LMFDB - Embedded newform 6762.2.a.cl.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6762, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6762.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$53.9948418468$
Analytic rank:	$0$
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			1.1
Root			$4.22985$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.22985 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.22985 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -3.22985 q^{10} +3.31243 q^{11} -1.00000 q^{12} +4.43192 q^{13} +3.22985 q^{15} +1.00000 q^{16} +0.0825866 q^{17} +1.00000 q^{18} -2.00000 q^{19} -3.22985 q^{20} +3.31243 q^{22} -1.00000 q^{23} -1.00000 q^{24} +5.43192 q^{25} +4.43192 q^{26} -1.00000 q^{27} +0.568085 q^{29} +3.22985 q^{30} -2.00000 q^{31} +1.00000 q^{32} -3.31243 q^{33} +0.0825866 q^{34} +1.00000 q^{36} -2.45970 q^{37} -2.00000 q^{38} -4.43192 q^{39} -3.22985 q^{40} +8.45970 q^{41} +2.00000 q^{43} +3.31243 q^{44} -3.22985 q^{45} -1.00000 q^{46} -7.62487 q^{47} -1.00000 q^{48} +5.43192 q^{50} -0.0825866 q^{51} +4.43192 q^{52} +14.0937 q^{53} -1.00000 q^{54} -10.6987 q^{55} +2.00000 q^{57} +0.568085 q^{58} -12.9194 q^{59} +3.22985 q^{60} -4.86383 q^{61} -2.00000 q^{62} +1.00000 q^{64} -14.3144 q^{65} -3.31243 q^{66} -10.0937 q^{67} +0.0825866 q^{68} +1.00000 q^{69} +7.69866 q^{71} +1.00000 q^{72} -3.86383 q^{73} -2.45970 q^{74} -5.43192 q^{75} -2.00000 q^{76} -4.43192 q^{78} +4.68757 q^{79} -3.22985 q^{80} +1.00000 q^{81} +8.45970 q^{82} -0.165173 q^{83} -0.266742 q^{85} +2.00000 q^{86} -0.568085 q^{87} +3.31243 q^{88} +11.3235 q^{89} -3.22985 q^{90} -1.00000 q^{92} +2.00000 q^{93} -7.62487 q^{94} +6.45970 q^{95} -1.00000 q^{96} -8.00000 q^{97} +3.31243 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−3.22985	−1.44443	−0.722216	−	0.691668i	$-0.756876\pi$
$5$	−3.22985	−1.44443	−0.722216	+	0.691668i	$0.756876\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−3.22985	−1.02137
$11$	3.31243	0.998736	0.499368	−	0.866390i	$-0.333565\pi$
$11$	3.31243	0.998736	0.499368	+	0.866390i	$0.333565\pi$
$12$	−1.00000	−0.288675
$13$	4.43192	1.22919	0.614596	−	0.788842i	$-0.289319\pi$
$13$	4.43192	1.22919	0.614596	+	0.788842i	$0.289319\pi$
$14$	0	0
$15$	3.22985	0.833943
$16$	1.00000	0.250000
$17$	0.0825866	0.0200302	0.0100151	−	0.999950i	$-0.496812\pi$
$17$	0.0825866	0.0200302	0.0100151	+	0.999950i	$0.496812\pi$
$18$	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	$0.573682\pi$
$20$	−3.22985	−0.722216
$21$	0	0
$22$	3.31243	0.706213
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.00000	−0.204124
$25$	5.43192	1.08638
$26$	4.43192	0.869170
$27$	−1.00000	−0.192450
$28$	0	0
$29$	0.568085	0.105491	0.0527453	−	0.998608i	$-0.483203\pi$
$29$	0.568085	0.105491	0.0527453	+	0.998608i	$0.483203\pi$
$30$	3.22985	0.589687
$31$	−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
$33$	−3.31243	−0.576621
$34$	0.0825866	0.0141635
$35$	0	0
$36$	1.00000	0.166667
$37$	−2.45970	−0.404371	−0.202186	−	0.979347i	$-0.564804\pi$
$37$	−2.45970	−0.404371	−0.202186	+	0.979347i	$0.564804\pi$
$38$	−2.00000	−0.324443
$39$	−4.43192	−0.709674
$40$	−3.22985	−0.510684
$41$	8.45970	1.32118	0.660591	−	0.750746i	$-0.270306\pi$
$41$	8.45970	1.32118	0.660591	+	0.750746i	$0.270306\pi$
$42$	0	0
$43$	2.00000	0.304997	0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000	0.304997	0.152499	+	0.988304i	$0.451268\pi$
$44$	3.31243	0.499368
$45$	−3.22985	−0.481477
$46$	−1.00000	−0.147442
$47$	−7.62487	−1.11220	−0.556101	−	0.831115i	$-0.687703\pi$
$47$	−7.62487	−1.11220	−0.556101	+	0.831115i	$0.687703\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	5.43192	0.768189
$51$	−0.0825866	−0.0115644
$52$	4.43192	0.614596
$53$	14.0937	1.93592	0.967958	−	0.251113i	$-0.0807965\pi$
$53$	14.0937	1.93592	0.967958	+	0.251113i	$0.0807965\pi$
$54$	−1.00000	−0.136083
$55$	−10.6987	−1.44261
$56$	0	0
$57$	2.00000	0.264906
$58$	0.568085	0.0745932
$59$	−12.9194	−1.68196	−0.840981	−	0.541065i	$-0.818021\pi$
$59$	−12.9194	−1.68196	−0.840981	+	0.541065i	$0.818021\pi$
$60$	3.22985	0.416972
$61$	−4.86383	−0.622750	−0.311375	−	0.950287i	$-0.600789\pi$
$61$	−4.86383	−0.622750	−0.311375	+	0.950287i	$0.600789\pi$
$62$	−2.00000	−0.254000
$63$	0	0
$64$	1.00000	0.125000
$65$	−14.3144	−1.77548
$66$	−3.31243	−0.407732
$67$	−10.0937	−1.23314	−0.616570	−	0.787300i	$-0.711478\pi$
$67$	−10.0937	−1.23314	−0.616570	+	0.787300i	$0.711478\pi$
$68$	0.0825866	0.0100151
$69$	1.00000	0.120386
$70$	0	0
$71$	7.69866	0.913663	0.456831	−	0.889553i	$-0.348984\pi$
$71$	7.69866	0.913663	0.456831	+	0.889553i	$0.348984\pi$
$72$	1.00000	0.117851
$73$	−3.86383	−0.452227	−0.226114	−	0.974101i	$-0.572602\pi$
$73$	−3.86383	−0.452227	−0.226114	+	0.974101i	$0.572602\pi$
$74$	−2.45970	−0.285934
$75$	−5.43192	−0.627224
$76$	−2.00000	−0.229416
$77$	0	0
$78$	−4.43192	−0.501816
$79$	4.68757	0.527392	0.263696	−	0.964606i	$-0.415058\pi$
$79$	4.68757	0.527392	0.263696	+	0.964606i	$0.415058\pi$
$80$	−3.22985	−0.361108
$81$	1.00000	0.111111
$82$	8.45970	0.934217
$83$	−0.165173	−0.0181301	−0.00906506	−	0.999959i	$-0.502886\pi$
$83$	−0.165173	−0.0181301	−0.00906506	+	0.999959i	$0.502886\pi$
$84$	0	0
$85$	−0.266742	−0.0289322
$86$	2.00000	0.215666
$87$	−0.568085	−0.0609051
$88$	3.31243	0.353107
$89$	11.3235	1.20029	0.600146	−	0.799891i	$-0.295109\pi$
$89$	11.3235	1.20029	0.600146	+	0.799891i	$0.295109\pi$
$90$	−3.22985	−0.340456
$91$	0	0
$92$	−1.00000	−0.104257
$93$	2.00000	0.207390
$94$	−7.62487	−0.786445
$95$	6.45970	0.662751
$96$	−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
$99$	3.31243	0.332912
$100$	5.43192	0.543192
$101$	9.43192	0.938511	0.469255	−	0.883063i	$-0.344522\pi$
$101$	9.43192	0.938511	0.469255	+	0.883063i	$0.344522\pi$
$102$	−0.0825866	−0.00817729
$103$	19.7006	1.94116	0.970581	−	0.240776i	$-0.0774021\pi$
$103$	19.7006	1.94116	0.970581	+	0.240776i	$0.0774021\pi$
$104$	4.43192	0.434585
$105$	0	0
$106$	14.0937	1.36890
$107$	14.6249	1.41384	0.706920	−	0.707294i	$-0.250084\pi$
$107$	14.6249	1.41384	0.706920	+	0.707294i	$0.250084\pi$
$108$	−1.00000	−0.0962250
$109$	−6.01109	−0.575758	−0.287879	−	0.957667i	$-0.592950\pi$
$109$	−6.01109	−0.575758	−0.287879	+	0.957667i	$0.592950\pi$
$110$	−10.6987	−1.02008
$111$	2.45970	0.233464
$112$	0	0
$113$	−1.39502	−0.131233	−0.0656163	−	0.997845i	$-0.520901\pi$
$113$	−1.39502	−0.131233	−0.0656163	+	0.997845i	$0.520901\pi$
$114$	2.00000	0.187317
$115$	3.22985	0.301185
$116$	0.568085	0.0527453
$117$	4.43192	0.409731
$118$	−12.9194	−1.18933
$119$	0	0
$120$	3.22985	0.294843
$121$	−0.0277798	−0.00252544
$122$	−4.86383	−0.440351
$123$	−8.45970	−0.762785
$124$	−2.00000	−0.179605
$125$	−1.39502	−0.124774
$126$	0	0
$127$	−13.3235	−1.18227	−0.591136	−	0.806572i	$-0.701320\pi$
$127$	−13.3235	−1.18227	−0.591136	+	0.806572i	$0.701320\pi$
$128$	1.00000	0.0883883
$129$	−2.00000	−0.176090
$130$	−14.3144	−1.25546
$131$	1.86261	0.162737	0.0813683	−	0.996684i	$-0.474071\pi$
$131$	1.86261	0.162737	0.0813683	+	0.996684i	$0.474071\pi$
$132$	−3.31243	−0.288310
$133$	0	0
$134$	−10.0937	−0.871961
$135$	3.22985	0.277981
$136$	0.0825866	0.00708174
$137$	14.2119	1.21421	0.607104	−	0.794623i	$-0.292331\pi$
$137$	14.2119	1.21421	0.607104	+	0.794623i	$0.292331\pi$
$138$	1.00000	0.0851257
$139$	3.59709	0.305101	0.152551	−	0.988296i	$-0.451251\pi$
$139$	3.59709	0.305101	0.152551	+	0.988296i	$0.451251\pi$
$140$	0	0
$141$	7.62487	0.642130
$142$	7.69866	0.646057
$143$	14.6804	1.22764
$144$	1.00000	0.0833333
$145$	−1.83483	−0.152374
$146$	−3.86383	−0.319773
$147$	0	0
$148$	−2.45970	−0.202186
$149$	−3.85472	−0.315791	−0.157895	−	0.987456i	$-0.550471\pi$
$149$	−3.85472	−0.315791	−0.157895	+	0.987456i	$0.550471\pi$
$150$	−5.43192	−0.443514
$151$	−5.59586	−0.455385	−0.227692	−	0.973733i	$-0.573118\pi$
$151$	−5.59586	−0.455385	−0.227692	+	0.973733i	$0.573118\pi$
$152$	−2.00000	−0.162221
$153$	0.0825866	0.00667673
$154$	0	0
$155$	6.45970	0.518855
$156$	−4.43192	−0.354837
$157$	18.1763	1.45062	0.725312	−	0.688420i	$-0.241696\pi$
$157$	18.1763	1.45062	0.725312	+	0.688420i	$0.241696\pi$
$158$	4.68757	0.372923
$159$	−14.0937	−1.11770
$160$	−3.22985	−0.255342
$161$	0	0
$162$	1.00000	0.0785674
$163$	−5.26674	−0.412523	−0.206262	−	0.978497i	$-0.566130\pi$
$163$	−5.26674	−0.412523	−0.206262	+	0.978497i	$0.566130\pi$
$164$	8.45970	0.660591
$165$	10.6987	0.832889
$166$	−0.165173	−0.0128199
$167$	−7.29575	−0.564562	−0.282281	−	0.959332i	$-0.591091\pi$
$167$	−7.29575	−0.564562	−0.282281	+	0.959332i	$0.591091\pi$
$168$	0	0
$169$	6.64187	0.510913
$170$	−0.266742	−0.0204582
$171$	−2.00000	−0.152944
$172$	2.00000	0.152499
$173$	−19.5613	−1.48722	−0.743608	−	0.668616i	$-0.766887\pi$
$173$	−19.5613	−1.48722	−0.743608	+	0.668616i	$0.766887\pi$
$174$	−0.568085	−0.0430664
$175$	0	0
$176$	3.31243	0.249684
$177$	12.9194	0.971081
$178$	11.3235	0.848734
$179$	2.35813	0.176255	0.0881273	−	0.996109i	$-0.471912\pi$
$179$	2.35813	0.176255	0.0881273	+	0.996109i	$0.471912\pi$
$180$	−3.22985	−0.240739
$181$	−11.0735	−0.823085	−0.411542	−	0.911391i	$-0.635010\pi$
$181$	−11.0735	−0.823085	−0.411542	+	0.911391i	$0.635010\pi$
$182$	0	0
$183$	4.86383	0.359545
$184$	−1.00000	−0.0737210
$185$	7.94444	0.584087
$186$	2.00000	0.146647
$187$	0.273563	0.0200049
$188$	−7.62487	−0.556101
$189$	0	0
$190$	6.45970	0.468636
$191$	11.3235	0.819342	0.409671	−	0.912233i	$-0.365644\pi$
$191$	11.3235	0.819342	0.409671	+	0.912233i	$0.365644\pi$
$192$	−1.00000	−0.0721688
$193$	12.4875	0.898868	0.449434	−	0.893314i	$-0.351626\pi$
$193$	12.4875	0.898868	0.449434	+	0.893314i	$0.351626\pi$
$194$	−8.00000	−0.574367
$195$	14.3144	1.02508
$196$	0	0
$197$	20.2957	1.44601	0.723006	−	0.690842i	$-0.242760\pi$
$197$	20.2957	1.44601	0.723006	+	0.690842i	$0.242760\pi$
$198$	3.31243	0.235404
$199$	9.60696	0.681019	0.340510	−	0.940241i	$-0.389400\pi$
$199$	9.60696	0.681019	0.340510	+	0.940241i	$0.389400\pi$
$200$	5.43192	0.384094
$201$	10.0937	0.711953
$202$	9.43192	0.663627
$203$	0	0
$204$	−0.0825866	−0.00578222
$205$	−27.3235	−1.90836
$206$	19.7006	1.37261
$207$	−1.00000	−0.0695048
$208$	4.43192	0.307298
$209$	−6.62487	−0.458252
$210$	0	0
$211$	9.19295	0.632869	0.316434	−	0.948614i	$-0.397514\pi$
$211$	9.19295	0.632869	0.316434	+	0.948614i	$0.397514\pi$
$212$	14.0937	0.967958
$213$	−7.69866	−0.527503
$214$	14.6249	0.999735
$215$	−6.45970	−0.440548
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−6.01109	−0.407123
$219$	3.86383	0.261093
$220$	−10.6987	−0.721303
$221$	0.366017	0.0246210
$222$	2.45970	0.165084
$223$	13.3791	0.895930	0.447965	−	0.894051i	$-0.352149\pi$
$223$	13.3791	0.895930	0.447965	+	0.894051i	$0.352149\pi$
$224$	0	0
$225$	5.43192	0.362128
$226$	−1.39502	−0.0927954
$227$	21.6070	1.43410	0.717052	−	0.697020i	$-0.245491\pi$
$227$	21.6070	1.43410	0.717052	+	0.697020i	$0.245491\pi$
$228$	2.00000	0.132453
$229$	27.2608	1.80145	0.900723	−	0.434394i	$-0.143037\pi$
$229$	27.2608	1.80145	0.900723	+	0.434394i	$0.143037\pi$
$230$	3.22985	0.212970
$231$	0	0
$232$	0.568085	0.0372966
$233$	9.24974	0.605970	0.302985	−	0.952995i	$-0.402017\pi$
$233$	9.24974	0.605970	0.302985	+	0.952995i	$0.402017\pi$
$234$	4.43192	0.289723
$235$	24.6272	1.60650
$236$	−12.9194	−0.840981
$237$	−4.68757	−0.304490
$238$	0	0
$239$	−13.2667	−0.858154	−0.429077	−	0.903268i	$-0.641161\pi$
$239$	−13.2667	−0.858154	−0.429077	+	0.903268i	$0.641161\pi$
$240$	3.22985	0.208486
$241$	25.0846	1.61584	0.807919	−	0.589293i	$-0.200594\pi$
$241$	25.0846	1.61584	0.807919	+	0.589293i	$0.200594\pi$
$242$	−0.0277798	−0.00178575
$243$	−1.00000	−0.0641500
$244$	−4.86383	−0.311375
$245$	0	0
$246$	−8.45970	−0.539370
$247$	−8.86383	−0.563992
$248$	−2.00000	−0.127000
$249$	0.165173	0.0104674
$250$	−1.39502	−0.0882289
$251$	20.7097	1.30719	0.653594	−	0.756845i	$-0.273260\pi$
$251$	20.7097	1.30719	0.653594	+	0.756845i	$0.273260\pi$
$252$	0	0
$253$	−3.31243	−0.208251
$254$	−13.3235	−0.835992
$255$	0.266742	0.0167040
$256$	1.00000	0.0625000
$257$	29.0846	1.81425	0.907123	−	0.420866i	$-0.138274\pi$
$257$	29.0846	1.81425	0.907123	+	0.420866i	$0.138274\pi$
$258$	−2.00000	−0.124515
$259$	0	0
$260$	−14.3144	−0.887742
$261$	0.568085	0.0351636
$262$	1.86261	0.115072
$263$	7.76104	0.478566	0.239283	−	0.970950i	$-0.423088\pi$
$263$	7.76104	0.478566	0.239283	+	0.970950i	$0.423088\pi$
$264$	−3.31243	−0.203866
$265$	−45.5204	−2.79630
$266$	0	0
$267$	−11.3235	−0.692989
$268$	−10.0937	−0.616570
$269$	−8.22196	−0.501302	−0.250651	−	0.968078i	$-0.580645\pi$
$269$	−8.22196	−0.501302	−0.250651	+	0.968078i	$0.580645\pi$
$270$	3.22985	0.196562
$271$	15.4887	0.940871	0.470436	−	0.882434i	$-0.344097\pi$
$271$	15.4887	0.940871	0.470436	+	0.882434i	$0.344097\pi$
$272$	0.0825866	0.00500755
$273$	0	0
$274$	14.2119	0.858574
$275$	17.9929	1.08501
$276$	1.00000	0.0601929
$277$	−25.5165	−1.53314	−0.766568	−	0.642163i	$-0.778037\pi$
$277$	−25.5165	−1.53314	−0.766568	+	0.642163i	$0.778037\pi$
$278$	3.59709	0.215739
$279$	−2.00000	−0.119737
$280$	0	0
$281$	−31.1155	−1.85620	−0.928099	−	0.372334i	$-0.878558\pi$
$281$	−31.1155	−1.85620	−0.928099	+	0.372334i	$0.878558\pi$
$282$	7.62487	0.454054
$283$	19.5244	1.16060	0.580302	−	0.814402i	$-0.302935\pi$
$283$	19.5244	1.16060	0.580302	+	0.814402i	$0.302935\pi$
$284$	7.69866	0.456831
$285$	−6.45970	−0.382639
$286$	14.6804	0.868072
$287$	0	0
$288$	1.00000	0.0589256
$289$	−16.9932	−0.999599
$290$	−1.83483	−0.107745
$291$	8.00000	0.468968
$292$	−3.86383	−0.226114
$293$	2.93533	0.171484	0.0857418	−	0.996317i	$-0.472674\pi$
$293$	2.93533	0.171484	0.0857418	+	0.996317i	$0.472674\pi$
$294$	0	0
$295$	41.7277	2.42948
$296$	−2.45970	−0.142967
$297$	−3.31243	−0.192207
$298$	−3.85472	−0.223298
$299$	−4.43192	−0.256304
$300$	−5.43192	−0.313612
$301$	0	0
$302$	−5.59586	−0.322006
$303$	−9.43192	−0.541849
$304$	−2.00000	−0.114708
$305$	15.7094	0.899519
$306$	0.0825866	0.00472116
$307$	−5.94322	−0.339197	−0.169599	−	0.985513i	$-0.554247\pi$
$307$	−5.94322	−0.339197	−0.169599	+	0.985513i	$0.554247\pi$
$308$	0	0
$309$	−19.7006	−1.12073
$310$	6.45970	0.366886
$311$	19.6249	1.11282	0.556412	−	0.830906i	$-0.312178\pi$
$311$	19.6249	1.11282	0.556412	+	0.830906i	$0.312178\pi$
$312$	−4.43192	−0.250908
$313$	9.24974	0.522826	0.261413	−	0.965227i	$-0.415812\pi$
$313$	9.24974	0.522826	0.261413	+	0.965227i	$0.415812\pi$
$314$	18.1763	1.02575
$315$	0	0
$316$	4.68757	0.263696
$317$	31.8388	1.78824	0.894122	−	0.447823i	$-0.147801\pi$
$317$	31.8388	1.78824	0.894122	+	0.447823i	$0.147801\pi$
$318$	−14.0937	−0.790334
$319$	1.88174	0.105357
$320$	−3.22985	−0.180554
$321$	−14.6249	−0.816281
$322$	0	0
$323$	−0.165173	−0.00919048
$324$	1.00000	0.0555556
$325$	24.0738	1.33537
$326$	−5.26674	−0.291698
$327$	6.01109	0.332414
$328$	8.45970	0.467109
$329$	0	0
$330$	10.6987	0.588942
$331$	29.1067	1.59985	0.799926	−	0.600099i	$-0.204872\pi$
$331$	29.1067	1.59985	0.799926	+	0.600099i	$0.204872\pi$
$332$	−0.165173	−0.00906506
$333$	−2.45970	−0.134790
$334$	−7.29575	−0.399205
$335$	32.6010	1.78119
$336$	0	0
$337$	5.13617	0.279785	0.139892	−	0.990167i	$-0.455324\pi$
$337$	5.13617	0.279785	0.139892	+	0.990167i	$0.455324\pi$
$338$	6.64187	0.361270
$339$	1.39502	0.0757671
$340$	−0.266742	−0.0144661
$341$	−6.62487	−0.358757
$342$	−2.00000	−0.108148
$343$	0	0
$344$	2.00000	0.107833
$345$	−3.22985	−0.173889
$346$	−19.5613	−1.05162
$347$	−16.0858	−0.863530	−0.431765	−	0.901986i	$-0.642109\pi$
$347$	−16.0858	−0.863530	−0.431765	+	0.901986i	$0.642109\pi$
$348$	−0.568085	−0.0304525
$349$	−11.8070	−0.632017	−0.316008	−	0.948756i	$-0.602343\pi$
$349$	−11.8070	−0.632017	−0.316008	+	0.948756i	$0.602343\pi$
$350$	0	0
$351$	−4.43192	−0.236558
$352$	3.31243	0.176553
$353$	32.4597	1.72766	0.863828	−	0.503787i	$-0.168061\pi$
$353$	32.4597	1.72766	0.863828	+	0.503787i	$0.168061\pi$
$354$	12.9194	0.686658
$355$	−24.8655	−1.31972
$356$	11.3235	0.600146
$357$	0	0
$358$	2.35813	0.124631
$359$	20.2945	1.07110	0.535552	−	0.844502i	$-0.320104\pi$
$359$	20.2945	1.07110	0.535552	+	0.844502i	$0.320104\pi$
$360$	−3.22985	−0.170228
$361$	−15.0000	−0.789474
$362$	−11.0735	−0.582009
$363$	0.0277798	0.00145806
$364$	0	0
$365$	12.4796	0.653211
$366$	4.86383	0.254237
$367$	−19.3434	−1.00972	−0.504859	−	0.863202i	$-0.668456\pi$
$367$	−19.3434	−1.00972	−0.504859	+	0.863202i	$0.668456\pi$
$368$	−1.00000	−0.0521286
$369$	8.45970	0.440394
$370$	7.94444	0.413012
$371$	0	0
$372$	2.00000	0.103695
$373$	16.8011	0.869930	0.434965	−	0.900447i	$-0.356761\pi$
$373$	16.8011	0.869930	0.434965	+	0.900447i	$0.356761\pi$
$374$	0.273563	0.0141456
$375$	1.39502	0.0720386
$376$	−7.62487	−0.393223
$377$	2.51770	0.129668
$378$	0	0
$379$	−11.2854	−0.579692	−0.289846	−	0.957073i	$-0.593604\pi$
$379$	−11.2854	−0.579692	−0.289846	+	0.957073i	$0.593604\pi$
$380$	6.45970	0.331375
$381$	13.3235	0.682585
$382$	11.3235	0.579362
$383$	26.5890	1.35864	0.679318	−	0.733844i	$-0.262276\pi$
$383$	26.5890	1.35864	0.679318	+	0.733844i	$0.262276\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	12.4875	0.635596
$387$	2.00000	0.101666
$388$	−8.00000	−0.406138
$389$	7.56249	0.383433	0.191717	−	0.981450i	$-0.438595\pi$
$389$	7.56249	0.383433	0.191717	+	0.981450i	$0.438595\pi$
$390$	14.3144	0.724838
$391$	−0.0825866	−0.00417658
$392$	0	0
$393$	−1.86261	−0.0939561
$394$	20.2957	1.02248
$395$	−15.1401	−0.761782
$396$	3.31243	0.166456
$397$	−15.4609	−0.775961	−0.387981	−	0.921668i	$-0.626827\pi$
$397$	−15.4609	−0.775961	−0.387981	+	0.921668i	$0.626827\pi$
$398$	9.60696	0.481553
$399$	0	0
$400$	5.43192	0.271596
$401$	1.45772	0.0727950	0.0363975	−	0.999337i	$-0.488412\pi$
$401$	1.45772	0.0727950	0.0363975	+	0.999337i	$0.488412\pi$
$402$	10.0937	0.503427
$403$	−8.86383	−0.441539
$404$	9.43192	0.469255
$405$	−3.22985	−0.160492
$406$	0	0
$407$	−8.14758	−0.403860
$408$	−0.0825866	−0.00408865
$409$	−4.26797	−0.211037	−0.105519	−	0.994417i	$-0.533650\pi$
$409$	−4.26797	−0.211037	−0.105519	+	0.994417i	$0.533650\pi$
$410$	−27.3235	−1.34941
$411$	−14.2119	−0.701023
$412$	19.7006	0.970581
$413$	0	0
$414$	−1.00000	−0.0491473
$415$	0.533484	0.0261877
$416$	4.43192	0.217293
$417$	−3.59709	−0.176150
$418$	−6.62487	−0.324033
$419$	−23.1694	−1.13190	−0.565951	−	0.824439i	$-0.691491\pi$
$419$	−23.1694	−1.13190	−0.565951	+	0.824439i	$0.691491\pi$
$420$	0	0
$421$	33.3124	1.62355	0.811774	−	0.583971i	$-0.198502\pi$
$421$	33.3124	1.62355	0.811774	+	0.583971i	$0.198502\pi$
$422$	9.19295	0.447506
$423$	−7.62487	−0.370734
$424$	14.0937	0.684450
$425$	0.448603	0.0217605
$426$	−7.69866	−0.373001
$427$	0	0
$428$	14.6249	0.706920
$429$	−14.6804	−0.708778
$430$	−6.45970	−0.311514
$431$	−9.72521	−0.468447	−0.234224	−	0.972183i	$-0.575255\pi$
$431$	−9.72521	−0.468447	−0.234224	+	0.972183i	$0.575255\pi$
$432$	−1.00000	−0.0481125
$433$	−24.7384	−1.18885	−0.594427	−	0.804150i	$-0.702621\pi$
$433$	−24.7384	−1.18885	−0.594427	+	0.804150i	$0.702621\pi$
$434$	0	0
$435$	1.83483	0.0879732
$436$	−6.01109	−0.287879
$437$	2.00000	0.0956730
$438$	3.86383	0.184621
$439$	−31.2719	−1.49253	−0.746264	−	0.665650i	$-0.768154\pi$
$439$	−31.2719	−1.49253	−0.746264	+	0.665650i	$0.768154\pi$
$440$	−10.6987	−0.510038
$441$	0	0
$442$	0.366017	0.0174096
$443$	−32.8956	−1.56292	−0.781458	−	0.623958i	$-0.785524\pi$
$443$	−32.8956	−1.56292	−0.781458	+	0.623958i	$0.785524\pi$
$444$	2.45970	0.116732
$445$	−36.5733	−1.73374
$446$	13.3791	0.633518
$447$	3.85472	0.182322
$448$	0	0
$449$	5.89039	0.277985	0.138992	−	0.990293i	$-0.455614\pi$
$449$	5.89039	0.277985	0.138992	+	0.990293i	$0.455614\pi$
$450$	5.43192	0.256063
$451$	28.0222	1.31951
$452$	−1.39502	−0.0656163
$453$	5.59586	0.262917
$454$	21.6070	1.01406
$455$	0	0
$456$	2.00000	0.0936586
$457$	−20.9194	−0.978568	−0.489284	−	0.872125i	$-0.662742\pi$
$457$	−20.9194	−0.978568	−0.489284	+	0.872125i	$0.662742\pi$
$458$	27.2608	1.27381
$459$	−0.0825866	−0.00385481
$460$	3.22985	0.150592
$461$	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
$463$	13.7277	0.637979	0.318989	−	0.947758i	$-0.396657\pi$
$463$	13.7277	0.637979	0.318989	+	0.947758i	$0.396657\pi$
$464$	0.568085	0.0263727
$465$	−6.45970	−0.299561
$466$	9.24974	0.428486
$467$	−1.88174	−0.0870767	−0.0435383	−	0.999052i	$-0.513863\pi$
$467$	−1.88174	−0.0870767	−0.0435383	+	0.999052i	$0.513863\pi$
$468$	4.43192	0.204865
$469$	0	0
$470$	24.6272	1.13597
$471$	−18.1763	−0.837518
$472$	−12.9194	−0.594663
$473$	6.62487	0.304612
$474$	−4.68757	−0.215307
$475$	−10.8638	−0.498467
$476$	0	0
$477$	14.0937	0.645305
$478$	−13.2667	−0.606807
$479$	29.7094	1.35746	0.678729	−	0.734389i	$-0.262531\pi$
$479$	29.7094	1.35746	0.678729	+	0.734389i	$0.262531\pi$
$480$	3.22985	0.147422
$481$	−10.9012	−0.497050
$482$	25.0846	1.14257
$483$	0	0
$484$	−0.0277798	−0.00126272
$485$	25.8388	1.17328
$486$	−1.00000	−0.0453609
$487$	−19.8904	−0.901319	−0.450660	−	0.892696i	$-0.648811\pi$
$487$	−19.8904	−0.901319	−0.450660	+	0.892696i	$0.648811\pi$
$488$	−4.86383	−0.220175
$489$	5.26674	0.238170
$490$	0	0
$491$	0.982995	0.0443619	0.0221810	−	0.999754i	$-0.492939\pi$
$491$	0.982995	0.0443619	0.0221810	+	0.999754i	$0.492939\pi$
$492$	−8.45970	−0.381393
$493$	0.0469162	0.00211300
$494$	−8.86383	−0.398803
$495$	−10.6987	−0.480869
$496$	−2.00000	−0.0898027
$497$	0	0
$498$	0.165173	0.00740159
$499$	−3.52330	−0.157725	−0.0788623	−	0.996886i	$-0.525129\pi$
$499$	−3.52330	−0.157725	−0.0788623	+	0.996886i	$0.525129\pi$
$500$	−1.39502	−0.0623872
$501$	7.29575	0.325950
$502$	20.7097	0.924321
$503$	−33.8054	−1.50731	−0.753654	−	0.657271i	$-0.771711\pi$
$503$	−33.8054	−1.50731	−0.753654	+	0.657271i	$0.771711\pi$
$504$	0	0
$505$	−30.4636	−1.35561
$506$	−3.31243	−0.147256
$507$	−6.64187	−0.294976
$508$	−13.3235	−0.591136
$509$	22.6817	1.00535	0.502673	−	0.864476i	$-0.332350\pi$
$509$	22.6817	1.00535	0.502673	+	0.864476i	$0.332350\pi$
$510$	0.266742	0.0118115
$511$	0	0
$512$	1.00000	0.0441942
$513$	2.00000	0.0883022
$514$	29.0846	1.28287
$515$	−63.6300	−2.80387
$516$	−2.00000	−0.0880451
$517$	−25.2569	−1.11080
$518$	0	0
$519$	19.5613	0.858644
$520$	−14.3144	−0.627728
$521$	−36.9615	−1.61931	−0.809656	−	0.586905i	$-0.800346\pi$
$521$	−36.9615	−1.61931	−0.809656	+	0.586905i	$0.800346\pi$
$522$	0.568085	0.0248644
$523$	8.64476	0.378009	0.189004	−	0.981976i	$-0.439474\pi$
$523$	8.64476	0.378009	0.189004	+	0.981976i	$0.439474\pi$
$524$	1.86261	0.0813683
$525$	0	0
$526$	7.76104	0.338397
$527$	−0.165173	−0.00719506
$528$	−3.31243	−0.144155
$529$	1.00000	0.0434783
$530$	−45.5204	−1.97728
$531$	−12.9194	−0.560654
$532$	0	0
$533$	37.4927	1.62399
$534$	−11.3235	−0.490017
$535$	−47.2361	−2.04219
$536$	−10.0937	−0.435980
$537$	−2.35813	−0.101761
$538$	−8.22196	−0.354474
$539$	0	0
$540$	3.22985	0.138991
$541$	−14.1571	−0.608662	−0.304331	−	0.952566i	$-0.598433\pi$
$541$	−14.1571	−0.608662	−0.304331	+	0.952566i	$0.598433\pi$
$542$	15.4887	0.665297
$543$	11.0735	0.475208
$544$	0.0825866	0.00354087
$545$	19.4149	0.831643
$546$	0	0
$547$	−19.0500	−0.814518	−0.407259	−	0.913313i	$-0.633515\pi$
$547$	−19.0500	−0.814518	−0.407259	+	0.913313i	$0.633515\pi$
$548$	14.2119	0.607104
$549$	−4.86383	−0.207583
$550$	17.9929	0.767218
$551$	−1.13617	−0.0484024
$552$	1.00000	0.0425628
$553$	0	0
$554$	−25.5165	−1.08409
$555$	−7.94444	−0.337223
$556$	3.59709	0.152551
$557$	−35.1981	−1.49139	−0.745696	−	0.666286i	$-0.767883\pi$
$557$	−35.1981	−1.49139	−0.745696	+	0.666286i	$0.767883\pi$
$558$	−2.00000	−0.0846668
$559$	8.86383	0.374900
$560$	0	0
$561$	−0.273563	−0.0115498
$562$	−31.1155	−1.31253
$563$	4.06665	0.171389	0.0856945	−	0.996321i	$-0.472689\pi$
$563$	4.06665	0.171389	0.0856945	+	0.996321i	$0.472689\pi$
$564$	7.62487	0.321065
$565$	4.50570	0.189556
$566$	19.5244	0.820670
$567$	0	0
$568$	7.69866	0.323028
$569$	8.73433	0.366162	0.183081	−	0.983098i	$-0.441393\pi$
$569$	8.73433	0.366162	0.183081	+	0.983098i	$0.441393\pi$
$570$	−6.45970	−0.270567
$571$	−47.1424	−1.97285	−0.986424	−	0.164216i	$-0.947491\pi$
$571$	−47.1424	−1.97285	−0.986424	+	0.164216i	$0.947491\pi$
$572$	14.6804	0.613820
$573$	−11.3235	−0.473047
$574$	0	0
$575$	−5.43192	−0.226527
$576$	1.00000	0.0416667
$577$	−20.7554	−0.864060	−0.432030	−	0.901859i	$-0.642203\pi$
$577$	−20.7554	−0.864060	−0.432030	+	0.901859i	$0.642203\pi$
$578$	−16.9932	−0.706823
$579$	−12.4875	−0.518962
$580$	−1.83483	−0.0761870
$581$	0	0
$582$	8.00000	0.331611
$583$	46.6844	1.93347
$584$	−3.86383	−0.159886
$585$	−14.3144	−0.591828
$586$	2.93533	0.121257
$587$	−26.8734	−1.10918	−0.554592	−	0.832123i	$-0.687125\pi$
$587$	−26.8734	−1.10918	−0.554592	+	0.832123i	$0.687125\pi$
$588$	0	0
$589$	4.00000	0.164817
$590$	41.7277	1.71790
$591$	−20.2957	−0.834855
$592$	−2.45970	−0.101093
$593$	−26.8122	−1.10105	−0.550523	−	0.834820i	$-0.685572\pi$
$593$	−26.8122	−1.10105	−0.550523	+	0.834820i	$0.685572\pi$
$594$	−3.31243	−0.135911
$595$	0	0
$596$	−3.85472	−0.157895
$597$	−9.60696	−0.393187
$598$	−4.43192	−0.181234
$599$	−31.2207	−1.27564	−0.637822	−	0.770184i	$-0.720165\pi$
$599$	−31.2207	−1.27564	−0.637822	+	0.770184i	$0.720165\pi$
$600$	−5.43192	−0.221757
$601$	−26.9194	−1.09806	−0.549032	−	0.835801i	$-0.685004\pi$
$601$	−26.9194	−1.09806	−0.549032	+	0.835801i	$0.685004\pi$
$602$	0	0
$603$	−10.0937	−0.411046
$604$	−5.59586	−0.227692
$605$	0.0897245	0.00364782
$606$	−9.43192	−0.383145
$607$	24.5153	0.995043	0.497522	−	0.867452i	$-0.334243\pi$
$607$	24.5153	0.995043	0.497522	+	0.867452i	$0.334243\pi$
$608$	−2.00000	−0.0811107
$609$	0	0
$610$	15.7094	0.636056
$611$	−33.7928	−1.36711
$612$	0.0825866	0.00333837
$613$	10.5224	0.424995	0.212498	−	0.977162i	$-0.431840\pi$
$613$	10.5224	0.424995	0.212498	+	0.977162i	$0.431840\pi$
$614$	−5.94322	−0.239849
$615$	27.3235	1.10179
$616$	0	0
$617$	46.1087	1.85627	0.928134	−	0.372247i	$-0.121413\pi$
$617$	46.1087	1.85627	0.928134	+	0.372247i	$0.121413\pi$
$618$	−19.7006	−0.792476
$619$	2.58920	0.104069	0.0520343	−	0.998645i	$-0.483429\pi$
$619$	2.58920	0.104069	0.0520343	+	0.998645i	$0.483429\pi$
$620$	6.45970	0.259428
$621$	1.00000	0.0401286
$622$	19.6249	0.786886
$623$	0	0
$624$	−4.43192	−0.177419
$625$	−22.6539	−0.906155
$626$	9.24974	0.369694
$627$	6.62487	0.264572
$628$	18.1763	0.725312
$629$	−0.203138	−0.00809964
$630$	0	0
$631$	44.6200	1.77630	0.888148	−	0.459558i	$-0.151992\pi$
$631$	44.6200	1.77630	0.888148	+	0.459558i	$0.151992\pi$
$632$	4.68757	0.186461
$633$	−9.19295	−0.365387
$634$	31.8388	1.26448
$635$	43.0330	1.70771
$636$	−14.0937	−0.558851
$637$	0	0
$638$	1.88174	0.0744989
$639$	7.69866	0.304554
$640$	−3.22985	−0.127671
$641$	22.7852	0.899961	0.449981	−	0.893038i	$-0.351431\pi$
$641$	22.7852	0.899961	0.449981	+	0.893038i	$0.351431\pi$
$642$	−14.6249	−0.577198
$643$	−7.13617	−0.281423	−0.140712	−	0.990051i	$-0.544939\pi$
$643$	−7.13617	−0.281423	−0.140712	+	0.990051i	$0.544939\pi$
$644$	0	0
$645$	6.45970	0.254350
$646$	−0.165173	−0.00649865
$647$	−2.51648	−0.0989330	−0.0494665	−	0.998776i	$-0.515752\pi$
$647$	−2.51648	−0.0989330	−0.0494665	+	0.998776i	$0.515752\pi$
$648$	1.00000	0.0392837
$649$	−42.7946	−1.67984
$650$	24.0738	0.944252
$651$	0	0
$652$	−5.26674	−0.206262
$653$	12.4943	0.488940	0.244470	−	0.969657i	$-0.421386\pi$
$653$	12.4943	0.488940	0.244470	+	0.969657i	$0.421386\pi$
$654$	6.01109	0.235052
$655$	−6.01594	−0.235062
$656$	8.45970	0.330296
$657$	−3.86383	−0.150742
$658$	0	0
$659$	−15.8635	−0.617955	−0.308977	−	0.951069i	$-0.599987\pi$
$659$	−15.8635	−0.617955	−0.308977	+	0.951069i	$0.599987\pi$
$660$	10.6987	0.416445
$661$	24.1802	0.940502	0.470251	−	0.882533i	$-0.344163\pi$
$661$	24.1802	0.940502	0.470251	+	0.882533i	$0.344163\pi$
$662$	29.1067	1.13127
$663$	−0.366017	−0.0142149
$664$	−0.165173	−0.00640996
$665$	0	0
$666$	−2.45970	−0.0953113
$667$	−0.568085	−0.0219963
$668$	−7.29575	−0.282281
$669$	−13.3791	−0.517265
$670$	32.6010	1.25949
$671$	−16.1111	−0.621963
$672$	0	0
$673$	51.4000	1.98133	0.990663	−	0.136333i	$-0.0435317\pi$
$673$	51.4000	1.98133	0.990663	+	0.136333i	$0.0435317\pi$
$674$	5.13617	0.197838
$675$	−5.43192	−0.209075
$676$	6.64187	0.255457
$677$	33.7117	1.29565	0.647823	−	0.761791i	$-0.275679\pi$
$677$	33.7117	1.29565	0.647823	+	0.761791i	$0.275679\pi$
$678$	1.39502	0.0535755
$679$	0	0
$680$	−0.266742	−0.0102291
$681$	−21.6070	−0.827980
$682$	−6.62487	−0.253679
$683$	34.2373	1.31005	0.655027	−	0.755605i	$-0.272657\pi$
$683$	34.2373	1.31005	0.655027	+	0.755605i	$0.272657\pi$
$684$	−2.00000	−0.0764719
$685$	−45.9024	−1.75384
$686$	0	0
$687$	−27.2608	−1.04007
$688$	2.00000	0.0762493
$689$	62.4620	2.37961
$690$	−3.22985	−0.122958
$691$	26.5903	1.01154	0.505771	−	0.862668i	$-0.331208\pi$
$691$	26.5903	1.01154	0.505771	+	0.862668i	$0.331208\pi$
$692$	−19.5613	−0.743608
$693$	0	0
$694$	−16.0858	−0.610608
$695$	−11.6180	−0.440698
$696$	−0.568085	−0.0215332
$697$	0.698658	0.0264635
$698$	−11.8070	−0.446903
$699$	−9.24974	−0.349857
$700$	0	0
$701$	−8.93533	−0.337483	−0.168741	−	0.985660i	$-0.553970\pi$
$701$	−8.93533	−0.337483	−0.168741	+	0.985660i	$0.553970\pi$
$702$	−4.43192	−0.167272
$703$	4.91939	0.185538
$704$	3.31243	0.124842
$705$	−24.6272	−0.927513
$706$	32.4597	1.22164
$707$	0	0
$708$	12.9194	0.485540
$709$	−8.28343	−0.311091	−0.155545	−	0.987829i	$-0.549713\pi$
$709$	−8.28343	−0.311091	−0.155545	+	0.987829i	$0.549713\pi$
$710$	−24.8655	−0.933185
$711$	4.68757	0.175797
$712$	11.3235	0.424367
$713$	2.00000	0.0749006
$714$	0	0
$715$	−47.4155	−1.77324
$716$	2.35813	0.0881273
$717$	13.2667	0.495456
$718$	20.2945	0.757385
$719$	−42.1413	−1.57161	−0.785804	−	0.618476i	$-0.787750\pi$
$719$	−42.1413	−1.57161	−0.785804	+	0.618476i	$0.787750\pi$
$720$	−3.22985	−0.120369
$721$	0	0
$722$	−15.0000	−0.558242
$723$	−25.0846	−0.932905
$724$	−11.0735	−0.411542
$725$	3.08579	0.114603
$726$	0.0277798	0.00103100
$727$	46.8789	1.73864	0.869321	−	0.494249i	$-0.164557\pi$
$727$	46.8789	1.73864	0.869321	+	0.494249i	$0.164557\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	12.4796	0.461890
$731$	0.165173	0.00610915
$732$	4.86383	0.179772
$733$	−53.5554	−1.97811	−0.989056	−	0.147541i	$-0.952864\pi$
$733$	−53.5554	−1.97811	−0.989056	+	0.147541i	$0.952864\pi$
$734$	−19.3434	−0.713978
$735$	0	0
$736$	−1.00000	−0.0368605
$737$	−33.4346	−1.23158
$738$	8.45970	0.311406
$739$	−12.7913	−0.470534	−0.235267	−	0.971931i	$-0.575597\pi$
$739$	−12.7913	−0.470534	−0.235267	+	0.971931i	$0.575597\pi$
$740$	7.94444	0.292043
$741$	8.86383	0.325621
$742$	0	0
$743$	−10.6987	−0.392496	−0.196248	−	0.980554i	$-0.562876\pi$
$743$	−10.6987	−0.392496	−0.196248	+	0.980554i	$0.562876\pi$
$744$	2.00000	0.0733236
$745$	12.4501	0.456138
$746$	16.8011	0.615133
$747$	−0.165173	−0.00604337
$748$	0.273563	0.0100024
$749$	0	0
$750$	1.39502	0.0509390
$751$	−31.8190	−1.16109	−0.580547	−	0.814227i	$-0.697161\pi$
$751$	−31.8190	−1.16109	−0.580547	+	0.814227i	$0.697161\pi$
$752$	−7.62487	−0.278050
$753$	−20.7097	−0.754705
$754$	2.51770	0.0916893
$755$	18.0738	0.657773
$756$	0	0
$757$	16.0000	0.581530	0.290765	−	0.956795i	$-0.406090\pi$
$757$	16.0000	0.581530	0.290765	+	0.956795i	$0.406090\pi$
$758$	−11.2854	−0.409904
$759$	3.31243	0.120234
$760$	6.45970	0.234318
$761$	13.4887	0.488965	0.244482	−	0.969654i	$-0.421382\pi$
$761$	13.4887	0.488965	0.244482	+	0.969654i	$0.421382\pi$
$762$	13.3235	0.482660
$763$	0	0
$764$	11.3235	0.409671
$765$	−0.266742	−0.00964408
$766$	26.5890	0.960701
$767$	−57.2576	−2.06745
$768$	−1.00000	−0.0360844
$769$	52.9971	1.91113	0.955563	−	0.294788i	$-0.0952490\pi$
$769$	52.9971	1.91113	0.955563	+	0.294788i	$0.0952490\pi$
$770$	0	0
$771$	−29.0846	−1.04745
$772$	12.4875	0.449434
$773$	−9.19647	−0.330774	−0.165387	−	0.986229i	$-0.552887\pi$
$773$	−9.19647	−0.330774	−0.165387	+	0.986229i	$0.552887\pi$
$774$	2.00000	0.0718885
$775$	−10.8638	−0.390240
$776$	−8.00000	−0.287183
$777$	0	0
$778$	7.56249	0.271128
$779$	−16.9194	−0.606200
$780$	14.3144	0.512538
$781$	25.5013	0.912508
$782$	−0.0825866	−0.00295329
$783$	−0.568085	−0.0203017
$784$	0	0
$785$	−58.7066	−2.09533
$786$	−1.86261	−0.0664370
$787$	−18.9393	−0.675112	−0.337556	−	0.941305i	$-0.609600\pi$
$787$	−18.9393	−0.675112	−0.337556	+	0.941305i	$0.609600\pi$
$788$	20.2957	0.723006
$789$	−7.76104	−0.276300
$790$	−15.1401	−0.538661
$791$	0	0
$792$	3.31243	0.117702
$793$	−21.5561	−0.765479
$794$	−15.4609	−0.548687
$795$	45.5204	1.61444
$796$	9.60696	0.340510
$797$	−24.5175	−0.868456	−0.434228	−	0.900803i	$-0.642979\pi$
$797$	−24.5175	−0.868456	−0.434228	+	0.900803i	$0.642979\pi$
$798$	0	0
$799$	−0.629712	−0.0222776
$800$	5.43192	0.192047
$801$	11.3235	0.400097
$802$	1.45772	0.0514738
$803$	−12.7987	−0.451656
$804$	10.0937	0.355977
$805$	0	0
$806$	−8.86383	−0.312215
$807$	8.22196	0.289427
$808$	9.43192	0.331814
$809$	−18.1318	−0.637480	−0.318740	−	0.947842i	$-0.603260\pi$
$809$	−18.1318	−0.637480	−0.318740	+	0.947842i	$0.603260\pi$
$810$	−3.22985	−0.113485
$811$	9.52330	0.334408	0.167204	−	0.985922i	$-0.446526\pi$
$811$	9.52330	0.334408	0.167204	+	0.985922i	$0.446526\pi$
$812$	0	0
$813$	−15.4887	−0.543212
$814$	−8.14758	−0.285572
$815$	17.0108	0.595861
$816$	−0.0825866	−0.00289111
$817$	−4.00000	−0.139942
$818$	−4.26797	−0.149226
$819$	0	0
$820$	−27.3235	−0.954179
$821$	28.6079	0.998421	0.499211	−	0.866481i	$-0.333623\pi$
$821$	28.6079	0.998421	0.499211	+	0.866481i	$0.333623\pi$
$822$	−14.2119	−0.495698
$823$	39.1426	1.36442	0.682212	−	0.731154i	$-0.261018\pi$
$823$	39.1426	1.36442	0.682212	+	0.731154i	$0.261018\pi$
$824$	19.7006	0.686304
$825$	−17.9929	−0.626431
$826$	0	0
$827$	−37.6625	−1.30965	−0.654827	−	0.755779i	$-0.727259\pi$
$827$	−37.6625	−1.30965	−0.654827	+	0.755779i	$0.727259\pi$
$828$	−1.00000	−0.0347524
$829$	−12.5430	−0.435638	−0.217819	−	0.975989i	$-0.569894\pi$
$829$	−12.5430	−0.435638	−0.217819	+	0.975989i	$0.569894\pi$
$830$	0.533484	0.0185175
$831$	25.5165	0.885157
$832$	4.43192	0.153649
$833$	0	0
$834$	−3.59709	−0.124557
$835$	23.5641	0.815471
$836$	−6.62487	−0.229126
$837$	2.00000	0.0691301
$838$	−23.1694	−0.800375
$839$	29.5084	1.01874	0.509372	−	0.860546i	$-0.329878\pi$
$839$	29.5084	1.01874	0.509372	+	0.860546i	$0.329878\pi$
$840$	0	0
$841$	−28.6773	−0.988872
$842$	33.3124	1.14802
$843$	31.1155	1.07168
$844$	9.19295	0.316434
$845$	−21.4522	−0.737979
$846$	−7.62487	−0.262148
$847$	0	0
$848$	14.0937	0.483979
$849$	−19.5244	−0.670075
$850$	0.448603	0.0153870
$851$	2.45970	0.0843173
$852$	−7.69866	−0.263752
$853$	−18.8280	−0.644659	−0.322329	−	0.946628i	$-0.604466\pi$
$853$	−18.8280	−0.644659	−0.322329	+	0.946628i	$0.604466\pi$
$854$	0	0
$855$	6.45970	0.220917
$856$	14.6249	0.499868
$857$	10.5693	0.361041	0.180520	−	0.983571i	$-0.442222\pi$
$857$	10.5693	0.361041	0.180520	+	0.983571i	$0.442222\pi$
$858$	−14.6804	−0.501182
$859$	−6.40291	−0.218465	−0.109232	−	0.994016i	$-0.534839\pi$
$859$	−6.40291	−0.218465	−0.109232	+	0.994016i	$0.534839\pi$
$860$	−6.45970	−0.220274
$861$	0	0
$862$	−9.72521	−0.331242
$863$	−15.2945	−0.520632	−0.260316	−	0.965524i	$-0.583827\pi$
$863$	−15.2945	−0.520632	−0.260316	+	0.965524i	$0.583827\pi$
$864$	−1.00000	−0.0340207
$865$	63.1799	2.14818
$866$	−24.7384	−0.840646
$867$	16.9932	0.577119
$868$	0	0
$869$	15.5273	0.526726
$870$	1.83483	0.0622065
$871$	−44.7343	−1.51576
$872$	−6.01109	−0.203561
$873$	−8.00000	−0.270759
$874$	2.00000	0.0676510
$875$	0	0
$876$	3.86383	0.130547
$877$	−5.69988	−0.192471	−0.0962357	−	0.995359i	$-0.530680\pi$
$877$	−5.69988	−0.192471	−0.0962357	+	0.995359i	$0.530680\pi$
$878$	−31.2719	−1.05538
$879$	−2.93533	−0.0990061
$880$	−10.6987	−0.360652
$881$	−1.27676	−0.0430153	−0.0215076	−	0.999769i	$-0.506847\pi$
$881$	−1.27676	−0.0430153	−0.0215076	+	0.999769i	$0.506847\pi$
$882$	0	0
$883$	−33.0305	−1.11157	−0.555783	−	0.831328i	$-0.687581\pi$
$883$	−33.0305	−1.11157	−0.555783	+	0.831328i	$0.687581\pi$
$884$	0.366017	0.0123105
$885$	−41.7277	−1.40266
$886$	−32.8956	−1.10515
$887$	41.8218	1.40424	0.702119	−	0.712060i	$-0.252237\pi$
$887$	41.8218	1.40424	0.702119	+	0.712060i	$0.252237\pi$
$888$	2.45970	0.0825420
$889$	0	0
$890$	−36.5733	−1.22594
$891$	3.31243	0.110971
$892$	13.3791	0.447965
$893$	15.2497	0.510313
$894$	3.85472	0.128921
$895$	−7.61639	−0.254588
$896$	0	0
$897$	4.43192	0.147977
$898$	5.89039	0.196565
$899$	−1.13617	−0.0378934
$900$	5.43192	0.181064
$901$	1.16395	0.0387768
$902$	28.0222	0.933037
$903$	0	0
$904$	−1.39502	−0.0463977
$905$	35.7656	1.18889
$906$	5.59586	0.185910
$907$	−12.1453	−0.403278	−0.201639	−	0.979460i	$-0.564627\pi$
$907$	−12.1453	−0.403278	−0.201639	+	0.979460i	$0.564627\pi$
$908$	21.6070	0.717052
$909$	9.43192	0.312837
$910$	0	0
$911$	5.05119	0.167353	0.0836767	−	0.996493i	$-0.473334\pi$
$911$	5.05119	0.167353	0.0836767	+	0.996493i	$0.473334\pi$
$912$	2.00000	0.0662266
$913$	−0.547125	−0.0181072
$914$	−20.9194	−0.691952
$915$	−15.7094	−0.519338
$916$	27.2608	0.900723
$917$	0	0
$918$	−0.0825866	−0.00272576
$919$	−7.51328	−0.247840	−0.123920	−	0.992292i	$-0.539547\pi$
$919$	−7.51328	−0.247840	−0.123920	+	0.992292i	$0.539547\pi$
$920$	3.22985	0.106485
$921$	5.94322	0.195836
$922$	6.00000	0.197599
$923$	34.1198	1.12307
$924$	0	0
$925$	−13.3609	−0.439302
$926$	13.7277	0.451119
$927$	19.7006	0.647054
$928$	0.568085	0.0186483
$929$	37.1243	1.21801	0.609005	−	0.793166i	$-0.291569\pi$
$929$	37.1243	1.21801	0.609005	+	0.793166i	$0.291569\pi$
$930$	−6.45970	−0.211822
$931$	0	0
$932$	9.24974	0.302985
$933$	−19.6249	−0.642489
$934$	−1.88174	−0.0615725
$935$	−0.883566	−0.0288957
$936$	4.43192	0.144862
$937$	−18.6288	−0.608577	−0.304289	−	0.952580i	$-0.598419\pi$
$937$	−18.6288	−0.608577	−0.304289	+	0.952580i	$0.598419\pi$
$938$	0	0
$939$	−9.24974	−0.301854
$940$	24.6272	0.803249
$941$	−42.7764	−1.39447	−0.697235	−	0.716842i	$-0.745587\pi$
$941$	−42.7764	−1.39447	−0.697235	+	0.716842i	$0.745587\pi$
$942$	−18.1763	−0.592215
$943$	−8.45970	−0.275486
$944$	−12.9194	−0.420490
$945$	0	0
$946$	6.62487	0.215393
$947$	50.2191	1.63190	0.815951	−	0.578122i	$-0.196214\pi$
$947$	50.2191	1.63190	0.815951	+	0.578122i	$0.196214\pi$
$948$	−4.68757	−0.152245
$949$	−17.1242	−0.555874
$950$	−10.8638	−0.352469
$951$	−31.8388	−1.03244
$952$	0	0
$953$	−4.96631	−0.160874	−0.0804372	−	0.996760i	$-0.525632\pi$
$953$	−4.96631	−0.160874	−0.0804372	+	0.996760i	$0.525632\pi$
$954$	14.0937	0.456300
$955$	−36.5733	−1.18348
$956$	−13.2667	−0.429077
$957$	−1.88174	−0.0608281
$958$	29.7094	0.959868
$959$	0	0
$960$	3.22985	0.104243
$961$	−27.0000	−0.870968
$962$	−10.9012	−0.351468
$963$	14.6249	0.471280
$964$	25.0846	0.807919
$965$	−40.3326	−1.29835
$966$	0	0
$967$	57.8649	1.86081	0.930405	−	0.366533i	$-0.119455\pi$
$967$	57.8649	1.86081	0.930405	+	0.366533i	$0.119455\pi$
$968$	−0.0277798	−0.000892876 0
$969$	0.165173	0.00530613
$970$	25.8388	0.829633
$971$	−46.0150	−1.47669	−0.738347	−	0.674422i	$-0.764393\pi$
$971$	−46.0150	−1.47669	−0.738347	+	0.674422i	$0.764393\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−19.8904	−0.637329
$975$	−24.0738	−0.770978
$976$	−4.86383	−0.155687
$977$	−8.53119	−0.272937	−0.136468	−	0.990644i	$-0.543575\pi$
$977$	−8.53119	−0.272937	−0.136468	+	0.990644i	$0.543575\pi$
$978$	5.26674	0.168412
$979$	37.5084	1.19877
$980$	0	0
$981$	−6.01109	−0.191919
$982$	0.982995	0.0313686
$983$	−39.5959	−1.26291	−0.631456	−	0.775412i	$-0.717542\pi$
$983$	−39.5959	−1.26291	−0.631456	+	0.775412i	$0.717542\pi$
$984$	−8.45970	−0.269685
$985$	−65.5522	−2.08867
$986$	0.0469162	0.00149412
$987$	0	0
$988$	−8.86383	−0.281996
$989$	−2.00000	−0.0635963
$990$	−10.6987	−0.340026
$991$	2.12539	0.0675154	0.0337577	−	0.999430i	$-0.489253\pi$
$991$	2.12539	0.0675154	0.0337577	+	0.999430i	$0.489253\pi$
$992$	−2.00000	−0.0635001
$993$	−29.1067	−0.923675
$994$	0	0
$995$	−31.0290	−0.983686
$996$	0.165173	0.00523371
$997$	−10.4439	−0.330762	−0.165381	−	0.986230i	$-0.552885\pi$
$997$	−10.4439	−0.330762	−0.165381	+	0.986230i	$0.552885\pi$
$998$	−3.52330	−0.111528
$999$	2.45970	0.0778213

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6762.2.a.cl.1.1		4
7.2	even	3		966.2.i.m.277.4	✓	8
7.4	even	3		966.2.i.m.415.4	yes	8
7.6	odd	2		6762.2.a.cr.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.m.277.4	✓	8	7.2	even	3
966.2.i.m.415.4	yes	8	7.4	even	3
6762.2.a.cl.1.1		4	1.1	even	1	trivial
6762.2.a.cr.1.4		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.22985 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.22985 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -3.22985 q^{10} +3.31243 q^{11} -1.00000 q^{12} +4.43192 q^{13} +3.22985 q^{15} +1.00000 q^{16} +0.0825866 q^{17} +1.00000 q^{18} -2.00000 q^{19} -3.22985 q^{20} +3.31243 q^{22} -1.00000 q^{23} -1.00000 q^{24} +5.43192 q^{25} +4.43192 q^{26} -1.00000 q^{27} +0.568085 q^{29} +3.22985 q^{30} -2.00000 q^{31} +1.00000 q^{32} -3.31243 q^{33} +0.0825866 q^{34} +1.00000 q^{36} -2.45970 q^{37} -2.00000 q^{38} -4.43192 q^{39} -3.22985 q^{40} +8.45970 q^{41} +2.00000 q^{43} +3.31243 q^{44} -3.22985 q^{45} -1.00000 q^{46} -7.62487 q^{47} -1.00000 q^{48} +5.43192 q^{50} -0.0825866 q^{51} +4.43192 q^{52} +14.0937 q^{53} -1.00000 q^{54} -10.6987 q^{55} +2.00000 q^{57} +0.568085 q^{58} -12.9194 q^{59} +3.22985 q^{60} -4.86383 q^{61} -2.00000 q^{62} +1.00000 q^{64} -14.3144 q^{65} -3.31243 q^{66} -10.0937 q^{67} +0.0825866 q^{68} +1.00000 q^{69} +7.69866 q^{71} +1.00000 q^{72} -3.86383 q^{73} -2.45970 q^{74} -5.43192 q^{75} -2.00000 q^{76} -4.43192 q^{78} +4.68757 q^{79} -3.22985 q^{80} +1.00000 q^{81} +8.45970 q^{82} -0.165173 q^{83} -0.266742 q^{85} +2.00000 q^{86} -0.568085 q^{87} +3.31243 q^{88} +11.3235 q^{89} -3.22985 q^{90} -1.00000 q^{92} +2.00000 q^{93} -7.62487 q^{94} +6.45970 q^{95} -1.00000 q^{96} -8.00000 q^{97} +3.31243 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 4 q^{6} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 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