LMFDB - Embedded newform 5054.2.a.v.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5054,2,Mod(1,5054)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5054, 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("5054.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 5054 = 2 \cdot 7 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5054.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,-4,-4,4,2,4,4,-4,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	yes
Analytic conductor:	$40.3563931816$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{20})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 5 $ x^4 - 5*x^2 + 5
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.90211$ of defining polynomial
Character	$\chi$	$=$	5054.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +0.902113 q^{3} +1.00000 q^{4} +0.557537 q^{5} -0.902113 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.18619 q^{9} -0.557537 q^{10} -1.35114 q^{11} +0.902113 q^{12} -1.45965 q^{13} -1.00000 q^{14} +0.502961 q^{15} +1.00000 q^{16} +2.34458 q^{17} +2.18619 q^{18} +0.557537 q^{20} +0.902113 q^{21} +1.35114 q^{22} +3.35114 q^{23} -0.902113 q^{24} -4.68915 q^{25} +1.45965 q^{26} -4.67853 q^{27} +1.00000 q^{28} +0.804226 q^{29} -0.502961 q^{30} -1.09132 q^{31} -1.00000 q^{32} -1.21888 q^{33} -2.34458 q^{34} +0.557537 q^{35} -2.18619 q^{36} -6.78298 q^{37} -1.31677 q^{39} -0.557537 q^{40} +5.03624 q^{41} -0.902113 q^{42} +2.49704 q^{43} -1.35114 q^{44} -1.21888 q^{45} -3.35114 q^{46} -2.24077 q^{47} +0.902113 q^{48} +1.00000 q^{49} +4.68915 q^{50} +2.11507 q^{51} -1.45965 q^{52} -5.37238 q^{53} +4.67853 q^{54} -0.753310 q^{55} -1.00000 q^{56} -0.804226 q^{58} -11.1850 q^{59} +0.502961 q^{60} +7.15067 q^{61} +1.09132 q^{62} -2.18619 q^{63} +1.00000 q^{64} -0.813808 q^{65} +1.21888 q^{66} +10.0498 q^{67} +2.34458 q^{68} +3.02311 q^{69} -0.557537 q^{70} -3.00592 q^{71} +2.18619 q^{72} +7.48089 q^{73} +6.78298 q^{74} -4.23015 q^{75} -1.35114 q^{77} +1.31677 q^{78} -1.96325 q^{79} +0.557537 q^{80} +2.33801 q^{81} -5.03624 q^{82} -9.06154 q^{83} +0.902113 q^{84} +1.30719 q^{85} -2.49704 q^{86} +0.725503 q^{87} +1.35114 q^{88} -3.12164 q^{89} +1.21888 q^{90} -1.45965 q^{91} +3.35114 q^{92} -0.984496 q^{93} +2.24077 q^{94} -0.902113 q^{96} -12.7935 q^{97} -1.00000 q^{98} +2.95385 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} + 4 q^{11} - 4 q^{12} + 2 q^{13} - 4 q^{14} - 2 q^{15} + 4 q^{16} + 2 q^{17} - 2 q^{18} + 2 q^{20} - 4 q^{21}+ \cdots + 2 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 + 4 * q^11 - 4 * q^12 + 2 * q^13 - 4 * q^14 - 2 * q^15 + 4 * q^16 + 2 * q^17 - 2 * q^18 + 2 * q^20 - 4 * q^21 - 4 * q^22 + 4 * q^23 + 4 * q^24 - 4 * q^25 - 2 * q^26 - 10 * q^27 + 4 * q^28 - 12 * q^29 + 2 * q^30 - 14 * q^31 - 4 * q^32 - 4 * q^33 - 2 * q^34 + 2 * q^35 + 2 * q^36 - 24 * q^37 - 12 * q^39 - 2 * q^40 + 4 * q^42 + 14 * q^43 + 4 * q^44 - 4 * q^45 - 4 * q^46 - 2 * q^47 - 4 * q^48 + 4 * q^49 + 4 * q^50 + 8 * q^51 + 2 * q^52 + 10 * q^54 - 18 * q^55 - 4 * q^56 + 12 * q^58 - 2 * q^59 - 2 * q^60 + 2 * q^61 + 14 * q^62 + 2 * q^63 + 4 * q^64 - 14 * q^65 + 4 * q^66 - 22 * q^67 + 2 * q^68 - 4 * q^69 - 2 * q^70 - 4 * q^71 - 2 * q^72 + 10 * q^73 + 24 * q^74 - 16 * q^75 + 4 * q^77 + 12 * q^78 - 2 * q^79 + 2 * q^80 + 4 * q^81 - 4 * q^84 - 14 * q^85 - 14 * q^86 + 32 * q^87 - 4 * q^88 - 10 * q^89 + 4 * q^90 + 2 * q^91 + 4 * q^92 + 14 * q^93 + 2 * q^94 + 4 * q^96 + 22 * q^97 - 4 * q^98 + 2 * 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
$3$	0.902113	0.520835	0.260418	−	0.965496i	$-0.416140\pi$
$3$	0.902113	0.520835	0.260418	+	0.965496i	$0.416140\pi$
$4$	1.00000	0.500000
$5$	0.557537	0.249338	0.124669	−	0.992198i	$-0.460213\pi$
$5$	0.557537	0.249338	0.124669	+	0.992198i	$0.460213\pi$
$6$	−0.902113	−0.368286
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−2.18619	−0.728731
$10$	−0.557537	−0.176309
$11$	−1.35114	−0.407384	−0.203692	−	0.979035i	$-0.565294\pi$
$11$	−1.35114	−0.407384	−0.203692	+	0.979035i	$0.565294\pi$
$12$	0.902113	0.260418
$13$	−1.45965	−0.404834	−0.202417	−	0.979299i	$-0.564880\pi$
$13$	−1.45965	−0.404834	−0.202417	+	0.979299i	$0.564880\pi$
$14$	−1.00000	−0.267261
$15$	0.502961	0.129864
$16$	1.00000	0.250000
$17$	2.34458	0.568643	0.284322	−	0.958729i	$-0.408232\pi$
$17$	2.34458	0.568643	0.284322	+	0.958729i	$0.408232\pi$
$18$	2.18619	0.515290
$19$	0	0
$19$	0	0
$20$	0.557537	0.124669
$21$	0.902113	0.196857
$22$	1.35114	0.288064
$23$	3.35114	0.698761	0.349381	−	0.936981i	$-0.386392\pi$
$23$	3.35114	0.698761	0.349381	+	0.936981i	$0.386392\pi$
$24$	−0.902113	−0.184143
$25$	−4.68915	−0.937831
$26$	1.45965	0.286261
$27$	−4.67853	−0.900384
$28$	1.00000	0.188982
$29$	0.804226	0.149341	0.0746705	−	0.997208i	$-0.476209\pi$
$29$	0.804226	0.149341	0.0746705	+	0.997208i	$0.476209\pi$
$30$	−0.502961	−0.0918277
$31$	−1.09132	−0.196007	−0.0980037	−	0.995186i	$-0.531246\pi$
$31$	−1.09132	−0.196007	−0.0980037	+	0.995186i	$0.531246\pi$
$32$	−1.00000	−0.176777
$33$	−1.21888	−0.212180
$34$	−2.34458	−0.402092
$35$	0.557537	0.0942409
$36$	−2.18619	−0.364365
$37$	−6.78298	−1.11512	−0.557558	−	0.830138i	$-0.688261\pi$
$37$	−6.78298	−1.11512	−0.557558	+	0.830138i	$0.688261\pi$
$38$	0	0
$39$	−1.31677	−0.210852
$40$	−0.557537	−0.0881543
$41$	5.03624	0.786528	0.393264	−	0.919426i	$-0.371346\pi$
$41$	5.03624	0.786528	0.393264	+	0.919426i	$0.371346\pi$
$42$	−0.902113	−0.139199
$43$	2.49704	0.380795	0.190397	−	0.981707i	$-0.439022\pi$
$43$	2.49704	0.380795	0.190397	+	0.981707i	$0.439022\pi$
$44$	−1.35114	−0.203692
$45$	−1.21888	−0.181700
$46$	−3.35114	−0.494099
$47$	−2.24077	−0.326850	−0.163425	−	0.986556i	$-0.552254\pi$
$47$	−2.24077	−0.326850	−0.163425	+	0.986556i	$0.552254\pi$
$48$	0.902113	0.130209
$49$	1.00000	0.142857
$50$	4.68915	0.663146
$51$	2.11507	0.296169
$52$	−1.45965	−0.202417
$53$	−5.37238	−0.737954	−0.368977	−	0.929439i	$-0.620292\pi$
$53$	−5.37238	−0.737954	−0.368977	+	0.929439i	$0.620292\pi$
$54$	4.67853	0.636667
$55$	−0.753310	−0.101576
$56$	−1.00000	−0.133631
$57$	0	0
$58$	−0.804226	−0.105600
$59$	−11.1850	−1.45617	−0.728084	−	0.685488i	$-0.759589\pi$
$59$	−11.1850	−1.45617	−0.728084	+	0.685488i	$0.759589\pi$
$60$	0.502961	0.0649320
$61$	7.15067	0.915549	0.457775	−	0.889068i	$-0.348647\pi$
$61$	7.15067	0.915549	0.457775	+	0.889068i	$0.348647\pi$
$62$	1.09132	0.138598
$63$	−2.18619	−0.275434
$64$	1.00000	0.125000
$65$	−0.813808	−0.100940
$66$	1.21888	0.150034
$67$	10.0498	1.22777	0.613887	−	0.789394i	$-0.289605\pi$
$67$	10.0498	1.22777	0.613887	+	0.789394i	$0.289605\pi$
$68$	2.34458	0.284322
$69$	3.02311	0.363939
$70$	−0.557537	−0.0666384
$71$	−3.00592	−0.356737	−0.178369	−	0.983964i	$-0.557082\pi$
$71$	−3.00592	−0.356737	−0.178369	+	0.983964i	$0.557082\pi$
$72$	2.18619	0.257645
$73$	7.48089	0.875572	0.437786	−	0.899079i	$-0.355763\pi$
$73$	7.48089	0.875572	0.437786	+	0.899079i	$0.355763\pi$
$74$	6.78298	0.788506
$75$	−4.23015	−0.488455
$76$	0	0
$77$	−1.35114	−0.153977
$78$	1.31677	0.149095
$79$	−1.96325	−0.220883	−0.110442	−	0.993883i	$-0.535227\pi$
$79$	−1.96325	−0.220883	−0.110442	+	0.993883i	$0.535227\pi$
$80$	0.557537	0.0623345
$81$	2.33801	0.259779
$82$	−5.03624	−0.556159
$83$	−9.06154	−0.994633	−0.497316	−	0.867569i	$-0.665681\pi$
$83$	−9.06154	−0.994633	−0.497316	+	0.867569i	$0.665681\pi$
$84$	0.902113	0.0984286
$85$	1.30719	0.141784
$86$	−2.49704	−0.269263
$87$	0.725503	0.0777821
$88$	1.35114	0.144032
$89$	−3.12164	−0.330893	−0.165446	−	0.986219i	$-0.552907\pi$
$89$	−3.12164	−0.330893	−0.165446	+	0.986219i	$0.552907\pi$
$90$	1.21888	0.128481
$91$	−1.45965	−0.153013
$92$	3.35114	0.349381
$93$	−0.984496	−0.102088
$94$	2.24077	0.231118
$95$	0	0
$96$	−0.902113	−0.0920715
$97$	−12.7935	−1.29898	−0.649491	−	0.760369i	$-0.725018\pi$
$97$	−12.7935	−1.29898	−0.649491	+	0.760369i	$0.725018\pi$
$98$	−1.00000	−0.101015
$99$	2.95385	0.296873
$100$	−4.68915	−0.468915
$101$	−10.7444	−1.06911	−0.534556	−	0.845133i	$-0.679521\pi$
$101$	−10.7444	−1.06911	−0.534556	+	0.845133i	$0.679521\pi$
$102$	−2.11507	−0.209423
$103$	−9.03624	−0.890367	−0.445183	−	0.895439i	$-0.646862\pi$
$103$	−9.03624	−0.890367	−0.445183	+	0.895439i	$0.646862\pi$
$104$	1.45965	0.143130
$105$	0.502961	0.0490840
$106$	5.37238	0.521812
$107$	−10.9808	−1.06156	−0.530779	−	0.847510i	$-0.678100\pi$
$107$	−10.9808	−1.06156	−0.530779	+	0.847510i	$0.678100\pi$
$108$	−4.67853	−0.450192
$109$	−4.15182	−0.397672	−0.198836	−	0.980033i	$-0.563716\pi$
$109$	−4.15182	−0.397672	−0.198836	+	0.980033i	$0.563716\pi$
$110$	0.753310	0.0718253
$111$	−6.11902	−0.580791
$112$	1.00000	0.0944911
$113$	−12.3072	−1.15776	−0.578881	−	0.815412i	$-0.696511\pi$
$113$	−12.3072	−1.15776	−0.578881	+	0.815412i	$0.696511\pi$
$114$	0	0
$115$	1.86838	0.174228
$116$	0.804226	0.0746705
$117$	3.19107	0.295015
$118$	11.1850	1.02967
$119$	2.34458	0.214927
$120$	−0.502961	−0.0459138
$121$	−9.17442	−0.834038
$122$	−7.15067	−0.647391
$123$	4.54325	0.409652
$124$	−1.09132	−0.0980037
$125$	−5.40206	−0.483175
$126$	2.18619	0.194761
$127$	0.301265	0.0267330	0.0133665	−	0.999911i	$-0.495745\pi$
$127$	0.301265	0.0267330	0.0133665	+	0.999911i	$0.495745\pi$
$128$	−1.00000	−0.0883883
$129$	2.25261	0.198331
$130$	0.813808	0.0713757
$131$	2.20815	0.192927	0.0964634	−	0.995337i	$-0.469247\pi$
$131$	2.20815	0.192927	0.0964634	+	0.995337i	$0.469247\pi$
$132$	−1.21888	−0.106090
$133$	0	0
$134$	−10.0498	−0.868167
$135$	−2.60845	−0.224500
$136$	−2.34458	−0.201046
$137$	9.12088	0.779250	0.389625	−	0.920974i	$-0.372605\pi$
$137$	9.12088	0.779250	0.389625	+	0.920974i	$0.372605\pi$
$138$	−3.02311	−0.257344
$139$	−20.6169	−1.74870	−0.874351	−	0.485295i	$-0.838712\pi$
$139$	−20.6169	−1.74870	−0.874351	+	0.485295i	$0.838712\pi$
$140$	0.557537	0.0471204
$141$	−2.02143	−0.170235
$142$	3.00592	0.252251
$143$	1.97219	0.164923
$144$	−2.18619	−0.182183
$145$	0.448385	0.0372364
$146$	−7.48089	−0.619123
$147$	0.902113	0.0744050
$148$	−6.78298	−0.557558
$149$	12.4376	1.01893	0.509463	−	0.860492i	$-0.329844\pi$
$149$	12.4376	1.01893	0.509463	+	0.860492i	$0.329844\pi$
$150$	4.23015	0.345390
$151$	−16.8636	−1.37234	−0.686169	−	0.727442i	$-0.740709\pi$
$151$	−16.8636	−1.37234	−0.686169	+	0.727442i	$0.740709\pi$
$152$	0	0
$153$	−5.12569	−0.414388
$154$	1.35114	0.108878
$155$	−0.608452	−0.0488721
$156$	−1.31677	−0.105426
$157$	8.99583	0.717945	0.358973	−	0.933348i	$-0.383127\pi$
$157$	8.99583	0.717945	0.358973	+	0.933348i	$0.383127\pi$
$158$	1.96325	0.156188
$159$	−4.84650	−0.384352
$160$	−0.557537	−0.0440771
$161$	3.35114	0.264107
$162$	−2.33801	−0.183692
$163$	15.2704	1.19607	0.598037	−	0.801469i	$-0.295948\pi$
$163$	15.2704	1.19607	0.598037	+	0.801469i	$0.295948\pi$
$164$	5.03624	0.393264
$165$	−0.679571	−0.0529045
$166$	9.06154	0.703312
$167$	−3.35333	−0.259489	−0.129744	−	0.991547i	$-0.541416\pi$
$167$	−3.35333	−0.259489	−0.129744	+	0.991547i	$0.541416\pi$
$168$	−0.902113	−0.0695995
$169$	−10.8694	−0.836109
$170$	−1.30719	−0.100257
$171$	0	0
$172$	2.49704	0.190397
$173$	18.8683	1.43453	0.717264	−	0.696801i	$-0.245394\pi$
$173$	18.8683	1.43453	0.717264	+	0.696801i	$0.245394\pi$
$174$	−0.725503	−0.0550002
$175$	−4.68915	−0.354467
$176$	−1.35114	−0.101846
$177$	−10.0902	−0.758424
$178$	3.12164	0.233977
$179$	−7.36280	−0.550322	−0.275161	−	0.961398i	$-0.588731\pi$
$179$	−7.36280	−0.550322	−0.275161	+	0.961398i	$0.588731\pi$
$180$	−1.21888	−0.0908501
$181$	−5.28918	−0.393141	−0.196571	−	0.980490i	$-0.562981\pi$
$181$	−5.28918	−0.393141	−0.196571	+	0.980490i	$0.562981\pi$
$182$	1.45965	0.108196
$183$	6.45071	0.476850
$184$	−3.35114	−0.247049
$185$	−3.78176	−0.278041
$186$	0.984496	0.0721868
$187$	−3.16785	−0.231656
$188$	−2.24077	−0.163425
$189$	−4.67853	−0.340313
$190$	0	0
$191$	−2.84233	−0.205664	−0.102832	−	0.994699i	$-0.532790\pi$
$191$	−2.84233	−0.205664	−0.102832	+	0.994699i	$0.532790\pi$
$192$	0.902113	0.0651044
$193$	−12.4128	−0.893492	−0.446746	−	0.894661i	$-0.647417\pi$
$193$	−12.4128	−0.893492	−0.446746	+	0.894661i	$0.647417\pi$
$194$	12.7935	0.918519
$195$	−0.734147	−0.0525733
$196$	1.00000	0.0714286
$197$	−16.8481	−1.20038	−0.600188	−	0.799859i	$-0.704907\pi$
$197$	−16.8481	−1.20038	−0.600188	+	0.799859i	$0.704907\pi$
$198$	−2.95385	−0.209921
$199$	−5.28053	−0.374327	−0.187163	−	0.982329i	$-0.559929\pi$
$199$	−5.28053	−0.374327	−0.187163	+	0.982329i	$0.559929\pi$
$200$	4.68915	0.331573
$201$	9.06602	0.639468
$202$	10.7444	0.755976
$203$	0.804226	0.0564456
$204$	2.11507	0.148085
$205$	2.80789	0.196111
$206$	9.03624	0.629584
$207$	−7.32624	−0.509209
$208$	−1.45965	−0.101208
$209$	0	0
$210$	−0.502961	−0.0347076
$211$	12.7557	0.878139	0.439069	−	0.898453i	$-0.355308\pi$
$211$	12.7557	0.878139	0.439069	+	0.898453i	$0.355308\pi$
$212$	−5.37238	−0.368977
$213$	−2.71168	−0.185801
$214$	10.9808	0.750635
$215$	1.39219	0.0949466
$216$	4.67853	0.318334
$217$	−1.09132	−0.0740838
$218$	4.15182	0.281197
$219$	6.74861	0.456029
$220$	−0.753310	−0.0507882
$221$	−3.42226	−0.230206
$222$	6.11902	0.410682
$223$	−22.9108	−1.53422	−0.767109	−	0.641517i	$-0.778305\pi$
$223$	−22.9108	−1.53422	−0.767109	+	0.641517i	$0.778305\pi$
$224$	−1.00000	−0.0668153
$225$	10.2514	0.683426
$226$	12.3072	0.818662
$227$	−10.3999	−0.690263	−0.345132	−	0.938554i	$-0.612166\pi$
$227$	−10.3999	−0.690263	−0.345132	+	0.938554i	$0.612166\pi$
$228$	0	0
$229$	−3.31741	−0.219221	−0.109610	−	0.993975i	$-0.534960\pi$
$229$	−3.31741	−0.219221	−0.109610	+	0.993975i	$0.534960\pi$
$230$	−1.86838	−0.123198
$231$	−1.21888	−0.0801965
$232$	−0.804226	−0.0528000
$233$	17.1708	1.12489	0.562447	−	0.826833i	$-0.309860\pi$
$233$	17.1708	1.12489	0.562447	+	0.826833i	$0.309860\pi$
$234$	−3.19107	−0.208607
$235$	−1.24931	−0.0814960
$236$	−11.1850	−0.728084
$237$	−1.77108	−0.115044
$238$	−2.34458	−0.151976
$239$	19.3878	1.25409	0.627045	−	0.778983i	$-0.284264\pi$
$239$	19.3878	1.25409	0.627045	+	0.778983i	$0.284264\pi$
$240$	0.502961	0.0324660
$241$	1.32553	0.0853846	0.0426923	−	0.999088i	$-0.486406\pi$
$241$	1.32553	0.0853846	0.0426923	+	0.999088i	$0.486406\pi$
$242$	9.17442	0.589754
$243$	16.1447	1.03569
$244$	7.15067	0.457775
$245$	0.557537	0.0356197
$246$	−4.54325	−0.289667
$247$	0	0
$248$	1.09132	0.0692990
$249$	−8.17453	−0.518040
$250$	5.40206	0.341656
$251$	11.9502	0.754290	0.377145	−	0.926154i	$-0.376906\pi$
$251$	11.9502	0.754290	0.377145	+	0.926154i	$0.376906\pi$
$252$	−2.18619	−0.137717
$253$	−4.52786	−0.284664
$254$	−0.301265	−0.0189031
$255$	1.17923	0.0738463
$256$	1.00000	0.0625000
$257$	−9.35957	−0.583834	−0.291917	−	0.956444i	$-0.594293\pi$
$257$	−9.35957	−0.583834	−0.291917	+	0.956444i	$0.594293\pi$
$258$	−2.25261	−0.140241
$259$	−6.78298	−0.421474
$260$	−0.813808	−0.0504702
$261$	−1.75819	−0.108829
$262$	−2.20815	−0.136420
$263$	5.94658	0.366682	0.183341	−	0.983049i	$-0.441309\pi$
$263$	5.94658	0.366682	0.183341	+	0.983049i	$0.441309\pi$
$264$	1.21888	0.0750170
$265$	−2.99530	−0.184000
$266$	0	0
$267$	−2.81607	−0.172341
$268$	10.0498	0.613887
$269$	26.5896	1.62120	0.810598	−	0.585602i	$-0.199142\pi$
$269$	26.5896	1.62120	0.810598	+	0.585602i	$0.199142\pi$
$270$	2.60845	0.158745
$271$	0.699775	0.0425083	0.0212541	−	0.999774i	$-0.493234\pi$
$271$	0.699775	0.0425083	0.0212541	+	0.999774i	$0.493234\pi$
$272$	2.34458	0.142161
$273$	−1.31677	−0.0796945
$274$	−9.12088	−0.551013
$275$	6.33571	0.382058
$276$	3.02311	0.181970
$277$	−12.9537	−0.778311	−0.389155	−	0.921172i	$-0.627233\pi$
$277$	−12.9537	−0.778311	−0.389155	+	0.921172i	$0.627233\pi$
$278$	20.6169	1.23652
$279$	2.38584	0.142837
$280$	−0.557537	−0.0333192
$281$	30.6736	1.82983	0.914917	−	0.403642i	$-0.132256\pi$
$281$	30.6736	1.82983	0.914917	+	0.403642i	$0.132256\pi$
$282$	2.02143	0.120374
$283$	23.3257	1.38657	0.693285	−	0.720663i	$-0.256163\pi$
$283$	23.3257	1.38657	0.693285	+	0.720663i	$0.256163\pi$
$284$	−3.00592	−0.178369
$285$	0	0
$286$	−1.97219	−0.116618
$287$	5.03624	0.297280
$288$	2.18619	0.128823
$289$	−11.5030	−0.676645
$290$	−0.448385	−0.0263301
$291$	−11.5412	−0.676556
$292$	7.48089	0.437786
$293$	5.50411	0.321554	0.160777	−	0.986991i	$-0.448600\pi$
$293$	5.50411	0.321554	0.160777	+	0.986991i	$0.448600\pi$
$294$	−0.902113	−0.0526123
$295$	−6.23607	−0.363078
$296$	6.78298	0.394253
$297$	6.32136	0.366802
$298$	−12.4376	−0.720490
$299$	−4.89149	−0.282882
$300$	−4.23015	−0.244228
$301$	2.49704	0.143927
$302$	16.8636	0.970389
$303$	−9.69270	−0.556831
$304$	0	0
$305$	3.98676	0.228281
$306$	5.12569	0.293016
$307$	−20.7235	−1.18275	−0.591377	−	0.806395i	$-0.701415\pi$
$307$	−20.7235	−1.18275	−0.591377	+	0.806395i	$0.701415\pi$
$308$	−1.35114	−0.0769884
$309$	−8.15171	−0.463734
$310$	0.608452	0.0345578
$311$	−11.5766	−0.656448	−0.328224	−	0.944600i	$-0.606450\pi$
$311$	−11.5766	−0.656448	−0.328224	+	0.944600i	$0.606450\pi$
$312$	1.31677	0.0745474
$313$	−34.0823	−1.92645	−0.963224	−	0.268700i	$-0.913406\pi$
$313$	−34.0823	−1.92645	−0.963224	+	0.268700i	$0.913406\pi$
$314$	−8.99583	−0.507664
$315$	−1.21888	−0.0686762
$316$	−1.96325	−0.110442
$317$	−3.86368	−0.217006	−0.108503	−	0.994096i	$-0.534606\pi$
$317$	−3.86368	−0.217006	−0.108503	+	0.994096i	$0.534606\pi$
$318$	4.84650	0.271778
$319$	−1.08662	−0.0608392
$320$	0.557537	0.0311672
$321$	−9.90596	−0.552897
$322$	−3.35114	−0.186752
$323$	0	0
$324$	2.33801	0.129890
$325$	6.84452	0.379666
$326$	−15.2704	−0.845751
$327$	−3.74541	−0.207122
$328$	−5.03624	−0.278080
$329$	−2.24077	−0.123538
$330$	0.679571	0.0374092
$331$	−2.54319	−0.139786	−0.0698931	−	0.997554i	$-0.522266\pi$
$331$	−2.54319	−0.139786	−0.0698931	+	0.997554i	$0.522266\pi$
$332$	−9.06154	−0.497316
$333$	14.8289	0.812619
$334$	3.35333	0.183486
$335$	5.60311	0.306131
$336$	0.902113	0.0492143
$337$	−21.6713	−1.18051	−0.590257	−	0.807216i	$-0.700973\pi$
$337$	−21.6713	−1.18051	−0.590257	+	0.807216i	$0.700973\pi$
$338$	10.8694	0.591219
$339$	−11.1025	−0.603004
$340$	1.30719	0.0708922
$341$	1.47453	0.0798503
$342$	0	0
$343$	1.00000	0.0539949
$344$	−2.49704	−0.134631
$345$	1.68549	0.0907439
$346$	−18.8683	−1.01436
$347$	22.7748	1.22261	0.611306	−	0.791394i	$-0.290644\pi$
$347$	22.7748	1.22261	0.611306	+	0.791394i	$0.290644\pi$
$348$	0.725503	0.0388910
$349$	−7.24669	−0.387906	−0.193953	−	0.981011i	$-0.562131\pi$
$349$	−7.24669	−0.387906	−0.193953	+	0.981011i	$0.562131\pi$
$350$	4.68915	0.250646
$351$	6.82902	0.364506
$352$	1.35114	0.0720161
$353$	−1.97470	−0.105103	−0.0525513	−	0.998618i	$-0.516735\pi$
$353$	−1.97470	−0.105103	−0.0525513	+	0.998618i	$0.516735\pi$
$354$	10.0902	0.536286
$355$	−1.67591	−0.0889481
$356$	−3.12164	−0.165446
$357$	2.11507	0.111942
$358$	7.36280	0.389136
$359$	23.5659	1.24376	0.621879	−	0.783113i	$-0.286370\pi$
$359$	23.5659	1.24376	0.621879	+	0.783113i	$0.286370\pi$
$360$	1.21888	0.0642407
$361$	0	0
$362$	5.28918	0.277993
$363$	−8.27636	−0.434396
$364$	−1.45965	−0.0765064
$365$	4.17087	0.218313
$366$	−6.45071	−0.337184
$367$	−25.5721	−1.33485	−0.667426	−	0.744676i	$-0.732604\pi$
$367$	−25.5721	−1.33485	−0.667426	+	0.744676i	$0.732604\pi$
$368$	3.35114	0.174690
$369$	−11.0102	−0.573167
$370$	3.78176	0.196604
$371$	−5.37238	−0.278920
$372$	−0.984496	−0.0510438
$373$	−34.4331	−1.78288	−0.891439	−	0.453141i	$-0.850303\pi$
$373$	−34.4331	−1.78288	−0.891439	+	0.453141i	$0.850303\pi$
$374$	3.16785	0.163806
$375$	−4.87327	−0.251654
$376$	2.24077	0.115559
$377$	−1.17389	−0.0604583
$378$	4.67853	0.240638
$379$	5.93250	0.304732	0.152366	−	0.988324i	$-0.451311\pi$
$379$	5.93250	0.304732	0.152366	+	0.988324i	$0.451311\pi$
$380$	0	0
$381$	0.271775	0.0139235
$382$	2.84233	0.145426
$383$	12.8493	0.656570	0.328285	−	0.944579i	$-0.393529\pi$
$383$	12.8493	0.656570	0.328285	+	0.944579i	$0.393529\pi$
$384$	−0.902113	−0.0460358
$385$	−0.753310	−0.0383923
$386$	12.4128	0.631794
$387$	−5.45901	−0.277497
$388$	−12.7935	−0.649491
$389$	−14.8885	−0.754876	−0.377438	−	0.926035i	$-0.623195\pi$
$389$	−14.8885	−0.754876	−0.377438	+	0.926035i	$0.623195\pi$
$390$	0.734147	0.0371750
$391$	7.85701	0.397346
$392$	−1.00000	−0.0505076
$393$	1.99200	0.100483
$394$	16.8481	0.848793
$395$	−1.09459	−0.0550746
$396$	2.95385	0.148437
$397$	−11.0623	−0.555201	−0.277600	−	0.960697i	$-0.589539\pi$
$397$	−11.0623	−0.555201	−0.277600	+	0.960697i	$0.589539\pi$
$398$	5.28053	0.264689
$399$	0	0
$400$	−4.68915	−0.234458
$401$	0.255119	0.0127400	0.00637001	−	0.999980i	$-0.497972\pi$
$401$	0.255119	0.0127400	0.00637001	+	0.999980i	$0.497972\pi$
$402$	−9.06602	−0.452172
$403$	1.59295	0.0793504
$404$	−10.7444	−0.534556
$405$	1.30353	0.0647728
$406$	−0.804226	−0.0399131
$407$	9.16477	0.454281
$408$	−2.11507	−0.104712
$409$	5.21766	0.257997	0.128998	−	0.991645i	$-0.458824\pi$
$409$	5.21766	0.257997	0.128998	+	0.991645i	$0.458824\pi$
$410$	−2.80789	−0.138672
$411$	8.22807	0.405861
$412$	−9.03624	−0.445183
$413$	−11.1850	−0.550380
$414$	7.32624	0.360065
$415$	−5.05214	−0.248000
$416$	1.45965	0.0715652
$417$	−18.5988	−0.910785
$418$	0	0
$419$	−27.6587	−1.35122	−0.675609	−	0.737261i	$-0.736119\pi$
$419$	−27.6587	−1.35122	−0.675609	+	0.737261i	$0.736119\pi$
$420$	0.502961	0.0245420
$421$	−5.70020	−0.277811	−0.138905	−	0.990306i	$-0.544358\pi$
$421$	−5.70020	−0.277811	−0.138905	+	0.990306i	$0.544358\pi$
$422$	−12.7557	−0.620938
$423$	4.89875	0.238185
$424$	5.37238	0.260906
$425$	−10.9941	−0.533291
$426$	2.71168	0.131381
$427$	7.15067	0.346045
$428$	−10.9808	−0.530779
$429$	1.77914	0.0858977
$430$	−1.39219	−0.0671374
$431$	−20.6656	−0.995427	−0.497714	−	0.867341i	$-0.665827\pi$
$431$	−20.6656	−0.995427	−0.497714	+	0.867341i	$0.665827\pi$
$432$	−4.67853	−0.225096
$433$	−16.1525	−0.776241	−0.388121	−	0.921609i	$-0.626876\pi$
$433$	−16.1525	−0.776241	−0.388121	+	0.921609i	$0.626876\pi$
$434$	1.09132	0.0523852
$435$	0.404494	0.0193940
$436$	−4.15182	−0.198836
$437$	0	0
$438$	−6.74861	−0.322461
$439$	7.66156	0.365666	0.182833	−	0.983144i	$-0.441473\pi$
$439$	7.66156	0.365666	0.182833	+	0.983144i	$0.441473\pi$
$440$	0.753310	0.0359127
$441$	−2.18619	−0.104104
$442$	3.42226	0.162780
$443$	14.7542	0.700995	0.350497	−	0.936564i	$-0.386013\pi$
$443$	14.7542	0.700995	0.350497	+	0.936564i	$0.386013\pi$
$444$	−6.11902	−0.290396
$445$	−1.74043	−0.0825041
$446$	22.9108	1.08486
$447$	11.2201	0.530693
$448$	1.00000	0.0472456
$449$	12.1341	0.572645	0.286322	−	0.958133i	$-0.407567\pi$
$449$	12.1341	0.572645	0.286322	+	0.958133i	$0.407567\pi$
$450$	−10.2514	−0.483255
$451$	−6.80467	−0.320419
$452$	−12.3072	−0.578881
$453$	−15.2128	−0.714762
$454$	10.3999	0.488090
$455$	−0.813808	−0.0381519
$456$	0	0
$457$	33.3891	1.56188	0.780939	−	0.624608i	$-0.214741\pi$
$457$	33.3891	1.56188	0.780939	+	0.624608i	$0.214741\pi$
$458$	3.31741	0.155012
$459$	−10.9692	−0.511997
$460$	1.86838	0.0871138
$461$	−1.44124	−0.0671253	−0.0335626	−	0.999437i	$-0.510685\pi$
$461$	−1.44124	−0.0671253	−0.0335626	+	0.999437i	$0.510685\pi$
$462$	1.21888	0.0567075
$463$	0.594599	0.0276333	0.0138167	−	0.999905i	$-0.495602\pi$
$463$	0.594599	0.0276333	0.0138167	+	0.999905i	$0.495602\pi$
$464$	0.804226	0.0373353
$465$	−0.548893	−0.0254543
$466$	−17.1708	−0.795420
$467$	39.3250	1.81974	0.909871	−	0.414890i	$-0.136180\pi$
$467$	39.3250	1.81974	0.909871	+	0.414890i	$0.136180\pi$
$468$	3.19107	0.147507
$469$	10.0498	0.464055
$470$	1.24931	0.0576264
$471$	8.11526	0.373931
$472$	11.1850	0.514833
$473$	−3.37385	−0.155130
$474$	1.77108	0.0813482
$475$	0	0
$476$	2.34458	0.107463
$477$	11.7451	0.537770
$478$	−19.3878	−0.886776
$479$	−16.1460	−0.737728	−0.368864	−	0.929483i	$-0.620253\pi$
$479$	−16.1460	−0.737728	−0.368864	+	0.929483i	$0.620253\pi$
$480$	−0.502961	−0.0229569
$481$	9.90078	0.451437
$482$	−1.32553	−0.0603760
$483$	3.02311	0.137556
$484$	−9.17442	−0.417019
$485$	−7.13284	−0.323886
$486$	−16.1447	−0.732341
$487$	−42.2190	−1.91312	−0.956562	−	0.291528i	$-0.905836\pi$
$487$	−42.2190	−1.91312	−0.956562	+	0.291528i	$0.905836\pi$
$488$	−7.15067	−0.323696
$489$	13.7757	0.622957
$490$	−0.557537	−0.0251869
$491$	−13.0440	−0.588669	−0.294334	−	0.955703i	$-0.595098\pi$
$491$	−13.0440	−0.588669	−0.294334	+	0.955703i	$0.595098\pi$
$492$	4.54325	0.204826
$493$	1.88557	0.0849218
$494$	0	0
$495$	1.64688	0.0740218
$496$	−1.09132	−0.0490018
$497$	−3.00592	−0.134834
$498$	8.17453	0.366309
$499$	−4.06154	−0.181819	−0.0909097	−	0.995859i	$-0.528977\pi$
$499$	−4.06154	−0.181819	−0.0909097	+	0.995859i	$0.528977\pi$
$500$	−5.40206	−0.241587
$501$	−3.02509	−0.135151
$502$	−11.9502	−0.533363
$503$	−36.1376	−1.61130	−0.805649	−	0.592394i	$-0.798183\pi$
$503$	−36.1376	−1.61130	−0.805649	+	0.592394i	$0.798183\pi$
$504$	2.18619	0.0973807
$505$	−5.99042	−0.266570
$506$	4.52786	0.201288
$507$	−9.80545	−0.435475
$508$	0.301265	0.0133665
$509$	42.2030	1.87062	0.935308	−	0.353835i	$-0.115123\pi$
$509$	42.2030	1.87062	0.935308	+	0.353835i	$0.115123\pi$
$510$	−1.17923	−0.0522172
$511$	7.48089	0.330935
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	9.35957	0.412833
$515$	−5.03803	−0.222002
$516$	2.25261	0.0991657
$517$	3.02759	0.133153
$518$	6.78298	0.298027
$519$	17.0213	0.747153
$520$	0.813808	0.0356878
$521$	30.8397	1.35111	0.675556	−	0.737309i	$-0.263904\pi$
$521$	30.8397	1.35111	0.675556	+	0.737309i	$0.263904\pi$
$522$	1.75819	0.0769540
$523$	−13.3220	−0.582530	−0.291265	−	0.956642i	$-0.594076\pi$
$523$	−13.3220	−0.582530	−0.291265	+	0.956642i	$0.594076\pi$
$524$	2.20815	0.0964634
$525$	−4.23015	−0.184619
$526$	−5.94658	−0.259283
$527$	−2.55869	−0.111458
$528$	−1.21888	−0.0530450
$529$	−11.7699	−0.511733
$530$	2.99530	0.130108
$531$	24.4526	1.06115
$532$	0	0
$533$	−7.35114	−0.318413
$534$	2.81607	0.121863
$535$	−6.12222	−0.264687
$536$	−10.0498	−0.434084
$537$	−6.64208	−0.286627
$538$	−26.5896	−1.14636
$539$	−1.35114	−0.0581978
$540$	−2.60845	−0.112250
$541$	6.55053	0.281629	0.140815	−	0.990036i	$-0.455028\pi$
$541$	6.55053	0.281629	0.140815	+	0.990036i	$0.455028\pi$
$542$	−0.699775	−0.0300579
$543$	−4.77143	−0.204762
$544$	−2.34458	−0.100523
$545$	−2.31479	−0.0991548
$546$	1.31677	0.0563525
$547$	9.52066	0.407074	0.203537	−	0.979067i	$-0.434756\pi$
$547$	9.52066	0.407074	0.203537	+	0.979067i	$0.434756\pi$
$548$	9.12088	0.389625
$549$	−15.6327	−0.667189
$550$	−6.33571	−0.270155
$551$	0	0
$552$	−3.02311	−0.128672
$553$	−1.96325	−0.0834860
$554$	12.9537	0.550349
$555$	−3.41158	−0.144813
$556$	−20.6169	−0.874351
$557$	19.9857	0.846823	0.423411	−	0.905937i	$-0.360832\pi$
$557$	19.9857	0.846823	0.423411	+	0.905937i	$0.360832\pi$
$558$	−2.38584	−0.101001
$559$	−3.64480	−0.154159
$560$	0.557537	0.0235602
$561$	−2.85776	−0.120655
$562$	−30.6736	−1.29389
$563$	−21.2600	−0.896003	−0.448002	−	0.894033i	$-0.647864\pi$
$563$	−21.2600	−0.896003	−0.448002	+	0.894033i	$0.647864\pi$
$564$	−2.02143	−0.0851174
$565$	−6.86171	−0.288674
$566$	−23.3257	−0.980453
$567$	2.33801	0.0981873
$568$	3.00592	0.126126
$569$	−16.6086	−0.696270	−0.348135	−	0.937444i	$-0.613185\pi$
$569$	−16.6086	−0.696270	−0.348135	+	0.937444i	$0.613185\pi$
$570$	0	0
$571$	19.2419	0.805247	0.402624	−	0.915366i	$-0.368098\pi$
$571$	19.2419	0.805247	0.402624	+	0.915366i	$0.368098\pi$
$572$	1.97219	0.0824615
$573$	−2.56410	−0.107117
$574$	−5.03624	−0.210208
$575$	−15.7140	−0.655320
$576$	−2.18619	−0.0910913
$577$	−32.8162	−1.36615	−0.683077	−	0.730346i	$-0.739359\pi$
$577$	−32.8162	−1.36615	−0.683077	+	0.730346i	$0.739359\pi$
$578$	11.5030	0.478460
$579$	−11.1977	−0.465362
$580$	0.448385	0.0186182
$581$	−9.06154	−0.375936
$582$	11.5412	0.478397
$583$	7.25885	0.300631
$584$	−7.48089	−0.309562
$585$	1.77914	0.0735584
$586$	−5.50411	−0.227373
$587$	−34.6571	−1.43045	−0.715225	−	0.698894i	$-0.753676\pi$
$587$	−34.6571	−1.43045	−0.715225	+	0.698894i	$0.753676\pi$
$588$	0.902113	0.0372025
$589$	0	0
$590$	6.23607	0.256735
$591$	−15.1989	−0.625198
$592$	−6.78298	−0.278779
$593$	37.5224	1.54086	0.770429	−	0.637525i	$-0.220042\pi$
$593$	37.5224	1.54086	0.770429	+	0.637525i	$0.220042\pi$
$594$	−6.32136	−0.259368
$595$	1.30719	0.0535894
$596$	12.4376	0.509463
$597$	−4.76364	−0.194963
$598$	4.89149	0.200028
$599$	24.3167	0.993552	0.496776	−	0.867879i	$-0.334517\pi$
$599$	24.3167	0.993552	0.496776	+	0.867879i	$0.334517\pi$
$600$	4.23015	0.172695
$601$	29.9333	1.22101	0.610503	−	0.792014i	$-0.290967\pi$
$601$	29.9333	1.22101	0.610503	+	0.792014i	$0.290967\pi$
$602$	−2.49704	−0.101772
$603$	−21.9707	−0.894717
$604$	−16.8636	−0.686169
$605$	−5.11507	−0.207957
$606$	9.69270	0.393739
$607$	45.0819	1.82982	0.914909	−	0.403660i	$-0.132262\pi$
$607$	45.0819	1.82982	0.914909	+	0.403660i	$0.132262\pi$
$608$	0	0
$609$	0.725503	0.0293989
$610$	−3.98676	−0.161419
$611$	3.27074	0.132320
$612$	−5.12569	−0.207194
$613$	11.4353	0.461869	0.230935	−	0.972969i	$-0.425822\pi$
$613$	11.4353	0.461869	0.230935	+	0.972969i	$0.425822\pi$
$614$	20.7235	0.836333
$615$	2.53303	0.102142
$616$	1.35114	0.0544390
$617$	−0.125562	−0.00505493	−0.00252747	−	0.999997i	$-0.500805\pi$
$617$	−0.125562	−0.00505493	−0.00252747	+	0.999997i	$0.500805\pi$
$618$	8.15171	0.327910
$619$	11.4218	0.459079	0.229539	−	0.973299i	$-0.426278\pi$
$619$	11.4218	0.459079	0.229539	+	0.973299i	$0.426278\pi$
$620$	−0.608452	−0.0244360
$621$	−15.6784	−0.629153
$622$	11.5766	0.464179
$623$	−3.12164	−0.125066
$624$	−1.31677	−0.0527129
$625$	20.4339	0.817357
$626$	34.0823	1.36220
$627$	0	0
$628$	8.99583	0.358973
$629$	−15.9032	−0.634103
$630$	1.21888	0.0485614
$631$	−3.65760	−0.145607	−0.0728034	−	0.997346i	$-0.523195\pi$
$631$	−3.65760	−0.145607	−0.0728034	+	0.997346i	$0.523195\pi$
$632$	1.96325	0.0780940
$633$	11.5071	0.457366
$634$	3.86368	0.153446
$635$	0.167966	0.00666554
$636$	−4.84650	−0.192176
$637$	−1.45965	−0.0578334
$638$	1.08662	0.0430198
$639$	6.57152	0.259965
$640$	−0.557537	−0.0220386
$641$	21.9096	0.865377	0.432689	−	0.901543i	$-0.357565\pi$
$641$	21.9096	0.865377	0.432689	+	0.901543i	$0.357565\pi$
$642$	9.90596	0.390957
$643$	−4.82120	−0.190129	−0.0950647	−	0.995471i	$-0.530306\pi$
$643$	−4.82120	−0.190129	−0.0950647	+	0.995471i	$0.530306\pi$
$644$	3.35114	0.132053
$645$	1.25591	0.0494515
$646$	0	0
$647$	4.25795	0.167397	0.0836987	−	0.996491i	$-0.473327\pi$
$647$	4.25795	0.167397	0.0836987	+	0.996491i	$0.473327\pi$
$648$	−2.33801	−0.0918458
$649$	15.1126	0.593220
$650$	−6.84452	−0.268464
$651$	−0.984496	−0.0385854
$652$	15.2704	0.598037
$653$	−34.8423	−1.36348	−0.681742	−	0.731593i	$-0.738777\pi$
$653$	−34.8423	−1.36348	−0.681742	+	0.731593i	$0.738777\pi$
$654$	3.74541	0.146457
$655$	1.23112	0.0481040
$656$	5.03624	0.196632
$657$	−16.3547	−0.638056
$658$	2.24077	0.0873542
$659$	−6.63471	−0.258452	−0.129226	−	0.991615i	$-0.541249\pi$
$659$	−6.63471	−0.258452	−0.129226	+	0.991615i	$0.541249\pi$
$660$	−0.679571	−0.0264523
$661$	−29.6118	−1.15176	−0.575882	−	0.817533i	$-0.695341\pi$
$661$	−29.6118	−1.15176	−0.575882	+	0.817533i	$0.695341\pi$
$662$	2.54319	0.0988437
$663$	−3.08727	−0.119899
$664$	9.06154	0.351656
$665$	0	0
$666$	−14.8289	−0.574608
$667$	2.69507	0.104354
$668$	−3.35333	−0.129744
$669$	−20.6681	−0.799075
$670$	−5.60311	−0.216467
$671$	−9.66156	−0.372980
$672$	−0.902113	−0.0347998
$673$	−9.24565	−0.356394	−0.178197	−	0.983995i	$-0.557026\pi$
$673$	−9.24565	−0.356394	−0.178197	+	0.983995i	$0.557026\pi$
$674$	21.6713	0.834749
$675$	21.9383	0.844407
$676$	−10.8694	−0.418055
$677$	20.8183	0.800111	0.400055	−	0.916491i	$-0.368991\pi$
$677$	20.8183	0.800111	0.400055	+	0.916491i	$0.368991\pi$
$678$	11.1025	0.426388
$679$	−12.7935	−0.490969
$680$	−1.30719	−0.0501283
$681$	−9.38185	−0.359513
$682$	−1.47453	−0.0564627
$683$	7.95243	0.304291	0.152146	−	0.988358i	$-0.451382\pi$
$683$	7.95243	0.304291	0.152146	+	0.988358i	$0.451382\pi$
$684$	0	0
$685$	5.08522	0.194296
$686$	−1.00000	−0.0381802
$687$	−2.99268	−0.114178
$688$	2.49704	0.0951987
$689$	7.84180	0.298749
$690$	−1.68549	−0.0641656
$691$	31.5801	1.20136	0.600682	−	0.799488i	$-0.294896\pi$
$691$	31.5801	1.20136	0.600682	+	0.799488i	$0.294896\pi$
$692$	18.8683	0.717264
$693$	2.95385	0.112208
$694$	−22.7748	−0.864518
$695$	−11.4947	−0.436017
$696$	−0.725503	−0.0275001
$697$	11.8078	0.447254
$698$	7.24669	0.274291
$699$	15.4900	0.585884
$700$	−4.68915	−0.177233
$701$	−24.7836	−0.936063	−0.468032	−	0.883712i	$-0.655037\pi$
$701$	−24.7836	−0.936063	−0.468032	+	0.883712i	$0.655037\pi$
$702$	−6.82902	−0.257745
$703$	0	0
$704$	−1.35114	−0.0509230
$705$	−1.12702	−0.0424460
$706$	1.97470	0.0743188
$707$	−10.7444	−0.404086
$708$	−10.0902	−0.379212
$709$	29.7249	1.11634	0.558172	−	0.829725i	$-0.311503\pi$
$709$	29.7249	1.11634	0.558172	+	0.829725i	$0.311503\pi$
$710$	1.67591	0.0628958
$711$	4.29205	0.160964
$712$	3.12164	0.116988
$713$	−3.65718	−0.136962
$714$	−2.11507	−0.0791546
$715$	1.09957	0.0411216
$716$	−7.36280	−0.275161
$717$	17.4900	0.653175
$718$	−23.5659	−0.879470
$719$	−48.0010	−1.79014	−0.895068	−	0.445931i	$-0.852873\pi$
$719$	−48.0010	−1.79014	−0.895068	+	0.445931i	$0.852873\pi$
$720$	−1.21888	−0.0454250
$721$	−9.03624	−0.336527
$722$	0	0
$723$	1.19577	0.0444713
$724$	−5.28918	−0.196571
$725$	−3.77114	−0.140057
$726$	8.27636	0.307165
$727$	4.02956	0.149448	0.0747240	−	0.997204i	$-0.476192\pi$
$727$	4.02956	0.149448	0.0747240	+	0.997204i	$0.476192\pi$
$728$	1.45965	0.0540982
$729$	7.55035	0.279643
$730$	−4.17087	−0.154371
$731$	5.85450	0.216536
$732$	6.45071	0.238425
$733$	7.81507	0.288656	0.144328	−	0.989530i	$-0.453898\pi$
$733$	7.81507	0.288656	0.144328	+	0.989530i	$0.453898\pi$
$734$	25.5721	0.943884
$735$	0.502961	0.0185520
$736$	−3.35114	−0.123525
$737$	−13.5786	−0.500176
$738$	11.0102	0.405290
$739$	−19.1280	−0.703634	−0.351817	−	0.936069i	$-0.614436\pi$
$739$	−19.1280	−0.703634	−0.351817	+	0.936069i	$0.614436\pi$
$740$	−3.78176	−0.139020
$741$	0	0
$742$	5.37238	0.197226
$743$	27.2286	0.998919	0.499460	−	0.866337i	$-0.333532\pi$
$743$	27.2286	0.998919	0.499460	+	0.866337i	$0.333532\pi$
$744$	0.984496	0.0360934
$745$	6.93441	0.254057
$746$	34.4331	1.26068
$747$	19.8103	0.724820
$748$	−3.16785	−0.115828
$749$	−10.9808	−0.401231
$750$	4.87327	0.177947
$751$	−27.1340	−0.990134	−0.495067	−	0.868855i	$-0.664857\pi$
$751$	−27.1340	−0.990134	−0.495067	+	0.868855i	$0.664857\pi$
$752$	−2.24077	−0.0817124
$753$	10.7804	0.392861
$754$	1.17389	0.0427505
$755$	−9.40206	−0.342176
$756$	−4.67853	−0.170157
$757$	−42.0071	−1.52677	−0.763387	−	0.645942i	$-0.776465\pi$
$757$	−42.0071	−1.52677	−0.763387	+	0.645942i	$0.776465\pi$
$758$	−5.93250	−0.215478
$759$	−4.08465	−0.148263
$760$	0	0
$761$	−32.1741	−1.16631	−0.583155	−	0.812361i	$-0.698182\pi$
$761$	−32.1741	−1.16631	−0.583155	+	0.812361i	$0.698182\pi$
$762$	−0.271775	−0.00984538
$763$	−4.15182	−0.150306
$764$	−2.84233	−0.102832
$765$	−2.85776	−0.103323
$766$	−12.8493	−0.464265
$767$	16.3262	0.589506
$768$	0.902113	0.0325522
$769$	−36.2064	−1.30564	−0.652818	−	0.757515i	$-0.726413\pi$
$769$	−36.2064	−1.30564	−0.652818	+	0.757515i	$0.726413\pi$
$770$	0.753310	0.0271474
$771$	−8.44339	−0.304081
$772$	−12.4128	−0.446746
$773$	−10.9365	−0.393358	−0.196679	−	0.980468i	$-0.563016\pi$
$773$	−10.9365	−0.393358	−0.196679	+	0.980468i	$0.563016\pi$
$774$	5.45901	0.196220
$775$	5.11738	0.183822
$776$	12.7935	0.459260
$777$	−6.11902	−0.219519
$778$	14.8885	0.533778
$779$	0	0
$780$	−0.734147	−0.0262867
$781$	4.06142	0.145329
$782$	−7.85701	−0.280966
$783$	−3.76260	−0.134464
$784$	1.00000	0.0357143
$785$	5.01550	0.179011
$786$	−1.99200	−0.0710522
$787$	53.2128	1.89683	0.948416	−	0.317028i	$-0.102685\pi$
$787$	53.2128	1.89683	0.948416	+	0.317028i	$0.102685\pi$
$788$	−16.8481	−0.600188
$789$	5.36448	0.190981
$790$	1.09459	0.0389436
$791$	−12.3072	−0.437593
$792$	−2.95385	−0.104961
$793$	−10.4375	−0.370645
$794$	11.0623	0.392586
$795$	−2.70210	−0.0958336
$796$	−5.28053	−0.187163
$797$	17.5340	0.621086	0.310543	−	0.950559i	$-0.399489\pi$
$797$	17.5340	0.621086	0.310543	+	0.950559i	$0.399489\pi$
$798$	0	0
$799$	−5.25365	−0.185861
$800$	4.68915	0.165787
$801$	6.82450	0.241132
$802$	−0.255119	−0.00900856
$803$	−10.1077	−0.356694
$804$	9.06602	0.319734
$805$	1.86838	0.0658519
$806$	−1.59295	−0.0561092
$807$	23.9868	0.844376
$808$	10.7444	0.377988
$809$	−46.6298	−1.63942	−0.819708	−	0.572782i	$-0.805864\pi$
$809$	−46.6298	−1.63942	−0.819708	+	0.572782i	$0.805864\pi$
$810$	−1.30353	−0.0458013
$811$	16.7623	0.588603	0.294302	−	0.955713i	$-0.404913\pi$
$811$	16.7623	0.588603	0.294302	+	0.955713i	$0.404913\pi$
$812$	0.804226	0.0282228
$813$	0.631276	0.0221398
$814$	−9.16477	−0.321225
$815$	8.51383	0.298226
$816$	2.11507	0.0740424
$817$	0	0
$818$	−5.21766	−0.182431
$819$	3.19107	0.111505
$820$	2.80789	0.0980556
$821$	−34.8319	−1.21564	−0.607821	−	0.794074i	$-0.707956\pi$
$821$	−34.8319	−1.21564	−0.607821	+	0.794074i	$0.707956\pi$
$822$	−8.22807	−0.286987
$823$	−47.0210	−1.63905	−0.819525	−	0.573044i	$-0.805763\pi$
$823$	−47.0210	−1.63905	−0.819525	+	0.573044i	$0.805763\pi$
$824$	9.03624	0.314792
$825$	5.71552	0.198989
$826$	11.1850	0.389177
$827$	17.6099	0.612357	0.306178	−	0.951974i	$-0.400950\pi$
$827$	17.6099	0.612357	0.306178	+	0.951974i	$0.400950\pi$
$828$	−7.32624	−0.254604
$829$	−3.41994	−0.118779	−0.0593896	−	0.998235i	$-0.518915\pi$
$829$	−3.41994	−0.118779	−0.0593896	+	0.998235i	$0.518915\pi$
$830$	5.05214	0.175362
$831$	−11.6857	−0.405372
$832$	−1.45965	−0.0506042
$833$	2.34458	0.0812348
$834$	18.5988	0.644022
$835$	−1.86961	−0.0647004
$836$	0	0
$837$	5.10579	0.176482
$838$	27.6587	0.955455
$839$	−1.50554	−0.0519769	−0.0259885	−	0.999662i	$-0.508273\pi$
$839$	−1.50554	−0.0519769	−0.0259885	+	0.999662i	$0.508273\pi$
$840$	−0.502961	−0.0173538
$841$	−28.3532	−0.977697
$842$	5.70020	0.196442
$843$	27.6711	0.953042
$844$	12.7557	0.439069
$845$	−6.06010	−0.208474
$846$	−4.89875	−0.168422
$847$	−9.17442	−0.315237
$848$	−5.37238	−0.184488
$849$	21.0424	0.722175
$850$	10.9941	0.377094
$851$	−22.7307	−0.779199
$852$	−2.71168	−0.0929007
$853$	−23.7732	−0.813977	−0.406989	−	0.913433i	$-0.633421\pi$
$853$	−23.7732	−0.813977	−0.406989	+	0.913433i	$0.633421\pi$
$854$	−7.15067	−0.244691
$855$	0	0
$856$	10.9808	0.375317
$857$	−33.6469	−1.14936	−0.574678	−	0.818380i	$-0.694873\pi$
$857$	−33.6469	−1.14936	−0.574678	+	0.818380i	$0.694873\pi$
$858$	−1.77914	−0.0607389
$859$	57.2061	1.95185	0.975923	−	0.218116i	$-0.0699913\pi$
$859$	57.2061	1.95185	0.975923	+	0.218116i	$0.0699913\pi$
$860$	1.39219	0.0474733
$861$	4.54325	0.154834
$862$	20.6656	0.703873
$863$	32.3878	1.10250	0.551248	−	0.834342i	$-0.314152\pi$
$863$	32.3878	1.10250	0.551248	+	0.834342i	$0.314152\pi$
$864$	4.67853	0.159167
$865$	10.5197	0.357682
$866$	16.1525	0.548885
$867$	−10.3770	−0.352420
$868$	−1.09132	−0.0370419
$869$	2.65263	0.0899844
$870$	−0.404494	−0.0137136
$871$	−14.6691	−0.497045
$872$	4.15182	0.140598
$873$	27.9690	0.946608
$874$	0	0
$875$	−5.40206	−0.182623
$876$	6.74861	0.228014
$877$	7.92285	0.267536	0.133768	−	0.991013i	$-0.457292\pi$
$877$	7.92285	0.267536	0.133768	+	0.991013i	$0.457292\pi$
$878$	−7.66156	−0.258565
$879$	4.96533	0.167477
$880$	−0.753310	−0.0253941
$881$	49.9603	1.68321	0.841603	−	0.540097i	$-0.181612\pi$
$881$	49.9603	1.68321	0.841603	+	0.540097i	$0.181612\pi$
$882$	2.18619	0.0736129
$883$	21.4970	0.723433	0.361716	−	0.932288i	$-0.382191\pi$
$883$	21.4970	0.723433	0.361716	+	0.932288i	$0.382191\pi$
$884$	−3.42226	−0.115103
$885$	−5.62564	−0.189104
$886$	−14.7542	−0.495678
$887$	8.68542	0.291628	0.145814	−	0.989312i	$-0.453420\pi$
$887$	8.68542	0.291628	0.145814	+	0.989312i	$0.453420\pi$
$888$	6.11902	0.205341
$889$	0.301265	0.0101041
$890$	1.74043	0.0583392
$891$	−3.15898	−0.105830
$892$	−22.9108	−0.767109
$893$	0	0
$894$	−11.2201	−0.375256
$895$	−4.10503	−0.137216
$896$	−1.00000	−0.0334077
$897$	−4.41268	−0.147335
$898$	−12.1341	−0.404921
$899$	−0.877670	−0.0292719
$900$	10.2514	0.341713
$901$	−12.5960	−0.419632
$902$	6.80467	0.226571
$903$	2.25261	0.0749622
$904$	12.3072	0.409331
$905$	−2.94891	−0.0980250
$906$	15.2128	0.505413
$907$	41.5715	1.38036	0.690179	−	0.723639i	$-0.257532\pi$
$907$	41.5715	1.38036	0.690179	+	0.723639i	$0.257532\pi$
$908$	−10.3999	−0.345132
$909$	23.4894	0.779095
$910$	0.813808	0.0269775
$911$	48.3972	1.60347	0.801735	−	0.597679i	$-0.203910\pi$
$911$	48.3972	1.60347	0.801735	+	0.597679i	$0.203910\pi$
$912$	0	0
$913$	12.2434	0.405198
$914$	−33.3891	−1.10441
$915$	3.59651	0.118897
$916$	−3.31741	−0.109610
$917$	2.20815	0.0729195
$918$	10.9692	0.362037
$919$	42.6200	1.40590	0.702952	−	0.711237i	$-0.251865\pi$
$919$	42.6200	1.40590	0.702952	+	0.711237i	$0.251865\pi$
$920$	−1.86838	−0.0615988
$921$	−18.6950	−0.616020
$922$	1.44124	0.0474648
$923$	4.38759	0.144419
$924$	−1.21888	−0.0400983
$925$	31.8064	1.04579
$926$	−0.594599	−0.0195397
$927$	19.7549	0.648838
$928$	−0.804226	−0.0264000
$929$	−27.5135	−0.902689	−0.451345	−	0.892350i	$-0.649055\pi$
$929$	−27.5135	−0.902689	−0.451345	+	0.892350i	$0.649055\pi$
$930$	0.548893	0.0179989
$931$	0	0
$932$	17.1708	0.562447
$933$	−10.4434	−0.341901
$934$	−39.3250	−1.28675
$935$	−1.76619	−0.0577607
$936$	−3.19107	−0.104304
$937$	−38.0399	−1.24271	−0.621354	−	0.783530i	$-0.713417\pi$
$937$	−38.0399	−1.24271	−0.621354	+	0.783530i	$0.713417\pi$
$938$	−10.0498	−0.328136
$939$	−30.7461	−1.00336
$940$	−1.24931	−0.0407480
$941$	−49.6889	−1.61981	−0.809906	−	0.586559i	$-0.800482\pi$
$941$	−49.6889	−1.61981	−0.809906	+	0.586559i	$0.800482\pi$
$942$	−8.11526	−0.264409
$943$	16.8771	0.549595
$944$	−11.1850	−0.364042
$945$	−2.60845	−0.0848530
$946$	3.37385	0.109693
$947$	−1.38642	−0.0450526	−0.0225263	−	0.999746i	$-0.507171\pi$
$947$	−1.38642	−0.0450526	−0.0225263	+	0.999746i	$0.507171\pi$
$948$	−1.77108	−0.0575219
$949$	−10.9195	−0.354461
$950$	0	0
$951$	−3.48548	−0.113024
$952$	−2.34458	−0.0759882
$953$	53.5740	1.73543	0.867716	−	0.497061i	$-0.165588\pi$
$953$	53.5740	1.73543	0.867716	+	0.497061i	$0.165588\pi$
$954$	−11.7451	−0.380260
$955$	−1.58470	−0.0512797
$956$	19.3878	0.627045
$957$	−0.980257	−0.0316872
$958$	16.1460	0.521653
$959$	9.12088	0.294529
$960$	0.502961	0.0162330
$961$	−29.8090	−0.961581
$962$	−9.90078	−0.319214
$963$	24.0062	0.773590
$964$	1.32553	0.0426923
$965$	−6.92058	−0.222781
$966$	−3.02311	−0.0972669
$967$	−22.5482	−0.725100	−0.362550	−	0.931964i	$-0.618094\pi$
$967$	−22.5482	−0.725100	−0.362550	+	0.931964i	$0.618094\pi$
$968$	9.17442	0.294877
$969$	0	0
$970$	7.13284	0.229022
$971$	−29.6013	−0.949952	−0.474976	−	0.879999i	$-0.657543\pi$
$971$	−29.6013	−0.949952	−0.474976	+	0.879999i	$0.657543\pi$
$972$	16.1447	0.517843
$973$	−20.6169	−0.660947
$974$	42.2190	1.35278
$975$	6.17453	0.197743
$976$	7.15067	0.228887
$977$	40.1954	1.28597	0.642983	−	0.765880i	$-0.277697\pi$
$977$	40.1954	1.28597	0.642983	+	0.765880i	$0.277697\pi$
$978$	−13.7757	−0.440497
$979$	4.21777	0.134801
$980$	0.557537	0.0178099
$981$	9.07668	0.289796
$982$	13.0440	0.416252
$983$	16.4837	0.525747	0.262873	−	0.964830i	$-0.415330\pi$
$983$	16.4837	0.525747	0.262873	+	0.964830i	$0.415330\pi$
$984$	−4.54325	−0.144834
$985$	−9.39341	−0.299299
$986$	−1.88557	−0.0600488
$987$	−2.02143	−0.0643427
$988$	0	0
$989$	8.36793	0.266085
$990$	−1.64688	−0.0523413
$991$	−33.4568	−1.06279	−0.531395	−	0.847124i	$-0.678332\pi$
$991$	−33.4568	−1.06279	−0.531395	+	0.847124i	$0.678332\pi$
$992$	1.09132	0.0346495
$993$	−2.29424	−0.0728055
$994$	3.00592	0.0953421
$995$	−2.94409	−0.0933339
$996$	−8.17453	−0.259020
$997$	11.5900	0.367060	0.183530	−	0.983014i	$-0.441247\pi$
$997$	11.5900	0.367060	0.183530	+	0.983014i	$0.441247\pi$
$998$	4.06154	0.128566
$999$	31.7344	1.00403

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5054.2.a.v.1.4	✓	4
19.18	odd	2		5054.2.a.y.1.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5054.2.a.v.1.4	✓	4	1.1	even	1	trivial
5054.2.a.y.1.1	yes	4	19.18	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:	\( N \)	\(=\)	\( 5054 = 2 \cdot 7 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5054.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.902113 q^{3} +1.00000 q^{4} +0.557537 q^{5} -0.902113 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.18619 q^{9} -0.557537 q^{10} -1.35114 q^{11} +0.902113 q^{12} -1.45965 q^{13} -1.00000 q^{14} +0.502961 q^{15} +1.00000 q^{16} +2.34458 q^{17} +2.18619 q^{18} +0.557537 q^{20} +0.902113 q^{21} +1.35114 q^{22} +3.35114 q^{23} -0.902113 q^{24} -4.68915 q^{25} +1.45965 q^{26} -4.67853 q^{27} +1.00000 q^{28} +0.804226 q^{29} -0.502961 q^{30} -1.09132 q^{31} -1.00000 q^{32} -1.21888 q^{33} -2.34458 q^{34} +0.557537 q^{35} -2.18619 q^{36} -6.78298 q^{37} -1.31677 q^{39} -0.557537 q^{40} +5.03624 q^{41} -0.902113 q^{42} +2.49704 q^{43} -1.35114 q^{44} -1.21888 q^{45} -3.35114 q^{46} -2.24077 q^{47} +0.902113 q^{48} +1.00000 q^{49} +4.68915 q^{50} +2.11507 q^{51} -1.45965 q^{52} -5.37238 q^{53} +4.67853 q^{54} -0.753310 q^{55} -1.00000 q^{56} -0.804226 q^{58} -11.1850 q^{59} +0.502961 q^{60} +7.15067 q^{61} +1.09132 q^{62} -2.18619 q^{63} +1.00000 q^{64} -0.813808 q^{65} +1.21888 q^{66} +10.0498 q^{67} +2.34458 q^{68} +3.02311 q^{69} -0.557537 q^{70} -3.00592 q^{71} +2.18619 q^{72} +7.48089 q^{73} +6.78298 q^{74} -4.23015 q^{75} -1.35114 q^{77} +1.31677 q^{78} -1.96325 q^{79} +0.557537 q^{80} +2.33801 q^{81} -5.03624 q^{82} -9.06154 q^{83} +0.902113 q^{84} +1.30719 q^{85} -2.49704 q^{86} +0.725503 q^{87} +1.35114 q^{88} -3.12164 q^{89} +1.21888 q^{90} -1.45965 q^{91} +3.35114 q^{92} -0.984496 q^{93} +2.24077 q^{94} -0.902113 q^{96} -12.7935 q^{97} -1.00000 q^{98} +2.95385 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{9} - 2 q^{10} + 4 q^{11} - 4 q^{12} + 2 q^{13} - 4 q^{14} - 2 q^{15} + 4 q^{16} + 2 q^{17} - 2 q^{18} + 2 q^{20} - 4 q^{21}+ \cdots + 2 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^9 - 2 * q^10 + 4 * q^11 - 4 * q^12 + 2 * q^13 - 4 * q^14 - 2 * q^15 + 4 * q^16 + 2 * q^17 - 2 * q^18 + 2 * q^20 - 4 * q^21 - 4 * q^22 + 4 * q^23 + 4 * q^24 - 4 * q^25 - 2 * q^26 - 10 * q^27 + 4 * q^28 - 12 * q^29 + 2 * q^30 - 14 * q^31 - 4 * q^32 - 4 * q^33 - 2 * q^34 + 2 * q^35 + 2 * q^36 - 24 * q^37 - 12 * q^39 - 2 * q^40 + 4 * q^42 + 14 * q^43 + 4 * q^44 - 4 * q^45 - 4 * q^46 - 2 * q^47 - 4 * q^48 + 4 * q^49 + 4 * q^50 + 8 * q^51 + 2 * q^52 + 10 * q^54 - 18 * q^55 - 4 * q^56 + 12 * q^58 - 2 * q^59 - 2 * q^60 + 2 * q^61 + 14 * q^62 + 2 * q^63 + 4 * q^64 - 14 * q^65 + 4 * q^66 - 22 * q^67 + 2 * q^68 - 4 * q^69 - 2 * q^70 - 4 * q^71 - 2 * q^72 + 10 * q^73 + 24 * q^74 - 16 * q^75 + 4 * q^77 + 12 * q^78 - 2 * q^79 + 2 * q^80 + 4 * q^81 - 4 * q^84 - 14 * q^85 - 14 * q^86 + 32 * q^87 - 4 * q^88 - 10 * q^89 + 4 * q^90 + 2 * q^91 + 4 * q^92 + 14 * q^93 + 2 * q^94 + 4 * q^96 + 22 * q^97 - 4 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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