 + 5 * q^64 + 5 * q^65 + 9 * q^66 - 4 * q^67 + 8 * q^68 + 14 * q^69 - 22 * q^71 + 8 * q^72 - 8 * q^74 - 34 * q^75 + 2 * q^76 + 18 * q^78 - 13 * q^79 + 7 * q^80 + 17 * q^81 + 23 * q^82 + 28 * q^83 - 7 * q^85 - 3 * q^86 - 3 * q^87 + 17 * q^89 + 4 * q^90 + q^92 + 17 * q^93 + 16 * q^94 - 9 * q^95 + 3 * q^96 + 42 * q^97 - 42 * 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
$3$	3.23497	1.86771	0.933854	−	0.357653i	$-0.116423\pi$
$3$	3.23497	1.86771	0.933854	+	0.357653i	$0.116423\pi$
$4$	1.00000	0.500000
$5$	1.14439	0.511789	0.255894	−	0.966705i	$-0.417630\pi$
$5$	1.14439	0.511789	0.255894	+	0.966705i	$0.417630\pi$
$6$	3.23497	1.32067
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	7.46501	2.48834
$10$	1.14439	0.361889
$11$	−0.850683	−0.256491	−0.128245	−	0.991742i	$-0.540934\pi$
$11$	−0.850683	−0.256491	−0.128245	+	0.991742i	$0.540934\pi$
$12$	3.23497	0.933854
$13$	3.66136	1.01548	0.507739	−	0.861511i	$-0.330481\pi$
$13$	3.66136	1.01548	0.507739	+	0.861511i	$0.330481\pi$
$14$	0	0
$15$	3.70208	0.955872
$16$	1.00000	0.250000
$17$	0.194248	0.0471121	0.0235561	−	0.999723i	$-0.492501\pi$
$17$	0.194248	0.0471121	0.0235561	+	0.999723i	$0.492501\pi$
$18$	7.46501	1.75952
$19$	−6.99369	−1.60446	−0.802231	−	0.597014i	$-0.796354\pi$
$19$	−6.99369	−1.60446	−0.802231	+	0.597014i	$0.796354\pi$
$20$	1.14439	0.255894
$21$	0	0
$22$	−0.850683	−0.181366
$23$	−3.46219	−0.721916	−0.360958	−	0.932582i	$-0.617550\pi$
$23$	−3.46219	−0.721916	−0.360958	+	0.932582i	$0.617550\pi$
$24$	3.23497	0.660335
$25$	−3.69036	−0.738072
$26$	3.66136	0.718051
$27$	14.4442	2.77978
$28$	0	0
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	3.70208	0.675904
$31$	−3.97423	−0.713792	−0.356896	−	0.934144i	$-0.616165\pi$
$31$	−3.97423	−0.713792	−0.356896	+	0.934144i	$0.616165\pi$
$32$	1.00000	0.176777
$33$	−2.75193	−0.479050
$34$	0.194248	0.0333133
$35$	0	0
$36$	7.46501	1.24417
$37$	7.20919	1.18518	0.592592	−	0.805503i	$-0.298105\pi$
$37$	7.20919	1.18518	0.592592	+	0.805503i	$0.298105\pi$
$38$	−6.99369	−1.13453
$39$	11.8444	1.89662
$40$	1.14439	0.180945
$41$	4.04493	0.631712	0.315856	−	0.948807i	$-0.397708\pi$
$41$	4.04493	0.631712	0.315856	+	0.948807i	$0.397708\pi$
$42$	0	0
$43$	9.77788	1.49111	0.745556	−	0.666443i	$-0.232184\pi$
$43$	9.77788	1.49111	0.745556	+	0.666443i	$0.232184\pi$
$44$	−0.850683	−0.128245
$45$	8.54291	1.27350
$46$	−3.46219	−0.510472
$47$	0.0538211	0.00785061	0.00392531	−	0.999992i	$-0.498751\pi$
$47$	0.0538211	0.00785061	0.00392531	+	0.999992i	$0.498751\pi$
$48$	3.23497	0.466927
$49$	0	0
$50$	−3.69036	−0.521896
$51$	0.628386	0.0879917
$52$	3.66136	0.507739
$53$	−2.67097	−0.366886	−0.183443	−	0.983030i	$-0.558724\pi$
$53$	−2.67097	−0.366886	−0.183443	+	0.983030i	$0.558724\pi$
$54$	14.4442	1.96560
$55$	−0.973516	−0.131269
$56$	0	0
$57$	−22.6244	−2.99667
$58$	−1.00000	−0.131306
$59$	−8.04354	−1.04718	−0.523590	−	0.851970i	$-0.675408\pi$
$59$	−8.04354	−1.04718	−0.523590	+	0.851970i	$0.675408\pi$
$60$	3.70208	0.477936
$61$	−5.08144	−0.650611	−0.325306	−	0.945609i	$-0.605467\pi$
$61$	−5.08144	−0.650611	−0.325306	+	0.945609i	$0.605467\pi$
$62$	−3.97423	−0.504727
$63$	0	0
$64$	1.00000	0.125000
$65$	4.19004	0.519710
$66$	−2.75193	−0.338739
$67$	−11.6003	−1.41720	−0.708599	−	0.705611i	$-0.750673\pi$
$67$	−11.6003	−1.41720	−0.708599	+	0.705611i	$0.750673\pi$
$68$	0.194248	0.0235561
$69$	−11.2001	−1.34833
$70$	0	0
$71$	−11.2825	−1.33898	−0.669492	−	0.742819i	$-0.733488\pi$
$71$	−11.2825	−1.33898	−0.669492	+	0.742819i	$0.733488\pi$
$72$	7.46501	0.879760
$73$	−7.31077	−0.855661	−0.427830	−	0.903859i	$-0.640722\pi$
$73$	−7.31077	−0.855661	−0.427830	+	0.903859i	$0.640722\pi$
$74$	7.20919	0.838052
$75$	−11.9382	−1.37850
$76$	−6.99369	−0.802231
$77$	0	0
$78$	11.8444	1.34111
$79$	−13.3564	−1.50271	−0.751357	−	0.659896i	$-0.770600\pi$
$79$	−13.3564	−1.50271	−0.751357	+	0.659896i	$0.770600\pi$
$80$	1.14439	0.127947
$81$	24.3314	2.70348
$82$	4.04493	0.446688
$83$	9.04564	0.992888	0.496444	−	0.868069i	$-0.334639\pi$
$83$	9.04564	0.992888	0.496444	+	0.868069i	$0.334639\pi$
$84$	0	0
$85$	0.222296	0.0241114
$86$	9.77788	1.05438
$87$	−3.23497	−0.346825
$88$	−0.850683	−0.0906831
$89$	14.2305	1.50843	0.754216	−	0.656626i	$-0.228017\pi$
$89$	14.2305	1.50843	0.754216	+	0.656626i	$0.228017\pi$
$90$	8.54291	0.900502
$91$	0	0
$92$	−3.46219	−0.360958
$93$	−12.8565	−1.33316
$94$	0.0538211	0.00555122
$95$	−8.00353	−0.821145
$96$	3.23497	0.330167
$97$	18.7779	1.90660	0.953302	−	0.302017i	$-0.0976601\pi$
$97$	18.7779	1.90660	0.953302	+	0.302017i	$0.0976601\pi$
$98$	0	0
$99$	−6.35036	−0.638235
$100$	−3.69036	−0.369036
$101$	13.7194	1.36513	0.682564	−	0.730826i	$-0.260865\pi$
$101$	13.7194	1.36513	0.682564	+	0.730826i	$0.260865\pi$
$102$	0.628386	0.0622195
$103$	1.18115	0.116382	0.0581909	−	0.998305i	$-0.481467\pi$
$103$	1.18115	0.116382	0.0581909	+	0.998305i	$0.481467\pi$
$104$	3.66136	0.359026
$105$	0	0
$106$	−2.67097	−0.259428
$107$	−1.79224	−0.173263	−0.0866313	−	0.996240i	$-0.527610\pi$
$107$	−1.79224	−0.173263	−0.0866313	+	0.996240i	$0.527610\pi$
$108$	14.4442	1.38989
$109$	3.64190	0.348830	0.174415	−	0.984672i	$-0.444197\pi$
$109$	3.64190	0.348830	0.174415	+	0.984672i	$0.444197\pi$
$110$	−0.973516	−0.0928211
$111$	23.3215	2.21358
$112$	0	0
$113$	−17.7718	−1.67183	−0.835915	−	0.548859i	$-0.815063\pi$
$113$	−17.7718	−1.67183	−0.835915	+	0.548859i	$0.815063\pi$
$114$	−22.6244	−2.11896
$115$	−3.96211	−0.369468
$116$	−1.00000	−0.0928477
$117$	27.3321	2.52685
$118$	−8.04354	−0.740468
$119$	0	0
$120$	3.70208	0.337952
$121$	−10.2763	−0.934213
$122$	−5.08144	−0.460052
$123$	13.0852	1.17985
$124$	−3.97423	−0.356896
$125$	−9.94520	−0.889526
$126$	0	0
$127$	−11.5789	−1.02746	−0.513732	−	0.857950i	$-0.671738\pi$
$127$	−11.5789	−1.02746	−0.513732	+	0.857950i	$0.671738\pi$
$128$	1.00000	0.0883883
$129$	31.6311	2.78496
$130$	4.19004	0.367490
$131$	−16.1976	−1.41519	−0.707593	−	0.706620i	$-0.750219\pi$
$131$	−16.1976	−1.41519	−0.707593	+	0.706620i	$0.750219\pi$
$132$	−2.75193	−0.239525
$133$	0	0
$134$	−11.6003	−1.00211
$135$	16.5298	1.42266
$136$	0.194248	0.0166566
$137$	−12.7842	−1.09223	−0.546116	−	0.837710i	$-0.683894\pi$
$137$	−12.7842	−1.09223	−0.546116	+	0.837710i	$0.683894\pi$
$138$	−11.2001	−0.953412
$139$	0.170575	0.0144679	0.00723397	−	0.999974i	$-0.497697\pi$
$139$	0.170575	0.0144679	0.00723397	+	0.999974i	$0.497697\pi$
$140$	0	0
$141$	0.174109	0.0146627
$142$	−11.2825	−0.946804
$143$	−3.11465	−0.260460
$144$	7.46501	0.622084
$145$	−1.14439	−0.0950367
$146$	−7.31077	−0.605044
$147$	0	0
$148$	7.20919	0.592592
$149$	14.0440	1.15053	0.575263	−	0.817969i	$-0.304900\pi$
$149$	14.0440	1.15053	0.575263	+	0.817969i	$0.304900\pi$
$150$	−11.9382	−0.974750
$151$	12.1976	0.992623	0.496311	−	0.868145i	$-0.334687\pi$
$151$	12.1976	0.992623	0.496311	+	0.868145i	$0.334687\pi$
$152$	−6.99369	−0.567263
$153$	1.45006	0.117231
$154$	0	0
$155$	−4.54808	−0.365311
$156$	11.8444	0.948309
$157$	14.3897	1.14842	0.574212	−	0.818707i	$-0.305309\pi$
$157$	14.3897	1.14842	0.574212	+	0.818707i	$0.305309\pi$
$158$	−13.3564	−1.06258
$159$	−8.64051	−0.685237
$160$	1.14439	0.0904723
$161$	0	0
$162$	24.3314	1.91165
$163$	16.7674	1.31332	0.656660	−	0.754186i	$-0.271969\pi$
$163$	16.7674	1.31332	0.656660	+	0.754186i	$0.271969\pi$
$164$	4.04493	0.315856
$165$	−3.14929	−0.245172
$166$	9.04564	0.702078
$167$	−10.6555	−0.824544	−0.412272	−	0.911061i	$-0.635265\pi$
$167$	−10.6555	−0.824544	−0.412272	+	0.911061i	$0.635265\pi$
$168$	0	0
$169$	0.405541	0.0311955
$170$	0.222296	0.0170494
$171$	−52.2080	−3.99244
$172$	9.77788	0.745556
$173$	17.9251	1.36282	0.681409	−	0.731902i	$-0.261367\pi$
$173$	17.9251	1.36282	0.681409	+	0.731902i	$0.261367\pi$
$174$	−3.23497	−0.245242
$175$	0	0
$176$	−0.850683	−0.0641226
$177$	−26.0206	−1.95583
$178$	14.2305	1.06662
$179$	5.28920	0.395333	0.197667	−	0.980269i	$-0.436664\pi$
$179$	5.28920	0.395333	0.197667	+	0.980269i	$0.436664\pi$
$180$	8.54291	0.636751
$181$	13.1711	0.978997	0.489498	−	0.872004i	$-0.337180\pi$
$181$	13.1711	0.978997	0.489498	+	0.872004i	$0.337180\pi$
$182$	0	0
$183$	−16.4383	−1.21515
$184$	−3.46219	−0.255236
$185$	8.25016	0.606564
$186$	−12.8565	−0.942684
$187$	−0.165244	−0.0120838
$188$	0.0538211	0.00392531
$189$	0	0
$190$	−8.00353	−0.580637
$191$	9.90869	0.716968	0.358484	−	0.933536i	$-0.383294\pi$
$191$	9.90869	0.716968	0.358484	+	0.933536i	$0.383294\pi$
$192$	3.23497	0.233464
$193$	−17.3950	−1.25212	−0.626061	−	0.779774i	$-0.715334\pi$
$193$	−17.3950	−1.25212	−0.626061	+	0.779774i	$0.715334\pi$
$194$	18.7779	1.34817
$195$	13.5546	0.970667
$196$	0	0
$197$	17.5961	1.25367	0.626834	−	0.779153i	$-0.284350\pi$
$197$	17.5961	1.25367	0.626834	+	0.779153i	$0.284350\pi$
$198$	−6.35036	−0.451300
$199$	11.2846	0.799943	0.399972	−	0.916528i	$-0.369020\pi$
$199$	11.2846	0.799943	0.399972	+	0.916528i	$0.369020\pi$
$200$	−3.69036	−0.260948
$201$	−37.5265	−2.64691
$202$	13.7194	0.965291
$203$	0	0
$204$	0.628386	0.0439958
$205$	4.62899	0.323303
$206$	1.18115	0.0822943
$207$	−25.8453	−1.79637
$208$	3.66136	0.253869
$209$	5.94941	0.411529
$210$	0	0
$211$	−9.87572	−0.679873	−0.339936	−	0.940448i	$-0.610406\pi$
$211$	−9.87572	−0.679873	−0.339936	+	0.940448i	$0.610406\pi$
$212$	−2.67097	−0.183443
$213$	−36.4984	−2.50083
$214$	−1.79224	−0.122515
$215$	11.1897	0.763134
$216$	14.4442	0.982801
$217$	0	0
$218$	3.64190	0.246660
$219$	−23.6501	−1.59813
$220$	−0.973516	−0.0656345
$221$	0.711212	0.0478413
$222$	23.3215	1.56524
$223$	−16.5982	−1.11150	−0.555748	−	0.831351i	$-0.687568\pi$
$223$	−16.5982	−1.11150	−0.555748	+	0.831351i	$0.687568\pi$
$224$	0	0
$225$	−27.5486	−1.83657
$226$	−17.7718	−1.18216
$227$	17.9930	1.19424	0.597120	−	0.802152i	$-0.296312\pi$
$227$	17.9930	1.19424	0.597120	+	0.802152i	$0.296312\pi$
$228$	−22.6244	−1.49833
$229$	−2.03821	−0.134689	−0.0673444	−	0.997730i	$-0.521453\pi$
$229$	−2.03821	−0.134689	−0.0673444	+	0.997730i	$0.521453\pi$
$230$	−3.96211	−0.261253
$231$	0	0
$232$	−1.00000	−0.0656532
$233$	−16.4989	−1.08088	−0.540441	−	0.841382i	$-0.681742\pi$
$233$	−16.4989	−1.08088	−0.540441	+	0.841382i	$0.681742\pi$
$234$	27.3321	1.78675
$235$	0.0615925	0.00401785
$236$	−8.04354	−0.523590
$237$	−43.2075	−2.80663
$238$	0	0
$239$	18.7414	1.21228	0.606141	−	0.795357i	$-0.292717\pi$
$239$	18.7414	1.21228	0.606141	+	0.795357i	$0.292717\pi$
$240$	3.70208	0.238968
$241$	17.8781	1.15163	0.575813	−	0.817581i	$-0.304685\pi$
$241$	17.8781	1.15163	0.575813	+	0.817581i	$0.304685\pi$
$242$	−10.2763	−0.660588
$243$	35.3786	2.26954
$244$	−5.08144	−0.325306
$245$	0	0
$246$	13.0852	0.834283
$247$	−25.6064	−1.62930
$248$	−3.97423	−0.252364
$249$	29.2624	1.85443
$250$	−9.94520	−0.628990
$251$	−1.69249	−0.106829	−0.0534144	−	0.998572i	$-0.517010\pi$
$251$	−1.69249	−0.106829	−0.0534144	+	0.998572i	$0.517010\pi$
$252$	0	0
$253$	2.94522	0.185165
$254$	−11.5789	−0.726527
$255$	0.719122	0.0450331
$256$	1.00000	0.0625000
$257$	3.55324	0.221645	0.110822	−	0.993840i	$-0.464652\pi$
$257$	3.55324	0.221645	0.110822	+	0.993840i	$0.464652\pi$
$258$	31.6311	1.96927
$259$	0	0
$260$	4.19004	0.259855
$261$	−7.46501	−0.462073
$262$	−16.1976	−1.00069
$263$	−18.3627	−1.13229	−0.566147	−	0.824304i	$-0.691567\pi$
$263$	−18.3627	−1.13229	−0.566147	+	0.824304i	$0.691567\pi$
$264$	−2.75193	−0.169370
$265$	−3.05665	−0.187768
$266$	0	0
$267$	46.0353	2.81731
$268$	−11.6003	−0.708599
$269$	18.1820	1.10858	0.554289	−	0.832324i	$-0.312990\pi$
$269$	18.1820	1.10858	0.554289	+	0.832324i	$0.312990\pi$
$270$	16.5298	1.00597
$271$	−7.30703	−0.443871	−0.221935	−	0.975061i	$-0.571237\pi$
$271$	−7.30703	−0.443871	−0.221935	+	0.975061i	$0.571237\pi$
$272$	0.194248	0.0117780
$273$	0	0
$274$	−12.7842	−0.772324
$275$	3.13933	0.189309
$276$	−11.2001	−0.674164
$277$	−16.6420	−0.999918	−0.499959	−	0.866049i	$-0.666652\pi$
$277$	−16.6420	−0.999918	−0.499959	+	0.866049i	$0.666652\pi$
$278$	0.170575	0.0102304
$279$	−29.6676	−1.77616
$280$	0	0
$281$	13.2562	0.790800	0.395400	−	0.918509i	$-0.370606\pi$
$281$	13.2562	0.790800	0.395400	+	0.918509i	$0.370606\pi$
$282$	0.174109	0.0103681
$283$	−15.2786	−0.908217	−0.454109	−	0.890946i	$-0.650042\pi$
$283$	−15.2786	−0.908217	−0.454109	+	0.890946i	$0.650042\pi$
$284$	−11.2825	−0.669492
$285$	−25.8912	−1.53366
$286$	−3.11465	−0.184173
$287$	0	0
$288$	7.46501	0.439880
$289$	−16.9623	−0.997780
$290$	−1.14439	−0.0672011
$291$	60.7458	3.56098
$292$	−7.31077	−0.427830
$293$	−15.5191	−0.906637	−0.453318	−	0.891349i	$-0.649760\pi$
$293$	−15.5191	−0.906637	−0.453318	+	0.891349i	$0.649760\pi$
$294$	0	0
$295$	−9.20498	−0.535935
$296$	7.20919	0.419026
$297$	−12.2874	−0.712987
$298$	14.0440	0.813544
$299$	−12.6763	−0.733090
$300$	−11.9382	−0.689252
$301$	0	0
$302$	12.1976	0.701890
$303$	44.3817	2.54966
$304$	−6.99369	−0.401116
$305$	−5.81517	−0.332975
$306$	1.45006	0.0828947
$307$	3.14277	0.179368	0.0896838	−	0.995970i	$-0.471414\pi$
$307$	3.14277	0.179368	0.0896838	+	0.995970i	$0.471414\pi$
$308$	0	0
$309$	3.82097	0.217367
$310$	−4.54808	−0.258314
$311$	24.2160	1.37316	0.686581	−	0.727053i	$-0.259111\pi$
$311$	24.2160	1.37316	0.686581	+	0.727053i	$0.259111\pi$
$312$	11.8444	0.670555
$313$	−10.3528	−0.585175	−0.292588	−	0.956239i	$-0.594516\pi$
$313$	−10.3528	−0.585175	−0.292588	+	0.956239i	$0.594516\pi$
$314$	14.3897	0.812058
$315$	0	0
$316$	−13.3564	−0.751357
$317$	−34.5329	−1.93956	−0.969780	−	0.243983i	$-0.921546\pi$
$317$	−34.5329	−1.93956	−0.969780	+	0.243983i	$0.921546\pi$
$318$	−8.64051	−0.484536
$319$	0.850683	0.0476291
$320$	1.14439	0.0639736
$321$	−5.79784	−0.323604
$322$	0	0
$323$	−1.35851	−0.0755896
$324$	24.3314	1.35174
$325$	−13.5117	−0.749496
$326$	16.7674	0.928658
$327$	11.7814	0.651514
$328$	4.04493	0.223344
$329$	0	0
$330$	−3.14929	−0.173363
$331$	5.10043	0.280345	0.140173	−	0.990127i	$-0.455234\pi$
$331$	5.10043	0.280345	0.140173	+	0.990127i	$0.455234\pi$
$332$	9.04564	0.496444
$333$	53.8167	2.94914
$334$	−10.6555	−0.583041
$335$	−13.2753	−0.725306
$336$	0	0
$337$	24.7613	1.34884	0.674418	−	0.738350i	$-0.264394\pi$
$337$	24.7613	1.34884	0.674418	+	0.738350i	$0.264394\pi$
$338$	0.405541	0.0220585
$339$	−57.4912	−3.12249
$340$	0.222296	0.0120557
$341$	3.38081	0.183081
$342$	−52.2080	−2.82308
$343$	0	0
$344$	9.77788	0.527188
$345$	−12.8173	−0.690059
$346$	17.9251	0.963658
$347$	6.42032	0.344661	0.172331	−	0.985039i	$-0.444870\pi$
$347$	6.42032	0.344661	0.172331	+	0.985039i	$0.444870\pi$
$348$	−3.23497	−0.173412
$349$	−2.54039	−0.135984	−0.0679920	−	0.997686i	$-0.521659\pi$
$349$	−2.54039	−0.135984	−0.0679920	+	0.997686i	$0.521659\pi$
$350$	0	0
$351$	52.8852	2.82281
$352$	−0.850683	−0.0453415
$353$	−1.20628	−0.0642038	−0.0321019	−	0.999485i	$-0.510220\pi$
$353$	−1.20628	−0.0642038	−0.0321019	+	0.999485i	$0.510220\pi$
$354$	−26.0206	−1.38298
$355$	−12.9116	−0.685276
$356$	14.2305	0.754216
$357$	0	0
$358$	5.28920	0.279543
$359$	0.315996	0.0166777	0.00833883	−	0.999965i	$-0.497346\pi$
$359$	0.315996	0.0166777	0.00833883	+	0.999965i	$0.497346\pi$
$360$	8.54291	0.450251
$361$	29.9117	1.57430
$362$	13.1711	0.692255
$363$	−33.2436	−1.74484
$364$	0	0
$365$	−8.36640	−0.437917
$366$	−16.4383	−0.859243
$367$	24.2997	1.26843	0.634217	−	0.773155i	$-0.281322\pi$
$367$	24.2997	1.26843	0.634217	+	0.773155i	$0.281322\pi$
$368$	−3.46219	−0.180479
$369$	30.1955	1.57191
$370$	8.25016	0.428905
$371$	0	0
$372$	−12.8565	−0.666578
$373$	−9.98510	−0.517009	−0.258504	−	0.966010i	$-0.583230\pi$
$373$	−9.98510	−0.517009	−0.258504	+	0.966010i	$0.583230\pi$
$374$	−0.165244	−0.00854454
$375$	−32.1724	−1.66137
$376$	0.0538211	0.00277561
$377$	−3.66136	−0.188570
$378$	0	0
$379$	−13.0891	−0.672343	−0.336172	−	0.941801i	$-0.609132\pi$
$379$	−13.0891	−0.672343	−0.336172	+	0.941801i	$0.609132\pi$
$380$	−8.00353	−0.410573
$381$	−37.4575	−1.91901
$382$	9.90869	0.506973
$383$	−2.96390	−0.151448	−0.0757241	−	0.997129i	$-0.524127\pi$
$383$	−2.96390	−0.151448	−0.0757241	+	0.997129i	$0.524127\pi$
$384$	3.23497	0.165084
$385$	0	0
$386$	−17.3950	−0.885384
$387$	72.9920	3.71039
$388$	18.7779	0.953302
$389$	−34.9114	−1.77008	−0.885040	−	0.465514i	$-0.845869\pi$
$389$	−34.9114	−1.77008	−0.885040	+	0.465514i	$0.845869\pi$
$390$	13.5546	0.686365
$391$	−0.672523	−0.0340110
$392$	0	0
$393$	−52.3985	−2.64316
$394$	17.5961	0.886477
$395$	−15.2850	−0.769072
$396$	−6.35036	−0.319117
$397$	15.4156	0.773685	0.386842	−	0.922146i	$-0.373566\pi$
$397$	15.4156	0.773685	0.386842	+	0.922146i	$0.373566\pi$
$398$	11.2846	0.565645
$399$	0	0
$400$	−3.69036	−0.184518
$401$	38.0366	1.89946	0.949728	−	0.313077i	$-0.101360\pi$
$401$	38.0366	1.89946	0.949728	+	0.313077i	$0.101360\pi$
$402$	−37.5265	−1.87165
$403$	−14.5511	−0.724840
$404$	13.7194	0.682564
$405$	27.8447	1.38361
$406$	0	0
$407$	−6.13274	−0.303989
$408$	0.628386	0.0311098
$409$	−29.2856	−1.44808	−0.724041	−	0.689757i	$-0.757717\pi$
$409$	−29.2856	−1.44808	−0.724041	+	0.689757i	$0.757717\pi$
$410$	4.62899	0.228610
$411$	−41.3566	−2.03997
$412$	1.18115	0.0581909
$413$	0	0
$414$	−25.8453	−1.27023
$415$	10.3518	0.508149
$416$	3.66136	0.179513
$417$	0.551803	0.0270219
$418$	5.94941	0.290995
$419$	−6.29412	−0.307488	−0.153744	−	0.988111i	$-0.549133\pi$
$419$	−6.29412	−0.307488	−0.153744	+	0.988111i	$0.549133\pi$
$420$	0	0
$421$	2.94479	0.143520	0.0717602	−	0.997422i	$-0.477138\pi$
$421$	2.94479	0.143520	0.0717602	+	0.997422i	$0.477138\pi$
$422$	−9.87572	−0.480743
$423$	0.401775	0.0195350
$424$	−2.67097	−0.129714
$425$	−0.716846	−0.0347721
$426$	−36.4984	−1.76836
$427$	0	0
$428$	−1.79224	−0.0866313
$429$	−10.0758	−0.486464
$430$	11.1897	0.539617
$431$	5.45942	0.262971	0.131486	−	0.991318i	$-0.458025\pi$
$431$	5.45942	0.262971	0.131486	+	0.991318i	$0.458025\pi$
$432$	14.4442	0.694945
$433$	−16.9899	−0.816482	−0.408241	−	0.912874i	$-0.633858\pi$
$433$	−16.9899	−0.816482	−0.408241	+	0.912874i	$0.633858\pi$
$434$	0	0
$435$	−3.70208	−0.177501
$436$	3.64190	0.174415
$437$	24.2135	1.15829
$438$	−23.6501	−1.13005
$439$	−22.6419	−1.08064	−0.540321	−	0.841459i	$-0.681697\pi$
$439$	−22.6419	−1.08064	−0.540321	+	0.841459i	$0.681697\pi$
$440$	−0.973516	−0.0464106
$441$	0	0
$442$	0.711212	0.0338289
$443$	−17.1387	−0.814285	−0.407143	−	0.913365i	$-0.633475\pi$
$443$	−17.1387	−0.814285	−0.407143	+	0.913365i	$0.633475\pi$
$444$	23.3215	1.10679
$445$	16.2853	0.771998
$446$	−16.5982	−0.785946
$447$	45.4317	2.14885
$448$	0	0
$449$	−12.1802	−0.574818	−0.287409	−	0.957808i	$-0.592794\pi$
$449$	−12.1802	−0.574818	−0.287409	+	0.957808i	$0.592794\pi$
$450$	−27.5486	−1.29865
$451$	−3.44095	−0.162028
$452$	−17.7718	−0.835915
$453$	39.4587	1.85393
$454$	17.9930	0.844455
$455$	0	0
$456$	−22.6244	−1.05948
$457$	31.5102	1.47398	0.736991	−	0.675902i	$-0.236246\pi$
$457$	31.5102	1.47398	0.736991	+	0.675902i	$0.236246\pi$
$458$	−2.03821	−0.0952394
$459$	2.80575	0.130961
$460$	−3.96211	−0.184734
$461$	−6.40796	−0.298448	−0.149224	−	0.988803i	$-0.547678\pi$
$461$	−6.40796	−0.298448	−0.149224	+	0.988803i	$0.547678\pi$
$462$	0	0
$463$	−0.902939	−0.0419632	−0.0209816	−	0.999780i	$-0.506679\pi$
$463$	−0.902939	−0.0419632	−0.0209816	+	0.999780i	$0.506679\pi$
$464$	−1.00000	−0.0464238
$465$	−14.7129	−0.682294
$466$	−16.4989	−0.764299
$467$	−36.4112	−1.68491	−0.842454	−	0.538768i	$-0.818890\pi$
$467$	−36.4112	−1.68491	−0.842454	+	0.538768i	$0.818890\pi$
$468$	27.3321	1.26343
$469$	0	0
$470$	0.0615925	0.00284105
$471$	46.5502	2.14492
$472$	−8.04354	−0.370234
$473$	−8.31787	−0.382456
$474$	−43.2075	−1.98459
$475$	25.8092	1.18421
$476$	0	0
$477$	−19.9388	−0.912937
$478$	18.7414	0.857213
$479$	31.4283	1.43600	0.717998	−	0.696045i	$-0.245059\pi$
$479$	31.4283	1.43600	0.717998	+	0.696045i	$0.245059\pi$
$480$	3.70208	0.168976
$481$	26.3954	1.20353
$482$	17.8781	0.814323
$483$	0	0
$484$	−10.2763	−0.467106
$485$	21.4893	0.975778
$486$	35.3786	1.60481
$487$	14.4460	0.654609	0.327304	−	0.944919i	$-0.393860\pi$
$487$	14.4460	0.654609	0.327304	+	0.944919i	$0.393860\pi$
$488$	−5.08144	−0.230026
$489$	54.2418	2.45290
$490$	0	0
$491$	29.2405	1.31961	0.659803	−	0.751439i	$-0.270640\pi$
$491$	29.2405	1.31961	0.659803	+	0.751439i	$0.270640\pi$
$492$	13.0852	0.589927
$493$	−0.194248	−0.00874850
$494$	−25.6064	−1.15209
$495$	−7.26731	−0.326641
$496$	−3.97423	−0.178448
$497$	0	0
$498$	29.2624	1.31128
$499$	28.4905	1.27541	0.637704	−	0.770282i	$-0.279884\pi$
$499$	28.4905	1.27541	0.637704	+	0.770282i	$0.279884\pi$
$500$	−9.94520	−0.444763
$501$	−34.4700	−1.54001
$502$	−1.69249	−0.0755393
$503$	19.9091	0.887701	0.443850	−	0.896101i	$-0.353612\pi$
$503$	19.9091	0.887701	0.443850	+	0.896101i	$0.353612\pi$
$504$	0	0
$505$	15.7004	0.698657
$506$	2.94522	0.130931
$507$	1.31191	0.0582641
$508$	−11.5789	−0.513732
$509$	3.57199	0.158326	0.0791628	−	0.996862i	$-0.474775\pi$
$509$	3.57199	0.158326	0.0791628	+	0.996862i	$0.474775\pi$
$510$	0.719122	0.0318432
$511$	0	0
$512$	1.00000	0.0441942
$513$	−101.018	−4.46005
$514$	3.55324	0.156727
$515$	1.35170	0.0595628
$516$	31.6311	1.39248
$517$	−0.0457847	−0.00201361
$518$	0	0
$519$	57.9871	2.54535
$520$	4.19004	0.183745
$521$	−9.36877	−0.410453	−0.205227	−	0.978714i	$-0.565793\pi$
$521$	−9.36877	−0.410453	−0.205227	+	0.978714i	$0.565793\pi$
$522$	−7.46501	−0.326735
$523$	−13.6159	−0.595381	−0.297690	−	0.954662i	$-0.596216\pi$
$523$	−13.6159	−0.595381	−0.297690	+	0.954662i	$0.596216\pi$
$524$	−16.1976	−0.707593
$525$	0	0
$526$	−18.3627	−0.800653
$527$	−0.771986	−0.0336283
$528$	−2.75193	−0.119762
$529$	−11.0133	−0.478838
$530$	−3.05665	−0.132772
$531$	−60.0451	−2.60574
$532$	0	0
$533$	14.8099	0.641490
$534$	46.0353	1.99214
$535$	−2.05103	−0.0886738
$536$	−11.6003	−0.501055
$537$	17.1104	0.738367
$538$	18.1820	0.783883
$539$	0	0
$540$	16.5298	0.711330
$541$	10.6970	0.459901	0.229951	−	0.973202i	$-0.426144\pi$
$541$	10.6970	0.459901	0.229951	+	0.973202i	$0.426144\pi$
$542$	−7.30703	−0.313864
$543$	42.6079	1.82848
$544$	0.194248	0.00832832
$545$	4.16776	0.178527
$546$	0	0
$547$	−23.6925	−1.01302	−0.506509	−	0.862235i	$-0.669064\pi$
$547$	−23.6925	−1.01302	−0.506509	+	0.862235i	$0.669064\pi$
$548$	−12.7842	−0.546116
$549$	−37.9330	−1.61894
$550$	3.13933	0.133861
$551$	6.99369	0.297941
$552$	−11.2001	−0.476706
$553$	0	0
$554$	−16.6420	−0.707049
$555$	26.6890	1.13288
$556$	0.170575	0.00723397
$557$	12.2781	0.520242	0.260121	−	0.965576i	$-0.416238\pi$
$557$	12.2781	0.520242	0.260121	+	0.965576i	$0.416238\pi$
$558$	−29.6676	−1.25593
$559$	35.8003	1.51419
$560$	0	0
$561$	−0.534558	−0.0225690
$562$	13.2562	0.559180
$563$	37.3831	1.57551	0.787755	−	0.615989i	$-0.211244\pi$
$563$	37.3831	1.57551	0.787755	+	0.615989i	$0.211244\pi$
$564$	0.174109	0.00733133
$565$	−20.3379	−0.855624
$566$	−15.2786	−0.642207
$567$	0	0
$568$	−11.2825	−0.473402
$569$	−14.2478	−0.597300	−0.298650	−	0.954363i	$-0.596536\pi$
$569$	−14.2478	−0.597300	−0.298650	+	0.954363i	$0.596536\pi$
$570$	−25.8912	−1.08446
$571$	−6.59865	−0.276145	−0.138072	−	0.990422i	$-0.544091\pi$
$571$	−6.59865	−0.276145	−0.138072	+	0.990422i	$0.544091\pi$
$572$	−3.11465	−0.130230
$573$	32.0543	1.33909
$574$	0	0
$575$	12.7767	0.532826
$576$	7.46501	0.311042
$577$	−21.0911	−0.878032	−0.439016	−	0.898479i	$-0.644673\pi$
$577$	−21.0911	−0.878032	−0.439016	+	0.898479i	$0.644673\pi$
$578$	−16.9623	−0.705537
$579$	−56.2723	−2.33860
$580$	−1.14439	−0.0475184
$581$	0	0
$582$	60.7458	2.51800
$583$	2.27215	0.0941029
$584$	−7.31077	−0.302522
$585$	31.2787	1.29321
$586$	−15.5191	−0.641089
$587$	23.5851	0.973459	0.486730	−	0.873553i	$-0.338190\pi$
$587$	23.5851	0.973459	0.486730	+	0.873553i	$0.338190\pi$
$588$	0	0
$589$	27.7945	1.14525
$590$	−9.20498	−0.378963
$591$	56.9227	2.34149
$592$	7.20919	0.296296
$593$	−24.8808	−1.02173	−0.510865	−	0.859661i	$-0.670675\pi$
$593$	−24.8808	−1.02173	−0.510865	+	0.859661i	$0.670675\pi$
$594$	−12.2874	−0.504158
$595$	0	0
$596$	14.0440	0.575263
$597$	36.5053	1.49406
$598$	−12.6763	−0.518373
$599$	4.77907	0.195268	0.0976338	−	0.995222i	$-0.468873\pi$
$599$	4.77907	0.195268	0.0976338	+	0.995222i	$0.468873\pi$
$600$	−11.9382	−0.487375
$601$	−44.3292	−1.80823	−0.904113	−	0.427292i	$-0.859467\pi$
$601$	−44.3292	−1.80823	−0.904113	+	0.427292i	$0.859467\pi$
$602$	0	0
$603$	−86.5961	−3.52647
$604$	12.1976	0.496311
$605$	−11.7602	−0.478119
$606$	44.3817	1.80288
$607$	42.8992	1.74123	0.870613	−	0.491968i	$-0.163722\pi$
$607$	42.8992	1.74123	0.870613	+	0.491968i	$0.163722\pi$
$608$	−6.99369	−0.283632
$609$	0	0
$610$	−5.81517	−0.235449
$611$	0.197058	0.00797212
$612$	1.45006	0.0586154
$613$	26.0405	1.05177	0.525884	−	0.850557i	$-0.323735\pi$
$613$	26.0405	1.05177	0.525884	+	0.850557i	$0.323735\pi$
$614$	3.14277	0.126832
$615$	14.9746	0.603836
$616$	0	0
$617$	−38.2301	−1.53909	−0.769543	−	0.638595i	$-0.779516\pi$
$617$	−38.2301	−1.53909	−0.769543	+	0.638595i	$0.779516\pi$
$618$	3.82097	0.153702
$619$	33.8413	1.36020	0.680098	−	0.733122i	$-0.261937\pi$
$619$	33.8413	1.36020	0.680098	+	0.733122i	$0.261937\pi$
$620$	−4.54808	−0.182655
$621$	−50.0084	−2.00677
$622$	24.2160	0.970973
$623$	0	0
$624$	11.8444	0.474154
$625$	7.07059	0.282823
$626$	−10.3528	−0.413781
$627$	19.2461	0.768617
$628$	14.3897	0.574212
$629$	1.40037	0.0558365
$630$	0	0
$631$	−36.3237	−1.44602	−0.723012	−	0.690835i	$-0.757243\pi$
$631$	−36.3237	−1.44602	−0.723012	+	0.690835i	$0.757243\pi$
$632$	−13.3564	−0.531290
$633$	−31.9476	−1.26980
$634$	−34.5329	−1.37148
$635$	−13.2509	−0.525845
$636$	−8.64051	−0.342618
$637$	0	0
$638$	0.850683	0.0336789
$639$	−84.2238	−3.33184
$640$	1.14439	0.0452361
$641$	−5.01376	−0.198031	−0.0990157	−	0.995086i	$-0.531569\pi$
$641$	−5.01376	−0.198031	−0.0990157	+	0.995086i	$0.531569\pi$
$642$	−5.79784	−0.228823
$643$	−21.6758	−0.854811	−0.427406	−	0.904060i	$-0.640572\pi$
$643$	−21.6758	−0.854811	−0.427406	+	0.904060i	$0.640572\pi$
$644$	0	0
$645$	36.1985	1.42531
$646$	−1.35851	−0.0534499
$647$	−23.0945	−0.907940	−0.453970	−	0.891017i	$-0.649993\pi$
$647$	−23.0945	−0.907940	−0.453970	+	0.891017i	$0.649993\pi$
$648$	24.3314	0.955826
$649$	6.84250	0.268592
$650$	−13.5117	−0.529974
$651$	0	0
$652$	16.7674	0.656660
$653$	−33.9240	−1.32755	−0.663774	−	0.747933i	$-0.731046\pi$
$653$	−33.9240	−1.32755	−0.663774	+	0.747933i	$0.731046\pi$
$654$	11.7814	0.460690
$655$	−18.5364	−0.724276
$656$	4.04493	0.157928
$657$	−54.5750	−2.12917
$658$	0	0
$659$	−5.52520	−0.215231	−0.107616	−	0.994193i	$-0.534322\pi$
$659$	−5.52520	−0.215231	−0.107616	+	0.994193i	$0.534322\pi$
$660$	−3.14929	−0.122586
$661$	−1.62365	−0.0631527	−0.0315763	−	0.999501i	$-0.510053\pi$
$661$	−1.62365	−0.0631527	−0.0315763	+	0.999501i	$0.510053\pi$
$662$	5.10043	0.198234
$663$	2.30075	0.0893536
$664$	9.04564	0.351039
$665$	0	0
$666$	53.8167	2.08536
$667$	3.46219	0.134056
$668$	−10.6555	−0.412272
$669$	−53.6945	−2.07595
$670$	−13.2753	−0.512869
$671$	4.32269	0.166876
$672$	0	0
$673$	−1.69886	−0.0654862	−0.0327431	−	0.999464i	$-0.510424\pi$
$673$	−1.69886	−0.0654862	−0.0327431	+	0.999464i	$0.510424\pi$
$674$	24.7613	0.953771
$675$	−53.3042	−2.05168
$676$	0.405541	0.0155977
$677$	20.7277	0.796628	0.398314	−	0.917249i	$-0.369595\pi$
$677$	20.7277	0.796628	0.398314	+	0.917249i	$0.369595\pi$
$678$	−57.4912	−2.20794
$679$	0	0
$680$	0.222296	0.00852468
$681$	58.2068	2.23049
$682$	3.38081	0.129458
$683$	−30.3817	−1.16252	−0.581261	−	0.813717i	$-0.697441\pi$
$683$	−30.3817	−1.16252	−0.581261	+	0.813717i	$0.697441\pi$
$684$	−52.2080	−1.99622
$685$	−14.6302	−0.558991
$686$	0	0
$687$	−6.59355	−0.251560
$688$	9.77788	0.372778
$689$	−9.77939	−0.372565
$690$	−12.8173	−0.487945
$691$	−4.62046	−0.175771	−0.0878853	−	0.996131i	$-0.528011\pi$
$691$	−4.62046	−0.175771	−0.0878853	+	0.996131i	$0.528011\pi$
$692$	17.9251	0.681409
$693$	0	0
$694$	6.42032	0.243712
$695$	0.195204	0.00740453
$696$	−3.23497	−0.122621
$697$	0.785720	0.0297613
$698$	−2.54039	−0.0961553
$699$	−53.3735	−2.01877
$700$	0	0
$701$	36.9179	1.39437	0.697186	−	0.716890i	$-0.254435\pi$
$701$	36.9179	1.39437	0.697186	+	0.716890i	$0.254435\pi$
$702$	52.8852	1.99602
$703$	−50.4189	−1.90158
$704$	−0.850683	−0.0320613
$705$	0.199250	0.00750418
$706$	−1.20628	−0.0453989
$707$	0	0
$708$	−26.0206	−0.977914
$709$	−32.0742	−1.20457	−0.602286	−	0.798281i	$-0.705743\pi$
$709$	−32.0742	−1.20457	−0.602286	+	0.798281i	$0.705743\pi$
$710$	−12.9116	−0.484564
$711$	−99.7058	−3.73926
$712$	14.2305	0.533311
$713$	13.7595	0.515298
$714$	0	0
$715$	−3.56439	−0.133301
$716$	5.28920	0.197667
$717$	60.6279	2.26419
$718$	0.315996	0.0117929
$719$	35.8354	1.33644	0.668218	−	0.743966i	$-0.267057\pi$
$719$	35.8354	1.33644	0.668218	+	0.743966i	$0.267057\pi$
$720$	8.54291	0.318376
$721$	0	0
$722$	29.9117	1.11320
$723$	57.8349	2.15090
$724$	13.1711	0.489498
$725$	3.69036	0.137057
$726$	−33.2436	−1.23379
$727$	−12.8401	−0.476215	−0.238107	−	0.971239i	$-0.576527\pi$
$727$	−12.8401	−0.476215	−0.238107	+	0.971239i	$0.576527\pi$
$728$	0	0
$729$	41.4546	1.53536
$730$	−8.36640	−0.309654
$731$	1.89934	0.0702495
$732$	−16.4383	−0.607576
$733$	−9.13293	−0.337332	−0.168666	−	0.985673i	$-0.553946\pi$
$733$	−9.13293	−0.337332	−0.168666	+	0.985673i	$0.553946\pi$
$734$	24.2997	0.896919
$735$	0	0
$736$	−3.46219	−0.127618
$737$	9.86815	0.363498
$738$	30.1955	1.11151
$739$	6.32454	0.232652	0.116326	−	0.993211i	$-0.462888\pi$
$739$	6.32454	0.232652	0.116326	+	0.993211i	$0.462888\pi$
$740$	8.25016	0.303282
$741$	−82.8358	−3.04305
$742$	0	0
$743$	32.2973	1.18487	0.592436	−	0.805618i	$-0.298166\pi$
$743$	32.2973	1.18487	0.592436	+	0.805618i	$0.298166\pi$
$744$	−12.8565	−0.471342
$745$	16.0718	0.588826
$746$	−9.98510	−0.365581
$747$	67.5258	2.47064
$748$	−0.165244	−0.00604190
$749$	0	0
$750$	−32.1724	−1.17477
$751$	19.8619	0.724771	0.362385	−	0.932028i	$-0.381962\pi$
$751$	19.8619	0.724771	0.362385	+	0.932028i	$0.381962\pi$
$752$	0.0538211	0.00196265
$753$	−5.47514	−0.199525
$754$	−3.66136	−0.133339
$755$	13.9588	0.508013
$756$	0	0
$757$	24.1136	0.876425	0.438213	−	0.898871i	$-0.355612\pi$
$757$	24.1136	0.876425	0.438213	+	0.898871i	$0.355612\pi$
$758$	−13.0891	−0.475419
$759$	9.52770	0.345834
$760$	−8.00353	−0.290319
$761$	39.6245	1.43639	0.718194	−	0.695843i	$-0.244969\pi$
$761$	39.6245	1.43639	0.718194	+	0.695843i	$0.244969\pi$
$762$	−37.4575	−1.35694
$763$	0	0
$764$	9.90869	0.358484
$765$	1.65945	0.0599974
$766$	−2.96390	−0.107090
$767$	−29.4503	−1.06339
$768$	3.23497	0.116732
$769$	−11.8143	−0.426034	−0.213017	−	0.977049i	$-0.568329\pi$
$769$	−11.8143	−0.426034	−0.213017	+	0.977049i	$0.568329\pi$
$770$	0	0
$771$	11.4946	0.413968
$772$	−17.3950	−0.626061
$773$	18.0208	0.648164	0.324082	−	0.946029i	$-0.394945\pi$
$773$	18.0208	0.648164	0.324082	+	0.946029i	$0.394945\pi$
$774$	72.9920	2.62364
$775$	14.6663	0.526830
$776$	18.7779	0.674087
$777$	0	0
$778$	−34.9114	−1.25164
$779$	−28.2890	−1.01356
$780$	13.5546	0.485334
$781$	9.59781	0.343437
$782$	−0.672523	−0.0240494
$783$	−14.4442	−0.516192
$784$	0	0
$785$	16.4675	0.587750
$786$	−52.3985	−1.86899
$787$	−7.31843	−0.260874	−0.130437	−	0.991457i	$-0.541638\pi$
$787$	−7.31843	−0.260874	−0.130437	+	0.991457i	$0.541638\pi$
$788$	17.5961	0.626834
$789$	−59.4028	−2.11480
$790$	−15.2850	−0.543816
$791$	0	0
$792$	−6.35036	−0.225650
$793$	−18.6050	−0.660682
$794$	15.4156	0.547078
$795$	−9.88815	−0.350696
$796$	11.2846	0.399972
$797$	53.5394	1.89646	0.948232	−	0.317578i	$-0.102869\pi$
$797$	53.5394	1.89646	0.948232	+	0.317578i	$0.102869\pi$
$798$	0	0
$799$	0.0104546	0.000369859 0
$800$	−3.69036	−0.130474
$801$	106.231	3.75349
$802$	38.0366	1.34312
$803$	6.21915	0.219469
$804$	−37.5265	−1.32346
$805$	0	0
$806$	−14.5511	−0.512540
$807$	58.8183	2.07050
$808$	13.7194	0.482646
$809$	8.89326	0.312670	0.156335	−	0.987704i	$-0.450032\pi$
$809$	8.89326	0.312670	0.156335	+	0.987704i	$0.450032\pi$
$810$	27.8447	0.978361
$811$	4.11053	0.144340	0.0721701	−	0.997392i	$-0.477008\pi$
$811$	4.11053	0.144340	0.0721701	+	0.997392i	$0.477008\pi$
$812$	0	0
$813$	−23.6380	−0.829021
$814$	−6.13274	−0.214952
$815$	19.1885	0.672142
$816$	0.628386	0.0219979
$817$	−68.3834	−2.39243
$818$	−29.2856	−1.02395
$819$	0	0
$820$	4.62899	0.161652
$821$	14.2064	0.495806	0.247903	−	0.968785i	$-0.420259\pi$
$821$	14.2064	0.495806	0.247903	+	0.968785i	$0.420259\pi$
$822$	−41.3566	−1.44248
$823$	18.8402	0.656728	0.328364	−	0.944551i	$-0.393503\pi$
$823$	18.8402	0.656728	0.328364	+	0.944551i	$0.393503\pi$
$824$	1.18115	0.0411472
$825$	10.1556	0.353573
$826$	0	0
$827$	7.13405	0.248075	0.124038	−	0.992278i	$-0.460416\pi$
$827$	7.13405	0.248075	0.124038	+	0.992278i	$0.460416\pi$
$828$	−25.8453	−0.898185
$829$	1.21203	0.0420956	0.0210478	−	0.999778i	$-0.493300\pi$
$829$	1.21203	0.0420956	0.0210478	+	0.999778i	$0.493300\pi$
$830$	10.3518	0.359315
$831$	−53.8362	−1.86756
$832$	3.66136	0.126935
$833$	0	0
$834$	0.551803	0.0191074
$835$	−12.1940	−0.421992
$836$	5.94941	0.205765
$837$	−57.4044	−1.98419
$838$	−6.29412	−0.217427
$839$	13.0004	0.448823	0.224412	−	0.974494i	$-0.427954\pi$
$839$	13.0004	0.448823	0.224412	+	0.974494i	$0.427954\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	2.94479	0.101484
$843$	42.8834	1.47698
$844$	−9.87572	−0.339936
$845$	0.464099	0.0159655
$846$	0.401775	0.0138133
$847$	0	0
$848$	−2.67097	−0.0917216
$849$	−49.4257	−1.69629
$850$	−0.716846	−0.0245876
$851$	−24.9596	−0.855603
$852$	−36.4984	−1.25042
$853$	23.8201	0.815584	0.407792	−	0.913075i	$-0.366299\pi$
$853$	23.8201	0.815584	0.407792	+	0.913075i	$0.366299\pi$
$854$	0	0
$855$	−59.7465	−2.04329
$856$	−1.79224	−0.0612576
$857$	−7.27140	−0.248386	−0.124193	−	0.992258i	$-0.539634\pi$
$857$	−7.27140	−0.248386	−0.124193	+	0.992258i	$0.539634\pi$
$858$	−10.0758	−0.343982
$859$	9.83263	0.335485	0.167742	−	0.985831i	$-0.446352\pi$
$859$	9.83263	0.335485	0.167742	+	0.985831i	$0.446352\pi$
$860$	11.1897	0.381567
$861$	0	0
$862$	5.45942	0.185949
$863$	21.9413	0.746890	0.373445	−	0.927652i	$-0.378176\pi$
$863$	21.9413	0.746890	0.373445	+	0.927652i	$0.378176\pi$
$864$	14.4442	0.491400
$865$	20.5134	0.697475
$866$	−16.9899	−0.577340
$867$	−54.8724	−1.86356
$868$	0	0
$869$	11.3621	0.385432
$870$	−3.70208	−0.125512
$871$	−42.4727	−1.43913
$872$	3.64190	0.123330
$873$	140.177	4.74427
$874$	24.2135	0.819032
$875$	0	0
$876$	−23.6501	−0.799063
$877$	36.5659	1.23474	0.617372	−	0.786672i	$-0.288197\pi$
$877$	36.5659	1.23474	0.617372	+	0.786672i	$0.288197\pi$
$878$	−22.6419	−0.764129
$879$	−50.2039	−1.69333
$880$	−0.973516	−0.0328172
$881$	−33.4505	−1.12698	−0.563489	−	0.826124i	$-0.690541\pi$
$881$	−33.4505	−1.12698	−0.563489	+	0.826124i	$0.690541\pi$
$882$	0	0
$883$	−23.9555	−0.806166	−0.403083	−	0.915163i	$-0.632061\pi$
$883$	−23.9555	−0.806166	−0.403083	+	0.915163i	$0.632061\pi$
$884$	0.711212	0.0239207
$885$	−29.7778	−1.00097
$886$	−17.1387	−0.575787
$887$	7.39554	0.248318	0.124159	−	0.992262i	$-0.460377\pi$
$887$	7.39554	0.248318	0.124159	+	0.992262i	$0.460377\pi$
$888$	23.3215	0.782618
$889$	0	0
$890$	16.2853	0.545885
$891$	−20.6983	−0.693418
$892$	−16.5982	−0.555748
$893$	−0.376408	−0.0125960
$894$	45.4317	1.51946
$895$	6.05292	0.202327
$896$	0	0
$897$	−41.0074	−1.36920
$898$	−12.1802	−0.406457
$899$	3.97423	0.132548
$900$	−27.5486	−0.918286
$901$	−0.518832	−0.0172848
$902$	−3.44095	−0.114571
$903$	0	0
$904$	−17.7718	−0.591081
$905$	15.0729	0.501039
$906$	39.4587	1.31093
$907$	28.5892	0.949289	0.474644	−	0.880178i	$-0.342577\pi$
$907$	28.5892	0.949289	0.474644	+	0.880178i	$0.342577\pi$
$908$	17.9930	0.597120
$909$	102.415	3.39690
$910$	0	0
$911$	−15.2600	−0.505587	−0.252793	−	0.967520i	$-0.581349\pi$
$911$	−15.2600	−0.505587	−0.252793	+	0.967520i	$0.581349\pi$
$912$	−22.6244	−0.749167
$913$	−7.69497	−0.254666
$914$	31.5102	1.04226
$915$	−18.8119	−0.621901
$916$	−2.03821	−0.0673444
$917$	0	0
$918$	2.80575	0.0926036
$919$	−22.3019	−0.735673	−0.367836	−	0.929891i	$-0.619901\pi$
$919$	−22.3019	−0.735673	−0.367836	+	0.929891i	$0.619901\pi$
$920$	−3.96211	−0.130627
$921$	10.1668	0.335006
$922$	−6.40796	−0.211035
$923$	−41.3092	−1.35971
$924$	0	0
$925$	−26.6045	−0.874752
$926$	−0.902939	−0.0296724
$927$	8.81727	0.289597
$928$	−1.00000	−0.0328266
$929$	−44.9700	−1.47542	−0.737710	−	0.675118i	$-0.764093\pi$
$929$	−44.9700	−1.47542	−0.737710	+	0.675118i	$0.764093\pi$
$930$	−14.7129	−0.482455
$931$	0	0
$932$	−16.4989	−0.540441
$933$	78.3379	2.56467
$934$	−36.4112	−1.19141
$935$	−0.189104	−0.00618435
$936$	27.3321	0.893377
$937$	20.6347	0.674105	0.337053	−	0.941486i	$-0.390570\pi$
$937$	20.6347	0.674105	0.337053	+	0.941486i	$0.390570\pi$
$938$	0	0
$939$	−33.4910	−1.09294
$940$	0.0615925	0.00200893
$941$	33.2588	1.08421	0.542103	−	0.840312i	$-0.317628\pi$
$941$	33.2588	1.08421	0.542103	+	0.840312i	$0.317628\pi$
$942$	46.5502	1.51669
$943$	−14.0043	−0.456043
$944$	−8.04354	−0.261795
$945$	0	0
$946$	−8.31787	−0.270437
$947$	0.0959893	0.00311923	0.00155962	−	0.999999i	$-0.499504\pi$
$947$	0.0959893	0.00311923	0.00155962	+	0.999999i	$0.499504\pi$
$948$	−43.2075	−1.40332
$949$	−26.7673	−0.868905
$950$	25.8092	0.837362
$951$	−111.713	−3.62253
$952$	0	0
$953$	−11.4213	−0.369974	−0.184987	−	0.982741i	$-0.559224\pi$
$953$	−11.4213	−0.369974	−0.184987	+	0.982741i	$0.559224\pi$
$954$	−19.9388	−0.645544
$955$	11.3394	0.366936
$956$	18.7414	0.606141
$957$	2.75193	0.0889573
$958$	31.4283	1.01540
$959$	0	0
$960$	3.70208	0.119484
$961$	−15.2055	−0.490501
$962$	26.3954	0.851023
$963$	−13.3791	−0.431136
$964$	17.8781	0.575813
$965$	−19.9068	−0.640822
$966$	0	0
$967$	−9.43755	−0.303491	−0.151746	−	0.988420i	$-0.548489\pi$
$967$	−9.43755	−0.303491	−0.151746	+	0.988420i	$0.548489\pi$
$968$	−10.2763	−0.330294
$969$	−4.39474	−0.141179
$970$	21.4893	0.689980
$971$	−18.5280	−0.594592	−0.297296	−	0.954785i	$-0.596085\pi$
$971$	−18.5280	−0.594592	−0.297296	+	0.954785i	$0.596085\pi$
$972$	35.3786	1.13477
$973$	0	0
$974$	14.4460	0.462878
$975$	−43.7100	−1.39984
$976$	−5.08144	−0.162653
$977$	−40.6766	−1.30136	−0.650680	−	0.759352i	$-0.725516\pi$
$977$	−40.6766	−1.30136	−0.650680	+	0.759352i	$0.725516\pi$
$978$	54.2418	1.73446
$979$	−12.1057	−0.386899
$980$	0	0
$981$	27.1868	0.868008
$982$	29.2405	0.933102
$983$	52.6149	1.67816	0.839078	−	0.544012i	$-0.183095\pi$
$983$	52.6149	1.67816	0.839078	+	0.544012i	$0.183095\pi$
$984$	13.0852	0.417142
$985$	20.1368	0.641613
$986$	−0.194248	−0.00618612
$987$	0	0
$988$	−25.6064	−0.814648
$989$	−33.8528	−1.07646
$990$	−7.26731	−0.230970
$991$	−24.7835	−0.787273	−0.393637	−	0.919266i	$-0.628783\pi$
$991$	−24.7835	−0.787273	−0.393637	+	0.919266i	$0.628783\pi$
$992$	−3.97423	−0.126182
$993$	16.4997	0.523603
$994$	0	0
$995$	12.9140	0.409402
$996$	29.2624	0.927213
$997$	16.1891	0.512713	0.256356	−	0.966582i	$-0.417478\pi$
$997$	16.1891	0.512713	0.256356	+	0.966582i	$0.417478\pi$
$998$	28.4905	0.901850
$999$	104.131	3.29455

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2842.2.a.z.1.5		5
7.2	even	3		406.2.e.a.291.1	yes	10
7.4	even	3		406.2.e.a.233.1	✓	10
7.6	odd	2		2842.2.a.x.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.e.a.233.1	✓	10	7.4	even	3
406.2.e.a.291.1	yes	10	7.2	even	3
2842.2.a.x.1.1		5	7.6	odd	2
2842.2.a.z.1.5		5	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:	\( N \)	\(=\)	\( 2842 = 2 \cdot 7^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2842.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.23497 q^{3} +1.00000 q^{4} +1.14439 q^{5} +3.23497 q^{6} +1.00000 q^{8} +7.46501 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.23497 q^{3} +1.00000 q^{4} +1.14439 q^{5} +3.23497 q^{6} +1.00000 q^{8} +7.46501 q^{9} +1.14439 q^{10} -0.850683 q^{11} +3.23497 q^{12} +3.66136 q^{13} +3.70208 q^{15} +1.00000 q^{16} +0.194248 q^{17} +7.46501 q^{18} -6.99369 q^{19} +1.14439 q^{20} -0.850683 q^{22} -3.46219 q^{23} +3.23497 q^{24} -3.69036 q^{25} +3.66136 q^{26} +14.4442 q^{27} -1.00000 q^{29} +3.70208 q^{30} -3.97423 q^{31} +1.00000 q^{32} -2.75193 q^{33} +0.194248 q^{34} +7.46501 q^{36} +7.20919 q^{37} -6.99369 q^{38} +11.8444 q^{39} +1.14439 q^{40} +4.04493 q^{41} +9.77788 q^{43} -0.850683 q^{44} +8.54291 q^{45} -3.46219 q^{46} +0.0538211 q^{47} +3.23497 q^{48} -3.69036 q^{50} +0.628386 q^{51} +3.66136 q^{52} -2.67097 q^{53} +14.4442 q^{54} -0.973516 q^{55} -22.6244 q^{57} -1.00000 q^{58} -8.04354 q^{59} +3.70208 q^{60} -5.08144 q^{61} -3.97423 q^{62} +1.00000 q^{64} +4.19004 q^{65} -2.75193 q^{66} -11.6003 q^{67} +0.194248 q^{68} -11.2001 q^{69} -11.2825 q^{71} +7.46501 q^{72} -7.31077 q^{73} +7.20919 q^{74} -11.9382 q^{75} -6.99369 q^{76} +11.8444 q^{78} -13.3564 q^{79} +1.14439 q^{80} +24.3314 q^{81} +4.04493 q^{82} +9.04564 q^{83} +0.222296 q^{85} +9.77788 q^{86} -3.23497 q^{87} -0.850683 q^{88} +14.2305 q^{89} +8.54291 q^{90} -3.46219 q^{92} -12.8565 q^{93} +0.0538211 q^{94} -8.00353 q^{95} +3.23497 q^{96} +18.7779 q^{97} -6.35036 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 3 q^{3} + 5 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{8} + 8 q^{9}+O(q^{10}) \) 5 * q + 5 * q^2 + 3 * q^3 + 5 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^8 + 8 * q^9	\( 5 q + 5 q^{2} + 3 q^{3} + 5 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{8} + 8 q^{9} + 7 q^{10} + 3 q^{12} + 10 q^{13} - 10 q^{15} + 5 q^{16} + 8 q^{17} + 8 q^{18} + 2 q^{19} + 7 q^{20} + q^{23} + 3 q^{24} + 12 q^{25} + 10 q^{26} + 15 q^{27} - 5 q^{29} - 10 q^{30} + 11 q^{31} + 5 q^{32} + 9 q^{33} + 8 q^{34} + 8 q^{36} - 8 q^{37} + 2 q^{38} + 18 q^{39} + 7 q^{40} + 23 q^{41} - 3 q^{43} + 4 q^{45} + q^{46} + 16 q^{47} + 3 q^{48} + 12 q^{50} + 7 q^{51} + 10 q^{52} + 7 q^{53} + 15 q^{54} + 6 q^{55} - 34 q^{57} - 5 q^{58} - 9 q^{59} - 10 q^{60} + 15 q^{61} + 11 q^{62} + 5 q^{64} + 5 q^{65} + 9 q^{66} - 4 q^{67} + 8 q^{68} + 14 q^{69} - 22 q^{71} + 8 q^{72} - 8 q^{74} - 34 q^{75} + 2 q^{76} + 18 q^{78} - 13 q^{79} + 7 q^{80} + 17 q^{81} + 23 q^{82} + 28 q^{83} - 7 q^{85} - 3 q^{86} - 3 q^{87} + 17 q^{89} + 4 q^{90} + q^{92} + 17 q^{93} + 16 q^{94} - 9 q^{95} + 3 q^{96} + 42 q^{97} - 42 q^{99}+O(q^{100}) \) 5 * q + 5 * q^2 + 3 * q^3 + 5 * q^4 + 7 * q^5 + 3 * q^6 + 5 * q^8 + 8 * q^9 + 7 * q^10 + 3 * q^12 + 10 * q^13 - 10 * q^15 + 5 * q^16 + 8 * q^17 + 8 * q^18 + 2 * q^19 + 7 * q^20 + q^23 + 3 * q^24 + 12 * q^25 + 10 * q^26 + 15 * q^27 - 5 * q^29 - 10 * q^30 + 11 * q^31 + 5 * q^32 + 9 * q^33 + 8 * q^34 + 8 * q^36 - 8 * q^37 + 2 * q^38 + 18 * q^39 + 7 * q^40 + 23 * q^41 - 3 * q^43 + 4 * q^45 + q^46 + 16 * q^47 + 3 * q^48 + 12 * q^50 + 7 * q^51 + 10 * q^52 + 7 * q^53 + 15 * q^54 + 6 * q^55 - 34 * q^57 - 5 * q^58 - 9 * q^59 - 10 * q^60 + 15 * q^61 + 11 * q^62 + 5 * q^64 + 5 * q^65 + 9 * q^66 - 4 * q^67 + 8 * q^68 + 14 * q^69 - 22 * q^71 + 8 * q^72 - 8 * q^74 - 34 * q^75 + 2 * q^76 + 18 * q^78 - 13 * q^79 + 7 * q^80 + 17 * q^81 + 23 * q^82 + 28 * q^83 - 7 * q^85 - 3 * q^86 - 3 * q^87 + 17 * q^89 + 4 * q^90 + q^92 + 17 * q^93 + 16 * q^94 - 9 * q^95 + 3 * q^96 + 42 * q^97 - 42 * q^99

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