LMFDB - Embedded newform 1859.2.a.t.1.6

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			1.6
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)

$f(q)$	$=$	$q-1.53678 q^{2} -3.28188 q^{3} +0.361702 q^{4} -1.21246 q^{5} +5.04353 q^{6} -1.98662 q^{7} +2.51771 q^{8} +7.77071 q^{9} +O(q^{10})$	\(q-1.53678 q^{2} -3.28188 q^{3} +0.361702 q^{4} -1.21246 q^{5} +5.04353 q^{6} -1.98662 q^{7} +2.51771 q^{8} +7.77071 q^{9} +1.86328 q^{10} +1.00000 q^{11} -1.18706 q^{12} +3.05300 q^{14} +3.97913 q^{15} -4.59258 q^{16} +6.12307 q^{17} -11.9419 q^{18} +3.70133 q^{19} -0.438548 q^{20} +6.51984 q^{21} -1.53678 q^{22} -5.04028 q^{23} -8.26281 q^{24} -3.52995 q^{25} -15.6569 q^{27} -0.718565 q^{28} +8.47487 q^{29} -6.11506 q^{30} +3.43530 q^{31} +2.02238 q^{32} -3.28188 q^{33} -9.40983 q^{34} +2.40869 q^{35} +2.81069 q^{36} -8.15204 q^{37} -5.68814 q^{38} -3.05261 q^{40} -3.80914 q^{41} -10.0196 q^{42} +1.79628 q^{43} +0.361702 q^{44} -9.42165 q^{45} +7.74582 q^{46} -5.02969 q^{47} +15.0723 q^{48} -3.05334 q^{49} +5.42477 q^{50} -20.0951 q^{51} +9.97705 q^{53} +24.0612 q^{54} -1.21246 q^{55} -5.00173 q^{56} -12.1473 q^{57} -13.0240 q^{58} -11.9103 q^{59} +1.43926 q^{60} +3.23779 q^{61} -5.27931 q^{62} -15.4374 q^{63} +6.07720 q^{64} +5.04353 q^{66} +0.832597 q^{67} +2.21473 q^{68} +16.5416 q^{69} -3.70163 q^{70} -5.22675 q^{71} +19.5644 q^{72} +9.29337 q^{73} +12.5279 q^{74} +11.5849 q^{75} +1.33878 q^{76} -1.98662 q^{77} +1.72080 q^{79} +5.56830 q^{80} +28.0718 q^{81} +5.85381 q^{82} -13.3621 q^{83} +2.35824 q^{84} -7.42395 q^{85} -2.76049 q^{86} -27.8135 q^{87} +2.51771 q^{88} +3.92753 q^{89} +14.4790 q^{90} -1.82308 q^{92} -11.2742 q^{93} +7.72954 q^{94} -4.48770 q^{95} -6.63719 q^{96} -13.3265 q^{97} +4.69233 q^{98} +7.77071 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.53678	−1.08667	−0.543335	−	0.839516i	$-0.682839\pi$
$2$	−1.53678	−1.08667	−0.543335	+	0.839516i	$0.682839\pi$
$3$	−3.28188	−1.89479	−0.947396	−	0.320064i	$-0.896296\pi$
$3$	−3.28188	−1.89479	−0.947396	+	0.320064i	$0.896296\pi$
$4$	0.361702	0.180851
$5$	−1.21246	−0.542227	−0.271113	−	0.962547i	$-0.587392\pi$
$5$	−1.21246	−0.542227	−0.271113	+	0.962547i	$0.587392\pi$
$6$	5.04353	2.05901
$7$	−1.98662	−0.750871	−0.375436	−	0.926848i	$-0.622507\pi$
$7$	−1.98662	−0.750871	−0.375436	+	0.926848i	$0.622507\pi$
$8$	2.51771	0.890144
$9$	7.77071	2.59024
$10$	1.86328	0.589222
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.18706	−0.342675
$13$	0	0
$13$	0	0
$14$	3.05300	0.815949
$15$	3.97913	1.02741
$16$	−4.59258	−1.14814
$17$	6.12307	1.48506	0.742531	−	0.669812i	$-0.233625\pi$
$17$	6.12307	1.48506	0.742531	+	0.669812i	$0.233625\pi$
$18$	−11.9419	−2.81473
$19$	3.70133	0.849143	0.424572	−	0.905394i	$-0.360425\pi$
$19$	3.70133	0.849143	0.424572	+	0.905394i	$0.360425\pi$
$20$	−0.438548	−0.0980624
$21$	6.51984	1.42275
$22$	−1.53678	−0.327643
$23$	−5.04028	−1.05097	−0.525485	−	0.850803i	$-0.676116\pi$
$23$	−5.04028	−1.05097	−0.525485	+	0.850803i	$0.676116\pi$
$24$	−8.26281	−1.68664
$25$	−3.52995	−0.705990
$26$	0	0
$27$	−15.6569	−3.01317
$28$	−0.718565	−0.135796
$29$	8.47487	1.57374	0.786872	−	0.617117i	$-0.211699\pi$
$29$	8.47487	1.57374	0.786872	+	0.617117i	$0.211699\pi$
$30$	−6.11506	−1.11645
$31$	3.43530	0.616998	0.308499	−	0.951225i	$-0.400173\pi$
$31$	3.43530	0.616998	0.308499	+	0.951225i	$0.400173\pi$
$32$	2.02238	0.357509
$33$	−3.28188	−0.571301
$34$	−9.40983	−1.61377
$35$	2.40869	0.407143
$36$	2.81069	0.468448
$37$	−8.15204	−1.34019	−0.670094	−	0.742276i	$-0.733746\pi$
$37$	−8.15204	−1.34019	−0.670094	+	0.742276i	$0.733746\pi$
$38$	−5.68814	−0.922738
$39$	0	0
$40$	−3.05261	−0.482660
$41$	−3.80914	−0.594887	−0.297443	−	0.954739i	$-0.596134\pi$
$41$	−3.80914	−0.594887	−0.297443	+	0.954739i	$0.596134\pi$
$42$	−10.0196	−1.54605
$43$	1.79628	0.273929	0.136965	−	0.990576i	$-0.456265\pi$
$43$	1.79628	0.273929	0.136965	+	0.990576i	$0.456265\pi$
$44$	0.361702	0.0545287
$45$	−9.42165	−1.40450
$46$	7.74582	1.14206
$47$	−5.02969	−0.733656	−0.366828	−	0.930289i	$-0.619556\pi$
$47$	−5.02969	−0.733656	−0.366828	+	0.930289i	$0.619556\pi$
$48$	15.0723	2.17549
$49$	−3.05334	−0.436192
$50$	5.42477	0.767178
$51$	−20.0951	−2.81388
$52$	0	0
$53$	9.97705	1.37045	0.685226	−	0.728330i	$-0.259703\pi$
$53$	9.97705	1.37045	0.685226	+	0.728330i	$0.259703\pi$
$54$	24.0612	3.27432
$55$	−1.21246	−0.163488
$56$	−5.00173	−0.668384
$57$	−12.1473	−1.60895
$58$	−13.0240	−1.71014
$59$	−11.9103	−1.55058	−0.775291	−	0.631604i	$-0.782397\pi$
$59$	−11.9103	−1.55058	−0.775291	+	0.631604i	$0.782397\pi$
$60$	1.43926	0.185808
$61$	3.23779	0.414557	0.207278	−	0.978282i	$-0.433539\pi$
$61$	3.23779	0.414557	0.207278	+	0.978282i	$0.433539\pi$
$62$	−5.27931	−0.670473
$63$	−15.4374	−1.94493
$64$	6.07720	0.759650
$65$	0	0
$66$	5.04353	0.620816
$67$	0.832597	0.101718	0.0508590	−	0.998706i	$-0.483804\pi$
$67$	0.832597	0.101718	0.0508590	+	0.998706i	$0.483804\pi$
$68$	2.21473	0.268575
$69$	16.5416	1.99137
$70$	−3.70163	−0.442430
$71$	−5.22675	−0.620301	−0.310150	−	0.950688i	$-0.600379\pi$
$71$	−5.22675	−0.620301	−0.310150	+	0.950688i	$0.600379\pi$
$72$	19.5644	2.30568
$73$	9.29337	1.08771	0.543853	−	0.839180i	$-0.316965\pi$
$73$	9.29337	1.08771	0.543853	+	0.839180i	$0.316965\pi$
$74$	12.5279	1.45634
$75$	11.5849	1.33770
$76$	1.33878	0.153569
$77$	−1.98662	−0.226396
$78$	0	0
$79$	1.72080	0.193605	0.0968026	−	0.995304i	$-0.469138\pi$
$79$	1.72080	0.193605	0.0968026	+	0.995304i	$0.469138\pi$
$80$	5.56830	0.622555
$81$	28.0718	3.11909
$82$	5.85381	0.646446
$83$	−13.3621	−1.46668	−0.733342	−	0.679860i	$-0.762041\pi$
$83$	−13.3621	−1.46668	−0.733342	+	0.679860i	$0.762041\pi$
$84$	2.35824	0.257305
$85$	−7.42395	−0.805241
$86$	−2.76049	−0.297671
$87$	−27.8135	−2.98192
$88$	2.51771	0.268389
$89$	3.92753	0.416317	0.208159	−	0.978095i	$-0.433253\pi$
$89$	3.92753	0.416317	0.208159	+	0.978095i	$0.433253\pi$
$90$	14.4790	1.52622
$91$	0	0
$92$	−1.82308	−0.190069
$93$	−11.2742	−1.16908
$94$	7.72954	0.797241
$95$	−4.48770	−0.460428
$96$	−6.63719	−0.677406
$97$	−13.3265	−1.35311	−0.676553	−	0.736394i	$-0.736527\pi$
$97$	−13.3265	−1.35311	−0.676553	+	0.736394i	$0.736527\pi$
$98$	4.69233	0.473997
$99$	7.77071	0.780986
$100$	−1.27679	−0.127679
$101$	4.16147	0.414081	0.207041	−	0.978332i	$-0.433617\pi$
$101$	4.16147	0.414081	0.207041	+	0.978332i	$0.433617\pi$
$102$	30.8819	3.05776
$103$	12.0087	1.18325	0.591624	−	0.806214i	$-0.298487\pi$
$103$	12.0087	1.18325	0.591624	+	0.806214i	$0.298487\pi$
$104$	0	0
$105$	−7.90502	−0.771451
$106$	−15.3326	−1.48923
$107$	3.84674	0.371878	0.185939	−	0.982561i	$-0.440467\pi$
$107$	3.84674	0.371878	0.185939	+	0.982561i	$0.440467\pi$
$108$	−5.66313	−0.544935
$109$	5.72918	0.548756	0.274378	−	0.961622i	$-0.411528\pi$
$109$	5.72918	0.548756	0.274378	+	0.961622i	$0.411528\pi$
$110$	1.86328	0.177657
$111$	26.7540	2.53938
$112$	9.12370	0.862109
$113$	−9.59740	−0.902847	−0.451424	−	0.892310i	$-0.649084\pi$
$113$	−9.59740	−0.902847	−0.451424	+	0.892310i	$0.649084\pi$
$114$	18.6678	1.74840
$115$	6.11112	0.569865
$116$	3.06538	0.284613
$117$	0	0
$118$	18.3035	1.68497
$119$	−12.1642	−1.11509
$120$	10.0183	0.914541
$121$	1.00000	0.0909091
$122$	−4.97578	−0.450486
$123$	12.5011	1.12719
$124$	1.24256	0.111585
$125$	10.3422	0.925034
$126$	23.7240	2.11350
$127$	−7.39494	−0.656195	−0.328097	−	0.944644i	$-0.606407\pi$
$127$	−7.39494	−0.656195	−0.328097	+	0.944644i	$0.606407\pi$
$128$	−13.3841	−1.18300
$129$	−5.89515	−0.519039
$130$	0	0
$131$	14.5630	1.27237	0.636187	−	0.771535i	$-0.280511\pi$
$131$	14.5630	1.27237	0.636187	+	0.771535i	$0.280511\pi$
$132$	−1.18706	−0.103321
$133$	−7.35313	−0.637597
$134$	−1.27952	−0.110534
$135$	18.9833	1.63382
$136$	15.4161	1.32192
$137$	1.85385	0.158385	0.0791924	−	0.996859i	$-0.474766\pi$
$137$	1.85385	0.158385	0.0791924	+	0.996859i	$0.474766\pi$
$138$	−25.4208	−2.16396
$139$	21.5418	1.82715	0.913576	−	0.406668i	$-0.133309\pi$
$139$	21.5418	1.82715	0.913576	+	0.406668i	$0.133309\pi$
$140$	0.871229	0.0736323
$141$	16.5068	1.39012
$142$	8.03237	0.674062
$143$	0	0
$144$	−35.6876	−2.97397
$145$	−10.2754	−0.853326
$146$	−14.2819	−1.18198
$147$	10.0207	0.826493
$148$	−2.94861	−0.242375
$149$	−14.8011	−1.21255	−0.606275	−	0.795255i	$-0.707337\pi$
$149$	−14.8011	−1.21255	−0.606275	+	0.795255i	$0.707337\pi$
$150$	−17.8034	−1.45364
$151$	10.3080	0.838856	0.419428	−	0.907789i	$-0.362231\pi$
$151$	10.3080	0.838856	0.419428	+	0.907789i	$0.362231\pi$
$152$	9.31887	0.755860
$153$	47.5806	3.84666
$154$	3.05300	0.246018
$155$	−4.16515	−0.334553
$156$	0	0
$157$	3.44935	0.275288	0.137644	−	0.990482i	$-0.456047\pi$
$157$	3.44935	0.275288	0.137644	+	0.990482i	$0.456047\pi$
$158$	−2.64450	−0.210385
$159$	−32.7434	−2.59672
$160$	−2.45204	−0.193851
$161$	10.0131	0.789144
$162$	−43.1403	−3.38942
$163$	−19.3269	−1.51380	−0.756899	−	0.653532i	$-0.773287\pi$
$163$	−19.3269	−1.51380	−0.756899	+	0.653532i	$0.773287\pi$
$164$	−1.37777	−0.107586
$165$	3.97913	0.309775
$166$	20.5347	1.59380
$167$	13.8906	1.07488	0.537442	−	0.843301i	$-0.319391\pi$
$167$	13.8906	1.07488	0.537442	+	0.843301i	$0.319391\pi$
$168$	16.4150	1.26645
$169$	0	0
$170$	11.4090	0.875031
$171$	28.7620	2.19948
$172$	0.649717	0.0495405
$173$	−20.4360	−1.55372	−0.776859	−	0.629675i	$-0.783188\pi$
$173$	−20.4360	−1.55372	−0.776859	+	0.629675i	$0.783188\pi$
$174$	42.7433	3.24036
$175$	7.01267	0.530108
$176$	−4.59258	−0.346178
$177$	39.0880	2.93803
$178$	−6.03576	−0.452400
$179$	−21.6947	−1.62154	−0.810771	−	0.585364i	$-0.800952\pi$
$179$	−21.6947	−1.62154	−0.810771	+	0.585364i	$0.800952\pi$
$180$	−3.40783	−0.254005
$181$	8.01583	0.595812	0.297906	−	0.954595i	$-0.403712\pi$
$181$	8.01583	0.595812	0.297906	+	0.954595i	$0.403712\pi$
$182$	0	0
$183$	−10.6260	−0.785499
$184$	−12.6900	−0.935516
$185$	9.88400	0.726686
$186$	17.3260	1.27041
$187$	6.12307	0.447763
$188$	−1.81925	−0.132683
$189$	31.1043	2.26250
$190$	6.89662	0.500333
$191$	−18.1275	−1.31166	−0.655828	−	0.754910i	$-0.727680\pi$
$191$	−18.1275	−1.31166	−0.655828	+	0.754910i	$0.727680\pi$
$192$	−19.9446	−1.43938
$193$	14.9366	1.07516	0.537582	−	0.843212i	$-0.319338\pi$
$193$	14.9366	1.07516	0.537582	+	0.843212i	$0.319338\pi$
$194$	20.4800	1.47038
$195$	0	0
$196$	−1.10440	−0.0788859
$197$	20.7866	1.48098	0.740491	−	0.672066i	$-0.234593\pi$
$197$	20.7866	1.48098	0.740491	+	0.672066i	$0.234593\pi$
$198$	−11.9419	−0.848674
$199$	3.75388	0.266105	0.133053	−	0.991109i	$-0.457522\pi$
$199$	3.75388	0.266105	0.133053	+	0.991109i	$0.457522\pi$
$200$	−8.88738	−0.628433
$201$	−2.73248	−0.192734
$202$	−6.39527	−0.449970
$203$	−16.8363	−1.18168
$204$	−7.26846	−0.508894
$205$	4.61841	0.322564
$206$	−18.4547	−1.28580
$207$	−39.1666	−2.72226
$208$	0	0
$209$	3.70133	0.256026
$210$	12.1483	0.838312
$211$	12.8237	0.882817	0.441408	−	0.897306i	$-0.354479\pi$
$211$	12.8237	0.882817	0.441408	+	0.897306i	$0.354479\pi$
$212$	3.60872	0.247848
$213$	17.1535	1.17534
$214$	−5.91160	−0.404109
$215$	−2.17791	−0.148532
$216$	−39.4195	−2.68215
$217$	−6.82463	−0.463286
$218$	−8.80450	−0.596316
$219$	−30.4997	−2.06098
$220$	−0.438548	−0.0295669
$221$	0	0
$222$	−41.1151	−2.75946
$223$	−14.4246	−0.965946	−0.482973	−	0.875635i	$-0.660443\pi$
$223$	−14.4246	−0.965946	−0.482973	+	0.875635i	$0.660443\pi$
$224$	−4.01769	−0.268443
$225$	−27.4302	−1.82868
$226$	14.7491	0.981097
$227$	16.7827	1.11390	0.556952	−	0.830544i	$-0.311971\pi$
$227$	16.7827	1.11390	0.556952	+	0.830544i	$0.311971\pi$
$228$	−4.39371	−0.290980
$229$	−4.78314	−0.316079	−0.158039	−	0.987433i	$-0.550517\pi$
$229$	−4.78314	−0.316079	−0.158039	+	0.987433i	$0.550517\pi$
$230$	−9.39146	−0.619255
$231$	6.51984	0.428974
$232$	21.3372	1.40086
$233$	−2.47540	−0.162169	−0.0810843	−	0.996707i	$-0.525838\pi$
$233$	−2.47540	−0.162169	−0.0810843	+	0.996707i	$0.525838\pi$
$234$	0	0
$235$	6.09828	0.397808
$236$	−4.30797	−0.280425
$237$	−5.64745	−0.366842
$238$	18.6937	1.21174
$239$	−17.6139	−1.13935	−0.569675	−	0.821870i	$-0.692931\pi$
$239$	−17.6139	−1.13935	−0.569675	+	0.821870i	$0.692931\pi$
$240$	−18.2745	−1.17961
$241$	3.16351	0.203779	0.101890	−	0.994796i	$-0.467511\pi$
$241$	3.16351	0.203779	0.101890	+	0.994796i	$0.467511\pi$
$242$	−1.53678	−0.0987882
$243$	−45.1576	−2.89686
$244$	1.17112	0.0749731
$245$	3.70205	0.236515
$246$	−19.2115	−1.22488
$247$	0	0
$248$	8.64908	0.549217
$249$	43.8529	2.77906
$250$	−15.8937	−1.00521
$251$	8.49701	0.536327	0.268163	−	0.963373i	$-0.413583\pi$
$251$	8.49701	0.536327	0.268163	+	0.963373i	$0.413583\pi$
$252$	−5.58376	−0.351744
$253$	−5.04028	−0.316880
$254$	11.3644	0.713067
$255$	24.3645	1.52576
$256$	8.41405	0.525878
$257$	−3.24187	−0.202222	−0.101111	−	0.994875i	$-0.532240\pi$
$257$	−3.24187	−0.202222	−0.101111	+	0.994875i	$0.532240\pi$
$258$	9.05957	0.564024
$259$	16.1950	1.00631
$260$	0	0
$261$	65.8557	4.07637
$262$	−22.3802	−1.38265
$263$	−2.08594	−0.128624	−0.0643122	−	0.997930i	$-0.520485\pi$
$263$	−2.08594	−0.128624	−0.0643122	+	0.997930i	$0.520485\pi$
$264$	−8.26281	−0.508541
$265$	−12.0967	−0.743096
$266$	11.3002	0.692858
$267$	−12.8897	−0.788835
$268$	0.301153	0.0183958
$269$	30.8543	1.88122	0.940610	−	0.339490i	$-0.110254\pi$
$269$	30.8543	1.88122	0.940610	+	0.339490i	$0.110254\pi$
$270$	−29.1732	−1.77542
$271$	−7.66076	−0.465358	−0.232679	−	0.972554i	$-0.574749\pi$
$271$	−7.66076	−0.465358	−0.232679	+	0.972554i	$0.574749\pi$
$272$	−28.1207	−1.70507
$273$	0	0
$274$	−2.84896	−0.172112
$275$	−3.52995	−0.212864
$276$	5.98313	0.360142
$277$	14.0673	0.845225	0.422612	−	0.906310i	$-0.361113\pi$
$277$	14.0673	0.845225	0.422612	+	0.906310i	$0.361113\pi$
$278$	−33.1051	−1.98551
$279$	26.6947	1.59817
$280$	6.06437	0.362416
$281$	3.17033	0.189126	0.0945629	−	0.995519i	$-0.469855\pi$
$281$	3.17033	0.189126	0.0945629	+	0.995519i	$0.469855\pi$
$282$	−25.3674	−1.51061
$283$	−2.04430	−0.121521	−0.0607604	−	0.998152i	$-0.519353\pi$
$283$	−2.04430	−0.121521	−0.0607604	+	0.998152i	$0.519353\pi$
$284$	−1.89053	−0.112182
$285$	14.7281	0.872416
$286$	0	0
$287$	7.56730	0.446684
$288$	15.7153	0.926034
$289$	20.4920	1.20541
$290$	15.7911	0.927284
$291$	43.7361	2.56385
$292$	3.36143	0.196713
$293$	9.77243	0.570911	0.285456	−	0.958392i	$-0.407855\pi$
$293$	9.77243	0.570911	0.285456	+	0.958392i	$0.407855\pi$
$294$	−15.3996	−0.898125
$295$	14.4407	0.840768
$296$	−20.5245	−1.19296
$297$	−15.6569	−0.908504
$298$	22.7460	1.31764
$299$	0	0
$300$	4.19027	0.241925
$301$	−3.56851	−0.205686
$302$	−15.8412	−0.911560
$303$	−13.6574	−0.784598
$304$	−16.9986	−0.974939
$305$	−3.92568	−0.224784
$306$	−73.1210	−4.18005
$307$	−13.0036	−0.742152	−0.371076	−	0.928603i	$-0.621011\pi$
$307$	−13.0036	−0.742152	−0.371076	+	0.928603i	$0.621011\pi$
$308$	−0.718565	−0.0409440
$309$	−39.4109	−2.24201
$310$	6.40093	0.363548
$311$	−20.9389	−1.18734	−0.593668	−	0.804710i	$-0.702321\pi$
$311$	−20.9389	−1.18734	−0.593668	+	0.804710i	$0.702321\pi$
$312$	0	0
$313$	0.484921	0.0274094	0.0137047	−	0.999906i	$-0.495638\pi$
$313$	0.484921	0.0274094	0.0137047	+	0.999906i	$0.495638\pi$
$314$	−5.30091	−0.299148
$315$	18.7172	1.05460
$316$	0.622418	0.0350137
$317$	−24.9983	−1.40404	−0.702021	−	0.712156i	$-0.747719\pi$
$317$	−24.9983	−1.40404	−0.702021	+	0.712156i	$0.747719\pi$
$318$	50.3196	2.82178
$319$	8.47487	0.474501
$320$	−7.36834	−0.411902
$321$	−12.6245	−0.704632
$322$	−15.3880	−0.857539
$323$	22.6635	1.26103
$324$	10.1536	0.564091
$325$	0	0
$326$	29.7012	1.64500
$327$	−18.8025	−1.03978
$328$	−9.59029	−0.529535
$329$	9.99208	0.550881
$330$	−6.11506	−0.336623
$331$	14.6088	0.802972	0.401486	−	0.915865i	$-0.368494\pi$
$331$	14.6088	0.802972	0.401486	+	0.915865i	$0.368494\pi$
$332$	−4.83312	−0.265252
$333$	−63.3472	−3.47140
$334$	−21.3468	−1.16804
$335$	−1.00949	−0.0551542
$336$	−29.9429	−1.63352
$337$	−12.3867	−0.674748	−0.337374	−	0.941371i	$-0.609539\pi$
$337$	−12.3867	−0.674748	−0.337374	+	0.941371i	$0.609539\pi$
$338$	0	0
$339$	31.4975	1.71071
$340$	−2.68526	−0.145629
$341$	3.43530	0.186032
$342$	−44.2009	−2.39011
$343$	19.9722	1.07840
$344$	4.52250	0.243837
$345$	−20.0559	−1.07978
$346$	31.4057	1.68838
$347$	−11.4789	−0.616221	−0.308111	−	0.951351i	$-0.599697\pi$
$347$	−11.4789	−0.616221	−0.308111	+	0.951351i	$0.599697\pi$
$348$	−10.0602	−0.539283
$349$	16.7829	0.898366	0.449183	−	0.893440i	$-0.351715\pi$
$349$	16.7829	0.898366	0.449183	+	0.893440i	$0.351715\pi$
$350$	−10.7769	−0.576052
$351$	0	0
$352$	2.02238	0.107793
$353$	17.8330	0.949156	0.474578	−	0.880213i	$-0.342601\pi$
$353$	17.8330	0.949156	0.474578	+	0.880213i	$0.342601\pi$
$354$	−60.0697	−3.19267
$355$	6.33720	0.336344
$356$	1.42060	0.0752915
$357$	39.9214	2.11286
$358$	33.3401	1.76208
$359$	−10.5901	−0.558922	−0.279461	−	0.960157i	$-0.590156\pi$
$359$	−10.5901	−0.558922	−0.279461	+	0.960157i	$0.590156\pi$
$360$	−23.7210	−1.25020
$361$	−5.30017	−0.278956
$362$	−12.3186	−0.647451
$363$	−3.28188	−0.172254
$364$	0	0
$365$	−11.2678	−0.589784
$366$	16.3299	0.853578
$367$	12.3094	0.642545	0.321272	−	0.946987i	$-0.395889\pi$
$367$	12.3094	0.642545	0.321272	+	0.946987i	$0.395889\pi$
$368$	23.1479	1.20667
$369$	−29.5997	−1.54090
$370$	−15.1896	−0.789668
$371$	−19.8206	−1.02903
$372$	−4.07791	−0.211430
$373$	4.19426	0.217171	0.108585	−	0.994087i	$-0.465368\pi$
$373$	4.19426	0.217171	0.108585	+	0.994087i	$0.465368\pi$
$374$	−9.40983	−0.486571
$375$	−33.9418	−1.75275
$376$	−12.6633	−0.653059
$377$	0	0
$378$	−47.8005	−2.45859
$379$	16.7368	0.859710	0.429855	−	0.902898i	$-0.358565\pi$
$379$	16.7368	0.859710	0.429855	+	0.902898i	$0.358565\pi$
$380$	−1.62321	−0.0832690
$381$	24.2693	1.24335
$382$	27.8580	1.42534
$383$	4.41154	0.225419	0.112709	−	0.993628i	$-0.464047\pi$
$383$	4.41154	0.225419	0.112709	+	0.993628i	$0.464047\pi$
$384$	43.9249	2.24153
$385$	2.40869	0.122758
$386$	−22.9544	−1.16835
$387$	13.9583	0.709542
$388$	−4.82024	−0.244711
$389$	15.4167	0.781658	0.390829	−	0.920463i	$-0.372188\pi$
$389$	15.4167	0.781658	0.390829	+	0.920463i	$0.372188\pi$
$390$	0	0
$391$	−30.8620	−1.56076
$392$	−7.68743	−0.388274
$393$	−47.7939	−2.41089
$394$	−31.9445	−1.60934
$395$	−2.08640	−0.104978
$396$	2.81069	0.141242
$397$	25.8026	1.29500	0.647498	−	0.762067i	$-0.275815\pi$
$397$	25.8026	1.29500	0.647498	+	0.762067i	$0.275815\pi$
$398$	−5.76890	−0.289169
$399$	24.1321	1.20811
$400$	16.2116	0.810578
$401$	−21.7169	−1.08449	−0.542246	−	0.840220i	$-0.682426\pi$
$401$	−21.7169	−1.08449	−0.542246	+	0.840220i	$0.682426\pi$
$402$	4.19923	0.209439
$403$	0	0
$404$	1.50521	0.0748871
$405$	−34.0358	−1.69125
$406$	25.8738	1.28409
$407$	−8.15204	−0.404082
$408$	−50.5937	−2.50476
$409$	11.1416	0.550917	0.275459	−	0.961313i	$-0.411170\pi$
$409$	11.1416	0.550917	0.275459	+	0.961313i	$0.411170\pi$
$410$	−7.09749	−0.350520
$411$	−6.08409	−0.300106
$412$	4.34356	0.213992
$413$	23.6611	1.16429
$414$	60.1905	2.95820
$415$	16.2010	0.795276
$416$	0	0
$417$	−70.6975	−3.46207
$418$	−5.68814	−0.278216
$419$	5.97393	0.291846	0.145923	−	0.989296i	$-0.453385\pi$
$419$	5.97393	0.291846	0.145923	+	0.989296i	$0.453385\pi$
$420$	−2.85926	−0.139518
$421$	−5.46498	−0.266347	−0.133173	−	0.991093i	$-0.542517\pi$
$421$	−5.46498	−0.266347	−0.133173	+	0.991093i	$0.542517\pi$
$422$	−19.7072	−0.959330
$423$	−39.0843	−1.90034
$424$	25.1193	1.21990
$425$	−21.6141	−1.04844
$426$	−26.3613	−1.27721
$427$	−6.43226	−0.311279
$428$	1.39137	0.0672546
$429$	0	0
$430$	3.34697	0.161405
$431$	8.56335	0.412482	0.206241	−	0.978501i	$-0.433877\pi$
$431$	8.56335	0.412482	0.206241	+	0.978501i	$0.433877\pi$
$432$	71.9054	3.45955
$433$	−0.526285	−0.0252917	−0.0126458	−	0.999920i	$-0.504025\pi$
$433$	−0.526285	−0.0252917	−0.0126458	+	0.999920i	$0.504025\pi$
$434$	10.4880	0.503439
$435$	33.7226	1.61688
$436$	2.07226	0.0992432
$437$	−18.6557	−0.892425
$438$	46.8714	2.23960
$439$	−2.41736	−0.115374	−0.0576871	−	0.998335i	$-0.518373\pi$
$439$	−2.41736	−0.115374	−0.0576871	+	0.998335i	$0.518373\pi$
$440$	−3.05261	−0.145528
$441$	−23.7267	−1.12984
$442$	0	0
$443$	−24.0014	−1.14034	−0.570171	−	0.821526i	$-0.693123\pi$
$443$	−24.0014	−1.14034	−0.570171	+	0.821526i	$0.693123\pi$
$444$	9.67699	0.459249
$445$	−4.76196	−0.225738
$446$	22.1676	1.04966
$447$	48.5752	2.29753
$448$	−12.0731	−0.570399
$449$	−7.41494	−0.349933	−0.174966	−	0.984574i	$-0.555982\pi$
$449$	−7.41494	−0.349933	−0.174966	+	0.984574i	$0.555982\pi$
$450$	42.1543	1.98717
$451$	−3.80914	−0.179365
$452$	−3.47140	−0.163281
$453$	−33.8297	−1.58946
$454$	−25.7913	−1.21045
$455$	0	0
$456$	−30.5834	−1.43220
$457$	−2.53108	−0.118399	−0.0591995	−	0.998246i	$-0.518855\pi$
$457$	−2.53108	−0.118399	−0.0591995	+	0.998246i	$0.518855\pi$
$458$	7.35065	0.343473
$459$	−95.8681	−4.47474
$460$	2.21041	0.103061
$461$	4.75026	0.221242	0.110621	−	0.993863i	$-0.464716\pi$
$461$	4.75026	0.221242	0.110621	+	0.993863i	$0.464716\pi$
$462$	−10.0196	−0.466153
$463$	−8.86195	−0.411850	−0.205925	−	0.978568i	$-0.566020\pi$
$463$	−8.86195	−0.411850	−0.205925	+	0.978568i	$0.566020\pi$
$464$	−38.9215	−1.80688
$465$	13.6695	0.633908
$466$	3.80415	0.176224
$467$	0.900979	0.0416923	0.0208462	−	0.999783i	$-0.493364\pi$
$467$	0.900979	0.0416923	0.0208462	+	0.999783i	$0.493364\pi$
$468$	0	0
$469$	−1.65405	−0.0763771
$470$	−9.37173	−0.432286
$471$	−11.3203	−0.521614
$472$	−29.9865	−1.38024
$473$	1.79628	0.0825928
$474$	8.67891	0.398636
$475$	−13.0655	−0.599486
$476$	−4.39982	−0.201666
$477$	77.5288	3.54980
$478$	27.0688	1.23810
$479$	−4.61882	−0.211039	−0.105520	−	0.994417i	$-0.533651\pi$
$479$	−4.61882	−0.211039	−0.105520	+	0.994417i	$0.533651\pi$
$480$	8.04731	0.367308
$481$	0	0
$482$	−4.86162	−0.221441
$483$	−32.8618	−1.49526
$484$	0.361702	0.0164410
$485$	16.1578	0.733690
$486$	69.3974	3.14793
$487$	22.0991	1.00141	0.500703	−	0.865619i	$-0.333075\pi$
$487$	22.0991	1.00141	0.500703	+	0.865619i	$0.333075\pi$
$488$	8.15181	0.369015
$489$	63.4284	2.86833
$490$	−5.68924	−0.257014
$491$	−6.73294	−0.303853	−0.151927	−	0.988392i	$-0.548548\pi$
$491$	−6.73294	−0.303853	−0.151927	+	0.988392i	$0.548548\pi$
$492$	4.52168	0.203853
$493$	51.8922	2.33711
$494$	0	0
$495$	−9.42165	−0.423472
$496$	−15.7769	−0.708402
$497$	10.3836	0.465766
$498$	−67.3923	−3.01992
$499$	38.3071	1.71486	0.857430	−	0.514600i	$-0.172060\pi$
$499$	38.3071	1.71486	0.857430	+	0.514600i	$0.172060\pi$
$500$	3.74080	0.167293
$501$	−45.5871	−2.03668
$502$	−13.0581	−0.582810
$503$	−10.1501	−0.452571	−0.226285	−	0.974061i	$-0.572658\pi$
$503$	−10.1501	−0.452571	−0.226285	+	0.974061i	$0.572658\pi$
$504$	−38.8670	−1.73127
$505$	−5.04560	−0.224526
$506$	7.74582	0.344344
$507$	0	0
$508$	−2.67477	−0.118674
$509$	−16.0023	−0.709289	−0.354644	−	0.935001i	$-0.615398\pi$
$509$	−16.0023	−0.709289	−0.354644	+	0.935001i	$0.615398\pi$
$510$	−37.4429	−1.65800
$511$	−18.4624	−0.816728
$512$	13.8376	0.611542
$513$	−57.9513	−2.55861
$514$	4.98204	0.219749
$515$	−14.5600	−0.641589
$516$	−2.13229	−0.0938689
$517$	−5.02969	−0.221205
$518$	−24.8882	−1.09353
$519$	67.0683	2.94397
$520$	0	0
$521$	38.9248	1.70533	0.852663	−	0.522461i	$-0.174986\pi$
$521$	38.9248	1.70533	0.852663	+	0.522461i	$0.174986\pi$
$522$	−101.206	−4.42967
$523$	40.0699	1.75214	0.876068	−	0.482188i	$-0.160158\pi$
$523$	40.0699	1.75214	0.876068	+	0.482188i	$0.160158\pi$
$524$	5.26747	0.230110
$525$	−23.0147	−1.00444
$526$	3.20563	0.139772
$527$	21.0346	0.916280
$528$	15.0723	0.655936
$529$	2.40442	0.104540
$530$	18.5901	0.807500
$531$	−92.5511	−4.01638
$532$	−2.65965	−0.115310
$533$	0	0
$534$	19.8086	0.857203
$535$	−4.66400	−0.201642
$536$	2.09624	0.0905437
$537$	71.1995	3.07248
$538$	−47.4164	−2.04426
$539$	−3.05334	−0.131517
$540$	6.86630	0.295479
$541$	34.1644	1.46884	0.734420	−	0.678695i	$-0.237454\pi$
$541$	34.1644	1.46884	0.734420	+	0.678695i	$0.237454\pi$
$542$	11.7729	0.505691
$543$	−26.3070	−1.12894
$544$	12.3832	0.530923
$545$	−6.94638	−0.297550
$546$	0	0
$547$	15.9397	0.681531	0.340766	−	0.940148i	$-0.389314\pi$
$547$	15.9397	0.681531	0.340766	+	0.940148i	$0.389314\pi$
$548$	0.670541	0.0286441
$549$	25.1599	1.07380
$550$	5.42477	0.231313
$551$	31.3683	1.33633
$552$	41.6469	1.77261
$553$	−3.41857	−0.145373
$554$	−21.6185	−0.918480
$555$	−32.4381	−1.37692
$556$	7.79172	0.330443
$557$	34.0051	1.44084	0.720421	−	0.693537i	$-0.243949\pi$
$557$	34.0051	1.44084	0.720421	+	0.693537i	$0.243949\pi$
$558$	−41.0240	−1.73668
$559$	0	0
$560$	−11.0621	−0.467458
$561$	−20.0951	−0.848418
$562$	−4.87210	−0.205517
$563$	−9.89124	−0.416866	−0.208433	−	0.978037i	$-0.566836\pi$
$563$	−9.89124	−0.416866	−0.208433	+	0.978037i	$0.566836\pi$
$564$	5.97056	0.251406
$565$	11.6364	0.489548
$566$	3.14164	0.132053
$567$	−55.7680	−2.34204
$568$	−13.1594	−0.552157
$569$	−8.41679	−0.352850	−0.176425	−	0.984314i	$-0.556453\pi$
$569$	−8.41679	−0.352850	−0.176425	+	0.984314i	$0.556453\pi$
$570$	−22.6339	−0.948028
$571$	34.0299	1.42411	0.712054	−	0.702125i	$-0.247765\pi$
$571$	34.0299	1.42411	0.712054	+	0.702125i	$0.247765\pi$
$572$	0	0
$573$	59.4920	2.48532
$574$	−11.6293	−0.485398
$575$	17.7919	0.741975
$576$	47.2241	1.96767
$577$	−12.1007	−0.503760	−0.251880	−	0.967759i	$-0.581049\pi$
$577$	−12.1007	−0.503760	−0.251880	+	0.967759i	$0.581049\pi$
$578$	−31.4917	−1.30988
$579$	−49.0202	−2.03721
$580$	−3.71664	−0.154325
$581$	26.5455	1.10129
$582$	−67.2128	−2.78606
$583$	9.97705	0.413207
$584$	23.3980	0.968216
$585$	0	0
$586$	−15.0181	−0.620392
$587$	38.9939	1.60945	0.804726	−	0.593647i	$-0.202312\pi$
$587$	38.9939	1.60945	0.804726	+	0.593647i	$0.202312\pi$
$588$	3.62451	0.149472
$589$	12.7152	0.523919
$590$	−22.1922	−0.913637
$591$	−68.2190	−2.80615
$592$	37.4389	1.53873
$593$	−24.7393	−1.01592	−0.507960	−	0.861381i	$-0.669600\pi$
$593$	−24.7393	−1.01592	−0.507960	+	0.861381i	$0.669600\pi$
$594$	24.0612	0.987244
$595$	14.7486	0.604632
$596$	−5.35358	−0.219291
$597$	−12.3198	−0.504215
$598$	0	0
$599$	3.54030	0.144653	0.0723264	−	0.997381i	$-0.476958\pi$
$599$	3.54030	0.144653	0.0723264	+	0.997381i	$0.476958\pi$
$600$	29.1673	1.19075
$601$	20.2708	0.826862	0.413431	−	0.910535i	$-0.364330\pi$
$601$	20.2708	0.826862	0.413431	+	0.910535i	$0.364330\pi$
$602$	5.48403	0.223513
$603$	6.46987	0.263474
$604$	3.72844	0.151708
$605$	−1.21246	−0.0492934
$606$	20.9885	0.852599
$607$	15.7189	0.638012	0.319006	−	0.947753i	$-0.396651\pi$
$607$	15.7189	0.638012	0.319006	+	0.947753i	$0.396651\pi$
$608$	7.48548	0.303576
$609$	55.2548	2.23904
$610$	6.03292	0.244266
$611$	0	0
$612$	17.2100	0.695674
$613$	43.5374	1.75846	0.879230	−	0.476397i	$-0.158057\pi$
$613$	43.5374	1.75846	0.879230	+	0.476397i	$0.158057\pi$
$614$	19.9836	0.806474
$615$	−15.1570	−0.611191
$616$	−5.00173	−0.201525
$617$	10.8608	0.437238	0.218619	−	0.975810i	$-0.429845\pi$
$617$	10.8608	0.437238	0.218619	+	0.975810i	$0.429845\pi$
$618$	60.5660	2.43632
$619$	21.8912	0.879883	0.439941	−	0.898027i	$-0.354999\pi$
$619$	21.8912	0.879883	0.439941	+	0.898027i	$0.354999\pi$
$620$	−1.50654	−0.0605043
$621$	78.9151	3.16675
$622$	32.1785	1.29024
$623$	−7.80251	−0.312601
$624$	0	0
$625$	5.11029	0.204412
$626$	−0.745219	−0.0297849
$627$	−12.1473	−0.485117
$628$	1.24764	0.0497862
$629$	−49.9155	−1.99026
$630$	−28.7643	−1.14600
$631$	29.9694	1.19306	0.596531	−	0.802590i	$-0.296545\pi$
$631$	29.9694	1.19306	0.596531	+	0.802590i	$0.296545\pi$
$632$	4.33247	0.172337
$633$	−42.0856	−1.67275
$634$	38.4169	1.52573
$635$	8.96604	0.355806
$636$	−11.8434	−0.469621
$637$	0	0
$638$	−13.0240	−0.515626
$639$	−40.6155	−1.60673
$640$	16.2276	0.641453
$641$	12.2732	0.484764	0.242382	−	0.970181i	$-0.422071\pi$
$641$	12.2732	0.484764	0.242382	+	0.970181i	$0.422071\pi$
$642$	19.4011	0.765702
$643$	−12.2900	−0.484671	−0.242335	−	0.970193i	$-0.577913\pi$
$643$	−12.2900	−0.484671	−0.242335	+	0.970193i	$0.577913\pi$
$644$	3.62177	0.142718
$645$	7.14762	0.281437
$646$	−34.8289	−1.37032
$647$	0.936707	0.0368258	0.0184129	−	0.999830i	$-0.494139\pi$
$647$	0.936707	0.0368258	0.0184129	+	0.999830i	$0.494139\pi$
$648$	70.6766	2.77644
$649$	−11.9103	−0.467518
$650$	0	0
$651$	22.3976	0.877830
$652$	−6.99058	−0.273772
$653$	−7.80246	−0.305334	−0.152667	−	0.988278i	$-0.548786\pi$
$653$	−7.80246	−0.305334	−0.152667	+	0.988278i	$0.548786\pi$
$654$	28.8953	1.12990
$655$	−17.6570	−0.689916
$656$	17.4937	0.683016
$657$	72.2161	2.81742
$658$	−15.3557	−0.598626
$659$	5.75064	0.224013	0.112007	−	0.993707i	$-0.464272\pi$
$659$	5.75064	0.224013	0.112007	+	0.993707i	$0.464272\pi$
$660$	1.43926	0.0560232
$661$	−28.9866	−1.12745	−0.563723	−	0.825964i	$-0.690632\pi$
$661$	−28.9866	−1.12745	−0.563723	+	0.825964i	$0.690632\pi$
$662$	−22.4506	−0.872566
$663$	0	0
$664$	−33.6419	−1.30556
$665$	8.91535	0.345722
$666$	97.3509	3.77227
$667$	−42.7157	−1.65396
$668$	5.02425	0.194394
$669$	47.3399	1.83027
$670$	1.55136	0.0599344
$671$	3.23779	0.124994
$672$	13.1856	0.508645
$673$	−25.7021	−0.990743	−0.495371	−	0.868681i	$-0.664968\pi$
$673$	−25.7021	−0.990743	−0.495371	+	0.868681i	$0.664968\pi$
$674$	19.0357	0.733229
$675$	55.2680	2.12727
$676$	0	0
$677$	38.2945	1.47178	0.735889	−	0.677102i	$-0.236764\pi$
$677$	38.2945	1.47178	0.735889	+	0.677102i	$0.236764\pi$
$678$	−48.4048	−1.85897
$679$	26.4748	1.01601
$680$	−18.6913	−0.716780
$681$	−55.0786	−2.11062
$682$	−5.27931	−0.202155
$683$	16.1752	0.618928	0.309464	−	0.950911i	$-0.399850\pi$
$683$	16.1752	0.618928	0.309464	+	0.950911i	$0.399850\pi$
$684$	10.4033	0.397779
$685$	−2.24771	−0.0858805
$686$	−30.6929	−1.17186
$687$	15.6977	0.598904
$688$	−8.24953	−0.314510
$689$	0	0
$690$	30.8216	1.17336
$691$	−32.0215	−1.21816	−0.609078	−	0.793111i	$-0.708460\pi$
$691$	−32.0215	−1.21816	−0.609078	+	0.793111i	$0.708460\pi$
$692$	−7.39174	−0.280992
$693$	−15.4374	−0.586420
$694$	17.6406	0.669629
$695$	−26.1185	−0.990731
$696$	−70.0262	−2.65434
$697$	−23.3236	−0.883444
$698$	−25.7916	−0.976228
$699$	8.12395	0.307276
$700$	2.53650	0.0958706
$701$	15.9319	0.601739	0.300870	−	0.953665i	$-0.402723\pi$
$701$	15.9319	0.601739	0.300870	+	0.953665i	$0.402723\pi$
$702$	0	0
$703$	−30.1734	−1.13801
$704$	6.07720	0.229043
$705$	−20.0138	−0.753763
$706$	−27.4055	−1.03142
$707$	−8.26725	−0.310922
$708$	14.1382	0.531347
$709$	−21.8336	−0.819976	−0.409988	−	0.912091i	$-0.634467\pi$
$709$	−21.8336	−0.819976	−0.409988	+	0.912091i	$0.634467\pi$
$710$	−9.73890	−0.365494
$711$	13.3718	0.501483
$712$	9.88837	0.370583
$713$	−17.3149	−0.648447
$714$	−61.3505	−2.29599
$715$	0	0
$716$	−7.84704	−0.293258
$717$	57.8068	2.15883
$718$	16.2746	0.607364
$719$	12.0186	0.448217	0.224108	−	0.974564i	$-0.428053\pi$
$719$	12.0186	0.448217	0.224108	+	0.974564i	$0.428053\pi$
$720$	43.2696	1.61256
$721$	−23.8566	−0.888467
$722$	8.14520	0.303133
$723$	−10.3822	−0.386119
$724$	2.89935	0.107753
$725$	−29.9159	−1.11105
$726$	5.04353	0.187183
$727$	46.1626	1.71208	0.856038	−	0.516913i	$-0.172919\pi$
$727$	46.1626	1.71208	0.856038	+	0.516913i	$0.172919\pi$
$728$	0	0
$729$	63.9861	2.36986
$730$	17.3162	0.640900
$731$	10.9987	0.406802
$732$	−3.84346	−0.142058
$733$	35.0574	1.29487	0.647437	−	0.762119i	$-0.275841\pi$
$733$	35.0574	1.29487	0.647437	+	0.762119i	$0.275841\pi$
$734$	−18.9169	−0.698234
$735$	−12.1497	−0.448147
$736$	−10.1933	−0.375732
$737$	0.832597	0.0306691
$738$	45.4883	1.67445
$739$	−14.7567	−0.542833	−0.271417	−	0.962462i	$-0.587492\pi$
$739$	−14.7567	−0.542833	−0.271417	+	0.962462i	$0.587492\pi$
$740$	3.57507	0.131422
$741$	0	0
$742$	30.4600	1.11822
$743$	9.96561	0.365603	0.182801	−	0.983150i	$-0.441483\pi$
$743$	9.96561	0.365603	0.182801	+	0.983150i	$0.441483\pi$
$744$	−28.3852	−1.04065
$745$	17.9456	0.657477
$746$	−6.44567	−0.235993
$747$	−103.833	−3.79906
$748$	2.21473	0.0809785
$749$	−7.64200	−0.279233
$750$	52.1612	1.90466
$751$	45.5216	1.66111	0.830553	−	0.556939i	$-0.188024\pi$
$751$	45.5216	1.66111	0.830553	+	0.556939i	$0.188024\pi$
$752$	23.0992	0.842342
$753$	−27.8861	−1.01623
$754$	0	0
$755$	−12.4980	−0.454850
$756$	11.2505	0.409176
$757$	−38.3244	−1.39292	−0.696462	−	0.717594i	$-0.745243\pi$
$757$	−38.3244	−1.39292	−0.696462	+	0.717594i	$0.745243\pi$
$758$	−25.7208	−0.934221
$759$	16.5416	0.600421
$760$	−11.2987	−0.409848
$761$	−15.9628	−0.578652	−0.289326	−	0.957231i	$-0.593431\pi$
$761$	−15.9628	−0.578652	−0.289326	+	0.957231i	$0.593431\pi$
$762$	−37.2966	−1.35111
$763$	−11.3817	−0.412045
$764$	−6.55674	−0.237215
$765$	−57.6894	−2.08576
$766$	−6.77957	−0.244956
$767$	0	0
$768$	−27.6139	−0.996430
$769$	−35.2975	−1.27286	−0.636431	−	0.771334i	$-0.719590\pi$
$769$	−35.2975	−1.27286	−0.636431	+	0.771334i	$0.719590\pi$
$770$	−3.70163	−0.133398
$771$	10.6394	0.383169
$772$	5.40262	0.194445
$773$	10.8588	0.390565	0.195283	−	0.980747i	$-0.437438\pi$
$773$	10.8588	0.390565	0.195283	+	0.980747i	$0.437438\pi$
$774$	−21.4509	−0.771038
$775$	−12.1264	−0.435594
$776$	−33.5523	−1.20446
$777$	−53.1500	−1.90675
$778$	−23.6921	−0.849404
$779$	−14.0989	−0.505144
$780$	0	0
$781$	−5.22675	−0.187028
$782$	47.4282	1.69603
$783$	−132.690	−4.74195
$784$	14.0227	0.500811
$785$	−4.18219	−0.149269
$786$	73.4489	2.61984
$787$	4.54676	0.162074	0.0810372	−	0.996711i	$-0.474177\pi$
$787$	4.54676	0.162074	0.0810372	+	0.996711i	$0.474177\pi$
$788$	7.51856	0.267838
$789$	6.84579	0.243716
$790$	3.20634	0.114076
$791$	19.0664	0.677922
$792$	19.5644	0.695190
$793$	0	0
$794$	−39.6530	−1.40723
$795$	39.7000	1.40801
$796$	1.35779	0.0481255
$797$	12.9330	0.458110	0.229055	−	0.973414i	$-0.426436\pi$
$797$	12.9330	0.458110	0.229055	+	0.973414i	$0.426436\pi$
$798$	−37.0857	−1.31282
$799$	−30.7971	−1.08952
$800$	−7.13889	−0.252398
$801$	30.5197	1.07836
$802$	33.3742	1.17848
$803$	9.29337	0.327956
$804$	−0.988345	−0.0348563
$805$	−12.1405	−0.427895
$806$	0	0
$807$	−101.260	−3.56452
$808$	10.4774	0.368592
$809$	−37.0363	−1.30213	−0.651064	−	0.759023i	$-0.725677\pi$
$809$	−37.0363	−1.30213	−0.651064	+	0.759023i	$0.725677\pi$
$810$	52.3057	1.83784
$811$	−30.7510	−1.07981	−0.539907	−	0.841725i	$-0.681541\pi$
$811$	−30.7510	−1.07981	−0.539907	+	0.841725i	$0.681541\pi$
$812$	−6.08974	−0.213708
$813$	25.1417	0.881757
$814$	12.5279	0.439104
$815$	23.4330	0.820822
$816$	92.2885	3.23074
$817$	6.64861	0.232605
$818$	−17.1222	−0.598665
$819$	0	0
$820$	1.67049	0.0583360
$821$	52.6472	1.83740	0.918699	−	0.394958i	$-0.129241\pi$
$821$	52.6472	1.83740	0.918699	+	0.394958i	$0.129241\pi$
$822$	9.34993	0.326116
$823$	−36.0179	−1.25551	−0.627753	−	0.778413i	$-0.716025\pi$
$823$	−36.0179	−1.25551	−0.627753	+	0.778413i	$0.716025\pi$
$824$	30.2343	1.05326
$825$	11.5849	0.403333
$826$	−36.3620	−1.26520
$827$	46.4535	1.61535	0.807673	−	0.589631i	$-0.200727\pi$
$827$	46.4535	1.61535	0.807673	+	0.589631i	$0.200727\pi$
$828$	−14.1666	−0.492325
$829$	−4.65695	−0.161743	−0.0808713	−	0.996725i	$-0.525770\pi$
$829$	−4.65695	−0.161743	−0.0808713	+	0.996725i	$0.525770\pi$
$830$	−24.8974	−0.864202
$831$	−46.1673	−1.60153
$832$	0	0
$833$	−18.6958	−0.647772
$834$	108.647	3.76213
$835$	−16.8417	−0.582831
$836$	1.33878	0.0463027
$837$	−53.7860	−1.85912
$838$	−9.18064	−0.317140
$839$	26.2967	0.907862	0.453931	−	0.891037i	$-0.350021\pi$
$839$	26.2967	0.907862	0.453931	+	0.891037i	$0.350021\pi$
$840$	−19.9025	−0.686702
$841$	42.8234	1.47667
$842$	8.39849	0.289431
$843$	−10.4046	−0.358354
$844$	4.63835	0.159658
$845$	0	0
$846$	60.0640	2.06504
$847$	−1.98662	−0.0682610
$848$	−45.8204	−1.57348
$849$	6.70913	0.230257
$850$	33.2162	1.13931
$851$	41.0886	1.40850
$852$	6.20447	0.212562
$853$	−4.97399	−0.170306	−0.0851530	−	0.996368i	$-0.527138\pi$
$853$	−4.97399	−0.170306	−0.0851530	+	0.996368i	$0.527138\pi$
$854$	9.88499	0.338257
$855$	−34.8726	−1.19262
$856$	9.68496	0.331025
$857$	16.7189	0.571106	0.285553	−	0.958363i	$-0.407823\pi$
$857$	16.7189	0.571106	0.285553	+	0.958363i	$0.407823\pi$
$858$	0	0
$859$	9.68953	0.330603	0.165301	−	0.986243i	$-0.447140\pi$
$859$	9.68953	0.330603	0.165301	+	0.986243i	$0.447140\pi$
$860$	−0.787754	−0.0268622
$861$	−24.8349	−0.846373
$862$	−13.1600	−0.448232
$863$	−2.96369	−0.100885	−0.0504426	−	0.998727i	$-0.516063\pi$
$863$	−2.96369	−0.100885	−0.0504426	+	0.998727i	$0.516063\pi$
$864$	−31.6641	−1.07724
$865$	24.7777	0.842468
$866$	0.808786	0.0274837
$867$	−67.2521	−2.28400
$868$	−2.46848	−0.0837858
$869$	1.72080	0.0583741
$870$	−51.8243	−1.75701
$871$	0	0
$872$	14.4244	0.488472
$873$	−103.557	−3.50486
$874$	28.6698	0.969771
$875$	−20.5460	−0.694581
$876$	−11.0318	−0.372730
$877$	−3.63010	−0.122580	−0.0612898	−	0.998120i	$-0.519521\pi$
$877$	−3.63010	−0.122580	−0.0612898	+	0.998120i	$0.519521\pi$
$878$	3.71495	0.125374
$879$	−32.0719	−1.08176
$880$	5.56830	0.187707
$881$	38.8671	1.30947	0.654733	−	0.755860i	$-0.272781\pi$
$881$	38.8671	1.30947	0.654733	+	0.755860i	$0.272781\pi$
$882$	36.4627	1.22776
$883$	−7.72302	−0.259900	−0.129950	−	0.991521i	$-0.541482\pi$
$883$	−7.72302	−0.259900	−0.129950	+	0.991521i	$0.541482\pi$
$884$	0	0
$885$	−47.3924	−1.59308
$886$	36.8850	1.23918
$887$	13.5579	0.455231	0.227616	−	0.973751i	$-0.426907\pi$
$887$	13.5579	0.455231	0.227616	+	0.973751i	$0.426907\pi$
$888$	67.3588	2.26041
$889$	14.6909	0.492718
$890$	7.31810	0.245303
$891$	28.0718	0.940441
$892$	−5.21743	−0.174692
$893$	−18.6165	−0.622979
$894$	−74.6496	−2.49666
$895$	26.3039	0.879243
$896$	26.5891	0.888279
$897$	0	0
$898$	11.3952	0.380261
$899$	29.1137	0.970996
$900$	−9.92158	−0.330719
$901$	61.0901	2.03521
$902$	5.85381	0.194911
$903$	11.7114	0.389732
$904$	−24.1634	−0.803664
$905$	−9.71885	−0.323065
$906$	51.9889	1.72722
$907$	54.1005	1.79638	0.898189	−	0.439609i	$-0.144883\pi$
$907$	54.1005	1.79638	0.898189	+	0.439609i	$0.144883\pi$
$908$	6.07033	0.201451
$909$	32.3376	1.07257
$910$	0	0
$911$	−7.17721	−0.237792	−0.118896	−	0.992907i	$-0.537935\pi$
$911$	−7.17721	−0.237792	−0.118896	+	0.992907i	$0.537935\pi$
$912$	55.7874	1.84731
$913$	−13.3621	−0.442222
$914$	3.88973	0.128661
$915$	12.8836	0.425919
$916$	−1.73007	−0.0571632
$917$	−28.9311	−0.955390
$918$	147.329	4.86257
$919$	−32.1437	−1.06032	−0.530162	−	0.847896i	$-0.677869\pi$
$919$	−32.1437	−1.06032	−0.530162	+	0.847896i	$0.677869\pi$
$920$	15.3860	0.507262
$921$	42.6760	1.40622
$922$	−7.30012	−0.240417
$923$	0	0
$924$	2.35824	0.0775804
$925$	28.7763	0.946159
$926$	13.6189	0.447545
$927$	93.3158	3.06489
$928$	17.1394	0.562628
$929$	37.2034	1.22061	0.610303	−	0.792168i	$-0.291048\pi$
$929$	37.2034	1.22061	0.610303	+	0.792168i	$0.291048\pi$
$930$	−21.0071	−0.688848
$931$	−11.3014	−0.370390
$932$	−0.895357	−0.0293284
$933$	68.7188	2.24975
$934$	−1.38461	−0.0453058
$935$	−7.42395	−0.242789
$936$	0	0
$937$	−34.5166	−1.12761	−0.563804	−	0.825909i	$-0.690662\pi$
$937$	−34.5166	−1.12761	−0.563804	+	0.825909i	$0.690662\pi$
$938$	2.54192	0.0829967
$939$	−1.59145	−0.0519351
$940$	2.20576	0.0719440
$941$	55.3190	1.80335	0.901674	−	0.432417i	$-0.142339\pi$
$941$	55.3190	1.80335	0.901674	+	0.432417i	$0.142339\pi$
$942$	17.3969	0.566822
$943$	19.1991	0.625209
$944$	54.6987	1.78029
$945$	−37.7126	−1.22679
$946$	−2.76049	−0.0897511
$947$	−2.49089	−0.0809430	−0.0404715	−	0.999181i	$-0.512886\pi$
$947$	−2.49089	−0.0809430	−0.0404715	+	0.999181i	$0.512886\pi$
$948$	−2.04270	−0.0663437
$949$	0	0
$950$	20.0788	0.651444
$951$	82.0412	2.66037
$952$	−30.6259	−0.992591
$953$	−27.7692	−0.899533	−0.449766	−	0.893146i	$-0.648493\pi$
$953$	−27.7692	−0.899533	−0.449766	+	0.893146i	$0.648493\pi$
$954$	−119.145	−3.85746
$955$	21.9787	0.711215
$956$	−6.37100	−0.206053
$957$	−27.8135	−0.899082
$958$	7.09813	0.229330
$959$	−3.68289	−0.118927
$960$	24.1820	0.780469
$961$	−19.1987	−0.619314
$962$	0	0
$963$	29.8919	0.963252
$964$	1.14425	0.0368537
$965$	−18.1100	−0.582982
$966$	50.5015	1.62486
$967$	47.5638	1.52955	0.764775	−	0.644298i	$-0.222850\pi$
$967$	47.5638	1.52955	0.764775	+	0.644298i	$0.222850\pi$
$968$	2.51771	0.0809222
$969$	−74.3788	−2.38939
$970$	−24.8311	−0.797279
$971$	−32.9713	−1.05810	−0.529050	−	0.848591i	$-0.677452\pi$
$971$	−32.9713	−1.05810	−0.529050	+	0.848591i	$0.677452\pi$
$972$	−16.3336	−0.523901
$973$	−42.7954	−1.37196
$974$	−33.9615	−1.08820
$975$	0	0
$976$	−14.8698	−0.475971
$977$	0.741037	0.0237079	0.0118539	−	0.999930i	$-0.496227\pi$
$977$	0.741037	0.0237079	0.0118539	+	0.999930i	$0.496227\pi$
$978$	−97.4758	−3.11693
$979$	3.92753	0.125524
$980$	1.33904	0.0427740
$981$	44.5198	1.42141
$982$	10.3471	0.330188
$983$	29.6646	0.946154	0.473077	−	0.881021i	$-0.343143\pi$
$983$	29.6646	0.946154	0.473077	+	0.881021i	$0.343143\pi$
$984$	31.4741	1.00336
$985$	−25.2028	−0.803029
$986$	−79.7470	−2.53966
$987$	−32.7928	−1.04380
$988$	0	0
$989$	−9.05373	−0.287892
$990$	14.4790	0.460174
$991$	18.6412	0.592158	0.296079	−	0.955163i	$-0.404321\pi$
$991$	18.6412	0.592158	0.296079	+	0.955163i	$0.404321\pi$
$992$	6.94747	0.220582
$993$	−47.9443	−1.52147
$994$	−15.9573	−0.506134
$995$	−4.55141	−0.144290
$996$	15.8617	0.502597
$997$	53.2981	1.68797	0.843984	−	0.536369i	$-0.180204\pi$
$997$	53.2981	1.68797	0.843984	+	0.536369i	$0.180204\pi$
$998$	−58.8697	−1.86349
$999$	127.636	4.03821

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.t.1.6	yes	21
13.12	even	2		1859.2.a.s.1.16	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.2.a.s.1.16	✓	21	13.12	even	2
1859.2.a.t.1.6	yes	21	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-1.53678 q^{2} -3.28188 q^{3} +0.361702 q^{4} -1.21246 q^{5} +5.04353 q^{6} -1.98662 q^{7} +2.51771 q^{8} +7.77071 q^{9} +O(q^{10})\)	\(q-1.53678 q^{2} -3.28188 q^{3} +0.361702 q^{4} -1.21246 q^{5} +5.04353 q^{6} -1.98662 q^{7} +2.51771 q^{8} +7.77071 q^{9} +1.86328 q^{10} +1.00000 q^{11} -1.18706 q^{12} +3.05300 q^{14} +3.97913 q^{15} -4.59258 q^{16} +6.12307 q^{17} -11.9419 q^{18} +3.70133 q^{19} -0.438548 q^{20} +6.51984 q^{21} -1.53678 q^{22} -5.04028 q^{23} -8.26281 q^{24} -3.52995 q^{25} -15.6569 q^{27} -0.718565 q^{28} +8.47487 q^{29} -6.11506 q^{30} +3.43530 q^{31} +2.02238 q^{32} -3.28188 q^{33} -9.40983 q^{34} +2.40869 q^{35} +2.81069 q^{36} -8.15204 q^{37} -5.68814 q^{38} -3.05261 q^{40} -3.80914 q^{41} -10.0196 q^{42} +1.79628 q^{43} +0.361702 q^{44} -9.42165 q^{45} +7.74582 q^{46} -5.02969 q^{47} +15.0723 q^{48} -3.05334 q^{49} +5.42477 q^{50} -20.0951 q^{51} +9.97705 q^{53} +24.0612 q^{54} -1.21246 q^{55} -5.00173 q^{56} -12.1473 q^{57} -13.0240 q^{58} -11.9103 q^{59} +1.43926 q^{60} +3.23779 q^{61} -5.27931 q^{62} -15.4374 q^{63} +6.07720 q^{64} +5.04353 q^{66} +0.832597 q^{67} +2.21473 q^{68} +16.5416 q^{69} -3.70163 q^{70} -5.22675 q^{71} +19.5644 q^{72} +9.29337 q^{73} +12.5279 q^{74} +11.5849 q^{75} +1.33878 q^{76} -1.98662 q^{77} +1.72080 q^{79} +5.56830 q^{80} +28.0718 q^{81} +5.85381 q^{82} -13.3621 q^{83} +2.35824 q^{84} -7.42395 q^{85} -2.76049 q^{86} -27.8135 q^{87} +2.51771 q^{88} +3.92753 q^{89} +14.4790 q^{90} -1.82308 q^{92} -11.2742 q^{93} +7.72954 q^{94} -4.48770 q^{95} -6.63719 q^{96} -13.3265 q^{97} +4.69233 q^{98} +7.77071 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 6 q^{3} + 32 q^{4} + 7 q^{5} - 19 q^{6} + q^{7} - 3 q^{8} + 33 q^{9}+O(q^{10}) \) 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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