LMFDB - Embedded newform 3549.2.a.bh.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:	$15$
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			1.2
Root			$-2.60515$ 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)

$f(q)$	$=$	$q-2.60515 q^{2} +1.00000 q^{3} +4.78683 q^{4} -1.51368 q^{5} -2.60515 q^{6} -1.00000 q^{7} -7.26012 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.60515 q^{2} +1.00000 q^{3} +4.78683 q^{4} -1.51368 q^{5} -2.60515 q^{6} -1.00000 q^{7} -7.26012 q^{8} +1.00000 q^{9} +3.94338 q^{10} -0.949498 q^{11} +4.78683 q^{12} +2.60515 q^{14} -1.51368 q^{15} +9.34008 q^{16} +5.20785 q^{17} -2.60515 q^{18} +5.53387 q^{19} -7.24575 q^{20} -1.00000 q^{21} +2.47359 q^{22} -3.94826 q^{23} -7.26012 q^{24} -2.70876 q^{25} +1.00000 q^{27} -4.78683 q^{28} +5.11085 q^{29} +3.94338 q^{30} +9.26508 q^{31} -9.81211 q^{32} -0.949498 q^{33} -13.5673 q^{34} +1.51368 q^{35} +4.78683 q^{36} +7.19721 q^{37} -14.4166 q^{38} +10.9895 q^{40} -2.01650 q^{41} +2.60515 q^{42} -10.1790 q^{43} -4.54509 q^{44} -1.51368 q^{45} +10.2858 q^{46} -6.97453 q^{47} +9.34008 q^{48} +1.00000 q^{49} +7.05674 q^{50} +5.20785 q^{51} -11.2203 q^{53} -2.60515 q^{54} +1.43724 q^{55} +7.26012 q^{56} +5.53387 q^{57} -13.3146 q^{58} -6.64104 q^{59} -7.24575 q^{60} -3.07927 q^{61} -24.1370 q^{62} -1.00000 q^{63} +6.88190 q^{64} +2.47359 q^{66} +12.8973 q^{67} +24.9291 q^{68} -3.94826 q^{69} -3.94338 q^{70} -7.77833 q^{71} -7.26012 q^{72} -8.64459 q^{73} -18.7499 q^{74} -2.70876 q^{75} +26.4897 q^{76} +0.949498 q^{77} +15.2689 q^{79} -14.1379 q^{80} +1.00000 q^{81} +5.25329 q^{82} -11.7165 q^{83} -4.78683 q^{84} -7.88304 q^{85} +26.5178 q^{86} +5.11085 q^{87} +6.89347 q^{88} +8.13994 q^{89} +3.94338 q^{90} -18.8997 q^{92} +9.26508 q^{93} +18.1697 q^{94} -8.37653 q^{95} -9.81211 q^{96} +14.8803 q^{97} -2.60515 q^{98} -0.949498 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.60515	−1.84212	−0.921061	−	0.389418i	$-0.872676\pi$
$2$	−2.60515	−1.84212	−0.921061	+	0.389418i	$0.872676\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.78683	2.39342
$5$	−1.51368	−0.676940	−0.338470	−	0.940977i	$-0.609909\pi$
$5$	−1.51368	−0.676940	−0.338470	+	0.940977i	$0.609909\pi$
$6$	−2.60515	−1.06355
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−7.26012	−2.56684
$9$	1.00000	0.333333
$10$	3.94338	1.24701
$11$	−0.949498	−0.286284	−0.143142	−	0.989702i	$-0.545721\pi$
$11$	−0.949498	−0.286284	−0.143142	+	0.989702i	$0.545721\pi$
$12$	4.78683	1.38184
$13$	0	0
$13$	0	0
$14$	2.60515	0.696257
$15$	−1.51368	−0.390832
$16$	9.34008	2.33502
$17$	5.20785	1.26309	0.631545	−	0.775340i	$-0.282421\pi$
$17$	5.20785	1.26309	0.631545	+	0.775340i	$0.282421\pi$
$18$	−2.60515	−0.614041
$19$	5.53387	1.26956	0.634778	−	0.772695i	$-0.281092\pi$
$19$	5.53387	1.26956	0.634778	+	0.772695i	$0.281092\pi$
$20$	−7.24575	−1.62020
$21$	−1.00000	−0.218218
$22$	2.47359	0.527371
$23$	−3.94826	−0.823269	−0.411635	−	0.911349i	$-0.635042\pi$
$23$	−3.94826	−0.823269	−0.411635	+	0.911349i	$0.635042\pi$
$24$	−7.26012	−1.48197
$25$	−2.70876	−0.541752
$26$	0	0
$27$	1.00000	0.192450
$28$	−4.78683	−0.904626
$29$	5.11085	0.949062	0.474531	−	0.880239i	$-0.342618\pi$
$29$	5.11085	0.949062	0.474531	+	0.880239i	$0.342618\pi$
$30$	3.94338	0.719960
$31$	9.26508	1.66406	0.832028	−	0.554733i	$-0.187180\pi$
$31$	9.26508	1.66406	0.832028	+	0.554733i	$0.187180\pi$
$32$	−9.81211	−1.73455
$33$	−0.949498	−0.165286
$34$	−13.5673	−2.32676
$35$	1.51368	0.255859
$36$	4.78683	0.797805
$37$	7.19721	1.18321	0.591607	−	0.806226i	$-0.298494\pi$
$37$	7.19721	1.18321	0.591607	+	0.806226i	$0.298494\pi$
$38$	−14.4166	−2.33868
$39$	0	0
$40$	10.9895	1.73760
$41$	−2.01650	−0.314924	−0.157462	−	0.987525i	$-0.550331\pi$
$41$	−2.01650	−0.314924	−0.157462	+	0.987525i	$0.550331\pi$
$42$	2.60515	0.401984
$43$	−10.1790	−1.55228	−0.776138	−	0.630563i	$-0.782824\pi$
$43$	−10.1790	−1.55228	−0.776138	+	0.630563i	$0.782824\pi$
$44$	−4.54509	−0.685197
$45$	−1.51368	−0.225647
$46$	10.2858	1.51656
$47$	−6.97453	−1.01734	−0.508670	−	0.860962i	$-0.669863\pi$
$47$	−6.97453	−1.01734	−0.508670	+	0.860962i	$0.669863\pi$
$48$	9.34008	1.34812
$49$	1.00000	0.142857
$50$	7.05674	0.997973
$51$	5.20785	0.729245
$52$	0	0
$53$	−11.2203	−1.54123	−0.770615	−	0.637301i	$-0.780051\pi$
$53$	−11.2203	−1.54123	−0.770615	+	0.637301i	$0.780051\pi$
$54$	−2.60515	−0.354517
$55$	1.43724	0.193797
$56$	7.26012	0.970175
$57$	5.53387	0.732979
$58$	−13.3146	−1.74829
$59$	−6.64104	−0.864590	−0.432295	−	0.901732i	$-0.642296\pi$
$59$	−6.64104	−0.864590	−0.432295	+	0.901732i	$0.642296\pi$
$60$	−7.24575	−0.935422
$61$	−3.07927	−0.394260	−0.197130	−	0.980377i	$-0.563162\pi$
$61$	−3.07927	−0.394260	−0.197130	+	0.980377i	$0.563162\pi$
$62$	−24.1370	−3.06540
$63$	−1.00000	−0.125988
$64$	6.88190	0.860238
$65$	0	0
$66$	2.47359	0.304478
$67$	12.8973	1.57565	0.787826	−	0.615898i	$-0.211207\pi$
$67$	12.8973	1.57565	0.787826	+	0.615898i	$0.211207\pi$
$68$	24.9291	3.02310
$69$	−3.94826	−0.475315
$70$	−3.94338	−0.471324
$71$	−7.77833	−0.923118	−0.461559	−	0.887110i	$-0.652710\pi$
$71$	−7.77833	−0.923118	−0.461559	+	0.887110i	$0.652710\pi$
$72$	−7.26012	−0.855614
$73$	−8.64459	−1.01177	−0.505886	−	0.862600i	$-0.668834\pi$
$73$	−8.64459	−1.01177	−0.505886	+	0.862600i	$0.668834\pi$
$74$	−18.7499	−2.17963
$75$	−2.70876	−0.312781
$76$	26.4897	3.03857
$77$	0.949498	0.108205
$78$	0	0
$79$	15.2689	1.71788	0.858941	−	0.512075i	$-0.171123\pi$
$79$	15.2689	1.71788	0.858941	+	0.512075i	$0.171123\pi$
$80$	−14.1379	−1.58067
$81$	1.00000	0.111111
$82$	5.25329	0.580129
$83$	−11.7165	−1.28605	−0.643024	−	0.765846i	$-0.722321\pi$
$83$	−11.7165	−1.28605	−0.643024	+	0.765846i	$0.722321\pi$
$84$	−4.78683	−0.522286
$85$	−7.88304	−0.855036
$86$	26.5178	2.85948
$87$	5.11085	0.547941
$88$	6.89347	0.734847
$89$	8.13994	0.862832	0.431416	−	0.902153i	$-0.358014\pi$
$89$	8.13994	0.862832	0.431416	+	0.902153i	$0.358014\pi$
$90$	3.94338	0.415669
$91$	0	0
$92$	−18.8997	−1.97043
$93$	9.26508	0.960744
$94$	18.1697	1.87406
$95$	−8.37653	−0.859414
$96$	−9.81211	−1.00144
$97$	14.8803	1.51086	0.755431	−	0.655229i	$-0.227428\pi$
$97$	14.8803	1.51086	0.755431	+	0.655229i	$0.227428\pi$
$98$	−2.60515	−0.263160
$99$	−0.949498	−0.0954281
$100$	−12.9664	−1.29664
$101$	−0.878824	−0.0874463	−0.0437231	−	0.999044i	$-0.513922\pi$
$101$	−0.878824	−0.0874463	−0.0437231	+	0.999044i	$0.513922\pi$
$102$	−13.5673	−1.34336
$103$	4.72585	0.465652	0.232826	−	0.972518i	$-0.425203\pi$
$103$	4.72585	0.465652	0.232826	+	0.972518i	$0.425203\pi$
$104$	0	0
$105$	1.51368	0.147720
$106$	29.2307	2.83914
$107$	14.5988	1.41132	0.705658	−	0.708553i	$-0.250652\pi$
$107$	14.5988	1.41132	0.705658	+	0.708553i	$0.250652\pi$
$108$	4.78683	0.460613
$109$	−14.4751	−1.38646	−0.693232	−	0.720714i	$-0.743814\pi$
$109$	−14.4751	−1.38646	−0.693232	+	0.720714i	$0.743814\pi$
$110$	−3.74423	−0.356999
$111$	7.19721	0.683129
$112$	−9.34008	−0.882555
$113$	−0.659804	−0.0620692	−0.0310346	−	0.999518i	$-0.509880\pi$
$113$	−0.659804	−0.0620692	−0.0310346	+	0.999518i	$0.509880\pi$
$114$	−14.4166	−1.35024
$115$	5.97642	0.557304
$116$	24.4648	2.27150
$117$	0	0
$118$	17.3009	1.59268
$119$	−5.20785	−0.477403
$120$	10.9895	1.00320
$121$	−10.0985	−0.918041
$122$	8.02197	0.726275
$123$	−2.01650	−0.181822
$124$	44.3503	3.98278
$125$	11.6686	1.04367
$126$	2.60515	0.232086
$127$	3.18132	0.282296	0.141148	−	0.989988i	$-0.454921\pi$
$127$	3.18132	0.282296	0.141148	+	0.989988i	$0.454921\pi$
$128$	1.69580	0.149889
$129$	−10.1790	−0.896207
$130$	0	0
$131$	22.2245	1.94177	0.970883	−	0.239555i	$-0.0770016\pi$
$131$	22.2245	1.94177	0.970883	+	0.239555i	$0.0770016\pi$
$132$	−4.54509	−0.395599
$133$	−5.53387	−0.479847
$134$	−33.5994	−2.90254
$135$	−1.51368	−0.130277
$136$	−37.8096	−3.24215
$137$	13.2437	1.13148	0.565742	−	0.824583i	$-0.308590\pi$
$137$	13.2437	1.13148	0.565742	+	0.824583i	$0.308590\pi$
$138$	10.2858	0.875588
$139$	14.4676	1.22713	0.613564	−	0.789645i	$-0.289735\pi$
$139$	14.4676	1.22713	0.613564	+	0.789645i	$0.289735\pi$
$140$	7.24575	0.612378
$141$	−6.97453	−0.587361
$142$	20.2637	1.70050
$143$	0	0
$144$	9.34008	0.778340
$145$	−7.73622	−0.642458
$146$	22.5205	1.86381
$147$	1.00000	0.0824786
$148$	34.4518	2.83192
$149$	15.5692	1.27548	0.637740	−	0.770252i	$-0.279869\pi$
$149$	15.5692	1.27548	0.637740	+	0.770252i	$0.279869\pi$
$150$	7.05674	0.576180
$151$	−7.76523	−0.631926	−0.315963	−	0.948772i	$-0.602327\pi$
$151$	−7.76523	−0.631926	−0.315963	+	0.948772i	$0.602327\pi$
$152$	−40.1766	−3.25875
$153$	5.20785	0.421030
$154$	−2.47359	−0.199327
$155$	−14.0244	−1.12647
$156$	0	0
$157$	−8.41794	−0.671825	−0.335913	−	0.941893i	$-0.609045\pi$
$157$	−8.41794	−0.671825	−0.335913	+	0.941893i	$0.609045\pi$
$158$	−39.7778	−3.16455
$159$	−11.2203	−0.889830
$160$	14.8524	1.17419
$161$	3.94826	0.311167
$162$	−2.60515	−0.204680
$163$	−6.67148	−0.522551	−0.261275	−	0.965264i	$-0.584143\pi$
$163$	−6.67148	−0.522551	−0.261275	+	0.965264i	$0.584143\pi$
$164$	−9.65264	−0.753744
$165$	1.43724	0.111889
$166$	30.5232	2.36906
$167$	0.768371	0.0594583	0.0297292	−	0.999558i	$-0.490536\pi$
$167$	0.768371	0.0594583	0.0297292	+	0.999558i	$0.490536\pi$
$168$	7.26012	0.560131
$169$	0	0
$170$	20.5365	1.57508
$171$	5.53387	0.423185
$172$	−48.7249	−3.71524
$173$	−0.606929	−0.0461440	−0.0230720	−	0.999734i	$-0.507345\pi$
$173$	−0.606929	−0.0461440	−0.0230720	+	0.999734i	$0.507345\pi$
$174$	−13.3146	−1.00937
$175$	2.70876	0.204763
$176$	−8.86839	−0.668480
$177$	−6.64104	−0.499171
$178$	−21.2058	−1.58944
$179$	7.43308	0.555575	0.277787	−	0.960643i	$-0.410399\pi$
$179$	7.43308	0.555575	0.277787	+	0.960643i	$0.410399\pi$
$180$	−7.24575	−0.540066
$181$	18.2820	1.35889	0.679445	−	0.733727i	$-0.262221\pi$
$181$	18.2820	1.35889	0.679445	+	0.733727i	$0.262221\pi$
$182$	0	0
$183$	−3.07927	−0.227626
$184$	28.6649	2.11320
$185$	−10.8943	−0.800966
$186$	−24.1370	−1.76981
$187$	−4.94484	−0.361603
$188$	−33.3859	−2.43492
$189$	−1.00000	−0.0727393
$190$	21.8222	1.58315
$191$	3.80093	0.275026	0.137513	−	0.990500i	$-0.456089\pi$
$191$	3.80093	0.275026	0.137513	+	0.990500i	$0.456089\pi$
$192$	6.88190	0.496659
$193$	−2.52606	−0.181830	−0.0909149	−	0.995859i	$-0.528979\pi$
$193$	−2.52606	−0.181830	−0.0909149	+	0.995859i	$0.528979\pi$
$194$	−38.7654	−2.78319
$195$	0	0
$196$	4.78683	0.341916
$197$	7.51285	0.535268	0.267634	−	0.963521i	$-0.413758\pi$
$197$	7.51285	0.535268	0.267634	+	0.963521i	$0.413758\pi$
$198$	2.47359	0.175790
$199$	8.40900	0.596098	0.298049	−	0.954550i	$-0.403664\pi$
$199$	8.40900	0.596098	0.298049	+	0.954550i	$0.403664\pi$
$200$	19.6659	1.39059
$201$	12.8973	0.909703
$202$	2.28947	0.161087
$203$	−5.11085	−0.358712
$204$	24.9291	1.74539
$205$	3.05234	0.213185
$206$	−12.3116	−0.857788
$207$	−3.94826	−0.274423
$208$	0	0
$209$	−5.25439	−0.363454
$210$	−3.94338	−0.272119
$211$	−17.0137	−1.17127	−0.585637	−	0.810573i	$-0.699156\pi$
$211$	−17.0137	−1.17127	−0.585637	+	0.810573i	$0.699156\pi$
$212$	−53.7098	−3.68880
$213$	−7.77833	−0.532962
$214$	−38.0320	−2.59982
$215$	15.4077	1.05080
$216$	−7.26012	−0.493989
$217$	−9.26508	−0.628954
$218$	37.7099	2.55404
$219$	−8.64459	−0.584147
$220$	6.87982	0.463838
$221$	0	0
$222$	−18.7499	−1.25841
$223$	8.43541	0.564877	0.282438	−	0.959285i	$-0.408857\pi$
$223$	8.43541	0.564877	0.282438	+	0.959285i	$0.408857\pi$
$224$	9.81211	0.655599
$225$	−2.70876	−0.180584
$226$	1.71889	0.114339
$227$	19.6940	1.30714	0.653569	−	0.756867i	$-0.273271\pi$
$227$	19.6940	1.30714	0.653569	+	0.756867i	$0.273271\pi$
$228$	26.4897	1.75432
$229$	−8.84860	−0.584732	−0.292366	−	0.956306i	$-0.594443\pi$
$229$	−8.84860	−0.584732	−0.292366	+	0.956306i	$0.594443\pi$
$230$	−15.5695	−1.02662
$231$	0.949498	0.0624724
$232$	−37.1054	−2.43609
$233$	0.554530	0.0363285	0.0181642	−	0.999835i	$-0.494218\pi$
$233$	0.554530	0.0363285	0.0181642	+	0.999835i	$0.494218\pi$
$234$	0	0
$235$	10.5572	0.688678
$236$	−31.7895	−2.06932
$237$	15.2689	0.991820
$238$	13.5673	0.879434
$239$	−0.0284300	−0.00183898	−0.000919490	−	1.00000i	$-0.500293\pi$
$239$	−0.0284300	−0.00183898	−0.000919490		1.00000i	$0.500293\pi$
$240$	−14.1379	−0.912600
$241$	21.0729	1.35742	0.678712	−	0.734405i	$-0.262538\pi$
$241$	21.0729	1.35742	0.678712	+	0.734405i	$0.262538\pi$
$242$	26.3080	1.69114
$243$	1.00000	0.0641500
$244$	−14.7399	−0.943627
$245$	−1.51368	−0.0967058
$246$	5.25329	0.334938
$247$	0	0
$248$	−67.2656	−4.27137
$249$	−11.7165	−0.742500
$250$	−30.3986	−1.92258
$251$	10.0148	0.632129	0.316064	−	0.948738i	$-0.397638\pi$
$251$	10.0148	0.632129	0.316064	+	0.948738i	$0.397638\pi$
$252$	−4.78683	−0.301542
$253$	3.74887	0.235689
$254$	−8.28782	−0.520024
$255$	−7.88304	−0.493655
$256$	−18.1816	−1.13635
$257$	2.05650	0.128281	0.0641404	−	0.997941i	$-0.479569\pi$
$257$	2.05650	0.128281	0.0641404	+	0.997941i	$0.479569\pi$
$258$	26.5178	1.65092
$259$	−7.19721	−0.447213
$260$	0	0
$261$	5.11085	0.316354
$262$	−57.8983	−3.57697
$263$	−25.5725	−1.57686	−0.788432	−	0.615121i	$-0.789107\pi$
$263$	−25.5725	−1.57686	−0.788432	+	0.615121i	$0.789107\pi$
$264$	6.89347	0.424264
$265$	16.9840	1.04332
$266$	14.4166	0.883937
$267$	8.13994	0.498156
$268$	61.7370	3.77119
$269$	18.2104	1.11031	0.555155	−	0.831747i	$-0.312659\pi$
$269$	18.2104	1.11031	0.555155	+	0.831747i	$0.312659\pi$
$270$	3.94338	0.239987
$271$	−0.286832	−0.0174238	−0.00871191	−	0.999962i	$-0.502773\pi$
$271$	−0.286832	−0.0174238	−0.00871191	+	0.999962i	$0.502773\pi$
$272$	48.6417	2.94934
$273$	0	0
$274$	−34.5018	−2.08433
$275$	2.57196	0.155095
$276$	−18.8997	−1.13763
$277$	−26.3811	−1.58509	−0.792543	−	0.609816i	$-0.791243\pi$
$277$	−26.3811	−1.58509	−0.792543	+	0.609816i	$0.791243\pi$
$278$	−37.6904	−2.26052
$279$	9.26508	0.554686
$280$	−10.9895	−0.656750
$281$	−20.1174	−1.20010	−0.600051	−	0.799961i	$-0.704853\pi$
$281$	−20.1174	−1.20010	−0.600051	+	0.799961i	$0.704853\pi$
$282$	18.1697	1.08199
$283$	27.2020	1.61699	0.808495	−	0.588503i	$-0.200283\pi$
$283$	27.2020	1.61699	0.808495	+	0.588503i	$0.200283\pi$
$284$	−37.2335	−2.20940
$285$	−8.37653	−0.496183
$286$	0	0
$287$	2.01650	0.119030
$288$	−9.81211	−0.578184
$289$	10.1217	0.595394
$290$	20.1540	1.18349
$291$	14.8803	0.872296
$292$	−41.3802	−2.42159
$293$	4.80538	0.280733	0.140367	−	0.990100i	$-0.455172\pi$
$293$	4.80538	0.280733	0.140367	+	0.990100i	$0.455172\pi$
$294$	−2.60515	−0.151936
$295$	10.0524	0.585276
$296$	−52.2527	−3.03712
$297$	−0.949498	−0.0550955
$298$	−40.5602	−2.34959
$299$	0	0
$300$	−12.9664	−0.748614
$301$	10.1790	0.586705
$302$	20.2296	1.16408
$303$	−0.878824	−0.0504871
$304$	51.6868	2.96444
$305$	4.66104	0.266890
$306$	−13.5673	−0.775588
$307$	−3.38773	−0.193348	−0.0966739	−	0.995316i	$-0.530820\pi$
$307$	−3.38773	−0.193348	−0.0966739	+	0.995316i	$0.530820\pi$
$308$	4.54509	0.258980
$309$	4.72585	0.268844
$310$	36.5357	2.07509
$311$	−1.19801	−0.0679327	−0.0339664	−	0.999423i	$-0.510814\pi$
$311$	−1.19801	−0.0679327	−0.0339664	+	0.999423i	$0.510814\pi$
$312$	0	0
$313$	7.65369	0.432612	0.216306	−	0.976326i	$-0.430599\pi$
$313$	7.65369	0.432612	0.216306	+	0.976326i	$0.430599\pi$
$314$	21.9300	1.23758
$315$	1.51368	0.0852865
$316$	73.0895	4.11160
$317$	16.9899	0.954249	0.477125	−	0.878836i	$-0.341679\pi$
$317$	16.9899	0.954249	0.477125	+	0.878836i	$0.341679\pi$
$318$	29.2307	1.63918
$319$	−4.85274	−0.271702
$320$	−10.4170	−0.582330
$321$	14.5988	0.814823
$322$	−10.2858	−0.573207
$323$	28.8195	1.60356
$324$	4.78683	0.265935
$325$	0	0
$326$	17.3802	0.962602
$327$	−14.4751	−0.800476
$328$	14.6400	0.808360
$329$	6.97453	0.384518
$330$	−3.74423	−0.206113
$331$	−29.4213	−1.61714	−0.808571	−	0.588399i	$-0.799759\pi$
$331$	−29.4213	−1.61714	−0.808571	+	0.588399i	$0.799759\pi$
$332$	−56.0847	−3.07805
$333$	7.19721	0.394405
$334$	−2.00172	−0.109529
$335$	−19.5224	−1.06662
$336$	−9.34008	−0.509543
$337$	11.6689	0.635647	0.317823	−	0.948150i	$-0.397048\pi$
$337$	11.6689	0.635647	0.317823	+	0.948150i	$0.397048\pi$
$338$	0	0
$339$	−0.659804	−0.0358356
$340$	−37.7348	−2.04646
$341$	−8.79717	−0.476393
$342$	−14.4166	−0.779559
$343$	−1.00000	−0.0539949
$344$	73.9005	3.98445
$345$	5.97642	0.321760
$346$	1.58114	0.0850028
$347$	27.0926	1.45441	0.727203	−	0.686422i	$-0.240820\pi$
$347$	27.0926	1.45441	0.727203	+	0.686422i	$0.240820\pi$
$348$	24.4648	1.31145
$349$	11.2409	0.601711	0.300855	−	0.953670i	$-0.402728\pi$
$349$	11.2409	0.601711	0.300855	+	0.953670i	$0.402728\pi$
$350$	−7.05674	−0.377198
$351$	0	0
$352$	9.31658	0.496575
$353$	−6.14521	−0.327077	−0.163538	−	0.986537i	$-0.552291\pi$
$353$	−6.14521	−0.327077	−0.163538	+	0.986537i	$0.552291\pi$
$354$	17.3009	0.919534
$355$	11.7739	0.624896
$356$	38.9645	2.06511
$357$	−5.20785	−0.275629
$358$	−19.3643	−1.02344
$359$	16.0261	0.845823	0.422911	−	0.906171i	$-0.361008\pi$
$359$	16.0261	0.845823	0.422911	+	0.906171i	$0.361008\pi$
$360$	10.9895	0.579199
$361$	11.6237	0.611773
$362$	−47.6274	−2.50324
$363$	−10.0985	−0.530031
$364$	0	0
$365$	13.0852	0.684910
$366$	8.02197	0.419315
$367$	13.1656	0.687241	0.343620	−	0.939109i	$-0.388347\pi$
$367$	13.1656	0.687241	0.343620	+	0.939109i	$0.388347\pi$
$368$	−36.8771	−1.92235
$369$	−2.01650	−0.104975
$370$	28.3814	1.47548
$371$	11.2203	0.582530
$372$	44.3503	2.29946
$373$	20.9338	1.08391	0.541954	−	0.840408i	$-0.317685\pi$
$373$	20.9338	1.08391	0.541954	+	0.840408i	$0.317685\pi$
$374$	12.8821	0.666116
$375$	11.6686	0.602565
$376$	50.6359	2.61135
$377$	0	0
$378$	2.60515	0.133995
$379$	21.9130	1.12560	0.562798	−	0.826595i	$-0.309725\pi$
$379$	21.9130	1.12560	0.562798	+	0.826595i	$0.309725\pi$
$380$	−40.0970	−2.05693
$381$	3.18132	0.162984
$382$	−9.90201	−0.506631
$383$	28.2588	1.44396	0.721979	−	0.691915i	$-0.243233\pi$
$383$	28.2588	1.44396	0.721979	+	0.691915i	$0.243233\pi$
$384$	1.69580	0.0865386
$385$	−1.43724	−0.0732485
$386$	6.58078	0.334953
$387$	−10.1790	−0.517426
$388$	71.2293	3.61612
$389$	−9.13748	−0.463288	−0.231644	−	0.972801i	$-0.574411\pi$
$389$	−9.13748	−0.463288	−0.231644	+	0.972801i	$0.574411\pi$
$390$	0	0
$391$	−20.5619	−1.03986
$392$	−7.26012	−0.366692
$393$	22.2245	1.12108
$394$	−19.5721	−0.986030
$395$	−23.1122	−1.16290
$396$	−4.54509	−0.228399
$397$	−16.6775	−0.837018	−0.418509	−	0.908213i	$-0.637447\pi$
$397$	−16.6775	−0.837018	−0.418509	+	0.908213i	$0.637447\pi$
$398$	−21.9068	−1.09809
$399$	−5.53387	−0.277040
$400$	−25.3000	−1.26500
$401$	31.7990	1.58796	0.793982	−	0.607941i	$-0.208004\pi$
$401$	31.7990	1.58796	0.793982	+	0.607941i	$0.208004\pi$
$402$	−33.5994	−1.67578
$403$	0	0
$404$	−4.20678	−0.209295
$405$	−1.51368	−0.0752156
$406$	13.3146	0.660791
$407$	−6.83374	−0.338736
$408$	−37.8096	−1.87186
$409$	9.94983	0.491987	0.245994	−	0.969271i	$-0.420886\pi$
$409$	9.94983	0.491987	0.245994	+	0.969271i	$0.420886\pi$
$410$	−7.95182	−0.392713
$411$	13.2437	0.653262
$412$	22.6218	1.11450
$413$	6.64104	0.326784
$414$	10.2858	0.505521
$415$	17.7350	0.870578
$416$	0	0
$417$	14.4676	0.708482
$418$	13.6885	0.669527
$419$	25.2181	1.23198	0.615991	−	0.787753i	$-0.288756\pi$
$419$	25.2181	1.23198	0.615991	+	0.787753i	$0.288756\pi$
$420$	7.24575	0.353556
$421$	14.6230	0.712683	0.356341	−	0.934356i	$-0.384024\pi$
$421$	14.6230	0.712683	0.356341	+	0.934356i	$0.384024\pi$
$422$	44.3234	2.15763
$423$	−6.97453	−0.339113
$424$	81.4610	3.95609
$425$	−14.1068	−0.684281
$426$	20.2637	0.981782
$427$	3.07927	0.149016
$428$	69.8818	3.37786
$429$	0	0
$430$	−40.1395	−1.93570
$431$	17.5855	0.847063	0.423532	−	0.905881i	$-0.360790\pi$
$431$	17.5855	0.847063	0.423532	+	0.905881i	$0.360790\pi$
$432$	9.34008	0.449375
$433$	−32.4471	−1.55931	−0.779654	−	0.626211i	$-0.784605\pi$
$433$	−32.4471	−1.55931	−0.779654	+	0.626211i	$0.784605\pi$
$434$	24.1370	1.15861
$435$	−7.73622	−0.370923
$436$	−69.2899	−3.31839
$437$	−21.8491	−1.04519
$438$	22.5205	1.07607
$439$	10.0106	0.477781	0.238890	−	0.971047i	$-0.423216\pi$
$439$	10.0106	0.477781	0.238890	+	0.971047i	$0.423216\pi$
$440$	−10.4345	−0.497447
$441$	1.00000	0.0476190
$442$	0	0
$443$	−5.83618	−0.277286	−0.138643	−	0.990342i	$-0.544274\pi$
$443$	−5.83618	−0.277286	−0.138643	+	0.990342i	$0.544274\pi$
$444$	34.4518	1.63501
$445$	−12.3213	−0.584086
$446$	−21.9755	−1.04057
$447$	15.5692	0.736399
$448$	−6.88190	−0.325139
$449$	18.4584	0.871105	0.435552	−	0.900163i	$-0.356553\pi$
$449$	18.4584	0.871105	0.435552	+	0.900163i	$0.356553\pi$
$450$	7.05674	0.332658
$451$	1.91466	0.0901579
$452$	−3.15837	−0.148557
$453$	−7.76523	−0.364842
$454$	−51.3059	−2.40791
$455$	0	0
$456$	−40.1766	−1.88144
$457$	−0.831673	−0.0389040	−0.0194520	−	0.999811i	$-0.506192\pi$
$457$	−0.831673	−0.0389040	−0.0194520	+	0.999811i	$0.506192\pi$
$458$	23.0520	1.07715
$459$	5.20785	0.243082
$460$	28.6081	1.33386
$461$	−31.3731	−1.46119	−0.730597	−	0.682809i	$-0.760758\pi$
$461$	−31.3731	−1.46119	−0.730597	+	0.682809i	$0.760758\pi$
$462$	−2.47359	−0.115082
$463$	−23.7154	−1.10215	−0.551074	−	0.834457i	$-0.685782\pi$
$463$	−23.7154	−1.10215	−0.551074	+	0.834457i	$0.685782\pi$
$464$	47.7358	2.21608
$465$	−14.0244	−0.650366
$466$	−1.44464	−0.0669215
$467$	−4.32173	−0.199986	−0.0999929	−	0.994988i	$-0.531882\pi$
$467$	−4.32173	−0.199986	−0.0999929	+	0.994988i	$0.531882\pi$
$468$	0	0
$469$	−12.8973	−0.595541
$470$	−27.5032	−1.26863
$471$	−8.41794	−0.387878
$472$	48.2148	2.21926
$473$	9.66490	0.444393
$474$	−39.7778	−1.82705
$475$	−14.9899	−0.687784
$476$	−24.9291	−1.14262
$477$	−11.2203	−0.513743
$478$	0.0740644	0.00338763
$479$	−33.2267	−1.51816	−0.759082	−	0.650995i	$-0.774352\pi$
$479$	−33.2267	−1.51816	−0.759082	+	0.650995i	$0.774352\pi$
$480$	14.8524	0.677918
$481$	0	0
$482$	−54.8981	−2.50054
$483$	3.94826	0.179652
$484$	−48.3396	−2.19725
$485$	−22.5240	−1.02276
$486$	−2.60515	−0.118172
$487$	38.7278	1.75492	0.877462	−	0.479646i	$-0.159235\pi$
$487$	38.7278	1.75492	0.877462	+	0.479646i	$0.159235\pi$
$488$	22.3559	1.01200
$489$	−6.67148	−0.301695
$490$	3.94338	0.178144
$491$	−8.21236	−0.370619	−0.185309	−	0.982680i	$-0.559329\pi$
$491$	−8.21236	−0.370619	−0.185309	+	0.982680i	$0.559329\pi$
$492$	−9.65264	−0.435174
$493$	26.6166	1.19875
$494$	0	0
$495$	1.43724	0.0645991
$496$	86.5366	3.88561
$497$	7.77833	0.348906
$498$	30.5232	1.36778
$499$	−3.44425	−0.154186	−0.0770930	−	0.997024i	$-0.524564\pi$
$499$	−3.44425	−0.154186	−0.0770930	+	0.997024i	$0.524564\pi$
$500$	55.8557	2.49794
$501$	0.768371	0.0343283
$502$	−26.0901	−1.16446
$503$	31.6929	1.41312	0.706559	−	0.707654i	$-0.250246\pi$
$503$	31.6929	1.41312	0.706559	+	0.707654i	$0.250246\pi$
$504$	7.26012	0.323392
$505$	1.33026	0.0591959
$506$	−9.76637	−0.434168
$507$	0	0
$508$	15.2284	0.675652
$509$	5.98899	0.265457	0.132729	−	0.991152i	$-0.457626\pi$
$509$	5.98899	0.265457	0.132729	+	0.991152i	$0.457626\pi$
$510$	20.5365	0.909373
$511$	8.64459	0.382414
$512$	43.9744	1.94341
$513$	5.53387	0.244326
$514$	−5.35750	−0.236309
$515$	−7.15344	−0.315218
$516$	−48.7249	−2.14500
$517$	6.62230	0.291248
$518$	18.7499	0.823821
$519$	−0.606929	−0.0266412
$520$	0	0
$521$	36.0714	1.58032	0.790159	−	0.612902i	$-0.209998\pi$
$521$	36.0714	1.58032	0.790159	+	0.612902i	$0.209998\pi$
$522$	−13.3146	−0.582763
$523$	−16.9852	−0.742710	−0.371355	−	0.928491i	$-0.621107\pi$
$523$	−16.9852	−0.742710	−0.371355	+	0.928491i	$0.621107\pi$
$524$	106.385	4.64745
$525$	2.70876	0.118220
$526$	66.6202	2.90478
$527$	48.2511	2.10185
$528$	−8.86839	−0.385947
$529$	−7.41124	−0.322228
$530$	−44.2460	−1.92192
$531$	−6.64104	−0.288197
$532$	−26.4897	−1.14847
$533$	0	0
$534$	−21.2058	−0.917665
$535$	−22.0979	−0.955376
$536$	−93.6358	−4.04445
$537$	7.43308	0.320761
$538$	−47.4410	−2.04533
$539$	−0.949498	−0.0408978
$540$	−7.24575	−0.311807
$541$	1.76197	0.0757532	0.0378766	−	0.999282i	$-0.487941\pi$
$541$	1.76197	0.0757532	0.0378766	+	0.999282i	$0.487941\pi$
$542$	0.747243	0.0320968
$543$	18.2820	0.784555
$544$	−51.1000	−2.19089
$545$	21.9108	0.938554
$546$	0	0
$547$	15.6128	0.667556	0.333778	−	0.942652i	$-0.391676\pi$
$547$	15.6128	0.667556	0.333778	+	0.942652i	$0.391676\pi$
$548$	63.3952	2.70811
$549$	−3.07927	−0.131420
$550$	−6.70036	−0.285704
$551$	28.2828	1.20489
$552$	28.6649	1.22006
$553$	−15.2689	−0.649298
$554$	68.7268	2.91992
$555$	−10.8943	−0.462438
$556$	69.2540	2.93702
$557$	−42.6449	−1.80692	−0.903461	−	0.428671i	$-0.858982\pi$
$557$	−42.6449	−1.80692	−0.903461	+	0.428671i	$0.858982\pi$
$558$	−24.1370	−1.02180
$559$	0	0
$560$	14.1379	0.597437
$561$	−4.94484	−0.208771
$562$	52.4089	2.21074
$563$	32.6273	1.37507	0.687537	−	0.726149i	$-0.258692\pi$
$563$	32.6273	1.37507	0.687537	+	0.726149i	$0.258692\pi$
$564$	−33.3859	−1.40580
$565$	0.998735	0.0420171
$566$	−70.8653	−2.97869
$567$	−1.00000	−0.0419961
$568$	56.4716	2.36950
$569$	41.3429	1.73318	0.866592	−	0.499017i	$-0.166306\pi$
$569$	41.3429	1.73318	0.866592	+	0.499017i	$0.166306\pi$
$570$	21.8222	0.914029
$571$	−42.3972	−1.77427	−0.887135	−	0.461511i	$-0.847308\pi$
$571$	−42.3972	−1.77427	−0.887135	+	0.461511i	$0.847308\pi$
$572$	0	0
$573$	3.80093	0.158786
$574$	−5.25329	−0.219268
$575$	10.6949	0.446008
$576$	6.88190	0.286746
$577$	−26.2118	−1.09121	−0.545606	−	0.838042i	$-0.683700\pi$
$577$	−26.2118	−1.09121	−0.545606	+	0.838042i	$0.683700\pi$
$578$	−26.3686	−1.09679
$579$	−2.52606	−0.104979
$580$	−37.0320	−1.53767
$581$	11.7165	0.486081
$582$	−38.7654	−1.60688
$583$	10.6537	0.441230
$584$	62.7608	2.59706
$585$	0	0
$586$	−12.5188	−0.517145
$587$	−30.8293	−1.27246	−0.636230	−	0.771499i	$-0.719507\pi$
$587$	−30.8293	−1.27246	−0.636230	+	0.771499i	$0.719507\pi$
$588$	4.78683	0.197406
$589$	51.2717	2.11261
$590$	−26.1882	−1.07815
$591$	7.51285	0.309037
$592$	67.2226	2.76283
$593$	−27.8372	−1.14314	−0.571568	−	0.820554i	$-0.693665\pi$
$593$	−27.8372	−1.14314	−0.571568	+	0.820554i	$0.693665\pi$
$594$	2.47359	0.101493
$595$	7.88304	0.323173
$596$	74.5272	3.05275
$597$	8.40900	0.344158
$598$	0	0
$599$	−11.0019	−0.449525	−0.224763	−	0.974414i	$-0.572161\pi$
$599$	−11.0019	−0.449525	−0.224763	+	0.974414i	$0.572161\pi$
$600$	19.6659	0.802858
$601$	−15.5029	−0.632377	−0.316188	−	0.948696i	$-0.602403\pi$
$601$	−15.5029	−0.632377	−0.316188	+	0.948696i	$0.602403\pi$
$602$	−26.5178	−1.08078
$603$	12.8973	0.525217
$604$	−37.1708	−1.51246
$605$	15.2859	0.621459
$606$	2.28947	0.0930035
$607$	−2.16091	−0.0877086	−0.0438543	−	0.999038i	$-0.513964\pi$
$607$	−2.16091	−0.0877086	−0.0438543	+	0.999038i	$0.513964\pi$
$608$	−54.2989	−2.20211
$609$	−5.11085	−0.207102
$610$	−12.1427	−0.491645
$611$	0	0
$612$	24.9291	1.00770
$613$	−18.3854	−0.742578	−0.371289	−	0.928517i	$-0.621084\pi$
$613$	−18.3854	−0.742578	−0.371289	+	0.928517i	$0.621084\pi$
$614$	8.82555	0.356170
$615$	3.05234	0.123082
$616$	−6.89347	−0.277746
$617$	26.0219	1.04760	0.523801	−	0.851841i	$-0.324514\pi$
$617$	26.0219	1.04760	0.523801	+	0.851841i	$0.324514\pi$
$618$	−12.3116	−0.495244
$619$	13.1006	0.526557	0.263278	−	0.964720i	$-0.415196\pi$
$619$	13.1006	0.526557	0.263278	+	0.964720i	$0.415196\pi$
$620$	−67.1324	−2.69610
$621$	−3.94826	−0.158438
$622$	3.12099	0.125140
$623$	−8.13994	−0.326120
$624$	0	0
$625$	−4.11883	−0.164753
$626$	−19.9390	−0.796925
$627$	−5.25439	−0.209840
$628$	−40.2953	−1.60796
$629$	37.4820	1.49451
$630$	−3.94338	−0.157108
$631$	10.3506	0.412052	0.206026	−	0.978547i	$-0.433947\pi$
$631$	10.3506	0.412052	0.206026	+	0.978547i	$0.433947\pi$
$632$	−110.854	−4.40953
$633$	−17.0137	−0.676235
$634$	−44.2614	−1.75784
$635$	−4.81551	−0.191098
$636$	−53.7098	−2.12973
$637$	0	0
$638$	12.6421	0.500507
$639$	−7.77833	−0.307706
$640$	−2.56691	−0.101466
$641$	16.7543	0.661754	0.330877	−	0.943674i	$-0.392655\pi$
$641$	16.7543	0.661754	0.330877	+	0.943674i	$0.392655\pi$
$642$	−38.0320	−1.50100
$643$	28.7346	1.13318	0.566592	−	0.823999i	$-0.308262\pi$
$643$	28.7346	1.13318	0.566592	+	0.823999i	$0.308262\pi$
$644$	18.8997	0.744751
$645$	15.4077	0.606679
$646$	−75.0794	−2.95396
$647$	−30.0734	−1.18231	−0.591154	−	0.806559i	$-0.701327\pi$
$647$	−30.0734	−1.18231	−0.591154	+	0.806559i	$0.701327\pi$
$648$	−7.26012	−0.285205
$649$	6.30565	0.247518
$650$	0	0
$651$	−9.26508	−0.363127
$652$	−31.9352	−1.25068
$653$	2.99613	0.117247	0.0586237	−	0.998280i	$-0.481329\pi$
$653$	2.99613	0.117247	0.0586237	+	0.998280i	$0.481329\pi$
$654$	37.7099	1.47457
$655$	−33.6409	−1.31446
$656$	−18.8343	−0.735354
$657$	−8.64459	−0.337258
$658$	−18.1697	−0.708330
$659$	18.0993	0.705047	0.352524	−	0.935803i	$-0.385324\pi$
$659$	18.0993	0.705047	0.352524	+	0.935803i	$0.385324\pi$
$660$	6.87982	0.267797
$661$	39.9992	1.55579	0.777895	−	0.628395i	$-0.216288\pi$
$661$	39.9992	1.55579	0.777895	+	0.628395i	$0.216288\pi$
$662$	76.6471	2.97897
$663$	0	0
$664$	85.0629	3.30108
$665$	8.37653	0.324828
$666$	−18.7499	−0.726542
$667$	−20.1790	−0.781333
$668$	3.67806	0.142308
$669$	8.43541	0.326132
$670$	50.8589	1.96485
$671$	2.92376	0.112870
$672$	9.81211	0.378510
$673$	4.21170	0.162349	0.0811745	−	0.996700i	$-0.474133\pi$
$673$	4.21170	0.162349	0.0811745	+	0.996700i	$0.474133\pi$
$674$	−30.3994	−1.17094
$675$	−2.70876	−0.104260
$676$	0	0
$677$	−31.9491	−1.22790	−0.613951	−	0.789344i	$-0.710421\pi$
$677$	−31.9491	−1.22790	−0.613951	+	0.789344i	$0.710421\pi$
$678$	1.71889	0.0660136
$679$	−14.8803	−0.571052
$680$	57.2319	2.19474
$681$	19.6940	0.754676
$682$	22.9180	0.877575
$683$	41.8402	1.60097	0.800484	−	0.599353i	$-0.204576\pi$
$683$	41.8402	1.60097	0.800484	+	0.599353i	$0.204576\pi$
$684$	26.4897	1.01286
$685$	−20.0467	−0.765947
$686$	2.60515	0.0994653
$687$	−8.84860	−0.337595
$688$	−95.0723	−3.62460
$689$	0	0
$690$	−15.5695	−0.592721
$691$	22.8484	0.869192	0.434596	−	0.900625i	$-0.356891\pi$
$691$	22.8484	0.869192	0.434596	+	0.900625i	$0.356891\pi$
$692$	−2.90527	−0.110442
$693$	0.949498	0.0360684
$694$	−70.5804	−2.67919
$695$	−21.8994	−0.830692
$696$	−37.1054	−1.40648
$697$	−10.5016	−0.397777
$698$	−29.2842	−1.10842
$699$	0.554530	0.0209743
$700$	12.9664	0.490083
$701$	14.1083	0.532862	0.266431	−	0.963854i	$-0.414156\pi$
$701$	14.1083	0.532862	0.266431	+	0.963854i	$0.414156\pi$
$702$	0	0
$703$	39.8284	1.50216
$704$	−6.53435	−0.246273
$705$	10.5572	0.397608
$706$	16.0092	0.602515
$707$	0.878824	0.0330516
$708$	−31.7895	−1.19472
$709$	39.8609	1.49701	0.748504	−	0.663130i	$-0.230772\pi$
$709$	39.8609	1.49701	0.748504	+	0.663130i	$0.230772\pi$
$710$	−30.6729	−1.15113
$711$	15.2689	0.572627
$712$	−59.0970	−2.21475
$713$	−36.5809	−1.36997
$714$	13.5673	0.507742
$715$	0	0
$716$	35.5809	1.32972
$717$	−0.0284300	−0.00106174
$718$	−41.7503	−1.55811
$719$	−21.0361	−0.784514	−0.392257	−	0.919856i	$-0.628306\pi$
$719$	−21.0361	−0.784514	−0.392257	+	0.919856i	$0.628306\pi$
$720$	−14.1379	−0.526890
$721$	−4.72585	−0.176000
$722$	−30.2815	−1.12696
$723$	21.0729	0.783709
$724$	87.5128	3.25239
$725$	−13.8441	−0.514156
$726$	26.3080	0.976383
$727$	−12.6534	−0.469288	−0.234644	−	0.972081i	$-0.575392\pi$
$727$	−12.6534	−0.469288	−0.234644	+	0.972081i	$0.575392\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−34.0889	−1.26169
$731$	−53.0105	−1.96066
$732$	−14.7399	−0.544803
$733$	−14.2854	−0.527643	−0.263821	−	0.964572i	$-0.584983\pi$
$733$	−14.2854	−0.527643	−0.263821	+	0.964572i	$0.584983\pi$
$734$	−34.2985	−1.26598
$735$	−1.51368	−0.0558331
$736$	38.7408	1.42800
$737$	−12.2459	−0.451085
$738$	5.25329	0.193376
$739$	8.90875	0.327714	0.163857	−	0.986484i	$-0.447606\pi$
$739$	8.90875	0.327714	0.163857	+	0.986484i	$0.447606\pi$
$740$	−52.1492	−1.91704
$741$	0	0
$742$	−29.2307	−1.07309
$743$	−28.1389	−1.03232	−0.516158	−	0.856493i	$-0.672638\pi$
$743$	−28.1389	−1.03232	−0.516158	+	0.856493i	$0.672638\pi$
$744$	−67.2656	−2.46608
$745$	−23.5669	−0.863424
$746$	−54.5357	−1.99669
$747$	−11.7165	−0.428683
$748$	−23.6701	−0.865465
$749$	−14.5988	−0.533427
$750$	−30.3986	−1.11000
$751$	44.6703	1.63004	0.815020	−	0.579432i	$-0.196726\pi$
$751$	44.6703	1.63004	0.815020	+	0.579432i	$0.196726\pi$
$752$	−65.1427	−2.37551
$753$	10.0148	0.364960
$754$	0	0
$755$	11.7541	0.427776
$756$	−4.78683	−0.174095
$757$	12.0887	0.439373	0.219686	−	0.975571i	$-0.429497\pi$
$757$	12.0887	0.439373	0.219686	+	0.975571i	$0.429497\pi$
$758$	−57.0867	−2.07348
$759$	3.74887	0.136075
$760$	60.8146	2.20598
$761$	17.8391	0.646667	0.323333	−	0.946285i	$-0.395197\pi$
$761$	17.8391	0.646667	0.323333	+	0.946285i	$0.395197\pi$
$762$	−8.28782	−0.300236
$763$	14.4751	0.524034
$764$	18.1944	0.658250
$765$	−7.88304	−0.285012
$766$	−73.6185	−2.65995
$767$	0	0
$768$	−18.1816	−0.656073
$769$	11.4506	0.412921	0.206460	−	0.978455i	$-0.433806\pi$
$769$	11.4506	0.412921	0.206460	+	0.978455i	$0.433806\pi$
$770$	3.74423	0.134933
$771$	2.05650	0.0740630
$772$	−12.0918	−0.435194
$773$	−11.1486	−0.400988	−0.200494	−	0.979695i	$-0.564255\pi$
$773$	−11.1486	−0.400988	−0.200494	+	0.979695i	$0.564255\pi$
$774$	26.5178	0.953161
$775$	−25.0969	−0.901506
$776$	−108.032	−3.87814
$777$	−7.19721	−0.258199
$778$	23.8045	0.853434
$779$	−11.1590	−0.399814
$780$	0	0
$781$	7.38551	0.264274
$782$	53.5671	1.91555
$783$	5.11085	0.182647
$784$	9.34008	0.333574
$785$	12.7421	0.454785
$786$	−57.8983	−2.06516
$787$	−49.5139	−1.76498	−0.882489	−	0.470332i	$-0.844134\pi$
$787$	−49.5139	−1.76498	−0.882489	+	0.470332i	$0.844134\pi$
$788$	35.9627	1.28112
$789$	−25.5725	−0.910403
$790$	60.2110	2.14221
$791$	0.659804	0.0234599
$792$	6.89347	0.244949
$793$	0	0
$794$	43.4474	1.54189
$795$	16.9840	0.602362
$796$	40.2525	1.42671
$797$	−33.7455	−1.19533	−0.597664	−	0.801747i	$-0.703904\pi$
$797$	−33.7455	−1.19533	−0.597664	+	0.801747i	$0.703904\pi$
$798$	14.4166	0.510341
$799$	−36.3223	−1.28499
$800$	26.5786	0.939697
$801$	8.13994	0.287611
$802$	−82.8412	−2.92522
$803$	8.20802	0.289655
$804$	61.7370	2.17730
$805$	−5.97642	−0.210641
$806$	0	0
$807$	18.2104	0.641037
$808$	6.38037	0.224461
$809$	28.4402	0.999906	0.499953	−	0.866053i	$-0.333351\pi$
$809$	28.4402	0.999906	0.499953	+	0.866053i	$0.333351\pi$
$810$	3.94338	0.138556
$811$	−2.84955	−0.100061	−0.0500306	−	0.998748i	$-0.515932\pi$
$811$	−2.84955	−0.100061	−0.0500306	+	0.998748i	$0.515932\pi$
$812$	−24.4648	−0.858546
$813$	−0.286832	−0.0100597
$814$	17.8029	0.623993
$815$	10.0985	0.353736
$816$	48.6417	1.70280
$817$	−56.3290	−1.97070
$818$	−25.9208	−0.906301
$819$	0	0
$820$	14.6110	0.510240
$821$	−34.9336	−1.21919	−0.609596	−	0.792712i	$-0.708668\pi$
$821$	−34.9336	−1.21919	−0.609596	+	0.792712i	$0.708668\pi$
$822$	−34.5018	−1.20339
$823$	−41.4188	−1.44377	−0.721884	−	0.692014i	$-0.756723\pi$
$823$	−41.4188	−1.44377	−0.721884	+	0.692014i	$0.756723\pi$
$824$	−34.3102	−1.19525
$825$	2.57196	0.0895442
$826$	−17.3009	−0.601976
$827$	−23.6924	−0.823866	−0.411933	−	0.911214i	$-0.635146\pi$
$827$	−23.6924	−0.823866	−0.411933	+	0.911214i	$0.635146\pi$
$828$	−18.8997	−0.656808
$829$	−40.0234	−1.39007	−0.695034	−	0.718977i	$-0.744611\pi$
$829$	−40.0234	−1.39007	−0.695034	+	0.718977i	$0.744611\pi$
$830$	−46.2025	−1.60371
$831$	−26.3811	−0.915150
$832$	0	0
$833$	5.20785	0.180441
$834$	−37.6904	−1.30511
$835$	−1.16307	−0.0402497
$836$	−25.1519	−0.869896
$837$	9.26508	0.320248
$838$	−65.6969	−2.26946
$839$	−43.8642	−1.51436	−0.757181	−	0.653206i	$-0.773424\pi$
$839$	−43.8642	−1.51436	−0.757181	+	0.653206i	$0.773424\pi$
$840$	−10.9895	−0.379175
$841$	−2.87918	−0.0992820
$842$	−38.0953	−1.31285
$843$	−20.1174	−0.692880
$844$	−81.4419	−2.80334
$845$	0	0
$846$	18.1697	0.624688
$847$	10.0985	0.346987
$848$	−104.799	−3.59880
$849$	27.2020	0.933569
$850$	36.7504	1.26053
$851$	−28.4165	−0.974104
$852$	−37.2335	−1.27560
$853$	−18.6397	−0.638210	−0.319105	−	0.947719i	$-0.603382\pi$
$853$	−18.6397	−0.638210	−0.319105	+	0.947719i	$0.603382\pi$
$854$	−8.02197	−0.274506
$855$	−8.37653	−0.286471
$856$	−105.989	−3.62262
$857$	−12.2408	−0.418139	−0.209069	−	0.977901i	$-0.567043\pi$
$857$	−12.2408	−0.418139	−0.209069	+	0.977901i	$0.567043\pi$
$858$	0	0
$859$	12.3049	0.419837	0.209919	−	0.977719i	$-0.432680\pi$
$859$	12.3049	0.419837	0.209919	+	0.977719i	$0.432680\pi$
$860$	73.7542	2.51500
$861$	2.01650	0.0687221
$862$	−45.8129	−1.56039
$863$	5.55448	0.189077	0.0945383	−	0.995521i	$-0.469863\pi$
$863$	5.55448	0.189077	0.0945383	+	0.995521i	$0.469863\pi$
$864$	−9.81211	−0.333815
$865$	0.918699	0.0312367
$866$	84.5297	2.87244
$867$	10.1217	0.343751
$868$	−44.3503	−1.50535
$869$	−14.4978	−0.491803
$870$	20.1540	0.683286
$871$	0	0
$872$	105.091	3.55883
$873$	14.8803	0.503620
$874$	56.9204	1.92536
$875$	−11.6686	−0.394472
$876$	−41.3802	−1.39811
$877$	2.68227	0.0905739	0.0452869	−	0.998974i	$-0.485580\pi$
$877$	2.68227	0.0905739	0.0452869	+	0.998974i	$0.485580\pi$
$878$	−26.0792	−0.880130
$879$	4.80538	0.162081
$880$	13.4239	0.452521
$881$	−32.4366	−1.09282	−0.546408	−	0.837519i	$-0.684005\pi$
$881$	−32.4366	−1.09282	−0.546408	+	0.837519i	$0.684005\pi$
$882$	−2.60515	−0.0877201
$883$	44.7188	1.50491	0.752453	−	0.658646i	$-0.228870\pi$
$883$	44.7188	1.50491	0.752453	+	0.658646i	$0.228870\pi$
$884$	0	0
$885$	10.0524	0.337909
$886$	15.2042	0.510794
$887$	−43.8406	−1.47202	−0.736012	−	0.676968i	$-0.763293\pi$
$887$	−43.8406	−1.47202	−0.736012	+	0.676968i	$0.763293\pi$
$888$	−52.2527	−1.75348
$889$	−3.18132	−0.106698
$890$	32.0989	1.07596
$891$	−0.949498	−0.0318094
$892$	40.3789	1.35198
$893$	−38.5961	−1.29157
$894$	−40.5602	−1.35654
$895$	−11.2513	−0.376091
$896$	−1.69580	−0.0566528
$897$	0	0
$898$	−48.0869	−1.60468
$899$	47.3524	1.57929
$900$	−12.9664	−0.432212
$901$	−58.4338	−1.94671
$902$	−4.98799	−0.166082
$903$	10.1790	0.338735
$904$	4.79026	0.159322
$905$	−27.6732	−0.919887
$906$	20.2296	0.672084
$907$	−21.3865	−0.710128	−0.355064	−	0.934842i	$-0.615541\pi$
$907$	−21.3865	−0.710128	−0.355064	+	0.934842i	$0.615541\pi$
$908$	94.2719	3.12852
$909$	−0.878824	−0.0291488
$910$	0	0
$911$	−20.5969	−0.682406	−0.341203	−	0.939990i	$-0.610834\pi$
$911$	−20.5969	−0.682406	−0.341203	+	0.939990i	$0.610834\pi$
$912$	51.6868	1.71152
$913$	11.1248	0.368176
$914$	2.16664	0.0716660
$915$	4.66104	0.154089
$916$	−42.3568	−1.39951
$917$	−22.2245	−0.733918
$918$	−13.5673	−0.447786
$919$	−7.11153	−0.234588	−0.117294	−	0.993097i	$-0.537422\pi$
$919$	−7.11153	−0.234588	−0.117294	+	0.993097i	$0.537422\pi$
$920$	−43.3896	−1.43051
$921$	−3.38773	−0.111629
$922$	81.7319	2.69170
$923$	0	0
$924$	4.54509	0.149522
$925$	−19.4955	−0.641009
$926$	61.7823	2.03029
$927$	4.72585	0.155217
$928$	−50.1483	−1.64620
$929$	13.4954	0.442769	0.221385	−	0.975187i	$-0.428942\pi$
$929$	13.4954	0.442769	0.221385	+	0.975187i	$0.428942\pi$
$930$	36.5357	1.19805
$931$	5.53387	0.181365
$932$	2.65444	0.0869492
$933$	−1.19801	−0.0392210
$934$	11.2588	0.368398
$935$	7.48493	0.244783
$936$	0	0
$937$	−7.61840	−0.248882	−0.124441	−	0.992227i	$-0.539714\pi$
$937$	−7.61840	−0.248882	−0.124441	+	0.992227i	$0.539714\pi$
$938$	33.5994	1.09706
$939$	7.65369	0.249769
$940$	50.5357	1.64829
$941$	9.15256	0.298365	0.149182	−	0.988810i	$-0.452336\pi$
$941$	9.15256	0.298365	0.149182	+	0.988810i	$0.452336\pi$
$942$	21.9300	0.714520
$943$	7.96166	0.259267
$944$	−62.0278	−2.01883
$945$	1.51368	0.0492402
$946$	−25.1786	−0.818625
$947$	2.69459	0.0875623	0.0437812	−	0.999041i	$-0.486060\pi$
$947$	2.69459	0.0875623	0.0437812	+	0.999041i	$0.486060\pi$
$948$	73.0895	2.37384
$949$	0	0
$950$	39.0510	1.26698
$951$	16.9899	0.550936
$952$	37.8096	1.22542
$953$	−16.1487	−0.523106	−0.261553	−	0.965189i	$-0.584235\pi$
$953$	−16.1487	−0.523106	−0.261553	+	0.965189i	$0.584235\pi$
$954$	29.2307	0.946378
$955$	−5.75341	−0.186176
$956$	−0.136089	−0.00440144
$957$	−4.85274	−0.156867
$958$	86.5606	2.79665
$959$	−13.2437	−0.427660
$960$	−10.4170	−0.336208
$961$	54.8416	1.76909
$962$	0	0
$963$	14.5988	0.470438
$964$	100.872	3.24888
$965$	3.82366	0.123088
$966$	−10.2858	−0.330941
$967$	−47.9571	−1.54220	−0.771098	−	0.636717i	$-0.780292\pi$
$967$	−47.9571	−1.54220	−0.771098	+	0.636717i	$0.780292\pi$
$968$	73.3160	2.35647
$969$	28.8195	0.925817
$970$	58.6785	1.88405
$971$	19.2626	0.618166	0.309083	−	0.951035i	$-0.399978\pi$
$971$	19.2626	0.618166	0.309083	+	0.951035i	$0.399978\pi$
$972$	4.78683	0.153538
$973$	−14.4676	−0.463810
$974$	−100.892	−3.23279
$975$	0	0
$976$	−28.7606	−0.920605
$977$	47.9655	1.53455	0.767276	−	0.641317i	$-0.221612\pi$
$977$	47.9655	1.53455	0.767276	+	0.641317i	$0.221612\pi$
$978$	17.3802	0.555759
$979$	−7.72885	−0.247015
$980$	−7.24575	−0.231457
$981$	−14.4751	−0.462155
$982$	21.3945	0.682725
$983$	36.7956	1.17360	0.586799	−	0.809733i	$-0.300388\pi$
$983$	36.7956	1.17360	0.586799	+	0.809733i	$0.300388\pi$
$984$	14.6400	0.466707
$985$	−11.3721	−0.362345
$986$	−69.3402	−2.20824
$987$	6.97453	0.222002
$988$	0	0
$989$	40.1892	1.27794
$990$	−3.74423	−0.119000
$991$	20.0508	0.636935	0.318467	−	0.947934i	$-0.396832\pi$
$991$	20.0508	0.636935	0.318467	+	0.947934i	$0.396832\pi$
$992$	−90.9100	−2.88639
$993$	−29.4213	−0.933657
$994$	−20.2637	−0.642727
$995$	−12.7286	−0.403523
$996$	−56.0847	−1.77711
$997$	−31.0874	−0.984549	−0.492274	−	0.870440i	$-0.663834\pi$
$997$	−31.0874	−0.984549	−0.492274	+	0.870440i	$0.663834\pi$
$998$	8.97282	0.284030
$999$	7.19721	0.227710

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bh.1.2	yes	15
13.12	even	2		3549.2.a.bg.1.14	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3549.2.a.bg.1.14	✓	15	13.12	even	2
3549.2.a.bh.1.2	yes	15	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)

\(f(q)\)	\(=\)	\(q-2.60515 q^{2} +1.00000 q^{3} +4.78683 q^{4} -1.51368 q^{5} -2.60515 q^{6} -1.00000 q^{7} -7.26012 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.60515 q^{2} +1.00000 q^{3} +4.78683 q^{4} -1.51368 q^{5} -2.60515 q^{6} -1.00000 q^{7} -7.26012 q^{8} +1.00000 q^{9} +3.94338 q^{10} -0.949498 q^{11} +4.78683 q^{12} +2.60515 q^{14} -1.51368 q^{15} +9.34008 q^{16} +5.20785 q^{17} -2.60515 q^{18} +5.53387 q^{19} -7.24575 q^{20} -1.00000 q^{21} +2.47359 q^{22} -3.94826 q^{23} -7.26012 q^{24} -2.70876 q^{25} +1.00000 q^{27} -4.78683 q^{28} +5.11085 q^{29} +3.94338 q^{30} +9.26508 q^{31} -9.81211 q^{32} -0.949498 q^{33} -13.5673 q^{34} +1.51368 q^{35} +4.78683 q^{36} +7.19721 q^{37} -14.4166 q^{38} +10.9895 q^{40} -2.01650 q^{41} +2.60515 q^{42} -10.1790 q^{43} -4.54509 q^{44} -1.51368 q^{45} +10.2858 q^{46} -6.97453 q^{47} +9.34008 q^{48} +1.00000 q^{49} +7.05674 q^{50} +5.20785 q^{51} -11.2203 q^{53} -2.60515 q^{54} +1.43724 q^{55} +7.26012 q^{56} +5.53387 q^{57} -13.3146 q^{58} -6.64104 q^{59} -7.24575 q^{60} -3.07927 q^{61} -24.1370 q^{62} -1.00000 q^{63} +6.88190 q^{64} +2.47359 q^{66} +12.8973 q^{67} +24.9291 q^{68} -3.94826 q^{69} -3.94338 q^{70} -7.77833 q^{71} -7.26012 q^{72} -8.64459 q^{73} -18.7499 q^{74} -2.70876 q^{75} +26.4897 q^{76} +0.949498 q^{77} +15.2689 q^{79} -14.1379 q^{80} +1.00000 q^{81} +5.25329 q^{82} -11.7165 q^{83} -4.78683 q^{84} -7.88304 q^{85} +26.5178 q^{86} +5.11085 q^{87} +6.89347 q^{88} +8.13994 q^{89} +3.94338 q^{90} -18.8997 q^{92} +9.26508 q^{93} +18.1697 q^{94} -8.37653 q^{95} -9.81211 q^{96} +14.8803 q^{97} -2.60515 q^{98} -0.949498 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 2 q^{2} + 15 q^{3} + 28 q^{4} - 9 q^{5} + 2 q^{6} - 15 q^{7} + 9 q^{8} + 15 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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