LMFDB - Embedded newform 3549.2.a.bf.1.2

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			1.2
Root			$-1.60159$ 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)

$f(q)$	$=$	$q-1.60159 q^{2} -1.00000 q^{3} +0.565099 q^{4} -2.27787 q^{5} +1.60159 q^{6} -1.00000 q^{7} +2.29813 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.60159 q^{2} -1.00000 q^{3} +0.565099 q^{4} -2.27787 q^{5} +1.60159 q^{6} -1.00000 q^{7} +2.29813 q^{8} +1.00000 q^{9} +3.64823 q^{10} -2.53947 q^{11} -0.565099 q^{12} +1.60159 q^{14} +2.27787 q^{15} -4.81086 q^{16} -4.05395 q^{17} -1.60159 q^{18} -7.93457 q^{19} -1.28722 q^{20} +1.00000 q^{21} +4.06719 q^{22} +0.458029 q^{23} -2.29813 q^{24} +0.188713 q^{25} -1.00000 q^{27} -0.565099 q^{28} +6.01106 q^{29} -3.64823 q^{30} +0.340678 q^{31} +3.10879 q^{32} +2.53947 q^{33} +6.49278 q^{34} +2.27787 q^{35} +0.565099 q^{36} -4.74702 q^{37} +12.7080 q^{38} -5.23485 q^{40} -8.88028 q^{41} -1.60159 q^{42} -2.14282 q^{43} -1.43505 q^{44} -2.27787 q^{45} -0.733576 q^{46} +7.16883 q^{47} +4.81086 q^{48} +1.00000 q^{49} -0.302241 q^{50} +4.05395 q^{51} +3.30421 q^{53} +1.60159 q^{54} +5.78459 q^{55} -2.29813 q^{56} +7.93457 q^{57} -9.62727 q^{58} -4.30373 q^{59} +1.28722 q^{60} -11.4865 q^{61} -0.545627 q^{62} -1.00000 q^{63} +4.64271 q^{64} -4.06719 q^{66} -10.4979 q^{67} -2.29088 q^{68} -0.458029 q^{69} -3.64823 q^{70} -4.25291 q^{71} +2.29813 q^{72} -1.59136 q^{73} +7.60279 q^{74} -0.188713 q^{75} -4.48382 q^{76} +2.53947 q^{77} -9.42077 q^{79} +10.9585 q^{80} +1.00000 q^{81} +14.2226 q^{82} -1.87743 q^{83} +0.565099 q^{84} +9.23439 q^{85} +3.43193 q^{86} -6.01106 q^{87} -5.83602 q^{88} -17.9934 q^{89} +3.64823 q^{90} +0.258832 q^{92} -0.340678 q^{93} -11.4815 q^{94} +18.0740 q^{95} -3.10879 q^{96} -18.9563 q^{97} -1.60159 q^{98} -2.53947 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.60159	−1.13250	−0.566248	−	0.824235i	$-0.691606\pi$
$2$	−1.60159	−1.13250	−0.566248	+	0.824235i	$0.691606\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.565099	0.282549
$5$	−2.27787	−1.01870	−0.509348	−	0.860560i	$-0.670113\pi$
$5$	−2.27787	−1.01870	−0.509348	+	0.860560i	$0.670113\pi$
$6$	1.60159	0.653847
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.29813	0.812511
$9$	1.00000	0.333333
$10$	3.64823	1.15367
$11$	−2.53947	−0.765678	−0.382839	−	0.923815i	$-0.625054\pi$
$11$	−2.53947	−0.765678	−0.382839	+	0.923815i	$0.625054\pi$
$12$	−0.565099	−0.163130
$13$	0	0
$13$	0	0
$14$	1.60159	0.428044
$15$	2.27787	0.588145
$16$	−4.81086	−1.20272
$17$	−4.05395	−0.983228	−0.491614	−	0.870813i	$-0.663593\pi$
$17$	−4.05395	−0.983228	−0.491614	+	0.870813i	$0.663593\pi$
$18$	−1.60159	−0.377499
$19$	−7.93457	−1.82032	−0.910158	−	0.414261i	$-0.864040\pi$
$19$	−7.93457	−1.82032	−0.910158	+	0.414261i	$0.864040\pi$
$20$	−1.28722	−0.287832
$21$	1.00000	0.218218
$22$	4.06719	0.867128
$23$	0.458029	0.0955057	0.0477529	−	0.998859i	$-0.484794\pi$
$23$	0.458029	0.0955057	0.0477529	+	0.998859i	$0.484794\pi$
$24$	−2.29813	−0.469103
$25$	0.188713	0.0377425
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−0.565099	−0.106794
$29$	6.01106	1.11623	0.558113	−	0.829765i	$-0.311526\pi$
$29$	6.01106	1.11623	0.558113	+	0.829765i	$0.311526\pi$
$30$	−3.64823	−0.666072
$31$	0.340678	0.0611875	0.0305938	−	0.999532i	$-0.490260\pi$
$31$	0.340678	0.0611875	0.0305938	+	0.999532i	$0.490260\pi$
$32$	3.10879	0.549561
$33$	2.53947	0.442064
$34$	6.49278	1.11350
$35$	2.27787	0.385031
$36$	0.565099	0.0941831
$37$	−4.74702	−0.780405	−0.390202	−	0.920729i	$-0.627595\pi$
$37$	−4.74702	−0.780405	−0.390202	+	0.920729i	$0.627595\pi$
$38$	12.7080	2.06150
$39$	0	0
$40$	−5.23485	−0.827702
$41$	−8.88028	−1.38687	−0.693433	−	0.720521i	$-0.743903\pi$
$41$	−8.88028	−1.38687	−0.693433	+	0.720521i	$0.743903\pi$
$42$	−1.60159	−0.247131
$43$	−2.14282	−0.326777	−0.163389	−	0.986562i	$-0.552242\pi$
$43$	−2.14282	−0.326777	−0.163389	+	0.986562i	$0.552242\pi$
$44$	−1.43505	−0.216342
$45$	−2.27787	−0.339565
$46$	−0.733576	−0.108160
$47$	7.16883	1.04568	0.522841	−	0.852430i	$-0.324872\pi$
$47$	7.16883	1.04568	0.522841	+	0.852430i	$0.324872\pi$
$48$	4.81086	0.694388
$49$	1.00000	0.142857
$50$	−0.302241	−0.0427433
$51$	4.05395	0.567667
$52$	0	0
$53$	3.30421	0.453868	0.226934	−	0.973910i	$-0.427130\pi$
$53$	3.30421	0.453868	0.226934	+	0.973910i	$0.427130\pi$
$54$	1.60159	0.217949
$55$	5.78459	0.779993
$56$	−2.29813	−0.307100
$57$	7.93457	1.05096
$58$	−9.62727	−1.26412
$59$	−4.30373	−0.560298	−0.280149	−	0.959957i	$-0.590384\pi$
$59$	−4.30373	−0.560298	−0.280149	+	0.959957i	$0.590384\pi$
$60$	1.28722	0.166180
$61$	−11.4865	−1.47069	−0.735347	−	0.677691i	$-0.762981\pi$
$61$	−11.4865	−1.47069	−0.735347	+	0.677691i	$0.762981\pi$
$62$	−0.545627	−0.0692947
$63$	−1.00000	−0.125988
$64$	4.64271	0.580339
$65$	0	0
$66$	−4.06719	−0.500637
$67$	−10.4979	−1.28252	−0.641258	−	0.767325i	$-0.721587\pi$
$67$	−10.4979	−1.28252	−0.641258	+	0.767325i	$0.721587\pi$
$68$	−2.29088	−0.277810
$69$	−0.458029	−0.0551402
$70$	−3.64823	−0.436047
$71$	−4.25291	−0.504727	−0.252364	−	0.967633i	$-0.581208\pi$
$71$	−4.25291	−0.504727	−0.252364	+	0.967633i	$0.581208\pi$
$72$	2.29813	0.270837
$73$	−1.59136	−0.186255	−0.0931273	−	0.995654i	$-0.529686\pi$
$73$	−1.59136	−0.186255	−0.0931273	+	0.995654i	$0.529686\pi$
$74$	7.60279	0.883806
$75$	−0.188713	−0.0217907
$76$	−4.48382	−0.514329
$77$	2.53947	0.289399
$78$	0	0
$79$	−9.42077	−1.05992	−0.529960	−	0.848023i	$-0.677793\pi$
$79$	−9.42077	−1.05992	−0.529960	+	0.848023i	$0.677793\pi$
$80$	10.9585	1.22520
$81$	1.00000	0.111111
$82$	14.2226	1.57062
$83$	−1.87743	−0.206074	−0.103037	−	0.994678i	$-0.532856\pi$
$83$	−1.87743	−0.206074	−0.103037	+	0.994678i	$0.532856\pi$
$84$	0.565099	0.0616573
$85$	9.23439	1.00161
$86$	3.43193	0.370074
$87$	−6.01106	−0.644453
$88$	−5.83602	−0.622121
$89$	−17.9934	−1.90730	−0.953648	−	0.300923i	$-0.902705\pi$
$89$	−17.9934	−1.90730	−0.953648	+	0.300923i	$0.902705\pi$
$90$	3.64823	0.384557
$91$	0	0
$92$	0.258832	0.0269851
$93$	−0.340678	−0.0353266
$94$	−11.4815	−1.18423
$95$	18.0740	1.85435
$96$	−3.10879	−0.317289
$97$	−18.9563	−1.92472	−0.962359	−	0.271780i	$-0.912388\pi$
$97$	−18.9563	−1.92472	−0.962359	+	0.271780i	$0.912388\pi$
$98$	−1.60159	−0.161785
$99$	−2.53947	−0.255226
$100$	0.106641	0.0106641
$101$	−4.02671	−0.400672	−0.200336	−	0.979727i	$-0.564203\pi$
$101$	−4.02671	−0.400672	−0.200336	+	0.979727i	$0.564203\pi$
$102$	−6.49278	−0.642881
$103$	−11.3431	−1.11767	−0.558835	−	0.829279i	$-0.688751\pi$
$103$	−11.3431	−1.11767	−0.558835	+	0.829279i	$0.688751\pi$
$104$	0	0
$105$	−2.27787	−0.222298
$106$	−5.29200	−0.514004
$107$	−15.8563	−1.53289	−0.766444	−	0.642311i	$-0.777976\pi$
$107$	−15.8563	−1.53289	−0.766444	+	0.642311i	$0.777976\pi$
$108$	−0.565099	−0.0543767
$109$	−13.1406	−1.25864	−0.629320	−	0.777146i	$-0.716666\pi$
$109$	−13.1406	−1.25864	−0.629320	+	0.777146i	$0.716666\pi$
$110$	−9.26455	−0.883340
$111$	4.74702	0.450567
$112$	4.81086	0.454584
$113$	0.392747	0.0369465	0.0184733	−	0.999829i	$-0.494119\pi$
$113$	0.392747	0.0369465	0.0184733	+	0.999829i	$0.494119\pi$
$114$	−12.7080	−1.19021
$115$	−1.04333	−0.0972913
$116$	3.39684	0.315389
$117$	0	0
$118$	6.89282	0.634535
$119$	4.05395	0.371625
$120$	5.23485	0.477874
$121$	−4.55111	−0.413737
$122$	18.3967	1.66556
$123$	8.88028	0.800708
$124$	0.192517	0.0172885
$125$	10.9595	0.980248
$126$	1.60159	0.142681
$127$	15.9958	1.41940	0.709701	−	0.704503i	$-0.248830\pi$
$127$	15.9958	1.41940	0.709701	+	0.704503i	$0.248830\pi$
$128$	−13.6533	−1.20679
$129$	2.14282	0.188665
$130$	0	0
$131$	16.6090	1.45113	0.725567	−	0.688151i	$-0.241577\pi$
$131$	16.6090	1.45113	0.725567	+	0.688151i	$0.241577\pi$
$132$	1.43505	0.124905
$133$	7.93457	0.688015
$134$	16.8133	1.45245
$135$	2.27787	0.196048
$136$	−9.31650	−0.798883
$137$	1.57748	0.134773	0.0673865	−	0.997727i	$-0.478534\pi$
$137$	1.57748	0.134773	0.0673865	+	0.997727i	$0.478534\pi$
$138$	0.733576	0.0624462
$139$	12.0257	1.02000	0.510001	−	0.860174i	$-0.329645\pi$
$139$	12.0257	1.02000	0.510001	+	0.860174i	$0.329645\pi$
$140$	1.28722	0.108790
$141$	−7.16883	−0.603724
$142$	6.81142	0.571602
$143$	0	0
$144$	−4.81086	−0.400905
$145$	−13.6924	−1.13710
$146$	2.54871	0.210933
$147$	−1.00000	−0.0824786
$148$	−2.68253	−0.220503
$149$	24.1801	1.98091	0.990456	−	0.137827i	$-0.0440120\pi$
$149$	24.1801	1.98091	0.990456	+	0.137827i	$0.0440120\pi$
$150$	0.302241	0.0246779
$151$	8.98472	0.731167	0.365583	−	0.930779i	$-0.380870\pi$
$151$	8.98472	0.731167	0.365583	+	0.930779i	$0.380870\pi$
$152$	−18.2347	−1.47903
$153$	−4.05395	−0.327743
$154$	−4.06719	−0.327744
$155$	−0.776021	−0.0623315
$156$	0	0
$157$	−2.71212	−0.216451	−0.108225	−	0.994126i	$-0.534517\pi$
$157$	−2.71212	−0.216451	−0.108225	+	0.994126i	$0.534517\pi$
$158$	15.0882	1.20036
$159$	−3.30421	−0.262041
$160$	−7.08142	−0.559836
$161$	−0.458029	−0.0360978
$162$	−1.60159	−0.125833
$163$	17.3562	1.35944	0.679722	−	0.733470i	$-0.262101\pi$
$163$	17.3562	1.35944	0.679722	+	0.733470i	$0.262101\pi$
$164$	−5.01823	−0.391858
$165$	−5.78459	−0.450329
$166$	3.00687	0.233379
$167$	−12.7077	−0.983349	−0.491674	−	0.870779i	$-0.663615\pi$
$167$	−12.7077	−0.983349	−0.491674	+	0.870779i	$0.663615\pi$
$168$	2.29813	0.177304
$169$	0	0
$170$	−14.7897	−1.13432
$171$	−7.93457	−0.606772
$172$	−1.21091	−0.0923307
$173$	1.35443	0.102975	0.0514876	−	0.998674i	$-0.483604\pi$
$173$	1.35443	0.102975	0.0514876	+	0.998674i	$0.483604\pi$
$174$	9.62727	0.729842
$175$	−0.188713	−0.0142653
$176$	12.2170	0.920892
$177$	4.30373	0.323488
$178$	28.8181	2.16001
$179$	21.0691	1.57478	0.787390	−	0.616456i	$-0.211432\pi$
$179$	21.0691	1.57478	0.787390	+	0.616456i	$0.211432\pi$
$180$	−1.28722	−0.0959440
$181$	−0.269780	−0.0200526	−0.0100263	−	0.999950i	$-0.503192\pi$
$181$	−0.269780	−0.0200526	−0.0100263	+	0.999950i	$0.503192\pi$
$182$	0	0
$183$	11.4865	0.849106
$184$	1.05261	0.0775994
$185$	10.8131	0.794995
$186$	0.545627	0.0400073
$187$	10.2949	0.752836
$188$	4.05110	0.295457
$189$	1.00000	0.0727393
$190$	−28.9471	−2.10005
$191$	−6.28281	−0.454608	−0.227304	−	0.973824i	$-0.572991\pi$
$191$	−6.28281	−0.454608	−0.227304	+	0.973824i	$0.572991\pi$
$192$	−4.64271	−0.335059
$193$	−19.3154	−1.39035	−0.695177	−	0.718839i	$-0.744674\pi$
$193$	−19.3154	−1.39035	−0.695177	+	0.718839i	$0.744674\pi$
$194$	30.3602	2.17974
$195$	0	0
$196$	0.565099	0.0403642
$197$	21.0050	1.49654	0.748272	−	0.663392i	$-0.230884\pi$
$197$	21.0050	1.49654	0.748272	+	0.663392i	$0.230884\pi$
$198$	4.06719	0.289043
$199$	17.0312	1.20731	0.603653	−	0.797247i	$-0.293711\pi$
$199$	17.0312	1.20731	0.603653	+	0.797247i	$0.293711\pi$
$200$	0.433686	0.0306662
$201$	10.4979	0.740461
$202$	6.44914	0.453760
$203$	−6.01106	−0.421894
$204$	2.29088	0.160394
$205$	20.2282	1.41280
$206$	18.1670	1.26576
$207$	0.458029	0.0318352
$208$	0	0
$209$	20.1496	1.39378
$210$	3.64823	0.251752
$211$	−10.0436	−0.691428	−0.345714	−	0.938340i	$-0.612363\pi$
$211$	−10.0436	−0.691428	−0.345714	+	0.938340i	$0.612363\pi$
$212$	1.86721	0.128240
$213$	4.25291	0.291404
$214$	25.3954	1.73599
$215$	4.88108	0.332887
$216$	−2.29813	−0.156368
$217$	−0.340678	−0.0231267
$218$	21.0459	1.42541
$219$	1.59136	0.107534
$220$	3.26886	0.220387
$221$	0	0
$222$	−7.60279	−0.510266
$223$	−1.30689	−0.0875156	−0.0437578	−	0.999042i	$-0.513933\pi$
$223$	−1.30689	−0.0875156	−0.0437578	+	0.999042i	$0.513933\pi$
$224$	−3.10879	−0.207714
$225$	0.188713	0.0125808
$226$	−0.629020	−0.0418418
$227$	−7.31823	−0.485728	−0.242864	−	0.970060i	$-0.578087\pi$
$227$	−7.31823	−0.485728	−0.242864	+	0.970060i	$0.578087\pi$
$228$	4.48382	0.296948
$229$	16.5282	1.09221	0.546107	−	0.837715i	$-0.316109\pi$
$229$	16.5282	1.09221	0.546107	+	0.837715i	$0.316109\pi$
$230$	1.67099	0.110182
$231$	−2.53947	−0.167085
$232$	13.8142	0.906946
$233$	5.48450	0.359302	0.179651	−	0.983730i	$-0.442503\pi$
$233$	5.48450	0.359302	0.179651	+	0.983730i	$0.442503\pi$
$234$	0	0
$235$	−16.3297	−1.06523
$236$	−2.43203	−0.158312
$237$	9.42077	0.611945
$238$	−6.49278	−0.420864
$239$	−17.8572	−1.15509	−0.577543	−	0.816360i	$-0.695988\pi$
$239$	−17.8572	−1.15509	−0.577543	+	0.816360i	$0.695988\pi$
$240$	−10.9585	−0.707371
$241$	−23.1081	−1.48852	−0.744262	−	0.667887i	$-0.767199\pi$
$241$	−23.1081	−1.48852	−0.744262	+	0.667887i	$0.767199\pi$
$242$	7.28903	0.468556
$243$	−1.00000	−0.0641500
$244$	−6.49100	−0.415544
$245$	−2.27787	−0.145528
$246$	−14.2226	−0.906799
$247$	0	0
$248$	0.782921	0.0497155
$249$	1.87743	0.118977
$250$	−17.5527	−1.11013
$251$	11.7442	0.741290	0.370645	−	0.928775i	$-0.379137\pi$
$251$	11.7442	0.741290	0.370645	+	0.928775i	$0.379137\pi$
$252$	−0.565099	−0.0355979
$253$	−1.16315	−0.0731266
$254$	−25.6188	−1.60747
$255$	−9.23439	−0.578280
$256$	12.5816	0.786350
$257$	−9.53811	−0.594971	−0.297486	−	0.954726i	$-0.596148\pi$
$257$	−9.53811	−0.594971	−0.297486	+	0.954726i	$0.596148\pi$
$258$	−3.43193	−0.213662
$259$	4.74702	0.294965
$260$	0	0
$261$	6.01106	0.372075
$262$	−26.6008	−1.64341
$263$	−5.26624	−0.324730	−0.162365	−	0.986731i	$-0.551912\pi$
$263$	−5.26624	−0.324730	−0.162365	+	0.986731i	$0.551912\pi$
$264$	5.83602	0.359182
$265$	−7.52658	−0.462354
$266$	−12.7080	−0.779175
$267$	17.9934	1.10118
$268$	−5.93232	−0.362374
$269$	0.602644	0.0367438	0.0183719	−	0.999831i	$-0.494152\pi$
$269$	0.602644	0.0367438	0.0183719	+	0.999831i	$0.494152\pi$
$270$	−3.64823	−0.222024
$271$	5.69585	0.345998	0.172999	−	0.984922i	$-0.444654\pi$
$271$	5.69585	0.345998	0.172999	+	0.984922i	$0.444654\pi$
$272$	19.5030	1.18254
$273$	0	0
$274$	−2.52648	−0.152630
$275$	−0.479229	−0.0288986
$276$	−0.258832	−0.0155798
$277$	−8.00692	−0.481089	−0.240545	−	0.970638i	$-0.577326\pi$
$277$	−8.00692	−0.481089	−0.240545	+	0.970638i	$0.577326\pi$
$278$	−19.2602	−1.15515
$279$	0.340678	0.0203958
$280$	5.23485	0.312842
$281$	3.01814	0.180047	0.0900236	−	0.995940i	$-0.471306\pi$
$281$	3.01814	0.180047	0.0900236	+	0.995940i	$0.471306\pi$
$282$	11.4815	0.683716
$283$	8.91703	0.530062	0.265031	−	0.964240i	$-0.414618\pi$
$283$	8.91703	0.530062	0.265031	+	0.964240i	$0.414618\pi$
$284$	−2.40331	−0.142610
$285$	−18.0740	−1.07061
$286$	0	0
$287$	8.88028	0.524186
$288$	3.10879	0.183187
$289$	−0.565477	−0.0332633
$290$	21.9297	1.28776
$291$	18.9563	1.11124
$292$	−0.899276	−0.0526261
$293$	5.32016	0.310807	0.155403	−	0.987851i	$-0.450332\pi$
$293$	5.32016	0.310807	0.155403	+	0.987851i	$0.450332\pi$
$294$	1.60159	0.0934068
$295$	9.80335	0.570773
$296$	−10.9092	−0.634087
$297$	2.53947	0.147355
$298$	−38.7267	−2.24338
$299$	0	0
$300$	−0.106641	−0.00615694
$301$	2.14282	0.123510
$302$	−14.3899	−0.828044
$303$	4.02671	0.231328
$304$	38.1721	2.18932
$305$	26.1648	1.49819
$306$	6.49278	0.371167
$307$	3.65245	0.208457	0.104228	−	0.994553i	$-0.466763\pi$
$307$	3.65245	0.208457	0.104228	+	0.994553i	$0.466763\pi$
$308$	1.43505	0.0817695
$309$	11.3431	0.645287
$310$	1.24287	0.0705903
$311$	4.97775	0.282262	0.141131	−	0.989991i	$-0.454926\pi$
$311$	4.97775	0.282262	0.141131	+	0.989991i	$0.454926\pi$
$312$	0	0
$313$	−30.8020	−1.74103	−0.870516	−	0.492140i	$-0.836215\pi$
$313$	−30.8020	−1.74103	−0.870516	+	0.492140i	$0.836215\pi$
$314$	4.34371	0.245130
$315$	2.27787	0.128344
$316$	−5.32367	−0.299480
$317$	22.5252	1.26514	0.632570	−	0.774503i	$-0.282000\pi$
$317$	22.5252	1.26514	0.632570	+	0.774503i	$0.282000\pi$
$318$	5.29200	0.296761
$319$	−15.2649	−0.854670
$320$	−10.5755	−0.591190
$321$	15.8563	0.885013
$322$	0.733576	0.0408806
$323$	32.1664	1.78979
$324$	0.565099	0.0313944
$325$	0	0
$326$	−27.7976	−1.53957
$327$	13.1406	0.726676
$328$	−20.4080	−1.12684
$329$	−7.16883	−0.395230
$330$	9.26455	0.509997
$331$	−4.73222	−0.260106	−0.130053	−	0.991507i	$-0.541515\pi$
$331$	−4.73222	−0.260106	−0.130053	+	0.991507i	$0.541515\pi$
$332$	−1.06093	−0.0582262
$333$	−4.74702	−0.260135
$334$	20.3525	1.11364
$335$	23.9128	1.30650
$336$	−4.81086	−0.262454
$337$	−27.2574	−1.48480	−0.742402	−	0.669955i	$-0.766313\pi$
$337$	−27.2574	−1.48480	−0.742402	+	0.669955i	$0.766313\pi$
$338$	0	0
$339$	−0.392747	−0.0213311
$340$	5.21834	0.283004
$341$	−0.865140	−0.0468499
$342$	12.7080	0.687168
$343$	−1.00000	−0.0539949
$344$	−4.92447	−0.265510
$345$	1.04333	0.0561712
$346$	−2.16924	−0.116619
$347$	−34.5372	−1.85406	−0.927028	−	0.374993i	$-0.877645\pi$
$347$	−34.5372	−1.85406	−0.927028	+	0.374993i	$0.877645\pi$
$348$	−3.39684	−0.182090
$349$	25.5552	1.36794	0.683969	−	0.729511i	$-0.260252\pi$
$349$	25.5552	1.36794	0.683969	+	0.729511i	$0.260252\pi$
$350$	0.302241	0.0161554
$351$	0	0
$352$	−7.89465	−0.420787
$353$	26.8466	1.42890	0.714450	−	0.699686i	$-0.246677\pi$
$353$	26.8466	1.42890	0.714450	+	0.699686i	$0.246677\pi$
$354$	−6.89282	−0.366349
$355$	9.68759	0.514164
$356$	−10.1680	−0.538906
$357$	−4.05395	−0.214558
$358$	−33.7441	−1.78343
$359$	23.6724	1.24938	0.624690	−	0.780873i	$-0.285225\pi$
$359$	23.6724	1.24938	0.624690	+	0.780873i	$0.285225\pi$
$360$	−5.23485	−0.275901
$361$	43.9575	2.31355
$362$	0.432077	0.0227095
$363$	4.55111	0.238871
$364$	0	0
$365$	3.62492	0.189737
$366$	−18.3967	−0.961610
$367$	11.5392	0.602341	0.301171	−	0.953570i	$-0.402623\pi$
$367$	11.5392	0.602341	0.301171	+	0.953570i	$0.402623\pi$
$368$	−2.20352	−0.114866
$369$	−8.88028	−0.462289
$370$	−17.3182	−0.900330
$371$	−3.30421	−0.171546
$372$	−0.192517	−0.00998152
$373$	1.52172	0.0787916	0.0393958	−	0.999224i	$-0.487457\pi$
$373$	1.52172	0.0787916	0.0393958	+	0.999224i	$0.487457\pi$
$374$	−16.4882	−0.852584
$375$	−10.9595	−0.565947
$376$	16.4749	0.849627
$377$	0	0
$378$	−1.60159	−0.0823770
$379$	34.4586	1.77002	0.885010	−	0.465571i	$-0.154151\pi$
$379$	34.4586	1.77002	0.885010	+	0.465571i	$0.154151\pi$
$380$	10.2136	0.523945
$381$	−15.9958	−0.819492
$382$	10.0625	0.514842
$383$	3.91678	0.200138	0.100069	−	0.994980i	$-0.468094\pi$
$383$	3.91678	0.200138	0.100069	+	0.994980i	$0.468094\pi$
$384$	13.6533	0.696742
$385$	−5.78459	−0.294810
$386$	30.9354	1.57457
$387$	−2.14282	−0.108926
$388$	−10.7122	−0.543828
$389$	−31.0836	−1.57600	−0.788002	−	0.615673i	$-0.788884\pi$
$389$	−31.0836	−1.57600	−0.788002	+	0.615673i	$0.788884\pi$
$390$	0	0
$391$	−1.85683	−0.0939039
$392$	2.29813	0.116073
$393$	−16.6090	−0.837813
$394$	−33.6414	−1.69483
$395$	21.4593	1.07974
$396$	−1.43505	−0.0721139
$397$	9.75019	0.489348	0.244674	−	0.969605i	$-0.421319\pi$
$397$	9.75019	0.489348	0.244674	+	0.969605i	$0.421319\pi$
$398$	−27.2770	−1.36727
$399$	−7.93457	−0.397226
$400$	−0.907870	−0.0453935
$401$	2.38904	0.119303	0.0596515	−	0.998219i	$-0.481001\pi$
$401$	2.38904	0.119303	0.0596515	+	0.998219i	$0.481001\pi$
$402$	−16.8133	−0.838570
$403$	0	0
$404$	−2.27549	−0.113210
$405$	−2.27787	−0.113188
$406$	9.62727	0.477793
$407$	12.0549	0.597539
$408$	9.31650	0.461235
$409$	−19.0527	−0.942094	−0.471047	−	0.882108i	$-0.656124\pi$
$409$	−19.0527	−0.942094	−0.471047	+	0.882108i	$0.656124\pi$
$410$	−32.3973	−1.59999
$411$	−1.57748	−0.0778113
$412$	−6.40997	−0.315797
$413$	4.30373	0.211773
$414$	−0.733576	−0.0360533
$415$	4.27654	0.209927
$416$	0	0
$417$	−12.0257	−0.588899
$418$	−32.2714	−1.57845
$419$	19.6916	0.961998	0.480999	−	0.876721i	$-0.340274\pi$
$419$	19.6916	0.961998	0.480999	+	0.876721i	$0.340274\pi$
$420$	−1.28722	−0.0628101
$421$	25.2278	1.22953	0.614765	−	0.788711i	$-0.289251\pi$
$421$	25.2278	1.22953	0.614765	+	0.788711i	$0.289251\pi$
$422$	16.0857	0.783040
$423$	7.16883	0.348560
$424$	7.59350	0.368773
$425$	−0.765032	−0.0371095
$426$	−6.81142	−0.330014
$427$	11.4865	0.555870
$428$	−8.96038	−0.433117
$429$	0	0
$430$	−7.81750	−0.376993
$431$	−7.87972	−0.379553	−0.189776	−	0.981827i	$-0.560776\pi$
$431$	−7.87972	−0.379553	−0.189776	+	0.981827i	$0.560776\pi$
$432$	4.81086	0.231463
$433$	−24.8346	−1.19348	−0.596738	−	0.802436i	$-0.703537\pi$
$433$	−24.8346	−1.19348	−0.596738	+	0.802436i	$0.703537\pi$
$434$	0.545627	0.0261909
$435$	13.6924	0.656502
$436$	−7.42573	−0.355628
$437$	−3.63427	−0.173851
$438$	−2.54871	−0.121782
$439$	−19.0971	−0.911457	−0.455728	−	0.890119i	$-0.650621\pi$
$439$	−19.0971	−0.911457	−0.455728	+	0.890119i	$0.650621\pi$
$440$	13.2937	0.633753
$441$	1.00000	0.0476190
$442$	0	0
$443$	39.1199	1.85864	0.929320	−	0.369275i	$-0.120394\pi$
$443$	39.1199	1.85864	0.929320	+	0.369275i	$0.120394\pi$
$444$	2.68253	0.127307
$445$	40.9867	1.94296
$446$	2.09310	0.0991112
$447$	−24.1801	−1.14368
$448$	−4.64271	−0.219348
$449$	−2.38383	−0.112500	−0.0562500	−	0.998417i	$-0.517914\pi$
$449$	−2.38383	−0.112500	−0.0562500	+	0.998417i	$0.517914\pi$
$450$	−0.302241	−0.0142478
$451$	22.5512	1.06189
$452$	0.221941	0.0104392
$453$	−8.98472	−0.422139
$454$	11.7208	0.550085
$455$	0	0
$456$	18.2347	0.853916
$457$	14.9656	0.700061	0.350031	−	0.936738i	$-0.386171\pi$
$457$	14.9656	0.700061	0.350031	+	0.936738i	$0.386171\pi$
$458$	−26.4714	−1.23693
$459$	4.05395	0.189222
$460$	−0.589586	−0.0274896
$461$	−33.0078	−1.53733	−0.768664	−	0.639653i	$-0.779078\pi$
$461$	−33.0078	−1.53733	−0.768664	+	0.639653i	$0.779078\pi$
$462$	4.06719	0.189223
$463$	−34.2144	−1.59008	−0.795039	−	0.606559i	$-0.792550\pi$
$463$	−34.2144	−1.59008	−0.795039	+	0.606559i	$0.792550\pi$
$464$	−28.9184	−1.34250
$465$	0.776021	0.0359871
$466$	−8.78393	−0.406908
$467$	−25.2750	−1.16959	−0.584795	−	0.811181i	$-0.698825\pi$
$467$	−25.2750	−1.16959	−0.584795	+	0.811181i	$0.698825\pi$
$468$	0	0
$469$	10.4979	0.484746
$470$	26.1535	1.20637
$471$	2.71212	0.124968
$472$	−9.89051	−0.455248
$473$	5.44162	0.250206
$474$	−15.0882	−0.693026
$475$	−1.49735	−0.0687033
$476$	2.29088	0.105002
$477$	3.30421	0.151289
$478$	28.5999	1.30813
$479$	37.4251	1.70999	0.854997	−	0.518633i	$-0.173559\pi$
$479$	37.4251	1.70999	0.854997	+	0.518633i	$0.173559\pi$
$480$	7.08142	0.323221
$481$	0	0
$482$	37.0098	1.68575
$483$	0.458029	0.0208411
$484$	−2.57183	−0.116901
$485$	43.1800	1.96070
$486$	1.60159	0.0726497
$487$	30.3596	1.37572	0.687862	−	0.725842i	$-0.258549\pi$
$487$	30.3596	1.37572	0.687862	+	0.725842i	$0.258549\pi$
$488$	−26.3974	−1.19495
$489$	−17.3562	−0.784875
$490$	3.64823	0.164810
$491$	−5.62758	−0.253969	−0.126984	−	0.991905i	$-0.540530\pi$
$491$	−5.62758	−0.253969	−0.126984	+	0.991905i	$0.540530\pi$
$492$	5.01823	0.226239
$493$	−24.3686	−1.09750
$494$	0	0
$495$	5.78459	0.259998
$496$	−1.63895	−0.0735912
$497$	4.25291	0.190769
$498$	−3.00687	−0.134741
$499$	−34.1534	−1.52892	−0.764459	−	0.644673i	$-0.776994\pi$
$499$	−34.1534	−1.52892	−0.764459	+	0.644673i	$0.776994\pi$
$500$	6.19321	0.276969
$501$	12.7077	0.567737
$502$	−18.8095	−0.839509
$503$	10.4426	0.465612	0.232806	−	0.972523i	$-0.425209\pi$
$503$	10.4426	0.465612	0.232806	+	0.972523i	$0.425209\pi$
$504$	−2.29813	−0.102367
$505$	9.17233	0.408163
$506$	1.86289	0.0828157
$507$	0	0
$508$	9.03923	0.401051
$509$	−18.2623	−0.809463	−0.404732	−	0.914436i	$-0.632635\pi$
$509$	−18.2623	−0.809463	−0.404732	+	0.914436i	$0.632635\pi$
$510$	14.7897	0.654901
$511$	1.59136	0.0703976
$512$	7.15601	0.316254
$513$	7.93457	0.350320
$514$	15.2762	0.673803
$515$	25.8382	1.13857
$516$	1.21091	0.0533071
$517$	−18.2050	−0.800655
$518$	−7.60279	−0.334047
$519$	−1.35443	−0.0594527
$520$	0	0
$521$	34.9086	1.52937	0.764687	−	0.644401i	$-0.222893\pi$
$521$	34.9086	1.52937	0.764687	+	0.644401i	$0.222893\pi$
$522$	−9.62727	−0.421374
$523$	−4.61292	−0.201709	−0.100854	−	0.994901i	$-0.532158\pi$
$523$	−4.61292	−0.201709	−0.100854	+	0.994901i	$0.532158\pi$
$524$	9.38572	0.410017
$525$	0.188713	0.00823609
$526$	8.43437	0.367756
$527$	−1.38109	−0.0601613
$528$	−12.2170	−0.531677
$529$	−22.7902	−0.990879
$530$	12.0545	0.523614
$531$	−4.30373	−0.186766
$532$	4.48382	0.194398
$533$	0	0
$534$	−28.8181	−1.24708
$535$	36.1187	1.56155
$536$	−24.1254	−1.04206
$537$	−21.0691	−0.909199
$538$	−0.965190	−0.0416123
$539$	−2.53947	−0.109383
$540$	1.28722	0.0553933
$541$	31.6729	1.36172	0.680862	−	0.732412i	$-0.261605\pi$
$541$	31.6729	1.36172	0.680862	+	0.732412i	$0.261605\pi$
$542$	−9.12243	−0.391842
$543$	0.269780	0.0115774
$544$	−12.6029	−0.540343
$545$	29.9326	1.28217
$546$	0	0
$547$	21.6899	0.927393	0.463697	−	0.885994i	$-0.346523\pi$
$547$	21.6899	0.927393	0.463697	+	0.885994i	$0.346523\pi$
$548$	0.891431	0.0380800
$549$	−11.4865	−0.490231
$550$	0.767530	0.0327276
$551$	−47.6952	−2.03188
$552$	−1.05261	−0.0448020
$553$	9.42077	0.400612
$554$	12.8238	0.544832
$555$	−10.8131	−0.458991
$556$	6.79568	0.288201
$557$	32.4871	1.37652	0.688262	−	0.725462i	$-0.258374\pi$
$557$	32.4871	1.37652	0.688262	+	0.725462i	$0.258374\pi$
$558$	−0.545627	−0.0230982
$559$	0	0
$560$	−10.9585	−0.463083
$561$	−10.2949	−0.434650
$562$	−4.83383	−0.203903
$563$	−13.0529	−0.550115	−0.275058	−	0.961428i	$-0.588697\pi$
$563$	−13.0529	−0.550115	−0.275058	+	0.961428i	$0.588697\pi$
$564$	−4.05110	−0.170582
$565$	−0.894628	−0.0376373
$566$	−14.2814	−0.600294
$567$	−1.00000	−0.0419961
$568$	−9.77372	−0.410096
$569$	−15.3184	−0.642182	−0.321091	−	0.947048i	$-0.604049\pi$
$569$	−15.3184	−0.642182	−0.321091	+	0.947048i	$0.604049\pi$
$570$	28.9471	1.21246
$571$	−44.0404	−1.84303	−0.921517	−	0.388337i	$-0.873050\pi$
$571$	−44.0404	−1.84303	−0.921517	+	0.388337i	$0.873050\pi$
$572$	0	0
$573$	6.28281	0.262468
$574$	−14.2226	−0.593639
$575$	0.0864359	0.00360463
$576$	4.64271	0.193446
$577$	−13.7961	−0.574338	−0.287169	−	0.957880i	$-0.592714\pi$
$577$	−13.7961	−0.574338	−0.287169	+	0.957880i	$0.592714\pi$
$578$	0.905663	0.0376706
$579$	19.3154	0.802721
$580$	−7.73758	−0.321286
$581$	1.87743	0.0778888
$582$	−30.3602	−1.25847
$583$	−8.39093	−0.347517
$584$	−3.65715	−0.151334
$585$	0	0
$586$	−8.52072	−0.351988
$587$	−29.7424	−1.22760	−0.613801	−	0.789461i	$-0.710360\pi$
$587$	−29.7424	−1.22760	−0.613801	+	0.789461i	$0.710360\pi$
$588$	−0.565099	−0.0233043
$589$	−2.70313	−0.111381
$590$	−15.7010	−0.646399
$591$	−21.0050	−0.864030
$592$	22.8372	0.938605
$593$	−26.2248	−1.07692	−0.538461	−	0.842650i	$-0.680994\pi$
$593$	−26.2248	−1.07692	−0.538461	+	0.842650i	$0.680994\pi$
$594$	−4.06719	−0.166879
$595$	−9.23439	−0.378573
$596$	13.6642	0.559706
$597$	−17.0312	−0.697039
$598$	0	0
$599$	−7.80961	−0.319092	−0.159546	−	0.987191i	$-0.551003\pi$
$599$	−7.80961	−0.319092	−0.159546	+	0.987191i	$0.551003\pi$
$600$	−0.433686	−0.0177051
$601$	13.4938	0.550422	0.275211	−	0.961384i	$-0.411252\pi$
$601$	13.4938	0.550422	0.275211	+	0.961384i	$0.411252\pi$
$602$	−3.43193	−0.139875
$603$	−10.4979	−0.427506
$604$	5.07726	0.206591
$605$	10.3669	0.421473
$606$	−6.44914	−0.261978
$607$	−18.5539	−0.753078	−0.376539	−	0.926401i	$-0.622886\pi$
$607$	−18.5539	−0.753078	−0.376539	+	0.926401i	$0.622886\pi$
$608$	−24.6669	−1.00037
$609$	6.01106	0.243580
$610$	−41.9053	−1.69670
$611$	0	0
$612$	−2.29088	−0.0926035
$613$	12.9374	0.522536	0.261268	−	0.965266i	$-0.415859\pi$
$613$	12.9374	0.522536	0.261268	+	0.965266i	$0.415859\pi$
$614$	−5.84974	−0.236076
$615$	−20.2282	−0.815678
$616$	5.83602	0.235140
$617$	33.2636	1.33914	0.669571	−	0.742748i	$-0.266478\pi$
$617$	33.2636	1.33914	0.669571	+	0.742748i	$0.266478\pi$
$618$	−18.1670	−0.730785
$619$	18.8470	0.757523	0.378762	−	0.925494i	$-0.376350\pi$
$619$	18.8470	0.757523	0.378762	+	0.925494i	$0.376350\pi$
$620$	−0.438529	−0.0176117
$621$	−0.458029	−0.0183801
$622$	−7.97233	−0.319661
$623$	17.9934	0.720890
$624$	0	0
$625$	−25.9080	−1.03632
$626$	49.3323	1.97171
$627$	−20.1496	−0.804697
$628$	−1.53262	−0.0611581
$629$	19.2442	0.767315
$630$	−3.64823	−0.145349
$631$	25.5434	1.01687	0.508433	−	0.861101i	$-0.330225\pi$
$631$	25.5434	1.01687	0.508433	+	0.861101i	$0.330225\pi$
$632$	−21.6501	−0.861196
$633$	10.0436	0.399196
$634$	−36.0762	−1.43277
$635$	−36.4365	−1.44594
$636$	−1.86721	−0.0740395
$637$	0	0
$638$	24.4481	0.967911
$639$	−4.25291	−0.168242
$640$	31.1005	1.22936
$641$	14.6984	0.580552	0.290276	−	0.956943i	$-0.406253\pi$
$641$	14.6984	0.580552	0.290276	+	0.956943i	$0.406253\pi$
$642$	−25.3954	−1.00227
$643$	8.13670	0.320880	0.160440	−	0.987046i	$-0.448709\pi$
$643$	8.13670	0.320880	0.160440	+	0.987046i	$0.448709\pi$
$644$	−0.258832	−0.0101994
$645$	−4.88108	−0.192192
$646$	−51.5174	−2.02693
$647$	−17.9914	−0.707315	−0.353658	−	0.935375i	$-0.615062\pi$
$647$	−17.9914	−0.707315	−0.353658	+	0.935375i	$0.615062\pi$
$648$	2.29813	0.0902790
$649$	10.9292	0.429008
$650$	0	0
$651$	0.340678	0.0133522
$652$	9.80798	0.384110
$653$	−9.74392	−0.381309	−0.190654	−	0.981657i	$-0.561061\pi$
$653$	−9.74392	−0.381309	−0.190654	+	0.981657i	$0.561061\pi$
$654$	−21.0459	−0.822958
$655$	−37.8332	−1.47827
$656$	42.7218	1.66801
$657$	−1.59136	−0.0620849
$658$	11.4815	0.447597
$659$	39.8534	1.55247	0.776234	−	0.630445i	$-0.217128\pi$
$659$	39.8534	1.55247	0.776234	+	0.630445i	$0.217128\pi$
$660$	−3.26886	−0.127240
$661$	4.70505	0.183005	0.0915025	−	0.995805i	$-0.470833\pi$
$661$	4.70505	0.183005	0.0915025	+	0.995805i	$0.470833\pi$
$662$	7.57908	0.294570
$663$	0	0
$664$	−4.31457	−0.167438
$665$	−18.0740	−0.700878
$666$	7.60279	0.294602
$667$	2.75324	0.106606
$668$	−7.18109	−0.277845
$669$	1.30689	0.0505272
$670$	−38.2985	−1.47960
$671$	29.1696	1.12608
$672$	3.10879	0.119924
$673$	−51.1974	−1.97351	−0.986757	−	0.162205i	$-0.948139\pi$
$673$	−51.1974	−1.97351	−0.986757	+	0.162205i	$0.948139\pi$
$674$	43.6552	1.68154
$675$	−0.188713	−0.00726355
$676$	0	0
$677$	−6.98340	−0.268394	−0.134197	−	0.990955i	$-0.542845\pi$
$677$	−6.98340	−0.268394	−0.134197	+	0.990955i	$0.542845\pi$
$678$	0.629020	0.0241574
$679$	18.9563	0.727475
$680$	21.2218	0.813819
$681$	7.31823	0.280435
$682$	1.38560	0.0530574
$683$	−14.7082	−0.562793	−0.281396	−	0.959592i	$-0.590798\pi$
$683$	−14.7082	−0.562793	−0.281396	+	0.959592i	$0.590798\pi$
$684$	−4.48382	−0.171443
$685$	−3.59330	−0.137293
$686$	1.60159	0.0611491
$687$	−16.5282	−0.630590
$688$	10.3088	0.393020
$689$	0	0
$690$	−1.67099	−0.0636137
$691$	−45.3789	−1.72629	−0.863147	−	0.504953i	$-0.831510\pi$
$691$	−45.3789	−1.72629	−0.863147	+	0.504953i	$0.831510\pi$
$692$	0.765385	0.0290956
$693$	2.53947	0.0964663
$694$	55.3146	2.09971
$695$	−27.3929	−1.03907
$696$	−13.8142	−0.523625
$697$	36.0002	1.36361
$698$	−40.9290	−1.54918
$699$	−5.48450	−0.207443
$700$	−0.106641	−0.00403066
$701$	−16.8794	−0.637525	−0.318763	−	0.947835i	$-0.603267\pi$
$701$	−16.8794	−0.637525	−0.318763	+	0.947835i	$0.603267\pi$
$702$	0	0
$703$	37.6656	1.42058
$704$	−11.7900	−0.444353
$705$	16.3297	0.615012
$706$	−42.9973	−1.61823
$707$	4.02671	0.151440
$708$	2.43203	0.0914014
$709$	41.2478	1.54909	0.774547	−	0.632516i	$-0.217978\pi$
$709$	41.2478	1.54909	0.774547	+	0.632516i	$0.217978\pi$
$710$	−15.5156	−0.582289
$711$	−9.42077	−0.353307
$712$	−41.3511	−1.54970
$713$	0.156040	0.00584376
$714$	6.49278	0.242986
$715$	0	0
$716$	11.9061	0.444953
$717$	17.8572	0.666889
$718$	−37.9135	−1.41492
$719$	14.8928	0.555409	0.277704	−	0.960667i	$-0.410426\pi$
$719$	14.8928	0.555409	0.277704	+	0.960667i	$0.410426\pi$
$720$	10.9585	0.408401
$721$	11.3431	0.422439
$722$	−70.4020	−2.62009
$723$	23.1081	0.859400
$724$	−0.152452	−0.00566584
$725$	1.13436	0.0421292
$726$	−7.28903	−0.270521
$727$	31.4330	1.16578	0.582892	−	0.812550i	$-0.301921\pi$
$727$	31.4330	1.16578	0.582892	+	0.812550i	$0.301921\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−5.80564	−0.214876
$731$	8.68689	0.321296
$732$	6.49100	0.239914
$733$	5.22860	0.193123	0.0965613	−	0.995327i	$-0.469216\pi$
$733$	5.22860	0.193123	0.0965613	+	0.995327i	$0.469216\pi$
$734$	−18.4811	−0.682150
$735$	2.27787	0.0840207
$736$	1.42391	0.0524862
$737$	26.6589	0.981995
$738$	14.2226	0.523541
$739$	23.0653	0.848469	0.424235	−	0.905552i	$-0.360543\pi$
$739$	23.0653	0.848469	0.424235	+	0.905552i	$0.360543\pi$
$740$	6.11047	0.224626
$741$	0	0
$742$	5.29200	0.194275
$743$	0.991530	0.0363757	0.0181878	−	0.999835i	$-0.494210\pi$
$743$	0.991530	0.0363757	0.0181878	+	0.999835i	$0.494210\pi$
$744$	−0.782921	−0.0287033
$745$	−55.0793	−2.01795
$746$	−2.43717	−0.0892312
$747$	−1.87743	−0.0686915
$748$	5.81762	0.212713
$749$	15.8563	0.579377
$750$	17.5527	0.640933
$751$	29.7806	1.08671	0.543356	−	0.839503i	$-0.317154\pi$
$751$	29.7806	1.08671	0.543356	+	0.839503i	$0.317154\pi$
$752$	−34.4882	−1.25766
$753$	−11.7442	−0.427984
$754$	0	0
$755$	−20.4661	−0.744837
$756$	0.565099	0.0205524
$757$	−9.12624	−0.331699	−0.165849	−	0.986151i	$-0.553037\pi$
$757$	−9.12624	−0.331699	−0.165849	+	0.986151i	$0.553037\pi$
$758$	−55.1887	−2.00454
$759$	1.16315	0.0422197
$760$	41.5363	1.50668
$761$	14.2507	0.516586	0.258293	−	0.966067i	$-0.416840\pi$
$761$	14.2507	0.516586	0.258293	+	0.966067i	$0.416840\pi$
$762$	25.6188	0.928072
$763$	13.1406	0.475721
$764$	−3.55041	−0.128449
$765$	9.23439	0.333870
$766$	−6.27309	−0.226656
$767$	0	0
$768$	−12.5816	−0.454000
$769$	43.0440	1.55221	0.776103	−	0.630606i	$-0.217193\pi$
$769$	43.0440	1.55221	0.776103	+	0.630606i	$0.217193\pi$
$770$	9.26455	0.333871
$771$	9.53811	0.343507
$772$	−10.9151	−0.392844
$773$	30.5971	1.10050	0.550251	−	0.834999i	$-0.314532\pi$
$773$	30.5971	1.10050	0.550251	+	0.834999i	$0.314532\pi$
$774$	3.43193	0.123358
$775$	0.0642902	0.00230937
$776$	−43.5639	−1.56385
$777$	−4.74702	−0.170298
$778$	49.7833	1.78482
$779$	70.4612	2.52453
$780$	0	0
$781$	10.8001	0.386458
$782$	2.97388	0.106346
$783$	−6.01106	−0.214818
$784$	−4.81086	−0.171816
$785$	6.17787	0.220498
$786$	26.6008	0.948820
$787$	23.2516	0.828830	0.414415	−	0.910088i	$-0.363986\pi$
$787$	23.2516	0.828830	0.414415	+	0.910088i	$0.363986\pi$
$788$	11.8699	0.422848
$789$	5.26624	0.187483
$790$	−34.3691	−1.22280
$791$	−0.392747	−0.0139645
$792$	−5.83602	−0.207374
$793$	0	0
$794$	−15.6158	−0.554185
$795$	7.52658	0.266940
$796$	9.62428	0.341124
$797$	−48.7696	−1.72751	−0.863754	−	0.503914i	$-0.831893\pi$
$797$	−48.7696	−1.72751	−0.863754	+	0.503914i	$0.831893\pi$
$798$	12.7080	0.449857
$799$	−29.0621	−1.02814
$800$	0.586667	0.0207418
$801$	−17.9934	−0.635766
$802$	−3.82627	−0.135110
$803$	4.04120	0.142611
$804$	5.93232	0.209217
$805$	1.04333	0.0367727
$806$	0	0
$807$	−0.602644	−0.0212141
$808$	−9.25388	−0.325550
$809$	−4.26862	−0.150077	−0.0750383	−	0.997181i	$-0.523908\pi$
$809$	−4.26862	−0.150077	−0.0750383	+	0.997181i	$0.523908\pi$
$810$	3.64823	0.128186
$811$	−16.1267	−0.566287	−0.283143	−	0.959078i	$-0.591377\pi$
$811$	−16.1267	−0.566287	−0.283143	+	0.959078i	$0.591377\pi$
$812$	−3.39684	−0.119206
$813$	−5.69585	−0.199762
$814$	−19.3070	−0.676711
$815$	−39.5353	−1.38486
$816$	−19.5030	−0.682741
$817$	17.0024	0.594838
$818$	30.5146	1.06692
$819$	0	0
$820$	11.4309	0.399185
$821$	−42.1403	−1.47071	−0.735354	−	0.677684i	$-0.762984\pi$
$821$	−42.1403	−1.47071	−0.735354	+	0.677684i	$0.762984\pi$
$822$	2.52648	0.0881210
$823$	34.5376	1.20391	0.601953	−	0.798531i	$-0.294389\pi$
$823$	34.5376	1.20391	0.601953	+	0.798531i	$0.294389\pi$
$824$	−26.0679	−0.908118
$825$	0.479229	0.0166846
$826$	−6.89282	−0.239832
$827$	−43.7311	−1.52068	−0.760340	−	0.649525i	$-0.774968\pi$
$827$	−43.7311	−1.52068	−0.760340	+	0.649525i	$0.774968\pi$
$828$	0.258832	0.00899503
$829$	−0.927355	−0.0322084	−0.0161042	−	0.999870i	$-0.505126\pi$
$829$	−0.927355	−0.0322084	−0.0161042	+	0.999870i	$0.505126\pi$
$830$	−6.84928	−0.237742
$831$	8.00692	0.277757
$832$	0	0
$833$	−4.05395	−0.140461
$834$	19.2602	0.666926
$835$	28.9465	1.00173
$836$	11.3865	0.393811
$837$	−0.340678	−0.0117755
$838$	−31.5379	−1.08946
$839$	−24.1448	−0.833571	−0.416785	−	0.909005i	$-0.636843\pi$
$839$	−24.1448	−0.833571	−0.416785	+	0.909005i	$0.636843\pi$
$840$	−5.23485	−0.180619
$841$	7.13286	0.245961
$842$	−40.4047	−1.39244
$843$	−3.01814	−0.103950
$844$	−5.67561	−0.195363
$845$	0	0
$846$	−11.4815	−0.394744
$847$	4.55111	0.156378
$848$	−15.8961	−0.545874
$849$	−8.91703	−0.306032
$850$	1.22527	0.0420264
$851$	−2.17427	−0.0745331
$852$	2.40331	0.0823361
$853$	−54.7857	−1.87583	−0.937914	−	0.346868i	$-0.887245\pi$
$853$	−54.7857	−1.87583	−0.937914	+	0.346868i	$0.887245\pi$
$854$	−18.3967	−0.629521
$855$	18.0740	0.618117
$856$	−36.4398	−1.24549
$857$	2.79688	0.0955396	0.0477698	−	0.998858i	$-0.484789\pi$
$857$	2.79688	0.0955396	0.0477698	+	0.998858i	$0.484789\pi$
$858$	0	0
$859$	−37.7430	−1.28778	−0.643888	−	0.765120i	$-0.722680\pi$
$859$	−37.7430	−1.28778	−0.643888	+	0.765120i	$0.722680\pi$
$860$	2.75829	0.0940569
$861$	−8.88028	−0.302639
$862$	12.6201	0.429843
$863$	−25.0401	−0.852376	−0.426188	−	0.904635i	$-0.640144\pi$
$863$	−25.0401	−0.852376	−0.426188	+	0.904635i	$0.640144\pi$
$864$	−3.10879	−0.105763
$865$	−3.08521	−0.104900
$866$	39.7749	1.35161
$867$	0.565477	0.0192046
$868$	−0.192517	−0.00653444
$869$	23.9237	0.811557
$870$	−21.9297	−0.743487
$871$	0	0
$872$	−30.1987	−1.02266
$873$	−18.9563	−0.641573
$874$	5.82062	0.196885
$875$	−10.9595	−0.370499
$876$	0.899276	0.0303837
$877$	32.5220	1.09819	0.549095	−	0.835760i	$-0.314973\pi$
$877$	32.5220	1.09819	0.549095	+	0.835760i	$0.314973\pi$
$878$	30.5858	1.03222
$879$	−5.32016	−0.179444
$880$	−27.8288	−0.938110
$881$	27.6515	0.931604	0.465802	−	0.884889i	$-0.345766\pi$
$881$	27.6515	0.931604	0.465802	+	0.884889i	$0.345766\pi$
$882$	−1.60159	−0.0539284
$883$	18.0601	0.607771	0.303885	−	0.952709i	$-0.401716\pi$
$883$	18.0601	0.607771	0.303885	+	0.952709i	$0.401716\pi$
$884$	0	0
$885$	−9.80335	−0.329536
$886$	−62.6541	−2.10490
$887$	44.6426	1.49895	0.749476	−	0.662032i	$-0.230306\pi$
$887$	44.6426	1.49895	0.749476	+	0.662032i	$0.230306\pi$
$888$	10.9092	0.366090
$889$	−15.9958	−0.536483
$890$	−65.6440	−2.20039
$891$	−2.53947	−0.0850753
$892$	−0.738520	−0.0247275
$893$	−56.8816	−1.90347
$894$	38.7267	1.29521
$895$	−47.9928	−1.60422
$896$	13.6533	0.456125
$897$	0	0
$898$	3.81793	0.127406
$899$	2.04783	0.0682991
$900$	0.106641	0.00355471
$901$	−13.3951	−0.446256
$902$	−36.1178	−1.20259
$903$	−2.14282	−0.0713086
$904$	0.902582	0.0300194
$905$	0.614524	0.0204275
$906$	14.3899	0.478071
$907$	−26.3976	−0.876517	−0.438259	−	0.898849i	$-0.644405\pi$
$907$	−26.3976	−0.876517	−0.438259	+	0.898849i	$0.644405\pi$
$908$	−4.13552	−0.137242
$909$	−4.02671	−0.133557
$910$	0	0
$911$	4.45669	0.147657	0.0738283	−	0.997271i	$-0.476478\pi$
$911$	4.45669	0.147657	0.0738283	+	0.997271i	$0.476478\pi$
$912$	−38.1721	−1.26401
$913$	4.76766	0.157787
$914$	−23.9688	−0.792817
$915$	−26.1648	−0.864981
$916$	9.34006	0.308604
$917$	−16.6090	−0.548477
$918$	−6.49278	−0.214294
$919$	−6.71089	−0.221372	−0.110686	−	0.993855i	$-0.535305\pi$
$919$	−6.71089	−0.221372	−0.110686	+	0.993855i	$0.535305\pi$
$920$	−2.39771	−0.0790502
$921$	−3.65245	−0.120352
$922$	52.8651	1.74102
$923$	0	0
$924$	−1.43505	−0.0472097
$925$	−0.895822	−0.0294544
$926$	54.7975	1.80076
$927$	−11.3431	−0.372556
$928$	18.6871	0.613434
$929$	28.2471	0.926759	0.463379	−	0.886160i	$-0.346637\pi$
$929$	28.2471	0.926759	0.463379	+	0.886160i	$0.346637\pi$
$930$	−1.24287	−0.0407553
$931$	−7.93457	−0.260045
$932$	3.09928	0.101520
$933$	−4.97775	−0.162964
$934$	40.4803	1.32456
$935$	−23.4504	−0.766911
$936$	0	0
$937$	−33.0728	−1.08044	−0.540220	−	0.841524i	$-0.681659\pi$
$937$	−33.0728	−1.08044	−0.540220	+	0.841524i	$0.681659\pi$
$938$	−16.8133	−0.548973
$939$	30.8020	1.00519
$940$	−9.22789	−0.300981
$941$	−40.0527	−1.30568	−0.652840	−	0.757495i	$-0.726423\pi$
$941$	−40.0527	−1.30568	−0.652840	+	0.757495i	$0.726423\pi$
$942$	−4.34371	−0.141526
$943$	−4.06743	−0.132454
$944$	20.7046	0.673879
$945$	−2.27787	−0.0740993
$946$	−8.71526	−0.283358
$947$	−52.8629	−1.71781	−0.858907	−	0.512132i	$-0.828856\pi$
$947$	−52.8629	−1.71781	−0.858907	+	0.512132i	$0.828856\pi$
$948$	5.32367	0.172905
$949$	0	0
$950$	2.39815	0.0778063
$951$	−22.5252	−0.730429
$952$	9.31650	0.301949
$953$	−47.6352	−1.54306	−0.771528	−	0.636196i	$-0.780507\pi$
$953$	−47.6352	−1.54306	−0.771528	+	0.636196i	$0.780507\pi$
$954$	−5.29200	−0.171335
$955$	14.3114	0.463108
$956$	−10.0911	−0.326369
$957$	15.2649	0.493444
$958$	−59.9397	−1.93656
$959$	−1.57748	−0.0509394
$960$	10.5755	0.341324
$961$	−30.8839	−0.996256
$962$	0	0
$963$	−15.8563	−0.510963
$964$	−13.0584	−0.420582
$965$	43.9981	1.41635
$966$	−0.733576	−0.0236024
$967$	34.0050	1.09353	0.546764	−	0.837287i	$-0.315860\pi$
$967$	34.0050	1.09353	0.546764	+	0.837287i	$0.315860\pi$
$968$	−10.4590	−0.336166
$969$	−32.1664	−1.03333
$970$	−69.1568	−2.22049
$971$	−1.28177	−0.0411338	−0.0205669	−	0.999788i	$-0.506547\pi$
$971$	−1.28177	−0.0411338	−0.0205669	+	0.999788i	$0.506547\pi$
$972$	−0.565099	−0.0181256
$973$	−12.0257	−0.385525
$974$	−48.6237	−1.55800
$975$	0	0
$976$	55.2599	1.76883
$977$	−53.5945	−1.71464	−0.857320	−	0.514783i	$-0.827872\pi$
$977$	−53.5945	−1.71464	−0.857320	+	0.514783i	$0.827872\pi$
$978$	27.7976	0.888869
$979$	45.6936	1.46037
$980$	−1.28722	−0.0411189
$981$	−13.1406	−0.419547
$982$	9.01309	0.287619
$983$	−12.2091	−0.389410	−0.194705	−	0.980862i	$-0.562375\pi$
$983$	−12.2091	−0.389410	−0.194705	+	0.980862i	$0.562375\pi$
$984$	20.4080	0.650583
$985$	−47.8468	−1.52452
$986$	39.0285	1.24292
$987$	7.16883	0.228186
$988$	0	0
$989$	−0.981475	−0.0312091
$990$	−9.26455	−0.294447
$991$	−7.83719	−0.248957	−0.124478	−	0.992222i	$-0.539726\pi$
$991$	−7.83719	−0.248957	−0.124478	+	0.992222i	$0.539726\pi$
$992$	1.05909	0.0336263
$993$	4.73222	0.150172
$994$	−6.81142	−0.216045
$995$	−38.7948	−1.22988
$996$	1.06093	0.0336169
$997$	57.3019	1.81477	0.907385	−	0.420302i	$-0.138076\pi$
$997$	57.3019	1.81477	0.907385	+	0.420302i	$0.138076\pi$
$998$	54.6999	1.73149
$999$	4.74702	0.150189

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bf.1.2	yes	9
13.12	even	2		3549.2.a.be.1.8	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3549.2.a.be.1.8	✓	9	13.12	even	2
3549.2.a.bf.1.2	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)

\(f(q)\)	\(=\)	\(q-1.60159 q^{2} -1.00000 q^{3} +0.565099 q^{4} -2.27787 q^{5} +1.60159 q^{6} -1.00000 q^{7} +2.29813 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.60159 q^{2} -1.00000 q^{3} +0.565099 q^{4} -2.27787 q^{5} +1.60159 q^{6} -1.00000 q^{7} +2.29813 q^{8} +1.00000 q^{9} +3.64823 q^{10} -2.53947 q^{11} -0.565099 q^{12} +1.60159 q^{14} +2.27787 q^{15} -4.81086 q^{16} -4.05395 q^{17} -1.60159 q^{18} -7.93457 q^{19} -1.28722 q^{20} +1.00000 q^{21} +4.06719 q^{22} +0.458029 q^{23} -2.29813 q^{24} +0.188713 q^{25} -1.00000 q^{27} -0.565099 q^{28} +6.01106 q^{29} -3.64823 q^{30} +0.340678 q^{31} +3.10879 q^{32} +2.53947 q^{33} +6.49278 q^{34} +2.27787 q^{35} +0.565099 q^{36} -4.74702 q^{37} +12.7080 q^{38} -5.23485 q^{40} -8.88028 q^{41} -1.60159 q^{42} -2.14282 q^{43} -1.43505 q^{44} -2.27787 q^{45} -0.733576 q^{46} +7.16883 q^{47} +4.81086 q^{48} +1.00000 q^{49} -0.302241 q^{50} +4.05395 q^{51} +3.30421 q^{53} +1.60159 q^{54} +5.78459 q^{55} -2.29813 q^{56} +7.93457 q^{57} -9.62727 q^{58} -4.30373 q^{59} +1.28722 q^{60} -11.4865 q^{61} -0.545627 q^{62} -1.00000 q^{63} +4.64271 q^{64} -4.06719 q^{66} -10.4979 q^{67} -2.29088 q^{68} -0.458029 q^{69} -3.64823 q^{70} -4.25291 q^{71} +2.29813 q^{72} -1.59136 q^{73} +7.60279 q^{74} -0.188713 q^{75} -4.48382 q^{76} +2.53947 q^{77} -9.42077 q^{79} +10.9585 q^{80} +1.00000 q^{81} +14.2226 q^{82} -1.87743 q^{83} +0.565099 q^{84} +9.23439 q^{85} +3.43193 q^{86} -6.01106 q^{87} -5.83602 q^{88} -17.9934 q^{89} +3.64823 q^{90} +0.258832 q^{92} -0.340678 q^{93} -11.4815 q^{94} +18.0740 q^{95} -3.10879 q^{96} -18.9563 q^{97} -1.60159 q^{98} -2.53947 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + q^{2} - 9 q^{3} + 5 q^{4} - 9 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 9 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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