LMFDB - Embedded newform 5819.2.a.u.1.12

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			1.12
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)

$f(q)$	$=$	\(q-1.77899 q^{2} -1.88973 q^{3} +1.16479 q^{4} +1.17802 q^{5} +3.36180 q^{6} -1.47227 q^{7} +1.48583 q^{8} +0.571076 q^{9} -2.09569 q^{10} +1.00000 q^{11} -2.20114 q^{12} -2.91011 q^{13} +2.61914 q^{14} -2.22614 q^{15} -4.97284 q^{16} -7.64172 q^{17} -1.01594 q^{18} +8.29282 q^{19} +1.37215 q^{20} +2.78219 q^{21} -1.77899 q^{22} -2.80781 q^{24} -3.61226 q^{25} +5.17704 q^{26} +4.59001 q^{27} -1.71488 q^{28} +1.86761 q^{29} +3.96028 q^{30} -3.39140 q^{31} +5.87496 q^{32} -1.88973 q^{33} +13.5945 q^{34} -1.73436 q^{35} +0.665183 q^{36} -9.70746 q^{37} -14.7528 q^{38} +5.49931 q^{39} +1.75034 q^{40} -2.49583 q^{41} -4.94947 q^{42} +4.71348 q^{43} +1.16479 q^{44} +0.672740 q^{45} -11.1406 q^{47} +9.39733 q^{48} -4.83243 q^{49} +6.42616 q^{50} +14.4408 q^{51} -3.38966 q^{52} +1.48214 q^{53} -8.16556 q^{54} +1.17802 q^{55} -2.18754 q^{56} -15.6712 q^{57} -3.32246 q^{58} +4.87652 q^{59} -2.59299 q^{60} -5.00863 q^{61} +6.03326 q^{62} -0.840776 q^{63} -0.505780 q^{64} -3.42817 q^{65} +3.36180 q^{66} -5.28241 q^{67} -8.90099 q^{68} +3.08541 q^{70} +1.24607 q^{71} +0.848520 q^{72} +14.9184 q^{73} +17.2694 q^{74} +6.82620 q^{75} +9.65938 q^{76} -1.47227 q^{77} -9.78320 q^{78} +10.4945 q^{79} -5.85812 q^{80} -10.3871 q^{81} +4.44004 q^{82} -2.32476 q^{83} +3.24066 q^{84} -9.00212 q^{85} -8.38522 q^{86} -3.52929 q^{87} +1.48583 q^{88} +16.5139 q^{89} -1.19679 q^{90} +4.28446 q^{91} +6.40884 q^{93} +19.8190 q^{94} +9.76913 q^{95} -11.1021 q^{96} -8.94688 q^{97} +8.59682 q^{98} +0.571076 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.77899	−1.25793	−0.628966	−	0.777433i	$-0.716522\pi$
$2$	−1.77899	−1.25793	−0.628966	+	0.777433i	$0.716522\pi$
$3$	−1.88973	−1.09104	−0.545518	−	0.838099i	$-0.683667\pi$
$3$	−1.88973	−1.09104	−0.545518	+	0.838099i	$0.683667\pi$
$4$	1.16479	0.582394
$5$	1.17802	0.526828	0.263414	−	0.964683i	$-0.415152\pi$
$5$	1.17802	0.526828	0.263414	+	0.964683i	$0.415152\pi$
$6$	3.36180	1.37245
$7$	−1.47227	−0.556465	−0.278232	−	0.960514i	$-0.589749\pi$
$7$	−1.47227	−0.556465	−0.278232	+	0.960514i	$0.589749\pi$
$8$	1.48583	0.525320
$9$	0.571076	0.190359
$10$	−2.09569	−0.662714
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.20114	−0.635413
$13$	−2.91011	−0.807119	−0.403559	−	0.914953i	$-0.632227\pi$
$13$	−2.91011	−0.807119	−0.403559	+	0.914953i	$0.632227\pi$
$14$	2.61914	0.699995
$15$	−2.22614	−0.574788
$16$	−4.97284	−1.24321
$17$	−7.64172	−1.85339	−0.926695	−	0.375815i	$-0.877363\pi$
$17$	−7.64172	−1.85339	−0.926695	+	0.375815i	$0.877363\pi$
$18$	−1.01594	−0.239458
$19$	8.29282	1.90250	0.951251	−	0.308417i	$-0.0997991\pi$
$19$	8.29282	1.90250	0.951251	+	0.308417i	$0.0997991\pi$
$20$	1.37215	0.306822
$21$	2.78219	0.607123
$22$	−1.77899	−0.379281
$23$	0	0
$23$	0	0
$24$	−2.80781	−0.573142
$25$	−3.61226	−0.722452
$26$	5.17704	1.01530
$27$	4.59001	0.883348
$28$	−1.71488	−0.324082
$29$	1.86761	0.346807	0.173404	−	0.984851i	$-0.444523\pi$
$29$	1.86761	0.346807	0.173404	+	0.984851i	$0.444523\pi$
$30$	3.96028	0.723044
$31$	−3.39140	−0.609114	−0.304557	−	0.952494i	$-0.598508\pi$
$31$	−3.39140	−0.609114	−0.304557	+	0.952494i	$0.598508\pi$
$32$	5.87496	1.03856
$33$	−1.88973	−0.328960
$34$	13.5945	2.33144
$35$	−1.73436	−0.293161
$36$	0.665183	0.110864
$37$	−9.70746	−1.59590	−0.797948	−	0.602726i	$-0.794081\pi$
$37$	−9.70746	−1.59590	−0.797948	+	0.602726i	$0.794081\pi$
$38$	−14.7528	−2.39322
$39$	5.49931	0.880595
$40$	1.75034	0.276753
$41$	−2.49583	−0.389783	−0.194891	−	0.980825i	$-0.562435\pi$
$41$	−2.49583	−0.389783	−0.194891	+	0.980825i	$0.562435\pi$
$42$	−4.94947	−0.763720
$43$	4.71348	0.718799	0.359400	−	0.933184i	$-0.382981\pi$
$43$	4.71348	0.718799	0.359400	+	0.933184i	$0.382981\pi$
$44$	1.16479	0.175599
$45$	0.672740	0.100286
$46$	0	0
$47$	−11.1406	−1.62503	−0.812515	−	0.582941i	$-0.801902\pi$
$47$	−11.1406	−1.62503	−0.812515	+	0.582941i	$0.801902\pi$
$48$	9.39733	1.35639
$49$	−4.83243	−0.690347
$50$	6.42616	0.908796
$51$	14.4408	2.02211
$52$	−3.38966	−0.470061
$53$	1.48214	0.203587	0.101794	−	0.994806i	$-0.467542\pi$
$53$	1.48214	0.203587	0.101794	+	0.994806i	$0.467542\pi$
$54$	−8.16556	−1.11119
$55$	1.17802	0.158845
$56$	−2.18754	−0.292322
$57$	−15.6712	−2.07570
$58$	−3.32246	−0.436260
$59$	4.87652	0.634868	0.317434	−	0.948280i	$-0.397179\pi$
$59$	4.87652	0.634868	0.317434	+	0.948280i	$0.397179\pi$
$60$	−2.59299	−0.334753
$61$	−5.00863	−0.641290	−0.320645	−	0.947199i	$-0.603900\pi$
$61$	−5.00863	−0.641290	−0.320645	+	0.947199i	$0.603900\pi$
$62$	6.03326	0.766225
$63$	−0.840776	−0.105928
$64$	−0.505780	−0.0632224
$65$	−3.42817	−0.425213
$66$	3.36180	0.413809
$67$	−5.28241	−0.645349	−0.322674	−	0.946510i	$-0.604582\pi$
$67$	−5.28241	−0.645349	−0.322674	+	0.946510i	$0.604582\pi$
$68$	−8.90099	−1.07940
$69$	0	0
$70$	3.08541	0.368777
$71$	1.24607	0.147882	0.0739408	−	0.997263i	$-0.476442\pi$
$71$	1.24607	0.147882	0.0739408	+	0.997263i	$0.476442\pi$
$72$	0.848520	0.0999991
$73$	14.9184	1.74607	0.873033	−	0.487662i	$-0.162150\pi$
$73$	14.9184	1.74607	0.873033	+	0.487662i	$0.162150\pi$
$74$	17.2694	2.00753
$75$	6.82620	0.788221
$76$	9.65938	1.10801
$77$	−1.47227	−0.167780
$78$	−9.78320	−1.10773
$79$	10.4945	1.18072	0.590362	−	0.807138i	$-0.298985\pi$
$79$	10.4945	1.18072	0.590362	+	0.807138i	$0.298985\pi$
$80$	−5.85812	−0.654958
$81$	−10.3871	−1.15412
$82$	4.44004	0.490321
$83$	−2.32476	−0.255175	−0.127588	−	0.991827i	$-0.540723\pi$
$83$	−2.32476	−0.255175	−0.127588	+	0.991827i	$0.540723\pi$
$84$	3.24066	0.353585
$85$	−9.00212	−0.976417
$86$	−8.38522	−0.904201
$87$	−3.52929	−0.378379
$88$	1.48583	0.158390
$89$	16.5139	1.75047	0.875237	−	0.483694i	$-0.160705\pi$
$89$	16.5139	1.75047	0.875237	+	0.483694i	$0.160705\pi$
$90$	−1.19679	−0.126153
$91$	4.28446	0.449133
$92$	0	0
$93$	6.40884	0.664565
$94$	19.8190	2.04418
$95$	9.76913	1.00229
$96$	−11.1021	−1.13310
$97$	−8.94688	−0.908418	−0.454209	−	0.890895i	$-0.650078\pi$
$97$	−8.94688	−0.908418	−0.454209	+	0.890895i	$0.650078\pi$
$98$	8.59682	0.868410
$99$	0.571076	0.0573953
$100$	−4.20752	−0.420752
$101$	1.89460	0.188519	0.0942597	−	0.995548i	$-0.469952\pi$
$101$	1.89460	0.188519	0.0942597	+	0.995548i	$0.469952\pi$
$102$	−25.6899	−2.54368
$103$	6.90660	0.680528	0.340264	−	0.940330i	$-0.389484\pi$
$103$	6.90660	0.680528	0.340264	+	0.940330i	$0.389484\pi$
$104$	−4.32392	−0.423995
$105$	3.27748	0.319849
$106$	−2.63670	−0.256099
$107$	−11.0879	−1.07191	−0.535956	−	0.844246i	$-0.680049\pi$
$107$	−11.0879	−1.07191	−0.535956	+	0.844246i	$0.680049\pi$
$108$	5.34639	0.514457
$109$	−2.27328	−0.217741	−0.108871	−	0.994056i	$-0.534723\pi$
$109$	−2.27328	−0.217741	−0.108871	+	0.994056i	$0.534723\pi$
$110$	−2.09569	−0.199816
$111$	18.3445	1.74118
$112$	7.32136	0.691803
$113$	−1.32432	−0.124582	−0.0622908	−	0.998058i	$-0.519841\pi$
$113$	−1.32432	−0.124582	−0.0622908	+	0.998058i	$0.519841\pi$
$114$	27.8788	2.61109
$115$	0	0
$116$	2.17538	0.201979
$117$	−1.66189	−0.153642
$118$	−8.67525	−0.798622
$119$	11.2507	1.03135
$120$	−3.30767	−0.301947
$121$	1.00000	0.0909091
$122$	8.91028	0.806699
$123$	4.71644	0.425267
$124$	−3.95027	−0.354745
$125$	−10.1454	−0.907436
$126$	1.49573	0.133250
$127$	−10.4223	−0.924829	−0.462415	−	0.886664i	$-0.653017\pi$
$127$	−10.4223	−0.924829	−0.462415	+	0.886664i	$0.653017\pi$
$128$	−10.8501	−0.959027
$129$	−8.90720	−0.784236
$130$	6.09867	0.534889
$131$	−1.68691	−0.147386	−0.0736932	−	0.997281i	$-0.523479\pi$
$131$	−1.68691	−0.147386	−0.0736932	+	0.997281i	$0.523479\pi$
$132$	−2.20114	−0.191584
$133$	−12.2092	−1.05868
$134$	9.39732	0.811805
$135$	5.40713	0.465372
$136$	−11.3543	−0.973622
$137$	18.2425	1.55856	0.779280	−	0.626676i	$-0.215585\pi$
$137$	18.2425	1.55856	0.779280	+	0.626676i	$0.215585\pi$
$138$	0	0
$139$	−21.6814	−1.83899	−0.919496	−	0.393099i	$-0.871403\pi$
$139$	−21.6814	−1.83899	−0.919496	+	0.393099i	$0.871403\pi$
$140$	−2.02017	−0.170735
$141$	21.0528	1.77296
$142$	−2.21675	−0.186025
$143$	−2.91011	−0.243355
$144$	−2.83987	−0.236656
$145$	2.20009	0.182708
$146$	−26.5396	−2.19643
$147$	9.13198	0.753193
$148$	−11.3071	−0.929441
$149$	14.4386	1.18286	0.591429	−	0.806357i	$-0.298564\pi$
$149$	14.4386	1.18286	0.591429	+	0.806357i	$0.298564\pi$
$150$	−12.1437	−0.991529
$151$	−4.25102	−0.345943	−0.172971	−	0.984927i	$-0.555337\pi$
$151$	−4.25102	−0.345943	−0.172971	+	0.984927i	$0.555337\pi$
$152$	12.3217	0.999422
$153$	−4.36400	−0.352809
$154$	2.61914	0.211057
$155$	−3.99515	−0.320898
$156$	6.40554	0.512854
$157$	−14.9517	−1.19327	−0.596637	−	0.802511i	$-0.703497\pi$
$157$	−14.9517	−1.19327	−0.596637	+	0.802511i	$0.703497\pi$
$158$	−18.6696	−1.48527
$159$	−2.80084	−0.222121
$160$	6.92084	0.547140
$161$	0	0
$162$	18.4785	1.45181
$163$	−3.40411	−0.266630	−0.133315	−	0.991074i	$-0.542562\pi$
$163$	−3.40411	−0.266630	−0.133315	+	0.991074i	$0.542562\pi$
$164$	−2.90711	−0.227007
$165$	−2.22614	−0.173305
$166$	4.13571	0.320993
$167$	−17.6557	−1.36624	−0.683120	−	0.730306i	$-0.739377\pi$
$167$	−17.6557	−1.36624	−0.683120	+	0.730306i	$0.739377\pi$
$168$	4.13385	0.318934
$169$	−4.53127	−0.348559
$170$	16.0146	1.22827
$171$	4.73583	0.362158
$172$	5.49021	0.418625
$173$	−11.3483	−0.862798	−0.431399	−	0.902161i	$-0.641980\pi$
$173$	−11.3483	−0.862798	−0.431399	+	0.902161i	$0.641980\pi$
$174$	6.27855	0.475975
$175$	5.31822	0.402019
$176$	−4.97284	−0.374842
$177$	−9.21530	−0.692664
$178$	−29.3781	−2.20198
$179$	5.18497	0.387543	0.193772	−	0.981047i	$-0.437928\pi$
$179$	5.18497	0.387543	0.193772	+	0.981047i	$0.437928\pi$
$180$	0.783600	0.0584061
$181$	−9.06688	−0.673936	−0.336968	−	0.941516i	$-0.609401\pi$
$181$	−9.06688	−0.673936	−0.336968	+	0.941516i	$0.609401\pi$
$182$	−7.62199	−0.564979
$183$	9.46496	0.699670
$184$	0	0
$185$	−11.4356	−0.840763
$186$	−11.4012	−0.835978
$187$	−7.64172	−0.558818
$188$	−12.9765	−0.946408
$189$	−6.75772	−0.491552
$190$	−17.3791	−1.26081
$191$	−15.1506	−1.09626	−0.548129	−	0.836394i	$-0.684660\pi$
$191$	−15.1506	−1.09626	−0.548129	+	0.836394i	$0.684660\pi$
$192$	0.955786	0.0689779
$193$	−9.25275	−0.666028	−0.333014	−	0.942922i	$-0.608066\pi$
$193$	−9.25275	−0.666028	−0.333014	+	0.942922i	$0.608066\pi$
$194$	15.9164	1.14273
$195$	6.47832	0.463922
$196$	−5.62876	−0.402054
$197$	−2.59222	−0.184688	−0.0923439	−	0.995727i	$-0.529436\pi$
$197$	−2.59222	−0.184688	−0.0923439	+	0.995727i	$0.529436\pi$
$198$	−1.01594	−0.0721994
$199$	14.9313	1.05845	0.529227	−	0.848480i	$-0.322482\pi$
$199$	14.9313	1.05845	0.529227	+	0.848480i	$0.322482\pi$
$200$	−5.36720	−0.379519
$201$	9.98232	0.704098
$202$	−3.37046	−0.237145
$203$	−2.74963	−0.192986
$204$	16.8205	1.17767
$205$	−2.94014	−0.205348
$206$	−12.2867	−0.856058
$207$	0	0
$208$	14.4715	1.00342
$209$	8.29282	0.573626
$210$	−5.83059	−0.402349
$211$	−15.6848	−1.07979	−0.539894	−	0.841733i	$-0.681536\pi$
$211$	−15.6848	−1.07979	−0.539894	+	0.841733i	$0.681536\pi$
$212$	1.72638	0.118568
$213$	−2.35474	−0.161344
$214$	19.7253	1.34839
$215$	5.55259	0.378683
$216$	6.81997	0.464040
$217$	4.99306	0.338951
$218$	4.04414	0.273904
$219$	−28.1917	−1.90502
$220$	1.37215	0.0925102
$221$	22.2382	1.49591
$222$	−32.6345	−2.19029
$223$	16.9577	1.13557	0.567786	−	0.823176i	$-0.307800\pi$
$223$	16.9577	1.13557	0.567786	+	0.823176i	$0.307800\pi$
$224$	−8.64951	−0.577920
$225$	−2.06288	−0.137525
$226$	2.35595	0.156715
$227$	20.3232	1.34890	0.674450	−	0.738320i	$-0.264381\pi$
$227$	20.3232	1.34890	0.674450	+	0.738320i	$0.264381\pi$
$228$	−18.2536	−1.20887
$229$	6.88626	0.455057	0.227528	−	0.973771i	$-0.426936\pi$
$229$	6.88626	0.455057	0.227528	+	0.973771i	$0.426936\pi$
$230$	0	0
$231$	2.78219	0.183054
$232$	2.77495	0.182185
$233$	−5.66004	−0.370801	−0.185401	−	0.982663i	$-0.559358\pi$
$233$	−5.66004	−0.370801	−0.185401	+	0.982663i	$0.559358\pi$
$234$	2.95648	0.193271
$235$	−13.1239	−0.856111
$236$	5.68011	0.369744
$237$	−19.8318	−1.28821
$238$	−20.0148	−1.29736
$239$	−20.0549	−1.29725	−0.648623	−	0.761110i	$-0.724655\pi$
$239$	−20.0549	−1.29725	−0.648623	+	0.761110i	$0.724655\pi$
$240$	11.0703	0.714583
$241$	−13.9290	−0.897244	−0.448622	−	0.893722i	$-0.648085\pi$
$241$	−13.9290	−0.897244	−0.448622	+	0.893722i	$0.648085\pi$
$242$	−1.77899	−0.114358
$243$	5.85878	0.375841
$244$	−5.83400	−0.373484
$245$	−5.69271	−0.363694
$246$	−8.39048	−0.534957
$247$	−24.1330	−1.53555
$248$	−5.03905	−0.319980
$249$	4.39316	0.278405
$250$	18.0486	1.14149
$251$	−6.30319	−0.397854	−0.198927	−	0.980014i	$-0.563746\pi$
$251$	−6.30319	−0.397854	−0.198927	+	0.980014i	$0.563746\pi$
$252$	−0.979327	−0.0616918
$253$	0	0
$254$	18.5411	1.16337
$255$	17.0116	1.06531
$256$	20.3138	1.26961
$257$	−1.57916	−0.0985054	−0.0492527	−	0.998786i	$-0.515684\pi$
$257$	−1.57916	−0.0985054	−0.0492527	+	0.998786i	$0.515684\pi$
$258$	15.8458	0.986515
$259$	14.2920	0.888060
$260$	−3.99310	−0.247641
$261$	1.06655	0.0660177
$262$	3.00100	0.185402
$263$	4.07808	0.251465	0.125733	−	0.992064i	$-0.459872\pi$
$263$	4.07808	0.251465	0.125733	+	0.992064i	$0.459872\pi$
$264$	−2.80781	−0.172809
$265$	1.74599	0.107255
$266$	21.7201	1.33174
$267$	−31.2069	−1.90983
$268$	−6.15289	−0.375847
$269$	−16.9352	−1.03256	−0.516279	−	0.856421i	$-0.672683\pi$
$269$	−16.9352	−1.03256	−0.516279	+	0.856421i	$0.672683\pi$
$270$	−9.61921	−0.585407
$271$	19.7028	1.19686	0.598431	−	0.801174i	$-0.295791\pi$
$271$	19.7028	1.19686	0.598431	+	0.801174i	$0.295791\pi$
$272$	38.0011	2.30415
$273$	−8.09646	−0.490020
$274$	−32.4531	−1.96056
$275$	−3.61226	−0.217828
$276$	0	0
$277$	29.0173	1.74348	0.871740	−	0.489968i	$-0.162992\pi$
$277$	29.0173	1.74348	0.871740	+	0.489968i	$0.162992\pi$
$278$	38.5709	2.31333
$279$	−1.93675	−0.115950
$280$	−2.57697	−0.154003
$281$	2.37569	0.141722	0.0708608	−	0.997486i	$-0.477425\pi$
$281$	2.37569	0.141722	0.0708608	+	0.997486i	$0.477425\pi$
$282$	−37.4526	−2.23027
$283$	−17.7144	−1.05301	−0.526507	−	0.850171i	$-0.676499\pi$
$283$	−17.7144	−1.05301	−0.526507	+	0.850171i	$0.676499\pi$
$284$	1.45141	0.0861255
$285$	−18.4610	−1.09354
$286$	5.17704	0.306125
$287$	3.67453	0.216901
$288$	3.35505	0.197698
$289$	41.3959	2.43505
$290$	−3.91393	−0.229834
$291$	16.9072	0.991116
$292$	17.3768	1.01690
$293$	−1.62082	−0.0946891	−0.0473445	−	0.998879i	$-0.515076\pi$
$293$	−1.62082	−0.0946891	−0.0473445	+	0.998879i	$0.515076\pi$
$294$	−16.2457	−0.947466
$295$	5.74465	0.334466
$296$	−14.4236	−0.838356
$297$	4.59001	0.266339
$298$	−25.6861	−1.48796
$299$	0	0
$300$	7.95108	0.459056
$301$	−6.93951	−0.399987
$302$	7.56250	0.435173
$303$	−3.58027	−0.205681
$304$	−41.2389	−2.36521
$305$	−5.90028	−0.337849
$306$	7.76349	0.443809
$307$	0.664207	0.0379083	0.0189541	−	0.999820i	$-0.493966\pi$
$307$	0.664207	0.0379083	0.0189541	+	0.999820i	$0.493966\pi$
$308$	−1.71488	−0.0977144
$309$	−13.0516	−0.742480
$310$	7.10732	0.403668
$311$	32.0445	1.81708	0.908540	−	0.417799i	$-0.137198\pi$
$311$	32.0445	1.81708	0.908540	+	0.417799i	$0.137198\pi$
$312$	8.17104	0.462594
$313$	21.6509	1.22378	0.611891	−	0.790942i	$-0.290409\pi$
$313$	21.6509	1.22378	0.611891	+	0.790942i	$0.290409\pi$
$314$	26.5988	1.50106
$315$	−0.990454	−0.0558057
$316$	12.2239	0.687648
$317$	−1.07598	−0.0604333	−0.0302166	−	0.999543i	$-0.509620\pi$
$317$	−1.07598	−0.0604333	−0.0302166	+	0.999543i	$0.509620\pi$
$318$	4.98265	0.279413
$319$	1.86761	0.104566
$320$	−0.595820	−0.0333073
$321$	20.9532	1.16949
$322$	0	0
$323$	−63.3714	−3.52608
$324$	−12.0988	−0.672154
$325$	10.5121	0.583105
$326$	6.05586	0.335403
$327$	4.29589	0.237563
$328$	−3.70837	−0.204761
$329$	16.4020	0.904272
$330$	3.96028	0.218006
$331$	15.2717	0.839410	0.419705	−	0.907661i	$-0.362134\pi$
$331$	15.2717	0.839410	0.419705	+	0.907661i	$0.362134\pi$
$332$	−2.70785	−0.148613
$333$	−5.54369	−0.303792
$334$	31.4092	1.71864
$335$	−6.22280	−0.339988
$336$	−13.8354	−0.754782
$337$	−11.5856	−0.631106	−0.315553	−	0.948908i	$-0.602190\pi$
$337$	−11.5856	−0.631106	−0.315553	+	0.948908i	$0.602190\pi$
$338$	8.06107	0.438464
$339$	2.50261	0.135923
$340$	−10.4856	−0.568660
$341$	−3.39140	−0.183655
$342$	−8.42496	−0.455570
$343$	17.4205	0.940619
$344$	7.00343	0.377599
$345$	0	0
$346$	20.1885	1.08534
$347$	−0.160098	−0.00859452	−0.00429726	−	0.999991i	$-0.501368\pi$
$347$	−0.160098	−0.00859452	−0.00429726	+	0.999991i	$0.501368\pi$
$348$	−4.11087	−0.220366
$349$	−6.27288	−0.335779	−0.167890	−	0.985806i	$-0.553695\pi$
$349$	−6.27288	−0.335779	−0.167890	+	0.985806i	$0.553695\pi$
$350$	−9.46103	−0.505713
$351$	−13.3574	−0.712966
$352$	5.87496	0.313136
$353$	17.0972	0.909993	0.454997	−	0.890493i	$-0.349640\pi$
$353$	17.0972	0.909993	0.454997	+	0.890493i	$0.349640\pi$
$354$	16.3939	0.871325
$355$	1.46790	0.0779082
$356$	19.2353	1.01947
$357$	−21.2607	−1.12524
$358$	−9.22399	−0.487503
$359$	−7.09556	−0.374489	−0.187245	−	0.982313i	$-0.559956\pi$
$359$	−7.09556	−0.374489	−0.187245	+	0.982313i	$0.559956\pi$
$360$	0.999576	0.0526823
$361$	49.7708	2.61952
$362$	16.1299	0.847766
$363$	−1.88973	−0.0991850
$364$	4.99049	0.261573
$365$	17.5742	0.919876
$366$	−16.8380	−0.880137
$367$	3.72910	0.194658	0.0973288	−	0.995252i	$-0.468970\pi$
$367$	3.72910	0.194658	0.0973288	+	0.995252i	$0.468970\pi$
$368$	0	0
$369$	−1.42531	−0.0741985
$370$	20.3438	1.05762
$371$	−2.18210	−0.113289
$372$	7.46494	0.387039
$373$	24.9200	1.29031	0.645153	−	0.764053i	$-0.276793\pi$
$373$	24.9200	1.29031	0.645153	+	0.764053i	$0.276793\pi$
$374$	13.5945	0.702955
$375$	19.1721	0.990045
$376$	−16.5531	−0.853660
$377$	−5.43496	−0.279915
$378$	12.0219	0.618339
$379$	14.7494	0.757626	0.378813	−	0.925473i	$-0.376332\pi$
$379$	14.7494	0.757626	0.378813	+	0.925473i	$0.376332\pi$
$380$	11.3790	0.583729
$381$	19.6953	1.00902
$382$	26.9526	1.37902
$383$	−7.82313	−0.399743	−0.199872	−	0.979822i	$-0.564053\pi$
$383$	−7.82313	−0.399743	−0.199872	+	0.979822i	$0.564053\pi$
$384$	20.5038	1.04633
$385$	−1.73436	−0.0883914
$386$	16.4605	0.837818
$387$	2.69175	0.136830
$388$	−10.4212	−0.529057
$389$	10.9813	0.556775	0.278388	−	0.960469i	$-0.410200\pi$
$389$	10.9813	0.556775	0.278388	+	0.960469i	$0.410200\pi$
$390$	−11.5248	−0.583583
$391$	0	0
$392$	−7.18016	−0.362653
$393$	3.18781	0.160804
$394$	4.61152	0.232325
$395$	12.3628	0.622039
$396$	0.665183	0.0334267
$397$	35.6270	1.78807	0.894033	−	0.448001i	$-0.147864\pi$
$397$	35.6270	1.78807	0.894033	+	0.448001i	$0.147864\pi$
$398$	−26.5626	−1.33146
$399$	23.0722	1.15505
$400$	17.9632	0.898161
$401$	−2.17225	−0.108477	−0.0542384	−	0.998528i	$-0.517273\pi$
$401$	−2.17225	−0.108477	−0.0542384	+	0.998528i	$0.517273\pi$
$402$	−17.7584	−0.885708
$403$	9.86935	0.491627
$404$	2.20681	0.109793
$405$	−12.2362	−0.608024
$406$	4.89155	0.242763
$407$	−9.70746	−0.481181
$408$	21.4565	1.06226
$409$	−7.24365	−0.358176	−0.179088	−	0.983833i	$-0.557315\pi$
$409$	−7.24365	−0.358176	−0.179088	+	0.983833i	$0.557315\pi$
$410$	5.23047	0.258315
$411$	−34.4733	−1.70044
$412$	8.04473	0.396336
$413$	−7.17954	−0.353282
$414$	0	0
$415$	−2.73861	−0.134433
$416$	−17.0968	−0.838238
$417$	40.9720	2.00641
$418$	−14.7528	−0.721583
$419$	−2.70576	−0.132185	−0.0660926	−	0.997813i	$-0.521053\pi$
$419$	−2.70576	−0.132185	−0.0660926	+	0.997813i	$0.521053\pi$
$420$	3.81757	0.186278
$421$	−20.4462	−0.996485	−0.498242	−	0.867038i	$-0.666021\pi$
$421$	−20.4462	−0.996485	−0.498242	+	0.867038i	$0.666021\pi$
$422$	27.9031	1.35830
$423$	−6.36215	−0.309338
$424$	2.20220	0.106948
$425$	27.6039	1.33899
$426$	4.18905	0.202960
$427$	7.37405	0.356855
$428$	−12.9151	−0.624275
$429$	5.49931	0.265509
$430$	−9.87797	−0.476358
$431$	−2.27340	−0.109506	−0.0547529	−	0.998500i	$-0.517437\pi$
$431$	−2.27340	−0.109506	−0.0547529	+	0.998500i	$0.517437\pi$
$432$	−22.8254	−1.09819
$433$	−10.2647	−0.493288	−0.246644	−	0.969106i	$-0.579328\pi$
$433$	−10.2647	−0.493288	−0.246644	+	0.969106i	$0.579328\pi$
$434$	−8.88257	−0.426377
$435$	−4.15758	−0.199341
$436$	−2.64789	−0.126811
$437$	0	0
$438$	50.1526	2.39639
$439$	5.36257	0.255941	0.127971	−	0.991778i	$-0.459154\pi$
$439$	5.36257	0.255941	0.127971	+	0.991778i	$0.459154\pi$
$440$	1.75034	0.0834442
$441$	−2.75968	−0.131413
$442$	−39.5615	−1.88175
$443$	−3.29069	−0.156345	−0.0781726	−	0.996940i	$-0.524909\pi$
$443$	−3.29069	−0.156345	−0.0781726	+	0.996940i	$0.524909\pi$
$444$	21.3674	1.01405
$445$	19.4538	0.922199
$446$	−30.1675	−1.42847
$447$	−27.2851	−1.29054
$448$	0.744643	0.0351811
$449$	−17.9872	−0.848871	−0.424435	−	0.905458i	$-0.639527\pi$
$449$	−17.9872	−0.848871	−0.424435	+	0.905458i	$0.639527\pi$
$450$	3.66982	0.172997
$451$	−2.49583	−0.117524
$452$	−1.54255	−0.0725556
$453$	8.03327	0.377436
$454$	−36.1547	−1.69683
$455$	5.04719	0.236616
$456$	−23.2847	−1.09041
$457$	−22.8271	−1.06781	−0.533904	−	0.845545i	$-0.679276\pi$
$457$	−22.8271	−1.06781	−0.533904	+	0.845545i	$0.679276\pi$
$458$	−12.2505	−0.572430
$459$	−35.0756	−1.63719
$460$	0	0
$461$	32.0936	1.49475	0.747375	−	0.664403i	$-0.231314\pi$
$461$	32.0936	1.49475	0.747375	+	0.664403i	$0.231314\pi$
$462$	−4.94947	−0.230270
$463$	29.6416	1.37756	0.688782	−	0.724969i	$-0.258146\pi$
$463$	29.6416	1.37756	0.688782	+	0.724969i	$0.258146\pi$
$464$	−9.28736	−0.431155
$465$	7.54975	0.350111
$466$	10.0691	0.466443
$467$	−42.2264	−1.95401	−0.977003	−	0.213225i	$-0.931603\pi$
$467$	−42.2264	−1.95401	−0.977003	+	0.213225i	$0.931603\pi$
$468$	−1.93575	−0.0894802
$469$	7.77712	0.359114
$470$	23.3473	1.07693
$471$	28.2546	1.30190
$472$	7.24567	0.333509
$473$	4.71348	0.216726
$474$	35.2805	1.62048
$475$	−29.9558	−1.37447
$476$	13.1046	0.600650
$477$	0.846412	0.0387545
$478$	35.6774	1.63185
$479$	−21.9761	−1.00411	−0.502056	−	0.864835i	$-0.667423\pi$
$479$	−21.9761	−1.00411	−0.502056	+	0.864835i	$0.667423\pi$
$480$	−13.0785	−0.596949
$481$	28.2497	1.28808
$482$	24.7794	1.12867
$483$	0	0
$484$	1.16479	0.0529449
$485$	−10.5396	−0.478580
$486$	−10.4227	−0.472782
$487$	22.1390	1.00321	0.501607	−	0.865095i	$-0.332742\pi$
$487$	22.1390	1.00321	0.501607	+	0.865095i	$0.332742\pi$
$488$	−7.44197	−0.336882
$489$	6.43284	0.290903
$490$	10.1272	0.457502
$491$	−1.19152	−0.0537727	−0.0268863	−	0.999638i	$-0.508559\pi$
$491$	−1.19152	−0.0537727	−0.0268863	+	0.999638i	$0.508559\pi$
$492$	5.49366	0.247673
$493$	−14.2718	−0.642769
$494$	42.9322	1.93161
$495$	0.672740	0.0302374
$496$	16.8649	0.757258
$497$	−1.83455	−0.0822909
$498$	−7.81536	−0.350215
$499$	18.8592	0.844253	0.422127	−	0.906537i	$-0.361284\pi$
$499$	18.8592	0.844253	0.422127	+	0.906537i	$0.361284\pi$
$500$	−11.8173	−0.528486
$501$	33.3645	1.49062
$502$	11.2133	0.500474
$503$	36.9360	1.64690	0.823448	−	0.567392i	$-0.192048\pi$
$503$	36.9360	1.64690	0.823448	+	0.567392i	$0.192048\pi$
$504$	−1.24925	−0.0556460
$505$	2.23188	0.0993173
$506$	0	0
$507$	8.56288	0.380291
$508$	−12.1398	−0.538615
$509$	−20.6141	−0.913704	−0.456852	−	0.889543i	$-0.651023\pi$
$509$	−20.6141	−0.913704	−0.456852	+	0.889543i	$0.651023\pi$
$510$	−30.2633	−1.34008
$511$	−21.9639	−0.971624
$512$	−14.4377	−0.638061
$513$	38.0641	1.68057
$514$	2.80931	0.123913
$515$	8.13613	0.358521
$516$	−10.3750	−0.456734
$517$	−11.1406	−0.489965
$518$	−25.4252	−1.11712
$519$	21.4453	0.941343
$520$	−5.09368	−0.223373
$521$	6.53030	0.286098	0.143049	−	0.989716i	$-0.454309\pi$
$521$	6.53030	0.286098	0.143049	+	0.989716i	$0.454309\pi$
$522$	−1.89738	−0.0830459
$523$	15.9545	0.697643	0.348821	−	0.937189i	$-0.386582\pi$
$523$	15.9545	0.697643	0.348821	+	0.937189i	$0.386582\pi$
$524$	−1.96490	−0.0858370
$525$	−10.0500	−0.438617
$526$	−7.25485	−0.316326
$527$	25.9162	1.12893
$528$	9.39733	0.408966
$529$	0	0
$530$	−3.10609	−0.134920
$531$	2.78486	0.120853
$532$	−14.2212	−0.616567
$533$	7.26313	0.314601
$534$	55.5166	2.40244
$535$	−13.0618	−0.564713
$536$	−7.84875	−0.339014
$537$	−9.79820	−0.422823
$538$	30.1275	1.29889
$539$	−4.83243	−0.208147
$540$	6.29817	0.271030
$541$	30.9141	1.32910	0.664550	−	0.747244i	$-0.268623\pi$
$541$	30.9141	1.32910	0.664550	+	0.747244i	$0.268623\pi$
$542$	−35.0510	−1.50557
$543$	17.1339	0.735288
$544$	−44.8948	−1.92485
$545$	−2.67798	−0.114712
$546$	14.4035	0.616412
$547$	25.5267	1.09144	0.545721	−	0.837967i	$-0.316256\pi$
$547$	25.5267	1.09144	0.545721	+	0.837967i	$0.316256\pi$
$548$	21.2486	0.907696
$549$	−2.86031	−0.122075
$550$	6.42616	0.274012
$551$	15.4878	0.659802
$552$	0	0
$553$	−15.4507	−0.657032
$554$	−51.6214	−2.19318
$555$	21.6102	0.917302
$556$	−25.2543	−1.07102
$557$	−7.40361	−0.313701	−0.156851	−	0.987622i	$-0.550134\pi$
$557$	−7.40361	−0.313701	−0.156851	+	0.987622i	$0.550134\pi$
$558$	3.44545	0.145857
$559$	−13.7167	−0.580156
$560$	8.62473	0.364461
$561$	14.4408	0.609690
$562$	−4.22631	−0.178276
$563$	−32.3268	−1.36241	−0.681207	−	0.732091i	$-0.738545\pi$
$563$	−32.3268	−1.36241	−0.681207	+	0.732091i	$0.738545\pi$
$564$	24.5221	1.03256
$565$	−1.56008	−0.0656331
$566$	31.5137	1.32462
$567$	15.2926	0.642228
$568$	1.85145	0.0776852
$569$	12.6352	0.529693	0.264847	−	0.964291i	$-0.414679\pi$
$569$	12.6352	0.529693	0.264847	+	0.964291i	$0.414679\pi$
$570$	32.8419	1.37559
$571$	4.77267	0.199730	0.0998650	−	0.995001i	$-0.468159\pi$
$571$	4.77267	0.199730	0.0998650	+	0.995001i	$0.468159\pi$
$572$	−3.38966	−0.141729
$573$	28.6305	1.19606
$574$	−6.53693	−0.272846
$575$	0	0
$576$	−0.288838	−0.0120349
$577$	−33.9889	−1.41498	−0.707489	−	0.706724i	$-0.750172\pi$
$577$	−33.9889	−1.41498	−0.707489	+	0.706724i	$0.750172\pi$
$578$	−73.6427	−3.06313
$579$	17.4852	0.726660
$580$	2.56264	0.106408
$581$	3.42266	0.141996
$582$	−30.0776	−1.24676
$583$	1.48214	0.0613838
$584$	22.1662	0.917243
$585$	−1.95775	−0.0809428
$586$	2.88341	0.119112
$587$	−0.107063	−0.00441898	−0.00220949	−	0.999998i	$-0.500703\pi$
$587$	−0.107063	−0.00441898	−0.00220949	+	0.999998i	$0.500703\pi$
$588$	10.6368	0.438655
$589$	−28.1243	−1.15884
$590$	−10.2196	−0.420736
$591$	4.89859	0.201501
$592$	48.2737	1.98404
$593$	39.0649	1.60420	0.802101	−	0.597188i	$-0.203715\pi$
$593$	39.0649	1.60420	0.802101	+	0.597188i	$0.203715\pi$
$594$	−8.16556	−0.335037
$595$	13.2535	0.543342
$596$	16.8179	0.688890
$597$	−28.2162	−1.15481
$598$	0	0
$599$	24.3793	0.996113	0.498056	−	0.867145i	$-0.334047\pi$
$599$	24.3793	0.996113	0.498056	+	0.867145i	$0.334047\pi$
$600$	10.1426	0.414068
$601$	10.6259	0.433439	0.216719	−	0.976234i	$-0.430464\pi$
$601$	10.6259	0.433439	0.216719	+	0.976234i	$0.430464\pi$
$602$	12.3453	0.503156
$603$	−3.01665	−0.122848
$604$	−4.95154	−0.201475
$605$	1.17802	0.0478934
$606$	6.36926	0.258733
$607$	16.1436	0.655247	0.327624	−	0.944808i	$-0.393752\pi$
$607$	16.1436	0.655247	0.327624	+	0.944808i	$0.393752\pi$
$608$	48.7200	1.97586
$609$	5.19605	0.210555
$610$	10.4965	0.424992
$611$	32.4205	1.31159
$612$	−5.08314	−0.205474
$613$	33.1283	1.33804	0.669019	−	0.743245i	$-0.266714\pi$
$613$	33.1283	1.33804	0.669019	+	0.743245i	$0.266714\pi$
$614$	−1.18161	−0.0476861
$615$	5.55607	0.224043
$616$	−2.18754	−0.0881384
$617$	32.5368	1.30988	0.654942	−	0.755679i	$-0.272693\pi$
$617$	32.5368	1.30988	0.654942	+	0.755679i	$0.272693\pi$
$618$	23.2186	0.933990
$619$	15.9871	0.642576	0.321288	−	0.946982i	$-0.395884\pi$
$619$	15.9871	0.642576	0.321288	+	0.946982i	$0.395884\pi$
$620$	−4.65351	−0.186889
$621$	0	0
$622$	−57.0068	−2.28576
$623$	−24.3129	−0.974077
$624$	−27.3472	−1.09477
$625$	6.10975	0.244390
$626$	−38.5167	−1.53944
$627$	−15.6712	−0.625847
$628$	−17.4155	−0.694956
$629$	74.1817	2.95782
$630$	1.76200	0.0701999
$631$	−1.83745	−0.0731476	−0.0365738	−	0.999331i	$-0.511644\pi$
$631$	−1.83745	−0.0731476	−0.0365738	+	0.999331i	$0.511644\pi$
$632$	15.5930	0.620258
$633$	29.6401	1.17809
$634$	1.91416	0.0760210
$635$	−12.2777	−0.487226
$636$	−3.26238	−0.129362
$637$	14.0629	0.557192
$638$	−3.32246	−0.131537
$639$	0.711602	0.0281505
$640$	−12.7817	−0.505242
$641$	9.20200	0.363457	0.181729	−	0.983349i	$-0.441831\pi$
$641$	9.20200	0.363457	0.181729	+	0.983349i	$0.441831\pi$
$642$	−37.2754	−1.47114
$643$	−10.5860	−0.417470	−0.208735	−	0.977972i	$-0.566935\pi$
$643$	−10.5860	−0.417470	−0.208735	+	0.977972i	$0.566935\pi$
$644$	0	0
$645$	−10.4929	−0.413157
$646$	112.737	4.43557
$647$	−11.9908	−0.471406	−0.235703	−	0.971825i	$-0.575739\pi$
$647$	−11.9908	−0.471406	−0.235703	+	0.971825i	$0.575739\pi$
$648$	−15.4334	−0.606283
$649$	4.87652	0.191420
$650$	−18.7008	−0.733507
$651$	−9.43552	−0.369807
$652$	−3.96507	−0.155284
$653$	−3.96070	−0.154994	−0.0774971	−	0.996993i	$-0.524693\pi$
$653$	−3.96070	−0.154994	−0.0774971	+	0.996993i	$0.524693\pi$
$654$	−7.64232	−0.298838
$655$	−1.98722	−0.0776472
$656$	12.4114	0.484583
$657$	8.51953	0.332378
$658$	−29.1789	−1.13751
$659$	−38.1614	−1.48656	−0.743279	−	0.668981i	$-0.766731\pi$
$659$	−38.1614	−1.48656	−0.743279	+	0.668981i	$0.766731\pi$
$660$	−2.59299	−0.100932
$661$	26.1891	1.01864	0.509318	−	0.860578i	$-0.329898\pi$
$661$	26.1891	1.01864	0.509318	+	0.860578i	$0.329898\pi$
$662$	−27.1682	−1.05592
$663$	−42.0242	−1.63209
$664$	−3.45419	−0.134048
$665$	−14.3828	−0.557740
$666$	9.86215	0.382150
$667$	0	0
$668$	−20.5652	−0.795690
$669$	−32.0454	−1.23895
$670$	11.0703	0.427682
$671$	−5.00863	−0.193356
$672$	16.3452	0.630531
$673$	−16.9110	−0.651871	−0.325935	−	0.945392i	$-0.605679\pi$
$673$	−16.9110	−0.651871	−0.325935	+	0.945392i	$0.605679\pi$
$674$	20.6106	0.793889
$675$	−16.5803	−0.638177
$676$	−5.27798	−0.202999
$677$	50.7708	1.95128	0.975640	−	0.219377i	$-0.0704024\pi$
$677$	50.7708	1.95128	0.975640	+	0.219377i	$0.0704024\pi$
$678$	−4.45210	−0.170982
$679$	13.1722	0.505502
$680$	−13.3756	−0.512931
$681$	−38.4054	−1.47170
$682$	6.03326	0.231025
$683$	−10.4515	−0.399917	−0.199959	−	0.979804i	$-0.564081\pi$
$683$	−10.4515	−0.399917	−0.199959	+	0.979804i	$0.564081\pi$
$684$	5.51624	0.210919
$685$	21.4901	0.821093
$686$	−30.9908	−1.18323
$687$	−13.0132	−0.496483
$688$	−23.4394	−0.893619
$689$	−4.31318	−0.164319
$690$	0	0
$691$	19.0341	0.724092	0.362046	−	0.932160i	$-0.382078\pi$
$691$	19.0341	0.724092	0.362046	+	0.932160i	$0.382078\pi$
$692$	−13.2184	−0.502489
$693$	−0.840776	−0.0319384
$694$	0.284812	0.0108113
$695$	−25.5412	−0.968832
$696$	−5.24391	−0.198770
$697$	19.0724	0.722420
$698$	11.1594	0.422388
$699$	10.6959	0.404558
$700$	6.19460	0.234134
$701$	−37.6400	−1.42164	−0.710821	−	0.703373i	$-0.751676\pi$
$701$	−37.6400	−1.42164	−0.710821	+	0.703373i	$0.751676\pi$
$702$	23.7627	0.896864
$703$	−80.5022	−3.03620
$704$	−0.505780	−0.0190623
$705$	24.8007	0.934047
$706$	−30.4157	−1.14471
$707$	−2.78935	−0.104904
$708$	−10.7339	−0.403404
$709$	27.7626	1.04265	0.521323	−	0.853359i	$-0.325439\pi$
$709$	27.7626	1.04265	0.521323	+	0.853359i	$0.325439\pi$
$710$	−2.61138	−0.0980032
$711$	5.99316	0.224761
$712$	24.5369	0.919559
$713$	0	0
$714$	37.8225	1.41547
$715$	−3.42817	−0.128206
$716$	6.03940	0.225703
$717$	37.8984	1.41534
$718$	12.6229	0.471082
$719$	15.0105	0.559797	0.279899	−	0.960030i	$-0.409699\pi$
$719$	15.0105	0.559797	0.279899	+	0.960030i	$0.409699\pi$
$720$	−3.34543	−0.124677
$721$	−10.1684	−0.378690
$722$	−88.5415	−3.29518
$723$	26.3220	0.978925
$724$	−10.5610	−0.392497
$725$	−6.74631	−0.250552
$726$	3.36180	0.124768
$727$	39.1531	1.45211	0.726053	−	0.687638i	$-0.241352\pi$
$727$	39.1531	1.45211	0.726053	+	0.687638i	$0.241352\pi$
$728$	6.36597	0.235939
$729$	20.0898	0.744067
$730$	−31.2642	−1.15714
$731$	−36.0191	−1.33222
$732$	11.0247	0.407484
$733$	−42.1742	−1.55774	−0.778871	−	0.627185i	$-0.784207\pi$
$733$	−42.1742	−1.55774	−0.778871	+	0.627185i	$0.784207\pi$
$734$	−6.63402	−0.244866
$735$	10.7577	0.396803
$736$	0	0
$737$	−5.28241	−0.194580
$738$	2.53560	0.0933367
$739$	−32.7037	−1.20303	−0.601513	−	0.798863i	$-0.705435\pi$
$739$	−32.7037	−1.20303	−0.601513	+	0.798863i	$0.705435\pi$
$740$	−13.3201	−0.489655
$741$	45.6048	1.67533
$742$	3.88193	0.142510
$743$	4.59040	0.168405	0.0842027	−	0.996449i	$-0.473166\pi$
$743$	4.59040	0.168405	0.0842027	+	0.996449i	$0.473166\pi$
$744$	9.52243	0.349109
$745$	17.0090	0.623162
$746$	−44.3323	−1.62312
$747$	−1.32761	−0.0485747
$748$	−8.90099	−0.325452
$749$	16.3244	0.596481
$750$	−34.1069	−1.24541
$751$	43.0737	1.57178	0.785891	−	0.618365i	$-0.212205\pi$
$751$	43.0737	1.57178	0.785891	+	0.618365i	$0.212205\pi$
$752$	55.4007	2.02025
$753$	11.9113	0.434073
$754$	9.66871	0.352114
$755$	−5.00779	−0.182252
$756$	−7.87132	−0.286277
$757$	−21.8767	−0.795123	−0.397562	−	0.917575i	$-0.630144\pi$
$757$	−21.8767	−0.795123	−0.397562	+	0.917575i	$0.630144\pi$
$758$	−26.2390	−0.953043
$759$	0	0
$760$	14.5152	0.526523
$761$	7.85990	0.284921	0.142461	−	0.989800i	$-0.454499\pi$
$761$	7.85990	0.284921	0.142461	+	0.989800i	$0.454499\pi$
$762$	−35.0377	−1.26928
$763$	3.34688	0.121165
$764$	−17.6472	−0.638454
$765$	−5.14089	−0.185869
$766$	13.9172	0.502850
$767$	−14.1912	−0.512414
$768$	−38.3876	−1.38519
$769$	−19.2418	−0.693878	−0.346939	−	0.937888i	$-0.612779\pi$
$769$	−19.2418	−0.693878	−0.346939	+	0.937888i	$0.612779\pi$
$770$	3.08541	0.111190
$771$	2.98419	0.107473
$772$	−10.7775	−0.387891
$773$	−12.0494	−0.433387	−0.216694	−	0.976240i	$-0.569527\pi$
$773$	−12.0494	−0.433387	−0.216694	+	0.976240i	$0.569527\pi$
$774$	−4.78859	−0.172122
$775$	12.2506	0.440056
$776$	−13.2935	−0.477210
$777$	−27.0080	−0.968905
$778$	−19.5356	−0.700385
$779$	−20.6974	−0.741563
$780$	7.54587	0.270186
$781$	1.24607	0.0445880
$782$	0	0
$783$	8.57237	0.306351
$784$	24.0309	0.858247
$785$	−17.6134	−0.628650
$786$	−5.67107	−0.202280
$787$	6.99779	0.249444	0.124722	−	0.992192i	$-0.460196\pi$
$787$	6.99779	0.249444	0.124722	+	0.992192i	$0.460196\pi$
$788$	−3.01938	−0.107561
$789$	−7.70647	−0.274358
$790$	−21.9932	−0.782483
$791$	1.94975	0.0693253
$792$	0.848520	0.0301509
$793$	14.5757	0.517597
$794$	−63.3798	−2.24927
$795$	−3.29945	−0.117019
$796$	17.3919	0.616438
$797$	5.77778	0.204659	0.102330	−	0.994751i	$-0.467370\pi$
$797$	5.77778	0.204659	0.102330	+	0.994751i	$0.467370\pi$
$798$	−41.0450	−1.45298
$799$	85.1337	3.01181
$800$	−21.2219	−0.750307
$801$	9.43071	0.333218
$802$	3.86440	0.136457
$803$	14.9184	0.526459
$804$	11.6273	0.410063
$805$	0	0
$806$	−17.5574	−0.618434
$807$	32.0029	1.12656
$808$	2.81505	0.0990330
$809$	11.9756	0.421040	0.210520	−	0.977590i	$-0.432484\pi$
$809$	11.9756	0.421040	0.210520	+	0.977590i	$0.432484\pi$
$810$	21.7681	0.764853
$811$	51.6373	1.81323	0.906615	−	0.421958i	$-0.138657\pi$
$811$	51.6373	1.81323	0.906615	+	0.421958i	$0.138657\pi$
$812$	−3.20274	−0.112394
$813$	−37.2330	−1.30582
$814$	17.2694	0.605293
$815$	−4.01012	−0.140468
$816$	−71.8118	−2.51391
$817$	39.0880	1.36752
$818$	12.8864	0.450561
$819$	2.44675	0.0854963
$820$	−3.42465	−0.119594
$821$	15.0823	0.526376	0.263188	−	0.964745i	$-0.415226\pi$
$821$	15.0823	0.526376	0.263188	+	0.964745i	$0.415226\pi$
$822$	61.3276	2.13904
$823$	22.8544	0.796654	0.398327	−	0.917244i	$-0.369591\pi$
$823$	22.8544	0.796654	0.398327	+	0.917244i	$0.369591\pi$
$824$	10.2620	0.357495
$825$	6.82620	0.237658
$826$	12.7723	0.444405
$827$	−34.3535	−1.19459	−0.597293	−	0.802023i	$-0.703757\pi$
$827$	−34.3535	−1.19459	−0.597293	+	0.802023i	$0.703757\pi$
$828$	0	0
$829$	49.6108	1.72305	0.861526	−	0.507713i	$-0.169509\pi$
$829$	49.6108	1.72305	0.861526	+	0.507713i	$0.169509\pi$
$830$	4.87195	0.169108
$831$	−54.8348	−1.90220
$832$	1.47187	0.0510280
$833$	36.9281	1.27948
$834$	−72.8885	−2.52392
$835$	−20.7988	−0.719773
$836$	9.65938	0.334077
$837$	−15.5666	−0.538060
$838$	4.81351	0.166280
$839$	39.0726	1.34894	0.674469	−	0.738304i	$-0.264373\pi$
$839$	39.0726	1.34894	0.674469	+	0.738304i	$0.264373\pi$
$840$	4.86977	0.168023
$841$	−25.5120	−0.879725
$842$	36.3734	1.25351
$843$	−4.48940	−0.154623
$844$	−18.2695	−0.628863
$845$	−5.33794	−0.183631
$846$	11.3182	0.389127
$847$	−1.47227	−0.0505877
$848$	−7.37043	−0.253102
$849$	33.4755	1.14888
$850$	−49.1069	−1.68435
$851$	0	0
$852$	−2.74278	−0.0939659
$853$	29.8901	1.02342	0.511708	−	0.859159i	$-0.329013\pi$
$853$	29.8901	1.02342	0.511708	+	0.859159i	$0.329013\pi$
$854$	−13.1183	−0.448900
$855$	5.57891	0.190795
$856$	−16.4748	−0.563096
$857$	57.6526	1.96937	0.984687	−	0.174330i	$-0.0557760\pi$
$857$	57.6526	1.96937	0.984687	+	0.174330i	$0.0557760\pi$
$858$	−9.78320	−0.333993
$859$	1.68688	0.0575557	0.0287778	−	0.999586i	$-0.490838\pi$
$859$	1.68688	0.0575557	0.0287778	+	0.999586i	$0.490838\pi$
$860$	6.46759	0.220543
$861$	−6.94386	−0.236646
$862$	4.04434	0.137751
$863$	−46.9695	−1.59886	−0.799431	−	0.600758i	$-0.794866\pi$
$863$	−46.9695	−1.59886	−0.799431	+	0.600758i	$0.794866\pi$
$864$	26.9661	0.917406
$865$	−13.3686	−0.454546
$866$	18.2607	0.620523
$867$	−78.2271	−2.65673
$868$	5.81586	0.197403
$869$	10.4945	0.356002
$870$	7.39627	0.250757
$871$	15.3724	0.520873
$872$	−3.37771	−0.114384
$873$	−5.10934	−0.172925
$874$	0	0
$875$	14.9368	0.504956
$876$	−32.8374	−1.10947
$877$	48.9606	1.65328	0.826640	−	0.562730i	$-0.190249\pi$
$877$	48.9606	1.65328	0.826640	+	0.562730i	$0.190249\pi$
$878$	−9.53993	−0.321957
$879$	3.06290	0.103309
$880$	−5.85812	−0.197477
$881$	14.3107	0.482138	0.241069	−	0.970508i	$-0.422502\pi$
$881$	14.3107	0.482138	0.241069	+	0.970508i	$0.422502\pi$
$882$	4.90943	0.165309
$883$	49.2746	1.65822	0.829111	−	0.559083i	$-0.188847\pi$
$883$	49.2746	1.65822	0.829111	+	0.559083i	$0.188847\pi$
$884$	25.9028	0.871207
$885$	−10.8558	−0.364915
$886$	5.85408	0.196672
$887$	16.2926	0.547053	0.273526	−	0.961865i	$-0.411810\pi$
$887$	16.2926	0.547053	0.273526	+	0.961865i	$0.411810\pi$
$888$	27.2567	0.914676
$889$	15.3444	0.514635
$890$	−34.6080	−1.16006
$891$	−10.3871	−0.347981
$892$	19.7521	0.661350
$893$	−92.3873	−3.09162
$894$	48.5398	1.62341
$895$	6.10802	0.204169
$896$	15.9743	0.533665
$897$	0	0
$898$	31.9991	1.06782
$899$	−6.33384	−0.211245
$900$	−2.40281	−0.0800938
$901$	−11.3261	−0.377326
$902$	4.44004	0.147837
$903$	13.1138	0.436400
$904$	−1.96771	−0.0654452
$905$	−10.6810	−0.355048
$906$	−14.2911	−0.474789
$907$	−9.86041	−0.327410	−0.163705	−	0.986509i	$-0.552344\pi$
$907$	−9.86041	−0.327410	−0.163705	+	0.986509i	$0.552344\pi$
$908$	23.6723	0.785592
$909$	1.08196	0.0358863
$910$	−8.97887	−0.297647
$911$	37.1508	1.23086	0.615431	−	0.788191i	$-0.288982\pi$
$911$	37.1508	1.23086	0.615431	+	0.788191i	$0.288982\pi$
$912$	77.9303	2.58053
$913$	−2.32476	−0.0769382
$914$	40.6091	1.34323
$915$	11.1499	0.368606
$916$	8.02103	0.265022
$917$	2.48359	0.0820153
$918$	62.3989	2.05947
$919$	24.7268	0.815662	0.407831	−	0.913057i	$-0.366285\pi$
$919$	24.7268	0.815662	0.407831	+	0.913057i	$0.366285\pi$
$920$	0	0
$921$	−1.25517	−0.0413593
$922$	−57.0941	−1.88029
$923$	−3.62621	−0.119358
$924$	3.24066	0.106610
$925$	35.0659	1.15296
$926$	−52.7320	−1.73288
$927$	3.94419	0.129544
$928$	10.9722	0.360179
$929$	49.8142	1.63435	0.817175	−	0.576390i	$-0.195539\pi$
$929$	49.8142	1.63435	0.817175	+	0.576390i	$0.195539\pi$
$930$	−13.4309	−0.440417
$931$	−40.0744	−1.31339
$932$	−6.59275	−0.215953
$933$	−60.5555	−1.98250
$934$	75.1202	2.45801
$935$	−9.00212	−0.294401
$936$	−2.46929	−0.0807111
$937$	−2.90796	−0.0949989	−0.0474994	−	0.998871i	$-0.515125\pi$
$937$	−2.90796	−0.0949989	−0.0474994	+	0.998871i	$0.515125\pi$
$938$	−13.8354	−0.451741
$939$	−40.9144	−1.33519
$940$	−15.2866	−0.498594
$941$	−27.6207	−0.900409	−0.450204	−	0.892926i	$-0.648649\pi$
$941$	−27.6207	−0.900409	−0.450204	+	0.892926i	$0.648649\pi$
$942$	−50.2645	−1.63771
$943$	0	0
$944$	−24.2502	−0.789276
$945$	−7.96075	−0.258963
$946$	−8.38522	−0.272627
$947$	7.54684	0.245239	0.122620	−	0.992454i	$-0.460870\pi$
$947$	7.54684	0.245239	0.122620	+	0.992454i	$0.460870\pi$
$948$	−23.0998	−0.750248
$949$	−43.4141	−1.40928
$950$	53.2910	1.72899
$951$	2.03332	0.0659349
$952$	16.7166	0.541787
$953$	−15.0773	−0.488400	−0.244200	−	0.969725i	$-0.578525\pi$
$953$	−15.0773	−0.488400	−0.244200	+	0.969725i	$0.578525\pi$
$954$	−1.50575	−0.0487506
$955$	−17.8477	−0.577539
$956$	−23.3598	−0.755509
$957$	−3.52929	−0.114086
$958$	39.0951	1.26311
$959$	−26.8578	−0.867284
$960$	1.12594	0.0363395
$961$	−19.4984	−0.628980
$962$	−50.2559	−1.62031
$963$	−6.33205	−0.204047
$964$	−16.2243	−0.522550
$965$	−10.9000	−0.350882
$966$	0	0
$967$	−49.5086	−1.59209	−0.796044	−	0.605239i	$-0.793078\pi$
$967$	−49.5086	−1.59209	−0.796044	+	0.605239i	$0.793078\pi$
$968$	1.48583	0.0477563
$969$	119.755	3.84708
$970$	18.7498	0.602021
$971$	−42.3810	−1.36007	−0.680036	−	0.733179i	$-0.738036\pi$
$971$	−42.3810	−1.36007	−0.680036	+	0.733179i	$0.738036\pi$
$972$	6.82424	0.218888
$973$	31.9208	1.02333
$974$	−39.3850	−1.26198
$975$	−19.8650	−0.636188
$976$	24.9072	0.797258
$977$	−19.5088	−0.624141	−0.312071	−	0.950059i	$-0.601023\pi$
$977$	−19.5088	−0.624141	−0.312071	+	0.950059i	$0.601023\pi$
$978$	−11.4439	−0.365937
$979$	16.5139	0.527788
$980$	−6.63081	−0.211813
$981$	−1.29822	−0.0414489
$982$	2.11970	0.0676424
$983$	−50.7450	−1.61851	−0.809257	−	0.587454i	$-0.800130\pi$
$983$	−50.7450	−1.61851	−0.809257	+	0.587454i	$0.800130\pi$
$984$	7.00782	0.223401
$985$	−3.05369	−0.0972987
$986$	25.3893	0.808560
$987$	−30.9953	−0.986593
$988$	−28.1098	−0.894293
$989$	0	0
$990$	−1.19679	−0.0380366
$991$	−19.2456	−0.611357	−0.305678	−	0.952135i	$-0.598883\pi$
$991$	−19.2456	−0.611357	−0.305678	+	0.952135i	$0.598883\pi$
$992$	−19.9244	−0.632599
$993$	−28.8594	−0.915826
$994$	3.26364	0.103516
$995$	17.5895	0.557623
$996$	5.11710	0.162142
$997$	−6.71283	−0.212597	−0.106299	−	0.994334i	$-0.533900\pi$
$997$	−6.71283	−0.212597	−0.106299	+	0.994334i	$0.533900\pi$
$998$	−33.5502	−1.06201
$999$	−44.5573	−1.40973

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5819.2.a.u.1.12		60
23.9	even	11		253.2.i.b.12.3	✓	120
23.18	even	11		253.2.i.b.232.3	yes	120
23.22	odd	2		5819.2.a.t.1.12		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.2.i.b.12.3	✓	120	23.9	even	11
253.2.i.b.232.3	yes	120	23.18	even	11
5819.2.a.t.1.12		60	23.22	odd	2
5819.2.a.u.1.12		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)

\(f(q)\)	\(=\)	\(q-1.77899 q^{2} -1.88973 q^{3} +1.16479 q^{4} +1.17802 q^{5} +3.36180 q^{6} -1.47227 q^{7} +1.48583 q^{8} +0.571076 q^{9} -2.09569 q^{10} +1.00000 q^{11} -2.20114 q^{12} -2.91011 q^{13} +2.61914 q^{14} -2.22614 q^{15} -4.97284 q^{16} -7.64172 q^{17} -1.01594 q^{18} +8.29282 q^{19} +1.37215 q^{20} +2.78219 q^{21} -1.77899 q^{22} -2.80781 q^{24} -3.61226 q^{25} +5.17704 q^{26} +4.59001 q^{27} -1.71488 q^{28} +1.86761 q^{29} +3.96028 q^{30} -3.39140 q^{31} +5.87496 q^{32} -1.88973 q^{33} +13.5945 q^{34} -1.73436 q^{35} +0.665183 q^{36} -9.70746 q^{37} -14.7528 q^{38} +5.49931 q^{39} +1.75034 q^{40} -2.49583 q^{41} -4.94947 q^{42} +4.71348 q^{43} +1.16479 q^{44} +0.672740 q^{45} -11.1406 q^{47} +9.39733 q^{48} -4.83243 q^{49} +6.42616 q^{50} +14.4408 q^{51} -3.38966 q^{52} +1.48214 q^{53} -8.16556 q^{54} +1.17802 q^{55} -2.18754 q^{56} -15.6712 q^{57} -3.32246 q^{58} +4.87652 q^{59} -2.59299 q^{60} -5.00863 q^{61} +6.03326 q^{62} -0.840776 q^{63} -0.505780 q^{64} -3.42817 q^{65} +3.36180 q^{66} -5.28241 q^{67} -8.90099 q^{68} +3.08541 q^{70} +1.24607 q^{71} +0.848520 q^{72} +14.9184 q^{73} +17.2694 q^{74} +6.82620 q^{75} +9.65938 q^{76} -1.47227 q^{77} -9.78320 q^{78} +10.4945 q^{79} -5.85812 q^{80} -10.3871 q^{81} +4.44004 q^{82} -2.32476 q^{83} +3.24066 q^{84} -9.00212 q^{85} -8.38522 q^{86} -3.52929 q^{87} +1.48583 q^{88} +16.5139 q^{89} -1.19679 q^{90} +4.28446 q^{91} +6.40884 q^{93} +19.8190 q^{94} +9.76913 q^{95} -11.1021 q^{96} -8.94688 q^{97} +8.59682 q^{98} +0.571076 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 5 q^{2} + 9 q^{3} + 73 q^{4} + 8 q^{5} + 26 q^{6} + 30 q^{8} + 75 q^{9} - 7 q^{10} + 60 q^{11} + 41 q^{12} + 46 q^{13} + 16 q^{14} + 4 q^{15} + 99 q^{16} - 5 q^{17} + 36 q^{18} - 8 q^{19} + 82 q^{20}+ \cdots + 75 q^{99}+O(q^{100}) \) 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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