LMFDB - Embedded newform 5819.2.a.u.1.14

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			1.14
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)

$f(q)$	$=$	\(q-1.66144 q^{2} -1.56821 q^{3} +0.760370 q^{4} -0.618995 q^{5} +2.60547 q^{6} +1.60957 q^{7} +2.05957 q^{8} -0.540729 q^{9} +1.02842 q^{10} +1.00000 q^{11} -1.19242 q^{12} -4.28258 q^{13} -2.67420 q^{14} +0.970711 q^{15} -4.94258 q^{16} -2.36953 q^{17} +0.898386 q^{18} -7.82169 q^{19} -0.470665 q^{20} -2.52414 q^{21} -1.66144 q^{22} -3.22982 q^{24} -4.61685 q^{25} +7.11523 q^{26} +5.55259 q^{27} +1.22387 q^{28} -9.55885 q^{29} -1.61278 q^{30} -6.15045 q^{31} +4.09265 q^{32} -1.56821 q^{33} +3.93682 q^{34} -0.996316 q^{35} -0.411154 q^{36} -8.68489 q^{37} +12.9952 q^{38} +6.71597 q^{39} -1.27486 q^{40} -2.31236 q^{41} +4.19370 q^{42} +4.99650 q^{43} +0.760370 q^{44} +0.334708 q^{45} +11.6513 q^{47} +7.75098 q^{48} -4.40928 q^{49} +7.67059 q^{50} +3.71591 q^{51} -3.25635 q^{52} -0.722668 q^{53} -9.22528 q^{54} -0.618995 q^{55} +3.31502 q^{56} +12.2660 q^{57} +15.8814 q^{58} -8.68909 q^{59} +0.738100 q^{60} -3.55721 q^{61} +10.2186 q^{62} -0.870341 q^{63} +3.08549 q^{64} +2.65089 q^{65} +2.60547 q^{66} +14.3884 q^{67} -1.80172 q^{68} +1.65532 q^{70} +1.36796 q^{71} -1.11367 q^{72} -10.2994 q^{73} +14.4294 q^{74} +7.24017 q^{75} -5.94738 q^{76} +1.60957 q^{77} -11.1582 q^{78} -7.06103 q^{79} +3.05943 q^{80} -7.08543 q^{81} +3.84184 q^{82} -14.1073 q^{83} -1.91928 q^{84} +1.46672 q^{85} -8.30136 q^{86} +14.9902 q^{87} +2.05957 q^{88} +3.97617 q^{89} -0.556096 q^{90} -6.89312 q^{91} +9.64518 q^{93} -19.3580 q^{94} +4.84159 q^{95} -6.41811 q^{96} +3.17407 q^{97} +7.32574 q^{98} -0.540729 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.66144	−1.17481	−0.587406	−	0.809292i	$-0.699851\pi$
$2$	−1.66144	−1.17481	−0.587406	+	0.809292i	$0.699851\pi$
$3$	−1.56821	−0.905404	−0.452702	−	0.891662i	$-0.649540\pi$
$3$	−1.56821	−0.905404	−0.452702	+	0.891662i	$0.649540\pi$
$4$	0.760370	0.380185
$5$	−0.618995	−0.276823	−0.138411	−	0.990375i	$-0.544200\pi$
$5$	−0.618995	−0.276823	−0.138411	+	0.990375i	$0.544200\pi$
$6$	2.60547	1.06368
$7$	1.60957	0.608361	0.304180	−	0.952614i	$-0.401617\pi$
$7$	1.60957	0.608361	0.304180	+	0.952614i	$0.401617\pi$
$8$	2.05957	0.728166
$9$	−0.540729	−0.180243
$10$	1.02842	0.325215
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.19242	−0.344221
$13$	−4.28258	−1.18777	−0.593887	−	0.804548i	$-0.702407\pi$
$13$	−4.28258	−1.18777	−0.593887	+	0.804548i	$0.702407\pi$
$14$	−2.67420	−0.714710
$15$	0.970711	0.250637
$16$	−4.94258	−1.23564
$17$	−2.36953	−0.574695	−0.287347	−	0.957826i	$-0.592773\pi$
$17$	−2.36953	−0.574695	−0.287347	+	0.957826i	$0.592773\pi$
$18$	0.898386	0.211752
$19$	−7.82169	−1.79442	−0.897210	−	0.441605i	$-0.854409\pi$
$19$	−7.82169	−1.79442	−0.897210	+	0.441605i	$0.854409\pi$
$20$	−0.470665	−0.105244
$21$	−2.52414	−0.550812
$22$	−1.66144	−0.354219
$23$	0	0
$23$	0	0
$24$	−3.22982	−0.659285
$25$	−4.61685	−0.923369
$26$	7.11523	1.39541
$27$	5.55259	1.06860
$28$	1.22387	0.231290
$29$	−9.55885	−1.77503	−0.887517	−	0.460776i	$-0.847571\pi$
$29$	−9.55885	−1.77503	−0.887517	+	0.460776i	$0.847571\pi$
$30$	−1.61278	−0.294451
$31$	−6.15045	−1.10465	−0.552327	−	0.833628i	$-0.686260\pi$
$31$	−6.15045	−1.10465	−0.552327	+	0.833628i	$0.686260\pi$
$32$	4.09265	0.723484
$33$	−1.56821	−0.272990
$34$	3.93682	0.675159
$35$	−0.996316	−0.168408
$36$	−0.411154	−0.0685256
$37$	−8.68489	−1.42779	−0.713894	−	0.700254i	$-0.753070\pi$
$37$	−8.68489	−1.42779	−0.713894	+	0.700254i	$0.753070\pi$
$38$	12.9952	2.10811
$39$	6.71597	1.07542
$40$	−1.27486	−0.201573
$41$	−2.31236	−0.361130	−0.180565	−	0.983563i	$-0.557793\pi$
$41$	−2.31236	−0.361130	−0.180565	+	0.983563i	$0.557793\pi$
$42$	4.19370	0.647102
$43$	4.99650	0.761959	0.380979	−	0.924584i	$-0.375587\pi$
$43$	4.99650	0.761959	0.380979	+	0.924584i	$0.375587\pi$
$44$	0.760370	0.114630
$45$	0.334708	0.0498953
$46$	0	0
$47$	11.6513	1.69952	0.849761	−	0.527167i	$-0.176746\pi$
$47$	11.6513	1.69952	0.849761	+	0.527167i	$0.176746\pi$
$48$	7.75098	1.11876
$49$	−4.40928	−0.629897
$50$	7.67059	1.08479
$51$	3.71591	0.520331
$52$	−3.25635	−0.451574
$53$	−0.722668	−0.0992661	−0.0496331	−	0.998768i	$-0.515805\pi$
$53$	−0.722668	−0.0992661	−0.0496331	+	0.998768i	$0.515805\pi$
$54$	−9.22528	−1.25540
$55$	−0.618995	−0.0834652
$56$	3.31502	0.442988
$57$	12.2660	1.62468
$58$	15.8814	2.08533
$59$	−8.68909	−1.13122	−0.565612	−	0.824672i	$-0.691360\pi$
$59$	−8.68909	−1.13122	−0.565612	+	0.824672i	$0.691360\pi$
$60$	0.738100	0.0952883
$61$	−3.55721	−0.455454	−0.227727	−	0.973725i	$-0.573129\pi$
$61$	−3.55721	−0.455454	−0.227727	+	0.973725i	$0.573129\pi$
$62$	10.2186	1.29776
$63$	−0.870341	−0.109653
$64$	3.08549	0.385686
$65$	2.65089	0.328803
$66$	2.60547	0.320712
$67$	14.3884	1.75782	0.878909	−	0.476990i	$-0.158272\pi$
$67$	14.3884	1.75782	0.878909	+	0.476990i	$0.158272\pi$
$68$	−1.80172	−0.218490
$69$	0	0
$70$	1.65532	0.197848
$71$	1.36796	0.162347	0.0811735	−	0.996700i	$-0.474133\pi$
$71$	1.36796	0.162347	0.0811735	+	0.996700i	$0.474133\pi$
$72$	−1.11367	−0.131247
$73$	−10.2994	−1.20545	−0.602725	−	0.797949i	$-0.705918\pi$
$73$	−10.2994	−1.20545	−0.602725	+	0.797949i	$0.705918\pi$
$74$	14.4294	1.67738
$75$	7.24017	0.836022
$76$	−5.94738	−0.682211
$77$	1.60957	0.183428
$78$	−11.1582	−1.26341
$79$	−7.06103	−0.794428	−0.397214	−	0.917726i	$-0.630023\pi$
$79$	−7.06103	−0.794428	−0.397214	+	0.917726i	$0.630023\pi$
$80$	3.05943	0.342055
$81$	−7.08543	−0.787270
$82$	3.84184	0.424260
$83$	−14.1073	−1.54848	−0.774240	−	0.632892i	$-0.781868\pi$
$83$	−14.1073	−1.54848	−0.774240	+	0.632892i	$0.781868\pi$
$84$	−1.91928	−0.209411
$85$	1.46672	0.159089
$86$	−8.30136	−0.895159
$87$	14.9902	1.60712
$88$	2.05957	0.219550
$89$	3.97617	0.421473	0.210737	−	0.977543i	$-0.432414\pi$
$89$	3.97617	0.421473	0.210737	+	0.977543i	$0.432414\pi$
$90$	−0.556096	−0.0586177
$91$	−6.89312	−0.722595
$92$	0	0
$93$	9.64518	1.00016
$94$	−19.3580	−1.99662
$95$	4.84159	0.496736
$96$	−6.41811	−0.655046
$97$	3.17407	0.322278	0.161139	−	0.986932i	$-0.448483\pi$
$97$	3.17407	0.322278	0.161139	+	0.986932i	$0.448483\pi$
$98$	7.32574	0.740011
$99$	−0.540729	−0.0543453
$100$	−3.51051	−0.351051
$101$	−4.22752	−0.420654	−0.210327	−	0.977631i	$-0.567453\pi$
$101$	−4.22752	−0.420654	−0.210327	+	0.977631i	$0.567453\pi$
$102$	−6.17374	−0.611292
$103$	5.15172	0.507614	0.253807	−	0.967255i	$-0.418317\pi$
$103$	5.15172	0.507614	0.253807	+	0.967255i	$0.418317\pi$
$104$	−8.82025	−0.864897
$105$	1.56243	0.152477
$106$	1.20067	0.116619
$107$	15.2074	1.47015	0.735077	−	0.677983i	$-0.237146\pi$
$107$	15.2074	1.47015	0.735077	+	0.677983i	$0.237146\pi$
$108$	4.22203	0.406265
$109$	−0.736074	−0.0705031	−0.0352515	−	0.999378i	$-0.511223\pi$
$109$	−0.736074	−0.0705031	−0.0352515	+	0.999378i	$0.511223\pi$
$110$	1.02842	0.0980560
$111$	13.6197	1.29272
$112$	−7.95543	−0.751717
$113$	−14.5947	−1.37295	−0.686476	−	0.727152i	$-0.740843\pi$
$113$	−14.5947	−1.37295	−0.686476	+	0.727152i	$0.740843\pi$
$114$	−20.3792	−1.90869
$115$	0	0
$116$	−7.26826	−0.674841
$117$	2.31571	0.214088
$118$	14.4364	1.32898
$119$	−3.81392	−0.349622
$120$	1.99924	0.182505
$121$	1.00000	0.0909091
$122$	5.91008	0.535073
$123$	3.62626	0.326969
$124$	−4.67662	−0.419973
$125$	5.95278	0.532432
$126$	1.44602	0.128821
$127$	−17.2343	−1.52930	−0.764648	−	0.644448i	$-0.777087\pi$
$127$	−17.2343	−1.52930	−0.764648	+	0.644448i	$0.777087\pi$
$128$	−13.3116	−1.17659
$129$	−7.83554	−0.689881
$130$	−4.40429	−0.386282
$131$	−0.660279	−0.0576888	−0.0288444	−	0.999584i	$-0.509183\pi$
$131$	−0.660279	−0.0576888	−0.0288444	+	0.999584i	$0.509183\pi$
$132$	−1.19242	−0.103787
$133$	−12.5896	−1.09165
$134$	−23.9053	−2.06511
$135$	−3.43703	−0.295812
$136$	−4.88020	−0.418473
$137$	−10.4980	−0.896902	−0.448451	−	0.893807i	$-0.648024\pi$
$137$	−10.4980	−0.896902	−0.448451	+	0.893807i	$0.648024\pi$
$138$	0	0
$139$	−3.07522	−0.260836	−0.130418	−	0.991459i	$-0.541632\pi$
$139$	−3.07522	−0.260836	−0.130418	+	0.991459i	$0.541632\pi$
$140$	−0.757569	−0.0640263
$141$	−18.2717	−1.53876
$142$	−2.27278	−0.190727
$143$	−4.28258	−0.358127
$144$	2.67259	0.222716
$145$	5.91687	0.491370
$146$	17.1117	1.41618
$147$	6.91466	0.570312
$148$	−6.60373	−0.542823
$149$	1.96657	0.161108	0.0805539	−	0.996750i	$-0.474331\pi$
$149$	1.96657	0.161108	0.0805539	+	0.996750i	$0.474331\pi$
$150$	−12.0291	−0.982170
$151$	9.92919	0.808026	0.404013	−	0.914753i	$-0.367615\pi$
$151$	9.92919	0.808026	0.404013	+	0.914753i	$0.367615\pi$
$152$	−16.1093	−1.30664
$153$	1.28127	0.103585
$154$	−2.67420	−0.215493
$155$	3.80710	0.305793
$156$	5.10662	0.408857
$157$	9.82429	0.784064	0.392032	−	0.919952i	$-0.371772\pi$
$157$	9.82429	0.784064	0.392032	+	0.919952i	$0.371772\pi$
$158$	11.7314	0.933304
$159$	1.13329	0.0898760
$160$	−2.53333	−0.200277
$161$	0	0
$162$	11.7720	0.924894
$163$	−1.99477	−0.156243	−0.0781213	−	0.996944i	$-0.524892\pi$
$163$	−1.99477	−0.156243	−0.0781213	+	0.996944i	$0.524892\pi$
$164$	−1.75825	−0.137296
$165$	0.970711	0.0755698
$166$	23.4384	1.81917
$167$	−3.14885	−0.243666	−0.121833	−	0.992551i	$-0.538877\pi$
$167$	−3.14885	−0.243666	−0.121833	+	0.992551i	$0.538877\pi$
$168$	−5.19863	−0.401083
$169$	5.34049	0.410807
$170$	−2.43687	−0.186899
$171$	4.22941	0.323431
$172$	3.79919	0.289685
$173$	5.96172	0.453261	0.226631	−	0.973981i	$-0.427229\pi$
$173$	5.96172	0.453261	0.226631	+	0.973981i	$0.427229\pi$
$174$	−24.9053	−1.88807
$175$	−7.43114	−0.561741
$176$	−4.94258	−0.372561
$177$	13.6263	1.02421
$178$	−6.60616	−0.495152
$179$	5.31241	0.397068	0.198534	−	0.980094i	$-0.436382\pi$
$179$	5.31241	0.397068	0.198534	+	0.980094i	$0.436382\pi$
$180$	0.254502	0.0189695
$181$	−15.7729	−1.17239	−0.586197	−	0.810169i	$-0.699376\pi$
$181$	−15.7729	−1.17239	−0.586197	+	0.810169i	$0.699376\pi$
$182$	11.4525	0.848914
$183$	5.57844	0.412370
$184$	0	0
$185$	5.37590	0.395244
$186$	−16.0248	−1.17500
$187$	−2.36953	−0.173277
$188$	8.85933	0.646133
$189$	8.93729	0.650092
$190$	−8.04399	−0.583572
$191$	−27.2318	−1.97042	−0.985212	−	0.171342i	$-0.945190\pi$
$191$	−27.2318	−1.97042	−0.985212	+	0.171342i	$0.945190\pi$
$192$	−4.83868	−0.349202
$193$	−2.37337	−0.170839	−0.0854195	−	0.996345i	$-0.527223\pi$
$193$	−2.37337	−0.170839	−0.0854195	+	0.996345i	$0.527223\pi$
$194$	−5.27351	−0.378616
$195$	−4.15715	−0.297700
$196$	−3.35269	−0.239478
$197$	−22.6702	−1.61519	−0.807593	−	0.589740i	$-0.799230\pi$
$197$	−22.6702	−1.61519	−0.807593	+	0.589740i	$0.799230\pi$
$198$	0.898386	0.0638455
$199$	27.8125	1.97158	0.985789	−	0.167988i	$-0.0537271\pi$
$199$	27.8125	1.97158	0.985789	+	0.167988i	$0.0537271\pi$
$200$	−9.50870	−0.672366
$201$	−22.5639	−1.59154
$202$	7.02375	0.494190
$203$	−15.3856	−1.07986
$204$	2.82547	0.197822
$205$	1.43134	0.0999690
$206$	−8.55926	−0.596352
$207$	0	0
$208$	21.1670	1.46767
$209$	−7.82169	−0.541038
$210$	−2.59588	−0.179132
$211$	10.9511	0.753906	0.376953	−	0.926232i	$-0.376972\pi$
$211$	10.9511	0.753906	0.376953	+	0.926232i	$0.376972\pi$
$212$	−0.549496	−0.0377395
$213$	−2.14524	−0.146990
$214$	−25.2661	−1.72716
$215$	−3.09281	−0.210928
$216$	11.4359	0.778117
$217$	−9.89959	−0.672028
$218$	1.22294	0.0828279
$219$	16.1515	1.09142
$220$	−0.470665	−0.0317322
$221$	10.1477	0.682608
$222$	−22.6283	−1.51871
$223$	−25.2390	−1.69013	−0.845063	−	0.534667i	$-0.820437\pi$
$223$	−25.2390	−1.69013	−0.845063	+	0.534667i	$0.820437\pi$
$224$	6.58740	0.440139
$225$	2.49646	0.166431
$226$	24.2481	1.61296
$227$	13.9598	0.926544	0.463272	−	0.886216i	$-0.346675\pi$
$227$	13.9598	0.926544	0.463272	+	0.886216i	$0.346675\pi$
$228$	9.32672	0.617677
$229$	5.97008	0.394514	0.197257	−	0.980352i	$-0.436797\pi$
$229$	5.97008	0.394514	0.197257	+	0.980352i	$0.436797\pi$
$230$	0	0
$231$	−2.52414	−0.166076
$232$	−19.6871	−1.29252
$233$	−17.7243	−1.16115	−0.580577	−	0.814205i	$-0.697173\pi$
$233$	−17.7243	−1.16115	−0.580577	+	0.814205i	$0.697173\pi$
$234$	−3.84741	−0.251513
$235$	−7.21212	−0.470467
$236$	−6.60692	−0.430074
$237$	11.0731	0.719278
$238$	6.33659	0.410740
$239$	−10.5599	−0.683062	−0.341531	−	0.939870i	$-0.610945\pi$
$239$	−10.5599	−0.683062	−0.341531	+	0.939870i	$0.610945\pi$
$240$	−4.79782	−0.309698
$241$	−12.1664	−0.783708	−0.391854	−	0.920027i	$-0.628166\pi$
$241$	−12.1664	−0.783708	−0.391854	+	0.920027i	$0.628166\pi$
$242$	−1.66144	−0.106801
$243$	−5.54637	−0.355800
$244$	−2.70480	−0.173157
$245$	2.72932	0.174370
$246$	−6.02480	−0.384127
$247$	33.4970	2.13136
$248$	−12.6673	−0.804372
$249$	22.1232	1.40200
$250$	−9.89016	−0.625508
$251$	9.31176	0.587753	0.293876	−	0.955843i	$-0.405055\pi$
$251$	9.31176	0.587753	0.293876	+	0.955843i	$0.405055\pi$
$252$	−0.661781	−0.0416883
$253$	0	0
$254$	28.6337	1.79664
$255$	−2.30013	−0.144040
$256$	15.9455	0.996591
$257$	−19.5798	−1.22136	−0.610678	−	0.791879i	$-0.709103\pi$
$257$	−19.5798	−1.22136	−0.610678	+	0.791879i	$0.709103\pi$
$258$	13.0183	0.810481
$259$	−13.9790	−0.868610
$260$	2.01566	0.125006
$261$	5.16874	0.319937
$262$	1.09701	0.0677736
$263$	4.32096	0.266442	0.133221	−	0.991086i	$-0.457468\pi$
$263$	4.32096	0.266442	0.133221	+	0.991086i	$0.457468\pi$
$264$	−3.22982	−0.198782
$265$	0.447328	0.0274791
$266$	20.9168	1.28249
$267$	−6.23546	−0.381604
$268$	10.9405	0.668296
$269$	19.2846	1.17580	0.587901	−	0.808933i	$-0.299955\pi$
$269$	19.2846	1.17580	0.587901	+	0.808933i	$0.299955\pi$
$270$	5.71040	0.347524
$271$	13.9372	0.846624	0.423312	−	0.905984i	$-0.360867\pi$
$271$	13.9372	0.846624	0.423312	+	0.905984i	$0.360867\pi$
$272$	11.7116	0.710118
$273$	10.8098	0.654241
$274$	17.4417	1.05369
$275$	−4.61685	−0.278406
$276$	0	0
$277$	−8.25234	−0.495835	−0.247917	−	0.968781i	$-0.579746\pi$
$277$	−8.25234	−0.495835	−0.247917	+	0.968781i	$0.579746\pi$
$278$	5.10927	0.306434
$279$	3.32572	0.199106
$280$	−2.05198	−0.122629
$281$	−6.03675	−0.360122	−0.180061	−	0.983655i	$-0.557630\pi$
$281$	−6.03675	−0.360122	−0.180061	+	0.983655i	$0.557630\pi$
$282$	30.3573	1.80775
$283$	21.2256	1.26173	0.630865	−	0.775893i	$-0.282700\pi$
$283$	21.2256	1.26173	0.630865	+	0.775893i	$0.282700\pi$
$284$	1.04016	0.0617219
$285$	−7.59261	−0.449747
$286$	7.11523	0.420733
$287$	−3.72191	−0.219697
$288$	−2.21301	−0.130403
$289$	−11.3853	−0.669726
$290$	−9.83051	−0.577267
$291$	−4.97759	−0.291792
$292$	−7.83133	−0.458294
$293$	13.6311	0.796340	0.398170	−	0.917312i	$-0.369645\pi$
$293$	13.6311	0.796340	0.398170	+	0.917312i	$0.369645\pi$
$294$	−11.4883	−0.670010
$295$	5.37850	0.313148
$296$	−17.8871	−1.03967
$297$	5.55259	0.322194
$298$	−3.26733	−0.189272
$299$	0	0
$300$	5.50521	0.317843
$301$	8.04222	0.463546
$302$	−16.4967	−0.949279
$303$	6.62962	0.380862
$304$	38.6593	2.21726
$305$	2.20189	0.126080
$306$	−2.12875	−0.121693
$307$	24.1392	1.37770	0.688848	−	0.724906i	$-0.258117\pi$
$307$	24.1392	1.37770	0.688848	+	0.724906i	$0.258117\pi$
$308$	1.22387	0.0697365
$309$	−8.07896	−0.459596
$310$	−6.32525	−0.359250
$311$	−26.5152	−1.50354	−0.751770	−	0.659426i	$-0.770799\pi$
$311$	−26.5152	−1.50354	−0.751770	+	0.659426i	$0.770799\pi$
$312$	13.8320	0.783082
$313$	−14.8723	−0.840632	−0.420316	−	0.907378i	$-0.638081\pi$
$313$	−14.8723	−0.840632	−0.420316	+	0.907378i	$0.638081\pi$
$314$	−16.3224	−0.921128
$315$	0.538736	0.0303544
$316$	−5.36899	−0.302030
$317$	13.6152	0.764707	0.382353	−	0.924016i	$-0.375114\pi$
$317$	13.6152	0.764707	0.382353	+	0.924016i	$0.375114\pi$
$318$	−1.88289	−0.105587
$319$	−9.55885	−0.535193
$320$	−1.90990	−0.106767
$321$	−23.8483	−1.33108
$322$	0	0
$323$	18.5337	1.03124
$324$	−5.38755	−0.299308
$325$	19.7720	1.09675
$326$	3.31419	0.183556
$327$	1.15432	0.0638338
$328$	−4.76246	−0.262963
$329$	18.7537	1.03392
$330$	−1.61278	−0.0887803
$331$	15.5614	0.855333	0.427666	−	0.903937i	$-0.359336\pi$
$331$	15.5614	0.855333	0.427666	+	0.903937i	$0.359336\pi$
$332$	−10.7268	−0.588709
$333$	4.69617	0.257348
$334$	5.23162	0.286261
$335$	−8.90632	−0.486604
$336$	12.4758	0.680608
$337$	−17.0840	−0.930624	−0.465312	−	0.885147i	$-0.654058\pi$
$337$	−17.0840	−0.930624	−0.465312	+	0.885147i	$0.654058\pi$
$338$	−8.87288	−0.482621
$339$	22.8875	1.24308
$340$	1.11525	0.0604831
$341$	−6.15045	−0.333066
$342$	−7.02690	−0.379971
$343$	−18.3640	−0.991565
$344$	10.2906	0.554833
$345$	0	0
$346$	−9.90502	−0.532497
$347$	25.7060	1.37997	0.689986	−	0.723823i	$-0.257617\pi$
$347$	25.7060	1.37997	0.689986	+	0.723823i	$0.257617\pi$
$348$	11.3981	0.611004
$349$	28.0255	1.50017	0.750086	−	0.661340i	$-0.230012\pi$
$349$	28.0255	1.50017	0.750086	+	0.661340i	$0.230012\pi$
$350$	12.3464	0.659941
$351$	−23.7794	−1.26925
$352$	4.09265	0.218139
$353$	1.01036	0.0537762	0.0268881	−	0.999638i	$-0.491440\pi$
$353$	1.01036	0.0537762	0.0268881	+	0.999638i	$0.491440\pi$
$354$	−22.6392	−1.20326
$355$	−0.846760	−0.0449414
$356$	3.02336	0.160238
$357$	5.98102	0.316549
$358$	−8.82623	−0.466481
$359$	−5.70273	−0.300978	−0.150489	−	0.988612i	$-0.548085\pi$
$359$	−5.70273	−0.300978	−0.150489	+	0.988612i	$0.548085\pi$
$360$	0.689353	0.0363321
$361$	42.1789	2.21994
$362$	26.2057	1.37734
$363$	−1.56821	−0.0823095
$364$	−5.24132	−0.274720
$365$	6.37525	0.333696
$366$	−9.26822	−0.484458
$367$	5.35487	0.279522	0.139761	−	0.990185i	$-0.455367\pi$
$367$	5.35487	0.279522	0.139761	+	0.990185i	$0.455367\pi$
$368$	0	0
$369$	1.25036	0.0650911
$370$	−8.93172	−0.464338
$371$	−1.16319	−0.0603896
$372$	7.33391	0.380245
$373$	0.235458	0.0121916	0.00609578	−	0.999981i	$-0.498060\pi$
$373$	0.235458	0.0121916	0.00609578	+	0.999981i	$0.498060\pi$
$374$	3.93682	0.203568
$375$	−9.33518	−0.482067
$376$	23.9967	1.23754
$377$	40.9365	2.10834
$378$	−14.8487	−0.763737
$379$	−6.96773	−0.357908	−0.178954	−	0.983857i	$-0.557271\pi$
$379$	−6.96773	−0.357908	−0.178954	+	0.983857i	$0.557271\pi$
$380$	3.68140	0.188852
$381$	27.0269	1.38463
$382$	45.2439	2.31488
$383$	−8.77251	−0.448254	−0.224127	−	0.974560i	$-0.571953\pi$
$383$	−8.77251	−0.448254	−0.224127	+	0.974560i	$0.571953\pi$
$384$	20.8754	1.06529
$385$	−0.996316	−0.0507770
$386$	3.94320	0.200704
$387$	−2.70175	−0.137338
$388$	2.41347	0.122525
$389$	8.75227	0.443758	0.221879	−	0.975074i	$-0.428781\pi$
$389$	8.75227	0.443758	0.221879	+	0.975074i	$0.428781\pi$
$390$	6.90684	0.349741
$391$	0	0
$392$	−9.08120	−0.458670
$393$	1.03545	0.0522317
$394$	37.6651	1.89754
$395$	4.37074	0.219916
$396$	−0.411154	−0.0206613
$397$	6.34338	0.318365	0.159183	−	0.987249i	$-0.449114\pi$
$397$	6.34338	0.318365	0.159183	+	0.987249i	$0.449114\pi$
$398$	−46.2087	−2.31624
$399$	19.7430	0.988389
$400$	22.8191	1.14096
$401$	−29.9288	−1.49457	−0.747287	−	0.664501i	$-0.768644\pi$
$401$	−29.9288	−1.49457	−0.747287	+	0.664501i	$0.768644\pi$
$402$	37.4885	1.86976
$403$	26.3398	1.31208
$404$	−3.21448	−0.159926
$405$	4.38584	0.217934
$406$	25.5623	1.26863
$407$	−8.68489	−0.430494
$408$	7.65316	0.378888
$409$	29.1785	1.44278	0.721392	−	0.692527i	$-0.243503\pi$
$409$	29.1785	1.44278	0.721392	+	0.692527i	$0.243503\pi$
$410$	−2.37808	−0.117445
$411$	16.4630	0.812059
$412$	3.91722	0.192987
$413$	−13.9857	−0.688192
$414$	0	0
$415$	8.73236	0.428655
$416$	−17.5271	−0.859336
$417$	4.82257	0.236162
$418$	12.9952	0.635618
$419$	−18.8284	−0.919827	−0.459914	−	0.887964i	$-0.652120\pi$
$419$	−18.8284	−0.919827	−0.459914	+	0.887964i	$0.652120\pi$
$420$	1.18802	0.0579697
$421$	−18.5020	−0.901731	−0.450865	−	0.892592i	$-0.648885\pi$
$421$	−18.5020	−0.901731	−0.450865	+	0.892592i	$0.648885\pi$
$422$	−18.1946	−0.885698
$423$	−6.30021	−0.306327
$424$	−1.48838	−0.0722823
$425$	10.9397	0.530655
$426$	3.56419	0.172685
$427$	−5.72558	−0.277080
$428$	11.5633	0.558931
$429$	6.71597	0.324250
$430$	5.13850	0.247800
$431$	5.02957	0.242266	0.121133	−	0.992636i	$-0.461347\pi$
$431$	5.02957	0.242266	0.121133	+	0.992636i	$0.461347\pi$
$432$	−27.4441	−1.32041
$433$	−9.96080	−0.478685	−0.239343	−	0.970935i	$-0.576932\pi$
$433$	−9.96080	−0.478685	−0.239343	+	0.970935i	$0.576932\pi$
$434$	16.4475	0.789507
$435$	−9.27888	−0.444888
$436$	−0.559688	−0.0268042
$437$	0	0
$438$	−26.8347	−1.28221
$439$	26.1168	1.24649	0.623244	−	0.782028i	$-0.285815\pi$
$439$	26.1168	1.24649	0.623244	+	0.782028i	$0.285815\pi$
$440$	−1.27486	−0.0607766
$441$	2.38422	0.113534
$442$	−16.8597	−0.801936
$443$	−19.2364	−0.913950	−0.456975	−	0.889480i	$-0.651067\pi$
$443$	−19.2364	−0.913950	−0.456975	+	0.889480i	$0.651067\pi$
$444$	10.3560	0.491475
$445$	−2.46123	−0.116673
$446$	41.9329	1.98558
$447$	−3.08399	−0.145868
$448$	4.96631	0.234636
$449$	10.6314	0.501726	0.250863	−	0.968023i	$-0.419286\pi$
$449$	10.6314	0.501726	0.250863	+	0.968023i	$0.419286\pi$
$450$	−4.14771	−0.195525
$451$	−2.31236	−0.108885
$452$	−11.0974	−0.521976
$453$	−15.5710	−0.731590
$454$	−23.1933	−1.08852
$455$	4.26680	0.200031
$456$	25.2627	1.18303
$457$	−19.9177	−0.931712	−0.465856	−	0.884861i	$-0.654254\pi$
$457$	−19.9177	−0.931712	−0.465856	+	0.884861i	$0.654254\pi$
$458$	−9.91891	−0.463480
$459$	−13.1570	−0.614117
$460$	0	0
$461$	−5.49988	−0.256155	−0.128078	−	0.991764i	$-0.540881\pi$
$461$	−5.49988	−0.256155	−0.128078	+	0.991764i	$0.540881\pi$
$462$	4.19370	0.195108
$463$	−21.6472	−1.00603	−0.503015	−	0.864277i	$-0.667776\pi$
$463$	−21.6472	−1.00603	−0.503015	+	0.864277i	$0.667776\pi$
$464$	47.2453	2.19331
$465$	−5.97031	−0.276867
$466$	29.4477	1.36414
$467$	11.0214	0.510011	0.255005	−	0.966940i	$-0.417923\pi$
$467$	11.0214	0.510011	0.255005	+	0.966940i	$0.417923\pi$
$468$	1.76080	0.0813930
$469$	23.1591	1.06939
$470$	11.9825	0.552710
$471$	−15.4065	−0.709895
$472$	−17.8958	−0.823719
$473$	4.99650	0.229739
$474$	−18.3973	−0.845017
$475$	36.1115	1.65691
$476$	−2.89999	−0.132921
$477$	0.390767	0.0178920
$478$	17.5446	0.802470
$479$	−7.53167	−0.344131	−0.172065	−	0.985086i	$-0.555044\pi$
$479$	−7.53167	−0.344131	−0.172065	+	0.985086i	$0.555044\pi$
$480$	3.97278	0.181332
$481$	37.1937	1.69589
$482$	20.2137	0.920710
$483$	0	0
$484$	0.760370	0.0345623
$485$	−1.96473	−0.0892138
$486$	9.21494	0.417998
$487$	17.1588	0.777539	0.388769	−	0.921335i	$-0.372900\pi$
$487$	17.1588	0.777539	0.388769	+	0.921335i	$0.372900\pi$
$488$	−7.32631	−0.331646
$489$	3.12822	0.141463
$490$	−4.53459	−0.204852
$491$	23.4006	1.05605	0.528027	−	0.849227i	$-0.322932\pi$
$491$	23.4006	1.05605	0.528027	+	0.849227i	$0.322932\pi$
$492$	2.75730	0.124309
$493$	22.6499	1.02010
$494$	−55.6532	−2.50395
$495$	0.334708	0.0150440
$496$	30.3991	1.36496
$497$	2.20183	0.0987655
$498$	−36.7563	−1.64709
$499$	21.1155	0.945261	0.472631	−	0.881261i	$-0.343304\pi$
$499$	21.1155	0.945261	0.472631	+	0.881261i	$0.343304\pi$
$500$	4.52631	0.202423
$501$	4.93805	0.220616
$502$	−15.4709	−0.690500
$503$	−13.1797	−0.587653	−0.293827	−	0.955859i	$-0.594929\pi$
$503$	−13.1797	−0.587653	−0.293827	+	0.955859i	$0.594929\pi$
$504$	−1.79252	−0.0798454
$505$	2.61681	0.116447
$506$	0	0
$507$	−8.37499	−0.371946
$508$	−13.1044	−0.581416
$509$	−5.50880	−0.244173	−0.122087	−	0.992519i	$-0.538959\pi$
$509$	−5.50880	−0.244173	−0.122087	+	0.992519i	$0.538959\pi$
$510$	3.82151	0.169220
$511$	−16.5776	−0.733348
$512$	0.130908	0.00578539
$513$	−43.4307	−1.91751
$514$	32.5306	1.43487
$515$	−3.18889	−0.140519
$516$	−5.95791	−0.262282
$517$	11.6513	0.512425
$518$	23.2251	1.02045
$519$	−9.34921	−0.410385
$520$	5.45969	0.239423
$521$	−21.3858	−0.936927	−0.468464	−	0.883483i	$-0.655192\pi$
$521$	−21.3858	−0.936927	−0.468464	+	0.883483i	$0.655192\pi$
$522$	−8.58753	−0.375866
$523$	−27.7437	−1.21315	−0.606575	−	0.795026i	$-0.707457\pi$
$523$	−27.7437	−1.21315	−0.606575	+	0.795026i	$0.707457\pi$
$524$	−0.502056	−0.0219324
$525$	11.6536	0.508603
$526$	−7.17900	−0.313019
$527$	14.5737	0.634839
$528$	7.75098	0.337318
$529$	0	0
$530$	−0.743207	−0.0322828
$531$	4.69844	0.203895
$532$	−9.57273	−0.415031
$533$	9.90287	0.428941
$534$	10.3598	0.448313
$535$	−9.41330	−0.406972
$536$	29.6338	1.27998
$537$	−8.33095	−0.359507
$538$	−32.0401	−1.38135
$539$	−4.40928	−0.189921
$540$	−2.61341	−0.112463
$541$	3.27579	0.140837	0.0704185	−	0.997518i	$-0.477567\pi$
$541$	3.27579	0.140837	0.0704185	+	0.997518i	$0.477567\pi$
$542$	−23.1557	−0.994624
$543$	24.7352	1.06149
$544$	−9.69764	−0.415783
$545$	0.455626	0.0195169
$546$	−17.9598	−0.768610
$547$	−26.4931	−1.13276	−0.566382	−	0.824143i	$-0.691657\pi$
$547$	−26.4931	−1.13276	−0.566382	+	0.824143i	$0.691657\pi$
$548$	−7.98234	−0.340989
$549$	1.92349	0.0820924
$550$	7.67059	0.327075
$551$	74.7664	3.18515
$552$	0	0
$553$	−11.3652	−0.483299
$554$	13.7107	0.582513
$555$	−8.43052	−0.357856
$556$	−2.33830	−0.0991661
$557$	−34.7407	−1.47201	−0.736005	−	0.676976i	$-0.763290\pi$
$557$	−34.7407	−1.47201	−0.736005	+	0.676976i	$0.763290\pi$
$558$	−5.52548	−0.233912
$559$	−21.3979	−0.905035
$560$	4.92437	0.208093
$561$	3.71591	0.156886
$562$	10.0297	0.423076
$563$	−1.85743	−0.0782813	−0.0391407	−	0.999234i	$-0.512462\pi$
$563$	−1.85743	−0.0782813	−0.0391407	+	0.999234i	$0.512462\pi$
$564$	−13.8933	−0.585012
$565$	9.03403	0.380064
$566$	−35.2650	−1.48230
$567$	−11.4045	−0.478944
$568$	2.81740	0.118216
$569$	−28.0289	−1.17503	−0.587516	−	0.809212i	$-0.699894\pi$
$569$	−28.0289	−1.17503	−0.587516	+	0.809212i	$0.699894\pi$
$570$	12.6146	0.528369
$571$	−23.3753	−0.978226	−0.489113	−	0.872220i	$-0.662679\pi$
$571$	−23.3753	−0.978226	−0.489113	+	0.872220i	$0.662679\pi$
$572$	−3.25635	−0.136155
$573$	42.7051	1.78403
$574$	6.18371	0.258103
$575$	0	0
$576$	−1.66841	−0.0695171
$577$	33.5017	1.39469	0.697346	−	0.716734i	$-0.254364\pi$
$577$	33.5017	1.39469	0.697346	+	0.716734i	$0.254364\pi$
$578$	18.9160	0.786803
$579$	3.72194	0.154678
$580$	4.49902	0.186811
$581$	−22.7067	−0.942035
$582$	8.26995	0.342800
$583$	−0.722668	−0.0299299
$584$	−21.2122	−0.877768
$585$	−1.43341	−0.0592644
$586$	−22.6473	−0.935550
$587$	−10.5456	−0.435262	−0.217631	−	0.976031i	$-0.569833\pi$
$587$	−10.5456	−0.435262	−0.217631	+	0.976031i	$0.569833\pi$
$588$	5.25770	0.216824
$589$	48.1069	1.98221
$590$	−8.93603	−0.367891
$591$	35.5516	1.46240
$592$	42.9257	1.76424
$593$	−19.6322	−0.806197	−0.403098	−	0.915157i	$-0.632067\pi$
$593$	−19.6322	−0.806197	−0.403098	+	0.915157i	$0.632067\pi$
$594$	−9.22528	−0.378518
$595$	2.36080	0.0967833
$596$	1.49532	0.0612508
$597$	−43.6158	−1.78508
$598$	0	0
$599$	9.40424	0.384247	0.192124	−	0.981371i	$-0.438463\pi$
$599$	9.40424	0.384247	0.192124	+	0.981371i	$0.438463\pi$
$600$	14.9116	0.608764
$601$	11.2566	0.459167	0.229583	−	0.973289i	$-0.426264\pi$
$601$	11.2566	0.459167	0.229583	+	0.973289i	$0.426264\pi$
$602$	−13.3616	−0.544580
$603$	−7.78020	−0.316834
$604$	7.54986	0.307199
$605$	−0.618995	−0.0251657
$606$	−11.0147	−0.447441
$607$	30.1996	1.22576	0.612881	−	0.790175i	$-0.290010\pi$
$607$	30.1996	1.22576	0.612881	+	0.790175i	$0.290010\pi$
$608$	−32.0114	−1.29823
$609$	24.1279	0.977710
$610$	−3.65831	−0.148121
$611$	−49.8978	−2.01865
$612$	0.974240	0.0393813
$613$	−14.3241	−0.578546	−0.289273	−	0.957247i	$-0.593414\pi$
$613$	−14.3241	−0.578546	−0.289273	+	0.957247i	$0.593414\pi$
$614$	−40.1057	−1.61853
$615$	−2.24463	−0.0905124
$616$	3.31502	0.133566
$617$	16.4854	0.663676	0.331838	−	0.943336i	$-0.392331\pi$
$617$	16.4854	0.663676	0.331838	+	0.943336i	$0.392331\pi$
$618$	13.4227	0.539940
$619$	−26.6043	−1.06932	−0.534658	−	0.845069i	$-0.679560\pi$
$619$	−26.6043	−1.06932	−0.534658	+	0.845069i	$0.679560\pi$
$620$	2.89480	0.116258
$621$	0	0
$622$	44.0533	1.76638
$623$	6.39993	0.256408
$624$	−33.1942	−1.32883
$625$	19.3995	0.775980
$626$	24.7094	0.987585
$627$	12.2660	0.489858
$628$	7.47010	0.298089
$629$	20.5791	0.820542
$630$	−0.895076	−0.0356607
$631$	−1.52350	−0.0606496	−0.0303248	−	0.999540i	$-0.509654\pi$
$631$	−1.52350	−0.0606496	−0.0303248	+	0.999540i	$0.509654\pi$
$632$	−14.5426	−0.578476
$633$	−17.1736	−0.682590
$634$	−22.6208	−0.898387
$635$	10.6679	0.423344
$636$	0.861722	0.0341695
$637$	18.8831	0.748176
$638$	15.8814	0.628751
$639$	−0.739695	−0.0292619
$640$	8.23983	0.325708
$641$	42.8758	1.69349	0.846746	−	0.531998i	$-0.178559\pi$
$641$	42.8758	1.69349	0.846746	+	0.531998i	$0.178559\pi$
$642$	39.6225	1.56378
$643$	48.7538	1.92266	0.961332	−	0.275393i	$-0.0888079\pi$
$643$	48.7538	1.92266	0.961332	+	0.275393i	$0.0888079\pi$
$644$	0	0
$645$	4.85016	0.190975
$646$	−30.7926	−1.21152
$647$	15.8590	0.623483	0.311741	−	0.950167i	$-0.399088\pi$
$647$	15.8590	0.623483	0.311741	+	0.950167i	$0.399088\pi$
$648$	−14.5929	−0.573263
$649$	−8.68909	−0.341077
$650$	−32.8499	−1.28848
$651$	15.5246	0.608457
$652$	−1.51677	−0.0594011
$653$	11.6310	0.455155	0.227577	−	0.973760i	$-0.426920\pi$
$653$	11.6310	0.455155	0.227577	+	0.973760i	$0.426920\pi$
$654$	−1.91782	−0.0749927
$655$	0.408709	0.0159696
$656$	11.4290	0.446228
$657$	5.56916	0.217274
$658$	−31.1580	−1.21467
$659$	−15.2980	−0.595926	−0.297963	−	0.954577i	$-0.596307\pi$
$659$	−15.2980	−0.595926	−0.297963	+	0.954577i	$0.596307\pi$
$660$	0.738100	0.0287305
$661$	33.6313	1.30810	0.654052	−	0.756449i	$-0.273068\pi$
$661$	33.6313	1.30810	0.654052	+	0.756449i	$0.273068\pi$
$662$	−25.8543	−1.00486
$663$	−15.9137	−0.618036
$664$	−29.0550	−1.12755
$665$	7.79288	0.302195
$666$	−7.80238	−0.302336
$667$	0	0
$668$	−2.39429	−0.0926380
$669$	39.5799	1.53025
$670$	14.7973	0.571669
$671$	−3.55721	−0.137325
$672$	−10.3304	−0.398504
$673$	49.7912	1.91931	0.959655	−	0.281181i	$-0.0907261\pi$
$673$	49.7912	1.91931	0.959655	+	0.281181i	$0.0907261\pi$
$674$	28.3840	1.09331
$675$	−25.6355	−0.986710
$676$	4.06075	0.156183
$677$	10.5029	0.403660	0.201830	−	0.979421i	$-0.435311\pi$
$677$	10.5029	0.403660	0.201830	+	0.979421i	$0.435311\pi$
$678$	−38.0261	−1.46038
$679$	5.10889	0.196061
$680$	3.02082	0.115843
$681$	−21.8918	−0.838897
$682$	10.2186	0.391290
$683$	−2.73910	−0.104809	−0.0524045	−	0.998626i	$-0.516689\pi$
$683$	−2.73910	−0.104809	−0.0524045	+	0.998626i	$0.516689\pi$
$684$	3.21592	0.122964
$685$	6.49819	0.248283
$686$	30.5107	1.16490
$687$	−9.36232	−0.357195
$688$	−24.6956	−0.941510
$689$	3.09489	0.117906
$690$	0	0
$691$	−10.0910	−0.383881	−0.191941	−	0.981407i	$-0.561478\pi$
$691$	−10.0910	−0.383881	−0.191941	+	0.981407i	$0.561478\pi$
$692$	4.53312	0.172323
$693$	−0.870341	−0.0330615
$694$	−42.7089	−1.62121
$695$	1.90354	0.0722055
$696$	30.8734	1.17025
$697$	5.47920	0.207540
$698$	−46.5626	−1.76242
$699$	27.7953	1.05131
$700$	−5.65042	−0.213566
$701$	−8.91178	−0.336593	−0.168297	−	0.985736i	$-0.553827\pi$
$701$	−8.91178	−0.336593	−0.168297	+	0.985736i	$0.553827\pi$
$702$	39.5080	1.49113
$703$	67.9305	2.56205
$704$	3.08549	0.116289
$705$	11.3101	0.425963
$706$	−1.67865	−0.0631770
$707$	−6.80449	−0.255909
$708$	10.3610	0.389391
$709$	8.43966	0.316958	0.158479	−	0.987362i	$-0.449341\pi$
$709$	8.43966	0.316958	0.158479	+	0.987362i	$0.449341\pi$
$710$	1.40684	0.0527977
$711$	3.81810	0.143190
$712$	8.18919	0.306903
$713$	0	0
$714$	−9.93708	−0.371886
$715$	2.65089	0.0991378
$716$	4.03940	0.150959
$717$	16.5601	0.618448
$718$	9.47472	0.353593
$719$	−7.71862	−0.287856	−0.143928	−	0.989588i	$-0.545973\pi$
$719$	−7.71862	−0.287856	−0.143928	+	0.989588i	$0.545973\pi$
$720$	−1.65432	−0.0616529
$721$	8.29206	0.308813
$722$	−70.0775	−2.60801
$723$	19.0795	0.709573
$724$	−11.9933	−0.445727
$725$	44.1317	1.63901
$726$	2.60547	0.0966982
$727$	−21.1775	−0.785429	−0.392714	−	0.919660i	$-0.628464\pi$
$727$	−21.1775	−0.785429	−0.392714	+	0.919660i	$0.628464\pi$
$728$	−14.1968	−0.526169
$729$	29.9541	1.10941
$730$	−10.5921	−0.392030
$731$	−11.8393	−0.437894
$732$	4.24168	0.156777
$733$	13.4252	0.495870	0.247935	−	0.968777i	$-0.420248\pi$
$733$	13.4252	0.495870	0.247935	+	0.968777i	$0.420248\pi$
$734$	−8.89677	−0.328386
$735$	−4.28014	−0.157875
$736$	0	0
$737$	14.3884	0.530002
$738$	−2.07739	−0.0764699
$739$	−45.1842	−1.66213	−0.831063	−	0.556178i	$-0.812267\pi$
$739$	−45.1842	−1.66213	−0.831063	+	0.556178i	$0.812267\pi$
$740$	4.08768	0.150266
$741$	−52.5302	−1.92975
$742$	1.93256	0.0709465
$743$	12.4616	0.457170	0.228585	−	0.973524i	$-0.426590\pi$
$743$	12.4616	0.457170	0.228585	+	0.973524i	$0.426590\pi$
$744$	19.8649	0.728282
$745$	−1.21730	−0.0445983
$746$	−0.391199	−0.0143228
$747$	7.62823	0.279103
$748$	−1.80172	−0.0658773
$749$	24.4774	0.894384
$750$	15.5098	0.566338
$751$	−19.8926	−0.725890	−0.362945	−	0.931811i	$-0.618229\pi$
$751$	−19.8926	−0.725890	−0.362945	+	0.931811i	$0.618229\pi$
$752$	−57.5877	−2.10001
$753$	−14.6028	−0.532154
$754$	−68.0134	−2.47690
$755$	−6.14612	−0.223680
$756$	6.79565	0.247155
$757$	−37.7019	−1.37030	−0.685149	−	0.728403i	$-0.740263\pi$
$757$	−37.7019	−1.37030	−0.685149	+	0.728403i	$0.740263\pi$
$758$	11.5764	0.420475
$759$	0	0
$760$	9.97156	0.361707
$761$	−19.9487	−0.723141	−0.361571	−	0.932345i	$-0.617759\pi$
$761$	−19.9487	−0.723141	−0.361571	+	0.932345i	$0.617759\pi$
$762$	−44.9035	−1.62668
$763$	−1.18476	−0.0428913
$764$	−20.7062	−0.749126
$765$	−0.793100	−0.0286746
$766$	14.5750	0.526615
$767$	37.2117	1.34364
$768$	−25.0058	−0.902318
$769$	−6.83927	−0.246631	−0.123315	−	0.992368i	$-0.539353\pi$
$769$	−6.83927	−0.246631	−0.123315	+	0.992368i	$0.539353\pi$
$770$	1.65532	0.0596534
$771$	30.7052	1.10582
$772$	−1.80464	−0.0649504
$773$	36.0368	1.29615	0.648077	−	0.761575i	$-0.275574\pi$
$773$	36.0368	1.29615	0.648077	+	0.761575i	$0.275574\pi$
$774$	4.48878	0.161346
$775$	28.3957	1.02000
$776$	6.53720	0.234672
$777$	21.9219	0.786443
$778$	−14.5413	−0.521332
$779$	18.0866	0.648019
$780$	−3.16097	−0.113181
$781$	1.36796	0.0489495
$782$	0	0
$783$	−53.0764	−1.89680
$784$	21.7932	0.778329
$785$	−6.08118	−0.217047
$786$	−1.72034	−0.0613625
$787$	−7.73134	−0.275593	−0.137796	−	0.990461i	$-0.544002\pi$
$787$	−7.73134	−0.275593	−0.137796	+	0.990461i	$0.544002\pi$
$788$	−17.2378	−0.614070
$789$	−6.77616	−0.241238
$790$	−7.26170	−0.258360
$791$	−23.4912	−0.835250
$792$	−1.11367	−0.0395724
$793$	15.2340	0.540977
$794$	−10.5391	−0.374020
$795$	−0.701502	−0.0248797
$796$	21.1478	0.749565
$797$	21.0466	0.745510	0.372755	−	0.927930i	$-0.378413\pi$
$797$	21.0466	0.745510	0.372755	+	0.927930i	$0.378413\pi$
$798$	−32.8018	−1.16117
$799$	−27.6082	−0.976707
$800$	−18.8951	−0.668043
$801$	−2.15003	−0.0759676
$802$	49.7248	1.75584
$803$	−10.2994	−0.363457
$804$	−17.1569	−0.605078
$805$	0	0
$806$	−43.7619	−1.54145
$807$	−30.2422	−1.06458
$808$	−8.70685	−0.306306
$809$	32.3982	1.13906	0.569531	−	0.821970i	$-0.307125\pi$
$809$	32.3982	1.13906	0.569531	+	0.821970i	$0.307125\pi$
$810$	−7.28680	−0.256032
$811$	11.3359	0.398057	0.199028	−	0.979994i	$-0.436221\pi$
$811$	11.3359	0.398057	0.199028	+	0.979994i	$0.436221\pi$
$812$	−11.6988	−0.410547
$813$	−21.8564	−0.766537
$814$	14.4294	0.505750
$815$	1.23475	0.0432515
$816$	−18.3662	−0.642944
$817$	−39.0811	−1.36727
$818$	−48.4782	−1.69500
$819$	3.72730	0.130243
$820$	1.08835	0.0380067
$821$	−0.998090	−0.0348336	−0.0174168	−	0.999848i	$-0.505544\pi$
$821$	−0.998090	−0.0348336	−0.0174168	+	0.999848i	$0.505544\pi$
$822$	−27.3522	−0.954017
$823$	−30.4306	−1.06074	−0.530372	−	0.847765i	$-0.677948\pi$
$823$	−30.4306	−1.06074	−0.530372	+	0.847765i	$0.677948\pi$
$824$	10.6103	0.369628
$825$	7.24017	0.252070
$826$	23.2364	0.808496
$827$	−10.0372	−0.349028	−0.174514	−	0.984655i	$-0.555835\pi$
$827$	−10.0372	−0.349028	−0.174514	+	0.984655i	$0.555835\pi$
$828$	0	0
$829$	10.5351	0.365899	0.182950	−	0.983122i	$-0.441435\pi$
$829$	10.5351	0.365899	0.182950	+	0.983122i	$0.441435\pi$
$830$	−14.5083	−0.503589
$831$	12.9414	0.448931
$832$	−13.2138	−0.458107
$833$	10.4479	0.361999
$834$	−8.01240	−0.277447
$835$	1.94912	0.0674522
$836$	−5.94738	−0.205695
$837$	−34.1510	−1.18043
$838$	31.2822	1.08062
$839$	25.4274	0.877850	0.438925	−	0.898524i	$-0.355359\pi$
$839$	25.4274	0.877850	0.438925	+	0.898524i	$0.355359\pi$
$840$	3.21793	0.111029
$841$	62.3716	2.15074
$842$	30.7398	1.05937
$843$	9.46687	0.326056
$844$	8.32690	0.286624
$845$	−3.30573	−0.113721
$846$	10.4674	0.359877
$847$	1.60957	0.0553055
$848$	3.57184	0.122658
$849$	−33.2861	−1.14238
$850$	−18.1757	−0.623421
$851$	0	0
$852$	−1.63118	−0.0558833
$853$	18.9160	0.647671	0.323835	−	0.946113i	$-0.395028\pi$
$853$	18.9160	0.647671	0.323835	+	0.946113i	$0.395028\pi$
$854$	9.51269	0.325518
$855$	−2.61798	−0.0895331
$856$	31.3206	1.07052
$857$	0.387282	0.0132293	0.00661465	−	0.999978i	$-0.497894\pi$
$857$	0.387282	0.0132293	0.00661465	+	0.999978i	$0.497894\pi$
$858$	−11.1582	−0.380933
$859$	5.13183	0.175096	0.0875478	−	0.996160i	$-0.472097\pi$
$859$	5.13183	0.175096	0.0875478	+	0.996160i	$0.472097\pi$
$860$	−2.35168	−0.0801915
$861$	5.83672	0.198915
$862$	−8.35631	−0.284617
$863$	16.5309	0.562719	0.281360	−	0.959602i	$-0.409215\pi$
$863$	16.5309	0.562719	0.281360	+	0.959602i	$0.409215\pi$
$864$	22.7248	0.773113
$865$	−3.69028	−0.125473
$866$	16.5492	0.562366
$867$	17.8546	0.606373
$868$	−7.52735	−0.255495
$869$	−7.06103	−0.239529
$870$	15.4163	0.522660
$871$	−61.6193	−2.08789
$872$	−1.51599	−0.0513380
$873$	−1.71631	−0.0580882
$874$	0	0
$875$	9.58142	0.323911
$876$	12.2811	0.414942
$877$	42.9346	1.44980	0.724899	−	0.688855i	$-0.241886\pi$
$877$	42.9346	1.44980	0.724899	+	0.688855i	$0.241886\pi$
$878$	−43.3914	−1.46439
$879$	−21.3764	−0.721010
$880$	3.05943	0.103133
$881$	3.94591	0.132941	0.0664706	−	0.997788i	$-0.478826\pi$
$881$	3.94591	0.132941	0.0664706	+	0.997788i	$0.478826\pi$
$882$	−3.96124	−0.133382
$883$	−3.43182	−0.115490	−0.0577450	−	0.998331i	$-0.518391\pi$
$883$	−3.43182	−0.115490	−0.0577450	+	0.998331i	$0.518391\pi$
$884$	7.71600	0.259517
$885$	−8.43460	−0.283526
$886$	31.9601	1.07372
$887$	−55.6303	−1.86788	−0.933941	−	0.357427i	$-0.883654\pi$
$887$	−55.6303	−1.86788	−0.933941	+	0.357427i	$0.883654\pi$
$888$	28.0507	0.941319
$889$	−27.7398	−0.930364
$890$	4.08918	0.137069
$891$	−7.08543	−0.237371
$892$	−19.1910	−0.642561
$893$	−91.1332	−3.04966
$894$	5.12385	0.171367
$895$	−3.28835	−0.109917
$896$	−21.4260	−0.715793
$897$	0	0
$898$	−17.6633	−0.589434
$899$	58.7912	1.96080
$900$	1.89823	0.0632745
$901$	1.71238	0.0570477
$902$	3.84184	0.127919
$903$	−12.6119	−0.419696
$904$	−30.0587	−0.999738
$905$	9.76337	0.324545
$906$	25.8703	0.859482
$907$	28.7837	0.955749	0.477874	−	0.878428i	$-0.341407\pi$
$907$	28.7837	0.955749	0.477874	+	0.878428i	$0.341407\pi$
$908$	10.6146	0.352258
$909$	2.28594	0.0758199
$910$	−7.08902	−0.234999
$911$	−18.4717	−0.611996	−0.305998	−	0.952032i	$-0.598990\pi$
$911$	−18.4717	−0.611996	−0.305998	+	0.952032i	$0.598990\pi$
$912$	−60.6258	−2.00752
$913$	−14.1073	−0.466884
$914$	33.0920	1.09459
$915$	−3.45302	−0.114153
$916$	4.53947	0.149988
$917$	−1.06277	−0.0350956
$918$	21.8596	0.721473
$919$	−13.5885	−0.448243	−0.224121	−	0.974561i	$-0.571951\pi$
$919$	−13.5885	−0.448243	−0.224121	+	0.974561i	$0.571951\pi$
$920$	0	0
$921$	−37.8552	−1.24737
$922$	9.13771	0.300934
$923$	−5.85840	−0.192832
$924$	−1.91928	−0.0631397
$925$	40.0968	1.31837
$926$	35.9654	1.18190
$927$	−2.78568	−0.0914938
$928$	−39.1210	−1.28421
$929$	11.5668	0.379495	0.189747	−	0.981833i	$-0.439233\pi$
$929$	11.5668	0.379495	0.189747	+	0.981833i	$0.439233\pi$
$930$	9.91929	0.325266
$931$	34.4880	1.13030
$932$	−13.4770	−0.441454
$933$	41.5813	1.36131
$934$	−18.3114	−0.599167
$935$	1.46672	0.0479670
$936$	4.76936	0.155892
$937$	−58.0108	−1.89513	−0.947565	−	0.319564i	$-0.896464\pi$
$937$	−58.0108	−1.89513	−0.947565	+	0.319564i	$0.896464\pi$
$938$	−38.4773	−1.25633
$939$	23.3228	0.761112
$940$	−5.48388	−0.178864
$941$	−32.4334	−1.05730	−0.528649	−	0.848840i	$-0.677301\pi$
$941$	−32.4334	−1.05730	−0.528649	+	0.848840i	$0.677301\pi$
$942$	25.5969	0.833994
$943$	0	0
$944$	42.9465	1.39779
$945$	−5.53214	−0.179960
$946$	−8.30136	−0.269901
$947$	−0.711323	−0.0231149	−0.0115574	−	0.999933i	$-0.503679\pi$
$947$	−0.711323	−0.0231149	−0.0115574	+	0.999933i	$0.503679\pi$
$948$	8.41969	0.273459
$949$	44.1079	1.43180
$950$	−59.9970	−1.94656
$951$	−21.3515	−0.692369
$952$	−7.85503	−0.254583
$953$	48.7544	1.57931	0.789655	−	0.613551i	$-0.210260\pi$
$953$	48.7544	1.57931	0.789655	+	0.613551i	$0.210260\pi$
$954$	−0.649235	−0.0210198
$955$	16.8563	0.545458
$956$	−8.02942	−0.259690
$957$	14.9902	0.484566
$958$	12.5134	0.404289
$959$	−16.8972	−0.545640
$960$	2.99512	0.0966669
$961$	6.82805	0.220260
$962$	−61.7950	−1.99235
$963$	−8.22307	−0.264985
$964$	−9.25098	−0.297954
$965$	1.46910	0.0472921
$966$	0	0
$967$	−14.9479	−0.480691	−0.240345	−	0.970687i	$-0.577261\pi$
$967$	−14.9479	−0.480691	−0.240345	+	0.970687i	$0.577261\pi$
$968$	2.05957	0.0661970
$969$	−29.0647	−0.933692
$970$	3.26427	0.104810
$971$	20.7716	0.666592	0.333296	−	0.942822i	$-0.391839\pi$
$971$	20.7716	0.666592	0.333296	+	0.942822i	$0.391839\pi$
$972$	−4.21729	−0.135270
$973$	−4.94978	−0.158683
$974$	−28.5082	−0.913463
$975$	−31.0066	−0.993006
$976$	17.5818	0.562779
$977$	−25.3681	−0.811598	−0.405799	−	0.913962i	$-0.633007\pi$
$977$	−25.3681	−0.811598	−0.405799	+	0.913962i	$0.633007\pi$
$978$	−5.19733	−0.166192
$979$	3.97617	0.127079
$980$	2.07529	0.0662929
$981$	0.398016	0.0127077
$982$	−38.8786	−1.24067
$983$	−21.3360	−0.680514	−0.340257	−	0.940332i	$-0.610514\pi$
$983$	−21.3360	−0.680514	−0.340257	+	0.940332i	$0.610514\pi$
$984$	7.46852	0.238088
$985$	14.0327	0.447121
$986$	−37.6314	−1.19843
$987$	−29.4096	−0.936118
$988$	25.4701	0.810313
$989$	0	0
$990$	−0.556096	−0.0176739
$991$	47.2508	1.50097	0.750486	−	0.660887i	$-0.229820\pi$
$991$	47.2508	1.50097	0.750486	+	0.660887i	$0.229820\pi$
$992$	−25.1716	−0.799200
$993$	−24.4035	−0.774422
$994$	−3.65820	−0.116031
$995$	−17.2158	−0.545778
$996$	16.8218	0.533020
$997$	7.49197	0.237273	0.118637	−	0.992938i	$-0.462148\pi$
$997$	7.49197	0.237273	0.118637	+	0.992938i	$0.462148\pi$
$998$	−35.0821	−1.11050
$999$	−48.2237	−1.52573

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5819.2.a.u.1.14		60
23.2	even	11		253.2.i.b.188.3	yes	120
23.12	even	11		253.2.i.b.144.3	✓	120
23.22	odd	2		5819.2.a.t.1.14		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.2.i.b.144.3	✓	120	23.12	even	11
253.2.i.b.188.3	yes	120	23.2	even	11
5819.2.a.t.1.14		60	23.22	odd	2
5819.2.a.u.1.14		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)

\(f(q)\)	\(=\)	\(q-1.66144 q^{2} -1.56821 q^{3} +0.760370 q^{4} -0.618995 q^{5} +2.60547 q^{6} +1.60957 q^{7} +2.05957 q^{8} -0.540729 q^{9} +1.02842 q^{10} +1.00000 q^{11} -1.19242 q^{12} -4.28258 q^{13} -2.67420 q^{14} +0.970711 q^{15} -4.94258 q^{16} -2.36953 q^{17} +0.898386 q^{18} -7.82169 q^{19} -0.470665 q^{20} -2.52414 q^{21} -1.66144 q^{22} -3.22982 q^{24} -4.61685 q^{25} +7.11523 q^{26} +5.55259 q^{27} +1.22387 q^{28} -9.55885 q^{29} -1.61278 q^{30} -6.15045 q^{31} +4.09265 q^{32} -1.56821 q^{33} +3.93682 q^{34} -0.996316 q^{35} -0.411154 q^{36} -8.68489 q^{37} +12.9952 q^{38} +6.71597 q^{39} -1.27486 q^{40} -2.31236 q^{41} +4.19370 q^{42} +4.99650 q^{43} +0.760370 q^{44} +0.334708 q^{45} +11.6513 q^{47} +7.75098 q^{48} -4.40928 q^{49} +7.67059 q^{50} +3.71591 q^{51} -3.25635 q^{52} -0.722668 q^{53} -9.22528 q^{54} -0.618995 q^{55} +3.31502 q^{56} +12.2660 q^{57} +15.8814 q^{58} -8.68909 q^{59} +0.738100 q^{60} -3.55721 q^{61} +10.2186 q^{62} -0.870341 q^{63} +3.08549 q^{64} +2.65089 q^{65} +2.60547 q^{66} +14.3884 q^{67} -1.80172 q^{68} +1.65532 q^{70} +1.36796 q^{71} -1.11367 q^{72} -10.2994 q^{73} +14.4294 q^{74} +7.24017 q^{75} -5.94738 q^{76} +1.60957 q^{77} -11.1582 q^{78} -7.06103 q^{79} +3.05943 q^{80} -7.08543 q^{81} +3.84184 q^{82} -14.1073 q^{83} -1.91928 q^{84} +1.46672 q^{85} -8.30136 q^{86} +14.9902 q^{87} +2.05957 q^{88} +3.97617 q^{89} -0.556096 q^{90} -6.89312 q^{91} +9.64518 q^{93} -19.3580 q^{94} +4.84159 q^{95} -6.41811 q^{96} +3.17407 q^{97} +7.32574 q^{98} -0.540729 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 5 q^{2} + 9 q^{3} + 73 q^{4} + 8 q^{5} + 26 q^{6} + 30 q^{8} + 75 q^{9} - 7 q^{10} + 60 q^{11} + 41 q^{12} + 46 q^{13} + 16 q^{14} + 4 q^{15} + 99 q^{16} - 5 q^{17} + 36 q^{18} - 8 q^{19} + 82 q^{20}+ \cdots + 75 q^{99}+O(q^{100}) \) 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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