LMFDB - Embedded newform 4998.2.a.bw.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4998,2,Mod(1,4998)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4998, 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("4998.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4998 = 2 \cdot 3 \cdot 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4998.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:	$39.9092309302$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{6}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 6 $ x^2 - 6
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 714)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.44949$ of defining polynomial
Character	$\chi$	$=$	4998.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -2.00000 q^{10} -4.89898 q^{11} -1.00000 q^{12} -2.89898 q^{13} +2.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -4.89898 q^{19} -2.00000 q^{20} -4.89898 q^{22} -4.00000 q^{23} -1.00000 q^{24} -1.00000 q^{25} -2.89898 q^{26} -1.00000 q^{27} +6.89898 q^{29} +2.00000 q^{30} +9.79796 q^{31} +1.00000 q^{32} +4.89898 q^{33} +1.00000 q^{34} +1.00000 q^{36} -6.89898 q^{37} -4.89898 q^{38} +2.89898 q^{39} -2.00000 q^{40} +2.00000 q^{41} +4.00000 q^{43} -4.89898 q^{44} -2.00000 q^{45} -4.00000 q^{46} +8.00000 q^{47} -1.00000 q^{48} -1.00000 q^{50} -1.00000 q^{51} -2.89898 q^{52} +6.00000 q^{53} -1.00000 q^{54} +9.79796 q^{55} +4.89898 q^{57} +6.89898 q^{58} -0.898979 q^{59} +2.00000 q^{60} -10.0000 q^{61} +9.79796 q^{62} +1.00000 q^{64} +5.79796 q^{65} +4.89898 q^{66} +5.79796 q^{67} +1.00000 q^{68} +4.00000 q^{69} -5.79796 q^{71} +1.00000 q^{72} +2.00000 q^{73} -6.89898 q^{74} +1.00000 q^{75} -4.89898 q^{76} +2.89898 q^{78} +9.79796 q^{79} -2.00000 q^{80} +1.00000 q^{81} +2.00000 q^{82} +7.10102 q^{83} -2.00000 q^{85} +4.00000 q^{86} -6.89898 q^{87} -4.89898 q^{88} +11.7980 q^{89} -2.00000 q^{90} -4.00000 q^{92} -9.79796 q^{93} +8.00000 q^{94} +9.79796 q^{95} -1.00000 q^{96} -6.00000 q^{97} -4.89898 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9} - 4 q^{10} - 2 q^{12} + 4 q^{13} + 4 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} - 4 q^{20} - 8 q^{23} - 2 q^{24} - 2 q^{25} + 4 q^{26} - 2 q^{27} + 4 q^{29} + 4 q^{30} + 2 q^{32} + 2 q^{34} + 2 q^{36} - 4 q^{37} - 4 q^{39} - 4 q^{40} + 4 q^{41} + 8 q^{43} - 4 q^{45} - 8 q^{46} + 16 q^{47} - 2 q^{48} - 2 q^{50} - 2 q^{51} + 4 q^{52} + 12 q^{53} - 2 q^{54} + 4 q^{58} + 8 q^{59} + 4 q^{60} - 20 q^{61} + 2 q^{64} - 8 q^{65} - 8 q^{67} + 2 q^{68} + 8 q^{69} + 8 q^{71} + 2 q^{72} + 4 q^{73} - 4 q^{74} + 2 q^{75} - 4 q^{78} - 4 q^{80} + 2 q^{81} + 4 q^{82} + 24 q^{83} - 4 q^{85} + 8 q^{86} - 4 q^{87} + 4 q^{89} - 4 q^{90} - 8 q^{92} + 16 q^{94} - 2 q^{96} - 12 q^{97}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9 - 4 * q^10 - 2 * q^12 + 4 * q^13 + 4 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 - 4 * q^20 - 8 * q^23 - 2 * q^24 - 2 * q^25 + 4 * q^26 - 2 * q^27 + 4 * q^29 + 4 * q^30 + 2 * q^32 + 2 * q^34 + 2 * q^36 - 4 * q^37 - 4 * q^39 - 4 * q^40 + 4 * q^41 + 8 * q^43 - 4 * q^45 - 8 * q^46 + 16 * q^47 - 2 * q^48 - 2 * q^50 - 2 * q^51 + 4 * q^52 + 12 * q^53 - 2 * q^54 + 4 * q^58 + 8 * q^59 + 4 * q^60 - 20 * q^61 + 2 * q^64 - 8 * q^65 - 8 * q^67 + 2 * q^68 + 8 * q^69 + 8 * q^71 + 2 * q^72 + 4 * q^73 - 4 * q^74 + 2 * q^75 - 4 * q^78 - 4 * q^80 + 2 * q^81 + 4 * q^82 + 24 * q^83 - 4 * q^85 + 8 * q^86 - 4 * q^87 + 4 * q^89 - 4 * q^90 - 8 * q^92 + 16 * q^94 - 2 * q^96 - 12 * 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
$5$	−2.00000	−0.894427	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000	−0.894427	−0.447214	+	0.894427i	$0.647584\pi$
$6$	−1.00000	−0.408248
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.00000	−0.632456
$11$	−4.89898	−1.47710	−0.738549	−	0.674200i	$-0.764489\pi$
$11$	−4.89898	−1.47710	−0.738549	+	0.674200i	$0.764489\pi$
$12$	−1.00000	−0.288675
$13$	−2.89898	−0.804032	−0.402016	−	0.915633i	$-0.631690\pi$
$13$	−2.89898	−0.804032	−0.402016	+	0.915633i	$0.631690\pi$
$14$	0	0
$15$	2.00000	0.516398
$16$	1.00000	0.250000
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	1.00000	0.235702
$19$	−4.89898	−1.12390	−0.561951	−	0.827170i	$-0.689949\pi$
$19$	−4.89898	−1.12390	−0.561951	+	0.827170i	$0.689949\pi$
$20$	−2.00000	−0.447214
$21$	0	0
$22$	−4.89898	−1.04447
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	−1.00000	−0.204124
$25$	−1.00000	−0.200000
$26$	−2.89898	−0.568537
$27$	−1.00000	−0.192450
$28$	0	0
$29$	6.89898	1.28111	0.640554	−	0.767913i	$-0.278705\pi$
$29$	6.89898	1.28111	0.640554	+	0.767913i	$0.278705\pi$
$30$	2.00000	0.365148
$31$	9.79796	1.75977	0.879883	−	0.475191i	$-0.157621\pi$
$31$	9.79796	1.75977	0.879883	+	0.475191i	$0.157621\pi$
$32$	1.00000	0.176777
$33$	4.89898	0.852803
$34$	1.00000	0.171499
$35$	0	0
$36$	1.00000	0.166667
$37$	−6.89898	−1.13419	−0.567093	−	0.823654i	$-0.691932\pi$
$37$	−6.89898	−1.13419	−0.567093	+	0.823654i	$0.691932\pi$
$38$	−4.89898	−0.794719
$39$	2.89898	0.464208
$40$	−2.00000	−0.316228
$41$	2.00000	0.312348	0.156174	−	0.987730i	$-0.450084\pi$
$41$	2.00000	0.312348	0.156174	+	0.987730i	$0.450084\pi$
$42$	0	0
$43$	4.00000	0.609994	0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000	0.609994	0.304997	+	0.952353i	$0.401344\pi$
$44$	−4.89898	−0.738549
$45$	−2.00000	−0.298142
$46$	−4.00000	−0.589768
$47$	8.00000	1.16692	0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000	1.16692	0.583460	+	0.812142i	$0.301699\pi$
$48$	−1.00000	−0.144338
$49$	0	0
$50$	−1.00000	−0.141421
$51$	−1.00000	−0.140028
$52$	−2.89898	−0.402016
$53$	6.00000	0.824163	0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000	0.824163	0.412082	+	0.911147i	$0.364802\pi$
$54$	−1.00000	−0.136083
$55$	9.79796	1.32116
$56$	0	0
$57$	4.89898	0.648886
$58$	6.89898	0.905880
$59$	−0.898979	−0.117037	−0.0585186	−	0.998286i	$-0.518638\pi$
$59$	−0.898979	−0.117037	−0.0585186	+	0.998286i	$0.518638\pi$
$60$	2.00000	0.258199
$61$	−10.0000	−1.28037	−0.640184	−	0.768221i	$-0.721142\pi$
$61$	−10.0000	−1.28037	−0.640184	+	0.768221i	$0.721142\pi$
$62$	9.79796	1.24434
$63$	0	0
$64$	1.00000	0.125000
$65$	5.79796	0.719148
$66$	4.89898	0.603023
$67$	5.79796	0.708333	0.354167	−	0.935182i	$-0.384765\pi$
$67$	5.79796	0.708333	0.354167	+	0.935182i	$0.384765\pi$
$68$	1.00000	0.121268
$69$	4.00000	0.481543
$70$	0	0
$71$	−5.79796	−0.688091	−0.344046	−	0.938953i	$-0.611797\pi$
$71$	−5.79796	−0.688091	−0.344046	+	0.938953i	$0.611797\pi$
$72$	1.00000	0.117851
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	−6.89898	−0.801990
$75$	1.00000	0.115470
$76$	−4.89898	−0.561951
$77$	0	0
$78$	2.89898	0.328245
$79$	9.79796	1.10236	0.551178	−	0.834388i	$-0.314178\pi$
$79$	9.79796	1.10236	0.551178	+	0.834388i	$0.314178\pi$
$80$	−2.00000	−0.223607
$81$	1.00000	0.111111
$82$	2.00000	0.220863
$83$	7.10102	0.779438	0.389719	−	0.920934i	$-0.372572\pi$
$83$	7.10102	0.779438	0.389719	+	0.920934i	$0.372572\pi$
$84$	0	0
$85$	−2.00000	−0.216930
$86$	4.00000	0.431331
$87$	−6.89898	−0.739648
$88$	−4.89898	−0.522233
$89$	11.7980	1.25058	0.625291	−	0.780392i	$-0.284980\pi$
$89$	11.7980	1.25058	0.625291	+	0.780392i	$0.284980\pi$
$90$	−2.00000	−0.210819
$91$	0	0
$92$	−4.00000	−0.417029
$93$	−9.79796	−1.01600
$94$	8.00000	0.825137
$95$	9.79796	1.00525
$96$	−1.00000	−0.102062
$97$	−6.00000	−0.609208	−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000	−0.609208	−0.304604	+	0.952479i	$0.598524\pi$
$98$	0	0
$99$	−4.89898	−0.492366
$100$	−1.00000	−0.100000
$101$	10.8990	1.08449	0.542244	−	0.840221i	$-0.317575\pi$
$101$	10.8990	1.08449	0.542244	+	0.840221i	$0.317575\pi$
$102$	−1.00000	−0.0990148
$103$	5.79796	0.571290	0.285645	−	0.958336i	$-0.407792\pi$
$103$	5.79796	0.571290	0.285645	+	0.958336i	$0.407792\pi$
$104$	−2.89898	−0.284268
$105$	0	0
$106$	6.00000	0.582772
$107$	−12.8990	−1.24699	−0.623496	−	0.781827i	$-0.714288\pi$
$107$	−12.8990	−1.24699	−0.623496	+	0.781827i	$0.714288\pi$
$108$	−1.00000	−0.0962250
$109$	−16.6969	−1.59928	−0.799638	−	0.600482i	$-0.794975\pi$
$109$	−16.6969	−1.59928	−0.799638	+	0.600482i	$0.794975\pi$
$110$	9.79796	0.934199
$111$	6.89898	0.654822
$112$	0	0
$113$	7.79796	0.733570	0.366785	−	0.930306i	$-0.380458\pi$
$113$	7.79796	0.733570	0.366785	+	0.930306i	$0.380458\pi$
$114$	4.89898	0.458831
$115$	8.00000	0.746004
$116$	6.89898	0.640554
$117$	−2.89898	−0.268011
$118$	−0.898979	−0.0827578
$119$	0	0
$120$	2.00000	0.182574
$121$	13.0000	1.18182
$122$	−10.0000	−0.905357
$123$	−2.00000	−0.180334
$124$	9.79796	0.879883
$125$	12.0000	1.07331
$126$	0	0
$127$	17.7980	1.57931	0.789657	−	0.613549i	$-0.210259\pi$
$127$	17.7980	1.57931	0.789657	+	0.613549i	$0.210259\pi$
$128$	1.00000	0.0883883
$129$	−4.00000	−0.352180
$130$	5.79796	0.508515
$131$	4.00000	0.349482	0.174741	−	0.984614i	$-0.444091\pi$
$131$	4.00000	0.349482	0.174741	+	0.984614i	$0.444091\pi$
$132$	4.89898	0.426401
$133$	0	0
$134$	5.79796	0.500867
$135$	2.00000	0.172133
$136$	1.00000	0.0857493
$137$	2.00000	0.170872	0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000	0.170872	0.0854358	+	0.996344i	$0.472772\pi$
$138$	4.00000	0.340503
$139$	−5.79796	−0.491776	−0.245888	−	0.969298i	$-0.579080\pi$
$139$	−5.79796	−0.491776	−0.245888	+	0.969298i	$0.579080\pi$
$140$	0	0
$141$	−8.00000	−0.673722
$142$	−5.79796	−0.486554
$143$	14.2020	1.18763
$144$	1.00000	0.0833333
$145$	−13.7980	−1.14586
$146$	2.00000	0.165521
$147$	0	0
$148$	−6.89898	−0.567093
$149$	−11.7980	−0.966526	−0.483263	−	0.875475i	$-0.660549\pi$
$149$	−11.7980	−0.966526	−0.483263	+	0.875475i	$0.660549\pi$
$150$	1.00000	0.0816497
$151$	−17.7980	−1.44838	−0.724189	−	0.689602i	$-0.757786\pi$
$151$	−17.7980	−1.44838	−0.724189	+	0.689602i	$0.757786\pi$
$152$	−4.89898	−0.397360
$153$	1.00000	0.0808452
$154$	0	0
$155$	−19.5959	−1.57398
$156$	2.89898	0.232104
$157$	−12.6969	−1.01333	−0.506663	−	0.862144i	$-0.669121\pi$
$157$	−12.6969	−1.01333	−0.506663	+	0.862144i	$0.669121\pi$
$158$	9.79796	0.779484
$159$	−6.00000	−0.475831
$160$	−2.00000	−0.158114
$161$	0	0
$162$	1.00000	0.0785674
$163$	−0.898979	−0.0704135	−0.0352068	−	0.999380i	$-0.511209\pi$
$163$	−0.898979	−0.0704135	−0.0352068	+	0.999380i	$0.511209\pi$
$164$	2.00000	0.156174
$165$	−9.79796	−0.762770
$166$	7.10102	0.551146
$167$	16.0000	1.23812	0.619059	−	0.785345i	$-0.287514\pi$
$167$	16.0000	1.23812	0.619059	+	0.785345i	$0.287514\pi$
$168$	0	0
$169$	−4.59592	−0.353532
$170$	−2.00000	−0.153393
$171$	−4.89898	−0.374634
$172$	4.00000	0.304997
$173$	−19.7980	−1.50521	−0.752605	−	0.658472i	$-0.771203\pi$
$173$	−19.7980	−1.50521	−0.752605	+	0.658472i	$0.771203\pi$
$174$	−6.89898	−0.523010
$175$	0	0
$176$	−4.89898	−0.369274
$177$	0.898979	0.0675714
$178$	11.7980	0.884294
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	−2.00000	−0.149071
$181$	15.7980	1.17425	0.587127	−	0.809495i	$-0.300259\pi$
$181$	15.7980	1.17425	0.587127	+	0.809495i	$0.300259\pi$
$182$	0	0
$183$	10.0000	0.739221
$184$	−4.00000	−0.294884
$185$	13.7980	1.01445
$186$	−9.79796	−0.718421
$187$	−4.89898	−0.358249
$188$	8.00000	0.583460
$189$	0	0
$190$	9.79796	0.710819
$191$	19.5959	1.41791	0.708955	−	0.705253i	$-0.249167\pi$
$191$	19.5959	1.41791	0.708955	+	0.705253i	$0.249167\pi$
$192$	−1.00000	−0.0721688
$193$	11.7980	0.849236	0.424618	−	0.905373i	$-0.360408\pi$
$193$	11.7980	0.849236	0.424618	+	0.905373i	$0.360408\pi$
$194$	−6.00000	−0.430775
$195$	−5.79796	−0.415200
$196$	0	0
$197$	22.8990	1.63148	0.815742	−	0.578415i	$-0.196329\pi$
$197$	22.8990	1.63148	0.815742	+	0.578415i	$0.196329\pi$
$198$	−4.89898	−0.348155
$199$	16.0000	1.13421	0.567105	−	0.823646i	$-0.308063\pi$
$199$	16.0000	1.13421	0.567105	+	0.823646i	$0.308063\pi$
$200$	−1.00000	−0.0707107
$201$	−5.79796	−0.408956
$202$	10.8990	0.766850
$203$	0	0
$204$	−1.00000	−0.0700140
$205$	−4.00000	−0.279372
$206$	5.79796	0.403963
$207$	−4.00000	−0.278019
$208$	−2.89898	−0.201008
$209$	24.0000	1.66011
$210$	0	0
$211$	15.1010	1.03960	0.519799	−	0.854289i	$-0.326007\pi$
$211$	15.1010	1.03960	0.519799	+	0.854289i	$0.326007\pi$
$212$	6.00000	0.412082
$213$	5.79796	0.397270
$214$	−12.8990	−0.881756
$215$	−8.00000	−0.545595
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−16.6969	−1.13086
$219$	−2.00000	−0.135147
$220$	9.79796	0.660578
$221$	−2.89898	−0.195006
$222$	6.89898	0.463029
$223$	−2.20204	−0.147460	−0.0737298	−	0.997278i	$-0.523490\pi$
$223$	−2.20204	−0.147460	−0.0737298	+	0.997278i	$0.523490\pi$
$224$	0	0
$225$	−1.00000	−0.0666667
$226$	7.79796	0.518713
$227$	15.5959	1.03514	0.517569	−	0.855642i	$-0.326837\pi$
$227$	15.5959	1.03514	0.517569	+	0.855642i	$0.326837\pi$
$228$	4.89898	0.324443
$229$	−9.10102	−0.601412	−0.300706	−	0.953717i	$-0.597222\pi$
$229$	−9.10102	−0.601412	−0.300706	+	0.953717i	$0.597222\pi$
$230$	8.00000	0.527504
$231$	0	0
$232$	6.89898	0.452940
$233$	−11.7980	−0.772910	−0.386455	−	0.922308i	$-0.626301\pi$
$233$	−11.7980	−0.772910	−0.386455	+	0.922308i	$0.626301\pi$
$234$	−2.89898	−0.189512
$235$	−16.0000	−1.04372
$236$	−0.898979	−0.0585186
$237$	−9.79796	−0.636446
$238$	0	0
$239$	17.7980	1.15125	0.575627	−	0.817712i	$-0.304758\pi$
$239$	17.7980	1.15125	0.575627	+	0.817712i	$0.304758\pi$
$240$	2.00000	0.129099
$241$	−17.5959	−1.13345	−0.566726	−	0.823906i	$-0.691790\pi$
$241$	−17.5959	−1.13345	−0.566726	+	0.823906i	$0.691790\pi$
$242$	13.0000	0.835672
$243$	−1.00000	−0.0641500
$244$	−10.0000	−0.640184
$245$	0	0
$246$	−2.00000	−0.127515
$247$	14.2020	0.903654
$248$	9.79796	0.622171
$249$	−7.10102	−0.450009
$250$	12.0000	0.758947
$251$	16.8990	1.06665	0.533327	−	0.845909i	$-0.320942\pi$
$251$	16.8990	1.06665	0.533327	+	0.845909i	$0.320942\pi$
$252$	0	0
$253$	19.5959	1.23198
$254$	17.7980	1.11674
$255$	2.00000	0.125245
$256$	1.00000	0.0625000
$257$	−15.7980	−0.985450	−0.492725	−	0.870185i	$-0.663999\pi$
$257$	−15.7980	−0.985450	−0.492725	+	0.870185i	$0.663999\pi$
$258$	−4.00000	−0.249029
$259$	0	0
$260$	5.79796	0.359574
$261$	6.89898	0.427036
$262$	4.00000	0.247121
$263$	−17.7980	−1.09747	−0.548735	−	0.835997i	$-0.684890\pi$
$263$	−17.7980	−1.09747	−0.548735	+	0.835997i	$0.684890\pi$
$264$	4.89898	0.301511
$265$	−12.0000	−0.737154
$266$	0	0
$267$	−11.7980	−0.722023
$268$	5.79796	0.354167
$269$	−3.79796	−0.231566	−0.115783	−	0.993275i	$-0.536938\pi$
$269$	−3.79796	−0.231566	−0.115783	+	0.993275i	$0.536938\pi$
$270$	2.00000	0.121716
$271$	−21.7980	−1.32413	−0.662066	−	0.749446i	$-0.730320\pi$
$271$	−21.7980	−1.32413	−0.662066	+	0.749446i	$0.730320\pi$
$272$	1.00000	0.0606339
$273$	0	0
$274$	2.00000	0.120824
$275$	4.89898	0.295420
$276$	4.00000	0.240772
$277$	28.6969	1.72423	0.862116	−	0.506711i	$-0.169139\pi$
$277$	28.6969	1.72423	0.862116	+	0.506711i	$0.169139\pi$
$278$	−5.79796	−0.347738
$279$	9.79796	0.586588
$280$	0	0
$281$	21.5959	1.28830	0.644152	−	0.764897i	$-0.277210\pi$
$281$	21.5959	1.28830	0.644152	+	0.764897i	$0.277210\pi$
$282$	−8.00000	−0.476393
$283$	21.7980	1.29575	0.647877	−	0.761745i	$-0.275657\pi$
$283$	21.7980	1.29575	0.647877	+	0.761745i	$0.275657\pi$
$284$	−5.79796	−0.344046
$285$	−9.79796	−0.580381
$286$	14.2020	0.839784
$287$	0	0
$288$	1.00000	0.0589256
$289$	1.00000	0.0588235
$290$	−13.7980	−0.810244
$291$	6.00000	0.351726
$292$	2.00000	0.117041
$293$	20.6969	1.20913	0.604564	−	0.796557i	$-0.293347\pi$
$293$	20.6969	1.20913	0.604564	+	0.796557i	$0.293347\pi$
$294$	0	0
$295$	1.79796	0.104681
$296$	−6.89898	−0.400995
$297$	4.89898	0.284268
$298$	−11.7980	−0.683437
$299$	11.5959	0.670609
$300$	1.00000	0.0577350
$301$	0	0
$302$	−17.7980	−1.02416
$303$	−10.8990	−0.626130
$304$	−4.89898	−0.280976
$305$	20.0000	1.14520
$306$	1.00000	0.0571662
$307$	3.10102	0.176985	0.0884923	−	0.996077i	$-0.471795\pi$
$307$	3.10102	0.176985	0.0884923	+	0.996077i	$0.471795\pi$
$308$	0	0
$309$	−5.79796	−0.329834
$310$	−19.5959	−1.11297
$311$	1.79796	0.101953	0.0509764	−	0.998700i	$-0.483767\pi$
$311$	1.79796	0.101953	0.0509764	+	0.998700i	$0.483767\pi$
$312$	2.89898	0.164122
$313$	−30.0000	−1.69570	−0.847850	−	0.530236i	$-0.822103\pi$
$313$	−30.0000	−1.69570	−0.847850	+	0.530236i	$0.822103\pi$
$314$	−12.6969	−0.716530
$315$	0	0
$316$	9.79796	0.551178
$317$	−4.69694	−0.263806	−0.131903	−	0.991263i	$-0.542109\pi$
$317$	−4.69694	−0.263806	−0.131903	+	0.991263i	$0.542109\pi$
$318$	−6.00000	−0.336463
$319$	−33.7980	−1.89232
$320$	−2.00000	−0.111803
$321$	12.8990	0.719951
$322$	0	0
$323$	−4.89898	−0.272587
$324$	1.00000	0.0555556
$325$	2.89898	0.160806
$326$	−0.898979	−0.0497899
$327$	16.6969	0.923343
$328$	2.00000	0.110432
$329$	0	0
$330$	−9.79796	−0.539360
$331$	12.0000	0.659580	0.329790	−	0.944054i	$-0.393022\pi$
$331$	12.0000	0.659580	0.329790	+	0.944054i	$0.393022\pi$
$332$	7.10102	0.389719
$333$	−6.89898	−0.378062
$334$	16.0000	0.875481
$335$	−11.5959	−0.633553
$336$	0	0
$337$	−17.5959	−0.958511	−0.479255	−	0.877676i	$-0.659093\pi$
$337$	−17.5959	−0.958511	−0.479255	+	0.877676i	$0.659093\pi$
$338$	−4.59592	−0.249985
$339$	−7.79796	−0.423527
$340$	−2.00000	−0.108465
$341$	−48.0000	−2.59935
$342$	−4.89898	−0.264906
$343$	0	0
$344$	4.00000	0.215666
$345$	−8.00000	−0.430706
$346$	−19.7980	−1.06434
$347$	−19.1010	−1.02540	−0.512698	−	0.858569i	$-0.671354\pi$
$347$	−19.1010	−1.02540	−0.512698	+	0.858569i	$0.671354\pi$
$348$	−6.89898	−0.369824
$349$	−26.8990	−1.43987	−0.719935	−	0.694042i	$-0.755828\pi$
$349$	−26.8990	−1.43987	−0.719935	+	0.694042i	$0.755828\pi$
$350$	0	0
$351$	2.89898	0.154736
$352$	−4.89898	−0.261116
$353$	8.20204	0.436551	0.218275	−	0.975887i	$-0.429957\pi$
$353$	8.20204	0.436551	0.218275	+	0.975887i	$0.429957\pi$
$354$	0.898979	0.0477802
$355$	11.5959	0.615447
$356$	11.7980	0.625291
$357$	0	0
$358$	12.0000	0.634220
$359$	25.7980	1.36156	0.680782	−	0.732486i	$-0.261640\pi$
$359$	25.7980	1.36156	0.680782	+	0.732486i	$0.261640\pi$
$360$	−2.00000	−0.105409
$361$	5.00000	0.263158
$362$	15.7980	0.830322
$363$	−13.0000	−0.682323
$364$	0	0
$365$	−4.00000	−0.209370
$366$	10.0000	0.522708
$367$	−33.7980	−1.76424	−0.882120	−	0.471026i	$-0.843884\pi$
$367$	−33.7980	−1.76424	−0.882120	+	0.471026i	$0.843884\pi$
$368$	−4.00000	−0.208514
$369$	2.00000	0.104116
$370$	13.7980	0.717322
$371$	0	0
$372$	−9.79796	−0.508001
$373$	31.7980	1.64644	0.823218	−	0.567725i	$-0.192176\pi$
$373$	31.7980	1.64644	0.823218	+	0.567725i	$0.192176\pi$
$374$	−4.89898	−0.253320
$375$	−12.0000	−0.619677
$376$	8.00000	0.412568
$377$	−20.0000	−1.03005
$378$	0	0
$379$	−15.1010	−0.775687	−0.387844	−	0.921725i	$-0.626780\pi$
$379$	−15.1010	−0.775687	−0.387844	+	0.921725i	$0.626780\pi$
$380$	9.79796	0.502625
$381$	−17.7980	−0.911817
$382$	19.5959	1.00261
$383$	1.79796	0.0918714	0.0459357	−	0.998944i	$-0.485373\pi$
$383$	1.79796	0.0918714	0.0459357	+	0.998944i	$0.485373\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	11.7980	0.600500
$387$	4.00000	0.203331
$388$	−6.00000	−0.304604
$389$	25.5959	1.29776	0.648882	−	0.760889i	$-0.275237\pi$
$389$	25.5959	1.29776	0.648882	+	0.760889i	$0.275237\pi$
$390$	−5.79796	−0.293591
$391$	−4.00000	−0.202289
$392$	0	0
$393$	−4.00000	−0.201773
$394$	22.8990	1.15363
$395$	−19.5959	−0.985978
$396$	−4.89898	−0.246183
$397$	27.3939	1.37486	0.687430	−	0.726251i	$-0.258739\pi$
$397$	27.3939	1.37486	0.687430	+	0.726251i	$0.258739\pi$
$398$	16.0000	0.802008
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	6.00000	0.299626	0.149813	−	0.988714i	$-0.452133\pi$
$401$	6.00000	0.299626	0.149813	+	0.988714i	$0.452133\pi$
$402$	−5.79796	−0.289176
$403$	−28.4041	−1.41491
$404$	10.8990	0.542244
$405$	−2.00000	−0.0993808
$406$	0	0
$407$	33.7980	1.67530
$408$	−1.00000	−0.0495074
$409$	7.79796	0.385584	0.192792	−	0.981240i	$-0.438246\pi$
$409$	7.79796	0.385584	0.192792	+	0.981240i	$0.438246\pi$
$410$	−4.00000	−0.197546
$411$	−2.00000	−0.0986527
$412$	5.79796	0.285645
$413$	0	0
$414$	−4.00000	−0.196589
$415$	−14.2020	−0.697151
$416$	−2.89898	−0.142134
$417$	5.79796	0.283927
$418$	24.0000	1.17388
$419$	−33.3939	−1.63140	−0.815699	−	0.578477i	$-0.803647\pi$
$419$	−33.3939	−1.63140	−0.815699	+	0.578477i	$0.803647\pi$
$420$	0	0
$421$	15.7980	0.769945	0.384973	−	0.922928i	$-0.374211\pi$
$421$	15.7980	0.769945	0.384973	+	0.922928i	$0.374211\pi$
$422$	15.1010	0.735106
$423$	8.00000	0.388973
$424$	6.00000	0.291386
$425$	−1.00000	−0.0485071
$426$	5.79796	0.280912
$427$	0	0
$428$	−12.8990	−0.623496
$429$	−14.2020	−0.685681
$430$	−8.00000	−0.385794
$431$	36.0000	1.73406	0.867029	−	0.498257i	$-0.166026\pi$
$431$	36.0000	1.73406	0.867029	+	0.498257i	$0.166026\pi$
$432$	−1.00000	−0.0481125
$433$	27.3939	1.31647	0.658233	−	0.752814i	$-0.271304\pi$
$433$	27.3939	1.31647	0.658233	+	0.752814i	$0.271304\pi$
$434$	0	0
$435$	13.7980	0.661561
$436$	−16.6969	−0.799638
$437$	19.5959	0.937400
$438$	−2.00000	−0.0955637
$439$	6.20204	0.296007	0.148004	−	0.988987i	$-0.452715\pi$
$439$	6.20204	0.296007	0.148004	+	0.988987i	$0.452715\pi$
$440$	9.79796	0.467099
$441$	0	0
$442$	−2.89898	−0.137890
$443$	10.2020	0.484714	0.242357	−	0.970187i	$-0.422080\pi$
$443$	10.2020	0.484714	0.242357	+	0.970187i	$0.422080\pi$
$444$	6.89898	0.327411
$445$	−23.5959	−1.11855
$446$	−2.20204	−0.104270
$447$	11.7980	0.558024
$448$	0	0
$449$	−13.5959	−0.641631	−0.320816	−	0.947142i	$-0.603957\pi$
$449$	−13.5959	−0.641631	−0.320816	+	0.947142i	$0.603957\pi$
$450$	−1.00000	−0.0471405
$451$	−9.79796	−0.461368
$452$	7.79796	0.366785
$453$	17.7980	0.836221
$454$	15.5959	0.731953
$455$	0	0
$456$	4.89898	0.229416
$457$	34.0000	1.59045	0.795226	−	0.606313i	$-0.207352\pi$
$457$	34.0000	1.59045	0.795226	+	0.606313i	$0.207352\pi$
$458$	−9.10102	−0.425263
$459$	−1.00000	−0.0466760
$460$	8.00000	0.373002
$461$	−22.8990	−1.06651	−0.533256	−	0.845954i	$-0.679032\pi$
$461$	−22.8990	−1.06651	−0.533256	+	0.845954i	$0.679032\pi$
$462$	0	0
$463$	27.5959	1.28249	0.641246	−	0.767336i	$-0.278418\pi$
$463$	27.5959	1.28249	0.641246	+	0.767336i	$0.278418\pi$
$464$	6.89898	0.320277
$465$	19.5959	0.908739
$466$	−11.7980	−0.546530
$467$	−30.2929	−1.40179	−0.700893	−	0.713266i	$-0.747215\pi$
$467$	−30.2929	−1.40179	−0.700893	+	0.713266i	$0.747215\pi$
$468$	−2.89898	−0.134005
$469$	0	0
$470$	−16.0000	−0.738025
$471$	12.6969	0.585044
$472$	−0.898979	−0.0413789
$473$	−19.5959	−0.901021
$474$	−9.79796	−0.450035
$475$	4.89898	0.224781
$476$	0	0
$477$	6.00000	0.274721
$478$	17.7980	0.814060
$479$	21.3939	0.977511	0.488756	−	0.872421i	$-0.337451\pi$
$479$	21.3939	0.977511	0.488756	+	0.872421i	$0.337451\pi$
$480$	2.00000	0.0912871
$481$	20.0000	0.911922
$482$	−17.5959	−0.801472
$483$	0	0
$484$	13.0000	0.590909
$485$	12.0000	0.544892
$486$	−1.00000	−0.0453609
$487$	−32.0000	−1.45006	−0.725029	−	0.688718i	$-0.758174\pi$
$487$	−32.0000	−1.45006	−0.725029	+	0.688718i	$0.758174\pi$
$488$	−10.0000	−0.452679
$489$	0.898979	0.0406533
$490$	0	0
$491$	−31.5959	−1.42590	−0.712952	−	0.701213i	$-0.752642\pi$
$491$	−31.5959	−1.42590	−0.712952	+	0.701213i	$0.752642\pi$
$492$	−2.00000	−0.0901670
$493$	6.89898	0.310714
$494$	14.2020	0.638980
$495$	9.79796	0.440386
$496$	9.79796	0.439941
$497$	0	0
$498$	−7.10102	−0.318204
$499$	7.10102	0.317885	0.158943	−	0.987288i	$-0.449191\pi$
$499$	7.10102	0.317885	0.158943	+	0.987288i	$0.449191\pi$
$500$	12.0000	0.536656
$501$	−16.0000	−0.714827
$502$	16.8990	0.754238
$503$	0	0		−	1.00000i	$-0.5\pi$
$503$	0	0			1.00000i	$0.5\pi$
$504$	0	0
$505$	−21.7980	−0.969996
$506$	19.5959	0.871145
$507$	4.59592	0.204112
$508$	17.7980	0.789657
$509$	−21.1010	−0.935286	−0.467643	−	0.883917i	$-0.654897\pi$
$509$	−21.1010	−0.935286	−0.467643	+	0.883917i	$0.654897\pi$
$510$	2.00000	0.0885615
$511$	0	0
$512$	1.00000	0.0441942
$513$	4.89898	0.216295
$514$	−15.7980	−0.696818
$515$	−11.5959	−0.510977
$516$	−4.00000	−0.176090
$517$	−39.1918	−1.72365
$518$	0	0
$519$	19.7980	0.869034
$520$	5.79796	0.254257
$521$	−6.00000	−0.262865	−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000	−0.262865	−0.131432	+	0.991325i	$0.541958\pi$
$522$	6.89898	0.301960
$523$	28.8990	1.26366	0.631832	−	0.775105i	$-0.282303\pi$
$523$	28.8990	1.26366	0.631832	+	0.775105i	$0.282303\pi$
$524$	4.00000	0.174741
$525$	0	0
$526$	−17.7980	−0.776028
$527$	9.79796	0.426806
$528$	4.89898	0.213201
$529$	−7.00000	−0.304348
$530$	−12.0000	−0.521247
$531$	−0.898979	−0.0390124
$532$	0	0
$533$	−5.79796	−0.251137
$534$	−11.7980	−0.510548
$535$	25.7980	1.11534
$536$	5.79796	0.250434
$537$	−12.0000	−0.517838
$538$	−3.79796	−0.163742
$539$	0	0
$540$	2.00000	0.0860663
$541$	14.4949	0.623184	0.311592	−	0.950216i	$-0.399138\pi$
$541$	14.4949	0.623184	0.311592	+	0.950216i	$0.399138\pi$
$542$	−21.7980	−0.936303
$543$	−15.7980	−0.677955
$544$	1.00000	0.0428746
$545$	33.3939	1.43044
$546$	0	0
$547$	−28.4949	−1.21835	−0.609177	−	0.793034i	$-0.708500\pi$
$547$	−28.4949	−1.21835	−0.609177	+	0.793034i	$0.708500\pi$
$548$	2.00000	0.0854358
$549$	−10.0000	−0.426790
$550$	4.89898	0.208893
$551$	−33.7980	−1.43984
$552$	4.00000	0.170251
$553$	0	0
$554$	28.6969	1.21922
$555$	−13.7980	−0.585691
$556$	−5.79796	−0.245888
$557$	33.5959	1.42350	0.711752	−	0.702430i	$-0.247902\pi$
$557$	33.5959	1.42350	0.711752	+	0.702430i	$0.247902\pi$
$558$	9.79796	0.414781
$559$	−11.5959	−0.490455
$560$	0	0
$561$	4.89898	0.206835
$562$	21.5959	0.910969
$563$	−22.2929	−0.939532	−0.469766	−	0.882791i	$-0.655662\pi$
$563$	−22.2929	−0.939532	−0.469766	+	0.882791i	$0.655662\pi$
$564$	−8.00000	−0.336861
$565$	−15.5959	−0.656125
$566$	21.7980	0.916237
$567$	0	0
$568$	−5.79796	−0.243277
$569$	−30.0000	−1.25767	−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000	−1.25767	−0.628833	+	0.777541i	$0.716467\pi$
$570$	−9.79796	−0.410391
$571$	−40.8990	−1.71157	−0.855785	−	0.517332i	$-0.826925\pi$
$571$	−40.8990	−1.71157	−0.855785	+	0.517332i	$0.826925\pi$
$572$	14.2020	0.593817
$573$	−19.5959	−0.818631
$574$	0	0
$575$	4.00000	0.166812
$576$	1.00000	0.0416667
$577$	9.59592	0.399483	0.199742	−	0.979849i	$-0.435990\pi$
$577$	9.59592	0.399483	0.199742	+	0.979849i	$0.435990\pi$
$578$	1.00000	0.0415945
$579$	−11.7980	−0.490306
$580$	−13.7980	−0.572929
$581$	0	0
$582$	6.00000	0.248708
$583$	−29.3939	−1.21737
$584$	2.00000	0.0827606
$585$	5.79796	0.239716
$586$	20.6969	0.854983
$587$	30.2929	1.25032	0.625160	−	0.780497i	$-0.285034\pi$
$587$	30.2929	1.25032	0.625160	+	0.780497i	$0.285034\pi$
$588$	0	0
$589$	−48.0000	−1.97781
$590$	1.79796	0.0740208
$591$	−22.8990	−0.941938
$592$	−6.89898	−0.283546
$593$	27.7980	1.14153	0.570763	−	0.821115i	$-0.306648\pi$
$593$	27.7980	1.14153	0.570763	+	0.821115i	$0.306648\pi$
$594$	4.89898	0.201008
$595$	0	0
$596$	−11.7980	−0.483263
$597$	−16.0000	−0.654836
$598$	11.5959	0.474192
$599$	−1.79796	−0.0734626	−0.0367313	−	0.999325i	$-0.511695\pi$
$599$	−1.79796	−0.0734626	−0.0367313	+	0.999325i	$0.511695\pi$
$600$	1.00000	0.0408248
$601$	−41.5959	−1.69673	−0.848366	−	0.529409i	$-0.822414\pi$
$601$	−41.5959	−1.69673	−0.848366	+	0.529409i	$0.822414\pi$
$602$	0	0
$603$	5.79796	0.236111
$604$	−17.7980	−0.724189
$605$	−26.0000	−1.05705
$606$	−10.8990	−0.442741
$607$	−11.5959	−0.470664	−0.235332	−	0.971915i	$-0.575618\pi$
$607$	−11.5959	−0.470664	−0.235332	+	0.971915i	$0.575618\pi$
$608$	−4.89898	−0.198680
$609$	0	0
$610$	20.0000	0.809776
$611$	−23.1918	−0.938241
$612$	1.00000	0.0404226
$613$	−0.202041	−0.00816036	−0.00408018	−	0.999992i	$-0.501299\pi$
$613$	−0.202041	−0.00816036	−0.00408018	+	0.999992i	$0.501299\pi$
$614$	3.10102	0.125147
$615$	4.00000	0.161296
$616$	0	0
$617$	−8.20204	−0.330202	−0.165101	−	0.986277i	$-0.552795\pi$
$617$	−8.20204	−0.330202	−0.165101	+	0.986277i	$0.552795\pi$
$618$	−5.79796	−0.233228
$619$	−4.00000	−0.160774	−0.0803868	−	0.996764i	$-0.525616\pi$
$619$	−4.00000	−0.160774	−0.0803868	+	0.996764i	$0.525616\pi$
$620$	−19.5959	−0.786991
$621$	4.00000	0.160514
$622$	1.79796	0.0720916
$623$	0	0
$624$	2.89898	0.116052
$625$	−19.0000	−0.760000
$626$	−30.0000	−1.19904
$627$	−24.0000	−0.958468
$628$	−12.6969	−0.506663
$629$	−6.89898	−0.275080
$630$	0	0
$631$	9.79796	0.390051	0.195025	−	0.980798i	$-0.437521\pi$
$631$	9.79796	0.390051	0.195025	+	0.980798i	$0.437521\pi$
$632$	9.79796	0.389742
$633$	−15.1010	−0.600212
$634$	−4.69694	−0.186539
$635$	−35.5959	−1.41258
$636$	−6.00000	−0.237915
$637$	0	0
$638$	−33.7980	−1.33807
$639$	−5.79796	−0.229364
$640$	−2.00000	−0.0790569
$641$	17.5959	0.694997	0.347498	−	0.937681i	$-0.387031\pi$
$641$	17.5959	0.694997	0.347498	+	0.937681i	$0.387031\pi$
$642$	12.8990	0.509082
$643$	−15.5959	−0.615043	−0.307521	−	0.951541i	$-0.599500\pi$
$643$	−15.5959	−0.615043	−0.307521	+	0.951541i	$0.599500\pi$
$644$	0	0
$645$	8.00000	0.315000
$646$	−4.89898	−0.192748
$647$	−11.5959	−0.455883	−0.227941	−	0.973675i	$-0.573199\pi$
$647$	−11.5959	−0.455883	−0.227941	+	0.973675i	$0.573199\pi$
$648$	1.00000	0.0392837
$649$	4.40408	0.172875
$650$	2.89898	0.113707
$651$	0	0
$652$	−0.898979	−0.0352068
$653$	−17.1010	−0.669215	−0.334607	−	0.942358i	$-0.608604\pi$
$653$	−17.1010	−0.669215	−0.334607	+	0.942358i	$0.608604\pi$
$654$	16.6969	0.652902
$655$	−8.00000	−0.312586
$656$	2.00000	0.0780869
$657$	2.00000	0.0780274
$658$	0	0
$659$	−2.20204	−0.0857793	−0.0428897	−	0.999080i	$-0.513656\pi$
$659$	−2.20204	−0.0857793	−0.0428897	+	0.999080i	$0.513656\pi$
$660$	−9.79796	−0.381385
$661$	−25.1010	−0.976317	−0.488158	−	0.872755i	$-0.662331\pi$
$661$	−25.1010	−0.976317	−0.488158	+	0.872755i	$0.662331\pi$
$662$	12.0000	0.466393
$663$	2.89898	0.112587
$664$	7.10102	0.275573
$665$	0	0
$666$	−6.89898	−0.267330
$667$	−27.5959	−1.06852
$668$	16.0000	0.619059
$669$	2.20204	0.0851358
$670$	−11.5959	−0.447989
$671$	48.9898	1.89123
$672$	0	0
$673$	−19.3939	−0.747579	−0.373790	−	0.927514i	$-0.621942\pi$
$673$	−19.3939	−0.747579	−0.373790	+	0.927514i	$0.621942\pi$
$674$	−17.5959	−0.677769
$675$	1.00000	0.0384900
$676$	−4.59592	−0.176766
$677$	14.0000	0.538064	0.269032	−	0.963131i	$-0.413296\pi$
$677$	14.0000	0.538064	0.269032	+	0.963131i	$0.413296\pi$
$678$	−7.79796	−0.299479
$679$	0	0
$680$	−2.00000	−0.0766965
$681$	−15.5959	−0.597637
$682$	−48.0000	−1.83801
$683$	24.4949	0.937271	0.468636	−	0.883392i	$-0.344746\pi$
$683$	24.4949	0.937271	0.468636	+	0.883392i	$0.344746\pi$
$684$	−4.89898	−0.187317
$685$	−4.00000	−0.152832
$686$	0	0
$687$	9.10102	0.347226
$688$	4.00000	0.152499
$689$	−17.3939	−0.662654
$690$	−8.00000	−0.304555
$691$	33.3939	1.27036	0.635181	−	0.772363i	$-0.280925\pi$
$691$	33.3939	1.27036	0.635181	+	0.772363i	$0.280925\pi$
$692$	−19.7980	−0.752605
$693$	0	0
$694$	−19.1010	−0.725065
$695$	11.5959	0.439858
$696$	−6.89898	−0.261505
$697$	2.00000	0.0757554
$698$	−26.8990	−1.01814
$699$	11.7980	0.446240
$700$	0	0
$701$	−35.7980	−1.35207	−0.676035	−	0.736869i	$-0.736303\pi$
$701$	−35.7980	−1.35207	−0.676035	+	0.736869i	$0.736303\pi$
$702$	2.89898	0.109415
$703$	33.7980	1.27471
$704$	−4.89898	−0.184637
$705$	16.0000	0.602595
$706$	8.20204	0.308688
$707$	0	0
$708$	0.898979	0.0337857
$709$	−40.6969	−1.52841	−0.764203	−	0.644976i	$-0.776867\pi$
$709$	−40.6969	−1.52841	−0.764203	+	0.644976i	$0.776867\pi$
$710$	11.5959	0.435187
$711$	9.79796	0.367452
$712$	11.7980	0.442147
$713$	−39.1918	−1.46775
$714$	0	0
$715$	−28.4041	−1.06225
$716$	12.0000	0.448461
$717$	−17.7980	−0.664677
$718$	25.7980	0.962771
$719$	−25.7980	−0.962102	−0.481051	−	0.876693i	$-0.659745\pi$
$719$	−25.7980	−0.962102	−0.481051	+	0.876693i	$0.659745\pi$
$720$	−2.00000	−0.0745356
$721$	0	0
$722$	5.00000	0.186081
$723$	17.5959	0.654399
$724$	15.7980	0.587127
$725$	−6.89898	−0.256222
$726$	−13.0000	−0.482475
$727$	12.0000	0.445055	0.222528	−	0.974926i	$-0.428569\pi$
$727$	12.0000	0.445055	0.222528	+	0.974926i	$0.428569\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−4.00000	−0.148047
$731$	4.00000	0.147945
$732$	10.0000	0.369611
$733$	22.8990	0.845793	0.422897	−	0.906178i	$-0.361013\pi$
$733$	22.8990	0.845793	0.422897	+	0.906178i	$0.361013\pi$
$734$	−33.7980	−1.24751
$735$	0	0
$736$	−4.00000	−0.147442
$737$	−28.4041	−1.04628
$738$	2.00000	0.0736210
$739$	−26.2020	−0.963858	−0.481929	−	0.876210i	$-0.660064\pi$
$739$	−26.2020	−0.963858	−0.481929	+	0.876210i	$0.660064\pi$
$740$	13.7980	0.507223
$741$	−14.2020	−0.521725
$742$	0	0
$743$	−29.7980	−1.09318	−0.546591	−	0.837400i	$-0.684075\pi$
$743$	−29.7980	−1.09318	−0.546591	+	0.837400i	$0.684075\pi$
$744$	−9.79796	−0.359211
$745$	23.5959	0.864488
$746$	31.7980	1.16421
$747$	7.10102	0.259813
$748$	−4.89898	−0.179124
$749$	0	0
$750$	−12.0000	−0.438178
$751$	4.40408	0.160707	0.0803536	−	0.996766i	$-0.474395\pi$
$751$	4.40408	0.160707	0.0803536	+	0.996766i	$0.474395\pi$
$752$	8.00000	0.291730
$753$	−16.8990	−0.615833
$754$	−20.0000	−0.728357
$755$	35.5959	1.29547
$756$	0	0
$757$	−23.3939	−0.850265	−0.425132	−	0.905131i	$-0.639772\pi$
$757$	−23.3939	−0.850265	−0.425132	+	0.905131i	$0.639772\pi$
$758$	−15.1010	−0.548494
$759$	−19.5959	−0.711287
$760$	9.79796	0.355409
$761$	37.5959	1.36285	0.681425	−	0.731888i	$-0.261360\pi$
$761$	37.5959	1.36285	0.681425	+	0.731888i	$0.261360\pi$
$762$	−17.7980	−0.644752
$763$	0	0
$764$	19.5959	0.708955
$765$	−2.00000	−0.0723102
$766$	1.79796	0.0649629
$767$	2.60612	0.0941017
$768$	−1.00000	−0.0360844
$769$	−19.7980	−0.713933	−0.356966	−	0.934117i	$-0.616189\pi$
$769$	−19.7980	−0.713933	−0.356966	+	0.934117i	$0.616189\pi$
$770$	0	0
$771$	15.7980	0.568950
$772$	11.7980	0.424618
$773$	−18.4949	−0.665215	−0.332608	−	0.943065i	$-0.607928\pi$
$773$	−18.4949	−0.665215	−0.332608	+	0.943065i	$0.607928\pi$
$774$	4.00000	0.143777
$775$	−9.79796	−0.351953
$776$	−6.00000	−0.215387
$777$	0	0
$778$	25.5959	0.917658
$779$	−9.79796	−0.351048
$780$	−5.79796	−0.207600
$781$	28.4041	1.01638
$782$	−4.00000	−0.143040
$783$	−6.89898	−0.246549
$784$	0	0
$785$	25.3939	0.906346
$786$	−4.00000	−0.142675
$787$	0.404082	0.0144040	0.00720198	−	0.999974i	$-0.497708\pi$
$787$	0.404082	0.0144040	0.00720198	+	0.999974i	$0.497708\pi$
$788$	22.8990	0.815742
$789$	17.7980	0.633624
$790$	−19.5959	−0.697191
$791$	0	0
$792$	−4.89898	−0.174078
$793$	28.9898	1.02946
$794$	27.3939	0.972172
$795$	12.0000	0.425596
$796$	16.0000	0.567105
$797$	25.1010	0.889124	0.444562	−	0.895748i	$-0.353359\pi$
$797$	25.1010	0.889124	0.444562	+	0.895748i	$0.353359\pi$
$798$	0	0
$799$	8.00000	0.283020
$800$	−1.00000	−0.0353553
$801$	11.7980	0.416860
$802$	6.00000	0.211867
$803$	−9.79796	−0.345762
$804$	−5.79796	−0.204478
$805$	0	0
$806$	−28.4041	−1.00049
$807$	3.79796	0.133694
$808$	10.8990	0.383425
$809$	−2.00000	−0.0703163	−0.0351581	−	0.999382i	$-0.511193\pi$
$809$	−2.00000	−0.0703163	−0.0351581	+	0.999382i	$0.511193\pi$
$810$	−2.00000	−0.0702728
$811$	49.3939	1.73445	0.867227	−	0.497913i	$-0.165900\pi$
$811$	49.3939	1.73445	0.867227	+	0.497913i	$0.165900\pi$
$812$	0	0
$813$	21.7980	0.764488
$814$	33.7980	1.18462
$815$	1.79796	0.0629798
$816$	−1.00000	−0.0350070
$817$	−19.5959	−0.685574
$818$	7.79796	0.272649
$819$	0	0
$820$	−4.00000	−0.139686
$821$	−9.10102	−0.317628	−0.158814	−	0.987309i	$-0.550767\pi$
$821$	−9.10102	−0.317628	−0.158814	+	0.987309i	$0.550767\pi$
$822$	−2.00000	−0.0697580
$823$	−9.79796	−0.341535	−0.170768	−	0.985311i	$-0.554625\pi$
$823$	−9.79796	−0.341535	−0.170768	+	0.985311i	$0.554625\pi$
$824$	5.79796	0.201981
$825$	−4.89898	−0.170561
$826$	0	0
$827$	28.8990	1.00492	0.502458	−	0.864602i	$-0.332429\pi$
$827$	28.8990	1.00492	0.502458	+	0.864602i	$0.332429\pi$
$828$	−4.00000	−0.139010
$829$	5.10102	0.177166	0.0885829	−	0.996069i	$-0.471766\pi$
$829$	5.10102	0.177166	0.0885829	+	0.996069i	$0.471766\pi$
$830$	−14.2020	−0.492960
$831$	−28.6969	−0.995486
$832$	−2.89898	−0.100504
$833$	0	0
$834$	5.79796	0.200767
$835$	−32.0000	−1.10741
$836$	24.0000	0.830057
$837$	−9.79796	−0.338667
$838$	−33.3939	−1.15357
$839$	−4.40408	−0.152046	−0.0760229	−	0.997106i	$-0.524222\pi$
$839$	−4.40408	−0.152046	−0.0760229	+	0.997106i	$0.524222\pi$
$840$	0	0
$841$	18.5959	0.641239
$842$	15.7980	0.544434
$843$	−21.5959	−0.743803
$844$	15.1010	0.519799
$845$	9.19184	0.316209
$846$	8.00000	0.275046
$847$	0	0
$848$	6.00000	0.206041
$849$	−21.7980	−0.748104
$850$	−1.00000	−0.0342997
$851$	27.5959	0.945976
$852$	5.79796	0.198635
$853$	37.1918	1.27342	0.636712	−	0.771102i	$-0.280294\pi$
$853$	37.1918	1.27342	0.636712	+	0.771102i	$0.280294\pi$
$854$	0	0
$855$	9.79796	0.335083
$856$	−12.8990	−0.440878
$857$	41.1918	1.40709	0.703543	−	0.710653i	$-0.251600\pi$
$857$	41.1918	1.40709	0.703543	+	0.710653i	$0.251600\pi$
$858$	−14.2020	−0.484850
$859$	38.6969	1.32032	0.660161	−	0.751124i	$-0.270488\pi$
$859$	38.6969	1.32032	0.660161	+	0.751124i	$0.270488\pi$
$860$	−8.00000	−0.272798
$861$	0	0
$862$	36.0000	1.22616
$863$	−9.79796	−0.333526	−0.166763	−	0.985997i	$-0.553332\pi$
$863$	−9.79796	−0.333526	−0.166763	+	0.985997i	$0.553332\pi$
$864$	−1.00000	−0.0340207
$865$	39.5959	1.34630
$866$	27.3939	0.930882
$867$	−1.00000	−0.0339618
$868$	0	0
$869$	−48.0000	−1.62829
$870$	13.7980	0.467795
$871$	−16.8082	−0.569523
$872$	−16.6969	−0.565430
$873$	−6.00000	−0.203069
$874$	19.5959	0.662842
$875$	0	0
$876$	−2.00000	−0.0675737
$877$	−21.1010	−0.712531	−0.356265	−	0.934385i	$-0.615950\pi$
$877$	−21.1010	−0.712531	−0.356265	+	0.934385i	$0.615950\pi$
$878$	6.20204	0.209309
$879$	−20.6969	−0.698090
$880$	9.79796	0.330289
$881$	13.5959	0.458058	0.229029	−	0.973420i	$-0.426445\pi$
$881$	13.5959	0.458058	0.229029	+	0.973420i	$0.426445\pi$
$882$	0	0
$883$	5.79796	0.195117	0.0975584	−	0.995230i	$-0.468897\pi$
$883$	5.79796	0.195117	0.0975584	+	0.995230i	$0.468897\pi$
$884$	−2.89898	−0.0975032
$885$	−1.79796	−0.0604377
$886$	10.2020	0.342744
$887$	33.7980	1.13482	0.567412	−	0.823434i	$-0.307945\pi$
$887$	33.7980	1.13482	0.567412	+	0.823434i	$0.307945\pi$
$888$	6.89898	0.231515
$889$	0	0
$890$	−23.5959	−0.790937
$891$	−4.89898	−0.164122
$892$	−2.20204	−0.0737298
$893$	−39.1918	−1.31150
$894$	11.7980	0.394583
$895$	−24.0000	−0.802232
$896$	0	0
$897$	−11.5959	−0.387176
$898$	−13.5959	−0.453702
$899$	67.5959	2.25445
$900$	−1.00000	−0.0333333
$901$	6.00000	0.199889
$902$	−9.79796	−0.326236
$903$	0	0
$904$	7.79796	0.259356
$905$	−31.5959	−1.05028
$906$	17.7980	0.591298
$907$	15.1010	0.501421	0.250711	−	0.968062i	$-0.419336\pi$
$907$	15.1010	0.501421	0.250711	+	0.968062i	$0.419336\pi$
$908$	15.5959	0.517569
$909$	10.8990	0.361496
$910$	0	0
$911$	49.3939	1.63649	0.818246	−	0.574868i	$-0.194947\pi$
$911$	49.3939	1.63649	0.818246	+	0.574868i	$0.194947\pi$
$912$	4.89898	0.162221
$913$	−34.7878	−1.15131
$914$	34.0000	1.12462
$915$	−20.0000	−0.661180
$916$	−9.10102	−0.300706
$917$	0	0
$918$	−1.00000	−0.0330049
$919$	−6.20204	−0.204586	−0.102293	−	0.994754i	$-0.532618\pi$
$919$	−6.20204	−0.204586	−0.102293	+	0.994754i	$0.532618\pi$
$920$	8.00000	0.263752
$921$	−3.10102	−0.102182
$922$	−22.8990	−0.754138
$923$	16.8082	0.553247
$924$	0	0
$925$	6.89898	0.226837
$926$	27.5959	0.906858
$927$	5.79796	0.190430
$928$	6.89898	0.226470
$929$	18.0000	0.590561	0.295280	−	0.955411i	$-0.404587\pi$
$929$	18.0000	0.590561	0.295280	+	0.955411i	$0.404587\pi$
$930$	19.5959	0.642575
$931$	0	0
$932$	−11.7980	−0.386455
$933$	−1.79796	−0.0588625
$934$	−30.2929	−0.991213
$935$	9.79796	0.320428
$936$	−2.89898	−0.0947561
$937$	−50.0000	−1.63343	−0.816714	−	0.577042i	$-0.804207\pi$
$937$	−50.0000	−1.63343	−0.816714	+	0.577042i	$0.804207\pi$
$938$	0	0
$939$	30.0000	0.979013
$940$	−16.0000	−0.521862
$941$	−58.9898	−1.92301	−0.961506	−	0.274783i	$-0.911394\pi$
$941$	−58.9898	−1.92301	−0.961506	+	0.274783i	$0.911394\pi$
$942$	12.6969	0.413689
$943$	−8.00000	−0.260516
$944$	−0.898979	−0.0292593
$945$	0	0
$946$	−19.5959	−0.637118
$947$	4.89898	0.159195	0.0795977	−	0.996827i	$-0.474636\pi$
$947$	4.89898	0.159195	0.0795977	+	0.996827i	$0.474636\pi$
$948$	−9.79796	−0.318223
$949$	−5.79796	−0.188210
$950$	4.89898	0.158944
$951$	4.69694	0.152309
$952$	0	0
$953$	−33.5959	−1.08828	−0.544139	−	0.838995i	$-0.683144\pi$
$953$	−33.5959	−1.08828	−0.544139	+	0.838995i	$0.683144\pi$
$954$	6.00000	0.194257
$955$	−39.1918	−1.26822
$956$	17.7980	0.575627
$957$	33.7980	1.09253
$958$	21.3939	0.691205
$959$	0	0
$960$	2.00000	0.0645497
$961$	65.0000	2.09677
$962$	20.0000	0.644826
$963$	−12.8990	−0.415664
$964$	−17.5959	−0.566726
$965$	−23.5959	−0.759579
$966$	0	0
$967$	4.40408	0.141626	0.0708129	−	0.997490i	$-0.477441\pi$
$967$	4.40408	0.141626	0.0708129	+	0.997490i	$0.477441\pi$
$968$	13.0000	0.417836
$969$	4.89898	0.157378
$970$	12.0000	0.385297
$971$	7.10102	0.227883	0.113941	−	0.993487i	$-0.463652\pi$
$971$	7.10102	0.227883	0.113941	+	0.993487i	$0.463652\pi$
$972$	−1.00000	−0.0320750
$973$	0	0
$974$	−32.0000	−1.02535
$975$	−2.89898	−0.0928416
$976$	−10.0000	−0.320092
$977$	5.59592	0.179029	0.0895146	−	0.995986i	$-0.471468\pi$
$977$	5.59592	0.179029	0.0895146	+	0.995986i	$0.471468\pi$
$978$	0.898979	0.0287462
$979$	−57.7980	−1.84723
$980$	0	0
$981$	−16.6969	−0.533092
$982$	−31.5959	−1.00827
$983$	−53.3939	−1.70300	−0.851500	−	0.524354i	$-0.824307\pi$
$983$	−53.3939	−1.70300	−0.851500	+	0.524354i	$0.824307\pi$
$984$	−2.00000	−0.0637577
$985$	−45.7980	−1.45924
$986$	6.89898	0.219708
$987$	0	0
$988$	14.2020	0.451827
$989$	−16.0000	−0.508770
$990$	9.79796	0.311400
$991$	57.7980	1.83601	0.918006	−	0.396566i	$-0.129798\pi$
$991$	57.7980	1.83601	0.918006	+	0.396566i	$0.129798\pi$
$992$	9.79796	0.311086
$993$	−12.0000	−0.380808
$994$	0	0
$995$	−32.0000	−1.01447
$996$	−7.10102	−0.225004
$997$	−2.00000	−0.0633406	−0.0316703	−	0.999498i	$-0.510083\pi$
$997$	−2.00000	−0.0633406	−0.0316703	+	0.999498i	$0.510083\pi$
$998$	7.10102	0.224779
$999$	6.89898	0.218274

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4998.2.a.bw.1.1		2
7.6	odd	2		714.2.a.m.1.1	✓	2
21.20	even	2		2142.2.a.v.1.2		2
28.27	even	2		5712.2.a.bm.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
714.2.a.m.1.1	✓	2	7.6	odd	2
2142.2.a.v.1.2		2	21.20	even	2
4998.2.a.bw.1.1		2	1.1	even	1	trivial
5712.2.a.bm.1.2		2	28.27	even	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:	\( N \)	\(=\)	\( 4998 = 2 \cdot 3 \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4998.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} -1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -2.00000 q^{10} -4.89898 q^{11} -1.00000 q^{12} -2.89898 q^{13} +2.00000 q^{15} +1.00000 q^{16} +1.00000 q^{17} +1.00000 q^{18} -4.89898 q^{19} -2.00000 q^{20} -4.89898 q^{22} -4.00000 q^{23} -1.00000 q^{24} -1.00000 q^{25} -2.89898 q^{26} -1.00000 q^{27} +6.89898 q^{29} +2.00000 q^{30} +9.79796 q^{31} +1.00000 q^{32} +4.89898 q^{33} +1.00000 q^{34} +1.00000 q^{36} -6.89898 q^{37} -4.89898 q^{38} +2.89898 q^{39} -2.00000 q^{40} +2.00000 q^{41} +4.00000 q^{43} -4.89898 q^{44} -2.00000 q^{45} -4.00000 q^{46} +8.00000 q^{47} -1.00000 q^{48} -1.00000 q^{50} -1.00000 q^{51} -2.89898 q^{52} +6.00000 q^{53} -1.00000 q^{54} +9.79796 q^{55} +4.89898 q^{57} +6.89898 q^{58} -0.898979 q^{59} +2.00000 q^{60} -10.0000 q^{61} +9.79796 q^{62} +1.00000 q^{64} +5.79796 q^{65} +4.89898 q^{66} +5.79796 q^{67} +1.00000 q^{68} +4.00000 q^{69} -5.79796 q^{71} +1.00000 q^{72} +2.00000 q^{73} -6.89898 q^{74} +1.00000 q^{75} -4.89898 q^{76} +2.89898 q^{78} +9.79796 q^{79} -2.00000 q^{80} +1.00000 q^{81} +2.00000 q^{82} +7.10102 q^{83} -2.00000 q^{85} +4.00000 q^{86} -6.89898 q^{87} -4.89898 q^{88} +11.7980 q^{89} -2.00000 q^{90} -4.00000 q^{92} -9.79796 q^{93} +8.00000 q^{94} +9.79796 q^{95} -1.00000 q^{96} -6.00000 q^{97} -4.89898 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} - 2 q^{6} + 2 q^{8} + 2 q^{9} - 4 q^{10} - 2 q^{12} + 4 q^{13} + 4 q^{15} + 2 q^{16} + 2 q^{17} + 2 q^{18} - 4 q^{20} - 8 q^{23} - 2 q^{24} - 2 q^{25} + 4 q^{26} - 2 q^{27} + 4 q^{29} + 4 q^{30} + 2 q^{32} + 2 q^{34} + 2 q^{36} - 4 q^{37} - 4 q^{39} - 4 q^{40} + 4 q^{41} + 8 q^{43} - 4 q^{45} - 8 q^{46} + 16 q^{47} - 2 q^{48} - 2 q^{50} - 2 q^{51} + 4 q^{52} + 12 q^{53} - 2 q^{54} + 4 q^{58} + 8 q^{59} + 4 q^{60} - 20 q^{61} + 2 q^{64} - 8 q^{65} - 8 q^{67} + 2 q^{68} + 8 q^{69} + 8 q^{71} + 2 q^{72} + 4 q^{73} - 4 q^{74} + 2 q^{75} - 4 q^{78} - 4 q^{80} + 2 q^{81} + 4 q^{82} + 24 q^{83} - 4 q^{85} + 8 q^{86} - 4 q^{87} + 4 q^{89} - 4 q^{90} - 8 q^{92} + 16 q^{94} - 2 q^{96} - 12 q^{97}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 - 2 * q^6 + 2 * q^8 + 2 * q^9 - 4 * q^10 - 2 * q^12 + 4 * q^13 + 4 * q^15 + 2 * q^16 + 2 * q^17 + 2 * q^18 - 4 * q^20 - 8 * q^23 - 2 * q^24 - 2 * q^25 + 4 * q^26 - 2 * q^27 + 4 * q^29 + 4 * q^30 + 2 * q^32 + 2 * q^34 + 2 * q^36 - 4 * q^37 - 4 * q^39 - 4 * q^40 + 4 * q^41 + 8 * q^43 - 4 * q^45 - 8 * q^46 + 16 * q^47 - 2 * q^48 - 2 * q^50 - 2 * q^51 + 4 * q^52 + 12 * q^53 - 2 * q^54 + 4 * q^58 + 8 * q^59 + 4 * q^60 - 20 * q^61 + 2 * q^64 - 8 * q^65 - 8 * q^67 + 2 * q^68 + 8 * q^69 + 8 * q^71 + 2 * q^72 + 4 * q^73 - 4 * q^74 + 2 * q^75 - 4 * q^78 - 4 * q^80 + 2 * q^81 + 4 * q^82 + 24 * q^83 - 4 * q^85 + 8 * q^86 - 4 * q^87 + 4 * q^89 - 4 * q^90 - 8 * q^92 + 16 * q^94 - 2 * q^96 - 12 * q^97

Introduction

L-functions

Modular forms

Varieties

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Database

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