LMFDB - Embedded newform 1617.2.a.u.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1617,2,Mod(1,1617)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1617, 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("1617.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1617 = 3 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1617.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:	$12.9118100068$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.2624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 3x^{2} + 2x + 1 $ x^4 - 2x^3 - 3x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.22833$ of defining polynomial
Character	$\chi$	$=$	1617.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.22833 q^{2} -1.00000 q^{3} +2.96545 q^{4} +4.15133 q^{5} +2.22833 q^{6} -2.15133 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.22833 q^{2} -1.00000 q^{3} +2.96545 q^{4} +4.15133 q^{5} +2.22833 q^{6} -2.15133 q^{8} +1.00000 q^{9} -9.25053 q^{10} +1.00000 q^{11} -2.96545 q^{12} -2.93089 q^{13} -4.15133 q^{15} -1.13702 q^{16} +1.36535 q^{17} -2.22833 q^{18} +4.10247 q^{19} +12.3106 q^{20} -2.22833 q^{22} +2.93732 q^{23} +2.15133 q^{24} +12.2336 q^{25} +6.53099 q^{26} -1.00000 q^{27} -8.97976 q^{29} +9.25053 q^{30} +4.10889 q^{31} +6.83632 q^{32} -1.00000 q^{33} -3.04244 q^{34} +2.96545 q^{36} +10.2160 q^{37} -9.14164 q^{38} +2.93089 q^{39} -8.93089 q^{40} -6.60157 q^{41} +10.8644 q^{43} +2.96545 q^{44} +4.15133 q^{45} -6.54530 q^{46} +6.22044 q^{47} +1.13702 q^{48} -27.2604 q^{50} -1.36535 q^{51} -8.69141 q^{52} -6.71954 q^{53} +2.22833 q^{54} +4.15133 q^{55} -4.10247 q^{57} +20.0099 q^{58} -0.797142 q^{59} -12.3106 q^{60} -7.77690 q^{61} -9.15595 q^{62} -12.9595 q^{64} -12.1671 q^{65} +2.22833 q^{66} -11.7751 q^{67} +4.04887 q^{68} -2.93732 q^{69} -5.68825 q^{71} -2.15133 q^{72} +13.5702 q^{73} -22.7645 q^{74} -12.2336 q^{75} +12.1656 q^{76} -6.53099 q^{78} -4.38755 q^{79} -4.72015 q^{80} +1.00000 q^{81} +14.7105 q^{82} +6.01116 q^{83} +5.66801 q^{85} -24.2096 q^{86} +8.97976 q^{87} -2.15133 q^{88} +1.32024 q^{89} -9.25053 q^{90} +8.71045 q^{92} -4.10889 q^{93} -13.8612 q^{94} +17.0307 q^{95} -6.83632 q^{96} +2.57463 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 4 q^{3} + 2 q^{4} + 8 q^{5} + 2 q^{6} + 4 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - 4 * q^3 + 2 * q^4 + 8 * q^5 + 2 * q^6 + 4 * q^9	$ 4 q - 2 q^{2} - 4 q^{3} + 2 q^{4} + 8 q^{5} + 2 q^{6} + 4 q^{9} - 2 q^{10} + 4 q^{11} - 2 q^{12} + 8 q^{13} - 8 q^{15} - 6 q^{16} - 2 q^{18} + 8 q^{19} + 14 q^{20} - 2 q^{22} + 12 q^{25} + 2 q^{26} - 4 q^{27} - 16 q^{29} + 2 q^{30} + 16 q^{31} - 2 q^{32} - 4 q^{33} - 4 q^{34} + 2 q^{36} - 4 q^{37} - 2 q^{38} - 8 q^{39} - 16 q^{40} + 4 q^{41} + 16 q^{43} + 2 q^{44} + 8 q^{45} + 8 q^{46} + 36 q^{47} + 6 q^{48} - 8 q^{50} - 22 q^{52} - 16 q^{53} + 2 q^{54} + 8 q^{55} - 8 q^{57} + 14 q^{58} - 14 q^{60} - 8 q^{61} + 8 q^{62} - 12 q^{64} - 4 q^{65} + 2 q^{66} + 20 q^{67} + 16 q^{68} - 20 q^{71} + 4 q^{73} - 30 q^{74} - 12 q^{75} + 30 q^{76} - 2 q^{78} + 16 q^{79} - 14 q^{80} + 4 q^{81} + 28 q^{82} + 24 q^{83} - 44 q^{86} + 16 q^{87} - 4 q^{89} - 2 q^{90} + 4 q^{92} - 16 q^{93} - 10 q^{94} + 28 q^{95} + 2 q^{96} + 16 q^{97} + 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 4 * q^3 + 2 * q^4 + 8 * q^5 + 2 * q^6 + 4 * q^9 - 2 * q^10 + 4 * q^11 - 2 * q^12 + 8 * q^13 - 8 * q^15 - 6 * q^16 - 2 * q^18 + 8 * q^19 + 14 * q^20 - 2 * q^22 + 12 * q^25 + 2 * q^26 - 4 * q^27 - 16 * q^29 + 2 * q^30 + 16 * q^31 - 2 * q^32 - 4 * q^33 - 4 * q^34 + 2 * q^36 - 4 * q^37 - 2 * q^38 - 8 * q^39 - 16 * q^40 + 4 * q^41 + 16 * q^43 + 2 * q^44 + 8 * q^45 + 8 * q^46 + 36 * q^47 + 6 * q^48 - 8 * q^50 - 22 * q^52 - 16 * q^53 + 2 * q^54 + 8 * q^55 - 8 * q^57 + 14 * q^58 - 14 * q^60 - 8 * q^61 + 8 * q^62 - 12 * q^64 - 4 * q^65 + 2 * q^66 + 20 * q^67 + 16 * q^68 - 20 * q^71 + 4 * q^73 - 30 * q^74 - 12 * q^75 + 30 * q^76 - 2 * q^78 + 16 * q^79 - 14 * q^80 + 4 * q^81 + 28 * q^82 + 24 * q^83 - 44 * q^86 + 16 * q^87 - 4 * q^89 - 2 * q^90 + 4 * q^92 - 16 * q^93 - 10 * q^94 + 28 * q^95 + 2 * q^96 + 16 * q^97 + 4 * 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 $

$2$	−2.22833	−1.57567	−0.787833	−	0.615889i	$-0.788797\pi$
$2$	−2.22833	−1.57567	−0.787833	+	0.615889i	$0.788797\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.96545	1.48272
$5$	4.15133	1.85653	0.928266	−	0.371917i	$-0.121299\pi$
$5$	4.15133	1.85653	0.928266	+	0.371917i	$0.121299\pi$
$6$	2.22833	0.909711
$7$	0	0
$7$	0	0
$8$	−2.15133	−0.760611
$9$	1.00000	0.333333
$10$	−9.25053	−2.92527
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.96545	−0.856051
$13$	−2.93089	−0.812884	−0.406442	−	0.913677i	$-0.633231\pi$
$13$	−2.93089	−0.812884	−0.406442	+	0.913677i	$0.633231\pi$
$14$	0	0
$15$	−4.15133	−1.07187
$16$	−1.13702	−0.284255
$17$	1.36535	0.331145	0.165573	−	0.986198i	$-0.447053\pi$
$17$	1.36535	0.331145	0.165573	+	0.986198i	$0.447053\pi$
$18$	−2.22833	−0.525222
$19$	4.10247	0.941170	0.470585	−	0.882355i	$-0.344043\pi$
$19$	4.10247	0.941170	0.470585	+	0.882355i	$0.344043\pi$
$20$	12.3106	2.75272
$21$	0	0
$22$	−2.22833	−0.475081
$23$	2.93732	0.612473	0.306236	−	0.951956i	$-0.400930\pi$
$23$	2.93732	0.612473	0.306236	+	0.951956i	$0.400930\pi$
$24$	2.15133	0.439139
$25$	12.2336	2.44671
$26$	6.53099	1.28083
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−8.97976	−1.66750	−0.833750	−	0.552143i	$-0.813810\pi$
$29$	−8.97976	−1.66750	−0.833750	+	0.552143i	$0.813810\pi$
$30$	9.25053	1.68891
$31$	4.10889	0.737978	0.368989	−	0.929434i	$-0.379704\pi$
$31$	4.10889	0.737978	0.368989	+	0.929434i	$0.379704\pi$
$32$	6.83632	1.20850
$33$	−1.00000	−0.174078
$34$	−3.04244	−0.521775
$35$	0	0
$36$	2.96545	0.494241
$37$	10.2160	1.67950	0.839748	−	0.542976i	$-0.182703\pi$
$37$	10.2160	1.67950	0.839748	+	0.542976i	$0.182703\pi$
$38$	−9.14164	−1.48297
$39$	2.93089	0.469319
$40$	−8.93089	−1.41210
$41$	−6.60157	−1.03099	−0.515496	−	0.856892i	$-0.672392\pi$
$41$	−6.60157	−1.03099	−0.515496	+	0.856892i	$0.672392\pi$
$42$	0	0
$43$	10.8644	1.65681	0.828406	−	0.560128i	$-0.189248\pi$
$43$	10.8644	1.65681	0.828406	+	0.560128i	$0.189248\pi$
$44$	2.96545	0.447058
$45$	4.15133	0.618844
$46$	−6.54530	−0.965053
$47$	6.22044	0.907344	0.453672	−	0.891169i	$-0.350114\pi$
$47$	6.22044	0.907344	0.453672	+	0.891169i	$0.350114\pi$
$48$	1.13702	0.164115
$49$	0	0
$50$	−27.2604	−3.85520
$51$	−1.36535	−0.191187
$52$	−8.69141	−1.20528
$53$	−6.71954	−0.923000	−0.461500	−	0.887140i	$-0.652688\pi$
$53$	−6.71954	−0.923000	−0.461500	+	0.887140i	$0.652688\pi$
$54$	2.22833	0.303237
$55$	4.15133	0.559765
$56$	0	0
$57$	−4.10247	−0.543385
$58$	20.0099	2.62742
$59$	−0.797142	−0.103779	−0.0518895	−	0.998653i	$-0.516524\pi$
$59$	−0.797142	−0.103779	−0.0518895	+	0.998653i	$0.516524\pi$
$60$	−12.3106	−1.58929
$61$	−7.77690	−0.995730	−0.497865	−	0.867255i	$-0.665883\pi$
$61$	−7.77690	−0.995730	−0.497865	+	0.867255i	$0.665883\pi$
$62$	−9.15595	−1.16281
$63$	0	0
$64$	−12.9595	−1.61994
$65$	−12.1671	−1.50914
$66$	2.22833	0.274288
$67$	−11.7751	−1.43856	−0.719279	−	0.694722i	$-0.755528\pi$
$67$	−11.7751	−1.43856	−0.719279	+	0.694722i	$0.755528\pi$
$68$	4.04887	0.490997
$69$	−2.93732	−0.353611
$70$	0	0
$71$	−5.68825	−0.675071	−0.337536	−	0.941313i	$-0.609593\pi$
$71$	−5.68825	−0.675071	−0.337536	+	0.941313i	$0.609593\pi$
$72$	−2.15133	−0.253537
$73$	13.5702	1.58827	0.794134	−	0.607743i	$-0.207925\pi$
$73$	13.5702	1.58827	0.794134	+	0.607743i	$0.207925\pi$
$74$	−22.7645	−2.64633
$75$	−12.2336	−1.41261
$76$	12.1656	1.39550
$77$	0	0
$78$	−6.53099	−0.739489
$79$	−4.38755	−0.493638	−0.246819	−	0.969062i	$-0.579385\pi$
$79$	−4.38755	−0.493638	−0.246819	+	0.969062i	$0.579385\pi$
$80$	−4.72015	−0.527728
$81$	1.00000	0.111111
$82$	14.7105	1.62450
$83$	6.01116	0.659810	0.329905	−	0.944014i	$-0.392983\pi$
$83$	6.01116	0.659810	0.329905	+	0.944014i	$0.392983\pi$
$84$	0	0
$85$	5.66801	0.614782
$86$	−24.2096	−2.61058
$87$	8.97976	0.962731
$88$	−2.15133	−0.229333
$89$	1.32024	0.139946	0.0699728	−	0.997549i	$-0.477709\pi$
$89$	1.32024	0.139946	0.0699728	+	0.997549i	$0.477709\pi$
$90$	−9.25053	−0.975091
$91$	0	0
$92$	8.71045	0.908128
$93$	−4.10889	−0.426072
$94$	−13.8612	−1.42967
$95$	17.0307	1.74731
$96$	−6.83632	−0.697729
$97$	2.57463	0.261414	0.130707	−	0.991421i	$-0.458275\pi$
$97$	2.57463	0.261414	0.130707	+	0.991421i	$0.458275\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	36.2780	3.62780
$101$	−8.79910	−0.875543	−0.437772	−	0.899086i	$-0.644232\pi$
$101$	−8.79910	−0.875543	−0.437772	+	0.899086i	$0.644232\pi$
$102$	3.04244	0.301247
$103$	17.5840	1.73260	0.866301	−	0.499523i	$-0.166491\pi$
$103$	17.5840	1.73260	0.866301	+	0.499523i	$0.166491\pi$
$104$	6.30532	0.618288
$105$	0	0
$106$	14.9733	1.45434
$107$	4.97976	0.481411	0.240706	−	0.970598i	$-0.422621\pi$
$107$	4.97976	0.481411	0.240706	+	0.970598i	$0.422621\pi$
$108$	−2.96545	−0.285350
$109$	−11.3249	−1.08473	−0.542363	−	0.840144i	$-0.682470\pi$
$109$	−11.3249	−1.08473	−0.542363	+	0.840144i	$0.682470\pi$
$110$	−9.25053	−0.882003
$111$	−10.2160	−0.969658
$112$	0	0
$113$	6.25842	0.588743	0.294371	−	0.955691i	$-0.404890\pi$
$113$	6.25842	0.588743	0.294371	+	0.955691i	$0.404890\pi$
$114$	9.14164	0.856193
$115$	12.1938	1.13708
$116$	−26.6290	−2.47244
$117$	−2.93089	−0.270961
$118$	1.77629	0.163521
$119$	0	0
$120$	8.93089	0.815275
$121$	1.00000	0.0909091
$122$	17.3295	1.56894
$123$	6.60157	0.595243
$124$	12.1847	1.09422
$125$	30.0289	2.68587
$126$	0	0
$127$	−7.04706	−0.625326	−0.312663	−	0.949864i	$-0.601221\pi$
$127$	−7.04706	−0.625326	−0.312663	+	0.949864i	$0.601221\pi$
$128$	15.2054	1.34398
$129$	−10.8644	−0.956561
$130$	27.1123	2.37791
$131$	10.6993	0.934802	0.467401	−	0.884045i	$-0.345190\pi$
$131$	10.6993	0.934802	0.467401	+	0.884045i	$0.345190\pi$
$132$	−2.96545	−0.258109
$133$	0	0
$134$	26.2388	2.26669
$135$	−4.15133	−0.357290
$136$	−2.93732	−0.251873
$137$	−13.7306	−1.17308	−0.586541	−	0.809919i	$-0.699511\pi$
$137$	−13.7306	−1.17308	−0.586541	+	0.809919i	$0.699511\pi$
$138$	6.54530	0.557173
$139$	4.63927	0.393498	0.196749	−	0.980454i	$-0.436962\pi$
$139$	4.63927	0.393498	0.196749	+	0.980454i	$0.436962\pi$
$140$	0	0
$141$	−6.22044	−0.523855
$142$	12.6753	1.06369
$143$	−2.93089	−0.245094
$144$	−1.13702	−0.0947516
$145$	−37.2780	−3.09577
$146$	−30.2388	−2.50258
$147$	0	0
$148$	30.2949	2.49023
$149$	2.32110	0.190152	0.0950761	−	0.995470i	$-0.469691\pi$
$149$	2.32110	0.190152	0.0950761	+	0.995470i	$0.469691\pi$
$150$	27.2604	2.22580
$151$	18.2435	1.48463	0.742317	−	0.670048i	$-0.233727\pi$
$151$	18.2435	1.48463	0.742317	+	0.670048i	$0.233727\pi$
$152$	−8.82577	−0.715864
$153$	1.36535	0.110382
$154$	0	0
$155$	17.0574	1.37008
$156$	8.69141	0.695870
$157$	24.1293	1.92573	0.962863	−	0.269989i	$-0.0870200\pi$
$157$	24.1293	1.92573	0.962863	+	0.269989i	$0.0870200\pi$
$158$	9.77690	0.777808
$159$	6.71954	0.532894
$160$	28.3798	2.24362
$161$	0	0
$162$	−2.22833	−0.175074
$163$	−23.1240	−1.81121	−0.905605	−	0.424123i	$-0.860582\pi$
$163$	−23.1240	−1.81121	−0.905605	+	0.424123i	$0.860582\pi$
$164$	−19.5766	−1.52867
$165$	−4.15133	−0.323181
$166$	−13.3948	−1.03964
$167$	11.2453	0.870188	0.435094	−	0.900385i	$-0.356715\pi$
$167$	11.2453	0.870188	0.435094	+	0.900385i	$0.356715\pi$
$168$	0	0
$169$	−4.40986	−0.339220
$170$	−12.6302	−0.968691
$171$	4.10247	0.313723
$172$	32.2179	2.45659
$173$	−6.61065	−0.502598	−0.251299	−	0.967909i	$-0.580858\pi$
$173$	−6.61065	−0.502598	−0.251299	+	0.967909i	$0.580858\pi$
$174$	−20.0099	−1.51694
$175$	0	0
$176$	−1.13702	−0.0857061
$177$	0.797142	0.0599168
$178$	−2.94194	−0.220508
$179$	8.05725	0.602227	0.301114	−	0.953588i	$-0.402642\pi$
$179$	8.05725	0.602227	0.301114	+	0.953588i	$0.402642\pi$
$180$	12.3106	0.917574
$181$	7.48794	0.556574	0.278287	−	0.960498i	$-0.410233\pi$
$181$	7.48794	0.556574	0.278287	+	0.960498i	$0.410233\pi$
$182$	0	0
$183$	7.77690	0.574885
$184$	−6.31914	−0.465853
$185$	42.4099	3.11804
$186$	9.15595	0.671347
$187$	1.36535	0.0998441
$188$	18.4464	1.34534
$189$	0	0
$190$	−37.9500	−2.75318
$191$	13.0184	0.941981	0.470991	−	0.882138i	$-0.343897\pi$
$191$	13.0184	0.941981	0.470991	+	0.882138i	$0.343897\pi$
$192$	12.9595	0.935273
$193$	−9.32487	−0.671219	−0.335609	−	0.942001i	$-0.608942\pi$
$193$	−9.32487	−0.671219	−0.335609	+	0.942001i	$0.608942\pi$
$194$	−5.73712	−0.411901
$195$	12.1671	0.871305
$196$	0	0
$197$	−17.6101	−1.25466	−0.627332	−	0.778752i	$-0.715853\pi$
$197$	−17.6101	−1.25466	−0.627332	+	0.778752i	$0.715853\pi$
$198$	−2.22833	−0.158360
$199$	13.8129	0.979172	0.489586	−	0.871955i	$-0.337148\pi$
$199$	13.8129	0.979172	0.489586	+	0.871955i	$0.337148\pi$
$200$	−26.3184	−1.86099
$201$	11.7751	0.830551
$202$	19.6073	1.37956
$203$	0	0
$204$	−4.04887	−0.283477
$205$	−27.4053	−1.91407
$206$	−39.1829	−2.73000
$207$	2.93732	0.204158
$208$	3.33248	0.231066
$209$	4.10247	0.283774
$210$	0	0
$211$	10.0572	0.692370	0.346185	−	0.938166i	$-0.387477\pi$
$211$	10.0572	0.692370	0.346185	+	0.938166i	$0.387477\pi$
$212$	−19.9264	−1.36855
$213$	5.68825	0.389753
$214$	−11.0965	−0.758544
$215$	45.1019	3.07593
$216$	2.15133	0.146380
$217$	0	0
$218$	25.2355	1.70916
$219$	−13.5702	−0.916987
$220$	12.3106	0.829977
$221$	−4.00169	−0.269183
$222$	22.7645	1.52786
$223$	16.0924	1.07763	0.538814	−	0.842425i	$-0.318873\pi$
$223$	16.0924	1.07763	0.538814	+	0.842425i	$0.318873\pi$
$224$	0	0
$225$	12.2336	0.815570
$226$	−13.9458	−0.927662
$227$	−28.7384	−1.90743	−0.953717	−	0.300707i	$-0.902777\pi$
$227$	−28.7384	−1.90743	−0.953717	+	0.300707i	$0.902777\pi$
$228$	−12.1656	−0.805689
$229$	16.0960	1.06366	0.531828	−	0.846852i	$-0.321505\pi$
$229$	16.0960	1.06366	0.531828	+	0.846852i	$0.321505\pi$
$230$	−27.1717	−1.79165
$231$	0	0
$232$	19.3184	1.26832
$233$	−11.5029	−0.753578	−0.376789	−	0.926299i	$-0.622972\pi$
$233$	−11.5029	−0.753578	−0.376789	+	0.926299i	$0.622972\pi$
$234$	6.53099	0.426944
$235$	25.8231	1.68451
$236$	−2.36388	−0.153876
$237$	4.38755	0.285002
$238$	0	0
$239$	1.00207	0.0648188	0.0324094	−	0.999475i	$-0.489682\pi$
$239$	1.00207	0.0648188	0.0324094	+	0.999475i	$0.489682\pi$
$240$	4.72015	0.304684
$241$	−2.84601	−0.183327	−0.0916637	−	0.995790i	$-0.529218\pi$
$241$	−2.84601	−0.183327	−0.0916637	+	0.995790i	$0.529218\pi$
$242$	−2.22833	−0.143242
$243$	−1.00000	−0.0641500
$244$	−23.0620	−1.47639
$245$	0	0
$246$	−14.7105	−0.937904
$247$	−12.0239	−0.765062
$248$	−8.83958	−0.561314
$249$	−6.01116	−0.380942
$250$	−66.9142	−4.23203
$251$	−15.0021	−0.946923	−0.473461	−	0.880815i	$-0.656996\pi$
$251$	−15.0021	−0.946923	−0.473461	+	0.880815i	$0.656996\pi$
$252$	0	0
$253$	2.93732	0.184667
$254$	15.7032	0.985305
$255$	−5.66801	−0.354945
$256$	−7.96365	−0.497728
$257$	25.3193	1.57937	0.789687	−	0.613510i	$-0.210243\pi$
$257$	25.3193	1.57937	0.789687	+	0.613510i	$0.210243\pi$
$258$	24.2096	1.50722
$259$	0	0
$260$	−36.0809	−2.23764
$261$	−8.97976	−0.555833
$262$	−23.8415	−1.47294
$263$	−19.9569	−1.23059	−0.615296	−	0.788296i	$-0.710964\pi$
$263$	−19.9569	−1.23059	−0.615296	+	0.788296i	$0.710964\pi$
$264$	2.15133	0.132405
$265$	−27.8950	−1.71358
$266$	0	0
$267$	−1.32024	−0.0807976
$268$	−34.9184	−2.13298
$269$	−6.87283	−0.419044	−0.209522	−	0.977804i	$-0.567191\pi$
$269$	−6.87283	−0.419044	−0.209522	+	0.977804i	$0.567191\pi$
$270$	9.25053	0.562969
$271$	1.85606	0.112748	0.0563739	−	0.998410i	$-0.482046\pi$
$271$	1.85606	0.112748	0.0563739	+	0.998410i	$0.482046\pi$
$272$	−1.55243	−0.0941297
$273$	0	0
$274$	30.5962	1.84839
$275$	12.2336	0.737711
$276$	−8.71045	−0.524308
$277$	27.4458	1.64906	0.824528	−	0.565821i	$-0.191441\pi$
$277$	27.4458	1.64906	0.824528	+	0.565821i	$0.191441\pi$
$278$	−10.3378	−0.620022
$279$	4.10889	0.245993
$280$	0	0
$281$	26.6172	1.58785	0.793925	−	0.608015i	$-0.208034\pi$
$281$	26.6172	1.58785	0.793925	+	0.608015i	$0.208034\pi$
$282$	13.8612	0.825421
$283$	−15.3524	−0.912605	−0.456302	−	0.889825i	$-0.650826\pi$
$283$	−15.3524	−0.912605	−0.456302	+	0.889825i	$0.650826\pi$
$284$	−16.8682	−1.00094
$285$	−17.0307	−1.00881
$286$	6.53099	0.386186
$287$	0	0
$288$	6.83632	0.402834
$289$	−15.1358	−0.890343
$290$	83.0675	4.87789
$291$	−2.57463	−0.150927
$292$	40.2416	2.35496
$293$	6.69021	0.390846	0.195423	−	0.980719i	$-0.437392\pi$
$293$	6.69021	0.390846	0.195423	+	0.980719i	$0.437392\pi$
$294$	0	0
$295$	−3.30920	−0.192669
$296$	−21.9780	−1.27744
$297$	−1.00000	−0.0580259
$298$	−5.17218	−0.299616
$299$	−8.60896	−0.497869
$300$	−36.2780	−2.09451
$301$	0	0
$302$	−40.6525	−2.33929
$303$	8.79910	0.505495
$304$	−4.66458	−0.267532
$305$	−32.2845	−1.84860
$306$	−3.04244	−0.173925
$307$	4.99820	0.285262	0.142631	−	0.989776i	$-0.454444\pi$
$307$	4.99820	0.285262	0.142631	+	0.989776i	$0.454444\pi$
$308$	0	0
$309$	−17.5840	−1.00032
$310$	−38.0094	−2.15879
$311$	−13.2851	−0.753328	−0.376664	−	0.926350i	$-0.622929\pi$
$311$	−13.2851	−0.753328	−0.376664	+	0.926350i	$0.622929\pi$
$312$	−6.30532	−0.356969
$313$	−26.7511	−1.51206	−0.756031	−	0.654536i	$-0.772864\pi$
$313$	−26.7511	−1.51206	−0.756031	+	0.654536i	$0.772864\pi$
$314$	−53.7680	−3.03430
$315$	0	0
$316$	−13.0110	−0.731928
$317$	−11.8100	−0.663315	−0.331657	−	0.943400i	$-0.607608\pi$
$317$	−11.8100	−0.663315	−0.331657	+	0.943400i	$0.607608\pi$
$318$	−14.9733	−0.839663
$319$	−8.97976	−0.502770
$320$	−53.7993	−3.00747
$321$	−4.97976	−0.277943
$322$	0	0
$323$	5.60129	0.311664
$324$	2.96545	0.164747
$325$	−35.8553	−1.98889
$326$	51.5278	2.85386
$327$	11.3249	0.626267
$328$	14.2022	0.784183
$329$	0	0
$330$	9.25053	0.509225
$331$	24.2493	1.33286	0.666432	−	0.745566i	$-0.267821\pi$
$331$	24.2493	1.33286	0.666432	+	0.745566i	$0.267821\pi$
$332$	17.8258	0.978316
$333$	10.2160	0.559832
$334$	−25.0582	−1.37112
$335$	−48.8823	−2.67073
$336$	0	0
$337$	−3.57781	−0.194895	−0.0974477	−	0.995241i	$-0.531068\pi$
$337$	−3.57781	−0.194895	−0.0974477	+	0.995241i	$0.531068\pi$
$338$	9.82663	0.534498
$339$	−6.25842	−0.339911
$340$	16.8082	0.911552
$341$	4.10889	0.222509
$342$	−9.14164	−0.494323
$343$	0	0
$344$	−23.3730	−1.26019
$345$	−12.1938	−0.656491
$346$	14.7307	0.791927
$347$	27.5601	1.47950	0.739752	−	0.672879i	$-0.234943\pi$
$347$	27.5601	1.47950	0.739752	+	0.672879i	$0.234943\pi$
$348$	26.6290	1.42746
$349$	9.76978	0.522964	0.261482	−	0.965208i	$-0.415789\pi$
$349$	9.76978	0.522964	0.261482	+	0.965208i	$0.415789\pi$
$350$	0	0
$351$	2.93089	0.156440
$352$	6.83632	0.364377
$353$	−5.73155	−0.305060	−0.152530	−	0.988299i	$-0.548742\pi$
$353$	−5.73155	−0.305060	−0.152530	+	0.988299i	$0.548742\pi$
$354$	−1.77629	−0.0944089
$355$	−23.6138	−1.25329
$356$	3.91511	0.207501
$357$	0	0
$358$	−17.9542	−0.948909
$359$	2.23888	0.118163	0.0590817	−	0.998253i	$-0.481183\pi$
$359$	2.23888	0.118163	0.0590817	+	0.998253i	$0.481183\pi$
$360$	−8.93089	−0.470699
$361$	−2.16977	−0.114198
$362$	−16.6856	−0.876975
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	56.3343	2.94867
$366$	−17.3295	−0.905827
$367$	20.5129	1.07077	0.535383	−	0.844610i	$-0.320167\pi$
$367$	20.5129	1.07077	0.535383	+	0.844610i	$0.320167\pi$
$368$	−3.33979	−0.174098
$369$	−6.60157	−0.343664
$370$	−94.5032	−4.91299
$371$	0	0
$372$	−12.1847	−0.631747
$373$	23.4031	1.21176	0.605882	−	0.795554i	$-0.292820\pi$
$373$	23.4031	1.21176	0.605882	+	0.795554i	$0.292820\pi$
$374$	−3.04244	−0.157321
$375$	−30.0289	−1.55069
$376$	−13.3822	−0.690136
$377$	26.3187	1.35548
$378$	0	0
$379$	5.34413	0.274510	0.137255	−	0.990536i	$-0.456172\pi$
$379$	5.34413	0.274510	0.137255	+	0.990536i	$0.456172\pi$
$380$	50.5036	2.59078
$381$	7.04706	0.361032
$382$	−29.0094	−1.48425
$383$	31.5344	1.61133	0.805667	−	0.592369i	$-0.201807\pi$
$383$	31.5344	1.61133	0.805667	+	0.592369i	$0.201807\pi$
$384$	−15.2054	−0.775949
$385$	0	0
$386$	20.7789	1.05762
$387$	10.8644	0.552271
$388$	7.63492	0.387605
$389$	−18.7309	−0.949692	−0.474846	−	0.880069i	$-0.657496\pi$
$389$	−18.7309	−0.949692	−0.474846	+	0.880069i	$0.657496\pi$
$390$	−27.1123	−1.37289
$391$	4.01046	0.202818
$392$	0	0
$393$	−10.6993	−0.539708
$394$	39.2410	1.97693
$395$	−18.2142	−0.916455
$396$	2.96545	0.149019
$397$	26.4506	1.32752	0.663760	−	0.747946i	$-0.268960\pi$
$397$	26.4506	1.32752	0.663760	+	0.747946i	$0.268960\pi$
$398$	−30.7797	−1.54285
$399$	0	0
$400$	−13.9098	−0.695490
$401$	−0.603254	−0.0301251	−0.0150625	−	0.999887i	$-0.504795\pi$
$401$	−0.603254	−0.0301251	−0.0150625	+	0.999887i	$0.504795\pi$
$402$	−26.2388	−1.30867
$403$	−12.0427	−0.599890
$404$	−26.0933	−1.29819
$405$	4.15133	0.206281
$406$	0	0
$407$	10.2160	0.506387
$408$	2.93732	0.145419
$409$	5.29261	0.261703	0.130851	−	0.991402i	$-0.458229\pi$
$409$	5.29261	0.261703	0.130851	+	0.991402i	$0.458229\pi$
$410$	61.0680	3.01593
$411$	13.7306	0.677280
$412$	52.1444	2.56897
$413$	0	0
$414$	−6.54530	−0.321684
$415$	24.9543	1.22496
$416$	−20.0365	−0.982371
$417$	−4.63927	−0.227186
$418$	−9.14164	−0.447132
$419$	0.251997	0.0123108	0.00615542	−	0.999981i	$-0.498041\pi$
$419$	0.251997	0.0123108	0.00615542	+	0.999981i	$0.498041\pi$
$420$	0	0
$421$	−28.5812	−1.39296	−0.696482	−	0.717575i	$-0.745252\pi$
$421$	−28.5812	−1.39296	−0.696482	+	0.717575i	$0.745252\pi$
$422$	−22.4109	−1.09094
$423$	6.22044	0.302448
$424$	14.4560	0.702043
$425$	16.7031	0.810217
$426$	−12.6753	−0.614120
$427$	0	0
$428$	14.7672	0.713800
$429$	2.93089	0.141505
$430$	−100.502	−4.84663
$431$	−25.3748	−1.22226	−0.611131	−	0.791529i	$-0.709285\pi$
$431$	−25.3748	−1.22226	−0.611131	+	0.791529i	$0.709285\pi$
$432$	1.13702	0.0547049
$433$	−27.9009	−1.34083	−0.670415	−	0.741986i	$-0.733884\pi$
$433$	−27.9009	−1.34083	−0.670415	+	0.741986i	$0.733884\pi$
$434$	0	0
$435$	37.2780	1.78734
$436$	−33.5833	−1.60835
$437$	12.0502	0.576441
$438$	30.2388	1.44487
$439$	9.84542	0.469896	0.234948	−	0.972008i	$-0.424508\pi$
$439$	9.84542	0.469896	0.234948	+	0.972008i	$0.424508\pi$
$440$	−8.93089	−0.425764
$441$	0	0
$442$	8.91708	0.424142
$443$	−5.45568	−0.259207	−0.129604	−	0.991566i	$-0.541371\pi$
$443$	−5.45568	−0.259207	−0.129604	+	0.991566i	$0.541371\pi$
$444$	−30.2949	−1.43773
$445$	5.48077	0.259814
$446$	−35.8592	−1.69798
$447$	−2.32110	−0.109784
$448$	0	0
$449$	−22.1735	−1.04643	−0.523217	−	0.852200i	$-0.675268\pi$
$449$	−22.1735	−1.04643	−0.523217	+	0.852200i	$0.675268\pi$
$450$	−27.2604	−1.28507
$451$	−6.60157	−0.310856
$452$	18.5590	0.872942
$453$	−18.2435	−0.857154
$454$	64.0385	3.00548
$455$	0	0
$456$	8.82577	0.413304
$457$	10.9245	0.511025	0.255513	−	0.966806i	$-0.417756\pi$
$457$	10.9245	0.511025	0.255513	+	0.966806i	$0.417756\pi$
$458$	−35.8673	−1.67597
$459$	−1.36535	−0.0637290
$460$	36.1600	1.68597
$461$	−24.0300	−1.11919	−0.559594	−	0.828767i	$-0.689043\pi$
$461$	−24.0300	−1.11919	−0.559594	+	0.828767i	$0.689043\pi$
$462$	0	0
$463$	15.5192	0.721240	0.360620	−	0.932713i	$-0.382565\pi$
$463$	15.5192	0.721240	0.360620	+	0.932713i	$0.382565\pi$
$464$	10.2102	0.473995
$465$	−17.0574	−0.791016
$466$	25.6322	1.18739
$467$	4.27670	0.197902	0.0989510	−	0.995092i	$-0.468451\pi$
$467$	4.27670	0.197902	0.0989510	+	0.995092i	$0.468451\pi$
$468$	−8.69141	−0.401760
$469$	0	0
$470$	−57.5424	−2.65423
$471$	−24.1293	−1.11182
$472$	1.71492	0.0789354
$473$	10.8644	0.499548
$474$	−9.77690	−0.449068
$475$	50.1878	2.30277
$476$	0	0
$477$	−6.71954	−0.307667
$478$	−2.23295	−0.102133
$479$	21.5428	0.984316	0.492158	−	0.870506i	$-0.336208\pi$
$479$	21.5428	0.984316	0.492158	+	0.870506i	$0.336208\pi$
$480$	−28.3798	−1.29536
$481$	−29.9419	−1.36523
$482$	6.34184	0.288863
$483$	0	0
$484$	2.96545	0.134793
$485$	10.6881	0.485323
$486$	2.22833	0.101079
$487$	4.21246	0.190885	0.0954423	−	0.995435i	$-0.469573\pi$
$487$	4.21246	0.190885	0.0954423	+	0.995435i	$0.469573\pi$
$488$	16.7307	0.757363
$489$	23.1240	1.04570
$490$	0	0
$491$	−7.33575	−0.331058	−0.165529	−	0.986205i	$-0.552933\pi$
$491$	−7.33575	−0.331058	−0.165529	+	0.986205i	$0.552933\pi$
$492$	19.5766	0.882581
$493$	−12.2605	−0.552185
$494$	26.7932	1.20548
$495$	4.15133	0.186588
$496$	−4.67189	−0.209774
$497$	0	0
$498$	13.3948	0.600237
$499$	10.2067	0.456916	0.228458	−	0.973554i	$-0.426632\pi$
$499$	10.2067	0.456916	0.228458	+	0.973554i	$0.426632\pi$
$500$	89.0491	3.98240
$501$	−11.2453	−0.502403
$502$	33.4295	1.49203
$503$	−0.843347	−0.0376030	−0.0188015	−	0.999823i	$-0.505985\pi$
$503$	−0.843347	−0.0376030	−0.0188015	+	0.999823i	$0.505985\pi$
$504$	0	0
$505$	−36.5280	−1.62547
$506$	−6.54530	−0.290974
$507$	4.40986	0.195849
$508$	−20.8977	−0.927185
$509$	−37.9401	−1.68167	−0.840833	−	0.541294i	$-0.817935\pi$
$509$	−37.9401	−1.68167	−0.840833	+	0.541294i	$0.817935\pi$
$510$	12.6302	0.559274
$511$	0	0
$512$	−12.6652	−0.559730
$513$	−4.10247	−0.181128
$514$	−56.4197	−2.48857
$515$	72.9970	3.21663
$516$	−32.2179	−1.41832
$517$	6.22044	0.273575
$518$	0	0
$519$	6.61065	0.290175
$520$	26.1755	1.14787
$521$	−2.65140	−0.116160	−0.0580800	−	0.998312i	$-0.518498\pi$
$521$	−2.65140	−0.116160	−0.0580800	+	0.998312i	$0.518498\pi$
$522$	20.0099	0.875807
$523$	−11.1984	−0.489672	−0.244836	−	0.969565i	$-0.578734\pi$
$523$	−11.1984	−0.489672	−0.244836	+	0.969565i	$0.578734\pi$
$524$	31.7282	1.38605
$525$	0	0
$526$	44.4704	1.93900
$527$	5.61006	0.244378
$528$	1.13702	0.0494824
$529$	−14.3722	−0.624877
$530$	62.1593	2.70003
$531$	−0.797142	−0.0345930
$532$	0	0
$533$	19.3485	0.838076
$534$	2.94194	0.127310
$535$	20.6726	0.893756
$536$	25.3321	1.09418
$537$	−8.05725	−0.347696
$538$	15.3149	0.660273
$539$	0	0
$540$	−12.3106	−0.529762
$541$	−7.34389	−0.315739	−0.157869	−	0.987460i	$-0.550462\pi$
$541$	−7.34389	−0.315739	−0.157869	+	0.987460i	$0.550462\pi$
$542$	−4.13592	−0.177653
$543$	−7.48794	−0.321338
$544$	9.33395	0.400190
$545$	−47.0133	−2.01383
$546$	0	0
$547$	−7.85901	−0.336027	−0.168014	−	0.985785i	$-0.553735\pi$
$547$	−7.85901	−0.336027	−0.168014	+	0.985785i	$0.553735\pi$
$548$	−40.7173	−1.73936
$549$	−7.77690	−0.331910
$550$	−27.2604	−1.16239
$551$	−36.8392	−1.56940
$552$	6.31914	0.268961
$553$	0	0
$554$	−61.1582	−2.59836
$555$	−42.4099	−1.80020
$556$	13.7575	0.583449
$557$	23.2643	0.985738	0.492869	−	0.870103i	$-0.335948\pi$
$557$	23.2643	0.985738	0.492869	+	0.870103i	$0.335948\pi$
$558$	−9.15595	−0.387602
$559$	−31.8425	−1.34680
$560$	0	0
$561$	−1.36535	−0.0576450
$562$	−59.3119	−2.50192
$563$	28.7199	1.21040	0.605200	−	0.796073i	$-0.293093\pi$
$563$	28.7199	1.21040	0.605200	+	0.796073i	$0.293093\pi$
$564$	−18.4464	−0.776733
$565$	25.9808	1.09302
$566$	34.2102	1.43796
$567$	0	0
$568$	12.2373	0.513467
$569$	20.8646	0.874689	0.437344	−	0.899294i	$-0.355919\pi$
$569$	20.8646	0.874689	0.437344	+	0.899294i	$0.355919\pi$
$570$	37.9500	1.58955
$571$	7.29832	0.305425	0.152712	−	0.988271i	$-0.451199\pi$
$571$	7.29832	0.305425	0.152712	+	0.988271i	$0.451199\pi$
$572$	−8.69141	−0.363406
$573$	−13.0184	−0.543853
$574$	0	0
$575$	35.9338	1.49854
$576$	−12.9595	−0.539980
$577$	−27.1280	−1.12935	−0.564677	−	0.825312i	$-0.690999\pi$
$577$	−27.1280	−1.12935	−0.564677	+	0.825312i	$0.690999\pi$
$578$	33.7276	1.40288
$579$	9.32487	0.387528
$580$	−110.546	−4.59016
$581$	0	0
$582$	5.73712	0.237811
$583$	−6.71954	−0.278295
$584$	−29.1939	−1.20805
$585$	−12.1671	−0.503048
$586$	−14.9080	−0.615843
$587$	−11.4493	−0.472562	−0.236281	−	0.971685i	$-0.575929\pi$
$587$	−11.4493	−0.472562	−0.236281	+	0.971685i	$0.575929\pi$
$588$	0	0
$589$	16.8566	0.694563
$590$	7.37398	0.303582
$591$	17.6101	0.724381
$592$	−11.6158	−0.477405
$593$	−13.0829	−0.537251	−0.268626	−	0.963245i	$-0.586569\pi$
$593$	−13.0829	−0.537251	−0.268626	+	0.963245i	$0.586569\pi$
$594$	2.22833	0.0914294
$595$	0	0
$596$	6.88311	0.281943
$597$	−13.8129	−0.565325
$598$	19.1836	0.784475
$599$	−11.8121	−0.482628	−0.241314	−	0.970447i	$-0.577578\pi$
$599$	−11.8121	−0.482628	−0.241314	+	0.970447i	$0.577578\pi$
$600$	26.3184	1.07445
$601$	10.3074	0.420448	0.210224	−	0.977653i	$-0.432581\pi$
$601$	10.3074	0.420448	0.210224	+	0.977653i	$0.432581\pi$
$602$	0	0
$603$	−11.7751	−0.479519
$604$	54.1001	2.20130
$605$	4.15133	0.168776
$606$	−19.6073	−0.796492
$607$	−39.4839	−1.60260	−0.801301	−	0.598262i	$-0.795858\pi$
$607$	−39.4839	−1.60260	−0.801301	+	0.598262i	$0.795858\pi$
$608$	28.0458	1.13741
$609$	0	0
$610$	71.9405	2.91278
$611$	−18.2314	−0.737565
$612$	4.04887	0.163666
$613$	−38.5827	−1.55834	−0.779170	−	0.626812i	$-0.784359\pi$
$613$	−38.5827	−1.55834	−0.779170	+	0.626812i	$0.784359\pi$
$614$	−11.1376	−0.449478
$615$	27.4053	1.10509
$616$	0	0
$617$	−6.06789	−0.244284	−0.122142	−	0.992513i	$-0.538976\pi$
$617$	−6.06789	−0.244284	−0.122142	+	0.992513i	$0.538976\pi$
$618$	39.1829	1.57617
$619$	19.3039	0.775890	0.387945	−	0.921682i	$-0.373185\pi$
$619$	19.3039	0.775890	0.387945	+	0.921682i	$0.373185\pi$
$620$	50.5827	2.03145
$621$	−2.93732	−0.117870
$622$	29.6035	1.18699
$623$	0	0
$624$	−3.33248	−0.133406
$625$	63.4921	2.53969
$626$	59.6102	2.38250
$627$	−4.10247	−0.163837
$628$	71.5541	2.85532
$629$	13.9484	0.556158
$630$	0	0
$631$	16.4894	0.656434	0.328217	−	0.944602i	$-0.393552\pi$
$631$	16.4894	0.656434	0.328217	+	0.944602i	$0.393552\pi$
$632$	9.43908	0.375466
$633$	−10.0572	−0.399740
$634$	26.3165	1.04516
$635$	−29.2547	−1.16094
$636$	19.9264	0.790134
$637$	0	0
$638$	20.0099	0.792198
$639$	−5.68825	−0.225024
$640$	63.1228	2.49515
$641$	1.31734	0.0520318	0.0260159	−	0.999662i	$-0.491718\pi$
$641$	1.31734	0.0520318	0.0260159	+	0.999662i	$0.491718\pi$
$642$	11.0965	0.437945
$643$	−31.5586	−1.24455	−0.622275	−	0.782799i	$-0.713791\pi$
$643$	−31.5586	−1.24455	−0.622275	+	0.782799i	$0.713791\pi$
$644$	0	0
$645$	−45.1019	−1.77589
$646$	−12.4815	−0.491079
$647$	30.7334	1.20825	0.604126	−	0.796888i	$-0.293522\pi$
$647$	30.7334	1.20825	0.604126	+	0.796888i	$0.293522\pi$
$648$	−2.15133	−0.0845123
$649$	−0.797142	−0.0312905
$650$	79.8973	3.13383
$651$	0	0
$652$	−68.5729	−2.68552
$653$	36.9929	1.44764	0.723822	−	0.689987i	$-0.242384\pi$
$653$	36.9929	1.44764	0.723822	+	0.689987i	$0.242384\pi$
$654$	−25.2355	−0.986787
$655$	44.4163	1.73549
$656$	7.50611	0.293064
$657$	13.5702	0.529423
$658$	0	0
$659$	−21.6348	−0.842773	−0.421386	−	0.906881i	$-0.638456\pi$
$659$	−21.6348	−0.842773	−0.421386	+	0.906881i	$0.638456\pi$
$660$	−12.3106	−0.479188
$661$	1.97068	0.0766504	0.0383252	−	0.999265i	$-0.487798\pi$
$661$	1.97068	0.0766504	0.0383252	+	0.999265i	$0.487798\pi$
$662$	−54.0355	−2.10015
$663$	4.00169	0.155413
$664$	−12.9320	−0.501859
$665$	0	0
$666$	−22.7645	−0.882108
$667$	−26.3764	−1.02130
$668$	33.3473	1.29025
$669$	−16.0924	−0.622169
$670$	108.926	4.20818
$671$	−7.77690	−0.300224
$672$	0	0
$673$	1.24081	0.0478297	0.0239148	−	0.999714i	$-0.492387\pi$
$673$	1.24081	0.0478297	0.0239148	+	0.999714i	$0.492387\pi$
$674$	7.97252	0.307090
$675$	−12.2336	−0.470870
$676$	−13.0772	−0.502970
$677$	8.82859	0.339310	0.169655	−	0.985504i	$-0.445735\pi$
$677$	8.82859	0.339310	0.169655	+	0.985504i	$0.445735\pi$
$678$	13.9458	0.535586
$679$	0	0
$680$	−12.1938	−0.467610
$681$	28.7384	1.10126
$682$	−9.15595	−0.350600
$683$	0.0255618	0.000978097 0	0.000489048	−	1.00000i	$-0.499844\pi$
$683$	0.0255618	0.000978097 0	0.000489048		1.00000i	$0.499844\pi$
$684$	12.1656	0.465165
$685$	−57.0002	−2.17787
$686$	0	0
$687$	−16.0960	−0.614102
$688$	−12.3531	−0.470957
$689$	19.6942	0.750291
$690$	27.1717	1.03441
$691$	−28.4635	−1.08280	−0.541402	−	0.840764i	$-0.682106\pi$
$691$	−28.4635	−1.08280	−0.541402	+	0.840764i	$0.682106\pi$
$692$	−19.6035	−0.745214
$693$	0	0
$694$	−61.4130	−2.33120
$695$	19.2592	0.730542
$696$	−19.3184	−0.732264
$697$	−9.01343	−0.341408
$698$	−21.7703	−0.824017
$699$	11.5029	0.435078
$700$	0	0
$701$	28.6422	1.08180	0.540901	−	0.841087i	$-0.318084\pi$
$701$	28.6422	1.08180	0.540901	+	0.841087i	$0.318084\pi$
$702$	−6.53099	−0.246496
$703$	41.9107	1.58069
$704$	−12.9595	−0.488430
$705$	−25.8231	−0.972554
$706$	12.7718	0.480672
$707$	0	0
$708$	2.36388	0.0888401
$709$	1.20078	0.0450964	0.0225482	−	0.999746i	$-0.492822\pi$
$709$	1.20078	0.0450964	0.0225482	+	0.999746i	$0.492822\pi$
$710$	52.6194	1.97477
$711$	−4.38755	−0.164546
$712$	−2.84028	−0.106444
$713$	12.0691	0.451992
$714$	0	0
$715$	−12.1671	−0.455024
$716$	23.8933	0.892936
$717$	−1.00207	−0.0374231
$718$	−4.98896	−0.186186
$719$	4.07177	0.151851	0.0759256	−	0.997113i	$-0.475809\pi$
$719$	4.07177	0.151851	0.0759256	+	0.997113i	$0.475809\pi$
$720$	−4.72015	−0.175909
$721$	0	0
$722$	4.83496	0.179939
$723$	2.84601	0.105844
$724$	22.2051	0.825246
$725$	−109.854	−4.07989
$726$	2.22833	0.0827010
$727$	−26.4800	−0.982088	−0.491044	−	0.871135i	$-0.663385\pi$
$727$	−26.4800	−0.982088	−0.491044	+	0.871135i	$0.663385\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−125.531	−4.64612
$731$	14.8337	0.548646
$732$	23.0620	0.852395
$733$	−6.65113	−0.245665	−0.122833	−	0.992427i	$-0.539198\pi$
$733$	−6.65113	−0.245665	−0.122833	+	0.992427i	$0.539198\pi$
$734$	−45.7095	−1.68717
$735$	0	0
$736$	20.0804	0.740174
$737$	−11.7751	−0.433741
$738$	14.7105	0.541499
$739$	−45.9618	−1.69073	−0.845365	−	0.534189i	$-0.820617\pi$
$739$	−45.9618	−1.69073	−0.845365	+	0.534189i	$0.820617\pi$
$740$	125.764	4.62319
$741$	12.0239	0.441709
$742$	0	0
$743$	−21.1782	−0.776951	−0.388476	−	0.921459i	$-0.626998\pi$
$743$	−21.1782	−0.776951	−0.388476	+	0.921459i	$0.626998\pi$
$744$	8.83958	0.324075
$745$	9.63567	0.353024
$746$	−52.1497	−1.90934
$747$	6.01116	0.219937
$748$	4.04887	0.148041
$749$	0	0
$750$	66.9142	2.44336
$751$	−12.1534	−0.443484	−0.221742	−	0.975105i	$-0.571174\pi$
$751$	−12.1534	−0.443484	−0.221742	+	0.975105i	$0.571174\pi$
$752$	−7.07276	−0.257917
$753$	15.0021	0.546706
$754$	−58.6467	−2.13579
$755$	75.7348	2.75627
$756$	0	0
$757$	9.19862	0.334330	0.167165	−	0.985929i	$-0.446539\pi$
$757$	9.19862	0.334330	0.167165	+	0.985929i	$0.446539\pi$
$758$	−11.9085	−0.432536
$759$	−2.93732	−0.106618
$760$	−36.6387	−1.32902
$761$	5.49123	0.199057	0.0995285	−	0.995035i	$-0.468267\pi$
$761$	5.49123	0.199057	0.0995285	+	0.995035i	$0.468267\pi$
$762$	−15.7032	−0.568866
$763$	0	0
$764$	38.6055	1.39670
$765$	5.66801	0.204927
$766$	−70.2690	−2.53892
$767$	2.33634	0.0843602
$768$	7.96365	0.287363
$769$	2.72497	0.0982650	0.0491325	−	0.998792i	$-0.484354\pi$
$769$	2.72497	0.0982650	0.0491325	+	0.998792i	$0.484354\pi$
$770$	0	0
$771$	−25.3193	−0.911852
$772$	−27.6524	−0.995231
$773$	−35.7910	−1.28731	−0.643657	−	0.765314i	$-0.722583\pi$
$773$	−35.7910	−1.28731	−0.643657	+	0.765314i	$0.722583\pi$
$774$	−24.2096	−0.870194
$775$	50.2663	1.80562
$776$	−5.53888	−0.198834
$777$	0	0
$778$	41.7385	1.49640
$779$	−27.0827	−0.970338
$780$	36.0809	1.29190
$781$	−5.68825	−0.203542
$782$	−8.93662	−0.319573
$783$	8.97976	0.320910
$784$	0	0
$785$	100.169	3.57517
$786$	23.8415	0.850400
$787$	−12.5410	−0.447037	−0.223518	−	0.974700i	$-0.571754\pi$
$787$	−12.5410	−0.447037	−0.223518	+	0.974700i	$0.571754\pi$
$788$	−52.2217	−1.86032
$789$	19.9569	0.710483
$790$	40.5872	1.44403
$791$	0	0
$792$	−2.15133	−0.0764443
$793$	22.7933	0.809413
$794$	−58.9407	−2.09173
$795$	27.8950	0.989335
$796$	40.9615	1.45184
$797$	22.4031	0.793557	0.396778	−	0.917914i	$-0.370128\pi$
$797$	22.4031	0.793557	0.396778	+	0.917914i	$0.370128\pi$
$798$	0	0
$799$	8.49306	0.300463
$800$	83.6325	2.95685
$801$	1.32024	0.0466485
$802$	1.34425	0.0474670
$803$	13.5702	0.478881
$804$	34.9184	1.23148
$805$	0	0
$806$	26.8351	0.945227
$807$	6.87283	0.241935
$808$	18.9298	0.665948
$809$	−11.0528	−0.388595	−0.194298	−	0.980943i	$-0.562243\pi$
$809$	−11.0528	−0.388595	−0.194298	+	0.980943i	$0.562243\pi$
$810$	−9.25053	−0.325030
$811$	44.6572	1.56813	0.784063	−	0.620682i	$-0.213144\pi$
$811$	44.6572	1.56813	0.784063	+	0.620682i	$0.213144\pi$
$812$	0	0
$813$	−1.85606	−0.0650950
$814$	−22.7645	−0.797897
$815$	−95.9953	−3.36257
$816$	1.55243	0.0543458
$817$	44.5710	1.55934
$818$	−11.7937	−0.412356
$819$	0	0
$820$	−81.2689	−2.83803
$821$	−4.67317	−0.163095	−0.0815474	−	0.996669i	$-0.525986\pi$
$821$	−4.67317	−0.163095	−0.0815474	+	0.996669i	$0.525986\pi$
$822$	−30.5962	−1.06717
$823$	−45.7856	−1.59598	−0.797992	−	0.602668i	$-0.794104\pi$
$823$	−45.7856	−1.59598	−0.797992	+	0.602668i	$0.794104\pi$
$824$	−37.8290	−1.31784
$825$	−12.2336	−0.425918
$826$	0	0
$827$	−54.7414	−1.90355	−0.951773	−	0.306803i	$-0.900741\pi$
$827$	−54.7414	−1.90355	−0.951773	+	0.306803i	$0.900741\pi$
$828$	8.71045	0.302709
$829$	2.42271	0.0841442	0.0420721	−	0.999115i	$-0.486604\pi$
$829$	2.42271	0.0841442	0.0420721	+	0.999115i	$0.486604\pi$
$830$	−55.6064	−1.93013
$831$	−27.4458	−0.952083
$832$	37.9830	1.31682
$833$	0	0
$834$	10.3378	0.357970
$835$	46.6830	1.61553
$836$	12.1656	0.420758
$837$	−4.10889	−0.142024
$838$	−0.561531	−0.0193978
$839$	−47.6581	−1.64534	−0.822670	−	0.568519i	$-0.807517\pi$
$839$	−47.6581	−1.64534	−0.822670	+	0.568519i	$0.807517\pi$
$840$	0	0
$841$	51.6361	1.78055
$842$	63.6883	2.19484
$843$	−26.6172	−0.916746
$844$	29.8242	1.02659
$845$	−18.3068	−0.629773
$846$	−13.8612	−0.476557
$847$	0	0
$848$	7.64025	0.262367
$849$	15.3524	0.526893
$850$	−37.2199	−1.27663
$851$	30.0076	1.02865
$852$	16.8682	0.577895
$853$	−33.7510	−1.15561	−0.577806	−	0.816174i	$-0.696091\pi$
$853$	−33.7510	−1.15561	−0.577806	+	0.816174i	$0.696091\pi$
$854$	0	0
$855$	17.0307	0.582438
$856$	−10.7131	−0.366167
$857$	14.5889	0.498347	0.249173	−	0.968459i	$-0.419841\pi$
$857$	14.5889	0.498347	0.249173	+	0.968459i	$0.419841\pi$
$858$	−6.53099	−0.222964
$859$	−19.2582	−0.657081	−0.328540	−	0.944490i	$-0.606557\pi$
$859$	−19.2582	−0.657081	−0.328540	+	0.944490i	$0.606557\pi$
$860$	133.747	4.56075
$861$	0	0
$862$	56.5435	1.92588
$863$	−19.2935	−0.656757	−0.328379	−	0.944546i	$-0.606502\pi$
$863$	−19.2935	−0.656757	−0.328379	+	0.944546i	$0.606502\pi$
$864$	−6.83632	−0.232576
$865$	−27.4430	−0.933090
$866$	62.1723	2.11270
$867$	15.1358	0.514040
$868$	0	0
$869$	−4.38755	−0.148837
$870$	−83.0675	−2.81625
$871$	34.5116	1.16938
$872$	24.3635	0.825054
$873$	2.57463	0.0871380
$874$	−26.8519	−0.908279
$875$	0	0
$876$	−40.2416	−1.35964
$877$	13.3358	0.450318	0.225159	−	0.974322i	$-0.427710\pi$
$877$	13.3358	0.450318	0.225159	+	0.974322i	$0.427710\pi$
$878$	−21.9388	−0.740400
$879$	−6.69021	−0.225655
$880$	−4.72015	−0.159116
$881$	−29.9312	−1.00841	−0.504203	−	0.863585i	$-0.668214\pi$
$881$	−29.9312	−1.00841	−0.504203	+	0.863585i	$0.668214\pi$
$882$	0	0
$883$	−12.0855	−0.406709	−0.203354	−	0.979105i	$-0.565184\pi$
$883$	−12.0855	−0.406709	−0.203354	+	0.979105i	$0.565184\pi$
$884$	−11.8668	−0.399123
$885$	3.30920	0.111238
$886$	12.1571	0.408424
$887$	−13.5112	−0.453663	−0.226832	−	0.973934i	$-0.572837\pi$
$887$	−13.5112	−0.453663	−0.226832	+	0.973934i	$0.572837\pi$
$888$	21.9780	0.737532
$889$	0	0
$890$	−12.2130	−0.409379
$891$	1.00000	0.0335013
$892$	47.7212	1.59782
$893$	25.5191	0.853965
$894$	5.17218	0.172984
$895$	33.4483	1.11805
$896$	0	0
$897$	8.60896	0.287445
$898$	49.4099	1.64883
$899$	−36.8968	−1.23058
$900$	36.2780	1.20927
$901$	−9.17451	−0.305647
$902$	14.7105	0.489805
$903$	0	0
$904$	−13.4639	−0.447804
$905$	31.0849	1.03330
$906$	40.6525	1.35059
$907$	55.3387	1.83749	0.918746	−	0.394849i	$-0.129203\pi$
$907$	55.3387	1.83749	0.918746	+	0.394849i	$0.129203\pi$
$908$	−85.2221	−2.82820
$909$	−8.79910	−0.291848
$910$	0	0
$911$	−55.5802	−1.84145	−0.920727	−	0.390207i	$-0.872403\pi$
$911$	−55.5802	−1.84145	−0.920727	+	0.390207i	$0.872403\pi$
$912$	4.66458	0.154460
$913$	6.01116	0.198940
$914$	−24.3433	−0.805205
$915$	32.2845	1.06729
$916$	47.7320	1.57711
$917$	0	0
$918$	3.04244	0.100416
$919$	6.73991	0.222329	0.111165	−	0.993802i	$-0.464542\pi$
$919$	6.73991	0.222329	0.111165	+	0.993802i	$0.464542\pi$
$920$	−26.2329	−0.864872
$921$	−4.99820	−0.164696
$922$	53.5467	1.76347
$923$	16.6717	0.548754
$924$	0	0
$925$	124.978	4.10924
$926$	−34.5819	−1.13643
$927$	17.5840	0.577534
$928$	−61.3885	−2.01518
$929$	−20.7649	−0.681275	−0.340637	−	0.940195i	$-0.610643\pi$
$929$	−20.7649	−0.681275	−0.340637	+	0.940195i	$0.610643\pi$
$930$	38.0094	1.24638
$931$	0	0
$932$	−34.1111	−1.11735
$933$	13.2851	0.434934
$934$	−9.52989	−0.311828
$935$	5.66801	0.185364
$936$	6.30532	0.206096
$937$	50.2053	1.64013	0.820067	−	0.572267i	$-0.193936\pi$
$937$	50.2053	1.64013	0.820067	+	0.572267i	$0.193936\pi$
$938$	0	0
$939$	26.7511	0.872989
$940$	76.5770	2.49767
$941$	16.0665	0.523753	0.261876	−	0.965101i	$-0.415659\pi$
$941$	16.0665	0.523753	0.261876	+	0.965101i	$0.415659\pi$
$942$	53.7680	1.75186
$943$	−19.3909	−0.631454
$944$	0.906366	0.0294997
$945$	0	0
$946$	−24.2096	−0.787120
$947$	−47.7275	−1.55094	−0.775468	−	0.631387i	$-0.782486\pi$
$947$	−47.7275	−1.55094	−0.775468	+	0.631387i	$0.782486\pi$
$948$	13.0110	0.422579
$949$	−39.7727	−1.29108
$950$	−111.835	−3.62840
$951$	11.8100	0.382965
$952$	0	0
$953$	9.32944	0.302210	0.151105	−	0.988518i	$-0.451717\pi$
$953$	9.32944	0.302210	0.151105	+	0.988518i	$0.451717\pi$
$954$	14.9733	0.484780
$955$	54.0439	1.74882
$956$	2.97160	0.0961083
$957$	8.97976	0.290274
$958$	−48.0044	−1.55095
$959$	0	0
$960$	53.7993	1.73636
$961$	−14.1170	−0.455388
$962$	66.7205	2.15115
$963$	4.97976	0.160470
$964$	−8.43968	−0.271824
$965$	−38.7106	−1.24614
$966$	0	0
$967$	−31.9165	−1.02637	−0.513183	−	0.858279i	$-0.671534\pi$
$967$	−31.9165	−1.02637	−0.513183	+	0.858279i	$0.671534\pi$
$968$	−2.15133	−0.0691464
$969$	−5.60129	−0.179939
$970$	−23.8167	−0.764708
$971$	24.8052	0.796037	0.398019	−	0.917377i	$-0.369698\pi$
$971$	24.8052	0.796037	0.398019	+	0.917377i	$0.369698\pi$
$972$	−2.96545	−0.0951167
$973$	0	0
$974$	−9.38674	−0.300770
$975$	35.8553	1.14829
$976$	8.84249	0.283041
$977$	−2.76926	−0.0885966	−0.0442983	−	0.999018i	$-0.514105\pi$
$977$	−2.76926	−0.0885966	−0.0442983	+	0.999018i	$0.514105\pi$
$978$	−51.5278	−1.64768
$979$	1.32024	0.0421952
$980$	0	0
$981$	−11.3249	−0.361575
$982$	16.3465	0.521637
$983$	−11.9348	−0.380661	−0.190331	−	0.981720i	$-0.560956\pi$
$983$	−11.9348	−0.380661	−0.190331	+	0.981720i	$0.560956\pi$
$984$	−14.2022	−0.452748
$985$	−73.1052	−2.32933
$986$	27.3204	0.870059
$987$	0	0
$988$	−35.6562	−1.13438
$989$	31.9123	1.01475
$990$	−9.25053	−0.294001
$991$	−10.4194	−0.330982	−0.165491	−	0.986211i	$-0.552921\pi$
$991$	−10.4194	−0.330982	−0.165491	+	0.986211i	$0.552921\pi$
$992$	28.0897	0.891848
$993$	−24.2493	−0.769529
$994$	0	0
$995$	57.3420	1.81786
$996$	−17.8258	−0.564831
$997$	−0.00770883	−0.000244141 0	−0.000122070	−	1.00000i	$-0.500039\pi$
$997$	−0.00770883	−0.000244141 0	−0.000122070		1.00000i	$0.500039\pi$
$998$	−22.7440	−0.719947
$999$	−10.2160	−0.323219

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1617.2.a.u.1.1	✓	4
3.2	odd	2		4851.2.a.bx.1.4		4
7.6	odd	2		1617.2.a.v.1.1	yes	4
21.20	even	2		4851.2.a.by.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1617.2.a.u.1.1	✓	4	1.1	even	1	trivial
1617.2.a.v.1.1	yes	4	7.6	odd	2
4851.2.a.bx.1.4		4	3.2	odd	2
4851.2.a.by.1.4		4	21.20	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:	\( N \)	\(=\)	\( 1617 = 3 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1617.a (trivial)

\(f(q)\)	\(=\)	\(q-2.22833 q^{2} -1.00000 q^{3} +2.96545 q^{4} +4.15133 q^{5} +2.22833 q^{6} -2.15133 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.22833 q^{2} -1.00000 q^{3} +2.96545 q^{4} +4.15133 q^{5} +2.22833 q^{6} -2.15133 q^{8} +1.00000 q^{9} -9.25053 q^{10} +1.00000 q^{11} -2.96545 q^{12} -2.93089 q^{13} -4.15133 q^{15} -1.13702 q^{16} +1.36535 q^{17} -2.22833 q^{18} +4.10247 q^{19} +12.3106 q^{20} -2.22833 q^{22} +2.93732 q^{23} +2.15133 q^{24} +12.2336 q^{25} +6.53099 q^{26} -1.00000 q^{27} -8.97976 q^{29} +9.25053 q^{30} +4.10889 q^{31} +6.83632 q^{32} -1.00000 q^{33} -3.04244 q^{34} +2.96545 q^{36} +10.2160 q^{37} -9.14164 q^{38} +2.93089 q^{39} -8.93089 q^{40} -6.60157 q^{41} +10.8644 q^{43} +2.96545 q^{44} +4.15133 q^{45} -6.54530 q^{46} +6.22044 q^{47} +1.13702 q^{48} -27.2604 q^{50} -1.36535 q^{51} -8.69141 q^{52} -6.71954 q^{53} +2.22833 q^{54} +4.15133 q^{55} -4.10247 q^{57} +20.0099 q^{58} -0.797142 q^{59} -12.3106 q^{60} -7.77690 q^{61} -9.15595 q^{62} -12.9595 q^{64} -12.1671 q^{65} +2.22833 q^{66} -11.7751 q^{67} +4.04887 q^{68} -2.93732 q^{69} -5.68825 q^{71} -2.15133 q^{72} +13.5702 q^{73} -22.7645 q^{74} -12.2336 q^{75} +12.1656 q^{76} -6.53099 q^{78} -4.38755 q^{79} -4.72015 q^{80} +1.00000 q^{81} +14.7105 q^{82} +6.01116 q^{83} +5.66801 q^{85} -24.2096 q^{86} +8.97976 q^{87} -2.15133 q^{88} +1.32024 q^{89} -9.25053 q^{90} +8.71045 q^{92} -4.10889 q^{93} -13.8612 q^{94} +17.0307 q^{95} -6.83632 q^{96} +2.57463 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 4 q^{3} + 2 q^{4} + 8 q^{5} + 2 q^{6} + 4 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 4 * q^3 + 2 * q^4 + 8 * q^5 + 2 * q^6 + 4 * q^9	\( 4 q - 2 q^{2} - 4 q^{3} + 2 q^{4} + 8 q^{5} + 2 q^{6} + 4 q^{9} - 2 q^{10} + 4 q^{11} - 2 q^{12} + 8 q^{13} - 8 q^{15} - 6 q^{16} - 2 q^{18} + 8 q^{19} + 14 q^{20} - 2 q^{22} + 12 q^{25} + 2 q^{26} - 4 q^{27} - 16 q^{29} + 2 q^{30} + 16 q^{31} - 2 q^{32} - 4 q^{33} - 4 q^{34} + 2 q^{36} - 4 q^{37} - 2 q^{38} - 8 q^{39} - 16 q^{40} + 4 q^{41} + 16 q^{43} + 2 q^{44} + 8 q^{45} + 8 q^{46} + 36 q^{47} + 6 q^{48} - 8 q^{50} - 22 q^{52} - 16 q^{53} + 2 q^{54} + 8 q^{55} - 8 q^{57} + 14 q^{58} - 14 q^{60} - 8 q^{61} + 8 q^{62} - 12 q^{64} - 4 q^{65} + 2 q^{66} + 20 q^{67} + 16 q^{68} - 20 q^{71} + 4 q^{73} - 30 q^{74} - 12 q^{75} + 30 q^{76} - 2 q^{78} + 16 q^{79} - 14 q^{80} + 4 q^{81} + 28 q^{82} + 24 q^{83} - 44 q^{86} + 16 q^{87} - 4 q^{89} - 2 q^{90} + 4 q^{92} - 16 q^{93} - 10 q^{94} + 28 q^{95} + 2 q^{96} + 16 q^{97} + 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 4 * q^3 + 2 * q^4 + 8 * q^5 + 2 * q^6 + 4 * q^9 - 2 * q^10 + 4 * q^11 - 2 * q^12 + 8 * q^13 - 8 * q^15 - 6 * q^16 - 2 * q^18 + 8 * q^19 + 14 * q^20 - 2 * q^22 + 12 * q^25 + 2 * q^26 - 4 * q^27 - 16 * q^29 + 2 * q^30 + 16 * q^31 - 2 * q^32 - 4 * q^33 - 4 * q^34 + 2 * q^36 - 4 * q^37 - 2 * q^38 - 8 * q^39 - 16 * q^40 + 4 * q^41 + 16 * q^43 + 2 * q^44 + 8 * q^45 + 8 * q^46 + 36 * q^47 + 6 * q^48 - 8 * q^50 - 22 * q^52 - 16 * q^53 + 2 * q^54 + 8 * q^55 - 8 * q^57 + 14 * q^58 - 14 * q^60 - 8 * q^61 + 8 * q^62 - 12 * q^64 - 4 * q^65 + 2 * q^66 + 20 * q^67 + 16 * q^68 - 20 * q^71 + 4 * q^73 - 30 * q^74 - 12 * q^75 + 30 * q^76 - 2 * q^78 + 16 * q^79 - 14 * q^80 + 4 * q^81 + 28 * q^82 + 24 * q^83 - 44 * q^86 + 16 * q^87 - 4 * q^89 - 2 * q^90 + 4 * q^92 - 16 * q^93 - 10 * q^94 + 28 * q^95 + 2 * q^96 + 16 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more