LMFDB - Embedded newform 1859.2.a.q.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,2,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, 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("1859.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1859.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:	$14.8441897358$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 10x^{7} - x^{6} + 31x^{5} + 9x^{4} - 31x^{3} - 15x^{2} + 2x + 1 $ x^9 - 10x^7 - x^6 + 31x^5 + 9x^4 - 31x^3 - 15x^2 + 2x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$2.07671$ of defining polynomial
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.07671 q^{2} -2.04022 q^{3} +2.31273 q^{4} -0.294310 q^{5} -4.23695 q^{6} +0.566818 q^{7} +0.649450 q^{8} +1.16251 q^{9} +O(q^{10})$	\(q+2.07671 q^{2} -2.04022 q^{3} +2.31273 q^{4} -0.294310 q^{5} -4.23695 q^{6} +0.566818 q^{7} +0.649450 q^{8} +1.16251 q^{9} -0.611198 q^{10} +1.00000 q^{11} -4.71848 q^{12} +1.17712 q^{14} +0.600459 q^{15} -3.27674 q^{16} +1.40786 q^{17} +2.41419 q^{18} -5.25551 q^{19} -0.680661 q^{20} -1.15643 q^{21} +2.07671 q^{22} -3.30517 q^{23} -1.32502 q^{24} -4.91338 q^{25} +3.74889 q^{27} +1.31090 q^{28} -2.18840 q^{29} +1.24698 q^{30} +5.10594 q^{31} -8.10374 q^{32} -2.04022 q^{33} +2.92371 q^{34} -0.166820 q^{35} +2.68857 q^{36} -2.65179 q^{37} -10.9142 q^{38} -0.191140 q^{40} -4.07096 q^{41} -2.40158 q^{42} -1.79546 q^{43} +2.31273 q^{44} -0.342138 q^{45} -6.86388 q^{46} -4.59839 q^{47} +6.68528 q^{48} -6.67872 q^{49} -10.2037 q^{50} -2.87234 q^{51} +5.09461 q^{53} +7.78537 q^{54} -0.294310 q^{55} +0.368120 q^{56} +10.7224 q^{57} -4.54469 q^{58} -13.4389 q^{59} +1.38870 q^{60} -2.78390 q^{61} +10.6036 q^{62} +0.658930 q^{63} -10.2757 q^{64} -4.23695 q^{66} -12.3475 q^{67} +3.25599 q^{68} +6.74328 q^{69} -0.346438 q^{70} +16.2074 q^{71} +0.754991 q^{72} -4.29006 q^{73} -5.50700 q^{74} +10.0244 q^{75} -12.1546 q^{76} +0.566818 q^{77} +7.13089 q^{79} +0.964379 q^{80} -11.1361 q^{81} -8.45421 q^{82} -13.6907 q^{83} -2.67452 q^{84} -0.414347 q^{85} -3.72865 q^{86} +4.46483 q^{87} +0.649450 q^{88} -10.5882 q^{89} -0.710523 q^{90} -7.64396 q^{92} -10.4173 q^{93} -9.54953 q^{94} +1.54675 q^{95} +16.5334 q^{96} +9.74381 q^{97} -13.8698 q^{98} +1.16251 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 5 q^{3} + 2 q^{4} - 4 q^{5} - 11 q^{6} + q^{7} + 3 q^{8} + 2 q^{9}+O(q^{10}) $ 9 * q - 5 * q^3 + 2 * q^4 - 4 * q^5 - 11 * q^6 + q^7 + 3 * q^8 + 2 * q^9	$ 9 q - 5 q^{3} + 2 q^{4} - 4 q^{5} - 11 q^{6} + q^{7} + 3 q^{8} + 2 q^{9} - 8 q^{10} + 9 q^{11} - 9 q^{12} + 3 q^{15} - 8 q^{16} - 8 q^{17} + 27 q^{18} - q^{19} + 12 q^{20} + 17 q^{21} - 6 q^{24} - 15 q^{25} - 23 q^{27} + 11 q^{28} - 22 q^{29} - 3 q^{30} - 6 q^{31} - 19 q^{32} - 5 q^{33} + 10 q^{34} - 15 q^{35} + 7 q^{36} - 15 q^{37} + q^{38} - 3 q^{40} + 10 q^{41} + 2 q^{42} - 19 q^{43} + 2 q^{44} - 2 q^{45} + 19 q^{46} - 2 q^{47} + 6 q^{48} - 20 q^{49} - 17 q^{50} - 2 q^{51} - 5 q^{53} - 27 q^{54} - 4 q^{55} - 16 q^{56} - 32 q^{57} - 11 q^{58} - 11 q^{59} - 6 q^{60} - 68 q^{61} - 21 q^{62} - 29 q^{63} - 23 q^{64} - 11 q^{66} + 5 q^{67} + 16 q^{68} - 34 q^{69} - 5 q^{70} - 34 q^{71} + 13 q^{72} + 26 q^{73} + q^{74} + 10 q^{75} - 11 q^{76} + q^{77} - 32 q^{79} + 8 q^{80} + 13 q^{81} - 42 q^{82} + 8 q^{83} - 13 q^{84} + 23 q^{85} + 30 q^{86} + 10 q^{87} + 3 q^{88} - 37 q^{89} + 21 q^{90} - 12 q^{92} + 20 q^{93} - 12 q^{94} - 4 q^{95} + 60 q^{96} + 3 q^{97} - 9 q^{98} + 2 q^{99}+O(q^{100}) $ 9 * q - 5 * q^3 + 2 * q^4 - 4 * q^5 - 11 * q^6 + q^7 + 3 * q^8 + 2 * q^9 - 8 * q^10 + 9 * q^11 - 9 * q^12 + 3 * q^15 - 8 * q^16 - 8 * q^17 + 27 * q^18 - q^19 + 12 * q^20 + 17 * q^21 - 6 * q^24 - 15 * q^25 - 23 * q^27 + 11 * q^28 - 22 * q^29 - 3 * q^30 - 6 * q^31 - 19 * q^32 - 5 * q^33 + 10 * q^34 - 15 * q^35 + 7 * q^36 - 15 * q^37 + q^38 - 3 * q^40 + 10 * q^41 + 2 * q^42 - 19 * q^43 + 2 * q^44 - 2 * q^45 + 19 * q^46 - 2 * q^47 + 6 * q^48 - 20 * q^49 - 17 * q^50 - 2 * q^51 - 5 * q^53 - 27 * q^54 - 4 * q^55 - 16 * q^56 - 32 * q^57 - 11 * q^58 - 11 * q^59 - 6 * q^60 - 68 * q^61 - 21 * q^62 - 29 * q^63 - 23 * q^64 - 11 * q^66 + 5 * q^67 + 16 * q^68 - 34 * q^69 - 5 * q^70 - 34 * q^71 + 13 * q^72 + 26 * q^73 + q^74 + 10 * q^75 - 11 * q^76 + q^77 - 32 * q^79 + 8 * q^80 + 13 * q^81 - 42 * q^82 + 8 * q^83 - 13 * q^84 + 23 * q^85 + 30 * q^86 + 10 * q^87 + 3 * q^88 - 37 * q^89 + 21 * q^90 - 12 * q^92 + 20 * q^93 - 12 * q^94 - 4 * q^95 + 60 * q^96 + 3 * q^97 - 9 * q^98 + 2 * q^99

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 $

$2$	2.07671	1.46846	0.734228	−	0.678903i	$-0.237544\pi$
$2$	2.07671	1.46846	0.734228	+	0.678903i	$0.237544\pi$
$3$	−2.04022	−1.17792	−0.588962	−	0.808161i	$-0.700463\pi$
$3$	−2.04022	−1.17792	−0.588962	+	0.808161i	$0.700463\pi$
$4$	2.31273	1.15636
$5$	−0.294310	−0.131620	−0.0658098	−	0.997832i	$-0.520963\pi$
$5$	−0.294310	−0.131620	−0.0658098	+	0.997832i	$0.520963\pi$
$6$	−4.23695	−1.72973
$7$	0.566818	0.214237	0.107118	−	0.994246i	$-0.465838\pi$
$7$	0.566818	0.214237	0.107118	+	0.994246i	$0.465838\pi$
$8$	0.649450	0.229615
$9$	1.16251	0.387503
$10$	−0.611198	−0.193278
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−4.71848	−1.36211
$13$	0	0
$13$	0	0
$14$	1.17712	0.314598
$15$	0.600459	0.155038
$16$	−3.27674	−0.819185
$17$	1.40786	0.341456	0.170728	−	0.985318i	$-0.445388\pi$
$17$	1.40786	0.341456	0.170728	+	0.985318i	$0.445388\pi$
$18$	2.41419	0.569031
$19$	−5.25551	−1.20570	−0.602848	−	0.797856i	$-0.705968\pi$
$19$	−5.25551	−1.20570	−0.602848	+	0.797856i	$0.705968\pi$
$20$	−0.680661	−0.152200
$21$	−1.15643	−0.252355
$22$	2.07671	0.442756
$23$	−3.30517	−0.689175	−0.344587	−	0.938754i	$-0.611981\pi$
$23$	−3.30517	−0.689175	−0.344587	+	0.938754i	$0.611981\pi$
$24$	−1.32502	−0.270469
$25$	−4.91338	−0.982676
$26$	0	0
$27$	3.74889	0.721475
$28$	1.31090	0.247736
$29$	−2.18840	−0.406377	−0.203188	−	0.979140i	$-0.565130\pi$
$29$	−2.18840	−0.406377	−0.203188	+	0.979140i	$0.565130\pi$
$30$	1.24698	0.227666
$31$	5.10594	0.917054	0.458527	−	0.888681i	$-0.348377\pi$
$31$	5.10594	0.917054	0.458527	+	0.888681i	$0.348377\pi$
$32$	−8.10374	−1.43255
$33$	−2.04022	−0.355157
$34$	2.92371	0.501413
$35$	−0.166820	−0.0281978
$36$	2.68857	0.448095
$37$	−2.65179	−0.435951	−0.217976	−	0.975954i	$-0.569945\pi$
$37$	−2.65179	−0.435951	−0.217976	+	0.975954i	$0.569945\pi$
$38$	−10.9142	−1.77051
$39$	0	0
$40$	−0.191140	−0.0302219
$41$	−4.07096	−0.635777	−0.317889	−	0.948128i	$-0.602974\pi$
$41$	−4.07096	−0.635777	−0.317889	+	0.948128i	$0.602974\pi$
$42$	−2.40158	−0.370572
$43$	−1.79546	−0.273805	−0.136903	−	0.990585i	$-0.543715\pi$
$43$	−1.79546	−0.273805	−0.136903	+	0.990585i	$0.543715\pi$
$44$	2.31273	0.348657
$45$	−0.342138	−0.0510030
$46$	−6.86388	−1.01202
$47$	−4.59839	−0.670745	−0.335372	−	0.942086i	$-0.608862\pi$
$47$	−4.59839	−0.670745	−0.335372	+	0.942086i	$0.608862\pi$
$48$	6.68528	0.964937
$49$	−6.67872	−0.954103
$50$	−10.2037	−1.44302
$51$	−2.87234	−0.402208
$52$	0	0
$53$	5.09461	0.699798	0.349899	−	0.936787i	$-0.386216\pi$
$53$	5.09461	0.699798	0.349899	+	0.936787i	$0.386216\pi$
$54$	7.78537	1.05945
$55$	−0.294310	−0.0396848
$56$	0.368120	0.0491921
$57$	10.7224	1.42022
$58$	−4.54469	−0.596746
$59$	−13.4389	−1.74959	−0.874796	−	0.484491i	$-0.839005\pi$
$59$	−13.4389	−1.74959	−0.874796	+	0.484491i	$0.839005\pi$
$60$	1.38870	0.179280
$61$	−2.78390	−0.356442	−0.178221	−	0.983991i	$-0.557034\pi$
$61$	−2.78390	−0.356442	−0.178221	+	0.983991i	$0.557034\pi$
$62$	10.6036	1.34665
$63$	0.658930	0.0830174
$64$	−10.2757	−1.28446
$65$	0	0
$66$	−4.23695	−0.521533
$67$	−12.3475	−1.50849	−0.754243	−	0.656596i	$-0.771996\pi$
$67$	−12.3475	−1.50849	−0.754243	+	0.656596i	$0.771996\pi$
$68$	3.25599	0.394847
$69$	6.74328	0.811795
$70$	−0.346438	−0.0414072
$71$	16.2074	1.92347	0.961735	−	0.273983i	$-0.0883411\pi$
$71$	16.2074	1.92347	0.961735	+	0.273983i	$0.0883411\pi$
$72$	0.754991	0.0889765
$73$	−4.29006	−0.502114	−0.251057	−	0.967972i	$-0.580778\pi$
$73$	−4.29006	−0.502114	−0.251057	+	0.967972i	$0.580778\pi$
$74$	−5.50700	−0.640176
$75$	10.0244	1.15752
$76$	−12.1546	−1.39423
$77$	0.566818	0.0645949
$78$	0	0
$79$	7.13089	0.802288	0.401144	−	0.916015i	$-0.368613\pi$
$79$	7.13089	0.802288	0.401144	+	0.916015i	$0.368613\pi$
$80$	0.964379	0.107821
$81$	−11.1361	−1.23734
$82$	−8.45421	−0.933612
$83$	−13.6907	−1.50275	−0.751377	−	0.659873i	$-0.770610\pi$
$83$	−13.6907	−1.50275	−0.751377	+	0.659873i	$0.770610\pi$
$84$	−2.67452	−0.291814
$85$	−0.414347	−0.0449423
$86$	−3.72865	−0.402071
$87$	4.46483	0.478680
$88$	0.649450	0.0692316
$89$	−10.5882	−1.12235	−0.561173	−	0.827699i	$-0.689650\pi$
$89$	−10.5882	−1.12235	−0.561173	+	0.827699i	$0.689650\pi$
$90$	−0.710523	−0.0748957
$91$	0	0
$92$	−7.64396	−0.796938
$93$	−10.4173	−1.08022
$94$	−9.54953	−0.984959
$95$	1.54675	0.158693
$96$	16.5334	1.68744
$97$	9.74381	0.989334	0.494667	−	0.869083i	$-0.335290\pi$
$97$	9.74381	0.989334	0.494667	+	0.869083i	$0.335290\pi$
$98$	−13.8698	−1.40106
$99$	1.16251	0.116836
$100$	−11.3633	−1.13633
$101$	−7.64298	−0.760505	−0.380253	−	0.924883i	$-0.624163\pi$
$101$	−7.64298	−0.760505	−0.380253	+	0.924883i	$0.624163\pi$
$102$	−5.96503	−0.590626
$103$	14.6165	1.44021	0.720105	−	0.693865i	$-0.244094\pi$
$103$	14.6165	1.44021	0.720105	+	0.693865i	$0.244094\pi$
$104$	0	0
$105$	0.340351	0.0332148
$106$	10.5800	1.02762
$107$	2.18507	0.211238	0.105619	−	0.994407i	$-0.466318\pi$
$107$	2.18507	0.211238	0.105619	+	0.994407i	$0.466318\pi$
$108$	8.67017	0.834288
$109$	18.3342	1.75610	0.878049	−	0.478571i	$-0.158845\pi$
$109$	18.3342	1.75610	0.878049	+	0.478571i	$0.158845\pi$
$110$	−0.611198	−0.0582754
$111$	5.41024	0.513517
$112$	−1.85731	−0.175500
$113$	−13.0632	−1.22889	−0.614444	−	0.788961i	$-0.710619\pi$
$113$	−13.0632	−1.22889	−0.614444	+	0.788961i	$0.710619\pi$
$114$	22.2673	2.08553
$115$	0.972745	0.0907089
$116$	−5.06119	−0.469920
$117$	0	0
$118$	−27.9087	−2.56920
$119$	0.797999	0.0731524
$120$	0.389968	0.0355990
$121$	1.00000	0.0909091
$122$	−5.78136	−0.523419
$123$	8.30567	0.748897
$124$	11.8087	1.06045
$125$	2.91761	0.260959
$126$	1.36841	0.121907
$127$	−15.7579	−1.39829	−0.699143	−	0.714982i	$-0.746435\pi$
$127$	−15.7579	−1.39829	−0.699143	+	0.714982i	$0.746435\pi$
$128$	−5.13208	−0.453616
$129$	3.66314	0.322521
$130$	0	0
$131$	4.20009	0.366964	0.183482	−	0.983023i	$-0.441263\pi$
$131$	4.20009	0.366964	0.183482	+	0.983023i	$0.441263\pi$
$132$	−4.71848	−0.410691
$133$	−2.97892	−0.258305
$134$	−25.6422	−2.21515
$135$	−1.10334	−0.0949602
$136$	0.914333	0.0784034
$137$	−2.60226	−0.222326	−0.111163	−	0.993802i	$-0.535458\pi$
$137$	−2.60226	−0.222326	−0.111163	+	0.993802i	$0.535458\pi$
$138$	14.0038	1.19209
$139$	−14.7193	−1.24848	−0.624238	−	0.781234i	$-0.714591\pi$
$139$	−14.7193	−1.24848	−0.624238	+	0.781234i	$0.714591\pi$
$140$	−0.385811	−0.0326069
$141$	9.38174	0.790085
$142$	33.6582	2.82453
$143$	0	0
$144$	−3.80924	−0.317436
$145$	0.644070	0.0534871
$146$	−8.90922	−0.737332
$147$	13.6261	1.12386
$148$	−6.13287	−0.504119
$149$	11.8963	0.974584	0.487292	−	0.873239i	$-0.337985\pi$
$149$	11.8963	0.974584	0.487292	+	0.873239i	$0.337985\pi$
$150$	20.8178	1.69976
$151$	20.8405	1.69598	0.847988	−	0.530015i	$-0.177814\pi$
$151$	20.8405	1.69598	0.847988	+	0.530015i	$0.177814\pi$
$152$	−3.41319	−0.276846
$153$	1.63665	0.132315
$154$	1.17712	0.0948548
$155$	−1.50273	−0.120702
$156$	0	0
$157$	6.23358	0.497494	0.248747	−	0.968568i	$-0.419981\pi$
$157$	6.23358	0.497494	0.248747	+	0.968568i	$0.419981\pi$
$158$	14.8088	1.17812
$159$	−10.3941	−0.824308
$160$	2.38502	0.188552
$161$	−1.87343	−0.147647
$162$	−23.1265	−1.81699
$163$	19.3863	1.51845	0.759225	−	0.650828i	$-0.225578\pi$
$163$	19.3863	1.51845	0.759225	+	0.650828i	$0.225578\pi$
$164$	−9.41503	−0.735191
$165$	0.600459	0.0467457
$166$	−28.4317	−2.20673
$167$	0.893805	0.0691647	0.0345823	−	0.999402i	$-0.488990\pi$
$167$	0.893805	0.0691647	0.0345823	+	0.999402i	$0.488990\pi$
$168$	−0.751046	−0.0579445
$169$	0	0
$170$	−0.860479	−0.0659958
$171$	−6.10957	−0.467211
$172$	−4.15242	−0.316619
$173$	−4.79275	−0.364386	−0.182193	−	0.983263i	$-0.558320\pi$
$173$	−4.79275	−0.364386	−0.182193	+	0.983263i	$0.558320\pi$
$174$	9.27217	0.702921
$175$	−2.78499	−0.210526
$176$	−3.27674	−0.246994
$177$	27.4183	2.06089
$178$	−21.9886	−1.64812
$179$	3.99682	0.298736	0.149368	−	0.988782i	$-0.452276\pi$
$179$	3.99682	0.298736	0.149368	+	0.988782i	$0.452276\pi$
$180$	−0.791274	−0.0589781
$181$	−11.3141	−0.840967	−0.420484	−	0.907300i	$-0.638140\pi$
$181$	−11.3141	−0.840967	−0.420484	+	0.907300i	$0.638140\pi$
$182$	0	0
$183$	5.67977	0.419861
$184$	−2.14654	−0.158245
$185$	0.780449	0.0573798
$186$	−21.6336	−1.58625
$187$	1.40786	0.102953
$188$	−10.6348	−0.775625
$189$	2.12494	0.154567
$190$	3.21216	0.233034
$191$	23.5654	1.70513	0.852566	−	0.522620i	$-0.175045\pi$
$191$	23.5654	1.70513	0.852566	+	0.522620i	$0.175045\pi$
$192$	20.9646	1.51299
$193$	−4.20586	−0.302744	−0.151372	−	0.988477i	$-0.548369\pi$
$193$	−4.20586	−0.302744	−0.151372	+	0.988477i	$0.548369\pi$
$194$	20.2351	1.45279
$195$	0	0
$196$	−15.4461	−1.10329
$197$	20.1630	1.43655	0.718277	−	0.695757i	$-0.244931\pi$
$197$	20.1630	1.43655	0.718277	+	0.695757i	$0.244931\pi$
$198$	2.41419	0.171569
$199$	−15.9132	−1.12806	−0.564030	−	0.825754i	$-0.690750\pi$
$199$	−15.9132	−1.12806	−0.564030	+	0.825754i	$0.690750\pi$
$200$	−3.19099	−0.225637
$201$	25.1916	1.77688
$202$	−15.8723	−1.11677
$203$	−1.24043	−0.0870609
$204$	−6.64295	−0.465100
$205$	1.19813	0.0836808
$206$	30.3543	2.11489
$207$	−3.84228	−0.267057
$208$	0	0
$209$	−5.25551	−0.363531
$210$	0.706810	0.0487745
$211$	11.5699	0.796502	0.398251	−	0.917277i	$-0.369617\pi$
$211$	11.5699	0.796502	0.398251	+	0.917277i	$0.369617\pi$
$212$	11.7825	0.809222
$213$	−33.0668	−2.26570
$214$	4.53775	0.310194
$215$	0.528423	0.0360381
$216$	2.43472	0.165662
$217$	2.89414	0.196467
$218$	38.0748	2.57875
$219$	8.75268	0.591452
$220$	−0.680661	−0.0458901
$221$	0	0
$222$	11.2355	0.754078
$223$	11.9562	0.800647	0.400324	−	0.916374i	$-0.368898\pi$
$223$	11.9562	0.800647	0.400324	+	0.916374i	$0.368898\pi$
$224$	−4.59335	−0.306906
$225$	−5.71185	−0.380790
$226$	−27.1286	−1.80457
$227$	18.5540	1.23147	0.615736	−	0.787952i	$-0.288859\pi$
$227$	18.5540	1.23147	0.615736	+	0.787952i	$0.288859\pi$
$228$	24.7980	1.64229
$229$	−5.53364	−0.365673	−0.182837	−	0.983143i	$-0.558528\pi$
$229$	−5.53364	−0.365673	−0.182837	+	0.983143i	$0.558528\pi$
$230$	2.02011	0.133202
$231$	−1.15643	−0.0760878
$232$	−1.42126	−0.0933102
$233$	−13.8555	−0.907703	−0.453851	−	0.891077i	$-0.649950\pi$
$233$	−13.8555	−0.907703	−0.453851	+	0.891077i	$0.649950\pi$
$234$	0	0
$235$	1.35335	0.0882831
$236$	−31.0805	−2.02317
$237$	−14.5486	−0.945033
$238$	1.65721	0.107421
$239$	17.6202	1.13976	0.569879	−	0.821729i	$-0.306990\pi$
$239$	17.6202	1.13976	0.569879	+	0.821729i	$0.306990\pi$
$240$	−1.96755	−0.127005
$241$	−12.1573	−0.783121	−0.391561	−	0.920152i	$-0.628065\pi$
$241$	−12.1573	−0.783121	−0.391561	+	0.920152i	$0.628065\pi$
$242$	2.07671	0.133496
$243$	11.4734	0.736022
$244$	−6.43841	−0.412177
$245$	1.96562	0.125579
$246$	17.2485	1.09972
$247$	0	0
$248$	3.31605	0.210569
$249$	27.9321	1.77013
$250$	6.05904	0.383207
$251$	−7.81876	−0.493515	−0.246758	−	0.969077i	$-0.579365\pi$
$251$	−7.81876	−0.493515	−0.246758	+	0.969077i	$0.579365\pi$
$252$	1.52393	0.0959984
$253$	−3.30517	−0.207794
$254$	−32.7246	−2.05332
$255$	0.845360	0.0529385
$256$	9.89345	0.618341
$257$	20.0537	1.25092	0.625459	−	0.780257i	$-0.284912\pi$
$257$	20.0537	1.25092	0.625459	+	0.780257i	$0.284912\pi$
$258$	7.60728	0.473609
$259$	−1.50308	−0.0933969
$260$	0	0
$261$	−2.54404	−0.157472
$262$	8.72238	0.538870
$263$	30.4092	1.87511	0.937557	−	0.347832i	$-0.113082\pi$
$263$	30.4092	1.87511	0.937557	+	0.347832i	$0.113082\pi$
$264$	−1.32502	−0.0815495
$265$	−1.49940	−0.0921072
$266$	−6.18635	−0.379309
$267$	21.6023	1.32204
$268$	−28.5564	−1.74436
$269$	−20.1423	−1.22810	−0.614048	−	0.789269i	$-0.710460\pi$
$269$	−20.1423	−1.22810	−0.614048	+	0.789269i	$0.710460\pi$
$270$	−2.29131	−0.139445
$271$	9.09891	0.552719	0.276360	−	0.961054i	$-0.410872\pi$
$271$	9.09891	0.552719	0.276360	+	0.961054i	$0.410872\pi$
$272$	−4.61318	−0.279715
$273$	0	0
$274$	−5.40415	−0.326477
$275$	−4.91338	−0.296288
$276$	15.5954	0.938731
$277$	−27.7612	−1.66801	−0.834003	−	0.551759i	$-0.813957\pi$
$277$	−27.7612	−1.66801	−0.834003	+	0.551759i	$0.813957\pi$
$278$	−30.5678	−1.83333
$279$	5.93570	0.355361
$280$	−0.108341	−0.00647464
$281$	0.638650	0.0380987	0.0190493	−	0.999819i	$-0.493936\pi$
$281$	0.638650	0.0380987	0.0190493	+	0.999819i	$0.493936\pi$
$282$	19.4832	1.16021
$283$	−26.4315	−1.57119	−0.785596	−	0.618740i	$-0.787643\pi$
$283$	−26.4315	−1.57119	−0.785596	+	0.618740i	$0.787643\pi$
$284$	37.4834	2.22423
$285$	−3.15572	−0.186929
$286$	0	0
$287$	−2.30749	−0.136207
$288$	−9.42067	−0.555118
$289$	−15.0179	−0.883408
$290$	1.33755	0.0785435
$291$	−19.8795	−1.16536
$292$	−9.92176	−0.580627
$293$	−18.8915	−1.10366	−0.551828	−	0.833958i	$-0.686069\pi$
$293$	−18.8915	−1.10366	−0.551828	+	0.833958i	$0.686069\pi$
$294$	28.2974	1.65034
$295$	3.95520	0.230281
$296$	−1.72220	−0.100101
$297$	3.74889	0.217533
$298$	24.7052	1.43113
$299$	0	0
$300$	23.1837	1.33851
$301$	−1.01770	−0.0586592
$302$	43.2797	2.49047
$303$	15.5934	0.895817
$304$	17.2209	0.987688
$305$	0.819331	0.0469147
$306$	3.39884	0.194299
$307$	5.66766	0.323471	0.161735	−	0.986834i	$-0.448291\pi$
$307$	5.66766	0.323471	0.161735	+	0.986834i	$0.448291\pi$
$308$	1.31090	0.0746953
$309$	−29.8210	−1.69646
$310$	−3.12074	−0.177246
$311$	−10.4217	−0.590962	−0.295481	−	0.955349i	$-0.595480\pi$
$311$	−10.4217	−0.590962	−0.295481	+	0.955349i	$0.595480\pi$
$312$	0	0
$313$	−27.6491	−1.56282	−0.781409	−	0.624019i	$-0.785499\pi$
$313$	−27.6491	−1.56282	−0.781409	+	0.624019i	$0.785499\pi$
$314$	12.9454	0.730548
$315$	−0.193930	−0.0109267
$316$	16.4918	0.927737
$317$	3.64100	0.204499	0.102249	−	0.994759i	$-0.467396\pi$
$317$	3.64100	0.204499	0.102249	+	0.994759i	$0.467396\pi$
$318$	−21.5856	−1.21046
$319$	−2.18840	−0.122527
$320$	3.02423	0.169060
$321$	−4.45802	−0.248823
$322$	−3.89057	−0.216813
$323$	−7.39901	−0.411692
$324$	−25.7548	−1.43082
$325$	0	0
$326$	40.2597	2.22978
$327$	−37.4058	−2.06855
$328$	−2.64389	−0.145984
$329$	−2.60645	−0.143698
$330$	1.24698	0.0686440
$331$	−2.99168	−0.164438	−0.0822188	−	0.996614i	$-0.526201\pi$
$331$	−2.99168	−0.164438	−0.0822188	+	0.996614i	$0.526201\pi$
$332$	−31.6630	−1.73773
$333$	−3.08273	−0.168932
$334$	1.85617	0.101565
$335$	3.63399	0.198546
$336$	3.78934	0.206725
$337$	1.16099	0.0632432	0.0316216	−	0.999500i	$-0.489933\pi$
$337$	1.16099	0.0632432	0.0316216	+	0.999500i	$0.489933\pi$
$338$	0	0
$339$	26.6519	1.44753
$340$	−0.958273	−0.0519697
$341$	5.10594	0.276502
$342$	−12.6878	−0.686079
$343$	−7.75334	−0.418641
$344$	−1.16606	−0.0628698
$345$	−1.98462	−0.106848
$346$	−9.95317	−0.535085
$347$	30.3573	1.62967	0.814834	−	0.579695i	$-0.196828\pi$
$347$	30.3573	1.62967	0.814834	+	0.579695i	$0.196828\pi$
$348$	10.3260	0.553529
$349$	19.7556	1.05749	0.528745	−	0.848781i	$-0.322663\pi$
$349$	19.7556	1.05749	0.528745	+	0.848781i	$0.322663\pi$
$350$	−5.78362	−0.309148
$351$	0	0
$352$	−8.10374	−0.431931
$353$	−19.8879	−1.05853	−0.529264	−	0.848457i	$-0.677532\pi$
$353$	−19.8879	−1.05853	−0.529264	+	0.848457i	$0.677532\pi$
$354$	56.9399	3.02632
$355$	−4.77002	−0.253166
$356$	−24.4876	−1.29784
$357$	−1.62809	−0.0861679
$358$	8.30025	0.438682
$359$	−20.8471	−1.10027	−0.550134	−	0.835076i	$-0.685423\pi$
$359$	−20.8471	−1.10027	−0.550134	+	0.835076i	$0.685423\pi$
$360$	−0.222202	−0.0117111
$361$	8.62037	0.453704
$362$	−23.4960	−1.23492
$363$	−2.04022	−0.107084
$364$	0	0
$365$	1.26261	0.0660880
$366$	11.7953	0.616548
$367$	−1.65713	−0.0865015	−0.0432508	−	0.999064i	$-0.513771\pi$
$367$	−1.65713	−0.0865015	−0.0432508	+	0.999064i	$0.513771\pi$
$368$	10.8302	0.564562
$369$	−4.73253	−0.246366
$370$	1.62077	0.0842597
$371$	2.88771	0.149923
$372$	−24.0923	−1.24913
$373$	−17.4288	−0.902427	−0.451213	−	0.892416i	$-0.649009\pi$
$373$	−17.4288	−0.902427	−0.451213	+	0.892416i	$0.649009\pi$
$374$	2.92371	0.151182
$375$	−5.95258	−0.307390
$376$	−2.98643	−0.154013
$377$	0	0
$378$	4.41288	0.226974
$379$	3.97944	0.204410	0.102205	−	0.994763i	$-0.467410\pi$
$379$	3.97944	0.204410	0.102205	+	0.994763i	$0.467410\pi$
$380$	3.57722	0.183507
$381$	32.1496	1.64707
$382$	48.9385	2.50391
$383$	1.09528	0.0559663	0.0279831	−	0.999608i	$-0.491092\pi$
$383$	1.09528	0.0559663	0.0279831	+	0.999608i	$0.491092\pi$
$384$	10.4706	0.534325
$385$	−0.166820	−0.00850195
$386$	−8.73435	−0.444567
$387$	−2.08724	−0.106100
$388$	22.5348	1.14403
$389$	−28.2973	−1.43473	−0.717366	−	0.696696i	$-0.754652\pi$
$389$	−28.2973	−1.43473	−0.717366	+	0.696696i	$0.754652\pi$
$390$	0	0
$391$	−4.65320	−0.235323
$392$	−4.33749	−0.219076
$393$	−8.56912	−0.432255
$394$	41.8727	2.10952
$395$	−2.09870	−0.105597
$396$	2.68857	0.135106
$397$	13.3464	0.669837	0.334919	−	0.942247i	$-0.391291\pi$
$397$	13.3464	0.669837	0.334919	+	0.942247i	$0.391291\pi$
$398$	−33.0472	−1.65651
$399$	6.07765	0.304263
$400$	16.0999	0.804994
$401$	5.14046	0.256702	0.128351	−	0.991729i	$-0.459032\pi$
$401$	5.14046	0.256702	0.128351	+	0.991729i	$0.459032\pi$
$402$	52.3157	2.60927
$403$	0	0
$404$	−17.6762	−0.879422
$405$	3.27747	0.162859
$406$	−2.57601	−0.127845
$407$	−2.65179	−0.131444
$408$	−1.86544	−0.0923532
$409$	−18.4298	−0.911293	−0.455647	−	0.890161i	$-0.650592\pi$
$409$	−18.4298	−0.911293	−0.455647	+	0.890161i	$0.650592\pi$
$410$	2.48816	0.122882
$411$	5.30920	0.261883
$412$	33.8041	1.66541
$413$	−7.61739	−0.374827
$414$	−7.97931	−0.392162
$415$	4.02933	0.197792
$416$	0	0
$417$	30.0307	1.47061
$418$	−10.9142	−0.533830
$419$	23.4639	1.14628	0.573142	−	0.819456i	$-0.305724\pi$
$419$	23.4639	1.14628	0.573142	+	0.819456i	$0.305724\pi$
$420$	0.787139	0.0384085
$421$	17.7161	0.863430	0.431715	−	0.902010i	$-0.357909\pi$
$421$	17.7161	0.863430	0.431715	+	0.902010i	$0.357909\pi$
$422$	24.0273	1.16963
$423$	−5.34567	−0.259915
$424$	3.30869	0.160684
$425$	−6.91734	−0.335540
$426$	−68.6702	−3.32708
$427$	−1.57796	−0.0763630
$428$	5.05347	0.244269
$429$	0	0
$430$	1.09738	0.0529204
$431$	−17.2675	−0.831748	−0.415874	−	0.909422i	$-0.636524\pi$
$431$	−17.2675	−0.831748	−0.415874	+	0.909422i	$0.636524\pi$
$432$	−12.2841	−0.591021
$433$	36.9970	1.77796	0.888982	−	0.457942i	$-0.151413\pi$
$433$	36.9970	1.77796	0.888982	+	0.457942i	$0.151413\pi$
$434$	6.01029	0.288503
$435$	−1.31405	−0.0630037
$436$	42.4020	2.03069
$437$	17.3703	0.830936
$438$	18.1768	0.868521
$439$	−28.0774	−1.34006	−0.670030	−	0.742334i	$-0.733719\pi$
$439$	−28.0774	−1.34006	−0.670030	+	0.742334i	$0.733719\pi$
$440$	−0.191140	−0.00911224
$441$	−7.76407	−0.369717
$442$	0	0
$443$	15.2641	0.725221	0.362610	−	0.931941i	$-0.381886\pi$
$443$	15.2641	0.725221	0.362610	+	0.931941i	$0.381886\pi$
$444$	12.5124	0.593813
$445$	3.11621	0.147723
$446$	24.8296	1.17572
$447$	−24.2711	−1.14798
$448$	−5.82442	−0.275178
$449$	13.8803	0.655052	0.327526	−	0.944842i	$-0.393785\pi$
$449$	13.8803	0.655052	0.327526	+	0.944842i	$0.393785\pi$
$450$	−11.8619	−0.559173
$451$	−4.07096	−0.191694
$452$	−30.2118	−1.42104
$453$	−42.5193	−1.99773
$454$	38.5313	1.80836
$455$	0	0
$456$	6.96367	0.326104
$457$	4.88885	0.228691	0.114345	−	0.993441i	$-0.463523\pi$
$457$	4.88885	0.228691	0.114345	+	0.993441i	$0.463523\pi$
$458$	−11.4918	−0.536975
$459$	5.27791	0.246352
$460$	2.24970	0.104893
$461$	8.90596	0.414792	0.207396	−	0.978257i	$-0.433501\pi$
$461$	8.90596	0.414792	0.207396	+	0.978257i	$0.433501\pi$
$462$	−2.40158	−0.111732
$463$	−15.9018	−0.739019	−0.369509	−	0.929227i	$-0.620474\pi$
$463$	−15.9018	−0.739019	−0.369509	+	0.929227i	$0.620474\pi$
$464$	7.17083	0.332898
$465$	3.06591	0.142178
$466$	−28.7738	−1.33292
$467$	−1.13636	−0.0525845	−0.0262923	−	0.999654i	$-0.508370\pi$
$467$	−1.13636	−0.0525845	−0.0262923	+	0.999654i	$0.508370\pi$
$468$	0	0
$469$	−6.99877	−0.323173
$470$	2.81053	0.129640
$471$	−12.7179	−0.586010
$472$	−8.72788	−0.401733
$473$	−1.79546	−0.0825554
$474$	−30.2132	−1.38774
$475$	25.8223	1.18481
$476$	1.84556	0.0845909
$477$	5.92252	0.271174
$478$	36.5921	1.67368
$479$	1.45859	0.0666447	0.0333224	−	0.999445i	$-0.489391\pi$
$479$	1.45859	0.0666447	0.0333224	+	0.999445i	$0.489391\pi$
$480$	−4.86596	−0.222100
$481$	0	0
$482$	−25.2472	−1.14998
$483$	3.82221	0.173917
$484$	2.31273	0.105124
$485$	−2.86771	−0.130216
$486$	23.8270	1.08082
$487$	−5.65570	−0.256284	−0.128142	−	0.991756i	$-0.540901\pi$
$487$	−5.65570	−0.256284	−0.128142	+	0.991756i	$0.540901\pi$
$488$	−1.80800	−0.0818445
$489$	−39.5523	−1.78862
$490$	4.08202	0.184407
$491$	−10.1648	−0.458730	−0.229365	−	0.973340i	$-0.573665\pi$
$491$	−10.1648	−0.458730	−0.229365	+	0.973340i	$0.573665\pi$
$492$	19.2088	0.865998
$493$	−3.08096	−0.138760
$494$	0	0
$495$	−0.342138	−0.0153780
$496$	−16.7308	−0.751237
$497$	9.18666	0.412078
$498$	58.0070	2.59936
$499$	−22.7197	−1.01708	−0.508538	−	0.861040i	$-0.669814\pi$
$499$	−22.7197	−1.01708	−0.508538	+	0.861040i	$0.669814\pi$
$500$	6.74765	0.301764
$501$	−1.82356	−0.0814707
$502$	−16.2373	−0.724706
$503$	12.2885	0.547918	0.273959	−	0.961741i	$-0.411667\pi$
$503$	12.2885	0.547918	0.273959	+	0.961741i	$0.411667\pi$
$504$	0.427942	0.0190621
$505$	2.24941	0.100097
$506$	−6.86388	−0.305137
$507$	0	0
$508$	−36.4437	−1.61693
$509$	19.2741	0.854308	0.427154	−	0.904179i	$-0.359516\pi$
$509$	19.2741	0.854308	0.427154	+	0.904179i	$0.359516\pi$
$510$	1.75557	0.0777379
$511$	−2.43168	−0.107571
$512$	30.8100	1.36162
$513$	−19.7023	−0.869879
$514$	41.6458	1.83692
$515$	−4.30180	−0.189560
$516$	8.47185	0.372952
$517$	−4.59839	−0.202237
$518$	−3.12147	−0.137149
$519$	9.77828	0.429219
$520$	0	0
$521$	27.4380	1.20208	0.601041	−	0.799218i	$-0.294753\pi$
$521$	27.4380	1.20208	0.601041	+	0.799218i	$0.294753\pi$
$522$	−5.28323	−0.231241
$523$	−22.5536	−0.986199	−0.493100	−	0.869973i	$-0.664136\pi$
$523$	−22.5536	−0.986199	−0.493100	+	0.869973i	$0.664136\pi$
$524$	9.71368	0.424344
$525$	5.68200	0.247983
$526$	63.1512	2.75352
$527$	7.18843	0.313133
$528$	6.68528	0.290939
$529$	−12.0759	−0.525038
$530$	−3.11381	−0.135255
$531$	−15.6228	−0.677972
$532$	−6.88943	−0.298695
$533$	0	0
$534$	44.8617	1.94135
$535$	−0.643088	−0.0278031
$536$	−8.01907	−0.346371
$537$	−8.15441	−0.351889
$538$	−41.8297	−1.80340
$539$	−6.67872	−0.287673
$540$	−2.55172	−0.109809
$541$	1.04709	0.0450180	0.0225090	−	0.999747i	$-0.492835\pi$
$541$	1.04709	0.0450180	0.0225090	+	0.999747i	$0.492835\pi$
$542$	18.8958	0.811644
$543$	23.0832	0.990595
$544$	−11.4089	−0.489153
$545$	−5.39594	−0.231137
$546$	0	0
$547$	−5.79777	−0.247895	−0.123947	−	0.992289i	$-0.539555\pi$
$547$	−5.79777	−0.247895	−0.123947	+	0.992289i	$0.539555\pi$
$548$	−6.01833	−0.257090
$549$	−3.23631	−0.138122
$550$	−10.2037	−0.435086
$551$	11.5012	0.489967
$552$	4.37942	0.186400
$553$	4.04191	0.171880
$554$	−57.6519	−2.44940
$555$	−1.59229	−0.0675890
$556$	−34.0418	−1.44369
$557$	15.6047	0.661193	0.330597	−	0.943772i	$-0.392750\pi$
$557$	15.6047	0.661193	0.330597	+	0.943772i	$0.392750\pi$
$558$	12.3267	0.521832
$559$	0	0
$560$	0.546627	0.0230992
$561$	−2.87234	−0.121270
$562$	1.32629	0.0559462
$563$	−27.1865	−1.14578	−0.572888	−	0.819634i	$-0.694177\pi$
$563$	−27.1865	−1.14578	−0.572888	+	0.819634i	$0.694177\pi$
$564$	21.6974	0.913627
$565$	3.84465	0.161746
$566$	−54.8907	−2.30723
$567$	−6.31214	−0.265085
$568$	10.5259	0.441658
$569$	−27.1093	−1.13648	−0.568241	−	0.822862i	$-0.692376\pi$
$569$	−27.1093	−1.13648	−0.568241	+	0.822862i	$0.692376\pi$
$570$	−6.55351	−0.274496
$571$	−34.5979	−1.44788	−0.723938	−	0.689865i	$-0.757670\pi$
$571$	−34.5979	−1.44788	−0.723938	+	0.689865i	$0.757670\pi$
$572$	0	0
$573$	−48.0786	−2.00851
$574$	−4.79200	−0.200014
$575$	16.2395	0.677236
$576$	−11.9455	−0.497731
$577$	21.5422	0.896812	0.448406	−	0.893830i	$-0.351992\pi$
$577$	21.5422	0.896812	0.448406	+	0.893830i	$0.351992\pi$
$578$	−31.1879	−1.29725
$579$	8.58089	0.356609
$580$	1.48956	0.0618506
$581$	−7.76015	−0.321945
$582$	−41.2841	−1.71128
$583$	5.09461	0.210997
$584$	−2.78618	−0.115293
$585$	0	0
$586$	−39.2323	−1.62067
$587$	−12.2616	−0.506091	−0.253045	−	0.967454i	$-0.581432\pi$
$587$	−12.2616	−0.506091	−0.253045	+	0.967454i	$0.581432\pi$
$588$	31.5134	1.29959
$589$	−26.8343	−1.10569
$590$	8.21381	0.338157
$591$	−41.1370	−1.69215
$592$	8.68922	0.357125
$593$	4.24915	0.174492	0.0872459	−	0.996187i	$-0.472193\pi$
$593$	4.24915	0.174492	0.0872459	+	0.996187i	$0.472193\pi$
$594$	7.78537	0.319437
$595$	−0.234859	−0.00962829
$596$	27.5130	1.12697
$597$	32.4666	1.32877
$598$	0	0
$599$	−26.8652	−1.09768	−0.548842	−	0.835926i	$-0.684931\pi$
$599$	−26.8652	−1.09768	−0.548842	+	0.835926i	$0.684931\pi$
$600$	6.51034	0.265784
$601$	−40.2925	−1.64357	−0.821783	−	0.569800i	$-0.807021\pi$
$601$	−40.2925	−1.64357	−0.821783	+	0.569800i	$0.807021\pi$
$602$	−2.11347	−0.0861385
$603$	−14.3541	−0.584542
$604$	48.1985	1.96117
$605$	−0.294310	−0.0119654
$606$	32.3830	1.31547
$607$	36.1401	1.46688	0.733441	−	0.679753i	$-0.237913\pi$
$607$	36.1401	1.46688	0.733441	+	0.679753i	$0.237913\pi$
$608$	42.5893	1.72722
$609$	2.53075	0.102551
$610$	1.70151	0.0688923
$611$	0	0
$612$	3.78512	0.153004
$613$	−14.4608	−0.584067	−0.292033	−	0.956408i	$-0.594332\pi$
$613$	−14.4608	−0.584067	−0.292033	+	0.956408i	$0.594332\pi$
$614$	11.7701	0.475003
$615$	−2.44444	−0.0985695
$616$	0.368120	0.0148320
$617$	−11.7996	−0.475034	−0.237517	−	0.971383i	$-0.576333\pi$
$617$	−11.7996	−0.475034	−0.237517	+	0.971383i	$0.576333\pi$
$618$	−61.9296	−2.49117
$619$	−43.3624	−1.74288	−0.871442	−	0.490499i	$-0.836815\pi$
$619$	−43.3624	−1.74288	−0.871442	+	0.490499i	$0.836815\pi$
$620$	−3.47541	−0.139576
$621$	−12.3907	−0.497222
$622$	−21.6429	−0.867803
$623$	−6.00157	−0.240448
$624$	0	0
$625$	23.7082	0.948329
$626$	−57.4192	−2.29493
$627$	10.7224	0.428212
$628$	14.4166	0.575285
$629$	−3.73334	−0.148858
$630$	−0.402737	−0.0160454
$631$	26.7071	1.06319	0.531596	−	0.846998i	$-0.321593\pi$
$631$	26.7071	1.06319	0.531596	+	0.846998i	$0.321593\pi$
$632$	4.63116	0.184217
$633$	−23.6051	−0.938218
$634$	7.56131	0.300298
$635$	4.63771	0.184042
$636$	−24.0388	−0.953201
$637$	0	0
$638$	−4.54469	−0.179926
$639$	18.8413	0.745350
$640$	1.51043	0.0597048
$641$	−19.9420	−0.787660	−0.393830	−	0.919183i	$-0.628850\pi$
$641$	−19.9420	−0.787660	−0.393830	+	0.919183i	$0.628850\pi$
$642$	−9.25803	−0.365385
$643$	4.60077	0.181437	0.0907184	−	0.995877i	$-0.471084\pi$
$643$	4.60077	0.181437	0.0907184	+	0.995877i	$0.471084\pi$
$644$	−4.33273	−0.170734
$645$	−1.07810	−0.0424501
$646$	−15.3656	−0.604552
$647$	32.5666	1.28032	0.640162	−	0.768240i	$-0.278867\pi$
$647$	32.5666	1.28032	0.640162	+	0.768240i	$0.278867\pi$
$648$	−7.23234	−0.284113
$649$	−13.4389	−0.527522
$650$	0	0
$651$	−5.90468	−0.231423
$652$	44.8352	1.75588
$653$	−9.89414	−0.387188	−0.193594	−	0.981082i	$-0.562014\pi$
$653$	−9.89414	−0.387188	−0.193594	+	0.981082i	$0.562014\pi$
$654$	−77.6811	−3.03757
$655$	−1.23613	−0.0482996
$656$	13.3395	0.520819
$657$	−4.98723	−0.194571
$658$	−5.41285	−0.211015
$659$	−42.7784	−1.66641	−0.833204	−	0.552965i	$-0.813496\pi$
$659$	−42.7784	−1.66641	−0.833204	+	0.552965i	$0.813496\pi$
$660$	1.38870	0.0540550
$661$	10.9503	0.425918	0.212959	−	0.977061i	$-0.431690\pi$
$661$	10.9503	0.425918	0.212959	+	0.977061i	$0.431690\pi$
$662$	−6.21285	−0.241469
$663$	0	0
$664$	−8.89145	−0.345055
$665$	0.876726	0.0339980
$666$	−6.40193	−0.248070
$667$	7.23304	0.280065
$668$	2.06713	0.0799796
$669$	−24.3933	−0.943101
$670$	7.54676	0.291557
$671$	−2.78390	−0.107471
$672$	9.37145	0.361511
$673$	14.8257	0.571490	0.285745	−	0.958306i	$-0.407759\pi$
$673$	14.8257	0.571490	0.285745	+	0.958306i	$0.407759\pi$
$674$	2.41104	0.0928699
$675$	−18.4197	−0.708976
$676$	0	0
$677$	−35.4925	−1.36409	−0.682045	−	0.731310i	$-0.738909\pi$
$677$	−35.4925	−1.36409	−0.682045	+	0.731310i	$0.738909\pi$
$678$	55.3484	2.12564
$679$	5.52297	0.211952
$680$	−0.269098	−0.0103194
$681$	−37.8543	−1.45058
$682$	10.6036	0.406031
$683$	6.80198	0.260270	0.130135	−	0.991496i	$-0.458459\pi$
$683$	6.80198	0.260270	0.130135	+	0.991496i	$0.458459\pi$
$684$	−14.1298	−0.540266
$685$	0.765873	0.0292625
$686$	−16.1014	−0.614756
$687$	11.2899	0.430735
$688$	5.88326	0.224297
$689$	0	0
$690$	−4.12148	−0.156902
$691$	−43.7587	−1.66466	−0.832329	−	0.554282i	$-0.812993\pi$
$691$	−43.7587	−1.66466	−0.832329	+	0.554282i	$0.812993\pi$
$692$	−11.0843	−0.421364
$693$	0.658930	0.0250307
$694$	63.0434	2.39310
$695$	4.33205	0.164324
$696$	2.89969	0.109912
$697$	−5.73133	−0.217090
$698$	41.0266	1.55288
$699$	28.2683	1.06920
$700$	−6.44093	−0.243444
$701$	−32.9829	−1.24575	−0.622874	−	0.782322i	$-0.714035\pi$
$701$	−32.9829	−1.24575	−0.622874	+	0.782322i	$0.714035\pi$
$702$	0	0
$703$	13.9365	0.525625
$704$	−10.2757	−0.387278
$705$	−2.76115	−0.103991
$706$	−41.3015	−1.55440
$707$	−4.33218	−0.162928
$708$	63.4111	2.38314
$709$	−38.9129	−1.46140	−0.730702	−	0.682697i	$-0.760807\pi$
$709$	−38.9129	−1.46140	−0.730702	+	0.682697i	$0.760807\pi$
$710$	−9.90595	−0.371764
$711$	8.28972	0.310889
$712$	−6.87650	−0.257708
$713$	−16.8760	−0.632010
$714$	−3.38108	−0.126534
$715$	0	0
$716$	9.24357	0.345448
$717$	−35.9492	−1.34255
$718$	−43.2934	−1.61570
$719$	−23.2229	−0.866068	−0.433034	−	0.901378i	$-0.642557\pi$
$719$	−23.2229	−0.866068	−0.433034	+	0.901378i	$0.642557\pi$
$720$	1.12110	0.0417809
$721$	8.28491	0.308546
$722$	17.9020	0.666244
$723$	24.8036	0.922457
$724$	−26.1664	−0.972465
$725$	10.7525	0.399337
$726$	−4.23695	−0.157248
$727$	23.4114	0.868282	0.434141	−	0.900845i	$-0.357052\pi$
$727$	23.4114	0.868282	0.434141	+	0.900845i	$0.357052\pi$
$728$	0	0
$729$	9.99991	0.370367
$730$	2.62208	0.0970474
$731$	−2.52775	−0.0934923
$732$	13.1358	0.485513
$733$	−52.8757	−1.95301	−0.976504	−	0.215499i	$-0.930862\pi$
$733$	−52.8757	−1.95301	−0.976504	+	0.215499i	$0.930862\pi$
$734$	−3.44138	−0.127024
$735$	−4.01029	−0.147922
$736$	26.7842	0.987279
$737$	−12.3475	−0.454825
$738$	−9.82809	−0.361777
$739$	12.3058	0.452678	0.226339	−	0.974049i	$-0.427324\pi$
$739$	12.3058	0.452678	0.226339	+	0.974049i	$0.427324\pi$
$740$	1.80497	0.0663520
$741$	0	0
$742$	5.99695	0.220155
$743$	46.3257	1.69953	0.849763	−	0.527165i	$-0.176745\pi$
$743$	46.3257	1.69953	0.849763	+	0.527165i	$0.176745\pi$
$744$	−6.76548	−0.248035
$745$	−3.50121	−0.128274
$746$	−36.1945	−1.32517
$747$	−15.9156	−0.582321
$748$	3.25599	0.119051
$749$	1.23853	0.0452551
$750$	−12.3618	−0.451389
$751$	26.5457	0.968666	0.484333	−	0.874884i	$-0.339062\pi$
$751$	26.5457	0.968666	0.484333	+	0.874884i	$0.339062\pi$
$752$	15.0677	0.549464
$753$	15.9520	0.581323
$754$	0	0
$755$	−6.13358	−0.223224
$756$	4.91441	0.178735
$757$	−18.9217	−0.687720	−0.343860	−	0.939021i	$-0.611735\pi$
$757$	−18.9217	−0.687720	−0.343860	+	0.939021i	$0.611735\pi$
$758$	8.26415	0.300168
$759$	6.74328	0.244765
$760$	1.00454	0.0364384
$761$	−41.6240	−1.50887	−0.754434	−	0.656376i	$-0.772088\pi$
$761$	−41.6240	−1.50887	−0.754434	+	0.656376i	$0.772088\pi$
$762$	66.7654	2.41866
$763$	10.3921	0.376221
$764$	54.5004	1.97175
$765$	−0.481682	−0.0174153
$766$	2.27458	0.0821840
$767$	0	0
$768$	−20.1849	−0.728358
$769$	32.7075	1.17946	0.589731	−	0.807600i	$-0.299234\pi$
$769$	32.7075	1.17946	0.589731	+	0.807600i	$0.299234\pi$
$770$	−0.346438	−0.0124848
$771$	−40.9141	−1.47348
$772$	−9.72701	−0.350083
$773$	−39.8587	−1.43362	−0.716809	−	0.697269i	$-0.754398\pi$
$773$	−39.8587	−1.43362	−0.716809	+	0.697269i	$0.754398\pi$
$774$	−4.33459	−0.155804
$775$	−25.0874	−0.901167
$776$	6.32812	0.227166
$777$	3.06662	0.110014
$778$	−58.7654	−2.10684
$779$	21.3950	0.766554
$780$	0	0
$781$	16.2074	0.579948
$782$	−9.66336	−0.345561
$783$	−8.20409	−0.293190
$784$	21.8844	0.781586
$785$	−1.83461	−0.0654800
$786$	−17.7956	−0.634748
$787$	46.8180	1.66888	0.834441	−	0.551097i	$-0.185791\pi$
$787$	46.8180	1.66888	0.834441	+	0.551097i	$0.185791\pi$
$788$	46.6316	1.66118
$789$	−62.0416	−2.20874
$790$	−4.35838	−0.155064
$791$	−7.40448	−0.263273
$792$	0.754991	0.0268274
$793$	0	0
$794$	27.7167	0.983627
$795$	3.05910	0.108495
$796$	−36.8030	−1.30445
$797$	−1.76366	−0.0624722	−0.0312361	−	0.999512i	$-0.509944\pi$
$797$	−1.76366	−0.0624722	−0.0312361	+	0.999512i	$0.509944\pi$
$798$	12.6215	0.446797
$799$	−6.47388	−0.229029
$800$	39.8168	1.40774
$801$	−12.3089	−0.434912
$802$	10.6753	0.376956
$803$	−4.29006	−0.151393
$804$	58.2614	2.05472
$805$	0.551369	0.0194332
$806$	0	0
$807$	41.0947	1.44660
$808$	−4.96374	−0.174624
$809$	40.7520	1.43276	0.716382	−	0.697708i	$-0.245797\pi$
$809$	40.7520	1.43276	0.716382	+	0.697708i	$0.245797\pi$
$810$	6.80636	0.239151
$811$	−31.3202	−1.09980	−0.549901	−	0.835230i	$-0.685335\pi$
$811$	−31.3202	−1.09980	−0.549901	+	0.835230i	$0.685335\pi$
$812$	−2.86877	−0.100674
$813$	−18.5638	−0.651061
$814$	−5.50700	−0.193020
$815$	−5.70558	−0.199858
$816$	9.41192	0.329483
$817$	9.43606	0.330126
$818$	−38.2733	−1.33819
$819$	0	0
$820$	2.77094	0.0967655
$821$	−4.55978	−0.159137	−0.0795687	−	0.996829i	$-0.525354\pi$
$821$	−4.55978	−0.159137	−0.0795687	+	0.996829i	$0.525354\pi$
$822$	11.0257	0.384564
$823$	−7.01614	−0.244567	−0.122284	−	0.992495i	$-0.539022\pi$
$823$	−7.01614	−0.244567	−0.122284	+	0.992495i	$0.539022\pi$
$824$	9.49271	0.330694
$825$	10.0244	0.349005
$826$	−15.8191	−0.550418
$827$	52.8832	1.83893	0.919465	−	0.393172i	$-0.128622\pi$
$827$	52.8832	1.83893	0.919465	+	0.393172i	$0.128622\pi$
$828$	−8.88617	−0.308816
$829$	22.9471	0.796987	0.398493	−	0.917171i	$-0.369533\pi$
$829$	22.9471	0.796987	0.398493	+	0.917171i	$0.369533\pi$
$830$	8.36775	0.290449
$831$	56.6390	1.96478
$832$	0	0
$833$	−9.40268	−0.325784
$834$	62.3651	2.15953
$835$	−0.263056	−0.00910343
$836$	−12.1546	−0.420375
$837$	19.1416	0.661631
$838$	48.7277	1.68327
$839$	49.3280	1.70299	0.851495	−	0.524362i	$-0.175696\pi$
$839$	49.3280	1.70299	0.851495	+	0.524362i	$0.175696\pi$
$840$	0.221041	0.00762663
$841$	−24.2109	−0.834858
$842$	36.7912	1.26791
$843$	−1.30299	−0.0448773
$844$	26.7580	0.921047
$845$	0	0
$846$	−11.1014	−0.381674
$847$	0.566818	0.0194761
$848$	−16.6937	−0.573264
$849$	53.9262	1.85074
$850$	−14.3653	−0.492726
$851$	8.76461	0.300447
$852$	−76.4745	−2.61997
$853$	7.06191	0.241795	0.120898	−	0.992665i	$-0.461423\pi$
$853$	7.06191	0.241795	0.120898	+	0.992665i	$0.461423\pi$
$854$	−3.27698	−0.112136
$855$	1.79811	0.0614941
$856$	1.41909	0.0485036
$857$	−46.5013	−1.58845	−0.794227	−	0.607622i	$-0.792124\pi$
$857$	−46.5013	−1.58845	−0.794227	+	0.607622i	$0.792124\pi$
$858$	0	0
$859$	−7.43316	−0.253616	−0.126808	−	0.991927i	$-0.540473\pi$
$859$	−7.43316	−0.253616	−0.126808	+	0.991927i	$0.540473\pi$
$860$	1.22210	0.0416732
$861$	4.70780	0.160441
$862$	−35.8597	−1.22139
$863$	9.77264	0.332664	0.166332	−	0.986070i	$-0.446808\pi$
$863$	9.77264	0.332664	0.166332	+	0.986070i	$0.446808\pi$
$864$	−30.3801	−1.03355
$865$	1.41056	0.0479604
$866$	76.8322	2.61086
$867$	30.6399	1.04059
$868$	6.69336	0.227187
$869$	7.13089	0.241899
$870$	−2.72890	−0.0925182
$871$	0	0
$872$	11.9071	0.403227
$873$	11.3273	0.383370
$874$	36.0732	1.22019
$875$	1.65375	0.0559071
$876$	20.2426	0.683934
$877$	−48.4576	−1.63630	−0.818148	−	0.575008i	$-0.804999\pi$
$877$	−48.4576	−1.63630	−0.818148	+	0.575008i	$0.804999\pi$
$878$	−58.3086	−1.96782
$879$	38.5429	1.30002
$880$	0.964379	0.0325092
$881$	−0.629656	−0.0212136	−0.0106068	−	0.999944i	$-0.503376\pi$
$881$	−0.629656	−0.0212136	−0.0106068	+	0.999944i	$0.503376\pi$
$882$	−16.1237	−0.542914
$883$	19.1333	0.643886	0.321943	−	0.946759i	$-0.395664\pi$
$883$	19.1333	0.643886	0.321943	+	0.946759i	$0.395664\pi$
$884$	0	0
$885$	−8.06949	−0.271253
$886$	31.6992	1.06496
$887$	−7.96912	−0.267577	−0.133789	−	0.991010i	$-0.542714\pi$
$887$	−7.96912	−0.267577	−0.133789	+	0.991010i	$0.542714\pi$
$888$	3.51368	0.117911
$889$	−8.93185	−0.299565
$890$	6.47148	0.216924
$891$	−11.1361	−0.373073
$892$	27.6515	0.925840
$893$	24.1669	0.808714
$894$	−50.4041	−1.68577
$895$	−1.17631	−0.0393196
$896$	−2.90896	−0.0971814
$897$	0	0
$898$	28.8254	0.961915
$899$	−11.1739	−0.372669
$900$	−13.2100	−0.440332
$901$	7.17248	0.238950
$902$	−8.45421	−0.281494
$903$	2.07633	0.0690960
$904$	−8.48393	−0.282171
$905$	3.32984	0.110688
$906$	−88.3003	−2.93358
$907$	12.1593	0.403744	0.201872	−	0.979412i	$-0.435297\pi$
$907$	12.1593	0.403744	0.201872	+	0.979412i	$0.435297\pi$
$908$	42.9104	1.42403
$909$	−8.88503	−0.294698
$910$	0	0
$911$	−6.14172	−0.203484	−0.101742	−	0.994811i	$-0.532442\pi$
$911$	−6.14172	−0.203484	−0.101742	+	0.994811i	$0.532442\pi$
$912$	−35.1345	−1.16342
$913$	−13.6907	−0.453097
$914$	10.1527	0.335823
$915$	−1.67162	−0.0552620
$916$	−12.7978	−0.422852
$917$	2.38069	0.0786172
$918$	10.9607	0.361757
$919$	−23.0673	−0.760919	−0.380459	−	0.924798i	$-0.624234\pi$
$919$	−23.0673	−0.760919	−0.380459	+	0.924798i	$0.624234\pi$
$920$	0.631749	0.0208282
$921$	−11.5633	−0.381023
$922$	18.4951	0.609104
$923$	0	0
$924$	−2.67452	−0.0879853
$925$	13.0293	0.428399
$926$	−33.0234	−1.08522
$927$	16.9918	0.558085
$928$	17.7343	0.582156
$929$	43.8243	1.43783	0.718914	−	0.695099i	$-0.244639\pi$
$929$	43.8243	1.43783	0.718914	+	0.695099i	$0.244639\pi$
$930$	6.36700	0.208782
$931$	35.1001	1.15036
$932$	−32.0440	−1.04964
$933$	21.2627	0.696108
$934$	−2.35989	−0.0772181
$935$	−0.414347	−0.0135506
$936$	0	0
$937$	−52.3292	−1.70952	−0.854760	−	0.519023i	$-0.826296\pi$
$937$	−52.3292	−1.70952	−0.854760	+	0.519023i	$0.826296\pi$
$938$	−14.5344	−0.474566
$939$	56.4103	1.84088
$940$	3.12994	0.102088
$941$	50.6533	1.65125	0.825625	−	0.564219i	$-0.190823\pi$
$941$	50.6533	1.65125	0.825625	+	0.564219i	$0.190823\pi$
$942$	−26.4114	−0.860530
$943$	13.4552	0.438162
$944$	44.0357	1.43324
$945$	−0.625392	−0.0203440
$946$	−3.72865	−0.121229
$947$	−28.7879	−0.935482	−0.467741	−	0.883866i	$-0.654932\pi$
$947$	−28.7879	−0.935482	−0.467741	+	0.883866i	$0.654932\pi$
$948$	−33.6470	−1.09280
$949$	0	0
$950$	53.6255	1.73984
$951$	−7.42845	−0.240884
$952$	0.518260	0.0167969
$953$	53.0353	1.71798	0.858991	−	0.511990i	$-0.171092\pi$
$953$	53.0353	1.71798	0.858991	+	0.511990i	$0.171092\pi$
$954$	12.2994	0.398207
$955$	−6.93554	−0.224429
$956$	40.7508	1.31798
$957$	4.46483	0.144328
$958$	3.02907	0.0978649
$959$	−1.47501	−0.0476305
$960$	−6.17011	−0.199139
$961$	−4.92939	−0.159013
$962$	0	0
$963$	2.54016	0.0818555
$964$	−28.1166	−0.905574
$965$	1.23783	0.0398471
$966$	7.93762	0.255389
$967$	22.1413	0.712016	0.356008	−	0.934483i	$-0.384138\pi$
$967$	22.1413	0.712016	0.356008	+	0.934483i	$0.384138\pi$
$968$	0.649450	0.0208741
$969$	15.0956	0.484941
$970$	−5.95540	−0.191216
$971$	−29.8710	−0.958606	−0.479303	−	0.877650i	$-0.659110\pi$
$971$	−29.8710	−0.958606	−0.479303	+	0.877650i	$0.659110\pi$
$972$	26.5350	0.851110
$973$	−8.34317	−0.267470
$974$	−11.7453	−0.376342
$975$	0	0
$976$	9.12211	0.291992
$977$	10.4762	0.335164	0.167582	−	0.985858i	$-0.446404\pi$
$977$	10.4762	0.335164	0.167582	+	0.985858i	$0.446404\pi$
$978$	−82.1387	−2.62651
$979$	−10.5882	−0.338400
$980$	4.54594	0.145215
$981$	21.3137	0.680493
$982$	−21.1093	−0.673625
$983$	51.6944	1.64880	0.824398	−	0.566011i	$-0.191514\pi$
$983$	51.6944	1.64880	0.824398	+	0.566011i	$0.191514\pi$
$984$	5.39411	0.171958
$985$	−5.93418	−0.189079
$986$	−6.39827	−0.203762
$987$	5.31774	0.169266
$988$	0	0
$989$	5.93430	0.188700
$990$	−0.710523	−0.0225819
$991$	25.8268	0.820415	0.410207	−	0.911992i	$-0.365456\pi$
$991$	25.8268	0.820415	0.410207	+	0.911992i	$0.365456\pi$
$992$	−41.3772	−1.31373
$993$	6.10369	0.193695
$994$	19.0781	0.605119
$995$	4.68343	0.148475
$996$	64.5995	2.04691
$997$	−46.7456	−1.48045	−0.740224	−	0.672361i	$-0.765280\pi$
$997$	−46.7456	−1.48045	−0.740224	+	0.672361i	$0.765280\pi$
$998$	−47.1824	−1.49353
$999$	−9.94127	−0.314528

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.q.1.9	✓	9
13.12	even	2		1859.2.a.r.1.1	yes	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.2.a.q.1.9	✓	9	1.1	even	1	trivial
1859.2.a.r.1.1	yes	9	13.12	even	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:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q+2.07671 q^{2} -2.04022 q^{3} +2.31273 q^{4} -0.294310 q^{5} -4.23695 q^{6} +0.566818 q^{7} +0.649450 q^{8} +1.16251 q^{9} +O(q^{10})\)	\(q+2.07671 q^{2} -2.04022 q^{3} +2.31273 q^{4} -0.294310 q^{5} -4.23695 q^{6} +0.566818 q^{7} +0.649450 q^{8} +1.16251 q^{9} -0.611198 q^{10} +1.00000 q^{11} -4.71848 q^{12} +1.17712 q^{14} +0.600459 q^{15} -3.27674 q^{16} +1.40786 q^{17} +2.41419 q^{18} -5.25551 q^{19} -0.680661 q^{20} -1.15643 q^{21} +2.07671 q^{22} -3.30517 q^{23} -1.32502 q^{24} -4.91338 q^{25} +3.74889 q^{27} +1.31090 q^{28} -2.18840 q^{29} +1.24698 q^{30} +5.10594 q^{31} -8.10374 q^{32} -2.04022 q^{33} +2.92371 q^{34} -0.166820 q^{35} +2.68857 q^{36} -2.65179 q^{37} -10.9142 q^{38} -0.191140 q^{40} -4.07096 q^{41} -2.40158 q^{42} -1.79546 q^{43} +2.31273 q^{44} -0.342138 q^{45} -6.86388 q^{46} -4.59839 q^{47} +6.68528 q^{48} -6.67872 q^{49} -10.2037 q^{50} -2.87234 q^{51} +5.09461 q^{53} +7.78537 q^{54} -0.294310 q^{55} +0.368120 q^{56} +10.7224 q^{57} -4.54469 q^{58} -13.4389 q^{59} +1.38870 q^{60} -2.78390 q^{61} +10.6036 q^{62} +0.658930 q^{63} -10.2757 q^{64} -4.23695 q^{66} -12.3475 q^{67} +3.25599 q^{68} +6.74328 q^{69} -0.346438 q^{70} +16.2074 q^{71} +0.754991 q^{72} -4.29006 q^{73} -5.50700 q^{74} +10.0244 q^{75} -12.1546 q^{76} +0.566818 q^{77} +7.13089 q^{79} +0.964379 q^{80} -11.1361 q^{81} -8.45421 q^{82} -13.6907 q^{83} -2.67452 q^{84} -0.414347 q^{85} -3.72865 q^{86} +4.46483 q^{87} +0.649450 q^{88} -10.5882 q^{89} -0.710523 q^{90} -7.64396 q^{92} -10.4173 q^{93} -9.54953 q^{94} +1.54675 q^{95} +16.5334 q^{96} +9.74381 q^{97} -13.8698 q^{98} +1.16251 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 5 q^{3} + 2 q^{4} - 4 q^{5} - 11 q^{6} + q^{7} + 3 q^{8} + 2 q^{9}+O(q^{10}) \) 9 * q - 5 * q^3 + 2 * q^4 - 4 * q^5 - 11 * q^6 + q^7 + 3 * q^8 + 2 * q^9	\( 9 q - 5 q^{3} + 2 q^{4} - 4 q^{5} - 11 q^{6} + q^{7} + 3 q^{8} + 2 q^{9} - 8 q^{10} + 9 q^{11} - 9 q^{12} + 3 q^{15} - 8 q^{16} - 8 q^{17} + 27 q^{18} - q^{19} + 12 q^{20} + 17 q^{21} - 6 q^{24} - 15 q^{25} - 23 q^{27} + 11 q^{28} - 22 q^{29} - 3 q^{30} - 6 q^{31} - 19 q^{32} - 5 q^{33} + 10 q^{34} - 15 q^{35} + 7 q^{36} - 15 q^{37} + q^{38} - 3 q^{40} + 10 q^{41} + 2 q^{42} - 19 q^{43} + 2 q^{44} - 2 q^{45} + 19 q^{46} - 2 q^{47} + 6 q^{48} - 20 q^{49} - 17 q^{50} - 2 q^{51} - 5 q^{53} - 27 q^{54} - 4 q^{55} - 16 q^{56} - 32 q^{57} - 11 q^{58} - 11 q^{59} - 6 q^{60} - 68 q^{61} - 21 q^{62} - 29 q^{63} - 23 q^{64} - 11 q^{66} + 5 q^{67} + 16 q^{68} - 34 q^{69} - 5 q^{70} - 34 q^{71} + 13 q^{72} + 26 q^{73} + q^{74} + 10 q^{75} - 11 q^{76} + q^{77} - 32 q^{79} + 8 q^{80} + 13 q^{81} - 42 q^{82} + 8 q^{83} - 13 q^{84} + 23 q^{85} + 30 q^{86} + 10 q^{87} + 3 q^{88} - 37 q^{89} + 21 q^{90} - 12 q^{92} + 20 q^{93} - 12 q^{94} - 4 q^{95} + 60 q^{96} + 3 q^{97} - 9 q^{98} + 2 q^{99}+O(q^{100}) \) 9 * q - 5 * q^3 + 2 * q^4 - 4 * q^5 - 11 * q^6 + q^7 + 3 * q^8 + 2 * q^9 - 8 * q^10 + 9 * q^11 - 9 * q^12 + 3 * q^15 - 8 * q^16 - 8 * q^17 + 27 * q^18 - q^19 + 12 * q^20 + 17 * q^21 - 6 * q^24 - 15 * q^25 - 23 * q^27 + 11 * q^28 - 22 * q^29 - 3 * q^30 - 6 * q^31 - 19 * q^32 - 5 * q^33 + 10 * q^34 - 15 * q^35 + 7 * q^36 - 15 * q^37 + q^38 - 3 * q^40 + 10 * q^41 + 2 * q^42 - 19 * q^43 + 2 * q^44 - 2 * q^45 + 19 * q^46 - 2 * q^47 + 6 * q^48 - 20 * q^49 - 17 * q^50 - 2 * q^51 - 5 * q^53 - 27 * q^54 - 4 * q^55 - 16 * q^56 - 32 * q^57 - 11 * q^58 - 11 * q^59 - 6 * q^60 - 68 * q^61 - 21 * q^62 - 29 * q^63 - 23 * q^64 - 11 * q^66 + 5 * q^67 + 16 * q^68 - 34 * q^69 - 5 * q^70 - 34 * q^71 + 13 * q^72 + 26 * q^73 + q^74 + 10 * q^75 - 11 * q^76 + q^77 - 32 * q^79 + 8 * q^80 + 13 * q^81 - 42 * q^82 + 8 * q^83 - 13 * q^84 + 23 * q^85 + 30 * q^86 + 10 * q^87 + 3 * q^88 - 37 * q^89 + 21 * q^90 - 12 * q^92 + 20 * q^93 - 12 * q^94 - 4 * q^95 + 60 * q^96 + 3 * q^97 - 9 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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