LMFDB - Embedded newform 2873.2.a.i.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2873,2,Mod(1,2873)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2873, 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("2873.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2873 = 13^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2873.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:	$22.9410205007$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{21}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 5 $ x^2 - x - 5
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 221)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.79129$ of defining polynomial
Character	$\chi$	$=$	2873.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.79129 q^{2} +2.79129 q^{3} +1.20871 q^{4} +1.00000 q^{5} -5.00000 q^{6} +4.79129 q^{7} +1.41742 q^{8} +4.79129 q^{9} +O(q^{10})$	\(q-1.79129 q^{2} +2.79129 q^{3} +1.20871 q^{4} +1.00000 q^{5} -5.00000 q^{6} +4.79129 q^{7} +1.41742 q^{8} +4.79129 q^{9} -1.79129 q^{10} -3.79129 q^{11} +3.37386 q^{12} -8.58258 q^{14} +2.79129 q^{15} -4.95644 q^{16} +1.00000 q^{17} -8.58258 q^{18} -0.208712 q^{19} +1.20871 q^{20} +13.3739 q^{21} +6.79129 q^{22} -1.58258 q^{23} +3.95644 q^{24} -4.00000 q^{25} +5.00000 q^{27} +5.79129 q^{28} +9.00000 q^{29} -5.00000 q^{30} -8.58258 q^{31} +6.04356 q^{32} -10.5826 q^{33} -1.79129 q^{34} +4.79129 q^{35} +5.79129 q^{36} +8.58258 q^{37} +0.373864 q^{38} +1.41742 q^{40} -23.9564 q^{42} +9.00000 q^{43} -4.58258 q^{44} +4.79129 q^{45} +2.83485 q^{46} +5.58258 q^{47} -13.8348 q^{48} +15.9564 q^{49} +7.16515 q^{50} +2.79129 q^{51} -3.20871 q^{53} -8.95644 q^{54} -3.79129 q^{55} +6.79129 q^{56} -0.582576 q^{57} -16.1216 q^{58} +0.582576 q^{59} +3.37386 q^{60} +7.20871 q^{61} +15.3739 q^{62} +22.9564 q^{63} -0.912878 q^{64} +18.9564 q^{66} +13.5826 q^{67} +1.20871 q^{68} -4.41742 q^{69} -8.58258 q^{70} -2.00000 q^{71} +6.79129 q^{72} +0.582576 q^{73} -15.3739 q^{74} -11.1652 q^{75} -0.252273 q^{76} -18.1652 q^{77} +0.582576 q^{79} -4.95644 q^{80} -0.417424 q^{81} +4.58258 q^{83} +16.1652 q^{84} +1.00000 q^{85} -16.1216 q^{86} +25.1216 q^{87} -5.37386 q^{88} -6.95644 q^{89} -8.58258 q^{90} -1.91288 q^{92} -23.9564 q^{93} -10.0000 q^{94} -0.208712 q^{95} +16.8693 q^{96} +7.95644 q^{97} -28.5826 q^{98} -18.1652 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + q^{3} + 7 q^{4} + 2 q^{5} - 10 q^{6} + 5 q^{7} + 12 q^{8} + 5 q^{9}+O(q^{10}) $ 2 * q + q^2 + q^3 + 7 * q^4 + 2 * q^5 - 10 * q^6 + 5 * q^7 + 12 * q^8 + 5 * q^9	$ 2 q + q^{2} + q^{3} + 7 q^{4} + 2 q^{5} - 10 q^{6} + 5 q^{7} + 12 q^{8} + 5 q^{9} + q^{10} - 3 q^{11} - 7 q^{12} - 8 q^{14} + q^{15} + 13 q^{16} + 2 q^{17} - 8 q^{18} - 5 q^{19} + 7 q^{20} + 13 q^{21} + 9 q^{22} + 6 q^{23} - 15 q^{24} - 8 q^{25} + 10 q^{27} + 7 q^{28} + 18 q^{29} - 10 q^{30} - 8 q^{31} + 35 q^{32} - 12 q^{33} + q^{34} + 5 q^{35} + 7 q^{36} + 8 q^{37} - 13 q^{38} + 12 q^{40} - 25 q^{42} + 18 q^{43} + 5 q^{45} + 24 q^{46} + 2 q^{47} - 46 q^{48} + 9 q^{49} - 4 q^{50} + q^{51} - 11 q^{53} + 5 q^{54} - 3 q^{55} + 9 q^{56} + 8 q^{57} + 9 q^{58} - 8 q^{59} - 7 q^{60} + 19 q^{61} + 17 q^{62} + 23 q^{63} + 44 q^{64} + 15 q^{66} + 18 q^{67} + 7 q^{68} - 18 q^{69} - 8 q^{70} - 4 q^{71} + 9 q^{72} - 8 q^{73} - 17 q^{74} - 4 q^{75} - 28 q^{76} - 18 q^{77} - 8 q^{79} + 13 q^{80} - 10 q^{81} + 14 q^{84} + 2 q^{85} + 9 q^{86} + 9 q^{87} + 3 q^{88} + 9 q^{89} - 8 q^{90} + 42 q^{92} - 25 q^{93} - 20 q^{94} - 5 q^{95} - 35 q^{96} - 7 q^{97} - 48 q^{98} - 18 q^{99}+O(q^{100}) $ 2 * q + q^2 + q^3 + 7 * q^4 + 2 * q^5 - 10 * q^6 + 5 * q^7 + 12 * q^8 + 5 * q^9 + q^10 - 3 * q^11 - 7 * q^12 - 8 * q^14 + q^15 + 13 * q^16 + 2 * q^17 - 8 * q^18 - 5 * q^19 + 7 * q^20 + 13 * q^21 + 9 * q^22 + 6 * q^23 - 15 * q^24 - 8 * q^25 + 10 * q^27 + 7 * q^28 + 18 * q^29 - 10 * q^30 - 8 * q^31 + 35 * q^32 - 12 * q^33 + q^34 + 5 * q^35 + 7 * q^36 + 8 * q^37 - 13 * q^38 + 12 * q^40 - 25 * q^42 + 18 * q^43 + 5 * q^45 + 24 * q^46 + 2 * q^47 - 46 * q^48 + 9 * q^49 - 4 * q^50 + q^51 - 11 * q^53 + 5 * q^54 - 3 * q^55 + 9 * q^56 + 8 * q^57 + 9 * q^58 - 8 * q^59 - 7 * q^60 + 19 * q^61 + 17 * q^62 + 23 * q^63 + 44 * q^64 + 15 * q^66 + 18 * q^67 + 7 * q^68 - 18 * q^69 - 8 * q^70 - 4 * q^71 + 9 * q^72 - 8 * q^73 - 17 * q^74 - 4 * q^75 - 28 * q^76 - 18 * q^77 - 8 * q^79 + 13 * q^80 - 10 * q^81 + 14 * q^84 + 2 * q^85 + 9 * q^86 + 9 * q^87 + 3 * q^88 + 9 * q^89 - 8 * q^90 + 42 * q^92 - 25 * q^93 - 20 * q^94 - 5 * q^95 - 35 * q^96 - 7 * q^97 - 48 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.79129	−1.26663	−0.633316	−	0.773893i	$-0.718307\pi$
$2$	−1.79129	−1.26663	−0.633316	+	0.773893i	$0.718307\pi$
$3$	2.79129	1.61155	0.805775	−	0.592221i	$-0.201749\pi$
$3$	2.79129	1.61155	0.805775	+	0.592221i	$0.201749\pi$
$4$	1.20871	0.604356
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	−5.00000	−2.04124
$7$	4.79129	1.81094	0.905468	−	0.424414i	$-0.139520\pi$
$7$	4.79129	1.81094	0.905468	+	0.424414i	$0.139520\pi$
$8$	1.41742	0.501135
$9$	4.79129	1.59710
$10$	−1.79129	−0.566455
$11$	−3.79129	−1.14312	−0.571558	−	0.820562i	$-0.693661\pi$
$11$	−3.79129	−1.14312	−0.571558	+	0.820562i	$0.693661\pi$
$12$	3.37386	0.973951
$13$	0	0
$13$	0	0
$14$	−8.58258	−2.29379
$15$	2.79129	0.720707
$16$	−4.95644	−1.23911
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−8.58258	−2.02293
$19$	−0.208712	−0.0478819	−0.0239409	−	0.999713i	$-0.507621\pi$
$19$	−0.208712	−0.0478819	−0.0239409	+	0.999713i	$0.507621\pi$
$20$	1.20871	0.270276
$21$	13.3739	2.91842
$22$	6.79129	1.44791
$23$	−1.58258	−0.329990	−0.164995	−	0.986294i	$-0.552761\pi$
$23$	−1.58258	−0.329990	−0.164995	+	0.986294i	$0.552761\pi$
$24$	3.95644	0.807605
$25$	−4.00000	−0.800000
$26$	0	0
$27$	5.00000	0.962250
$28$	5.79129	1.09445
$29$	9.00000	1.67126	0.835629	−	0.549294i	$-0.185103\pi$
$29$	9.00000	1.67126	0.835629	+	0.549294i	$0.185103\pi$
$30$	−5.00000	−0.912871
$31$	−8.58258	−1.54148	−0.770738	−	0.637152i	$-0.780112\pi$
$31$	−8.58258	−1.54148	−0.770738	+	0.637152i	$0.780112\pi$
$32$	6.04356	1.06836
$33$	−10.5826	−1.84219
$34$	−1.79129	−0.307203
$35$	4.79129	0.809875
$36$	5.79129	0.965215
$37$	8.58258	1.41097	0.705483	−	0.708726i	$-0.250730\pi$
$37$	8.58258	1.41097	0.705483	+	0.708726i	$0.250730\pi$
$38$	0.373864	0.0606487
$39$	0	0
$40$	1.41742	0.224114
$41$	0	0		−	1.00000i	$-0.5\pi$
$41$	0	0			1.00000i	$0.5\pi$
$42$	−23.9564	−3.69656
$43$	9.00000	1.37249	0.686244	−	0.727372i	$-0.259258\pi$
$43$	9.00000	1.37249	0.686244	+	0.727372i	$0.259258\pi$
$44$	−4.58258	−0.690849
$45$	4.79129	0.714243
$46$	2.83485	0.417976
$47$	5.58258	0.814302	0.407151	−	0.913361i	$-0.366522\pi$
$47$	5.58258	0.814302	0.407151	+	0.913361i	$0.366522\pi$
$48$	−13.8348	−1.99689
$49$	15.9564	2.27949
$50$	7.16515	1.01331
$51$	2.79129	0.390858
$52$	0	0
$53$	−3.20871	−0.440751	−0.220375	−	0.975415i	$-0.570728\pi$
$53$	−3.20871	−0.440751	−0.220375	+	0.975415i	$0.570728\pi$
$54$	−8.95644	−1.21882
$55$	−3.79129	−0.511217
$56$	6.79129	0.907524
$57$	−0.582576	−0.0771640
$58$	−16.1216	−2.11687
$59$	0.582576	0.0758449	0.0379224	−	0.999281i	$-0.487926\pi$
$59$	0.582576	0.0758449	0.0379224	+	0.999281i	$0.487926\pi$
$60$	3.37386	0.435564
$61$	7.20871	0.922981	0.461491	−	0.887145i	$-0.347315\pi$
$61$	7.20871	0.922981	0.461491	+	0.887145i	$0.347315\pi$
$62$	15.3739	1.95248
$63$	22.9564	2.89224
$64$	−0.912878	−0.114110
$65$	0	0
$66$	18.9564	2.33338
$67$	13.5826	1.65938	0.829688	−	0.558228i	$-0.188518\pi$
$67$	13.5826	1.65938	0.829688	+	0.558228i	$0.188518\pi$
$68$	1.20871	0.146578
$69$	−4.41742	−0.531795
$70$	−8.58258	−1.02581
$71$	−2.00000	−0.237356	−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000	−0.237356	−0.118678	+	0.992933i	$0.537866\pi$
$72$	6.79129	0.800361
$73$	0.582576	0.0681853	0.0340927	−	0.999419i	$-0.489146\pi$
$73$	0.582576	0.0681853	0.0340927	+	0.999419i	$0.489146\pi$
$74$	−15.3739	−1.78718
$75$	−11.1652	−1.28924
$76$	−0.252273	−0.0289377
$77$	−18.1652	−2.07011
$78$	0	0
$79$	0.582576	0.0655449	0.0327724	−	0.999463i	$-0.489566\pi$
$79$	0.582576	0.0655449	0.0327724	+	0.999463i	$0.489566\pi$
$80$	−4.95644	−0.554147
$81$	−0.417424	−0.0463805
$82$	0	0
$83$	4.58258	0.503003	0.251502	−	0.967857i	$-0.419076\pi$
$83$	4.58258	0.503003	0.251502	+	0.967857i	$0.419076\pi$
$84$	16.1652	1.76376
$85$	1.00000	0.108465
$86$	−16.1216	−1.73844
$87$	25.1216	2.69332
$88$	−5.37386	−0.572856
$89$	−6.95644	−0.737381	−0.368691	−	0.929552i	$-0.620194\pi$
$89$	−6.95644	−0.737381	−0.368691	+	0.929552i	$0.620194\pi$
$90$	−8.58258	−0.904683
$91$	0	0
$92$	−1.91288	−0.199431
$93$	−23.9564	−2.48417
$94$	−10.0000	−1.03142
$95$	−0.208712	−0.0214134
$96$	16.8693	1.72172
$97$	7.95644	0.807854	0.403927	−	0.914791i	$-0.367645\pi$
$97$	7.95644	0.807854	0.403927	+	0.914791i	$0.367645\pi$
$98$	−28.5826	−2.88728
$99$	−18.1652	−1.82567
$100$	−4.83485	−0.483485
$101$	−12.1652	−1.21048	−0.605239	−	0.796044i	$-0.706922\pi$
$101$	−12.1652	−1.21048	−0.605239	+	0.796044i	$0.706922\pi$
$102$	−5.00000	−0.495074
$103$	−1.00000	−0.0985329	−0.0492665	−	0.998786i	$-0.515688\pi$
$103$	−1.00000	−0.0985329	−0.0492665	+	0.998786i	$0.515688\pi$
$104$	0	0
$105$	13.3739	1.30516
$106$	5.74773	0.558269
$107$	−7.37386	−0.712858	−0.356429	−	0.934322i	$-0.616006\pi$
$107$	−7.37386	−0.712858	−0.356429	+	0.934322i	$0.616006\pi$
$108$	6.04356	0.581542
$109$	−5.95644	−0.570523	−0.285262	−	0.958450i	$-0.592081\pi$
$109$	−5.95644	−0.570523	−0.285262	+	0.958450i	$0.592081\pi$
$110$	6.79129	0.647524
$111$	23.9564	2.27384
$112$	−23.7477	−2.24395
$113$	0.791288	0.0744381	0.0372190	−	0.999307i	$-0.488150\pi$
$113$	0.791288	0.0744381	0.0372190	+	0.999307i	$0.488150\pi$
$114$	1.04356	0.0977384
$115$	−1.58258	−0.147576
$116$	10.8784	1.01003
$117$	0	0
$118$	−1.04356	−0.0960676
$119$	4.79129	0.439217
$120$	3.95644	0.361172
$121$	3.37386	0.306715
$122$	−12.9129	−1.16908
$123$	0	0
$124$	−10.3739	−0.931600
$125$	−9.00000	−0.804984
$126$	−41.1216	−3.66340
$127$	16.9564	1.50464	0.752320	−	0.658797i	$-0.228935\pi$
$127$	16.9564	1.50464	0.752320	+	0.658797i	$0.228935\pi$
$128$	−10.4519	−0.923826
$129$	25.1216	2.21183
$130$	0	0
$131$	1.41742	0.123841	0.0619205	−	0.998081i	$-0.480277\pi$
$131$	1.41742	0.123841	0.0619205	+	0.998081i	$0.480277\pi$
$132$	−12.7913	−1.11334
$133$	−1.00000	−0.0867110
$134$	−24.3303	−2.10182
$135$	5.00000	0.430331
$136$	1.41742	0.121543
$137$	−3.79129	−0.323912	−0.161956	−	0.986798i	$-0.551780\pi$
$137$	−3.79129	−0.323912	−0.161956	+	0.986798i	$0.551780\pi$
$138$	7.91288	0.673589
$139$	20.7477	1.75980	0.879900	−	0.475160i	$-0.157610\pi$
$139$	20.7477	1.75980	0.879900	+	0.475160i	$0.157610\pi$
$140$	5.79129	0.489453
$141$	15.5826	1.31229
$142$	3.58258	0.300643
$143$	0	0
$144$	−23.7477	−1.97898
$145$	9.00000	0.747409
$146$	−1.04356	−0.0863657
$147$	44.5390	3.67352
$148$	10.3739	0.852726
$149$	18.9564	1.55297	0.776486	−	0.630134i	$-0.217000\pi$
$149$	18.9564	1.55297	0.776486	+	0.630134i	$0.217000\pi$
$150$	20.0000	1.63299
$151$	8.74773	0.711880	0.355940	−	0.934509i	$-0.384161\pi$
$151$	8.74773	0.711880	0.355940	+	0.934509i	$0.384161\pi$
$152$	−0.295834	−0.0239953
$153$	4.79129	0.387353
$154$	32.5390	2.62207
$155$	−8.58258	−0.689369
$156$	0	0
$157$	−14.5826	−1.16382	−0.581908	−	0.813255i	$-0.697694\pi$
$157$	−14.5826	−1.16382	−0.581908	+	0.813255i	$0.697694\pi$
$158$	−1.04356	−0.0830212
$159$	−8.95644	−0.710292
$160$	6.04356	0.477785
$161$	−7.58258	−0.597591
$162$	0.747727	0.0587470
$163$	−11.2087	−0.877934	−0.438967	−	0.898503i	$-0.644656\pi$
$163$	−11.2087	−0.877934	−0.438967	+	0.898503i	$0.644656\pi$
$164$	0	0
$165$	−10.5826	−0.823852
$166$	−8.20871	−0.637120
$167$	−25.3303	−1.96012	−0.980059	−	0.198708i	$-0.936326\pi$
$167$	−25.3303	−1.96012	−0.980059	+	0.198708i	$0.936326\pi$
$168$	18.9564	1.46252
$169$	0	0
$170$	−1.79129	−0.137386
$171$	−1.00000	−0.0764719
$172$	10.8784	0.829471
$173$	−10.1652	−0.772842	−0.386421	−	0.922322i	$-0.626289\pi$
$173$	−10.1652	−0.772842	−0.386421	+	0.922322i	$0.626289\pi$
$174$	−45.0000	−3.41144
$175$	−19.1652	−1.44875
$176$	18.7913	1.41645
$177$	1.62614	0.122228
$178$	12.4610	0.933990
$179$	−18.1652	−1.35773	−0.678864	−	0.734264i	$-0.737527\pi$
$179$	−18.1652	−1.35773	−0.678864	+	0.734264i	$0.737527\pi$
$180$	5.79129	0.431657
$181$	−15.2087	−1.13045	−0.565227	−	0.824935i	$-0.691212\pi$
$181$	−15.2087	−1.13045	−0.565227	+	0.824935i	$0.691212\pi$
$182$	0	0
$183$	20.1216	1.48743
$184$	−2.24318	−0.165370
$185$	8.58258	0.631004
$186$	42.9129	3.14652
$187$	−3.79129	−0.277246
$188$	6.74773	0.492129
$189$	23.9564	1.74257
$190$	0.373864	0.0271229
$191$	−17.7477	−1.28418	−0.642090	−	0.766629i	$-0.721933\pi$
$191$	−17.7477	−1.28418	−0.642090	+	0.766629i	$0.721933\pi$
$192$	−2.54811	−0.183894
$193$	−9.58258	−0.689769	−0.344884	−	0.938645i	$-0.612082\pi$
$193$	−9.58258	−0.689769	−0.344884	+	0.938645i	$0.612082\pi$
$194$	−14.2523	−1.02325
$195$	0	0
$196$	19.2867	1.37762
$197$	4.74773	0.338262	0.169131	−	0.985594i	$-0.445904\pi$
$197$	4.74773	0.338262	0.169131	+	0.985594i	$0.445904\pi$
$198$	32.5390	2.31245
$199$	11.0000	0.779769	0.389885	−	0.920864i	$-0.372515\pi$
$199$	11.0000	0.779769	0.389885	+	0.920864i	$0.372515\pi$
$200$	−5.66970	−0.400908
$201$	37.9129	2.67417
$202$	21.7913	1.53323
$203$	43.1216	3.02654
$204$	3.37386	0.236218
$205$	0	0
$206$	1.79129	0.124805
$207$	−7.58258	−0.527025
$208$	0	0
$209$	0.791288	0.0547345
$210$	−23.9564	−1.65315
$211$	20.5826	1.41696	0.708481	−	0.705729i	$-0.249381\pi$
$211$	20.5826	1.41696	0.708481	+	0.705729i	$0.249381\pi$
$212$	−3.87841	−0.266370
$213$	−5.58258	−0.382512
$214$	13.2087	0.902929
$215$	9.00000	0.613795
$216$	7.08712	0.482218
$217$	−41.1216	−2.79152
$218$	10.6697	0.722643
$219$	1.62614	0.109884
$220$	−4.58258	−0.308957
$221$	0	0
$222$	−42.9129	−2.88012
$223$	−12.7913	−0.856568	−0.428284	−	0.903644i	$-0.640882\pi$
$223$	−12.7913	−0.856568	−0.428284	+	0.903644i	$0.640882\pi$
$224$	28.9564	1.93473
$225$	−19.1652	−1.27768
$226$	−1.41742	−0.0942857
$227$	−1.58258	−0.105039	−0.0525196	−	0.998620i	$-0.516725\pi$
$227$	−1.58258	−0.105039	−0.0525196	+	0.998620i	$0.516725\pi$
$228$	−0.704166	−0.0466346
$229$	−1.41742	−0.0936660	−0.0468330	−	0.998903i	$-0.514913\pi$
$229$	−1.41742	−0.0936660	−0.0468330	+	0.998903i	$0.514913\pi$
$230$	2.83485	0.186924
$231$	−50.7042	−3.33609
$232$	12.7568	0.837526
$233$	−26.9129	−1.76312	−0.881561	−	0.472071i	$-0.843507\pi$
$233$	−26.9129	−1.76312	−0.881561	+	0.472071i	$0.843507\pi$
$234$	0	0
$235$	5.58258	0.364167
$236$	0.704166	0.0458373
$237$	1.62614	0.105629
$238$	−8.58258	−0.556326
$239$	−1.74773	−0.113051	−0.0565255	−	0.998401i	$-0.518002\pi$
$239$	−1.74773	−0.113051	−0.0565255	+	0.998401i	$0.518002\pi$
$240$	−13.8348	−0.893036
$241$	9.74773	0.627906	0.313953	−	0.949438i	$-0.398347\pi$
$241$	9.74773	0.627906	0.313953	+	0.949438i	$0.398347\pi$
$242$	−6.04356	−0.388495
$243$	−16.1652	−1.03699
$244$	8.71326	0.557809
$245$	15.9564	1.01942
$246$	0	0
$247$	0	0
$248$	−12.1652	−0.772488
$249$	12.7913	0.810615
$250$	16.1216	1.01962
$251$	−10.3739	−0.654792	−0.327396	−	0.944887i	$-0.606171\pi$
$251$	−10.3739	−0.654792	−0.327396	+	0.944887i	$0.606171\pi$
$252$	27.7477	1.74794
$253$	6.00000	0.377217
$254$	−30.3739	−1.90583
$255$	2.79129	0.174797
$256$	20.5481	1.28426
$257$	8.16515	0.509328	0.254664	−	0.967030i	$-0.418035\pi$
$257$	8.16515	0.509328	0.254664	+	0.967030i	$0.418035\pi$
$258$	−45.0000	−2.80158
$259$	41.1216	2.55517
$260$	0	0
$261$	43.1216	2.66916
$262$	−2.53901	−0.156861
$263$	−2.00000	−0.123325	−0.0616626	−	0.998097i	$-0.519640\pi$
$263$	−2.00000	−0.123325	−0.0616626	+	0.998097i	$0.519640\pi$
$264$	−15.0000	−0.923186
$265$	−3.20871	−0.197110
$266$	1.79129	0.109831
$267$	−19.4174	−1.18833
$268$	16.4174	1.00285
$269$	−6.62614	−0.404003	−0.202001	−	0.979385i	$-0.564745\pi$
$269$	−6.62614	−0.404003	−0.202001	+	0.979385i	$0.564745\pi$
$270$	−8.95644	−0.545072
$271$	−30.3739	−1.84508	−0.922540	−	0.385901i	$-0.873891\pi$
$271$	−30.3739	−1.84508	−0.922540	+	0.385901i	$0.873891\pi$
$272$	−4.95644	−0.300528
$273$	0	0
$274$	6.79129	0.410277
$275$	15.1652	0.914493
$276$	−5.33939	−0.321394
$277$	−6.83485	−0.410666	−0.205333	−	0.978692i	$-0.565828\pi$
$277$	−6.83485	−0.410666	−0.205333	+	0.978692i	$0.565828\pi$
$278$	−37.1652	−2.22902
$279$	−41.1216	−2.46189
$280$	6.79129	0.405857
$281$	29.1216	1.73725	0.868624	−	0.495471i	$-0.165005\pi$
$281$	29.1216	1.73725	0.868624	+	0.495471i	$0.165005\pi$
$282$	−27.9129	−1.66219
$283$	5.20871	0.309626	0.154813	−	0.987944i	$-0.450523\pi$
$283$	5.20871	0.309626	0.154813	+	0.987944i	$0.450523\pi$
$284$	−2.41742	−0.143448
$285$	−0.582576	−0.0345088
$286$	0	0
$287$	0	0
$288$	28.9564	1.70627
$289$	1.00000	0.0588235
$290$	−16.1216	−0.946692
$291$	22.2087	1.30190
$292$	0.704166	0.0412082
$293$	−17.6261	−1.02973	−0.514865	−	0.857271i	$-0.672158\pi$
$293$	−17.6261	−1.02973	−0.514865	+	0.857271i	$0.672158\pi$
$294$	−79.7822	−4.65299
$295$	0.582576	0.0339189
$296$	12.1652	0.707085
$297$	−18.9564	−1.09996
$298$	−33.9564	−1.96704
$299$	0	0
$300$	−13.4955	−0.779160
$301$	43.1216	2.48549
$302$	−15.6697	−0.901690
$303$	−33.9564	−1.95075
$304$	1.03447	0.0593309
$305$	7.20871	0.412770
$306$	−8.58258	−0.490633
$307$	−19.7913	−1.12955	−0.564774	−	0.825245i	$-0.691037\pi$
$307$	−19.7913	−1.12955	−0.564774	+	0.825245i	$0.691037\pi$
$308$	−21.9564	−1.25108
$309$	−2.79129	−0.158791
$310$	15.3739	0.873177
$311$	22.5826	1.28054	0.640270	−	0.768150i	$-0.278822\pi$
$311$	22.5826	1.28054	0.640270	+	0.768150i	$0.278822\pi$
$312$	0	0
$313$	−1.00000	−0.0565233	−0.0282617	−	0.999601i	$-0.508997\pi$
$313$	−1.00000	−0.0565233	−0.0282617	+	0.999601i	$0.508997\pi$
$314$	26.1216	1.47413
$315$	22.9564	1.29345
$316$	0.704166	0.0396125
$317$	−17.0000	−0.954815	−0.477408	−	0.878682i	$-0.658423\pi$
$317$	−17.0000	−0.954815	−0.477408	+	0.878682i	$0.658423\pi$
$318$	16.0436	0.899678
$319$	−34.1216	−1.91044
$320$	−0.912878	−0.0510315
$321$	−20.5826	−1.14881
$322$	13.5826	0.756927
$323$	−0.208712	−0.0116131
$324$	−0.504546	−0.0280303
$325$	0	0
$326$	20.0780	1.11202
$327$	−16.6261	−0.919427
$328$	0	0
$329$	26.7477	1.47465
$330$	18.9564	1.04352
$331$	11.0000	0.604615	0.302307	−	0.953211i	$-0.402243\pi$
$331$	11.0000	0.604615	0.302307	+	0.953211i	$0.402243\pi$
$332$	5.53901	0.303993
$333$	41.1216	2.25345
$334$	45.3739	2.48275
$335$	13.5826	0.742095
$336$	−66.2867	−3.61624
$337$	−6.20871	−0.338210	−0.169105	−	0.985598i	$-0.554088\pi$
$337$	−6.20871	−0.338210	−0.169105	+	0.985598i	$0.554088\pi$
$338$	0	0
$339$	2.20871	0.119961
$340$	1.20871	0.0655516
$341$	32.5390	1.76209
$342$	1.79129	0.0968618
$343$	42.9129	2.31708
$344$	12.7568	0.687802
$345$	−4.41742	−0.237826
$346$	18.2087	0.978906
$347$	11.7477	0.630651	0.315326	−	0.948984i	$-0.397886\pi$
$347$	11.7477	0.630651	0.315326	+	0.948984i	$0.397886\pi$
$348$	30.3648	1.62772
$349$	−10.6261	−0.568804	−0.284402	−	0.958705i	$-0.591795\pi$
$349$	−10.6261	−0.568804	−0.284402	+	0.958705i	$0.591795\pi$
$350$	34.3303	1.83503
$351$	0	0
$352$	−22.9129	−1.22126
$353$	−22.3303	−1.18852	−0.594261	−	0.804272i	$-0.702555\pi$
$353$	−22.3303	−1.18852	−0.594261	+	0.804272i	$0.702555\pi$
$354$	−2.91288	−0.154818
$355$	−2.00000	−0.106149
$356$	−8.40833	−0.445641
$357$	13.3739	0.707820
$358$	32.5390	1.71974
$359$	16.7913	0.886210	0.443105	−	0.896470i	$-0.353877\pi$
$359$	16.7913	0.886210	0.443105	+	0.896470i	$0.353877\pi$
$360$	6.79129	0.357932
$361$	−18.9564	−0.997707
$362$	27.2432	1.43187
$363$	9.41742	0.494287
$364$	0	0
$365$	0.582576	0.0304934
$366$	−36.0436	−1.88403
$367$	−2.04356	−0.106673	−0.0533365	−	0.998577i	$-0.516986\pi$
$367$	−2.04356	−0.106673	−0.0533365	+	0.998577i	$0.516986\pi$
$368$	7.84394	0.408894
$369$	0	0
$370$	−15.3739	−0.799249
$371$	−15.3739	−0.798171
$372$	−28.9564	−1.50132
$373$	27.1216	1.40430	0.702151	−	0.712028i	$-0.252223\pi$
$373$	27.1216	1.40430	0.702151	+	0.712028i	$0.252223\pi$
$374$	6.79129	0.351169
$375$	−25.1216	−1.29727
$376$	7.91288	0.408076
$377$	0	0
$378$	−42.9129	−2.20720
$379$	18.7477	0.963006	0.481503	−	0.876444i	$-0.340091\pi$
$379$	18.7477	0.963006	0.481503	+	0.876444i	$0.340091\pi$
$380$	−0.252273	−0.0129413
$381$	47.3303	2.42480
$382$	31.7913	1.62658
$383$	−28.9129	−1.47738	−0.738690	−	0.674046i	$-0.764555\pi$
$383$	−28.9129	−1.47738	−0.738690	+	0.674046i	$0.764555\pi$
$384$	−29.1742	−1.48879
$385$	−18.1652	−0.925782
$386$	17.1652	0.873683
$387$	43.1216	2.19199
$388$	9.61704	0.488231
$389$	−1.04356	−0.0529106	−0.0264553	−	0.999650i	$-0.508422\pi$
$389$	−1.04356	−0.0529106	−0.0264553	+	0.999650i	$0.508422\pi$
$390$	0	0
$391$	−1.58258	−0.0800343
$392$	22.6170	1.14233
$393$	3.95644	0.199576
$394$	−8.50455	−0.428453
$395$	0.582576	0.0293126
$396$	−21.9564	−1.10335
$397$	17.1652	0.861494	0.430747	−	0.902473i	$-0.358250\pi$
$397$	17.1652	0.861494	0.430747	+	0.902473i	$0.358250\pi$
$398$	−19.7042	−0.987681
$399$	−2.79129	−0.139739
$400$	19.8258	0.991288
$401$	18.9564	0.946639	0.473320	−	0.880891i	$-0.343056\pi$
$401$	18.9564	0.946639	0.473320	+	0.880891i	$0.343056\pi$
$402$	−67.9129	−3.38719
$403$	0	0
$404$	−14.7042	−0.731560
$405$	−0.417424	−0.0207420
$406$	−77.2432	−3.83351
$407$	−32.5390	−1.61290
$408$	3.95644	0.195873
$409$	5.16515	0.255400	0.127700	−	0.991813i	$-0.459240\pi$
$409$	5.16515	0.255400	0.127700	+	0.991813i	$0.459240\pi$
$410$	0	0
$411$	−10.5826	−0.522000
$412$	−1.20871	−0.0595490
$413$	2.79129	0.137350
$414$	13.5826	0.667547
$415$	4.58258	0.224950
$416$	0	0
$417$	57.9129	2.83601
$418$	−1.41742	−0.0693285
$419$	−10.6261	−0.519121	−0.259560	−	0.965727i	$-0.583578\pi$
$419$	−10.6261	−0.519121	−0.259560	+	0.965727i	$0.583578\pi$
$420$	16.1652	0.788779
$421$	6.20871	0.302594	0.151297	−	0.988488i	$-0.451655\pi$
$421$	6.20871	0.302594	0.151297	+	0.988488i	$0.451655\pi$
$422$	−36.8693	−1.79477
$423$	26.7477	1.30052
$424$	−4.54811	−0.220876
$425$	−4.00000	−0.194029
$426$	10.0000	0.484502
$427$	34.5390	1.67146
$428$	−8.91288	−0.430820
$429$	0	0
$430$	−16.1216	−0.777452
$431$	20.8348	1.00358	0.501790	−	0.864990i	$-0.332675\pi$
$431$	20.8348	1.00358	0.501790	+	0.864990i	$0.332675\pi$
$432$	−24.7822	−1.19233
$433$	−9.16515	−0.440449	−0.220225	−	0.975449i	$-0.570679\pi$
$433$	−9.16515	−0.440449	−0.220225	+	0.975449i	$0.570679\pi$
$434$	73.6606	3.53582
$435$	25.1216	1.20449
$436$	−7.19962	−0.344799
$437$	0.330303	0.0158005
$438$	−2.91288	−0.139183
$439$	−18.3739	−0.876937	−0.438468	−	0.898747i	$-0.644479\pi$
$439$	−18.3739	−0.876937	−0.438468	+	0.898747i	$0.644479\pi$
$440$	−5.37386	−0.256189
$441$	76.4519	3.64057
$442$	0	0
$443$	0.582576	0.0276790	0.0138395	−	0.999904i	$-0.495595\pi$
$443$	0.582576	0.0276790	0.0138395	+	0.999904i	$0.495595\pi$
$444$	28.9564	1.37421
$445$	−6.95644	−0.329767
$446$	22.9129	1.08496
$447$	52.9129	2.50269
$448$	−4.37386	−0.206646
$449$	15.1216	0.713632	0.356816	−	0.934175i	$-0.383862\pi$
$449$	15.1216	0.713632	0.356816	+	0.934175i	$0.383862\pi$
$450$	34.3303	1.61835
$451$	0	0
$452$	0.956439	0.0449871
$453$	24.4174	1.14723
$454$	2.83485	0.133046
$455$	0	0
$456$	−0.825757	−0.0386696
$457$	−24.7042	−1.15561	−0.577806	−	0.816174i	$-0.696091\pi$
$457$	−24.7042	−1.15561	−0.577806	+	0.816174i	$0.696091\pi$
$458$	2.53901	0.118640
$459$	5.00000	0.233380
$460$	−1.91288	−0.0891884
$461$	−27.7477	−1.29234	−0.646170	−	0.763193i	$-0.723630\pi$
$461$	−27.7477	−1.29234	−0.646170	+	0.763193i	$0.723630\pi$
$462$	90.8258	4.22560
$463$	−15.7477	−0.731859	−0.365929	−	0.930643i	$-0.619249\pi$
$463$	−15.7477	−0.731859	−0.365929	+	0.930643i	$0.619249\pi$
$464$	−44.6080	−2.07087
$465$	−23.9564	−1.11095
$466$	48.2087	2.23323
$467$	4.79129	0.221714	0.110857	−	0.993836i	$-0.464640\pi$
$467$	4.79129	0.221714	0.110857	+	0.993836i	$0.464640\pi$
$468$	0	0
$469$	65.0780	3.00502
$470$	−10.0000	−0.461266
$471$	−40.7042	−1.87555
$472$	0.825757	0.0380085
$473$	−34.1216	−1.56891
$474$	−2.91288	−0.133793
$475$	0.834849	0.0383055
$476$	5.79129	0.265443
$477$	−15.3739	−0.703921
$478$	3.13068	0.143194
$479$	−35.1216	−1.60475	−0.802373	−	0.596823i	$-0.796430\pi$
$479$	−35.1216	−1.60475	−0.802373	+	0.596823i	$0.796430\pi$
$480$	16.8693	0.769975
$481$	0	0
$482$	−17.4610	−0.795326
$483$	−21.1652	−0.963048
$484$	4.07803	0.185365
$485$	7.95644	0.361283
$486$	28.9564	1.31349
$487$	23.0000	1.04223	0.521115	−	0.853487i	$-0.325516\pi$
$487$	23.0000	1.04223	0.521115	+	0.853487i	$0.325516\pi$
$488$	10.2178	0.462538
$489$	−31.2867	−1.41484
$490$	−28.5826	−1.29123
$491$	−12.9564	−0.584716	−0.292358	−	0.956309i	$-0.594440\pi$
$491$	−12.9564	−0.584716	−0.292358	+	0.956309i	$0.594440\pi$
$492$	0	0
$493$	9.00000	0.405340
$494$	0	0
$495$	−18.1652	−0.816463
$496$	42.5390	1.91006
$497$	−9.58258	−0.429837
$498$	−22.9129	−1.02675
$499$	13.1652	0.589353	0.294677	−	0.955597i	$-0.404788\pi$
$499$	13.1652	0.589353	0.294677	+	0.955597i	$0.404788\pi$
$500$	−10.8784	−0.486497
$501$	−70.7042	−3.15883
$502$	18.5826	0.829381
$503$	31.3739	1.39889	0.699446	−	0.714686i	$-0.253430\pi$
$503$	31.3739	1.39889	0.699446	+	0.714686i	$0.253430\pi$
$504$	32.5390	1.44940
$505$	−12.1652	−0.541342
$506$	−10.7477	−0.477795
$507$	0	0
$508$	20.4955	0.909339
$509$	17.4174	0.772014	0.386007	−	0.922496i	$-0.373854\pi$
$509$	17.4174	0.772014	0.386007	+	0.922496i	$0.373854\pi$
$510$	−5.00000	−0.221404
$511$	2.79129	0.123479
$512$	−15.9038	−0.702855
$513$	−1.04356	−0.0460743
$514$	−14.6261	−0.645131
$515$	−1.00000	−0.0440653
$516$	30.3648	1.33673
$517$	−21.1652	−0.930842
$518$	−73.6606	−3.23646
$519$	−28.3739	−1.24547
$520$	0	0
$521$	13.4174	0.587828	0.293914	−	0.955832i	$-0.405042\pi$
$521$	13.4174	0.587828	0.293914	+	0.955832i	$0.405042\pi$
$522$	−77.2432	−3.38084
$523$	−24.8693	−1.08746	−0.543730	−	0.839260i	$-0.682988\pi$
$523$	−24.8693	−1.08746	−0.543730	+	0.839260i	$0.682988\pi$
$524$	1.71326	0.0748440
$525$	−53.4955	−2.33473
$526$	3.58258	0.156208
$527$	−8.58258	−0.373863
$528$	52.4519	2.28268
$529$	−20.4955	−0.891107
$530$	5.74773	0.249665
$531$	2.79129	0.121132
$532$	−1.20871	−0.0524043
$533$	0	0
$534$	34.7822	1.50517
$535$	−7.37386	−0.318800
$536$	19.2523	0.831572
$537$	−50.7042	−2.18805
$538$	11.8693	0.511723
$539$	−60.4955	−2.60572
$540$	6.04356	0.260073
$541$	−1.79129	−0.0770135	−0.0385067	−	0.999258i	$-0.512260\pi$
$541$	−1.79129	−0.0770135	−0.0385067	+	0.999258i	$0.512260\pi$
$542$	54.4083	2.33704
$543$	−42.4519	−1.82179
$544$	6.04356	0.259116
$545$	−5.95644	−0.255146
$546$	0	0
$547$	−35.8693	−1.53366	−0.766831	−	0.641849i	$-0.778167\pi$
$547$	−35.8693	−1.53366	−0.766831	+	0.641849i	$0.778167\pi$
$548$	−4.58258	−0.195758
$549$	34.5390	1.47409
$550$	−27.1652	−1.15833
$551$	−1.87841	−0.0800229
$552$	−6.26136	−0.266501
$553$	2.79129	0.118698
$554$	12.2432	0.520163
$555$	23.9564	1.01689
$556$	25.0780	1.06355
$557$	−14.4174	−0.610886	−0.305443	−	0.952210i	$-0.598805\pi$
$557$	−14.4174	−0.610886	−0.305443	+	0.952210i	$0.598805\pi$
$558$	73.6606	3.11830
$559$	0	0
$560$	−23.7477	−1.00352
$561$	−10.5826	−0.446797
$562$	−52.1652	−2.20045
$563$	39.9564	1.68396	0.841982	−	0.539506i	$-0.181389\pi$
$563$	39.9564	1.68396	0.841982	+	0.539506i	$0.181389\pi$
$564$	18.8348	0.793090
$565$	0.791288	0.0332897
$566$	−9.33030	−0.392182
$567$	−2.00000	−0.0839921
$568$	−2.83485	−0.118948
$569$	−21.3739	−0.896039	−0.448019	−	0.894024i	$-0.647870\pi$
$569$	−21.3739	−0.896039	−0.448019	+	0.894024i	$0.647870\pi$
$570$	1.04356	0.0437100
$571$	35.1652	1.47162	0.735808	−	0.677190i	$-0.236803\pi$
$571$	35.1652	1.47162	0.735808	+	0.677190i	$0.236803\pi$
$572$	0	0
$573$	−49.5390	−2.06952
$574$	0	0
$575$	6.33030	0.263992
$576$	−4.37386	−0.182244
$577$	−30.2867	−1.26085	−0.630427	−	0.776249i	$-0.717120\pi$
$577$	−30.2867	−1.26085	−0.630427	+	0.776249i	$0.717120\pi$
$578$	−1.79129	−0.0745078
$579$	−26.7477	−1.11160
$580$	10.8784	0.451701
$581$	21.9564	0.910907
$582$	−39.7822	−1.64903
$583$	12.1652	0.503829
$584$	0.825757	0.0341701
$585$	0	0
$586$	31.5735	1.30429
$587$	21.9564	0.906239	0.453120	−	0.891450i	$-0.350311\pi$
$587$	21.9564	0.906239	0.453120	+	0.891450i	$0.350311\pi$
$588$	53.8348	2.22011
$589$	1.79129	0.0738087
$590$	−1.04356	−0.0429627
$591$	13.2523	0.545126
$592$	−42.5390	−1.74834
$593$	11.6261	0.477428	0.238714	−	0.971090i	$-0.423274\pi$
$593$	11.6261	0.477428	0.238714	+	0.971090i	$0.423274\pi$
$594$	33.9564	1.39325
$595$	4.79129	0.196424
$596$	22.9129	0.938548
$597$	30.7042	1.25664
$598$	0	0
$599$	5.00000	0.204294	0.102147	−	0.994769i	$-0.467429\pi$
$599$	5.00000	0.204294	0.102147	+	0.994769i	$0.467429\pi$
$600$	−15.8258	−0.646084
$601$	−35.4519	−1.44611	−0.723056	−	0.690789i	$-0.757263\pi$
$601$	−35.4519	−1.44611	−0.723056	+	0.690789i	$0.757263\pi$
$602$	−77.2432	−3.14820
$603$	65.0780	2.65018
$604$	10.5735	0.430229
$605$	3.37386	0.137167
$606$	60.8258	2.47088
$607$	1.41742	0.0575315	0.0287657	−	0.999586i	$-0.490842\pi$
$607$	1.41742	0.0575315	0.0287657	+	0.999586i	$0.490842\pi$
$608$	−1.26136	−0.0511551
$609$	120.365	4.87743
$610$	−12.9129	−0.522827
$611$	0	0
$612$	5.79129	0.234099
$613$	43.7477	1.76695	0.883477	−	0.468474i	$-0.155196\pi$
$613$	43.7477	1.76695	0.883477	+	0.468474i	$0.155196\pi$
$614$	35.4519	1.43072
$615$	0	0
$616$	−25.7477	−1.03741
$617$	−20.5826	−0.828623	−0.414312	−	0.910135i	$-0.635978\pi$
$617$	−20.5826	−0.828623	−0.414312	+	0.910135i	$0.635978\pi$
$618$	5.00000	0.201129
$619$	−29.8348	−1.19916	−0.599582	−	0.800313i	$-0.704666\pi$
$619$	−29.8348	−1.19916	−0.599582	+	0.800313i	$0.704666\pi$
$620$	−10.3739	−0.416624
$621$	−7.91288	−0.317533
$622$	−40.4519	−1.62197
$623$	−33.3303	−1.33535
$624$	0	0
$625$	11.0000	0.440000
$626$	1.79129	0.0715943
$627$	2.20871	0.0882075
$628$	−17.6261	−0.703359
$629$	8.58258	0.342210
$630$	−41.1216	−1.63832
$631$	−13.8348	−0.550757	−0.275378	−	0.961336i	$-0.588803\pi$
$631$	−13.8348	−0.550757	−0.275378	+	0.961336i	$0.588803\pi$
$632$	0.825757	0.0328468
$633$	57.4519	2.28351
$634$	30.4519	1.20940
$635$	16.9564	0.672896
$636$	−10.8258	−0.429269
$637$	0	0
$638$	61.1216	2.41983
$639$	−9.58258	−0.379081
$640$	−10.4519	−0.413147
$641$	2.58258	0.102006	0.0510028	−	0.998699i	$-0.483758\pi$
$641$	2.58258	0.102006	0.0510028	+	0.998699i	$0.483758\pi$
$642$	36.8693	1.45512
$643$	−28.7042	−1.13198	−0.565991	−	0.824411i	$-0.691506\pi$
$643$	−28.7042	−1.13198	−0.565991	+	0.824411i	$0.691506\pi$
$644$	−9.16515	−0.361158
$645$	25.1216	0.989162
$646$	0.373864	0.0147095
$647$	−25.2087	−0.991057	−0.495528	−	0.868592i	$-0.665026\pi$
$647$	−25.2087	−0.991057	−0.495528	+	0.868592i	$0.665026\pi$
$648$	−0.591667	−0.0232429
$649$	−2.20871	−0.0866995
$650$	0	0
$651$	−114.782	−4.49867
$652$	−13.5481	−0.530585
$653$	42.0780	1.64664	0.823320	−	0.567577i	$-0.192119\pi$
$653$	42.0780	1.64664	0.823320	+	0.567577i	$0.192119\pi$
$654$	29.7822	1.16458
$655$	1.41742	0.0553834
$656$	0	0
$657$	2.79129	0.108899
$658$	−47.9129	−1.86784
$659$	10.9129	0.425105	0.212553	−	0.977150i	$-0.431822\pi$
$659$	10.9129	0.425105	0.212553	+	0.977150i	$0.431822\pi$
$660$	−12.7913	−0.497900
$661$	−38.7477	−1.50711	−0.753556	−	0.657384i	$-0.771663\pi$
$661$	−38.7477	−1.50711	−0.753556	+	0.657384i	$0.771663\pi$
$662$	−19.7042	−0.765824
$663$	0	0
$664$	6.49545	0.252073
$665$	−1.00000	−0.0387783
$666$	−73.6606	−2.85429
$667$	−14.2432	−0.551498
$668$	−30.6170	−1.18461
$669$	−35.7042	−1.38040
$670$	−24.3303	−0.939962
$671$	−27.3303	−1.05507
$672$	80.8258	3.11792
$673$	31.9129	1.23015	0.615076	−	0.788468i	$-0.289126\pi$
$673$	31.9129	1.23015	0.615076	+	0.788468i	$0.289126\pi$
$674$	11.1216	0.428388
$675$	−20.0000	−0.769800
$676$	0	0
$677$	−45.8693	−1.76290	−0.881451	−	0.472276i	$-0.843432\pi$
$677$	−45.8693	−1.76290	−0.881451	+	0.472276i	$0.843432\pi$
$678$	−3.95644	−0.151946
$679$	38.1216	1.46297
$680$	1.41742	0.0543557
$681$	−4.41742	−0.169276
$682$	−58.2867	−2.23191
$683$	−13.9129	−0.532361	−0.266181	−	0.963923i	$-0.585762\pi$
$683$	−13.9129	−0.532361	−0.266181	+	0.963923i	$0.585762\pi$
$684$	−1.20871	−0.0462163
$685$	−3.79129	−0.144858
$686$	−76.8693	−2.93488
$687$	−3.95644	−0.150948
$688$	−44.6080	−1.70066
$689$	0	0
$690$	7.91288	0.301238
$691$	−4.08712	−0.155481	−0.0777407	−	0.996974i	$-0.524771\pi$
$691$	−4.08712	−0.155481	−0.0777407	+	0.996974i	$0.524771\pi$
$692$	−12.2867	−0.467072
$693$	−87.0345	−3.30617
$694$	−21.0436	−0.798803
$695$	20.7477	0.787006
$696$	35.6080	1.34972
$697$	0	0
$698$	19.0345	0.720465
$699$	−75.1216	−2.84136
$700$	−23.1652	−0.875560
$701$	−26.9564	−1.01813	−0.509065	−	0.860728i	$-0.670009\pi$
$701$	−26.9564	−1.01813	−0.509065	+	0.860728i	$0.670009\pi$
$702$	0	0
$703$	−1.79129	−0.0675597
$704$	3.46099	0.130441
$705$	15.5826	0.586874
$706$	40.0000	1.50542
$707$	−58.2867	−2.19210
$708$	1.96553	0.0738692
$709$	30.5390	1.14692	0.573458	−	0.819235i	$-0.305601\pi$
$709$	30.5390	1.14692	0.573458	+	0.819235i	$0.305601\pi$
$710$	3.58258	0.134452
$711$	2.79129	0.104681
$712$	−9.86023	−0.369528
$713$	13.5826	0.508671
$714$	−23.9564	−0.896547
$715$	0	0
$716$	−21.9564	−0.820551
$717$	−4.87841	−0.182188
$718$	−30.0780	−1.12250
$719$	−17.1652	−0.640152	−0.320076	−	0.947392i	$-0.603708\pi$
$719$	−17.1652	−0.640152	−0.320076	+	0.947392i	$0.603708\pi$
$720$	−23.7477	−0.885026
$721$	−4.79129	−0.178437
$722$	33.9564	1.26373
$723$	27.2087	1.01190
$724$	−18.3830	−0.683197
$725$	−36.0000	−1.33701
$726$	−16.8693	−0.626079
$727$	32.3303	1.19906	0.599532	−	0.800351i	$-0.295353\pi$
$727$	32.3303	1.19906	0.599532	+	0.800351i	$0.295353\pi$
$728$	0	0
$729$	−43.8693	−1.62479
$730$	−1.04356	−0.0386239
$731$	9.00000	0.332877
$732$	24.3212	0.898938
$733$	−22.1652	−0.818689	−0.409344	−	0.912380i	$-0.634242\pi$
$733$	−22.1652	−0.818689	−0.409344	+	0.912380i	$0.634242\pi$
$734$	3.66061	0.135115
$735$	44.5390	1.64285
$736$	−9.56439	−0.352548
$737$	−51.4955	−1.89686
$738$	0	0
$739$	−12.7042	−0.467330	−0.233665	−	0.972317i	$-0.575072\pi$
$739$	−12.7042	−0.467330	−0.233665	+	0.972317i	$0.575072\pi$
$740$	10.3739	0.381351
$741$	0	0
$742$	27.5390	1.01099
$743$	−22.7477	−0.834533	−0.417267	−	0.908784i	$-0.637012\pi$
$743$	−22.7477	−0.834533	−0.417267	+	0.908784i	$0.637012\pi$
$744$	−33.9564	−1.24490
$745$	18.9564	0.694510
$746$	−48.5826	−1.77873
$747$	21.9564	0.803344
$748$	−4.58258	−0.167556
$749$	−35.3303	−1.29094
$750$	45.0000	1.64317
$751$	14.3303	0.522920	0.261460	−	0.965214i	$-0.415796\pi$
$751$	14.3303	0.522920	0.261460	+	0.965214i	$0.415796\pi$
$752$	−27.6697	−1.00901
$753$	−28.9564	−1.05523
$754$	0	0
$755$	8.74773	0.318362
$756$	28.9564	1.05314
$757$	5.37386	0.195316	0.0976582	−	0.995220i	$-0.468865\pi$
$757$	5.37386	0.195316	0.0976582	+	0.995220i	$0.468865\pi$
$758$	−33.5826	−1.21977
$759$	16.7477	0.607904
$760$	−0.295834	−0.0107310
$761$	2.91288	0.105592	0.0527959	−	0.998605i	$-0.483187\pi$
$761$	2.91288	0.105592	0.0527959	+	0.998605i	$0.483187\pi$
$762$	−84.7822	−3.07133
$763$	−28.5390	−1.03318
$764$	−21.4519	−0.776102
$765$	4.79129	0.173229
$766$	51.7913	1.87130
$767$	0	0
$768$	57.3557	2.06964
$769$	40.7913	1.47097	0.735486	−	0.677540i	$-0.236954\pi$
$769$	40.7913	1.47097	0.735486	+	0.677540i	$0.236954\pi$
$770$	32.5390	1.17262
$771$	22.7913	0.820808
$772$	−11.5826	−0.416866
$773$	−9.79129	−0.352168	−0.176084	−	0.984375i	$-0.556343\pi$
$773$	−9.79129	−0.352168	−0.176084	+	0.984375i	$0.556343\pi$
$774$	−77.2432	−2.77645
$775$	34.3303	1.23318
$776$	11.2777	0.404844
$777$	114.782	4.11779
$778$	1.86932	0.0670183
$779$	0	0
$780$	0	0
$781$	7.58258	0.271326
$782$	2.83485	0.101374
$783$	45.0000	1.60817
$784$	−79.0871	−2.82454
$785$	−14.5826	−0.520474
$786$	−7.08712	−0.252789
$787$	−31.2432	−1.11370	−0.556850	−	0.830613i	$-0.687990\pi$
$787$	−31.2432	−1.11370	−0.556850	+	0.830613i	$0.687990\pi$
$788$	5.73864	0.204430
$789$	−5.58258	−0.198745
$790$	−1.04356	−0.0371282
$791$	3.79129	0.134803
$792$	−25.7477	−0.914906
$793$	0	0
$794$	−30.7477	−1.09120
$795$	−8.95644	−0.317652
$796$	13.2958	0.471258
$797$	44.8693	1.58935	0.794676	−	0.607033i	$-0.207641\pi$
$797$	44.8693	1.58935	0.794676	+	0.607033i	$0.207641\pi$
$798$	5.00000	0.176998
$799$	5.58258	0.197497
$800$	−24.1742	−0.854689
$801$	−33.3303	−1.17767
$802$	−33.9564	−1.19904
$803$	−2.20871	−0.0779438
$804$	45.8258	1.61615
$805$	−7.58258	−0.267251
$806$	0	0
$807$	−18.4955	−0.651071
$808$	−17.2432	−0.606613
$809$	−34.3303	−1.20699	−0.603495	−	0.797367i	$-0.706226\pi$
$809$	−34.3303	−1.20699	−0.603495	+	0.797367i	$0.706226\pi$
$810$	0.747727	0.0262725
$811$	−30.1652	−1.05924	−0.529621	−	0.848234i	$-0.677666\pi$
$811$	−30.1652	−1.05924	−0.529621	+	0.848234i	$0.677666\pi$
$812$	52.1216	1.82911
$813$	−84.7822	−2.97344
$814$	58.2867	2.04295
$815$	−11.2087	−0.392624
$816$	−13.8348	−0.484317
$817$	−1.87841	−0.0657172
$818$	−9.25227	−0.323498
$819$	0	0
$820$	0	0
$821$	−46.4083	−1.61966	−0.809831	−	0.586663i	$-0.800441\pi$
$821$	−46.4083	−1.61966	−0.809831	+	0.586663i	$0.800441\pi$
$822$	18.9564	0.661182
$823$	7.41742	0.258555	0.129278	−	0.991608i	$-0.458734\pi$
$823$	7.41742	0.258555	0.129278	+	0.991608i	$0.458734\pi$
$824$	−1.41742	−0.0493783
$825$	42.3303	1.47375
$826$	−5.00000	−0.173972
$827$	−37.4519	−1.30233	−0.651165	−	0.758936i	$-0.725719\pi$
$827$	−37.4519	−1.30233	−0.651165	+	0.758936i	$0.725719\pi$
$828$	−9.16515	−0.318511
$829$	6.41742	0.222886	0.111443	−	0.993771i	$-0.464453\pi$
$829$	6.41742	0.222886	0.111443	+	0.993771i	$0.464453\pi$
$830$	−8.20871	−0.284929
$831$	−19.0780	−0.661810
$832$	0	0
$833$	15.9564	0.552858
$834$	−103.739	−3.59218
$835$	−25.3303	−0.876591
$836$	0.956439	0.0330791
$837$	−42.9129	−1.48329
$838$	19.0345	0.657535
$839$	8.20871	0.283396	0.141698	−	0.989910i	$-0.454744\pi$
$839$	8.20871	0.283396	0.141698	+	0.989910i	$0.454744\pi$
$840$	18.9564	0.654059
$841$	52.0000	1.79310
$842$	−11.1216	−0.383275
$843$	81.2867	2.79966
$844$	24.8784	0.856350
$845$	0	0
$846$	−47.9129	−1.64728
$847$	16.1652	0.555441
$848$	15.9038	0.546138
$849$	14.5390	0.498978
$850$	7.16515	0.245763
$851$	−13.5826	−0.465605
$852$	−6.74773	−0.231173
$853$	44.1652	1.51219	0.756093	−	0.654464i	$-0.227106\pi$
$853$	44.1652	1.51219	0.756093	+	0.654464i	$0.227106\pi$
$854$	−61.8693	−2.11712
$855$	−1.00000	−0.0341993
$856$	−10.4519	−0.357238
$857$	−28.0780	−0.959127	−0.479564	−	0.877507i	$-0.659205\pi$
$857$	−28.0780	−0.959127	−0.479564	+	0.877507i	$0.659205\pi$
$858$	0	0
$859$	18.5390	0.632543	0.316272	−	0.948669i	$-0.397569\pi$
$859$	18.5390	0.632543	0.316272	+	0.948669i	$0.397569\pi$
$860$	10.8784	0.370951
$861$	0	0
$862$	−37.3212	−1.27117
$863$	39.0000	1.32758	0.663788	−	0.747921i	$-0.268948\pi$
$863$	39.0000	1.32758	0.663788	+	0.747921i	$0.268948\pi$
$864$	30.2178	1.02803
$865$	−10.1652	−0.345626
$866$	16.4174	0.557887
$867$	2.79129	0.0947971
$868$	−49.7042	−1.68707
$869$	−2.20871	−0.0749254
$870$	−45.0000	−1.52564
$871$	0	0
$872$	−8.44280	−0.285909
$873$	38.1216	1.29022
$874$	−0.591667	−0.0200134
$875$	−43.1216	−1.45778
$876$	1.96553	0.0664091
$877$	−27.3739	−0.924350	−0.462175	−	0.886789i	$-0.652931\pi$
$877$	−27.3739	−0.924350	−0.462175	+	0.886789i	$0.652931\pi$
$878$	32.9129	1.11076
$879$	−49.1996	−1.65946
$880$	18.7913	0.633454
$881$	−1.46099	−0.0492218	−0.0246109	−	0.999697i	$-0.507835\pi$
$881$	−1.46099	−0.0492218	−0.0246109	+	0.999697i	$0.507835\pi$
$882$	−136.947	−4.61126
$883$	−19.0000	−0.639401	−0.319700	−	0.947519i	$-0.603582\pi$
$883$	−19.0000	−0.639401	−0.319700	+	0.947519i	$0.603582\pi$
$884$	0	0
$885$	1.62614	0.0546620
$886$	−1.04356	−0.0350591
$887$	−50.9564	−1.71095	−0.855475	−	0.517844i	$-0.826735\pi$
$887$	−50.9564	−1.71095	−0.855475	+	0.517844i	$0.826735\pi$
$888$	33.9564	1.13950
$889$	81.2432	2.72481
$890$	12.4610	0.417693
$891$	1.58258	0.0530183
$892$	−15.4610	−0.517672
$893$	−1.16515	−0.0389903
$894$	−94.7822	−3.16999
$895$	−18.1652	−0.607194
$896$	−50.0780	−1.67299
$897$	0	0
$898$	−27.0871	−0.903909
$899$	−77.2432	−2.57620
$900$	−23.1652	−0.772172
$901$	−3.20871	−0.106898
$902$	0	0
$903$	120.365	4.00549
$904$	1.12159	0.0373035
$905$	−15.2087	−0.505555
$906$	−43.7386	−1.45312
$907$	22.6261	0.751289	0.375644	−	0.926764i	$-0.377421\pi$
$907$	22.6261	0.751289	0.375644	+	0.926764i	$0.377421\pi$
$908$	−1.91288	−0.0634811
$909$	−58.2867	−1.93325
$910$	0	0
$911$	−23.8348	−0.789684	−0.394842	−	0.918749i	$-0.629201\pi$
$911$	−23.8348	−0.789684	−0.394842	+	0.918749i	$0.629201\pi$
$912$	2.88750	0.0956147
$913$	−17.3739	−0.574991
$914$	44.2523	1.46374
$915$	20.1216	0.665199
$916$	−1.71326	−0.0566076
$917$	6.79129	0.224268
$918$	−8.95644	−0.295607
$919$	−34.4174	−1.13533	−0.567663	−	0.823261i	$-0.692152\pi$
$919$	−34.4174	−1.13533	−0.567663	+	0.823261i	$0.692152\pi$
$920$	−2.24318	−0.0739555
$921$	−55.2432	−1.82032
$922$	49.7042	1.63692
$923$	0	0
$924$	−61.2867	−2.01619
$925$	−34.3303	−1.12877
$926$	28.2087	0.926996
$927$	−4.79129	−0.157367
$928$	54.3920	1.78551
$929$	4.62614	0.151779	0.0758893	−	0.997116i	$-0.475820\pi$
$929$	4.62614	0.151779	0.0758893	+	0.997116i	$0.475820\pi$
$930$	42.9129	1.40717
$931$	−3.33030	−0.109146
$932$	−32.5299	−1.06555
$933$	63.0345	2.06366
$934$	−8.58258	−0.280830
$935$	−3.79129	−0.123988
$936$	0	0
$937$	−0.252273	−0.00824140	−0.00412070	−	0.999992i	$-0.501312\pi$
$937$	−0.252273	−0.00824140	−0.00412070	+	0.999992i	$0.501312\pi$
$938$	−116.573	−3.80626
$939$	−2.79129	−0.0910902
$940$	6.74773	0.220087
$941$	29.7913	0.971168	0.485584	−	0.874190i	$-0.338607\pi$
$941$	29.7913	0.971168	0.485584	+	0.874190i	$0.338607\pi$
$942$	72.9129	2.37563
$943$	0	0
$944$	−2.88750	−0.0939802
$945$	23.9564	0.779303
$946$	61.1216	1.98723
$947$	4.00000	0.129983	0.0649913	−	0.997886i	$-0.479298\pi$
$947$	4.00000	0.129983	0.0649913	+	0.997886i	$0.479298\pi$
$948$	1.96553	0.0638375
$949$	0	0
$950$	−1.49545	−0.0485189
$951$	−47.4519	−1.53873
$952$	6.79129	0.220107
$953$	27.5826	0.893487	0.446744	−	0.894662i	$-0.352584\pi$
$953$	27.5826	0.893487	0.446744	+	0.894662i	$0.352584\pi$
$954$	27.5390	0.891609
$955$	−17.7477	−0.574303
$956$	−2.11250	−0.0683231
$957$	−95.2432	−3.07877
$958$	62.9129	2.03262
$959$	−18.1652	−0.586583
$960$	−2.54811	−0.0822398
$961$	42.6606	1.37615
$962$	0	0
$963$	−35.3303	−1.13850
$964$	11.7822	0.379479
$965$	−9.58258	−0.308474
$966$	37.9129	1.21983
$967$	44.5826	1.43368	0.716839	−	0.697238i	$-0.245588\pi$
$967$	44.5826	1.43368	0.716839	+	0.697238i	$0.245588\pi$
$968$	4.78220	0.153706
$969$	−0.582576	−0.0187150
$970$	−14.2523	−0.457613
$971$	26.0436	0.835778	0.417889	−	0.908498i	$-0.362770\pi$
$971$	26.0436	0.835778	0.417889	+	0.908498i	$0.362770\pi$
$972$	−19.5390	−0.626714
$973$	99.4083	3.18688
$974$	−41.1996	−1.32012
$975$	0	0
$976$	−35.7295	−1.14367
$977$	−33.9564	−1.08636	−0.543181	−	0.839615i	$-0.682780\pi$
$977$	−33.9564	−1.08636	−0.543181	+	0.839615i	$0.682780\pi$
$978$	56.0436	1.79208
$979$	26.3739	0.842912
$980$	19.2867	0.616092
$981$	−28.5390	−0.911181
$982$	23.2087	0.740620
$983$	28.0780	0.895550	0.447775	−	0.894146i	$-0.352217\pi$
$983$	28.0780	0.895550	0.447775	+	0.894146i	$0.352217\pi$
$984$	0	0
$985$	4.74773	0.151275
$986$	−16.1216	−0.513416
$987$	74.6606	2.37647
$988$	0	0
$989$	−14.2432	−0.452907
$990$	32.5390	1.03416
$991$	−7.79129	−0.247498	−0.123749	−	0.992314i	$-0.539492\pi$
$991$	−7.79129	−0.247498	−0.123749	+	0.992314i	$0.539492\pi$
$992$	−51.8693	−1.64685
$993$	30.7042	0.974367
$994$	17.1652	0.544446
$995$	11.0000	0.348723
$996$	15.4610	0.489900
$997$	−42.0780	−1.33262	−0.666312	−	0.745673i	$-0.732128\pi$
$997$	−42.0780	−1.33262	−0.666312	+	0.745673i	$0.732128\pi$
$998$	−23.5826	−0.746493
$999$	42.9129	1.35770

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2873.2.a.i.1.1		2
13.12	even	2		221.2.a.d.1.2	✓	2
39.38	odd	2		1989.2.a.h.1.1		2
52.51	odd	2		3536.2.a.r.1.1		2
65.64	even	2		5525.2.a.p.1.1		2
221.220	even	2		3757.2.a.g.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
221.2.a.d.1.2	✓	2	13.12	even	2
1989.2.a.h.1.1		2	39.38	odd	2
2873.2.a.i.1.1		2	1.1	even	1	trivial
3536.2.a.r.1.1		2	52.51	odd	2
3757.2.a.g.1.2		2	221.220	even	2
5525.2.a.p.1.1		2	65.64	even	2

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:	\( N \)	\(=\)	\( 2873 = 13^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2873.a (trivial)

\(f(q)\)	\(=\)	\(q-1.79129 q^{2} +2.79129 q^{3} +1.20871 q^{4} +1.00000 q^{5} -5.00000 q^{6} +4.79129 q^{7} +1.41742 q^{8} +4.79129 q^{9} +O(q^{10})\)	\(q-1.79129 q^{2} +2.79129 q^{3} +1.20871 q^{4} +1.00000 q^{5} -5.00000 q^{6} +4.79129 q^{7} +1.41742 q^{8} +4.79129 q^{9} -1.79129 q^{10} -3.79129 q^{11} +3.37386 q^{12} -8.58258 q^{14} +2.79129 q^{15} -4.95644 q^{16} +1.00000 q^{17} -8.58258 q^{18} -0.208712 q^{19} +1.20871 q^{20} +13.3739 q^{21} +6.79129 q^{22} -1.58258 q^{23} +3.95644 q^{24} -4.00000 q^{25} +5.00000 q^{27} +5.79129 q^{28} +9.00000 q^{29} -5.00000 q^{30} -8.58258 q^{31} +6.04356 q^{32} -10.5826 q^{33} -1.79129 q^{34} +4.79129 q^{35} +5.79129 q^{36} +8.58258 q^{37} +0.373864 q^{38} +1.41742 q^{40} -23.9564 q^{42} +9.00000 q^{43} -4.58258 q^{44} +4.79129 q^{45} +2.83485 q^{46} +5.58258 q^{47} -13.8348 q^{48} +15.9564 q^{49} +7.16515 q^{50} +2.79129 q^{51} -3.20871 q^{53} -8.95644 q^{54} -3.79129 q^{55} +6.79129 q^{56} -0.582576 q^{57} -16.1216 q^{58} +0.582576 q^{59} +3.37386 q^{60} +7.20871 q^{61} +15.3739 q^{62} +22.9564 q^{63} -0.912878 q^{64} +18.9564 q^{66} +13.5826 q^{67} +1.20871 q^{68} -4.41742 q^{69} -8.58258 q^{70} -2.00000 q^{71} +6.79129 q^{72} +0.582576 q^{73} -15.3739 q^{74} -11.1652 q^{75} -0.252273 q^{76} -18.1652 q^{77} +0.582576 q^{79} -4.95644 q^{80} -0.417424 q^{81} +4.58258 q^{83} +16.1652 q^{84} +1.00000 q^{85} -16.1216 q^{86} +25.1216 q^{87} -5.37386 q^{88} -6.95644 q^{89} -8.58258 q^{90} -1.91288 q^{92} -23.9564 q^{93} -10.0000 q^{94} -0.208712 q^{95} +16.8693 q^{96} +7.95644 q^{97} -28.5826 q^{98} -18.1652 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + q^{3} + 7 q^{4} + 2 q^{5} - 10 q^{6} + 5 q^{7} + 12 q^{8} + 5 q^{9}+O(q^{10}) \) 2 * q + q^2 + q^3 + 7 * q^4 + 2 * q^5 - 10 * q^6 + 5 * q^7 + 12 * q^8 + 5 * q^9	\( 2 q + q^{2} + q^{3} + 7 q^{4} + 2 q^{5} - 10 q^{6} + 5 q^{7} + 12 q^{8} + 5 q^{9} + q^{10} - 3 q^{11} - 7 q^{12} - 8 q^{14} + q^{15} + 13 q^{16} + 2 q^{17} - 8 q^{18} - 5 q^{19} + 7 q^{20} + 13 q^{21} + 9 q^{22} + 6 q^{23} - 15 q^{24} - 8 q^{25} + 10 q^{27} + 7 q^{28} + 18 q^{29} - 10 q^{30} - 8 q^{31} + 35 q^{32} - 12 q^{33} + q^{34} + 5 q^{35} + 7 q^{36} + 8 q^{37} - 13 q^{38} + 12 q^{40} - 25 q^{42} + 18 q^{43} + 5 q^{45} + 24 q^{46} + 2 q^{47} - 46 q^{48} + 9 q^{49} - 4 q^{50} + q^{51} - 11 q^{53} + 5 q^{54} - 3 q^{55} + 9 q^{56} + 8 q^{57} + 9 q^{58} - 8 q^{59} - 7 q^{60} + 19 q^{61} + 17 q^{62} + 23 q^{63} + 44 q^{64} + 15 q^{66} + 18 q^{67} + 7 q^{68} - 18 q^{69} - 8 q^{70} - 4 q^{71} + 9 q^{72} - 8 q^{73} - 17 q^{74} - 4 q^{75} - 28 q^{76} - 18 q^{77} - 8 q^{79} + 13 q^{80} - 10 q^{81} + 14 q^{84} + 2 q^{85} + 9 q^{86} + 9 q^{87} + 3 q^{88} + 9 q^{89} - 8 q^{90} + 42 q^{92} - 25 q^{93} - 20 q^{94} - 5 q^{95} - 35 q^{96} - 7 q^{97} - 48 q^{98} - 18 q^{99}+O(q^{100}) \) 2 * q + q^2 + q^3 + 7 * q^4 + 2 * q^5 - 10 * q^6 + 5 * q^7 + 12 * q^8 + 5 * q^9 + q^10 - 3 * q^11 - 7 * q^12 - 8 * q^14 + q^15 + 13 * q^16 + 2 * q^17 - 8 * q^18 - 5 * q^19 + 7 * q^20 + 13 * q^21 + 9 * q^22 + 6 * q^23 - 15 * q^24 - 8 * q^25 + 10 * q^27 + 7 * q^28 + 18 * q^29 - 10 * q^30 - 8 * q^31 + 35 * q^32 - 12 * q^33 + q^34 + 5 * q^35 + 7 * q^36 + 8 * q^37 - 13 * q^38 + 12 * q^40 - 25 * q^42 + 18 * q^43 + 5 * q^45 + 24 * q^46 + 2 * q^47 - 46 * q^48 + 9 * q^49 - 4 * q^50 + q^51 - 11 * q^53 + 5 * q^54 - 3 * q^55 + 9 * q^56 + 8 * q^57 + 9 * q^58 - 8 * q^59 - 7 * q^60 + 19 * q^61 + 17 * q^62 + 23 * q^63 + 44 * q^64 + 15 * q^66 + 18 * q^67 + 7 * q^68 - 18 * q^69 - 8 * q^70 - 4 * q^71 + 9 * q^72 - 8 * q^73 - 17 * q^74 - 4 * q^75 - 28 * q^76 - 18 * q^77 - 8 * q^79 + 13 * q^80 - 10 * q^81 + 14 * q^84 + 2 * q^85 + 9 * q^86 + 9 * q^87 + 3 * q^88 + 9 * q^89 - 8 * q^90 + 42 * q^92 - 25 * q^93 - 20 * q^94 - 5 * q^95 - 35 * q^96 - 7 * q^97 - 48 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

Properties

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