LMFDB - Embedded newform 3822.2.a.bx.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3822,2,Mod(1,3822)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3822, 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("3822.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3822.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:	$30.5188236525$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.10304.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 7x^{2} + 8x + 8 $ x^4 - 2x^3 - 7x^2 + 8*x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.692297$ of defining polynomial
Character	$\chi$	$=$	3822.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.69230 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.69230 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +2.69230 q^{10} -4.49978 q^{11} -1.00000 q^{12} +1.00000 q^{13} +2.69230 q^{15} +1.00000 q^{16} -7.88438 q^{17} -1.00000 q^{18} -6.03500 q^{19} -2.69230 q^{20} +4.49978 q^{22} +2.65041 q^{23} +1.00000 q^{24} +2.24846 q^{25} -1.00000 q^{26} -1.00000 q^{27} -1.64173 q^{29} -2.69230 q^{30} -1.84937 q^{31} -1.00000 q^{32} +4.49978 q^{33} +7.88438 q^{34} +1.00000 q^{36} -5.44922 q^{37} +6.03500 q^{38} -1.00000 q^{39} +2.69230 q^{40} -3.56484 q^{41} +1.34959 q^{43} -4.49978 q^{44} -2.69230 q^{45} -2.65041 q^{46} +3.16246 q^{47} -1.00000 q^{48} -2.24846 q^{50} +7.88438 q^{51} +1.00000 q^{52} -5.16246 q^{53} +1.00000 q^{54} +12.1147 q^{55} +6.03500 q^{57} +1.64173 q^{58} -13.4643 q^{59} +2.69230 q^{60} +14.6290 q^{61} +1.84937 q^{62} +1.00000 q^{64} -2.69230 q^{65} -4.49978 q^{66} +4.85805 q^{67} -7.88438 q^{68} -2.65041 q^{69} +1.80748 q^{71} -1.00000 q^{72} -15.9641 q^{73} +5.44922 q^{74} -2.24846 q^{75} -6.03500 q^{76} +1.00000 q^{78} -5.89126 q^{79} -2.69230 q^{80} +1.00000 q^{81} +3.56484 q^{82} -3.72774 q^{83} +21.2271 q^{85} -1.34959 q^{86} +1.64173 q^{87} +4.49978 q^{88} -12.7569 q^{89} +2.69230 q^{90} +2.65041 q^{92} +1.84937 q^{93} -3.16246 q^{94} +16.2480 q^{95} +1.00000 q^{96} -5.28347 q^{97} -4.49978 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 6 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 - 6 * q^5 + 4 * q^6 - 4 * q^8 + 4 * q^9	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 6 q^{5} + 4 q^{6} - 4 q^{8} + 4 q^{9} + 6 q^{10} + 2 q^{11} - 4 q^{12} + 4 q^{13} + 6 q^{15} + 4 q^{16} - 2 q^{17} - 4 q^{18} - 2 q^{19} - 6 q^{20} - 2 q^{22} - 2 q^{23} + 4 q^{24} + 6 q^{25} - 4 q^{26} - 4 q^{27} + 6 q^{29} - 6 q^{30} - 4 q^{32} - 2 q^{33} + 2 q^{34} + 4 q^{36} + 6 q^{37} + 2 q^{38} - 4 q^{39} + 6 q^{40} - 16 q^{41} + 18 q^{43} + 2 q^{44} - 6 q^{45} + 2 q^{46} - 16 q^{47} - 4 q^{48} - 6 q^{50} + 2 q^{51} + 4 q^{52} + 8 q^{53} + 4 q^{54} - 2 q^{55} + 2 q^{57} - 6 q^{58} - 16 q^{59} + 6 q^{60} + 2 q^{61} + 4 q^{64} - 6 q^{65} + 2 q^{66} + 12 q^{67} - 2 q^{68} + 2 q^{69} - 8 q^{71} - 4 q^{72} - 6 q^{73} - 6 q^{74} - 6 q^{75} - 2 q^{76} + 4 q^{78} - 24 q^{79} - 6 q^{80} + 4 q^{81} + 16 q^{82} - 28 q^{83} + 38 q^{85} - 18 q^{86} - 6 q^{87} - 2 q^{88} - 28 q^{89} + 6 q^{90} - 2 q^{92} + 16 q^{94} + 22 q^{95} + 4 q^{96} + 4 q^{97} + 2 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 6 * q^5 + 4 * q^6 - 4 * q^8 + 4 * q^9 + 6 * q^10 + 2 * q^11 - 4 * q^12 + 4 * q^13 + 6 * q^15 + 4 * q^16 - 2 * q^17 - 4 * q^18 - 2 * q^19 - 6 * q^20 - 2 * q^22 - 2 * q^23 + 4 * q^24 + 6 * q^25 - 4 * q^26 - 4 * q^27 + 6 * q^29 - 6 * q^30 - 4 * q^32 - 2 * q^33 + 2 * q^34 + 4 * q^36 + 6 * q^37 + 2 * q^38 - 4 * q^39 + 6 * q^40 - 16 * q^41 + 18 * q^43 + 2 * q^44 - 6 * q^45 + 2 * q^46 - 16 * q^47 - 4 * q^48 - 6 * q^50 + 2 * q^51 + 4 * q^52 + 8 * q^53 + 4 * q^54 - 2 * q^55 + 2 * q^57 - 6 * q^58 - 16 * q^59 + 6 * q^60 + 2 * q^61 + 4 * q^64 - 6 * q^65 + 2 * q^66 + 12 * q^67 - 2 * q^68 + 2 * q^69 - 8 * q^71 - 4 * q^72 - 6 * q^73 - 6 * q^74 - 6 * q^75 - 2 * q^76 + 4 * q^78 - 24 * q^79 - 6 * q^80 + 4 * q^81 + 16 * q^82 - 28 * q^83 + 38 * q^85 - 18 * q^86 - 6 * q^87 - 2 * q^88 - 28 * q^89 + 6 * q^90 - 2 * q^92 + 16 * q^94 + 22 * q^95 + 4 * q^96 + 4 * q^97 + 2 * q^99

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
$5$	−2.69230	−1.20403	−0.602016	−	0.798484i	$-0.705636\pi$
$5$	−2.69230	−1.20403	−0.602016	+	0.798484i	$0.705636\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	2.69230	0.851379
$11$	−4.49978	−1.35673	−0.678367	−	0.734723i	$-0.737312\pi$
$11$	−4.49978	−1.35673	−0.678367	+	0.734723i	$0.737312\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0	0
$15$	2.69230	0.695148
$16$	1.00000	0.250000
$17$	−7.88438	−1.91224	−0.956121	−	0.292972i	$-0.905356\pi$
$17$	−7.88438	−1.91224	−0.956121	+	0.292972i	$0.905356\pi$
$18$	−1.00000	−0.235702
$19$	−6.03500	−1.38452	−0.692262	−	0.721646i	$-0.743386\pi$
$19$	−6.03500	−1.38452	−0.692262	+	0.721646i	$0.743386\pi$
$20$	−2.69230	−0.602016
$21$	0	0
$22$	4.49978	0.959356
$23$	2.65041	0.552649	0.276324	−	0.961064i	$-0.410884\pi$
$23$	2.65041	0.552649	0.276324	+	0.961064i	$0.410884\pi$
$24$	1.00000	0.204124
$25$	2.24846	0.449693
$26$	−1.00000	−0.196116
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−1.64173	−0.304862	−0.152431	−	0.988314i	$-0.548710\pi$
$29$	−1.64173	−0.304862	−0.152431	+	0.988314i	$0.548710\pi$
$30$	−2.69230	−0.491544
$31$	−1.84937	−0.332157	−0.166078	−	0.986113i	$-0.553110\pi$
$31$	−1.84937	−0.332157	−0.166078	+	0.986113i	$0.553110\pi$
$32$	−1.00000	−0.176777
$33$	4.49978	0.783311
$34$	7.88438	1.35216
$35$	0	0
$36$	1.00000	0.166667
$37$	−5.44922	−0.895846	−0.447923	−	0.894072i	$-0.647836\pi$
$37$	−5.44922	−0.895846	−0.447923	+	0.894072i	$0.647836\pi$
$38$	6.03500	0.979007
$39$	−1.00000	−0.160128
$40$	2.69230	0.425690
$41$	−3.56484	−0.556735	−0.278367	−	0.960475i	$-0.589793\pi$
$41$	−3.56484	−0.556735	−0.278367	+	0.960475i	$0.589793\pi$
$42$	0	0
$43$	1.34959	0.205811	0.102905	−	0.994691i	$-0.467186\pi$
$43$	1.34959	0.205811	0.102905	+	0.994691i	$0.467186\pi$
$44$	−4.49978	−0.678367
$45$	−2.69230	−0.401344
$46$	−2.65041	−0.390782
$47$	3.16246	0.461292	0.230646	−	0.973038i	$-0.425916\pi$
$47$	3.16246	0.461292	0.230646	+	0.973038i	$0.425916\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	−2.24846	−0.317981
$51$	7.88438	1.10403
$52$	1.00000	0.138675
$53$	−5.16246	−0.709118	−0.354559	−	0.935034i	$-0.615369\pi$
$53$	−5.16246	−0.709118	−0.354559	+	0.935034i	$0.615369\pi$
$54$	1.00000	0.136083
$55$	12.1147	1.63355
$56$	0	0
$57$	6.03500	0.799356
$58$	1.64173	0.215570
$59$	−13.4643	−1.75291	−0.876454	−	0.481486i	$-0.840097\pi$
$59$	−13.4643	−1.75291	−0.876454	+	0.481486i	$0.840097\pi$
$60$	2.69230	0.347574
$61$	14.6290	1.87306	0.936528	−	0.350594i	$-0.114020\pi$
$61$	14.6290	1.87306	0.936528	+	0.350594i	$0.114020\pi$
$62$	1.84937	0.234870
$63$	0	0
$64$	1.00000	0.125000
$65$	−2.69230	−0.333938
$66$	−4.49978	−0.553885
$67$	4.85805	0.593505	0.296752	−	0.954954i	$-0.404096\pi$
$67$	4.85805	0.593505	0.296752	+	0.954954i	$0.404096\pi$
$68$	−7.88438	−0.956121
$69$	−2.65041	−0.319072
$70$	0	0
$71$	1.80748	0.214509	0.107254	−	0.994232i	$-0.465794\pi$
$71$	1.80748	0.214509	0.107254	+	0.994232i	$0.465794\pi$
$72$	−1.00000	−0.117851
$73$	−15.9641	−1.86846	−0.934229	−	0.356673i	$-0.883911\pi$
$73$	−15.9641	−1.86846	−0.934229	+	0.356673i	$0.883911\pi$
$74$	5.44922	0.633459
$75$	−2.24846	−0.259630
$76$	−6.03500	−0.692262
$77$	0	0
$78$	1.00000	0.113228
$79$	−5.89126	−0.662818	−0.331409	−	0.943487i	$-0.607524\pi$
$79$	−5.89126	−0.662818	−0.331409	+	0.943487i	$0.607524\pi$
$80$	−2.69230	−0.301008
$81$	1.00000	0.111111
$82$	3.56484	0.393671
$83$	−3.72774	−0.409173	−0.204586	−	0.978849i	$-0.565585\pi$
$83$	−3.72774	−0.409173	−0.204586	+	0.978849i	$0.565585\pi$
$84$	0	0
$85$	21.2271	2.30240
$86$	−1.34959	−0.145530
$87$	1.64173	0.176012
$88$	4.49978	0.479678
$89$	−12.7569	−1.35223	−0.676115	−	0.736796i	$-0.736338\pi$
$89$	−12.7569	−1.35223	−0.676115	+	0.736796i	$0.736338\pi$
$90$	2.69230	0.283793
$91$	0	0
$92$	2.65041	0.276324
$93$	1.84937	0.191771
$94$	−3.16246	−0.326183
$95$	16.2480	1.66701
$96$	1.00000	0.102062
$97$	−5.28347	−0.536455	−0.268228	−	0.963356i	$-0.586438\pi$
$97$	−5.28347	−0.536455	−0.268228	+	0.963356i	$0.586438\pi$
$98$	0	0
$99$	−4.49978	−0.452245
$100$	2.24846	0.224846
$101$	2.27988	0.226856	0.113428	−	0.993546i	$-0.463817\pi$
$101$	2.27988	0.226856	0.113428	+	0.993546i	$0.463817\pi$
$102$	−7.88438	−0.780669
$103$	−2.57890	−0.254107	−0.127053	−	0.991896i	$-0.540552\pi$
$103$	−2.57890	−0.254107	−0.127053	+	0.991896i	$0.540552\pi$
$104$	−1.00000	−0.0980581
$105$	0	0
$106$	5.16246	0.501422
$107$	−13.7146	−1.32584	−0.662920	−	0.748690i	$-0.730683\pi$
$107$	−13.7146	−1.32584	−0.662920	+	0.748690i	$0.730683\pi$
$108$	−1.00000	−0.0962250
$109$	15.1653	1.45257	0.726287	−	0.687392i	$-0.241245\pi$
$109$	15.1653	1.45257	0.726287	+	0.687392i	$0.241245\pi$
$110$	−12.1147	−1.15510
$111$	5.44922	0.517217
$112$	0	0
$113$	4.71969	0.443991	0.221995	−	0.975048i	$-0.428743\pi$
$113$	4.71969	0.443991	0.221995	+	0.975048i	$0.428743\pi$
$114$	−6.03500	−0.565230
$115$	−7.13569	−0.665407
$116$	−1.64173	−0.152431
$117$	1.00000	0.0924500
$118$	13.4643	1.23949
$119$	0	0
$120$	−2.69230	−0.245772
$121$	9.24803	0.840730
$122$	−14.6290	−1.32445
$123$	3.56484	0.321431
$124$	−1.84937	−0.166078
$125$	7.40795	0.662587
$126$	0	0
$127$	−9.67736	−0.858727	−0.429363	−	0.903132i	$-0.641262\pi$
$127$	−9.67736	−0.858727	−0.429363	+	0.903132i	$0.641262\pi$
$128$	−1.00000	−0.0883883
$129$	−1.34959	−0.118825
$130$	2.69230	0.236130
$131$	−9.90173	−0.865118	−0.432559	−	0.901606i	$-0.642389\pi$
$131$	−9.90173	−0.865118	−0.432559	+	0.901606i	$0.642389\pi$
$132$	4.49978	0.391656
$133$	0	0
$134$	−4.85805	−0.419671
$135$	2.69230	0.231716
$136$	7.88438	0.676080
$137$	13.5702	1.15938	0.579691	−	0.814836i	$-0.303173\pi$
$137$	13.5702	1.15938	0.579691	+	0.814836i	$0.303173\pi$
$138$	2.65041	0.225618
$139$	−1.08780	−0.0922658	−0.0461329	−	0.998935i	$-0.514690\pi$
$139$	−1.08780	−0.0922658	−0.0461329	+	0.998935i	$0.514690\pi$
$140$	0	0
$141$	−3.16246	−0.266327
$142$	−1.80748	−0.151681
$143$	−4.49978	−0.376291
$144$	1.00000	0.0833333
$145$	4.42004	0.367064
$146$	15.9641	1.32120
$147$	0	0
$148$	−5.44922	−0.447923
$149$	−4.55617	−0.373256	−0.186628	−	0.982431i	$-0.559756\pi$
$149$	−4.55617	−0.373256	−0.186628	+	0.982431i	$0.559756\pi$
$150$	2.24846	0.183586
$151$	−2.78369	−0.226533	−0.113267	−	0.993565i	$-0.536131\pi$
$151$	−2.78369	−0.226533	−0.113267	+	0.993565i	$0.536131\pi$
$152$	6.03500	0.489503
$153$	−7.88438	−0.637414
$154$	0	0
$155$	4.97906	0.399927
$156$	−1.00000	−0.0800641
$157$	1.22796	0.0980019	0.0490009	−	0.998799i	$-0.484396\pi$
$157$	1.22796	0.0980019	0.0490009	+	0.998799i	$0.484396\pi$
$158$	5.89126	0.468683
$159$	5.16246	0.409410
$160$	2.69230	0.212845
$161$	0	0
$162$	−1.00000	−0.0785674
$163$	−19.5047	−1.52773	−0.763864	−	0.645377i	$-0.776700\pi$
$163$	−19.5047	−1.52773	−0.763864	+	0.645377i	$0.776700\pi$
$164$	−3.56484	−0.278367
$165$	−12.1147	−0.943132
$166$	3.72774	0.289329
$167$	25.3686	1.96308	0.981541	−	0.191254i	$-0.0612555\pi$
$167$	25.3686	1.96308	0.981541	+	0.191254i	$0.0612555\pi$
$168$	0	0
$169$	1.00000	0.0769231
$170$	−21.2271	−1.62804
$171$	−6.03500	−0.461508
$172$	1.34959	0.102905
$173$	−17.6355	−1.34080	−0.670400	−	0.742000i	$-0.733877\pi$
$173$	−17.6355	−1.34080	−0.670400	+	0.742000i	$0.733877\pi$
$174$	−1.64173	−0.124460
$175$	0	0
$176$	−4.49978	−0.339184
$177$	13.4643	1.01204
$178$	12.7569	0.956172
$179$	8.41377	0.628875	0.314438	−	0.949278i	$-0.398184\pi$
$179$	8.41377	0.628875	0.314438	+	0.949278i	$0.398184\pi$
$180$	−2.69230	−0.200672
$181$	16.1119	1.19759	0.598794	−	0.800903i	$-0.295647\pi$
$181$	16.1119	1.19759	0.598794	+	0.800903i	$0.295647\pi$
$182$	0	0
$183$	−14.6290	−1.08141
$184$	−2.65041	−0.195391
$185$	14.6709	1.07863
$186$	−1.84937	−0.135602
$187$	35.4780	2.59441
$188$	3.16246	0.230646
$189$	0	0
$190$	−16.2480	−1.17876
$191$	17.2766	1.25009	0.625045	−	0.780589i	$-0.285081\pi$
$191$	17.2766	1.25009	0.625045	+	0.780589i	$0.285081\pi$
$192$	−1.00000	−0.0721688
$193$	11.2211	0.807711	0.403855	−	0.914823i	$-0.367670\pi$
$193$	11.2211	0.807711	0.403855	+	0.914823i	$0.367670\pi$
$194$	5.28347	0.379331
$195$	2.69230	0.192799
$196$	0	0
$197$	22.5940	1.60976	0.804879	−	0.593439i	$-0.202230\pi$
$197$	22.5940	1.60976	0.804879	+	0.593439i	$0.202230\pi$
$198$	4.49978	0.319785
$199$	19.9635	1.41517	0.707587	−	0.706626i	$-0.249784\pi$
$199$	19.9635	1.41517	0.707587	+	0.706626i	$0.249784\pi$
$200$	−2.24846	−0.158990
$201$	−4.85805	−0.342660
$202$	−2.27988	−0.160412
$203$	0	0
$204$	7.88438	0.552017
$205$	9.59762	0.670327
$206$	2.57890	0.179681
$207$	2.65041	0.184216
$208$	1.00000	0.0693375
$209$	27.1562	1.87843
$210$	0	0
$211$	−18.2364	−1.25544	−0.627722	−	0.778438i	$-0.716013\pi$
$211$	−18.2364	−1.25544	−0.627722	+	0.778438i	$0.716013\pi$
$212$	−5.16246	−0.354559
$213$	−1.80748	−0.123847
$214$	13.7146	0.937510
$215$	−3.63350	−0.247803
$216$	1.00000	0.0680414
$217$	0	0
$218$	−15.1653	−1.02712
$219$	15.9641	1.07876
$220$	12.1147	0.816776
$221$	−7.88438	−0.530360
$222$	−5.44922	−0.365728
$223$	−11.7442	−0.786451	−0.393225	−	0.919442i	$-0.628641\pi$
$223$	−11.7442	−0.786451	−0.393225	+	0.919442i	$0.628641\pi$
$224$	0	0
$225$	2.24846	0.149898
$226$	−4.71969	−0.313949
$227$	15.5170	1.02990	0.514950	−	0.857220i	$-0.327811\pi$
$227$	15.5170	1.02990	0.514950	+	0.857220i	$0.327811\pi$
$228$	6.03500	0.399678
$229$	−5.13284	−0.339188	−0.169594	−	0.985514i	$-0.554246\pi$
$229$	−5.13284	−0.339188	−0.169594	+	0.985514i	$0.554246\pi$
$230$	7.13569	0.470514
$231$	0	0
$232$	1.64173	0.107785
$233$	27.7861	1.82033	0.910164	−	0.414248i	$-0.135955\pi$
$233$	27.7861	1.82033	0.910164	+	0.414248i	$0.135955\pi$
$234$	−1.00000	−0.0653720
$235$	−8.51428	−0.555410
$236$	−13.4643	−0.876454
$237$	5.89126	0.382678
$238$	0	0
$239$	7.54811	0.488247	0.244123	−	0.969744i	$-0.421500\pi$
$239$	7.54811	0.488247	0.244123	+	0.969744i	$0.421500\pi$
$240$	2.69230	0.173787
$241$	−28.7857	−1.85425	−0.927124	−	0.374755i	$-0.877727\pi$
$241$	−28.7857	−1.85425	−0.927124	+	0.374755i	$0.877727\pi$
$242$	−9.24803	−0.594486
$243$	−1.00000	−0.0641500
$244$	14.6290	0.936528
$245$	0	0
$246$	−3.56484	−0.227286
$247$	−6.03500	−0.383998
$248$	1.84937	0.117435
$249$	3.72774	0.236236
$250$	−7.40795	−0.468520
$251$	−23.6112	−1.49033	−0.745164	−	0.666881i	$-0.767629\pi$
$251$	−23.6112	−1.49033	−0.745164	+	0.666881i	$0.767629\pi$
$252$	0	0
$253$	−11.9263	−0.749798
$254$	9.67736	0.607212
$255$	−21.2271	−1.32929
$256$	1.00000	0.0625000
$257$	8.31415	0.518622	0.259311	−	0.965794i	$-0.416504\pi$
$257$	8.31415	0.518622	0.259311	+	0.965794i	$0.416504\pi$
$258$	1.34959	0.0840218
$259$	0	0
$260$	−2.69230	−0.166969
$261$	−1.64173	−0.101621
$262$	9.90173	0.611731
$263$	10.8877	0.671362	0.335681	−	0.941976i	$-0.391034\pi$
$263$	10.8877	0.671362	0.335681	+	0.941976i	$0.391034\pi$
$264$	−4.49978	−0.276942
$265$	13.8989	0.853801
$266$	0	0
$267$	12.7569	0.780711
$268$	4.85805	0.296752
$269$	−22.0486	−1.34433	−0.672164	−	0.740402i	$-0.734635\pi$
$269$	−22.0486	−1.34433	−0.672164	+	0.740402i	$0.734635\pi$
$270$	−2.69230	−0.163848
$271$	19.9613	1.21256	0.606280	−	0.795251i	$-0.292661\pi$
$271$	19.9613	1.21256	0.606280	+	0.795251i	$0.292661\pi$
$272$	−7.88438	−0.478060
$273$	0	0
$274$	−13.5702	−0.819807
$275$	−10.1176	−0.610114
$276$	−2.65041	−0.159536
$277$	6.76157	0.406264	0.203132	−	0.979151i	$-0.434888\pi$
$277$	6.76157	0.406264	0.203132	+	0.979151i	$0.434888\pi$
$278$	1.08780	0.0652418
$279$	−1.84937	−0.110719
$280$	0	0
$281$	−8.69830	−0.518897	−0.259449	−	0.965757i	$-0.583541\pi$
$281$	−8.69830	−0.518897	−0.259449	+	0.965757i	$0.583541\pi$
$282$	3.16246	0.188322
$283$	13.3556	0.793908	0.396954	−	0.917839i	$-0.370067\pi$
$283$	13.3556	0.793908	0.396954	+	0.917839i	$0.370067\pi$
$284$	1.80748	0.107254
$285$	−16.2480	−0.962450
$286$	4.49978	0.266078
$287$	0	0
$288$	−1.00000	−0.0589256
$289$	45.1634	2.65667
$290$	−4.42004	−0.259554
$291$	5.28347	0.309722
$292$	−15.9641	−0.934229
$293$	−30.5553	−1.78506	−0.892530	−	0.450989i	$-0.851071\pi$
$293$	−30.5553	−1.78506	−0.892530	+	0.450989i	$0.851071\pi$
$294$	0	0
$295$	36.2500	2.11056
$296$	5.44922	0.316729
$297$	4.49978	0.261104
$298$	4.55617	0.263932
$299$	2.65041	0.153277
$300$	−2.24846	−0.129815
$301$	0	0
$302$	2.78369	0.160183
$303$	−2.27988	−0.130975
$304$	−6.03500	−0.346131
$305$	−39.3857	−2.25522
$306$	7.88438	0.450720
$307$	12.6145	0.719949	0.359975	−	0.932962i	$-0.382785\pi$
$307$	12.6145	0.719949	0.359975	+	0.932962i	$0.382785\pi$
$308$	0	0
$309$	2.57890	0.146709
$310$	−4.97906	−0.282791
$311$	10.6746	0.605303	0.302652	−	0.953101i	$-0.402128\pi$
$311$	10.6746	0.605303	0.302652	+	0.953101i	$0.402128\pi$
$312$	1.00000	0.0566139
$313$	13.2604	0.749524	0.374762	−	0.927121i	$-0.377724\pi$
$313$	13.2604	0.749524	0.374762	+	0.927121i	$0.377724\pi$
$314$	−1.22796	−0.0692978
$315$	0	0
$316$	−5.89126	−0.331409
$317$	−22.1743	−1.24543	−0.622716	−	0.782448i	$-0.713971\pi$
$317$	−22.1743	−1.24543	−0.622716	+	0.782448i	$0.713971\pi$
$318$	−5.16246	−0.289496
$319$	7.38745	0.413618
$320$	−2.69230	−0.150504
$321$	13.7146	0.765474
$322$	0	0
$323$	47.5822	2.64755
$324$	1.00000	0.0555556
$325$	2.24846	0.124722
$326$	19.5047	1.08027
$327$	−15.1653	−0.838644
$328$	3.56484	0.196836
$329$	0	0
$330$	12.1147	0.666895
$331$	−32.1523	−1.76725	−0.883625	−	0.468196i	$-0.844904\pi$
$331$	−32.1523	−1.76725	−0.883625	+	0.468196i	$0.844904\pi$
$332$	−3.72774	−0.204586
$333$	−5.44922	−0.298615
$334$	−25.3686	−1.38811
$335$	−13.0793	−0.714599
$336$	0	0
$337$	9.13657	0.497701	0.248850	−	0.968542i	$-0.419947\pi$
$337$	9.13657	0.497701	0.248850	+	0.968542i	$0.419947\pi$
$338$	−1.00000	−0.0543928
$339$	−4.71969	−0.256338
$340$	21.2271	1.15120
$341$	8.32176	0.450649
$342$	6.03500	0.326336
$343$	0	0
$344$	−1.34959	−0.0727650
$345$	7.13569	0.384173
$346$	17.6355	0.948089
$347$	−6.45566	−0.346558	−0.173279	−	0.984873i	$-0.555436\pi$
$347$	−6.45566	−0.346558	−0.173279	+	0.984873i	$0.555436\pi$
$348$	1.64173	0.0880062
$349$	18.0971	0.968715	0.484358	−	0.874870i	$-0.339053\pi$
$349$	18.0971	0.968715	0.484358	+	0.874870i	$0.339053\pi$
$350$	0	0
$351$	−1.00000	−0.0533761
$352$	4.49978	0.239839
$353$	15.3091	0.814819	0.407409	−	0.913246i	$-0.366432\pi$
$353$	15.3091	0.814819	0.407409	+	0.913246i	$0.366432\pi$
$354$	−13.4643	−0.715621
$355$	−4.86628	−0.258275
$356$	−12.7569	−0.676115
$357$	0	0
$358$	−8.41377	−0.444682
$359$	−5.01691	−0.264782	−0.132391	−	0.991198i	$-0.542266\pi$
$359$	−5.01691	−0.264782	−0.132391	+	0.991198i	$0.542266\pi$
$360$	2.69230	0.141897
$361$	17.4213	0.916909
$362$	−16.1119	−0.846822
$363$	−9.24803	−0.485395
$364$	0	0
$365$	42.9802	2.24968
$366$	14.6290	0.764672
$367$	10.5644	0.551457	0.275729	−	0.961235i	$-0.411081\pi$
$367$	10.5644	0.551457	0.275729	+	0.961235i	$0.411081\pi$
$368$	2.65041	0.138162
$369$	−3.56484	−0.185578
$370$	−14.6709	−0.762705
$371$	0	0
$372$	1.84937	0.0958854
$373$	−7.53435	−0.390114	−0.195057	−	0.980792i	$-0.562489\pi$
$373$	−7.53435	−0.390114	−0.195057	+	0.980792i	$0.562489\pi$
$374$	−35.4780	−1.83452
$375$	−7.40795	−0.382545
$376$	−3.16246	−0.163091
$377$	−1.64173	−0.0845536
$378$	0	0
$379$	−29.3541	−1.50782	−0.753909	−	0.656978i	$-0.771834\pi$
$379$	−29.3541	−1.50782	−0.753909	+	0.656978i	$0.771834\pi$
$380$	16.2480	0.833506
$381$	9.67736	0.495786
$382$	−17.2766	−0.883947
$383$	14.4564	0.738687	0.369344	−	0.929293i	$-0.379583\pi$
$383$	14.4564	0.738687	0.369344	+	0.929293i	$0.379583\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	−11.2211	−0.571138
$387$	1.34959	0.0686035
$388$	−5.28347	−0.268228
$389$	−20.1504	−1.02166	−0.510832	−	0.859680i	$-0.670663\pi$
$389$	−20.1504	−1.02166	−0.510832	+	0.859680i	$0.670663\pi$
$390$	−2.69230	−0.136330
$391$	−20.8968	−1.05680
$392$	0	0
$393$	9.90173	0.499476
$394$	−22.5940	−1.13827
$395$	15.8610	0.798054
$396$	−4.49978	−0.226122
$397$	19.5860	0.982992	0.491496	−	0.870880i	$-0.336450\pi$
$397$	19.5860	0.982992	0.491496	+	0.870880i	$0.336450\pi$
$398$	−19.9635	−1.00068
$399$	0	0
$400$	2.24846	0.112423
$401$	15.6987	0.783958	0.391979	−	0.919974i	$-0.371791\pi$
$401$	15.6987	0.783958	0.391979	+	0.919974i	$0.371791\pi$
$402$	4.85805	0.242297
$403$	−1.84937	−0.0921237
$404$	2.27988	0.113428
$405$	−2.69230	−0.133781
$406$	0	0
$407$	24.5203	1.21543
$408$	−7.88438	−0.390335
$409$	−26.9161	−1.33091	−0.665457	−	0.746436i	$-0.731764\pi$
$409$	−26.9161	−1.33091	−0.665457	+	0.746436i	$0.731764\pi$
$410$	−9.59762	−0.473992
$411$	−13.5702	−0.669370
$412$	−2.57890	−0.127053
$413$	0	0
$414$	−2.65041	−0.130261
$415$	10.0362	0.492657
$416$	−1.00000	−0.0490290
$417$	1.08780	0.0532697
$418$	−27.1562	−1.32825
$419$	−23.1735	−1.13210	−0.566051	−	0.824370i	$-0.691529\pi$
$419$	−23.1735	−1.13210	−0.566051	+	0.824370i	$0.691529\pi$
$420$	0	0
$421$	−5.04969	−0.246107	−0.123053	−	0.992400i	$-0.539269\pi$
$421$	−5.04969	−0.246107	−0.123053	+	0.992400i	$0.539269\pi$
$422$	18.2364	0.887733
$423$	3.16246	0.153764
$424$	5.16246	0.250711
$425$	−17.7277	−0.859922
$426$	1.80748	0.0875729
$427$	0	0
$428$	−13.7146	−0.662920
$429$	4.49978	0.217251
$430$	3.63350	0.175223
$431$	23.5665	1.13516	0.567579	−	0.823319i	$-0.307880\pi$
$431$	23.5665	1.13516	0.567579	+	0.823319i	$0.307880\pi$
$432$	−1.00000	−0.0481125
$433$	36.0319	1.73158	0.865791	−	0.500405i	$-0.166816\pi$
$433$	36.0319	1.73158	0.865791	+	0.500405i	$0.166816\pi$
$434$	0	0
$435$	−4.42004	−0.211925
$436$	15.1653	0.726287
$437$	−15.9952	−0.765156
$438$	−15.9641	−0.762795
$439$	26.1939	1.25017	0.625083	−	0.780559i	$-0.285065\pi$
$439$	26.1939	1.25017	0.625083	+	0.780559i	$0.285065\pi$
$440$	−12.1147	−0.577548
$441$	0	0
$442$	7.88438	0.375021
$443$	−13.6304	−0.647599	−0.323800	−	0.946126i	$-0.604960\pi$
$443$	−13.6304	−0.647599	−0.323800	+	0.946126i	$0.604960\pi$
$444$	5.44922	0.258608
$445$	34.3454	1.62813
$446$	11.7442	0.556105
$447$	4.55617	0.215499
$448$	0	0
$449$	5.28274	0.249308	0.124654	−	0.992200i	$-0.460218\pi$
$449$	5.28274	0.249308	0.124654	+	0.992200i	$0.460218\pi$
$450$	−2.24846	−0.105994
$451$	16.0410	0.755342
$452$	4.71969	0.221995
$453$	2.78369	0.130789
$454$	−15.5170	−0.728249
$455$	0	0
$456$	−6.03500	−0.282615
$457$	34.4510	1.61155	0.805775	−	0.592222i	$-0.201749\pi$
$457$	34.4510	1.61155	0.805775	+	0.592222i	$0.201749\pi$
$458$	5.13284	0.239842
$459$	7.88438	0.368011
$460$	−7.13569	−0.332703
$461$	36.7860	1.71329	0.856647	−	0.515904i	$-0.172544\pi$
$461$	36.7860	1.71329	0.856647	+	0.515904i	$0.172544\pi$
$462$	0	0
$463$	−2.95694	−0.137421	−0.0687103	−	0.997637i	$-0.521888\pi$
$463$	−2.95694	−0.137421	−0.0687103	+	0.997637i	$0.521888\pi$
$464$	−1.64173	−0.0762156
$465$	−4.97906	−0.230898
$466$	−27.7861	−1.28717
$467$	35.3821	1.63729	0.818644	−	0.574301i	$-0.194726\pi$
$467$	35.3821	1.63729	0.818644	+	0.574301i	$0.194726\pi$
$468$	1.00000	0.0462250
$469$	0	0
$470$	8.51428	0.392734
$471$	−1.22796	−0.0565814
$472$	13.4643	0.619746
$473$	−6.07286	−0.279230
$474$	−5.89126	−0.270594
$475$	−13.5695	−0.622611
$476$	0	0
$477$	−5.16246	−0.236373
$478$	−7.54811	−0.345243
$479$	−27.9002	−1.27479	−0.637397	−	0.770536i	$-0.719989\pi$
$479$	−27.9002	−1.27479	−0.637397	+	0.770536i	$0.719989\pi$
$480$	−2.69230	−0.122886
$481$	−5.44922	−0.248463
$482$	28.7857	1.31115
$483$	0	0
$484$	9.24803	0.420365
$485$	14.2247	0.645909
$486$	1.00000	0.0453609
$487$	9.04057	0.409667	0.204834	−	0.978797i	$-0.434335\pi$
$487$	9.04057	0.409667	0.204834	+	0.978797i	$0.434335\pi$
$488$	−14.6290	−0.662225
$489$	19.5047	0.882034
$490$	0	0
$491$	−31.3219	−1.41354	−0.706770	−	0.707444i	$-0.749848\pi$
$491$	−31.3219	−1.41354	−0.706770	+	0.707444i	$0.749848\pi$
$492$	3.56484	0.160716
$493$	12.9441	0.582971
$494$	6.03500	0.271528
$495$	12.1147	0.544517
$496$	−1.84937	−0.0830392
$497$	0	0
$498$	−3.72774	−0.167044
$499$	−2.46943	−0.110547	−0.0552734	−	0.998471i	$-0.517603\pi$
$499$	−2.46943	−0.110547	−0.0552734	+	0.998471i	$0.517603\pi$
$500$	7.40795	0.331294
$501$	−25.3686	−1.13339
$502$	23.6112	1.05382
$503$	−0.193757	−0.00863921	−0.00431961	−	0.999991i	$-0.501375\pi$
$503$	−0.193757	−0.00863921	−0.00431961	+	0.999991i	$0.501375\pi$
$504$	0	0
$505$	−6.13810	−0.273142
$506$	11.9263	0.530187
$507$	−1.00000	−0.0444116
$508$	−9.67736	−0.429363
$509$	−37.2347	−1.65040	−0.825200	−	0.564841i	$-0.808937\pi$
$509$	−37.2347	−1.65040	−0.825200	+	0.564841i	$0.808937\pi$
$510$	21.2271	0.939951
$511$	0	0
$512$	−1.00000	−0.0441942
$513$	6.03500	0.266452
$514$	−8.31415	−0.366721
$515$	6.94317	0.305953
$516$	−1.34959	−0.0594124
$517$	−14.2304	−0.625851
$518$	0	0
$519$	17.6355	0.774111
$520$	2.69230	0.118065
$521$	9.79702	0.429215	0.214608	−	0.976700i	$-0.431153\pi$
$521$	9.79702	0.429215	0.214608	+	0.976700i	$0.431153\pi$
$522$	1.64173	0.0718568
$523$	2.80792	0.122782	0.0613909	−	0.998114i	$-0.480446\pi$
$523$	2.80792	0.122782	0.0613909	+	0.998114i	$0.480446\pi$
$524$	−9.90173	−0.432559
$525$	0	0
$526$	−10.8877	−0.474725
$527$	14.5811	0.635164
$528$	4.49978	0.195828
$529$	−15.9753	−0.694579
$530$	−13.8989	−0.603729
$531$	−13.4643	−0.584302
$532$	0	0
$533$	−3.56484	−0.154410
$534$	−12.7569	−0.552046
$535$	36.9238	1.59635
$536$	−4.85805	−0.209836
$537$	−8.41377	−0.363081
$538$	22.0486	0.950584
$539$	0	0
$540$	2.69230	0.115858
$541$	−9.04771	−0.388992	−0.194496	−	0.980903i	$-0.562307\pi$
$541$	−9.04771	−0.388992	−0.194496	+	0.980903i	$0.562307\pi$
$542$	−19.9613	−0.857410
$543$	−16.1119	−0.691428
$544$	7.88438	0.338040
$545$	−40.8295	−1.74894
$546$	0	0
$547$	−10.9822	−0.469565	−0.234783	−	0.972048i	$-0.575438\pi$
$547$	−10.9822	−0.469565	−0.234783	+	0.972048i	$0.575438\pi$
$548$	13.5702	0.579691
$549$	14.6290	0.624352
$550$	10.1176	0.431416
$551$	9.90788	0.422090
$552$	2.65041	0.112809
$553$	0	0
$554$	−6.76157	−0.287272
$555$	−14.6709	−0.622746
$556$	−1.08780	−0.0461329
$557$	24.2701	1.02836	0.514179	−	0.857683i	$-0.328097\pi$
$557$	24.2701	1.02836	0.514179	+	0.857683i	$0.328097\pi$
$558$	1.84937	0.0782901
$559$	1.34959	0.0570816
$560$	0	0
$561$	−35.4780	−1.49788
$562$	8.69830	0.366916
$563$	40.2742	1.69736	0.848678	−	0.528909i	$-0.177399\pi$
$563$	40.2742	1.69736	0.848678	+	0.528909i	$0.177399\pi$
$564$	−3.16246	−0.133164
$565$	−12.7068	−0.534579
$566$	−13.3556	−0.561378
$567$	0	0
$568$	−1.80748	−0.0758403
$569$	14.7878	0.619936	0.309968	−	0.950747i	$-0.399682\pi$
$569$	14.7878	0.619936	0.309968	+	0.950747i	$0.399682\pi$
$570$	16.2480	0.680555
$571$	7.58597	0.317463	0.158731	−	0.987322i	$-0.449260\pi$
$571$	7.58597	0.317463	0.158731	+	0.987322i	$0.449260\pi$
$572$	−4.49978	−0.188145
$573$	−17.2766	−0.721740
$574$	0	0
$575$	5.95935	0.248522
$576$	1.00000	0.0416667
$577$	1.68673	0.0702195	0.0351097	−	0.999383i	$-0.488822\pi$
$577$	1.68673	0.0702195	0.0351097	+	0.999383i	$0.488822\pi$
$578$	−45.1634	−1.87855
$579$	−11.2211	−0.466332
$580$	4.42004	0.183532
$581$	0	0
$582$	−5.28347	−0.219007
$583$	23.2299	0.962086
$584$	15.9641	0.660600
$585$	−2.69230	−0.111313
$586$	30.5553	1.26223
$587$	−43.9528	−1.81413	−0.907063	−	0.420996i	$-0.861681\pi$
$587$	−43.9528	−1.81413	−0.907063	+	0.420996i	$0.861681\pi$
$588$	0	0
$589$	11.1610	0.459879
$590$	−36.2500	−1.49239
$591$	−22.5940	−0.929394
$592$	−5.44922	−0.223961
$593$	5.78548	0.237581	0.118791	−	0.992919i	$-0.462098\pi$
$593$	5.78548	0.237581	0.118791	+	0.992919i	$0.462098\pi$
$594$	−4.49978	−0.184628
$595$	0	0
$596$	−4.55617	−0.186628
$597$	−19.9635	−0.817052
$598$	−2.65041	−0.108383
$599$	−22.3189	−0.911926	−0.455963	−	0.889999i	$-0.650705\pi$
$599$	−22.3189	−0.911926	−0.455963	+	0.889999i	$0.650705\pi$
$600$	2.24846	0.0917932
$601$	−21.4802	−0.876195	−0.438098	−	0.898927i	$-0.644348\pi$
$601$	−21.4802	−0.876195	−0.438098	+	0.898927i	$0.644348\pi$
$602$	0	0
$603$	4.85805	0.197835
$604$	−2.78369	−0.113267
$605$	−24.8984	−1.01227
$606$	2.27988	0.0926136
$607$	−38.8676	−1.57759	−0.788794	−	0.614657i	$-0.789294\pi$
$607$	−38.8676	−1.57759	−0.788794	+	0.614657i	$0.789294\pi$
$608$	6.03500	0.244752
$609$	0	0
$610$	39.3857	1.59468
$611$	3.16246	0.127939
$612$	−7.88438	−0.318707
$613$	28.2196	1.13978	0.569890	−	0.821721i	$-0.306986\pi$
$613$	28.2196	1.13978	0.569890	+	0.821721i	$0.306986\pi$
$614$	−12.6145	−0.509081
$615$	−9.59762	−0.387013
$616$	0	0
$617$	−0.332231	−0.0133751	−0.00668755	−	0.999978i	$-0.502129\pi$
$617$	−0.332231	−0.0133751	−0.00668755	+	0.999978i	$0.502129\pi$
$618$	−2.57890	−0.103739
$619$	−21.5973	−0.868069	−0.434035	−	0.900896i	$-0.642910\pi$
$619$	−21.5973	−0.868069	−0.434035	+	0.900896i	$0.642910\pi$
$620$	4.97906	0.199964
$621$	−2.65041	−0.106357
$622$	−10.6746	−0.428014
$623$	0	0
$624$	−1.00000	−0.0400320
$625$	−31.1867	−1.24747
$626$	−13.2604	−0.529993
$627$	−27.1562	−1.08451
$628$	1.22796	0.0490009
$629$	42.9637	1.71307
$630$	0	0
$631$	−39.8790	−1.58756	−0.793780	−	0.608205i	$-0.791890\pi$
$631$	−39.8790	−1.58756	−0.793780	+	0.608205i	$0.791890\pi$
$632$	5.89126	0.234342
$633$	18.2364	0.724831
$634$	22.1743	0.880654
$635$	26.0543	1.03393
$636$	5.16246	0.204705
$637$	0	0
$638$	−7.38745	−0.292472
$639$	1.80748	0.0715029
$640$	2.69230	0.106422
$641$	3.18131	0.125654	0.0628270	−	0.998024i	$-0.479988\pi$
$641$	3.18131	0.125654	0.0628270	+	0.998024i	$0.479988\pi$
$642$	−13.7146	−0.541272
$643$	−34.3447	−1.35442	−0.677211	−	0.735789i	$-0.736812\pi$
$643$	−34.3447	−1.35442	−0.677211	+	0.735789i	$0.736812\pi$
$644$	0	0
$645$	3.63350	0.143069
$646$	−47.5822	−1.87210
$647$	−35.3700	−1.39054	−0.695268	−	0.718750i	$-0.744714\pi$
$647$	−35.3700	−1.39054	−0.695268	+	0.718750i	$0.744714\pi$
$648$	−1.00000	−0.0392837
$649$	60.5866	2.37823
$650$	−2.24846	−0.0881920
$651$	0	0
$652$	−19.5047	−0.763864
$653$	−0.192833	−0.00754615	−0.00377307	−	0.999993i	$-0.501201\pi$
$653$	−0.192833	−0.00754615	−0.00377307	+	0.999993i	$0.501201\pi$
$654$	15.1653	0.593011
$655$	26.6584	1.04163
$656$	−3.56484	−0.139184
$657$	−15.9641	−0.622820
$658$	0	0
$659$	−25.4811	−0.992601	−0.496301	−	0.868151i	$-0.665309\pi$
$659$	−25.4811	−0.992601	−0.496301	+	0.868151i	$0.665309\pi$
$660$	−12.1147	−0.471566
$661$	18.1400	0.705565	0.352782	−	0.935705i	$-0.385236\pi$
$661$	18.1400	0.705565	0.352782	+	0.935705i	$0.385236\pi$
$662$	32.1523	1.24963
$663$	7.88438	0.306204
$664$	3.72774	0.144664
$665$	0	0
$666$	5.44922	0.211153
$667$	−4.35127	−0.168482
$668$	25.3686	0.981541
$669$	11.7442	0.454058
$670$	13.0793	0.505298
$671$	−65.8274	−2.54124
$672$	0	0
$673$	−44.8883	−1.73032	−0.865159	−	0.501498i	$-0.832783\pi$
$673$	−44.8883	−1.73032	−0.865159	+	0.501498i	$0.832783\pi$
$674$	−9.13657	−0.351927
$675$	−2.24846	−0.0865435
$676$	1.00000	0.0384615
$677$	16.8320	0.646907	0.323453	−	0.946244i	$-0.395156\pi$
$677$	16.8320	0.646907	0.323453	+	0.946244i	$0.395156\pi$
$678$	4.71969	0.181258
$679$	0	0
$680$	−21.2271	−0.814021
$681$	−15.5170	−0.594613
$682$	−8.32176	−0.318657
$683$	−35.1260	−1.34406	−0.672029	−	0.740525i	$-0.734577\pi$
$683$	−35.1260	−1.34406	−0.672029	+	0.740525i	$0.734577\pi$
$684$	−6.03500	−0.230754
$685$	−36.5351	−1.39593
$686$	0	0
$687$	5.13284	0.195830
$688$	1.34959	0.0514526
$689$	−5.16246	−0.196674
$690$	−7.13569	−0.271651
$691$	−4.99956	−0.190192	−0.0950961	−	0.995468i	$-0.530316\pi$
$691$	−4.99956	−0.190192	−0.0950961	+	0.995468i	$0.530316\pi$
$692$	−17.6355	−0.670400
$693$	0	0
$694$	6.45566	0.245054
$695$	2.92868	0.111091
$696$	−1.64173	−0.0622298
$697$	28.1066	1.06461
$698$	−18.0971	−0.684985
$699$	−27.7861	−1.05097
$700$	0	0
$701$	49.7133	1.87764	0.938822	−	0.344401i	$-0.111918\pi$
$701$	49.7133	1.87764	0.938822	+	0.344401i	$0.111918\pi$
$702$	1.00000	0.0377426
$703$	32.8861	1.24032
$704$	−4.49978	−0.169592
$705$	8.51428	0.320666
$706$	−15.3091	−0.576164
$707$	0	0
$708$	13.4643	0.506021
$709$	−30.2805	−1.13721	−0.568604	−	0.822611i	$-0.692516\pi$
$709$	−30.2805	−1.13721	−0.568604	+	0.822611i	$0.692516\pi$
$710$	4.86628	0.182628
$711$	−5.89126	−0.220939
$712$	12.7569	0.478086
$713$	−4.90159	−0.183566
$714$	0	0
$715$	12.1147	0.453066
$716$	8.41377	0.314438
$717$	−7.54811	−0.281889
$718$	5.01691	0.187229
$719$	−8.93629	−0.333267	−0.166634	−	0.986019i	$-0.553290\pi$
$719$	−8.93629	−0.333267	−0.166634	+	0.986019i	$0.553290\pi$
$720$	−2.69230	−0.100336
$721$	0	0
$722$	−17.4213	−0.648353
$723$	28.7857	1.07055
$724$	16.1119	0.598794
$725$	−3.69138	−0.137095
$726$	9.24803	0.343226
$727$	15.9333	0.590932	0.295466	−	0.955353i	$-0.404525\pi$
$727$	15.9333	0.590932	0.295466	+	0.955353i	$0.404525\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−42.9802	−1.59077
$731$	−10.6407	−0.393560
$732$	−14.6290	−0.540704
$733$	32.7897	1.21111	0.605557	−	0.795802i	$-0.292950\pi$
$733$	32.7897	1.21111	0.605557	+	0.795802i	$0.292950\pi$
$734$	−10.5644	−0.389939
$735$	0	0
$736$	−2.65041	−0.0976954
$737$	−21.8601	−0.805229
$738$	3.56484	0.131224
$739$	−13.4218	−0.493730	−0.246865	−	0.969050i	$-0.579400\pi$
$739$	−13.4218	−0.493730	−0.246865	+	0.969050i	$0.579400\pi$
$740$	14.6709	0.539314
$741$	6.03500	0.221701
$742$	0	0
$743$	45.3828	1.66493	0.832467	−	0.554074i	$-0.186928\pi$
$743$	45.3828	1.66493	0.832467	+	0.554074i	$0.186928\pi$
$744$	−1.84937	−0.0678012
$745$	12.2666	0.449412
$746$	7.53435	0.275852
$747$	−3.72774	−0.136391
$748$	35.4780	1.29720
$749$	0	0
$750$	7.40795	0.270500
$751$	−7.58070	−0.276624	−0.138312	−	0.990389i	$-0.544168\pi$
$751$	−7.58070	−0.276624	−0.138312	+	0.990389i	$0.544168\pi$
$752$	3.16246	0.115323
$753$	23.6112	0.860441
$754$	1.64173	0.0597884
$755$	7.49452	0.272753
$756$	0	0
$757$	−39.4808	−1.43495	−0.717477	−	0.696582i	$-0.754703\pi$
$757$	−39.4808	−1.43495	−0.717477	+	0.696582i	$0.754703\pi$
$758$	29.3541	1.06619
$759$	11.9263	0.432896
$760$	−16.2480	−0.589378
$761$	−5.32370	−0.192984	−0.0964920	−	0.995334i	$-0.530762\pi$
$761$	−5.32370	−0.192984	−0.0964920	+	0.995334i	$0.530762\pi$
$762$	−9.67736	−0.350574
$763$	0	0
$764$	17.2766	0.625045
$765$	21.2271	0.767467
$766$	−14.4564	−0.522331
$767$	−13.4643	−0.486169
$768$	−1.00000	−0.0360844
$769$	−10.3557	−0.373437	−0.186719	−	0.982413i	$-0.559785\pi$
$769$	−10.3557	−0.373437	−0.186719	+	0.982413i	$0.559785\pi$
$770$	0	0
$771$	−8.31415	−0.299427
$772$	11.2211	0.403855
$773$	7.88841	0.283726	0.141863	−	0.989886i	$-0.454691\pi$
$773$	7.88841	0.283726	0.141863	+	0.989886i	$0.454691\pi$
$774$	−1.34959	−0.0485100
$775$	−4.15825	−0.149369
$776$	5.28347	0.189665
$777$	0	0
$778$	20.1504	0.722426
$779$	21.5138	0.770813
$780$	2.69230	0.0963997
$781$	−8.13328	−0.291032
$782$	20.8968	0.747269
$783$	1.64173	0.0586708
$784$	0	0
$785$	−3.30603	−0.117997
$786$	−9.90173	−0.353183
$787$	−13.7939	−0.491698	−0.245849	−	0.969308i	$-0.579067\pi$
$787$	−13.7939	−0.491698	−0.245849	+	0.969308i	$0.579067\pi$
$788$	22.5940	0.804879
$789$	−10.8877	−0.387611
$790$	−15.8610	−0.564310
$791$	0	0
$792$	4.49978	0.159893
$793$	14.6290	0.519492
$794$	−19.5860	−0.695080
$795$	−13.8989	−0.492942
$796$	19.9635	0.707587
$797$	28.5094	1.00985	0.504927	−	0.863162i	$-0.331519\pi$
$797$	28.5094	1.00985	0.504927	+	0.863162i	$0.331519\pi$
$798$	0	0
$799$	−24.9340	−0.882102
$800$	−2.24846	−0.0794952
$801$	−12.7569	−0.450744
$802$	−15.6987	−0.554342
$803$	71.8350	2.53500
$804$	−4.85805	−0.171330
$805$	0	0
$806$	1.84937	0.0651413
$807$	22.0486	0.776148
$808$	−2.27988	−0.0802058
$809$	4.67568	0.164388	0.0821941	−	0.996616i	$-0.473807\pi$
$809$	4.67568	0.164388	0.0821941	+	0.996616i	$0.473807\pi$
$810$	2.69230	0.0945977
$811$	−15.5444	−0.545837	−0.272919	−	0.962037i	$-0.587989\pi$
$811$	−15.5444	−0.545837	−0.272919	+	0.962037i	$0.587989\pi$
$812$	0	0
$813$	−19.9613	−0.700072
$814$	−24.5203	−0.859436
$815$	52.5125	1.83943
$816$	7.88438	0.276008
$817$	−8.14478	−0.284950
$818$	26.9161	0.941099
$819$	0	0
$820$	9.59762	0.335163
$821$	−21.9617	−0.766468	−0.383234	−	0.923651i	$-0.625190\pi$
$821$	−21.9617	−0.766468	−0.383234	+	0.923651i	$0.625190\pi$
$822$	13.5702	0.473316
$823$	3.49965	0.121990	0.0609950	−	0.998138i	$-0.480573\pi$
$823$	3.49965	0.121990	0.0609950	+	0.998138i	$0.480573\pi$
$824$	2.57890	0.0898404
$825$	10.1176	0.352250
$826$	0	0
$827$	−20.1450	−0.700510	−0.350255	−	0.936654i	$-0.613905\pi$
$827$	−20.1450	−0.700510	−0.350255	+	0.936654i	$0.613905\pi$
$828$	2.65041	0.0921081
$829$	4.20211	0.145945	0.0729726	−	0.997334i	$-0.476751\pi$
$829$	4.20211	0.145945	0.0729726	+	0.997334i	$0.476751\pi$
$830$	−10.0362	−0.348361
$831$	−6.76157	−0.234556
$832$	1.00000	0.0346688
$833$	0	0
$834$	−1.08780	−0.0376674
$835$	−68.2998	−2.36361
$836$	27.1562	0.939217
$837$	1.84937	0.0639236
$838$	23.1735	0.800517
$839$	19.0605	0.658040	0.329020	−	0.944323i	$-0.393282\pi$
$839$	19.0605	0.658040	0.329020	+	0.944323i	$0.393282\pi$
$840$	0	0
$841$	−26.3047	−0.907059
$842$	5.04969	0.174024
$843$	8.69830	0.299585
$844$	−18.2364	−0.627722
$845$	−2.69230	−0.0926178
$846$	−3.16246	−0.108728
$847$	0	0
$848$	−5.16246	−0.177280
$849$	−13.3556	−0.458363
$850$	17.7277	0.608056
$851$	−14.4427	−0.495088
$852$	−1.80748	−0.0619234
$853$	−0.957674	−0.0327901	−0.0163951	−	0.999866i	$-0.505219\pi$
$853$	−0.957674	−0.0327901	−0.0163951	+	0.999866i	$0.505219\pi$
$854$	0	0
$855$	16.2480	0.555671
$856$	13.7146	0.468755
$857$	3.21134	0.109697	0.0548487	−	0.998495i	$-0.482532\pi$
$857$	3.21134	0.109697	0.0548487	+	0.998495i	$0.482532\pi$
$858$	−4.49978	−0.153620
$859$	8.85209	0.302029	0.151015	−	0.988532i	$-0.451746\pi$
$859$	8.85209	0.302029	0.151015	+	0.988532i	$0.451746\pi$
$860$	−3.63350	−0.123901
$861$	0	0
$862$	−23.5665	−0.802678
$863$	−56.7277	−1.93103	−0.965516	−	0.260343i	$-0.916164\pi$
$863$	−56.7277	−1.93103	−0.965516	+	0.260343i	$0.916164\pi$
$864$	1.00000	0.0340207
$865$	47.4799	1.61437
$866$	−36.0319	−1.22441
$867$	−45.1634	−1.53383
$868$	0	0
$869$	26.5094	0.899269
$870$	4.42004	0.149853
$871$	4.85805	0.164609
$872$	−15.1653	−0.513562
$873$	−5.28347	−0.178818
$874$	15.9952	0.541047
$875$	0	0
$876$	15.9641	0.539378
$877$	28.2985	0.955571	0.477785	−	0.878477i	$-0.341440\pi$
$877$	28.2985	0.955571	0.477785	+	0.878477i	$0.341440\pi$
$878$	−26.1939	−0.884000
$879$	30.5553	1.03060
$880$	12.1147	0.408388
$881$	42.7828	1.44139	0.720695	−	0.693253i	$-0.243823\pi$
$881$	42.7828	1.44139	0.720695	+	0.693253i	$0.243823\pi$
$882$	0	0
$883$	18.8162	0.633216	0.316608	−	0.948557i	$-0.397456\pi$
$883$	18.8162	0.633216	0.316608	+	0.948557i	$0.397456\pi$
$884$	−7.88438	−0.265180
$885$	−36.2500	−1.21853
$886$	13.6304	0.457922
$887$	−11.3962	−0.382648	−0.191324	−	0.981527i	$-0.561278\pi$
$887$	−11.3962	−0.382648	−0.191324	+	0.981527i	$0.561278\pi$
$888$	−5.44922	−0.182864
$889$	0	0
$890$	−34.3454	−1.15126
$891$	−4.49978	−0.150748
$892$	−11.7442	−0.393225
$893$	−19.0855	−0.638670
$894$	−4.55617	−0.152381
$895$	−22.6524	−0.757186
$896$	0	0
$897$	−2.65041	−0.0884946
$898$	−5.28274	−0.176287
$899$	3.03618	0.101262
$900$	2.24846	0.0749488
$901$	40.7028	1.35601
$902$	−16.0410	−0.534107
$903$	0	0
$904$	−4.71969	−0.156974
$905$	−43.3780	−1.44193
$906$	−2.78369	−0.0924819
$907$	−0.939083	−0.0311817	−0.0155909	−	0.999878i	$-0.504963\pi$
$907$	−0.939083	−0.0311817	−0.0155909	+	0.999878i	$0.504963\pi$
$908$	15.5170	0.514950
$909$	2.27988	0.0756187
$910$	0	0
$911$	−17.4543	−0.578287	−0.289143	−	0.957286i	$-0.593370\pi$
$911$	−17.4543	−0.578287	−0.289143	+	0.957286i	$0.593370\pi$
$912$	6.03500	0.199839
$913$	16.7740	0.555139
$914$	−34.4510	−1.13954
$915$	39.3857	1.30205
$916$	−5.13284	−0.169594
$917$	0	0
$918$	−7.88438	−0.260223
$919$	−31.5976	−1.04231	−0.521155	−	0.853462i	$-0.674499\pi$
$919$	−31.5976	−1.04231	−0.521155	+	0.853462i	$0.674499\pi$
$920$	7.13569	0.235257
$921$	−12.6145	−0.415663
$922$	−36.7860	−1.21148
$923$	1.80748	0.0594940
$924$	0	0
$925$	−12.2524	−0.402856
$926$	2.95694	0.0971711
$927$	−2.57890	−0.0847023
$928$	1.64173	0.0538926
$929$	−5.25640	−0.172457	−0.0862284	−	0.996275i	$-0.527481\pi$
$929$	−5.25640	−0.172457	−0.0862284	+	0.996275i	$0.527481\pi$
$930$	4.97906	0.163270
$931$	0	0
$932$	27.7861	0.910164
$933$	−10.6746	−0.349472
$934$	−35.3821	−1.15774
$935$	−95.5172	−3.12375
$936$	−1.00000	−0.0326860
$937$	−37.5309	−1.22608	−0.613041	−	0.790051i	$-0.710054\pi$
$937$	−37.5309	−1.22608	−0.613041	+	0.790051i	$0.710054\pi$
$938$	0	0
$939$	−13.2604	−0.432738
$940$	−8.51428	−0.277705
$941$	46.7865	1.52520	0.762599	−	0.646872i	$-0.223923\pi$
$941$	46.7865	1.52520	0.762599	+	0.646872i	$0.223923\pi$
$942$	1.22796	0.0400091
$943$	−9.44829	−0.307679
$944$	−13.4643	−0.438227
$945$	0	0
$946$	6.07286	0.197446
$947$	40.1513	1.30474	0.652371	−	0.757900i	$-0.273774\pi$
$947$	40.1513	1.30474	0.652371	+	0.757900i	$0.273774\pi$
$948$	5.89126	0.191339
$949$	−15.9641	−0.518217
$950$	13.5695	0.440253
$951$	22.1743	0.719051
$952$	0	0
$953$	−19.5428	−0.633055	−0.316527	−	0.948583i	$-0.602517\pi$
$953$	−19.5428	−0.633055	−0.316527	+	0.948583i	$0.602517\pi$
$954$	5.16246	0.167141
$955$	−46.5137	−1.50515
$956$	7.54811	0.244123
$957$	−7.38745	−0.238802
$958$	27.9002	0.901415
$959$	0	0
$960$	2.69230	0.0868935
$961$	−27.5798	−0.889672
$962$	5.44922	0.175690
$963$	−13.7146	−0.441947
$964$	−28.7857	−0.927124
$965$	−30.2105	−0.972510
$966$	0	0
$967$	13.9146	0.447464	0.223732	−	0.974651i	$-0.428176\pi$
$967$	13.9146	0.447464	0.223732	+	0.974651i	$0.428176\pi$
$968$	−9.24803	−0.297243
$969$	−47.5822	−1.52856
$970$	−14.2247	−0.456727
$971$	−44.5544	−1.42982	−0.714910	−	0.699217i	$-0.753532\pi$
$971$	−44.5544	−1.42982	−0.714910	+	0.699217i	$0.753532\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−9.04057	−0.289679
$975$	−2.24846	−0.0720085
$976$	14.6290	0.468264
$977$	−50.7580	−1.62389	−0.811946	−	0.583732i	$-0.801592\pi$
$977$	−50.7580	−1.62389	−0.811946	+	0.583732i	$0.801592\pi$
$978$	−19.5047	−0.623692
$979$	57.4033	1.83462
$980$	0	0
$981$	15.1653	0.484191
$982$	31.3219	0.999523
$983$	−14.8704	−0.474293	−0.237146	−	0.971474i	$-0.576212\pi$
$983$	−14.8704	−0.474293	−0.237146	+	0.971474i	$0.576212\pi$
$984$	−3.56484	−0.113643
$985$	−60.8298	−1.93820
$986$	−12.9441	−0.412223
$987$	0	0
$988$	−6.03500	−0.191999
$989$	3.57697	0.113741
$990$	−12.1147	−0.385032
$991$	−30.6681	−0.974203	−0.487102	−	0.873345i	$-0.661946\pi$
$991$	−30.6681	−0.974203	−0.487102	+	0.873345i	$0.661946\pi$
$992$	1.84937	0.0587176
$993$	32.1523	1.02032
$994$	0	0
$995$	−53.7477	−1.70392
$996$	3.72774	0.118118
$997$	−34.8339	−1.10320	−0.551600	−	0.834109i	$-0.685982\pi$
$997$	−34.8339	−1.10320	−0.551600	+	0.834109i	$0.685982\pi$
$998$	2.46943	0.0781684
$999$	5.44922	0.172406

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3822.2.a.bx.1.2	✓	4
7.6	odd	2		3822.2.a.by.1.3	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3822.2.a.bx.1.2	✓	4	1.1	even	1	trivial
3822.2.a.by.1.3	yes	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:	\( N \)	\(=\)	\( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3822.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.69230 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.69230 q^{5} +1.00000 q^{6} -1.00000 q^{8} +1.00000 q^{9} +2.69230 q^{10} -4.49978 q^{11} -1.00000 q^{12} +1.00000 q^{13} +2.69230 q^{15} +1.00000 q^{16} -7.88438 q^{17} -1.00000 q^{18} -6.03500 q^{19} -2.69230 q^{20} +4.49978 q^{22} +2.65041 q^{23} +1.00000 q^{24} +2.24846 q^{25} -1.00000 q^{26} -1.00000 q^{27} -1.64173 q^{29} -2.69230 q^{30} -1.84937 q^{31} -1.00000 q^{32} +4.49978 q^{33} +7.88438 q^{34} +1.00000 q^{36} -5.44922 q^{37} +6.03500 q^{38} -1.00000 q^{39} +2.69230 q^{40} -3.56484 q^{41} +1.34959 q^{43} -4.49978 q^{44} -2.69230 q^{45} -2.65041 q^{46} +3.16246 q^{47} -1.00000 q^{48} -2.24846 q^{50} +7.88438 q^{51} +1.00000 q^{52} -5.16246 q^{53} +1.00000 q^{54} +12.1147 q^{55} +6.03500 q^{57} +1.64173 q^{58} -13.4643 q^{59} +2.69230 q^{60} +14.6290 q^{61} +1.84937 q^{62} +1.00000 q^{64} -2.69230 q^{65} -4.49978 q^{66} +4.85805 q^{67} -7.88438 q^{68} -2.65041 q^{69} +1.80748 q^{71} -1.00000 q^{72} -15.9641 q^{73} +5.44922 q^{74} -2.24846 q^{75} -6.03500 q^{76} +1.00000 q^{78} -5.89126 q^{79} -2.69230 q^{80} +1.00000 q^{81} +3.56484 q^{82} -3.72774 q^{83} +21.2271 q^{85} -1.34959 q^{86} +1.64173 q^{87} +4.49978 q^{88} -12.7569 q^{89} +2.69230 q^{90} +2.65041 q^{92} +1.84937 q^{93} -3.16246 q^{94} +16.2480 q^{95} +1.00000 q^{96} -5.28347 q^{97} -4.49978 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 6 q^{5} + 4 q^{6} - 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 6 * q^5 + 4 * q^6 - 4 * q^8 + 4 * q^9	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} - 6 q^{5} + 4 q^{6} - 4 q^{8} + 4 q^{9} + 6 q^{10} + 2 q^{11} - 4 q^{12} + 4 q^{13} + 6 q^{15} + 4 q^{16} - 2 q^{17} - 4 q^{18} - 2 q^{19} - 6 q^{20} - 2 q^{22} - 2 q^{23} + 4 q^{24} + 6 q^{25} - 4 q^{26} - 4 q^{27} + 6 q^{29} - 6 q^{30} - 4 q^{32} - 2 q^{33} + 2 q^{34} + 4 q^{36} + 6 q^{37} + 2 q^{38} - 4 q^{39} + 6 q^{40} - 16 q^{41} + 18 q^{43} + 2 q^{44} - 6 q^{45} + 2 q^{46} - 16 q^{47} - 4 q^{48} - 6 q^{50} + 2 q^{51} + 4 q^{52} + 8 q^{53} + 4 q^{54} - 2 q^{55} + 2 q^{57} - 6 q^{58} - 16 q^{59} + 6 q^{60} + 2 q^{61} + 4 q^{64} - 6 q^{65} + 2 q^{66} + 12 q^{67} - 2 q^{68} + 2 q^{69} - 8 q^{71} - 4 q^{72} - 6 q^{73} - 6 q^{74} - 6 q^{75} - 2 q^{76} + 4 q^{78} - 24 q^{79} - 6 q^{80} + 4 q^{81} + 16 q^{82} - 28 q^{83} + 38 q^{85} - 18 q^{86} - 6 q^{87} - 2 q^{88} - 28 q^{89} + 6 q^{90} - 2 q^{92} + 16 q^{94} + 22 q^{95} + 4 q^{96} + 4 q^{97} + 2 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 - 6 * q^5 + 4 * q^6 - 4 * q^8 + 4 * q^9 + 6 * q^10 + 2 * q^11 - 4 * q^12 + 4 * q^13 + 6 * q^15 + 4 * q^16 - 2 * q^17 - 4 * q^18 - 2 * q^19 - 6 * q^20 - 2 * q^22 - 2 * q^23 + 4 * q^24 + 6 * q^25 - 4 * q^26 - 4 * q^27 + 6 * q^29 - 6 * q^30 - 4 * q^32 - 2 * q^33 + 2 * q^34 + 4 * q^36 + 6 * q^37 + 2 * q^38 - 4 * q^39 + 6 * q^40 - 16 * q^41 + 18 * q^43 + 2 * q^44 - 6 * q^45 + 2 * q^46 - 16 * q^47 - 4 * q^48 - 6 * q^50 + 2 * q^51 + 4 * q^52 + 8 * q^53 + 4 * q^54 - 2 * q^55 + 2 * q^57 - 6 * q^58 - 16 * q^59 + 6 * q^60 + 2 * q^61 + 4 * q^64 - 6 * q^65 + 2 * q^66 + 12 * q^67 - 2 * q^68 + 2 * q^69 - 8 * q^71 - 4 * q^72 - 6 * q^73 - 6 * q^74 - 6 * q^75 - 2 * q^76 + 4 * q^78 - 24 * q^79 - 6 * q^80 + 4 * q^81 + 16 * q^82 - 28 * q^83 + 38 * q^85 - 18 * q^86 - 6 * q^87 - 2 * q^88 - 28 * q^89 + 6 * q^90 - 2 * q^92 + 16 * q^94 + 22 * q^95 + 4 * q^96 + 4 * q^97 + 2 * q^99

Introduction

L-functions

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Database

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