LMFDB - Embedded newform 5586.2.a.bd.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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 798)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.73205$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.46410 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.46410 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -3.46410 q^{10} -5.46410 q^{11} +1.00000 q^{12} +3.46410 q^{13} +3.46410 q^{15} +1.00000 q^{16} -7.46410 q^{17} -1.00000 q^{18} -1.00000 q^{19} +3.46410 q^{20} +5.46410 q^{22} -5.46410 q^{23} -1.00000 q^{24} +7.00000 q^{25} -3.46410 q^{26} +1.00000 q^{27} -6.00000 q^{29} -3.46410 q^{30} -6.92820 q^{31} -1.00000 q^{32} -5.46410 q^{33} +7.46410 q^{34} +1.00000 q^{36} +10.0000 q^{37} +1.00000 q^{38} +3.46410 q^{39} -3.46410 q^{40} +2.00000 q^{41} -6.92820 q^{43} -5.46410 q^{44} +3.46410 q^{45} +5.46410 q^{46} -10.9282 q^{47} +1.00000 q^{48} -7.00000 q^{50} -7.46410 q^{51} +3.46410 q^{52} +2.00000 q^{53} -1.00000 q^{54} -18.9282 q^{55} -1.00000 q^{57} +6.00000 q^{58} -4.00000 q^{59} +3.46410 q^{60} +4.92820 q^{61} +6.92820 q^{62} +1.00000 q^{64} +12.0000 q^{65} +5.46410 q^{66} +9.46410 q^{67} -7.46410 q^{68} -5.46410 q^{69} +2.92820 q^{71} -1.00000 q^{72} -10.0000 q^{73} -10.0000 q^{74} +7.00000 q^{75} -1.00000 q^{76} -3.46410 q^{78} -12.3923 q^{79} +3.46410 q^{80} +1.00000 q^{81} -2.00000 q^{82} -8.00000 q^{83} -25.8564 q^{85} +6.92820 q^{86} -6.00000 q^{87} +5.46410 q^{88} +2.00000 q^{89} -3.46410 q^{90} -5.46410 q^{92} -6.92820 q^{93} +10.9282 q^{94} -3.46410 q^{95} -1.00000 q^{96} -4.53590 q^{97} -5.46410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} - 2 q^{8} + 2 q^{9} - 4 q^{11} + 2 q^{12} + 2 q^{16} - 8 q^{17} - 2 q^{18} - 2 q^{19} + 4 q^{22} - 4 q^{23} - 2 q^{24} + 14 q^{25} + 2 q^{27} - 12 q^{29} - 2 q^{32} - 4 q^{33} + 8 q^{34} + 2 q^{36} + 20 q^{37} + 2 q^{38} + 4 q^{41} - 4 q^{44} + 4 q^{46} - 8 q^{47} + 2 q^{48} - 14 q^{50} - 8 q^{51} + 4 q^{53} - 2 q^{54} - 24 q^{55} - 2 q^{57} + 12 q^{58} - 8 q^{59} - 4 q^{61} + 2 q^{64} + 24 q^{65} + 4 q^{66} + 12 q^{67} - 8 q^{68} - 4 q^{69} - 8 q^{71} - 2 q^{72} - 20 q^{73} - 20 q^{74} + 14 q^{75} - 2 q^{76} - 4 q^{79} + 2 q^{81} - 4 q^{82} - 16 q^{83} - 24 q^{85} - 12 q^{87} + 4 q^{88} + 4 q^{89} - 4 q^{92} + 8 q^{94} - 2 q^{96} - 16 q^{97} - 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 - 2 * q^8 + 2 * q^9 - 4 * q^11 + 2 * q^12 + 2 * q^16 - 8 * q^17 - 2 * q^18 - 2 * q^19 + 4 * q^22 - 4 * q^23 - 2 * q^24 + 14 * q^25 + 2 * q^27 - 12 * q^29 - 2 * q^32 - 4 * q^33 + 8 * q^34 + 2 * q^36 + 20 * q^37 + 2 * q^38 + 4 * q^41 - 4 * q^44 + 4 * q^46 - 8 * q^47 + 2 * q^48 - 14 * q^50 - 8 * q^51 + 4 * q^53 - 2 * q^54 - 24 * q^55 - 2 * q^57 + 12 * q^58 - 8 * q^59 - 4 * q^61 + 2 * q^64 + 24 * q^65 + 4 * q^66 + 12 * q^67 - 8 * q^68 - 4 * q^69 - 8 * q^71 - 2 * q^72 - 20 * q^73 - 20 * q^74 + 14 * q^75 - 2 * q^76 - 4 * q^79 + 2 * q^81 - 4 * q^82 - 16 * q^83 - 24 * q^85 - 12 * q^87 + 4 * q^88 + 4 * q^89 - 4 * q^92 + 8 * q^94 - 2 * q^96 - 16 * 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
$5$	3.46410	1.54919	0.774597	−	0.632456i	$-0.217953\pi$
$5$	3.46410	1.54919	0.774597	+	0.632456i	$0.217953\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.46410	−1.09545
$11$	−5.46410	−1.64749	−0.823744	−	0.566961i	$-0.808119\pi$
$11$	−5.46410	−1.64749	−0.823744	+	0.566961i	$0.808119\pi$
$12$	1.00000	0.288675
$13$	3.46410	0.960769	0.480384	−	0.877058i	$-0.340497\pi$
$13$	3.46410	0.960769	0.480384	+	0.877058i	$0.340497\pi$
$14$	0	0
$15$	3.46410	0.894427
$16$	1.00000	0.250000
$17$	−7.46410	−1.81031	−0.905155	−	0.425081i	$-0.860246\pi$
$17$	−7.46410	−1.81031	−0.905155	+	0.425081i	$0.860246\pi$
$18$	−1.00000	−0.235702
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	3.46410	0.774597
$21$	0	0
$22$	5.46410	1.16495
$23$	−5.46410	−1.13934	−0.569672	−	0.821872i	$-0.692930\pi$
$23$	−5.46410	−1.13934	−0.569672	+	0.821872i	$0.692930\pi$
$24$	−1.00000	−0.204124
$25$	7.00000	1.40000
$26$	−3.46410	−0.679366
$27$	1.00000	0.192450
$28$	0	0
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	−3.46410	−0.632456
$31$	−6.92820	−1.24434	−0.622171	−	0.782881i	$-0.713749\pi$
$31$	−6.92820	−1.24434	−0.622171	+	0.782881i	$0.713749\pi$
$32$	−1.00000	−0.176777
$33$	−5.46410	−0.951178
$34$	7.46410	1.28008
$35$	0	0
$36$	1.00000	0.166667
$37$	10.0000	1.64399	0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000	1.64399	0.821995	+	0.569495i	$0.192861\pi$
$38$	1.00000	0.162221
$39$	3.46410	0.554700
$40$	−3.46410	−0.547723
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	0	0
$43$	−6.92820	−1.05654	−0.528271	−	0.849076i	$-0.677159\pi$
$43$	−6.92820	−1.05654	−0.528271	+	0.849076i	$0.677159\pi$
$44$	−5.46410	−0.823744
$45$	3.46410	0.516398
$46$	5.46410	0.805638
$47$	−10.9282	−1.59404	−0.797021	−	0.603951i	$-0.793592\pi$
$47$	−10.9282	−1.59404	−0.797021	+	0.603951i	$0.793592\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	−7.00000	−0.989949
$51$	−7.46410	−1.04518
$52$	3.46410	0.480384
$53$	2.00000	0.274721	0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000	0.274721	0.137361	+	0.990521i	$0.456138\pi$
$54$	−1.00000	−0.136083
$55$	−18.9282	−2.55228
$56$	0	0
$57$	−1.00000	−0.132453
$58$	6.00000	0.787839
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	3.46410	0.447214
$61$	4.92820	0.630992	0.315496	−	0.948927i	$-0.397829\pi$
$61$	4.92820	0.630992	0.315496	+	0.948927i	$0.397829\pi$
$62$	6.92820	0.879883
$63$	0	0
$64$	1.00000	0.125000
$65$	12.0000	1.48842
$66$	5.46410	0.672584
$67$	9.46410	1.15622	0.578112	−	0.815957i	$-0.303790\pi$
$67$	9.46410	1.15622	0.578112	+	0.815957i	$0.303790\pi$
$68$	−7.46410	−0.905155
$69$	−5.46410	−0.657801
$70$	0	0
$71$	2.92820	0.347514	0.173757	−	0.984789i	$-0.444409\pi$
$71$	2.92820	0.347514	0.173757	+	0.984789i	$0.444409\pi$
$72$	−1.00000	−0.117851
$73$	−10.0000	−1.17041	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000	−1.17041	−0.585206	+	0.810885i	$0.698986\pi$
$74$	−10.0000	−1.16248
$75$	7.00000	0.808290
$76$	−1.00000	−0.114708
$77$	0	0
$78$	−3.46410	−0.392232
$79$	−12.3923	−1.39424	−0.697122	−	0.716953i	$-0.745536\pi$
$79$	−12.3923	−1.39424	−0.697122	+	0.716953i	$0.745536\pi$
$80$	3.46410	0.387298
$81$	1.00000	0.111111
$82$	−2.00000	−0.220863
$83$	−8.00000	−0.878114	−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000	−0.878114	−0.439057	+	0.898459i	$0.644687\pi$
$84$	0	0
$85$	−25.8564	−2.80452
$86$	6.92820	0.747087
$87$	−6.00000	−0.643268
$88$	5.46410	0.582475
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	−3.46410	−0.365148
$91$	0	0
$92$	−5.46410	−0.569672
$93$	−6.92820	−0.718421
$94$	10.9282	1.12716
$95$	−3.46410	−0.355409
$96$	−1.00000	−0.102062
$97$	−4.53590	−0.460551	−0.230275	−	0.973126i	$-0.573963\pi$
$97$	−4.53590	−0.460551	−0.230275	+	0.973126i	$0.573963\pi$
$98$	0	0
$99$	−5.46410	−0.549163
$100$	7.00000	0.700000
$101$	−4.53590	−0.451339	−0.225669	−	0.974204i	$-0.572457\pi$
$101$	−4.53590	−0.451339	−0.225669	+	0.974204i	$0.572457\pi$
$102$	7.46410	0.739056
$103$	6.92820	0.682656	0.341328	−	0.939944i	$-0.389123\pi$
$103$	6.92820	0.682656	0.341328	+	0.939944i	$0.389123\pi$
$104$	−3.46410	−0.339683
$105$	0	0
$106$	−2.00000	−0.194257
$107$	−4.00000	−0.386695	−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000	−0.386695	−0.193347	+	0.981130i	$0.561934\pi$
$108$	1.00000	0.0962250
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	18.9282	1.80473
$111$	10.0000	0.949158
$112$	0	0
$113$	11.8564	1.11536	0.557678	−	0.830057i	$-0.311692\pi$
$113$	11.8564	1.11536	0.557678	+	0.830057i	$0.311692\pi$
$114$	1.00000	0.0936586
$115$	−18.9282	−1.76506
$116$	−6.00000	−0.557086
$117$	3.46410	0.320256
$118$	4.00000	0.368230
$119$	0	0
$120$	−3.46410	−0.316228
$121$	18.8564	1.71422
$122$	−4.92820	−0.446179
$123$	2.00000	0.180334
$124$	−6.92820	−0.622171
$125$	6.92820	0.619677
$126$	0	0
$127$	−17.4641	−1.54969	−0.774844	−	0.632152i	$-0.782172\pi$
$127$	−17.4641	−1.54969	−0.774844	+	0.632152i	$0.782172\pi$
$128$	−1.00000	−0.0883883
$129$	−6.92820	−0.609994
$130$	−12.0000	−1.05247
$131$	5.07180	0.443125	0.221562	−	0.975146i	$-0.428884\pi$
$131$	5.07180	0.443125	0.221562	+	0.975146i	$0.428884\pi$
$132$	−5.46410	−0.475589
$133$	0	0
$134$	−9.46410	−0.817574
$135$	3.46410	0.298142
$136$	7.46410	0.640041
$137$	−0.928203	−0.0793018	−0.0396509	−	0.999214i	$-0.512625\pi$
$137$	−0.928203	−0.0793018	−0.0396509	+	0.999214i	$0.512625\pi$
$138$	5.46410	0.465135
$139$	−9.85641	−0.836009	−0.418005	−	0.908445i	$-0.637270\pi$
$139$	−9.85641	−0.836009	−0.418005	+	0.908445i	$0.637270\pi$
$140$	0	0
$141$	−10.9282	−0.920321
$142$	−2.92820	−0.245729
$143$	−18.9282	−1.58286
$144$	1.00000	0.0833333
$145$	−20.7846	−1.72607
$146$	10.0000	0.827606
$147$	0	0
$148$	10.0000	0.821995
$149$	−3.07180	−0.251651	−0.125826	−	0.992052i	$-0.540158\pi$
$149$	−3.07180	−0.251651	−0.125826	+	0.992052i	$0.540158\pi$
$150$	−7.00000	−0.571548
$151$	1.46410	0.119147	0.0595734	−	0.998224i	$-0.481026\pi$
$151$	1.46410	0.119147	0.0595734	+	0.998224i	$0.481026\pi$
$152$	1.00000	0.0811107
$153$	−7.46410	−0.603437
$154$	0	0
$155$	−24.0000	−1.92773
$156$	3.46410	0.277350
$157$	−19.8564	−1.58471	−0.792357	−	0.610058i	$-0.791146\pi$
$157$	−19.8564	−1.58471	−0.792357	+	0.610058i	$0.791146\pi$
$158$	12.3923	0.985879
$159$	2.00000	0.158610
$160$	−3.46410	−0.273861
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	1.07180	0.0839496	0.0419748	−	0.999119i	$-0.486635\pi$
$163$	1.07180	0.0839496	0.0419748	+	0.999119i	$0.486635\pi$
$164$	2.00000	0.156174
$165$	−18.9282	−1.47356
$166$	8.00000	0.620920
$167$	18.9282	1.46471	0.732354	−	0.680924i	$-0.238422\pi$
$167$	18.9282	1.46471	0.732354	+	0.680924i	$0.238422\pi$
$168$	0	0
$169$	−1.00000	−0.0769231
$170$	25.8564	1.98310
$171$	−1.00000	−0.0764719
$172$	−6.92820	−0.528271
$173$	0.928203	0.0705700	0.0352850	−	0.999377i	$-0.488766\pi$
$173$	0.928203	0.0705700	0.0352850	+	0.999377i	$0.488766\pi$
$174$	6.00000	0.454859
$175$	0	0
$176$	−5.46410	−0.411872
$177$	−4.00000	−0.300658
$178$	−2.00000	−0.149906
$179$	−9.85641	−0.736702	−0.368351	−	0.929687i	$-0.620078\pi$
$179$	−9.85641	−0.736702	−0.368351	+	0.929687i	$0.620078\pi$
$180$	3.46410	0.258199
$181$	8.53590	0.634468	0.317234	−	0.948347i	$-0.397246\pi$
$181$	8.53590	0.634468	0.317234	+	0.948347i	$0.397246\pi$
$182$	0	0
$183$	4.92820	0.364303
$184$	5.46410	0.402819
$185$	34.6410	2.54686
$186$	6.92820	0.508001
$187$	40.7846	2.98247
$188$	−10.9282	−0.797021
$189$	0	0
$190$	3.46410	0.251312
$191$	−5.46410	−0.395369	−0.197684	−	0.980266i	$-0.563342\pi$
$191$	−5.46410	−0.395369	−0.197684	+	0.980266i	$0.563342\pi$
$192$	1.00000	0.0721688
$193$	−22.0000	−1.58359	−0.791797	−	0.610784i	$-0.790854\pi$
$193$	−22.0000	−1.58359	−0.791797	+	0.610784i	$0.790854\pi$
$194$	4.53590	0.325659
$195$	12.0000	0.859338
$196$	0	0
$197$	4.92820	0.351120	0.175560	−	0.984469i	$-0.443826\pi$
$197$	4.92820	0.351120	0.175560	+	0.984469i	$0.443826\pi$
$198$	5.46410	0.388317
$199$	24.7846	1.75693	0.878467	−	0.477803i	$-0.158567\pi$
$199$	24.7846	1.75693	0.878467	+	0.477803i	$0.158567\pi$
$200$	−7.00000	−0.494975
$201$	9.46410	0.667546
$202$	4.53590	0.319145
$203$	0	0
$204$	−7.46410	−0.522592
$205$	6.92820	0.483887
$206$	−6.92820	−0.482711
$207$	−5.46410	−0.379781
$208$	3.46410	0.240192
$209$	5.46410	0.377960
$210$	0	0
$211$	1.46410	0.100793	0.0503965	−	0.998729i	$-0.483952\pi$
$211$	1.46410	0.100793	0.0503965	+	0.998729i	$0.483952\pi$
$212$	2.00000	0.137361
$213$	2.92820	0.200637
$214$	4.00000	0.273434
$215$	−24.0000	−1.63679
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−2.00000	−0.135457
$219$	−10.0000	−0.675737
$220$	−18.9282	−1.27614
$221$	−25.8564	−1.73929
$222$	−10.0000	−0.671156
$223$	12.0000	0.803579	0.401790	−	0.915732i	$-0.368388\pi$
$223$	12.0000	0.803579	0.401790	+	0.915732i	$0.368388\pi$
$224$	0	0
$225$	7.00000	0.466667
$226$	−11.8564	−0.788676
$227$	−14.9282	−0.990820	−0.495410	−	0.868659i	$-0.664982\pi$
$227$	−14.9282	−0.990820	−0.495410	+	0.868659i	$0.664982\pi$
$228$	−1.00000	−0.0662266
$229$	−3.07180	−0.202990	−0.101495	−	0.994836i	$-0.532363\pi$
$229$	−3.07180	−0.202990	−0.101495	+	0.994836i	$0.532363\pi$
$230$	18.9282	1.24809
$231$	0	0
$232$	6.00000	0.393919
$233$	26.7846	1.75472	0.877359	−	0.479834i	$-0.159303\pi$
$233$	26.7846	1.75472	0.877359	+	0.479834i	$0.159303\pi$
$234$	−3.46410	−0.226455
$235$	−37.8564	−2.46948
$236$	−4.00000	−0.260378
$237$	−12.3923	−0.804967
$238$	0	0
$239$	30.2487	1.95663	0.978313	−	0.207131i	$-0.0664126\pi$
$239$	30.2487	1.95663	0.978313	+	0.207131i	$0.0664126\pi$
$240$	3.46410	0.223607
$241$	−21.3205	−1.37337	−0.686687	−	0.726953i	$-0.740936\pi$
$241$	−21.3205	−1.37337	−0.686687	+	0.726953i	$0.740936\pi$
$242$	−18.8564	−1.21214
$243$	1.00000	0.0641500
$244$	4.92820	0.315496
$245$	0	0
$246$	−2.00000	−0.127515
$247$	−3.46410	−0.220416
$248$	6.92820	0.439941
$249$	−8.00000	−0.506979
$250$	−6.92820	−0.438178
$251$	−5.07180	−0.320129	−0.160064	−	0.987107i	$-0.551170\pi$
$251$	−5.07180	−0.320129	−0.160064	+	0.987107i	$0.551170\pi$
$252$	0	0
$253$	29.8564	1.87706
$254$	17.4641	1.09580
$255$	−25.8564	−1.61919
$256$	1.00000	0.0625000
$257$	−24.9282	−1.55498	−0.777489	−	0.628896i	$-0.783507\pi$
$257$	−24.9282	−1.55498	−0.777489	+	0.628896i	$0.783507\pi$
$258$	6.92820	0.431331
$259$	0	0
$260$	12.0000	0.744208
$261$	−6.00000	−0.371391
$262$	−5.07180	−0.313337
$263$	11.3205	0.698052	0.349026	−	0.937113i	$-0.386512\pi$
$263$	11.3205	0.698052	0.349026	+	0.937113i	$0.386512\pi$
$264$	5.46410	0.336292
$265$	6.92820	0.425596
$266$	0	0
$267$	2.00000	0.122398
$268$	9.46410	0.578112
$269$	16.9282	1.03213	0.516065	−	0.856549i	$-0.327396\pi$
$269$	16.9282	1.03213	0.516065	+	0.856549i	$0.327396\pi$
$270$	−3.46410	−0.210819
$271$	29.8564	1.81365	0.906824	−	0.421510i	$-0.138500\pi$
$271$	29.8564	1.81365	0.906824	+	0.421510i	$0.138500\pi$
$272$	−7.46410	−0.452578
$273$	0	0
$274$	0.928203	0.0560748
$275$	−38.2487	−2.30648
$276$	−5.46410	−0.328900
$277$	22.0000	1.32185	0.660926	−	0.750451i	$-0.270164\pi$
$277$	22.0000	1.32185	0.660926	+	0.750451i	$0.270164\pi$
$278$	9.85641	0.591148
$279$	−6.92820	−0.414781
$280$	0	0
$281$	−26.0000	−1.55103	−0.775515	−	0.631329i	$-0.782510\pi$
$281$	−26.0000	−1.55103	−0.775515	+	0.631329i	$0.782510\pi$
$282$	10.9282	0.650765
$283$	20.0000	1.18888	0.594438	−	0.804141i	$-0.297374\pi$
$283$	20.0000	1.18888	0.594438	+	0.804141i	$0.297374\pi$
$284$	2.92820	0.173757
$285$	−3.46410	−0.205196
$286$	18.9282	1.11925
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	38.7128	2.27722
$290$	20.7846	1.22051
$291$	−4.53590	−0.265899
$292$	−10.0000	−0.585206
$293$	−7.07180	−0.413139	−0.206569	−	0.978432i	$-0.566230\pi$
$293$	−7.07180	−0.413139	−0.206569	+	0.978432i	$0.566230\pi$
$294$	0	0
$295$	−13.8564	−0.806751
$296$	−10.0000	−0.581238
$297$	−5.46410	−0.317059
$298$	3.07180	0.177944
$299$	−18.9282	−1.09465
$300$	7.00000	0.404145
$301$	0	0
$302$	−1.46410	−0.0842496
$303$	−4.53590	−0.260581
$304$	−1.00000	−0.0573539
$305$	17.0718	0.977528
$306$	7.46410	0.426694
$307$	−20.7846	−1.18624	−0.593120	−	0.805114i	$-0.702104\pi$
$307$	−20.7846	−1.18624	−0.593120	+	0.805114i	$0.702104\pi$
$308$	0	0
$309$	6.92820	0.394132
$310$	24.0000	1.36311
$311$	−2.14359	−0.121552	−0.0607760	−	0.998151i	$-0.519358\pi$
$311$	−2.14359	−0.121552	−0.0607760	+	0.998151i	$0.519358\pi$
$312$	−3.46410	−0.196116
$313$	6.00000	0.339140	0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000	0.339140	0.169570	+	0.985518i	$0.445762\pi$
$314$	19.8564	1.12056
$315$	0	0
$316$	−12.3923	−0.697122
$317$	7.85641	0.441260	0.220630	−	0.975358i	$-0.429189\pi$
$317$	7.85641	0.441260	0.220630	+	0.975358i	$0.429189\pi$
$318$	−2.00000	−0.112154
$319$	32.7846	1.83559
$320$	3.46410	0.193649
$321$	−4.00000	−0.223258
$322$	0	0
$323$	7.46410	0.415314
$324$	1.00000	0.0555556
$325$	24.2487	1.34508
$326$	−1.07180	−0.0593613
$327$	2.00000	0.110600
$328$	−2.00000	−0.110432
$329$	0	0
$330$	18.9282	1.04196
$331$	14.5359	0.798965	0.399483	−	0.916741i	$-0.369190\pi$
$331$	14.5359	0.798965	0.399483	+	0.916741i	$0.369190\pi$
$332$	−8.00000	−0.439057
$333$	10.0000	0.547997
$334$	−18.9282	−1.03571
$335$	32.7846	1.79121
$336$	0	0
$337$	10.7846	0.587475	0.293738	−	0.955886i	$-0.405101\pi$
$337$	10.7846	0.587475	0.293738	+	0.955886i	$0.405101\pi$
$338$	1.00000	0.0543928
$339$	11.8564	0.643952
$340$	−25.8564	−1.40226
$341$	37.8564	2.05004
$342$	1.00000	0.0540738
$343$	0	0
$344$	6.92820	0.373544
$345$	−18.9282	−1.01906
$346$	−0.928203	−0.0499005
$347$	27.3205	1.46664	0.733321	−	0.679883i	$-0.237969\pi$
$347$	27.3205	1.46664	0.733321	+	0.679883i	$0.237969\pi$
$348$	−6.00000	−0.321634
$349$	−35.8564	−1.91935	−0.959675	−	0.281113i	$-0.909296\pi$
$349$	−35.8564	−1.91935	−0.959675	+	0.281113i	$0.909296\pi$
$350$	0	0
$351$	3.46410	0.184900
$352$	5.46410	0.291238
$353$	−5.32051	−0.283182	−0.141591	−	0.989925i	$-0.545222\pi$
$353$	−5.32051	−0.283182	−0.141591	+	0.989925i	$0.545222\pi$
$354$	4.00000	0.212598
$355$	10.1436	0.538366
$356$	2.00000	0.106000
$357$	0	0
$358$	9.85641	0.520927
$359$	35.3205	1.86415	0.932073	−	0.362272i	$-0.117999\pi$
$359$	35.3205	1.86415	0.932073	+	0.362272i	$0.117999\pi$
$360$	−3.46410	−0.182574
$361$	1.00000	0.0526316
$362$	−8.53590	−0.448637
$363$	18.8564	0.989705
$364$	0	0
$365$	−34.6410	−1.81319
$366$	−4.92820	−0.257601
$367$	−8.00000	−0.417597	−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000	−0.417597	−0.208798	+	0.977959i	$0.566955\pi$
$368$	−5.46410	−0.284836
$369$	2.00000	0.104116
$370$	−34.6410	−1.80090
$371$	0	0
$372$	−6.92820	−0.359211
$373$	10.7846	0.558406	0.279203	−	0.960232i	$-0.409930\pi$
$373$	10.7846	0.558406	0.279203	+	0.960232i	$0.409930\pi$
$374$	−40.7846	−2.10892
$375$	6.92820	0.357771
$376$	10.9282	0.563579
$377$	−20.7846	−1.07046
$378$	0	0
$379$	−1.46410	−0.0752058	−0.0376029	−	0.999293i	$-0.511972\pi$
$379$	−1.46410	−0.0752058	−0.0376029	+	0.999293i	$0.511972\pi$
$380$	−3.46410	−0.177705
$381$	−17.4641	−0.894713
$382$	5.46410	0.279568
$383$	−8.00000	−0.408781	−0.204390	−	0.978889i	$-0.565521\pi$
$383$	−8.00000	−0.408781	−0.204390	+	0.978889i	$0.565521\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	22.0000	1.11977
$387$	−6.92820	−0.352180
$388$	−4.53590	−0.230275
$389$	29.7128	1.50650	0.753250	−	0.657735i	$-0.228485\pi$
$389$	29.7128	1.50650	0.753250	+	0.657735i	$0.228485\pi$
$390$	−12.0000	−0.607644
$391$	40.7846	2.06257
$392$	0	0
$393$	5.07180	0.255838
$394$	−4.92820	−0.248279
$395$	−42.9282	−2.15995
$396$	−5.46410	−0.274581
$397$	−19.8564	−0.996564	−0.498282	−	0.867015i	$-0.666036\pi$
$397$	−19.8564	−0.996564	−0.498282	+	0.867015i	$0.666036\pi$
$398$	−24.7846	−1.24234
$399$	0	0
$400$	7.00000	0.350000
$401$	19.8564	0.991582	0.495791	−	0.868442i	$-0.334878\pi$
$401$	19.8564	0.991582	0.495791	+	0.868442i	$0.334878\pi$
$402$	−9.46410	−0.472026
$403$	−24.0000	−1.19553
$404$	−4.53590	−0.225669
$405$	3.46410	0.172133
$406$	0	0
$407$	−54.6410	−2.70845
$408$	7.46410	0.369528
$409$	31.1769	1.54160	0.770800	−	0.637078i	$-0.219857\pi$
$409$	31.1769	1.54160	0.770800	+	0.637078i	$0.219857\pi$
$410$	−6.92820	−0.342160
$411$	−0.928203	−0.0457849
$412$	6.92820	0.341328
$413$	0	0
$414$	5.46410	0.268546
$415$	−27.7128	−1.36037
$416$	−3.46410	−0.169842
$417$	−9.85641	−0.482670
$418$	−5.46410	−0.267258
$419$	−18.9282	−0.924703	−0.462352	−	0.886697i	$-0.652994\pi$
$419$	−18.9282	−0.924703	−0.462352	+	0.886697i	$0.652994\pi$
$420$	0	0
$421$	18.7846	0.915506	0.457753	−	0.889079i	$-0.348654\pi$
$421$	18.7846	0.915506	0.457753	+	0.889079i	$0.348654\pi$
$422$	−1.46410	−0.0712714
$423$	−10.9282	−0.531347
$424$	−2.00000	−0.0971286
$425$	−52.2487	−2.53443
$426$	−2.92820	−0.141872
$427$	0	0
$428$	−4.00000	−0.193347
$429$	−18.9282	−0.913862
$430$	24.0000	1.15738
$431$	−34.9282	−1.68243	−0.841216	−	0.540699i	$-0.818160\pi$
$431$	−34.9282	−1.68243	−0.841216	+	0.540699i	$0.818160\pi$
$432$	1.00000	0.0481125
$433$	−6.67949	−0.320996	−0.160498	−	0.987036i	$-0.551310\pi$
$433$	−6.67949	−0.320996	−0.160498	+	0.987036i	$0.551310\pi$
$434$	0	0
$435$	−20.7846	−0.996546
$436$	2.00000	0.0957826
$437$	5.46410	0.261383
$438$	10.0000	0.477818
$439$	4.78461	0.228357	0.114178	−	0.993460i	$-0.463576\pi$
$439$	4.78461	0.228357	0.114178	+	0.993460i	$0.463576\pi$
$440$	18.9282	0.902367
$441$	0	0
$442$	25.8564	1.22986
$443$	−11.3205	−0.537854	−0.268927	−	0.963161i	$-0.586669\pi$
$443$	−11.3205	−0.537854	−0.268927	+	0.963161i	$0.586669\pi$
$444$	10.0000	0.474579
$445$	6.92820	0.328428
$446$	−12.0000	−0.568216
$447$	−3.07180	−0.145291
$448$	0	0
$449$	−7.85641	−0.370767	−0.185383	−	0.982666i	$-0.559353\pi$
$449$	−7.85641	−0.370767	−0.185383	+	0.982666i	$0.559353\pi$
$450$	−7.00000	−0.329983
$451$	−10.9282	−0.514589
$452$	11.8564	0.557678
$453$	1.46410	0.0687895
$454$	14.9282	0.700615
$455$	0	0
$456$	1.00000	0.0468293
$457$	12.1436	0.568053	0.284027	−	0.958816i	$-0.408330\pi$
$457$	12.1436	0.568053	0.284027	+	0.958816i	$0.408330\pi$
$458$	3.07180	0.143536
$459$	−7.46410	−0.348394
$460$	−18.9282	−0.882532
$461$	−38.1051	−1.77473	−0.887366	−	0.461065i	$-0.847467\pi$
$461$	−38.1051	−1.77473	−0.887366	+	0.461065i	$0.847467\pi$
$462$	0	0
$463$	24.0000	1.11537	0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000	1.11537	0.557687	+	0.830051i	$0.311689\pi$
$464$	−6.00000	−0.278543
$465$	−24.0000	−1.11297
$466$	−26.7846	−1.24077
$467$	−35.7128	−1.65259	−0.826296	−	0.563236i	$-0.809556\pi$
$467$	−35.7128	−1.65259	−0.826296	+	0.563236i	$0.809556\pi$
$468$	3.46410	0.160128
$469$	0	0
$470$	37.8564	1.74619
$471$	−19.8564	−0.914935
$472$	4.00000	0.184115
$473$	37.8564	1.74064
$474$	12.3923	0.569197
$475$	−7.00000	−0.321182
$476$	0	0
$477$	2.00000	0.0915737
$478$	−30.2487	−1.38354
$479$	−27.7128	−1.26623	−0.633115	−	0.774057i	$-0.718224\pi$
$479$	−27.7128	−1.26623	−0.633115	+	0.774057i	$0.718224\pi$
$480$	−3.46410	−0.158114
$481$	34.6410	1.57949
$482$	21.3205	0.971123
$483$	0	0
$484$	18.8564	0.857109
$485$	−15.7128	−0.713482
$486$	−1.00000	−0.0453609
$487$	−39.3205	−1.78178	−0.890891	−	0.454217i	$-0.849919\pi$
$487$	−39.3205	−1.78178	−0.890891	+	0.454217i	$0.849919\pi$
$488$	−4.92820	−0.223089
$489$	1.07180	0.0484683
$490$	0	0
$491$	−40.3923	−1.82288	−0.911440	−	0.411434i	$-0.865028\pi$
$491$	−40.3923	−1.82288	−0.911440	+	0.411434i	$0.865028\pi$
$492$	2.00000	0.0901670
$493$	44.7846	2.01700
$494$	3.46410	0.155857
$495$	−18.9282	−0.850759
$496$	−6.92820	−0.311086
$497$	0	0
$498$	8.00000	0.358489
$499$	−22.9282	−1.02641	−0.513204	−	0.858267i	$-0.671541\pi$
$499$	−22.9282	−1.02641	−0.513204	+	0.858267i	$0.671541\pi$
$500$	6.92820	0.309839
$501$	18.9282	0.845650
$502$	5.07180	0.226365
$503$	21.8564	0.974529	0.487264	−	0.873254i	$-0.337995\pi$
$503$	21.8564	0.974529	0.487264	+	0.873254i	$0.337995\pi$
$504$	0	0
$505$	−15.7128	−0.699211
$506$	−29.8564	−1.32728
$507$	−1.00000	−0.0444116
$508$	−17.4641	−0.774844
$509$	44.6410	1.97868	0.989339	−	0.145630i	$-0.0465209\pi$
$509$	44.6410	1.97868	0.989339	+	0.145630i	$0.0465209\pi$
$510$	25.8564	1.14494
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	24.9282	1.09954
$515$	24.0000	1.05757
$516$	−6.92820	−0.304997
$517$	59.7128	2.62617
$518$	0	0
$519$	0.928203	0.0407436
$520$	−12.0000	−0.526235
$521$	−25.7128	−1.12650	−0.563249	−	0.826287i	$-0.690449\pi$
$521$	−25.7128	−1.12650	−0.563249	+	0.826287i	$0.690449\pi$
$522$	6.00000	0.262613
$523$	−26.6410	−1.16493	−0.582465	−	0.812856i	$-0.697912\pi$
$523$	−26.6410	−1.16493	−0.582465	+	0.812856i	$0.697912\pi$
$524$	5.07180	0.221562
$525$	0	0
$526$	−11.3205	−0.493598
$527$	51.7128	2.25265
$528$	−5.46410	−0.237795
$529$	6.85641	0.298105
$530$	−6.92820	−0.300942
$531$	−4.00000	−0.173585
$532$	0	0
$533$	6.92820	0.300094
$534$	−2.00000	−0.0865485
$535$	−13.8564	−0.599065
$536$	−9.46410	−0.408787
$537$	−9.85641	−0.425335
$538$	−16.9282	−0.729827
$539$	0	0
$540$	3.46410	0.149071
$541$	−34.0000	−1.46177	−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000	−1.46177	−0.730887	+	0.682498i	$0.760893\pi$
$542$	−29.8564	−1.28244
$543$	8.53590	0.366310
$544$	7.46410	0.320021
$545$	6.92820	0.296772
$546$	0	0
$547$	−10.2487	−0.438203	−0.219102	−	0.975702i	$-0.570313\pi$
$547$	−10.2487	−0.438203	−0.219102	+	0.975702i	$0.570313\pi$
$548$	−0.928203	−0.0396509
$549$	4.92820	0.210331
$550$	38.2487	1.63093
$551$	6.00000	0.255609
$552$	5.46410	0.232568
$553$	0	0
$554$	−22.0000	−0.934690
$555$	34.6410	1.47043
$556$	−9.85641	−0.418005
$557$	4.92820	0.208815	0.104407	−	0.994535i	$-0.466705\pi$
$557$	4.92820	0.208815	0.104407	+	0.994535i	$0.466705\pi$
$558$	6.92820	0.293294
$559$	−24.0000	−1.01509
$560$	0	0
$561$	40.7846	1.72193
$562$	26.0000	1.09674
$563$	−25.8564	−1.08972	−0.544859	−	0.838528i	$-0.683417\pi$
$563$	−25.8564	−1.08972	−0.544859	+	0.838528i	$0.683417\pi$
$564$	−10.9282	−0.460160
$565$	41.0718	1.72790
$566$	−20.0000	−0.840663
$567$	0	0
$568$	−2.92820	−0.122865
$569$	−45.7128	−1.91638	−0.958190	−	0.286131i	$-0.907631\pi$
$569$	−45.7128	−1.91638	−0.958190	+	0.286131i	$0.907631\pi$
$570$	3.46410	0.145095
$571$	37.5692	1.57222	0.786111	−	0.618085i	$-0.212091\pi$
$571$	37.5692	1.57222	0.786111	+	0.618085i	$0.212091\pi$
$572$	−18.9282	−0.791428
$573$	−5.46410	−0.228266
$574$	0	0
$575$	−38.2487	−1.59508
$576$	1.00000	0.0416667
$577$	3.85641	0.160544	0.0802722	−	0.996773i	$-0.474421\pi$
$577$	3.85641	0.160544	0.0802722	+	0.996773i	$0.474421\pi$
$578$	−38.7128	−1.61024
$579$	−22.0000	−0.914289
$580$	−20.7846	−0.863034
$581$	0	0
$582$	4.53590	0.188019
$583$	−10.9282	−0.452600
$584$	10.0000	0.413803
$585$	12.0000	0.496139
$586$	7.07180	0.292133
$587$	8.00000	0.330195	0.165098	−	0.986277i	$-0.447206\pi$
$587$	8.00000	0.330195	0.165098	+	0.986277i	$0.447206\pi$
$588$	0	0
$589$	6.92820	0.285472
$590$	13.8564	0.570459
$591$	4.92820	0.202719
$592$	10.0000	0.410997
$593$	−12.5359	−0.514788	−0.257394	−	0.966307i	$-0.582864\pi$
$593$	−12.5359	−0.514788	−0.257394	+	0.966307i	$0.582864\pi$
$594$	5.46410	0.224195
$595$	0	0
$596$	−3.07180	−0.125826
$597$	24.7846	1.01437
$598$	18.9282	0.774032
$599$	13.0718	0.534099	0.267050	−	0.963683i	$-0.413951\pi$
$599$	13.0718	0.534099	0.267050	+	0.963683i	$0.413951\pi$
$600$	−7.00000	−0.285774
$601$	−6.67949	−0.272462	−0.136231	−	0.990677i	$-0.543499\pi$
$601$	−6.67949	−0.272462	−0.136231	+	0.990677i	$0.543499\pi$
$602$	0	0
$603$	9.46410	0.385408
$604$	1.46410	0.0595734
$605$	65.3205	2.65566
$606$	4.53590	0.184258
$607$	17.8564	0.724769	0.362385	−	0.932029i	$-0.381963\pi$
$607$	17.8564	0.724769	0.362385	+	0.932029i	$0.381963\pi$
$608$	1.00000	0.0405554
$609$	0	0
$610$	−17.0718	−0.691217
$611$	−37.8564	−1.53151
$612$	−7.46410	−0.301718
$613$	−23.8564	−0.963551	−0.481776	−	0.876295i	$-0.660008\pi$
$613$	−23.8564	−0.963551	−0.481776	+	0.876295i	$0.660008\pi$
$614$	20.7846	0.838799
$615$	6.92820	0.279372
$616$	0	0
$617$	12.9282	0.520470	0.260235	−	0.965545i	$-0.416200\pi$
$617$	12.9282	0.520470	0.260235	+	0.965545i	$0.416200\pi$
$618$	−6.92820	−0.278693
$619$	−26.6410	−1.07079	−0.535396	−	0.844601i	$-0.679838\pi$
$619$	−26.6410	−1.07079	−0.535396	+	0.844601i	$0.679838\pi$
$620$	−24.0000	−0.963863
$621$	−5.46410	−0.219267
$622$	2.14359	0.0859503
$623$	0	0
$624$	3.46410	0.138675
$625$	−11.0000	−0.440000
$626$	−6.00000	−0.239808
$627$	5.46410	0.218215
$628$	−19.8564	−0.792357
$629$	−74.6410	−2.97613
$630$	0	0
$631$	16.7846	0.668185	0.334092	−	0.942540i	$-0.391570\pi$
$631$	16.7846	0.668185	0.334092	+	0.942540i	$0.391570\pi$
$632$	12.3923	0.492939
$633$	1.46410	0.0581928
$634$	−7.85641	−0.312018
$635$	−60.4974	−2.40077
$636$	2.00000	0.0793052
$637$	0	0
$638$	−32.7846	−1.29796
$639$	2.92820	0.115838
$640$	−3.46410	−0.136931
$641$	−15.8564	−0.626290	−0.313145	−	0.949705i	$-0.601383\pi$
$641$	−15.8564	−0.626290	−0.313145	+	0.949705i	$0.601383\pi$
$642$	4.00000	0.157867
$643$	14.9282	0.588711	0.294355	−	0.955696i	$-0.404895\pi$
$643$	14.9282	0.588711	0.294355	+	0.955696i	$0.404895\pi$
$644$	0	0
$645$	−24.0000	−0.944999
$646$	−7.46410	−0.293671
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	−1.00000	−0.0392837
$649$	21.8564	0.857939
$650$	−24.2487	−0.951113
$651$	0	0
$652$	1.07180	0.0419748
$653$	−33.7128	−1.31928	−0.659642	−	0.751580i	$-0.729292\pi$
$653$	−33.7128	−1.31928	−0.659642	+	0.751580i	$0.729292\pi$
$654$	−2.00000	−0.0782062
$655$	17.5692	0.686486
$656$	2.00000	0.0780869
$657$	−10.0000	−0.390137
$658$	0	0
$659$	14.1436	0.550956	0.275478	−	0.961307i	$-0.411164\pi$
$659$	14.1436	0.550956	0.275478	+	0.961307i	$0.411164\pi$
$660$	−18.9282	−0.736779
$661$	−45.3205	−1.76276	−0.881382	−	0.472405i	$-0.843386\pi$
$661$	−45.3205	−1.76276	−0.881382	+	0.472405i	$0.843386\pi$
$662$	−14.5359	−0.564954
$663$	−25.8564	−1.00418
$664$	8.00000	0.310460
$665$	0	0
$666$	−10.0000	−0.387492
$667$	32.7846	1.26943
$668$	18.9282	0.732354
$669$	12.0000	0.463947
$670$	−32.7846	−1.26658
$671$	−26.9282	−1.03955
$672$	0	0
$673$	−16.9282	−0.652534	−0.326267	−	0.945278i	$-0.605791\pi$
$673$	−16.9282	−0.652534	−0.326267	+	0.945278i	$0.605791\pi$
$674$	−10.7846	−0.415408
$675$	7.00000	0.269430
$676$	−1.00000	−0.0384615
$677$	19.8564	0.763144	0.381572	−	0.924339i	$-0.375383\pi$
$677$	19.8564	0.763144	0.381572	+	0.924339i	$0.375383\pi$
$678$	−11.8564	−0.455343
$679$	0	0
$680$	25.8564	0.991548
$681$	−14.9282	−0.572050
$682$	−37.8564	−1.44960
$683$	30.9282	1.18343	0.591717	−	0.806145i	$-0.298450\pi$
$683$	30.9282	1.18343	0.591717	+	0.806145i	$0.298450\pi$
$684$	−1.00000	−0.0382360
$685$	−3.21539	−0.122854
$686$	0	0
$687$	−3.07180	−0.117196
$688$	−6.92820	−0.264135
$689$	6.92820	0.263944
$690$	18.9282	0.720584
$691$	20.0000	0.760836	0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000	0.760836	0.380418	+	0.924815i	$0.375780\pi$
$692$	0.928203	0.0352850
$693$	0	0
$694$	−27.3205	−1.03707
$695$	−34.1436	−1.29514
$696$	6.00000	0.227429
$697$	−14.9282	−0.565446
$698$	35.8564	1.35718
$699$	26.7846	1.01309
$700$	0	0
$701$	13.7128	0.517926	0.258963	−	0.965887i	$-0.416619\pi$
$701$	13.7128	0.517926	0.258963	+	0.965887i	$0.416619\pi$
$702$	−3.46410	−0.130744
$703$	−10.0000	−0.377157
$704$	−5.46410	−0.205936
$705$	−37.8564	−1.42575
$706$	5.32051	0.200240
$707$	0	0
$708$	−4.00000	−0.150329
$709$	14.0000	0.525781	0.262891	−	0.964826i	$-0.415324\pi$
$709$	14.0000	0.525781	0.262891	+	0.964826i	$0.415324\pi$
$710$	−10.1436	−0.380682
$711$	−12.3923	−0.464748
$712$	−2.00000	−0.0749532
$713$	37.8564	1.41773
$714$	0	0
$715$	−65.5692	−2.45215
$716$	−9.85641	−0.368351
$717$	30.2487	1.12966
$718$	−35.3205	−1.31815
$719$	−16.0000	−0.596699	−0.298350	−	0.954457i	$-0.596436\pi$
$719$	−16.0000	−0.596699	−0.298350	+	0.954457i	$0.596436\pi$
$720$	3.46410	0.129099
$721$	0	0
$722$	−1.00000	−0.0372161
$723$	−21.3205	−0.792918
$724$	8.53590	0.317234
$725$	−42.0000	−1.55984
$726$	−18.8564	−0.699827
$727$	−8.00000	−0.296704	−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000	−0.296704	−0.148352	+	0.988935i	$0.547397\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	34.6410	1.28212
$731$	51.7128	1.91267
$732$	4.92820	0.182152
$733$	2.00000	0.0738717	0.0369358	−	0.999318i	$-0.488240\pi$
$733$	2.00000	0.0738717	0.0369358	+	0.999318i	$0.488240\pi$
$734$	8.00000	0.295285
$735$	0	0
$736$	5.46410	0.201409
$737$	−51.7128	−1.90487
$738$	−2.00000	−0.0736210
$739$	−9.85641	−0.362574	−0.181287	−	0.983430i	$-0.558026\pi$
$739$	−9.85641	−0.362574	−0.181287	+	0.983430i	$0.558026\pi$
$740$	34.6410	1.27343
$741$	−3.46410	−0.127257
$742$	0	0
$743$	27.7128	1.01668	0.508342	−	0.861155i	$-0.330258\pi$
$743$	27.7128	1.01668	0.508342	+	0.861155i	$0.330258\pi$
$744$	6.92820	0.254000
$745$	−10.6410	−0.389857
$746$	−10.7846	−0.394853
$747$	−8.00000	−0.292705
$748$	40.7846	1.49123
$749$	0	0
$750$	−6.92820	−0.252982
$751$	20.3923	0.744126	0.372063	−	0.928208i	$-0.378651\pi$
$751$	20.3923	0.744126	0.372063	+	0.928208i	$0.378651\pi$
$752$	−10.9282	−0.398511
$753$	−5.07180	−0.184827
$754$	20.7846	0.756931
$755$	5.07180	0.184582
$756$	0	0
$757$	3.85641	0.140163	0.0700817	−	0.997541i	$-0.477674\pi$
$757$	3.85641	0.140163	0.0700817	+	0.997541i	$0.477674\pi$
$758$	1.46410	0.0531786
$759$	29.8564	1.08372
$760$	3.46410	0.125656
$761$	−4.53590	−0.164426	−0.0822131	−	0.996615i	$-0.526199\pi$
$761$	−4.53590	−0.164426	−0.0822131	+	0.996615i	$0.526199\pi$
$762$	17.4641	0.632658
$763$	0	0
$764$	−5.46410	−0.197684
$765$	−25.8564	−0.934840
$766$	8.00000	0.289052
$767$	−13.8564	−0.500326
$768$	1.00000	0.0360844
$769$	19.8564	0.716040	0.358020	−	0.933714i	$-0.383452\pi$
$769$	19.8564	0.716040	0.358020	+	0.933714i	$0.383452\pi$
$770$	0	0
$771$	−24.9282	−0.897767
$772$	−22.0000	−0.791797
$773$	−2.78461	−0.100155	−0.0500777	−	0.998745i	$-0.515947\pi$
$773$	−2.78461	−0.100155	−0.0500777	+	0.998745i	$0.515947\pi$
$774$	6.92820	0.249029
$775$	−48.4974	−1.74208
$776$	4.53590	0.162829
$777$	0	0
$778$	−29.7128	−1.06526
$779$	−2.00000	−0.0716574
$780$	12.0000	0.429669
$781$	−16.0000	−0.572525
$782$	−40.7846	−1.45845
$783$	−6.00000	−0.214423
$784$	0	0
$785$	−68.7846	−2.45503
$786$	−5.07180	−0.180905
$787$	11.2154	0.399785	0.199893	−	0.979818i	$-0.435941\pi$
$787$	11.2154	0.399785	0.199893	+	0.979818i	$0.435941\pi$
$788$	4.92820	0.175560
$789$	11.3205	0.403021
$790$	42.9282	1.52732
$791$	0	0
$792$	5.46410	0.194158
$793$	17.0718	0.606237
$794$	19.8564	0.704677
$795$	6.92820	0.245718
$796$	24.7846	0.878467
$797$	44.6410	1.58127	0.790633	−	0.612290i	$-0.209752\pi$
$797$	44.6410	1.58127	0.790633	+	0.612290i	$0.209752\pi$
$798$	0	0
$799$	81.5692	2.88571
$800$	−7.00000	−0.247487
$801$	2.00000	0.0706665
$802$	−19.8564	−0.701154
$803$	54.6410	1.92824
$804$	9.46410	0.333773
$805$	0	0
$806$	24.0000	0.845364
$807$	16.9282	0.595901
$808$	4.53590	0.159572
$809$	18.0000	0.632846	0.316423	−	0.948618i	$-0.397518\pi$
$809$	18.0000	0.632846	0.316423	+	0.948618i	$0.397518\pi$
$810$	−3.46410	−0.121716
$811$	−33.0718	−1.16131	−0.580654	−	0.814150i	$-0.697203\pi$
$811$	−33.0718	−1.16131	−0.580654	+	0.814150i	$0.697203\pi$
$812$	0	0
$813$	29.8564	1.04711
$814$	54.6410	1.91517
$815$	3.71281	0.130054
$816$	−7.46410	−0.261296
$817$	6.92820	0.242387
$818$	−31.1769	−1.09008
$819$	0	0
$820$	6.92820	0.241943
$821$	−48.9282	−1.70761	−0.853803	−	0.520596i	$-0.825710\pi$
$821$	−48.9282	−1.70761	−0.853803	+	0.520596i	$0.825710\pi$
$822$	0.928203	0.0323748
$823$	−21.8564	−0.761866	−0.380933	−	0.924603i	$-0.624397\pi$
$823$	−21.8564	−0.761866	−0.380933	+	0.924603i	$0.624397\pi$
$824$	−6.92820	−0.241355
$825$	−38.2487	−1.33165
$826$	0	0
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	−5.46410	−0.189891
$829$	5.60770	0.194763	0.0973817	−	0.995247i	$-0.468953\pi$
$829$	5.60770	0.194763	0.0973817	+	0.995247i	$0.468953\pi$
$830$	27.7128	0.961926
$831$	22.0000	0.763172
$832$	3.46410	0.120096
$833$	0	0
$834$	9.85641	0.341299
$835$	65.5692	2.26912
$836$	5.46410	0.188980
$837$	−6.92820	−0.239474
$838$	18.9282	0.653864
$839$	5.07180	0.175098	0.0875489	−	0.996160i	$-0.472097\pi$
$839$	5.07180	0.175098	0.0875489	+	0.996160i	$0.472097\pi$
$840$	0	0
$841$	7.00000	0.241379
$842$	−18.7846	−0.647360
$843$	−26.0000	−0.895488
$844$	1.46410	0.0503965
$845$	−3.46410	−0.119169
$846$	10.9282	0.375719
$847$	0	0
$848$	2.00000	0.0686803
$849$	20.0000	0.686398
$850$	52.2487	1.79212
$851$	−54.6410	−1.87307
$852$	2.92820	0.100319
$853$	−35.0718	−1.20084	−0.600418	−	0.799687i	$-0.704999\pi$
$853$	−35.0718	−1.20084	−0.600418	+	0.799687i	$0.704999\pi$
$854$	0	0
$855$	−3.46410	−0.118470
$856$	4.00000	0.136717
$857$	−47.5692	−1.62493	−0.812467	−	0.583007i	$-0.801876\pi$
$857$	−47.5692	−1.62493	−0.812467	+	0.583007i	$0.801876\pi$
$858$	18.9282	0.646198
$859$	28.7846	0.982118	0.491059	−	0.871126i	$-0.336610\pi$
$859$	28.7846	0.982118	0.491059	+	0.871126i	$0.336610\pi$
$860$	−24.0000	−0.818393
$861$	0	0
$862$	34.9282	1.18966
$863$	18.1436	0.617615	0.308808	−	0.951125i	$-0.400070\pi$
$863$	18.1436	0.617615	0.308808	+	0.951125i	$0.400070\pi$
$864$	−1.00000	−0.0340207
$865$	3.21539	0.109327
$866$	6.67949	0.226978
$867$	38.7128	1.31476
$868$	0	0
$869$	67.7128	2.29700
$870$	20.7846	0.704664
$871$	32.7846	1.11086
$872$	−2.00000	−0.0677285
$873$	−4.53590	−0.153517
$874$	−5.46410	−0.184826
$875$	0	0
$876$	−10.0000	−0.337869
$877$	2.00000	0.0675352	0.0337676	−	0.999430i	$-0.489249\pi$
$877$	2.00000	0.0675352	0.0337676	+	0.999430i	$0.489249\pi$
$878$	−4.78461	−0.161473
$879$	−7.07180	−0.238526
$880$	−18.9282	−0.638070
$881$	−43.1769	−1.45467	−0.727334	−	0.686284i	$-0.759241\pi$
$881$	−43.1769	−1.45467	−0.727334	+	0.686284i	$0.759241\pi$
$882$	0	0
$883$	48.4974	1.63207	0.816034	−	0.578004i	$-0.196168\pi$
$883$	48.4974	1.63207	0.816034	+	0.578004i	$0.196168\pi$
$884$	−25.8564	−0.869645
$885$	−13.8564	−0.465778
$886$	11.3205	0.380320
$887$	27.7128	0.930505	0.465253	−	0.885178i	$-0.345963\pi$
$887$	27.7128	0.930505	0.465253	+	0.885178i	$0.345963\pi$
$888$	−10.0000	−0.335578
$889$	0	0
$890$	−6.92820	−0.232234
$891$	−5.46410	−0.183054
$892$	12.0000	0.401790
$893$	10.9282	0.365698
$894$	3.07180	0.102736
$895$	−34.1436	−1.14129
$896$	0	0
$897$	−18.9282	−0.631994
$898$	7.85641	0.262172
$899$	41.5692	1.38641
$900$	7.00000	0.233333
$901$	−14.9282	−0.497331
$902$	10.9282	0.363869
$903$	0	0
$904$	−11.8564	−0.394338
$905$	29.5692	0.982914
$906$	−1.46410	−0.0486415
$907$	−41.4641	−1.37679	−0.688396	−	0.725335i	$-0.741685\pi$
$907$	−41.4641	−1.37679	−0.688396	+	0.725335i	$0.741685\pi$
$908$	−14.9282	−0.495410
$909$	−4.53590	−0.150446
$910$	0	0
$911$	22.6410	0.750130	0.375065	−	0.926998i	$-0.377620\pi$
$911$	22.6410	0.750130	0.375065	+	0.926998i	$0.377620\pi$
$912$	−1.00000	−0.0331133
$913$	43.7128	1.44668
$914$	−12.1436	−0.401674
$915$	17.0718	0.564376
$916$	−3.07180	−0.101495
$917$	0	0
$918$	7.46410	0.246352
$919$	−49.5692	−1.63514	−0.817569	−	0.575831i	$-0.804679\pi$
$919$	−49.5692	−1.63514	−0.817569	+	0.575831i	$0.804679\pi$
$920$	18.9282	0.624044
$921$	−20.7846	−0.684876
$922$	38.1051	1.25493
$923$	10.1436	0.333880
$924$	0	0
$925$	70.0000	2.30159
$926$	−24.0000	−0.788689
$927$	6.92820	0.227552
$928$	6.00000	0.196960
$929$	−25.6077	−0.840161	−0.420081	−	0.907487i	$-0.637998\pi$
$929$	−25.6077	−0.840161	−0.420081	+	0.907487i	$0.637998\pi$
$930$	24.0000	0.786991
$931$	0	0
$932$	26.7846	0.877359
$933$	−2.14359	−0.0701781
$934$	35.7128	1.16856
$935$	141.282	4.62042
$936$	−3.46410	−0.113228
$937$	−20.9282	−0.683695	−0.341847	−	0.939756i	$-0.611053\pi$
$937$	−20.9282	−0.683695	−0.341847	+	0.939756i	$0.611053\pi$
$938$	0	0
$939$	6.00000	0.195803
$940$	−37.8564	−1.23474
$941$	5.21539	0.170017	0.0850084	−	0.996380i	$-0.472908\pi$
$941$	5.21539	0.170017	0.0850084	+	0.996380i	$0.472908\pi$
$942$	19.8564	0.646957
$943$	−10.9282	−0.355871
$944$	−4.00000	−0.130189
$945$	0	0
$946$	−37.8564	−1.23082
$947$	−28.1051	−0.913294	−0.456647	−	0.889648i	$-0.650950\pi$
$947$	−28.1051	−0.913294	−0.456647	+	0.889648i	$0.650950\pi$
$948$	−12.3923	−0.402483
$949$	−34.6410	−1.12449
$950$	7.00000	0.227110
$951$	7.85641	0.254761
$952$	0	0
$953$	−31.8564	−1.03193	−0.515965	−	0.856610i	$-0.672567\pi$
$953$	−31.8564	−1.03193	−0.515965	+	0.856610i	$0.672567\pi$
$954$	−2.00000	−0.0647524
$955$	−18.9282	−0.612502
$956$	30.2487	0.978313
$957$	32.7846	1.05978
$958$	27.7128	0.895360
$959$	0	0
$960$	3.46410	0.111803
$961$	17.0000	0.548387
$962$	−34.6410	−1.11687
$963$	−4.00000	−0.128898
$964$	−21.3205	−0.686687
$965$	−76.2102	−2.45329
$966$	0	0
$967$	−18.9282	−0.608690	−0.304345	−	0.952562i	$-0.598438\pi$
$967$	−18.9282	−0.608690	−0.304345	+	0.952562i	$0.598438\pi$
$968$	−18.8564	−0.606068
$969$	7.46410	0.239781
$970$	15.7128	0.504508
$971$	10.6410	0.341486	0.170743	−	0.985316i	$-0.445383\pi$
$971$	10.6410	0.341486	0.170743	+	0.985316i	$0.445383\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	39.3205	1.25991
$975$	24.2487	0.776580
$976$	4.92820	0.157748
$977$	−7.85641	−0.251349	−0.125674	−	0.992072i	$-0.540109\pi$
$977$	−7.85641	−0.251349	−0.125674	+	0.992072i	$0.540109\pi$
$978$	−1.07180	−0.0342723
$979$	−10.9282	−0.349267
$980$	0	0
$981$	2.00000	0.0638551
$982$	40.3923	1.28897
$983$	32.7846	1.04567	0.522833	−	0.852435i	$-0.324875\pi$
$983$	32.7846	1.04567	0.522833	+	0.852435i	$0.324875\pi$
$984$	−2.00000	−0.0637577
$985$	17.0718	0.543953
$986$	−44.7846	−1.42623
$987$	0	0
$988$	−3.46410	−0.110208
$989$	37.8564	1.20376
$990$	18.9282	0.601578
$991$	35.6077	1.13112	0.565558	−	0.824709i	$-0.308661\pi$
$991$	35.6077	1.13112	0.565558	+	0.824709i	$0.308661\pi$
$992$	6.92820	0.219971
$993$	14.5359	0.461283
$994$	0	0
$995$	85.8564	2.72183
$996$	−8.00000	−0.253490
$997$	47.8564	1.51563	0.757814	−	0.652471i	$-0.226268\pi$
$997$	47.8564	1.51563	0.757814	+	0.652471i	$0.226268\pi$
$998$	22.9282	0.725780
$999$	10.0000	0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5586.2.a.bd.1.2		2
7.6	odd	2		798.2.a.k.1.1	✓	2
21.20	even	2		2394.2.a.x.1.2		2
28.27	even	2		6384.2.a.br.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.a.k.1.1	✓	2	7.6	odd	2
2394.2.a.x.1.2		2	21.20	even	2
5586.2.a.bd.1.2		2	1.1	even	1	trivial
6384.2.a.br.1.1		2	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.46410 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.46410 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -3.46410 q^{10} -5.46410 q^{11} +1.00000 q^{12} +3.46410 q^{13} +3.46410 q^{15} +1.00000 q^{16} -7.46410 q^{17} -1.00000 q^{18} -1.00000 q^{19} +3.46410 q^{20} +5.46410 q^{22} -5.46410 q^{23} -1.00000 q^{24} +7.00000 q^{25} -3.46410 q^{26} +1.00000 q^{27} -6.00000 q^{29} -3.46410 q^{30} -6.92820 q^{31} -1.00000 q^{32} -5.46410 q^{33} +7.46410 q^{34} +1.00000 q^{36} +10.0000 q^{37} +1.00000 q^{38} +3.46410 q^{39} -3.46410 q^{40} +2.00000 q^{41} -6.92820 q^{43} -5.46410 q^{44} +3.46410 q^{45} +5.46410 q^{46} -10.9282 q^{47} +1.00000 q^{48} -7.00000 q^{50} -7.46410 q^{51} +3.46410 q^{52} +2.00000 q^{53} -1.00000 q^{54} -18.9282 q^{55} -1.00000 q^{57} +6.00000 q^{58} -4.00000 q^{59} +3.46410 q^{60} +4.92820 q^{61} +6.92820 q^{62} +1.00000 q^{64} +12.0000 q^{65} +5.46410 q^{66} +9.46410 q^{67} -7.46410 q^{68} -5.46410 q^{69} +2.92820 q^{71} -1.00000 q^{72} -10.0000 q^{73} -10.0000 q^{74} +7.00000 q^{75} -1.00000 q^{76} -3.46410 q^{78} -12.3923 q^{79} +3.46410 q^{80} +1.00000 q^{81} -2.00000 q^{82} -8.00000 q^{83} -25.8564 q^{85} +6.92820 q^{86} -6.00000 q^{87} +5.46410 q^{88} +2.00000 q^{89} -3.46410 q^{90} -5.46410 q^{92} -6.92820 q^{93} +10.9282 q^{94} -3.46410 q^{95} -1.00000 q^{96} -4.53590 q^{97} -5.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} - 2 q^{8} + 2 q^{9} - 4 q^{11} + 2 q^{12} + 2 q^{16} - 8 q^{17} - 2 q^{18} - 2 q^{19} + 4 q^{22} - 4 q^{23} - 2 q^{24} + 14 q^{25} + 2 q^{27} - 12 q^{29} - 2 q^{32} - 4 q^{33} + 8 q^{34} + 2 q^{36} + 20 q^{37} + 2 q^{38} + 4 q^{41} - 4 q^{44} + 4 q^{46} - 8 q^{47} + 2 q^{48} - 14 q^{50} - 8 q^{51} + 4 q^{53} - 2 q^{54} - 24 q^{55} - 2 q^{57} + 12 q^{58} - 8 q^{59} - 4 q^{61} + 2 q^{64} + 24 q^{65} + 4 q^{66} + 12 q^{67} - 8 q^{68} - 4 q^{69} - 8 q^{71} - 2 q^{72} - 20 q^{73} - 20 q^{74} + 14 q^{75} - 2 q^{76} - 4 q^{79} + 2 q^{81} - 4 q^{82} - 16 q^{83} - 24 q^{85} - 12 q^{87} + 4 q^{88} + 4 q^{89} - 4 q^{92} + 8 q^{94} - 2 q^{96} - 16 q^{97} - 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 - 2 * q^8 + 2 * q^9 - 4 * q^11 + 2 * q^12 + 2 * q^16 - 8 * q^17 - 2 * q^18 - 2 * q^19 + 4 * q^22 - 4 * q^23 - 2 * q^24 + 14 * q^25 + 2 * q^27 - 12 * q^29 - 2 * q^32 - 4 * q^33 + 8 * q^34 + 2 * q^36 + 20 * q^37 + 2 * q^38 + 4 * q^41 - 4 * q^44 + 4 * q^46 - 8 * q^47 + 2 * q^48 - 14 * q^50 - 8 * q^51 + 4 * q^53 - 2 * q^54 - 24 * q^55 - 2 * q^57 + 12 * q^58 - 8 * q^59 - 4 * q^61 + 2 * q^64 + 24 * q^65 + 4 * q^66 + 12 * q^67 - 8 * q^68 - 4 * q^69 - 8 * q^71 - 2 * q^72 - 20 * q^73 - 20 * q^74 + 14 * q^75 - 2 * q^76 - 4 * q^79 + 2 * q^81 - 4 * q^82 - 16 * q^83 - 24 * q^85 - 12 * q^87 + 4 * q^88 + 4 * q^89 - 4 * q^92 + 8 * q^94 - 2 * q^96 - 16 * q^97 - 4 * q^99

Introduction

L-functions

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