LMFDB - Embedded newform 3721.2.a.l.1.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3721,2,Mod(1,3721)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3721.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3721, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 3721 = 61^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3721.a (trivial)

Newform invariants

comment:select newform

sage:traces = [16,5,-2,15,-12,-9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$29.7123345921$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} - 11 x^{14} + 86 x^{13} + 5 x^{12} - 562 x^{11} + 362 x^{10} + 1761 x^{9} - 1799 x^{8} + \cdots - 9 $ x^16 - 5x^15 - 11x^14 + 86x^13 + 5x^12 - 562x^11 + 362x^10 + 1761x^9 - 1799x^8 - 2672x^7 + 3614x^6 + 1572x^5 - 3212x^4 + 144x^3 + 1005x^2 - 279*x - 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 61)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$1.33501$ of defining polynomial
Character	$\chi$	$=$	3721.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.33501 q^{2} -2.85085 q^{3} -0.217749 q^{4} -2.94702 q^{5} -3.80591 q^{6} -3.02640 q^{7} -2.96072 q^{8} +5.12735 q^{9} -3.93430 q^{10} -0.399822 q^{11} +0.620769 q^{12} -0.299852 q^{13} -4.04027 q^{14} +8.40150 q^{15} -3.51709 q^{16} +7.66680 q^{17} +6.84506 q^{18} +3.49748 q^{19} +0.641709 q^{20} +8.62781 q^{21} -0.533766 q^{22} +1.54138 q^{23} +8.44056 q^{24} +3.68491 q^{25} -0.400306 q^{26} -6.06474 q^{27} +0.658994 q^{28} +7.82582 q^{29} +11.2161 q^{30} -3.12298 q^{31} +1.22609 q^{32} +1.13983 q^{33} +10.2353 q^{34} +8.91885 q^{35} -1.11647 q^{36} -2.57617 q^{37} +4.66917 q^{38} +0.854834 q^{39} +8.72528 q^{40} -7.17350 q^{41} +11.5182 q^{42} -10.5500 q^{43} +0.0870607 q^{44} -15.1104 q^{45} +2.05776 q^{46} +5.72065 q^{47} +10.0267 q^{48} +2.15909 q^{49} +4.91939 q^{50} -21.8569 q^{51} +0.0652924 q^{52} +6.02358 q^{53} -8.09649 q^{54} +1.17828 q^{55} +8.96031 q^{56} -9.97079 q^{57} +10.4475 q^{58} -4.73292 q^{59} -1.82942 q^{60} -4.16921 q^{62} -15.5174 q^{63} +8.67101 q^{64} +0.883670 q^{65} +1.52169 q^{66} -1.62571 q^{67} -1.66944 q^{68} -4.39424 q^{69} +11.9068 q^{70} -1.86466 q^{71} -15.1806 q^{72} -0.931489 q^{73} -3.43921 q^{74} -10.5051 q^{75} -0.761571 q^{76} +1.21002 q^{77} +1.14121 q^{78} +2.57646 q^{79} +10.3649 q^{80} +1.90764 q^{81} -9.57669 q^{82} +7.68195 q^{83} -1.87869 q^{84} -22.5942 q^{85} -14.0844 q^{86} -22.3102 q^{87} +1.18376 q^{88} -1.17865 q^{89} -20.1725 q^{90} +0.907473 q^{91} -0.335634 q^{92} +8.90316 q^{93} +7.63713 q^{94} -10.3071 q^{95} -3.49539 q^{96} -2.09382 q^{97} +2.88241 q^{98} -2.05003 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 5 q^{2} - 2 q^{3} + 15 q^{4} - 12 q^{5} - 9 q^{6} - 4 q^{7} + 12 q^{8} + 4 q^{9} - 20 q^{10} + 9 q^{11} - 17 q^{12} - 11 q^{14} - 12 q^{15} + 9 q^{16} - 4 q^{17} + 35 q^{18} - 19 q^{19} - 17 q^{20}+ \cdots - 47 q^{99}+O(q^{100}) $ 16 * q + 5 * q^2 - 2 * q^3 + 15 * q^4 - 12 * q^5 - 9 * q^6 - 4 * q^7 + 12 * q^8 + 4 * q^9 - 20 * q^10 + 9 * q^11 - 17 * q^12 - 11 * q^14 - 12 * q^15 + 9 * q^16 - 4 * q^17 + 35 * q^18 - 19 * q^19 - 17 * q^20 - 3 * q^21 - 11 * q^22 - 4 * q^23 - 15 * q^24 - 8 * q^25 - 19 * q^26 - 5 * q^27 - 22 * q^28 - 4 * q^29 + 24 * q^30 + 9 * q^31 + 34 * q^32 - 10 * q^33 - 6 * q^34 + 37 * q^35 + 20 * q^36 - 38 * q^37 - 18 * q^38 - 12 * q^39 - 60 * q^40 - 37 * q^41 + 17 * q^42 - 15 * q^43 + 34 * q^44 - 32 * q^45 - 41 * q^46 - 40 * q^47 - 43 * q^48 + 24 * q^49 + 28 * q^50 - 19 * q^51 - 56 * q^52 + 19 * q^53 - 6 * q^54 + 30 * q^55 - 58 * q^56 + 8 * q^57 - 21 * q^58 - q^59 - 10 * q^60 - 37 * q^62 + 17 * q^63 + 28 * q^64 - 34 * q^65 - 59 * q^66 - 3 * q^67 + 2 * q^68 + 31 * q^69 + 17 * q^70 + 8 * q^71 - 9 * q^72 + 6 * q^73 + 10 * q^74 - q^75 - 65 * q^76 - 39 * q^77 - 68 * q^78 + 56 * q^79 - 14 * q^80 - 56 * q^81 + 39 * q^82 + 6 * q^83 - 65 * q^84 - 53 * q^85 - 54 * q^86 - 83 * q^87 - 5 * q^88 - 66 * q^89 - 60 * q^90 - 5 * q^91 + 37 * q^92 + 67 * q^93 - 43 * q^94 - 39 * q^95 + 14 * q^96 + 13 * q^97 - 16 * q^98 - 47 * q^99

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 $

$2$	1.33501	0.943995	0.471997	−	0.881600i	$-0.343533\pi$
$2$	1.33501	0.943995	0.471997	+	0.881600i	$0.343533\pi$
$3$	−2.85085	−1.64594	−0.822970	−	0.568086i	$-0.807684\pi$
$3$	−2.85085	−1.64594	−0.822970	+	0.568086i	$0.807684\pi$
$4$	−0.217749	−0.108874
$5$	−2.94702	−1.31795	−0.658973	−	0.752167i	$-0.729009\pi$
$5$	−2.94702	−1.31795	−0.658973	+	0.752167i	$0.729009\pi$
$6$	−3.80591	−1.55376
$7$	−3.02640	−1.14387	−0.571936	−	0.820298i	$-0.693807\pi$
$7$	−3.02640	−1.14387	−0.571936	+	0.820298i	$0.693807\pi$
$8$	−2.96072	−1.04677
$9$	5.12735	1.70912
$10$	−3.93430	−1.24413
$11$	−0.399822	−0.120551	−0.0602754	−	0.998182i	$-0.519198\pi$
$11$	−0.399822	−0.120551	−0.0602754	+	0.998182i	$0.519198\pi$
$12$	0.620769	0.179201
$13$	−0.299852	−0.0831640	−0.0415820	−	0.999135i	$-0.513240\pi$
$13$	−0.299852	−0.0831640	−0.0415820	+	0.999135i	$0.513240\pi$
$14$	−4.04027	−1.07981
$15$	8.40150	2.16926
$16$	−3.51709	−0.879272
$17$	7.66680	1.85947	0.929736	−	0.368226i	$-0.120035\pi$
$17$	7.66680	1.85947	0.929736	+	0.368226i	$0.120035\pi$
$18$	6.84506	1.61340
$19$	3.49748	0.802377	0.401188	−	0.915996i	$-0.368597\pi$
$19$	3.49748	0.802377	0.401188	+	0.915996i	$0.368597\pi$
$20$	0.641709	0.143491
$21$	8.62781	1.88274
$22$	−0.533766	−0.113799
$23$	1.54138	0.321400	0.160700	−	0.987003i	$-0.448625\pi$
$23$	1.54138	0.321400	0.160700	+	0.987003i	$0.448625\pi$
$24$	8.44056	1.72292
$25$	3.68491	0.736982
$26$	−0.400306	−0.0785064
$27$	−6.06474	−1.16716
$28$	0.658994	0.124538
$29$	7.82582	1.45322	0.726609	−	0.687051i	$-0.241095\pi$
$29$	7.82582	1.45322	0.726609	+	0.687051i	$0.241095\pi$
$30$	11.2161	2.04777
$31$	−3.12298	−0.560904	−0.280452	−	0.959868i	$-0.590484\pi$
$31$	−3.12298	−0.560904	−0.280452	+	0.959868i	$0.590484\pi$
$32$	1.22609	0.216743
$33$	1.13983	0.198419
$34$	10.2353	1.75533
$35$	8.91885	1.50756
$36$	−1.11647	−0.186079
$37$	−2.57617	−0.423520	−0.211760	−	0.977322i	$-0.567920\pi$
$37$	−2.57617	−0.423520	−0.211760	+	0.977322i	$0.567920\pi$
$38$	4.66917	0.757439
$39$	0.854834	0.136883
$40$	8.72528	1.37959
$41$	−7.17350	−1.12031	−0.560156	−	0.828387i	$-0.689259\pi$
$41$	−7.17350	−1.12031	−0.560156	+	0.828387i	$0.689259\pi$
$42$	11.5182	1.77730
$43$	−10.5500	−1.60887	−0.804434	−	0.594043i	$-0.797531\pi$
$43$	−10.5500	−1.60887	−0.804434	+	0.594043i	$0.797531\pi$
$44$	0.0870607	0.0131249
$45$	−15.1104	−2.25252
$46$	2.05776	0.303400
$47$	5.72065	0.834443	0.417221	−	0.908805i	$-0.363004\pi$
$47$	5.72065	0.834443	0.417221	+	0.908805i	$0.363004\pi$
$48$	10.0267	1.44723
$49$	2.15909	0.308442
$50$	4.91939	0.695707
$51$	−21.8569	−3.06058
$52$	0.0652924	0.00905443
$53$	6.02358	0.827402	0.413701	−	0.910413i	$-0.364236\pi$
$53$	6.02358	0.827402	0.413701	+	0.910413i	$0.364236\pi$
$54$	−8.09649	−1.10179
$55$	1.17828	0.158880
$56$	8.96031	1.19737
$57$	−9.97079	−1.32066
$58$	10.4475	1.37183
$59$	−4.73292	−0.616174	−0.308087	−	0.951358i	$-0.599689\pi$
$59$	−4.73292	−0.616174	−0.308087	+	0.951358i	$0.599689\pi$
$60$	−1.82942	−0.236177
$61$	0	0
$61$	0	0
$62$	−4.16921	−0.529491
$63$	−15.5174	−1.95501
$64$	8.67101	1.08388
$65$	0.883670	0.109606
$66$	1.52169	0.187307
$67$	−1.62571	−0.198612	−0.0993059	−	0.995057i	$-0.531662\pi$
$67$	−1.62571	−0.198612	−0.0993059	+	0.995057i	$0.531662\pi$
$68$	−1.66944	−0.202449
$69$	−4.39424	−0.529005
$70$	11.9068	1.42313
$71$	−1.86466	−0.221295	−0.110647	−	0.993860i	$-0.535292\pi$
$71$	−1.86466	−0.221295	−0.110647	+	0.993860i	$0.535292\pi$
$72$	−15.1806	−1.78905
$73$	−0.931489	−0.109023	−0.0545113	−	0.998513i	$-0.517360\pi$
$73$	−0.931489	−0.109023	−0.0545113	+	0.998513i	$0.517360\pi$
$74$	−3.43921	−0.399801
$75$	−10.5051	−1.21303
$76$	−0.761571	−0.0873582
$77$	1.21002	0.137895
$78$	1.14121	0.129217
$79$	2.57646	0.289874	0.144937	−	0.989441i	$-0.453702\pi$
$79$	2.57646	0.289874	0.144937	+	0.989441i	$0.453702\pi$
$80$	10.3649	1.15883
$81$	1.90764	0.211960
$82$	−9.57669	−1.05757
$83$	7.68195	0.843203	0.421602	−	0.906781i	$-0.361468\pi$
$83$	7.68195	0.843203	0.421602	+	0.906781i	$0.361468\pi$
$84$	−1.87869	−0.204982
$85$	−22.5942	−2.45068
$86$	−14.0844	−1.51876
$87$	−22.3102	−2.39191
$88$	1.18376	0.126189
$89$	−1.17865	−0.124936	−0.0624681	−	0.998047i	$-0.519897\pi$
$89$	−1.17865	−0.124936	−0.0624681	+	0.998047i	$0.519897\pi$
$90$	−20.1725	−2.12637
$91$	0.907473	0.0951290
$92$	−0.335634	−0.0349922
$93$	8.90316	0.923214
$94$	7.63713	0.787709
$95$	−10.3071	−1.05749
$96$	−3.49539	−0.356746
$97$	−2.09382	−0.212595	−0.106298	−	0.994334i	$-0.533900\pi$
$97$	−2.09382	−0.212595	−0.106298	+	0.994334i	$0.533900\pi$
$98$	2.88241	0.291168
$99$	−2.05003	−0.206035
$100$	−0.802384	−0.0802384
$101$	−1.07049	−0.106518	−0.0532591	−	0.998581i	$-0.516961\pi$
$101$	−1.07049	−0.106518	−0.0532591	+	0.998581i	$0.516961\pi$
$102$	−29.1792	−2.88917
$103$	−8.45092	−0.832694	−0.416347	−	0.909206i	$-0.636690\pi$
$103$	−8.45092	−0.832694	−0.416347	+	0.909206i	$0.636690\pi$
$104$	0.887777	0.0870537
$105$	−25.4263	−2.48135
$106$	8.04153	0.781063
$107$	15.4802	1.49653	0.748265	−	0.663399i	$-0.230887\pi$
$107$	15.4802	1.49653	0.748265	+	0.663399i	$0.230887\pi$
$108$	1.32059	0.127074
$109$	19.7887	1.89542	0.947709	−	0.319137i	$-0.103393\pi$
$109$	19.7887	1.89542	0.947709	+	0.319137i	$0.103393\pi$
$110$	1.57302	0.149981
$111$	7.34428	0.697088
$112$	10.6441	1.00577
$113$	7.66276	0.720852	0.360426	−	0.932788i	$-0.382631\pi$
$113$	7.66276	0.720852	0.360426	+	0.932788i	$0.382631\pi$
$114$	−13.3111	−1.24670
$115$	−4.54247	−0.423588
$116$	−1.70406	−0.158218
$117$	−1.53745	−0.142137
$118$	−6.31850	−0.581665
$119$	−23.2028	−2.12700
$120$	−24.8745	−2.27072
$121$	−10.8401	−0.985467
$122$	0	0
$123$	20.4506	1.84397
$124$	0.680025	0.0610681
$125$	3.87559	0.346644
$126$	−20.7159	−1.84552
$127$	−7.04218	−0.624893	−0.312446	−	0.949935i	$-0.601148\pi$
$127$	−7.04218	−0.624893	−0.312446	+	0.949935i	$0.601148\pi$
$128$	9.12372	0.806430
$129$	30.0766	2.64810
$130$	1.17971	0.103467
$131$	1.36006	0.118829	0.0594147	−	0.998233i	$-0.481077\pi$
$131$	1.36006	0.118829	0.0594147	+	0.998233i	$0.481077\pi$
$132$	−0.248197	−0.0216028
$133$	−10.5848	−0.917816
$134$	−2.17033	−0.187488
$135$	17.8729	1.53825
$136$	−22.6992	−1.94644
$137$	7.65724	0.654202	0.327101	−	0.944989i	$-0.393928\pi$
$137$	7.65724	0.654202	0.327101	+	0.944989i	$0.393928\pi$
$138$	−5.86636	−0.499378
$139$	−7.79896	−0.661499	−0.330750	−	0.943719i	$-0.607302\pi$
$139$	−7.79896	−0.661499	−0.330750	+	0.943719i	$0.607302\pi$
$140$	−1.94207	−0.164135
$141$	−16.3087	−1.37344
$142$	−2.48934	−0.208901
$143$	0.119887	0.0100255
$144$	−18.0333	−1.50278
$145$	−23.0628	−1.91526
$146$	−1.24355	−0.102917
$147$	−6.15525	−0.507677
$148$	0.560958	0.0461105
$149$	5.41144	0.443323	0.221661	−	0.975124i	$-0.428852\pi$
$149$	5.41144	0.443323	0.221661	+	0.975124i	$0.428852\pi$
$150$	−14.0244	−1.14509
$151$	−5.78347	−0.470652	−0.235326	−	0.971916i	$-0.575616\pi$
$151$	−5.78347	−0.470652	−0.235326	+	0.971916i	$0.575616\pi$
$152$	−10.3550	−0.839905
$153$	39.3103	3.17805
$154$	1.61539	0.130172
$155$	9.20348	0.739242
$156$	−0.186139	−0.0149030
$157$	3.24533	0.259006	0.129503	−	0.991579i	$-0.458662\pi$
$157$	3.24533	0.259006	0.129503	+	0.991579i	$0.458662\pi$
$158$	3.43960	0.273640
$159$	−17.1723	−1.36185
$160$	−3.61329	−0.285656
$161$	−4.66483	−0.367640
$162$	2.54671	0.200089
$163$	18.5273	1.45117	0.725586	−	0.688131i	$-0.241569\pi$
$163$	18.5273	1.45117	0.725586	+	0.688131i	$0.241569\pi$
$164$	1.56202	0.121973
$165$	−3.35911	−0.261506
$166$	10.2555	0.795979
$167$	−9.36309	−0.724538	−0.362269	−	0.932074i	$-0.617998\pi$
$167$	−9.36309	−0.724538	−0.362269	+	0.932074i	$0.617998\pi$
$168$	−25.5445	−1.97080
$169$	−12.9101	−0.993084
$170$	−30.1635	−2.31343
$171$	17.9328	1.37135
$172$	2.29726	0.175164
$173$	−1.25294	−0.0952591	−0.0476296	−	0.998865i	$-0.515167\pi$
$173$	−1.25294	−0.0952591	−0.0476296	+	0.998865i	$0.515167\pi$
$174$	−29.7844	−2.25795
$175$	−11.1520	−0.843013
$176$	1.40621	0.105997
$177$	13.4928	1.01418
$178$	−1.57350	−0.117939
$179$	−11.9939	−0.896468	−0.448234	−	0.893916i	$-0.647947\pi$
$179$	−11.9939	−0.896468	−0.448234	+	0.893916i	$0.647947\pi$
$180$	3.29026	0.245242
$181$	23.2071	1.72497	0.862486	−	0.506082i	$-0.168907\pi$
$181$	23.2071	1.72497	0.862486	+	0.506082i	$0.168907\pi$
$182$	1.21148	0.0898012
$183$	0	0
$184$	−4.56359	−0.336432
$185$	7.59202	0.558177
$186$	11.8858	0.871509
$187$	−3.06536	−0.224161
$188$	−1.24566	−0.0908494
$189$	18.3543	1.33508
$190$	−13.7601	−0.998264
$191$	−17.2440	−1.24773	−0.623866	−	0.781531i	$-0.714439\pi$
$191$	−17.2440	−1.24773	−0.623866	+	0.781531i	$0.714439\pi$
$192$	−24.7198	−1.78399
$193$	21.9944	1.58319	0.791597	−	0.611044i	$-0.209250\pi$
$193$	21.9944	1.58319	0.791597	+	0.611044i	$0.209250\pi$
$194$	−2.79527	−0.200689
$195$	−2.51921	−0.180404
$196$	−0.470140	−0.0335814
$197$	18.2116	1.29752	0.648762	−	0.760991i	$-0.275287\pi$
$197$	18.2116	1.29752	0.648762	+	0.760991i	$0.275287\pi$
$198$	−2.73680	−0.194496
$199$	3.82547	0.271180	0.135590	−	0.990765i	$-0.456707\pi$
$199$	3.82547	0.271180	0.135590	+	0.990765i	$0.456707\pi$
$200$	−10.9100	−0.771452
$201$	4.63465	0.326903
$202$	−1.42912	−0.100553
$203$	−23.6841	−1.66229
$204$	4.75931	0.333218
$205$	21.1404	1.47651
$206$	−11.2821	−0.786059
$207$	7.90319	0.549310
$208$	1.05461	0.0731238
$209$	−1.39837	−0.0967272
$210$	−33.9444	−2.34238
$211$	10.0466	0.691634	0.345817	−	0.938302i	$-0.387602\pi$
$211$	10.0466	0.691634	0.345817	+	0.938302i	$0.387602\pi$
$212$	−1.31163	−0.0900828
$213$	5.31587	0.364237
$214$	20.6663	1.41272
$215$	31.0912	2.12040
$216$	17.9560	1.22175
$217$	9.45139	0.641602
$218$	26.4182	1.78926
$219$	2.65554	0.179445
$220$	−0.256569	−0.0172979
$221$	−2.29891	−0.154641
$222$	9.80468	0.658047
$223$	−4.70859	−0.315311	−0.157655	−	0.987494i	$-0.550393\pi$
$223$	−4.70859	−0.315311	−0.157655	+	0.987494i	$0.550393\pi$
$224$	−3.71062	−0.247926
$225$	18.8938	1.25959
$226$	10.2299	0.680481
$227$	17.8908	1.18746	0.593728	−	0.804666i	$-0.297655\pi$
$227$	17.8908	1.18746	0.593728	+	0.804666i	$0.297655\pi$
$228$	2.17113	0.143786
$229$	−22.4294	−1.48217	−0.741087	−	0.671409i	$-0.765690\pi$
$229$	−22.4294	−1.48217	−0.741087	+	0.671409i	$0.765690\pi$
$230$	−6.06425	−0.399865
$231$	−3.44959	−0.226966
$232$	−23.1700	−1.52119
$233$	−17.8701	−1.17071	−0.585356	−	0.810777i	$-0.699045\pi$
$233$	−17.8701	−1.17071	−0.585356	+	0.810777i	$0.699045\pi$
$234$	−2.05251	−0.134176
$235$	−16.8589	−1.09975
$236$	1.03059	0.0670855
$237$	−7.34509	−0.477115
$238$	−30.9760	−2.00787
$239$	−15.9647	−1.03267	−0.516334	−	0.856387i	$-0.672704\pi$
$239$	−15.9647	−1.03267	−0.516334	+	0.856387i	$0.672704\pi$
$240$	−29.5488	−1.90737
$241$	−3.38895	−0.218302	−0.109151	−	0.994025i	$-0.534813\pi$
$241$	−3.38895	−0.218302	−0.109151	+	0.994025i	$0.534813\pi$
$242$	−14.4717	−0.930276
$243$	12.7558	0.818288
$244$	0	0
$245$	−6.36289	−0.406510
$246$	27.3017	1.74069
$247$	−1.04873	−0.0667289
$248$	9.24627	0.587139
$249$	−21.9001	−1.38786
$250$	5.17396	0.327230
$251$	−21.3416	−1.34707	−0.673536	−	0.739154i	$-0.735225\pi$
$251$	−21.3416	−1.34707	−0.673536	+	0.739154i	$0.735225\pi$
$252$	3.37889	0.212850
$253$	−0.616278	−0.0387450
$254$	−9.40138	−0.589895
$255$	64.4127	4.03368
$256$	−5.16177	−0.322611
$257$	−2.94877	−0.183939	−0.0919696	−	0.995762i	$-0.529316\pi$
$257$	−2.94877	−0.183939	−0.0919696	+	0.995762i	$0.529316\pi$
$258$	40.1526	2.49979
$259$	7.79652	0.484452
$260$	−0.192418	−0.0119333
$261$	40.1257	2.48372
$262$	1.81570	0.112174
$263$	−0.290703	−0.0179255	−0.00896275	−	0.999960i	$-0.502853\pi$
$263$	−0.290703	−0.0179255	−0.00896275	+	0.999960i	$0.502853\pi$
$264$	−3.37472	−0.207700
$265$	−17.7516	−1.09047
$266$	−14.1308	−0.866413
$267$	3.36014	0.205638
$268$	0.353996	0.0216237
$269$	−22.4073	−1.36620	−0.683098	−	0.730326i	$-0.739368\pi$
$269$	−22.4073	−1.36620	−0.683098	+	0.730326i	$0.739368\pi$
$270$	23.8605	1.45210
$271$	−8.33794	−0.506494	−0.253247	−	0.967402i	$-0.581499\pi$
$271$	−8.33794	−0.506494	−0.253247	+	0.967402i	$0.581499\pi$
$272$	−26.9648	−1.63498
$273$	−2.58707	−0.156576
$274$	10.2225	0.617563
$275$	−1.47331	−0.0888438
$276$	0.956841	0.0575951
$277$	−11.7269	−0.704600	−0.352300	−	0.935887i	$-0.614600\pi$
$277$	−11.7269	−0.704600	−0.352300	+	0.935887i	$0.614600\pi$
$278$	−10.4117	−0.624452
$279$	−16.0126	−0.958650
$280$	−26.4062	−1.57807
$281$	−11.4692	−0.684192	−0.342096	−	0.939665i	$-0.611137\pi$
$281$	−11.4692	−0.684192	−0.342096	+	0.939665i	$0.611137\pi$
$282$	−21.7723	−1.29652
$283$	−17.1905	−1.02187	−0.510936	−	0.859619i	$-0.670701\pi$
$283$	−17.1905	−1.02187	−0.510936	+	0.859619i	$0.670701\pi$
$284$	0.406027	0.0240933
$285$	29.3841	1.74056
$286$	0.160051	0.00946401
$287$	21.7099	1.28149
$288$	6.28656	0.370439
$289$	41.7798	2.45764
$290$	−30.7891	−1.80800
$291$	5.96917	0.349919
$292$	0.202831	0.0118698
$293$	−15.7956	−0.922790	−0.461395	−	0.887195i	$-0.652651\pi$
$293$	−15.7956	−0.922790	−0.461395	+	0.887195i	$0.652651\pi$
$294$	−8.21732	−0.479244
$295$	13.9480	0.812084
$296$	7.62731	0.443329
$297$	2.42482	0.140702
$298$	7.22433	0.418494
$299$	−0.462186	−0.0267289
$300$	2.28748	0.132068
$301$	31.9287	1.84034
$302$	−7.72099	−0.444293
$303$	3.05182	0.175322
$304$	−12.3009	−0.705507
$305$	0	0
$306$	52.4797	3.00006
$307$	−33.1675	−1.89297	−0.946484	−	0.322750i	$-0.895393\pi$
$307$	−33.1675	−1.89297	−0.946484	+	0.322750i	$0.895393\pi$
$308$	−0.263480	−0.0150132
$309$	24.0923	1.37056
$310$	12.2867	0.697840
$311$	−21.8042	−1.23640	−0.618201	−	0.786020i	$-0.712138\pi$
$311$	−21.8042	−1.23640	−0.618201	+	0.786020i	$0.712138\pi$
$312$	−2.53092	−0.143285
$313$	−26.2274	−1.48246	−0.741229	−	0.671252i	$-0.765757\pi$
$313$	−26.2274	−1.48246	−0.741229	+	0.671252i	$0.765757\pi$
$314$	4.33255	0.244500
$315$	45.7300	2.57660
$316$	−0.561020	−0.0315598
$317$	14.7802	0.830141	0.415071	−	0.909789i	$-0.363757\pi$
$317$	14.7802	0.830141	0.415071	+	0.909789i	$0.363757\pi$
$318$	−22.9252	−1.28558
$319$	−3.12893	−0.175187
$320$	−25.5536	−1.42849
$321$	−44.1318	−2.46320
$322$	−6.22760	−0.347050
$323$	26.8145	1.49200
$324$	−0.415385	−0.0230770
$325$	−1.10493	−0.0612904
$326$	24.7342	1.36990
$327$	−56.4147	−3.11974
$328$	21.2387	1.17271
$329$	−17.3130	−0.954495
$330$	−4.48444	−0.246860
$331$	−2.30323	−0.126597	−0.0632985	−	0.997995i	$-0.520162\pi$
$331$	−2.30323	−0.126597	−0.0632985	+	0.997995i	$0.520162\pi$
$332$	−1.67273	−0.0918032
$333$	−13.2089	−0.723845
$334$	−12.4998	−0.683960
$335$	4.79099	0.261760
$336$	−30.3448	−1.65544
$337$	10.0387	0.546845	0.273423	−	0.961894i	$-0.411844\pi$
$337$	10.0387	0.546845	0.273423	+	0.961894i	$0.411844\pi$
$338$	−17.2351	−0.937466
$339$	−21.8454	−1.18648
$340$	4.91986	0.266817
$341$	1.24864	0.0676175
$342$	23.9404	1.29455
$343$	14.6505	0.791053
$344$	31.2357	1.68412
$345$	12.9499	0.697200
$346$	−1.67268	−0.0899241
$347$	−24.9512	−1.33945	−0.669725	−	0.742609i	$-0.733588\pi$
$347$	−24.9512	−1.33945	−0.669725	+	0.742609i	$0.733588\pi$
$348$	4.85802	0.260417
$349$	3.51638	0.188227	0.0941137	−	0.995561i	$-0.469998\pi$
$349$	3.51638	0.188227	0.0941137	+	0.995561i	$0.469998\pi$
$350$	−14.8880	−0.795799
$351$	1.81853	0.0970658
$352$	−0.490216	−0.0261286
$353$	−6.99234	−0.372165	−0.186082	−	0.982534i	$-0.559579\pi$
$353$	−6.99234	−0.372165	−0.186082	+	0.982534i	$0.559579\pi$
$354$	18.0131	0.957385
$355$	5.49519	0.291654
$356$	0.256649	0.0136024
$357$	66.1477	3.50091
$358$	−16.0120	−0.846261
$359$	20.3345	1.07321	0.536607	−	0.843832i	$-0.319706\pi$
$359$	20.3345	1.07321	0.536607	+	0.843832i	$0.319706\pi$
$360$	44.7375	2.35788
$361$	−6.76764	−0.356192
$362$	30.9817	1.62836
$363$	30.9036	1.62202
$364$	−0.197601	−0.0103571
$365$	2.74512	0.143686
$366$	0	0
$367$	3.22811	0.168506	0.0842531	−	0.996444i	$-0.473150\pi$
$367$	3.22811	0.168506	0.0842531	+	0.996444i	$0.473150\pi$
$368$	−5.42117	−0.282598
$369$	−36.7810	−1.91474
$370$	10.1354	0.526916
$371$	−18.2298	−0.946442
$372$	−1.93865	−0.100514
$373$	2.26622	0.117340	0.0586702	−	0.998277i	$-0.481314\pi$
$373$	2.26622	0.117340	0.0586702	+	0.998277i	$0.481314\pi$
$374$	−4.09228	−0.211607
$375$	−11.0487	−0.570554
$376$	−16.9372	−0.873471
$377$	−2.34659	−0.120855
$378$	24.5032	1.26031
$379$	32.9645	1.69327	0.846636	−	0.532172i	$-0.178624\pi$
$379$	32.9645	1.69327	0.846636	+	0.532172i	$0.178624\pi$
$380$	2.24436	0.115133
$381$	20.0762	1.02854
$382$	−23.0209	−1.17785
$383$	−14.6400	−0.748071	−0.374035	−	0.927414i	$-0.622026\pi$
$383$	−14.6400	−0.748071	−0.374035	+	0.927414i	$0.622026\pi$
$384$	−26.0103	−1.32733
$385$	−3.56595	−0.181738
$386$	29.3628	1.49453
$387$	−54.0937	−2.74974
$388$	0.455927	0.0231462
$389$	14.8158	0.751191	0.375595	−	0.926784i	$-0.377438\pi$
$389$	14.8158	0.751191	0.375595	+	0.926784i	$0.377438\pi$
$390$	−3.36317	−0.170301
$391$	11.8175	0.597635
$392$	−6.39246	−0.322868
$393$	−3.87734	−0.195586
$394$	24.3127	1.22486
$395$	−7.59286	−0.382038
$396$	0.446390	0.0224320
$397$	−26.8844	−1.34929	−0.674644	−	0.738144i	$-0.735703\pi$
$397$	−26.8844	−1.34929	−0.674644	+	0.738144i	$0.735703\pi$
$398$	5.10704	0.255993
$399$	30.1756	1.51067
$400$	−12.9602	−0.648008
$401$	−5.44924	−0.272122	−0.136061	−	0.990700i	$-0.543444\pi$
$401$	−5.44924	−0.272122	−0.136061	+	0.990700i	$0.543444\pi$
$402$	6.18730	0.308594
$403$	0.936433	0.0466471
$404$	0.233099	0.0115971
$405$	−5.62184	−0.279351
$406$	−31.6184	−1.56920
$407$	1.03001	0.0510557
$408$	64.7121	3.20373
$409$	9.89180	0.489118	0.244559	−	0.969634i	$-0.421357\pi$
$409$	9.89180	0.489118	0.244559	+	0.969634i	$0.421357\pi$
$410$	28.2227	1.39382
$411$	−21.8296	−1.07678
$412$	1.84018	0.0906590
$413$	14.3237	0.704824
$414$	10.5508	0.518545
$415$	−22.6388	−1.11130
$416$	−0.367644	−0.0180252
$417$	22.2337	1.08879
$418$	−1.86684	−0.0913099
$419$	5.64312	0.275685	0.137842	−	0.990454i	$-0.455983\pi$
$419$	5.64312	0.275685	0.137842	+	0.990454i	$0.455983\pi$
$420$	5.53654	0.270156
$421$	−14.4009	−0.701858	−0.350929	−	0.936402i	$-0.614134\pi$
$421$	−14.4009	−0.701858	−0.350929	+	0.936402i	$0.614134\pi$
$422$	13.4123	0.652899
$423$	29.3318	1.42616
$424$	−17.8341	−0.866101
$425$	28.2515	1.37040
$426$	7.09674	0.343838
$427$	0	0
$428$	−3.37080	−0.162934
$429$	−0.341781	−0.0165014
$430$	41.5070	2.00165
$431$	16.2943	0.784867	0.392433	−	0.919780i	$-0.371633\pi$
$431$	16.2943	0.784867	0.392433	+	0.919780i	$0.371633\pi$
$432$	21.3302	1.02625
$433$	20.2338	0.972374	0.486187	−	0.873855i	$-0.338387\pi$
$433$	20.2338	0.972374	0.486187	+	0.873855i	$0.338387\pi$
$434$	12.6177	0.605669
$435$	65.7486	3.15241
$436$	−4.30897	−0.206362
$437$	5.39095	0.257884
$438$	3.54517	0.169395
$439$	−7.83578	−0.373982	−0.186991	−	0.982362i	$-0.559873\pi$
$439$	−7.83578	−0.373982	−0.186991	+	0.982362i	$0.559873\pi$
$440$	−3.48856	−0.166311
$441$	11.0704	0.527163
$442$	−3.06906	−0.145980
$443$	26.5171	1.25986	0.629932	−	0.776650i	$-0.283083\pi$
$443$	26.5171	1.25986	0.629932	+	0.776650i	$0.283083\pi$
$444$	−1.59921	−0.0758950
$445$	3.47349	0.164659
$446$	−6.28602	−0.297652
$447$	−15.4272	−0.729682
$448$	−26.2419	−1.23982
$449$	−3.77710	−0.178252	−0.0891262	−	0.996020i	$-0.528407\pi$
$449$	−3.77710	−0.178252	−0.0891262	+	0.996020i	$0.528407\pi$
$450$	25.2234	1.18904
$451$	2.86812	0.135055
$452$	−1.66856	−0.0784823
$453$	16.4878	0.774665
$454$	23.8844	1.12095
$455$	−2.67434	−0.125375
$456$	29.5207	1.38243
$457$	10.2352	0.478782	0.239391	−	0.970923i	$-0.423052\pi$
$457$	10.2352	0.478782	0.239391	+	0.970923i	$0.423052\pi$
$458$	−29.9434	−1.39916
$459$	−46.4972	−2.17030
$460$	0.989118	0.0461179
$461$	−13.0371	−0.607197	−0.303598	−	0.952800i	$-0.598188\pi$
$461$	−13.0371	−0.607197	−0.303598	+	0.952800i	$0.598188\pi$
$462$	−4.60523	−0.214255
$463$	16.2771	0.756463	0.378231	−	0.925711i	$-0.376532\pi$
$463$	16.2771	0.756463	0.378231	+	0.925711i	$0.376532\pi$
$464$	−27.5241	−1.27777
$465$	−26.2378	−1.21675
$466$	−23.8568	−1.10514
$467$	13.4847	0.623997	0.311998	−	0.950083i	$-0.399002\pi$
$467$	13.4847	0.623997	0.311998	+	0.950083i	$0.399002\pi$
$468$	0.334777	0.0154751
$469$	4.92004	0.227186
$470$	−22.5067	−1.03816
$471$	−9.25196	−0.426308
$472$	14.0128	0.644993
$473$	4.21814	0.193950
$474$	−9.80577	−0.450394
$475$	12.8879	0.591337
$476$	5.05238	0.231575
$477$	30.8850	1.41413
$478$	−21.3130	−0.974833
$479$	−38.3825	−1.75374	−0.876872	−	0.480725i	$-0.840374\pi$
$479$	−38.3825	−1.75374	−0.876872	+	0.480725i	$0.840374\pi$
$480$	10.3010	0.470172
$481$	0.772471	0.0352216
$482$	−4.52429	−0.206076
$483$	13.2987	0.605114
$484$	2.36043	0.107292
$485$	6.17052	0.280189
$486$	17.0292	0.772459
$487$	−11.6942	−0.529913	−0.264957	−	0.964260i	$-0.585358\pi$
$487$	−11.6942	−0.529913	−0.264957	+	0.964260i	$0.585358\pi$
$488$	0	0
$489$	−52.8186	−2.38854
$490$	−8.49452	−0.383743
$491$	−39.2115	−1.76959	−0.884796	−	0.465979i	$-0.845702\pi$
$491$	−39.2115	−1.76959	−0.884796	+	0.465979i	$0.845702\pi$
$492$	−4.45308	−0.200760
$493$	59.9990	2.70222
$494$	−1.40006	−0.0629917
$495$	6.04146	0.271543
$496$	10.9838	0.493187
$497$	5.64321	0.253132
$498$	−29.2368	−1.31013
$499$	−38.5025	−1.72361	−0.861804	−	0.507242i	$-0.830665\pi$
$499$	−38.5025	−1.72361	−0.861804	+	0.507242i	$0.830665\pi$
$500$	−0.843905	−0.0377406
$501$	26.6928	1.19254
$502$	−28.4913	−1.27163
$503$	−34.7951	−1.55144	−0.775719	−	0.631078i	$-0.782613\pi$
$503$	−34.7951	−1.55144	−0.775719	+	0.631078i	$0.782613\pi$
$504$	45.9426	2.04645
$505$	3.15477	0.140385
$506$	−0.822737	−0.0365751
$507$	36.8047	1.63456
$508$	1.53343	0.0680348
$509$	24.5529	1.08829	0.544143	−	0.838992i	$-0.316855\pi$
$509$	24.5529	1.08829	0.544143	+	0.838992i	$0.316855\pi$
$510$	85.9915	3.80777
$511$	2.81906	0.124708
$512$	−25.1385	−1.11097
$513$	−21.2113	−0.936502
$514$	−3.93663	−0.173638
$515$	24.9050	1.09745
$516$	−6.54914	−0.288310
$517$	−2.28724	−0.100593
$518$	10.4084	0.457320
$519$	3.57194	0.156791
$520$	−2.61630	−0.114732
$521$	−19.3486	−0.847679	−0.423840	−	0.905737i	$-0.639318\pi$
$521$	−19.3486	−0.847679	−0.423840	+	0.905737i	$0.639318\pi$
$522$	53.5682	2.34462
$523$	20.8350	0.911049	0.455525	−	0.890223i	$-0.349452\pi$
$523$	20.8350	0.911049	0.455525	+	0.890223i	$0.349452\pi$
$524$	−0.296152	−0.0129375
$525$	31.7927	1.38755
$526$	−0.388091	−0.0169216
$527$	−23.9433	−1.04299
$528$	−4.00889	−0.174465
$529$	−20.6241	−0.896702
$530$	−23.6985	−1.02940
$531$	−24.2673	−1.05311
$532$	2.30482	0.0999266
$533$	2.15099	0.0931697
$534$	4.48583	0.194121
$535$	−45.6205	−1.97235
$536$	4.81326	0.207901
$537$	34.1929	1.47553
$538$	−29.9140	−1.28968
$539$	−0.863253	−0.0371829
$540$	−3.89180	−0.167476
$541$	12.1355	0.521748	0.260874	−	0.965373i	$-0.415989\pi$
$541$	12.1355	0.521748	0.260874	+	0.965373i	$0.415989\pi$
$542$	−11.1312	−0.478128
$543$	−66.1600	−2.83920
$544$	9.40015	0.403028
$545$	−58.3178	−2.49806
$546$	−3.45376	−0.147807
$547$	−8.73055	−0.373291	−0.186646	−	0.982427i	$-0.559762\pi$
$547$	−8.73055	−0.373291	−0.186646	+	0.982427i	$0.559762\pi$
$548$	−1.66735	−0.0712258
$549$	0	0
$550$	−1.96688	−0.0838681
$551$	27.3706	1.16603
$552$	13.0101	0.553747
$553$	−7.79739	−0.331579
$554$	−15.6555	−0.665139
$555$	−21.6437	−0.918725
$556$	1.69821	0.0720203
$557$	−13.7986	−0.584665	−0.292332	−	0.956317i	$-0.594431\pi$
$557$	−13.7986	−0.584665	−0.292332	+	0.956317i	$0.594431\pi$
$558$	−21.3770	−0.904960
$559$	3.16346	0.133800
$560$	−31.3684	−1.32556
$561$	8.73887	0.368955
$562$	−15.3114	−0.645874
$563$	−15.9610	−0.672674	−0.336337	−	0.941742i	$-0.609188\pi$
$563$	−15.9610	−0.672674	−0.336337	+	0.941742i	$0.609188\pi$
$564$	3.55120	0.149533
$565$	−22.5823	−0.950044
$566$	−22.9496	−0.964642
$567$	−5.77327	−0.242455
$568$	5.52073	0.231645
$569$	−38.9632	−1.63342	−0.816712	−	0.577046i	$-0.804205\pi$
$569$	−38.9632	−1.63342	−0.816712	+	0.577046i	$0.804205\pi$
$570$	39.2280	1.64308
$571$	38.4942	1.61093	0.805466	−	0.592642i	$-0.201915\pi$
$571$	38.4942	1.61093	0.805466	+	0.592642i	$0.201915\pi$
$572$	−0.0261053	−0.00109152
$573$	49.1601	2.05369
$574$	28.9829	1.20972
$575$	5.67985	0.236866
$576$	44.4593	1.85247
$577$	8.50330	0.353997	0.176998	−	0.984211i	$-0.443361\pi$
$577$	8.50330	0.353997	0.176998	+	0.984211i	$0.443361\pi$
$578$	55.7765	2.32000
$579$	−62.7028	−2.60584
$580$	5.02190	0.208523
$581$	−23.2486	−0.964516
$582$	7.96890	0.330321
$583$	−2.40836	−0.0997440
$584$	2.75788	0.114122
$585$	4.53088	0.187329
$586$	−21.0873	−0.871109
$587$	32.6717	1.34851	0.674253	−	0.738501i	$-0.264466\pi$
$587$	32.6717	1.34851	0.674253	+	0.738501i	$0.264466\pi$
$588$	1.34030	0.0552730
$589$	−10.9226	−0.450056
$590$	18.6207	0.766603
$591$	−51.9186	−2.13565
$592$	9.06062	0.372389
$593$	5.47641	0.224889	0.112445	−	0.993658i	$-0.464132\pi$
$593$	5.47641	0.224889	0.112445	+	0.993658i	$0.464132\pi$
$594$	3.23716	0.132822
$595$	68.3791	2.80327
$596$	−1.17833	−0.0482664
$597$	−10.9058	−0.446346
$598$	−0.617023	−0.0252320
$599$	1.13106	0.0462139	0.0231070	−	0.999733i	$-0.492644\pi$
$599$	1.13106	0.0462139	0.0231070	+	0.999733i	$0.492644\pi$
$600$	31.1027	1.26976
$601$	−4.28154	−0.174647	−0.0873237	−	0.996180i	$-0.527831\pi$
$601$	−4.28154	−0.174647	−0.0873237	+	0.996180i	$0.527831\pi$
$602$	42.6251	1.73727
$603$	−8.33556	−0.339450
$604$	1.25934	0.0512420
$605$	31.9461	1.29879
$606$	4.07421	0.165503
$607$	38.0413	1.54405	0.772025	−	0.635593i	$-0.219244\pi$
$607$	38.0413	1.54405	0.772025	+	0.635593i	$0.219244\pi$
$608$	4.28821	0.173910
$609$	67.5197	2.73604
$610$	0	0
$611$	−1.71535	−0.0693956
$612$	−8.55977	−0.346008
$613$	−30.3166	−1.22448	−0.612238	−	0.790674i	$-0.709730\pi$
$613$	−30.3166	−1.22448	−0.612238	+	0.790674i	$0.709730\pi$
$614$	−44.2789	−1.78695
$615$	−60.2682	−2.43025
$616$	−3.58253	−0.144344
$617$	32.5615	1.31088	0.655438	−	0.755249i	$-0.272484\pi$
$617$	32.5615	1.31088	0.655438	+	0.755249i	$0.272484\pi$
$618$	32.1635	1.29380
$619$	−10.2570	−0.412265	−0.206132	−	0.978524i	$-0.566088\pi$
$619$	−10.2570	−0.412265	−0.206132	+	0.978524i	$0.566088\pi$
$620$	−2.00405	−0.0804844
$621$	−9.34808	−0.375125
$622$	−29.1088	−1.16716
$623$	3.56706	0.142911
$624$	−3.00653	−0.120357
$625$	−29.8460	−1.19384
$626$	−35.0138	−1.39943
$627$	3.98654	0.159207
$628$	−0.706667	−0.0281991
$629$	−19.7510	−0.787524
$630$	61.0500	2.43229
$631$	−3.57768	−0.142425	−0.0712125	−	0.997461i	$-0.522687\pi$
$631$	−3.57768	−0.142425	−0.0712125	+	0.997461i	$0.522687\pi$
$632$	−7.62816	−0.303432
$633$	−28.6413	−1.13839
$634$	19.7318	0.783649
$635$	20.7534	0.823575
$636$	3.73925	0.148271
$637$	−0.647409	−0.0256513
$638$	−4.17716	−0.165375
$639$	−9.56076	−0.378218
$640$	−26.8877	−1.06283
$641$	11.2511	0.444390	0.222195	−	0.975002i	$-0.428678\pi$
$641$	11.2511	0.444390	0.222195	+	0.975002i	$0.428678\pi$
$642$	−58.9164	−2.32525
$643$	25.8125	1.01795	0.508974	−	0.860782i	$-0.330025\pi$
$643$	25.8125	1.01795	0.508974	+	0.860782i	$0.330025\pi$
$644$	1.01576	0.0400266
$645$	−88.6363	−3.49005
$646$	35.7976	1.40844
$647$	4.94451	0.194389	0.0971943	−	0.995265i	$-0.469013\pi$
$647$	4.94451	0.194389	0.0971943	+	0.995265i	$0.469013\pi$
$648$	−5.64797	−0.221873
$649$	1.89233	0.0742803
$650$	−1.47509	−0.0578578
$651$	−26.9445	−1.05604
$652$	−4.03430	−0.157995
$653$	−38.2880	−1.49832	−0.749162	−	0.662387i	$-0.769544\pi$
$653$	−38.2880	−1.49832	−0.749162	+	0.662387i	$0.769544\pi$
$654$	−75.3142	−2.94502
$655$	−4.00813	−0.156611
$656$	25.2298	0.985059
$657$	−4.77607	−0.186332
$658$	−23.1130	−0.901038
$659$	19.0846	0.743430	0.371715	−	0.928347i	$-0.378770\pi$
$659$	19.0846	0.743430	0.371715	+	0.928347i	$0.378770\pi$
$660$	0.731441	0.0284713
$661$	16.2051	0.630307	0.315154	−	0.949041i	$-0.397944\pi$
$661$	16.2051	0.630307	0.315154	+	0.949041i	$0.397944\pi$
$662$	−3.07483	−0.119507
$663$	6.55384	0.254530
$664$	−22.7441	−0.882641
$665$	31.1935	1.20963
$666$	−17.6340	−0.683305
$667$	12.0626	0.467064
$668$	2.03880	0.0788835
$669$	13.4235	0.518982
$670$	6.39601	0.247100
$671$	0	0
$672$	10.5784	0.408072
$673$	28.6996	1.10629	0.553145	−	0.833085i	$-0.313428\pi$
$673$	28.6996	1.10629	0.553145	+	0.833085i	$0.313428\pi$
$674$	13.4018	0.516219
$675$	−22.3480	−0.860176
$676$	2.81115	0.108121
$677$	−39.3935	−1.51401	−0.757007	−	0.653406i	$-0.773339\pi$
$677$	−39.3935	−1.51401	−0.757007	+	0.653406i	$0.773339\pi$
$678$	−29.1638	−1.12003
$679$	6.33674	0.243182
$680$	66.8950	2.56531
$681$	−51.0041	−1.95448
$682$	1.66694	0.0638305
$683$	0.198967	0.00761325	0.00380663	−	0.999993i	$-0.498788\pi$
$683$	0.198967	0.00761325	0.00380663	+	0.999993i	$0.498788\pi$
$684$	−3.90484	−0.149305
$685$	−22.5660	−0.862203
$686$	19.5586	0.746750
$687$	63.9428	2.43957
$688$	37.1054	1.41463
$689$	−1.80618	−0.0688101
$690$	17.2883	0.658153
$691$	16.7000	0.635299	0.317649	−	0.948208i	$-0.397107\pi$
$691$	16.7000	0.635299	0.317649	+	0.948208i	$0.397107\pi$
$692$	0.272826	0.0103713
$693$	6.20420	0.235678
$694$	−33.3101	−1.26443
$695$	22.9837	0.871821
$696$	66.0543	2.50378
$697$	−54.9978	−2.08319
$698$	4.69440	0.177686
$699$	50.9451	1.92692
$700$	2.42834	0.0917824
$701$	38.3276	1.44762	0.723808	−	0.690002i	$-0.242390\pi$
$701$	38.3276	1.44762	0.723808	+	0.690002i	$0.242390\pi$
$702$	2.42775	0.0916296
$703$	−9.01011	−0.339823
$704$	−3.46686	−0.130662
$705$	48.0621	1.81012
$706$	−9.33484	−0.351321
$707$	3.23974	0.121843
$708$	−2.93805	−0.110419
$709$	29.8957	1.12276	0.561378	−	0.827560i	$-0.310272\pi$
$709$	29.8957	1.12276	0.561378	+	0.827560i	$0.310272\pi$
$710$	7.33613	0.275320
$711$	13.2104	0.495428
$712$	3.48964	0.130780
$713$	−4.81370	−0.180275
$714$	88.3079	3.30484
$715$	−0.353310	−0.0132131
$716$	2.61166	0.0976023
$717$	45.5128	1.69971
$718$	27.1468	1.01311
$719$	−47.8534	−1.78463	−0.892315	−	0.451412i	$-0.850920\pi$
$719$	−47.8534	−1.78463	−0.892315	+	0.451412i	$0.850920\pi$
$720$	53.1445	1.98058
$721$	25.5759	0.952495
$722$	−9.03487	−0.336243
$723$	9.66140	0.359311
$724$	−5.05332	−0.187805
$725$	28.8374	1.07100
$726$	41.2566	1.53118
$727$	−38.2100	−1.41713	−0.708565	−	0.705646i	$-0.750657\pi$
$727$	−38.2100	−1.41713	−0.708565	+	0.705646i	$0.750657\pi$
$728$	−2.68677	−0.0995783
$729$	−42.0879	−1.55881
$730$	3.66476	0.135639
$731$	−80.8851	−2.99164
$732$	0	0
$733$	−41.8494	−1.54574	−0.772871	−	0.634563i	$-0.781180\pi$
$733$	−41.8494	−1.54574	−0.772871	+	0.634563i	$0.781180\pi$
$734$	4.30956	0.159069
$735$	18.1396	0.669091
$736$	1.88986	0.0696613
$737$	0.649993	0.0239428
$738$	−49.1030	−1.80751
$739$	34.1689	1.25692	0.628461	−	0.777841i	$-0.283685\pi$
$739$	34.1689	1.25692	0.628461	+	0.777841i	$0.283685\pi$
$740$	−1.65315	−0.0607711
$741$	2.98976	0.109832
$742$	−24.3369	−0.893436
$743$	17.0680	0.626165	0.313082	−	0.949726i	$-0.398638\pi$
$743$	17.0680	0.626165	0.313082	+	0.949726i	$0.398638\pi$
$744$	−26.3597	−0.966394
$745$	−15.9476	−0.584275
$746$	3.02543	0.110769
$747$	39.3880	1.44113
$748$	0.667477	0.0244054
$749$	−46.8494	−1.71184
$750$	−14.7502	−0.538600
$751$	−14.0478	−0.512610	−0.256305	−	0.966596i	$-0.582505\pi$
$751$	−14.0478	−0.512610	−0.256305	+	0.966596i	$0.582505\pi$
$752$	−20.1200	−0.733702
$753$	60.8418	2.21720
$754$	−3.13272	−0.114087
$755$	17.0440	0.620294
$756$	−3.99663	−0.145356
$757$	−14.5106	−0.527397	−0.263698	−	0.964605i	$-0.584942\pi$
$757$	−14.5106	−0.527397	−0.263698	+	0.964605i	$0.584942\pi$
$758$	44.0079	1.59844
$759$	1.75692	0.0637720
$760$	30.5165	1.10695
$761$	4.24490	0.153877	0.0769387	−	0.997036i	$-0.475485\pi$
$761$	4.24490	0.153877	0.0769387	+	0.997036i	$0.475485\pi$
$762$	26.8019	0.970932
$763$	−59.8886	−2.16811
$764$	3.75486	0.135846
$765$	−115.848	−4.18850
$766$	−19.5446	−0.706175
$767$	1.41918	0.0512435
$768$	14.7154	0.530998
$769$	34.0992	1.22965	0.614824	−	0.788664i	$-0.289227\pi$
$769$	34.0992	1.22965	0.614824	+	0.788664i	$0.289227\pi$
$770$	−4.76058	−0.171559
$771$	8.40650	0.302753
$772$	−4.78926	−0.172369
$773$	−21.0356	−0.756599	−0.378299	−	0.925683i	$-0.623491\pi$
$773$	−21.0356	−0.756599	−0.378299	+	0.925683i	$0.623491\pi$
$774$	−72.2157	−2.59574
$775$	−11.5079	−0.413376
$776$	6.19921	0.222539
$777$	−22.2267	−0.797379
$778$	19.7792	0.709120
$779$	−25.0891	−0.898912
$780$	0.548555	0.0196414
$781$	0.745532	0.0266772
$782$	15.7764	0.564164
$783$	−47.4616	−1.69614
$784$	−7.59372	−0.271204
$785$	−9.56405	−0.341356
$786$	−5.17629	−0.184632
$787$	42.0877	1.50026	0.750132	−	0.661288i	$-0.229990\pi$
$787$	42.0877	1.50026	0.750132	+	0.661288i	$0.229990\pi$
$788$	−3.96556	−0.141267
$789$	0.828750	0.0295043
$790$	−10.1365	−0.360642
$791$	−23.1906	−0.824562
$792$	6.06954	0.215672
$793$	0	0
$794$	−35.8909	−1.27372
$795$	50.6071	1.79485
$796$	−0.832991	−0.0295246
$797$	52.8282	1.87127	0.935635	−	0.352968i	$-0.114828\pi$
$797$	52.8282	1.87127	0.935635	+	0.352968i	$0.114828\pi$
$798$	40.2847	1.42606
$799$	43.8591	1.55162
$800$	4.51801	0.159736
$801$	−6.04333	−0.213531
$802$	−7.27479	−0.256882
$803$	0.372430	0.0131428
$804$	−1.00919	−0.0355913
$805$	13.7473	0.484530
$806$	1.25015	0.0440346
$807$	63.8798	2.24868
$808$	3.16943	0.111500
$809$	2.14947	0.0755713	0.0377856	−	0.999286i	$-0.487970\pi$
$809$	2.14947	0.0755713	0.0377856	+	0.999286i	$0.487970\pi$
$810$	−7.50521	−0.263706
$811$	−37.4503	−1.31506	−0.657528	−	0.753430i	$-0.728398\pi$
$811$	−37.4503	−1.31506	−0.657528	+	0.753430i	$0.728398\pi$
$812$	5.15717	0.180981
$813$	23.7702	0.833658
$814$	1.37507	0.0481963
$815$	−54.6004	−1.91257
$816$	76.8726	2.69108
$817$	−36.8986	−1.29092
$818$	13.2057	0.461725
$819$	4.65293	0.162586
$820$	−4.60330	−0.160754
$821$	22.4623	0.783940	0.391970	−	0.919978i	$-0.371794\pi$
$821$	22.4623	0.783940	0.391970	+	0.919978i	$0.371794\pi$
$822$	−29.1428	−1.01647
$823$	−6.18053	−0.215440	−0.107720	−	0.994181i	$-0.534355\pi$
$823$	−6.18053	−0.215440	−0.107720	+	0.994181i	$0.534355\pi$
$824$	25.0208	0.871640
$825$	4.20018	0.146231
$826$	19.1223	0.665350
$827$	35.1700	1.22298	0.611490	−	0.791252i	$-0.290570\pi$
$827$	35.1700	1.22298	0.611490	+	0.791252i	$0.290570\pi$
$828$	−1.72091	−0.0598057
$829$	−44.0764	−1.53084	−0.765418	−	0.643533i	$-0.777468\pi$
$829$	−44.0764	−1.53084	−0.765418	+	0.643533i	$0.777468\pi$
$830$	−30.2231	−1.04906
$831$	33.4316	1.15973
$832$	−2.60002	−0.0901396
$833$	16.5533	0.573539
$834$	29.6822	1.02781
$835$	27.5932	0.954901
$836$	0.304493	0.0105311
$837$	18.9401	0.654665
$838$	7.53363	0.260245
$839$	−41.8931	−1.44631	−0.723155	−	0.690686i	$-0.757309\pi$
$839$	−41.8931	−1.44631	−0.723155	+	0.690686i	$0.757309\pi$
$840$	75.2801	2.59741
$841$	32.2434	1.11184
$842$	−19.2254	−0.662550
$843$	32.6968	1.12614
$844$	−2.18763	−0.0753012
$845$	38.0463	1.30883
$846$	39.1582	1.34629
$847$	32.8066	1.12725
$848$	−21.1855	−0.727511
$849$	49.0077	1.68194
$850$	37.7160	1.29365
$851$	−3.97086	−0.136119
$852$	−1.15752	−0.0396561
$853$	45.4221	1.55522	0.777612	−	0.628745i	$-0.216431\pi$
$853$	45.4221	1.55522	0.777612	+	0.628745i	$0.216431\pi$
$854$	0	0
$855$	−52.8482	−1.80737
$856$	−45.8326	−1.56653
$857$	32.5899	1.11325	0.556626	−	0.830763i	$-0.312096\pi$
$857$	32.5899	1.11325	0.556626	+	0.830763i	$0.312096\pi$
$858$	−0.456281	−0.0155772
$859$	−43.1281	−1.47151	−0.735756	−	0.677246i	$-0.763173\pi$
$859$	−43.1281	−1.47151	−0.735756	+	0.677246i	$0.763173\pi$
$860$	−6.77006	−0.230857
$861$	−61.8916	−2.10926
$862$	21.7530	0.740910
$863$	18.6553	0.635033	0.317516	−	0.948253i	$-0.397151\pi$
$863$	18.6553	0.635033	0.317516	+	0.948253i	$0.397151\pi$
$864$	−7.43589	−0.252974
$865$	3.69243	0.125546
$866$	27.0123	0.917915
$867$	−119.108	−4.04512
$868$	−2.05803	−0.0698540
$869$	−1.03012	−0.0349446
$870$	87.7751	2.97585
$871$	0.487472	0.0165174
$872$	−58.5888	−1.98407
$873$	−10.7357	−0.363350
$874$	7.19697	0.243441
$875$	−11.7291	−0.396516
$876$	−0.578240	−0.0195369
$877$	−29.2438	−0.987494	−0.493747	−	0.869606i	$-0.664373\pi$
$877$	−29.2438	−0.987494	−0.493747	+	0.869606i	$0.664373\pi$
$878$	−10.4609	−0.353037
$879$	45.0309	1.51886
$880$	−4.14412	−0.139698
$881$	14.9569	0.503911	0.251955	−	0.967739i	$-0.418926\pi$
$881$	14.9569	0.503911	0.251955	+	0.967739i	$0.418926\pi$
$882$	14.7791	0.497639
$883$	43.4183	1.46114	0.730570	−	0.682837i	$-0.239254\pi$
$883$	43.4183	1.46114	0.730570	+	0.682837i	$0.239254\pi$
$884$	0.500584	0.0168365
$885$	−39.7637	−1.33664
$886$	35.4006	1.18931
$887$	−58.8225	−1.97507	−0.987534	−	0.157406i	$-0.949687\pi$
$887$	−58.8225	−1.97507	−0.987534	+	0.157406i	$0.949687\pi$
$888$	−21.7443	−0.729692
$889$	21.3125	0.714797
$890$	4.63715	0.155437
$891$	−0.762715	−0.0255519
$892$	1.02529	0.0343292
$893$	20.0079	0.669537
$894$	−20.5955	−0.688816
$895$	35.3463	1.18150
$896$	−27.6120	−0.922453
$897$	1.31762	0.0439942
$898$	−5.04247	−0.168269
$899$	−24.4399	−0.815116
$900$	−4.11410	−0.137137
$901$	46.1816	1.53853
$902$	3.82897	0.127491
$903$	−91.0238	−3.02908
$904$	−22.6873	−0.754567
$905$	−68.3918	−2.27342
$906$	22.0114	0.731280
$907$	−40.3589	−1.34009	−0.670047	−	0.742319i	$-0.733726\pi$
$907$	−40.3589	−1.34009	−0.670047	+	0.742319i	$0.733726\pi$
$908$	−3.89571	−0.129284
$909$	−5.48879	−0.182052
$910$	−3.57027	−0.118353
$911$	9.28025	0.307469	0.153734	−	0.988112i	$-0.450870\pi$
$911$	9.28025	0.307469	0.153734	+	0.988112i	$0.450870\pi$
$912$	35.0681	1.16122
$913$	−3.07141	−0.101649
$914$	13.6641	0.451968
$915$	0	0
$916$	4.88397	0.161371
$917$	−4.11610	−0.135926
$918$	−62.0742	−2.04875
$919$	−29.7738	−0.982147	−0.491074	−	0.871118i	$-0.663395\pi$
$919$	−29.7738	−0.982147	−0.491074	+	0.871118i	$0.663395\pi$
$920$	13.4490	0.443400
$921$	94.5555	3.11571
$922$	−17.4046	−0.573190
$923$	0.559123	0.0184037
$924$	0.751143	0.0247108
$925$	−9.49296	−0.312127
$926$	21.7301	0.714097
$927$	−43.3308	−1.42317
$928$	9.59512	0.314975
$929$	−11.7400	−0.385176	−0.192588	−	0.981280i	$-0.561688\pi$
$929$	−11.7400	−0.385176	−0.192588	+	0.981280i	$0.561688\pi$
$930$	−35.0277	−1.14860
$931$	7.55139	0.247487
$932$	3.89120	0.127460
$933$	62.1605	2.03504
$934$	18.0022	0.589050
$935$	9.03365	0.295432
$936$	4.55194	0.148785
$937$	39.8729	1.30259	0.651295	−	0.758825i	$-0.274226\pi$
$937$	39.8729	1.30259	0.651295	+	0.758825i	$0.274226\pi$
$938$	6.56830	0.214463
$939$	74.7703	2.44004
$940$	3.67099	0.119735
$941$	13.2350	0.431449	0.215724	−	0.976454i	$-0.430789\pi$
$941$	13.2350	0.431449	0.215724	+	0.976454i	$0.430789\pi$
$942$	−12.3515	−0.402432
$943$	−11.0571	−0.360068
$944$	16.6461	0.541784
$945$	−54.0905	−1.75957
$946$	5.63126	0.183088
$947$	−46.4358	−1.50896	−0.754480	−	0.656323i	$-0.772111\pi$
$947$	−46.4358	−1.50896	−0.754480	+	0.656323i	$0.772111\pi$
$948$	1.59938	0.0519456
$949$	0.279309	0.00906676
$950$	17.2055	0.558219
$951$	−42.1363	−1.36636
$952$	68.6969	2.22648
$953$	−7.08096	−0.229375	−0.114687	−	0.993402i	$-0.536587\pi$
$953$	−7.08096	−0.229375	−0.114687	+	0.993402i	$0.536587\pi$
$954$	41.2317	1.33493
$955$	50.8184	1.64444
$956$	3.47628	0.112431
$957$	8.92012	0.288347
$958$	−51.2411	−1.65552
$959$	−23.1739	−0.748323
$960$	72.8495	2.35121
$961$	−21.2470	−0.685386
$962$	1.03126	0.0332490
$963$	79.3725	2.55774
$964$	0.737940	0.0237675
$965$	−64.8180	−2.08656
$966$	17.7539	0.571224
$967$	3.04447	0.0979036	0.0489518	−	0.998801i	$-0.484412\pi$
$967$	3.04447	0.0979036	0.0489518	+	0.998801i	$0.484412\pi$
$968$	32.0946	1.03156
$969$	−76.4440	−2.45574
$970$	8.23771	0.264497
$971$	−4.63627	−0.148785	−0.0743924	−	0.997229i	$-0.523702\pi$
$971$	−4.63627	−0.148785	−0.0743924	+	0.997229i	$0.523702\pi$
$972$	−2.77757	−0.0890905
$973$	23.6028	0.756670
$974$	−15.6118	−0.500235
$975$	3.14999	0.100880
$976$	0	0
$977$	9.58007	0.306494	0.153247	−	0.988188i	$-0.451027\pi$
$977$	9.58007	0.306494	0.153247	+	0.988188i	$0.451027\pi$
$978$	−70.5134	−2.25477
$979$	0.471249	0.0150612
$980$	1.38551	0.0442585
$981$	101.464	3.23949
$982$	−52.3478	−1.67048
$983$	−34.5346	−1.10148	−0.550741	−	0.834676i	$-0.685655\pi$
$983$	−34.5346	−1.10148	−0.550741	+	0.834676i	$0.685655\pi$
$984$	−60.5483	−1.93021
$985$	−53.6700	−1.71007
$986$	80.0992	2.55088
$987$	49.3567	1.57104
$988$	0.228359	0.00726506
$989$	−16.2616	−0.517090
$990$	8.06541	0.256335
$991$	−32.8383	−1.04314	−0.521571	−	0.853208i	$-0.674654\pi$
$991$	−32.8383	−1.04314	−0.521571	+	0.853208i	$0.674654\pi$
$992$	−3.82904	−0.121572
$993$	6.56616	0.208371
$994$	7.53374	0.238956
$995$	−11.2737	−0.357401
$996$	4.76871	0.151102
$997$	28.6486	0.907309	0.453655	−	0.891178i	$-0.350120\pi$
$997$	28.6486	0.907309	0.453655	+	0.891178i	$0.350120\pi$
$998$	−51.4012	−1.62708
$999$	15.6238	0.494316

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3721.2.a.l.1.11		16
61.4	even	30		61.2.i.a.16.4	✓	32
61.46	even	30		61.2.i.a.42.4	yes	32
61.60	even	2		3721.2.a.j.1.6		16
183.65	odd	30		549.2.bl.b.199.1		32
183.107	odd	30		549.2.bl.b.469.1		32
244.107	odd	30		976.2.bw.c.225.4		32
244.187	odd	30		976.2.bw.c.321.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.i.a.16.4	✓	32	61.4	even	30
61.2.i.a.42.4	yes	32	61.46	even	30
549.2.bl.b.199.1		32	183.65	odd	30
549.2.bl.b.469.1		32	183.107	odd	30
976.2.bw.c.225.4		32	244.107	odd	30
976.2.bw.c.321.4		32	244.187	odd	30
3721.2.a.j.1.6		16	61.60	even	2
3721.2.a.l.1.11		16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3721 = 61^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3721.a (trivial)

\(f(q)\)	\(=\)	\(q+1.33501 q^{2} -2.85085 q^{3} -0.217749 q^{4} -2.94702 q^{5} -3.80591 q^{6} -3.02640 q^{7} -2.96072 q^{8} +5.12735 q^{9} -3.93430 q^{10} -0.399822 q^{11} +0.620769 q^{12} -0.299852 q^{13} -4.04027 q^{14} +8.40150 q^{15} -3.51709 q^{16} +7.66680 q^{17} +6.84506 q^{18} +3.49748 q^{19} +0.641709 q^{20} +8.62781 q^{21} -0.533766 q^{22} +1.54138 q^{23} +8.44056 q^{24} +3.68491 q^{25} -0.400306 q^{26} -6.06474 q^{27} +0.658994 q^{28} +7.82582 q^{29} +11.2161 q^{30} -3.12298 q^{31} +1.22609 q^{32} +1.13983 q^{33} +10.2353 q^{34} +8.91885 q^{35} -1.11647 q^{36} -2.57617 q^{37} +4.66917 q^{38} +0.854834 q^{39} +8.72528 q^{40} -7.17350 q^{41} +11.5182 q^{42} -10.5500 q^{43} +0.0870607 q^{44} -15.1104 q^{45} +2.05776 q^{46} +5.72065 q^{47} +10.0267 q^{48} +2.15909 q^{49} +4.91939 q^{50} -21.8569 q^{51} +0.0652924 q^{52} +6.02358 q^{53} -8.09649 q^{54} +1.17828 q^{55} +8.96031 q^{56} -9.97079 q^{57} +10.4475 q^{58} -4.73292 q^{59} -1.82942 q^{60} -4.16921 q^{62} -15.5174 q^{63} +8.67101 q^{64} +0.883670 q^{65} +1.52169 q^{66} -1.62571 q^{67} -1.66944 q^{68} -4.39424 q^{69} +11.9068 q^{70} -1.86466 q^{71} -15.1806 q^{72} -0.931489 q^{73} -3.43921 q^{74} -10.5051 q^{75} -0.761571 q^{76} +1.21002 q^{77} +1.14121 q^{78} +2.57646 q^{79} +10.3649 q^{80} +1.90764 q^{81} -9.57669 q^{82} +7.68195 q^{83} -1.87869 q^{84} -22.5942 q^{85} -14.0844 q^{86} -22.3102 q^{87} +1.18376 q^{88} -1.17865 q^{89} -20.1725 q^{90} +0.907473 q^{91} -0.335634 q^{92} +8.90316 q^{93} +7.63713 q^{94} -10.3071 q^{95} -3.49539 q^{96} -2.09382 q^{97} +2.88241 q^{98} -2.05003 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{2} - 2 q^{3} + 15 q^{4} - 12 q^{5} - 9 q^{6} - 4 q^{7} + 12 q^{8} + 4 q^{9} - 20 q^{10} + 9 q^{11} - 17 q^{12} - 11 q^{14} - 12 q^{15} + 9 q^{16} - 4 q^{17} + 35 q^{18} - 19 q^{19} - 17 q^{20}+ \cdots - 47 q^{99}+O(q^{100}) \) 16 * q + 5 * q^2 - 2 * q^3 + 15 * q^4 - 12 * q^5 - 9 * q^6 - 4 * q^7 + 12 * q^8 + 4 * q^9 - 20 * q^10 + 9 * q^11 - 17 * q^12 - 11 * q^14 - 12 * q^15 + 9 * q^16 - 4 * q^17 + 35 * q^18 - 19 * q^19 - 17 * q^20 - 3 * q^21 - 11 * q^22 - 4 * q^23 - 15 * q^24 - 8 * q^25 - 19 * q^26 - 5 * q^27 - 22 * q^28 - 4 * q^29 + 24 * q^30 + 9 * q^31 + 34 * q^32 - 10 * q^33 - 6 * q^34 + 37 * q^35 + 20 * q^36 - 38 * q^37 - 18 * q^38 - 12 * q^39 - 60 * q^40 - 37 * q^41 + 17 * q^42 - 15 * q^43 + 34 * q^44 - 32 * q^45 - 41 * q^46 - 40 * q^47 - 43 * q^48 + 24 * q^49 + 28 * q^50 - 19 * q^51 - 56 * q^52 + 19 * q^53 - 6 * q^54 + 30 * q^55 - 58 * q^56 + 8 * q^57 - 21 * q^58 - q^59 - 10 * q^60 - 37 * q^62 + 17 * q^63 + 28 * q^64 - 34 * q^65 - 59 * q^66 - 3 * q^67 + 2 * q^68 + 31 * q^69 + 17 * q^70 + 8 * q^71 - 9 * q^72 + 6 * q^73 + 10 * q^74 - q^75 - 65 * q^76 - 39 * q^77 - 68 * q^78 + 56 * q^79 - 14 * q^80 - 56 * q^81 + 39 * q^82 + 6 * q^83 - 65 * q^84 - 53 * q^85 - 54 * q^86 - 83 * q^87 - 5 * q^88 - 66 * q^89 - 60 * q^90 - 5 * q^91 + 37 * q^92 + 67 * q^93 - 43 * q^94 - 39 * q^95 + 14 * q^96 + 13 * q^97 - 16 * q^98 - 47 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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