LMFDB - Embedded newform 1338.2.a.j.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1338,2,Mod(1,1338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1338, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1338.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1338 = 2 \cdot 3 \cdot 223 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1338.a (trivial)

Newform invariants

comment:select newform

sage:traces = [7,7,-7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	yes
Analytic conductor:	$10.6839837904$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 18x^{5} - 8x^{4} + 51x^{3} + 47x^{2} - 2x - 8 $ x^7 - 18x^5 - 8x^4 + 51x^3 + 47x^2 - 2*x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-3.57857$ of defining polynomial
Character	$\chi$	$=$	1338.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.27125 q^{5} -1.00000 q^{6} +3.11004 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.27125 q^{10} +5.01780 q^{11} -1.00000 q^{12} -2.25689 q^{13} +3.11004 q^{14} -3.27125 q^{15} +1.00000 q^{16} +1.75903 q^{17} +1.00000 q^{18} -7.20855 q^{19} +3.27125 q^{20} -3.11004 q^{21} +5.01780 q^{22} +4.20547 q^{23} -1.00000 q^{24} +5.70110 q^{25} -2.25689 q^{26} -1.00000 q^{27} +3.11004 q^{28} -10.3333 q^{29} -3.27125 q^{30} -5.41158 q^{31} +1.00000 q^{32} -5.01780 q^{33} +1.75903 q^{34} +10.1737 q^{35} +1.00000 q^{36} +5.01681 q^{37} -7.20855 q^{38} +2.25689 q^{39} +3.27125 q^{40} +3.29171 q^{41} -3.11004 q^{42} -12.3131 q^{43} +5.01780 q^{44} +3.27125 q^{45} +4.20547 q^{46} -5.32237 q^{47} -1.00000 q^{48} +2.67235 q^{49} +5.70110 q^{50} -1.75903 q^{51} -2.25689 q^{52} -10.9467 q^{53} -1.00000 q^{54} +16.4145 q^{55} +3.11004 q^{56} +7.20855 q^{57} -10.3333 q^{58} +1.70199 q^{59} -3.27125 q^{60} +14.3333 q^{61} -5.41158 q^{62} +3.11004 q^{63} +1.00000 q^{64} -7.38284 q^{65} -5.01780 q^{66} -9.78502 q^{67} +1.75903 q^{68} -4.20547 q^{69} +10.1737 q^{70} -0.0747454 q^{71} +1.00000 q^{72} +8.00222 q^{73} +5.01681 q^{74} -5.70110 q^{75} -7.20855 q^{76} +15.6055 q^{77} +2.25689 q^{78} +7.81235 q^{79} +3.27125 q^{80} +1.00000 q^{81} +3.29171 q^{82} +6.06193 q^{83} -3.11004 q^{84} +5.75425 q^{85} -12.3131 q^{86} +10.3333 q^{87} +5.01780 q^{88} +7.54971 q^{89} +3.27125 q^{90} -7.01900 q^{91} +4.20547 q^{92} +5.41158 q^{93} -5.32237 q^{94} -23.5810 q^{95} -1.00000 q^{96} +7.00311 q^{97} +2.67235 q^{98} +5.01780 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 7 q^{2} - 7 q^{3} + 7 q^{4} + 6 q^{5} - 7 q^{6} + 3 q^{7} + 7 q^{8} + 7 q^{9} + 6 q^{10} - q^{11} - 7 q^{12} + 8 q^{13} + 3 q^{14} - 6 q^{15} + 7 q^{16} + 16 q^{17} + 7 q^{18} + 2 q^{19} + 6 q^{20}+ \cdots - q^{99}+O(q^{100}) $ 7 * q + 7 * q^2 - 7 * q^3 + 7 * q^4 + 6 * q^5 - 7 * q^6 + 3 * q^7 + 7 * q^8 + 7 * q^9 + 6 * q^10 - q^11 - 7 * q^12 + 8 * q^13 + 3 * q^14 - 6 * q^15 + 7 * q^16 + 16 * q^17 + 7 * q^18 + 2 * q^19 + 6 * q^20 - 3 * q^21 - q^22 + 8 * q^23 - 7 * q^24 + 19 * q^25 + 8 * q^26 - 7 * q^27 + 3 * q^28 + 4 * q^29 - 6 * q^30 + 11 * q^31 + 7 * q^32 + q^33 + 16 * q^34 + 7 * q^36 + 17 * q^37 + 2 * q^38 - 8 * q^39 + 6 * q^40 + 18 * q^41 - 3 * q^42 - q^43 - q^44 + 6 * q^45 + 8 * q^46 + 5 * q^47 - 7 * q^48 + 24 * q^49 + 19 * q^50 - 16 * q^51 + 8 * q^52 + 6 * q^53 - 7 * q^54 + 21 * q^55 + 3 * q^56 - 2 * q^57 + 4 * q^58 - 7 * q^59 - 6 * q^60 + 24 * q^61 + 11 * q^62 + 3 * q^63 + 7 * q^64 + 11 * q^65 + q^66 - 4 * q^67 + 16 * q^68 - 8 * q^69 - 7 * q^71 + 7 * q^72 + 28 * q^73 + 17 * q^74 - 19 * q^75 + 2 * q^76 - 2 * q^77 - 8 * q^78 + 6 * q^80 + 7 * q^81 + 18 * q^82 - 2 * q^83 - 3 * q^84 + 4 * q^85 - q^86 - 4 * q^87 - q^88 + 5 * q^89 + 6 * q^90 + 2 * q^91 + 8 * q^92 - 11 * q^93 + 5 * q^94 - 14 * q^95 - 7 * q^96 + 23 * q^97 + 24 * q^98 - q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	3.27125	1.46295	0.731475	−	0.681869i	$-0.238833\pi$
$5$	3.27125	1.46295	0.731475	+	0.681869i	$0.238833\pi$
$6$	−1.00000	−0.408248
$7$	3.11004	1.17548	0.587742	−	0.809048i	$-0.300017\pi$
$7$	3.11004	1.17548	0.587742	+	0.809048i	$0.300017\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.27125	1.03446
$11$	5.01780	1.51292	0.756461	−	0.654038i	$-0.226927\pi$
$11$	5.01780	1.51292	0.756461	+	0.654038i	$0.226927\pi$
$12$	−1.00000	−0.288675
$13$	−2.25689	−0.625947	−0.312974	−	0.949762i	$-0.601325\pi$
$13$	−2.25689	−0.625947	−0.312974	+	0.949762i	$0.601325\pi$
$14$	3.11004	0.831193
$15$	−3.27125	−0.844634
$16$	1.00000	0.250000
$17$	1.75903	0.426628	0.213314	−	0.976984i	$-0.431574\pi$
$17$	1.75903	0.426628	0.213314	+	0.976984i	$0.431574\pi$
$18$	1.00000	0.235702
$19$	−7.20855	−1.65376	−0.826878	−	0.562382i	$-0.809885\pi$
$19$	−7.20855	−1.65376	−0.826878	+	0.562382i	$0.809885\pi$
$20$	3.27125	0.731475
$21$	−3.11004	−0.678666
$22$	5.01780	1.06980
$23$	4.20547	0.876901	0.438451	−	0.898755i	$-0.355527\pi$
$23$	4.20547	0.876901	0.438451	+	0.898755i	$0.355527\pi$
$24$	−1.00000	−0.204124
$25$	5.70110	1.14022
$26$	−2.25689	−0.442612
$27$	−1.00000	−0.192450
$28$	3.11004	0.587742
$29$	−10.3333	−1.91885	−0.959423	−	0.281970i	$-0.909012\pi$
$29$	−10.3333	−1.91885	−0.959423	+	0.281970i	$0.909012\pi$
$30$	−3.27125	−0.597246
$31$	−5.41158	−0.971949	−0.485974	−	0.873973i	$-0.661535\pi$
$31$	−5.41158	−0.971949	−0.485974	+	0.873973i	$0.661535\pi$
$32$	1.00000	0.176777
$33$	−5.01780	−0.873486
$34$	1.75903	0.301672
$35$	10.1737	1.71967
$36$	1.00000	0.166667
$37$	5.01681	0.824759	0.412379	−	0.911012i	$-0.364698\pi$
$37$	5.01681	0.824759	0.412379	+	0.911012i	$0.364698\pi$
$38$	−7.20855	−1.16938
$39$	2.25689	0.361391
$40$	3.27125	0.517231
$41$	3.29171	0.514079	0.257039	−	0.966401i	$-0.417253\pi$
$41$	3.29171	0.514079	0.257039	+	0.966401i	$0.417253\pi$
$42$	−3.11004	−0.479890
$43$	−12.3131	−1.87773	−0.938863	−	0.344292i	$-0.888119\pi$
$43$	−12.3131	−1.87773	−0.938863	+	0.344292i	$0.888119\pi$
$44$	5.01780	0.756461
$45$	3.27125	0.487650
$46$	4.20547	0.620063
$47$	−5.32237	−0.776348	−0.388174	−	0.921586i	$-0.626894\pi$
$47$	−5.32237	−0.776348	−0.388174	+	0.921586i	$0.626894\pi$
$48$	−1.00000	−0.144338
$49$	2.67235	0.381764
$50$	5.70110	0.806257
$51$	−1.75903	−0.246314
$52$	−2.25689	−0.312974
$53$	−10.9467	−1.50364	−0.751822	−	0.659366i	$-0.770825\pi$
$53$	−10.9467	−1.50364	−0.751822	+	0.659366i	$0.770825\pi$
$54$	−1.00000	−0.136083
$55$	16.4145	2.21333
$56$	3.11004	0.415597
$57$	7.20855	0.954796
$58$	−10.3333	−1.35683
$59$	1.70199	0.221580	0.110790	−	0.993844i	$-0.464662\pi$
$59$	1.70199	0.221580	0.110790	+	0.993844i	$0.464662\pi$
$60$	−3.27125	−0.422317
$61$	14.3333	1.83519	0.917596	−	0.397515i	$-0.130127\pi$
$61$	14.3333	1.83519	0.917596	+	0.397515i	$0.130127\pi$
$62$	−5.41158	−0.687271
$63$	3.11004	0.391828
$64$	1.00000	0.125000
$65$	−7.38284	−0.915729
$66$	−5.01780	−0.617648
$67$	−9.78502	−1.19543	−0.597716	−	0.801708i	$-0.703925\pi$
$67$	−9.78502	−1.19543	−0.597716	+	0.801708i	$0.703925\pi$
$68$	1.75903	0.213314
$69$	−4.20547	−0.506279
$70$	10.1737	1.21599
$71$	−0.0747454	−0.00887065	−0.00443532	−	0.999990i	$-0.501412\pi$
$71$	−0.0747454	−0.00887065	−0.00443532	+	0.999990i	$0.501412\pi$
$72$	1.00000	0.117851
$73$	8.00222	0.936589	0.468295	−	0.883572i	$-0.344869\pi$
$73$	8.00222	0.936589	0.468295	+	0.883572i	$0.344869\pi$
$74$	5.01681	0.583192
$75$	−5.70110	−0.658306
$76$	−7.20855	−0.826878
$77$	15.6055	1.77842
$78$	2.25689	0.255542
$79$	7.81235	0.878957	0.439479	−	0.898253i	$-0.355163\pi$
$79$	7.81235	0.878957	0.439479	+	0.898253i	$0.355163\pi$
$80$	3.27125	0.365737
$81$	1.00000	0.111111
$82$	3.29171	0.363509
$83$	6.06193	0.665383	0.332691	−	0.943036i	$-0.392043\pi$
$83$	6.06193	0.665383	0.332691	+	0.943036i	$0.392043\pi$
$84$	−3.11004	−0.339333
$85$	5.75425	0.624136
$86$	−12.3131	−1.32775
$87$	10.3333	1.10785
$88$	5.01780	0.534899
$89$	7.54971	0.800268	0.400134	−	0.916457i	$-0.368964\pi$
$89$	7.54971	0.800268	0.400134	+	0.916457i	$0.368964\pi$
$90$	3.27125	0.344820
$91$	−7.01900	−0.735791
$92$	4.20547	0.438451
$93$	5.41158	0.561155
$94$	−5.32237	−0.548961
$95$	−23.5810	−2.41936
$96$	−1.00000	−0.102062
$97$	7.00311	0.711058	0.355529	−	0.934665i	$-0.384301\pi$
$97$	7.00311	0.711058	0.355529	+	0.934665i	$0.384301\pi$
$98$	2.67235	0.269948
$99$	5.01780	0.504308
$100$	5.70110	0.570110
$101$	10.7033	1.06502	0.532510	−	0.846424i	$-0.321249\pi$
$101$	10.7033	1.06502	0.532510	+	0.846424i	$0.321249\pi$
$102$	−1.75903	−0.174170
$103$	10.1428	0.999397	0.499698	−	0.866199i	$-0.333444\pi$
$103$	10.1428	0.999397	0.499698	+	0.866199i	$0.333444\pi$
$104$	−2.25689	−0.221306
$105$	−10.1737	−0.992854
$106$	−10.9467	−1.06324
$107$	−1.78715	−0.172770	−0.0863851	−	0.996262i	$-0.527532\pi$
$107$	−1.78715	−0.172770	−0.0863851	+	0.996262i	$0.527532\pi$
$108$	−1.00000	−0.0962250
$109$	−12.5753	−1.20449	−0.602246	−	0.798311i	$-0.705727\pi$
$109$	−12.5753	−1.20449	−0.602246	+	0.798311i	$0.705727\pi$
$110$	16.4145	1.56506
$111$	−5.01681	−0.476175
$112$	3.11004	0.293871
$113$	−16.2276	−1.52656	−0.763280	−	0.646068i	$-0.776412\pi$
$113$	−16.2276	−1.52656	−0.763280	+	0.646068i	$0.776412\pi$
$114$	7.20855	0.675143
$115$	13.7572	1.28286
$116$	−10.3333	−0.959423
$117$	−2.25689	−0.208649
$118$	1.70199	0.156681
$119$	5.47067	0.501495
$120$	−3.27125	−0.298623
$121$	14.1783	1.28893
$122$	14.3333	1.29768
$123$	−3.29171	−0.296804
$124$	−5.41158	−0.485974
$125$	2.29347	0.205134
$126$	3.11004	0.277064
$127$	−14.9452	−1.32617	−0.663086	−	0.748543i	$-0.730754\pi$
$127$	−14.9452	−1.32617	−0.663086	+	0.748543i	$0.730754\pi$
$128$	1.00000	0.0883883
$129$	12.3131	1.08411
$130$	−7.38284	−0.647518
$131$	−8.50744	−0.743298	−0.371649	−	0.928373i	$-0.621208\pi$
$131$	−8.50744	−0.743298	−0.371649	+	0.928373i	$0.621208\pi$
$132$	−5.01780	−0.436743
$133$	−22.4189	−1.94396
$134$	−9.78502	−0.845297
$135$	−3.27125	−0.281545
$136$	1.75903	0.150836
$137$	3.64306	0.311248	0.155624	−	0.987816i	$-0.450261\pi$
$137$	3.64306	0.311248	0.155624	+	0.987816i	$0.450261\pi$
$138$	−4.20547	−0.357993
$139$	−17.2902	−1.46654	−0.733268	−	0.679940i	$-0.762006\pi$
$139$	−17.2902	−1.46654	−0.733268	+	0.679940i	$0.762006\pi$
$140$	10.1737	0.859837
$141$	5.32237	0.448225
$142$	−0.0747454	−0.00627250
$143$	−11.3246	−0.947010
$144$	1.00000	0.0833333
$145$	−33.8029	−2.80717
$146$	8.00222	0.662269
$147$	−2.67235	−0.220411
$148$	5.01681	0.412379
$149$	11.9004	0.974916	0.487458	−	0.873146i	$-0.337924\pi$
$149$	11.9004	0.974916	0.487458	+	0.873146i	$0.337924\pi$
$150$	−5.70110	−0.465493
$151$	14.0944	1.14699	0.573495	−	0.819209i	$-0.305587\pi$
$151$	14.0944	1.14699	0.573495	+	0.819209i	$0.305587\pi$
$152$	−7.20855	−0.584691
$153$	1.75903	0.142209
$154$	15.6055	1.25753
$155$	−17.7027	−1.42191
$156$	2.25689	0.180695
$157$	6.30275	0.503014	0.251507	−	0.967855i	$-0.419074\pi$
$157$	6.30275	0.503014	0.251507	+	0.967855i	$0.419074\pi$
$158$	7.81235	0.621517
$159$	10.9467	0.868130
$160$	3.27125	0.258615
$161$	13.0792	1.03078
$162$	1.00000	0.0785674
$163$	−3.84555	−0.301206	−0.150603	−	0.988594i	$-0.548122\pi$
$163$	−3.84555	−0.301206	−0.150603	+	0.988594i	$0.548122\pi$
$164$	3.29171	0.257039
$165$	−16.4145	−1.27787
$166$	6.06193	0.470497
$167$	−7.21959	−0.558669	−0.279334	−	0.960194i	$-0.590114\pi$
$167$	−7.21959	−0.558669	−0.279334	+	0.960194i	$0.590114\pi$
$168$	−3.11004	−0.239945
$169$	−7.90647	−0.608190
$170$	5.75425	0.441331
$171$	−7.20855	−0.551252
$172$	−12.3131	−0.938863
$173$	8.24128	0.626573	0.313287	−	0.949659i	$-0.398570\pi$
$173$	8.24128	0.626573	0.313287	+	0.949659i	$0.398570\pi$
$174$	10.3333	0.783366
$175$	17.7306	1.34031
$176$	5.01780	0.378231
$177$	−1.70199	−0.127929
$178$	7.54971	0.565875
$179$	1.76632	0.132021	0.0660105	−	0.997819i	$-0.478973\pi$
$179$	1.76632	0.132021	0.0660105	+	0.997819i	$0.478973\pi$
$180$	3.27125	0.243825
$181$	21.0143	1.56198	0.780990	−	0.624544i	$-0.214715\pi$
$181$	21.0143	1.56198	0.780990	+	0.624544i	$0.214715\pi$
$182$	−7.01900	−0.520283
$183$	−14.3333	−1.05955
$184$	4.20547	0.310031
$185$	16.4113	1.20658
$186$	5.41158	0.396796
$187$	8.82648	0.645456
$188$	−5.32237	−0.388174
$189$	−3.11004	−0.226222
$190$	−23.5810	−1.71075
$191$	−16.3741	−1.18479	−0.592394	−	0.805648i	$-0.701817\pi$
$191$	−16.3741	−1.18479	−0.592394	+	0.805648i	$0.701817\pi$
$192$	−1.00000	−0.0721688
$193$	19.9818	1.43832	0.719162	−	0.694843i	$-0.244526\pi$
$193$	19.9818	1.43832	0.719162	+	0.694843i	$0.244526\pi$
$194$	7.00311	0.502794
$195$	7.38284	0.528697
$196$	2.67235	0.190882
$197$	−27.9554	−1.99174	−0.995871	−	0.0907781i	$-0.971065\pi$
$197$	−27.9554	−1.99174	−0.995871	+	0.0907781i	$0.971065\pi$
$198$	5.01780	0.356599
$199$	−4.56995	−0.323955	−0.161977	−	0.986794i	$-0.551787\pi$
$199$	−4.56995	−0.323955	−0.161977	+	0.986794i	$0.551787\pi$
$200$	5.70110	0.403129
$201$	9.78502	0.690182
$202$	10.7033	0.753083
$203$	−32.1370	−2.25557
$204$	−1.75903	−0.123157
$205$	10.7680	0.752071
$206$	10.1428	0.706680
$207$	4.20547	0.292300
$208$	−2.25689	−0.156487
$209$	−36.1711	−2.50200
$210$	−10.1737	−0.702054
$211$	0.0340811	0.00234624	0.00117312	−	0.999999i	$-0.499627\pi$
$211$	0.0340811	0.00234624	0.00117312	+	0.999999i	$0.499627\pi$
$212$	−10.9467	−0.751822
$213$	0.0747454	0.00512147
$214$	−1.78715	−0.122167
$215$	−40.2792	−2.74702
$216$	−1.00000	−0.0680414
$217$	−16.8302	−1.14251
$218$	−12.5753	−0.851704
$219$	−8.00222	−0.540740
$220$	16.4145	1.10666
$221$	−3.96994	−0.267047
$222$	−5.01681	−0.336706
$223$	−1.00000	−0.0669650
$223$	−1.00000	−0.0669650
$224$	3.11004	0.207798
$225$	5.70110	0.380073
$226$	−16.2276	−1.07944
$227$	15.4023	1.02228	0.511142	−	0.859496i	$-0.329223\pi$
$227$	15.4023	1.02228	0.511142	+	0.859496i	$0.329223\pi$
$228$	7.20855	0.477398
$229$	−2.84010	−0.187679	−0.0938396	−	0.995587i	$-0.529914\pi$
$229$	−2.84010	−0.187679	−0.0938396	+	0.995587i	$0.529914\pi$
$230$	13.7572	0.907120
$231$	−15.6055	−1.02677
$232$	−10.3333	−0.678415
$233$	−4.45436	−0.291815	−0.145907	−	0.989298i	$-0.546610\pi$
$233$	−4.45436	−0.291815	−0.145907	+	0.989298i	$0.546610\pi$
$234$	−2.25689	−0.147537
$235$	−17.4108	−1.13576
$236$	1.70199	0.110790
$237$	−7.81235	−0.507466
$238$	5.47067	0.354611
$239$	−15.3887	−0.995411	−0.497705	−	0.867346i	$-0.665824\pi$
$239$	−15.3887	−0.995411	−0.497705	+	0.867346i	$0.665824\pi$
$240$	−3.27125	−0.211158
$241$	7.60381	0.489805	0.244902	−	0.969548i	$-0.421244\pi$
$241$	7.60381	0.489805	0.244902	+	0.969548i	$0.421244\pi$
$242$	14.1783	0.911415
$243$	−1.00000	−0.0641500
$244$	14.3333	0.917596
$245$	8.74192	0.558501
$246$	−3.29171	−0.209872
$247$	16.2689	1.03516
$248$	−5.41158	−0.343636
$249$	−6.06193	−0.384159
$250$	2.29347	0.145052
$251$	−9.96260	−0.628834	−0.314417	−	0.949285i	$-0.601809\pi$
$251$	−9.96260	−0.628834	−0.314417	+	0.949285i	$0.601809\pi$
$252$	3.11004	0.195914
$253$	21.1022	1.32668
$254$	−14.9452	−0.937745
$255$	−5.75425	−0.360345
$256$	1.00000	0.0625000
$257$	24.1357	1.50554	0.752772	−	0.658281i	$-0.228716\pi$
$257$	24.1357	1.50554	0.752772	+	0.658281i	$0.228716\pi$
$258$	12.3131	0.766578
$259$	15.6025	0.969491
$260$	−7.38284	−0.457865
$261$	−10.3333	−0.639616
$262$	−8.50744	−0.525591
$263$	−16.9293	−1.04391	−0.521953	−	0.852974i	$-0.674796\pi$
$263$	−16.9293	−1.04391	−0.521953	+	0.852974i	$0.674796\pi$
$264$	−5.01780	−0.308824
$265$	−35.8094	−2.19976
$266$	−22.4189	−1.37459
$267$	−7.54971	−0.462035
$268$	−9.78502	−0.597716
$269$	−7.14497	−0.435637	−0.217818	−	0.975989i	$-0.569894\pi$
$269$	−7.14497	−0.435637	−0.217818	+	0.975989i	$0.569894\pi$
$270$	−3.27125	−0.199082
$271$	−1.20312	−0.0730846	−0.0365423	−	0.999332i	$-0.511634\pi$
$271$	−1.20312	−0.0730846	−0.0365423	+	0.999332i	$0.511634\pi$
$272$	1.75903	0.106657
$273$	7.01900	0.424809
$274$	3.64306	0.220085
$275$	28.6070	1.72506
$276$	−4.20547	−0.253140
$277$	24.9595	1.49967	0.749834	−	0.661626i	$-0.230133\pi$
$277$	24.9595	1.49967	0.749834	+	0.661626i	$0.230133\pi$
$278$	−17.2902	−1.03700
$279$	−5.41158	−0.323983
$280$	10.1737	0.607996
$281$	−0.597109	−0.0356206	−0.0178103	−	0.999841i	$-0.505669\pi$
$281$	−0.597109	−0.0356206	−0.0178103	+	0.999841i	$0.505669\pi$
$282$	5.32237	0.316943
$283$	11.4252	0.679157	0.339578	−	0.940578i	$-0.389716\pi$
$283$	11.4252	0.679157	0.339578	+	0.940578i	$0.389716\pi$
$284$	−0.0747454	−0.00443532
$285$	23.5810	1.39682
$286$	−11.3246	−0.669637
$287$	10.2374	0.604292
$288$	1.00000	0.0589256
$289$	−13.9058	−0.817988
$290$	−33.8029	−1.98497
$291$	−7.00311	−0.410530
$292$	8.00222	0.468295
$293$	18.6579	1.09000	0.545002	−	0.838435i	$-0.316529\pi$
$293$	18.6579	1.09000	0.545002	+	0.838435i	$0.316529\pi$
$294$	−2.67235	−0.155854
$295$	5.56764	0.324160
$296$	5.01681	0.291596
$297$	−5.01780	−0.291162
$298$	11.9004	0.689370
$299$	−9.49126	−0.548894
$300$	−5.70110	−0.329153
$301$	−38.2941	−2.20724
$302$	14.0944	0.811044
$303$	−10.7033	−0.614890
$304$	−7.20855	−0.413439
$305$	46.8879	2.68479
$306$	1.75903	0.100557
$307$	−6.04278	−0.344880	−0.172440	−	0.985020i	$-0.555165\pi$
$307$	−6.04278	−0.344880	−0.172440	+	0.985020i	$0.555165\pi$
$308$	15.6055	0.889208
$309$	−10.1428	−0.577002
$310$	−17.7027	−1.00544
$311$	−23.0971	−1.30972	−0.654858	−	0.755752i	$-0.727272\pi$
$311$	−23.0971	−1.30972	−0.654858	+	0.755752i	$0.727272\pi$
$312$	2.25689	0.127771
$313$	15.4613	0.873927	0.436963	−	0.899479i	$-0.356054\pi$
$313$	15.4613	0.873927	0.436963	+	0.899479i	$0.356054\pi$
$314$	6.30275	0.355685
$315$	10.1737	0.573225
$316$	7.81235	0.439479
$317$	−23.5816	−1.32447	−0.662236	−	0.749295i	$-0.730393\pi$
$317$	−23.5816	−1.32447	−0.662236	+	0.749295i	$0.730393\pi$
$318$	10.9467	0.613860
$319$	−51.8504	−2.90307
$320$	3.27125	0.182869
$321$	1.78715	0.0997490
$322$	13.0792	0.728874
$323$	−12.6801	−0.705539
$324$	1.00000	0.0555556
$325$	−12.8667	−0.713718
$326$	−3.84555	−0.212985
$327$	12.5753	0.695413
$328$	3.29171	0.181754
$329$	−16.5528	−0.912585
$330$	−16.4145	−0.903588
$331$	3.49155	0.191913	0.0959565	−	0.995386i	$-0.469409\pi$
$331$	3.49155	0.191913	0.0959565	+	0.995386i	$0.469409\pi$
$332$	6.06193	0.332691
$333$	5.01681	0.274920
$334$	−7.21959	−0.395038
$335$	−32.0093	−1.74885
$336$	−3.11004	−0.169667
$337$	33.8121	1.84187	0.920933	−	0.389722i	$-0.127429\pi$
$337$	33.8121	1.84187	0.920933	+	0.389722i	$0.127429\pi$
$338$	−7.90647	−0.430055
$339$	16.2276	0.881360
$340$	5.75425	0.312068
$341$	−27.1542	−1.47048
$342$	−7.20855	−0.389794
$343$	−13.4592	−0.726727
$344$	−12.3131	−0.663876
$345$	−13.7572	−0.740660
$346$	8.24128	0.443054
$347$	−7.87613	−0.422813	−0.211407	−	0.977398i	$-0.567804\pi$
$347$	−7.87613	−0.422813	−0.211407	+	0.977398i	$0.567804\pi$
$348$	10.3333	0.553923
$349$	−24.1375	−1.29205	−0.646024	−	0.763317i	$-0.723570\pi$
$349$	−24.1375	−1.29205	−0.646024	+	0.763317i	$0.723570\pi$
$350$	17.7306	0.947743
$351$	2.25689	0.120464
$352$	5.01780	0.267449
$353$	7.82351	0.416403	0.208202	−	0.978086i	$-0.433239\pi$
$353$	7.82351	0.416403	0.208202	+	0.978086i	$0.433239\pi$
$354$	−1.70199	−0.0904597
$355$	−0.244511	−0.0129773
$356$	7.54971	0.400134
$357$	−5.47067	−0.289538
$358$	1.76632	0.0933529
$359$	5.84778	0.308634	0.154317	−	0.988021i	$-0.450682\pi$
$359$	5.84778	0.308634	0.154317	+	0.988021i	$0.450682\pi$
$360$	3.27125	0.172410
$361$	32.9632	1.73491
$362$	21.0143	1.10449
$363$	−14.1783	−0.744167
$364$	−7.01900	−0.367896
$365$	26.1773	1.37018
$366$	−14.3333	−0.749214
$367$	22.2229	1.16003	0.580013	−	0.814607i	$-0.303048\pi$
$367$	22.2229	1.16003	0.580013	+	0.814607i	$0.303048\pi$
$368$	4.20547	0.219225
$369$	3.29171	0.171360
$370$	16.4113	0.853181
$371$	−34.0447	−1.76751
$372$	5.41158	0.280577
$373$	−34.0109	−1.76102	−0.880509	−	0.474029i	$-0.842799\pi$
$373$	−34.0109	−1.76102	−0.880509	+	0.474029i	$0.842799\pi$
$374$	8.82648	0.456406
$375$	−2.29347	−0.118434
$376$	−5.32237	−0.274480
$377$	23.3211	1.20110
$378$	−3.11004	−0.159963
$379$	−10.3035	−0.529257	−0.264628	−	0.964350i	$-0.585249\pi$
$379$	−10.3035	−0.529257	−0.264628	+	0.964350i	$0.585249\pi$
$380$	−23.5810	−1.20968
$381$	14.9452	0.765666
$382$	−16.3741	−0.837772
$383$	6.63837	0.339205	0.169602	−	0.985513i	$-0.445752\pi$
$383$	6.63837	0.339205	0.169602	+	0.985513i	$0.445752\pi$
$384$	−1.00000	−0.0510310
$385$	51.0497	2.60173
$386$	19.9818	1.01705
$387$	−12.3131	−0.625908
$388$	7.00311	0.355529
$389$	20.4264	1.03566	0.517830	−	0.855483i	$-0.326740\pi$
$389$	20.4264	1.03566	0.517830	+	0.855483i	$0.326740\pi$
$390$	7.38284	0.373845
$391$	7.39756	0.374111
$392$	2.67235	0.134974
$393$	8.50744	0.429144
$394$	−27.9554	−1.40837
$395$	25.5562	1.28587
$396$	5.01780	0.252154
$397$	37.9844	1.90638	0.953192	−	0.302367i	$-0.0977768\pi$
$397$	37.9844	1.90638	0.953192	+	0.302367i	$0.0977768\pi$
$398$	−4.56995	−0.229071
$399$	22.4189	1.12235
$400$	5.70110	0.285055
$401$	−4.37080	−0.218268	−0.109134	−	0.994027i	$-0.534808\pi$
$401$	−4.37080	−0.218268	−0.109134	+	0.994027i	$0.534808\pi$
$402$	9.78502	0.488033
$403$	12.2133	0.608389
$404$	10.7033	0.532510
$405$	3.27125	0.162550
$406$	−32.1370	−1.59493
$407$	25.1733	1.24780
$408$	−1.75903	−0.0870852
$409$	−13.8293	−0.683817	−0.341908	−	0.939733i	$-0.611073\pi$
$409$	−13.8293	−0.683817	−0.341908	+	0.939733i	$0.611073\pi$
$410$	10.7680	0.531795
$411$	−3.64306	−0.179699
$412$	10.1428	0.499698
$413$	5.29325	0.260464
$414$	4.20547	0.206688
$415$	19.8301	0.973421
$416$	−2.25689	−0.110653
$417$	17.2902	0.846705
$418$	−36.1711	−1.76918
$419$	−15.7703	−0.770429	−0.385215	−	0.922827i	$-0.625873\pi$
$419$	−15.7703	−0.770429	−0.385215	+	0.922827i	$0.625873\pi$
$420$	−10.1737	−0.496427
$421$	40.1185	1.95526	0.977628	−	0.210341i	$-0.0674575\pi$
$421$	40.1185	1.95526	0.977628	+	0.210341i	$0.0674575\pi$
$422$	0.0340811	0.00165904
$423$	−5.32237	−0.258783
$424$	−10.9467	−0.531619
$425$	10.0284	0.486450
$426$	0.0747454	0.00362143
$427$	44.5771	2.15724
$428$	−1.78715	−0.0863851
$429$	11.3246	0.546757
$430$	−40.2792	−1.94243
$431$	19.6960	0.948722	0.474361	−	0.880330i	$-0.342679\pi$
$431$	19.6960	0.948722	0.474361	+	0.880330i	$0.342679\pi$
$432$	−1.00000	−0.0481125
$433$	−8.75740	−0.420854	−0.210427	−	0.977610i	$-0.567485\pi$
$433$	−8.75740	−0.420854	−0.210427	+	0.977610i	$0.567485\pi$
$434$	−16.8302	−0.807877
$435$	33.8029	1.62072
$436$	−12.5753	−0.602246
$437$	−30.3154	−1.45018
$438$	−8.00222	−0.382361
$439$	−11.4726	−0.547559	−0.273779	−	0.961793i	$-0.588274\pi$
$439$	−11.4726	−0.547559	−0.273779	+	0.961793i	$0.588274\pi$
$440$	16.4145	0.782530
$441$	2.67235	0.127255
$442$	−3.96994	−0.188831
$443$	37.1871	1.76681	0.883405	−	0.468610i	$-0.155245\pi$
$443$	37.1871	1.76681	0.883405	+	0.468610i	$0.155245\pi$
$444$	−5.01681	−0.238087
$445$	24.6970	1.17075
$446$	−1.00000	−0.0473514
$447$	−11.9004	−0.562868
$448$	3.11004	0.146936
$449$	−15.9340	−0.751974	−0.375987	−	0.926625i	$-0.622696\pi$
$449$	−15.9340	−0.751974	−0.375987	+	0.926625i	$0.622696\pi$
$450$	5.70110	0.268752
$451$	16.5171	0.777762
$452$	−16.2276	−0.763280
$453$	−14.0944	−0.662215
$454$	15.4023	0.722864
$455$	−22.9609	−1.07643
$456$	7.20855	0.337571
$457$	7.42897	0.347512	0.173756	−	0.984789i	$-0.444410\pi$
$457$	7.42897	0.347512	0.173756	+	0.984789i	$0.444410\pi$
$458$	−2.84010	−0.132709
$459$	−1.75903	−0.0821047
$460$	13.7572	0.641431
$461$	−28.5862	−1.33139	−0.665695	−	0.746224i	$-0.731865\pi$
$461$	−28.5862	−1.33139	−0.665695	+	0.746224i	$0.731865\pi$
$462$	−15.6055	−0.726036
$463$	24.1021	1.12012	0.560059	−	0.828452i	$-0.310778\pi$
$463$	24.1021	1.12012	0.560059	+	0.828452i	$0.310778\pi$
$464$	−10.3333	−0.479712
$465$	17.7027	0.820941
$466$	−4.45436	−0.206344
$467$	20.0021	0.925585	0.462792	−	0.886467i	$-0.346848\pi$
$467$	20.0021	0.925585	0.462792	+	0.886467i	$0.346848\pi$
$468$	−2.25689	−0.104325
$469$	−30.4318	−1.40521
$470$	−17.4108	−0.803101
$471$	−6.30275	−0.290415
$472$	1.70199	0.0783404
$473$	−61.7845	−2.84085
$474$	−7.81235	−0.358833
$475$	−41.0967	−1.88564
$476$	5.47067	0.250748
$477$	−10.9467	−0.501215
$478$	−15.3887	−0.703862
$479$	−13.3758	−0.611156	−0.305578	−	0.952167i	$-0.598850\pi$
$479$	−13.3758	−0.611156	−0.305578	+	0.952167i	$0.598850\pi$
$480$	−3.27125	−0.149312
$481$	−11.3224	−0.516255
$482$	7.60381	0.346344
$483$	−13.0792	−0.595123
$484$	14.1783	0.644467
$485$	22.9090	1.04024
$486$	−1.00000	−0.0453609
$487$	−25.4804	−1.15463	−0.577314	−	0.816522i	$-0.695899\pi$
$487$	−25.4804	−1.15463	−0.577314	+	0.816522i	$0.695899\pi$
$488$	14.3333	0.648838
$489$	3.84555	0.173902
$490$	8.74192	0.394920
$491$	22.4454	1.01295	0.506473	−	0.862256i	$-0.330949\pi$
$491$	22.4454	1.01295	0.506473	+	0.862256i	$0.330949\pi$
$492$	−3.29171	−0.148402
$493$	−18.1766	−0.818635
$494$	16.2689	0.731972
$495$	16.4145	0.737776
$496$	−5.41158	−0.242987
$497$	−0.232461	−0.0104273
$498$	−6.06193	−0.271641
$499$	34.9827	1.56604	0.783021	−	0.621995i	$-0.213678\pi$
$499$	34.9827	1.56604	0.783021	+	0.621995i	$0.213678\pi$
$500$	2.29347	0.102567
$501$	7.21959	0.322547
$502$	−9.96260	−0.444653
$503$	10.9861	0.489845	0.244922	−	0.969543i	$-0.421238\pi$
$503$	10.9861	0.489845	0.244922	+	0.969543i	$0.421238\pi$
$504$	3.11004	0.138532
$505$	35.0133	1.55807
$506$	21.1022	0.938107
$507$	7.90647	0.351139
$508$	−14.9452	−0.663086
$509$	19.3410	0.857275	0.428637	−	0.903477i	$-0.358994\pi$
$509$	19.3410	0.857275	0.428637	+	0.903477i	$0.358994\pi$
$510$	−5.75425	−0.254802
$511$	24.8872	1.10095
$512$	1.00000	0.0441942
$513$	7.20855	0.318265
$514$	24.1357	1.06458
$515$	33.1796	1.46207
$516$	12.3131	0.542053
$517$	−26.7066	−1.17455
$518$	15.6025	0.685534
$519$	−8.24128	−0.361752
$520$	−7.38284	−0.323759
$521$	−19.1494	−0.838949	−0.419474	−	0.907767i	$-0.637786\pi$
$521$	−19.1494	−0.838949	−0.419474	+	0.907767i	$0.637786\pi$
$522$	−10.3333	−0.452277
$523$	31.3698	1.37170	0.685852	−	0.727741i	$-0.259430\pi$
$523$	31.3698	1.37170	0.685852	+	0.727741i	$0.259430\pi$
$524$	−8.50744	−0.371649
$525$	−17.7306	−0.773829
$526$	−16.9293	−0.738153
$527$	−9.51915	−0.414661
$528$	−5.01780	−0.218372
$529$	−5.31403	−0.231045
$530$	−35.8094	−1.55546
$531$	1.70199	0.0738600
$532$	−22.4189	−0.971982
$533$	−7.42902	−0.321786
$534$	−7.54971	−0.326708
$535$	−5.84622	−0.252754
$536$	−9.78502	−0.422649
$537$	−1.76632	−0.0762224
$538$	−7.14497	−0.308042
$539$	13.4093	0.577579
$540$	−3.27125	−0.140772
$541$	−35.5504	−1.52843	−0.764215	−	0.644961i	$-0.776873\pi$
$541$	−35.5504	−1.52843	−0.764215	+	0.644961i	$0.776873\pi$
$542$	−1.20312	−0.0516786
$543$	−21.0143	−0.901809
$544$	1.75903	0.0754180
$545$	−41.1369	−1.76211
$546$	7.01900	0.300386
$547$	−4.50929	−0.192803	−0.0964016	−	0.995343i	$-0.530733\pi$
$547$	−4.50929	−0.192803	−0.0964016	+	0.995343i	$0.530733\pi$
$548$	3.64306	0.155624
$549$	14.3333	0.611731
$550$	28.6070	1.21980
$551$	74.4882	3.17330
$552$	−4.20547	−0.178997
$553$	24.2967	1.03320
$554$	24.9595	1.06043
$555$	−16.4113	−0.696619
$556$	−17.2902	−0.733268
$557$	8.72524	0.369700	0.184850	−	0.982767i	$-0.440820\pi$
$557$	8.72524	0.369700	0.184850	+	0.982767i	$0.440820\pi$
$558$	−5.41158	−0.229090
$559$	27.7892	1.17536
$560$	10.1737	0.429918
$561$	−8.82648	−0.372654
$562$	−0.597109	−0.0251875
$563$	−11.5480	−0.486688	−0.243344	−	0.969940i	$-0.578244\pi$
$563$	−11.5480	−0.486688	−0.243344	+	0.969940i	$0.578244\pi$
$564$	5.32237	0.224112
$565$	−53.0845	−2.23328
$566$	11.4252	0.480236
$567$	3.11004	0.130609
$568$	−0.0747454	−0.00313625
$569$	−21.5937	−0.905255	−0.452628	−	0.891700i	$-0.649513\pi$
$569$	−21.5937	−0.905255	−0.452628	+	0.891700i	$0.649513\pi$
$570$	23.5810	0.987700
$571$	3.77657	0.158044	0.0790222	−	0.996873i	$-0.474820\pi$
$571$	3.77657	0.158044	0.0790222	+	0.996873i	$0.474820\pi$
$572$	−11.3246	−0.473505
$573$	16.3741	0.684038
$574$	10.2374	0.427299
$575$	23.9758	0.999860
$576$	1.00000	0.0416667
$577$	2.70883	0.112770	0.0563851	−	0.998409i	$-0.482043\pi$
$577$	2.70883	0.112770	0.0563851	+	0.998409i	$0.482043\pi$
$578$	−13.9058	−0.578405
$579$	−19.9818	−0.830417
$580$	−33.8029	−1.40359
$581$	18.8528	0.782147
$582$	−7.00311	−0.290288
$583$	−54.9283	−2.27490
$584$	8.00222	0.331134
$585$	−7.38284	−0.305243
$586$	18.6579	0.770749
$587$	−24.8743	−1.02667	−0.513337	−	0.858187i	$-0.671591\pi$
$587$	−24.8743	−1.02667	−0.513337	+	0.858187i	$0.671591\pi$
$588$	−2.67235	−0.110206
$589$	39.0097	1.60737
$590$	5.56764	0.229216
$591$	27.9554	1.14993
$592$	5.01681	0.206190
$593$	14.6929	0.603365	0.301683	−	0.953408i	$-0.402452\pi$
$593$	14.6929	0.603365	0.301683	+	0.953408i	$0.402452\pi$
$594$	−5.01780	−0.205883
$595$	17.8959	0.733662
$596$	11.9004	0.487458
$597$	4.56995	0.187035
$598$	−9.49126	−0.388127
$599$	−20.1347	−0.822683	−0.411342	−	0.911481i	$-0.634940\pi$
$599$	−20.1347	−0.822683	−0.411342	+	0.911481i	$0.634940\pi$
$600$	−5.70110	−0.232746
$601$	−4.29457	−0.175179	−0.0875896	−	0.996157i	$-0.527916\pi$
$601$	−4.29457	−0.175179	−0.0875896	+	0.996157i	$0.527916\pi$
$602$	−38.2941	−1.56075
$603$	−9.78502	−0.398477
$604$	14.0944	0.573495
$605$	46.3808	1.88565
$606$	−10.7033	−0.434793
$607$	−10.0890	−0.409501	−0.204750	−	0.978814i	$-0.565638\pi$
$607$	−10.0890	−0.409501	−0.204750	+	0.978814i	$0.565638\pi$
$608$	−7.20855	−0.292345
$609$	32.1370	1.30226
$610$	46.8879	1.89843
$611$	12.0120	0.485953
$612$	1.75903	0.0711047
$613$	−11.9776	−0.483771	−0.241886	−	0.970305i	$-0.577766\pi$
$613$	−11.9776	−0.483771	−0.241886	+	0.970305i	$0.577766\pi$
$614$	−6.04278	−0.243867
$615$	−10.7680	−0.434209
$616$	15.6055	0.628765
$617$	−11.1459	−0.448716	−0.224358	−	0.974507i	$-0.572029\pi$
$617$	−11.1459	−0.448716	−0.224358	+	0.974507i	$0.572029\pi$
$618$	−10.1428	−0.408002
$619$	−39.8046	−1.59988	−0.799940	−	0.600080i	$-0.795135\pi$
$619$	−39.8046	−1.59988	−0.799940	+	0.600080i	$0.795135\pi$
$620$	−17.7027	−0.710956
$621$	−4.20547	−0.168760
$622$	−23.0971	−0.926109
$623$	23.4799	0.940703
$624$	2.25689	0.0903477
$625$	−21.0030	−0.840119
$626$	15.4613	0.617960
$627$	36.1711	1.44453
$628$	6.30275	0.251507
$629$	8.82474	0.351865
$630$	10.1737	0.405331
$631$	40.7835	1.62356	0.811782	−	0.583961i	$-0.198498\pi$
$631$	40.7835	1.62356	0.811782	+	0.583961i	$0.198498\pi$
$632$	7.81235	0.310758
$633$	−0.0340811	−0.00135460
$634$	−23.5816	−0.936544
$635$	−48.8895	−1.94012
$636$	10.9467	0.434065
$637$	−6.03118	−0.238964
$638$	−51.8504	−2.05278
$639$	−0.0747454	−0.00295688
$640$	3.27125	0.129308
$641$	−35.4113	−1.39866	−0.699331	−	0.714798i	$-0.746519\pi$
$641$	−35.4113	−1.39866	−0.699331	+	0.714798i	$0.746519\pi$
$642$	1.78715	0.0705332
$643$	33.2796	1.31242	0.656209	−	0.754579i	$-0.272159\pi$
$643$	33.2796	1.31242	0.656209	+	0.754579i	$0.272159\pi$
$644$	13.0792	0.515392
$645$	40.2792	1.58599
$646$	−12.6801	−0.498892
$647$	31.1506	1.22466	0.612329	−	0.790603i	$-0.290233\pi$
$647$	31.1506	1.22466	0.612329	+	0.790603i	$0.290233\pi$
$648$	1.00000	0.0392837
$649$	8.54024	0.335234
$650$	−12.8667	−0.504675
$651$	16.8302	0.659629
$652$	−3.84555	−0.150603
$653$	48.7883	1.90923	0.954617	−	0.297837i	$-0.0962651\pi$
$653$	48.7883	1.90923	0.954617	+	0.297837i	$0.0962651\pi$
$654$	12.5753	0.491732
$655$	−27.8300	−1.08741
$656$	3.29171	0.128520
$657$	8.00222	0.312196
$658$	−16.5528	−0.645295
$659$	−11.2361	−0.437696	−0.218848	−	0.975759i	$-0.570230\pi$
$659$	−11.2361	−0.437696	−0.218848	+	0.975759i	$0.570230\pi$
$660$	−16.4145	−0.638933
$661$	−24.0571	−0.935714	−0.467857	−	0.883804i	$-0.654974\pi$
$661$	−24.0571	−0.935714	−0.467857	+	0.883804i	$0.654974\pi$
$662$	3.49155	0.135703
$663$	3.96994	0.154180
$664$	6.06193	0.235248
$665$	−73.3379	−2.84392
$666$	5.01681	0.194397
$667$	−43.4564	−1.68264
$668$	−7.21959	−0.279334
$669$	1.00000	0.0386622
$670$	−32.0093	−1.23663
$671$	71.9216	2.77650
$672$	−3.11004	−0.119972
$673$	20.5088	0.790555	0.395277	−	0.918562i	$-0.370648\pi$
$673$	20.5088	0.790555	0.395277	+	0.918562i	$0.370648\pi$
$674$	33.8121	1.30240
$675$	−5.70110	−0.219435
$676$	−7.90647	−0.304095
$677$	−17.9714	−0.690695	−0.345348	−	0.938475i	$-0.612239\pi$
$677$	−17.9714	−0.690695	−0.345348	+	0.938475i	$0.612239\pi$
$678$	16.2276	0.623216
$679$	21.7800	0.835838
$680$	5.75425	0.220665
$681$	−15.4023	−0.590216
$682$	−27.1542	−1.03979
$683$	42.1183	1.61161	0.805806	−	0.592179i	$-0.201732\pi$
$683$	42.1183	1.61161	0.805806	+	0.592179i	$0.201732\pi$
$684$	−7.20855	−0.275626
$685$	11.9174	0.455340
$686$	−13.4592	−0.513874
$687$	2.84010	0.108357
$688$	−12.3131	−0.469431
$689$	24.7055	0.941203
$690$	−13.7572	−0.523726
$691$	−2.46310	−0.0937007	−0.0468503	−	0.998902i	$-0.514918\pi$
$691$	−2.46310	−0.0937007	−0.0468503	+	0.998902i	$0.514918\pi$
$692$	8.24128	0.313287
$693$	15.6055	0.592806
$694$	−7.87613	−0.298974
$695$	−56.5606	−2.14547
$696$	10.3333	0.391683
$697$	5.79023	0.219321
$698$	−24.1375	−0.913616
$699$	4.45436	0.168479
$700$	17.7306	0.670155
$701$	−25.1740	−0.950809	−0.475405	−	0.879767i	$-0.657698\pi$
$701$	−25.1740	−0.950809	−0.475405	+	0.879767i	$0.657698\pi$
$702$	2.25689	0.0851807
$703$	−36.1639	−1.36395
$704$	5.01780	0.189115
$705$	17.4108	0.655730
$706$	7.82351	0.294442
$707$	33.2878	1.25191
$708$	−1.70199	−0.0639647
$709$	23.7385	0.891519	0.445760	−	0.895153i	$-0.352934\pi$
$709$	23.7385	0.891519	0.445760	+	0.895153i	$0.352934\pi$
$710$	−0.244511	−0.00917634
$711$	7.81235	0.292986
$712$	7.54971	0.282938
$713$	−22.7582	−0.852303
$714$	−5.47067	−0.204735
$715$	−37.0456	−1.38543
$716$	1.76632	0.0660105
$717$	15.3887	0.574701
$718$	5.84778	0.218237
$719$	−40.5322	−1.51160	−0.755798	−	0.654805i	$-0.772751\pi$
$719$	−40.5322	−1.51160	−0.755798	+	0.654805i	$0.772751\pi$
$720$	3.27125	0.121912
$721$	31.5444	1.17478
$722$	32.9632	1.22676
$723$	−7.60381	−0.282789
$724$	21.0143	0.780990
$725$	−58.9112	−2.18791
$726$	−14.1783	−0.526205
$727$	33.4553	1.24079	0.620394	−	0.784291i	$-0.286973\pi$
$727$	33.4553	1.24079	0.620394	+	0.784291i	$0.286973\pi$
$728$	−7.01900	−0.260142
$729$	1.00000	0.0370370
$730$	26.1773	0.968865
$731$	−21.6591	−0.801091
$732$	−14.3333	−0.529774
$733$	−30.6796	−1.13318	−0.566589	−	0.824001i	$-0.691737\pi$
$733$	−30.6796	−1.13318	−0.566589	+	0.824001i	$0.691737\pi$
$734$	22.2229	0.820262
$735$	−8.74192	−0.322451
$736$	4.20547	0.155016
$737$	−49.0993	−1.80859
$738$	3.29171	0.121170
$739$	35.3510	1.30041	0.650203	−	0.759760i	$-0.274684\pi$
$739$	35.3510	1.30041	0.650203	+	0.759760i	$0.274684\pi$
$740$	16.4113	0.603290
$741$	−16.2689	−0.597652
$742$	−34.0447	−1.24982
$743$	−42.5668	−1.56162	−0.780812	−	0.624766i	$-0.785194\pi$
$743$	−42.5668	−1.56162	−0.780812	+	0.624766i	$0.785194\pi$
$744$	5.41158	0.198398
$745$	38.9291	1.42625
$746$	−34.0109	−1.24523
$747$	6.06193	0.221794
$748$	8.82648	0.322728
$749$	−5.55811	−0.203089
$750$	−2.29347	−0.0837458
$751$	−18.5767	−0.677872	−0.338936	−	0.940809i	$-0.610067\pi$
$751$	−18.5767	−0.677872	−0.338936	+	0.940809i	$0.610067\pi$
$752$	−5.32237	−0.194087
$753$	9.96260	0.363057
$754$	23.3211	0.849304
$755$	46.1065	1.67799
$756$	−3.11004	−0.113111
$757$	−1.40756	−0.0511585	−0.0255793	−	0.999673i	$-0.508143\pi$
$757$	−1.40756	−0.0511585	−0.0255793	+	0.999673i	$0.508143\pi$
$758$	−10.3035	−0.374241
$759$	−21.1022	−0.765961
$760$	−23.5810	−0.855373
$761$	6.58828	0.238825	0.119413	−	0.992845i	$-0.461899\pi$
$761$	6.58828	0.238825	0.119413	+	0.992845i	$0.461899\pi$
$762$	14.9452	0.541407
$763$	−39.1095	−1.41586
$764$	−16.3741	−0.592394
$765$	5.75425	0.208045
$766$	6.63837	0.239854
$767$	−3.84120	−0.138698
$768$	−1.00000	−0.0360844
$769$	30.7297	1.10814	0.554070	−	0.832470i	$-0.313074\pi$
$769$	30.7297	1.10814	0.554070	+	0.832470i	$0.313074\pi$
$770$	51.0497	1.83970
$771$	−24.1357	−0.869226
$772$	19.9818	0.719162
$773$	29.0705	1.04559	0.522797	−	0.852457i	$-0.324889\pi$
$773$	29.0705	1.04559	0.522797	+	0.852457i	$0.324889\pi$
$774$	−12.3131	−0.442584
$775$	−30.8520	−1.10823
$776$	7.00311	0.251397
$777$	−15.6025	−0.559736
$778$	20.4264	0.732322
$779$	−23.7285	−0.850161
$780$	7.38284	0.264348
$781$	−0.375057	−0.0134206
$782$	7.39756	0.264536
$783$	10.3333	0.369282
$784$	2.67235	0.0954409
$785$	20.6179	0.735884
$786$	8.50744	0.303450
$787$	−43.8451	−1.56291	−0.781455	−	0.623961i	$-0.785522\pi$
$787$	−43.8451	−1.56291	−0.781455	+	0.623961i	$0.785522\pi$
$788$	−27.9554	−0.995871
$789$	16.9293	0.602699
$790$	25.5562	0.909247
$791$	−50.4683	−1.79445
$792$	5.01780	0.178300
$793$	−32.3486	−1.14873
$794$	37.9844	1.34802
$795$	35.8094	1.27003
$796$	−4.56995	−0.161977
$797$	−21.6122	−0.765544	−0.382772	−	0.923843i	$-0.625030\pi$
$797$	−21.6122	−0.765544	−0.382772	+	0.923843i	$0.625030\pi$
$798$	22.4189	0.793620
$799$	−9.36223	−0.331212
$800$	5.70110	0.201564
$801$	7.54971	0.266756
$802$	−4.37080	−0.154338
$803$	40.1535	1.41699
$804$	9.78502	0.345091
$805$	42.7853	1.50798
$806$	12.2133	0.430196
$807$	7.14497	0.251515
$808$	10.7033	0.376542
$809$	32.0006	1.12508	0.562540	−	0.826770i	$-0.309824\pi$
$809$	32.0006	1.12508	0.562540	+	0.826770i	$0.309824\pi$
$810$	3.27125	0.114940
$811$	−55.7756	−1.95855	−0.979273	−	0.202543i	$-0.935079\pi$
$811$	−55.7756	−1.95855	−0.979273	+	0.202543i	$0.935079\pi$
$812$	−32.1370	−1.12779
$813$	1.20312	0.0421954
$814$	25.1733	0.882325
$815$	−12.5798	−0.440650
$816$	−1.75903	−0.0615785
$817$	88.7594	3.10530
$818$	−13.8293	−0.483531
$819$	−7.01900	−0.245264
$820$	10.7680	0.376036
$821$	−23.7910	−0.830313	−0.415157	−	0.909750i	$-0.636273\pi$
$821$	−23.7910	−0.830313	−0.415157	+	0.909750i	$0.636273\pi$
$822$	−3.64306	−0.127066
$823$	24.1272	0.841023	0.420511	−	0.907287i	$-0.361851\pi$
$823$	24.1272	0.841023	0.420511	+	0.907287i	$0.361851\pi$
$824$	10.1428	0.353340
$825$	−28.6070	−0.995966
$826$	5.29325	0.184176
$827$	−7.51262	−0.261239	−0.130620	−	0.991433i	$-0.541697\pi$
$827$	−7.51262	−0.261239	−0.130620	+	0.991433i	$0.541697\pi$
$828$	4.20547	0.146150
$829$	−30.8250	−1.07060	−0.535298	−	0.844663i	$-0.679801\pi$
$829$	−30.8250	−1.07060	−0.535298	+	0.844663i	$0.679801\pi$
$830$	19.8301	0.688313
$831$	−24.9595	−0.865834
$832$	−2.25689	−0.0782434
$833$	4.70075	0.162871
$834$	17.2902	0.598711
$835$	−23.6171	−0.817304
$836$	−36.1711	−1.25100
$837$	5.41158	0.187052
$838$	−15.7703	−0.544776
$839$	34.8573	1.20341	0.601703	−	0.798720i	$-0.294489\pi$
$839$	34.8573	1.20341	0.601703	+	0.798720i	$0.294489\pi$
$840$	−10.1737	−0.351027
$841$	77.7772	2.68197
$842$	40.1185	1.38257
$843$	0.597109	0.0205655
$844$	0.0340811	0.00117312
$845$	−25.8641	−0.889751
$846$	−5.32237	−0.182987
$847$	44.0950	1.51512
$848$	−10.9467	−0.375911
$849$	−11.4252	−0.392111
$850$	10.0284	0.343972
$851$	21.0980	0.723232
$852$	0.0747454	0.00256074
$853$	−32.5835	−1.11564	−0.557819	−	0.829963i	$-0.688362\pi$
$853$	−32.5835	−1.11564	−0.557819	+	0.829963i	$0.688362\pi$
$854$	44.5771	1.52540
$855$	−23.5810	−0.806453
$856$	−1.78715	−0.0610835
$857$	26.7989	0.915433	0.457717	−	0.889098i	$-0.348667\pi$
$857$	26.7989	0.915433	0.457717	+	0.889098i	$0.348667\pi$
$858$	11.3246	0.386615
$859$	−32.3965	−1.10536	−0.552678	−	0.833395i	$-0.686394\pi$
$859$	−32.3965	−1.10536	−0.552678	+	0.833395i	$0.686394\pi$
$860$	−40.2792	−1.37351
$861$	−10.2374	−0.348888
$862$	19.6960	0.670848
$863$	6.82638	0.232373	0.116186	−	0.993227i	$-0.462933\pi$
$863$	6.82638	0.232373	0.116186	+	0.993227i	$0.462933\pi$
$864$	−1.00000	−0.0340207
$865$	26.9593	0.916645
$866$	−8.75740	−0.297589
$867$	13.9058	0.472266
$868$	−16.8302	−0.571255
$869$	39.2008	1.32979
$870$	33.8029	1.14602
$871$	22.0837	0.748277
$872$	−12.5753	−0.425852
$873$	7.00311	0.237019
$874$	−30.3154	−1.02543
$875$	7.13279	0.241132
$876$	−8.00222	−0.270370
$877$	−23.8938	−0.806838	−0.403419	−	0.915015i	$-0.632178\pi$
$877$	−23.8938	−0.806838	−0.403419	+	0.915015i	$0.632178\pi$
$878$	−11.4726	−0.387182
$879$	−18.6579	−0.629314
$880$	16.4145	0.553332
$881$	32.9039	1.10856	0.554280	−	0.832330i	$-0.312994\pi$
$881$	32.9039	1.10856	0.554280	+	0.832330i	$0.312994\pi$
$882$	2.67235	0.0899825
$883$	24.7641	0.833380	0.416690	−	0.909049i	$-0.363190\pi$
$883$	24.7641	0.833380	0.416690	+	0.909049i	$0.363190\pi$
$884$	−3.96994	−0.133523
$885$	−5.56764	−0.187154
$886$	37.1871	1.24932
$887$	35.7133	1.19913	0.599567	−	0.800324i	$-0.295339\pi$
$887$	35.7133	1.19913	0.599567	+	0.800324i	$0.295339\pi$
$888$	−5.01681	−0.168353
$889$	−46.4801	−1.55889
$890$	24.6970	0.827846
$891$	5.01780	0.168103
$892$	−1.00000	−0.0334825
$893$	38.3666	1.28389
$894$	−11.9004	−0.398008
$895$	5.77808	0.193140
$896$	3.11004	0.103899
$897$	9.49126	0.316904
$898$	−15.9340	−0.531726
$899$	55.9195	1.86502
$900$	5.70110	0.190037
$901$	−19.2556	−0.641498
$902$	16.5171	0.549961
$903$	38.2941	1.27435
$904$	−16.2276	−0.539721
$905$	68.7431	2.28510
$906$	−14.0944	−0.468257
$907$	4.31143	0.143159	0.0715793	−	0.997435i	$-0.477196\pi$
$907$	4.31143	0.143159	0.0715793	+	0.997435i	$0.477196\pi$
$908$	15.4023	0.511142
$909$	10.7033	0.355007
$910$	−22.9609	−0.761148
$911$	−11.1292	−0.368727	−0.184364	−	0.982858i	$-0.559022\pi$
$911$	−11.1292	−0.368727	−0.184364	+	0.982858i	$0.559022\pi$
$912$	7.20855	0.238699
$913$	30.4175	1.00667
$914$	7.42897	0.245728
$915$	−46.8879	−1.55007
$916$	−2.84010	−0.0938396
$917$	−26.4585	−0.873736
$918$	−1.75903	−0.0580568
$919$	26.4793	0.873472	0.436736	−	0.899590i	$-0.356134\pi$
$919$	26.4793	0.873472	0.436736	+	0.899590i	$0.356134\pi$
$920$	13.7572	0.453560
$921$	6.04278	0.199116
$922$	−28.5862	−0.941435
$923$	0.168692	0.00555256
$924$	−15.6055	−0.513385
$925$	28.6013	0.940406
$926$	24.1021	0.792044
$927$	10.1428	0.333132
$928$	−10.3333	−0.339207
$929$	−4.16163	−0.136539	−0.0682694	−	0.997667i	$-0.521748\pi$
$929$	−4.16163	−0.136539	−0.0682694	+	0.997667i	$0.521748\pi$
$930$	17.7027	0.580493
$931$	−19.2637	−0.631344
$932$	−4.45436	−0.145907
$933$	23.0971	0.756165
$934$	20.0021	0.654487
$935$	28.8736	0.944269
$936$	−2.25689	−0.0737686
$937$	−53.5209	−1.74845	−0.874227	−	0.485518i	$-0.838631\pi$
$937$	−53.5209	−1.74845	−0.874227	+	0.485518i	$0.838631\pi$
$938$	−30.4318	−0.993634
$939$	−15.4613	−0.504562
$940$	−17.4108	−0.567878
$941$	7.45231	0.242938	0.121469	−	0.992595i	$-0.461239\pi$
$941$	7.45231	0.242938	0.121469	+	0.992595i	$0.461239\pi$
$942$	−6.30275	−0.205355
$943$	13.8432	0.450796
$944$	1.70199	0.0553950
$945$	−10.1737	−0.330951
$946$	−61.7845	−2.00879
$947$	28.8887	0.938756	0.469378	−	0.882997i	$-0.344478\pi$
$947$	28.8887	0.938756	0.469378	+	0.882997i	$0.344478\pi$
$948$	−7.81235	−0.253733
$949$	−18.0601	−0.586256
$950$	−41.0967	−1.33335
$951$	23.5816	0.764685
$952$	5.47067	0.177305
$953$	28.3803	0.919328	0.459664	−	0.888093i	$-0.347970\pi$
$953$	28.3803	0.919328	0.459664	+	0.888093i	$0.347970\pi$
$954$	−10.9467	−0.354413
$955$	−53.5638	−1.73329
$956$	−15.3887	−0.497705
$957$	51.8504	1.67609
$958$	−13.3758	−0.432153
$959$	11.3301	0.365867
$960$	−3.27125	−0.105579
$961$	−1.71480	−0.0553160
$962$	−11.3224	−0.365048
$963$	−1.78715	−0.0575901
$964$	7.60381	0.244902
$965$	65.3656	2.10419
$966$	−13.0792	−0.420816
$967$	16.9049	0.543625	0.271812	−	0.962350i	$-0.412377\pi$
$967$	16.9049	0.543625	0.271812	+	0.962350i	$0.412377\pi$
$968$	14.1783	0.455707
$969$	12.6801	0.407343
$970$	22.9090	0.735562
$971$	−9.61604	−0.308593	−0.154297	−	0.988025i	$-0.549311\pi$
$971$	−9.61604	−0.308593	−0.154297	+	0.988025i	$0.549311\pi$
$972$	−1.00000	−0.0320750
$973$	−53.7732	−1.72389
$974$	−25.4804	−0.816446
$975$	12.8667	0.412065
$976$	14.3333	0.458798
$977$	18.0948	0.578904	0.289452	−	0.957193i	$-0.406527\pi$
$977$	18.0948	0.578904	0.289452	+	0.957193i	$0.406527\pi$
$978$	3.84555	0.122967
$979$	37.8829	1.21074
$980$	8.74192	0.279250
$981$	−12.5753	−0.401497
$982$	22.4454	0.716261
$983$	35.4606	1.13102	0.565508	−	0.824743i	$-0.308680\pi$
$983$	35.4606	1.13102	0.565508	+	0.824743i	$0.308680\pi$
$984$	−3.29171	−0.104936
$985$	−91.4493	−2.91382
$986$	−18.1766	−0.578862
$987$	16.5528	0.526881
$988$	16.2689	0.517582
$989$	−51.7822	−1.64658
$990$	16.4145	0.521687
$991$	−6.42746	−0.204175	−0.102087	−	0.994775i	$-0.532552\pi$
$991$	−6.42746	−0.204175	−0.102087	+	0.994775i	$0.532552\pi$
$992$	−5.41158	−0.171818
$993$	−3.49155	−0.110801
$994$	−0.232461	−0.00737322
$995$	−14.9495	−0.473929
$996$	−6.06193	−0.192080
$997$	−26.9300	−0.852881	−0.426440	−	0.904516i	$-0.640233\pi$
$997$	−26.9300	−0.852881	−0.426440	+	0.904516i	$0.640233\pi$
$998$	34.9827	1.10736
$999$	−5.01681	−0.158725

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1338.2.a.j.1.6	✓	7
3.2	odd	2		4014.2.a.v.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1338.2.a.j.1.6	✓	7	1.1	even	1	trivial
4014.2.a.v.1.2		7	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1338 = 2 \cdot 3 \cdot 223 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1338.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.27125 q^{5} -1.00000 q^{6} +3.11004 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.27125 q^{10} +5.01780 q^{11} -1.00000 q^{12} -2.25689 q^{13} +3.11004 q^{14} -3.27125 q^{15} +1.00000 q^{16} +1.75903 q^{17} +1.00000 q^{18} -7.20855 q^{19} +3.27125 q^{20} -3.11004 q^{21} +5.01780 q^{22} +4.20547 q^{23} -1.00000 q^{24} +5.70110 q^{25} -2.25689 q^{26} -1.00000 q^{27} +3.11004 q^{28} -10.3333 q^{29} -3.27125 q^{30} -5.41158 q^{31} +1.00000 q^{32} -5.01780 q^{33} +1.75903 q^{34} +10.1737 q^{35} +1.00000 q^{36} +5.01681 q^{37} -7.20855 q^{38} +2.25689 q^{39} +3.27125 q^{40} +3.29171 q^{41} -3.11004 q^{42} -12.3131 q^{43} +5.01780 q^{44} +3.27125 q^{45} +4.20547 q^{46} -5.32237 q^{47} -1.00000 q^{48} +2.67235 q^{49} +5.70110 q^{50} -1.75903 q^{51} -2.25689 q^{52} -10.9467 q^{53} -1.00000 q^{54} +16.4145 q^{55} +3.11004 q^{56} +7.20855 q^{57} -10.3333 q^{58} +1.70199 q^{59} -3.27125 q^{60} +14.3333 q^{61} -5.41158 q^{62} +3.11004 q^{63} +1.00000 q^{64} -7.38284 q^{65} -5.01780 q^{66} -9.78502 q^{67} +1.75903 q^{68} -4.20547 q^{69} +10.1737 q^{70} -0.0747454 q^{71} +1.00000 q^{72} +8.00222 q^{73} +5.01681 q^{74} -5.70110 q^{75} -7.20855 q^{76} +15.6055 q^{77} +2.25689 q^{78} +7.81235 q^{79} +3.27125 q^{80} +1.00000 q^{81} +3.29171 q^{82} +6.06193 q^{83} -3.11004 q^{84} +5.75425 q^{85} -12.3131 q^{86} +10.3333 q^{87} +5.01780 q^{88} +7.54971 q^{89} +3.27125 q^{90} -7.01900 q^{91} +4.20547 q^{92} +5.41158 q^{93} -5.32237 q^{94} -23.5810 q^{95} -1.00000 q^{96} +7.00311 q^{97} +2.67235 q^{98} +5.01780 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 7 q^{2} - 7 q^{3} + 7 q^{4} + 6 q^{5} - 7 q^{6} + 3 q^{7} + 7 q^{8} + 7 q^{9} + 6 q^{10} - q^{11} - 7 q^{12} + 8 q^{13} + 3 q^{14} - 6 q^{15} + 7 q^{16} + 16 q^{17} + 7 q^{18} + 2 q^{19} + 6 q^{20}+ \cdots - q^{99}+O(q^{100}) \) 7 * q + 7 * q^2 - 7 * q^3 + 7 * q^4 + 6 * q^5 - 7 * q^6 + 3 * q^7 + 7 * q^8 + 7 * q^9 + 6 * q^10 - q^11 - 7 * q^12 + 8 * q^13 + 3 * q^14 - 6 * q^15 + 7 * q^16 + 16 * q^17 + 7 * q^18 + 2 * q^19 + 6 * q^20 - 3 * q^21 - q^22 + 8 * q^23 - 7 * q^24 + 19 * q^25 + 8 * q^26 - 7 * q^27 + 3 * q^28 + 4 * q^29 - 6 * q^30 + 11 * q^31 + 7 * q^32 + q^33 + 16 * q^34 + 7 * q^36 + 17 * q^37 + 2 * q^38 - 8 * q^39 + 6 * q^40 + 18 * q^41 - 3 * q^42 - q^43 - q^44 + 6 * q^45 + 8 * q^46 + 5 * q^47 - 7 * q^48 + 24 * q^49 + 19 * q^50 - 16 * q^51 + 8 * q^52 + 6 * q^53 - 7 * q^54 + 21 * q^55 + 3 * q^56 - 2 * q^57 + 4 * q^58 - 7 * q^59 - 6 * q^60 + 24 * q^61 + 11 * q^62 + 3 * q^63 + 7 * q^64 + 11 * q^65 + q^66 - 4 * q^67 + 16 * q^68 - 8 * q^69 - 7 * q^71 + 7 * q^72 + 28 * q^73 + 17 * q^74 - 19 * q^75 + 2 * q^76 - 2 * q^77 - 8 * q^78 + 6 * q^80 + 7 * q^81 + 18 * q^82 - 2 * q^83 - 3 * q^84 + 4 * q^85 - q^86 - 4 * q^87 - q^88 + 5 * q^89 + 6 * q^90 + 2 * q^91 + 8 * q^92 - 11 * q^93 + 5 * q^94 - 14 * q^95 - 7 * q^96 + 23 * q^97 + 24 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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