LMFDB - Embedded newform 6762.2.a.ce.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6762,2,Mod(1,6762)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6762, 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("6762.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6762.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:	$53.9948418468$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.3132.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 15x - 6 $ x^3 - 15*x - 6
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 966)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.65491$ of defining polynomial
Character	$\chi$	$=$	6762.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -3.65491 q^{11} -1.00000 q^{12} -0.851731 q^{13} -1.00000 q^{15} +1.00000 q^{16} -6.16155 q^{17} -1.00000 q^{18} +5.50664 q^{19} +1.00000 q^{20} +3.65491 q^{22} -1.00000 q^{23} +1.00000 q^{24} -4.00000 q^{25} +0.851731 q^{26} -1.00000 q^{27} +4.14827 q^{29} +1.00000 q^{30} +3.35837 q^{31} -1.00000 q^{32} +3.65491 q^{33} +6.16155 q^{34} +1.00000 q^{36} +6.81646 q^{37} -5.50664 q^{38} +0.851731 q^{39} -1.00000 q^{40} -2.49336 q^{41} +7.30982 q^{43} -3.65491 q^{44} +1.00000 q^{45} +1.00000 q^{46} +2.35837 q^{47} -1.00000 q^{48} +4.00000 q^{50} +6.16155 q^{51} -0.851731 q^{52} +6.30982 q^{53} +1.00000 q^{54} -3.65491 q^{55} -5.50664 q^{57} -4.14827 q^{58} +3.16155 q^{59} -1.00000 q^{60} +10.0000 q^{61} -3.35837 q^{62} +1.00000 q^{64} -0.851731 q^{65} -3.65491 q^{66} -10.3584 q^{67} -6.16155 q^{68} +1.00000 q^{69} -8.45809 q^{71} -1.00000 q^{72} +1.34509 q^{73} -6.81646 q^{74} +4.00000 q^{75} +5.50664 q^{76} -0.851731 q^{78} -11.4581 q^{79} +1.00000 q^{80} +1.00000 q^{81} +2.49336 q^{82} -7.65491 q^{83} -6.16155 q^{85} -7.30982 q^{86} -4.14827 q^{87} +3.65491 q^{88} -6.81646 q^{89} -1.00000 q^{90} -1.00000 q^{92} -3.35837 q^{93} -2.35837 q^{94} +5.50664 q^{95} +1.00000 q^{96} +0.444807 q^{97} -3.65491 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} - 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 - 3 * q^8 + 3 * q^9	$ 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} - 3 q^{8} + 3 q^{9} - 3 q^{10} - 3 q^{12} - 3 q^{13} - 3 q^{15} + 3 q^{16} + 3 q^{17} - 3 q^{18} + 6 q^{19} + 3 q^{20} - 3 q^{23} + 3 q^{24} - 12 q^{25} + 3 q^{26} - 3 q^{27} + 12 q^{29} + 3 q^{30} - 3 q^{32} - 3 q^{34} + 3 q^{36} - 12 q^{37} - 6 q^{38} + 3 q^{39} - 3 q^{40} - 18 q^{41} + 3 q^{45} + 3 q^{46} - 3 q^{47} - 3 q^{48} + 12 q^{50} - 3 q^{51} - 3 q^{52} - 3 q^{53} + 3 q^{54} - 6 q^{57} - 12 q^{58} - 12 q^{59} - 3 q^{60} + 30 q^{61} + 3 q^{64} - 3 q^{65} - 21 q^{67} + 3 q^{68} + 3 q^{69} - 3 q^{71} - 3 q^{72} + 15 q^{73} + 12 q^{74} + 12 q^{75} + 6 q^{76} - 3 q^{78} - 12 q^{79} + 3 q^{80} + 3 q^{81} + 18 q^{82} - 12 q^{83} + 3 q^{85} - 12 q^{87} + 12 q^{89} - 3 q^{90} - 3 q^{92} + 3 q^{94} + 6 q^{95} + 3 q^{96}+O(q^{100}) $ 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 - 3 * q^8 + 3 * q^9 - 3 * q^10 - 3 * q^12 - 3 * q^13 - 3 * q^15 + 3 * q^16 + 3 * q^17 - 3 * q^18 + 6 * q^19 + 3 * q^20 - 3 * q^23 + 3 * q^24 - 12 * q^25 + 3 * q^26 - 3 * q^27 + 12 * q^29 + 3 * q^30 - 3 * q^32 - 3 * q^34 + 3 * q^36 - 12 * q^37 - 6 * q^38 + 3 * q^39 - 3 * q^40 - 18 * q^41 + 3 * q^45 + 3 * q^46 - 3 * q^47 - 3 * q^48 + 12 * q^50 - 3 * q^51 - 3 * q^52 - 3 * q^53 + 3 * q^54 - 6 * q^57 - 12 * q^58 - 12 * q^59 - 3 * q^60 + 30 * q^61 + 3 * q^64 - 3 * q^65 - 21 * q^67 + 3 * q^68 + 3 * q^69 - 3 * q^71 - 3 * q^72 + 15 * q^73 + 12 * q^74 + 12 * q^75 + 6 * q^76 - 3 * q^78 - 12 * q^79 + 3 * q^80 + 3 * q^81 + 18 * q^82 - 12 * q^83 + 3 * q^85 - 12 * q^87 + 12 * q^89 - 3 * q^90 - 3 * q^92 + 3 * q^94 + 6 * q^95 + 3 * q^96

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214	0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000	0.447214	0.223607	+	0.974679i	$0.428217\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	−3.65491	−1.10200	−0.550999	−	0.834506i	$-0.685753\pi$
$11$	−3.65491	−1.10200	−0.550999	+	0.834506i	$0.685753\pi$
$12$	−1.00000	−0.288675
$13$	−0.851731	−0.236228	−0.118114	−	0.993000i	$-0.537685\pi$
$13$	−0.851731	−0.236228	−0.118114	+	0.993000i	$0.537685\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−6.16155	−1.49440	−0.747198	−	0.664601i	$-0.768601\pi$
$17$	−6.16155	−1.49440	−0.747198	+	0.664601i	$0.768601\pi$
$18$	−1.00000	−0.235702
$19$	5.50664	1.26331	0.631655	−	0.775249i	$-0.282376\pi$
$19$	5.50664	1.26331	0.631655	+	0.775249i	$0.282376\pi$
$20$	1.00000	0.223607
$21$	0	0
$22$	3.65491	0.779230
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.00000	0.204124
$25$	−4.00000	−0.800000
$26$	0.851731	0.167038
$27$	−1.00000	−0.192450
$28$	0	0
$29$	4.14827	0.770314	0.385157	−	0.922851i	$-0.374147\pi$
$29$	4.14827	0.770314	0.385157	+	0.922851i	$0.374147\pi$
$30$	1.00000	0.182574
$31$	3.35837	0.603182	0.301591	−	0.953437i	$-0.402482\pi$
$31$	3.35837	0.603182	0.301591	+	0.953437i	$0.402482\pi$
$32$	−1.00000	−0.176777
$33$	3.65491	0.636238
$34$	6.16155	1.05670
$35$	0	0
$36$	1.00000	0.166667
$37$	6.81646	1.12062	0.560310	−	0.828283i	$-0.310682\pi$
$37$	6.81646	1.12062	0.560310	+	0.828283i	$0.310682\pi$
$38$	−5.50664	−0.893295
$39$	0.851731	0.136386
$40$	−1.00000	−0.158114
$41$	−2.49336	−0.389397	−0.194699	−	0.980863i	$-0.562373\pi$
$41$	−2.49336	−0.389397	−0.194699	+	0.980863i	$0.562373\pi$
$42$	0	0
$43$	7.30982	1.11474	0.557369	−	0.830265i	$-0.311811\pi$
$43$	7.30982	1.11474	0.557369	+	0.830265i	$0.311811\pi$
$44$	−3.65491	−0.550999
$45$	1.00000	0.149071
$46$	1.00000	0.147442
$47$	2.35837	0.344004	0.172002	−	0.985097i	$-0.444976\pi$
$47$	2.35837	0.344004	0.172002	+	0.985097i	$0.444976\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	4.00000	0.565685
$51$	6.16155	0.862790
$52$	−0.851731	−0.118114
$53$	6.30982	0.866721	0.433360	−	0.901221i	$-0.357328\pi$
$53$	6.30982	0.866721	0.433360	+	0.901221i	$0.357328\pi$
$54$	1.00000	0.136083
$55$	−3.65491	−0.492828
$56$	0	0
$57$	−5.50664	−0.729373
$58$	−4.14827	−0.544694
$59$	3.16155	0.411599	0.205800	−	0.978594i	$-0.434021\pi$
$59$	3.16155	0.411599	0.205800	+	0.978594i	$0.434021\pi$
$60$	−1.00000	−0.129099
$61$	10.0000	1.28037	0.640184	−	0.768221i	$-0.278858\pi$
$61$	10.0000	1.28037	0.640184	+	0.768221i	$0.278858\pi$
$62$	−3.35837	−0.426514
$63$	0	0
$64$	1.00000	0.125000
$65$	−0.851731	−0.105644
$66$	−3.65491	−0.449888
$67$	−10.3584	−1.26548	−0.632738	−	0.774366i	$-0.718069\pi$
$67$	−10.3584	−1.26548	−0.632738	+	0.774366i	$0.718069\pi$
$68$	−6.16155	−0.747198
$69$	1.00000	0.120386
$70$	0	0
$71$	−8.45809	−1.00379	−0.501895	−	0.864928i	$-0.667364\pi$
$71$	−8.45809	−1.00379	−0.501895	+	0.864928i	$0.667364\pi$
$72$	−1.00000	−0.117851
$73$	1.34509	0.157431	0.0787154	−	0.996897i	$-0.474918\pi$
$73$	1.34509	0.157431	0.0787154	+	0.996897i	$0.474918\pi$
$74$	−6.81646	−0.792398
$75$	4.00000	0.461880
$76$	5.50664	0.631655
$77$	0	0
$78$	−0.851731	−0.0964396
$79$	−11.4581	−1.28914	−0.644568	−	0.764547i	$-0.722963\pi$
$79$	−11.4581	−1.28914	−0.644568	+	0.764547i	$0.722963\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	2.49336	0.275345
$83$	−7.65491	−0.840236	−0.420118	−	0.907470i	$-0.638011\pi$
$83$	−7.65491	−0.840236	−0.420118	+	0.907470i	$0.638011\pi$
$84$	0	0
$85$	−6.16155	−0.668314
$86$	−7.30982	−0.788238
$87$	−4.14827	−0.444741
$88$	3.65491	0.389615
$89$	−6.81646	−0.722544	−0.361272	−	0.932461i	$-0.617657\pi$
$89$	−6.81646	−0.722544	−0.361272	+	0.932461i	$0.617657\pi$
$90$	−1.00000	−0.105409
$91$	0	0
$92$	−1.00000	−0.104257
$93$	−3.35837	−0.348247
$94$	−2.35837	−0.243248
$95$	5.50664	0.564970
$96$	1.00000	0.102062
$97$	0.444807	0.0451633	0.0225816	−	0.999745i	$-0.492811\pi$
$97$	0.444807	0.0451633	0.0225816	+	0.999745i	$0.492811\pi$
$98$	0	0
$99$	−3.65491	−0.367332
$100$	−4.00000	−0.400000
$101$	1.30982	0.130332	0.0651661	−	0.997874i	$-0.479242\pi$
$101$	1.30982	0.130332	0.0651661	+	0.997874i	$0.479242\pi$
$102$	−6.16155	−0.610085
$103$	3.64163	0.358820	0.179410	−	0.983774i	$-0.442581\pi$
$103$	3.64163	0.358820	0.179410	+	0.983774i	$0.442581\pi$
$104$	0.851731	0.0835191
$105$	0	0
$106$	−6.30982	−0.612864
$107$	−6.34509	−0.613403	−0.306701	−	0.951806i	$-0.599225\pi$
$107$	−6.34509	−0.613403	−0.306701	+	0.951806i	$0.599225\pi$
$108$	−1.00000	−0.0962250
$109$	3.30982	0.317023	0.158512	−	0.987357i	$-0.449330\pi$
$109$	3.30982	0.317023	0.158512	+	0.987357i	$0.449330\pi$
$110$	3.65491	0.348482
$111$	−6.81646	−0.646990
$112$	0	0
$113$	9.17484	0.863096	0.431548	−	0.902090i	$-0.357968\pi$
$113$	9.17484	0.863096	0.431548	+	0.902090i	$0.357968\pi$
$114$	5.50664	0.515744
$115$	−1.00000	−0.0932505
$116$	4.14827	0.385157
$117$	−0.851731	−0.0787426
$118$	−3.16155	−0.291045
$119$	0	0
$120$	1.00000	0.0912871
$121$	2.35837	0.214398
$122$	−10.0000	−0.905357
$123$	2.49336	0.224819
$124$	3.35837	0.301591
$125$	−9.00000	−0.804984
$126$	0	0
$127$	−8.34509	−0.740507	−0.370253	−	0.928931i	$-0.620729\pi$
$127$	−8.34509	−0.740507	−0.370253	+	0.928931i	$0.620729\pi$
$128$	−1.00000	−0.0883883
$129$	−7.30982	−0.643594
$130$	0.851731	0.0747018
$131$	5.09972	0.445564	0.222782	−	0.974868i	$-0.428486\pi$
$131$	5.09972	0.445564	0.222782	+	0.974868i	$0.428486\pi$
$132$	3.65491	0.318119
$133$	0	0
$134$	10.3584	0.894827
$135$	−1.00000	−0.0860663
$136$	6.16155	0.528349
$137$	−2.95145	−0.252159	−0.126080	−	0.992020i	$-0.540239\pi$
$137$	−2.95145	−0.252159	−0.126080	+	0.992020i	$0.540239\pi$
$138$	−1.00000	−0.0851257
$139$	16.0266	1.35936	0.679678	−	0.733511i	$-0.262120\pi$
$139$	16.0266	1.35936	0.679678	+	0.733511i	$0.262120\pi$
$140$	0	0
$141$	−2.35837	−0.198611
$142$	8.45809	0.709787
$143$	3.11300	0.260322
$144$	1.00000	0.0833333
$145$	4.14827	0.344495
$146$	−1.34509	−0.111320
$147$	0	0
$148$	6.81646	0.560310
$149$	−19.9647	−1.63557	−0.817787	−	0.575521i	$-0.804799\pi$
$149$	−19.9647	−1.63557	−0.817787	+	0.575521i	$0.804799\pi$
$150$	−4.00000	−0.326599
$151$	2.34509	0.190841	0.0954203	−	0.995437i	$-0.469580\pi$
$151$	2.34509	0.190841	0.0954203	+	0.995437i	$0.469580\pi$
$152$	−5.50664	−0.446648
$153$	−6.16155	−0.498132
$154$	0	0
$155$	3.35837	0.269751
$156$	0.851731	0.0681931
$157$	−24.8430	−1.98269	−0.991345	−	0.131283i	$-0.958090\pi$
$157$	−24.8430	−1.98269	−0.991345	+	0.131283i	$0.958090\pi$
$158$	11.4581	0.911557
$159$	−6.30982	−0.500401
$160$	−1.00000	−0.0790569
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	−22.8430	−1.78920	−0.894602	−	0.446864i	$-0.852541\pi$
$163$	−22.8430	−1.78920	−0.894602	+	0.446864i	$0.852541\pi$
$164$	−2.49336	−0.194699
$165$	3.65491	0.284534
$166$	7.65491	0.594136
$167$	4.06184	0.314314	0.157157	−	0.987574i	$-0.449767\pi$
$167$	4.06184	0.314314	0.157157	+	0.987574i	$0.449767\pi$
$168$	0	0
$169$	−12.2746	−0.944196
$170$	6.16155	0.472570
$171$	5.50664	0.421103
$172$	7.30982	0.557369
$173$	−3.70346	−0.281569	−0.140785	−	0.990040i	$-0.544962\pi$
$173$	−3.70346	−0.281569	−0.140785	+	0.990040i	$0.544962\pi$
$174$	4.14827	0.314479
$175$	0	0
$176$	−3.65491	−0.275499
$177$	−3.16155	−0.237637
$178$	6.81646	0.510916
$179$	14.9780	1.11951	0.559755	−	0.828658i	$-0.310895\pi$
$179$	14.9780	1.11951	0.559755	+	0.828658i	$0.310895\pi$
$180$	1.00000	0.0745356
$181$	−1.70346	−0.126617	−0.0633087	−	0.997994i	$-0.520165\pi$
$181$	−1.70346	−0.126617	−0.0633087	+	0.997994i	$0.520165\pi$
$182$	0	0
$183$	−10.0000	−0.739221
$184$	1.00000	0.0737210
$185$	6.81646	0.501156
$186$	3.35837	0.246248
$187$	22.5199	1.64682
$188$	2.35837	0.172002
$189$	0	0
$190$	−5.50664	−0.399494
$191$	−22.8430	−1.65286	−0.826432	−	0.563037i	$-0.809633\pi$
$191$	−22.8430	−1.65286	−0.826432	+	0.563037i	$0.809633\pi$
$192$	−1.00000	−0.0721688
$193$	−17.9162	−1.28963	−0.644817	−	0.764337i	$-0.723067\pi$
$193$	−17.9162	−1.28963	−0.644817	+	0.764337i	$0.723067\pi$
$194$	−0.444807	−0.0319353
$195$	0.851731	0.0609937
$196$	0	0
$197$	5.01328	0.357182	0.178591	−	0.983923i	$-0.442846\pi$
$197$	5.01328	0.357182	0.178591	+	0.983923i	$0.442846\pi$
$198$	3.65491	0.259743
$199$	14.3231	1.01534	0.507669	−	0.861552i	$-0.330507\pi$
$199$	14.3231	1.01534	0.507669	+	0.861552i	$0.330507\pi$
$200$	4.00000	0.282843
$201$	10.3584	0.730623
$202$	−1.30982	−0.0921587
$203$	0	0
$204$	6.16155	0.431395
$205$	−2.49336	−0.174144
$206$	−3.64163	−0.253724
$207$	−1.00000	−0.0695048
$208$	−0.851731	−0.0590569
$209$	−20.1263	−1.39216
$210$	0	0
$211$	−9.01328	−0.620500	−0.310250	−	0.950655i	$-0.600413\pi$
$211$	−9.01328	−0.620500	−0.310250	+	0.950655i	$0.600413\pi$
$212$	6.30982	0.433360
$213$	8.45809	0.579539
$214$	6.34509	0.433741
$215$	7.30982	0.498526
$216$	1.00000	0.0680414
$217$	0	0
$218$	−3.30982	−0.224169
$219$	−1.34509	−0.0908927
$220$	−3.65491	−0.246414
$221$	5.24799	0.353018
$222$	6.81646	0.457491
$223$	−15.9780	−1.06997	−0.534984	−	0.844862i	$-0.679682\pi$
$223$	−15.9780	−1.06997	−0.534984	+	0.844862i	$0.679682\pi$
$224$	0	0
$225$	−4.00000	−0.266667
$226$	−9.17484	−0.610301
$227$	−13.9780	−0.927754	−0.463877	−	0.885900i	$-0.653542\pi$
$227$	−13.9780	−0.927754	−0.463877	+	0.885900i	$0.653542\pi$
$228$	−5.50664	−0.364686
$229$	28.5199	1.88465	0.942325	−	0.334700i	$-0.108635\pi$
$229$	28.5199	1.88465	0.942325	+	0.334700i	$0.108635\pi$
$230$	1.00000	0.0659380
$231$	0	0
$232$	−4.14827	−0.272347
$233$	11.1396	0.729777	0.364889	−	0.931051i	$-0.381107\pi$
$233$	11.1396	0.729777	0.364889	+	0.931051i	$0.381107\pi$
$234$	0.851731	0.0556794
$235$	2.35837	0.153843
$236$	3.16155	0.205800
$237$	11.4581	0.744283
$238$	0	0
$239$	−16.0000	−1.03495	−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000	−1.03495	−0.517477	+	0.855697i	$0.673129\pi$
$240$	−1.00000	−0.0645497
$241$	16.5685	1.06727	0.533635	−	0.845715i	$-0.320826\pi$
$241$	16.5685	1.06727	0.533635	+	0.845715i	$0.320826\pi$
$242$	−2.35837	−0.151602
$243$	−1.00000	−0.0641500
$244$	10.0000	0.640184
$245$	0	0
$246$	−2.49336	−0.158971
$247$	−4.69018	−0.298429
$248$	−3.35837	−0.213257
$249$	7.65491	0.485110
$250$	9.00000	0.569210
$251$	30.2746	1.91091	0.955456	−	0.295132i	$-0.0953637\pi$
$251$	30.2746	1.91091	0.955456	+	0.295132i	$0.0953637\pi$
$252$	0	0
$253$	3.65491	0.229782
$254$	8.34509	0.523617
$255$	6.16155	0.385851
$256$	1.00000	0.0625000
$257$	−14.1263	−0.881173	−0.440587	−	0.897710i	$-0.645230\pi$
$257$	−14.1263	−0.881173	−0.440587	+	0.897710i	$0.645230\pi$
$258$	7.30982	0.455090
$259$	0	0
$260$	−0.851731	−0.0528221
$261$	4.14827	0.256771
$262$	−5.09972	−0.315062
$263$	−15.3098	−0.944044	−0.472022	−	0.881587i	$-0.656476\pi$
$263$	−15.3098	−0.944044	−0.472022	+	0.881587i	$0.656476\pi$
$264$	−3.65491	−0.224944
$265$	6.30982	0.387609
$266$	0	0
$267$	6.81646	0.417161
$268$	−10.3584	−0.632738
$269$	−22.4714	−1.37010	−0.685052	−	0.728494i	$-0.740221\pi$
$269$	−22.4714	−1.37010	−0.685052	+	0.728494i	$0.740221\pi$
$270$	1.00000	0.0608581
$271$	−14.3717	−0.873016	−0.436508	−	0.899700i	$-0.643785\pi$
$271$	−14.3717	−0.873016	−0.436508	+	0.899700i	$0.643785\pi$
$272$	−6.16155	−0.373599
$273$	0	0
$274$	2.95145	0.178304
$275$	14.6196	0.881598
$276$	1.00000	0.0601929
$277$	−11.9647	−0.718891	−0.359446	−	0.933166i	$-0.617034\pi$
$277$	−11.9647	−0.718891	−0.359446	+	0.933166i	$0.617034\pi$
$278$	−16.0266	−0.961210
$279$	3.35837	0.201061
$280$	0	0
$281$	11.0512	0.659257	0.329629	−	0.944111i	$-0.393076\pi$
$281$	11.0512	0.659257	0.329629	+	0.944111i	$0.393076\pi$
$282$	2.35837	0.140439
$283$	3.93816	0.234100	0.117050	−	0.993126i	$-0.462656\pi$
$283$	3.93816	0.234100	0.117050	+	0.993126i	$0.462656\pi$
$284$	−8.45809	−0.501895
$285$	−5.50664	−0.326185
$286$	−3.11300	−0.184076
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	20.9647	1.23322
$290$	−4.14827	−0.243595
$291$	−0.444807	−0.0260750
$292$	1.34509	0.0787154
$293$	13.0266	0.761020	0.380510	−	0.924777i	$-0.375748\pi$
$293$	13.0266	0.761020	0.380510	+	0.924777i	$0.375748\pi$
$294$	0	0
$295$	3.16155	0.184073
$296$	−6.81646	−0.396199
$297$	3.65491	0.212079
$298$	19.9647	1.15653
$299$	0.851731	0.0492569
$300$	4.00000	0.230940
$301$	0	0
$302$	−2.34509	−0.134945
$303$	−1.30982	−0.0752473
$304$	5.50664	0.315828
$305$	10.0000	0.572598
$306$	6.16155	0.352233
$307$	−25.4095	−1.45020	−0.725099	−	0.688644i	$-0.758206\pi$
$307$	−25.4095	−1.45020	−0.725099	+	0.688644i	$0.758206\pi$
$308$	0	0
$309$	−3.64163	−0.207165
$310$	−3.35837	−0.190743
$311$	−5.54191	−0.314253	−0.157126	−	0.987578i	$-0.550223\pi$
$311$	−5.54191	−0.314253	−0.157126	+	0.987578i	$0.550223\pi$
$312$	−0.851731	−0.0482198
$313$	19.1616	1.08307	0.541537	−	0.840677i	$-0.317842\pi$
$313$	19.1616	1.08307	0.541537	+	0.840677i	$0.317842\pi$
$314$	24.8430	1.40197
$315$	0	0
$316$	−11.4581	−0.644568
$317$	8.56848	0.481254	0.240627	−	0.970618i	$-0.422647\pi$
$317$	8.56848	0.481254	0.240627	+	0.970618i	$0.422647\pi$
$318$	6.30982	0.353837
$319$	−15.1616	−0.848884
$320$	1.00000	0.0559017
$321$	6.34509	0.354148
$322$	0	0
$323$	−33.9295	−1.88789
$324$	1.00000	0.0555556
$325$	3.40692	0.188982
$326$	22.8430	1.26516
$327$	−3.30982	−0.183034
$328$	2.49336	0.137673
$329$	0	0
$330$	−3.65491	−0.201196
$331$	17.1396	0.942076	0.471038	−	0.882113i	$-0.343879\pi$
$331$	17.1396	0.942076	0.471038	+	0.882113i	$0.343879\pi$
$332$	−7.65491	−0.420118
$333$	6.81646	0.373540
$334$	−4.06184	−0.222254
$335$	−10.3584	−0.565938
$336$	0	0
$337$	−14.5685	−0.793596	−0.396798	−	0.917906i	$-0.629879\pi$
$337$	−14.5685	−0.793596	−0.396798	+	0.917906i	$0.629879\pi$
$338$	12.2746	0.667648
$339$	−9.17484	−0.498309
$340$	−6.16155	−0.334157
$341$	−12.2746	−0.664704
$342$	−5.50664	−0.297765
$343$	0	0
$344$	−7.30982	−0.394119
$345$	1.00000	0.0538382
$346$	3.70346	0.199099
$347$	7.04855	0.378386	0.189193	−	0.981940i	$-0.439413\pi$
$347$	7.04855	0.378386	0.189193	+	0.981940i	$0.439413\pi$
$348$	−4.14827	−0.222371
$349$	22.4581	1.20215	0.601077	−	0.799191i	$-0.294738\pi$
$349$	22.4581	1.20215	0.601077	+	0.799191i	$0.294738\pi$
$350$	0	0
$351$	0.851731	0.0454620
$352$	3.65491	0.194807
$353$	11.1396	0.592899	0.296450	−	0.955048i	$-0.404197\pi$
$353$	11.1396	0.592899	0.296450	+	0.955048i	$0.404197\pi$
$354$	3.16155	0.168035
$355$	−8.45809	−0.448909
$356$	−6.81646	−0.361272
$357$	0	0
$358$	−14.9780	−0.791613
$359$	−28.0266	−1.47919	−0.739593	−	0.673055i	$-0.764982\pi$
$359$	−28.0266	−1.47919	−0.739593	+	0.673055i	$0.764982\pi$
$360$	−1.00000	−0.0527046
$361$	11.3231	0.595953
$362$	1.70346	0.0895320
$363$	−2.35837	−0.123782
$364$	0	0
$365$	1.34509	0.0704052
$366$	10.0000	0.522708
$367$	−7.78990	−0.406629	−0.203315	−	0.979113i	$-0.565171\pi$
$367$	−7.78990	−0.406629	−0.203315	+	0.979113i	$0.565171\pi$
$368$	−1.00000	−0.0521286
$369$	−2.49336	−0.129799
$370$	−6.81646	−0.354371
$371$	0	0
$372$	−3.35837	−0.174124
$373$	12.7167	0.658448	0.329224	−	0.944252i	$-0.393213\pi$
$373$	12.7167	0.658448	0.329224	+	0.944252i	$0.393213\pi$
$374$	−22.5199	−1.16448
$375$	9.00000	0.464758
$376$	−2.35837	−0.121624
$377$	−3.53321	−0.181970
$378$	0	0
$379$	−22.2613	−1.14348	−0.571742	−	0.820433i	$-0.693732\pi$
$379$	−22.2613	−1.14348	−0.571742	+	0.820433i	$0.693732\pi$
$380$	5.50664	0.282485
$381$	8.34509	0.427532
$382$	22.8430	1.16875
$383$	−22.2234	−1.13556	−0.567781	−	0.823180i	$-0.692198\pi$
$383$	−22.2234	−1.13556	−0.567781	+	0.823180i	$0.692198\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	17.9162	0.911910
$387$	7.30982	0.371579
$388$	0.444807	0.0225816
$389$	−30.7433	−1.55875	−0.779374	−	0.626559i	$-0.784463\pi$
$389$	−30.7433	−1.55875	−0.779374	+	0.626559i	$0.784463\pi$
$390$	−0.851731	−0.0431291
$391$	6.16155	0.311603
$392$	0	0
$393$	−5.09972	−0.257247
$394$	−5.01328	−0.252566
$395$	−11.4581	−0.576519
$396$	−3.65491	−0.183666
$397$	−6.16155	−0.309239	−0.154620	−	0.987974i	$-0.549415\pi$
$397$	−6.16155	−0.309239	−0.154620	+	0.987974i	$0.549415\pi$
$398$	−14.3231	−0.717952
$399$	0	0
$400$	−4.00000	−0.200000
$401$	−15.9647	−0.797241	−0.398620	−	0.917116i	$-0.630511\pi$
$401$	−15.9647	−0.797241	−0.398620	+	0.917116i	$0.630511\pi$
$402$	−10.3584	−0.516629
$403$	−2.86043	−0.142488
$404$	1.30982	0.0651661
$405$	1.00000	0.0496904
$406$	0	0
$407$	−24.9136	−1.23492
$408$	−6.16155	−0.305042
$409$	−14.7300	−0.728353	−0.364177	−	0.931330i	$-0.618650\pi$
$409$	−14.7300	−0.728353	−0.364177	+	0.931330i	$0.618650\pi$
$410$	2.49336	0.123138
$411$	2.95145	0.145584
$412$	3.64163	0.179410
$413$	0	0
$414$	1.00000	0.0491473
$415$	−7.65491	−0.375765
$416$	0.851731	0.0417596
$417$	−16.0266	−0.784824
$418$	20.1263	0.984409
$419$	24.9427	1.21853	0.609267	−	0.792966i	$-0.291464\pi$
$419$	24.9427	1.21853	0.609267	+	0.792966i	$0.291464\pi$
$420$	0	0
$421$	32.3497	1.57663	0.788313	−	0.615274i	$-0.210955\pi$
$421$	32.3497	1.57663	0.788313	+	0.615274i	$0.210955\pi$
$422$	9.01328	0.438760
$423$	2.35837	0.114668
$424$	−6.30982	−0.306432
$425$	24.6462	1.19552
$426$	−8.45809	−0.409796
$427$	0	0
$428$	−6.34509	−0.306701
$429$	−3.11300	−0.150297
$430$	−7.30982	−0.352511
$431$	4.59308	0.221241	0.110620	−	0.993863i	$-0.464716\pi$
$431$	4.59308	0.221241	0.110620	+	0.993863i	$0.464716\pi$
$432$	−1.00000	−0.0481125
$433$	27.2393	1.30904	0.654518	−	0.756046i	$-0.272871\pi$
$433$	27.2393	1.30904	0.654518	+	0.756046i	$0.272871\pi$
$434$	0	0
$435$	−4.14827	−0.198894
$436$	3.30982	0.158512
$437$	−5.50664	−0.263418
$438$	1.34509	0.0642708
$439$	−15.9514	−0.761321	−0.380661	−	0.924715i	$-0.624303\pi$
$439$	−15.9514	−0.761321	−0.380661	+	0.924715i	$0.624303\pi$
$440$	3.65491	0.174241
$441$	0	0
$442$	−5.24799	−0.249621
$443$	−29.1263	−1.38383	−0.691916	−	0.721978i	$-0.743233\pi$
$443$	−29.1263	−1.38383	−0.691916	+	0.721978i	$0.743233\pi$
$444$	−6.81646	−0.323495
$445$	−6.81646	−0.323131
$446$	15.9780	0.756581
$447$	19.9647	0.944299
$448$	0	0
$449$	−18.2234	−0.860015	−0.430007	−	0.902825i	$-0.641489\pi$
$449$	−18.2234	−0.860015	−0.430007	+	0.902825i	$0.641489\pi$
$450$	4.00000	0.188562
$451$	9.11300	0.429114
$452$	9.17484	0.431548
$453$	−2.34509	−0.110182
$454$	13.9780	0.656021
$455$	0	0
$456$	5.50664	0.257872
$457$	10.2719	0.480501	0.240251	−	0.970711i	$-0.422770\pi$
$457$	10.2719	0.480501	0.240251	+	0.970711i	$0.422770\pi$
$458$	−28.5199	−1.33265
$459$	6.16155	0.287597
$460$	−1.00000	−0.0466252
$461$	20.6196	0.960353	0.480176	−	0.877172i	$-0.340573\pi$
$461$	20.6196	0.960353	0.480176	+	0.877172i	$0.340573\pi$
$462$	0	0
$463$	15.3098	0.711508	0.355754	−	0.934580i	$-0.384224\pi$
$463$	15.3098	0.711508	0.355754	+	0.934580i	$0.384224\pi$
$464$	4.14827	0.192579
$465$	−3.35837	−0.155741
$466$	−11.1396	−0.516031
$467$	7.30982	0.338258	0.169129	−	0.985594i	$-0.445905\pi$
$467$	7.30982	0.338258	0.169129	+	0.985594i	$0.445905\pi$
$468$	−0.851731	−0.0393713
$469$	0	0
$470$	−2.35837	−0.108784
$471$	24.8430	1.14471
$472$	−3.16155	−0.145522
$473$	−26.7167	−1.22844
$474$	−11.4581	−0.526288
$475$	−22.0266	−1.01065
$476$	0	0
$477$	6.30982	0.288907
$478$	16.0000	0.731823
$479$	−33.1130	−1.51297	−0.756486	−	0.654010i	$-0.773085\pi$
$479$	−33.1130	−1.51297	−0.756486	+	0.654010i	$0.773085\pi$
$480$	1.00000	0.0456435
$481$	−5.80579	−0.264721
$482$	−16.5685	−0.754673
$483$	0	0
$484$	2.35837	0.107199
$485$	0.444807	0.0201976
$486$	1.00000	0.0453609
$487$	−27.3849	−1.24093	−0.620465	−	0.784234i	$-0.713056\pi$
$487$	−27.3849	−1.24093	−0.620465	+	0.784234i	$0.713056\pi$
$488$	−10.0000	−0.452679
$489$	22.8430	1.03300
$490$	0	0
$491$	19.8165	0.894304	0.447152	−	0.894458i	$-0.352438\pi$
$491$	19.8165	0.894304	0.447152	+	0.894458i	$0.352438\pi$
$492$	2.49336	0.112409
$493$	−25.5598	−1.15115
$494$	4.69018	0.211021
$495$	−3.65491	−0.164276
$496$	3.35837	0.150795
$497$	0	0
$498$	−7.65491	−0.343025
$499$	−36.3497	−1.62723	−0.813617	−	0.581401i	$-0.802505\pi$
$499$	−36.3497	−1.62723	−0.813617	+	0.581401i	$0.802505\pi$
$500$	−9.00000	−0.402492
$501$	−4.06184	−0.181469
$502$	−30.2746	−1.35122
$503$	−38.9427	−1.73637	−0.868186	−	0.496239i	$-0.834714\pi$
$503$	−38.9427	−1.73637	−0.868186	+	0.496239i	$0.834714\pi$
$504$	0	0
$505$	1.30982	0.0582863
$506$	−3.65491	−0.162481
$507$	12.2746	0.545132
$508$	−8.34509	−0.370253
$509$	16.1748	0.716937	0.358469	−	0.933542i	$-0.383299\pi$
$509$	16.1748	0.716937	0.358469	+	0.933542i	$0.383299\pi$
$510$	−6.16155	−0.272838
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−5.50664	−0.243124
$514$	14.1263	0.623084
$515$	3.64163	0.160469
$516$	−7.30982	−0.321797
$517$	−8.61964	−0.379091
$518$	0	0
$519$	3.70346	0.162564
$520$	0.851731	0.0373509
$521$	−20.9780	−0.919064	−0.459532	−	0.888161i	$-0.651983\pi$
$521$	−20.9780	−0.919064	−0.459532	+	0.888161i	$0.651983\pi$
$522$	−4.14827	−0.181565
$523$	−26.2613	−1.14833	−0.574163	−	0.818741i	$-0.694672\pi$
$523$	−26.2613	−1.14833	−0.574163	+	0.818741i	$0.694672\pi$
$524$	5.09972	0.222782
$525$	0	0
$526$	15.3098	0.667540
$527$	−20.6928	−0.901392
$528$	3.65491	0.159060
$529$	1.00000	0.0434783
$530$	−6.30982	−0.274081
$531$	3.16155	0.137200
$532$	0	0
$533$	2.12367	0.0919864
$534$	−6.81646	−0.294977
$535$	−6.34509	−0.274322
$536$	10.3584	0.447414
$537$	−14.9780	−0.646349
$538$	22.4714	0.968810
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	8.16155	0.350893	0.175446	−	0.984489i	$-0.443863\pi$
$541$	8.16155	0.350893	0.175446	+	0.984489i	$0.443863\pi$
$542$	14.3717	0.617316
$543$	1.70346	0.0731026
$544$	6.16155	0.264174
$545$	3.30982	0.141777
$546$	0	0
$547$	21.7326	0.929221	0.464610	−	0.885515i	$-0.346194\pi$
$547$	21.7326	0.929221	0.464610	+	0.885515i	$0.346194\pi$
$548$	−2.95145	−0.126080
$549$	10.0000	0.426790
$550$	−14.6196	−0.623384
$551$	22.8430	0.973146
$552$	−1.00000	−0.0425628
$553$	0	0
$554$	11.9647	0.508333
$555$	−6.81646	−0.289343
$556$	16.0266	0.679678
$557$	−36.5977	−1.55069	−0.775346	−	0.631536i	$-0.782425\pi$
$557$	−36.5977	−1.55069	−0.775346	+	0.631536i	$0.782425\pi$
$558$	−3.35837	−0.142171
$559$	−6.22600	−0.263332
$560$	0	0
$561$	−22.5199	−0.950792
$562$	−11.0512	−0.466165
$563$	7.28784	0.307146	0.153573	−	0.988137i	$-0.450922\pi$
$563$	7.28784	0.307146	0.153573	+	0.988137i	$0.450922\pi$
$564$	−2.35837	−0.0993054
$565$	9.17484	0.385988
$566$	−3.93816	−0.165533
$567$	0	0
$568$	8.45809	0.354894
$569$	−13.3451	−0.559455	−0.279728	−	0.960079i	$-0.590244\pi$
$569$	−13.3451	−0.559455	−0.279728	+	0.960079i	$0.590244\pi$
$570$	5.50664	0.230648
$571$	−31.5950	−1.32221	−0.661106	−	0.750293i	$-0.729913\pi$
$571$	−31.5950	−1.32221	−0.661106	+	0.750293i	$0.729913\pi$
$572$	3.11300	0.130161
$573$	22.8430	0.954281
$574$	0	0
$575$	4.00000	0.166812
$576$	1.00000	0.0416667
$577$	0.738730	0.0307537	0.0153769	−	0.999882i	$-0.495105\pi$
$577$	0.738730	0.0307537	0.0153769	+	0.999882i	$0.495105\pi$
$578$	−20.9647	−0.872018
$579$	17.9162	0.744571
$580$	4.14827	0.172247
$581$	0	0
$582$	0.444807	0.0184378
$583$	−23.0618	−0.955124
$584$	−1.34509	−0.0556602
$585$	−0.851731	−0.0352147
$586$	−13.0266	−0.538123
$587$	−42.2367	−1.74329	−0.871647	−	0.490134i	$-0.836948\pi$
$587$	−42.2367	−1.74329	−0.871647	+	0.490134i	$0.836948\pi$
$588$	0	0
$589$	18.4934	0.762006
$590$	−3.16155	−0.130159
$591$	−5.01328	−0.206219
$592$	6.81646	0.280155
$593$	−0.663611	−0.0272512	−0.0136256	−	0.999907i	$-0.504337\pi$
$593$	−0.663611	−0.0272512	−0.0136256	+	0.999907i	$0.504337\pi$
$594$	−3.65491	−0.149963
$595$	0	0
$596$	−19.9647	−0.817787
$597$	−14.3231	−0.586206
$598$	−0.851731	−0.0348299
$599$	29.8916	1.22134	0.610668	−	0.791886i	$-0.290901\pi$
$599$	29.8916	1.22134	0.610668	+	0.791886i	$0.290901\pi$
$600$	−4.00000	−0.163299
$601$	−18.9647	−0.773588	−0.386794	−	0.922166i	$-0.626417\pi$
$601$	−18.9647	−0.773588	−0.386794	+	0.922166i	$0.626417\pi$
$602$	0	0
$603$	−10.3584	−0.421826
$604$	2.34509	0.0954203
$605$	2.35837	0.0958815
$606$	1.30982	0.0532079
$607$	23.5578	0.956182	0.478091	−	0.878310i	$-0.341329\pi$
$607$	23.5578	0.956182	0.478091	+	0.878310i	$0.341329\pi$
$608$	−5.50664	−0.223324
$609$	0	0
$610$	−10.0000	−0.404888
$611$	−2.00870	−0.0812633
$612$	−6.16155	−0.249066
$613$	−43.9295	−1.77429	−0.887147	−	0.461487i	$-0.847316\pi$
$613$	−43.9295	−1.77429	−0.887147	+	0.461487i	$0.847316\pi$
$614$	25.4095	1.02545
$615$	2.49336	0.100542
$616$	0	0
$617$	30.2878	1.21934	0.609671	−	0.792654i	$-0.291301\pi$
$617$	30.2878	1.21934	0.609671	+	0.792654i	$0.291301\pi$
$618$	3.64163	0.146488
$619$	−24.9049	−1.00101	−0.500506	−	0.865733i	$-0.666853\pi$
$619$	−24.9049	−1.00101	−0.500506	+	0.865733i	$0.666853\pi$
$620$	3.35837	0.134876
$621$	1.00000	0.0401286
$622$	5.54191	0.222210
$623$	0	0
$624$	0.851731	0.0340965
$625$	11.0000	0.440000
$626$	−19.1616	−0.765850
$627$	20.1263	0.803766
$628$	−24.8430	−0.991345
$629$	−42.0000	−1.67465
$630$	0	0
$631$	−28.4095	−1.13097	−0.565483	−	0.824760i	$-0.691310\pi$
$631$	−28.4095	−1.13097	−0.565483	+	0.824760i	$0.691310\pi$
$632$	11.4581	0.455778
$633$	9.01328	0.358246
$634$	−8.56848	−0.340298
$635$	−8.34509	−0.331165
$636$	−6.30982	−0.250201
$637$	0	0
$638$	15.1616	0.600252
$639$	−8.45809	−0.334597
$640$	−1.00000	−0.0395285
$641$	−15.0512	−0.594485	−0.297243	−	0.954802i	$-0.596067\pi$
$641$	−15.0512	−0.594485	−0.297243	+	0.954802i	$0.596067\pi$
$642$	−6.34509	−0.250421
$643$	9.80318	0.386600	0.193300	−	0.981140i	$-0.438081\pi$
$643$	9.80318	0.386600	0.193300	+	0.981140i	$0.438081\pi$
$644$	0	0
$645$	−7.30982	−0.287824
$646$	33.9295	1.33494
$647$	−31.5093	−1.23876	−0.619378	−	0.785093i	$-0.712615\pi$
$647$	−31.5093	−1.23876	−0.619378	+	0.785093i	$0.712615\pi$
$648$	−1.00000	−0.0392837
$649$	−11.5552	−0.453581
$650$	−3.40692	−0.133631
$651$	0	0
$652$	−22.8430	−0.894602
$653$	−41.5112	−1.62446	−0.812230	−	0.583337i	$-0.801747\pi$
$653$	−41.5112	−1.62446	−0.812230	+	0.583337i	$0.801747\pi$
$654$	3.30982	0.129424
$655$	5.09972	0.199262
$656$	−2.49336	−0.0973493
$657$	1.34509	0.0524769
$658$	0	0
$659$	−43.6329	−1.69970	−0.849849	−	0.527027i	$-0.823307\pi$
$659$	−43.6329	−1.69970	−0.849849	+	0.527027i	$0.823307\pi$
$660$	3.65491	0.142267
$661$	37.9826	1.47735	0.738676	−	0.674061i	$-0.235451\pi$
$661$	37.9826	1.47735	0.738676	+	0.674061i	$0.235451\pi$
$662$	−17.1396	−0.666148
$663$	−5.24799	−0.203815
$664$	7.65491	0.297068
$665$	0	0
$666$	−6.81646	−0.264133
$667$	−4.14827	−0.160622
$668$	4.06184	0.157157
$669$	15.9780	0.617746
$670$	10.3584	0.400179
$671$	−36.5491	−1.41096
$672$	0	0
$673$	36.2040	1.39556	0.697781	−	0.716311i	$-0.254171\pi$
$673$	36.2040	1.39556	0.697781	+	0.716311i	$0.254171\pi$
$674$	14.5685	0.561157
$675$	4.00000	0.153960
$676$	−12.2746	−0.472098
$677$	−29.6196	−1.13838	−0.569188	−	0.822208i	$-0.692742\pi$
$677$	−29.6196	−1.13838	−0.569188	+	0.822208i	$0.692742\pi$
$678$	9.17484	0.352357
$679$	0	0
$680$	6.16155	0.236285
$681$	13.9780	0.535639
$682$	12.2746	0.470017
$683$	36.8563	1.41027	0.705134	−	0.709074i	$-0.250887\pi$
$683$	36.8563	1.41027	0.705134	+	0.709074i	$0.250887\pi$
$684$	5.50664	0.210552
$685$	−2.95145	−0.112769
$686$	0	0
$687$	−28.5199	−1.08810
$688$	7.30982	0.278684
$689$	−5.37427	−0.204743
$690$	−1.00000	−0.0380693
$691$	−12.5465	−0.477291	−0.238646	−	0.971107i	$-0.576703\pi$
$691$	−12.5465	−0.477291	−0.238646	+	0.971107i	$0.576703\pi$
$692$	−3.70346	−0.140785
$693$	0	0
$694$	−7.04855	−0.267559
$695$	16.0266	0.607922
$696$	4.14827	0.157240
$697$	15.3630	0.581913
$698$	−22.4581	−0.850051
$699$	−11.1396	−0.421337
$700$	0	0
$701$	−12.6769	−0.478800	−0.239400	−	0.970921i	$-0.576951\pi$
$701$	−12.6769	−0.478800	−0.239400	+	0.970921i	$0.576951\pi$
$702$	−0.851731	−0.0321465
$703$	37.5358	1.41569
$704$	−3.65491	−0.137750
$705$	−2.35837	−0.0888215
$706$	−11.1396	−0.419243
$707$	0	0
$708$	−3.16155	−0.118818
$709$	−28.0292	−1.05266	−0.526329	−	0.850281i	$-0.676432\pi$
$709$	−28.0292	−1.05266	−0.526329	+	0.850281i	$0.676432\pi$
$710$	8.45809	0.317426
$711$	−11.4581	−0.429712
$712$	6.81646	0.255458
$713$	−3.35837	−0.125772
$714$	0	0
$715$	3.11300	0.116420
$716$	14.9780	0.559755
$717$	16.0000	0.597531
$718$	28.0266	1.04594
$719$	−15.2746	−0.569645	−0.284822	−	0.958580i	$-0.591935\pi$
$719$	−15.2746	−0.569645	−0.284822	+	0.958580i	$0.591935\pi$
$720$	1.00000	0.0372678
$721$	0	0
$722$	−11.3231	−0.421402
$723$	−16.5685	−0.616188
$724$	−1.70346	−0.0633087
$725$	−16.5931	−0.616251
$726$	2.35837	0.0875274
$727$	−2.51534	−0.0932889	−0.0466444	−	0.998912i	$-0.514853\pi$
$727$	−2.51534	−0.0932889	−0.0466444	+	0.998912i	$0.514853\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−1.34509	−0.0497840
$731$	−45.0399	−1.66586
$732$	−10.0000	−0.369611
$733$	44.8696	1.65730	0.828648	−	0.559770i	$-0.189110\pi$
$733$	44.8696	1.65730	0.828648	+	0.559770i	$0.189110\pi$
$734$	7.78990	0.287530
$735$	0	0
$736$	1.00000	0.0368605
$737$	37.8589	1.39455
$738$	2.49336	0.0917818
$739$	34.9693	1.28637	0.643184	−	0.765712i	$-0.277613\pi$
$739$	34.9693	1.28637	0.643184	+	0.765712i	$0.277613\pi$
$740$	6.81646	0.250578
$741$	4.69018	0.172298
$742$	0	0
$743$	−39.4627	−1.44775	−0.723873	−	0.689934i	$-0.757640\pi$
$743$	−39.4627	−1.44775	−0.723873	+	0.689934i	$0.757640\pi$
$744$	3.35837	0.123124
$745$	−19.9647	−0.731451
$746$	−12.7167	−0.465593
$747$	−7.65491	−0.280079
$748$	22.5199	0.823410
$749$	0	0
$750$	−9.00000	−0.328634
$751$	19.0644	0.695672	0.347836	−	0.937555i	$-0.386917\pi$
$751$	19.0644	0.695672	0.347836	+	0.937555i	$0.386917\pi$
$752$	2.35837	0.0860010
$753$	−30.2746	−1.10327
$754$	3.53321	0.128672
$755$	2.34509	0.0853465
$756$	0	0
$757$	13.2101	0.480129	0.240065	−	0.970757i	$-0.422831\pi$
$757$	13.2101	0.480129	0.240065	+	0.970757i	$0.422831\pi$
$758$	22.2613	0.808566
$759$	−3.65491	−0.132665
$760$	−5.50664	−0.199747
$761$	50.3523	1.82527	0.912635	−	0.408777i	$-0.134044\pi$
$761$	50.3523	1.82527	0.912635	+	0.408777i	$0.134044\pi$
$762$	−8.34509	−0.302311
$763$	0	0
$764$	−22.8430	−0.826432
$765$	−6.16155	−0.222771
$766$	22.2234	0.802964
$767$	−2.69279	−0.0972311
$768$	−1.00000	−0.0360844
$769$	42.4008	1.52901	0.764507	−	0.644616i	$-0.222983\pi$
$769$	42.4008	1.52901	0.764507	+	0.644616i	$0.222983\pi$
$770$	0	0
$771$	14.1263	0.508746
$772$	−17.9162	−0.644817
$773$	17.6682	0.635481	0.317740	−	0.948178i	$-0.397076\pi$
$773$	17.6682	0.635481	0.317740	+	0.948178i	$0.397076\pi$
$774$	−7.30982	−0.262746
$775$	−13.4335	−0.482545
$776$	−0.444807	−0.0159676
$777$	0	0
$778$	30.7433	1.10220
$779$	−13.7300	−0.491929
$780$	0.851731	0.0304969
$781$	30.9136	1.10617
$782$	−6.16155	−0.220337
$783$	−4.14827	−0.148247
$784$	0	0
$785$	−24.8430	−0.886686
$786$	5.09972	0.181901
$787$	29.3717	1.04699	0.523493	−	0.852030i	$-0.324629\pi$
$787$	29.3717	1.04699	0.523493	+	0.852030i	$0.324629\pi$
$788$	5.01328	0.178591
$789$	15.3098	0.545044
$790$	11.4581	0.407661
$791$	0	0
$792$	3.65491	0.129872
$793$	−8.51731	−0.302459
$794$	6.16155	0.218665
$795$	−6.30982	−0.223786
$796$	14.3231	0.507669
$797$	−12.6064	−0.446540	−0.223270	−	0.974757i	$-0.571673\pi$
$797$	−12.6064	−0.446540	−0.223270	+	0.974757i	$0.571673\pi$
$798$	0	0
$799$	−14.5312	−0.514078
$800$	4.00000	0.141421
$801$	−6.81646	−0.240848
$802$	15.9647	0.563734
$803$	−4.91618	−0.173488
$804$	10.3584	0.365312
$805$	0	0
$806$	2.86043	0.100754
$807$	22.4714	0.791030
$808$	−1.30982	−0.0460794
$809$	36.4494	1.28149	0.640746	−	0.767753i	$-0.278625\pi$
$809$	36.4494	1.28149	0.640746	+	0.767753i	$0.278625\pi$
$810$	−1.00000	−0.0351364
$811$	22.6462	0.795216	0.397608	−	0.917555i	$-0.369840\pi$
$811$	22.6462	0.795216	0.397608	+	0.917555i	$0.369840\pi$
$812$	0	0
$813$	14.3717	0.504036
$814$	24.9136	0.873220
$815$	−22.8430	−0.800156
$816$	6.16155	0.215697
$817$	40.2526	1.40826
$818$	14.7300	0.515023
$819$	0	0
$820$	−2.49336	−0.0870718
$821$	−34.1483	−1.19178	−0.595891	−	0.803065i	$-0.703201\pi$
$821$	−34.1483	−1.19178	−0.595891	+	0.803065i	$0.703201\pi$
$822$	−2.95145	−0.102944
$823$	−4.12367	−0.143742	−0.0718711	−	0.997414i	$-0.522897\pi$
$823$	−4.12367	−0.143742	−0.0718711	+	0.997414i	$0.522897\pi$
$824$	−3.64163	−0.126862
$825$	−14.6196	−0.508991
$826$	0	0
$827$	−50.6508	−1.76130	−0.880650	−	0.473767i	$-0.842894\pi$
$827$	−50.6508	−1.76130	−0.880650	+	0.473767i	$0.842894\pi$
$828$	−1.00000	−0.0347524
$829$	47.8942	1.66343	0.831717	−	0.555200i	$-0.187358\pi$
$829$	47.8942	1.66343	0.831717	+	0.555200i	$0.187358\pi$
$830$	7.65491	0.265706
$831$	11.9647	0.415052
$832$	−0.851731	−0.0295285
$833$	0	0
$834$	16.0266	0.554955
$835$	4.06184	0.140566
$836$	−20.1263	−0.696082
$837$	−3.35837	−0.116082
$838$	−24.9427	−0.861633
$839$	14.7899	0.510604	0.255302	−	0.966861i	$-0.417825\pi$
$839$	14.7899	0.510604	0.255302	+	0.966861i	$0.417825\pi$
$840$	0	0
$841$	−11.7919	−0.406616
$842$	−32.3497	−1.11484
$843$	−11.0512	−0.380622
$844$	−9.01328	−0.310250
$845$	−12.2746	−0.422257
$846$	−2.35837	−0.0810825
$847$	0	0
$848$	6.30982	0.216680
$849$	−3.93816	−0.135157
$850$	−24.6462	−0.845358
$851$	−6.81646	−0.233665
$852$	8.45809	0.289769
$853$	−21.6064	−0.739788	−0.369894	−	0.929074i	$-0.620606\pi$
$853$	−21.6064	−0.739788	−0.369894	+	0.929074i	$0.620606\pi$
$854$	0	0
$855$	5.50664	0.188323
$856$	6.34509	0.216871
$857$	13.7326	0.469098	0.234549	−	0.972104i	$-0.424639\pi$
$857$	13.7326	0.469098	0.234549	+	0.972104i	$0.424639\pi$
$858$	3.11300	0.106276
$859$	−35.7858	−1.22100	−0.610498	−	0.792018i	$-0.709030\pi$
$859$	−35.7858	−1.22100	−0.610498	+	0.792018i	$0.709030\pi$
$860$	7.30982	0.249263
$861$	0	0
$862$	−4.59308	−0.156441
$863$	6.09102	0.207341	0.103670	−	0.994612i	$-0.466941\pi$
$863$	6.09102	0.207341	0.103670	+	0.994612i	$0.466941\pi$
$864$	1.00000	0.0340207
$865$	−3.70346	−0.125921
$866$	−27.2393	−0.925629
$867$	−20.9647	−0.712000
$868$	0	0
$869$	41.8783	1.42062
$870$	4.14827	0.140639
$871$	8.82255	0.298941
$872$	−3.30982	−0.112085
$873$	0.444807	0.0150544
$874$	5.50664	0.186265
$875$	0	0
$876$	−1.34509	−0.0454464
$877$	−38.4847	−1.29953	−0.649767	−	0.760133i	$-0.725134\pi$
$877$	−38.4847	−1.29953	−0.649767	+	0.760133i	$0.725134\pi$
$878$	15.9514	0.538335
$879$	−13.0266	−0.439375
$880$	−3.65491	−0.123207
$881$	−21.9647	−0.740011	−0.370005	−	0.929030i	$-0.620644\pi$
$881$	−21.9647	−0.740011	−0.370005	+	0.929030i	$0.620644\pi$
$882$	0	0
$883$	−16.4228	−0.552672	−0.276336	−	0.961061i	$-0.589120\pi$
$883$	−16.4228	−0.552672	−0.276336	+	0.961061i	$0.589120\pi$
$884$	5.24799	0.176509
$885$	−3.16155	−0.106274
$886$	29.1263	0.978517
$887$	17.3804	0.583575	0.291788	−	0.956483i	$-0.405750\pi$
$887$	17.3804	0.583575	0.291788	+	0.956483i	$0.405750\pi$
$888$	6.81646	0.228746
$889$	0	0
$890$	6.81646	0.228488
$891$	−3.65491	−0.122444
$892$	−15.9780	−0.534984
$893$	12.9867	0.434584
$894$	−19.9647	−0.667721
$895$	14.9780	0.500660
$896$	0	0
$897$	−0.851731	−0.0284385
$898$	18.2234	0.608122
$899$	13.9314	0.464639
$900$	−4.00000	−0.133333
$901$	−38.8783	−1.29522
$902$	−9.11300	−0.303430
$903$	0	0
$904$	−9.17484	−0.305151
$905$	−1.70346	−0.0566250
$906$	2.34509	0.0779104
$907$	−18.8517	−0.625961	−0.312981	−	0.949759i	$-0.601328\pi$
$907$	−18.8517	−0.625961	−0.312981	+	0.949759i	$0.601328\pi$
$908$	−13.9780	−0.463877
$909$	1.30982	0.0434440
$910$	0	0
$911$	57.9826	1.92105	0.960525	−	0.278195i	$-0.0897361\pi$
$911$	57.9826	1.92105	0.960525	+	0.278195i	$0.0897361\pi$
$912$	−5.50664	−0.182343
$913$	27.9780	0.925937
$914$	−10.2719	−0.339766
$915$	−10.0000	−0.330590
$916$	28.5199	0.942325
$917$	0	0
$918$	−6.16155	−0.203362
$919$	38.2613	1.26212	0.631061	−	0.775733i	$-0.282620\pi$
$919$	38.2613	1.26212	0.631061	+	0.775733i	$0.282620\pi$
$920$	1.00000	0.0329690
$921$	25.4095	0.837273
$922$	−20.6196	−0.679072
$923$	7.20402	0.237123
$924$	0	0
$925$	−27.2659	−0.896496
$926$	−15.3098	−0.503112
$927$	3.64163	0.119607
$928$	−4.14827	−0.136174
$929$	−43.8829	−1.43975	−0.719875	−	0.694103i	$-0.755801\pi$
$929$	−43.8829	−1.43975	−0.719875	+	0.694103i	$0.755801\pi$
$930$	3.35837	0.110125
$931$	0	0
$932$	11.1396	0.364889
$933$	5.54191	0.181434
$934$	−7.30982	−0.239185
$935$	22.5199	0.736480
$936$	0.851731	0.0278397
$937$	−56.6974	−1.85222	−0.926111	−	0.377250i	$-0.876870\pi$
$937$	−56.6974	−1.85222	−0.926111	+	0.377250i	$0.876870\pi$
$938$	0	0
$939$	−19.1616	−0.625314
$940$	2.35837	0.0769216
$941$	42.2746	1.37811	0.689056	−	0.724709i	$-0.258026\pi$
$941$	42.2746	1.37811	0.689056	+	0.724709i	$0.258026\pi$
$942$	−24.8430	−0.809430
$943$	2.49336	0.0811949
$944$	3.16155	0.102900
$945$	0	0
$946$	26.7167	0.868636
$947$	−36.0618	−1.17185	−0.585926	−	0.810364i	$-0.699269\pi$
$947$	−36.0618	−1.17185	−0.585926	+	0.810364i	$0.699269\pi$
$948$	11.4581	0.372141
$949$	−1.14565	−0.0371895
$950$	22.0266	0.714636
$951$	−8.56848	−0.277852
$952$	0	0
$953$	29.0133	0.939832	0.469916	−	0.882711i	$-0.344284\pi$
$953$	29.0133	0.939832	0.469916	+	0.882711i	$0.344284\pi$
$954$	−6.30982	−0.204288
$955$	−22.8430	−0.739183
$956$	−16.0000	−0.517477
$957$	15.1616	0.490103
$958$	33.1130	1.06983
$959$	0	0
$960$	−1.00000	−0.0322749
$961$	−19.7213	−0.636172
$962$	5.80579	0.187186
$963$	−6.34509	−0.204468
$964$	16.5685	0.533635
$965$	−17.9162	−0.576742
$966$	0	0
$967$	35.5844	1.14432	0.572158	−	0.820143i	$-0.306106\pi$
$967$	35.5844	1.14432	0.572158	+	0.820143i	$0.306106\pi$
$968$	−2.35837	−0.0758010
$969$	33.9295	1.08997
$970$	−0.444807	−0.0142819
$971$	−25.6549	−0.823305	−0.411653	−	0.911341i	$-0.635048\pi$
$971$	−25.6549	−0.823305	−0.411653	+	0.911341i	$0.635048\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	27.3849	0.877470
$975$	−3.40692	−0.109109
$976$	10.0000	0.320092
$977$	19.0751	0.610267	0.305134	−	0.952310i	$-0.401299\pi$
$977$	19.0751	0.610267	0.305134	+	0.952310i	$0.401299\pi$
$978$	−22.8430	−0.730440
$979$	24.9136	0.796241
$980$	0	0
$981$	3.30982	0.105674
$982$	−19.8165	−0.632369
$983$	−33.1396	−1.05699	−0.528494	−	0.848937i	$-0.677243\pi$
$983$	−33.1396	−1.05699	−0.528494	+	0.848937i	$0.677243\pi$
$984$	−2.49336	−0.0794854
$985$	5.01328	0.159737
$986$	25.5598	0.813989
$987$	0	0
$988$	−4.69018	−0.149214
$989$	−7.30982	−0.232439
$990$	3.65491	0.116161
$991$	1.28784	0.0409095	0.0204548	−	0.999791i	$-0.493489\pi$
$991$	1.28784	0.0409095	0.0204548	+	0.999791i	$0.493489\pi$
$992$	−3.35837	−0.106628
$993$	−17.1396	−0.543908
$994$	0	0
$995$	14.3231	0.454073
$996$	7.65491	0.242555
$997$	20.1968	0.639640	0.319820	−	0.947478i	$-0.396378\pi$
$997$	20.1968	0.639640	0.319820	+	0.947478i	$0.396378\pi$
$998$	36.3497	1.15063
$999$	−6.81646	−0.215663

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6762.2.a.ce.1.1		3
7.2	even	3		966.2.i.k.277.1	✓	6
7.4	even	3		966.2.i.k.415.1	yes	6
7.6	odd	2		6762.2.a.cf.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.k.277.1	✓	6	7.2	even	3
966.2.i.k.415.1	yes	6	7.4	even	3
6762.2.a.ce.1.1		3	1.1	even	1	trivial
6762.2.a.cf.1.1		3	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6762 = 2 \cdot 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6762.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -3.65491 q^{11} -1.00000 q^{12} -0.851731 q^{13} -1.00000 q^{15} +1.00000 q^{16} -6.16155 q^{17} -1.00000 q^{18} +5.50664 q^{19} +1.00000 q^{20} +3.65491 q^{22} -1.00000 q^{23} +1.00000 q^{24} -4.00000 q^{25} +0.851731 q^{26} -1.00000 q^{27} +4.14827 q^{29} +1.00000 q^{30} +3.35837 q^{31} -1.00000 q^{32} +3.65491 q^{33} +6.16155 q^{34} +1.00000 q^{36} +6.81646 q^{37} -5.50664 q^{38} +0.851731 q^{39} -1.00000 q^{40} -2.49336 q^{41} +7.30982 q^{43} -3.65491 q^{44} +1.00000 q^{45} +1.00000 q^{46} +2.35837 q^{47} -1.00000 q^{48} +4.00000 q^{50} +6.16155 q^{51} -0.851731 q^{52} +6.30982 q^{53} +1.00000 q^{54} -3.65491 q^{55} -5.50664 q^{57} -4.14827 q^{58} +3.16155 q^{59} -1.00000 q^{60} +10.0000 q^{61} -3.35837 q^{62} +1.00000 q^{64} -0.851731 q^{65} -3.65491 q^{66} -10.3584 q^{67} -6.16155 q^{68} +1.00000 q^{69} -8.45809 q^{71} -1.00000 q^{72} +1.34509 q^{73} -6.81646 q^{74} +4.00000 q^{75} +5.50664 q^{76} -0.851731 q^{78} -11.4581 q^{79} +1.00000 q^{80} +1.00000 q^{81} +2.49336 q^{82} -7.65491 q^{83} -6.16155 q^{85} -7.30982 q^{86} -4.14827 q^{87} +3.65491 q^{88} -6.81646 q^{89} -1.00000 q^{90} -1.00000 q^{92} -3.35837 q^{93} -2.35837 q^{94} +5.50664 q^{95} +1.00000 q^{96} +0.444807 q^{97} -3.65491 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 - 3 * q^8 + 3 * q^9	\( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} - 3 q^{8} + 3 q^{9} - 3 q^{10} - 3 q^{12} - 3 q^{13} - 3 q^{15} + 3 q^{16} + 3 q^{17} - 3 q^{18} + 6 q^{19} + 3 q^{20} - 3 q^{23} + 3 q^{24} - 12 q^{25} + 3 q^{26} - 3 q^{27} + 12 q^{29} + 3 q^{30} - 3 q^{32} - 3 q^{34} + 3 q^{36} - 12 q^{37} - 6 q^{38} + 3 q^{39} - 3 q^{40} - 18 q^{41} + 3 q^{45} + 3 q^{46} - 3 q^{47} - 3 q^{48} + 12 q^{50} - 3 q^{51} - 3 q^{52} - 3 q^{53} + 3 q^{54} - 6 q^{57} - 12 q^{58} - 12 q^{59} - 3 q^{60} + 30 q^{61} + 3 q^{64} - 3 q^{65} - 21 q^{67} + 3 q^{68} + 3 q^{69} - 3 q^{71} - 3 q^{72} + 15 q^{73} + 12 q^{74} + 12 q^{75} + 6 q^{76} - 3 q^{78} - 12 q^{79} + 3 q^{80} + 3 q^{81} + 18 q^{82} - 12 q^{83} + 3 q^{85} - 12 q^{87} + 12 q^{89} - 3 q^{90} - 3 q^{92} + 3 q^{94} + 6 q^{95} + 3 q^{96}+O(q^{100}) \) 3 * q - 3 * q^2 - 3 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 - 3 * q^8 + 3 * q^9 - 3 * q^10 - 3 * q^12 - 3 * q^13 - 3 * q^15 + 3 * q^16 + 3 * q^17 - 3 * q^18 + 6 * q^19 + 3 * q^20 - 3 * q^23 + 3 * q^24 - 12 * q^25 + 3 * q^26 - 3 * q^27 + 12 * q^29 + 3 * q^30 - 3 * q^32 - 3 * q^34 + 3 * q^36 - 12 * q^37 - 6 * q^38 + 3 * q^39 - 3 * q^40 - 18 * q^41 + 3 * q^45 + 3 * q^46 - 3 * q^47 - 3 * q^48 + 12 * q^50 - 3 * q^51 - 3 * q^52 - 3 * q^53 + 3 * q^54 - 6 * q^57 - 12 * q^58 - 12 * q^59 - 3 * q^60 + 30 * q^61 + 3 * q^64 - 3 * q^65 - 21 * q^67 + 3 * q^68 + 3 * q^69 - 3 * q^71 - 3 * q^72 + 15 * q^73 + 12 * q^74 + 12 * q^75 + 6 * q^76 - 3 * q^78 - 12 * q^79 + 3 * q^80 + 3 * q^81 + 18 * q^82 - 12 * q^83 + 3 * q^85 - 12 * q^87 + 12 * q^89 - 3 * q^90 - 3 * q^92 + 3 * q^94 + 6 * q^95 + 3 * q^96

Introduction

L-functions

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