LMFDB - Embedded newform 7381.2.a.v.1.13

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			1.13
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)

$f(q)$	$=$	$q-1.86589 q^{2} +3.07680 q^{3} +1.48156 q^{4} +3.54844 q^{5} -5.74097 q^{6} -1.55335 q^{7} +0.967361 q^{8} +6.46667 q^{9} +O(q^{10})$	\(q-1.86589 q^{2} +3.07680 q^{3} +1.48156 q^{4} +3.54844 q^{5} -5.74097 q^{6} -1.55335 q^{7} +0.967361 q^{8} +6.46667 q^{9} -6.62101 q^{10} +4.55845 q^{12} +3.04877 q^{13} +2.89838 q^{14} +10.9178 q^{15} -4.76810 q^{16} +0.800394 q^{17} -12.0661 q^{18} +1.70018 q^{19} +5.25721 q^{20} -4.77934 q^{21} +7.89486 q^{23} +2.97637 q^{24} +7.59142 q^{25} -5.68867 q^{26} +10.6663 q^{27} -2.30137 q^{28} +5.64016 q^{29} -20.3715 q^{30} +2.30970 q^{31} +6.96205 q^{32} -1.49345 q^{34} -5.51197 q^{35} +9.58074 q^{36} +2.52959 q^{37} -3.17236 q^{38} +9.38043 q^{39} +3.43262 q^{40} -4.65850 q^{41} +8.91774 q^{42} +7.17708 q^{43} +22.9466 q^{45} -14.7310 q^{46} -11.4007 q^{47} -14.6705 q^{48} -4.58710 q^{49} -14.1648 q^{50} +2.46265 q^{51} +4.51692 q^{52} +11.9207 q^{53} -19.9021 q^{54} -1.50265 q^{56} +5.23111 q^{57} -10.5239 q^{58} +3.26479 q^{59} +16.1754 q^{60} +1.00000 q^{61} -4.30965 q^{62} -10.0450 q^{63} -3.45423 q^{64} +10.8184 q^{65} -4.85551 q^{67} +1.18583 q^{68} +24.2909 q^{69} +10.2847 q^{70} -12.7023 q^{71} +6.25561 q^{72} -15.4387 q^{73} -4.71995 q^{74} +23.3572 q^{75} +2.51892 q^{76} -17.5029 q^{78} +0.573217 q^{79} -16.9193 q^{80} +13.4179 q^{81} +8.69226 q^{82} -11.6048 q^{83} -7.08086 q^{84} +2.84015 q^{85} -13.3917 q^{86} +17.3536 q^{87} -5.34002 q^{89} -42.8159 q^{90} -4.73580 q^{91} +11.6967 q^{92} +7.10647 q^{93} +21.2726 q^{94} +6.03299 q^{95} +21.4208 q^{96} -18.2114 q^{97} +8.55904 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.86589	−1.31939	−0.659693	−	0.751535i	$-0.729314\pi$
$2$	−1.86589	−1.31939	−0.659693	+	0.751535i	$0.729314\pi$
$3$	3.07680	1.77639	0.888195	−	0.459468i	$-0.151960\pi$
$3$	3.07680	1.77639	0.888195	+	0.459468i	$0.151960\pi$
$4$	1.48156	0.740778
$5$	3.54844	1.58691	0.793455	−	0.608629i	$-0.208280\pi$
$5$	3.54844	1.58691	0.793455	+	0.608629i	$0.208280\pi$
$6$	−5.74097	−2.34374
$7$	−1.55335	−0.587111	−0.293556	−	0.955942i	$-0.594839\pi$
$7$	−1.55335	−0.587111	−0.293556	+	0.955942i	$0.594839\pi$
$8$	0.967361	0.342014
$9$	6.46667	2.15556
$10$	−6.62101	−2.09375
$11$	0	0
$11$	0	0
$12$	4.55845	1.31591
$13$	3.04877	0.845575	0.422788	−	0.906229i	$-0.361052\pi$
$13$	3.04877	0.845575	0.422788	+	0.906229i	$0.361052\pi$
$14$	2.89838	0.774626
$15$	10.9178	2.81897
$16$	−4.76810	−1.19203
$17$	0.800394	0.194124	0.0970620	−	0.995278i	$-0.469055\pi$
$17$	0.800394	0.194124	0.0970620	+	0.995278i	$0.469055\pi$
$18$	−12.0661	−2.84401
$19$	1.70018	0.390049	0.195024	−	0.980798i	$-0.437521\pi$
$19$	1.70018	0.390049	0.195024	+	0.980798i	$0.437521\pi$
$20$	5.25721	1.17555
$21$	−4.77934	−1.04294
$22$	0	0
$23$	7.89486	1.64619	0.823096	−	0.567902i	$-0.192245\pi$
$23$	7.89486	1.64619	0.823096	+	0.567902i	$0.192245\pi$
$24$	2.97637	0.607549
$25$	7.59142	1.51828
$26$	−5.68867	−1.11564
$27$	10.6663	2.05272
$28$	−2.30137	−0.434919
$29$	5.64016	1.04735	0.523676	−	0.851917i	$-0.324560\pi$
$29$	5.64016	1.04735	0.523676	+	0.851917i	$0.324560\pi$
$30$	−20.3715	−3.71931
$31$	2.30970	0.414834	0.207417	−	0.978253i	$-0.433494\pi$
$31$	2.30970	0.414834	0.207417	+	0.978253i	$0.433494\pi$
$32$	6.96205	1.23073
$33$	0	0
$34$	−1.49345	−0.256124
$35$	−5.51197	−0.931692
$36$	9.58074	1.59679
$37$	2.52959	0.415862	0.207931	−	0.978143i	$-0.433327\pi$
$37$	2.52959	0.415862	0.207931	+	0.978143i	$0.433327\pi$
$38$	−3.17236	−0.514624
$39$	9.38043	1.50207
$40$	3.43262	0.542745
$41$	−4.65850	−0.727535	−0.363768	−	0.931490i	$-0.618510\pi$
$41$	−4.65850	−0.727535	−0.363768	+	0.931490i	$0.618510\pi$
$42$	8.91774	1.37604
$43$	7.17708	1.09449	0.547247	−	0.836971i	$-0.315676\pi$
$43$	7.17708	1.09449	0.547247	+	0.836971i	$0.315676\pi$
$44$	0	0
$45$	22.9466	3.42068
$46$	−14.7310	−2.17196
$47$	−11.4007	−1.66297	−0.831484	−	0.555549i	$-0.812508\pi$
$47$	−11.4007	−1.66297	−0.831484	+	0.555549i	$0.812508\pi$
$48$	−14.6705	−2.11750
$49$	−4.58710	−0.655301
$50$	−14.1648	−2.00320
$51$	2.46265	0.344840
$52$	4.51692	0.626384
$53$	11.9207	1.63744	0.818720	−	0.574193i	$-0.194684\pi$
$53$	11.9207	1.63744	0.818720	+	0.574193i	$0.194684\pi$
$54$	−19.9021	−2.70833
$55$	0	0
$56$	−1.50265	−0.200800
$57$	5.23111	0.692878
$58$	−10.5239	−1.38186
$59$	3.26479	0.425040	0.212520	−	0.977157i	$-0.431833\pi$
$59$	3.26479	0.425040	0.212520	+	0.977157i	$0.431833\pi$
$60$	16.1754	2.08823
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−4.30965	−0.547326
$63$	−10.0450	−1.26555
$64$	−3.45423	−0.431779
$65$	10.8184	1.34185
$66$	0	0
$67$	−4.85551	−0.593195	−0.296597	−	0.955003i	$-0.595852\pi$
$67$	−4.85551	−0.593195	−0.296597	+	0.955003i	$0.595852\pi$
$68$	1.18583	0.143803
$69$	24.2909	2.92428
$70$	10.2847	1.22926
$71$	−12.7023	−1.50748	−0.753741	−	0.657172i	$-0.771753\pi$
$71$	−12.7023	−1.50748	−0.753741	+	0.657172i	$0.771753\pi$
$72$	6.25561	0.737230
$73$	−15.4387	−1.80697	−0.903483	−	0.428624i	$-0.858999\pi$
$73$	−15.4387	−1.80697	−0.903483	+	0.428624i	$0.858999\pi$
$74$	−4.71995	−0.548683
$75$	23.3572	2.69706
$76$	2.51892	0.288939
$77$	0	0
$78$	−17.5029	−1.98181
$79$	0.573217	0.0644920	0.0322460	−	0.999480i	$-0.489734\pi$
$79$	0.573217	0.0644920	0.0322460	+	0.999480i	$0.489734\pi$
$80$	−16.9193	−1.89164
$81$	13.4179	1.49087
$82$	8.69226	0.959900
$83$	−11.6048	−1.27379	−0.636894	−	0.770951i	$-0.719781\pi$
$83$	−11.6048	−1.27379	−0.636894	+	0.770951i	$0.719781\pi$
$84$	−7.08086	−0.772585
$85$	2.84015	0.308057
$86$	−13.3917	−1.44406
$87$	17.3536	1.86050
$88$	0	0
$89$	−5.34002	−0.566041	−0.283020	−	0.959114i	$-0.591336\pi$
$89$	−5.34002	−0.566041	−0.283020	+	0.959114i	$0.591336\pi$
$90$	−42.8159	−4.51319
$91$	−4.73580	−0.496447
$92$	11.6967	1.21946
$93$	7.10647	0.736907
$94$	21.2726	2.19410
$95$	6.03299	0.618972
$96$	21.4208	2.18625
$97$	−18.2114	−1.84909	−0.924545	−	0.381072i	$-0.875555\pi$
$97$	−18.2114	−1.84909	−0.924545	+	0.381072i	$0.875555\pi$
$98$	8.55904	0.864594
$99$	0	0
$100$	11.2471	1.12471
$101$	−13.4899	−1.34230	−0.671149	−	0.741322i	$-0.734199\pi$
$101$	−13.4899	−1.34230	−0.671149	+	0.741322i	$0.734199\pi$
$102$	−4.59504	−0.454977
$103$	3.59271	0.354001	0.177000	−	0.984211i	$-0.443361\pi$
$103$	3.59271	0.354001	0.177000	+	0.984211i	$0.443361\pi$
$104$	2.94926	0.289198
$105$	−16.9592	−1.65505
$106$	−22.2428	−2.16041
$107$	10.0546	0.972011	0.486006	−	0.873956i	$-0.338453\pi$
$107$	10.0546	0.972011	0.486006	+	0.873956i	$0.338453\pi$
$108$	15.8026	1.52061
$109$	10.4595	1.00183	0.500917	−	0.865495i	$-0.332996\pi$
$109$	10.4595	1.00183	0.500917	+	0.865495i	$0.332996\pi$
$110$	0	0
$111$	7.78304	0.738733
$112$	7.40653	0.699852
$113$	−11.1627	−1.05010	−0.525049	−	0.851072i	$-0.675953\pi$
$113$	−11.1627	−1.05010	−0.525049	+	0.851072i	$0.675953\pi$
$114$	−9.76070	−0.914173
$115$	28.0144	2.61236
$116$	8.35622	0.775855
$117$	19.7154	1.82269
$118$	−6.09175	−0.560791
$119$	−1.24329	−0.113972
$120$	10.5615	0.964126
$121$	0	0
$122$	−1.86589	−0.168930
$123$	−14.3333	−1.29239
$124$	3.42195	0.307300
$125$	9.19549	0.822469
$126$	18.7429	1.66975
$127$	5.75374	0.510561	0.255281	−	0.966867i	$-0.417832\pi$
$127$	5.75374	0.510561	0.255281	+	0.966867i	$0.417832\pi$
$128$	−7.47888	−0.661045
$129$	22.0824	1.94425
$130$	−20.1859	−1.77042
$131$	−1.00276	−0.0876118	−0.0438059	−	0.999040i	$-0.513948\pi$
$131$	−1.00276	−0.0876118	−0.0438059	+	0.999040i	$0.513948\pi$
$132$	0	0
$133$	−2.64098	−0.229002
$134$	9.05986	0.782653
$135$	37.8485	3.25748
$136$	0.774270	0.0663931
$137$	−16.8123	−1.43637	−0.718187	−	0.695850i	$-0.755028\pi$
$137$	−16.8123	−1.43637	−0.718187	+	0.695850i	$0.755028\pi$
$138$	−45.3242	−3.85825
$139$	−5.06384	−0.429510	−0.214755	−	0.976668i	$-0.568895\pi$
$139$	−5.06384	−0.429510	−0.214755	+	0.976668i	$0.568895\pi$
$140$	−8.16629	−0.690177
$141$	−35.0777	−2.95408
$142$	23.7011	1.98895
$143$	0	0
$144$	−30.8338	−2.56948
$145$	20.0138	1.66205
$146$	28.8070	2.38409
$147$	−14.1136	−1.16407
$148$	3.74773	0.308062
$149$	−12.9582	−1.06158	−0.530790	−	0.847503i	$-0.678105\pi$
$149$	−12.9582	−1.06158	−0.530790	+	0.847503i	$0.678105\pi$
$150$	−43.5821	−3.55846
$151$	−19.4766	−1.58498	−0.792492	−	0.609882i	$-0.791217\pi$
$151$	−19.4766	−1.58498	−0.792492	+	0.609882i	$0.791217\pi$
$152$	1.64469	0.133402
$153$	5.17589	0.418446
$154$	0	0
$155$	8.19583	0.658305
$156$	13.8976	1.11270
$157$	−2.68956	−0.214650	−0.107325	−	0.994224i	$-0.534229\pi$
$157$	−2.68956	−0.214650	−0.107325	+	0.994224i	$0.534229\pi$
$158$	−1.06956	−0.0850898
$159$	36.6777	2.90873
$160$	24.7044	1.95305
$161$	−12.2635	−0.966498
$162$	−25.0363	−1.96704
$163$	19.4330	1.52211	0.761054	−	0.648688i	$-0.224682\pi$
$163$	19.4330	1.52211	0.761054	+	0.648688i	$0.224682\pi$
$164$	−6.90183	−0.538942
$165$	0	0
$166$	21.6532	1.68062
$167$	−10.2879	−0.796098	−0.398049	−	0.917364i	$-0.630313\pi$
$167$	−10.2879	−0.796098	−0.398049	+	0.917364i	$0.630313\pi$
$168$	−4.62335	−0.356699
$169$	−3.70503	−0.285002
$170$	−5.29941	−0.406446
$171$	10.9945	0.840772
$172$	10.6332	0.810777
$173$	8.71867	0.662869	0.331434	−	0.943478i	$-0.392467\pi$
$173$	8.71867	0.662869	0.331434	+	0.943478i	$0.392467\pi$
$174$	−32.3800	−2.45472
$175$	−11.7921	−0.891401
$176$	0	0
$177$	10.0451	0.755036
$178$	9.96390	0.746826
$179$	−5.48322	−0.409835	−0.204918	−	0.978779i	$-0.565693\pi$
$179$	−5.48322	−0.409835	−0.204918	+	0.978779i	$0.565693\pi$
$180$	33.9967	2.53396
$181$	−1.87067	−0.139046	−0.0695231	−	0.997580i	$-0.522148\pi$
$181$	−1.87067	−0.139046	−0.0695231	+	0.997580i	$0.522148\pi$
$182$	8.83649	0.655005
$183$	3.07680	0.227443
$184$	7.63718	0.563020
$185$	8.97610	0.659936
$186$	−13.2599	−0.972265
$187$	0	0
$188$	−16.8908	−1.23189
$189$	−16.5684	−1.20518
$190$	−11.2569	−0.816663
$191$	−10.1255	−0.732655	−0.366327	−	0.930486i	$-0.619385\pi$
$191$	−10.1255	−0.732655	−0.366327	+	0.930486i	$0.619385\pi$
$192$	−10.6280	−0.767007
$193$	20.7592	1.49428	0.747140	−	0.664666i	$-0.231426\pi$
$193$	20.7592	1.49428	0.747140	+	0.664666i	$0.231426\pi$
$194$	33.9806	2.43966
$195$	33.2859	2.38365
$196$	−6.79605	−0.485432
$197$	4.92603	0.350965	0.175483	−	0.984483i	$-0.443851\pi$
$197$	4.92603	0.350965	0.175483	+	0.984483i	$0.443851\pi$
$198$	0	0
$199$	21.7101	1.53899	0.769496	−	0.638652i	$-0.220508\pi$
$199$	21.7101	1.53899	0.769496	+	0.638652i	$0.220508\pi$
$200$	7.34364	0.519274
$201$	−14.9394	−1.05375
$202$	25.1708	1.77101
$203$	−8.76115	−0.614912
$204$	3.64855	0.255450
$205$	−16.5304	−1.15453
$206$	−6.70362	−0.467063
$207$	51.0535	3.54846
$208$	−14.5368	−1.00795
$209$	0	0
$210$	31.6440	2.18365
$211$	1.13294	0.0779946	0.0389973	−	0.999239i	$-0.487584\pi$
$211$	1.13294	0.0779946	0.0389973	+	0.999239i	$0.487584\pi$
$212$	17.6612	1.21298
$213$	−39.0823	−2.67787
$214$	−18.7607	−1.28246
$215$	25.4674	1.73686
$216$	10.3181	0.702059
$217$	−3.58777	−0.243554
$218$	−19.5162	−1.32181
$219$	−47.5018	−3.20988
$220$	0	0
$221$	2.44021	0.164147
$222$	−14.5223	−0.974674
$223$	−6.78174	−0.454139	−0.227070	−	0.973879i	$-0.572914\pi$
$223$	−6.78174	−0.454139	−0.227070	+	0.973879i	$0.572914\pi$
$224$	−10.8145	−0.722574
$225$	49.0912	3.27275
$226$	20.8284	1.38549
$227$	17.2952	1.14792	0.573962	−	0.818882i	$-0.305406\pi$
$227$	17.2952	1.14792	0.573962	+	0.818882i	$0.305406\pi$
$228$	7.75019	0.513269
$229$	−1.65629	−0.109450	−0.0547252	−	0.998501i	$-0.517428\pi$
$229$	−1.65629	−0.109450	−0.0547252	+	0.998501i	$0.517428\pi$
$230$	−52.2719	−3.44671
$231$	0	0
$232$	5.45607	0.358209
$233$	−12.1522	−0.796116	−0.398058	−	0.917360i	$-0.630316\pi$
$233$	−12.1522	−0.796116	−0.398058	+	0.917360i	$0.630316\pi$
$234$	−36.7868	−2.40483
$235$	−40.4548	−2.63898
$236$	4.83697	0.314860
$237$	1.76367	0.114563
$238$	2.31985	0.150374
$239$	6.36230	0.411543	0.205771	−	0.978600i	$-0.434030\pi$
$239$	6.36230	0.411543	0.205771	+	0.978600i	$0.434030\pi$
$240$	−52.0573	−3.36029
$241$	−15.2833	−0.984484	−0.492242	−	0.870458i	$-0.663823\pi$
$241$	−15.2833	−0.984484	−0.492242	+	0.870458i	$0.663823\pi$
$242$	0	0
$243$	9.28526	0.595649
$244$	1.48156	0.0948469
$245$	−16.2771	−1.03990
$246$	26.7443	1.70516
$247$	5.18346	0.329815
$248$	2.23431	0.141879
$249$	−35.7055	−2.26274
$250$	−17.1578	−1.08515
$251$	5.91760	0.373516	0.186758	−	0.982406i	$-0.440202\pi$
$251$	5.91760	0.373516	0.186758	+	0.982406i	$0.440202\pi$
$252$	−14.8822	−0.937493
$253$	0	0
$254$	−10.7359	−0.673627
$255$	8.73856	0.547230
$256$	20.8632	1.30395
$257$	7.41501	0.462535	0.231268	−	0.972890i	$-0.425713\pi$
$257$	7.41501	0.462535	0.231268	+	0.972890i	$0.425713\pi$
$258$	−41.2034	−2.56521
$259$	−3.92934	−0.244157
$260$	16.0280	0.994015
$261$	36.4731	2.25763
$262$	1.87105	0.115594
$263$	26.9425	1.66135	0.830674	−	0.556759i	$-0.187955\pi$
$263$	26.9425	1.66135	0.830674	+	0.556759i	$0.187955\pi$
$264$	0	0
$265$	42.3000	2.59847
$266$	4.92778	0.302142
$267$	−16.4301	−1.00551
$268$	−7.19371	−0.439426
$269$	28.5468	1.74053	0.870264	−	0.492586i	$-0.163948\pi$
$269$	28.5468	1.74053	0.870264	+	0.492586i	$0.163948\pi$
$270$	−70.6213	−4.29788
$271$	1.70191	0.103384	0.0516919	−	0.998663i	$-0.483539\pi$
$271$	1.70191	0.103384	0.0516919	+	0.998663i	$0.483539\pi$
$272$	−3.81636	−0.231401
$273$	−14.5711	−0.881882
$274$	31.3700	1.89513
$275$	0	0
$276$	35.9883	2.16624
$277$	26.8662	1.61423	0.807117	−	0.590392i	$-0.201027\pi$
$277$	26.8662	1.61423	0.807117	+	0.590392i	$0.201027\pi$
$278$	9.44859	0.566689
$279$	14.9361	0.894199
$280$	−5.33206	−0.318652
$281$	12.0693	0.719996	0.359998	−	0.932953i	$-0.382777\pi$
$281$	12.0693	0.719996	0.359998	+	0.932953i	$0.382777\pi$
$282$	65.4513	3.89757
$283$	28.9485	1.72081	0.860406	−	0.509609i	$-0.170210\pi$
$283$	28.9485	1.72081	0.860406	+	0.509609i	$0.170210\pi$
$284$	−18.8191	−1.11671
$285$	18.5623	1.09954
$286$	0	0
$287$	7.23628	0.427144
$288$	45.0213	2.65291
$289$	−16.3594	−0.962316
$290$	−37.3436	−2.19289
$291$	−56.0329	−3.28470
$292$	−22.8733	−1.33856
$293$	6.50722	0.380156	0.190078	−	0.981769i	$-0.439126\pi$
$293$	6.50722	0.380156	0.190078	+	0.981769i	$0.439126\pi$
$294$	26.3344	1.53586
$295$	11.5849	0.674500
$296$	2.44703	0.142231
$297$	0	0
$298$	24.1787	1.40063
$299$	24.0696	1.39198
$300$	34.6051	1.99792
$301$	−11.1485	−0.642590
$302$	36.3413	2.09121
$303$	−41.5058	−2.38444
$304$	−8.10665	−0.464948
$305$	3.54844	0.203183
$306$	−9.65765	−0.552091
$307$	−13.9135	−0.794083	−0.397041	−	0.917801i	$-0.629963\pi$
$307$	−13.9135	−0.794083	−0.397041	+	0.917801i	$0.629963\pi$
$308$	0	0
$309$	11.0540	0.628843
$310$	−15.2925	−0.868558
$311$	−13.0378	−0.739306	−0.369653	−	0.929170i	$-0.620524\pi$
$311$	−13.0378	−0.739306	−0.369653	+	0.929170i	$0.620524\pi$
$312$	9.07426	0.513729
$313$	10.9343	0.618043	0.309022	−	0.951055i	$-0.399998\pi$
$313$	10.9343	0.618043	0.309022	+	0.951055i	$0.399998\pi$
$314$	5.01842	0.283206
$315$	−35.6441	−2.00832
$316$	0.849254	0.0477742
$317$	5.06481	0.284468	0.142234	−	0.989833i	$-0.454571\pi$
$317$	5.06481	0.284468	0.142234	+	0.989833i	$0.454571\pi$
$318$	−68.4366	−3.83774
$319$	0	0
$320$	−12.2571	−0.685194
$321$	30.9358	1.72667
$322$	22.8823	1.27518
$323$	1.36082	0.0757178
$324$	19.8793	1.10441
$325$	23.1445	1.28382
$326$	−36.2599	−2.00825
$327$	32.1816	1.77965
$328$	−4.50645	−0.248827
$329$	17.7093	0.976347
$330$	0	0
$331$	−2.83615	−0.155889	−0.0779444	−	0.996958i	$-0.524836\pi$
$331$	−2.83615	−0.155889	−0.0779444	+	0.996958i	$0.524836\pi$
$332$	−17.1931	−0.943594
$333$	16.3580	0.896415
$334$	19.1960	1.05036
$335$	−17.2295	−0.941347
$336$	22.7884	1.24321
$337$	−15.3768	−0.837628	−0.418814	−	0.908072i	$-0.637554\pi$
$337$	−15.3768	−0.837628	−0.418814	+	0.908072i	$0.637554\pi$
$338$	6.91319	0.376028
$339$	−34.3454	−1.86538
$340$	4.20784	0.228202
$341$	0	0
$342$	−20.5146	−1.10930
$343$	17.9988	0.971845
$344$	6.94282	0.374332
$345$	86.1947	4.64057
$346$	−16.2681	−0.874579
$347$	−21.2674	−1.14169	−0.570847	−	0.821056i	$-0.693385\pi$
$347$	−21.2674	−1.14169	−0.570847	+	0.821056i	$0.693385\pi$
$348$	25.7104	1.37822
$349$	0.448039	0.0239830	0.0119915	−	0.999928i	$-0.496183\pi$
$349$	0.448039	0.0239830	0.0119915	+	0.999928i	$0.496183\pi$
$350$	22.0028	1.17610
$351$	32.5189	1.73573
$352$	0	0
$353$	0.314670	0.0167482	0.00837410	−	0.999965i	$-0.497334\pi$
$353$	0.314670	0.0167482	0.00837410	+	0.999965i	$0.497334\pi$
$354$	−18.7431	−0.996184
$355$	−45.0732	−2.39224
$356$	−7.91153	−0.419310
$357$	−3.82536	−0.202459
$358$	10.2311	0.540731
$359$	12.9469	0.683312	0.341656	−	0.939825i	$-0.389012\pi$
$359$	12.9469	0.683312	0.341656	+	0.939825i	$0.389012\pi$
$360$	22.1976	1.16992
$361$	−16.1094	−0.847862
$362$	3.49048	0.183455
$363$	0	0
$364$	−7.01635	−0.367757
$365$	−54.7834	−2.86749
$366$	−5.74097	−0.300085
$367$	13.4783	0.703564	0.351782	−	0.936082i	$-0.385576\pi$
$367$	13.4783	0.703564	0.351782	+	0.936082i	$0.385576\pi$
$368$	−37.6435	−1.96230
$369$	−30.1250	−1.56825
$370$	−16.7484	−0.870710
$371$	−18.5171	−0.961359
$372$	10.5286	0.545885
$373$	14.0874	0.729417	0.364709	−	0.931122i	$-0.381169\pi$
$373$	14.0874	0.729417	0.364709	+	0.931122i	$0.381169\pi$
$374$	0	0
$375$	28.2926	1.46103
$376$	−11.0286	−0.568758
$377$	17.1955	0.885615
$378$	30.9149	1.59009
$379$	28.1274	1.44481	0.722403	−	0.691472i	$-0.243038\pi$
$379$	28.1274	1.44481	0.722403	+	0.691472i	$0.243038\pi$
$380$	8.93822	0.458521
$381$	17.7031	0.906956
$382$	18.8931	0.966654
$383$	−3.34109	−0.170722	−0.0853608	−	0.996350i	$-0.527204\pi$
$383$	−3.34109	−0.170722	−0.0853608	+	0.996350i	$0.527204\pi$
$384$	−23.0110	−1.17427
$385$	0	0
$386$	−38.7345	−1.97153
$387$	46.4118	2.35925
$388$	−26.9813	−1.36977
$389$	8.83381	0.447892	0.223946	−	0.974602i	$-0.428106\pi$
$389$	8.83381	0.447892	0.223946	+	0.974602i	$0.428106\pi$
$390$	−62.1079	−3.14496
$391$	6.31900	0.319565
$392$	−4.43738	−0.224122
$393$	−3.08530	−0.155633
$394$	−9.19145	−0.463059
$395$	2.03403	0.102343
$396$	0	0
$397$	−23.5458	−1.18173	−0.590864	−	0.806771i	$-0.701213\pi$
$397$	−23.5458	−1.18173	−0.590864	+	0.806771i	$0.701213\pi$
$398$	−40.5088	−2.03052
$399$	−8.12575	−0.406796
$400$	−36.1967	−1.80983
$401$	11.4282	0.570696	0.285348	−	0.958424i	$-0.407891\pi$
$401$	11.4282	0.570696	0.285348	+	0.958424i	$0.407891\pi$
$402$	27.8753	1.39030
$403$	7.04173	0.350774
$404$	−19.9861	−0.994345
$405$	47.6124	2.36588
$406$	16.3474	0.811306
$407$	0	0
$408$	2.38227	0.117940
$409$	2.26489	0.111992	0.0559958	−	0.998431i	$-0.482167\pi$
$409$	2.26489	0.111992	0.0559958	+	0.998431i	$0.482167\pi$
$410$	30.8440	1.52327
$411$	−51.7281	−2.55156
$412$	5.32281	0.262236
$413$	−5.07137	−0.249546
$414$	−95.2603	−4.68179
$415$	−41.1788	−2.02139
$416$	21.2257	1.04067
$417$	−15.5804	−0.762976
$418$	0	0
$419$	19.0250	0.929431	0.464716	−	0.885460i	$-0.346157\pi$
$419$	19.0250	0.929431	0.464716	+	0.885460i	$0.346157\pi$
$420$	−25.1260	−1.22602
$421$	−18.2575	−0.889814	−0.444907	−	0.895577i	$-0.646763\pi$
$421$	−18.2575	−0.889814	−0.444907	+	0.895577i	$0.646763\pi$
$422$	−2.11394	−0.102905
$423$	−73.7248	−3.58462
$424$	11.5317	0.560027
$425$	6.07613	0.294735
$426$	72.9234	3.53315
$427$	−1.55335	−0.0751719
$428$	14.8964	0.720045
$429$	0	0
$430$	−47.5195	−2.29159
$431$	−19.3988	−0.934410	−0.467205	−	0.884149i	$-0.654739\pi$
$431$	−19.3988	−0.934410	−0.467205	+	0.884149i	$0.654739\pi$
$432$	−50.8578	−2.44690
$433$	33.5882	1.61414	0.807072	−	0.590453i	$-0.201051\pi$
$433$	33.5882	1.61414	0.807072	+	0.590453i	$0.201051\pi$
$434$	6.69440	0.321341
$435$	61.5783	2.95245
$436$	15.4963	0.742137
$437$	13.4227	0.642095
$438$	88.6333	4.23506
$439$	−25.3058	−1.20778	−0.603890	−	0.797067i	$-0.706383\pi$
$439$	−25.3058	−1.20778	−0.603890	+	0.797067i	$0.706383\pi$
$440$	0	0
$441$	−29.6633	−1.41254
$442$	−4.55318	−0.216573
$443$	−32.5399	−1.54602	−0.773009	−	0.634395i	$-0.781249\pi$
$443$	−32.5399	−1.54602	−0.773009	+	0.634395i	$0.781249\pi$
$444$	11.5310	0.547237
$445$	−18.9487	−0.898256
$446$	12.6540	0.599184
$447$	−39.8699	−1.88578
$448$	5.36563	0.253502
$449$	6.78893	0.320390	0.160195	−	0.987085i	$-0.448788\pi$
$449$	6.78893	0.320390	0.160195	+	0.987085i	$0.448788\pi$
$450$	−91.5990	−4.31802
$451$	0	0
$452$	−16.5382	−0.777890
$453$	−59.9256	−2.81555
$454$	−32.2710	−1.51455
$455$	−16.8047	−0.787816
$456$	5.06037	0.236974
$457$	−6.54879	−0.306339	−0.153170	−	0.988200i	$-0.548948\pi$
$457$	−6.54879	−0.306339	−0.153170	+	0.988200i	$0.548948\pi$
$458$	3.09045	0.144407
$459$	8.53720	0.398483
$460$	41.5049	1.93518
$461$	−26.0536	−1.21344	−0.606718	−	0.794917i	$-0.707514\pi$
$461$	−26.0536	−1.21344	−0.606718	+	0.794917i	$0.707514\pi$
$462$	0	0
$463$	11.9128	0.553637	0.276818	−	0.960922i	$-0.410720\pi$
$463$	11.9128	0.553637	0.276818	+	0.960922i	$0.410720\pi$
$464$	−26.8929	−1.24847
$465$	25.2169	1.16941
$466$	22.6747	1.05038
$467$	−25.6220	−1.18565	−0.592823	−	0.805333i	$-0.701987\pi$
$467$	−25.6220	−1.18565	−0.592823	+	0.805333i	$0.701987\pi$
$468$	29.2094	1.35021
$469$	7.54231	0.348271
$470$	75.4843	3.48183
$471$	−8.27521	−0.381302
$472$	3.15823	0.145369
$473$	0	0
$474$	−3.29082	−0.151153
$475$	12.9068	0.592204
$476$	−1.84201	−0.0844282
$477$	77.0876	3.52960
$478$	−11.8714	−0.542984
$479$	−18.9518	−0.865928	−0.432964	−	0.901411i	$-0.642532\pi$
$479$	−18.9518	−0.865928	−0.432964	+	0.901411i	$0.642532\pi$
$480$	76.0104	3.46938
$481$	7.71213	0.351643
$482$	28.5170	1.29891
$483$	−37.7322	−1.71688
$484$	0	0
$485$	−64.6222	−2.93434
$486$	−17.3253	−0.785891
$487$	8.32987	0.377463	0.188731	−	0.982029i	$-0.439562\pi$
$487$	8.32987	0.377463	0.188731	+	0.982029i	$0.439562\pi$
$488$	0.967361	0.0437904
$489$	59.7913	2.70386
$490$	30.3712	1.37203
$491$	30.4696	1.37507	0.687537	−	0.726150i	$-0.258692\pi$
$491$	30.4696	1.37507	0.687537	+	0.726150i	$0.258692\pi$
$492$	−21.2355	−0.957371
$493$	4.51435	0.203316
$494$	−9.67177	−0.435154
$495$	0	0
$496$	−11.0129	−0.494493
$497$	19.7311	0.885059
$498$	66.6226	2.98543
$499$	7.28785	0.326249	0.163124	−	0.986605i	$-0.447843\pi$
$499$	7.28785	0.326249	0.163124	+	0.986605i	$0.447843\pi$
$500$	13.6236	0.609267
$501$	−31.6536	−1.41418
$502$	−11.0416	−0.492811
$503$	28.1274	1.25414	0.627069	−	0.778963i	$-0.284254\pi$
$503$	28.1274	1.25414	0.627069	+	0.778963i	$0.284254\pi$
$504$	−9.71715	−0.432836
$505$	−47.8682	−2.13011
$506$	0	0
$507$	−11.3996	−0.506275
$508$	8.52448	0.378213
$509$	−41.7084	−1.84869	−0.924347	−	0.381553i	$-0.875389\pi$
$509$	−41.7084	−1.84869	−0.924347	+	0.381553i	$0.875389\pi$
$510$	−16.3052	−0.722007
$511$	23.9817	1.06089
$512$	−23.9708	−1.05937
$513$	18.1346	0.800661
$514$	−13.8356	−0.610263
$515$	12.7485	0.561767
$516$	32.7163	1.44026
$517$	0	0
$518$	7.33173	0.322138
$519$	26.8256	1.17751
$520$	10.4653	0.458932
$521$	0.181227	0.00793970	0.00396985	−	0.999992i	$-0.498736\pi$
$521$	0.181227	0.00793970	0.00396985	+	0.999992i	$0.498736\pi$
$522$	−68.0549	−2.97868
$523$	−45.3097	−1.98126	−0.990628	−	0.136590i	$-0.956386\pi$
$523$	−45.3097	−1.98126	−0.990628	+	0.136590i	$0.956386\pi$
$524$	−1.48565	−0.0649009
$525$	−36.2820	−1.58348
$526$	−50.2719	−2.19196
$527$	1.84867	0.0805293
$528$	0	0
$529$	39.3288	1.70995
$530$	−78.9273	−3.42838
$531$	21.1124	0.916198
$532$	−3.91276	−0.169640
$533$	−14.2027	−0.615186
$534$	30.6569	1.32665
$535$	35.6780	1.54249
$536$	−4.69703	−0.202881
$537$	−16.8708	−0.728027
$538$	−53.2652	−2.29643
$539$	0	0
$540$	56.0747	2.41307
$541$	−8.61042	−0.370191	−0.185095	−	0.982721i	$-0.559259\pi$
$541$	−8.61042	−0.370191	−0.185095	+	0.982721i	$0.559259\pi$
$542$	−3.17559	−0.136403
$543$	−5.75568	−0.247000
$544$	5.57238	0.238914
$545$	37.1147	1.58982
$546$	27.1881	1.16354
$547$	−16.9870	−0.726311	−0.363155	−	0.931729i	$-0.618301\pi$
$547$	−16.9870	−0.726311	−0.363155	+	0.931729i	$0.618301\pi$
$548$	−24.9084	−1.06403
$549$	6.46667	0.275991
$550$	0	0
$551$	9.58931	0.408518
$552$	23.4980	1.00014
$553$	−0.890407	−0.0378640
$554$	−50.1295	−2.12980
$555$	27.6176	1.17230
$556$	−7.50237	−0.318171
$557$	−24.8717	−1.05385	−0.526923	−	0.849913i	$-0.676654\pi$
$557$	−24.8717	−1.05385	−0.526923	+	0.849913i	$0.676654\pi$
$558$	−27.8691	−1.17979
$559$	21.8812	0.925477
$560$	26.2816	1.11060
$561$	0	0
$562$	−22.5201	−0.949952
$563$	15.7969	0.665760	0.332880	−	0.942969i	$-0.391980\pi$
$563$	15.7969	0.665760	0.332880	+	0.942969i	$0.391980\pi$
$564$	−51.9696	−2.18832
$565$	−39.6102	−1.66641
$566$	−54.0149	−2.27041
$567$	−20.8426	−0.875308
$568$	−12.2877	−0.515579
$569$	−26.6993	−1.11929	−0.559647	−	0.828731i	$-0.689063\pi$
$569$	−26.6993	−1.11929	−0.559647	+	0.828731i	$0.689063\pi$
$570$	−34.6352	−1.45071
$571$	14.9692	0.626443	0.313222	−	0.949680i	$-0.398592\pi$
$571$	14.9692	0.626443	0.313222	+	0.949680i	$0.398592\pi$
$572$	0	0
$573$	−31.1541	−1.30148
$574$	−13.5021	−0.563568
$575$	59.9332	2.49939
$576$	−22.3374	−0.930724
$577$	18.6266	0.775434	0.387717	−	0.921779i	$-0.373264\pi$
$577$	18.6266	0.775434	0.387717	+	0.921779i	$0.373264\pi$
$578$	30.5248	1.26967
$579$	63.8719	2.65442
$580$	29.6515	1.23121
$581$	18.0263	0.747855
$582$	104.551	4.33379
$583$	0	0
$584$	−14.9348	−0.618007
$585$	69.9588	2.89244
$586$	−12.1418	−0.501572
$587$	9.56248	0.394686	0.197343	−	0.980335i	$-0.436769\pi$
$587$	9.56248	0.394686	0.197343	+	0.980335i	$0.436769\pi$
$588$	−20.9101	−0.862317
$589$	3.92691	0.161806
$590$	−21.6162	−0.889926
$591$	15.1564	0.623451
$592$	−12.0614	−0.495719
$593$	16.8226	0.690820	0.345410	−	0.938452i	$-0.387740\pi$
$593$	16.8226	0.690820	0.345410	+	0.938452i	$0.387740\pi$
$594$	0	0
$595$	−4.41175	−0.180864
$596$	−19.1984	−0.786395
$597$	66.7977	2.73385
$598$	−44.9112	−1.83656
$599$	−18.3221	−0.748620	−0.374310	−	0.927304i	$-0.622120\pi$
$599$	−18.3221	−0.748620	−0.374310	+	0.927304i	$0.622120\pi$
$600$	22.5949	0.922432
$601$	−35.9478	−1.46634	−0.733171	−	0.680044i	$-0.761961\pi$
$601$	−35.9478	−1.46634	−0.733171	+	0.680044i	$0.761961\pi$
$602$	20.8019	0.847823
$603$	−31.3990	−1.27867
$604$	−28.8557	−1.17412
$605$	0	0
$606$	77.4453	3.14600
$607$	−2.09016	−0.0848371	−0.0424185	−	0.999100i	$-0.513506\pi$
$607$	−2.09016	−0.0848371	−0.0424185	+	0.999100i	$0.513506\pi$
$608$	11.8368	0.480044
$609$	−26.9563	−1.09232
$610$	−6.62101	−0.268077
$611$	−34.7582	−1.40616
$612$	7.66837	0.309975
$613$	−48.4647	−1.95747	−0.978735	−	0.205130i	$-0.934238\pi$
$613$	−48.4647	−1.95747	−0.978735	+	0.205130i	$0.934238\pi$
$614$	25.9610	1.04770
$615$	−50.8607	−2.05090
$616$	0	0
$617$	43.5442	1.75302	0.876512	−	0.481381i	$-0.159865\pi$
$617$	43.5442	1.75302	0.876512	+	0.481381i	$0.159865\pi$
$618$	−20.6257	−0.829686
$619$	−33.5356	−1.34791	−0.673954	−	0.738773i	$-0.735406\pi$
$619$	−33.5356	−1.34791	−0.673954	+	0.738773i	$0.735406\pi$
$620$	12.1426	0.487658
$621$	84.2086	3.37917
$622$	24.3272	0.975430
$623$	8.29491	0.332329
$624$	−44.7269	−1.79051
$625$	−5.32746	−0.213099
$626$	−20.4022	−0.815438
$627$	0	0
$628$	−3.98473	−0.159008
$629$	2.02467	0.0807289
$630$	66.5081	2.64974
$631$	30.6945	1.22193	0.610964	−	0.791658i	$-0.290782\pi$
$631$	30.6945	1.22193	0.610964	+	0.791658i	$0.290782\pi$
$632$	0.554508	0.0220571
$633$	3.48582	0.138549
$634$	−9.45039	−0.375323
$635$	20.4168	0.810215
$636$	54.3401	2.15472
$637$	−13.9850	−0.554106
$638$	0	0
$639$	−82.1414	−3.24946
$640$	−26.5383	−1.04902
$641$	−17.4271	−0.688329	−0.344164	−	0.938909i	$-0.611838\pi$
$641$	−17.4271	−0.688329	−0.344164	+	0.938909i	$0.611838\pi$
$642$	−57.7230	−2.27814
$643$	−10.6873	−0.421464	−0.210732	−	0.977544i	$-0.567585\pi$
$643$	−10.6873	−0.421464	−0.210732	+	0.977544i	$0.567585\pi$
$644$	−18.1690	−0.715960
$645$	78.3581	3.08535
$646$	−2.53914	−0.0999010
$647$	15.4570	0.607677	0.303838	−	0.952724i	$-0.401732\pi$
$647$	15.4570	0.607677	0.303838	+	0.952724i	$0.401732\pi$
$648$	12.9799	0.509899
$649$	0	0
$650$	−43.1851	−1.69386
$651$	−11.0388	−0.432646
$652$	28.7910	1.12754
$653$	23.2031	0.908006	0.454003	−	0.891000i	$-0.349995\pi$
$653$	23.2031	0.908006	0.454003	+	0.891000i	$0.349995\pi$
$654$	−60.0475	−2.34804
$655$	−3.55824	−0.139032
$656$	22.2122	0.867241
$657$	−99.8372	−3.89502
$658$	−33.0437	−1.28818
$659$	−37.4716	−1.45969	−0.729843	−	0.683615i	$-0.760407\pi$
$659$	−37.4716	−1.45969	−0.729843	+	0.683615i	$0.760407\pi$
$660$	0	0
$661$	−21.4337	−0.833674	−0.416837	−	0.908981i	$-0.636861\pi$
$661$	−21.4337	−0.833674	−0.416837	+	0.908981i	$0.636861\pi$
$662$	5.29195	0.205677
$663$	7.50804	0.291588
$664$	−11.2260	−0.435653
$665$	−9.37135	−0.363405
$666$	−30.5224	−1.18272
$667$	44.5283	1.72414
$668$	−15.2420	−0.589732
$669$	−20.8660	−0.806728
$670$	32.1484	1.24200
$671$	0	0
$672$	−33.2740	−1.28357
$673$	−44.3547	−1.70975	−0.854874	−	0.518835i	$-0.826366\pi$
$673$	−44.3547	−1.70975	−0.854874	+	0.518835i	$0.826366\pi$
$674$	28.6915	1.10515
$675$	80.9720	3.11661
$676$	−5.48921	−0.211123
$677$	−26.0686	−1.00190	−0.500949	−	0.865477i	$-0.667015\pi$
$677$	−26.0686	−1.00190	−0.500949	+	0.865477i	$0.667015\pi$
$678$	64.0848	2.46116
$679$	28.2887	1.08562
$680$	2.74745	0.105360
$681$	53.2138	2.03916
$682$	0	0
$683$	9.77992	0.374218	0.187109	−	0.982339i	$-0.440088\pi$
$683$	9.77992	0.374218	0.187109	+	0.982339i	$0.440088\pi$
$684$	16.2890	0.622826
$685$	−59.6575	−2.27940
$686$	−33.5839	−1.28224
$687$	−5.09606	−0.194427
$688$	−34.2211	−1.30467
$689$	36.3435	1.38458
$690$	−160.830	−6.12269
$691$	36.8678	1.40252	0.701258	−	0.712908i	$-0.252622\pi$
$691$	36.8678	1.40252	0.701258	+	0.712908i	$0.252622\pi$
$692$	12.9172	0.491038
$693$	0	0
$694$	39.6827	1.50634
$695$	−17.9687	−0.681593
$696$	16.7872	0.636318
$697$	−3.72864	−0.141232
$698$	−0.835993	−0.0316428
$699$	−37.3898	−1.41421
$700$	−17.4707	−0.660330
$701$	32.7780	1.23801	0.619004	−	0.785388i	$-0.287537\pi$
$701$	32.7780	1.23801	0.619004	+	0.785388i	$0.287537\pi$
$702$	−60.6768	−2.29010
$703$	4.30077	0.162206
$704$	0	0
$705$	−124.471	−4.68786
$706$	−0.587141	−0.0220973
$707$	20.9546	0.788078
$708$	14.8824	0.559314
$709$	−36.7777	−1.38121	−0.690607	−	0.723230i	$-0.742657\pi$
$709$	−36.7777	−1.38121	−0.690607	+	0.723230i	$0.742657\pi$
$710$	84.1018	3.15628
$711$	3.70681	0.139016
$712$	−5.16572	−0.193594
$713$	18.2348	0.682897
$714$	7.13770	0.267122
$715$	0	0
$716$	−8.12370	−0.303597
$717$	19.5755	0.731060
$718$	−24.1576	−0.901552
$719$	−12.3220	−0.459533	−0.229767	−	0.973246i	$-0.573796\pi$
$719$	−12.3220	−0.459533	−0.229767	+	0.973246i	$0.573796\pi$
$720$	−109.412	−4.07754
$721$	−5.58074	−0.207838
$722$	30.0584	1.11866
$723$	−47.0236	−1.74883
$724$	−2.77151	−0.103002
$725$	42.8168	1.59018
$726$	0	0
$727$	−17.1376	−0.635597	−0.317798	−	0.948158i	$-0.602944\pi$
$727$	−17.1376	−0.635597	−0.317798	+	0.948158i	$0.602944\pi$
$728$	−4.58123	−0.169792
$729$	−11.6847	−0.432768
$730$	102.220	3.78333
$731$	5.74449	0.212468
$732$	4.55845	0.168485
$733$	−2.84672	−0.105146	−0.0525729	−	0.998617i	$-0.516742\pi$
$733$	−2.84672	−0.105146	−0.0525729	+	0.998617i	$0.516742\pi$
$734$	−25.1491	−0.928272
$735$	−50.0812	−1.84727
$736$	54.9644	2.02601
$737$	0	0
$738$	56.2100	2.06912
$739$	34.4566	1.26751	0.633754	−	0.773535i	$-0.281513\pi$
$739$	34.4566	1.26751	0.633754	+	0.773535i	$0.281513\pi$
$740$	13.2986	0.488866
$741$	15.9484	0.585881
$742$	34.5509	1.26840
$743$	18.0946	0.663828	0.331914	−	0.943310i	$-0.392306\pi$
$743$	18.0946	0.663828	0.331914	+	0.943310i	$0.392306\pi$
$744$	6.87453	0.252032
$745$	−45.9815	−1.68463
$746$	−26.2856	−0.962382
$747$	−75.0442	−2.74572
$748$	0	0
$749$	−15.6183	−0.570679
$750$	−52.7910	−1.92766
$751$	35.5526	1.29733	0.648666	−	0.761073i	$-0.275327\pi$
$751$	35.5526	1.29733	0.648666	+	0.761073i	$0.275327\pi$
$752$	54.3599	1.98230
$753$	18.2072	0.663509
$754$	−32.0850	−1.16847
$755$	−69.1116	−2.51523
$756$	−24.5470	−0.892767
$757$	40.8378	1.48427	0.742137	−	0.670248i	$-0.233812\pi$
$757$	40.8378	1.48427	0.742137	+	0.670248i	$0.233812\pi$
$758$	−52.4826	−1.90626
$759$	0	0
$760$	5.83608	0.211697
$761$	16.3078	0.591156	0.295578	−	0.955319i	$-0.404488\pi$
$761$	16.3078	0.591156	0.295578	+	0.955319i	$0.404488\pi$
$762$	−33.0320	−1.19662
$763$	−16.2472	−0.588188
$764$	−15.0015	−0.542734
$765$	18.3663	0.664036
$766$	6.23411	0.225248
$767$	9.95359	0.359403
$768$	64.1919	2.31633
$769$	46.8187	1.68833	0.844163	−	0.536087i	$-0.180098\pi$
$769$	46.8187	1.68833	0.844163	+	0.536087i	$0.180098\pi$
$770$	0	0
$771$	22.8145	0.821643
$772$	30.7559	1.10693
$773$	18.1410	0.652487	0.326243	−	0.945286i	$-0.394217\pi$
$773$	18.1410	0.652487	0.326243	+	0.945286i	$0.394217\pi$
$774$	−86.5995	−3.11275
$775$	17.5339	0.629836
$776$	−17.6170	−0.632414
$777$	−12.0898	−0.433718
$778$	−16.4829	−0.590942
$779$	−7.92030	−0.283774
$780$	49.3149	1.76576
$781$	0	0
$782$	−11.7906	−0.421630
$783$	60.1594	2.14992
$784$	21.8718	0.781135
$785$	−9.54372	−0.340630
$786$	5.75683	0.205339
$787$	8.01072	0.285551	0.142776	−	0.989755i	$-0.454397\pi$
$787$	8.01072	0.285551	0.142776	+	0.989755i	$0.454397\pi$
$788$	7.29820	0.259987
$789$	82.8967	2.95120
$790$	−3.79528	−0.135030
$791$	17.3396	0.616525
$792$	0	0
$793$	3.04877	0.108265
$794$	43.9339	1.55915
$795$	130.149	4.61589
$796$	32.1648	1.14005
$797$	−6.29544	−0.222996	−0.111498	−	0.993765i	$-0.535565\pi$
$797$	−6.29544	−0.222996	−0.111498	+	0.993765i	$0.535565\pi$
$798$	15.1618	0.536721
$799$	−9.12508	−0.322822
$800$	52.8518	1.86859
$801$	−34.5321	−1.22013
$802$	−21.3238	−0.752968
$803$	0	0
$804$	−22.1336	−0.780591
$805$	−43.5162	−1.53374
$806$	−13.1391	−0.462806
$807$	87.8326	3.09185
$808$	−13.0496	−0.459084
$809$	−36.0907	−1.26888	−0.634440	−	0.772972i	$-0.718769\pi$
$809$	−36.0907	−1.26888	−0.634440	+	0.772972i	$0.718769\pi$
$810$	−88.8397	−3.12151
$811$	33.6272	1.18081	0.590405	−	0.807107i	$-0.298968\pi$
$811$	33.6272	1.18081	0.590405	+	0.807107i	$0.298968\pi$
$812$	−12.9801	−0.455513
$813$	5.23644	0.183650
$814$	0	0
$815$	68.9567	2.41545
$816$	−11.7422	−0.411058
$817$	12.2023	0.426906
$818$	−4.22605	−0.147760
$819$	−30.6249	−1.07012
$820$	−24.4907	−0.855253
$821$	−16.8632	−0.588528	−0.294264	−	0.955724i	$-0.595075\pi$
$821$	−16.8632	−0.588528	−0.294264	+	0.955724i	$0.595075\pi$
$822$	96.5191	3.36649
$823$	−22.6690	−0.790190	−0.395095	−	0.918640i	$-0.629288\pi$
$823$	−22.6690	−0.790190	−0.395095	+	0.918640i	$0.629288\pi$
$824$	3.47545	0.121073
$825$	0	0
$826$	9.46263	0.329247
$827$	0.394679	0.0137243	0.00686216	−	0.999976i	$-0.497816\pi$
$827$	0.394679	0.0137243	0.00686216	+	0.999976i	$0.497816\pi$
$828$	75.6386	2.62862
$829$	−1.56754	−0.0544428	−0.0272214	−	0.999629i	$-0.508666\pi$
$829$	−1.56754	−0.0544428	−0.0272214	+	0.999629i	$0.508666\pi$
$830$	76.8352	2.66699
$831$	82.6618	2.86751
$832$	−10.5311	−0.365101
$833$	−3.67149	−0.127210
$834$	29.0714	1.00666
$835$	−36.5058	−1.26334
$836$	0	0
$837$	24.6358	0.851539
$838$	−35.4986	−1.22628
$839$	−2.75246	−0.0950254	−0.0475127	−	0.998871i	$-0.515129\pi$
$839$	−2.75246	−0.0950254	−0.0475127	+	0.998871i	$0.515129\pi$
$840$	−16.4057	−0.566049
$841$	2.81145	0.0969466
$842$	34.0665	1.17401
$843$	37.1349	1.27899
$844$	1.67851	0.0577767
$845$	−13.1471	−0.452273
$846$	137.563	4.72950
$847$	0	0
$848$	−56.8393	−1.95187
$849$	89.0688	3.05683
$850$	−11.3374	−0.388870
$851$	19.9708	0.684589
$852$	−57.9026	−1.98371
$853$	2.00865	0.0687750	0.0343875	−	0.999409i	$-0.489052\pi$
$853$	2.00865	0.0687750	0.0343875	+	0.999409i	$0.489052\pi$
$854$	2.89838	0.0991807
$855$	39.0134	1.33423
$856$	9.72639	0.332441
$857$	22.5503	0.770304	0.385152	−	0.922853i	$-0.374149\pi$
$857$	22.5503	0.770304	0.385152	+	0.922853i	$0.374149\pi$
$858$	0	0
$859$	41.4688	1.41490	0.707448	−	0.706765i	$-0.249846\pi$
$859$	41.4688	1.41490	0.707448	+	0.706765i	$0.249846\pi$
$860$	37.7314	1.28663
$861$	22.2646	0.758774
$862$	36.1962	1.23285
$863$	39.6779	1.35065	0.675326	−	0.737519i	$-0.264003\pi$
$863$	39.6779	1.35065	0.675326	+	0.737519i	$0.264003\pi$
$864$	74.2590	2.52634
$865$	30.9377	1.05191
$866$	−62.6719	−2.12968
$867$	−50.3344	−1.70945
$868$	−5.31548	−0.180419
$869$	0	0
$870$	−114.899	−3.89542
$871$	−14.8033	−0.501591
$872$	10.1181	0.342641
$873$	−117.767	−3.98582
$874$	−25.0453	−0.847171
$875$	−14.2838	−0.482881
$876$	−70.3766	−2.37781
$877$	14.3414	0.484274	0.242137	−	0.970242i	$-0.422152\pi$
$877$	14.3414	0.484274	0.242137	+	0.970242i	$0.422152\pi$
$878$	47.2179	1.59353
$879$	20.0214	0.675305
$880$	0	0
$881$	8.52542	0.287229	0.143614	−	0.989634i	$-0.454128\pi$
$881$	8.52542	0.287229	0.143614	+	0.989634i	$0.454128\pi$
$882$	55.3486	1.86368
$883$	0.376314	0.0126640	0.00633199	−	0.999980i	$-0.497984\pi$
$883$	0.376314	0.0126640	0.00633199	+	0.999980i	$0.497984\pi$
$884$	3.61531	0.121596
$885$	35.6444	1.19817
$886$	60.7160	2.03979
$887$	−13.5552	−0.455139	−0.227570	−	0.973762i	$-0.573078\pi$
$887$	−13.5552	−0.455139	−0.227570	+	0.973762i	$0.573078\pi$
$888$	7.52900	0.252657
$889$	−8.93756	−0.299756
$890$	35.3563	1.18515
$891$	0	0
$892$	−10.0475	−0.336416
$893$	−19.3833	−0.648638
$894$	74.3929	2.48807
$895$	−19.4569	−0.650372
$896$	11.6173	0.388107
$897$	74.0572	2.47270
$898$	−12.6674	−0.422717
$899$	13.0271	0.434478
$900$	72.7314	2.42438
$901$	9.54129	0.317866
$902$	0	0
$903$	−34.3017	−1.14149
$904$	−10.7984	−0.359148
$905$	−6.63797	−0.220654
$906$	111.815	3.71479
$907$	−17.7877	−0.590631	−0.295316	−	0.955400i	$-0.595425\pi$
$907$	−17.7877	−0.590631	−0.295316	+	0.955400i	$0.595425\pi$
$908$	25.6238	0.850356
$909$	−87.2350	−2.89340
$910$	31.3558	1.03943
$911$	25.6031	0.848267	0.424134	−	0.905600i	$-0.360579\pi$
$911$	25.6031	0.848267	0.424134	+	0.905600i	$0.360579\pi$
$912$	−24.9425	−0.825929
$913$	0	0
$914$	12.2193	0.404180
$915$	10.9178	0.360932
$916$	−2.45388	−0.0810785
$917$	1.55764	0.0514379
$918$	−15.9295	−0.525752
$919$	−43.1410	−1.42309	−0.711546	−	0.702640i	$-0.752005\pi$
$919$	−43.1410	−1.42309	−0.711546	+	0.702640i	$0.752005\pi$
$920$	27.1001	0.893462
$921$	−42.8089	−1.41060
$922$	48.6132	1.60099
$923$	−38.7262	−1.27469
$924$	0	0
$925$	19.2032	0.631397
$926$	−22.2281	−0.730460
$927$	23.2329	0.763069
$928$	39.2671	1.28901
$929$	43.2912	1.42034	0.710169	−	0.704032i	$-0.248619\pi$
$929$	43.2912	1.42034	0.710169	+	0.704032i	$0.248619\pi$
$930$	−47.0520	−1.54290
$931$	−7.79891	−0.255599
$932$	−18.0041	−0.589745
$933$	−40.1147	−1.31330
$934$	47.8080	1.56432
$935$	0	0
$936$	19.0719	0.623384
$937$	24.4235	0.797883	0.398941	−	0.916976i	$-0.369378\pi$
$937$	24.4235	0.797883	0.398941	+	0.916976i	$0.369378\pi$
$938$	−14.0731	−0.459504
$939$	33.6426	1.09789
$940$	−59.9361	−1.95490
$941$	50.6827	1.65221	0.826104	−	0.563518i	$-0.190553\pi$
$941$	50.6827	1.65221	0.826104	+	0.563518i	$0.190553\pi$
$942$	15.4407	0.503084
$943$	−36.7782	−1.19766
$944$	−15.5669	−0.506659
$945$	−58.7920	−1.91250
$946$	0	0
$947$	19.8576	0.645286	0.322643	−	0.946521i	$-0.395429\pi$
$947$	19.8576	0.645286	0.322643	+	0.946521i	$0.395429\pi$
$948$	2.61298	0.0848656
$949$	−47.0691	−1.52793
$950$	−24.0827	−0.781346
$951$	15.5834	0.505326
$952$	−1.20271	−0.0389801
$953$	14.9912	0.485611	0.242806	−	0.970075i	$-0.421932\pi$
$953$	14.9912	0.485611	0.242806	+	0.970075i	$0.421932\pi$
$954$	−143.837	−4.65690
$955$	−35.9297	−1.16266
$956$	9.42610	0.304862
$957$	0	0
$958$	35.3620	1.14249
$959$	26.1154	0.843311
$960$	−37.7127	−1.21717
$961$	−25.6653	−0.827913
$962$	−14.3900	−0.463952
$963$	65.0196	2.09523
$964$	−22.6431	−0.729284
$965$	73.6628	2.37129
$966$	70.4043	2.26522
$967$	24.0634	0.773825	0.386913	−	0.922116i	$-0.373542\pi$
$967$	24.0634	0.773825	0.386913	+	0.922116i	$0.373542\pi$
$968$	0	0
$969$	4.18695	0.134504
$970$	120.578	3.87153
$971$	9.22640	0.296089	0.148045	−	0.988981i	$-0.452702\pi$
$971$	9.22640	0.296089	0.148045	+	0.988981i	$0.452702\pi$
$972$	13.7566	0.441244
$973$	7.86592	0.252170
$974$	−15.5426	−0.498019
$975$	71.2108	2.28057
$976$	−4.76810	−0.152623
$977$	−2.43926	−0.0780390	−0.0390195	−	0.999238i	$-0.512423\pi$
$977$	−2.43926	−0.0780390	−0.0390195	+	0.999238i	$0.512423\pi$
$978$	−111.564	−3.56743
$979$	0	0
$980$	−24.1154	−0.770337
$981$	67.6379	2.15951
$982$	−56.8530	−1.81425
$983$	48.4860	1.54646	0.773232	−	0.634124i	$-0.218639\pi$
$983$	48.4860	1.54646	0.773232	+	0.634124i	$0.218639\pi$
$984$	−13.8654	−0.442014
$985$	17.4797	0.556951
$986$	−8.42330	−0.268252
$987$	54.4880	1.73437
$988$	7.67958	0.244320
$989$	56.6620	1.80175
$990$	0	0
$991$	−47.9696	−1.52381	−0.761903	−	0.647691i	$-0.775735\pi$
$991$	−47.9696	−1.52381	−0.761903	+	0.647691i	$0.775735\pi$
$992$	16.0802	0.510548
$993$	−8.72625	−0.276919
$994$	−36.8161	−1.16773
$995$	77.0371	2.44224
$996$	−52.8997	−1.67619
$997$	−50.3263	−1.59385	−0.796924	−	0.604079i	$-0.793541\pi$
$997$	−50.3263	−1.59385	−0.796924	+	0.604079i	$0.793541\pi$
$998$	−13.5983	−0.430448
$999$	26.9813	0.853649

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7381.2.a.v.1.13		64
11.5	even	5		671.2.j.c.245.27	✓	128
11.9	even	5		671.2.j.c.367.27	yes	128
11.10	odd	2		7381.2.a.u.1.52		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
671.2.j.c.245.27	✓	128	11.5	even	5
671.2.j.c.367.27	yes	128	11.9	even	5
7381.2.a.u.1.52		64	11.10	odd	2
7381.2.a.v.1.13		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)

\(f(q)\)	\(=\)	\(q-1.86589 q^{2} +3.07680 q^{3} +1.48156 q^{4} +3.54844 q^{5} -5.74097 q^{6} -1.55335 q^{7} +0.967361 q^{8} +6.46667 q^{9} +O(q^{10})\)	\(q-1.86589 q^{2} +3.07680 q^{3} +1.48156 q^{4} +3.54844 q^{5} -5.74097 q^{6} -1.55335 q^{7} +0.967361 q^{8} +6.46667 q^{9} -6.62101 q^{10} +4.55845 q^{12} +3.04877 q^{13} +2.89838 q^{14} +10.9178 q^{15} -4.76810 q^{16} +0.800394 q^{17} -12.0661 q^{18} +1.70018 q^{19} +5.25721 q^{20} -4.77934 q^{21} +7.89486 q^{23} +2.97637 q^{24} +7.59142 q^{25} -5.68867 q^{26} +10.6663 q^{27} -2.30137 q^{28} +5.64016 q^{29} -20.3715 q^{30} +2.30970 q^{31} +6.96205 q^{32} -1.49345 q^{34} -5.51197 q^{35} +9.58074 q^{36} +2.52959 q^{37} -3.17236 q^{38} +9.38043 q^{39} +3.43262 q^{40} -4.65850 q^{41} +8.91774 q^{42} +7.17708 q^{43} +22.9466 q^{45} -14.7310 q^{46} -11.4007 q^{47} -14.6705 q^{48} -4.58710 q^{49} -14.1648 q^{50} +2.46265 q^{51} +4.51692 q^{52} +11.9207 q^{53} -19.9021 q^{54} -1.50265 q^{56} +5.23111 q^{57} -10.5239 q^{58} +3.26479 q^{59} +16.1754 q^{60} +1.00000 q^{61} -4.30965 q^{62} -10.0450 q^{63} -3.45423 q^{64} +10.8184 q^{65} -4.85551 q^{67} +1.18583 q^{68} +24.2909 q^{69} +10.2847 q^{70} -12.7023 q^{71} +6.25561 q^{72} -15.4387 q^{73} -4.71995 q^{74} +23.3572 q^{75} +2.51892 q^{76} -17.5029 q^{78} +0.573217 q^{79} -16.9193 q^{80} +13.4179 q^{81} +8.69226 q^{82} -11.6048 q^{83} -7.08086 q^{84} +2.84015 q^{85} -13.3917 q^{86} +17.3536 q^{87} -5.34002 q^{89} -42.8159 q^{90} -4.73580 q^{91} +11.6967 q^{92} +7.10647 q^{93} +21.2726 q^{94} +6.03299 q^{95} +21.4208 q^{96} -18.2114 q^{97} +8.55904 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 5 q^{2} + 19 q^{3} + 73 q^{4} + 21 q^{5} - q^{6} + 6 q^{7} + 3 q^{8} + 81 q^{9}+O(q^{10}) \) 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

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