LMFDB - Embedded newform 1859.2.a.s.1.2

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:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-2.56428 q^{2} +1.12676 q^{3} +4.57554 q^{4} -1.24792 q^{5} -2.88933 q^{6} -2.50384 q^{7} -6.60441 q^{8} -1.73041 q^{9} +O(q^{10})$	\(q-2.56428 q^{2} +1.12676 q^{3} +4.57554 q^{4} -1.24792 q^{5} -2.88933 q^{6} -2.50384 q^{7} -6.60441 q^{8} -1.73041 q^{9} +3.20001 q^{10} -1.00000 q^{11} +5.15554 q^{12} +6.42056 q^{14} -1.40611 q^{15} +7.78448 q^{16} +2.78965 q^{17} +4.43726 q^{18} +5.79085 q^{19} -5.70990 q^{20} -2.82123 q^{21} +2.56428 q^{22} -8.60804 q^{23} -7.44158 q^{24} -3.44270 q^{25} -5.33004 q^{27} -11.4564 q^{28} -0.584987 q^{29} +3.60565 q^{30} +5.56093 q^{31} -6.75278 q^{32} -1.12676 q^{33} -7.15346 q^{34} +3.12459 q^{35} -7.91757 q^{36} -8.21491 q^{37} -14.8494 q^{38} +8.24176 q^{40} -0.167741 q^{41} +7.23443 q^{42} +9.05070 q^{43} -4.57554 q^{44} +2.15941 q^{45} +22.0734 q^{46} +10.5184 q^{47} +8.77124 q^{48} -0.730769 q^{49} +8.82805 q^{50} +3.14327 q^{51} -1.39208 q^{53} +13.6677 q^{54} +1.24792 q^{55} +16.5364 q^{56} +6.52490 q^{57} +1.50007 q^{58} -5.61213 q^{59} -6.43369 q^{60} +12.3950 q^{61} -14.2598 q^{62} +4.33268 q^{63} +1.74708 q^{64} +2.88933 q^{66} +10.9688 q^{67} +12.7642 q^{68} -9.69919 q^{69} -8.01234 q^{70} -3.69804 q^{71} +11.4283 q^{72} -7.96670 q^{73} +21.0653 q^{74} -3.87910 q^{75} +26.4963 q^{76} +2.50384 q^{77} +14.8194 q^{79} -9.71440 q^{80} -0.814441 q^{81} +0.430136 q^{82} -9.73406 q^{83} -12.9087 q^{84} -3.48126 q^{85} -23.2085 q^{86} -0.659140 q^{87} +6.60441 q^{88} -0.577135 q^{89} -5.53734 q^{90} -39.3864 q^{92} +6.26583 q^{93} -26.9721 q^{94} -7.22651 q^{95} -7.60877 q^{96} +3.91481 q^{97} +1.87390 q^{98} +1.73041 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9}+O(q^{10}) $ 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9	\( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9} + 18 q^{10} - 21 q^{11} + 23 q^{12} + 20 q^{14} - 16 q^{15} + 50 q^{16} + 16 q^{17} - 3 q^{18} + 11 q^{19} - 24 q^{20} + 5 q^{21} - 9 q^{23} + 54 q^{24} + 36 q^{25} + 11 q^{28} + 28 q^{29} + 21 q^{30} - 15 q^{31} + 61 q^{32} - 6 q^{33} + 6 q^{34} - 3 q^{35} + 45 q^{36} + 12 q^{37} + q^{38} + 55 q^{40} + 4 q^{41} - 34 q^{42} + 17 q^{43} - 32 q^{44} - 9 q^{45} - 11 q^{46} - 36 q^{47} + 24 q^{48} + 72 q^{49} + 9 q^{50} + 2 q^{51} + 19 q^{53} - q^{54} + 7 q^{55} + 44 q^{56} + 4 q^{57} + 33 q^{58} - 54 q^{59} - 64 q^{60} + 98 q^{61} - 29 q^{62} + 81 q^{63} + 63 q^{64} - 19 q^{66} - 25 q^{67} + 4 q^{68} + 89 q^{69} - 65 q^{70} - 37 q^{71} - 55 q^{72} - 8 q^{73} - 11 q^{74} + 24 q^{75} - 13 q^{76} + q^{77} + 24 q^{79} - 26 q^{80} + 81 q^{81} + 26 q^{82} + 34 q^{83} + 103 q^{84} + 11 q^{85} - 30 q^{86} + 32 q^{87} - 3 q^{88} - 6 q^{89} + 47 q^{90} - 80 q^{92} - 41 q^{93} + 40 q^{94} + 20 q^{95} + 98 q^{96} + 5 q^{98} - 33 q^{99}+O(q^{100}) \) 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9 + 18 * q^10 - 21 * q^11 + 23 * q^12 + 20 * q^14 - 16 * q^15 + 50 * q^16 + 16 * q^17 - 3 * q^18 + 11 * q^19 - 24 * q^20 + 5 * q^21 - 9 * q^23 + 54 * q^24 + 36 * q^25 + 11 * q^28 + 28 * q^29 + 21 * q^30 - 15 * q^31 + 61 * q^32 - 6 * q^33 + 6 * q^34 - 3 * q^35 + 45 * q^36 + 12 * q^37 + q^38 + 55 * q^40 + 4 * q^41 - 34 * q^42 + 17 * q^43 - 32 * q^44 - 9 * q^45 - 11 * q^46 - 36 * q^47 + 24 * q^48 + 72 * q^49 + 9 * q^50 + 2 * q^51 + 19 * q^53 - q^54 + 7 * q^55 + 44 * q^56 + 4 * q^57 + 33 * q^58 - 54 * q^59 - 64 * q^60 + 98 * q^61 - 29 * q^62 + 81 * q^63 + 63 * q^64 - 19 * q^66 - 25 * q^67 + 4 * q^68 + 89 * q^69 - 65 * q^70 - 37 * q^71 - 55 * q^72 - 8 * q^73 - 11 * q^74 + 24 * q^75 - 13 * q^76 + q^77 + 24 * q^79 - 26 * q^80 + 81 * q^81 + 26 * q^82 + 34 * q^83 + 103 * q^84 + 11 * q^85 - 30 * q^86 + 32 * q^87 - 3 * q^88 - 6 * q^89 + 47 * q^90 - 80 * q^92 - 41 * q^93 + 40 * q^94 + 20 * q^95 + 98 * q^96 + 5 * q^98 - 33 * 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 $

$2$	−2.56428	−1.81322	−0.906610	−	0.421969i	$-0.861339\pi$
$2$	−2.56428	−1.81322	−0.906610	+	0.421969i	$0.861339\pi$
$3$	1.12676	0.650535	0.325268	−	0.945622i	$-0.394546\pi$
$3$	1.12676	0.650535	0.325268	+	0.945622i	$0.394546\pi$
$4$	4.57554	2.28777
$5$	−1.24792	−0.558086	−0.279043	−	0.960279i	$-0.590017\pi$
$5$	−1.24792	−0.558086	−0.279043	+	0.960279i	$0.590017\pi$
$6$	−2.88933	−1.17956
$7$	−2.50384	−0.946364	−0.473182	−	0.880965i	$-0.656895\pi$
$7$	−2.50384	−0.946364	−0.473182	+	0.880965i	$0.656895\pi$
$8$	−6.60441	−2.33501
$9$	−1.73041	−0.576804
$10$	3.20001	1.01193
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	5.15554	1.48827
$13$	0	0
$13$	0	0
$14$	6.42056	1.71597
$15$	−1.40611	−0.363055
$16$	7.78448	1.94612
$17$	2.78965	0.676590	0.338295	−	0.941040i	$-0.390150\pi$
$17$	2.78965	0.676590	0.338295	+	0.941040i	$0.390150\pi$
$18$	4.43726	1.04587
$19$	5.79085	1.32851	0.664256	−	0.747505i	$-0.268748\pi$
$19$	5.79085	1.32851	0.664256	+	0.747505i	$0.268748\pi$
$20$	−5.70990	−1.27677
$21$	−2.82123	−0.615643
$22$	2.56428	0.546707
$23$	−8.60804	−1.79490	−0.897450	−	0.441116i	$-0.854583\pi$
$23$	−8.60804	−1.79490	−0.897450	+	0.441116i	$0.854583\pi$
$24$	−7.44158	−1.51901
$25$	−3.44270	−0.688540
$26$	0	0
$27$	−5.33004	−1.02577
$28$	−11.4564	−2.16506
$29$	−0.584987	−0.108629	−0.0543147	−	0.998524i	$-0.517297\pi$
$29$	−0.584987	−0.108629	−0.0543147	+	0.998524i	$0.517297\pi$
$30$	3.60565	0.658298
$31$	5.56093	0.998772	0.499386	−	0.866379i	$-0.333559\pi$
$31$	5.56093	0.998772	0.499386	+	0.866379i	$0.333559\pi$
$32$	−6.75278	−1.19373
$33$	−1.12676	−0.196144
$34$	−7.15346	−1.22681
$35$	3.12459	0.528153
$36$	−7.91757	−1.31959
$37$	−8.21491	−1.35052	−0.675261	−	0.737579i	$-0.735969\pi$
$37$	−8.21491	−1.35052	−0.675261	+	0.737579i	$0.735969\pi$
$38$	−14.8494	−2.40889
$39$	0	0
$40$	8.24176	1.30314
$41$	−0.167741	−0.0261968	−0.0130984	−	0.999914i	$-0.504169\pi$
$41$	−0.167741	−0.0261968	−0.0130984	+	0.999914i	$0.504169\pi$
$42$	7.23443	1.11630
$43$	9.05070	1.38022	0.690109	−	0.723705i	$-0.257562\pi$
$43$	9.05070	1.38022	0.690109	+	0.723705i	$0.257562\pi$
$44$	−4.57554	−0.689788
$45$	2.15941	0.321906
$46$	22.0734	3.25455
$47$	10.5184	1.53426	0.767132	−	0.641489i	$-0.221683\pi$
$47$	10.5184	1.53426	0.767132	+	0.641489i	$0.221683\pi$
$48$	8.77124	1.26602
$49$	−0.730769	−0.104396
$50$	8.82805	1.24847
$51$	3.14327	0.440146
$52$	0	0
$53$	−1.39208	−0.191217	−0.0956086	−	0.995419i	$-0.530480\pi$
$53$	−1.39208	−0.191217	−0.0956086	+	0.995419i	$0.530480\pi$
$54$	13.6677	1.85994
$55$	1.24792	0.168269
$56$	16.5364	2.20977
$57$	6.52490	0.864244
$58$	1.50007	0.196969
$59$	−5.61213	−0.730637	−0.365318	−	0.930883i	$-0.619040\pi$
$59$	−5.61213	−0.730637	−0.365318	+	0.930883i	$0.619040\pi$
$60$	−6.43369	−0.830586
$61$	12.3950	1.58702	0.793511	−	0.608556i	$-0.208251\pi$
$61$	12.3950	1.58702	0.793511	+	0.608556i	$0.208251\pi$
$62$	−14.2598	−1.81100
$63$	4.33268	0.545866
$64$	1.74708	0.218385
$65$	0	0
$66$	2.88933	0.355652
$67$	10.9688	1.34005	0.670027	−	0.742337i	$-0.266282\pi$
$67$	10.9688	1.34005	0.670027	+	0.742337i	$0.266282\pi$
$68$	12.7642	1.54788
$69$	−9.69919	−1.16765
$70$	−8.01234	−0.957657
$71$	−3.69804	−0.438877	−0.219438	−	0.975626i	$-0.570423\pi$
$71$	−3.69804	−0.438877	−0.219438	+	0.975626i	$0.570423\pi$
$72$	11.4283	1.34684
$73$	−7.96670	−0.932432	−0.466216	−	0.884671i	$-0.654383\pi$
$73$	−7.96670	−0.932432	−0.466216	+	0.884671i	$0.654383\pi$
$74$	21.0653	2.44880
$75$	−3.87910	−0.447919
$76$	26.4963	3.03933
$77$	2.50384	0.285339
$78$	0	0
$79$	14.8194	1.66732	0.833658	−	0.552282i	$-0.186243\pi$
$79$	14.8194	1.66732	0.833658	+	0.552282i	$0.186243\pi$
$80$	−9.71440	−1.08610
$81$	−0.814441	−0.0904935
$82$	0.430136	0.0475006
$83$	−9.73406	−1.06845	−0.534226	−	0.845342i	$-0.679397\pi$
$83$	−9.73406	−1.06845	−0.534226	+	0.845342i	$0.679397\pi$
$84$	−12.9087	−1.40845
$85$	−3.48126	−0.377596
$86$	−23.2085	−2.50264
$87$	−0.659140	−0.0706672
$88$	6.60441	0.704032
$89$	−0.577135	−0.0611762	−0.0305881	−	0.999532i	$-0.509738\pi$
$89$	−0.577135	−0.0611762	−0.0305881	+	0.999532i	$0.509738\pi$
$90$	−5.53734	−0.583687
$91$	0	0
$92$	−39.3864	−4.10632
$93$	6.26583	0.649737
$94$	−26.9721	−2.78196
$95$	−7.22651	−0.741424
$96$	−7.60877	−0.776567
$97$	3.91481	0.397488	0.198744	−	0.980051i	$-0.436314\pi$
$97$	3.91481	0.397488	0.198744	+	0.980051i	$0.436314\pi$
$98$	1.87390	0.189292
$99$	1.73041	0.173913
$100$	−15.7522	−1.57522
$101$	16.0136	1.59341	0.796705	−	0.604368i	$-0.206574\pi$
$101$	16.0136	1.59341	0.796705	+	0.604368i	$0.206574\pi$
$102$	−8.06023	−0.798082
$103$	13.0066	1.28158	0.640790	−	0.767716i	$-0.278607\pi$
$103$	13.0066	1.28158	0.640790	+	0.767716i	$0.278607\pi$
$104$	0	0
$105$	3.52067	0.343582
$106$	3.56969	0.346719
$107$	−8.67224	−0.838377	−0.419189	−	0.907899i	$-0.637685\pi$
$107$	−8.67224	−0.838377	−0.419189	+	0.907899i	$0.637685\pi$
$108$	−24.3878	−2.34672
$109$	16.9033	1.61904	0.809519	−	0.587093i	$-0.199728\pi$
$109$	16.9033	1.61904	0.809519	+	0.587093i	$0.199728\pi$
$110$	−3.20001	−0.305109
$111$	−9.25623	−0.878563
$112$	−19.4911	−1.84174
$113$	16.1408	1.51840	0.759201	−	0.650857i	$-0.225590\pi$
$113$	16.1408	1.51840	0.759201	+	0.650857i	$0.225590\pi$
$114$	−16.7317	−1.56707
$115$	10.7421	1.00171
$116$	−2.67663	−0.248519
$117$	0	0
$118$	14.3911	1.32481
$119$	−6.98486	−0.640301
$120$	9.28649	0.847737
$121$	1.00000	0.0909091
$122$	−31.7844	−2.87762
$123$	−0.189004	−0.0170419
$124$	25.4443	2.28496
$125$	10.5358	0.942351
$126$	−11.1102	−0.989776
$127$	−7.14827	−0.634306	−0.317153	−	0.948374i	$-0.602727\pi$
$127$	−7.14827	−0.634306	−0.317153	+	0.948374i	$0.602727\pi$
$128$	9.02557	0.797755
$129$	10.1980	0.897881
$130$	0	0
$131$	−14.4094	−1.25895	−0.629476	−	0.777020i	$-0.716730\pi$
$131$	−14.4094	−1.25895	−0.629476	+	0.777020i	$0.716730\pi$
$132$	−5.15554	−0.448732
$133$	−14.4994	−1.25726
$134$	−28.1271	−2.42981
$135$	6.65146	0.572466
$136$	−18.4240	−1.57985
$137$	−13.9533	−1.19211	−0.596056	−	0.802943i	$-0.703267\pi$
$137$	−13.9533	−1.19211	−0.596056	+	0.802943i	$0.703267\pi$
$138$	24.8715	2.11720
$139$	−9.73754	−0.825928	−0.412964	−	0.910747i	$-0.635506\pi$
$139$	−9.73754	−0.825928	−0.412964	+	0.910747i	$0.635506\pi$
$140$	14.2967	1.20829
$141$	11.8517	0.998093
$142$	9.48282	0.795781
$143$	0	0
$144$	−13.4704	−1.12253
$145$	0.730016	0.0606245
$146$	20.4289	1.69071
$147$	−0.823401	−0.0679130
$148$	−37.5876	−3.08968
$149$	6.20284	0.508157	0.254078	−	0.967184i	$-0.418228\pi$
$149$	6.20284	0.508157	0.254078	+	0.967184i	$0.418228\pi$
$150$	9.94709	0.812177
$151$	−0.456330	−0.0371356	−0.0185678	−	0.999828i	$-0.505911\pi$
$151$	−0.456330	−0.0371356	−0.0185678	+	0.999828i	$0.505911\pi$
$152$	−38.2451	−3.10209
$153$	−4.82725	−0.390260
$154$	−6.42056	−0.517383
$155$	−6.93959	−0.557401
$156$	0	0
$157$	0.891307	0.0711340	0.0355670	−	0.999367i	$-0.488676\pi$
$157$	0.891307	0.0711340	0.0355670	+	0.999367i	$0.488676\pi$
$158$	−38.0012	−3.02321
$159$	−1.56854	−0.124394
$160$	8.42692	0.666207
$161$	21.5532	1.69863
$162$	2.08846	0.164085
$163$	4.99937	0.391581	0.195790	−	0.980646i	$-0.437273\pi$
$163$	4.99937	0.391581	0.195790	+	0.980646i	$0.437273\pi$
$164$	−0.767507	−0.0599323
$165$	1.40611	0.109465
$166$	24.9609	1.93734
$167$	4.44898	0.344272	0.172136	−	0.985073i	$-0.444933\pi$
$167$	4.44898	0.344272	0.172136	+	0.985073i	$0.444933\pi$
$168$	18.6326	1.43753
$169$	0	0
$170$	8.92693	0.684664
$171$	−10.0206	−0.766291
$172$	41.4118	3.15762
$173$	−2.28893	−0.174024	−0.0870120	−	0.996207i	$-0.527732\pi$
$173$	−2.28893	−0.174024	−0.0870120	+	0.996207i	$0.527732\pi$
$174$	1.69022	0.128135
$175$	8.61998	0.651609
$176$	−7.78448	−0.586777
$177$	−6.32352	−0.475305
$178$	1.47994	0.110926
$179$	8.16758	0.610473	0.305237	−	0.952277i	$-0.401264\pi$
$179$	8.16758	0.610473	0.305237	+	0.952277i	$0.401264\pi$
$180$	9.88048	0.736447
$181$	−2.05898	−0.153043	−0.0765213	−	0.997068i	$-0.524381\pi$
$181$	−2.05898	−0.153043	−0.0765213	+	0.997068i	$0.524381\pi$
$182$	0	0
$183$	13.9662	1.03241
$184$	56.8510	4.19111
$185$	10.2515	0.753708
$186$	−16.0674	−1.17812
$187$	−2.78965	−0.204000
$188$	48.1273	3.51004
$189$	13.3456	0.970748
$190$	18.5308	1.34437
$191$	25.7569	1.86371	0.931853	−	0.362836i	$-0.118191\pi$
$191$	25.7569	1.86371	0.931853	+	0.362836i	$0.118191\pi$
$192$	1.96854	0.142067
$193$	−6.26933	−0.451276	−0.225638	−	0.974211i	$-0.572447\pi$
$193$	−6.26933	−0.451276	−0.225638	+	0.974211i	$0.572447\pi$
$194$	−10.0387	−0.720734
$195$	0	0
$196$	−3.34366	−0.238833
$197$	15.2472	1.08632	0.543160	−	0.839629i	$-0.317228\pi$
$197$	15.2472	1.08632	0.543160	+	0.839629i	$0.317228\pi$
$198$	−4.43726	−0.315342
$199$	24.4661	1.73436	0.867180	−	0.497996i	$-0.165930\pi$
$199$	24.4661	1.73436	0.867180	+	0.497996i	$0.165930\pi$
$200$	22.7370	1.60775
$201$	12.3592	0.871753
$202$	−41.0633	−2.88921
$203$	1.46472	0.102803
$204$	14.3822	1.00695
$205$	0.209328	0.0146201
$206$	−33.3526	−2.32379
$207$	14.8954	1.03531
$208$	0	0
$209$	−5.79085	−0.400562
$210$	−9.02798	−0.622990
$211$	−4.75526	−0.327366	−0.163683	−	0.986513i	$-0.552337\pi$
$211$	−4.75526	−0.327366	−0.163683	+	0.986513i	$0.552337\pi$
$212$	−6.36953	−0.437461
$213$	−4.16681	−0.285505
$214$	22.2381	1.52016
$215$	−11.2945	−0.770281
$216$	35.2017	2.39518
$217$	−13.9237	−0.945202
$218$	−43.3447	−2.93567
$219$	−8.97656	−0.606580
$220$	5.70990	0.384961
$221$	0	0
$222$	23.7356	1.59303
$223$	4.01280	0.268717	0.134359	−	0.990933i	$-0.457103\pi$
$223$	4.01280	0.268717	0.134359	+	0.990933i	$0.457103\pi$
$224$	16.9079	1.12971
$225$	5.95729	0.397152
$226$	−41.3896	−2.75320
$227$	11.8314	0.785279	0.392640	−	0.919692i	$-0.371562\pi$
$227$	11.8314	0.785279	0.392640	+	0.919692i	$0.371562\pi$
$228$	29.8549	1.97719
$229$	15.3381	1.01357	0.506786	−	0.862072i	$-0.330833\pi$
$229$	15.3381	1.01357	0.506786	+	0.862072i	$0.330833\pi$
$230$	−27.5458	−1.81632
$231$	2.82123	0.185623
$232$	3.86349	0.253651
$233$	15.7577	1.03232	0.516162	−	0.856491i	$-0.327360\pi$
$233$	15.7577	1.03232	0.516162	+	0.856491i	$0.327360\pi$
$234$	0	0
$235$	−13.1261	−0.856252
$236$	−25.6785	−1.67153
$237$	16.6979	1.08465
$238$	17.9111	1.16101
$239$	−6.15946	−0.398422	−0.199211	−	0.979957i	$-0.563838\pi$
$239$	−6.15946	−0.398422	−0.199211	+	0.979957i	$0.563838\pi$
$240$	−10.9458	−0.706548
$241$	−5.60829	−0.361262	−0.180631	−	0.983551i	$-0.557814\pi$
$241$	−5.60829	−0.361262	−0.180631	+	0.983551i	$0.557814\pi$
$242$	−2.56428	−0.164838
$243$	15.0724	0.966897
$244$	56.7140	3.63074
$245$	0.911940	0.0582617
$246$	0.484660	0.0309008
$247$	0	0
$248$	−36.7266	−2.33214
$249$	−10.9679	−0.695065
$250$	−27.0168	−1.70869
$251$	−6.73306	−0.424987	−0.212494	−	0.977162i	$-0.568158\pi$
$251$	−6.73306	−0.424987	−0.212494	+	0.977162i	$0.568158\pi$
$252$	19.8243	1.24882
$253$	8.60804	0.541183
$254$	18.3302	1.15014
$255$	−3.92255	−0.245639
$256$	−26.6383	−1.66489
$257$	−12.9127	−0.805471	−0.402736	−	0.915316i	$-0.631941\pi$
$257$	−12.9127	−0.805471	−0.402736	+	0.915316i	$0.631941\pi$
$258$	−26.1505	−1.62806
$259$	20.5688	1.27809
$260$	0	0
$261$	1.01227	0.0626578
$262$	36.9497	2.28276
$263$	4.81118	0.296670	0.148335	−	0.988937i	$-0.452609\pi$
$263$	4.81118	0.296670	0.148335	+	0.988937i	$0.452609\pi$
$264$	7.44158	0.457998
$265$	1.73721	0.106716
$266$	37.1805	2.27968
$267$	−0.650293	−0.0397973
$268$	50.1883	3.06574
$269$	−8.82230	−0.537905	−0.268953	−	0.963153i	$-0.586678\pi$
$269$	−8.82230	−0.537905	−0.268953	+	0.963153i	$0.586678\pi$
$270$	−17.0562	−1.03801
$271$	25.6898	1.56054	0.780271	−	0.625441i	$-0.215081\pi$
$271$	25.6898	1.56054	0.780271	+	0.625441i	$0.215081\pi$
$272$	21.7160	1.31673
$273$	0	0
$274$	35.7802	2.16156
$275$	3.44270	0.207603
$276$	−44.3790	−2.67130
$277$	−14.1090	−0.847728	−0.423864	−	0.905726i	$-0.639326\pi$
$277$	−14.1090	−0.847728	−0.423864	+	0.905726i	$0.639326\pi$
$278$	24.9698	1.49759
$279$	−9.62270	−0.576096
$280$	−20.6361	−1.23324
$281$	10.9738	0.654640	0.327320	−	0.944914i	$-0.393854\pi$
$281$	10.9738	0.654640	0.327320	+	0.944914i	$0.393854\pi$
$282$	−30.3911	−1.80976
$283$	17.7418	1.05464	0.527321	−	0.849666i	$-0.323196\pi$
$283$	17.7418	1.05464	0.527321	+	0.849666i	$0.323196\pi$
$284$	−16.9205	−1.00405
$285$	−8.14255	−0.482323
$286$	0	0
$287$	0.419998	0.0247917
$288$	11.6851	0.688551
$289$	−9.21783	−0.542225
$290$	−1.87197	−0.109926
$291$	4.41105	0.258580
$292$	−36.4520	−2.13319
$293$	−13.3395	−0.779301	−0.389650	−	0.920963i	$-0.627404\pi$
$293$	−13.3395	−0.779301	−0.389650	+	0.920963i	$0.627404\pi$
$294$	2.11143	0.123141
$295$	7.00348	0.407758
$296$	54.2546	3.15348
$297$	5.33004	0.309280
$298$	−15.9058	−0.921400
$299$	0	0
$300$	−17.7490	−1.02474
$301$	−22.6615	−1.30619
$302$	1.17016	0.0673350
$303$	18.0435	1.03657
$304$	45.0788	2.58544
$305$	−15.4680	−0.885695
$306$	12.3784	0.707627
$307$	−32.3554	−1.84662	−0.923310	−	0.384054i	$-0.874528\pi$
$307$	−32.3554	−1.84662	−0.923310	+	0.384054i	$0.874528\pi$
$308$	11.4564	0.652791
$309$	14.6553	0.833713
$310$	17.7951	1.01069
$311$	−7.67368	−0.435135	−0.217567	−	0.976045i	$-0.569812\pi$
$311$	−7.67368	−0.435135	−0.217567	+	0.976045i	$0.569812\pi$
$312$	0	0
$313$	29.7474	1.68142	0.840711	−	0.541484i	$-0.182137\pi$
$313$	29.7474	1.68142	0.840711	+	0.541484i	$0.182137\pi$
$314$	−2.28556	−0.128982
$315$	−5.40683	−0.304640
$316$	67.8068	3.81443
$317$	25.0006	1.40418	0.702088	−	0.712090i	$-0.252251\pi$
$317$	25.0006	1.40418	0.702088	+	0.712090i	$0.252251\pi$
$318$	4.02219	0.225553
$319$	0.584987	0.0327530
$320$	−2.18021	−0.121877
$321$	−9.77154	−0.545394
$322$	−55.2684	−3.07999
$323$	16.1545	0.898859
$324$	−3.72651	−0.207028
$325$	0	0
$326$	−12.8198	−0.710023
$327$	19.0459	1.05324
$328$	1.10783	0.0611698
$329$	−26.3364	−1.45197
$330$	−3.60565	−0.198484
$331$	−3.63629	−0.199869	−0.0999343	−	0.994994i	$-0.531863\pi$
$331$	−3.63629	−0.199869	−0.0999343	+	0.994994i	$0.531863\pi$
$332$	−44.5386	−2.44437
$333$	14.2152	0.778987
$334$	−11.4084	−0.624242
$335$	−13.6882	−0.747866
$336$	−21.9618	−1.19812
$337$	5.62870	0.306615	0.153307	−	0.988179i	$-0.451008\pi$
$337$	5.62870	0.306615	0.153307	+	0.988179i	$0.451008\pi$
$338$	0	0
$339$	18.1868	0.987774
$340$	−15.9286	−0.863852
$341$	−5.56093	−0.301141
$342$	25.6955	1.38945
$343$	19.3566	1.04516
$344$	−59.7745	−3.22282
$345$	12.1038	0.651647
$346$	5.86946	0.315544
$347$	−12.3838	−0.664797	−0.332399	−	0.943139i	$-0.607858\pi$
$347$	−12.3838	−0.664797	−0.332399	+	0.943139i	$0.607858\pi$
$348$	−3.01592	−0.161670
$349$	1.12141	0.0600278	0.0300139	−	0.999549i	$-0.490445\pi$
$349$	1.12141	0.0600278	0.0300139	+	0.999549i	$0.490445\pi$
$350$	−22.1041	−1.18151
$351$	0	0
$352$	6.75278	0.359925
$353$	−13.4843	−0.717698	−0.358849	−	0.933396i	$-0.616831\pi$
$353$	−13.4843	−0.717698	−0.358849	+	0.933396i	$0.616831\pi$
$354$	16.2153	0.861833
$355$	4.61486	0.244931
$356$	−2.64071	−0.139957
$357$	−7.87026	−0.416538
$358$	−20.9440	−1.10692
$359$	−6.36974	−0.336182	−0.168091	−	0.985771i	$-0.553760\pi$
$359$	−6.36974	−0.336182	−0.168091	+	0.985771i	$0.553760\pi$
$360$	−14.2616	−0.751655
$361$	14.5340	0.764945
$362$	5.27980	0.277500
$363$	1.12676	0.0591396
$364$	0	0
$365$	9.94180	0.520378
$366$	−35.8133	−1.87199
$367$	−25.6153	−1.33711	−0.668555	−	0.743663i	$-0.733087\pi$
$367$	−25.6153	−1.33711	−0.668555	+	0.743663i	$0.733087\pi$
$368$	−67.0091	−3.49309
$369$	0.290262	0.0151104
$370$	−26.2878	−1.36664
$371$	3.48556	0.180961
$372$	28.6696	1.48645
$373$	23.1071	1.19644	0.598220	−	0.801332i	$-0.295875\pi$
$373$	23.1071	1.19644	0.598220	+	0.801332i	$0.295875\pi$
$374$	7.15346	0.369896
$375$	11.8713	0.613032
$376$	−69.4677	−3.58252
$377$	0	0
$378$	−34.2218	−1.76018
$379$	−6.76975	−0.347739	−0.173869	−	0.984769i	$-0.555627\pi$
$379$	−6.76975	−0.347739	−0.173869	+	0.984769i	$0.555627\pi$
$380$	−33.0652	−1.69621
$381$	−8.05438	−0.412639
$382$	−66.0480	−3.37931
$383$	−18.6735	−0.954173	−0.477086	−	0.878856i	$-0.658307\pi$
$383$	−18.6735	−0.954173	−0.477086	+	0.878856i	$0.658307\pi$
$384$	10.1697	0.518968
$385$	−3.12459	−0.159244
$386$	16.0763	0.818263
$387$	−15.6614	−0.796115
$388$	17.9123	0.909362
$389$	1.02338	0.0518874	0.0259437	−	0.999663i	$-0.491741\pi$
$389$	1.02338	0.0518874	0.0259437	+	0.999663i	$0.491741\pi$
$390$	0	0
$391$	−24.0134	−1.21441
$392$	4.82629	0.243765
$393$	−16.2359	−0.818993
$394$	−39.0982	−1.96974
$395$	−18.4934	−0.930506
$396$	7.91757	0.397873
$397$	−6.22967	−0.312658	−0.156329	−	0.987705i	$-0.549966\pi$
$397$	−6.22967	−0.312658	−0.156329	+	0.987705i	$0.549966\pi$
$398$	−62.7381	−3.14478
$399$	−16.3373	−0.817889
$400$	−26.7996	−1.33998
$401$	5.07583	0.253475	0.126737	−	0.991936i	$-0.459549\pi$
$401$	5.07583	0.253475	0.126737	+	0.991936i	$0.459549\pi$
$402$	−31.6925	−1.58068
$403$	0	0
$404$	73.2708	3.64536
$405$	1.01636	0.0505031
$406$	−3.75594	−0.186404
$407$	8.21491	0.407198
$408$	−20.7594	−1.02775
$409$	2.99383	0.148036	0.0740178	−	0.997257i	$-0.476418\pi$
$409$	2.99383	0.148036	0.0740178	+	0.997257i	$0.476418\pi$
$410$	−0.536775	−0.0265094
$411$	−15.7220	−0.775511
$412$	59.5123	2.93196
$413$	14.0519	0.691448
$414$	−38.1961	−1.87724
$415$	12.1473	0.596288
$416$	0	0
$417$	−10.9719	−0.537295
$418$	14.8494	0.726307
$419$	36.3647	1.77653	0.888265	−	0.459331i	$-0.151911\pi$
$419$	36.3647	1.77653	0.888265	+	0.459331i	$0.151911\pi$
$420$	16.1089	0.786036
$421$	−8.03914	−0.391804	−0.195902	−	0.980624i	$-0.562763\pi$
$421$	−8.03914	−0.391804	−0.195902	+	0.980624i	$0.562763\pi$
$422$	12.1938	0.593586
$423$	−18.2011	−0.884970
$424$	9.19388	0.446494
$425$	−9.60394	−0.465859
$426$	10.6849	0.517683
$427$	−31.0352	−1.50190
$428$	−39.6802	−1.91801
$429$	0	0
$430$	28.9624	1.39669
$431$	37.6681	1.81441	0.907205	−	0.420688i	$-0.138211\pi$
$431$	37.6681	1.81441	0.907205	+	0.420688i	$0.138211\pi$
$432$	−41.4916	−1.99626
$433$	−32.4341	−1.55869	−0.779343	−	0.626598i	$-0.784447\pi$
$433$	−32.4341	−1.55869	−0.779343	+	0.626598i	$0.784447\pi$
$434$	35.7043	1.71386
$435$	0.822553	0.0394384
$436$	77.3415	3.70399
$437$	−49.8479	−2.38455
$438$	23.0184	1.09986
$439$	−5.61852	−0.268157	−0.134079	−	0.990971i	$-0.542807\pi$
$439$	−5.61852	−0.268157	−0.134079	+	0.990971i	$0.542807\pi$
$440$	−8.24176	−0.392911
$441$	1.26453	0.0602157
$442$	0	0
$443$	−27.5046	−1.30678	−0.653392	−	0.757020i	$-0.726655\pi$
$443$	−27.5046	−1.30678	−0.653392	+	0.757020i	$0.726655\pi$
$444$	−42.3523	−2.00995
$445$	0.720218	0.0341416
$446$	−10.2900	−0.487244
$447$	6.98912	0.330574
$448$	−4.37441	−0.206671
$449$	7.54668	0.356150	0.178075	−	0.984017i	$-0.443013\pi$
$449$	7.54668	0.356150	0.178075	+	0.984017i	$0.443013\pi$
$450$	−15.2762	−0.720125
$451$	0.167741	0.00789863
$452$	73.8530	3.47375
$453$	−0.514174	−0.0241580
$454$	−30.3391	−1.42388
$455$	0	0
$456$	−43.0931	−2.01802
$457$	9.37175	0.438392	0.219196	−	0.975681i	$-0.429657\pi$
$457$	9.37175	0.438392	0.219196	+	0.975681i	$0.429657\pi$
$458$	−39.3313	−1.83783
$459$	−14.8690	−0.694024
$460$	49.1510	2.29168
$461$	−1.83146	−0.0852994	−0.0426497	−	0.999090i	$-0.513580\pi$
$461$	−1.83146	−0.0852994	−0.0426497	+	0.999090i	$0.513580\pi$
$462$	−7.23443	−0.336576
$463$	11.8569	0.551038	0.275519	−	0.961296i	$-0.411150\pi$
$463$	11.8569	0.551038	0.275519	+	0.961296i	$0.411150\pi$
$464$	−4.55382	−0.211406
$465$	−7.81925	−0.362609
$466$	−40.4073	−1.87183
$467$	−18.4522	−0.853865	−0.426933	−	0.904283i	$-0.640406\pi$
$467$	−18.4522	−0.853865	−0.426933	+	0.904283i	$0.640406\pi$
$468$	0	0
$469$	−27.4642	−1.26818
$470$	33.6590	1.55257
$471$	1.00429	0.0462752
$472$	37.0648	1.70604
$473$	−9.05070	−0.416152
$474$	−42.8182	−1.96670
$475$	−19.9362	−0.914734
$476$	−31.9595	−1.46486
$477$	2.40888	0.110295
$478$	15.7946	0.722427
$479$	15.4749	0.707068	0.353534	−	0.935422i	$-0.384980\pi$
$479$	15.4749	0.707068	0.353534	+	0.935422i	$0.384980\pi$
$480$	9.49512	0.433391
$481$	0	0
$482$	14.3812	0.655047
$483$	24.2853	1.10502
$484$	4.57554	0.207979
$485$	−4.88536	−0.221833
$486$	−38.6500	−1.75320
$487$	−33.9060	−1.53643	−0.768213	−	0.640194i	$-0.778854\pi$
$487$	−33.9060	−1.53643	−0.768213	+	0.640194i	$0.778854\pi$
$488$	−81.8618	−3.70571
$489$	5.63309	0.254737
$490$	−2.33847	−0.105641
$491$	−32.5583	−1.46934	−0.734668	−	0.678427i	$-0.762662\pi$
$491$	−32.5583	−1.46934	−0.734668	+	0.678427i	$0.762662\pi$
$492$	−0.864797	−0.0389880
$493$	−1.63191	−0.0734976
$494$	0	0
$495$	−2.15941	−0.0970584
$496$	43.2889	1.94373
$497$	9.25932	0.415337
$498$	28.1249	1.26031
$499$	18.4678	0.826731	0.413366	−	0.910565i	$-0.364353\pi$
$499$	18.4678	0.826731	0.413366	+	0.910565i	$0.364353\pi$
$500$	48.2070	2.15588
$501$	5.01293	0.223961
$502$	17.2655	0.770595
$503$	18.6770	0.832768	0.416384	−	0.909189i	$-0.363297\pi$
$503$	18.6770	0.832768	0.416384	+	0.909189i	$0.363297\pi$
$504$	−28.6148	−1.27460
$505$	−19.9836	−0.889261
$506$	−22.0734	−0.981284
$507$	0	0
$508$	−32.7072	−1.45115
$509$	24.5276	1.08717	0.543584	−	0.839355i	$-0.317067\pi$
$509$	24.5276	1.08717	0.543584	+	0.839355i	$0.317067\pi$
$510$	10.0585	0.445398
$511$	19.9474	0.882420
$512$	50.2568	2.22106
$513$	−30.8655	−1.36274
$514$	33.1118	1.46050
$515$	−16.2312	−0.715232
$516$	46.6612	2.05414
$517$	−10.5184	−0.462598
$518$	−52.7443	−2.31745
$519$	−2.57907	−0.113209
$520$	0	0
$521$	−22.8034	−0.999037	−0.499519	−	0.866303i	$-0.666490\pi$
$521$	−22.8034	−0.999037	−0.499519	+	0.866303i	$0.666490\pi$
$522$	−2.59574	−0.113612
$523$	21.3824	0.934988	0.467494	−	0.883996i	$-0.345157\pi$
$523$	21.3824	0.934988	0.467494	+	0.883996i	$0.345157\pi$
$524$	−65.9306	−2.88019
$525$	9.71265	0.423895
$526$	−12.3372	−0.537928
$527$	15.5131	0.675760
$528$	−8.77124	−0.381719
$529$	51.0983	2.22167
$530$	−4.45468	−0.193499
$531$	9.71129	0.421434
$532$	−66.3425	−2.87631
$533$	0	0
$534$	1.66753	0.0721613
$535$	10.8223	0.467887
$536$	−72.4425	−3.12904
$537$	9.20290	0.397134
$538$	22.6229	0.975341
$539$	0.730769	0.0314764
$540$	30.4340	1.30967
$541$	17.3168	0.744509	0.372254	−	0.928131i	$-0.378585\pi$
$541$	17.3168	0.744509	0.372254	+	0.928131i	$0.378585\pi$
$542$	−65.8758	−2.82961
$543$	−2.31998	−0.0995597
$544$	−18.8379	−0.807670
$545$	−21.0939	−0.903563
$546$	0	0
$547$	−1.06272	−0.0454385	−0.0227192	−	0.999742i	$-0.507232\pi$
$547$	−1.06272	−0.0454385	−0.0227192	+	0.999742i	$0.507232\pi$
$548$	−63.8440	−2.72728
$549$	−21.4485	−0.915400
$550$	−8.82805	−0.376429
$551$	−3.38757	−0.144315
$552$	64.0574	2.72646
$553$	−37.1055	−1.57789
$554$	36.1794	1.53712
$555$	11.5510	0.490314
$556$	−44.5545	−1.88953
$557$	−29.9774	−1.27018	−0.635091	−	0.772437i	$-0.719037\pi$
$557$	−29.9774	−1.27018	−0.635091	+	0.772437i	$0.719037\pi$
$558$	24.6753	1.04459
$559$	0	0
$560$	24.3233	1.02785
$561$	−3.14327	−0.132709
$562$	−28.1398	−1.18701
$563$	4.95951	0.209018	0.104509	−	0.994524i	$-0.466673\pi$
$563$	4.95951	0.209018	0.104509	+	0.994524i	$0.466673\pi$
$564$	54.2279	2.28341
$565$	−20.1424	−0.847399
$566$	−45.4951	−1.91230
$567$	2.03923	0.0856397
$568$	24.4234	1.02478
$569$	21.5456	0.903238	0.451619	−	0.892211i	$-0.350847\pi$
$569$	21.5456	0.903238	0.451619	+	0.892211i	$0.350847\pi$
$570$	20.8798	0.874558
$571$	−2.51139	−0.105099	−0.0525493	−	0.998618i	$-0.516735\pi$
$571$	−2.51139	−0.105099	−0.0525493	+	0.998618i	$0.516735\pi$
$572$	0	0
$573$	29.0219	1.21241
$574$	−1.07699	−0.0449528
$575$	29.6349	1.23586
$576$	−3.02316	−0.125965
$577$	−14.1555	−0.589302	−0.294651	−	0.955605i	$-0.595203\pi$
$577$	−14.1555	−0.589302	−0.294651	+	0.955605i	$0.595203\pi$
$578$	23.6371	0.983174
$579$	−7.06403	−0.293571
$580$	3.34022	0.138695
$581$	24.3726	1.01114
$582$	−11.3112	−0.468863
$583$	1.39208	0.0576542
$584$	52.6154	2.17724
$585$	0	0
$586$	34.2062	1.41304
$587$	−1.24274	−0.0512935	−0.0256468	−	0.999671i	$-0.508165\pi$
$587$	−1.24274	−0.0512935	−0.0256468	+	0.999671i	$0.508165\pi$
$588$	−3.76750	−0.155369
$589$	32.2025	1.32688
$590$	−17.9589	−0.739356
$591$	17.1800	0.706689
$592$	−63.9488	−2.62828
$593$	42.7713	1.75641	0.878204	−	0.478287i	$-0.158742\pi$
$593$	42.7713	1.75641	0.878204	+	0.478287i	$0.158742\pi$
$594$	−13.6677	−0.560793
$595$	8.71653	0.357343
$596$	28.3813	1.16255
$597$	27.5675	1.12826
$598$	0	0
$599$	−7.82462	−0.319705	−0.159853	−	0.987141i	$-0.551102\pi$
$599$	−7.82462	−0.319705	−0.159853	+	0.987141i	$0.551102\pi$
$600$	25.6191	1.04590
$601$	33.9176	1.38353	0.691764	−	0.722124i	$-0.256834\pi$
$601$	33.9176	1.38353	0.691764	+	0.722124i	$0.256834\pi$
$602$	58.1105	2.36841
$603$	−18.9806	−0.772949
$604$	−2.08795	−0.0849576
$605$	−1.24792	−0.0507351
$606$	−46.2685	−1.87953
$607$	−35.9927	−1.46090	−0.730448	−	0.682968i	$-0.760689\pi$
$607$	−35.9927	−1.46090	−0.730448	+	0.682968i	$0.760689\pi$
$608$	−39.1044	−1.58589
$609$	1.65038	0.0668769
$610$	39.6643	1.60596
$611$	0	0
$612$	−22.0873	−0.892825
$613$	−24.8304	−1.00289	−0.501445	−	0.865190i	$-0.667198\pi$
$613$	−24.8304	−1.00289	−0.501445	+	0.865190i	$0.667198\pi$
$614$	82.9684	3.34833
$615$	0.235862	0.00951087
$616$	−16.5364	−0.666271
$617$	6.06632	0.244221	0.122110	−	0.992517i	$-0.461034\pi$
$617$	6.06632	0.244221	0.122110	+	0.992517i	$0.461034\pi$
$618$	−37.5804	−1.51171
$619$	8.17737	0.328676	0.164338	−	0.986404i	$-0.447451\pi$
$619$	8.17737	0.328676	0.164338	+	0.986404i	$0.447451\pi$
$620$	−31.7524	−1.27521
$621$	45.8812	1.84115
$622$	19.6775	0.788995
$623$	1.44506	0.0578950
$624$	0	0
$625$	4.06567	0.162627
$626$	−76.2807	−3.04879
$627$	−6.52490	−0.260579
$628$	4.07821	0.162738
$629$	−22.9168	−0.913751
$630$	13.8646	0.552380
$631$	37.2790	1.48405	0.742027	−	0.670370i	$-0.233864\pi$
$631$	37.2790	1.48405	0.742027	+	0.670370i	$0.233864\pi$
$632$	−97.8735	−3.89320
$633$	−5.35804	−0.212963
$634$	−64.1087	−2.54608
$635$	8.92046	0.353998
$636$	−7.17693	−0.284584
$637$	0	0
$638$	−1.50007	−0.0593884
$639$	6.39913	0.253146
$640$	−11.2632	−0.445216
$641$	9.72543	0.384131	0.192066	−	0.981382i	$-0.438481\pi$
$641$	9.72543	0.384131	0.192066	+	0.981382i	$0.438481\pi$
$642$	25.0570	0.988920
$643$	−37.6960	−1.48659	−0.743293	−	0.668966i	$-0.766737\pi$
$643$	−37.6960	−1.48659	−0.743293	+	0.668966i	$0.766737\pi$
$644$	98.6174	3.88607
$645$	−12.7262	−0.501095
$646$	−41.4246	−1.62983
$647$	1.71968	0.0676076	0.0338038	−	0.999428i	$-0.489238\pi$
$647$	1.71968	0.0676076	0.0338038	+	0.999428i	$0.489238\pi$
$648$	5.37890	0.211303
$649$	5.61213	0.220295
$650$	0	0
$651$	−15.6887	−0.614887
$652$	22.8748	0.895847
$653$	23.6607	0.925913	0.462957	−	0.886381i	$-0.346789\pi$
$653$	23.6607	0.925913	0.462957	+	0.886381i	$0.346789\pi$
$654$	−48.8391	−1.90976
$655$	17.9817	0.702604
$656$	−1.30578	−0.0509821
$657$	13.7857	0.537830
$658$	67.5339	2.63275
$659$	−22.8352	−0.889533	−0.444767	−	0.895647i	$-0.646713\pi$
$659$	−22.8352	−0.889533	−0.444767	+	0.895647i	$0.646713\pi$
$660$	6.43369	0.250431
$661$	−47.8311	−1.86042	−0.930208	−	0.367033i	$-0.880373\pi$
$661$	−47.8311	−1.86042	−0.930208	+	0.367033i	$0.880373\pi$
$662$	9.32447	0.362406
$663$	0	0
$664$	64.2877	2.49485
$665$	18.0941	0.701657
$666$	−36.4517	−1.41247
$667$	5.03559	0.194979
$668$	20.3565	0.787616
$669$	4.52147	0.174810
$670$	35.1004	1.35605
$671$	−12.3950	−0.478505
$672$	19.0512	0.734915
$673$	17.0698	0.657991	0.328996	−	0.944331i	$-0.393290\pi$
$673$	17.0698	0.657991	0.328996	+	0.944331i	$0.393290\pi$
$674$	−14.4336	−0.555960
$675$	18.3497	0.706281
$676$	0	0
$677$	20.8935	0.803002	0.401501	−	0.915859i	$-0.368489\pi$
$677$	20.8935	0.803002	0.401501	+	0.915859i	$0.368489\pi$
$678$	−46.6362	−1.79105
$679$	−9.80206	−0.376169
$680$	22.9917	0.881690
$681$	13.3312	0.510852
$682$	14.2598	0.546036
$683$	16.5245	0.632293	0.316146	−	0.948710i	$-0.397611\pi$
$683$	16.5245	0.632293	0.316146	+	0.948710i	$0.397611\pi$
$684$	−45.8494	−1.75310
$685$	17.4126	0.665302
$686$	−49.6359	−1.89511
$687$	17.2824	0.659365
$688$	70.4550	2.68607
$689$	0	0
$690$	−31.0376	−1.18158
$691$	−40.5014	−1.54075	−0.770373	−	0.637593i	$-0.779930\pi$
$691$	−40.5014	−1.54075	−0.770373	+	0.637593i	$0.779930\pi$
$692$	−10.4731	−0.398127
$693$	−4.33268	−0.164585
$694$	31.7556	1.20542
$695$	12.1517	0.460939
$696$	4.35323	0.165009
$697$	−0.467940	−0.0177245
$698$	−2.87561	−0.108844
$699$	17.7552	0.671563
$700$	39.4411	1.49073
$701$	−11.6750	−0.440957	−0.220479	−	0.975392i	$-0.570762\pi$
$701$	−11.6750	−0.440957	−0.220479	+	0.975392i	$0.570762\pi$
$702$	0	0
$703$	−47.5713	−1.79419
$704$	−1.74708	−0.0658455
$705$	−14.7900	−0.557022
$706$	34.5776	1.30135
$707$	−40.0955	−1.50795
$708$	−28.9335	−1.08739
$709$	31.8177	1.19494	0.597469	−	0.801892i	$-0.296173\pi$
$709$	31.8177	1.19494	0.597469	+	0.801892i	$0.296173\pi$
$710$	−11.8338	−0.444114
$711$	−25.6437	−0.961714
$712$	3.81164	0.142847
$713$	−47.8687	−1.79270
$714$	20.1816	0.755276
$715$	0	0
$716$	37.3711	1.39662
$717$	−6.94023	−0.259188
$718$	16.3338	0.609572
$719$	−6.08912	−0.227086	−0.113543	−	0.993533i	$-0.536220\pi$
$719$	−6.08912	−0.227086	−0.113543	+	0.993533i	$0.536220\pi$
$720$	16.8099	0.626468
$721$	−32.5665	−1.21284
$722$	−37.2692	−1.38701
$723$	−6.31920	−0.235014
$724$	−9.42094	−0.350126
$725$	2.01393	0.0747956
$726$	−2.88933	−0.107233
$727$	19.7169	0.731259	0.365630	−	0.930760i	$-0.380854\pi$
$727$	19.7169	0.731259	0.365630	+	0.930760i	$0.380854\pi$
$728$	0	0
$729$	19.4263	0.719494
$730$	−25.4936	−0.943559
$731$	25.2483	0.933843
$732$	63.9030	2.36192
$733$	−17.3470	−0.640726	−0.320363	−	0.947295i	$-0.603805\pi$
$733$	−17.3470	−0.640726	−0.320363	+	0.947295i	$0.603805\pi$
$734$	65.6850	2.42448
$735$	1.02754	0.0379013
$736$	58.1282	2.14263
$737$	−10.9688	−0.404042
$738$	−0.744313	−0.0273985
$739$	−18.7748	−0.690643	−0.345322	−	0.938484i	$-0.612230\pi$
$739$	−18.7748	−0.690643	−0.345322	+	0.938484i	$0.612230\pi$
$740$	46.9063	1.72431
$741$	0	0
$742$	−8.93795	−0.328122
$743$	1.93836	0.0711114	0.0355557	−	0.999368i	$-0.488680\pi$
$743$	1.93836	0.0711114	0.0355557	+	0.999368i	$0.488680\pi$
$744$	−41.3821	−1.51714
$745$	−7.74064	−0.283595
$746$	−59.2530	−2.16941
$747$	16.8439	0.616287
$748$	−12.7642	−0.466704
$749$	21.7139	0.793410
$750$	−30.4414	−1.11156
$751$	−34.0402	−1.24214	−0.621072	−	0.783754i	$-0.713302\pi$
$751$	−34.0402	−1.24214	−0.621072	+	0.783754i	$0.713302\pi$
$752$	81.8802	2.98586
$753$	−7.58654	−0.276469
$754$	0	0
$755$	0.569462	0.0207248
$756$	61.0632	2.22085
$757$	−36.9488	−1.34293	−0.671463	−	0.741038i	$-0.734334\pi$
$757$	−36.9488	−1.34293	−0.671463	+	0.741038i	$0.734334\pi$
$758$	17.3595	0.630527
$759$	9.69919	0.352058
$760$	47.7268	1.73123
$761$	14.4568	0.524058	0.262029	−	0.965060i	$-0.415608\pi$
$761$	14.4568	0.524058	0.262029	+	0.965060i	$0.415608\pi$
$762$	20.6537	0.748205
$763$	−42.3231	−1.53220
$764$	117.852	4.26373
$765$	6.02401	0.217799
$766$	47.8842	1.73013
$767$	0	0
$768$	−30.0149	−1.08307
$769$	−38.8243	−1.40004	−0.700019	−	0.714124i	$-0.746825\pi$
$769$	−38.8243	−1.40004	−0.700019	+	0.714124i	$0.746825\pi$
$770$	8.01234	0.288745
$771$	−14.5495	−0.523987
$772$	−28.6855	−1.03242
$773$	−23.5321	−0.846389	−0.423195	−	0.906039i	$-0.639091\pi$
$773$	−23.5321	−0.846389	−0.423195	+	0.906039i	$0.639091\pi$
$774$	40.1603	1.44353
$775$	−19.1446	−0.687695
$776$	−25.8550	−0.928140
$777$	23.1762	0.831440
$778$	−2.62423	−0.0940833
$779$	−0.971365	−0.0348028
$780$	0	0
$781$	3.69804	0.132326
$782$	61.5772	2.20200
$783$	3.11800	0.111428
$784$	−5.68866	−0.203166
$785$	−1.11228	−0.0396989
$786$	41.6334	1.48501
$787$	−28.5968	−1.01937	−0.509683	−	0.860362i	$-0.670237\pi$
$787$	−28.5968	−1.01937	−0.509683	+	0.860362i	$0.670237\pi$
$788$	69.7643	2.48525
$789$	5.42104	0.192994
$790$	47.4224	1.68721
$791$	−40.4141	−1.43696
$792$	−11.4283	−0.406088
$793$	0	0
$794$	15.9746	0.566919
$795$	1.95741	0.0694223
$796$	111.946	3.96781
$797$	6.23715	0.220931	0.110466	−	0.993880i	$-0.464766\pi$
$797$	6.23715	0.220931	0.110466	+	0.993880i	$0.464766\pi$
$798$	41.8935	1.48301
$799$	29.3427	1.03807
$800$	23.2478	0.821934
$801$	0.998682	0.0352867
$802$	−13.0159	−0.459606
$803$	7.96670	0.281139
$804$	56.5501	1.99437
$805$	−26.8966	−0.947981
$806$	0	0
$807$	−9.94062	−0.349926
$808$	−105.760	−3.72063
$809$	18.0119	0.633265	0.316632	−	0.948548i	$-0.397448\pi$
$809$	18.0119	0.633265	0.316632	+	0.948548i	$0.397448\pi$
$810$	−2.60622	−0.0915734
$811$	−24.2212	−0.850520	−0.425260	−	0.905071i	$-0.639817\pi$
$811$	−24.2212	−0.850520	−0.425260	+	0.905071i	$0.639817\pi$
$812$	6.70186	0.235189
$813$	28.9462	1.01519
$814$	−21.0653	−0.738340
$815$	−6.23881	−0.218536
$816$	24.4687	0.856577
$817$	52.4112	1.83364
$818$	−7.67703	−0.268421
$819$	0	0
$820$	0.957787	0.0334474
$821$	39.6901	1.38520	0.692598	−	0.721324i	$-0.256466\pi$
$821$	39.6901	1.38520	0.692598	+	0.721324i	$0.256466\pi$
$822$	40.3158	1.40617
$823$	4.14004	0.144313	0.0721563	−	0.997393i	$-0.477012\pi$
$823$	4.14004	0.144313	0.0721563	+	0.997393i	$0.477012\pi$
$824$	−85.9010	−2.99250
$825$	3.87910	0.135053
$826$	−36.0330	−1.25375
$827$	44.2318	1.53809	0.769046	−	0.639194i	$-0.220732\pi$
$827$	44.2318	1.53809	0.769046	+	0.639194i	$0.220732\pi$
$828$	68.1547	2.36854
$829$	−9.58938	−0.333053	−0.166526	−	0.986037i	$-0.553255\pi$
$829$	−9.58938	−0.333053	−0.166526	+	0.986037i	$0.553255\pi$
$830$	−31.1491	−1.08120
$831$	−15.8975	−0.551477
$832$	0	0
$833$	−2.03859	−0.0706330
$834$	28.1350	0.974235
$835$	−5.55196	−0.192134
$836$	−26.4963	−0.916393
$837$	−29.6400	−1.02451
$838$	−93.2492	−3.22124
$839$	−3.93357	−0.135802	−0.0679010	−	0.997692i	$-0.521630\pi$
$839$	−3.93357	−0.135802	−0.0679010	+	0.997692i	$0.521630\pi$
$840$	−23.2519	−0.802267
$841$	−28.6578	−0.988200
$842$	20.6146	0.710427
$843$	12.3648	0.425866
$844$	−21.7579	−0.748937
$845$	0	0
$846$	46.6729	1.60465
$847$	−2.50384	−0.0860331
$848$	−10.8366	−0.372132
$849$	19.9908	0.686082
$850$	24.6272	0.844706
$851$	70.7142	2.42405
$852$	−19.0654	−0.653169
$853$	13.7652	0.471312	0.235656	−	0.971837i	$-0.424276\pi$
$853$	13.7652	0.471312	0.235656	+	0.971837i	$0.424276\pi$
$854$	79.5830	2.72328
$855$	12.5048	0.427656
$856$	57.2750	1.95762
$857$	42.3398	1.44630	0.723151	−	0.690690i	$-0.242693\pi$
$857$	42.3398	1.44630	0.723151	+	0.690690i	$0.242693\pi$
$858$	0	0
$859$	36.3610	1.24062	0.620311	−	0.784356i	$-0.287006\pi$
$859$	36.3610	1.24062	0.620311	+	0.784356i	$0.287006\pi$
$860$	−51.6786	−1.76223
$861$	0.473237	0.0161279
$862$	−96.5917	−3.28993
$863$	0.577464	0.0196571	0.00982854	−	0.999952i	$-0.496871\pi$
$863$	0.577464	0.0196571	0.00982854	+	0.999952i	$0.496871\pi$
$864$	35.9926	1.22449
$865$	2.85640	0.0971204
$866$	83.1703	2.82624
$867$	−10.3863	−0.352737
$868$	−63.7084	−2.16240
$869$	−14.8194	−0.502714
$870$	−2.10926	−0.0715105
$871$	0	0
$872$	−111.636	−3.78047
$873$	−6.77423	−0.229273
$874$	127.824	4.32371
$875$	−26.3800	−0.891807
$876$	−41.0726	−1.38772
$877$	−12.7360	−0.430064	−0.215032	−	0.976607i	$-0.568986\pi$
$877$	−12.7360	−0.430064	−0.215032	+	0.976607i	$0.568986\pi$
$878$	14.4075	0.486228
$879$	−15.0304	−0.506963
$880$	9.71440	0.327472
$881$	31.5739	1.06375	0.531875	−	0.846823i	$-0.321488\pi$
$881$	31.5739	1.06375	0.531875	+	0.846823i	$0.321488\pi$
$882$	−3.24261	−0.109184
$883$	−39.2725	−1.32163	−0.660813	−	0.750551i	$-0.729788\pi$
$883$	−39.2725	−1.32163	−0.660813	+	0.750551i	$0.729788\pi$
$884$	0	0
$885$	7.89124	0.265261
$886$	70.5296	2.36949
$887$	−28.8294	−0.967995	−0.483997	−	0.875069i	$-0.660816\pi$
$887$	−28.8294	−0.967995	−0.483997	+	0.875069i	$0.660816\pi$
$888$	61.1319	2.05145
$889$	17.8981	0.600285
$890$	−1.84684	−0.0619063
$891$	0.814441	0.0272848
$892$	18.3607	0.614763
$893$	60.9104	2.03829
$894$	−17.9221	−0.599403
$895$	−10.1925	−0.340697
$896$	−22.5986	−0.754967
$897$	0	0
$898$	−19.3518	−0.645779
$899$	−3.25307	−0.108496
$900$	27.2578	0.908593
$901$	−3.88343	−0.129376
$902$	−0.430136	−0.0143220
$903$	−25.5341	−0.849722
$904$	−106.601	−3.54548
$905$	2.56944	0.0854110
$906$	1.31849	0.0438038
$907$	−19.1993	−0.637501	−0.318751	−	0.947839i	$-0.603263\pi$
$907$	−19.1993	−0.637501	−0.318751	+	0.947839i	$0.603263\pi$
$908$	54.1351	1.79654
$909$	−27.7101	−0.919086
$910$	0	0
$911$	−34.2901	−1.13608	−0.568041	−	0.823000i	$-0.692299\pi$
$911$	−34.2901	−1.13608	−0.568041	+	0.823000i	$0.692299\pi$
$912$	50.7930	1.68192
$913$	9.73406	0.322150
$914$	−24.0318	−0.794901
$915$	−17.4287	−0.576176
$916$	70.1802	2.31882
$917$	36.0788	1.19143
$918$	38.1282	1.25842
$919$	−26.5997	−0.877443	−0.438722	−	0.898623i	$-0.644569\pi$
$919$	−26.5997	−0.877443	−0.438722	+	0.898623i	$0.644569\pi$
$920$	−70.9454	−2.33900
$921$	−36.4568	−1.20129
$922$	4.69637	0.154667
$923$	0	0
$924$	12.9087	0.424663
$925$	28.2815	0.929889
$926$	−30.4045	−0.999153
$927$	−22.5068	−0.739221
$928$	3.95029	0.129675
$929$	−54.4680	−1.78704	−0.893519	−	0.449025i	$-0.851772\pi$
$929$	−54.4680	−1.78704	−0.893519	+	0.449025i	$0.851772\pi$
$930$	20.0508	0.657490
$931$	−4.23177	−0.138691
$932$	72.1002	2.36172
$933$	−8.64640	−0.283070
$934$	47.3166	1.54825
$935$	3.48126	0.113849
$936$	0	0
$937$	−29.5997	−0.966979	−0.483490	−	0.875350i	$-0.660631\pi$
$937$	−29.5997	−0.966979	−0.483490	+	0.875350i	$0.660631\pi$
$938$	70.4259	2.29949
$939$	33.5182	1.09382
$940$	−60.0590	−1.95891
$941$	−15.3105	−0.499109	−0.249555	−	0.968361i	$-0.580284\pi$
$941$	−15.3105	−0.499109	−0.249555	+	0.968361i	$0.580284\pi$
$942$	−2.57528	−0.0839071
$943$	1.44392	0.0470206
$944$	−43.6875	−1.42191
$945$	−16.6542	−0.541761
$946$	23.2085	0.754575
$947$	42.5752	1.38351	0.691754	−	0.722133i	$-0.256838\pi$
$947$	42.5752	1.38351	0.691754	+	0.722133i	$0.256838\pi$
$948$	76.4020	2.48142
$949$	0	0
$950$	51.1219	1.65861
$951$	28.1697	0.913466
$952$	46.1308	1.49511
$953$	38.6005	1.25039	0.625196	−	0.780468i	$-0.285019\pi$
$953$	38.6005	1.25039	0.625196	+	0.780468i	$0.285019\pi$
$954$	−6.17704	−0.199989
$955$	−32.1426	−1.04011
$956$	−28.1828	−0.911498
$957$	0.659140	0.0213070
$958$	−39.6821	−1.28207
$959$	34.9369	1.12817
$960$	−2.45657	−0.0792856
$961$	−0.0760599	−0.00245355
$962$	0	0
$963$	15.0065	0.483579
$964$	−25.6610	−0.826484
$965$	7.82361	0.251851
$966$	−62.2742	−2.00364
$967$	−38.0349	−1.22312	−0.611560	−	0.791198i	$-0.709458\pi$
$967$	−38.0349	−1.22312	−0.611560	+	0.791198i	$0.709458\pi$
$968$	−6.60441	−0.212274
$969$	18.2022	0.584739
$970$	12.5274	0.402232
$971$	−22.7230	−0.729216	−0.364608	−	0.931161i	$-0.618797\pi$
$971$	−22.7230	−0.729216	−0.364608	+	0.931161i	$0.618797\pi$
$972$	68.9645	2.21204
$973$	24.3813	0.781628
$974$	86.9445	2.78588
$975$	0	0
$976$	96.4889	3.08853
$977$	−53.2418	−1.70336	−0.851678	−	0.524066i	$-0.824415\pi$
$977$	−53.2418	−1.70336	−0.851678	+	0.524066i	$0.824415\pi$
$978$	−14.4448	−0.461895
$979$	0.577135	0.0184453
$980$	4.17262	0.133289
$981$	−29.2496	−0.933868
$982$	83.4887	2.66423
$983$	−51.8219	−1.65286	−0.826431	−	0.563039i	$-0.809632\pi$
$983$	−51.8219	−1.65286	−0.826431	+	0.563039i	$0.809632\pi$
$984$	1.24826	0.0397931
$985$	−19.0273	−0.606260
$986$	4.18468	0.133267
$987$	−29.6748	−0.944559
$988$	0	0
$989$	−77.9087	−2.47735
$990$	5.53734	0.175988
$991$	25.0586	0.796014	0.398007	−	0.917382i	$-0.369702\pi$
$991$	25.0586	0.796014	0.398007	+	0.917382i	$0.369702\pi$
$992$	−37.5518	−1.19227
$993$	−4.09723	−0.130022
$994$	−23.7435	−0.753098
$995$	−30.5318	−0.967922
$996$	−50.1843	−1.59015
$997$	−3.35266	−0.106180	−0.0530899	−	0.998590i	$-0.516907\pi$
$997$	−3.35266	−0.106180	−0.0530899	+	0.998590i	$0.516907\pi$
$998$	−47.3566	−1.49905
$999$	43.7858	1.38532

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.s.1.2	✓	21
13.12	even	2		1859.2.a.t.1.20	yes	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.2.a.s.1.2	✓	21	1.1	even	1	trivial
1859.2.a.t.1.20	yes	21	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)

\(f(q)\)	\(=\)	\(q-2.56428 q^{2} +1.12676 q^{3} +4.57554 q^{4} -1.24792 q^{5} -2.88933 q^{6} -2.50384 q^{7} -6.60441 q^{8} -1.73041 q^{9} +O(q^{10})\)	\(q-2.56428 q^{2} +1.12676 q^{3} +4.57554 q^{4} -1.24792 q^{5} -2.88933 q^{6} -2.50384 q^{7} -6.60441 q^{8} -1.73041 q^{9} +3.20001 q^{10} -1.00000 q^{11} +5.15554 q^{12} +6.42056 q^{14} -1.40611 q^{15} +7.78448 q^{16} +2.78965 q^{17} +4.43726 q^{18} +5.79085 q^{19} -5.70990 q^{20} -2.82123 q^{21} +2.56428 q^{22} -8.60804 q^{23} -7.44158 q^{24} -3.44270 q^{25} -5.33004 q^{27} -11.4564 q^{28} -0.584987 q^{29} +3.60565 q^{30} +5.56093 q^{31} -6.75278 q^{32} -1.12676 q^{33} -7.15346 q^{34} +3.12459 q^{35} -7.91757 q^{36} -8.21491 q^{37} -14.8494 q^{38} +8.24176 q^{40} -0.167741 q^{41} +7.23443 q^{42} +9.05070 q^{43} -4.57554 q^{44} +2.15941 q^{45} +22.0734 q^{46} +10.5184 q^{47} +8.77124 q^{48} -0.730769 q^{49} +8.82805 q^{50} +3.14327 q^{51} -1.39208 q^{53} +13.6677 q^{54} +1.24792 q^{55} +16.5364 q^{56} +6.52490 q^{57} +1.50007 q^{58} -5.61213 q^{59} -6.43369 q^{60} +12.3950 q^{61} -14.2598 q^{62} +4.33268 q^{63} +1.74708 q^{64} +2.88933 q^{66} +10.9688 q^{67} +12.7642 q^{68} -9.69919 q^{69} -8.01234 q^{70} -3.69804 q^{71} +11.4283 q^{72} -7.96670 q^{73} +21.0653 q^{74} -3.87910 q^{75} +26.4963 q^{76} +2.50384 q^{77} +14.8194 q^{79} -9.71440 q^{80} -0.814441 q^{81} +0.430136 q^{82} -9.73406 q^{83} -12.9087 q^{84} -3.48126 q^{85} -23.2085 q^{86} -0.659140 q^{87} +6.60441 q^{88} -0.577135 q^{89} -5.53734 q^{90} -39.3864 q^{92} +6.26583 q^{93} -26.9721 q^{94} -7.22651 q^{95} -7.60877 q^{96} +3.91481 q^{97} +1.87390 q^{98} +1.73041 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9}+O(q^{10}) \) 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9	\( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9} + 18 q^{10} - 21 q^{11} + 23 q^{12} + 20 q^{14} - 16 q^{15} + 50 q^{16} + 16 q^{17} - 3 q^{18} + 11 q^{19} - 24 q^{20} + 5 q^{21} - 9 q^{23} + 54 q^{24} + 36 q^{25} + 11 q^{28} + 28 q^{29} + 21 q^{30} - 15 q^{31} + 61 q^{32} - 6 q^{33} + 6 q^{34} - 3 q^{35} + 45 q^{36} + 12 q^{37} + q^{38} + 55 q^{40} + 4 q^{41} - 34 q^{42} + 17 q^{43} - 32 q^{44} - 9 q^{45} - 11 q^{46} - 36 q^{47} + 24 q^{48} + 72 q^{49} + 9 q^{50} + 2 q^{51} + 19 q^{53} - q^{54} + 7 q^{55} + 44 q^{56} + 4 q^{57} + 33 q^{58} - 54 q^{59} - 64 q^{60} + 98 q^{61} - 29 q^{62} + 81 q^{63} + 63 q^{64} - 19 q^{66} - 25 q^{67} + 4 q^{68} + 89 q^{69} - 65 q^{70} - 37 q^{71} - 55 q^{72} - 8 q^{73} - 11 q^{74} + 24 q^{75} - 13 q^{76} + q^{77} + 24 q^{79} - 26 q^{80} + 81 q^{81} + 26 q^{82} + 34 q^{83} + 103 q^{84} + 11 q^{85} - 30 q^{86} + 32 q^{87} - 3 q^{88} - 6 q^{89} + 47 q^{90} - 80 q^{92} - 41 q^{93} + 40 q^{94} + 20 q^{95} + 98 q^{96} + 5 q^{98} - 33 q^{99}+O(q^{100}) \) 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9 + 18 * q^10 - 21 * q^11 + 23 * q^12 + 20 * q^14 - 16 * q^15 + 50 * q^16 + 16 * q^17 - 3 * q^18 + 11 * q^19 - 24 * q^20 + 5 * q^21 - 9 * q^23 + 54 * q^24 + 36 * q^25 + 11 * q^28 + 28 * q^29 + 21 * q^30 - 15 * q^31 + 61 * q^32 - 6 * q^33 + 6 * q^34 - 3 * q^35 + 45 * q^36 + 12 * q^37 + q^38 + 55 * q^40 + 4 * q^41 - 34 * q^42 + 17 * q^43 - 32 * q^44 - 9 * q^45 - 11 * q^46 - 36 * q^47 + 24 * q^48 + 72 * q^49 + 9 * q^50 + 2 * q^51 + 19 * q^53 - q^54 + 7 * q^55 + 44 * q^56 + 4 * q^57 + 33 * q^58 - 54 * q^59 - 64 * q^60 + 98 * q^61 - 29 * q^62 + 81 * q^63 + 63 * q^64 - 19 * q^66 - 25 * q^67 + 4 * q^68 + 89 * q^69 - 65 * q^70 - 37 * q^71 - 55 * q^72 - 8 * q^73 - 11 * q^74 + 24 * q^75 - 13 * q^76 + q^77 + 24 * q^79 - 26 * q^80 + 81 * q^81 + 26 * q^82 + 34 * q^83 + 103 * q^84 + 11 * q^85 - 30 * q^86 + 32 * q^87 - 3 * q^88 - 6 * q^89 + 47 * q^90 - 80 * q^92 - 41 * q^93 + 40 * q^94 + 20 * q^95 + 98 * q^96 + 5 * q^98 - 33 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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