LMFDB - Embedded newform 5586.2.a.bz.1.3

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:	$1$
Dimension:	$4$
Coefficient field:	4.4.29268.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 9x^{2} + 5x + 16 $ x^4 - x^3 - 9x^2 + 5x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 798)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.25548$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.14924 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.14924 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -1.14924 q^{10} -2.16830 q^{11} +1.00000 q^{12} -2.29847 q^{13} +1.14924 q^{15} +1.00000 q^{16} +4.99679 q^{17} -1.00000 q^{18} -1.00000 q^{19} +1.14924 q^{20} +2.16830 q^{22} -6.91567 q^{23} -1.00000 q^{24} -3.67925 q^{25} +2.29847 q^{26} +1.00000 q^{27} +3.76643 q^{29} -1.14924 q^{30} -4.38565 q^{31} -1.00000 q^{32} -2.16830 q^{33} -4.99679 q^{34} +1.00000 q^{36} +0.660191 q^{37} +1.00000 q^{38} -2.29847 q^{39} -1.14924 q^{40} -0.806583 q^{41} -2.08397 q^{43} -2.16830 q^{44} +1.14924 q^{45} +6.91567 q^{46} +3.72225 q^{47} +1.00000 q^{48} +3.67925 q^{50} +4.99679 q^{51} -2.29847 q^{52} -11.2713 q^{53} -1.00000 q^{54} -2.49189 q^{55} -1.00000 q^{57} -3.76643 q^{58} -10.4266 q^{59} +1.14924 q^{60} -2.57622 q^{61} +4.38565 q^{62} +1.00000 q^{64} -2.64149 q^{65} +2.16830 q^{66} +8.88568 q^{67} +4.99679 q^{68} -6.91567 q^{69} -0.323591 q^{71} -1.00000 q^{72} +4.72830 q^{73} -0.660191 q^{74} -3.67925 q^{75} -1.00000 q^{76} +2.29847 q^{78} -7.59208 q^{79} +1.14924 q^{80} +1.00000 q^{81} +0.806583 q^{82} -3.17435 q^{83} +5.74250 q^{85} +2.08397 q^{86} +3.76643 q^{87} +2.16830 q^{88} -12.3776 q^{89} -1.14924 q^{90} -6.91567 q^{92} -4.38565 q^{93} -3.72225 q^{94} -1.14924 q^{95} -1.00000 q^{96} +5.91567 q^{97} -2.16830 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^6 - 4 * q^8 + 4 * q^9	$ 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{8} + 4 q^{9} - 2 q^{11} + 4 q^{12} + 4 q^{16} - 10 q^{17} - 4 q^{18} - 4 q^{19} + 2 q^{22} - 5 q^{23} - 4 q^{24} + 4 q^{25} + 4 q^{27} - 3 q^{29} - 9 q^{31} - 4 q^{32} - 2 q^{33} + 10 q^{34} + 4 q^{36} - 14 q^{37} + 4 q^{38} - 4 q^{41} + 21 q^{43} - 2 q^{44} + 5 q^{46} - 7 q^{47} + 4 q^{48} - 4 q^{50} - 10 q^{51} - 7 q^{53} - 4 q^{54} - 4 q^{57} + 3 q^{58} - 7 q^{59} - 23 q^{61} + 9 q^{62} + 4 q^{64} - 48 q^{65} + 2 q^{66} + 6 q^{67} - 10 q^{68} - 5 q^{69} + 2 q^{71} - 4 q^{72} + 5 q^{73} + 14 q^{74} + 4 q^{75} - 4 q^{76} - 11 q^{79} + 4 q^{81} + 4 q^{82} - 14 q^{83} + 6 q^{85} - 21 q^{86} - 3 q^{87} + 2 q^{88} - 10 q^{89} - 5 q^{92} - 9 q^{93} + 7 q^{94} - 4 q^{96} + q^{97} - 2 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^6 - 4 * q^8 + 4 * q^9 - 2 * q^11 + 4 * q^12 + 4 * q^16 - 10 * q^17 - 4 * q^18 - 4 * q^19 + 2 * q^22 - 5 * q^23 - 4 * q^24 + 4 * q^25 + 4 * q^27 - 3 * q^29 - 9 * q^31 - 4 * q^32 - 2 * q^33 + 10 * q^34 + 4 * q^36 - 14 * q^37 + 4 * q^38 - 4 * q^41 + 21 * q^43 - 2 * q^44 + 5 * q^46 - 7 * q^47 + 4 * q^48 - 4 * q^50 - 10 * q^51 - 7 * q^53 - 4 * q^54 - 4 * q^57 + 3 * q^58 - 7 * q^59 - 23 * q^61 + 9 * q^62 + 4 * q^64 - 48 * q^65 + 2 * q^66 + 6 * q^67 - 10 * q^68 - 5 * q^69 + 2 * q^71 - 4 * q^72 + 5 * q^73 + 14 * q^74 + 4 * q^75 - 4 * q^76 - 11 * q^79 + 4 * q^81 + 4 * q^82 - 14 * q^83 + 6 * q^85 - 21 * q^86 - 3 * q^87 + 2 * q^88 - 10 * q^89 - 5 * q^92 - 9 * q^93 + 7 * q^94 - 4 * q^96 + q^97 - 2 * 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
$5$	1.14924	0.513954	0.256977	−	0.966417i	$-0.417273\pi$
$5$	1.14924	0.513954	0.256977	+	0.966417i	$0.417273\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.14924	−0.363421
$11$	−2.16830	−0.653767	−0.326884	−	0.945065i	$-0.605998\pi$
$11$	−2.16830	−0.653767	−0.326884	+	0.945065i	$0.605998\pi$
$12$	1.00000	0.288675
$13$	−2.29847	−0.637482	−0.318741	−	0.947842i	$-0.603260\pi$
$13$	−2.29847	−0.637482	−0.318741	+	0.947842i	$0.603260\pi$
$14$	0	0
$15$	1.14924	0.296732
$16$	1.00000	0.250000
$17$	4.99679	1.21190	0.605950	−	0.795503i	$-0.292793\pi$
$17$	4.99679	1.21190	0.605950	+	0.795503i	$0.292793\pi$
$18$	−1.00000	−0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	1.14924	0.256977
$21$	0	0
$22$	2.16830	0.462283
$23$	−6.91567	−1.44202	−0.721008	−	0.692926i	$-0.756321\pi$
$23$	−6.91567	−1.44202	−0.721008	+	0.692926i	$0.756321\pi$
$24$	−1.00000	−0.204124
$25$	−3.67925	−0.735851
$26$	2.29847	0.450768
$27$	1.00000	0.192450
$28$	0	0
$29$	3.76643	0.699409	0.349704	−	0.936860i	$-0.386282\pi$
$29$	3.76643	0.699409	0.349704	+	0.936860i	$0.386282\pi$
$30$	−1.14924	−0.209821
$31$	−4.38565	−0.787686	−0.393843	−	0.919178i	$-0.628855\pi$
$31$	−4.38565	−0.787686	−0.393843	+	0.919178i	$0.628855\pi$
$32$	−1.00000	−0.176777
$33$	−2.16830	−0.377453
$34$	−4.99679	−0.856943
$35$	0	0
$36$	1.00000	0.166667
$37$	0.660191	0.108535	0.0542674	−	0.998526i	$-0.482718\pi$
$37$	0.660191	0.108535	0.0542674	+	0.998526i	$0.482718\pi$
$38$	1.00000	0.162221
$39$	−2.29847	−0.368050
$40$	−1.14924	−0.181710
$41$	−0.806583	−0.125967	−0.0629836	−	0.998015i	$-0.520062\pi$
$41$	−0.806583	−0.125967	−0.0629836	+	0.998015i	$0.520062\pi$
$42$	0	0
$43$	−2.08397	−0.317802	−0.158901	−	0.987295i	$-0.550795\pi$
$43$	−2.08397	−0.317802	−0.158901	+	0.987295i	$0.550795\pi$
$44$	−2.16830	−0.326884
$45$	1.14924	0.171318
$46$	6.91567	1.01966
$47$	3.72225	0.542946	0.271473	−	0.962446i	$-0.412489\pi$
$47$	3.72225	0.542946	0.271473	+	0.962446i	$0.412489\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	3.67925	0.520325
$51$	4.99679	0.699691
$52$	−2.29847	−0.318741
$53$	−11.2713	−1.54824	−0.774118	−	0.633041i	$-0.781806\pi$
$53$	−11.2713	−1.54824	−0.774118	+	0.633041i	$0.781806\pi$
$54$	−1.00000	−0.136083
$55$	−2.49189	−0.336006
$56$	0	0
$57$	−1.00000	−0.132453
$58$	−3.76643	−0.494557
$59$	−10.4266	−1.35743	−0.678715	−	0.734401i	$-0.737463\pi$
$59$	−10.4266	−1.35743	−0.678715	+	0.734401i	$0.737463\pi$
$60$	1.14924	0.148366
$61$	−2.57622	−0.329852	−0.164926	−	0.986306i	$-0.552738\pi$
$61$	−2.57622	−0.329852	−0.164926	+	0.986306i	$0.552738\pi$
$62$	4.38565	0.556978
$63$	0	0
$64$	1.00000	0.125000
$65$	−2.64149	−0.327637
$66$	2.16830	0.266899
$67$	8.88568	1.08556	0.542779	−	0.839875i	$-0.317372\pi$
$67$	8.88568	1.08556	0.542779	+	0.839875i	$0.317372\pi$
$68$	4.99679	0.605950
$69$	−6.91567	−0.832549
$70$	0	0
$71$	−0.323591	−0.0384031	−0.0192016	−	0.999816i	$-0.506112\pi$
$71$	−0.323591	−0.0384031	−0.0192016	+	0.999816i	$0.506112\pi$
$72$	−1.00000	−0.117851
$73$	4.72830	0.553406	0.276703	−	0.960955i	$-0.410758\pi$
$73$	4.72830	0.553406	0.276703	+	0.960955i	$0.410758\pi$
$74$	−0.660191	−0.0767457
$75$	−3.67925	−0.424844
$76$	−1.00000	−0.114708
$77$	0	0
$78$	2.29847	0.260251
$79$	−7.59208	−0.854175	−0.427088	−	0.904210i	$-0.640460\pi$
$79$	−7.59208	−0.854175	−0.427088	+	0.904210i	$0.640460\pi$
$80$	1.14924	0.128489
$81$	1.00000	0.111111
$82$	0.806583	0.0890722
$83$	−3.17435	−0.348431	−0.174215	−	0.984708i	$-0.555739\pi$
$83$	−3.17435	−0.348431	−0.174215	+	0.984708i	$0.555739\pi$
$84$	0	0
$85$	5.74250	0.622861
$86$	2.08397	0.224720
$87$	3.76643	0.403804
$88$	2.16830	0.231142
$89$	−12.3776	−1.31202	−0.656010	−	0.754752i	$-0.727757\pi$
$89$	−12.3776	−1.31202	−0.656010	+	0.754752i	$0.727757\pi$
$90$	−1.14924	−0.121140
$91$	0	0
$92$	−6.91567	−0.721008
$93$	−4.38565	−0.454771
$94$	−3.72225	−0.383921
$95$	−1.14924	−0.117909
$96$	−1.00000	−0.102062
$97$	5.91567	0.600645	0.300323	−	0.953838i	$-0.402906\pi$
$97$	5.91567	0.600645	0.300323	+	0.953838i	$0.402906\pi$
$98$	0	0
$99$	−2.16830	−0.217922
$100$	−3.67925	−0.367925
$101$	12.8683	1.28044	0.640221	−	0.768191i	$-0.278843\pi$
$101$	12.8683	1.28044	0.640221	+	0.768191i	$0.278843\pi$
$102$	−4.99679	−0.494756
$103$	−6.95582	−0.685377	−0.342689	−	0.939449i	$-0.611338\pi$
$103$	−6.95582	−0.685377	−0.342689	+	0.939449i	$0.611338\pi$
$104$	2.29847	0.225384
$105$	0	0
$106$	11.2713	1.09477
$107$	−12.3987	−1.19862	−0.599312	−	0.800516i	$-0.704559\pi$
$107$	−12.3987	−1.19862	−0.599312	+	0.800516i	$0.704559\pi$
$108$	1.00000	0.0962250
$109$	18.0568	1.72953	0.864765	−	0.502176i	$-0.167467\pi$
$109$	18.0568	1.72953	0.864765	+	0.502176i	$0.167467\pi$
$110$	2.49189	0.237592
$111$	0.660191	0.0626626
$112$	0	0
$113$	−8.63792	−0.812587	−0.406294	−	0.913743i	$-0.633179\pi$
$113$	−8.63792	−0.812587	−0.406294	+	0.913743i	$0.633179\pi$
$114$	1.00000	0.0936586
$115$	−7.94774	−0.741131
$116$	3.76643	0.349704
$117$	−2.29847	−0.212494
$118$	10.4266	0.959848
$119$	0	0
$120$	−1.14924	−0.104911
$121$	−6.29847	−0.572589
$122$	2.57622	0.233240
$123$	−0.806583	−0.0727271
$124$	−4.38565	−0.393843
$125$	−9.97452	−0.892148
$126$	0	0
$127$	−13.8683	−1.23061	−0.615305	−	0.788289i	$-0.710967\pi$
$127$	−13.8683	−1.23061	−0.615305	+	0.788289i	$0.710967\pi$
$128$	−1.00000	−0.0883883
$129$	−2.08397	−0.183483
$130$	2.64149	0.231674
$131$	−12.2113	−1.06691	−0.533453	−	0.845830i	$-0.679106\pi$
$131$	−12.2113	−1.06691	−0.533453	+	0.845830i	$0.679106\pi$
$132$	−2.16830	−0.188726
$133$	0	0
$134$	−8.88568	−0.767606
$135$	1.14924	0.0989106
$136$	−4.99679	−0.428471
$137$	11.0808	0.946693	0.473347	−	0.880876i	$-0.343046\pi$
$137$	11.0808	0.946693	0.473347	+	0.880876i	$0.343046\pi$
$138$	6.91567	0.588701
$139$	11.0175	0.934494	0.467247	−	0.884127i	$-0.345246\pi$
$139$	11.0175	0.934494	0.467247	+	0.884127i	$0.345246\pi$
$140$	0	0
$141$	3.72225	0.313470
$142$	0.323591	0.0271551
$143$	4.98378	0.416765
$144$	1.00000	0.0833333
$145$	4.32852	0.359464
$146$	−4.72830	−0.391317
$147$	0	0
$148$	0.660191	0.0542674
$149$	−21.2170	−1.73816	−0.869082	−	0.494669i	$-0.835289\pi$
$149$	−21.2170	−1.73816	−0.869082	+	0.494669i	$0.835289\pi$
$150$	3.67925	0.300410
$151$	9.40187	0.765113	0.382557	−	0.923932i	$-0.375044\pi$
$151$	9.40187	0.765113	0.382557	+	0.923932i	$0.375044\pi$
$152$	1.00000	0.0811107
$153$	4.99679	0.403967
$154$	0	0
$155$	−5.04015	−0.404835
$156$	−2.29847	−0.184025
$157$	−6.14721	−0.490601	−0.245300	−	0.969447i	$-0.578887\pi$
$157$	−6.14721	−0.490601	−0.245300	+	0.969447i	$0.578887\pi$
$158$	7.59208	0.603993
$159$	−11.2713	−0.893875
$160$	−1.14924	−0.0908552
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	−8.60793	−0.674225	−0.337113	−	0.941464i	$-0.609450\pi$
$163$	−8.60793	−0.674225	−0.337113	+	0.941464i	$0.609450\pi$
$164$	−0.806583	−0.0629836
$165$	−2.49189	−0.193993
$166$	3.17435	0.246378
$167$	−11.9749	−0.926644	−0.463322	−	0.886190i	$-0.653343\pi$
$167$	−11.9749	−0.926644	−0.463322	+	0.886190i	$0.653343\pi$
$168$	0	0
$169$	−7.71702	−0.593617
$170$	−5.74250	−0.440429
$171$	−1.00000	−0.0764719
$172$	−2.08397	−0.158901
$173$	−8.10185	−0.615972	−0.307986	−	0.951391i	$-0.599655\pi$
$173$	−8.10185	−0.615972	−0.307986	+	0.951391i	$0.599655\pi$
$174$	−3.76643	−0.285532
$175$	0	0
$176$	−2.16830	−0.163442
$177$	−10.4266	−0.783713
$178$	12.3776	0.927738
$179$	−6.84755	−0.511810	−0.255905	−	0.966702i	$-0.582373\pi$
$179$	−6.84755	−0.511810	−0.255905	+	0.966702i	$0.582373\pi$
$180$	1.14924	0.0856591
$181$	16.5905	1.23316	0.616582	−	0.787291i	$-0.288517\pi$
$181$	16.5905	1.23316	0.616582	+	0.787291i	$0.288517\pi$
$182$	0	0
$183$	−2.57622	−0.190440
$184$	6.91567	0.509830
$185$	0.758716	0.0557819
$186$	4.38565	0.321572
$187$	−10.8345	−0.792300
$188$	3.72225	0.271473
$189$	0	0
$190$	1.14924	0.0833744
$191$	15.8902	1.14977	0.574887	−	0.818233i	$-0.305046\pi$
$191$	15.8902	1.14977	0.574887	+	0.818233i	$0.305046\pi$
$192$	1.00000	0.0721688
$193$	6.49676	0.467647	0.233824	−	0.972279i	$-0.424876\pi$
$193$	6.49676	0.467647	0.233824	+	0.972279i	$0.424876\pi$
$194$	−5.91567	−0.424720
$195$	−2.64149	−0.189161
$196$	0	0
$197$	1.06491	0.0758713	0.0379357	−	0.999280i	$-0.487922\pi$
$197$	1.06491	0.0758713	0.0379357	+	0.999280i	$0.487922\pi$
$198$	2.16830	0.154094
$199$	−23.5917	−1.67237	−0.836186	−	0.548446i	$-0.815220\pi$
$199$	−23.5917	−1.67237	−0.836186	+	0.548446i	$0.815220\pi$
$200$	3.67925	0.260163
$201$	8.88568	0.626748
$202$	−12.8683	−0.905409
$203$	0	0
$204$	4.99679	0.349845
$205$	−0.926955	−0.0647414
$206$	6.95582	0.484635
$207$	−6.91567	−0.480672
$208$	−2.29847	−0.159370
$209$	2.16830	0.149984
$210$	0	0
$211$	17.8699	1.23022	0.615109	−	0.788442i	$-0.289112\pi$
$211$	17.8699	1.23022	0.615109	+	0.788442i	$0.289112\pi$
$212$	−11.2713	−0.774118
$213$	−0.323591	−0.0221721
$214$	12.3987	0.847555
$215$	−2.39497	−0.163336
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−18.0568	−1.22296
$219$	4.72830	0.319509
$220$	−2.49189	−0.168003
$221$	−11.4850	−0.772564
$222$	−0.660191	−0.0443091
$223$	−4.44605	−0.297729	−0.148865	−	0.988858i	$-0.547562\pi$
$223$	−4.44605	−0.297729	−0.148865	+	0.988858i	$0.547562\pi$
$224$	0	0
$225$	−3.67925	−0.245284
$226$	8.63792	0.574586
$227$	−20.0938	−1.33367	−0.666835	−	0.745205i	$-0.732351\pi$
$227$	−20.0938	−1.33367	−0.666835	+	0.745205i	$0.732351\pi$
$228$	−1.00000	−0.0662266
$229$	−17.9555	−1.18653	−0.593265	−	0.805007i	$-0.702161\pi$
$229$	−17.9555	−1.18653	−0.593265	+	0.805007i	$0.702161\pi$
$230$	7.94774	0.524059
$231$	0	0
$232$	−3.76643	−0.247278
$233$	10.2539	0.671757	0.335879	−	0.941905i	$-0.390967\pi$
$233$	10.2539	0.671757	0.335879	+	0.941905i	$0.390967\pi$
$234$	2.29847	0.150256
$235$	4.27775	0.279050
$236$	−10.4266	−0.678715
$237$	−7.59208	−0.493158
$238$	0	0
$239$	1.73965	0.112529	0.0562644	−	0.998416i	$-0.482081\pi$
$239$	1.73965	0.112529	0.0562644	+	0.998416i	$0.482081\pi$
$240$	1.14924	0.0741829
$241$	20.8492	1.34302	0.671508	−	0.740997i	$-0.265647\pi$
$241$	20.8492	1.34302	0.671508	+	0.740997i	$0.265647\pi$
$242$	6.29847	0.404881
$243$	1.00000	0.0641500
$244$	−2.57622	−0.164926
$245$	0	0
$246$	0.806583	0.0514259
$247$	2.29847	0.146248
$248$	4.38565	0.278489
$249$	−3.17435	−0.201166
$250$	9.97452	0.630844
$251$	−3.19663	−0.201769	−0.100885	−	0.994898i	$-0.532167\pi$
$251$	−3.19663	−0.201769	−0.100885	+	0.994898i	$0.532167\pi$
$252$	0	0
$253$	14.9952	0.942743
$254$	13.8683	0.870173
$255$	5.74250	0.359609
$256$	1.00000	0.0625000
$257$	15.0219	0.937041	0.468520	−	0.883453i	$-0.344787\pi$
$257$	15.0219	0.937041	0.468520	+	0.883453i	$0.344787\pi$
$258$	2.08397	0.129742
$259$	0	0
$260$	−2.64149	−0.163818
$261$	3.76643	0.233136
$262$	12.2113	0.754416
$263$	10.6760	0.658313	0.329157	−	0.944275i	$-0.393236\pi$
$263$	10.6760	0.658313	0.329157	+	0.944275i	$0.393236\pi$
$264$	2.16830	0.133450
$265$	−12.9534	−0.795723
$266$	0	0
$267$	−12.3776	−0.757495
$268$	8.88568	0.542779
$269$	3.24906	0.198099	0.0990494	−	0.995083i	$-0.468420\pi$
$269$	3.24906	0.198099	0.0990494	+	0.995083i	$0.468420\pi$
$270$	−1.14924	−0.0699403
$271$	−18.0349	−1.09554	−0.547772	−	0.836628i	$-0.684524\pi$
$271$	−18.0349	−1.09554	−0.547772	+	0.836628i	$0.684524\pi$
$272$	4.99679	0.302975
$273$	0	0
$274$	−11.0808	−0.669413
$275$	7.97773	0.481075
$276$	−6.91567	−0.416274
$277$	22.2839	1.33891	0.669455	−	0.742852i	$-0.266528\pi$
$277$	22.2839	1.33891	0.669455	+	0.742852i	$0.266528\pi$
$278$	−11.0175	−0.660787
$279$	−4.38565	−0.262562
$280$	0	0
$281$	7.10790	0.424022	0.212011	−	0.977267i	$-0.431999\pi$
$281$	7.10790	0.424022	0.212011	+	0.977267i	$0.431999\pi$
$282$	−3.72225	−0.221657
$283$	15.7474	0.936084	0.468042	−	0.883706i	$-0.344960\pi$
$283$	15.7474	0.936084	0.468042	+	0.883706i	$0.344960\pi$
$284$	−0.323591	−0.0192016
$285$	−1.14924	−0.0680749
$286$	−4.98378	−0.294697
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	7.96793	0.468702
$290$	−4.32852	−0.254180
$291$	5.91567	0.346783
$292$	4.72830	0.276703
$293$	−22.0139	−1.28607	−0.643034	−	0.765837i	$-0.722325\pi$
$293$	−22.0139	−1.28607	−0.643034	+	0.765837i	$0.722325\pi$
$294$	0	0
$295$	−11.9827	−0.697657
$296$	−0.660191	−0.0383728
$297$	−2.16830	−0.125818
$298$	21.2170	1.22907
$299$	15.8955	0.919260
$300$	−3.67925	−0.212422
$301$	0	0
$302$	−9.40187	−0.541017
$303$	12.8683	0.739263
$304$	−1.00000	−0.0573539
$305$	−2.96069	−0.169529
$306$	−4.99679	−0.285648
$307$	−14.3776	−0.820571	−0.410286	−	0.911957i	$-0.634571\pi$
$307$	−14.3776	−0.820571	−0.410286	+	0.911957i	$0.634571\pi$
$308$	0	0
$309$	−6.95582	−0.395703
$310$	5.04015	0.286261
$311$	2.97452	0.168670	0.0843348	−	0.996437i	$-0.473123\pi$
$311$	2.97452	0.168670	0.0843348	+	0.996437i	$0.473123\pi$
$312$	2.29847	0.130125
$313$	16.7588	0.947265	0.473633	−	0.880723i	$-0.342942\pi$
$313$	16.7588	0.947265	0.473633	+	0.880723i	$0.342942\pi$
$314$	6.14721	0.346907
$315$	0	0
$316$	−7.59208	−0.427088
$317$	−2.81061	−0.157860	−0.0789298	−	0.996880i	$-0.525150\pi$
$317$	−2.81061	−0.157860	−0.0789298	+	0.996880i	$0.525150\pi$
$318$	11.2713	0.632065
$319$	−8.16675	−0.457250
$320$	1.14924	0.0642443
$321$	−12.3987	−0.692026
$322$	0	0
$323$	−4.99679	−0.278029
$324$	1.00000	0.0555556
$325$	8.45667	0.469092
$326$	8.60793	0.476749
$327$	18.0568	0.998545
$328$	0.806583	0.0445361
$329$	0	0
$330$	2.49189	0.137174
$331$	−10.1391	−0.557294	−0.278647	−	0.960394i	$-0.589886\pi$
$331$	−10.1391	−0.557294	−0.278647	+	0.960394i	$0.589886\pi$
$332$	−3.17435	−0.174215
$333$	0.660191	0.0361782
$334$	11.9749	0.655236
$335$	10.2118	0.557928
$336$	0	0
$337$	21.4364	1.16772	0.583858	−	0.811856i	$-0.301542\pi$
$337$	21.4364	1.16772	0.583858	+	0.811856i	$0.301542\pi$
$338$	7.71702	0.419750
$339$	−8.63792	−0.469147
$340$	5.74250	0.311431
$341$	9.50941	0.514963
$342$	1.00000	0.0540738
$343$	0	0
$344$	2.08397	0.112360
$345$	−7.94774	−0.427892
$346$	8.10185	0.435558
$347$	29.1826	1.56660	0.783302	−	0.621641i	$-0.213534\pi$
$347$	29.1826	1.56660	0.783302	+	0.621641i	$0.213534\pi$
$348$	3.76643	0.201902
$349$	−9.36208	−0.501141	−0.250570	−	0.968098i	$-0.580618\pi$
$349$	−9.36208	−0.501141	−0.250570	+	0.968098i	$0.580618\pi$
$350$	0	0
$351$	−2.29847	−0.122683
$352$	2.16830	0.115571
$353$	−33.5994	−1.78832	−0.894159	−	0.447750i	$-0.852225\pi$
$353$	−33.5994	−1.78832	−0.894159	+	0.447750i	$0.852225\pi$
$354$	10.4266	0.554169
$355$	−0.371882	−0.0197375
$356$	−12.3776	−0.656010
$357$	0	0
$358$	6.84755	0.361905
$359$	−24.3630	−1.28583	−0.642915	−	0.765937i	$-0.722275\pi$
$359$	−24.3630	−1.28583	−0.642915	+	0.765937i	$0.722275\pi$
$360$	−1.14924	−0.0605701
$361$	1.00000	0.0526316
$362$	−16.5905	−0.871979
$363$	−6.29847	−0.330584
$364$	0	0
$365$	5.43394	0.284426
$366$	2.57622	0.134661
$367$	33.1571	1.73079	0.865394	−	0.501092i	$-0.167068\pi$
$367$	33.1571	1.73079	0.865394	+	0.501092i	$0.167068\pi$
$368$	−6.91567	−0.360504
$369$	−0.806583	−0.0419890
$370$	−0.758716	−0.0394438
$371$	0	0
$372$	−4.38565	−0.227385
$373$	−22.5460	−1.16739	−0.583693	−	0.811974i	$-0.698393\pi$
$373$	−22.5460	−1.16739	−0.583693	+	0.811974i	$0.698393\pi$
$374$	10.8345	0.560241
$375$	−9.97452	−0.515082
$376$	−3.72225	−0.191960
$377$	−8.65704	−0.445860
$378$	0	0
$379$	18.7616	0.963717	0.481858	−	0.876249i	$-0.339962\pi$
$379$	18.7616	0.963717	0.481858	+	0.876249i	$0.339962\pi$
$380$	−1.14924	−0.0589546
$381$	−13.8683	−0.710494
$382$	−15.8902	−0.813013
$383$	8.11770	0.414795	0.207398	−	0.978257i	$-0.433501\pi$
$383$	8.11770	0.414795	0.207398	+	0.978257i	$0.433501\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−6.49676	−0.330676
$387$	−2.08397	−0.105934
$388$	5.91567	0.300323
$389$	−35.0034	−1.77474	−0.887371	−	0.461056i	$-0.847471\pi$
$389$	−35.0034	−1.77474	−0.887371	+	0.461056i	$0.847471\pi$
$390$	2.64149	0.133757
$391$	−34.5562	−1.74758
$392$	0	0
$393$	−12.2113	−0.615978
$394$	−1.06491	−0.0536491
$395$	−8.72510	−0.439007
$396$	−2.16830	−0.108961
$397$	−15.0219	−0.753928	−0.376964	−	0.926228i	$-0.623032\pi$
$397$	−15.0219	−0.753928	−0.376964	+	0.926228i	$0.623032\pi$
$398$	23.5917	1.18255
$399$	0	0
$400$	−3.67925	−0.183963
$401$	−26.6287	−1.32977	−0.664886	−	0.746945i	$-0.731520\pi$
$401$	−26.6287	−1.32977	−0.664886	+	0.746945i	$0.731520\pi$
$402$	−8.88568	−0.443178
$403$	10.0803	0.502136
$404$	12.8683	0.640221
$405$	1.14924	0.0571060
$406$	0	0
$407$	−1.43149	−0.0709565
$408$	−4.99679	−0.247378
$409$	−27.6489	−1.36715	−0.683575	−	0.729880i	$-0.739576\pi$
$409$	−27.6489	−1.36715	−0.683575	+	0.729880i	$0.739576\pi$
$410$	0.926955	0.0457791
$411$	11.0808	0.546574
$412$	−6.95582	−0.342689
$413$	0	0
$414$	6.91567	0.339887
$415$	−3.64808	−0.179077
$416$	2.29847	0.112692
$417$	11.0175	0.539530
$418$	−2.16830	−0.106055
$419$	−1.91888	−0.0937433	−0.0468716	−	0.998901i	$-0.514925\pi$
$419$	−1.91888	−0.0937433	−0.0468716	+	0.998901i	$0.514925\pi$
$420$	0	0
$421$	25.9815	1.26626	0.633130	−	0.774046i	$-0.281770\pi$
$421$	25.9815	1.26626	0.633130	+	0.774046i	$0.281770\pi$
$422$	−17.8699	−0.869895
$423$	3.72225	0.180982
$424$	11.2713	0.547384
$425$	−18.3845	−0.891778
$426$	0.323591	0.0156780
$427$	0	0
$428$	−12.3987	−0.599312
$429$	4.98378	0.240619
$430$	2.39497	0.115496
$431$	0.965082	0.0464864	0.0232432	−	0.999730i	$-0.492601\pi$
$431$	0.965082	0.0464864	0.0232432	+	0.999730i	$0.492601\pi$
$432$	1.00000	0.0481125
$433$	5.93960	0.285439	0.142720	−	0.989763i	$-0.454415\pi$
$433$	5.93960	0.285439	0.142720	+	0.989763i	$0.454415\pi$
$434$	0	0
$435$	4.32852	0.207537
$436$	18.0568	0.864765
$437$	6.91567	0.330821
$438$	−4.72830	−0.225927
$439$	−21.5921	−1.03053	−0.515267	−	0.857030i	$-0.672307\pi$
$439$	−21.5921	−1.03053	−0.515267	+	0.857030i	$0.672307\pi$
$440$	2.49189	0.118796
$441$	0	0
$442$	11.4850	0.546286
$443$	13.9344	0.662042	0.331021	−	0.943623i	$-0.392607\pi$
$443$	13.9344	0.662042	0.331021	+	0.943623i	$0.392607\pi$
$444$	0.660191	0.0313313
$445$	−14.2248	−0.674318
$446$	4.44605	0.210527
$447$	−21.2170	−1.00353
$448$	0	0
$449$	14.3273	0.676149	0.338074	−	0.941119i	$-0.390224\pi$
$449$	14.3273	0.676149	0.338074	+	0.941119i	$0.390224\pi$
$450$	3.67925	0.173442
$451$	1.74891	0.0823532
$452$	−8.63792	−0.406294
$453$	9.40187	0.441738
$454$	20.0938	0.943047
$455$	0	0
$456$	1.00000	0.0468293
$457$	32.2981	1.51084	0.755421	−	0.655240i	$-0.227432\pi$
$457$	32.2981	1.51084	0.755421	+	0.655240i	$0.227432\pi$
$458$	17.9555	0.839003
$459$	4.99679	0.233230
$460$	−7.94774	−0.370565
$461$	−0.375849	−0.0175050	−0.00875252	−	0.999962i	$-0.502786\pi$
$461$	−0.375849	−0.0175050	−0.00875252	+	0.999962i	$0.502786\pi$
$462$	0	0
$463$	7.80824	0.362880	0.181440	−	0.983402i	$-0.441924\pi$
$463$	7.80824	0.362880	0.181440	+	0.983402i	$0.441924\pi$
$464$	3.76643	0.174852
$465$	−5.04015	−0.233731
$466$	−10.2539	−0.475004
$467$	12.2555	0.567116	0.283558	−	0.958955i	$-0.408485\pi$
$467$	12.2555	0.567116	0.283558	+	0.958955i	$0.408485\pi$
$468$	−2.29847	−0.106247
$469$	0	0
$470$	−4.27775	−0.197318
$471$	−6.14721	−0.283249
$472$	10.4266	0.479924
$473$	4.51867	0.207769
$474$	7.59208	0.348716
$475$	3.67925	0.168816
$476$	0	0
$477$	−11.2713	−0.516079
$478$	−1.73965	−0.0795699
$479$	−27.0751	−1.23709	−0.618546	−	0.785749i	$-0.712278\pi$
$479$	−27.0751	−1.23709	−0.618546	+	0.785749i	$0.712278\pi$
$480$	−1.14924	−0.0524553
$481$	−1.51743	−0.0691889
$482$	−20.8492	−0.949656
$483$	0	0
$484$	−6.29847	−0.286294
$485$	6.79850	0.308704
$486$	−1.00000	−0.0453609
$487$	29.7498	1.34809	0.674047	−	0.738688i	$-0.264554\pi$
$487$	29.7498	1.34809	0.674047	+	0.738688i	$0.264554\pi$
$488$	2.57622	0.116620
$489$	−8.60793	−0.389264
$490$	0	0
$491$	18.4381	0.832099	0.416050	−	0.909342i	$-0.363414\pi$
$491$	18.4381	0.832099	0.416050	+	0.909342i	$0.363414\pi$
$492$	−0.806583	−0.0363636
$493$	18.8201	0.847613
$494$	−2.29847	−0.103413
$495$	−2.49189	−0.112002
$496$	−4.38565	−0.196922
$497$	0	0
$498$	3.17435	0.142246
$499$	33.1570	1.48431	0.742156	−	0.670227i	$-0.233803\pi$
$499$	33.1570	1.48431	0.742156	+	0.670227i	$0.233803\pi$
$500$	−9.97452	−0.446074
$501$	−11.9749	−0.534998
$502$	3.19663	0.142672
$503$	−12.8678	−0.573747	−0.286873	−	0.957968i	$-0.592616\pi$
$503$	−12.8678	−0.573747	−0.286873	+	0.957968i	$0.592616\pi$
$504$	0	0
$505$	14.7887	0.658089
$506$	−14.9952	−0.666620
$507$	−7.71702	−0.342725
$508$	−13.8683	−0.615305
$509$	−8.70235	−0.385725	−0.192862	−	0.981226i	$-0.561777\pi$
$509$	−8.70235	−0.385725	−0.192862	+	0.981226i	$0.561777\pi$
$510$	−5.74250	−0.254282
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	−15.0219	−0.662588
$515$	−7.99389	−0.352253
$516$	−2.08397	−0.0917416
$517$	−8.07096	−0.354960
$518$	0	0
$519$	−8.10185	−0.355632
$520$	2.64149	0.115837
$521$	−37.7965	−1.65590	−0.827948	−	0.560805i	$-0.810492\pi$
$521$	−37.7965	−1.65590	−0.827948	+	0.560805i	$0.810492\pi$
$522$	−3.76643	−0.164852
$523$	−42.3364	−1.85124	−0.925620	−	0.378455i	$-0.876455\pi$
$523$	−42.3364	−1.85124	−0.925620	+	0.378455i	$0.876455\pi$
$524$	−12.2113	−0.533453
$525$	0	0
$526$	−10.6760	−0.465498
$527$	−21.9142	−0.954597
$528$	−2.16830	−0.0943632
$529$	24.8265	1.07941
$530$	12.9534	0.562661
$531$	−10.4266	−0.452477
$532$	0	0
$533$	1.85391	0.0803018
$534$	12.3776	0.535630
$535$	−14.2490	−0.616038
$536$	−8.88568	−0.383803
$537$	−6.84755	−0.295494
$538$	−3.24906	−0.140077
$539$	0	0
$540$	1.14924	0.0494553
$541$	8.01146	0.344440	0.172220	−	0.985059i	$-0.444906\pi$
$541$	8.01146	0.344440	0.172220	+	0.985059i	$0.444906\pi$
$542$	18.0349	0.774666
$543$	16.5905	0.711968
$544$	−4.99679	−0.214236
$545$	20.7516	0.888900
$546$	0	0
$547$	−34.1587	−1.46052	−0.730260	−	0.683170i	$-0.760601\pi$
$547$	−34.1587	−1.46052	−0.730260	+	0.683170i	$0.760601\pi$
$548$	11.0808	0.473347
$549$	−2.57622	−0.109951
$550$	−7.97773	−0.340171
$551$	−3.76643	−0.160455
$552$	6.91567	0.294350
$553$	0	0
$554$	−22.2839	−0.946753
$555$	0.758716	0.0322057
$556$	11.0175	0.467247
$557$	−40.4791	−1.71515	−0.857576	−	0.514357i	$-0.828031\pi$
$557$	−40.4791	−1.71515	−0.857576	+	0.514357i	$0.828031\pi$
$558$	4.38565	0.185659
$559$	4.78995	0.202593
$560$	0	0
$561$	−10.8345	−0.457435
$562$	−7.10790	−0.299829
$563$	−18.2044	−0.767224	−0.383612	−	0.923494i	$-0.625320\pi$
$563$	−18.2044	−0.767224	−0.383612	+	0.923494i	$0.625320\pi$
$564$	3.72225	0.156735
$565$	−9.92702	−0.417633
$566$	−15.7474	−0.661911
$567$	0	0
$568$	0.323591	0.0135776
$569$	−16.0253	−0.671815	−0.335908	−	0.941895i	$-0.609043\pi$
$569$	−16.0253	−0.671815	−0.335908	+	0.941895i	$0.609043\pi$
$570$	1.14924	0.0481362
$571$	7.02630	0.294041	0.147021	−	0.989133i	$-0.453032\pi$
$571$	7.02630	0.294041	0.147021	+	0.989133i	$0.453032\pi$
$572$	4.98378	0.208382
$573$	15.8902	0.663822
$574$	0	0
$575$	25.4445	1.06111
$576$	1.00000	0.0416667
$577$	−22.9109	−0.953794	−0.476897	−	0.878959i	$-0.658238\pi$
$577$	−22.9109	−0.953794	−0.476897	+	0.878959i	$0.658238\pi$
$578$	−7.96793	−0.331422
$579$	6.49676	0.269996
$580$	4.32852	0.179732
$581$	0	0
$582$	−5.91567	−0.245212
$583$	24.4396	1.01219
$584$	−4.72830	−0.195659
$585$	−2.64149	−0.109212
$586$	22.0139	0.909388
$587$	9.55395	0.394334	0.197167	−	0.980370i	$-0.436826\pi$
$587$	9.55395	0.394334	0.197167	+	0.980370i	$0.436826\pi$
$588$	0	0
$589$	4.38565	0.180708
$590$	11.9827	0.493318
$591$	1.06491	0.0438043
$592$	0.660191	0.0271337
$593$	−8.10672	−0.332903	−0.166452	−	0.986050i	$-0.553231\pi$
$593$	−8.10672	−0.332903	−0.166452	+	0.986050i	$0.553231\pi$
$594$	2.16830	0.0889664
$595$	0	0
$596$	−21.2170	−0.869082
$597$	−23.5917	−0.965545
$598$	−15.8955	−0.650015
$599$	−18.3172	−0.748419	−0.374210	−	0.927344i	$-0.622086\pi$
$599$	−18.3172	−0.748419	−0.374210	+	0.927344i	$0.622086\pi$
$600$	3.67925	0.150205
$601$	−15.5629	−0.634824	−0.317412	−	0.948288i	$-0.602814\pi$
$601$	−15.5629	−0.634824	−0.317412	+	0.948288i	$0.602814\pi$
$602$	0	0
$603$	8.88568	0.361853
$604$	9.40187	0.382557
$605$	−7.23844	−0.294284
$606$	−12.8683	−0.522738
$607$	−28.3918	−1.15239	−0.576193	−	0.817314i	$-0.695462\pi$
$607$	−28.3918	−1.15239	−0.576193	+	0.817314i	$0.695462\pi$
$608$	1.00000	0.0405554
$609$	0	0
$610$	2.96069	0.119875
$611$	−8.55550	−0.346118
$612$	4.99679	0.201983
$613$	−35.4409	−1.43145	−0.715723	−	0.698384i	$-0.753903\pi$
$613$	−35.4409	−1.43145	−0.715723	+	0.698384i	$0.753903\pi$
$614$	14.3776	0.580232
$615$	−0.926955	−0.0373784
$616$	0	0
$617$	27.6964	1.11502	0.557508	−	0.830172i	$-0.311758\pi$
$617$	27.6964	1.11502	0.557508	+	0.830172i	$0.311758\pi$
$618$	6.95582	0.279804
$619$	26.3914	1.06076	0.530380	−	0.847760i	$-0.322049\pi$
$619$	26.3914	1.06076	0.530380	+	0.847760i	$0.322049\pi$
$620$	−5.04015	−0.202417
$621$	−6.91567	−0.277516
$622$	−2.97452	−0.119267
$623$	0	0
$624$	−2.29847	−0.0920126
$625$	6.93318	0.277327
$626$	−16.7588	−0.669818
$627$	2.16830	0.0865936
$628$	−6.14721	−0.245300
$629$	3.29884	0.131533
$630$	0	0
$631$	21.3293	0.849105	0.424553	−	0.905403i	$-0.360431\pi$
$631$	21.3293	0.849105	0.424553	+	0.905403i	$0.360431\pi$
$632$	7.59208	0.301997
$633$	17.8699	0.710266
$634$	2.81061	0.111624
$635$	−15.9379	−0.632478
$636$	−11.2713	−0.446937
$637$	0	0
$638$	8.16675	0.323325
$639$	−0.323591	−0.0128010
$640$	−1.14924	−0.0454276
$641$	19.0070	0.750730	0.375365	−	0.926877i	$-0.377517\pi$
$641$	19.0070	0.750730	0.375365	+	0.926877i	$0.377517\pi$
$642$	12.3987	0.489336
$643$	−3.46630	−0.136697	−0.0683487	−	0.997661i	$-0.521773\pi$
$643$	−3.46630	−0.136697	−0.0683487	+	0.997661i	$0.521773\pi$
$644$	0	0
$645$	−2.39497	−0.0943020
$646$	4.99679	0.196596
$647$	−12.3609	−0.485957	−0.242979	−	0.970032i	$-0.578124\pi$
$647$	−12.3609	−0.485957	−0.242979	+	0.970032i	$0.578124\pi$
$648$	−1.00000	−0.0392837
$649$	22.6080	0.887444
$650$	−8.45667	−0.331698
$651$	0	0
$652$	−8.60793	−0.337113
$653$	50.7123	1.98452	0.992262	−	0.124161i	$-0.0396239\pi$
$653$	50.7123	1.98452	0.992262	+	0.124161i	$0.0396239\pi$
$654$	−18.0568	−0.706078
$655$	−14.0337	−0.548341
$656$	−0.806583	−0.0314918
$657$	4.72830	0.184469
$658$	0	0
$659$	−29.4985	−1.14910	−0.574549	−	0.818470i	$-0.694822\pi$
$659$	−29.4985	−1.14910	−0.574549	+	0.818470i	$0.694822\pi$
$660$	−2.49189	−0.0969967
$661$	37.8979	1.47406	0.737029	−	0.675861i	$-0.236228\pi$
$661$	37.8979	1.47406	0.737029	+	0.675861i	$0.236228\pi$
$662$	10.1391	0.394066
$663$	−11.4850	−0.446040
$664$	3.17435	0.123189
$665$	0	0
$666$	−0.660191	−0.0255819
$667$	−26.0474	−1.00856
$668$	−11.9749	−0.463322
$669$	−4.44605	−0.171894
$670$	−10.2118	−0.394514
$671$	5.58602	0.215646
$672$	0	0
$673$	−0.234048	−0.00902187	−0.00451094	−	0.999990i	$-0.501436\pi$
$673$	−0.234048	−0.00902187	−0.00451094	+	0.999990i	$0.501436\pi$
$674$	−21.4364	−0.825700
$675$	−3.67925	−0.141615
$676$	−7.71702	−0.296808
$677$	11.2235	0.431353	0.215676	−	0.976465i	$-0.430804\pi$
$677$	11.2235	0.431353	0.215676	+	0.976465i	$0.430804\pi$
$678$	8.63792	0.331737
$679$	0	0
$680$	−5.74250	−0.220215
$681$	−20.0938	−0.769995
$682$	−9.50941	−0.364134
$683$	16.5187	0.632072	0.316036	−	0.948747i	$-0.397648\pi$
$683$	16.5187	0.632072	0.316036	+	0.948747i	$0.397648\pi$
$684$	−1.00000	−0.0382360
$685$	12.7344	0.486557
$686$	0	0
$687$	−17.9555	−0.685043
$688$	−2.08397	−0.0794506
$689$	25.9069	0.986973
$690$	7.94774	0.302565
$691$	−41.4575	−1.57712	−0.788559	−	0.614959i	$-0.789173\pi$
$691$	−41.4575	−1.57712	−0.788559	+	0.614959i	$0.789173\pi$
$692$	−8.10185	−0.307986
$693$	0	0
$694$	−29.1826	−1.10776
$695$	12.6617	0.480287
$696$	−3.76643	−0.142766
$697$	−4.03033	−0.152660
$698$	9.36208	0.354360
$699$	10.2539	0.387839
$700$	0	0
$701$	26.9202	1.01676	0.508380	−	0.861133i	$-0.330244\pi$
$701$	26.9202	1.01676	0.508380	+	0.861133i	$0.330244\pi$
$702$	2.29847	0.0867503
$703$	−0.660191	−0.0248996
$704$	−2.16830	−0.0817209
$705$	4.27775	0.161109
$706$	33.5994	1.26453
$707$	0	0
$708$	−10.4266	−0.391856
$709$	29.6206	1.11242	0.556212	−	0.831040i	$-0.312254\pi$
$709$	29.6206	1.11242	0.556212	+	0.831040i	$0.312254\pi$
$710$	0.371882	0.0139565
$711$	−7.59208	−0.284725
$712$	12.3776	0.463869
$713$	30.3297	1.13586
$714$	0	0
$715$	5.72755	0.214198
$716$	−6.84755	−0.255905
$717$	1.73965	0.0649685
$718$	24.3630	0.909220
$719$	26.5038	0.988425	0.494213	−	0.869341i	$-0.335456\pi$
$719$	26.5038	0.988425	0.494213	+	0.869341i	$0.335456\pi$
$720$	1.14924	0.0428295
$721$	0	0
$722$	−1.00000	−0.0372161
$723$	20.8492	0.775391
$724$	16.5905	0.616582
$725$	−13.8577	−0.514661
$726$	6.29847	0.233758
$727$	−27.4510	−1.01810	−0.509051	−	0.860736i	$-0.670004\pi$
$727$	−27.4510	−1.01810	−0.509051	+	0.860736i	$0.670004\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−5.43394	−0.201119
$731$	−10.4132	−0.385144
$732$	−2.57622	−0.0952199
$733$	14.1651	0.523200	0.261600	−	0.965176i	$-0.415750\pi$
$733$	14.1651	0.523200	0.261600	+	0.965176i	$0.415750\pi$
$734$	−33.1571	−1.22385
$735$	0	0
$736$	6.91567	0.254915
$737$	−19.2668	−0.709703
$738$	0.806583	0.0296907
$739$	7.54018	0.277370	0.138685	−	0.990337i	$-0.455712\pi$
$739$	7.54018	0.277370	0.138685	+	0.990337i	$0.455712\pi$
$740$	0.758716	0.0278910
$741$	2.29847	0.0844365
$742$	0	0
$743$	−53.8226	−1.97456	−0.987279	−	0.158997i	$-0.949174\pi$
$743$	−53.8226	−1.97456	−0.987279	+	0.158997i	$0.949174\pi$
$744$	4.38565	0.160786
$745$	−24.3833	−0.893337
$746$	22.5460	0.825467
$747$	−3.17435	−0.116144
$748$	−10.8345	−0.396150
$749$	0	0
$750$	9.97452	0.364218
$751$	20.7762	0.758136	0.379068	−	0.925369i	$-0.376245\pi$
$751$	20.7762	0.758136	0.379068	+	0.925369i	$0.376245\pi$
$752$	3.72225	0.135737
$753$	−3.19663	−0.116492
$754$	8.65704	0.315271
$755$	10.8050	0.393233
$756$	0	0
$757$	−15.9757	−0.580647	−0.290323	−	0.956929i	$-0.593763\pi$
$757$	−15.9757	−0.580647	−0.290323	+	0.956929i	$0.593763\pi$
$758$	−18.7616	−0.681451
$759$	14.9952	0.544293
$760$	1.14924	0.0416872
$761$	−14.1830	−0.514132	−0.257066	−	0.966394i	$-0.582756\pi$
$761$	−14.1830	−0.514132	−0.257066	+	0.966394i	$0.582756\pi$
$762$	13.8683	0.502395
$763$	0	0
$764$	15.8902	0.574887
$765$	5.74250	0.207620
$766$	−8.11770	−0.293305
$767$	23.9653	0.865338
$768$	1.00000	0.0360844
$769$	39.7426	1.43316	0.716578	−	0.697507i	$-0.245708\pi$
$769$	39.7426	1.43316	0.716578	+	0.697507i	$0.245708\pi$
$770$	0	0
$771$	15.0219	0.541001
$772$	6.49676	0.233824
$773$	−0.183792	−0.00661053	−0.00330527	−	0.999995i	$-0.501052\pi$
$773$	−0.183792	−0.00661053	−0.00330527	+	0.999995i	$0.501052\pi$
$774$	2.08397	0.0749067
$775$	16.1359	0.579620
$776$	−5.91567	−0.212360
$777$	0	0
$778$	35.0034	1.25493
$779$	0.806583	0.0288988
$780$	−2.64149	−0.0945806
$781$	0.701641	0.0251067
$782$	34.5562	1.23573
$783$	3.76643	0.134601
$784$	0	0
$785$	−7.06460	−0.252146
$786$	12.2113	0.435563
$787$	20.2158	0.720616	0.360308	−	0.932833i	$-0.382672\pi$
$787$	20.2158	0.720616	0.360308	+	0.932833i	$0.382672\pi$
$788$	1.06491	0.0379357
$789$	10.6760	0.380077
$790$	8.72510	0.310425
$791$	0	0
$792$	2.16830	0.0770472
$793$	5.92138	0.210274
$794$	15.0219	0.533108
$795$	−12.9534	−0.459411
$796$	−23.5917	−0.836186
$797$	33.9377	1.20213	0.601067	−	0.799198i	$-0.294742\pi$
$797$	33.9377	1.20213	0.601067	+	0.799198i	$0.294742\pi$
$798$	0	0
$799$	18.5993	0.657996
$800$	3.67925	0.130081
$801$	−12.3776	−0.437340
$802$	26.6287	0.940291
$803$	−10.2524	−0.361799
$804$	8.88568	0.313374
$805$	0	0
$806$	−10.0803	−0.355064
$807$	3.24906	0.114372
$808$	−12.8683	−0.452705
$809$	−34.7190	−1.22066	−0.610328	−	0.792149i	$-0.708962\pi$
$809$	−34.7190	−1.22066	−0.610328	+	0.792149i	$0.708962\pi$
$810$	−1.14924	−0.0403801
$811$	−44.1620	−1.55074	−0.775369	−	0.631509i	$-0.782436\pi$
$811$	−44.1620	−1.55074	−0.775369	+	0.631509i	$0.782436\pi$
$812$	0	0
$813$	−18.0349	−0.632512
$814$	1.43149	0.0501738
$815$	−9.89255	−0.346521
$816$	4.99679	0.174923
$817$	2.08397	0.0729088
$818$	27.6489	0.966721
$819$	0	0
$820$	−0.926955	−0.0323707
$821$	12.1074	0.422552	0.211276	−	0.977426i	$-0.432238\pi$
$821$	12.1074	0.422552	0.211276	+	0.977426i	$0.432238\pi$
$822$	−11.0808	−0.386486
$823$	3.69623	0.128843	0.0644213	−	0.997923i	$-0.479480\pi$
$823$	3.69623	0.128843	0.0644213	+	0.997923i	$0.479480\pi$
$824$	6.95582	0.242317
$825$	7.97773	0.277749
$826$	0	0
$827$	−11.8614	−0.412461	−0.206230	−	0.978503i	$-0.566120\pi$
$827$	−11.8614	−0.412461	−0.206230	+	0.978503i	$0.566120\pi$
$828$	−6.91567	−0.240336
$829$	−34.2921	−1.19101	−0.595506	−	0.803351i	$-0.703048\pi$
$829$	−34.2921	−1.19101	−0.595506	+	0.803351i	$0.703048\pi$
$830$	3.64808	0.126627
$831$	22.2839	0.773021
$832$	−2.29847	−0.0796852
$833$	0	0
$834$	−11.0175	−0.381505
$835$	−13.7620	−0.476253
$836$	2.16830	0.0749922
$837$	−4.38565	−0.151590
$838$	1.91888	0.0662865
$839$	−23.5395	−0.812672	−0.406336	−	0.913724i	$-0.633194\pi$
$839$	−23.5395	−0.812672	−0.406336	+	0.913724i	$0.633194\pi$
$840$	0	0
$841$	−14.8140	−0.510827
$842$	−25.9815	−0.895381
$843$	7.10790	0.244809
$844$	17.8699	0.615109
$845$	−8.86868	−0.305092
$846$	−3.72225	−0.127974
$847$	0	0
$848$	−11.2713	−0.387059
$849$	15.7474	0.540448
$850$	18.3845	0.630582
$851$	−4.56566	−0.156509
$852$	−0.323591	−0.0110860
$853$	54.9855	1.88267	0.941334	−	0.337477i	$-0.109573\pi$
$853$	54.9855	1.88267	0.941334	+	0.337477i	$0.109573\pi$
$854$	0	0
$855$	−1.14924	−0.0393031
$856$	12.3987	0.423777
$857$	−58.1333	−1.98579	−0.992897	−	0.118976i	$-0.962039\pi$
$857$	−58.1333	−1.98579	−0.992897	+	0.118976i	$0.962039\pi$
$858$	−4.98378	−0.170143
$859$	−11.6517	−0.397550	−0.198775	−	0.980045i	$-0.563696\pi$
$859$	−11.6517	−0.397550	−0.198775	+	0.980045i	$0.563696\pi$
$860$	−2.39497	−0.0816679
$861$	0	0
$862$	−0.965082	−0.0328708
$863$	−9.64470	−0.328309	−0.164155	−	0.986435i	$-0.552490\pi$
$863$	−9.64470	−0.328309	−0.164155	+	0.986435i	$0.552490\pi$
$864$	−1.00000	−0.0340207
$865$	−9.31094	−0.316582
$866$	−5.93960	−0.201836
$867$	7.96793	0.270605
$868$	0	0
$869$	16.4619	0.558432
$870$	−4.32852	−0.146751
$871$	−20.4235	−0.692024
$872$	−18.0568	−0.611481
$873$	5.91567	0.200215
$874$	−6.91567	−0.233926
$875$	0	0
$876$	4.72830	0.159755
$877$	−51.9199	−1.75321	−0.876605	−	0.481211i	$-0.840197\pi$
$877$	−51.9199	−1.75321	−0.876605	+	0.481211i	$0.840197\pi$
$878$	21.5921	0.728697
$879$	−22.0139	−0.742512
$880$	−2.49189	−0.0840016
$881$	−1.32443	−0.0446213	−0.0223106	−	0.999751i	$-0.507102\pi$
$881$	−1.32443	−0.0446213	−0.0223106	+	0.999751i	$0.507102\pi$
$882$	0	0
$883$	−45.6432	−1.53602	−0.768009	−	0.640439i	$-0.778752\pi$
$883$	−45.6432	−1.53602	−0.768009	+	0.640439i	$0.778752\pi$
$884$	−11.4850	−0.386282
$885$	−11.9827	−0.402793
$886$	−13.9344	−0.468134
$887$	−5.18089	−0.173957	−0.0869786	−	0.996210i	$-0.527721\pi$
$887$	−5.18089	−0.173957	−0.0869786	+	0.996210i	$0.527721\pi$
$888$	−0.660191	−0.0221546
$889$	0	0
$890$	14.2248	0.476815
$891$	−2.16830	−0.0726408
$892$	−4.44605	−0.148865
$893$	−3.72225	−0.124560
$894$	21.2170	0.709602
$895$	−7.86946	−0.263047
$896$	0	0
$897$	15.8955	0.530735
$898$	−14.3273	−0.478109
$899$	−16.5183	−0.550915
$900$	−3.67925	−0.122642
$901$	−56.3205	−1.87631
$902$	−1.74891	−0.0582325
$903$	0	0
$904$	8.63792	0.287293
$905$	19.0665	0.633790
$906$	−9.40187	−0.312356
$907$	58.5017	1.94252	0.971258	−	0.238028i	$-0.0765008\pi$
$907$	58.5017	1.94252	0.971258	+	0.238028i	$0.0765008\pi$
$908$	−20.0938	−0.666835
$909$	12.8683	0.426814
$910$	0	0
$911$	23.2344	0.769790	0.384895	−	0.922960i	$-0.374238\pi$
$911$	23.2344	0.769790	0.384895	+	0.922960i	$0.374238\pi$
$912$	−1.00000	−0.0331133
$913$	6.88295	0.227792
$914$	−32.2981	−1.06833
$915$	−2.96069	−0.0978774
$916$	−17.9555	−0.593265
$917$	0	0
$918$	−4.99679	−0.164919
$919$	17.8751	0.589644	0.294822	−	0.955552i	$-0.404740\pi$
$919$	17.8751	0.589644	0.294822	+	0.955552i	$0.404740\pi$
$920$	7.94774	0.262029
$921$	−14.3776	−0.473757
$922$	0.375849	0.0123779
$923$	0.743764	0.0244813
$924$	0	0
$925$	−2.42901	−0.0798654
$926$	−7.80824	−0.256595
$927$	−6.95582	−0.228459
$928$	−3.76643	−0.123639
$929$	−46.4492	−1.52395	−0.761974	−	0.647607i	$-0.775770\pi$
$929$	−46.4492	−1.52395	−0.761974	+	0.647607i	$0.775770\pi$
$930$	5.04015	0.165273
$931$	0	0
$932$	10.2539	0.335879
$933$	2.97452	0.0973814
$934$	−12.2555	−0.401011
$935$	−12.4515	−0.407206
$936$	2.29847	0.0751280
$937$	42.3561	1.38371	0.691857	−	0.722034i	$-0.256793\pi$
$937$	42.3561	1.38371	0.691857	+	0.722034i	$0.256793\pi$
$938$	0	0
$939$	16.7588	0.546904
$940$	4.27775	0.139525
$941$	46.4969	1.51576	0.757878	−	0.652396i	$-0.226236\pi$
$941$	46.4969	1.51576	0.757878	+	0.652396i	$0.226236\pi$
$942$	6.14721	0.200287
$943$	5.57806	0.181647
$944$	−10.4266	−0.339358
$945$	0	0
$946$	−4.51867	−0.146915
$947$	47.2657	1.53593	0.767964	−	0.640493i	$-0.221270\pi$
$947$	47.2657	1.53593	0.767964	+	0.640493i	$0.221270\pi$
$948$	−7.59208	−0.246579
$949$	−10.8679	−0.352786
$950$	−3.67925	−0.119371
$951$	−2.81061	−0.0911403
$952$	0	0
$953$	−0.673201	−0.0218071	−0.0109036	−	0.999941i	$-0.503471\pi$
$953$	−0.673201	−0.0218071	−0.0109036	+	0.999941i	$0.503471\pi$
$954$	11.2713	0.364923
$955$	18.2616	0.590931
$956$	1.73965	0.0562644
$957$	−8.16675	−0.263994
$958$	27.0751	0.874756
$959$	0	0
$960$	1.14924	0.0370915
$961$	−11.7661	−0.379551
$962$	1.51743	0.0489240
$963$	−12.3987	−0.399541
$964$	20.8492	0.671508
$965$	7.46632	0.240349
$966$	0	0
$967$	1.83609	0.0590447	0.0295224	−	0.999564i	$-0.490601\pi$
$967$	1.83609	0.0590447	0.0295224	+	0.999564i	$0.490601\pi$
$968$	6.29847	0.202441
$969$	−4.99679	−0.160520
$970$	−6.79850	−0.218287
$971$	−12.6488	−0.405921	−0.202960	−	0.979187i	$-0.565056\pi$
$971$	−12.6488	−0.405921	−0.202960	+	0.979187i	$0.565056\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	−29.7498	−0.953247
$975$	8.45667	0.270830
$976$	−2.57622	−0.0824629
$977$	21.3457	0.682909	0.341454	−	0.939898i	$-0.389081\pi$
$977$	21.3457	0.682909	0.341454	+	0.939898i	$0.389081\pi$
$978$	8.60793	0.275251
$979$	26.8383	0.857756
$980$	0	0
$981$	18.0568	0.576510
$982$	−18.4381	−0.588383
$983$	−25.7268	−0.820558	−0.410279	−	0.911960i	$-0.634569\pi$
$983$	−25.7268	−0.820558	−0.410279	+	0.911960i	$0.634569\pi$
$984$	0.806583	0.0257129
$985$	1.22383	0.0389944
$986$	−18.8201	−0.599353
$987$	0	0
$988$	2.29847	0.0731242
$989$	14.4120	0.458276
$990$	2.49189	0.0791975
$991$	−58.1823	−1.84822	−0.924111	−	0.382124i	$-0.875193\pi$
$991$	−58.1823	−1.84822	−0.924111	+	0.382124i	$0.875193\pi$
$992$	4.38565	0.139245
$993$	−10.1391	−0.321754
$994$	0	0
$995$	−27.1125	−0.859523
$996$	−3.17435	−0.100583
$997$	51.2792	1.62403	0.812014	−	0.583638i	$-0.198371\pi$
$997$	51.2792	1.62403	0.812014	+	0.583638i	$0.198371\pi$
$998$	−33.1570	−1.04957
$999$	0.660191	0.0208875

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5586.2.a.bz.1.3		4
7.3	odd	6		798.2.j.l.457.3	✓	8
7.5	odd	6		798.2.j.l.571.3	yes	8
7.6	odd	2		5586.2.a.bw.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.j.l.457.3	✓	8	7.3	odd	6
798.2.j.l.571.3	yes	8	7.5	odd	6
5586.2.a.bw.1.2		4	7.6	odd	2
5586.2.a.bz.1.3		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5586 = 2 \cdot 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5586.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.14924 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.14924 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -1.14924 q^{10} -2.16830 q^{11} +1.00000 q^{12} -2.29847 q^{13} +1.14924 q^{15} +1.00000 q^{16} +4.99679 q^{17} -1.00000 q^{18} -1.00000 q^{19} +1.14924 q^{20} +2.16830 q^{22} -6.91567 q^{23} -1.00000 q^{24} -3.67925 q^{25} +2.29847 q^{26} +1.00000 q^{27} +3.76643 q^{29} -1.14924 q^{30} -4.38565 q^{31} -1.00000 q^{32} -2.16830 q^{33} -4.99679 q^{34} +1.00000 q^{36} +0.660191 q^{37} +1.00000 q^{38} -2.29847 q^{39} -1.14924 q^{40} -0.806583 q^{41} -2.08397 q^{43} -2.16830 q^{44} +1.14924 q^{45} +6.91567 q^{46} +3.72225 q^{47} +1.00000 q^{48} +3.67925 q^{50} +4.99679 q^{51} -2.29847 q^{52} -11.2713 q^{53} -1.00000 q^{54} -2.49189 q^{55} -1.00000 q^{57} -3.76643 q^{58} -10.4266 q^{59} +1.14924 q^{60} -2.57622 q^{61} +4.38565 q^{62} +1.00000 q^{64} -2.64149 q^{65} +2.16830 q^{66} +8.88568 q^{67} +4.99679 q^{68} -6.91567 q^{69} -0.323591 q^{71} -1.00000 q^{72} +4.72830 q^{73} -0.660191 q^{74} -3.67925 q^{75} -1.00000 q^{76} +2.29847 q^{78} -7.59208 q^{79} +1.14924 q^{80} +1.00000 q^{81} +0.806583 q^{82} -3.17435 q^{83} +5.74250 q^{85} +2.08397 q^{86} +3.76643 q^{87} +2.16830 q^{88} -12.3776 q^{89} -1.14924 q^{90} -6.91567 q^{92} -4.38565 q^{93} -3.72225 q^{94} -1.14924 q^{95} -1.00000 q^{96} +5.91567 q^{97} -2.16830 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^6 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} + 4 q^{3} + 4 q^{4} - 4 q^{6} - 4 q^{8} + 4 q^{9} - 2 q^{11} + 4 q^{12} + 4 q^{16} - 10 q^{17} - 4 q^{18} - 4 q^{19} + 2 q^{22} - 5 q^{23} - 4 q^{24} + 4 q^{25} + 4 q^{27} - 3 q^{29} - 9 q^{31} - 4 q^{32} - 2 q^{33} + 10 q^{34} + 4 q^{36} - 14 q^{37} + 4 q^{38} - 4 q^{41} + 21 q^{43} - 2 q^{44} + 5 q^{46} - 7 q^{47} + 4 q^{48} - 4 q^{50} - 10 q^{51} - 7 q^{53} - 4 q^{54} - 4 q^{57} + 3 q^{58} - 7 q^{59} - 23 q^{61} + 9 q^{62} + 4 q^{64} - 48 q^{65} + 2 q^{66} + 6 q^{67} - 10 q^{68} - 5 q^{69} + 2 q^{71} - 4 q^{72} + 5 q^{73} + 14 q^{74} + 4 q^{75} - 4 q^{76} - 11 q^{79} + 4 q^{81} + 4 q^{82} - 14 q^{83} + 6 q^{85} - 21 q^{86} - 3 q^{87} + 2 q^{88} - 10 q^{89} - 5 q^{92} - 9 q^{93} + 7 q^{94} - 4 q^{96} + q^{97} - 2 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^3 + 4 * q^4 - 4 * q^6 - 4 * q^8 + 4 * q^9 - 2 * q^11 + 4 * q^12 + 4 * q^16 - 10 * q^17 - 4 * q^18 - 4 * q^19 + 2 * q^22 - 5 * q^23 - 4 * q^24 + 4 * q^25 + 4 * q^27 - 3 * q^29 - 9 * q^31 - 4 * q^32 - 2 * q^33 + 10 * q^34 + 4 * q^36 - 14 * q^37 + 4 * q^38 - 4 * q^41 + 21 * q^43 - 2 * q^44 + 5 * q^46 - 7 * q^47 + 4 * q^48 - 4 * q^50 - 10 * q^51 - 7 * q^53 - 4 * q^54 - 4 * q^57 + 3 * q^58 - 7 * q^59 - 23 * q^61 + 9 * q^62 + 4 * q^64 - 48 * q^65 + 2 * q^66 + 6 * q^67 - 10 * q^68 - 5 * q^69 + 2 * q^71 - 4 * q^72 + 5 * q^73 + 14 * q^74 + 4 * q^75 - 4 * q^76 - 11 * q^79 + 4 * q^81 + 4 * q^82 - 14 * q^83 + 6 * q^85 - 21 * q^86 - 3 * q^87 + 2 * q^88 - 10 * q^89 - 5 * q^92 - 9 * q^93 + 7 * q^94 - 4 * q^96 + q^97 - 2 * q^99

Introduction

L-functions

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