LMFDB - Embedded newform 3549.2.a.bg.1.7

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:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 2 x^{14} - 27 x^{13} + 51 x^{12} + 290 x^{11} - 510 x^{10} - 1575 x^{9} + 2522 x^{8} + \cdots + 281 $ x^15 - 2x^14 - 27x^13 + 51x^12 + 290x^11 - 510x^10 - 1575x^9 + 2522x^8 + 4553x^7 - 6393x^6 - 6785x^5 + 7806x^4 + 4632x^3 - 3811x^2 - 1041x + 281
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			1.7
Root			$1.02667$ 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)

$f(q)$	$=$	$q-1.02667 q^{2} +1.00000 q^{3} -0.945953 q^{4} +3.27646 q^{5} -1.02667 q^{6} +1.00000 q^{7} +3.02452 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.02667 q^{2} +1.00000 q^{3} -0.945953 q^{4} +3.27646 q^{5} -1.02667 q^{6} +1.00000 q^{7} +3.02452 q^{8} +1.00000 q^{9} -3.36384 q^{10} +3.64615 q^{11} -0.945953 q^{12} -1.02667 q^{14} +3.27646 q^{15} -1.21327 q^{16} -6.88794 q^{17} -1.02667 q^{18} +6.29215 q^{19} -3.09937 q^{20} +1.00000 q^{21} -3.74338 q^{22} +7.44525 q^{23} +3.02452 q^{24} +5.73518 q^{25} +1.00000 q^{27} -0.945953 q^{28} +9.42061 q^{29} -3.36384 q^{30} -10.7607 q^{31} -4.80341 q^{32} +3.64615 q^{33} +7.07162 q^{34} +3.27646 q^{35} -0.945953 q^{36} -0.298388 q^{37} -6.45995 q^{38} +9.90970 q^{40} +3.91963 q^{41} -1.02667 q^{42} -5.28378 q^{43} -3.44908 q^{44} +3.27646 q^{45} -7.64380 q^{46} +1.78548 q^{47} -1.21327 q^{48} +1.00000 q^{49} -5.88813 q^{50} -6.88794 q^{51} +4.92587 q^{53} -1.02667 q^{54} +11.9464 q^{55} +3.02452 q^{56} +6.29215 q^{57} -9.67184 q^{58} -5.56609 q^{59} -3.09937 q^{60} +4.34575 q^{61} +11.0477 q^{62} +1.00000 q^{63} +7.35804 q^{64} -3.74338 q^{66} -12.7392 q^{67} +6.51566 q^{68} +7.44525 q^{69} -3.36384 q^{70} +5.67644 q^{71} +3.02452 q^{72} +6.72651 q^{73} +0.306346 q^{74} +5.73518 q^{75} -5.95208 q^{76} +3.64615 q^{77} +3.24335 q^{79} -3.97522 q^{80} +1.00000 q^{81} -4.02416 q^{82} +15.6734 q^{83} -0.945953 q^{84} -22.5680 q^{85} +5.42469 q^{86} +9.42061 q^{87} +11.0278 q^{88} -4.85592 q^{89} -3.36384 q^{90} -7.04286 q^{92} -10.7607 q^{93} -1.83309 q^{94} +20.6160 q^{95} -4.80341 q^{96} -4.26503 q^{97} -1.02667 q^{98} +3.64615 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 2 q^{2} + 15 q^{3} + 28 q^{4} + 9 q^{5} - 2 q^{6} + 15 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) $ 15 * q - 2 * q^2 + 15 * q^3 + 28 * q^4 + 9 * q^5 - 2 * q^6 + 15 * q^7 - 9 * q^8 + 15 * q^9	\( 15 q - 2 q^{2} + 15 q^{3} + 28 q^{4} + 9 q^{5} - 2 q^{6} + 15 q^{7} - 9 q^{8} + 15 q^{9} + 21 q^{10} - 5 q^{11} + 28 q^{12} - 2 q^{14} + 9 q^{15} + 50 q^{16} - q^{17} - 2 q^{18} - 3 q^{19} + 23 q^{20} + 15 q^{21} + 21 q^{22} + 4 q^{23} - 9 q^{24} + 50 q^{25} + 15 q^{27} + 28 q^{28} + 9 q^{29} + 21 q^{30} - 7 q^{31} - 35 q^{32} - 5 q^{33} + 2 q^{34} + 9 q^{35} + 28 q^{36} - 17 q^{37} - 12 q^{38} + 46 q^{40} + 22 q^{41} - 2 q^{42} + 36 q^{43} - 29 q^{44} + 9 q^{45} + q^{46} + 12 q^{47} + 50 q^{48} + 15 q^{49} - 53 q^{50} - q^{51} - 5 q^{53} - 2 q^{54} + 43 q^{55} - 9 q^{56} - 3 q^{57} - 29 q^{58} + 29 q^{59} + 23 q^{60} + 12 q^{61} + 14 q^{62} + 15 q^{63} + 95 q^{64} + 21 q^{66} + 12 q^{67} - 16 q^{68} + 4 q^{69} + 21 q^{70} - 36 q^{71} - 9 q^{72} + 29 q^{73} - 5 q^{74} + 50 q^{75} - 25 q^{76} - 5 q^{77} + 35 q^{79} + 89 q^{80} + 15 q^{81} + 51 q^{82} + 10 q^{83} + 28 q^{84} - 23 q^{85} - 19 q^{86} + 9 q^{87} + 73 q^{88} - 25 q^{89} + 21 q^{90} - 31 q^{92} - 7 q^{93} - 19 q^{94} - 7 q^{95} - 35 q^{96} + 26 q^{97} - 2 q^{98} - 5 q^{99}+O(q^{100}) \) 15 * q - 2 * q^2 + 15 * q^3 + 28 * q^4 + 9 * q^5 - 2 * q^6 + 15 * q^7 - 9 * q^8 + 15 * q^9 + 21 * q^10 - 5 * q^11 + 28 * q^12 - 2 * q^14 + 9 * q^15 + 50 * q^16 - q^17 - 2 * q^18 - 3 * q^19 + 23 * q^20 + 15 * q^21 + 21 * q^22 + 4 * q^23 - 9 * q^24 + 50 * q^25 + 15 * q^27 + 28 * q^28 + 9 * q^29 + 21 * q^30 - 7 * q^31 - 35 * q^32 - 5 * q^33 + 2 * q^34 + 9 * q^35 + 28 * q^36 - 17 * q^37 - 12 * q^38 + 46 * q^40 + 22 * q^41 - 2 * q^42 + 36 * q^43 - 29 * q^44 + 9 * q^45 + q^46 + 12 * q^47 + 50 * q^48 + 15 * q^49 - 53 * q^50 - q^51 - 5 * q^53 - 2 * q^54 + 43 * q^55 - 9 * q^56 - 3 * q^57 - 29 * q^58 + 29 * q^59 + 23 * q^60 + 12 * q^61 + 14 * q^62 + 15 * q^63 + 95 * q^64 + 21 * q^66 + 12 * q^67 - 16 * q^68 + 4 * q^69 + 21 * q^70 - 36 * q^71 - 9 * q^72 + 29 * q^73 - 5 * q^74 + 50 * q^75 - 25 * q^76 - 5 * q^77 + 35 * q^79 + 89 * q^80 + 15 * q^81 + 51 * q^82 + 10 * q^83 + 28 * q^84 - 23 * q^85 - 19 * q^86 + 9 * q^87 + 73 * q^88 - 25 * q^89 + 21 * q^90 - 31 * q^92 - 7 * q^93 - 19 * q^94 - 7 * q^95 - 35 * q^96 + 26 * q^97 - 2 * q^98 - 5 * 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 $

$2$	−1.02667	−0.725964	−0.362982	−	0.931796i	$-0.618241\pi$
$2$	−1.02667	−0.725964	−0.362982	+	0.931796i	$0.618241\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.945953	−0.472976
$5$	3.27646	1.46528	0.732638	−	0.680618i	$-0.238289\pi$
$5$	3.27646	1.46528	0.732638	+	0.680618i	$0.238289\pi$
$6$	−1.02667	−0.419135
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	3.02452	1.06933
$9$	1.00000	0.333333
$10$	−3.36384	−1.06374
$11$	3.64615	1.09935	0.549677	−	0.835377i	$-0.314751\pi$
$11$	3.64615	1.09935	0.549677	+	0.835377i	$0.314751\pi$
$12$	−0.945953	−0.273073
$13$	0	0
$13$	0	0
$14$	−1.02667	−0.274389
$15$	3.27646	0.845978
$16$	−1.21327	−0.303317
$17$	−6.88794	−1.67057	−0.835285	−	0.549817i	$-0.814697\pi$
$17$	−6.88794	−1.67057	−0.835285	+	0.549817i	$0.814697\pi$
$18$	−1.02667	−0.241988
$19$	6.29215	1.44352	0.721759	−	0.692144i	$-0.243334\pi$
$19$	6.29215	1.44352	0.721759	+	0.692144i	$0.243334\pi$
$20$	−3.09937	−0.693041
$21$	1.00000	0.218218
$22$	−3.74338	−0.798092
$23$	7.44525	1.55244	0.776221	−	0.630461i	$-0.217134\pi$
$23$	7.44525	1.55244	0.776221	+	0.630461i	$0.217134\pi$
$24$	3.02452	0.617377
$25$	5.73518	1.14704
$26$	0	0
$27$	1.00000	0.192450
$28$	−0.945953	−0.178768
$29$	9.42061	1.74936	0.874682	−	0.484697i	$-0.161070\pi$
$29$	9.42061	1.74936	0.874682	+	0.484697i	$0.161070\pi$
$30$	−3.36384	−0.614149
$31$	−10.7607	−1.93269	−0.966343	−	0.257257i	$-0.917181\pi$
$31$	−10.7607	−1.93269	−0.966343	+	0.257257i	$0.917181\pi$
$32$	−4.80341	−0.849130
$33$	3.64615	0.634712
$34$	7.07162	1.21277
$35$	3.27646	0.553823
$36$	−0.945953	−0.157659
$37$	−0.298388	−0.0490547	−0.0245274	−	0.999699i	$-0.507808\pi$
$37$	−0.298388	−0.0490547	−0.0245274	+	0.999699i	$0.507808\pi$
$38$	−6.45995	−1.04794
$39$	0	0
$40$	9.90970	1.56686
$41$	3.91963	0.612144	0.306072	−	0.952008i	$-0.400985\pi$
$41$	3.91963	0.612144	0.306072	+	0.952008i	$0.400985\pi$
$42$	−1.02667	−0.158418
$43$	−5.28378	−0.805769	−0.402885	−	0.915251i	$-0.631992\pi$
$43$	−5.28378	−0.805769	−0.402885	+	0.915251i	$0.631992\pi$
$44$	−3.44908	−0.519969
$45$	3.27646	0.488426
$46$	−7.64380	−1.12702
$47$	1.78548	0.260438	0.130219	−	0.991485i	$-0.458432\pi$
$47$	1.78548	0.260438	0.130219	+	0.991485i	$0.458432\pi$
$48$	−1.21327	−0.175120
$49$	1.00000	0.142857
$50$	−5.88813	−0.832707
$51$	−6.88794	−0.964504
$52$	0	0
$53$	4.92587	0.676621	0.338310	−	0.941035i	$-0.390145\pi$
$53$	4.92587	0.676621	0.338310	+	0.941035i	$0.390145\pi$
$54$	−1.02667	−0.139712
$55$	11.9464	1.61086
$56$	3.02452	0.404168
$57$	6.29215	0.833416
$58$	−9.67184	−1.26998
$59$	−5.56609	−0.724643	−0.362322	−	0.932053i	$-0.618016\pi$
$59$	−5.56609	−0.724643	−0.362322	+	0.932053i	$0.618016\pi$
$60$	−3.09937	−0.400128
$61$	4.34575	0.556416	0.278208	−	0.960521i	$-0.410259\pi$
$61$	4.34575	0.556416	0.278208	+	0.960521i	$0.410259\pi$
$62$	11.0477	1.40306
$63$	1.00000	0.125988
$64$	7.35804	0.919755
$65$	0	0
$66$	−3.74338	−0.460778
$67$	−12.7392	−1.55634	−0.778170	−	0.628054i	$-0.783852\pi$
$67$	−12.7392	−1.55634	−0.778170	+	0.628054i	$0.783852\pi$
$68$	6.51566	0.790140
$69$	7.44525	0.896303
$70$	−3.36384	−0.402055
$71$	5.67644	0.673669	0.336835	−	0.941564i	$-0.390644\pi$
$71$	5.67644	0.673669	0.336835	+	0.941564i	$0.390644\pi$
$72$	3.02452	0.356443
$73$	6.72651	0.787279	0.393639	−	0.919265i	$-0.371216\pi$
$73$	6.72651	0.787279	0.393639	+	0.919265i	$0.371216\pi$
$74$	0.306346	0.0356120
$75$	5.73518	0.662242
$76$	−5.95208	−0.682750
$77$	3.64615	0.415517
$78$	0	0
$79$	3.24335	0.364905	0.182453	−	0.983215i	$-0.441596\pi$
$79$	3.24335	0.364905	0.182453	+	0.983215i	$0.441596\pi$
$80$	−3.97522	−0.444443
$81$	1.00000	0.111111
$82$	−4.02416	−0.444394
$83$	15.6734	1.72038	0.860190	−	0.509973i	$-0.170345\pi$
$83$	15.6734	1.72038	0.860190	+	0.509973i	$0.170345\pi$
$84$	−0.945953	−0.103212
$85$	−22.5680	−2.44785
$86$	5.42469	0.584959
$87$	9.42061	1.01000
$88$	11.0278	1.17557
$89$	−4.85592	−0.514726	−0.257363	−	0.966315i	$-0.582854\pi$
$89$	−4.85592	−0.514726	−0.257363	+	0.966315i	$0.582854\pi$
$90$	−3.36384	−0.354579
$91$	0	0
$92$	−7.04286	−0.734269
$93$	−10.7607	−1.11584
$94$	−1.83309	−0.189069
$95$	20.6160	2.11515
$96$	−4.80341	−0.490246
$97$	−4.26503	−0.433048	−0.216524	−	0.976277i	$-0.569472\pi$
$97$	−4.26503	−0.433048	−0.216524	+	0.976277i	$0.569472\pi$
$98$	−1.02667	−0.103709
$99$	3.64615	0.366451
$100$	−5.42521	−0.542521
$101$	−6.34614	−0.631464	−0.315732	−	0.948848i	$-0.602250\pi$
$101$	−6.34614	−0.631464	−0.315732	+	0.948848i	$0.602250\pi$
$102$	7.07162	0.700195
$103$	−9.87950	−0.973456	−0.486728	−	0.873553i	$-0.661810\pi$
$103$	−9.87950	−0.973456	−0.486728	+	0.873553i	$0.661810\pi$
$104$	0	0
$105$	3.27646	0.319750
$106$	−5.05724	−0.491202
$107$	−17.3396	−1.67628	−0.838140	−	0.545456i	$-0.816357\pi$
$107$	−17.3396	−1.67628	−0.838140	+	0.545456i	$0.816357\pi$
$108$	−0.945953	−0.0910243
$109$	−7.94895	−0.761372	−0.380686	−	0.924704i	$-0.624312\pi$
$109$	−7.94895	−0.761372	−0.380686	+	0.924704i	$0.624312\pi$
$110$	−12.2650	−1.16943
$111$	−0.298388	−0.0283218
$112$	−1.21327	−0.114643
$113$	−17.4746	−1.64387	−0.821936	−	0.569579i	$-0.807106\pi$
$113$	−17.4746	−1.64387	−0.821936	+	0.569579i	$0.807106\pi$
$114$	−6.45995	−0.605030
$115$	24.3941	2.27476
$116$	−8.91145	−0.827408
$117$	0	0
$118$	5.71453	0.526065
$119$	−6.88794	−0.631416
$120$	9.90970	0.904628
$121$	2.29438	0.208580
$122$	−4.46164	−0.403938
$123$	3.91963	0.353421
$124$	10.1792	0.914115
$125$	2.40879	0.215448
$126$	−1.02667	−0.0914629
$127$	−4.25486	−0.377557	−0.188779	−	0.982020i	$-0.560453\pi$
$127$	−4.25486	−0.377557	−0.188779	+	0.982020i	$0.560453\pi$
$128$	2.05255	0.181421
$129$	−5.28378	−0.465211
$130$	0	0
$131$	3.88999	0.339870	0.169935	−	0.985455i	$-0.445644\pi$
$131$	3.88999	0.339870	0.169935	+	0.985455i	$0.445644\pi$
$132$	−3.44908	−0.300204
$133$	6.29215	0.545599
$134$	13.0789	1.12985
$135$	3.27646	0.281993
$136$	−20.8327	−1.78639
$137$	−7.07777	−0.604695	−0.302347	−	0.953198i	$-0.597770\pi$
$137$	−7.07777	−0.604695	−0.302347	+	0.953198i	$0.597770\pi$
$138$	−7.64380	−0.650684
$139$	15.8222	1.34202	0.671012	−	0.741446i	$-0.265860\pi$
$139$	15.8222	1.34202	0.671012	+	0.741446i	$0.265860\pi$
$140$	−3.09937	−0.261945
$141$	1.78548	0.150364
$142$	−5.82782	−0.489059
$143$	0	0
$144$	−1.21327	−0.101106
$145$	30.8662	2.56330
$146$	−6.90589	−0.571536
$147$	1.00000	0.0824786
$148$	0.282261	0.0232017
$149$	8.53252	0.699011	0.349505	−	0.936934i	$-0.386350\pi$
$149$	8.53252	0.699011	0.349505	+	0.936934i	$0.386350\pi$
$150$	−5.88813	−0.480763
$151$	−6.95074	−0.565643	−0.282822	−	0.959173i	$-0.591270\pi$
$151$	−6.95074	−0.565643	−0.282822	+	0.959173i	$0.591270\pi$
$152$	19.0307	1.54359
$153$	−6.88794	−0.556857
$154$	−3.74338	−0.301650
$155$	−35.2571	−2.83192
$156$	0	0
$157$	12.7344	1.01632	0.508159	−	0.861263i	$-0.330326\pi$
$157$	12.7344	1.01632	0.508159	+	0.861263i	$0.330326\pi$
$158$	−3.32984	−0.264908
$159$	4.92587	0.390647
$160$	−15.7382	−1.24421
$161$	7.44525	0.586768
$162$	−1.02667	−0.0806627
$163$	−3.92353	−0.307315	−0.153657	−	0.988124i	$-0.549105\pi$
$163$	−3.92353	−0.307315	−0.153657	+	0.988124i	$0.549105\pi$
$164$	−3.70779	−0.289530
$165$	11.9464	0.930029
$166$	−16.0914	−1.24893
$167$	−5.39579	−0.417539	−0.208769	−	0.977965i	$-0.566946\pi$
$167$	−5.39579	−0.417539	−0.208769	+	0.977965i	$0.566946\pi$
$168$	3.02452	0.233346
$169$	0	0
$170$	23.1699	1.77705
$171$	6.29215	0.481173
$172$	4.99821	0.381110
$173$	2.03101	0.154415	0.0772076	−	0.997015i	$-0.475400\pi$
$173$	2.03101	0.154415	0.0772076	+	0.997015i	$0.475400\pi$
$174$	−9.67184	−0.733220
$175$	5.73518	0.433539
$176$	−4.42375	−0.333453
$177$	−5.56609	−0.418373
$178$	4.98541	0.373673
$179$	12.0826	0.903097	0.451548	−	0.892247i	$-0.350872\pi$
$179$	12.0826	0.903097	0.451548	+	0.892247i	$0.350872\pi$
$180$	−3.09937	−0.231014
$181$	17.6432	1.31141	0.655703	−	0.755019i	$-0.272372\pi$
$181$	17.6432	1.31141	0.655703	+	0.755019i	$0.272372\pi$
$182$	0	0
$183$	4.34575	0.321247
$184$	22.5183	1.66007
$185$	−0.977656	−0.0718787
$186$	11.0477	0.810057
$187$	−25.1144	−1.83655
$188$	−1.68898	−0.123181
$189$	1.00000	0.0727393
$190$	−21.1658	−1.53553
$191$	6.67101	0.482697	0.241349	−	0.970438i	$-0.422410\pi$
$191$	6.67101	0.482697	0.241349	+	0.970438i	$0.422410\pi$
$192$	7.35804	0.531021
$193$	−15.9900	−1.15099	−0.575493	−	0.817807i	$-0.695190\pi$
$193$	−15.9900	−1.15099	−0.575493	+	0.817807i	$0.695190\pi$
$194$	4.37877	0.314377
$195$	0	0
$196$	−0.945953	−0.0675680
$197$	−7.34567	−0.523357	−0.261679	−	0.965155i	$-0.584276\pi$
$197$	−7.34567	−0.523357	−0.261679	+	0.965155i	$0.584276\pi$
$198$	−3.74338	−0.266031
$199$	−0.202957	−0.0143873	−0.00719363	−	0.999974i	$-0.502290\pi$
$199$	−0.202957	−0.0143873	−0.00719363	+	0.999974i	$0.502290\pi$
$200$	17.3461	1.22656
$201$	−12.7392	−0.898553
$202$	6.51538	0.458420
$203$	9.42061	0.661197
$204$	6.51566	0.456188
$205$	12.8425	0.896960
$206$	10.1430	0.706694
$207$	7.44525	0.517481
$208$	0	0
$209$	22.9421	1.58694
$210$	−3.36384	−0.232127
$211$	8.62718	0.593920	0.296960	−	0.954890i	$-0.404027\pi$
$211$	8.62718	0.593920	0.296960	+	0.954890i	$0.404027\pi$
$212$	−4.65964	−0.320026
$213$	5.67644	0.388943
$214$	17.8020	1.21692
$215$	−17.3121	−1.18067
$216$	3.02452	0.205792
$217$	−10.7607	−0.730487
$218$	8.16094	0.552728
$219$	6.72651	0.454536
$220$	−11.3008	−0.761898
$221$	0	0
$222$	0.306346	0.0205606
$223$	1.66736	0.111655	0.0558275	−	0.998440i	$-0.482220\pi$
$223$	1.66736	0.111655	0.0558275	+	0.998440i	$0.482220\pi$
$224$	−4.80341	−0.320941
$225$	5.73518	0.382345
$226$	17.9406	1.19339
$227$	−22.3102	−1.48078	−0.740391	−	0.672176i	$-0.765360\pi$
$227$	−22.3102	−1.48078	−0.740391	+	0.672176i	$0.765360\pi$
$228$	−5.95208	−0.394186
$229$	24.3840	1.61134	0.805669	−	0.592365i	$-0.201806\pi$
$229$	24.3840	1.61134	0.805669	+	0.592365i	$0.201806\pi$
$230$	−25.0446	−1.65139
$231$	3.64615	0.239899
$232$	28.4928	1.87064
$233$	−17.2618	−1.13086	−0.565431	−	0.824796i	$-0.691290\pi$
$233$	−17.2618	−1.13086	−0.565431	+	0.824796i	$0.691290\pi$
$234$	0	0
$235$	5.85004	0.381614
$236$	5.26526	0.342739
$237$	3.24335	0.210678
$238$	7.07162	0.458385
$239$	−6.12302	−0.396065	−0.198033	−	0.980195i	$-0.563455\pi$
$239$	−6.12302	−0.396065	−0.198033	+	0.980195i	$0.563455\pi$
$240$	−3.97522	−0.256600
$241$	−4.04969	−0.260863	−0.130432	−	0.991457i	$-0.541636\pi$
$241$	−4.04969	−0.260863	−0.130432	+	0.991457i	$0.541636\pi$
$242$	−2.35556	−0.151421
$243$	1.00000	0.0641500
$244$	−4.11088	−0.263172
$245$	3.27646	0.209325
$246$	−4.02416	−0.256571
$247$	0	0
$248$	−32.5460	−2.06667
$249$	15.6734	0.993262
$250$	−2.47302	−0.156408
$251$	17.6643	1.11496	0.557479	−	0.830191i	$-0.311769\pi$
$251$	17.6643	1.11496	0.557479	+	0.830191i	$0.311769\pi$
$252$	−0.945953	−0.0595894
$253$	27.1465	1.70668
$254$	4.36832	0.274093
$255$	−22.5680	−1.41327
$256$	−16.8234	−1.05146
$257$	−1.45219	−0.0905854	−0.0452927	−	0.998974i	$-0.514422\pi$
$257$	−1.45219	−0.0905854	−0.0452927	+	0.998974i	$0.514422\pi$
$258$	5.42469	0.337726
$259$	−0.298388	−0.0185409
$260$	0	0
$261$	9.42061	0.583121
$262$	−3.99373	−0.246733
$263$	3.02641	0.186617	0.0933083	−	0.995637i	$-0.470256\pi$
$263$	3.02641	0.186617	0.0933083	+	0.995637i	$0.470256\pi$
$264$	11.0278	0.678716
$265$	16.1394	0.991436
$266$	−6.45995	−0.396085
$267$	−4.85592	−0.297177
$268$	12.0507	0.736112
$269$	−8.80840	−0.537058	−0.268529	−	0.963272i	$-0.586537\pi$
$269$	−8.80840	−0.537058	−0.268529	+	0.963272i	$0.586537\pi$
$270$	−3.36384	−0.204716
$271$	−2.79485	−0.169775	−0.0848877	−	0.996391i	$-0.527053\pi$
$271$	−2.79485	−0.169775	−0.0848877	+	0.996391i	$0.527053\pi$
$272$	8.35691	0.506712
$273$	0	0
$274$	7.26652	0.438987
$275$	20.9113	1.26100
$276$	−7.04286	−0.423930
$277$	24.2433	1.45664	0.728318	−	0.685239i	$-0.240302\pi$
$277$	24.2433	1.45664	0.728318	+	0.685239i	$0.240302\pi$
$278$	−16.2442	−0.974262
$279$	−10.7607	−0.644229
$280$	9.90970	0.592218
$281$	2.10017	0.125286	0.0626428	−	0.998036i	$-0.480047\pi$
$281$	2.10017	0.125286	0.0626428	+	0.998036i	$0.480047\pi$
$282$	−1.83309	−0.109159
$283$	7.28606	0.433112	0.216556	−	0.976270i	$-0.430518\pi$
$283$	7.28606	0.433112	0.216556	+	0.976270i	$0.430518\pi$
$284$	−5.36964	−0.318630
$285$	20.6160	1.22118
$286$	0	0
$287$	3.91963	0.231369
$288$	−4.80341	−0.283043
$289$	30.4437	1.79080
$290$	−31.6894	−1.86086
$291$	−4.26503	−0.250020
$292$	−6.36296	−0.372364
$293$	−2.85760	−0.166943	−0.0834715	−	0.996510i	$-0.526601\pi$
$293$	−2.85760	−0.166943	−0.0834715	+	0.996510i	$0.526601\pi$
$294$	−1.02667	−0.0598765
$295$	−18.2371	−1.06180
$296$	−0.902480	−0.0524556
$297$	3.64615	0.211571
$298$	−8.76006	−0.507457
$299$	0	0
$300$	−5.42521	−0.313225
$301$	−5.28378	−0.304552
$302$	7.13610	0.410637
$303$	−6.34614	−0.364576
$304$	−7.63407	−0.437844
$305$	14.2387	0.815304
$306$	7.07162	0.404258
$307$	29.8167	1.70173	0.850865	−	0.525384i	$-0.176078\pi$
$307$	29.8167	1.70173	0.850865	+	0.525384i	$0.176078\pi$
$308$	−3.44908	−0.196530
$309$	−9.87950	−0.562025
$310$	36.1974	2.05587
$311$	1.71131	0.0970393	0.0485197	−	0.998822i	$-0.484550\pi$
$311$	1.71131	0.0970393	0.0485197	+	0.998822i	$0.484550\pi$
$312$	0	0
$313$	−1.74425	−0.0985909	−0.0492954	−	0.998784i	$-0.515698\pi$
$313$	−1.74425	−0.0985909	−0.0492954	+	0.998784i	$0.515698\pi$
$314$	−13.0740	−0.737811
$315$	3.27646	0.184608
$316$	−3.06805	−0.172592
$317$	1.64195	0.0922210	0.0461105	−	0.998936i	$-0.485317\pi$
$317$	1.64195	0.0922210	0.0461105	+	0.998936i	$0.485317\pi$
$318$	−5.05724	−0.283596
$319$	34.3489	1.92317
$320$	24.1083	1.34770
$321$	−17.3396	−0.967800
$322$	−7.64380	−0.425972
$323$	−43.3399	−2.41150
$324$	−0.945953	−0.0525529
$325$	0	0
$326$	4.02817	0.223099
$327$	−7.94895	−0.439578
$328$	11.8550	0.654583
$329$	1.78548	0.0984365
$330$	−12.2650	−0.675168
$331$	−21.9051	−1.20401	−0.602006	−	0.798491i	$-0.705632\pi$
$331$	−21.9051	−1.20401	−0.602006	+	0.798491i	$0.705632\pi$
$332$	−14.8263	−0.813699
$333$	−0.298388	−0.0163516
$334$	5.53968	0.303118
$335$	−41.7394	−2.28047
$336$	−1.21327	−0.0661892
$337$	22.0335	1.20024	0.600121	−	0.799909i	$-0.295119\pi$
$337$	22.0335	1.20024	0.600121	+	0.799909i	$0.295119\pi$
$338$	0	0
$339$	−17.4746	−0.949090
$340$	21.3483	1.15777
$341$	−39.2352	−2.12471
$342$	−6.45995	−0.349314
$343$	1.00000	0.0539949
$344$	−15.9809	−0.861631
$345$	24.3941	1.31333
$346$	−2.08518	−0.112100
$347$	−11.7986	−0.633383	−0.316692	−	0.948529i	$-0.602572\pi$
$347$	−11.7986	−0.633383	−0.316692	+	0.948529i	$0.602572\pi$
$348$	−8.91145	−0.477704
$349$	−0.644467	−0.0344975	−0.0172488	−	0.999851i	$-0.505491\pi$
$349$	−0.644467	−0.0344975	−0.0172488	+	0.999851i	$0.505491\pi$
$350$	−5.88813	−0.314734
$351$	0	0
$352$	−17.5139	−0.933495
$353$	24.3481	1.29592	0.647960	−	0.761674i	$-0.275622\pi$
$353$	24.3481	1.29592	0.647960	+	0.761674i	$0.275622\pi$
$354$	5.71453	0.303724
$355$	18.5986	0.987112
$356$	4.59347	0.243453
$357$	−6.88794	−0.364548
$358$	−12.4048	−0.655616
$359$	−0.163028	−0.00860429	−0.00430214	−	0.999991i	$-0.501369\pi$
$359$	−0.163028	−0.00860429	−0.00430214	+	0.999991i	$0.501369\pi$
$360$	9.90970	0.522287
$361$	20.5912	1.08375
$362$	−18.1137	−0.952034
$363$	2.29438	0.120424
$364$	0	0
$365$	22.0391	1.15358
$366$	−4.46164	−0.233214
$367$	18.1404	0.946920	0.473460	−	0.880815i	$-0.343005\pi$
$367$	18.1404	0.946920	0.473460	+	0.880815i	$0.343005\pi$
$368$	−9.03309	−0.470882
$369$	3.91963	0.204048
$370$	1.00373	0.0521814
$371$	4.92587	0.255739
$372$	10.1792	0.527764
$373$	4.28760	0.222004	0.111002	−	0.993820i	$-0.464594\pi$
$373$	4.28760	0.222004	0.111002	+	0.993820i	$0.464594\pi$
$374$	25.7842	1.33327
$375$	2.40879	0.124389
$376$	5.40020	0.278494
$377$	0	0
$378$	−1.02667	−0.0528061
$379$	−21.7188	−1.11562	−0.557809	−	0.829969i	$-0.688358\pi$
$379$	−21.7188	−1.11562	−0.557809	+	0.829969i	$0.688358\pi$
$380$	−19.5017	−1.00042
$381$	−4.25486	−0.217983
$382$	−6.84891	−0.350421
$383$	22.4712	1.14822	0.574112	−	0.818777i	$-0.305347\pi$
$383$	22.4712	1.14822	0.574112	+	0.818777i	$0.305347\pi$
$384$	2.05255	0.104744
$385$	11.9464	0.608847
$386$	16.4164	0.835574
$387$	−5.28378	−0.268590
$388$	4.03451	0.204821
$389$	−3.28401	−0.166506	−0.0832530	−	0.996528i	$-0.526531\pi$
$389$	−3.28401	−0.166506	−0.0832530	+	0.996528i	$0.526531\pi$
$390$	0	0
$391$	−51.2824	−2.59346
$392$	3.02452	0.152761
$393$	3.88999	0.196224
$394$	7.54156	0.379938
$395$	10.6267	0.534687
$396$	−3.44908	−0.173323
$397$	−4.46062	−0.223872	−0.111936	−	0.993715i	$-0.535705\pi$
$397$	−4.46062	−0.223872	−0.111936	+	0.993715i	$0.535705\pi$
$398$	0.208370	0.0104446
$399$	6.29215	0.315002
$400$	−6.95831	−0.347916
$401$	−2.96473	−0.148052	−0.0740258	−	0.997256i	$-0.523585\pi$
$401$	−2.96473	−0.148052	−0.0740258	+	0.997256i	$0.523585\pi$
$402$	13.0789	0.652317
$403$	0	0
$404$	6.00315	0.298668
$405$	3.27646	0.162809
$406$	−9.67184	−0.480005
$407$	−1.08797	−0.0539285
$408$	−20.8327	−1.03137
$409$	19.5362	0.966004	0.483002	−	0.875619i	$-0.339546\pi$
$409$	19.5362	0.966004	0.483002	+	0.875619i	$0.339546\pi$
$410$	−13.1850	−0.651161
$411$	−7.07777	−0.349121
$412$	9.34554	0.460422
$413$	−5.56609	−0.273889
$414$	−7.64380	−0.375672
$415$	51.3533	2.52083
$416$	0	0
$417$	15.8222	0.774818
$418$	−23.5539	−1.15206
$419$	−25.9290	−1.26671	−0.633357	−	0.773860i	$-0.718323\pi$
$419$	−25.9290	−1.26671	−0.633357	+	0.773860i	$0.718323\pi$
$420$	−3.09937	−0.151234
$421$	−6.59832	−0.321583	−0.160791	−	0.986988i	$-0.551405\pi$
$421$	−6.59832	−0.321583	−0.160791	+	0.986988i	$0.551405\pi$
$422$	−8.85725	−0.431164
$423$	1.78548	0.0868128
$424$	14.8984	0.723529
$425$	−39.5035	−1.91620
$426$	−5.82782	−0.282359
$427$	4.34575	0.210306
$428$	16.4024	0.792841
$429$	0	0
$430$	17.7738	0.857127
$431$	9.76500	0.470363	0.235182	−	0.971951i	$-0.424431\pi$
$431$	9.76500	0.470363	0.235182	+	0.971951i	$0.424431\pi$
$432$	−1.21327	−0.0583734
$433$	31.1719	1.49802	0.749012	−	0.662556i	$-0.230528\pi$
$433$	31.1719	1.49802	0.749012	+	0.662556i	$0.230528\pi$
$434$	11.0477	0.530307
$435$	30.8662	1.47992
$436$	7.51933	0.360111
$437$	46.8467	2.24098
$438$	−6.90589	−0.329976
$439$	0.0700703	0.00334427	0.00167214	−	0.999999i	$-0.499468\pi$
$439$	0.0700703	0.00334427	0.00167214	+	0.999999i	$0.499468\pi$
$440$	36.1322	1.72254
$441$	1.00000	0.0476190
$442$	0	0
$443$	−13.9060	−0.660692	−0.330346	−	0.943860i	$-0.607166\pi$
$443$	−13.9060	−0.660692	−0.330346	+	0.943860i	$0.607166\pi$
$444$	0.282261	0.0133955
$445$	−15.9102	−0.754216
$446$	−1.71183	−0.0810575
$447$	8.53252	0.403574
$448$	7.35804	0.347635
$449$	−41.9051	−1.97762	−0.988812	−	0.149164i	$-0.952342\pi$
$449$	−41.9051	−1.97762	−0.988812	+	0.149164i	$0.952342\pi$
$450$	−5.88813	−0.277569
$451$	14.2916	0.672963
$452$	16.5302	0.777513
$453$	−6.95074	−0.326574
$454$	22.9052	1.07499
$455$	0	0
$456$	19.0307	0.891195
$457$	11.9231	0.557738	0.278869	−	0.960329i	$-0.410040\pi$
$457$	11.9231	0.557738	0.278869	+	0.960329i	$0.410040\pi$
$458$	−25.0343	−1.16977
$459$	−6.88794	−0.321501
$460$	−23.0756	−1.07591
$461$	−18.0671	−0.841470	−0.420735	−	0.907184i	$-0.638228\pi$
$461$	−18.0671	−0.841470	−0.420735	+	0.907184i	$0.638228\pi$
$462$	−3.74338	−0.174158
$463$	7.47553	0.347417	0.173709	−	0.984797i	$-0.444425\pi$
$463$	7.47553	0.347417	0.173709	+	0.984797i	$0.444425\pi$
$464$	−11.4297	−0.530612
$465$	−35.2571	−1.63501
$466$	17.7222	0.820964
$467$	33.0758	1.53056	0.765282	−	0.643695i	$-0.222600\pi$
$467$	33.0758	1.53056	0.765282	+	0.643695i	$0.222600\pi$
$468$	0	0
$469$	−12.7392	−0.588241
$470$	−6.00605	−0.277038
$471$	12.7344	0.586772
$472$	−16.8347	−0.774881
$473$	−19.2654	−0.885826
$474$	−3.32984	−0.152945
$475$	36.0866	1.65577
$476$	6.51566	0.298645
$477$	4.92587	0.225540
$478$	6.28631	0.287529
$479$	−10.4405	−0.477037	−0.238519	−	0.971138i	$-0.576662\pi$
$479$	−10.4405	−0.477037	−0.238519	+	0.971138i	$0.576662\pi$
$480$	−15.7382	−0.718346
$481$	0	0
$482$	4.15769	0.189377
$483$	7.44525	0.338771
$484$	−2.17037	−0.0986533
$485$	−13.9742	−0.634535
$486$	−1.02667	−0.0465706
$487$	39.3547	1.78333	0.891665	−	0.452695i	$-0.149537\pi$
$487$	39.3547	1.78333	0.891665	+	0.452695i	$0.149537\pi$
$488$	13.1438	0.594992
$489$	−3.92353	−0.177428
$490$	−3.36384	−0.151963
$491$	32.2361	1.45479	0.727397	−	0.686217i	$-0.240730\pi$
$491$	32.2361	1.45479	0.727397	+	0.686217i	$0.240730\pi$
$492$	−3.70779	−0.167160
$493$	−64.8886	−2.92243
$494$	0	0
$495$	11.9464	0.536953
$496$	13.0557	0.586217
$497$	5.67644	0.254623
$498$	−16.0914	−0.721073
$499$	6.32415	0.283108	0.141554	−	0.989931i	$-0.454790\pi$
$499$	6.32415	0.283108	0.141554	+	0.989931i	$0.454790\pi$
$500$	−2.27860	−0.101902
$501$	−5.39579	−0.241066
$502$	−18.1353	−0.809420
$503$	11.6484	0.519377	0.259689	−	0.965692i	$-0.416380\pi$
$503$	11.6484	0.519377	0.259689	+	0.965692i	$0.416380\pi$
$504$	3.02452	0.134723
$505$	−20.7929	−0.925270
$506$	−27.8704	−1.23899
$507$	0	0
$508$	4.02489	0.178576
$509$	13.0251	0.577328	0.288664	−	0.957430i	$-0.406789\pi$
$509$	13.0251	0.577328	0.288664	+	0.957430i	$0.406789\pi$
$510$	23.1699	1.02598
$511$	6.72651	0.297563
$512$	13.1669	0.581901
$513$	6.29215	0.277805
$514$	1.49092	0.0657617
$515$	−32.3698	−1.42638
$516$	4.99821	0.220034
$517$	6.51011	0.286314
$518$	0.306346	0.0134601
$519$	2.03101	0.0891516
$520$	0	0
$521$	−23.3360	−1.02237	−0.511185	−	0.859471i	$-0.670793\pi$
$521$	−23.3360	−1.02237	−0.511185	+	0.859471i	$0.670793\pi$
$522$	−9.67184	−0.423325
$523$	−38.8457	−1.69860	−0.849301	−	0.527908i	$-0.822977\pi$
$523$	−38.8457	−1.69860	−0.849301	+	0.527908i	$0.822977\pi$
$524$	−3.67975	−0.160750
$525$	5.73518	0.250304
$526$	−3.10712	−0.135477
$527$	74.1193	3.22869
$528$	−4.42375	−0.192519
$529$	32.4318	1.41008
$530$	−16.5698	−0.719747
$531$	−5.56609	−0.241548
$532$	−5.95208	−0.258055
$533$	0	0
$534$	4.98541	0.215740
$535$	−56.8124	−2.45621
$536$	−38.5299	−1.66424
$537$	12.0826	0.521403
$538$	9.04330	0.389884
$539$	3.64615	0.157051
$540$	−3.09937	−0.133376
$541$	−38.2152	−1.64300	−0.821499	−	0.570210i	$-0.806862\pi$
$541$	−38.2152	−1.64300	−0.821499	+	0.570210i	$0.806862\pi$
$542$	2.86939	0.123251
$543$	17.6432	0.757141
$544$	33.0856	1.41853
$545$	−26.0444	−1.11562
$546$	0	0
$547$	−41.3324	−1.76724	−0.883622	−	0.468200i	$-0.844903\pi$
$547$	−41.3324	−1.76724	−0.883622	+	0.468200i	$0.844903\pi$
$548$	6.69524	0.286006
$549$	4.34575	0.185472
$550$	−21.4690	−0.915440
$551$	59.2759	2.52524
$552$	22.5183	0.958442
$553$	3.24335	0.137921
$554$	−24.8898	−1.05747
$555$	−0.977656	−0.0414992
$556$	−14.9671	−0.634746
$557$	−10.4059	−0.440913	−0.220456	−	0.975397i	$-0.570755\pi$
$557$	−10.4059	−0.440913	−0.220456	+	0.975397i	$0.570755\pi$
$558$	11.0477	0.467687
$559$	0	0
$560$	−3.97522	−0.167984
$561$	−25.1144	−1.06033
$562$	−2.15618	−0.0909528
$563$	−4.99675	−0.210588	−0.105294	−	0.994441i	$-0.533578\pi$
$563$	−4.99675	−0.210588	−0.105294	+	0.994441i	$0.533578\pi$
$564$	−1.68898	−0.0711187
$565$	−57.2548	−2.40873
$566$	−7.48037	−0.314423
$567$	1.00000	0.0419961
$568$	17.1685	0.720373
$569$	−26.4626	−1.10937	−0.554686	−	0.832060i	$-0.687161\pi$
$569$	−26.4626	−1.10937	−0.554686	+	0.832060i	$0.687161\pi$
$570$	−21.1658	−0.886536
$571$	16.4007	0.686349	0.343175	−	0.939272i	$-0.388498\pi$
$571$	16.4007	0.686349	0.343175	+	0.939272i	$0.388498\pi$
$572$	0	0
$573$	6.67101	0.278685
$574$	−4.02416	−0.167965
$575$	42.6999	1.78071
$576$	7.35804	0.306585
$577$	−10.3983	−0.432887	−0.216443	−	0.976295i	$-0.569446\pi$
$577$	−10.3983	−0.432887	−0.216443	+	0.976295i	$0.569446\pi$
$578$	−31.2555	−1.30006
$579$	−15.9900	−0.664522
$580$	−29.1980	−1.21238
$581$	15.6734	0.650243
$582$	4.37877	0.181506
$583$	17.9604	0.743846
$584$	20.3444	0.841859
$585$	0	0
$586$	2.93381	0.121195
$587$	−20.2156	−0.834388	−0.417194	−	0.908818i	$-0.636986\pi$
$587$	−20.2156	−0.834388	−0.417194	+	0.908818i	$0.636986\pi$
$588$	−0.945953	−0.0390104
$589$	−67.7082	−2.78987
$590$	18.7234	0.770831
$591$	−7.34567	−0.302160
$592$	0.362025	0.0148791
$593$	−0.815771	−0.0334997	−0.0167499	−	0.999860i	$-0.505332\pi$
$593$	−0.815771	−0.0334997	−0.0167499	+	0.999860i	$0.505332\pi$
$594$	−3.74338	−0.153593
$595$	−22.5680	−0.925199
$596$	−8.07136	−0.330616
$597$	−0.202957	−0.00830649
$598$	0	0
$599$	−17.0984	−0.698623	−0.349312	−	0.937007i	$-0.613585\pi$
$599$	−17.0984	−0.698623	−0.349312	+	0.937007i	$0.613585\pi$
$600$	17.3461	0.708153
$601$	−4.62318	−0.188584	−0.0942918	−	0.995545i	$-0.530059\pi$
$601$	−4.62318	−0.188584	−0.0942918	+	0.995545i	$0.530059\pi$
$602$	5.42469	0.221094
$603$	−12.7392	−0.518780
$604$	6.57507	0.267536
$605$	7.51743	0.305627
$606$	6.51538	0.264669
$607$	−41.9476	−1.70260	−0.851300	−	0.524679i	$-0.824185\pi$
$607$	−41.9476	−1.70260	−0.851300	+	0.524679i	$0.824185\pi$
$608$	−30.2238	−1.22574
$609$	9.42061	0.381742
$610$	−14.6184	−0.591881
$611$	0	0
$612$	6.51566	0.263380
$613$	−44.3300	−1.79047	−0.895237	−	0.445591i	$-0.852994\pi$
$613$	−44.3300	−1.79047	−0.895237	+	0.445591i	$0.852994\pi$
$614$	−30.6119	−1.23539
$615$	12.8425	0.517860
$616$	11.0278	0.444324
$617$	−10.6983	−0.430699	−0.215350	−	0.976537i	$-0.569089\pi$
$617$	−10.6983	−0.430699	−0.215350	+	0.976537i	$0.569089\pi$
$618$	10.1430	0.408010
$619$	9.90538	0.398131	0.199065	−	0.979986i	$-0.436209\pi$
$619$	9.90538	0.398131	0.199065	+	0.979986i	$0.436209\pi$
$620$	33.3516	1.33943
$621$	7.44525	0.298768
$622$	−1.75694	−0.0704471
$623$	−4.85592	−0.194548
$624$	0	0
$625$	−20.7836	−0.831345
$626$	1.79077	0.0715734
$627$	22.9421	0.916219
$628$	−12.0462	−0.480695
$629$	2.05528	0.0819493
$630$	−3.36384	−0.134018
$631$	37.4082	1.48920	0.744599	−	0.667512i	$-0.232641\pi$
$631$	37.4082	1.48920	0.744599	+	0.667512i	$0.232641\pi$
$632$	9.80956	0.390203
$633$	8.62718	0.342900
$634$	−1.68574	−0.0669491
$635$	−13.9409	−0.553226
$636$	−4.65964	−0.184767
$637$	0	0
$638$	−35.2649	−1.39615
$639$	5.67644	0.224556
$640$	6.72509	0.265833
$641$	9.02222	0.356356	0.178178	−	0.983998i	$-0.442980\pi$
$641$	9.02222	0.356356	0.178178	+	0.983998i	$0.442980\pi$
$642$	17.8020	0.702588
$643$	−37.7554	−1.48893	−0.744463	−	0.667663i	$-0.767295\pi$
$643$	−37.7554	−1.48893	−0.744463	+	0.667663i	$0.767295\pi$
$644$	−7.04286	−0.277527
$645$	−17.3121	−0.681663
$646$	44.4957	1.75066
$647$	16.3059	0.641051	0.320526	−	0.947240i	$-0.396140\pi$
$647$	16.3059	0.641051	0.320526	+	0.947240i	$0.396140\pi$
$648$	3.02452	0.118814
$649$	−20.2948	−0.796640
$650$	0	0
$651$	−10.7607	−0.421747
$652$	3.71148	0.145353
$653$	15.6155	0.611082	0.305541	−	0.952179i	$-0.401163\pi$
$653$	15.6155	0.611082	0.305541	+	0.952179i	$0.401163\pi$
$654$	8.16094	0.319118
$655$	12.7454	0.498003
$656$	−4.75557	−0.185674
$657$	6.72651	0.262426
$658$	−1.83309	−0.0714613
$659$	13.2703	0.516936	0.258468	−	0.966020i	$-0.416782\pi$
$659$	13.2703	0.516936	0.258468	+	0.966020i	$0.416782\pi$
$660$	−11.3008	−0.439882
$661$	−37.7744	−1.46925	−0.734627	−	0.678472i	$-0.762643\pi$
$661$	−37.7744	−1.46925	−0.734627	+	0.678472i	$0.762643\pi$
$662$	22.4893	0.874070
$663$	0	0
$664$	47.4045	1.83965
$665$	20.6160	0.799453
$666$	0.306346	0.0118707
$667$	70.1388	2.71579
$668$	5.10416	0.197486
$669$	1.66736	0.0644640
$670$	42.8525	1.65554
$671$	15.8452	0.611699
$672$	−4.80341	−0.185295
$673$	32.3855	1.24837	0.624185	−	0.781277i	$-0.285431\pi$
$673$	32.3855	1.24837	0.624185	+	0.781277i	$0.285431\pi$
$674$	−22.6211	−0.871333
$675$	5.73518	0.220747
$676$	0	0
$677$	22.4981	0.864672	0.432336	−	0.901713i	$-0.357689\pi$
$677$	22.4981	0.864672	0.432336	+	0.901713i	$0.357689\pi$
$678$	17.9406	0.689005
$679$	−4.26503	−0.163677
$680$	−68.2574	−2.61755
$681$	−22.3102	−0.854930
$682$	40.2816	1.54246
$683$	−10.4531	−0.399978	−0.199989	−	0.979798i	$-0.564091\pi$
$683$	−10.4531	−0.399978	−0.199989	+	0.979798i	$0.564091\pi$
$684$	−5.95208	−0.227583
$685$	−23.1900	−0.886045
$686$	−1.02667	−0.0391984
$687$	24.3840	0.930307
$688$	6.41064	0.244404
$689$	0	0
$690$	−25.0446	−0.953432
$691$	18.9877	0.722326	0.361163	−	0.932503i	$-0.382380\pi$
$691$	18.9877	0.722326	0.361163	+	0.932503i	$0.382380\pi$
$692$	−1.92124	−0.0730347
$693$	3.64615	0.138506
$694$	12.1133	0.459813
$695$	51.8409	1.96644
$696$	28.4928	1.08002
$697$	−26.9982	−1.02263
$698$	0.661653	0.0250439
$699$	−17.2618	−0.652903
$700$	−5.42521	−0.205054
$701$	−24.2484	−0.915848	−0.457924	−	0.888991i	$-0.651407\pi$
$701$	−24.2484	−0.915848	−0.457924	+	0.888991i	$0.651407\pi$
$702$	0	0
$703$	−1.87750	−0.0708114
$704$	26.8285	1.01114
$705$	5.85004	0.220325
$706$	−24.9975	−0.940792
$707$	−6.34614	−0.238671
$708$	5.26526	0.197881
$709$	−44.4465	−1.66922	−0.834611	−	0.550839i	$-0.814308\pi$
$709$	−44.4465	−1.66922	−0.834611	+	0.550839i	$0.814308\pi$
$710$	−19.0946	−0.716607
$711$	3.24335	0.121635
$712$	−14.6868	−0.550411
$713$	−80.1164	−3.00038
$714$	7.07162	0.264649
$715$	0	0
$716$	−11.4296	−0.427143
$717$	−6.12302	−0.228668
$718$	0.167376	0.00624640
$719$	5.93676	0.221404	0.110702	−	0.993854i	$-0.464690\pi$
$719$	5.93676	0.221404	0.110702	+	0.993854i	$0.464690\pi$
$720$	−3.97522	−0.148148
$721$	−9.87950	−0.367932
$722$	−21.1403	−0.786760
$723$	−4.04969	−0.150610
$724$	−16.6896	−0.620264
$725$	54.0289	2.00658
$726$	−2.35556	−0.0874232
$727$	27.7128	1.02781	0.513905	−	0.857847i	$-0.328198\pi$
$727$	27.7128	1.02781	0.513905	+	0.857847i	$0.328198\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−22.6269	−0.837458
$731$	36.3943	1.34609
$732$	−4.11088	−0.151942
$733$	−22.0420	−0.814141	−0.407071	−	0.913397i	$-0.633450\pi$
$733$	−22.0420	−0.814141	−0.407071	+	0.913397i	$0.633450\pi$
$734$	−18.6242	−0.687430
$735$	3.27646	0.120854
$736$	−35.7626	−1.31823
$737$	−46.4489	−1.71097
$738$	−4.02416	−0.148131
$739$	0.984398	0.0362117	0.0181058	−	0.999836i	$-0.494236\pi$
$739$	0.984398	0.0362117	0.0181058	+	0.999836i	$0.494236\pi$
$740$	0.924817	0.0339969
$741$	0	0
$742$	−5.05724	−0.185657
$743$	−36.9260	−1.35468	−0.677341	−	0.735669i	$-0.736868\pi$
$743$	−36.9260	−1.35468	−0.677341	+	0.735669i	$0.736868\pi$
$744$	−32.5460	−1.19320
$745$	27.9564	1.02424
$746$	−4.40194	−0.161167
$747$	15.6734	0.573460
$748$	23.7570	0.868644
$749$	−17.3396	−0.633574
$750$	−2.47302	−0.0903020
$751$	−2.42350	−0.0884349	−0.0442174	−	0.999022i	$-0.514079\pi$
$751$	−2.42350	−0.0884349	−0.0442174	+	0.999022i	$0.514079\pi$
$752$	−2.16626	−0.0789954
$753$	17.6643	0.643722
$754$	0	0
$755$	−22.7738	−0.828824
$756$	−0.945953	−0.0344040
$757$	17.2323	0.626320	0.313160	−	0.949700i	$-0.398612\pi$
$757$	17.2323	0.626320	0.313160	+	0.949700i	$0.398612\pi$
$758$	22.2980	0.809898
$759$	27.1465	0.985355
$760$	62.3533	2.26179
$761$	25.2003	0.913509	0.456754	−	0.889593i	$-0.349012\pi$
$761$	25.2003	0.913509	0.456754	+	0.889593i	$0.349012\pi$
$762$	4.36832	0.158248
$763$	−7.94895	−0.287771
$764$	−6.31046	−0.228304
$765$	−22.5680	−0.815949
$766$	−23.0705	−0.833569
$767$	0	0
$768$	−16.8234	−0.607061
$769$	15.1674	0.546950	0.273475	−	0.961879i	$-0.411827\pi$
$769$	15.1674	0.546950	0.273475	+	0.961879i	$0.411827\pi$
$770$	−12.2650	−0.442001
$771$	−1.45219	−0.0522995
$772$	15.1258	0.544389
$773$	39.0898	1.40596	0.702981	−	0.711209i	$-0.251852\pi$
$773$	39.0898	1.40596	0.702981	+	0.711209i	$0.251852\pi$
$774$	5.42469	0.194986
$775$	−61.7148	−2.21686
$776$	−12.8996	−0.463070
$777$	−0.298388	−0.0107046
$778$	3.37159	0.120877
$779$	24.6629	0.883641
$780$	0	0
$781$	20.6971	0.740601
$782$	52.6500	1.88276
$783$	9.42061	0.336665
$784$	−1.21327	−0.0433310
$785$	41.7238	1.48919
$786$	−3.99373	−0.142452
$787$	−34.6046	−1.23352	−0.616761	−	0.787151i	$-0.711555\pi$
$787$	−34.6046	−1.23352	−0.616761	+	0.787151i	$0.711555\pi$
$788$	6.94865	0.247536
$789$	3.02641	0.107743
$790$	−10.9101	−0.388164
$791$	−17.4746	−0.621326
$792$	11.0278	0.391857
$793$	0	0
$794$	4.57958	0.162523
$795$	16.1394	0.572406
$796$	0.191988	0.00680483
$797$	−26.6138	−0.942708	−0.471354	−	0.881944i	$-0.656235\pi$
$797$	−26.6138	−0.942708	−0.471354	+	0.881944i	$0.656235\pi$
$798$	−6.45995	−0.228680
$799$	−12.2982	−0.435081
$800$	−27.5484	−0.973983
$801$	−4.85592	−0.171575
$802$	3.04379	0.107480
$803$	24.5258	0.865498
$804$	12.0507	0.424994
$805$	24.3941	0.859778
$806$	0	0
$807$	−8.80840	−0.310070
$808$	−19.1940	−0.675242
$809$	−42.4083	−1.49100	−0.745499	−	0.666507i	$-0.767789\pi$
$809$	−42.4083	−1.49100	−0.745499	+	0.666507i	$0.767789\pi$
$810$	−3.36384	−0.118193
$811$	2.66908	0.0937242	0.0468621	−	0.998901i	$-0.485078\pi$
$811$	2.66908	0.0937242	0.0468621	+	0.998901i	$0.485078\pi$
$812$	−8.91145	−0.312731
$813$	−2.79485	−0.0980198
$814$	1.11698	0.0391502
$815$	−12.8553	−0.450301
$816$	8.35691	0.292550
$817$	−33.2463	−1.16314
$818$	−20.0572	−0.701284
$819$	0	0
$820$	−12.1484	−0.424241
$821$	−26.1841	−0.913831	−0.456915	−	0.889510i	$-0.651046\pi$
$821$	−26.1841	−0.913831	−0.456915	+	0.889510i	$0.651046\pi$
$822$	7.26652	0.253449
$823$	26.1469	0.911423	0.455712	−	0.890128i	$-0.349385\pi$
$823$	26.1469	0.911423	0.455712	+	0.890128i	$0.349385\pi$
$824$	−29.8807	−1.04094
$825$	20.9113	0.728038
$826$	5.71453	0.198834
$827$	−23.2089	−0.807053	−0.403526	−	0.914968i	$-0.632216\pi$
$827$	−23.2089	−0.807053	−0.403526	+	0.914968i	$0.632216\pi$
$828$	−7.04286	−0.244756
$829$	−18.1602	−0.630728	−0.315364	−	0.948971i	$-0.602127\pi$
$829$	−18.1602	−0.630728	−0.315364	+	0.948971i	$0.602127\pi$
$830$	−52.7228	−1.83003
$831$	24.2433	0.840989
$832$	0	0
$833$	−6.88794	−0.238653
$834$	−16.2442	−0.562490
$835$	−17.6791	−0.611810
$836$	−21.7021	−0.750584
$837$	−10.7607	−0.371946
$838$	26.6205	0.919588
$839$	−1.18110	−0.0407762	−0.0203881	−	0.999792i	$-0.506490\pi$
$839$	−1.18110	−0.0407762	−0.0203881	+	0.999792i	$0.506490\pi$
$840$	9.90970	0.341917
$841$	59.7479	2.06027
$842$	6.77429	0.233457
$843$	2.10017	0.0723336
$844$	−8.16090	−0.280910
$845$	0	0
$846$	−1.83309	−0.0630230
$847$	2.29438	0.0788358
$848$	−5.97640	−0.205231
$849$	7.28606	0.250057
$850$	40.5570	1.39109
$851$	−2.22158	−0.0761546
$852$	−5.36964	−0.183961
$853$	−15.2735	−0.522955	−0.261477	−	0.965210i	$-0.584210\pi$
$853$	−15.2735	−0.522955	−0.261477	+	0.965210i	$0.584210\pi$
$854$	−4.46164	−0.152674
$855$	20.6160	0.705051
$856$	−52.4438	−1.79249
$857$	5.54169	0.189301	0.0946503	−	0.995511i	$-0.469827\pi$
$857$	5.54169	0.189301	0.0946503	+	0.995511i	$0.469827\pi$
$858$	0	0
$859$	30.5667	1.04292	0.521461	−	0.853275i	$-0.325387\pi$
$859$	30.5667	1.04292	0.521461	+	0.853275i	$0.325387\pi$
$860$	16.3764	0.558431
$861$	3.91963	0.133581
$862$	−10.0254	−0.341467
$863$	−46.0379	−1.56715	−0.783574	−	0.621299i	$-0.786605\pi$
$863$	−46.0379	−1.56715	−0.783574	+	0.621299i	$0.786605\pi$
$864$	−4.80341	−0.163415
$865$	6.65453	0.226261
$866$	−32.0032	−1.08751
$867$	30.4437	1.03392
$868$	10.1792	0.345503
$869$	11.8257	0.401160
$870$	−31.6894	−1.07437
$871$	0	0
$872$	−24.0417	−0.814156
$873$	−4.26503	−0.144349
$874$	−48.0960	−1.62687
$875$	2.40879	0.0814318
$876$	−6.36296	−0.214985
$877$	14.8745	0.502277	0.251138	−	0.967951i	$-0.419195\pi$
$877$	14.8745	0.502277	0.251138	+	0.967951i	$0.419195\pi$
$878$	−0.0719390	−0.00242782
$879$	−2.85760	−0.0963845
$880$	−14.4942	−0.488601
$881$	−16.6031	−0.559371	−0.279686	−	0.960092i	$-0.590230\pi$
$881$	−16.6031	−0.559371	−0.279686	+	0.960092i	$0.590230\pi$
$882$	−1.02667	−0.0345697
$883$	−24.9994	−0.841298	−0.420649	−	0.907223i	$-0.638198\pi$
$883$	−24.9994	−0.841298	−0.420649	+	0.907223i	$0.638198\pi$
$884$	0	0
$885$	−18.2371	−0.613032
$886$	14.2768	0.479639
$887$	−2.86708	−0.0962672	−0.0481336	−	0.998841i	$-0.515327\pi$
$887$	−2.86708	−0.0962672	−0.0481336	+	0.998841i	$0.515327\pi$
$888$	−0.902480	−0.0302852
$889$	−4.25486	−0.142703
$890$	16.3345	0.547534
$891$	3.64615	0.122150
$892$	−1.57725	−0.0528102
$893$	11.2345	0.375948
$894$	−8.76006	−0.292980
$895$	39.5882	1.32329
$896$	2.05255	0.0685708
$897$	0	0
$898$	43.0227	1.43568
$899$	−101.373	−3.38097
$900$	−5.42521	−0.180840
$901$	−33.9291	−1.13034
$902$	−14.6727	−0.488547
$903$	−5.28378	−0.175833
$904$	−52.8522	−1.75784
$905$	57.8071	1.92157
$906$	7.13610	0.237081
$907$	−21.7144	−0.721014	−0.360507	−	0.932757i	$-0.617396\pi$
$907$	−21.7144	−0.721014	−0.360507	+	0.932757i	$0.617396\pi$
$908$	21.1044	0.700375
$909$	−6.34614	−0.210488
$910$	0	0
$911$	15.6928	0.519925	0.259962	−	0.965619i	$-0.416290\pi$
$911$	15.6928	0.519925	0.259962	+	0.965619i	$0.416290\pi$
$912$	−7.63407	−0.252789
$913$	57.1476	1.89131
$914$	−12.2410	−0.404898
$915$	14.2387	0.470716
$916$	−23.0661	−0.762125
$917$	3.88999	0.128459
$918$	7.07162	0.233398
$919$	−20.1788	−0.665637	−0.332819	−	0.942991i	$-0.608000\pi$
$919$	−20.1788	−0.665637	−0.332819	+	0.942991i	$0.608000\pi$
$920$	73.7802	2.43246
$921$	29.8167	0.982494
$922$	18.5489	0.610877
$923$	0	0
$924$	−3.44908	−0.113466
$925$	−1.71131	−0.0562675
$926$	−7.67489	−0.252212
$927$	−9.87950	−0.324485
$928$	−45.2510	−1.48544
$929$	34.7349	1.13961	0.569807	−	0.821779i	$-0.307018\pi$
$929$	34.7349	1.13961	0.569807	+	0.821779i	$0.307018\pi$
$930$	36.1974	1.18696
$931$	6.29215	0.206217
$932$	16.3289	0.534871
$933$	1.71131	0.0560257
$934$	−33.9578	−1.11113
$935$	−82.2863	−2.69105
$936$	0	0
$937$	−43.6472	−1.42589	−0.712947	−	0.701218i	$-0.752640\pi$
$937$	−43.6472	−1.42589	−0.712947	+	0.701218i	$0.752640\pi$
$938$	13.0789	0.427042
$939$	−1.74425	−0.0569215
$940$	−5.53386	−0.180495
$941$	−34.2059	−1.11508	−0.557541	−	0.830150i	$-0.688255\pi$
$941$	−34.2059	−1.11508	−0.557541	+	0.830150i	$0.688255\pi$
$942$	−13.0740	−0.425975
$943$	29.1827	0.950318
$944$	6.75316	0.219797
$945$	3.27646	0.106583
$946$	19.7792	0.643078
$947$	47.6701	1.54907	0.774534	−	0.632532i	$-0.217984\pi$
$947$	47.6701	1.54907	0.774534	+	0.632532i	$0.217984\pi$
$948$	−3.06805	−0.0996458
$949$	0	0
$950$	−37.0490	−1.20203
$951$	1.64195	0.0532438
$952$	−20.8327	−0.675191
$953$	−48.2855	−1.56412	−0.782060	−	0.623204i	$-0.785831\pi$
$953$	−48.2855	−1.56412	−0.782060	+	0.623204i	$0.785831\pi$
$954$	−5.05724	−0.163734
$955$	21.8573	0.707285
$956$	5.79209	0.187329
$957$	34.3489	1.11034
$958$	10.7189	0.346312
$959$	−7.07777	−0.228553
$960$	24.1083	0.778093
$961$	84.7935	2.73528
$962$	0	0
$963$	−17.3396	−0.558760
$964$	3.83082	0.123382
$965$	−52.3906	−1.68651
$966$	−7.64380	−0.245935
$967$	−2.78480	−0.0895533	−0.0447766	−	0.998997i	$-0.514258\pi$
$967$	−2.78480	−0.0895533	−0.0447766	+	0.998997i	$0.514258\pi$
$968$	6.93938	0.223040
$969$	−43.3399	−1.39228
$970$	14.3468	0.460650
$971$	6.50695	0.208818	0.104409	−	0.994534i	$-0.466705\pi$
$971$	6.50695	0.208818	0.104409	+	0.994534i	$0.466705\pi$
$972$	−0.945953	−0.0303414
$973$	15.8222	0.507238
$974$	−40.4042	−1.29463
$975$	0	0
$976$	−5.27256	−0.168771
$977$	−25.8860	−0.828165	−0.414083	−	0.910239i	$-0.635898\pi$
$977$	−25.8860	−0.828165	−0.414083	+	0.910239i	$0.635898\pi$
$978$	4.02817	0.128807
$979$	−17.7054	−0.565866
$980$	−3.09937	−0.0990059
$981$	−7.94895	−0.253791
$982$	−33.0958	−1.05613
$983$	−23.2474	−0.741476	−0.370738	−	0.928738i	$-0.620895\pi$
$983$	−23.2474	−0.741476	−0.370738	+	0.928738i	$0.620895\pi$
$984$	11.8550	0.377923
$985$	−24.0678	−0.766863
$986$	66.6190	2.12158
$987$	1.78548	0.0568323
$988$	0	0
$989$	−39.3391	−1.25091
$990$	−12.2650	−0.389808
$991$	44.6377	1.41796	0.708981	−	0.705228i	$-0.249155\pi$
$991$	44.6377	1.41796	0.708981	+	0.705228i	$0.249155\pi$
$992$	51.6882	1.64110
$993$	−21.9051	−0.695137
$994$	−5.82782	−0.184847
$995$	−0.664981	−0.0210813
$996$	−14.8263	−0.469790
$997$	−15.0365	−0.476210	−0.238105	−	0.971239i	$-0.576526\pi$
$997$	−15.0365	−0.476210	−0.238105	+	0.971239i	$0.576526\pi$
$998$	−6.49280	−0.205526
$999$	−0.298388	−0.00944058

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bg.1.7	✓	15
13.12	even	2		3549.2.a.bh.1.9	yes	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3549.2.a.bg.1.7	✓	15	1.1	even	1	trivial
3549.2.a.bh.1.9	yes	15	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q-1.02667 q^{2} +1.00000 q^{3} -0.945953 q^{4} +3.27646 q^{5} -1.02667 q^{6} +1.00000 q^{7} +3.02452 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.02667 q^{2} +1.00000 q^{3} -0.945953 q^{4} +3.27646 q^{5} -1.02667 q^{6} +1.00000 q^{7} +3.02452 q^{8} +1.00000 q^{9} -3.36384 q^{10} +3.64615 q^{11} -0.945953 q^{12} -1.02667 q^{14} +3.27646 q^{15} -1.21327 q^{16} -6.88794 q^{17} -1.02667 q^{18} +6.29215 q^{19} -3.09937 q^{20} +1.00000 q^{21} -3.74338 q^{22} +7.44525 q^{23} +3.02452 q^{24} +5.73518 q^{25} +1.00000 q^{27} -0.945953 q^{28} +9.42061 q^{29} -3.36384 q^{30} -10.7607 q^{31} -4.80341 q^{32} +3.64615 q^{33} +7.07162 q^{34} +3.27646 q^{35} -0.945953 q^{36} -0.298388 q^{37} -6.45995 q^{38} +9.90970 q^{40} +3.91963 q^{41} -1.02667 q^{42} -5.28378 q^{43} -3.44908 q^{44} +3.27646 q^{45} -7.64380 q^{46} +1.78548 q^{47} -1.21327 q^{48} +1.00000 q^{49} -5.88813 q^{50} -6.88794 q^{51} +4.92587 q^{53} -1.02667 q^{54} +11.9464 q^{55} +3.02452 q^{56} +6.29215 q^{57} -9.67184 q^{58} -5.56609 q^{59} -3.09937 q^{60} +4.34575 q^{61} +11.0477 q^{62} +1.00000 q^{63} +7.35804 q^{64} -3.74338 q^{66} -12.7392 q^{67} +6.51566 q^{68} +7.44525 q^{69} -3.36384 q^{70} +5.67644 q^{71} +3.02452 q^{72} +6.72651 q^{73} +0.306346 q^{74} +5.73518 q^{75} -5.95208 q^{76} +3.64615 q^{77} +3.24335 q^{79} -3.97522 q^{80} +1.00000 q^{81} -4.02416 q^{82} +15.6734 q^{83} -0.945953 q^{84} -22.5680 q^{85} +5.42469 q^{86} +9.42061 q^{87} +11.0278 q^{88} -4.85592 q^{89} -3.36384 q^{90} -7.04286 q^{92} -10.7607 q^{93} -1.83309 q^{94} +20.6160 q^{95} -4.80341 q^{96} -4.26503 q^{97} -1.02667 q^{98} +3.64615 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 2 q^{2} + 15 q^{3} + 28 q^{4} + 9 q^{5} - 2 q^{6} + 15 q^{7} - 9 q^{8} + 15 q^{9}+O(q^{10}) \) 15 * q - 2 * q^2 + 15 * q^3 + 28 * q^4 + 9 * q^5 - 2 * q^6 + 15 * q^7 - 9 * q^8 + 15 * q^9	\( 15 q - 2 q^{2} + 15 q^{3} + 28 q^{4} + 9 q^{5} - 2 q^{6} + 15 q^{7} - 9 q^{8} + 15 q^{9} + 21 q^{10} - 5 q^{11} + 28 q^{12} - 2 q^{14} + 9 q^{15} + 50 q^{16} - q^{17} - 2 q^{18} - 3 q^{19} + 23 q^{20} + 15 q^{21} + 21 q^{22} + 4 q^{23} - 9 q^{24} + 50 q^{25} + 15 q^{27} + 28 q^{28} + 9 q^{29} + 21 q^{30} - 7 q^{31} - 35 q^{32} - 5 q^{33} + 2 q^{34} + 9 q^{35} + 28 q^{36} - 17 q^{37} - 12 q^{38} + 46 q^{40} + 22 q^{41} - 2 q^{42} + 36 q^{43} - 29 q^{44} + 9 q^{45} + q^{46} + 12 q^{47} + 50 q^{48} + 15 q^{49} - 53 q^{50} - q^{51} - 5 q^{53} - 2 q^{54} + 43 q^{55} - 9 q^{56} - 3 q^{57} - 29 q^{58} + 29 q^{59} + 23 q^{60} + 12 q^{61} + 14 q^{62} + 15 q^{63} + 95 q^{64} + 21 q^{66} + 12 q^{67} - 16 q^{68} + 4 q^{69} + 21 q^{70} - 36 q^{71} - 9 q^{72} + 29 q^{73} - 5 q^{74} + 50 q^{75} - 25 q^{76} - 5 q^{77} + 35 q^{79} + 89 q^{80} + 15 q^{81} + 51 q^{82} + 10 q^{83} + 28 q^{84} - 23 q^{85} - 19 q^{86} + 9 q^{87} + 73 q^{88} - 25 q^{89} + 21 q^{90} - 31 q^{92} - 7 q^{93} - 19 q^{94} - 7 q^{95} - 35 q^{96} + 26 q^{97} - 2 q^{98} - 5 q^{99}+O(q^{100}) \) 15 * q - 2 * q^2 + 15 * q^3 + 28 * q^4 + 9 * q^5 - 2 * q^6 + 15 * q^7 - 9 * q^8 + 15 * q^9 + 21 * q^10 - 5 * q^11 + 28 * q^12 - 2 * q^14 + 9 * q^15 + 50 * q^16 - q^17 - 2 * q^18 - 3 * q^19 + 23 * q^20 + 15 * q^21 + 21 * q^22 + 4 * q^23 - 9 * q^24 + 50 * q^25 + 15 * q^27 + 28 * q^28 + 9 * q^29 + 21 * q^30 - 7 * q^31 - 35 * q^32 - 5 * q^33 + 2 * q^34 + 9 * q^35 + 28 * q^36 - 17 * q^37 - 12 * q^38 + 46 * q^40 + 22 * q^41 - 2 * q^42 + 36 * q^43 - 29 * q^44 + 9 * q^45 + q^46 + 12 * q^47 + 50 * q^48 + 15 * q^49 - 53 * q^50 - q^51 - 5 * q^53 - 2 * q^54 + 43 * q^55 - 9 * q^56 - 3 * q^57 - 29 * q^58 + 29 * q^59 + 23 * q^60 + 12 * q^61 + 14 * q^62 + 15 * q^63 + 95 * q^64 + 21 * q^66 + 12 * q^67 - 16 * q^68 + 4 * q^69 + 21 * q^70 - 36 * q^71 - 9 * q^72 + 29 * q^73 - 5 * q^74 + 50 * q^75 - 25 * q^76 - 5 * q^77 + 35 * q^79 + 89 * q^80 + 15 * q^81 + 51 * q^82 + 10 * q^83 + 28 * q^84 - 23 * q^85 - 19 * q^86 + 9 * q^87 + 73 * q^88 - 25 * q^89 + 21 * q^90 - 31 * q^92 - 7 * q^93 - 19 * q^94 - 7 * q^95 - 35 * q^96 + 26 * q^97 - 2 * q^98 - 5 * q^99

Introduction

L-functions

Modular forms

Varieties

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