LMFDB - Embedded newform 1849.2.a.m.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,2,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1849.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:	$14.7643393337$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{44})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 11x^{8} + 44x^{6} - 77x^{4} + 55x^{2} - 11 $ x^10 - 11x^8 + 44x^6 - 77x^4 + 55x^2 - 11
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$1.08128$ of defining polynomial
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.08128 q^{2} +3.06092 q^{3} -0.830830 q^{4} -2.59278 q^{5} +3.30972 q^{6} -0.985960 q^{7} -3.06092 q^{8} +6.36926 q^{9} +O(q^{10})$	\(q+1.08128 q^{2} +3.06092 q^{3} -0.830830 q^{4} -2.59278 q^{5} +3.30972 q^{6} -0.985960 q^{7} -3.06092 q^{8} +6.36926 q^{9} -2.80353 q^{10} -4.60149 q^{11} -2.54311 q^{12} +0.224463 q^{13} -1.06610 q^{14} -7.93631 q^{15} -1.64806 q^{16} -3.99444 q^{17} +6.88696 q^{18} -1.95251 q^{19} +2.15416 q^{20} -3.01795 q^{21} -4.97551 q^{22} -2.30326 q^{23} -9.36926 q^{24} +1.72251 q^{25} +0.242707 q^{26} +10.3130 q^{27} +0.819165 q^{28} +0.226582 q^{29} -8.58138 q^{30} -0.470746 q^{31} +4.33983 q^{32} -14.0848 q^{33} -4.31912 q^{34} +2.55638 q^{35} -5.29177 q^{36} -11.6484 q^{37} -2.11121 q^{38} +0.687063 q^{39} +7.93631 q^{40} +7.81225 q^{41} -3.26325 q^{42} +3.82306 q^{44} -16.5141 q^{45} -2.49048 q^{46} +2.56573 q^{47} -5.04459 q^{48} -6.02788 q^{49} +1.86252 q^{50} -12.2267 q^{51} -0.186490 q^{52} -5.89326 q^{53} +11.1513 q^{54} +11.9307 q^{55} +3.01795 q^{56} -5.97649 q^{57} +0.244999 q^{58} +3.36298 q^{59} +6.59372 q^{60} +4.73833 q^{61} -0.509009 q^{62} -6.27984 q^{63} +7.98870 q^{64} -0.581982 q^{65} -15.2297 q^{66} +12.6260 q^{67} +3.31870 q^{68} -7.05012 q^{69} +2.76417 q^{70} +2.28626 q^{71} -19.4958 q^{72} +8.33340 q^{73} -12.5952 q^{74} +5.27248 q^{75} +1.62221 q^{76} +4.53689 q^{77} +0.742909 q^{78} -14.4964 q^{79} +4.27306 q^{80} +12.4597 q^{81} +8.44724 q^{82} -10.1357 q^{83} +2.50740 q^{84} +10.3567 q^{85} +0.693550 q^{87} +14.0848 q^{88} -5.02757 q^{89} -17.8564 q^{90} -0.221311 q^{91} +1.91362 q^{92} -1.44092 q^{93} +2.77428 q^{94} +5.06243 q^{95} +13.2839 q^{96} +16.5056 q^{97} -6.51784 q^{98} -29.3081 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{4} + 22 q^{6} + 14 q^{9}+O(q^{10}) $ 10 * q + 2 * q^4 + 22 * q^6 + 14 * q^9	$ 10 q + 2 q^{4} + 22 q^{6} + 14 q^{9} - 22 q^{10} - 10 q^{11} - 14 q^{13} - 22 q^{14} - 22 q^{15} - 26 q^{16} - 16 q^{17} - 44 q^{21} - 18 q^{23} - 44 q^{24} - 6 q^{25} - 2 q^{31} - 28 q^{36} - 22 q^{38} + 22 q^{40} - 2 q^{44} - 18 q^{47} + 18 q^{49} + 28 q^{52} + 2 q^{53} + 44 q^{56} - 22 q^{57} - 22 q^{58} + 14 q^{59} + 8 q^{64} - 22 q^{66} + 26 q^{67} + 32 q^{68} + 44 q^{74} - 44 q^{78} - 56 q^{79} + 2 q^{81} - 38 q^{83} - 22 q^{87} - 22 q^{90} - 74 q^{92} + 22 q^{96} + 34 q^{97} - 36 q^{99}+O(q^{100}) $ 10 * q + 2 * q^4 + 22 * q^6 + 14 * q^9 - 22 * q^10 - 10 * q^11 - 14 * q^13 - 22 * q^14 - 22 * q^15 - 26 * q^16 - 16 * q^17 - 44 * q^21 - 18 * q^23 - 44 * q^24 - 6 * q^25 - 2 * q^31 - 28 * q^36 - 22 * q^38 + 22 * q^40 - 2 * q^44 - 18 * q^47 + 18 * q^49 + 28 * q^52 + 2 * q^53 + 44 * q^56 - 22 * q^57 - 22 * q^58 + 14 * q^59 + 8 * q^64 - 22 * q^66 + 26 * q^67 + 32 * q^68 + 44 * q^74 - 44 * q^78 - 56 * q^79 + 2 * q^81 - 38 * q^83 - 22 * q^87 - 22 * q^90 - 74 * q^92 + 22 * q^96 + 34 * q^97 - 36 * 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 $

$2$	1.08128	0.764582	0.382291	−	0.924042i	$-0.375135\pi$
$2$	1.08128	0.764582	0.382291	+	0.924042i	$0.375135\pi$
$3$	3.06092	1.76723	0.883613	−	0.468218i	$-0.155104\pi$
$3$	3.06092	1.76723	0.883613	+	0.468218i	$0.155104\pi$
$4$	−0.830830	−0.415415
$5$	−2.59278	−1.15953	−0.579763	−	0.814785i	$-0.696855\pi$
$5$	−2.59278	−1.15953	−0.579763	+	0.814785i	$0.696855\pi$
$6$	3.30972	1.35119
$7$	−0.985960	−0.372658	−0.186329	−	0.982487i	$-0.559659\pi$
$7$	−0.985960	−0.372658	−0.186329	+	0.982487i	$0.559659\pi$
$8$	−3.06092	−1.08220
$9$	6.36926	2.12309
$10$	−2.80353	−0.886553
$11$	−4.60149	−1.38740	−0.693701	−	0.720263i	$-0.744021\pi$
$11$	−4.60149	−1.38740	−0.693701	+	0.720263i	$0.744021\pi$
$12$	−2.54311	−0.734132
$13$	0.224463	0.0622547	0.0311274	−	0.999515i	$-0.490090\pi$
$13$	0.224463	0.0622547	0.0311274	+	0.999515i	$0.490090\pi$
$14$	−1.06610	−0.284927
$15$	−7.93631	−2.04915
$16$	−1.64806	−0.412015
$17$	−3.99444	−0.968794	−0.484397	−	0.874848i	$-0.660961\pi$
$17$	−3.99444	−0.968794	−0.484397	+	0.874848i	$0.660961\pi$
$18$	6.88696	1.62327
$19$	−1.95251	−0.447937	−0.223968	−	0.974596i	$-0.571901\pi$
$19$	−1.95251	−0.447937	−0.223968	+	0.974596i	$0.571901\pi$
$20$	2.15416	0.481685
$21$	−3.01795	−0.658571
$22$	−4.97551	−1.06078
$23$	−2.30326	−0.480264	−0.240132	−	0.970740i	$-0.577191\pi$
$23$	−2.30326	−0.480264	−0.240132	+	0.970740i	$0.577191\pi$
$24$	−9.36926	−1.91249
$25$	1.72251	0.344502
$26$	0.242707	0.0475988
$27$	10.3130	1.98475
$28$	0.819165	0.154808
$29$	0.226582	0.0420752	0.0210376	−	0.999779i	$-0.493303\pi$
$29$	0.226582	0.0420752	0.0210376	+	0.999779i	$0.493303\pi$
$30$	−8.58138	−1.56674
$31$	−0.470746	−0.0845484	−0.0422742	−	0.999106i	$-0.513460\pi$
$31$	−0.470746	−0.0845484	−0.0422742	+	0.999106i	$0.513460\pi$
$32$	4.33983	0.767181
$33$	−14.0848	−2.45185
$34$	−4.31912	−0.740722
$35$	2.55638	0.432107
$36$	−5.29177	−0.881962
$37$	−11.6484	−1.91498	−0.957492	−	0.288459i	$-0.906857\pi$
$37$	−11.6484	−1.91498	−0.957492	+	0.288459i	$0.906857\pi$
$38$	−2.11121	−0.342484
$39$	0.687063	0.110018
$40$	7.93631	1.25484
$41$	7.81225	1.22007	0.610034	−	0.792375i	$-0.291156\pi$
$41$	7.81225	1.22007	0.610034	+	0.792375i	$0.291156\pi$
$42$	−3.26325	−0.503531
$43$	0	0
$43$	0	0
$44$	3.82306	0.576348
$45$	−16.5141	−2.46178
$46$	−2.49048	−0.367201
$47$	2.56573	0.374251	0.187125	−	0.982336i	$-0.440083\pi$
$47$	2.56573	0.374251	0.187125	+	0.982336i	$0.440083\pi$
$48$	−5.04459	−0.728124
$49$	−6.02788	−0.861126
$50$	1.86252	0.263400
$51$	−12.2267	−1.71208
$52$	−0.186490	−0.0258616
$53$	−5.89326	−0.809502	−0.404751	−	0.914427i	$-0.632642\pi$
$53$	−5.89326	−0.809502	−0.404751	+	0.914427i	$0.632642\pi$
$54$	11.1513	1.51750
$55$	11.9307	1.60873
$56$	3.01795	0.403291
$57$	−5.97649	−0.791606
$58$	0.244999	0.0321699
$59$	3.36298	0.437823	0.218911	−	0.975745i	$-0.429749\pi$
$59$	3.36298	0.437823	0.218911	+	0.975745i	$0.429749\pi$
$60$	6.59372	0.851246
$61$	4.73833	0.606681	0.303340	−	0.952882i	$-0.401898\pi$
$61$	4.73833	0.606681	0.303340	+	0.952882i	$0.401898\pi$
$62$	−0.509009	−0.0646442
$63$	−6.27984	−0.791185
$64$	7.98870	0.998588
$65$	−0.581982	−0.0721860
$66$	−15.2297	−1.87464
$67$	12.6260	1.54251	0.771253	−	0.636529i	$-0.219630\pi$
$67$	12.6260	1.54251	0.771253	+	0.636529i	$0.219630\pi$
$68$	3.31870	0.402452
$69$	−7.05012	−0.848735
$70$	2.76417	0.330381
$71$	2.28626	0.271329	0.135665	−	0.990755i	$-0.456683\pi$
$71$	2.28626	0.271329	0.135665	+	0.990755i	$0.456683\pi$
$72$	−19.4958	−2.29760
$73$	8.33340	0.975351	0.487676	−	0.873025i	$-0.337845\pi$
$73$	8.33340	0.975351	0.487676	+	0.873025i	$0.337845\pi$
$74$	−12.5952	−1.46416
$75$	5.27248	0.608814
$76$	1.62221	0.186080
$77$	4.53689	0.517027
$78$	0.742909	0.0841179
$79$	−14.4964	−1.63098	−0.815489	−	0.578773i	$-0.803532\pi$
$79$	−14.4964	−1.63098	−0.815489	+	0.578773i	$0.803532\pi$
$80$	4.27306	0.477743
$81$	12.4597	1.38441
$82$	8.44724	0.932842
$83$	−10.1357	−1.11254	−0.556268	−	0.831003i	$-0.687767\pi$
$83$	−10.1357	−1.11254	−0.556268	+	0.831003i	$0.687767\pi$
$84$	2.50740	0.273580
$85$	10.3567	1.12334
$86$	0	0
$87$	0.693550	0.0743563
$88$	14.0848	1.50145
$89$	−5.02757	−0.532922	−0.266461	−	0.963846i	$-0.585854\pi$
$89$	−5.02757	−0.532922	−0.266461	+	0.963846i	$0.585854\pi$
$90$	−17.8564	−1.88223
$91$	−0.221311	−0.0231997
$92$	1.91362	0.199509
$93$	−1.44092	−0.149416
$94$	2.77428	0.286145
$95$	5.06243	0.519395
$96$	13.2839	1.35578
$97$	16.5056	1.67589	0.837946	−	0.545753i	$-0.183756\pi$
$97$	16.5056	1.67589	0.837946	+	0.545753i	$0.183756\pi$
$98$	−6.51784	−0.658401
$99$	−29.3081	−2.94557
$100$	−1.43111	−0.143111
$101$	−5.37500	−0.534832	−0.267416	−	0.963581i	$-0.586170\pi$
$101$	−5.37500	−0.534832	−0.267416	+	0.963581i	$0.586170\pi$
$102$	−13.2205	−1.30902
$103$	3.33992	0.329092	0.164546	−	0.986369i	$-0.447384\pi$
$103$	3.33992	0.329092	0.164546	+	0.986369i	$0.447384\pi$
$104$	−0.687063	−0.0673721
$105$	7.82488	0.763630
$106$	−6.37228	−0.618930
$107$	−12.8228	−1.23963	−0.619814	−	0.784749i	$-0.712792\pi$
$107$	−12.8228	−1.23963	−0.619814	+	0.784749i	$0.712792\pi$
$108$	−8.56839	−0.824494
$109$	5.93751	0.568711	0.284355	−	0.958719i	$-0.408220\pi$
$109$	5.93751	0.568711	0.284355	+	0.958719i	$0.408220\pi$
$110$	12.9004	1.23001
$111$	−35.6549	−3.38421
$112$	1.62492	0.153541
$113$	−12.8324	−1.20717	−0.603584	−	0.797300i	$-0.706261\pi$
$113$	−12.8324	−1.20717	−0.603584	+	0.797300i	$0.706261\pi$
$114$	−6.46227	−0.605247
$115$	5.97186	0.556879
$116$	−0.188251	−0.0174787
$117$	1.42966	0.132172
$118$	3.63633	0.334751
$119$	3.93836	0.361029
$120$	24.2924	2.21759
$121$	10.1737	0.924885
$122$	5.12347	0.463857
$123$	23.9127	2.15614
$124$	0.391110	0.0351227
$125$	8.49781	0.760067
$126$	−6.79027	−0.604925
$127$	−16.7536	−1.48664	−0.743322	−	0.668934i	$-0.766751\pi$
$127$	−16.7536	−1.48664	−0.743322	+	0.668934i	$0.766751\pi$
$128$	−0.0416244	−0.00367911
$129$	0	0
$130$	−0.629287	−0.0551921
$131$	4.36963	0.381776	0.190888	−	0.981612i	$-0.438863\pi$
$131$	4.36963	0.381776	0.190888	+	0.981612i	$0.438863\pi$
$132$	11.7021	1.01854
$133$	1.92510	0.166927
$134$	13.6522	1.17937
$135$	−26.7395	−2.30137
$136$	12.2267	1.04843
$137$	−14.7308	−1.25854	−0.629270	−	0.777187i	$-0.716646\pi$
$137$	−14.7308	−1.25854	−0.629270	+	0.777187i	$0.716646\pi$
$138$	−7.62316	−0.648927
$139$	−5.15768	−0.437468	−0.218734	−	0.975784i	$-0.570193\pi$
$139$	−5.15768	−0.437468	−0.218734	+	0.975784i	$0.570193\pi$
$140$	−2.12392	−0.179504
$141$	7.85351	0.661385
$142$	2.47209	0.207453
$143$	−1.03286	−0.0863724
$144$	−10.4969	−0.874744
$145$	−0.587477	−0.0487873
$146$	9.01076	0.745736
$147$	−18.4509	−1.52180
$148$	9.67784	0.795513
$149$	4.32423	0.354255	0.177128	−	0.984188i	$-0.443319\pi$
$149$	4.32423	0.354255	0.177128	+	0.984188i	$0.443319\pi$
$150$	5.70104	0.465488
$151$	20.0658	1.63293	0.816464	−	0.577396i	$-0.195931\pi$
$151$	20.0658	1.63293	0.816464	+	0.577396i	$0.195931\pi$
$152$	5.97649	0.484757
$153$	−25.4416	−2.05683
$154$	4.90566	0.395309
$155$	1.22054	0.0980362
$156$	−0.570833	−0.0457032
$157$	7.03748	0.561652	0.280826	−	0.959759i	$-0.409392\pi$
$157$	7.03748	0.561652	0.280826	+	0.959759i	$0.409392\pi$
$158$	−15.6747	−1.24702
$159$	−18.0388	−1.43057
$160$	−11.2522	−0.889567
$161$	2.27093	0.178974
$162$	13.4724	1.05849
$163$	6.89488	0.540049	0.270024	−	0.962854i	$-0.412968\pi$
$163$	6.89488	0.540049	0.270024	+	0.962854i	$0.412968\pi$
$164$	−6.49065	−0.506835
$165$	36.5189	2.84299
$166$	−10.9595	−0.850624
$167$	−18.8690	−1.46013	−0.730063	−	0.683379i	$-0.760510\pi$
$167$	−18.8690	−1.46013	−0.730063	+	0.683379i	$0.760510\pi$
$168$	9.23772	0.712705
$169$	−12.9496	−0.996124
$170$	11.1985	0.858887
$171$	−12.4361	−0.951009
$172$	0	0
$173$	11.7053	0.889935	0.444968	−	0.895547i	$-0.353215\pi$
$173$	11.7053	0.889935	0.444968	+	0.895547i	$0.353215\pi$
$174$	0.749923	0.0568515
$175$	−1.69833	−0.128382
$176$	7.58354	0.571631
$177$	10.2938	0.773732
$178$	−5.43622	−0.407462
$179$	17.1956	1.28526	0.642631	−	0.766176i	$-0.277843\pi$
$179$	17.1956	1.28526	0.642631	+	0.766176i	$0.277843\pi$
$180$	13.7204	1.02266
$181$	1.28168	0.0952666	0.0476333	−	0.998865i	$-0.484832\pi$
$181$	1.28168	0.0952666	0.0476333	+	0.998865i	$0.484832\pi$
$182$	−0.239300	−0.0177381
$183$	14.5037	1.07214
$184$	7.05012	0.519742
$185$	30.2017	2.22048
$186$	−1.55804	−0.114241
$187$	18.3804	1.34411
$188$	−2.13169	−0.155469
$189$	−10.1683	−0.739632
$190$	5.47392	0.397120
$191$	−18.6667	−1.35067	−0.675337	−	0.737509i	$-0.736002\pi$
$191$	−18.6667	−1.35067	−0.675337	+	0.737509i	$0.736002\pi$
$192$	24.4528	1.76473
$193$	7.79518	0.561109	0.280555	−	0.959838i	$-0.409482\pi$
$193$	7.79518	0.561109	0.280555	+	0.959838i	$0.409482\pi$
$194$	17.8472	1.28136
$195$	−1.78140	−0.127569
$196$	5.00815	0.357725
$197$	−6.52348	−0.464779	−0.232389	−	0.972623i	$-0.574654\pi$
$197$	−6.52348	−0.464779	−0.232389	+	0.972623i	$0.574654\pi$
$198$	−31.6903	−2.25213
$199$	−12.4668	−0.883750	−0.441875	−	0.897077i	$-0.645686\pi$
$199$	−12.4668	−0.883750	−0.441875	+	0.897077i	$0.645686\pi$
$200$	−5.27248	−0.372821
$201$	38.6471	2.72596
$202$	−5.81189	−0.408923
$203$	−0.223401	−0.0156797
$204$	10.1583	0.711223
$205$	−20.2555	−1.41470
$206$	3.61140	0.251618
$207$	−14.6701	−1.01964
$208$	−0.369928	−0.0256499
$209$	8.98447	0.621469
$210$	8.46090	0.583858
$211$	4.84351	0.333441	0.166720	−	0.986004i	$-0.446682\pi$
$211$	4.84351	0.333441	0.166720	+	0.986004i	$0.446682\pi$
$212$	4.89630	0.336279
$213$	6.99808	0.479500
$214$	−13.8651	−0.947796
$215$	0	0
$216$	−31.5675	−2.14789
$217$	0.464137	0.0315076
$218$	6.42013	0.434826
$219$	25.5079	1.72367
$220$	−9.91235	−0.668291
$221$	−0.896603	−0.0603120
$222$	−38.5529	−2.58750
$223$	12.8758	0.862226	0.431113	−	0.902298i	$-0.358121\pi$
$223$	12.8758	0.862226	0.431113	+	0.902298i	$0.358121\pi$
$224$	−4.27890	−0.285896
$225$	10.9711	0.731408
$226$	−13.8754	−0.922978
$227$	3.12163	0.207190	0.103595	−	0.994620i	$-0.466965\pi$
$227$	3.12163	0.207190	0.103595	+	0.994620i	$0.466965\pi$
$228$	4.96545	0.328845
$229$	−5.18504	−0.342637	−0.171318	−	0.985216i	$-0.554803\pi$
$229$	−5.18504	−0.342637	−0.171318	+	0.985216i	$0.554803\pi$
$230$	6.45726	0.425779
$231$	13.8871	0.913702
$232$	−0.693550	−0.0455338
$233$	17.5285	1.14833	0.574164	−	0.818740i	$-0.305327\pi$
$233$	17.5285	1.14833	0.574164	+	0.818740i	$0.305327\pi$
$234$	1.54587	0.101056
$235$	−6.65238	−0.433954
$236$	−2.79407	−0.181878
$237$	−44.3725	−2.88231
$238$	4.25848	0.276036
$239$	5.58667	0.361372	0.180686	−	0.983541i	$-0.442168\pi$
$239$	5.58667	0.361372	0.180686	+	0.983541i	$0.442168\pi$
$240$	13.0795	0.844279
$241$	20.4467	1.31709	0.658544	−	0.752542i	$-0.271173\pi$
$241$	20.4467	1.31709	0.658544	+	0.752542i	$0.271173\pi$
$242$	11.0007	0.707150
$243$	7.19901	0.461816
$244$	−3.93674	−0.252024
$245$	15.6290	0.998499
$246$	25.8564	1.64854
$247$	−0.438266	−0.0278862
$248$	1.44092	0.0914983
$249$	−31.0245	−1.96610
$250$	9.18852	0.581133
$251$	−6.76796	−0.427190	−0.213595	−	0.976922i	$-0.568517\pi$
$251$	−6.76796	−0.427190	−0.213595	+	0.976922i	$0.568517\pi$
$252$	5.21748	0.328670
$253$	10.5985	0.666319
$254$	−18.1154	−1.13666
$255$	31.7011	1.98520
$256$	−16.0224	−1.00140
$257$	15.8683	0.989836	0.494918	−	0.868940i	$-0.335198\pi$
$257$	15.8683	0.989836	0.494918	+	0.868940i	$0.335198\pi$
$258$	0	0
$259$	11.4849	0.713634
$260$	0.483528	0.0299872
$261$	1.44316	0.0893293
$262$	4.72480	0.291899
$263$	12.1831	0.751244	0.375622	−	0.926773i	$-0.377429\pi$
$263$	12.1831	0.751244	0.375622	+	0.926773i	$0.377429\pi$
$264$	43.1126	2.65340
$265$	15.2799	0.938639
$266$	2.08157	0.127629
$267$	−15.3890	−0.941793
$268$	−10.4900	−0.640780
$269$	−26.9462	−1.64294	−0.821471	−	0.570251i	$-0.806846\pi$
$269$	−26.9462	−1.64294	−0.821471	+	0.570251i	$0.806846\pi$
$270$	−28.9129	−1.75958
$271$	−13.2715	−0.806185	−0.403092	−	0.915159i	$-0.632065\pi$
$271$	−13.2715	−0.806185	−0.403092	+	0.915159i	$0.632065\pi$
$272$	6.58308	0.399158
$273$	−0.677417	−0.0409991
$274$	−15.9282	−0.962256
$275$	−7.92613	−0.477963
$276$	5.85745	0.352577
$277$	−7.66042	−0.460270	−0.230135	−	0.973159i	$-0.573917\pi$
$277$	−7.66042	−0.460270	−0.230135	+	0.973159i	$0.573917\pi$
$278$	−5.57690	−0.334480
$279$	−2.99830	−0.179504
$280$	−7.82488	−0.467626
$281$	2.55271	0.152282	0.0761410	−	0.997097i	$-0.475740\pi$
$281$	2.55271	0.152282	0.0761410	+	0.997097i	$0.475740\pi$
$282$	8.49186	0.505683
$283$	23.7366	1.41099	0.705497	−	0.708713i	$-0.250724\pi$
$283$	23.7366	1.41099	0.705497	+	0.708713i	$0.250724\pi$
$284$	−1.89950	−0.112714
$285$	15.4957	0.917888
$286$	−1.11682	−0.0660387
$287$	−7.70257	−0.454668
$288$	27.6415	1.62879
$289$	−1.04444	−0.0614379
$290$	−0.635228	−0.0373019
$291$	50.5225	2.96168
$292$	−6.92364	−0.405176
$293$	−27.5298	−1.60831	−0.804154	−	0.594421i	$-0.797381\pi$
$293$	−27.5298	−1.60831	−0.804154	+	0.594421i	$0.797381\pi$
$294$	−19.9506	−1.16354
$295$	−8.71947	−0.507667
$296$	35.6549	2.07240
$297$	−47.4554	−2.75364
$298$	4.67572	0.270857
$299$	−0.516997	−0.0298987
$300$	−4.38053	−0.252910
$301$	0	0
$302$	21.6967	1.24851
$303$	−16.4525	−0.945169
$304$	3.21786	0.184557
$305$	−12.2854	−0.703462
$306$	−27.5096	−1.57262
$307$	18.3789	1.04894	0.524471	−	0.851429i	$-0.324263\pi$
$307$	18.3789	1.04894	0.524471	+	0.851429i	$0.324263\pi$
$308$	−3.76938	−0.214781
$309$	10.2233	0.581580
$310$	1.31975	0.0749567
$311$	−20.2210	−1.14663	−0.573313	−	0.819336i	$-0.694342\pi$
$311$	−20.2210	−1.14663	−0.573313	+	0.819336i	$0.694342\pi$
$312$	−2.10305	−0.119062
$313$	−9.75291	−0.551267	−0.275633	−	0.961263i	$-0.588888\pi$
$313$	−9.75291	−0.551267	−0.275633	+	0.961263i	$0.588888\pi$
$314$	7.60950	0.429429
$315$	16.2822	0.917400
$316$	12.0441	0.677533
$317$	−19.7360	−1.10848	−0.554241	−	0.832356i	$-0.686992\pi$
$317$	−19.7360	−1.10848	−0.554241	+	0.832356i	$0.686992\pi$
$318$	−19.5051	−1.09379
$319$	−1.04261	−0.0583752
$320$	−20.7130	−1.15789
$321$	−39.2496	−2.19070
$322$	2.45551	0.136840
$323$	7.79919	0.433959
$324$	−10.3519	−0.575104
$325$	0.386640	0.0214469
$326$	7.45531	0.412911
$327$	18.1743	1.00504
$328$	−23.9127	−1.32036
$329$	−2.52971	−0.139467
$330$	39.4872	2.17370
$331$	−13.9247	−0.765368	−0.382684	−	0.923879i	$-0.625000\pi$
$331$	−13.9247	−0.765368	−0.382684	+	0.923879i	$0.625000\pi$
$332$	8.42102	0.462164
$333$	−74.1917	−4.06568
$334$	−20.4027	−1.11639
$335$	−32.7363	−1.78858
$336$	4.97377	0.271341
$337$	−15.4290	−0.840470	−0.420235	−	0.907415i	$-0.638052\pi$
$337$	−15.4290	−0.840470	−0.420235	+	0.907415i	$0.638052\pi$
$338$	−14.0022	−0.761618
$339$	−39.2789	−2.13334
$340$	−8.60466	−0.466653
$341$	2.16613	0.117303
$342$	−13.4469	−0.727124
$343$	12.8450	0.693563
$344$	0	0
$345$	18.2794	0.984131
$346$	12.6567	0.680428
$347$	−20.1717	−1.08287	−0.541436	−	0.840742i	$-0.682119\pi$
$347$	−20.1717	−1.08287	−0.541436	+	0.840742i	$0.682119\pi$
$348$	−0.576222	−0.0308887
$349$	−28.2864	−1.51414	−0.757069	−	0.653335i	$-0.773369\pi$
$349$	−28.2864	−1.51414	−0.757069	+	0.653335i	$0.773369\pi$
$350$	−1.83637	−0.0981582
$351$	2.31489	0.123560
$352$	−19.9697	−1.06439
$353$	5.23666	0.278720	0.139360	−	0.990242i	$-0.455496\pi$
$353$	5.23666	0.278720	0.139360	+	0.990242i	$0.455496\pi$
$354$	11.1305	0.591581
$355$	−5.92778	−0.314614
$356$	4.17706	0.221384
$357$	12.0550	0.638019
$358$	18.5933	0.982687
$359$	−23.7307	−1.25246	−0.626229	−	0.779640i	$-0.715402\pi$
$359$	−23.7307	−1.25246	−0.626229	+	0.779640i	$0.715402\pi$
$360$	50.5484	2.66413
$361$	−15.1877	−0.799353
$362$	1.38586	0.0728391
$363$	31.1410	1.63448
$364$	0.183872	0.00963751
$365$	−21.6067	−1.13095
$366$	15.6825	0.819740
$367$	4.57431	0.238777	0.119388	−	0.992848i	$-0.461907\pi$
$367$	4.57431	0.238777	0.119388	+	0.992848i	$0.461907\pi$
$368$	3.79592	0.197876
$369$	49.7582	2.59031
$370$	32.6566	1.69774
$371$	5.81052	0.301667
$372$	1.19716	0.0620697
$373$	3.66773	0.189908	0.0949538	−	0.995482i	$-0.469730\pi$
$373$	3.66773	0.189908	0.0949538	+	0.995482i	$0.469730\pi$
$374$	19.8744	1.02768
$375$	26.0111	1.34321
$376$	−7.85351	−0.405014
$377$	0.0508592	0.00261938
$378$	−10.9947	−0.565509
$379$	22.0164	1.13091	0.565454	−	0.824780i	$-0.308701\pi$
$379$	22.0164	1.13091	0.565454	+	0.824780i	$0.308701\pi$
$380$	−4.20602	−0.215764
$381$	−51.2816	−2.62724
$382$	−20.1839	−1.03270
$383$	1.23252	0.0629787	0.0314893	−	0.999504i	$-0.489975\pi$
$383$	1.23252	0.0629787	0.0314893	+	0.999504i	$0.489975\pi$
$384$	−0.127409	−0.00650182
$385$	−11.7632	−0.599506
$386$	8.42878	0.429014
$387$	0	0
$388$	−13.7134	−0.696191
$389$	−0.426505	−0.0216247	−0.0108123	−	0.999942i	$-0.503442\pi$
$389$	−0.426505	−0.0216247	−0.0108123	+	0.999942i	$0.503442\pi$
$390$	−1.92620	−0.0975369
$391$	9.20025	0.465277
$392$	18.4509	0.931911
$393$	13.3751	0.674685
$394$	−7.05372	−0.355361
$395$	37.5861	1.89116
$396$	24.3500	1.22364
$397$	30.3250	1.52197	0.760984	−	0.648771i	$-0.224717\pi$
$397$	30.3250	1.52197	0.760984	+	0.648771i	$0.224717\pi$
$398$	−13.4801	−0.675699
$399$	5.89258	0.294998
$400$	−2.83881	−0.141940
$401$	−26.5707	−1.32688	−0.663438	−	0.748232i	$-0.730903\pi$
$401$	−26.5707	−1.32688	−0.663438	+	0.748232i	$0.730903\pi$
$402$	41.7884	2.08422
$403$	−0.105665	−0.00526354
$404$	4.46571	0.222177
$405$	−32.3052	−1.60526
$406$	−0.241559	−0.0119884
$407$	53.6000	2.65685
$408$	37.4249	1.85281
$409$	−7.56596	−0.374113	−0.187056	−	0.982349i	$-0.559895\pi$
$409$	−7.56596	−0.374113	−0.187056	+	0.982349i	$0.559895\pi$
$410$	−21.9018	−1.08166
$411$	−45.0900	−2.22412
$412$	−2.77491	−0.136710
$413$	−3.31577	−0.163158
$414$	−15.8625	−0.779599
$415$	26.2796	1.29001
$416$	0.974130	0.0477606
$417$	−15.7873	−0.773105
$418$	9.71474	0.475164
$419$	9.58791	0.468400	0.234200	−	0.972188i	$-0.424753\pi$
$419$	9.58791	0.468400	0.234200	+	0.972188i	$0.424753\pi$
$420$	−6.50115	−0.317224
$421$	38.7122	1.88671	0.943357	−	0.331778i	$-0.107649\pi$
$421$	38.7122	1.88671	0.943357	+	0.331778i	$0.107649\pi$
$422$	5.23720	0.254943
$423$	16.3418	0.794566
$424$	18.0388	0.876043
$425$	−6.88047	−0.333752
$426$	7.56689	0.366617
$427$	−4.67180	−0.226084
$428$	10.6536	0.514960
$429$	−3.16152	−0.152639
$430$	0	0
$431$	−39.7032	−1.91243	−0.956217	−	0.292659i	$-0.905460\pi$
$431$	−39.7032	−1.91243	−0.956217	+	0.292659i	$0.905460\pi$
$432$	−16.9965	−0.817746
$433$	−22.5695	−1.08462	−0.542311	−	0.840178i	$-0.682451\pi$
$433$	−22.5695	−1.08462	−0.542311	+	0.840178i	$0.682451\pi$
$434$	0.501862	0.0240902
$435$	−1.79822	−0.0862182
$436$	−4.93307	−0.236251
$437$	4.49715	0.215128
$438$	27.5812	1.31788
$439$	−40.5553	−1.93560	−0.967801	−	0.251718i	$-0.919004\pi$
$439$	−40.5553	−1.93560	−0.967801	+	0.251718i	$0.919004\pi$
$440$	−36.5189	−1.74097
$441$	−38.3931	−1.82824
$442$	−0.969480	−0.0461135
$443$	17.2919	0.821561	0.410781	−	0.911734i	$-0.365256\pi$
$443$	17.2919	0.821561	0.410781	+	0.911734i	$0.365256\pi$
$444$	29.6231	1.40585
$445$	13.0354	0.617937
$446$	13.9223	0.659242
$447$	13.2362	0.626049
$448$	−7.87654	−0.372132
$449$	3.93060	0.185497	0.0927483	−	0.995690i	$-0.470435\pi$
$449$	3.93060	0.185497	0.0927483	+	0.995690i	$0.470435\pi$
$450$	11.8629	0.559221
$451$	−35.9480	−1.69273
$452$	10.6615	0.501476
$453$	61.4198	2.88575
$454$	3.37536	0.158414
$455$	0.573812	0.0269007
$456$	18.2936	0.856676
$457$	17.4814	0.817747	0.408873	−	0.912591i	$-0.365922\pi$
$457$	17.4814	0.817747	0.408873	+	0.912591i	$0.365922\pi$
$458$	−5.60648	−0.261974
$459$	−41.1949	−1.92281
$460$	−4.96160	−0.231336
$461$	−28.8299	−1.34274	−0.671371	−	0.741121i	$-0.734294\pi$
$461$	−28.8299	−1.34274	−0.671371	+	0.741121i	$0.734294\pi$
$462$	15.0158	0.698600
$463$	−30.9980	−1.44060	−0.720299	−	0.693664i	$-0.755995\pi$
$463$	−30.9980	−1.44060	−0.720299	+	0.693664i	$0.755995\pi$
$464$	−0.373421	−0.0173356
$465$	3.73598	0.173252
$466$	18.9532	0.877991
$467$	8.35064	0.386422	0.193211	−	0.981157i	$-0.438110\pi$
$467$	8.35064	0.386422	0.193211	+	0.981157i	$0.438110\pi$
$468$	−1.18780	−0.0549063
$469$	−12.4487	−0.574827
$470$	−7.19310	−0.331793
$471$	21.5412	0.992566
$472$	−10.2938	−0.473812
$473$	0	0
$474$	−47.9792	−2.20376
$475$	−3.36323	−0.154315
$476$	−3.27211	−0.149977
$477$	−37.5357	−1.71864
$478$	6.04076	0.276298
$479$	−23.0351	−1.05250	−0.526251	−	0.850329i	$-0.676403\pi$
$479$	−23.0351	−1.05250	−0.526251	+	0.850329i	$0.676403\pi$
$480$	−34.4422	−1.57207
$481$	−2.61463	−0.119217
$482$	22.1087	1.00702
$483$	6.95114	0.316288
$484$	−8.45265	−0.384211
$485$	−42.7955	−1.94324
$486$	7.78415	0.353096
$487$	16.3284	0.739910	0.369955	−	0.929050i	$-0.379373\pi$
$487$	16.3284	0.739910	0.369955	+	0.929050i	$0.379373\pi$
$488$	−14.5037	−0.656550
$489$	21.1047	0.954388
$490$	16.8993	0.763434
$491$	−28.9800	−1.30785	−0.653925	−	0.756559i	$-0.726879\pi$
$491$	−28.9800	−1.30785	−0.653925	+	0.756559i	$0.726879\pi$
$492$	−19.8674	−0.895691
$493$	−0.905068	−0.0407622
$494$	−0.473889	−0.0213213
$495$	75.9895	3.41547
$496$	0.775818	0.0348353
$497$	−2.25416	−0.101113
$498$	−33.5463	−1.50324
$499$	−1.08708	−0.0486642	−0.0243321	−	0.999704i	$-0.507746\pi$
$499$	−1.08708	−0.0486642	−0.0243321	+	0.999704i	$0.507746\pi$
$500$	−7.06023	−0.315743
$501$	−57.7566	−2.58037
$502$	−7.31807	−0.326622
$503$	10.5159	0.468883	0.234441	−	0.972130i	$-0.424674\pi$
$503$	10.5159	0.468883	0.234441	+	0.972130i	$0.424674\pi$
$504$	19.2221	0.856221
$505$	13.9362	0.620152
$506$	11.4599	0.509455
$507$	−39.6378	−1.76038
$508$	13.9194	0.617574
$509$	2.01653	0.0893809	0.0446905	−	0.999001i	$-0.485770\pi$
$509$	2.01653	0.0893809	0.0446905	+	0.999001i	$0.485770\pi$
$510$	34.2778	1.51785
$511$	−8.21641	−0.363472
$512$	−17.2415	−0.761973
$513$	−20.1363	−0.889041
$514$	17.1581	0.756811
$515$	−8.65969	−0.381591
$516$	0	0
$517$	−11.8062	−0.519236
$518$	12.4184	0.545632
$519$	35.8290	1.57272
$520$	1.78140	0.0781197
$521$	37.7802	1.65518	0.827590	−	0.561333i	$-0.189711\pi$
$521$	37.7802	1.65518	0.827590	+	0.561333i	$0.189711\pi$
$522$	1.56046	0.0682995
$523$	−24.2078	−1.05853	−0.529267	−	0.848455i	$-0.677533\pi$
$523$	−24.2078	−1.05853	−0.529267	+	0.848455i	$0.677533\pi$
$524$	−3.63042	−0.158596
$525$	−5.19846	−0.226879
$526$	13.1734	0.574387
$527$	1.88037	0.0819100
$528$	23.2127	1.01020
$529$	−17.6950	−0.769347
$530$	16.5219	0.717666
$531$	21.4197	0.929536
$532$	−1.59943	−0.0693441
$533$	1.75356	0.0759550
$534$	−16.6399	−0.720078
$535$	33.2467	1.43738
$536$	−38.6471	−1.66930
$537$	52.6345	2.27135
$538$	−29.1365	−1.25616
$539$	27.7373	1.19473
$540$	22.2160	0.956022
$541$	−6.10175	−0.262335	−0.131167	−	0.991360i	$-0.541873\pi$
$541$	−6.10175	−0.262335	−0.131167	+	0.991360i	$0.541873\pi$
$542$	−14.3502	−0.616394
$543$	3.92313	0.168358
$544$	−17.3352	−0.743240
$545$	−15.3947	−0.659435
$546$	−0.732479	−0.0313472
$547$	−17.8123	−0.761600	−0.380800	−	0.924657i	$-0.624351\pi$
$547$	−17.8123	−0.761600	−0.380800	+	0.924657i	$0.624351\pi$
$548$	12.2388	0.522816
$549$	30.1796	1.28804
$550$	−8.57038	−0.365442
$551$	−0.442404	−0.0188470
$552$	21.5799	0.918501
$553$	14.2929	0.607797
$554$	−8.28307	−0.351914
$555$	92.4452	3.92408
$556$	4.28515	0.181731
$557$	−12.1364	−0.514238	−0.257119	−	0.966380i	$-0.582773\pi$
$557$	−12.1364	−0.514238	−0.257119	+	0.966380i	$0.582773\pi$
$558$	−3.24201	−0.137245
$559$	0	0
$560$	−4.21307	−0.178035
$561$	56.2610	2.37534
$562$	2.76020	0.116432
$563$	6.78970	0.286152	0.143076	−	0.989712i	$-0.454301\pi$
$563$	6.78970	0.286152	0.143076	+	0.989712i	$0.454301\pi$
$564$	−6.52494	−0.274749
$565$	33.2715	1.39974
$566$	25.6659	1.07882
$567$	−12.2848	−0.515911
$568$	−6.99808	−0.293633
$569$	23.8382	0.999350	0.499675	−	0.866213i	$-0.333453\pi$
$569$	23.8382	0.999350	0.499675	+	0.866213i	$0.333453\pi$
$570$	16.7552	0.701800
$571$	−16.8133	−0.703616	−0.351808	−	0.936072i	$-0.614433\pi$
$571$	−16.8133	−0.703616	−0.351808	+	0.936072i	$0.614433\pi$
$572$	0.858134	0.0358804
$573$	−57.1373	−2.38694
$574$	−8.32865	−0.347631
$575$	−3.96740	−0.165452
$576$	50.8821	2.12009
$577$	−13.5990	−0.566134	−0.283067	−	0.959100i	$-0.591352\pi$
$577$	−13.5990	−0.566134	−0.283067	+	0.959100i	$0.591352\pi$
$578$	−1.12934	−0.0469743
$579$	23.8604	0.991606
$580$	0.488094	0.0202670
$581$	9.99337	0.414595
$582$	54.6290	2.26445
$583$	27.1178	1.12311
$584$	−25.5079	−1.05553
$585$	−3.70680	−0.153257
$586$	−29.7675	−1.22968
$587$	21.2806	0.878346	0.439173	−	0.898403i	$-0.355272\pi$
$587$	21.2806	0.878346	0.439173	+	0.898403i	$0.355272\pi$
$588$	15.3296	0.632180
$589$	0.919137	0.0378724
$590$	−9.42821	−0.388153
$591$	−19.9679	−0.821369
$592$	19.1973	0.789003
$593$	19.3470	0.794487	0.397244	−	0.917713i	$-0.369967\pi$
$593$	19.3470	0.794487	0.397244	+	0.917713i	$0.369967\pi$
$594$	−51.3127	−2.10538
$595$	−10.2113	−0.418623
$596$	−3.59270	−0.147163
$597$	−38.1600	−1.56178
$598$	−0.559019	−0.0228600
$599$	−18.0395	−0.737075	−0.368537	−	0.929613i	$-0.620141\pi$
$599$	−18.0395	−0.737075	−0.368537	+	0.929613i	$0.620141\pi$
$600$	−16.1387	−0.658858
$601$	47.8912	1.95352	0.976762	−	0.214328i	$-0.0687562\pi$
$601$	47.8912	1.95352	0.976762	+	0.214328i	$0.0687562\pi$
$602$	0	0
$603$	80.4180	3.27487
$604$	−16.6712	−0.678343
$605$	−26.3783	−1.07243
$606$	−17.7897	−0.722659
$607$	24.3008	0.986338	0.493169	−	0.869934i	$-0.335838\pi$
$607$	24.3008	0.986338	0.493169	+	0.869934i	$0.335838\pi$
$608$	−8.47357	−0.343649
$609$	−0.683813	−0.0277095
$610$	−13.2840	−0.537854
$611$	0.575911	0.0232989
$612$	21.1377	0.854440
$613$	32.4494	1.31062	0.655310	−	0.755360i	$-0.272538\pi$
$613$	32.4494	1.31062	0.655310	+	0.755360i	$0.272538\pi$
$614$	19.8728	0.802001
$615$	−62.0004	−2.50010
$616$	−13.8871	−0.559526
$617$	−27.8423	−1.12089	−0.560445	−	0.828192i	$-0.689370\pi$
$617$	−27.8423	−1.12089	−0.560445	+	0.828192i	$0.689370\pi$
$618$	11.0542	0.444666
$619$	27.2945	1.09706	0.548528	−	0.836132i	$-0.315188\pi$
$619$	27.2945	1.09706	0.548528	+	0.836132i	$0.315188\pi$
$620$	−1.01406	−0.0407257
$621$	−23.7537	−0.953202
$622$	−21.8646	−0.876689
$623$	4.95699	0.198598
$624$	−1.13232	−0.0453292
$625$	−30.6455	−1.22582
$626$	−10.5456	−0.421489
$627$	27.5008	1.09828
$628$	−5.84695	−0.233319
$629$	46.5288	1.85523
$630$	17.6057	0.701427
$631$	31.5792	1.25715	0.628574	−	0.777749i	$-0.283639\pi$
$631$	31.5792	1.25715	0.628574	+	0.777749i	$0.283639\pi$
$632$	44.3725	1.76504
$633$	14.8256	0.589265
$634$	−21.3402	−0.847526
$635$	43.4385	1.72380
$636$	14.9872	0.594281
$637$	−1.35303	−0.0536092
$638$	−1.12736	−0.0446326
$639$	14.5618	0.576056
$640$	0.107923	0.00426603
$641$	−5.27969	−0.208535	−0.104268	−	0.994549i	$-0.533250\pi$
$641$	−5.27969	−0.208535	−0.104268	+	0.994549i	$0.533250\pi$
$642$	−42.4399	−1.67497
$643$	14.6074	0.576061	0.288031	−	0.957621i	$-0.407000\pi$
$643$	14.6074	0.576061	0.288031	+	0.957621i	$0.407000\pi$
$644$	−1.88675	−0.0743486
$645$	0	0
$646$	8.43312	0.331797
$647$	14.3624	0.564644	0.282322	−	0.959320i	$-0.408895\pi$
$647$	14.3624	0.564644	0.282322	+	0.959320i	$0.408895\pi$
$648$	−38.1381	−1.49821
$649$	−15.4747	−0.607436
$650$	0.418066	0.0163979
$651$	1.42069	0.0556811
$652$	−5.72847	−0.224344
$653$	−14.7070	−0.575531	−0.287766	−	0.957701i	$-0.592912\pi$
$653$	−14.7070	−0.575531	−0.287766	+	0.957701i	$0.592912\pi$
$654$	19.6515	0.768435
$655$	−11.3295	−0.442680
$656$	−12.8751	−0.502687
$657$	53.0776	2.07075
$658$	−2.73533	−0.106634
$659$	38.9417	1.51695	0.758476	−	0.651701i	$-0.225944\pi$
$659$	38.9417	1.51695	0.758476	+	0.651701i	$0.225944\pi$
$660$	−30.3410	−1.18102
$661$	11.2000	0.435629	0.217815	−	0.975990i	$-0.430107\pi$
$661$	11.2000	0.435629	0.217815	+	0.975990i	$0.430107\pi$
$662$	−15.0565	−0.585186
$663$	−2.74443	−0.106585
$664$	31.0245	1.20399
$665$	−4.99136	−0.193557
$666$	−80.2221	−3.10854
$667$	−0.521878	−0.0202072
$668$	15.6769	0.606559
$669$	39.4118	1.52375
$670$	−35.3972	−1.36751
$671$	−21.8034	−0.841710
$672$	−13.0974	−0.505243
$673$	−22.5219	−0.868157	−0.434079	−	0.900875i	$-0.642926\pi$
$673$	−22.5219	−0.868157	−0.434079	+	0.900875i	$0.642926\pi$
$674$	−16.6831	−0.642608
$675$	17.7643	0.683750
$676$	10.7589	0.413805
$677$	10.0434	0.386000	0.193000	−	0.981199i	$-0.438178\pi$
$677$	10.0434	0.386000	0.193000	+	0.981199i	$0.438178\pi$
$678$	−42.4716	−1.63111
$679$	−16.2739	−0.624534
$680$	−31.7011	−1.21568
$681$	9.55508	0.366151
$682$	2.34220	0.0896875
$683$	31.6971	1.21286	0.606428	−	0.795139i	$-0.292602\pi$
$683$	31.6971	1.21286	0.606428	+	0.795139i	$0.292602\pi$
$684$	10.3322	0.395063
$685$	38.1938	1.45931
$686$	13.8890	0.530286
$687$	−15.8710	−0.605517
$688$	0	0
$689$	−1.32282	−0.0503953
$690$	19.7652	0.752448
$691$	−15.7326	−0.598495	−0.299247	−	0.954176i	$-0.596736\pi$
$691$	−15.7326	−0.598495	−0.299247	+	0.954176i	$0.596736\pi$
$692$	−9.72509	−0.369692
$693$	28.8966	1.09769
$694$	−21.8113	−0.827945
$695$	13.3727	0.507256
$696$	−2.12290	−0.0804685
$697$	−31.2056	−1.18200
$698$	−30.5856	−1.15768
$699$	53.6533	2.02936
$700$	1.41102	0.0533316
$701$	8.04169	0.303731	0.151865	−	0.988401i	$-0.451472\pi$
$701$	8.04169	0.303731	0.151865	+	0.988401i	$0.451472\pi$
$702$	2.50305	0.0944716
$703$	22.7436	0.857792
$704$	−36.7600	−1.38544
$705$	−20.3624	−0.766894
$706$	5.66231	0.213104
$707$	5.29953	0.199309
$708$	−8.55242	−0.321420
$709$	21.8569	0.820853	0.410426	−	0.911894i	$-0.365380\pi$
$709$	21.8569	0.820853	0.410426	+	0.911894i	$0.365380\pi$
$710$	−6.40960	−0.240548
$711$	−92.3316	−3.46271
$712$	15.3890	0.576728
$713$	1.08425	0.0406056
$714$	13.0349	0.487818
$715$	2.67799	0.100151
$716$	−14.2866	−0.533917
$717$	17.1004	0.638625
$718$	−25.6595	−0.957606
$719$	18.4136	0.686710	0.343355	−	0.939206i	$-0.388437\pi$
$719$	18.4136	0.686710	0.343355	+	0.939206i	$0.388437\pi$
$720$	27.2162	1.01429
$721$	−3.29303	−0.122639
$722$	−16.4222	−0.611170
$723$	62.5858	2.32759
$724$	−1.06486	−0.0395752
$725$	0.390290	0.0144950
$726$	33.6722	1.24969
$727$	−37.4773	−1.38996	−0.694979	−	0.719030i	$-0.744586\pi$
$727$	−37.4773	−1.38996	−0.694979	+	0.719030i	$0.744586\pi$
$728$	0.677417	0.0251067
$729$	−15.3434	−0.568275
$730$	−23.3629	−0.864700
$731$	0	0
$732$	−12.0501	−0.445384
$733$	−18.9603	−0.700315	−0.350158	−	0.936691i	$-0.613872\pi$
$733$	−18.9603	−0.700315	−0.350158	+	0.936691i	$0.613872\pi$
$734$	4.94612	0.182564
$735$	47.8391	1.76457
$736$	−9.99578	−0.368449
$737$	−58.0982	−2.14008
$738$	53.8027	1.98050
$739$	16.1459	0.593938	0.296969	−	0.954887i	$-0.404024\pi$
$739$	16.1459	0.593938	0.296969	+	0.954887i	$0.404024\pi$
$740$	−25.0925	−0.922419
$741$	−1.34150	−0.0492812
$742$	6.28281	0.230649
$743$	−35.8243	−1.31427	−0.657133	−	0.753775i	$-0.728231\pi$
$743$	−35.8243	−1.31427	−0.657133	+	0.753775i	$0.728231\pi$
$744$	4.41054	0.161698
$745$	−11.2118	−0.410768
$746$	3.96584	0.145200
$747$	−64.5568	−2.36201
$748$	−15.2710	−0.558362
$749$	12.6428	0.461957
$750$	28.1254	1.02699
$751$	3.57779	0.130555	0.0652777	−	0.997867i	$-0.479207\pi$
$751$	3.57779	0.130555	0.0652777	+	0.997867i	$0.479207\pi$
$752$	−4.22849	−0.154197
$753$	−20.7162	−0.754941
$754$	0.0549931	0.00200273
$755$	−52.0261	−1.89342
$756$	8.44809	0.307254
$757$	−39.0616	−1.41972	−0.709858	−	0.704345i	$-0.751241\pi$
$757$	−39.0616	−1.41972	−0.709858	+	0.704345i	$0.751241\pi$
$758$	23.8060	0.864672
$759$	32.4411	1.17754
$760$	−15.4957	−0.562089
$761$	−34.4953	−1.25045	−0.625227	−	0.780443i	$-0.714994\pi$
$761$	−34.4953	−1.25045	−0.625227	+	0.780443i	$0.714994\pi$
$762$	−55.4498	−2.00874
$763$	−5.85415	−0.211935
$764$	15.5088	0.561090
$765$	65.9646	2.38495
$766$	1.33270	0.0481523
$767$	0.754864	0.0272565
$768$	−49.0434	−1.76970
$769$	37.8009	1.36314	0.681568	−	0.731754i	$-0.261298\pi$
$769$	37.8009	1.36314	0.681568	+	0.731754i	$0.261298\pi$
$770$	−12.7193	−0.458371
$771$	48.5716	1.74926
$772$	−6.47647	−0.233093
$773$	−28.1539	−1.01262	−0.506312	−	0.862350i	$-0.668992\pi$
$773$	−28.1539	−1.01262	−0.506312	+	0.862350i	$0.668992\pi$
$774$	0	0
$775$	−0.810865	−0.0291271
$776$	−50.5225	−1.81365
$777$	35.1543	1.26115
$778$	−0.461172	−0.0165338
$779$	−15.2535	−0.546514
$780$	1.48004	0.0529941
$781$	−10.5202	−0.376443
$782$	9.94807	0.355742
$783$	2.33675	0.0835086
$784$	9.93432	0.354797
$785$	−18.2466	−0.651251
$786$	14.4623	0.515852
$787$	−34.2719	−1.22166	−0.610830	−	0.791761i	$-0.709164\pi$
$787$	−34.2719	−1.22166	−0.610830	+	0.791761i	$0.709164\pi$
$788$	5.41991	0.193076
$789$	37.2916	1.32762
$790$	40.6412	1.44595
$791$	12.6522	0.449861
$792$	89.7099	3.18770
$793$	1.06358	0.0377687
$794$	32.7899	1.16367
$795$	46.7708	1.65879
$796$	10.3578	0.367123
$797$	−14.6068	−0.517400	−0.258700	−	0.965958i	$-0.583294\pi$
$797$	−14.6068	−0.517400	−0.258700	+	0.965958i	$0.583294\pi$
$798$	6.37154	0.225550
$799$	−10.2487	−0.362572
$800$	7.47541	0.264296
$801$	−32.0219	−1.13144
$802$	−28.7304	−1.01450
$803$	−38.3461	−1.35320
$804$	−32.1092	−1.13240
$805$	−5.88802	−0.207525
$806$	−0.114253	−0.00402441
$807$	−82.4804	−2.90345
$808$	16.4525	0.578796
$809$	33.6149	1.18184	0.590919	−	0.806731i	$-0.298765\pi$
$809$	33.6149	1.18184	0.590919	+	0.806731i	$0.298765\pi$
$810$	−34.9310	−1.22735
$811$	−3.35930	−0.117961	−0.0589805	−	0.998259i	$-0.518785\pi$
$811$	−3.35930	−0.117961	−0.0589805	+	0.998259i	$0.518785\pi$
$812$	0.185608	0.00651356
$813$	−40.6230	−1.42471
$814$	57.9567	2.03138
$815$	−17.8769	−0.626201
$816$	20.1503	0.705402
$817$	0	0
$818$	−8.18093	−0.286040
$819$	−1.40959	−0.0492550
$820$	16.8288	0.587689
$821$	−8.16708	−0.285033	−0.142517	−	0.989792i	$-0.545519\pi$
$821$	−8.16708	−0.285033	−0.142517	+	0.989792i	$0.545519\pi$
$822$	−48.7549	−1.70052
$823$	50.5759	1.76297	0.881483	−	0.472216i	$-0.156546\pi$
$823$	50.5759	1.76297	0.881483	+	0.472216i	$0.156546\pi$
$824$	−10.2233	−0.356144
$825$	−24.2613	−0.844669
$826$	−3.58528	−0.124748
$827$	−27.9755	−0.972805	−0.486402	−	0.873735i	$-0.661691\pi$
$827$	−27.9755	−0.972805	−0.486402	+	0.873735i	$0.661691\pi$
$828$	12.1884	0.423574
$829$	39.6472	1.37700	0.688502	−	0.725234i	$-0.258268\pi$
$829$	39.6472	1.37700	0.688502	+	0.725234i	$0.258268\pi$
$830$	28.4156	0.986321
$831$	−23.4480	−0.813401
$832$	1.79317	0.0621668
$833$	24.0780	0.834254
$834$	−17.0705	−0.591102
$835$	48.9232	1.69306
$836$	−7.46457	−0.258167
$837$	−4.85482	−0.167807
$838$	10.3672	0.358130
$839$	−27.8807	−0.962549	−0.481274	−	0.876570i	$-0.659826\pi$
$839$	−27.8807	−0.962549	−0.481274	+	0.876570i	$0.659826\pi$
$840$	−23.9514	−0.826401
$841$	−28.9487	−0.998230
$842$	41.8587	1.44255
$843$	7.81366	0.269117
$844$	−4.02413	−0.138516
$845$	33.5755	1.15503
$846$	17.6701	0.607511
$847$	−10.0309	−0.344666
$848$	9.71246	0.333527
$849$	72.6559	2.49354
$850$	−7.43973	−0.255181
$851$	26.8293	0.919698
$852$	−5.81421	−0.199192
$853$	−2.72468	−0.0932912	−0.0466456	−	0.998912i	$-0.514853\pi$
$853$	−2.72468	−0.0932912	−0.0466456	+	0.998912i	$0.514853\pi$
$854$	−5.05153	−0.172860
$855$	32.2440	1.10272
$856$	39.2496	1.34152
$857$	−56.9502	−1.94538	−0.972690	−	0.232108i	$-0.925438\pi$
$857$	−56.9502	−1.94538	−0.972690	+	0.232108i	$0.925438\pi$
$858$	−3.41849	−0.116705
$859$	17.8672	0.609621	0.304810	−	0.952413i	$-0.401407\pi$
$859$	17.8672	0.609621	0.304810	+	0.952413i	$0.401407\pi$
$860$	0	0
$861$	−23.5770	−0.803501
$862$	−42.9303	−1.46221
$863$	12.1428	0.413346	0.206673	−	0.978410i	$-0.433736\pi$
$863$	12.1428	0.413346	0.206673	+	0.978410i	$0.433736\pi$
$864$	44.7569	1.52266
$865$	−30.3492	−1.03190
$866$	−24.4040	−0.829282
$867$	−3.19697	−0.108575
$868$	−0.385619	−0.0130887
$869$	66.7053	2.26282
$870$	−1.94439	−0.0659208
$871$	2.83406	0.0960283
$872$	−18.1743	−0.615459
$873$	105.129	3.55806
$874$	4.86269	0.164483
$875$	−8.37850	−0.283245
$876$	−21.1927	−0.716037
$877$	−36.3990	−1.22911	−0.614553	−	0.788876i	$-0.710663\pi$
$877$	−36.3990	−1.22911	−0.614553	+	0.788876i	$0.710663\pi$
$878$	−43.8518	−1.47993
$879$	−84.2666	−2.84224
$880$	−19.6625	−0.662822
$881$	−44.9915	−1.51580	−0.757901	−	0.652369i	$-0.773775\pi$
$881$	−44.9915	−1.51580	−0.757901	+	0.652369i	$0.773775\pi$
$882$	−41.5138	−1.39784
$883$	−27.6040	−0.928950	−0.464475	−	0.885586i	$-0.653757\pi$
$883$	−27.6040	−0.928950	−0.464475	+	0.885586i	$0.653757\pi$
$884$	0.744924	0.0250545
$885$	−26.6896	−0.897163
$886$	18.6974	0.628150
$887$	−32.7789	−1.10061	−0.550304	−	0.834964i	$-0.685488\pi$
$887$	−32.7789	−1.10061	−0.550304	+	0.834964i	$0.685488\pi$
$888$	109.137	3.66239
$889$	16.5184	0.554010
$890$	14.0949	0.472463
$891$	−57.3331	−1.92073
$892$	−10.6976	−0.358181
$893$	−5.00962	−0.167641
$894$	14.3120	0.478665
$895$	−44.5845	−1.49030
$896$	0.0410400	0.00137105
$897$	−1.58249	−0.0528377
$898$	4.25009	0.141827
$899$	−0.106662	−0.00355739
$900$	−9.11514	−0.303838
$901$	23.5403	0.784241
$902$	−38.8699	−1.29423
$903$	0	0
$904$	39.2789	1.30640
$905$	−3.32312	−0.110464
$906$	66.4121	2.20639
$907$	42.7768	1.42038	0.710191	−	0.704010i	$-0.248609\pi$
$907$	42.7768	1.42038	0.710191	+	0.704010i	$0.248609\pi$
$908$	−2.59355	−0.0860698
$909$	−34.2348	−1.13550
$910$	0.620452	0.0205678
$911$	−29.8027	−0.987408	−0.493704	−	0.869630i	$-0.664357\pi$
$911$	−29.8027	−0.987408	−0.493704	+	0.869630i	$0.664357\pi$
$912$	9.84962	0.326154
$913$	46.6392	1.54353
$914$	18.9024	0.625234
$915$	−37.6048	−1.24318
$916$	4.30788	0.142336
$917$	−4.30828	−0.142272
$918$	−44.5432	−1.47015
$919$	−36.8550	−1.21573	−0.607866	−	0.794039i	$-0.707974\pi$
$919$	−36.8550	−1.21573	−0.607866	+	0.794039i	$0.707974\pi$
$920$	−18.2794	−0.602654
$921$	56.2565	1.85372
$922$	−31.1733	−1.02664
$923$	0.513180	0.0168915
$924$	−11.5378	−0.379566
$925$	−20.0645	−0.659717
$926$	−33.5175	−1.10145
$927$	21.2728	0.698691
$928$	0.983327	0.0322793
$929$	−31.0932	−1.02014	−0.510068	−	0.860134i	$-0.670380\pi$
$929$	−31.0932	−1.02014	−0.510068	+	0.860134i	$0.670380\pi$
$930$	4.03965	0.132465
$931$	11.7695	0.385730
$932$	−14.5632	−0.477033
$933$	−61.8949	−2.02635
$934$	9.02940	0.295451
$935$	−47.6563	−1.55853
$936$	−4.37608	−0.143037
$937$	−35.6318	−1.16404	−0.582020	−	0.813174i	$-0.697738\pi$
$937$	−35.6318	−1.16404	−0.582020	+	0.813174i	$0.697738\pi$
$938$	−13.4605	−0.439502
$939$	−29.8529	−0.974213
$940$	5.52700	0.180271
$941$	18.2470	0.594836	0.297418	−	0.954747i	$-0.403875\pi$
$941$	18.2470	0.594836	0.297418	+	0.954747i	$0.403875\pi$
$942$	23.2921	0.758898
$943$	−17.9937	−0.585955
$944$	−5.54240	−0.180390
$945$	26.3641	0.857623
$946$	0	0
$947$	−1.69966	−0.0552316	−0.0276158	−	0.999619i	$-0.508792\pi$
$947$	−1.69966	−0.0552316	−0.0276158	+	0.999619i	$0.508792\pi$
$948$	36.8660	1.19735
$949$	1.87054	0.0607202
$950$	−3.63659	−0.117987
$951$	−60.4103	−1.95894
$952$	−12.0550	−0.390705
$953$	35.5925	1.15295	0.576477	−	0.817113i	$-0.304427\pi$
$953$	35.5925	1.15295	0.576477	+	0.817113i	$0.304427\pi$
$954$	−40.5867	−1.31404
$955$	48.3986	1.56614
$956$	−4.64157	−0.150119
$957$	−3.19136	−0.103162
$958$	−24.9075	−0.804724
$959$	14.5240	0.469005
$960$	−63.4008	−2.04625
$961$	−30.7784	−0.992852
$962$	−2.82715	−0.0911510
$963$	−81.6718	−2.63184
$964$	−16.9877	−0.547138
$965$	−20.2112	−0.650621
$966$	7.51614	0.241828
$967$	0.795474	0.0255807	0.0127904	−	0.999918i	$-0.495929\pi$
$967$	0.795474	0.0255807	0.0127904	+	0.999918i	$0.495929\pi$
$968$	−31.1410	−1.00091
$969$	23.8727	0.766903
$970$	−46.2739	−1.48577
$971$	28.1935	0.904774	0.452387	−	0.891822i	$-0.350573\pi$
$971$	28.1935	0.904774	0.452387	+	0.891822i	$0.350573\pi$
$972$	−5.98115	−0.191845
$973$	5.08526	0.163026
$974$	17.6556	0.565722
$975$	1.18347	0.0379015
$976$	−7.80905	−0.249962
$977$	0.284795	0.00911141	0.00455570	−	0.999990i	$-0.498550\pi$
$977$	0.284795	0.00911141	0.00455570	+	0.999990i	$0.498550\pi$
$978$	22.8201	0.729707
$979$	23.1343	0.739377
$980$	−12.9850	−0.414791
$981$	37.8176	1.20742
$982$	−31.3356	−0.999959
$983$	32.9099	1.04966	0.524832	−	0.851206i	$-0.324128\pi$
$983$	32.9099	1.04966	0.524832	+	0.851206i	$0.324128\pi$
$984$	−73.1950	−2.33337
$985$	16.9140	0.538924
$986$	−0.978633	−0.0311660
$987$	−7.74325	−0.246470
$988$	0.364124	0.0115843
$989$	0	0
$990$	82.1660	2.61141
$991$	13.8032	0.438473	0.219237	−	0.975672i	$-0.429643\pi$
$991$	13.8032	0.438473	0.219237	+	0.975672i	$0.429643\pi$
$992$	−2.04296	−0.0648639
$993$	−42.6223	−1.35258
$994$	−2.43739	−0.0773092
$995$	32.3237	1.02473
$996$	25.7761	0.816748
$997$	7.24936	0.229589	0.114795	−	0.993389i	$-0.463379\pi$
$997$	7.24936	0.229589	0.114795	+	0.993389i	$0.463379\pi$
$998$	−1.17544	−0.0372078
$999$	−120.130	−3.80076

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.2.a.m.1.7	yes	10
43.42	odd	2	inner	1849.2.a.m.1.4	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1849.2.a.m.1.4	✓	10	43.42	odd	2	inner
1849.2.a.m.1.7	yes	10	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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q+1.08128 q^{2} +3.06092 q^{3} -0.830830 q^{4} -2.59278 q^{5} +3.30972 q^{6} -0.985960 q^{7} -3.06092 q^{8} +6.36926 q^{9} +O(q^{10})\)	\(q+1.08128 q^{2} +3.06092 q^{3} -0.830830 q^{4} -2.59278 q^{5} +3.30972 q^{6} -0.985960 q^{7} -3.06092 q^{8} +6.36926 q^{9} -2.80353 q^{10} -4.60149 q^{11} -2.54311 q^{12} +0.224463 q^{13} -1.06610 q^{14} -7.93631 q^{15} -1.64806 q^{16} -3.99444 q^{17} +6.88696 q^{18} -1.95251 q^{19} +2.15416 q^{20} -3.01795 q^{21} -4.97551 q^{22} -2.30326 q^{23} -9.36926 q^{24} +1.72251 q^{25} +0.242707 q^{26} +10.3130 q^{27} +0.819165 q^{28} +0.226582 q^{29} -8.58138 q^{30} -0.470746 q^{31} +4.33983 q^{32} -14.0848 q^{33} -4.31912 q^{34} +2.55638 q^{35} -5.29177 q^{36} -11.6484 q^{37} -2.11121 q^{38} +0.687063 q^{39} +7.93631 q^{40} +7.81225 q^{41} -3.26325 q^{42} +3.82306 q^{44} -16.5141 q^{45} -2.49048 q^{46} +2.56573 q^{47} -5.04459 q^{48} -6.02788 q^{49} +1.86252 q^{50} -12.2267 q^{51} -0.186490 q^{52} -5.89326 q^{53} +11.1513 q^{54} +11.9307 q^{55} +3.01795 q^{56} -5.97649 q^{57} +0.244999 q^{58} +3.36298 q^{59} +6.59372 q^{60} +4.73833 q^{61} -0.509009 q^{62} -6.27984 q^{63} +7.98870 q^{64} -0.581982 q^{65} -15.2297 q^{66} +12.6260 q^{67} +3.31870 q^{68} -7.05012 q^{69} +2.76417 q^{70} +2.28626 q^{71} -19.4958 q^{72} +8.33340 q^{73} -12.5952 q^{74} +5.27248 q^{75} +1.62221 q^{76} +4.53689 q^{77} +0.742909 q^{78} -14.4964 q^{79} +4.27306 q^{80} +12.4597 q^{81} +8.44724 q^{82} -10.1357 q^{83} +2.50740 q^{84} +10.3567 q^{85} +0.693550 q^{87} +14.0848 q^{88} -5.02757 q^{89} -17.8564 q^{90} -0.221311 q^{91} +1.91362 q^{92} -1.44092 q^{93} +2.77428 q^{94} +5.06243 q^{95} +13.2839 q^{96} +16.5056 q^{97} -6.51784 q^{98} -29.3081 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{4} + 22 q^{6} + 14 q^{9}+O(q^{10}) \) 10 * q + 2 * q^4 + 22 * q^6 + 14 * q^9	\( 10 q + 2 q^{4} + 22 q^{6} + 14 q^{9} - 22 q^{10} - 10 q^{11} - 14 q^{13} - 22 q^{14} - 22 q^{15} - 26 q^{16} - 16 q^{17} - 44 q^{21} - 18 q^{23} - 44 q^{24} - 6 q^{25} - 2 q^{31} - 28 q^{36} - 22 q^{38} + 22 q^{40} - 2 q^{44} - 18 q^{47} + 18 q^{49} + 28 q^{52} + 2 q^{53} + 44 q^{56} - 22 q^{57} - 22 q^{58} + 14 q^{59} + 8 q^{64} - 22 q^{66} + 26 q^{67} + 32 q^{68} + 44 q^{74} - 44 q^{78} - 56 q^{79} + 2 q^{81} - 38 q^{83} - 22 q^{87} - 22 q^{90} - 74 q^{92} + 22 q^{96} + 34 q^{97} - 36 q^{99}+O(q^{100}) \) 10 * q + 2 * q^4 + 22 * q^6 + 14 * q^9 - 22 * q^10 - 10 * q^11 - 14 * q^13 - 22 * q^14 - 22 * q^15 - 26 * q^16 - 16 * q^17 - 44 * q^21 - 18 * q^23 - 44 * q^24 - 6 * q^25 - 2 * q^31 - 28 * q^36 - 22 * q^38 + 22 * q^40 - 2 * q^44 - 18 * q^47 + 18 * q^49 + 28 * q^52 + 2 * q^53 + 44 * q^56 - 22 * q^57 - 22 * q^58 + 14 * q^59 + 8 * q^64 - 22 * q^66 + 26 * q^67 + 32 * q^68 + 44 * q^74 - 44 * q^78 - 56 * q^79 + 2 * q^81 - 38 * q^83 - 22 * q^87 - 22 * q^90 - 74 * q^92 + 22 * q^96 + 34 * q^97 - 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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