LMFDB - Embedded newform 5239.2.a.t.1.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5239,2,Mod(1,5239)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5239.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5239, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 5239 = 13^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5239.a (trivial)

Newform invariants

comment:select newform

sage:traces = [36,2,-5,28,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$41.8336256189$
Analytic rank:	$1$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	5239.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.33705 q^{2} +2.56782 q^{3} -0.212302 q^{4} -1.42532 q^{5} -3.43329 q^{6} +2.10054 q^{7} +2.95795 q^{8} +3.59368 q^{9} +1.90573 q^{10} +4.03430 q^{11} -0.545153 q^{12} -2.80852 q^{14} -3.65997 q^{15} -3.53032 q^{16} -0.0164471 q^{17} -4.80493 q^{18} -1.87489 q^{19} +0.302600 q^{20} +5.39380 q^{21} -5.39405 q^{22} -8.64037 q^{23} +7.59549 q^{24} -2.96845 q^{25} +1.52447 q^{27} -0.445949 q^{28} -8.05850 q^{29} +4.89356 q^{30} -1.00000 q^{31} -1.19570 q^{32} +10.3593 q^{33} +0.0219905 q^{34} -2.99395 q^{35} -0.762947 q^{36} -7.64204 q^{37} +2.50682 q^{38} -4.21605 q^{40} +6.36287 q^{41} -7.21177 q^{42} -7.57422 q^{43} -0.856491 q^{44} -5.12216 q^{45} +11.5526 q^{46} -2.01909 q^{47} -9.06522 q^{48} -2.58774 q^{49} +3.96896 q^{50} -0.0422331 q^{51} -0.597398 q^{53} -2.03829 q^{54} -5.75019 q^{55} +6.21330 q^{56} -4.81438 q^{57} +10.7746 q^{58} -12.6781 q^{59} +0.777021 q^{60} +0.0410727 q^{61} +1.33705 q^{62} +7.54867 q^{63} +8.65935 q^{64} -13.8509 q^{66} -5.97968 q^{67} +0.00349175 q^{68} -22.1869 q^{69} +4.00305 q^{70} +7.55012 q^{71} +10.6299 q^{72} +0.874248 q^{73} +10.2178 q^{74} -7.62243 q^{75} +0.398044 q^{76} +8.47420 q^{77} -1.71482 q^{79} +5.03186 q^{80} -6.86650 q^{81} -8.50747 q^{82} -0.609918 q^{83} -1.14512 q^{84} +0.0234424 q^{85} +10.1271 q^{86} -20.6928 q^{87} +11.9333 q^{88} -9.35368 q^{89} +6.84858 q^{90} +1.83437 q^{92} -2.56782 q^{93} +2.69963 q^{94} +2.67233 q^{95} -3.07033 q^{96} -2.07646 q^{97} +3.45993 q^{98} +14.4980 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 2 q^{2} - 5 q^{3} + 28 q^{4} + 5 q^{5} - 3 q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9} - 15 q^{10} - q^{11} - 13 q^{12} - 19 q^{14} - 10 q^{15} + 4 q^{16} - 46 q^{17} - 9 q^{18} + 8 q^{19} - 5 q^{20} - 16 q^{21}+ \cdots - 47 q^{99}+O(q^{100}) $ 36 * q + 2 * q^2 - 5 * q^3 + 28 * q^4 + 5 * q^5 - 3 * q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9 - 15 * q^10 - q^11 - 13 * q^12 - 19 * q^14 - 10 * q^15 + 4 * q^16 - 46 * q^17 - 9 * q^18 + 8 * q^19 - 5 * q^20 - 16 * q^21 - 21 * q^22 - 24 * q^23 + 57 * q^24 + 5 * q^25 - 11 * q^27 - 32 * q^28 - 73 * q^29 - 31 * q^30 - 36 * q^31 + 3 * q^32 - 8 * q^33 - 37 * q^34 - 31 * q^35 - 31 * q^36 + 6 * q^37 - 25 * q^38 - 22 * q^40 + 6 * q^41 - 37 * q^42 - 37 * q^43 - 16 * q^45 - 45 * q^46 + 13 * q^47 - 46 * q^48 - 5 * q^49 + 24 * q^50 - 46 * q^51 - 42 * q^53 - 26 * q^54 - 47 * q^55 - 95 * q^56 + 33 * q^57 + 9 * q^58 + 20 * q^59 - 40 * q^60 - 48 * q^61 - 2 * q^62 + 52 * q^63 + 21 * q^64 - 4 * q^66 - 50 * q^67 - 76 * q^68 - 33 * q^69 + 93 * q^70 + 16 * q^71 - 52 * q^72 - 43 * q^73 - 76 * q^74 - 40 * q^75 + 62 * q^76 - 47 * q^77 - 43 * q^79 - 46 * q^80 - 96 * q^81 + 7 * q^82 + 9 * q^83 - 77 * q^84 - 5 * q^85 + 64 * q^86 - 8 * q^87 - 54 * q^88 + 6 * q^89 + 27 * q^90 - 35 * q^92 + 5 * q^93 - 76 * q^94 - 63 * q^95 + 72 * q^96 - 4 * q^97 - 41 * q^98 - 47 * 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 $

$2$	−1.33705	−0.945436	−0.472718	−	0.881214i	$-0.656727\pi$
$2$	−1.33705	−0.945436	−0.472718	+	0.881214i	$0.656727\pi$
$3$	2.56782	1.48253	0.741265	−	0.671213i	$-0.234226\pi$
$3$	2.56782	1.48253	0.741265	+	0.671213i	$0.234226\pi$
$4$	−0.212302	−0.106151
$5$	−1.42532	−0.637425	−0.318712	−	0.947852i	$-0.603250\pi$
$5$	−1.42532	−0.637425	−0.318712	+	0.947852i	$0.603250\pi$
$6$	−3.43329	−1.40164
$7$	2.10054	0.793929	0.396964	−	0.917834i	$-0.370064\pi$
$7$	2.10054	0.793929	0.396964	+	0.917834i	$0.370064\pi$
$8$	2.95795	1.04579
$9$	3.59368	1.19789
$10$	1.90573	0.602644
$11$	4.03430	1.21639	0.608193	−	0.793789i	$-0.291895\pi$
$11$	4.03430	1.21639	0.608193	+	0.793789i	$0.291895\pi$
$12$	−0.545153	−0.157372
$13$	0	0
$13$	0	0
$14$	−2.80852	−0.750609
$15$	−3.65997	−0.945001
$16$	−3.53032	−0.882581
$17$	−0.0164471	−0.00398900	−0.00199450	−	0.999998i	$-0.500635\pi$
$17$	−0.0164471	−0.00398900	−0.00199450	+	0.999998i	$0.500635\pi$
$18$	−4.80493	−1.13253
$19$	−1.87489	−0.430130	−0.215065	−	0.976600i	$-0.568996\pi$
$19$	−1.87489	−0.430130	−0.215065	+	0.976600i	$0.568996\pi$
$20$	0.302600	0.0676634
$21$	5.39380	1.17702
$22$	−5.39405	−1.15002
$23$	−8.64037	−1.80164	−0.900821	−	0.434191i	$-0.857034\pi$
$23$	−8.64037	−1.80164	−0.900821	+	0.434191i	$0.857034\pi$
$24$	7.59549	1.55042
$25$	−2.96845	−0.593690
$26$	0	0
$27$	1.52447	0.293384
$28$	−0.445949	−0.0842765
$29$	−8.05850	−1.49643	−0.748213	−	0.663458i	$-0.769088\pi$
$29$	−8.05850	−1.49643	−0.748213	+	0.663458i	$0.769088\pi$
$30$	4.89356	0.893438
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−1.19570	−0.211371
$33$	10.3593	1.80333
$34$	0.0219905	0.00377135
$35$	−2.99395	−0.506070
$36$	−0.762947	−0.127158
$37$	−7.64204	−1.25634	−0.628172	−	0.778075i	$-0.716197\pi$
$37$	−7.64204	−1.25634	−0.628172	+	0.778075i	$0.716197\pi$
$38$	2.50682	0.406660
$39$	0	0
$40$	−4.21605	−0.666615
$41$	6.36287	0.993714	0.496857	−	0.867832i	$-0.334487\pi$
$41$	6.36287	0.993714	0.496857	+	0.867832i	$0.334487\pi$
$42$	−7.21177	−1.11280
$43$	−7.57422	−1.15506	−0.577529	−	0.816370i	$-0.695983\pi$
$43$	−7.57422	−1.15506	−0.577529	+	0.816370i	$0.695983\pi$
$44$	−0.856491	−0.129121
$45$	−5.12216	−0.763567
$46$	11.5526	1.70334
$47$	−2.01909	−0.294515	−0.147258	−	0.989098i	$-0.547045\pi$
$47$	−2.01909	−0.294515	−0.147258	+	0.989098i	$0.547045\pi$
$48$	−9.06522	−1.30845
$49$	−2.58774	−0.369677
$50$	3.96896	0.561296
$51$	−0.0422331	−0.00591381
$52$	0	0
$53$	−0.597398	−0.0820590	−0.0410295	−	0.999158i	$-0.513064\pi$
$53$	−0.597398	−0.0820590	−0.0410295	+	0.999158i	$0.513064\pi$
$54$	−2.03829	−0.277376
$55$	−5.75019	−0.775355
$56$	6.21330	0.830287
$57$	−4.81438	−0.637680
$58$	10.7746	1.41478
$59$	−12.6781	−1.65055	−0.825274	−	0.564733i	$-0.808979\pi$
$59$	−12.6781	−1.65055	−0.825274	+	0.564733i	$0.808979\pi$
$60$	0.777021	0.100313
$61$	0.0410727	0.00525882	0.00262941	−	0.999997i	$-0.499163\pi$
$61$	0.0410727	0.00525882	0.00262941	+	0.999997i	$0.499163\pi$
$62$	1.33705	0.169805
$63$	7.54867	0.951043
$64$	8.65935	1.08242
$65$	0	0
$66$	−13.8509	−1.70493
$67$	−5.97968	−0.730534	−0.365267	−	0.930903i	$-0.619022\pi$
$67$	−5.97968	−0.730534	−0.365267	+	0.930903i	$0.619022\pi$
$68$	0.00349175	0.000423437 0
$69$	−22.1869	−2.67099
$70$	4.00305	0.478456
$71$	7.55012	0.896034	0.448017	−	0.894025i	$-0.352130\pi$
$71$	7.55012	0.896034	0.448017	+	0.894025i	$0.352130\pi$
$72$	10.6299	1.25275
$73$	0.874248	0.102323	0.0511615	−	0.998690i	$-0.483708\pi$
$73$	0.874248	0.102323	0.0511615	+	0.998690i	$0.483708\pi$
$74$	10.2178	1.18779
$75$	−7.62243	−0.880163
$76$	0.398044	0.0456588
$77$	8.47420	0.965725
$78$	0	0
$79$	−1.71482	−0.192932	−0.0964662	−	0.995336i	$-0.530754\pi$
$79$	−1.71482	−0.192932	−0.0964662	+	0.995336i	$0.530754\pi$
$80$	5.03186	0.562579
$81$	−6.86650	−0.762944
$82$	−8.50747	−0.939493
$83$	−0.609918	−0.0669472	−0.0334736	−	0.999440i	$-0.510657\pi$
$83$	−0.609918	−0.0669472	−0.0334736	+	0.999440i	$0.510657\pi$
$84$	−1.14512	−0.124942
$85$	0.0234424	0.00254269
$86$	10.1271	1.09203
$87$	−20.6928	−2.21850
$88$	11.9333	1.27209
$89$	−9.35368	−0.991488	−0.495744	−	0.868469i	$-0.665105\pi$
$89$	−9.35368	−0.991488	−0.495744	+	0.868469i	$0.665105\pi$
$90$	6.84858	0.721904
$91$	0	0
$92$	1.83437	0.191246
$93$	−2.56782	−0.266270
$94$	2.69963	0.278445
$95$	2.67233	0.274175
$96$	−3.07033	−0.313364
$97$	−2.07646	−0.210833	−0.105416	−	0.994428i	$-0.533618\pi$
$97$	−2.07646	−0.210833	−0.105416	+	0.994428i	$0.533618\pi$
$98$	3.45993	0.349506
$99$	14.4980	1.45710
$100$	0.630209	0.0630209
$101$	−2.99814	−0.298327	−0.149163	−	0.988813i	$-0.547658\pi$
$101$	−2.99814	−0.298327	−0.149163	+	0.988813i	$0.547658\pi$
$102$	0.0564677	0.00559113
$103$	11.2861	1.11205	0.556025	−	0.831166i	$-0.312326\pi$
$103$	11.2861	1.11205	0.556025	+	0.831166i	$0.312326\pi$
$104$	0	0
$105$	−7.68791	−0.750263
$106$	0.798750	0.0775815
$107$	−1.72168	−0.166441	−0.0832204	−	0.996531i	$-0.526521\pi$
$107$	−1.72168	−0.166441	−0.0832204	+	0.996531i	$0.526521\pi$
$108$	−0.323648	−0.0311430
$109$	−14.6807	−1.40615	−0.703076	−	0.711114i	$-0.748191\pi$
$109$	−14.6807	−1.40615	−0.703076	+	0.711114i	$0.748191\pi$
$110$	7.68827	0.733048
$111$	−19.6234	−1.86257
$112$	−7.41558	−0.700706
$113$	−10.1246	−0.952441	−0.476220	−	0.879326i	$-0.657994\pi$
$113$	−10.1246	−0.952441	−0.476220	+	0.879326i	$0.657994\pi$
$114$	6.43706	0.602886
$115$	12.3153	1.14841
$116$	1.71084	0.158847
$117$	0	0
$118$	16.9512	1.56049
$119$	−0.0345477	−0.00316698
$120$	−10.8260	−0.988277
$121$	5.27557	0.479597
$122$	−0.0549162	−0.00497188
$123$	16.3387	1.47321
$124$	0.212302	0.0190653
$125$	11.3576	1.01586
$126$	−10.0929	−0.899150
$127$	18.1165	1.60758	0.803791	−	0.594912i	$-0.202813\pi$
$127$	18.1165	1.60758	0.803791	+	0.594912i	$0.202813\pi$
$128$	−9.18657	−0.811986
$129$	−19.4492	−1.71241
$130$	0	0
$131$	9.21433	0.805060	0.402530	−	0.915407i	$-0.368131\pi$
$131$	9.21433	0.805060	0.402530	+	0.915407i	$0.368131\pi$
$132$	−2.19931	−0.191426
$133$	−3.93828	−0.341493
$134$	7.99511	0.690673
$135$	−2.17286	−0.187010
$136$	−0.0486497	−0.00417168
$137$	−5.09013	−0.434879	−0.217440	−	0.976074i	$-0.569771\pi$
$137$	−5.09013	−0.434879	−0.217440	+	0.976074i	$0.569771\pi$
$138$	29.6649	2.52525
$139$	4.48117	0.380088	0.190044	−	0.981776i	$-0.439137\pi$
$139$	4.48117	0.380088	0.190044	+	0.981776i	$0.439137\pi$
$140$	0.635622	0.0537199
$141$	−5.18466	−0.436627
$142$	−10.0949	−0.847143
$143$	0	0
$144$	−12.6869	−1.05724
$145$	11.4860	0.953859
$146$	−1.16891	−0.0967398
$147$	−6.64484	−0.548057
$148$	1.62242	0.133362
$149$	23.9803	1.96454	0.982272	−	0.187460i	$-0.0600256\pi$
$149$	23.9803	1.96454	0.982272	+	0.187460i	$0.0600256\pi$
$150$	10.1916	0.832137
$151$	16.0690	1.30768	0.653840	−	0.756633i	$-0.273157\pi$
$151$	16.0690	1.30768	0.653840	+	0.756633i	$0.273157\pi$
$152$	−5.54585	−0.449828
$153$	−0.0591056	−0.00477840
$154$	−11.3304	−0.913031
$155$	1.42532	0.114485
$156$	0	0
$157$	23.6539	1.88779	0.943894	−	0.330249i	$-0.107133\pi$
$157$	23.6539	1.88779	0.943894	+	0.330249i	$0.107133\pi$
$158$	2.29280	0.182405
$159$	−1.53401	−0.121655
$160$	1.70426	0.134733
$161$	−18.1494	−1.43038
$162$	9.18083	0.721314
$163$	−0.610632	−0.0478284	−0.0239142	−	0.999714i	$-0.507613\pi$
$163$	−0.610632	−0.0478284	−0.0239142	+	0.999714i	$0.507613\pi$
$164$	−1.35085	−0.105484
$165$	−14.7654	−1.14949
$166$	0.815490	0.0632943
$167$	15.6320	1.20964	0.604821	−	0.796361i	$-0.293245\pi$
$167$	15.6320	1.20964	0.604821	+	0.796361i	$0.293245\pi$
$168$	15.9546	1.23092
$169$	0	0
$170$	−0.0313437	−0.00240395
$171$	−6.73777	−0.515250
$172$	1.60802	0.122611
$173$	−25.1668	−1.91340	−0.956700	−	0.291076i	$-0.905987\pi$
$173$	−25.1668	−1.91340	−0.956700	+	0.291076i	$0.905987\pi$
$174$	27.6672	2.09745
$175$	−6.23534	−0.471348
$176$	−14.2424	−1.07356
$177$	−32.5550	−2.44699
$178$	12.5063	0.937388
$179$	−10.6107	−0.793082	−0.396541	−	0.918017i	$-0.629790\pi$
$179$	−10.6107	−0.793082	−0.396541	+	0.918017i	$0.629790\pi$
$180$	1.08745	0.0810535
$181$	16.1834	1.20291	0.601453	−	0.798908i	$-0.294589\pi$
$181$	16.1834	1.20291	0.601453	+	0.798908i	$0.294589\pi$
$182$	0	0
$183$	0.105467	0.00779636
$184$	−25.5578	−1.88415
$185$	10.8924	0.800824
$186$	3.43329	0.251741
$187$	−0.0663524	−0.00485217
$188$	0.428658	0.0312631
$189$	3.20220	0.232926
$190$	−3.57303	−0.259215
$191$	−13.7500	−0.994912	−0.497456	−	0.867489i	$-0.665732\pi$
$191$	−13.7500	−0.994912	−0.497456	+	0.867489i	$0.665732\pi$
$192$	22.2356	1.60472
$193$	18.9509	1.36411	0.682056	−	0.731300i	$-0.261086\pi$
$193$	18.9509	1.36411	0.682056	+	0.731300i	$0.261086\pi$
$194$	2.77633	0.199329
$195$	0	0
$196$	0.549383	0.0392416
$197$	22.2195	1.58308	0.791538	−	0.611120i	$-0.209281\pi$
$197$	22.2195	1.58308	0.791538	+	0.611120i	$0.209281\pi$
$198$	−19.3845	−1.37760
$199$	−4.66216	−0.330492	−0.165246	−	0.986252i	$-0.552842\pi$
$199$	−4.66216	−0.330492	−0.165246	+	0.986252i	$0.552842\pi$
$200$	−8.78054	−0.620878
$201$	−15.3547	−1.08304
$202$	4.00866	0.282049
$203$	−16.9272	−1.18806
$204$	0.00896618	0.000627758 0
$205$	−9.06916	−0.633418
$206$	−15.0900	−1.05137
$207$	−31.0507	−2.15818
$208$	0	0
$209$	−7.56388	−0.523204
$210$	10.2791	0.709326
$211$	−10.4552	−0.719769	−0.359884	−	0.932997i	$-0.617184\pi$
$211$	−10.4552	−0.719769	−0.359884	+	0.932997i	$0.617184\pi$
$212$	0.126829	0.00871065
$213$	19.3873	1.32840
$214$	2.30197	0.157359
$215$	10.7957	0.736262
$216$	4.50930	0.306819
$217$	−2.10054	−0.142594
$218$	19.6288	1.32943
$219$	2.24491	0.151697
$220$	1.22078	0.0823048
$221$	0	0
$222$	26.2374	1.76094
$223$	−2.62263	−0.175624	−0.0878122	−	0.996137i	$-0.527988\pi$
$223$	−2.62263	−0.175624	−0.0878122	+	0.996137i	$0.527988\pi$
$224$	−2.51161	−0.167814
$225$	−10.6677	−0.711178
$226$	13.5371	0.900471
$227$	0.249112	0.0165342	0.00826708	−	0.999966i	$-0.497368\pi$
$227$	0.249112	0.0165342	0.00826708	+	0.999966i	$0.497368\pi$
$228$	1.02210	0.0676905
$229$	−10.7722	−0.711848	−0.355924	−	0.934515i	$-0.615834\pi$
$229$	−10.7722	−0.711848	−0.355924	+	0.934515i	$0.615834\pi$
$230$	−16.4662	−1.08575
$231$	21.7602	1.43172
$232$	−23.8367	−1.56496
$233$	−15.3667	−1.00671	−0.503354	−	0.864080i	$-0.667901\pi$
$233$	−15.3667	−1.00671	−0.503354	+	0.864080i	$0.667901\pi$
$234$	0	0
$235$	2.87786	0.187731
$236$	2.69159	0.175208
$237$	−4.40334	−0.286028
$238$	0.0461920	0.00299418
$239$	−8.10070	−0.523991	−0.261995	−	0.965069i	$-0.584381\pi$
$239$	−8.10070	−0.523991	−0.261995	+	0.965069i	$0.584381\pi$
$240$	12.9209	0.834040
$241$	−10.5809	−0.681574	−0.340787	−	0.940141i	$-0.610694\pi$
$241$	−10.5809	−0.681574	−0.340787	+	0.940141i	$0.610694\pi$
$242$	−7.05369	−0.453428
$243$	−22.2053	−1.42447
$244$	−0.00871983	−0.000558230 0
$245$	3.68837	0.235641
$246$	−21.8456	−1.39283
$247$	0	0
$248$	−2.95795	−0.187830
$249$	−1.56616	−0.0992513
$250$	−15.1857	−0.960428
$251$	−15.7876	−0.996507	−0.498254	−	0.867031i	$-0.666025\pi$
$251$	−15.7876	−0.996507	−0.498254	+	0.867031i	$0.666025\pi$
$252$	−1.60260	−0.100954
$253$	−34.8578	−2.19149
$254$	−24.2227	−1.51987
$255$	0.0601959	0.00376961
$256$	−5.03581	−0.314738
$257$	−16.5299	−1.03111	−0.515554	−	0.856857i	$-0.672414\pi$
$257$	−16.5299	−1.03111	−0.515554	+	0.856857i	$0.672414\pi$
$258$	26.0045	1.61897
$259$	−16.0524	−0.997447
$260$	0	0
$261$	−28.9597	−1.79256
$262$	−12.3200	−0.761132
$263$	9.97680	0.615196	0.307598	−	0.951516i	$-0.400475\pi$
$263$	9.97680	0.615196	0.307598	+	0.951516i	$0.400475\pi$
$264$	30.6425	1.88591
$265$	0.851486	0.0523064
$266$	5.26568	0.322859
$267$	−24.0185	−1.46991
$268$	1.26950	0.0775470
$269$	16.8578	1.02784	0.513918	−	0.857839i	$-0.328194\pi$
$269$	16.8578	1.02784	0.513918	+	0.857839i	$0.328194\pi$
$270$	2.90522	0.176806
$271$	6.39352	0.388379	0.194189	−	0.980964i	$-0.437792\pi$
$271$	6.39352	0.388379	0.194189	+	0.980964i	$0.437792\pi$
$272$	0.0580635	0.00352062
$273$	0	0
$274$	6.80575	0.411150
$275$	−11.9756	−0.722157
$276$	4.71033	0.283528
$277$	−13.5224	−0.812480	−0.406240	−	0.913766i	$-0.633160\pi$
$277$	−13.5224	−0.812480	−0.406240	+	0.913766i	$0.633160\pi$
$278$	−5.99154	−0.359349
$279$	−3.59368	−0.215148
$280$	−8.85597	−0.529245
$281$	1.43056	0.0853401	0.0426701	−	0.999089i	$-0.486414\pi$
$281$	1.43056	0.0853401	0.0426701	+	0.999089i	$0.486414\pi$
$282$	6.93214	0.412803
$283$	11.0118	0.654582	0.327291	−	0.944924i	$-0.393864\pi$
$283$	11.0118	0.654582	0.327291	+	0.944924i	$0.393864\pi$
$284$	−1.60291	−0.0951150
$285$	6.86206	0.406473
$286$	0	0
$287$	13.3655	0.788938
$288$	−4.29696	−0.253201
$289$	−16.9997	−0.999984
$290$	−15.3573	−0.901812
$291$	−5.33197	−0.312566
$292$	−0.185605	−0.0108617
$293$	−15.4462	−0.902379	−0.451190	−	0.892428i	$-0.649000\pi$
$293$	−15.4462	−0.902379	−0.451190	+	0.892428i	$0.649000\pi$
$294$	8.88447	0.518153
$295$	18.0704	1.05210
$296$	−22.6048	−1.31388
$297$	6.15015	0.356868
$298$	−32.0628	−1.85735
$299$	0	0
$300$	1.61826	0.0934303
$301$	−15.9099	−0.917034
$302$	−21.4851	−1.23633
$303$	−7.69869	−0.442278
$304$	6.61898	0.379624
$305$	−0.0585420	−0.00335210
$306$	0.0790270	0.00451767
$307$	31.2288	1.78232	0.891162	−	0.453685i	$-0.149891\pi$
$307$	31.2288	1.78232	0.891162	+	0.453685i	$0.149891\pi$
$308$	−1.79909	−0.102513
$309$	28.9806	1.64865
$310$	−1.90573	−0.108238
$311$	27.6307	1.56679	0.783396	−	0.621523i	$-0.213486\pi$
$311$	27.6307	1.56679	0.783396	+	0.621523i	$0.213486\pi$
$312$	0	0
$313$	−8.46905	−0.478699	−0.239349	−	0.970933i	$-0.576934\pi$
$313$	−8.46905	−0.478699	−0.239349	+	0.970933i	$0.576934\pi$
$314$	−31.6264	−1.78478
$315$	−10.7593	−0.606218
$316$	0.364060	0.0204800
$317$	22.3123	1.25318	0.626592	−	0.779347i	$-0.284449\pi$
$317$	22.3123	1.25318	0.626592	+	0.779347i	$0.284449\pi$
$318$	2.05104	0.115017
$319$	−32.5104	−1.82023
$320$	−12.3424	−0.689960
$321$	−4.42095	−0.246753
$322$	24.2667	1.35233
$323$	0.0308365	0.00171579
$324$	1.45777	0.0809874
$325$	0	0
$326$	0.816444	0.0452187
$327$	−37.6973	−2.08466
$328$	18.8211	1.03922
$329$	−4.24118	−0.233824
$330$	19.7421	1.08677
$331$	−19.6971	−1.08265	−0.541326	−	0.840813i	$-0.682078\pi$
$331$	−19.6971	−1.08265	−0.541326	+	0.840813i	$0.682078\pi$
$332$	0.129487	0.00710653
$333$	−27.4631	−1.50497
$334$	−20.9008	−1.14364
$335$	8.52298	0.465660
$336$	−19.0418	−1.03882
$337$	14.7663	0.804373	0.402186	−	0.915558i	$-0.368250\pi$
$337$	14.7663	0.804373	0.402186	+	0.915558i	$0.368250\pi$
$338$	0	0
$339$	−25.9981	−1.41202
$340$	−0.00497688	−0.000269909 0
$341$	−4.03430	−0.218470
$342$	9.00872	0.487136
$343$	−20.1394	−1.08743
$344$	−22.4042	−1.20795
$345$	31.6235	1.70255
$346$	33.6493	1.80900
$347$	27.5314	1.47796	0.738982	−	0.673725i	$-0.235307\pi$
$347$	27.5314	1.47796	0.738982	+	0.673725i	$0.235307\pi$
$348$	4.39312	0.235496
$349$	0.0998581	0.00534528	0.00267264	−	0.999996i	$-0.499149\pi$
$349$	0.0998581	0.00534528	0.00267264	+	0.999996i	$0.499149\pi$
$350$	8.33695	0.445629
$351$	0	0
$352$	−4.82380	−0.257109
$353$	−23.9520	−1.27484	−0.637418	−	0.770518i	$-0.719998\pi$
$353$	−23.9520	−1.27484	−0.637418	+	0.770518i	$0.719998\pi$
$354$	43.5276	2.31347
$355$	−10.7614	−0.571154
$356$	1.98581	0.105248
$357$	−0.0887122	−0.00469515
$358$	14.1870	0.749808
$359$	−2.63001	−0.138807	−0.0694033	−	0.997589i	$-0.522110\pi$
$359$	−2.63001	−0.138807	−0.0694033	+	0.997589i	$0.522110\pi$
$360$	−15.1511	−0.798535
$361$	−15.4848	−0.814988
$362$	−21.6380	−1.13727
$363$	13.5467	0.711017
$364$	0	0
$365$	−1.24609	−0.0652232
$366$	−0.141015	−0.00737096
$367$	−6.41524	−0.334873	−0.167436	−	0.985883i	$-0.553549\pi$
$367$	−6.41524	−0.334873	−0.167436	+	0.985883i	$0.553549\pi$
$368$	30.5033	1.59009
$369$	22.8661	1.19036
$370$	−14.5636	−0.757128
$371$	−1.25486	−0.0651490
$372$	0.545153	0.0282649
$373$	35.4958	1.83790	0.918952	−	0.394369i	$-0.129037\pi$
$373$	35.4958	1.83790	0.918952	+	0.394369i	$0.129037\pi$
$374$	0.0887164	0.00458742
$375$	29.1643	1.50604
$376$	−5.97239	−0.308002
$377$	0	0
$378$	−4.28150	−0.220216
$379$	1.74807	0.0897924	0.0448962	−	0.998992i	$-0.485704\pi$
$379$	1.74807	0.0897924	0.0448962	+	0.998992i	$0.485704\pi$
$380$	−0.567342	−0.0291040
$381$	46.5199	2.38329
$382$	18.3844	0.940626
$383$	−28.9265	−1.47808	−0.739038	−	0.673664i	$-0.764720\pi$
$383$	−28.9265	−1.47808	−0.739038	+	0.673664i	$0.764720\pi$
$384$	−23.5894	−1.20379
$385$	−12.0785	−0.615577
$386$	−25.3382	−1.28968
$387$	−27.2193	−1.38364
$388$	0.440837	0.0223801
$389$	27.6900	1.40394	0.701969	−	0.712208i	$-0.252305\pi$
$389$	27.6900	1.40394	0.701969	+	0.712208i	$0.252305\pi$
$390$	0	0
$391$	0.142109	0.00718675
$392$	−7.65441	−0.386606
$393$	23.6607	1.19352
$394$	−29.7086	−1.49670
$395$	2.44418	0.122980
$396$	−3.07796	−0.154673
$397$	23.9754	1.20329	0.601645	−	0.798764i	$-0.294512\pi$
$397$	23.9754	1.20329	0.601645	+	0.798764i	$0.294512\pi$
$398$	6.23354	0.312459
$399$	−10.1128	−0.506273
$400$	10.4796	0.523979
$401$	−5.25188	−0.262266	−0.131133	−	0.991365i	$-0.541862\pi$
$401$	−5.25188	−0.262266	−0.131133	+	0.991365i	$0.541862\pi$
$402$	20.5300	1.02394
$403$	0	0
$404$	0.636513	0.0316677
$405$	9.78699	0.486319
$406$	22.6325	1.12323
$407$	−30.8303	−1.52820
$408$	−0.124924	−0.00618464
$409$	−0.121700	−0.00601767	−0.00300883	−	0.999995i	$-0.500958\pi$
$409$	−0.121700	−0.00601767	−0.00300883	+	0.999995i	$0.500958\pi$
$410$	12.1259	0.598856
$411$	−13.0705	−0.644721
$412$	−2.39606	−0.118045
$413$	−26.6308	−1.31042
$414$	41.5163	2.04042
$415$	0.869332	0.0426738
$416$	0	0
$417$	11.5068	0.563491
$418$	10.1133	0.494656
$419$	−21.3135	−1.04123	−0.520616	−	0.853791i	$-0.674298\pi$
$419$	−21.3135	−1.04123	−0.520616	+	0.853791i	$0.674298\pi$
$420$	1.63216	0.0796413
$421$	19.3803	0.944538	0.472269	−	0.881455i	$-0.343435\pi$
$421$	19.3803	0.944538	0.472269	+	0.881455i	$0.343435\pi$
$422$	13.9792	0.680495
$423$	−7.25598	−0.352798
$424$	−1.76708	−0.0858168
$425$	0.0488223	0.00236823
$426$	−25.9218	−1.25591
$427$	0.0862748	0.00417513
$428$	0.365516	0.0176679
$429$	0	0
$430$	−14.4344	−0.696089
$431$	−30.0225	−1.44614	−0.723068	−	0.690777i	$-0.757269\pi$
$431$	−30.0225	−1.44614	−0.723068	+	0.690777i	$0.757269\pi$
$432$	−5.38186	−0.258935
$433$	−26.8912	−1.29231	−0.646155	−	0.763206i	$-0.723624\pi$
$433$	−26.8912	−1.29231	−0.646155	+	0.763206i	$0.723624\pi$
$434$	2.80852	0.134813
$435$	29.4939	1.41412
$436$	3.11674	0.149265
$437$	16.1998	0.774940
$438$	−3.00155	−0.143420
$439$	−1.48920	−0.0710755	−0.0355378	−	0.999368i	$-0.511314\pi$
$439$	−1.48920	−0.0710755	−0.0355378	+	0.999368i	$0.511314\pi$
$440$	−17.0088	−0.810862
$441$	−9.29951	−0.442834
$442$	0	0
$443$	13.9431	0.662457	0.331228	−	0.943551i	$-0.392537\pi$
$443$	13.9431	0.662457	0.331228	+	0.943551i	$0.392537\pi$
$444$	4.16608	0.197714
$445$	13.3320	0.631999
$446$	3.50659	0.166042
$447$	61.5771	2.91250
$448$	18.1893	0.859364
$449$	−26.8813	−1.26861	−0.634304	−	0.773084i	$-0.718713\pi$
$449$	−26.8813	−1.26861	−0.634304	+	0.773084i	$0.718713\pi$
$450$	14.2632	0.672373
$451$	25.6697	1.20874
$452$	2.14947	0.101103
$453$	41.2623	1.93867
$454$	−0.333075	−0.0156320
$455$	0	0
$456$	−14.2407	−0.666883
$457$	10.1838	0.476378	0.238189	−	0.971219i	$-0.423446\pi$
$457$	10.1838	0.476378	0.238189	+	0.971219i	$0.423446\pi$
$458$	14.4030	0.673006
$459$	−0.0250730	−0.00117031
$460$	−2.61457	−0.121905
$461$	21.2608	0.990212	0.495106	−	0.868833i	$-0.335129\pi$
$461$	21.2608	0.990212	0.495106	+	0.868833i	$0.335129\pi$
$462$	−29.0944	−1.35359
$463$	−20.5840	−0.956621	−0.478311	−	0.878191i	$-0.658751\pi$
$463$	−20.5840	−0.956621	−0.478311	+	0.878191i	$0.658751\pi$
$464$	28.4491	1.32072
$465$	3.65997	0.169727
$466$	20.5461	0.951778
$467$	−31.8339	−1.47310	−0.736548	−	0.676385i	$-0.763546\pi$
$467$	−31.8339	−1.47310	−0.736548	+	0.676385i	$0.763546\pi$
$468$	0	0
$469$	−12.5605	−0.579992
$470$	−3.84784	−0.177488
$471$	60.7389	2.79870
$472$	−37.5012	−1.72613
$473$	−30.5567	−1.40500
$474$	5.88748	0.270421
$475$	5.56552	0.255364
$476$	0.00733456	0.000336179 0
$477$	−2.14686	−0.0982979
$478$	10.8310	0.495400
$479$	−1.53857	−0.0702990	−0.0351495	−	0.999382i	$-0.511191\pi$
$479$	−1.53857	−0.0702990	−0.0351495	+	0.999382i	$0.511191\pi$
$480$	4.37622	0.199746
$481$	0	0
$482$	14.1471	0.644385
$483$	−46.6044	−2.12057
$484$	−1.12001	−0.0509098
$485$	2.95963	0.134390
$486$	29.6896	1.34675
$487$	3.23073	0.146398	0.0731992	−	0.997317i	$-0.476679\pi$
$487$	3.23073	0.146398	0.0731992	+	0.997317i	$0.476679\pi$
$488$	0.121491	0.00549965
$489$	−1.56799	−0.0709070
$490$	−4.93153	−0.222784
$491$	1.50855	0.0680799	0.0340399	−	0.999420i	$-0.489163\pi$
$491$	1.50855	0.0680799	0.0340399	+	0.999420i	$0.489163\pi$
$492$	−3.46874	−0.156383
$493$	0.132539	0.00596925
$494$	0	0
$495$	−20.6643	−0.928793
$496$	3.53032	0.158516
$497$	15.8593	0.711387
$498$	2.09403	0.0938357
$499$	13.8204	0.618686	0.309343	−	0.950950i	$-0.399891\pi$
$499$	13.8204	0.618686	0.309343	+	0.950950i	$0.399891\pi$
$500$	−2.41125	−0.107834
$501$	40.1402	1.79333
$502$	21.1088	0.942134
$503$	−17.1588	−0.765073	−0.382536	−	0.923940i	$-0.624949\pi$
$503$	−17.1588	−0.765073	−0.382536	+	0.923940i	$0.624949\pi$
$504$	22.3286	0.994596
$505$	4.27333	0.190161
$506$	46.6066	2.07192
$507$	0	0
$508$	−3.84618	−0.170647
$509$	24.8200	1.10013	0.550064	−	0.835122i	$-0.314603\pi$
$509$	24.8200	1.10013	0.550064	+	0.835122i	$0.314603\pi$
$510$	−0.0804847	−0.00356392
$511$	1.83639	0.0812372
$512$	25.1063	1.10955
$513$	−2.85821	−0.126193
$514$	22.1013	0.974846
$515$	−16.0863	−0.708848
$516$	4.12911	0.181774
$517$	−8.14563	−0.358244
$518$	21.4628	0.943023
$519$	−64.6238	−2.83667
$520$	0	0
$521$	−40.2422	−1.76304	−0.881520	−	0.472146i	$-0.843479\pi$
$521$	−40.2422	−1.76304	−0.881520	+	0.472146i	$0.843479\pi$
$522$	38.7205	1.69475
$523$	−11.9605	−0.522997	−0.261499	−	0.965204i	$-0.584217\pi$
$523$	−11.9605	−0.522997	−0.261499	+	0.965204i	$0.584217\pi$
$524$	−1.95622	−0.0854580
$525$	−16.0112	−0.698787
$526$	−13.3395	−0.581628
$527$	0.0164471	0.000716446 0
$528$	−36.5718	−1.59158
$529$	51.6560	2.24591
$530$	−1.13848	−0.0494523
$531$	−45.5610	−1.97718
$532$	0.836107	0.0362498
$533$	0	0
$534$	32.1139	1.38971
$535$	2.45395	0.106093
$536$	−17.6876	−0.763988
$537$	−27.2464	−1.17577
$538$	−22.5396	−0.971752
$539$	−10.4397	−0.449670
$540$	0.461303	0.0198513
$541$	27.2011	1.16947	0.584733	−	0.811226i	$-0.301199\pi$
$541$	27.2011	1.16947	0.584733	+	0.811226i	$0.301199\pi$
$542$	−8.54845	−0.367187
$543$	41.5561	1.78334
$544$	0.0196657	0.000843161 0
$545$	20.9247	0.896316
$546$	0	0
$547$	9.62388	0.411488	0.205744	−	0.978606i	$-0.434039\pi$
$547$	9.62388	0.411488	0.205744	+	0.978606i	$0.434039\pi$
$548$	1.08065	0.0461629
$549$	0.147602	0.00629951
$550$	16.0120	0.682753
$551$	15.1088	0.643658
$552$	−65.6278	−2.79331
$553$	−3.60205	−0.153175
$554$	18.0801	0.768148
$555$	27.9697	1.18725
$556$	−0.951363	−0.0403468
$557$	17.6937	0.749707	0.374854	−	0.927084i	$-0.377693\pi$
$557$	17.6937	0.749707	0.374854	+	0.927084i	$0.377693\pi$
$558$	4.80493	0.203409
$559$	0	0
$560$	10.5696	0.446647
$561$	−0.170381	−0.00719349
$562$	−1.91273	−0.0806836
$563$	5.53995	0.233481	0.116740	−	0.993162i	$-0.462755\pi$
$563$	5.53995	0.233481	0.116740	+	0.993162i	$0.462755\pi$
$564$	1.10072	0.0463485
$565$	14.4308	0.607109
$566$	−14.7233	−0.618865
$567$	−14.4233	−0.605723
$568$	22.3329	0.937068
$569$	10.8728	0.455811	0.227906	−	0.973683i	$-0.426812\pi$
$569$	10.8728	0.455811	0.227906	+	0.973683i	$0.426812\pi$
$570$	−9.17490	−0.384294
$571$	17.4474	0.730153	0.365076	−	0.930978i	$-0.381043\pi$
$571$	17.4474	0.730153	0.365076	+	0.930978i	$0.381043\pi$
$572$	0	0
$573$	−35.3074	−1.47499
$574$	−17.8703	−0.745890
$575$	25.6485	1.06962
$576$	31.1190	1.29662
$577$	19.1962	0.799150	0.399575	−	0.916701i	$-0.369158\pi$
$577$	19.1962	0.799150	0.399575	+	0.916701i	$0.369158\pi$
$578$	22.7295	0.945421
$579$	48.6623	2.02234
$580$	−2.43850	−0.101253
$581$	−1.28116	−0.0531514
$582$	7.12910	0.295511
$583$	−2.41008	−0.0998154
$584$	2.58599	0.107009
$585$	0	0
$586$	20.6524	0.853142
$587$	−47.5323	−1.96187	−0.980935	−	0.194338i	$-0.937744\pi$
$587$	−47.5323	−1.96187	−0.980935	+	0.194338i	$0.937744\pi$
$588$	1.41071	0.0581769
$589$	1.87489	0.0772536
$590$	−24.1610	−0.994692
$591$	57.0557	2.34696
$592$	26.9789	1.10882
$593$	−36.8014	−1.51125	−0.755627	−	0.655002i	$-0.772668\pi$
$593$	−36.8014	−1.51125	−0.755627	+	0.655002i	$0.772668\pi$
$594$	−8.22305	−0.337396
$595$	0.0492417	0.00201871
$596$	−5.09108	−0.208539
$597$	−11.9716	−0.489964
$598$	0	0
$599$	11.3893	0.465355	0.232678	−	0.972554i	$-0.425251\pi$
$599$	11.3893	0.465355	0.232678	+	0.972554i	$0.425251\pi$
$600$	−22.5468	−0.920470
$601$	21.6702	0.883947	0.441974	−	0.897028i	$-0.354278\pi$
$601$	21.6702	0.883947	0.441974	+	0.897028i	$0.354278\pi$
$602$	21.2724	0.866997
$603$	−21.4891	−0.875102
$604$	−3.41149	−0.138812
$605$	−7.51939	−0.305707
$606$	10.2935	0.418145
$607$	33.5350	1.36114	0.680571	−	0.732682i	$-0.261732\pi$
$607$	33.5350	1.36114	0.680571	+	0.732682i	$0.261732\pi$
$608$	2.24180	0.0909172
$609$	−43.4659	−1.76133
$610$	0.0782734	0.00316920
$611$	0	0
$612$	0.0125483	0.000507233 0
$613$	36.2209	1.46295	0.731474	−	0.681869i	$-0.238833\pi$
$613$	36.2209	1.46295	0.731474	+	0.681869i	$0.238833\pi$
$614$	−41.7545	−1.68507
$615$	−23.2879	−0.939060
$616$	25.0663	1.00995
$617$	32.0991	1.29226	0.646131	−	0.763227i	$-0.276386\pi$
$617$	32.0991	1.29226	0.646131	+	0.763227i	$0.276386\pi$
$618$	−38.7484	−1.55869
$619$	5.95611	0.239396	0.119698	−	0.992810i	$-0.461807\pi$
$619$	5.95611	0.239396	0.119698	+	0.992810i	$0.461807\pi$
$620$	−0.302600	−0.0121527
$621$	−13.1720	−0.528572
$622$	−36.9436	−1.48130
$623$	−19.6478	−0.787171
$624$	0	0
$625$	−1.34606	−0.0538424
$626$	11.3235	0.452579
$627$	−19.4226	−0.775666
$628$	−5.02178	−0.200391
$629$	0.125689	0.00501156
$630$	14.3857	0.573140
$631$	−26.7521	−1.06498	−0.532492	−	0.846435i	$-0.678744\pi$
$631$	−26.7521	−1.06498	−0.532492	+	0.846435i	$0.678744\pi$
$632$	−5.07236	−0.201768
$633$	−26.8471	−1.06708
$634$	−29.8326	−1.18481
$635$	−25.8219	−1.02471
$636$	0.325674	0.0129138
$637$	0	0
$638$	43.4680	1.72091
$639$	27.1327	1.07335
$640$	13.0939	0.517580
$641$	34.8042	1.37468	0.687342	−	0.726334i	$-0.258778\pi$
$641$	34.8042	1.37468	0.687342	+	0.726334i	$0.258778\pi$
$642$	5.91102	0.233290
$643$	28.7699	1.13457	0.567287	−	0.823520i	$-0.307993\pi$
$643$	28.7699	1.13457	0.567287	+	0.823520i	$0.307993\pi$
$644$	3.85317	0.151836
$645$	27.7214	1.09153
$646$	−0.0412299	−0.00162217
$647$	−7.32163	−0.287843	−0.143921	−	0.989589i	$-0.545971\pi$
$647$	−7.32163	−0.287843	−0.143921	+	0.989589i	$0.545971\pi$
$648$	−20.3108	−0.797883
$649$	−51.1472	−2.00770
$650$	0	0
$651$	−5.39380	−0.211400
$652$	0.129639	0.00507704
$653$	−46.9350	−1.83671	−0.918354	−	0.395761i	$-0.870481\pi$
$653$	−46.9350	−1.83671	−0.918354	+	0.395761i	$0.870481\pi$
$654$	50.4031	1.97092
$655$	−13.1334	−0.513165
$656$	−22.4630	−0.877033
$657$	3.14177	0.122572
$658$	5.67067	0.221066
$659$	13.3860	0.521443	0.260722	−	0.965414i	$-0.416040\pi$
$659$	13.3860	0.521443	0.260722	+	0.965414i	$0.416040\pi$
$660$	3.13473	0.122019
$661$	−6.50063	−0.252845	−0.126423	−	0.991976i	$-0.540350\pi$
$661$	−6.50063	−0.252845	−0.126423	+	0.991976i	$0.540350\pi$
$662$	26.3360	1.02358
$663$	0	0
$664$	−1.80411	−0.0700131
$665$	5.61333	0.217676
$666$	36.7194	1.42285
$667$	69.6285	2.69602
$668$	−3.31872	−0.128405
$669$	−6.73444	−0.260368
$670$	−11.3956	−0.440252
$671$	0.165700	0.00639676
$672$	−6.44935	−0.248789
$673$	−6.76665	−0.260835	−0.130418	−	0.991459i	$-0.541632\pi$
$673$	−6.76665	−0.260835	−0.130418	+	0.991459i	$0.541632\pi$
$674$	−19.7433	−0.760483
$675$	−4.52530	−0.174179
$676$	0	0
$677$	−47.3270	−1.81893	−0.909463	−	0.415785i	$-0.863507\pi$
$677$	−47.3270	−1.81893	−0.909463	+	0.415785i	$0.863507\pi$
$678$	34.7607	1.33498
$679$	−4.36168	−0.167386
$680$	0.0693416	0.00265913
$681$	0.639675	0.0245124
$682$	5.39405	0.206549
$683$	36.1273	1.38237	0.691186	−	0.722677i	$-0.257089\pi$
$683$	36.1273	1.38237	0.691186	+	0.722677i	$0.257089\pi$
$684$	1.43044	0.0546944
$685$	7.25509	0.277203
$686$	26.9274	1.02809
$687$	−27.6611	−1.05534
$688$	26.7394	1.01943
$689$	0	0
$690$	−42.2822	−1.60965
$691$	−38.5583	−1.46683	−0.733413	−	0.679783i	$-0.762074\pi$
$691$	−38.5583	−1.46683	−0.733413	+	0.679783i	$0.762074\pi$
$692$	5.34298	0.203110
$693$	30.4536	1.15684
$694$	−36.8108	−1.39732
$695$	−6.38712	−0.242277
$696$	−61.2082	−2.32009
$697$	−0.104651	−0.00396393
$698$	−0.133515	−0.00505362
$699$	−39.4590	−1.49248
$700$	1.32378	0.0500341
$701$	−14.8160	−0.559594	−0.279797	−	0.960059i	$-0.590267\pi$
$701$	−14.8160	−0.559594	−0.279797	+	0.960059i	$0.590267\pi$
$702$	0	0
$703$	14.3280	0.540391
$704$	34.9344	1.31664
$705$	7.38983	0.278317
$706$	32.0250	1.20528
$707$	−6.29772	−0.236850
$708$	6.91151	0.259750
$709$	−24.5278	−0.921162	−0.460581	−	0.887618i	$-0.652359\pi$
$709$	−24.5278	−0.921162	−0.460581	+	0.887618i	$0.652359\pi$
$710$	14.3885	0.539989
$711$	−6.16252	−0.231113
$712$	−27.6678	−1.03689
$713$	8.64037	0.323584
$714$	0.118612	0.00443896
$715$	0	0
$716$	2.25268	0.0841866
$717$	−20.8011	−0.776832
$718$	3.51645	0.131233
$719$	−41.2110	−1.53691	−0.768456	−	0.639903i	$-0.778974\pi$
$719$	−41.2110	−1.53691	−0.768456	+	0.639903i	$0.778974\pi$
$720$	18.0829	0.673910
$721$	23.7068	0.882889
$722$	20.7039	0.770519
$723$	−27.1697	−1.01045
$724$	−3.43578	−0.127690
$725$	23.9213	0.888413
$726$	−18.1126	−0.672221
$727$	26.4051	0.979312	0.489656	−	0.871916i	$-0.337122\pi$
$727$	26.4051	0.979312	0.489656	+	0.871916i	$0.337122\pi$
$728$	0	0
$729$	−36.4197	−1.34888
$730$	1.66608	0.0616643
$731$	0.124574	0.00460753
$732$	−0.0223909	−0.000827593 0
$733$	−7.74570	−0.286094	−0.143047	−	0.989716i	$-0.545690\pi$
$733$	−7.74570	−0.286094	−0.143047	+	0.989716i	$0.545690\pi$
$734$	8.57749	0.316601
$735$	9.47105	0.349345
$736$	10.3313	0.380816
$737$	−24.1238	−0.888611
$738$	−30.5731	−1.12541
$739$	19.3502	0.711808	0.355904	−	0.934523i	$-0.384173\pi$
$739$	19.3502	0.711808	0.355904	+	0.934523i	$0.384173\pi$
$740$	−2.31248	−0.0850084
$741$	0	0
$742$	1.67781	0.0615942
$743$	−8.44821	−0.309935	−0.154967	−	0.987920i	$-0.549527\pi$
$743$	−8.44821	−0.309935	−0.154967	+	0.987920i	$0.549527\pi$
$744$	−7.59549	−0.278464
$745$	−34.1797	−1.25225
$746$	−47.4596	−1.73762
$747$	−2.19185	−0.0801957
$748$	0.0140868	0.000515063 0
$749$	−3.61645	−0.132142
$750$	−38.9941	−1.42386
$751$	12.3289	0.449887	0.224944	−	0.974372i	$-0.427780\pi$
$751$	12.3289	0.449887	0.224944	+	0.974372i	$0.427780\pi$
$752$	7.12805	0.259933
$753$	−40.5398	−1.47735
$754$	0	0
$755$	−22.9036	−0.833547
$756$	−0.679835	−0.0247253
$757$	−41.5370	−1.50969	−0.754844	−	0.655904i	$-0.772288\pi$
$757$	−41.5370	−1.50969	−0.754844	+	0.655904i	$0.772288\pi$
$758$	−2.33726	−0.0848929
$759$	−89.5085	−3.24895
$760$	7.90463	0.286731
$761$	−21.4649	−0.778102	−0.389051	−	0.921216i	$-0.627197\pi$
$761$	−21.4649	−0.778102	−0.389051	+	0.921216i	$0.627197\pi$
$762$	−62.1994	−2.25325
$763$	−30.8373	−1.11639
$764$	2.91915	0.105611
$765$	0.0842446	0.00304587
$766$	38.6762	1.39743
$767$	0	0
$768$	−12.9310	−0.466609
$769$	9.70089	0.349823	0.174911	−	0.984584i	$-0.444036\pi$
$769$	9.70089	0.349823	0.174911	+	0.984584i	$0.444036\pi$
$770$	16.1495	0.581988
$771$	−42.4458	−1.52865
$772$	−4.02331	−0.144802
$773$	−31.1116	−1.11901	−0.559504	−	0.828828i	$-0.689008\pi$
$773$	−31.1116	−1.11901	−0.559504	+	0.828828i	$0.689008\pi$
$774$	36.3936	1.30814
$775$	2.96845	0.106630
$776$	−6.14207	−0.220488
$777$	−41.2196	−1.47875
$778$	−37.0228	−1.32733
$779$	−11.9297	−0.427426
$780$	0	0
$781$	30.4594	1.08992
$782$	−0.190006	−0.00679461
$783$	−12.2849	−0.439027
$784$	9.13555	0.326270
$785$	−33.7145	−1.20332
$786$	−31.6355	−1.12840
$787$	12.1713	0.433860	0.216930	−	0.976187i	$-0.430396\pi$
$787$	12.1713	0.433860	0.216930	+	0.976187i	$0.430396\pi$
$788$	−4.71726	−0.168045
$789$	25.6186	0.912046
$790$	−3.26798	−0.116270
$791$	−21.2671	−0.756170
$792$	42.8844	1.52383
$793$	0	0
$794$	−32.0562	−1.13763
$795$	2.18646	0.0775458
$796$	0.989788	0.0350821
$797$	47.5670	1.68491	0.842454	−	0.538768i	$-0.181110\pi$
$797$	47.5670	1.68491	0.842454	+	0.538768i	$0.181110\pi$
$798$	13.5213	0.478648
$799$	0.0332082	0.00117482
$800$	3.54937	0.125489
$801$	−33.6142	−1.18770
$802$	7.02202	0.247956
$803$	3.52698	0.124464
$804$	3.25984	0.114966
$805$	25.8688	0.911757
$806$	0	0
$807$	43.2876	1.52380
$808$	−8.86838	−0.311988
$809$	−18.5449	−0.652006	−0.326003	−	0.945369i	$-0.605702\pi$
$809$	−18.5449	−0.652006	−0.326003	+	0.945369i	$0.605702\pi$
$810$	−13.0857	−0.459784
$811$	−9.31360	−0.327045	−0.163522	−	0.986540i	$-0.552286\pi$
$811$	−9.31360	−0.327045	−0.163522	+	0.986540i	$0.552286\pi$
$812$	3.59368	0.126114
$813$	16.4174	0.575783
$814$	41.2216	1.44481
$815$	0.870349	0.0304870
$816$	0.149096	0.00521942
$817$	14.2009	0.496825
$818$	0.162719	0.00568932
$819$	0	0
$820$	1.92540	0.0672380
$821$	43.2457	1.50928	0.754642	−	0.656137i	$-0.227811\pi$
$821$	43.2457	1.50928	0.754642	+	0.656137i	$0.227811\pi$
$822$	17.4759	0.609543
$823$	−21.7577	−0.758427	−0.379214	−	0.925309i	$-0.623805\pi$
$823$	−21.7577	−0.758427	−0.379214	+	0.925309i	$0.623805\pi$
$824$	33.3837	1.16298
$825$	−30.7512	−1.07062
$826$	35.6067	1.23892
$827$	−17.1833	−0.597521	−0.298761	−	0.954328i	$-0.596573\pi$
$827$	−17.1833	−0.597521	−0.298761	+	0.954328i	$0.596573\pi$
$828$	6.59215	0.229093
$829$	−4.73505	−0.164455	−0.0822276	−	0.996614i	$-0.526203\pi$
$829$	−4.73505	−0.164455	−0.0822276	+	0.996614i	$0.526203\pi$
$830$	−1.16234	−0.0403454
$831$	−34.7230	−1.20453
$832$	0	0
$833$	0.0425607	0.00147464
$834$	−15.3852	−0.532745
$835$	−22.2807	−0.771056
$836$	1.60583	0.0555388
$837$	−1.52447	−0.0526933
$838$	28.4972	0.984419
$839$	2.34123	0.0808283	0.0404141	−	0.999183i	$-0.487132\pi$
$839$	2.34123	0.0808283	0.0404141	+	0.999183i	$0.487132\pi$
$840$	−22.7405	−0.784622
$841$	35.9395	1.23929
$842$	−25.9124	−0.893000
$843$	3.67342	0.126519
$844$	2.21967	0.0764043
$845$	0	0
$846$	9.70160	0.333548
$847$	11.0815	0.380766
$848$	2.10901	0.0724237
$849$	28.2762	0.970437
$850$	−0.0652778	−0.00223901
$851$	66.0301	2.26348
$852$	−4.11597	−0.141011
$853$	−37.8828	−1.29708	−0.648542	−	0.761179i	$-0.724621\pi$
$853$	−37.8828	−1.29708	−0.648542	+	0.761179i	$0.724621\pi$
$854$	−0.115354	−0.00394732
$855$	9.60351	0.328433
$856$	−5.09264	−0.174063
$857$	−18.6049	−0.635532	−0.317766	−	0.948169i	$-0.602933\pi$
$857$	−18.6049	−0.635532	−0.317766	+	0.948169i	$0.602933\pi$
$858$	0	0
$859$	−3.79631	−0.129528	−0.0647642	−	0.997901i	$-0.520630\pi$
$859$	−3.79631	−0.129528	−0.0647642	+	0.997901i	$0.520630\pi$
$860$	−2.29196	−0.0781551
$861$	34.3200	1.16962
$862$	40.1416	1.36723
$863$	−8.65975	−0.294781	−0.147391	−	0.989078i	$-0.547087\pi$
$863$	−8.65975	−0.294781	−0.147391	+	0.989078i	$0.547087\pi$
$864$	−1.82280	−0.0620130
$865$	35.8709	1.21965
$866$	35.9549	1.22180
$867$	−43.6522	−1.48251
$868$	0.445949	0.0151365
$869$	−6.91810	−0.234680
$870$	−39.4348	−1.33696
$871$	0	0
$872$	−43.4247	−1.47055
$873$	−7.46214	−0.252555
$874$	−21.6599	−0.732656
$875$	23.8571	0.806518
$876$	−0.476599	−0.0161028
$877$	−11.2999	−0.381572	−0.190786	−	0.981632i	$-0.561104\pi$
$877$	−11.2999	−0.381572	−0.190786	+	0.981632i	$0.561104\pi$
$878$	1.99113	0.0671973
$879$	−39.6631	−1.33780
$880$	20.3000	0.684313
$881$	−44.4888	−1.49887	−0.749433	−	0.662080i	$-0.769674\pi$
$881$	−44.4888	−1.49887	−0.749433	+	0.662080i	$0.769674\pi$
$882$	12.4339	0.418671
$883$	1.32840	0.0447043	0.0223522	−	0.999750i	$-0.492884\pi$
$883$	1.32840	0.0447043	0.0223522	+	0.999750i	$0.492884\pi$
$884$	0	0
$885$	46.4015	1.55977
$886$	−18.6426	−0.626310
$887$	15.2509	0.512074	0.256037	−	0.966667i	$-0.417583\pi$
$887$	15.2509	0.512074	0.256037	+	0.966667i	$0.417583\pi$
$888$	−58.0450	−1.94786
$889$	38.0545	1.27631
$890$	−17.8256	−0.597514
$891$	−27.7015	−0.928035
$892$	0.556791	0.0186427
$893$	3.78558	0.126680
$894$	−82.3315	−2.75358
$895$	15.1237	0.505530
$896$	−19.2968	−0.644659
$897$	0	0
$898$	35.9416	1.19939
$899$	8.05850	0.268766
$900$	2.26477	0.0754923
$901$	0.00982545	0.000327333 0
$902$	−34.3217	−1.14279
$903$	−40.8538	−1.35953
$904$	−29.9481	−0.996057
$905$	−23.0667	−0.766762
$906$	−55.1697	−1.83289
$907$	−44.2883	−1.47057	−0.735284	−	0.677759i	$-0.762951\pi$
$907$	−44.2883	−1.47057	−0.735284	+	0.677759i	$0.762951\pi$
$908$	−0.0528871	−0.00175512
$909$	−10.7744	−0.357364
$910$	0	0
$911$	−41.1437	−1.36315	−0.681576	−	0.731748i	$-0.738705\pi$
$911$	−41.1437	−1.36315	−0.681576	+	0.731748i	$0.738705\pi$
$912$	16.9963	0.562804
$913$	−2.46059	−0.0814338
$914$	−13.6162	−0.450385
$915$	−0.150325	−0.00496959
$916$	2.28696	0.0755634
$917$	19.3551	0.639160
$918$	0.0335238	0.00110645
$919$	−18.6755	−0.616048	−0.308024	−	0.951379i	$-0.599668\pi$
$919$	−18.6755	−0.616048	−0.308024	+	0.951379i	$0.599668\pi$
$920$	36.4282	1.20100
$921$	80.1899	2.64235
$922$	−28.4266	−0.936182
$923$	0	0
$924$	−4.61974	−0.151978
$925$	22.6850	0.745879
$926$	27.5218	0.904424
$927$	40.5586	1.33212
$928$	9.63553	0.316302
$929$	35.4781	1.16400	0.581999	−	0.813190i	$-0.302271\pi$
$929$	35.4781	1.16400	0.581999	+	0.813190i	$0.302271\pi$
$930$	−4.89356	−0.160466
$931$	4.85173	0.159009
$932$	3.26239	0.106863
$933$	70.9505	2.32282
$934$	42.5634	1.39272
$935$	0.0945737	0.00309289
$936$	0	0
$937$	−25.0262	−0.817570	−0.408785	−	0.912631i	$-0.634047\pi$
$937$	−25.0262	−0.817570	−0.408785	+	0.912631i	$0.634047\pi$
$938$	16.7940	0.548345
$939$	−21.7470	−0.709685
$940$	−0.610977	−0.0199279
$941$	8.53670	0.278289	0.139144	−	0.990272i	$-0.455565\pi$
$941$	8.53670	0.278289	0.139144	+	0.990272i	$0.455565\pi$
$942$	−81.2108	−2.64599
$943$	−54.9776	−1.79032
$944$	44.7578	1.45674
$945$	−4.56418	−0.148473
$946$	40.8557	1.32833
$947$	−51.3960	−1.67015	−0.835073	−	0.550138i	$-0.814575\pi$
$947$	−51.3960	−1.67015	−0.835073	+	0.550138i	$0.814575\pi$
$948$	0.934840	0.0303622
$949$	0	0
$950$	−7.44137	−0.241430
$951$	57.2939	1.85788
$952$	−0.102191	−0.00331202
$953$	21.4764	0.695690	0.347845	−	0.937552i	$-0.386914\pi$
$953$	21.4764	0.695690	0.347845	+	0.937552i	$0.386914\pi$
$954$	2.87045	0.0929344
$955$	19.5982	0.634182
$956$	1.71980	0.0556222
$957$	−83.4808	−2.69855
$958$	2.05714	0.0664631
$959$	−10.6920	−0.345263
$960$	−31.6930	−1.02289
$961$	1.00000	0.0322581
$962$	0	0
$963$	−6.18716	−0.199378
$964$	2.24634	0.0723499
$965$	−27.0111	−0.869519
$966$	62.3123	2.00487
$967$	36.5435	1.17516	0.587580	−	0.809166i	$-0.300081\pi$
$967$	36.5435	1.17516	0.587580	+	0.809166i	$0.300081\pi$
$968$	15.6049	0.501560
$969$	0.0791825	0.00254371
$970$	−3.95717	−0.127057
$971$	−59.7630	−1.91788	−0.958942	−	0.283601i	$-0.908471\pi$
$971$	−59.7630	−1.91788	−0.958942	+	0.283601i	$0.908471\pi$
$972$	4.71424	0.151209
$973$	9.41287	0.301763
$974$	−4.31964	−0.138410
$975$	0	0
$976$	−0.145000	−0.00464134
$977$	54.7276	1.75089	0.875446	−	0.483315i	$-0.160568\pi$
$977$	54.7276	1.75089	0.875446	+	0.483315i	$0.160568\pi$
$978$	2.09648	0.0670380
$979$	−37.7355	−1.20603
$980$	−0.783049	−0.0250136
$981$	−52.7577	−1.68442
$982$	−2.01700	−0.0643651
$983$	−41.4614	−1.32241	−0.661206	−	0.750204i	$-0.729955\pi$
$983$	−41.4614	−1.32241	−0.661206	+	0.750204i	$0.729955\pi$
$984$	48.3291	1.54068
$985$	−31.6700	−1.00909
$986$	−0.177211	−0.00564354
$987$	−10.8906	−0.346651
$988$	0	0
$989$	65.4441	2.08100
$990$	27.6292	0.878114
$991$	4.13712	0.131420	0.0657099	−	0.997839i	$-0.479069\pi$
$991$	4.13712	0.131420	0.0657099	+	0.997839i	$0.479069\pi$
$992$	1.19570	0.0379634
$993$	−50.5786	−1.60506
$994$	−21.2047	−0.672571
$995$	6.64510	0.210664
$996$	0.332499	0.0105356
$997$	−46.5359	−1.47381	−0.736904	−	0.675997i	$-0.763713\pi$
$997$	−46.5359	−1.47381	−0.736904	+	0.675997i	$0.763713\pi$
$998$	−18.4785	−0.584928
$999$	−11.6500	−0.368591

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5239.2.a.t.1.10	yes	36
13.12	even	2		5239.2.a.s.1.27	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5239.2.a.s.1.27	✓	36	13.12	even	2
5239.2.a.t.1.10	yes	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5239 = 13^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5239.a (trivial)

\(f(q)\)	\(=\)	\(q-1.33705 q^{2} +2.56782 q^{3} -0.212302 q^{4} -1.42532 q^{5} -3.43329 q^{6} +2.10054 q^{7} +2.95795 q^{8} +3.59368 q^{9} +1.90573 q^{10} +4.03430 q^{11} -0.545153 q^{12} -2.80852 q^{14} -3.65997 q^{15} -3.53032 q^{16} -0.0164471 q^{17} -4.80493 q^{18} -1.87489 q^{19} +0.302600 q^{20} +5.39380 q^{21} -5.39405 q^{22} -8.64037 q^{23} +7.59549 q^{24} -2.96845 q^{25} +1.52447 q^{27} -0.445949 q^{28} -8.05850 q^{29} +4.89356 q^{30} -1.00000 q^{31} -1.19570 q^{32} +10.3593 q^{33} +0.0219905 q^{34} -2.99395 q^{35} -0.762947 q^{36} -7.64204 q^{37} +2.50682 q^{38} -4.21605 q^{40} +6.36287 q^{41} -7.21177 q^{42} -7.57422 q^{43} -0.856491 q^{44} -5.12216 q^{45} +11.5526 q^{46} -2.01909 q^{47} -9.06522 q^{48} -2.58774 q^{49} +3.96896 q^{50} -0.0422331 q^{51} -0.597398 q^{53} -2.03829 q^{54} -5.75019 q^{55} +6.21330 q^{56} -4.81438 q^{57} +10.7746 q^{58} -12.6781 q^{59} +0.777021 q^{60} +0.0410727 q^{61} +1.33705 q^{62} +7.54867 q^{63} +8.65935 q^{64} -13.8509 q^{66} -5.97968 q^{67} +0.00349175 q^{68} -22.1869 q^{69} +4.00305 q^{70} +7.55012 q^{71} +10.6299 q^{72} +0.874248 q^{73} +10.2178 q^{74} -7.62243 q^{75} +0.398044 q^{76} +8.47420 q^{77} -1.71482 q^{79} +5.03186 q^{80} -6.86650 q^{81} -8.50747 q^{82} -0.609918 q^{83} -1.14512 q^{84} +0.0234424 q^{85} +10.1271 q^{86} -20.6928 q^{87} +11.9333 q^{88} -9.35368 q^{89} +6.84858 q^{90} +1.83437 q^{92} -2.56782 q^{93} +2.69963 q^{94} +2.67233 q^{95} -3.07033 q^{96} -2.07646 q^{97} +3.45993 q^{98} +14.4980 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} - 5 q^{3} + 28 q^{4} + 5 q^{5} - 3 q^{6} + 5 q^{7} + 3 q^{8} + 5 q^{9} - 15 q^{10} - q^{11} - 13 q^{12} - 19 q^{14} - 10 q^{15} + 4 q^{16} - 46 q^{17} - 9 q^{18} + 8 q^{19} - 5 q^{20} - 16 q^{21}+ \cdots - 47 q^{99}+O(q^{100}) \) 36 * q + 2 * q^2 - 5 * q^3 + 28 * q^4 + 5 * q^5 - 3 * q^6 + 5 * q^7 + 3 * q^8 + 5 * q^9 - 15 * q^10 - q^11 - 13 * q^12 - 19 * q^14 - 10 * q^15 + 4 * q^16 - 46 * q^17 - 9 * q^18 + 8 * q^19 - 5 * q^20 - 16 * q^21 - 21 * q^22 - 24 * q^23 + 57 * q^24 + 5 * q^25 - 11 * q^27 - 32 * q^28 - 73 * q^29 - 31 * q^30 - 36 * q^31 + 3 * q^32 - 8 * q^33 - 37 * q^34 - 31 * q^35 - 31 * q^36 + 6 * q^37 - 25 * q^38 - 22 * q^40 + 6 * q^41 - 37 * q^42 - 37 * q^43 - 16 * q^45 - 45 * q^46 + 13 * q^47 - 46 * q^48 - 5 * q^49 + 24 * q^50 - 46 * q^51 - 42 * q^53 - 26 * q^54 - 47 * q^55 - 95 * q^56 + 33 * q^57 + 9 * q^58 + 20 * q^59 - 40 * q^60 - 48 * q^61 - 2 * q^62 + 52 * q^63 + 21 * q^64 - 4 * q^66 - 50 * q^67 - 76 * q^68 - 33 * q^69 + 93 * q^70 + 16 * q^71 - 52 * q^72 - 43 * q^73 - 76 * q^74 - 40 * q^75 + 62 * q^76 - 47 * q^77 - 43 * q^79 - 46 * q^80 - 96 * q^81 + 7 * q^82 + 9 * q^83 - 77 * q^84 - 5 * q^85 + 64 * q^86 - 8 * q^87 - 54 * q^88 + 6 * q^89 + 27 * q^90 - 35 * q^92 + 5 * q^93 - 76 * q^94 - 63 * q^95 + 72 * q^96 - 4 * q^97 - 41 * q^98 - 47 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more