LMFDB - Embedded newform 5819.2.a.u.1.16

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			1.16
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)

$f(q)$	$=$	\(q-1.41986 q^{2} -1.33152 q^{3} +0.0159886 q^{4} -3.46743 q^{5} +1.89056 q^{6} -4.25485 q^{7} +2.81701 q^{8} -1.22706 q^{9} +4.92324 q^{10} +1.00000 q^{11} -0.0212892 q^{12} +4.11273 q^{13} +6.04128 q^{14} +4.61694 q^{15} -4.03172 q^{16} +4.97059 q^{17} +1.74224 q^{18} -4.15019 q^{19} -0.0554394 q^{20} +5.66542 q^{21} -1.41986 q^{22} -3.75090 q^{24} +7.02304 q^{25} -5.83949 q^{26} +5.62841 q^{27} -0.0680293 q^{28} -4.41798 q^{29} -6.55539 q^{30} -5.73794 q^{31} +0.0904432 q^{32} -1.33152 q^{33} -7.05752 q^{34} +14.7534 q^{35} -0.0196190 q^{36} +8.00763 q^{37} +5.89267 q^{38} -5.47619 q^{39} -9.76777 q^{40} -8.40892 q^{41} -8.04408 q^{42} -2.20336 q^{43} +0.0159886 q^{44} +4.25472 q^{45} +5.39036 q^{47} +5.36832 q^{48} +11.1038 q^{49} -9.97170 q^{50} -6.61844 q^{51} +0.0657570 q^{52} +1.58092 q^{53} -7.99152 q^{54} -3.46743 q^{55} -11.9860 q^{56} +5.52606 q^{57} +6.27290 q^{58} +2.29767 q^{59} +0.0738187 q^{60} -11.8411 q^{61} +8.14704 q^{62} +5.22094 q^{63} +7.93503 q^{64} -14.2606 q^{65} +1.89056 q^{66} -11.8408 q^{67} +0.0794730 q^{68} -20.9477 q^{70} -2.81554 q^{71} -3.45663 q^{72} +8.31668 q^{73} -11.3697 q^{74} -9.35131 q^{75} -0.0663559 q^{76} -4.25485 q^{77} +7.77539 q^{78} -7.13322 q^{79} +13.9797 q^{80} -3.81317 q^{81} +11.9394 q^{82} +1.35058 q^{83} +0.0905824 q^{84} -17.2352 q^{85} +3.12846 q^{86} +5.88263 q^{87} +2.81701 q^{88} -2.64145 q^{89} -6.04109 q^{90} -17.4991 q^{91} +7.64017 q^{93} -7.65353 q^{94} +14.3905 q^{95} -0.120427 q^{96} -10.2232 q^{97} -15.7658 q^{98} -1.22706 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.41986	−1.00399	−0.501995	−	0.864871i	$-0.667400\pi$
$2$	−1.41986	−1.00399	−0.501995	+	0.864871i	$0.667400\pi$
$3$	−1.33152	−0.768753	−0.384377	−	0.923176i	$-0.625584\pi$
$3$	−1.33152	−0.768753	−0.384377	+	0.923176i	$0.625584\pi$
$4$	0.0159886	0.00799432
$5$	−3.46743	−1.55068	−0.775340	−	0.631544i	$-0.782421\pi$
$5$	−3.46743	−1.55068	−0.775340	+	0.631544i	$0.782421\pi$
$6$	1.89056	0.771820
$7$	−4.25485	−1.60818	−0.804092	−	0.594505i	$-0.797348\pi$
$7$	−4.25485	−1.60818	−0.804092	+	0.594505i	$0.797348\pi$
$8$	2.81701	0.995963
$9$	−1.22706	−0.409019
$10$	4.92324	1.55687
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.0212892	−0.00614566
$13$	4.11273	1.14067	0.570334	−	0.821413i	$-0.306814\pi$
$13$	4.11273	1.14067	0.570334	+	0.821413i	$0.306814\pi$
$14$	6.04128	1.61460
$15$	4.61694	1.19209
$16$	−4.03172	−1.00793
$17$	4.97059	1.20555	0.602773	−	0.797913i	$-0.294063\pi$
$17$	4.97059	1.20555	0.602773	+	0.797913i	$0.294063\pi$
$18$	1.74224	0.410650
$19$	−4.15019	−0.952119	−0.476060	−	0.879413i	$-0.657935\pi$
$19$	−4.15019	−0.952119	−0.476060	+	0.879413i	$0.657935\pi$
$20$	−0.0554394	−0.0123966
$21$	5.66542	1.23630
$22$	−1.41986	−0.302714
$23$	0	0
$23$	0	0
$24$	−3.75090	−0.765650
$25$	7.02304	1.40461
$26$	−5.83949	−1.14522
$27$	5.62841	1.08319
$28$	−0.0680293	−0.0128563
$29$	−4.41798	−0.820399	−0.410199	−	0.911996i	$-0.634541\pi$
$29$	−4.41798	−0.820399	−0.410199	+	0.911996i	$0.634541\pi$
$30$	−6.55539	−1.19685
$31$	−5.73794	−1.03056	−0.515282	−	0.857021i	$-0.672313\pi$
$31$	−5.73794	−1.03056	−0.515282	+	0.857021i	$0.672313\pi$
$32$	0.0904432	0.0159883
$33$	−1.33152	−0.231788
$34$	−7.05752	−1.21035
$35$	14.7534	2.49378
$36$	−0.0196190	−0.00326983
$37$	8.00763	1.31645	0.658223	−	0.752823i	$-0.271308\pi$
$37$	8.00763	1.31645	0.658223	+	0.752823i	$0.271308\pi$
$38$	5.89267	0.955917
$39$	−5.47619	−0.876892
$40$	−9.76777	−1.54442
$41$	−8.40892	−1.31325	−0.656626	−	0.754216i	$-0.728017\pi$
$41$	−8.40892	−1.31325	−0.656626	+	0.754216i	$0.728017\pi$
$42$	−8.04408	−1.24123
$43$	−2.20336	−0.336010	−0.168005	−	0.985786i	$-0.553732\pi$
$43$	−2.20336	−0.336010	−0.168005	+	0.985786i	$0.553732\pi$
$44$	0.0159886	0.00241038
$45$	4.25472	0.634257
$46$	0	0
$47$	5.39036	0.786265	0.393133	−	0.919482i	$-0.371391\pi$
$47$	5.39036	0.786265	0.393133	+	0.919482i	$0.371391\pi$
$48$	5.36832	0.774850
$49$	11.1038	1.58625
$50$	−9.97170	−1.41021
$51$	−6.61844	−0.926767
$52$	0.0657570	0.00911886
$53$	1.58092	0.217156	0.108578	−	0.994088i	$-0.465370\pi$
$53$	1.58092	0.217156	0.108578	+	0.994088i	$0.465370\pi$
$54$	−7.99152	−1.08751
$55$	−3.46743	−0.467548
$56$	−11.9860	−1.60169
$57$	5.52606	0.731945
$58$	6.27290	0.823672
$59$	2.29767	0.299131	0.149565	−	0.988752i	$-0.452213\pi$
$59$	2.29767	0.299131	0.149565	+	0.988752i	$0.452213\pi$
$60$	0.0738187	0.00952995
$61$	−11.8411	−1.51610	−0.758051	−	0.652195i	$-0.773848\pi$
$61$	−11.8411	−1.51610	−0.758051	+	0.652195i	$0.773848\pi$
$62$	8.14704	1.03467
$63$	5.22094	0.657777
$64$	7.93503	0.991878
$65$	−14.2606	−1.76881
$66$	1.89056	0.232712
$67$	−11.8408	−1.44658	−0.723289	−	0.690545i	$-0.757371\pi$
$67$	−11.8408	−1.44658	−0.723289	+	0.690545i	$0.757371\pi$
$68$	0.0794730	0.00963752
$69$	0	0
$70$	−20.9477	−2.50373
$71$	−2.81554	−0.334143	−0.167072	−	0.985945i	$-0.553431\pi$
$71$	−2.81554	−0.334143	−0.167072	+	0.985945i	$0.553431\pi$
$72$	−3.45663	−0.407367
$73$	8.31668	0.973393	0.486697	−	0.873571i	$-0.338202\pi$
$73$	8.31668	0.973393	0.486697	+	0.873571i	$0.338202\pi$
$74$	−11.3697	−1.32170
$75$	−9.35131	−1.07980
$76$	−0.0663559	−0.00761155
$77$	−4.25485	−0.484886
$78$	7.77539	0.880390
$79$	−7.13322	−0.802550	−0.401275	−	0.915958i	$-0.631433\pi$
$79$	−7.13322	−0.802550	−0.401275	+	0.915958i	$0.631433\pi$
$80$	13.9797	1.56298
$81$	−3.81317	−0.423685
$82$	11.9394	1.31849
$83$	1.35058	0.148245	0.0741225	−	0.997249i	$-0.476384\pi$
$83$	1.35058	0.148245	0.0741225	+	0.997249i	$0.476384\pi$
$84$	0.0905824	0.00988335
$85$	−17.2352	−1.86942
$86$	3.12846	0.337350
$87$	5.88263	0.630684
$88$	2.81701	0.300294
$89$	−2.64145	−0.279993	−0.139997	−	0.990152i	$-0.544709\pi$
$89$	−2.64145	−0.279993	−0.139997	+	0.990152i	$0.544709\pi$
$90$	−6.04109	−0.636787
$91$	−17.4991	−1.83440
$92$	0	0
$93$	7.64017	0.792249
$94$	−7.65353	−0.789402
$95$	14.3905	1.47643
$96$	−0.120427	−0.0122910
$97$	−10.2232	−1.03801	−0.519006	−	0.854771i	$-0.673698\pi$
$97$	−10.2232	−1.03801	−0.519006	+	0.854771i	$0.673698\pi$
$98$	−15.7658	−1.59258
$99$	−1.22706	−0.123324
$100$	0.112289	0.0112289
$101$	−8.37347	−0.833191	−0.416596	−	0.909092i	$-0.636777\pi$
$101$	−8.37347	−0.833191	−0.416596	+	0.909092i	$0.636777\pi$
$102$	9.39723	0.930464
$103$	−15.8814	−1.56484	−0.782422	−	0.622749i	$-0.786016\pi$
$103$	−15.8814	−1.56484	−0.782422	+	0.622749i	$0.786016\pi$
$104$	11.5856	1.13606
$105$	−19.6444	−1.91710
$106$	−2.24468	−0.218023
$107$	−10.8092	−1.04497	−0.522484	−	0.852649i	$-0.674994\pi$
$107$	−10.8092	−1.04497	−0.522484	+	0.852649i	$0.674994\pi$
$108$	0.0899906	0.00865935
$109$	2.15190	0.206115	0.103057	−	0.994675i	$-0.467137\pi$
$109$	2.15190	0.206115	0.103057	+	0.994675i	$0.467137\pi$
$110$	4.92324	0.469413
$111$	−10.6623	−1.01202
$112$	17.1544	1.62094
$113$	−13.8690	−1.30468	−0.652342	−	0.757925i	$-0.726213\pi$
$113$	−13.8690	−1.30468	−0.652342	+	0.757925i	$0.726213\pi$
$114$	−7.84621	−0.734865
$115$	0	0
$116$	−0.0706375	−0.00655853
$117$	−5.04656	−0.466554
$118$	−3.26236	−0.300324
$119$	−21.1491	−1.93874
$120$	13.0060	1.18728
$121$	1.00000	0.0909091
$122$	16.8127	1.52215
$123$	11.1966	1.00957
$124$	−0.0917418	−0.00823866
$125$	−7.01473	−0.627417
$126$	−7.41298	−0.660401
$127$	8.98982	0.797718	0.398859	−	0.917012i	$-0.369406\pi$
$127$	8.98982	0.797718	0.398859	+	0.917012i	$0.369406\pi$
$128$	−11.4475	−1.01182
$129$	2.93382	0.258309
$130$	20.2480	1.77587
$131$	3.56452	0.311434	0.155717	−	0.987802i	$-0.450231\pi$
$131$	3.56452	0.311434	0.155717	+	0.987802i	$0.450231\pi$
$132$	−0.0212892	−0.00185299
$133$	17.6585	1.53118
$134$	16.8122	1.45235
$135$	−19.5161	−1.67968
$136$	14.0022	1.20068
$137$	−5.76972	−0.492940	−0.246470	−	0.969150i	$-0.579271\pi$
$137$	−5.76972	−0.492940	−0.246470	+	0.969150i	$0.579271\pi$
$138$	0	0
$139$	−10.0047	−0.848589	−0.424294	−	0.905524i	$-0.639478\pi$
$139$	−10.0047	−0.848589	−0.424294	+	0.905524i	$0.639478\pi$
$140$	0.235887	0.0199361
$141$	−7.17737	−0.604444
$142$	3.99766	0.335476
$143$	4.11273	0.343924
$144$	4.94715	0.412262
$145$	15.3190	1.27218
$146$	−11.8085	−0.977276
$147$	−14.7849	−1.21944
$148$	0.128031	0.0105241
$149$	11.4806	0.940525	0.470263	−	0.882526i	$-0.344159\pi$
$149$	11.4806	0.940525	0.470263	+	0.882526i	$0.344159\pi$
$150$	13.2775	1.08410
$151$	−15.2754	−1.24309	−0.621547	−	0.783377i	$-0.713495\pi$
$151$	−15.2754	−1.24309	−0.621547	+	0.783377i	$0.713495\pi$
$152$	−11.6911	−0.948276
$153$	−6.09920	−0.493091
$154$	6.04128	0.486820
$155$	19.8959	1.59807
$156$	−0.0875568	−0.00701015
$157$	−12.3833	−0.988291	−0.494146	−	0.869379i	$-0.664519\pi$
$157$	−12.3833	−0.988291	−0.494146	+	0.869379i	$0.664519\pi$
$158$	10.1281	0.805751
$159$	−2.10503	−0.166940
$160$	−0.313605	−0.0247927
$161$	0	0
$162$	5.41414	0.425375
$163$	−5.80185	−0.454436	−0.227218	−	0.973844i	$-0.572963\pi$
$163$	−5.80185	−0.454436	−0.227218	+	0.973844i	$0.572963\pi$
$164$	−0.134447	−0.0104986
$165$	4.61694	0.359429
$166$	−1.91762	−0.148836
$167$	−7.39060	−0.571902	−0.285951	−	0.958244i	$-0.592309\pi$
$167$	−7.39060	−0.571902	−0.285951	+	0.958244i	$0.592309\pi$
$168$	15.9595	1.23131
$169$	3.91459	0.301122
$170$	24.4714	1.87687
$171$	5.09252	0.389435
$172$	−0.0352288	−0.00268617
$173$	18.2061	1.38418	0.692092	−	0.721809i	$-0.256689\pi$
$173$	18.2061	1.38418	0.692092	+	0.721809i	$0.256689\pi$
$174$	−8.35248	−0.633200
$175$	−29.8820	−2.25887
$176$	−4.03172	−0.303902
$177$	−3.05939	−0.229958
$178$	3.75048	0.281110
$179$	−15.8020	−1.18110	−0.590550	−	0.807001i	$-0.701089\pi$
$179$	−15.8020	−1.18110	−0.590550	+	0.807001i	$0.701089\pi$
$180$	0.0680273	0.00507045
$181$	−6.12247	−0.455079	−0.227540	−	0.973769i	$-0.573068\pi$
$181$	−6.12247	−0.455079	−0.227540	+	0.973769i	$0.573068\pi$
$182$	24.8462	1.84172
$183$	15.7667	1.16551
$184$	0	0
$185$	−27.7659	−2.04139
$186$	−10.8479	−0.795410
$187$	4.97059	0.363486
$188$	0.0861846	0.00628566
$189$	−23.9480	−1.74196
$190$	−20.4324	−1.48232
$191$	−6.73135	−0.487063	−0.243532	−	0.969893i	$-0.578306\pi$
$191$	−6.73135	−0.487063	−0.243532	+	0.969893i	$0.578306\pi$
$192$	−10.5656	−0.762510
$193$	24.4458	1.75965	0.879825	−	0.475298i	$-0.157660\pi$
$193$	24.4458	1.75965	0.879825	+	0.475298i	$0.157660\pi$
$194$	14.5155	1.04215
$195$	18.9883	1.35978
$196$	0.177534	0.0126810
$197$	5.51418	0.392869	0.196434	−	0.980517i	$-0.437064\pi$
$197$	5.51418	0.392869	0.196434	+	0.980517i	$0.437064\pi$
$198$	1.74224	0.123816
$199$	26.7245	1.89445	0.947224	−	0.320573i	$-0.103875\pi$
$199$	26.7245	1.89445	0.947224	+	0.320573i	$0.103875\pi$
$200$	19.7840	1.39894
$201$	15.7662	1.11206
$202$	11.8891	0.836515
$203$	18.7979	1.31935
$204$	−0.105820	−0.00740887
$205$	29.1573	2.03643
$206$	22.5493	1.57109
$207$	0	0
$208$	−16.5814	−1.14971
$209$	−4.15019	−0.287075
$210$	27.8922	1.92475
$211$	−3.52799	−0.242877	−0.121438	−	0.992599i	$-0.538751\pi$
$211$	−3.52799	−0.242877	−0.121438	+	0.992599i	$0.538751\pi$
$212$	0.0252768	0.00173602
$213$	3.74895	0.256874
$214$	15.3475	1.04914
$215$	7.64000	0.521043
$216$	15.8553	1.07881
$217$	24.4141	1.65734
$218$	−3.05539	−0.206937
$219$	−11.0738	−0.748299
$220$	−0.0554394	−0.00373772
$221$	20.4427	1.37513
$222$	15.1389	1.01606
$223$	4.70392	0.314998	0.157499	−	0.987519i	$-0.449657\pi$
$223$	4.70392	0.314998	0.157499	+	0.987519i	$0.449657\pi$
$224$	−0.384823	−0.0257121
$225$	−8.61766	−0.574511
$226$	19.6919	1.30989
$227$	−2.79246	−0.185342	−0.0926710	−	0.995697i	$-0.529540\pi$
$227$	−2.79246	−0.185342	−0.0926710	+	0.995697i	$0.529540\pi$
$228$	0.0883542	0.00585140
$229$	−16.4011	−1.08382	−0.541908	−	0.840438i	$-0.682298\pi$
$229$	−16.4011	−1.08382	−0.541908	+	0.840438i	$0.682298\pi$
$230$	0	0
$231$	5.66542	0.372757
$232$	−12.4455	−0.817087
$233$	−25.5279	−1.67239	−0.836195	−	0.548432i	$-0.815225\pi$
$233$	−25.5279	−1.67239	−0.836195	+	0.548432i	$0.815225\pi$
$234$	7.16538	0.468415
$235$	−18.6907	−1.21925
$236$	0.0367366	0.00239135
$237$	9.49802	0.616963
$238$	30.0287	1.94647
$239$	10.2850	0.665282	0.332641	−	0.943053i	$-0.392060\pi$
$239$	10.2850	0.665282	0.332641	+	0.943053i	$0.392060\pi$
$240$	−18.6142	−1.20154
$241$	28.1266	1.81179	0.905895	−	0.423502i	$-0.139199\pi$
$241$	28.1266	1.81179	0.905895	+	0.423502i	$0.139199\pi$
$242$	−1.41986	−0.0912717
$243$	−11.8079	−0.757478
$244$	−0.189324	−0.0121202
$245$	−38.5015	−2.45977
$246$	−15.8976	−1.01359
$247$	−17.0686	−1.08605
$248$	−16.1638	−1.02640
$249$	−1.79832	−0.113964
$250$	9.95990	0.629920
$251$	−17.5538	−1.10799	−0.553993	−	0.832521i	$-0.686897\pi$
$251$	−17.5538	−1.10799	−0.553993	+	0.832521i	$0.686897\pi$
$252$	0.0834758	0.00525848
$253$	0	0
$254$	−12.7642	−0.800900
$255$	22.9489	1.43712
$256$	0.383703	0.0239814
$257$	22.4943	1.40316	0.701579	−	0.712591i	$-0.252479\pi$
$257$	22.4943	1.40316	0.701579	+	0.712591i	$0.252479\pi$
$258$	−4.16560	−0.259339
$259$	−34.0713	−2.11709
$260$	−0.228008	−0.0141404
$261$	5.42111	0.335558
$262$	−5.06111	−0.312676
$263$	−7.92185	−0.488482	−0.244241	−	0.969715i	$-0.578539\pi$
$263$	−7.92185	−0.488482	−0.244241	+	0.969715i	$0.578539\pi$
$264$	−3.75090	−0.230852
$265$	−5.48173	−0.336740
$266$	−25.0725	−1.53729
$267$	3.51714	0.215246
$268$	−0.189317	−0.0115644
$269$	27.0233	1.64764	0.823819	−	0.566853i	$-0.191839\pi$
$269$	27.0233	1.64764	0.823819	+	0.566853i	$0.191839\pi$
$270$	27.7100	1.68638
$271$	15.1859	0.922476	0.461238	−	0.887276i	$-0.347405\pi$
$271$	15.1859	0.922476	0.461238	+	0.887276i	$0.347405\pi$
$272$	−20.0400	−1.21511
$273$	23.3004	1.41020
$274$	8.19216	0.494907
$275$	7.02304	0.423505
$276$	0	0
$277$	13.5783	0.815844	0.407922	−	0.913017i	$-0.366254\pi$
$277$	13.5783	0.815844	0.407922	+	0.913017i	$0.366254\pi$
$278$	14.2052	0.851974
$279$	7.04077	0.421520
$280$	41.5604	2.48371
$281$	−1.23677	−0.0737795	−0.0368898	−	0.999319i	$-0.511745\pi$
$281$	−1.23677	−0.0737795	−0.0368898	+	0.999319i	$0.511745\pi$
$282$	10.1908	0.606855
$283$	−7.34610	−0.436680	−0.218340	−	0.975873i	$-0.570064\pi$
$283$	−7.34610	−0.436680	−0.218340	+	0.975873i	$0.570064\pi$
$284$	−0.0450166	−0.00267125
$285$	−19.1612	−1.13501
$286$	−5.83949	−0.345296
$287$	35.7787	2.11195
$288$	−0.110979	−0.00653950
$289$	7.70679	0.453340
$290$	−21.7508	−1.27725
$291$	13.6124	0.797975
$292$	0.132972	0.00778162
$293$	−28.7651	−1.68047	−0.840236	−	0.542220i	$-0.817584\pi$
$293$	−28.7651	−1.68047	−0.840236	+	0.542220i	$0.817584\pi$
$294$	20.9924	1.22430
$295$	−7.96699	−0.463856
$296$	22.5576	1.31113
$297$	5.62841	0.326593
$298$	−16.3008	−0.944277
$299$	0	0
$300$	−0.149515	−0.00863224
$301$	9.37499	0.540365
$302$	21.6888	1.24805
$303$	11.1494	0.640518
$304$	16.7324	0.959670
$305$	41.0583	2.35099
$306$	8.65997	0.495058
$307$	−29.3547	−1.67536	−0.837681	−	0.546160i	$-0.816089\pi$
$307$	−29.3547	−1.67536	−0.837681	+	0.546160i	$0.816089\pi$
$308$	−0.0680293	−0.00387633
$309$	21.1464	1.20298
$310$	−28.2492	−1.60445
$311$	−12.4466	−0.705781	−0.352891	−	0.935665i	$-0.614801\pi$
$311$	−12.4466	−0.705781	−0.352891	+	0.935665i	$0.614801\pi$
$312$	−15.4265	−0.873352
$313$	−12.7455	−0.720417	−0.360208	−	0.932872i	$-0.617294\pi$
$313$	−12.7455	−0.720417	−0.360208	+	0.932872i	$0.617294\pi$
$314$	17.5824	0.992234
$315$	−18.1032	−1.02000
$316$	−0.114050	−0.00641584
$317$	−13.1679	−0.739584	−0.369792	−	0.929115i	$-0.620571\pi$
$317$	−13.1679	−0.739584	−0.369792	+	0.929115i	$0.620571\pi$
$318$	2.98884	0.167606
$319$	−4.41798	−0.247360
$320$	−27.5141	−1.53809
$321$	14.3927	0.803322
$322$	0	0
$323$	−20.6289	−1.14782
$324$	−0.0609673	−0.00338707
$325$	28.8839	1.60219
$326$	8.23779	0.456249
$327$	−2.86530	−0.158451
$328$	−23.6880	−1.30795
$329$	−22.9352	−1.26446
$330$	−6.55539	−0.360862
$331$	11.3673	0.624801	0.312401	−	0.949950i	$-0.398867\pi$
$331$	11.3673	0.624801	0.312401	+	0.949950i	$0.398867\pi$
$332$	0.0215939	0.00118512
$333$	−9.82581	−0.538451
$334$	10.4936	0.574183
$335$	41.0569	2.24318
$336$	−22.8414	−1.24610
$337$	1.94561	0.105984	0.0529921	−	0.998595i	$-0.483124\pi$
$337$	1.94561	0.105984	0.0529921	+	0.998595i	$0.483124\pi$
$338$	−5.55815	−0.302323
$339$	18.4668	1.00298
$340$	−0.275567	−0.0149447
$341$	−5.73794	−0.310727
$342$	−7.23064	−0.390988
$343$	−17.4610	−0.942804
$344$	−6.20689	−0.334653
$345$	0	0
$346$	−25.8500	−1.38971
$347$	14.5545	0.781326	0.390663	−	0.920534i	$-0.372246\pi$
$347$	14.5545	0.781326	0.390663	+	0.920534i	$0.372246\pi$
$348$	0.0940552	0.00504189
$349$	−2.44728	−0.131000	−0.0655000	−	0.997853i	$-0.520864\pi$
$349$	−2.44728	−0.131000	−0.0655000	+	0.997853i	$0.520864\pi$
$350$	42.4281	2.26788
$351$	23.1481	1.23556
$352$	0.0904432	0.00482064
$353$	2.74658	0.146185	0.0730927	−	0.997325i	$-0.476713\pi$
$353$	2.74658	0.146185	0.0730927	+	0.997325i	$0.476713\pi$
$354$	4.34389	0.230875
$355$	9.76267	0.518149
$356$	−0.0422332	−0.00223836
$357$	28.1605	1.49041
$358$	22.4366	1.18581
$359$	−20.0584	−1.05864	−0.529322	−	0.848421i	$-0.677553\pi$
$359$	−20.0584	−1.05864	−0.529322	+	0.848421i	$0.677553\pi$
$360$	11.9856	0.631696
$361$	−1.77591	−0.0934689
$362$	8.69301	0.456895
$363$	−1.33152	−0.0698866
$364$	−0.279787	−0.0146648
$365$	−28.8375	−1.50942
$366$	−22.3864	−1.17016
$367$	20.1214	1.05033	0.525164	−	0.851001i	$-0.324004\pi$
$367$	20.1214	1.05033	0.525164	+	0.851001i	$0.324004\pi$
$368$	0	0
$369$	10.3182	0.537145
$370$	39.4235	2.04953
$371$	−6.72659	−0.349227
$372$	0.122156	0.00633349
$373$	11.1779	0.578772	0.289386	−	0.957212i	$-0.406549\pi$
$373$	11.1779	0.578772	0.289386	+	0.957212i	$0.406549\pi$
$374$	−7.05752	−0.364936
$375$	9.34025	0.482328
$376$	15.1847	0.783091
$377$	−18.1700	−0.935802
$378$	34.0028	1.74891
$379$	9.06120	0.465443	0.232721	−	0.972543i	$-0.425237\pi$
$379$	9.06120	0.465443	0.232721	+	0.972543i	$0.425237\pi$
$380$	0.230084	0.0118031
$381$	−11.9701	−0.613248
$382$	9.55754	0.489006
$383$	−24.2624	−1.23975	−0.619876	−	0.784700i	$-0.712817\pi$
$383$	−24.2624	−1.23975	−0.619876	+	0.784700i	$0.712817\pi$
$384$	15.2425	0.777842
$385$	14.7534	0.751902
$386$	−34.7095	−1.76667
$387$	2.70365	0.137434
$388$	−0.163455	−0.00829820
$389$	11.6427	0.590309	0.295155	−	0.955450i	$-0.404629\pi$
$389$	11.6427	0.590309	0.295155	+	0.955450i	$0.404629\pi$
$390$	−26.9606	−1.36520
$391$	0	0
$392$	31.2794	1.57985
$393$	−4.74623	−0.239416
$394$	−7.82933	−0.394436
$395$	24.7339	1.24450
$396$	−0.0196190	−0.000985890 0
$397$	13.1831	0.661643	0.330822	−	0.943693i	$-0.392674\pi$
$397$	13.1831	0.661643	0.330822	+	0.943693i	$0.392674\pi$
$398$	−37.9449	−1.90200
$399$	−23.5126	−1.17710
$400$	−28.3149	−1.41575
$401$	−19.0198	−0.949801	−0.474901	−	0.880039i	$-0.657516\pi$
$401$	−19.0198	−0.949801	−0.474901	+	0.880039i	$0.657516\pi$
$402$	−22.3857	−1.11650
$403$	−23.5986	−1.17553
$404$	−0.133880	−0.00666080
$405$	13.2219	0.657000
$406$	−26.6903	−1.32462
$407$	8.00763	0.396924
$408$	−18.6442	−0.923026
$409$	3.24464	0.160437	0.0802185	−	0.996777i	$-0.474438\pi$
$409$	3.24464	0.160437	0.0802185	+	0.996777i	$0.474438\pi$
$410$	−41.3991	−2.04456
$411$	7.68249	0.378949
$412$	−0.253922	−0.0125099
$413$	−9.77624	−0.481057
$414$	0	0
$415$	−4.68302	−0.229880
$416$	0.371969	0.0182373
$417$	13.3215	0.652355
$418$	5.89267	0.288220
$419$	23.0669	1.12689	0.563447	−	0.826153i	$-0.309475\pi$
$419$	23.0669	1.12689	0.563447	+	0.826153i	$0.309475\pi$
$420$	−0.314088	−0.0153259
$421$	−6.57652	−0.320520	−0.160260	−	0.987075i	$-0.551233\pi$
$421$	−6.57652	−0.320520	−0.160260	+	0.987075i	$0.551233\pi$
$422$	5.00923	0.243846
$423$	−6.61428	−0.321597
$424$	4.45347	0.216280
$425$	34.9087	1.69332
$426$	−5.32296	−0.257898
$427$	50.3823	2.43817
$428$	−0.172825	−0.00835380
$429$	−5.47619	−0.264393
$430$	−10.8477	−0.523122
$431$	17.4665	0.841331	0.420665	−	0.907216i	$-0.361797\pi$
$431$	17.4665	0.841331	0.420665	+	0.907216i	$0.361797\pi$
$432$	−22.6922	−1.09178
$433$	−30.8815	−1.48407	−0.742036	−	0.670360i	$-0.766140\pi$
$433$	−30.8815	−1.48407	−0.742036	+	0.670360i	$0.766140\pi$
$434$	−34.6645	−1.66395
$435$	−20.3976	−0.977989
$436$	0.0344060	0.00164775
$437$	0	0
$438$	15.7232	0.751284
$439$	−22.6301	−1.08007	−0.540037	−	0.841641i	$-0.681590\pi$
$439$	−22.6301	−1.08007	−0.540037	+	0.841641i	$0.681590\pi$
$440$	−9.76777	−0.465660
$441$	−13.6250	−0.648808
$442$	−29.0257	−1.38061
$443$	−10.9018	−0.517959	−0.258980	−	0.965883i	$-0.583386\pi$
$443$	−10.9018	−0.517959	−0.258980	+	0.965883i	$0.583386\pi$
$444$	−0.170476	−0.00809043
$445$	9.15903	0.434180
$446$	−6.67889	−0.316254
$447$	−15.2866	−0.723032
$448$	−33.7624	−1.59512
$449$	14.0363	0.662414	0.331207	−	0.943558i	$-0.392544\pi$
$449$	14.0363	0.662414	0.331207	+	0.943558i	$0.392544\pi$
$450$	12.2358	0.576803
$451$	−8.40892	−0.395960
$452$	−0.221746	−0.0104301
$453$	20.3395	0.955632
$454$	3.96489	0.186081
$455$	60.6768	2.84457
$456$	15.5670	0.728990
$457$	−16.1729	−0.756537	−0.378268	−	0.925696i	$-0.623480\pi$
$457$	−16.1729	−0.756537	−0.378268	+	0.925696i	$0.623480\pi$
$458$	23.2872	1.08814
$459$	27.9765	1.30583
$460$	0	0
$461$	−7.55235	−0.351748	−0.175874	−	0.984413i	$-0.556275\pi$
$461$	−7.55235	−0.351748	−0.175874	+	0.984413i	$0.556275\pi$
$462$	−8.04408	−0.374244
$463$	−0.844737	−0.0392583	−0.0196291	−	0.999807i	$-0.506249\pi$
$463$	−0.844737	−0.0392583	−0.0196291	+	0.999807i	$0.506249\pi$
$464$	17.8121	0.826905
$465$	−26.4917	−1.22852
$466$	36.2460	1.67906
$467$	−13.9752	−0.646693	−0.323347	−	0.946281i	$-0.604808\pi$
$467$	−13.9752	−0.646693	−0.323347	+	0.946281i	$0.604808\pi$
$468$	−0.0806876	−0.00372978
$469$	50.3807	2.32636
$470$	26.5381	1.22411
$471$	16.4885	0.759752
$472$	6.47255	0.297923
$473$	−2.20336	−0.101311
$474$	−13.4858	−0.619424
$475$	−29.1470	−1.33735
$476$	−0.338146	−0.0154989
$477$	−1.93988	−0.0888210
$478$	−14.6032	−0.667936
$479$	−35.2408	−1.61019	−0.805096	−	0.593144i	$-0.797886\pi$
$479$	−35.2408	−1.61019	−0.805096	+	0.593144i	$0.797886\pi$
$480$	0.417571	0.0190594
$481$	32.9333	1.50163
$482$	−39.9356	−1.81902
$483$	0	0
$484$	0.0159886	0.000726756 0
$485$	35.4483	1.60962
$486$	16.7655	0.760500
$487$	20.8769	0.946022	0.473011	−	0.881056i	$-0.343167\pi$
$487$	20.8769	0.946022	0.473011	+	0.881056i	$0.343167\pi$
$488$	−33.3566	−1.50998
$489$	7.72528	0.349349
$490$	54.6666	2.46958
$491$	−40.9526	−1.84817	−0.924083	−	0.382193i	$-0.875169\pi$
$491$	−40.9526	−1.84817	−0.924083	+	0.382193i	$0.875169\pi$
$492$	0.179019	0.00807080
$493$	−21.9600	−0.989028
$494$	24.2350	1.09038
$495$	4.25472	0.191236
$496$	23.1338	1.03874
$497$	11.9797	0.537363
$498$	2.55335	0.114418
$499$	13.8839	0.621528	0.310764	−	0.950487i	$-0.399415\pi$
$499$	13.8839	0.621528	0.310764	+	0.950487i	$0.399415\pi$
$500$	−0.112156	−0.00501577
$501$	9.84073	0.439651
$502$	24.9239	1.11241
$503$	18.9508	0.844974	0.422487	−	0.906369i	$-0.361157\pi$
$503$	18.9508	0.844974	0.422487	+	0.906369i	$0.361157\pi$
$504$	14.7074	0.655122
$505$	29.0344	1.29201
$506$	0	0
$507$	−5.21235	−0.231489
$508$	0.143735	0.00637721
$509$	−39.6112	−1.75574	−0.877868	−	0.478903i	$-0.841034\pi$
$509$	−39.6112	−1.75574	−0.877868	+	0.478903i	$0.841034\pi$
$510$	−32.5842	−1.44285
$511$	−35.3862	−1.56540
$512$	22.3501	0.987746
$513$	−23.3590	−1.03132
$514$	−31.9387	−1.40876
$515$	55.0677	2.42657
$516$	0.0469078	0.00206500
$517$	5.39036	0.237068
$518$	48.3763	2.12553
$519$	−24.2418	−1.06410
$520$	−40.1722	−1.76167
$521$	−1.80696	−0.0791644	−0.0395822	−	0.999216i	$-0.512603\pi$
$521$	−1.80696	−0.0791644	−0.0395822	+	0.999216i	$0.512603\pi$
$522$	−7.69719	−0.336897
$523$	27.5551	1.20490	0.602450	−	0.798157i	$-0.294191\pi$
$523$	27.5551	1.20490	0.602450	+	0.798157i	$0.294191\pi$
$524$	0.0569919	0.00248970
$525$	39.7885	1.73651
$526$	11.2479	0.490431
$527$	−28.5209	−1.24239
$528$	5.36832	0.233626
$529$	0	0
$530$	7.78326	0.338083
$531$	−2.81937	−0.122350
$532$	0.282335	0.0122408
$533$	−34.5837	−1.49798
$534$	−4.99383	−0.216104
$535$	37.4802	1.62041
$536$	−33.3555	−1.44074
$537$	21.0407	0.907974
$538$	−38.3691	−1.65421
$539$	11.1038	0.478274
$540$	−0.312036	−0.0134279
$541$	15.6261	0.671819	0.335910	−	0.941894i	$-0.390956\pi$
$541$	15.6261	0.671819	0.335910	+	0.941894i	$0.390956\pi$
$542$	−21.5617	−0.926156
$543$	8.15218	0.349844
$544$	0.449556	0.0192746
$545$	−7.46156	−0.319618
$546$	−33.0832	−1.41583
$547$	−2.25864	−0.0965723	−0.0482862	−	0.998834i	$-0.515376\pi$
$547$	−2.25864	−0.0965723	−0.0482862	+	0.998834i	$0.515376\pi$
$548$	−0.0922499	−0.00394072
$549$	14.5297	0.620114
$550$	−9.97170	−0.425195
$551$	18.3355	0.781118
$552$	0	0
$553$	30.3508	1.29065
$554$	−19.2793	−0.819098
$555$	36.9708	1.56932
$556$	−0.159962	−0.00678389
$557$	−29.4630	−1.24839	−0.624193	−	0.781270i	$-0.714572\pi$
$557$	−29.4630	−1.24839	−0.624193	+	0.781270i	$0.714572\pi$
$558$	−9.99687	−0.423201
$559$	−9.06185	−0.383275
$560$	−59.4815	−2.51355
$561$	−6.61844	−0.279431
$562$	1.75603	0.0740739
$563$	−33.7612	−1.42287	−0.711433	−	0.702754i	$-0.751954\pi$
$563$	−33.7612	−1.42287	−0.711433	+	0.702754i	$0.751954\pi$
$564$	−0.114756	−0.00483212
$565$	48.0896	2.02315
$566$	10.4304	0.438422
$567$	16.2245	0.681363
$568$	−7.93140	−0.332794
$569$	−11.2979	−0.473631	−0.236816	−	0.971555i	$-0.576104\pi$
$569$	−11.2979	−0.473631	−0.236816	+	0.971555i	$0.576104\pi$
$570$	27.2061	1.13954
$571$	−15.6585	−0.655286	−0.327643	−	0.944802i	$-0.606254\pi$
$571$	−15.6585	−0.655286	−0.327643	+	0.944802i	$0.606254\pi$
$572$	0.0657570	0.00274944
$573$	8.96292	0.374431
$574$	−50.8006	−2.12038
$575$	0	0
$576$	−9.73672	−0.405697
$577$	12.1962	0.507734	0.253867	−	0.967239i	$-0.418297\pi$
$577$	12.1962	0.507734	0.253867	+	0.967239i	$0.418297\pi$
$578$	−10.9425	−0.455149
$579$	−32.5501	−1.35274
$580$	0.244930	0.0101702
$581$	−5.74650	−0.238405
$582$	−19.3277	−0.801158
$583$	1.58092	0.0654751
$584$	23.4281	0.969464
$585$	17.4986	0.723476
$586$	40.8422	1.68718
$587$	−27.1900	−1.12225	−0.561125	−	0.827731i	$-0.689631\pi$
$587$	−27.1900	−1.12225	−0.561125	+	0.827731i	$0.689631\pi$
$588$	−0.236390	−0.00974858
$589$	23.8135	0.981220
$590$	11.3120	0.465707
$591$	−7.34223	−0.302019
$592$	−32.2845	−1.32689
$593$	−22.9836	−0.943824	−0.471912	−	0.881646i	$-0.656436\pi$
$593$	−22.9836	−0.943824	−0.471912	+	0.881646i	$0.656436\pi$
$594$	−7.99152	−0.327896
$595$	73.3331	3.00636
$596$	0.183559	0.00751886
$597$	−35.5842	−1.45636
$598$	0	0
$599$	27.7948	1.13566	0.567832	−	0.823144i	$-0.307782\pi$
$599$	27.7948	1.13566	0.567832	+	0.823144i	$0.307782\pi$
$600$	−26.3427	−1.07544
$601$	−3.73280	−0.152264	−0.0761320	−	0.997098i	$-0.524257\pi$
$601$	−3.73280	−0.152264	−0.0761320	+	0.997098i	$0.524257\pi$
$602$	−13.3111	−0.542521
$603$	14.5293	0.591677
$604$	−0.244233	−0.00993768
$605$	−3.46743	−0.140971
$606$	−15.8306	−0.643073
$607$	19.9846	0.811152	0.405576	−	0.914061i	$-0.367071\pi$
$607$	19.9846	0.811152	0.405576	+	0.914061i	$0.367071\pi$
$608$	−0.375357	−0.0152227
$609$	−25.0297	−1.01426
$610$	−58.2968	−2.36037
$611$	22.1691	0.896867
$612$	−0.0975178	−0.00394192
$613$	24.0550	0.971572	0.485786	−	0.874078i	$-0.338533\pi$
$613$	24.0550	0.971572	0.485786	+	0.874078i	$0.338533\pi$
$614$	41.6794	1.68204
$615$	−38.8235	−1.56551
$616$	−11.9860	−0.482928
$617$	2.45556	0.0988570	0.0494285	−	0.998778i	$-0.484260\pi$
$617$	2.45556	0.0988570	0.0494285	+	0.998778i	$0.484260\pi$
$618$	−30.0249	−1.20778
$619$	35.5760	1.42992	0.714959	−	0.699166i	$-0.246445\pi$
$619$	35.5760	1.42992	0.714959	+	0.699166i	$0.246445\pi$
$620$	0.318108	0.0127755
$621$	0	0
$622$	17.6723	0.708597
$623$	11.2390	0.450281
$624$	22.0785	0.883846
$625$	−10.7921	−0.431685
$626$	18.0967	0.723291
$627$	5.52606	0.220690
$628$	−0.197991	−0.00790072
$629$	39.8027	1.58704
$630$	25.7040	1.02407
$631$	16.9418	0.674443	0.337221	−	0.941425i	$-0.390513\pi$
$631$	16.9418	0.674443	0.337221	+	0.941425i	$0.390513\pi$
$632$	−20.0943	−0.799310
$633$	4.69758	0.186712
$634$	18.6965	0.742534
$635$	−31.1715	−1.23700
$636$	−0.0336565	−0.00133457
$637$	45.6669	1.80939
$638$	6.27290	0.248346
$639$	3.45482	0.136671
$640$	39.6933	1.56901
$641$	−6.63528	−0.262078	−0.131039	−	0.991377i	$-0.541831\pi$
$641$	−6.63528	−0.262078	−0.131039	+	0.991377i	$0.541831\pi$
$642$	−20.4355	−0.806527
$643$	23.8403	0.940169	0.470084	−	0.882621i	$-0.344223\pi$
$643$	23.8403	0.940169	0.470084	+	0.882621i	$0.344223\pi$
$644$	0	0
$645$	−10.1728	−0.400554
$646$	29.2901	1.15240
$647$	−5.87955	−0.231149	−0.115574	−	0.993299i	$-0.536871\pi$
$647$	−5.87955	−0.231149	−0.115574	+	0.993299i	$0.536871\pi$
$648$	−10.7417	−0.421975
$649$	2.29767	0.0901913
$650$	−41.0109	−1.60858
$651$	−32.5078	−1.27408
$652$	−0.0927637	−0.00363291
$653$	−22.6519	−0.886438	−0.443219	−	0.896413i	$-0.646164\pi$
$653$	−22.6519	−0.886438	−0.443219	+	0.896413i	$0.646164\pi$
$654$	4.06831	0.159084
$655$	−12.3597	−0.482934
$656$	33.9024	1.32367
$657$	−10.2050	−0.398136
$658$	32.5647	1.26950
$659$	4.12553	0.160708	0.0803540	−	0.996766i	$-0.474395\pi$
$659$	4.12553	0.160708	0.0803540	+	0.996766i	$0.474395\pi$
$660$	0.0738187	0.00287339
$661$	0.776084	0.0301862	0.0150931	−	0.999886i	$-0.495196\pi$
$661$	0.776084	0.0301862	0.0150931	+	0.999886i	$0.495196\pi$
$662$	−16.1399	−0.627294
$663$	−27.2199	−1.05713
$664$	3.80458	0.147647
$665$	−61.2294	−2.37437
$666$	13.9512	0.540599
$667$	0	0
$668$	−0.118166	−0.00457197
$669$	−6.26336	−0.242156
$670$	−58.2949	−2.25213
$671$	−11.8411	−0.457122
$672$	0.512399	0.0197662
$673$	32.0088	1.23385	0.616923	−	0.787023i	$-0.288379\pi$
$673$	32.0088	1.23385	0.616923	+	0.787023i	$0.288379\pi$
$674$	−2.76249	−0.106407
$675$	39.5285	1.52145
$676$	0.0625890	0.00240727
$677$	1.56026	0.0599658	0.0299829	−	0.999550i	$-0.490455\pi$
$677$	1.56026	0.0599658	0.0299829	+	0.999550i	$0.490455\pi$
$678$	−26.2202	−1.00698
$679$	43.4983	1.66931
$680$	−48.5516	−1.86187
$681$	3.71821	0.142482
$682$	8.14704	0.311966
$683$	−24.1143	−0.922710	−0.461355	−	0.887216i	$-0.652636\pi$
$683$	−24.1143	−0.922710	−0.461355	+	0.887216i	$0.652636\pi$
$684$	0.0814224	0.00311326
$685$	20.0061	0.764392
$686$	24.7921	0.946565
$687$	21.8384	0.833188
$688$	8.88335	0.338674
$689$	6.50191	0.247703
$690$	0	0
$691$	−0.591070	−0.0224854	−0.0112427	−	0.999937i	$-0.503579\pi$
$691$	−0.591070	−0.0224854	−0.0112427	+	0.999937i	$0.503579\pi$
$692$	0.291091	0.0110656
$693$	5.22094	0.198327
$694$	−20.6653	−0.784443
$695$	34.6906	1.31589
$696$	16.5714	0.628138
$697$	−41.7973	−1.58319
$698$	3.47478	0.131523
$699$	33.9909	1.28566
$700$	−0.477772	−0.0180581
$701$	−10.6367	−0.401741	−0.200871	−	0.979618i	$-0.564377\pi$
$701$	−10.6367	−0.401741	−0.200871	+	0.979618i	$0.564377\pi$
$702$	−32.8670	−1.24049
$703$	−33.2332	−1.25341
$704$	7.93503	0.299063
$705$	24.8870	0.937299
$706$	−3.89974	−0.146769
$707$	35.6279	1.33992
$708$	−0.0489155	−0.00183836
$709$	31.2629	1.17410	0.587052	−	0.809549i	$-0.300288\pi$
$709$	31.2629	1.17410	0.587052	+	0.809549i	$0.300288\pi$
$710$	−13.8616	−0.520216
$711$	8.75286	0.328258
$712$	−7.44099	−0.278863
$713$	0	0
$714$	−39.9838	−1.49636
$715$	−14.2606	−0.533316
$716$	−0.252653	−0.00944209
$717$	−13.6947	−0.511438
$718$	28.4801	1.06287
$719$	−28.2585	−1.05386	−0.526932	−	0.849908i	$-0.676658\pi$
$719$	−28.2585	−1.05386	−0.526932	+	0.849908i	$0.676658\pi$
$720$	−17.1539	−0.639287
$721$	67.5732	2.51656
$722$	2.52153	0.0938418
$723$	−37.4511	−1.39282
$724$	−0.0978899	−0.00363805
$725$	−31.0277	−1.15234
$726$	1.89056	0.0701654
$727$	−2.96743	−0.110056	−0.0550279	−	0.998485i	$-0.517525\pi$
$727$	−2.96743	−0.110056	−0.0550279	+	0.998485i	$0.517525\pi$
$728$	−49.2951	−1.82700
$729$	27.1620	1.00600
$730$	40.9450	1.51544
$731$	−10.9520	−0.405075
$732$	0.252088	0.00931744
$733$	17.5760	0.649184	0.324592	−	0.945854i	$-0.394773\pi$
$733$	17.5760	0.649184	0.324592	+	0.945854i	$0.394773\pi$
$734$	−28.5695	−1.05452
$735$	51.2655	1.89096
$736$	0	0
$737$	−11.8408	−0.436160
$738$	−14.6504	−0.539288
$739$	7.67789	0.282436	0.141218	−	0.989979i	$-0.454898\pi$
$739$	7.67789	0.282436	0.141218	+	0.989979i	$0.454898\pi$
$740$	−0.443938	−0.0163195
$741$	22.7272	0.834905
$742$	9.55079	0.350620
$743$	−8.77222	−0.321822	−0.160911	−	0.986969i	$-0.551443\pi$
$743$	−8.77222	−0.321822	−0.160911	+	0.986969i	$0.551443\pi$
$744$	21.5224	0.789051
$745$	−39.8080	−1.45845
$746$	−15.8711	−0.581081
$747$	−1.65723	−0.0606350
$748$	0.0794730	0.00290582
$749$	45.9917	1.68050
$750$	−13.2618	−0.484253
$751$	32.8460	1.19857	0.599284	−	0.800537i	$-0.295452\pi$
$751$	32.8460	1.19857	0.599284	+	0.800537i	$0.295452\pi$
$752$	−21.7324	−0.792501
$753$	23.3732	0.851768
$754$	25.7988	0.939535
$755$	52.9663	1.92764
$756$	−0.382897	−0.0139258
$757$	−19.3913	−0.704789	−0.352395	−	0.935851i	$-0.614633\pi$
$757$	−19.3913	−0.704789	−0.352395	+	0.935851i	$0.614633\pi$
$758$	−12.8656	−0.467299
$759$	0	0
$760$	40.5381	1.47047
$761$	−14.3064	−0.518608	−0.259304	−	0.965796i	$-0.583493\pi$
$761$	−14.3064	−0.518608	−0.259304	+	0.965796i	$0.583493\pi$
$762$	16.9958	0.615694
$763$	−9.15603	−0.331471
$764$	−0.107625	−0.00389374
$765$	21.1485	0.764626
$766$	34.4491	1.24470
$767$	9.44970	0.341209
$768$	−0.510908	−0.0184358
$769$	−39.8563	−1.43725	−0.718627	−	0.695395i	$-0.755229\pi$
$769$	−39.8563	−1.43725	−0.718627	+	0.695395i	$0.755229\pi$
$770$	−20.9477	−0.754902
$771$	−29.9517	−1.07868
$772$	0.390856	0.0140672
$773$	46.4739	1.67155	0.835776	−	0.549071i	$-0.185018\pi$
$773$	46.4739	1.67155	0.835776	+	0.549071i	$0.185018\pi$
$774$	−3.83879	−0.137982
$775$	−40.2977	−1.44754
$776$	−28.7989	−1.03382
$777$	45.3666	1.62752
$778$	−16.5310	−0.592664
$779$	34.8986	1.25037
$780$	0.303597	0.0108705
$781$	−2.81554	−0.100748
$782$	0	0
$783$	−24.8662	−0.888646
$784$	−44.7673	−1.59883
$785$	42.9380	1.53252
$786$	6.73896	0.240371
$787$	9.44081	0.336529	0.168264	−	0.985742i	$-0.446184\pi$
$787$	9.44081	0.336529	0.168264	+	0.985742i	$0.446184\pi$
$788$	0.0881642	0.00314072
$789$	10.5481	0.375522
$790$	−35.1185	−1.24946
$791$	59.0105	2.09817
$792$	−3.45663	−0.122826
$793$	−48.6995	−1.72937
$794$	−18.7182	−0.664282
$795$	7.29903	0.258870
$796$	0.427288	0.0151448
$797$	16.7897	0.594721	0.297360	−	0.954765i	$-0.403894\pi$
$797$	16.7897	0.594721	0.297360	+	0.954765i	$0.403894\pi$
$798$	33.3845	1.18180
$799$	26.7933	0.947879
$800$	0.635186	0.0224572
$801$	3.24121	0.114522
$802$	27.0053	0.953590
$803$	8.31668	0.293489
$804$	0.252080	0.00889017
$805$	0	0
$806$	33.5066	1.18022
$807$	−35.9820	−1.26663
$808$	−23.5881	−0.829828
$809$	−14.6664	−0.515645	−0.257822	−	0.966192i	$-0.583005\pi$
$809$	−14.6664	−0.515645	−0.257822	+	0.966192i	$0.583005\pi$
$810$	−18.7731	−0.659621
$811$	6.55103	0.230038	0.115019	−	0.993363i	$-0.463307\pi$
$811$	6.55103	0.230038	0.115019	+	0.993363i	$0.463307\pi$
$812$	0.300552	0.0105473
$813$	−20.2203	−0.709156
$814$	−11.3697	−0.398507
$815$	20.1175	0.704685
$816$	26.6837	0.934117
$817$	9.14438	0.319921
$818$	−4.60691	−0.161077
$819$	21.4724	0.750305
$820$	0.466185	0.0162799
$821$	−27.7284	−0.967727	−0.483864	−	0.875143i	$-0.660767\pi$
$821$	−27.7284	−0.967727	−0.483864	+	0.875143i	$0.660767\pi$
$822$	−10.9080	−0.380461
$823$	−4.52589	−0.157763	−0.0788813	−	0.996884i	$-0.525135\pi$
$823$	−4.52589	−0.157763	−0.0788813	+	0.996884i	$0.525135\pi$
$824$	−44.7381	−1.55853
$825$	−9.35131	−0.325571
$826$	13.8808	0.482976
$827$	25.7608	0.895789	0.447895	−	0.894086i	$-0.352174\pi$
$827$	25.7608	0.895789	0.447895	+	0.894086i	$0.352174\pi$
$828$	0	0
$829$	48.0559	1.66905	0.834525	−	0.550971i	$-0.185742\pi$
$829$	48.0559	1.66905	0.834525	+	0.550971i	$0.185742\pi$
$830$	6.64921	0.230798
$831$	−18.0798	−0.627183
$832$	32.6347	1.13140
$833$	55.1924	1.91230
$834$	−18.9146	−0.654957
$835$	25.6264	0.886837
$836$	−0.0663559	−0.00229497
$837$	−32.2954	−1.11629
$838$	−32.7517	−1.13139
$839$	52.4223	1.80982	0.904909	−	0.425605i	$-0.139939\pi$
$839$	52.4223	1.80982	0.904909	+	0.425605i	$0.139939\pi$
$840$	−55.3385	−1.90936
$841$	−9.48143	−0.326946
$842$	9.33771	0.321799
$843$	1.64678	0.0567182
$844$	−0.0564077	−0.00194163
$845$	−13.5735	−0.466944
$846$	9.39132	0.322880
$847$	−4.25485	−0.146199
$848$	−6.37384	−0.218878
$849$	9.78148	0.335699
$850$	−49.5652	−1.70007
$851$	0	0
$852$	0.0599405	0.00205353
$853$	9.62649	0.329605	0.164802	−	0.986327i	$-0.447301\pi$
$853$	9.62649	0.329605	0.164802	+	0.986327i	$0.447301\pi$
$854$	−71.5356	−2.44790
$855$	−17.6579	−0.603888
$856$	−30.4497	−1.04075
$857$	−39.4771	−1.34851	−0.674257	−	0.738497i	$-0.735536\pi$
$857$	−39.4771	−1.34851	−0.674257	+	0.738497i	$0.735536\pi$
$858$	7.77539	0.265447
$859$	−13.2627	−0.452516	−0.226258	−	0.974067i	$-0.572649\pi$
$859$	−13.2627	−0.452516	−0.226258	+	0.974067i	$0.572649\pi$
$860$	0.122153	0.00416539
$861$	−47.6401	−1.62357
$862$	−24.7999	−0.844687
$863$	−51.7611	−1.76197	−0.880983	−	0.473147i	$-0.843118\pi$
$863$	−51.7611	−1.76197	−0.880983	+	0.473147i	$0.843118\pi$
$864$	0.509051	0.0173183
$865$	−63.1283	−2.14643
$866$	43.8473	1.48999
$867$	−10.2617	−0.348507
$868$	0.390348	0.0132493
$869$	−7.13322	−0.241978
$870$	28.9616	0.981890
$871$	−48.6979	−1.65006
$872$	6.06193	0.205283
$873$	12.5445	0.424566
$874$	0	0
$875$	29.8467	1.00900
$876$	−0.177055	−0.00598214
$877$	14.9319	0.504214	0.252107	−	0.967699i	$-0.418876\pi$
$877$	14.9319	0.504214	0.252107	+	0.967699i	$0.418876\pi$
$878$	32.1314	1.08438
$879$	38.3012	1.29187
$880$	13.9797	0.471255
$881$	38.7572	1.30576	0.652882	−	0.757460i	$-0.273560\pi$
$881$	38.7572	1.30576	0.652882	+	0.757460i	$0.273560\pi$
$882$	19.3455	0.651396
$883$	−58.1505	−1.95692	−0.978461	−	0.206433i	$-0.933814\pi$
$883$	−58.1505	−1.95692	−0.978461	+	0.206433i	$0.933814\pi$
$884$	0.326851	0.0109932
$885$	10.6082	0.356591
$886$	15.4790	0.520026
$887$	18.4519	0.619554	0.309777	−	0.950809i	$-0.399746\pi$
$887$	18.4519	0.619554	0.309777	+	0.950809i	$0.399746\pi$
$888$	−30.0358	−1.00794
$889$	−38.2504	−1.28288
$890$	−13.0045	−0.435912
$891$	−3.81317	−0.127746
$892$	0.0752093	0.00251819
$893$	−22.3710	−0.748618
$894$	21.7048	0.725916
$895$	54.7924	1.83151
$896$	48.7073	1.62720
$897$	0	0
$898$	−19.9295	−0.665056
$899$	25.3501	0.845473
$900$	−0.137785	−0.00459282
$901$	7.85812	0.261792
$902$	11.9394	0.397540
$903$	−12.4830	−0.415407
$904$	−39.0690	−1.29942
$905$	21.2292	0.705682
$906$	−28.8791	−0.959444
$907$	−39.6171	−1.31547	−0.657733	−	0.753251i	$-0.728484\pi$
$907$	−39.6171	−1.31547	−0.657733	+	0.753251i	$0.728484\pi$
$908$	−0.0446476	−0.00148168
$909$	10.2747	0.340791
$910$	−86.1522	−2.85592
$911$	−47.2068	−1.56403	−0.782015	−	0.623260i	$-0.785808\pi$
$911$	−47.2068	−1.56403	−0.782015	+	0.623260i	$0.785808\pi$
$912$	−22.2795	−0.737749
$913$	1.35058	0.0446975
$914$	22.9632	0.759555
$915$	−54.6699	−1.80733
$916$	−0.262232	−0.00866438
$917$	−15.1665	−0.500843
$918$	−39.7226	−1.31104
$919$	−24.0575	−0.793585	−0.396792	−	0.917908i	$-0.629877\pi$
$919$	−24.0575	−0.793585	−0.396792	+	0.917908i	$0.629877\pi$
$920$	0	0
$921$	39.0864	1.28794
$922$	10.7232	0.353151
$923$	−11.5796	−0.381146
$924$	0.0905824	0.00297994
$925$	56.2379	1.84909
$926$	1.19940	0.0394149
$927$	19.4874	0.640050
$928$	−0.399577	−0.0131167
$929$	43.4438	1.42535	0.712673	−	0.701497i	$-0.247485\pi$
$929$	43.4438	1.42535	0.712673	+	0.701497i	$0.247485\pi$
$930$	37.6144	1.23343
$931$	−46.0828	−1.51030
$932$	−0.408157	−0.0133696
$933$	16.5729	0.542571
$934$	19.8427	0.649273
$935$	−17.2352	−0.563650
$936$	−14.2162	−0.464671
$937$	3.90690	0.127633	0.0638165	−	0.997962i	$-0.479673\pi$
$937$	3.90690	0.127633	0.0638165	+	0.997962i	$0.479673\pi$
$938$	−71.5332	−2.33564
$939$	16.9708	0.553823
$940$	−0.298839	−0.00974704
$941$	16.7034	0.544515	0.272258	−	0.962224i	$-0.412230\pi$
$941$	16.7034	0.544515	0.272258	+	0.962224i	$0.412230\pi$
$942$	−23.4113	−0.762783
$943$	0	0
$944$	−9.26356	−0.301503
$945$	83.0381	2.70123
$946$	3.12846	0.101715
$947$	52.4203	1.70343	0.851715	−	0.524005i	$-0.175563\pi$
$947$	52.4203	1.70343	0.851715	+	0.524005i	$0.175563\pi$
$948$	0.151860	0.00493220
$949$	34.2043	1.11032
$950$	41.3844	1.34269
$951$	17.5333	0.568558
$952$	−59.5773	−1.93091
$953$	−18.5139	−0.599723	−0.299861	−	0.953983i	$-0.596940\pi$
$953$	−18.5139	−0.599723	−0.299861	+	0.953983i	$0.596940\pi$
$954$	2.75435	0.0891753
$955$	23.3404	0.755279
$956$	0.164443	0.00531848
$957$	5.88263	0.190158
$958$	50.0368	1.61662
$959$	24.5493	0.792738
$960$	36.6356	1.18241
$961$	1.92392	0.0620618
$962$	−46.7605	−1.50762
$963$	13.2635	0.427411
$964$	0.449705	0.0144840
$965$	−84.7641	−2.72865
$966$	0	0
$967$	10.1487	0.326359	0.163180	−	0.986596i	$-0.447825\pi$
$967$	10.1487	0.326359	0.163180	+	0.986596i	$0.447825\pi$
$968$	2.81701	0.0905421
$969$	27.4678	0.882393
$970$	−50.3314	−1.61604
$971$	−26.4379	−0.848433	−0.424216	−	0.905561i	$-0.639450\pi$
$971$	−26.4379	−0.848433	−0.424216	+	0.905561i	$0.639450\pi$
$972$	−0.188793	−0.00605552
$973$	42.5686	1.36469
$974$	−29.6422	−0.949796
$975$	−38.4595	−1.23169
$976$	47.7402	1.52813
$977$	31.3077	1.00162	0.500810	−	0.865557i	$-0.333035\pi$
$977$	31.3077	1.00162	0.500810	+	0.865557i	$0.333035\pi$
$978$	−10.9688	−0.350743
$979$	−2.64145	−0.0844211
$980$	−0.615587	−0.0196642
$981$	−2.64051	−0.0843048
$982$	58.1468	1.85554
$983$	−32.8529	−1.04785	−0.523923	−	0.851766i	$-0.675532\pi$
$983$	−32.8529	−1.04785	−0.523923	+	0.851766i	$0.675532\pi$
$984$	31.5410	1.00549
$985$	−19.1200	−0.609214
$986$	31.1800	0.992974
$987$	30.5387	0.972057
$988$	−0.272904	−0.00868224
$989$	0	0
$990$	−6.04109	−0.191999
$991$	−16.7864	−0.533236	−0.266618	−	0.963802i	$-0.585906\pi$
$991$	−16.7864	−0.533236	−0.266618	+	0.963802i	$0.585906\pi$
$992$	−0.518958	−0.0164769
$993$	−15.1357	−0.480318
$994$	−17.0095	−0.539507
$995$	−92.6651	−2.93768
$996$	−0.0287527	−0.000911063 0
$997$	58.5350	1.85382	0.926911	−	0.375281i	$-0.122454\pi$
$997$	58.5350	1.85382	0.926911	+	0.375281i	$0.122454\pi$
$998$	−19.7131	−0.624007
$999$	45.0702	1.42596

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5819.2.a.u.1.16		60
23.13	even	11		253.2.i.b.100.9	✓	120
23.16	even	11		253.2.i.b.210.9	yes	120
23.22	odd	2		5819.2.a.t.1.16		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.2.i.b.100.9	✓	120	23.13	even	11
253.2.i.b.210.9	yes	120	23.16	even	11
5819.2.a.t.1.16		60	23.22	odd	2
5819.2.a.u.1.16		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)

\(f(q)\)	\(=\)	\(q-1.41986 q^{2} -1.33152 q^{3} +0.0159886 q^{4} -3.46743 q^{5} +1.89056 q^{6} -4.25485 q^{7} +2.81701 q^{8} -1.22706 q^{9} +4.92324 q^{10} +1.00000 q^{11} -0.0212892 q^{12} +4.11273 q^{13} +6.04128 q^{14} +4.61694 q^{15} -4.03172 q^{16} +4.97059 q^{17} +1.74224 q^{18} -4.15019 q^{19} -0.0554394 q^{20} +5.66542 q^{21} -1.41986 q^{22} -3.75090 q^{24} +7.02304 q^{25} -5.83949 q^{26} +5.62841 q^{27} -0.0680293 q^{28} -4.41798 q^{29} -6.55539 q^{30} -5.73794 q^{31} +0.0904432 q^{32} -1.33152 q^{33} -7.05752 q^{34} +14.7534 q^{35} -0.0196190 q^{36} +8.00763 q^{37} +5.89267 q^{38} -5.47619 q^{39} -9.76777 q^{40} -8.40892 q^{41} -8.04408 q^{42} -2.20336 q^{43} +0.0159886 q^{44} +4.25472 q^{45} +5.39036 q^{47} +5.36832 q^{48} +11.1038 q^{49} -9.97170 q^{50} -6.61844 q^{51} +0.0657570 q^{52} +1.58092 q^{53} -7.99152 q^{54} -3.46743 q^{55} -11.9860 q^{56} +5.52606 q^{57} +6.27290 q^{58} +2.29767 q^{59} +0.0738187 q^{60} -11.8411 q^{61} +8.14704 q^{62} +5.22094 q^{63} +7.93503 q^{64} -14.2606 q^{65} +1.89056 q^{66} -11.8408 q^{67} +0.0794730 q^{68} -20.9477 q^{70} -2.81554 q^{71} -3.45663 q^{72} +8.31668 q^{73} -11.3697 q^{74} -9.35131 q^{75} -0.0663559 q^{76} -4.25485 q^{77} +7.77539 q^{78} -7.13322 q^{79} +13.9797 q^{80} -3.81317 q^{81} +11.9394 q^{82} +1.35058 q^{83} +0.0905824 q^{84} -17.2352 q^{85} +3.12846 q^{86} +5.88263 q^{87} +2.81701 q^{88} -2.64145 q^{89} -6.04109 q^{90} -17.4991 q^{91} +7.64017 q^{93} -7.65353 q^{94} +14.3905 q^{95} -0.120427 q^{96} -10.2232 q^{97} -15.7658 q^{98} -1.22706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 5 q^{2} + 9 q^{3} + 73 q^{4} + 8 q^{5} + 26 q^{6} + 30 q^{8} + 75 q^{9} - 7 q^{10} + 60 q^{11} + 41 q^{12} + 46 q^{13} + 16 q^{14} + 4 q^{15} + 99 q^{16} - 5 q^{17} + 36 q^{18} - 8 q^{19} + 82 q^{20}+ \cdots + 75 q^{99}+O(q^{100}) \) 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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