LMFDB - Embedded newform 5819.2.a.t.1.20

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			1.20
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)

$f(q)$	$=$	\(q-1.12774 q^{2} +2.11139 q^{3} -0.728194 q^{4} -0.943998 q^{5} -2.38110 q^{6} -1.55399 q^{7} +3.07670 q^{8} +1.45795 q^{9} +1.06459 q^{10} -1.00000 q^{11} -1.53750 q^{12} -4.10851 q^{13} +1.75250 q^{14} -1.99315 q^{15} -2.01334 q^{16} -7.48754 q^{17} -1.64420 q^{18} -5.65746 q^{19} +0.687414 q^{20} -3.28107 q^{21} +1.12774 q^{22} +6.49611 q^{24} -4.10887 q^{25} +4.63335 q^{26} -3.25586 q^{27} +1.13161 q^{28} +5.46487 q^{29} +2.24776 q^{30} +0.647562 q^{31} -3.88287 q^{32} -2.11139 q^{33} +8.44402 q^{34} +1.46696 q^{35} -1.06167 q^{36} -7.47778 q^{37} +6.38017 q^{38} -8.67466 q^{39} -2.90440 q^{40} +8.11294 q^{41} +3.70021 q^{42} +10.1683 q^{43} +0.728194 q^{44} -1.37630 q^{45} +2.48881 q^{47} -4.25095 q^{48} -4.58512 q^{49} +4.63375 q^{50} -15.8091 q^{51} +2.99180 q^{52} -0.738321 q^{53} +3.67177 q^{54} +0.943998 q^{55} -4.78116 q^{56} -11.9451 q^{57} -6.16297 q^{58} +11.7423 q^{59} +1.45140 q^{60} -2.61676 q^{61} -0.730284 q^{62} -2.26564 q^{63} +8.40557 q^{64} +3.87843 q^{65} +2.38110 q^{66} +9.92380 q^{67} +5.45238 q^{68} -1.65436 q^{70} +1.04399 q^{71} +4.48569 q^{72} +2.25470 q^{73} +8.43302 q^{74} -8.67541 q^{75} +4.11973 q^{76} +1.55399 q^{77} +9.78279 q^{78} +11.5540 q^{79} +1.90059 q^{80} -11.2482 q^{81} -9.14932 q^{82} +11.4873 q^{83} +2.38926 q^{84} +7.06822 q^{85} -11.4672 q^{86} +11.5385 q^{87} -3.07670 q^{88} -1.78171 q^{89} +1.55212 q^{90} +6.38459 q^{91} +1.36725 q^{93} -2.80674 q^{94} +5.34064 q^{95} -8.19824 q^{96} -15.3288 q^{97} +5.17084 q^{98} -1.45795 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.12774	−0.797435	−0.398718	−	0.917074i	$-0.630545\pi$
$2$	−1.12774	−0.797435	−0.398718	+	0.917074i	$0.630545\pi$
$3$	2.11139	1.21901	0.609505	−	0.792782i	$-0.291368\pi$
$3$	2.11139	1.21901	0.609505	+	0.792782i	$0.291368\pi$
$4$	−0.728194	−0.364097
$5$	−0.943998	−0.422169	−0.211084	−	0.977468i	$-0.567700\pi$
$5$	−0.943998	−0.422169	−0.211084	+	0.977468i	$0.567700\pi$
$6$	−2.38110	−0.972081
$7$	−1.55399	−0.587353	−0.293676	−	0.955905i	$-0.594879\pi$
$7$	−1.55399	−0.587353	−0.293676	+	0.955905i	$0.594879\pi$
$8$	3.07670	1.08778
$9$	1.45795	0.485984
$10$	1.06459	0.336652
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.53750	−0.443838
$13$	−4.10851	−1.13950	−0.569748	−	0.821819i	$-0.692959\pi$
$13$	−4.10851	−1.13950	−0.569748	+	0.821819i	$0.692959\pi$
$14$	1.75250	0.468376
$15$	−1.99315	−0.514628
$16$	−2.01334	−0.503336
$17$	−7.48754	−1.81599	−0.907997	−	0.418976i	$-0.862389\pi$
$17$	−7.48754	−1.81599	−0.907997	+	0.418976i	$0.862389\pi$
$18$	−1.64420	−0.387541
$19$	−5.65746	−1.29791	−0.648956	−	0.760826i	$-0.724794\pi$
$19$	−5.65746	−1.29791	−0.648956	+	0.760826i	$0.724794\pi$
$20$	0.687414	0.153711
$21$	−3.28107	−0.715988
$22$	1.12774	0.240436
$23$	0	0
$23$	0	0
$24$	6.49611	1.32601
$25$	−4.10887	−0.821773
$26$	4.63335	0.908675
$27$	−3.25586	−0.626590
$28$	1.13161	0.213853
$29$	5.46487	1.01480	0.507401	−	0.861710i	$-0.330606\pi$
$29$	5.46487	1.01480	0.507401	+	0.861710i	$0.330606\pi$
$30$	2.24776	0.410382
$31$	0.647562	0.116306	0.0581528	−	0.998308i	$-0.481479\pi$
$31$	0.647562	0.116306	0.0581528	+	0.998308i	$0.481479\pi$
$32$	−3.88287	−0.686401
$33$	−2.11139	−0.367545
$34$	8.44402	1.44814
$35$	1.46696	0.247962
$36$	−1.06167	−0.176946
$37$	−7.47778	−1.22934	−0.614670	−	0.788785i	$-0.710711\pi$
$37$	−7.47778	−1.22934	−0.614670	+	0.788785i	$0.710711\pi$
$38$	6.38017	1.03500
$39$	−8.67466	−1.38906
$40$	−2.90440	−0.459226
$41$	8.11294	1.26703	0.633514	−	0.773731i	$-0.281612\pi$
$41$	8.11294	1.26703	0.633514	+	0.773731i	$0.281612\pi$
$42$	3.70021	0.570954
$43$	10.1683	1.55065	0.775323	−	0.631564i	$-0.217587\pi$
$43$	10.1683	1.55065	0.775323	+	0.631564i	$0.217587\pi$
$44$	0.728194	0.109779
$45$	−1.37630	−0.205167
$46$	0	0
$47$	2.48881	0.363030	0.181515	−	0.983388i	$-0.441900\pi$
$47$	2.48881	0.363030	0.181515	+	0.983388i	$0.441900\pi$
$48$	−4.25095	−0.613571
$49$	−4.58512	−0.655017
$50$	4.63375	0.655311
$51$	−15.8091	−2.21371
$52$	2.99180	0.414888
$53$	−0.738321	−0.101416	−0.0507081	−	0.998714i	$-0.516148\pi$
$53$	−0.738321	−0.101416	−0.0507081	+	0.998714i	$0.516148\pi$
$54$	3.67177	0.499665
$55$	0.943998	0.127289
$56$	−4.78116	−0.638910
$57$	−11.9451	−1.58217
$58$	−6.16297	−0.809238
$59$	11.7423	1.52871	0.764357	−	0.644794i	$-0.223057\pi$
$59$	11.7423	1.52871	0.764357	+	0.644794i	$0.223057\pi$
$60$	1.45140	0.187375
$61$	−2.61676	−0.335041	−0.167521	−	0.985869i	$-0.553576\pi$
$61$	−2.61676	−0.335041	−0.167521	+	0.985869i	$0.553576\pi$
$62$	−0.730284	−0.0927461
$63$	−2.26564	−0.285444
$64$	8.40557	1.05070
$65$	3.87843	0.481060
$66$	2.38110	0.293093
$67$	9.92380	1.21238	0.606192	−	0.795318i	$-0.292696\pi$
$67$	9.92380	1.21238	0.606192	+	0.795318i	$0.292696\pi$
$68$	5.45238	0.661199
$69$	0	0
$70$	−1.65436	−0.197734
$71$	1.04399	0.123899	0.0619497	−	0.998079i	$-0.480268\pi$
$71$	1.04399	0.123899	0.0619497	+	0.998079i	$0.480268\pi$
$72$	4.48569	0.528643
$73$	2.25470	0.263893	0.131947	−	0.991257i	$-0.457877\pi$
$73$	2.25470	0.263893	0.131947	+	0.991257i	$0.457877\pi$
$74$	8.43302	0.980318
$75$	−8.67541	−1.00175
$76$	4.11973	0.472566
$77$	1.55399	0.177093
$78$	9.78279	1.10768
$79$	11.5540	1.29993	0.649965	−	0.759964i	$-0.274784\pi$
$79$	11.5540	1.29993	0.649965	+	0.759964i	$0.274784\pi$
$80$	1.90059	0.212493
$81$	−11.2482	−1.24980
$82$	−9.14932	−1.01037
$83$	11.4873	1.26089	0.630447	−	0.776232i	$-0.282871\pi$
$83$	11.4873	1.26089	0.630447	+	0.776232i	$0.282871\pi$
$84$	2.38926	0.260689
$85$	7.06822	0.766656
$86$	−11.4672	−1.23654
$87$	11.5385	1.23705
$88$	−3.07670	−0.327978
$89$	−1.78171	−0.188861	−0.0944303	−	0.995531i	$-0.530103\pi$
$89$	−1.78171	−0.188861	−0.0944303	+	0.995531i	$0.530103\pi$
$90$	1.55212	0.163608
$91$	6.38459	0.669286
$92$	0	0
$93$	1.36725	0.141778
$94$	−2.80674	−0.289493
$95$	5.34064	0.547938
$96$	−8.19824	−0.836730
$97$	−15.3288	−1.55641	−0.778204	−	0.628012i	$-0.783869\pi$
$97$	−15.3288	−1.55641	−0.778204	+	0.628012i	$0.783869\pi$
$98$	5.17084	0.522334
$99$	−1.45795	−0.146530
$100$	2.99205	0.299205
$101$	17.3241	1.72381	0.861906	−	0.507068i	$-0.169271\pi$
$101$	17.3241	1.72381	0.861906	+	0.507068i	$0.169271\pi$
$102$	17.8286	1.76529
$103$	7.31971	0.721233	0.360616	−	0.932714i	$-0.382566\pi$
$103$	7.31971	0.721233	0.360616	+	0.932714i	$0.382566\pi$
$104$	−12.6407	−1.23952
$105$	3.09733	0.302268
$106$	0.832637	0.0808728
$107$	−1.64268	−0.158804	−0.0794022	−	0.996843i	$-0.525301\pi$
$107$	−1.64268	−0.158804	−0.0794022	+	0.996843i	$0.525301\pi$
$108$	2.37090	0.228140
$109$	0.759916	0.0727868	0.0363934	−	0.999338i	$-0.488413\pi$
$109$	0.759916	0.0727868	0.0363934	+	0.999338i	$0.488413\pi$
$110$	−1.06459	−0.101504
$111$	−15.7885	−1.49858
$112$	3.12871	0.295636
$113$	−7.83050	−0.736631	−0.368316	−	0.929701i	$-0.620065\pi$
$113$	−7.83050	−0.736631	−0.368316	+	0.929701i	$0.620065\pi$
$114$	13.4710	1.26168
$115$	0	0
$116$	−3.97949	−0.369486
$117$	−5.99002	−0.553778
$118$	−13.2423	−1.21905
$119$	11.6355	1.06663
$120$	−6.13232	−0.559801
$121$	1.00000	0.0909091
$122$	2.95103	0.267174
$123$	17.1296	1.54452
$124$	−0.471551	−0.0423465
$125$	8.59875	0.769096
$126$	2.55506	0.227623
$127$	−2.61296	−0.231863	−0.115931	−	0.993257i	$-0.536985\pi$
$127$	−2.61296	−0.231863	−0.115931	+	0.993257i	$0.536985\pi$
$128$	−1.71359	−0.151461
$129$	21.4691	1.89025
$130$	−4.37388	−0.383614
$131$	14.8098	1.29394	0.646970	−	0.762516i	$-0.276036\pi$
$131$	14.8098	1.29394	0.646970	+	0.762516i	$0.276036\pi$
$132$	1.53750	0.133822
$133$	8.79164	0.762332
$134$	−11.1915	−0.966798
$135$	3.07352	0.264527
$136$	−23.0369	−1.97540
$137$	7.78130	0.664801	0.332401	−	0.943138i	$-0.392141\pi$
$137$	7.78130	0.664801	0.332401	+	0.943138i	$0.392141\pi$
$138$	0	0
$139$	12.0941	1.02581	0.512903	−	0.858446i	$-0.328570\pi$
$139$	12.0941	1.02581	0.512903	+	0.858446i	$0.328570\pi$
$140$	−1.06823	−0.0902823
$141$	5.25484	0.442537
$142$	−1.17736	−0.0988017
$143$	4.10851	0.343571
$144$	−2.93536	−0.244613
$145$	−5.15883	−0.428418
$146$	−2.54273	−0.210438
$147$	−9.68096	−0.798472
$148$	5.44528	0.447599
$149$	−18.0995	−1.48277	−0.741385	−	0.671080i	$-0.765831\pi$
$149$	−18.0995	−1.48277	−0.741385	+	0.671080i	$0.765831\pi$
$150$	9.78363	0.798830
$151$	3.66819	0.298513	0.149256	−	0.988799i	$-0.452312\pi$
$151$	3.66819	0.298513	0.149256	+	0.988799i	$0.452312\pi$
$152$	−17.4063	−1.41184
$153$	−10.9165	−0.882545
$154$	−1.75250	−0.141221
$155$	−0.611297	−0.0491006
$156$	6.31684	0.505752
$157$	−0.962631	−0.0768263	−0.0384132	−	0.999262i	$-0.512230\pi$
$157$	−0.962631	−0.0768263	−0.0384132	+	0.999262i	$0.512230\pi$
$158$	−13.0300	−1.03661
$159$	−1.55888	−0.123627
$160$	3.66542	0.289777
$161$	0	0
$162$	12.6851	0.996637
$163$	−23.9300	−1.87434	−0.937172	−	0.348868i	$-0.886566\pi$
$163$	−23.9300	−1.87434	−0.937172	+	0.348868i	$0.886566\pi$
$164$	−5.90780	−0.461322
$165$	1.99315	0.155166
$166$	−12.9547	−1.00548
$167$	−11.1686	−0.864251	−0.432125	−	0.901814i	$-0.642236\pi$
$167$	−11.1686	−0.864251	−0.432125	+	0.901814i	$0.642236\pi$
$168$	−10.0949	−0.778837
$169$	3.87989	0.298453
$170$	−7.97114	−0.611359
$171$	−8.24832	−0.630764
$172$	−7.40448	−0.564586
$173$	−13.6091	−1.03468	−0.517342	−	0.855779i	$-0.673078\pi$
$173$	−13.6091	−1.03468	−0.517342	+	0.855779i	$0.673078\pi$
$174$	−13.0124	−0.986469
$175$	6.38513	0.482671
$176$	2.01334	0.151762
$177$	24.7925	1.86352
$178$	2.00931	0.150604
$179$	2.61118	0.195169	0.0975844	−	0.995227i	$-0.468888\pi$
$179$	2.61118	0.195169	0.0975844	+	0.995227i	$0.468888\pi$
$180$	1.00222	0.0747009
$181$	−14.0713	−1.04591	−0.522956	−	0.852359i	$-0.675171\pi$
$181$	−14.0713	−1.04591	−0.522956	+	0.852359i	$0.675171\pi$
$182$	−7.20017	−0.533712
$183$	−5.52498	−0.408419
$184$	0	0
$185$	7.05901	0.518989
$186$	−1.54191	−0.113058
$187$	7.48754	0.547543
$188$	−1.81234	−0.132178
$189$	5.05957	0.368029
$190$	−6.02287	−0.436945
$191$	−13.2854	−0.961299	−0.480650	−	0.876913i	$-0.659599\pi$
$191$	−13.2854	−0.961299	−0.480650	+	0.876913i	$0.659599\pi$
$192$	17.7474	1.28081
$193$	13.0763	0.941253	0.470626	−	0.882333i	$-0.344028\pi$
$193$	13.0763	0.941253	0.470626	+	0.882333i	$0.344028\pi$
$194$	17.2870	1.24113
$195$	8.18887	0.586417
$196$	3.33886	0.238490
$197$	−21.1377	−1.50600	−0.753000	−	0.658021i	$-0.771394\pi$
$197$	−21.1377	−1.50600	−0.753000	+	0.658021i	$0.771394\pi$
$198$	1.64420	0.116848
$199$	−2.03252	−0.144082	−0.0720408	−	0.997402i	$-0.522951\pi$
$199$	−2.03252	−0.144082	−0.0720408	+	0.997402i	$0.522951\pi$
$200$	−12.6418	−0.893908
$201$	20.9530	1.47791
$202$	−19.5371	−1.37463
$203$	−8.49235	−0.596046
$204$	11.5121	0.806007
$205$	−7.65860	−0.534900
$206$	−8.25476	−0.575136
$207$	0	0
$208$	8.27185	0.573550
$209$	5.65746	0.391335
$210$	−3.49299	−0.241039
$211$	−2.59363	−0.178553	−0.0892763	−	0.996007i	$-0.528455\pi$
$211$	−2.59363	−0.178553	−0.0892763	+	0.996007i	$0.528455\pi$
$212$	0.537641	0.0369253
$213$	2.20428	0.151034
$214$	1.85253	0.126636
$215$	−9.59883	−0.654635
$216$	−10.0173	−0.681592
$217$	−1.00630	−0.0683124
$218$	−0.856991	−0.0580427
$219$	4.76055	0.321688
$220$	−0.687414	−0.0463455
$221$	30.7627	2.06932
$222$	17.8054	1.19502
$223$	−7.01687	−0.469884	−0.234942	−	0.972009i	$-0.575490\pi$
$223$	−7.01687	−0.469884	−0.234942	+	0.972009i	$0.575490\pi$
$224$	6.03394	0.403160
$225$	−5.99053	−0.399369
$226$	8.83079	0.587416
$227$	−4.90623	−0.325638	−0.162819	−	0.986656i	$-0.552059\pi$
$227$	−4.90623	−0.325638	−0.162819	+	0.986656i	$0.552059\pi$
$228$	8.69835	0.576062
$229$	−6.22401	−0.411294	−0.205647	−	0.978626i	$-0.565930\pi$
$229$	−6.22401	−0.411294	−0.205647	+	0.978626i	$0.565930\pi$
$230$	0	0
$231$	3.28107	0.215879
$232$	16.8138	1.10388
$233$	7.32162	0.479655	0.239828	−	0.970815i	$-0.422909\pi$
$233$	7.32162	0.479655	0.239828	+	0.970815i	$0.422909\pi$
$234$	6.75521	0.441602
$235$	−2.34943	−0.153260
$236$	−8.55066	−0.556600
$237$	24.3950	1.58463
$238$	−13.1219	−0.850567
$239$	25.5011	1.64953	0.824765	−	0.565476i	$-0.191308\pi$
$239$	25.5011	1.64953	0.824765	+	0.565476i	$0.191308\pi$
$240$	4.01289	0.259031
$241$	20.8432	1.34263	0.671313	−	0.741174i	$-0.265731\pi$
$241$	20.8432	1.34263	0.671313	+	0.741174i	$0.265731\pi$
$242$	−1.12774	−0.0724941
$243$	−13.9818	−0.896932
$244$	1.90551	0.121988
$245$	4.32834	0.276528
$246$	−19.3177	−1.23165
$247$	23.2438	1.47897
$248$	1.99236	0.126515
$249$	24.2541	1.53704
$250$	−9.69719	−0.613304
$251$	−2.98135	−0.188181	−0.0940905	−	0.995564i	$-0.529994\pi$
$251$	−2.98135	−0.188181	−0.0940905	+	0.995564i	$0.529994\pi$
$252$	1.64983	0.103929
$253$	0	0
$254$	2.94675	0.184895
$255$	14.9237	0.934561
$256$	−14.8787	−0.929916
$257$	6.90477	0.430708	0.215354	−	0.976536i	$-0.430910\pi$
$257$	6.90477	0.430708	0.215354	+	0.976536i	$0.430910\pi$
$258$	−24.2117	−1.50735
$259$	11.6204	0.722056
$260$	−2.82425	−0.175153
$261$	7.96753	0.493177
$262$	−16.7017	−1.03183
$263$	7.35770	0.453696	0.226848	−	0.973930i	$-0.427158\pi$
$263$	7.35770	0.453696	0.226848	+	0.973930i	$0.427158\pi$
$264$	−6.49611	−0.399808
$265$	0.696974	0.0428147
$266$	−9.91471	−0.607910
$267$	−3.76187	−0.230223
$268$	−7.22646	−0.441426
$269$	30.7554	1.87519	0.937595	−	0.347729i	$-0.113047\pi$
$269$	30.7554	1.87519	0.937595	+	0.347729i	$0.113047\pi$
$270$	−3.46615	−0.210943
$271$	8.05485	0.489297	0.244649	−	0.969612i	$-0.421327\pi$
$271$	8.05485	0.489297	0.244649	+	0.969612i	$0.421327\pi$
$272$	15.0750	0.914055
$273$	13.4803	0.815866
$274$	−8.77531	−0.530136
$275$	4.10887	0.247774
$276$	0	0
$277$	−23.4213	−1.40725	−0.703626	−	0.710571i	$-0.748437\pi$
$277$	−23.4213	−1.40725	−0.703626	+	0.710571i	$0.748437\pi$
$278$	−13.6390	−0.818014
$279$	0.944114	0.0565227
$280$	4.51341	0.269728
$281$	−1.08512	−0.0647326	−0.0323663	−	0.999476i	$-0.510304\pi$
$281$	−1.08512	−0.0647326	−0.0323663	+	0.999476i	$0.510304\pi$
$282$	−5.92611	−0.352895
$283$	25.0169	1.48710	0.743549	−	0.668682i	$-0.233141\pi$
$283$	25.0169	1.48710	0.743549	+	0.668682i	$0.233141\pi$
$284$	−0.760231	−0.0451114
$285$	11.2761	0.667941
$286$	−4.63335	−0.273976
$287$	−12.6074	−0.744192
$288$	−5.66104	−0.333580
$289$	39.0632	2.29784
$290$	5.81784	0.341635
$291$	−32.3651	−1.89728
$292$	−1.64186	−0.0960828
$293$	−13.0930	−0.764902	−0.382451	−	0.923976i	$-0.624920\pi$
$293$	−13.0930	−0.764902	−0.382451	+	0.923976i	$0.624920\pi$
$294$	10.9176	0.636730
$295$	−11.0847	−0.645375
$296$	−23.0069	−1.33725
$297$	3.25586	0.188924
$298$	20.4116	1.18241
$299$	0	0
$300$	6.31738	0.364734
$301$	−15.8014	−0.910776
$302$	−4.13677	−0.238045
$303$	36.5779	2.10134
$304$	11.3904	0.653285
$305$	2.47021	0.141444
$306$	12.3110	0.703772
$307$	0.163593	0.00933677	0.00466839	−	0.999989i	$-0.498514\pi$
$307$	0.163593	0.00933677	0.00466839	+	0.999989i	$0.498514\pi$
$308$	−1.13161	−0.0644792
$309$	15.4547	0.879190
$310$	0.689387	0.0391545
$311$	18.7208	1.06156	0.530779	−	0.847510i	$-0.321899\pi$
$311$	18.7208	1.06156	0.530779	+	0.847510i	$0.321899\pi$
$312$	−26.6894	−1.51099
$313$	−11.1702	−0.631375	−0.315688	−	0.948863i	$-0.602235\pi$
$313$	−11.1702	−0.631375	−0.315688	+	0.948863i	$0.602235\pi$
$314$	1.08560	0.0612640
$315$	2.13876	0.120506
$316$	−8.41358	−0.473301
$317$	4.79170	0.269129	0.134564	−	0.990905i	$-0.457036\pi$
$317$	4.79170	0.269129	0.134564	+	0.990905i	$0.457036\pi$
$318$	1.75802	0.0985847
$319$	−5.46487	−0.305974
$320$	−7.93484	−0.443571
$321$	−3.46834	−0.193584
$322$	0	0
$323$	42.3605	2.35700
$324$	8.19090	0.455050
$325$	16.8813	0.936408
$326$	26.9869	1.49467
$327$	1.60448	0.0887278
$328$	24.9611	1.37825
$329$	−3.86758	−0.213227
$330$	−2.24776	−0.123735
$331$	2.66261	0.146350	0.0731751	−	0.997319i	$-0.476687\pi$
$331$	2.66261	0.146350	0.0731751	+	0.997319i	$0.476687\pi$
$332$	−8.36499	−0.459088
$333$	−10.9022	−0.597439
$334$	12.5953	0.689184
$335$	−9.36805	−0.511831
$336$	6.60592	0.360383
$337$	−15.7353	−0.857154	−0.428577	−	0.903505i	$-0.640985\pi$
$337$	−15.7353	−0.857154	−0.428577	+	0.903505i	$0.640985\pi$
$338$	−4.37552	−0.237997
$339$	−16.5332	−0.897961
$340$	−5.14704	−0.279137
$341$	−0.647562	−0.0350674
$342$	9.30199	0.502994
$343$	18.0031	0.972078
$344$	31.2848	1.68676
$345$	0	0
$346$	15.3476	0.825093
$347$	−20.2894	−1.08919	−0.544595	−	0.838699i	$-0.683317\pi$
$347$	−20.2894	−1.08919	−0.544595	+	0.838699i	$0.683317\pi$
$348$	−8.40224	−0.450407
$349$	−6.26662	−0.335444	−0.167722	−	0.985834i	$-0.553641\pi$
$349$	−6.26662	−0.335444	−0.167722	+	0.985834i	$0.553641\pi$
$350$	−7.20079	−0.384899
$351$	13.3767	0.713998
$352$	3.88287	0.206958
$353$	−19.0784	−1.01544	−0.507720	−	0.861522i	$-0.669511\pi$
$353$	−19.0784	−1.01544	−0.507720	+	0.861522i	$0.669511\pi$
$354$	−27.9595	−1.48603
$355$	−0.985529	−0.0523064
$356$	1.29743	0.0687636
$357$	24.5671	1.30023
$358$	−2.94474	−0.155634
$359$	14.7488	0.778410	0.389205	−	0.921151i	$-0.372750\pi$
$359$	14.7488	0.778410	0.389205	+	0.921151i	$0.372750\pi$
$360$	−4.23448	−0.223177
$361$	13.0069	0.684574
$362$	15.8688	0.834048
$363$	2.11139	0.110819
$364$	−4.64922	−0.243685
$365$	−2.12844	−0.111407
$366$	6.23076	0.325687
$367$	9.85129	0.514233	0.257116	−	0.966380i	$-0.417228\pi$
$367$	9.85129	0.514233	0.257116	+	0.966380i	$0.417228\pi$
$368$	0	0
$369$	11.8283	0.615756
$370$	−7.96075	−0.413860
$371$	1.14734	0.0595670
$372$	−0.995626	−0.0516208
$373$	−7.17076	−0.371288	−0.185644	−	0.982617i	$-0.559437\pi$
$373$	−7.17076	−0.371288	−0.185644	+	0.982617i	$0.559437\pi$
$374$	−8.44402	−0.436630
$375$	18.1553	0.937535
$376$	7.65733	0.394897
$377$	−22.4525	−1.15636
$378$	−5.70589	−0.293479
$379$	−29.7862	−1.53001	−0.765007	−	0.644021i	$-0.777265\pi$
$379$	−29.7862	−1.53001	−0.765007	+	0.644021i	$0.777265\pi$
$380$	−3.88902	−0.199503
$381$	−5.51697	−0.282643
$382$	14.9825	0.766574
$383$	8.24992	0.421551	0.210776	−	0.977534i	$-0.432401\pi$
$383$	8.24992	0.421551	0.210776	+	0.977534i	$0.432401\pi$
$384$	−3.61804	−0.184632
$385$	−1.46696	−0.0747633
$386$	−14.7467	−0.750588
$387$	14.8249	0.753590
$388$	11.1624	0.566684
$389$	−26.7898	−1.35830	−0.679148	−	0.734002i	$-0.737650\pi$
$389$	−26.7898	−1.35830	−0.679148	+	0.734002i	$0.737650\pi$
$390$	−9.23494	−0.467629
$391$	0	0
$392$	−14.1071	−0.712514
$393$	31.2692	1.57732
$394$	23.8379	1.20094
$395$	−10.9070	−0.548790
$396$	1.06167	0.0533511
$397$	11.8752	0.595998	0.297999	−	0.954566i	$-0.403681\pi$
$397$	11.8752	0.595998	0.297999	+	0.954566i	$0.403681\pi$
$398$	2.29216	0.114896
$399$	18.5625	0.929289
$400$	8.27256	0.413628
$401$	−6.96778	−0.347954	−0.173977	−	0.984750i	$-0.555662\pi$
$401$	−6.96778	−0.347954	−0.173977	+	0.984750i	$0.555662\pi$
$402$	−23.6296	−1.17854
$403$	−2.66052	−0.132530
$404$	−12.6153	−0.627635
$405$	10.6183	0.527628
$406$	9.57719	0.475308
$407$	7.47778	0.370660
$408$	−48.6399	−2.40803
$409$	−22.6496	−1.11995	−0.559974	−	0.828510i	$-0.689189\pi$
$409$	−22.6496	−1.11995	−0.559974	+	0.828510i	$0.689189\pi$
$410$	8.63694	0.426548
$411$	16.4293	0.810399
$412$	−5.33018	−0.262599
$413$	−18.2474	−0.897894
$414$	0	0
$415$	−10.8440	−0.532311
$416$	15.9528	0.782152
$417$	25.5353	1.25047
$418$	−6.38017	−0.312064
$419$	6.83510	0.333917	0.166958	−	0.985964i	$-0.446605\pi$
$419$	6.83510	0.333917	0.166958	+	0.985964i	$0.446605\pi$
$420$	−2.25546	−0.110055
$421$	36.4268	1.77533	0.887666	−	0.460487i	$-0.152325\pi$
$421$	36.4268	1.77533	0.887666	+	0.460487i	$0.152325\pi$
$422$	2.92494	0.142384
$423$	3.62857	0.176427
$424$	−2.27159	−0.110318
$425$	30.7653	1.49234
$426$	−2.48586	−0.120440
$427$	4.06641	0.196787
$428$	1.19619	0.0578202
$429$	8.67466	0.418817
$430$	10.8250	0.522029
$431$	36.8664	1.77579	0.887896	−	0.460044i	$-0.152166\pi$
$431$	36.8664	1.77579	0.887896	+	0.460044i	$0.152166\pi$
$432$	6.55516	0.315385
$433$	−4.91612	−0.236253	−0.118127	−	0.992999i	$-0.537689\pi$
$433$	−4.91612	−0.236253	−0.118127	+	0.992999i	$0.537689\pi$
$434$	1.13485	0.0544747
$435$	−10.8923	−0.522245
$436$	−0.553367	−0.0265015
$437$	0	0
$438$	−5.36868	−0.256526
$439$	5.54972	0.264874	0.132437	−	0.991191i	$-0.457720\pi$
$439$	5.54972	0.264874	0.132437	+	0.991191i	$0.457720\pi$
$440$	2.90440	0.138462
$441$	−6.68489	−0.318328
$442$	−34.6924	−1.65015
$443$	4.65314	0.221078	0.110539	−	0.993872i	$-0.464742\pi$
$443$	4.65314	0.221078	0.110539	+	0.993872i	$0.464742\pi$
$444$	11.4971	0.545627
$445$	1.68193	0.0797310
$446$	7.91323	0.374702
$447$	−38.2151	−1.80751
$448$	−13.0622	−0.617129
$449$	16.6080	0.783782	0.391891	−	0.920012i	$-0.371821\pi$
$449$	16.6080	0.783782	0.391891	+	0.920012i	$0.371821\pi$
$450$	6.75579	0.318471
$451$	−8.11294	−0.382023
$452$	5.70213	0.268205
$453$	7.74496	0.363890
$454$	5.53297	0.259675
$455$	−6.02704	−0.282552
$456$	−36.7515	−1.72105
$457$	0.100842	0.00471721	0.00235860	−	0.999997i	$-0.499249\pi$
$457$	0.100842	0.00471721	0.00235860	+	0.999997i	$0.499249\pi$
$458$	7.01908	0.327980
$459$	24.3784	1.13788
$460$	0	0
$461$	−16.1631	−0.752791	−0.376395	−	0.926459i	$-0.622837\pi$
$461$	−16.1631	−0.752791	−0.376395	+	0.926459i	$0.622837\pi$
$462$	−3.70021	−0.172149
$463$	4.07637	0.189445	0.0947225	−	0.995504i	$-0.469804\pi$
$463$	4.07637	0.189445	0.0947225	+	0.995504i	$0.469804\pi$
$464$	−11.0027	−0.510786
$465$	−1.29068	−0.0598541
$466$	−8.25691	−0.382494
$467$	−26.3131	−1.21762	−0.608812	−	0.793314i	$-0.708354\pi$
$467$	−26.3131	−1.21762	−0.608812	+	0.793314i	$0.708354\pi$
$468$	4.36190	0.201629
$469$	−15.4215	−0.712097
$470$	2.64956	0.122215
$471$	−2.03249	−0.0936520
$472$	36.1275	1.66290
$473$	−10.1683	−0.467538
$474$	−27.5113	−1.26364
$475$	23.2458	1.06659
$476$	−8.47294	−0.388357
$477$	−1.07644	−0.0492867
$478$	−28.7587	−1.31539
$479$	−15.4158	−0.704366	−0.352183	−	0.935931i	$-0.614561\pi$
$479$	−15.4158	−0.704366	−0.352183	+	0.935931i	$0.614561\pi$
$480$	7.73913	0.353241
$481$	30.7226	1.40083
$482$	−23.5057	−1.07066
$483$	0	0
$484$	−0.728194	−0.0330997
$485$	14.4704	0.657067
$486$	15.7679	0.715245
$487$	42.9334	1.94550	0.972749	−	0.231861i	$-0.0744814\pi$
$487$	42.9334	1.94550	0.972749	+	0.231861i	$0.0744814\pi$
$488$	−8.05098	−0.364451
$489$	−50.5255	−2.28484
$490$	−4.88126	−0.220513
$491$	−8.08837	−0.365023	−0.182511	−	0.983204i	$-0.558423\pi$
$491$	−8.08837	−0.365023	−0.182511	+	0.983204i	$0.558423\pi$
$492$	−12.4736	−0.562355
$493$	−40.9184	−1.84287
$494$	−26.2130	−1.17938
$495$	1.37630	0.0618603
$496$	−1.30376	−0.0585408
$497$	−1.62236	−0.0727726
$498$	−27.3524	−1.22569
$499$	27.1368	1.21481	0.607404	−	0.794393i	$-0.292211\pi$
$499$	27.1368	1.21481	0.607404	+	0.794393i	$0.292211\pi$
$500$	−6.26157	−0.280026
$501$	−23.5812	−1.05353
$502$	3.36219	0.150062
$503$	−34.7664	−1.55016	−0.775078	−	0.631865i	$-0.782290\pi$
$503$	−34.7664	−1.55016	−0.775078	+	0.631865i	$0.782290\pi$
$504$	−6.97071	−0.310500
$505$	−16.3539	−0.727740
$506$	0	0
$507$	8.19195	0.363817
$508$	1.90274	0.0844206
$509$	−40.9939	−1.81702	−0.908512	−	0.417858i	$-0.862781\pi$
$509$	−40.9939	−1.81702	−0.908512	+	0.417858i	$0.862781\pi$
$510$	−16.8302	−0.745252
$511$	−3.50379	−0.154998
$512$	20.2065	0.893009
$513$	18.4199	0.813258
$514$	−7.78681	−0.343461
$515$	−6.90980	−0.304482
$516$	−15.6337	−0.688236
$517$	−2.48881	−0.109458
$518$	−13.1048	−0.575792
$519$	−28.7341	−1.26129
$520$	11.9328	0.523287
$521$	−9.92597	−0.434865	−0.217432	−	0.976075i	$-0.569768\pi$
$521$	−9.92597	−0.434865	−0.217432	+	0.976075i	$0.569768\pi$
$522$	−8.98533	−0.393277
$523$	11.5471	0.504918	0.252459	−	0.967608i	$-0.418761\pi$
$523$	11.5471	0.504918	0.252459	+	0.967608i	$0.418761\pi$
$524$	−10.7844	−0.471120
$525$	13.4815	0.588380
$526$	−8.29760	−0.361793
$527$	−4.84864	−0.211210
$528$	4.25095	0.184999
$529$	0	0
$530$	−0.786008	−0.0341420
$531$	17.1197	0.742930
$532$	−6.40202	−0.277563
$533$	−33.3321	−1.44378
$534$	4.24243	0.183588
$535$	1.55069	0.0670422
$536$	30.5326	1.31881
$537$	5.51321	0.237913
$538$	−34.6842	−1.49534
$539$	4.58512	0.197495
$540$	−2.23812	−0.0963135
$541$	17.6371	0.758279	0.379139	−	0.925340i	$-0.376220\pi$
$541$	17.6371	0.758279	0.379139	+	0.925340i	$0.376220\pi$
$542$	−9.08380	−0.390183
$543$	−29.7100	−1.27498
$544$	29.0732	1.24650
$545$	−0.717360	−0.0307283
$546$	−15.2024	−0.650601
$547$	14.4093	0.616096	0.308048	−	0.951371i	$-0.400324\pi$
$547$	14.4093	0.616096	0.308048	+	0.951371i	$0.400324\pi$
$548$	−5.66630	−0.242052
$549$	−3.81511	−0.162825
$550$	−4.63375	−0.197584
$551$	−30.9173	−1.31712
$552$	0	0
$553$	−17.9548	−0.763517
$554$	26.4133	1.12219
$555$	14.9043	0.632652
$556$	−8.80684	−0.373493
$557$	15.3176	0.649027	0.324513	−	0.945881i	$-0.394799\pi$
$557$	15.3176	0.649027	0.324513	+	0.945881i	$0.394799\pi$
$558$	−1.06472	−0.0450732
$559$	−41.7765	−1.76696
$560$	−2.95350	−0.124808
$561$	15.8091	0.667460
$562$	1.22373	0.0516200
$563$	28.9249	1.21904	0.609519	−	0.792772i	$-0.291363\pi$
$563$	28.9249	1.21904	0.609519	+	0.792772i	$0.291363\pi$
$564$	−3.82655	−0.161127
$565$	7.39198	0.310983
$566$	−28.2126	−1.18586
$567$	17.4796	0.734075
$568$	3.21206	0.134775
$569$	12.9460	0.542723	0.271361	−	0.962478i	$-0.412526\pi$
$569$	12.9460	0.542723	0.271361	+	0.962478i	$0.412526\pi$
$570$	−12.7166	−0.532640
$571$	−30.9748	−1.29626	−0.648129	−	0.761531i	$-0.724448\pi$
$571$	−30.9748	−1.29626	−0.648129	+	0.761531i	$0.724448\pi$
$572$	−2.99180	−0.125093
$573$	−28.0506	−1.17183
$574$	14.2179	0.593445
$575$	0	0
$576$	12.2549	0.510622
$577$	−12.2699	−0.510804	−0.255402	−	0.966835i	$-0.582208\pi$
$577$	−12.2699	−0.510804	−0.255402	+	0.966835i	$0.582208\pi$
$578$	−44.0533	−1.83238
$579$	27.6091	1.14740
$580$	3.75663	0.155986
$581$	−17.8511	−0.740590
$582$	36.4995	1.51295
$583$	0.738321	0.0305781
$584$	6.93706	0.287057
$585$	5.65457	0.233788
$586$	14.7656	0.609960
$587$	7.34814	0.303290	0.151645	−	0.988435i	$-0.451543\pi$
$587$	7.34814	0.303290	0.151645	+	0.988435i	$0.451543\pi$
$588$	7.04962	0.290721
$589$	−3.66356	−0.150954
$590$	12.5007	0.514645
$591$	−44.6299	−1.83583
$592$	15.0553	0.618771
$593$	29.7346	1.22105	0.610527	−	0.791996i	$-0.290958\pi$
$593$	29.7346	1.22105	0.610527	+	0.791996i	$0.290958\pi$
$594$	−3.67177	−0.150655
$595$	−10.9839	−0.450298
$596$	13.1800	0.539873
$597$	−4.29144	−0.175637
$598$	0	0
$599$	38.7237	1.58221	0.791103	−	0.611683i	$-0.209507\pi$
$599$	38.7237	1.58221	0.791103	+	0.611683i	$0.209507\pi$
$600$	−26.6917	−1.08968
$601$	−32.3899	−1.32121	−0.660607	−	0.750732i	$-0.729701\pi$
$601$	−32.3899	−1.32121	−0.660607	+	0.750732i	$0.729701\pi$
$602$	17.8199	0.726285
$603$	14.4684	0.589200
$604$	−2.67115	−0.108688
$605$	−0.943998	−0.0383790
$606$	−41.2505	−1.67569
$607$	−0.895589	−0.0363508	−0.0181754	−	0.999835i	$-0.505786\pi$
$607$	−0.895589	−0.0363508	−0.0181754	+	0.999835i	$0.505786\pi$
$608$	21.9672	0.890888
$609$	−17.9306	−0.726586
$610$	−2.78577	−0.112792
$611$	−10.2253	−0.413672
$612$	7.94932	0.321332
$613$	20.8119	0.840586	0.420293	−	0.907388i	$-0.361927\pi$
$613$	20.8119	0.840586	0.420293	+	0.907388i	$0.361927\pi$
$614$	−0.184491	−0.00744547
$615$	−16.1703	−0.652048
$616$	4.78116	0.192639
$617$	−0.129106	−0.00519760	−0.00259880	−	0.999997i	$-0.500827\pi$
$617$	−0.129106	−0.00519760	−0.00259880	+	0.999997i	$0.500827\pi$
$618$	−17.4290	−0.701097
$619$	46.0045	1.84908	0.924539	−	0.381087i	$-0.124450\pi$
$619$	46.0045	1.84908	0.924539	+	0.381087i	$0.124450\pi$
$620$	0.445143	0.0178774
$621$	0	0
$622$	−21.1122	−0.846524
$623$	2.76875	0.110928
$624$	17.4651	0.699163
$625$	12.4271	0.497085
$626$	12.5971	0.503481
$627$	11.9451	0.477041
$628$	0.700983	0.0279722
$629$	55.9902	2.23247
$630$	−2.41198	−0.0960954
$631$	−2.55441	−0.101690	−0.0508448	−	0.998707i	$-0.516191\pi$
$631$	−2.55441	−0.101690	−0.0508448	+	0.998707i	$0.516191\pi$
$632$	35.5483	1.41404
$633$	−5.47615	−0.217657
$634$	−5.40381	−0.214613
$635$	2.46663	0.0978852
$636$	1.13517	0.0450124
$637$	18.8380	0.746390
$638$	6.16297	0.243994
$639$	1.52209	0.0602131
$640$	1.61762	0.0639421
$641$	6.07687	0.240022	0.120011	−	0.992773i	$-0.461707\pi$
$641$	6.07687	0.240022	0.120011	+	0.992773i	$0.461707\pi$
$642$	3.91140	0.154371
$643$	−32.1547	−1.26806	−0.634029	−	0.773309i	$-0.718600\pi$
$643$	−32.1547	−1.26806	−0.634029	+	0.773309i	$0.718600\pi$
$644$	0	0
$645$	−20.2668	−0.798006
$646$	−47.7718	−1.87955
$647$	−44.4290	−1.74669	−0.873343	−	0.487106i	$-0.838053\pi$
$647$	−44.4290	−1.74669	−0.873343	+	0.487106i	$0.838053\pi$
$648$	−34.6075	−1.35951
$649$	−11.7423	−0.460924
$650$	−19.0378	−0.746725
$651$	−2.12470	−0.0832734
$652$	17.4257	0.682444
$653$	49.1250	1.92241	0.961205	−	0.275834i	$-0.0889540\pi$
$653$	49.1250	1.92241	0.961205	+	0.275834i	$0.0889540\pi$
$654$	−1.80944	−0.0707547
$655$	−13.9804	−0.546261
$656$	−16.3341	−0.637741
$657$	3.28725	0.128248
$658$	4.36164	0.170035
$659$	−9.40434	−0.366341	−0.183171	−	0.983081i	$-0.558636\pi$
$659$	−9.40434	−0.366341	−0.183171	+	0.983081i	$0.558636\pi$
$660$	−1.45140	−0.0564956
$661$	38.3424	1.49135	0.745673	−	0.666312i	$-0.232128\pi$
$661$	38.3424	1.49135	0.745673	+	0.666312i	$0.232128\pi$
$662$	−3.00274	−0.116705
$663$	64.9519	2.52252
$664$	35.3430	1.37157
$665$	−8.29929	−0.321833
$666$	12.2949	0.476419
$667$	0	0
$668$	8.13290	0.314671
$669$	−14.8153	−0.572793
$670$	10.5648	0.408152
$671$	2.61676	0.101019
$672$	12.7400	0.491455
$673$	−0.633561	−0.0244220	−0.0122110	−	0.999925i	$-0.503887\pi$
$673$	−0.633561	−0.0244220	−0.0122110	+	0.999925i	$0.503887\pi$
$674$	17.7453	0.683524
$675$	13.3779	0.514915
$676$	−2.82532	−0.108666
$677$	10.5852	0.406823	0.203412	−	0.979093i	$-0.434797\pi$
$677$	10.5852	0.406823	0.203412	+	0.979093i	$0.434797\pi$
$678$	18.6452	0.716065
$679$	23.8208	0.914160
$680$	21.7468	0.833953
$681$	−10.3590	−0.396956
$682$	0.730284	0.0279640
$683$	−36.3263	−1.38999	−0.694994	−	0.719016i	$-0.744593\pi$
$683$	−36.3263	−1.38999	−0.694994	+	0.719016i	$0.744593\pi$
$684$	6.00638	0.229660
$685$	−7.34553	−0.280658
$686$	−20.3029	−0.775169
$687$	−13.1413	−0.501371
$688$	−20.4722	−0.780496
$689$	3.03340	0.115563
$690$	0	0
$691$	−20.4187	−0.776763	−0.388382	−	0.921499i	$-0.626966\pi$
$691$	−20.4187	−0.776763	−0.388382	+	0.921499i	$0.626966\pi$
$692$	9.91009	0.376725
$693$	2.26564	0.0860646
$694$	22.8812	0.868559
$695$	−11.4168	−0.433064
$696$	35.5004	1.34564
$697$	−60.7460	−2.30092
$698$	7.06714	0.267495
$699$	15.4588	0.584705
$700$	−4.64962	−0.175739
$701$	31.5055	1.18995	0.594974	−	0.803745i	$-0.297162\pi$
$701$	31.5055	1.18995	0.594974	+	0.803745i	$0.297162\pi$
$702$	−15.0855	−0.569367
$703$	42.3053	1.59557
$704$	−8.40557	−0.316797
$705$	−4.96056	−0.186826
$706$	21.5155	0.809747
$707$	−26.9215	−1.01249
$708$	−18.0537	−0.678501
$709$	−34.4572	−1.29407	−0.647033	−	0.762462i	$-0.723991\pi$
$709$	−34.4572	−1.29407	−0.647033	+	0.762462i	$0.723991\pi$
$710$	1.11142	0.0417110
$711$	16.8452	0.631745
$712$	−5.48178	−0.205439
$713$	0	0
$714$	−27.7054	−1.03685
$715$	−3.87843	−0.145045
$716$	−1.90145	−0.0710604
$717$	53.8427	2.01079
$718$	−16.6328	−0.620731
$719$	4.56669	0.170309	0.0851543	−	0.996368i	$-0.472862\pi$
$719$	4.56669	0.170309	0.0851543	+	0.996368i	$0.472862\pi$
$720$	2.77097	0.103268
$721$	−11.3748	−0.423618
$722$	−14.6685	−0.545903
$723$	44.0079	1.63667
$724$	10.2467	0.380814
$725$	−22.4544	−0.833937
$726$	−2.38110	−0.0883710
$727$	44.6661	1.65657	0.828286	−	0.560305i	$-0.189316\pi$
$727$	44.6661	1.65657	0.828286	+	0.560305i	$0.189316\pi$
$728$	19.6435	0.728036
$729$	4.22373	0.156435
$730$	2.40033	0.0888402
$731$	−76.1353	−2.81597
$732$	4.02326	0.148704
$733$	13.5339	0.499886	0.249943	−	0.968261i	$-0.419588\pi$
$733$	13.5339	0.499886	0.249943	+	0.968261i	$0.419588\pi$
$734$	−11.1097	−0.410067
$735$	9.13881	0.337090
$736$	0	0
$737$	−9.92380	−0.365548
$738$	−13.3393	−0.491025
$739$	17.3255	0.637330	0.318665	−	0.947867i	$-0.396765\pi$
$739$	17.3255	0.637330	0.318665	+	0.947867i	$0.396765\pi$
$740$	−5.14033	−0.188962
$741$	49.0766	1.80287
$742$	−1.29391	−0.0475009
$743$	−3.73057	−0.136861	−0.0684307	−	0.997656i	$-0.521799\pi$
$743$	−3.73057	−0.136861	−0.0684307	+	0.997656i	$0.521799\pi$
$744$	4.20663	0.154223
$745$	17.0859	0.625980
$746$	8.08678	0.296078
$747$	16.7479	0.612775
$748$	−5.45238	−0.199359
$749$	2.55271	0.0932741
$750$	−20.4745	−0.747624
$751$	−24.0681	−0.878257	−0.439129	−	0.898424i	$-0.644713\pi$
$751$	−24.0681	−0.878257	−0.439129	+	0.898424i	$0.644713\pi$
$752$	−5.01083	−0.182726
$753$	−6.29477	−0.229394
$754$	25.3207	0.922124
$755$	−3.46276	−0.126023
$756$	−3.68435	−0.133998
$757$	−45.6344	−1.65861	−0.829306	−	0.558795i	$-0.811264\pi$
$757$	−45.6344	−1.65861	−0.829306	+	0.558795i	$0.811264\pi$
$758$	33.5912	1.22009
$759$	0	0
$760$	16.4316	0.596035
$761$	−30.4837	−1.10503	−0.552517	−	0.833501i	$-0.686333\pi$
$761$	−30.4837	−1.10503	−0.552517	+	0.833501i	$0.686333\pi$
$762$	6.22172	0.225389
$763$	−1.18090	−0.0427515
$764$	9.67437	0.350006
$765$	10.3051	0.372583
$766$	−9.30379	−0.336160
$767$	−48.2433	−1.74196
$768$	−31.4146	−1.13358
$769$	−6.28482	−0.226636	−0.113318	−	0.993559i	$-0.536148\pi$
$769$	−6.28482	−0.226636	−0.113318	+	0.993559i	$0.536148\pi$
$770$	1.65436	0.0596189
$771$	14.5786	0.525037
$772$	−9.52209	−0.342708
$773$	−33.1780	−1.19333	−0.596665	−	0.802490i	$-0.703508\pi$
$773$	−33.1780	−1.19333	−0.596665	+	0.802490i	$0.703508\pi$
$774$	−16.7186	−0.600939
$775$	−2.66075	−0.0955768
$776$	−47.1623	−1.69303
$777$	24.5351	0.880193
$778$	30.2120	1.08315
$779$	−45.8987	−1.64449
$780$	−5.96309	−0.213513
$781$	−1.04399	−0.0373570
$782$	0	0
$783$	−17.7928	−0.635864
$784$	9.23142	0.329694
$785$	0.908722	0.0324337
$786$	−35.2637	−1.25781
$787$	47.1122	1.67937	0.839684	−	0.543075i	$-0.182740\pi$
$787$	47.1122	1.67937	0.839684	+	0.543075i	$0.182740\pi$
$788$	15.3924	0.548330
$789$	15.5350	0.553059
$790$	12.3003	0.437624
$791$	12.1685	0.432662
$792$	−4.48569	−0.159392
$793$	10.7510	0.381779
$794$	−13.3922	−0.475270
$795$	1.47158	0.0521916
$796$	1.48007	0.0524597
$797$	0.301803	0.0106904	0.00534520	−	0.999986i	$-0.498299\pi$
$797$	0.301803	0.0106904	0.00534520	+	0.999986i	$0.498299\pi$
$798$	−20.9338	−0.741048
$799$	−18.6351	−0.659261
$800$	15.9542	0.564066
$801$	−2.59764	−0.0917832
$802$	7.85787	0.277471
$803$	−2.25470	−0.0795668
$804$	−15.2578	−0.538103
$805$	0	0
$806$	3.00038	0.105684
$807$	64.9365	2.28587
$808$	53.3011	1.87513
$809$	14.1882	0.498831	0.249416	−	0.968397i	$-0.419761\pi$
$809$	14.1882	0.498831	0.249416	+	0.968397i	$0.419761\pi$
$810$	−11.9747	−0.420749
$811$	24.2418	0.851245	0.425623	−	0.904901i	$-0.360055\pi$
$811$	24.2418	0.851245	0.425623	+	0.904901i	$0.360055\pi$
$812$	6.18408	0.217019
$813$	17.0069	0.596458
$814$	−8.43302	−0.295577
$815$	22.5899	0.791290
$816$	31.8291	1.11424
$817$	−57.5266	−2.01260
$818$	25.5429	0.893086
$819$	9.30842	0.325263
$820$	5.57695	0.194756
$821$	3.77128	0.131618	0.0658092	−	0.997832i	$-0.479037\pi$
$821$	3.77128	0.131618	0.0658092	+	0.997832i	$0.479037\pi$
$822$	−18.5281	−0.646241
$823$	35.7647	1.24668	0.623339	−	0.781952i	$-0.285776\pi$
$823$	35.7647	1.24668	0.623339	+	0.781952i	$0.285776\pi$
$824$	22.5206	0.784542
$825$	8.67541	0.302039
$826$	20.5783	0.716012
$827$	4.73807	0.164759	0.0823794	−	0.996601i	$-0.473748\pi$
$827$	4.73807	0.164759	0.0823794	+	0.996601i	$0.473748\pi$
$828$	0	0
$829$	27.7132	0.962519	0.481259	−	0.876578i	$-0.340180\pi$
$829$	27.7132	0.962519	0.481259	+	0.876578i	$0.340180\pi$
$830$	12.2292	0.424483
$831$	−49.4515	−1.71545
$832$	−34.5344	−1.19727
$833$	34.3313	1.18951
$834$	−28.7972	−0.997167
$835$	10.5431	0.364860
$836$	−4.11973	−0.142484
$837$	−2.10837	−0.0728759
$838$	−7.70824	−0.266277
$839$	7.29543	0.251866	0.125933	−	0.992039i	$-0.459808\pi$
$839$	7.29543	0.251866	0.125933	+	0.992039i	$0.459808\pi$
$840$	9.52955	0.328801
$841$	0.864829	0.0298217
$842$	−41.0801	−1.41571
$843$	−2.29110	−0.0789096
$844$	1.88866	0.0650105
$845$	−3.66261	−0.125998
$846$	−4.09209	−0.140689
$847$	−1.55399	−0.0533957
$848$	1.48649	0.0510464
$849$	52.8202	1.81279
$850$	−34.6954	−1.19004
$851$	0	0
$852$	−1.60514	−0.0549912
$853$	50.3906	1.72534	0.862671	−	0.505765i	$-0.168790\pi$
$853$	50.3906	1.72534	0.862671	+	0.505765i	$0.168790\pi$
$854$	−4.58587	−0.156925
$855$	7.78640	0.266289
$856$	−5.05405	−0.172744
$857$	−31.2679	−1.06809	−0.534045	−	0.845456i	$-0.679329\pi$
$857$	−31.2679	−1.06809	−0.534045	+	0.845456i	$0.679329\pi$
$858$	−9.78279	−0.333979
$859$	−45.5291	−1.55343	−0.776716	−	0.629851i	$-0.783116\pi$
$859$	−45.5291	−1.55343	−0.776716	+	0.629851i	$0.783116\pi$
$860$	6.98982	0.238351
$861$	−26.6191	−0.907178
$862$	−41.5759	−1.41608
$863$	25.1496	0.856102	0.428051	−	0.903755i	$-0.359200\pi$
$863$	25.1496	0.856102	0.428051	+	0.903755i	$0.359200\pi$
$864$	12.6421	0.430092
$865$	12.8470	0.436811
$866$	5.54412	0.188397
$867$	82.4776	2.80108
$868$	0.732785	0.0248723
$869$	−11.5540	−0.391944
$870$	12.2837	0.416457
$871$	−40.7721	−1.38151
$872$	2.33804	0.0791759
$873$	−22.3487	−0.756389
$874$	0	0
$875$	−13.3624	−0.451731
$876$	−3.46661	−0.117126
$877$	−45.3237	−1.53047	−0.765236	−	0.643750i	$-0.777378\pi$
$877$	−45.3237	−1.53047	−0.765236	+	0.643750i	$0.777378\pi$
$878$	−6.25866	−0.211220
$879$	−27.6444	−0.932423
$880$	−1.90059	−0.0640690
$881$	−27.7285	−0.934197	−0.467098	−	0.884205i	$-0.654701\pi$
$881$	−27.7285	−0.934197	−0.467098	+	0.884205i	$0.654701\pi$
$882$	7.53884	0.253846
$883$	48.0009	1.61536	0.807680	−	0.589621i	$-0.200723\pi$
$883$	48.0009	1.61536	0.807680	+	0.589621i	$0.200723\pi$
$884$	−22.4012	−0.753434
$885$	−23.4040	−0.786718
$886$	−5.24755	−0.176295
$887$	48.1989	1.61836	0.809180	−	0.587561i	$-0.199912\pi$
$887$	48.1989	1.61836	0.809180	+	0.587561i	$0.199912\pi$
$888$	−48.5765	−1.63012
$889$	4.06051	0.136185
$890$	−1.89678	−0.0635803
$891$	11.2482	0.376830
$892$	5.10964	0.171084
$893$	−14.0804	−0.471181
$894$	43.0968	1.44137
$895$	−2.46495	−0.0823942
$896$	2.66289	0.0889610
$897$	0	0
$898$	−18.7296	−0.625015
$899$	3.53884	0.118027
$900$	4.36227	0.145409
$901$	5.52821	0.184171
$902$	9.14932	0.304639
$903$	−33.3628	−1.11024
$904$	−24.0921	−0.801292
$905$	13.2833	0.441552
$906$	−8.73433	−0.290179
$907$	22.4489	0.745405	0.372702	−	0.927951i	$-0.378431\pi$
$907$	22.4489	0.745405	0.372702	+	0.927951i	$0.378431\pi$
$908$	3.57269	0.118564
$909$	25.2577	0.837746
$910$	6.79695	0.225317
$911$	24.2176	0.802364	0.401182	−	0.915998i	$-0.368600\pi$
$911$	24.2176	0.802364	0.401182	+	0.915998i	$0.368600\pi$
$912$	24.0496	0.796361
$913$	−11.4873	−0.380174
$914$	−0.113724	−0.00376167
$915$	5.21558	0.172422
$916$	4.53229	0.149751
$917$	−23.0143	−0.759999
$918$	−27.4925	−0.907389
$919$	−2.87860	−0.0949563	−0.0474781	−	0.998872i	$-0.515118\pi$
$919$	−2.87860	−0.0949563	−0.0474781	+	0.998872i	$0.515118\pi$
$920$	0	0
$921$	0.345409	0.0113816
$922$	18.2278	0.600302
$923$	−4.28927	−0.141183
$924$	−2.38926	−0.0786008
$925$	30.7252	1.01024
$926$	−4.59710	−0.151070
$927$	10.6718	0.350508
$928$	−21.2194	−0.696561
$929$	−25.1540	−0.825275	−0.412637	−	0.910895i	$-0.635392\pi$
$929$	−25.1540	−0.825275	−0.412637	+	0.910895i	$0.635392\pi$
$930$	1.45556	0.0477297
$931$	25.9401	0.850154
$932$	−5.33157	−0.174641
$933$	39.5268	1.29405
$934$	29.6744	0.970977
$935$	−7.06822	−0.231156
$936$	−18.4295	−0.602388
$937$	53.0570	1.73330	0.866649	−	0.498919i	$-0.166269\pi$
$937$	53.0570	1.73330	0.866649	+	0.498919i	$0.166269\pi$
$938$	17.3915	0.567851
$939$	−23.5845	−0.769653
$940$	1.71084	0.0558016
$941$	14.8995	0.485711	0.242855	−	0.970063i	$-0.421916\pi$
$941$	14.8995	0.485711	0.242855	+	0.970063i	$0.421916\pi$
$942$	2.29212	0.0746814
$943$	0	0
$944$	−23.6412	−0.769456
$945$	−4.77622	−0.155371
$946$	11.4672	0.372831
$947$	−55.4878	−1.80311	−0.901556	−	0.432663i	$-0.857574\pi$
$947$	−55.4878	−1.80311	−0.901556	+	0.432663i	$0.857574\pi$
$948$	−17.7643	−0.576958
$949$	−9.26349	−0.300705
$950$	−26.2153	−0.850536
$951$	10.1171	0.328071
$952$	35.7991	1.16026
$953$	34.9473	1.13205	0.566027	−	0.824387i	$-0.308480\pi$
$953$	34.9473	1.13205	0.566027	+	0.824387i	$0.308480\pi$
$954$	1.21394	0.0393029
$955$	12.5414	0.405831
$956$	−18.5698	−0.600589
$957$	−11.5385	−0.372985
$958$	17.3851	0.561686
$959$	−12.0920	−0.390473
$960$	−16.7535	−0.540718
$961$	−30.5807	−0.986473
$962$	−34.6472	−1.11707
$963$	−2.39496	−0.0771764
$964$	−15.1779	−0.488846
$965$	−12.3440	−0.397368
$966$	0	0
$967$	22.6734	0.729127	0.364563	−	0.931179i	$-0.381218\pi$
$967$	22.6734	0.729127	0.364563	+	0.931179i	$0.381218\pi$
$968$	3.07670	0.0988890
$969$	89.4393	2.87321
$970$	−16.3189	−0.523968
$971$	57.5531	1.84697	0.923483	−	0.383640i	$-0.125330\pi$
$971$	57.5531	1.84697	0.923483	+	0.383640i	$0.125330\pi$
$972$	10.1815	0.326571
$973$	−18.7941	−0.602510
$974$	−48.4179	−1.55141
$975$	35.6430	1.14149
$976$	5.26843	0.168638
$977$	−4.62307	−0.147905	−0.0739525	−	0.997262i	$-0.523561\pi$
$977$	−4.62307	−0.147905	−0.0739525	+	0.997262i	$0.523561\pi$
$978$	56.9798	1.82201
$979$	1.78171	0.0569436
$980$	−3.15188	−0.100683
$981$	1.10792	0.0353732
$982$	9.12160	0.291082
$983$	9.92441	0.316539	0.158270	−	0.987396i	$-0.449408\pi$
$983$	9.92441	0.316539	0.158270	+	0.987396i	$0.449408\pi$
$984$	52.7026	1.68010
$985$	19.9540	0.635786
$986$	46.1455	1.46957
$987$	−8.16596	−0.259925
$988$	−16.9260	−0.538487
$989$	0	0
$990$	−1.55212	−0.0493296
$991$	−15.3200	−0.486656	−0.243328	−	0.969944i	$-0.578239\pi$
$991$	−15.3200	−0.486656	−0.243328	+	0.969944i	$0.578239\pi$
$992$	−2.51440	−0.0798323
$993$	5.62179	0.178402
$994$	1.82960	0.0580314
$995$	1.91870	0.0608267
$996$	−17.6617	−0.559633
$997$	45.7887	1.45014	0.725072	−	0.688673i	$-0.241807\pi$
$997$	45.7887	1.45014	0.725072	+	0.688673i	$0.241807\pi$
$998$	−30.6033	−0.968730
$999$	24.3466	0.770292

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5819.2.a.t.1.20		60
23.11	odd	22		253.2.i.b.144.5	✓	120
23.21	odd	22		253.2.i.b.188.5	yes	120
23.22	odd	2		5819.2.a.u.1.20		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
253.2.i.b.144.5	✓	120	23.11	odd	22
253.2.i.b.188.5	yes	120	23.21	odd	22
5819.2.a.t.1.20		60	1.1	even	1	trivial
5819.2.a.u.1.20		60	23.22	odd	2

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)

\(f(q)\)	\(=\)	\(q-1.12774 q^{2} +2.11139 q^{3} -0.728194 q^{4} -0.943998 q^{5} -2.38110 q^{6} -1.55399 q^{7} +3.07670 q^{8} +1.45795 q^{9} +1.06459 q^{10} -1.00000 q^{11} -1.53750 q^{12} -4.10851 q^{13} +1.75250 q^{14} -1.99315 q^{15} -2.01334 q^{16} -7.48754 q^{17} -1.64420 q^{18} -5.65746 q^{19} +0.687414 q^{20} -3.28107 q^{21} +1.12774 q^{22} +6.49611 q^{24} -4.10887 q^{25} +4.63335 q^{26} -3.25586 q^{27} +1.13161 q^{28} +5.46487 q^{29} +2.24776 q^{30} +0.647562 q^{31} -3.88287 q^{32} -2.11139 q^{33} +8.44402 q^{34} +1.46696 q^{35} -1.06167 q^{36} -7.47778 q^{37} +6.38017 q^{38} -8.67466 q^{39} -2.90440 q^{40} +8.11294 q^{41} +3.70021 q^{42} +10.1683 q^{43} +0.728194 q^{44} -1.37630 q^{45} +2.48881 q^{47} -4.25095 q^{48} -4.58512 q^{49} +4.63375 q^{50} -15.8091 q^{51} +2.99180 q^{52} -0.738321 q^{53} +3.67177 q^{54} +0.943998 q^{55} -4.78116 q^{56} -11.9451 q^{57} -6.16297 q^{58} +11.7423 q^{59} +1.45140 q^{60} -2.61676 q^{61} -0.730284 q^{62} -2.26564 q^{63} +8.40557 q^{64} +3.87843 q^{65} +2.38110 q^{66} +9.92380 q^{67} +5.45238 q^{68} -1.65436 q^{70} +1.04399 q^{71} +4.48569 q^{72} +2.25470 q^{73} +8.43302 q^{74} -8.67541 q^{75} +4.11973 q^{76} +1.55399 q^{77} +9.78279 q^{78} +11.5540 q^{79} +1.90059 q^{80} -11.2482 q^{81} -9.14932 q^{82} +11.4873 q^{83} +2.38926 q^{84} +7.06822 q^{85} -11.4672 q^{86} +11.5385 q^{87} -3.07670 q^{88} -1.78171 q^{89} +1.55212 q^{90} +6.38459 q^{91} +1.36725 q^{93} -2.80674 q^{94} +5.34064 q^{95} -8.19824 q^{96} -15.3288 q^{97} +5.17084 q^{98} -1.45795 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 5 q^{2} + 9 q^{3} + 73 q^{4} - 8 q^{5} + 26 q^{6} + 30 q^{8} + 75 q^{9} + 7 q^{10} - 60 q^{11} + 41 q^{12} + 46 q^{13} - 16 q^{14} - 4 q^{15} + 99 q^{16} + 5 q^{17} + 36 q^{18} + 8 q^{19} - 82 q^{20}+ \cdots - 75 q^{99}+O(q^{100}) \) 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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