LMFDB - Embedded newform 3971.2.a.t.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3971,2,Mod(1,3971)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3971.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3971, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 3971 = 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3971.a (trivial)

Newform invariants

comment:select newform

sage:traces = [21,6,15] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$31.7085946427$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	no (minimal twist has level 209)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	3971.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.68287 q^{2} +0.146409 q^{3} +0.832058 q^{4} +3.02083 q^{5} -0.246387 q^{6} -2.73938 q^{7} +1.96550 q^{8} -2.97856 q^{9} -5.08367 q^{10} +1.00000 q^{11} +0.121821 q^{12} -3.11321 q^{13} +4.61003 q^{14} +0.442276 q^{15} -4.97180 q^{16} -4.43069 q^{17} +5.01254 q^{18} +2.51351 q^{20} -0.401070 q^{21} -1.68287 q^{22} -4.74211 q^{23} +0.287766 q^{24} +4.12540 q^{25} +5.23914 q^{26} -0.875315 q^{27} -2.27933 q^{28} -3.88758 q^{29} -0.744294 q^{30} -3.90204 q^{31} +4.43590 q^{32} +0.146409 q^{33} +7.45628 q^{34} -8.27520 q^{35} -2.47834 q^{36} +2.67887 q^{37} -0.455802 q^{39} +5.93743 q^{40} +11.1225 q^{41} +0.674949 q^{42} -5.11919 q^{43} +0.832058 q^{44} -8.99773 q^{45} +7.98036 q^{46} +9.02479 q^{47} -0.727915 q^{48} +0.504216 q^{49} -6.94252 q^{50} -0.648692 q^{51} -2.59037 q^{52} +8.09736 q^{53} +1.47304 q^{54} +3.02083 q^{55} -5.38425 q^{56} +6.54230 q^{58} +6.73170 q^{59} +0.367999 q^{60} -13.7126 q^{61} +6.56663 q^{62} +8.15943 q^{63} +2.47853 q^{64} -9.40448 q^{65} -0.246387 q^{66} +2.31270 q^{67} -3.68659 q^{68} -0.694287 q^{69} +13.9261 q^{70} +14.4450 q^{71} -5.85436 q^{72} +1.07891 q^{73} -4.50819 q^{74} +0.603995 q^{75} -2.73938 q^{77} +0.767056 q^{78} -2.29927 q^{79} -15.0189 q^{80} +8.80754 q^{81} -18.7178 q^{82} +8.04434 q^{83} -0.333714 q^{84} -13.3843 q^{85} +8.61494 q^{86} -0.569176 q^{87} +1.96550 q^{88} +1.45068 q^{89} +15.1420 q^{90} +8.52828 q^{91} -3.94571 q^{92} -0.571293 q^{93} -15.1876 q^{94} +0.649456 q^{96} +6.93562 q^{97} -0.848531 q^{98} -2.97856 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 6 q^{2} + 15 q^{3} + 18 q^{4} + 6 q^{5} - 6 q^{6} + 6 q^{7} + 15 q^{8} + 18 q^{9} - 6 q^{10} + 21 q^{11} + 30 q^{12} + 36 q^{13} + 12 q^{14} + 12 q^{15} + 12 q^{16} + 21 q^{17} + 6 q^{18} + 15 q^{20}+ \cdots + 18 q^{99}+O(q^{100}) $ 21 * q + 6 * q^2 + 15 * q^3 + 18 * q^4 + 6 * q^5 - 6 * q^6 + 6 * q^7 + 15 * q^8 + 18 * q^9 - 6 * q^10 + 21 * q^11 + 30 * q^12 + 36 * q^13 + 12 * q^14 + 12 * q^15 + 12 * q^16 + 21 * q^17 + 6 * q^18 + 15 * q^20 - 3 * q^21 + 6 * q^22 + 6 * q^23 - 18 * q^24 + 3 * q^25 + 6 * q^26 + 24 * q^27 + 27 * q^29 - 30 * q^30 + 54 * q^31 + 21 * q^32 + 15 * q^33 + 39 * q^34 - 33 * q^35 + 54 * q^36 + 57 * q^37 - 27 * q^40 + 24 * q^41 + 6 * q^42 + 12 * q^43 + 18 * q^44 - 3 * q^45 + 15 * q^46 + 12 * q^47 - 39 * q^48 + 21 * q^49 + 33 * q^50 - 18 * q^51 - 18 * q^52 + 39 * q^53 + 30 * q^54 + 6 * q^55 + 57 * q^56 + 30 * q^58 + 27 * q^59 + 12 * q^60 - 30 * q^61 + 21 * q^62 - 18 * q^63 - 15 * q^64 - 24 * q^65 - 6 * q^66 + 27 * q^67 - 48 * q^68 + 54 * q^69 + 51 * q^70 + 42 * q^71 + 15 * q^72 + 6 * q^73 + 84 * q^74 + 27 * q^75 + 6 * q^77 - 48 * q^78 + 39 * q^79 - 27 * q^80 - 27 * q^81 - 15 * q^82 + 12 * q^83 - 48 * q^84 - 42 * q^85 - 45 * q^86 + 75 * q^87 + 15 * q^88 + 75 * q^89 - 87 * q^90 + 45 * q^91 + 12 * q^92 + 66 * q^93 + 42 * q^94 - 3 * q^96 + 39 * q^97 - 45 * q^98 + 18 * 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 $

$2$	−1.68287	−1.18997	−0.594985	−	0.803737i	$-0.702842\pi$
$2$	−1.68287	−1.18997	−0.594985	+	0.803737i	$0.702842\pi$
$3$	0.146409	0.0845292	0.0422646	−	0.999106i	$-0.486543\pi$
$3$	0.146409	0.0845292	0.0422646	+	0.999106i	$0.486543\pi$
$4$	0.832058	0.416029
$5$	3.02083	1.35096	0.675478	−	0.737380i	$-0.263937\pi$
$5$	3.02083	1.35096	0.675478	+	0.737380i	$0.263937\pi$
$6$	−0.246387	−0.100587
$7$	−2.73938	−1.03539	−0.517695	−	0.855565i	$-0.673210\pi$
$7$	−2.73938	−1.03539	−0.517695	+	0.855565i	$0.673210\pi$
$8$	1.96550	0.694908
$9$	−2.97856	−0.992855
$10$	−5.08367	−1.60760
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.121821	0.0351666
$13$	−3.11321	−0.863450	−0.431725	−	0.902005i	$-0.642095\pi$
$13$	−3.11321	−0.863450	−0.431725	+	0.902005i	$0.642095\pi$
$14$	4.61003	1.23208
$15$	0.442276	0.114195
$16$	−4.97180	−1.24295
$17$	−4.43069	−1.07460	−0.537300	−	0.843391i	$-0.680556\pi$
$17$	−4.43069	−1.07460	−0.537300	+	0.843391i	$0.680556\pi$
$18$	5.01254	1.18147
$19$	0	0
$19$	0	0
$20$	2.51351	0.562037
$21$	−0.401070	−0.0875206
$22$	−1.68287	−0.358790
$23$	−4.74211	−0.988798	−0.494399	−	0.869235i	$-0.664612\pi$
$23$	−4.74211	−0.988798	−0.494399	+	0.869235i	$0.664612\pi$
$24$	0.287766	0.0587400
$25$	4.12540	0.825080
$26$	5.23914	1.02748
$27$	−0.875315	−0.168454
$28$	−2.27933	−0.430752
$29$	−3.88758	−0.721906	−0.360953	−	0.932584i	$-0.617548\pi$
$29$	−3.88758	−0.721906	−0.360953	+	0.932584i	$0.617548\pi$
$30$	−0.744294	−0.135889
$31$	−3.90204	−0.700827	−0.350413	−	0.936595i	$-0.613959\pi$
$31$	−3.90204	−0.700827	−0.350413	+	0.936595i	$0.613959\pi$
$32$	4.43590	0.784164
$33$	0.146409	0.0254865
$34$	7.45628	1.27874
$35$	−8.27520	−1.39876
$36$	−2.47834	−0.413057
$37$	2.67887	0.440403	0.220202	−	0.975454i	$-0.429328\pi$
$37$	2.67887	0.440403	0.220202	+	0.975454i	$0.429328\pi$
$38$	0	0
$39$	−0.455802	−0.0729867
$40$	5.93743	0.938790
$41$	11.1225	1.73704	0.868522	−	0.495650i	$-0.165070\pi$
$41$	11.1225	1.73704	0.868522	+	0.495650i	$0.165070\pi$
$42$	0.674949	0.104147
$43$	−5.11919	−0.780669	−0.390335	−	0.920673i	$-0.627641\pi$
$43$	−5.11919	−0.780669	−0.390335	+	0.920673i	$0.627641\pi$
$44$	0.832058	0.125438
$45$	−8.99773	−1.34130
$46$	7.98036	1.17664
$47$	9.02479	1.31640	0.658200	−	0.752843i	$-0.271318\pi$
$47$	9.02479	1.31640	0.658200	+	0.752843i	$0.271318\pi$
$48$	−0.727915	−0.105065
$49$	0.504216	0.0720309
$50$	−6.94252	−0.981821
$51$	−0.648692	−0.0908350
$52$	−2.59037	−0.359220
$53$	8.09736	1.11226	0.556129	−	0.831096i	$-0.312286\pi$
$53$	8.09736	1.11226	0.556129	+	0.831096i	$0.312286\pi$
$54$	1.47304	0.200456
$55$	3.02083	0.407328
$56$	−5.38425	−0.719500
$57$	0	0
$58$	6.54230	0.859046
$59$	6.73170	0.876393	0.438196	−	0.898879i	$-0.355617\pi$
$59$	6.73170	0.876393	0.438196	+	0.898879i	$0.355617\pi$
$60$	0.367999	0.0475085
$61$	−13.7126	−1.75572	−0.877859	−	0.478919i	$-0.841029\pi$
$61$	−13.7126	−1.75572	−0.877859	+	0.478919i	$0.841029\pi$
$62$	6.56663	0.833963
$63$	8.15943	1.02799
$64$	2.47853	0.309817
$65$	−9.40448	−1.16648
$66$	−0.246387	−0.0303282
$67$	2.31270	0.282541	0.141270	−	0.989971i	$-0.454881\pi$
$67$	2.31270	0.282541	0.141270	+	0.989971i	$0.454881\pi$
$68$	−3.68659	−0.447065
$69$	−0.694287	−0.0835823
$70$	13.9261	1.66449
$71$	14.4450	1.71431	0.857156	−	0.515057i	$-0.172229\pi$
$71$	14.4450	1.71431	0.857156	+	0.515057i	$0.172229\pi$
$72$	−5.85436	−0.689943
$73$	1.07891	0.126277	0.0631386	−	0.998005i	$-0.479889\pi$
$73$	1.07891	0.126277	0.0631386	+	0.998005i	$0.479889\pi$
$74$	−4.50819	−0.524067
$75$	0.603995	0.0697434
$76$	0	0
$77$	−2.73938	−0.312182
$78$	0.767056	0.0868520
$79$	−2.29927	−0.258688	−0.129344	−	0.991600i	$-0.541287\pi$
$79$	−2.29927	−0.258688	−0.129344	+	0.991600i	$0.541287\pi$
$80$	−15.0189	−1.67917
$81$	8.80754	0.978615
$82$	−18.7178	−2.06703
$83$	8.04434	0.882981	0.441490	−	0.897266i	$-0.354450\pi$
$83$	8.04434	0.882981	0.441490	+	0.897266i	$0.354450\pi$
$84$	−0.333714	−0.0364111
$85$	−13.3843	−1.45174
$86$	8.61494	0.928973
$87$	−0.569176	−0.0610221
$88$	1.96550	0.209523
$89$	1.45068	0.153771	0.0768857	−	0.997040i	$-0.475502\pi$
$89$	1.45068	0.153771	0.0768857	+	0.997040i	$0.475502\pi$
$90$	15.1420	1.59611
$91$	8.52828	0.894006
$92$	−3.94571	−0.411369
$93$	−0.571293	−0.0592403
$94$	−15.1876	−1.56648
$95$	0	0
$96$	0.649456	0.0662848
$97$	6.93562	0.704206	0.352103	−	0.935961i	$-0.385467\pi$
$97$	6.93562	0.704206	0.352103	+	0.935961i	$0.385467\pi$
$98$	−0.848531	−0.0857146
$99$	−2.97856	−0.299357
$100$	3.43258	0.343258
$101$	19.8015	1.97032	0.985159	−	0.171642i	$-0.0549071\pi$
$101$	19.8015	1.97032	0.985159	+	0.171642i	$0.0549071\pi$
$102$	1.09167	0.108091
$103$	0.466338	0.0459497	0.0229748	−	0.999736i	$-0.492686\pi$
$103$	0.466338	0.0459497	0.0229748	+	0.999736i	$0.492686\pi$
$104$	−6.11901	−0.600018
$105$	−1.21156	−0.118236
$106$	−13.6268	−1.32355
$107$	18.9846	1.83531	0.917657	−	0.397373i	$-0.130078\pi$
$107$	18.9846	1.83531	0.917657	+	0.397373i	$0.130078\pi$
$108$	−0.728313	−0.0700820
$109$	12.8593	1.23170	0.615848	−	0.787865i	$-0.288813\pi$
$109$	12.8593	1.23170	0.615848	+	0.787865i	$0.288813\pi$
$110$	−5.08367	−0.484709
$111$	0.392210	0.0372269
$112$	13.6196	1.28694
$113$	−0.947234	−0.0891083	−0.0445541	−	0.999007i	$-0.514187\pi$
$113$	−0.947234	−0.0891083	−0.0445541	+	0.999007i	$0.514187\pi$
$114$	0	0
$115$	−14.3251	−1.33582
$116$	−3.23469	−0.300334
$117$	9.27290	0.857280
$118$	−11.3286	−1.04288
$119$	12.1373	1.11263
$120$	0.869292	0.0793551
$121$	1.00000	0.0909091
$122$	23.0766	2.08925
$123$	1.62843	0.146831
$124$	−3.24672	−0.291564
$125$	−2.64201	−0.236308
$126$	−13.7313	−1.22328
$127$	−7.62107	−0.676261	−0.338130	−	0.941099i	$-0.609795\pi$
$127$	−7.62107	−0.676261	−0.338130	+	0.941099i	$0.609795\pi$
$128$	−13.0429	−1.15284
$129$	−0.749495	−0.0659894
$130$	15.8265	1.38808
$131$	5.40172	0.471950	0.235975	−	0.971759i	$-0.424172\pi$
$131$	5.40172	0.471950	0.235975	+	0.971759i	$0.424172\pi$
$132$	0.121821	0.0106031
$133$	0	0
$134$	−3.89197	−0.336215
$135$	−2.64418	−0.227574
$136$	−8.70850	−0.746748
$137$	−7.93722	−0.678123	−0.339061	−	0.940764i	$-0.610109\pi$
$137$	−7.93722	−0.678123	−0.339061	+	0.940764i	$0.610109\pi$
$138$	1.16840	0.0994605
$139$	0.150496	0.0127649	0.00638244	−	0.999980i	$-0.497968\pi$
$139$	0.150496	0.0127649	0.00638244	+	0.999980i	$0.497968\pi$
$140$	−6.88545	−0.581927
$141$	1.32131	0.111274
$142$	−24.3092	−2.03998
$143$	−3.11321	−0.260340
$144$	14.8088	1.23407
$145$	−11.7437	−0.975262
$146$	−1.81567	−0.150266
$147$	0.0738217	0.00608871
$148$	2.22898	0.183221
$149$	11.2114	0.918471	0.459236	−	0.888315i	$-0.348123\pi$
$149$	11.2114	0.918471	0.459236	+	0.888315i	$0.348123\pi$
$150$	−1.01645	−0.0829926
$151$	−13.1344	−1.06887	−0.534433	−	0.845211i	$-0.679475\pi$
$151$	−13.1344	−1.06887	−0.534433	+	0.845211i	$0.679475\pi$
$152$	0	0
$153$	13.1971	1.06692
$154$	4.61003	0.371487
$155$	−11.7874	−0.946785
$156$	−0.379254	−0.0303646
$157$	17.9137	1.42967	0.714835	−	0.699293i	$-0.246502\pi$
$157$	17.9137	1.42967	0.714835	+	0.699293i	$0.246502\pi$
$158$	3.86937	0.307831
$159$	1.18553	0.0940183
$160$	13.4001	1.05937
$161$	12.9905	1.02379
$162$	−14.8220	−1.16452
$163$	−15.2702	−1.19605	−0.598027	−	0.801476i	$-0.704049\pi$
$163$	−15.2702	−1.19605	−0.598027	+	0.801476i	$0.704049\pi$
$164$	9.25458	0.722661
$165$	0.442276	0.0344311
$166$	−13.5376	−1.05072
$167$	−16.6892	−1.29145	−0.645726	−	0.763570i	$-0.723445\pi$
$167$	−16.6892	−1.29145	−0.645726	+	0.763570i	$0.723445\pi$
$168$	−0.788301	−0.0608188
$169$	−3.30791	−0.254455
$170$	22.5241	1.72752
$171$	0	0
$172$	−4.25947	−0.324781
$173$	−6.99073	−0.531496	−0.265748	−	0.964043i	$-0.585619\pi$
$173$	−6.99073	−0.531496	−0.265748	+	0.964043i	$0.585619\pi$
$174$	0.957851	0.0726145
$175$	−11.3011	−0.854279
$176$	−4.97180	−0.374763
$177$	0.985581	0.0740808
$178$	−2.44130	−0.182983
$179$	2.41602	0.180582	0.0902911	−	0.995915i	$-0.471220\pi$
$179$	2.41602	0.180582	0.0902911	+	0.995915i	$0.471220\pi$
$180$	−7.48664	−0.558021
$181$	16.5726	1.23183	0.615915	−	0.787813i	$-0.288787\pi$
$181$	16.5726	1.23183	0.615915	+	0.787813i	$0.288787\pi$
$182$	−14.3520	−1.06384
$183$	−2.00765	−0.148409
$184$	−9.32060	−0.687124
$185$	8.09240	0.594965
$186$	0.961413	0.0704942
$187$	−4.43069	−0.324004
$188$	7.50915	0.547661
$189$	2.39782	0.174416
$190$	0	0
$191$	21.9959	1.59157	0.795783	−	0.605582i	$-0.207060\pi$
$191$	21.9959	1.59157	0.795783	+	0.605582i	$0.207060\pi$
$192$	0.362879	0.0261886
$193$	9.01705	0.649061	0.324531	−	0.945875i	$-0.394794\pi$
$193$	9.01705	0.649061	0.324531	+	0.945875i	$0.394794\pi$
$194$	−11.6718	−0.837984
$195$	−1.37690	−0.0986018
$196$	0.419537	0.0299669
$197$	−7.42582	−0.529068	−0.264534	−	0.964376i	$-0.585218\pi$
$197$	−7.42582	−0.529068	−0.264534	+	0.964376i	$0.585218\pi$
$198$	5.01254	0.356226
$199$	−23.2961	−1.65142	−0.825709	−	0.564097i	$-0.809225\pi$
$199$	−23.2961	−1.65142	−0.825709	+	0.564097i	$0.809225\pi$
$200$	8.10846	0.573355
$201$	0.338599	0.0238830
$202$	−33.3233	−2.34462
$203$	10.6496	0.747453
$204$	−0.539750	−0.0377900
$205$	33.5992	2.34667
$206$	−0.784787	−0.0546787
$207$	14.1247	0.981733
$208$	15.4783	1.07322
$209$	0	0
$210$	2.03891	0.140698
$211$	−19.3575	−1.33262	−0.666311	−	0.745674i	$-0.732128\pi$
$211$	−19.3575	−1.33262	−0.666311	+	0.745674i	$0.732128\pi$
$212$	6.73748	0.462732
$213$	2.11488	0.144909
$214$	−31.9487	−2.18397
$215$	−15.4642	−1.05465
$216$	−1.72043	−0.117060
$217$	10.6892	0.725628
$218$	−21.6405	−1.46568
$219$	0.157962	0.0106741
$220$	2.51351	0.169460
$221$	13.7937	0.927863
$222$	−0.660039	−0.0442989
$223$	−4.96632	−0.332569	−0.166285	−	0.986078i	$-0.553177\pi$
$223$	−4.96632	−0.332569	−0.166285	+	0.986078i	$0.553177\pi$
$224$	−12.1516	−0.811915
$225$	−12.2878	−0.819185
$226$	1.59407	0.106036
$227$	−14.0397	−0.931846	−0.465923	−	0.884825i	$-0.654278\pi$
$227$	−14.0397	−0.931846	−0.465923	+	0.884825i	$0.654278\pi$
$228$	0	0
$229$	12.5658	0.830374	0.415187	−	0.909736i	$-0.363716\pi$
$229$	12.5658	0.830374	0.415187	+	0.909736i	$0.363716\pi$
$230$	24.1073	1.58959
$231$	−0.401070	−0.0263885
$232$	−7.64103	−0.501658
$233$	−20.5279	−1.34483	−0.672413	−	0.740176i	$-0.734742\pi$
$233$	−20.5279	−1.34483	−0.672413	+	0.740176i	$0.734742\pi$
$234$	−15.6051	−1.02014
$235$	27.2623	1.77840
$236$	5.60117	0.364605
$237$	−0.336633	−0.0218667
$238$	−20.4256	−1.32400
$239$	−4.21758	−0.272812	−0.136406	−	0.990653i	$-0.543555\pi$
$239$	−4.21758	−0.272812	−0.136406	+	0.990653i	$0.543555\pi$
$240$	−2.19891	−0.141939
$241$	−12.9479	−0.834049	−0.417025	−	0.908895i	$-0.636927\pi$
$241$	−12.9479	−0.834049	−0.417025	+	0.908895i	$0.636927\pi$
$242$	−1.68287	−0.108179
$243$	3.91545	0.251176
$244$	−11.4097	−0.730430
$245$	1.52315	0.0973105
$246$	−2.74045	−0.174724
$247$	0	0
$248$	−7.66944	−0.487010
$249$	1.17776	0.0746376
$250$	4.44616	0.281200
$251$	20.9888	1.32480	0.662402	−	0.749148i	$-0.269537\pi$
$251$	20.9888	1.32480	0.662402	+	0.749148i	$0.269537\pi$
$252$	6.78912	0.427674
$253$	−4.74211	−0.298134
$254$	12.8253	0.804730
$255$	−1.95959	−0.122714
$256$	16.9924	1.06203
$257$	−17.5287	−1.09341	−0.546705	−	0.837325i	$-0.684118\pi$
$257$	−17.5287	−1.09341	−0.546705	+	0.837325i	$0.684118\pi$
$258$	1.26130	0.0785254
$259$	−7.33845	−0.455989
$260$	−7.82507	−0.485291
$261$	11.5794	0.716748
$262$	−9.09040	−0.561607
$263$	7.41725	0.457367	0.228684	−	0.973501i	$-0.426558\pi$
$263$	7.41725	0.457367	0.228684	+	0.973501i	$0.426558\pi$
$264$	0.287766	0.0177108
$265$	24.4607	1.50261
$266$	0	0
$267$	0.212392	0.0129982
$268$	1.92430	0.117545
$269$	17.3161	1.05578	0.527892	−	0.849311i	$-0.322983\pi$
$269$	17.3161	1.05578	0.527892	+	0.849311i	$0.322983\pi$
$270$	4.44981	0.270807
$271$	−1.92665	−0.117036	−0.0585179	−	0.998286i	$-0.518637\pi$
$271$	−1.92665	−0.117036	−0.0585179	+	0.998286i	$0.518637\pi$
$272$	22.0285	1.33567
$273$	1.24862	0.0755696
$274$	13.3573	0.806946
$275$	4.12540	0.248771
$276$	−0.577687	−0.0347727
$277$	5.38591	0.323608	0.161804	−	0.986823i	$-0.448269\pi$
$277$	5.38591	0.323608	0.161804	+	0.986823i	$0.448269\pi$
$278$	−0.253265	−0.0151898
$279$	11.6225	0.695819
$280$	−16.2649	−0.972013
$281$	19.3355	1.15346	0.576731	−	0.816934i	$-0.304328\pi$
$281$	19.3355	1.15346	0.576731	+	0.816934i	$0.304328\pi$
$282$	−2.22359	−0.132413
$283$	−6.83280	−0.406168	−0.203084	−	0.979161i	$-0.565096\pi$
$283$	−6.83280	−0.406168	−0.203084	+	0.979161i	$0.565096\pi$
$284$	12.0191	0.713204
$285$	0	0
$286$	5.23914	0.309797
$287$	−30.4688	−1.79852
$288$	−13.2126	−0.778561
$289$	2.63099	0.154764
$290$	19.7632	1.16053
$291$	1.01544	0.0595260
$292$	0.897718	0.0525350
$293$	−28.5890	−1.67019	−0.835094	−	0.550108i	$-0.814587\pi$
$293$	−28.5890	−1.67019	−0.835094	+	0.550108i	$0.814587\pi$
$294$	−0.124232	−0.00724538
$295$	20.3353	1.18397
$296$	5.26531	0.306040
$297$	−0.875315	−0.0507909
$298$	−18.8673	−1.09295
$299$	14.7632	0.853777
$300$	0.502559	0.0290153
$301$	14.0234	0.808297
$302$	22.1036	1.27192
$303$	2.89911	0.166549
$304$	0	0
$305$	−41.4234	−2.37190
$306$	−22.2090	−1.26960
$307$	18.6587	1.06491	0.532454	−	0.846459i	$-0.321270\pi$
$307$	18.6587	1.06491	0.532454	+	0.846459i	$0.321270\pi$
$308$	−2.27933	−0.129877
$309$	0.0682760	0.00388409
$310$	19.8367	1.12665
$311$	4.75786	0.269793	0.134897	−	0.990860i	$-0.456930\pi$
$311$	4.75786	0.269793	0.134897	+	0.990860i	$0.456930\pi$
$312$	−0.895877	−0.0507190
$313$	11.5658	0.653736	0.326868	−	0.945070i	$-0.394007\pi$
$313$	11.5658	0.653736	0.326868	+	0.945070i	$0.394007\pi$
$314$	−30.1465	−1.70126
$315$	24.6482	1.38877
$316$	−1.91313	−0.107622
$317$	25.8412	1.45139	0.725693	−	0.688019i	$-0.241519\pi$
$317$	25.8412	1.45139	0.725693	+	0.688019i	$0.241519\pi$
$318$	−1.99509	−0.111879
$319$	−3.88758	−0.217663
$320$	7.48722	0.418549
$321$	2.77952	0.155138
$322$	−21.8613	−1.21828
$323$	0	0
$324$	7.32839	0.407133
$325$	−12.8433	−0.712415
$326$	25.6978	1.42327
$327$	1.88271	0.104114
$328$	21.8613	1.20709
$329$	−24.7224	−1.36299
$330$	−0.744294	−0.0409720
$331$	−11.9015	−0.654164	−0.327082	−	0.944996i	$-0.606065\pi$
$331$	−11.9015	−0.654164	−0.327082	+	0.944996i	$0.606065\pi$
$332$	6.69336	0.367346
$333$	−7.97918	−0.437257
$334$	28.0858	1.53679
$335$	6.98626	0.381700
$336$	1.99404	0.108784
$337$	−5.64567	−0.307539	−0.153770	−	0.988107i	$-0.549141\pi$
$337$	−5.64567	−0.307539	−0.153770	+	0.988107i	$0.549141\pi$
$338$	5.56679	0.302794
$339$	−0.138683	−0.00753225
$340$	−11.1366	−0.603965
$341$	−3.90204	−0.211307
$342$	0	0
$343$	17.7944	0.960809
$344$	−10.0618	−0.542493
$345$	−2.09732	−0.112916
$346$	11.7645	0.632464
$347$	5.33345	0.286314	0.143157	−	0.989700i	$-0.454275\pi$
$347$	5.33345	0.286314	0.143157	+	0.989700i	$0.454275\pi$
$348$	−0.473588	−0.0253870
$349$	−2.10061	−0.112443	−0.0562215	−	0.998418i	$-0.517905\pi$
$349$	−2.10061	−0.112443	−0.0562215	+	0.998418i	$0.517905\pi$
$350$	19.0182	1.01657
$351$	2.72504	0.145452
$352$	4.43590	0.236434
$353$	4.21622	0.224407	0.112203	−	0.993685i	$-0.464209\pi$
$353$	4.21622	0.224407	0.112203	+	0.993685i	$0.464209\pi$
$354$	−1.65861	−0.0881539
$355$	43.6360	2.31596
$356$	1.20705	0.0639734
$357$	1.77702	0.0940496
$358$	−4.06586	−0.214887
$359$	−0.632715	−0.0333934	−0.0166967	−	0.999861i	$-0.505315\pi$
$359$	−0.632715	−0.0333934	−0.0166967	+	0.999861i	$0.505315\pi$
$360$	−17.6850	−0.932082
$361$	0	0
$362$	−27.8895	−1.46584
$363$	0.146409	0.00768447
$364$	7.09602	0.371933
$365$	3.25921	0.170595
$366$	3.37861	0.176603
$367$	21.0594	1.09929	0.549646	−	0.835397i	$-0.314762\pi$
$367$	21.0594	1.09929	0.549646	+	0.835397i	$0.314762\pi$
$368$	23.5768	1.22903
$369$	−33.1291	−1.72463
$370$	−13.6185	−0.707991
$371$	−22.1818	−1.15162
$372$	−0.475349	−0.0246457
$373$	16.7265	0.866063	0.433032	−	0.901379i	$-0.357444\pi$
$373$	16.7265	0.866063	0.433032	+	0.901379i	$0.357444\pi$
$374$	7.45628	0.385555
$375$	−0.386814	−0.0199750
$376$	17.7382	0.914777
$377$	12.1029	0.623329
$378$	−4.03523	−0.207550
$379$	−8.48098	−0.435639	−0.217819	−	0.975989i	$-0.569894\pi$
$379$	−8.48098	−0.435639	−0.217819	+	0.975989i	$0.569894\pi$
$380$	0	0
$381$	−1.11579	−0.0571638
$382$	−37.0162	−1.89392
$383$	−14.4497	−0.738344	−0.369172	−	0.929361i	$-0.620359\pi$
$383$	−14.4497	−0.738344	−0.369172	+	0.929361i	$0.620359\pi$
$384$	−1.90959	−0.0974484
$385$	−8.27520	−0.421743
$386$	−15.1745	−0.772364
$387$	15.2478	0.775091
$388$	5.77084	0.292970
$389$	12.6489	0.641325	0.320663	−	0.947194i	$-0.396094\pi$
$389$	12.6489	0.641325	0.320663	+	0.947194i	$0.396094\pi$
$390$	2.31714	0.117333
$391$	21.0108	1.06256
$392$	0.991035	0.0500548
$393$	0.790859	0.0398936
$394$	12.4967	0.629575
$395$	−6.94569	−0.349476
$396$	−2.47834	−0.124541
$397$	5.12134	0.257033	0.128516	−	0.991707i	$-0.458979\pi$
$397$	5.12134	0.257033	0.128516	+	0.991707i	$0.458979\pi$
$398$	39.2044	1.96514
$399$	0	0
$400$	−20.5107	−1.02553
$401$	39.1602	1.95557	0.977785	−	0.209612i	$-0.0672201\pi$
$401$	39.1602	1.95557	0.977785	+	0.209612i	$0.0672201\pi$
$402$	−0.569819	−0.0284200
$403$	12.1479	0.605128
$404$	16.4760	0.819710
$405$	26.6061	1.32207
$406$	−17.9219	−0.889447
$407$	2.67887	0.132787
$408$	−1.27500	−0.0631220
$409$	13.4305	0.664094	0.332047	−	0.943263i	$-0.392261\pi$
$409$	13.4305	0.664094	0.332047	+	0.943263i	$0.392261\pi$
$410$	−56.5431	−2.79247
$411$	−1.16208	−0.0573212
$412$	0.388020	0.0191164
$413$	−18.4407	−0.907408
$414$	−23.7700	−1.16823
$415$	24.3006	1.19287
$416$	−13.8099	−0.677086
$417$	0.0220339	0.00107900
$418$	0	0
$419$	−6.55196	−0.320084	−0.160042	−	0.987110i	$-0.551163\pi$
$419$	−6.55196	−0.320084	−0.160042	+	0.987110i	$0.551163\pi$
$420$	−1.00809	−0.0491898
$421$	−6.18732	−0.301552	−0.150776	−	0.988568i	$-0.548177\pi$
$421$	−6.18732	−0.301552	−0.150776	+	0.988568i	$0.548177\pi$
$422$	32.5761	1.58578
$423$	−26.8809	−1.30700
$424$	15.9153	0.772917
$425$	−18.2784	−0.886631
$426$	−3.55908	−0.172438
$427$	37.5641	1.81785
$428$	15.7963	0.763544
$429$	−0.455802	−0.0220063
$430$	26.0243	1.25500
$431$	31.2369	1.50463	0.752315	−	0.658803i	$-0.228937\pi$
$431$	31.2369	1.50463	0.752315	+	0.658803i	$0.228937\pi$
$432$	4.35189	0.209380
$433$	23.8590	1.14659	0.573296	−	0.819349i	$-0.305665\pi$
$433$	23.8590	1.14659	0.573296	+	0.819349i	$0.305665\pi$
$434$	−17.9885	−0.863476
$435$	−1.71938	−0.0824381
$436$	10.6997	0.512422
$437$	0	0
$438$	−0.265830	−0.0127019
$439$	−9.61741	−0.459014	−0.229507	−	0.973307i	$-0.573711\pi$
$439$	−9.61741	−0.459014	−0.229507	+	0.973307i	$0.573711\pi$
$440$	5.93743	0.283056
$441$	−1.50184	−0.0715162
$442$	−23.2130	−1.10413
$443$	−13.3447	−0.634024	−0.317012	−	0.948422i	$-0.602680\pi$
$443$	−13.3447	−0.634024	−0.317012	+	0.948422i	$0.602680\pi$
$444$	0.326342	0.0154875
$445$	4.38224	0.207738
$446$	8.35768	0.395748
$447$	1.64144	0.0776376
$448$	−6.78965	−0.320781
$449$	29.6953	1.40141	0.700704	−	0.713452i	$-0.252869\pi$
$449$	29.6953	1.40141	0.700704	+	0.713452i	$0.252869\pi$
$450$	20.6788	0.974806
$451$	11.1225	0.523739
$452$	−0.788154	−0.0370716
$453$	−1.92300	−0.0903504
$454$	23.6270	1.10887
$455$	25.7625	1.20776
$456$	0	0
$457$	7.31038	0.341965	0.170983	−	0.985274i	$-0.445306\pi$
$457$	7.31038	0.341965	0.170983	+	0.985274i	$0.445306\pi$
$458$	−21.1467	−0.988121
$459$	3.87825	0.181021
$460$	−11.9193	−0.555741
$461$	6.41757	0.298896	0.149448	−	0.988770i	$-0.452250\pi$
$461$	6.41757	0.298896	0.149448	+	0.988770i	$0.452250\pi$
$462$	0.674949	0.0314015
$463$	18.7396	0.870904	0.435452	−	0.900212i	$-0.356589\pi$
$463$	18.7396	0.870904	0.435452	+	0.900212i	$0.356589\pi$
$464$	19.3283	0.897292
$465$	−1.72578	−0.0800310
$466$	34.5458	1.60030
$467$	30.5291	1.41272	0.706359	−	0.707853i	$-0.250336\pi$
$467$	30.5291	1.41272	0.706359	+	0.707853i	$0.250336\pi$
$468$	7.71560	0.356654
$469$	−6.33536	−0.292540
$470$	−45.8790	−2.11624
$471$	2.62273	0.120849
$472$	13.2311	0.609012
$473$	−5.11919	−0.235381
$474$	0.566511	0.0260207
$475$	0	0
$476$	10.0990	0.462886
$477$	−24.1185	−1.10431
$478$	7.09764	0.324639
$479$	−28.1218	−1.28492	−0.642459	−	0.766320i	$-0.722086\pi$
$479$	−28.1218	−1.28492	−0.642459	+	0.766320i	$0.722086\pi$
$480$	1.96189	0.0895478
$481$	−8.33988	−0.380266
$482$	21.7897	0.992494
$483$	1.90192	0.0865402
$484$	0.832058	0.0378208
$485$	20.9513	0.951351
$486$	−6.58920	−0.298892
$487$	33.0398	1.49718	0.748589	−	0.663034i	$-0.230732\pi$
$487$	33.0398	1.49718	0.748589	+	0.663034i	$0.230732\pi$
$488$	−26.9521	−1.22006
$489$	−2.23569	−0.101102
$490$	−2.56327	−0.115797
$491$	−22.7858	−1.02831	−0.514154	−	0.857698i	$-0.671894\pi$
$491$	−22.7858	−1.02831	−0.514154	+	0.857698i	$0.671894\pi$
$492$	1.35495	0.0610860
$493$	17.2247	0.775760
$494$	0	0
$495$	−8.99773	−0.404418
$496$	19.4001	0.871092
$497$	−39.5705	−1.77498
$498$	−1.98202	−0.0888166
$499$	−42.7320	−1.91295	−0.956473	−	0.291820i	$-0.905739\pi$
$499$	−42.7320	−1.91295	−0.956473	+	0.291820i	$0.905739\pi$
$500$	−2.19831	−0.0983112
$501$	−2.44345	−0.109165
$502$	−35.3215	−1.57648
$503$	22.2573	0.992402	0.496201	−	0.868208i	$-0.334728\pi$
$503$	22.2573	0.992402	0.496201	+	0.868208i	$0.334728\pi$
$504$	16.0373	0.714359
$505$	59.8168	2.66181
$506$	7.98036	0.354770
$507$	−0.484308	−0.0215089
$508$	−6.34118	−0.281344
$509$	−39.3241	−1.74301	−0.871505	−	0.490387i	$-0.836855\pi$
$509$	−39.3241	−1.74301	−0.871505	+	0.490387i	$0.836855\pi$
$510$	3.29773	0.146026
$511$	−2.95555	−0.130746
$512$	−2.51031	−0.110941
$513$	0	0
$514$	29.4986	1.30113
$515$	1.40873	0.0620759
$516$	−0.623624	−0.0274535
$517$	9.02479	0.396910
$518$	12.3497	0.542613
$519$	−1.02351	−0.0449269
$520$	−18.4845	−0.810597
$521$	34.1490	1.49610	0.748048	−	0.663645i	$-0.230991\pi$
$521$	34.1490	1.49610	0.748048	+	0.663645i	$0.230991\pi$
$522$	−19.4867	−0.852908
$523$	−3.59852	−0.157352	−0.0786761	−	0.996900i	$-0.525069\pi$
$523$	−3.59852	−0.157352	−0.0786761	+	0.996900i	$0.525069\pi$
$524$	4.49455	0.196345
$525$	−1.65457	−0.0722116
$526$	−12.4823	−0.544254
$527$	17.2887	0.753108
$528$	−0.727915	−0.0316784
$529$	−0.512397	−0.0222781
$530$	−41.1643	−1.78806
$531$	−20.0508	−0.870131
$532$	0	0
$533$	−34.6267	−1.49985
$534$	−0.357428	−0.0154674
$535$	57.3493	2.47943
$536$	4.54560	0.196340
$537$	0.353727	0.0152645
$538$	−29.1409	−1.25635
$539$	0.504216	0.0217181
$540$	−2.20011	−0.0946776
$541$	−22.4253	−0.964138	−0.482069	−	0.876133i	$-0.660115\pi$
$541$	−22.4253	−0.964138	−0.482069	+	0.876133i	$0.660115\pi$
$542$	3.24231	0.139269
$543$	2.42637	0.104126
$544$	−19.6541	−0.842663
$545$	38.8457	1.66397
$546$	−2.10126	−0.0899256
$547$	−13.1967	−0.564249	−0.282125	−	0.959378i	$-0.591039\pi$
$547$	−13.1967	−0.564249	−0.282125	+	0.959378i	$0.591039\pi$
$548$	−6.60423	−0.282119
$549$	40.8439	1.74317
$550$	−6.94252	−0.296030
$551$	0	0
$552$	−1.36462	−0.0580820
$553$	6.29857	0.267843
$554$	−9.06380	−0.385084
$555$	1.18480	0.0502919
$556$	0.125221	0.00531056
$557$	−39.5188	−1.67446	−0.837232	−	0.546848i	$-0.815828\pi$
$557$	−39.5188	−1.67446	−0.837232	+	0.546848i	$0.815828\pi$
$558$	−19.5591	−0.828004
$559$	15.9371	0.674069
$560$	41.1426	1.73859
$561$	−0.648692	−0.0273878
$562$	−32.5392	−1.37259
$563$	−9.60572	−0.404833	−0.202416	−	0.979300i	$-0.564879\pi$
$563$	−9.60572	−0.404833	−0.202416	+	0.979300i	$0.564879\pi$
$564$	1.09941	0.0462934
$565$	−2.86143	−0.120381
$566$	11.4987	0.483328
$567$	−24.1272	−1.01325
$568$	28.3917	1.19129
$569$	36.9325	1.54829	0.774146	−	0.633007i	$-0.218179\pi$
$569$	36.9325	1.54829	0.774146	+	0.633007i	$0.218179\pi$
$570$	0	0
$571$	35.0368	1.46624	0.733122	−	0.680097i	$-0.238062\pi$
$571$	35.0368	1.46624	0.733122	+	0.680097i	$0.238062\pi$
$572$	−2.59037	−0.108309
$573$	3.22039	0.134534
$574$	51.2751	2.14018
$575$	−19.5631	−0.815838
$576$	−7.38247	−0.307603
$577$	−21.8967	−0.911573	−0.455786	−	0.890089i	$-0.650642\pi$
$577$	−21.8967	−0.911573	−0.455786	+	0.890089i	$0.650642\pi$
$578$	−4.42762	−0.184165
$579$	1.32018	0.0548646
$580$	−9.77146	−0.405738
$581$	−22.0365	−0.914229
$582$	−1.70885	−0.0708341
$583$	8.09736	0.335358
$584$	2.12060	0.0877510
$585$	28.0118	1.15815
$586$	48.1116	1.98747
$587$	−33.9537	−1.40142	−0.700711	−	0.713446i	$-0.747134\pi$
$587$	−33.9537	−1.40142	−0.700711	+	0.713446i	$0.747134\pi$
$588$	0.0614240	0.00253308
$589$	0	0
$590$	−34.2217	−1.40889
$591$	−1.08721	−0.0447217
$592$	−13.3188	−0.547399
$593$	8.63723	0.354689	0.177344	−	0.984149i	$-0.443249\pi$
$593$	8.63723	0.354689	0.177344	+	0.984149i	$0.443249\pi$
$594$	1.47304	0.0604397
$595$	36.6648	1.50311
$596$	9.32851	0.382111
$597$	−3.41076	−0.139593
$598$	−24.8446	−1.01597
$599$	−16.8842	−0.689869	−0.344934	−	0.938627i	$-0.612099\pi$
$599$	−16.8842	−0.689869	−0.344934	+	0.938627i	$0.612099\pi$
$600$	1.18715	0.0484652
$601$	−28.6569	−1.16894	−0.584469	−	0.811416i	$-0.698697\pi$
$601$	−28.6569	−1.16894	−0.584469	+	0.811416i	$0.698697\pi$
$602$	−23.5996	−0.961849
$603$	−6.88852	−0.280522
$604$	−10.9286	−0.444680
$605$	3.02083	0.122814
$606$	−4.87883	−0.198189
$607$	−34.4975	−1.40021	−0.700106	−	0.714039i	$-0.746864\pi$
$607$	−34.4975	−1.40021	−0.700106	+	0.714039i	$0.746864\pi$
$608$	0	0
$609$	1.55919	0.0631816
$610$	69.7103	2.82249
$611$	−28.0961	−1.13665
$612$	10.9807	0.443870
$613$	47.4139	1.91503	0.957514	−	0.288387i	$-0.0931191\pi$
$613$	47.4139	1.91503	0.957514	+	0.288387i	$0.0931191\pi$
$614$	−31.4002	−1.26721
$615$	4.91922	0.198362
$616$	−5.38425	−0.216937
$617$	−16.0914	−0.647815	−0.323907	−	0.946089i	$-0.604997\pi$
$617$	−16.0914	−0.647815	−0.323907	+	0.946089i	$0.604997\pi$
$618$	−0.114900	−0.00462195
$619$	24.4989	0.984696	0.492348	−	0.870398i	$-0.336139\pi$
$619$	24.4989	0.984696	0.492348	+	0.870398i	$0.336139\pi$
$620$	−9.80779	−0.393890
$621$	4.15084	0.166567
$622$	−8.00687	−0.321046
$623$	−3.97396	−0.159213
$624$	2.26615	0.0907187
$625$	−28.6081	−1.14432
$626$	−19.4637	−0.777926
$627$	0	0
$628$	14.9053	0.594784
$629$	−11.8692	−0.473257
$630$	−41.4798	−1.65260
$631$	15.6922	0.624698	0.312349	−	0.949967i	$-0.398884\pi$
$631$	15.6922	0.624698	0.312349	+	0.949967i	$0.398884\pi$
$632$	−4.51920	−0.179764
$633$	−2.83410	−0.112646
$634$	−43.4874	−1.72711
$635$	−23.0220	−0.913598
$636$	0.986426	0.0391143
$637$	−1.56973	−0.0621950
$638$	6.54230	0.259012
$639$	−43.0255	−1.70206
$640$	−39.4002	−1.55743
$641$	7.08845	0.279977	0.139988	−	0.990153i	$-0.455293\pi$
$641$	7.08845	0.279977	0.139988	+	0.990153i	$0.455293\pi$
$642$	−4.67758	−0.184609
$643$	−43.7524	−1.72543	−0.862713	−	0.505694i	$-0.831236\pi$
$643$	−43.7524	−1.72543	−0.862713	+	0.505694i	$0.831236\pi$
$644$	10.8088	0.425927
$645$	−2.26410	−0.0891487
$646$	0	0
$647$	−9.79736	−0.385174	−0.192587	−	0.981280i	$-0.561688\pi$
$647$	−9.79736	−0.385174	−0.192587	+	0.981280i	$0.561688\pi$
$648$	17.3112	0.680048
$649$	6.73170	0.264242
$650$	21.6135	0.847753
$651$	1.56499	0.0613368
$652$	−12.7057	−0.497594
$653$	20.7746	0.812974	0.406487	−	0.913657i	$-0.366754\pi$
$653$	20.7746	0.812974	0.406487	+	0.913657i	$0.366754\pi$
$654$	−3.16837	−0.123893
$655$	16.3177	0.637584
$656$	−55.2988	−2.15906
$657$	−3.21361	−0.125375
$658$	41.6046	1.62191
$659$	−13.6273	−0.530846	−0.265423	−	0.964132i	$-0.585512\pi$
$659$	−13.6273	−0.530846	−0.265423	+	0.964132i	$0.585512\pi$
$660$	0.367999	0.0143244
$661$	−14.4743	−0.562987	−0.281493	−	0.959563i	$-0.590830\pi$
$661$	−14.4743	−0.562987	−0.281493	+	0.959563i	$0.590830\pi$
$662$	20.0287	0.778436
$663$	2.01952	0.0784315
$664$	15.8111	0.613590
$665$	0	0
$666$	13.4279	0.520322
$667$	18.4353	0.713819
$668$	−13.8864	−0.537281
$669$	−0.727113	−0.0281118
$670$	−11.7570	−0.454212
$671$	−13.7126	−0.529369
$672$	−1.77911	−0.0686305
$673$	9.40765	0.362638	0.181319	−	0.983424i	$-0.441963\pi$
$673$	9.40765	0.362638	0.181319	+	0.983424i	$0.441963\pi$
$674$	9.50094	0.365963
$675$	−3.61103	−0.138988
$676$	−2.75238	−0.105861
$677$	20.4389	0.785532	0.392766	−	0.919639i	$-0.371518\pi$
$677$	20.4389	0.785532	0.392766	+	0.919639i	$0.371518\pi$
$678$	0.233387	0.00896315
$679$	−18.9993	−0.729127
$680$	−26.3069	−1.00882
$681$	−2.05553	−0.0787682
$682$	6.56663	0.251449
$683$	13.3968	0.512615	0.256308	−	0.966595i	$-0.417494\pi$
$683$	13.3968	0.512615	0.256308	+	0.966595i	$0.417494\pi$
$684$	0	0
$685$	−23.9770	−0.916113
$686$	−29.9458	−1.14333
$687$	1.83975	0.0701909
$688$	25.4516	0.970332
$689$	−25.2088	−0.960379
$690$	3.52952	0.134367
$691$	48.6746	1.85167	0.925834	−	0.377930i	$-0.123364\pi$
$691$	48.6746	1.85167	0.925834	+	0.377930i	$0.123364\pi$
$692$	−5.81670	−0.221118
$693$	8.15943	0.309951
$694$	−8.97551	−0.340706
$695$	0.454621	0.0172448
$696$	−1.11871	−0.0424047
$697$	−49.2804	−1.86663
$698$	3.53506	0.133804
$699$	−3.00546	−0.113677
$700$	−9.40314	−0.355405
$701$	14.7366	0.556595	0.278298	−	0.960495i	$-0.410230\pi$
$701$	14.7366	0.556595	0.278298	+	0.960495i	$0.410230\pi$
$702$	−4.58589	−0.173083
$703$	0	0
$704$	2.47853	0.0934132
$705$	3.99145	0.150327
$706$	−7.09536	−0.267037
$707$	−54.2438	−2.04005
$708$	0.820061	0.0308198
$709$	−10.5648	−0.396769	−0.198384	−	0.980124i	$-0.563569\pi$
$709$	−10.5648	−0.396769	−0.198384	+	0.980124i	$0.563569\pi$
$710$	−73.4338	−2.75592
$711$	6.84852	0.256839
$712$	2.85130	0.106857
$713$	18.5039	0.692976
$714$	−2.99049	−0.111916
$715$	−9.40448	−0.351708
$716$	2.01027	0.0751274
$717$	−0.617491	−0.0230606
$718$	1.06478	0.0397372
$719$	−16.1382	−0.601854	−0.300927	−	0.953647i	$-0.597296\pi$
$719$	−16.1382	−0.601854	−0.300927	+	0.953647i	$0.597296\pi$
$720$	44.7349	1.66717
$721$	−1.27748	−0.0475758
$722$	0	0
$723$	−1.89569	−0.0705015
$724$	13.7893	0.512477
$725$	−16.0378	−0.595630
$726$	−0.246387	−0.00914429
$727$	−4.27672	−0.158615	−0.0793073	−	0.996850i	$-0.525271\pi$
$727$	−4.27672	−0.158615	−0.0793073	+	0.996850i	$0.525271\pi$
$728$	16.7623	0.621252
$729$	−25.8494	−0.957384
$730$	−5.48483	−0.203003
$731$	22.6815	0.838907
$732$	−1.67048	−0.0617427
$733$	18.9894	0.701389	0.350694	−	0.936490i	$-0.385946\pi$
$733$	18.9894	0.701389	0.350694	+	0.936490i	$0.385946\pi$
$734$	−35.4403	−1.30813
$735$	0.223003	0.00822558
$736$	−21.0355	−0.775380
$737$	2.31270	0.0851893
$738$	55.7521	2.05226
$739$	−32.7358	−1.20421	−0.602103	−	0.798418i	$-0.705670\pi$
$739$	−32.7358	−1.20421	−0.602103	+	0.798418i	$0.705670\pi$
$740$	6.73335	0.247523
$741$	0	0
$742$	37.3291	1.37039
$743$	−8.37190	−0.307135	−0.153568	−	0.988138i	$-0.549076\pi$
$743$	−8.37190	−0.307135	−0.153568	+	0.988138i	$0.549076\pi$
$744$	−1.12287	−0.0411666
$745$	33.8676	1.24081
$746$	−28.1485	−1.03059
$747$	−23.9606	−0.876672
$748$	−3.68659	−0.134795
$749$	−52.0062	−1.90026
$750$	0.650958	0.0237696
$751$	23.2556	0.848609	0.424304	−	0.905520i	$-0.360519\pi$
$751$	23.2556	0.848609	0.424304	+	0.905520i	$0.360519\pi$
$752$	−44.8694	−1.63622
$753$	3.07295	0.111985
$754$	−20.3676	−0.741743
$755$	−39.6769	−1.44399
$756$	1.99513	0.0725621
$757$	44.3078	1.61040	0.805198	−	0.593006i	$-0.202059\pi$
$757$	44.3078	1.61040	0.805198	+	0.593006i	$0.202059\pi$
$758$	14.2724	0.518397
$759$	−0.694287	−0.0252010
$760$	0	0
$761$	34.2261	1.24069	0.620347	−	0.784327i	$-0.286992\pi$
$761$	34.2261	1.24069	0.620347	+	0.784327i	$0.286992\pi$
$762$	1.87774	0.0680232
$763$	−35.2265	−1.27529
$764$	18.3019	0.662138
$765$	39.8661	1.44136
$766$	24.3170	0.878608
$767$	−20.9572	−0.756721
$768$	2.48784	0.0897721
$769$	18.0250	0.649996	0.324998	−	0.945715i	$-0.394636\pi$
$769$	18.0250	0.649996	0.324998	+	0.945715i	$0.394636\pi$
$770$	13.9261	0.501862
$771$	−2.56636	−0.0924251
$772$	7.50271	0.270028
$773$	−47.1420	−1.69558	−0.847790	−	0.530332i	$-0.822067\pi$
$773$	−47.1420	−1.69558	−0.847790	+	0.530332i	$0.822067\pi$
$774$	−25.6602	−0.922336
$775$	−16.0975	−0.578238
$776$	13.6319	0.489358
$777$	−1.07441	−0.0385444
$778$	−21.2865	−0.763158
$779$	0	0
$780$	−1.14566	−0.0410212
$781$	14.4450	0.516884
$782$	−35.3585	−1.26442
$783$	3.40286	0.121608
$784$	−2.50686	−0.0895307
$785$	54.1142	1.93142
$786$	−1.33092	−0.0474722
$787$	−5.48812	−0.195630	−0.0978151	−	0.995205i	$-0.531185\pi$
$787$	−5.48812	−0.195630	−0.0978151	+	0.995205i	$0.531185\pi$
$788$	−6.17872	−0.220108
$789$	1.08595	0.0386609
$790$	11.6887	0.415866
$791$	2.59484	0.0922618
$792$	−5.85436	−0.208026
$793$	42.6902	1.51597
$794$	−8.61856	−0.305861
$795$	3.58127	0.127014
$796$	−19.3837	−0.687038
$797$	−26.0730	−0.923552	−0.461776	−	0.886996i	$-0.652788\pi$
$797$	−26.0730	−0.923552	−0.461776	+	0.886996i	$0.652788\pi$
$798$	0	0
$799$	−39.9860	−1.41460
$800$	18.2999	0.646999
$801$	−4.32093	−0.152673
$802$	−65.9017	−2.32707
$803$	1.07891	0.0380740
$804$	0.281734	0.00993601
$805$	39.2419	1.38310
$806$	−20.4433	−0.720085
$807$	2.53524	0.0892446
$808$	38.9197	1.36919
$809$	−40.8941	−1.43776	−0.718880	−	0.695134i	$-0.755345\pi$
$809$	−40.8941	−1.43776	−0.718880	+	0.695134i	$0.755345\pi$
$810$	−44.7746	−1.57322
$811$	17.6300	0.619074	0.309537	−	0.950887i	$-0.399826\pi$
$811$	17.6300	0.619074	0.309537	+	0.950887i	$0.399826\pi$
$812$	8.86107	0.310962
$813$	−0.282079	−0.00989295
$814$	−4.50819	−0.158012
$815$	−46.1287	−1.61582
$816$	3.22516	0.112903
$817$	0	0
$818$	−22.6018	−0.790252
$819$	−25.4020	−0.887619
$820$	27.9565	0.976283
$821$	13.7336	0.479305	0.239653	−	0.970859i	$-0.422966\pi$
$821$	13.7336	0.479305	0.239653	+	0.970859i	$0.422966\pi$
$822$	1.95563	0.0682105
$823$	37.9263	1.32203	0.661014	−	0.750374i	$-0.270127\pi$
$823$	37.9263	1.32203	0.661014	+	0.750374i	$0.270127\pi$
$824$	0.916586	0.0319308
$825$	0.603995	0.0210284
$826$	31.0333	1.07979
$827$	−10.9660	−0.381326	−0.190663	−	0.981656i	$-0.561064\pi$
$827$	−10.9660	−0.381326	−0.190663	+	0.981656i	$0.561064\pi$
$828$	11.7526	0.408430
$829$	50.2347	1.74472	0.872362	−	0.488861i	$-0.162588\pi$
$829$	50.2347	1.74472	0.872362	+	0.488861i	$0.162588\pi$
$830$	−40.8947	−1.41948
$831$	0.788545	0.0273543
$832$	−7.71620	−0.267511
$833$	−2.23402	−0.0774043
$834$	−0.0370802	−0.00128398
$835$	−50.4153	−1.74469
$836$	0	0
$837$	3.41551	0.118057
$838$	11.0261	0.380891
$839$	6.77707	0.233970	0.116985	−	0.993134i	$-0.462677\pi$
$839$	6.77707	0.233970	0.116985	+	0.993134i	$0.462677\pi$
$840$	−2.38132	−0.0821634
$841$	−13.8867	−0.478852
$842$	10.4125	0.358837
$843$	2.83089	0.0975012
$844$	−16.1065	−0.554410
$845$	−9.99264	−0.343757
$846$	45.2371	1.55529
$847$	−2.73938	−0.0941263
$848$	−40.2584	−1.38248
$849$	−1.00038	−0.0343330
$850$	30.7602	1.05506
$851$	−12.7035	−0.435470
$852$	1.75971	0.0602865
$853$	−9.01075	−0.308522	−0.154261	−	0.988030i	$-0.549300\pi$
$853$	−9.01075	−0.308522	−0.154261	+	0.988030i	$0.549300\pi$
$854$	−63.2155	−2.16319
$855$	0	0
$856$	37.3142	1.27537
$857$	10.0303	0.342629	0.171315	−	0.985216i	$-0.445199\pi$
$857$	10.0303	0.342629	0.171315	+	0.985216i	$0.445199\pi$
$858$	0.767056	0.0261869
$859$	24.8891	0.849204	0.424602	−	0.905380i	$-0.360414\pi$
$859$	24.8891	0.849204	0.424602	+	0.905380i	$0.360414\pi$
$860$	−12.8671	−0.438765
$861$	−4.46090	−0.152027
$862$	−52.5678	−1.79047
$863$	−35.2512	−1.19997	−0.599983	−	0.800013i	$-0.704826\pi$
$863$	−35.2512	−1.19997	−0.599983	+	0.800013i	$0.704826\pi$
$864$	−3.88281	−0.132096
$865$	−21.1178	−0.718027
$866$	−40.1517	−1.36441
$867$	0.385200	0.0130821
$868$	8.89402	0.301883
$869$	−2.29927	−0.0779973
$870$	2.89350	0.0980989
$871$	−7.19992	−0.243960
$872$	25.2749	0.855916
$873$	−20.6582	−0.699174
$874$	0	0
$875$	7.23747	0.244671
$876$	0.131434	0.00444074
$877$	20.2240	0.682916	0.341458	−	0.939897i	$-0.389079\pi$
$877$	20.2240	0.682916	0.341458	+	0.939897i	$0.389079\pi$
$878$	16.1849	0.546213
$879$	−4.18568	−0.141180
$880$	−15.0189	−0.506288
$881$	53.6736	1.80831	0.904155	−	0.427204i	$-0.140501\pi$
$881$	53.6736	1.80831	0.904155	+	0.427204i	$0.140501\pi$
$882$	2.52740	0.0851021
$883$	−53.9771	−1.81647	−0.908237	−	0.418457i	$-0.862571\pi$
$883$	−53.9771	−1.81647	−0.908237	+	0.418457i	$0.862571\pi$
$884$	11.4771	0.386018
$885$	2.97727	0.100080
$886$	22.4574	0.754469
$887$	−31.7801	−1.06707	−0.533536	−	0.845778i	$-0.679137\pi$
$887$	−31.7801	−1.06707	−0.533536	+	0.845778i	$0.679137\pi$
$888$	0.770887	0.0258693
$889$	20.8770	0.700193
$890$	−7.37476	−0.247202
$891$	8.80754	0.295064
$892$	−4.13227	−0.138359
$893$	0	0
$894$	−2.76234	−0.0923865
$895$	7.29839	0.243958
$896$	35.7294	1.19363
$897$	2.16146	0.0721691
$898$	−49.9734	−1.66763
$899$	15.1695	0.505931
$900$	−10.2241	−0.340805
$901$	−35.8769	−1.19523
$902$	−18.7178	−0.623233
$903$	2.05315	0.0683247
$904$	−1.86178	−0.0619220
$905$	50.0629	1.66415
$906$	3.23616	0.107514
$907$	−40.3207	−1.33883	−0.669414	−	0.742890i	$-0.733455\pi$
$907$	−40.3207	−1.33883	−0.669414	+	0.742890i	$0.733455\pi$
$908$	−11.6818	−0.387675
$909$	−58.9799	−1.95624
$910$	−43.3549	−1.43720
$911$	16.2257	0.537583	0.268791	−	0.963198i	$-0.413376\pi$
$911$	16.2257	0.537583	0.268791	+	0.963198i	$0.413376\pi$
$912$	0	0
$913$	8.04434	0.266229
$914$	−12.3024	−0.406928
$915$	−6.06475	−0.200495
$916$	10.4555	0.345460
$917$	−14.7974	−0.488652
$918$	−6.52659	−0.215410
$919$	32.6377	1.07662	0.538309	−	0.842748i	$-0.319063\pi$
$919$	32.6377	1.07662	0.538309	+	0.842748i	$0.319063\pi$
$920$	−28.1559	−0.928273
$921$	2.73180	0.0900158
$922$	−10.7999	−0.355677
$923$	−44.9705	−1.48022
$924$	−0.333714	−0.0109784
$925$	11.0514	0.363368
$926$	−31.5364	−1.03635
$927$	−1.38902	−0.0456213
$928$	−17.2449	−0.566093
$929$	−11.9251	−0.391251	−0.195625	−	0.980679i	$-0.562674\pi$
$929$	−11.9251	−0.391251	−0.195625	+	0.980679i	$0.562674\pi$
$930$	2.90426	0.0952345
$931$	0	0
$932$	−17.0804	−0.559487
$933$	0.696593	0.0228054
$934$	−51.3766	−1.68109
$935$	−13.3843	−0.437715
$936$	18.2259	0.595731
$937$	31.5377	1.03029	0.515146	−	0.857102i	$-0.327738\pi$
$937$	31.5377	1.03029	0.515146	+	0.857102i	$0.327738\pi$
$938$	10.6616	0.348114
$939$	1.69333	0.0552598
$940$	22.6839	0.739866
$941$	10.0598	0.327942	0.163971	−	0.986465i	$-0.447570\pi$
$941$	10.0598	0.327942	0.163971	+	0.986465i	$0.447570\pi$
$942$	−4.41371	−0.143806
$943$	−52.7442	−1.71759
$944$	−33.4686	−1.08931
$945$	7.24341	0.235628
$946$	8.61494	0.280096
$947$	−9.22460	−0.299759	−0.149880	−	0.988704i	$-0.547889\pi$
$947$	−9.22460	−0.299759	−0.149880	+	0.988704i	$0.547889\pi$
$948$	−0.280098	−0.00909718
$949$	−3.35888	−0.109034
$950$	0	0
$951$	3.78338	0.122684
$952$	23.8559	0.773175
$953$	48.8886	1.58366	0.791829	−	0.610743i	$-0.209129\pi$
$953$	48.8886	1.58366	0.791829	+	0.610743i	$0.209129\pi$
$954$	40.5884	1.31410
$955$	66.4458	2.15013
$956$	−3.50927	−0.113498
$957$	−0.569176	−0.0183989
$958$	47.3254	1.52901
$959$	21.7431	0.702121
$960$	1.09620	0.0353796
$961$	−15.7741	−0.508842
$962$	14.0350	0.452505
$963$	−56.5470	−1.82220
$964$	−10.7734	−0.346989
$965$	27.2390	0.876853
$966$	−3.20068	−0.102980
$967$	−15.9082	−0.511572	−0.255786	−	0.966733i	$-0.582334\pi$
$967$	−15.9082	−0.511572	−0.255786	+	0.966733i	$0.582334\pi$
$968$	1.96550	0.0631734
$969$	0	0
$970$	−35.2584	−1.13208
$971$	47.1624	1.51351	0.756757	−	0.653697i	$-0.226783\pi$
$971$	47.1624	1.51351	0.756757	+	0.653697i	$0.226783\pi$
$972$	3.25788	0.104497
$973$	−0.412265	−0.0132166
$974$	−55.6018	−1.78160
$975$	−1.88037	−0.0602199
$976$	68.1763	2.18227
$977$	42.9519	1.37415	0.687077	−	0.726585i	$-0.258893\pi$
$977$	42.9519	1.37415	0.687077	+	0.726585i	$0.258893\pi$
$978$	3.76239	0.120308
$979$	1.45068	0.0463638
$980$	1.26735	0.0404840
$981$	−38.3022	−1.22290
$982$	38.3456	1.22366
$983$	32.3928	1.03317	0.516585	−	0.856236i	$-0.327203\pi$
$983$	32.3928	1.03317	0.516585	+	0.856236i	$0.327203\pi$
$984$	3.20068	0.102034
$985$	−22.4321	−0.714747
$986$	−28.9869	−0.923131
$987$	−3.61957	−0.115212
$988$	0	0
$989$	24.2758	0.771924
$990$	15.1420	0.481245
$991$	−37.8794	−1.20328	−0.601639	−	0.798768i	$-0.705485\pi$
$991$	−37.8794	−1.20328	−0.601639	+	0.798768i	$0.705485\pi$
$992$	−17.3091	−0.549563
$993$	−1.74248	−0.0552960
$994$	66.5921	2.11217
$995$	−70.3735	−2.23099
$996$	0.979967	0.0310514
$997$	2.31900	0.0734435	0.0367218	−	0.999326i	$-0.488308\pi$
$997$	2.31900	0.0734435	0.0367218	+	0.999326i	$0.488308\pi$
$998$	71.9125	2.27635
$999$	−2.34485	−0.0741879

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3971.2.a.t.1.4		21
19.6	even	9		209.2.j.b.188.1	✓	42
19.16	even	9		209.2.j.b.199.1	yes	42
19.18	odd	2		3971.2.a.s.1.18		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.2.j.b.188.1	✓	42	19.6	even	9
209.2.j.b.199.1	yes	42	19.16	even	9
3971.2.a.s.1.18		21	19.18	odd	2
3971.2.a.t.1.4		21	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:	\( N \)	\(=\)	\( 3971 = 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3971.a (trivial)

\(f(q)\)	\(=\)	\(q-1.68287 q^{2} +0.146409 q^{3} +0.832058 q^{4} +3.02083 q^{5} -0.246387 q^{6} -2.73938 q^{7} +1.96550 q^{8} -2.97856 q^{9} -5.08367 q^{10} +1.00000 q^{11} +0.121821 q^{12} -3.11321 q^{13} +4.61003 q^{14} +0.442276 q^{15} -4.97180 q^{16} -4.43069 q^{17} +5.01254 q^{18} +2.51351 q^{20} -0.401070 q^{21} -1.68287 q^{22} -4.74211 q^{23} +0.287766 q^{24} +4.12540 q^{25} +5.23914 q^{26} -0.875315 q^{27} -2.27933 q^{28} -3.88758 q^{29} -0.744294 q^{30} -3.90204 q^{31} +4.43590 q^{32} +0.146409 q^{33} +7.45628 q^{34} -8.27520 q^{35} -2.47834 q^{36} +2.67887 q^{37} -0.455802 q^{39} +5.93743 q^{40} +11.1225 q^{41} +0.674949 q^{42} -5.11919 q^{43} +0.832058 q^{44} -8.99773 q^{45} +7.98036 q^{46} +9.02479 q^{47} -0.727915 q^{48} +0.504216 q^{49} -6.94252 q^{50} -0.648692 q^{51} -2.59037 q^{52} +8.09736 q^{53} +1.47304 q^{54} +3.02083 q^{55} -5.38425 q^{56} +6.54230 q^{58} +6.73170 q^{59} +0.367999 q^{60} -13.7126 q^{61} +6.56663 q^{62} +8.15943 q^{63} +2.47853 q^{64} -9.40448 q^{65} -0.246387 q^{66} +2.31270 q^{67} -3.68659 q^{68} -0.694287 q^{69} +13.9261 q^{70} +14.4450 q^{71} -5.85436 q^{72} +1.07891 q^{73} -4.50819 q^{74} +0.603995 q^{75} -2.73938 q^{77} +0.767056 q^{78} -2.29927 q^{79} -15.0189 q^{80} +8.80754 q^{81} -18.7178 q^{82} +8.04434 q^{83} -0.333714 q^{84} -13.3843 q^{85} +8.61494 q^{86} -0.569176 q^{87} +1.96550 q^{88} +1.45068 q^{89} +15.1420 q^{90} +8.52828 q^{91} -3.94571 q^{92} -0.571293 q^{93} -15.1876 q^{94} +0.649456 q^{96} +6.93562 q^{97} -0.848531 q^{98} -2.97856 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 6 q^{2} + 15 q^{3} + 18 q^{4} + 6 q^{5} - 6 q^{6} + 6 q^{7} + 15 q^{8} + 18 q^{9} - 6 q^{10} + 21 q^{11} + 30 q^{12} + 36 q^{13} + 12 q^{14} + 12 q^{15} + 12 q^{16} + 21 q^{17} + 6 q^{18} + 15 q^{20}+ \cdots + 18 q^{99}+O(q^{100}) \) 21 * q + 6 * q^2 + 15 * q^3 + 18 * q^4 + 6 * q^5 - 6 * q^6 + 6 * q^7 + 15 * q^8 + 18 * q^9 - 6 * q^10 + 21 * q^11 + 30 * q^12 + 36 * q^13 + 12 * q^14 + 12 * q^15 + 12 * q^16 + 21 * q^17 + 6 * q^18 + 15 * q^20 - 3 * q^21 + 6 * q^22 + 6 * q^23 - 18 * q^24 + 3 * q^25 + 6 * q^26 + 24 * q^27 + 27 * q^29 - 30 * q^30 + 54 * q^31 + 21 * q^32 + 15 * q^33 + 39 * q^34 - 33 * q^35 + 54 * q^36 + 57 * q^37 - 27 * q^40 + 24 * q^41 + 6 * q^42 + 12 * q^43 + 18 * q^44 - 3 * q^45 + 15 * q^46 + 12 * q^47 - 39 * q^48 + 21 * q^49 + 33 * q^50 - 18 * q^51 - 18 * q^52 + 39 * q^53 + 30 * q^54 + 6 * q^55 + 57 * q^56 + 30 * q^58 + 27 * q^59 + 12 * q^60 - 30 * q^61 + 21 * q^62 - 18 * q^63 - 15 * q^64 - 24 * q^65 - 6 * q^66 + 27 * q^67 - 48 * q^68 + 54 * q^69 + 51 * q^70 + 42 * q^71 + 15 * q^72 + 6 * q^73 + 84 * q^74 + 27 * q^75 + 6 * q^77 - 48 * q^78 + 39 * q^79 - 27 * q^80 - 27 * q^81 - 15 * q^82 + 12 * q^83 - 48 * q^84 - 42 * q^85 - 45 * q^86 + 75 * q^87 + 15 * q^88 + 75 * q^89 - 87 * q^90 + 45 * q^91 + 12 * q^92 + 66 * q^93 + 42 * q^94 - 3 * q^96 + 39 * q^97 - 45 * q^98 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

Properties

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