LMFDB - Embedded newform 7381.2.a.u.1.54

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			1.54
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	$-0.232921\pi$
$2$	2.10438	1.48802	0.744010	+	0.668168i	$0.232921\pi$
$3$	−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	$-0.751344\pi$
$7$	−3.75742	−1.42017	−0.710086	+	0.704115i	$0.751344\pi$
$8$	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	$-0.718688\pi$
$13$	−4.57358	−1.26848	−0.634242	+	0.773135i	$0.718688\pi$
$14$	−7.90705	−2.11325
$15$	−5.22094	−1.34804
$16$	−2.95964	−0.739909
$17$	−3.31839	−0.804828	−0.402414	−	0.915458i	$-0.631829\pi$
$17$	−3.31839	−0.804828	−0.402414	+	0.915458i	$0.631829\pi$
$18$	2.49935	0.589104
$19$	−4.20479	−0.964644	−0.482322	−	0.875994i	$-0.660206\pi$
$19$	−4.20479	−0.964644	−0.482322	+	0.875994i	$0.660206\pi$
$20$	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	$-0.384773\pi$
$29$	3.81423	0.708284	0.354142	+	0.935192i	$0.384773\pi$
$30$	−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	$-0.333854\pi$
$41$	6.38496	0.997163	0.498582	+	0.866843i	$0.333854\pi$
$42$	16.1809	2.49676
$43$	8.90134	1.35744	0.678721	−	0.734396i	$-0.262535\pi$
$43$	8.90134	1.35744	0.678721	+	0.734396i	$0.262535\pi$
$44$	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	$-0.612642\pi$
$73$	−5.92160	−0.693071	−0.346536	+	0.938037i	$0.612642\pi$
$74$	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	$-0.392761\pi$
$79$	5.87622	0.661126	0.330563	+	0.943784i	$0.392761\pi$
$80$	−7.55092	−0.844219
$81$	−11.1525	−1.23916
$82$	13.4364	1.48380
$83$	7.55980	0.829796	0.414898	−	0.909868i	$-0.363817\pi$
$83$	7.55980	0.829796	0.414898	+	0.909868i	$0.363817\pi$
$84$	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	$-0.531673\pi$
$101$	−1.99672	−0.198681	−0.0993405	+	0.995053i	$0.531673\pi$
$102$	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	$-0.384843\pi$
$107$	7.32227	0.707871	0.353935	+	0.935270i	$0.384843\pi$
$108$	9.00621	0.866623
$109$	0.927090	0.0887991	0.0443996	−	0.999014i	$-0.485863\pi$
$109$	0.927090	0.0887991	0.0443996	+	0.999014i	$0.485863\pi$
$110$	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	$-0.797532\pi$
$127$	−18.1310	−1.60887	−0.804435	+	0.594041i	$0.797532\pi$
$128$	−7.04688	−0.622862
$129$	−18.2156	−1.60379
$130$	−24.5551	−2.15363
$131$	−0.130245	−0.0113796	−0.00568979	−	0.999984i	$-0.501811\pi$
$131$	−0.130245	−0.0113796	−0.00568979	+	0.999984i	$0.501811\pi$
$132$	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	$-0.481576\pi$
$139$	1.36407	0.115699	0.0578495	+	0.998325i	$0.481576\pi$
$140$	−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	$-0.715815\pi$
$149$	−15.3129	−1.25448	−0.627239	+	0.778827i	$0.715815\pi$
$150$	−6.49888	−0.530631
$151$	−2.48840	−0.202503	−0.101252	−	0.994861i	$-0.532285\pi$
$151$	−2.48840	−0.202503	−0.101252	+	0.994861i	$0.532285\pi$
$152$	−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	$-0.389614\pi$
$167$	8.78437	0.679755	0.339878	+	0.940470i	$0.389614\pi$
$168$	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	$-0.929690\pi$
$173$	−25.6668	−1.95141	−0.975704	+	0.219095i	$0.929690\pi$
$174$	−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	$-0.739185\pi$
$193$	−18.9681	−1.36536	−0.682678	+	0.730719i	$0.739185\pi$
$194$	−7.49233	−0.537918
$195$	23.8784	1.70997
$196$	17.2860	1.23472
$197$	−7.97079	−0.567895	−0.283948	−	0.958840i	$-0.591644\pi$
$197$	−7.97079	−0.567895	−0.283948	+	0.958840i	$0.591644\pi$
$198$	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	$-0.277468\pi$
$211$	18.6957	1.28707	0.643533	+	0.765418i	$0.277468\pi$
$212$	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	$-0.470234\pi$
$227$	2.81372	0.186753	0.0933767	+	0.995631i	$0.470234\pi$
$228$	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	$-0.179049\pi$
$233$	25.8250	1.69185	0.845925	+	0.533302i	$0.179049\pi$
$234$	−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	$-0.554648\pi$
$239$	−5.28225	−0.341680	−0.170840	+	0.985299i	$0.554648\pi$
$240$	15.4521	0.997428
$241$	23.5563	1.51739	0.758697	−	0.651443i	$-0.225836\pi$
$241$	23.5563	1.51739	0.758697	+	0.651443i	$0.225836\pi$
$242$	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	$-0.527828\pi$
$263$	−2.83194	−0.174625	−0.0873124	+	0.996181i	$0.527828\pi$
$264$	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	$-0.344168\pi$
$271$	15.4822	0.940478	0.470239	+	0.882539i	$0.344168\pi$
$272$	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	$-0.479764\pi$
$277$	2.11468	0.127059	0.0635293	+	0.997980i	$0.479764\pi$
$278$	2.87052	0.172163
$279$	−4.52697	−0.271023
$280$	−8.64248	−0.516487
$281$	16.4766	0.982912	0.491456	−	0.870903i	$-0.336465\pi$
$281$	16.4766	0.982912	0.491456	+	0.870903i	$0.336465\pi$
$282$	−18.6269	−1.10922
$283$	7.92549	0.471121	0.235561	−	0.971860i	$-0.424307\pi$
$283$	7.92549	0.471121	0.235561	+	0.971860i	$0.424307\pi$
$284$	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	$-0.625954\pi$
$293$	−13.1957	−0.770902	−0.385451	+	0.922728i	$0.625954\pi$
$294$	−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	$-0.752672\pi$
$307$	−24.9862	−1.42604	−0.713018	+	0.701146i	$0.752672\pi$
$308$	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	$-0.206373\pi$
$337$	29.2652	1.59418	0.797088	+	0.603863i	$0.206373\pi$
$338$	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	$-0.528620\pi$
$347$	−3.34524	−0.179582	−0.0897909	+	0.995961i	$0.528620\pi$
$348$	−18.9547	−1.01608
$349$	25.7880	1.38040	0.690201	−	0.723618i	$-0.257522\pi$
$349$	25.7880	1.38040	0.690201	+	0.723618i	$0.257522\pi$
$350$	−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	$-0.334365\pi$
$359$	18.8408	0.994380	0.497190	+	0.867642i	$0.334365\pi$
$360$	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	$-0.285284\pi$
$373$	24.1240	1.24909	0.624546	+	0.780988i	$0.285284\pi$
$374$	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	$-0.323593\pi$
$409$	21.2860	1.05253	0.526263	+	0.850322i	$0.323593\pi$
$410$	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	$-0.831513\pi$
$431$	−35.8390	−1.72630	−0.863151	+	0.504945i	$0.831513\pi$
$432$	−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	$-0.240404\pi$
$439$	30.5108	1.45620	0.728100	+	0.685471i	$0.240404\pi$
$440$	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	$-0.510365\pi$
$457$	−1.39196	−0.0651132	−0.0325566	+	0.999470i	$0.510365\pi$
$458$	37.8866	1.77032
$459$	−12.3068	−0.574434
$460$	39.8681	1.85886
$461$	2.65455	0.123635	0.0618175	−	0.998087i	$-0.480310\pi$
$461$	2.65455	0.123635	0.0618175	+	0.998087i	$0.480310\pi$
$462$	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	$-0.515139\pi$
$479$	−2.08109	−0.0950873	−0.0475437	+	0.998869i	$0.515139\pi$
$480$	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	$-0.157211\pi$
$491$	39.0209	1.76099	0.880494	+	0.474057i	$0.157211\pi$
$492$	−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	$-0.636677\pi$
$503$	−18.6738	−0.832623	−0.416311	+	0.909222i	$0.636677\pi$
$504$	−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	$-0.474696\pi$
$523$	3.63218	0.158824	0.0794121	+	0.996842i	$0.474696\pi$
$524$	−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	$-0.790540\pi$
$541$	−36.8054	−1.58239	−0.791193	+	0.611566i	$0.790540\pi$
$542$	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	$-0.584196\pi$
$547$	−12.2289	−0.522871	−0.261436	+	0.965221i	$0.584196\pi$
$548$	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	$-0.336952\pi$
$557$	23.1346	0.980245	0.490123	+	0.871653i	$0.336952\pi$
$558$	−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	$-0.503290\pi$
$563$	−0.490429	−0.0206691	−0.0103346	+	0.999947i	$0.503290\pi$
$564$	−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	$-0.346517\pi$
$569$	22.1225	0.927425	0.463712	+	0.885986i	$0.346517\pi$
$570$	46.1973	1.93499
$571$	0.679250	0.0284257	0.0142129	−	0.999899i	$-0.495476\pi$
$571$	0.679250	0.0284257	0.0142129	+	0.999899i	$0.495476\pi$
$572$	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	$-0.666484\pi$
$593$	−24.3274	−0.999007	−0.499503	+	0.866312i	$0.666484\pi$
$594$	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	$-0.536859\pi$
$601$	−5.66484	−0.231074	−0.115537	+	0.993303i	$0.536859\pi$
$602$	−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	$-0.611619\pi$
$607$	−16.9268	−0.687037	−0.343518	+	0.939146i	$0.611619\pi$
$608$	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	$-0.251445\pi$
$613$	34.8550	1.40778	0.703891	+	0.710308i	$0.251445\pi$
$614$	−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	$-0.637094\pi$
$659$	−21.4353	−0.835001	−0.417501	+	0.908677i	$0.637094\pi$
$660$	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	$-0.536125\pi$
$673$	−5.87580	−0.226496	−0.113248	+	0.993567i	$0.536125\pi$
$674$	61.5851	2.37217
$675$	5.59689	0.215424
$676$	19.2274	0.739515
$677$	−3.77568	−0.145111	−0.0725555	−	0.997364i	$-0.523115\pi$
$677$	−3.77568	−0.145111	−0.0725555	+	0.997364i	$0.523115\pi$
$678$	−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	$-0.294851\pi$
$701$	31.8138	1.20159	0.600795	+	0.799403i	$0.294851\pi$
$702$	−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	$-0.146538\pi$
$733$	48.5107	1.79178	0.895892	+	0.444272i	$0.146538\pi$
$734$	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	$-0.449128\pi$
$739$	8.65220	0.318276	0.159138	+	0.987256i	$0.449128\pi$
$740$	18.7427	0.688997
$741$	−39.3539	−1.44570
$742$	−13.0881	−0.480480
$743$	−9.83052	−0.360647	−0.180323	−	0.983607i	$-0.557714\pi$
$743$	−9.83052	−0.360647	−0.180323	+	0.983607i	$0.557714\pi$
$744$	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	$-0.346893\pi$
$761$	25.5265	0.925334	0.462667	+	0.886532i	$0.346893\pi$
$762$	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	$-0.652008\pi$
$769$	−25.4903	−0.919202	−0.459601	+	0.888125i	$0.652008\pi$
$770$	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	$-0.726953\pi$
$787$	−36.6996	−1.30820	−0.654101	+	0.756408i	$0.726953\pi$
$788$	−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	$-0.680668\pi$
$809$	−30.5817	−1.07519	−0.537597	+	0.843202i	$0.680668\pi$
$810$	−59.8765	−2.10385
$811$	16.0980	0.565276	0.282638	−	0.959227i	$-0.408791\pi$
$811$	16.0980	0.565276	0.282638	+	0.959227i	$0.408791\pi$
$812$	−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	$-0.210967\pi$
$821$	45.1739	1.57658	0.788290	+	0.615304i	$0.210967\pi$
$822$	−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	$-0.749099\pi$
$827$	−40.5541	−1.41021	−0.705103	+	0.709105i	$0.749099\pi$
$828$	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	$-0.424336\pi$
$853$	13.7546	0.470947	0.235474	+	0.971881i	$0.424336\pi$
$854$	7.90705	0.270574
$855$	−12.7412	−0.435739
$856$	6.60135	0.225629
$857$	13.0885	0.447095	0.223548	−	0.974693i	$-0.428236\pi$
$857$	13.0885	0.447095	0.223548	+	0.974693i	$0.428236\pi$
$858$	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	$-0.234975\pi$
$877$	43.8103	1.47937	0.739684	+	0.672955i	$0.234975\pi$
$878$	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	$-0.688795\pi$
$887$	−33.2938	−1.11790	−0.558948	+	0.829202i	$0.688795\pi$
$888$	−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	$-0.334174\pi$
$919$	30.1762	0.995421	0.497710	+	0.867343i	$0.334174\pi$
$920$	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	$-0.353398\pi$
$937$	27.2099	0.888908	0.444454	+	0.895802i	$0.353398\pi$
$938$	−105.529	−3.44565
$939$	44.5242	1.45299
$940$	26.7987	0.874078
$941$	13.5420	0.441458	0.220729	−	0.975335i	$-0.429156\pi$
$941$	13.5420	0.441458	0.220729	+	0.975335i	$0.429156\pi$
$942$	−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	$-0.520291\pi$
$953$	−3.93314	−0.127407	−0.0637035	+	0.997969i	$0.520291\pi$
$954$	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	$-0.251836\pi$
$967$	43.7228	1.40603	0.703016	+	0.711174i	$0.251836\pi$
$968$	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	$-0.212067\pi$
$997$	49.6464	1.57232	0.786158	+	0.618026i	$0.212067\pi$
$998$	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.u.1.54		64
11.2	odd	10		671.2.j.c.367.28	yes	128
11.6	odd	10		671.2.j.c.245.28	✓	128
11.10	odd	2		7381.2.a.v.1.11		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.j.c.245.28	✓	128	11.6	odd	10
671.2.j.c.367.28	yes	128	11.2	odd	10
7381.2.a.u.1.54		64	1.1	even	1	trivial
7381.2.a.v.1.11		64	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

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Database

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