LMFDB - Embedded newform 5586.2.a.cc.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5586,2,Mod(1,5586)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5586, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("5586.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5586.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:	$44.6044345691$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.207085568.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 13x^{4} + 28x^{3} + 10x^{2} - 12x + 2 $ x^6 - 2x^5 - 13x^4 + 28x^3 + 10x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$0.341967$ of defining polynomial
Character	$\chi$	$=$	5586.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.72132 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.72132 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +2.72132 q^{10} +3.36491 q^{11} -1.00000 q^{12} -6.56984 q^{13} +2.72132 q^{15} +1.00000 q^{16} -0.683933 q^{17} -1.00000 q^{18} +1.00000 q^{19} -2.72132 q^{20} -3.36491 q^{22} +1.07836 q^{23} +1.00000 q^{24} +2.40556 q^{25} +6.56984 q^{26} -1.00000 q^{27} -1.51236 q^{29} -2.72132 q^{30} +0.107111 q^{31} -1.00000 q^{32} -3.36491 q^{33} +0.683933 q^{34} +1.00000 q^{36} +6.09488 q^{37} -1.00000 q^{38} +6.56984 q^{39} +2.72132 q^{40} -1.46352 q^{41} -2.23399 q^{43} +3.36491 q^{44} -2.72132 q^{45} -1.07836 q^{46} -8.70864 q^{47} -1.00000 q^{48} -2.40556 q^{50} +0.683933 q^{51} -6.56984 q^{52} -6.07477 q^{53} +1.00000 q^{54} -9.15698 q^{55} -1.00000 q^{57} +1.51236 q^{58} -10.7094 q^{59} +2.72132 q^{60} +7.84450 q^{61} -0.107111 q^{62} +1.00000 q^{64} +17.8786 q^{65} +3.36491 q^{66} -8.33214 q^{67} -0.683933 q^{68} -1.07836 q^{69} -4.27106 q^{71} -1.00000 q^{72} +8.19334 q^{73} -6.09488 q^{74} -2.40556 q^{75} +1.00000 q^{76} -6.56984 q^{78} +7.69257 q^{79} -2.72132 q^{80} +1.00000 q^{81} +1.46352 q^{82} -1.95981 q^{83} +1.86120 q^{85} +2.23399 q^{86} +1.51236 q^{87} -3.36491 q^{88} +7.93969 q^{89} +2.72132 q^{90} +1.07836 q^{92} -0.107111 q^{93} +8.70864 q^{94} -2.72132 q^{95} +1.00000 q^{96} -12.6700 q^{97} +3.36491 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} + 6 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 + 6 * q^6 - 6 * q^8 + 6 * q^9	$ 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} + 6 q^{6} - 6 q^{8} + 6 q^{9} + 4 q^{11} - 6 q^{12} + 6 q^{16} - 4 q^{17} - 6 q^{18} + 6 q^{19} - 4 q^{22} + 16 q^{23} + 6 q^{24} + 10 q^{25} - 6 q^{27} + 8 q^{29} - 6 q^{32} - 4 q^{33} + 4 q^{34} + 6 q^{36} - 6 q^{38} - 8 q^{41} + 8 q^{43} + 4 q^{44} - 16 q^{46} - 16 q^{47} - 6 q^{48} - 10 q^{50} + 4 q^{51} - 4 q^{53} + 6 q^{54} + 32 q^{55} - 6 q^{57} - 8 q^{58} - 24 q^{59} + 6 q^{64} + 16 q^{65} + 4 q^{66} - 20 q^{67} - 4 q^{68} - 16 q^{69} + 24 q^{71} - 6 q^{72} + 16 q^{73} - 10 q^{75} + 6 q^{76} + 40 q^{79} + 6 q^{81} + 8 q^{82} - 24 q^{83} + 8 q^{85} - 8 q^{86} - 8 q^{87} - 4 q^{88} - 24 q^{89} + 16 q^{92} + 16 q^{94} + 6 q^{96} + 4 q^{97} + 4 q^{99}+O(q^{100}) $ 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 + 6 * q^6 - 6 * q^8 + 6 * q^9 + 4 * q^11 - 6 * q^12 + 6 * q^16 - 4 * q^17 - 6 * q^18 + 6 * q^19 - 4 * q^22 + 16 * q^23 + 6 * q^24 + 10 * q^25 - 6 * q^27 + 8 * q^29 - 6 * q^32 - 4 * q^33 + 4 * q^34 + 6 * q^36 - 6 * q^38 - 8 * q^41 + 8 * q^43 + 4 * q^44 - 16 * q^46 - 16 * q^47 - 6 * q^48 - 10 * q^50 + 4 * q^51 - 4 * q^53 + 6 * q^54 + 32 * q^55 - 6 * q^57 - 8 * q^58 - 24 * q^59 + 6 * q^64 + 16 * q^65 + 4 * q^66 - 20 * q^67 - 4 * q^68 - 16 * q^69 + 24 * q^71 - 6 * q^72 + 16 * q^73 - 10 * q^75 + 6 * q^76 + 40 * q^79 + 6 * q^81 + 8 * q^82 - 24 * q^83 + 8 * q^85 - 8 * q^86 - 8 * q^87 - 4 * q^88 - 24 * q^89 + 16 * q^92 + 16 * q^94 + 6 * q^96 + 4 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−2.72132	−1.21701	−0.608505	−	0.793550i	$-0.708230\pi$
$5$	−2.72132	−1.21701	−0.608505	+	0.793550i	$0.708230\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.72132	0.860556
$11$	3.36491	1.01456	0.507279	−	0.861782i	$-0.330651\pi$
$11$	3.36491	1.01456	0.507279	+	0.861782i	$0.330651\pi$
$12$	−1.00000	−0.288675
$13$	−6.56984	−1.82215	−0.911073	−	0.412246i	$-0.864745\pi$
$13$	−6.56984	−1.82215	−0.911073	+	0.412246i	$0.864745\pi$
$14$	0	0
$15$	2.72132	0.702641
$16$	1.00000	0.250000
$17$	−0.683933	−0.165878	−0.0829391	−	0.996555i	$-0.526431\pi$
$17$	−0.683933	−0.165878	−0.0829391	+	0.996555i	$0.526431\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−2.72132	−0.608505
$21$	0	0
$22$	−3.36491	−0.717401
$23$	1.07836	0.224854	0.112427	−	0.993660i	$-0.464137\pi$
$23$	1.07836	0.224854	0.112427	+	0.993660i	$0.464137\pi$
$24$	1.00000	0.204124
$25$	2.40556	0.481112
$26$	6.56984	1.28845
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−1.51236	−0.280838	−0.140419	−	0.990092i	$-0.544845\pi$
$29$	−1.51236	−0.280838	−0.140419	+	0.990092i	$0.544845\pi$
$30$	−2.72132	−0.496842
$31$	0.107111	0.0192377	0.00961884	−	0.999954i	$-0.496938\pi$
$31$	0.107111	0.0192377	0.00961884	+	0.999954i	$0.496938\pi$
$32$	−1.00000	−0.176777
$33$	−3.36491	−0.585755
$34$	0.683933	0.117294
$35$	0	0
$36$	1.00000	0.166667
$37$	6.09488	1.00199	0.500996	−	0.865450i	$-0.332967\pi$
$37$	6.09488	1.00199	0.500996	+	0.865450i	$0.332967\pi$
$38$	−1.00000	−0.162221
$39$	6.56984	1.05202
$40$	2.72132	0.430278
$41$	−1.46352	−0.228563	−0.114282	−	0.993448i	$-0.536457\pi$
$41$	−1.46352	−0.228563	−0.114282	+	0.993448i	$0.536457\pi$
$42$	0	0
$43$	−2.23399	−0.340680	−0.170340	−	0.985385i	$-0.554487\pi$
$43$	−2.23399	−0.340680	−0.170340	+	0.985385i	$0.554487\pi$
$44$	3.36491	0.507279
$45$	−2.72132	−0.405670
$46$	−1.07836	−0.158996
$47$	−8.70864	−1.27029	−0.635143	−	0.772395i	$-0.719059\pi$
$47$	−8.70864	−1.27029	−0.635143	+	0.772395i	$0.719059\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	−2.40556	−0.340198
$51$	0.683933	0.0957698
$52$	−6.56984	−0.911073
$53$	−6.07477	−0.834433	−0.417217	−	0.908807i	$-0.636994\pi$
$53$	−6.07477	−0.834433	−0.417217	+	0.908807i	$0.636994\pi$
$54$	1.00000	0.136083
$55$	−9.15698	−1.23473
$56$	0	0
$57$	−1.00000	−0.132453
$58$	1.51236	0.198583
$59$	−10.7094	−1.39424	−0.697122	−	0.716952i	$-0.745536\pi$
$59$	−10.7094	−1.39424	−0.697122	+	0.716952i	$0.745536\pi$
$60$	2.72132	0.351320
$61$	7.84450	1.00438	0.502192	−	0.864756i	$-0.332527\pi$
$61$	7.84450	1.00438	0.502192	+	0.864756i	$0.332527\pi$
$62$	−0.107111	−0.0136031
$63$	0	0
$64$	1.00000	0.125000
$65$	17.8786	2.21757
$66$	3.36491	0.414192
$67$	−8.33214	−1.01793	−0.508966	−	0.860786i	$-0.669972\pi$
$67$	−8.33214	−1.01793	−0.508966	+	0.860786i	$0.669972\pi$
$68$	−0.683933	−0.0829391
$69$	−1.07836	−0.129820
$70$	0	0
$71$	−4.27106	−0.506882	−0.253441	−	0.967351i	$-0.581562\pi$
$71$	−4.27106	−0.506882	−0.253441	+	0.967351i	$0.581562\pi$
$72$	−1.00000	−0.117851
$73$	8.19334	0.958957	0.479479	−	0.877554i	$-0.340826\pi$
$73$	8.19334	0.958957	0.479479	+	0.877554i	$0.340826\pi$
$74$	−6.09488	−0.708515
$75$	−2.40556	−0.277770
$76$	1.00000	0.114708
$77$	0	0
$78$	−6.56984	−0.743888
$79$	7.69257	0.865482	0.432741	−	0.901518i	$-0.357547\pi$
$79$	7.69257	0.865482	0.432741	+	0.901518i	$0.357547\pi$
$80$	−2.72132	−0.304252
$81$	1.00000	0.111111
$82$	1.46352	0.161619
$83$	−1.95981	−0.215117	−0.107559	−	0.994199i	$-0.534303\pi$
$83$	−1.95981	−0.215117	−0.107559	+	0.994199i	$0.534303\pi$
$84$	0	0
$85$	1.86120	0.201875
$86$	2.23399	0.240897
$87$	1.51236	0.162142
$88$	−3.36491	−0.358700
$89$	7.93969	0.841605	0.420802	−	0.907152i	$-0.361749\pi$
$89$	7.93969	0.841605	0.420802	+	0.907152i	$0.361749\pi$
$90$	2.72132	0.286852
$91$	0	0
$92$	1.07836	0.112427
$93$	−0.107111	−0.0111069
$94$	8.70864	0.898228
$95$	−2.72132	−0.279201
$96$	1.00000	0.102062
$97$	−12.6700	−1.28644	−0.643220	−	0.765681i	$-0.722402\pi$
$97$	−12.6700	−1.28644	−0.643220	+	0.765681i	$0.722402\pi$
$98$	0	0
$99$	3.36491	0.338186
$100$	2.40556	0.240556
$101$	1.74604	0.173737	0.0868686	−	0.996220i	$-0.472314\pi$
$101$	1.74604	0.173737	0.0868686	+	0.996220i	$0.472314\pi$
$102$	−0.683933	−0.0677195
$103$	10.8588	1.06995	0.534976	−	0.844867i	$-0.320321\pi$
$103$	10.8588	1.06995	0.534976	+	0.844867i	$0.320321\pi$
$104$	6.56984	0.644226
$105$	0	0
$106$	6.07477	0.590033
$107$	−6.85638	−0.662832	−0.331416	−	0.943485i	$-0.607526\pi$
$107$	−6.85638	−0.662832	−0.331416	+	0.943485i	$0.607526\pi$
$108$	−1.00000	−0.0962250
$109$	−3.81114	−0.365041	−0.182520	−	0.983202i	$-0.558426\pi$
$109$	−3.81114	−0.365041	−0.182520	+	0.983202i	$0.558426\pi$
$110$	9.15698	0.873084
$111$	−6.09488	−0.578500
$112$	0	0
$113$	−5.19703	−0.488896	−0.244448	−	0.969662i	$-0.578607\pi$
$113$	−5.19703	−0.488896	−0.244448	+	0.969662i	$0.578607\pi$
$114$	1.00000	0.0936586
$115$	−2.93457	−0.273650
$116$	−1.51236	−0.140419
$117$	−6.56984	−0.607382
$118$	10.7094	0.985880
$119$	0	0
$120$	−2.72132	−0.248421
$121$	0.322609	0.0293280
$122$	−7.84450	−0.710207
$123$	1.46352	0.131961
$124$	0.107111	0.00961884
$125$	7.06029	0.631491
$126$	0	0
$127$	9.62703	0.854260	0.427130	−	0.904190i	$-0.359525\pi$
$127$	9.62703	0.854260	0.427130	+	0.904190i	$0.359525\pi$
$128$	−1.00000	−0.0883883
$129$	2.23399	0.196692
$130$	−17.8786	−1.56806
$131$	−0.192110	−0.0167847	−0.00839237	−	0.999965i	$-0.502671\pi$
$131$	−0.192110	−0.0167847	−0.00839237	+	0.999965i	$0.502671\pi$
$132$	−3.36491	−0.292878
$133$	0	0
$134$	8.33214	0.719787
$135$	2.72132	0.234214
$136$	0.683933	0.0586468
$137$	−17.1972	−1.46925	−0.734627	−	0.678472i	$-0.762643\pi$
$137$	−17.1972	−1.46925	−0.734627	+	0.678472i	$0.762643\pi$
$138$	1.07836	0.0917965
$139$	−16.3409	−1.38602	−0.693008	−	0.720930i	$-0.743715\pi$
$139$	−16.3409	−1.38602	−0.693008	+	0.720930i	$0.743715\pi$
$140$	0	0
$141$	8.70864	0.733400
$142$	4.27106	0.358419
$143$	−22.1069	−1.84867
$144$	1.00000	0.0833333
$145$	4.11561	0.341783
$146$	−8.19334	−0.678085
$147$	0	0
$148$	6.09488	0.500996
$149$	−17.1069	−1.40145	−0.700726	−	0.713431i	$-0.747140\pi$
$149$	−17.1069	−1.40145	−0.700726	+	0.713431i	$0.747140\pi$
$150$	2.40556	0.196413
$151$	3.46633	0.282086	0.141043	−	0.990003i	$-0.454954\pi$
$151$	3.46633	0.282086	0.141043	+	0.990003i	$0.454954\pi$
$152$	−1.00000	−0.0811107
$153$	−0.683933	−0.0552927
$154$	0	0
$155$	−0.291483	−0.0234124
$156$	6.56984	0.526008
$157$	19.5007	1.55632	0.778162	−	0.628063i	$-0.216152\pi$
$157$	19.5007	1.55632	0.778162	+	0.628063i	$0.216152\pi$
$158$	−7.69257	−0.611988
$159$	6.07477	0.481760
$160$	2.72132	0.215139
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	−5.63955	−0.441724	−0.220862	−	0.975305i	$-0.570887\pi$
$163$	−5.63955	−0.441724	−0.220862	+	0.975305i	$0.570887\pi$
$164$	−1.46352	−0.114282
$165$	9.15698	0.712870
$166$	1.95981	0.152111
$167$	−20.4853	−1.58520	−0.792599	−	0.609743i	$-0.791273\pi$
$167$	−20.4853	−1.58520	−0.792599	+	0.609743i	$0.791273\pi$
$168$	0	0
$169$	30.1628	2.32021
$170$	−1.86120	−0.142747
$171$	1.00000	0.0764719
$172$	−2.23399	−0.170340
$173$	3.14833	0.239363	0.119681	−	0.992812i	$-0.461813\pi$
$173$	3.14833	0.239363	0.119681	+	0.992812i	$0.461813\pi$
$174$	−1.51236	−0.114652
$175$	0	0
$176$	3.36491	0.253640
$177$	10.7094	0.804967
$178$	−7.93969	−0.595105
$179$	3.86304	0.288737	0.144369	−	0.989524i	$-0.453885\pi$
$179$	3.86304	0.288737	0.144369	+	0.989524i	$0.453885\pi$
$180$	−2.72132	−0.202835
$181$	−2.26384	−0.168270	−0.0841349	−	0.996454i	$-0.526813\pi$
$181$	−2.26384	−0.168270	−0.0841349	+	0.996454i	$0.526813\pi$
$182$	0	0
$183$	−7.84450	−0.579882
$184$	−1.07836	−0.0794981
$185$	−16.5861	−1.21943
$186$	0.107111	0.00785375
$187$	−2.30137	−0.168293
$188$	−8.70864	−0.635143
$189$	0	0
$190$	2.72132	0.197425
$191$	−5.85234	−0.423461	−0.211730	−	0.977328i	$-0.567910\pi$
$191$	−5.85234	−0.423461	−0.211730	+	0.977328i	$0.567910\pi$
$192$	−1.00000	−0.0721688
$193$	7.34402	0.528634	0.264317	−	0.964436i	$-0.414853\pi$
$193$	7.34402	0.528634	0.264317	+	0.964436i	$0.414853\pi$
$194$	12.6700	0.909651
$195$	−17.8786	−1.28031
$196$	0	0
$197$	16.3314	1.16356	0.581781	−	0.813346i	$-0.302356\pi$
$197$	16.3314	1.16356	0.581781	+	0.813346i	$0.302356\pi$
$198$	−3.36491	−0.239134
$199$	16.0738	1.13944	0.569722	−	0.821837i	$-0.307051\pi$
$199$	16.0738	1.13944	0.569722	+	0.821837i	$0.307051\pi$
$200$	−2.40556	−0.170099
$201$	8.33214	0.587704
$202$	−1.74604	−0.122851
$203$	0	0
$204$	0.683933	0.0478849
$205$	3.98270	0.278164
$206$	−10.8588	−0.756570
$207$	1.07836	0.0749515
$208$	−6.56984	−0.455536
$209$	3.36491	0.232756
$210$	0	0
$211$	−8.46374	−0.582668	−0.291334	−	0.956621i	$-0.594099\pi$
$211$	−8.46374	−0.582668	−0.291334	+	0.956621i	$0.594099\pi$
$212$	−6.07477	−0.417217
$213$	4.27106	0.292648
$214$	6.85638	0.468693
$215$	6.07939	0.414611
$216$	1.00000	0.0680414
$217$	0	0
$218$	3.81114	0.258123
$219$	−8.19334	−0.553654
$220$	−9.15698	−0.617363
$221$	4.49333	0.302254
$222$	6.09488	0.409061
$223$	9.39257	0.628973	0.314487	−	0.949262i	$-0.398168\pi$
$223$	9.39257	0.628973	0.314487	+	0.949262i	$0.398168\pi$
$224$	0	0
$225$	2.40556	0.160371
$226$	5.19703	0.345702
$227$	−8.93835	−0.593259	−0.296629	−	0.954993i	$-0.595863\pi$
$227$	−8.93835	−0.593259	−0.296629	+	0.954993i	$0.595863\pi$
$228$	−1.00000	−0.0662266
$229$	26.9276	1.77942	0.889712	−	0.456523i	$-0.150905\pi$
$229$	26.9276	1.77942	0.889712	+	0.456523i	$0.150905\pi$
$230$	2.93457	0.193500
$231$	0	0
$232$	1.51236	0.0992913
$233$	26.0429	1.70613	0.853063	−	0.521809i	$-0.174742\pi$
$233$	26.0429	1.70613	0.853063	+	0.521809i	$0.174742\pi$
$234$	6.56984	0.429484
$235$	23.6990	1.54595
$236$	−10.7094	−0.697122
$237$	−7.69257	−0.499686
$238$	0	0
$239$	14.6307	0.946381	0.473191	−	0.880960i	$-0.343102\pi$
$239$	14.6307	0.946381	0.473191	+	0.880960i	$0.343102\pi$
$240$	2.72132	0.175660
$241$	12.5618	0.809175	0.404588	−	0.914499i	$-0.367415\pi$
$241$	12.5618	0.809175	0.404588	+	0.914499i	$0.367415\pi$
$242$	−0.322609	−0.0207381
$243$	−1.00000	−0.0641500
$244$	7.84450	0.502192
$245$	0	0
$246$	−1.46352	−0.0933105
$247$	−6.56984	−0.418029
$248$	−0.107111	−0.00680155
$249$	1.95981	0.124198
$250$	−7.06029	−0.446532
$251$	−25.8096	−1.62909	−0.814545	−	0.580100i	$-0.803013\pi$
$251$	−25.8096	−1.62909	−0.814545	+	0.580100i	$0.803013\pi$
$252$	0	0
$253$	3.62860	0.228128
$254$	−9.62703	−0.604053
$255$	−1.86120	−0.116553
$256$	1.00000	0.0625000
$257$	1.40616	0.0877140	0.0438570	−	0.999038i	$-0.486035\pi$
$257$	1.40616	0.0877140	0.0438570	+	0.999038i	$0.486035\pi$
$258$	−2.23399	−0.139082
$259$	0	0
$260$	17.8786	1.10878
$261$	−1.51236	−0.0936128
$262$	0.192110	0.0118686
$263$	7.26198	0.447793	0.223896	−	0.974613i	$-0.428122\pi$
$263$	7.26198	0.447793	0.223896	+	0.974613i	$0.428122\pi$
$264$	3.36491	0.207096
$265$	16.5314	1.01551
$266$	0	0
$267$	−7.93969	−0.485901
$268$	−8.33214	−0.508966
$269$	29.0985	1.77417	0.887083	−	0.461611i	$-0.152728\pi$
$269$	29.0985	1.77417	0.887083	+	0.461611i	$0.152728\pi$
$270$	−2.72132	−0.165614
$271$	27.7712	1.68698	0.843490	−	0.537145i	$-0.180497\pi$
$271$	27.7712	1.68698	0.843490	+	0.537145i	$0.180497\pi$
$272$	−0.683933	−0.0414696
$273$	0	0
$274$	17.1972	1.03892
$275$	8.09450	0.488117
$276$	−1.07836	−0.0649099
$277$	−17.3786	−1.04418	−0.522089	−	0.852891i	$-0.674847\pi$
$277$	−17.3786	−1.04418	−0.522089	+	0.852891i	$0.674847\pi$
$278$	16.3409	0.980062
$279$	0.107111	0.00641256
$280$	0	0
$281$	−2.39009	−0.142581	−0.0712905	−	0.997456i	$-0.522712\pi$
$281$	−2.39009	−0.142581	−0.0712905	+	0.997456i	$0.522712\pi$
$282$	−8.70864	−0.518592
$283$	14.6445	0.870525	0.435263	−	0.900303i	$-0.356655\pi$
$283$	14.6445	0.870525	0.435263	+	0.900303i	$0.356655\pi$
$284$	−4.27106	−0.253441
$285$	2.72132	0.161197
$286$	22.1069	1.30721
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	−16.5322	−0.972484
$290$	−4.11561	−0.241677
$291$	12.6700	0.742727
$292$	8.19334	0.479479
$293$	−29.8716	−1.74512	−0.872559	−	0.488509i	$-0.837541\pi$
$293$	−29.8716	−1.74512	−0.872559	+	0.488509i	$0.837541\pi$
$294$	0	0
$295$	29.1436	1.69681
$296$	−6.09488	−0.354257
$297$	−3.36491	−0.195252
$298$	17.1069	0.990976
$299$	−7.08468	−0.409718
$300$	−2.40556	−0.138885
$301$	0	0
$302$	−3.46633	−0.199465
$303$	−1.74604	−0.100307
$304$	1.00000	0.0573539
$305$	−21.3474	−1.22235
$306$	0.683933	0.0390979
$307$	2.44652	0.139630	0.0698152	−	0.997560i	$-0.477759\pi$
$307$	2.44652	0.139630	0.0698152	+	0.997560i	$0.477759\pi$
$308$	0	0
$309$	−10.8588	−0.617737
$310$	0.291483	0.0165551
$311$	−2.97617	−0.168763	−0.0843816	−	0.996434i	$-0.526891\pi$
$311$	−2.97617	−0.168763	−0.0843816	+	0.996434i	$0.526891\pi$
$312$	−6.56984	−0.371944
$313$	−23.1344	−1.30763	−0.653816	−	0.756654i	$-0.726833\pi$
$313$	−23.1344	−1.30763	−0.653816	+	0.756654i	$0.726833\pi$
$314$	−19.5007	−1.10049
$315$	0	0
$316$	7.69257	0.432741
$317$	7.41309	0.416361	0.208180	−	0.978090i	$-0.433246\pi$
$317$	7.41309	0.416361	0.208180	+	0.978090i	$0.433246\pi$
$318$	−6.07477	−0.340656
$319$	−5.08895	−0.284927
$320$	−2.72132	−0.152126
$321$	6.85638	0.382686
$322$	0	0
$323$	−0.683933	−0.0380551
$324$	1.00000	0.0555556
$325$	−15.8042	−0.876657
$326$	5.63955	0.312346
$327$	3.81114	0.210756
$328$	1.46352	0.0808093
$329$	0	0
$330$	−9.15698	−0.504075
$331$	23.4786	1.29050	0.645250	−	0.763972i	$-0.276753\pi$
$331$	23.4786	1.29050	0.645250	+	0.763972i	$0.276753\pi$
$332$	−1.95981	−0.107559
$333$	6.09488	0.333997
$334$	20.4853	1.12090
$335$	22.6744	1.23883
$336$	0	0
$337$	−24.3615	−1.32706	−0.663529	−	0.748151i	$-0.730942\pi$
$337$	−24.3615	−1.32706	−0.663529	+	0.748151i	$0.730942\pi$
$338$	−30.1628	−1.64064
$339$	5.19703	0.282264
$340$	1.86120	0.100938
$341$	0.360418	0.0195177
$342$	−1.00000	−0.0540738
$343$	0	0
$344$	2.23399	0.120449
$345$	2.93457	0.157992
$346$	−3.14833	−0.169255
$347$	14.8585	0.797648	0.398824	−	0.917028i	$-0.369418\pi$
$347$	14.8585	0.797648	0.398824	+	0.917028i	$0.369418\pi$
$348$	1.51236	0.0810710
$349$	26.0515	1.39451	0.697253	−	0.716825i	$-0.254405\pi$
$349$	26.0515	1.39451	0.697253	+	0.716825i	$0.254405\pi$
$350$	0	0
$351$	6.56984	0.350672
$352$	−3.36491	−0.179350
$353$	28.1537	1.49847	0.749234	−	0.662305i	$-0.230422\pi$
$353$	28.1537	1.49847	0.749234	+	0.662305i	$0.230422\pi$
$354$	−10.7094	−0.569198
$355$	11.6229	0.616880
$356$	7.93969	0.420802
$357$	0	0
$358$	−3.86304	−0.204168
$359$	25.7949	1.36140	0.680701	−	0.732562i	$-0.261675\pi$
$359$	25.7949	1.36140	0.680701	+	0.732562i	$0.261675\pi$
$360$	2.72132	0.143426
$361$	1.00000	0.0526316
$362$	2.26384	0.118985
$363$	−0.322609	−0.0169326
$364$	0	0
$365$	−22.2967	−1.16706
$366$	7.84450	0.410038
$367$	31.5322	1.64597	0.822985	−	0.568064i	$-0.192307\pi$
$367$	31.5322	1.64597	0.822985	+	0.568064i	$0.192307\pi$
$368$	1.07836	0.0562136
$369$	−1.46352	−0.0761877
$370$	16.5861	0.862270
$371$	0	0
$372$	−0.107111	−0.00555344
$373$	0.0683518	0.00353912	0.00176956	−	0.999998i	$-0.499437\pi$
$373$	0.0683518	0.00353912	0.00176956	+	0.999998i	$0.499437\pi$
$374$	2.30137	0.119001
$375$	−7.06029	−0.364592
$376$	8.70864	0.449114
$377$	9.93596	0.511728
$378$	0	0
$379$	−14.6773	−0.753923	−0.376961	−	0.926229i	$-0.623031\pi$
$379$	−14.6773	−0.753923	−0.376961	+	0.926229i	$0.623031\pi$
$380$	−2.72132	−0.139601
$381$	−9.62703	−0.493207
$382$	5.85234	0.299432
$383$	−6.81112	−0.348032	−0.174016	−	0.984743i	$-0.555674\pi$
$383$	−6.81112	−0.348032	−0.174016	+	0.984743i	$0.555674\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−7.34402	−0.373801
$387$	−2.23399	−0.113560
$388$	−12.6700	−0.643220
$389$	14.0850	0.714138	0.357069	−	0.934078i	$-0.383776\pi$
$389$	14.0850	0.714138	0.357069	+	0.934078i	$0.383776\pi$
$390$	17.8786	0.905319
$391$	−0.737529	−0.0372985
$392$	0	0
$393$	0.192110	0.00969067
$394$	−16.3314	−0.822762
$395$	−20.9339	−1.05330
$396$	3.36491	0.169093
$397$	−24.0169	−1.20538	−0.602688	−	0.797977i	$-0.705904\pi$
$397$	−24.0169	−1.20538	−0.602688	+	0.797977i	$0.705904\pi$
$398$	−16.0738	−0.805709
$399$	0	0
$400$	2.40556	0.120278
$401$	−13.3924	−0.668785	−0.334392	−	0.942434i	$-0.608531\pi$
$401$	−13.3924	−0.668785	−0.334392	+	0.942434i	$0.608531\pi$
$402$	−8.33214	−0.415569
$403$	−0.703701	−0.0350538
$404$	1.74604	0.0868686
$405$	−2.72132	−0.135223
$406$	0	0
$407$	20.5087	1.01658
$408$	−0.683933	−0.0338598
$409$	−4.06253	−0.200879	−0.100440	−	0.994943i	$-0.532025\pi$
$409$	−4.06253	−0.200879	−0.100440	+	0.994943i	$0.532025\pi$
$410$	−3.98270	−0.196691
$411$	17.1972	0.848274
$412$	10.8588	0.534976
$413$	0	0
$414$	−1.07836	−0.0529987
$415$	5.33326	0.261800
$416$	6.56984	0.322113
$417$	16.3409	0.800217
$418$	−3.36491	−0.164583
$419$	28.1766	1.37652	0.688259	−	0.725465i	$-0.258375\pi$
$419$	28.1766	1.37652	0.688259	+	0.725465i	$0.258375\pi$
$420$	0	0
$421$	29.3034	1.42816	0.714081	−	0.700063i	$-0.246845\pi$
$421$	29.3034	1.42816	0.714081	+	0.700063i	$0.246845\pi$
$422$	8.46374	0.412008
$423$	−8.70864	−0.423429
$424$	6.07477	0.295017
$425$	−1.64524	−0.0798061
$426$	−4.27106	−0.206934
$427$	0	0
$428$	−6.85638	−0.331416
$429$	22.1069	1.06733
$430$	−6.07939	−0.293174
$431$	25.5517	1.23078	0.615391	−	0.788222i	$-0.288998\pi$
$431$	25.5517	1.23078	0.615391	+	0.788222i	$0.288998\pi$
$432$	−1.00000	−0.0481125
$433$	14.8483	0.713564	0.356782	−	0.934188i	$-0.383874\pi$
$433$	14.8483	0.713564	0.356782	+	0.934188i	$0.383874\pi$
$434$	0	0
$435$	−4.11561	−0.197328
$436$	−3.81114	−0.182520
$437$	1.07836	0.0515852
$438$	8.19334	0.391493
$439$	28.9070	1.37965	0.689827	−	0.723974i	$-0.257687\pi$
$439$	28.9070	1.37965	0.689827	+	0.723974i	$0.257687\pi$
$440$	9.15698	0.436542
$441$	0	0
$442$	−4.49333	−0.213726
$443$	29.3515	1.39453	0.697266	−	0.716813i	$-0.254400\pi$
$443$	29.3515	1.39453	0.697266	+	0.716813i	$0.254400\pi$
$444$	−6.09488	−0.289250
$445$	−21.6064	−1.02424
$446$	−9.39257	−0.444751
$447$	17.1069	0.809128
$448$	0	0
$449$	36.1441	1.70574	0.852872	−	0.522119i	$-0.174858\pi$
$449$	36.1441	1.70574	0.852872	+	0.522119i	$0.174858\pi$
$450$	−2.40556	−0.113399
$451$	−4.92461	−0.231891
$452$	−5.19703	−0.244448
$453$	−3.46633	−0.162862
$454$	8.93835	0.419497
$455$	0	0
$456$	1.00000	0.0468293
$457$	9.65685	0.451729	0.225864	−	0.974159i	$-0.427479\pi$
$457$	9.65685	0.451729	0.225864	+	0.974159i	$0.427479\pi$
$458$	−26.9276	−1.25824
$459$	0.683933	0.0319233
$460$	−2.93457	−0.136825
$461$	−13.9819	−0.651200	−0.325600	−	0.945508i	$-0.605566\pi$
$461$	−13.9819	−0.651200	−0.325600	+	0.945508i	$0.605566\pi$
$462$	0	0
$463$	4.73140	0.219887	0.109943	−	0.993938i	$-0.464933\pi$
$463$	4.73140	0.219887	0.109943	+	0.993938i	$0.464933\pi$
$464$	−1.51236	−0.0702096
$465$	0.291483	0.0135172
$466$	−26.0429	−1.20641
$467$	41.2055	1.90676	0.953381	−	0.301770i	$-0.0975775\pi$
$467$	41.2055	1.90676	0.953381	+	0.301770i	$0.0975775\pi$
$468$	−6.56984	−0.303691
$469$	0	0
$470$	−23.6990	−1.09315
$471$	−19.5007	−0.898545
$472$	10.7094	0.492940
$473$	−7.51717	−0.345640
$474$	7.69257	0.353331
$475$	2.40556	0.110375
$476$	0	0
$477$	−6.07477	−0.278144
$478$	−14.6307	−0.669193
$479$	−30.0110	−1.37124	−0.685618	−	0.727961i	$-0.740468\pi$
$479$	−30.0110	−1.37124	−0.685618	+	0.727961i	$0.740468\pi$
$480$	−2.72132	−0.124211
$481$	−40.0424	−1.82577
$482$	−12.5618	−0.572173
$483$	0	0
$484$	0.322609	0.0146640
$485$	34.4790	1.56561
$486$	1.00000	0.0453609
$487$	18.7173	0.848161	0.424081	−	0.905624i	$-0.360597\pi$
$487$	18.7173	0.848161	0.424081	+	0.905624i	$0.360597\pi$
$488$	−7.84450	−0.355104
$489$	5.63955	0.255029
$490$	0	0
$491$	−15.4712	−0.698204	−0.349102	−	0.937085i	$-0.613513\pi$
$491$	−15.4712	−0.698204	−0.349102	+	0.937085i	$0.613513\pi$
$492$	1.46352	0.0659805
$493$	1.03435	0.0465850
$494$	6.56984	0.295591
$495$	−9.15698	−0.411576
$496$	0.107111	0.00480942
$497$	0	0
$498$	−1.95981	−0.0878212
$499$	33.3724	1.49395	0.746977	−	0.664850i	$-0.231505\pi$
$499$	33.3724	1.49395	0.746977	+	0.664850i	$0.231505\pi$
$500$	7.06029	0.315746
$501$	20.4853	0.915215
$502$	25.8096	1.15194
$503$	−3.27322	−0.145946	−0.0729728	−	0.997334i	$-0.523249\pi$
$503$	−3.27322	−0.145946	−0.0729728	+	0.997334i	$0.523249\pi$
$504$	0	0
$505$	−4.75152	−0.211440
$506$	−3.62860	−0.161311
$507$	−30.1628	−1.33958
$508$	9.62703	0.427130
$509$	−7.26986	−0.322231	−0.161115	−	0.986936i	$-0.551509\pi$
$509$	−7.26986	−0.322231	−0.161115	+	0.986936i	$0.551509\pi$
$510$	1.86120	0.0824153
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	−1.40616	−0.0620232
$515$	−29.5503	−1.30214
$516$	2.23399	0.0983459
$517$	−29.3038	−1.28878
$518$	0	0
$519$	−3.14833	−0.138196
$520$	−17.8786	−0.784029
$521$	−13.8371	−0.606214	−0.303107	−	0.952957i	$-0.598024\pi$
$521$	−13.8371	−0.606214	−0.303107	+	0.952957i	$0.598024\pi$
$522$	1.51236	0.0661942
$523$	5.17727	0.226386	0.113193	−	0.993573i	$-0.463892\pi$
$523$	5.17727	0.226386	0.113193	+	0.993573i	$0.463892\pi$
$524$	−0.192110	−0.00839237
$525$	0	0
$526$	−7.26198	−0.316637
$527$	−0.0732567	−0.00319111
$528$	−3.36491	−0.146439
$529$	−21.8371	−0.949440
$530$	−16.5314	−0.718076
$531$	−10.7094	−0.464748
$532$	0	0
$533$	9.61508	0.416475
$534$	7.93969	0.343584
$535$	18.6584	0.806672
$536$	8.33214	0.359893
$537$	−3.86304	−0.166702
$538$	−29.0985	−1.25452
$539$	0	0
$540$	2.72132	0.117107
$541$	−9.26868	−0.398492	−0.199246	−	0.979950i	$-0.563849\pi$
$541$	−9.26868	−0.398492	−0.199246	+	0.979950i	$0.563849\pi$
$542$	−27.7712	−1.19287
$543$	2.26384	0.0971506
$544$	0.683933	0.0293234
$545$	10.3713	0.444258
$546$	0	0
$547$	−27.4128	−1.17209	−0.586043	−	0.810280i	$-0.699315\pi$
$547$	−27.4128	−1.17209	−0.586043	+	0.810280i	$0.699315\pi$
$548$	−17.1972	−0.734627
$549$	7.84450	0.334795
$550$	−8.09450	−0.345150
$551$	−1.51236	−0.0644287
$552$	1.07836	0.0458982
$553$	0	0
$554$	17.3786	0.738346
$555$	16.5861	0.704040
$556$	−16.3409	−0.693008
$557$	−30.0280	−1.27233	−0.636164	−	0.771553i	$-0.719480\pi$
$557$	−30.0280	−1.27233	−0.636164	+	0.771553i	$0.719480\pi$
$558$	−0.107111	−0.00453436
$559$	14.6769	0.620769
$560$	0	0
$561$	2.30137	0.0971641
$562$	2.39009	0.100820
$563$	−23.5700	−0.993355	−0.496678	−	0.867935i	$-0.665447\pi$
$563$	−23.5700	−0.993355	−0.496678	+	0.867935i	$0.665447\pi$
$564$	8.70864	0.366700
$565$	14.1428	0.594991
$566$	−14.6445	−0.615554
$567$	0	0
$568$	4.27106	0.179210
$569$	16.9950	0.712469	0.356234	−	0.934397i	$-0.384060\pi$
$569$	16.9950	0.712469	0.356234	+	0.934397i	$0.384060\pi$
$570$	−2.72132	−0.113983
$571$	−2.67842	−0.112089	−0.0560443	−	0.998428i	$-0.517849\pi$
$571$	−2.67842	−0.112089	−0.0560443	+	0.998428i	$0.517849\pi$
$572$	−22.1069	−0.924336
$573$	5.85234	0.244485
$574$	0	0
$575$	2.59407	0.108180
$576$	1.00000	0.0416667
$577$	−11.2501	−0.468346	−0.234173	−	0.972195i	$-0.575238\pi$
$577$	−11.2501	−0.468346	−0.234173	+	0.972195i	$0.575238\pi$
$578$	16.5322	0.687650
$579$	−7.34402	−0.305207
$580$	4.11561	0.170891
$581$	0	0
$582$	−12.6700	−0.525187
$583$	−20.4410	−0.846581
$584$	−8.19334	−0.339043
$585$	17.8786	0.739189
$586$	29.8716	1.23398
$587$	−7.45379	−0.307651	−0.153825	−	0.988098i	$-0.549159\pi$
$587$	−7.45379	−0.307651	−0.153825	+	0.988098i	$0.549159\pi$
$588$	0	0
$589$	0.107111	0.00441343
$590$	−29.1436	−1.19982
$591$	−16.3314	−0.671782
$592$	6.09488	0.250498
$593$	10.5040	0.431347	0.215673	−	0.976466i	$-0.430805\pi$
$593$	10.5040	0.431347	0.215673	+	0.976466i	$0.430805\pi$
$594$	3.36491	0.138064
$595$	0	0
$596$	−17.1069	−0.700726
$597$	−16.0738	−0.657858
$598$	7.08468	0.289714
$599$	33.1817	1.35577	0.677883	−	0.735170i	$-0.262898\pi$
$599$	33.1817	1.35577	0.677883	+	0.735170i	$0.262898\pi$
$600$	2.40556	0.0982067
$601$	−29.1036	−1.18716	−0.593580	−	0.804775i	$-0.702286\pi$
$601$	−29.1036	−1.18716	−0.593580	+	0.804775i	$0.702286\pi$
$602$	0	0
$603$	−8.33214	−0.339311
$604$	3.46633	0.141043
$605$	−0.877920	−0.0356925
$606$	1.74604	0.0709279
$607$	11.6424	0.472550	0.236275	−	0.971686i	$-0.424073\pi$
$607$	11.6424	0.472550	0.236275	+	0.971686i	$0.424073\pi$
$608$	−1.00000	−0.0405554
$609$	0	0
$610$	21.3474	0.864329
$611$	57.2144	2.31465
$612$	−0.683933	−0.0276464
$613$	45.4600	1.83611	0.918055	−	0.396453i	$-0.129759\pi$
$613$	45.4600	1.83611	0.918055	+	0.396453i	$0.129759\pi$
$614$	−2.44652	−0.0987336
$615$	−3.98270	−0.160598
$616$	0	0
$617$	−35.2228	−1.41802	−0.709008	−	0.705201i	$-0.750857\pi$
$617$	−35.2228	−1.41802	−0.709008	+	0.705201i	$0.750857\pi$
$618$	10.8588	0.436806
$619$	2.51954	0.101269	0.0506343	−	0.998717i	$-0.483876\pi$
$619$	2.51954	0.101269	0.0506343	+	0.998717i	$0.483876\pi$
$620$	−0.291483	−0.0117062
$621$	−1.07836	−0.0432733
$622$	2.97617	0.119334
$623$	0	0
$624$	6.56984	0.263004
$625$	−31.2411	−1.24964
$626$	23.1344	0.924635
$627$	−3.36491	−0.134381
$628$	19.5007	0.778162
$629$	−4.16849	−0.166209
$630$	0	0
$631$	24.3452	0.969167	0.484584	−	0.874745i	$-0.338971\pi$
$631$	24.3452	0.969167	0.484584	+	0.874745i	$0.338971\pi$
$632$	−7.69257	−0.305994
$633$	8.46374	0.336403
$634$	−7.41309	−0.294412
$635$	−26.1982	−1.03964
$636$	6.07477	0.240880
$637$	0	0
$638$	5.08895	0.201474
$639$	−4.27106	−0.168961
$640$	2.72132	0.107569
$641$	24.8155	0.980155	0.490077	−	0.871679i	$-0.336969\pi$
$641$	24.8155	0.980155	0.490077	+	0.871679i	$0.336969\pi$
$642$	−6.85638	−0.270600
$643$	−19.4583	−0.767361	−0.383680	−	0.923466i	$-0.625344\pi$
$643$	−19.4583	−0.767361	−0.383680	+	0.923466i	$0.625344\pi$
$644$	0	0
$645$	−6.07939	−0.239376
$646$	0.683933	0.0269090
$647$	34.4839	1.35570	0.677852	−	0.735199i	$-0.262911\pi$
$647$	34.4839	1.35570	0.677852	+	0.735199i	$0.262911\pi$
$648$	−1.00000	−0.0392837
$649$	−36.0361	−1.41454
$650$	15.8042	0.619890
$651$	0	0
$652$	−5.63955	−0.220862
$653$	20.3341	0.795736	0.397868	−	0.917443i	$-0.369750\pi$
$653$	20.3341	0.795736	0.397868	+	0.917443i	$0.369750\pi$
$654$	−3.81114	−0.149027
$655$	0.522792	0.0204272
$656$	−1.46352	−0.0571408
$657$	8.19334	0.319652
$658$	0	0
$659$	36.4052	1.41814	0.709072	−	0.705136i	$-0.249114\pi$
$659$	36.4052	1.41814	0.709072	+	0.705136i	$0.249114\pi$
$660$	9.15698	0.356435
$661$	35.3651	1.37554	0.687771	−	0.725928i	$-0.258589\pi$
$661$	35.3651	1.37554	0.687771	+	0.725928i	$0.258589\pi$
$662$	−23.4786	−0.912521
$663$	−4.49333	−0.174507
$664$	1.95981	0.0760554
$665$	0	0
$666$	−6.09488	−0.236172
$667$	−1.63088	−0.0631478
$668$	−20.4853	−0.792599
$669$	−9.39257	−0.363138
$670$	−22.6744	−0.875988
$671$	26.3960	1.01901
$672$	0	0
$673$	44.4898	1.71496	0.857478	−	0.514521i	$-0.172030\pi$
$673$	44.4898	1.71496	0.857478	+	0.514521i	$0.172030\pi$
$674$	24.3615	0.938372
$675$	−2.40556	−0.0925901
$676$	30.1628	1.16011
$677$	−10.1106	−0.388582	−0.194291	−	0.980944i	$-0.562241\pi$
$677$	−10.1106	−0.388582	−0.194291	+	0.980944i	$0.562241\pi$
$678$	−5.19703	−0.199591
$679$	0	0
$680$	−1.86120	−0.0713737
$681$	8.93835	0.342518
$682$	−0.360418	−0.0138011
$683$	26.9622	1.03168	0.515840	−	0.856685i	$-0.327480\pi$
$683$	26.9622	1.03168	0.515840	+	0.856685i	$0.327480\pi$
$684$	1.00000	0.0382360
$685$	46.7989	1.78810
$686$	0	0
$687$	−26.9276	−1.02735
$688$	−2.23399	−0.0851700
$689$	39.9102	1.52046
$690$	−2.93457	−0.111717
$691$	−48.6933	−1.85238	−0.926191	−	0.377055i	$-0.876937\pi$
$691$	−48.6933	−1.85238	−0.926191	+	0.377055i	$0.876937\pi$
$692$	3.14833	0.119681
$693$	0	0
$694$	−14.8585	−0.564022
$695$	44.4687	1.68680
$696$	−1.51236	−0.0573259
$697$	1.00095	0.0379137
$698$	−26.0515	−0.986065
$699$	−26.0429	−0.985032
$700$	0	0
$701$	7.57186	0.285985	0.142993	−	0.989724i	$-0.454328\pi$
$701$	7.57186	0.285985	0.142993	+	0.989724i	$0.454328\pi$
$702$	−6.56984	−0.247963
$703$	6.09488	0.229873
$704$	3.36491	0.126820
$705$	−23.6990	−0.892555
$706$	−28.1537	−1.05958
$707$	0	0
$708$	10.7094	0.402484
$709$	−53.0985	−1.99415	−0.997077	−	0.0764022i	$-0.975657\pi$
$709$	−53.0985	−1.99415	−0.997077	+	0.0764022i	$0.975657\pi$
$710$	−11.6229	−0.436200
$711$	7.69257	0.288494
$712$	−7.93969	−0.297552
$713$	0.115505	0.00432568
$714$	0	0
$715$	60.1599	2.24985
$716$	3.86304	0.144369
$717$	−14.6307	−0.546394
$718$	−25.7949	−0.962656
$719$	2.31650	0.0863910	0.0431955	−	0.999067i	$-0.486246\pi$
$719$	2.31650	0.0863910	0.0431955	+	0.999067i	$0.486246\pi$
$720$	−2.72132	−0.101417
$721$	0	0
$722$	−1.00000	−0.0372161
$723$	−12.5618	−0.467178
$724$	−2.26384	−0.0841349
$725$	−3.63808	−0.135115
$726$	0.322609	0.0119731
$727$	−37.4938	−1.39057	−0.695285	−	0.718735i	$-0.744722\pi$
$727$	−37.4938	−1.39057	−0.695285	+	0.718735i	$0.744722\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	22.2967	0.825236
$731$	1.52790	0.0565114
$732$	−7.84450	−0.289941
$733$	38.4259	1.41929	0.709646	−	0.704558i	$-0.248855\pi$
$733$	38.4259	1.41929	0.709646	+	0.704558i	$0.248855\pi$
$734$	−31.5322	−1.16388
$735$	0	0
$736$	−1.07836	−0.0397490
$737$	−28.0369	−1.03275
$738$	1.46352	0.0538729
$739$	−7.00722	−0.257765	−0.128882	−	0.991660i	$-0.541139\pi$
$739$	−7.00722	−0.257765	−0.128882	+	0.991660i	$0.541139\pi$
$740$	−16.5861	−0.609717
$741$	6.56984	0.241349
$742$	0	0
$743$	−38.2499	−1.40325	−0.701626	−	0.712545i	$-0.747542\pi$
$743$	−38.2499	−1.40325	−0.701626	+	0.712545i	$0.747542\pi$
$744$	0.107111	0.00392687
$745$	46.5533	1.70558
$746$	−0.0683518	−0.00250254
$747$	−1.95981	−0.0717057
$748$	−2.30137	−0.0841465
$749$	0	0
$750$	7.06029	0.257805
$751$	−0.0659087	−0.00240504	−0.00120252	−	0.999999i	$-0.500383\pi$
$751$	−0.0659087	−0.00240504	−0.00120252	+	0.999999i	$0.500383\pi$
$752$	−8.70864	−0.317571
$753$	25.8096	0.940556
$754$	−9.93596	−0.361846
$755$	−9.43297	−0.343301
$756$	0	0
$757$	22.6479	0.823154	0.411577	−	0.911375i	$-0.364978\pi$
$757$	22.6479	0.823154	0.411577	+	0.911375i	$0.364978\pi$
$758$	14.6773	0.533104
$759$	−3.62860	−0.131710
$760$	2.72132	0.0987125
$761$	−32.2554	−1.16926	−0.584628	−	0.811302i	$-0.698759\pi$
$761$	−32.2554	−1.16926	−0.584628	+	0.811302i	$0.698759\pi$
$762$	9.62703	0.348750
$763$	0	0
$764$	−5.85234	−0.211730
$765$	1.86120	0.0672918
$766$	6.81112	0.246096
$767$	70.3590	2.54052
$768$	−1.00000	−0.0360844
$769$	48.3581	1.74384	0.871918	−	0.489652i	$-0.162876\pi$
$769$	48.3581	1.74384	0.871918	+	0.489652i	$0.162876\pi$
$770$	0	0
$771$	−1.40616	−0.0506417
$772$	7.34402	0.264317
$773$	−5.82068	−0.209355	−0.104678	−	0.994506i	$-0.533381\pi$
$773$	−5.82068	−0.209355	−0.104678	+	0.994506i	$0.533381\pi$
$774$	2.23399	0.0802991
$775$	0.257662	0.00925549
$776$	12.6700	0.454825
$777$	0	0
$778$	−14.0850	−0.504972
$779$	−1.46352	−0.0524360
$780$	−17.8786	−0.640157
$781$	−14.3717	−0.514261
$782$	0.737529	0.0263740
$783$	1.51236	0.0540474
$784$	0	0
$785$	−53.0676	−1.89406
$786$	−0.192110	−0.00685234
$787$	13.9871	0.498587	0.249293	−	0.968428i	$-0.419802\pi$
$787$	13.9871	0.498587	0.249293	+	0.968428i	$0.419802\pi$
$788$	16.3314	0.581781
$789$	−7.26198	−0.258533
$790$	20.9339	0.744795
$791$	0	0
$792$	−3.36491	−0.119567
$793$	−51.5371	−1.83014
$794$	24.0169	0.852330
$795$	−16.5314	−0.586307
$796$	16.0738	0.569722
$797$	7.32026	0.259297	0.129649	−	0.991560i	$-0.458615\pi$
$797$	7.32026	0.259297	0.129649	+	0.991560i	$0.458615\pi$
$798$	0	0
$799$	5.95613	0.210713
$800$	−2.40556	−0.0850495
$801$	7.93969	0.280535
$802$	13.3924	0.472902
$803$	27.5698	0.972918
$804$	8.33214	0.293852
$805$	0	0
$806$	0.703701	0.0247868
$807$	−29.0985	−1.02431
$808$	−1.74604	−0.0614254
$809$	−1.81692	−0.0638794	−0.0319397	−	0.999490i	$-0.510168\pi$
$809$	−1.81692	−0.0638794	−0.0319397	+	0.999490i	$0.510168\pi$
$810$	2.72132	0.0956173
$811$	−31.1521	−1.09390	−0.546950	−	0.837165i	$-0.684211\pi$
$811$	−31.1521	−1.09390	−0.546950	+	0.837165i	$0.684211\pi$
$812$	0	0
$813$	−27.7712	−0.973978
$814$	−20.5087	−0.718830
$815$	15.3470	0.537582
$816$	0.683933	0.0239425
$817$	−2.23399	−0.0781574
$818$	4.06253	0.142043
$819$	0	0
$820$	3.98270	0.139082
$821$	41.4231	1.44568	0.722838	−	0.691018i	$-0.242837\pi$
$821$	41.4231	1.44568	0.722838	+	0.691018i	$0.242837\pi$
$822$	−17.1972	−0.599820
$823$	−22.2976	−0.777245	−0.388622	−	0.921397i	$-0.627049\pi$
$823$	−22.2976	−0.777245	−0.388622	+	0.921397i	$0.627049\pi$
$824$	−10.8588	−0.378285
$825$	−8.09450	−0.281814
$826$	0	0
$827$	−43.1224	−1.49951	−0.749756	−	0.661715i	$-0.769829\pi$
$827$	−43.1224	−1.49951	−0.749756	+	0.661715i	$0.769829\pi$
$828$	1.07836	0.0374757
$829$	−53.3381	−1.85251	−0.926255	−	0.376897i	$-0.876991\pi$
$829$	−53.3381	−1.85251	−0.926255	+	0.376897i	$0.876991\pi$
$830$	−5.33326	−0.185120
$831$	17.3786	0.602857
$832$	−6.56984	−0.227768
$833$	0	0
$834$	−16.3409	−0.565839
$835$	55.7469	1.92920
$836$	3.36491	0.116378
$837$	−0.107111	−0.00370229
$838$	−28.1766	−0.973346
$839$	33.0927	1.14249	0.571244	−	0.820780i	$-0.306461\pi$
$839$	33.0927	1.14249	0.571244	+	0.820780i	$0.306461\pi$
$840$	0	0
$841$	−26.7128	−0.921130
$842$	−29.3034	−1.00986
$843$	2.39009	0.0823192
$844$	−8.46374	−0.291334
$845$	−82.0825	−2.82372
$846$	8.70864	0.299409
$847$	0	0
$848$	−6.07477	−0.208608
$849$	−14.6445	−0.502598
$850$	1.64524	0.0564314
$851$	6.57250	0.225302
$852$	4.27106	0.146324
$853$	−32.8513	−1.12481	−0.562403	−	0.826863i	$-0.690123\pi$
$853$	−32.8513	−1.12481	−0.562403	+	0.826863i	$0.690123\pi$
$854$	0	0
$855$	−2.72132	−0.0930671
$856$	6.85638	0.234346
$857$	−2.69836	−0.0921744	−0.0460872	−	0.998937i	$-0.514675\pi$
$857$	−2.69836	−0.0921744	−0.0460872	+	0.998937i	$0.514675\pi$
$858$	−22.1069	−0.754717
$859$	33.0520	1.12772	0.563860	−	0.825870i	$-0.309316\pi$
$859$	33.0520	1.12772	0.563860	+	0.825870i	$0.309316\pi$
$860$	6.07939	0.207306
$861$	0	0
$862$	−25.5517	−0.870294
$863$	41.9124	1.42671	0.713357	−	0.700801i	$-0.247174\pi$
$863$	41.9124	1.42671	0.713357	+	0.700801i	$0.247174\pi$
$864$	1.00000	0.0340207
$865$	−8.56760	−0.291307
$866$	−14.8483	−0.504566
$867$	16.5322	0.561464
$868$	0	0
$869$	25.8848	0.878081
$870$	4.11561	0.139532
$871$	54.7408	1.85482
$872$	3.81114	0.129061
$873$	−12.6700	−0.428813
$874$	−1.07836	−0.0364762
$875$	0	0
$876$	−8.19334	−0.276827
$877$	−26.7418	−0.903008	−0.451504	−	0.892269i	$-0.649112\pi$
$877$	−26.7418	−0.903008	−0.451504	+	0.892269i	$0.649112\pi$
$878$	−28.9070	−0.975563
$879$	29.8716	1.00754
$880$	−9.15698	−0.308682
$881$	21.8329	0.735568	0.367784	−	0.929911i	$-0.380117\pi$
$881$	21.8329	0.735568	0.367784	+	0.929911i	$0.380117\pi$
$882$	0	0
$883$	−11.5496	−0.388676	−0.194338	−	0.980935i	$-0.562256\pi$
$883$	−11.5496	−0.388676	−0.194338	+	0.980935i	$0.562256\pi$
$884$	4.49333	0.151127
$885$	−29.1436	−0.979653
$886$	−29.3515	−0.986082
$887$	26.0116	0.873385	0.436693	−	0.899611i	$-0.356150\pi$
$887$	26.0116	0.873385	0.436693	+	0.899611i	$0.356150\pi$
$888$	6.09488	0.204531
$889$	0	0
$890$	21.6064	0.724248
$891$	3.36491	0.112729
$892$	9.39257	0.314487
$893$	−8.70864	−0.291424
$894$	−17.1069	−0.572140
$895$	−10.5126	−0.351396
$896$	0	0
$897$	7.08468	0.236551
$898$	−36.1441	−1.20614
$899$	−0.161990	−0.00540268
$900$	2.40556	0.0801854
$901$	4.15474	0.138414
$902$	4.92461	0.163971
$903$	0	0
$904$	5.19703	0.172851
$905$	6.16062	0.204786
$906$	3.46633	0.115161
$907$	−6.93870	−0.230396	−0.115198	−	0.993343i	$-0.536750\pi$
$907$	−6.93870	−0.230396	−0.115198	+	0.993343i	$0.536750\pi$
$908$	−8.93835	−0.296629
$909$	1.74604	0.0579124
$910$	0	0
$911$	−14.8252	−0.491181	−0.245591	−	0.969374i	$-0.578982\pi$
$911$	−14.8252	−0.491181	−0.245591	+	0.969374i	$0.578982\pi$
$912$	−1.00000	−0.0331133
$913$	−6.59458	−0.218249
$914$	−9.65685	−0.319420
$915$	21.3474	0.705722
$916$	26.9276	0.889712
$917$	0	0
$918$	−0.683933	−0.0225732
$919$	−29.6584	−0.978340	−0.489170	−	0.872189i	$-0.662700\pi$
$919$	−29.6584	−0.978340	−0.489170	+	0.872189i	$0.662700\pi$
$920$	2.93457	0.0967499
$921$	−2.44652	−0.0806157
$922$	13.9819	0.460468
$923$	28.0602	0.923612
$924$	0	0
$925$	14.6616	0.482071
$926$	−4.73140	−0.155483
$927$	10.8588	0.356651
$928$	1.51236	0.0496457
$929$	13.6489	0.447807	0.223903	−	0.974611i	$-0.428120\pi$
$929$	13.6489	0.447807	0.223903	+	0.974611i	$0.428120\pi$
$930$	−0.291483	−0.00955809
$931$	0	0
$932$	26.0429	0.853063
$933$	2.97617	0.0974354
$934$	−41.2055	−1.34828
$935$	6.26276	0.204814
$936$	6.56984	0.214742
$937$	57.3244	1.87271	0.936353	−	0.351059i	$-0.114178\pi$
$937$	57.3244	1.87271	0.936353	+	0.351059i	$0.114178\pi$
$938$	0	0
$939$	23.1344	0.754961
$940$	23.6990	0.772975
$941$	38.6660	1.26047	0.630237	−	0.776403i	$-0.282958\pi$
$941$	38.6660	1.26047	0.630237	+	0.776403i	$0.282958\pi$
$942$	19.5007	0.635367
$943$	−1.57821	−0.0513935
$944$	−10.7094	−0.348561
$945$	0	0
$946$	7.51717	0.244404
$947$	−4.61344	−0.149917	−0.0749584	−	0.997187i	$-0.523882\pi$
$947$	−4.61344	−0.149917	−0.0749584	+	0.997187i	$0.523882\pi$
$948$	−7.69257	−0.249843
$949$	−53.8289	−1.74736
$950$	−2.40556	−0.0780467
$951$	−7.41309	−0.240386
$952$	0	0
$953$	8.92780	0.289200	0.144600	−	0.989490i	$-0.453810\pi$
$953$	8.92780	0.289200	0.144600	+	0.989490i	$0.453810\pi$
$954$	6.07477	0.196678
$955$	15.9261	0.515356
$956$	14.6307	0.473191
$957$	5.08895	0.164503
$958$	30.0110	0.969610
$959$	0	0
$960$	2.72132	0.0878301
$961$	−30.9885	−0.999630
$962$	40.0424	1.29102
$963$	−6.85638	−0.220944
$964$	12.5618	0.404588
$965$	−19.9854	−0.643353
$966$	0	0
$967$	32.0691	1.03127	0.515637	−	0.856807i	$-0.327555\pi$
$967$	32.0691	1.03127	0.515637	+	0.856807i	$0.327555\pi$
$968$	−0.322609	−0.0103690
$969$	0.683933	0.0219711
$970$	−34.4790	−1.10705
$971$	−39.7074	−1.27427	−0.637135	−	0.770752i	$-0.719881\pi$
$971$	−39.7074	−1.27427	−0.637135	+	0.770752i	$0.719881\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−18.7173	−0.599741
$975$	15.8042	0.506138
$976$	7.84450	0.251096
$977$	−30.8573	−0.987211	−0.493606	−	0.869686i	$-0.664321\pi$
$977$	−30.8573	−0.987211	−0.493606	+	0.869686i	$0.664321\pi$
$978$	−5.63955	−0.180333
$979$	26.7163	0.853857
$980$	0	0
$981$	−3.81114	−0.121680
$982$	15.4712	0.493705
$983$	56.9036	1.81494	0.907472	−	0.420112i	$-0.138009\pi$
$983$	56.9036	1.81494	0.907472	+	0.420112i	$0.138009\pi$
$984$	−1.46352	−0.0466553
$985$	−44.4428	−1.41607
$986$	−1.03435	−0.0329405
$987$	0	0
$988$	−6.56984	−0.209014
$989$	−2.40905	−0.0766035
$990$	9.15698	0.291028
$991$	−12.3386	−0.391948	−0.195974	−	0.980609i	$-0.562787\pi$
$991$	−12.3386	−0.391948	−0.195974	+	0.980609i	$0.562787\pi$
$992$	−0.107111	−0.00340077
$993$	−23.4786	−0.745070
$994$	0	0
$995$	−43.7420	−1.38671
$996$	1.95981	0.0620989
$997$	10.3523	0.327862	0.163931	−	0.986472i	$-0.447583\pi$
$997$	10.3523	0.327862	0.163931	+	0.986472i	$0.447583\pi$
$998$	−33.3724	−1.05638
$999$	−6.09488	−0.192833

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5586.2.a.cc.1.2	✓	6
7.6	odd	2		5586.2.a.cd.1.5	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5586.2.a.cc.1.2	✓	6	1.1	even	1	trivial
5586.2.a.cd.1.5	yes	6	7.6	odd	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:	\( N \)	\(=\)	\( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5586.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.72132 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.72132 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +2.72132 q^{10} +3.36491 q^{11} -1.00000 q^{12} -6.56984 q^{13} +2.72132 q^{15} +1.00000 q^{16} -0.683933 q^{17} -1.00000 q^{18} +1.00000 q^{19} -2.72132 q^{20} -3.36491 q^{22} +1.07836 q^{23} +1.00000 q^{24} +2.40556 q^{25} +6.56984 q^{26} -1.00000 q^{27} -1.51236 q^{29} -2.72132 q^{30} +0.107111 q^{31} -1.00000 q^{32} -3.36491 q^{33} +0.683933 q^{34} +1.00000 q^{36} +6.09488 q^{37} -1.00000 q^{38} +6.56984 q^{39} +2.72132 q^{40} -1.46352 q^{41} -2.23399 q^{43} +3.36491 q^{44} -2.72132 q^{45} -1.07836 q^{46} -8.70864 q^{47} -1.00000 q^{48} -2.40556 q^{50} +0.683933 q^{51} -6.56984 q^{52} -6.07477 q^{53} +1.00000 q^{54} -9.15698 q^{55} -1.00000 q^{57} +1.51236 q^{58} -10.7094 q^{59} +2.72132 q^{60} +7.84450 q^{61} -0.107111 q^{62} +1.00000 q^{64} +17.8786 q^{65} +3.36491 q^{66} -8.33214 q^{67} -0.683933 q^{68} -1.07836 q^{69} -4.27106 q^{71} -1.00000 q^{72} +8.19334 q^{73} -6.09488 q^{74} -2.40556 q^{75} +1.00000 q^{76} -6.56984 q^{78} +7.69257 q^{79} -2.72132 q^{80} +1.00000 q^{81} +1.46352 q^{82} -1.95981 q^{83} +1.86120 q^{85} +2.23399 q^{86} +1.51236 q^{87} -3.36491 q^{88} +7.93969 q^{89} +2.72132 q^{90} +1.07836 q^{92} -0.107111 q^{93} +8.70864 q^{94} -2.72132 q^{95} +1.00000 q^{96} -12.6700 q^{97} +3.36491 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} + 6 q^{6} - 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 + 6 * q^6 - 6 * q^8 + 6 * q^9	\( 6 q - 6 q^{2} - 6 q^{3} + 6 q^{4} + 6 q^{6} - 6 q^{8} + 6 q^{9} + 4 q^{11} - 6 q^{12} + 6 q^{16} - 4 q^{17} - 6 q^{18} + 6 q^{19} - 4 q^{22} + 16 q^{23} + 6 q^{24} + 10 q^{25} - 6 q^{27} + 8 q^{29} - 6 q^{32} - 4 q^{33} + 4 q^{34} + 6 q^{36} - 6 q^{38} - 8 q^{41} + 8 q^{43} + 4 q^{44} - 16 q^{46} - 16 q^{47} - 6 q^{48} - 10 q^{50} + 4 q^{51} - 4 q^{53} + 6 q^{54} + 32 q^{55} - 6 q^{57} - 8 q^{58} - 24 q^{59} + 6 q^{64} + 16 q^{65} + 4 q^{66} - 20 q^{67} - 4 q^{68} - 16 q^{69} + 24 q^{71} - 6 q^{72} + 16 q^{73} - 10 q^{75} + 6 q^{76} + 40 q^{79} + 6 q^{81} + 8 q^{82} - 24 q^{83} + 8 q^{85} - 8 q^{86} - 8 q^{87} - 4 q^{88} - 24 q^{89} + 16 q^{92} + 16 q^{94} + 6 q^{96} + 4 q^{97} + 4 q^{99}+O(q^{100}) \) 6 * q - 6 * q^2 - 6 * q^3 + 6 * q^4 + 6 * q^6 - 6 * q^8 + 6 * q^9 + 4 * q^11 - 6 * q^12 + 6 * q^16 - 4 * q^17 - 6 * q^18 + 6 * q^19 - 4 * q^22 + 16 * q^23 + 6 * q^24 + 10 * q^25 - 6 * q^27 + 8 * q^29 - 6 * q^32 - 4 * q^33 + 4 * q^34 + 6 * q^36 - 6 * q^38 - 8 * q^41 + 8 * q^43 + 4 * q^44 - 16 * q^46 - 16 * q^47 - 6 * q^48 - 10 * q^50 + 4 * q^51 - 4 * q^53 + 6 * q^54 + 32 * q^55 - 6 * q^57 - 8 * q^58 - 24 * q^59 + 6 * q^64 + 16 * q^65 + 4 * q^66 - 20 * q^67 - 4 * q^68 - 16 * q^69 + 24 * q^71 - 6 * q^72 + 16 * q^73 - 10 * q^75 + 6 * q^76 + 40 * q^79 + 6 * q^81 + 8 * q^82 - 24 * q^83 + 8 * q^85 - 8 * q^86 - 8 * q^87 - 4 * q^88 - 24 * q^89 + 16 * q^92 + 16 * q^94 + 6 * q^96 + 4 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

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Database

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