LMFDB - Embedded newform 4998.2.a.co.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4998,2,Mod(1,4998)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4998, 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("4998.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4998 = 2 \cdot 3 \cdot 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4998.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:	$39.9092309302$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.16448.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 7x^{2} + 8x + 14 $ x^4 - 2x^3 - 7x^2 + 8*x + 14
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.18398$ of defining polynomial
Character	$\chi$	$=$	4998.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.230234 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.230234 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -0.230234 q^{10} -2.27259 q^{11} -1.00000 q^{12} -4.59819 q^{13} +0.230234 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +1.67440 q^{19} -0.230234 q^{20} -2.27259 q^{22} +3.08861 q^{23} -1.00000 q^{24} -4.94699 q^{25} -4.59819 q^{26} -1.00000 q^{27} +0.845973 q^{29} +0.230234 q^{30} +0.325600 q^{31} +1.00000 q^{32} +2.27259 q^{33} -1.00000 q^{34} +1.00000 q^{36} +7.68681 q^{37} +1.67440 q^{38} +4.59819 q^{39} -0.230234 q^{40} +2.69356 q^{41} +10.1801 q^{43} -2.27259 q^{44} -0.230234 q^{45} +3.08861 q^{46} -3.02320 q^{47} -1.00000 q^{48} -4.94699 q^{50} +1.00000 q^{51} -4.59819 q^{52} +14.3150 q^{53} -1.00000 q^{54} +0.523229 q^{55} -1.67440 q^{57} +0.845973 q^{58} -0.0829597 q^{59} +0.230234 q^{60} -5.71676 q^{61} +0.325600 q^{62} +1.00000 q^{64} +1.05866 q^{65} +2.27259 q^{66} -0.733061 q^{67} -1.00000 q^{68} -3.08861 q^{69} -1.78217 q^{71} +1.00000 q^{72} +9.88709 q^{73} +7.68681 q^{74} +4.94699 q^{75} +1.67440 q^{76} +4.59819 q^{78} +11.1609 q^{79} -0.230234 q^{80} +1.00000 q^{81} +2.69356 q^{82} -7.20879 q^{83} +0.230234 q^{85} +10.1801 q^{86} -0.845973 q^{87} -2.27259 q^{88} +14.4075 q^{89} -0.230234 q^{90} +3.08861 q^{92} -0.325600 q^{93} -3.02320 q^{94} -0.385504 q^{95} -1.00000 q^{96} +4.03950 q^{97} -2.27259 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} - 2 q^{10} + 10 q^{11} - 4 q^{12} - 6 q^{13} + 2 q^{15} + 4 q^{16} - 4 q^{17} + 4 q^{18} - 2 q^{20} + 10 q^{22} - 4 q^{24} + 6 q^{25} - 6 q^{26} - 4 q^{27} + 8 q^{29} + 2 q^{30} + 8 q^{31} + 4 q^{32} - 10 q^{33} - 4 q^{34} + 4 q^{36} + 6 q^{37} + 6 q^{39} - 2 q^{40} + 4 q^{41} + 6 q^{43} + 10 q^{44} - 2 q^{45} + 8 q^{47} - 4 q^{48} + 6 q^{50} + 4 q^{51} - 6 q^{52} + 18 q^{53} - 4 q^{54} - 10 q^{55} + 8 q^{58} - 24 q^{59} + 2 q^{60} + 4 q^{61} + 8 q^{62} + 4 q^{64} - 6 q^{65} - 10 q^{66} + 14 q^{67} - 4 q^{68} + 12 q^{71} + 4 q^{72} + 18 q^{73} + 6 q^{74} - 6 q^{75} + 6 q^{78} + 10 q^{79} - 2 q^{80} + 4 q^{81} + 4 q^{82} + 14 q^{83} + 2 q^{85} + 6 q^{86} - 8 q^{87} + 10 q^{88} + 34 q^{89} - 2 q^{90} - 8 q^{93} + 8 q^{94} - 4 q^{95} - 4 q^{96} + 6 q^{97} + 10 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 - 2 * q^10 + 10 * q^11 - 4 * q^12 - 6 * q^13 + 2 * q^15 + 4 * q^16 - 4 * q^17 + 4 * q^18 - 2 * q^20 + 10 * q^22 - 4 * q^24 + 6 * q^25 - 6 * q^26 - 4 * q^27 + 8 * q^29 + 2 * q^30 + 8 * q^31 + 4 * q^32 - 10 * q^33 - 4 * q^34 + 4 * q^36 + 6 * q^37 + 6 * q^39 - 2 * q^40 + 4 * q^41 + 6 * q^43 + 10 * q^44 - 2 * q^45 + 8 * q^47 - 4 * q^48 + 6 * q^50 + 4 * q^51 - 6 * q^52 + 18 * q^53 - 4 * q^54 - 10 * q^55 + 8 * q^58 - 24 * q^59 + 2 * q^60 + 4 * q^61 + 8 * q^62 + 4 * q^64 - 6 * q^65 - 10 * q^66 + 14 * q^67 - 4 * q^68 + 12 * q^71 + 4 * q^72 + 18 * q^73 + 6 * q^74 - 6 * q^75 + 6 * q^78 + 10 * q^79 - 2 * q^80 + 4 * q^81 + 4 * q^82 + 14 * q^83 + 2 * q^85 + 6 * q^86 - 8 * q^87 + 10 * q^88 + 34 * q^89 - 2 * q^90 - 8 * q^93 + 8 * q^94 - 4 * q^95 - 4 * q^96 + 6 * q^97 + 10 * 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
$5$	−0.230234	−0.102964	−0.0514819	−	0.998674i	$-0.516394\pi$
$5$	−0.230234	−0.102964	−0.0514819	+	0.998674i	$0.516394\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.230234	−0.0728065
$11$	−2.27259	−0.685212	−0.342606	−	0.939479i	$-0.611310\pi$
$11$	−2.27259	−0.685212	−0.342606	+	0.939479i	$0.611310\pi$
$12$	−1.00000	−0.288675
$13$	−4.59819	−1.27531	−0.637655	−	0.770322i	$-0.720095\pi$
$13$	−4.59819	−1.27531	−0.637655	+	0.770322i	$0.720095\pi$
$14$	0	0
$15$	0.230234	0.0594462
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.00000	0.235702
$19$	1.67440	0.384134	0.192067	−	0.981382i	$-0.438481\pi$
$19$	1.67440	0.384134	0.192067	+	0.981382i	$0.438481\pi$
$20$	−0.230234	−0.0514819
$21$	0	0
$22$	−2.27259	−0.484518
$23$	3.08861	0.644020	0.322010	−	0.946736i	$-0.395641\pi$
$23$	3.08861	0.644020	0.322010	+	0.946736i	$0.395641\pi$
$24$	−1.00000	−0.204124
$25$	−4.94699	−0.989398
$26$	−4.59819	−0.901780
$27$	−1.00000	−0.192450
$28$	0	0
$29$	0.845973	0.157093	0.0785466	−	0.996910i	$-0.474972\pi$
$29$	0.845973	0.157093	0.0785466	+	0.996910i	$0.474972\pi$
$30$	0.230234	0.0420348
$31$	0.325600	0.0584795	0.0292398	−	0.999572i	$-0.490691\pi$
$31$	0.325600	0.0584795	0.0292398	+	0.999572i	$0.490691\pi$
$32$	1.00000	0.176777
$33$	2.27259	0.395608
$34$	−1.00000	−0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	7.68681	1.26370	0.631852	−	0.775089i	$-0.282295\pi$
$37$	7.68681	1.26370	0.631852	+	0.775089i	$0.282295\pi$
$38$	1.67440	0.271623
$39$	4.59819	0.736300
$40$	−0.230234	−0.0364032
$41$	2.69356	0.420663	0.210332	−	0.977630i	$-0.432546\pi$
$41$	2.69356	0.420663	0.210332	+	0.977630i	$0.432546\pi$
$42$	0	0
$43$	10.1801	1.55245	0.776224	−	0.630457i	$-0.217133\pi$
$43$	10.1801	1.55245	0.776224	+	0.630457i	$0.217133\pi$
$44$	−2.27259	−0.342606
$45$	−0.230234	−0.0343213
$46$	3.08861	0.455391
$47$	−3.02320	−0.440979	−0.220489	−	0.975389i	$-0.570765\pi$
$47$	−3.02320	−0.440979	−0.220489	+	0.975389i	$0.570765\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	−4.94699	−0.699610
$51$	1.00000	0.140028
$52$	−4.59819	−0.637655
$53$	14.3150	1.96631	0.983155	−	0.182774i	$-0.0585078\pi$
$53$	14.3150	1.96631	0.983155	+	0.182774i	$0.0585078\pi$
$54$	−1.00000	−0.136083
$55$	0.523229	0.0705521
$56$	0	0
$57$	−1.67440	−0.221780
$58$	0.845973	0.111082
$59$	−0.0829597	−0.0108004	−0.00540021	−	0.999985i	$-0.501719\pi$
$59$	−0.0829597	−0.0108004	−0.00540021	+	0.999985i	$0.501719\pi$
$60$	0.230234	0.0297231
$61$	−5.71676	−0.731956	−0.365978	−	0.930624i	$-0.619265\pi$
$61$	−5.71676	−0.731956	−0.365978	+	0.930624i	$0.619265\pi$
$62$	0.325600	0.0413513
$63$	0	0
$64$	1.00000	0.125000
$65$	1.05866	0.131311
$66$	2.27259	0.279737
$67$	−0.733061	−0.0895577	−0.0447788	−	0.998997i	$-0.514258\pi$
$67$	−0.733061	−0.0895577	−0.0447788	+	0.998997i	$0.514258\pi$
$68$	−1.00000	−0.121268
$69$	−3.08861	−0.371825
$70$	0	0
$71$	−1.78217	−0.211505	−0.105752	−	0.994392i	$-0.533725\pi$
$71$	−1.78217	−0.211505	−0.105752	+	0.994392i	$0.533725\pi$
$72$	1.00000	0.117851
$73$	9.88709	1.15720	0.578598	−	0.815613i	$-0.303600\pi$
$73$	9.88709	1.15720	0.578598	+	0.815613i	$0.303600\pi$
$74$	7.68681	0.893573
$75$	4.94699	0.571229
$76$	1.67440	0.192067
$77$	0	0
$78$	4.59819	0.520643
$79$	11.1609	1.25570	0.627851	−	0.778334i	$-0.283935\pi$
$79$	11.1609	1.25570	0.627851	+	0.778334i	$0.283935\pi$
$80$	−0.230234	−0.0257410
$81$	1.00000	0.111111
$82$	2.69356	0.297454
$83$	−7.20879	−0.791268	−0.395634	−	0.918408i	$-0.629475\pi$
$83$	−7.20879	−0.791268	−0.395634	+	0.918408i	$0.629475\pi$
$84$	0	0
$85$	0.230234	0.0249724
$86$	10.1801	1.09775
$87$	−0.845973	−0.0906978
$88$	−2.27259	−0.242259
$89$	14.4075	1.52719	0.763594	−	0.645697i	$-0.223433\pi$
$89$	14.4075	1.52719	0.763594	+	0.645697i	$0.223433\pi$
$90$	−0.230234	−0.0242688
$91$	0	0
$92$	3.08861	0.322010
$93$	−0.325600	−0.0337632
$94$	−3.02320	−0.311819
$95$	−0.385504	−0.0395519
$96$	−1.00000	−0.102062
$97$	4.03950	0.410149	0.205075	−	0.978746i	$-0.434256\pi$
$97$	4.03950	0.410149	0.205075	+	0.978746i	$0.434256\pi$
$98$	0	0
$99$	−2.27259	−0.228404
$100$	−4.94699	−0.494699
$101$	8.41987	0.837808	0.418904	−	0.908031i	$-0.362414\pi$
$101$	8.41987	0.837808	0.418904	+	0.908031i	$0.362414\pi$
$102$	1.00000	0.0990148
$103$	−1.18398	−0.116661	−0.0583305	−	0.998297i	$-0.518578\pi$
$103$	−1.18398	−0.116661	−0.0583305	+	0.998297i	$0.518578\pi$
$104$	−4.59819	−0.450890
$105$	0	0
$106$	14.3150	1.39039
$107$	1.26408	0.122203	0.0611017	−	0.998132i	$-0.480539\pi$
$107$	1.26408	0.122203	0.0611017	+	0.998132i	$0.480539\pi$
$108$	−1.00000	−0.0962250
$109$	8.80537	0.843402	0.421701	−	0.906735i	$-0.361433\pi$
$109$	8.80537	0.843402	0.421701	+	0.906735i	$0.361433\pi$
$110$	0.523229	0.0498879
$111$	−7.68681	−0.729599
$112$	0	0
$113$	−11.3437	−1.06712	−0.533561	−	0.845762i	$-0.679146\pi$
$113$	−11.3437	−1.06712	−0.533561	+	0.845762i	$0.679146\pi$
$114$	−1.67440	−0.156822
$115$	−0.711104	−0.0663108
$116$	0.845973	0.0785466
$117$	−4.59819	−0.425103
$118$	−0.0829597	−0.00763706
$119$	0	0
$120$	0.230234	0.0210174
$121$	−5.83532	−0.530484
$122$	−5.71676	−0.517571
$123$	−2.69356	−0.242870
$124$	0.325600	0.0292398
$125$	2.29014	0.204836
$126$	0	0
$127$	−12.2619	−1.08807	−0.544036	−	0.839062i	$-0.683104\pi$
$127$	−12.2619	−1.08807	−0.544036	+	0.839062i	$0.683104\pi$
$128$	1.00000	0.0883883
$129$	−10.1801	−0.896306
$130$	1.05866	0.0928507
$131$	−0.190732	−0.0166644	−0.00833218	−	0.999965i	$-0.502652\pi$
$131$	−0.190732	−0.0166644	−0.00833218	+	0.999965i	$0.502652\pi$
$132$	2.27259	0.197804
$133$	0	0
$134$	−0.733061	−0.0633268
$135$	0.230234	0.0198154
$136$	−1.00000	−0.0857493
$137$	−0.753463	−0.0643727	−0.0321863	−	0.999482i	$-0.510247\pi$
$137$	−0.753463	−0.0643727	−0.0321863	+	0.999482i	$0.510247\pi$
$138$	−3.08861	−0.262920
$139$	−11.2183	−0.951527	−0.475764	−	0.879573i	$-0.657828\pi$
$139$	−11.2183	−0.951527	−0.475764	+	0.879573i	$0.657828\pi$
$140$	0	0
$141$	3.02320	0.254599
$142$	−1.78217	−0.149557
$143$	10.4498	0.873858
$144$	1.00000	0.0833333
$145$	−0.194772	−0.0161749
$146$	9.88709	0.818261
$147$	0	0
$148$	7.68681	0.631852
$149$	12.4458	1.01960	0.509799	−	0.860294i	$-0.329720\pi$
$149$	12.4458	1.01960	0.509799	+	0.860294i	$0.329720\pi$
$150$	4.94699	0.403920
$151$	10.3178	0.839651	0.419826	−	0.907605i	$-0.362091\pi$
$151$	10.3178	0.839651	0.419826	+	0.907605i	$0.362091\pi$
$152$	1.67440	0.135812
$153$	−1.00000	−0.0808452
$154$	0	0
$155$	−0.0749643	−0.00602128
$156$	4.59819	0.368150
$157$	−1.52603	−0.121790	−0.0608951	−	0.998144i	$-0.519395\pi$
$157$	−1.52603	−0.121790	−0.0608951	+	0.998144i	$0.519395\pi$
$158$	11.1609	0.887915
$159$	−14.3150	−1.13525
$160$	−0.230234	−0.0182016
$161$	0	0
$162$	1.00000	0.0785674
$163$	19.7822	1.54946	0.774730	−	0.632293i	$-0.217886\pi$
$163$	19.7822	1.54946	0.774730	+	0.632293i	$0.217886\pi$
$164$	2.69356	0.210332
$165$	−0.523229	−0.0407333
$166$	−7.20879	−0.559511
$167$	4.80647	0.371936	0.185968	−	0.982556i	$-0.440458\pi$
$167$	4.80647	0.371936	0.185968	+	0.982556i	$0.440458\pi$
$168$	0	0
$169$	8.14338	0.626414
$170$	0.230234	0.0176582
$171$	1.67440	0.128045
$172$	10.1801	0.776224
$173$	19.5508	1.48642	0.743211	−	0.669057i	$-0.233302\pi$
$173$	19.5508	1.48642	0.743211	+	0.669057i	$0.233302\pi$
$174$	−0.845973	−0.0641330
$175$	0	0
$176$	−2.27259	−0.171303
$177$	0.0829597	0.00623563
$178$	14.4075	1.07988
$179$	−6.19477	−0.463019	−0.231509	−	0.972833i	$-0.574366\pi$
$179$	−6.19477	−0.463019	−0.231509	+	0.972833i	$0.574366\pi$
$180$	−0.230234	−0.0171606
$181$	−17.9747	−1.33605	−0.668023	−	0.744141i	$-0.732859\pi$
$181$	−17.9747	−1.33605	−0.668023	+	0.744141i	$0.732859\pi$
$182$	0	0
$183$	5.71676	0.422595
$184$	3.08861	0.227696
$185$	−1.76977	−0.130116
$186$	−0.325600	−0.0238742
$187$	2.27259	0.166188
$188$	−3.02320	−0.220489
$189$	0	0
$190$	−0.385504	−0.0279674
$191$	20.1067	1.45487	0.727434	−	0.686178i	$-0.240713\pi$
$191$	20.1067	1.45487	0.727434	+	0.686178i	$0.240713\pi$
$192$	−1.00000	−0.0721688
$193$	−20.1519	−1.45056	−0.725282	−	0.688452i	$-0.758291\pi$
$193$	−20.1519	−1.45056	−0.725282	+	0.688452i	$0.758291\pi$
$194$	4.03950	0.290019
$195$	−1.05866	−0.0758123
$196$	0	0
$197$	−13.6067	−0.969437	−0.484719	−	0.874670i	$-0.661078\pi$
$197$	−13.6067	−0.969437	−0.484719	+	0.874670i	$0.661078\pi$
$198$	−2.27259	−0.161506
$199$	15.6393	1.10864	0.554321	−	0.832303i	$-0.312978\pi$
$199$	15.6393	1.10864	0.554321	+	0.832303i	$0.312978\pi$
$200$	−4.94699	−0.349805
$201$	0.733061	0.0517061
$202$	8.41987	0.592420
$203$	0	0
$204$	1.00000	0.0700140
$205$	−0.620149	−0.0433131
$206$	−1.18398	−0.0824917
$207$	3.08861	0.214673
$208$	−4.59819	−0.318827
$209$	−3.80523	−0.263213
$210$	0	0
$211$	17.9243	1.23396	0.616980	−	0.786979i	$-0.288356\pi$
$211$	17.9243	1.23396	0.616980	+	0.786979i	$0.288356\pi$
$212$	14.3150	0.983155
$213$	1.78217	0.122112
$214$	1.26408	0.0864109
$215$	−2.34380	−0.159846
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	8.80537	0.596375
$219$	−9.88709	−0.668108
$220$	0.523229	0.0352761
$221$	4.59819	0.309308
$222$	−7.68681	−0.515905
$223$	−8.87630	−0.594401	−0.297200	−	0.954815i	$-0.596053\pi$
$223$	−8.87630	−0.594401	−0.297200	+	0.954815i	$0.596053\pi$
$224$	0	0
$225$	−4.94699	−0.329799
$226$	−11.3437	−0.754569
$227$	20.9706	1.39187	0.695933	−	0.718107i	$-0.254991\pi$
$227$	20.9706	1.39187	0.695933	+	0.718107i	$0.254991\pi$
$228$	−1.67440	−0.110890
$229$	−17.3341	−1.14547	−0.572735	−	0.819740i	$-0.694118\pi$
$229$	−17.3341	−1.14547	−0.572735	+	0.819740i	$0.694118\pi$
$230$	−0.711104	−0.0468888
$231$	0	0
$232$	0.845973	0.0555408
$233$	14.0874	0.922894	0.461447	−	0.887168i	$-0.347330\pi$
$233$	14.0874	0.922894	0.461447	+	0.887168i	$0.347330\pi$
$234$	−4.59819	−0.300593
$235$	0.696044	0.0454049
$236$	−0.0829597	−0.00540021
$237$	−11.1609	−0.724980
$238$	0	0
$239$	18.4498	1.19342	0.596710	−	0.802457i	$-0.296474\pi$
$239$	18.4498	1.19342	0.596710	+	0.802457i	$0.296474\pi$
$240$	0.230234	0.0148616
$241$	20.9380	1.34873	0.674366	−	0.738397i	$-0.264417\pi$
$241$	20.9380	1.34873	0.674366	+	0.738397i	$0.264417\pi$
$242$	−5.83532	−0.375109
$243$	−1.00000	−0.0641500
$244$	−5.71676	−0.365978
$245$	0	0
$246$	−2.69356	−0.171735
$247$	−7.69921	−0.489889
$248$	0.325600	0.0206756
$249$	7.20879	0.456839
$250$	2.29014	0.144841
$251$	−3.20879	−0.202537	−0.101269	−	0.994859i	$-0.532290\pi$
$251$	−3.20879	−0.202537	−0.101269	+	0.994859i	$0.532290\pi$
$252$	0	0
$253$	−7.01916	−0.441291
$254$	−12.2619	−0.769383
$255$	−0.230234	−0.0144178
$256$	1.00000	0.0625000
$257$	18.5982	1.16012	0.580062	−	0.814573i	$-0.303028\pi$
$257$	18.5982	1.16012	0.580062	+	0.814573i	$0.303028\pi$
$258$	−10.1801	−0.633784
$259$	0	0
$260$	1.05866	0.0656554
$261$	0.845973	0.0523644
$262$	−0.190732	−0.0117835
$263$	−6.89119	−0.424929	−0.212464	−	0.977169i	$-0.568149\pi$
$263$	−6.89119	−0.424929	−0.212464	+	0.977169i	$0.568149\pi$
$264$	2.27259	0.139868
$265$	−3.29579	−0.202459
$266$	0	0
$267$	−14.4075	−0.881722
$268$	−0.733061	−0.0447788
$269$	1.01916	0.0621392	0.0310696	−	0.999517i	$-0.490109\pi$
$269$	1.01916	0.0621392	0.0310696	+	0.999517i	$0.490109\pi$
$270$	0.230234	0.0140116
$271$	−5.09926	−0.309758	−0.154879	−	0.987933i	$-0.549499\pi$
$271$	−5.09926	−0.309758	−0.154879	+	0.987933i	$0.549499\pi$
$272$	−1.00000	−0.0606339
$273$	0	0
$274$	−0.753463	−0.0455184
$275$	11.2425	0.677948
$276$	−3.08861	−0.185913
$277$	−17.9419	−1.07802	−0.539011	−	0.842299i	$-0.681202\pi$
$277$	−17.9419	−1.07802	−0.539011	+	0.842299i	$0.681202\pi$
$278$	−11.2183	−0.672831
$279$	0.325600	0.0194932
$280$	0	0
$281$	−19.4909	−1.16273	−0.581366	−	0.813642i	$-0.697481\pi$
$281$	−19.4909	−1.16273	−0.581366	+	0.813642i	$0.697481\pi$
$282$	3.02320	0.180029
$283$	8.48242	0.504228	0.252114	−	0.967698i	$-0.418874\pi$
$283$	8.48242	0.504228	0.252114	+	0.967698i	$0.418874\pi$
$284$	−1.78217	−0.105752
$285$	0.385504	0.0228353
$286$	10.4498	0.617911
$287$	0	0
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−0.194772	−0.0114374
$291$	−4.03950	−0.236800
$292$	9.88709	0.578598
$293$	−22.7625	−1.32980	−0.664899	−	0.746933i	$-0.731526\pi$
$293$	−22.7625	−1.32980	−0.664899	+	0.746933i	$0.731526\pi$
$294$	0	0
$295$	0.0191002	0.00111205
$296$	7.68681	0.446787
$297$	2.27259	0.131869
$298$	12.4458	0.720965
$299$	−14.2020	−0.821325
$300$	4.94699	0.285615
$301$	0	0
$302$	10.3178	0.593723
$303$	−8.41987	−0.483709
$304$	1.67440	0.0960334
$305$	1.31619	0.0753650
$306$	−1.00000	−0.0571662
$307$	−5.03826	−0.287549	−0.143774	−	0.989611i	$-0.545924\pi$
$307$	−5.03826	−0.287549	−0.143774	+	0.989611i	$0.545924\pi$
$308$	0	0
$309$	1.18398	0.0673542
$310$	−0.0749643	−0.00425769
$311$	10.5558	0.598566	0.299283	−	0.954164i	$-0.403252\pi$
$311$	10.5558	0.598566	0.299283	+	0.954164i	$0.403252\pi$
$312$	4.59819	0.260321
$313$	11.8015	0.667059	0.333529	−	0.942740i	$-0.391760\pi$
$313$	11.8015	0.667059	0.333529	+	0.942740i	$0.391760\pi$
$314$	−1.52603	−0.0861186
$315$	0	0
$316$	11.1609	0.627851
$317$	−4.41436	−0.247935	−0.123967	−	0.992286i	$-0.539562\pi$
$317$	−4.41436	−0.247935	−0.123967	+	0.992286i	$0.539562\pi$
$318$	−14.3150	−0.802743
$319$	−1.92255	−0.107642
$320$	−0.230234	−0.0128705
$321$	−1.26408	−0.0705542
$322$	0	0
$323$	−1.67440	−0.0931661
$324$	1.00000	0.0555556
$325$	22.7472	1.26179
$326$	19.7822	1.09563
$327$	−8.80537	−0.486938
$328$	2.69356	0.148727
$329$	0	0
$330$	−0.523229	−0.0288028
$331$	−11.2918	−0.620651	−0.310325	−	0.950630i	$-0.600438\pi$
$331$	−11.2918	−0.620651	−0.310325	+	0.950630i	$0.600438\pi$
$332$	−7.20879	−0.395634
$333$	7.68681	0.421234
$334$	4.80647	0.262998
$335$	0.168776	0.00922120
$336$	0	0
$337$	0.0383188	0.00208736	0.00104368	−	0.999999i	$-0.499668\pi$
$337$	0.0383188	0.00208736	0.00104368	+	0.999999i	$0.499668\pi$
$338$	8.14338	0.442941
$339$	11.3437	0.616103
$340$	0.230234	0.0124862
$341$	−0.739957	−0.0400709
$342$	1.67440	0.0905412
$343$	0	0
$344$	10.1801	0.548873
$345$	0.711104	0.0382846
$346$	19.5508	1.05106
$347$	−2.54804	−0.136786	−0.0683930	−	0.997658i	$-0.521787\pi$
$347$	−2.54804	−0.136786	−0.0683930	+	0.997658i	$0.521787\pi$
$348$	−0.845973	−0.0453489
$349$	3.81616	0.204275	0.102137	−	0.994770i	$-0.467432\pi$
$349$	3.81616	0.204275	0.102137	+	0.994770i	$0.467432\pi$
$350$	0	0
$351$	4.59819	0.245433
$352$	−2.27259	−0.121130
$353$	8.93106	0.475352	0.237676	−	0.971344i	$-0.423614\pi$
$353$	8.93106	0.475352	0.237676	+	0.971344i	$0.423614\pi$
$354$	0.0829597	0.00440926
$355$	0.410317	0.0217774
$356$	14.4075	0.763594
$357$	0	0
$358$	−6.19477	−0.327404
$359$	26.0960	1.37730	0.688648	−	0.725096i	$-0.258205\pi$
$359$	26.0960	1.37730	0.688648	+	0.725096i	$0.258205\pi$
$360$	−0.230234	−0.0121344
$361$	−16.1964	−0.852441
$362$	−17.9747	−0.944727
$363$	5.83532	0.306275
$364$	0	0
$365$	−2.27635	−0.119149
$366$	5.71676	0.298820
$367$	28.9706	1.51225	0.756126	−	0.654427i	$-0.227090\pi$
$367$	28.9706	1.51225	0.756126	+	0.654427i	$0.227090\pi$
$368$	3.08861	0.161005
$369$	2.69356	0.140221
$370$	−1.76977	−0.0920057
$371$	0	0
$372$	−0.325600	−0.0168816
$373$	−27.1653	−1.40657	−0.703284	−	0.710909i	$-0.748284\pi$
$373$	−27.1653	−1.40657	−0.703284	+	0.710909i	$0.748284\pi$
$374$	2.27259	0.117513
$375$	−2.29014	−0.118262
$376$	−3.02320	−0.155910
$377$	−3.88994	−0.200342
$378$	0	0
$379$	26.4096	1.35657	0.678285	−	0.734799i	$-0.262724\pi$
$379$	26.4096	1.35657	0.678285	+	0.734799i	$0.262724\pi$
$380$	−0.385504	−0.0197759
$381$	12.2619	0.628198
$382$	20.1067	1.02875
$383$	15.2738	0.780457	0.390228	−	0.920718i	$-0.372396\pi$
$383$	15.2738	0.780457	0.390228	+	0.920718i	$0.372396\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−20.1519	−1.02570
$387$	10.1801	0.517483
$388$	4.03950	0.205075
$389$	−14.5587	−0.738155	−0.369077	−	0.929399i	$-0.620326\pi$
$389$	−14.5587	−0.738155	−0.369077	+	0.929399i	$0.620326\pi$
$390$	−1.05866	−0.0536074
$391$	−3.08861	−0.156198
$392$	0	0
$393$	0.190732	0.00962117
$394$	−13.6067	−0.685496
$395$	−2.56963	−0.129292
$396$	−2.27259	−0.114202
$397$	−8.40056	−0.421612	−0.210806	−	0.977528i	$-0.567609\pi$
$397$	−8.40056	−0.421612	−0.210806	+	0.977528i	$0.567609\pi$
$398$	15.6393	0.783928
$399$	0	0
$400$	−4.94699	−0.247350
$401$	14.0592	0.702082	0.351041	−	0.936360i	$-0.385828\pi$
$401$	14.0592	0.702082	0.351041	+	0.936360i	$0.385828\pi$
$402$	0.733061	0.0365618
$403$	−1.49717	−0.0745795
$404$	8.41987	0.418904
$405$	−0.230234	−0.0114404
$406$	0	0
$407$	−17.4690	−0.865905
$408$	1.00000	0.0495074
$409$	−24.4582	−1.20938	−0.604690	−	0.796461i	$-0.706703\pi$
$409$	−24.4582	−1.20938	−0.604690	+	0.796461i	$0.706703\pi$
$410$	−0.620149	−0.0306270
$411$	0.753463	0.0371656
$412$	−1.18398	−0.0583305
$413$	0	0
$414$	3.08861	0.151797
$415$	1.65971	0.0814720
$416$	−4.59819	−0.225445
$417$	11.2183	0.549365
$418$	−3.80523	−0.186120
$419$	22.3777	1.09322	0.546611	−	0.837386i	$-0.315918\pi$
$419$	22.3777	1.09322	0.546611	+	0.837386i	$0.315918\pi$
$420$	0	0
$421$	−4.74775	−0.231391	−0.115696	−	0.993285i	$-0.536910\pi$
$421$	−4.74775	−0.231391	−0.115696	+	0.993285i	$0.536910\pi$
$422$	17.9243	0.872542
$423$	−3.02320	−0.146993
$424$	14.3150	0.695195
$425$	4.94699	0.239964
$426$	1.78217	0.0863465
$427$	0	0
$428$	1.26408	0.0611017
$429$	−10.4498	−0.504522
$430$	−2.34380	−0.113028
$431$	17.3546	0.835941	0.417971	−	0.908460i	$-0.362741\pi$
$431$	17.3546	0.835941	0.417971	+	0.908460i	$0.362741\pi$
$432$	−1.00000	−0.0481125
$433$	13.1693	0.632876	0.316438	−	0.948613i	$-0.397513\pi$
$433$	13.1693	0.632876	0.316438	+	0.948613i	$0.397513\pi$
$434$	0	0
$435$	0.194772	0.00933859
$436$	8.80537	0.421701
$437$	5.17157	0.247390
$438$	−9.88709	−0.472423
$439$	−1.49717	−0.0714562	−0.0357281	−	0.999362i	$-0.511375\pi$
$439$	−1.49717	−0.0714562	−0.0357281	+	0.999362i	$0.511375\pi$
$440$	0.523229	0.0249439
$441$	0	0
$442$	4.59819	0.218714
$443$	−1.10763	−0.0526251	−0.0263125	−	0.999654i	$-0.508377\pi$
$443$	−1.10763	−0.0526251	−0.0263125	+	0.999654i	$0.508377\pi$
$444$	−7.68681	−0.364800
$445$	−3.31709	−0.157245
$446$	−8.87630	−0.420305
$447$	−12.4458	−0.588665
$448$	0	0
$449$	−14.4826	−0.683477	−0.341739	−	0.939795i	$-0.611016\pi$
$449$	−14.4826	−0.683477	−0.341739	+	0.939795i	$0.611016\pi$
$450$	−4.94699	−0.233203
$451$	−6.12136	−0.288244
$452$	−11.3437	−0.533561
$453$	−10.3178	−0.484773
$454$	20.9706	0.984197
$455$	0	0
$456$	−1.67440	−0.0784109
$457$	1.33088	0.0622560	0.0311280	−	0.999515i	$-0.490090\pi$
$457$	1.33088	0.0622560	0.0311280	+	0.999515i	$0.490090\pi$
$458$	−17.3341	−0.809970
$459$	1.00000	0.0466760
$460$	−0.711104	−0.0331554
$461$	28.2637	1.31637	0.658186	−	0.752855i	$-0.271324\pi$
$461$	28.2637	1.31637	0.658186	+	0.752855i	$0.271324\pi$
$462$	0	0
$463$	41.6579	1.93601	0.968003	−	0.250939i	$-0.0807392\pi$
$463$	41.6579	1.93601	0.968003	+	0.250939i	$0.0807392\pi$
$464$	0.845973	0.0392733
$465$	0.0749643	0.00347639
$466$	14.0874	0.652585
$467$	18.1351	0.839191	0.419595	−	0.907711i	$-0.362172\pi$
$467$	18.1351	0.839191	0.419595	+	0.907711i	$0.362172\pi$
$468$	−4.59819	−0.212552
$469$	0	0
$470$	0.696044	0.0321061
$471$	1.52603	0.0703156
$472$	−0.0829597	−0.00381853
$473$	−23.1352	−1.06376
$474$	−11.1609	−0.512638
$475$	−8.28324	−0.380061
$476$	0	0
$477$	14.3150	0.655437
$478$	18.4498	0.843875
$479$	7.73871	0.353591	0.176795	−	0.984248i	$-0.443427\pi$
$479$	7.73871	0.353591	0.176795	+	0.984248i	$0.443427\pi$
$480$	0.230234	0.0105087
$481$	−35.3454	−1.61161
$482$	20.9380	0.953698
$483$	0	0
$484$	−5.83532	−0.265242
$485$	−0.930032	−0.0422306
$486$	−1.00000	−0.0453609
$487$	10.4959	0.475616	0.237808	−	0.971312i	$-0.423571\pi$
$487$	10.4959	0.475616	0.237808	+	0.971312i	$0.423571\pi$
$488$	−5.71676	−0.258785
$489$	−19.7822	−0.894581
$490$	0	0
$491$	−11.2004	−0.505468	−0.252734	−	0.967536i	$-0.581330\pi$
$491$	−11.2004	−0.505468	−0.252734	+	0.967536i	$0.581330\pi$
$492$	−2.69356	−0.121435
$493$	−0.845973	−0.0381007
$494$	−7.69921	−0.346404
$495$	0.523229	0.0235174
$496$	0.325600	0.0146199
$497$	0	0
$498$	7.20879	0.323034
$499$	−30.6850	−1.37365	−0.686825	−	0.726822i	$-0.740996\pi$
$499$	−30.6850	−1.37365	−0.686825	+	0.726822i	$0.740996\pi$
$500$	2.29014	0.102418
$501$	−4.80647	−0.214737
$502$	−3.20879	−0.143215
$503$	28.4878	1.27021	0.635103	−	0.772427i	$-0.280957\pi$
$503$	28.4878	1.27021	0.635103	+	0.772427i	$0.280957\pi$
$504$	0	0
$505$	−1.93854	−0.0862640
$506$	−7.01916	−0.312040
$507$	−8.14338	−0.361660
$508$	−12.2619	−0.544036
$509$	−34.7129	−1.53862	−0.769310	−	0.638875i	$-0.779400\pi$
$509$	−34.7129	−1.53862	−0.769310	+	0.638875i	$0.779400\pi$
$510$	−0.230234	−0.0101949
$511$	0	0
$512$	1.00000	0.0441942
$513$	−1.67440	−0.0739266
$514$	18.5982	0.820331
$515$	0.272593	0.0120119
$516$	−10.1801	−0.448153
$517$	6.87050	0.302164
$518$	0	0
$519$	−19.5508	−0.858187
$520$	1.05866	0.0464254
$521$	9.30644	0.407723	0.203861	−	0.979000i	$-0.434651\pi$
$521$	9.30644	0.407723	0.203861	+	0.979000i	$0.434651\pi$
$522$	0.845973	0.0370272
$523$	−30.5101	−1.33411	−0.667057	−	0.745007i	$-0.732446\pi$
$523$	−30.5101	−1.33411	−0.667057	+	0.745007i	$0.732446\pi$
$524$	−0.190732	−0.00833218
$525$	0	0
$526$	−6.89119	−0.300470
$527$	−0.325600	−0.0141834
$528$	2.27259	0.0989019
$529$	−13.4605	−0.585238
$530$	−3.29579	−0.143160
$531$	−0.0829597	−0.00360014
$532$	0	0
$533$	−12.3855	−0.536476
$534$	−14.4075	−0.623472
$535$	−0.291035	−0.0125825
$536$	−0.733061	−0.0316634
$537$	6.19477	0.267324
$538$	1.01916	0.0439391
$539$	0	0
$540$	0.230234	0.00990770
$541$	−5.48477	−0.235809	−0.117904	−	0.993025i	$-0.537618\pi$
$541$	−5.48477	−0.235809	−0.117904	+	0.993025i	$0.537618\pi$
$542$	−5.09926	−0.219032
$543$	17.9747	0.771367
$544$	−1.00000	−0.0428746
$545$	−2.02730	−0.0868399
$546$	0	0
$547$	12.1078	0.517691	0.258845	−	0.965919i	$-0.416658\pi$
$547$	12.1078	0.517691	0.258845	+	0.965919i	$0.416658\pi$
$548$	−0.753463	−0.0321863
$549$	−5.71676	−0.243985
$550$	11.2425	0.479382
$551$	1.41650	0.0603448
$552$	−3.08861	−0.131460
$553$	0	0
$554$	−17.9419	−0.762276
$555$	1.76977	0.0751224
$556$	−11.2183	−0.475764
$557$	−8.77660	−0.371877	−0.185938	−	0.982561i	$-0.559532\pi$
$557$	−8.77660	−0.371877	−0.185938	+	0.982561i	$0.559532\pi$
$558$	0.325600	0.0137838
$559$	−46.8100	−1.97985
$560$	0	0
$561$	−2.27259	−0.0959489
$562$	−19.4909	−0.822175
$563$	30.6533	1.29188	0.645942	−	0.763387i	$-0.276465\pi$
$563$	30.6533	1.29188	0.645942	+	0.763387i	$0.276465\pi$
$564$	3.02320	0.127300
$565$	2.61170	0.109875
$566$	8.48242	0.356543
$567$	0	0
$568$	−1.78217	−0.0747783
$569$	−6.28573	−0.263511	−0.131756	−	0.991282i	$-0.542061\pi$
$569$	−6.28573	−0.263511	−0.131756	+	0.991282i	$0.542061\pi$
$570$	0.385504	0.0161470
$571$	−39.5408	−1.65473	−0.827365	−	0.561665i	$-0.810161\pi$
$571$	−39.5408	−1.65473	−0.827365	+	0.561665i	$0.810161\pi$
$572$	10.4498	0.436929
$573$	−20.1067	−0.839968
$574$	0	0
$575$	−15.2793	−0.637193
$576$	1.00000	0.0416667
$577$	−29.4488	−1.22597	−0.612984	−	0.790095i	$-0.710031\pi$
$577$	−29.4488	−1.22597	−0.612984	+	0.790095i	$0.710031\pi$
$578$	1.00000	0.0415945
$579$	20.1519	0.837484
$580$	−0.194772	−0.00808746
$581$	0	0
$582$	−4.03950	−0.167443
$583$	−32.5321	−1.34734
$584$	9.88709	0.409131
$585$	1.05866	0.0437703
$586$	−22.7625	−0.940310
$587$	−11.8104	−0.487466	−0.243733	−	0.969842i	$-0.578372\pi$
$587$	−11.8104	−0.487466	−0.243733	+	0.969842i	$0.578372\pi$
$588$	0	0
$589$	0.545185	0.0224640
$590$	0.0191002	0.000786341 0
$591$	13.6067	0.559705
$592$	7.68681	0.315926
$593$	−35.1233	−1.44234	−0.721170	−	0.692758i	$-0.756395\pi$
$593$	−35.1233	−1.44234	−0.721170	+	0.692758i	$0.756395\pi$
$594$	2.27259	0.0932456
$595$	0	0
$596$	12.4458	0.509799
$597$	−15.6393	−0.640074
$598$	−14.2020	−0.580765
$599$	−29.3849	−1.20064	−0.600318	−	0.799762i	$-0.704959\pi$
$599$	−29.3849	−1.20064	−0.600318	+	0.799762i	$0.704959\pi$
$600$	4.94699	0.201960
$601$	−11.3952	−0.464820	−0.232410	−	0.972618i	$-0.574661\pi$
$601$	−11.3952	−0.464820	−0.232410	+	0.972618i	$0.574661\pi$
$602$	0	0
$603$	−0.733061	−0.0298526
$604$	10.3178	0.419826
$605$	1.34349	0.0546207
$606$	−8.41987	−0.342034
$607$	20.1136	0.816385	0.408192	−	0.912896i	$-0.366159\pi$
$607$	20.1136	0.816385	0.408192	+	0.912896i	$0.366159\pi$
$608$	1.67440	0.0679059
$609$	0	0
$610$	1.31619	0.0532911
$611$	13.9013	0.562384
$612$	−1.00000	−0.0404226
$613$	7.56590	0.305584	0.152792	−	0.988258i	$-0.451174\pi$
$613$	7.56590	0.305584	0.152792	+	0.988258i	$0.451174\pi$
$614$	−5.03826	−0.203328
$615$	0.620149	0.0250068
$616$	0	0
$617$	16.4961	0.664109	0.332055	−	0.943260i	$-0.392258\pi$
$617$	16.4961	0.664109	0.332055	+	0.943260i	$0.392258\pi$
$618$	1.18398	0.0476266
$619$	−20.6055	−0.828203	−0.414102	−	0.910231i	$-0.635904\pi$
$619$	−20.6055	−0.828203	−0.414102	+	0.910231i	$0.635904\pi$
$620$	−0.0749643	−0.00301064
$621$	−3.08861	−0.123942
$622$	10.5558	0.423250
$623$	0	0
$624$	4.59819	0.184075
$625$	24.2077	0.968308
$626$	11.8015	0.471682
$627$	3.80523	0.151966
$628$	−1.52603	−0.0608951
$629$	−7.68681	−0.306493
$630$	0	0
$631$	−13.6336	−0.542745	−0.271372	−	0.962474i	$-0.587478\pi$
$631$	−13.6336	−0.542745	−0.271372	+	0.962474i	$0.587478\pi$
$632$	11.1609	0.443958
$633$	−17.9243	−0.712427
$634$	−4.41436	−0.175316
$635$	2.82312	0.112032
$636$	−14.3150	−0.567625
$637$	0	0
$638$	−1.92255	−0.0761145
$639$	−1.78217	−0.0705016
$640$	−0.230234	−0.00910081
$641$	11.8888	0.469581	0.234791	−	0.972046i	$-0.424560\pi$
$641$	11.8888	0.469581	0.234791	+	0.972046i	$0.424560\pi$
$642$	−1.26408	−0.0498894
$643$	1.59658	0.0629629	0.0314815	−	0.999504i	$-0.489977\pi$
$643$	1.59658	0.0629629	0.0314815	+	0.999504i	$0.489977\pi$
$644$	0	0
$645$	2.34380	0.0922872
$646$	−1.67440	−0.0658784
$647$	27.2468	1.07118	0.535592	−	0.844477i	$-0.320089\pi$
$647$	27.2468	1.07118	0.535592	+	0.844477i	$0.320089\pi$
$648$	1.00000	0.0392837
$649$	0.188534	0.00740059
$650$	22.7472	0.892220
$651$	0	0
$652$	19.7822	0.774730
$653$	−27.3736	−1.07121	−0.535606	−	0.844468i	$-0.679917\pi$
$653$	−27.3736	−1.07121	−0.535606	+	0.844468i	$0.679917\pi$
$654$	−8.80537	−0.344317
$655$	0.0439131	0.00171583
$656$	2.69356	0.105166
$657$	9.88709	0.385732
$658$	0	0
$659$	−29.7586	−1.15923	−0.579615	−	0.814890i	$-0.696797\pi$
$659$	−29.7586	−1.15923	−0.579615	+	0.814890i	$0.696797\pi$
$660$	−0.523229	−0.0203666
$661$	−34.4424	−1.33965	−0.669827	−	0.742517i	$-0.733632\pi$
$661$	−34.4424	−1.33965	−0.669827	+	0.742517i	$0.733632\pi$
$662$	−11.2918	−0.438866
$663$	−4.59819	−0.178579
$664$	−7.20879	−0.279755
$665$	0	0
$666$	7.68681	0.297858
$667$	2.61288	0.101171
$668$	4.80647	0.185968
$669$	8.87630	0.343177
$670$	0.168776	0.00652038
$671$	12.9919	0.501545
$672$	0	0
$673$	1.99025	0.0767184	0.0383592	−	0.999264i	$-0.487787\pi$
$673$	1.99025	0.0767184	0.0383592	+	0.999264i	$0.487787\pi$
$674$	0.0383188	0.00147598
$675$	4.94699	0.190410
$676$	8.14338	0.313207
$677$	47.2068	1.81430	0.907152	−	0.420803i	$-0.138251\pi$
$677$	47.2068	1.81430	0.907152	+	0.420803i	$0.138251\pi$
$678$	11.3437	0.435651
$679$	0	0
$680$	0.230234	0.00882908
$681$	−20.9706	−0.803594
$682$	−0.739957	−0.0283344
$683$	−0.937957	−0.0358899	−0.0179450	−	0.999839i	$-0.505712\pi$
$683$	−0.937957	−0.0358899	−0.0179450	+	0.999839i	$0.505712\pi$
$684$	1.67440	0.0640223
$685$	0.173473	0.00662806
$686$	0	0
$687$	17.3341	0.661338
$688$	10.1801	0.388112
$689$	−65.8229	−2.50765
$690$	0.711104	0.0270713
$691$	−3.25095	−0.123672	−0.0618360	−	0.998086i	$-0.519696\pi$
$691$	−3.25095	−0.123672	−0.0618360	+	0.998086i	$0.519696\pi$
$692$	19.5508	0.743211
$693$	0	0
$694$	−2.54804	−0.0967223
$695$	2.58285	0.0979729
$696$	−0.845973	−0.0320665
$697$	−2.69356	−0.102026
$698$	3.81616	0.144444
$699$	−14.0874	−0.532833
$700$	0	0
$701$	−16.3036	−0.615780	−0.307890	−	0.951422i	$-0.599623\pi$
$701$	−16.3036	−0.615780	−0.307890	+	0.951422i	$0.599623\pi$
$702$	4.59819	0.173548
$703$	12.8708	0.485431
$704$	−2.27259	−0.0856516
$705$	−0.696044	−0.0262145
$706$	8.93106	0.336125
$707$	0	0
$708$	0.0829597	0.00311782
$709$	−44.1012	−1.65625	−0.828127	−	0.560541i	$-0.810593\pi$
$709$	−44.1012	−1.65625	−0.828127	+	0.560541i	$0.810593\pi$
$710$	0.410317	0.0153989
$711$	11.1609	0.418567
$712$	14.4075	0.539942
$713$	1.00565	0.0376620
$714$	0	0
$715$	−2.40591	−0.0899758
$716$	−6.19477	−0.231509
$717$	−18.4498	−0.689021
$718$	26.0960	0.973895
$719$	29.4367	1.09781	0.548903	−	0.835886i	$-0.315046\pi$
$719$	29.4367	1.09781	0.548903	+	0.835886i	$0.315046\pi$
$720$	−0.230234	−0.00858032
$721$	0	0
$722$	−16.1964	−0.602767
$723$	−20.9380	−0.778691
$724$	−17.9747	−0.668023
$725$	−4.18502	−0.155428
$726$	5.83532	0.216569
$727$	5.52815	0.205028	0.102514	−	0.994732i	$-0.467311\pi$
$727$	5.52815	0.205028	0.102514	+	0.994732i	$0.467311\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−2.27635	−0.0842513
$731$	−10.1801	−0.376524
$732$	5.71676	0.211297
$733$	6.82271	0.252003	0.126001	−	0.992030i	$-0.459786\pi$
$733$	6.82271	0.252003	0.126001	+	0.992030i	$0.459786\pi$
$734$	28.9706	1.06932
$735$	0	0
$736$	3.08861	0.113848
$737$	1.66595	0.0613660
$738$	2.69356	0.0991513
$739$	−17.8862	−0.657954	−0.328977	−	0.944338i	$-0.606704\pi$
$739$	−17.8862	−0.657954	−0.328977	+	0.944338i	$0.606704\pi$
$740$	−1.76977	−0.0650579
$741$	7.69921	0.282838
$742$	0	0
$743$	−44.9340	−1.64847	−0.824234	−	0.566249i	$-0.808394\pi$
$743$	−44.9340	−1.64847	−0.824234	+	0.566249i	$0.808394\pi$
$744$	−0.325600	−0.0119371
$745$	−2.86544	−0.104982
$746$	−27.1653	−0.994594
$747$	−7.20879	−0.263756
$748$	2.27259	0.0830942
$749$	0	0
$750$	−2.29014	−0.0836240
$751$	13.7607	0.502134	0.251067	−	0.967970i	$-0.419219\pi$
$751$	13.7607	0.502134	0.251067	+	0.967970i	$0.419219\pi$
$752$	−3.02320	−0.110245
$753$	3.20879	0.116935
$754$	−3.88994	−0.141663
$755$	−2.37551	−0.0864537
$756$	0	0
$757$	−17.9857	−0.653701	−0.326850	−	0.945076i	$-0.605987\pi$
$757$	−17.9857	−0.653701	−0.326850	+	0.945076i	$0.605987\pi$
$758$	26.4096	0.959239
$759$	7.01916	0.254779
$760$	−0.385504	−0.0139837
$761$	−5.54643	−0.201058	−0.100529	−	0.994934i	$-0.532053\pi$
$761$	−5.54643	−0.201058	−0.100529	+	0.994934i	$0.532053\pi$
$762$	12.2619	0.444203
$763$	0	0
$764$	20.1067	0.727434
$765$	0.230234	0.00832414
$766$	15.2738	0.551866
$767$	0.381465	0.0137739
$768$	−1.00000	−0.0360844
$769$	36.9324	1.33182	0.665909	−	0.746033i	$-0.268044\pi$
$769$	36.9324	1.33182	0.665909	+	0.746033i	$0.268044\pi$
$770$	0	0
$771$	−18.5982	−0.669798
$772$	−20.1519	−0.725282
$773$	−47.2829	−1.70065	−0.850323	−	0.526261i	$-0.823594\pi$
$773$	−47.2829	−1.70065	−0.850323	+	0.526261i	$0.823594\pi$
$774$	10.1801	0.365916
$775$	−1.61074	−0.0578596
$776$	4.03950	0.145010
$777$	0	0
$778$	−14.5587	−0.521954
$779$	4.51009	0.161591
$780$	−1.05866	−0.0379062
$781$	4.05015	0.144926
$782$	−3.08861	−0.110449
$783$	−0.845973	−0.0302326
$784$	0	0
$785$	0.351343	0.0125400
$786$	0.190732	0.00680319
$787$	42.7072	1.52235	0.761174	−	0.648548i	$-0.224624\pi$
$787$	42.7072	1.52235	0.761174	+	0.648548i	$0.224624\pi$
$788$	−13.6067	−0.484719
$789$	6.89119	0.245333
$790$	−2.56963	−0.0914232
$791$	0	0
$792$	−2.27259	−0.0807531
$793$	26.2868	0.933470
$794$	−8.40056	−0.298125
$795$	3.29579	0.116890
$796$	15.6393	0.554321
$797$	12.6452	0.447915	0.223957	−	0.974599i	$-0.428102\pi$
$797$	12.6452	0.447915	0.223957	+	0.974599i	$0.428102\pi$
$798$	0	0
$799$	3.02320	0.106953
$800$	−4.94699	−0.174903
$801$	14.4075	0.509063
$802$	14.0592	0.496447
$803$	−22.4693	−0.792925
$804$	0.733061	0.0258531
$805$	0	0
$806$	−1.49717	−0.0527357
$807$	−1.01916	−0.0358761
$808$	8.41987	0.296210
$809$	2.64973	0.0931595	0.0465798	−	0.998915i	$-0.485168\pi$
$809$	2.64973	0.0931595	0.0465798	+	0.998915i	$0.485168\pi$
$810$	−0.230234	−0.00808961
$811$	6.47435	0.227345	0.113673	−	0.993518i	$-0.463739\pi$
$811$	6.47435	0.227345	0.113673	+	0.993518i	$0.463739\pi$
$812$	0	0
$813$	5.09926	0.178839
$814$	−17.4690	−0.612287
$815$	−4.55453	−0.159538
$816$	1.00000	0.0350070
$817$	17.0455	0.596348
$818$	−24.4582	−0.855160
$819$	0	0
$820$	−0.620149	−0.0216566
$821$	−7.82433	−0.273071	−0.136535	−	0.990635i	$-0.543597\pi$
$821$	−7.82433	−0.273071	−0.136535	+	0.990635i	$0.543597\pi$
$822$	0.753463	0.0262800
$823$	−7.21275	−0.251421	−0.125710	−	0.992067i	$-0.540121\pi$
$823$	−7.21275	−0.251421	−0.125710	+	0.992067i	$0.540121\pi$
$824$	−1.18398	−0.0412459
$825$	−11.2425	−0.391414
$826$	0	0
$827$	−26.4069	−0.918259	−0.459130	−	0.888369i	$-0.651839\pi$
$827$	−26.4069	−0.918259	−0.459130	+	0.888369i	$0.651839\pi$
$828$	3.08861	0.107337
$829$	−39.4762	−1.37107	−0.685533	−	0.728041i	$-0.740431\pi$
$829$	−39.4762	−1.37107	−0.685533	+	0.728041i	$0.740431\pi$
$830$	1.65971	0.0576094
$831$	17.9419	0.622396
$832$	−4.59819	−0.159414
$833$	0	0
$834$	11.2183	0.388459
$835$	−1.10661	−0.0382960
$836$	−3.80523	−0.131607
$837$	−0.325600	−0.0112544
$838$	22.3777	0.773025
$839$	−53.5572	−1.84900	−0.924500	−	0.381182i	$-0.875517\pi$
$839$	−53.5572	−1.84900	−0.924500	+	0.381182i	$0.875517\pi$
$840$	0	0
$841$	−28.2843	−0.975322
$842$	−4.74775	−0.163618
$843$	19.4909	0.671303
$844$	17.9243	0.616980
$845$	−1.87488	−0.0644980
$846$	−3.02320	−0.103940
$847$	0	0
$848$	14.3150	0.491577
$849$	−8.48242	−0.291116
$850$	4.94699	0.169680
$851$	23.7416	0.813851
$852$	1.78217	0.0610562
$853$	−2.43721	−0.0834485	−0.0417242	−	0.999129i	$-0.513285\pi$
$853$	−2.43721	−0.0834485	−0.0417242	+	0.999129i	$0.513285\pi$
$854$	0	0
$855$	−0.385504	−0.0131840
$856$	1.26408	0.0432055
$857$	−5.58916	−0.190922	−0.0954610	−	0.995433i	$-0.530433\pi$
$857$	−5.58916	−0.190922	−0.0954610	+	0.995433i	$0.530433\pi$
$858$	−10.4498	−0.356751
$859$	−21.0680	−0.718832	−0.359416	−	0.933177i	$-0.617024\pi$
$859$	−21.0680	−0.718832	−0.359416	+	0.933177i	$0.617024\pi$
$860$	−2.34380	−0.0799230
$861$	0	0
$862$	17.3546	0.591100
$863$	−1.04360	−0.0355246	−0.0177623	−	0.999842i	$-0.505654\pi$
$863$	−1.04360	−0.0355246	−0.0177623	+	0.999842i	$0.505654\pi$
$864$	−1.00000	−0.0340207
$865$	−4.50127	−0.153048
$866$	13.1693	0.447511
$867$	−1.00000	−0.0339618
$868$	0	0
$869$	−25.3642	−0.860423
$870$	0.194772	0.00660338
$871$	3.37076	0.114214
$872$	8.80537	0.298187
$873$	4.03950	0.136716
$874$	5.17157	0.174931
$875$	0	0
$876$	−9.88709	−0.334054
$877$	8.99803	0.303842	0.151921	−	0.988393i	$-0.451454\pi$
$877$	8.99803	0.303842	0.151921	+	0.988393i	$0.451454\pi$
$878$	−1.49717	−0.0505271
$879$	22.7625	0.767760
$880$	0.523229	0.0176380
$881$	48.6681	1.63967	0.819835	−	0.572600i	$-0.194065\pi$
$881$	48.6681	1.63967	0.819835	+	0.572600i	$0.194065\pi$
$882$	0	0
$883$	10.8203	0.364134	0.182067	−	0.983286i	$-0.441721\pi$
$883$	10.8203	0.364134	0.182067	+	0.983286i	$0.441721\pi$
$884$	4.59819	0.154654
$885$	−0.0191002	−0.000642045 0
$886$	−1.10763	−0.0372115
$887$	−30.5402	−1.02544	−0.512721	−	0.858556i	$-0.671362\pi$
$887$	−30.5402	−1.02544	−0.512721	+	0.858556i	$0.671362\pi$
$888$	−7.68681	−0.257952
$889$	0	0
$890$	−3.31709	−0.111189
$891$	−2.27259	−0.0761347
$892$	−8.87630	−0.297200
$893$	−5.06204	−0.169395
$894$	−12.4458	−0.416249
$895$	1.42625	0.0476742
$896$	0	0
$897$	14.2020	0.474192
$898$	−14.4826	−0.483292
$899$	0.275449	0.00918674
$900$	−4.94699	−0.164900
$901$	−14.3150	−0.476900
$902$	−6.12136	−0.203819
$903$	0	0
$904$	−11.3437	−0.377285
$905$	4.13838	0.137564
$906$	−10.3178	−0.342786
$907$	56.7331	1.88379	0.941896	−	0.335905i	$-0.109042\pi$
$907$	56.7331	1.88379	0.941896	+	0.335905i	$0.109042\pi$
$908$	20.9706	0.695933
$909$	8.41987	0.279269
$910$	0	0
$911$	29.2716	0.969810	0.484905	−	0.874567i	$-0.338854\pi$
$911$	29.2716	0.969810	0.484905	+	0.874567i	$0.338854\pi$
$912$	−1.67440	−0.0554449
$913$	16.3826	0.542187
$914$	1.33088	0.0440217
$915$	−1.31619	−0.0435120
$916$	−17.3341	−0.572735
$917$	0	0
$918$	1.00000	0.0330049
$919$	−37.7777	−1.24617	−0.623086	−	0.782154i	$-0.714121\pi$
$919$	−37.7777	−1.24617	−0.623086	+	0.782154i	$0.714121\pi$
$920$	−0.711104	−0.0234444
$921$	5.03826	0.166016
$922$	28.2637	0.930815
$923$	8.19477	0.269734
$924$	0	0
$925$	−38.0266	−1.25031
$926$	41.6579	1.36896
$927$	−1.18398	−0.0388870
$928$	0.845973	0.0277704
$929$	47.0992	1.54527	0.772637	−	0.634848i	$-0.218937\pi$
$929$	47.0992	1.54527	0.772637	+	0.634848i	$0.218937\pi$
$930$	0.0749643	0.00245818
$931$	0	0
$932$	14.0874	0.461447
$933$	−10.5558	−0.345583
$934$	18.1351	0.593398
$935$	−0.523229	−0.0171114
$936$	−4.59819	−0.150297
$937$	12.2410	0.399895	0.199947	−	0.979807i	$-0.435923\pi$
$937$	12.2410	0.399895	0.199947	+	0.979807i	$0.435923\pi$
$938$	0	0
$939$	−11.8015	−0.385127
$940$	0.696044	0.0227024
$941$	−4.34433	−0.141621	−0.0708105	−	0.997490i	$-0.522559\pi$
$941$	−4.34433	−0.141621	−0.0708105	+	0.997490i	$0.522559\pi$
$942$	1.52603	0.0497206
$943$	8.31936	0.270916
$944$	−0.0829597	−0.00270011
$945$	0	0
$946$	−23.1352	−0.752190
$947$	−16.7224	−0.543405	−0.271703	−	0.962381i	$-0.587587\pi$
$947$	−16.7224	−0.543405	−0.271703	+	0.962381i	$0.587587\pi$
$948$	−11.1609	−0.362490
$949$	−45.4627	−1.47578
$950$	−8.28324	−0.268744
$951$	4.41436	0.143145
$952$	0	0
$953$	24.0264	0.778290	0.389145	−	0.921176i	$-0.372770\pi$
$953$	24.0264	0.778290	0.389145	+	0.921176i	$0.372770\pi$
$954$	14.3150	0.463464
$955$	−4.62924	−0.149799
$956$	18.4498	0.596710
$957$	1.92255	0.0621472
$958$	7.73871	0.250027
$959$	0	0
$960$	0.230234	0.00743078
$961$	−30.8940	−0.996580
$962$	−35.3454	−1.13958
$963$	1.26408	0.0407345
$964$	20.9380	0.674366
$965$	4.63965	0.149356
$966$	0	0
$967$	19.1189	0.614824	0.307412	−	0.951577i	$-0.400537\pi$
$967$	19.1189	0.614824	0.307412	+	0.951577i	$0.400537\pi$
$968$	−5.83532	−0.187554
$969$	1.67440	0.0537895
$970$	−0.930032	−0.0298615
$971$	19.1592	0.614847	0.307423	−	0.951573i	$-0.400533\pi$
$971$	19.1592	0.614847	0.307423	+	0.951573i	$0.400533\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	10.4959	0.336311
$975$	−22.7472	−0.728494
$976$	−5.71676	−0.182989
$977$	−2.75318	−0.0880819	−0.0440410	−	0.999030i	$-0.514023\pi$
$977$	−2.75318	−0.0880819	−0.0440410	+	0.999030i	$0.514023\pi$
$978$	−19.7822	−0.632564
$979$	−32.7423	−1.04645
$980$	0	0
$981$	8.80537	0.281134
$982$	−11.2004	−0.357420
$983$	−15.9436	−0.508522	−0.254261	−	0.967136i	$-0.581832\pi$
$983$	−15.9436	−0.508522	−0.254261	+	0.967136i	$0.581832\pi$
$984$	−2.69356	−0.0858675
$985$	3.13273	0.0998170
$986$	−0.845973	−0.0269413
$987$	0	0
$988$	−7.69921	−0.244945
$989$	31.4423	0.999808
$990$	0.523229	0.0166293
$991$	−3.92622	−0.124720	−0.0623602	−	0.998054i	$-0.519863\pi$
$991$	−3.92622	−0.124720	−0.0623602	+	0.998054i	$0.519863\pi$
$992$	0.325600	0.0103378
$993$	11.2918	0.358333
$994$	0	0
$995$	−3.60070	−0.114150
$996$	7.20879	0.228419
$997$	−54.6836	−1.73185	−0.865923	−	0.500177i	$-0.833268\pi$
$997$	−54.6836	−1.73185	−0.865923	+	0.500177i	$0.833268\pi$
$998$	−30.6850	−0.971318
$999$	−7.68681	−0.243200

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4998.2.a.co.1.3	✓	4
7.6	odd	2		4998.2.a.cp.1.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4998.2.a.co.1.3	✓	4	1.1	even	1	trivial
4998.2.a.cp.1.2	yes	4	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4998 = 2 \cdot 3 \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4998.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.230234 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.230234 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -0.230234 q^{10} -2.27259 q^{11} -1.00000 q^{12} -4.59819 q^{13} +0.230234 q^{15} +1.00000 q^{16} -1.00000 q^{17} +1.00000 q^{18} +1.67440 q^{19} -0.230234 q^{20} -2.27259 q^{22} +3.08861 q^{23} -1.00000 q^{24} -4.94699 q^{25} -4.59819 q^{26} -1.00000 q^{27} +0.845973 q^{29} +0.230234 q^{30} +0.325600 q^{31} +1.00000 q^{32} +2.27259 q^{33} -1.00000 q^{34} +1.00000 q^{36} +7.68681 q^{37} +1.67440 q^{38} +4.59819 q^{39} -0.230234 q^{40} +2.69356 q^{41} +10.1801 q^{43} -2.27259 q^{44} -0.230234 q^{45} +3.08861 q^{46} -3.02320 q^{47} -1.00000 q^{48} -4.94699 q^{50} +1.00000 q^{51} -4.59819 q^{52} +14.3150 q^{53} -1.00000 q^{54} +0.523229 q^{55} -1.67440 q^{57} +0.845973 q^{58} -0.0829597 q^{59} +0.230234 q^{60} -5.71676 q^{61} +0.325600 q^{62} +1.00000 q^{64} +1.05866 q^{65} +2.27259 q^{66} -0.733061 q^{67} -1.00000 q^{68} -3.08861 q^{69} -1.78217 q^{71} +1.00000 q^{72} +9.88709 q^{73} +7.68681 q^{74} +4.94699 q^{75} +1.67440 q^{76} +4.59819 q^{78} +11.1609 q^{79} -0.230234 q^{80} +1.00000 q^{81} +2.69356 q^{82} -7.20879 q^{83} +0.230234 q^{85} +10.1801 q^{86} -0.845973 q^{87} -2.27259 q^{88} +14.4075 q^{89} -0.230234 q^{90} +3.08861 q^{92} -0.325600 q^{93} -3.02320 q^{94} -0.385504 q^{95} -1.00000 q^{96} +4.03950 q^{97} -2.27259 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} - 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} - 2 q^{10} + 10 q^{11} - 4 q^{12} - 6 q^{13} + 2 q^{15} + 4 q^{16} - 4 q^{17} + 4 q^{18} - 2 q^{20} + 10 q^{22} - 4 q^{24} + 6 q^{25} - 6 q^{26} - 4 q^{27} + 8 q^{29} + 2 q^{30} + 8 q^{31} + 4 q^{32} - 10 q^{33} - 4 q^{34} + 4 q^{36} + 6 q^{37} + 6 q^{39} - 2 q^{40} + 4 q^{41} + 6 q^{43} + 10 q^{44} - 2 q^{45} + 8 q^{47} - 4 q^{48} + 6 q^{50} + 4 q^{51} - 6 q^{52} + 18 q^{53} - 4 q^{54} - 10 q^{55} + 8 q^{58} - 24 q^{59} + 2 q^{60} + 4 q^{61} + 8 q^{62} + 4 q^{64} - 6 q^{65} - 10 q^{66} + 14 q^{67} - 4 q^{68} + 12 q^{71} + 4 q^{72} + 18 q^{73} + 6 q^{74} - 6 q^{75} + 6 q^{78} + 10 q^{79} - 2 q^{80} + 4 q^{81} + 4 q^{82} + 14 q^{83} + 2 q^{85} + 6 q^{86} - 8 q^{87} + 10 q^{88} + 34 q^{89} - 2 q^{90} - 8 q^{93} + 8 q^{94} - 4 q^{95} - 4 q^{96} + 6 q^{97} + 10 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 - 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 - 2 * q^10 + 10 * q^11 - 4 * q^12 - 6 * q^13 + 2 * q^15 + 4 * q^16 - 4 * q^17 + 4 * q^18 - 2 * q^20 + 10 * q^22 - 4 * q^24 + 6 * q^25 - 6 * q^26 - 4 * q^27 + 8 * q^29 + 2 * q^30 + 8 * q^31 + 4 * q^32 - 10 * q^33 - 4 * q^34 + 4 * q^36 + 6 * q^37 + 6 * q^39 - 2 * q^40 + 4 * q^41 + 6 * q^43 + 10 * q^44 - 2 * q^45 + 8 * q^47 - 4 * q^48 + 6 * q^50 + 4 * q^51 - 6 * q^52 + 18 * q^53 - 4 * q^54 - 10 * q^55 + 8 * q^58 - 24 * q^59 + 2 * q^60 + 4 * q^61 + 8 * q^62 + 4 * q^64 - 6 * q^65 - 10 * q^66 + 14 * q^67 - 4 * q^68 + 12 * q^71 + 4 * q^72 + 18 * q^73 + 6 * q^74 - 6 * q^75 + 6 * q^78 + 10 * q^79 - 2 * q^80 + 4 * q^81 + 4 * q^82 + 14 * q^83 + 2 * q^85 + 6 * q^86 - 8 * q^87 + 10 * q^88 + 34 * q^89 - 2 * q^90 - 8 * q^93 + 8 * q^94 - 4 * q^95 - 4 * q^96 + 6 * q^97 + 10 * q^99

Introduction

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