LMFDB - Embedded newform 6027.2.a.bo.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, 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("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69245 q^{2} +1.00000 q^{3} +5.24930 q^{4} +3.40876 q^{5} -2.69245 q^{6} -8.74860 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.69245 q^{2} +1.00000 q^{3} +5.24930 q^{4} +3.40876 q^{5} -2.69245 q^{6} -8.74860 q^{8} +1.00000 q^{9} -9.17792 q^{10} +2.47740 q^{11} +5.24930 q^{12} -2.61944 q^{13} +3.40876 q^{15} +13.0566 q^{16} -5.06684 q^{17} -2.69245 q^{18} -2.94589 q^{19} +17.8936 q^{20} -6.67027 q^{22} +2.48116 q^{23} -8.74860 q^{24} +6.61964 q^{25} +7.05272 q^{26} +1.00000 q^{27} +0.267181 q^{29} -9.17792 q^{30} -6.04056 q^{31} -17.6570 q^{32} +2.47740 q^{33} +13.6422 q^{34} +5.24930 q^{36} +9.78122 q^{37} +7.93167 q^{38} -2.61944 q^{39} -29.8219 q^{40} -1.00000 q^{41} +7.25634 q^{43} +13.0046 q^{44} +3.40876 q^{45} -6.68041 q^{46} -8.30624 q^{47} +13.0566 q^{48} -17.8231 q^{50} -5.06684 q^{51} -13.7502 q^{52} +10.8096 q^{53} -2.69245 q^{54} +8.44485 q^{55} -2.94589 q^{57} -0.719372 q^{58} -2.98222 q^{59} +17.8936 q^{60} -7.07265 q^{61} +16.2639 q^{62} +21.4276 q^{64} -8.92904 q^{65} -6.67027 q^{66} +14.1114 q^{67} -26.5974 q^{68} +2.48116 q^{69} +8.21376 q^{71} -8.74860 q^{72} -6.66722 q^{73} -26.3355 q^{74} +6.61964 q^{75} -15.4639 q^{76} +7.05272 q^{78} -10.7721 q^{79} +44.5067 q^{80} +1.00000 q^{81} +2.69245 q^{82} +14.0497 q^{83} -17.2716 q^{85} -19.5374 q^{86} +0.267181 q^{87} -21.6737 q^{88} +15.6068 q^{89} -9.17792 q^{90} +13.0244 q^{92} -6.04056 q^{93} +22.3642 q^{94} -10.0418 q^{95} -17.6570 q^{96} -7.72850 q^{97} +2.47740 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) $ 24 * q + 8 * q^2 + 24 * q^3 + 32 * q^4 + 4 * q^5 + 8 * q^6 + 24 * q^8 + 24 * q^9	$ 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9} - 4 q^{10} + 12 q^{11} + 32 q^{12} + 4 q^{15} + 44 q^{16} + 8 q^{17} + 8 q^{18} - 4 q^{19} + 28 q^{20} + 16 q^{22} + 20 q^{23} + 24 q^{24} + 48 q^{25} + 32 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 4 q^{31} + 36 q^{32} + 12 q^{33} + 16 q^{34} + 32 q^{36} + 64 q^{37} + 20 q^{38} - 48 q^{40} - 24 q^{41} + 20 q^{43} + 48 q^{44} + 4 q^{45} + 28 q^{46} + 32 q^{47} + 44 q^{48} - 20 q^{50} + 8 q^{51} + 76 q^{53} + 8 q^{54} - 24 q^{55} - 4 q^{57} + 28 q^{58} + 28 q^{59} + 28 q^{60} - 28 q^{61} - 4 q^{62} + 48 q^{64} + 28 q^{65} + 16 q^{66} + 44 q^{67} - 32 q^{68} + 20 q^{69} + 20 q^{71} + 24 q^{72} - 16 q^{73} + 44 q^{74} + 48 q^{75} - 16 q^{76} + 32 q^{78} + 4 q^{79} + 44 q^{80} + 24 q^{81} - 8 q^{82} + 8 q^{83} + 28 q^{85} + 56 q^{86} + 24 q^{87} + 60 q^{88} + 60 q^{89} - 4 q^{90} + 60 q^{92} - 4 q^{93} + 24 q^{94} + 28 q^{95} + 36 q^{96} - 48 q^{97} + 12 q^{99}+O(q^{100}) $ 24 * q + 8 * q^2 + 24 * q^3 + 32 * q^4 + 4 * q^5 + 8 * q^6 + 24 * q^8 + 24 * q^9 - 4 * q^10 + 12 * q^11 + 32 * q^12 + 4 * q^15 + 44 * q^16 + 8 * q^17 + 8 * q^18 - 4 * q^19 + 28 * q^20 + 16 * q^22 + 20 * q^23 + 24 * q^24 + 48 * q^25 + 32 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 4 * q^31 + 36 * q^32 + 12 * q^33 + 16 * q^34 + 32 * q^36 + 64 * q^37 + 20 * q^38 - 48 * q^40 - 24 * q^41 + 20 * q^43 + 48 * q^44 + 4 * q^45 + 28 * q^46 + 32 * q^47 + 44 * q^48 - 20 * q^50 + 8 * q^51 + 76 * q^53 + 8 * q^54 - 24 * q^55 - 4 * q^57 + 28 * q^58 + 28 * q^59 + 28 * q^60 - 28 * q^61 - 4 * q^62 + 48 * q^64 + 28 * q^65 + 16 * q^66 + 44 * q^67 - 32 * q^68 + 20 * q^69 + 20 * q^71 + 24 * q^72 - 16 * q^73 + 44 * q^74 + 48 * q^75 - 16 * q^76 + 32 * q^78 + 4 * q^79 + 44 * q^80 + 24 * q^81 - 8 * q^82 + 8 * q^83 + 28 * q^85 + 56 * q^86 + 24 * q^87 + 60 * q^88 + 60 * q^89 - 4 * q^90 + 60 * q^92 - 4 * q^93 + 24 * q^94 + 28 * q^95 + 36 * q^96 - 48 * q^97 + 12 * 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 $

$2$	−2.69245	−1.90385	−0.951926	−	0.306328i	$-0.900899\pi$
$2$	−2.69245	−1.90385	−0.951926	+	0.306328i	$0.900899\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	5.24930	2.62465
$5$	3.40876	1.52444	0.762222	−	0.647316i	$-0.224109\pi$
$5$	3.40876	1.52444	0.762222	+	0.647316i	$0.224109\pi$
$6$	−2.69245	−1.09919
$7$	0	0
$7$	0	0
$8$	−8.74860	−3.09310
$9$	1.00000	0.333333
$10$	−9.17792	−2.90231
$11$	2.47740	0.746963	0.373482	−	0.927638i	$-0.378164\pi$
$11$	2.47740	0.746963	0.373482	+	0.927638i	$0.378164\pi$
$12$	5.24930	1.51534
$13$	−2.61944	−0.726502	−0.363251	−	0.931691i	$-0.618333\pi$
$13$	−2.61944	−0.726502	−0.363251	+	0.931691i	$0.618333\pi$
$14$	0	0
$15$	3.40876	0.880138
$16$	13.0566	3.26414
$17$	−5.06684	−1.22889	−0.614445	−	0.788960i	$-0.710620\pi$
$17$	−5.06684	−1.22889	−0.614445	+	0.788960i	$0.710620\pi$
$18$	−2.69245	−0.634617
$19$	−2.94589	−0.675833	−0.337917	−	0.941176i	$-0.609722\pi$
$19$	−2.94589	−0.675833	−0.337917	+	0.941176i	$0.609722\pi$
$20$	17.8936	4.00113
$21$	0	0
$22$	−6.67027	−1.42211
$23$	2.48116	0.517358	0.258679	−	0.965963i	$-0.416713\pi$
$23$	2.48116	0.517358	0.258679	+	0.965963i	$0.416713\pi$
$24$	−8.74860	−1.78580
$25$	6.61964	1.32393
$26$	7.05272	1.38315
$27$	1.00000	0.192450
$28$	0	0
$29$	0.267181	0.0496142	0.0248071	−	0.999692i	$-0.492103\pi$
$29$	0.267181	0.0496142	0.0248071	+	0.999692i	$0.492103\pi$
$30$	−9.17792	−1.67565
$31$	−6.04056	−1.08492	−0.542459	−	0.840083i	$-0.682506\pi$
$31$	−6.04056	−1.08492	−0.542459	+	0.840083i	$0.682506\pi$
$32$	−17.6570	−3.12135
$33$	2.47740	0.431259
$34$	13.6422	2.33962
$35$	0	0
$36$	5.24930	0.874884
$37$	9.78122	1.60802	0.804012	−	0.594614i	$-0.202695\pi$
$37$	9.78122	1.60802	0.804012	+	0.594614i	$0.202695\pi$
$38$	7.93167	1.28669
$39$	−2.61944	−0.419446
$40$	−29.8219	−4.71525
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	7.25634	1.10658	0.553291	−	0.832988i	$-0.313372\pi$
$43$	7.25634	1.10658	0.553291	+	0.832988i	$0.313372\pi$
$44$	13.0046	1.96052
$45$	3.40876	0.508148
$46$	−6.68041	−0.984973
$47$	−8.30624	−1.21159	−0.605795	−	0.795621i	$-0.707145\pi$
$47$	−8.30624	−1.21159	−0.605795	+	0.795621i	$0.707145\pi$
$48$	13.0566	1.88455
$49$	0	0
$50$	−17.8231	−2.52056
$51$	−5.06684	−0.709500
$52$	−13.7502	−1.90682
$53$	10.8096	1.48481	0.742406	−	0.669951i	$-0.233685\pi$
$53$	10.8096	1.48481	0.742406	+	0.669951i	$0.233685\pi$
$54$	−2.69245	−0.366396
$55$	8.44485	1.13870
$56$	0	0
$57$	−2.94589	−0.390192
$58$	−0.719372	−0.0944581
$59$	−2.98222	−0.388252	−0.194126	−	0.980977i	$-0.562187\pi$
$59$	−2.98222	−0.388252	−0.194126	+	0.980977i	$0.562187\pi$
$60$	17.8936	2.31005
$61$	−7.07265	−0.905560	−0.452780	−	0.891622i	$-0.649568\pi$
$61$	−7.07265	−0.905560	−0.452780	+	0.891622i	$0.649568\pi$
$62$	16.2639	2.06552
$63$	0	0
$64$	21.4276	2.67845
$65$	−8.92904	−1.10751
$66$	−6.67027	−0.821054
$67$	14.1114	1.72398	0.861989	−	0.506927i	$-0.169219\pi$
$67$	14.1114	1.72398	0.861989	+	0.506927i	$0.169219\pi$
$68$	−26.5974	−3.22541
$69$	2.48116	0.298697
$70$	0	0
$71$	8.21376	0.974794	0.487397	−	0.873181i	$-0.337946\pi$
$71$	8.21376	0.974794	0.487397	+	0.873181i	$0.337946\pi$
$72$	−8.74860	−1.03103
$73$	−6.66722	−0.780339	−0.390169	−	0.920743i	$-0.627584\pi$
$73$	−6.66722	−0.780339	−0.390169	+	0.920743i	$0.627584\pi$
$74$	−26.3355	−3.06144
$75$	6.61964	0.764370
$76$	−15.4639	−1.77383
$77$	0	0
$78$	7.05272	0.798564
$79$	−10.7721	−1.21196	−0.605979	−	0.795481i	$-0.707218\pi$
$79$	−10.7721	−1.21196	−0.605979	+	0.795481i	$0.707218\pi$
$80$	44.5067	4.97600
$81$	1.00000	0.111111
$82$	2.69245	0.297332
$83$	14.0497	1.54215	0.771077	−	0.636743i	$-0.219719\pi$
$83$	14.0497	1.54215	0.771077	+	0.636743i	$0.219719\pi$
$84$	0	0
$85$	−17.2716	−1.87337
$86$	−19.5374	−2.10677
$87$	0.267181	0.0286448
$88$	−21.6737	−2.31043
$89$	15.6068	1.65432	0.827161	−	0.561966i	$-0.189955\pi$
$89$	15.6068	1.65432	0.827161	+	0.561966i	$0.189955\pi$
$90$	−9.17792	−0.967438
$91$	0	0
$92$	13.0244	1.35788
$93$	−6.04056	−0.626377
$94$	22.3642	2.30669
$95$	−10.0418	−1.03027
$96$	−17.6570	−1.80211
$97$	−7.72850	−0.784710	−0.392355	−	0.919814i	$-0.628340\pi$
$97$	−7.72850	−0.784710	−0.392355	+	0.919814i	$0.628340\pi$
$98$	0	0
$99$	2.47740	0.248988
$100$	34.7485	3.47485
$101$	9.67726	0.962923	0.481462	−	0.876467i	$-0.340106\pi$
$101$	9.67726	0.962923	0.481462	+	0.876467i	$0.340106\pi$
$102$	13.6422	1.35078
$103$	−4.45587	−0.439050	−0.219525	−	0.975607i	$-0.570451\pi$
$103$	−4.45587	−0.439050	−0.219525	+	0.975607i	$0.570451\pi$
$104$	22.9164	2.24714
$105$	0	0
$106$	−29.1043	−2.82686
$107$	10.3878	1.00423	0.502115	−	0.864801i	$-0.332555\pi$
$107$	10.3878	1.00423	0.502115	+	0.864801i	$0.332555\pi$
$108$	5.24930	0.505114
$109$	−7.88580	−0.755322	−0.377661	−	0.925944i	$-0.623272\pi$
$109$	−7.88580	−0.755322	−0.377661	+	0.925944i	$0.623272\pi$
$110$	−22.7373	−2.16792
$111$	9.78122	0.928393
$112$	0	0
$113$	18.9778	1.78528	0.892641	−	0.450768i	$-0.148850\pi$
$113$	18.9778	1.78528	0.892641	+	0.450768i	$0.148850\pi$
$114$	7.93167	0.742869
$115$	8.45768	0.788683
$116$	1.40251	0.130220
$117$	−2.61944	−0.242167
$118$	8.02950	0.739175
$119$	0	0
$120$	−29.8219	−2.72235
$121$	−4.86251	−0.442046
$122$	19.0428	1.72405
$123$	−1.00000	−0.0901670
$124$	−31.7087	−2.84753
$125$	5.52095	0.493809
$126$	0	0
$127$	13.4451	1.19306	0.596529	−	0.802592i	$-0.296546\pi$
$127$	13.4451	1.19306	0.596529	+	0.802592i	$0.296546\pi$
$128$	−22.3787	−1.97801
$129$	7.25634	0.638885
$130$	24.0410	2.10854
$131$	1.31500	0.114892	0.0574460	−	0.998349i	$-0.481704\pi$
$131$	1.31500	0.114892	0.0574460	+	0.998349i	$0.481704\pi$
$132$	13.0046	1.13191
$133$	0	0
$134$	−37.9942	−3.28220
$135$	3.40876	0.293379
$136$	44.3278	3.80107
$137$	14.4957	1.23845	0.619224	−	0.785214i	$-0.287447\pi$
$137$	14.4957	1.23845	0.619224	+	0.785214i	$0.287447\pi$
$138$	−6.68041	−0.568674
$139$	3.68532	0.312585	0.156292	−	0.987711i	$-0.450046\pi$
$139$	3.68532	0.312585	0.156292	+	0.987711i	$0.450046\pi$
$140$	0	0
$141$	−8.30624	−0.699512
$142$	−22.1152	−1.85586
$143$	−6.48939	−0.542670
$144$	13.0566	1.08805
$145$	0.910755	0.0756341
$146$	17.9512	1.48565
$147$	0	0
$148$	51.3446	4.22050
$149$	15.8559	1.29897	0.649485	−	0.760375i	$-0.274985\pi$
$149$	15.8559	1.29897	0.649485	+	0.760375i	$0.274985\pi$
$150$	−17.8231	−1.45525
$151$	11.0469	0.898987	0.449493	−	0.893284i	$-0.351605\pi$
$151$	11.0469	0.898987	0.449493	+	0.893284i	$0.351605\pi$
$152$	25.7724	2.09042
$153$	−5.06684	−0.409630
$154$	0	0
$155$	−20.5908	−1.65389
$156$	−13.7502	−1.10090
$157$	8.18928	0.653576	0.326788	−	0.945098i	$-0.394034\pi$
$157$	8.18928	0.653576	0.326788	+	0.945098i	$0.394034\pi$
$158$	29.0034	2.30739
$159$	10.8096	0.857256
$160$	−60.1885	−4.75832
$161$	0	0
$162$	−2.69245	−0.211539
$163$	−0.540625	−0.0423450	−0.0211725	−	0.999776i	$-0.506740\pi$
$163$	−0.540625	−0.0423450	−0.0211725	+	0.999776i	$0.506740\pi$
$164$	−5.24930	−0.409902
$165$	8.44485	0.657430
$166$	−37.8281	−2.93603
$167$	22.1797	1.71631	0.858157	−	0.513388i	$-0.171610\pi$
$167$	22.1797	1.71631	0.858157	+	0.513388i	$0.171610\pi$
$168$	0	0
$169$	−6.13853	−0.472194
$170$	46.5031	3.56662
$171$	−2.94589	−0.225278
$172$	38.0908	2.90439
$173$	18.9158	1.43814	0.719070	−	0.694937i	$-0.244568\pi$
$173$	18.9158	1.43814	0.719070	+	0.694937i	$0.244568\pi$
$174$	−0.719372	−0.0545354
$175$	0	0
$176$	32.3463	2.43820
$177$	−2.98222	−0.224158
$178$	−42.0207	−3.14958
$179$	−4.70118	−0.351383	−0.175691	−	0.984445i	$-0.556216\pi$
$179$	−4.70118	−0.351383	−0.175691	+	0.984445i	$0.556216\pi$
$180$	17.8936	1.33371
$181$	20.8428	1.54923	0.774616	−	0.632432i	$-0.217943\pi$
$181$	20.8428	1.54923	0.774616	+	0.632432i	$0.217943\pi$
$182$	0	0
$183$	−7.07265	−0.522825
$184$	−21.7067	−1.60024
$185$	33.3418	2.45134
$186$	16.2639	1.19253
$187$	−12.5526	−0.917935
$188$	−43.6020	−3.18000
$189$	0	0
$190$	27.0371	1.96148
$191$	2.02143	0.146266	0.0731329	−	0.997322i	$-0.476700\pi$
$191$	2.02143	0.146266	0.0731329	+	0.997322i	$0.476700\pi$
$192$	21.4276	1.54640
$193$	0.759337	0.0546583	0.0273291	−	0.999626i	$-0.491300\pi$
$193$	0.759337	0.0546583	0.0273291	+	0.999626i	$0.491300\pi$
$194$	20.8086	1.49397
$195$	−8.92904	−0.639422
$196$	0	0
$197$	17.2289	1.22751	0.613755	−	0.789496i	$-0.289658\pi$
$197$	17.2289	1.22751	0.613755	+	0.789496i	$0.289658\pi$
$198$	−6.67027	−0.474036
$199$	20.8621	1.47887	0.739436	−	0.673227i	$-0.235092\pi$
$199$	20.8621	1.47887	0.739436	+	0.673227i	$0.235092\pi$
$200$	−57.9125	−4.09503
$201$	14.1114	0.995339
$202$	−26.0556	−1.83326
$203$	0	0
$204$	−26.5974	−1.86219
$205$	−3.40876	−0.238078
$206$	11.9972	0.835887
$207$	2.48116	0.172453
$208$	−34.2009	−2.37141
$209$	−7.29813	−0.504822
$210$	0	0
$211$	−12.7824	−0.879978	−0.439989	−	0.898003i	$-0.645018\pi$
$211$	−12.7824	−0.879978	−0.439989	+	0.898003i	$0.645018\pi$
$212$	56.7428	3.89711
$213$	8.21376	0.562798
$214$	−27.9688	−1.91190
$215$	24.7351	1.68692
$216$	−8.74860	−0.595267
$217$	0	0
$218$	21.2321	1.43802
$219$	−6.66722	−0.450529
$220$	44.3296	2.98870
$221$	13.2723	0.892791
$222$	−26.3355	−1.76752
$223$	7.42145	0.496977	0.248489	−	0.968635i	$-0.420066\pi$
$223$	7.42145	0.496977	0.248489	+	0.968635i	$0.420066\pi$
$224$	0	0
$225$	6.61964	0.441309
$226$	−51.0969	−3.39891
$227$	12.4666	0.827437	0.413718	−	0.910405i	$-0.364230\pi$
$227$	12.4666	0.827437	0.413718	+	0.910405i	$0.364230\pi$
$228$	−15.4639	−1.02412
$229$	−14.2997	−0.944948	−0.472474	−	0.881345i	$-0.656639\pi$
$229$	−14.2997	−0.944948	−0.472474	+	0.881345i	$0.656639\pi$
$230$	−22.7719	−1.50154
$231$	0	0
$232$	−2.33746	−0.153462
$233$	−23.7816	−1.55798	−0.778991	−	0.627035i	$-0.784268\pi$
$233$	−23.7816	−1.55798	−0.778991	+	0.627035i	$0.784268\pi$
$234$	7.05272	0.461051
$235$	−28.3140	−1.84700
$236$	−15.6546	−1.01903
$237$	−10.7721	−0.699724
$238$	0	0
$239$	10.0560	0.650472	0.325236	−	0.945633i	$-0.394556\pi$
$239$	10.0560	0.650472	0.325236	+	0.945633i	$0.394556\pi$
$240$	44.5067	2.87290
$241$	−9.20788	−0.593132	−0.296566	−	0.955012i	$-0.595841\pi$
$241$	−9.20788	−0.593132	−0.296566	+	0.955012i	$0.595841\pi$
$242$	13.0921	0.841591
$243$	1.00000	0.0641500
$244$	−37.1265	−2.37678
$245$	0	0
$246$	2.69245	0.171665
$247$	7.71658	0.490994
$248$	52.8464	3.35575
$249$	14.0497	0.890362
$250$	−14.8649	−0.940138
$251$	−25.0778	−1.58290	−0.791450	−	0.611234i	$-0.790673\pi$
$251$	−25.0778	−1.58290	−0.791450	+	0.611234i	$0.790673\pi$
$252$	0	0
$253$	6.14682	0.386447
$254$	−36.2002	−2.27140
$255$	−17.2716	−1.08159
$256$	17.3983	1.08740
$257$	22.7564	1.41950	0.709752	−	0.704452i	$-0.248807\pi$
$257$	22.7564	1.41950	0.709752	+	0.704452i	$0.248807\pi$
$258$	−19.5374	−1.21634
$259$	0	0
$260$	−46.8713	−2.90683
$261$	0.267181	0.0165381
$262$	−3.54057	−0.218737
$263$	−5.98638	−0.369136	−0.184568	−	0.982820i	$-0.559089\pi$
$263$	−5.98638	−0.369136	−0.184568	+	0.982820i	$0.559089\pi$
$264$	−21.6737	−1.33393
$265$	36.8473	2.26351
$266$	0	0
$267$	15.6068	0.955123
$268$	74.0749	4.52484
$269$	−31.2140	−1.90315	−0.951575	−	0.307418i	$-0.900535\pi$
$269$	−31.2140	−1.90315	−0.951575	+	0.307418i	$0.900535\pi$
$270$	−9.17792	−0.558551
$271$	−6.47522	−0.393342	−0.196671	−	0.980470i	$-0.563013\pi$
$271$	−6.47522	−0.393342	−0.196671	+	0.980470i	$0.563013\pi$
$272$	−66.1556	−4.01127
$273$	0	0
$274$	−39.0289	−2.35782
$275$	16.3995	0.988925
$276$	13.0244	0.783975
$277$	20.3614	1.22340	0.611699	−	0.791091i	$-0.290486\pi$
$277$	20.3614	1.22340	0.611699	+	0.791091i	$0.290486\pi$
$278$	−9.92255	−0.595115
$279$	−6.04056	−0.361639
$280$	0	0
$281$	18.5325	1.10556	0.552778	−	0.833328i	$-0.313568\pi$
$281$	18.5325	1.10556	0.552778	+	0.833328i	$0.313568\pi$
$282$	22.3642	1.33177
$283$	−5.17781	−0.307789	−0.153894	−	0.988087i	$-0.549182\pi$
$283$	−5.17781	−0.307789	−0.153894	+	0.988087i	$0.549182\pi$
$284$	43.1165	2.55849
$285$	−10.0418	−0.594826
$286$	17.4724	1.03316
$287$	0	0
$288$	−17.6570	−1.04045
$289$	8.67290	0.510171
$290$	−2.45216	−0.143996
$291$	−7.72850	−0.453053
$292$	−34.9982	−2.04812
$293$	−5.72975	−0.334735	−0.167368	−	0.985895i	$-0.553527\pi$
$293$	−5.72975	−0.334735	−0.167368	+	0.985895i	$0.553527\pi$
$294$	0	0
$295$	−10.1657	−0.591869
$296$	−85.5720	−4.97377
$297$	2.47740	0.143753
$298$	−42.6914	−2.47305
$299$	−6.49926	−0.375862
$300$	34.7485	2.00620
$301$	0	0
$302$	−29.7434	−1.71154
$303$	9.67726	0.555944
$304$	−38.4632	−2.20602
$305$	−24.1089	−1.38047
$306$	13.6422	0.779875
$307$	1.87189	0.106835	0.0534173	−	0.998572i	$-0.482989\pi$
$307$	1.87189	0.106835	0.0534173	+	0.998572i	$0.482989\pi$
$308$	0	0
$309$	−4.45587	−0.253486
$310$	55.4398	3.14877
$311$	−14.0836	−0.798608	−0.399304	−	0.916819i	$-0.630748\pi$
$311$	−14.0836	−0.798608	−0.399304	+	0.916819i	$0.630748\pi$
$312$	22.9164	1.29739
$313$	26.4775	1.49659	0.748297	−	0.663363i	$-0.230872\pi$
$313$	26.4775	1.49659	0.748297	+	0.663363i	$0.230872\pi$
$314$	−22.0493	−1.24431
$315$	0	0
$316$	−56.5461	−3.18097
$317$	−2.22286	−0.124848	−0.0624242	−	0.998050i	$-0.519883\pi$
$317$	−2.22286	−0.124848	−0.0624242	+	0.998050i	$0.519883\pi$
$318$	−29.1043	−1.63209
$319$	0.661913	0.0370600
$320$	73.0414	4.08314
$321$	10.3878	0.579792
$322$	0	0
$323$	14.9264	0.830525
$324$	5.24930	0.291628
$325$	−17.3397	−0.961836
$326$	1.45561	0.0806187
$327$	−7.88580	−0.436086
$328$	8.74860	0.483060
$329$	0	0
$330$	−22.7373	−1.25165
$331$	−18.1534	−0.997800	−0.498900	−	0.866660i	$-0.666262\pi$
$331$	−18.1534	−0.997800	−0.498900	+	0.866660i	$0.666262\pi$
$332$	73.7510	4.04761
$333$	9.78122	0.536008
$334$	−59.7177	−3.26761
$335$	48.1023	2.62811
$336$	0	0
$337$	−7.69887	−0.419384	−0.209692	−	0.977767i	$-0.567246\pi$
$337$	−7.69887	−0.419384	−0.209692	+	0.977767i	$0.567246\pi$
$338$	16.5277	0.898988
$339$	18.9778	1.03073
$340$	−90.6641	−4.91695
$341$	−14.9649	−0.810393
$342$	7.93167	0.428895
$343$	0	0
$344$	−63.4828	−3.42276
$345$	8.45768	0.455346
$346$	−50.9299	−2.73801
$347$	−28.2126	−1.51453	−0.757266	−	0.653107i	$-0.773465\pi$
$347$	−28.2126	−1.51453	−0.757266	+	0.653107i	$0.773465\pi$
$348$	1.40251	0.0751826
$349$	24.3427	1.30303	0.651517	−	0.758634i	$-0.274133\pi$
$349$	24.3427	1.30303	0.651517	+	0.758634i	$0.274133\pi$
$350$	0	0
$351$	−2.61944	−0.139815
$352$	−43.7435	−2.33153
$353$	−34.9906	−1.86236	−0.931180	−	0.364559i	$-0.881220\pi$
$353$	−34.9906	−1.86236	−0.931180	+	0.364559i	$0.881220\pi$
$354$	8.02950	0.426763
$355$	27.9987	1.48602
$356$	81.9250	4.34202
$357$	0	0
$358$	12.6577	0.668980
$359$	−34.5993	−1.82608	−0.913039	−	0.407871i	$-0.866271\pi$
$359$	−34.5993	−1.82608	−0.913039	+	0.407871i	$0.866271\pi$
$360$	−29.8219	−1.57175
$361$	−10.3217	−0.543250
$362$	−56.1182	−2.94951
$363$	−4.86251	−0.255216
$364$	0	0
$365$	−22.7269	−1.18958
$366$	19.0428	0.995381
$367$	−23.3100	−1.21677	−0.608387	−	0.793640i	$-0.708183\pi$
$367$	−23.3100	−1.21677	−0.608387	+	0.793640i	$0.708183\pi$
$368$	32.3955	1.68873
$369$	−1.00000	−0.0520579
$370$	−89.7713	−4.66699
$371$	0	0
$372$	−31.7087	−1.64402
$373$	−19.5468	−1.01209	−0.506047	−	0.862506i	$-0.668894\pi$
$373$	−19.5468	−1.01209	−0.506047	+	0.862506i	$0.668894\pi$
$374$	33.7972	1.74761
$375$	5.52095	0.285101
$376$	72.6679	3.74756
$377$	−0.699865	−0.0360449
$378$	0	0
$379$	3.74324	0.192277	0.0961386	−	0.995368i	$-0.469351\pi$
$379$	3.74324	0.192277	0.0961386	+	0.995368i	$0.469351\pi$
$380$	−52.7126	−2.70410
$381$	13.4451	0.688812
$382$	−5.44262	−0.278468
$383$	−4.35761	−0.222664	−0.111332	−	0.993783i	$-0.535512\pi$
$383$	−4.35761	−0.222664	−0.111332	+	0.993783i	$0.535512\pi$
$384$	−22.3787	−1.14201
$385$	0	0
$386$	−2.04448	−0.104061
$387$	7.25634	0.368861
$388$	−40.5692	−2.05959
$389$	−28.6074	−1.45045	−0.725226	−	0.688511i	$-0.758265\pi$
$389$	−28.6074	−1.45045	−0.725226	+	0.688511i	$0.758265\pi$
$390$	24.0410	1.21736
$391$	−12.5717	−0.635776
$392$	0	0
$393$	1.31500	0.0663329
$394$	−46.3881	−2.33700
$395$	−36.7195	−1.84756
$396$	13.0046	0.653506
$397$	−11.4747	−0.575898	−0.287949	−	0.957646i	$-0.592973\pi$
$397$	−11.4747	−0.575898	−0.287949	+	0.957646i	$0.592973\pi$
$398$	−56.1701	−2.81555
$399$	0	0
$400$	86.4298	4.32149
$401$	−16.8298	−0.840442	−0.420221	−	0.907422i	$-0.638047\pi$
$401$	−16.8298	−0.840442	−0.420221	+	0.907422i	$0.638047\pi$
$402$	−37.9942	−1.89498
$403$	15.8229	0.788195
$404$	50.7989	2.52734
$405$	3.40876	0.169383
$406$	0	0
$407$	24.2320	1.20113
$408$	44.3278	2.19455
$409$	33.7391	1.66829	0.834144	−	0.551546i	$-0.185962\pi$
$409$	33.7391	1.66829	0.834144	+	0.551546i	$0.185962\pi$
$410$	9.17792	0.453265
$411$	14.4957	0.715019
$412$	−23.3902	−1.15235
$413$	0	0
$414$	−6.68041	−0.328324
$415$	47.8920	2.35092
$416$	46.2516	2.26767
$417$	3.68532	0.180471
$418$	19.6499	0.961107
$419$	13.3241	0.650923	0.325461	−	0.945555i	$-0.394480\pi$
$419$	13.3241	0.650923	0.325461	+	0.945555i	$0.394480\pi$
$420$	0	0
$421$	−25.0597	−1.22134	−0.610668	−	0.791887i	$-0.709099\pi$
$421$	−25.0597	−1.22134	−0.610668	+	0.791887i	$0.709099\pi$
$422$	34.4161	1.67535
$423$	−8.30624	−0.403863
$424$	−94.5687	−4.59266
$425$	−33.5407	−1.62696
$426$	−22.1152	−1.07148
$427$	0	0
$428$	54.5289	2.63575
$429$	−6.48939	−0.313311
$430$	−66.5982	−3.21165
$431$	6.65870	0.320738	0.160369	−	0.987057i	$-0.448732\pi$
$431$	6.65870	0.320738	0.160369	+	0.987057i	$0.448732\pi$
$432$	13.0566	0.628185
$433$	30.8114	1.48070	0.740352	−	0.672220i	$-0.234659\pi$
$433$	30.8114	1.48070	0.740352	+	0.672220i	$0.234659\pi$
$434$	0	0
$435$	0.910755	0.0436674
$436$	−41.3949	−1.98246
$437$	−7.30923	−0.349648
$438$	17.9512	0.857740
$439$	−9.81611	−0.468497	−0.234249	−	0.972177i	$-0.575263\pi$
$439$	−9.81611	−0.468497	−0.234249	+	0.972177i	$0.575263\pi$
$440$	−73.8805	−3.52212
$441$	0	0
$442$	−35.7350	−1.69974
$443$	−21.1360	−1.00420	−0.502101	−	0.864809i	$-0.667439\pi$
$443$	−21.1360	−1.00420	−0.502101	+	0.864809i	$0.667439\pi$
$444$	51.3446	2.43671
$445$	53.1999	2.52192
$446$	−19.9819	−0.946171
$447$	15.8559	0.749960
$448$	0	0
$449$	29.6148	1.39761	0.698805	−	0.715312i	$-0.253715\pi$
$449$	29.6148	1.39761	0.698805	+	0.715312i	$0.253715\pi$
$450$	−17.8231	−0.840187
$451$	−2.47740	−0.116656
$452$	99.6203	4.68574
$453$	11.0469	0.519030
$454$	−33.5657	−1.57532
$455$	0	0
$456$	25.7724	1.20690
$457$	−8.41928	−0.393837	−0.196919	−	0.980420i	$-0.563094\pi$
$457$	−8.41928	−0.393837	−0.196919	+	0.980420i	$0.563094\pi$
$458$	38.5012	1.79904
$459$	−5.06684	−0.236500
$460$	44.3969	2.07002
$461$	−16.5792	−0.772171	−0.386086	−	0.922463i	$-0.626173\pi$
$461$	−16.5792	−0.772171	−0.386086	+	0.922463i	$0.626173\pi$
$462$	0	0
$463$	7.25788	0.337302	0.168651	−	0.985676i	$-0.446059\pi$
$463$	7.25788	0.337302	0.168651	+	0.985676i	$0.446059\pi$
$464$	3.48847	0.161948
$465$	−20.5908	−0.954876
$466$	64.0307	2.96617
$467$	−33.5488	−1.55245	−0.776226	−	0.630454i	$-0.782869\pi$
$467$	−33.5488	−1.55245	−0.776226	+	0.630454i	$0.782869\pi$
$468$	−13.7502	−0.635605
$469$	0	0
$470$	76.2340	3.51641
$471$	8.18928	0.377342
$472$	26.0903	1.20090
$473$	17.9768	0.826576
$474$	29.0034	1.33217
$475$	−19.5007	−0.894754
$476$	0	0
$477$	10.8096	0.494937
$478$	−27.0754	−1.23840
$479$	18.5081	0.845656	0.422828	−	0.906210i	$-0.361037\pi$
$479$	18.5081	0.845656	0.422828	+	0.906210i	$0.361037\pi$
$480$	−60.1885	−2.74722
$481$	−25.6213	−1.16823
$482$	24.7918	1.12923
$483$	0	0
$484$	−25.5248	−1.16022
$485$	−26.3446	−1.19625
$486$	−2.69245	−0.122132
$487$	−43.5938	−1.97542	−0.987711	−	0.156290i	$-0.950046\pi$
$487$	−43.5938	−1.97542	−0.987711	+	0.156290i	$0.950046\pi$
$488$	61.8757	2.80098
$489$	−0.540625	−0.0244479
$490$	0	0
$491$	33.8439	1.52735	0.763676	−	0.645599i	$-0.223392\pi$
$491$	33.8439	1.52735	0.763676	+	0.645599i	$0.223392\pi$
$492$	−5.24930	−0.236657
$493$	−1.35376	−0.0609704
$494$	−20.7765	−0.934781
$495$	8.44485	0.379568
$496$	−78.8691	−3.54133
$497$	0	0
$498$	−37.8281	−1.69512
$499$	35.4016	1.58479	0.792396	−	0.610008i	$-0.208834\pi$
$499$	35.4016	1.58479	0.792396	+	0.610008i	$0.208834\pi$
$500$	28.9811	1.29608
$501$	22.1797	0.990914
$502$	67.5209	3.01361
$503$	35.0856	1.56439	0.782195	−	0.623033i	$-0.214100\pi$
$503$	35.0856	1.56439	0.782195	+	0.623033i	$0.214100\pi$
$504$	0	0
$505$	32.9874	1.46792
$506$	−16.5500	−0.735738
$507$	−6.13853	−0.272622
$508$	70.5773	3.13136
$509$	−24.7682	−1.09783	−0.548917	−	0.835877i	$-0.684960\pi$
$509$	−24.7682	−1.09783	−0.548917	+	0.835877i	$0.684960\pi$
$510$	46.5031	2.05919
$511$	0	0
$512$	−2.08691	−0.0922294
$513$	−2.94589	−0.130064
$514$	−61.2705	−2.70253
$515$	−15.1890	−0.669307
$516$	38.0908	1.67685
$517$	−20.5778	−0.905013
$518$	0	0
$519$	18.9158	0.830311
$520$	78.1166	3.42564
$521$	−20.6917	−0.906520	−0.453260	−	0.891378i	$-0.649739\pi$
$521$	−20.6917	−0.906520	−0.453260	+	0.891378i	$0.649739\pi$
$522$	−0.719372	−0.0314860
$523$	3.14418	0.137485	0.0687426	−	0.997634i	$-0.478101\pi$
$523$	3.14418	0.137485	0.0687426	+	0.997634i	$0.478101\pi$
$524$	6.90283	0.301551
$525$	0	0
$526$	16.1180	0.702780
$527$	30.6066	1.33324
$528$	32.3463	1.40769
$529$	−16.8438	−0.732341
$530$	−99.2096	−4.30939
$531$	−2.98222	−0.129417
$532$	0	0
$533$	2.61944	0.113461
$534$	−42.0207	−1.81841
$535$	35.4096	1.53089
$536$	−123.455	−5.33243
$537$	−4.70118	−0.202871
$538$	84.0421	3.62331
$539$	0	0
$540$	17.8936	0.770018
$541$	−1.25034	−0.0537565	−0.0268782	−	0.999639i	$-0.508557\pi$
$541$	−1.25034	−0.0537565	−0.0268782	+	0.999639i	$0.508557\pi$
$542$	17.4342	0.748864
$543$	20.8428	0.894449
$544$	89.4654	3.83580
$545$	−26.8808	−1.15145
$546$	0	0
$547$	−27.9208	−1.19381	−0.596903	−	0.802313i	$-0.703602\pi$
$547$	−27.9208	−1.19381	−0.596903	+	0.802313i	$0.703602\pi$
$548$	76.0922	3.25050
$549$	−7.07265	−0.301853
$550$	−44.1548	−1.88277
$551$	−0.787085	−0.0335309
$552$	−21.7067	−0.923898
$553$	0	0
$554$	−54.8221	−2.32917
$555$	33.3418	1.41528
$556$	19.3454	0.820426
$557$	−3.83843	−0.162639	−0.0813197	−	0.996688i	$-0.525913\pi$
$557$	−3.83843	−0.162639	−0.0813197	+	0.996688i	$0.525913\pi$
$558$	16.2639	0.688507
$559$	−19.0076	−0.803935
$560$	0	0
$561$	−12.5526	−0.529970
$562$	−49.8979	−2.10482
$563$	−19.5595	−0.824335	−0.412167	−	0.911108i	$-0.635228\pi$
$563$	−19.5595	−0.824335	−0.412167	+	0.911108i	$0.635228\pi$
$564$	−43.6020	−1.83597
$565$	64.6908	2.72156
$566$	13.9410	0.585984
$567$	0	0
$568$	−71.8589	−3.01513
$569$	−4.77753	−0.200284	−0.100142	−	0.994973i	$-0.531930\pi$
$569$	−4.77753	−0.200284	−0.100142	+	0.994973i	$0.531930\pi$
$570$	27.0371	1.13246
$571$	16.0786	0.672870	0.336435	−	0.941707i	$-0.390779\pi$
$571$	16.0786	0.672870	0.336435	+	0.941707i	$0.390779\pi$
$572$	−34.0648	−1.42432
$573$	2.02143	0.0844466
$574$	0	0
$575$	16.4244	0.684944
$576$	21.4276	0.892815
$577$	2.45923	0.102379	0.0511896	−	0.998689i	$-0.483699\pi$
$577$	2.45923	0.102379	0.0511896	+	0.998689i	$0.483699\pi$
$578$	−23.3514	−0.971289
$579$	0.759337	0.0315570
$580$	4.78083	0.198513
$581$	0	0
$582$	20.8086	0.862545
$583$	26.7796	1.10910
$584$	58.3288	2.41366
$585$	−8.92904	−0.369171
$586$	15.4271	0.637286
$587$	−16.0272	−0.661512	−0.330756	−	0.943716i	$-0.607304\pi$
$587$	−16.0272	−0.661512	−0.330756	+	0.943716i	$0.607304\pi$
$588$	0	0
$589$	17.7948	0.733223
$590$	27.3706	1.12683
$591$	17.2289	0.708704
$592$	127.709	5.24882
$593$	15.5184	0.637266	0.318633	−	0.947878i	$-0.396776\pi$
$593$	15.5184	0.637266	0.318633	+	0.947878i	$0.396776\pi$
$594$	−6.67027	−0.273685
$595$	0	0
$596$	83.2327	3.40934
$597$	20.8621	0.853827
$598$	17.4989	0.715585
$599$	21.8286	0.891892	0.445946	−	0.895060i	$-0.352867\pi$
$599$	21.8286	0.891892	0.445946	+	0.895060i	$0.352867\pi$
$600$	−57.9125	−2.36427
$601$	2.88582	0.117715	0.0588575	−	0.998266i	$-0.481254\pi$
$601$	2.88582	0.117715	0.0588575	+	0.998266i	$0.481254\pi$
$602$	0	0
$603$	14.1114	0.574659
$604$	57.9887	2.35953
$605$	−16.5751	−0.673874
$606$	−26.0556	−1.05844
$607$	−6.38555	−0.259182	−0.129591	−	0.991568i	$-0.541366\pi$
$607$	−6.38555	−0.259182	−0.129591	+	0.991568i	$0.541366\pi$
$608$	52.0156	2.10951
$609$	0	0
$610$	64.9122	2.62822
$611$	21.7577	0.880223
$612$	−26.5974	−1.07514
$613$	17.3087	0.699092	0.349546	−	0.936919i	$-0.386336\pi$
$613$	17.3087	0.699092	0.349546	+	0.936919i	$0.386336\pi$
$614$	−5.03998	−0.203397
$615$	−3.40876	−0.137454
$616$	0	0
$617$	2.81470	0.113316	0.0566579	−	0.998394i	$-0.481956\pi$
$617$	2.81470	0.113316	0.0566579	+	0.998394i	$0.481956\pi$
$618$	11.9972	0.482599
$619$	−28.7390	−1.15512	−0.577559	−	0.816349i	$-0.695995\pi$
$619$	−28.7390	−1.15512	−0.577559	+	0.816349i	$0.695995\pi$
$620$	−108.087	−4.34090
$621$	2.48116	0.0995656
$622$	37.9194	1.52043
$623$	0	0
$624$	−34.2009	−1.36913
$625$	−14.2786	−0.571144
$626$	−71.2893	−2.84929
$627$	−7.29813	−0.291459
$628$	42.9880	1.71541
$629$	−49.5599	−1.97608
$630$	0	0
$631$	0.108140	0.00430497	0.00215249	−	0.999998i	$-0.499315\pi$
$631$	0.108140	0.00430497	0.00215249	+	0.999998i	$0.499315\pi$
$632$	94.2409	3.74870
$633$	−12.7824	−0.508056
$634$	5.98496	0.237693
$635$	45.8310	1.81875
$636$	56.7428	2.25000
$637$	0	0
$638$	−1.78217	−0.0705567
$639$	8.21376	0.324931
$640$	−76.2834	−3.01537
$641$	14.5924	0.576366	0.288183	−	0.957575i	$-0.406949\pi$
$641$	14.5924	0.576366	0.288183	+	0.957575i	$0.406949\pi$
$642$	−27.9688	−1.10384
$643$	−19.0479	−0.751178	−0.375589	−	0.926786i	$-0.622560\pi$
$643$	−19.0479	−0.751178	−0.375589	+	0.926786i	$0.622560\pi$
$644$	0	0
$645$	24.7351	0.973945
$646$	−40.1885	−1.58120
$647$	−2.49785	−0.0982008	−0.0491004	−	0.998794i	$-0.515635\pi$
$647$	−2.49785	−0.0982008	−0.0491004	+	0.998794i	$0.515635\pi$
$648$	−8.74860	−0.343677
$649$	−7.38815	−0.290010
$650$	46.6865	1.83119
$651$	0	0
$652$	−2.83791	−0.111141
$653$	7.16644	0.280444	0.140222	−	0.990120i	$-0.455218\pi$
$653$	7.16644	0.280444	0.140222	+	0.990120i	$0.455218\pi$
$654$	21.2321	0.830242
$655$	4.48251	0.175146
$656$	−13.0566	−0.509774
$657$	−6.66722	−0.260113
$658$	0	0
$659$	24.4135	0.951016	0.475508	−	0.879712i	$-0.342264\pi$
$659$	24.4135	0.951016	0.475508	+	0.879712i	$0.342264\pi$
$660$	44.3296	1.72553
$661$	−22.6127	−0.879530	−0.439765	−	0.898113i	$-0.644938\pi$
$661$	−22.6127	−0.879530	−0.439765	+	0.898113i	$0.644938\pi$
$662$	48.8771	1.89966
$663$	13.2723	0.515453
$664$	−122.915	−4.77003
$665$	0	0
$666$	−26.3355	−1.02048
$667$	0.662919	0.0256683
$668$	116.428	4.50473
$669$	7.42145	0.286930
$670$	−129.513	−5.00353
$671$	−17.5217	−0.676419
$672$	0	0
$673$	11.8973	0.458607	0.229303	−	0.973355i	$-0.426355\pi$
$673$	11.8973	0.458607	0.229303	+	0.973355i	$0.426355\pi$
$674$	20.7288	0.798445
$675$	6.61964	0.254790
$676$	−32.2230	−1.23935
$677$	−4.70172	−0.180702	−0.0903509	−	0.995910i	$-0.528799\pi$
$677$	−4.70172	−0.180702	−0.0903509	+	0.995910i	$0.528799\pi$
$678$	−51.0969	−1.96236
$679$	0	0
$680$	151.103	5.79452
$681$	12.4666	0.477721
$682$	40.2922	1.54287
$683$	−16.7037	−0.639149	−0.319575	−	0.947561i	$-0.603540\pi$
$683$	−16.7037	−0.639149	−0.319575	+	0.947561i	$0.603540\pi$
$684$	−15.4639	−0.591276
$685$	49.4122	1.88794
$686$	0	0
$687$	−14.2997	−0.545566
$688$	94.7430	3.61204
$689$	−28.3151	−1.07872
$690$	−22.7719	−0.866912
$691$	−1.53565	−0.0584187	−0.0292093	−	0.999573i	$-0.509299\pi$
$691$	−1.53565	−0.0584187	−0.0292093	+	0.999573i	$0.509299\pi$
$692$	99.2947	3.77462
$693$	0	0
$694$	75.9611	2.88344
$695$	12.5624	0.476518
$696$	−2.33746	−0.0886011
$697$	5.06684	0.191920
$698$	−65.5415	−2.48078
$699$	−23.7816	−0.899501
$700$	0	0
$701$	−18.6576	−0.704687	−0.352343	−	0.935871i	$-0.614615\pi$
$701$	−18.6576	−0.704687	−0.352343	+	0.935871i	$0.614615\pi$
$702$	7.05272	0.266188
$703$	−28.8144	−1.08676
$704$	53.0846	2.00070
$705$	−28.3140	−1.06637
$706$	94.2105	3.54566
$707$	0	0
$708$	−15.6546	−0.588336
$709$	17.4961	0.657079	0.328540	−	0.944490i	$-0.393444\pi$
$709$	17.4961	0.657079	0.328540	+	0.944490i	$0.393444\pi$
$710$	−75.3853	−2.82916
$711$	−10.7721	−0.403986
$712$	−136.538	−5.11697
$713$	−14.9876	−0.561291
$714$	0	0
$715$	−22.1208	−0.827270
$716$	−24.6779	−0.922257
$717$	10.0560	0.375550
$718$	93.1569	3.47658
$719$	10.4177	0.388513	0.194257	−	0.980951i	$-0.437771\pi$
$719$	10.4177	0.388513	0.194257	+	0.980951i	$0.437771\pi$
$720$	44.5067	1.65867
$721$	0	0
$722$	27.7908	1.03427
$723$	−9.20788	−0.342445
$724$	109.410	4.06619
$725$	1.76864	0.0656856
$726$	13.0921	0.485893
$727$	13.3290	0.494346	0.247173	−	0.968971i	$-0.420498\pi$
$727$	13.3290	0.494346	0.247173	+	0.968971i	$0.420498\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	61.1912	2.26479
$731$	−36.7668	−1.35987
$732$	−37.1265	−1.37223
$733$	10.0515	0.371262	0.185631	−	0.982620i	$-0.440567\pi$
$733$	10.0515	0.371262	0.185631	+	0.982620i	$0.440567\pi$
$734$	62.7612	2.31656
$735$	0	0
$736$	−43.8099	−1.61486
$737$	34.9595	1.28775
$738$	2.69245	0.0991106
$739$	22.6282	0.832392	0.416196	−	0.909275i	$-0.363363\pi$
$739$	22.6282	0.832392	0.416196	+	0.909275i	$0.363363\pi$
$740$	175.021	6.43391
$741$	7.71658	0.283476
$742$	0	0
$743$	45.5658	1.67165	0.835823	−	0.548999i	$-0.184991\pi$
$743$	45.5658	1.67165	0.835823	+	0.548999i	$0.184991\pi$
$744$	52.8464	1.93744
$745$	54.0491	1.98021
$746$	52.6288	1.92688
$747$	14.0497	0.514051
$748$	−65.8923	−2.40926
$749$	0	0
$750$	−14.8649	−0.542789
$751$	−24.9793	−0.911507	−0.455753	−	0.890106i	$-0.650630\pi$
$751$	−24.9793	−0.911507	−0.455753	+	0.890106i	$0.650630\pi$
$752$	−108.451	−3.95480
$753$	−25.0778	−0.913888
$754$	1.88435	0.0686241
$755$	37.6563	1.37045
$756$	0	0
$757$	−25.3070	−0.919799	−0.459899	−	0.887971i	$-0.652115\pi$
$757$	−25.3070	−0.919799	−0.459899	+	0.887971i	$0.652115\pi$
$758$	−10.0785	−0.366067
$759$	6.14682	0.223115
$760$	87.8518	3.18672
$761$	−23.9832	−0.869391	−0.434695	−	0.900578i	$-0.643144\pi$
$761$	−23.9832	−0.869391	−0.434695	+	0.900578i	$0.643144\pi$
$762$	−36.2002	−1.31140
$763$	0	0
$764$	10.6111	0.383897
$765$	−17.2716	−0.624458
$766$	11.7327	0.423919
$767$	7.81176	0.282066
$768$	17.3983	0.627809
$769$	−9.22042	−0.332497	−0.166248	−	0.986084i	$-0.553165\pi$
$769$	−9.22042	−0.332497	−0.166248	+	0.986084i	$0.553165\pi$
$770$	0	0
$771$	22.7564	0.819551
$772$	3.98599	0.143459
$773$	12.9567	0.466020	0.233010	−	0.972474i	$-0.425142\pi$
$773$	12.9567	0.466020	0.233010	+	0.972474i	$0.425142\pi$
$774$	−19.5374	−0.702256
$775$	−39.9863	−1.43635
$776$	67.6135	2.42718
$777$	0	0
$778$	77.0240	2.76144
$779$	2.94589	0.105547
$780$	−46.8713	−1.67826
$781$	20.3487	0.728135
$782$	33.8486	1.21042
$783$	0.267181	0.00954826
$784$	0	0
$785$	27.9153	0.996339
$786$	−3.54057	−0.126288
$787$	−21.9896	−0.783845	−0.391923	−	0.919998i	$-0.628190\pi$
$787$	−21.9896	−0.783845	−0.391923	+	0.919998i	$0.628190\pi$
$788$	90.4399	3.22179
$789$	−5.98638	−0.213121
$790$	98.8656	3.51748
$791$	0	0
$792$	−21.6737	−0.770143
$793$	18.5264	0.657891
$794$	30.8950	1.09642
$795$	36.8473	1.30684
$796$	109.511	3.88152
$797$	54.7322	1.93871	0.969356	−	0.245658i	$-0.0790041\pi$
$797$	54.7322	1.93871	0.969356	+	0.245658i	$0.0790041\pi$
$798$	0	0
$799$	42.0864	1.48891
$800$	−116.883	−4.13244
$801$	15.6068	0.551440
$802$	45.3136	1.60008
$803$	−16.5173	−0.582884
$804$	74.0749	2.61242
$805$	0	0
$806$	−42.6024	−1.50061
$807$	−31.2140	−1.09878
$808$	−84.6624	−2.97841
$809$	43.6588	1.53496	0.767482	−	0.641071i	$-0.221510\pi$
$809$	43.6588	1.53496	0.767482	+	0.641071i	$0.221510\pi$
$810$	−9.17792	−0.322479
$811$	−1.40296	−0.0492645	−0.0246322	−	0.999697i	$-0.507841\pi$
$811$	−1.40296	−0.0492645	−0.0246322	+	0.999697i	$0.507841\pi$
$812$	0	0
$813$	−6.47522	−0.227096
$814$	−65.2434	−2.28678
$815$	−1.84286	−0.0645526
$816$	−66.1556	−2.31591
$817$	−21.3764	−0.747865
$818$	−90.8408	−3.17617
$819$	0	0
$820$	−17.8936	−0.624872
$821$	−31.7107	−1.10671	−0.553355	−	0.832946i	$-0.686653\pi$
$821$	−31.7107	−1.10671	−0.553355	+	0.832946i	$0.686653\pi$
$822$	−39.0289	−1.36129
$823$	−31.6705	−1.10396	−0.551981	−	0.833856i	$-0.686128\pi$
$823$	−31.6705	−1.10396	−0.551981	+	0.833856i	$0.686128\pi$
$824$	38.9826	1.35802
$825$	16.3995	0.570956
$826$	0	0
$827$	−11.7291	−0.407861	−0.203931	−	0.978985i	$-0.565372\pi$
$827$	−11.7291	−0.407861	−0.203931	+	0.978985i	$0.565372\pi$
$828$	13.0244	0.452628
$829$	−37.7160	−1.30993	−0.654965	−	0.755659i	$-0.727317\pi$
$829$	−37.7160	−1.30993	−0.654965	+	0.755659i	$0.727317\pi$
$830$	−128.947	−4.47581
$831$	20.3614	0.706329
$832$	−56.1283	−1.94590
$833$	0	0
$834$	−9.92255	−0.343590
$835$	75.6051	2.61642
$836$	−38.3101	−1.32498
$837$	−6.04056	−0.208792
$838$	−35.8744	−1.23926
$839$	−26.0811	−0.900420	−0.450210	−	0.892923i	$-0.648651\pi$
$839$	−26.0811	−0.900420	−0.450210	+	0.892923i	$0.648651\pi$
$840$	0	0
$841$	−28.9286	−0.997538
$842$	67.4721	2.32524
$843$	18.5325	0.638293
$844$	−67.0988	−2.30964
$845$	−20.9248	−0.719833
$846$	22.3642	0.768896
$847$	0	0
$848$	141.136	4.84664
$849$	−5.17781	−0.177702
$850$	90.3066	3.09749
$851$	24.2688	0.831924
$852$	43.1165	1.47715
$853$	−48.0414	−1.64491	−0.822453	−	0.568833i	$-0.807395\pi$
$853$	−48.0414	−1.64491	−0.822453	+	0.568833i	$0.807395\pi$
$854$	0	0
$855$	−10.0418	−0.343423
$856$	−90.8790	−3.10618
$857$	−41.5181	−1.41823	−0.709116	−	0.705092i	$-0.750906\pi$
$857$	−41.5181	−1.41823	−0.709116	+	0.705092i	$0.750906\pi$
$858$	17.4724	0.596498
$859$	47.5478	1.62231	0.811156	−	0.584830i	$-0.198839\pi$
$859$	47.5478	1.62231	0.811156	+	0.584830i	$0.198839\pi$
$860$	129.842	4.42758
$861$	0	0
$862$	−17.9282	−0.610638
$863$	3.80787	0.129621	0.0648107	−	0.997898i	$-0.479356\pi$
$863$	3.80787	0.129621	0.0648107	+	0.997898i	$0.479356\pi$
$864$	−17.6570	−0.600704
$865$	64.4794	2.19236
$866$	−82.9584	−2.81904
$867$	8.67290	0.294547
$868$	0	0
$869$	−26.6868	−0.905288
$870$	−2.45216	−0.0831362
$871$	−36.9639	−1.25247
$872$	68.9897	2.33628
$873$	−7.72850	−0.261570
$874$	19.6797	0.665677
$875$	0	0
$876$	−34.9982	−1.18248
$877$	−46.2498	−1.56175	−0.780873	−	0.624690i	$-0.785226\pi$
$877$	−46.2498	−1.56175	−0.780873	+	0.624690i	$0.785226\pi$
$878$	26.4294	0.891949
$879$	−5.72975	−0.193260
$880$	110.261	3.71689
$881$	−8.19976	−0.276257	−0.138128	−	0.990414i	$-0.544109\pi$
$881$	−8.19976	−0.276257	−0.138128	+	0.990414i	$0.544109\pi$
$882$	0	0
$883$	−37.2720	−1.25430	−0.627151	−	0.778898i	$-0.715779\pi$
$883$	−37.2720	−1.25430	−0.627151	+	0.778898i	$0.715779\pi$
$884$	69.6703	2.34327
$885$	−10.1657	−0.341716
$886$	56.9077	1.91185
$887$	−24.8683	−0.834996	−0.417498	−	0.908678i	$-0.637093\pi$
$887$	−24.8683	−0.834996	−0.417498	+	0.908678i	$0.637093\pi$
$888$	−85.5720	−2.87161
$889$	0	0
$890$	−143.238	−4.80136
$891$	2.47740	0.0829959
$892$	38.9574	1.30439
$893$	24.4693	0.818832
$894$	−42.6914	−1.42781
$895$	−16.0252	−0.535663
$896$	0	0
$897$	−6.49926	−0.217004
$898$	−79.7366	−2.66084
$899$	−1.61392	−0.0538273
$900$	34.7485	1.15828
$901$	−54.7705	−1.82467
$902$	6.67027	0.222096
$903$	0	0
$904$	−166.029	−5.52205
$905$	71.0480	2.36172
$906$	−29.7434	−0.988157
$907$	−10.1610	−0.337389	−0.168694	−	0.985668i	$-0.553955\pi$
$907$	−10.1610	−0.337389	−0.168694	+	0.985668i	$0.553955\pi$
$908$	65.4409	2.17173
$909$	9.67726	0.320974
$910$	0	0
$911$	−16.7737	−0.555738	−0.277869	−	0.960619i	$-0.589628\pi$
$911$	−16.7737	−0.555738	−0.277869	+	0.960619i	$0.589628\pi$
$912$	−38.4632	−1.27364
$913$	34.8066	1.15193
$914$	22.6685	0.749808
$915$	−24.1089	−0.797017
$916$	−75.0632	−2.48016
$917$	0	0
$918$	13.6422	0.450261
$919$	2.31695	0.0764290	0.0382145	−	0.999270i	$-0.487833\pi$
$919$	2.31695	0.0764290	0.0382145	+	0.999270i	$0.487833\pi$
$920$	−73.9928	−2.43947
$921$	1.87189	0.0616810
$922$	44.6388	1.47010
$923$	−21.5155	−0.708190
$924$	0	0
$925$	64.7481	2.12891
$926$	−19.5415	−0.642173
$927$	−4.45587	−0.146350
$928$	−4.71762	−0.154863
$929$	48.6233	1.59528	0.797640	−	0.603134i	$-0.206082\pi$
$929$	48.6233	1.59528	0.797640	+	0.603134i	$0.206082\pi$
$930$	55.4398	1.81794
$931$	0	0
$932$	−124.837	−4.08916
$933$	−14.0836	−0.461077
$934$	90.3285	2.95564
$935$	−42.7887	−1.39934
$936$	22.9164	0.749047
$937$	9.53054	0.311349	0.155675	−	0.987808i	$-0.450245\pi$
$937$	9.53054	0.311349	0.155675	+	0.987808i	$0.450245\pi$
$938$	0	0
$939$	26.4775	0.864059
$940$	−148.629	−4.84773
$941$	47.8808	1.56087	0.780434	−	0.625238i	$-0.214998\pi$
$941$	47.8808	1.56087	0.780434	+	0.625238i	$0.214998\pi$
$942$	−22.0493	−0.718403
$943$	−2.48116	−0.0807977
$944$	−38.9376	−1.26731
$945$	0	0
$946$	−48.4018	−1.57368
$947$	−40.4665	−1.31498	−0.657492	−	0.753461i	$-0.728383\pi$
$947$	−40.4665	−1.31498	−0.657492	+	0.753461i	$0.728383\pi$
$948$	−56.5461	−1.83653
$949$	17.4644	0.566918
$950$	52.5047	1.70348
$951$	−2.22286	−0.0720813
$952$	0	0
$953$	−39.0547	−1.26511	−0.632554	−	0.774517i	$-0.717993\pi$
$953$	−39.0547	−1.26511	−0.632554	+	0.774517i	$0.717993\pi$
$954$	−29.1043	−0.942287
$955$	6.89058	0.222974
$956$	52.7872	1.70726
$957$	0.661913	0.0213966
$958$	−49.8321	−1.61000
$959$	0	0
$960$	73.0414	2.35740
$961$	5.48840	0.177045
$962$	68.9843	2.22414
$963$	10.3878	0.334743
$964$	−48.3350	−1.55676
$965$	2.58840	0.0833234
$966$	0	0
$967$	−18.3993	−0.591681	−0.295840	−	0.955237i	$-0.595600\pi$
$967$	−18.3993	−0.591681	−0.295840	+	0.955237i	$0.595600\pi$
$968$	42.5401	1.36729
$969$	14.9264	0.479504
$970$	70.9316	2.27748
$971$	31.1119	0.998429	0.499215	−	0.866478i	$-0.333622\pi$
$971$	31.1119	0.998429	0.499215	+	0.866478i	$0.333622\pi$
$972$	5.24930	0.168371
$973$	0	0
$974$	117.374	3.76091
$975$	−17.3397	−0.555316
$976$	−92.3445	−2.95588
$977$	−13.4478	−0.430232	−0.215116	−	0.976588i	$-0.569013\pi$
$977$	−13.4478	−0.430232	−0.215116	+	0.976588i	$0.569013\pi$
$978$	1.45561	0.0465452
$979$	38.6643	1.23572
$980$	0	0
$981$	−7.88580	−0.251774
$982$	−91.1230	−2.90785
$983$	−23.3009	−0.743184	−0.371592	−	0.928396i	$-0.621188\pi$
$983$	−23.3009	−0.743184	−0.371592	+	0.928396i	$0.621188\pi$
$984$	8.74860	0.278895
$985$	58.7293	1.87127
$986$	3.64494	0.116079
$987$	0	0
$988$	40.5067	1.28869
$989$	18.0042	0.572499
$990$	−22.7373	−0.722640
$991$	23.4475	0.744835	0.372417	−	0.928065i	$-0.378529\pi$
$991$	23.4475	0.744835	0.372417	+	0.928065i	$0.378529\pi$
$992$	106.658	3.38641
$993$	−18.1534	−0.576080
$994$	0	0
$995$	71.1137	2.25446
$996$	73.7510	2.33689
$997$	0.865413	0.0274079	0.0137039	−	0.999906i	$-0.495638\pi$
$997$	0.865413	0.0274079	0.0137039	+	0.999906i	$0.495638\pi$
$998$	−95.3170	−3.01721
$999$	9.78122	0.309464

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bo.1.1	yes	24
7.6	odd	2		6027.2.a.bn.1.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6027.2.a.bn.1.1	✓	24	7.6	odd	2
6027.2.a.bo.1.1	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69245 q^{2} +1.00000 q^{3} +5.24930 q^{4} +3.40876 q^{5} -2.69245 q^{6} -8.74860 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.69245 q^{2} +1.00000 q^{3} +5.24930 q^{4} +3.40876 q^{5} -2.69245 q^{6} -8.74860 q^{8} +1.00000 q^{9} -9.17792 q^{10} +2.47740 q^{11} +5.24930 q^{12} -2.61944 q^{13} +3.40876 q^{15} +13.0566 q^{16} -5.06684 q^{17} -2.69245 q^{18} -2.94589 q^{19} +17.8936 q^{20} -6.67027 q^{22} +2.48116 q^{23} -8.74860 q^{24} +6.61964 q^{25} +7.05272 q^{26} +1.00000 q^{27} +0.267181 q^{29} -9.17792 q^{30} -6.04056 q^{31} -17.6570 q^{32} +2.47740 q^{33} +13.6422 q^{34} +5.24930 q^{36} +9.78122 q^{37} +7.93167 q^{38} -2.61944 q^{39} -29.8219 q^{40} -1.00000 q^{41} +7.25634 q^{43} +13.0046 q^{44} +3.40876 q^{45} -6.68041 q^{46} -8.30624 q^{47} +13.0566 q^{48} -17.8231 q^{50} -5.06684 q^{51} -13.7502 q^{52} +10.8096 q^{53} -2.69245 q^{54} +8.44485 q^{55} -2.94589 q^{57} -0.719372 q^{58} -2.98222 q^{59} +17.8936 q^{60} -7.07265 q^{61} +16.2639 q^{62} +21.4276 q^{64} -8.92904 q^{65} -6.67027 q^{66} +14.1114 q^{67} -26.5974 q^{68} +2.48116 q^{69} +8.21376 q^{71} -8.74860 q^{72} -6.66722 q^{73} -26.3355 q^{74} +6.61964 q^{75} -15.4639 q^{76} +7.05272 q^{78} -10.7721 q^{79} +44.5067 q^{80} +1.00000 q^{81} +2.69245 q^{82} +14.0497 q^{83} -17.2716 q^{85} -19.5374 q^{86} +0.267181 q^{87} -21.6737 q^{88} +15.6068 q^{89} -9.17792 q^{90} +13.0244 q^{92} -6.04056 q^{93} +22.3642 q^{94} -10.0418 q^{95} -17.6570 q^{96} -7.72850 q^{97} +2.47740 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9}+O(q^{10}) \) 24 * q + 8 * q^2 + 24 * q^3 + 32 * q^4 + 4 * q^5 + 8 * q^6 + 24 * q^8 + 24 * q^9	\( 24 q + 8 q^{2} + 24 q^{3} + 32 q^{4} + 4 q^{5} + 8 q^{6} + 24 q^{8} + 24 q^{9} - 4 q^{10} + 12 q^{11} + 32 q^{12} + 4 q^{15} + 44 q^{16} + 8 q^{17} + 8 q^{18} - 4 q^{19} + 28 q^{20} + 16 q^{22} + 20 q^{23} + 24 q^{24} + 48 q^{25} + 32 q^{26} + 24 q^{27} + 24 q^{29} - 4 q^{30} - 4 q^{31} + 36 q^{32} + 12 q^{33} + 16 q^{34} + 32 q^{36} + 64 q^{37} + 20 q^{38} - 48 q^{40} - 24 q^{41} + 20 q^{43} + 48 q^{44} + 4 q^{45} + 28 q^{46} + 32 q^{47} + 44 q^{48} - 20 q^{50} + 8 q^{51} + 76 q^{53} + 8 q^{54} - 24 q^{55} - 4 q^{57} + 28 q^{58} + 28 q^{59} + 28 q^{60} - 28 q^{61} - 4 q^{62} + 48 q^{64} + 28 q^{65} + 16 q^{66} + 44 q^{67} - 32 q^{68} + 20 q^{69} + 20 q^{71} + 24 q^{72} - 16 q^{73} + 44 q^{74} + 48 q^{75} - 16 q^{76} + 32 q^{78} + 4 q^{79} + 44 q^{80} + 24 q^{81} - 8 q^{82} + 8 q^{83} + 28 q^{85} + 56 q^{86} + 24 q^{87} + 60 q^{88} + 60 q^{89} - 4 q^{90} + 60 q^{92} - 4 q^{93} + 24 q^{94} + 28 q^{95} + 36 q^{96} - 48 q^{97} + 12 q^{99}+O(q^{100}) \) 24 * q + 8 * q^2 + 24 * q^3 + 32 * q^4 + 4 * q^5 + 8 * q^6 + 24 * q^8 + 24 * q^9 - 4 * q^10 + 12 * q^11 + 32 * q^12 + 4 * q^15 + 44 * q^16 + 8 * q^17 + 8 * q^18 - 4 * q^19 + 28 * q^20 + 16 * q^22 + 20 * q^23 + 24 * q^24 + 48 * q^25 + 32 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 4 * q^31 + 36 * q^32 + 12 * q^33 + 16 * q^34 + 32 * q^36 + 64 * q^37 + 20 * q^38 - 48 * q^40 - 24 * q^41 + 20 * q^43 + 48 * q^44 + 4 * q^45 + 28 * q^46 + 32 * q^47 + 44 * q^48 - 20 * q^50 + 8 * q^51 + 76 * q^53 + 8 * q^54 - 24 * q^55 - 4 * q^57 + 28 * q^58 + 28 * q^59 + 28 * q^60 - 28 * q^61 - 4 * q^62 + 48 * q^64 + 28 * q^65 + 16 * q^66 + 44 * q^67 - 32 * q^68 + 20 * q^69 + 20 * q^71 + 24 * q^72 - 16 * q^73 + 44 * q^74 + 48 * q^75 - 16 * q^76 + 32 * q^78 + 4 * q^79 + 44 * q^80 + 24 * q^81 - 8 * q^82 + 8 * q^83 + 28 * q^85 + 56 * q^86 + 24 * q^87 + 60 * q^88 + 60 * q^89 - 4 * q^90 + 60 * q^92 - 4 * q^93 + 24 * q^94 + 28 * q^95 + 36 * q^96 - 48 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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