LMFDB - Embedded newform 9295.2.a.bn.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9295,2,Mod(1,9295)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9295, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("9295.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9295 = 5 \cdot 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9295.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:	$74.2209486788$
Analytic rank:	$0$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	9295.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.717895 q^{2} -2.94870 q^{3} -1.48463 q^{4} +1.00000 q^{5} -2.11685 q^{6} -0.587136 q^{7} -2.50160 q^{8} +5.69480 q^{9} +O(q^{10})$	\(q+0.717895 q^{2} -2.94870 q^{3} -1.48463 q^{4} +1.00000 q^{5} -2.11685 q^{6} -0.587136 q^{7} -2.50160 q^{8} +5.69480 q^{9} +0.717895 q^{10} +1.00000 q^{11} +4.37771 q^{12} -0.421502 q^{14} -2.94870 q^{15} +1.17337 q^{16} +5.09079 q^{17} +4.08827 q^{18} +0.808186 q^{19} -1.48463 q^{20} +1.73128 q^{21} +0.717895 q^{22} +1.18065 q^{23} +7.37644 q^{24} +1.00000 q^{25} -7.94616 q^{27} +0.871677 q^{28} +1.01718 q^{29} -2.11685 q^{30} -4.25282 q^{31} +5.84555 q^{32} -2.94870 q^{33} +3.65465 q^{34} -0.587136 q^{35} -8.45466 q^{36} +10.6622 q^{37} +0.580193 q^{38} -2.50160 q^{40} +4.80611 q^{41} +1.24288 q^{42} +3.10017 q^{43} -1.48463 q^{44} +5.69480 q^{45} +0.847585 q^{46} +5.76127 q^{47} -3.45992 q^{48} -6.65527 q^{49} +0.717895 q^{50} -15.0112 q^{51} -4.90876 q^{53} -5.70450 q^{54} +1.00000 q^{55} +1.46878 q^{56} -2.38310 q^{57} +0.730229 q^{58} -4.99774 q^{59} +4.37771 q^{60} +12.4062 q^{61} -3.05308 q^{62} -3.34362 q^{63} +1.84974 q^{64} -2.11685 q^{66} -10.3632 q^{67} -7.55793 q^{68} -3.48139 q^{69} -0.421502 q^{70} +14.2767 q^{71} -14.2461 q^{72} -0.230278 q^{73} +7.65431 q^{74} -2.94870 q^{75} -1.19986 q^{76} -0.587136 q^{77} -7.08489 q^{79} +1.17337 q^{80} +6.34638 q^{81} +3.45028 q^{82} -9.62601 q^{83} -2.57031 q^{84} +5.09079 q^{85} +2.22560 q^{86} -2.99936 q^{87} -2.50160 q^{88} +1.35865 q^{89} +4.08827 q^{90} -1.75283 q^{92} +12.5403 q^{93} +4.13599 q^{94} +0.808186 q^{95} -17.2367 q^{96} +5.88623 q^{97} -4.77778 q^{98} +5.69480 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q + 8 q^{2} + 12 q^{3} + 38 q^{4} + 33 q^{5} + 18 q^{6} + 4 q^{7} + 21 q^{8} + 35 q^{9}+O(q^{10}) $ 33 * q + 8 * q^2 + 12 * q^3 + 38 * q^4 + 33 * q^5 + 18 * q^6 + 4 * q^7 + 21 * q^8 + 35 * q^9	\( 33 q + 8 q^{2} + 12 q^{3} + 38 q^{4} + 33 q^{5} + 18 q^{6} + 4 q^{7} + 21 q^{8} + 35 q^{9} + 8 q^{10} + 33 q^{11} + 24 q^{12} - 5 q^{14} + 12 q^{15} + 44 q^{16} + 9 q^{17} + 18 q^{18} + 8 q^{19} + 38 q^{20} + 9 q^{21} + 8 q^{22} + 7 q^{23} + 54 q^{24} + 33 q^{25} + 42 q^{27} + 15 q^{28} - 11 q^{29} + 18 q^{30} + 13 q^{31} + 85 q^{32} + 12 q^{33} + 31 q^{34} + 4 q^{35} + 26 q^{36} + 22 q^{37} - 2 q^{38} + 21 q^{40} + 36 q^{41} + 11 q^{42} + 26 q^{43} + 38 q^{44} + 35 q^{45} - q^{46} + 46 q^{47} + 36 q^{48} + 29 q^{49} + 8 q^{50} - 41 q^{51} + 9 q^{53} + 70 q^{54} + 33 q^{55} - 10 q^{56} + 70 q^{57} - 23 q^{58} + 18 q^{59} + 24 q^{60} - 42 q^{61} - 24 q^{62} + 68 q^{63} + 39 q^{64} + 18 q^{66} + 26 q^{67} + 8 q^{68} + 12 q^{69} - 5 q^{70} + 43 q^{71} + 46 q^{72} + 21 q^{73} - 22 q^{74} + 12 q^{75} + 2 q^{76} + 4 q^{77} - 22 q^{79} + 44 q^{80} + 41 q^{81} + 156 q^{82} + 26 q^{83} + 11 q^{84} + 9 q^{85} + 17 q^{86} - 30 q^{87} + 21 q^{88} + 95 q^{89} + 18 q^{90} + 37 q^{92} + 62 q^{93} - 14 q^{94} + 8 q^{95} + 53 q^{96} + 40 q^{97} + 132 q^{98} + 35 q^{99}+O(q^{100}) \) 33 * q + 8 * q^2 + 12 * q^3 + 38 * q^4 + 33 * q^5 + 18 * q^6 + 4 * q^7 + 21 * q^8 + 35 * q^9 + 8 * q^10 + 33 * q^11 + 24 * q^12 - 5 * q^14 + 12 * q^15 + 44 * q^16 + 9 * q^17 + 18 * q^18 + 8 * q^19 + 38 * q^20 + 9 * q^21 + 8 * q^22 + 7 * q^23 + 54 * q^24 + 33 * q^25 + 42 * q^27 + 15 * q^28 - 11 * q^29 + 18 * q^30 + 13 * q^31 + 85 * q^32 + 12 * q^33 + 31 * q^34 + 4 * q^35 + 26 * q^36 + 22 * q^37 - 2 * q^38 + 21 * q^40 + 36 * q^41 + 11 * q^42 + 26 * q^43 + 38 * q^44 + 35 * q^45 - q^46 + 46 * q^47 + 36 * q^48 + 29 * q^49 + 8 * q^50 - 41 * q^51 + 9 * q^53 + 70 * q^54 + 33 * q^55 - 10 * q^56 + 70 * q^57 - 23 * q^58 + 18 * q^59 + 24 * q^60 - 42 * q^61 - 24 * q^62 + 68 * q^63 + 39 * q^64 + 18 * q^66 + 26 * q^67 + 8 * q^68 + 12 * q^69 - 5 * q^70 + 43 * q^71 + 46 * q^72 + 21 * q^73 - 22 * q^74 + 12 * q^75 + 2 * q^76 + 4 * q^77 - 22 * q^79 + 44 * q^80 + 41 * q^81 + 156 * q^82 + 26 * q^83 + 11 * q^84 + 9 * q^85 + 17 * q^86 - 30 * q^87 + 21 * q^88 + 95 * q^89 + 18 * q^90 + 37 * q^92 + 62 * q^93 - 14 * q^94 + 8 * q^95 + 53 * q^96 + 40 * q^97 + 132 * q^98 + 35 * 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 $

$2$	0.717895	0.507628	0.253814	−	0.967253i	$-0.418315\pi$
$2$	0.717895	0.507628	0.253814	+	0.967253i	$0.418315\pi$
$3$	−2.94870	−1.70243	−0.851215	−	0.524817i	$-0.824134\pi$
$3$	−2.94870	−1.70243	−0.851215	+	0.524817i	$0.824134\pi$
$4$	−1.48463	−0.742314
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.11685	−0.864202
$7$	−0.587136	−0.221916	−0.110958	−	0.993825i	$-0.535392\pi$
$7$	−0.587136	−0.221916	−0.110958	+	0.993825i	$0.535392\pi$
$8$	−2.50160	−0.884448
$9$	5.69480	1.89827
$10$	0.717895	0.227018
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	4.37771	1.26374
$13$	0	0
$13$	0	0
$14$	−0.421502	−0.112651
$15$	−2.94870	−0.761350
$16$	1.17337	0.293343
$17$	5.09079	1.23470	0.617350	−	0.786689i	$-0.288206\pi$
$17$	5.09079	1.23470	0.617350	+	0.786689i	$0.288206\pi$
$18$	4.08827	0.963614
$19$	0.808186	0.185411	0.0927053	−	0.995694i	$-0.470449\pi$
$19$	0.808186	0.185411	0.0927053	+	0.995694i	$0.470449\pi$
$20$	−1.48463	−0.331973
$21$	1.73128	0.377797
$22$	0.717895	0.153056
$23$	1.18065	0.246183	0.123092	−	0.992395i	$-0.460719\pi$
$23$	1.18065	0.246183	0.123092	+	0.992395i	$0.460719\pi$
$24$	7.37644	1.50571
$25$	1.00000	0.200000
$26$	0	0
$27$	−7.94616	−1.52924
$28$	0.871677	0.164732
$29$	1.01718	0.188886	0.0944429	−	0.995530i	$-0.469893\pi$
$29$	1.01718	0.188886	0.0944429	+	0.995530i	$0.469893\pi$
$30$	−2.11685	−0.386483
$31$	−4.25282	−0.763830	−0.381915	−	0.924198i	$-0.624735\pi$
$31$	−4.25282	−0.763830	−0.381915	+	0.924198i	$0.624735\pi$
$32$	5.84555	1.03336
$33$	−2.94870	−0.513302
$34$	3.65465	0.626768
$35$	−0.587136	−0.0992440
$36$	−8.45466	−1.40911
$37$	10.6622	1.75285	0.876424	−	0.481540i	$-0.159922\pi$
$37$	10.6622	1.75285	0.876424	+	0.481540i	$0.159922\pi$
$38$	0.580193	0.0941197
$39$	0	0
$40$	−2.50160	−0.395537
$41$	4.80611	0.750588	0.375294	−	0.926906i	$-0.377542\pi$
$41$	4.80611	0.750588	0.375294	+	0.926906i	$0.377542\pi$
$42$	1.24288	0.191780
$43$	3.10017	0.472772	0.236386	−	0.971659i	$-0.424037\pi$
$43$	3.10017	0.472772	0.236386	+	0.971659i	$0.424037\pi$
$44$	−1.48463	−0.223816
$45$	5.69480	0.848931
$46$	0.847585	0.124970
$47$	5.76127	0.840368	0.420184	−	0.907439i	$-0.361965\pi$
$47$	5.76127	0.840368	0.420184	+	0.907439i	$0.361965\pi$
$48$	−3.45992	−0.499396
$49$	−6.65527	−0.950753
$50$	0.717895	0.101526
$51$	−15.0112	−2.10199
$52$	0	0
$53$	−4.90876	−0.674271	−0.337135	−	0.941456i	$-0.609458\pi$
$53$	−4.90876	−0.674271	−0.337135	+	0.941456i	$0.609458\pi$
$54$	−5.70450	−0.776285
$55$	1.00000	0.134840
$56$	1.46878	0.196273
$57$	−2.38310	−0.315649
$58$	0.730229	0.0958837
$59$	−4.99774	−0.650651	−0.325325	−	0.945602i	$-0.605474\pi$
$59$	−4.99774	−0.650651	−0.325325	+	0.945602i	$0.605474\pi$
$60$	4.37771	0.565160
$61$	12.4062	1.58845	0.794227	−	0.607621i	$-0.207876\pi$
$61$	12.4062	1.58845	0.794227	+	0.607621i	$0.207876\pi$
$62$	−3.05308	−0.387741
$63$	−3.34362	−0.421257
$64$	1.84974	0.231218
$65$	0	0
$66$	−2.11685	−0.260567
$67$	−10.3632	−1.26607	−0.633035	−	0.774123i	$-0.718191\pi$
$67$	−10.3632	−1.26607	−0.633035	+	0.774123i	$0.718191\pi$
$68$	−7.55793	−0.916534
$69$	−3.48139	−0.419110
$70$	−0.421502	−0.0503791
$71$	14.2767	1.69434	0.847168	−	0.531325i	$-0.178306\pi$
$71$	14.2767	1.69434	0.847168	+	0.531325i	$0.178306\pi$
$72$	−14.2461	−1.67892
$73$	−0.230278	−0.0269520	−0.0134760	−	0.999909i	$-0.504290\pi$
$73$	−0.230278	−0.0269520	−0.0134760	+	0.999909i	$0.504290\pi$
$74$	7.65431	0.889795
$75$	−2.94870	−0.340486
$76$	−1.19986	−0.137633
$77$	−0.587136	−0.0669103
$78$	0	0
$79$	−7.08489	−0.797112	−0.398556	−	0.917144i	$-0.630489\pi$
$79$	−7.08489	−0.797112	−0.398556	+	0.917144i	$0.630489\pi$
$80$	1.17337	0.131187
$81$	6.34638	0.705154
$82$	3.45028	0.381020
$83$	−9.62601	−1.05659	−0.528296	−	0.849060i	$-0.677169\pi$
$83$	−9.62601	−1.05659	−0.528296	+	0.849060i	$0.677169\pi$
$84$	−2.57031	−0.280444
$85$	5.09079	0.552174
$86$	2.22560	0.239993
$87$	−2.99936	−0.321565
$88$	−2.50160	−0.266671
$89$	1.35865	0.144017	0.0720084	−	0.997404i	$-0.477059\pi$
$89$	1.35865	0.144017	0.0720084	+	0.997404i	$0.477059\pi$
$90$	4.08827	0.430941
$91$	0	0
$92$	−1.75283	−0.182745
$93$	12.5403	1.30037
$94$	4.13599	0.426595
$95$	0.808186	0.0829182
$96$	−17.2367	−1.75922
$97$	5.88623	0.597656	0.298828	−	0.954307i	$-0.403404\pi$
$97$	5.88623	0.597656	0.298828	+	0.954307i	$0.403404\pi$
$98$	−4.77778	−0.482629
$99$	5.69480	0.572349
$100$	−1.48463	−0.148463
$101$	−9.85980	−0.981087	−0.490543	−	0.871417i	$-0.663202\pi$
$101$	−9.85980	−0.981087	−0.490543	+	0.871417i	$0.663202\pi$
$102$	−10.7765	−1.06703
$103$	−18.2212	−1.79539	−0.897694	−	0.440620i	$-0.854759\pi$
$103$	−18.2212	−1.79539	−0.897694	+	0.440620i	$0.854759\pi$
$104$	0	0
$105$	1.73128	0.168956
$106$	−3.52398	−0.342279
$107$	3.93242	0.380161	0.190080	−	0.981769i	$-0.439125\pi$
$107$	3.93242	0.380161	0.190080	+	0.981769i	$0.439125\pi$
$108$	11.7971	1.13517
$109$	−3.40255	−0.325906	−0.162953	−	0.986634i	$-0.552102\pi$
$109$	−3.40255	−0.325906	−0.162953	+	0.986634i	$0.552102\pi$
$110$	0.717895	0.0684486
$111$	−31.4395	−2.98410
$112$	−0.688929	−0.0650976
$113$	7.16866	0.674371	0.337185	−	0.941438i	$-0.390525\pi$
$113$	7.16866	0.674371	0.337185	+	0.941438i	$0.390525\pi$
$114$	−1.71081	−0.160232
$115$	1.18065	0.110097
$116$	−1.51013	−0.140212
$117$	0	0
$118$	−3.58785	−0.330289
$119$	−2.98899	−0.274000
$120$	7.37644	0.673374
$121$	1.00000	0.0909091
$122$	8.90636	0.806344
$123$	−14.1718	−1.27782
$124$	6.31386	0.567001
$125$	1.00000	0.0894427
$126$	−2.40037	−0.213842
$127$	13.8831	1.23193	0.615965	−	0.787774i	$-0.288766\pi$
$127$	13.8831	1.23193	0.615965	+	0.787774i	$0.288766\pi$
$128$	−10.3632	−0.915984
$129$	−9.14147	−0.804862
$130$	0	0
$131$	−2.23506	−0.195278	−0.0976392	−	0.995222i	$-0.531129\pi$
$131$	−2.23506	−0.195278	−0.0976392	+	0.995222i	$0.531129\pi$
$132$	4.37771	0.381031
$133$	−0.474515	−0.0411457
$134$	−7.43971	−0.642693
$135$	−7.94616	−0.683896
$136$	−12.7351	−1.09203
$137$	−10.7742	−0.920504	−0.460252	−	0.887788i	$-0.652241\pi$
$137$	−10.7742	−0.920504	−0.460252	+	0.887788i	$0.652241\pi$
$138$	−2.49927	−0.212752
$139$	19.0735	1.61779	0.808896	−	0.587952i	$-0.200066\pi$
$139$	19.0735	1.61779	0.808896	+	0.587952i	$0.200066\pi$
$140$	0.871677	0.0736702
$141$	−16.9882	−1.43067
$142$	10.2492	0.860093
$143$	0	0
$144$	6.68213	0.556844
$145$	1.01718	0.0844723
$146$	−0.165315	−0.0136816
$147$	19.6244	1.61859
$148$	−15.8293	−1.30116
$149$	−15.2327	−1.24791	−0.623954	−	0.781461i	$-0.714475\pi$
$149$	−15.2327	−1.24791	−0.623954	+	0.781461i	$0.714475\pi$
$150$	−2.11685	−0.172840
$151$	14.1983	1.15544	0.577722	−	0.816233i	$-0.303942\pi$
$151$	14.1983	1.15544	0.577722	+	0.816233i	$0.303942\pi$
$152$	−2.02176	−0.163986
$153$	28.9911	2.34379
$154$	−0.421502	−0.0339656
$155$	−4.25282	−0.341595
$156$	0	0
$157$	3.15854	0.252079	0.126039	−	0.992025i	$-0.459773\pi$
$157$	3.15854	0.252079	0.126039	+	0.992025i	$0.459773\pi$
$158$	−5.08620	−0.404637
$159$	14.4745	1.14790
$160$	5.84555	0.462131
$161$	−0.693204	−0.0546321
$162$	4.55603	0.357956
$163$	−10.0538	−0.787471	−0.393735	−	0.919224i	$-0.628817\pi$
$163$	−10.0538	−0.787471	−0.393735	+	0.919224i	$0.628817\pi$
$164$	−7.13528	−0.557172
$165$	−2.94870	−0.229556
$166$	−6.91046	−0.536356
$167$	6.15403	0.476213	0.238107	−	0.971239i	$-0.423473\pi$
$167$	6.15403	0.476213	0.238107	+	0.971239i	$0.423473\pi$
$168$	−4.33097	−0.334142
$169$	0	0
$170$	3.65465	0.280299
$171$	4.60246	0.351959
$172$	−4.60260	−0.350945
$173$	−9.04873	−0.687962	−0.343981	−	0.938977i	$-0.611776\pi$
$173$	−9.04873	−0.687962	−0.343981	+	0.938977i	$0.611776\pi$
$174$	−2.15322	−0.163235
$175$	−0.587136	−0.0443833
$176$	1.17337	0.0884463
$177$	14.7368	1.10769
$178$	0.975369	0.0731070
$179$	10.4726	0.782758	0.391379	−	0.920230i	$-0.371998\pi$
$179$	10.4726	0.782758	0.391379	+	0.920230i	$0.371998\pi$
$180$	−8.45466	−0.630173
$181$	−12.7827	−0.950127	−0.475064	−	0.879951i	$-0.657575\pi$
$181$	−12.7827	−0.950127	−0.475064	+	0.879951i	$0.657575\pi$
$182$	0	0
$183$	−36.5822	−2.70423
$184$	−2.95352	−0.217736
$185$	10.6622	0.783898
$186$	9.00260	0.660103
$187$	5.09079	0.372276
$188$	−8.55335	−0.623817
$189$	4.66547	0.339363
$190$	0.580193	0.0420916
$191$	−4.96865	−0.359519	−0.179759	−	0.983711i	$-0.557532\pi$
$191$	−4.96865	−0.359519	−0.179759	+	0.983711i	$0.557532\pi$
$192$	−5.45433	−0.393632
$193$	14.4125	1.03744	0.518719	−	0.854945i	$-0.326409\pi$
$193$	14.4125	1.03744	0.518719	+	0.854945i	$0.326409\pi$
$194$	4.22570	0.303387
$195$	0	0
$196$	9.88060	0.705757
$197$	0.743494	0.0529718	0.0264859	−	0.999649i	$-0.491568\pi$
$197$	0.743494	0.0529718	0.0264859	+	0.999649i	$0.491568\pi$
$198$	4.08827	0.290541
$199$	−8.08735	−0.573297	−0.286648	−	0.958036i	$-0.592541\pi$
$199$	−8.08735	−0.573297	−0.286648	+	0.958036i	$0.592541\pi$
$200$	−2.50160	−0.176890
$201$	30.5580	2.15540
$202$	−7.07830	−0.498027
$203$	−0.597223	−0.0419168
$204$	22.2860	1.56033
$205$	4.80611	0.335673
$206$	−13.0809	−0.911389
$207$	6.72359	0.467322
$208$	0	0
$209$	0.808186	0.0559034
$210$	1.24288	0.0857668
$211$	−22.6155	−1.55691	−0.778456	−	0.627699i	$-0.783997\pi$
$211$	−22.6155	−1.55691	−0.778456	+	0.627699i	$0.783997\pi$
$212$	7.28769	0.500520
$213$	−42.0977	−2.88449
$214$	2.82306	0.192980
$215$	3.10017	0.211430
$216$	19.8781	1.35253
$217$	2.49698	0.169506
$218$	−2.44268	−0.165439
$219$	0.679019	0.0458838
$220$	−1.48463	−0.100094
$221$	0	0
$222$	−22.5702	−1.51481
$223$	−6.55233	−0.438777	−0.219388	−	0.975638i	$-0.570406\pi$
$223$	−6.55233	−0.438777	−0.219388	+	0.975638i	$0.570406\pi$
$224$	−3.43213	−0.229319
$225$	5.69480	0.379654
$226$	5.14634	0.342330
$227$	−6.50628	−0.431837	−0.215919	−	0.976411i	$-0.569275\pi$
$227$	−6.50628	−0.431837	−0.215919	+	0.976411i	$0.569275\pi$
$228$	3.53801	0.234310
$229$	−15.8043	−1.04438	−0.522188	−	0.852830i	$-0.674884\pi$
$229$	−15.8043	−1.04438	−0.522188	+	0.852830i	$0.674884\pi$
$230$	0.847585	0.0558881
$231$	1.73128	0.113910
$232$	−2.54457	−0.167060
$233$	21.9774	1.43979	0.719894	−	0.694084i	$-0.244190\pi$
$233$	21.9774	1.43979	0.719894	+	0.694084i	$0.244190\pi$
$234$	0	0
$235$	5.76127	0.375824
$236$	7.41979	0.482987
$237$	20.8912	1.35703
$238$	−2.14578	−0.139090
$239$	−23.5456	−1.52304	−0.761518	−	0.648144i	$-0.775545\pi$
$239$	−23.5456	−1.52304	−0.761518	+	0.648144i	$0.775545\pi$
$240$	−3.45992	−0.223337
$241$	29.4887	1.89953	0.949766	−	0.312962i	$-0.101321\pi$
$241$	29.4887	1.89953	0.949766	+	0.312962i	$0.101321\pi$
$242$	0.717895	0.0461480
$243$	5.12492	0.328764
$244$	−18.4186	−1.17913
$245$	−6.65527	−0.425190
$246$	−10.1738	−0.648660
$247$	0	0
$248$	10.6388	0.675567
$249$	28.3842	1.79877
$250$	0.717895	0.0454036
$251$	−16.9575	−1.07035	−0.535174	−	0.844742i	$-0.679754\pi$
$251$	−16.9575	−1.07035	−0.535174	+	0.844742i	$0.679754\pi$
$252$	4.96403	0.312705
$253$	1.18065	0.0742271
$254$	9.96663	0.625362
$255$	−15.0112	−0.940038
$256$	−11.1392	−0.696197
$257$	−2.31516	−0.144416	−0.0722079	−	0.997390i	$-0.523005\pi$
$257$	−2.31516	−0.144416	−0.0722079	+	0.997390i	$0.523005\pi$
$258$	−6.56261	−0.408570
$259$	−6.26013	−0.388986
$260$	0	0
$261$	5.79265	0.358556
$262$	−1.60454	−0.0991288
$263$	10.4049	0.641591	0.320796	−	0.947148i	$-0.396050\pi$
$263$	10.4049	0.641591	0.320796	+	0.947148i	$0.396050\pi$
$264$	7.37644	0.453989
$265$	−4.90876	−0.301543
$266$	−0.340652	−0.0208867
$267$	−4.00625	−0.245179
$268$	15.3855	0.939821
$269$	16.6226	1.01350	0.506748	−	0.862094i	$-0.330847\pi$
$269$	16.6226	1.01350	0.506748	+	0.862094i	$0.330847\pi$
$270$	−5.70450	−0.347165
$271$	−19.3366	−1.17462	−0.587309	−	0.809363i	$-0.699813\pi$
$271$	−19.3366	−1.17462	−0.587309	+	0.809363i	$0.699813\pi$
$272$	5.97340	0.362190
$273$	0	0
$274$	−7.73475	−0.467274
$275$	1.00000	0.0603023
$276$	5.16856	0.311111
$277$	27.4526	1.64947	0.824733	−	0.565523i	$-0.191326\pi$
$277$	27.4526	1.64947	0.824733	+	0.565523i	$0.191326\pi$
$278$	13.6928	0.821237
$279$	−24.2190	−1.44995
$280$	1.46878	0.0877761
$281$	−0.946149	−0.0564425	−0.0282213	−	0.999602i	$-0.508984\pi$
$281$	−0.946149	−0.0564425	−0.0282213	+	0.999602i	$0.508984\pi$
$282$	−12.1958	−0.726248
$283$	17.7532	1.05532	0.527660	−	0.849455i	$-0.323069\pi$
$283$	17.7532	1.05532	0.527660	+	0.849455i	$0.323069\pi$
$284$	−21.1956	−1.25773
$285$	−2.38310	−0.141162
$286$	0	0
$287$	−2.82184	−0.166568
$288$	33.2893	1.96159
$289$	8.91619	0.524482
$290$	0.730229	0.0428805
$291$	−17.3567	−1.01747
$292$	0.341876	0.0200068
$293$	12.6408	0.738484	0.369242	−	0.929333i	$-0.379617\pi$
$293$	12.6408	0.738484	0.369242	+	0.929333i	$0.379617\pi$
$294$	14.0882	0.821642
$295$	−4.99774	−0.290980
$296$	−26.6724	−1.55030
$297$	−7.94616	−0.461083
$298$	−10.9354	−0.633473
$299$	0	0
$300$	4.37771	0.252747
$301$	−1.82022	−0.104916
$302$	10.1929	0.586536
$303$	29.0735	1.67023
$304$	0.948303	0.0543889
$305$	12.4062	0.710378
$306$	20.8125	1.18977
$307$	3.74701	0.213853	0.106927	−	0.994267i	$-0.465899\pi$
$307$	3.74701	0.213853	0.106927	+	0.994267i	$0.465899\pi$
$308$	0.871677	0.0496684
$309$	53.7287	3.05652
$310$	−3.05308	−0.173403
$311$	4.46458	0.253163	0.126581	−	0.991956i	$-0.459599\pi$
$311$	4.46458	0.253163	0.126581	+	0.991956i	$0.459599\pi$
$312$	0	0
$313$	11.5873	0.654954	0.327477	−	0.944859i	$-0.393802\pi$
$313$	11.5873	0.654954	0.327477	+	0.944859i	$0.393802\pi$
$314$	2.26750	0.127962
$315$	−3.34362	−0.188392
$316$	10.5184	0.591707
$317$	35.3154	1.98351	0.991755	−	0.128147i	$-0.0409031\pi$
$317$	35.3154	1.98351	0.991755	+	0.128147i	$0.0409031\pi$
$318$	10.3911	0.582706
$319$	1.01718	0.0569512
$320$	1.84974	0.103404
$321$	−11.5955	−0.647197
$322$	−0.497647	−0.0277328
$323$	4.11431	0.228926
$324$	−9.42201	−0.523445
$325$	0	0
$326$	−7.21753	−0.399742
$327$	10.0331	0.554832
$328$	−12.0229	−0.663856
$329$	−3.38265	−0.186491
$330$	−2.11685	−0.116529
$331$	0.718369	0.0394852	0.0197426	−	0.999805i	$-0.493715\pi$
$331$	0.718369	0.0394852	0.0197426	+	0.999805i	$0.493715\pi$
$332$	14.2910	0.784323
$333$	60.7189	3.32738
$334$	4.41795	0.241739
$335$	−10.3632	−0.566204
$336$	2.03144	0.110824
$337$	−17.2505	−0.939694	−0.469847	−	0.882748i	$-0.655691\pi$
$337$	−17.2505	−0.939694	−0.469847	+	0.882748i	$0.655691\pi$
$338$	0	0
$339$	−21.1382	−1.14807
$340$	−7.55793	−0.409886
$341$	−4.25282	−0.230303
$342$	3.30408	0.178664
$343$	8.01750	0.432904
$344$	−7.75538	−0.418142
$345$	−3.48139	−0.187432
$346$	−6.49603	−0.349229
$347$	26.8124	1.43936	0.719682	−	0.694304i	$-0.244288\pi$
$347$	26.8124	1.43936	0.719682	+	0.694304i	$0.244288\pi$
$348$	4.45293	0.238702
$349$	18.5965	0.995447	0.497723	−	0.867336i	$-0.334169\pi$
$349$	18.5965	0.995447	0.497723	+	0.867336i	$0.334169\pi$
$350$	−0.421502	−0.0225302
$351$	0	0
$352$	5.84555	0.311569
$353$	17.6914	0.941618	0.470809	−	0.882235i	$-0.343962\pi$
$353$	17.6914	0.941618	0.470809	+	0.882235i	$0.343962\pi$
$354$	10.5795	0.562293
$355$	14.2767	0.757730
$356$	−2.01709	−0.106906
$357$	8.81361	0.466466
$358$	7.51821	0.397350
$359$	−21.3937	−1.12912	−0.564558	−	0.825393i	$-0.690953\pi$
$359$	−21.3937	−1.12912	−0.564558	+	0.825393i	$0.690953\pi$
$360$	−14.2461	−0.750835
$361$	−18.3468	−0.965623
$362$	−9.17660	−0.482311
$363$	−2.94870	−0.154766
$364$	0	0
$365$	−0.230278	−0.0120533
$366$	−26.2621	−1.37274
$367$	26.1290	1.36392	0.681960	−	0.731389i	$-0.261128\pi$
$367$	26.1290	1.36392	0.681960	+	0.731389i	$0.261128\pi$
$368$	1.38535	0.0722162
$369$	27.3699	1.42482
$370$	7.65431	0.397929
$371$	2.88211	0.149632
$372$	−18.6176	−0.965280
$373$	26.2127	1.35724	0.678622	−	0.734488i	$-0.262577\pi$
$373$	26.2127	1.35724	0.678622	+	0.734488i	$0.262577\pi$
$374$	3.65465	0.188978
$375$	−2.94870	−0.152270
$376$	−14.4124	−0.743262
$377$	0	0
$378$	3.34932	0.172270
$379$	−3.81800	−0.196117	−0.0980587	−	0.995181i	$-0.531263\pi$
$379$	−3.81800	−0.196117	−0.0980587	+	0.995181i	$0.531263\pi$
$380$	−1.19986	−0.0615513
$381$	−40.9371	−2.09727
$382$	−3.56697	−0.182502
$383$	−3.59885	−0.183892	−0.0919462	−	0.995764i	$-0.529309\pi$
$383$	−3.59885	−0.183892	−0.0919462	+	0.995764i	$0.529309\pi$
$384$	30.5578	1.55940
$385$	−0.587136	−0.0299232
$386$	10.3467	0.526632
$387$	17.6549	0.897448
$388$	−8.73886	−0.443649
$389$	−1.08708	−0.0551172	−0.0275586	−	0.999620i	$-0.508773\pi$
$389$	−1.08708	−0.0551172	−0.0275586	+	0.999620i	$0.508773\pi$
$390$	0	0
$391$	6.01047	0.303962
$392$	16.6488	0.840891
$393$	6.59052	0.332448
$394$	0.533751	0.0268900
$395$	−7.08489	−0.356479
$396$	−8.45466	−0.424863
$397$	−37.2204	−1.86804	−0.934019	−	0.357223i	$-0.883724\pi$
$397$	−37.2204	−1.86804	−0.934019	+	0.357223i	$0.883724\pi$
$398$	−5.80587	−0.291022
$399$	1.39920	0.0700476
$400$	1.17337	0.0586686
$401$	34.6118	1.72843	0.864216	−	0.503121i	$-0.167815\pi$
$401$	34.6118	1.72843	0.864216	+	0.503121i	$0.167815\pi$
$402$	21.9374	1.09414
$403$	0	0
$404$	14.6381	0.728274
$405$	6.34638	0.315354
$406$	−0.428743	−0.0212782
$407$	10.6622	0.528504
$408$	37.5520	1.85910
$409$	35.9611	1.77816	0.889080	−	0.457752i	$-0.151345\pi$
$409$	35.9611	1.77816	0.889080	+	0.457752i	$0.151345\pi$
$410$	3.45028	0.170397
$411$	31.7699	1.56709
$412$	27.0517	1.33274
$413$	2.93435	0.144390
$414$	4.82683	0.237226
$415$	−9.62601	−0.472522
$416$	0	0
$417$	−56.2419	−2.75418
$418$	0.580193	0.0283782
$419$	−36.0933	−1.76327	−0.881637	−	0.471927i	$-0.843558\pi$
$419$	−36.0933	−1.76327	−0.881637	+	0.471927i	$0.843558\pi$
$420$	−2.57031	−0.125418
$421$	−1.57495	−0.0767583	−0.0383792	−	0.999263i	$-0.512219\pi$
$421$	−1.57495	−0.0767583	−0.0383792	+	0.999263i	$0.512219\pi$
$422$	−16.2355	−0.790333
$423$	32.8093	1.59524
$424$	12.2797	0.596357
$425$	5.09079	0.246940
$426$	−30.2217	−1.46425
$427$	−7.28413	−0.352504
$428$	−5.83817	−0.282199
$429$	0	0
$430$	2.22560	0.107328
$431$	−17.1519	−0.826179	−0.413090	−	0.910690i	$-0.635550\pi$
$431$	−17.1519	−0.826179	−0.413090	+	0.910690i	$0.635550\pi$
$432$	−9.32380	−0.448592
$433$	−24.4852	−1.17668	−0.588342	−	0.808612i	$-0.700219\pi$
$433$	−24.4852	−1.17668	−0.588342	+	0.808612i	$0.700219\pi$
$434$	1.79257	0.0860462
$435$	−2.99936	−0.143808
$436$	5.05153	0.241924
$437$	0.954188	0.0456450
$438$	0.487464	0.0232919
$439$	27.7898	1.32633	0.663166	−	0.748472i	$-0.269212\pi$
$439$	27.7898	1.32633	0.663166	+	0.748472i	$0.269212\pi$
$440$	−2.50160	−0.119259
$441$	−37.9005	−1.80478
$442$	0	0
$443$	13.7497	0.653270	0.326635	−	0.945151i	$-0.394085\pi$
$443$	13.7497	0.653270	0.326635	+	0.945151i	$0.394085\pi$
$444$	46.6759	2.21514
$445$	1.35865	0.0644063
$446$	−4.70389	−0.222735
$447$	44.9165	2.12448
$448$	−1.08605	−0.0513111
$449$	−5.19338	−0.245091	−0.122545	−	0.992463i	$-0.539106\pi$
$449$	−5.19338	−0.245091	−0.122545	+	0.992463i	$0.539106\pi$
$450$	4.08827	0.192723
$451$	4.80611	0.226311
$452$	−10.6428	−0.500595
$453$	−41.8666	−1.96706
$454$	−4.67083	−0.219213
$455$	0	0
$456$	5.96154	0.279175
$457$	−1.53656	−0.0718771	−0.0359386	−	0.999354i	$-0.511442\pi$
$457$	−1.53656	−0.0718771	−0.0359386	+	0.999354i	$0.511442\pi$
$458$	−11.3458	−0.530155
$459$	−40.4523	−1.88815
$460$	−1.75283	−0.0817261
$461$	28.8263	1.34258	0.671288	−	0.741197i	$-0.265742\pi$
$461$	28.8263	1.34258	0.671288	+	0.741197i	$0.265742\pi$
$462$	1.24288	0.0578240
$463$	10.5358	0.489642	0.244821	−	0.969568i	$-0.421271\pi$
$463$	10.5358	0.489642	0.244821	+	0.969568i	$0.421271\pi$
$464$	1.19353	0.0554083
$465$	12.5403	0.581542
$466$	15.7775	0.730877
$467$	−4.11703	−0.190514	−0.0952568	−	0.995453i	$-0.530367\pi$
$467$	−4.11703	−0.190514	−0.0952568	+	0.995453i	$0.530367\pi$
$468$	0	0
$469$	6.08462	0.280962
$470$	4.13599	0.190779
$471$	−9.31357	−0.429147
$472$	12.5023	0.575466
$473$	3.10017	0.142546
$474$	14.9977	0.688866
$475$	0.808186	0.0370821
$476$	4.43753	0.203394
$477$	−27.9545	−1.27995
$478$	−16.9032	−0.773136
$479$	16.8391	0.769400	0.384700	−	0.923042i	$-0.374305\pi$
$479$	16.8391	0.769400	0.384700	+	0.923042i	$0.374305\pi$
$480$	−17.2367	−0.786746
$481$	0	0
$482$	21.1698	0.964256
$483$	2.04405	0.0930073
$484$	−1.48463	−0.0674831
$485$	5.88623	0.267280
$486$	3.67915	0.166890
$487$	21.9527	0.994771	0.497385	−	0.867530i	$-0.334294\pi$
$487$	21.9527	0.994771	0.497385	+	0.867530i	$0.334294\pi$
$488$	−31.0353	−1.40490
$489$	29.6454	1.34061
$490$	−4.77778	−0.215838
$491$	−13.7339	−0.619803	−0.309902	−	0.950769i	$-0.600296\pi$
$491$	−13.7339	−0.619803	−0.309902	+	0.950769i	$0.600296\pi$
$492$	21.0398	0.948546
$493$	5.17826	0.233217
$494$	0	0
$495$	5.69480	0.255962
$496$	−4.99014	−0.224064
$497$	−8.38238	−0.376001
$498$	20.3769	0.913109
$499$	24.0502	1.07664	0.538318	−	0.842742i	$-0.319060\pi$
$499$	24.0502	1.07664	0.538318	+	0.842742i	$0.319060\pi$
$500$	−1.48463	−0.0663945
$501$	−18.1464	−0.810720
$502$	−12.1737	−0.543339
$503$	−7.92371	−0.353301	−0.176650	−	0.984274i	$-0.556526\pi$
$503$	−7.92371	−0.353301	−0.176650	+	0.984274i	$0.556526\pi$
$504$	8.36439	0.372580
$505$	−9.85980	−0.438755
$506$	0.847585	0.0376797
$507$	0	0
$508$	−20.6113	−0.914478
$509$	1.08533	0.0481065	0.0240532	−	0.999711i	$-0.492343\pi$
$509$	1.08533	0.0481065	0.0240532	+	0.999711i	$0.492343\pi$
$510$	−10.7765	−0.477190
$511$	0.135204	0.00598108
$512$	12.7296	0.562575
$513$	−6.42198	−0.283537
$514$	−1.66204	−0.0733095
$515$	−18.2212	−0.802922
$516$	13.5717	0.597460
$517$	5.76127	0.253381
$518$	−4.49412	−0.197460
$519$	26.6819	1.17121
$520$	0	0
$521$	35.0616	1.53608	0.768039	−	0.640403i	$-0.221233\pi$
$521$	35.0616	1.53608	0.768039	+	0.640403i	$0.221233\pi$
$522$	4.15851	0.182013
$523$	28.5874	1.25004	0.625019	−	0.780609i	$-0.285091\pi$
$523$	28.5874	1.25004	0.625019	+	0.780609i	$0.285091\pi$
$524$	3.31824	0.144958
$525$	1.73128	0.0755594
$526$	7.46960	0.325690
$527$	−21.6502	−0.943100
$528$	−3.45992	−0.150574
$529$	−21.6061	−0.939394
$530$	−3.52398	−0.153072
$531$	−28.4612	−1.23511
$532$	0.704478	0.0305430
$533$	0	0
$534$	−2.87607	−0.124460
$535$	3.93242	0.170013
$536$	25.9246	1.11977
$537$	−30.8805	−1.33259
$538$	11.9333	0.514480
$539$	−6.65527	−0.286663
$540$	11.7971	0.507666
$541$	1.62257	0.0697595	0.0348798	−	0.999392i	$-0.488895\pi$
$541$	1.62257	0.0697595	0.0348798	+	0.999392i	$0.488895\pi$
$542$	−13.8817	−0.596269
$543$	37.6922	1.61753
$544$	29.7585	1.27588
$545$	−3.40255	−0.145749
$546$	0	0
$547$	6.26802	0.268001	0.134001	−	0.990981i	$-0.457218\pi$
$547$	6.26802	0.268001	0.134001	+	0.990981i	$0.457218\pi$
$548$	15.9957	0.683302
$549$	70.6510	3.01531
$550$	0.717895	0.0306111
$551$	0.822072	0.0350214
$552$	8.70902	0.370681
$553$	4.15979	0.176892
$554$	19.7081	0.837315
$555$	−31.4395	−1.33453
$556$	−28.3170	−1.20091
$557$	12.9920	0.550488	0.275244	−	0.961374i	$-0.411241\pi$
$557$	12.9920	0.550488	0.275244	+	0.961374i	$0.411241\pi$
$558$	−17.3867	−0.736037
$559$	0	0
$560$	−0.688929	−0.0291125
$561$	−15.0112	−0.633774
$562$	−0.679235	−0.0286518
$563$	−23.3598	−0.984498	−0.492249	−	0.870454i	$-0.663825\pi$
$563$	−23.3598	−0.984498	−0.492249	+	0.870454i	$0.663825\pi$
$564$	25.2212	1.06200
$565$	7.16866	0.301588
$566$	12.7450	0.535711
$567$	−3.72619	−0.156485
$568$	−35.7146	−1.49855
$569$	−40.7605	−1.70877	−0.854385	−	0.519641i	$-0.826066\pi$
$569$	−40.7605	−1.70877	−0.854385	+	0.519641i	$0.826066\pi$
$570$	−1.71081	−0.0716580
$571$	28.1752	1.17909	0.589547	−	0.807734i	$-0.299306\pi$
$571$	28.1752	1.17909	0.589547	+	0.807734i	$0.299306\pi$
$572$	0	0
$573$	14.6510	0.612056
$574$	−2.02578	−0.0845545
$575$	1.18065	0.0492367
$576$	10.5339	0.438914
$577$	34.8474	1.45072	0.725359	−	0.688371i	$-0.241674\pi$
$577$	34.8474	1.45072	0.725359	+	0.688371i	$0.241674\pi$
$578$	6.40089	0.266242
$579$	−42.4982	−1.76616
$580$	−1.51013	−0.0627049
$581$	5.65177	0.234475
$582$	−12.4603	−0.516496
$583$	−4.90876	−0.203300
$584$	0.576061	0.0238376
$585$	0	0
$586$	9.07477	0.374875
$587$	41.7147	1.72175	0.860874	−	0.508818i	$-0.169917\pi$
$587$	41.7147	1.72175	0.860874	+	0.508818i	$0.169917\pi$
$588$	−29.1349	−1.20150
$589$	−3.43707	−0.141622
$590$	−3.58785	−0.147710
$591$	−2.19234	−0.0901808
$592$	12.5107	0.514186
$593$	−36.2488	−1.48856	−0.744281	−	0.667867i	$-0.767207\pi$
$593$	−36.2488	−1.48856	−0.744281	+	0.667867i	$0.767207\pi$
$594$	−5.70450	−0.234059
$595$	−2.98899	−0.122537
$596$	22.6148	0.926339
$597$	23.8471	0.975998
$598$	0	0
$599$	13.5733	0.554590	0.277295	−	0.960785i	$-0.410562\pi$
$599$	13.5733	0.554590	0.277295	+	0.960785i	$0.410562\pi$
$600$	7.37644	0.301142
$601$	−30.6401	−1.24983	−0.624917	−	0.780691i	$-0.714867\pi$
$601$	−30.6401	−1.24983	−0.624917	+	0.780691i	$0.714867\pi$
$602$	−1.30673	−0.0532583
$603$	−59.0166	−2.40334
$604$	−21.0792	−0.857702
$605$	1.00000	0.0406558
$606$	20.8717	0.847857
$607$	44.5831	1.80957	0.904786	−	0.425866i	$-0.140031\pi$
$607$	44.5831	1.80957	0.904786	+	0.425866i	$0.140031\pi$
$608$	4.72429	0.191595
$609$	1.76103	0.0713605
$610$	8.90636	0.360608
$611$	0	0
$612$	−43.0409	−1.73983
$613$	−4.81321	−0.194404	−0.0972019	−	0.995265i	$-0.530989\pi$
$613$	−4.81321	−0.194404	−0.0972019	+	0.995265i	$0.530989\pi$
$614$	2.68996	0.108558
$615$	−14.1718	−0.571460
$616$	1.46878	0.0591787
$617$	−21.7832	−0.876960	−0.438480	−	0.898741i	$-0.644483\pi$
$617$	−21.7832	−0.876960	−0.438480	+	0.898741i	$0.644483\pi$
$618$	38.5716	1.55158
$619$	9.32860	0.374948	0.187474	−	0.982270i	$-0.439970\pi$
$619$	9.32860	0.374948	0.187474	+	0.982270i	$0.439970\pi$
$620$	6.31386	0.253571
$621$	−9.38166	−0.376473
$622$	3.20510	0.128513
$623$	−0.797713	−0.0319597
$624$	0	0
$625$	1.00000	0.0400000
$626$	8.31847	0.332473
$627$	−2.38310	−0.0951717
$628$	−4.68925	−0.187122
$629$	54.2789	2.16424
$630$	−2.40037	−0.0956330
$631$	33.7195	1.34235	0.671176	−	0.741298i	$-0.265789\pi$
$631$	33.7195	1.34235	0.671176	+	0.741298i	$0.265789\pi$
$632$	17.7235	0.705004
$633$	66.6861	2.65054
$634$	25.3527	1.00689
$635$	13.8831	0.550935
$636$	−21.4892	−0.852101
$637$	0	0
$638$	0.730229	0.0289100
$639$	81.3032	3.21630
$640$	−10.3632	−0.409640
$641$	−35.8922	−1.41766	−0.708828	−	0.705381i	$-0.750776\pi$
$641$	−35.8922	−1.41766	−0.708828	+	0.705381i	$0.750776\pi$
$642$	−8.32434	−0.328536
$643$	23.4944	0.926530	0.463265	−	0.886220i	$-0.346678\pi$
$643$	23.4944	0.926530	0.463265	+	0.886220i	$0.346678\pi$
$644$	1.02915	0.0405542
$645$	−9.14147	−0.359945
$646$	2.95364	0.116209
$647$	−42.8409	−1.68425	−0.842126	−	0.539281i	$-0.818696\pi$
$647$	−42.8409	−1.68425	−0.842126	+	0.539281i	$0.818696\pi$
$648$	−15.8761	−0.623671
$649$	−4.99774	−0.196179
$650$	0	0
$651$	−7.36284	−0.288573
$652$	14.9261	0.584550
$653$	46.4151	1.81636	0.908182	−	0.418576i	$-0.137471\pi$
$653$	46.4151	1.81636	0.908182	+	0.418576i	$0.137471\pi$
$654$	7.20271	0.281648
$655$	−2.23506	−0.0873312
$656$	5.63936	0.220180
$657$	−1.31139	−0.0511620
$658$	−2.42839	−0.0946683
$659$	−36.1433	−1.40794	−0.703972	−	0.710228i	$-0.748592\pi$
$659$	−36.1433	−1.40794	−0.703972	+	0.710228i	$0.748592\pi$
$660$	4.37771	0.170402
$661$	−16.0734	−0.625184	−0.312592	−	0.949888i	$-0.601197\pi$
$661$	−16.0734	−0.625184	−0.312592	+	0.949888i	$0.601197\pi$
$662$	0.515714	0.0200438
$663$	0	0
$664$	24.0804	0.934500
$665$	−0.474515	−0.0184009
$666$	43.5898	1.68907
$667$	1.20094	0.0465005
$668$	−9.13644	−0.353499
$669$	19.3208	0.746987
$670$	−7.43971	−0.287421
$671$	12.4062	0.478937
$672$	10.1203	0.390399
$673$	−10.8709	−0.419041	−0.209521	−	0.977804i	$-0.567190\pi$
$673$	−10.8709	−0.419041	−0.209521	+	0.977804i	$0.567190\pi$
$674$	−12.3840	−0.477015
$675$	−7.94616	−0.305848
$676$	0	0
$677$	14.7019	0.565041	0.282520	−	0.959261i	$-0.408830\pi$
$677$	14.7019	0.565041	0.282520	+	0.959261i	$0.408830\pi$
$678$	−15.1750	−0.582792
$679$	−3.45602	−0.132630
$680$	−12.7351	−0.488369
$681$	19.1850	0.735173
$682$	−3.05308	−0.116908
$683$	−1.07456	−0.0411170	−0.0205585	−	0.999789i	$-0.506544\pi$
$683$	−1.07456	−0.0411170	−0.0205585	+	0.999789i	$0.506544\pi$
$684$	−6.83294	−0.261264
$685$	−10.7742	−0.411662
$686$	5.75572	0.219754
$687$	46.6020	1.77798
$688$	3.63766	0.138684
$689$	0	0
$690$	−2.49927	−0.0951456
$691$	−35.3469	−1.34466	−0.672329	−	0.740252i	$-0.734706\pi$
$691$	−35.3469	−1.34466	−0.672329	+	0.740252i	$0.734706\pi$
$692$	13.4340	0.510684
$693$	−3.34362	−0.127014
$694$	19.2485	0.730662
$695$	19.0735	0.723498
$696$	7.50318	0.284407
$697$	24.4669	0.926751
$698$	13.3503	0.505317
$699$	−64.8047	−2.45114
$700$	0.871677	0.0329463
$701$	−24.8855	−0.939913	−0.469957	−	0.882690i	$-0.655730\pi$
$701$	−24.8855	−0.939913	−0.469957	+	0.882690i	$0.655730\pi$
$702$	0	0
$703$	8.61701	0.324997
$704$	1.84974	0.0697148
$705$	−16.9882	−0.639814
$706$	12.7006	0.477992
$707$	5.78904	0.217719
$708$	−21.8787	−0.822251
$709$	13.6025	0.510852	0.255426	−	0.966829i	$-0.417784\pi$
$709$	13.6025	0.510852	0.255426	+	0.966829i	$0.417784\pi$
$710$	10.2492	0.384645
$711$	−40.3470	−1.51313
$712$	−3.39880	−0.127375
$713$	−5.02111	−0.188042
$714$	6.32725	0.236791
$715$	0	0
$716$	−15.5479	−0.581052
$717$	69.4287	2.59286
$718$	−15.3584	−0.573171
$719$	12.0436	0.449149	0.224575	−	0.974457i	$-0.427901\pi$
$719$	12.0436	0.449149	0.224575	+	0.974457i	$0.427901\pi$
$720$	6.68213	0.249028
$721$	10.6983	0.398426
$722$	−13.1711	−0.490177
$723$	−86.9531	−3.23382
$724$	18.9775	0.705292
$725$	1.01718	0.0377771
$726$	−2.11685	−0.0785638
$727$	−23.3689	−0.866703	−0.433352	−	0.901225i	$-0.642669\pi$
$727$	−23.3689	−0.866703	−0.433352	+	0.901225i	$0.642669\pi$
$728$	0	0
$729$	−34.1510	−1.26485
$730$	−0.165315	−0.00611859
$731$	15.7824	0.583731
$732$	54.3109	2.00739
$733$	−18.6667	−0.689470	−0.344735	−	0.938700i	$-0.612031\pi$
$733$	−18.6667	−0.689470	−0.344735	+	0.938700i	$0.612031\pi$
$734$	18.7578	0.692365
$735$	19.6244	0.723856
$736$	6.90157	0.254395
$737$	−10.3632	−0.381734
$738$	19.6487	0.723278
$739$	−19.1608	−0.704843	−0.352421	−	0.935841i	$-0.614642\pi$
$739$	−19.1608	−0.704843	−0.352421	+	0.935841i	$0.614642\pi$
$740$	−15.8293	−0.581898
$741$	0	0
$742$	2.06905	0.0759573
$743$	0.249612	0.00915738	0.00457869	−	0.999990i	$-0.498543\pi$
$743$	0.249612	0.00915738	0.00457869	+	0.999990i	$0.498543\pi$
$744$	−31.3707	−1.15011
$745$	−15.2327	−0.558081
$746$	18.8180	0.688976
$747$	−54.8183	−2.00570
$748$	−7.55793	−0.276345
$749$	−2.30886	−0.0843639
$750$	−2.11685	−0.0772965
$751$	−13.6797	−0.499178	−0.249589	−	0.968352i	$-0.580295\pi$
$751$	−13.6797	−0.499178	−0.249589	+	0.968352i	$0.580295\pi$
$752$	6.76012	0.246516
$753$	50.0025	1.82219
$754$	0	0
$755$	14.1983	0.516731
$756$	−6.92649	−0.251914
$757$	51.2665	1.86331	0.931656	−	0.363342i	$-0.118364\pi$
$757$	51.2665	1.86331	0.931656	+	0.363342i	$0.118364\pi$
$758$	−2.74092	−0.0995547
$759$	−3.48139	−0.126366
$760$	−2.02176	−0.0733368
$761$	1.48419	0.0538020	0.0269010	−	0.999638i	$-0.491436\pi$
$761$	1.48419	0.0538020	0.0269010	+	0.999638i	$0.491436\pi$
$762$	−29.3886	−1.06464
$763$	1.99776	0.0723238
$764$	7.37659	0.266876
$765$	28.9911	1.04817
$766$	−2.58359	−0.0933490
$767$	0	0
$768$	32.8460	1.18523
$769$	7.85094	0.283112	0.141556	−	0.989930i	$-0.454789\pi$
$769$	7.85094	0.283112	0.141556	+	0.989930i	$0.454789\pi$
$770$	−0.421502	−0.0151899
$771$	6.82671	0.245858
$772$	−21.3972	−0.770104
$773$	41.1336	1.47947	0.739737	−	0.672896i	$-0.234950\pi$
$773$	41.1336	1.47947	0.739737	+	0.672896i	$0.234950\pi$
$774$	12.6744	0.455570
$775$	−4.25282	−0.152766
$776$	−14.7250	−0.528596
$777$	18.4592	0.662221
$778$	−0.780409	−0.0279790
$779$	3.88423	0.139167
$780$	0	0
$781$	14.2767	0.510862
$782$	4.31488	0.154300
$783$	−8.08268	−0.288851
$784$	−7.80911	−0.278897
$785$	3.15854	0.112733
$786$	4.73130	0.168760
$787$	−20.7794	−0.740706	−0.370353	−	0.928891i	$-0.620763\pi$
$787$	−20.7794	−0.740706	−0.370353	+	0.928891i	$0.620763\pi$
$788$	−1.10381	−0.0393217
$789$	−30.6808	−1.09226
$790$	−5.08620	−0.180959
$791$	−4.20898	−0.149654
$792$	−14.2461	−0.506213
$793$	0	0
$794$	−26.7203	−0.948269
$795$	14.4745	0.513356
$796$	12.0067	0.425566
$797$	−45.3480	−1.60631	−0.803154	−	0.595772i	$-0.796846\pi$
$797$	−45.3480	−1.60631	−0.803154	+	0.595772i	$0.796846\pi$
$798$	1.00448	0.0355581
$799$	29.3295	1.03760
$800$	5.84555	0.206671
$801$	7.73726	0.273383
$802$	24.8476	0.877401
$803$	−0.230278	−0.00812632
$804$	−45.3672	−1.59998
$805$	−0.693204	−0.0244322
$806$	0	0
$807$	−49.0149	−1.72541
$808$	24.6652	0.867720
$809$	37.4187	1.31557	0.657786	−	0.753205i	$-0.271493\pi$
$809$	37.4187	1.31557	0.657786	+	0.753205i	$0.271493\pi$
$810$	4.55603	0.160083
$811$	−26.6480	−0.935737	−0.467869	−	0.883798i	$-0.654978\pi$
$811$	−26.6480	−0.935737	−0.467869	+	0.883798i	$0.654978\pi$
$812$	0.886654	0.0311154
$813$	57.0179	1.99970
$814$	7.65431	0.268283
$815$	−10.0538	−0.352168
$816$	−17.6137	−0.616604
$817$	2.50552	0.0876570
$818$	25.8163	0.902644
$819$	0	0
$820$	−7.13528	−0.249175
$821$	47.2074	1.64755	0.823775	−	0.566916i	$-0.191864\pi$
$821$	47.2074	1.64755	0.823775	+	0.566916i	$0.191864\pi$
$822$	22.8074	0.795501
$823$	27.4870	0.958138	0.479069	−	0.877777i	$-0.340974\pi$
$823$	27.4870	0.958138	0.479069	+	0.877777i	$0.340974\pi$
$824$	45.5820	1.58793
$825$	−2.94870	−0.102660
$826$	2.10656	0.0732965
$827$	−9.24737	−0.321563	−0.160781	−	0.986990i	$-0.551401\pi$
$827$	−9.24737	−0.321563	−0.160781	+	0.986990i	$0.551401\pi$
$828$	−9.98203	−0.346899
$829$	−40.0373	−1.39055	−0.695276	−	0.718743i	$-0.744718\pi$
$829$	−40.0373	−1.39055	−0.695276	+	0.718743i	$0.744718\pi$
$830$	−6.91046	−0.239866
$831$	−80.9493	−2.80810
$832$	0	0
$833$	−33.8806	−1.17389
$834$	−40.3758	−1.39810
$835$	6.15403	0.212969
$836$	−1.19986	−0.0414979
$837$	33.7936	1.16808
$838$	−25.9112	−0.895088
$839$	−0.0939057	−0.00324198	−0.00162099	−	0.999999i	$-0.500516\pi$
$839$	−0.0939057	−0.00324198	−0.00162099	+	0.999999i	$0.500516\pi$
$840$	−4.33097	−0.149433
$841$	−27.9653	−0.964322
$842$	−1.13065	−0.0389647
$843$	2.78990	0.0960894
$844$	33.5755	1.15572
$845$	0	0
$846$	23.5536	0.809791
$847$	−0.587136	−0.0201742
$848$	−5.75981	−0.197793
$849$	−52.3489	−1.79661
$850$	3.65465	0.125354
$851$	12.5883	0.431522
$852$	62.4994	2.14120
$853$	−47.9779	−1.64273	−0.821365	−	0.570403i	$-0.806787\pi$
$853$	−47.9779	−1.64273	−0.821365	+	0.570403i	$0.806787\pi$
$854$	−5.22924	−0.178941
$855$	4.60246	0.157401
$856$	−9.83731	−0.336232
$857$	46.2150	1.57867	0.789337	−	0.613960i	$-0.210424\pi$
$857$	46.2150	1.57867	0.789337	+	0.613960i	$0.210424\pi$
$858$	0	0
$859$	43.5968	1.48750	0.743752	−	0.668455i	$-0.233044\pi$
$859$	43.5968	1.48750	0.743752	+	0.668455i	$0.233044\pi$
$860$	−4.60260	−0.156947
$861$	8.32074	0.283570
$862$	−12.3133	−0.419392
$863$	−29.8157	−1.01494	−0.507469	−	0.861670i	$-0.669419\pi$
$863$	−29.8157	−1.01494	−0.507469	+	0.861670i	$0.669419\pi$
$864$	−46.4496	−1.58025
$865$	−9.04873	−0.307666
$866$	−17.5778	−0.597318
$867$	−26.2911	−0.892894
$868$	−3.70709	−0.125827
$869$	−7.08489	−0.240338
$870$	−2.15322	−0.0730011
$871$	0	0
$872$	8.51182	0.288246
$873$	33.5209	1.13451
$874$	0.685007	0.0231707
$875$	−0.587136	−0.0198488
$876$	−1.00809	−0.0340602
$877$	−29.3516	−0.991134	−0.495567	−	0.868570i	$-0.665040\pi$
$877$	−29.3516	−0.991134	−0.495567	+	0.868570i	$0.665040\pi$
$878$	19.9501	0.673284
$879$	−37.2739	−1.25722
$880$	1.17337	0.0395544
$881$	−16.4269	−0.553437	−0.276718	−	0.960951i	$-0.589247\pi$
$881$	−16.4269	−0.553437	−0.276718	+	0.960951i	$0.589247\pi$
$882$	−27.2085	−0.916159
$883$	2.13335	0.0717930	0.0358965	−	0.999356i	$-0.488571\pi$
$883$	2.13335	0.0717930	0.0358965	+	0.999356i	$0.488571\pi$
$884$	0	0
$885$	14.7368	0.495373
$886$	9.87087	0.331618
$887$	−56.7524	−1.90556	−0.952779	−	0.303665i	$-0.901790\pi$
$887$	−56.7524	−1.90556	−0.952779	+	0.303665i	$0.901790\pi$
$888$	78.6488	2.63928
$889$	−8.15128	−0.273385
$890$	0.975369	0.0326944
$891$	6.34638	0.212612
$892$	9.72777	0.325710
$893$	4.65618	0.155813
$894$	32.2453	1.07844
$895$	10.4726	0.350060
$896$	6.08459	0.203272
$897$	0	0
$898$	−3.72830	−0.124415
$899$	−4.32589	−0.144277
$900$	−8.45466	−0.281822
$901$	−24.9895	−0.832521
$902$	3.45028	0.114882
$903$	5.36728	0.178612
$904$	−17.9331	−0.596446
$905$	−12.7827	−0.424910
$906$	−30.0558	−0.998537
$907$	6.08391	0.202013	0.101007	−	0.994886i	$-0.467794\pi$
$907$	6.08391	0.202013	0.101007	+	0.994886i	$0.467794\pi$
$908$	9.65941	0.320559
$909$	−56.1496	−1.86237
$910$	0	0
$911$	−13.2424	−0.438741	−0.219370	−	0.975642i	$-0.570400\pi$
$911$	−13.2424	−0.438741	−0.219370	+	0.975642i	$0.570400\pi$
$912$	−2.79626	−0.0925934
$913$	−9.62601	−0.318575
$914$	−1.10309	−0.0364869
$915$	−36.5822	−1.20937
$916$	23.4635	0.775254
$917$	1.31229	0.0433355
$918$	−29.0405	−0.958478
$919$	−16.1581	−0.533007	−0.266503	−	0.963834i	$-0.585868\pi$
$919$	−16.1581	−0.533007	−0.266503	+	0.963834i	$0.585868\pi$
$920$	−2.95352	−0.0973746
$921$	−11.0488	−0.364070
$922$	20.6943	0.681529
$923$	0	0
$924$	−2.57031	−0.0845570
$925$	10.6622	0.350570
$926$	7.56363	0.248556
$927$	−103.766	−3.40813
$928$	5.94598	0.195186
$929$	19.1699	0.628945	0.314473	−	0.949267i	$-0.398172\pi$
$929$	19.1699	0.628945	0.314473	+	0.949267i	$0.398172\pi$
$930$	9.00260	0.295207
$931$	−5.37870	−0.176280
$932$	−32.6283	−1.06877
$933$	−13.1647	−0.430992
$934$	−2.95560	−0.0967101
$935$	5.09079	0.166487
$936$	0	0
$937$	−36.7103	−1.19927	−0.599637	−	0.800272i	$-0.704688\pi$
$937$	−36.7103	−1.19927	−0.599637	+	0.800272i	$0.704688\pi$
$938$	4.36812	0.142624
$939$	−34.1675	−1.11501
$940$	−8.55335	−0.278979
$941$	−56.8699	−1.85390	−0.926952	−	0.375179i	$-0.877581\pi$
$941$	−56.8699	−1.85390	−0.926952	+	0.375179i	$0.877581\pi$
$942$	−6.68617	−0.217847
$943$	5.67435	0.184782
$944$	−5.86421	−0.190864
$945$	4.66547	0.151768
$946$	2.22560	0.0723605
$947$	−33.1151	−1.07610	−0.538049	−	0.842914i	$-0.680838\pi$
$947$	−33.1151	−1.07610	−0.538049	+	0.842914i	$0.680838\pi$
$948$	−31.0156	−1.00734
$949$	0	0
$950$	0.580193	0.0188239
$951$	−104.134	−3.37679
$952$	7.47724	0.242339
$953$	23.3488	0.756343	0.378172	−	0.925735i	$-0.376553\pi$
$953$	23.3488	0.756343	0.378172	+	0.925735i	$0.376553\pi$
$954$	−20.0684	−0.649737
$955$	−4.96865	−0.160782
$956$	34.9564	1.13057
$957$	−2.99936	−0.0969554
$958$	12.0887	0.390569
$959$	6.32593	0.204275
$960$	−5.45433	−0.176038
$961$	−12.9135	−0.416564
$962$	0	0
$963$	22.3943	0.721647
$964$	−43.7797	−1.41005
$965$	14.4125	0.463956
$966$	1.46741	0.0472132
$967$	−47.6491	−1.53229	−0.766145	−	0.642667i	$-0.777828\pi$
$967$	−47.6491	−1.53229	−0.766145	+	0.642667i	$0.777828\pi$
$968$	−2.50160	−0.0804043
$969$	−12.1318	−0.389731
$970$	4.22570	0.135679
$971$	−3.09463	−0.0993116	−0.0496558	−	0.998766i	$-0.515812\pi$
$971$	−3.09463	−0.0993116	−0.0496558	+	0.998766i	$0.515812\pi$
$972$	−7.60860	−0.244046
$973$	−11.1987	−0.359014
$974$	15.7597	0.504974
$975$	0	0
$976$	14.5571	0.465962
$977$	35.9043	1.14868	0.574340	−	0.818617i	$-0.305259\pi$
$977$	35.9043	1.14868	0.574340	+	0.818617i	$0.305259\pi$
$978$	21.2823	0.680533
$979$	1.35865	0.0434227
$980$	9.88060	0.315624
$981$	−19.3769	−0.618656
$982$	−9.85951	−0.314630
$983$	18.2412	0.581803	0.290901	−	0.956753i	$-0.406045\pi$
$983$	18.2412	0.581803	0.290901	+	0.956753i	$0.406045\pi$
$984$	35.4520	1.13017
$985$	0.743494	0.0236897
$986$	3.71744	0.118388
$987$	9.97440	0.317489
$988$	0	0
$989$	3.66023	0.116389
$990$	4.08827	0.129934
$991$	−15.7427	−0.500083	−0.250042	−	0.968235i	$-0.580444\pi$
$991$	−15.7427	−0.500083	−0.250042	+	0.968235i	$0.580444\pi$
$992$	−24.8601	−0.789308
$993$	−2.11825	−0.0672207
$994$	−6.01766	−0.190869
$995$	−8.08735	−0.256386
$996$	−42.1399	−1.33525
$997$	−14.5139	−0.459658	−0.229829	−	0.973231i	$-0.573817\pi$
$997$	−14.5139	−0.459658	−0.229829	+	0.973231i	$0.573817\pi$
$998$	17.2655	0.546530
$999$	−84.7232	−2.68052

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9295.2.a.bn.1.19	yes	33
13.12	even	2		9295.2.a.bm.1.15	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9295.2.a.bm.1.15	✓	33	13.12	even	2
9295.2.a.bn.1.19	yes	33	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:	\( N \)	\(=\)	\( 9295 = 5 \cdot 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9295.a (trivial)

\(f(q)\)	\(=\)	\(q+0.717895 q^{2} -2.94870 q^{3} -1.48463 q^{4} +1.00000 q^{5} -2.11685 q^{6} -0.587136 q^{7} -2.50160 q^{8} +5.69480 q^{9} +O(q^{10})\)	\(q+0.717895 q^{2} -2.94870 q^{3} -1.48463 q^{4} +1.00000 q^{5} -2.11685 q^{6} -0.587136 q^{7} -2.50160 q^{8} +5.69480 q^{9} +0.717895 q^{10} +1.00000 q^{11} +4.37771 q^{12} -0.421502 q^{14} -2.94870 q^{15} +1.17337 q^{16} +5.09079 q^{17} +4.08827 q^{18} +0.808186 q^{19} -1.48463 q^{20} +1.73128 q^{21} +0.717895 q^{22} +1.18065 q^{23} +7.37644 q^{24} +1.00000 q^{25} -7.94616 q^{27} +0.871677 q^{28} +1.01718 q^{29} -2.11685 q^{30} -4.25282 q^{31} +5.84555 q^{32} -2.94870 q^{33} +3.65465 q^{34} -0.587136 q^{35} -8.45466 q^{36} +10.6622 q^{37} +0.580193 q^{38} -2.50160 q^{40} +4.80611 q^{41} +1.24288 q^{42} +3.10017 q^{43} -1.48463 q^{44} +5.69480 q^{45} +0.847585 q^{46} +5.76127 q^{47} -3.45992 q^{48} -6.65527 q^{49} +0.717895 q^{50} -15.0112 q^{51} -4.90876 q^{53} -5.70450 q^{54} +1.00000 q^{55} +1.46878 q^{56} -2.38310 q^{57} +0.730229 q^{58} -4.99774 q^{59} +4.37771 q^{60} +12.4062 q^{61} -3.05308 q^{62} -3.34362 q^{63} +1.84974 q^{64} -2.11685 q^{66} -10.3632 q^{67} -7.55793 q^{68} -3.48139 q^{69} -0.421502 q^{70} +14.2767 q^{71} -14.2461 q^{72} -0.230278 q^{73} +7.65431 q^{74} -2.94870 q^{75} -1.19986 q^{76} -0.587136 q^{77} -7.08489 q^{79} +1.17337 q^{80} +6.34638 q^{81} +3.45028 q^{82} -9.62601 q^{83} -2.57031 q^{84} +5.09079 q^{85} +2.22560 q^{86} -2.99936 q^{87} -2.50160 q^{88} +1.35865 q^{89} +4.08827 q^{90} -1.75283 q^{92} +12.5403 q^{93} +4.13599 q^{94} +0.808186 q^{95} -17.2367 q^{96} +5.88623 q^{97} -4.77778 q^{98} +5.69480 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q + 8 q^{2} + 12 q^{3} + 38 q^{4} + 33 q^{5} + 18 q^{6} + 4 q^{7} + 21 q^{8} + 35 q^{9}+O(q^{10}) \) 33 * q + 8 * q^2 + 12 * q^3 + 38 * q^4 + 33 * q^5 + 18 * q^6 + 4 * q^7 + 21 * q^8 + 35 * q^9	\( 33 q + 8 q^{2} + 12 q^{3} + 38 q^{4} + 33 q^{5} + 18 q^{6} + 4 q^{7} + 21 q^{8} + 35 q^{9} + 8 q^{10} + 33 q^{11} + 24 q^{12} - 5 q^{14} + 12 q^{15} + 44 q^{16} + 9 q^{17} + 18 q^{18} + 8 q^{19} + 38 q^{20} + 9 q^{21} + 8 q^{22} + 7 q^{23} + 54 q^{24} + 33 q^{25} + 42 q^{27} + 15 q^{28} - 11 q^{29} + 18 q^{30} + 13 q^{31} + 85 q^{32} + 12 q^{33} + 31 q^{34} + 4 q^{35} + 26 q^{36} + 22 q^{37} - 2 q^{38} + 21 q^{40} + 36 q^{41} + 11 q^{42} + 26 q^{43} + 38 q^{44} + 35 q^{45} - q^{46} + 46 q^{47} + 36 q^{48} + 29 q^{49} + 8 q^{50} - 41 q^{51} + 9 q^{53} + 70 q^{54} + 33 q^{55} - 10 q^{56} + 70 q^{57} - 23 q^{58} + 18 q^{59} + 24 q^{60} - 42 q^{61} - 24 q^{62} + 68 q^{63} + 39 q^{64} + 18 q^{66} + 26 q^{67} + 8 q^{68} + 12 q^{69} - 5 q^{70} + 43 q^{71} + 46 q^{72} + 21 q^{73} - 22 q^{74} + 12 q^{75} + 2 q^{76} + 4 q^{77} - 22 q^{79} + 44 q^{80} + 41 q^{81} + 156 q^{82} + 26 q^{83} + 11 q^{84} + 9 q^{85} + 17 q^{86} - 30 q^{87} + 21 q^{88} + 95 q^{89} + 18 q^{90} + 37 q^{92} + 62 q^{93} - 14 q^{94} + 8 q^{95} + 53 q^{96} + 40 q^{97} + 132 q^{98} + 35 q^{99}+O(q^{100}) \) 33 * q + 8 * q^2 + 12 * q^3 + 38 * q^4 + 33 * q^5 + 18 * q^6 + 4 * q^7 + 21 * q^8 + 35 * q^9 + 8 * q^10 + 33 * q^11 + 24 * q^12 - 5 * q^14 + 12 * q^15 + 44 * q^16 + 9 * q^17 + 18 * q^18 + 8 * q^19 + 38 * q^20 + 9 * q^21 + 8 * q^22 + 7 * q^23 + 54 * q^24 + 33 * q^25 + 42 * q^27 + 15 * q^28 - 11 * q^29 + 18 * q^30 + 13 * q^31 + 85 * q^32 + 12 * q^33 + 31 * q^34 + 4 * q^35 + 26 * q^36 + 22 * q^37 - 2 * q^38 + 21 * q^40 + 36 * q^41 + 11 * q^42 + 26 * q^43 + 38 * q^44 + 35 * q^45 - q^46 + 46 * q^47 + 36 * q^48 + 29 * q^49 + 8 * q^50 - 41 * q^51 + 9 * q^53 + 70 * q^54 + 33 * q^55 - 10 * q^56 + 70 * q^57 - 23 * q^58 + 18 * q^59 + 24 * q^60 - 42 * q^61 - 24 * q^62 + 68 * q^63 + 39 * q^64 + 18 * q^66 + 26 * q^67 + 8 * q^68 + 12 * q^69 - 5 * q^70 + 43 * q^71 + 46 * q^72 + 21 * q^73 - 22 * q^74 + 12 * q^75 + 2 * q^76 + 4 * q^77 - 22 * q^79 + 44 * q^80 + 41 * q^81 + 156 * q^82 + 26 * q^83 + 11 * q^84 + 9 * q^85 + 17 * q^86 - 30 * q^87 + 21 * q^88 + 95 * q^89 + 18 * q^90 + 37 * q^92 + 62 * q^93 - 14 * q^94 + 8 * q^95 + 53 * q^96 + 40 * q^97 + 132 * q^98 + 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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