LMFDB - Embedded newform 6762.2.a.cf.1.3

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			1.3
Root			$4.05932$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +4.05932 q^{11} +1.00000 q^{12} +6.26870 q^{13} -1.00000 q^{15} +1.00000 q^{16} -3.84994 q^{17} -1.00000 q^{18} -3.20938 q^{19} -1.00000 q^{20} -4.05932 q^{22} -1.00000 q^{23} -1.00000 q^{24} -4.00000 q^{25} -6.26870 q^{26} +1.00000 q^{27} -1.26870 q^{29} +1.00000 q^{30} -6.47808 q^{31} -1.00000 q^{32} +4.05932 q^{33} +3.84994 q^{34} +1.00000 q^{36} -10.9093 q^{37} +3.20938 q^{38} +6.26870 q^{39} +1.00000 q^{40} +4.79062 q^{41} -8.11864 q^{43} +4.05932 q^{44} -1.00000 q^{45} +1.00000 q^{46} -5.47808 q^{47} +1.00000 q^{48} +4.00000 q^{50} -3.84994 q^{51} +6.26870 q^{52} -9.11864 q^{53} -1.00000 q^{54} -4.05932 q^{55} -3.20938 q^{57} +1.26870 q^{58} +6.84994 q^{59} -1.00000 q^{60} -10.0000 q^{61} +6.47808 q^{62} +1.00000 q^{64} -6.26870 q^{65} -4.05932 q^{66} -13.4781 q^{67} -3.84994 q^{68} -1.00000 q^{69} +12.3873 q^{71} -1.00000 q^{72} -9.05932 q^{73} +10.9093 q^{74} -4.00000 q^{75} -3.20938 q^{76} -6.26870 q^{78} +9.38734 q^{79} -1.00000 q^{80} +1.00000 q^{81} -4.79062 q^{82} -0.0593201 q^{83} +3.84994 q^{85} +8.11864 q^{86} -1.26870 q^{87} -4.05932 q^{88} -10.9093 q^{89} +1.00000 q^{90} -1.00000 q^{92} -6.47808 q^{93} +5.47808 q^{94} +3.20938 q^{95} -1.00000 q^{96} +15.8061 q^{97} +4.05932 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.571783\pi$
$5$	−1.00000	−0.447214	−0.223607	+	0.974679i	$0.571783\pi$
$6$	−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
$11$	4.05932	1.22393	0.611966	−	0.790884i	$-0.290379\pi$
$11$	4.05932	1.22393	0.611966	+	0.790884i	$0.290379\pi$
$12$	1.00000	0.288675
$13$	6.26870	1.73862	0.869312	−	0.494263i	$-0.164562\pi$
$13$	6.26870	1.73862	0.869312	+	0.494263i	$0.164562\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−3.84994	−0.933748	−0.466874	−	0.884324i	$-0.654620\pi$
$17$	−3.84994	−0.933748	−0.466874	+	0.884324i	$0.654620\pi$
$18$	−1.00000	−0.235702
$19$	−3.20938	−0.736282	−0.368141	−	0.929770i	$-0.620006\pi$
$19$	−3.20938	−0.736282	−0.368141	+	0.929770i	$0.620006\pi$
$20$	−1.00000	−0.223607
$21$	0	0
$22$	−4.05932	−0.865450
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.00000	−0.204124
$25$	−4.00000	−0.800000
$26$	−6.26870	−1.22939
$27$	1.00000	0.192450
$28$	0	0
$29$	−1.26870	−0.235592	−0.117796	−	0.993038i	$-0.537583\pi$
$29$	−1.26870	−0.235592	−0.117796	+	0.993038i	$0.537583\pi$
$30$	1.00000	0.182574
$31$	−6.47808	−1.16350	−0.581749	−	0.813369i	$-0.697631\pi$
$31$	−6.47808	−1.16350	−0.581749	+	0.813369i	$0.697631\pi$
$32$	−1.00000	−0.176777
$33$	4.05932	0.706637
$34$	3.84994	0.660259
$35$	0	0
$36$	1.00000	0.166667
$37$	−10.9093	−1.79347	−0.896736	−	0.442567i	$-0.854068\pi$
$37$	−10.9093	−1.79347	−0.896736	+	0.442567i	$0.854068\pi$
$38$	3.20938	0.520630
$39$	6.26870	1.00380
$40$	1.00000	0.158114
$41$	4.79062	0.748169	0.374085	−	0.927395i	$-0.377957\pi$
$41$	4.79062	0.748169	0.374085	+	0.927395i	$0.377957\pi$
$42$	0	0
$43$	−8.11864	−1.23808	−0.619041	−	0.785359i	$-0.712478\pi$
$43$	−8.11864	−1.23808	−0.619041	+	0.785359i	$0.712478\pi$
$44$	4.05932	0.611966
$45$	−1.00000	−0.149071
$46$	1.00000	0.147442
$47$	−5.47808	−0.799060	−0.399530	−	0.916720i	$-0.630827\pi$
$47$	−5.47808	−0.799060	−0.399530	+	0.916720i	$0.630827\pi$
$48$	1.00000	0.144338
$49$	0	0
$50$	4.00000	0.565685
$51$	−3.84994	−0.539099
$52$	6.26870	0.869312
$53$	−9.11864	−1.25254	−0.626271	−	0.779606i	$-0.715420\pi$
$53$	−9.11864	−1.25254	−0.626271	+	0.779606i	$0.715420\pi$
$54$	−1.00000	−0.136083
$55$	−4.05932	−0.547359
$56$	0	0
$57$	−3.20938	−0.425093
$58$	1.26870	0.166588
$59$	6.84994	0.891786	0.445893	−	0.895086i	$-0.352886\pi$
$59$	6.84994	0.891786	0.445893	+	0.895086i	$0.352886\pi$
$60$	−1.00000	−0.129099
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	6.47808	0.822717
$63$	0	0
$64$	1.00000	0.125000
$65$	−6.26870	−0.777537
$66$	−4.05932	−0.499668
$67$	−13.4781	−1.64661	−0.823305	−	0.567600i	$-0.807872\pi$
$67$	−13.4781	−1.64661	−0.823305	+	0.567600i	$0.807872\pi$
$68$	−3.84994	−0.466874
$69$	−1.00000	−0.120386
$70$	0	0
$71$	12.3873	1.47011	0.735053	−	0.678009i	$-0.237157\pi$
$71$	12.3873	1.47011	0.735053	+	0.678009i	$0.237157\pi$
$72$	−1.00000	−0.117851
$73$	−9.05932	−1.06031	−0.530157	−	0.847900i	$-0.677867\pi$
$73$	−9.05932	−1.06031	−0.530157	+	0.847900i	$0.677867\pi$
$74$	10.9093	1.26818
$75$	−4.00000	−0.461880
$76$	−3.20938	−0.368141
$77$	0	0
$78$	−6.26870	−0.709791
$79$	9.38734	1.05616	0.528079	−	0.849195i	$-0.322912\pi$
$79$	9.38734	1.05616	0.528079	+	0.849195i	$0.322912\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−4.79062	−0.529035
$83$	−0.0593201	−0.00651123	−0.00325562	−	0.999995i	$-0.501036\pi$
$83$	−0.0593201	−0.00651123	−0.00325562	+	0.999995i	$0.501036\pi$
$84$	0	0
$85$	3.84994	0.417585
$86$	8.11864	0.875455
$87$	−1.26870	−0.136019
$88$	−4.05932	−0.432725
$89$	−10.9093	−1.15638	−0.578190	−	0.815902i	$-0.696241\pi$
$89$	−10.9093	−1.15638	−0.578190	+	0.815902i	$0.696241\pi$
$90$	1.00000	0.105409
$91$	0	0
$92$	−1.00000	−0.104257
$93$	−6.47808	−0.671746
$94$	5.47808	0.565021
$95$	3.20938	0.329275
$96$	−1.00000	−0.102062
$97$	15.8061	1.60487	0.802433	−	0.596742i	$-0.203538\pi$
$97$	15.8061	1.60487	0.802433	+	0.596742i	$0.203538\pi$
$98$	0	0
$99$	4.05932	0.407977
$100$	−4.00000	−0.400000
$101$	14.1186	1.40486	0.702429	−	0.711754i	$-0.252099\pi$
$101$	14.1186	1.40486	0.702429	+	0.711754i	$0.252099\pi$
$102$	3.84994	0.381201
$103$	−0.521920	−0.0514263	−0.0257132	−	0.999669i	$-0.508186\pi$
$103$	−0.521920	−0.0514263	−0.0257132	+	0.999669i	$0.508186\pi$
$104$	−6.26870	−0.614697
$105$	0	0
$106$	9.11864	0.885681
$107$	−14.0593	−1.35917	−0.679583	−	0.733599i	$-0.737839\pi$
$107$	−14.0593	−1.35917	−0.679583	+	0.733599i	$0.737839\pi$
$108$	1.00000	0.0962250
$109$	−12.1186	−1.16076	−0.580378	−	0.814347i	$-0.697095\pi$
$109$	−12.1186	−1.16076	−0.580378	+	0.814347i	$0.697095\pi$
$110$	4.05932	0.387041
$111$	−10.9093	−1.03546
$112$	0	0
$113$	−5.43118	−0.510922	−0.255461	−	0.966819i	$-0.582227\pi$
$113$	−5.43118	−0.510922	−0.255461	+	0.966819i	$0.582227\pi$
$114$	3.20938	0.300586
$115$	1.00000	0.0932505
$116$	−1.26870	−0.117796
$117$	6.26870	0.579542
$118$	−6.84994	−0.630588
$119$	0	0
$120$	1.00000	0.0912871
$121$	5.47808	0.498007
$122$	10.0000	0.905357
$123$	4.79062	0.431956
$124$	−6.47808	−0.581749
$125$	9.00000	0.804984
$126$	0	0
$127$	−16.0593	−1.42503	−0.712517	−	0.701655i	$-0.752445\pi$
$127$	−16.0593	−1.42503	−0.712517	+	0.701655i	$0.752445\pi$
$128$	−1.00000	−0.0883883
$129$	−8.11864	−0.714806
$130$	6.26870	0.549801
$131$	18.8654	1.64828	0.824140	−	0.566387i	$-0.191659\pi$
$131$	18.8654	1.64828	0.824140	+	0.566387i	$0.191659\pi$
$132$	4.05932	0.353318
$133$	0	0
$134$	13.4781	1.16433
$135$	−1.00000	−0.0860663
$136$	3.84994	0.330130
$137$	15.5967	1.33252	0.666259	−	0.745721i	$-0.267895\pi$
$137$	15.5967	1.33252	0.666259	+	0.745721i	$0.267895\pi$
$138$	1.00000	0.0851257
$139$	−6.83752	−0.579951	−0.289975	−	0.957034i	$-0.593647\pi$
$139$	−6.83752	−0.579951	−0.289975	+	0.957034i	$0.593647\pi$
$140$	0	0
$141$	−5.47808	−0.461338
$142$	−12.3873	−1.03952
$143$	25.4467	2.12796
$144$	1.00000	0.0833333
$145$	1.26870	0.105360
$146$	9.05932	0.749755
$147$	0	0
$148$	−10.9093	−0.896736
$149$	3.17796	0.260349	0.130174	−	0.991491i	$-0.458446\pi$
$149$	3.17796	0.260349	0.130174	+	0.991491i	$0.458446\pi$
$150$	4.00000	0.326599
$151$	10.0593	0.818616	0.409308	−	0.912396i	$-0.365770\pi$
$151$	10.0593	0.818616	0.409308	+	0.912396i	$0.365770\pi$
$152$	3.20938	0.260315
$153$	−3.84994	−0.311249
$154$	0	0
$155$	6.47808	0.520332
$156$	6.26870	0.501898
$157$	−2.07174	−0.165343	−0.0826714	−	0.996577i	$-0.526345\pi$
$157$	−2.07174	−0.165343	−0.0826714	+	0.996577i	$0.526345\pi$
$158$	−9.38734	−0.746817
$159$	−9.11864	−0.723155
$160$	1.00000	0.0790569
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	4.07174	0.318923	0.159462	−	0.987204i	$-0.449024\pi$
$163$	4.07174	0.318923	0.159462	+	0.987204i	$0.449024\pi$
$164$	4.79062	0.374085
$165$	−4.05932	−0.316018
$166$	0.0593201	0.00460414
$167$	−18.0155	−1.39408	−0.697040	−	0.717032i	$-0.745500\pi$
$167$	−18.0155	−1.39408	−0.697040	+	0.717032i	$0.745500\pi$
$168$	0	0
$169$	26.2966	2.02282
$170$	−3.84994	−0.295277
$171$	−3.20938	−0.245427
$172$	−8.11864	−0.619041
$173$	14.5374	1.10526	0.552629	−	0.833427i	$-0.313625\pi$
$173$	14.5374	1.10526	0.552629	+	0.833427i	$0.313625\pi$
$174$	1.26870	0.0961799
$175$	0	0
$176$	4.05932	0.305983
$177$	6.84994	0.514873
$178$	10.9093	0.817684
$179$	−12.7592	−0.953667	−0.476834	−	0.878994i	$-0.658216\pi$
$179$	−12.7592	−0.953667	−0.476834	+	0.878994i	$0.658216\pi$
$180$	−1.00000	−0.0745356
$181$	12.5374	0.931898	0.465949	−	0.884812i	$-0.345713\pi$
$181$	12.5374	0.931898	0.465949	+	0.884812i	$0.345713\pi$
$182$	0	0
$183$	−10.0000	−0.739221
$184$	1.00000	0.0737210
$185$	10.9093	0.802065
$186$	6.47808	0.474996
$187$	−15.6281	−1.14284
$188$	−5.47808	−0.399530
$189$	0	0
$190$	−3.20938	−0.232833
$191$	4.07174	0.294621	0.147310	−	0.989090i	$-0.452938\pi$
$191$	4.07174	0.294621	0.147310	+	0.989090i	$0.452938\pi$
$192$	1.00000	0.0721688
$193$	23.7747	1.71134	0.855669	−	0.517523i	$-0.173146\pi$
$193$	23.7747	1.71134	0.855669	+	0.517523i	$0.173146\pi$
$194$	−15.8061	−1.13481
$195$	−6.26870	−0.448911
$196$	0	0
$197$	0.418760	0.0298354	0.0149177	−	0.999889i	$-0.495251\pi$
$197$	0.418760	0.0298354	0.0149177	+	0.999889i	$0.495251\pi$
$198$	−4.05932	−0.288483
$199$	5.69988	0.404054	0.202027	−	0.979380i	$-0.435247\pi$
$199$	5.69988	0.404054	0.202027	+	0.979380i	$0.435247\pi$
$200$	4.00000	0.282843
$201$	−13.4781	−0.950670
$202$	−14.1186	−0.993384
$203$	0	0
$204$	−3.84994	−0.269550
$205$	−4.79062	−0.334591
$206$	0.521920	0.0363639
$207$	−1.00000	−0.0695048
$208$	6.26870	0.434656
$209$	−13.0279	−0.901159
$210$	0	0
$211$	−4.41876	−0.304200	−0.152100	−	0.988365i	$-0.548604\pi$
$211$	−4.41876	−0.304200	−0.152100	+	0.988365i	$0.548604\pi$
$212$	−9.11864	−0.626271
$213$	12.3873	0.848767
$214$	14.0593	0.961075
$215$	8.11864	0.553687
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	12.1186	0.820778
$219$	−9.05932	−0.612172
$220$	−4.05932	−0.273679
$221$	−24.1341	−1.62344
$222$	10.9093	0.732182
$223$	−11.7592	−0.787454	−0.393727	−	0.919227i	$-0.628815\pi$
$223$	−11.7592	−0.787454	−0.393727	+	0.919227i	$0.628815\pi$
$224$	0	0
$225$	−4.00000	−0.266667
$226$	5.43118	0.361277
$227$	−13.7592	−0.913230	−0.456615	−	0.889664i	$-0.650938\pi$
$227$	−13.7592	−0.913230	−0.456615	+	0.889664i	$0.650938\pi$
$228$	−3.20938	−0.212546
$229$	−21.6281	−1.42923	−0.714614	−	0.699519i	$-0.753398\pi$
$229$	−21.6281	−1.42923	−0.714614	+	0.699519i	$0.753398\pi$
$230$	−1.00000	−0.0659380
$231$	0	0
$232$	1.26870	0.0832942
$233$	−26.6091	−1.74322	−0.871611	−	0.490198i	$-0.836925\pi$
$233$	−26.6091	−1.74322	−0.871611	+	0.490198i	$0.836925\pi$
$234$	−6.26870	−0.409798
$235$	5.47808	0.357351
$236$	6.84994	0.445893
$237$	9.38734	0.609773
$238$	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
$241$	−28.2249	−1.81812	−0.909062	−	0.416662i	$-0.863200\pi$
$241$	−28.2249	−1.81812	−0.909062	+	0.416662i	$0.863200\pi$
$242$	−5.47808	−0.352144
$243$	1.00000	0.0641500
$244$	−10.0000	−0.640184
$245$	0	0
$246$	−4.79062	−0.305439
$247$	−20.1186	−1.28012
$248$	6.47808	0.411358
$249$	−0.0593201	−0.00375926
$250$	−9.00000	−0.569210
$251$	8.29660	0.523677	0.261838	−	0.965112i	$-0.415671\pi$
$251$	8.29660	0.523677	0.261838	+	0.965112i	$0.415671\pi$
$252$	0	0
$253$	−4.05932	−0.255207
$254$	16.0593	1.00765
$255$	3.84994	0.241093
$256$	1.00000	0.0625000
$257$	−19.0279	−1.18693	−0.593464	−	0.804861i	$-0.702240\pi$
$257$	−19.0279	−1.18693	−0.593464	+	0.804861i	$0.702240\pi$
$258$	8.11864	0.505444
$259$	0	0
$260$	−6.26870	−0.388768
$261$	−1.26870	−0.0785306
$262$	−18.8654	−1.16551
$263$	0.118640	0.00731567	0.00365784	−	0.999993i	$-0.498836\pi$
$263$	0.118640	0.00731567	0.00365784	+	0.999993i	$0.498836\pi$
$264$	−4.05932	−0.249834
$265$	9.11864	0.560154
$266$	0	0
$267$	−10.9093	−0.667636
$268$	−13.4781	−0.823305
$269$	−2.96858	−0.180998	−0.0904988	−	0.995897i	$-0.528846\pi$
$269$	−2.96858	−0.180998	−0.0904988	+	0.995897i	$0.528846\pi$
$270$	1.00000	0.0608581
$271$	12.8968	0.783427	0.391714	−	0.920087i	$-0.371882\pi$
$271$	12.8968	0.783427	0.391714	+	0.920087i	$0.371882\pi$
$272$	−3.84994	−0.233437
$273$	0	0
$274$	−15.5967	−0.942232
$275$	−16.2373	−0.979145
$276$	−1.00000	−0.0601929
$277$	11.1780	0.671619	0.335809	−	0.941930i	$-0.390990\pi$
$277$	11.1780	0.671619	0.335809	+	0.941930i	$0.390990\pi$
$278$	6.83752	0.410087
$279$	−6.47808	−0.387833
$280$	0	0
$281$	−31.4621	−1.87687	−0.938437	−	0.345450i	$-0.887726\pi$
$281$	−31.4621	−1.87687	−0.938437	+	0.345450i	$0.887726\pi$
$282$	5.47808	0.326215
$283$	10.0155	0.595358	0.297679	−	0.954666i	$-0.403787\pi$
$283$	10.0155	0.595358	0.297679	+	0.954666i	$0.403787\pi$
$284$	12.3873	0.735053
$285$	3.20938	0.190107
$286$	−25.4467	−1.50469
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	−2.17796	−0.128115
$290$	−1.26870	−0.0745006
$291$	15.8061	0.926570
$292$	−9.05932	−0.530157
$293$	−3.83752	−0.224190	−0.112095	−	0.993697i	$-0.535756\pi$
$293$	−3.83752	−0.224190	−0.112095	+	0.993697i	$0.535756\pi$
$294$	0	0
$295$	−6.84994	−0.398819
$296$	10.9093	0.634088
$297$	4.05932	0.235546
$298$	−3.17796	−0.184094
$299$	−6.26870	−0.362528
$300$	−4.00000	−0.230940
$301$	0	0
$302$	−10.0593	−0.578849
$303$	14.1186	0.811095
$304$	−3.20938	−0.184071
$305$	10.0000	0.572598
$306$	3.84994	0.220086
$307$	−13.9841	−0.798112	−0.399056	−	0.916926i	$-0.630662\pi$
$307$	−13.9841	−0.798112	−0.399056	+	0.916926i	$0.630662\pi$
$308$	0	0
$309$	−0.521920	−0.0296910
$310$	−6.47808	−0.367930
$311$	26.3873	1.49629	0.748144	−	0.663536i	$-0.230945\pi$
$311$	26.3873	1.49629	0.748144	+	0.663536i	$0.230945\pi$
$312$	−6.26870	−0.354895
$313$	−9.15006	−0.517192	−0.258596	−	0.965986i	$-0.583260\pi$
$313$	−9.15006	−0.517192	−0.258596	+	0.965986i	$0.583260\pi$
$314$	2.07174	0.116915
$315$	0	0
$316$	9.38734	0.528079
$317$	20.2249	1.13594	0.567971	−	0.823049i	$-0.307729\pi$
$317$	20.2249	1.13594	0.567971	+	0.823049i	$0.307729\pi$
$318$	9.11864	0.511348
$319$	−5.15006	−0.288348
$320$	−1.00000	−0.0559017
$321$	−14.0593	−0.784715
$322$	0	0
$323$	12.3559	0.687502
$324$	1.00000	0.0555556
$325$	−25.0748	−1.39090
$326$	−4.07174	−0.225513
$327$	−12.1186	−0.670162
$328$	−4.79062	−0.264518
$329$	0	0
$330$	4.05932	0.223458
$331$	−20.6091	−1.13278	−0.566390	−	0.824137i	$-0.691661\pi$
$331$	−20.6091	−1.13278	−0.566390	+	0.824137i	$0.691661\pi$
$332$	−0.0593201	−0.00325562
$333$	−10.9093	−0.597824
$334$	18.0155	0.985763
$335$	13.4781	0.736386
$336$	0	0
$337$	−26.2249	−1.42856	−0.714280	−	0.699860i	$-0.753245\pi$
$337$	−26.2249	−1.42856	−0.714280	+	0.699860i	$0.753245\pi$
$338$	−26.2966	−1.43035
$339$	−5.43118	−0.294981
$340$	3.84994	0.208792
$341$	−26.2966	−1.42404
$342$	3.20938	0.173543
$343$	0	0
$344$	8.11864	0.437728
$345$	1.00000	0.0538382
$346$	−14.5374	−0.781535
$347$	25.5967	1.37410	0.687052	−	0.726608i	$-0.258904\pi$
$347$	25.5967	1.37410	0.687052	+	0.726608i	$0.258904\pi$
$348$	−1.26870	−0.0680095
$349$	−1.61266	−0.0863237	−0.0431618	−	0.999068i	$-0.513743\pi$
$349$	−1.61266	−0.0863237	−0.0431618	+	0.999068i	$0.513743\pi$
$350$	0	0
$351$	6.26870	0.334598
$352$	−4.05932	−0.216362
$353$	26.6091	1.41626	0.708131	−	0.706081i	$-0.249539\pi$
$353$	26.6091	1.41626	0.708131	+	0.706081i	$0.249539\pi$
$354$	−6.84994	−0.364070
$355$	−12.3873	−0.657452
$356$	−10.9093	−0.578190
$357$	0	0
$358$	12.7592	0.674345
$359$	−18.8375	−0.994206	−0.497103	−	0.867691i	$-0.665603\pi$
$359$	−18.8375	−0.994206	−0.497103	+	0.867691i	$0.665603\pi$
$360$	1.00000	0.0527046
$361$	−8.69988	−0.457888
$362$	−12.5374	−0.658951
$363$	5.47808	0.287525
$364$	0	0
$365$	9.05932	0.474186
$366$	10.0000	0.522708
$367$	−0.746780	−0.0389816	−0.0194908	−	0.999810i	$-0.506205\pi$
$367$	−0.746780	−0.0389816	−0.0194908	+	0.999810i	$0.506205\pi$
$368$	−1.00000	−0.0521286
$369$	4.79062	0.249390
$370$	−10.9093	−0.567145
$371$	0	0
$372$	−6.47808	−0.335873
$373$	18.9562	0.981513	0.490756	−	0.871297i	$-0.336721\pi$
$373$	18.9562	0.981513	0.490756	+	0.871297i	$0.336721\pi$
$374$	15.6281	0.808112
$375$	9.00000	0.464758
$376$	5.47808	0.282510
$377$	−7.95310	−0.409606
$378$	0	0
$379$	11.7154	0.601778	0.300889	−	0.953659i	$-0.402717\pi$
$379$	11.7154	0.601778	0.300889	+	0.953659i	$0.402717\pi$
$380$	3.20938	0.164638
$381$	−16.0593	−0.822744
$382$	−4.07174	−0.208328
$383$	26.1655	1.33700	0.668498	−	0.743714i	$-0.266937\pi$
$383$	26.1655	1.33700	0.668498	+	0.743714i	$0.266937\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−23.7747	−1.21010
$387$	−8.11864	−0.412694
$388$	15.8061	0.802433
$389$	−27.7937	−1.40920	−0.704598	−	0.709607i	$-0.748873\pi$
$389$	−27.7937	−1.40920	−0.704598	+	0.709607i	$0.748873\pi$
$390$	6.26870	0.317428
$391$	3.84994	0.194700
$392$	0	0
$393$	18.8654	0.951635
$394$	−0.418760	−0.0210968
$395$	−9.38734	−0.472328
$396$	4.05932	0.203989
$397$	−3.84994	−0.193223	−0.0966115	−	0.995322i	$-0.530800\pi$
$397$	−3.84994	−0.193223	−0.0966115	+	0.995322i	$0.530800\pi$
$398$	−5.69988	−0.285709
$399$	0	0
$400$	−4.00000	−0.200000
$401$	7.17796	0.358450	0.179225	−	0.983808i	$-0.442641\pi$
$401$	7.17796	0.358450	0.179225	+	0.983808i	$0.442641\pi$
$402$	13.4781	0.672226
$403$	−40.6091	−2.02289
$404$	14.1186	0.702429
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	−44.2842	−2.19509
$408$	3.84994	0.190600
$409$	16.3749	0.809688	0.404844	−	0.914386i	$-0.367326\pi$
$409$	16.3749	0.809688	0.404844	+	0.914386i	$0.367326\pi$
$410$	4.79062	0.236592
$411$	15.5967	0.769329
$412$	−0.521920	−0.0257132
$413$	0	0
$414$	1.00000	0.0491473
$415$	0.0593201	0.00291191
$416$	−6.26870	−0.307348
$417$	−6.83752	−0.334835
$418$	13.0279	0.637215
$419$	25.9372	1.26711	0.633557	−	0.773696i	$-0.281594\pi$
$419$	25.9372	1.26711	0.633557	+	0.773696i	$0.281594\pi$
$420$	0	0
$421$	3.13764	0.152919	0.0764596	−	0.997073i	$-0.475638\pi$
$421$	3.13764	0.152919	0.0764596	+	0.997073i	$0.475638\pi$
$422$	4.41876	0.215102
$423$	−5.47808	−0.266353
$424$	9.11864	0.442840
$425$	15.3998	0.746998
$426$	−12.3873	−0.600169
$427$	0	0
$428$	−14.0593	−0.679583
$429$	25.4467	1.22858
$430$	−8.11864	−0.391516
$431$	−17.0748	−0.822464	−0.411232	−	0.911531i	$-0.634901\pi$
$431$	−17.0748	−0.822464	−0.411232	+	0.911531i	$0.634901\pi$
$432$	1.00000	0.0481125
$433$	34.4746	1.65674	0.828371	−	0.560180i	$-0.189268\pi$
$433$	34.4746	1.65674	0.828371	+	0.560180i	$0.189268\pi$
$434$	0	0
$435$	1.26870	0.0608295
$436$	−12.1186	−0.580378
$437$	3.20938	0.153525
$438$	9.05932	0.432871
$439$	−2.59672	−0.123935	−0.0619673	−	0.998078i	$-0.519737\pi$
$439$	−2.59672	−0.123935	−0.0619673	+	0.998078i	$0.519737\pi$
$440$	4.05932	0.193520
$441$	0	0
$442$	24.1341	1.14794
$443$	4.02790	0.191371	0.0956857	−	0.995412i	$-0.469496\pi$
$443$	4.02790	0.191371	0.0956857	+	0.995412i	$0.469496\pi$
$444$	−10.9093	−0.517731
$445$	10.9093	0.517149
$446$	11.7592	0.556814
$447$	3.17796	0.150312
$448$	0	0
$449$	−22.1655	−1.04606	−0.523028	−	0.852315i	$-0.675198\pi$
$449$	−22.1655	−1.04606	−0.523028	+	0.852315i	$0.675198\pi$
$450$	4.00000	0.188562
$451$	19.4467	0.915707
$452$	−5.43118	−0.255461
$453$	10.0593	0.472628
$454$	13.7592	0.645751
$455$	0	0
$456$	3.20938	0.150293
$457$	32.7623	1.53255	0.766277	−	0.642510i	$-0.222107\pi$
$457$	32.7623	1.53255	0.766277	+	0.642510i	$0.222107\pi$
$458$	21.6281	1.01062
$459$	−3.84994	−0.179700
$460$	1.00000	0.0466252
$461$	10.2373	0.476798	0.238399	−	0.971167i	$-0.423377\pi$
$461$	10.2373	0.476798	0.238399	+	0.971167i	$0.423377\pi$
$462$	0	0
$463$	−0.118640	−0.00551368	−0.00275684	−	0.999996i	$-0.500878\pi$
$463$	−0.118640	−0.00551368	−0.00275684	+	0.999996i	$0.500878\pi$
$464$	−1.26870	−0.0588979
$465$	6.47808	0.300414
$466$	26.6091	1.23264
$467$	8.11864	0.375686	0.187843	−	0.982199i	$-0.439850\pi$
$467$	8.11864	0.375686	0.187843	+	0.982199i	$0.439850\pi$
$468$	6.26870	0.289771
$469$	0	0
$470$	−5.47808	−0.252685
$471$	−2.07174	−0.0954608
$472$	−6.84994	−0.315294
$473$	−32.9562	−1.51533
$474$	−9.38734	−0.431175
$475$	12.8375	0.589026
$476$	0	0
$477$	−9.11864	−0.417514
$478$	16.0000	0.731823
$479$	4.55334	0.208047	0.104024	−	0.994575i	$-0.466828\pi$
$479$	4.55334	0.208047	0.104024	+	0.994575i	$0.466828\pi$
$480$	1.00000	0.0456435
$481$	−68.3869	−3.11817
$482$	28.2249	1.28561
$483$	0	0
$484$	5.47808	0.249004
$485$	−15.8061	−0.717718
$486$	−1.00000	−0.0453609
$487$	−21.3156	−0.965902	−0.482951	−	0.875647i	$-0.660435\pi$
$487$	−21.3156	−0.965902	−0.482951	+	0.875647i	$0.660435\pi$
$488$	10.0000	0.452679
$489$	4.07174	0.184130
$490$	0	0
$491$	2.09074	0.0943538	0.0471769	−	0.998887i	$-0.484978\pi$
$491$	2.09074	0.0943538	0.0471769	+	0.998887i	$0.484978\pi$
$492$	4.79062	0.215978
$493$	4.88442	0.219983
$494$	20.1186	0.905180
$495$	−4.05932	−0.182453
$496$	−6.47808	−0.290874
$497$	0	0
$498$	0.0593201	0.00265820
$499$	−7.13764	−0.319525	−0.159762	−	0.987156i	$-0.551073\pi$
$499$	−7.13764	−0.319525	−0.159762	+	0.987156i	$0.551073\pi$
$500$	9.00000	0.402492
$501$	−18.0155	−0.804872
$502$	−8.29660	−0.370295
$503$	−11.9372	−0.532252	−0.266126	−	0.963938i	$-0.585744\pi$
$503$	−11.9372	−0.532252	−0.266126	+	0.963938i	$0.585744\pi$
$504$	0	0
$505$	−14.1186	−0.628271
$506$	4.05932	0.180459
$507$	26.2966	1.16787
$508$	−16.0593	−0.712517
$509$	−1.56882	−0.0695367	−0.0347684	−	0.999395i	$-0.511069\pi$
$509$	−1.56882	−0.0695367	−0.0347684	+	0.999395i	$0.511069\pi$
$510$	−3.84994	−0.170478
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	−3.20938	−0.141698
$514$	19.0279	0.839285
$515$	0.521920	0.0229985
$516$	−8.11864	−0.357403
$517$	−22.2373	−0.977994
$518$	0	0
$519$	14.5374	0.638121
$520$	6.26870	0.274901
$521$	−6.75920	−0.296126	−0.148063	−	0.988978i	$-0.547304\pi$
$521$	−6.75920	−0.296126	−0.148063	+	0.988978i	$0.547304\pi$
$522$	1.26870	0.0555295
$523$	−7.71536	−0.337369	−0.168685	−	0.985670i	$-0.553952\pi$
$523$	−7.71536	−0.337369	−0.168685	+	0.985670i	$0.553952\pi$
$524$	18.8654	0.824140
$525$	0	0
$526$	−0.118640	−0.00517296
$527$	24.9402	1.08641
$528$	4.05932	0.176659
$529$	1.00000	0.0434783
$530$	−9.11864	−0.396088
$531$	6.84994	0.297262
$532$	0	0
$533$	30.0310	1.30079
$534$	10.9093	0.472090
$535$	14.0593	0.607837
$536$	13.4781	0.582164
$537$	−12.7592	−0.550600
$538$	2.96858	0.127985
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	−1.84994	−0.0795351	−0.0397676	−	0.999209i	$-0.512662\pi$
$541$	−1.84994	−0.0795351	−0.0397676	+	0.999209i	$0.512662\pi$
$542$	−12.8968	−0.553967
$543$	12.5374	0.538031
$544$	3.84994	0.165065
$545$	12.1186	0.519106
$546$	0	0
$547$	−37.6839	−1.61125	−0.805624	−	0.592427i	$-0.798170\pi$
$547$	−37.6839	−1.61125	−0.805624	+	0.592427i	$0.798170\pi$
$548$	15.5967	0.666259
$549$	−10.0000	−0.426790
$550$	16.2373	0.692360
$551$	4.07174	0.173462
$552$	1.00000	0.0425628
$553$	0	0
$554$	−11.1780	−0.474906
$555$	10.9093	0.463072
$556$	−6.83752	−0.289975
$557$	21.9965	0.932021	0.466010	−	0.884779i	$-0.345691\pi$
$557$	21.9965	0.932021	0.466010	+	0.884779i	$0.345691\pi$
$558$	6.47808	0.274239
$559$	−50.8933	−2.15256
$560$	0	0
$561$	−15.6281	−0.659821
$562$	31.4621	1.32715
$563$	35.8778	1.51207	0.756035	−	0.654531i	$-0.227134\pi$
$563$	35.8778	1.51207	0.756035	+	0.654531i	$0.227134\pi$
$564$	−5.47808	−0.230669
$565$	5.43118	0.228491
$566$	−10.0155	−0.420982
$567$	0	0
$568$	−12.3873	−0.519761
$569$	−21.0593	−0.882853	−0.441426	−	0.897298i	$-0.645527\pi$
$569$	−21.0593	−0.882853	−0.441426	+	0.897298i	$0.645527\pi$
$570$	−3.20938	−0.134426
$571$	−34.0624	−1.42547	−0.712733	−	0.701435i	$-0.752543\pi$
$571$	−34.0624	−1.42547	−0.712733	+	0.701435i	$0.752543\pi$
$572$	25.4467	1.06398
$573$	4.07174	0.170099
$574$	0	0
$575$	4.00000	0.166812
$576$	1.00000	0.0416667
$577$	−34.7154	−1.44522	−0.722610	−	0.691256i	$-0.757058\pi$
$577$	−34.7154	−1.44522	−0.722610	+	0.691256i	$0.757058\pi$
$578$	2.17796	0.0905912
$579$	23.7747	0.988042
$580$	1.26870	0.0526799
$581$	0	0
$582$	−15.8061	−0.655184
$583$	−37.0155	−1.53302
$584$	9.05932	0.374877
$585$	−6.26870	−0.259179
$586$	3.83752	0.158526
$587$	41.5843	1.71637	0.858184	−	0.513342i	$-0.171593\pi$
$587$	41.5843	1.71637	0.858184	+	0.513342i	$0.171593\pi$
$588$	0	0
$589$	20.7906	0.856663
$590$	6.84994	0.282008
$591$	0.418760	0.0172255
$592$	−10.9093	−0.448368
$593$	25.2811	1.03817	0.519086	−	0.854722i	$-0.326273\pi$
$593$	25.2811	1.03817	0.519086	+	0.854722i	$0.326273\pi$
$594$	−4.05932	−0.166556
$595$	0	0
$596$	3.17796	0.130174
$597$	5.69988	0.233281
$598$	6.26870	0.256346
$599$	21.5250	0.879487	0.439743	−	0.898123i	$-0.355069\pi$
$599$	21.5250	0.879487	0.439743	+	0.898123i	$0.355069\pi$
$600$	4.00000	0.163299
$601$	−4.17796	−0.170423	−0.0852113	−	0.996363i	$-0.527157\pi$
$601$	−4.17796	−0.170423	−0.0852113	+	0.996363i	$0.527157\pi$
$602$	0	0
$603$	−13.4781	−0.548870
$604$	10.0593	0.409308
$605$	−5.47808	−0.222716
$606$	−14.1186	−0.573531
$607$	21.2528	0.862623	0.431311	−	0.902203i	$-0.358051\pi$
$607$	21.2528	0.862623	0.431311	+	0.902203i	$0.358051\pi$
$608$	3.20938	0.130158
$609$	0	0
$610$	−10.0000	−0.404888
$611$	−34.3404	−1.38927
$612$	−3.84994	−0.155625
$613$	2.35592	0.0951547	0.0475774	−	0.998868i	$-0.484850\pi$
$613$	2.35592	0.0951547	0.0475774	+	0.998868i	$0.484850\pi$
$614$	13.9841	0.564351
$615$	−4.79062	−0.193176
$616$	0	0
$617$	−12.8778	−0.518442	−0.259221	−	0.965818i	$-0.583466\pi$
$617$	−12.8778	−0.518442	−0.259221	+	0.965818i	$0.583466\pi$
$618$	0.521920	0.0209947
$619$	11.9437	0.480059	0.240030	−	0.970766i	$-0.422843\pi$
$619$	11.9437	0.480059	0.240030	+	0.970766i	$0.422843\pi$
$620$	6.47808	0.260166
$621$	−1.00000	−0.0401286
$622$	−26.3873	−1.05804
$623$	0	0
$624$	6.26870	0.250949
$625$	11.0000	0.440000
$626$	9.15006	0.365710
$627$	−13.0279	−0.520284
$628$	−2.07174	−0.0826714
$629$	42.0000	1.67465
$630$	0	0
$631$	10.9841	0.437269	0.218634	−	0.975807i	$-0.429840\pi$
$631$	10.9841	0.437269	0.218634	+	0.975807i	$0.429840\pi$
$632$	−9.38734	−0.373408
$633$	−4.41876	−0.175630
$634$	−20.2249	−0.803232
$635$	16.0593	0.637295
$636$	−9.11864	−0.361578
$637$	0	0
$638$	5.15006	0.203893
$639$	12.3873	0.490036
$640$	1.00000	0.0395285
$641$	27.4621	1.08469	0.542345	−	0.840156i	$-0.317537\pi$
$641$	27.4621	1.08469	0.542345	+	0.840156i	$0.317537\pi$
$642$	14.0593	0.554877
$643$	3.32802	0.131244	0.0656222	−	0.997845i	$-0.479097\pi$
$643$	3.32802	0.131244	0.0656222	+	0.997845i	$0.479097\pi$
$644$	0	0
$645$	8.11864	0.319671
$646$	−12.3559	−0.486137
$647$	−31.8495	−1.25213	−0.626066	−	0.779770i	$-0.715336\pi$
$647$	−31.8495	−1.25213	−0.626066	+	0.779770i	$0.715336\pi$
$648$	−1.00000	−0.0392837
$649$	27.8061	1.09148
$650$	25.0748	0.983515
$651$	0	0
$652$	4.07174	0.159462
$653$	−2.28770	−0.0895246	−0.0447623	−	0.998998i	$-0.514253\pi$
$653$	−2.28770	−0.0895246	−0.0447623	+	0.998998i	$0.514253\pi$
$654$	12.1186	0.473876
$655$	−18.8654	−0.737133
$656$	4.79062	0.187042
$657$	−9.05932	−0.353438
$658$	0	0
$659$	−8.18148	−0.318705	−0.159353	−	0.987222i	$-0.550941\pi$
$659$	−8.18148	−0.318705	−0.159353	+	0.987222i	$0.550941\pi$
$660$	−4.05932	−0.158009
$661$	26.6809	1.03777	0.518883	−	0.854845i	$-0.326348\pi$
$661$	26.6809	1.03777	0.518883	+	0.854845i	$0.326348\pi$
$662$	20.6091	0.800997
$663$	−24.1341	−0.937292
$664$	0.0593201	0.00230207
$665$	0	0
$666$	10.9093	0.422725
$667$	1.26870	0.0491243
$668$	−18.0155	−0.697040
$669$	−11.7592	−0.454637
$670$	−13.4781	−0.520704
$671$	−40.5932	−1.56708
$672$	0	0
$673$	−48.6525	−1.87542	−0.937708	−	0.347423i	$-0.887057\pi$
$673$	−48.6525	−1.87542	−0.937708	+	0.347423i	$0.887057\pi$
$674$	26.2249	1.01014
$675$	−4.00000	−0.153960
$676$	26.2966	1.01141
$677$	−1.23728	−0.0475526	−0.0237763	−	0.999717i	$-0.507569\pi$
$677$	−1.23728	−0.0475526	−0.0237763	+	0.999717i	$0.507569\pi$
$678$	5.43118	0.208583
$679$	0	0
$680$	−3.84994	−0.147638
$681$	−13.7592	−0.527254
$682$	26.2966	1.00695
$683$	5.34702	0.204598	0.102299	−	0.994754i	$-0.467380\pi$
$683$	5.34702	0.204598	0.102299	+	0.994754i	$0.467380\pi$
$684$	−3.20938	−0.122714
$685$	−15.5967	−0.595920
$686$	0	0
$687$	−21.6281	−0.825165
$688$	−8.11864	−0.309520
$689$	−57.1620	−2.17770
$690$	−1.00000	−0.0380693
$691$	−3.53434	−0.134453	−0.0672263	−	0.997738i	$-0.521415\pi$
$691$	−3.53434	−0.134453	−0.0672263	+	0.997738i	$0.521415\pi$
$692$	14.5374	0.552629
$693$	0	0
$694$	−25.5967	−0.971638
$695$	6.83752	0.259362
$696$	1.26870	0.0480900
$697$	−18.4436	−0.698601
$698$	1.61266	0.0610401
$699$	−26.6091	−1.00645
$700$	0	0
$701$	−32.6999	−1.23506	−0.617529	−	0.786548i	$-0.711866\pi$
$701$	−32.6999	−1.23506	−0.617529	+	0.786548i	$0.711866\pi$
$702$	−6.26870	−0.236597
$703$	35.0120	1.32050
$704$	4.05932	0.152991
$705$	5.47808	0.206316
$706$	−26.6091	−1.00145
$707$	0	0
$708$	6.84994	0.257437
$709$	42.2213	1.58566	0.792828	−	0.609446i	$-0.208608\pi$
$709$	42.2213	1.58566	0.792828	+	0.609446i	$0.208608\pi$
$710$	12.3873	0.464889
$711$	9.38734	0.352053
$712$	10.9093	0.408842
$713$	6.47808	0.242606
$714$	0	0
$715$	−25.4467	−0.951651
$716$	−12.7592	−0.476834
$717$	−16.0000	−0.597531
$718$	18.8375	0.703010
$719$	−23.2966	−0.868817	−0.434408	−	0.900716i	$-0.643042\pi$
$719$	−23.2966	−0.868817	−0.434408	+	0.900716i	$0.643042\pi$
$720$	−1.00000	−0.0372678
$721$	0	0
$722$	8.69988	0.323776
$723$	−28.2249	−1.04969
$724$	12.5374	0.465949
$725$	5.07480	0.188473
$726$	−5.47808	−0.203311
$727$	32.5498	1.20721	0.603603	−	0.797285i	$-0.293731\pi$
$727$	32.5498	1.20721	0.603603	+	0.797285i	$0.293731\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−9.05932	−0.335300
$731$	31.2563	1.15606
$732$	−10.0000	−0.369611
$733$	−8.76578	−0.323771	−0.161886	−	0.986810i	$-0.551758\pi$
$733$	−8.76578	−0.323771	−0.161886	+	0.986810i	$0.551758\pi$
$734$	0.746780	0.0275642
$735$	0	0
$736$	1.00000	0.0368605
$737$	−54.7118	−2.01534
$738$	−4.79062	−0.176345
$739$	−25.0996	−0.923305	−0.461653	−	0.887061i	$-0.652743\pi$
$739$	−25.0996	−0.923305	−0.461653	+	0.887061i	$0.652743\pi$
$740$	10.9093	0.401032
$741$	−20.1186	−0.739077
$742$	0	0
$743$	18.3090	0.671693	0.335846	−	0.941917i	$-0.390978\pi$
$743$	18.3090	0.671693	0.335846	+	0.941917i	$0.390978\pi$
$744$	6.47808	0.237498
$745$	−3.17796	−0.116431
$746$	−18.9562	−0.694034
$747$	−0.0593201	−0.00217041
$748$	−15.6281	−0.571421
$749$	0	0
$750$	−9.00000	−0.328634
$751$	−28.0434	−1.02332	−0.511659	−	0.859189i	$-0.670969\pi$
$751$	−28.0434	−1.02332	−0.511659	+	0.859189i	$0.670969\pi$
$752$	−5.47808	−0.199765
$753$	8.29660	0.302345
$754$	7.95310	0.289635
$755$	−10.0593	−0.366096
$756$	0	0
$757$	21.7468	0.790400	0.395200	−	0.918595i	$-0.370675\pi$
$757$	21.7468	0.790400	0.395200	+	0.918595i	$0.370675\pi$
$758$	−11.7154	−0.425521
$759$	−4.05932	−0.147344
$760$	−3.20938	−0.116416
$761$	39.9212	1.44714	0.723572	−	0.690249i	$-0.242499\pi$
$761$	39.9212	1.44714	0.723572	+	0.690249i	$0.242499\pi$
$762$	16.0593	0.581768
$763$	0	0
$764$	4.07174	0.147310
$765$	3.84994	0.139195
$766$	−26.1655	−0.945399
$767$	42.9402	1.55048
$768$	1.00000	0.0360844
$769$	29.3245	1.05747	0.528734	−	0.848787i	$-0.322667\pi$
$769$	29.3245	1.05747	0.528734	+	0.848787i	$0.322667\pi$
$770$	0	0
$771$	−19.0279	−0.685273
$772$	23.7747	0.855669
$773$	−5.35944	−0.192766	−0.0963828	−	0.995344i	$-0.530727\pi$
$773$	−5.35944	−0.192766	−0.0963828	+	0.995344i	$0.530727\pi$
$774$	8.11864	0.291818
$775$	25.9123	0.930798
$776$	−15.8061	−0.567406
$777$	0	0
$778$	27.7937	0.996452
$779$	−15.3749	−0.550864
$780$	−6.26870	−0.224455
$781$	50.2842	1.79931
$782$	−3.84994	−0.137674
$783$	−1.26870	−0.0453396
$784$	0	0
$785$	2.07174	0.0739436
$786$	−18.8654	−0.672907
$787$	−27.8968	−0.994415	−0.497207	−	0.867632i	$-0.665641\pi$
$787$	−27.8968	−0.994415	−0.497207	+	0.867632i	$0.665641\pi$
$788$	0.418760	0.0149177
$789$	0.118640	0.00422371
$790$	9.38734	0.333987
$791$	0	0
$792$	−4.05932	−0.144242
$793$	−62.6870	−2.22608
$794$	3.84994	0.136629
$795$	9.11864	0.323405
$796$	5.69988	0.202027
$797$	−13.6560	−0.483722	−0.241861	−	0.970311i	$-0.577758\pi$
$797$	−13.6560	−0.483722	−0.241861	+	0.970311i	$0.577758\pi$
$798$	0	0
$799$	21.0903	0.746120
$800$	4.00000	0.141421
$801$	−10.9093	−0.385460
$802$	−7.17796	−0.253463
$803$	−36.7747	−1.29775
$804$	−13.4781	−0.475335
$805$	0	0
$806$	40.6091	1.43040
$807$	−2.96858	−0.104499
$808$	−14.1186	−0.496692
$809$	−16.7278	−0.588117	−0.294059	−	0.955787i	$-0.595006\pi$
$809$	−16.7278	−0.588117	−0.294059	+	0.955787i	$0.595006\pi$
$810$	1.00000	0.0351364
$811$	17.3998	0.610988	0.305494	−	0.952194i	$-0.401178\pi$
$811$	17.3998	0.610988	0.305494	+	0.952194i	$0.401178\pi$
$812$	0	0
$813$	12.8968	0.452312
$814$	44.2842	1.55216
$815$	−4.07174	−0.142627
$816$	−3.84994	−0.134775
$817$	26.0558	0.911577
$818$	−16.3749	−0.572536
$819$	0	0
$820$	−4.79062	−0.167296
$821$	−28.7313	−1.00273	−0.501365	−	0.865236i	$-0.667168\pi$
$821$	−28.7313	−1.00273	−0.501365	+	0.865236i	$0.667168\pi$
$822$	−15.5967	−0.543998
$823$	−32.0310	−1.11653	−0.558265	−	0.829663i	$-0.688533\pi$
$823$	−32.0310	−1.11653	−0.558265	+	0.829663i	$0.688533\pi$
$824$	0.521920	0.0181819
$825$	−16.2373	−0.565310
$826$	0	0
$827$	26.3214	0.915286	0.457643	−	0.889136i	$-0.348694\pi$
$827$	26.3214	0.915286	0.457643	+	0.889136i	$0.348694\pi$
$828$	−1.00000	−0.0347524
$829$	21.5339	0.747903	0.373951	−	0.927448i	$-0.378003\pi$
$829$	21.5339	0.747903	0.373951	+	0.927448i	$0.378003\pi$
$830$	−0.0593201	−0.00205903
$831$	11.1780	0.387759
$832$	6.26870	0.217328
$833$	0	0
$834$	6.83752	0.236764
$835$	18.0155	0.623451
$836$	−13.0279	−0.450579
$837$	−6.47808	−0.223915
$838$	−25.9372	−0.895984
$839$	−6.25322	−0.215885	−0.107943	−	0.994157i	$-0.534426\pi$
$839$	−6.25322	−0.215885	−0.107943	+	0.994157i	$0.534426\pi$
$840$	0	0
$841$	−27.3904	−0.944497
$842$	−3.13764	−0.108130
$843$	−31.4621	−1.08361
$844$	−4.41876	−0.152100
$845$	−26.2966	−0.904631
$846$	5.47808	0.188340
$847$	0	0
$848$	−9.11864	−0.313135
$849$	10.0155	0.343730
$850$	−15.3998	−0.528207
$851$	10.9093	0.373965
$852$	12.3873	0.424383
$853$	−4.65604	−0.159420	−0.0797099	−	0.996818i	$-0.525399\pi$
$853$	−4.65604	−0.159420	−0.0797099	+	0.996818i	$0.525399\pi$
$854$	0	0
$855$	3.20938	0.109758
$856$	14.0593	0.480538
$857$	45.6839	1.56053	0.780267	−	0.625447i	$-0.215083\pi$
$857$	45.6839	1.56053	0.780267	+	0.625447i	$0.215083\pi$
$858$	−25.4467	−0.868735
$859$	−42.0089	−1.43333	−0.716663	−	0.697420i	$-0.754331\pi$
$859$	−42.0089	−1.43333	−0.716663	+	0.697420i	$0.754331\pi$
$860$	8.11864	0.276843
$861$	0	0
$862$	17.0748	0.581570
$863$	−50.2059	−1.70903	−0.854514	−	0.519429i	$-0.826145\pi$
$863$	−50.2059	−1.70903	−0.854514	+	0.519429i	$0.826145\pi$
$864$	−1.00000	−0.0340207
$865$	−14.5374	−0.494286
$866$	−34.4746	−1.17149
$867$	−2.17796	−0.0739674
$868$	0	0
$869$	38.1062	1.29266
$870$	−1.26870	−0.0430130
$871$	−84.4900	−2.86284
$872$	12.1186	0.410389
$873$	15.8061	0.534955
$874$	−3.20938	−0.108559
$875$	0	0
$876$	−9.05932	−0.306086
$877$	−8.45018	−0.285342	−0.142671	−	0.989770i	$-0.545569\pi$
$877$	−8.45018	−0.285342	−0.142671	+	0.989770i	$0.545569\pi$
$878$	2.59672	0.0876351
$879$	−3.83752	−0.129436
$880$	−4.05932	−0.136840
$881$	−1.17796	−0.0396865	−0.0198432	−	0.999803i	$-0.506317\pi$
$881$	−1.17796	−0.0396865	−0.0198432	+	0.999803i	$0.506317\pi$
$882$	0	0
$883$	27.5653	0.927646	0.463823	−	0.885928i	$-0.346477\pi$
$883$	27.5653	0.927646	0.463823	+	0.885928i	$0.346477\pi$
$884$	−24.1341	−0.811718
$885$	−6.84994	−0.230258
$886$	−4.02790	−0.135320
$887$	−48.2373	−1.61965	−0.809825	−	0.586672i	$-0.800438\pi$
$887$	−48.2373	−1.61965	−0.809825	+	0.586672i	$0.800438\pi$
$888$	10.9093	0.366091
$889$	0	0
$890$	−10.9093	−0.365679
$891$	4.05932	0.135992
$892$	−11.7592	−0.393727
$893$	17.5812	0.588334
$894$	−3.17796	−0.106287
$895$	12.7592	0.426493
$896$	0	0
$897$	−6.26870	−0.209306
$898$	22.1655	0.739674
$899$	8.21874	0.274110
$900$	−4.00000	−0.133333
$901$	35.1062	1.16956
$902$	−19.4467	−0.647503
$903$	0	0
$904$	5.43118	0.180638
$905$	−12.5374	−0.416757
$906$	−10.0593	−0.334199
$907$	−24.2687	−0.805829	−0.402914	−	0.915238i	$-0.632003\pi$
$907$	−24.2687	−0.805829	−0.402914	+	0.915238i	$0.632003\pi$
$908$	−13.7592	−0.456615
$909$	14.1186	0.468286
$910$	0	0
$911$	−6.68088	−0.221347	−0.110674	−	0.993857i	$-0.535301\pi$
$911$	−6.68088	−0.221347	−0.110674	+	0.993857i	$0.535301\pi$
$912$	−3.20938	−0.106273
$913$	−0.240799	−0.00796930
$914$	−32.7623	−1.08368
$915$	10.0000	0.330590
$916$	−21.6281	−0.714614
$917$	0	0
$918$	3.84994	0.127067
$919$	4.28464	0.141337	0.0706686	−	0.997500i	$-0.477487\pi$
$919$	4.28464	0.141337	0.0706686	+	0.997500i	$0.477487\pi$
$920$	−1.00000	−0.0329690
$921$	−13.9841	−0.460790
$922$	−10.2373	−0.337147
$923$	77.6525	2.55596
$924$	0	0
$925$	43.6370	1.43478
$926$	0.118640	0.00389876
$927$	−0.521920	−0.0171421
$928$	1.26870	0.0416471
$929$	3.18454	0.104481	0.0522407	−	0.998635i	$-0.483364\pi$
$929$	3.18454	0.104481	0.0522407	+	0.998635i	$0.483364\pi$
$930$	−6.47808	−0.212425
$931$	0	0
$932$	−26.6091	−0.871611
$933$	26.3873	0.863883
$934$	−8.11864	−0.265650
$935$	15.6281	0.511095
$936$	−6.26870	−0.204899
$937$	−25.8619	−0.844871	−0.422436	−	0.906393i	$-0.638825\pi$
$937$	−25.8619	−0.844871	−0.422436	+	0.906393i	$0.638825\pi$
$938$	0	0
$939$	−9.15006	−0.298601
$940$	5.47808	0.178675
$941$	−3.70340	−0.120727	−0.0603637	−	0.998176i	$-0.519226\pi$
$941$	−3.70340	−0.120727	−0.0603637	+	0.998176i	$0.519226\pi$
$942$	2.07174	0.0675010
$943$	−4.79062	−0.156004
$944$	6.84994	0.222947
$945$	0	0
$946$	32.9562	1.07150
$947$	−50.0155	−1.62528	−0.812642	−	0.582763i	$-0.801972\pi$
$947$	−50.0155	−1.62528	−0.812642	+	0.582763i	$0.801972\pi$
$948$	9.38734	0.304887
$949$	−56.7902	−1.84349
$950$	−12.8375	−0.416504
$951$	20.2249	0.655836
$952$	0	0
$953$	24.4188	0.791001	0.395501	−	0.918466i	$-0.370571\pi$
$953$	24.4188	0.791001	0.395501	+	0.918466i	$0.370571\pi$
$954$	9.11864	0.295227
$955$	−4.07174	−0.131758
$956$	−16.0000	−0.517477
$957$	−5.15006	−0.166478
$958$	−4.55334	−0.147112
$959$	0	0
$960$	−1.00000	−0.0322749
$961$	10.9655	0.353726
$962$	68.3869	2.20488
$963$	−14.0593	−0.453055
$964$	−28.2249	−0.909062
$965$	−23.7747	−0.765334
$966$	0	0
$967$	−18.4152	−0.592194	−0.296097	−	0.955158i	$-0.595685\pi$
$967$	−18.4152	−0.592194	−0.296097	+	0.955158i	$0.595685\pi$
$968$	−5.47808	−0.176072
$969$	12.3559	0.396929
$970$	15.8061	0.507503
$971$	17.9407	0.575744	0.287872	−	0.957669i	$-0.407052\pi$
$971$	17.9407	0.575744	0.287872	+	0.957669i	$0.407052\pi$
$972$	1.00000	0.0320750
$973$	0	0
$974$	21.3156	0.682996
$975$	−25.0748	−0.803036
$976$	−10.0000	−0.320092
$977$	28.4342	0.909692	0.454846	−	0.890570i	$-0.349694\pi$
$977$	28.4342	0.909692	0.454846	+	0.890570i	$0.349694\pi$
$978$	−4.07174	−0.130200
$979$	−44.2842	−1.41533
$980$	0	0
$981$	−12.1186	−0.386918
$982$	−2.09074	−0.0667182
$983$	−4.60914	−0.147009	−0.0735044	−	0.997295i	$-0.523418\pi$
$983$	−4.60914	−0.147009	−0.0735044	+	0.997295i	$0.523418\pi$
$984$	−4.79062	−0.152719
$985$	−0.418760	−0.0133428
$986$	−4.88442	−0.155552
$987$	0	0
$988$	−20.1186	−0.640059
$989$	8.11864	0.258158
$990$	4.05932	0.129014
$991$	−41.8778	−1.33029	−0.665147	−	0.746713i	$-0.731631\pi$
$991$	−41.8778	−1.33029	−0.665147	+	0.746713i	$0.731631\pi$
$992$	6.47808	0.205679
$993$	−20.6091	−0.654011
$994$	0	0
$995$	−5.69988	−0.180698
$996$	−0.0593201	−0.00187963
$997$	−33.3280	−1.05551	−0.527754	−	0.849397i	$-0.676966\pi$
$997$	−33.3280	−1.05551	−0.527754	+	0.849397i	$0.676966\pi$
$998$	7.13764	0.225938
$999$	−10.9093	−0.345154

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6762.2.a.cf.1.3		3
7.3	odd	6		966.2.i.k.415.2	yes	6
7.5	odd	6		966.2.i.k.277.2	✓	6
7.6	odd	2		6762.2.a.ce.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.k.277.2	✓	6	7.5	odd	6
966.2.i.k.415.2	yes	6	7.3	odd	6
6762.2.a.ce.1.3		3	7.6	odd	2
6762.2.a.cf.1.3		3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} +4.05932 q^{11} +1.00000 q^{12} +6.26870 q^{13} -1.00000 q^{15} +1.00000 q^{16} -3.84994 q^{17} -1.00000 q^{18} -3.20938 q^{19} -1.00000 q^{20} -4.05932 q^{22} -1.00000 q^{23} -1.00000 q^{24} -4.00000 q^{25} -6.26870 q^{26} +1.00000 q^{27} -1.26870 q^{29} +1.00000 q^{30} -6.47808 q^{31} -1.00000 q^{32} +4.05932 q^{33} +3.84994 q^{34} +1.00000 q^{36} -10.9093 q^{37} +3.20938 q^{38} +6.26870 q^{39} +1.00000 q^{40} +4.79062 q^{41} -8.11864 q^{43} +4.05932 q^{44} -1.00000 q^{45} +1.00000 q^{46} -5.47808 q^{47} +1.00000 q^{48} +4.00000 q^{50} -3.84994 q^{51} +6.26870 q^{52} -9.11864 q^{53} -1.00000 q^{54} -4.05932 q^{55} -3.20938 q^{57} +1.26870 q^{58} +6.84994 q^{59} -1.00000 q^{60} -10.0000 q^{61} +6.47808 q^{62} +1.00000 q^{64} -6.26870 q^{65} -4.05932 q^{66} -13.4781 q^{67} -3.84994 q^{68} -1.00000 q^{69} +12.3873 q^{71} -1.00000 q^{72} -9.05932 q^{73} +10.9093 q^{74} -4.00000 q^{75} -3.20938 q^{76} -6.26870 q^{78} +9.38734 q^{79} -1.00000 q^{80} +1.00000 q^{81} -4.79062 q^{82} -0.0593201 q^{83} +3.84994 q^{85} +8.11864 q^{86} -1.26870 q^{87} -4.05932 q^{88} -10.9093 q^{89} +1.00000 q^{90} -1.00000 q^{92} -6.47808 q^{93} +5.47808 q^{94} +3.20938 q^{95} -1.00000 q^{96} +15.8061 q^{97} +4.05932 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} - 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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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