LMFDB - Embedded newform 3549.2.a.bf.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3549,2,Mod(1,3549)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, 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("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3549 = 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3549.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:	$28.3389076774$
Analytic rank:	$0$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - x^{8} - 11x^{7} + 8x^{6} + 37x^{5} - 18x^{4} - 41x^{3} + 12x^{2} + 6x - 1 $ x^9 - x^8 - 11x^7 + 8x^6 + 37x^5 - 18x^4 - 41x^3 + 12x^2 + 6*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.494186$ of defining polynomial
Character	$\chi$	$=$	3549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.494186 q^{2} -1.00000 q^{3} -1.75578 q^{4} +1.64627 q^{5} -0.494186 q^{6} -1.00000 q^{7} -1.85605 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.494186 q^{2} -1.00000 q^{3} -1.75578 q^{4} +1.64627 q^{5} -0.494186 q^{6} -1.00000 q^{7} -1.85605 q^{8} +1.00000 q^{9} +0.813565 q^{10} +1.00650 q^{11} +1.75578 q^{12} -0.494186 q^{14} -1.64627 q^{15} +2.59432 q^{16} -4.38900 q^{17} +0.494186 q^{18} +1.17541 q^{19} -2.89049 q^{20} +1.00000 q^{21} +0.497400 q^{22} +2.62816 q^{23} +1.85605 q^{24} -2.28979 q^{25} -1.00000 q^{27} +1.75578 q^{28} +5.13954 q^{29} -0.813565 q^{30} -0.705141 q^{31} +4.99419 q^{32} -1.00650 q^{33} -2.16898 q^{34} -1.64627 q^{35} -1.75578 q^{36} +2.72506 q^{37} +0.580871 q^{38} -3.05557 q^{40} -3.05611 q^{41} +0.494186 q^{42} -10.5077 q^{43} -1.76720 q^{44} +1.64627 q^{45} +1.29880 q^{46} -2.16111 q^{47} -2.59432 q^{48} +1.00000 q^{49} -1.13158 q^{50} +4.38900 q^{51} -1.96782 q^{53} -0.494186 q^{54} +1.65698 q^{55} +1.85605 q^{56} -1.17541 q^{57} +2.53989 q^{58} -4.90995 q^{59} +2.89049 q^{60} +0.563211 q^{61} -0.348471 q^{62} -1.00000 q^{63} -2.72059 q^{64} -0.497400 q^{66} +13.1061 q^{67} +7.70611 q^{68} -2.62816 q^{69} -0.813565 q^{70} +15.3807 q^{71} -1.85605 q^{72} +13.5942 q^{73} +1.34669 q^{74} +2.28979 q^{75} -2.06376 q^{76} -1.00650 q^{77} +7.63275 q^{79} +4.27096 q^{80} +1.00000 q^{81} -1.51029 q^{82} +0.0542580 q^{83} -1.75578 q^{84} -7.22548 q^{85} -5.19278 q^{86} -5.13954 q^{87} -1.86813 q^{88} -0.601205 q^{89} +0.813565 q^{90} -4.61447 q^{92} +0.705141 q^{93} -1.06799 q^{94} +1.93504 q^{95} -4.99419 q^{96} +1.74080 q^{97} +0.494186 q^{98} +1.00650 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + q^{2} - 9 q^{3} + 5 q^{4} - 9 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + q^2 - 9 * q^3 + 5 * q^4 - 9 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 9 * q^9	$ 9 q + q^{2} - 9 q^{3} + 5 q^{4} - 9 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 9 q^{9} + q^{10} + q^{11} - 5 q^{12} - q^{14} + 9 q^{15} + 5 q^{16} + 11 q^{17} + q^{18} - 7 q^{19} - 23 q^{20} + 9 q^{21} - 3 q^{22} + 22 q^{23} - 6 q^{24} - 8 q^{25} - 9 q^{27} - 5 q^{28} + 11 q^{29} - q^{30} - 7 q^{31} + 18 q^{32} - q^{33} + 6 q^{34} + 9 q^{35} + 5 q^{36} + q^{37} - 6 q^{38} - 14 q^{40} - 16 q^{41} + q^{42} + 32 q^{43} - 18 q^{44} - 9 q^{45} + 9 q^{46} + 12 q^{47} - 5 q^{48} + 9 q^{49} - 10 q^{50} - 11 q^{51} + 13 q^{53} - q^{54} + 9 q^{55} - 6 q^{56} + 7 q^{57} - 4 q^{58} - 29 q^{59} + 23 q^{60} - 12 q^{61} + 30 q^{62} - 9 q^{63} + 6 q^{64} + 3 q^{66} + 20 q^{67} + 34 q^{68} - 22 q^{69} - q^{70} + 2 q^{71} + 6 q^{72} - q^{73} + 43 q^{74} + 8 q^{75} - 13 q^{76} - q^{77} + 3 q^{79} + 39 q^{80} + 9 q^{81} - 19 q^{82} - 24 q^{83} + 5 q^{84} - 15 q^{85} + 28 q^{86} - 11 q^{87} - 19 q^{88} - 11 q^{89} + q^{90} + 73 q^{92} + 7 q^{93} + 15 q^{94} + 39 q^{95} - 18 q^{96} - 20 q^{97} + q^{98} + q^{99}+O(q^{100}) $ 9 * q + q^2 - 9 * q^3 + 5 * q^4 - 9 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 9 * q^9 + q^10 + q^11 - 5 * q^12 - q^14 + 9 * q^15 + 5 * q^16 + 11 * q^17 + q^18 - 7 * q^19 - 23 * q^20 + 9 * q^21 - 3 * q^22 + 22 * q^23 - 6 * q^24 - 8 * q^25 - 9 * q^27 - 5 * q^28 + 11 * q^29 - q^30 - 7 * q^31 + 18 * q^32 - q^33 + 6 * q^34 + 9 * q^35 + 5 * q^36 + q^37 - 6 * q^38 - 14 * q^40 - 16 * q^41 + q^42 + 32 * q^43 - 18 * q^44 - 9 * q^45 + 9 * q^46 + 12 * q^47 - 5 * q^48 + 9 * q^49 - 10 * q^50 - 11 * q^51 + 13 * q^53 - q^54 + 9 * q^55 - 6 * q^56 + 7 * q^57 - 4 * q^58 - 29 * q^59 + 23 * q^60 - 12 * q^61 + 30 * q^62 - 9 * q^63 + 6 * q^64 + 3 * q^66 + 20 * q^67 + 34 * q^68 - 22 * q^69 - q^70 + 2 * q^71 + 6 * q^72 - q^73 + 43 * q^74 + 8 * q^75 - 13 * q^76 - q^77 + 3 * q^79 + 39 * q^80 + 9 * q^81 - 19 * q^82 - 24 * q^83 + 5 * q^84 - 15 * q^85 + 28 * q^86 - 11 * q^87 - 19 * q^88 - 11 * q^89 + q^90 + 73 * q^92 + 7 * q^93 + 15 * q^94 + 39 * q^95 - 18 * q^96 - 20 * q^97 + q^98 + 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 $

$2$	0.494186	0.349442	0.174721	−	0.984618i	$-0.444098\pi$
$2$	0.494186	0.349442	0.174721	+	0.984618i	$0.444098\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.75578	−0.877890
$5$	1.64627	0.736236	0.368118	−	0.929779i	$-0.380002\pi$
$5$	1.64627	0.736236	0.368118	+	0.929779i	$0.380002\pi$
$6$	−0.494186	−0.201751
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.85605	−0.656214
$9$	1.00000	0.333333
$10$	0.813565	0.257272
$11$	1.00650	0.303472	0.151736	−	0.988421i	$-0.451514\pi$
$11$	1.00650	0.303472	0.151736	+	0.988421i	$0.451514\pi$
$12$	1.75578	0.506850
$13$	0	0
$13$	0	0
$14$	−0.494186	−0.132077
$15$	−1.64627	−0.425066
$16$	2.59432	0.648581
$17$	−4.38900	−1.06449	−0.532244	−	0.846591i	$-0.678651\pi$
$17$	−4.38900	−1.06449	−0.532244	+	0.846591i	$0.678651\pi$
$18$	0.494186	0.116481
$19$	1.17541	0.269657	0.134829	−	0.990869i	$-0.456952\pi$
$19$	1.17541	0.269657	0.134829	+	0.990869i	$0.456952\pi$
$20$	−2.89049	−0.646334
$21$	1.00000	0.218218
$22$	0.497400	0.106046
$23$	2.62816	0.548010	0.274005	−	0.961728i	$-0.411652\pi$
$23$	2.62816	0.548010	0.274005	+	0.961728i	$0.411652\pi$
$24$	1.85605	0.378866
$25$	−2.28979	−0.457957
$26$	0	0
$27$	−1.00000	−0.192450
$28$	1.75578	0.331811
$29$	5.13954	0.954388	0.477194	−	0.878798i	$-0.341654\pi$
$29$	5.13954	0.954388	0.477194	+	0.878798i	$0.341654\pi$
$30$	−0.813565	−0.148536
$31$	−0.705141	−0.126647	−0.0633235	−	0.997993i	$-0.520170\pi$
$31$	−0.705141	−0.126647	−0.0633235	+	0.997993i	$0.520170\pi$
$32$	4.99419	0.882856
$33$	−1.00650	−0.175210
$34$	−2.16898	−0.371977
$35$	−1.64627	−0.278271
$36$	−1.75578	−0.292630
$37$	2.72506	0.447997	0.223999	−	0.974589i	$-0.428089\pi$
$37$	2.72506	0.447997	0.223999	+	0.974589i	$0.428089\pi$
$38$	0.580871	0.0942297
$39$	0	0
$40$	−3.05557	−0.483128
$41$	−3.05611	−0.477284	−0.238642	−	0.971108i	$-0.576702\pi$
$41$	−3.05611	−0.477284	−0.238642	+	0.971108i	$0.576702\pi$
$42$	0.494186	0.0762546
$43$	−10.5077	−1.60242	−0.801208	−	0.598386i	$-0.795809\pi$
$43$	−10.5077	−1.60242	−0.801208	+	0.598386i	$0.795809\pi$
$44$	−1.76720	−0.266415
$45$	1.64627	0.245412
$46$	1.29880	0.191498
$47$	−2.16111	−0.315231	−0.157615	−	0.987501i	$-0.550381\pi$
$47$	−2.16111	−0.315231	−0.157615	+	0.987501i	$0.550381\pi$
$48$	−2.59432	−0.374458
$49$	1.00000	0.142857
$50$	−1.13158	−0.160030
$51$	4.38900	0.614582
$52$	0	0
$53$	−1.96782	−0.270301	−0.135150	−	0.990825i	$-0.543152\pi$
$53$	−1.96782	−0.270301	−0.135150	+	0.990825i	$0.543152\pi$
$54$	−0.494186	−0.0672502
$55$	1.65698	0.223427
$56$	1.85605	0.248026
$57$	−1.17541	−0.155687
$58$	2.53989	0.333504
$59$	−4.90995	−0.639221	−0.319611	−	0.947549i	$-0.603552\pi$
$59$	−4.90995	−0.639221	−0.319611	+	0.947549i	$0.603552\pi$
$60$	2.89049	0.373161
$61$	0.563211	0.0721117	0.0360559	−	0.999350i	$-0.488521\pi$
$61$	0.563211	0.0721117	0.0360559	+	0.999350i	$0.488521\pi$
$62$	−0.348471	−0.0442558
$63$	−1.00000	−0.125988
$64$	−2.72059	−0.340073
$65$	0	0
$66$	−0.497400	−0.0612258
$67$	13.1061	1.60116	0.800580	−	0.599225i	$-0.204525\pi$
$67$	13.1061	1.60116	0.800580	+	0.599225i	$0.204525\pi$
$68$	7.70611	0.934503
$69$	−2.62816	−0.316394
$70$	−0.813565	−0.0972397
$71$	15.3807	1.82536	0.912678	−	0.408678i	$-0.134010\pi$
$71$	15.3807	1.82536	0.912678	+	0.408678i	$0.134010\pi$
$72$	−1.85605	−0.218738
$73$	13.5942	1.59108	0.795541	−	0.605900i	$-0.207187\pi$
$73$	13.5942	1.59108	0.795541	+	0.605900i	$0.207187\pi$
$74$	1.34669	0.156549
$75$	2.28979	0.264402
$76$	−2.06376	−0.236729
$77$	−1.00650	−0.114702
$78$	0	0
$79$	7.63275	0.858751	0.429376	−	0.903126i	$-0.358734\pi$
$79$	7.63275	0.858751	0.429376	+	0.903126i	$0.358734\pi$
$80$	4.27096	0.477508
$81$	1.00000	0.111111
$82$	−1.51029	−0.166783
$83$	0.0542580	0.00595559	0.00297779	−	0.999996i	$-0.499052\pi$
$83$	0.0542580	0.00595559	0.00297779	+	0.999996i	$0.499052\pi$
$84$	−1.75578	−0.191571
$85$	−7.22548	−0.783714
$86$	−5.19278	−0.559952
$87$	−5.13954	−0.551016
$88$	−1.86813	−0.199143
$89$	−0.601205	−0.0637276	−0.0318638	−	0.999492i	$-0.510144\pi$
$89$	−0.601205	−0.0637276	−0.0318638	+	0.999492i	$0.510144\pi$
$90$	0.813565	0.0857573
$91$	0	0
$92$	−4.61447	−0.481092
$93$	0.705141	0.0731197
$94$	−1.06799	−0.110155
$95$	1.93504	0.198531
$96$	−4.99419	−0.509717
$97$	1.74080	0.176751	0.0883757	−	0.996087i	$-0.471832\pi$
$97$	1.74080	0.176751	0.0883757	+	0.996087i	$0.471832\pi$
$98$	0.494186	0.0499203
$99$	1.00650	0.101157
$100$	4.02036	0.402036
$101$	12.8587	1.27949	0.639746	−	0.768586i	$-0.279039\pi$
$101$	12.8587	1.27949	0.639746	+	0.768586i	$0.279039\pi$
$102$	2.16898	0.214761
$103$	14.6917	1.44761	0.723806	−	0.690004i	$-0.242391\pi$
$103$	14.6917	1.44761	0.723806	+	0.690004i	$0.242391\pi$
$104$	0	0
$105$	1.64627	0.160660
$106$	−0.972469	−0.0944546
$107$	3.37556	0.326328	0.163164	−	0.986599i	$-0.447830\pi$
$107$	3.37556	0.326328	0.163164	+	0.986599i	$0.447830\pi$
$108$	1.75578	0.168950
$109$	−9.90520	−0.948746	−0.474373	−	0.880324i	$-0.657325\pi$
$109$	−9.90520	−0.948746	−0.474373	+	0.880324i	$0.657325\pi$
$110$	0.818857	0.0780749
$111$	−2.72506	−0.258651
$112$	−2.59432	−0.245141
$113$	−13.5673	−1.27631	−0.638154	−	0.769909i	$-0.720302\pi$
$113$	−13.5673	−1.27631	−0.638154	+	0.769909i	$0.720302\pi$
$114$	−0.580871	−0.0544035
$115$	4.32667	0.403464
$116$	−9.02390	−0.837848
$117$	0	0
$118$	−2.42643	−0.223371
$119$	4.38900	0.402339
$120$	3.05557	0.278934
$121$	−9.98695	−0.907905
$122$	0.278331	0.0251989
$123$	3.05611	0.275560
$124$	1.23807	0.111182
$125$	−12.0010	−1.07340
$126$	−0.494186	−0.0440256
$127$	7.65651	0.679405	0.339703	−	0.940533i	$-0.389674\pi$
$127$	7.65651	0.679405	0.339703	+	0.940533i	$0.389674\pi$
$128$	−11.3329	−1.00169
$129$	10.5077	0.925155
$130$	0	0
$131$	1.25502	0.109652	0.0548258	−	0.998496i	$-0.482540\pi$
$131$	1.25502	0.109652	0.0548258	+	0.998496i	$0.482540\pi$
$132$	1.76720	0.153815
$133$	−1.17541	−0.101921
$134$	6.47684	0.559514
$135$	−1.64627	−0.141689
$136$	8.14622	0.698532
$137$	2.55836	0.218576	0.109288	−	0.994010i	$-0.465143\pi$
$137$	2.55836	0.218576	0.109288	+	0.994010i	$0.465143\pi$
$138$	−1.29880	−0.110561
$139$	5.63993	0.478373	0.239186	−	0.970974i	$-0.423119\pi$
$139$	5.63993	0.478373	0.239186	+	0.970974i	$0.423119\pi$
$140$	2.89049	0.244291
$141$	2.16111	0.181999
$142$	7.60094	0.637857
$143$	0	0
$144$	2.59432	0.216194
$145$	8.46108	0.702655
$146$	6.71807	0.555992
$147$	−1.00000	−0.0824786
$148$	−4.78461	−0.393292
$149$	5.49922	0.450514	0.225257	−	0.974299i	$-0.427678\pi$
$149$	5.49922	0.450514	0.225257	+	0.974299i	$0.427678\pi$
$150$	1.13158	0.0923932
$151$	8.31087	0.676329	0.338165	−	0.941087i	$-0.390194\pi$
$151$	8.31087	0.676329	0.338165	+	0.941087i	$0.390194\pi$
$152$	−2.18162	−0.176953
$153$	−4.38900	−0.354829
$154$	−0.497400	−0.0400817
$155$	−1.16085	−0.0932420
$156$	0	0
$157$	12.8123	1.02253	0.511265	−	0.859423i	$-0.329177\pi$
$157$	12.8123	1.02253	0.511265	+	0.859423i	$0.329177\pi$
$158$	3.77200	0.300084
$159$	1.96782	0.156058
$160$	8.22180	0.649990
$161$	−2.62816	−0.207128
$162$	0.494186	0.0388269
$163$	10.7587	0.842684	0.421342	−	0.906902i	$-0.361559\pi$
$163$	10.7587	0.842684	0.421342	+	0.906902i	$0.361559\pi$
$164$	5.36585	0.419003
$165$	−1.65698	−0.128996
$166$	0.0268135	0.00208113
$167$	−25.0059	−1.93502	−0.967509	−	0.252838i	$-0.918636\pi$
$167$	−25.0059	−1.93502	−0.967509	+	0.252838i	$0.918636\pi$
$168$	−1.85605	−0.143198
$169$	0	0
$170$	−3.57073	−0.273863
$171$	1.17541	0.0898857
$172$	18.4493	1.40675
$173$	16.7347	1.27232	0.636159	−	0.771558i	$-0.280522\pi$
$173$	16.7347	1.27232	0.636159	+	0.771558i	$0.280522\pi$
$174$	−2.53989	−0.192549
$175$	2.28979	0.173092
$176$	2.61120	0.196826
$177$	4.90995	0.369055
$178$	−0.297107	−0.0222691
$179$	12.2780	0.917699	0.458849	−	0.888514i	$-0.348262\pi$
$179$	12.2780	0.917699	0.458849	+	0.888514i	$0.348262\pi$
$180$	−2.89049	−0.215445
$181$	22.8077	1.69528	0.847640	−	0.530572i	$-0.178023\pi$
$181$	22.8077	1.69528	0.847640	+	0.530572i	$0.178023\pi$
$182$	0	0
$183$	−0.563211	−0.0416337
$184$	−4.87801	−0.359612
$185$	4.48619	0.329831
$186$	0.348471	0.0255511
$187$	−4.41754	−0.323043
$188$	3.79444	0.276738
$189$	1.00000	0.0727393
$190$	0.956271	0.0693752
$191$	27.4058	1.98302	0.991508	−	0.130047i	$-0.0415128\pi$
$191$	27.4058	1.98302	0.991508	+	0.130047i	$0.0415128\pi$
$192$	2.72059	0.196342
$193$	−6.41304	−0.461621	−0.230810	−	0.972999i	$-0.574138\pi$
$193$	−6.41304	−0.461621	−0.230810	+	0.972999i	$0.574138\pi$
$194$	0.860279	0.0617644
$195$	0	0
$196$	−1.75578	−0.125413
$197$	−17.2081	−1.22603	−0.613014	−	0.790072i	$-0.710043\pi$
$197$	−17.2081	−1.22603	−0.613014	+	0.790072i	$0.710043\pi$
$198$	0.497400	0.0353487
$199$	−3.01028	−0.213393	−0.106696	−	0.994292i	$-0.534027\pi$
$199$	−3.01028	−0.213393	−0.106696	+	0.994292i	$0.534027\pi$
$200$	4.24997	0.300518
$201$	−13.1061	−0.924431
$202$	6.35461	0.447109
$203$	−5.13954	−0.360725
$204$	−7.70611	−0.539536
$205$	−5.03119	−0.351393
$206$	7.26041	0.505857
$207$	2.62816	0.182670
$208$	0	0
$209$	1.18305	0.0818335
$210$	0.813565	0.0561413
$211$	26.6548	1.83499	0.917497	−	0.397743i	$-0.130207\pi$
$211$	26.6548	1.83499	0.917497	+	0.397743i	$0.130207\pi$
$212$	3.45506	0.237294
$213$	−15.3807	−1.05387
$214$	1.66815	0.114033
$215$	−17.2986	−1.17976
$216$	1.85605	0.126289
$217$	0.705141	0.0478681
$218$	−4.89501	−0.331532
$219$	−13.5942	−0.918612
$220$	−2.90929	−0.196144
$221$	0	0
$222$	−1.34669	−0.0903837
$223$	13.8795	0.929443	0.464722	−	0.885457i	$-0.346154\pi$
$223$	13.8795	0.929443	0.464722	+	0.885457i	$0.346154\pi$
$224$	−4.99419	−0.333688
$225$	−2.28979	−0.152652
$226$	−6.70479	−0.445996
$227$	13.7180	0.910496	0.455248	−	0.890365i	$-0.349551\pi$
$227$	13.7180	0.910496	0.455248	+	0.890365i	$0.349551\pi$
$228$	2.06376	0.136676
$229$	9.93225	0.656342	0.328171	−	0.944618i	$-0.393568\pi$
$229$	9.93225	0.656342	0.328171	+	0.944618i	$0.393568\pi$
$230$	2.13818	0.140988
$231$	1.00650	0.0662231
$232$	−9.53927	−0.626283
$233$	19.4424	1.27371	0.636857	−	0.770982i	$-0.280234\pi$
$233$	19.4424	1.27371	0.636857	+	0.770982i	$0.280234\pi$
$234$	0	0
$235$	−3.55778	−0.232084
$236$	8.62080	0.561166
$237$	−7.63275	−0.495800
$238$	2.16898	0.140594
$239$	16.3885	1.06009	0.530043	−	0.847971i	$-0.322176\pi$
$239$	16.3885	1.06009	0.530043	+	0.847971i	$0.322176\pi$
$240$	−4.27096	−0.275690
$241$	−16.0048	−1.03096	−0.515479	−	0.856902i	$-0.672386\pi$
$241$	−16.0048	−1.03096	−0.515479	+	0.856902i	$0.672386\pi$
$242$	−4.93541	−0.317260
$243$	−1.00000	−0.0641500
$244$	−0.988874	−0.0633062
$245$	1.64627	0.105177
$246$	1.51029	0.0962923
$247$	0	0
$248$	1.30878	0.0831076
$249$	−0.0542580	−0.00343846
$250$	−5.93072	−0.375091
$251$	−13.7389	−0.867193	−0.433597	−	0.901107i	$-0.642756\pi$
$251$	−13.7389	−0.867193	−0.433597	+	0.901107i	$0.642756\pi$
$252$	1.75578	0.110604
$253$	2.64526	0.166306
$254$	3.78374	0.237413
$255$	7.22548	0.452477
$256$	−0.159364	−0.00996028
$257$	25.1001	1.56570	0.782851	−	0.622210i	$-0.213765\pi$
$257$	25.1001	1.56570	0.782851	+	0.622210i	$0.213765\pi$
$258$	5.19278	0.323289
$259$	−2.72506	−0.169327
$260$	0	0
$261$	5.13954	0.318129
$262$	0.620214	0.0383169
$263$	6.86224	0.423144	0.211572	−	0.977362i	$-0.432142\pi$
$263$	6.86224	0.423144	0.211572	+	0.977362i	$0.432142\pi$
$264$	1.86813	0.114975
$265$	−3.23957	−0.199005
$266$	−0.580871	−0.0356155
$267$	0.601205	0.0367931
$268$	−23.0114	−1.40564
$269$	18.2175	1.11074	0.555369	−	0.831604i	$-0.312577\pi$
$269$	18.2175	1.11074	0.555369	+	0.831604i	$0.312577\pi$
$270$	−0.813565	−0.0495120
$271$	15.0414	0.913697	0.456849	−	0.889544i	$-0.348978\pi$
$271$	15.0414	0.913697	0.456849	+	0.889544i	$0.348978\pi$
$272$	−11.3865	−0.690406
$273$	0	0
$274$	1.26431	0.0763797
$275$	−2.30468	−0.138977
$276$	4.61447	0.277759
$277$	1.39436	0.0837787	0.0418894	−	0.999122i	$-0.486662\pi$
$277$	1.39436	0.0837787	0.0418894	+	0.999122i	$0.486662\pi$
$278$	2.78718	0.167164
$279$	−0.705141	−0.0422157
$280$	3.05557	0.182605
$281$	11.2011	0.668200	0.334100	−	0.942538i	$-0.391568\pi$
$281$	11.2011	0.668200	0.334100	+	0.942538i	$0.391568\pi$
$282$	1.06799	0.0635981
$283$	−14.8446	−0.882422	−0.441211	−	0.897403i	$-0.645451\pi$
$283$	−14.8446	−0.882422	−0.441211	+	0.897403i	$0.645451\pi$
$284$	−27.0052	−1.60246
$285$	−1.93504	−0.114622
$286$	0	0
$287$	3.05611	0.180396
$288$	4.99419	0.294285
$289$	2.26328	0.133134
$290$	4.18135	0.245537
$291$	−1.74080	−0.102047
$292$	−23.8684	−1.39680
$293$	−17.8257	−1.04139	−0.520695	−	0.853743i	$-0.674327\pi$
$293$	−17.8257	−1.04139	−0.520695	+	0.853743i	$0.674327\pi$
$294$	−0.494186	−0.0288215
$295$	−8.08312	−0.470618
$296$	−5.05786	−0.293982
$297$	−1.00650	−0.0584033
$298$	2.71764	0.157429
$299$	0	0
$300$	−4.02036	−0.232116
$301$	10.5077	0.605656
$302$	4.10712	0.236338
$303$	−12.8587	−0.738716
$304$	3.04939	0.174894
$305$	0.927198	0.0530912
$306$	−2.16898	−0.123992
$307$	−30.6385	−1.74863	−0.874317	−	0.485356i	$-0.838690\pi$
$307$	−30.6385	−1.74863	−0.874317	+	0.485356i	$0.838690\pi$
$308$	1.76720	0.100696
$309$	−14.6917	−0.835779
$310$	−0.573678	−0.0325827
$311$	9.27236	0.525788	0.262894	−	0.964825i	$-0.415323\pi$
$311$	9.27236	0.525788	0.262894	+	0.964825i	$0.415323\pi$
$312$	0	0
$313$	−25.7441	−1.45514	−0.727572	−	0.686031i	$-0.759351\pi$
$313$	−25.7441	−1.45514	−0.727572	+	0.686031i	$0.759351\pi$
$314$	6.33164	0.357315
$315$	−1.64627	−0.0927570
$316$	−13.4014	−0.753889
$317$	5.98521	0.336163	0.168082	−	0.985773i	$-0.446243\pi$
$317$	5.98521	0.336163	0.168082	+	0.985773i	$0.446243\pi$
$318$	0.972469	0.0545334
$319$	5.17297	0.289631
$320$	−4.47883	−0.250374
$321$	−3.37556	−0.188405
$322$	−1.29880	−0.0723794
$323$	−5.15886	−0.287047
$324$	−1.75578	−0.0975433
$325$	0	0
$326$	5.31679	0.294470
$327$	9.90520	0.547759
$328$	5.67230	0.313200
$329$	2.16111	0.119146
$330$	−0.818857	−0.0450766
$331$	−24.7010	−1.35769	−0.678846	−	0.734281i	$-0.737520\pi$
$331$	−24.7010	−1.35769	−0.678846	+	0.734281i	$0.737520\pi$
$332$	−0.0952651	−0.00522835
$333$	2.72506	0.149332
$334$	−12.3576	−0.676177
$335$	21.5762	1.17883
$336$	2.59432	0.141532
$337$	−6.44446	−0.351052	−0.175526	−	0.984475i	$-0.556163\pi$
$337$	−6.44446	−0.351052	−0.175526	+	0.984475i	$0.556163\pi$
$338$	0	0
$339$	13.5673	0.736877
$340$	12.6864	0.688014
$341$	−0.709727	−0.0384339
$342$	0.580871	0.0314099
$343$	−1.00000	−0.0539949
$344$	19.5029	1.05153
$345$	−4.32667	−0.232940
$346$	8.27008	0.444602
$347$	15.7956	0.847955	0.423977	−	0.905673i	$-0.360634\pi$
$347$	15.7956	0.847955	0.423977	+	0.905673i	$0.360634\pi$
$348$	9.02390	0.483732
$349$	21.2652	1.13830	0.569150	−	0.822234i	$-0.307273\pi$
$349$	21.2652	1.13830	0.569150	+	0.822234i	$0.307273\pi$
$350$	1.13158	0.0604855
$351$	0	0
$352$	5.02667	0.267922
$353$	10.0764	0.536311	0.268156	−	0.963376i	$-0.413586\pi$
$353$	10.0764	0.536311	0.268156	+	0.963376i	$0.413586\pi$
$354$	2.42643	0.128963
$355$	25.3209	1.34389
$356$	1.05558	0.0559458
$357$	−4.38900	−0.232290
$358$	6.06761	0.320683
$359$	−22.7145	−1.19883	−0.599413	−	0.800440i	$-0.704599\pi$
$359$	−22.7145	−1.19883	−0.599413	+	0.800440i	$0.704599\pi$
$360$	−3.05557	−0.161043
$361$	−17.6184	−0.927285
$362$	11.2712	0.592403
$363$	9.98695	0.524179
$364$	0	0
$365$	22.3798	1.17141
$366$	−0.278331	−0.0145486
$367$	−19.7830	−1.03267	−0.516333	−	0.856388i	$-0.672703\pi$
$367$	−19.7830	−1.03267	−0.516333	+	0.856388i	$0.672703\pi$
$368$	6.81830	0.355429
$369$	−3.05611	−0.159095
$370$	2.21701	0.115257
$371$	1.96782	0.102164
$372$	−1.23807	−0.0641910
$373$	−4.21238	−0.218109	−0.109054	−	0.994036i	$-0.534782\pi$
$373$	−4.21238	−0.218109	−0.109054	+	0.994036i	$0.534782\pi$
$374$	−2.18309	−0.112885
$375$	12.0010	0.619728
$376$	4.01115	0.206859
$377$	0	0
$378$	0.494186	0.0254182
$379$	1.62828	0.0836393	0.0418197	−	0.999125i	$-0.486685\pi$
$379$	1.62828	0.0836393	0.0418197	+	0.999125i	$0.486685\pi$
$380$	−3.39751	−0.174289
$381$	−7.65651	−0.392255
$382$	13.5436	0.692950
$383$	3.21481	0.164269	0.0821346	−	0.996621i	$-0.473826\pi$
$383$	3.21481	0.164269	0.0821346	+	0.996621i	$0.473826\pi$
$384$	11.3329	0.578327
$385$	−1.65698	−0.0844475
$386$	−3.16924	−0.161310
$387$	−10.5077	−0.534139
$388$	−3.05646	−0.155168
$389$	−4.30323	−0.218183	−0.109091	−	0.994032i	$-0.534794\pi$
$389$	−4.30323	−0.218183	−0.109091	+	0.994032i	$0.534794\pi$
$390$	0	0
$391$	−11.5350	−0.583350
$392$	−1.85605	−0.0937449
$393$	−1.25502	−0.0633074
$394$	−8.50402	−0.428426
$395$	12.5656	0.632243
$396$	−1.76720	−0.0888051
$397$	−31.5480	−1.58335	−0.791673	−	0.610945i	$-0.790790\pi$
$397$	−31.5480	−1.58335	−0.791673	+	0.610945i	$0.790790\pi$
$398$	−1.48764	−0.0745685
$399$	1.17541	0.0588440
$400$	−5.94045	−0.297022
$401$	21.7130	1.08429	0.542147	−	0.840284i	$-0.317612\pi$
$401$	21.7130	1.08429	0.542147	+	0.840284i	$0.317612\pi$
$402$	−6.47684	−0.323035
$403$	0	0
$404$	−22.5771	−1.12325
$405$	1.64627	0.0818040
$406$	−2.53989	−0.126053
$407$	2.74278	0.135955
$408$	−8.14622	−0.403298
$409$	−9.98412	−0.493683	−0.246842	−	0.969056i	$-0.579393\pi$
$409$	−9.98412	−0.493683	−0.246842	+	0.969056i	$0.579393\pi$
$410$	−2.48634	−0.122792
$411$	−2.55836	−0.126195
$412$	−25.7953	−1.27084
$413$	4.90995	0.241603
$414$	1.29880	0.0638326
$415$	0.0893234	0.00438472
$416$	0	0
$417$	−5.63993	−0.276189
$418$	0.584649	0.0285961
$419$	−25.9114	−1.26586	−0.632928	−	0.774211i	$-0.718147\pi$
$419$	−25.9114	−1.26586	−0.632928	+	0.774211i	$0.718147\pi$
$420$	−2.89049	−0.141042
$421$	22.8898	1.11558	0.557791	−	0.829981i	$-0.311649\pi$
$421$	22.8898	1.11558	0.557791	+	0.829981i	$0.311649\pi$
$422$	13.1724	0.641225
$423$	−2.16111	−0.105077
$424$	3.65238	0.177375
$425$	10.0499	0.487490
$426$	−7.60094	−0.368267
$427$	−0.563211	−0.0272557
$428$	−5.92674	−0.286480
$429$	0	0
$430$	−8.54874	−0.412257
$431$	−18.1818	−0.875787	−0.437893	−	0.899027i	$-0.644275\pi$
$431$	−18.1818	−0.875787	−0.437893	+	0.899027i	$0.644275\pi$
$432$	−2.59432	−0.124819
$433$	−22.5154	−1.08202	−0.541010	−	0.841016i	$-0.681958\pi$
$433$	−22.5154	−1.08202	−0.541010	+	0.841016i	$0.681958\pi$
$434$	0.348471	0.0167271
$435$	−8.46108	−0.405678
$436$	17.3913	0.832894
$437$	3.08916	0.147775
$438$	−6.71807	−0.321002
$439$	7.31288	0.349025	0.174512	−	0.984655i	$-0.444165\pi$
$439$	7.31288	0.349025	0.174512	+	0.984655i	$0.444165\pi$
$440$	−3.07545	−0.146616
$441$	1.00000	0.0476190
$442$	0	0
$443$	−7.00281	−0.332714	−0.166357	−	0.986066i	$-0.553200\pi$
$443$	−7.00281	−0.332714	−0.166357	+	0.986066i	$0.553200\pi$
$444$	4.78461	0.227067
$445$	−0.989747	−0.0469185
$446$	6.85908	0.324787
$447$	−5.49922	−0.260104
$448$	2.72059	0.128536
$449$	1.74630	0.0824132	0.0412066	−	0.999151i	$-0.486880\pi$
$449$	1.74630	0.0824132	0.0412066	+	0.999151i	$0.486880\pi$
$450$	−1.13158	−0.0533432
$451$	−3.07598	−0.144842
$452$	23.8213	1.12046
$453$	−8.31087	−0.390479
$454$	6.77925	0.318166
$455$	0	0
$456$	2.18162	0.102164
$457$	−18.2001	−0.851367	−0.425683	−	0.904872i	$-0.639966\pi$
$457$	−18.2001	−0.851367	−0.425683	+	0.904872i	$0.639966\pi$
$458$	4.90838	0.229354
$459$	4.38900	0.204861
$460$	−7.59668	−0.354197
$461$	−36.4349	−1.69694	−0.848471	−	0.529242i	$-0.822477\pi$
$461$	−36.4349	−1.69694	−0.848471	+	0.529242i	$0.822477\pi$
$462$	0.497400	0.0231412
$463$	33.5410	1.55878	0.779391	−	0.626538i	$-0.215529\pi$
$463$	33.5410	1.55878	0.779391	+	0.626538i	$0.215529\pi$
$464$	13.3336	0.618998
$465$	1.16085	0.0538333
$466$	9.60817	0.445090
$467$	3.86589	0.178892	0.0894461	−	0.995992i	$-0.471490\pi$
$467$	3.86589	0.178892	0.0894461	+	0.995992i	$0.471490\pi$
$468$	0	0
$469$	−13.1061	−0.605182
$470$	−1.75821	−0.0811001
$471$	−12.8123	−0.590358
$472$	9.11314	0.419466
$473$	−10.5761	−0.486289
$474$	−3.77200	−0.173254
$475$	−2.69143	−0.123491
$476$	−7.70611	−0.353209
$477$	−1.96782	−0.0901003
$478$	8.09899	0.370439
$479$	37.2104	1.70019	0.850094	−	0.526631i	$-0.176545\pi$
$479$	37.2104	1.70019	0.850094	+	0.526631i	$0.176545\pi$
$480$	−8.22180	−0.375272
$481$	0	0
$482$	−7.90934	−0.360261
$483$	2.62816	0.119586
$484$	17.5349	0.797040
$485$	2.86583	0.130131
$486$	−0.494186	−0.0224167
$487$	19.0179	0.861783	0.430892	−	0.902404i	$-0.358199\pi$
$487$	19.0179	0.861783	0.430892	+	0.902404i	$0.358199\pi$
$488$	−1.04535	−0.0473208
$489$	−10.7587	−0.486524
$490$	0.813565	0.0367531
$491$	14.7990	0.667868	0.333934	−	0.942596i	$-0.391624\pi$
$491$	14.7990	0.667868	0.333934	+	0.942596i	$0.391624\pi$
$492$	−5.36585	−0.241911
$493$	−22.5574	−1.01593
$494$	0	0
$495$	1.65698	0.0744757
$496$	−1.82936	−0.0821408
$497$	−15.3807	−0.689920
$498$	−0.0268135	−0.00120154
$499$	−27.5937	−1.23526	−0.617632	−	0.786467i	$-0.711908\pi$
$499$	−27.5937	−1.23526	−0.617632	+	0.786467i	$0.711908\pi$
$500$	21.0711	0.942327
$501$	25.0059	1.11718
$502$	−6.78959	−0.303034
$503$	42.9458	1.91486	0.957428	−	0.288671i	$-0.0932135\pi$
$503$	42.9458	1.91486	0.957428	+	0.288671i	$0.0932135\pi$
$504$	1.85605	0.0826752
$505$	21.1690	0.942008
$506$	1.30725	0.0581143
$507$	0	0
$508$	−13.4431	−0.596443
$509$	−25.7321	−1.14056	−0.570278	−	0.821452i	$-0.693165\pi$
$509$	−25.7321	−1.14056	−0.570278	+	0.821452i	$0.693165\pi$
$510$	3.57073	0.158115
$511$	−13.5942	−0.601373
$512$	22.5870	0.998212
$513$	−1.17541	−0.0518955
$514$	12.4041	0.547122
$515$	24.1865	1.06578
$516$	−18.4493	−0.812185
$517$	−2.17517	−0.0956639
$518$	−1.34669	−0.0591700
$519$	−16.7347	−0.734573
$520$	0	0
$521$	33.4269	1.46446	0.732229	−	0.681059i	$-0.238480\pi$
$521$	33.4269	1.46446	0.732229	+	0.681059i	$0.238480\pi$
$522$	2.53989	0.111168
$523$	−23.8931	−1.04477	−0.522386	−	0.852709i	$-0.674958\pi$
$523$	−23.8931	−1.04477	−0.522386	+	0.852709i	$0.674958\pi$
$524$	−2.20354	−0.0962621
$525$	−2.28979	−0.0999345
$526$	3.39123	0.147864
$527$	3.09486	0.134814
$528$	−2.61120	−0.113638
$529$	−16.0928	−0.699685
$530$	−1.60095	−0.0695408
$531$	−4.90995	−0.213074
$532$	2.06376	0.0894753
$533$	0	0
$534$	0.297107	0.0128571
$535$	5.55709	0.240254
$536$	−24.3256	−1.05070
$537$	−12.2780	−0.529834
$538$	9.00282	0.388139
$539$	1.00650	0.0433532
$540$	2.89049	0.124387
$541$	5.29873	0.227810	0.113905	−	0.993492i	$-0.463664\pi$
$541$	5.29873	0.227810	0.113905	+	0.993492i	$0.463664\pi$
$542$	7.43323	0.319285
$543$	−22.8077	−0.978770
$544$	−21.9195	−0.939789
$545$	−16.3067	−0.698500
$546$	0	0
$547$	37.2193	1.59138	0.795691	−	0.605703i	$-0.207108\pi$
$547$	37.2193	1.59138	0.795691	+	0.605703i	$0.207108\pi$
$548$	−4.49192	−0.191886
$549$	0.563211	0.0240372
$550$	−1.13894	−0.0485646
$551$	6.04106	0.257358
$552$	4.87801	0.207622
$553$	−7.63275	−0.324577
$554$	0.689072	0.0292758
$555$	−4.48619	−0.190428
$556$	−9.90248	−0.419959
$557$	5.40182	0.228883	0.114441	−	0.993430i	$-0.463492\pi$
$557$	5.40182	0.228883	0.114441	+	0.993430i	$0.463492\pi$
$558$	−0.348471	−0.0147519
$559$	0	0
$560$	−4.27096	−0.180481
$561$	4.41754	0.186509
$562$	5.53541	0.233497
$563$	−10.9360	−0.460898	−0.230449	−	0.973084i	$-0.574019\pi$
$563$	−10.9360	−0.460898	−0.230449	+	0.973084i	$0.574019\pi$
$564$	−3.79444	−0.159775
$565$	−22.3355	−0.939663
$566$	−7.33602	−0.308356
$567$	−1.00000	−0.0419961
$568$	−28.5475	−1.19783
$569$	−30.5762	−1.28182	−0.640911	−	0.767615i	$-0.721443\pi$
$569$	−30.5762	−1.28182	−0.640911	+	0.767615i	$0.721443\pi$
$570$	−0.956271	−0.0400538
$571$	6.37732	0.266882	0.133441	−	0.991057i	$-0.457397\pi$
$571$	6.37732	0.266882	0.133441	+	0.991057i	$0.457397\pi$
$572$	0	0
$573$	−27.4058	−1.14489
$574$	1.51029	0.0630381
$575$	−6.01793	−0.250965
$576$	−2.72059	−0.113358
$577$	0.900721	0.0374975	0.0187487	−	0.999824i	$-0.494032\pi$
$577$	0.900721	0.0374975	0.0187487	+	0.999824i	$0.494032\pi$
$578$	1.11848	0.0465227
$579$	6.41304	0.266517
$580$	−14.8558	−0.616854
$581$	−0.0542580	−0.00225100
$582$	−0.860279	−0.0356597
$583$	−1.98062	−0.0820288
$584$	−25.2316	−1.04409
$585$	0	0
$586$	−8.80923	−0.363906
$587$	−43.8262	−1.80890	−0.904451	−	0.426577i	$-0.859719\pi$
$587$	−43.8262	−1.80890	−0.904451	+	0.426577i	$0.859719\pi$
$588$	1.75578	0.0724071
$589$	−0.828828	−0.0341513
$590$	−3.99457	−0.164454
$591$	17.2081	0.707848
$592$	7.06969	0.290562
$593$	−30.8733	−1.26781	−0.633907	−	0.773409i	$-0.718550\pi$
$593$	−30.8733	−1.26781	−0.633907	+	0.773409i	$0.718550\pi$
$594$	−0.497400	−0.0204086
$595$	7.22548	0.296216
$596$	−9.65543	−0.395502
$597$	3.01028	0.123202
$598$	0	0
$599$	33.0466	1.35025	0.675123	−	0.737705i	$-0.264091\pi$
$599$	33.0466	1.35025	0.675123	+	0.737705i	$0.264091\pi$
$600$	−4.24997	−0.173504
$601$	−23.2566	−0.948658	−0.474329	−	0.880348i	$-0.657309\pi$
$601$	−23.2566	−0.948658	−0.474329	+	0.880348i	$0.657309\pi$
$602$	5.19278	0.211642
$603$	13.1061	0.533720
$604$	−14.5921	−0.593743
$605$	−16.4412	−0.668432
$606$	−6.35461	−0.258139
$607$	36.9583	1.50009	0.750045	−	0.661386i	$-0.230032\pi$
$607$	36.9583	1.50009	0.750045	+	0.661386i	$0.230032\pi$
$608$	5.87021	0.238068
$609$	5.13954	0.208265
$610$	0.458209	0.0185523
$611$	0	0
$612$	7.70611	0.311501
$613$	−6.74925	−0.272600	−0.136300	−	0.990668i	$-0.543521\pi$
$613$	−6.74925	−0.272600	−0.136300	+	0.990668i	$0.543521\pi$
$614$	−15.1411	−0.611047
$615$	5.03119	0.202877
$616$	1.86813	0.0752690
$617$	34.7076	1.39727	0.698637	−	0.715476i	$-0.253790\pi$
$617$	34.7076	1.39727	0.698637	+	0.715476i	$0.253790\pi$
$618$	−7.26041	−0.292057
$619$	7.42759	0.298540	0.149270	−	0.988796i	$-0.452308\pi$
$619$	7.42759	0.298540	0.149270	+	0.988796i	$0.452308\pi$
$620$	2.03820	0.0818562
$621$	−2.62816	−0.105465
$622$	4.58227	0.183732
$623$	0.601205	0.0240868
$624$	0	0
$625$	−8.30795	−0.332318
$626$	−12.7224	−0.508489
$627$	−1.18305	−0.0472466
$628$	−22.4955	−0.897668
$629$	−11.9603	−0.476887
$630$	−0.813565	−0.0324132
$631$	−30.4787	−1.21334	−0.606669	−	0.794954i	$-0.707495\pi$
$631$	−30.4787	−1.21334	−0.606669	+	0.794954i	$0.707495\pi$
$632$	−14.1668	−0.563525
$633$	−26.6548	−1.05943
$634$	2.95781	0.117470
$635$	12.6047	0.500202
$636$	−3.45506	−0.137002
$637$	0	0
$638$	2.55641	0.101209
$639$	15.3807	0.608452
$640$	−18.6570	−0.737481
$641$	27.6795	1.09328	0.546638	−	0.837369i	$-0.315907\pi$
$641$	27.6795	1.09328	0.546638	+	0.837369i	$0.315907\pi$
$642$	−1.66815	−0.0658368
$643$	−29.0749	−1.14660	−0.573302	−	0.819344i	$-0.694338\pi$
$643$	−29.0749	−1.14660	−0.573302	+	0.819344i	$0.694338\pi$
$644$	4.61447	0.181836
$645$	17.2986	0.681132
$646$	−2.54944	−0.100306
$647$	8.93804	0.351391	0.175695	−	0.984445i	$-0.443783\pi$
$647$	8.93804	0.351391	0.175695	+	0.984445i	$0.443783\pi$
$648$	−1.85605	−0.0729127
$649$	−4.94189	−0.193986
$650$	0	0
$651$	−0.705141	−0.0276366
$652$	−18.8899	−0.739784
$653$	−27.1525	−1.06256	−0.531280	−	0.847196i	$-0.678289\pi$
$653$	−27.1525	−1.06256	−0.531280	+	0.847196i	$0.678289\pi$
$654$	4.89501	0.191410
$655$	2.06611	0.0807295
$656$	−7.92853	−0.309557
$657$	13.5942	0.530361
$658$	1.06799	0.0416347
$659$	−5.63077	−0.219344	−0.109672	−	0.993968i	$-0.534980\pi$
$659$	−5.63077	−0.219344	−0.109672	+	0.993968i	$0.534980\pi$
$660$	2.90929	0.113244
$661$	−12.6352	−0.491453	−0.245727	−	0.969339i	$-0.579027\pi$
$661$	−12.6352	−0.491453	−0.245727	+	0.969339i	$0.579027\pi$
$662$	−12.2069	−0.474435
$663$	0	0
$664$	−0.100706	−0.00390814
$665$	−1.93504	−0.0750377
$666$	1.34669	0.0521831
$667$	13.5075	0.523014
$668$	43.9049	1.69873
$669$	−13.8795	−0.536614
$670$	10.6626	0.411934
$671$	0.566874	0.0218839
$672$	4.99419	0.192655
$673$	−45.5652	−1.75641	−0.878204	−	0.478286i	$-0.841258\pi$
$673$	−45.5652	−1.75641	−0.878204	+	0.478286i	$0.841258\pi$
$674$	−3.18476	−0.122673
$675$	2.28979	0.0881339
$676$	0	0
$677$	−26.6074	−1.02261	−0.511303	−	0.859400i	$-0.670837\pi$
$677$	−26.6074	−1.02261	−0.511303	+	0.859400i	$0.670837\pi$
$678$	6.70479	0.257496
$679$	−1.74080	−0.0668057
$680$	13.4109	0.514284
$681$	−13.7180	−0.525675
$682$	−0.350737	−0.0134304
$683$	21.5696	0.825338	0.412669	−	0.910881i	$-0.364597\pi$
$683$	21.5696	0.825338	0.412669	+	0.910881i	$0.364597\pi$
$684$	−2.06376	−0.0789098
$685$	4.21177	0.160923
$686$	−0.494186	−0.0188681
$687$	−9.93225	−0.378939
$688$	−27.2605	−1.03930
$689$	0	0
$690$	−2.13818	−0.0813992
$691$	−36.2297	−1.37824	−0.689121	−	0.724646i	$-0.742003\pi$
$691$	−36.2297	−1.37824	−0.689121	+	0.724646i	$0.742003\pi$
$692$	−29.3825	−1.11696
$693$	−1.00650	−0.0382339
$694$	7.80599	0.296311
$695$	9.28487	0.352195
$696$	9.53927	0.361585
$697$	13.4132	0.508063
$698$	10.5090	0.397770
$699$	−19.4424	−0.735379
$700$	−4.02036	−0.151955
$701$	4.73093	0.178685	0.0893424	−	0.996001i	$-0.471523\pi$
$701$	4.73093	0.178685	0.0893424	+	0.996001i	$0.471523\pi$
$702$	0	0
$703$	3.20306	0.120806
$704$	−2.73828	−0.103203
$705$	3.55778	0.133994
$706$	4.97961	0.187410
$707$	−12.8587	−0.483603
$708$	−8.62080	−0.323989
$709$	23.5959	0.886163	0.443082	−	0.896481i	$-0.353885\pi$
$709$	23.5959	0.886163	0.443082	+	0.896481i	$0.353885\pi$
$710$	12.5132	0.469613
$711$	7.63275	0.286250
$712$	1.11587	0.0418190
$713$	−1.85322	−0.0694038
$714$	−2.16898	−0.0811721
$715$	0	0
$716$	−21.5574	−0.805639
$717$	−16.3885	−0.612041
$718$	−11.2252	−0.418921
$719$	16.1744	0.603203	0.301601	−	0.953434i	$-0.402479\pi$
$719$	16.1744	0.603203	0.301601	+	0.953434i	$0.402479\pi$
$720$	4.27096	0.159169
$721$	−14.6917	−0.547146
$722$	−8.70678	−0.324033
$723$	16.0048	0.595224
$724$	−40.0452	−1.48827
$725$	−11.7684	−0.437069
$726$	4.93541	0.183170
$727$	−12.1774	−0.451633	−0.225817	−	0.974170i	$-0.572505\pi$
$727$	−12.1774	−0.451633	−0.225817	+	0.974170i	$0.572505\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	11.0598	0.409341
$731$	46.1184	1.70575
$732$	0.988874	0.0365498
$733$	−35.6552	−1.31695	−0.658477	−	0.752601i	$-0.728799\pi$
$733$	−35.6552	−1.31695	−0.658477	+	0.752601i	$0.728799\pi$
$734$	−9.77650	−0.360857
$735$	−1.64627	−0.0607237
$736$	13.1255	0.483814
$737$	13.1913	0.485908
$738$	−1.51029	−0.0555944
$739$	−18.0473	−0.663880	−0.331940	−	0.943300i	$-0.607703\pi$
$739$	−18.0473	−0.663880	−0.331940	+	0.943300i	$0.607703\pi$
$740$	−7.87677	−0.289556
$741$	0	0
$742$	0.972469	0.0357005
$743$	−52.9988	−1.94434	−0.972168	−	0.234285i	$-0.924725\pi$
$743$	−52.9988	−1.94434	−0.972168	+	0.234285i	$0.924725\pi$
$744$	−1.30878	−0.0479822
$745$	9.05322	0.331684
$746$	−2.08170	−0.0762165
$747$	0.0542580	0.00198520
$748$	7.75623	0.283596
$749$	−3.37556	−0.123340
$750$	5.93072	0.216559
$751$	38.3089	1.39791	0.698956	−	0.715165i	$-0.253648\pi$
$751$	38.3089	1.39791	0.698956	+	0.715165i	$0.253648\pi$
$752$	−5.60663	−0.204453
$753$	13.7389	0.500674
$754$	0	0
$755$	13.6820	0.497938
$756$	−1.75578	−0.0638571
$757$	26.3033	0.956010	0.478005	−	0.878357i	$-0.341360\pi$
$757$	26.3033	0.956010	0.478005	+	0.878357i	$0.341360\pi$
$758$	0.804675	0.0292271
$759$	−2.64526	−0.0960167
$760$	−3.59155	−0.130279
$761$	41.3290	1.49818	0.749088	−	0.662470i	$-0.230492\pi$
$761$	41.3290	1.49818	0.749088	+	0.662470i	$0.230492\pi$
$762$	−3.78374	−0.137071
$763$	9.90520	0.358592
$764$	−48.1186	−1.74087
$765$	−7.22548	−0.261238
$766$	1.58872	0.0574026
$767$	0	0
$768$	0.159364	0.00575057
$769$	−19.8950	−0.717431	−0.358715	−	0.933447i	$-0.616785\pi$
$769$	−19.8950	−0.717431	−0.358715	+	0.933447i	$0.616785\pi$
$770$	−0.818857	−0.0295095
$771$	−25.1001	−0.903958
$772$	11.2599	0.405252
$773$	−37.3499	−1.34338	−0.671692	−	0.740831i	$-0.734432\pi$
$773$	−37.3499	−1.34338	−0.671692	+	0.740831i	$0.734432\pi$
$774$	−5.19278	−0.186651
$775$	1.61462	0.0579989
$776$	−3.23102	−0.115987
$777$	2.72506	0.0977610
$778$	−2.12660	−0.0762422
$779$	−3.59217	−0.128703
$780$	0	0
$781$	15.4808	0.553945
$782$	−5.70043	−0.203847
$783$	−5.13954	−0.183672
$784$	2.59432	0.0926544
$785$	21.0925	0.752822
$786$	−0.620214	−0.0221223
$787$	15.9051	0.566955	0.283478	−	0.958979i	$-0.408512\pi$
$787$	15.9051	0.566955	0.283478	+	0.958979i	$0.408512\pi$
$788$	30.2137	1.07632
$789$	−6.86224	−0.244302
$790$	6.20974	0.220933
$791$	13.5673	0.482399
$792$	−1.86813	−0.0663810
$793$	0	0
$794$	−15.5906	−0.553288
$795$	3.23957	0.114896
$796$	5.28538	0.187335
$797$	13.5259	0.479111	0.239555	−	0.970883i	$-0.422998\pi$
$797$	13.5259	0.479111	0.239555	+	0.970883i	$0.422998\pi$
$798$	0.580871	0.0205626
$799$	9.48512	0.335560
$800$	−11.4356	−0.404310
$801$	−0.601205	−0.0212425
$802$	10.7302	0.378898
$803$	13.6826	0.482849
$804$	23.0114	0.811548
$805$	−4.32667	−0.152495
$806$	0	0
$807$	−18.2175	−0.641285
$808$	−23.8665	−0.839622
$809$	7.60313	0.267312	0.133656	−	0.991028i	$-0.457328\pi$
$809$	7.60313	0.267312	0.133656	+	0.991028i	$0.457328\pi$
$810$	0.813565	0.0285858
$811$	−23.9460	−0.840859	−0.420429	−	0.907325i	$-0.638121\pi$
$811$	−23.9460	−0.840859	−0.420429	+	0.907325i	$0.638121\pi$
$812$	9.02390	0.316677
$813$	−15.0414	−0.527523
$814$	1.35545	0.0475084
$815$	17.7117	0.620414
$816$	11.3865	0.398606
$817$	−12.3509	−0.432103
$818$	−4.93402	−0.172514
$819$	0	0
$820$	8.83366	0.308485
$821$	13.5062	0.471370	0.235685	−	0.971829i	$-0.424267\pi$
$821$	13.5062	0.471370	0.235685	+	0.971829i	$0.424267\pi$
$822$	−1.26431	−0.0440978
$823$	26.6348	0.928430	0.464215	−	0.885723i	$-0.346336\pi$
$823$	26.6348	0.928430	0.464215	+	0.885723i	$0.346336\pi$
$824$	−27.2685	−0.949944
$825$	2.30468	0.0802386
$826$	2.42643	0.0844263
$827$	32.3365	1.12445	0.562225	−	0.826984i	$-0.309945\pi$
$827$	32.3365	1.12445	0.562225	+	0.826984i	$0.309945\pi$
$828$	−4.61447	−0.160364
$829$	−38.3742	−1.33279	−0.666395	−	0.745598i	$-0.732164\pi$
$829$	−38.3742	−1.33279	−0.666395	+	0.745598i	$0.732164\pi$
$830$	0.0441424	0.00153221
$831$	−1.39436	−0.0483697
$832$	0	0
$833$	−4.38900	−0.152070
$834$	−2.78718	−0.0965120
$835$	−41.1666	−1.42463
$836$	−2.07718	−0.0718408
$837$	0.705141	0.0243732
$838$	−12.8051	−0.442344
$839$	−15.9684	−0.551290	−0.275645	−	0.961260i	$-0.588891\pi$
$839$	−15.9684	−0.551290	−0.275645	+	0.961260i	$0.588891\pi$
$840$	−3.05557	−0.105427
$841$	−2.58514	−0.0891427
$842$	11.3118	0.389832
$843$	−11.2011	−0.385785
$844$	−46.8000	−1.61092
$845$	0	0
$846$	−1.06799	−0.0367184
$847$	9.98695	0.343156
$848$	−5.10516	−0.175312
$849$	14.8446	0.509467
$850$	4.96650	0.170350
$851$	7.16190	0.245507
$852$	27.0052	0.925182
$853$	17.3245	0.593181	0.296590	−	0.955005i	$-0.404150\pi$
$853$	17.3245	0.593181	0.296590	+	0.955005i	$0.404150\pi$
$854$	−0.278331	−0.00952429
$855$	1.93504	0.0661771
$856$	−6.26522	−0.214141
$857$	−42.8681	−1.46435	−0.732174	−	0.681118i	$-0.761494\pi$
$857$	−42.8681	−1.46435	−0.732174	+	0.681118i	$0.761494\pi$
$858$	0	0
$859$	−5.98645	−0.204255	−0.102128	−	0.994771i	$-0.532565\pi$
$859$	−5.98645	−0.204255	−0.102128	+	0.994771i	$0.532565\pi$
$860$	30.3726	1.03570
$861$	−3.05611	−0.104152
$862$	−8.98520	−0.306037
$863$	9.24121	0.314575	0.157287	−	0.987553i	$-0.449725\pi$
$863$	9.24121	0.314575	0.157287	+	0.987553i	$0.449725\pi$
$864$	−4.99419	−0.169906
$865$	27.5499	0.936726
$866$	−11.1268	−0.378104
$867$	−2.26328	−0.0768650
$868$	−1.23807	−0.0420229
$869$	7.68239	0.260607
$870$	−4.18135	−0.141761
$871$	0	0
$872$	18.3846	0.622581
$873$	1.74080	0.0589171
$874$	1.52662	0.0516388
$875$	12.0010	0.405707
$876$	23.8684	0.806440
$877$	−36.2804	−1.22510	−0.612551	−	0.790431i	$-0.709856\pi$
$877$	−36.2804	−1.22510	−0.612551	+	0.790431i	$0.709856\pi$
$878$	3.61392	0.121964
$879$	17.8257	0.601247
$880$	4.29874	0.144911
$881$	35.8216	1.20686	0.603431	−	0.797416i	$-0.293800\pi$
$881$	35.8216	1.20686	0.603431	+	0.797416i	$0.293800\pi$
$882$	0.494186	0.0166401
$883$	2.07802	0.0699311	0.0349655	−	0.999389i	$-0.488868\pi$
$883$	2.07802	0.0699311	0.0349655	+	0.999389i	$0.488868\pi$
$884$	0	0
$885$	8.08312	0.271711
$886$	−3.46069	−0.116264
$887$	5.39229	0.181055	0.0905277	−	0.995894i	$-0.471145\pi$
$887$	5.39229	0.181055	0.0905277	+	0.995894i	$0.471145\pi$
$888$	5.05786	0.169731
$889$	−7.65651	−0.256791
$890$	−0.489119	−0.0163953
$891$	1.00650	0.0337191
$892$	−24.3694	−0.815949
$893$	−2.54019	−0.0850043
$894$	−2.71764	−0.0908915
$895$	20.2129	0.675642
$896$	11.3329	0.378604
$897$	0	0
$898$	0.862999	0.0287987
$899$	−3.62410	−0.120870
$900$	4.02036	0.134012
$901$	8.63675	0.287732
$902$	−1.52011	−0.0506141
$903$	−10.5077	−0.349676
$904$	25.1817	0.837532
$905$	37.5476	1.24813
$906$	−4.10712	−0.136450
$907$	−22.5753	−0.749601	−0.374801	−	0.927105i	$-0.622289\pi$
$907$	−22.5753	−0.749601	−0.374801	+	0.927105i	$0.622289\pi$
$908$	−24.0858	−0.799315
$909$	12.8587	0.426498
$910$	0	0
$911$	55.3163	1.83271	0.916355	−	0.400367i	$-0.131117\pi$
$911$	55.3163	1.83271	0.916355	+	0.400367i	$0.131117\pi$
$912$	−3.04939	−0.100975
$913$	0.0546109	0.00180736
$914$	−8.99426	−0.297504
$915$	−0.927198	−0.0306522
$916$	−17.4388	−0.576196
$917$	−1.25502	−0.0414444
$918$	2.16898	0.0715870
$919$	−13.0981	−0.432067	−0.216034	−	0.976386i	$-0.569312\pi$
$919$	−13.0981	−0.432067	−0.216034	+	0.976386i	$0.569312\pi$
$920$	−8.03054	−0.264759
$921$	30.6385	1.00957
$922$	−18.0056	−0.592984
$923$	0	0
$924$	−1.76720	−0.0581366
$925$	−6.23980	−0.205164
$926$	16.5755	0.544704
$927$	14.6917	0.482537
$928$	25.6678	0.842588
$929$	−35.5476	−1.16628	−0.583139	−	0.812372i	$-0.698176\pi$
$929$	−35.5476	−1.16628	−0.583139	+	0.812372i	$0.698176\pi$
$930$	0.573678	0.0188116
$931$	1.17541	0.0385225
$932$	−34.1366	−1.11818
$933$	−9.27236	−0.303564
$934$	1.91047	0.0625125
$935$	−7.27248	−0.237835
$936$	0	0
$937$	−2.01075	−0.0656884	−0.0328442	−	0.999460i	$-0.510457\pi$
$937$	−2.01075	−0.0656884	−0.0328442	+	0.999460i	$0.510457\pi$
$938$	−6.47684	−0.211476
$939$	25.7441	0.840128
$940$	6.24669	0.203744
$941$	47.7893	1.55789	0.778943	−	0.627095i	$-0.215756\pi$
$941$	47.7893	1.55789	0.778943	+	0.627095i	$0.215756\pi$
$942$	−6.33164	−0.206296
$943$	−8.03194	−0.261556
$944$	−12.7380	−0.414587
$945$	1.64627	0.0535533
$946$	−5.22656	−0.169930
$947$	40.3924	1.31258	0.656288	−	0.754510i	$-0.272126\pi$
$947$	40.3924	1.31258	0.656288	+	0.754510i	$0.272126\pi$
$948$	13.4014	0.435258
$949$	0	0
$950$	−1.33007	−0.0431531
$951$	−5.98521	−0.194084
$952$	−8.14622	−0.264020
$953$	27.0429	0.876007	0.438003	−	0.898973i	$-0.355686\pi$
$953$	27.0429	0.876007	0.438003	+	0.898973i	$0.355686\pi$
$954$	−0.972469	−0.0314849
$955$	45.1175	1.45997
$956$	−28.7747	−0.930639
$957$	−5.17297	−0.167218
$958$	18.3889	0.594118
$959$	−2.55836	−0.0826139
$960$	4.47883	0.144554
$961$	−30.5028	−0.983961
$962$	0	0
$963$	3.37556	0.108776
$964$	28.1009	0.905069
$965$	−10.5576	−0.339862
$966$	1.29880	0.0417882
$967$	33.5839	1.07998	0.539992	−	0.841670i	$-0.318427\pi$
$967$	33.5839	1.07998	0.539992	+	0.841670i	$0.318427\pi$
$968$	18.5363	0.595780
$969$	5.15886	0.165727
$970$	1.41625	0.0454732
$971$	37.0838	1.19008	0.595038	−	0.803698i	$-0.297137\pi$
$971$	37.0838	1.19008	0.595038	+	0.803698i	$0.297137\pi$
$972$	1.75578	0.0563167
$973$	−5.63993	−0.180808
$974$	9.39838	0.301144
$975$	0	0
$976$	1.46115	0.0467703
$977$	−44.9088	−1.43676	−0.718379	−	0.695652i	$-0.755116\pi$
$977$	−44.9088	−1.43676	−0.718379	+	0.695652i	$0.755116\pi$
$978$	−5.31679	−0.170012
$979$	−0.605115	−0.0193396
$980$	−2.89049	−0.0923334
$981$	−9.90520	−0.316249
$982$	7.31344	0.233381
$983$	6.22613	0.198583	0.0992914	−	0.995058i	$-0.468342\pi$
$983$	6.22613	0.198583	0.0992914	+	0.995058i	$0.468342\pi$
$984$	−5.67230	−0.180826
$985$	−28.3293	−0.902646
$986$	−11.1476	−0.355011
$987$	−2.16111	−0.0687890
$988$	0	0
$989$	−27.6161	−0.878139
$990$	0.818857	0.0260250
$991$	23.7212	0.753529	0.376765	−	0.926309i	$-0.377037\pi$
$991$	23.7212	0.753529	0.376765	+	0.926309i	$0.377037\pi$
$992$	−3.52160	−0.111811
$993$	24.7010	0.783864
$994$	−7.60094	−0.241087
$995$	−4.95573	−0.157107
$996$	0.0952651	0.00301859
$997$	−55.6549	−1.76261	−0.881303	−	0.472551i	$-0.843333\pi$
$997$	−55.6549	−1.76261	−0.881303	+	0.472551i	$0.843333\pi$
$998$	−13.6364	−0.431654
$999$	−2.72506	−0.0862171

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bf.1.6	yes	9
13.12	even	2		3549.2.a.be.1.4	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3549.2.a.be.1.4	✓	9	13.12	even	2
3549.2.a.bf.1.6	yes	9	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:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q+0.494186 q^{2} -1.00000 q^{3} -1.75578 q^{4} +1.64627 q^{5} -0.494186 q^{6} -1.00000 q^{7} -1.85605 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.494186 q^{2} -1.00000 q^{3} -1.75578 q^{4} +1.64627 q^{5} -0.494186 q^{6} -1.00000 q^{7} -1.85605 q^{8} +1.00000 q^{9} +0.813565 q^{10} +1.00650 q^{11} +1.75578 q^{12} -0.494186 q^{14} -1.64627 q^{15} +2.59432 q^{16} -4.38900 q^{17} +0.494186 q^{18} +1.17541 q^{19} -2.89049 q^{20} +1.00000 q^{21} +0.497400 q^{22} +2.62816 q^{23} +1.85605 q^{24} -2.28979 q^{25} -1.00000 q^{27} +1.75578 q^{28} +5.13954 q^{29} -0.813565 q^{30} -0.705141 q^{31} +4.99419 q^{32} -1.00650 q^{33} -2.16898 q^{34} -1.64627 q^{35} -1.75578 q^{36} +2.72506 q^{37} +0.580871 q^{38} -3.05557 q^{40} -3.05611 q^{41} +0.494186 q^{42} -10.5077 q^{43} -1.76720 q^{44} +1.64627 q^{45} +1.29880 q^{46} -2.16111 q^{47} -2.59432 q^{48} +1.00000 q^{49} -1.13158 q^{50} +4.38900 q^{51} -1.96782 q^{53} -0.494186 q^{54} +1.65698 q^{55} +1.85605 q^{56} -1.17541 q^{57} +2.53989 q^{58} -4.90995 q^{59} +2.89049 q^{60} +0.563211 q^{61} -0.348471 q^{62} -1.00000 q^{63} -2.72059 q^{64} -0.497400 q^{66} +13.1061 q^{67} +7.70611 q^{68} -2.62816 q^{69} -0.813565 q^{70} +15.3807 q^{71} -1.85605 q^{72} +13.5942 q^{73} +1.34669 q^{74} +2.28979 q^{75} -2.06376 q^{76} -1.00650 q^{77} +7.63275 q^{79} +4.27096 q^{80} +1.00000 q^{81} -1.51029 q^{82} +0.0542580 q^{83} -1.75578 q^{84} -7.22548 q^{85} -5.19278 q^{86} -5.13954 q^{87} -1.86813 q^{88} -0.601205 q^{89} +0.813565 q^{90} -4.61447 q^{92} +0.705141 q^{93} -1.06799 q^{94} +1.93504 q^{95} -4.99419 q^{96} +1.74080 q^{97} +0.494186 q^{98} +1.00650 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + q^{2} - 9 q^{3} + 5 q^{4} - 9 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + q^2 - 9 * q^3 + 5 * q^4 - 9 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 9 * q^9	\( 9 q + q^{2} - 9 q^{3} + 5 q^{4} - 9 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 9 q^{9} + q^{10} + q^{11} - 5 q^{12} - q^{14} + 9 q^{15} + 5 q^{16} + 11 q^{17} + q^{18} - 7 q^{19} - 23 q^{20} + 9 q^{21} - 3 q^{22} + 22 q^{23} - 6 q^{24} - 8 q^{25} - 9 q^{27} - 5 q^{28} + 11 q^{29} - q^{30} - 7 q^{31} + 18 q^{32} - q^{33} + 6 q^{34} + 9 q^{35} + 5 q^{36} + q^{37} - 6 q^{38} - 14 q^{40} - 16 q^{41} + q^{42} + 32 q^{43} - 18 q^{44} - 9 q^{45} + 9 q^{46} + 12 q^{47} - 5 q^{48} + 9 q^{49} - 10 q^{50} - 11 q^{51} + 13 q^{53} - q^{54} + 9 q^{55} - 6 q^{56} + 7 q^{57} - 4 q^{58} - 29 q^{59} + 23 q^{60} - 12 q^{61} + 30 q^{62} - 9 q^{63} + 6 q^{64} + 3 q^{66} + 20 q^{67} + 34 q^{68} - 22 q^{69} - q^{70} + 2 q^{71} + 6 q^{72} - q^{73} + 43 q^{74} + 8 q^{75} - 13 q^{76} - q^{77} + 3 q^{79} + 39 q^{80} + 9 q^{81} - 19 q^{82} - 24 q^{83} + 5 q^{84} - 15 q^{85} + 28 q^{86} - 11 q^{87} - 19 q^{88} - 11 q^{89} + q^{90} + 73 q^{92} + 7 q^{93} + 15 q^{94} + 39 q^{95} - 18 q^{96} - 20 q^{97} + q^{98} + q^{99}+O(q^{100}) \) 9 * q + q^2 - 9 * q^3 + 5 * q^4 - 9 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 9 * q^9 + q^10 + q^11 - 5 * q^12 - q^14 + 9 * q^15 + 5 * q^16 + 11 * q^17 + q^18 - 7 * q^19 - 23 * q^20 + 9 * q^21 - 3 * q^22 + 22 * q^23 - 6 * q^24 - 8 * q^25 - 9 * q^27 - 5 * q^28 + 11 * q^29 - q^30 - 7 * q^31 + 18 * q^32 - q^33 + 6 * q^34 + 9 * q^35 + 5 * q^36 + q^37 - 6 * q^38 - 14 * q^40 - 16 * q^41 + q^42 + 32 * q^43 - 18 * q^44 - 9 * q^45 + 9 * q^46 + 12 * q^47 - 5 * q^48 + 9 * q^49 - 10 * q^50 - 11 * q^51 + 13 * q^53 - q^54 + 9 * q^55 - 6 * q^56 + 7 * q^57 - 4 * q^58 - 29 * q^59 + 23 * q^60 - 12 * q^61 + 30 * q^62 - 9 * q^63 + 6 * q^64 + 3 * q^66 + 20 * q^67 + 34 * q^68 - 22 * q^69 - q^70 + 2 * q^71 + 6 * q^72 - q^73 + 43 * q^74 + 8 * q^75 - 13 * q^76 - q^77 + 3 * q^79 + 39 * q^80 + 9 * q^81 - 19 * q^82 - 24 * q^83 + 5 * q^84 - 15 * q^85 + 28 * q^86 - 11 * q^87 - 19 * q^88 - 11 * q^89 + q^90 + 73 * q^92 + 7 * q^93 + 15 * q^94 + 39 * q^95 - 18 * q^96 - 20 * q^97 + q^98 + q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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