LMFDB - Embedded newform 6762.2.a.cl.1.2

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:	$0$
Dimension:	$4$
Coefficient field:	4.4.473376.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 13x^{2} + 8x + 30 $ x^4 - 2x^3 - 13x^2 + 8*x + 30
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
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			1.2
Root			$1.83178$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.831776 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.831776 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -0.831776 q^{10} -2.45526 q^{11} -1.00000 q^{12} -5.30815 q^{13} +0.831776 q^{15} +1.00000 q^{16} -3.28704 q^{17} +1.00000 q^{18} -2.00000 q^{19} -0.831776 q^{20} -2.45526 q^{22} -1.00000 q^{23} -1.00000 q^{24} -4.30815 q^{25} -5.30815 q^{26} -1.00000 q^{27} +10.3081 q^{29} +0.831776 q^{30} -2.00000 q^{31} +1.00000 q^{32} +2.45526 q^{33} -3.28704 q^{34} +1.00000 q^{36} +2.33645 q^{37} -2.00000 q^{38} +5.30815 q^{39} -0.831776 q^{40} +3.66355 q^{41} +2.00000 q^{43} -2.45526 q^{44} -0.831776 q^{45} -1.00000 q^{46} +3.91052 q^{47} -1.00000 q^{48} -4.30815 q^{50} +3.28704 q^{51} -5.30815 q^{52} -7.78452 q^{53} -1.00000 q^{54} +2.04223 q^{55} +2.00000 q^{57} +10.3081 q^{58} -3.32710 q^{59} +0.831776 q^{60} +14.6163 q^{61} -2.00000 q^{62} +1.00000 q^{64} +4.41519 q^{65} +2.45526 q^{66} +11.7845 q^{67} -3.28704 q^{68} +1.00000 q^{69} -5.04223 q^{71} +1.00000 q^{72} +15.6163 q^{73} +2.33645 q^{74} +4.30815 q^{75} -2.00000 q^{76} +5.30815 q^{78} +10.4553 q^{79} -0.831776 q^{80} +1.00000 q^{81} +3.66355 q^{82} +6.57407 q^{83} +2.73408 q^{85} +2.00000 q^{86} -10.3081 q^{87} -2.45526 q^{88} -12.9527 q^{89} -0.831776 q^{90} -1.00000 q^{92} +2.00000 q^{93} +3.91052 q^{94} +1.66355 q^{95} -1.00000 q^{96} -8.00000 q^{97} -2.45526 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} + 2 q^{10} - 4 q^{12} + 6 q^{13} - 2 q^{15} + 4 q^{16} + 2 q^{17} + 4 q^{18} - 8 q^{19} + 2 q^{20} - 4 q^{23} - 4 q^{24} + 10 q^{25} + 6 q^{26} - 4 q^{27} + 14 q^{29} - 2 q^{30} - 8 q^{31} + 4 q^{32} + 2 q^{34} + 4 q^{36} + 20 q^{37} - 8 q^{38} - 6 q^{39} + 2 q^{40} + 4 q^{41} + 8 q^{43} + 2 q^{45} - 4 q^{46} - 4 q^{47} - 4 q^{48} + 10 q^{50} - 2 q^{51} + 6 q^{52} + 18 q^{53} - 4 q^{54} - 16 q^{55} + 8 q^{57} + 14 q^{58} + 8 q^{59} - 2 q^{60} + 4 q^{61} - 8 q^{62} + 4 q^{64} + 14 q^{65} - 2 q^{67} + 2 q^{68} + 4 q^{69} + 4 q^{71} + 4 q^{72} + 8 q^{73} + 20 q^{74} - 10 q^{75} - 8 q^{76} - 6 q^{78} + 32 q^{79} + 2 q^{80} + 4 q^{81} + 4 q^{82} - 4 q^{83} + 14 q^{85} + 8 q^{86} - 14 q^{87} - 8 q^{89} + 2 q^{90} - 4 q^{92} + 8 q^{93} - 4 q^{94} - 4 q^{95} - 4 q^{96} - 32 q^{97}+O(q^{100}) $ 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 + 2 * q^10 - 4 * q^12 + 6 * q^13 - 2 * q^15 + 4 * q^16 + 2 * q^17 + 4 * q^18 - 8 * q^19 + 2 * q^20 - 4 * q^23 - 4 * q^24 + 10 * q^25 + 6 * q^26 - 4 * q^27 + 14 * q^29 - 2 * q^30 - 8 * q^31 + 4 * q^32 + 2 * q^34 + 4 * q^36 + 20 * q^37 - 8 * q^38 - 6 * q^39 + 2 * q^40 + 4 * q^41 + 8 * q^43 + 2 * q^45 - 4 * q^46 - 4 * q^47 - 4 * q^48 + 10 * q^50 - 2 * q^51 + 6 * q^52 + 18 * q^53 - 4 * q^54 - 16 * q^55 + 8 * q^57 + 14 * q^58 + 8 * q^59 - 2 * q^60 + 4 * q^61 - 8 * q^62 + 4 * q^64 + 14 * q^65 - 2 * q^67 + 2 * q^68 + 4 * q^69 + 4 * q^71 + 4 * q^72 + 8 * q^73 + 20 * q^74 - 10 * q^75 - 8 * q^76 - 6 * q^78 + 32 * q^79 + 2 * q^80 + 4 * q^81 + 4 * q^82 - 4 * q^83 + 14 * q^85 + 8 * q^86 - 14 * q^87 - 8 * q^89 + 2 * q^90 - 4 * q^92 + 8 * q^93 - 4 * q^94 - 4 * q^95 - 4 * q^96 - 32 * q^97

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−0.831776	−0.371982	−0.185991	−	0.982551i	$-0.559549\pi$
$5$	−0.831776	−0.371982	−0.185991	+	0.982551i	$0.559549\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−0.831776	−0.263031
$11$	−2.45526	−0.740289	−0.370144	−	0.928974i	$-0.620692\pi$
$11$	−2.45526	−0.740289	−0.370144	+	0.928974i	$0.620692\pi$
$12$	−1.00000	−0.288675
$13$	−5.30815	−1.47222	−0.736108	−	0.676864i	$-0.763338\pi$
$13$	−5.30815	−1.47222	−0.736108	+	0.676864i	$0.763338\pi$
$14$	0	0
$15$	0.831776	0.214764
$16$	1.00000	0.250000
$17$	−3.28704	−0.797223	−0.398612	−	0.917120i	$-0.630508\pi$
$17$	−3.28704	−0.797223	−0.398612	+	0.917120i	$0.630508\pi$
$18$	1.00000	0.235702
$19$	−2.00000	−0.458831	−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000	−0.458831	−0.229416	+	0.973329i	$0.573682\pi$
$20$	−0.831776	−0.185991
$21$	0	0
$22$	−2.45526	−0.523463
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.00000	−0.204124
$25$	−4.30815	−0.861630
$26$	−5.30815	−1.04101
$27$	−1.00000	−0.192450
$28$	0	0
$29$	10.3081	1.91418	0.957088	−	0.289799i	$-0.0935884\pi$
$29$	10.3081	1.91418	0.957088	+	0.289799i	$0.0935884\pi$
$30$	0.831776	0.151861
$31$	−2.00000	−0.359211	−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000	−0.359211	−0.179605	+	0.983739i	$0.557482\pi$
$32$	1.00000	0.176777
$33$	2.45526	0.427406
$34$	−3.28704	−0.563722
$35$	0	0
$36$	1.00000	0.166667
$37$	2.33645	0.384110	0.192055	−	0.981384i	$-0.438485\pi$
$37$	2.33645	0.384110	0.192055	+	0.981384i	$0.438485\pi$
$38$	−2.00000	−0.324443
$39$	5.30815	0.849984
$40$	−0.831776	−0.131515
$41$	3.66355	0.572151	0.286075	−	0.958207i	$-0.407649\pi$
$41$	3.66355	0.572151	0.286075	+	0.958207i	$0.407649\pi$
$42$	0	0
$43$	2.00000	0.304997	0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000	0.304997	0.152499	+	0.988304i	$0.451268\pi$
$44$	−2.45526	−0.370144
$45$	−0.831776	−0.123994
$46$	−1.00000	−0.147442
$47$	3.91052	0.570408	0.285204	−	0.958467i	$-0.407939\pi$
$47$	3.91052	0.570408	0.285204	+	0.958467i	$0.407939\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	−4.30815	−0.609264
$51$	3.28704	0.460277
$52$	−5.30815	−0.736108
$53$	−7.78452	−1.06929	−0.534643	−	0.845078i	$-0.679554\pi$
$53$	−7.78452	−1.06929	−0.534643	+	0.845078i	$0.679554\pi$
$54$	−1.00000	−0.136083
$55$	2.04223	0.275374
$56$	0	0
$57$	2.00000	0.264906
$58$	10.3081	1.35353
$59$	−3.32710	−0.433152	−0.216576	−	0.976266i	$-0.569489\pi$
$59$	−3.32710	−0.433152	−0.216576	+	0.976266i	$0.569489\pi$
$60$	0.831776	0.107382
$61$	14.6163	1.87143	0.935713	−	0.352763i	$-0.114758\pi$
$61$	14.6163	1.87143	0.935713	+	0.352763i	$0.114758\pi$
$62$	−2.00000	−0.254000
$63$	0	0
$64$	1.00000	0.125000
$65$	4.41519	0.547637
$66$	2.45526	0.302222
$67$	11.7845	1.43971	0.719854	−	0.694125i	$-0.244209\pi$
$67$	11.7845	1.43971	0.719854	+	0.694125i	$0.244209\pi$
$68$	−3.28704	−0.398612
$69$	1.00000	0.120386
$70$	0	0
$71$	−5.04223	−0.598402	−0.299201	−	0.954190i	$-0.596720\pi$
$71$	−5.04223	−0.598402	−0.299201	+	0.954190i	$0.596720\pi$
$72$	1.00000	0.117851
$73$	15.6163	1.82775	0.913875	−	0.405996i	$-0.133075\pi$
$73$	15.6163	1.82775	0.913875	+	0.405996i	$0.133075\pi$
$74$	2.33645	0.271607
$75$	4.30815	0.497462
$76$	−2.00000	−0.229416
$77$	0	0
$78$	5.30815	0.601029
$79$	10.4553	1.17631	0.588154	−	0.808749i	$-0.299855\pi$
$79$	10.4553	1.17631	0.588154	+	0.808749i	$0.299855\pi$
$80$	−0.831776	−0.0929954
$81$	1.00000	0.111111
$82$	3.66355	0.404572
$83$	6.57407	0.721598	0.360799	−	0.932644i	$-0.382504\pi$
$83$	6.57407	0.721598	0.360799	+	0.932644i	$0.382504\pi$
$84$	0	0
$85$	2.73408	0.296552
$86$	2.00000	0.215666
$87$	−10.3081	−1.10515
$88$	−2.45526	−0.261732
$89$	−12.9527	−1.37299	−0.686494	−	0.727135i	$-0.740851\pi$
$89$	−12.9527	−1.37299	−0.686494	+	0.727135i	$0.740851\pi$
$90$	−0.831776	−0.0876769
$91$	0	0
$92$	−1.00000	−0.104257
$93$	2.00000	0.207390
$94$	3.91052	0.403339
$95$	1.66355	0.170677
$96$	−1.00000	−0.102062
$97$	−8.00000	−0.812277	−0.406138	−	0.913812i	$-0.633125\pi$
$97$	−8.00000	−0.812277	−0.406138	+	0.913812i	$0.633125\pi$
$98$	0	0
$99$	−2.45526	−0.246763
$100$	−4.30815	−0.430815
$101$	−0.308149	−0.0306619	−0.0153310	−	0.999882i	$-0.504880\pi$
$101$	−0.308149	−0.0306619	−0.0153310	+	0.999882i	$0.504880\pi$
$102$	3.28704	0.325465
$103$	−6.00216	−0.591410	−0.295705	−	0.955279i	$-0.595555\pi$
$103$	−6.00216	−0.591410	−0.295705	+	0.955279i	$0.595555\pi$
$104$	−5.30815	−0.520507
$105$	0	0
$106$	−7.78452	−0.756100
$107$	3.08948	0.298671	0.149336	−	0.988787i	$-0.452286\pi$
$107$	3.08948	0.298671	0.149336	+	0.988787i	$0.452286\pi$
$108$	−1.00000	−0.0962250
$109$	12.4975	1.19704	0.598521	−	0.801107i	$-0.295755\pi$
$109$	12.4975	1.19704	0.598521	+	0.801107i	$0.295755\pi$
$110$	2.04223	0.194719
$111$	−2.33645	−0.221766
$112$	0	0
$113$	7.74230	0.728334	0.364167	−	0.931334i	$-0.381354\pi$
$113$	7.74230	0.728334	0.364167	+	0.931334i	$0.381354\pi$
$114$	2.00000	0.187317
$115$	0.831776	0.0775635
$116$	10.3081	0.957088
$117$	−5.30815	−0.490739
$118$	−3.32710	−0.306285
$119$	0	0
$120$	0.831776	0.0759304
$121$	−4.97170	−0.451973
$122$	14.6163	1.32330
$123$	−3.66355	−0.330331
$124$	−2.00000	−0.179605
$125$	7.74230	0.692492
$126$	0	0
$127$	10.9527	0.971899	0.485949	−	0.873987i	$-0.338474\pi$
$127$	10.9527	0.971899	0.485949	+	0.873987i	$0.338474\pi$
$128$	1.00000	0.0883883
$129$	−2.00000	−0.176090
$130$	4.41519	0.387238
$131$	13.5458	1.18350	0.591750	−	0.806122i	$-0.298437\pi$
$131$	13.5458	1.18350	0.591750	+	0.806122i	$0.298437\pi$
$132$	2.45526	0.213703
$133$	0	0
$134$	11.7845	1.01803
$135$	0.831776	0.0715879
$136$	−3.28704	−0.281861
$137$	19.5247	1.66810	0.834052	−	0.551686i	$-0.186015\pi$
$137$	19.5247	1.66810	0.834052	+	0.551686i	$0.186015\pi$
$138$	1.00000	0.0851257
$139$	−12.8822	−1.09266	−0.546328	−	0.837571i	$-0.683975\pi$
$139$	−12.8822	−1.09266	−0.546328	+	0.837571i	$0.683975\pi$
$140$	0	0
$141$	−3.91052	−0.329325
$142$	−5.04223	−0.423134
$143$	13.0329	1.08986
$144$	1.00000	0.0833333
$145$	−8.57407	−0.712038
$146$	15.6163	1.29241
$147$	0	0
$148$	2.33645	0.192055
$149$	10.0787	0.825683	0.412841	−	0.910803i	$-0.364536\pi$
$149$	10.0787	0.825683	0.412841	+	0.910803i	$0.364536\pi$
$150$	4.30815	0.351759
$151$	−20.2798	−1.65035	−0.825175	−	0.564877i	$-0.808924\pi$
$151$	−20.2798	−1.65035	−0.825175	+	0.564877i	$0.808924\pi$
$152$	−2.00000	−0.162221
$153$	−3.28704	−0.265741
$154$	0	0
$155$	1.66355	0.133620
$156$	5.30815	0.424992
$157$	−7.07156	−0.564372	−0.282186	−	0.959360i	$-0.591059\pi$
$157$	−7.07156	−0.564372	−0.282186	+	0.959360i	$0.591059\pi$
$158$	10.4553	0.831776
$159$	7.78452	0.617353
$160$	−0.831776	−0.0657577
$161$	0	0
$162$	1.00000	0.0785674
$163$	−2.26592	−0.177481	−0.0887404	−	0.996055i	$-0.528284\pi$
$163$	−2.26592	−0.177481	−0.0887404	+	0.996055i	$0.528284\pi$
$164$	3.66355	0.286075
$165$	−2.04223	−0.158987
$166$	6.57407	0.510247
$167$	21.9244	1.69656	0.848282	−	0.529544i	$-0.177637\pi$
$167$	21.9244	1.69656	0.848282	+	0.529544i	$0.177637\pi$
$168$	0	0
$169$	15.1764	1.16742
$170$	2.73408	0.209694
$171$	−2.00000	−0.152944
$172$	2.00000	0.152499
$173$	−18.5035	−1.40680	−0.703399	−	0.710795i	$-0.748335\pi$
$173$	−18.5035	−1.40680	−0.703399	+	0.710795i	$0.748335\pi$
$174$	−10.3081	−0.781459
$175$	0	0
$176$	−2.45526	−0.185072
$177$	3.32710	0.250080
$178$	−12.9527	−0.970849
$179$	−6.17644	−0.461649	−0.230824	−	0.972995i	$-0.574142\pi$
$179$	−6.17644	−0.461649	−0.230824	+	0.972995i	$0.574142\pi$
$180$	−0.831776	−0.0619969
$181$	−13.2505	−0.984903	−0.492452	−	0.870340i	$-0.663899\pi$
$181$	−13.2505	−0.984903	−0.492452	+	0.870340i	$0.663899\pi$
$182$	0	0
$183$	−14.6163	−1.08047
$184$	−1.00000	−0.0737210
$185$	−1.94340	−0.142882
$186$	2.00000	0.146647
$187$	8.07053	0.590175
$188$	3.91052	0.285204
$189$	0	0
$190$	1.66355	0.120687
$191$	−12.9527	−0.937228	−0.468614	−	0.883403i	$-0.655246\pi$
$191$	−12.9527	−0.937228	−0.468614	+	0.883403i	$0.655246\pi$
$192$	−1.00000	−0.0721688
$193$	12.6353	0.909505	0.454753	−	0.890618i	$-0.349728\pi$
$193$	12.6353	0.909505	0.454753	+	0.890618i	$0.349728\pi$
$194$	−8.00000	−0.574367
$195$	−4.41519	−0.316178
$196$	0	0
$197$	−8.92445	−0.635840	−0.317920	−	0.948117i	$-0.602984\pi$
$197$	−8.92445	−0.635840	−0.317920	+	0.948117i	$0.602984\pi$
$198$	−2.45526	−0.174488
$199$	5.78236	0.409901	0.204950	−	0.978772i	$-0.434297\pi$
$199$	5.78236	0.409901	0.204950	+	0.978772i	$0.434297\pi$
$200$	−4.30815	−0.304632
$201$	−11.7845	−0.831216
$202$	−0.308149	−0.0216813
$203$	0	0
$204$	3.28704	0.230139
$205$	−3.04725	−0.212830
$206$	−6.00216	−0.418190
$207$	−1.00000	−0.0695048
$208$	−5.30815	−0.368054
$209$	4.91052	0.339668
$210$	0	0
$211$	7.39763	0.509274	0.254637	−	0.967037i	$-0.418044\pi$
$211$	7.39763	0.509274	0.254637	+	0.967037i	$0.418044\pi$
$212$	−7.78452	−0.534643
$213$	5.04223	0.345488
$214$	3.08948	0.211193
$215$	−1.66355	−0.113453
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	12.4975	0.846437
$219$	−15.6163	−1.05525
$220$	2.04223	0.137687
$221$	17.4481	1.17368
$222$	−2.33645	−0.156812
$223$	−1.00934	−0.0675907	−0.0337953	−	0.999429i	$-0.510759\pi$
$223$	−1.00934	−0.0675907	−0.0337953	+	0.999429i	$0.510759\pi$
$224$	0	0
$225$	−4.30815	−0.287210
$226$	7.74230	0.515010
$227$	17.7824	1.18026	0.590128	−	0.807309i	$-0.299077\pi$
$227$	17.7824	1.18026	0.590128	+	0.807309i	$0.299077\pi$
$228$	2.00000	0.132453
$229$	−14.3185	−0.946195	−0.473097	−	0.881010i	$-0.656864\pi$
$229$	−14.3185	−0.946195	−0.473097	+	0.881010i	$0.656864\pi$
$230$	0.831776	0.0548457
$231$	0	0
$232$	10.3081	0.676763
$233$	−13.8210	−0.905446	−0.452723	−	0.891651i	$-0.649547\pi$
$233$	−13.8210	−0.905446	−0.452723	+	0.891651i	$0.649547\pi$
$234$	−5.30815	−0.347005
$235$	−3.25268	−0.212181
$236$	−3.32710	−0.216576
$237$	−10.4553	−0.679142
$238$	0	0
$239$	−10.2659	−0.664047	−0.332024	−	0.943271i	$-0.607731\pi$
$239$	−10.2659	−0.664047	−0.332024	+	0.943271i	$0.607731\pi$
$240$	0.831776	0.0536909
$241$	8.75303	0.563832	0.281916	−	0.959439i	$-0.409030\pi$
$241$	8.75303	0.563832	0.281916	+	0.959439i	$0.409030\pi$
$242$	−4.97170	−0.319593
$243$	−1.00000	−0.0641500
$244$	14.6163	0.935713
$245$	0	0
$246$	−3.66355	−0.233580
$247$	10.6163	0.675499
$248$	−2.00000	−0.127000
$249$	−6.57407	−0.416615
$250$	7.74230	0.489666
$251$	−10.5397	−0.665261	−0.332630	−	0.943057i	$-0.607936\pi$
$251$	−10.5397	−0.665261	−0.332630	+	0.943057i	$0.607936\pi$
$252$	0	0
$253$	2.45526	0.154361
$254$	10.9527	0.687236
$255$	−2.73408	−0.171215
$256$	1.00000	0.0625000
$257$	12.7530	0.795512	0.397756	−	0.917491i	$-0.369789\pi$
$257$	12.7530	0.795512	0.397756	+	0.917491i	$0.369789\pi$
$258$	−2.00000	−0.124515
$259$	0	0
$260$	4.41519	0.273819
$261$	10.3081	0.638058
$262$	13.5458	0.836861
$263$	15.7058	0.968460	0.484230	−	0.874941i	$-0.339100\pi$
$263$	15.7058	0.968460	0.484230	+	0.874941i	$0.339100\pi$
$264$	2.45526	0.151111
$265$	6.47498	0.397755
$266$	0	0
$267$	12.9527	0.792695
$268$	11.7845	0.719854
$269$	19.7927	1.20678	0.603392	−	0.797445i	$-0.293815\pi$
$269$	19.7927	1.20678	0.603392	+	0.797445i	$0.293815\pi$
$270$	0.831776	0.0506203
$271$	−15.5268	−0.943187	−0.471593	−	0.881816i	$-0.656321\pi$
$271$	−15.5268	−0.943187	−0.471593	+	0.881816i	$0.656321\pi$
$272$	−3.28704	−0.199306
$273$	0	0
$274$	19.5247	1.17953
$275$	10.5776	0.637855
$276$	1.00000	0.0601929
$277$	0.555116	0.0333537	0.0166768	−	0.999861i	$-0.494691\pi$
$277$	0.555116	0.0333537	0.0166768	+	0.999861i	$0.494691\pi$
$278$	−12.8822	−0.772624
$279$	−2.00000	−0.119737
$280$	0	0
$281$	24.3973	1.45542	0.727709	−	0.685886i	$-0.240585\pi$
$281$	24.3973	1.45542	0.727709	+	0.685886i	$0.240585\pi$
$282$	−3.91052	−0.232868
$283$	19.0694	1.13356	0.566779	−	0.823870i	$-0.308189\pi$
$283$	19.0694	1.13356	0.566779	+	0.823870i	$0.308189\pi$
$284$	−5.04223	−0.299201
$285$	−1.66355	−0.0985403
$286$	13.0329	0.770650
$287$	0	0
$288$	1.00000	0.0589256
$289$	−6.19540	−0.364435
$290$	−8.57407	−0.503487
$291$	8.00000	0.468968
$292$	15.6163	0.913875
$293$	−1.40585	−0.0821305	−0.0410652	−	0.999156i	$-0.513075\pi$
$293$	−1.40585	−0.0821305	−0.0410652	+	0.999156i	$0.513075\pi$
$294$	0	0
$295$	2.76741	0.161125
$296$	2.33645	0.135803
$297$	2.45526	0.142469
$298$	10.0787	0.583846
$299$	5.30815	0.306978
$300$	4.30815	0.248731
$301$	0	0
$302$	−20.2798	−1.16697
$303$	0.308149	0.0177027
$304$	−2.00000	−0.114708
$305$	−12.1575	−0.696136
$306$	−3.28704	−0.187907
$307$	−27.2187	−1.55345	−0.776726	−	0.629839i	$-0.783121\pi$
$307$	−27.2187	−1.55345	−0.776726	+	0.629839i	$0.783121\pi$
$308$	0	0
$309$	6.00216	0.341451
$310$	1.66355	0.0944834
$311$	8.08948	0.458712	0.229356	−	0.973343i	$-0.426338\pi$
$311$	8.08948	0.458712	0.229356	+	0.973343i	$0.426338\pi$
$312$	5.30815	0.300515
$313$	−13.8210	−0.781211	−0.390606	−	0.920558i	$-0.627734\pi$
$313$	−13.8210	−0.781211	−0.390606	+	0.920558i	$0.627734\pi$
$314$	−7.07156	−0.399071
$315$	0	0
$316$	10.4553	0.588154
$317$	12.6542	0.710731	0.355366	−	0.934727i	$-0.384356\pi$
$317$	12.6542	0.710731	0.355366	+	0.934727i	$0.384356\pi$
$318$	7.78452	0.436534
$319$	−25.3092	−1.41704
$320$	−0.831776	−0.0464977
$321$	−3.08948	−0.172438
$322$	0	0
$323$	6.57407	0.365791
$324$	1.00000	0.0555556
$325$	22.8683	1.26850
$326$	−2.26592	−0.125498
$327$	−12.4975	−0.691113
$328$	3.66355	0.202286
$329$	0	0
$330$	−2.04223	−0.112421
$331$	−24.2419	−1.33246	−0.666229	−	0.745747i	$-0.732093\pi$
$331$	−24.2419	−1.33246	−0.666229	+	0.745747i	$0.732093\pi$
$332$	6.57407	0.360799
$333$	2.33645	0.128037
$334$	21.9244	1.19965
$335$	−9.80208	−0.535545
$336$	0	0
$337$	24.6163	1.34094	0.670468	−	0.741939i	$-0.266094\pi$
$337$	24.6163	1.34094	0.670468	+	0.741939i	$0.266094\pi$
$338$	15.1764	0.825490
$339$	−7.74230	−0.420504
$340$	2.73408	0.148276
$341$	4.91052	0.265920
$342$	−2.00000	−0.108148
$343$	0	0
$344$	2.00000	0.107833
$345$	−0.831776	−0.0447813
$346$	−18.5035	−0.994757
$347$	31.4090	1.68613	0.843063	−	0.537815i	$-0.180750\pi$
$347$	31.4090	1.68613	0.843063	+	0.537815i	$0.180750\pi$
$348$	−10.3081	−0.552575
$349$	−13.6024	−0.728118	−0.364059	−	0.931376i	$-0.618609\pi$
$349$	−13.6024	−0.728118	−0.364059	+	0.931376i	$0.618609\pi$
$350$	0	0
$351$	5.30815	0.283328
$352$	−2.45526	−0.130866
$353$	27.6636	1.47238	0.736191	−	0.676774i	$-0.236622\pi$
$353$	27.6636	1.47238	0.736191	+	0.676774i	$0.236622\pi$
$354$	3.32710	0.176834
$355$	4.19400	0.222595
$356$	−12.9527	−0.686494
$357$	0	0
$358$	−6.17644	−0.326435
$359$	22.2376	1.17366	0.586828	−	0.809711i	$-0.300376\pi$
$359$	22.2376	1.17366	0.586828	+	0.809711i	$0.300376\pi$
$360$	−0.831776	−0.0438384
$361$	−15.0000	−0.789474
$362$	−13.2505	−0.696432
$363$	4.97170	0.260947
$364$	0	0
$365$	−12.9893	−0.679889
$366$	−14.6163	−0.764006
$367$	25.6056	1.33660	0.668300	−	0.743892i	$-0.267022\pi$
$367$	25.6056	1.33660	0.668300	+	0.743892i	$0.267022\pi$
$368$	−1.00000	−0.0521286
$369$	3.66355	0.190717
$370$	−1.94340	−0.101033
$371$	0	0
$372$	2.00000	0.103695
$373$	−19.9821	−1.03463	−0.517316	−	0.855794i	$-0.673069\pi$
$373$	−19.9821	−1.03463	−0.517316	+	0.855794i	$0.673069\pi$
$374$	8.07053	0.417317
$375$	−7.74230	−0.399810
$376$	3.91052	0.201670
$377$	−54.7172	−2.81808
$378$	0	0
$379$	−18.7752	−0.964416	−0.482208	−	0.876057i	$-0.660165\pi$
$379$	−18.7752	−0.964416	−0.482208	+	0.876057i	$0.660165\pi$
$380$	1.66355	0.0853384
$381$	−10.9527	−0.561126
$382$	−12.9527	−0.662720
$383$	30.4752	1.55721	0.778606	−	0.627513i	$-0.215927\pi$
$383$	30.4752	1.55721	0.778606	+	0.627513i	$0.215927\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	12.6353	0.643117
$387$	2.00000	0.101666
$388$	−8.00000	−0.406138
$389$	−24.6585	−1.25024	−0.625118	−	0.780530i	$-0.714949\pi$
$389$	−24.6585	−1.25024	−0.625118	+	0.780530i	$0.714949\pi$
$390$	−4.41519	−0.223572
$391$	3.28704	0.166233
$392$	0	0
$393$	−13.5458	−0.683294
$394$	−8.92445	−0.449607
$395$	−8.69643	−0.437565
$396$	−2.45526	−0.123381
$397$	20.4985	1.02879	0.514396	−	0.857553i	$-0.328016\pi$
$397$	20.4985	1.02879	0.514396	+	0.857553i	$0.328016\pi$
$398$	5.78236	0.289844
$399$	0	0
$400$	−4.30815	−0.215407
$401$	9.62348	0.480574	0.240287	−	0.970702i	$-0.422758\pi$
$401$	9.62348	0.480574	0.240287	+	0.970702i	$0.422758\pi$
$402$	−11.7845	−0.587758
$403$	10.6163	0.528835
$404$	−0.308149	−0.0153310
$405$	−0.831776	−0.0413313
$406$	0	0
$407$	−5.73659	−0.284352
$408$	3.28704	0.162733
$409$	29.8961	1.47827	0.739135	−	0.673558i	$-0.235235\pi$
$409$	29.8961	1.47827	0.739135	+	0.673558i	$0.235235\pi$
$410$	−3.04725	−0.150493
$411$	−19.5247	−0.963080
$412$	−6.00216	−0.295705
$413$	0	0
$414$	−1.00000	−0.0491473
$415$	−5.46815	−0.268421
$416$	−5.30815	−0.260253
$417$	12.8822	0.630845
$418$	4.91052	0.240181
$419$	12.8762	0.629042	0.314521	−	0.949251i	$-0.398156\pi$
$419$	12.8762	0.629042	0.314521	+	0.949251i	$0.398156\pi$
$420$	0	0
$421$	27.5447	1.34245	0.671224	−	0.741254i	$-0.265769\pi$
$421$	27.5447	1.34245	0.671224	+	0.741254i	$0.265769\pi$
$422$	7.39763	0.360111
$423$	3.91052	0.190136
$424$	−7.78452	−0.378050
$425$	14.1610	0.686911
$426$	5.04223	0.244297
$427$	0	0
$428$	3.08948	0.149336
$429$	−13.0329	−0.629233
$430$	−1.66355	−0.0802236
$431$	−33.0915	−1.59396	−0.796982	−	0.604003i	$-0.793571\pi$
$431$	−33.0915	−1.59396	−0.796982	+	0.604003i	$0.793571\pi$
$432$	−1.00000	−0.0481125
$433$	29.3479	1.41037	0.705184	−	0.709024i	$-0.250864\pi$
$433$	29.3479	1.41037	0.705184	+	0.709024i	$0.250864\pi$
$434$	0	0
$435$	8.57407	0.411095
$436$	12.4975	0.598521
$437$	2.00000	0.0956730
$438$	−15.6163	−0.746176
$439$	28.8160	1.37531	0.687657	−	0.726036i	$-0.258640\pi$
$439$	28.8160	1.37531	0.687657	+	0.726036i	$0.258640\pi$
$440$	2.04223	0.0973593
$441$	0	0
$442$	17.4481	0.829920
$443$	7.56446	0.359398	0.179699	−	0.983722i	$-0.442488\pi$
$443$	7.56446	0.359398	0.179699	+	0.983722i	$0.442488\pi$
$444$	−2.33645	−0.110883
$445$	10.7738	0.510726
$446$	−1.00934	−0.0477938
$447$	−10.0787	−0.476708
$448$	0	0
$449$	22.5175	1.06267	0.531333	−	0.847163i	$-0.321691\pi$
$449$	22.5175	1.06267	0.531333	+	0.847163i	$0.321691\pi$
$450$	−4.30815	−0.203088
$451$	−8.99497	−0.423557
$452$	7.74230	0.364167
$453$	20.2798	0.952830
$454$	17.7824	0.834568
$455$	0	0
$456$	2.00000	0.0936586
$457$	−11.3271	−0.529860	−0.264930	−	0.964268i	$-0.585349\pi$
$457$	−11.3271	−0.529860	−0.264930	+	0.964268i	$0.585349\pi$
$458$	−14.3185	−0.669061
$459$	3.28704	0.153426
$460$	0.831776	0.0387818
$461$	6.00000	0.279448	0.139724	−	0.990190i	$-0.455378\pi$
$461$	6.00000	0.279448	0.139724	+	0.990190i	$0.455378\pi$
$462$	0	0
$463$	−25.2326	−1.17266	−0.586329	−	0.810073i	$-0.699427\pi$
$463$	−25.2326	−1.17266	−0.586329	+	0.810073i	$0.699427\pi$
$464$	10.3081	0.478544
$465$	−1.66355	−0.0771454
$466$	−13.8210	−0.640247
$467$	25.3092	1.17117	0.585585	−	0.810611i	$-0.300865\pi$
$467$	25.3092	1.17117	0.585585	+	0.810611i	$0.300865\pi$
$468$	−5.30815	−0.245369
$469$	0	0
$470$	−3.25268	−0.150035
$471$	7.07156	0.325840
$472$	−3.32710	−0.153142
$473$	−4.91052	−0.225786
$474$	−10.4553	−0.480226
$475$	8.61630	0.395343
$476$	0	0
$477$	−7.78452	−0.356429
$478$	−10.2659	−0.469552
$479$	1.84251	0.0841866	0.0420933	−	0.999114i	$-0.486597\pi$
$479$	1.84251	0.0841866	0.0420933	+	0.999114i	$0.486597\pi$
$480$	0.831776	0.0379652
$481$	−12.4022	−0.565492
$482$	8.75303	0.398690
$483$	0	0
$484$	−4.97170	−0.225986
$485$	6.65421	0.302152
$486$	−1.00000	−0.0453609
$487$	−36.5175	−1.65476	−0.827382	−	0.561639i	$-0.810171\pi$
$487$	−36.5175	−1.65476	−0.827382	+	0.561639i	$0.810171\pi$
$488$	14.6163	0.661649
$489$	2.26592	0.102469
$490$	0	0
$491$	−19.0870	−0.861382	−0.430691	−	0.902499i	$-0.641730\pi$
$491$	−19.0870	−0.861382	−0.430691	+	0.902499i	$0.641730\pi$
$492$	−3.66355	−0.165166
$493$	−33.8833	−1.52602
$494$	10.6163	0.477650
$495$	2.04223	0.0917912
$496$	−2.00000	−0.0898027
$497$	0	0
$498$	−6.57407	−0.294591
$499$	11.7505	0.526025	0.263013	−	0.964792i	$-0.415284\pi$
$499$	11.7505	0.526025	0.263013	+	0.964792i	$0.415284\pi$
$500$	7.74230	0.346246
$501$	−21.9244	−0.979512
$502$	−10.5397	−0.470410
$503$	32.2842	1.43948	0.719740	−	0.694244i	$-0.244261\pi$
$503$	32.2842	1.43948	0.719740	+	0.694244i	$0.244261\pi$
$504$	0	0
$505$	0.256311	0.0114057
$506$	2.45526	0.109150
$507$	−15.1764	−0.674009
$508$	10.9527	0.485949
$509$	−10.1292	−0.448968	−0.224484	−	0.974478i	$-0.572070\pi$
$509$	−10.1292	−0.448968	−0.224484	+	0.974478i	$0.572070\pi$
$510$	−2.73408	−0.121067
$511$	0	0
$512$	1.00000	0.0441942
$513$	2.00000	0.0883022
$514$	12.7530	0.562512
$515$	4.99245	0.219994
$516$	−2.00000	−0.0880451
$517$	−9.60134	−0.422266
$518$	0	0
$519$	18.5035	0.812216
$520$	4.41519	0.193619
$521$	30.3207	1.32837	0.664187	−	0.747567i	$-0.268778\pi$
$521$	30.3207	1.32837	0.664187	+	0.747567i	$0.268778\pi$
$522$	10.3081	0.451175
$523$	−23.5633	−1.03035	−0.515176	−	0.857084i	$-0.672274\pi$
$523$	−23.5633	−1.03035	−0.515176	+	0.857084i	$0.672274\pi$
$524$	13.5458	0.591750
$525$	0	0
$526$	15.7058	0.684804
$527$	6.57407	0.286371
$528$	2.45526	0.106851
$529$	1.00000	0.0434783
$530$	6.47498	0.281255
$531$	−3.32710	−0.144384
$532$	0	0
$533$	−19.4467	−0.842329
$534$	12.9527	0.560520
$535$	−2.56976	−0.111100
$536$	11.7845	0.509014
$537$	6.17644	0.266533
$538$	19.7927	0.853326
$539$	0	0
$540$	0.831776	0.0357939
$541$	−27.7834	−1.19450	−0.597251	−	0.802055i	$-0.703740\pi$
$541$	−27.7834	−1.19450	−0.597251	+	0.802055i	$0.703740\pi$
$542$	−15.5268	−0.666934
$543$	13.2505	0.568634
$544$	−3.28704	−0.140930
$545$	−10.3951	−0.445278
$546$	0	0
$547$	13.0233	0.556835	0.278417	−	0.960460i	$-0.410190\pi$
$547$	13.0233	0.556835	0.278417	+	0.960460i	$0.410190\pi$
$548$	19.5247	0.834052
$549$	14.6163	0.623808
$550$	10.5776	0.451031
$551$	−20.6163	−0.878284
$552$	1.00000	0.0425628
$553$	0	0
$554$	0.555116	0.0235846
$555$	1.94340	0.0824928
$556$	−12.8822	−0.546328
$557$	23.6843	1.00354	0.501768	−	0.865002i	$-0.332683\pi$
$557$	23.6843	1.00354	0.501768	+	0.865002i	$0.332683\pi$
$558$	−2.00000	−0.0846668
$559$	−10.6163	−0.449022
$560$	0	0
$561$	−8.07053	−0.340738
$562$	24.3973	1.02914
$563$	−4.55408	−0.191932	−0.0959659	−	0.995385i	$-0.530594\pi$
$563$	−4.55408	−0.191932	−0.0959659	+	0.995385i	$0.530594\pi$
$564$	−3.91052	−0.164663
$565$	−6.43986	−0.270927
$566$	19.0694	0.801547
$567$	0	0
$568$	−5.04223	−0.211567
$569$	26.5540	1.11320	0.556601	−	0.830780i	$-0.312105\pi$
$569$	26.5540	1.11320	0.556601	+	0.830780i	$0.312105\pi$
$570$	−1.66355	−0.0696785
$571$	−24.3543	−1.01919	−0.509597	−	0.860413i	$-0.670206\pi$
$571$	−24.3543	−1.01919	−0.509597	+	0.860413i	$0.670206\pi$
$572$	13.0329	0.544932
$573$	12.9527	0.541109
$574$	0	0
$575$	4.30815	0.179662
$576$	1.00000	0.0416667
$577$	13.2609	0.552058	0.276029	−	0.961149i	$-0.410981\pi$
$577$	13.2609	0.552058	0.276029	+	0.961149i	$0.410981\pi$
$578$	−6.19540	−0.257695
$579$	−12.6353	−0.525103
$580$	−8.57407	−0.356019
$581$	0	0
$582$	8.00000	0.331611
$583$	19.1130	0.791580
$584$	15.6163	0.646207
$585$	4.41519	0.182546
$586$	−1.40585	−0.0580750
$587$	−23.4305	−0.967081	−0.483540	−	0.875322i	$-0.660649\pi$
$587$	−23.4305	−0.967081	−0.483540	+	0.875322i	$0.660649\pi$
$588$	0	0
$589$	4.00000	0.164817
$590$	2.76741	0.113932
$591$	8.92445	0.367103
$592$	2.33645	0.0960274
$593$	28.4796	1.16952	0.584758	−	0.811208i	$-0.301190\pi$
$593$	28.4796	1.16952	0.584758	+	0.811208i	$0.301190\pi$
$594$	2.45526	0.100741
$595$	0	0
$596$	10.0787	0.412841
$597$	−5.78236	−0.236656
$598$	5.30815	0.217066
$599$	−34.3693	−1.40429	−0.702146	−	0.712033i	$-0.747775\pi$
$599$	−34.3693	−1.40429	−0.702146	+	0.712033i	$0.747775\pi$
$600$	4.30815	0.175879
$601$	−17.3271	−0.706787	−0.353394	−	0.935475i	$-0.614972\pi$
$601$	−17.3271	−0.706787	−0.353394	+	0.935475i	$0.614972\pi$
$602$	0	0
$603$	11.7845	0.479903
$604$	−20.2798	−0.825175
$605$	4.13534	0.168126
$606$	0.308149	0.0125177
$607$	29.6070	1.20171	0.600855	−	0.799358i	$-0.294827\pi$
$607$	29.6070	1.20171	0.600855	+	0.799358i	$0.294827\pi$
$608$	−2.00000	−0.0811107
$609$	0	0
$610$	−12.1575	−0.492242
$611$	−20.7576	−0.839763
$612$	−3.28704	−0.132871
$613$	23.0293	0.930146	0.465073	−	0.885272i	$-0.346028\pi$
$613$	23.0293	0.930146	0.465073	+	0.885272i	$0.346028\pi$
$614$	−27.2187	−1.09846
$615$	3.04725	0.122877
$616$	0	0
$617$	−20.2019	−0.813297	−0.406648	−	0.913585i	$-0.633303\pi$
$617$	−20.2019	−0.813297	−0.406648	+	0.913585i	$0.633303\pi$
$618$	6.00216	0.241442
$619$	−39.5067	−1.58791	−0.793955	−	0.607977i	$-0.791981\pi$
$619$	−39.5067	−1.58791	−0.793955	+	0.607977i	$0.791981\pi$
$620$	1.66355	0.0668099
$621$	1.00000	0.0401286
$622$	8.08948	0.324359
$623$	0	0
$624$	5.30815	0.212496
$625$	15.1009	0.604035
$626$	−13.8210	−0.552400
$627$	−4.91052	−0.196107
$628$	−7.07156	−0.282186
$629$	−7.67999	−0.306221
$630$	0	0
$631$	9.32495	0.371220	0.185610	−	0.982623i	$-0.440574\pi$
$631$	9.32495	0.371220	0.185610	+	0.982623i	$0.440574\pi$
$632$	10.4553	0.415888
$633$	−7.39763	−0.294029
$634$	12.6542	0.502563
$635$	−9.11023	−0.361528
$636$	7.78452	0.308676
$637$	0	0
$638$	−25.3092	−1.00200
$639$	−5.04223	−0.199467
$640$	−0.831776	−0.0328788
$641$	−19.2491	−0.760295	−0.380147	−	0.924926i	$-0.624127\pi$
$641$	−19.2491	−0.760295	−0.380147	+	0.924926i	$0.624127\pi$
$642$	−3.08948	−0.121932
$643$	−26.6163	−1.04964	−0.524822	−	0.851212i	$-0.675868\pi$
$643$	−26.6163	−1.04964	−0.524822	+	0.851212i	$0.675868\pi$
$644$	0	0
$645$	1.66355	0.0655023
$646$	6.57407	0.258653
$647$	23.5551	0.926047	0.463024	−	0.886346i	$-0.346765\pi$
$647$	23.5551	0.926047	0.463024	+	0.886346i	$0.346765\pi$
$648$	1.00000	0.0392837
$649$	8.16890	0.320658
$650$	22.8683	0.896968
$651$	0	0
$652$	−2.26592	−0.0887404
$653$	23.4399	0.917272	0.458636	−	0.888624i	$-0.348338\pi$
$653$	23.4399	0.917272	0.458636	+	0.888624i	$0.348338\pi$
$654$	−12.4975	−0.488690
$655$	−11.2670	−0.440240
$656$	3.66355	0.143038
$657$	15.6163	0.609250
$658$	0	0
$659$	0.234072	0.00911813	0.00455907	−	0.999990i	$-0.498549\pi$
$659$	0.234072	0.00911813	0.00455907	+	0.999990i	$0.498549\pi$
$660$	−2.04223	−0.0794935
$661$	−26.9914	−1.04984	−0.524922	−	0.851150i	$-0.675906\pi$
$661$	−26.9914	−1.04984	−0.524922	+	0.851150i	$0.675906\pi$
$662$	−24.2419	−0.942190
$663$	−17.4481	−0.677627
$664$	6.57407	0.255123
$665$	0	0
$666$	2.33645	0.0905355
$667$	−10.3081	−0.399133
$668$	21.9244	0.848282
$669$	1.00934	0.0390235
$670$	−9.80208	−0.378687
$671$	−35.8868	−1.38539
$672$	0	0
$673$	31.1578	1.20104	0.600522	−	0.799609i	$-0.294960\pi$
$673$	31.1578	1.20104	0.600522	+	0.799609i	$0.294960\pi$
$674$	24.6163	0.948184
$675$	4.30815	0.165821
$676$	15.1764	0.583709
$677$	−10.4996	−0.403534	−0.201767	−	0.979434i	$-0.564668\pi$
$677$	−10.4996	−0.403534	−0.201767	+	0.979434i	$0.564668\pi$
$678$	−7.74230	−0.297341
$679$	0	0
$680$	2.73408	0.104847
$681$	−17.7824	−0.681422
$682$	4.91052	0.188033
$683$	−41.5923	−1.59149	−0.795743	−	0.605635i	$-0.792919\pi$
$683$	−41.5923	−1.59149	−0.795743	+	0.605635i	$0.792919\pi$
$684$	−2.00000	−0.0764719
$685$	−16.2401	−0.620504
$686$	0	0
$687$	14.3185	0.546286
$688$	2.00000	0.0762493
$689$	41.3214	1.57422
$690$	−0.831776	−0.0316652
$691$	−0.686823	−0.0261280	−0.0130640	−	0.999915i	$-0.504159\pi$
$691$	−0.686823	−0.0261280	−0.0130640	+	0.999915i	$0.504159\pi$
$692$	−18.5035	−0.703399
$693$	0	0
$694$	31.4090	1.19227
$695$	10.7151	0.406448
$696$	−10.3081	−0.390729
$697$	−12.0422	−0.456132
$698$	−13.6024	−0.514857
$699$	13.8210	0.522760
$700$	0	0
$701$	−4.59415	−0.173519	−0.0867594	−	0.996229i	$-0.527651\pi$
$701$	−4.59415	−0.173519	−0.0867594	+	0.996229i	$0.527651\pi$
$702$	5.30815	0.200343
$703$	−4.67290	−0.176242
$704$	−2.45526	−0.0925361
$705$	3.25268	0.122503
$706$	27.6636	1.04113
$707$	0	0
$708$	3.32710	0.125040
$709$	−28.7351	−1.07917	−0.539585	−	0.841931i	$-0.681419\pi$
$709$	−28.7351	−1.07917	−0.539585	+	0.841931i	$0.681419\pi$
$710$	4.19400	0.157398
$711$	10.4553	0.392103
$712$	−12.9527	−0.485425
$713$	2.00000	0.0749006
$714$	0	0
$715$	−10.8404	−0.405409
$716$	−6.17644	−0.230824
$717$	10.2659	0.383388
$718$	22.2376	0.829901
$719$	−4.53437	−0.169103	−0.0845516	−	0.996419i	$-0.526946\pi$
$719$	−4.53437	−0.169103	−0.0845516	+	0.996419i	$0.526946\pi$
$720$	−0.831776	−0.0309985
$721$	0	0
$722$	−15.0000	−0.558242
$723$	−8.75303	−0.325529
$724$	−13.2505	−0.492452
$725$	−44.4090	−1.64931
$726$	4.97170	0.184517
$727$	−17.0336	−0.631743	−0.315871	−	0.948802i	$-0.602297\pi$
$727$	−17.0336	−0.631743	−0.315871	+	0.948802i	$0.602297\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−12.9893	−0.480754
$731$	−6.57407	−0.243151
$732$	−14.6163	−0.540234
$733$	−13.9191	−0.514114	−0.257057	−	0.966396i	$-0.582753\pi$
$733$	−13.9191	−0.514114	−0.257057	+	0.966396i	$0.582753\pi$
$734$	25.6056	0.945118
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	−28.9341	−1.06580
$738$	3.66355	0.134857
$739$	36.6467	1.34807	0.674035	−	0.738700i	$-0.264560\pi$
$739$	36.6467	1.34807	0.674035	+	0.738700i	$0.264560\pi$
$740$	−1.94340	−0.0714409
$741$	−10.6163	−0.389999
$742$	0	0
$743$	2.04223	0.0749220	0.0374610	−	0.999298i	$-0.488073\pi$
$743$	2.04223	0.0749220	0.0374610	+	0.999298i	$0.488073\pi$
$744$	2.00000	0.0733236
$745$	−8.38326	−0.307139
$746$	−19.9821	−0.731596
$747$	6.57407	0.240533
$748$	8.07053	0.295088
$749$	0	0
$750$	−7.74230	−0.282709
$751$	12.6750	0.462516	0.231258	−	0.972892i	$-0.425716\pi$
$751$	12.6750	0.462516	0.231258	+	0.972892i	$0.425716\pi$
$752$	3.91052	0.142602
$753$	10.5397	0.384088
$754$	−54.7172	−1.99268
$755$	16.8683	0.613900
$756$	0	0
$757$	16.0000	0.581530	0.290765	−	0.956795i	$-0.406090\pi$
$757$	16.0000	0.581530	0.290765	+	0.956795i	$0.406090\pi$
$758$	−18.7752	−0.681945
$759$	−2.45526	−0.0891203
$760$	1.66355	0.0603434
$761$	−17.5268	−0.635347	−0.317673	−	0.948200i	$-0.602902\pi$
$761$	−17.5268	−0.635347	−0.317673	+	0.948200i	$0.602902\pi$
$762$	−10.9527	−0.396776
$763$	0	0
$764$	−12.9527	−0.468614
$765$	2.73408	0.0988508
$766$	30.4752	1.10112
$767$	17.6608	0.637693
$768$	−1.00000	−0.0360844
$769$	16.2755	0.586911	0.293455	−	0.955973i	$-0.405195\pi$
$769$	16.2755	0.586911	0.293455	+	0.955973i	$0.405195\pi$
$770$	0	0
$771$	−12.7530	−0.459289
$772$	12.6353	0.454753
$773$	40.1066	1.44253	0.721267	−	0.692657i	$-0.243560\pi$
$773$	40.1066	1.44253	0.721267	+	0.692657i	$0.243560\pi$
$774$	2.00000	0.0718885
$775$	8.61630	0.309507
$776$	−8.00000	−0.287183
$777$	0	0
$778$	−24.6585	−0.884051
$779$	−7.32710	−0.262521
$780$	−4.41519	−0.158089
$781$	12.3800	0.442990
$782$	3.28704	0.117544
$783$	−10.3081	−0.368383
$784$	0	0
$785$	5.88195	0.209936
$786$	−13.5458	−0.483162
$787$	11.3257	0.403718	0.201859	−	0.979415i	$-0.435302\pi$
$787$	11.3257	0.403718	0.201859	+	0.979415i	$0.435302\pi$
$788$	−8.92445	−0.317920
$789$	−15.7058	−0.559141
$790$	−8.69643	−0.309405
$791$	0	0
$792$	−2.45526	−0.0872438
$793$	−77.5855	−2.75514
$794$	20.4985	0.727465
$795$	−6.47498	−0.229644
$796$	5.78236	0.204950
$797$	−13.2648	−0.469863	−0.234932	−	0.972012i	$-0.575487\pi$
$797$	−13.2648	−0.469863	−0.234932	+	0.972012i	$0.575487\pi$
$798$	0	0
$799$	−12.8540	−0.454742
$800$	−4.30815	−0.152316
$801$	−12.9527	−0.457663
$802$	9.62348	0.339817
$803$	−38.3421	−1.35306
$804$	−11.7845	−0.415608
$805$	0	0
$806$	10.6163	0.373943
$807$	−19.7927	−0.696737
$808$	−0.308149	−0.0108406
$809$	35.5124	1.24855	0.624276	−	0.781204i	$-0.285394\pi$
$809$	35.5124	1.24855	0.624276	+	0.781204i	$0.285394\pi$
$810$	−0.831776	−0.0292256
$811$	−5.75051	−0.201928	−0.100964	−	0.994890i	$-0.532193\pi$
$811$	−5.75051	−0.201928	−0.100964	+	0.994890i	$0.532193\pi$
$812$	0	0
$813$	15.5268	0.544549
$814$	−5.73659	−0.201067
$815$	1.88474	0.0660196
$816$	3.28704	0.115069
$817$	−4.00000	−0.139942
$818$	29.8961	1.04529
$819$	0	0
$820$	−3.04725	−0.106415
$821$	−2.99748	−0.104613	−0.0523064	−	0.998631i	$-0.516657\pi$
$821$	−2.99748	−0.104613	−0.0523064	+	0.998631i	$0.516657\pi$
$822$	−19.5247	−0.681001
$823$	−29.6277	−1.03276	−0.516378	−	0.856361i	$-0.672720\pi$
$823$	−29.6277	−1.03276	−0.516378	+	0.856361i	$0.672720\pi$
$824$	−6.00216	−0.209095
$825$	−10.5776	−0.368266
$826$	0	0
$827$	−43.7258	−1.52049	−0.760247	−	0.649634i	$-0.774922\pi$
$827$	−43.7258	−1.52049	−0.760247	+	0.649634i	$0.774922\pi$
$828$	−1.00000	−0.0347524
$829$	−22.5787	−0.784189	−0.392095	−	0.919925i	$-0.628249\pi$
$829$	−22.5787	−0.784189	−0.392095	+	0.919925i	$0.628249\pi$
$830$	−5.46815	−0.189802
$831$	−0.555116	−0.0192567
$832$	−5.30815	−0.184027
$833$	0	0
$834$	12.8822	0.446075
$835$	−18.2362	−0.631091
$836$	4.91052	0.169834
$837$	2.00000	0.0691301
$838$	12.8762	0.444800
$839$	23.8024	0.821748	0.410874	−	0.911692i	$-0.365224\pi$
$839$	23.8024	0.821748	0.410874	+	0.911692i	$0.365224\pi$
$840$	0	0
$841$	77.2579	2.66407
$842$	27.5447	0.949254
$843$	−24.3973	−0.840286
$844$	7.39763	0.254637
$845$	−12.6234	−0.434258
$846$	3.91052	0.134446
$847$	0	0
$848$	−7.78452	−0.267322
$849$	−19.0694	−0.654460
$850$	14.1610	0.485720
$851$	−2.33645	−0.0800924
$852$	5.04223	0.172744
$853$	−14.7695	−0.505697	−0.252848	−	0.967506i	$-0.581367\pi$
$853$	−14.7695	−0.505697	−0.252848	+	0.967506i	$0.581367\pi$
$854$	0	0
$855$	1.66355	0.0568923
$856$	3.08948	0.105596
$857$	−10.8539	−0.370763	−0.185381	−	0.982667i	$-0.559352\pi$
$857$	−10.8539	−0.370763	−0.185381	+	0.982667i	$0.559352\pi$
$858$	−13.0329	−0.444935
$859$	−22.8822	−0.780731	−0.390366	−	0.920660i	$-0.627651\pi$
$859$	−22.8822	−0.780731	−0.390366	+	0.920660i	$0.627651\pi$
$860$	−1.66355	−0.0567267
$861$	0	0
$862$	−33.0915	−1.12710
$863$	−17.2376	−0.586776	−0.293388	−	0.955994i	$-0.594783\pi$
$863$	−17.2376	−0.586776	−0.293388	+	0.955994i	$0.594783\pi$
$864$	−1.00000	−0.0340207
$865$	15.3908	0.523303
$866$	29.3479	0.997281
$867$	6.19540	0.210407
$868$	0	0
$869$	−25.6704	−0.870808
$870$	8.57407	0.290688
$871$	−62.5540	−2.11956
$872$	12.4975	0.423218
$873$	−8.00000	−0.270759
$874$	2.00000	0.0676510
$875$	0	0
$876$	−15.6163	−0.527626
$877$	38.2043	1.29007	0.645034	−	0.764154i	$-0.276843\pi$
$877$	38.2043	1.29007	0.645034	+	0.764154i	$0.276843\pi$
$878$	28.8160	0.972493
$879$	1.40585	0.0474180
$880$	2.04223	0.0688434
$881$	35.0515	1.18091	0.590457	−	0.807069i	$-0.298947\pi$
$881$	35.0515	1.18091	0.590457	+	0.807069i	$0.298947\pi$
$882$	0	0
$883$	−43.2139	−1.45426	−0.727132	−	0.686498i	$-0.759147\pi$
$883$	−43.2139	−1.45426	−0.727132	+	0.686498i	$0.759147\pi$
$884$	17.4481	0.586842
$885$	−2.76741	−0.0930253
$886$	7.56446	0.254133
$887$	2.56725	0.0861997	0.0430999	−	0.999071i	$-0.486277\pi$
$887$	2.56725	0.0861997	0.0430999	+	0.999071i	$0.486277\pi$
$888$	−2.33645	−0.0784061
$889$	0	0
$890$	10.7738	0.361138
$891$	−2.45526	−0.0822543
$892$	−1.00934	−0.0337953
$893$	−7.82104	−0.261721
$894$	−10.0787	−0.337084
$895$	5.13742	0.171725
$896$	0	0
$897$	−5.30815	−0.177234
$898$	22.5175	0.751418
$899$	−20.6163	−0.687592
$900$	−4.30815	−0.143605
$901$	25.5880	0.852460
$902$	−8.99497	−0.299500
$903$	0	0
$904$	7.74230	0.257505
$905$	11.0215	0.366366
$906$	20.2798	0.673753
$907$	−26.0787	−0.865930	−0.432965	−	0.901411i	$-0.642533\pi$
$907$	−26.0787	−0.865930	−0.432965	+	0.901411i	$0.642533\pi$
$908$	17.7824	0.590128
$909$	−0.308149	−0.0102206
$910$	0	0
$911$	−58.1853	−1.92777	−0.963883	−	0.266325i	$-0.914190\pi$
$911$	−58.1853	−1.92777	−0.963883	+	0.266325i	$0.914190\pi$
$912$	2.00000	0.0662266
$913$	−16.1411	−0.534191
$914$	−11.3271	−0.374667
$915$	12.1575	0.401914
$916$	−14.3185	−0.473097
$917$	0	0
$918$	3.28704	0.108488
$919$	−25.5669	−0.843374	−0.421687	−	0.906742i	$-0.638562\pi$
$919$	−25.5669	−0.843374	−0.421687	+	0.906742i	$0.638562\pi$
$920$	0.831776	0.0274228
$921$	27.2187	0.896886
$922$	6.00000	0.197599
$923$	26.7649	0.880977
$924$	0	0
$925$	−10.0658	−0.330960
$926$	−25.2326	−0.829195
$927$	−6.00216	−0.197137
$928$	10.3081	0.338382
$929$	−20.5526	−0.674309	−0.337154	−	0.941449i	$-0.609464\pi$
$929$	−20.5526	−0.674309	−0.337154	+	0.941449i	$0.609464\pi$
$930$	−1.66355	−0.0545500
$931$	0	0
$932$	−13.8210	−0.452723
$933$	−8.08948	−0.264838
$934$	25.3092	0.828142
$935$	−6.71287	−0.219534
$936$	−5.30815	−0.173502
$937$	18.8304	0.615162	0.307581	−	0.951522i	$-0.400481\pi$
$937$	18.8304	0.615162	0.307581	+	0.951522i	$0.400481\pi$
$938$	0	0
$939$	13.8210	0.451033
$940$	−3.25268	−0.106091
$941$	−2.90620	−0.0947395	−0.0473698	−	0.998877i	$-0.515084\pi$
$941$	−2.90620	−0.0947395	−0.0473698	+	0.998877i	$0.515084\pi$
$942$	7.07156	0.230404
$943$	−3.66355	−0.119302
$944$	−3.32710	−0.108288
$945$	0	0
$946$	−4.91052	−0.159655
$947$	−14.5172	−0.471746	−0.235873	−	0.971784i	$-0.575795\pi$
$947$	−14.5172	−0.471746	−0.235873	+	0.971784i	$0.575795\pi$
$948$	−10.4553	−0.339571
$949$	−82.8936	−2.69084
$950$	8.61630	0.279550
$951$	−12.6542	−0.410341
$952$	0	0
$953$	38.5561	1.24896	0.624478	−	0.781042i	$-0.285312\pi$
$953$	38.5561	1.24896	0.624478	+	0.781042i	$0.285312\pi$
$954$	−7.78452	−0.252033
$955$	10.7738	0.348631
$956$	−10.2659	−0.332024
$957$	25.3092	0.818130
$958$	1.84251	0.0595289
$959$	0	0
$960$	0.831776	0.0268455
$961$	−27.0000	−0.870968
$962$	−12.4022	−0.399863
$963$	3.08948	0.0995571
$964$	8.75303	0.281916
$965$	−10.5097	−0.338319
$966$	0	0
$967$	−24.2606	−0.780169	−0.390085	−	0.920779i	$-0.627554\pi$
$967$	−24.2606	−0.780169	−0.390085	+	0.920779i	$0.627554\pi$
$968$	−4.97170	−0.159797
$969$	−6.57407	−0.211190
$970$	6.65421	0.213654
$971$	−1.58265	−0.0507897	−0.0253949	−	0.999677i	$-0.508084\pi$
$971$	−1.58265	−0.0507897	−0.0253949	+	0.999677i	$0.508084\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−36.5175	−1.17010
$975$	−22.8683	−0.732372
$976$	14.6163	0.467856
$977$	−18.8740	−0.603833	−0.301916	−	0.953334i	$-0.597626\pi$
$977$	−18.8740	−0.603833	−0.301916	+	0.953334i	$0.597626\pi$
$978$	2.26592	0.0724562
$979$	31.8024	1.01641
$980$	0	0
$981$	12.4975	0.399014
$982$	−19.0870	−0.609089
$983$	−54.2798	−1.73126	−0.865629	−	0.500686i	$-0.833081\pi$
$983$	−54.2798	−1.73126	−0.865629	+	0.500686i	$0.833081\pi$
$984$	−3.66355	−0.116790
$985$	7.42314	0.236521
$986$	−33.8833	−1.07906
$987$	0	0
$988$	10.6163	0.337749
$989$	−2.00000	−0.0635963
$990$	2.04223	0.0649062
$991$	36.7316	1.16682	0.583408	−	0.812179i	$-0.301719\pi$
$991$	36.7316	1.16682	0.583408	+	0.812179i	$0.301719\pi$
$992$	−2.00000	−0.0635001
$993$	24.2419	0.769295
$994$	0	0
$995$	−4.80963	−0.152476
$996$	−6.57407	−0.208307
$997$	45.5855	1.44371	0.721853	−	0.692046i	$-0.243291\pi$
$997$	45.5855	1.44371	0.721853	+	0.692046i	$0.243291\pi$
$998$	11.7505	0.371956
$999$	−2.33645	−0.0739219

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6762.2.a.cl.1.2		4
7.2	even	3		966.2.i.m.277.3	✓	8
7.4	even	3		966.2.i.m.415.3	yes	8
7.6	odd	2		6762.2.a.cr.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.m.277.3	✓	8	7.2	even	3
966.2.i.m.415.3	yes	8	7.4	even	3
6762.2.a.cl.1.2		4	1.1	even	1	trivial
6762.2.a.cr.1.3		4	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.831776 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -0.831776 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -0.831776 q^{10} -2.45526 q^{11} -1.00000 q^{12} -5.30815 q^{13} +0.831776 q^{15} +1.00000 q^{16} -3.28704 q^{17} +1.00000 q^{18} -2.00000 q^{19} -0.831776 q^{20} -2.45526 q^{22} -1.00000 q^{23} -1.00000 q^{24} -4.30815 q^{25} -5.30815 q^{26} -1.00000 q^{27} +10.3081 q^{29} +0.831776 q^{30} -2.00000 q^{31} +1.00000 q^{32} +2.45526 q^{33} -3.28704 q^{34} +1.00000 q^{36} +2.33645 q^{37} -2.00000 q^{38} +5.30815 q^{39} -0.831776 q^{40} +3.66355 q^{41} +2.00000 q^{43} -2.45526 q^{44} -0.831776 q^{45} -1.00000 q^{46} +3.91052 q^{47} -1.00000 q^{48} -4.30815 q^{50} +3.28704 q^{51} -5.30815 q^{52} -7.78452 q^{53} -1.00000 q^{54} +2.04223 q^{55} +2.00000 q^{57} +10.3081 q^{58} -3.32710 q^{59} +0.831776 q^{60} +14.6163 q^{61} -2.00000 q^{62} +1.00000 q^{64} +4.41519 q^{65} +2.45526 q^{66} +11.7845 q^{67} -3.28704 q^{68} +1.00000 q^{69} -5.04223 q^{71} +1.00000 q^{72} +15.6163 q^{73} +2.33645 q^{74} +4.30815 q^{75} -2.00000 q^{76} +5.30815 q^{78} +10.4553 q^{79} -0.831776 q^{80} +1.00000 q^{81} +3.66355 q^{82} +6.57407 q^{83} +2.73408 q^{85} +2.00000 q^{86} -10.3081 q^{87} -2.45526 q^{88} -12.9527 q^{89} -0.831776 q^{90} -1.00000 q^{92} +2.00000 q^{93} +3.91052 q^{94} +1.66355 q^{95} -1.00000 q^{96} -8.00000 q^{97} -2.45526 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9} + 2 q^{10} - 4 q^{12} + 6 q^{13} - 2 q^{15} + 4 q^{16} + 2 q^{17} + 4 q^{18} - 8 q^{19} + 2 q^{20} - 4 q^{23} - 4 q^{24} + 10 q^{25} + 6 q^{26} - 4 q^{27} + 14 q^{29} - 2 q^{30} - 8 q^{31} + 4 q^{32} + 2 q^{34} + 4 q^{36} + 20 q^{37} - 8 q^{38} - 6 q^{39} + 2 q^{40} + 4 q^{41} + 8 q^{43} + 2 q^{45} - 4 q^{46} - 4 q^{47} - 4 q^{48} + 10 q^{50} - 2 q^{51} + 6 q^{52} + 18 q^{53} - 4 q^{54} - 16 q^{55} + 8 q^{57} + 14 q^{58} + 8 q^{59} - 2 q^{60} + 4 q^{61} - 8 q^{62} + 4 q^{64} + 14 q^{65} - 2 q^{67} + 2 q^{68} + 4 q^{69} + 4 q^{71} + 4 q^{72} + 8 q^{73} + 20 q^{74} - 10 q^{75} - 8 q^{76} - 6 q^{78} + 32 q^{79} + 2 q^{80} + 4 q^{81} + 4 q^{82} - 4 q^{83} + 14 q^{85} + 8 q^{86} - 14 q^{87} - 8 q^{89} + 2 q^{90} - 4 q^{92} + 8 q^{93} - 4 q^{94} - 4 q^{95} - 4 q^{96} - 32 q^{97}+O(q^{100}) \) 4 * q + 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 4 * q^6 + 4 * q^8 + 4 * q^9 + 2 * q^10 - 4 * q^12 + 6 * q^13 - 2 * q^15 + 4 * q^16 + 2 * q^17 + 4 * q^18 - 8 * q^19 + 2 * q^20 - 4 * q^23 - 4 * q^24 + 10 * q^25 + 6 * q^26 - 4 * q^27 + 14 * q^29 - 2 * q^30 - 8 * q^31 + 4 * q^32 + 2 * q^34 + 4 * q^36 + 20 * q^37 - 8 * q^38 - 6 * q^39 + 2 * q^40 + 4 * q^41 + 8 * q^43 + 2 * q^45 - 4 * q^46 - 4 * q^47 - 4 * q^48 + 10 * q^50 - 2 * q^51 + 6 * q^52 + 18 * q^53 - 4 * q^54 - 16 * q^55 + 8 * q^57 + 14 * q^58 + 8 * q^59 - 2 * q^60 + 4 * q^61 - 8 * q^62 + 4 * q^64 + 14 * q^65 - 2 * q^67 + 2 * q^68 + 4 * q^69 + 4 * q^71 + 4 * q^72 + 8 * q^73 + 20 * q^74 - 10 * q^75 - 8 * q^76 - 6 * q^78 + 32 * q^79 + 2 * q^80 + 4 * q^81 + 4 * q^82 - 4 * q^83 + 14 * q^85 + 8 * q^86 - 14 * q^87 - 8 * q^89 + 2 * q^90 - 4 * q^92 + 8 * q^93 - 4 * q^94 - 4 * q^95 - 4 * q^96 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more