LMFDB - Embedded newform 538.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [538,2,Mod(1,538)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(538, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("538.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 538 = 2 \cdot 269 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	538.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$4.29595162874$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.4913.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 6x^{2} + x + 1 $ x^4 - x^3 - 6*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.90570$ of defining polynomial
Character	$\chi$	$=$	538.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} -1.90570 q^{3} +1.00000 q^{4} +0.655849 q^{5} +1.90570 q^{6} +2.04948 q^{7} -1.00000 q^{8} +0.631706 q^{9} -0.655849 q^{10} +1.51207 q^{11} -1.90570 q^{12} -1.53741 q^{13} -2.04948 q^{14} -1.24985 q^{15} +1.00000 q^{16} +0.126749 q^{17} -0.631706 q^{18} -4.09896 q^{19} +0.655849 q^{20} -3.90570 q^{21} -1.51207 q^{22} +7.24985 q^{23} +1.90570 q^{24} -4.56986 q^{25} +1.53741 q^{26} +4.51327 q^{27} +2.04948 q^{28} +8.20504 q^{29} +1.24985 q^{30} +1.17623 q^{31} -1.00000 q^{32} -2.88156 q^{33} -0.126749 q^{34} +1.34415 q^{35} +0.631706 q^{36} +7.34882 q^{37} +4.09896 q^{38} +2.92985 q^{39} -0.655849 q^{40} -4.61103 q^{41} +3.90570 q^{42} +8.19673 q^{43} +1.51207 q^{44} +0.414304 q^{45} -7.24985 q^{46} +7.49140 q^{47} -1.90570 q^{48} -2.79963 q^{49} +4.56986 q^{50} -0.241545 q^{51} -1.53741 q^{52} +11.1231 q^{53} -4.51327 q^{54} +0.991691 q^{55} -2.04948 q^{56} +7.81141 q^{57} -8.20504 q^{58} +10.4190 q^{59} -1.24985 q^{60} -2.46259 q^{61} -1.17623 q^{62} +1.29467 q^{63} +1.00000 q^{64} -1.00831 q^{65} +2.88156 q^{66} +6.04948 q^{67} +0.126749 q^{68} -13.8161 q^{69} -1.34415 q^{70} +3.67288 q^{71} -0.631706 q^{72} -12.2957 q^{73} -7.34882 q^{74} +8.70880 q^{75} -4.09896 q^{76} +3.09896 q^{77} -2.92985 q^{78} -4.60756 q^{79} +0.655849 q^{80} -10.4961 q^{81} +4.61103 q^{82} -0.483091 q^{83} -3.90570 q^{84} +0.0831280 q^{85} -8.19673 q^{86} -15.6364 q^{87} -1.51207 q^{88} +4.00711 q^{89} -0.414304 q^{90} -3.15089 q^{91} +7.24985 q^{92} -2.24155 q^{93} -7.49140 q^{94} -2.68830 q^{95} +1.90570 q^{96} +13.1991 q^{97} +2.79963 q^{98} +0.955185 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 3 q^{3} + 4 q^{4} + 5 q^{5} - 3 q^{6} - q^{7} - 4 q^{8} + 3 q^{9} - 5 q^{10} + 7 q^{11} + 3 q^{12} + 4 q^{13} + q^{14} + 8 q^{15} + 4 q^{16} + 4 q^{17} - 3 q^{18} + 2 q^{19} + 5 q^{20}+ \cdots - 16 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 3 * q^3 + 4 * q^4 + 5 * q^5 - 3 * q^6 - q^7 - 4 * q^8 + 3 * q^9 - 5 * q^10 + 7 * q^11 + 3 * q^12 + 4 * q^13 + q^14 + 8 * q^15 + 4 * q^16 + 4 * q^17 - 3 * q^18 + 2 * q^19 + 5 * q^20 - 5 * q^21 - 7 * q^22 + 16 * q^23 - 3 * q^24 - q^25 - 4 * q^26 + 6 * q^27 - q^28 - 8 * q^30 - q^31 - 4 * q^32 + q^33 - 4 * q^34 + 3 * q^35 + 3 * q^36 - 2 * q^37 - 2 * q^38 + 3 * q^39 - 5 * q^40 - q^41 + 5 * q^42 + 9 * q^43 + 7 * q^44 + 8 * q^45 - 16 * q^46 + 13 * q^47 + 3 * q^48 - 15 * q^49 + q^50 + 3 * q^51 + 4 * q^52 + 28 * q^53 - 6 * q^54 + 13 * q^55 + q^56 + 10 * q^57 + 19 * q^59 + 8 * q^60 - 20 * q^61 + q^62 + 12 * q^63 + 4 * q^64 + 5 * q^65 - q^66 + 15 * q^67 + 4 * q^68 - 5 * q^69 - 3 * q^70 + 15 * q^71 - 3 * q^72 - 7 * q^73 + 2 * q^74 + 12 * q^75 + 2 * q^76 - 6 * q^77 - 3 * q^78 - 17 * q^79 + 5 * q^80 + 4 * q^81 + q^82 + 6 * q^83 - 5 * q^84 - 29 * q^85 - 9 * q^86 - 34 * q^87 - 7 * q^88 + 20 * q^89 - 8 * q^90 - 18 * q^91 + 16 * q^92 - 5 * q^93 - 13 * q^94 - 6 * q^95 - 3 * q^96 + 3 * q^97 + 15 * q^98 - 16 * q^99

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.90570	−1.10026	−0.550129	−	0.835080i	$-0.685422\pi$
$3$	−1.90570	−1.10026	−0.550129	+	0.835080i	$0.685422\pi$
$4$	1.00000	0.500000
$5$	0.655849	0.293305	0.146652	−	0.989188i	$-0.453150\pi$
$5$	0.655849	0.293305	0.146652	+	0.989188i	$0.453150\pi$
$6$	1.90570	0.778000
$7$	2.04948	0.774631	0.387316	−	0.921947i	$-0.373402\pi$
$7$	2.04948	0.774631	0.387316	+	0.921947i	$0.373402\pi$
$8$	−1.00000	−0.353553
$9$	0.631706	0.210569
$10$	−0.655849	−0.207398
$11$	1.51207	0.455907	0.227953	−	0.973672i	$-0.426797\pi$
$11$	1.51207	0.455907	0.227953	+	0.973672i	$0.426797\pi$
$12$	−1.90570	−0.550129
$13$	−1.53741	−0.426401	−0.213200	−	0.977009i	$-0.568389\pi$
$13$	−1.53741	−0.426401	−0.213200	+	0.977009i	$0.568389\pi$
$14$	−2.04948	−0.547747
$15$	−1.24985	−0.322711
$16$	1.00000	0.250000
$17$	0.126749	0.0307411	0.0153705	−	0.999882i	$-0.495107\pi$
$17$	0.126749	0.0307411	0.0153705	+	0.999882i	$0.495107\pi$
$18$	−0.631706	−0.148895
$19$	−4.09896	−0.940366	−0.470183	−	0.882569i	$-0.655812\pi$
$19$	−4.09896	−0.940366	−0.470183	+	0.882569i	$0.655812\pi$
$20$	0.655849	0.146652
$21$	−3.90570	−0.852294
$22$	−1.51207	−0.322375
$23$	7.24985	1.51170	0.755850	−	0.654745i	$-0.227224\pi$
$23$	7.24985	1.51170	0.755850	+	0.654745i	$0.227224\pi$
$24$	1.90570	0.389000
$25$	−4.56986	−0.913972
$26$	1.53741	0.301511
$27$	4.51327	0.868578
$28$	2.04948	0.387316
$29$	8.20504	1.52364	0.761819	−	0.647790i	$-0.224307\pi$
$29$	8.20504	1.52364	0.761819	+	0.647790i	$0.224307\pi$
$30$	1.24985	0.228191
$31$	1.17623	0.211257	0.105629	−	0.994406i	$-0.466315\pi$
$31$	1.17623	0.211257	0.105629	+	0.994406i	$0.466315\pi$
$32$	−1.00000	−0.176777
$33$	−2.88156	−0.501615
$34$	−0.126749	−0.0217372
$35$	1.34415	0.227203
$36$	0.631706	0.105284
$37$	7.34882	1.20814	0.604069	−	0.796932i	$-0.293545\pi$
$37$	7.34882	1.20814	0.604069	+	0.796932i	$0.293545\pi$
$38$	4.09896	0.664939
$39$	2.92985	0.469151
$40$	−0.655849	−0.103699
$41$	−4.61103	−0.720123	−0.360061	−	0.932929i	$-0.617244\pi$
$41$	−4.61103	−0.720123	−0.360061	+	0.932929i	$0.617244\pi$
$42$	3.90570	0.602663
$43$	8.19673	1.24999	0.624995	−	0.780629i	$-0.285101\pi$
$43$	8.19673	1.24999	0.624995	+	0.780629i	$0.285101\pi$
$44$	1.51207	0.227953
$45$	0.414304	0.0617608
$46$	−7.24985	−1.06893
$47$	7.49140	1.09273	0.546366	−	0.837546i	$-0.316011\pi$
$47$	7.49140	1.09273	0.546366	+	0.837546i	$0.316011\pi$
$48$	−1.90570	−0.275065
$49$	−2.79963	−0.399947
$50$	4.56986	0.646276
$51$	−0.241545	−0.0338231
$52$	−1.53741	−0.213200
$53$	11.1231	1.52788	0.763938	−	0.645290i	$-0.223263\pi$
$53$	11.1231	1.52788	0.763938	+	0.645290i	$0.223263\pi$
$54$	−4.51327	−0.614178
$55$	0.991691	0.133720
$56$	−2.04948	−0.273873
$57$	7.81141	1.03465
$58$	−8.20504	−1.07737
$59$	10.4190	1.35643	0.678217	−	0.734862i	$-0.262753\pi$
$59$	10.4190	1.35643	0.678217	+	0.734862i	$0.262753\pi$
$60$	−1.24985	−0.161355
$61$	−2.46259	−0.315302	−0.157651	−	0.987495i	$-0.550392\pi$
$61$	−2.46259	−0.315302	−0.157651	+	0.987495i	$0.550392\pi$
$62$	−1.17623	−0.149381
$63$	1.29467	0.163113
$64$	1.00000	0.125000
$65$	−1.00831	−0.125065
$66$	2.88156	0.354696
$67$	6.04948	0.739062	0.369531	−	0.929218i	$-0.379518\pi$
$67$	6.04948	0.739062	0.369531	+	0.929218i	$0.379518\pi$
$68$	0.126749	0.0153705
$69$	−13.8161	−1.66326
$70$	−1.34415	−0.160657
$71$	3.67288	0.435890	0.217945	−	0.975961i	$-0.430065\pi$
$71$	3.67288	0.435890	0.217945	+	0.975961i	$0.430065\pi$
$72$	−0.631706	−0.0744473
$73$	−12.2957	−1.43910	−0.719551	−	0.694440i	$-0.755652\pi$
$73$	−12.2957	−1.43910	−0.719551	+	0.694440i	$0.755652\pi$
$74$	−7.34882	−0.854283
$75$	8.70880	1.00561
$76$	−4.09896	−0.470183
$77$	3.09896	0.353160
$78$	−2.92985	−0.331740
$79$	−4.60756	−0.518391	−0.259196	−	0.965825i	$-0.583457\pi$
$79$	−4.60756	−0.518391	−0.259196	+	0.965825i	$0.583457\pi$
$80$	0.655849	0.0733262
$81$	−10.4961	−1.16623
$82$	4.61103	0.509204
$83$	−0.483091	−0.0530261	−0.0265130	−	0.999648i	$-0.508440\pi$
$83$	−0.483091	−0.0530261	−0.0265130	+	0.999648i	$0.508440\pi$
$84$	−3.90570	−0.426147
$85$	0.0831280	0.00901650
$86$	−8.19673	−0.883876
$87$	−15.6364	−1.67640
$88$	−1.51207	−0.161187
$89$	4.00711	0.424753	0.212377	−	0.977188i	$-0.431880\pi$
$89$	4.00711	0.424753	0.212377	+	0.977188i	$0.431880\pi$
$90$	−0.414304	−0.0436715
$91$	−3.15089	−0.330303
$92$	7.24985	0.755850
$93$	−2.24155	−0.232437
$94$	−7.49140	−0.772679
$95$	−2.68830	−0.275814
$96$	1.90570	0.194500
$97$	13.1991	1.34017	0.670084	−	0.742285i	$-0.266258\pi$
$97$	13.1991	1.34017	0.670084	+	0.742285i	$0.266258\pi$
$98$	2.79963	0.282805
$99$	0.955185	0.0959997
$100$	−4.56986	−0.456986
$101$	−7.79438	−0.775570	−0.387785	−	0.921750i	$-0.626760\pi$
$101$	−7.79438	−0.775570	−0.387785	+	0.921750i	$0.626760\pi$
$102$	0.241545	0.0239166
$103$	0.0807387	0.00795542	0.00397771	−	0.999992i	$-0.498734\pi$
$103$	0.0807387	0.00795542	0.00397771	+	0.999992i	$0.498734\pi$
$104$	1.53741	0.150755
$105$	−2.56155	−0.249982
$106$	−11.1231	−1.08037
$107$	0.175035	0.0169213	0.00846065	−	0.999964i	$-0.497307\pi$
$107$	0.175035	0.0169213	0.00846065	+	0.999964i	$0.497307\pi$
$108$	4.51327	0.434289
$109$	3.52505	0.337638	0.168819	−	0.985647i	$-0.446005\pi$
$109$	3.52505	0.337638	0.168819	+	0.985647i	$0.446005\pi$
$110$	−0.991691	−0.0945540
$111$	−14.0047	−1.32926
$112$	2.04948	0.193658
$113$	−21.0041	−1.97590	−0.987949	−	0.154780i	$-0.950533\pi$
$113$	−21.0041	−1.97590	−0.987949	+	0.154780i	$0.950533\pi$
$114$	−7.81141	−0.731605
$115$	4.75481	0.443388
$116$	8.20504	0.761819
$117$	−0.971191	−0.0897866
$118$	−10.4190	−0.959144
$119$	0.259769	0.0238130
$120$	1.24985	0.114096
$121$	−8.71364	−0.792149
$122$	2.46259	0.222952
$123$	8.78726	0.792321
$124$	1.17623	0.105629
$125$	−6.27639	−0.561377
$126$	−1.29467	−0.115338
$127$	7.86436	0.697849	0.348925	−	0.937151i	$-0.386547\pi$
$127$	7.86436	0.697849	0.348925	+	0.937151i	$0.386547\pi$
$128$	−1.00000	−0.0883883
$129$	−15.6205	−1.37531
$130$	1.00831	0.0884345
$131$	−6.21029	−0.542595	−0.271298	−	0.962495i	$-0.587453\pi$
$131$	−6.21029	−0.542595	−0.271298	+	0.962495i	$0.587453\pi$
$132$	−2.88156	−0.250808
$133$	−8.40075	−0.728437
$134$	−6.04948	−0.522596
$135$	2.96002	0.254758
$136$	−0.126749	−0.0108686
$137$	−1.23096	−0.105168	−0.0525840	−	0.998617i	$-0.516746\pi$
$137$	−1.23096	−0.105168	−0.0525840	+	0.998617i	$0.516746\pi$
$138$	13.8161	1.17610
$139$	14.6311	1.24100	0.620498	−	0.784208i	$-0.286931\pi$
$139$	14.6311	1.24100	0.620498	+	0.784208i	$0.286931\pi$
$140$	1.34415	0.113601
$141$	−14.2764	−1.20229
$142$	−3.67288	−0.308221
$143$	−2.32467	−0.194399
$144$	0.631706	0.0526422
$145$	5.38127	0.446890
$146$	12.2957	1.01760
$147$	5.33526	0.440045
$148$	7.34882	0.604069
$149$	2.96390	0.242813	0.121406	−	0.992603i	$-0.461260\pi$
$149$	2.96390	0.242813	0.121406	+	0.992603i	$0.461260\pi$
$150$	−8.70880	−0.711071
$151$	6.51327	0.530042	0.265021	−	0.964243i	$-0.414621\pi$
$151$	6.51327	0.530042	0.265021	+	0.964243i	$0.414621\pi$
$152$	4.09896	0.332470
$153$	0.0800679	0.00647310
$154$	−3.09896	−0.249722
$155$	0.771429	0.0619627
$156$	2.92985	0.234575
$157$	−4.54977	−0.363111	−0.181556	−	0.983381i	$-0.558113\pi$
$157$	−4.54977	−0.363111	−0.181556	+	0.983381i	$0.558113\pi$
$158$	4.60756	0.366558
$159$	−21.1973	−1.68106
$160$	−0.655849	−0.0518494
$161$	14.8584	1.17101
$162$	10.4961	0.824649
$163$	−14.5249	−1.13768	−0.568838	−	0.822450i	$-0.692607\pi$
$163$	−14.5249	−1.13768	−0.568838	+	0.822450i	$0.692607\pi$
$164$	−4.61103	−0.360061
$165$	−1.88987	−0.147126
$166$	0.483091	0.0374951
$167$	4.69542	0.363342	0.181671	−	0.983359i	$-0.441849\pi$
$167$	4.69542	0.363342	0.181671	+	0.983359i	$0.441849\pi$
$168$	3.90570	0.301332
$169$	−10.6364	−0.818182
$170$	−0.0831280	−0.00637563
$171$	−2.58934	−0.198012
$172$	8.19673	0.624995
$173$	14.9376	1.13568	0.567841	−	0.823138i	$-0.307779\pi$
$173$	14.9376	1.13568	0.567841	+	0.823138i	$0.307779\pi$
$174$	15.6364	1.18539
$175$	−9.36585	−0.707991
$176$	1.51207	0.113977
$177$	−19.8555	−1.49243
$178$	−4.00711	−0.300346
$179$	−5.17445	−0.386757	−0.193378	−	0.981124i	$-0.561944\pi$
$179$	−5.17445	−0.386757	−0.193378	+	0.981124i	$0.561944\pi$
$180$	0.414304	0.0308804
$181$	3.97341	0.295341	0.147671	−	0.989037i	$-0.452822\pi$
$181$	3.97341	0.295341	0.147671	+	0.989037i	$0.452822\pi$
$182$	3.15089	0.233560
$183$	4.69297	0.346914
$184$	−7.24985	−0.534466
$185$	4.81972	0.354353
$186$	2.24155	0.164358
$187$	0.191653	0.0140151
$188$	7.49140	0.546366
$189$	9.24985	0.672828
$190$	2.68830	0.195030
$191$	21.6735	1.56824	0.784119	−	0.620610i	$-0.213115\pi$
$191$	21.6735	1.56824	0.784119	+	0.620610i	$0.213115\pi$
$192$	−1.90570	−0.137532
$193$	−4.17742	−0.300698	−0.150349	−	0.988633i	$-0.548040\pi$
$193$	−4.17742	−0.300698	−0.150349	+	0.988633i	$0.548040\pi$
$194$	−13.1991	−0.947642
$195$	1.92154	0.137604
$196$	−2.79963	−0.199973
$197$	−1.51799	−0.108152	−0.0540762	−	0.998537i	$-0.517221\pi$
$197$	−1.51799	−0.108152	−0.0540762	+	0.998537i	$0.517221\pi$
$198$	−0.955185	−0.0678820
$199$	−12.1661	−0.862435	−0.431218	−	0.902248i	$-0.641916\pi$
$199$	−12.1661	−0.862435	−0.431218	+	0.902248i	$0.641916\pi$
$200$	4.56986	0.323138
$201$	−11.5285	−0.813159
$202$	7.79438	0.548411
$203$	16.8161	1.18026
$204$	−0.241545	−0.0169116
$205$	−3.02414	−0.211215
$206$	−0.0807387	−0.00562533
$207$	4.57978	0.318316
$208$	−1.53741	−0.106600
$209$	−6.19792	−0.428719
$210$	2.56155	0.176764
$211$	−24.7554	−1.70423	−0.852117	−	0.523352i	$-0.824681\pi$
$211$	−24.7554	−1.70423	−0.852117	+	0.523352i	$0.824681\pi$
$212$	11.1231	0.763938
$213$	−6.99942	−0.479592
$214$	−0.175035	−0.0119652
$215$	5.37582	0.366628
$216$	−4.51327	−0.307089
$217$	2.41066	0.163646
$218$	−3.52505	−0.238746
$219$	23.4319	1.58338
$220$	0.991691	0.0668598
$221$	−0.194865	−0.0131080
$222$	14.0047	0.939932
$223$	5.36710	0.359408	0.179704	−	0.983721i	$-0.442486\pi$
$223$	5.36710	0.359408	0.179704	+	0.983721i	$0.442486\pi$
$224$	−2.04948	−0.136937
$225$	−2.88681	−0.192454
$226$	21.0041	1.39717
$227$	−25.4413	−1.68860	−0.844298	−	0.535873i	$-0.819982\pi$
$227$	−25.4413	−1.68860	−0.844298	+	0.535873i	$0.819982\pi$
$228$	7.81141	0.517323
$229$	−2.13547	−0.141116	−0.0705579	−	0.997508i	$-0.522478\pi$
$229$	−2.13547	−0.141116	−0.0705579	+	0.997508i	$0.522478\pi$
$230$	−4.75481	−0.313523
$231$	−5.90570	−0.388567
$232$	−8.20504	−0.538687
$233$	13.8645	0.908296	0.454148	−	0.890926i	$-0.349944\pi$
$233$	13.8645	0.908296	0.454148	+	0.890926i	$0.349944\pi$
$234$	0.971191	0.0634887
$235$	4.91323	0.320504
$236$	10.4190	0.678217
$237$	8.78065	0.570364
$238$	−0.259769	−0.0168383
$239$	17.5309	1.13398	0.566990	−	0.823725i	$-0.308108\pi$
$239$	17.5309	1.13398	0.566990	+	0.823725i	$0.308108\pi$
$240$	−1.24985	−0.0806777
$241$	−6.65118	−0.428440	−0.214220	−	0.976785i	$-0.568721\pi$
$241$	−6.65118	−0.428440	−0.214220	+	0.976785i	$0.568721\pi$
$242$	8.71364	0.560134
$243$	6.46259	0.414575
$244$	−2.46259	−0.157651
$245$	−1.83613	−0.117306
$246$	−8.78726	−0.560255
$247$	6.30178	0.400973
$248$	−1.17623	−0.0746907
$249$	0.920628	0.0583424
$250$	6.27639	0.396954
$251$	−4.46726	−0.281971	−0.140985	−	0.990012i	$-0.545027\pi$
$251$	−4.46726	−0.281971	−0.140985	+	0.990012i	$0.545027\pi$
$252$	1.29467	0.0815565
$253$	10.9623	0.689194
$254$	−7.86436	−0.493454
$255$	−0.158417	−0.00992048
$256$	1.00000	0.0625000
$257$	23.0811	1.43976	0.719879	−	0.694099i	$-0.244197\pi$
$257$	23.0811	1.43976	0.719879	+	0.694099i	$0.244197\pi$
$258$	15.6205	0.972492
$259$	15.0613	0.935861
$260$	−1.00831	−0.0625327
$261$	5.18317	0.320830
$262$	6.21029	0.383673
$263$	−10.4537	−0.644603	−0.322301	−	0.946637i	$-0.604456\pi$
$263$	−10.4537	−0.644603	−0.322301	+	0.946637i	$0.604456\pi$
$264$	2.88156	0.177348
$265$	7.29508	0.448133
$266$	8.40075	0.515083
$267$	−7.63637	−0.467338
$268$	6.04948	0.369531
$269$	1.00000	0.0609711
$269$	1.00000	0.0609711
$270$	−2.96002	−0.180141
$271$	−3.04464	−0.184949	−0.0924745	−	0.995715i	$-0.529478\pi$
$271$	−3.04464	−0.184949	−0.0924745	+	0.995715i	$0.529478\pi$
$272$	0.126749	0.00768527
$273$	6.00467	0.363419
$274$	1.23096	0.0743650
$275$	−6.90996	−0.416686
$276$	−13.8161	−0.831630
$277$	16.3641	0.983222	0.491611	−	0.870815i	$-0.336408\pi$
$277$	16.3641	0.983222	0.491611	+	0.870815i	$0.336408\pi$
$278$	−14.6311	−0.877516
$279$	0.743031	0.0444841
$280$	−1.34415	−0.0803284
$281$	−21.7013	−1.29459	−0.647295	−	0.762240i	$-0.724100\pi$
$281$	−21.7013	−1.29459	−0.647295	+	0.762240i	$0.724100\pi$
$282$	14.2764	0.850146
$283$	−17.9315	−1.06592	−0.532958	−	0.846142i	$-0.678920\pi$
$283$	−17.9315	−1.06592	−0.532958	+	0.846142i	$0.678920\pi$
$284$	3.67288	0.217945
$285$	5.12311	0.303467
$286$	2.32467	0.137461
$287$	−9.45023	−0.557829
$288$	−0.631706	−0.0372236
$289$	−16.9839	−0.999055
$290$	−5.38127	−0.315999
$291$	−25.1536	−1.47453
$292$	−12.2957	−0.719551
$293$	14.9994	0.876275	0.438138	−	0.898908i	$-0.355638\pi$
$293$	14.9994	0.876275	0.438138	+	0.898908i	$0.355638\pi$
$294$	−5.33526	−0.311159
$295$	6.83327	0.397849
$296$	−7.34882	−0.427141
$297$	6.82438	0.395991
$298$	−2.96390	−0.171694
$299$	−11.1460	−0.644590
$300$	8.70880	0.502803
$301$	16.7990	0.968281
$302$	−6.51327	−0.374796
$303$	14.8538	0.853327
$304$	−4.09896	−0.235092
$305$	−1.61509	−0.0924797
$306$	−0.0800679	−0.00457718
$307$	−8.26528	−0.471724	−0.235862	−	0.971787i	$-0.575791\pi$
$307$	−8.26528	−0.471724	−0.235862	+	0.971787i	$0.575791\pi$
$308$	3.09896	0.176580
$309$	−0.153864	−0.00875302
$310$	−0.771429	−0.0438142
$311$	−24.5863	−1.39416	−0.697081	−	0.716993i	$-0.745518\pi$
$311$	−24.5863	−1.39416	−0.697081	+	0.716993i	$0.745518\pi$
$312$	−2.92985	−0.165870
$313$	7.63678	0.431656	0.215828	−	0.976431i	$-0.430755\pi$
$313$	7.63678	0.431656	0.215828	+	0.976431i	$0.430755\pi$
$314$	4.54977	0.256759
$315$	0.849108	0.0478418
$316$	−4.60756	−0.259196
$317$	2.77674	0.155957	0.0779786	−	0.996955i	$-0.475153\pi$
$317$	2.77674	0.155957	0.0779786	+	0.996955i	$0.475153\pi$
$318$	21.1973	1.18869
$319$	12.4066	0.694637
$320$	0.655849	0.0366631
$321$	−0.333565	−0.0186178
$322$	−14.8584	−0.828028
$323$	−0.519538	−0.0289079
$324$	−10.4961	−0.583115
$325$	7.02575	0.389718
$326$	14.5249	0.804458
$327$	−6.71769	−0.371489
$328$	4.61103	0.254602
$329$	15.3535	0.846465
$330$	1.88987	0.104034
$331$	17.3778	0.955170	0.477585	−	0.878586i	$-0.341512\pi$
$331$	17.3778	0.955170	0.477585	+	0.878586i	$0.341512\pi$
$332$	−0.483091	−0.0265130
$333$	4.64229	0.254396
$334$	−4.69542	−0.256922
$335$	3.96755	0.216770
$336$	−3.90570	−0.213074
$337$	25.8896	1.41030	0.705149	−	0.709059i	$-0.250880\pi$
$337$	25.8896	1.41030	0.705149	+	0.709059i	$0.250880\pi$
$338$	10.6364	0.578542
$339$	40.0276	2.17400
$340$	0.0831280	0.00450825
$341$	1.77854	0.0963135
$342$	2.58934	0.140015
$343$	−20.0842	−1.08444
$344$	−8.19673	−0.441938
$345$	−9.06126	−0.487842
$346$	−14.9376	−0.803049
$347$	15.1101	0.811151	0.405576	−	0.914062i	$-0.367071\pi$
$347$	15.1101	0.811151	0.405576	+	0.914062i	$0.367071\pi$
$348$	−15.6364	−0.838198
$349$	−28.2744	−1.51350	−0.756748	−	0.653707i	$-0.773213\pi$
$349$	−28.2744	−1.51350	−0.756748	+	0.653707i	$0.773213\pi$
$350$	9.36585	0.500626
$351$	−6.93874	−0.370362
$352$	−1.51207	−0.0805937
$353$	−28.8928	−1.53781	−0.768903	−	0.639365i	$-0.779197\pi$
$353$	−28.8928	−1.53781	−0.768903	+	0.639365i	$0.779197\pi$
$354$	19.8555	1.05531
$355$	2.40885	0.127849
$356$	4.00711	0.212377
$357$	−0.495043	−0.0262004
$358$	5.17445	0.273478
$359$	15.5962	0.823137	0.411569	−	0.911379i	$-0.364981\pi$
$359$	15.5962	0.823137	0.411569	+	0.911379i	$0.364981\pi$
$360$	−0.414304	−0.0218357
$361$	−2.19851	−0.115711
$362$	−3.97341	−0.208838
$363$	16.6056	0.871569
$364$	−3.15089	−0.165152
$365$	−8.06412	−0.422095
$366$	−4.69297	−0.245305
$367$	−20.3158	−1.06048	−0.530238	−	0.847849i	$-0.677897\pi$
$367$	−20.3158	−1.06048	−0.530238	+	0.847849i	$0.677897\pi$
$368$	7.24985	0.377925
$369$	−2.91282	−0.151635
$370$	−4.81972	−0.250565
$371$	22.7966	1.18354
$372$	−2.24155	−0.116219
$373$	−12.5876	−0.651759	−0.325880	−	0.945411i	$-0.605660\pi$
$373$	−12.5876	−0.651759	−0.325880	+	0.945411i	$0.605660\pi$
$374$	−0.191653	−0.00991014
$375$	11.9609	0.617660
$376$	−7.49140	−0.386339
$377$	−12.6145	−0.649680
$378$	−9.24985	−0.475761
$379$	5.09132	0.261524	0.130762	−	0.991414i	$-0.458258\pi$
$379$	5.09132	0.261524	0.130762	+	0.991414i	$0.458258\pi$
$380$	−2.68830	−0.137907
$381$	−14.9871	−0.767814
$382$	−21.6735	−1.10891
$383$	−0.881036	−0.0450189	−0.0225094	−	0.999747i	$-0.507166\pi$
$383$	−0.881036	−0.0450189	−0.0225094	+	0.999747i	$0.507166\pi$
$384$	1.90570	0.0972500
$385$	2.03245	0.103583
$386$	4.17742	0.212625
$387$	5.17792	0.263209
$388$	13.1991	0.670084
$389$	0.0718469	0.00364278	0.00182139	−	0.999998i	$-0.499420\pi$
$389$	0.0718469	0.00364278	0.00182139	+	0.999998i	$0.499420\pi$
$390$	−1.92154	−0.0973009
$391$	0.918909	0.0464712
$392$	2.79963	0.141403
$393$	11.8350	0.596995
$394$	1.51799	0.0764753
$395$	−3.02187	−0.152047
$396$	0.955185	0.0479998
$397$	28.8218	1.44652	0.723261	−	0.690574i	$-0.242642\pi$
$397$	28.8218	1.44652	0.723261	+	0.690574i	$0.242642\pi$
$398$	12.1661	0.609834
$399$	16.0093	0.801469
$400$	−4.56986	−0.228493
$401$	−16.9670	−0.847290	−0.423645	−	0.905828i	$-0.639250\pi$
$401$	−16.9670	−0.847290	−0.423645	+	0.905828i	$0.639250\pi$
$402$	11.5285	0.574990
$403$	−1.80835	−0.0900802
$404$	−7.79438	−0.387785
$405$	−6.88384	−0.342061
$406$	−16.8161	−0.834568
$407$	11.1119	0.550798
$408$	0.241545	0.0119583
$409$	−15.4405	−0.763483	−0.381742	−	0.924269i	$-0.624676\pi$
$409$	−15.4405	−0.763483	−0.381742	+	0.924269i	$0.624676\pi$
$410$	3.02414	0.149352
$411$	2.34584	0.115712
$412$	0.0807387	0.00397771
$413$	21.3535	1.05074
$414$	−4.57978	−0.225084
$415$	−0.316835	−0.0155528
$416$	1.53741	0.0753777
$417$	−27.8826	−1.36542
$418$	6.19792	0.303150
$419$	33.4401	1.63365	0.816827	−	0.576882i	$-0.195731\pi$
$419$	33.4401	1.63365	0.816827	+	0.576882i	$0.195731\pi$
$420$	−2.56155	−0.124991
$421$	28.3340	1.38091	0.690457	−	0.723373i	$-0.257409\pi$
$421$	28.3340	1.38091	0.690457	+	0.723373i	$0.257409\pi$
$422$	24.7554	1.20508
$423$	4.73236	0.230095
$424$	−11.1231	−0.540186
$425$	−0.579224	−0.0280965
$426$	6.99942	0.339123
$427$	−5.04703	−0.244243
$428$	0.175035	0.00846065
$429$	4.43014	0.213889
$430$	−5.37582	−0.259245
$431$	−40.9834	−1.97410	−0.987049	−	0.160417i	$-0.948716\pi$
$431$	−40.9834	−1.97410	−0.987049	+	0.160417i	$0.948716\pi$
$432$	4.51327	0.217145
$433$	17.0843	0.821020	0.410510	−	0.911856i	$-0.365351\pi$
$433$	17.0843	0.821020	0.410510	+	0.911856i	$0.365351\pi$
$434$	−2.41066	−0.115715
$435$	−10.2551	−0.491695
$436$	3.52505	0.168819
$437$	−29.7169	−1.42155
$438$	−23.4319	−1.11962
$439$	0.240874	0.0114963	0.00574816	−	0.999983i	$-0.498170\pi$
$439$	0.240874	0.0114963	0.00574816	+	0.999983i	$0.498170\pi$
$440$	−0.991691	−0.0472770
$441$	−1.76854	−0.0842162
$442$	0.194865	0.00926876
$443$	−22.3711	−1.06288	−0.531442	−	0.847095i	$-0.678350\pi$
$443$	−22.3711	−1.06288	−0.531442	+	0.847095i	$0.678350\pi$
$444$	−14.0047	−0.664632
$445$	2.62806	0.124582
$446$	−5.36710	−0.254140
$447$	−5.64832	−0.267157
$448$	2.04948	0.0968289
$449$	18.9102	0.892427	0.446214	−	0.894926i	$-0.352772\pi$
$449$	18.9102	0.892427	0.446214	+	0.894926i	$0.352772\pi$
$450$	2.88681	0.136085
$451$	−6.97221	−0.328309
$452$	−21.0041	−0.987949
$453$	−12.4124	−0.583183
$454$	25.4413	1.19402
$455$	−2.06651	−0.0968795
$456$	−7.81141	−0.365803
$457$	−34.3164	−1.60525	−0.802627	−	0.596482i	$-0.796565\pi$
$457$	−34.3164	−1.60525	−0.802627	+	0.596482i	$0.796565\pi$
$458$	2.13547	0.0997839
$459$	0.572050	0.0267010
$460$	4.75481	0.221694
$461$	3.84608	0.179130	0.0895648	−	0.995981i	$-0.471452\pi$
$461$	3.84608	0.179130	0.0895648	+	0.995981i	$0.471452\pi$
$462$	5.90570	0.274758
$463$	−6.87308	−0.319419	−0.159710	−	0.987164i	$-0.551056\pi$
$463$	−6.87308	−0.319419	−0.159710	+	0.987164i	$0.551056\pi$
$464$	8.20504	0.380909
$465$	−1.47012	−0.0681750
$466$	−13.8645	−0.642262
$467$	−22.8376	−1.05680	−0.528399	−	0.848996i	$-0.677207\pi$
$467$	−22.8376	−1.05680	−0.528399	+	0.848996i	$0.677207\pi$
$468$	−0.971191	−0.0448933
$469$	12.3983	0.572500
$470$	−4.91323	−0.226630
$471$	8.67052	0.399516
$472$	−10.4190	−0.479572
$473$	12.3940	0.569879
$474$	−8.78065	−0.403309
$475$	18.7317	0.859469
$476$	0.259769	0.0119065
$477$	7.02653	0.321723
$478$	−17.5309	−0.801845
$479$	−27.1928	−1.24247	−0.621236	−	0.783623i	$-0.713369\pi$
$479$	−27.1928	−1.24247	−0.621236	+	0.783623i	$0.713369\pi$
$480$	1.24985	0.0570478
$481$	−11.2981	−0.515151
$482$	6.65118	0.302953
$483$	−28.3158	−1.28841
$484$	−8.71364	−0.396075
$485$	8.65663	0.393077
$486$	−6.46259	−0.293149
$487$	−24.5938	−1.11445	−0.557225	−	0.830361i	$-0.688134\pi$
$487$	−24.5938	−1.11445	−0.557225	+	0.830361i	$0.688134\pi$
$488$	2.46259	0.111476
$489$	27.6801	1.25174
$490$	1.83613	0.0829480
$491$	13.8920	0.626936	0.313468	−	0.949599i	$-0.398509\pi$
$491$	13.8920	0.626936	0.313468	+	0.949599i	$0.398509\pi$
$492$	8.78726	0.396160
$493$	1.03998	0.0468382
$494$	−6.30178	−0.283531
$495$	0.626457	0.0281572
$496$	1.17623	0.0528143
$497$	7.52749	0.337654
$498$	−0.920628	−0.0412543
$499$	6.88806	0.308352	0.154176	−	0.988043i	$-0.450728\pi$
$499$	6.88806	0.308352	0.154176	+	0.988043i	$0.450728\pi$
$500$	−6.27639	−0.280689
$501$	−8.94807	−0.399770
$502$	4.46726	0.199383
$503$	−5.92646	−0.264248	−0.132124	−	0.991233i	$-0.542180\pi$
$503$	−5.92646	−0.264248	−0.132124	+	0.991233i	$0.542180\pi$
$504$	−1.29467	−0.0576692
$505$	−5.11194	−0.227478
$506$	−10.9623	−0.487334
$507$	20.2698	0.900212
$508$	7.86436	0.348925
$509$	−20.5149	−0.909307	−0.454653	−	0.890668i	$-0.650237\pi$
$509$	−20.5149	−0.909307	−0.454653	+	0.890668i	$0.650237\pi$
$510$	0.158417	0.00701484
$511$	−25.1998	−1.11477
$512$	−1.00000	−0.0441942
$513$	−18.4997	−0.816782
$514$	−23.0811	−1.01806
$515$	0.0529524	0.00233336
$516$	−15.6205	−0.687656
$517$	11.3275	0.498184
$518$	−15.0613	−0.661754
$519$	−28.4666	−1.24954
$520$	1.00831	0.0442173
$521$	−29.2417	−1.28110	−0.640552	−	0.767915i	$-0.721294\pi$
$521$	−29.2417	−1.28110	−0.640552	+	0.767915i	$0.721294\pi$
$522$	−5.18317	−0.226861
$523$	22.0758	0.965309	0.482655	−	0.875811i	$-0.339673\pi$
$523$	22.0758	0.965309	0.482655	+	0.875811i	$0.339673\pi$
$524$	−6.21029	−0.271298
$525$	17.8485	0.778974
$526$	10.4537	0.455803
$527$	0.149086	0.00649427
$528$	−2.88156	−0.125404
$529$	29.5604	1.28523
$530$	−7.29508	−0.316878
$531$	6.58173	0.285623
$532$	−8.40075	−0.364219
$533$	7.08905	0.307061
$534$	7.63637	0.330458
$535$	0.114797	0.00496309
$536$	−6.04948	−0.261298
$537$	9.86097	0.425532
$538$	−1.00000	−0.0431131
$539$	−4.23324	−0.182338
$540$	2.96002	0.127379
$541$	−31.1201	−1.33796	−0.668978	−	0.743282i	$-0.733268\pi$
$541$	−31.1201	−1.33796	−0.668978	+	0.743282i	$0.733268\pi$
$542$	3.04464	0.130779
$543$	−7.57214	−0.324952
$544$	−0.126749	−0.00543430
$545$	2.31190	0.0990309
$546$	−6.00467	−0.256976
$547$	31.5507	1.34901	0.674506	−	0.738269i	$-0.264357\pi$
$547$	31.5507	1.34901	0.674506	+	0.738269i	$0.264357\pi$
$548$	−1.23096	−0.0525840
$549$	−1.55563	−0.0663928
$550$	6.90996	0.294642
$551$	−33.6321	−1.43278
$552$	13.8161	0.588051
$553$	−9.44311	−0.401562
$554$	−16.3641	−0.695243
$555$	−9.18495	−0.389879
$556$	14.6311	0.620498
$557$	9.73717	0.412577	0.206289	−	0.978491i	$-0.433861\pi$
$557$	9.73717	0.412577	0.206289	+	0.978491i	$0.433861\pi$
$558$	−0.743031	−0.0314550
$559$	−12.6017	−0.532996
$560$	1.34415	0.0568007
$561$	−0.365234	−0.0154202
$562$	21.7013	0.915413
$563$	7.10499	0.299440	0.149720	−	0.988728i	$-0.452163\pi$
$563$	7.10499	0.299440	0.149720	+	0.988728i	$0.452163\pi$
$564$	−14.2764	−0.601144
$565$	−13.7755	−0.579540
$566$	17.9315	0.753716
$567$	−21.5115	−0.903398
$568$	−3.67288	−0.154111
$569$	46.0004	1.92844	0.964219	−	0.265106i	$-0.0854068\pi$
$569$	46.0004	1.92844	0.964219	+	0.265106i	$0.0854068\pi$
$570$	−5.12311	−0.214583
$571$	1.07721	0.0450798	0.0225399	−	0.999746i	$-0.492825\pi$
$571$	1.07721	0.0450798	0.0225399	+	0.999746i	$0.492825\pi$
$572$	−2.32467	−0.0971995
$573$	−41.3032	−1.72547
$574$	9.45023	0.394445
$575$	−33.1308	−1.38165
$576$	0.631706	0.0263211
$577$	−25.0292	−1.04198	−0.520991	−	0.853562i	$-0.674437\pi$
$577$	−25.0292	−1.04198	−0.520991	+	0.853562i	$0.674437\pi$
$578$	16.9839	0.706439
$579$	7.96093	0.330845
$580$	5.38127	0.223445
$581$	−0.990085	−0.0410757
$582$	25.1536	1.04265
$583$	16.8189	0.696569
$584$	12.2957	0.508799
$585$	−0.636955	−0.0263348
$586$	−14.9994	−0.619620
$587$	−7.94399	−0.327883	−0.163942	−	0.986470i	$-0.552421\pi$
$587$	−7.94399	−0.327883	−0.163942	+	0.986470i	$0.552421\pi$
$588$	5.33526	0.220022
$589$	−4.82132	−0.198659
$590$	−6.83327	−0.281321
$591$	2.89284	0.118996
$592$	7.34882	0.302035
$593$	−13.1071	−0.538244	−0.269122	−	0.963106i	$-0.586733\pi$
$593$	−13.1071	−0.538244	−0.269122	+	0.963106i	$0.586733\pi$
$594$	−6.82438	−0.280008
$595$	0.170369	0.00698446
$596$	2.96390	0.121406
$597$	23.1851	0.948901
$598$	11.1460	0.455794
$599$	11.3859	0.465217	0.232608	−	0.972570i	$-0.425274\pi$
$599$	11.3859	0.465217	0.232608	+	0.972570i	$0.425274\pi$
$600$	−8.70880	−0.355535
$601$	−30.2421	−1.23360	−0.616800	−	0.787120i	$-0.711571\pi$
$601$	−30.2421	−1.23360	−0.616800	+	0.787120i	$0.711571\pi$
$602$	−16.7990	−0.684678
$603$	3.82149	0.155623
$604$	6.51327	0.265021
$605$	−5.71483	−0.232341
$606$	−14.8538	−0.603393
$607$	18.0109	0.731041	0.365521	−	0.930803i	$-0.380891\pi$
$607$	18.0109	0.731041	0.365521	+	0.930803i	$0.380891\pi$
$608$	4.09896	0.166235
$609$	−32.0464	−1.29859
$610$	1.61509	0.0653930
$611$	−11.5173	−0.465942
$612$	0.0800679	0.00323655
$613$	14.5045	0.585833	0.292917	−	0.956138i	$-0.405374\pi$
$613$	14.5045	0.585833	0.292917	+	0.956138i	$0.405374\pi$
$614$	8.26528	0.333559
$615$	5.76312	0.232391
$616$	−3.09896	−0.124861
$617$	24.0246	0.967196	0.483598	−	0.875290i	$-0.339330\pi$
$617$	24.0246	0.967196	0.483598	+	0.875290i	$0.339330\pi$
$618$	0.153864	0.00618932
$619$	0.432758	0.0173940	0.00869701	−	0.999962i	$-0.497232\pi$
$619$	0.432758	0.0173940	0.00869701	+	0.999962i	$0.497232\pi$
$620$	0.771429	0.0309814
$621$	32.7205	1.31303
$622$	24.5863	0.985821
$623$	8.21251	0.329027
$624$	2.92985	0.117288
$625$	18.7329	0.749318
$626$	−7.63678	−0.305227
$627$	11.8114	0.471702
$628$	−4.54977	−0.181556
$629$	0.931453	0.0371394
$630$	−0.849108	−0.0338293
$631$	17.5719	0.699527	0.349763	−	0.936838i	$-0.386262\pi$
$631$	17.5719	0.699527	0.349763	+	0.936838i	$0.386262\pi$
$632$	4.60756	0.183279
$633$	47.1765	1.87510
$634$	−2.77674	−0.110278
$635$	5.15783	0.204682
$636$	−21.1973	−0.840529
$637$	4.30417	0.170538
$638$	−12.4066	−0.491182
$639$	2.32018	0.0917849
$640$	−0.655849	−0.0259247
$641$	−5.93265	−0.234325	−0.117163	−	0.993113i	$-0.537380\pi$
$641$	−5.93265	−0.234325	−0.117163	+	0.993113i	$0.537380\pi$
$642$	0.333565	0.0131648
$643$	37.8427	1.49237	0.746185	−	0.665739i	$-0.231884\pi$
$643$	37.8427	1.49237	0.746185	+	0.665739i	$0.231884\pi$
$644$	14.8584	0.585505
$645$	−10.2447	−0.403385
$646$	0.519538	0.0204409
$647$	32.2568	1.26815	0.634073	−	0.773273i	$-0.281382\pi$
$647$	32.2568	1.26815	0.634073	+	0.773273i	$0.281382\pi$
$648$	10.4961	0.412324
$649$	15.7542	0.618408
$650$	−7.02575	−0.275573
$651$	−4.59401	−0.180053
$652$	−14.5249	−0.568838
$653$	−23.0126	−0.900554	−0.450277	−	0.892889i	$-0.648675\pi$
$653$	−23.0126	−0.900554	−0.450277	+	0.892889i	$0.648675\pi$
$654$	6.71769	0.262683
$655$	−4.07301	−0.159146
$656$	−4.61103	−0.180031
$657$	−7.76726	−0.303030
$658$	−15.3535	−0.598541
$659$	−13.0493	−0.508329	−0.254164	−	0.967161i	$-0.581800\pi$
$659$	−13.0493	−0.508329	−0.254164	+	0.967161i	$0.581800\pi$
$660$	−1.88987	−0.0735631
$661$	15.4042	0.599152	0.299576	−	0.954072i	$-0.403155\pi$
$661$	15.4042	0.599152	0.299576	+	0.954072i	$0.403155\pi$
$662$	−17.3778	−0.675407
$663$	0.371354	0.0144222
$664$	0.483091	0.0187476
$665$	−5.50962	−0.213654
$666$	−4.64229	−0.179885
$667$	59.4853	2.30328
$668$	4.69542	0.181671
$669$	−10.2281	−0.395441
$670$	−3.96755	−0.153280
$671$	−3.72361	−0.143748
$672$	3.90570	0.150666
$673$	49.7199	1.91656	0.958281	−	0.285826i	$-0.0922681\pi$
$673$	49.7199	1.91656	0.958281	+	0.285826i	$0.0922681\pi$
$674$	−25.8896	−0.997232
$675$	−20.6250	−0.793857
$676$	−10.6364	−0.409091
$677$	−6.97568	−0.268097	−0.134049	−	0.990975i	$-0.542798\pi$
$677$	−6.97568	−0.268097	−0.134049	+	0.990975i	$0.542798\pi$
$678$	−40.0276	−1.53725
$679$	27.0513	1.03814
$680$	−0.0831280	−0.00318781
$681$	48.4835	1.85789
$682$	−1.77854	−0.0681040
$683$	18.6007	0.711737	0.355868	−	0.934536i	$-0.384185\pi$
$683$	18.6007	0.711737	0.355868	+	0.934536i	$0.384185\pi$
$684$	−2.58934	−0.0990059
$685$	−0.807324	−0.0308463
$686$	20.0842	0.766816
$687$	4.06957	0.155264
$688$	8.19673	0.312497
$689$	−17.1008	−0.651487
$690$	9.06126	0.344956
$691$	5.18428	0.197219	0.0986096	−	0.995126i	$-0.468560\pi$
$691$	5.18428	0.197219	0.0986096	+	0.995126i	$0.468560\pi$
$692$	14.9376	0.567841
$693$	1.95763	0.0743643
$694$	−15.1101	−0.573570
$695$	9.59581	0.363990
$696$	15.6364	0.592695
$697$	−0.584442	−0.0221373
$698$	28.2744	1.07020
$699$	−26.4217	−0.999360
$700$	−9.36585	−0.353996
$701$	−41.5972	−1.57111	−0.785553	−	0.618794i	$-0.787621\pi$
$701$	−41.5972	−1.57111	−0.785553	+	0.618794i	$0.787621\pi$
$702$	6.93874	0.261886
$703$	−30.1225	−1.13609
$704$	1.51207	0.0569883
$705$	−9.36316	−0.352637
$706$	28.8928	1.08739
$707$	−15.9744	−0.600780
$708$	−19.8555	−0.746214
$709$	23.0558	0.865880	0.432940	−	0.901423i	$-0.357476\pi$
$709$	23.0558	0.865880	0.432940	+	0.901423i	$0.357476\pi$
$710$	−2.40885	−0.0904027
$711$	−2.91063	−0.109157
$712$	−4.00711	−0.150173
$713$	8.52749	0.319357
$714$	0.495043	0.0185265
$715$	−1.52464	−0.0570181
$716$	−5.17445	−0.193378
$717$	−33.4087	−1.24767
$718$	−15.5962	−0.582046
$719$	17.5791	0.655589	0.327795	−	0.944749i	$-0.393695\pi$
$719$	17.5791	0.655589	0.327795	+	0.944749i	$0.393695\pi$
$720$	0.414304	0.0154402
$721$	0.165473	0.00616252
$722$	2.19851	0.0818200
$723$	12.6752	0.471395
$724$	3.97341	0.147671
$725$	−37.4959	−1.39256
$726$	−16.6056	−0.616292
$727$	10.2445	0.379947	0.189974	−	0.981789i	$-0.439160\pi$
$727$	10.2445	0.379947	0.189974	+	0.981789i	$0.439160\pi$
$728$	3.15089	0.116780
$729$	19.1724	0.710089
$730$	8.06412	0.298467
$731$	1.03892	0.0384260
$732$	4.69297	0.173457
$733$	48.1234	1.77748	0.888739	−	0.458414i	$-0.151582\pi$
$733$	48.1234	1.77748	0.888739	+	0.458414i	$0.151582\pi$
$734$	20.3158	0.749869
$735$	3.49913	0.129067
$736$	−7.24985	−0.267233
$737$	9.14725	0.336943
$738$	2.91282	0.107222
$739$	39.7903	1.46371	0.731856	−	0.681460i	$-0.238655\pi$
$739$	39.7903	1.46371	0.731856	+	0.681460i	$0.238655\pi$
$740$	4.81972	0.177176
$741$	−12.0093	−0.441174
$742$	−22.7966	−0.836889
$743$	17.2101	0.631378	0.315689	−	0.948863i	$-0.397764\pi$
$743$	17.2101	0.631378	0.315689	+	0.948863i	$0.397764\pi$
$744$	2.24155	0.0821790
$745$	1.94387	0.0712181
$746$	12.5876	0.460863
$747$	−0.305171	−0.0111656
$748$	0.191653	0.00700753
$749$	0.358731	0.0131078
$750$	−11.9609	−0.436752
$751$	39.8722	1.45496	0.727479	−	0.686130i	$-0.240692\pi$
$751$	39.8722	1.45496	0.727479	+	0.686130i	$0.240692\pi$
$752$	7.49140	0.273183
$753$	8.51327	0.310241
$754$	12.6145	0.459393
$755$	4.27172	0.155464
$756$	9.24985	0.336414
$757$	−22.4779	−0.816973	−0.408487	−	0.912764i	$-0.633943\pi$
$757$	−22.4779	−0.816973	−0.408487	+	0.912764i	$0.633943\pi$
$758$	−5.09132	−0.184925
$759$	−20.8909	−0.758291
$760$	2.68830	0.0975149
$761$	32.3862	1.17400	0.586999	−	0.809588i	$-0.300309\pi$
$761$	32.3862	1.17400	0.586999	+	0.809588i	$0.300309\pi$
$762$	14.9871	0.542927
$763$	7.22452	0.261545
$764$	21.6735	0.784119
$765$	0.0525125	0.00189859
$766$	0.881036	0.0318331
$767$	−16.0182	−0.578385
$768$	−1.90570	−0.0687662
$769$	−8.93195	−0.322094	−0.161047	−	0.986947i	$-0.551487\pi$
$769$	−8.93195	−0.322094	−0.161047	+	0.986947i	$0.551487\pi$
$770$	−2.03245	−0.0732445
$771$	−43.9857	−1.58411
$772$	−4.17742	−0.150349
$773$	16.4396	0.591291	0.295645	−	0.955298i	$-0.404465\pi$
$773$	16.4396	0.591291	0.295645	+	0.955298i	$0.404465\pi$
$774$	−5.17792	−0.186117
$775$	−5.37521	−0.193083
$776$	−13.1991	−0.473821
$777$	−28.7023	−1.02969
$778$	−0.0718469	−0.00257584
$779$	18.9005	0.677179
$780$	1.92154	0.0688021
$781$	5.55366	0.198725
$782$	−0.918909	−0.0328601
$783$	37.0315	1.32340
$784$	−2.79963	−0.0999867
$785$	−2.98397	−0.106502
$786$	−11.8350	−0.422139
$787$	5.86692	0.209133	0.104567	−	0.994518i	$-0.466654\pi$
$787$	5.86692	0.209133	0.104567	+	0.994518i	$0.466654\pi$
$788$	−1.51799	−0.0540762
$789$	19.9217	0.709230
$790$	3.02187	0.107513
$791$	−43.0475	−1.53059
$792$	−0.955185	−0.0339410
$793$	3.78601	0.134445
$794$	−28.8218	−1.02285
$795$	−13.9023	−0.493062
$796$	−12.1661	−0.431218
$797$	−25.0566	−0.887551	−0.443776	−	0.896138i	$-0.646361\pi$
$797$	−25.0566	−0.887551	−0.443776	+	0.896138i	$0.646361\pi$
$798$	−16.0093	−0.566724
$799$	0.949525	0.0335918
$800$	4.56986	0.161569
$801$	2.53132	0.0894397
$802$	16.9670	0.599124
$803$	−18.5920	−0.656096
$804$	−11.5285	−0.406579
$805$	9.74490	0.343462
$806$	1.80835	0.0636963
$807$	−1.90570	−0.0670839
$808$	7.79438	0.274205
$809$	30.2413	1.06323	0.531614	−	0.846987i	$-0.321586\pi$
$809$	30.2413	1.06323	0.531614	+	0.846987i	$0.321586\pi$
$810$	6.88384	0.241873
$811$	9.86022	0.346239	0.173120	−	0.984901i	$-0.444615\pi$
$811$	9.86022	0.346239	0.173120	+	0.984901i	$0.444615\pi$
$812$	16.8161	0.590128
$813$	5.80219	0.203492
$814$	−11.1119	−0.389473
$815$	−9.52613	−0.333686
$816$	−0.241545	−0.00845578
$817$	−33.5981	−1.17545
$818$	15.4405	0.539864
$819$	−1.99044	−0.0695515
$820$	−3.02414	−0.105608
$821$	18.4713	0.644651	0.322326	−	0.946629i	$-0.395535\pi$
$821$	18.4713	0.644651	0.322326	+	0.946629i	$0.395535\pi$
$822$	−2.34584	−0.0818207
$823$	−43.0467	−1.50051	−0.750257	−	0.661147i	$-0.770070\pi$
$823$	−43.0467	−1.50051	−0.750257	+	0.661147i	$0.770070\pi$
$824$	−0.0807387	−0.00281267
$825$	13.1683	0.458462
$826$	−21.3535	−0.742983
$827$	9.32820	0.324373	0.162187	−	0.986760i	$-0.448145\pi$
$827$	9.32820	0.324373	0.162187	+	0.986760i	$0.448145\pi$
$828$	4.57978	0.159158
$829$	−37.7005	−1.30939	−0.654697	−	0.755892i	$-0.727204\pi$
$829$	−37.7005	−1.30939	−0.654697	+	0.755892i	$0.727204\pi$
$830$	0.316835	0.0109975
$831$	−31.1851	−1.08180
$832$	−1.53741	−0.0533001
$833$	−0.354849	−0.0122948
$834$	27.8826	0.965495
$835$	3.07948	0.106570
$836$	−6.19792	−0.214360
$837$	5.30864	0.183493
$838$	−33.4401	−1.15517
$839$	22.7247	0.784543	0.392271	−	0.919850i	$-0.371689\pi$
$839$	22.7247	0.784543	0.392271	+	0.919850i	$0.371689\pi$
$840$	2.56155	0.0883820
$841$	38.3227	1.32147
$842$	−28.3340	−0.976454
$843$	41.3562	1.42438
$844$	−24.7554	−0.852117
$845$	−6.97586	−0.239977
$846$	−4.73236	−0.162702
$847$	−17.8584	−0.613623
$848$	11.1231	0.381969
$849$	34.1721	1.17278
$850$	0.579224	0.0198672
$851$	53.2778	1.82634
$852$	−6.99942	−0.239796
$853$	−47.3368	−1.62078	−0.810391	−	0.585890i	$-0.800745\pi$
$853$	−47.3368	−1.62078	−0.810391	+	0.585890i	$0.800745\pi$
$854$	5.04703	0.172706
$855$	−1.69822	−0.0580778
$856$	−0.175035	−0.00598258
$857$	−55.0546	−1.88063	−0.940315	−	0.340304i	$-0.889470\pi$
$857$	−55.0546	−1.88063	−0.940315	+	0.340304i	$0.889470\pi$
$858$	−4.43014	−0.151242
$859$	13.9751	0.476824	0.238412	−	0.971164i	$-0.423373\pi$
$859$	13.9751	0.476824	0.238412	+	0.971164i	$0.423373\pi$
$860$	5.37582	0.183314
$861$	18.0093	0.613756
$862$	40.9834	1.39590
$863$	−36.0098	−1.22579	−0.612893	−	0.790166i	$-0.709995\pi$
$863$	−36.0098	−1.22579	−0.612893	+	0.790166i	$0.709995\pi$
$864$	−4.51327	−0.153544
$865$	9.79680	0.333101
$866$	−17.0843	−0.580549
$867$	32.3663	1.09922
$868$	2.41066	0.0818232
$869$	−6.96696	−0.236338
$870$	10.2551	0.347681
$871$	−9.30053	−0.315136
$872$	−3.52505	−0.119373
$873$	8.33796	0.282197
$874$	29.7169	1.00519
$875$	−12.8633	−0.434860
$876$	23.4319	0.791692
$877$	31.5675	1.06596	0.532979	−	0.846129i	$-0.321073\pi$
$877$	31.5675	1.06596	0.532979	+	0.846129i	$0.321073\pi$
$878$	−0.240874	−0.00812912
$879$	−28.5844	−0.964129
$880$	0.991691	0.0334299
$881$	25.2649	0.851195	0.425597	−	0.904913i	$-0.360064\pi$
$881$	25.2649	0.851195	0.425597	+	0.904913i	$0.360064\pi$
$882$	1.76854	0.0595499
$883$	−39.3854	−1.32543	−0.662713	−	0.748874i	$-0.730595\pi$
$883$	−39.3854	−1.32543	−0.662713	+	0.748874i	$0.730595\pi$
$884$	−0.194865	−0.00655401
$885$	−13.0222	−0.437736
$886$	22.3711	0.751573
$887$	25.7106	0.863278	0.431639	−	0.902047i	$-0.357935\pi$
$887$	25.7106	0.863278	0.431639	+	0.902047i	$0.357935\pi$
$888$	14.0047	0.469966
$889$	16.1179	0.540576
$890$	−2.62806	−0.0880929
$891$	−15.8708	−0.531692
$892$	5.36710	0.179704
$893$	−30.7070	−1.02757
$894$	5.64832	0.188908
$895$	−3.39366	−0.113438
$896$	−2.04948	−0.0684684
$897$	21.2410	0.709215
$898$	−18.9102	−0.631041
$899$	9.65101	0.321879
$900$	−2.88681	−0.0962270
$901$	1.40984	0.0469685
$902$	6.97221	0.232149
$903$	−32.0140	−1.06536
$904$	21.0041	0.698585
$905$	2.60596	0.0866249
$906$	12.4124	0.412373
$907$	−43.7944	−1.45417	−0.727084	−	0.686548i	$-0.759125\pi$
$907$	−43.7944	−1.45417	−0.727084	+	0.686548i	$0.759125\pi$
$908$	−25.4413	−0.844298
$909$	−4.92376	−0.163311
$910$	2.06651	0.0685041
$911$	−45.0976	−1.49415	−0.747075	−	0.664739i	$-0.768543\pi$
$911$	−45.0976	−1.49415	−0.747075	+	0.664739i	$0.768543\pi$
$912$	7.81141	0.258662
$913$	−0.730468	−0.0241750
$914$	34.3164	1.13509
$915$	3.07788	0.101752
$916$	−2.13547	−0.0705579
$917$	−12.7279	−0.420311
$918$	−0.572050	−0.0188805
$919$	1.62104	0.0534731	0.0267365	−	0.999643i	$-0.491488\pi$
$919$	1.62104	0.0534731	0.0267365	+	0.999643i	$0.491488\pi$
$920$	−4.75481	−0.156761
$921$	15.7512	0.519019
$922$	−3.84608	−0.126664
$923$	−5.64672	−0.185864
$924$	−5.90570	−0.194283
$925$	−33.5831	−1.10420
$926$	6.87308	0.225863
$927$	0.0510031	0.00167516
$928$	−8.20504	−0.269344
$929$	−3.81619	−0.125205	−0.0626025	−	0.998039i	$-0.519940\pi$
$929$	−3.81619	−0.125205	−0.0626025	+	0.998039i	$0.519940\pi$
$930$	1.47012	0.0482070
$931$	11.4756	0.376096
$932$	13.8645	0.454148
$933$	46.8542	1.53394
$934$	22.8376	0.747269
$935$	0.125696	0.00411068
$936$	0.971191	0.0317444
$937$	−27.9150	−0.911944	−0.455972	−	0.889994i	$-0.650708\pi$
$937$	−27.9150	−0.911944	−0.455972	+	0.889994i	$0.650708\pi$
$938$	−12.3983	−0.404819
$939$	−14.5534	−0.474934
$940$	4.91323	0.160252
$941$	9.29342	0.302957	0.151478	−	0.988461i	$-0.451597\pi$
$941$	9.29342	0.302957	0.151478	+	0.988461i	$0.451597\pi$
$942$	−8.67052	−0.282501
$943$	−33.4293	−1.08861
$944$	10.4190	0.339109
$945$	6.06651	0.197344
$946$	−12.3940	−0.402965
$947$	−46.0615	−1.49680	−0.748398	−	0.663250i	$-0.769177\pi$
$947$	−46.0615	−1.49680	−0.748398	+	0.663250i	$0.769177\pi$
$948$	8.78065	0.285182
$949$	18.9035	0.613634
$950$	−18.7317	−0.607736
$951$	−5.29164	−0.171593
$952$	−0.259769	−0.00841916
$953$	51.0765	1.65453	0.827265	−	0.561811i	$-0.189895\pi$
$953$	51.0765	1.65453	0.827265	+	0.561811i	$0.189895\pi$
$954$	−7.02653	−0.227492
$955$	14.2145	0.459972
$956$	17.5309	0.566990
$957$	−23.6433	−0.764280
$958$	27.1928	0.878561
$959$	−2.52283	−0.0814664
$960$	−1.24985	−0.0403389
$961$	−29.6165	−0.955370
$962$	11.2981	0.364267
$963$	0.110571	0.00356309
$964$	−6.65118	−0.214220
$965$	−2.73976	−0.0881960
$966$	28.3158	0.911045
$967$	11.5052	0.369983	0.184992	−	0.982740i	$-0.440774\pi$
$967$	11.5052	0.369983	0.184992	+	0.982740i	$0.440774\pi$
$968$	8.71364	0.280067
$969$	0.990085	0.0318061
$970$	−8.65663	−0.277948
$971$	−22.6394	−0.726532	−0.363266	−	0.931685i	$-0.618338\pi$
$971$	−22.6394	−0.726532	−0.363266	+	0.931685i	$0.618338\pi$
$972$	6.46259	0.207288
$973$	29.9862	0.961314
$974$	24.5938	0.788035
$975$	−13.3890	−0.428791
$976$	−2.46259	−0.0788256
$977$	38.4642	1.23058	0.615290	−	0.788301i	$-0.289039\pi$
$977$	38.4642	1.23058	0.615290	+	0.788301i	$0.289039\pi$
$978$	−27.6801	−0.885112
$979$	6.05904	0.193648
$980$	−1.83613	−0.0586531
$981$	2.22679	0.0710960
$982$	−13.8920	−0.443311
$983$	−53.2201	−1.69746	−0.848729	−	0.528828i	$-0.822632\pi$
$983$	−53.2201	−1.69746	−0.848729	+	0.528828i	$0.822632\pi$
$984$	−8.78726	−0.280128
$985$	−0.995573	−0.0317216
$986$	−1.03998	−0.0331196
$987$	−29.2592	−0.931330
$988$	6.30178	0.200486
$989$	59.4251	1.88961
$990$	−0.626457	−0.0199101
$991$	−6.96323	−0.221194	−0.110597	−	0.993865i	$-0.535276\pi$
$991$	−6.96323	−0.221194	−0.110597	+	0.993865i	$0.535276\pi$
$992$	−1.17623	−0.0373453
$993$	−33.1169	−1.05093
$994$	−7.52749	−0.238758
$995$	−7.97916	−0.252956
$996$	0.920628	0.0291712
$997$	−50.0522	−1.58517	−0.792585	−	0.609761i	$-0.791265\pi$
$997$	−50.0522	−1.58517	−0.792585	+	0.609761i	$0.791265\pi$
$998$	−6.88806	−0.218038
$999$	33.1672	1.04936

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	538.2.a.c.1.1	✓	4
3.2	odd	2		4842.2.a.j.1.3		4
4.3	odd	2		4304.2.a.e.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
538.2.a.c.1.1	✓	4	1.1	even	1	trivial
4304.2.a.e.1.4		4	4.3	odd	2
4842.2.a.j.1.3		4	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 538 = 2 \cdot 269 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	538.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.90570 q^{3} +1.00000 q^{4} +0.655849 q^{5} +1.90570 q^{6} +2.04948 q^{7} -1.00000 q^{8} +0.631706 q^{9} -0.655849 q^{10} +1.51207 q^{11} -1.90570 q^{12} -1.53741 q^{13} -2.04948 q^{14} -1.24985 q^{15} +1.00000 q^{16} +0.126749 q^{17} -0.631706 q^{18} -4.09896 q^{19} +0.655849 q^{20} -3.90570 q^{21} -1.51207 q^{22} +7.24985 q^{23} +1.90570 q^{24} -4.56986 q^{25} +1.53741 q^{26} +4.51327 q^{27} +2.04948 q^{28} +8.20504 q^{29} +1.24985 q^{30} +1.17623 q^{31} -1.00000 q^{32} -2.88156 q^{33} -0.126749 q^{34} +1.34415 q^{35} +0.631706 q^{36} +7.34882 q^{37} +4.09896 q^{38} +2.92985 q^{39} -0.655849 q^{40} -4.61103 q^{41} +3.90570 q^{42} +8.19673 q^{43} +1.51207 q^{44} +0.414304 q^{45} -7.24985 q^{46} +7.49140 q^{47} -1.90570 q^{48} -2.79963 q^{49} +4.56986 q^{50} -0.241545 q^{51} -1.53741 q^{52} +11.1231 q^{53} -4.51327 q^{54} +0.991691 q^{55} -2.04948 q^{56} +7.81141 q^{57} -8.20504 q^{58} +10.4190 q^{59} -1.24985 q^{60} -2.46259 q^{61} -1.17623 q^{62} +1.29467 q^{63} +1.00000 q^{64} -1.00831 q^{65} +2.88156 q^{66} +6.04948 q^{67} +0.126749 q^{68} -13.8161 q^{69} -1.34415 q^{70} +3.67288 q^{71} -0.631706 q^{72} -12.2957 q^{73} -7.34882 q^{74} +8.70880 q^{75} -4.09896 q^{76} +3.09896 q^{77} -2.92985 q^{78} -4.60756 q^{79} +0.655849 q^{80} -10.4961 q^{81} +4.61103 q^{82} -0.483091 q^{83} -3.90570 q^{84} +0.0831280 q^{85} -8.19673 q^{86} -15.6364 q^{87} -1.51207 q^{88} +4.00711 q^{89} -0.414304 q^{90} -3.15089 q^{91} +7.24985 q^{92} -2.24155 q^{93} -7.49140 q^{94} -2.68830 q^{95} +1.90570 q^{96} +13.1991 q^{97} +2.79963 q^{98} +0.955185 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 3 q^{3} + 4 q^{4} + 5 q^{5} - 3 q^{6} - q^{7} - 4 q^{8} + 3 q^{9} - 5 q^{10} + 7 q^{11} + 3 q^{12} + 4 q^{13} + q^{14} + 8 q^{15} + 4 q^{16} + 4 q^{17} - 3 q^{18} + 2 q^{19} + 5 q^{20}+ \cdots - 16 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 3 * q^3 + 4 * q^4 + 5 * q^5 - 3 * q^6 - q^7 - 4 * q^8 + 3 * q^9 - 5 * q^10 + 7 * q^11 + 3 * q^12 + 4 * q^13 + q^14 + 8 * q^15 + 4 * q^16 + 4 * q^17 - 3 * q^18 + 2 * q^19 + 5 * q^20 - 5 * q^21 - 7 * q^22 + 16 * q^23 - 3 * q^24 - q^25 - 4 * q^26 + 6 * q^27 - q^28 - 8 * q^30 - q^31 - 4 * q^32 + q^33 - 4 * q^34 + 3 * q^35 + 3 * q^36 - 2 * q^37 - 2 * q^38 + 3 * q^39 - 5 * q^40 - q^41 + 5 * q^42 + 9 * q^43 + 7 * q^44 + 8 * q^45 - 16 * q^46 + 13 * q^47 + 3 * q^48 - 15 * q^49 + q^50 + 3 * q^51 + 4 * q^52 + 28 * q^53 - 6 * q^54 + 13 * q^55 + q^56 + 10 * q^57 + 19 * q^59 + 8 * q^60 - 20 * q^61 + q^62 + 12 * q^63 + 4 * q^64 + 5 * q^65 - q^66 + 15 * q^67 + 4 * q^68 - 5 * q^69 - 3 * q^70 + 15 * q^71 - 3 * q^72 - 7 * q^73 + 2 * q^74 + 12 * q^75 + 2 * q^76 - 6 * q^77 - 3 * q^78 - 17 * q^79 + 5 * q^80 + 4 * q^81 + q^82 + 6 * q^83 - 5 * q^84 - 29 * q^85 - 9 * q^86 - 34 * q^87 - 7 * q^88 + 20 * q^89 - 8 * q^90 - 18 * q^91 + 16 * q^92 - 5 * q^93 - 13 * q^94 - 6 * q^95 - 3 * q^96 + 3 * q^97 + 15 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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