LMFDB - Embedded newform 2842.2.a.z.1.1

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			1.1
Root			$-0.298978$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.44245 q^{3} +1.00000 q^{4} +4.14347 q^{5} -2.44245 q^{6} +1.00000 q^{8} +2.96555 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.44245 q^{3} +1.00000 q^{4} +4.14347 q^{5} -2.44245 q^{6} +1.00000 q^{8} +2.96555 q^{9} +4.14347 q^{10} -4.70697 q^{11} -2.44245 q^{12} -1.91061 q^{13} -10.1202 q^{15} +1.00000 q^{16} +2.76714 q^{17} +2.96555 q^{18} +4.04040 q^{19} +4.14347 q^{20} -4.70697 q^{22} -2.17268 q^{23} -2.44245 q^{24} +12.1683 q^{25} -1.91061 q^{26} +0.0841506 q^{27} -1.00000 q^{29} -10.1202 q^{30} -0.969044 q^{31} +1.00000 q^{32} +11.4965 q^{33} +2.76714 q^{34} +2.96555 q^{36} -1.47340 q^{37} +4.04040 q^{38} +4.66657 q^{39} +4.14347 q^{40} +10.4741 q^{41} +7.84520 q^{43} -4.70697 q^{44} +12.2876 q^{45} -2.17268 q^{46} +11.7294 q^{47} -2.44245 q^{48} +12.1683 q^{50} -6.75860 q^{51} -1.91061 q^{52} -2.78082 q^{53} +0.0841506 q^{54} -19.5032 q^{55} -9.86847 q^{57} -1.00000 q^{58} +3.41673 q^{59} -10.1202 q^{60} +11.4192 q^{61} -0.969044 q^{62} +1.00000 q^{64} -7.91656 q^{65} +11.4965 q^{66} -2.27575 q^{67} +2.76714 q^{68} +5.30667 q^{69} -6.24653 q^{71} +2.96555 q^{72} -13.5230 q^{73} -1.47340 q^{74} -29.7205 q^{75} +4.04040 q^{76} +4.66657 q^{78} -4.46293 q^{79} +4.14347 q^{80} -9.10217 q^{81} +10.4741 q^{82} -6.06003 q^{83} +11.4656 q^{85} +7.84520 q^{86} +2.44245 q^{87} -4.70697 q^{88} +13.2662 q^{89} +12.2876 q^{90} -2.17268 q^{92} +2.36684 q^{93} +11.7294 q^{94} +16.7413 q^{95} -2.44245 q^{96} +16.8452 q^{97} -13.9587 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.44245	−1.41015	−0.705074	−	0.709134i	$-0.749086\pi$
$3$	−2.44245	−1.41015	−0.705074	+	0.709134i	$0.749086\pi$
$4$	1.00000	0.500000
$5$	4.14347	1.85302	0.926508	−	0.376276i	$-0.122795\pi$
$5$	4.14347	1.85302	0.926508	+	0.376276i	$0.122795\pi$
$6$	−2.44245	−0.997125
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	2.96555	0.988516
$10$	4.14347	1.31028
$11$	−4.70697	−1.41921	−0.709603	−	0.704602i	$-0.751126\pi$
$11$	−4.70697	−1.41921	−0.709603	+	0.704602i	$0.751126\pi$
$12$	−2.44245	−0.705074
$13$	−1.91061	−0.529908	−0.264954	−	0.964261i	$-0.585357\pi$
$13$	−1.91061	−0.529908	−0.264954	+	0.964261i	$0.585357\pi$
$14$	0	0
$15$	−10.1202	−2.61302
$16$	1.00000	0.250000
$17$	2.76714	0.671131	0.335565	−	0.942017i	$-0.391073\pi$
$17$	2.76714	0.671131	0.335565	+	0.942017i	$0.391073\pi$
$18$	2.96555	0.698986
$19$	4.04040	0.926932	0.463466	−	0.886115i	$-0.346606\pi$
$19$	4.04040	0.926932	0.463466	+	0.886115i	$0.346606\pi$
$20$	4.14347	0.926508
$21$	0	0
$22$	−4.70697	−1.00353
$23$	−2.17268	−0.453036	−0.226518	−	0.974007i	$-0.572734\pi$
$23$	−2.17268	−0.453036	−0.226518	+	0.974007i	$0.572734\pi$
$24$	−2.44245	−0.498562
$25$	12.1683	2.43367
$26$	−1.91061	−0.374702
$27$	0.0841506	0.0161948
$28$	0	0
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	−10.1202	−1.84769
$31$	−0.969044	−0.174045	−0.0870227	−	0.996206i	$-0.527735\pi$
$31$	−0.969044	−0.174045	−0.0870227	+	0.996206i	$0.527735\pi$
$32$	1.00000	0.176777
$33$	11.4965	2.00129
$34$	2.76714	0.474561
$35$	0	0
$36$	2.96555	0.494258
$37$	−1.47340	−0.242226	−0.121113	−	0.992639i	$-0.538646\pi$
$37$	−1.47340	−0.242226	−0.121113	+	0.992639i	$0.538646\pi$
$38$	4.04040	0.655440
$39$	4.66657	0.747249
$40$	4.14347	0.655140
$41$	10.4741	1.63578	0.817891	−	0.575373i	$-0.195143\pi$
$41$	10.4741	1.63578	0.817891	+	0.575373i	$0.195143\pi$
$42$	0	0
$43$	7.84520	1.19638	0.598191	−	0.801353i	$-0.295886\pi$
$43$	7.84520	1.19638	0.598191	+	0.801353i	$0.295886\pi$
$44$	−4.70697	−0.709603
$45$	12.2876	1.83173
$46$	−2.17268	−0.320345
$47$	11.7294	1.71091	0.855453	−	0.517880i	$-0.173279\pi$
$47$	11.7294	1.71091	0.855453	+	0.517880i	$0.173279\pi$
$48$	−2.44245	−0.352537
$49$	0	0
$50$	12.1683	1.72086
$51$	−6.75860	−0.946393
$52$	−1.91061	−0.264954
$53$	−2.78082	−0.381975	−0.190988	−	0.981592i	$-0.561169\pi$
$53$	−2.78082	−0.381975	−0.190988	+	0.981592i	$0.561169\pi$
$54$	0.0841506	0.0114514
$55$	−19.5032	−2.62981
$56$	0	0
$57$	−9.86847	−1.30711
$58$	−1.00000	−0.131306
$59$	3.41673	0.444820	0.222410	−	0.974953i	$-0.428608\pi$
$59$	3.41673	0.444820	0.222410	+	0.974953i	$0.428608\pi$
$60$	−10.1202	−1.30651
$61$	11.4192	1.46208	0.731038	−	0.682337i	$-0.239036\pi$
$61$	11.4192	1.46208	0.731038	+	0.682337i	$0.239036\pi$
$62$	−0.969044	−0.123069
$63$	0	0
$64$	1.00000	0.125000
$65$	−7.91656	−0.981929
$66$	11.4965	1.41512
$67$	−2.27575	−0.278027	−0.139014	−	0.990290i	$-0.544393\pi$
$67$	−2.27575	−0.278027	−0.139014	+	0.990290i	$0.544393\pi$
$68$	2.76714	0.335565
$69$	5.30667	0.638848
$70$	0	0
$71$	−6.24653	−0.741327	−0.370664	−	0.928767i	$-0.620870\pi$
$71$	−6.24653	−0.741327	−0.370664	+	0.928767i	$0.620870\pi$
$72$	2.96555	0.349493
$73$	−13.5230	−1.58274	−0.791371	−	0.611336i	$-0.790632\pi$
$73$	−13.5230	−1.58274	−0.791371	+	0.611336i	$0.790632\pi$
$74$	−1.47340	−0.171280
$75$	−29.7205	−3.43183
$76$	4.04040	0.463466
$77$	0	0
$78$	4.66657	0.528385
$79$	−4.46293	−0.502119	−0.251059	−	0.967972i	$-0.580779\pi$
$79$	−4.46293	−0.502119	−0.251059	+	0.967972i	$0.580779\pi$
$80$	4.14347	0.463254
$81$	−9.10217	−1.01135
$82$	10.4741	1.15667
$83$	−6.06003	−0.665175	−0.332587	−	0.943072i	$-0.607922\pi$
$83$	−6.06003	−0.665175	−0.332587	+	0.943072i	$0.607922\pi$
$84$	0	0
$85$	11.4656	1.24362
$86$	7.84520	0.845970
$87$	2.44245	0.261858
$88$	−4.70697	−0.501765
$89$	13.2662	1.40621	0.703105	−	0.711086i	$-0.251796\pi$
$89$	13.2662	1.40621	0.703105	+	0.711086i	$0.251796\pi$
$90$	12.2876	1.29523
$91$	0	0
$92$	−2.17268	−0.226518
$93$	2.36684	0.245430
$94$	11.7294	1.20979
$95$	16.7413	1.71762
$96$	−2.44245	−0.249281
$97$	16.8452	1.71037	0.855186	−	0.518322i	$-0.173443\pi$
$97$	16.8452	1.71037	0.855186	+	0.518322i	$0.173443\pi$
$98$	0	0
$99$	−13.9587	−1.40291
$100$	12.1683	1.21683
$101$	−12.4261	−1.23644	−0.618219	−	0.786006i	$-0.712146\pi$
$101$	−12.4261	−1.23644	−0.618219	+	0.786006i	$0.712146\pi$
$102$	−6.75860	−0.669201
$103$	−16.1718	−1.59346	−0.796729	−	0.604337i	$-0.793438\pi$
$103$	−16.1718	−1.59346	−0.796729	+	0.604337i	$0.793438\pi$
$104$	−1.91061	−0.187351
$105$	0	0
$106$	−2.78082	−0.270097
$107$	10.6246	1.02712	0.513558	−	0.858055i	$-0.328327\pi$
$107$	10.6246	1.02712	0.513558	+	0.858055i	$0.328327\pi$
$108$	0.0841506	0.00809739
$109$	6.09884	0.584162	0.292081	−	0.956394i	$-0.405652\pi$
$109$	6.09884	0.584162	0.292081	+	0.956394i	$0.405652\pi$
$110$	−19.5032	−1.85956
$111$	3.59871	0.341574
$112$	0	0
$113$	14.5875	1.37228	0.686139	−	0.727471i	$-0.259304\pi$
$113$	14.5875	1.37228	0.686139	+	0.727471i	$0.259304\pi$
$114$	−9.86847	−0.924267
$115$	−9.00245	−0.839483
$116$	−1.00000	−0.0928477
$117$	−5.66601	−0.523823
$118$	3.41673	0.314535
$119$	0	0
$120$	−10.1202	−0.923844
$121$	11.1556	1.01414
$122$	11.4192	1.03384
$123$	−25.5825	−2.30669
$124$	−0.969044	−0.0870227
$125$	29.7018	2.65661
$126$	0	0
$127$	5.46381	0.484835	0.242418	−	0.970172i	$-0.422060\pi$
$127$	5.46381	0.484835	0.242418	+	0.970172i	$0.422060\pi$
$128$	1.00000	0.0883883
$129$	−19.1615	−1.68708
$130$	−7.91656	−0.694328
$131$	−13.4182	−1.17235	−0.586176	−	0.810184i	$-0.699367\pi$
$131$	−13.4182	−1.17235	−0.586176	+	0.810184i	$0.699367\pi$
$132$	11.4965	1.00064
$133$	0	0
$134$	−2.27575	−0.196595
$135$	0.348675	0.0300092
$136$	2.76714	0.237281
$137$	17.1032	1.46123	0.730613	−	0.682791i	$-0.239234\pi$
$137$	17.1032	1.46123	0.730613	+	0.682791i	$0.239234\pi$
$138$	5.30667	0.451734
$139$	−3.90711	−0.331397	−0.165699	−	0.986176i	$-0.552988\pi$
$139$	−3.90711	−0.331397	−0.165699	+	0.986176i	$0.552988\pi$
$140$	0	0
$141$	−28.6484	−2.41263
$142$	−6.24653	−0.524198
$143$	8.99320	0.752049
$144$	2.96555	0.247129
$145$	−4.14347	−0.344096
$146$	−13.5230	−1.11917
$147$	0	0
$148$	−1.47340	−0.121113
$149$	−7.49827	−0.614282	−0.307141	−	0.951664i	$-0.599372\pi$
$149$	−7.49827	−0.614282	−0.307141	+	0.951664i	$0.599372\pi$
$150$	−29.7205	−2.42667
$151$	9.41817	0.766440	0.383220	−	0.923657i	$-0.374815\pi$
$151$	9.41817	0.766440	0.383220	+	0.923657i	$0.374815\pi$
$152$	4.04040	0.327720
$153$	8.20609	0.663423
$154$	0	0
$155$	−4.01520	−0.322509
$156$	4.66657	0.373625
$157$	17.8286	1.42288	0.711439	−	0.702747i	$-0.248044\pi$
$157$	17.8286	1.42288	0.711439	+	0.702747i	$0.248044\pi$
$158$	−4.46293	−0.355051
$159$	6.79201	0.538641
$160$	4.14347	0.327570
$161$	0	0
$162$	−9.10217	−0.715134
$163$	−10.8789	−0.852102	−0.426051	−	0.904699i	$-0.640096\pi$
$163$	−10.8789	−0.852102	−0.426051	+	0.904699i	$0.640096\pi$
$164$	10.4741	0.817891
$165$	47.6355	3.70842
$166$	−6.06003	−0.470350
$167$	16.0326	1.24064	0.620318	−	0.784350i	$-0.287003\pi$
$167$	16.0326	1.24064	0.620318	+	0.784350i	$0.287003\pi$
$168$	0	0
$169$	−9.34956	−0.719197
$170$	11.4656	0.879369
$171$	11.9820	0.916287
$172$	7.84520	0.598191
$173$	−6.18878	−0.470524	−0.235262	−	0.971932i	$-0.575595\pi$
$173$	−6.18878	−0.470524	−0.235262	+	0.971932i	$0.575595\pi$
$174$	2.44245	0.185161
$175$	0	0
$176$	−4.70697	−0.354801
$177$	−8.34518	−0.627262
$178$	13.2662	0.994341
$179$	1.20540	0.0900957	0.0450479	−	0.998985i	$-0.485656\pi$
$179$	1.20540	0.0900957	0.0450479	+	0.998985i	$0.485656\pi$
$180$	12.2876	0.915867
$181$	6.95105	0.516668	0.258334	−	0.966056i	$-0.416827\pi$
$181$	6.95105	0.516668	0.258334	+	0.966056i	$0.416827\pi$
$182$	0	0
$183$	−27.8907	−2.06174
$184$	−2.17268	−0.160172
$185$	−6.10500	−0.448848
$186$	2.36684	0.173545
$187$	−13.0249	−0.952472
$188$	11.7294	0.855453
$189$	0	0
$190$	16.7413	1.21454
$191$	−6.80847	−0.492644	−0.246322	−	0.969188i	$-0.579222\pi$
$191$	−6.80847	−0.492644	−0.246322	+	0.969188i	$0.579222\pi$
$192$	−2.44245	−0.176268
$193$	−3.89664	−0.280486	−0.140243	−	0.990117i	$-0.544788\pi$
$193$	−3.89664	−0.280486	−0.140243	+	0.990117i	$0.544788\pi$
$194$	16.8452	1.20942
$195$	19.3358	1.38466
$196$	0	0
$197$	15.5624	1.10877	0.554386	−	0.832260i	$-0.312953\pi$
$197$	15.5624	1.10877	0.554386	+	0.832260i	$0.312953\pi$
$198$	−13.9587	−0.992005
$199$	24.5735	1.74197	0.870986	−	0.491308i	$-0.163481\pi$
$199$	24.5735	1.74197	0.870986	+	0.491308i	$0.163481\pi$
$200$	12.1683	0.860431
$201$	5.55840	0.392059
$202$	−12.4261	−0.874294
$203$	0	0
$204$	−6.75860	−0.473197
$205$	43.3992	3.03113
$206$	−16.1718	−1.12674
$207$	−6.44320	−0.447833
$208$	−1.91061	−0.132477
$209$	−19.0181	−1.31551
$210$	0	0
$211$	8.65646	0.595935	0.297968	−	0.954576i	$-0.403691\pi$
$211$	8.65646	0.595935	0.297968	+	0.954576i	$0.403691\pi$
$212$	−2.78082	−0.190988
$213$	15.2568	1.04538
$214$	10.6246	0.726281
$215$	32.5064	2.21691
$216$	0.0841506	0.00572572
$217$	0	0
$218$	6.09884	0.413065
$219$	33.0291	2.23190
$220$	−19.5032	−1.31490
$221$	−5.28694	−0.355638
$222$	3.59871	0.241529
$223$	−10.9191	−0.731194	−0.365597	−	0.930773i	$-0.619135\pi$
$223$	−10.9191	−0.731194	−0.365597	+	0.930773i	$0.619135\pi$
$224$	0	0
$225$	36.0858	2.40572
$226$	14.5875	0.970347
$227$	−10.4951	−0.696583	−0.348292	−	0.937386i	$-0.613238\pi$
$227$	−10.4951	−0.696583	−0.348292	+	0.937386i	$0.613238\pi$
$228$	−9.86847	−0.653555
$229$	−7.51525	−0.496622	−0.248311	−	0.968680i	$-0.579875\pi$
$229$	−7.51525	−0.496622	−0.248311	+	0.968680i	$0.579875\pi$
$230$	−9.00245	−0.593604
$231$	0	0
$232$	−1.00000	−0.0656532
$233$	5.14262	0.336904	0.168452	−	0.985710i	$-0.446123\pi$
$233$	5.14262	0.336904	0.168452	+	0.985710i	$0.446123\pi$
$234$	−5.66601	−0.370399
$235$	48.6003	3.17034
$236$	3.41673	0.222410
$237$	10.9005	0.708061
$238$	0	0
$239$	0.749673	0.0484923	0.0242462	−	0.999706i	$-0.492281\pi$
$239$	0.749673	0.0484923	0.0242462	+	0.999706i	$0.492281\pi$
$240$	−10.1202	−0.653256
$241$	−9.01959	−0.581003	−0.290501	−	0.956875i	$-0.593822\pi$
$241$	−9.01959	−0.581003	−0.290501	+	0.956875i	$0.593822\pi$
$242$	11.1556	0.717108
$243$	21.9791	1.40996
$244$	11.4192	0.731038
$245$	0	0
$246$	−25.5825	−1.63108
$247$	−7.71964	−0.491189
$248$	−0.969044	−0.0615344
$249$	14.8013	0.937994
$250$	29.7018	1.87850
$251$	−29.1169	−1.83784	−0.918921	−	0.394441i	$-0.870938\pi$
$251$	−29.1169	−1.83784	−0.918921	+	0.394441i	$0.870938\pi$
$252$	0	0
$253$	10.2268	0.642951
$254$	5.46381	0.342830
$255$	−28.0041	−1.75368
$256$	1.00000	0.0625000
$257$	−23.2275	−1.44889	−0.724447	−	0.689330i	$-0.757905\pi$
$257$	−23.2275	−1.44889	−0.724447	+	0.689330i	$0.757905\pi$
$258$	−19.1615	−1.19294
$259$	0	0
$260$	−7.91656	−0.490964
$261$	−2.96555	−0.183563
$262$	−13.4182	−0.828978
$263$	−20.5033	−1.26429	−0.632145	−	0.774850i	$-0.717825\pi$
$263$	−20.5033	−1.26429	−0.632145	+	0.774850i	$0.717825\pi$
$264$	11.4965	0.707562
$265$	−11.5222	−0.707806
$266$	0	0
$267$	−32.4019	−1.98296
$268$	−2.27575	−0.139014
$269$	−11.3952	−0.694778	−0.347389	−	0.937721i	$-0.612932\pi$
$269$	−11.3952	−0.694778	−0.347389	+	0.937721i	$0.612932\pi$
$270$	0.348675	0.0212197
$271$	17.9751	1.09191	0.545954	−	0.837815i	$-0.316167\pi$
$271$	17.9751	1.09191	0.545954	+	0.837815i	$0.316167\pi$
$272$	2.76714	0.167783
$273$	0	0
$274$	17.1032	1.03324
$275$	−57.2760	−3.45387
$276$	5.30667	0.319424
$277$	−2.08032	−0.124994	−0.0624971	−	0.998045i	$-0.519906\pi$
$277$	−2.08032	−0.124994	−0.0624971	+	0.998045i	$0.519906\pi$
$278$	−3.90711	−0.234333
$279$	−2.87375	−0.172047
$280$	0	0
$281$	7.35741	0.438906	0.219453	−	0.975623i	$-0.429573\pi$
$281$	7.35741	0.438906	0.219453	+	0.975623i	$0.429573\pi$
$282$	−28.6484	−1.70599
$283$	−6.08053	−0.361450	−0.180725	−	0.983534i	$-0.557844\pi$
$283$	−6.08053	−0.361450	−0.180725	+	0.983534i	$0.557844\pi$
$284$	−6.24653	−0.370664
$285$	−40.8897	−2.42210
$286$	8.99320	0.531779
$287$	0	0
$288$	2.96555	0.174747
$289$	−9.34292	−0.549583
$290$	−4.14347	−0.243313
$291$	−41.1435	−2.41188
$292$	−13.5230	−0.791371
$293$	13.7159	0.801291	0.400646	−	0.916233i	$-0.368786\pi$
$293$	13.7159	0.801291	0.400646	+	0.916233i	$0.368786\pi$
$294$	0	0
$295$	14.1571	0.824259
$296$	−1.47340	−0.0856398
$297$	−0.396094	−0.0229837
$298$	−7.49827	−0.434363
$299$	4.15116	0.240068
$300$	−29.7205	−1.71591
$301$	0	0
$302$	9.41817	0.541955
$303$	30.3500	1.74356
$304$	4.04040	0.231733
$305$	47.3150	2.70925
$306$	8.20609	0.469111
$307$	7.64494	0.436320	0.218160	−	0.975913i	$-0.429995\pi$
$307$	7.64494	0.436320	0.218160	+	0.975913i	$0.429995\pi$
$308$	0	0
$309$	39.4988	2.24701
$310$	−4.01520	−0.228048
$311$	24.4252	1.38502	0.692512	−	0.721406i	$-0.256504\pi$
$311$	24.4252	1.38502	0.692512	+	0.721406i	$0.256504\pi$
$312$	4.66657	0.264192
$313$	−18.2645	−1.03237	−0.516185	−	0.856477i	$-0.672648\pi$
$313$	−18.2645	−1.03237	−0.516185	+	0.856477i	$0.672648\pi$
$314$	17.8286	1.00613
$315$	0	0
$316$	−4.46293	−0.251059
$317$	−10.4217	−0.585342	−0.292671	−	0.956213i	$-0.594544\pi$
$317$	−10.4217	−0.585342	−0.292671	+	0.956213i	$0.594544\pi$
$318$	6.79201	0.380877
$319$	4.70697	0.263540
$320$	4.14347	0.231627
$321$	−25.9500	−1.44839
$322$	0	0
$323$	11.1804	0.622093
$324$	−9.10217	−0.505676
$325$	−23.2490	−1.28962
$326$	−10.8789	−0.602527
$327$	−14.8961	−0.823755
$328$	10.4741	0.578336
$329$	0	0
$330$	47.6355	2.62225
$331$	4.68351	0.257429	0.128715	−	0.991682i	$-0.458915\pi$
$331$	4.68351	0.257429	0.128715	+	0.991682i	$0.458915\pi$
$332$	−6.06003	−0.332587
$333$	−4.36944	−0.239444
$334$	16.0326	0.877262
$335$	−9.42950	−0.515189
$336$	0	0
$337$	−25.3719	−1.38210	−0.691048	−	0.722809i	$-0.742851\pi$
$337$	−25.3719	−1.38210	−0.691048	+	0.722809i	$0.742851\pi$
$338$	−9.34956	−0.508549
$339$	−35.6292	−1.93511
$340$	11.4656	0.621808
$341$	4.56126	0.247006
$342$	11.9820	0.647913
$343$	0	0
$344$	7.84520	0.422985
$345$	21.9880	1.18379
$346$	−6.18878	−0.332711
$347$	−1.93057	−0.103639	−0.0518193	−	0.998656i	$-0.516502\pi$
$347$	−1.93057	−0.103639	−0.0518193	+	0.998656i	$0.516502\pi$
$348$	2.44245	0.130929
$349$	1.95782	0.104800	0.0523998	−	0.998626i	$-0.483313\pi$
$349$	1.95782	0.104800	0.0523998	+	0.998626i	$0.483313\pi$
$350$	0	0
$351$	−0.160779	−0.00858175
$352$	−4.70697	−0.250882
$353$	−16.3330	−0.869317	−0.434658	−	0.900595i	$-0.643131\pi$
$353$	−16.3330	−0.869317	−0.434658	+	0.900595i	$0.643131\pi$
$354$	−8.34518	−0.443541
$355$	−25.8823	−1.37369
$356$	13.2662	0.703105
$357$	0	0
$358$	1.20540	0.0637073
$359$	−11.7801	−0.621729	−0.310865	−	0.950454i	$-0.600619\pi$
$359$	−11.7801	−0.621729	−0.310865	+	0.950454i	$0.600619\pi$
$360$	12.2876	0.647616
$361$	−2.67514	−0.140797
$362$	6.95105	0.365339
$363$	−27.2469	−1.43009
$364$	0	0
$365$	−56.0320	−2.93285
$366$	−27.8907	−1.45787
$367$	35.6438	1.86059	0.930295	−	0.366813i	$-0.119551\pi$
$367$	35.6438	1.86059	0.930295	+	0.366813i	$0.119551\pi$
$368$	−2.17268	−0.113259
$369$	31.0615	1.61700
$370$	−6.10500	−0.317384
$371$	0	0
$372$	2.36684	0.122715
$373$	17.7483	0.918971	0.459486	−	0.888185i	$-0.348034\pi$
$373$	17.7483	0.918971	0.459486	+	0.888185i	$0.348034\pi$
$374$	−13.0249	−0.673500
$375$	−72.5450	−3.74621
$376$	11.7294	0.604897
$377$	1.91061	0.0984015
$378$	0	0
$379$	−15.2263	−0.782124	−0.391062	−	0.920364i	$-0.627892\pi$
$379$	−15.2263	−0.782124	−0.391062	+	0.920364i	$0.627892\pi$
$380$	16.7413	0.858810
$381$	−13.3451	−0.683689
$382$	−6.80847	−0.348352
$383$	−15.8118	−0.807943	−0.403971	−	0.914772i	$-0.632371\pi$
$383$	−15.8118	−0.807943	−0.403971	+	0.914772i	$0.632371\pi$
$384$	−2.44245	−0.124641
$385$	0	0
$386$	−3.89664	−0.198334
$387$	23.2653	1.18264
$388$	16.8452	0.855186
$389$	−21.7172	−1.10110	−0.550552	−	0.834801i	$-0.685583\pi$
$389$	−21.7172	−1.10110	−0.550552	+	0.834801i	$0.685583\pi$
$390$	19.3358	0.979105
$391$	−6.01213	−0.304047
$392$	0	0
$393$	32.7732	1.65319
$394$	15.5624	0.784020
$395$	−18.4920	−0.930434
$396$	−13.9587	−0.701453
$397$	1.26033	0.0632543	0.0316272	−	0.999500i	$-0.489931\pi$
$397$	1.26033	0.0632543	0.0316272	+	0.999500i	$0.489931\pi$
$398$	24.5735	1.23176
$399$	0	0
$400$	12.1683	0.608417
$401$	−1.91181	−0.0954713	−0.0477356	−	0.998860i	$-0.515201\pi$
$401$	−1.91181	−0.0954713	−0.0477356	+	0.998860i	$0.515201\pi$
$402$	5.55840	0.277228
$403$	1.85147	0.0922282
$404$	−12.4261	−0.618219
$405$	−37.7146	−1.87405
$406$	0	0
$407$	6.93526	0.343768
$408$	−6.75860	−0.334601
$409$	−3.01815	−0.149238	−0.0746189	−	0.997212i	$-0.523774\pi$
$409$	−3.01815	−0.149238	−0.0746189	+	0.997212i	$0.523774\pi$
$410$	43.3992	2.14333
$411$	−41.7737	−2.06054
$412$	−16.1718	−0.796729
$413$	0	0
$414$	−6.44320	−0.316666
$415$	−25.1095	−1.23258
$416$	−1.91061	−0.0936755
$417$	9.54292	0.467319
$418$	−19.0181	−0.930204
$419$	4.64504	0.226925	0.113463	−	0.993542i	$-0.463806\pi$
$419$	4.64504	0.226925	0.113463	+	0.993542i	$0.463806\pi$
$420$	0	0
$421$	−26.6202	−1.29739	−0.648695	−	0.761048i	$-0.724685\pi$
$421$	−26.6202	−1.29739	−0.648695	+	0.761048i	$0.724685\pi$
$422$	8.65646	0.421390
$423$	34.7840	1.69126
$424$	−2.78082	−0.135049
$425$	33.6715	1.63331
$426$	15.2568	0.739196
$427$	0	0
$428$	10.6246	0.513558
$429$	−21.9654	−1.06050
$430$	32.5064	1.56760
$431$	−9.63869	−0.464279	−0.232140	−	0.972682i	$-0.574573\pi$
$431$	−9.63869	−0.464279	−0.232140	+	0.972682i	$0.574573\pi$
$432$	0.0841506	0.00404870
$433$	−3.16466	−0.152084	−0.0760420	−	0.997105i	$-0.524228\pi$
$433$	−3.16466	−0.152084	−0.0760420	+	0.997105i	$0.524228\pi$
$434$	0	0
$435$	10.1202	0.485227
$436$	6.09884	0.292081
$437$	−8.77852	−0.419934
$438$	33.0291	1.57819
$439$	13.8900	0.662933	0.331467	−	0.943467i	$-0.392457\pi$
$439$	13.8900	0.662933	0.331467	+	0.943467i	$0.392457\pi$
$440$	−19.5032	−0.929778
$441$	0	0
$442$	−5.28694	−0.251474
$443$	20.3708	0.967845	0.483923	−	0.875111i	$-0.339212\pi$
$443$	20.3708	0.967845	0.483923	+	0.875111i	$0.339212\pi$
$444$	3.59871	0.170787
$445$	54.9679	2.60573
$446$	−10.9191	−0.517032
$447$	18.3141	0.866228
$448$	0	0
$449$	33.1442	1.56417	0.782086	−	0.623170i	$-0.214156\pi$
$449$	33.1442	1.56417	0.782086	+	0.623170i	$0.214156\pi$
$450$	36.0858	1.70110
$451$	−49.3014	−2.32151
$452$	14.5875	0.686139
$453$	−23.0034	−1.08079
$454$	−10.4951	−0.492559
$455$	0	0
$456$	−9.86847	−0.462133
$457$	−18.2087	−0.851767	−0.425883	−	0.904778i	$-0.640037\pi$
$457$	−18.2087	−0.851767	−0.425883	+	0.904778i	$0.640037\pi$
$458$	−7.51525	−0.351165
$459$	0.232857	0.0108688
$460$	−9.00245	−0.419741
$461$	−3.52484	−0.164168	−0.0820841	−	0.996625i	$-0.526158\pi$
$461$	−3.52484	−0.164168	−0.0820841	+	0.996625i	$0.526158\pi$
$462$	0	0
$463$	10.7653	0.500304	0.250152	−	0.968207i	$-0.419519\pi$
$463$	10.7653	0.500304	0.250152	+	0.968207i	$0.419519\pi$
$464$	−1.00000	−0.0464238
$465$	9.80692	0.454785
$466$	5.14262	0.238227
$467$	12.0199	0.556214	0.278107	−	0.960550i	$-0.410293\pi$
$467$	12.0199	0.556214	0.278107	+	0.960550i	$0.410293\pi$
$468$	−5.66601	−0.261911
$469$	0	0
$470$	48.6003	2.24177
$471$	−43.5455	−2.00647
$472$	3.41673	0.157268
$473$	−36.9271	−1.69791
$474$	10.9005	0.500675
$475$	49.1650	2.25584
$476$	0	0
$477$	−8.24666	−0.377588
$478$	0.749673	0.0342893
$479$	8.29202	0.378872	0.189436	−	0.981893i	$-0.439334\pi$
$479$	8.29202	0.378872	0.189436	+	0.981893i	$0.439334\pi$
$480$	−10.1202	−0.461922
$481$	2.81510	0.128358
$482$	−9.01959	−0.410831
$483$	0	0
$484$	11.1556	0.507072
$485$	69.7976	3.16934
$486$	21.9791	0.996993
$487$	7.89345	0.357687	0.178843	−	0.983878i	$-0.442764\pi$
$487$	7.89345	0.357687	0.178843	+	0.983878i	$0.442764\pi$
$488$	11.4192	0.516922
$489$	26.5711	1.20159
$490$	0	0
$491$	−37.7250	−1.70250	−0.851252	−	0.524757i	$-0.824156\pi$
$491$	−37.7250	−1.70250	−0.851252	+	0.524757i	$0.824156\pi$
$492$	−25.5825	−1.15335
$493$	−2.76714	−0.124626
$494$	−7.71964	−0.347323
$495$	−57.8376	−2.59961
$496$	−0.969044	−0.0435114
$497$	0	0
$498$	14.8013	0.663262
$499$	−8.47942	−0.379591	−0.189796	−	0.981824i	$-0.560783\pi$
$499$	−8.47942	−0.379591	−0.189796	+	0.981824i	$0.560783\pi$
$500$	29.7018	1.32830
$501$	−39.1587	−1.74948
$502$	−29.1169	−1.29955
$503$	−25.2796	−1.12716	−0.563581	−	0.826061i	$-0.690577\pi$
$503$	−25.2796	−1.12716	−0.563581	+	0.826061i	$0.690577\pi$
$504$	0	0
$505$	−51.4870	−2.29114
$506$	10.2268	0.454635
$507$	22.8358	1.01417
$508$	5.46381	0.242418
$509$	4.96964	0.220275	0.110138	−	0.993916i	$-0.464871\pi$
$509$	4.96964	0.220275	0.110138	+	0.993916i	$0.464871\pi$
$510$	−28.0041	−1.24004
$511$	0	0
$512$	1.00000	0.0441942
$513$	0.340002	0.0150115
$514$	−23.2275	−1.02452
$515$	−67.0075	−2.95270
$516$	−19.1615	−0.843538
$517$	−55.2099	−2.42813
$518$	0	0
$519$	15.1158	0.663508
$520$	−7.91656	−0.347164
$521$	26.9628	1.18126	0.590631	−	0.806942i	$-0.298879\pi$
$521$	26.9628	1.18126	0.590631	+	0.806942i	$0.298879\pi$
$522$	−2.96555	−0.129798
$523$	−10.4899	−0.458691	−0.229345	−	0.973345i	$-0.573659\pi$
$523$	−10.4899	−0.458691	−0.229345	+	0.973345i	$0.573659\pi$
$524$	−13.4182	−0.586176
$525$	0	0
$526$	−20.5033	−0.893988
$527$	−2.68148	−0.116807
$528$	11.4965	0.500322
$529$	−18.2794	−0.794758
$530$	−11.5222	−0.500494
$531$	10.1325	0.439712
$532$	0	0
$533$	−20.0120	−0.866815
$534$	−32.4019	−1.40217
$535$	44.0226	1.90326
$536$	−2.27575	−0.0982975
$537$	−2.94412	−0.127048
$538$	−11.3952	−0.491282
$539$	0	0
$540$	0.348675	0.0150046
$541$	−44.5694	−1.91619	−0.958093	−	0.286456i	$-0.907523\pi$
$541$	−44.5694	−1.91619	−0.958093	+	0.286456i	$0.907523\pi$
$542$	17.9751	0.772095
$543$	−16.9776	−0.728578
$544$	2.76714	0.118640
$545$	25.2703	1.08246
$546$	0	0
$547$	34.8005	1.48796	0.743980	−	0.668202i	$-0.232936\pi$
$547$	34.8005	1.48796	0.743980	+	0.668202i	$0.232936\pi$
$548$	17.1032	0.730613
$549$	33.8641	1.44529
$550$	−57.2760	−2.44226
$551$	−4.04040	−0.172127
$552$	5.30667	0.225867
$553$	0	0
$554$	−2.08032	−0.0883843
$555$	14.9111	0.632942
$556$	−3.90711	−0.165699
$557$	−33.7665	−1.43073	−0.715365	−	0.698751i	$-0.753740\pi$
$557$	−33.7665	−1.43073	−0.715365	+	0.698751i	$0.753740\pi$
$558$	−2.87375	−0.121655
$559$	−14.9891	−0.633973
$560$	0	0
$561$	31.8125	1.34313
$562$	7.35741	0.310354
$563$	41.2408	1.73809	0.869047	−	0.494730i	$-0.164733\pi$
$563$	41.2408	1.73809	0.869047	+	0.494730i	$0.164733\pi$
$564$	−28.6484	−1.20632
$565$	60.4429	2.54285
$566$	−6.08053	−0.255584
$567$	0	0
$568$	−6.24653	−0.262099
$569$	−25.9185	−1.08656	−0.543281	−	0.839551i	$-0.682818\pi$
$569$	−25.9185	−1.08656	−0.543281	+	0.839551i	$0.682818\pi$
$570$	−40.8897	−1.71268
$571$	15.8953	0.665196	0.332598	−	0.943069i	$-0.392075\pi$
$571$	15.8953	0.665196	0.332598	+	0.943069i	$0.392075\pi$
$572$	8.99320	0.376024
$573$	16.6293	0.694700
$574$	0	0
$575$	−26.4380	−1.10254
$576$	2.96555	0.123564
$577$	−10.2723	−0.427639	−0.213820	−	0.976873i	$-0.568591\pi$
$577$	−10.2723	−0.427639	−0.213820	+	0.976873i	$0.568591\pi$
$578$	−9.34292	−0.388614
$579$	9.51734	0.395527
$580$	−4.14347	−0.172048
$581$	0	0
$582$	−41.1435	−1.70545
$583$	13.0892	0.542101
$584$	−13.5230	−0.559584
$585$	−23.4769	−0.970652
$586$	13.7159	0.566599
$587$	−23.9902	−0.990183	−0.495091	−	0.868841i	$-0.664865\pi$
$587$	−23.9902	−0.990183	−0.495091	+	0.868841i	$0.664865\pi$
$588$	0	0
$589$	−3.91533	−0.161328
$590$	14.1571	0.582839
$591$	−38.0102	−1.56353
$592$	−1.47340	−0.0605565
$593$	−15.5367	−0.638014	−0.319007	−	0.947752i	$-0.603349\pi$
$593$	−15.5367	−0.638014	−0.319007	+	0.947752i	$0.603349\pi$
$594$	−0.396094	−0.0162519
$595$	0	0
$596$	−7.49827	−0.307141
$597$	−60.0196	−2.45644
$598$	4.15116	0.169753
$599$	−20.8308	−0.851122	−0.425561	−	0.904930i	$-0.639923\pi$
$599$	−20.8308	−0.851122	−0.425561	+	0.904930i	$0.639923\pi$
$600$	−29.7205	−1.21333
$601$	17.7149	0.722606	0.361303	−	0.932448i	$-0.382332\pi$
$601$	17.7149	0.722606	0.361303	+	0.932448i	$0.382332\pi$
$602$	0	0
$603$	−6.74884	−0.274834
$604$	9.41817	0.383220
$605$	46.2228	1.87922
$606$	30.3500	1.23288
$607$	−2.44517	−0.0992466	−0.0496233	−	0.998768i	$-0.515802\pi$
$607$	−2.44517	−0.0992466	−0.0496233	+	0.998768i	$0.515802\pi$
$608$	4.04040	0.163860
$609$	0	0
$610$	47.3150	1.91573
$611$	−22.4103	−0.906624
$612$	8.20609	0.331712
$613$	−1.80610	−0.0729477	−0.0364739	−	0.999335i	$-0.511613\pi$
$613$	−1.80610	−0.0729477	−0.0364739	+	0.999335i	$0.511613\pi$
$614$	7.64494	0.308525
$615$	−106.000	−4.27434
$616$	0	0
$617$	−15.0917	−0.607567	−0.303784	−	0.952741i	$-0.598250\pi$
$617$	−15.0917	−0.607567	−0.303784	+	0.952741i	$0.598250\pi$
$618$	39.4988	1.58888
$619$	−44.5910	−1.79227	−0.896133	−	0.443786i	$-0.853635\pi$
$619$	−44.5910	−1.79227	−0.896133	+	0.443786i	$0.853635\pi$
$620$	−4.01520	−0.161254
$621$	−0.182833	−0.00733682
$622$	24.4252	0.979360
$623$	0	0
$624$	4.66657	0.186812
$625$	62.2267	2.48907
$626$	−18.2645	−0.729996
$627$	46.4506	1.85506
$628$	17.8286	0.711439
$629$	−4.07712	−0.162565
$630$	0	0
$631$	−14.3265	−0.570328	−0.285164	−	0.958479i	$-0.592048\pi$
$631$	−14.3265	−0.570328	−0.285164	+	0.958479i	$0.592048\pi$
$632$	−4.46293	−0.177526
$633$	−21.1429	−0.840357
$634$	−10.4217	−0.413899
$635$	22.6391	0.898407
$636$	6.79201	0.269321
$637$	0	0
$638$	4.70697	0.186351
$639$	−18.5244	−0.732814
$640$	4.14347	0.163785
$641$	−17.4354	−0.688658	−0.344329	−	0.938849i	$-0.611894\pi$
$641$	−17.4354	−0.688658	−0.344329	+	0.938849i	$0.611894\pi$
$642$	−25.9500	−1.02416
$643$	−6.99067	−0.275685	−0.137843	−	0.990454i	$-0.544017\pi$
$643$	−6.99067	−0.275685	−0.137843	+	0.990454i	$0.544017\pi$
$644$	0	0
$645$	−79.3950	−3.12618
$646$	11.1804	0.439886
$647$	−16.2341	−0.638227	−0.319113	−	0.947717i	$-0.603385\pi$
$647$	−16.2341	−0.638227	−0.319113	+	0.947717i	$0.603385\pi$
$648$	−9.10217	−0.357567
$649$	−16.0824	−0.631291
$650$	−23.2490	−0.911899
$651$	0	0
$652$	−10.8789	−0.426051
$653$	22.5201	0.881281	0.440641	−	0.897684i	$-0.354751\pi$
$653$	22.5201	0.881281	0.440641	+	0.897684i	$0.354751\pi$
$654$	−14.8961	−0.582483
$655$	−55.5978	−2.17239
$656$	10.4741	0.408945
$657$	−40.1030	−1.56457
$658$	0	0
$659$	−6.71682	−0.261650	−0.130825	−	0.991405i	$-0.541763\pi$
$659$	−6.71682	−0.261650	−0.130825	+	0.991405i	$0.541763\pi$
$660$	47.6355	1.85421
$661$	−35.3608	−1.37538	−0.687689	−	0.726006i	$-0.741375\pi$
$661$	−35.3608	−1.37538	−0.687689	+	0.726006i	$0.741375\pi$
$662$	4.68351	0.182030
$663$	12.9131	0.501502
$664$	−6.06003	−0.235175
$665$	0	0
$666$	−4.36944	−0.169313
$667$	2.17268	0.0841267
$668$	16.0326	0.620318
$669$	26.6692	1.03109
$670$	−9.42950	−0.364293
$671$	−53.7498	−2.07499
$672$	0	0
$673$	−23.1388	−0.891935	−0.445967	−	0.895049i	$-0.647140\pi$
$673$	−23.1388	−0.891935	−0.445967	+	0.895049i	$0.647140\pi$
$674$	−25.3719	−0.977290
$675$	1.02397	0.0394127
$676$	−9.34956	−0.359599
$677$	22.7344	0.873755	0.436878	−	0.899521i	$-0.356084\pi$
$677$	22.7344	0.873755	0.436878	+	0.899521i	$0.356084\pi$
$678$	−35.6292	−1.36833
$679$	0	0
$680$	11.4656	0.439685
$681$	25.6337	0.982285
$682$	4.56126	0.174660
$683$	20.2928	0.776483	0.388242	−	0.921558i	$-0.373083\pi$
$683$	20.2928	0.776483	0.388242	+	0.921558i	$0.373083\pi$
$684$	11.9820	0.458143
$685$	70.8667	2.70768
$686$	0	0
$687$	18.3556	0.700310
$688$	7.84520	0.299096
$689$	5.31307	0.202412
$690$	21.9880	0.837069
$691$	2.01180	0.0765324	0.0382662	−	0.999268i	$-0.487817\pi$
$691$	2.01180	0.0765324	0.0382662	+	0.999268i	$0.487817\pi$
$692$	−6.18878	−0.235262
$693$	0	0
$694$	−1.93057	−0.0732836
$695$	−16.1890	−0.614084
$696$	2.44245	0.0925807
$697$	28.9834	1.09782
$698$	1.95782	0.0741045
$699$	−12.5606	−0.475084
$700$	0	0
$701$	−3.02432	−0.114227	−0.0571136	−	0.998368i	$-0.518190\pi$
$701$	−3.02432	−0.114227	−0.0571136	+	0.998368i	$0.518190\pi$
$702$	−0.160779	−0.00606822
$703$	−5.95314	−0.224527
$704$	−4.70697	−0.177401
$705$	−118.704	−4.47064
$706$	−16.3330	−0.614700
$707$	0	0
$708$	−8.34518	−0.313631
$709$	−45.4669	−1.70754	−0.853772	−	0.520647i	$-0.825691\pi$
$709$	−45.4669	−1.70754	−0.853772	+	0.520647i	$0.825691\pi$
$710$	−25.8823	−0.971346
$711$	−13.2350	−0.496352
$712$	13.2662	0.497170
$713$	2.10543	0.0788489
$714$	0	0
$715$	37.2630	1.39356
$716$	1.20540	0.0450479
$717$	−1.83104	−0.0683813
$718$	−11.7801	−0.439629
$719$	30.1441	1.12418	0.562092	−	0.827075i	$-0.309997\pi$
$719$	30.1441	1.12418	0.562092	+	0.827075i	$0.309997\pi$
$720$	12.2876	0.457934
$721$	0	0
$722$	−2.67514	−0.0995585
$723$	22.0299	0.819300
$724$	6.95105	0.258334
$725$	−12.1683	−0.451921
$726$	−27.2469	−1.01123
$727$	45.6599	1.69343	0.846717	−	0.532044i	$-0.178576\pi$
$727$	45.6599	1.69343	0.846717	+	0.532044i	$0.178576\pi$
$728$	0	0
$729$	−26.3763	−0.976901
$730$	−56.0320	−2.07384
$731$	21.7088	0.802929
$732$	−27.8907	−1.03087
$733$	−27.3458	−1.01004	−0.505020	−	0.863107i	$-0.668515\pi$
$733$	−27.3458	−1.01004	−0.505020	+	0.863107i	$0.668515\pi$
$734$	35.6438	1.31564
$735$	0	0
$736$	−2.17268	−0.0800862
$737$	10.7119	0.394578
$738$	31.0615	1.14339
$739$	49.9166	1.83621	0.918106	−	0.396335i	$-0.129718\pi$
$739$	49.9166	1.83621	0.918106	+	0.396335i	$0.129718\pi$
$740$	−6.10500	−0.224424
$741$	18.8548	0.692649
$742$	0	0
$743$	28.6655	1.05164	0.525818	−	0.850597i	$-0.323759\pi$
$743$	28.6655	1.05164	0.525818	+	0.850597i	$0.323759\pi$
$744$	2.36684	0.0867725
$745$	−31.0688	−1.13827
$746$	17.7483	0.649811
$747$	−17.9713	−0.657536
$748$	−13.0249	−0.476236
$749$	0	0
$750$	−72.5450	−2.64897
$751$	−19.0316	−0.694473	−0.347236	−	0.937778i	$-0.612880\pi$
$751$	−19.0316	−0.694473	−0.347236	+	0.937778i	$0.612880\pi$
$752$	11.7294	0.427727
$753$	71.1165	2.59163
$754$	1.91061	0.0695804
$755$	39.0239	1.42023
$756$	0	0
$757$	−9.39694	−0.341538	−0.170769	−	0.985311i	$-0.554625\pi$
$757$	−9.39694	−0.341538	−0.170769	+	0.985311i	$0.554625\pi$
$758$	−15.2263	−0.553045
$759$	−24.9783	−0.906656
$760$	16.7413	0.607270
$761$	−10.7493	−0.389661	−0.194831	−	0.980837i	$-0.562416\pi$
$761$	−10.7493	−0.389661	−0.194831	+	0.980837i	$0.562416\pi$
$762$	−13.3451	−0.483441
$763$	0	0
$764$	−6.80847	−0.246322
$765$	34.0017	1.22933
$766$	−15.8118	−0.571302
$767$	−6.52804	−0.235714
$768$	−2.44245	−0.0881342
$769$	39.3774	1.41998	0.709992	−	0.704209i	$-0.248698\pi$
$769$	39.3774	1.41998	0.709992	+	0.704209i	$0.248698\pi$
$770$	0	0
$771$	56.7321	2.04316
$772$	−3.89664	−0.140243
$773$	−19.0471	−0.685078	−0.342539	−	0.939504i	$-0.611287\pi$
$773$	−19.0471	−0.685078	−0.342539	+	0.939504i	$0.611287\pi$
$774$	23.2653	0.836254
$775$	−11.7917	−0.423569
$776$	16.8452	0.604708
$777$	0	0
$778$	−21.7172	−0.778598
$779$	42.3196	1.51626
$780$	19.3358	0.692332
$781$	29.4023	1.05210
$782$	−6.01213	−0.214993
$783$	−0.0841506	−0.00300730
$784$	0	0
$785$	73.8723	2.63662
$786$	32.7732	1.16898
$787$	26.4446	0.942650	0.471325	−	0.881960i	$-0.343776\pi$
$787$	26.4446	0.942650	0.471325	+	0.881960i	$0.343776\pi$
$788$	15.5624	0.554386
$789$	50.0783	1.78283
$790$	−18.4920	−0.657916
$791$	0	0
$792$	−13.9587	−0.496002
$793$	−21.8176	−0.774767
$794$	1.26033	0.0447275
$795$	28.1425	0.998111
$796$	24.5735	0.870986
$797$	−42.8772	−1.51879	−0.759395	−	0.650630i	$-0.774505\pi$
$797$	−42.8772	−1.51879	−0.759395	+	0.650630i	$0.774505\pi$
$798$	0	0
$799$	32.4569	1.14824
$800$	12.1683	0.430216
$801$	39.3414	1.39006
$802$	−1.91181	−0.0675084
$803$	63.6522	2.24624
$804$	5.55840	0.196030
$805$	0	0
$806$	1.85147	0.0652152
$807$	27.8322	0.979739
$808$	−12.4261	−0.437147
$809$	−1.72392	−0.0606097	−0.0303048	−	0.999541i	$-0.509648\pi$
$809$	−1.72392	−0.0606097	−0.0303048	+	0.999541i	$0.509648\pi$
$810$	−37.7146	−1.32515
$811$	7.23311	0.253989	0.126995	−	0.991903i	$-0.459467\pi$
$811$	7.23311	0.253989	0.126995	+	0.991903i	$0.459467\pi$
$812$	0	0
$813$	−43.9031	−1.53975
$814$	6.93526	0.243081
$815$	−45.0764	−1.57896
$816$	−6.75860	−0.236598
$817$	31.6978	1.10896
$818$	−3.01815	−0.105527
$819$	0	0
$820$	43.3992	1.51556
$821$	30.7040	1.07158	0.535789	−	0.844352i	$-0.320014\pi$
$821$	30.7040	1.07158	0.535789	+	0.844352i	$0.320014\pi$
$822$	−41.7737	−1.45703
$823$	−9.58578	−0.334139	−0.167070	−	0.985945i	$-0.553430\pi$
$823$	−9.58578	−0.334139	−0.167070	+	0.985945i	$0.553430\pi$
$824$	−16.1718	−0.563372
$825$	139.894	4.87047
$826$	0	0
$827$	−6.26986	−0.218025	−0.109012	−	0.994040i	$-0.534769\pi$
$827$	−6.26986	−0.218025	−0.109012	+	0.994040i	$0.534769\pi$
$828$	−6.44320	−0.223917
$829$	11.2898	0.392110	0.196055	−	0.980593i	$-0.437187\pi$
$829$	11.2898	0.392110	0.196055	+	0.980593i	$0.437187\pi$
$830$	−25.1095	−0.871565
$831$	5.08107	0.176260
$832$	−1.91061	−0.0662386
$833$	0	0
$834$	9.54292	0.330444
$835$	66.4304	2.29892
$836$	−19.0181	−0.657753
$837$	−0.0815456	−0.00281863
$838$	4.64504	0.160460
$839$	−44.0101	−1.51940	−0.759698	−	0.650276i	$-0.774653\pi$
$839$	−44.0101	−1.51940	−0.759698	+	0.650276i	$0.774653\pi$
$840$	0	0
$841$	1.00000	0.0344828
$842$	−26.6202	−0.917394
$843$	−17.9701	−0.618923
$844$	8.65646	0.297968
$845$	−38.7396	−1.33268
$846$	34.7840	1.19590
$847$	0	0
$848$	−2.78082	−0.0954938
$849$	14.8514	0.509698
$850$	33.6715	1.15492
$851$	3.20124	0.109737
$852$	15.2568	0.522690
$853$	10.9272	0.374141	0.187070	−	0.982347i	$-0.440101\pi$
$853$	10.9272	0.374141	0.187070	+	0.982347i	$0.440101\pi$
$854$	0	0
$855$	49.6471	1.69789
$856$	10.6246	0.363141
$857$	29.2754	1.00003	0.500015	−	0.866017i	$-0.333328\pi$
$857$	29.2754	1.00003	0.500015	+	0.866017i	$0.333328\pi$
$858$	−21.9654	−0.749887
$859$	−43.3222	−1.47813	−0.739067	−	0.673632i	$-0.764733\pi$
$859$	−43.3222	−1.47813	−0.739067	+	0.673632i	$0.764733\pi$
$860$	32.5064	1.10846
$861$	0	0
$862$	−9.63869	−0.328295
$863$	−43.8381	−1.49227	−0.746133	−	0.665797i	$-0.768092\pi$
$863$	−43.8381	−1.49227	−0.746133	+	0.665797i	$0.768092\pi$
$864$	0.0841506	0.00286286
$865$	−25.6430	−0.871888
$866$	−3.16466	−0.107540
$867$	22.8196	0.774994
$868$	0	0
$869$	21.0069	0.712609
$870$	10.1202	0.343107
$871$	4.34808	0.147329
$872$	6.09884	0.206533
$873$	49.9552	1.69073
$874$	−8.77852	−0.296938
$875$	0	0
$876$	33.0291	1.11595
$877$	29.5072	0.996388	0.498194	−	0.867066i	$-0.333997\pi$
$877$	29.5072	0.996388	0.498194	+	0.867066i	$0.333997\pi$
$878$	13.8900	0.468764
$879$	−33.5004	−1.12994
$880$	−19.5032	−0.657452
$881$	−13.1060	−0.441554	−0.220777	−	0.975324i	$-0.570859\pi$
$881$	−13.1060	−0.441554	−0.220777	+	0.975324i	$0.570859\pi$
$882$	0	0
$883$	−7.44435	−0.250522	−0.125261	−	0.992124i	$-0.539977\pi$
$883$	−7.44435	−0.250522	−0.125261	+	0.992124i	$0.539977\pi$
$884$	−5.28694	−0.177819
$885$	−34.5780	−1.16233
$886$	20.3708	0.684370
$887$	38.6833	1.29886	0.649430	−	0.760422i	$-0.275008\pi$
$887$	38.6833	1.29886	0.649430	+	0.760422i	$0.275008\pi$
$888$	3.59871	0.120765
$889$	0	0
$890$	54.9679	1.84253
$891$	42.8437	1.43532
$892$	−10.9191	−0.365597
$893$	47.3914	1.58589
$894$	18.3141	0.612516
$895$	4.99453	0.166949
$896$	0	0
$897$	−10.1390	−0.338531
$898$	33.1442	1.10604
$899$	0.969044	0.0323194
$900$	36.0858	1.20286
$901$	−7.69493	−0.256355
$902$	−49.3014	−1.64156
$903$	0	0
$904$	14.5875	0.485173
$905$	28.8015	0.957393
$906$	−23.0034	−0.764236
$907$	2.42625	0.0805624	0.0402812	−	0.999188i	$-0.487175\pi$
$907$	2.42625	0.0805624	0.0402812	+	0.999188i	$0.487175\pi$
$908$	−10.4951	−0.348292
$909$	−36.8500	−1.22224
$910$	0	0
$911$	−1.86661	−0.0618435	−0.0309218	−	0.999522i	$-0.509844\pi$
$911$	−1.86661	−0.0618435	−0.0309218	+	0.999522i	$0.509844\pi$
$912$	−9.86847	−0.326778
$913$	28.5244	0.944020
$914$	−18.2087	−0.602290
$915$	−115.564	−3.82044
$916$	−7.51525	−0.248311
$917$	0	0
$918$	0.232857	0.00768542
$919$	27.4057	0.904031	0.452015	−	0.892010i	$-0.350705\pi$
$919$	27.4057	0.904031	0.452015	+	0.892010i	$0.350705\pi$
$920$	−9.00245	−0.296802
$921$	−18.6724	−0.615275
$922$	−3.52484	−0.116084
$923$	11.9347	0.392836
$924$	0	0
$925$	−17.9289	−0.589497
$926$	10.7653	0.353768
$927$	−47.9583	−1.57516
$928$	−1.00000	−0.0328266
$929$	43.9595	1.44227	0.721133	−	0.692797i	$-0.243622\pi$
$929$	43.9595	1.44227	0.721133	+	0.692797i	$0.243622\pi$
$930$	9.80692	0.321582
$931$	0	0
$932$	5.14262	0.168452
$933$	−59.6572	−1.95309
$934$	12.0199	0.393303
$935$	−53.9681	−1.76495
$936$	−5.66601	−0.185199
$937$	−29.9446	−0.978246	−0.489123	−	0.872215i	$-0.662683\pi$
$937$	−29.9446	−0.978246	−0.489123	+	0.872215i	$0.662683\pi$
$938$	0	0
$939$	44.6101	1.45579
$940$	48.6003	1.58517
$941$	21.5723	0.703236	0.351618	−	0.936144i	$-0.385632\pi$
$941$	21.5723	0.703236	0.351618	+	0.936144i	$0.385632\pi$
$942$	−43.5455	−1.41879
$943$	−22.7570	−0.741068
$944$	3.41673	0.111205
$945$	0	0
$946$	−36.9271	−1.20061
$947$	4.39212	0.142725	0.0713624	−	0.997450i	$-0.477265\pi$
$947$	4.39212	0.142725	0.0713624	+	0.997450i	$0.477265\pi$
$948$	10.9005	0.354031
$949$	25.8371	0.838709
$950$	49.1650	1.59512
$951$	25.4545	0.825418
$952$	0	0
$953$	32.9052	1.06591	0.532953	−	0.846145i	$-0.321082\pi$
$953$	32.9052	1.06591	0.532953	+	0.846145i	$0.321082\pi$
$954$	−8.24666	−0.266995
$955$	−28.2107	−0.912876
$956$	0.749673	0.0242462
$957$	−11.4965	−0.371630
$958$	8.29202	0.267903
$959$	0	0
$960$	−10.1202	−0.326628
$961$	−30.0610	−0.969708
$962$	2.81510	0.0907625
$963$	31.5077	1.01532
$964$	−9.01959	−0.290501
$965$	−16.1456	−0.519745
$966$	0	0
$967$	4.50365	0.144827	0.0724137	−	0.997375i	$-0.476930\pi$
$967$	4.50365	0.144827	0.0724137	+	0.997375i	$0.476930\pi$
$968$	11.1556	0.358554
$969$	−27.3075	−0.877242
$970$	69.7976	2.24107
$971$	30.4189	0.976187	0.488094	−	0.872791i	$-0.337692\pi$
$971$	30.4189	0.976187	0.488094	+	0.872791i	$0.337692\pi$
$972$	21.9791	0.704981
$973$	0	0
$974$	7.89345	0.252923
$975$	56.7844	1.81856
$976$	11.4192	0.365519
$977$	37.5202	1.20038	0.600189	−	0.799858i	$-0.295092\pi$
$977$	37.5202	1.20038	0.600189	+	0.799858i	$0.295092\pi$
$978$	26.5711	0.849652
$979$	−62.4434	−1.99570
$980$	0	0
$981$	18.0864	0.577454
$982$	−37.7250	−1.20385
$983$	43.4878	1.38705	0.693523	−	0.720435i	$-0.256058\pi$
$983$	43.4878	1.38705	0.693523	+	0.720435i	$0.256058\pi$
$984$	−25.5825	−0.815539
$985$	64.4821	2.05457
$986$	−2.76714	−0.0881238
$987$	0	0
$988$	−7.71964	−0.245595
$989$	−17.0452	−0.542004
$990$	−57.8376	−1.83820
$991$	−55.4198	−1.76047	−0.880233	−	0.474541i	$-0.842614\pi$
$991$	−55.4198	−1.76047	−0.880233	+	0.474541i	$0.842614\pi$
$992$	−0.969044	−0.0307672
$993$	−11.4392	−0.363013
$994$	0	0
$995$	101.820	3.22790
$996$	14.8013	0.468997
$997$	−23.8889	−0.756570	−0.378285	−	0.925689i	$-0.623486\pi$
$997$	−23.8889	−0.756570	−0.378285	+	0.925689i	$0.623486\pi$
$998$	−8.47942	−0.268411
$999$	−0.123988	−0.00392280

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2842.2.a.z.1.1		5
7.2	even	3		406.2.e.a.291.5	yes	10
7.4	even	3		406.2.e.a.233.5	✓	10
7.6	odd	2		2842.2.a.x.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
406.2.e.a.233.5	✓	10	7.4	even	3
406.2.e.a.291.5	yes	10	7.2	even	3
2842.2.a.x.1.5		5	7.6	odd	2
2842.2.a.z.1.1		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.44245 q^{3} +1.00000 q^{4} +4.14347 q^{5} -2.44245 q^{6} +1.00000 q^{8} +2.96555 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.44245 q^{3} +1.00000 q^{4} +4.14347 q^{5} -2.44245 q^{6} +1.00000 q^{8} +2.96555 q^{9} +4.14347 q^{10} -4.70697 q^{11} -2.44245 q^{12} -1.91061 q^{13} -10.1202 q^{15} +1.00000 q^{16} +2.76714 q^{17} +2.96555 q^{18} +4.04040 q^{19} +4.14347 q^{20} -4.70697 q^{22} -2.17268 q^{23} -2.44245 q^{24} +12.1683 q^{25} -1.91061 q^{26} +0.0841506 q^{27} -1.00000 q^{29} -10.1202 q^{30} -0.969044 q^{31} +1.00000 q^{32} +11.4965 q^{33} +2.76714 q^{34} +2.96555 q^{36} -1.47340 q^{37} +4.04040 q^{38} +4.66657 q^{39} +4.14347 q^{40} +10.4741 q^{41} +7.84520 q^{43} -4.70697 q^{44} +12.2876 q^{45} -2.17268 q^{46} +11.7294 q^{47} -2.44245 q^{48} +12.1683 q^{50} -6.75860 q^{51} -1.91061 q^{52} -2.78082 q^{53} +0.0841506 q^{54} -19.5032 q^{55} -9.86847 q^{57} -1.00000 q^{58} +3.41673 q^{59} -10.1202 q^{60} +11.4192 q^{61} -0.969044 q^{62} +1.00000 q^{64} -7.91656 q^{65} +11.4965 q^{66} -2.27575 q^{67} +2.76714 q^{68} +5.30667 q^{69} -6.24653 q^{71} +2.96555 q^{72} -13.5230 q^{73} -1.47340 q^{74} -29.7205 q^{75} +4.04040 q^{76} +4.66657 q^{78} -4.46293 q^{79} +4.14347 q^{80} -9.10217 q^{81} +10.4741 q^{82} -6.06003 q^{83} +11.4656 q^{85} +7.84520 q^{86} +2.44245 q^{87} -4.70697 q^{88} +13.2662 q^{89} +12.2876 q^{90} -2.17268 q^{92} +2.36684 q^{93} +11.7294 q^{94} +16.7413 q^{95} -2.44245 q^{96} +16.8452 q^{97} -13.9587 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 5 q^{2} + 3 q^{3} + 5 q^{4} + 7 q^{5} + 3 q^{6} + 5 q^{8} + 8 q^{9}+O(q^{10}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more