LMFDB - Embedded newform 8026.2.a.d.1.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [8026,2,Mod(1,8026)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("8026.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8026, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.a (trivial)

Newform invariants

comment:select newform

sage:traces = [96] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$64.0879326623$
Analytic rank:	$0$
Dimension:	$96$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8026.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} -3.15603 q^{3} +1.00000 q^{4} +0.126707 q^{5} -3.15603 q^{6} +5.16404 q^{7} +1.00000 q^{8} +6.96052 q^{9} +0.126707 q^{10} -3.20397 q^{11} -3.15603 q^{12} +0.276972 q^{13} +5.16404 q^{14} -0.399891 q^{15} +1.00000 q^{16} +2.29296 q^{17} +6.96052 q^{18} -4.61432 q^{19} +0.126707 q^{20} -16.2979 q^{21} -3.20397 q^{22} +0.949092 q^{23} -3.15603 q^{24} -4.98395 q^{25} +0.276972 q^{26} -12.4995 q^{27} +5.16404 q^{28} -4.64072 q^{29} -0.399891 q^{30} +0.973237 q^{31} +1.00000 q^{32} +10.1118 q^{33} +2.29296 q^{34} +0.654321 q^{35} +6.96052 q^{36} +9.85731 q^{37} -4.61432 q^{38} -0.874131 q^{39} +0.126707 q^{40} +5.49741 q^{41} -16.2979 q^{42} +6.34943 q^{43} -3.20397 q^{44} +0.881947 q^{45} +0.949092 q^{46} +7.68155 q^{47} -3.15603 q^{48} +19.6673 q^{49} -4.98395 q^{50} -7.23664 q^{51} +0.276972 q^{52} +5.93359 q^{53} -12.4995 q^{54} -0.405966 q^{55} +5.16404 q^{56} +14.5629 q^{57} -4.64072 q^{58} -5.08216 q^{59} -0.399891 q^{60} -3.09134 q^{61} +0.973237 q^{62} +35.9444 q^{63} +1.00000 q^{64} +0.0350943 q^{65} +10.1118 q^{66} +0.425022 q^{67} +2.29296 q^{68} -2.99536 q^{69} +0.654321 q^{70} +1.39943 q^{71} +6.96052 q^{72} -3.07623 q^{73} +9.85731 q^{74} +15.7295 q^{75} -4.61432 q^{76} -16.5455 q^{77} -0.874131 q^{78} -14.3331 q^{79} +0.126707 q^{80} +18.5672 q^{81} +5.49741 q^{82} +3.20258 q^{83} -16.2979 q^{84} +0.290534 q^{85} +6.34943 q^{86} +14.6462 q^{87} -3.20397 q^{88} +14.2139 q^{89} +0.881947 q^{90} +1.43029 q^{91} +0.949092 q^{92} -3.07156 q^{93} +7.68155 q^{94} -0.584667 q^{95} -3.15603 q^{96} -12.5799 q^{97} +19.6673 q^{98} -22.3013 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19}+ \cdots + 42 q^{99}+O(q^{100}) $ 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9 + 39 * q^10 + 36 * q^11 + 8 * q^12 + 63 * q^13 + 19 * q^14 + 17 * q^15 + 96 * q^16 + 56 * q^17 + 130 * q^18 + 17 * q^19 + 39 * q^20 + 51 * q^21 + 36 * q^22 + 47 * q^23 + 8 * q^24 + 147 * q^25 + 63 * q^26 + 17 * q^27 + 19 * q^28 + 60 * q^29 + 17 * q^30 + 63 * q^31 + 96 * q^32 + 55 * q^33 + 56 * q^34 + 45 * q^35 + 130 * q^36 + 46 * q^37 + 17 * q^38 + 22 * q^39 + 39 * q^40 + 101 * q^41 + 51 * q^42 - 3 * q^43 + 36 * q^44 + 106 * q^45 + 47 * q^46 + 99 * q^47 + 8 * q^48 + 175 * q^49 + 147 * q^50 - q^51 + 63 * q^52 + 75 * q^53 + 17 * q^54 + 80 * q^55 + 19 * q^56 + 35 * q^57 + 60 * q^58 + 129 * q^59 + 17 * q^60 + 75 * q^61 + 63 * q^62 + 20 * q^63 + 96 * q^64 + 55 * q^65 + 55 * q^66 + 2 * q^67 + 56 * q^68 + 57 * q^69 + 45 * q^70 + 87 * q^71 + 130 * q^72 + 120 * q^73 + 46 * q^74 - 15 * q^75 + 17 * q^76 + 95 * q^77 + 22 * q^78 + 21 * q^79 + 39 * q^80 + 180 * q^81 + 101 * q^82 + 69 * q^83 + 51 * q^84 + 59 * q^85 - 3 * q^86 + 63 * q^87 + 36 * q^88 + 144 * q^89 + 106 * q^90 - 5 * q^91 + 47 * q^92 + 59 * q^93 + 99 * q^94 + 23 * q^95 + 8 * q^96 + 99 * q^97 + 175 * q^98 + 42 * 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
$3$	−3.15603	−1.82213	−0.911067	−	0.412258i	$-0.864740\pi$
$3$	−3.15603	−1.82213	−0.911067	+	0.412258i	$0.864740\pi$
$4$	1.00000	0.500000
$5$	0.126707	0.0566651	0.0283326	−	0.999599i	$-0.490980\pi$
$5$	0.126707	0.0566651	0.0283326	+	0.999599i	$0.490980\pi$
$6$	−3.15603	−1.28844
$7$	5.16404	1.95182	0.975912	−	0.218165i	$-0.0700069\pi$
$7$	5.16404	1.95182	0.975912	+	0.218165i	$0.0700069\pi$
$8$	1.00000	0.353553
$9$	6.96052	2.32017
$10$	0.126707	0.0400683
$11$	−3.20397	−0.966035	−0.483017	−	0.875611i	$-0.660459\pi$
$11$	−3.20397	−0.966035	−0.483017	+	0.875611i	$0.660459\pi$
$12$	−3.15603	−0.911067
$13$	0.276972	0.0768181	0.0384091	−	0.999262i	$-0.487771\pi$
$13$	0.276972	0.0768181	0.0384091	+	0.999262i	$0.487771\pi$
$14$	5.16404	1.38015
$15$	−0.399891	−0.103251
$16$	1.00000	0.250000
$17$	2.29296	0.556124	0.278062	−	0.960563i	$-0.410308\pi$
$17$	2.29296	0.556124	0.278062	+	0.960563i	$0.410308\pi$
$18$	6.96052	1.64061
$19$	−4.61432	−1.05860	−0.529299	−	0.848436i	$-0.677545\pi$
$19$	−4.61432	−1.05860	−0.529299	+	0.848436i	$0.677545\pi$
$20$	0.126707	0.0283326
$21$	−16.2979	−3.55648
$22$	−3.20397	−0.683090
$23$	0.949092	0.197899	0.0989497	−	0.995092i	$-0.468452\pi$
$23$	0.949092	0.197899	0.0989497	+	0.995092i	$0.468452\pi$
$24$	−3.15603	−0.644222
$25$	−4.98395	−0.996789
$26$	0.276972	0.0543186
$27$	−12.4995	−2.40553
$28$	5.16404	0.975912
$29$	−4.64072	−0.861760	−0.430880	−	0.902409i	$-0.641797\pi$
$29$	−4.64072	−0.861760	−0.430880	+	0.902409i	$0.641797\pi$
$30$	−0.399891	−0.0730098
$31$	0.973237	0.174799	0.0873993	−	0.996173i	$-0.472144\pi$
$31$	0.973237	0.174799	0.0873993	+	0.996173i	$0.472144\pi$
$32$	1.00000	0.176777
$33$	10.1118	1.76024
$34$	2.29296	0.393239
$35$	0.654321	0.110600
$36$	6.96052	1.16009
$37$	9.85731	1.62053	0.810266	−	0.586062i	$-0.199323\pi$
$37$	9.85731	1.62053	0.810266	+	0.586062i	$0.199323\pi$
$38$	−4.61432	−0.748541
$39$	−0.874131	−0.139973
$40$	0.126707	0.0200342
$41$	5.49741	0.858551	0.429275	−	0.903174i	$-0.358769\pi$
$41$	5.49741	0.858551	0.429275	+	0.903174i	$0.358769\pi$
$42$	−16.2979	−2.51481
$43$	6.34943	0.968279	0.484139	−	0.874991i	$-0.339133\pi$
$43$	6.34943	0.968279	0.484139	+	0.874991i	$0.339133\pi$
$44$	−3.20397	−0.483017
$45$	0.881947	0.131473
$46$	0.949092	0.139936
$47$	7.68155	1.12047	0.560235	−	0.828334i	$-0.310711\pi$
$47$	7.68155	1.12047	0.560235	+	0.828334i	$0.310711\pi$
$48$	−3.15603	−0.455533
$49$	19.6673	2.80962
$50$	−4.98395	−0.704836
$51$	−7.23664	−1.01333
$52$	0.276972	0.0384091
$53$	5.93359	0.815041	0.407521	−	0.913196i	$-0.366393\pi$
$53$	5.93359	0.815041	0.407521	+	0.913196i	$0.366393\pi$
$54$	−12.4995	−1.70097
$55$	−0.405966	−0.0547405
$56$	5.16404	0.690074
$57$	14.5629	1.92891
$58$	−4.64072	−0.609356
$59$	−5.08216	−0.661641	−0.330820	−	0.943694i	$-0.607325\pi$
$59$	−5.08216	−0.661641	−0.330820	+	0.943694i	$0.607325\pi$
$60$	−0.399891	−0.0516257
$61$	−3.09134	−0.395805	−0.197903	−	0.980222i	$-0.563413\pi$
$61$	−3.09134	−0.395805	−0.197903	+	0.980222i	$0.563413\pi$
$62$	0.973237	0.123601
$63$	35.9444	4.52857
$64$	1.00000	0.125000
$65$	0.0350943	0.00435291
$66$	10.1118	1.24468
$67$	0.425022	0.0519247	0.0259623	−	0.999663i	$-0.491735\pi$
$67$	0.425022	0.0519247	0.0259623	+	0.999663i	$0.491735\pi$
$68$	2.29296	0.278062
$69$	−2.99536	−0.360599
$70$	0.654321	0.0782063
$71$	1.39943	0.166081	0.0830406	−	0.996546i	$-0.473537\pi$
$71$	1.39943	0.166081	0.0830406	+	0.996546i	$0.473537\pi$
$72$	6.96052	0.820305
$73$	−3.07623	−0.360046	−0.180023	−	0.983662i	$-0.557617\pi$
$73$	−3.07623	−0.360046	−0.180023	+	0.983662i	$0.557617\pi$
$74$	9.85731	1.14589
$75$	15.7295	1.81628
$76$	−4.61432	−0.529299
$77$	−16.5455	−1.88553
$78$	−0.874131	−0.0989758
$79$	−14.3331	−1.61259	−0.806297	−	0.591510i	$-0.798532\pi$
$79$	−14.3331	−1.61259	−0.806297	+	0.591510i	$0.798532\pi$
$80$	0.126707	0.0141663
$81$	18.5672	2.06303
$82$	5.49741	0.607087
$83$	3.20258	0.351529	0.175764	−	0.984432i	$-0.443760\pi$
$83$	3.20258	0.351529	0.175764	+	0.984432i	$0.443760\pi$
$84$	−16.2979	−1.77824
$85$	0.290534	0.0315129
$86$	6.34943	0.684676
$87$	14.6462	1.57024
$88$	−3.20397	−0.341545
$89$	14.2139	1.50667	0.753337	−	0.657635i	$-0.228443\pi$
$89$	14.2139	1.50667	0.753337	+	0.657635i	$0.228443\pi$
$90$	0.881947	0.0929654
$91$	1.43029	0.149936
$92$	0.949092	0.0989497
$93$	−3.07156	−0.318506
$94$	7.68155	0.792292
$95$	−0.584667	−0.0599856
$96$	−3.15603	−0.322111
$97$	−12.5799	−1.27730	−0.638649	−	0.769498i	$-0.720507\pi$
$97$	−12.5799	−1.27730	−0.638649	+	0.769498i	$0.720507\pi$
$98$	19.6673	1.98670
$99$	−22.3013	−2.24137
$100$	−4.98395	−0.498395
$101$	0.599044	0.0596071	0.0298035	−	0.999556i	$-0.490512\pi$
$101$	0.599044	0.0596071	0.0298035	+	0.999556i	$0.490512\pi$
$102$	−7.23664	−0.716534
$103$	7.14033	0.703557	0.351779	−	0.936083i	$-0.385577\pi$
$103$	7.14033	0.703557	0.351779	+	0.936083i	$0.385577\pi$
$104$	0.276972	0.0271593
$105$	−2.06505	−0.201529
$106$	5.93359	0.576321
$107$	−18.9606	−1.83299	−0.916494	−	0.400049i	$-0.868993\pi$
$107$	−18.9606	−1.83299	−0.916494	+	0.400049i	$0.868993\pi$
$108$	−12.4995	−1.20276
$109$	−11.0546	−1.05884	−0.529420	−	0.848360i	$-0.677590\pi$
$109$	−11.0546	−1.05884	−0.529420	+	0.848360i	$0.677590\pi$
$110$	−0.405966	−0.0387074
$111$	−31.1100	−2.95283
$112$	5.16404	0.487956
$113$	15.9633	1.50170	0.750849	−	0.660473i	$-0.229644\pi$
$113$	15.9633	1.50170	0.750849	+	0.660473i	$0.229644\pi$
$114$	14.5629	1.36394
$115$	0.120257	0.0112140
$116$	−4.64072	−0.430880
$117$	1.92787	0.178231
$118$	−5.08216	−0.467851
$119$	11.8409	1.08546
$120$	−0.399891	−0.0365049
$121$	−0.734548	−0.0667771
$122$	−3.09134	−0.279876
$123$	−17.3500	−1.56439
$124$	0.973237	0.0873993
$125$	−1.26504	−0.113148
$126$	35.9444	3.20218
$127$	10.2657	0.910933	0.455467	−	0.890253i	$-0.349472\pi$
$127$	10.2657	0.910933	0.455467	+	0.890253i	$0.349472\pi$
$128$	1.00000	0.0883883
$129$	−20.0390	−1.76433
$130$	0.0350943	0.00307797
$131$	16.8058	1.46833	0.734164	−	0.678972i	$-0.237574\pi$
$131$	16.8058	1.46833	0.734164	+	0.678972i	$0.237574\pi$
$132$	10.1118	0.880122
$133$	−23.8285	−2.06620
$134$	0.425022	0.0367163
$135$	−1.58378	−0.136310
$136$	2.29296	0.196620
$137$	4.73370	0.404427	0.202213	−	0.979341i	$-0.435187\pi$
$137$	4.73370	0.404427	0.202213	+	0.979341i	$0.435187\pi$
$138$	−2.99536	−0.254982
$139$	−3.84059	−0.325755	−0.162877	−	0.986646i	$-0.552078\pi$
$139$	−3.84059	−0.325755	−0.162877	+	0.986646i	$0.552078\pi$
$140$	0.654321	0.0553002
$141$	−24.2432	−2.04165
$142$	1.39943	0.117437
$143$	−0.887411	−0.0742090
$144$	6.96052	0.580043
$145$	−0.588012	−0.0488317
$146$	−3.07623	−0.254591
$147$	−62.0706	−5.11950
$148$	9.85731	0.810266
$149$	−11.2899	−0.924901	−0.462451	−	0.886645i	$-0.653030\pi$
$149$	−11.2899	−0.924901	−0.462451	+	0.886645i	$0.653030\pi$
$150$	15.7295	1.28431
$151$	−1.17424	−0.0955585	−0.0477793	−	0.998858i	$-0.515214\pi$
$151$	−1.17424	−0.0955585	−0.0477793	+	0.998858i	$0.515214\pi$
$152$	−4.61432	−0.374271
$153$	15.9602	1.29030
$154$	−16.5455	−1.33327
$155$	0.123316	0.00990498
$156$	−0.874131	−0.0699865
$157$	13.6147	1.08658	0.543288	−	0.839547i	$-0.317179\pi$
$157$	13.6147	1.08658	0.543288	+	0.839547i	$0.317179\pi$
$158$	−14.3331	−1.14028
$159$	−18.7266	−1.48511
$160$	0.126707	0.0100171
$161$	4.90115	0.386265
$162$	18.5672	1.45878
$163$	13.1528	1.03021	0.515104	−	0.857127i	$-0.327753\pi$
$163$	13.1528	1.03021	0.515104	+	0.857127i	$0.327753\pi$
$164$	5.49741	0.429275
$165$	1.28124	0.0997445
$166$	3.20258	0.248568
$167$	16.3881	1.26815	0.634074	−	0.773272i	$-0.281381\pi$
$167$	16.3881	1.26815	0.634074	+	0.773272i	$0.281381\pi$
$168$	−16.2979	−1.25741
$169$	−12.9233	−0.994099
$170$	0.290534	0.0222830
$171$	−32.1180	−2.45613
$172$	6.34943	0.484139
$173$	18.7770	1.42759	0.713796	−	0.700354i	$-0.246974\pi$
$173$	18.7770	1.42759	0.713796	+	0.700354i	$0.246974\pi$
$174$	14.6462	1.11033
$175$	−25.7373	−1.94556
$176$	−3.20397	−0.241509
$177$	16.0394	1.20560
$178$	14.2139	1.06538
$179$	−6.43092	−0.480670	−0.240335	−	0.970690i	$-0.577257\pi$
$179$	−6.43092	−0.480670	−0.240335	+	0.970690i	$0.577257\pi$
$180$	0.881947	0.0657364
$181$	24.5274	1.82311	0.911555	−	0.411179i	$-0.134883\pi$
$181$	24.5274	1.82311	0.911555	+	0.411179i	$0.134883\pi$
$182$	1.43029	0.106020
$183$	9.75635	0.721210
$184$	0.949092	0.0699680
$185$	1.24899	0.0918277
$186$	−3.07156	−0.225218
$187$	−7.34658	−0.537235
$188$	7.68155	0.560235
$189$	−64.5479	−4.69517
$190$	−0.584667	−0.0424162
$191$	9.54659	0.690767	0.345384	−	0.938462i	$-0.387749\pi$
$191$	9.54659	0.690767	0.345384	+	0.938462i	$0.387749\pi$
$192$	−3.15603	−0.227767
$193$	−5.97063	−0.429775	−0.214888	−	0.976639i	$-0.568939\pi$
$193$	−5.97063	−0.429775	−0.214888	+	0.976639i	$0.568939\pi$
$194$	−12.5799	−0.903187
$195$	−0.110759	−0.00793159
$196$	19.6673	1.40481
$197$	11.6397	0.829293	0.414646	−	0.909983i	$-0.363905\pi$
$197$	11.6397	0.829293	0.414646	+	0.909983i	$0.363905\pi$
$198$	−22.3013	−1.58489
$199$	−13.0399	−0.924375	−0.462188	−	0.886782i	$-0.652935\pi$
$199$	−13.0399	−0.924375	−0.462188	+	0.886782i	$0.652935\pi$
$200$	−4.98395	−0.352418
$201$	−1.34138	−0.0946137
$202$	0.599044	0.0421486
$203$	−23.9649	−1.68200
$204$	−7.23664	−0.506666
$205$	0.696561	0.0486499
$206$	7.14033	0.497490
$207$	6.60617	0.459161
$208$	0.276972	0.0192045
$209$	14.7842	1.02264
$210$	−2.06505	−0.142502
$211$	−22.7856	−1.56862	−0.784311	−	0.620368i	$-0.786983\pi$
$211$	−22.7856	−1.56862	−0.784311	+	0.620368i	$0.786983\pi$
$212$	5.93359	0.407521
$213$	−4.41663	−0.302622
$214$	−18.9606	−1.29612
$215$	0.804518	0.0548676
$216$	−12.4995	−0.850483
$217$	5.02584	0.341176
$218$	−11.0546	−0.748713
$219$	9.70868	0.656052
$220$	−0.405966	−0.0273702
$221$	0.635085	0.0427204
$222$	−31.1100	−2.08796
$223$	−2.39151	−0.160147	−0.0800736	−	0.996789i	$-0.525516\pi$
$223$	−2.39151	−0.160147	−0.0800736	+	0.996789i	$0.525516\pi$
$224$	5.16404	0.345037
$225$	−34.6908	−2.31272
$226$	15.9633	1.06186
$227$	−5.07995	−0.337168	−0.168584	−	0.985687i	$-0.553920\pi$
$227$	−5.07995	−0.337168	−0.168584	+	0.985687i	$0.553920\pi$
$228$	14.5629	0.964453
$229$	5.32645	0.351982	0.175991	−	0.984392i	$-0.443687\pi$
$229$	5.32645	0.351982	0.175991	+	0.984392i	$0.443687\pi$
$230$	0.120257	0.00792949
$231$	52.2179	3.43569
$232$	−4.64072	−0.304678
$233$	2.68052	0.175607	0.0878035	−	0.996138i	$-0.472015\pi$
$233$	2.68052	0.175607	0.0878035	+	0.996138i	$0.472015\pi$
$234$	1.92787	0.126029
$235$	0.973308	0.0634916
$236$	−5.08216	−0.330820
$237$	45.2355	2.93836
$238$	11.8409	0.767534
$239$	−11.0564	−0.715179	−0.357590	−	0.933879i	$-0.616401\pi$
$239$	−11.0564	−0.715179	−0.357590	+	0.933879i	$0.616401\pi$
$240$	−0.399891	−0.0258129
$241$	5.22346	0.336472	0.168236	−	0.985747i	$-0.446193\pi$
$241$	5.22346	0.336472	0.168236	+	0.985747i	$0.446193\pi$
$242$	−0.734548	−0.0472185
$243$	−21.1002	−1.35358
$244$	−3.09134	−0.197903
$245$	2.49199	0.159207
$246$	−17.3500	−1.10619
$247$	−1.27804	−0.0813195
$248$	0.973237	0.0618006
$249$	−10.1074	−0.640532
$250$	−1.26504	−0.0800080
$251$	−8.53704	−0.538853	−0.269427	−	0.963021i	$-0.586834\pi$
$251$	−8.53704	−0.538853	−0.269427	+	0.963021i	$0.586834\pi$
$252$	35.9444	2.26428
$253$	−3.04087	−0.191178
$254$	10.2657	0.644127
$255$	−0.916934	−0.0574206
$256$	1.00000	0.0625000
$257$	4.55007	0.283825	0.141913	−	0.989879i	$-0.454675\pi$
$257$	4.55007	0.283825	0.141913	+	0.989879i	$0.454675\pi$
$258$	−20.0390	−1.24757
$259$	50.9036	3.16299
$260$	0.0350943	0.00217646
$261$	−32.3018	−1.99943
$262$	16.8058	1.03826
$263$	19.6713	1.21299	0.606493	−	0.795088i	$-0.292576\pi$
$263$	19.6713	1.21299	0.606493	+	0.795088i	$0.292576\pi$
$264$	10.1118	0.622340
$265$	0.751828	0.0461844
$266$	−23.8285	−1.46102
$267$	−44.8596	−2.74536
$268$	0.425022	0.0259623
$269$	−5.55897	−0.338936	−0.169468	−	0.985536i	$-0.554205\pi$
$269$	−5.55897	−0.338936	−0.169468	+	0.985536i	$0.554205\pi$
$270$	−1.58378	−0.0963855
$271$	0.188715	0.0114636	0.00573181	−	0.999984i	$-0.498175\pi$
$271$	0.188715	0.0114636	0.00573181	+	0.999984i	$0.498175\pi$
$272$	2.29296	0.139031
$273$	−4.51405	−0.273203
$274$	4.73370	0.285973
$275$	15.9684	0.962933
$276$	−2.99536	−0.180300
$277$	10.0013	0.600918	0.300459	−	0.953795i	$-0.402860\pi$
$277$	10.0013	0.600918	0.300459	+	0.953795i	$0.402860\pi$
$278$	−3.84059	−0.230344
$279$	6.77423	0.405563
$280$	0.654321	0.0391031
$281$	13.2302	0.789250	0.394625	−	0.918842i	$-0.370874\pi$
$281$	13.2302	0.789250	0.394625	+	0.918842i	$0.370874\pi$
$282$	−24.2432	−1.44366
$283$	−14.8058	−0.880111	−0.440056	−	0.897970i	$-0.645041\pi$
$283$	−14.8058	−0.880111	−0.440056	+	0.897970i	$0.645041\pi$
$284$	1.39943	0.0830406
$285$	1.84523	0.109302
$286$	−0.887411	−0.0524737
$287$	28.3888	1.67574
$288$	6.96052	0.410152
$289$	−11.7423	−0.690726
$290$	−0.588012	−0.0345292
$291$	39.7026	2.32741
$292$	−3.07623	−0.180023
$293$	27.9134	1.63072	0.815358	−	0.578956i	$-0.196540\pi$
$293$	27.9134	1.63072	0.815358	+	0.578956i	$0.196540\pi$
$294$	−62.0706	−3.62003
$295$	−0.643946	−0.0374920
$296$	9.85731	0.572945
$297$	40.0481	2.32383
$298$	−11.2899	−0.654004
$299$	0.262872	0.0152023
$300$	15.7295	0.908142
$301$	32.7887	1.88991
$302$	−1.17424	−0.0675701
$303$	−1.89060	−0.108612
$304$	−4.61432	−0.264649
$305$	−0.391694	−0.0224284
$306$	15.9602	0.912382
$307$	−11.6931	−0.667360	−0.333680	−	0.942686i	$-0.608290\pi$
$307$	−11.6931	−0.667360	−0.333680	+	0.942686i	$0.608290\pi$
$308$	−16.5455	−0.942765
$309$	−22.5351	−1.28198
$310$	0.123316	0.00700388
$311$	12.6235	0.715813	0.357907	−	0.933757i	$-0.383491\pi$
$311$	12.6235	0.715813	0.357907	+	0.933757i	$0.383491\pi$
$312$	−0.874131	−0.0494879
$313$	−10.0057	−0.565555	−0.282777	−	0.959186i	$-0.591256\pi$
$313$	−10.0057	−0.565555	−0.282777	+	0.959186i	$0.591256\pi$
$314$	13.6147	0.768325
$315$	4.55441	0.256612
$316$	−14.3331	−0.806297
$317$	−4.36072	−0.244922	−0.122461	−	0.992473i	$-0.539079\pi$
$317$	−4.36072	−0.244922	−0.122461	+	0.992473i	$0.539079\pi$
$318$	−18.7266	−1.05013
$319$	14.8687	0.832490
$320$	0.126707	0.00708314
$321$	59.8401	3.33995
$322$	4.90115	0.273130
$323$	−10.5804	−0.588711
$324$	18.5672	1.03151
$325$	−1.38041	−0.0765715
$326$	13.1528	0.728468
$327$	34.8887	1.92935
$328$	5.49741	0.303544
$329$	39.6679	2.18696
$330$	1.28124	0.0705300
$331$	22.9812	1.26316	0.631582	−	0.775309i	$-0.282406\pi$
$331$	22.9812	1.26316	0.631582	+	0.775309i	$0.282406\pi$
$332$	3.20258	0.175764
$333$	68.6120	3.75991
$334$	16.3881	0.896717
$335$	0.0538533	0.00294232
$336$	−16.2979	−0.889121
$337$	31.8141	1.73302	0.866512	−	0.499156i	$-0.166357\pi$
$337$	31.8141	1.73302	0.866512	+	0.499156i	$0.166357\pi$
$338$	−12.9233	−0.702934
$339$	−50.3806	−2.73630
$340$	0.290534	0.0157564
$341$	−3.11823	−0.168861
$342$	−32.1180	−1.73674
$343$	65.4146	3.53205
$344$	6.34943	0.342338
$345$	−0.379534	−0.0204334
$346$	18.7770	1.00946
$347$	28.0310	1.50478	0.752392	−	0.658716i	$-0.228900\pi$
$347$	28.0310	1.50478	0.752392	+	0.658716i	$0.228900\pi$
$348$	14.6462	0.785121
$349$	13.5611	0.725911	0.362955	−	0.931807i	$-0.381768\pi$
$349$	13.5611	0.725911	0.362955	+	0.931807i	$0.381768\pi$
$350$	−25.7373	−1.37572
$351$	−3.46201	−0.184788
$352$	−3.20397	−0.170772
$353$	−0.301078	−0.0160248	−0.00801239	−	0.999968i	$-0.502550\pi$
$353$	−0.301078	−0.0160248	−0.00801239	+	0.999968i	$0.502550\pi$
$354$	16.0394	0.852487
$355$	0.177317	0.00941102
$356$	14.2139	0.753337
$357$	−37.3703	−1.97785
$358$	−6.43092	−0.339885
$359$	−25.4313	−1.34221	−0.671105	−	0.741362i	$-0.734180\pi$
$359$	−25.4313	−1.34221	−0.671105	+	0.741362i	$0.734180\pi$
$360$	0.881947	0.0464827
$361$	2.29193	0.120628
$362$	24.5274	1.28913
$363$	2.31825	0.121677
$364$	1.43029	0.0749678
$365$	−0.389781	−0.0204021
$366$	9.75635	0.509972
$367$	7.17017	0.374280	0.187140	−	0.982333i	$-0.440078\pi$
$367$	7.17017	0.374280	0.187140	+	0.982333i	$0.440078\pi$
$368$	0.949092	0.0494749
$369$	38.2648	1.99199
$370$	1.24899	0.0649320
$371$	30.6413	1.59082
$372$	−3.07156	−0.159253
$373$	28.5144	1.47642	0.738209	−	0.674573i	$-0.235672\pi$
$373$	28.5144	1.47642	0.738209	+	0.674573i	$0.235672\pi$
$374$	−7.34658	−0.379883
$375$	3.99249	0.206171
$376$	7.68155	0.396146
$377$	−1.28535	−0.0661988
$378$	−64.5479	−3.31999
$379$	−15.5128	−0.796841	−0.398421	−	0.917203i	$-0.630442\pi$
$379$	−15.5128	−0.796841	−0.398421	+	0.917203i	$0.630442\pi$
$380$	−0.584667	−0.0299928
$381$	−32.3988	−1.65984
$382$	9.54659	0.488446
$383$	8.94598	0.457118	0.228559	−	0.973530i	$-0.426599\pi$
$383$	8.94598	0.457118	0.228559	+	0.973530i	$0.426599\pi$
$384$	−3.15603	−0.161055
$385$	−2.09643	−0.106844
$386$	−5.97063	−0.303897
$387$	44.1953	2.24657
$388$	−12.5799	−0.638649
$389$	−19.0030	−0.963488	−0.481744	−	0.876312i	$-0.659996\pi$
$389$	−19.0030	−0.963488	−0.481744	+	0.876312i	$0.659996\pi$
$390$	−0.110759	−0.00560848
$391$	2.17623	0.110057
$392$	19.6673	0.993350
$393$	−53.0395	−2.67549
$394$	11.6397	0.586399
$395$	−1.81610	−0.0913779
$396$	−22.3013	−1.12068
$397$	−7.25878	−0.364308	−0.182154	−	0.983270i	$-0.558307\pi$
$397$	−7.25878	−0.364308	−0.182154	+	0.983270i	$0.558307\pi$
$398$	−13.0399	−0.653632
$399$	75.2035	3.76488
$400$	−4.98395	−0.249197
$401$	17.3981	0.868820	0.434410	−	0.900715i	$-0.356957\pi$
$401$	17.3981	0.868820	0.434410	+	0.900715i	$0.356957\pi$
$402$	−1.34138	−0.0669020
$403$	0.269559	0.0134277
$404$	0.599044	0.0298035
$405$	2.35260	0.116902
$406$	−23.9649	−1.18936
$407$	−31.5826	−1.56549
$408$	−7.23664	−0.358267
$409$	27.3242	1.35109	0.675547	−	0.737317i	$-0.263907\pi$
$409$	27.3242	1.35109	0.675547	+	0.737317i	$0.263907\pi$
$410$	0.696561	0.0344007
$411$	−14.9397	−0.736920
$412$	7.14033	0.351779
$413$	−26.2445	−1.29141
$414$	6.60617	0.324676
$415$	0.405790	0.0199194
$416$	0.276972	0.0135797
$417$	12.1210	0.593569
$418$	14.7842	0.723117
$419$	5.09022	0.248674	0.124337	−	0.992240i	$-0.460320\pi$
$419$	5.09022	0.248674	0.124337	+	0.992240i	$0.460320\pi$
$420$	−2.06505	−0.100764
$421$	−22.2268	−1.08327	−0.541635	−	0.840614i	$-0.682194\pi$
$421$	−22.2268	−1.08327	−0.541635	+	0.840614i	$0.682194\pi$
$422$	−22.7856	−1.10918
$423$	53.4676	2.59968
$424$	5.93359	0.288161
$425$	−11.4280	−0.554338
$426$	−4.41663	−0.213986
$427$	−15.9638	−0.772542
$428$	−18.9606	−0.916494
$429$	2.80069	0.135219
$430$	0.804518	0.0387973
$431$	−9.66923	−0.465751	−0.232875	−	0.972507i	$-0.574813\pi$
$431$	−9.66923	−0.465751	−0.232875	+	0.972507i	$0.574813\pi$
$432$	−12.4995	−0.601382
$433$	−6.21118	−0.298490	−0.149245	−	0.988800i	$-0.547684\pi$
$433$	−6.21118	−0.298490	−0.149245	+	0.988800i	$0.547684\pi$
$434$	5.02584	0.241248
$435$	1.85578	0.0889780
$436$	−11.0546	−0.529420
$437$	−4.37941	−0.209496
$438$	9.70868	0.463899
$439$	−27.4061	−1.30802	−0.654012	−	0.756485i	$-0.726915\pi$
$439$	−27.4061	−1.30802	−0.654012	+	0.756485i	$0.726915\pi$
$440$	−0.405966	−0.0193537
$441$	136.895	6.51879
$442$	0.635085	0.0302079
$443$	13.2401	0.629055	0.314527	−	0.949248i	$-0.398154\pi$
$443$	13.2401	0.629055	0.314527	+	0.949248i	$0.398154\pi$
$444$	−31.1100	−1.47641
$445$	1.80101	0.0853759
$446$	−2.39151	−0.113241
$447$	35.6311	1.68529
$448$	5.16404	0.243978
$449$	−21.4786	−1.01364	−0.506818	−	0.862053i	$-0.669178\pi$
$449$	−21.4786	−1.01364	−0.506818	+	0.862053i	$0.669178\pi$
$450$	−34.6908	−1.63534
$451$	−17.6136	−0.829390
$452$	15.9633	0.750849
$453$	3.70594	0.174120
$454$	−5.07995	−0.238414
$455$	0.181228	0.00849612
$456$	14.5629	0.681971
$457$	−3.44567	−0.161182	−0.0805909	−	0.996747i	$-0.525681\pi$
$457$	−3.44567	−0.161182	−0.0805909	+	0.996747i	$0.525681\pi$
$458$	5.32645	0.248889
$459$	−28.6608	−1.33777
$460$	0.120257	0.00560700
$461$	−18.1362	−0.844689	−0.422345	−	0.906435i	$-0.638793\pi$
$461$	−18.1362	−0.844689	−0.422345	+	0.906435i	$0.638793\pi$
$462$	52.2179	2.42940
$463$	25.2513	1.17353	0.586763	−	0.809758i	$-0.300402\pi$
$463$	25.2513	1.17353	0.586763	+	0.809758i	$0.300402\pi$
$464$	−4.64072	−0.215440
$465$	−0.389189	−0.0180482
$466$	2.68052	0.124173
$467$	27.4955	1.27234	0.636171	−	0.771548i	$-0.280517\pi$
$467$	27.4955	1.27234	0.636171	+	0.771548i	$0.280517\pi$
$468$	1.92787	0.0891157
$469$	2.19483	0.101348
$470$	0.973308	0.0448953
$471$	−42.9685	−1.97989
$472$	−5.08216	−0.233925
$473$	−20.3434	−0.935391
$474$	45.2355	2.07774
$475$	22.9975	1.05520
$476$	11.8409	0.542728
$477$	41.3008	1.89104
$478$	−11.0564	−0.505708
$479$	2.36031	0.107845	0.0539227	−	0.998545i	$-0.482828\pi$
$479$	2.36031	0.107845	0.0539227	+	0.998545i	$0.482828\pi$
$480$	−0.399891	−0.0182525
$481$	2.73020	0.124486
$482$	5.22346	0.237922
$483$	−15.4682	−0.703826
$484$	−0.734548	−0.0333885
$485$	−1.59397	−0.0723783
$486$	−21.1002	−0.957125
$487$	−29.1500	−1.32091	−0.660455	−	0.750865i	$-0.729637\pi$
$487$	−29.1500	−1.32091	−0.660455	+	0.750865i	$0.729637\pi$
$488$	−3.09134	−0.139938
$489$	−41.5107	−1.87718
$490$	2.49199	0.112577
$491$	−15.4451	−0.697029	−0.348515	−	0.937303i	$-0.613314\pi$
$491$	−15.4451	−0.697029	−0.348515	+	0.937303i	$0.613314\pi$
$492$	−17.3500	−0.782197
$493$	−10.6410	−0.479245
$494$	−1.27804	−0.0575015
$495$	−2.82574	−0.127007
$496$	0.973237	0.0436996
$497$	7.22669	0.324161
$498$	−10.1074	−0.452925
$499$	37.4525	1.67660	0.838302	−	0.545206i	$-0.183549\pi$
$499$	37.4525	1.67660	0.838302	+	0.545206i	$0.183549\pi$
$500$	−1.26504	−0.0565742
$501$	−51.7213	−2.31074
$502$	−8.53704	−0.381027
$503$	−1.16967	−0.0521532	−0.0260766	−	0.999660i	$-0.508301\pi$
$503$	−1.16967	−0.0521532	−0.0260766	+	0.999660i	$0.508301\pi$
$504$	35.9444	1.60109
$505$	0.0759031	0.00337764
$506$	−3.04087	−0.135183
$507$	40.7863	1.81138
$508$	10.2657	0.455467
$509$	21.2307	0.941033	0.470516	−	0.882391i	$-0.344068\pi$
$509$	21.2307	0.941033	0.470516	+	0.882391i	$0.344068\pi$
$510$	−0.916934	−0.0406025
$511$	−15.8858	−0.702746
$512$	1.00000	0.0441942
$513$	57.6767	2.54649
$514$	4.55007	0.200695
$515$	0.904730	0.0398672
$516$	−20.0390	−0.882167
$517$	−24.6115	−1.08241
$518$	50.9036	2.23657
$519$	−59.2609	−2.60126
$520$	0.0350943	0.00153899
$521$	15.7364	0.689425	0.344713	−	0.938708i	$-0.387976\pi$
$521$	15.7364	0.689425	0.344713	+	0.938708i	$0.387976\pi$
$522$	−32.3018	−1.41381
$523$	−2.89234	−0.126473	−0.0632367	−	0.997999i	$-0.520142\pi$
$523$	−2.89234	−0.126473	−0.0632367	+	0.997999i	$0.520142\pi$
$524$	16.8058	0.734164
$525$	81.2276	3.54507
$526$	19.6713	0.857711
$527$	2.23159	0.0972097
$528$	10.1118	0.440061
$529$	−22.0992	−0.960836
$530$	0.751828	0.0326573
$531$	−35.3745	−1.53512
$532$	−23.8285	−1.03310
$533$	1.52263	0.0659523
$534$	−44.8596	−1.94126
$535$	−2.40244	−0.103867
$536$	0.425022	0.0183581
$537$	20.2962	0.875845
$538$	−5.55897	−0.239664
$539$	−63.0136	−2.71419
$540$	−1.58378	−0.0681549
$541$	−18.1605	−0.780783	−0.390392	−	0.920649i	$-0.627660\pi$
$541$	−18.1605	−0.780783	−0.390392	+	0.920649i	$0.627660\pi$
$542$	0.188715	0.00810600
$543$	−77.4093	−3.32195
$544$	2.29296	0.0983098
$545$	−1.40070	−0.0599993
$546$	−4.51405	−0.193183
$547$	−24.3052	−1.03921	−0.519607	−	0.854405i	$-0.673922\pi$
$547$	−24.3052	−1.03921	−0.519607	+	0.854405i	$0.673922\pi$
$548$	4.73370	0.202213
$549$	−21.5173	−0.918336
$550$	15.9684	0.680896
$551$	21.4137	0.912256
$552$	−2.99536	−0.127491
$553$	−74.0165	−3.14750
$554$	10.0013	0.424913
$555$	−3.94185	−0.167322
$556$	−3.84059	−0.162877
$557$	14.0010	0.593242	0.296621	−	0.954995i	$-0.404140\pi$
$557$	14.0010	0.593242	0.296621	+	0.954995i	$0.404140\pi$
$558$	6.77423	0.286776
$559$	1.75861	0.0743814
$560$	0.654321	0.0276501
$561$	23.1860	0.978914
$562$	13.2302	0.558084
$563$	−25.1531	−1.06008	−0.530039	−	0.847973i	$-0.677823\pi$
$563$	−25.1531	−1.06008	−0.530039	+	0.847973i	$0.677823\pi$
$564$	−24.2432	−1.02082
$565$	2.02266	0.0850940
$566$	−14.8058	−0.622333
$567$	95.8819	4.02666
$568$	1.39943	0.0587186
$569$	−37.9840	−1.59237	−0.796187	−	0.605051i	$-0.793153\pi$
$569$	−37.9840	−1.59237	−0.796187	+	0.605051i	$0.793153\pi$
$570$	1.84523	0.0772880
$571$	16.5001	0.690508	0.345254	−	0.938509i	$-0.387793\pi$
$571$	16.5001	0.690508	0.345254	+	0.938509i	$0.387793\pi$
$572$	−0.887411	−0.0371045
$573$	−30.1293	−1.25867
$574$	28.3888	1.18493
$575$	−4.73022	−0.197264
$576$	6.96052	0.290021
$577$	0.833535	0.0347005	0.0173503	−	0.999849i	$-0.494477\pi$
$577$	0.833535	0.0347005	0.0173503	+	0.999849i	$0.494477\pi$
$578$	−11.7423	−0.488417
$579$	18.8435	0.783108
$580$	−0.588012	−0.0244159
$581$	16.5382	0.686122
$582$	39.7026	1.64573
$583$	−19.0111	−0.787358
$584$	−3.07623	−0.127295
$585$	0.244274	0.0100995
$586$	27.9134	1.15309
$587$	6.27248	0.258893	0.129446	−	0.991586i	$-0.458680\pi$
$587$	6.27248	0.258893	0.129446	+	0.991586i	$0.458680\pi$
$588$	−62.0706	−2.55975
$589$	−4.49082	−0.185041
$590$	−0.643946	−0.0265108
$591$	−36.7352	−1.51108
$592$	9.85731	0.405133
$593$	7.97567	0.327522	0.163761	−	0.986500i	$-0.447637\pi$
$593$	7.97567	0.327522	0.163761	+	0.986500i	$0.447637\pi$
$594$	40.0481	1.64319
$595$	1.50033	0.0615076
$596$	−11.2899	−0.462451
$597$	41.1544	1.68434
$598$	0.262872	0.0107496
$599$	−8.52043	−0.348135	−0.174068	−	0.984734i	$-0.555691\pi$
$599$	−8.52043	−0.348135	−0.174068	+	0.984734i	$0.555691\pi$
$600$	15.7295	0.642153
$601$	−25.6594	−1.04667	−0.523335	−	0.852127i	$-0.675312\pi$
$601$	−25.6594	−1.04667	−0.523335	+	0.852127i	$0.675312\pi$
$602$	32.7887	1.33637
$603$	2.95837	0.120474
$604$	−1.17424	−0.0477793
$605$	−0.0930724	−0.00378393
$606$	−1.89060	−0.0768003
$607$	−33.8877	−1.37546	−0.687729	−	0.725968i	$-0.741392\pi$
$607$	−33.8877	−1.37546	−0.687729	+	0.725968i	$0.741392\pi$
$608$	−4.61432	−0.187135
$609$	75.6338	3.06483
$610$	−0.391694	−0.0158592
$611$	2.12757	0.0860724
$612$	15.9602	0.645152
$613$	−16.7655	−0.677154	−0.338577	−	0.940939i	$-0.609946\pi$
$613$	−16.7655	−0.677154	−0.338577	+	0.940939i	$0.609946\pi$
$614$	−11.6931	−0.471895
$615$	−2.19837	−0.0886466
$616$	−16.5455	−0.666635
$617$	36.3913	1.46506	0.732530	−	0.680735i	$-0.238340\pi$
$617$	36.3913	1.46506	0.732530	+	0.680735i	$0.238340\pi$
$618$	−22.5351	−0.906494
$619$	−8.33228	−0.334903	−0.167451	−	0.985880i	$-0.553554\pi$
$619$	−8.33228	−0.334903	−0.167451	+	0.985880i	$0.553554\pi$
$620$	0.123316	0.00495249
$621$	−11.8632	−0.476053
$622$	12.6235	0.506156
$623$	73.4013	2.94076
$624$	−0.874131	−0.0349932
$625$	24.7594	0.990377
$626$	−10.0057	−0.399907
$627$	−46.6592	−1.86339
$628$	13.6147	0.543288
$629$	22.6024	0.901217
$630$	4.55441	0.181452
$631$	26.1353	1.04043	0.520215	−	0.854036i	$-0.325852\pi$
$631$	26.1353	1.04043	0.520215	+	0.854036i	$0.325852\pi$
$632$	−14.3331	−0.570138
$633$	71.9118	2.85824
$634$	−4.36072	−0.173186
$635$	1.30074	0.0516182
$636$	−18.7266	−0.742557
$637$	5.44729	0.215830
$638$	14.8687	0.588659
$639$	9.74073	0.385337
$640$	0.126707	0.00500854
$641$	4.85837	0.191894	0.0959470	−	0.995386i	$-0.469412\pi$
$641$	4.85837	0.191894	0.0959470	+	0.995386i	$0.469412\pi$
$642$	59.8401	2.36170
$643$	14.2210	0.560821	0.280411	−	0.959880i	$-0.409529\pi$
$643$	14.2210	0.560821	0.280411	+	0.959880i	$0.409529\pi$
$644$	4.90115	0.193132
$645$	−2.53908	−0.0999762
$646$	−10.5804	−0.416282
$647$	27.7257	1.09001	0.545005	−	0.838433i	$-0.316528\pi$
$647$	27.7257	1.09001	0.545005	+	0.838433i	$0.316528\pi$
$648$	18.5672	0.729390
$649$	16.2831	0.639168
$650$	−1.38041	−0.0541442
$651$	−15.8617	−0.621668
$652$	13.1528	0.515104
$653$	−7.83766	−0.306712	−0.153356	−	0.988171i	$-0.549008\pi$
$653$	−7.83766	−0.306712	−0.153356	+	0.988171i	$0.549008\pi$
$654$	34.8887	1.36426
$655$	2.12941	0.0832030
$656$	5.49741	0.214638
$657$	−21.4122	−0.835369
$658$	39.6679	1.54641
$659$	−39.1494	−1.52504	−0.762522	−	0.646963i	$-0.776039\pi$
$659$	−39.1494	−1.52504	−0.762522	+	0.646963i	$0.776039\pi$
$660$	1.28124	0.0498723
$661$	7.86361	0.305859	0.152929	−	0.988237i	$-0.451129\pi$
$661$	7.86361	0.305859	0.152929	+	0.988237i	$0.451129\pi$
$662$	22.9812	0.893192
$663$	−2.00435	−0.0778423
$664$	3.20258	0.124284
$665$	−3.01924	−0.117081
$666$	68.6120	2.65866
$667$	−4.40447	−0.170542
$668$	16.3881	0.634074
$669$	7.54766	0.291810
$670$	0.0538533	0.00208053
$671$	9.90456	0.382361
$672$	−16.2979	−0.628704
$673$	48.5101	1.86993	0.934964	−	0.354742i	$-0.115431\pi$
$673$	48.5101	1.86993	0.934964	+	0.354742i	$0.115431\pi$
$674$	31.8141	1.22543
$675$	62.2968	2.39781
$676$	−12.9233	−0.497049
$677$	37.4073	1.43768	0.718840	−	0.695176i	$-0.244673\pi$
$677$	37.4073	1.43768	0.718840	+	0.695176i	$0.244673\pi$
$678$	−50.3806	−1.93485
$679$	−64.9633	−2.49306
$680$	0.290534	0.0111415
$681$	16.0325	0.614366
$682$	−3.11823	−0.119403
$683$	−3.91544	−0.149820	−0.0749100	−	0.997190i	$-0.523867\pi$
$683$	−3.91544	−0.149820	−0.0749100	+	0.997190i	$0.523867\pi$
$684$	−32.1180	−1.22806
$685$	0.599793	0.0229169
$686$	65.4146	2.49754
$687$	−16.8104	−0.641358
$688$	6.34943	0.242070
$689$	1.64344	0.0626100
$690$	−0.379534	−0.0144486
$691$	31.4259	1.19550	0.597749	−	0.801683i	$-0.296062\pi$
$691$	31.4259	1.19550	0.597749	+	0.801683i	$0.296062\pi$
$692$	18.7770	0.713796
$693$	−115.165	−4.37475
$694$	28.0310	1.06404
$695$	−0.486631	−0.0184590
$696$	14.6462	0.555164
$697$	12.6053	0.477461
$698$	13.5611	0.513296
$699$	−8.45981	−0.319979
$700$	−25.7373	−0.972778
$701$	30.8684	1.16588	0.582942	−	0.812514i	$-0.301902\pi$
$701$	30.8684	1.16588	0.582942	+	0.812514i	$0.301902\pi$
$702$	−3.46201	−0.130665
$703$	−45.4848	−1.71549
$704$	−3.20397	−0.120754
$705$	−3.07179	−0.115690
$706$	−0.301078	−0.0113312
$707$	3.09349	0.116343
$708$	16.0394	0.602799
$709$	50.8639	1.91023	0.955117	−	0.296230i	$-0.0957293\pi$
$709$	50.8639	1.91023	0.955117	+	0.296230i	$0.0957293\pi$
$710$	0.177317	0.00665460
$711$	−99.7654	−3.74150
$712$	14.2139	0.532690
$713$	0.923692	0.0345925
$714$	−37.3703	−1.39855
$715$	−0.112441	−0.00420506
$716$	−6.43092	−0.240335
$717$	34.8943	1.30315
$718$	−25.4313	−0.949086
$719$	52.5879	1.96120	0.980599	−	0.196025i	$-0.0628035\pi$
$719$	52.5879	1.96120	0.980599	+	0.196025i	$0.0628035\pi$
$720$	0.881947	0.0328682
$721$	36.8729	1.37322
$722$	2.29193	0.0852967
$723$	−16.4854	−0.613098
$724$	24.5274	0.911555
$725$	23.1291	0.858992
$726$	2.31825	0.0860385
$727$	−7.98148	−0.296017	−0.148008	−	0.988986i	$-0.547286\pi$
$727$	−7.98148	−0.296017	−0.148008	+	0.988986i	$0.547286\pi$
$728$	1.43029	0.0530102
$729$	10.8912	0.403377
$730$	−0.389781	−0.0144264
$731$	14.5590	0.538483
$732$	9.75635	0.360605
$733$	−25.5918	−0.945253	−0.472627	−	0.881263i	$-0.656694\pi$
$733$	−25.5918	−0.945253	−0.472627	+	0.881263i	$0.656694\pi$
$734$	7.17017	0.264656
$735$	−7.86479	−0.290097
$736$	0.949092	0.0349840
$737$	−1.36176	−0.0501610
$738$	38.2648	1.40855
$739$	20.0865	0.738894	0.369447	−	0.929252i	$-0.379547\pi$
$739$	20.0865	0.738894	0.369447	+	0.929252i	$0.379547\pi$
$740$	1.24899	0.0459138
$741$	4.03352	0.148175
$742$	30.6413	1.12488
$743$	−47.6511	−1.74815	−0.874074	−	0.485793i	$-0.838531\pi$
$743$	−47.6511	−1.74815	−0.874074	+	0.485793i	$0.838531\pi$
$744$	−3.07156	−0.112609
$745$	−1.43051	−0.0524097
$746$	28.5144	1.04398
$747$	22.2916	0.815607
$748$	−7.34658	−0.268618
$749$	−97.9132	−3.57767
$750$	3.99249	0.145785
$751$	5.80813	0.211942	0.105971	−	0.994369i	$-0.466205\pi$
$751$	5.80813	0.211942	0.105971	+	0.994369i	$0.466205\pi$
$752$	7.68155	0.280117
$753$	26.9431	0.981863
$754$	−1.28535	−0.0468096
$755$	−0.148785	−0.00541484
$756$	−64.5479	−2.34759
$757$	19.8269	0.720620	0.360310	−	0.932833i	$-0.382671\pi$
$757$	19.8269	0.720620	0.360310	+	0.932833i	$0.382671\pi$
$758$	−15.5128	−0.563452
$759$	9.59706	0.348351
$760$	−0.584667	−0.0212081
$761$	37.1860	1.34799	0.673995	−	0.738736i	$-0.264577\pi$
$761$	37.1860	1.34799	0.673995	+	0.738736i	$0.264577\pi$
$762$	−32.3988	−1.17369
$763$	−57.0865	−2.06667
$764$	9.54659	0.345384
$765$	2.02227	0.0731152
$766$	8.94598	0.323232
$767$	−1.40761	−0.0508260
$768$	−3.15603	−0.113883
$769$	−22.5934	−0.814739	−0.407369	−	0.913263i	$-0.633554\pi$
$769$	−22.5934	−0.814739	−0.407369	+	0.913263i	$0.633554\pi$
$770$	−2.09643	−0.0755500
$771$	−14.3601	−0.517168
$772$	−5.97063	−0.214888
$773$	−0.112206	−0.00403578	−0.00201789	−	0.999998i	$-0.500642\pi$
$773$	−0.112206	−0.00403578	−0.00201789	+	0.999998i	$0.500642\pi$
$774$	44.1953	1.58857
$775$	−4.85056	−0.174237
$776$	−12.5799	−0.451593
$777$	−160.653	−5.76340
$778$	−19.0030	−0.681289
$779$	−25.3668	−0.908859
$780$	−0.110759	−0.00396579
$781$	−4.48372	−0.160440
$782$	2.17623	0.0778218
$783$	58.0066	2.07299
$784$	19.6673	0.702404
$785$	1.72509	0.0615709
$786$	−53.0395	−1.89186
$787$	−47.4574	−1.69167	−0.845836	−	0.533443i	$-0.820898\pi$
$787$	−47.4574	−1.69167	−0.845836	+	0.533443i	$0.820898\pi$
$788$	11.6397	0.414646
$789$	−62.0833	−2.21022
$790$	−1.81610	−0.0646139
$791$	82.4350	2.93105
$792$	−22.3013	−0.792443
$793$	−0.856213	−0.0304050
$794$	−7.25878	−0.257605
$795$	−2.37279	−0.0841542
$796$	−13.0399	−0.462188
$797$	22.5840	0.799967	0.399983	−	0.916522i	$-0.369016\pi$
$797$	22.5840	0.799967	0.399983	+	0.916522i	$0.369016\pi$
$798$	75.2035	2.66218
$799$	17.6135	0.623120
$800$	−4.98395	−0.176209
$801$	98.9363	3.49574
$802$	17.3981	0.614348
$803$	9.85618	0.347817
$804$	−1.34138	−0.0473068
$805$	0.621011	0.0218878
$806$	0.269559	0.00949482
$807$	17.5443	0.617587
$808$	0.599044	0.0210743
$809$	−6.94987	−0.244344	−0.122172	−	0.992509i	$-0.538986\pi$
$809$	−6.94987	−0.244344	−0.122172	+	0.992509i	$0.538986\pi$
$810$	2.35260	0.0826620
$811$	39.2392	1.37787	0.688937	−	0.724821i	$-0.258078\pi$
$811$	39.2392	1.37787	0.688937	+	0.724821i	$0.258078\pi$
$812$	−23.9649	−0.841001
$813$	−0.595590	−0.0208882
$814$	−31.5826	−1.10697
$815$	1.66656	0.0583769
$816$	−7.23664	−0.253333
$817$	−29.2983	−1.02502
$818$	27.3242	0.955368
$819$	9.95558	0.347876
$820$	0.696561	0.0243250
$821$	42.6889	1.48985	0.744927	−	0.667147i	$-0.232485\pi$
$821$	42.6889	1.48985	0.744927	+	0.667147i	$0.232485\pi$
$822$	−14.9397	−0.521081
$823$	−44.6437	−1.55618	−0.778092	−	0.628151i	$-0.783812\pi$
$823$	−44.6437	−1.55618	−0.778092	+	0.628151i	$0.783812\pi$
$824$	7.14033	0.248745
$825$	−50.3968	−1.75459
$826$	−26.2445	−0.913162
$827$	−45.1598	−1.57036	−0.785180	−	0.619268i	$-0.787430\pi$
$827$	−45.1598	−1.57036	−0.785180	+	0.619268i	$0.787430\pi$
$828$	6.60617	0.229580
$829$	−31.9968	−1.11129	−0.555647	−	0.831418i	$-0.687529\pi$
$829$	−31.9968	−1.11129	−0.555647	+	0.831418i	$0.687529\pi$
$830$	0.405790	0.0140852
$831$	−31.5643	−1.09495
$832$	0.276972	0.00960227
$833$	45.0963	1.56250
$834$	12.1210	0.419717
$835$	2.07649	0.0718598
$836$	14.7842	0.511321
$837$	−12.1650	−0.420483
$838$	5.09022	0.175839
$839$	3.06882	0.105948	0.0529738	−	0.998596i	$-0.483130\pi$
$839$	3.06882	0.105948	0.0529738	+	0.998596i	$0.483130\pi$
$840$	−2.06505	−0.0712512
$841$	−7.46374	−0.257371
$842$	−22.2268	−0.765987
$843$	−41.7550	−1.43812
$844$	−22.7856	−0.784311
$845$	−1.63747	−0.0563308
$846$	53.4676	1.83825
$847$	−3.79323	−0.130337
$848$	5.93359	0.203760
$849$	46.7274	1.60368
$850$	−11.4280	−0.391976
$851$	9.35550	0.320702
$852$	−4.41663	−0.151311
$853$	−11.6490	−0.398855	−0.199427	−	0.979913i	$-0.563908\pi$
$853$	−11.6490	−0.398855	−0.199427	+	0.979913i	$0.563908\pi$
$854$	−15.9638	−0.546270
$855$	−4.06958	−0.139177
$856$	−18.9606	−0.648059
$857$	3.11166	0.106292	0.0531462	−	0.998587i	$-0.483075\pi$
$857$	3.11166	0.106292	0.0531462	+	0.998587i	$0.483075\pi$
$858$	2.80069	0.0956141
$859$	28.2804	0.964915	0.482457	−	0.875919i	$-0.339744\pi$
$859$	28.2804	0.964915	0.482457	+	0.875919i	$0.339744\pi$
$860$	0.804518	0.0274338
$861$	−89.5960	−3.05342
$862$	−9.66923	−0.329335
$863$	3.93034	0.133790	0.0668952	−	0.997760i	$-0.478691\pi$
$863$	3.93034	0.133790	0.0668952	+	0.997760i	$0.478691\pi$
$864$	−12.4995	−0.425242
$865$	2.37919	0.0808947
$866$	−6.21118	−0.211064
$867$	37.0592	1.25860
$868$	5.02584	0.170588
$869$	45.9227	1.55782
$870$	1.85578	0.0629169
$871$	0.117719	0.00398876
$872$	−11.0546	−0.374357
$873$	−87.5628	−2.96355
$874$	−4.37941	−0.148136
$875$	−6.53270	−0.220846
$876$	9.70868	0.328026
$877$	40.6211	1.37168	0.685838	−	0.727754i	$-0.259436\pi$
$877$	40.6211	1.37168	0.685838	+	0.727754i	$0.259436\pi$
$878$	−27.4061	−0.924912
$879$	−88.0954	−2.97138
$880$	−0.405966	−0.0136851
$881$	−9.52411	−0.320876	−0.160438	−	0.987046i	$-0.551291\pi$
$881$	−9.52411	−0.320876	−0.160438	+	0.987046i	$0.551291\pi$
$882$	136.895	4.60948
$883$	−8.35845	−0.281284	−0.140642	−	0.990061i	$-0.544917\pi$
$883$	−8.35845	−0.281284	−0.140642	+	0.990061i	$0.544917\pi$
$884$	0.635085	0.0213602
$885$	2.03231	0.0683154
$886$	13.2401	0.444809
$887$	8.13444	0.273128	0.136564	−	0.990631i	$-0.456394\pi$
$887$	8.13444	0.273128	0.136564	+	0.990631i	$0.456394\pi$
$888$	−31.1100	−1.04398
$889$	53.0125	1.77798
$890$	1.80101	0.0603699
$891$	−59.4889	−1.99295
$892$	−2.39151	−0.0800736
$893$	−35.4451	−1.18613
$894$	35.6311	1.19168
$895$	−0.814844	−0.0272372
$896$	5.16404	0.172518
$897$	−0.829631	−0.0277006
$898$	−21.4786	−0.716749
$899$	−4.51652	−0.150634
$900$	−34.6908	−1.15636
$901$	13.6055	0.453264
$902$	−17.6136	−0.586467
$903$	−103.482	−3.44367
$904$	15.9633	0.530931
$905$	3.10780	0.103307
$906$	3.70594	0.123122
$907$	−4.77501	−0.158552	−0.0792758	−	0.996853i	$-0.525261\pi$
$907$	−4.77501	−0.158552	−0.0792758	+	0.996853i	$0.525261\pi$
$908$	−5.07995	−0.168584
$909$	4.16965	0.138299
$910$	0.181228	0.00600766
$911$	8.45562	0.280147	0.140074	−	0.990141i	$-0.455266\pi$
$911$	8.45562	0.280147	0.140074	+	0.990141i	$0.455266\pi$
$912$	14.5629	0.482226
$913$	−10.2610	−0.339589
$914$	−3.44567	−0.113973
$915$	1.23620	0.0408675
$916$	5.32645	0.175991
$917$	86.7858	2.86592
$918$	−28.6608	−0.945949
$919$	−23.2429	−0.766712	−0.383356	−	0.923601i	$-0.625232\pi$
$919$	−23.2429	−0.766712	−0.383356	+	0.923601i	$0.625232\pi$
$920$	0.120257	0.00396475
$921$	36.9037	1.21602
$922$	−18.1362	−0.597285
$923$	0.387601	0.0127581
$924$	52.2179	1.71784
$925$	−49.1283	−1.61533
$926$	25.2513	0.829809
$927$	49.7004	1.63237
$928$	−4.64072	−0.152339
$929$	35.3596	1.16011	0.580055	−	0.814577i	$-0.303031\pi$
$929$	35.3596	1.16011	0.580055	+	0.814577i	$0.303031\pi$
$930$	−0.389189	−0.0127620
$931$	−90.7513	−2.97425
$932$	2.68052	0.0878035
$933$	−39.8401	−1.30431
$934$	27.4955	0.899682
$935$	−0.930864	−0.0304425
$936$	1.92787	0.0630143
$937$	31.8521	1.04056	0.520281	−	0.853995i	$-0.325827\pi$
$937$	31.8521	1.04056	0.520281	+	0.853995i	$0.325827\pi$
$938$	2.19483	0.0716637
$939$	31.5782	1.03052
$940$	0.973308	0.0317458
$941$	55.2658	1.80161	0.900807	−	0.434219i	$-0.142976\pi$
$941$	55.2658	1.80161	0.900807	+	0.434219i	$0.142976\pi$
$942$	−42.9685	−1.39999
$943$	5.21755	0.169907
$944$	−5.08216	−0.165410
$945$	−8.17868	−0.266053
$946$	−20.3434	−0.661421
$947$	−23.1857	−0.753433	−0.376717	−	0.926329i	$-0.622947\pi$
$947$	−23.1857	−0.753433	−0.376717	+	0.926329i	$0.622947\pi$
$948$	45.2355	1.46918
$949$	−0.852030	−0.0276581
$950$	22.9975	0.746138
$951$	13.7626	0.446281
$952$	11.8409	0.383767
$953$	34.9846	1.13326	0.566631	−	0.823972i	$-0.308247\pi$
$953$	34.9846	1.13326	0.566631	+	0.823972i	$0.308247\pi$
$954$	41.3008	1.33716
$955$	1.20962	0.0391424
$956$	−11.0564	−0.357590
$957$	−46.9262	−1.51691
$958$	2.36031	0.0762582
$959$	24.4450	0.789370
$960$	−0.399891	−0.0129064
$961$	−30.0528	−0.969445
$962$	2.73020	0.0880251
$963$	−131.975	−4.25285
$964$	5.22346	0.168236
$965$	−0.756521	−0.0243533
$966$	−15.4682	−0.497680
$967$	−0.935053	−0.0300693	−0.0150346	−	0.999887i	$-0.504786\pi$
$967$	−0.935053	−0.0300693	−0.0150346	+	0.999887i	$0.504786\pi$
$968$	−0.734548	−0.0236093
$969$	33.3922	1.07271
$970$	−1.59397	−0.0511792
$971$	−11.9326	−0.382936	−0.191468	−	0.981499i	$-0.561325\pi$
$971$	−11.9326	−0.382936	−0.191468	+	0.981499i	$0.561325\pi$
$972$	−21.1002	−0.676790
$973$	−19.8330	−0.635816
$974$	−29.1500	−0.934025
$975$	4.35662	0.139524
$976$	−3.09134	−0.0989513
$977$	−17.9356	−0.573812	−0.286906	−	0.957959i	$-0.592627\pi$
$977$	−17.9356	−0.573812	−0.286906	+	0.957959i	$0.592627\pi$
$978$	−41.5107	−1.32737
$979$	−45.5411	−1.45550
$980$	2.49199	0.0796037
$981$	−76.9458	−2.45669
$982$	−15.4451	−0.492874
$983$	38.5877	1.23076	0.615378	−	0.788232i	$-0.289004\pi$
$983$	38.5877	1.23076	0.615378	+	0.788232i	$0.289004\pi$
$984$	−17.3500	−0.553097
$985$	1.47483	0.0469920
$986$	−10.6410	−0.338878
$987$	−125.193	−3.98493
$988$	−1.27804	−0.0406597
$989$	6.02619	0.191622
$990$	−2.82574	−0.0898078
$991$	−57.1812	−1.81642	−0.908211	−	0.418512i	$-0.862552\pi$
$991$	−57.1812	−1.81642	−0.908211	+	0.418512i	$0.862552\pi$
$992$	0.973237	0.0309003
$993$	−72.5295	−2.30165
$994$	7.22669	0.229217
$995$	−1.65225	−0.0523799
$996$	−10.1074	−0.320266
$997$	33.9164	1.07414	0.537072	−	0.843537i	$-0.319530\pi$
$997$	33.9164	1.07414	0.537072	+	0.843537i	$0.319530\pi$
$998$	37.4525	1.18554
$999$	−123.211	−3.89824

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.d.1.6	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.d.1.6	✓	96	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.15603 q^{3} +1.00000 q^{4} +0.126707 q^{5} -3.15603 q^{6} +5.16404 q^{7} +1.00000 q^{8} +6.96052 q^{9} +0.126707 q^{10} -3.20397 q^{11} -3.15603 q^{12} +0.276972 q^{13} +5.16404 q^{14} -0.399891 q^{15} +1.00000 q^{16} +2.29296 q^{17} +6.96052 q^{18} -4.61432 q^{19} +0.126707 q^{20} -16.2979 q^{21} -3.20397 q^{22} +0.949092 q^{23} -3.15603 q^{24} -4.98395 q^{25} +0.276972 q^{26} -12.4995 q^{27} +5.16404 q^{28} -4.64072 q^{29} -0.399891 q^{30} +0.973237 q^{31} +1.00000 q^{32} +10.1118 q^{33} +2.29296 q^{34} +0.654321 q^{35} +6.96052 q^{36} +9.85731 q^{37} -4.61432 q^{38} -0.874131 q^{39} +0.126707 q^{40} +5.49741 q^{41} -16.2979 q^{42} +6.34943 q^{43} -3.20397 q^{44} +0.881947 q^{45} +0.949092 q^{46} +7.68155 q^{47} -3.15603 q^{48} +19.6673 q^{49} -4.98395 q^{50} -7.23664 q^{51} +0.276972 q^{52} +5.93359 q^{53} -12.4995 q^{54} -0.405966 q^{55} +5.16404 q^{56} +14.5629 q^{57} -4.64072 q^{58} -5.08216 q^{59} -0.399891 q^{60} -3.09134 q^{61} +0.973237 q^{62} +35.9444 q^{63} +1.00000 q^{64} +0.0350943 q^{65} +10.1118 q^{66} +0.425022 q^{67} +2.29296 q^{68} -2.99536 q^{69} +0.654321 q^{70} +1.39943 q^{71} +6.96052 q^{72} -3.07623 q^{73} +9.85731 q^{74} +15.7295 q^{75} -4.61432 q^{76} -16.5455 q^{77} -0.874131 q^{78} -14.3331 q^{79} +0.126707 q^{80} +18.5672 q^{81} +5.49741 q^{82} +3.20258 q^{83} -16.2979 q^{84} +0.290534 q^{85} +6.34943 q^{86} +14.6462 q^{87} -3.20397 q^{88} +14.2139 q^{89} +0.881947 q^{90} +1.43029 q^{91} +0.949092 q^{92} -3.07156 q^{93} +7.68155 q^{94} -0.584667 q^{95} -3.15603 q^{96} -12.5799 q^{97} +19.6673 q^{98} -22.3013 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19}+ \cdots + 42 q^{99}+O(q^{100}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9 + 39 * q^10 + 36 * q^11 + 8 * q^12 + 63 * q^13 + 19 * q^14 + 17 * q^15 + 96 * q^16 + 56 * q^17 + 130 * q^18 + 17 * q^19 + 39 * q^20 + 51 * q^21 + 36 * q^22 + 47 * q^23 + 8 * q^24 + 147 * q^25 + 63 * q^26 + 17 * q^27 + 19 * q^28 + 60 * q^29 + 17 * q^30 + 63 * q^31 + 96 * q^32 + 55 * q^33 + 56 * q^34 + 45 * q^35 + 130 * q^36 + 46 * q^37 + 17 * q^38 + 22 * q^39 + 39 * q^40 + 101 * q^41 + 51 * q^42 - 3 * q^43 + 36 * q^44 + 106 * q^45 + 47 * q^46 + 99 * q^47 + 8 * q^48 + 175 * q^49 + 147 * q^50 - q^51 + 63 * q^52 + 75 * q^53 + 17 * q^54 + 80 * q^55 + 19 * q^56 + 35 * q^57 + 60 * q^58 + 129 * q^59 + 17 * q^60 + 75 * q^61 + 63 * q^62 + 20 * q^63 + 96 * q^64 + 55 * q^65 + 55 * q^66 + 2 * q^67 + 56 * q^68 + 57 * q^69 + 45 * q^70 + 87 * q^71 + 130 * q^72 + 120 * q^73 + 46 * q^74 - 15 * q^75 + 17 * q^76 + 95 * q^77 + 22 * q^78 + 21 * q^79 + 39 * q^80 + 180 * q^81 + 101 * q^82 + 69 * q^83 + 51 * q^84 + 59 * q^85 - 3 * q^86 + 63 * q^87 + 36 * q^88 + 144 * q^89 + 106 * q^90 - 5 * q^91 + 47 * q^92 + 59 * q^93 + 99 * q^94 + 23 * q^95 + 8 * q^96 + 99 * q^97 + 175 * q^98 + 42 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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