LMFDB - Embedded newform 7381.2.a.v.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7381,2,Mod(1,7381)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7381, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("7381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7381 = 11^{2} \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7381.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$58.9375817319$
Analytic rank:	$0$
Dimension:	$64$
Twist minimal:	no (minimal twist has level 671)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	7381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.10438 q^{2} -2.04639 q^{3} +2.42841 q^{4} +2.55130 q^{5} +4.30637 q^{6} +3.75742 q^{7} -0.901543 q^{8} +1.18769 q^{9} +O(q^{10})$	\(q-2.10438 q^{2} -2.04639 q^{3} +2.42841 q^{4} +2.55130 q^{5} +4.30637 q^{6} +3.75742 q^{7} -0.901543 q^{8} +1.18769 q^{9} -5.36890 q^{10} -4.96947 q^{12} +4.57358 q^{13} -7.90705 q^{14} -5.22094 q^{15} -2.95964 q^{16} +3.31839 q^{17} -2.49935 q^{18} +4.20479 q^{19} +6.19561 q^{20} -7.68914 q^{21} +6.43489 q^{23} +1.84491 q^{24} +1.50913 q^{25} -9.62456 q^{26} +3.70868 q^{27} +9.12458 q^{28} -3.81423 q^{29} +10.9868 q^{30} -3.81157 q^{31} +8.03128 q^{32} -6.98315 q^{34} +9.58632 q^{35} +2.88421 q^{36} +3.02517 q^{37} -8.84846 q^{38} -9.35931 q^{39} -2.30011 q^{40} -6.38496 q^{41} +16.1809 q^{42} -8.90134 q^{43} +3.03016 q^{45} -13.5414 q^{46} +4.32544 q^{47} +6.05656 q^{48} +7.11823 q^{49} -3.17578 q^{50} -6.79070 q^{51} +11.1066 q^{52} +1.65525 q^{53} -7.80447 q^{54} -3.38748 q^{56} -8.60461 q^{57} +8.02658 q^{58} +1.42242 q^{59} -12.6786 q^{60} +1.00000 q^{61} +8.02099 q^{62} +4.46266 q^{63} -10.9816 q^{64} +11.6686 q^{65} +13.3462 q^{67} +8.05842 q^{68} -13.1683 q^{69} -20.1732 q^{70} +5.86076 q^{71} -1.07076 q^{72} +5.92160 q^{73} -6.36610 q^{74} -3.08826 q^{75} +10.2110 q^{76} +19.6955 q^{78} -5.87622 q^{79} -7.55092 q^{80} -11.1525 q^{81} +13.4364 q^{82} -7.55980 q^{83} -18.6724 q^{84} +8.46621 q^{85} +18.7318 q^{86} +7.80538 q^{87} +10.2868 q^{89} -6.37660 q^{90} +17.1849 q^{91} +15.6266 q^{92} +7.79994 q^{93} -9.10236 q^{94} +10.7277 q^{95} -16.4351 q^{96} -3.56035 q^{97} -14.9795 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9}+O(q^{10}) $ 64 * q + 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 - q^6 + 6 * q^7 + 3 * q^8 + 81 * q^9	\( 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9} - 4 q^{10} + 41 q^{12} - q^{13} + 41 q^{14} + 28 q^{15} + 107 q^{16} + 13 q^{17} + 38 q^{18} - q^{19} + 65 q^{20} + q^{21} + 52 q^{23} + 3 q^{24} + 87 q^{25} + 37 q^{26} + 88 q^{27} - q^{28} + 19 q^{29} - 19 q^{30} + 45 q^{31} - 24 q^{32} - 23 q^{34} + 10 q^{35} + 146 q^{36} + 26 q^{37} - 4 q^{38} - 6 q^{39} + 84 q^{40} - 12 q^{41} + 28 q^{42} + 5 q^{43} + 71 q^{45} - 5 q^{46} + 63 q^{47} + 85 q^{48} + 78 q^{49} + 14 q^{50} + 22 q^{51} - 24 q^{52} + 86 q^{53} - 114 q^{54} + 119 q^{56} - 29 q^{57} + q^{58} + 119 q^{59} - 22 q^{60} + 64 q^{61} + 13 q^{62} - 28 q^{63} + 135 q^{64} - 30 q^{65} + 2 q^{67} + 59 q^{68} + 63 q^{69} - 2 q^{70} + 126 q^{71} + 48 q^{72} + 8 q^{73} - 27 q^{74} + 107 q^{75} - 82 q^{76} - 13 q^{78} - 5 q^{79} + 119 q^{80} + 96 q^{81} - 27 q^{82} + 14 q^{83} + 182 q^{84} - 52 q^{85} + 60 q^{86} - 8 q^{87} + 59 q^{89} - 45 q^{90} + 83 q^{91} + 111 q^{92} - 7 q^{93} + 21 q^{94} - 26 q^{95} - 86 q^{96} - 39 q^{97} - 57 q^{98}+O(q^{100}) \) 64 * q + 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 - q^6 + 6 * q^7 + 3 * q^8 + 81 * q^9 - 4 * q^10 + 41 * q^12 - q^13 + 41 * q^14 + 28 * q^15 + 107 * q^16 + 13 * q^17 + 38 * q^18 - q^19 + 65 * q^20 + q^21 + 52 * q^23 + 3 * q^24 + 87 * q^25 + 37 * q^26 + 88 * q^27 - q^28 + 19 * q^29 - 19 * q^30 + 45 * q^31 - 24 * q^32 - 23 * q^34 + 10 * q^35 + 146 * q^36 + 26 * q^37 - 4 * q^38 - 6 * q^39 + 84 * q^40 - 12 * q^41 + 28 * q^42 + 5 * q^43 + 71 * q^45 - 5 * q^46 + 63 * q^47 + 85 * q^48 + 78 * q^49 + 14 * q^50 + 22 * q^51 - 24 * q^52 + 86 * q^53 - 114 * q^54 + 119 * q^56 - 29 * q^57 + q^58 + 119 * q^59 - 22 * q^60 + 64 * q^61 + 13 * q^62 - 28 * q^63 + 135 * q^64 - 30 * q^65 + 2 * q^67 + 59 * q^68 + 63 * q^69 - 2 * q^70 + 126 * q^71 + 48 * q^72 + 8 * q^73 - 27 * q^74 + 107 * q^75 - 82 * q^76 - 13 * q^78 - 5 * q^79 + 119 * q^80 + 96 * q^81 - 27 * q^82 + 14 * q^83 + 182 * q^84 - 52 * q^85 + 60 * q^86 - 8 * q^87 + 59 * q^89 - 45 * q^90 + 83 * q^91 + 111 * q^92 - 7 * q^93 + 21 * q^94 - 26 * q^95 - 86 * q^96 - 39 * q^97 - 57 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	−2.10438	−1.48802	−0.744010	−	0.668168i	$-0.767079\pi$
$2$	−2.10438	−1.48802	−0.744010	+	0.668168i	$0.767079\pi$
$3$	−2.04639	−1.18148	−0.590741	−	0.806862i	$-0.701164\pi$
$3$	−2.04639	−1.18148	−0.590741	+	0.806862i	$0.701164\pi$
$4$	2.42841	1.21421
$5$	2.55130	1.14098	0.570488	−	0.821306i	$-0.306754\pi$
$5$	2.55130	1.14098	0.570488	+	0.821306i	$0.306754\pi$
$6$	4.30637	1.75807
$7$	3.75742	1.42017	0.710086	−	0.704115i	$-0.248656\pi$
$7$	3.75742	1.42017	0.710086	+	0.704115i	$0.248656\pi$
$8$	−0.901543	−0.318744
$9$	1.18769	0.395897
$10$	−5.36890	−1.69780
$11$	0	0
$11$	0	0
$12$	−4.96947	−1.43456
$13$	4.57358	1.26848	0.634242	−	0.773135i	$-0.281312\pi$
$13$	4.57358	1.26848	0.634242	+	0.773135i	$0.281312\pi$
$14$	−7.90705	−2.11325
$15$	−5.22094	−1.34804
$16$	−2.95964	−0.739909
$17$	3.31839	0.804828	0.402414	−	0.915458i	$-0.368171\pi$
$17$	3.31839	0.804828	0.402414	+	0.915458i	$0.368171\pi$
$18$	−2.49935	−0.589104
$19$	4.20479	0.964644	0.482322	−	0.875994i	$-0.339794\pi$
$19$	4.20479	0.964644	0.482322	+	0.875994i	$0.339794\pi$
$20$	6.19561	1.38538
$21$	−7.68914	−1.67791
$22$	0	0
$23$	6.43489	1.34177	0.670883	−	0.741563i	$-0.265915\pi$
$23$	6.43489	1.34177	0.670883	+	0.741563i	$0.265915\pi$
$24$	1.84491	0.376590
$25$	1.50913	0.301826
$26$	−9.62456	−1.88753
$27$	3.70868	0.713736
$28$	9.12458	1.72438
$29$	−3.81423	−0.708284	−0.354142	−	0.935192i	$-0.615227\pi$
$29$	−3.81423	−0.708284	−0.354142	+	0.935192i	$0.615227\pi$
$30$	10.9868	2.00591
$31$	−3.81157	−0.684579	−0.342289	−	0.939595i	$-0.611202\pi$
$31$	−3.81157	−0.684579	−0.342289	+	0.939595i	$0.611202\pi$
$32$	8.03128	1.41974
$33$	0	0
$34$	−6.98315	−1.19760
$35$	9.58632	1.62038
$36$	2.88421	0.480701
$37$	3.02517	0.497334	0.248667	−	0.968589i	$-0.420007\pi$
$37$	3.02517	0.497334	0.248667	+	0.968589i	$0.420007\pi$
$38$	−8.84846	−1.43541
$39$	−9.35931	−1.49869
$40$	−2.30011	−0.363679
$41$	−6.38496	−0.997163	−0.498582	−	0.866843i	$-0.666146\pi$
$41$	−6.38496	−0.997163	−0.498582	+	0.866843i	$0.666146\pi$
$42$	16.1809	2.49676
$43$	−8.90134	−1.35744	−0.678721	−	0.734396i	$-0.737465\pi$
$43$	−8.90134	−1.35744	−0.678721	+	0.734396i	$0.737465\pi$
$44$	0	0
$45$	3.03016	0.451709
$46$	−13.5414	−1.99658
$47$	4.32544	0.630930	0.315465	−	0.948937i	$-0.397840\pi$
$47$	4.32544	0.630930	0.315465	+	0.948937i	$0.397840\pi$
$48$	6.05656	0.874189
$49$	7.11823	1.01689
$50$	−3.17578	−0.449124
$51$	−6.79070	−0.950888
$52$	11.1066	1.54020
$53$	1.65525	0.227366	0.113683	−	0.993517i	$-0.463735\pi$
$53$	1.65525	0.227366	0.113683	+	0.993517i	$0.463735\pi$
$54$	−7.80447	−1.06205
$55$	0	0
$56$	−3.38748	−0.452671
$57$	−8.60461	−1.13971
$58$	8.02658	1.05394
$59$	1.42242	0.185183	0.0925914	−	0.995704i	$-0.470485\pi$
$59$	1.42242	0.185183	0.0925914	+	0.995704i	$0.470485\pi$
$60$	−12.6786	−1.63680
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	8.02099	1.01867
$63$	4.46266	0.562243
$64$	−10.9816	−1.37270
$65$	11.6686	1.44731
$66$	0	0
$67$	13.3462	1.63050	0.815250	−	0.579109i	$-0.196599\pi$
$67$	13.3462	1.63050	0.815250	+	0.579109i	$0.196599\pi$
$68$	8.05842	0.977227
$69$	−13.1683	−1.58527
$70$	−20.1732	−2.41116
$71$	5.86076	0.695544	0.347772	−	0.937579i	$-0.386938\pi$
$71$	5.86076	0.695544	0.347772	+	0.937579i	$0.386938\pi$
$72$	−1.07076	−0.126190
$73$	5.92160	0.693071	0.346536	−	0.938037i	$-0.387358\pi$
$73$	5.92160	0.693071	0.346536	+	0.938037i	$0.387358\pi$
$74$	−6.36610	−0.740044
$75$	−3.08826	−0.356602
$76$	10.2110	1.17128
$77$	0	0
$78$	19.6955	2.23008
$79$	−5.87622	−0.661126	−0.330563	−	0.943784i	$-0.607239\pi$
$79$	−5.87622	−0.661126	−0.330563	+	0.943784i	$0.607239\pi$
$80$	−7.55092	−0.844219
$81$	−11.1525	−1.23916
$82$	13.4364	1.48380
$83$	−7.55980	−0.829796	−0.414898	−	0.909868i	$-0.636183\pi$
$83$	−7.55980	−0.829796	−0.414898	+	0.909868i	$0.636183\pi$
$84$	−18.6724	−2.03733
$85$	8.46621	0.918289
$86$	18.7318	2.01990
$87$	7.80538	0.836824
$88$	0	0
$89$	10.2868	1.09040	0.545198	−	0.838307i	$-0.316454\pi$
$89$	10.2868	1.09040	0.545198	+	0.838307i	$0.316454\pi$
$90$	−6.37660	−0.672153
$91$	17.1849	1.80147
$92$	15.6266	1.62918
$93$	7.79994	0.808817
$94$	−9.10236	−0.938836
$95$	10.7277	1.10064
$96$	−16.4351	−1.67740
$97$	−3.56035	−0.361499	−0.180749	−	0.983529i	$-0.557852\pi$
$97$	−3.56035	−0.361499	−0.180749	+	0.983529i	$0.557852\pi$
$98$	−14.9795	−1.51315
$99$	0	0
$100$	3.66479	0.366479
$101$	1.99672	0.198681	0.0993405	−	0.995053i	$-0.468327\pi$
$101$	1.99672	0.198681	0.0993405	+	0.995053i	$0.468327\pi$
$102$	14.2902	1.41494
$103$	3.08800	0.304270	0.152135	−	0.988360i	$-0.451385\pi$
$103$	3.08800	0.304270	0.152135	+	0.988360i	$0.451385\pi$
$104$	−4.12328	−0.404321
$105$	−19.6173	−1.91445
$106$	−3.48327	−0.338325
$107$	−7.32227	−0.707871	−0.353935	−	0.935270i	$-0.615157\pi$
$107$	−7.32227	−0.707871	−0.353935	+	0.935270i	$0.615157\pi$
$108$	9.00621	0.866623
$109$	−0.927090	−0.0887991	−0.0443996	−	0.999014i	$-0.514137\pi$
$109$	−0.927090	−0.0887991	−0.0443996	+	0.999014i	$0.514137\pi$
$110$	0	0
$111$	−6.19065	−0.587591
$112$	−11.1206	−1.05080
$113$	19.4586	1.83052	0.915258	−	0.402869i	$-0.131987\pi$
$113$	19.4586	1.83052	0.915258	+	0.402869i	$0.131987\pi$
$114$	18.1074	1.69591
$115$	16.4173	1.53092
$116$	−9.26252	−0.860003
$117$	5.43201	0.502189
$118$	−2.99330	−0.275556
$119$	12.4686	1.14299
$120$	4.70691	0.429680
$121$	0	0
$122$	−2.10438	−0.190522
$123$	13.0661	1.17813
$124$	−9.25607	−0.831220
$125$	−8.90625	−0.796599
$126$	−9.39114	−0.836629
$127$	18.1310	1.60887	0.804435	−	0.594041i	$-0.202468\pi$
$127$	18.1310	1.60887	0.804435	+	0.594041i	$0.202468\pi$
$128$	7.04688	0.622862
$129$	18.2156	1.60379
$130$	−24.5551	−2.15363
$131$	0.130245	0.0113796	0.00568979	−	0.999984i	$-0.498189\pi$
$131$	0.130245	0.0113796	0.00568979	+	0.999984i	$0.498189\pi$
$132$	0	0
$133$	15.7992	1.36996
$134$	−28.0855	−2.42622
$135$	9.46195	0.814355
$136$	−2.99167	−0.256534
$137$	15.0415	1.28508	0.642542	−	0.766250i	$-0.277880\pi$
$137$	15.0415	1.28508	0.642542	+	0.766250i	$0.277880\pi$
$138$	27.7110	2.35892
$139$	−1.36407	−0.115699	−0.0578495	−	0.998325i	$-0.518424\pi$
$139$	−1.36407	−0.115699	−0.0578495	+	0.998325i	$0.518424\pi$
$140$	23.2795	1.96748
$141$	−8.85151	−0.745431
$142$	−12.3333	−1.03498
$143$	0	0
$144$	−3.51514	−0.292928
$145$	−9.73124	−0.808135
$146$	−12.4613	−1.03130
$147$	−14.5666	−1.20144
$148$	7.34635	0.603866
$149$	15.3129	1.25448	0.627239	−	0.778827i	$-0.284185\pi$
$149$	15.3129	1.25448	0.627239	+	0.778827i	$0.284185\pi$
$150$	6.49888	0.530631
$151$	2.48840	0.202503	0.101252	−	0.994861i	$-0.467715\pi$
$151$	2.48840	0.202503	0.101252	+	0.994861i	$0.467715\pi$
$152$	−3.79080	−0.307474
$153$	3.94122	0.318629
$154$	0	0
$155$	−9.72446	−0.781088
$156$	−22.7283	−1.81972
$157$	2.35511	0.187959	0.0939793	−	0.995574i	$-0.470041\pi$
$157$	2.35511	0.187959	0.0939793	+	0.995574i	$0.470041\pi$
$158$	12.3658	0.983770
$159$	−3.38727	−0.268628
$160$	20.4902	1.61989
$161$	24.1786	1.90554
$162$	23.4690	1.84390
$163$	−10.9962	−0.861287	−0.430644	−	0.902522i	$-0.641713\pi$
$163$	−10.9962	−0.861287	−0.430644	+	0.902522i	$0.641713\pi$
$164$	−15.5053	−1.21076
$165$	0	0
$166$	15.9087	1.23475
$167$	−8.78437	−0.679755	−0.339878	−	0.940470i	$-0.610386\pi$
$167$	−8.78437	−0.679755	−0.339878	+	0.940470i	$0.610386\pi$
$168$	6.93209	0.534822
$169$	7.91767	0.609052
$170$	−17.8161	−1.36643
$171$	4.99399	0.381900
$172$	−21.6161	−1.64821
$173$	25.6668	1.95141	0.975704	−	0.219095i	$-0.0703105\pi$
$173$	25.6668	1.95141	0.975704	+	0.219095i	$0.0703105\pi$
$174$	−16.4255	−1.24521
$175$	5.67045	0.428645
$176$	0	0
$177$	−2.91081	−0.218790
$178$	−21.6473	−1.62253
$179$	24.4547	1.82783	0.913915	−	0.405906i	$-0.133044\pi$
$179$	24.4547	1.82783	0.913915	+	0.405906i	$0.133044\pi$
$180$	7.35848	0.548468
$181$	−25.0288	−1.86038	−0.930189	−	0.367081i	$-0.880357\pi$
$181$	−25.0288	−1.86038	−0.930189	+	0.367081i	$0.880357\pi$
$182$	−36.1635	−2.68062
$183$	−2.04639	−0.151273
$184$	−5.80133	−0.427680
$185$	7.71811	0.567446
$186$	−16.4140	−1.20354
$187$	0	0
$188$	10.5039	0.766079
$189$	13.9351	1.01363
$190$	−22.5751	−1.63777
$191$	−24.2774	−1.75665	−0.878327	−	0.478060i	$-0.841340\pi$
$191$	−24.2774	−1.75665	−0.878327	+	0.478060i	$0.841340\pi$
$192$	22.4726	1.62182
$193$	18.9681	1.36536	0.682678	−	0.730719i	$-0.260815\pi$
$193$	18.9681	1.36536	0.682678	+	0.730719i	$0.260815\pi$
$194$	7.49233	0.537918
$195$	−23.8784	−1.70997
$196$	17.2860	1.23472
$197$	7.97079	0.567895	0.283948	−	0.958840i	$-0.408356\pi$
$197$	7.97079	0.567895	0.283948	+	0.958840i	$0.408356\pi$
$198$	0	0
$199$	−22.7745	−1.61444	−0.807222	−	0.590248i	$-0.799030\pi$
$199$	−22.7745	−1.61444	−0.807222	+	0.590248i	$0.799030\pi$
$200$	−1.36055	−0.0962052
$201$	−27.3115	−1.92641
$202$	−4.20186	−0.295642
$203$	−14.3317	−1.00589
$204$	−16.4906	−1.15457
$205$	−16.2899	−1.13774
$206$	−6.49833	−0.452760
$207$	7.64267	0.531202
$208$	−13.5361	−0.938563
$209$	0	0
$210$	41.2822	2.84874
$211$	−18.6957	−1.28707	−0.643533	−	0.765418i	$-0.722532\pi$
$211$	−18.6957	−1.28707	−0.643533	+	0.765418i	$0.722532\pi$
$212$	4.01962	0.276069
$213$	−11.9934	−0.821773
$214$	15.4088	1.05333
$215$	−22.7100	−1.54881
$216$	−3.34354	−0.227499
$217$	−14.3217	−0.972220
$218$	1.95095	0.132135
$219$	−12.1179	−0.818851
$220$	0	0
$221$	15.1769	1.02091
$222$	13.0275	0.874348
$223$	−2.50249	−0.167579	−0.0837897	−	0.996483i	$-0.526702\pi$
$223$	−2.50249	−0.167579	−0.0837897	+	0.996483i	$0.526702\pi$
$224$	30.1769	2.01628
$225$	1.79238	0.119492
$226$	−40.9484	−2.72385
$227$	−2.81372	−0.186753	−0.0933767	−	0.995631i	$-0.529766\pi$
$227$	−2.81372	−0.186753	−0.0933767	+	0.995631i	$0.529766\pi$
$228$	−20.8955	−1.38384
$229$	18.0037	1.18972	0.594859	−	0.803830i	$-0.297208\pi$
$229$	18.0037	1.18972	0.594859	+	0.803830i	$0.297208\pi$
$230$	−34.5483	−2.27805
$231$	0	0
$232$	3.43869	0.225761
$233$	−25.8250	−1.69185	−0.845925	−	0.533302i	$-0.820951\pi$
$233$	−25.8250	−1.69185	−0.845925	+	0.533302i	$0.820951\pi$
$234$	−11.4310	−0.747268
$235$	11.0355	0.719876
$236$	3.45422	0.224850
$237$	12.0250	0.781108
$238$	−26.2387	−1.70080
$239$	5.28225	0.341680	0.170840	−	0.985299i	$-0.445352\pi$
$239$	5.28225	0.341680	0.170840	+	0.985299i	$0.445352\pi$
$240$	15.4521	0.997428
$241$	−23.5563	−1.51739	−0.758697	−	0.651443i	$-0.774164\pi$
$241$	−23.5563	−1.51739	−0.758697	+	0.651443i	$0.774164\pi$
$242$	0	0
$243$	11.6962	0.750311
$244$	2.42841	0.155463
$245$	18.1607	1.16025
$246$	−27.4960	−1.75308
$247$	19.2309	1.22364
$248$	3.43630	0.218205
$249$	15.4703	0.980388
$250$	18.7421	1.18536
$251$	12.5147	0.789918	0.394959	−	0.918699i	$-0.370759\pi$
$251$	12.5147	0.789918	0.394959	+	0.918699i	$0.370759\pi$
$252$	10.8372	0.682679
$253$	0	0
$254$	−38.1546	−2.39403
$255$	−17.3251	−1.08494
$256$	7.13389	0.445868
$257$	−17.4583	−1.08902	−0.544511	−	0.838754i	$-0.683285\pi$
$257$	−17.4583	−1.08902	−0.544511	+	0.838754i	$0.683285\pi$
$258$	−38.3325	−2.38648
$259$	11.3668	0.706301
$260$	28.3361	1.75733
$261$	−4.53013	−0.280408
$262$	−0.274085	−0.0169330
$263$	2.83194	0.174625	0.0873124	−	0.996181i	$-0.472172\pi$
$263$	2.83194	0.174625	0.0873124	+	0.996181i	$0.472172\pi$
$264$	0	0
$265$	4.22303	0.259419
$266$	−33.2474	−2.03853
$267$	−21.0507	−1.28828
$268$	32.4101	1.97976
$269$	−22.9866	−1.40152	−0.700758	−	0.713399i	$-0.747155\pi$
$269$	−22.9866	−1.40152	−0.700758	+	0.713399i	$0.747155\pi$
$270$	−19.9115	−1.21178
$271$	−15.4822	−0.940478	−0.470239	−	0.882539i	$-0.655832\pi$
$271$	−15.4822	−0.940478	−0.470239	+	0.882539i	$0.655832\pi$
$272$	−9.82122	−0.595499
$273$	−35.1669	−2.12840
$274$	−31.6531	−1.91223
$275$	0	0
$276$	−31.9780	−1.92485
$277$	−2.11468	−0.127059	−0.0635293	−	0.997980i	$-0.520236\pi$
$277$	−2.11468	−0.127059	−0.0635293	+	0.997980i	$0.520236\pi$
$278$	2.87052	0.172163
$279$	−4.52697	−0.271023
$280$	−8.64248	−0.516487
$281$	−16.4766	−0.982912	−0.491456	−	0.870903i	$-0.663535\pi$
$281$	−16.4766	−0.982912	−0.491456	+	0.870903i	$0.663535\pi$
$282$	18.6269	1.10922
$283$	−7.92549	−0.471121	−0.235561	−	0.971860i	$-0.575693\pi$
$283$	−7.92549	−0.471121	−0.235561	+	0.971860i	$0.575693\pi$
$284$	14.2323	0.844535
$285$	−21.9529	−1.30038
$286$	0	0
$287$	−23.9910	−1.41614
$288$	9.53869	0.562073
$289$	−5.98829	−0.352253
$290$	20.4782	1.20252
$291$	7.28585	0.427104
$292$	14.3801	0.841532
$293$	13.1957	0.770902	0.385451	−	0.922728i	$-0.374046\pi$
$293$	13.1957	0.770902	0.385451	+	0.922728i	$0.374046\pi$
$294$	30.6538	1.78776
$295$	3.62901	0.211289
$296$	−2.72732	−0.158522
$297$	0	0
$298$	−32.2241	−1.86669
$299$	29.4305	1.70201
$300$	−7.49958	−0.432988
$301$	−33.4461	−1.92780
$302$	−5.23655	−0.301329
$303$	−4.08606	−0.234738
$304$	−12.4446	−0.713749
$305$	2.55130	0.146087
$306$	−8.29383	−0.474127
$307$	24.9862	1.42604	0.713018	−	0.701146i	$-0.247328\pi$
$307$	24.9862	1.42604	0.713018	+	0.701146i	$0.247328\pi$
$308$	0	0
$309$	−6.31924	−0.359489
$310$	20.4640	1.16227
$311$	28.5564	1.61929	0.809643	−	0.586923i	$-0.199661\pi$
$311$	28.5564	1.61929	0.809643	+	0.586923i	$0.199661\pi$
$312$	8.43783	0.477698
$313$	−21.7575	−1.22981	−0.614903	−	0.788603i	$-0.710805\pi$
$313$	−21.7575	−1.22981	−0.614903	+	0.788603i	$0.710805\pi$
$314$	−4.95605	−0.279686
$315$	11.3856	0.641505
$316$	−14.2699	−0.802744
$317$	−28.8829	−1.62223	−0.811113	−	0.584889i	$-0.801138\pi$
$317$	−28.8829	−1.62223	−0.811113	+	0.584889i	$0.801138\pi$
$318$	7.12811	0.399724
$319$	0	0
$320$	−28.0174	−1.56622
$321$	14.9842	0.836336
$322$	−50.8810	−2.83548
$323$	13.9531	0.776372
$324$	−27.0828	−1.50460
$325$	6.90214	0.382862
$326$	23.1401	1.28161
$327$	1.89718	0.104914
$328$	5.75632	0.317839
$329$	16.2525	0.896029
$330$	0	0
$331$	31.1914	1.71443	0.857216	−	0.514957i	$-0.172192\pi$
$331$	31.1914	1.71443	0.857216	+	0.514957i	$0.172192\pi$
$332$	−18.3583	−1.00754
$333$	3.59297	0.196893
$334$	18.4857	1.01149
$335$	34.0502	1.86036
$336$	22.7570	1.24150
$337$	−29.2652	−1.59418	−0.797088	−	0.603863i	$-0.793627\pi$
$337$	−29.2652	−1.59418	−0.797088	+	0.603863i	$0.793627\pi$
$338$	−16.6618	−0.906282
$339$	−39.8199	−2.16272
$340$	20.5594	1.11499
$341$	0	0
$342$	−10.5093	−0.568275
$343$	0.444255	0.0239875
$344$	8.02494	0.432676
$345$	−33.5962	−1.80876
$346$	−54.0126	−2.90373
$347$	3.34524	0.179582	0.0897909	−	0.995961i	$-0.471380\pi$
$347$	3.34524	0.179582	0.0897909	+	0.995961i	$0.471380\pi$
$348$	18.9547	1.01608
$349$	−25.7880	−1.38040	−0.690201	−	0.723618i	$-0.742478\pi$
$349$	−25.7880	−1.38040	−0.690201	+	0.723618i	$0.742478\pi$
$350$	−11.9328	−0.637833
$351$	16.9620	0.905362
$352$	0	0
$353$	9.18321	0.488773	0.244387	−	0.969678i	$-0.421413\pi$
$353$	9.18321	0.488773	0.244387	+	0.969678i	$0.421413\pi$
$354$	6.12545	0.325564
$355$	14.9526	0.793600
$356$	24.9805	1.32397
$357$	−25.5155	−1.35043
$358$	−51.4620	−2.71985
$359$	−18.8408	−0.994380	−0.497190	−	0.867642i	$-0.665635\pi$
$359$	−18.8408	−0.994380	−0.497190	+	0.867642i	$0.665635\pi$
$360$	−2.73182	−0.143980
$361$	−1.31978	−0.0694622
$362$	52.6701	2.76828
$363$	0	0
$364$	41.7320	2.18735
$365$	15.1078	0.790778
$366$	4.30637	0.225098
$367$	37.9788	1.98248	0.991239	−	0.132082i	$-0.0421662\pi$
$367$	37.9788	1.98248	0.991239	+	0.132082i	$0.0421662\pi$
$368$	−19.0449	−0.992786
$369$	−7.58337	−0.394774
$370$	−16.2418	−0.844372
$371$	6.21946	0.322898
$372$	18.9415	0.982070
$373$	−24.1240	−1.24909	−0.624546	−	0.780988i	$-0.714716\pi$
$373$	−24.1240	−1.24909	−0.624546	+	0.780988i	$0.714716\pi$
$374$	0	0
$375$	18.2256	0.941167
$376$	−3.89957	−0.201105
$377$	−17.4447	−0.898447
$378$	−29.3247	−1.50830
$379$	38.1041	1.95728	0.978639	−	0.205585i	$-0.0659097\pi$
$379$	38.1041	1.95728	0.978639	+	0.205585i	$0.0659097\pi$
$380$	26.0512	1.33640
$381$	−37.1031	−1.90085
$382$	51.0889	2.61394
$383$	−8.90836	−0.455196	−0.227598	−	0.973755i	$-0.573087\pi$
$383$	−8.90836	−0.455196	−0.227598	+	0.973755i	$0.573087\pi$
$384$	−14.4206	−0.735900
$385$	0	0
$386$	−39.9161	−2.03168
$387$	−10.5720	−0.537407
$388$	−8.64600	−0.438934
$389$	−17.1457	−0.869323	−0.434662	−	0.900594i	$-0.643132\pi$
$389$	−17.1457	−0.869323	−0.434662	+	0.900594i	$0.643132\pi$
$390$	50.2493	2.54447
$391$	21.3535	1.07989
$392$	−6.41740	−0.324128
$393$	−0.266532	−0.0134448
$394$	−16.7736	−0.845040
$395$	−14.9920	−0.754329
$396$	0	0
$397$	−14.8749	−0.746550	−0.373275	−	0.927721i	$-0.621765\pi$
$397$	−14.8749	−0.746550	−0.373275	+	0.927721i	$0.621765\pi$
$398$	47.9263	2.40233
$399$	−32.3312	−1.61858
$400$	−4.46648	−0.223324
$401$	3.81168	0.190346	0.0951732	−	0.995461i	$-0.469660\pi$
$401$	3.81168	0.190346	0.0951732	+	0.995461i	$0.469660\pi$
$402$	57.4738	2.86653
$403$	−17.4325	−0.868377
$404$	4.84886	0.241240
$405$	−28.4533	−1.41385
$406$	30.1593	1.49678
$407$	0	0
$408$	6.12211	0.303090
$409$	−21.2860	−1.05253	−0.526263	−	0.850322i	$-0.676407\pi$
$409$	−21.2860	−1.05253	−0.526263	+	0.850322i	$0.676407\pi$
$410$	34.2802	1.69298
$411$	−30.7808	−1.51830
$412$	7.49894	0.369446
$413$	5.34462	0.262992
$414$	−16.0831	−0.790440
$415$	−19.2873	−0.946777
$416$	36.7318	1.80092
$417$	2.79141	0.136696
$418$	0	0
$419$	15.9167	0.777579	0.388790	−	0.921327i	$-0.372893\pi$
$419$	15.9167	0.777579	0.388790	+	0.921327i	$0.372893\pi$
$420$	−47.6389	−2.32454
$421$	5.70967	0.278272	0.139136	−	0.990273i	$-0.455567\pi$
$421$	5.70967	0.278272	0.139136	+	0.990273i	$0.455567\pi$
$422$	39.3429	1.91518
$423$	5.13729	0.249783
$424$	−1.49228	−0.0724714
$425$	5.00788	0.242918
$426$	25.2386	1.22281
$427$	3.75742	0.181834
$428$	−17.7815	−0.859501
$429$	0	0
$430$	47.7904	2.30466
$431$	35.8390	1.72630	0.863151	−	0.504945i	$-0.168487\pi$
$431$	35.8390	1.72630	0.863151	+	0.504945i	$0.168487\pi$
$432$	−10.9763	−0.528100
$433$	26.3138	1.26456	0.632281	−	0.774739i	$-0.282119\pi$
$433$	26.3138	1.26456	0.632281	+	0.774739i	$0.282119\pi$
$434$	30.1383	1.44668
$435$	19.9139	0.954796
$436$	−2.25136	−0.107820
$437$	27.0573	1.29433
$438$	25.5006	1.21847
$439$	−30.5108	−1.45620	−0.728100	−	0.685471i	$-0.759596\pi$
$439$	−30.5108	−1.45620	−0.728100	+	0.685471i	$0.759596\pi$
$440$	0	0
$441$	8.45427	0.402584
$442$	−31.9380	−1.51914
$443$	0.306243	0.0145500	0.00727502	−	0.999974i	$-0.497684\pi$
$443$	0.306243	0.0145500	0.00727502	+	0.999974i	$0.497684\pi$
$444$	−15.0335	−0.713457
$445$	26.2447	1.24412
$446$	5.26620	0.249362
$447$	−31.3360	−1.48214
$448$	−41.2625	−1.94947
$449$	14.6645	0.692060	0.346030	−	0.938224i	$-0.387530\pi$
$449$	14.6645	0.692060	0.346030	+	0.938224i	$0.387530\pi$
$450$	−3.77185	−0.177807
$451$	0	0
$452$	47.2536	2.22262
$453$	−5.09223	−0.239254
$454$	5.92114	0.277893
$455$	43.8438	2.05543
$456$	7.75743	0.363275
$457$	1.39196	0.0651132	0.0325566	−	0.999470i	$-0.489635\pi$
$457$	1.39196	0.0651132	0.0325566	+	0.999470i	$0.489635\pi$
$458$	−37.8866	−1.77032
$459$	12.3068	0.574434
$460$	39.8681	1.85886
$461$	−2.65455	−0.123635	−0.0618175	−	0.998087i	$-0.519690\pi$
$461$	−2.65455	−0.123635	−0.0618175	+	0.998087i	$0.519690\pi$
$462$	0	0
$463$	−15.1281	−0.703064	−0.351532	−	0.936176i	$-0.614339\pi$
$463$	−15.1281	−0.703064	−0.351532	+	0.936176i	$0.614339\pi$
$464$	11.2887	0.524066
$465$	19.9000	0.922840
$466$	54.3455	2.51751
$467$	22.8423	1.05702	0.528508	−	0.848929i	$-0.322752\pi$
$467$	22.8423	1.05702	0.528508	+	0.848929i	$0.322752\pi$
$468$	13.1912	0.609762
$469$	50.1474	2.31559
$470$	−23.2228	−1.07119
$471$	−4.81947	−0.222069
$472$	−1.28237	−0.0590259
$473$	0	0
$474$	−25.3052	−1.16231
$475$	6.34557	0.291155
$476$	30.2789	1.38783
$477$	1.96592	0.0900134
$478$	−11.1158	−0.508427
$479$	2.08109	0.0950873	0.0475437	−	0.998869i	$-0.484861\pi$
$479$	2.08109	0.0950873	0.0475437	+	0.998869i	$0.484861\pi$
$480$	−41.9309	−1.91387
$481$	13.8359	0.630861
$482$	49.5714	2.25792
$483$	−49.4787	−2.25136
$484$	0	0
$485$	−9.08353	−0.412462
$486$	−24.6132	−1.11648
$487$	−33.3425	−1.51089	−0.755447	−	0.655210i	$-0.772580\pi$
$487$	−33.3425	−1.51089	−0.755447	+	0.655210i	$0.772580\pi$
$488$	−0.901543	−0.0408110
$489$	22.5024	1.01759
$490$	−38.2171	−1.72647
$491$	−39.0209	−1.76099	−0.880494	−	0.474057i	$-0.842789\pi$
$491$	−39.0209	−1.76099	−0.880494	+	0.474057i	$0.842789\pi$
$492$	31.7298	1.43049
$493$	−12.6571	−0.570047
$494$	−40.4692	−1.82080
$495$	0	0
$496$	11.2809	0.506526
$497$	22.0214	0.987793
$498$	−32.5553	−1.45884
$499$	12.5654	0.562507	0.281253	−	0.959634i	$-0.409250\pi$
$499$	12.5654	0.562507	0.281253	+	0.959634i	$0.409250\pi$
$500$	−21.6281	−0.967236
$501$	17.9762	0.803118
$502$	−26.3356	−1.17541
$503$	18.6738	0.832623	0.416311	−	0.909222i	$-0.363323\pi$
$503$	18.6738	0.832623	0.416311	+	0.909222i	$0.363323\pi$
$504$	−4.02328	−0.179211
$505$	5.09423	0.226690
$506$	0	0
$507$	−16.2026	−0.719583
$508$	44.0297	1.95350
$509$	−8.83352	−0.391539	−0.195769	−	0.980650i	$-0.562720\pi$
$509$	−8.83352	−0.391539	−0.195769	+	0.980650i	$0.562720\pi$
$510$	36.4586	1.61441
$511$	22.2500	0.984281
$512$	−29.1062	−1.28632
$513$	15.5942	0.688501
$514$	36.7390	1.62049
$515$	7.87842	0.347165
$516$	44.2349	1.94733
$517$	0	0
$518$	−23.9201	−1.05099
$519$	−52.5241	−2.30555
$520$	−10.5197	−0.461321
$521$	29.0591	1.27310	0.636552	−	0.771234i	$-0.280360\pi$
$521$	29.0591	1.27310	0.636552	+	0.771234i	$0.280360\pi$
$522$	9.53311	0.417253
$523$	−3.63218	−0.158824	−0.0794121	−	0.996842i	$-0.525304\pi$
$523$	−3.63218	−0.158824	−0.0794121	+	0.996842i	$0.525304\pi$
$524$	0.316289	0.0138172
$525$	−11.6039	−0.506436
$526$	−5.95947	−0.259845
$527$	−12.6483	−0.550968
$528$	0	0
$529$	18.4078	0.800339
$530$	−8.88686	−0.386020
$531$	1.68939	0.0733134
$532$	38.3669	1.66342
$533$	−29.2021	−1.26489
$534$	44.2987	1.91699
$535$	−18.6813	−0.807664
$536$	−12.0322	−0.519712
$537$	−50.0437	−2.15955
$538$	48.3725	2.08548
$539$	0	0
$540$	22.9775	0.988796
$541$	36.8054	1.58239	0.791193	−	0.611566i	$-0.209460\pi$
$541$	36.8054	1.58239	0.791193	+	0.611566i	$0.209460\pi$
$542$	32.5805	1.39945
$543$	51.2186	2.19800
$544$	26.6509	1.14265
$545$	−2.36528	−0.101318
$546$	74.0045	3.16710
$547$	12.2289	0.522871	0.261436	−	0.965221i	$-0.415804\pi$
$547$	12.2289	0.522871	0.261436	+	0.965221i	$0.415804\pi$
$548$	36.5270	1.56036
$549$	1.18769	0.0506895
$550$	0	0
$551$	−16.0380	−0.683242
$552$	11.8718	0.505296
$553$	−22.0794	−0.938913
$554$	4.45008	0.189066
$555$	−15.7942	−0.670427
$556$	−3.31253	−0.140482
$557$	−23.1346	−0.980245	−0.490123	−	0.871653i	$-0.663048\pi$
$557$	−23.1346	−0.980245	−0.490123	+	0.871653i	$0.663048\pi$
$558$	9.52647	0.403288
$559$	−40.7110	−1.72189
$560$	−28.3720	−1.19894
$561$	0	0
$562$	34.6730	1.46259
$563$	0.490429	0.0206691	0.0103346	−	0.999947i	$-0.496710\pi$
$563$	0.490429	0.0206691	0.0103346	+	0.999947i	$0.496710\pi$
$564$	−21.4951	−0.905108
$565$	49.6448	2.08857
$566$	16.6782	0.701038
$567$	−41.9045	−1.75982
$568$	−5.28373	−0.221700
$569$	−22.1225	−0.927425	−0.463712	−	0.885986i	$-0.653483\pi$
$569$	−22.1225	−0.927425	−0.463712	+	0.885986i	$0.653483\pi$
$570$	46.1973	1.93499
$571$	−0.679250	−0.0284257	−0.0142129	−	0.999899i	$-0.504524\pi$
$571$	−0.679250	−0.0284257	−0.0142129	+	0.999899i	$0.504524\pi$
$572$	0	0
$573$	49.6810	2.07545
$574$	50.4862	2.10725
$575$	9.71109	0.404981
$576$	−13.0428	−0.543448
$577$	−39.3622	−1.63867	−0.819335	−	0.573315i	$-0.805657\pi$
$577$	−39.3622	−1.63867	−0.819335	+	0.573315i	$0.805657\pi$
$578$	12.6016	0.524159
$579$	−38.8161	−1.61314
$580$	−23.6315	−0.981243
$581$	−28.4054	−1.17845
$582$	−15.3322	−0.635540
$583$	0	0
$584$	−5.33858	−0.220912
$585$	13.8587	0.572986
$586$	−27.7688	−1.14712
$587$	5.75711	0.237621	0.118811	−	0.992917i	$-0.462092\pi$
$587$	5.75711	0.237621	0.118811	+	0.992917i	$0.462092\pi$
$588$	−35.3738	−1.45879
$589$	−16.0268	−0.660375
$590$	−7.63682	−0.314403
$591$	−16.3113	−0.670958
$592$	−8.95339	−0.367982
$593$	24.3274	0.999007	0.499503	−	0.866312i	$-0.333516\pi$
$593$	24.3274	0.999007	0.499503	+	0.866312i	$0.333516\pi$
$594$	0	0
$595$	31.8111	1.30413
$596$	37.1860	1.52320
$597$	46.6055	1.90743
$598$	−61.9329	−2.53263
$599$	−5.18608	−0.211897	−0.105949	−	0.994372i	$-0.533788\pi$
$599$	−5.18608	−0.211897	−0.105949	+	0.994372i	$0.533788\pi$
$600$	2.78420	0.113665
$601$	5.66484	0.231074	0.115537	−	0.993303i	$-0.463141\pi$
$601$	5.66484	0.231074	0.115537	+	0.993303i	$0.463141\pi$
$602$	70.3833	2.86861
$603$	15.8512	0.645511
$604$	6.04287	0.245881
$605$	0	0
$606$	8.59862	0.349295
$607$	16.9268	0.687037	0.343518	−	0.939146i	$-0.388381\pi$
$607$	16.9268	0.687037	0.343518	+	0.939146i	$0.388381\pi$
$608$	33.7698	1.36955
$609$	29.3281	1.18843
$610$	−5.36890	−0.217381
$611$	19.7827	0.800324
$612$	9.57092	0.386882
$613$	−34.8550	−1.40778	−0.703891	−	0.710308i	$-0.748555\pi$
$613$	−34.8550	−1.40778	−0.703891	+	0.710308i	$0.748555\pi$
$614$	−52.5803	−2.12197
$615$	33.3355	1.34422
$616$	0	0
$617$	15.0847	0.607289	0.303645	−	0.952785i	$-0.401796\pi$
$617$	15.0847	0.607289	0.303645	+	0.952785i	$0.401796\pi$
$618$	13.2981	0.534927
$619$	39.5482	1.58958	0.794788	−	0.606887i	$-0.207582\pi$
$619$	39.5482	1.58958	0.794788	+	0.606887i	$0.207582\pi$
$620$	−23.6150	−0.948402
$621$	23.8649	0.957667
$622$	−60.0935	−2.40953
$623$	38.6518	1.54855
$624$	27.7002	1.10889
$625$	−30.2682	−1.21073
$626$	45.7860	1.82998
$627$	0	0
$628$	5.71919	0.228220
$629$	10.0387	0.400268
$630$	−23.9596	−0.954573
$631$	13.6086	0.541748	0.270874	−	0.962615i	$-0.412687\pi$
$631$	13.6086	0.541748	0.270874	+	0.962615i	$0.412687\pi$
$632$	5.29767	0.210730
$633$	38.2586	1.52064
$634$	60.7806	2.41391
$635$	46.2577	1.83568
$636$	−8.22569	−0.326170
$637$	32.5558	1.28991
$638$	0	0
$639$	6.96078	0.275364
$640$	17.9787	0.710671
$641$	5.45256	0.215363	0.107682	−	0.994185i	$-0.465657\pi$
$641$	5.45256	0.215363	0.107682	+	0.994185i	$0.465657\pi$
$642$	−31.5324	−1.24449
$643$	17.6216	0.694927	0.347464	−	0.937693i	$-0.387043\pi$
$643$	17.6216	0.694927	0.347464	+	0.937693i	$0.387043\pi$
$644$	58.7156	2.31372
$645$	46.4734	1.82989
$646$	−29.3626	−1.15526
$647$	43.9177	1.72658	0.863292	−	0.504704i	$-0.168398\pi$
$647$	43.9177	1.72658	0.863292	+	0.504704i	$0.168398\pi$
$648$	10.0544	0.394975
$649$	0	0
$650$	−14.5247	−0.569706
$651$	29.3077	1.14866
$652$	−26.7033	−1.04578
$653$	−12.6974	−0.496887	−0.248443	−	0.968646i	$-0.579919\pi$
$653$	−12.6974	−0.496887	−0.248443	+	0.968646i	$0.579919\pi$
$654$	−3.99239	−0.156115
$655$	0.332295	0.0129838
$656$	18.8972	0.737810
$657$	7.03304	0.274385
$658$	−34.2014	−1.33331
$659$	21.4353	0.835001	0.417501	−	0.908677i	$-0.362906\pi$
$659$	21.4353	0.835001	0.417501	+	0.908677i	$0.362906\pi$
$660$	0	0
$661$	13.0944	0.509313	0.254657	−	0.967032i	$-0.418038\pi$
$661$	13.0944	0.509313	0.254657	+	0.967032i	$0.418038\pi$
$662$	−65.6385	−2.55111
$663$	−31.0578	−1.20619
$664$	6.81549	0.264492
$665$	40.3084	1.56309
$666$	−7.56096	−0.292981
$667$	−24.5441	−0.950352
$668$	−21.3321	−0.825363
$669$	5.12106	0.197992
$670$	−71.6546	−2.76826
$671$	0	0
$672$	−61.7536	−2.38220
$673$	5.87580	0.226496	0.113248	−	0.993567i	$-0.463875\pi$
$673$	5.87580	0.226496	0.113248	+	0.993567i	$0.463875\pi$
$674$	61.5851	2.37217
$675$	5.59689	0.215424
$676$	19.2274	0.739515
$677$	3.77568	0.145111	0.0725555	−	0.997364i	$-0.476885\pi$
$677$	3.77568	0.145111	0.0725555	+	0.997364i	$0.476885\pi$
$678$	83.7962	3.21817
$679$	−13.3778	−0.513391
$680$	−7.63265	−0.292699
$681$	5.75796	0.220646
$682$	0	0
$683$	−35.5748	−1.36123	−0.680616	−	0.732640i	$-0.738288\pi$
$683$	−35.5748	−1.36123	−0.680616	+	0.732640i	$0.738288\pi$
$684$	12.1275	0.463705
$685$	38.3754	1.46625
$686$	−0.934881	−0.0356939
$687$	−36.8425	−1.40563
$688$	26.3447	1.00438
$689$	7.57041	0.288410
$690$	70.6991	2.69147
$691$	19.4282	0.739083	0.369542	−	0.929214i	$-0.379515\pi$
$691$	19.4282	0.739083	0.369542	+	0.929214i	$0.379515\pi$
$692$	62.3295	2.36941
$693$	0	0
$694$	−7.03965	−0.267221
$695$	−3.48015	−0.132010
$696$	−7.03689	−0.266732
$697$	−21.1878	−0.802544
$698$	54.2678	2.05407
$699$	52.8478	1.99889
$700$	13.7702	0.520464
$701$	−31.8138	−1.20159	−0.600795	−	0.799403i	$-0.705149\pi$
$701$	−31.8138	−1.20159	−0.600795	+	0.799403i	$0.705149\pi$
$702$	−35.6944	−1.34720
$703$	12.7202	0.479750
$704$	0	0
$705$	−22.5828	−0.850519
$706$	−19.3250	−0.727305
$707$	7.50252	0.282161
$708$	−7.06865	−0.265656
$709$	−14.7262	−0.553056	−0.276528	−	0.961006i	$-0.589184\pi$
$709$	−14.7262	−0.553056	−0.276528	+	0.961006i	$0.589184\pi$
$710$	−31.4659	−1.18089
$711$	−6.97914	−0.261738
$712$	−9.27398	−0.347557
$713$	−24.5270	−0.918545
$714$	53.6944	2.00946
$715$	0	0
$716$	59.3861	2.21936
$717$	−10.8095	−0.403688
$718$	39.6482	1.47966
$719$	7.38443	0.275393	0.137696	−	0.990474i	$-0.456030\pi$
$719$	7.38443	0.275393	0.137696	+	0.990474i	$0.456030\pi$
$720$	−8.96817	−0.334224
$721$	11.6029	0.432116
$722$	2.77732	0.103361
$723$	48.2053	1.79277
$724$	−60.7803	−2.25888
$725$	−5.75617	−0.213779
$726$	0	0
$727$	17.8867	0.663380	0.331690	−	0.943389i	$-0.392381\pi$
$727$	17.8867	0.663380	0.331690	+	0.943389i	$0.392381\pi$
$728$	−15.4929	−0.574206
$729$	9.52247	0.352684
$730$	−31.7925	−1.17669
$731$	−29.5381	−1.09251
$732$	−4.96947	−0.183677
$733$	−48.5107	−1.79178	−0.895892	−	0.444272i	$-0.853462\pi$
$733$	−48.5107	−1.79178	−0.895892	+	0.444272i	$0.853462\pi$
$734$	−79.9218	−2.94997
$735$	−37.1639	−1.37081
$736$	51.6804	1.90497
$737$	0	0
$738$	15.9583	0.587432
$739$	−8.65220	−0.318276	−0.159138	−	0.987256i	$-0.550872\pi$
$739$	−8.65220	−0.318276	−0.159138	+	0.987256i	$0.550872\pi$
$740$	18.7427	0.688997
$741$	−39.3539	−1.44570
$742$	−13.0881	−0.480480
$743$	9.83052	0.360647	0.180323	−	0.983607i	$-0.442286\pi$
$743$	9.83052	0.360647	0.180323	+	0.983607i	$0.442286\pi$
$744$	−7.03199	−0.257805
$745$	39.0677	1.43133
$746$	50.7660	1.85868
$747$	−8.97871	−0.328514
$748$	0	0
$749$	−27.5129	−1.00530
$750$	−38.3536	−1.40048
$751$	43.1881	1.57596	0.787978	−	0.615704i	$-0.211128\pi$
$751$	43.1881	1.57596	0.787978	+	0.615704i	$0.211128\pi$
$752$	−12.8017	−0.466831
$753$	−25.6098	−0.933273
$754$	36.7102	1.33691
$755$	6.34866	0.231052
$756$	33.8401	1.23075
$757$	−21.6303	−0.786166	−0.393083	−	0.919503i	$-0.628591\pi$
$757$	−21.6303	−0.786166	−0.393083	+	0.919503i	$0.628591\pi$
$758$	−80.1856	−2.91247
$759$	0	0
$760$	−9.67146	−0.350821
$761$	−25.5265	−0.925334	−0.462667	−	0.886532i	$-0.653107\pi$
$761$	−25.5265	−0.925334	−0.462667	+	0.886532i	$0.653107\pi$
$762$	78.0790	2.82850
$763$	−3.48347	−0.126110
$764$	−58.9557	−2.13294
$765$	10.0552	0.363548
$766$	18.7466	0.677341
$767$	6.50554	0.234902
$768$	−14.5987	−0.526784
$769$	25.4903	0.919202	0.459601	−	0.888125i	$-0.347992\pi$
$769$	25.4903	0.919202	0.459601	+	0.888125i	$0.347992\pi$
$770$	0	0
$771$	35.7265	1.28666
$772$	46.0625	1.65782
$773$	−45.0386	−1.61992	−0.809962	−	0.586482i	$-0.800512\pi$
$773$	−45.0386	−1.61992	−0.809962	+	0.586482i	$0.800512\pi$
$774$	22.2476	0.799674
$775$	−5.75216	−0.206624
$776$	3.20981	0.115226
$777$	−23.2609	−0.834481
$778$	36.0811	1.29357
$779$	−26.8474	−0.961907
$780$	−57.9867	−2.07626
$781$	0	0
$782$	−44.9358	−1.60690
$783$	−14.1457	−0.505528
$784$	−21.0674	−0.752407
$785$	6.00860	0.214456
$786$	0.560884	0.0200061
$787$	36.6996	1.30820	0.654101	−	0.756408i	$-0.273047\pi$
$787$	36.6996	1.30820	0.654101	+	0.756408i	$0.273047\pi$
$788$	19.3564	0.689542
$789$	−5.79524	−0.206316
$790$	31.5488	1.12246
$791$	73.1144	2.59965
$792$	0	0
$793$	4.57358	0.162413
$794$	31.3024	1.11088
$795$	−8.64195	−0.306498
$796$	−55.3060	−1.96027
$797$	28.1282	0.996354	0.498177	−	0.867075i	$-0.334003\pi$
$797$	28.1282	0.996354	0.498177	+	0.867075i	$0.334003\pi$
$798$	68.0370	2.40849
$799$	14.3535	0.507790
$800$	12.1203	0.428516
$801$	12.2175	0.431685
$802$	−8.02123	−0.283239
$803$	0	0
$804$	−66.3236	−2.33905
$805$	61.6869	2.17418
$806$	36.6847	1.29216
$807$	47.0394	1.65586
$808$	−1.80013	−0.0633283
$809$	30.5817	1.07519	0.537597	−	0.843202i	$-0.319332\pi$
$809$	30.5817	1.07519	0.537597	+	0.843202i	$0.319332\pi$
$810$	59.8765	2.10385
$811$	−16.0980	−0.565276	−0.282638	−	0.959227i	$-0.591209\pi$
$811$	−16.0980	−0.565276	−0.282638	+	0.959227i	$0.591209\pi$
$812$	−34.8032	−1.22135
$813$	31.6826	1.11116
$814$	0	0
$815$	−28.0546	−0.982708
$816$	20.0980	0.703571
$817$	−37.4282	−1.30945
$818$	44.7939	1.56618
$819$	20.4104	0.713196
$820$	−39.5587	−1.38145
$821$	−45.1739	−1.57658	−0.788290	−	0.615304i	$-0.789033\pi$
$821$	−45.1739	−1.57658	−0.788290	+	0.615304i	$0.789033\pi$
$822$	64.7744	2.25927
$823$	−0.460596	−0.0160554	−0.00802769	−	0.999968i	$-0.502555\pi$
$823$	−0.460596	−0.0160554	−0.00802769	+	0.999968i	$0.502555\pi$
$824$	−2.78397	−0.0969841
$825$	0	0
$826$	−11.2471	−0.391337
$827$	40.5541	1.41021	0.705103	−	0.709105i	$-0.250901\pi$
$827$	40.5541	1.41021	0.705103	+	0.709105i	$0.250901\pi$
$828$	18.5595	0.644989
$829$	−28.6084	−0.993611	−0.496806	−	0.867862i	$-0.665494\pi$
$829$	−28.6084	−0.993611	−0.496806	+	0.867862i	$0.665494\pi$
$830$	40.5878	1.40882
$831$	4.32744	0.150117
$832$	−50.2253	−1.74125
$833$	23.6211	0.818422
$834$	−5.87420	−0.203407
$835$	−22.4116	−0.775584
$836$	0	0
$837$	−14.1359	−0.488608
$838$	−33.4947	−1.15705
$839$	8.80602	0.304017	0.152009	−	0.988379i	$-0.451426\pi$
$839$	8.80602	0.304017	0.152009	+	0.988379i	$0.451426\pi$
$840$	17.6858	0.610220
$841$	−14.4517	−0.498334
$842$	−12.0153	−0.414075
$843$	33.7175	1.16129
$844$	−45.4009	−1.56276
$845$	20.2004	0.694913
$846$	−10.8108	−0.371683
$847$	0	0
$848$	−4.89893	−0.168230
$849$	16.2186	0.556621
$850$	−10.5385	−0.361467
$851$	19.4666	0.667307
$852$	−29.1249	−0.997802
$853$	−13.7546	−0.470947	−0.235474	−	0.971881i	$-0.575664\pi$
$853$	−13.7546	−0.470947	−0.235474	+	0.971881i	$0.575664\pi$
$854$	−7.90705	−0.270574
$855$	12.7412	0.435739
$856$	6.60135	0.225629
$857$	−13.0885	−0.447095	−0.223548	−	0.974693i	$-0.571764\pi$
$857$	−13.0885	−0.447095	−0.223548	+	0.974693i	$0.571764\pi$
$858$	0	0
$859$	−9.67910	−0.330247	−0.165123	−	0.986273i	$-0.552802\pi$
$859$	−9.67910	−0.330247	−0.165123	+	0.986273i	$0.552802\pi$
$860$	−55.1492	−1.88057
$861$	49.0948	1.67315
$862$	−75.4188	−2.56877
$863$	8.06978	0.274698	0.137349	−	0.990523i	$-0.456142\pi$
$863$	8.06978	0.274698	0.137349	+	0.990523i	$0.456142\pi$
$864$	29.7855	1.01332
$865$	65.4836	2.22651
$866$	−55.3742	−1.88169
$867$	12.2544	0.416180
$868$	−34.7790	−1.18048
$869$	0	0
$870$	−41.9063	−1.42076
$871$	61.0401	2.06826
$872$	0.835812	0.0283042
$873$	−4.22860	−0.143116
$874$	−56.9389	−1.92599
$875$	−33.4646	−1.13131
$876$	−29.4272	−0.994254
$877$	−43.8103	−1.47937	−0.739684	−	0.672955i	$-0.765025\pi$
$877$	−43.8103	−1.47937	−0.739684	+	0.672955i	$0.765025\pi$
$878$	64.2062	2.16685
$879$	−27.0035	−0.910806
$880$	0	0
$881$	−10.4120	−0.350788	−0.175394	−	0.984498i	$-0.556120\pi$
$881$	−10.4120	−0.350788	−0.175394	+	0.984498i	$0.556120\pi$
$882$	−17.7910	−0.599054
$883$	−15.9570	−0.536995	−0.268497	−	0.963280i	$-0.586527\pi$
$883$	−15.9570	−0.536995	−0.268497	+	0.963280i	$0.586527\pi$
$884$	36.8559	1.23960
$885$	−7.42636	−0.249634
$886$	−0.644451	−0.0216508
$887$	33.2938	1.11790	0.558948	−	0.829202i	$-0.311205\pi$
$887$	33.2938	1.11790	0.558948	+	0.829202i	$0.311205\pi$
$888$	5.58114	0.187291
$889$	68.1260	2.28487
$890$	−55.2287	−1.85127
$891$	0	0
$892$	−6.07709	−0.203476
$893$	18.1875	0.608622
$894$	65.9429	2.20546
$895$	62.3913	2.08551
$896$	26.4781	0.884572
$897$	−60.2261	−2.01089
$898$	−30.8596	−1.02980
$899$	14.5382	0.484876
$900$	4.35265	0.145088
$901$	5.49275	0.182990
$902$	0	0
$903$	68.4436	2.27766
$904$	−17.5428	−0.583465
$905$	−63.8560	−2.12265
$906$	10.7160	0.356015
$907$	−35.7513	−1.18710	−0.593551	−	0.804797i	$-0.702274\pi$
$907$	−35.7513	−1.18710	−0.593551	+	0.804797i	$0.702274\pi$
$908$	−6.83289	−0.226757
$909$	2.37149	0.0786573
$910$	−92.2640	−3.05852
$911$	28.5203	0.944921	0.472461	−	0.881352i	$-0.343366\pi$
$911$	28.5203	0.944921	0.472461	+	0.881352i	$0.343366\pi$
$912$	25.4665	0.843281
$913$	0	0
$914$	−2.92922	−0.0968899
$915$	−5.22094	−0.172599
$916$	43.7204	1.44456
$917$	0.489386	0.0161610
$918$	−25.8983	−0.854770
$919$	−30.1762	−0.995421	−0.497710	−	0.867343i	$-0.665826\pi$
$919$	−30.1762	−0.995421	−0.497710	+	0.867343i	$0.665826\pi$
$920$	−14.8009	−0.487972
$921$	−51.1313	−1.68483
$922$	5.58619	0.183971
$923$	26.8047	0.882287
$924$	0	0
$925$	4.56537	0.150109
$926$	31.8353	1.04617
$927$	3.66759	0.120460
$928$	−30.6331	−1.00558
$929$	17.5521	0.575866	0.287933	−	0.957650i	$-0.407032\pi$
$929$	17.5521	0.575866	0.287933	+	0.957650i	$0.407032\pi$
$930$	−41.8771	−1.37321
$931$	29.9306	0.980937
$932$	−62.7137	−2.05426
$933$	−58.4374	−1.91316
$934$	−48.0689	−1.57286
$935$	0	0
$936$	−4.89719	−0.160070
$937$	−27.2099	−0.888908	−0.444454	−	0.895802i	$-0.646602\pi$
$937$	−27.2099	−0.888908	−0.444454	+	0.895802i	$0.646602\pi$
$938$	−105.529	−3.44565
$939$	44.5242	1.45299
$940$	26.7987	0.874078
$941$	−13.5420	−0.441458	−0.220729	−	0.975335i	$-0.570844\pi$
$941$	−13.5420	−0.441458	−0.220729	+	0.975335i	$0.570844\pi$
$942$	10.1420	0.330444
$943$	−41.0865	−1.33796
$944$	−4.20984	−0.137019
$945$	35.5526	1.15653
$946$	0	0
$947$	−14.7906	−0.480630	−0.240315	−	0.970695i	$-0.577251\pi$
$947$	−14.7906	−0.480630	−0.240315	+	0.970695i	$0.577251\pi$
$948$	29.2017	0.948427
$949$	27.0830	0.879150
$950$	−13.3535	−0.433245
$951$	59.1056	1.91663
$952$	−11.2410	−0.364322
$953$	3.93314	0.127407	0.0637035	−	0.997969i	$-0.479709\pi$
$953$	3.93314	0.127407	0.0637035	+	0.997969i	$0.479709\pi$
$954$	−4.13705	−0.133942
$955$	−61.9390	−2.00430
$956$	12.8275	0.414870
$957$	0	0
$958$	−4.37940	−0.141492
$959$	56.5174	1.82504
$960$	57.3343	1.85046
$961$	−16.4719	−0.531352
$962$	−29.1159	−0.938734
$963$	−8.69661	−0.280244
$964$	−57.2044	−1.84243
$965$	48.3934	1.55784
$966$	104.122	3.35007
$967$	−43.7228	−1.40603	−0.703016	−	0.711174i	$-0.748164\pi$
$967$	−43.7228	−1.40603	−0.703016	+	0.711174i	$0.748164\pi$
$968$	0	0
$969$	−28.5534	−0.917269
$970$	19.1152	0.613752
$971$	−39.7799	−1.27660	−0.638299	−	0.769789i	$-0.720362\pi$
$971$	−39.7799	−1.27660	−0.638299	+	0.769789i	$0.720362\pi$
$972$	28.4032	0.911033
$973$	−5.12539	−0.164313
$974$	70.1653	2.24824
$975$	−14.1244	−0.452344
$976$	−2.95964	−0.0947357
$977$	0.272003	0.00870216	0.00435108	−	0.999991i	$-0.498615\pi$
$977$	0.272003	0.00870216	0.00435108	+	0.999991i	$0.498615\pi$
$978$	−47.3536	−1.51420
$979$	0	0
$980$	44.1018	1.40878
$981$	−1.10110	−0.0351553
$982$	82.1148	2.62039
$983$	−34.9358	−1.11428	−0.557139	−	0.830419i	$-0.688101\pi$
$983$	−34.9358	−1.11428	−0.557139	+	0.830419i	$0.688101\pi$
$984$	−11.7796	−0.375521
$985$	20.3359	0.647955
$986$	26.6353	0.848241
$987$	−33.2589	−1.05864
$988$	46.7007	1.48575
$989$	−57.2791	−1.82137
$990$	0	0
$991$	−49.4128	−1.56965	−0.784825	−	0.619717i	$-0.787247\pi$
$991$	−49.4128	−1.56965	−0.784825	+	0.619717i	$0.787247\pi$
$992$	−30.6118	−0.971926
$993$	−63.8295	−2.02557
$994$	−46.3413	−1.46986
$995$	−58.1047	−1.84204
$996$	37.5682	1.19039
$997$	−49.6464	−1.57232	−0.786158	−	0.618026i	$-0.787933\pi$
$997$	−49.6464	−1.57232	−0.786158	+	0.618026i	$0.787933\pi$
$998$	−26.4425	−0.837022
$999$	11.2194	0.354965

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.v.1.11		64
11.5	even	5		671.2.j.c.245.28	✓	128
11.9	even	5		671.2.j.c.367.28	yes	128
11.10	odd	2		7381.2.a.u.1.54		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.j.c.245.28	✓	128	11.5	even	5
671.2.j.c.367.28	yes	128	11.9	even	5
7381.2.a.u.1.54		64	11.10	odd	2
7381.2.a.v.1.11		64	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 7381 = 11^{2} \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7381.a (trivial)

\(f(q)\)	\(=\)	\(q-2.10438 q^{2} -2.04639 q^{3} +2.42841 q^{4} +2.55130 q^{5} +4.30637 q^{6} +3.75742 q^{7} -0.901543 q^{8} +1.18769 q^{9} +O(q^{10})\)	\(q-2.10438 q^{2} -2.04639 q^{3} +2.42841 q^{4} +2.55130 q^{5} +4.30637 q^{6} +3.75742 q^{7} -0.901543 q^{8} +1.18769 q^{9} -5.36890 q^{10} -4.96947 q^{12} +4.57358 q^{13} -7.90705 q^{14} -5.22094 q^{15} -2.95964 q^{16} +3.31839 q^{17} -2.49935 q^{18} +4.20479 q^{19} +6.19561 q^{20} -7.68914 q^{21} +6.43489 q^{23} +1.84491 q^{24} +1.50913 q^{25} -9.62456 q^{26} +3.70868 q^{27} +9.12458 q^{28} -3.81423 q^{29} +10.9868 q^{30} -3.81157 q^{31} +8.03128 q^{32} -6.98315 q^{34} +9.58632 q^{35} +2.88421 q^{36} +3.02517 q^{37} -8.84846 q^{38} -9.35931 q^{39} -2.30011 q^{40} -6.38496 q^{41} +16.1809 q^{42} -8.90134 q^{43} +3.03016 q^{45} -13.5414 q^{46} +4.32544 q^{47} +6.05656 q^{48} +7.11823 q^{49} -3.17578 q^{50} -6.79070 q^{51} +11.1066 q^{52} +1.65525 q^{53} -7.80447 q^{54} -3.38748 q^{56} -8.60461 q^{57} +8.02658 q^{58} +1.42242 q^{59} -12.6786 q^{60} +1.00000 q^{61} +8.02099 q^{62} +4.46266 q^{63} -10.9816 q^{64} +11.6686 q^{65} +13.3462 q^{67} +8.05842 q^{68} -13.1683 q^{69} -20.1732 q^{70} +5.86076 q^{71} -1.07076 q^{72} +5.92160 q^{73} -6.36610 q^{74} -3.08826 q^{75} +10.2110 q^{76} +19.6955 q^{78} -5.87622 q^{79} -7.55092 q^{80} -11.1525 q^{81} +13.4364 q^{82} -7.55980 q^{83} -18.6724 q^{84} +8.46621 q^{85} +18.7318 q^{86} +7.80538 q^{87} +10.2868 q^{89} -6.37660 q^{90} +17.1849 q^{91} +15.6266 q^{92} +7.79994 q^{93} -9.10236 q^{94} +10.7277 q^{95} -16.4351 q^{96} -3.56035 q^{97} -14.9795 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9}+O(q^{10}) \) 64 * q + 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 - q^6 + 6 * q^7 + 3 * q^8 + 81 * q^9	\( 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9} - 4 q^{10} + 41 q^{12} - q^{13} + 41 q^{14} + 28 q^{15} + 107 q^{16} + 13 q^{17} + 38 q^{18} - q^{19} + 65 q^{20} + q^{21} + 52 q^{23} + 3 q^{24} + 87 q^{25} + 37 q^{26} + 88 q^{27} - q^{28} + 19 q^{29} - 19 q^{30} + 45 q^{31} - 24 q^{32} - 23 q^{34} + 10 q^{35} + 146 q^{36} + 26 q^{37} - 4 q^{38} - 6 q^{39} + 84 q^{40} - 12 q^{41} + 28 q^{42} + 5 q^{43} + 71 q^{45} - 5 q^{46} + 63 q^{47} + 85 q^{48} + 78 q^{49} + 14 q^{50} + 22 q^{51} - 24 q^{52} + 86 q^{53} - 114 q^{54} + 119 q^{56} - 29 q^{57} + q^{58} + 119 q^{59} - 22 q^{60} + 64 q^{61} + 13 q^{62} - 28 q^{63} + 135 q^{64} - 30 q^{65} + 2 q^{67} + 59 q^{68} + 63 q^{69} - 2 q^{70} + 126 q^{71} + 48 q^{72} + 8 q^{73} - 27 q^{74} + 107 q^{75} - 82 q^{76} - 13 q^{78} - 5 q^{79} + 119 q^{80} + 96 q^{81} - 27 q^{82} + 14 q^{83} + 182 q^{84} - 52 q^{85} + 60 q^{86} - 8 q^{87} + 59 q^{89} - 45 q^{90} + 83 q^{91} + 111 q^{92} - 7 q^{93} + 21 q^{94} - 26 q^{95} - 86 q^{96} - 39 q^{97} - 57 q^{98}+O(q^{100}) \) 64 * q + 5 * q^2 + 19 * q^3 + 73 * q^4 + 21 * q^5 - q^6 + 6 * q^7 + 3 * q^8 + 81 * q^9 - 4 * q^10 + 41 * q^12 - q^13 + 41 * q^14 + 28 * q^15 + 107 * q^16 + 13 * q^17 + 38 * q^18 - q^19 + 65 * q^20 + q^21 + 52 * q^23 + 3 * q^24 + 87 * q^25 + 37 * q^26 + 88 * q^27 - q^28 + 19 * q^29 - 19 * q^30 + 45 * q^31 - 24 * q^32 - 23 * q^34 + 10 * q^35 + 146 * q^36 + 26 * q^37 - 4 * q^38 - 6 * q^39 + 84 * q^40 - 12 * q^41 + 28 * q^42 + 5 * q^43 + 71 * q^45 - 5 * q^46 + 63 * q^47 + 85 * q^48 + 78 * q^49 + 14 * q^50 + 22 * q^51 - 24 * q^52 + 86 * q^53 - 114 * q^54 + 119 * q^56 - 29 * q^57 + q^58 + 119 * q^59 - 22 * q^60 + 64 * q^61 + 13 * q^62 - 28 * q^63 + 135 * q^64 - 30 * q^65 + 2 * q^67 + 59 * q^68 + 63 * q^69 - 2 * q^70 + 126 * q^71 + 48 * q^72 + 8 * q^73 - 27 * q^74 + 107 * q^75 - 82 * q^76 - 13 * q^78 - 5 * q^79 + 119 * q^80 + 96 * q^81 - 27 * q^82 + 14 * q^83 + 182 * q^84 - 52 * q^85 + 60 * q^86 - 8 * q^87 + 59 * q^89 - 45 * q^90 + 83 * q^91 + 111 * q^92 - 7 * q^93 + 21 * q^94 - 26 * q^95 - 86 * q^96 - 39 * q^97 - 57 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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