LMFDB - Embedded newform 5819.2.a.u.1.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [5819,2,Mod(1,5819)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5819, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("5819.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 5819 = 11 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5819.a (trivial)

Newform invariants

comment:select newform

sage:traces = [60,5,9,73,8] 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:	$46.4649489362$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	no (minimal twist has level 253)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	5819.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.03269 q^{2} +1.07604 q^{3} +2.13185 q^{4} +0.410257 q^{5} -2.18727 q^{6} +4.26763 q^{7} -0.268004 q^{8} -1.84213 q^{9} -0.833927 q^{10} +1.00000 q^{11} +2.29396 q^{12} -1.13363 q^{13} -8.67478 q^{14} +0.441455 q^{15} -3.71892 q^{16} +1.83597 q^{17} +3.74449 q^{18} +5.52428 q^{19} +0.874605 q^{20} +4.59216 q^{21} -2.03269 q^{22} -0.288384 q^{24} -4.83169 q^{25} +2.30432 q^{26} -5.21034 q^{27} +9.09793 q^{28} -7.28033 q^{29} -0.897342 q^{30} -9.07836 q^{31} +8.09544 q^{32} +1.07604 q^{33} -3.73197 q^{34} +1.75082 q^{35} -3.92714 q^{36} +10.0489 q^{37} -11.2292 q^{38} -1.21983 q^{39} -0.109950 q^{40} +9.84403 q^{41} -9.33445 q^{42} +2.29332 q^{43} +2.13185 q^{44} -0.755746 q^{45} +2.36835 q^{47} -4.00173 q^{48} +11.2126 q^{49} +9.82135 q^{50} +1.97559 q^{51} -2.41672 q^{52} -4.17752 q^{53} +10.5910 q^{54} +0.410257 q^{55} -1.14374 q^{56} +5.94437 q^{57} +14.7987 q^{58} -4.33626 q^{59} +0.941114 q^{60} -5.04035 q^{61} +18.4535 q^{62} -7.86152 q^{63} -9.01771 q^{64} -0.465078 q^{65} -2.18727 q^{66} +11.8136 q^{67} +3.91401 q^{68} -3.55889 q^{70} -5.38445 q^{71} +0.493698 q^{72} +10.9055 q^{73} -20.4264 q^{74} -5.19911 q^{75} +11.7769 q^{76} +4.26763 q^{77} +2.47955 q^{78} +8.85428 q^{79} -1.52571 q^{80} -0.0801725 q^{81} -20.0099 q^{82} +2.55026 q^{83} +9.78977 q^{84} +0.753220 q^{85} -4.66162 q^{86} -7.83396 q^{87} -0.268004 q^{88} +2.04836 q^{89} +1.53620 q^{90} -4.83789 q^{91} -9.76872 q^{93} -4.81413 q^{94} +2.26638 q^{95} +8.71105 q^{96} -9.82847 q^{97} -22.7919 q^{98} -1.84213 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 5 q^{2} + 9 q^{3} + 73 q^{4} + 8 q^{5} + 26 q^{6} + 30 q^{8} + 75 q^{9} - 7 q^{10} + 60 q^{11} + 41 q^{12} + 46 q^{13} + 16 q^{14} + 4 q^{15} + 99 q^{16} - 5 q^{17} + 36 q^{18} - 8 q^{19} + 82 q^{20}+ \cdots + 75 q^{99}+O(q^{100}) $ 60 * q + 5 * q^2 + 9 * q^3 + 73 * q^4 + 8 * q^5 + 26 * q^6 + 30 * q^8 + 75 * q^9 - 7 * q^10 + 60 * q^11 + 41 * q^12 + 46 * q^13 + 16 * q^14 + 4 * q^15 + 99 * q^16 - 5 * q^17 + 36 * q^18 - 8 * q^19 + 82 * q^20 - 13 * q^21 + 5 * q^22 + 54 * q^24 + 96 * q^25 + 31 * q^26 + 54 * q^27 - 29 * q^28 + 42 * q^29 - 14 * q^30 + 71 * q^31 + 40 * q^32 + 9 * q^33 + 10 * q^34 + 9 * q^35 + 93 * q^36 - 5 * q^37 - 11 * q^38 + 56 * q^39 - 40 * q^40 + 62 * q^41 + 43 * q^42 - 2 * q^43 + 73 * q^44 - q^45 - q^47 + 71 * q^48 + 138 * q^49 - 18 * q^50 - 27 * q^51 + 102 * q^52 + 11 * q^53 + 69 * q^54 + 8 * q^55 + 13 * q^56 + 38 * q^57 + 58 * q^58 + 57 * q^59 - 49 * q^60 - 26 * q^61 + 17 * q^62 - 41 * q^63 + 184 * q^64 - 19 * q^65 + 26 * q^66 + 7 * q^67 - 76 * q^68 + 43 * q^70 + 33 * q^71 + 100 * q^72 + 108 * q^73 - 63 * q^74 + q^75 - 42 * q^76 - 3 * q^78 - 25 * q^79 + 148 * q^80 + 68 * q^81 + 59 * q^82 - 41 * q^83 - 97 * q^84 + 160 * q^85 + 78 * q^86 + 41 * q^87 + 30 * q^88 + 51 * q^89 - 53 * q^90 + 65 * q^93 + 121 * q^94 - 14 * q^95 + 82 * q^96 - 13 * q^97 - 75 * q^98 + 75 * 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 $

$2$	−2.03269	−1.43733	−0.718666	−	0.695355i	$-0.755247\pi$
$2$	−2.03269	−1.43733	−0.718666	+	0.695355i	$0.755247\pi$
$3$	1.07604	0.621254	0.310627	−	0.950532i	$-0.399461\pi$
$3$	1.07604	0.621254	0.310627	+	0.950532i	$0.399461\pi$
$4$	2.13185	1.06592
$5$	0.410257	0.183473	0.0917363	−	0.995783i	$-0.470758\pi$
$5$	0.410257	0.183473	0.0917363	+	0.995783i	$0.470758\pi$
$6$	−2.18727	−0.892949
$7$	4.26763	1.61301	0.806506	−	0.591226i	$-0.201356\pi$
$7$	4.26763	1.61301	0.806506	+	0.591226i	$0.201356\pi$
$8$	−0.268004	−0.0947536
$9$	−1.84213	−0.614043
$10$	−0.833927	−0.263711
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.29396	0.662209
$13$	−1.13363	−0.314411	−0.157206	−	0.987566i	$-0.550249\pi$
$13$	−1.13363	−0.314411	−0.157206	+	0.987566i	$0.550249\pi$
$14$	−8.67478	−2.31843
$15$	0.441455	0.113983
$16$	−3.71892	−0.929731
$17$	1.83597	0.445288	0.222644	−	0.974900i	$-0.428531\pi$
$17$	1.83597	0.445288	0.222644	+	0.974900i	$0.428531\pi$
$18$	3.74449	0.882584
$19$	5.52428	1.26736	0.633679	−	0.773596i	$-0.281544\pi$
$19$	5.52428	1.26736	0.633679	+	0.773596i	$0.281544\pi$
$20$	0.874605	0.195568
$21$	4.59216	1.00209
$22$	−2.03269	−0.433372
$23$	0	0
$23$	0	0
$24$	−0.288384	−0.0588661
$25$	−4.83169	−0.966338
$26$	2.30432	0.451913
$27$	−5.21034	−1.00273
$28$	9.09793	1.71935
$29$	−7.28033	−1.35192	−0.675962	−	0.736937i	$-0.736272\pi$
$29$	−7.28033	−1.35192	−0.675962	+	0.736937i	$0.736272\pi$
$30$	−0.897342	−0.163832
$31$	−9.07836	−1.63052	−0.815261	−	0.579094i	$-0.803406\pi$
$31$	−9.07836	−1.63052	−0.815261	+	0.579094i	$0.803406\pi$
$32$	8.09544	1.43109
$33$	1.07604	0.187315
$34$	−3.73197	−0.640027
$35$	1.75082	0.295943
$36$	−3.92714	−0.654523
$37$	10.0489	1.65203	0.826016	−	0.563647i	$-0.190602\pi$
$37$	10.0489	1.65203	0.826016	+	0.563647i	$0.190602\pi$
$38$	−11.2292	−1.82161
$39$	−1.21983	−0.195329
$40$	−0.109950	−0.0173847
$41$	9.84403	1.53738	0.768690	−	0.639622i	$-0.220909\pi$
$41$	9.84403	1.53738	0.768690	+	0.639622i	$0.220909\pi$
$42$	−9.33445	−1.44034
$43$	2.29332	0.349728	0.174864	−	0.984593i	$-0.444051\pi$
$43$	2.29332	0.349728	0.174864	+	0.984593i	$0.444051\pi$
$44$	2.13185	0.321388
$45$	−0.755746	−0.112660
$46$	0	0
$47$	2.36835	0.345459	0.172730	−	0.984969i	$-0.444741\pi$
$47$	2.36835	0.345459	0.172730	+	0.984969i	$0.444741\pi$
$48$	−4.00173	−0.577599
$49$	11.2126	1.60181
$50$	9.82135	1.38895
$51$	1.97559	0.276637
$52$	−2.41672	−0.335138
$53$	−4.17752	−0.573826	−0.286913	−	0.957957i	$-0.592629\pi$
$53$	−4.17752	−0.573826	−0.286913	+	0.957957i	$0.592629\pi$
$54$	10.5910	1.44126
$55$	0.410257	0.0553190
$56$	−1.14374	−0.152839
$57$	5.94437	0.787351
$58$	14.7987	1.94316
$59$	−4.33626	−0.564533	−0.282266	−	0.959336i	$-0.591086\pi$
$59$	−4.33626	−0.564533	−0.282266	+	0.959336i	$0.591086\pi$
$60$	0.941114	0.121497
$61$	−5.04035	−0.645351	−0.322676	−	0.946510i	$-0.604582\pi$
$61$	−5.04035	−0.645351	−0.322676	+	0.946510i	$0.604582\pi$
$62$	18.4535	2.34360
$63$	−7.86152	−0.990459
$64$	−9.01771	−1.12721
$65$	−0.465078	−0.0576858
$66$	−2.18727	−0.269234
$67$	11.8136	1.44326	0.721632	−	0.692277i	$-0.243392\pi$
$67$	11.8136	1.44326	0.721632	+	0.692277i	$0.243392\pi$
$68$	3.91401	0.474643
$69$	0	0
$70$	−3.55889	−0.425369
$71$	−5.38445	−0.639016	−0.319508	−	0.947584i	$-0.603518\pi$
$71$	−5.38445	−0.639016	−0.319508	+	0.947584i	$0.603518\pi$
$72$	0.493698	0.0581828
$73$	10.9055	1.27639	0.638194	−	0.769875i	$-0.279682\pi$
$73$	10.9055	1.27639	0.638194	+	0.769875i	$0.279682\pi$
$74$	−20.4264	−2.37452
$75$	−5.19911	−0.600342
$76$	11.7769	1.35091
$77$	4.26763	0.486341
$78$	2.47955	0.280753
$79$	8.85428	0.996184	0.498092	−	0.867124i	$-0.334034\pi$
$79$	8.85428	0.996184	0.498092	+	0.867124i	$0.334034\pi$
$80$	−1.52571	−0.170580
$81$	−0.0801725	−0.00890805
$82$	−20.0099	−2.20973
$83$	2.55026	0.279927	0.139964	−	0.990157i	$-0.455301\pi$
$83$	2.55026	0.279927	0.139964	+	0.990157i	$0.455301\pi$
$84$	9.78977	1.06815
$85$	0.753220	0.0816982
$86$	−4.66162	−0.502675
$87$	−7.83396	−0.839888
$88$	−0.268004	−0.0285693
$89$	2.04836	0.217126	0.108563	−	0.994090i	$-0.465375\pi$
$89$	2.04836	0.217126	0.108563	+	0.994090i	$0.465375\pi$
$90$	1.53620	0.161930
$91$	−4.83789	−0.507149
$92$	0	0
$93$	−9.76872	−1.01297
$94$	−4.81413	−0.496540
$95$	2.26638	0.232525
$96$	8.71105	0.889068
$97$	−9.82847	−0.997930	−0.498965	−	0.866622i	$-0.666286\pi$
$97$	−9.82847	−0.997930	−0.498965	+	0.866622i	$0.666286\pi$
$98$	−22.7919	−2.30233
$99$	−1.84213	−0.185141
$100$	−10.3004	−1.03004
$101$	11.8548	1.17960	0.589800	−	0.807550i	$-0.299207\pi$
$101$	11.8548	1.17960	0.589800	+	0.807550i	$0.299207\pi$
$102$	−4.01576	−0.397620
$103$	14.1414	1.39339	0.696697	−	0.717366i	$-0.254652\pi$
$103$	14.1414	1.39339	0.696697	+	0.717366i	$0.254652\pi$
$104$	0.303816	0.0297916
$105$	1.88396	0.183856
$106$	8.49161	0.824778
$107$	14.0842	1.36157	0.680786	−	0.732483i	$-0.261639\pi$
$107$	14.0842	1.36157	0.680786	+	0.732483i	$0.261639\pi$
$108$	−11.1077	−1.06883
$109$	1.64522	0.157583	0.0787916	−	0.996891i	$-0.474894\pi$
$109$	1.64522	0.157583	0.0787916	+	0.996891i	$0.474894\pi$
$110$	−0.833927	−0.0795118
$111$	10.8131	1.02633
$112$	−15.8710	−1.49967
$113$	1.19898	0.112791	0.0563954	−	0.998409i	$-0.482039\pi$
$113$	1.19898	0.112791	0.0563954	+	0.998409i	$0.482039\pi$
$114$	−12.0831	−1.13169
$115$	0	0
$116$	−15.5205	−1.44105
$117$	2.08829	0.193062
$118$	8.81429	0.811421
$119$	7.83524	0.718255
$120$	−0.118312	−0.0108003
$121$	1.00000	0.0909091
$122$	10.2455	0.927584
$123$	10.5926	0.955104
$124$	−19.3537	−1.73801
$125$	−4.03352	−0.360769
$126$	15.9801	1.42362
$127$	17.9572	1.59344	0.796721	−	0.604348i	$-0.206566\pi$
$127$	17.9572	1.59344	0.796721	+	0.604348i	$0.206566\pi$
$128$	2.13937	0.189095
$129$	2.46771	0.217270
$130$	0.945362	0.0829137
$131$	−13.6801	−1.19524	−0.597618	−	0.801781i	$-0.703886\pi$
$131$	−13.6801	−1.19524	−0.597618	+	0.801781i	$0.703886\pi$
$132$	2.29396	0.199664
$133$	23.5756	2.04426
$134$	−24.0135	−2.07445
$135$	−2.13758	−0.183974
$136$	−0.492047	−0.0421927
$137$	20.1737	1.72355	0.861777	−	0.507288i	$-0.169352\pi$
$137$	20.1737	1.72355	0.861777	+	0.507288i	$0.169352\pi$
$138$	0	0
$139$	−0.829831	−0.0703853	−0.0351927	−	0.999381i	$-0.511204\pi$
$139$	−0.829831	−0.0703853	−0.0351927	+	0.999381i	$0.511204\pi$
$140$	3.73249	0.315453
$141$	2.54845	0.214618
$142$	10.9449	0.918478
$143$	−1.13363	−0.0947986
$144$	6.85074	0.570895
$145$	−2.98681	−0.248041
$146$	−22.1675	−1.83459
$147$	12.0653	0.995129
$148$	21.4227	1.76094
$149$	−7.69477	−0.630380	−0.315190	−	0.949029i	$-0.602068\pi$
$149$	−7.69477	−0.630380	−0.315190	+	0.949029i	$0.602068\pi$
$150$	10.5682	0.862890
$151$	13.1253	1.06812	0.534062	−	0.845445i	$-0.320665\pi$
$151$	13.1253	1.06812	0.534062	+	0.845445i	$0.320665\pi$
$152$	−1.48053	−0.120087
$153$	−3.38209	−0.273426
$154$	−8.67478	−0.699034
$155$	−3.72446	−0.299156
$156$	−2.60049	−0.208206
$157$	5.16506	0.412216	0.206108	−	0.978529i	$-0.433920\pi$
$157$	5.16506	0.412216	0.206108	+	0.978529i	$0.433920\pi$
$158$	−17.9980	−1.43185
$159$	−4.49519	−0.356492
$160$	3.32121	0.262565
$161$	0	0
$162$	0.162966	0.0128038
$163$	9.97894	0.781611	0.390806	−	0.920473i	$-0.372196\pi$
$163$	9.97894	0.781611	0.390806	+	0.920473i	$0.372196\pi$
$164$	20.9860	1.63873
$165$	0.441455	0.0343672
$166$	−5.18389	−0.402348
$167$	−10.1447	−0.785018	−0.392509	−	0.919748i	$-0.628393\pi$
$167$	−10.1447	−0.785018	−0.392509	+	0.919748i	$0.628393\pi$
$168$	−1.23071	−0.0949517
$169$	−11.7149	−0.901146
$170$	−1.53107	−0.117427
$171$	−10.1764	−0.778212
$172$	4.88900	0.372783
$173$	12.4819	0.948982	0.474491	−	0.880260i	$-0.342632\pi$
$173$	12.4819	0.948982	0.474491	+	0.880260i	$0.342632\pi$
$174$	15.9240	1.20720
$175$	−20.6198	−1.55871
$176$	−3.71892	−0.280324
$177$	−4.66601	−0.350718
$178$	−4.16369	−0.312082
$179$	4.29725	0.321192	0.160596	−	0.987020i	$-0.448658\pi$
$179$	4.29725	0.321192	0.160596	+	0.987020i	$0.448658\pi$
$180$	−1.61114	−0.120087
$181$	4.64826	0.345502	0.172751	−	0.984966i	$-0.444734\pi$
$181$	4.64826	0.345502	0.172751	+	0.984966i	$0.444734\pi$
$182$	9.83396	0.728942
$183$	−5.42364	−0.400927
$184$	0	0
$185$	4.12264	0.303102
$186$	19.8568	1.45597
$187$	1.83597	0.134259
$188$	5.04896	0.368233
$189$	−22.2358	−1.61742
$190$	−4.60685	−0.334216
$191$	8.89964	0.643955	0.321978	−	0.946747i	$-0.395652\pi$
$191$	8.89964	0.643955	0.321978	+	0.946747i	$0.395652\pi$
$192$	−9.70346	−0.700287
$193$	−18.1016	−1.30298	−0.651491	−	0.758656i	$-0.725856\pi$
$193$	−18.1016	−1.30298	−0.651491	+	0.758656i	$0.725856\pi$
$194$	19.9783	1.43436
$195$	−0.500445	−0.0358376
$196$	23.9036	1.70740
$197$	6.56843	0.467981	0.233991	−	0.972239i	$-0.424822\pi$
$197$	6.56843	0.467981	0.233991	+	0.972239i	$0.424822\pi$
$198$	3.74449	0.266109
$199$	3.07539	0.218009	0.109004	−	0.994041i	$-0.465234\pi$
$199$	3.07539	0.218009	0.109004	+	0.994041i	$0.465234\pi$
$200$	1.29491	0.0915640
$201$	12.7120	0.896634
$202$	−24.0972	−1.69548
$203$	−31.0697	−2.18067
$204$	4.21164	0.294874
$205$	4.03858	0.282067
$206$	−28.7451	−2.00277
$207$	0	0
$208$	4.21587	0.292318
$209$	5.52428	0.382123
$210$	−3.82952	−0.264262
$211$	−12.3299	−0.848825	−0.424413	−	0.905469i	$-0.639519\pi$
$211$	−12.3299	−0.848825	−0.424413	+	0.905469i	$0.639519\pi$
$212$	−8.90582	−0.611654
$213$	−5.79390	−0.396992
$214$	−28.6289	−1.95703
$215$	0.940850	0.0641654
$216$	1.39639	0.0950124
$217$	−38.7431	−2.63005
$218$	−3.34422	−0.226499
$219$	11.7348	0.792962
$220$	0.874605	0.0589659
$221$	−2.08130	−0.140004
$222$	−21.9797	−1.47518
$223$	25.7156	1.72204	0.861021	−	0.508569i	$-0.169825\pi$
$223$	25.7156	1.72204	0.861021	+	0.508569i	$0.169825\pi$
$224$	34.5483	2.30836
$225$	8.90060	0.593373
$226$	−2.43716	−0.162118
$227$	−2.01299	−0.133607	−0.0668035	−	0.997766i	$-0.521280\pi$
$227$	−2.01299	−0.133607	−0.0668035	+	0.997766i	$0.521280\pi$
$228$	12.6725	0.839256
$229$	19.9468	1.31812	0.659061	−	0.752089i	$-0.270954\pi$
$229$	19.9468	1.31812	0.659061	+	0.752089i	$0.270954\pi$
$230$	0	0
$231$	4.59216	0.302142
$232$	1.95116	0.128100
$233$	−13.7177	−0.898677	−0.449338	−	0.893362i	$-0.648340\pi$
$233$	−13.7177	−0.898677	−0.449338	+	0.893362i	$0.648340\pi$
$234$	−4.24485	−0.277494
$235$	0.971632	0.0633823
$236$	−9.24424	−0.601749
$237$	9.52759	0.618884
$238$	−15.9266	−1.03237
$239$	−8.72044	−0.564078	−0.282039	−	0.959403i	$-0.591011\pi$
$239$	−8.72044	−0.564078	−0.282039	+	0.959403i	$0.591011\pi$
$240$	−1.64174	−0.105974
$241$	5.35123	0.344703	0.172351	−	0.985036i	$-0.444864\pi$
$241$	5.35123	0.344703	0.172351	+	0.985036i	$0.444864\pi$
$242$	−2.03269	−0.130667
$243$	15.5448	0.997197
$244$	−10.7453	−0.687895
$245$	4.60007	0.293887
$246$	−21.5315	−1.37280
$247$	−6.26247	−0.398472
$248$	2.43303	0.154498
$249$	2.74419	0.173906
$250$	8.19891	0.518545
$251$	−16.3988	−1.03508	−0.517541	−	0.855659i	$-0.673152\pi$
$251$	−16.3988	−1.03508	−0.517541	+	0.855659i	$0.673152\pi$
$252$	−16.7596	−1.05575
$253$	0	0
$254$	−36.5014	−2.29030
$255$	0.810498	0.0507553
$256$	13.6867	0.855421
$257$	−8.13632	−0.507530	−0.253765	−	0.967266i	$-0.581669\pi$
$257$	−8.13632	−0.507530	−0.253765	+	0.967266i	$0.581669\pi$
$258$	−5.01610	−0.312289
$259$	42.8850	2.66475
$260$	−0.991475	−0.0614887
$261$	13.4113	0.830139
$262$	27.8075	1.71795
$263$	−21.1511	−1.30423	−0.652116	−	0.758120i	$-0.726118\pi$
$263$	−21.1511	−1.30423	−0.652116	+	0.758120i	$0.726118\pi$
$264$	−0.288384	−0.0177488
$265$	−1.71386	−0.105281
$266$	−47.9220	−2.93828
$267$	2.20413	0.134890
$268$	25.1848	1.53841
$269$	−28.7752	−1.75445	−0.877226	−	0.480077i	$-0.840609\pi$
$269$	−28.7752	−1.75445	−0.877226	+	0.480077i	$0.840609\pi$
$270$	4.34505	0.264431
$271$	8.54800	0.519254	0.259627	−	0.965709i	$-0.416400\pi$
$271$	8.54800	0.519254	0.259627	+	0.965709i	$0.416400\pi$
$272$	−6.82783	−0.413998
$273$	−5.20579	−0.315069
$274$	−41.0069	−2.47732
$275$	−4.83169	−0.291362
$276$	0	0
$277$	3.57776	0.214967	0.107483	−	0.994207i	$-0.465721\pi$
$277$	3.57776	0.214967	0.107483	+	0.994207i	$0.465721\pi$
$278$	1.68679	0.101167
$279$	16.7235	1.00121
$280$	−0.469227	−0.0280417
$281$	−20.2428	−1.20759	−0.603793	−	0.797141i	$-0.706345\pi$
$281$	−20.2428	−1.20759	−0.603793	+	0.797141i	$0.706345\pi$
$282$	−5.18022	−0.308478
$283$	15.7206	0.934492	0.467246	−	0.884127i	$-0.345246\pi$
$283$	15.7206	0.934492	0.467246	+	0.884127i	$0.345246\pi$
$284$	−11.4788	−0.681142
$285$	2.43872	0.144457
$286$	2.30432	0.136257
$287$	42.0107	2.47981
$288$	−14.9129	−0.878748
$289$	−13.6292	−0.801718
$290$	6.07127	0.356517
$291$	−10.5759	−0.619969
$292$	23.2488	1.36053
$293$	6.24189	0.364655	0.182328	−	0.983238i	$-0.441637\pi$
$293$	6.24189	0.364655	0.182328	+	0.983238i	$0.441637\pi$
$294$	−24.5251	−1.43033
$295$	−1.77898	−0.103576
$296$	−2.69315	−0.156536
$297$	−5.21034	−0.302335
$298$	15.6411	0.906065
$299$	0	0
$300$	−11.0837	−0.639918
$301$	9.78703	0.564115
$302$	−26.6798	−1.53525
$303$	12.7563	0.732831
$304$	−20.5444	−1.17830
$305$	−2.06784	−0.118404
$306$	6.87477	0.393004
$307$	6.72906	0.384048	0.192024	−	0.981390i	$-0.438495\pi$
$307$	6.72906	0.384048	0.192024	+	0.981390i	$0.438495\pi$
$308$	9.09793	0.518402
$309$	15.2168	0.865652
$310$	7.57069	0.429986
$311$	−18.9075	−1.07214	−0.536072	−	0.844172i	$-0.680093\pi$
$311$	−18.9075	−1.07214	−0.536072	+	0.844172i	$0.680093\pi$
$312$	0.326919	0.0185082
$313$	−8.44851	−0.477538	−0.238769	−	0.971076i	$-0.576744\pi$
$313$	−8.44851	−0.477538	−0.238769	+	0.971076i	$0.576744\pi$
$314$	−10.4990	−0.592492
$315$	−3.22524	−0.181722
$316$	18.8760	1.06186
$317$	21.1314	1.18686	0.593429	−	0.804886i	$-0.297774\pi$
$317$	21.1314	1.18686	0.593429	+	0.804886i	$0.297774\pi$
$318$	9.13735	0.512397
$319$	−7.28033	−0.407620
$320$	−3.69958	−0.206813
$321$	15.1552	0.845882
$322$	0	0
$323$	10.1424	0.564339
$324$	−0.170915	−0.00949530
$325$	5.47733	0.303828
$326$	−20.2841	−1.12343
$327$	1.77033	0.0978992
$328$	−2.63824	−0.145672
$329$	10.1072	0.557230
$330$	−0.897342	−0.0493971
$331$	−8.78571	−0.482906	−0.241453	−	0.970412i	$-0.577624\pi$
$331$	−8.78571	−0.482906	−0.241453	+	0.970412i	$0.577624\pi$
$332$	5.43676	0.298381
$333$	−18.5114	−1.01442
$334$	20.6210	1.12833
$335$	4.84662	0.264799
$336$	−17.0779	−0.931674
$337$	9.46485	0.515583	0.257792	−	0.966201i	$-0.417005\pi$
$337$	9.46485	0.515583	0.257792	+	0.966201i	$0.417005\pi$
$338$	23.8128	1.29525
$339$	1.29016	0.0700717
$340$	1.60575	0.0870840
$341$	−9.07836	−0.491621
$342$	20.6856	1.11855
$343$	17.9780	0.970721
$344$	−0.614618	−0.0331380
$345$	0	0
$346$	−25.3719	−1.36400
$347$	−13.5027	−0.724866	−0.362433	−	0.932010i	$-0.618054\pi$
$347$	−13.5027	−0.724866	−0.362433	+	0.932010i	$0.618054\pi$
$348$	−16.7008	−0.895257
$349$	22.9371	1.22780	0.613898	−	0.789385i	$-0.289600\pi$
$349$	22.9371	1.22780	0.613898	+	0.789385i	$0.289600\pi$
$350$	41.9139	2.24039
$351$	5.90658	0.315270
$352$	8.09544	0.431489
$353$	−13.2279	−0.704052	−0.352026	−	0.935990i	$-0.614507\pi$
$353$	−13.2279	−0.704052	−0.352026	+	0.935990i	$0.614507\pi$
$354$	9.48456	0.504099
$355$	−2.20901	−0.117242
$356$	4.36679	0.231439
$357$	8.43106	0.446219
$358$	−8.73500	−0.461659
$359$	4.69699	0.247898	0.123949	−	0.992289i	$-0.460444\pi$
$359$	4.69699	0.247898	0.123949	+	0.992289i	$0.460444\pi$
$360$	0.202543	0.0106749
$361$	11.5177	0.606195
$362$	−9.44849	−0.496601
$363$	1.07604	0.0564777
$364$	−10.3136	−0.540582
$365$	4.47404	0.234182
$366$	11.0246	0.576265
$367$	33.1406	1.72993	0.864963	−	0.501835i	$-0.167342\pi$
$367$	33.1406	1.72993	0.864963	+	0.501835i	$0.167342\pi$
$368$	0	0
$369$	−18.1340	−0.944017
$370$	−8.38006	−0.435659
$371$	−17.8281	−0.925588
$372$	−20.8254	−1.07975
$373$	−11.1381	−0.576706	−0.288353	−	0.957524i	$-0.593108\pi$
$373$	−11.1381	−0.576706	−0.288353	+	0.957524i	$0.593108\pi$
$374$	−3.73197	−0.192975
$375$	−4.34025	−0.224129
$376$	−0.634727	−0.0327335
$377$	8.25317	0.425060
$378$	45.1986	2.32477
$379$	−7.06630	−0.362972	−0.181486	−	0.983394i	$-0.558091\pi$
$379$	−7.06630	−0.362972	−0.181486	+	0.983394i	$0.558091\pi$
$380$	4.83157	0.247854
$381$	19.3227	0.989932
$382$	−18.0903	−0.925578
$383$	12.0185	0.614119	0.307060	−	0.951690i	$-0.400655\pi$
$383$	12.0185	0.614119	0.307060	+	0.951690i	$0.400655\pi$
$384$	2.30206	0.117476
$385$	1.75082	0.0892303
$386$	36.7950	1.87282
$387$	−4.22459	−0.214748
$388$	−20.9528	−1.06372
$389$	−4.81673	−0.244218	−0.122109	−	0.992517i	$-0.538966\pi$
$389$	−4.81673	−0.244218	−0.122109	+	0.992517i	$0.538966\pi$
$390$	1.01725	0.0515105
$391$	0	0
$392$	−3.00503	−0.151777
$393$	−14.7204	−0.742546
$394$	−13.3516	−0.672644
$395$	3.63253	0.182772
$396$	−3.92714	−0.197346
$397$	−27.5316	−1.38177	−0.690886	−	0.722964i	$-0.742779\pi$
$397$	−27.5316	−1.38177	−0.690886	+	0.722964i	$0.742779\pi$
$398$	−6.25133	−0.313351
$399$	25.3684	1.27001
$400$	17.9687	0.898434
$401$	−28.1334	−1.40492	−0.702458	−	0.711725i	$-0.747914\pi$
$401$	−28.1334	−1.40492	−0.702458	+	0.711725i	$0.747914\pi$
$402$	−25.8396	−1.28876
$403$	10.2915	0.512654
$404$	25.2727	1.25736
$405$	−0.0328913	−0.00163438
$406$	63.1553	3.13434
$407$	10.0489	0.498106
$408$	−0.529464	−0.0262124
$409$	−29.6682	−1.46700	−0.733500	−	0.679689i	$-0.762115\pi$
$409$	−29.6682	−1.46700	−0.733500	+	0.679689i	$0.762115\pi$
$410$	−8.20921	−0.405424
$411$	21.7078	1.07076
$412$	30.1473	1.48525
$413$	−18.5055	−0.910598
$414$	0	0
$415$	1.04626	0.0513589
$416$	−9.17721	−0.449950
$417$	−0.892935	−0.0437272
$418$	−11.2292	−0.549237
$419$	0.114691	0.00560304	0.00280152	−	0.999996i	$-0.499108\pi$
$419$	0.114691	0.00560304	0.00280152	+	0.999996i	$0.499108\pi$
$420$	4.01632	0.195976
$421$	−33.9728	−1.65573	−0.827866	−	0.560926i	$-0.810445\pi$
$421$	−33.9728	−1.65573	−0.827866	+	0.560926i	$0.810445\pi$
$422$	25.0629	1.22004
$423$	−4.36281	−0.212127
$424$	1.11959	0.0543721
$425$	−8.87084	−0.430299
$426$	11.7772	0.570609
$427$	−21.5103	−1.04096
$428$	30.0254	1.45133
$429$	−1.21983	−0.0588940
$430$	−1.91246	−0.0922270
$431$	32.2604	1.55393	0.776964	−	0.629545i	$-0.216759\pi$
$431$	32.2604	1.55393	0.776964	+	0.629545i	$0.216759\pi$
$432$	19.3769	0.932270
$433$	27.4907	1.32112	0.660558	−	0.750775i	$-0.270320\pi$
$433$	27.4907	1.32112	0.660558	+	0.750775i	$0.270320\pi$
$434$	78.7528	3.78026
$435$	−3.21394	−0.154096
$436$	3.50735	0.167972
$437$	0	0
$438$	−23.8532	−1.13975
$439$	9.23889	0.440948	0.220474	−	0.975393i	$-0.429240\pi$
$439$	9.23889	0.440948	0.220474	+	0.975393i	$0.429240\pi$
$440$	−0.109950	−0.00524168
$441$	−20.6551	−0.983578
$442$	4.23066	0.201232
$443$	35.3646	1.68022	0.840111	−	0.542415i	$-0.182490\pi$
$443$	35.3646	1.68022	0.840111	+	0.542415i	$0.182490\pi$
$444$	23.0518	1.09399
$445$	0.840354	0.0398366
$446$	−52.2719	−2.47515
$447$	−8.27991	−0.391626
$448$	−38.4842	−1.81821
$449$	−0.833433	−0.0393321	−0.0196661	−	0.999807i	$-0.506260\pi$
$449$	−0.833433	−0.0393321	−0.0196661	+	0.999807i	$0.506260\pi$
$450$	−18.0922	−0.852874
$451$	9.84403	0.463537
$452$	2.55605	0.120226
$453$	14.1234	0.663577
$454$	4.09180	0.192038
$455$	−1.98478	−0.0930479
$456$	−1.59311	−0.0746044
$457$	12.6635	0.592372	0.296186	−	0.955130i	$-0.404285\pi$
$457$	12.6635	0.592372	0.296186	+	0.955130i	$0.404285\pi$
$458$	−40.5458	−1.89458
$459$	−9.56604	−0.446504
$460$	0	0
$461$	7.42632	0.345878	0.172939	−	0.984933i	$-0.444674\pi$
$461$	7.42632	0.345878	0.172939	+	0.984933i	$0.444674\pi$
$462$	−9.33445	−0.434278
$463$	8.53991	0.396883	0.198442	−	0.980113i	$-0.436412\pi$
$463$	8.53991	0.396883	0.198442	+	0.980113i	$0.436412\pi$
$464$	27.0750	1.25693
$465$	−4.00768	−0.185852
$466$	27.8839	1.29170
$467$	29.4128	1.36106	0.680532	−	0.732718i	$-0.261749\pi$
$467$	29.4128	1.36106	0.680532	+	0.732718i	$0.261749\pi$
$468$	4.45191	0.205789
$469$	50.4161	2.32800
$470$	−1.97503	−0.0911014
$471$	5.55783	0.256091
$472$	1.16213	0.0534915
$473$	2.29332	0.105447
$474$	−19.3667	−0.889541
$475$	−26.6916	−1.22470
$476$	16.7035	0.765605
$477$	7.69552	0.352354
$478$	17.7260	0.810768
$479$	−36.5558	−1.67028	−0.835140	−	0.550038i	$-0.814613\pi$
$479$	−36.5558	−1.67028	−0.835140	+	0.550038i	$0.814613\pi$
$480$	3.57377	0.163120
$481$	−11.3917	−0.519417
$482$	−10.8774	−0.495453
$483$	0	0
$484$	2.13185	0.0969021
$485$	−4.03220	−0.183093
$486$	−31.5978	−1.43330
$487$	−5.53035	−0.250604	−0.125302	−	0.992119i	$-0.539990\pi$
$487$	−5.53035	−0.250604	−0.125302	+	0.992119i	$0.539990\pi$
$488$	1.35083	0.0611494
$489$	10.7378	0.485579
$490$	−9.35053	−0.422414
$491$	−10.7545	−0.485344	−0.242672	−	0.970108i	$-0.578024\pi$
$491$	−10.7545	−0.485344	−0.242672	+	0.970108i	$0.578024\pi$
$492$	22.5818	1.01807
$493$	−13.3665	−0.601996
$494$	12.7297	0.572736
$495$	−0.755746	−0.0339683
$496$	33.7617	1.51595
$497$	−22.9788	−1.03074
$498$	−5.57810	−0.249961
$499$	13.3349	0.596950	0.298475	−	0.954417i	$-0.403522\pi$
$499$	13.3349	0.596950	0.298475	+	0.954417i	$0.403522\pi$
$500$	−8.59885	−0.384552
$501$	−10.9161	−0.487696
$502$	33.3337	1.48776
$503$	5.06433	0.225807	0.112904	−	0.993606i	$-0.463985\pi$
$503$	5.06433	0.225807	0.112904	+	0.993606i	$0.463985\pi$
$504$	2.10692	0.0938495
$505$	4.86353	0.216424
$506$	0	0
$507$	−12.6057	−0.559841
$508$	38.2819	1.69849
$509$	−31.3068	−1.38765	−0.693825	−	0.720143i	$-0.744076\pi$
$509$	−31.3068	−1.38765	−0.693825	+	0.720143i	$0.744076\pi$
$510$	−1.64749	−0.0729523
$511$	46.5405	2.05883
$512$	−32.0997	−1.41862
$513$	−28.7834	−1.27082
$514$	16.5386	0.729489
$515$	5.80161	0.255649
$516$	5.26078	0.231593
$517$	2.36835	0.104160
$518$	−87.1722	−3.83012
$519$	13.4311	0.589559
$520$	0.124643	0.00546594
$521$	4.33674	0.189996	0.0949979	−	0.995477i	$-0.469716\pi$
$521$	4.33674	0.189996	0.0949979	+	0.995477i	$0.469716\pi$
$522$	−27.2611	−1.19319
$523$	28.5934	1.25030	0.625150	−	0.780504i	$-0.285038\pi$
$523$	28.5934	1.25030	0.625150	+	0.780504i	$0.285038\pi$
$524$	−29.1639	−1.27403
$525$	−22.1879	−0.968358
$526$	42.9937	1.87461
$527$	−16.6676	−0.726052
$528$	−4.00173	−0.174153
$529$	0	0
$530$	3.48374	0.151324
$531$	7.98795	0.346647
$532$	50.2595	2.17903
$533$	−11.1595	−0.483370
$534$	−4.48031	−0.193882
$535$	5.77814	0.249811
$536$	−3.16609	−0.136754
$537$	4.62403	0.199542
$538$	58.4911	2.52173
$539$	11.2126	0.482963
$540$	−4.55699	−0.196102
$541$	1.32806	0.0570976	0.0285488	−	0.999592i	$-0.490911\pi$
$541$	1.32806	0.0570976	0.0285488	+	0.999592i	$0.490911\pi$
$542$	−17.3755	−0.746341
$543$	5.00173	0.214645
$544$	14.8630	0.637246
$545$	0.674962	0.0289122
$546$	10.5818	0.452858
$547$	17.0258	0.727972	0.363986	−	0.931404i	$-0.381416\pi$
$547$	17.0258	0.727972	0.363986	+	0.931404i	$0.381416\pi$
$548$	43.0072	1.83718
$549$	9.28498	0.396273
$550$	9.82135	0.418784
$551$	−40.2186	−1.71337
$552$	0	0
$553$	37.7868	1.60686
$554$	−7.27249	−0.308978
$555$	4.43614	0.188304
$556$	−1.76907	−0.0750254
$557$	20.3391	0.861793	0.430897	−	0.902401i	$-0.358197\pi$
$557$	20.3391	0.861793	0.430897	+	0.902401i	$0.358197\pi$
$558$	−33.9938	−1.43907
$559$	−2.59977	−0.109958
$560$	−6.51118	−0.275148
$561$	1.97559	0.0834093
$562$	41.1475	1.73570
$563$	23.3518	0.984163	0.492081	−	0.870549i	$-0.336236\pi$
$563$	23.3518	0.984163	0.492081	+	0.870549i	$0.336236\pi$
$564$	5.43290	0.228766
$565$	0.491891	0.0206940
$566$	−31.9552	−1.34318
$567$	−0.342146	−0.0143688
$568$	1.44305	0.0605491
$569$	9.05297	0.379520	0.189760	−	0.981830i	$-0.439229\pi$
$569$	9.05297	0.379520	0.189760	+	0.981830i	$0.439229\pi$
$570$	−4.95717	−0.207633
$571$	22.0070	0.920966	0.460483	−	0.887668i	$-0.347676\pi$
$571$	22.0070	0.920966	0.460483	+	0.887668i	$0.347676\pi$
$572$	−2.41672	−0.101048
$573$	9.57641	0.400060
$574$	−85.3948	−3.56431
$575$	0	0
$576$	16.6118	0.692158
$577$	17.2914	0.719852	0.359926	−	0.932981i	$-0.382802\pi$
$577$	17.2914	0.719852	0.359926	+	0.932981i	$0.382802\pi$
$578$	27.7040	1.15234
$579$	−19.4781	−0.809483
$580$	−6.36742	−0.264393
$581$	10.8835	0.451526
$582$	21.4975	0.891101
$583$	−4.17752	−0.173015
$584$	−2.92271	−0.120942
$585$	0.856734	0.0354216
$586$	−12.6879	−0.524130
$587$	17.0879	0.705292	0.352646	−	0.935757i	$-0.385282\pi$
$587$	17.0879	0.705292	0.352646	+	0.935757i	$0.385282\pi$
$588$	25.7214	1.06073
$589$	−50.1514	−2.06645
$590$	3.61612	0.148873
$591$	7.06792	0.290735
$592$	−37.3711	−1.53594
$593$	−40.4915	−1.66279	−0.831394	−	0.555684i	$-0.812456\pi$
$593$	−40.4915	−1.66279	−0.831394	+	0.555684i	$0.812456\pi$
$594$	10.5910	0.434556
$595$	3.21446	0.131780
$596$	−16.4041	−0.671936
$597$	3.30926	0.135439
$598$	0	0
$599$	20.1843	0.824708	0.412354	−	0.911024i	$-0.364707\pi$
$599$	20.1843	0.824708	0.412354	+	0.911024i	$0.364707\pi$
$600$	1.39338	0.0568845
$601$	−3.60034	−0.146861	−0.0734306	−	0.997300i	$-0.523395\pi$
$601$	−3.60034	−0.146861	−0.0734306	+	0.997300i	$0.523395\pi$
$602$	−19.8940	−0.810820
$603$	−21.7622	−0.886226
$604$	27.9812	1.13854
$605$	0.410257	0.0166793
$606$	−25.9297	−1.05332
$607$	−39.0252	−1.58399	−0.791993	−	0.610530i	$-0.790956\pi$
$607$	−39.0252	−1.58399	−0.791993	+	0.610530i	$0.790956\pi$
$608$	44.7215	1.81370
$609$	−33.4324	−1.35475
$610$	4.20329	0.170186
$611$	−2.68482	−0.108616
$612$	−7.21011	−0.291451
$613$	−42.2888	−1.70803	−0.854014	−	0.520250i	$-0.825839\pi$
$613$	−42.2888	−1.70803	−0.854014	+	0.520250i	$0.825839\pi$
$614$	−13.6781	−0.552004
$615$	4.34569	0.175235
$616$	−1.14374	−0.0460826
$617$	18.8486	0.758817	0.379409	−	0.925229i	$-0.376127\pi$
$617$	18.8486	0.758817	0.379409	+	0.925229i	$0.376127\pi$
$618$	−30.9310	−1.24423
$619$	−3.79490	−0.152530	−0.0762650	−	0.997088i	$-0.524300\pi$
$619$	−3.79490	−0.152530	−0.0762650	+	0.997088i	$0.524300\pi$
$620$	−7.93998	−0.318877
$621$	0	0
$622$	38.4331	1.54103
$623$	8.74164	0.350226
$624$	4.53646	0.181604
$625$	22.5037	0.900147
$626$	17.1732	0.686381
$627$	5.94437	0.237395
$628$	11.0111	0.439391
$629$	18.4495	0.735630
$630$	6.55594	0.261195
$631$	12.0419	0.479382	0.239691	−	0.970849i	$-0.422954\pi$
$631$	12.0419	0.479382	0.239691	+	0.970849i	$0.422954\pi$
$632$	−2.37298	−0.0943921
$633$	−13.2675	−0.527336
$634$	−42.9537	−1.70591
$635$	7.36706	0.292353
$636$	−9.58306	−0.379993
$637$	−12.7109	−0.503626
$638$	14.7987	0.585886
$639$	9.91884	0.392383
$640$	0.877692	0.0346938
$641$	−35.9629	−1.42045	−0.710224	−	0.703976i	$-0.751406\pi$
$641$	−35.9629	−1.42045	−0.710224	+	0.703976i	$0.751406\pi$
$642$	−30.8059	−1.21581
$643$	8.57269	0.338074	0.169037	−	0.985610i	$-0.445934\pi$
$643$	8.57269	0.338074	0.169037	+	0.985610i	$0.445934\pi$
$644$	0	0
$645$	1.01240	0.0398631
$646$	−20.6164	−0.811143
$647$	34.3946	1.35219	0.676097	−	0.736813i	$-0.263670\pi$
$647$	34.3946	1.35219	0.676097	+	0.736813i	$0.263670\pi$
$648$	0.0214865	0.000844070 0
$649$	−4.33626	−0.170213
$650$	−11.1337	−0.436701
$651$	−41.6892	−1.63393
$652$	21.2736	0.833138
$653$	−14.5224	−0.568306	−0.284153	−	0.958779i	$-0.591712\pi$
$653$	−14.5224	−0.568306	−0.284153	+	0.958779i	$0.591712\pi$
$654$	−3.59853	−0.140714
$655$	−5.61236	−0.219293
$656$	−36.6092	−1.42935
$657$	−20.0893	−0.783757
$658$	−20.5449	−0.800924
$659$	−41.6501	−1.62246	−0.811228	−	0.584729i	$-0.801201\pi$
$659$	−41.6501	−1.62246	−0.811228	+	0.584729i	$0.801201\pi$
$660$	0.941114	0.0366328
$661$	−5.31246	−0.206631	−0.103315	−	0.994649i	$-0.532945\pi$
$661$	−5.31246	−0.206631	−0.103315	+	0.994649i	$0.532945\pi$
$662$	17.8587	0.694097
$663$	−2.23958	−0.0869779
$664$	−0.683479	−0.0265241
$665$	9.67205	0.375066
$666$	37.6280	1.45806
$667$	0	0
$668$	−21.6269	−0.836769
$669$	27.6711	1.06983
$670$	−9.85170	−0.380604
$671$	−5.04035	−0.194581
$672$	37.1755	1.43408
$673$	37.3690	1.44047	0.720234	−	0.693731i	$-0.244035\pi$
$673$	37.3690	1.44047	0.720234	+	0.693731i	$0.244035\pi$
$674$	−19.2391	−0.741064
$675$	25.1748	0.968977
$676$	−24.9744	−0.960552
$677$	4.70224	0.180722	0.0903609	−	0.995909i	$-0.471198\pi$
$677$	4.70224	0.180722	0.0903609	+	0.995909i	$0.471198\pi$
$678$	−2.62250	−0.100716
$679$	−41.9443	−1.60967
$680$	−0.201866	−0.00774120
$681$	−2.16607	−0.0830039
$682$	18.4535	0.706622
$683$	10.6020	0.405675	0.202837	−	0.979212i	$-0.434984\pi$
$683$	10.6020	0.405675	0.202837	+	0.979212i	$0.434984\pi$
$684$	−21.6946	−0.829514
$685$	8.27639	0.316225
$686$	−36.5438	−1.39525
$687$	21.4636	0.818889
$688$	−8.52868	−0.325153
$689$	4.73574	0.180417
$690$	0	0
$691$	29.4870	1.12174	0.560869	−	0.827904i	$-0.310467\pi$
$691$	29.4870	1.12174	0.560869	+	0.827904i	$0.310467\pi$
$692$	26.6095	1.01154
$693$	−7.86152	−0.298634
$694$	27.4470	1.04187
$695$	−0.340444	−0.0129138
$696$	2.09953	0.0795825
$697$	18.0734	0.684577
$698$	−46.6242	−1.76475
$699$	−14.7609	−0.558307
$700$	−43.9584	−1.66147
$701$	28.9427	1.09315	0.546575	−	0.837410i	$-0.315931\pi$
$701$	28.9427	1.09315	0.546575	+	0.837410i	$0.315931\pi$
$702$	−12.0063	−0.453148
$703$	55.5131	2.09371
$704$	−9.01771	−0.339868
$705$	1.04552	0.0393765
$706$	26.8884	1.01196
$707$	50.5920	1.90271
$708$	−9.94721	−0.373839
$709$	−33.4099	−1.25473	−0.627367	−	0.778723i	$-0.715868\pi$
$709$	−33.4099	−1.25473	−0.627367	+	0.778723i	$0.715868\pi$
$710$	4.49024	0.168516
$711$	−16.3107	−0.611700
$712$	−0.548968	−0.0205735
$713$	0	0
$714$	−17.1378	−0.641365
$715$	−0.465078	−0.0173929
$716$	9.16108	0.342366
$717$	−9.38357	−0.350436
$718$	−9.54755	−0.356312
$719$	10.3377	0.385533	0.192766	−	0.981245i	$-0.438254\pi$
$719$	10.3377	0.385533	0.192766	+	0.981245i	$0.438254\pi$
$720$	2.81056	0.104744
$721$	60.3502	2.24756
$722$	−23.4120	−0.871304
$723$	5.75816	0.214148
$724$	9.90937	0.368279
$725$	35.1763	1.30641
$726$	−2.18727	−0.0811772
$727$	48.3261	1.79232	0.896158	−	0.443736i	$-0.146347\pi$
$727$	48.3261	1.79232	0.896158	+	0.443736i	$0.146347\pi$
$728$	1.29657	0.0480542
$729$	16.9674	0.628421
$730$	−9.09436	−0.336598
$731$	4.21047	0.155730
$732$	−11.5624	−0.427358
$733$	−40.7229	−1.50413	−0.752067	−	0.659086i	$-0.770943\pi$
$733$	−40.7229	−1.50413	−0.752067	+	0.659086i	$0.770943\pi$
$734$	−67.3647	−2.48648
$735$	4.94987	0.182579
$736$	0	0
$737$	11.8136	0.435160
$738$	36.8608	1.35687
$739$	−11.7025	−0.430485	−0.215243	−	0.976561i	$-0.569054\pi$
$739$	−11.7025	−0.430485	−0.215243	+	0.976561i	$0.569054\pi$
$740$	8.78883	0.323084
$741$	−6.73870	−0.247552
$742$	36.2390	1.33038
$743$	−39.1523	−1.43636	−0.718179	−	0.695858i	$-0.755024\pi$
$743$	−39.1523	−1.43636	−0.718179	+	0.695858i	$0.755024\pi$
$744$	2.61805	0.0959825
$745$	−3.15683	−0.115657
$746$	22.6403	0.828919
$747$	−4.69790	−0.171887
$748$	3.91401	0.143110
$749$	60.1061	2.19623
$750$	8.82239	0.322148
$751$	−53.0501	−1.93583	−0.967913	−	0.251287i	$-0.919146\pi$
$751$	−53.0501	−1.93583	−0.967913	+	0.251287i	$0.919146\pi$
$752$	−8.80771	−0.321184
$753$	−17.6458	−0.643049
$754$	−16.7762	−0.610953
$755$	5.38476	0.195972
$756$	−47.4033	−1.72404
$757$	−3.83293	−0.139310	−0.0696551	−	0.997571i	$-0.522190\pi$
$757$	−3.83293	−0.139310	−0.0696551	+	0.997571i	$0.522190\pi$
$758$	14.3636	0.521711
$759$	0	0
$760$	−0.607397	−0.0220326
$761$	−28.9474	−1.04934	−0.524671	−	0.851305i	$-0.675812\pi$
$761$	−28.9474	−1.04934	−0.524671	+	0.851305i	$0.675812\pi$
$762$	−39.2772	−1.42286
$763$	7.02117	0.254183
$764$	18.9727	0.686407
$765$	−1.38753	−0.0501662
$766$	−24.4300	−0.882693
$767$	4.91570	0.177496
$768$	14.7275	0.531434
$769$	14.5000	0.522883	0.261442	−	0.965219i	$-0.415802\pi$
$769$	14.5000	0.522883	0.261442	+	0.965219i	$0.415802\pi$
$770$	−3.55889	−0.128254
$771$	−8.75504	−0.315305
$772$	−38.5898	−1.38888
$773$	15.3948	0.553714	0.276857	−	0.960911i	$-0.410707\pi$
$773$	15.3948	0.553714	0.276857	+	0.960911i	$0.410707\pi$
$774$	8.58730	0.308664
$775$	43.8638	1.57563
$776$	2.63407	0.0945575
$777$	46.1462	1.65548
$778$	9.79093	0.351022
$779$	54.3812	1.94841
$780$	−1.06687	−0.0382001
$781$	−5.38445	−0.192671
$782$	0	0
$783$	37.9330	1.35562
$784$	−41.6990	−1.48925
$785$	2.11900	0.0756304
$786$	29.9221	1.06729
$787$	−2.41008	−0.0859102	−0.0429551	−	0.999077i	$-0.513677\pi$
$787$	−2.41008	−0.0859102	−0.0429551	+	0.999077i	$0.513677\pi$
$788$	14.0029	0.498832
$789$	−22.7595	−0.810259
$790$	−7.38382	−0.262705
$791$	5.11681	0.181933
$792$	0.493698	0.0175428
$793$	5.71388	0.202906
$794$	55.9633	1.98606
$795$	−1.84418	−0.0654064
$796$	6.55626	0.232381
$797$	36.9527	1.30893	0.654465	−	0.756092i	$-0.272894\pi$
$797$	36.9527	1.30893	0.654465	+	0.756092i	$0.272894\pi$
$798$	−51.5661	−1.82542
$799$	4.34822	0.153829
$800$	−39.1147	−1.38291
$801$	−3.77334	−0.133325
$802$	57.1867	2.01933
$803$	10.9055	0.384846
$804$	27.1000	0.955743
$805$	0	0
$806$	−20.9194	−0.736855
$807$	−30.9633	−1.08996
$808$	−3.17714	−0.111771
$809$	16.6912	0.586831	0.293415	−	0.955985i	$-0.405208\pi$
$809$	16.6912	0.586831	0.293415	+	0.955985i	$0.405208\pi$
$810$	0.0668580	0.00234915
$811$	20.8060	0.730597	0.365298	−	0.930890i	$-0.380967\pi$
$811$	20.8060	0.730597	0.365298	+	0.930890i	$0.380967\pi$
$812$	−66.2359	−2.32443
$813$	9.19803	0.322589
$814$	−20.4264	−0.715944
$815$	4.09393	0.143404
$816$	−7.34705	−0.257198
$817$	12.6689	0.443230
$818$	60.3065	2.10857
$819$	8.91203	0.311411
$820$	8.60964	0.300662
$821$	35.7565	1.24791	0.623955	−	0.781460i	$-0.285525\pi$
$821$	35.7565	1.24791	0.623955	+	0.781460i	$0.285525\pi$
$822$	−44.1252	−1.53904
$823$	13.1104	0.457001	0.228501	−	0.973544i	$-0.426618\pi$
$823$	13.1104	0.457001	0.228501	+	0.973544i	$0.426618\pi$
$824$	−3.78995	−0.132029
$825$	−5.19911	−0.181010
$826$	37.6161	1.30883
$827$	−40.6838	−1.41471	−0.707356	−	0.706857i	$-0.750112\pi$
$827$	−40.6838	−1.41471	−0.707356	+	0.706857i	$0.750112\pi$
$828$	0	0
$829$	45.9617	1.59632	0.798158	−	0.602448i	$-0.205808\pi$
$829$	45.9617	1.59632	0.798158	+	0.602448i	$0.205808\pi$
$830$	−2.12673	−0.0738198
$831$	3.84982	0.133549
$832$	10.2227	0.354409
$833$	20.5861	0.713266
$834$	1.81506	0.0628505
$835$	−4.16192	−0.144029
$836$	11.7769	0.407313
$837$	47.3014	1.63497
$838$	−0.233133	−0.00805343
$839$	27.8644	0.961986	0.480993	−	0.876724i	$-0.340276\pi$
$839$	27.8644	0.961986	0.480993	+	0.876724i	$0.340276\pi$
$840$	−0.504909	−0.0174210
$841$	24.0032	0.827698
$842$	69.0563	2.37984
$843$	−21.7822	−0.750218
$844$	−26.2855	−0.904783
$845$	−4.80612	−0.165335
$846$	8.86825	0.304897
$847$	4.26763	0.146637
$848$	15.5359	0.533504
$849$	16.9160	0.580557
$850$	18.0317	0.618482
$851$	0	0
$852$	−12.3517	−0.423163
$853$	2.79580	0.0957263	0.0478631	−	0.998854i	$-0.484759\pi$
$853$	2.79580	0.0957263	0.0478631	+	0.998854i	$0.484759\pi$
$854$	43.7240	1.49620
$855$	−4.17496	−0.142781
$856$	−3.77462	−0.129014
$857$	−23.2507	−0.794227	−0.397114	−	0.917769i	$-0.629988\pi$
$857$	−23.2507	−0.794227	−0.397114	+	0.917769i	$0.629988\pi$
$858$	2.47955	0.0846503
$859$	−32.2635	−1.10082	−0.550408	−	0.834896i	$-0.685528\pi$
$859$	−32.2635	−1.10082	−0.550408	+	0.834896i	$0.685528\pi$
$860$	2.00575	0.0683954
$861$	45.2053	1.54059
$862$	−65.5755	−2.23351
$863$	−23.4834	−0.799383	−0.399692	−	0.916650i	$-0.630883\pi$
$863$	−23.4834	−0.799383	−0.399692	+	0.916650i	$0.630883\pi$
$864$	−42.1800	−1.43499
$865$	5.12079	0.174112
$866$	−55.8801	−1.89888
$867$	−14.6656	−0.498071
$868$	−82.5943	−2.80343
$869$	8.85428	0.300361
$870$	6.53295	0.221488
$871$	−13.3922	−0.453778
$872$	−0.440924	−0.0149316
$873$	18.1053	0.612772
$874$	0	0
$875$	−17.2136	−0.581925
$876$	25.0167	0.845236
$877$	48.6987	1.64444	0.822219	−	0.569172i	$-0.192736\pi$
$877$	48.6987	1.64444	0.822219	+	0.569172i	$0.192736\pi$
$878$	−18.7798	−0.633789
$879$	6.71655	0.226544
$880$	−1.52571	−0.0514318
$881$	−6.48150	−0.218367	−0.109184	−	0.994022i	$-0.534824\pi$
$881$	−6.48150	−0.218367	−0.109184	+	0.994022i	$0.534824\pi$
$882$	41.9856	1.41373
$883$	−25.6058	−0.861704	−0.430852	−	0.902423i	$-0.641787\pi$
$883$	−25.6058	−0.861704	−0.430852	+	0.902423i	$0.641787\pi$
$884$	−4.43702	−0.149233
$885$	−1.91426	−0.0643472
$886$	−71.8853	−2.41504
$887$	36.4018	1.22225	0.611126	−	0.791533i	$-0.290717\pi$
$887$	36.4018	1.22225	0.611126	+	0.791533i	$0.290717\pi$
$888$	−2.89794	−0.0972487
$889$	76.6345	2.57024
$890$	−1.70818	−0.0572584
$891$	−0.0801725	−0.00268588
$892$	54.8217	1.83557
$893$	13.0834	0.437821
$894$	16.8305	0.562897
$895$	1.76298	0.0589298
$896$	9.13004	0.305013
$897$	0	0
$898$	1.69411	0.0565333
$899$	66.0935	2.20434
$900$	18.9747	0.632490
$901$	−7.66979	−0.255518
$902$	−20.0099	−0.666257
$903$	10.5313	0.350459
$904$	−0.321332	−0.0106873
$905$	1.90698	0.0633902
$906$	−28.7086	−0.953781
$907$	−11.1176	−0.369155	−0.184578	−	0.982818i	$-0.559092\pi$
$907$	−11.1176	−0.369155	−0.184578	+	0.982818i	$0.559092\pi$
$908$	−4.29139	−0.142415
$909$	−21.8381	−0.724325
$910$	4.03445	0.133741
$911$	30.2628	1.00265	0.501326	−	0.865259i	$-0.332846\pi$
$911$	30.2628	1.00265	0.501326	+	0.865259i	$0.332846\pi$
$912$	−22.1067	−0.732025
$913$	2.55026	0.0844012
$914$	−25.7410	−0.851435
$915$	−2.22509	−0.0735591
$916$	42.5235	1.40502
$917$	−58.3816	−1.92793
$918$	19.4448	0.641775
$919$	54.5872	1.80067	0.900333	−	0.435202i	$-0.143323\pi$
$919$	54.5872	1.80067	0.900333	+	0.435202i	$0.143323\pi$
$920$	0	0
$921$	7.24076	0.238591
$922$	−15.0954	−0.497142
$923$	6.10395	0.200914
$924$	9.78977	0.322060
$925$	−48.5532	−1.59642
$926$	−17.3590	−0.570453
$927$	−26.0503	−0.855603
$928$	−58.9375	−1.93472
$929$	−3.22809	−0.105910	−0.0529551	−	0.998597i	$-0.516864\pi$
$929$	−3.22809	−0.105910	−0.0529551	+	0.998597i	$0.516864\pi$
$930$	8.14640	0.267131
$931$	61.9418	2.03006
$932$	−29.2440	−0.957920
$933$	−20.3453	−0.666075
$934$	−59.7873	−1.95630
$935$	0.753220	0.0246329
$936$	−0.559668	−0.0182933
$937$	10.3788	0.339059	0.169530	−	0.985525i	$-0.445775\pi$
$937$	10.3788	0.339059	0.169530	+	0.985525i	$0.445775\pi$
$938$	−102.481	−3.34611
$939$	−9.09097	−0.296673
$940$	2.07137	0.0675607
$941$	7.63093	0.248761	0.124381	−	0.992235i	$-0.460306\pi$
$941$	7.63093	0.248761	0.124381	+	0.992235i	$0.460306\pi$
$942$	−11.2974	−0.368088
$943$	0	0
$944$	16.1262	0.524864
$945$	−9.12240	−0.296752
$946$	−4.66162	−0.151562
$947$	−59.4124	−1.93064	−0.965321	−	0.261065i	$-0.915926\pi$
$947$	−59.4124	−1.93064	−0.965321	+	0.261065i	$0.915926\pi$
$948$	20.3114	0.659683
$949$	−12.3627	−0.401311
$950$	54.2559	1.76029
$951$	22.7383	0.737341
$952$	−2.09987	−0.0680573
$953$	44.3346	1.43614	0.718069	−	0.695972i	$-0.245026\pi$
$953$	44.3346	1.43614	0.718069	+	0.695972i	$0.245026\pi$
$954$	−15.6426	−0.506449
$955$	3.65114	0.118148
$956$	−18.5906	−0.601264
$957$	−7.83396	−0.253236
$958$	74.3069	2.40075
$959$	86.0937	2.78011
$960$	−3.98091	−0.128483
$961$	51.4166	1.65860
$962$	23.1559	0.746575
$963$	−25.9449	−0.836063
$964$	11.4080	0.367427
$965$	−7.42631	−0.239061
$966$	0	0
$967$	−42.3917	−1.36323	−0.681613	−	0.731713i	$-0.738721\pi$
$967$	−42.3917	−1.36323	−0.681613	+	0.731713i	$0.738721\pi$
$968$	−0.268004	−0.00861397
$969$	10.9137	0.350598
$970$	8.19623	0.263165
$971$	−17.6998	−0.568013	−0.284006	−	0.958822i	$-0.591664\pi$
$971$	−17.6998	−0.568013	−0.284006	+	0.958822i	$0.591664\pi$
$972$	33.1391	1.06294
$973$	−3.54141	−0.113532
$974$	11.2415	0.360201
$975$	5.89385	0.188754
$976$	18.7447	0.600003
$977$	54.7336	1.75108	0.875541	−	0.483143i	$-0.160505\pi$
$977$	54.7336	1.75108	0.875541	+	0.483143i	$0.160505\pi$
$978$	−21.8266	−0.697939
$979$	2.04836	0.0654659
$980$	9.80664	0.313261
$981$	−3.03070	−0.0967629
$982$	21.8606	0.697600
$983$	44.5482	1.42087	0.710434	−	0.703764i	$-0.248499\pi$
$983$	44.5482	1.42087	0.710434	+	0.703764i	$0.248499\pi$
$984$	−2.83886	−0.0904996
$985$	2.69474	0.0858617
$986$	27.1700	0.865268
$987$	10.8758	0.346182
$988$	−13.3506	−0.424740
$989$	0	0
$990$	1.53620	0.0488237
$991$	−35.5303	−1.12866	−0.564329	−	0.825550i	$-0.690865\pi$
$991$	−35.5303	−1.12866	−0.564329	+	0.825550i	$0.690865\pi$
$992$	−73.4933	−2.33342
$993$	−9.45381	−0.300008
$994$	46.7089	1.48152
$995$	1.26170	0.0399986
$996$	5.85019	0.185370
$997$	−28.6339	−0.906846	−0.453423	−	0.891295i	$-0.649797\pi$
$997$	−28.6339	−0.906846	−0.453423	+	0.891295i	$0.649797\pi$
$998$	−27.1057	−0.858015
$999$	−52.3583	−1.65654

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5819.2.a.u.1.11		60
23.13	even	11		253.2.i.b.100.11	✓	120
23.16	even	11		253.2.i.b.210.11	yes	120
23.22	odd	2		5819.2.a.t.1.11		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.2.i.b.100.11	✓	120	23.13	even	11
253.2.i.b.210.11	yes	120	23.16	even	11
5819.2.a.t.1.11		60	23.22	odd	2
5819.2.a.u.1.11		60	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:	\( N \)	\(=\)	\( 5819 = 11 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5819.a (trivial)

\(f(q)\)	\(=\)	\(q-2.03269 q^{2} +1.07604 q^{3} +2.13185 q^{4} +0.410257 q^{5} -2.18727 q^{6} +4.26763 q^{7} -0.268004 q^{8} -1.84213 q^{9} -0.833927 q^{10} +1.00000 q^{11} +2.29396 q^{12} -1.13363 q^{13} -8.67478 q^{14} +0.441455 q^{15} -3.71892 q^{16} +1.83597 q^{17} +3.74449 q^{18} +5.52428 q^{19} +0.874605 q^{20} +4.59216 q^{21} -2.03269 q^{22} -0.288384 q^{24} -4.83169 q^{25} +2.30432 q^{26} -5.21034 q^{27} +9.09793 q^{28} -7.28033 q^{29} -0.897342 q^{30} -9.07836 q^{31} +8.09544 q^{32} +1.07604 q^{33} -3.73197 q^{34} +1.75082 q^{35} -3.92714 q^{36} +10.0489 q^{37} -11.2292 q^{38} -1.21983 q^{39} -0.109950 q^{40} +9.84403 q^{41} -9.33445 q^{42} +2.29332 q^{43} +2.13185 q^{44} -0.755746 q^{45} +2.36835 q^{47} -4.00173 q^{48} +11.2126 q^{49} +9.82135 q^{50} +1.97559 q^{51} -2.41672 q^{52} -4.17752 q^{53} +10.5910 q^{54} +0.410257 q^{55} -1.14374 q^{56} +5.94437 q^{57} +14.7987 q^{58} -4.33626 q^{59} +0.941114 q^{60} -5.04035 q^{61} +18.4535 q^{62} -7.86152 q^{63} -9.01771 q^{64} -0.465078 q^{65} -2.18727 q^{66} +11.8136 q^{67} +3.91401 q^{68} -3.55889 q^{70} -5.38445 q^{71} +0.493698 q^{72} +10.9055 q^{73} -20.4264 q^{74} -5.19911 q^{75} +11.7769 q^{76} +4.26763 q^{77} +2.47955 q^{78} +8.85428 q^{79} -1.52571 q^{80} -0.0801725 q^{81} -20.0099 q^{82} +2.55026 q^{83} +9.78977 q^{84} +0.753220 q^{85} -4.66162 q^{86} -7.83396 q^{87} -0.268004 q^{88} +2.04836 q^{89} +1.53620 q^{90} -4.83789 q^{91} -9.76872 q^{93} -4.81413 q^{94} +2.26638 q^{95} +8.71105 q^{96} -9.82847 q^{97} -22.7919 q^{98} -1.84213 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 5 q^{2} + 9 q^{3} + 73 q^{4} + 8 q^{5} + 26 q^{6} + 30 q^{8} + 75 q^{9} - 7 q^{10} + 60 q^{11} + 41 q^{12} + 46 q^{13} + 16 q^{14} + 4 q^{15} + 99 q^{16} - 5 q^{17} + 36 q^{18} - 8 q^{19} + 82 q^{20}+ \cdots + 75 q^{99}+O(q^{100}) \) 60 * q + 5 * q^2 + 9 * q^3 + 73 * q^4 + 8 * q^5 + 26 * q^6 + 30 * q^8 + 75 * q^9 - 7 * q^10 + 60 * q^11 + 41 * q^12 + 46 * q^13 + 16 * q^14 + 4 * q^15 + 99 * q^16 - 5 * q^17 + 36 * q^18 - 8 * q^19 + 82 * q^20 - 13 * q^21 + 5 * q^22 + 54 * q^24 + 96 * q^25 + 31 * q^26 + 54 * q^27 - 29 * q^28 + 42 * q^29 - 14 * q^30 + 71 * q^31 + 40 * q^32 + 9 * q^33 + 10 * q^34 + 9 * q^35 + 93 * q^36 - 5 * q^37 - 11 * q^38 + 56 * q^39 - 40 * q^40 + 62 * q^41 + 43 * q^42 - 2 * q^43 + 73 * q^44 - q^45 - q^47 + 71 * q^48 + 138 * q^49 - 18 * q^50 - 27 * q^51 + 102 * q^52 + 11 * q^53 + 69 * q^54 + 8 * q^55 + 13 * q^56 + 38 * q^57 + 58 * q^58 + 57 * q^59 - 49 * q^60 - 26 * q^61 + 17 * q^62 - 41 * q^63 + 184 * q^64 - 19 * q^65 + 26 * q^66 + 7 * q^67 - 76 * q^68 + 43 * q^70 + 33 * q^71 + 100 * q^72 + 108 * q^73 - 63 * q^74 + q^75 - 42 * q^76 - 3 * q^78 - 25 * q^79 + 148 * q^80 + 68 * q^81 + 59 * q^82 - 41 * q^83 - 97 * q^84 + 160 * q^85 + 78 * q^86 + 41 * q^87 + 30 * q^88 + 51 * q^89 - 53 * q^90 + 65 * q^93 + 121 * q^94 - 14 * q^95 + 82 * q^96 - 13 * q^97 - 75 * q^98 + 75 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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