LMFDB - Embedded newform 1859.2.a.s.1.17

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			1.17
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)

$f(q)$	$=$	$q+1.77144 q^{2} +2.92005 q^{3} +1.13800 q^{4} +2.22672 q^{5} +5.17269 q^{6} -0.178675 q^{7} -1.52699 q^{8} +5.52669 q^{9} +O(q^{10})$	\(q+1.77144 q^{2} +2.92005 q^{3} +1.13800 q^{4} +2.22672 q^{5} +5.17269 q^{6} -0.178675 q^{7} -1.52699 q^{8} +5.52669 q^{9} +3.94449 q^{10} -1.00000 q^{11} +3.32300 q^{12} -0.316511 q^{14} +6.50213 q^{15} -4.98096 q^{16} +6.50615 q^{17} +9.79020 q^{18} +0.965988 q^{19} +2.53399 q^{20} -0.521739 q^{21} -1.77144 q^{22} +0.589490 q^{23} -4.45888 q^{24} -0.0417290 q^{25} +7.37807 q^{27} -0.203331 q^{28} -3.89138 q^{29} +11.5181 q^{30} -10.3044 q^{31} -5.76948 q^{32} -2.92005 q^{33} +11.5252 q^{34} -0.397858 q^{35} +6.28935 q^{36} -10.2469 q^{37} +1.71119 q^{38} -3.40017 q^{40} +9.88582 q^{41} -0.924228 q^{42} -8.16609 q^{43} -1.13800 q^{44} +12.3064 q^{45} +1.04425 q^{46} +4.46747 q^{47} -14.5446 q^{48} -6.96808 q^{49} -0.0739203 q^{50} +18.9983 q^{51} +13.8672 q^{53} +13.0698 q^{54} -2.22672 q^{55} +0.272834 q^{56} +2.82073 q^{57} -6.89334 q^{58} +2.76812 q^{59} +7.39939 q^{60} +10.1417 q^{61} -18.2535 q^{62} -0.987480 q^{63} -0.258371 q^{64} -5.17269 q^{66} -6.80874 q^{67} +7.40397 q^{68} +1.72134 q^{69} -0.704781 q^{70} +3.55307 q^{71} -8.43920 q^{72} -3.73345 q^{73} -18.1518 q^{74} -0.121851 q^{75} +1.09929 q^{76} +0.178675 q^{77} +15.5728 q^{79} -11.0912 q^{80} +4.96425 q^{81} +17.5121 q^{82} -8.32835 q^{83} -0.593736 q^{84} +14.4874 q^{85} -14.4657 q^{86} -11.3630 q^{87} +1.52699 q^{88} -1.71654 q^{89} +21.8000 q^{90} +0.670837 q^{92} -30.0893 q^{93} +7.91384 q^{94} +2.15098 q^{95} -16.8472 q^{96} -15.2627 q^{97} -12.3435 q^{98} -5.52669 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.77144	1.25260	0.626298	−	0.779584i	$-0.284569\pi$
$2$	1.77144	1.25260	0.626298	+	0.779584i	$0.284569\pi$
$3$	2.92005	1.68589	0.842946	−	0.537998i	$-0.180819\pi$
$3$	2.92005	1.68589	0.842946	+	0.537998i	$0.180819\pi$
$4$	1.13800	0.568998
$5$	2.22672	0.995818	0.497909	−	0.867229i	$-0.334101\pi$
$5$	2.22672	0.995818	0.497909	+	0.867229i	$0.334101\pi$
$6$	5.17269	2.11174
$7$	−0.178675	−0.0675327	−0.0337663	−	0.999430i	$-0.510750\pi$
$7$	−0.178675	−0.0675327	−0.0337663	+	0.999430i	$0.510750\pi$
$8$	−1.52699	−0.539872
$9$	5.52669	1.84223
$10$	3.94449	1.24736
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	3.32300	0.959268
$13$	0	0
$13$	0	0
$14$	−0.316511	−0.0845912
$15$	6.50213	1.67884
$16$	−4.98096	−1.24524
$17$	6.50615	1.57797	0.788986	−	0.614411i	$-0.210606\pi$
$17$	6.50615	1.57797	0.788986	+	0.614411i	$0.210606\pi$
$18$	9.79020	2.30757
$19$	0.965988	0.221613	0.110806	−	0.993842i	$-0.464657\pi$
$19$	0.965988	0.221613	0.110806	+	0.993842i	$0.464657\pi$
$20$	2.53399	0.566618
$21$	−0.521739	−0.113853
$22$	−1.77144	−0.377672
$23$	0.589490	0.122917	0.0614586	−	0.998110i	$-0.480425\pi$
$23$	0.589490	0.122917	0.0614586	+	0.998110i	$0.480425\pi$
$24$	−4.45888	−0.910166
$25$	−0.0417290	−0.00834579
$26$	0	0
$27$	7.37807	1.41991
$28$	−0.203331	−0.0384259
$29$	−3.89138	−0.722611	−0.361306	−	0.932447i	$-0.617669\pi$
$29$	−3.89138	−0.722611	−0.361306	+	0.932447i	$0.617669\pi$
$30$	11.5181	2.10291
$31$	−10.3044	−1.85072	−0.925359	−	0.379091i	$-0.876237\pi$
$31$	−10.3044	−1.85072	−0.925359	+	0.379091i	$0.876237\pi$
$32$	−5.76948	−1.01991
$33$	−2.92005	−0.508315
$34$	11.5252	1.97656
$35$	−0.397858	−0.0672503
$36$	6.28935	1.04822
$37$	−10.2469	−1.68459	−0.842293	−	0.539019i	$-0.818795\pi$
$37$	−10.2469	−1.68459	−0.842293	+	0.539019i	$0.818795\pi$
$38$	1.71119	0.277591
$39$	0	0
$40$	−3.40017	−0.537615
$41$	9.88582	1.54391	0.771953	−	0.635680i	$-0.219280\pi$
$41$	9.88582	1.54391	0.771953	+	0.635680i	$0.219280\pi$
$42$	−0.924228	−0.142612
$43$	−8.16609	−1.24532	−0.622658	−	0.782494i	$-0.713947\pi$
$43$	−8.16609	−1.24532	−0.622658	+	0.782494i	$0.713947\pi$
$44$	−1.13800	−0.171559
$45$	12.3064	1.83453
$46$	1.04425	0.153966
$47$	4.46747	0.651647	0.325824	−	0.945431i	$-0.394358\pi$
$47$	4.46747	0.651647	0.325824	+	0.945431i	$0.394358\pi$
$48$	−14.5446	−2.09934
$49$	−6.96808	−0.995439
$50$	−0.0739203	−0.0104539
$51$	18.9983	2.66029
$52$	0	0
$53$	13.8672	1.90481	0.952404	−	0.304838i	$-0.0986022\pi$
$53$	13.8672	1.90481	0.952404	+	0.304838i	$0.0986022\pi$
$54$	13.0698	1.77857
$55$	−2.22672	−0.300251
$56$	0.272834	0.0364590
$57$	2.82073	0.373615
$58$	−6.89334	−0.905140
$59$	2.76812	0.360379	0.180189	−	0.983632i	$-0.442329\pi$
$59$	2.76812	0.360379	0.180189	+	0.983632i	$0.442329\pi$
$60$	7.39939	0.955257
$61$	10.1417	1.29851	0.649255	−	0.760571i	$-0.275081\pi$
$61$	10.1417	1.29851	0.649255	+	0.760571i	$0.275081\pi$
$62$	−18.2535	−2.31820
$63$	−0.987480	−0.124411
$64$	−0.258371	−0.0322964
$65$	0	0
$66$	−5.17269	−0.636714
$67$	−6.80874	−0.831820	−0.415910	−	0.909406i	$-0.636537\pi$
$67$	−6.80874	−0.831820	−0.415910	+	0.909406i	$0.636537\pi$
$68$	7.40397	0.897863
$69$	1.72134	0.207225
$70$	−0.704781	−0.0842374
$71$	3.55307	0.421672	0.210836	−	0.977521i	$-0.432381\pi$
$71$	3.55307	0.421672	0.210836	+	0.977521i	$0.432381\pi$
$72$	−8.43920	−0.994569
$73$	−3.73345	−0.436968	−0.218484	−	0.975841i	$-0.570111\pi$
$73$	−3.73345	−0.436968	−0.218484	+	0.975841i	$0.570111\pi$
$74$	−18.1518	−2.11011
$75$	−0.121851	−0.0140701
$76$	1.09929	0.126097
$77$	0.178675	0.0203619
$78$	0	0
$79$	15.5728	1.75208	0.876039	−	0.482240i	$-0.160177\pi$
$79$	15.5728	1.75208	0.876039	+	0.482240i	$0.160177\pi$
$80$	−11.0912	−1.24003
$81$	4.96425	0.551583
$82$	17.5121	1.93389
$83$	−8.32835	−0.914155	−0.457078	−	0.889427i	$-0.651104\pi$
$83$	−8.32835	−0.914155	−0.457078	+	0.889427i	$0.651104\pi$
$84$	−0.593736	−0.0647819
$85$	14.4874	1.57137
$86$	−14.4657	−1.55988
$87$	−11.3630	−1.21824
$88$	1.52699	0.162778
$89$	−1.71654	−0.181953	−0.0909763	−	0.995853i	$-0.528999\pi$
$89$	−1.71654	−0.181953	−0.0909763	+	0.995853i	$0.528999\pi$
$90$	21.8000	2.29792
$91$	0	0
$92$	0.670837	0.0699396
$93$	−30.0893	−3.12011
$94$	7.91384	0.816251
$95$	2.15098	0.220686
$96$	−16.8472	−1.71946
$97$	−15.2627	−1.54970	−0.774848	−	0.632147i	$-0.782174\pi$
$97$	−15.2627	−1.54970	−0.774848	+	0.632147i	$0.782174\pi$
$98$	−12.3435	−1.24688
$99$	−5.52669	−0.555453
$100$	−0.0474873	−0.00474873
$101$	0.739323	0.0735654	0.0367827	−	0.999323i	$-0.488289\pi$
$101$	0.739323	0.0735654	0.0367827	+	0.999323i	$0.488289\pi$
$102$	33.6543	3.33227
$103$	2.71468	0.267486	0.133743	−	0.991016i	$-0.457300\pi$
$103$	2.71468	0.267486	0.133743	+	0.991016i	$0.457300\pi$
$104$	0	0
$105$	−1.16176	−0.113377
$106$	24.5649	2.38596
$107$	−10.3232	−0.997981	−0.498991	−	0.866607i	$-0.666296\pi$
$107$	−10.3232	−0.997981	−0.498991	+	0.866607i	$0.666296\pi$
$108$	8.39620	0.807925
$109$	−8.31422	−0.796358	−0.398179	−	0.917308i	$-0.630358\pi$
$109$	−8.31422	−0.796358	−0.398179	+	0.917308i	$0.630358\pi$
$110$	−3.94449	−0.376093
$111$	−29.9216	−2.84003
$112$	0.889971	0.0840943
$113$	10.3923	0.977626	0.488813	−	0.872389i	$-0.337430\pi$
$113$	10.3923	0.977626	0.488813	+	0.872389i	$0.337430\pi$
$114$	4.99676	0.467989
$115$	1.31263	0.122403
$116$	−4.42837	−0.411164
$117$	0	0
$118$	4.90356	0.451409
$119$	−1.16248	−0.106565
$120$	−9.92867	−0.906360
$121$	1.00000	0.0909091
$122$	17.9654	1.62651
$123$	28.8671	2.60286
$124$	−11.7263	−1.05305
$125$	−11.2265	−1.00413
$126$	−1.74926	−0.155836
$127$	−1.77339	−0.157363	−0.0786813	−	0.996900i	$-0.525071\pi$
$127$	−1.77339	−0.157363	−0.0786813	+	0.996900i	$0.525071\pi$
$128$	11.0813	0.979456
$129$	−23.8454	−2.09947
$130$	0	0
$131$	−18.0081	−1.57337	−0.786687	−	0.617353i	$-0.788205\pi$
$131$	−18.0081	−1.57337	−0.786687	+	0.617353i	$0.788205\pi$
$132$	−3.32300	−0.289230
$133$	−0.172598	−0.0149661
$134$	−12.0613	−1.04194
$135$	16.4289	1.41397
$136$	−9.93482	−0.851904
$137$	−0.668527	−0.0571161	−0.0285581	−	0.999592i	$-0.509092\pi$
$137$	−0.668527	−0.0571161	−0.0285581	+	0.999592i	$0.509092\pi$
$138$	3.04925	0.259569
$139$	−1.23457	−0.104715	−0.0523574	−	0.998628i	$-0.516674\pi$
$139$	−1.23457	−0.104715	−0.0523574	+	0.998628i	$0.516674\pi$
$140$	−0.452760	−0.0382652
$141$	13.0452	1.09861
$142$	6.29405	0.528185
$143$	0	0
$144$	−27.5282	−2.29402
$145$	−8.66501	−0.719590
$146$	−6.61359	−0.547344
$147$	−20.3471	−1.67820
$148$	−11.6610	−0.958526
$149$	15.1931	1.24467	0.622335	−	0.782751i	$-0.286184\pi$
$149$	15.1931	1.24467	0.622335	+	0.782751i	$0.286184\pi$
$150$	−0.215851	−0.0176242
$151$	−1.45184	−0.118149	−0.0590746	−	0.998254i	$-0.518815\pi$
$151$	−1.45184	−0.118149	−0.0590746	+	0.998254i	$0.518815\pi$
$152$	−1.47505	−0.119643
$153$	35.9575	2.90699
$154$	0.316511	0.0255052
$155$	−22.9449	−1.84298
$156$	0	0
$157$	9.41597	0.751476	0.375738	−	0.926726i	$-0.377389\pi$
$157$	9.41597	0.751476	0.375738	+	0.926726i	$0.377389\pi$
$158$	27.5863	2.19465
$159$	40.4930	3.21130
$160$	−12.8470	−1.01565
$161$	−0.105327	−0.00830092
$162$	8.79386	0.690911
$163$	−12.9318	−1.01290	−0.506449	−	0.862270i	$-0.669042\pi$
$163$	−12.9318	−1.01290	−0.506449	+	0.862270i	$0.669042\pi$
$164$	11.2500	0.878479
$165$	−6.50213	−0.506190
$166$	−14.7532	−1.14507
$167$	9.71696	0.751921	0.375961	−	0.926636i	$-0.377313\pi$
$167$	9.71696	0.751921	0.375961	+	0.926636i	$0.377313\pi$
$168$	0.796689	0.0614659
$169$	0	0
$170$	25.6635	1.96830
$171$	5.33872	0.408262
$172$	−9.29296	−0.708582
$173$	16.2905	1.23855	0.619274	−	0.785175i	$-0.287427\pi$
$173$	16.2905	1.23855	0.619274	+	0.785175i	$0.287427\pi$
$174$	−20.1289	−1.52597
$175$	0.00745591	0.000563613 0
$176$	4.98096	0.375454
$177$	8.08305	0.607559
$178$	−3.04074	−0.227913
$179$	1.71092	0.127880	0.0639402	−	0.997954i	$-0.479633\pi$
$179$	1.71092	0.127880	0.0639402	+	0.997954i	$0.479633\pi$
$180$	14.0046	1.04384
$181$	−5.69203	−0.423086	−0.211543	−	0.977369i	$-0.567849\pi$
$181$	−5.69203	−0.423086	−0.211543	+	0.977369i	$0.567849\pi$
$182$	0	0
$183$	29.6142	2.18915
$184$	−0.900145	−0.0663596
$185$	−22.8170	−1.67754
$186$	−53.3013	−3.90824
$187$	−6.50615	−0.475777
$188$	5.08396	0.370786
$189$	−1.31827	−0.0958903
$190$	3.81033	0.276431
$191$	−3.15825	−0.228523	−0.114261	−	0.993451i	$-0.536450\pi$
$191$	−3.15825	−0.228523	−0.114261	+	0.993451i	$0.536450\pi$
$192$	−0.754456	−0.0544482
$193$	−6.38389	−0.459523	−0.229761	−	0.973247i	$-0.573795\pi$
$193$	−6.38389	−0.459523	−0.229761	+	0.973247i	$0.573795\pi$
$194$	−27.0370	−1.94114
$195$	0	0
$196$	−7.92964	−0.566403
$197$	14.4147	1.02701	0.513504	−	0.858087i	$-0.328347\pi$
$197$	14.4147	1.02701	0.513504	+	0.858087i	$0.328347\pi$
$198$	−9.79020	−0.695759
$199$	7.92326	0.561665	0.280832	−	0.959757i	$-0.409389\pi$
$199$	7.92326	0.561665	0.280832	+	0.959757i	$0.409389\pi$
$200$	0.0637197	0.00450566
$201$	−19.8819	−1.40236
$202$	1.30967	0.0921478
$203$	0.695291	0.0487999
$204$	21.6200	1.51370
$205$	22.0129	1.53745
$206$	4.80889	0.335052
$207$	3.25793	0.226442
$208$	0	0
$209$	−0.965988	−0.0668188
$210$	−2.05800	−0.142015
$211$	−12.2684	−0.844591	−0.422295	−	0.906458i	$-0.638775\pi$
$211$	−12.2684	−0.844591	−0.422295	+	0.906458i	$0.638775\pi$
$212$	15.7808	1.08383
$213$	10.3752	0.710894
$214$	−18.2869	−1.25007
$215$	−18.1836	−1.24011
$216$	−11.2662	−0.766570
$217$	1.84113	0.124984
$218$	−14.7281	−0.997515
$219$	−10.9019	−0.736680
$220$	−2.53399	−0.170842
$221$	0	0
$222$	−53.0042	−3.55741
$223$	−16.1348	−1.08047	−0.540235	−	0.841514i	$-0.681664\pi$
$223$	−16.1348	−1.08047	−0.540235	+	0.841514i	$0.681664\pi$
$224$	1.03086	0.0688772
$225$	−0.230623	−0.0153749
$226$	18.4093	1.22457
$227$	5.35288	0.355283	0.177642	−	0.984095i	$-0.443153\pi$
$227$	5.35288	0.355283	0.177642	+	0.984095i	$0.443153\pi$
$228$	3.20998	0.212586
$229$	−0.166944	−0.0110320	−0.00551598	−	0.999985i	$-0.501756\pi$
$229$	−0.166944	−0.0110320	−0.00551598	+	0.999985i	$0.501756\pi$
$230$	2.32524	0.153322
$231$	0.521739	0.0343279
$232$	5.94210	0.390118
$233$	−7.12342	−0.466671	−0.233336	−	0.972396i	$-0.574964\pi$
$233$	−7.12342	−0.466671	−0.233336	+	0.972396i	$0.574964\pi$
$234$	0	0
$235$	9.94779	0.648922
$236$	3.15011	0.205055
$237$	45.4734	2.95381
$238$	−2.05927	−0.133483
$239$	−12.9333	−0.836584	−0.418292	−	0.908313i	$-0.637371\pi$
$239$	−12.9333	−0.836584	−0.418292	+	0.908313i	$0.637371\pi$
$240$	−32.3868	−2.09056
$241$	17.6998	1.14014	0.570071	−	0.821596i	$-0.306916\pi$
$241$	17.6998	1.14014	0.570071	+	0.821596i	$0.306916\pi$
$242$	1.77144	0.113872
$243$	−7.63835	−0.490000
$244$	11.5412	0.738849
$245$	−15.5159	−0.991277
$246$	51.1363	3.26033
$247$	0	0
$248$	15.7346	0.999151
$249$	−24.3192	−1.54117
$250$	−19.8871	−1.25777
$251$	15.7897	0.996637	0.498319	−	0.866994i	$-0.333951\pi$
$251$	15.7897	0.996637	0.498319	+	0.866994i	$0.333951\pi$
$252$	−1.12375	−0.0707894
$253$	−0.589490	−0.0370609
$254$	−3.14144	−0.197112
$255$	42.3038	2.64917
$256$	20.1465	1.25916
$257$	−13.9258	−0.868670	−0.434335	−	0.900751i	$-0.643017\pi$
$257$	−13.9258	−0.868670	−0.434335	+	0.900751i	$0.643017\pi$
$258$	−42.2406	−2.62979
$259$	1.83087	0.113765
$260$	0	0
$261$	−21.5065	−1.33122
$262$	−31.9002	−1.97080
$263$	1.71796	0.105934	0.0529669	−	0.998596i	$-0.483132\pi$
$263$	1.71796	0.105934	0.0529669	+	0.998596i	$0.483132\pi$
$264$	4.45888	0.274425
$265$	30.8784	1.89684
$266$	−0.305746	−0.0187465
$267$	−5.01238	−0.306753
$268$	−7.74832	−0.473304
$269$	18.1935	1.10928	0.554639	−	0.832091i	$-0.312857\pi$
$269$	18.1935	1.10928	0.554639	+	0.832091i	$0.312857\pi$
$270$	29.1027	1.77114
$271$	8.77796	0.533223	0.266612	−	0.963804i	$-0.414096\pi$
$271$	8.77796	0.533223	0.266612	+	0.963804i	$0.414096\pi$
$272$	−32.4069	−1.96495
$273$	0	0
$274$	−1.18425	−0.0715434
$275$	0.0417290	0.00251635
$276$	1.95888	0.117911
$277$	−8.60169	−0.516826	−0.258413	−	0.966035i	$-0.583199\pi$
$277$	−8.60169	−0.516826	−0.258413	+	0.966035i	$0.583199\pi$
$278$	−2.18697	−0.131165
$279$	−56.9490	−3.40945
$280$	0.607525	0.0363065
$281$	15.1370	0.903000	0.451500	−	0.892271i	$-0.350889\pi$
$281$	15.1370	0.903000	0.451500	+	0.892271i	$0.350889\pi$
$282$	23.1088	1.37611
$283$	13.4648	0.800400	0.400200	−	0.916428i	$-0.368941\pi$
$283$	13.4648	0.800400	0.400200	+	0.916428i	$0.368941\pi$
$284$	4.04338	0.239930
$285$	6.28098	0.372053
$286$	0	0
$287$	−1.76635	−0.104264
$288$	−31.8862	−1.87891
$289$	25.3300	1.49000
$290$	−15.3495	−0.901355
$291$	−44.5680	−2.61262
$292$	−4.24865	−0.248634
$293$	19.7772	1.15540	0.577698	−	0.816250i	$-0.303951\pi$
$293$	19.7772	1.15540	0.577698	+	0.816250i	$0.303951\pi$
$294$	−36.0437	−2.10211
$295$	6.16382	0.358872
$296$	15.6470	0.909461
$297$	−7.37807	−0.428119
$298$	26.9137	1.55907
$299$	0	0
$300$	−0.138665	−0.00800585
$301$	1.45907	0.0840995
$302$	−2.57185	−0.147993
$303$	2.15886	0.124023
$304$	−4.81154	−0.275961
$305$	22.5827	1.29308
$306$	63.6965	3.64129
$307$	30.0992	1.71785	0.858927	−	0.512099i	$-0.171132\pi$
$307$	30.0992	1.71785	0.858927	+	0.512099i	$0.171132\pi$
$308$	0.203331	0.0115858
$309$	7.92701	0.450952
$310$	−40.6455	−2.30851
$311$	−15.5528	−0.881919	−0.440960	−	0.897527i	$-0.645362\pi$
$311$	−15.5528	−0.881919	−0.440960	+	0.897527i	$0.645362\pi$
$312$	0	0
$313$	−32.6323	−1.84448	−0.922242	−	0.386613i	$-0.873645\pi$
$313$	−32.6323	−1.84448	−0.922242	+	0.386613i	$0.873645\pi$
$314$	16.6798	0.941296
$315$	−2.19884	−0.123890
$316$	17.7218	0.996929
$317$	5.09101	0.285940	0.142970	−	0.989727i	$-0.454335\pi$
$317$	5.09101	0.285940	0.142970	+	0.989727i	$0.454335\pi$
$318$	71.7308	4.02246
$319$	3.89138	0.217876
$320$	−0.575319	−0.0321613
$321$	−30.1443	−1.68249
$322$	−0.186580	−0.0103977
$323$	6.28486	0.349699
$324$	5.64929	0.313849
$325$	0	0
$326$	−22.9079	−1.26875
$327$	−24.2779	−1.34257
$328$	−15.0955	−0.833512
$329$	−0.798223	−0.0440075
$330$	−11.5181	−0.634052
$331$	−5.26653	−0.289475	−0.144737	−	0.989470i	$-0.546234\pi$
$331$	−5.26653	−0.289475	−0.144737	+	0.989470i	$0.546234\pi$
$332$	−9.47762	−0.520152
$333$	−56.6317	−3.10340
$334$	17.2130	0.941854
$335$	−15.1611	−0.828342
$336$	2.59876	0.141774
$337$	26.3404	1.43485	0.717427	−	0.696633i	$-0.245320\pi$
$337$	26.3404	1.43485	0.717427	+	0.696633i	$0.245320\pi$
$338$	0	0
$339$	30.3461	1.64817
$340$	16.4865	0.894108
$341$	10.3044	0.558013
$342$	9.45721	0.511387
$343$	2.49574	0.134757
$344$	12.4695	0.672311
$345$	3.83294	0.206359
$346$	28.8577	1.55140
$347$	7.40784	0.397674	0.198837	−	0.980033i	$-0.436284\pi$
$347$	7.40784	0.397674	0.198837	+	0.980033i	$0.436284\pi$
$348$	−12.9311	−0.693178
$349$	−22.3166	−1.19458	−0.597289	−	0.802026i	$-0.703756\pi$
$349$	−22.3166	−1.19458	−0.597289	+	0.802026i	$0.703756\pi$
$350$	0.0132077	0.000705980 0
$351$	0	0
$352$	5.76948	0.307514
$353$	−33.6995	−1.79364	−0.896821	−	0.442393i	$-0.854130\pi$
$353$	−33.6995	−1.79364	−0.896821	+	0.442393i	$0.854130\pi$
$354$	14.3186	0.761027
$355$	7.91169	0.419909
$356$	−1.95341	−0.103531
$357$	−3.39451	−0.179657
$358$	3.03080	0.160183
$359$	−13.1965	−0.696486	−0.348243	−	0.937404i	$-0.613222\pi$
$359$	−13.1965	−0.696486	−0.348243	+	0.937404i	$0.613222\pi$
$360$	−18.7917	−0.990410
$361$	−18.0669	−0.950888
$362$	−10.0831	−0.529955
$363$	2.92005	0.153263
$364$	0	0
$365$	−8.31335	−0.435141
$366$	52.4598	2.74212
$367$	−8.16049	−0.425974	−0.212987	−	0.977055i	$-0.568319\pi$
$367$	−8.16049	−0.425974	−0.212987	+	0.977055i	$0.568319\pi$
$368$	−2.93623	−0.153061
$369$	54.6359	2.84423
$370$	−40.4190	−2.10128
$371$	−2.47772	−0.128637
$372$	−34.2414	−1.77534
$373$	21.4960	1.11302	0.556511	−	0.830840i	$-0.312140\pi$
$373$	21.4960	1.11302	0.556511	+	0.830840i	$0.312140\pi$
$374$	−11.5252	−0.595956
$375$	−32.7820	−1.69285
$376$	−6.82177	−0.351806
$377$	0	0
$378$	−2.33524	−0.120112
$379$	−6.54091	−0.335984	−0.167992	−	0.985788i	$-0.553728\pi$
$379$	−6.54091	−0.335984	−0.167992	+	0.985788i	$0.553728\pi$
$380$	2.44781	0.125570
$381$	−5.17838	−0.265296
$382$	−5.59464	−0.286247
$383$	−4.86063	−0.248367	−0.124183	−	0.992259i	$-0.539631\pi$
$383$	−4.86063	−0.248367	−0.124183	+	0.992259i	$0.539631\pi$
$384$	32.3579	1.65126
$385$	0.397858	0.0202767
$386$	−11.3087	−0.575596
$387$	−45.1314	−2.29416
$388$	−17.3689	−0.881774
$389$	−7.22398	−0.366270	−0.183135	−	0.983088i	$-0.558625\pi$
$389$	−7.22398	−0.366270	−0.183135	+	0.983088i	$0.558625\pi$
$390$	0	0
$391$	3.83531	0.193960
$392$	10.6402	0.537410
$393$	−52.5845	−2.65254
$394$	25.5348	1.28643
$395$	34.6763	1.74475
$396$	−6.28935	−0.316052
$397$	1.87644	0.0941760	0.0470880	−	0.998891i	$-0.485006\pi$
$397$	1.87644	0.0941760	0.0470880	+	0.998891i	$0.485006\pi$
$398$	14.0356	0.703539
$399$	−0.503993	−0.0252312
$400$	0.207850	0.0103925
$401$	34.6406	1.72987	0.864934	−	0.501886i	$-0.167360\pi$
$401$	34.6406	1.72987	0.864934	+	0.501886i	$0.167360\pi$
$402$	−35.2195	−1.75659
$403$	0	0
$404$	0.841346	0.0418585
$405$	11.0540	0.549277
$406$	1.23167	0.0611265
$407$	10.2469	0.507922
$408$	−29.0102	−1.43622
$409$	4.98986	0.246733	0.123366	−	0.992361i	$-0.460631\pi$
$409$	4.98986	0.246733	0.123366	+	0.992361i	$0.460631\pi$
$410$	38.9946	1.92580
$411$	−1.95213	−0.0962916
$412$	3.08930	0.152199
$413$	−0.494593	−0.0243373
$414$	5.77122	0.283640
$415$	−18.5449	−0.910332
$416$	0	0
$417$	−3.60501	−0.176538
$418$	−1.71119	−0.0836970
$419$	−25.5225	−1.24685	−0.623427	−	0.781881i	$-0.714260\pi$
$419$	−25.5225	−1.24685	−0.623427	+	0.781881i	$0.714260\pi$
$420$	−1.32208	−0.0645110
$421$	17.7562	0.865384	0.432692	−	0.901542i	$-0.357564\pi$
$421$	17.7562	0.865384	0.432692	+	0.901542i	$0.357564\pi$
$422$	−21.7327	−1.05793
$423$	24.6903	1.20048
$424$	−21.1751	−1.02835
$425$	−0.271495	−0.0131694
$426$	18.3789	0.890463
$427$	−1.81206	−0.0876919
$428$	−11.7478	−0.567849
$429$	0	0
$430$	−32.2111	−1.55336
$431$	14.0545	0.676982	0.338491	−	0.940970i	$-0.390084\pi$
$431$	14.0545	0.676982	0.338491	+	0.940970i	$0.390084\pi$
$432$	−36.7498	−1.76813
$433$	−24.0476	−1.15566	−0.577828	−	0.816159i	$-0.696099\pi$
$433$	−24.0476	−1.15566	−0.577828	+	0.816159i	$0.696099\pi$
$434$	3.26145	0.156554
$435$	−25.3023	−1.21315
$436$	−9.46155	−0.453126
$437$	0.569440	0.0272400
$438$	−19.3120	−0.922763
$439$	−28.6927	−1.36943	−0.684713	−	0.728812i	$-0.740073\pi$
$439$	−28.6927	−1.36943	−0.684713	+	0.728812i	$0.740073\pi$
$440$	3.40017	0.162097
$441$	−38.5104	−1.83383
$442$	0	0
$443$	31.5118	1.49717	0.748585	−	0.663039i	$-0.230734\pi$
$443$	31.5118	1.49717	0.748585	+	0.663039i	$0.230734\pi$
$444$	−34.0506	−1.61597
$445$	−3.82225	−0.181192
$446$	−28.5819	−1.35339
$447$	44.3647	2.09838
$448$	0.0461643	0.00218106
$449$	−0.166083	−0.00783795	−0.00391897	−	0.999992i	$-0.501247\pi$
$449$	−0.166083	−0.00783795	−0.00391897	+	0.999992i	$0.501247\pi$
$450$	−0.408535	−0.0192585
$451$	−9.88582	−0.465505
$452$	11.8264	0.556267
$453$	−4.23945	−0.199187
$454$	9.48230	0.445026
$455$	0	0
$456$	−4.30723	−0.201704
$457$	33.5143	1.56773	0.783866	−	0.620930i	$-0.213245\pi$
$457$	33.5143	1.56773	0.783866	+	0.620930i	$0.213245\pi$
$458$	−0.295731	−0.0138186
$459$	48.0028	2.24058
$460$	1.49376	0.0696471
$461$	9.88111	0.460209	0.230104	−	0.973166i	$-0.426093\pi$
$461$	9.88111	0.460209	0.230104	+	0.973166i	$0.426093\pi$
$462$	0.924228	0.0429990
$463$	12.1670	0.565447	0.282723	−	0.959201i	$-0.408762\pi$
$463$	12.1670	0.565447	0.282723	+	0.959201i	$0.408762\pi$
$464$	19.3828	0.899824
$465$	−67.0003	−3.10706
$466$	−12.6187	−0.584550
$467$	39.4207	1.82417	0.912086	−	0.410000i	$-0.134471\pi$
$467$	39.4207	1.82417	0.912086	+	0.410000i	$0.134471\pi$
$468$	0	0
$469$	1.21655	0.0561750
$470$	17.6219	0.812837
$471$	27.4951	1.26691
$472$	−4.22689	−0.194558
$473$	8.16609	0.375477
$474$	80.5533	3.69994
$475$	−0.0403097	−0.00184953
$476$	−1.32290	−0.0606351
$477$	76.6398	3.50910
$478$	−22.9105	−1.04790
$479$	23.7287	1.08419	0.542097	−	0.840316i	$-0.317631\pi$
$479$	23.7287	1.08419	0.542097	+	0.840316i	$0.317631\pi$
$480$	−37.5139	−1.71227
$481$	0	0
$482$	31.3540	1.42814
$483$	−0.307560	−0.0139945
$484$	1.13800	0.0517271
$485$	−33.9858	−1.54322
$486$	−13.5309	−0.613772
$487$	14.0421	0.636310	0.318155	−	0.948039i	$-0.396937\pi$
$487$	14.0421	0.636310	0.318155	+	0.948039i	$0.396937\pi$
$488$	−15.4862	−0.701030
$489$	−37.7616	−1.70764
$490$	−27.4855	−1.24167
$491$	27.7148	1.25075	0.625376	−	0.780323i	$-0.284946\pi$
$491$	27.7148	1.25075	0.625376	+	0.780323i	$0.284946\pi$
$492$	32.8506	1.48102
$493$	−25.3179	−1.14026
$494$	0	0
$495$	−12.3064	−0.553131
$496$	51.3256	2.30459
$497$	−0.634844	−0.0284766
$498$	−43.0800	−1.93046
$499$	16.9503	0.758798	0.379399	−	0.925233i	$-0.376131\pi$
$499$	16.9503	0.758798	0.379399	+	0.925233i	$0.376131\pi$
$500$	−12.7757	−0.571347
$501$	28.3740	1.26766
$502$	27.9705	1.24838
$503$	22.9472	1.02316	0.511582	−	0.859234i	$-0.329060\pi$
$503$	22.9472	1.02316	0.511582	+	0.859234i	$0.329060\pi$
$504$	1.50787	0.0671659
$505$	1.64626	0.0732578
$506$	−1.04425	−0.0464224
$507$	0	0
$508$	−2.01810	−0.0895389
$509$	37.1832	1.64812	0.824059	−	0.566504i	$-0.191704\pi$
$509$	37.1832	1.64812	0.824059	+	0.566504i	$0.191704\pi$
$510$	74.9386	3.31834
$511$	0.667074	0.0295096
$512$	13.5258	0.597762
$513$	7.12712	0.314670
$514$	−24.6688	−1.08809
$515$	6.04483	0.266367
$516$	−27.1359	−1.19459
$517$	−4.46747	−0.196479
$518$	3.24327	0.142501
$519$	47.5692	2.08806
$520$	0	0
$521$	3.07759	0.134832	0.0674158	−	0.997725i	$-0.478525\pi$
$521$	3.07759	0.134832	0.0674158	+	0.997725i	$0.478525\pi$
$522$	−38.0974	−1.66748
$523$	−20.5697	−0.899450	−0.449725	−	0.893167i	$-0.648478\pi$
$523$	−20.5697	−0.899450	−0.449725	+	0.893167i	$0.648478\pi$
$524$	−20.4931	−0.895245
$525$	0.0217716	0.000950191 0
$526$	3.04326	0.132692
$527$	−67.0417	−2.92038
$528$	14.5446	0.632974
$529$	−22.6525	−0.984891
$530$	54.6991	2.37598
$531$	15.2986	0.663901
$532$	−0.196415	−0.00851568
$533$	0	0
$534$	−8.87912	−0.384237
$535$	−22.9868	−0.993808
$536$	10.3969	0.449077
$537$	4.99598	0.215593
$538$	32.2287	1.38948
$539$	6.96808	0.300136
$540$	18.6960	0.804547
$541$	17.5477	0.754433	0.377216	−	0.926125i	$-0.376881\pi$
$541$	17.5477	0.754433	0.377216	+	0.926125i	$0.376881\pi$
$542$	15.5496	0.667913
$543$	−16.6210	−0.713277
$544$	−37.5371	−1.60939
$545$	−18.5134	−0.793028
$546$	0	0
$547$	−6.57955	−0.281321	−0.140661	−	0.990058i	$-0.544923\pi$
$547$	−6.57955	−0.281321	−0.140661	+	0.990058i	$0.544923\pi$
$548$	−0.760781	−0.0324989
$549$	56.0500	2.39216
$550$	0.0739203	0.00315197
$551$	−3.75903	−0.160140
$552$	−2.62847	−0.111875
$553$	−2.78247	−0.118323
$554$	−15.2374	−0.647374
$555$	−66.6269	−2.82815
$556$	−1.40493	−0.0595825
$557$	40.1019	1.69917	0.849586	−	0.527450i	$-0.176852\pi$
$557$	40.1019	1.69917	0.849586	+	0.527450i	$0.176852\pi$
$558$	−100.882	−4.27066
$559$	0	0
$560$	1.98171	0.0837427
$561$	−18.9983	−0.802108
$562$	26.8143	1.13109
$563$	−30.1885	−1.27229	−0.636146	−	0.771568i	$-0.719473\pi$
$563$	−30.1885	−1.27229	−0.636146	+	0.771568i	$0.719473\pi$
$564$	14.8454	0.625104
$565$	23.1407	0.973538
$566$	23.8521	1.00258
$567$	−0.886985	−0.0372499
$568$	−5.42550	−0.227649
$569$	−24.6659	−1.03405	−0.517024	−	0.855971i	$-0.672960\pi$
$569$	−24.6659	−1.03405	−0.517024	+	0.855971i	$0.672960\pi$
$570$	11.1264	0.466032
$571$	40.1493	1.68019	0.840097	−	0.542436i	$-0.182498\pi$
$571$	40.1493	1.68019	0.840097	+	0.542436i	$0.182498\pi$
$572$	0	0
$573$	−9.22224	−0.385265
$574$	−3.12897	−0.130601
$575$	−0.0245988	−0.00102584
$576$	−1.42794	−0.0594973
$577$	−7.60534	−0.316614	−0.158307	−	0.987390i	$-0.550604\pi$
$577$	−7.60534	−0.316614	−0.158307	+	0.987390i	$0.550604\pi$
$578$	44.8705	1.86637
$579$	−18.6413	−0.774705
$580$	−9.86074	−0.409445
$581$	1.48806	0.0617353
$582$	−78.9494	−3.27256
$583$	−13.8672	−0.574321
$584$	5.70094	0.235907
$585$	0	0
$586$	35.0341	1.44725
$587$	−1.32368	−0.0546339	−0.0273170	−	0.999627i	$-0.508696\pi$
$587$	−1.32368	−0.0546339	−0.0273170	+	0.999627i	$0.508696\pi$
$588$	−23.1549	−0.954893
$589$	−9.95389	−0.410143
$590$	10.9188	0.449521
$591$	42.0917	1.73142
$592$	51.0396	2.09771
$593$	−27.4172	−1.12589	−0.562944	−	0.826495i	$-0.690331\pi$
$593$	−27.4172	−1.12589	−0.562944	+	0.826495i	$0.690331\pi$
$594$	−13.0698	−0.536260
$595$	−2.58852	−0.106119
$596$	17.2897	0.708214
$597$	23.1363	0.946906
$598$	0	0
$599$	−36.9299	−1.50891	−0.754457	−	0.656350i	$-0.772099\pi$
$599$	−36.9299	−1.50891	−0.754457	+	0.656350i	$0.772099\pi$
$600$	0.186065	0.00759605
$601$	−8.81319	−0.359498	−0.179749	−	0.983713i	$-0.557528\pi$
$601$	−8.81319	−0.359498	−0.179749	+	0.983713i	$0.557528\pi$
$602$	2.58466	0.105343
$603$	−37.6298	−1.53240
$604$	−1.65219	−0.0672266
$605$	2.22672	0.0905289
$606$	3.82429	0.155351
$607$	7.65070	0.310532	0.155266	−	0.987873i	$-0.450376\pi$
$607$	7.65070	0.310532	0.155266	+	0.987873i	$0.450376\pi$
$608$	−5.57325	−0.226025
$609$	2.03028	0.0822713
$610$	40.0038	1.61971
$611$	0	0
$612$	40.9194	1.65407
$613$	−34.0091	−1.37361	−0.686807	−	0.726840i	$-0.740988\pi$
$613$	−34.0091	−1.37361	−0.686807	+	0.726840i	$0.740988\pi$
$614$	53.3189	2.15178
$615$	64.2789	2.59197
$616$	−0.272834	−0.0109928
$617$	22.4272	0.902885	0.451443	−	0.892300i	$-0.350910\pi$
$617$	22.4272	0.902885	0.451443	+	0.892300i	$0.350910\pi$
$618$	14.0422	0.564861
$619$	3.83671	0.154210	0.0771052	−	0.997023i	$-0.475432\pi$
$619$	3.83671	0.154210	0.0771052	+	0.997023i	$0.475432\pi$
$620$	−26.1112	−1.04865
$621$	4.34930	0.174531
$622$	−27.5509	−1.10469
$623$	0.306702	0.0122877
$624$	0	0
$625$	−24.7896	−0.991585
$626$	−57.8060	−2.31039
$627$	−2.82073	−0.112649
$628$	10.7153	0.427588
$629$	−66.6681	−2.65823
$630$	−3.89511	−0.155185
$631$	32.3528	1.28794	0.643972	−	0.765049i	$-0.277285\pi$
$631$	32.3528	1.28794	0.643972	+	0.765049i	$0.277285\pi$
$632$	−23.7795	−0.945898
$633$	−35.8243	−1.42389
$634$	9.01841	0.358167
$635$	−3.94883	−0.156705
$636$	46.0808	1.82722
$637$	0	0
$638$	6.89334	0.272910
$639$	19.6367	0.776817
$640$	24.6749	0.975360
$641$	−15.4337	−0.609596	−0.304798	−	0.952417i	$-0.598589\pi$
$641$	−15.4337	−0.609596	−0.304798	+	0.952417i	$0.598589\pi$
$642$	−53.3987	−2.10748
$643$	−2.71607	−0.107111	−0.0535557	−	0.998565i	$-0.517055\pi$
$643$	−2.71607	−0.107111	−0.0535557	+	0.998565i	$0.517055\pi$
$644$	−0.119862	−0.00472321
$645$	−53.0969	−2.09069
$646$	11.1332	0.438032
$647$	−24.2910	−0.954979	−0.477490	−	0.878637i	$-0.658453\pi$
$647$	−24.2910	−0.954979	−0.477490	+	0.878637i	$0.658453\pi$
$648$	−7.58035	−0.297784
$649$	−2.76812	−0.108658
$650$	0	0
$651$	5.37619	0.210709
$652$	−14.7163	−0.576337
$653$	29.9403	1.17165	0.585826	−	0.810437i	$-0.300770\pi$
$653$	29.9403	1.17165	0.585826	+	0.810437i	$0.300770\pi$
$654$	−43.0069	−1.68170
$655$	−40.0989	−1.56679
$656$	−49.2409	−1.92253
$657$	−20.6337	−0.804996
$658$	−1.41400	−0.0551236
$659$	2.80382	0.109221	0.0546107	−	0.998508i	$-0.482608\pi$
$659$	2.80382	0.109221	0.0546107	+	0.998508i	$0.482608\pi$
$660$	−7.39939	−0.288021
$661$	−12.1680	−0.473281	−0.236640	−	0.971597i	$-0.576046\pi$
$661$	−12.1680	−0.473281	−0.236640	+	0.971597i	$0.576046\pi$
$662$	−9.32934	−0.362595
$663$	0	0
$664$	12.7173	0.493527
$665$	−0.384326	−0.0149035
$666$	−100.320	−3.88730
$667$	−2.29393	−0.0888214
$668$	11.0579	0.427841
$669$	−47.1146	−1.82155
$670$	−26.8570	−1.03758
$671$	−10.1417	−0.391516
$672$	3.01016	0.116120
$673$	36.7456	1.41644	0.708220	−	0.705992i	$-0.249498\pi$
$673$	36.7456	1.41644	0.708220	+	0.705992i	$0.249498\pi$
$674$	46.6605	1.79729
$675$	−0.307879	−0.0118503
$676$	0	0
$677$	−27.8412	−1.07002	−0.535011	−	0.844845i	$-0.679693\pi$
$677$	−27.8412	−1.07002	−0.535011	+	0.844845i	$0.679693\pi$
$678$	53.7562	2.06449
$679$	2.72706	0.104655
$680$	−22.1220	−0.848341
$681$	15.6307	0.598969
$682$	18.2535	0.698965
$683$	4.51413	0.172728	0.0863642	−	0.996264i	$-0.472475\pi$
$683$	4.51413	0.172728	0.0863642	+	0.996264i	$0.472475\pi$
$684$	6.07543	0.232300
$685$	−1.48862	−0.0568773
$686$	4.42105	0.168797
$687$	−0.487484	−0.0185987
$688$	40.6749	1.55072
$689$	0	0
$690$	6.78982	0.258484
$691$	31.1907	1.18655	0.593275	−	0.805000i	$-0.297835\pi$
$691$	31.1907	1.18655	0.593275	+	0.805000i	$0.297835\pi$
$692$	18.5386	0.704730
$693$	0.987480	0.0375112
$694$	13.1225	0.498124
$695$	−2.74904	−0.104277
$696$	17.3512	0.657696
$697$	64.3186	2.43624
$698$	−39.5324	−1.49632
$699$	−20.8008	−0.786757
$700$	0.00848478	0.000320695 0
$701$	16.6915	0.630430	0.315215	−	0.949020i	$-0.397923\pi$
$701$	16.6915	0.630430	0.315215	+	0.949020i	$0.397923\pi$
$702$	0	0
$703$	−9.89842	−0.373326
$704$	0.258371	0.00973772
$705$	29.0480	1.09401
$706$	−59.6966	−2.24671
$707$	−0.132098	−0.00496807
$708$	9.19847	0.345700
$709$	−25.2842	−0.949569	−0.474784	−	0.880102i	$-0.657474\pi$
$709$	−25.2842	−0.949569	−0.474784	+	0.880102i	$0.657474\pi$
$710$	14.0151	0.525976
$711$	86.0662	3.22773
$712$	2.62113	0.0982312
$713$	−6.07432	−0.227485
$714$	−6.01317	−0.225037
$715$	0	0
$716$	1.94702	0.0727637
$717$	−37.7658	−1.41039
$718$	−23.3768	−0.872416
$719$	42.9188	1.60060	0.800300	−	0.599600i	$-0.204673\pi$
$719$	42.9188	1.60060	0.800300	+	0.599600i	$0.204673\pi$
$720$	−61.2976	−2.28443
$721$	−0.485045	−0.0180640
$722$	−32.0043	−1.19108
$723$	51.6842	1.92215
$724$	−6.47751	−0.240735
$725$	0.162383	0.00603076
$726$	5.17269	0.191977
$727$	−22.2288	−0.824421	−0.412210	−	0.911089i	$-0.635243\pi$
$727$	−22.2288	−0.824421	−0.412210	+	0.911089i	$0.635243\pi$
$728$	0	0
$729$	−37.1971	−1.37767
$730$	−14.7266	−0.545055
$731$	−53.1298	−1.96508
$732$	33.7009	1.24562
$733$	0.484687	0.0179023	0.00895117	−	0.999960i	$-0.497151\pi$
$733$	0.484687	0.0179023	0.00895117	+	0.999960i	$0.497151\pi$
$734$	−14.4558	−0.533574
$735$	−45.3073	−1.67119
$736$	−3.40105	−0.125364
$737$	6.80874	0.250803
$738$	96.7841	3.56267
$739$	−35.5891	−1.30917	−0.654583	−	0.755990i	$-0.727156\pi$
$739$	−35.5891	−1.30917	−0.654583	+	0.755990i	$0.727156\pi$
$740$	−25.9657	−0.954518
$741$	0	0
$742$	−4.38913	−0.161130
$743$	−20.7277	−0.760425	−0.380212	−	0.924899i	$-0.624149\pi$
$743$	−20.7277	−0.760425	−0.380212	+	0.924899i	$0.624149\pi$
$744$	45.9460	1.68446
$745$	33.8308	1.23946
$746$	38.0789	1.39417
$747$	−46.0282	−1.68408
$748$	−7.40397	−0.270716
$749$	1.84449	0.0673963
$750$	−58.0712	−2.12046
$751$	44.5213	1.62460	0.812302	−	0.583237i	$-0.198214\pi$
$751$	44.5213	1.62460	0.812302	+	0.583237i	$0.198214\pi$
$752$	−22.2523	−0.811457
$753$	46.1067	1.68022
$754$	0	0
$755$	−3.23284	−0.117655
$756$	−1.50019	−0.0545613
$757$	−31.3200	−1.13834	−0.569172	−	0.822219i	$-0.692736\pi$
$757$	−31.3200	−1.13834	−0.569172	+	0.822219i	$0.692736\pi$
$758$	−11.5868	−0.420852
$759$	−1.72134	−0.0624807
$760$	−3.28453	−0.119142
$761$	13.4570	0.487815	0.243908	−	0.969798i	$-0.421571\pi$
$761$	13.4570	0.487815	0.243908	+	0.969798i	$0.421571\pi$
$762$	−9.17318	−0.332309
$763$	1.48554	0.0537802
$764$	−3.59407	−0.130029
$765$	80.0672	2.89483
$766$	−8.61031	−0.311103
$767$	0	0
$768$	58.8289	2.12281
$769$	−22.6741	−0.817649	−0.408824	−	0.912613i	$-0.634061\pi$
$769$	−22.6741	−0.817649	−0.408824	+	0.912613i	$0.634061\pi$
$770$	0.704781	0.0253985
$771$	−40.6641	−1.46448
$772$	−7.26484	−0.261467
$773$	7.36132	0.264768	0.132384	−	0.991198i	$-0.457737\pi$
$773$	7.36132	0.264768	0.132384	+	0.991198i	$0.457737\pi$
$774$	−79.9476	−2.87366
$775$	0.429990	0.0154457
$776$	23.3060	0.836638
$777$	5.34623	0.191795
$778$	−12.7968	−0.458789
$779$	9.54959	0.342149
$780$	0	0
$781$	−3.55307	−0.127139
$782$	6.79402	0.242954
$783$	−28.7109	−1.02604
$784$	34.7077	1.23956
$785$	20.9667	0.748334
$786$	−93.1502	−3.32256
$787$	36.1126	1.28727	0.643637	−	0.765331i	$-0.277424\pi$
$787$	36.1126	1.28727	0.643637	+	0.765331i	$0.277424\pi$
$788$	16.4039	0.584365
$789$	5.01652	0.178593
$790$	61.4269	2.18547
$791$	−1.85684	−0.0660217
$792$	8.43920	0.299874
$793$	0	0
$794$	3.32400	0.117964
$795$	90.1664	3.19787
$796$	9.01663	0.319586
$797$	−32.1086	−1.13734	−0.568672	−	0.822564i	$-0.692543\pi$
$797$	−32.1086	−1.13734	−0.568672	+	0.822564i	$0.692543\pi$
$798$	−0.892793	−0.0316045
$799$	29.0660	1.02828
$800$	0.240755	0.00851196
$801$	−9.48678	−0.335199
$802$	61.3637	2.16683
$803$	3.73345	0.131751
$804$	−22.6255	−0.797939
$805$	−0.234533	−0.00826621
$806$	0	0
$807$	53.1259	1.87012
$808$	−1.12894	−0.0397159
$809$	−4.95375	−0.174165	−0.0870823	−	0.996201i	$-0.527754\pi$
$809$	−4.95375	−0.174165	−0.0870823	+	0.996201i	$0.527754\pi$
$810$	19.5814	0.688022
$811$	−25.6456	−0.900537	−0.450269	−	0.892893i	$-0.648672\pi$
$811$	−25.6456	−0.900537	−0.450269	+	0.892893i	$0.648672\pi$
$812$	0.791238	0.0277670
$813$	25.6321	0.898957
$814$	18.1518	0.636221
$815$	−28.7955	−1.00866
$816$	−94.6296	−3.31270
$817$	−7.88834	−0.275978
$818$	8.83923	0.309056
$819$	0	0
$820$	25.0506	0.874805
$821$	15.3700	0.536418	0.268209	−	0.963361i	$-0.413568\pi$
$821$	15.3700	0.536418	0.268209	+	0.963361i	$0.413568\pi$
$822$	−3.45808	−0.120614
$823$	−28.0334	−0.977182	−0.488591	−	0.872513i	$-0.662489\pi$
$823$	−28.0334	−0.977182	−0.488591	+	0.872513i	$0.662489\pi$
$824$	−4.14529	−0.144408
$825$	0.121851	0.00424229
$826$	−0.876141	−0.0304849
$827$	22.8631	0.795027	0.397513	−	0.917596i	$-0.369873\pi$
$827$	22.8631	0.795027	0.397513	+	0.917596i	$0.369873\pi$
$828$	3.70751	0.128845
$829$	15.1985	0.527865	0.263933	−	0.964541i	$-0.414980\pi$
$829$	15.1985	0.527865	0.263933	+	0.964541i	$0.414980\pi$
$830$	−32.8511	−1.14028
$831$	−25.1174	−0.871312
$832$	0	0
$833$	−45.3353	−1.57078
$834$	−6.38605	−0.221131
$835$	21.6369	0.748777
$836$	−1.09929	−0.0380197
$837$	−76.0263	−2.62785
$838$	−45.2115	−1.56181
$839$	−41.6910	−1.43933	−0.719666	−	0.694320i	$-0.755705\pi$
$839$	−41.6910	−1.43933	−0.719666	+	0.694320i	$0.755705\pi$
$840$	1.77400	0.0612089
$841$	−13.8572	−0.477833
$842$	31.4540	1.08398
$843$	44.2009	1.52236
$844$	−13.9614	−0.480570
$845$	0	0
$846$	43.7374	1.50372
$847$	−0.178675	−0.00613933
$848$	−69.0720	−2.37194
$849$	39.3179	1.34939
$850$	−0.480936	−0.0164960
$851$	−6.04047	−0.207065
$852$	11.8069	0.404497
$853$	−30.2106	−1.03439	−0.517195	−	0.855868i	$-0.673024\pi$
$853$	−30.2106	−1.03439	−0.517195	+	0.855868i	$0.673024\pi$
$854$	−3.20996	−0.109843
$855$	11.8878	0.406555
$856$	15.7634	0.538782
$857$	−46.0952	−1.57458	−0.787291	−	0.616581i	$-0.788517\pi$
$857$	−46.0952	−1.57458	−0.787291	+	0.616581i	$0.788517\pi$
$858$	0	0
$859$	−14.3640	−0.490095	−0.245047	−	0.969511i	$-0.578804\pi$
$859$	−14.3640	−0.490095	−0.245047	+	0.969511i	$0.578804\pi$
$860$	−20.6928	−0.705619
$861$	−5.15782	−0.175778
$862$	24.8967	0.847985
$863$	−2.48206	−0.0844904	−0.0422452	−	0.999107i	$-0.513451\pi$
$863$	−2.48206	−0.0844904	−0.0422452	+	0.999107i	$0.513451\pi$
$864$	−42.5676	−1.44818
$865$	36.2744	1.23337
$866$	−42.5989	−1.44757
$867$	73.9648	2.51198
$868$	2.09520	0.0711156
$869$	−15.5728	−0.528272
$870$	−44.8214	−1.51959
$871$	0	0
$872$	12.6957	0.429932
$873$	−84.3525	−2.85490
$874$	1.00873	0.0341208
$875$	2.00589	0.0678115
$876$	−12.4063	−0.419169
$877$	39.7910	1.34365	0.671823	−	0.740711i	$-0.265511\pi$
$877$	39.7910	1.34365	0.671823	+	0.740711i	$0.265511\pi$
$878$	−50.8273	−1.71534
$879$	57.7504	1.94787
$880$	11.0912	0.373884
$881$	−4.48082	−0.150963	−0.0754813	−	0.997147i	$-0.524049\pi$
$881$	−4.48082	−0.150963	−0.0754813	+	0.997147i	$0.524049\pi$
$882$	−68.2188	−2.29705
$883$	−46.0539	−1.54984	−0.774919	−	0.632061i	$-0.782209\pi$
$883$	−46.0539	−1.54984	−0.774919	+	0.632061i	$0.782209\pi$
$884$	0	0
$885$	17.9987	0.605019
$886$	55.8212	1.87535
$887$	9.09326	0.305322	0.152661	−	0.988279i	$-0.451216\pi$
$887$	9.09326	0.305322	0.152661	+	0.988279i	$0.451216\pi$
$888$	45.6899	1.53325
$889$	0.316859	0.0106271
$890$	−6.77087	−0.226960
$891$	−4.96425	−0.166309
$892$	−18.3614	−0.614784
$893$	4.31552	0.144413
$894$	78.5893	2.62842
$895$	3.80974	0.127346
$896$	−1.97994	−0.0661453
$897$	0	0
$898$	−0.294206	−0.00981778
$899$	40.0982	1.33735
$900$	−0.262448	−0.00874827
$901$	90.2222	3.00574
$902$	−17.5121	−0.583090
$903$	4.26056	0.141783
$904$	−15.8689	−0.527793
$905$	−12.6746	−0.421316
$906$	−7.50992	−0.249500
$907$	36.7395	1.21992	0.609958	−	0.792434i	$-0.291186\pi$
$907$	36.7395	1.21992	0.609958	+	0.792434i	$0.291186\pi$
$908$	6.09155	0.202155
$909$	4.08601	0.135524
$910$	0	0
$911$	−12.5537	−0.415921	−0.207961	−	0.978137i	$-0.566683\pi$
$911$	−12.5537	−0.415921	−0.207961	+	0.978137i	$0.566683\pi$
$912$	−14.0500	−0.465240
$913$	8.32835	0.275628
$914$	59.3685	1.96373
$915$	65.9426	2.17999
$916$	−0.189981	−0.00627715
$917$	3.21759	0.106254
$918$	85.0340	2.80654
$919$	−1.43660	−0.0473891	−0.0236946	−	0.999719i	$-0.507543\pi$
$919$	−1.43660	−0.0473891	−0.0236946	+	0.999719i	$0.507543\pi$
$920$	−2.00437	−0.0660821
$921$	87.8912	2.89611
$922$	17.5038	0.576456
$923$	0	0
$924$	0.593736	0.0195325
$925$	0.427594	0.0140592
$926$	21.5530	0.708277
$927$	15.0032	0.492770
$928$	22.4513	0.736999
$929$	36.2456	1.18918	0.594590	−	0.804029i	$-0.297315\pi$
$929$	36.2456	1.18918	0.594590	+	0.804029i	$0.297315\pi$
$930$	−118.687	−3.89190
$931$	−6.73108	−0.220602
$932$	−8.10642	−0.265535
$933$	−45.4150	−1.48682
$934$	69.8313	2.28495
$935$	−14.4874	−0.473787
$936$	0	0
$937$	30.8671	1.00839	0.504193	−	0.863591i	$-0.331790\pi$
$937$	30.8671	1.00839	0.504193	+	0.863591i	$0.331790\pi$
$938$	2.15504	0.0703646
$939$	−95.2878	−3.10960
$940$	11.3205	0.369235
$941$	13.3120	0.433958	0.216979	−	0.976176i	$-0.430380\pi$
$941$	13.3120	0.433958	0.216979	+	0.976176i	$0.430380\pi$
$942$	48.7059	1.58692
$943$	5.82759	0.189773
$944$	−13.7879	−0.448758
$945$	−2.93542	−0.0954893
$946$	14.4657	0.470321
$947$	54.4711	1.77007	0.885036	−	0.465522i	$-0.154133\pi$
$947$	54.4711	1.77007	0.885036	+	0.465522i	$0.154133\pi$
$948$	51.7485	1.68071
$949$	0	0
$950$	−0.0714061	−0.00231672
$951$	14.8660	0.482063
$952$	1.77510	0.0575313
$953$	27.8332	0.901607	0.450804	−	0.892623i	$-0.351138\pi$
$953$	27.8332	0.901607	0.450804	+	0.892623i	$0.351138\pi$
$954$	135.763	4.39548
$955$	−7.03253	−0.227567
$956$	−14.7180	−0.476014
$957$	11.3630	0.367315
$958$	42.0340	1.35806
$959$	0.119449	0.00385720
$960$	−1.67996	−0.0542205
$961$	75.1799	2.42516
$962$	0	0
$963$	−57.0531	−1.83851
$964$	20.1422	0.648738
$965$	−14.2151	−0.457601
$966$	−0.544823	−0.0175294
$967$	16.1542	0.519483	0.259741	−	0.965678i	$-0.416363\pi$
$967$	16.1542	0.519483	0.259741	+	0.965678i	$0.416363\pi$
$968$	−1.52699	−0.0490793
$969$	18.3521	0.589555
$970$	−60.2038	−1.93303
$971$	−26.8095	−0.860357	−0.430179	−	0.902744i	$-0.641549\pi$
$971$	−26.8095	−0.860357	−0.430179	+	0.902744i	$0.641549\pi$
$972$	−8.69240	−0.278809
$973$	0.220586	0.00707167
$974$	24.8748	0.797040
$975$	0	0
$976$	−50.5153	−1.61696
$977$	−28.3771	−0.907862	−0.453931	−	0.891037i	$-0.649979\pi$
$977$	−28.3771	−0.907862	−0.453931	+	0.891037i	$0.649979\pi$
$978$	−66.8923	−2.13898
$979$	1.71654	0.0548608
$980$	−17.6571	−0.564034
$981$	−45.9502	−1.46708
$982$	49.0951	1.56669
$983$	43.0228	1.37221	0.686107	−	0.727501i	$-0.259318\pi$
$983$	43.0228	1.37221	0.686107	+	0.727501i	$0.259318\pi$
$984$	−44.0797	−1.40521
$985$	32.0975	1.02271
$986$	−44.8491	−1.42829
$987$	−2.33085	−0.0741918
$988$	0	0
$989$	−4.81383	−0.153071
$990$	−21.8000	−0.692850
$991$	−42.6381	−1.35444	−0.677222	−	0.735779i	$-0.736816\pi$
$991$	−42.6381	−1.35444	−0.677222	+	0.735779i	$0.736816\pi$
$992$	59.4509	1.88757
$993$	−15.3785	−0.488023
$994$	−1.12459	−0.0356697
$995$	17.6429	0.559316
$996$	−27.6751	−0.876920
$997$	−22.2208	−0.703740	−0.351870	−	0.936049i	$-0.614454\pi$
$997$	−22.2208	−0.703740	−0.351870	+	0.936049i	$0.614454\pi$
$998$	30.0264	0.950468
$999$	−75.6026	−2.39196

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.s.1.17	✓	21
13.12	even	2		1859.2.a.t.1.5	yes	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.2.a.s.1.17	✓	21	1.1	even	1	trivial
1859.2.a.t.1.5	yes	21	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.77144 q^{2} +2.92005 q^{3} +1.13800 q^{4} +2.22672 q^{5} +5.17269 q^{6} -0.178675 q^{7} -1.52699 q^{8} +5.52669 q^{9} +O(q^{10})\)	\(q+1.77144 q^{2} +2.92005 q^{3} +1.13800 q^{4} +2.22672 q^{5} +5.17269 q^{6} -0.178675 q^{7} -1.52699 q^{8} +5.52669 q^{9} +3.94449 q^{10} -1.00000 q^{11} +3.32300 q^{12} -0.316511 q^{14} +6.50213 q^{15} -4.98096 q^{16} +6.50615 q^{17} +9.79020 q^{18} +0.965988 q^{19} +2.53399 q^{20} -0.521739 q^{21} -1.77144 q^{22} +0.589490 q^{23} -4.45888 q^{24} -0.0417290 q^{25} +7.37807 q^{27} -0.203331 q^{28} -3.89138 q^{29} +11.5181 q^{30} -10.3044 q^{31} -5.76948 q^{32} -2.92005 q^{33} +11.5252 q^{34} -0.397858 q^{35} +6.28935 q^{36} -10.2469 q^{37} +1.71119 q^{38} -3.40017 q^{40} +9.88582 q^{41} -0.924228 q^{42} -8.16609 q^{43} -1.13800 q^{44} +12.3064 q^{45} +1.04425 q^{46} +4.46747 q^{47} -14.5446 q^{48} -6.96808 q^{49} -0.0739203 q^{50} +18.9983 q^{51} +13.8672 q^{53} +13.0698 q^{54} -2.22672 q^{55} +0.272834 q^{56} +2.82073 q^{57} -6.89334 q^{58} +2.76812 q^{59} +7.39939 q^{60} +10.1417 q^{61} -18.2535 q^{62} -0.987480 q^{63} -0.258371 q^{64} -5.17269 q^{66} -6.80874 q^{67} +7.40397 q^{68} +1.72134 q^{69} -0.704781 q^{70} +3.55307 q^{71} -8.43920 q^{72} -3.73345 q^{73} -18.1518 q^{74} -0.121851 q^{75} +1.09929 q^{76} +0.178675 q^{77} +15.5728 q^{79} -11.0912 q^{80} +4.96425 q^{81} +17.5121 q^{82} -8.32835 q^{83} -0.593736 q^{84} +14.4874 q^{85} -14.4657 q^{86} -11.3630 q^{87} +1.52699 q^{88} -1.71654 q^{89} +21.8000 q^{90} +0.670837 q^{92} -30.0893 q^{93} +7.91384 q^{94} +2.15098 q^{95} -16.8472 q^{96} -15.2627 q^{97} -12.3435 q^{98} -5.52669 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9}+O(q^{10}) \) 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

Related objects

Downloads

Learn more