LMFDB - Embedded newform 2793.2.a.x.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2793,2,Mod(1,2793)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2793, 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("2793.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2793 = 3 \cdot 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2793.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:	$22.3022172845$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 399)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$2.17009$ of defining polynomial
Character	$\chi$	$=$	2793.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.17009 q^{2} +1.00000 q^{3} +2.70928 q^{4} -3.70928 q^{5} +2.17009 q^{6} +1.53919 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.17009 q^{2} +1.00000 q^{3} +2.70928 q^{4} -3.70928 q^{5} +2.17009 q^{6} +1.53919 q^{8} +1.00000 q^{9} -8.04945 q^{10} -1.07838 q^{11} +2.70928 q^{12} -0.921622 q^{13} -3.70928 q^{15} -2.07838 q^{16} -0.290725 q^{17} +2.17009 q^{18} -1.00000 q^{19} -10.0494 q^{20} -2.34017 q^{22} -7.60197 q^{23} +1.53919 q^{24} +8.75872 q^{25} -2.00000 q^{26} +1.00000 q^{27} +5.36910 q^{29} -8.04945 q^{30} -8.49693 q^{31} -7.58864 q^{32} -1.07838 q^{33} -0.630898 q^{34} +2.70928 q^{36} -10.6803 q^{37} -2.17009 q^{38} -0.921622 q^{39} -5.70928 q^{40} +3.75872 q^{41} -8.49693 q^{43} -2.92162 q^{44} -3.70928 q^{45} -16.4969 q^{46} +6.20620 q^{47} -2.07838 q^{48} +19.0072 q^{50} -0.290725 q^{51} -2.49693 q^{52} +4.78765 q^{53} +2.17009 q^{54} +4.00000 q^{55} -1.00000 q^{57} +11.6514 q^{58} -4.00000 q^{59} -10.0494 q^{60} +2.68035 q^{61} -18.4391 q^{62} -12.3112 q^{64} +3.41855 q^{65} -2.34017 q^{66} +1.26180 q^{67} -0.787653 q^{68} -7.60197 q^{69} -3.86603 q^{71} +1.53919 q^{72} -1.41855 q^{73} -23.1773 q^{74} +8.75872 q^{75} -2.70928 q^{76} -2.00000 q^{78} -10.5236 q^{79} +7.70928 q^{80} +1.00000 q^{81} +8.15676 q^{82} -8.72979 q^{83} +1.07838 q^{85} -18.4391 q^{86} +5.36910 q^{87} -1.65983 q^{88} +3.75872 q^{89} -8.04945 q^{90} -20.5958 q^{92} -8.49693 q^{93} +13.4680 q^{94} +3.70928 q^{95} -7.58864 q^{96} +13.5174 q^{97} -1.07838 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + q^{2} + 3 q^{3} + q^{4} - 4 q^{5} + q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + q^2 + 3 * q^3 + q^4 - 4 * q^5 + q^6 + 3 * q^8 + 3 * q^9	$ 3 q + q^{2} + 3 q^{3} + q^{4} - 4 q^{5} + q^{6} + 3 q^{8} + 3 q^{9} - 6 q^{10} + q^{12} - 6 q^{13} - 4 q^{15} - 3 q^{16} - 8 q^{17} + q^{18} - 3 q^{19} - 12 q^{20} + 4 q^{22} - 4 q^{23} + 3 q^{24} + q^{25} - 6 q^{26} + 3 q^{27} + 20 q^{29} - 6 q^{30} - 8 q^{31} - 3 q^{32} + 2 q^{34} + q^{36} - 10 q^{37} - q^{38} - 6 q^{39} - 10 q^{40} - 14 q^{41} - 8 q^{43} - 12 q^{44} - 4 q^{45} - 32 q^{46} - 6 q^{47} - 3 q^{48} + 23 q^{50} - 8 q^{51} + 10 q^{52} + 4 q^{53} + q^{54} + 12 q^{55} - 3 q^{57} - 2 q^{58} - 12 q^{59} - 12 q^{60} - 14 q^{61} - 8 q^{62} - 11 q^{64} - 4 q^{65} + 4 q^{66} - 4 q^{67} + 8 q^{68} - 4 q^{69} + 2 q^{71} + 3 q^{72} + 10 q^{73} - 30 q^{74} + q^{75} - q^{76} - 6 q^{78} - 16 q^{79} + 16 q^{80} + 3 q^{81} + 18 q^{82} + 14 q^{83} - 8 q^{86} + 20 q^{87} - 16 q^{88} - 14 q^{89} - 6 q^{90} - 8 q^{92} - 8 q^{93} + 8 q^{94} + 4 q^{95} - 3 q^{96} - 10 q^{97}+O(q^{100}) $ 3 * q + q^2 + 3 * q^3 + q^4 - 4 * q^5 + q^6 + 3 * q^8 + 3 * q^9 - 6 * q^10 + q^12 - 6 * q^13 - 4 * q^15 - 3 * q^16 - 8 * q^17 + q^18 - 3 * q^19 - 12 * q^20 + 4 * q^22 - 4 * q^23 + 3 * q^24 + q^25 - 6 * q^26 + 3 * q^27 + 20 * q^29 - 6 * q^30 - 8 * q^31 - 3 * q^32 + 2 * q^34 + q^36 - 10 * q^37 - q^38 - 6 * q^39 - 10 * q^40 - 14 * q^41 - 8 * q^43 - 12 * q^44 - 4 * q^45 - 32 * q^46 - 6 * q^47 - 3 * q^48 + 23 * q^50 - 8 * q^51 + 10 * q^52 + 4 * q^53 + q^54 + 12 * q^55 - 3 * q^57 - 2 * q^58 - 12 * q^59 - 12 * q^60 - 14 * q^61 - 8 * q^62 - 11 * q^64 - 4 * q^65 + 4 * q^66 - 4 * q^67 + 8 * q^68 - 4 * q^69 + 2 * q^71 + 3 * q^72 + 10 * q^73 - 30 * q^74 + q^75 - q^76 - 6 * q^78 - 16 * q^79 + 16 * q^80 + 3 * q^81 + 18 * q^82 + 14 * q^83 - 8 * q^86 + 20 * q^87 - 16 * q^88 - 14 * q^89 - 6 * q^90 - 8 * q^92 - 8 * q^93 + 8 * q^94 + 4 * q^95 - 3 * q^96 - 10 * q^97

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 $

$2$	2.17009	1.53448	0.767241	−	0.641358i	$-0.221629\pi$
$2$	2.17009	1.53448	0.767241	+	0.641358i	$0.221629\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.70928	1.35464
$5$	−3.70928	−1.65884	−0.829419	−	0.558627i	$-0.811328\pi$
$5$	−3.70928	−1.65884	−0.829419	+	0.558627i	$0.811328\pi$
$6$	2.17009	0.885934
$7$	0	0
$7$	0	0
$8$	1.53919	0.544185
$9$	1.00000	0.333333
$10$	−8.04945	−2.54546
$11$	−1.07838	−0.325143	−0.162572	−	0.986697i	$-0.551979\pi$
$11$	−1.07838	−0.325143	−0.162572	+	0.986697i	$0.551979\pi$
$12$	2.70928	0.782100
$13$	−0.921622	−0.255612	−0.127806	−	0.991799i	$-0.540793\pi$
$13$	−0.921622	−0.255612	−0.127806	+	0.991799i	$0.540793\pi$
$14$	0	0
$15$	−3.70928	−0.957731
$16$	−2.07838	−0.519594
$17$	−0.290725	−0.0705111	−0.0352555	−	0.999378i	$-0.511225\pi$
$17$	−0.290725	−0.0705111	−0.0352555	+	0.999378i	$0.511225\pi$
$18$	2.17009	0.511494
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−10.0494	−2.24712
$21$	0	0
$22$	−2.34017	−0.498927
$23$	−7.60197	−1.58512	−0.792560	−	0.609794i	$-0.791252\pi$
$23$	−7.60197	−1.58512	−0.792560	+	0.609794i	$0.791252\pi$
$24$	1.53919	0.314186
$25$	8.75872	1.75174
$26$	−2.00000	−0.392232
$27$	1.00000	0.192450
$28$	0	0
$29$	5.36910	0.997017	0.498509	−	0.866885i	$-0.333881\pi$
$29$	5.36910	0.997017	0.498509	+	0.866885i	$0.333881\pi$
$30$	−8.04945	−1.46962
$31$	−8.49693	−1.52609	−0.763047	−	0.646343i	$-0.776297\pi$
$31$	−8.49693	−1.52609	−0.763047	+	0.646343i	$0.776297\pi$
$32$	−7.58864	−1.34149
$33$	−1.07838	−0.187721
$34$	−0.630898	−0.108198
$35$	0	0
$36$	2.70928	0.451546
$37$	−10.6803	−1.75584	−0.877919	−	0.478809i	$-0.841069\pi$
$37$	−10.6803	−1.75584	−0.877919	+	0.478809i	$0.841069\pi$
$38$	−2.17009	−0.352035
$39$	−0.921622	−0.147578
$40$	−5.70928	−0.902716
$41$	3.75872	0.587014	0.293507	−	0.955957i	$-0.405178\pi$
$41$	3.75872	0.587014	0.293507	+	0.955957i	$0.405178\pi$
$42$	0	0
$43$	−8.49693	−1.29577	−0.647885	−	0.761738i	$-0.724346\pi$
$43$	−8.49693	−1.29577	−0.647885	+	0.761738i	$0.724346\pi$
$44$	−2.92162	−0.440451
$45$	−3.70928	−0.552946
$46$	−16.4969	−2.43234
$47$	6.20620	0.905268	0.452634	−	0.891696i	$-0.350484\pi$
$47$	6.20620	0.905268	0.452634	+	0.891696i	$0.350484\pi$
$48$	−2.07838	−0.299988
$49$	0	0
$50$	19.0072	2.68802
$51$	−0.290725	−0.0407096
$52$	−2.49693	−0.346262
$53$	4.78765	0.657635	0.328817	−	0.944394i	$-0.393350\pi$
$53$	4.78765	0.657635	0.328817	+	0.944394i	$0.393350\pi$
$54$	2.17009	0.295311
$55$	4.00000	0.539360
$56$	0	0
$57$	−1.00000	−0.132453
$58$	11.6514	1.52991
$59$	−4.00000	−0.520756	−0.260378	−	0.965507i	$-0.583847\pi$
$59$	−4.00000	−0.520756	−0.260378	+	0.965507i	$0.583847\pi$
$60$	−10.0494	−1.29738
$61$	2.68035	0.343183	0.171592	−	0.985168i	$-0.445109\pi$
$61$	2.68035	0.343183	0.171592	+	0.985168i	$0.445109\pi$
$62$	−18.4391	−2.34176
$63$	0	0
$64$	−12.3112	−1.53891
$65$	3.41855	0.424019
$66$	−2.34017	−0.288055
$67$	1.26180	0.154153	0.0770764	−	0.997025i	$-0.475441\pi$
$67$	1.26180	0.154153	0.0770764	+	0.997025i	$0.475441\pi$
$68$	−0.787653	−0.0955170
$69$	−7.60197	−0.915169
$70$	0	0
$71$	−3.86603	−0.458813	−0.229407	−	0.973331i	$-0.573679\pi$
$71$	−3.86603	−0.458813	−0.229407	+	0.973331i	$0.573679\pi$
$72$	1.53919	0.181395
$73$	−1.41855	−0.166029	−0.0830144	−	0.996548i	$-0.526455\pi$
$73$	−1.41855	−0.166029	−0.0830144	+	0.996548i	$0.526455\pi$
$74$	−23.1773	−2.69430
$75$	8.75872	1.01137
$76$	−2.70928	−0.310775
$77$	0	0
$78$	−2.00000	−0.226455
$79$	−10.5236	−1.18400	−0.591998	−	0.805939i	$-0.701661\pi$
$79$	−10.5236	−1.18400	−0.591998	+	0.805939i	$0.701661\pi$
$80$	7.70928	0.861923
$81$	1.00000	0.111111
$82$	8.15676	0.900763
$83$	−8.72979	−0.958219	−0.479110	−	0.877755i	$-0.659040\pi$
$83$	−8.72979	−0.958219	−0.479110	+	0.877755i	$0.659040\pi$
$84$	0	0
$85$	1.07838	0.116966
$86$	−18.4391	−1.98834
$87$	5.36910	0.575628
$88$	−1.65983	−0.176938
$89$	3.75872	0.398424	0.199212	−	0.979956i	$-0.436162\pi$
$89$	3.75872	0.398424	0.199212	+	0.979956i	$0.436162\pi$
$90$	−8.04945	−0.848486
$91$	0	0
$92$	−20.5958	−2.14726
$93$	−8.49693	−0.881090
$94$	13.4680	1.38912
$95$	3.70928	0.380564
$96$	−7.58864	−0.774512
$97$	13.5174	1.37249	0.686244	−	0.727371i	$-0.259258\pi$
$97$	13.5174	1.37249	0.686244	+	0.727371i	$0.259258\pi$
$98$	0	0
$99$	−1.07838	−0.108381
$100$	23.7298	2.37298
$101$	2.44748	0.243533	0.121767	−	0.992559i	$-0.461144\pi$
$101$	2.44748	0.243533	0.121767	+	0.992559i	$0.461144\pi$
$102$	−0.630898	−0.0624682
$103$	−19.5174	−1.92311	−0.961556	−	0.274610i	$-0.911451\pi$
$103$	−19.5174	−1.92311	−0.961556	+	0.274610i	$0.911451\pi$
$104$	−1.41855	−0.139100
$105$	0	0
$106$	10.3896	1.00913
$107$	15.6514	1.51308	0.756540	−	0.653948i	$-0.226888\pi$
$107$	15.6514	1.51308	0.756540	+	0.653948i	$0.226888\pi$
$108$	2.70928	0.260700
$109$	14.0989	1.35043	0.675215	−	0.737621i	$-0.264051\pi$
$109$	14.0989	1.35043	0.675215	+	0.737621i	$0.264051\pi$
$110$	8.68035	0.827639
$111$	−10.6803	−1.01373
$112$	0	0
$113$	18.7298	1.76195	0.880975	−	0.473162i	$-0.156887\pi$
$113$	18.7298	1.76195	0.880975	+	0.473162i	$0.156887\pi$
$114$	−2.17009	−0.203247
$115$	28.1978	2.62946
$116$	14.5464	1.35060
$117$	−0.921622	−0.0852040
$118$	−8.68035	−0.799091
$119$	0	0
$120$	−5.70928	−0.521183
$121$	−9.83710	−0.894282
$122$	5.81658	0.526609
$123$	3.75872	0.338913
$124$	−23.0205	−2.06730
$125$	−13.9421	−1.24702
$126$	0	0
$127$	−15.7854	−1.40073	−0.700363	−	0.713787i	$-0.746979\pi$
$127$	−15.7854	−1.40073	−0.700363	+	0.713787i	$0.746979\pi$
$128$	−11.5392	−1.01993
$129$	−8.49693	−0.748113
$130$	7.41855	0.650650
$131$	−6.10731	−0.533598	−0.266799	−	0.963752i	$-0.585966\pi$
$131$	−6.10731	−0.533598	−0.266799	+	0.963752i	$0.585966\pi$
$132$	−2.92162	−0.254295
$133$	0	0
$134$	2.73820	0.236545
$135$	−3.70928	−0.319244
$136$	−0.447480	−0.0383711
$137$	18.9939	1.62275	0.811377	−	0.584523i	$-0.198718\pi$
$137$	18.9939	1.62275	0.811377	+	0.584523i	$0.198718\pi$
$138$	−16.4969	−1.40431
$139$	−0.894960	−0.0759095	−0.0379548	−	0.999279i	$-0.512084\pi$
$139$	−0.894960	−0.0759095	−0.0379548	+	0.999279i	$0.512084\pi$
$140$	0	0
$141$	6.20620	0.522657
$142$	−8.38962	−0.704041
$143$	0.993857	0.0831105
$144$	−2.07838	−0.173198
$145$	−19.9155	−1.65389
$146$	−3.07838	−0.254768
$147$	0	0
$148$	−28.9360	−2.37852
$149$	20.9360	1.71514	0.857572	−	0.514364i	$-0.171972\pi$
$149$	20.9360	1.71514	0.857572	+	0.514364i	$0.171972\pi$
$150$	19.0072	1.55193
$151$	13.9421	1.13460	0.567298	−	0.823513i	$-0.307989\pi$
$151$	13.9421	1.13460	0.567298	+	0.823513i	$0.307989\pi$
$152$	−1.53919	−0.124845
$153$	−0.290725	−0.0235037
$154$	0	0
$155$	31.5174	2.53154
$156$	−2.49693	−0.199914
$157$	2.31351	0.184638	0.0923191	−	0.995729i	$-0.470572\pi$
$157$	2.31351	0.184638	0.0923191	+	0.995729i	$0.470572\pi$
$158$	−22.8371	−1.81682
$159$	4.78765	0.379686
$160$	28.1483	2.22532
$161$	0	0
$162$	2.17009	0.170498
$163$	−17.6598	−1.38322	−0.691612	−	0.722269i	$-0.743099\pi$
$163$	−17.6598	−1.38322	−0.691612	+	0.722269i	$0.743099\pi$
$164$	10.1834	0.795191
$165$	4.00000	0.311400
$166$	−18.9444	−1.47037
$167$	−3.05172	−0.236149	−0.118074	−	0.993005i	$-0.537672\pi$
$167$	−3.05172	−0.236149	−0.118074	+	0.993005i	$0.537672\pi$
$168$	0	0
$169$	−12.1506	−0.934662
$170$	2.34017	0.179483
$171$	−1.00000	−0.0764719
$172$	−23.0205	−1.75530
$173$	−9.60197	−0.730024	−0.365012	−	0.931003i	$-0.618935\pi$
$173$	−9.60197	−0.730024	−0.365012	+	0.931003i	$0.618935\pi$
$174$	11.6514	0.883292
$175$	0	0
$176$	2.24128	0.168943
$177$	−4.00000	−0.300658
$178$	8.15676	0.611375
$179$	−0.814315	−0.0608648	−0.0304324	−	0.999537i	$-0.509688\pi$
$179$	−0.814315	−0.0608648	−0.0304324	+	0.999537i	$0.509688\pi$
$180$	−10.0494	−0.749042
$181$	−20.1568	−1.49824	−0.749120	−	0.662434i	$-0.769523\pi$
$181$	−20.1568	−1.49824	−0.749120	+	0.662434i	$0.769523\pi$
$182$	0	0
$183$	2.68035	0.198137
$184$	−11.7009	−0.862599
$185$	39.6163	2.91265
$186$	−18.4391	−1.35202
$187$	0.313511	0.0229262
$188$	16.8143	1.22631
$189$	0	0
$190$	8.04945	0.583968
$191$	5.44521	0.394002	0.197001	−	0.980403i	$-0.436880\pi$
$191$	5.44521	0.394002	0.197001	+	0.980403i	$0.436880\pi$
$192$	−12.3112	−0.888487
$193$	1.68649	0.121396	0.0606981	−	0.998156i	$-0.480667\pi$
$193$	1.68649	0.121396	0.0606981	+	0.998156i	$0.480667\pi$
$194$	29.3340	2.10606
$195$	3.41855	0.244808
$196$	0	0
$197$	−10.3668	−0.738606	−0.369303	−	0.929309i	$-0.620404\pi$
$197$	−10.3668	−0.738606	−0.369303	+	0.929309i	$0.620404\pi$
$198$	−2.34017	−0.166309
$199$	2.42469	0.171882	0.0859410	−	0.996300i	$-0.472610\pi$
$199$	2.42469	0.171882	0.0859410	+	0.996300i	$0.472610\pi$
$200$	13.4813	0.953274
$201$	1.26180	0.0890002
$202$	5.31124	0.373698
$203$	0	0
$204$	−0.787653	−0.0551467
$205$	−13.9421	−0.973761
$206$	−42.3545	−2.95098
$207$	−7.60197	−0.528373
$208$	1.91548	0.132815
$209$	1.07838	0.0745929
$210$	0	0
$211$	19.5174	1.34364	0.671818	−	0.740716i	$-0.265514\pi$
$211$	19.5174	1.34364	0.671818	+	0.740716i	$0.265514\pi$
$212$	12.9711	0.890857
$213$	−3.86603	−0.264896
$214$	33.9649	2.32179
$215$	31.5174	2.14947
$216$	1.53919	0.104729
$217$	0	0
$218$	30.5958	2.07221
$219$	−1.41855	−0.0958568
$220$	10.8371	0.730637
$221$	0.267938	0.0180235
$222$	−23.1773	−1.55556
$223$	−19.0205	−1.27371	−0.636854	−	0.770984i	$-0.719765\pi$
$223$	−19.0205	−1.27371	−0.636854	+	0.770984i	$0.719765\pi$
$224$	0	0
$225$	8.75872	0.583915
$226$	40.6453	2.70368
$227$	−11.7321	−0.778684	−0.389342	−	0.921093i	$-0.627298\pi$
$227$	−11.7321	−0.778684	−0.389342	+	0.921093i	$0.627298\pi$
$228$	−2.70928	−0.179426
$229$	27.4596	1.81458	0.907290	−	0.420505i	$-0.138147\pi$
$229$	27.4596	1.81458	0.907290	+	0.420505i	$0.138147\pi$
$230$	61.1917	4.03486
$231$	0	0
$232$	8.26406	0.542562
$233$	−5.10504	−0.334442	−0.167221	−	0.985919i	$-0.553479\pi$
$233$	−5.10504	−0.334442	−0.167221	+	0.985919i	$0.553479\pi$
$234$	−2.00000	−0.130744
$235$	−23.0205	−1.50169
$236$	−10.8371	−0.705435
$237$	−10.5236	−0.683581
$238$	0	0
$239$	−10.6537	−0.689130	−0.344565	−	0.938763i	$-0.611973\pi$
$239$	−10.6537	−0.689130	−0.344565	+	0.938763i	$0.611973\pi$
$240$	7.70928	0.497632
$241$	13.5174	0.870735	0.435368	−	0.900253i	$-0.356618\pi$
$241$	13.5174	0.870735	0.435368	+	0.900253i	$0.356618\pi$
$242$	−21.3474	−1.37226
$243$	1.00000	0.0641500
$244$	7.26180	0.464889
$245$	0	0
$246$	8.15676	0.520056
$247$	0.921622	0.0586414
$248$	−13.0784	−0.830478
$249$	−8.72979	−0.553228
$250$	−30.2557	−1.91354
$251$	18.2062	1.14917	0.574583	−	0.818447i	$-0.305164\pi$
$251$	18.2062	1.14917	0.574583	+	0.818447i	$0.305164\pi$
$252$	0	0
$253$	8.19779	0.515391
$254$	−34.2557	−2.14939
$255$	1.07838	0.0675306
$256$	−0.418551	−0.0261594
$257$	−12.3402	−0.769759	−0.384879	−	0.922967i	$-0.625757\pi$
$257$	−12.3402	−0.769759	−0.384879	+	0.922967i	$0.625757\pi$
$258$	−18.4391	−1.14797
$259$	0	0
$260$	9.26180	0.574392
$261$	5.36910	0.332339
$262$	−13.2534	−0.818797
$263$	7.50307	0.462659	0.231330	−	0.972875i	$-0.425692\pi$
$263$	7.50307	0.462659	0.231330	+	0.972875i	$0.425692\pi$
$264$	−1.65983	−0.102155
$265$	−17.7587	−1.09091
$266$	0	0
$267$	3.75872	0.230030
$268$	3.41855	0.208821
$269$	4.34017	0.264625	0.132313	−	0.991208i	$-0.457760\pi$
$269$	4.34017	0.264625	0.132313	+	0.991208i	$0.457760\pi$
$270$	−8.04945	−0.489874
$271$	−26.0410	−1.58188	−0.790940	−	0.611893i	$-0.790408\pi$
$271$	−26.0410	−1.58188	−0.790940	+	0.611893i	$0.790408\pi$
$272$	0.604236	0.0366372
$273$	0	0
$274$	41.2183	2.49009
$275$	−9.44521	−0.569568
$276$	−20.5958	−1.23972
$277$	6.59583	0.396305	0.198152	−	0.980171i	$-0.436506\pi$
$277$	6.59583	0.396305	0.198152	+	0.980171i	$0.436506\pi$
$278$	−1.94214	−0.116482
$279$	−8.49693	−0.508698
$280$	0	0
$281$	−11.6248	−0.693475	−0.346737	−	0.937962i	$-0.612710\pi$
$281$	−11.6248	−0.693475	−0.346737	+	0.937962i	$0.612710\pi$
$282$	13.4680	0.802008
$283$	17.9421	1.06655	0.533275	−	0.845942i	$-0.320961\pi$
$283$	17.9421	1.06655	0.533275	+	0.845942i	$0.320961\pi$
$284$	−10.4741	−0.621526
$285$	3.70928	0.219719
$286$	2.15676	0.127532
$287$	0	0
$288$	−7.58864	−0.447165
$289$	−16.9155	−0.995028
$290$	−43.2183	−2.53787
$291$	13.5174	0.792407
$292$	−3.84324	−0.224909
$293$	23.7587	1.38800	0.694000	−	0.719975i	$-0.255847\pi$
$293$	23.7587	1.38800	0.694000	+	0.719975i	$0.255847\pi$
$294$	0	0
$295$	14.8371	0.863849
$296$	−16.4391	−0.955502
$297$	−1.07838	−0.0625738
$298$	45.4329	2.63186
$299$	7.00614	0.405176
$300$	23.7298	1.37004
$301$	0	0
$302$	30.2557	1.74102
$303$	2.44748	0.140604
$304$	2.07838	0.119203
$305$	−9.94214	−0.569285
$306$	−0.630898	−0.0360660
$307$	24.0144	1.37057	0.685286	−	0.728274i	$-0.259677\pi$
$307$	24.0144	1.37057	0.685286	+	0.728274i	$0.259677\pi$
$308$	0	0
$309$	−19.5174	−1.11031
$310$	68.3956	3.88461
$311$	−22.9854	−1.30339	−0.651693	−	0.758483i	$-0.725941\pi$
$311$	−22.9854	−1.30339	−0.651693	+	0.758483i	$0.725941\pi$
$312$	−1.41855	−0.0803096
$313$	−0.523590	−0.0295951	−0.0147975	−	0.999891i	$-0.504710\pi$
$313$	−0.523590	−0.0295951	−0.0147975	+	0.999891i	$0.504710\pi$
$314$	5.02052	0.283324
$315$	0	0
$316$	−28.5113	−1.60389
$317$	−17.1012	−0.960497	−0.480249	−	0.877132i	$-0.659454\pi$
$317$	−17.1012	−0.960497	−0.480249	+	0.877132i	$0.659454\pi$
$318$	10.3896	0.582621
$319$	−5.78992	−0.324173
$320$	45.6658	2.55280
$321$	15.6514	0.873577
$322$	0	0
$323$	0.290725	0.0161764
$324$	2.70928	0.150515
$325$	−8.07223	−0.447767
$326$	−38.3234	−2.12253
$327$	14.0989	0.779671
$328$	5.78539	0.319444
$329$	0	0
$330$	8.68035	0.477837
$331$	25.1461	1.38215	0.691077	−	0.722781i	$-0.257137\pi$
$331$	25.1461	1.38215	0.691077	+	0.722781i	$0.257137\pi$
$332$	−23.6514	−1.29804
$333$	−10.6803	−0.585279
$334$	−6.62249	−0.362366
$335$	−4.68035	−0.255715
$336$	0	0
$337$	−11.5753	−0.630547	−0.315274	−	0.949001i	$-0.602096\pi$
$337$	−11.5753	−0.630547	−0.315274	+	0.949001i	$0.602096\pi$
$338$	−26.3679	−1.43422
$339$	18.7298	1.01726
$340$	2.92162	0.158447
$341$	9.16290	0.496199
$342$	−2.17009	−0.117345
$343$	0	0
$344$	−13.0784	−0.705139
$345$	28.1978	1.51812
$346$	−20.8371	−1.12021
$347$	−32.0144	−1.71862	−0.859311	−	0.511454i	$-0.829107\pi$
$347$	−32.0144	−1.71862	−0.859311	+	0.511454i	$0.829107\pi$
$348$	14.5464	0.779768
$349$	2.36683	0.126694	0.0633469	−	0.997992i	$-0.479823\pi$
$349$	2.36683	0.126694	0.0633469	+	0.997992i	$0.479823\pi$
$350$	0	0
$351$	−0.921622	−0.0491926
$352$	8.18342	0.436178
$353$	−15.4413	−0.821859	−0.410930	−	0.911667i	$-0.634796\pi$
$353$	−15.4413	−0.821859	−0.410930	+	0.911667i	$0.634796\pi$
$354$	−8.68035	−0.461355
$355$	14.3402	0.761097
$356$	10.1834	0.539720
$357$	0	0
$358$	−1.76713	−0.0933959
$359$	23.4329	1.23674	0.618371	−	0.785886i	$-0.287793\pi$
$359$	23.4329	1.23674	0.618371	+	0.785886i	$0.287793\pi$
$360$	−5.70928	−0.300905
$361$	1.00000	0.0526316
$362$	−43.7419	−2.29902
$363$	−9.83710	−0.516314
$364$	0	0
$365$	5.26180	0.275415
$366$	5.81658	0.304038
$367$	31.3028	1.63399	0.816997	−	0.576642i	$-0.195637\pi$
$367$	31.3028	1.63399	0.816997	+	0.576642i	$0.195637\pi$
$368$	15.7998	0.823620
$369$	3.75872	0.195671
$370$	85.9709	4.46941
$371$	0	0
$372$	−23.0205	−1.19356
$373$	−23.6742	−1.22580	−0.612902	−	0.790159i	$-0.709998\pi$
$373$	−23.6742	−1.22580	−0.612902	+	0.790159i	$0.709998\pi$
$374$	0.680346	0.0351799
$375$	−13.9421	−0.719969
$376$	9.55252	0.492634
$377$	−4.94828	−0.254850
$378$	0	0
$379$	−7.41855	−0.381065	−0.190533	−	0.981681i	$-0.561022\pi$
$379$	−7.41855	−0.381065	−0.190533	+	0.981681i	$0.561022\pi$
$380$	10.0494	0.515526
$381$	−15.7854	−0.808710
$382$	11.8166	0.604589
$383$	7.10504	0.363051	0.181525	−	0.983386i	$-0.441897\pi$
$383$	7.10504	0.363051	0.181525	+	0.983386i	$0.441897\pi$
$384$	−11.5392	−0.588857
$385$	0	0
$386$	3.65983	0.186280
$387$	−8.49693	−0.431923
$388$	36.6225	1.85923
$389$	16.2557	0.824194	0.412097	−	0.911140i	$-0.364796\pi$
$389$	16.2557	0.824194	0.412097	+	0.911140i	$0.364796\pi$
$390$	7.41855	0.375653
$391$	2.21008	0.111769
$392$	0	0
$393$	−6.10731	−0.308073
$394$	−22.4969	−1.13338
$395$	39.0349	1.96406
$396$	−2.92162	−0.146817
$397$	−26.5113	−1.33056	−0.665282	−	0.746592i	$-0.731689\pi$
$397$	−26.5113	−1.33056	−0.665282	+	0.746592i	$0.731689\pi$
$398$	5.26180	0.263750
$399$	0	0
$400$	−18.2039	−0.910197
$401$	−6.04945	−0.302095	−0.151048	−	0.988527i	$-0.548265\pi$
$401$	−6.04945	−0.302095	−0.151048	+	0.988527i	$0.548265\pi$
$402$	2.73820	0.136569
$403$	7.83096	0.390088
$404$	6.63090	0.329899
$405$	−3.70928	−0.184315
$406$	0	0
$407$	11.5174	0.570899
$408$	−0.447480	−0.0221536
$409$	−37.1194	−1.83544	−0.917718	−	0.397231i	$-0.869971\pi$
$409$	−37.1194	−1.83544	−0.917718	+	0.397231i	$0.869971\pi$
$410$	−30.2557	−1.49422
$411$	18.9939	0.936898
$412$	−52.8781	−2.60512
$413$	0	0
$414$	−16.4969	−0.810780
$415$	32.3812	1.58953
$416$	6.99386	0.342902
$417$	−0.894960	−0.0438264
$418$	2.34017	0.114462
$419$	23.3523	1.14083	0.570417	−	0.821355i	$-0.306782\pi$
$419$	23.3523	1.14083	0.570417	+	0.821355i	$0.306782\pi$
$420$	0	0
$421$	7.57531	0.369198	0.184599	−	0.982814i	$-0.440901\pi$
$421$	7.57531	0.369198	0.184599	+	0.982814i	$0.440901\pi$
$422$	42.3545	2.06179
$423$	6.20620	0.301756
$424$	7.36910	0.357875
$425$	−2.54638	−0.123517
$426$	−8.38962	−0.406478
$427$	0	0
$428$	42.4040	2.04967
$429$	0.993857	0.0479839
$430$	68.3956	3.29833
$431$	−5.90707	−0.284533	−0.142267	−	0.989828i	$-0.545439\pi$
$431$	−5.90707	−0.284533	−0.142267	+	0.989828i	$0.545439\pi$
$432$	−2.07838	−0.0999960
$433$	7.47641	0.359293	0.179647	−	0.983731i	$-0.442505\pi$
$433$	7.47641	0.359293	0.179647	+	0.983731i	$0.442505\pi$
$434$	0	0
$435$	−19.9155	−0.954874
$436$	38.1978	1.82934
$437$	7.60197	0.363651
$438$	−3.07838	−0.147091
$439$	9.49079	0.452970	0.226485	−	0.974015i	$-0.427276\pi$
$439$	9.49079	0.452970	0.226485	+	0.974015i	$0.427276\pi$
$440$	6.15676	0.293512
$441$	0	0
$442$	0.581449	0.0276567
$443$	−25.1773	−1.19621	−0.598104	−	0.801418i	$-0.704079\pi$
$443$	−25.1773	−1.19621	−0.598104	+	0.801418i	$0.704079\pi$
$444$	−28.9360	−1.37324
$445$	−13.9421	−0.660921
$446$	−41.2762	−1.95448
$447$	20.9360	0.990239
$448$	0	0
$449$	−32.4040	−1.52924	−0.764620	−	0.644482i	$-0.777073\pi$
$449$	−32.4040	−1.52924	−0.764620	+	0.644482i	$0.777073\pi$
$450$	19.0072	0.896007
$451$	−4.05332	−0.190864
$452$	50.7442	2.38680
$453$	13.9421	0.655059
$454$	−25.4596	−1.19488
$455$	0	0
$456$	−1.53919	−0.0720791
$457$	8.86830	0.414841	0.207421	−	0.978252i	$-0.433493\pi$
$457$	8.86830	0.414841	0.207421	+	0.978252i	$0.433493\pi$
$458$	59.5897	2.78444
$459$	−0.290725	−0.0135699
$460$	76.3956	3.56196
$461$	−8.70313	−0.405345	−0.202673	−	0.979247i	$-0.564963\pi$
$461$	−8.70313	−0.405345	−0.202673	+	0.979247i	$0.564963\pi$
$462$	0	0
$463$	−6.21008	−0.288607	−0.144303	−	0.989533i	$-0.546094\pi$
$463$	−6.21008	−0.288607	−0.144303	+	0.989533i	$0.546094\pi$
$464$	−11.1590	−0.518045
$465$	31.5174	1.46159
$466$	−11.0784	−0.513196
$467$	−16.4619	−0.761764	−0.380882	−	0.924624i	$-0.624380\pi$
$467$	−16.4619	−0.761764	−0.380882	+	0.924624i	$0.624380\pi$
$468$	−2.49693	−0.115421
$469$	0	0
$470$	−49.9565	−2.30432
$471$	2.31351	0.106601
$472$	−6.15676	−0.283388
$473$	9.16290	0.421311
$474$	−22.8371	−1.04894
$475$	−8.75872	−0.401878
$476$	0	0
$477$	4.78765	0.219212
$478$	−23.1194	−1.05746
$479$	−16.5320	−0.755366	−0.377683	−	0.925935i	$-0.623279\pi$
$479$	−16.5320	−0.755366	−0.377683	+	0.925935i	$0.623279\pi$
$480$	28.1483	1.28479
$481$	9.84324	0.448813
$482$	29.3340	1.33613
$483$	0	0
$484$	−26.6514	−1.21143
$485$	−50.1399	−2.27674
$486$	2.17009	0.0984371
$487$	−25.6742	−1.16341	−0.581705	−	0.813400i	$-0.697614\pi$
$487$	−25.6742	−1.16341	−0.581705	+	0.813400i	$0.697614\pi$
$488$	4.12556	0.186755
$489$	−17.6598	−0.798605
$490$	0	0
$491$	27.3340	1.23357	0.616784	−	0.787133i	$-0.288435\pi$
$491$	27.3340	1.23357	0.616784	+	0.787133i	$0.288435\pi$
$492$	10.1834	0.459104
$493$	−1.56093	−0.0703008
$494$	2.00000	0.0899843
$495$	4.00000	0.179787
$496$	17.6598	0.792950
$497$	0	0
$498$	−18.9444	−0.848919
$499$	−10.0410	−0.449499	−0.224749	−	0.974417i	$-0.572156\pi$
$499$	−10.0410	−0.449499	−0.224749	+	0.974417i	$0.572156\pi$
$500$	−37.7731	−1.68926
$501$	−3.05172	−0.136341
$502$	39.5090	1.76337
$503$	−36.8287	−1.64211	−0.821055	−	0.570849i	$-0.806614\pi$
$503$	−36.8287	−1.64211	−0.821055	+	0.570849i	$0.806614\pi$
$504$	0	0
$505$	−9.07838	−0.403983
$506$	17.7899	0.790858
$507$	−12.1506	−0.539628
$508$	−42.7670	−1.89748
$509$	14.1301	0.626305	0.313153	−	0.949703i	$-0.398615\pi$
$509$	14.1301	0.626305	0.313153	+	0.949703i	$0.398615\pi$
$510$	2.34017	0.103625
$511$	0	0
$512$	22.1701	0.979789
$513$	−1.00000	−0.0441511
$514$	−26.7792	−1.18118
$515$	72.3956	3.19013
$516$	−23.0205	−1.01342
$517$	−6.69263	−0.294342
$518$	0	0
$519$	−9.60197	−0.421480
$520$	5.26180	0.230745
$521$	−28.1711	−1.23420	−0.617100	−	0.786885i	$-0.711693\pi$
$521$	−28.1711	−1.23420	−0.617100	+	0.786885i	$0.711693\pi$
$522$	11.6514	0.509969
$523$	32.1834	1.40728	0.703641	−	0.710555i	$-0.251556\pi$
$523$	32.1834	1.40728	0.703641	+	0.710555i	$0.251556\pi$
$524$	−16.5464	−0.722832
$525$	0	0
$526$	16.2823	0.709943
$527$	2.47027	0.107606
$528$	2.24128	0.0975390
$529$	34.7899	1.51261
$530$	−38.5380	−1.67398
$531$	−4.00000	−0.173585
$532$	0	0
$533$	−3.46412	−0.150048
$534$	8.15676	0.352977
$535$	−58.0554	−2.50995
$536$	1.94214	0.0838877
$537$	−0.814315	−0.0351403
$538$	9.41855	0.406063
$539$	0	0
$540$	−10.0494	−0.432459
$541$	−41.0349	−1.76423	−0.882114	−	0.471036i	$-0.843880\pi$
$541$	−41.0349	−1.76423	−0.882114	+	0.471036i	$0.843880\pi$
$542$	−56.5113	−2.42737
$543$	−20.1568	−0.865009
$544$	2.20620	0.0945902
$545$	−52.2967	−2.24014
$546$	0	0
$547$	9.67420	0.413639	0.206820	−	0.978379i	$-0.433689\pi$
$547$	9.67420	0.413639	0.206820	+	0.978379i	$0.433689\pi$
$548$	51.4596	2.19824
$549$	2.68035	0.114394
$550$	−20.4969	−0.873992
$551$	−5.36910	−0.228731
$552$	−11.7009	−0.498022
$553$	0	0
$554$	14.3135	0.608123
$555$	39.6163	1.68162
$556$	−2.42469	−0.102830
$557$	−40.1399	−1.70078	−0.850392	−	0.526150i	$-0.823635\pi$
$557$	−40.1399	−1.70078	−0.850392	+	0.526150i	$0.823635\pi$
$558$	−18.4391	−0.780588
$559$	7.83096	0.331214
$560$	0	0
$561$	0.313511	0.0132364
$562$	−25.2267	−1.06413
$563$	−44.0989	−1.85855	−0.929273	−	0.369393i	$-0.879566\pi$
$563$	−44.0989	−1.85855	−0.929273	+	0.369393i	$0.879566\pi$
$564$	16.8143	0.708010
$565$	−69.4740	−2.92279
$566$	38.9360	1.63660
$567$	0	0
$568$	−5.95055	−0.249680
$569$	−13.4147	−0.562372	−0.281186	−	0.959653i	$-0.590728\pi$
$569$	−13.4147	−0.562372	−0.281186	+	0.959653i	$0.590728\pi$
$570$	8.04945	0.337154
$571$	−27.8310	−1.16469	−0.582345	−	0.812942i	$-0.697865\pi$
$571$	−27.8310	−1.16469	−0.582345	+	0.812942i	$0.697865\pi$
$572$	2.69263	0.112585
$573$	5.44521	0.227477
$574$	0	0
$575$	−66.5835	−2.77673
$576$	−12.3112	−0.512968
$577$	34.1978	1.42367	0.711836	−	0.702345i	$-0.247864\pi$
$577$	34.1978	1.42367	0.711836	+	0.702345i	$0.247864\pi$
$578$	−36.7081	−1.52685
$579$	1.68649	0.0700881
$580$	−53.9565	−2.24042
$581$	0	0
$582$	29.3340	1.21593
$583$	−5.16290	−0.213825
$584$	−2.18342	−0.0903505
$585$	3.41855	0.141340
$586$	51.5585	2.12986
$587$	−33.1422	−1.36793	−0.683963	−	0.729517i	$-0.739745\pi$
$587$	−33.1422	−1.36793	−0.683963	+	0.729517i	$0.739745\pi$
$588$	0	0
$589$	8.49693	0.350110
$590$	32.1978	1.32556
$591$	−10.3668	−0.426435
$592$	22.1978	0.912324
$593$	−29.7503	−1.22170	−0.610849	−	0.791747i	$-0.709172\pi$
$593$	−29.7503	−1.22170	−0.610849	+	0.791747i	$0.709172\pi$
$594$	−2.34017	−0.0960185
$595$	0	0
$596$	56.7214	2.32340
$597$	2.42469	0.0992361
$598$	15.2039	0.621735
$599$	2.19183	0.0895557	0.0447778	−	0.998997i	$-0.485742\pi$
$599$	2.19183	0.0895557	0.0447778	+	0.998997i	$0.485742\pi$
$600$	13.4813	0.550373
$601$	−31.9877	−1.30481	−0.652403	−	0.757872i	$-0.726239\pi$
$601$	−31.9877	−1.30481	−0.652403	+	0.757872i	$0.726239\pi$
$602$	0	0
$603$	1.26180	0.0513843
$604$	37.7731	1.53697
$605$	36.4885	1.48347
$606$	5.31124	0.215755
$607$	27.5174	1.11690	0.558449	−	0.829539i	$-0.311397\pi$
$607$	27.5174	1.11690	0.558449	+	0.829539i	$0.311397\pi$
$608$	7.58864	0.307760
$609$	0	0
$610$	−21.5753	−0.873559
$611$	−5.71978	−0.231397
$612$	−0.787653	−0.0318390
$613$	6.59583	0.266403	0.133201	−	0.991089i	$-0.457474\pi$
$613$	6.59583	0.266403	0.133201	+	0.991089i	$0.457474\pi$
$614$	52.1133	2.10312
$615$	−13.9421	−0.562201
$616$	0	0
$617$	−3.47641	−0.139955	−0.0699775	−	0.997549i	$-0.522293\pi$
$617$	−3.47641	−0.139955	−0.0699775	+	0.997549i	$0.522293\pi$
$618$	−42.3545	−1.70375
$619$	−26.9893	−1.08479	−0.542396	−	0.840123i	$-0.682483\pi$
$619$	−26.9893	−1.08479	−0.542396	+	0.840123i	$0.682483\pi$
$620$	85.3894	3.42932
$621$	−7.60197	−0.305056
$622$	−49.8804	−2.00002
$623$	0	0
$624$	1.91548	0.0766805
$625$	7.92162	0.316865
$626$	−1.13624	−0.0454131
$627$	1.07838	0.0430663
$628$	6.26794	0.250118
$629$	3.10504	0.123806
$630$	0	0
$631$	−10.3402	−0.411636	−0.205818	−	0.978590i	$-0.565985\pi$
$631$	−10.3402	−0.411636	−0.205818	+	0.978590i	$0.565985\pi$
$632$	−16.1978	−0.644314
$633$	19.5174	0.775749
$634$	−37.1110	−1.47387
$635$	58.5523	2.32358
$636$	12.9711	0.514336
$637$	0	0
$638$	−12.5646	−0.497438
$639$	−3.86603	−0.152938
$640$	42.8020	1.69190
$641$	35.1955	1.39014	0.695070	−	0.718942i	$-0.255373\pi$
$641$	35.1955	1.39014	0.695070	+	0.718942i	$0.255373\pi$
$642$	33.9649	1.34049
$643$	−12.4657	−0.491600	−0.245800	−	0.969321i	$-0.579051\pi$
$643$	−12.4657	−0.491600	−0.245800	+	0.969321i	$0.579051\pi$
$644$	0	0
$645$	31.5174	1.24100
$646$	0.630898	0.0248223
$647$	11.8804	0.467067	0.233533	−	0.972349i	$-0.424971\pi$
$647$	11.8804	0.467067	0.233533	+	0.972349i	$0.424971\pi$
$648$	1.53919	0.0604650
$649$	4.31351	0.169320
$650$	−17.5174	−0.687091
$651$	0	0
$652$	−47.8453	−1.87377
$653$	6.00000	0.234798	0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000	0.234798	0.117399	+	0.993085i	$0.462544\pi$
$654$	30.5958	1.19639
$655$	22.6537	0.885153
$656$	−7.81205	−0.305009
$657$	−1.41855	−0.0553429
$658$	0	0
$659$	12.5464	0.488737	0.244369	−	0.969682i	$-0.421419\pi$
$659$	12.5464	0.488737	0.244369	+	0.969682i	$0.421419\pi$
$660$	10.8371	0.421834
$661$	−11.6430	−0.452860	−0.226430	−	0.974027i	$-0.572706\pi$
$661$	−11.6430	−0.452860	−0.226430	+	0.974027i	$0.572706\pi$
$662$	54.5692	2.12089
$663$	0.267938	0.0104059
$664$	−13.4368	−0.521449
$665$	0	0
$666$	−23.1773	−0.898101
$667$	−40.8157	−1.58039
$668$	−8.26794	−0.319896
$669$	−19.0205	−0.735376
$670$	−10.1568	−0.392390
$671$	−2.89043	−0.111584
$672$	0	0
$673$	41.3484	1.59386	0.796932	−	0.604069i	$-0.206455\pi$
$673$	41.3484	1.59386	0.796932	+	0.604069i	$0.206455\pi$
$674$	−25.1194	−0.967564
$675$	8.75872	0.337123
$676$	−32.9194	−1.26613
$677$	19.1773	0.737043	0.368521	−	0.929619i	$-0.379864\pi$
$677$	19.1773	0.737043	0.368521	+	0.929619i	$0.379864\pi$
$678$	40.6453	1.56097
$679$	0	0
$680$	1.65983	0.0636515
$681$	−11.7321	−0.449574
$682$	19.8843	0.761409
$683$	−22.2907	−0.852931	−0.426465	−	0.904504i	$-0.640241\pi$
$683$	−22.2907	−0.852931	−0.426465	+	0.904504i	$0.640241\pi$
$684$	−2.70928	−0.103592
$685$	−70.4534	−2.69189
$686$	0	0
$687$	27.4596	1.04765
$688$	17.6598	0.673275
$689$	−4.41241	−0.168099
$690$	61.1917	2.32953
$691$	30.0410	1.14281	0.571407	−	0.820666i	$-0.306398\pi$
$691$	30.0410	1.14281	0.571407	+	0.820666i	$0.306398\pi$
$692$	−26.0144	−0.988918
$693$	0	0
$694$	−69.4740	−2.63720
$695$	3.31965	0.125922
$696$	8.26406	0.313248
$697$	−1.09275	−0.0413910
$698$	5.13624	0.194409
$699$	−5.10504	−0.193090
$700$	0	0
$701$	−1.20394	−0.0454721	−0.0227360	−	0.999742i	$-0.507238\pi$
$701$	−1.20394	−0.0454721	−0.0227360	+	0.999742i	$0.507238\pi$
$702$	−2.00000	−0.0754851
$703$	10.6803	0.402817
$704$	13.2762	0.500365
$705$	−23.0205	−0.867003
$706$	−33.5090	−1.26113
$707$	0	0
$708$	−10.8371	−0.407283
$709$	−33.2351	−1.24817	−0.624086	−	0.781356i	$-0.714528\pi$
$709$	−33.2351	−1.24817	−0.624086	+	0.781356i	$0.714528\pi$
$710$	31.1194	1.16789
$711$	−10.5236	−0.394665
$712$	5.78539	0.216816
$713$	64.5934	2.41904
$714$	0	0
$715$	−3.68649	−0.137867
$716$	−2.20620	−0.0824497
$717$	−10.6537	−0.397869
$718$	50.8515	1.89776
$719$	−10.2062	−0.380627	−0.190314	−	0.981723i	$-0.560950\pi$
$719$	−10.2062	−0.380627	−0.190314	+	0.981723i	$0.560950\pi$
$720$	7.70928	0.287308
$721$	0	0
$722$	2.17009	0.0807623
$723$	13.5174	0.502719
$724$	−54.6102	−2.02957
$725$	47.0265	1.74652
$726$	−21.3474	−0.792275
$727$	26.8371	0.995333	0.497666	−	0.867368i	$-0.334190\pi$
$727$	26.8371	0.995333	0.497666	+	0.867368i	$0.334190\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	11.4186	0.422620
$731$	2.47027	0.0913661
$732$	7.26180	0.268404
$733$	−2.46573	−0.0910739	−0.0455369	−	0.998963i	$-0.514500\pi$
$733$	−2.46573	−0.0910739	−0.0455369	+	0.998963i	$0.514500\pi$
$734$	67.9299	2.50734
$735$	0	0
$736$	57.6886	2.12643
$737$	−1.36069	−0.0501217
$738$	8.15676	0.300254
$739$	0.863763	0.0317741	0.0158870	−	0.999874i	$-0.494943\pi$
$739$	0.863763	0.0317741	0.0158870	+	0.999874i	$0.494943\pi$
$740$	107.332	3.94559
$741$	0.921622	0.0338566
$742$	0	0
$743$	−36.1171	−1.32501	−0.662505	−	0.749058i	$-0.730507\pi$
$743$	−36.1171	−1.32501	−0.662505	+	0.749058i	$0.730507\pi$
$744$	−13.0784	−0.479477
$745$	−77.6574	−2.84515
$746$	−51.3751	−1.88097
$747$	−8.72979	−0.319406
$748$	0.849388	0.0310567
$749$	0	0
$750$	−30.2557	−1.10478
$751$	−33.8264	−1.23434	−0.617172	−	0.786828i	$-0.711722\pi$
$751$	−33.8264	−1.23434	−0.617172	+	0.786828i	$0.711722\pi$
$752$	−12.8988	−0.470372
$753$	18.2062	0.663471
$754$	−10.7382	−0.391062
$755$	−51.7152	−1.88211
$756$	0	0
$757$	−13.6865	−0.497444	−0.248722	−	0.968575i	$-0.580011\pi$
$757$	−13.6865	−0.497444	−0.248722	+	0.968575i	$0.580011\pi$
$758$	−16.0989	−0.584738
$759$	8.19779	0.297561
$760$	5.70928	0.207097
$761$	7.86150	0.284979	0.142490	−	0.989796i	$-0.454489\pi$
$761$	7.86150	0.284979	0.142490	+	0.989796i	$0.454489\pi$
$762$	−34.2557	−1.24095
$763$	0	0
$764$	14.7526	0.533730
$765$	1.07838	0.0389888
$766$	15.4186	0.557095
$767$	3.68649	0.133111
$768$	−0.418551	−0.0151031
$769$	−2.31351	−0.0834273	−0.0417137	−	0.999130i	$-0.513282\pi$
$769$	−2.31351	−0.0834273	−0.0417137	+	0.999130i	$0.513282\pi$
$770$	0	0
$771$	−12.3402	−0.444420
$772$	4.56916	0.164448
$773$	32.9216	1.18411	0.592054	−	0.805898i	$-0.298317\pi$
$773$	32.9216	1.18411	0.592054	+	0.805898i	$0.298317\pi$
$774$	−18.4391	−0.662779
$775$	−74.4222	−2.67333
$776$	20.8059	0.746888
$777$	0	0
$778$	35.2762	1.26471
$779$	−3.75872	−0.134670
$780$	9.26180	0.331625
$781$	4.16904	0.149180
$782$	4.79606	0.171507
$783$	5.36910	0.191876
$784$	0	0
$785$	−8.58145	−0.306285
$786$	−13.2534	−0.472733
$787$	−24.8104	−0.884397	−0.442198	−	0.896917i	$-0.645801\pi$
$787$	−24.8104	−0.884397	−0.442198	+	0.896917i	$0.645801\pi$
$788$	−28.0866	−1.00054
$789$	7.50307	0.267116
$790$	84.7091	3.01381
$791$	0	0
$792$	−1.65983	−0.0589794
$793$	−2.47027	−0.0877217
$794$	−57.5318	−2.04173
$795$	−17.7587	−0.629837
$796$	6.56916	0.232838
$797$	−2.59583	−0.0919488	−0.0459744	−	0.998943i	$-0.514639\pi$
$797$	−2.59583	−0.0919488	−0.0459744	+	0.998943i	$0.514639\pi$
$798$	0	0
$799$	−1.80430	−0.0638314
$800$	−66.4668	−2.34996
$801$	3.75872	0.132808
$802$	−13.1278	−0.463560
$803$	1.52973	0.0539831
$804$	3.41855	0.120563
$805$	0	0
$806$	16.9939	0.598583
$807$	4.34017	0.152781
$808$	3.76713	0.132527
$809$	38.6803	1.35993	0.679964	−	0.733245i	$-0.261995\pi$
$809$	38.6803	1.35993	0.679964	+	0.733245i	$0.261995\pi$
$810$	−8.04945	−0.282829
$811$	44.9939	1.57995	0.789974	−	0.613140i	$-0.210094\pi$
$811$	44.9939	1.57995	0.789974	+	0.613140i	$0.210094\pi$
$812$	0	0
$813$	−26.0410	−0.913299
$814$	24.9939	0.876034
$815$	65.5052	2.29455
$816$	0.604236	0.0211525
$817$	8.49693	0.297270
$818$	−80.5523	−2.81645
$819$	0	0
$820$	−37.7731	−1.31909
$821$	3.77310	0.131682	0.0658410	−	0.997830i	$-0.479027\pi$
$821$	3.77310	0.131682	0.0658410	+	0.997830i	$0.479027\pi$
$822$	41.2183	1.43765
$823$	−14.6537	−0.510795	−0.255398	−	0.966836i	$-0.582206\pi$
$823$	−14.6537	−0.510795	−0.255398	+	0.966836i	$0.582206\pi$
$824$	−30.0410	−1.04653
$825$	−9.44521	−0.328840
$826$	0	0
$827$	−15.4368	−0.536790	−0.268395	−	0.963309i	$-0.586493\pi$
$827$	−15.4368	−0.536790	−0.268395	+	0.963309i	$0.586493\pi$
$828$	−20.5958	−0.715754
$829$	−8.57691	−0.297889	−0.148944	−	0.988846i	$-0.547588\pi$
$829$	−8.57691	−0.297889	−0.148944	+	0.988846i	$0.547588\pi$
$830$	70.2700	2.43911
$831$	6.59583	0.228807
$832$	11.3463	0.393363
$833$	0	0
$834$	−1.94214	−0.0672508
$835$	11.3197	0.391733
$836$	2.92162	0.101046
$837$	−8.49693	−0.293697
$838$	50.6765	1.75059
$839$	−31.0349	−1.07144	−0.535722	−	0.844395i	$-0.679960\pi$
$839$	−31.0349	−1.07144	−0.535722	+	0.844395i	$0.679960\pi$
$840$	0	0
$841$	−0.172740	−0.00595654
$842$	16.4391	0.566528
$843$	−11.6248	−0.400378
$844$	52.8781	1.82014
$845$	45.0700	1.55045
$846$	13.4680	0.463039
$847$	0	0
$848$	−9.95055	−0.341703
$849$	17.9421	0.615773
$850$	−5.52586	−0.189535
$851$	81.1917	2.78321
$852$	−10.4741	−0.358838
$853$	−11.4140	−0.390808	−0.195404	−	0.980723i	$-0.562602\pi$
$853$	−11.4140	−0.390808	−0.195404	+	0.980723i	$0.562602\pi$
$854$	0	0
$855$	3.70928	0.126855
$856$	24.0905	0.823396
$857$	−22.7936	−0.778615	−0.389308	−	0.921108i	$-0.627286\pi$
$857$	−22.7936	−0.778615	−0.389308	+	0.921108i	$0.627286\pi$
$858$	2.15676	0.0736304
$859$	30.7838	1.05033	0.525164	−	0.851001i	$-0.324004\pi$
$859$	30.7838	1.05033	0.525164	+	0.851001i	$0.324004\pi$
$860$	85.3894	2.91176
$861$	0	0
$862$	−12.8188	−0.436612
$863$	10.0228	0.341180	0.170590	−	0.985342i	$-0.445433\pi$
$863$	10.0228	0.341180	0.170590	+	0.985342i	$0.445433\pi$
$864$	−7.58864	−0.258171
$865$	35.6163	1.21099
$866$	16.2245	0.551329
$867$	−16.9155	−0.574480
$868$	0	0
$869$	11.3484	0.384968
$870$	−43.2183	−1.46524
$871$	−1.16290	−0.0394033
$872$	21.7009	0.734884
$873$	13.5174	0.457496
$874$	16.4969	0.558017
$875$	0	0
$876$	−3.84324	−0.129851
$877$	−32.8371	−1.10883	−0.554415	−	0.832240i	$-0.687058\pi$
$877$	−32.8371	−1.10883	−0.554415	+	0.832240i	$0.687058\pi$
$878$	20.5958	0.695075
$879$	23.7587	0.801362
$880$	−8.31351	−0.280248
$881$	45.0700	1.51845	0.759223	−	0.650831i	$-0.225579\pi$
$881$	45.0700	1.51845	0.759223	+	0.650831i	$0.225579\pi$
$882$	0	0
$883$	54.5523	1.83583	0.917916	−	0.396774i	$-0.129870\pi$
$883$	54.5523	1.83583	0.917916	+	0.396774i	$0.129870\pi$
$884$	0.725919	0.0244153
$885$	14.8371	0.498744
$886$	−54.6369	−1.83556
$887$	−16.4657	−0.552865	−0.276433	−	0.961033i	$-0.589152\pi$
$887$	−16.4657	−0.552865	−0.276433	+	0.961033i	$0.589152\pi$
$888$	−16.4391	−0.551659
$889$	0	0
$890$	−30.2557	−1.01417
$891$	−1.07838	−0.0361270
$892$	−51.5318	−1.72541
$893$	−6.20620	−0.207683
$894$	45.4329	1.51950
$895$	3.02052	0.100965
$896$	0	0
$897$	7.00614	0.233928
$898$	−70.3195	−2.34659
$899$	−45.6209	−1.52154
$900$	23.7298	0.790993
$901$	−1.39189	−0.0463705
$902$	−8.79606	−0.292877
$903$	0	0
$904$	28.8287	0.958828
$905$	74.7670	2.48534
$906$	30.2557	1.00518
$907$	−23.5708	−0.782655	−0.391327	−	0.920252i	$-0.627984\pi$
$907$	−23.5708	−0.782655	−0.391327	+	0.920252i	$0.627984\pi$
$908$	−31.7854	−1.05484
$909$	2.44748	0.0811778
$910$	0	0
$911$	−0.616522	−0.0204263	−0.0102131	−	0.999948i	$-0.503251\pi$
$911$	−0.616522	−0.0204263	−0.0102131	+	0.999948i	$0.503251\pi$
$912$	2.07838	0.0688220
$913$	9.41402	0.311558
$914$	19.2450	0.636567
$915$	−9.94214	−0.328677
$916$	74.3956	2.45810
$917$	0	0
$918$	−0.630898	−0.0208227
$919$	53.6742	1.77055	0.885274	−	0.465069i	$-0.153971\pi$
$919$	53.6742	1.77055	0.885274	+	0.465069i	$0.153971\pi$
$920$	43.4017	1.43091
$921$	24.0144	0.791301
$922$	−18.8865	−0.621995
$923$	3.56302	0.117278
$924$	0	0
$925$	−93.5462	−3.07578
$926$	−13.4764	−0.442862
$927$	−19.5174	−0.641037
$928$	−40.7442	−1.33749
$929$	50.2616	1.64903	0.824515	−	0.565840i	$-0.191448\pi$
$929$	50.2616	1.64903	0.824515	+	0.565840i	$0.191448\pi$
$930$	68.3956	2.24278
$931$	0	0
$932$	−13.8310	−0.453048
$933$	−22.9854	−0.752510
$934$	−35.7237	−1.16891
$935$	−1.16290	−0.0380308
$936$	−1.41855	−0.0463668
$937$	−8.63931	−0.282234	−0.141117	−	0.989993i	$-0.545069\pi$
$937$	−8.63931	−0.282234	−0.141117	+	0.989993i	$0.545069\pi$
$938$	0	0
$939$	−0.523590	−0.0170867
$940$	−62.3689	−2.03425
$941$	−30.2122	−0.984889	−0.492444	−	0.870344i	$-0.663896\pi$
$941$	−30.2122	−0.984889	−0.492444	+	0.870344i	$0.663896\pi$
$942$	5.02052	0.163577
$943$	−28.5737	−0.930488
$944$	8.31351	0.270582
$945$	0	0
$946$	19.8843	0.646494
$947$	27.1727	0.882995	0.441498	−	0.897262i	$-0.354447\pi$
$947$	27.1727	0.882995	0.441498	+	0.897262i	$0.354447\pi$
$948$	−28.5113	−0.926004
$949$	1.30737	0.0424390
$950$	−19.0072	−0.616675
$951$	−17.1012	−0.554543
$952$	0	0
$953$	44.5029	1.44159	0.720795	−	0.693148i	$-0.243777\pi$
$953$	44.5029	1.44159	0.720795	+	0.693148i	$0.243777\pi$
$954$	10.3896	0.336376
$955$	−20.1978	−0.653585
$956$	−28.8638	−0.933521
$957$	−5.78992	−0.187162
$958$	−35.8759	−1.15910
$959$	0	0
$960$	45.6658	1.47386
$961$	41.1978	1.32896
$962$	21.3607	0.688696
$963$	15.6514	0.504360
$964$	36.6225	1.17953
$965$	−6.25565	−0.201377
$966$	0	0
$967$	−18.6004	−0.598147	−0.299074	−	0.954230i	$-0.596678\pi$
$967$	−18.6004	−0.598147	−0.299074	+	0.954230i	$0.596678\pi$
$968$	−15.1412	−0.486655
$969$	0.290725	0.00933942
$970$	−108.808	−3.49361
$971$	−16.0533	−0.515176	−0.257588	−	0.966255i	$-0.582928\pi$
$971$	−16.0533	−0.515176	−0.257588	+	0.966255i	$0.582928\pi$
$972$	2.70928	0.0869000
$973$	0	0
$974$	−55.7152	−1.78523
$975$	−8.07223	−0.258518
$976$	−5.57077	−0.178316
$977$	−15.8394	−0.506746	−0.253373	−	0.967369i	$-0.581540\pi$
$977$	−15.8394	−0.506746	−0.253373	+	0.967369i	$0.581540\pi$
$978$	−38.3234	−1.22545
$979$	−4.05332	−0.129545
$980$	0	0
$981$	14.0989	0.450143
$982$	59.3172	1.89289
$983$	23.0349	0.734699	0.367350	−	0.930083i	$-0.380265\pi$
$983$	23.0349	0.734699	0.367350	+	0.930083i	$0.380265\pi$
$984$	5.78539	0.184431
$985$	38.4534	1.22523
$986$	−3.38735	−0.107875
$987$	0	0
$988$	2.49693	0.0794379
$989$	64.5934	2.05395
$990$	8.68035	0.275880
$991$	−42.8371	−1.36077	−0.680383	−	0.732857i	$-0.738186\pi$
$991$	−42.8371	−1.36077	−0.680383	+	0.732857i	$0.738186\pi$
$992$	64.4801	2.04725
$993$	25.1461	0.797987
$994$	0	0
$995$	−8.99386	−0.285124
$996$	−23.6514	−0.749424
$997$	23.7899	0.753434	0.376717	−	0.926328i	$-0.377053\pi$
$997$	23.7899	0.753434	0.376717	+	0.926328i	$0.377053\pi$
$998$	−21.7899	−0.689748
$999$	−10.6803	−0.337911

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2793.2.a.x.1.3		3
3.2	odd	2		8379.2.a.bp.1.1		3
7.6	odd	2		399.2.a.d.1.3	✓	3
21.20	even	2		1197.2.a.l.1.1		3
28.27	even	2		6384.2.a.bx.1.3		3
35.34	odd	2		9975.2.a.z.1.1		3
133.132	even	2		7581.2.a.n.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
399.2.a.d.1.3	✓	3	7.6	odd	2
1197.2.a.l.1.1		3	21.20	even	2
2793.2.a.x.1.3		3	1.1	even	1	trivial
6384.2.a.bx.1.3		3	28.27	even	2
7581.2.a.n.1.1		3	133.132	even	2
8379.2.a.bp.1.1		3	3.2	odd	2
9975.2.a.z.1.1		3	35.34	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:	\( N \)	\(=\)	\( 2793 = 3 \cdot 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2793.a (trivial)

\(f(q)\)	\(=\)	\(q+2.17009 q^{2} +1.00000 q^{3} +2.70928 q^{4} -3.70928 q^{5} +2.17009 q^{6} +1.53919 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.17009 q^{2} +1.00000 q^{3} +2.70928 q^{4} -3.70928 q^{5} +2.17009 q^{6} +1.53919 q^{8} +1.00000 q^{9} -8.04945 q^{10} -1.07838 q^{11} +2.70928 q^{12} -0.921622 q^{13} -3.70928 q^{15} -2.07838 q^{16} -0.290725 q^{17} +2.17009 q^{18} -1.00000 q^{19} -10.0494 q^{20} -2.34017 q^{22} -7.60197 q^{23} +1.53919 q^{24} +8.75872 q^{25} -2.00000 q^{26} +1.00000 q^{27} +5.36910 q^{29} -8.04945 q^{30} -8.49693 q^{31} -7.58864 q^{32} -1.07838 q^{33} -0.630898 q^{34} +2.70928 q^{36} -10.6803 q^{37} -2.17009 q^{38} -0.921622 q^{39} -5.70928 q^{40} +3.75872 q^{41} -8.49693 q^{43} -2.92162 q^{44} -3.70928 q^{45} -16.4969 q^{46} +6.20620 q^{47} -2.07838 q^{48} +19.0072 q^{50} -0.290725 q^{51} -2.49693 q^{52} +4.78765 q^{53} +2.17009 q^{54} +4.00000 q^{55} -1.00000 q^{57} +11.6514 q^{58} -4.00000 q^{59} -10.0494 q^{60} +2.68035 q^{61} -18.4391 q^{62} -12.3112 q^{64} +3.41855 q^{65} -2.34017 q^{66} +1.26180 q^{67} -0.787653 q^{68} -7.60197 q^{69} -3.86603 q^{71} +1.53919 q^{72} -1.41855 q^{73} -23.1773 q^{74} +8.75872 q^{75} -2.70928 q^{76} -2.00000 q^{78} -10.5236 q^{79} +7.70928 q^{80} +1.00000 q^{81} +8.15676 q^{82} -8.72979 q^{83} +1.07838 q^{85} -18.4391 q^{86} +5.36910 q^{87} -1.65983 q^{88} +3.75872 q^{89} -8.04945 q^{90} -20.5958 q^{92} -8.49693 q^{93} +13.4680 q^{94} +3.70928 q^{95} -7.58864 q^{96} +13.5174 q^{97} -1.07838 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + q^{2} + 3 q^{3} + q^{4} - 4 q^{5} + q^{6} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + q^2 + 3 * q^3 + q^4 - 4 * q^5 + q^6 + 3 * q^8 + 3 * q^9	\( 3 q + q^{2} + 3 q^{3} + q^{4} - 4 q^{5} + q^{6} + 3 q^{8} + 3 q^{9} - 6 q^{10} + q^{12} - 6 q^{13} - 4 q^{15} - 3 q^{16} - 8 q^{17} + q^{18} - 3 q^{19} - 12 q^{20} + 4 q^{22} - 4 q^{23} + 3 q^{24} + q^{25} - 6 q^{26} + 3 q^{27} + 20 q^{29} - 6 q^{30} - 8 q^{31} - 3 q^{32} + 2 q^{34} + q^{36} - 10 q^{37} - q^{38} - 6 q^{39} - 10 q^{40} - 14 q^{41} - 8 q^{43} - 12 q^{44} - 4 q^{45} - 32 q^{46} - 6 q^{47} - 3 q^{48} + 23 q^{50} - 8 q^{51} + 10 q^{52} + 4 q^{53} + q^{54} + 12 q^{55} - 3 q^{57} - 2 q^{58} - 12 q^{59} - 12 q^{60} - 14 q^{61} - 8 q^{62} - 11 q^{64} - 4 q^{65} + 4 q^{66} - 4 q^{67} + 8 q^{68} - 4 q^{69} + 2 q^{71} + 3 q^{72} + 10 q^{73} - 30 q^{74} + q^{75} - q^{76} - 6 q^{78} - 16 q^{79} + 16 q^{80} + 3 q^{81} + 18 q^{82} + 14 q^{83} - 8 q^{86} + 20 q^{87} - 16 q^{88} - 14 q^{89} - 6 q^{90} - 8 q^{92} - 8 q^{93} + 8 q^{94} + 4 q^{95} - 3 q^{96} - 10 q^{97}+O(q^{100}) \) 3 * q + q^2 + 3 * q^3 + q^4 - 4 * q^5 + q^6 + 3 * q^8 + 3 * q^9 - 6 * q^10 + q^12 - 6 * q^13 - 4 * q^15 - 3 * q^16 - 8 * q^17 + q^18 - 3 * q^19 - 12 * q^20 + 4 * q^22 - 4 * q^23 + 3 * q^24 + q^25 - 6 * q^26 + 3 * q^27 + 20 * q^29 - 6 * q^30 - 8 * q^31 - 3 * q^32 + 2 * q^34 + q^36 - 10 * q^37 - q^38 - 6 * q^39 - 10 * q^40 - 14 * q^41 - 8 * q^43 - 12 * q^44 - 4 * q^45 - 32 * q^46 - 6 * q^47 - 3 * q^48 + 23 * q^50 - 8 * q^51 + 10 * q^52 + 4 * q^53 + q^54 + 12 * q^55 - 3 * q^57 - 2 * q^58 - 12 * q^59 - 12 * q^60 - 14 * q^61 - 8 * q^62 - 11 * q^64 - 4 * q^65 + 4 * q^66 - 4 * q^67 + 8 * q^68 - 4 * q^69 + 2 * q^71 + 3 * q^72 + 10 * q^73 - 30 * q^74 + q^75 - q^76 - 6 * q^78 - 16 * q^79 + 16 * q^80 + 3 * q^81 + 18 * q^82 + 14 * q^83 - 8 * q^86 + 20 * q^87 - 16 * q^88 - 14 * q^89 - 6 * q^90 - 8 * q^92 - 8 * q^93 + 8 * q^94 + 4 * q^95 - 3 * q^96 - 10 * q^97

Introduction

L-functions

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