LMFDB - Embedded newform 1682.2.a.t.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1682,2,Mod(1,1682)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1682.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1682, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1682 = 2 \cdot 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1682.a (trivial)

Newform invariants

comment:select newform

sage:traces = [6,6,2,6,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$13.4308376200$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.13716913.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 13x^{4} + 17x^{3} + 52x^{2} - 32x - 64 $ x^6 - 2x^5 - 13x^4 + 17x^3 + 52x^2 - 32*x - 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 58)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.63883$ of defining polynomial
Character	$\chi$	$=$	1682.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.63883 q^{3} +1.00000 q^{4} +1.19379 q^{5} +1.63883 q^{6} +2.04359 q^{7} +1.00000 q^{8} -0.314239 q^{9} +1.19379 q^{10} +3.68242 q^{11} +1.63883 q^{12} +2.15646 q^{13} +2.04359 q^{14} +1.95641 q^{15} +1.00000 q^{16} -6.53517 q^{17} -0.314239 q^{18} +5.31424 q^{19} +1.19379 q^{20} +3.34909 q^{21} +3.68242 q^{22} -5.89351 q^{23} +1.63883 q^{24} -3.57487 q^{25} +2.15646 q^{26} -5.43147 q^{27} +2.04359 q^{28} +1.95641 q^{30} +8.99665 q^{31} +1.00000 q^{32} +6.03485 q^{33} -6.53517 q^{34} +2.43961 q^{35} -0.314239 q^{36} +1.82798 q^{37} +5.31424 q^{38} +3.53407 q^{39} +1.19379 q^{40} -8.32895 q^{41} +3.34909 q^{42} -3.68242 q^{43} +3.68242 q^{44} -0.375134 q^{45} -5.89351 q^{46} -0.992767 q^{47} +1.63883 q^{48} -2.82375 q^{49} -3.57487 q^{50} -10.7100 q^{51} +2.15646 q^{52} -5.66449 q^{53} -5.43147 q^{54} +4.39602 q^{55} +2.04359 q^{56} +8.70913 q^{57} +2.94918 q^{59} +1.95641 q^{60} -1.80894 q^{61} +8.99665 q^{62} -0.642174 q^{63} +1.00000 q^{64} +2.57436 q^{65} +6.03485 q^{66} +6.04359 q^{67} -6.53517 q^{68} -9.65846 q^{69} +2.43961 q^{70} +3.75696 q^{71} -0.314239 q^{72} +12.7248 q^{73} +1.82798 q^{74} -5.85860 q^{75} +5.31424 q^{76} +7.52534 q^{77} +3.53407 q^{78} +14.1329 q^{79} +1.19379 q^{80} -7.95854 q^{81} -8.32895 q^{82} +2.05232 q^{83} +3.34909 q^{84} -7.80161 q^{85} -3.68242 q^{86} +3.68242 q^{88} -16.5120 q^{89} -0.375134 q^{90} +4.40692 q^{91} -5.89351 q^{92} +14.7440 q^{93} -0.992767 q^{94} +6.34407 q^{95} +1.63883 q^{96} -4.59626 q^{97} -2.82375 q^{98} -1.15716 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 2 q^{3} + 6 q^{4} + 2 q^{6} - 3 q^{7} + 6 q^{8} + 12 q^{9} - q^{11} + 2 q^{12} - 3 q^{13} - 3 q^{14} + 27 q^{15} + 6 q^{16} - 6 q^{17} + 12 q^{18} + 18 q^{19} - 10 q^{21} - q^{22} - 14 q^{23}+ \cdots - 4 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 + 2 * q^6 - 3 * q^7 + 6 * q^8 + 12 * q^9 - q^11 + 2 * q^12 - 3 * q^13 - 3 * q^14 + 27 * q^15 + 6 * q^16 - 6 * q^17 + 12 * q^18 + 18 * q^19 - 10 * q^21 - q^22 - 14 * q^23 + 2 * q^24 + 4 * q^25 - 3 * q^26 + 23 * q^27 - 3 * q^28 + 27 * q^30 + 17 * q^31 + 6 * q^32 + 20 * q^33 - 6 * q^34 - 9 * q^35 + 12 * q^36 + 12 * q^37 + 18 * q^38 + 10 * q^39 - 15 * q^41 - 10 * q^42 + q^43 - q^44 + 18 * q^45 - 14 * q^46 + 8 * q^47 + 2 * q^48 + q^49 + 4 * q^50 - 11 * q^51 - 3 * q^52 + 3 * q^53 + 23 * q^54 + 18 * q^55 - 3 * q^56 - 19 * q^57 + 19 * q^59 + 27 * q^60 + 15 * q^61 + 17 * q^62 - 33 * q^63 + 6 * q^64 + 11 * q^65 + 20 * q^66 + 21 * q^67 - 6 * q^68 - 11 * q^69 - 9 * q^70 - 9 * q^71 + 12 * q^72 + 31 * q^73 + 12 * q^74 - q^75 + 18 * q^76 + 33 * q^77 + 10 * q^78 - 2 * q^79 + 2 * q^81 - 15 * q^82 - 2 * q^83 - 10 * q^84 + 19 * q^85 + q^86 - q^88 + 2 * q^89 + 18 * q^90 - 22 * q^91 - 14 * q^92 + q^93 + 8 * q^94 - 18 * q^95 + 2 * q^96 + 43 * q^97 + q^98 - 4 * q^99

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.63883	0.946178	0.473089	−	0.881015i	$-0.343139\pi$
$3$	1.63883	0.946178	0.473089	+	0.881015i	$0.343139\pi$
$4$	1.00000	0.500000
$5$	1.19379	0.533878	0.266939	−	0.963713i	$-0.413988\pi$
$5$	1.19379	0.533878	0.266939	+	0.963713i	$0.413988\pi$
$6$	1.63883	0.669049
$7$	2.04359	0.772403	0.386202	−	0.922414i	$-0.373787\pi$
$7$	2.04359	0.772403	0.386202	+	0.922414i	$0.373787\pi$
$8$	1.00000	0.353553
$9$	−0.314239	−0.104746
$10$	1.19379	0.377509
$11$	3.68242	1.11029	0.555145	−	0.831754i	$-0.312663\pi$
$11$	3.68242	1.11029	0.555145	+	0.831754i	$0.312663\pi$
$12$	1.63883	0.473089
$13$	2.15646	0.598095	0.299047	−	0.954238i	$-0.403331\pi$
$13$	2.15646	0.598095	0.299047	+	0.954238i	$0.403331\pi$
$14$	2.04359	0.546171
$15$	1.95641	0.505144
$16$	1.00000	0.250000
$17$	−6.53517	−1.58501	−0.792506	−	0.609864i	$-0.791224\pi$
$17$	−6.53517	−1.58501	−0.792506	+	0.609864i	$0.791224\pi$
$18$	−0.314239	−0.0740668
$19$	5.31424	1.21917	0.609585	−	0.792721i	$-0.291336\pi$
$19$	5.31424	1.21917	0.609585	+	0.792721i	$0.291336\pi$
$20$	1.19379	0.266939
$21$	3.34909	0.730831
$22$	3.68242	0.785094
$23$	−5.89351	−1.22888	−0.614441	−	0.788963i	$-0.710618\pi$
$23$	−5.89351	−1.22888	−0.614441	+	0.788963i	$0.710618\pi$
$24$	1.63883	0.334525
$25$	−3.57487	−0.714974
$26$	2.15646	0.422917
$27$	−5.43147	−1.04529
$28$	2.04359	0.386202
$29$	0	0
$29$	0	0
$30$	1.95641	0.357191
$31$	8.99665	1.61585	0.807923	−	0.589287i	$-0.200591\pi$
$31$	8.99665	1.61585	0.807923	+	0.589287i	$0.200591\pi$
$32$	1.00000	0.176777
$33$	6.03485	1.05053
$34$	−6.53517	−1.12077
$35$	2.43961	0.412369
$36$	−0.314239	−0.0523732
$37$	1.82798	0.300519	0.150259	−	0.988647i	$-0.451989\pi$
$37$	1.82798	0.300519	0.150259	+	0.988647i	$0.451989\pi$
$38$	5.31424	0.862083
$39$	3.53407	0.565904
$40$	1.19379	0.188754
$41$	−8.32895	−1.30076	−0.650382	−	0.759608i	$-0.725391\pi$
$41$	−8.32895	−1.30076	−0.650382	+	0.759608i	$0.725391\pi$
$42$	3.34909	0.516776
$43$	−3.68242	−0.561563	−0.280782	−	0.959772i	$-0.590594\pi$
$43$	−3.68242	−0.561563	−0.280782	+	0.959772i	$0.590594\pi$
$44$	3.68242	0.555145
$45$	−0.375134	−0.0559217
$46$	−5.89351	−0.868951
$47$	−0.992767	−0.144810	−0.0724050	−	0.997375i	$-0.523067\pi$
$47$	−0.992767	−0.144810	−0.0724050	+	0.997375i	$0.523067\pi$
$48$	1.63883	0.236545
$49$	−2.82375	−0.403393
$50$	−3.57487	−0.505563
$51$	−10.7100	−1.49970
$52$	2.15646	0.299047
$53$	−5.66449	−0.778077	−0.389039	−	0.921221i	$-0.627193\pi$
$53$	−5.66449	−0.778077	−0.389039	+	0.921221i	$0.627193\pi$
$54$	−5.43147	−0.739130
$55$	4.39602	0.592759
$56$	2.04359	0.273086
$57$	8.70913	1.15355
$58$	0	0
$59$	2.94918	0.383951	0.191975	−	0.981400i	$-0.438511\pi$
$59$	2.94918	0.383951	0.191975	+	0.981400i	$0.438511\pi$
$60$	1.95641	0.252572
$61$	−1.80894	−0.231612	−0.115806	−	0.993272i	$-0.536945\pi$
$61$	−1.80894	−0.231612	−0.115806	+	0.993272i	$0.536945\pi$
$62$	8.99665	1.14258
$63$	−0.642174	−0.0809064
$64$	1.00000	0.125000
$65$	2.57436	0.319310
$66$	6.03485	0.742839
$67$	6.04359	0.738342	0.369171	−	0.929362i	$-0.379642\pi$
$67$	6.04359	0.738342	0.369171	+	0.929362i	$0.379642\pi$
$68$	−6.53517	−0.792506
$69$	−9.65846	−1.16274
$70$	2.43961	0.291589
$71$	3.75696	0.445870	0.222935	−	0.974833i	$-0.428436\pi$
$71$	3.75696	0.445870	0.222935	+	0.974833i	$0.428436\pi$
$72$	−0.314239	−0.0370334
$73$	12.7248	1.48933	0.744665	−	0.667438i	$-0.232609\pi$
$73$	12.7248	1.48933	0.744665	+	0.667438i	$0.232609\pi$
$74$	1.82798	0.212499
$75$	−5.85860	−0.676493
$76$	5.31424	0.609585
$77$	7.52534	0.857592
$78$	3.53407	0.400155
$79$	14.1329	1.59008	0.795039	−	0.606559i	$-0.207450\pi$
$79$	14.1329	1.59008	0.795039	+	0.606559i	$0.207450\pi$
$80$	1.19379	0.133469
$81$	−7.95854	−0.884282
$82$	−8.32895	−0.919778
$83$	2.05232	0.225272	0.112636	−	0.993636i	$-0.464071\pi$
$83$	2.05232	0.225272	0.112636	+	0.993636i	$0.464071\pi$
$84$	3.34909	0.365416
$85$	−7.80161	−0.846203
$86$	−3.68242	−0.397085
$87$	0	0
$88$	3.68242	0.392547
$89$	−16.5120	−1.75027	−0.875134	−	0.483880i	$-0.839227\pi$
$89$	−16.5120	−1.75027	−0.875134	+	0.483880i	$0.839227\pi$
$90$	−0.375134	−0.0395426
$91$	4.40692	0.461970
$92$	−5.89351	−0.614441
$93$	14.7440	1.52888
$94$	−0.992767	−0.102396
$95$	6.34407	0.650888
$96$	1.63883	0.167262
$97$	−4.59626	−0.466679	−0.233340	−	0.972395i	$-0.574965\pi$
$97$	−4.59626	−0.466679	−0.233340	+	0.972395i	$0.574965\pi$
$98$	−2.82375	−0.285242
$99$	−1.15716	−0.116299
$100$	−3.57487	−0.357487
$101$	0.209757	0.0208716	0.0104358	−	0.999946i	$-0.496678\pi$
$101$	0.209757	0.0208716	0.0104358	+	0.999946i	$0.496678\pi$
$102$	−10.7100	−1.06045
$103$	−11.1276	−1.09643	−0.548217	−	0.836336i	$-0.684693\pi$
$103$	−11.1276	−1.09643	−0.548217	+	0.836336i	$0.684693\pi$
$104$	2.15646	0.211458
$105$	3.99810	0.390175
$106$	−5.66449	−0.550184
$107$	−4.04580	−0.391122	−0.195561	−	0.980691i	$-0.562653\pi$
$107$	−4.04580	−0.391122	−0.195561	+	0.980691i	$0.562653\pi$
$108$	−5.43147	−0.522644
$109$	−15.6335	−1.49742	−0.748711	−	0.662896i	$-0.769327\pi$
$109$	−15.6335	−1.49742	−0.748711	+	0.662896i	$0.769327\pi$
$110$	4.39602	0.419144
$111$	2.99575	0.284344
$112$	2.04359	0.193101
$113$	18.4609	1.73665	0.868326	−	0.495994i	$-0.165196\pi$
$113$	18.4609	1.73665	0.868326	+	0.495994i	$0.165196\pi$
$114$	8.70913	0.815685
$115$	−7.03560	−0.656073
$116$	0	0
$117$	−0.677644	−0.0626482
$118$	2.94918	0.271494
$119$	−13.3552	−1.22427
$120$	1.95641	0.178595
$121$	2.56019	0.232744
$122$	−1.80894	−0.163774
$123$	−13.6497	−1.23075
$124$	8.99665	0.807923
$125$	−10.2366	−0.915587
$126$	−0.642174	−0.0572095
$127$	18.8979	1.67692	0.838461	−	0.544962i	$-0.183456\pi$
$127$	18.8979	1.67692	0.838461	+	0.544962i	$0.183456\pi$
$128$	1.00000	0.0883883
$129$	−6.03485	−0.531339
$130$	2.57436	0.225786
$131$	4.90775	0.428792	0.214396	−	0.976747i	$-0.431222\pi$
$131$	4.90775	0.428792	0.214396	+	0.976747i	$0.431222\pi$
$132$	6.03485	0.525266
$133$	10.8601	0.941691
$134$	6.04359	0.522086
$135$	−6.48402	−0.558056
$136$	−6.53517	−0.560386
$137$	3.81665	0.326078	0.163039	−	0.986620i	$-0.447870\pi$
$137$	3.81665	0.326078	0.163039	+	0.986620i	$0.447870\pi$
$138$	−9.65846	−0.822183
$139$	−12.1312	−1.02896	−0.514479	−	0.857503i	$-0.672015\pi$
$139$	−12.1312	−1.02896	−0.514479	+	0.857503i	$0.672015\pi$
$140$	2.43961	0.206184
$141$	−1.62697	−0.137016
$142$	3.75696	0.315277
$143$	7.94099	0.664059
$144$	−0.314239	−0.0261866
$145$	0	0
$146$	12.7248	1.05312
$147$	−4.62765	−0.381682
$148$	1.82798	0.150259
$149$	−7.19773	−0.589661	−0.294831	−	0.955550i	$-0.595263\pi$
$149$	−7.19773	−0.589661	−0.294831	+	0.955550i	$0.595263\pi$
$150$	−5.85860	−0.478353
$151$	−9.28245	−0.755395	−0.377698	−	0.925929i	$-0.623284\pi$
$151$	−9.28245	−0.755395	−0.377698	+	0.925929i	$0.623284\pi$
$152$	5.31424	0.431042
$153$	2.05361	0.166024
$154$	7.52534	0.606409
$155$	10.7401	0.862665
$156$	3.53407	0.282952
$157$	−1.99480	−0.159202	−0.0796011	−	0.996827i	$-0.525365\pi$
$157$	−1.99480	−0.159202	−0.0796011	+	0.996827i	$0.525365\pi$
$158$	14.1329	1.12435
$159$	−9.28313	−0.736200
$160$	1.19379	0.0943772
$161$	−12.0439	−0.949192
$162$	−7.95854	−0.625282
$163$	−4.09106	−0.320437	−0.160218	−	0.987082i	$-0.551220\pi$
$163$	−4.09106	−0.320437	−0.160218	+	0.987082i	$0.551220\pi$
$164$	−8.32895	−0.650382
$165$	7.20433	0.560856
$166$	2.05232	0.159291
$167$	7.36310	0.569774	0.284887	−	0.958561i	$-0.408044\pi$
$167$	7.36310	0.569774	0.284887	+	0.958561i	$0.408044\pi$
$168$	3.34909	0.258388
$169$	−8.34968	−0.642283
$170$	−7.80161	−0.598356
$171$	−1.66994	−0.127704
$172$	−3.68242	−0.280782
$173$	−9.85163	−0.749005	−0.374503	−	0.927226i	$-0.622187\pi$
$173$	−9.85163	−0.749005	−0.374503	+	0.927226i	$0.622187\pi$
$174$	0	0
$175$	−7.30556	−0.552248
$176$	3.68242	0.277573
$177$	4.83320	0.363286
$178$	−16.5120	−1.23763
$179$	−12.2877	−0.918425	−0.459213	−	0.888326i	$-0.651868\pi$
$179$	−12.2877	−0.918425	−0.459213	+	0.888326i	$0.651868\pi$
$180$	−0.375134	−0.0279609
$181$	13.7840	1.02455	0.512277	−	0.858821i	$-0.328802\pi$
$181$	13.7840	1.02455	0.512277	+	0.858821i	$0.328802\pi$
$182$	4.40692	0.326662
$183$	−2.96455	−0.219146
$184$	−5.89351	−0.434475
$185$	2.18222	0.160440
$186$	14.7440	1.08108
$187$	−24.0652	−1.75982
$188$	−0.992767	−0.0724050
$189$	−11.0997	−0.807383
$190$	6.34407	0.460247
$191$	15.8384	1.14603	0.573015	−	0.819545i	$-0.305774\pi$
$191$	15.8384	1.14603	0.573015	+	0.819545i	$0.305774\pi$
$192$	1.63883	0.118272
$193$	16.4251	1.18230	0.591151	−	0.806561i	$-0.298674\pi$
$193$	16.4251	1.18230	0.591151	+	0.806561i	$0.298674\pi$
$194$	−4.59626	−0.329992
$195$	4.21893	0.302124
$196$	−2.82375	−0.201697
$197$	14.6400	1.04306	0.521530	−	0.853233i	$-0.325362\pi$
$197$	14.6400	1.04306	0.521530	+	0.853233i	$0.325362\pi$
$198$	−1.15716	−0.0822357
$199$	1.41885	0.100579	0.0502897	−	0.998735i	$-0.483986\pi$
$199$	1.41885	0.100579	0.0502897	+	0.998735i	$0.483986\pi$
$200$	−3.57487	−0.252782
$201$	9.90441	0.698603
$202$	0.209757	0.0147584
$203$	0	0
$204$	−10.7100	−0.749852
$205$	−9.94299	−0.694449
$206$	−11.1276	−0.775295
$207$	1.85197	0.128721
$208$	2.15646	0.149524
$209$	19.5692	1.35363
$210$	3.99810	0.275895
$211$	−25.7685	−1.77398	−0.886988	−	0.461793i	$-0.847206\pi$
$211$	−25.7685	−1.77398	−0.886988	+	0.461793i	$0.847206\pi$
$212$	−5.66449	−0.389039
$213$	6.15702	0.421872
$214$	−4.04580	−0.276565
$215$	−4.39602	−0.299806
$216$	−5.43147	−0.369565
$217$	18.3854	1.24809
$218$	−15.6335	−1.05884
$219$	20.8538	1.40917
$220$	4.39602	0.296380
$221$	−14.0928	−0.947988
$222$	2.99575	0.201062
$223$	−2.37303	−0.158910	−0.0794548	−	0.996838i	$-0.525318\pi$
$223$	−2.37303	−0.158910	−0.0794548	+	0.996838i	$0.525318\pi$
$224$	2.04359	0.136543
$225$	1.12336	0.0748909
$226$	18.4609	1.22800
$227$	12.9823	0.861666	0.430833	−	0.902432i	$-0.358220\pi$
$227$	12.9823	0.861666	0.430833	+	0.902432i	$0.358220\pi$
$228$	8.70913	0.576776
$229$	−25.7082	−1.69884	−0.849422	−	0.527714i	$-0.823049\pi$
$229$	−25.7082	−1.69884	−0.849422	+	0.527714i	$0.823049\pi$
$230$	−7.03560	−0.463914
$231$	12.3327	0.811435
$232$	0	0
$233$	−7.05047	−0.461891	−0.230946	−	0.972967i	$-0.574182\pi$
$233$	−7.05047	−0.461891	−0.230946	+	0.972967i	$0.574182\pi$
$234$	−0.677644	−0.0442990
$235$	−1.18515	−0.0773108
$236$	2.94918	0.191975
$237$	23.1614	1.50450
$238$	−13.3552	−0.865689
$239$	−3.52639	−0.228103	−0.114052	−	0.993475i	$-0.536383\pi$
$239$	−3.52639	−0.228103	−0.114052	+	0.993475i	$0.536383\pi$
$240$	1.95641	0.126286
$241$	11.8721	0.764746	0.382373	−	0.924008i	$-0.375107\pi$
$241$	11.8721	0.764746	0.382373	+	0.924008i	$0.375107\pi$
$242$	2.56019	0.164575
$243$	3.25173	0.208599
$244$	−1.80894	−0.115806
$245$	−3.37096	−0.215363
$246$	−13.6497	−0.870275
$247$	11.4599	0.729179
$248$	8.99665	0.571288
$249$	3.36341	0.213147
$250$	−10.2366	−0.647418
$251$	−9.31251	−0.587800	−0.293900	−	0.955836i	$-0.594953\pi$
$251$	−9.31251	−0.587800	−0.293900	+	0.955836i	$0.594953\pi$
$252$	−0.642174	−0.0404532
$253$	−21.7024	−1.36442
$254$	18.8979	1.18576
$255$	−12.7855	−0.800659
$256$	1.00000	0.0625000
$257$	−11.5210	−0.718660	−0.359330	−	0.933211i	$-0.616995\pi$
$257$	−11.5210	−0.718660	−0.359330	+	0.933211i	$0.616995\pi$
$258$	−6.03485	−0.375713
$259$	3.73564	0.232121
$260$	2.57436	0.159655
$261$	0	0
$262$	4.90775	0.303202
$263$	10.0654	0.620658	0.310329	−	0.950629i	$-0.399561\pi$
$263$	10.0654	0.620658	0.310329	+	0.950629i	$0.399561\pi$
$264$	6.03485	0.371419
$265$	−6.76219	−0.415398
$266$	10.8601	0.665876
$267$	−27.0603	−1.65607
$268$	6.04359	0.369171
$269$	−8.40756	−0.512618	−0.256309	−	0.966595i	$-0.582506\pi$
$269$	−8.40756	−0.512618	−0.256309	+	0.966595i	$0.582506\pi$
$270$	−6.48402	−0.394605
$271$	8.66180	0.526167	0.263084	−	0.964773i	$-0.415261\pi$
$271$	8.66180	0.526167	0.263084	+	0.964773i	$0.415261\pi$
$272$	−6.53517	−0.396253
$273$	7.22218	0.437106
$274$	3.81665	0.230572
$275$	−13.1642	−0.793829
$276$	−9.65846	−0.581371
$277$	−19.3500	−1.16263	−0.581313	−	0.813680i	$-0.697461\pi$
$277$	−19.3500	−1.16263	−0.581313	+	0.813680i	$0.697461\pi$
$278$	−12.1312	−0.727584
$279$	−2.82710	−0.169254
$280$	2.43961	0.145794
$281$	−15.1993	−0.906715	−0.453358	−	0.891329i	$-0.649774\pi$
$281$	−15.1993	−0.906715	−0.453358	+	0.891329i	$0.649774\pi$
$282$	−1.62697	−0.0968850
$283$	15.0356	0.893774	0.446887	−	0.894591i	$-0.352533\pi$
$283$	15.0356	0.893774	0.446887	+	0.894591i	$0.352533\pi$
$284$	3.75696	0.222935
$285$	10.3968	0.615856
$286$	7.94099	0.469560
$287$	−17.0209	−1.00471
$288$	−0.314239	−0.0185167
$289$	25.7085	1.51226
$290$	0	0
$291$	−7.53248	−0.441562
$292$	12.7248	0.744665
$293$	29.4644	1.72133	0.860665	−	0.509171i	$-0.170048\pi$
$293$	29.4644	1.72133	0.860665	+	0.509171i	$0.170048\pi$
$294$	−4.62765	−0.269890
$295$	3.52069	0.204983
$296$	1.82798	0.106249
$297$	−20.0009	−1.16057
$298$	−7.19773	−0.416953
$299$	−12.7091	−0.734988
$300$	−5.85860	−0.338247
$301$	−7.52534	−0.433753
$302$	−9.28245	−0.534145
$303$	0.343756	0.0197482
$304$	5.31424	0.304793
$305$	−2.15949	−0.123652
$306$	2.05361	0.117397
$307$	−5.88515	−0.335883	−0.167942	−	0.985797i	$-0.553712\pi$
$307$	−5.88515	−0.335883	−0.167942	+	0.985797i	$0.553712\pi$
$308$	7.52534	0.428796
$309$	−18.2362	−1.03742
$310$	10.7401	0.609996
$311$	−22.9969	−1.30404	−0.652018	−	0.758203i	$-0.726077\pi$
$311$	−22.9969	−1.30404	−0.652018	+	0.758203i	$0.726077\pi$
$312$	3.53407	0.200077
$313$	20.5485	1.16147	0.580735	−	0.814093i	$-0.302765\pi$
$313$	20.5485	1.16147	0.580735	+	0.814093i	$0.302765\pi$
$314$	−1.99480	−0.112573
$315$	−0.766620	−0.0431941
$316$	14.1329	0.795039
$317$	7.04928	0.395927	0.197964	−	0.980209i	$-0.436567\pi$
$317$	7.04928	0.395927	0.197964	+	0.980209i	$0.436567\pi$
$318$	−9.28313	−0.520572
$319$	0	0
$320$	1.19379	0.0667347
$321$	−6.63038	−0.370072
$322$	−12.0439	−0.671180
$323$	−34.7295	−1.93240
$324$	−7.95854	−0.442141
$325$	−7.70907	−0.427622
$326$	−4.09106	−0.226583
$327$	−25.6207	−1.41683
$328$	−8.32895	−0.459889
$329$	−2.02880	−0.111852
$330$	7.20433	0.396585
$331$	20.4930	1.12640	0.563200	−	0.826321i	$-0.309570\pi$
$331$	20.4930	1.12640	0.563200	+	0.826321i	$0.309570\pi$
$332$	2.05232	0.112636
$333$	−0.574423	−0.0314782
$334$	7.36310	0.402891
$335$	7.21476	0.394184
$336$	3.34909	0.182708
$337$	−7.42412	−0.404418	−0.202209	−	0.979342i	$-0.564812\pi$
$337$	−7.42412	−0.404418	−0.202209	+	0.979342i	$0.564812\pi$
$338$	−8.34968	−0.454162
$339$	30.2542	1.64318
$340$	−7.80161	−0.423102
$341$	33.1294	1.79406
$342$	−1.66994	−0.0903001
$343$	−20.0757	−1.08399
$344$	−3.68242	−0.198543
$345$	−11.5301	−0.620762
$346$	−9.85163	−0.529627
$347$	−20.9493	−1.12462	−0.562308	−	0.826928i	$-0.690087\pi$
$347$	−20.9493	−1.12462	−0.562308	+	0.826928i	$0.690087\pi$
$348$	0	0
$349$	−13.5931	−0.727620	−0.363810	−	0.931473i	$-0.618524\pi$
$349$	−13.5931	−0.727620	−0.363810	+	0.931473i	$0.618524\pi$
$350$	−7.30556	−0.390499
$351$	−11.7128	−0.625181
$352$	3.68242	0.196273
$353$	18.2706	0.972445	0.486222	−	0.873835i	$-0.338375\pi$
$353$	18.2706	0.972445	0.486222	+	0.873835i	$0.338375\pi$
$354$	4.83320	0.256882
$355$	4.48502	0.238040
$356$	−16.5120	−0.875134
$357$	−21.8869	−1.15838
$358$	−12.2877	−0.649425
$359$	−8.73615	−0.461076	−0.230538	−	0.973063i	$-0.574049\pi$
$359$	−8.73615	−0.461076	−0.230538	+	0.973063i	$0.574049\pi$
$360$	−0.375134	−0.0197713
$361$	9.24114	0.486376
$362$	13.7840	0.724469
$363$	4.19571	0.220217
$364$	4.40692	0.230985
$365$	15.1908	0.795121
$366$	−2.96455	−0.154959
$367$	−14.9484	−0.780299	−0.390150	−	0.920751i	$-0.627577\pi$
$367$	−14.9484	−0.780299	−0.390150	+	0.920751i	$0.627577\pi$
$368$	−5.89351	−0.307221
$369$	2.61728	0.136250
$370$	2.18222	0.113448
$371$	−11.5759	−0.600989
$372$	14.7440	0.764440
$373$	35.0947	1.81713	0.908567	−	0.417738i	$-0.137177\pi$
$373$	35.0947	1.81713	0.908567	+	0.417738i	$0.137177\pi$
$374$	−24.0652	−1.24438
$375$	−16.7760	−0.866309
$376$	−0.992767	−0.0511980
$377$	0	0
$378$	−11.0997	−0.570906
$379$	33.0878	1.69961	0.849804	−	0.527098i	$-0.176720\pi$
$379$	33.0878	1.69961	0.849804	+	0.527098i	$0.176720\pi$
$380$	6.34407	0.325444
$381$	30.9705	1.58667
$382$	15.8384	0.810365
$383$	−8.55301	−0.437038	−0.218519	−	0.975833i	$-0.570123\pi$
$383$	−8.55301	−0.437038	−0.218519	+	0.975833i	$0.570123\pi$
$384$	1.63883	0.0836312
$385$	8.98365	0.457849
$386$	16.4251	0.836013
$387$	1.15716	0.0588217
$388$	−4.59626	−0.233340
$389$	−25.7864	−1.30742	−0.653710	−	0.756745i	$-0.726788\pi$
$389$	−25.7864	−1.30742	−0.653710	+	0.756745i	$0.726788\pi$
$390$	4.21893	0.213634
$391$	38.5151	1.94779
$392$	−2.82375	−0.142621
$393$	8.04297	0.405714
$394$	14.6400	0.737555
$395$	16.8717	0.848907
$396$	−1.15716	−0.0581494
$397$	8.52545	0.427880	0.213940	−	0.976847i	$-0.431370\pi$
$397$	8.52545	0.427880	0.213940	+	0.976847i	$0.431370\pi$
$398$	1.41885	0.0711204
$399$	17.7979	0.891007
$400$	−3.57487	−0.178744
$401$	15.7621	0.787122	0.393561	−	0.919298i	$-0.371243\pi$
$401$	15.7621	0.787122	0.393561	+	0.919298i	$0.371243\pi$
$402$	9.90441	0.493987
$403$	19.4009	0.966429
$404$	0.209757	0.0104358
$405$	−9.50080	−0.472099
$406$	0	0
$407$	6.73139	0.333663
$408$	−10.7100	−0.530226
$409$	22.8654	1.13062	0.565311	−	0.824878i	$-0.308756\pi$
$409$	22.8654	1.13062	0.565311	+	0.824878i	$0.308756\pi$
$410$	−9.94299	−0.491049
$411$	6.25483	0.308528
$412$	−11.1276	−0.548217
$413$	6.02690	0.296565
$414$	1.85197	0.0910194
$415$	2.45004	0.120268
$416$	2.15646	0.105729
$417$	−19.8810	−0.973579
$418$	19.5692	0.957163
$419$	20.3457	0.993950	0.496975	−	0.867765i	$-0.334444\pi$
$419$	20.3457	0.993950	0.496975	+	0.867765i	$0.334444\pi$
$420$	3.99810	0.195087
$421$	−19.3581	−0.943458	−0.471729	−	0.881744i	$-0.656370\pi$
$421$	−19.3581	−0.943458	−0.471729	+	0.881744i	$0.656370\pi$
$422$	−25.7685	−1.25439
$423$	0.311966	0.0151683
$424$	−5.66449	−0.275092
$425$	23.3624	1.13324
$426$	6.15702	0.298309
$427$	−3.69673	−0.178897
$428$	−4.04580	−0.195561
$429$	13.0139	0.628318
$430$	−4.39602	−0.211995
$431$	4.55906	0.219602	0.109801	−	0.993954i	$-0.464979\pi$
$431$	4.55906	0.219602	0.109801	+	0.993954i	$0.464979\pi$
$432$	−5.43147	−0.261322
$433$	−18.3691	−0.882760	−0.441380	−	0.897320i	$-0.645511\pi$
$433$	−18.3691	−0.882760	−0.441380	+	0.897320i	$0.645511\pi$
$434$	18.3854	0.882529
$435$	0	0
$436$	−15.6335	−0.748711
$437$	−31.3195	−1.49822
$438$	20.8538	0.996435
$439$	−19.1652	−0.914707	−0.457353	−	0.889285i	$-0.651203\pi$
$439$	−19.1652	−0.914707	−0.457353	+	0.889285i	$0.651203\pi$
$440$	4.39602	0.209572
$441$	0.887334	0.0422540
$442$	−14.0928	−0.670328
$443$	2.26565	0.107644	0.0538222	−	0.998551i	$-0.482860\pi$
$443$	2.26565	0.107644	0.0538222	+	0.998551i	$0.482860\pi$
$444$	2.99575	0.142172
$445$	−19.7118	−0.934430
$446$	−2.37303	−0.112366
$447$	−11.7959	−0.557925
$448$	2.04359	0.0965504
$449$	−24.3823	−1.15067	−0.575336	−	0.817917i	$-0.695129\pi$
$449$	−24.3823	−1.15067	−0.575336	+	0.817917i	$0.695129\pi$
$450$	1.12336	0.0529559
$451$	−30.6706	−1.44422
$452$	18.4609	0.868326
$453$	−15.2123	−0.714738
$454$	12.9823	0.609290
$455$	5.26092	0.246636
$456$	8.70913	0.407842
$457$	−26.0136	−1.21687	−0.608433	−	0.793605i	$-0.708202\pi$
$457$	−26.0136	−1.21687	−0.608433	+	0.793605i	$0.708202\pi$
$458$	−25.7082	−1.20126
$459$	35.4956	1.65679
$460$	−7.03560	−0.328037
$461$	−26.1593	−1.21836	−0.609181	−	0.793031i	$-0.708502\pi$
$461$	−26.1593	−1.21836	−0.609181	+	0.793031i	$0.708502\pi$
$462$	12.3327	0.573771
$463$	−28.3236	−1.31631	−0.658155	−	0.752882i	$-0.728663\pi$
$463$	−28.3236	−1.31631	−0.658155	+	0.752882i	$0.728663\pi$
$464$	0	0
$465$	17.6012	0.816235
$466$	−7.05047	−0.326607
$467$	−0.164856	−0.00762865	−0.00381432	−	0.999993i	$-0.501214\pi$
$467$	−0.164856	−0.00762865	−0.00381432	+	0.999993i	$0.501214\pi$
$468$	−0.677644	−0.0313241
$469$	12.3506	0.570297
$470$	−1.18515	−0.0546670
$471$	−3.26913	−0.150634
$472$	2.94918	0.135747
$473$	−13.5602	−0.623498
$474$	23.1614	1.06384
$475$	−18.9977	−0.871675
$476$	−13.3552	−0.612134
$477$	1.78000	0.0815007
$478$	−3.52639	−0.161293
$479$	−11.4544	−0.523363	−0.261682	−	0.965154i	$-0.584277\pi$
$479$	−11.4544	−0.523363	−0.261682	+	0.965154i	$0.584277\pi$
$480$	1.95641	0.0892976
$481$	3.94197	0.179739
$482$	11.8721	0.540757
$483$	−19.7379	−0.898105
$484$	2.56019	0.116372
$485$	−5.48695	−0.249150
$486$	3.25173	0.147502
$487$	23.2025	1.05141	0.525703	−	0.850668i	$-0.323802\pi$
$487$	23.2025	1.05141	0.525703	+	0.850668i	$0.323802\pi$
$488$	−1.80894	−0.0818870
$489$	−6.70455	−0.303190
$490$	−3.37096	−0.152285
$491$	14.1185	0.637158	0.318579	−	0.947896i	$-0.396794\pi$
$491$	14.1185	0.637158	0.318579	+	0.947896i	$0.396794\pi$
$492$	−13.6497	−0.615377
$493$	0	0
$494$	11.4599	0.515608
$495$	−1.38140	−0.0620894
$496$	8.99665	0.403962
$497$	7.67768	0.344391
$498$	3.36341	0.150718
$499$	−7.59719	−0.340097	−0.170049	−	0.985436i	$-0.554392\pi$
$499$	−7.59719	−0.340097	−0.170049	+	0.985436i	$0.554392\pi$
$500$	−10.2366	−0.457793
$501$	12.0669	0.539108
$502$	−9.31251	−0.415638
$503$	−1.68662	−0.0752028	−0.0376014	−	0.999293i	$-0.511972\pi$
$503$	−1.68662	−0.0752028	−0.0376014	+	0.999293i	$0.511972\pi$
$504$	−0.642174	−0.0286047
$505$	0.250405	0.0111429
$506$	−21.7024	−0.964788
$507$	−13.6837	−0.607714
$508$	18.8979	0.838461
$509$	41.3978	1.83492	0.917462	−	0.397823i	$-0.130234\pi$
$509$	41.3978	1.83492	0.917462	+	0.397823i	$0.130234\pi$
$510$	−12.7855	−0.566152
$511$	26.0043	1.15036
$512$	1.00000	0.0441942
$513$	−28.8641	−1.27438
$514$	−11.5210	−0.508169
$515$	−13.2840	−0.585362
$516$	−6.03485	−0.265669
$517$	−3.65578	−0.160781
$518$	3.73564	0.164135
$519$	−16.1451	−0.708693
$520$	2.57436	0.112893
$521$	−5.78621	−0.253498	−0.126749	−	0.991935i	$-0.540454\pi$
$521$	−5.78621	−0.253498	−0.126749	+	0.991935i	$0.540454\pi$
$522$	0	0
$523$	−14.4968	−0.633899	−0.316949	−	0.948442i	$-0.602659\pi$
$523$	−14.4968	−0.633899	−0.316949	+	0.948442i	$0.602659\pi$
$524$	4.90775	0.214396
$525$	−11.9726	−0.522526
$526$	10.0654	0.438871
$527$	−58.7947	−2.56114
$528$	6.03485	0.262633
$529$	11.7335	0.510151
$530$	−6.76219	−0.293731
$531$	−0.926747	−0.0402174
$532$	10.8601	0.470845
$533$	−17.9611	−0.777980
$534$	−27.0603	−1.17102
$535$	−4.82983	−0.208812
$536$	6.04359	0.261043
$537$	−20.1374	−0.868994
$538$	−8.40756	−0.362476
$539$	−10.3982	−0.447884
$540$	−6.48402	−0.279028
$541$	−2.23993	−0.0963022	−0.0481511	−	0.998840i	$-0.515333\pi$
$541$	−2.23993	−0.0963022	−0.0481511	+	0.998840i	$0.515333\pi$
$542$	8.66180	0.372056
$543$	22.5895	0.969410
$544$	−6.53517	−0.280193
$545$	−18.6631	−0.799441
$546$	7.22218	0.309081
$547$	41.7431	1.78481	0.892403	−	0.451239i	$-0.149018\pi$
$547$	41.7431	1.78481	0.892403	+	0.451239i	$0.149018\pi$
$548$	3.81665	0.163039
$549$	0.568441	0.0242605
$550$	−13.1642	−0.561322
$551$	0	0
$552$	−9.65846	−0.411091
$553$	28.8818	1.22818
$554$	−19.3500	−0.822101
$555$	3.57629	0.151805
$556$	−12.1312	−0.514479
$557$	−20.5159	−0.869287	−0.434644	−	0.900603i	$-0.643126\pi$
$557$	−20.5159	−0.869287	−0.434644	+	0.900603i	$0.643126\pi$
$558$	−2.82710	−0.119681
$559$	−7.94099	−0.335868
$560$	2.43961	0.103092
$561$	−39.4388	−1.66511
$562$	−15.1993	−0.641144
$563$	19.9670	0.841511	0.420755	−	0.907174i	$-0.361765\pi$
$563$	19.9670	0.841511	0.420755	+	0.907174i	$0.361765\pi$
$564$	−1.62697	−0.0685080
$565$	22.0383	0.927160
$566$	15.0356	0.631993
$567$	−16.2640	−0.683022
$568$	3.75696	0.157639
$569$	−6.11008	−0.256148	−0.128074	−	0.991765i	$-0.540879\pi$
$569$	−6.11008	−0.256148	−0.128074	+	0.991765i	$0.540879\pi$
$570$	10.3968	0.435476
$571$	21.5427	0.901534	0.450767	−	0.892642i	$-0.351150\pi$
$571$	21.5427	0.901534	0.450767	+	0.892642i	$0.351150\pi$
$572$	7.94099	0.332029
$573$	25.9565	1.08435
$574$	−17.0209	−0.710440
$575$	21.0686	0.878619
$576$	−0.314239	−0.0130933
$577$	13.5261	0.563101	0.281550	−	0.959546i	$-0.409151\pi$
$577$	13.5261	0.563101	0.281550	+	0.959546i	$0.409151\pi$
$578$	25.7085	1.06933
$579$	26.9179	1.11867
$580$	0	0
$581$	4.19410	0.174001
$582$	−7.53248	−0.312231
$583$	−20.8590	−0.863891
$584$	12.7248	0.526558
$585$	−0.808963	−0.0334465
$586$	29.4644	1.21716
$587$	−5.75838	−0.237674	−0.118837	−	0.992914i	$-0.537917\pi$
$587$	−5.75838	−0.237674	−0.118837	+	0.992914i	$0.537917\pi$
$588$	−4.62765	−0.190841
$589$	47.8104	1.96999
$590$	3.52069	0.144945
$591$	23.9925	0.986921
$592$	1.82798	0.0751296
$593$	18.6393	0.765426	0.382713	−	0.923867i	$-0.374990\pi$
$593$	18.6393	0.765426	0.382713	+	0.923867i	$0.374990\pi$
$594$	−20.0009	−0.820648
$595$	−15.9433	−0.653610
$596$	−7.19773	−0.294831
$597$	2.32525	0.0951661
$598$	−12.7091	−0.519715
$599$	6.79409	0.277599	0.138799	−	0.990321i	$-0.455676\pi$
$599$	6.79409	0.277599	0.138799	+	0.990321i	$0.455676\pi$
$600$	−5.85860	−0.239177
$601$	32.1799	1.31265	0.656324	−	0.754480i	$-0.272111\pi$
$601$	32.1799	1.31265	0.656324	+	0.754480i	$0.272111\pi$
$602$	−7.52534	−0.306710
$603$	−1.89913	−0.0773386
$604$	−9.28245	−0.377698
$605$	3.05632	0.124257
$606$	0.343756	0.0139641
$607$	−7.82054	−0.317426	−0.158713	−	0.987325i	$-0.550734\pi$
$607$	−7.82054	−0.317426	−0.158713	+	0.987325i	$0.550734\pi$
$608$	5.31424	0.215521
$609$	0	0
$610$	−2.15949	−0.0874354
$611$	−2.14086	−0.0866100
$612$	2.05361	0.0830121
$613$	−12.9346	−0.522423	−0.261212	−	0.965282i	$-0.584122\pi$
$613$	−12.9346	−0.522423	−0.261212	+	0.965282i	$0.584122\pi$
$614$	−5.88515	−0.237505
$615$	−16.2949	−0.657072
$616$	7.52534	0.303204
$617$	39.8389	1.60385	0.801927	−	0.597422i	$-0.203808\pi$
$617$	39.8389	1.60385	0.801927	+	0.597422i	$0.203808\pi$
$618$	−18.2362	−0.733568
$619$	5.35941	0.215413	0.107706	−	0.994183i	$-0.465649\pi$
$619$	5.35941	0.215413	0.107706	+	0.994183i	$0.465649\pi$
$620$	10.7401	0.431332
$621$	32.0104	1.28453
$622$	−22.9969	−0.922093
$623$	−33.7437	−1.35191
$624$	3.53407	0.141476
$625$	5.65407	0.226163
$626$	20.5485	0.821283
$627$	32.0706	1.28078
$628$	−1.99480	−0.0796011
$629$	−11.9462	−0.476326
$630$	−0.766620	−0.0305429
$631$	−22.2190	−0.884526	−0.442263	−	0.896885i	$-0.645824\pi$
$631$	−22.2190	−0.884526	−0.442263	+	0.896885i	$0.645824\pi$
$632$	14.1329	0.562177
$633$	−42.2301	−1.67850
$634$	7.04928	0.279963
$635$	22.5601	0.895271
$636$	−9.28313	−0.368100
$637$	−6.08932	−0.241267
$638$	0	0
$639$	−1.18058	−0.0467032
$640$	1.19379	0.0471886
$641$	−18.8545	−0.744710	−0.372355	−	0.928090i	$-0.621450\pi$
$641$	−18.8545	−0.744710	−0.372355	+	0.928090i	$0.621450\pi$
$642$	−6.63038	−0.261680
$643$	−7.54108	−0.297391	−0.148696	−	0.988883i	$-0.547507\pi$
$643$	−7.54108	−0.297391	−0.148696	+	0.988883i	$0.547507\pi$
$644$	−12.0439	−0.474596
$645$	−7.20433	−0.283670
$646$	−34.7295	−1.36641
$647$	34.2334	1.34585	0.672927	−	0.739709i	$-0.265037\pi$
$647$	34.2334	1.34585	0.672927	+	0.739709i	$0.265037\pi$
$648$	−7.95854	−0.312641
$649$	10.8601	0.426296
$650$	−7.70907	−0.302375
$651$	30.1306	1.18091
$652$	−4.09106	−0.160218
$653$	26.5709	1.03980	0.519900	−	0.854227i	$-0.325969\pi$
$653$	26.5709	1.03980	0.519900	+	0.854227i	$0.325969\pi$
$654$	−25.6207	−1.00185
$655$	5.85881	0.228923
$656$	−8.32895	−0.325191
$657$	−3.99864	−0.156002
$658$	−2.02880	−0.0790910
$659$	−18.6729	−0.727394	−0.363697	−	0.931517i	$-0.618486\pi$
$659$	−18.6729	−0.727394	−0.363697	+	0.931517i	$0.618486\pi$
$660$	7.20433	0.280428
$661$	22.3030	0.867486	0.433743	−	0.901037i	$-0.357193\pi$
$661$	22.3030	0.867486	0.433743	+	0.901037i	$0.357193\pi$
$662$	20.4930	0.796484
$663$	−23.0958	−0.896965
$664$	2.05232	0.0796456
$665$	12.9647	0.502748
$666$	−0.574423	−0.0222585
$667$	0	0
$668$	7.36310	0.284887
$669$	−3.88898	−0.150357
$670$	7.21476	0.278730
$671$	−6.66128	−0.257156
$672$	3.34909	0.129194
$673$	31.0215	1.19579	0.597896	−	0.801574i	$-0.296004\pi$
$673$	31.0215	1.19579	0.597896	+	0.801574i	$0.296004\pi$
$674$	−7.42412	−0.285967
$675$	19.4168	0.747354
$676$	−8.34968	−0.321141
$677$	12.8063	0.492186	0.246093	−	0.969246i	$-0.420853\pi$
$677$	12.8063	0.492186	0.246093	+	0.969246i	$0.420853\pi$
$678$	30.2542	1.16191
$679$	−9.39285	−0.360464
$680$	−7.80161	−0.299178
$681$	21.2758	0.815289
$682$	33.1294	1.26859
$683$	43.0174	1.64602	0.823008	−	0.568029i	$-0.192294\pi$
$683$	43.0174	1.64602	0.823008	+	0.568029i	$0.192294\pi$
$684$	−1.66994	−0.0638518
$685$	4.55626	0.174086
$686$	−20.0757	−0.766493
$687$	−42.1313	−1.60741
$688$	−3.68242	−0.140391
$689$	−12.2152	−0.465364
$690$	−11.5301	−0.438945
$691$	−42.9824	−1.63513	−0.817565	−	0.575837i	$-0.804676\pi$
$691$	−42.9824	−1.63513	−0.817565	+	0.575837i	$0.804676\pi$
$692$	−9.85163	−0.374503
$693$	−2.36475	−0.0898296
$694$	−20.9493	−0.795224
$695$	−14.4821	−0.549338
$696$	0	0
$697$	54.4311	2.06173
$698$	−13.5931	−0.514505
$699$	−11.5545	−0.437032
$700$	−7.30556	−0.276124
$701$	40.5781	1.53261	0.766307	−	0.642475i	$-0.222092\pi$
$701$	40.5781	1.53261	0.766307	+	0.642475i	$0.222092\pi$
$702$	−11.7128	−0.442070
$703$	9.71434	0.366383
$704$	3.68242	0.138786
$705$	−1.94226	−0.0731498
$706$	18.2706	0.687622
$707$	0.428656	0.0161213
$708$	4.83320	0.181643
$709$	−34.5861	−1.29891	−0.649453	−	0.760401i	$-0.725002\pi$
$709$	−34.5861	−1.29891	−0.649453	+	0.760401i	$0.725002\pi$
$710$	4.48502	0.168320
$711$	−4.44111	−0.166555
$712$	−16.5120	−0.618813
$713$	−53.0219	−1.98569
$714$	−21.8869	−0.819096
$715$	9.47985	0.354526
$716$	−12.2877	−0.459213
$717$	−5.77915	−0.215826
$718$	−8.73615	−0.326030
$719$	6.19210	0.230926	0.115463	−	0.993312i	$-0.463165\pi$
$719$	6.19210	0.230926	0.115463	+	0.993312i	$0.463165\pi$
$720$	−0.375134	−0.0139804
$721$	−22.7402	−0.846889
$722$	9.24114	0.343919
$723$	19.4563	0.723587
$724$	13.7840	0.512277
$725$	0	0
$726$	4.19571	0.155717
$727$	20.1213	0.746259	0.373129	−	0.927779i	$-0.378285\pi$
$727$	20.1213	0.746259	0.373129	+	0.927779i	$0.378285\pi$
$728$	4.40692	0.163331
$729$	29.2046	1.08165
$730$	15.1908	0.562235
$731$	24.0652	0.890084
$732$	−2.96455	−0.109573
$733$	−14.7072	−0.543224	−0.271612	−	0.962407i	$-0.587557\pi$
$733$	−14.7072	−0.543224	−0.271612	+	0.962407i	$0.587557\pi$
$734$	−14.9484	−0.551755
$735$	−5.52443	−0.203772
$736$	−5.89351	−0.217238
$737$	22.2550	0.819773
$738$	2.61728	0.0963434
$739$	−14.1566	−0.520759	−0.260379	−	0.965506i	$-0.583848\pi$
$739$	−14.1566	−0.520759	−0.260379	+	0.965506i	$0.583848\pi$
$740$	2.18222	0.0802201
$741$	18.7809	0.689934
$742$	−11.5759	−0.424964
$743$	−26.5698	−0.974752	−0.487376	−	0.873192i	$-0.662046\pi$
$743$	−26.5698	−0.974752	−0.487376	+	0.873192i	$0.662046\pi$
$744$	14.7440	0.540541
$745$	−8.59256	−0.314807
$746$	35.0947	1.28491
$747$	−0.644920	−0.0235964
$748$	−24.0652	−0.879912
$749$	−8.26795	−0.302104
$750$	−16.7760	−0.612573
$751$	37.2142	1.35797	0.678983	−	0.734154i	$-0.262421\pi$
$751$	37.2142	1.35797	0.678983	+	0.734154i	$0.262421\pi$
$752$	−0.992767	−0.0362025
$753$	−15.2616	−0.556164
$754$	0	0
$755$	−11.0813	−0.403289
$756$	−11.0997	−0.403692
$757$	22.9244	0.833201	0.416601	−	0.909090i	$-0.363221\pi$
$757$	22.9244	0.833201	0.416601	+	0.909090i	$0.363221\pi$
$758$	33.0878	1.20180
$759$	−35.5665	−1.29098
$760$	6.34407	0.230124
$761$	30.8221	1.11730	0.558651	−	0.829403i	$-0.311319\pi$
$761$	30.8221	1.11730	0.558651	+	0.829403i	$0.311319\pi$
$762$	30.9705	1.12194
$763$	−31.9485	−1.15661
$764$	15.8384	0.573015
$765$	2.45157	0.0886367
$766$	−8.55301	−0.309033
$767$	6.35979	0.229639
$768$	1.63883	0.0591362
$769$	−13.1631	−0.474674	−0.237337	−	0.971427i	$-0.576275\pi$
$769$	−13.1631	−0.474674	−0.237337	+	0.971427i	$0.576275\pi$
$770$	8.98365	0.323748
$771$	−18.8809	−0.679980
$772$	16.4251	0.591151
$773$	−1.05704	−0.0380192	−0.0190096	−	0.999819i	$-0.506051\pi$
$773$	−1.05704	−0.0380192	−0.0190096	+	0.999819i	$0.506051\pi$
$774$	1.15716	0.0415932
$775$	−32.1619	−1.15529
$776$	−4.59626	−0.164996
$777$	6.12208	0.219628
$778$	−25.7864	−0.924486
$779$	−44.2620	−1.58585
$780$	4.21893	0.151062
$781$	13.8347	0.495045
$782$	38.5151	1.37730
$783$	0	0
$784$	−2.82375	−0.100848
$785$	−2.38136	−0.0849946
$786$	8.04297	0.286883
$787$	21.1399	0.753558	0.376779	−	0.926303i	$-0.377032\pi$
$787$	21.1399	0.753558	0.376779	+	0.926303i	$0.377032\pi$
$788$	14.6400	0.521530
$789$	16.4954	0.587253
$790$	16.8717	0.600268
$791$	37.7264	1.34140
$792$	−1.15716	−0.0411178
$793$	−3.90092	−0.138526
$794$	8.52545	0.302557
$795$	−11.0821	−0.393041
$796$	1.41885	0.0502897
$797$	28.2846	1.00189	0.500945	−	0.865479i	$-0.332986\pi$
$797$	28.2846	1.00189	0.500945	+	0.865479i	$0.332986\pi$
$798$	17.7979	0.630037
$799$	6.48790	0.229525
$800$	−3.57487	−0.126391
$801$	5.18871	0.183334
$802$	15.7621	0.556580
$803$	46.8582	1.65359
$804$	9.90441	0.349301
$805$	−14.3779	−0.506753
$806$	19.4009	0.683369
$807$	−13.7786	−0.485028
$808$	0.209757	0.00737922
$809$	14.7831	0.519745	0.259873	−	0.965643i	$-0.416319\pi$
$809$	14.7831	0.519745	0.259873	+	0.965643i	$0.416319\pi$
$810$	−9.50080	−0.333824
$811$	36.6892	1.28833	0.644166	−	0.764886i	$-0.277205\pi$
$811$	36.6892	1.28833	0.644166	+	0.764886i	$0.277205\pi$
$812$	0	0
$813$	14.1952	0.497848
$814$	6.73139	0.235935
$815$	−4.88386	−0.171074
$816$	−10.7100	−0.374926
$817$	−19.5692	−0.684641
$818$	22.8654	0.799471
$819$	−1.38482	−0.0483897
$820$	−9.94299	−0.347224
$821$	−11.3932	−0.397625	−0.198813	−	0.980038i	$-0.563709\pi$
$821$	−11.3932	−0.397625	−0.198813	+	0.980038i	$0.563709\pi$
$822$	6.25483	0.218162
$823$	40.8530	1.42405	0.712023	−	0.702156i	$-0.247779\pi$
$823$	40.8530	1.42405	0.712023	+	0.702156i	$0.247779\pi$
$824$	−11.1276	−0.387648
$825$	−21.5738	−0.751104
$826$	6.02690	0.209703
$827$	−36.0491	−1.25355	−0.626775	−	0.779200i	$-0.715625\pi$
$827$	−36.0491	−1.25355	−0.626775	+	0.779200i	$0.715625\pi$
$828$	1.85197	0.0643604
$829$	23.8361	0.827862	0.413931	−	0.910308i	$-0.364155\pi$
$829$	23.8361	0.827862	0.413931	+	0.910308i	$0.364155\pi$
$830$	2.45004	0.0850420
$831$	−31.7113	−1.10005
$832$	2.15646	0.0747618
$833$	18.4537	0.639384
$834$	−19.8810	−0.688424
$835$	8.78998	0.304190
$836$	19.5692	0.676816
$837$	−48.8651	−1.68902
$838$	20.3457	0.702829
$839$	−41.7136	−1.44011	−0.720056	−	0.693916i	$-0.755884\pi$
$839$	−41.7136	−1.44011	−0.720056	+	0.693916i	$0.755884\pi$
$840$	3.99810	0.137948
$841$	0	0
$842$	−19.3581	−0.667126
$843$	−24.9091	−0.857914
$844$	−25.7685	−0.886988
$845$	−9.96774	−0.342901
$846$	0.311966	0.0107256
$847$	5.23196	0.179772
$848$	−5.66449	−0.194519
$849$	24.6408	0.845669
$850$	23.3624	0.801324
$851$	−10.7732	−0.369302
$852$	6.15702	0.210936
$853$	46.4024	1.58879	0.794395	−	0.607402i	$-0.207788\pi$
$853$	46.4024	1.58879	0.794395	+	0.607402i	$0.207788\pi$
$854$	−3.69673	−0.126500
$855$	−1.99355	−0.0681781
$856$	−4.04580	−0.138283
$857$	20.1932	0.689788	0.344894	−	0.938642i	$-0.387915\pi$
$857$	20.1932	0.689788	0.344894	+	0.938642i	$0.387915\pi$
$858$	13.0139	0.444288
$859$	10.7622	0.367202	0.183601	−	0.983001i	$-0.441224\pi$
$859$	10.7622	0.367202	0.183601	+	0.983001i	$0.441224\pi$
$860$	−4.39602	−0.149903
$861$	−27.8944	−0.950638
$862$	4.55906	0.155282
$863$	21.0643	0.717039	0.358519	−	0.933522i	$-0.383282\pi$
$863$	21.0643	0.717039	0.358519	+	0.933522i	$0.383282\pi$
$864$	−5.43147	−0.184782
$865$	−11.7607	−0.399877
$866$	−18.3691	−0.624206
$867$	42.1318	1.43087
$868$	18.3854	0.624043
$869$	52.0433	1.76545
$870$	0	0
$871$	13.0328	0.441598
$872$	−15.6335	−0.529419
$873$	1.44432	0.0488829
$874$	−31.3195	−1.05940
$875$	−20.9193	−0.707202
$876$	20.8538	0.704586
$877$	19.0046	0.641741	0.320871	−	0.947123i	$-0.396025\pi$
$877$	19.0046	0.641741	0.320871	+	0.947123i	$0.396025\pi$
$878$	−19.1652	−0.646795
$879$	48.2872	1.62869
$880$	4.39602	0.148190
$881$	32.2859	1.08774	0.543870	−	0.839170i	$-0.316959\pi$
$881$	32.2859	1.08774	0.543870	+	0.839170i	$0.316959\pi$
$882$	0.887334	0.0298781
$883$	23.1577	0.779317	0.389659	−	0.920959i	$-0.372593\pi$
$883$	23.1577	0.779317	0.389659	+	0.920959i	$0.372593\pi$
$884$	−14.0928	−0.473994
$885$	5.76982	0.193950
$886$	2.26565	0.0761160
$887$	−46.3944	−1.55777	−0.778886	−	0.627165i	$-0.784215\pi$
$887$	−46.3944	−1.55777	−0.778886	+	0.627165i	$0.784215\pi$
$888$	2.99575	0.100531
$889$	38.6196	1.29526
$890$	−19.7118	−0.660741
$891$	−29.3066	−0.981809
$892$	−2.37303	−0.0794548
$893$	−5.27580	−0.176548
$894$	−11.7959	−0.394512
$895$	−14.6689	−0.490327
$896$	2.04359	0.0682714
$897$	−20.8281	−0.695430
$898$	−24.3823	−0.813648
$899$	0	0
$900$	1.12336	0.0374455
$901$	37.0184	1.23326
$902$	−30.6706	−1.02122
$903$	−12.3327	−0.410408
$904$	18.4609	0.613999
$905$	16.4551	0.546986
$906$	−15.2123	−0.505396
$907$	−21.7273	−0.721444	−0.360722	−	0.932673i	$-0.617470\pi$
$907$	−21.7273	−0.721444	−0.360722	+	0.932673i	$0.617470\pi$
$908$	12.9823	0.430833
$909$	−0.0659138	−0.00218622
$910$	5.26092	0.174398
$911$	−28.1482	−0.932591	−0.466295	−	0.884629i	$-0.654412\pi$
$911$	−28.1482	−0.932591	−0.466295	+	0.884629i	$0.654412\pi$
$912$	8.70913	0.288388
$913$	7.55751	0.250117
$914$	−26.0136	−0.860455
$915$	−3.53904	−0.116997
$916$	−25.7082	−0.849422
$917$	10.0294	0.331200
$918$	35.4956	1.17153
$919$	47.3273	1.56119	0.780593	−	0.625040i	$-0.214917\pi$
$919$	47.3273	1.56119	0.780593	+	0.625040i	$0.214917\pi$
$920$	−7.03560	−0.231957
$921$	−9.64475	−0.317805
$922$	−26.1593	−0.861512
$923$	8.10175	0.266672
$924$	12.3327	0.405717
$925$	−6.53480	−0.214863
$926$	−28.3236	−0.930772
$927$	3.49672	0.114847
$928$	0	0
$929$	−14.6578	−0.480908	−0.240454	−	0.970661i	$-0.577296\pi$
$929$	−14.6578	−0.480908	−0.240454	+	0.970661i	$0.577296\pi$
$930$	17.6012	0.577165
$931$	−15.0061	−0.491805
$932$	−7.05047	−0.230946
$933$	−37.6880	−1.23385
$934$	−0.164856	−0.00539427
$935$	−28.7288	−0.939531
$936$	−0.677644	−0.0221495
$937$	14.9637	0.488843	0.244421	−	0.969669i	$-0.421402\pi$
$937$	14.9637	0.488843	0.244421	+	0.969669i	$0.421402\pi$
$938$	12.3506	0.403261
$939$	33.6755	1.09896
$940$	−1.18515	−0.0386554
$941$	6.43177	0.209670	0.104835	−	0.994490i	$-0.466569\pi$
$941$	6.43177	0.209670	0.104835	+	0.994490i	$0.466569\pi$
$942$	−3.26913	−0.106514
$943$	49.0868	1.59848
$944$	2.94918	0.0959876
$945$	−13.2507	−0.431044
$946$	−13.5602	−0.440880
$947$	7.34323	0.238623	0.119311	−	0.992857i	$-0.461931\pi$
$947$	7.34323	0.238623	0.119311	+	0.992857i	$0.461931\pi$
$948$	23.1614	0.752249
$949$	27.4406	0.890761
$950$	−18.9977	−0.616368
$951$	11.5526	0.374618
$952$	−13.3552	−0.432844
$953$	15.9585	0.516946	0.258473	−	0.966018i	$-0.416781\pi$
$953$	15.9585	0.516946	0.258473	+	0.966018i	$0.416781\pi$
$954$	1.78000	0.0576297
$955$	18.9077	0.611840
$956$	−3.52639	−0.114052
$957$	0	0
$958$	−11.4544	−0.370074
$959$	7.79965	0.251864
$960$	1.95641	0.0631430
$961$	49.9398	1.61096
$962$	3.94197	0.127094
$963$	1.27135	0.0409686
$964$	11.8721	0.382373
$965$	19.6080	0.631205
$966$	−19.7379	−0.635056
$967$	16.0536	0.516249	0.258124	−	0.966112i	$-0.416896\pi$
$967$	16.0536	0.516249	0.258124	+	0.966112i	$0.416896\pi$
$968$	2.56019	0.0822875
$969$	−56.9157	−1.82839
$970$	−5.48695	−0.176175
$971$	−33.5504	−1.07668	−0.538342	−	0.842726i	$-0.680949\pi$
$971$	−33.5504	−1.07668	−0.538342	+	0.842726i	$0.680949\pi$
$972$	3.25173	0.104299
$973$	−24.7912	−0.794771
$974$	23.2025	0.743456
$975$	−12.6339	−0.404607
$976$	−1.80894	−0.0579029
$977$	−7.98092	−0.255332	−0.127666	−	0.991817i	$-0.540749\pi$
$977$	−7.98092	−0.255332	−0.127666	+	0.991817i	$0.540749\pi$
$978$	−6.70455	−0.214388
$979$	−60.8040	−1.94331
$980$	−3.37096	−0.107681
$981$	4.91267	0.156849
$982$	14.1185	0.450539
$983$	54.2687	1.73090	0.865452	−	0.500992i	$-0.167031\pi$
$983$	54.2687	1.73090	0.865452	+	0.500992i	$0.167031\pi$
$984$	−13.6497	−0.435137
$985$	17.4771	0.556867
$986$	0	0
$987$	−3.32486	−0.105832
$988$	11.4599	0.364590
$989$	21.7024	0.690095
$990$	−1.38140	−0.0439038
$991$	3.49201	0.110927	0.0554636	−	0.998461i	$-0.482336\pi$
$991$	3.49201	0.110927	0.0554636	+	0.998461i	$0.482336\pi$
$992$	8.99665	0.285644
$993$	33.5846	1.06577
$994$	7.67768	0.243521
$995$	1.69380	0.0536971
$996$	3.36341	0.106574
$997$	−13.2368	−0.419214	−0.209607	−	0.977786i	$-0.567218\pi$
$997$	−13.2368	−0.419214	−0.209607	+	0.977786i	$0.567218\pi$
$998$	−7.59719	−0.240485
$999$	−9.92864	−0.314128

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1682.2.a.t.1.4		6
29.7	even	7		58.2.d.b.49.2	yes	12
29.12	odd	4		1682.2.b.i.1681.10		12
29.17	odd	4		1682.2.b.i.1681.3		12
29.25	even	7		58.2.d.b.45.2	✓	12
29.28	even	2		1682.2.a.q.1.3		6
87.65	odd	14		522.2.k.h.397.2		12
87.83	odd	14		522.2.k.h.451.2		12
116.7	odd	14		464.2.u.h.49.1		12
116.83	odd	14		464.2.u.h.161.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.2.d.b.45.2	✓	12	29.25	even	7
58.2.d.b.49.2	yes	12	29.7	even	7
464.2.u.h.49.1		12	116.7	odd	14
464.2.u.h.161.1		12	116.83	odd	14
522.2.k.h.397.2		12	87.65	odd	14
522.2.k.h.451.2		12	87.83	odd	14
1682.2.a.q.1.3		6	29.28	even	2
1682.2.a.t.1.4		6	1.1	even	1	trivial
1682.2.b.i.1681.3		12	29.17	odd	4
1682.2.b.i.1681.10		12	29.12	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1682 = 2 \cdot 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1682.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.63883 q^{3} +1.00000 q^{4} +1.19379 q^{5} +1.63883 q^{6} +2.04359 q^{7} +1.00000 q^{8} -0.314239 q^{9} +1.19379 q^{10} +3.68242 q^{11} +1.63883 q^{12} +2.15646 q^{13} +2.04359 q^{14} +1.95641 q^{15} +1.00000 q^{16} -6.53517 q^{17} -0.314239 q^{18} +5.31424 q^{19} +1.19379 q^{20} +3.34909 q^{21} +3.68242 q^{22} -5.89351 q^{23} +1.63883 q^{24} -3.57487 q^{25} +2.15646 q^{26} -5.43147 q^{27} +2.04359 q^{28} +1.95641 q^{30} +8.99665 q^{31} +1.00000 q^{32} +6.03485 q^{33} -6.53517 q^{34} +2.43961 q^{35} -0.314239 q^{36} +1.82798 q^{37} +5.31424 q^{38} +3.53407 q^{39} +1.19379 q^{40} -8.32895 q^{41} +3.34909 q^{42} -3.68242 q^{43} +3.68242 q^{44} -0.375134 q^{45} -5.89351 q^{46} -0.992767 q^{47} +1.63883 q^{48} -2.82375 q^{49} -3.57487 q^{50} -10.7100 q^{51} +2.15646 q^{52} -5.66449 q^{53} -5.43147 q^{54} +4.39602 q^{55} +2.04359 q^{56} +8.70913 q^{57} +2.94918 q^{59} +1.95641 q^{60} -1.80894 q^{61} +8.99665 q^{62} -0.642174 q^{63} +1.00000 q^{64} +2.57436 q^{65} +6.03485 q^{66} +6.04359 q^{67} -6.53517 q^{68} -9.65846 q^{69} +2.43961 q^{70} +3.75696 q^{71} -0.314239 q^{72} +12.7248 q^{73} +1.82798 q^{74} -5.85860 q^{75} +5.31424 q^{76} +7.52534 q^{77} +3.53407 q^{78} +14.1329 q^{79} +1.19379 q^{80} -7.95854 q^{81} -8.32895 q^{82} +2.05232 q^{83} +3.34909 q^{84} -7.80161 q^{85} -3.68242 q^{86} +3.68242 q^{88} -16.5120 q^{89} -0.375134 q^{90} +4.40692 q^{91} -5.89351 q^{92} +14.7440 q^{93} -0.992767 q^{94} +6.34407 q^{95} +1.63883 q^{96} -4.59626 q^{97} -2.82375 q^{98} -1.15716 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 2 q^{3} + 6 q^{4} + 2 q^{6} - 3 q^{7} + 6 q^{8} + 12 q^{9} - q^{11} + 2 q^{12} - 3 q^{13} - 3 q^{14} + 27 q^{15} + 6 q^{16} - 6 q^{17} + 12 q^{18} + 18 q^{19} - 10 q^{21} - q^{22} - 14 q^{23}+ \cdots - 4 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 2 * q^3 + 6 * q^4 + 2 * q^6 - 3 * q^7 + 6 * q^8 + 12 * q^9 - q^11 + 2 * q^12 - 3 * q^13 - 3 * q^14 + 27 * q^15 + 6 * q^16 - 6 * q^17 + 12 * q^18 + 18 * q^19 - 10 * q^21 - q^22 - 14 * q^23 + 2 * q^24 + 4 * q^25 - 3 * q^26 + 23 * q^27 - 3 * q^28 + 27 * q^30 + 17 * q^31 + 6 * q^32 + 20 * q^33 - 6 * q^34 - 9 * q^35 + 12 * q^36 + 12 * q^37 + 18 * q^38 + 10 * q^39 - 15 * q^41 - 10 * q^42 + q^43 - q^44 + 18 * q^45 - 14 * q^46 + 8 * q^47 + 2 * q^48 + q^49 + 4 * q^50 - 11 * q^51 - 3 * q^52 + 3 * q^53 + 23 * q^54 + 18 * q^55 - 3 * q^56 - 19 * q^57 + 19 * q^59 + 27 * q^60 + 15 * q^61 + 17 * q^62 - 33 * q^63 + 6 * q^64 + 11 * q^65 + 20 * q^66 + 21 * q^67 - 6 * q^68 - 11 * q^69 - 9 * q^70 - 9 * q^71 + 12 * q^72 + 31 * q^73 + 12 * q^74 - q^75 + 18 * q^76 + 33 * q^77 + 10 * q^78 - 2 * q^79 + 2 * q^81 - 15 * q^82 - 2 * q^83 - 10 * q^84 + 19 * q^85 + q^86 - q^88 + 2 * q^89 + 18 * q^90 - 22 * q^91 - 14 * q^92 + q^93 + 8 * q^94 - 18 * q^95 + 2 * q^96 + 43 * q^97 + q^98 - 4 * q^99

Introduction

L-functions

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Varieties

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Representations

Groups

Database

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