LMFDB - Embedded newform 3549.2.a.bf.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

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

Embedding invariants

Embedding label			1.9
Root			$2.67225$ 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)

$f(q)$	$=$	$q+2.67225 q^{2} -1.00000 q^{3} +5.14091 q^{4} -1.32568 q^{5} -2.67225 q^{6} -1.00000 q^{7} +8.39329 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.67225 q^{2} -1.00000 q^{3} +5.14091 q^{4} -1.32568 q^{5} -2.67225 q^{6} -1.00000 q^{7} +8.39329 q^{8} +1.00000 q^{9} -3.54256 q^{10} -3.03214 q^{11} -5.14091 q^{12} -2.67225 q^{14} +1.32568 q^{15} +12.1471 q^{16} +4.56435 q^{17} +2.67225 q^{18} +0.940093 q^{19} -6.81522 q^{20} +1.00000 q^{21} -8.10263 q^{22} +8.55552 q^{23} -8.39329 q^{24} -3.24256 q^{25} -1.00000 q^{27} -5.14091 q^{28} +5.79888 q^{29} +3.54256 q^{30} +1.00569 q^{31} +15.6736 q^{32} +3.03214 q^{33} +12.1971 q^{34} +1.32568 q^{35} +5.14091 q^{36} +11.3326 q^{37} +2.51216 q^{38} -11.1269 q^{40} -7.71076 q^{41} +2.67225 q^{42} +7.20423 q^{43} -15.5880 q^{44} -1.32568 q^{45} +22.8625 q^{46} +12.8237 q^{47} -12.1471 q^{48} +1.00000 q^{49} -8.66492 q^{50} -4.56435 q^{51} +5.26290 q^{53} -2.67225 q^{54} +4.01966 q^{55} -8.39329 q^{56} -0.940093 q^{57} +15.4960 q^{58} -13.1834 q^{59} +6.81522 q^{60} +5.82817 q^{61} +2.68746 q^{62} -1.00000 q^{63} +17.5894 q^{64} +8.10263 q^{66} +3.02297 q^{67} +23.4649 q^{68} -8.55552 q^{69} +3.54256 q^{70} -6.04396 q^{71} +8.39329 q^{72} -12.2757 q^{73} +30.2835 q^{74} +3.24256 q^{75} +4.83293 q^{76} +3.03214 q^{77} +1.46368 q^{79} -16.1033 q^{80} +1.00000 q^{81} -20.6051 q^{82} +4.31767 q^{83} +5.14091 q^{84} -6.05089 q^{85} +19.2515 q^{86} -5.79888 q^{87} -25.4496 q^{88} -3.22598 q^{89} -3.54256 q^{90} +43.9832 q^{92} -1.00569 q^{93} +34.2681 q^{94} -1.24627 q^{95} -15.6736 q^{96} -5.51764 q^{97} +2.67225 q^{98} -3.03214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + q^{2} - 9 q^{3} + 5 q^{4} - 9 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 9 q^{9}+O(q^{10}) $ 9 * q + q^2 - 9 * q^3 + 5 * q^4 - 9 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 9 * q^9	$ 9 q + q^{2} - 9 q^{3} + 5 q^{4} - 9 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 9 q^{9} + q^{10} + q^{11} - 5 q^{12} - q^{14} + 9 q^{15} + 5 q^{16} + 11 q^{17} + q^{18} - 7 q^{19} - 23 q^{20} + 9 q^{21} - 3 q^{22} + 22 q^{23} - 6 q^{24} - 8 q^{25} - 9 q^{27} - 5 q^{28} + 11 q^{29} - q^{30} - 7 q^{31} + 18 q^{32} - q^{33} + 6 q^{34} + 9 q^{35} + 5 q^{36} + q^{37} - 6 q^{38} - 14 q^{40} - 16 q^{41} + q^{42} + 32 q^{43} - 18 q^{44} - 9 q^{45} + 9 q^{46} + 12 q^{47} - 5 q^{48} + 9 q^{49} - 10 q^{50} - 11 q^{51} + 13 q^{53} - q^{54} + 9 q^{55} - 6 q^{56} + 7 q^{57} - 4 q^{58} - 29 q^{59} + 23 q^{60} - 12 q^{61} + 30 q^{62} - 9 q^{63} + 6 q^{64} + 3 q^{66} + 20 q^{67} + 34 q^{68} - 22 q^{69} - q^{70} + 2 q^{71} + 6 q^{72} - q^{73} + 43 q^{74} + 8 q^{75} - 13 q^{76} - q^{77} + 3 q^{79} + 39 q^{80} + 9 q^{81} - 19 q^{82} - 24 q^{83} + 5 q^{84} - 15 q^{85} + 28 q^{86} - 11 q^{87} - 19 q^{88} - 11 q^{89} + q^{90} + 73 q^{92} + 7 q^{93} + 15 q^{94} + 39 q^{95} - 18 q^{96} - 20 q^{97} + q^{98} + q^{99}+O(q^{100}) $ 9 * q + q^2 - 9 * q^3 + 5 * q^4 - 9 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 9 * q^9 + q^10 + q^11 - 5 * q^12 - q^14 + 9 * q^15 + 5 * q^16 + 11 * q^17 + q^18 - 7 * q^19 - 23 * q^20 + 9 * q^21 - 3 * q^22 + 22 * q^23 - 6 * q^24 - 8 * q^25 - 9 * q^27 - 5 * q^28 + 11 * q^29 - q^30 - 7 * q^31 + 18 * q^32 - q^33 + 6 * q^34 + 9 * q^35 + 5 * q^36 + q^37 - 6 * q^38 - 14 * q^40 - 16 * q^41 + q^42 + 32 * q^43 - 18 * q^44 - 9 * q^45 + 9 * q^46 + 12 * q^47 - 5 * q^48 + 9 * q^49 - 10 * q^50 - 11 * q^51 + 13 * q^53 - q^54 + 9 * q^55 - 6 * q^56 + 7 * q^57 - 4 * q^58 - 29 * q^59 + 23 * q^60 - 12 * q^61 + 30 * q^62 - 9 * q^63 + 6 * q^64 + 3 * q^66 + 20 * q^67 + 34 * q^68 - 22 * q^69 - q^70 + 2 * q^71 + 6 * q^72 - q^73 + 43 * q^74 + 8 * q^75 - 13 * q^76 - q^77 + 3 * q^79 + 39 * q^80 + 9 * q^81 - 19 * q^82 - 24 * q^83 + 5 * q^84 - 15 * q^85 + 28 * q^86 - 11 * q^87 - 19 * q^88 - 11 * q^89 + q^90 + 73 * q^92 + 7 * q^93 + 15 * q^94 + 39 * q^95 - 18 * q^96 - 20 * q^97 + q^98 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.67225	1.88956	0.944782	−	0.327699i	$-0.106273\pi$
$2$	2.67225	1.88956	0.944782	+	0.327699i	$0.106273\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	5.14091	2.57045
$5$	−1.32568	−0.592864	−0.296432	−	0.955054i	$-0.595797\pi$
$5$	−1.32568	−0.592864	−0.296432	+	0.955054i	$0.595797\pi$
$6$	−2.67225	−1.09094
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	8.39329	2.96748
$9$	1.00000	0.333333
$10$	−3.54256	−1.12026
$11$	−3.03214	−0.914225	−0.457112	−	0.889409i	$-0.651116\pi$
$11$	−3.03214	−0.914225	−0.457112	+	0.889409i	$0.651116\pi$
$12$	−5.14091	−1.48405
$13$	0	0
$13$	0	0
$14$	−2.67225	−0.714188
$15$	1.32568	0.342290
$16$	12.1471	3.03678
$17$	4.56435	1.10702	0.553509	−	0.832843i	$-0.313288\pi$
$17$	4.56435	1.10702	0.553509	+	0.832843i	$0.313288\pi$
$18$	2.67225	0.629855
$19$	0.940093	0.215672	0.107836	−	0.994169i	$-0.465608\pi$
$19$	0.940093	0.215672	0.107836	+	0.994169i	$0.465608\pi$
$20$	−6.81522	−1.52393
$21$	1.00000	0.218218
$22$	−8.10263	−1.72749
$23$	8.55552	1.78395	0.891975	−	0.452085i	$-0.149320\pi$
$23$	8.55552	1.78395	0.891975	+	0.452085i	$0.149320\pi$
$24$	−8.39329	−1.71327
$25$	−3.24256	−0.648512
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−5.14091	−0.971540
$29$	5.79888	1.07682	0.538412	−	0.842681i	$-0.319024\pi$
$29$	5.79888	1.07682	0.538412	+	0.842681i	$0.319024\pi$
$30$	3.54256	0.646780
$31$	1.00569	0.180628	0.0903138	−	0.995913i	$-0.471213\pi$
$31$	1.00569	0.180628	0.0903138	+	0.995913i	$0.471213\pi$
$32$	15.6736	2.77072
$33$	3.03214	0.527828
$34$	12.1971	2.09178
$35$	1.32568	0.224082
$36$	5.14091	0.856818
$37$	11.3326	1.86306	0.931532	−	0.363658i	$-0.118472\pi$
$37$	11.3326	1.86306	0.931532	+	0.363658i	$0.118472\pi$
$38$	2.51216	0.407526
$39$	0	0
$40$	−11.1269	−1.75931
$41$	−7.71076	−1.20422	−0.602109	−	0.798414i	$-0.705673\pi$
$41$	−7.71076	−1.20422	−0.602109	+	0.798414i	$0.705673\pi$
$42$	2.67225	0.412337
$43$	7.20423	1.09864	0.549318	−	0.835614i	$-0.314888\pi$
$43$	7.20423	1.09864	0.549318	+	0.835614i	$0.314888\pi$
$44$	−15.5880	−2.34997
$45$	−1.32568	−0.197621
$46$	22.8625	3.37089
$47$	12.8237	1.87053	0.935264	−	0.353952i	$-0.115162\pi$
$47$	12.8237	1.87053	0.935264	+	0.353952i	$0.115162\pi$
$48$	−12.1471	−1.75329
$49$	1.00000	0.142857
$50$	−8.66492	−1.22541
$51$	−4.56435	−0.639137
$52$	0	0
$53$	5.26290	0.722915	0.361458	−	0.932389i	$-0.382279\pi$
$53$	5.26290	0.722915	0.361458	+	0.932389i	$0.382279\pi$
$54$	−2.67225	−0.363647
$55$	4.01966	0.542011
$56$	−8.39329	−1.12160
$57$	−0.940093	−0.124518
$58$	15.4960	2.03473
$59$	−13.1834	−1.71634	−0.858169	−	0.513368i	$-0.828398\pi$
$59$	−13.1834	−1.71634	−0.858169	+	0.513368i	$0.828398\pi$
$60$	6.81522	0.879842
$61$	5.82817	0.746221	0.373111	−	0.927787i	$-0.378291\pi$
$61$	5.82817	0.746221	0.373111	+	0.927787i	$0.378291\pi$
$62$	2.68746	0.341308
$63$	−1.00000	−0.125988
$64$	17.5894	2.19867
$65$	0	0
$66$	8.10263	0.997365
$67$	3.02297	0.369315	0.184657	−	0.982803i	$-0.440882\pi$
$67$	3.02297	0.369315	0.184657	+	0.982803i	$0.440882\pi$
$68$	23.4649	2.84554
$69$	−8.55552	−1.02996
$70$	3.54256	0.423417
$71$	−6.04396	−0.717286	−0.358643	−	0.933475i	$-0.616760\pi$
$71$	−6.04396	−0.717286	−0.358643	+	0.933475i	$0.616760\pi$
$72$	8.39329	0.989158
$73$	−12.2757	−1.43676	−0.718381	−	0.695650i	$-0.755117\pi$
$73$	−12.2757	−1.43676	−0.718381	+	0.695650i	$0.755117\pi$
$74$	30.2835	3.52038
$75$	3.24256	0.374419
$76$	4.83293	0.554375
$77$	3.03214	0.345544
$78$	0	0
$79$	1.46368	0.164677	0.0823384	−	0.996604i	$-0.473761\pi$
$79$	1.46368	0.164677	0.0823384	+	0.996604i	$0.473761\pi$
$80$	−16.1033	−1.80040
$81$	1.00000	0.111111
$82$	−20.6051	−2.27545
$83$	4.31767	0.473926	0.236963	−	0.971519i	$-0.423848\pi$
$83$	4.31767	0.473926	0.236963	+	0.971519i	$0.423848\pi$
$84$	5.14091	0.560919
$85$	−6.05089	−0.656311
$86$	19.2515	2.07594
$87$	−5.79888	−0.621705
$88$	−25.4496	−2.71294
$89$	−3.22598	−0.341953	−0.170976	−	0.985275i	$-0.554692\pi$
$89$	−3.22598	−0.341953	−0.170976	+	0.985275i	$0.554692\pi$
$90$	−3.54256	−0.373418
$91$	0	0
$92$	43.9832	4.58556
$93$	−1.00569	−0.104285
$94$	34.2681	3.53448
$95$	−1.24627	−0.127864
$96$	−15.6736	−1.59968
$97$	−5.51764	−0.560231	−0.280116	−	0.959966i	$-0.590373\pi$
$97$	−5.51764	−0.560231	−0.280116	+	0.959966i	$0.590373\pi$
$98$	2.67225	0.269938
$99$	−3.03214	−0.304742
$100$	−16.6697	−1.66697
$101$	−15.6199	−1.55424	−0.777118	−	0.629355i	$-0.783319\pi$
$101$	−15.6199	−1.55424	−0.777118	+	0.629355i	$0.783319\pi$
$102$	−12.1971	−1.20769
$103$	3.64829	0.359477	0.179739	−	0.983714i	$-0.442475\pi$
$103$	3.64829	0.359477	0.179739	+	0.983714i	$0.442475\pi$
$104$	0	0
$105$	−1.32568	−0.129374
$106$	14.0638	1.36600
$107$	−13.8712	−1.34098	−0.670491	−	0.741917i	$-0.733917\pi$
$107$	−13.8712	−1.34098	−0.670491	+	0.741917i	$0.733917\pi$
$108$	−5.14091	−0.494684
$109$	4.46904	0.428057	0.214028	−	0.976827i	$-0.431341\pi$
$109$	4.46904	0.428057	0.214028	+	0.976827i	$0.431341\pi$
$110$	10.7415	1.02416
$111$	−11.3326	−1.07564
$112$	−12.1471	−1.14780
$113$	−6.59144	−0.620070	−0.310035	−	0.950725i	$-0.600341\pi$
$113$	−6.59144	−0.620070	−0.310035	+	0.950725i	$0.600341\pi$
$114$	−2.51216	−0.235285
$115$	−11.3419	−1.05764
$116$	29.8115	2.76793
$117$	0	0
$118$	−35.2294	−3.24313
$119$	−4.56435	−0.418413
$120$	11.1269	1.01574
$121$	−1.80613	−0.164193
$122$	15.5743	1.41003
$123$	7.71076	0.695256
$124$	5.17017	0.464295
$125$	10.9270	0.977344
$126$	−2.67225	−0.238063
$127$	−3.34415	−0.296746	−0.148373	−	0.988931i	$-0.547404\pi$
$127$	−3.34415	−0.296746	−0.148373	+	0.988931i	$0.547404\pi$
$128$	15.6561	1.38382
$129$	−7.20423	−0.634297
$130$	0	0
$131$	17.5766	1.53567	0.767836	−	0.640646i	$-0.221334\pi$
$131$	17.5766	1.53567	0.767836	+	0.640646i	$0.221334\pi$
$132$	15.5880	1.35676
$133$	−0.940093	−0.0815164
$134$	8.07813	0.697844
$135$	1.32568	0.114097
$136$	38.3099	3.28505
$137$	8.33789	0.712354	0.356177	−	0.934418i	$-0.384080\pi$
$137$	8.33789	0.712354	0.356177	+	0.934418i	$0.384080\pi$
$138$	−22.8625	−1.94618
$139$	9.03188	0.766074	0.383037	−	0.923733i	$-0.374878\pi$
$139$	9.03188	0.766074	0.383037	+	0.923733i	$0.374878\pi$
$140$	6.81522	0.575992
$141$	−12.8237	−1.07995
$142$	−16.1509	−1.35536
$143$	0	0
$144$	12.1471	1.01226
$145$	−7.68749	−0.638411
$146$	−32.8037	−2.71486
$147$	−1.00000	−0.0824786
$148$	58.2598	4.78892
$149$	−11.5763	−0.948364	−0.474182	−	0.880427i	$-0.657256\pi$
$149$	−11.5763	−0.948364	−0.474182	+	0.880427i	$0.657256\pi$
$150$	8.66492	0.707488
$151$	12.8069	1.04221	0.521106	−	0.853492i	$-0.325519\pi$
$151$	12.8069	1.04221	0.521106	+	0.853492i	$0.325519\pi$
$152$	7.89047	0.640001
$153$	4.56435	0.369006
$154$	8.10263	0.652929
$155$	−1.33323	−0.107088
$156$	0	0
$157$	21.2317	1.69448	0.847238	−	0.531213i	$-0.178264\pi$
$157$	21.2317	1.69448	0.847238	+	0.531213i	$0.178264\pi$
$158$	3.91132	0.311168
$159$	−5.26290	−0.417375
$160$	−20.7782	−1.64266
$161$	−8.55552	−0.674270
$162$	2.67225	0.209952
$163$	−9.58992	−0.751140	−0.375570	−	0.926794i	$-0.622553\pi$
$163$	−9.58992	−0.751140	−0.375570	+	0.926794i	$0.622553\pi$
$164$	−39.6403	−3.09539
$165$	−4.01966	−0.312930
$166$	11.5379	0.895514
$167$	18.3054	1.41652	0.708258	−	0.705954i	$-0.249481\pi$
$167$	18.3054	1.41652	0.708258	+	0.705954i	$0.249481\pi$
$168$	8.39329	0.647556
$169$	0	0
$170$	−16.1695	−1.24014
$171$	0.940093	0.0718907
$172$	37.0363	2.82399
$173$	−14.3907	−1.09410	−0.547051	−	0.837100i	$-0.684249\pi$
$173$	−14.3907	−1.09410	−0.547051	+	0.837100i	$0.684249\pi$
$174$	−15.4960	−1.17475
$175$	3.24256	0.245115
$176$	−36.8318	−2.77630
$177$	13.1834	0.990928
$178$	−8.62061	−0.646142
$179$	11.4813	0.858156	0.429078	−	0.903267i	$-0.358838\pi$
$179$	11.4813	0.858156	0.429078	+	0.903267i	$0.358838\pi$
$180$	−6.81522	−0.507977
$181$	−26.5739	−1.97522	−0.987612	−	0.156914i	$-0.949845\pi$
$181$	−26.5739	−1.97522	−0.987612	+	0.156914i	$0.949845\pi$
$182$	0	0
$183$	−5.82817	−0.430831
$184$	71.8090	5.29383
$185$	−15.0234	−1.10454
$186$	−2.68746	−0.197054
$187$	−13.8398	−1.01206
$188$	65.9254	4.80810
$189$	1.00000	0.0727393
$190$	−3.33033	−0.241608
$191$	−0.582610	−0.0421562	−0.0210781	−	0.999778i	$-0.506710\pi$
$191$	−0.582610	−0.0421562	−0.0210781	+	0.999778i	$0.506710\pi$
$192$	−17.5894	−1.26940
$193$	−4.20527	−0.302702	−0.151351	−	0.988480i	$-0.548362\pi$
$193$	−4.20527	−0.302702	−0.151351	+	0.988480i	$0.548362\pi$
$194$	−14.7445	−1.05859
$195$	0	0
$196$	5.14091	0.367208
$197$	20.0883	1.43123	0.715616	−	0.698494i	$-0.246146\pi$
$197$	20.0883	1.43123	0.715616	+	0.698494i	$0.246146\pi$
$198$	−8.10263	−0.575829
$199$	−26.6158	−1.88675	−0.943374	−	0.331732i	$-0.892367\pi$
$199$	−26.6158	−1.88675	−0.943374	+	0.331732i	$0.892367\pi$
$200$	−27.2157	−1.92444
$201$	−3.02297	−0.213224
$202$	−41.7402	−2.93683
$203$	−5.79888	−0.407002
$204$	−23.4649	−1.64287
$205$	10.2220	0.713938
$206$	9.74915	0.679255
$207$	8.55552	0.594650
$208$	0	0
$209$	−2.85049	−0.197173
$210$	−3.54256	−0.244460
$211$	−22.5261	−1.55076	−0.775379	−	0.631497i	$-0.782441\pi$
$211$	−22.5261	−1.55076	−0.775379	+	0.631497i	$0.782441\pi$
$212$	27.0561	1.85822
$213$	6.04396	0.414125
$214$	−37.0674	−2.53387
$215$	−9.55054	−0.651342
$216$	−8.39329	−0.571091
$217$	−1.00569	−0.0682708
$218$	11.9424	0.808841
$219$	12.2757	0.829515
$220$	20.6647	1.39321
$221$	0	0
$222$	−30.2835	−2.03249
$223$	9.50381	0.636422	0.318211	−	0.948020i	$-0.396918\pi$
$223$	9.50381	0.636422	0.318211	+	0.948020i	$0.396918\pi$
$224$	−15.6736	−1.04723
$225$	−3.24256	−0.216171
$226$	−17.6140	−1.17166
$227$	−14.9121	−0.989749	−0.494874	−	0.868965i	$-0.664786\pi$
$227$	−14.9121	−0.989749	−0.494874	+	0.868965i	$0.664786\pi$
$228$	−4.83293	−0.320069
$229$	−14.1266	−0.933513	−0.466757	−	0.884386i	$-0.654578\pi$
$229$	−14.1266	−0.933513	−0.466757	+	0.884386i	$0.654578\pi$
$230$	−30.3084	−1.99848
$231$	−3.03214	−0.199500
$232$	48.6717	3.19545
$233$	−15.0580	−0.986481	−0.493241	−	0.869893i	$-0.664188\pi$
$233$	−15.0580	−0.986481	−0.493241	+	0.869893i	$0.664188\pi$
$234$	0	0
$235$	−17.0002	−1.10897
$236$	−67.7749	−4.41177
$237$	−1.46368	−0.0950762
$238$	−12.1971	−0.790619
$239$	4.14971	0.268423	0.134211	−	0.990953i	$-0.457150\pi$
$239$	4.14971	0.268423	0.134211	+	0.990953i	$0.457150\pi$
$240$	16.1033	1.03946
$241$	−18.1010	−1.16599	−0.582995	−	0.812476i	$-0.698119\pi$
$241$	−18.1010	−1.16599	−0.582995	+	0.812476i	$0.698119\pi$
$242$	−4.82642	−0.310254
$243$	−1.00000	−0.0641500
$244$	29.9621	1.91813
$245$	−1.32568	−0.0846949
$246$	20.6051	1.31373
$247$	0	0
$248$	8.44106	0.536008
$249$	−4.31767	−0.273621
$250$	29.1997	1.84675
$251$	4.22142	0.266454	0.133227	−	0.991086i	$-0.457466\pi$
$251$	4.22142	0.266454	0.133227	+	0.991086i	$0.457466\pi$
$252$	−5.14091	−0.323847
$253$	−25.9415	−1.63093
$254$	−8.93641	−0.560720
$255$	6.05089	0.378922
$256$	6.65816	0.416135
$257$	11.8550	0.739493	0.369747	−	0.929133i	$-0.379444\pi$
$257$	11.8550	0.739493	0.369747	+	0.929133i	$0.379444\pi$
$258$	−19.2515	−1.19855
$259$	−11.3326	−0.704172
$260$	0	0
$261$	5.79888	0.358942
$262$	46.9690	2.90175
$263$	12.5753	0.775425	0.387712	−	0.921780i	$-0.373265\pi$
$263$	12.5753	0.775425	0.387712	+	0.921780i	$0.373265\pi$
$264$	25.4496	1.56632
$265$	−6.97695	−0.428591
$266$	−2.51216	−0.154030
$267$	3.22598	0.197427
$268$	15.5408	0.949307
$269$	12.5342	0.764221	0.382110	−	0.924117i	$-0.375197\pi$
$269$	12.5342	0.764221	0.382110	+	0.924117i	$0.375197\pi$
$270$	3.54256	0.215593
$271$	−3.47597	−0.211150	−0.105575	−	0.994411i	$-0.533668\pi$
$271$	−3.47597	−0.211150	−0.105575	+	0.994411i	$0.533668\pi$
$272$	55.4438	3.36177
$273$	0	0
$274$	22.2809	1.34604
$275$	9.83190	0.592886
$276$	−43.9832	−2.64748
$277$	−6.76964	−0.406748	−0.203374	−	0.979101i	$-0.565191\pi$
$277$	−6.76964	−0.406748	−0.203374	+	0.979101i	$0.565191\pi$
$278$	24.1354	1.44755
$279$	1.00569	0.0602092
$280$	11.1269	0.664957
$281$	4.18616	0.249725	0.124863	−	0.992174i	$-0.460151\pi$
$281$	4.18616	0.249725	0.124863	+	0.992174i	$0.460151\pi$
$282$	−34.2681	−2.04063
$283$	5.21985	0.310288	0.155144	−	0.987892i	$-0.450416\pi$
$283$	5.21985	0.310288	0.155144	+	0.987892i	$0.450416\pi$
$284$	−31.0714	−1.84375
$285$	1.24627	0.0738224
$286$	0	0
$287$	7.71076	0.455152
$288$	15.6736	0.923574
$289$	3.83331	0.225489
$290$	−20.5429	−1.20632
$291$	5.51764	0.323450
$292$	−63.1083	−3.69313
$293$	10.0063	0.584573	0.292286	−	0.956331i	$-0.405584\pi$
$293$	10.0063	0.584573	0.292286	+	0.956331i	$0.405584\pi$
$294$	−2.67225	−0.155849
$295$	17.4771	1.01756
$296$	95.1176	5.52860
$297$	3.03214	0.175943
$298$	−30.9346	−1.79199
$299$	0	0
$300$	16.6697	0.962426
$301$	−7.20423	−0.415245
$302$	34.2233	1.96933
$303$	15.6199	0.897338
$304$	11.4194	0.654949
$305$	−7.72632	−0.442408
$306$	12.1971	0.697261
$307$	−0.476202	−0.0271783	−0.0135891	−	0.999908i	$-0.504326\pi$
$307$	−0.476202	−0.0271783	−0.0135891	+	0.999908i	$0.504326\pi$
$308$	15.5880	0.888206
$309$	−3.64829	−0.207544
$310$	−3.56272	−0.202349
$311$	22.0675	1.25133	0.625666	−	0.780091i	$-0.284827\pi$
$311$	22.0675	1.25133	0.625666	+	0.780091i	$0.284827\pi$
$312$	0	0
$313$	−6.17383	−0.348966	−0.174483	−	0.984660i	$-0.555825\pi$
$313$	−6.17383	−0.348966	−0.174483	+	0.984660i	$0.555825\pi$
$314$	56.7364	3.20182
$315$	1.32568	0.0746939
$316$	7.52465	0.423294
$317$	12.1948	0.684930	0.342465	−	0.939531i	$-0.388738\pi$
$317$	12.1948	0.684930	0.342465	+	0.939531i	$0.388738\pi$
$318$	−14.0638	−0.788658
$319$	−17.5830	−0.984460
$320$	−23.3180	−1.30351
$321$	13.8712	0.774217
$322$	−22.8625	−1.27408
$323$	4.29091	0.238753
$324$	5.14091	0.285606
$325$	0	0
$326$	−25.6266	−1.41933
$327$	−4.46904	−0.247139
$328$	−64.7187	−3.57349
$329$	−12.8237	−0.706993
$330$	−10.7415	−0.591302
$331$	−21.9157	−1.20459	−0.602297	−	0.798272i	$-0.705748\pi$
$331$	−21.9157	−1.20459	−0.602297	+	0.798272i	$0.705748\pi$
$332$	22.1968	1.21821
$333$	11.3326	0.621022
$334$	48.9166	2.67660
$335$	−4.00751	−0.218953
$336$	12.1471	0.662680
$337$	−9.16559	−0.499281	−0.249641	−	0.968339i	$-0.580312\pi$
$337$	−9.16559	−0.499281	−0.249641	+	0.968339i	$0.580312\pi$
$338$	0	0
$339$	6.59144	0.357998
$340$	−31.1071	−1.68702
$341$	−3.04940	−0.165134
$342$	2.51216	0.135842
$343$	−1.00000	−0.0539949
$344$	60.4672	3.26017
$345$	11.3419	0.610629
$346$	−38.4554	−2.06738
$347$	11.2649	0.604734	0.302367	−	0.953192i	$-0.402223\pi$
$347$	11.2649	0.604734	0.302367	+	0.953192i	$0.402223\pi$
$348$	−29.8115	−1.59806
$349$	10.6412	0.569610	0.284805	−	0.958585i	$-0.408071\pi$
$349$	10.6412	0.569610	0.284805	+	0.958585i	$0.408071\pi$
$350$	8.66492	0.463160
$351$	0	0
$352$	−47.5244	−2.53306
$353$	−9.03769	−0.481027	−0.240514	−	0.970646i	$-0.577316\pi$
$353$	−9.03769	−0.481027	−0.240514	+	0.970646i	$0.577316\pi$
$354$	35.2294	1.87242
$355$	8.01238	0.425253
$356$	−16.5845	−0.878974
$357$	4.56435	0.241571
$358$	30.6810	1.62154
$359$	−2.34727	−0.123884	−0.0619421	−	0.998080i	$-0.519729\pi$
$359$	−2.34727	−0.123884	−0.0619421	+	0.998080i	$0.519729\pi$
$360$	−11.1269	−0.586437
$361$	−18.1162	−0.953486
$362$	−71.0121	−3.73231
$363$	1.80613	0.0947970
$364$	0	0
$365$	16.2737	0.851805
$366$	−15.5743	−0.814083
$367$	30.1391	1.57325	0.786623	−	0.617433i	$-0.211827\pi$
$367$	30.1391	1.57325	0.786623	+	0.617433i	$0.211827\pi$
$368$	103.925	5.41747
$369$	−7.71076	−0.401406
$370$	−40.1463	−2.08711
$371$	−5.26290	−0.273236
$372$	−5.17017	−0.268061
$373$	−1.86802	−0.0967222	−0.0483611	−	0.998830i	$-0.515400\pi$
$373$	−1.86802	−0.0967222	−0.0483611	+	0.998830i	$0.515400\pi$
$374$	−36.9833	−1.91236
$375$	−10.9270	−0.564270
$376$	107.633	5.55074
$377$	0	0
$378$	2.67225	0.137446
$379$	−31.2686	−1.60616	−0.803080	−	0.595871i	$-0.796807\pi$
$379$	−31.2686	−1.60616	−0.803080	+	0.595871i	$0.796807\pi$
$380$	−6.40694	−0.328669
$381$	3.34415	0.171326
$382$	−1.55688	−0.0796568
$383$	−5.27451	−0.269515	−0.134757	−	0.990879i	$-0.543026\pi$
$383$	−5.27451	−0.269515	−0.134757	+	0.990879i	$0.543026\pi$
$384$	−15.6561	−0.798946
$385$	−4.01966	−0.204861
$386$	−11.2375	−0.571975
$387$	7.20423	0.366212
$388$	−28.3657	−1.44005
$389$	31.9519	1.62002	0.810012	−	0.586413i	$-0.199460\pi$
$389$	31.9519	1.62002	0.810012	+	0.586413i	$0.199460\pi$
$390$	0	0
$391$	39.0504	1.97486
$392$	8.39329	0.423925
$393$	−17.5766	−0.886621
$394$	53.6809	2.70440
$395$	−1.94038	−0.0976310
$396$	−15.5880	−0.783324
$397$	0.115785	0.00581111	0.00290555	−	0.999996i	$-0.499075\pi$
$397$	0.115785	0.00581111	0.00290555	+	0.999996i	$0.499075\pi$
$398$	−71.1241	−3.56513
$399$	0.940093	0.0470635
$400$	−39.3878	−1.96939
$401$	−17.7168	−0.884734	−0.442367	−	0.896834i	$-0.645861\pi$
$401$	−17.7168	−0.884734	−0.442367	+	0.896834i	$0.645861\pi$
$402$	−8.07813	−0.402900
$403$	0	0
$404$	−80.3003	−3.99509
$405$	−1.32568	−0.0658738
$406$	−15.4960	−0.769056
$407$	−34.3620	−1.70326
$408$	−38.3099	−1.89662
$409$	18.5393	0.916708	0.458354	−	0.888770i	$-0.348439\pi$
$409$	18.5393	0.916708	0.458354	+	0.888770i	$0.348439\pi$
$410$	27.3158	1.34903
$411$	−8.33789	−0.411278
$412$	18.7555	0.924019
$413$	13.1834	0.648715
$414$	22.8625	1.12363
$415$	−5.72387	−0.280974
$416$	0	0
$417$	−9.03188	−0.442293
$418$	−7.61722	−0.372571
$419$	20.2670	0.990107	0.495053	−	0.868863i	$-0.335148\pi$
$419$	20.2670	0.990107	0.495053	+	0.868863i	$0.335148\pi$
$420$	−6.81522	−0.332549
$421$	−38.6779	−1.88504	−0.942522	−	0.334144i	$-0.891553\pi$
$421$	−38.6779	−1.88504	−0.942522	+	0.334144i	$0.891553\pi$
$422$	−60.1952	−2.93026
$423$	12.8237	0.623509
$424$	44.1731	2.14523
$425$	−14.8002	−0.717914
$426$	16.1509	0.782516
$427$	−5.82817	−0.282045
$428$	−71.3108	−3.44694
$429$	0	0
$430$	−25.5214	−1.23075
$431$	−27.4790	−1.32362	−0.661808	−	0.749673i	$-0.730211\pi$
$431$	−27.4790	−1.32362	−0.661808	+	0.749673i	$0.730211\pi$
$432$	−12.1471	−0.584429
$433$	−35.8813	−1.72435	−0.862173	−	0.506613i	$-0.830897\pi$
$433$	−35.8813	−1.72435	−0.862173	+	0.506613i	$0.830897\pi$
$434$	−2.68746	−0.129002
$435$	7.68749	0.368587
$436$	22.9749	1.10030
$437$	8.04298	0.384748
$438$	32.8037	1.56742
$439$	−12.6382	−0.603187	−0.301593	−	0.953437i	$-0.597519\pi$
$439$	−12.6382	−0.603187	−0.301593	+	0.953437i	$0.597519\pi$
$440$	33.7382	1.60840
$441$	1.00000	0.0476190
$442$	0	0
$443$	4.86153	0.230978	0.115489	−	0.993309i	$-0.463156\pi$
$443$	4.86153	0.230978	0.115489	+	0.993309i	$0.463156\pi$
$444$	−58.2598	−2.76489
$445$	4.27663	0.202732
$446$	25.3965	1.20256
$447$	11.5763	0.547538
$448$	−17.5894	−0.831021
$449$	−26.0682	−1.23024	−0.615118	−	0.788435i	$-0.710891\pi$
$449$	−26.0682	−1.23024	−0.615118	+	0.788435i	$0.710891\pi$
$450$	−8.66492	−0.408468
$451$	23.3801	1.10093
$452$	−33.8860	−1.59386
$453$	−12.8069	−0.601722
$454$	−39.8487	−1.87019
$455$	0	0
$456$	−7.89047	−0.369505
$457$	2.32931	0.108960	0.0544802	−	0.998515i	$-0.482650\pi$
$457$	2.32931	0.108960	0.0544802	+	0.998515i	$0.482650\pi$
$458$	−37.7498	−1.76393
$459$	−4.56435	−0.213046
$460$	−58.3078	−2.71862
$461$	−11.6874	−0.544338	−0.272169	−	0.962249i	$-0.587741\pi$
$461$	−11.6874	−0.544338	−0.272169	+	0.962249i	$0.587741\pi$
$462$	−8.10263	−0.376968
$463$	25.3264	1.17702	0.588509	−	0.808490i	$-0.299715\pi$
$463$	25.3264	1.17702	0.588509	+	0.808490i	$0.299715\pi$
$464$	70.4397	3.27008
$465$	1.33323	0.0618271
$466$	−40.2387	−1.86402
$467$	4.69774	0.217385	0.108693	−	0.994075i	$-0.465334\pi$
$467$	4.69774	0.217385	0.108693	+	0.994075i	$0.465334\pi$
$468$	0	0
$469$	−3.02297	−0.139588
$470$	−45.4287	−2.09547
$471$	−21.2317	−0.978306
$472$	−110.652	−5.09319
$473$	−21.8442	−1.00440
$474$	−3.91132	−0.179653
$475$	−3.04831	−0.139866
$476$	−23.4649	−1.07551
$477$	5.26290	0.240972
$478$	11.0891	0.507202
$479$	−25.7413	−1.17615	−0.588075	−	0.808806i	$-0.700114\pi$
$479$	−25.7413	−1.17615	−0.588075	+	0.808806i	$0.700114\pi$
$480$	20.7782	0.948391
$481$	0	0
$482$	−48.3704	−2.20321
$483$	8.55552	0.389290
$484$	−9.28513	−0.422051
$485$	7.31465	0.332141
$486$	−2.67225	−0.121216
$487$	−8.77825	−0.397780	−0.198890	−	0.980022i	$-0.563734\pi$
$487$	−8.77825	−0.397780	−0.198890	+	0.980022i	$0.563734\pi$
$488$	48.9175	2.21439
$489$	9.58992	0.433671
$490$	−3.54256	−0.160036
$491$	34.6420	1.56337	0.781686	−	0.623672i	$-0.214360\pi$
$491$	34.6420	1.56337	0.781686	+	0.623672i	$0.214360\pi$
$492$	39.6403	1.78712
$493$	26.4681	1.19206
$494$	0	0
$495$	4.01966	0.180670
$496$	12.2163	0.548527
$497$	6.04396	0.271108
$498$	−11.5379	−0.517025
$499$	15.2931	0.684612	0.342306	−	0.939589i	$-0.388792\pi$
$499$	15.2931	0.684612	0.342306	+	0.939589i	$0.388792\pi$
$500$	56.1749	2.51222
$501$	−18.3054	−0.817826
$502$	11.2807	0.503482
$503$	−8.70136	−0.387974	−0.193987	−	0.981004i	$-0.562142\pi$
$503$	−8.70136	−0.387974	−0.193987	+	0.981004i	$0.562142\pi$
$504$	−8.39329	−0.373867
$505$	20.7070	0.921450
$506$	−69.3222	−3.08175
$507$	0	0
$508$	−17.1920	−0.762771
$509$	26.9261	1.19348	0.596739	−	0.802435i	$-0.296463\pi$
$509$	26.9261	1.19348	0.596739	+	0.802435i	$0.296463\pi$
$510$	16.1695	0.715997
$511$	12.2757	0.543045
$512$	−13.5199	−0.597501
$513$	−0.940093	−0.0415061
$514$	31.6794	1.39732
$515$	−4.83649	−0.213121
$516$	−37.0363	−1.63043
$517$	−38.8832	−1.71008
$518$	−30.2835	−1.33058
$519$	14.3907	0.631680
$520$	0	0
$521$	0.805919	0.0353079	0.0176540	−	0.999844i	$-0.494380\pi$
$521$	0.805919	0.0353079	0.0176540	+	0.999844i	$0.494380\pi$
$522$	15.4960	0.678243
$523$	37.1587	1.62484	0.812418	−	0.583075i	$-0.198151\pi$
$523$	37.1587	1.62484	0.812418	+	0.583075i	$0.198151\pi$
$524$	90.3596	3.94738
$525$	−3.24256	−0.141517
$526$	33.6043	1.46522
$527$	4.59033	0.199958
$528$	36.8318	1.60290
$529$	50.1970	2.18248
$530$	−18.6441	−0.809850
$531$	−13.1834	−0.572113
$532$	−4.83293	−0.209534
$533$	0	0
$534$	8.62061	0.373050
$535$	18.3889	0.795021
$536$	25.3727	1.09593
$537$	−11.4813	−0.495457
$538$	33.4944	1.44404
$539$	−3.03214	−0.130604
$540$	6.81522	0.293281
$541$	22.5963	0.971492	0.485746	−	0.874100i	$-0.338548\pi$
$541$	22.5963	0.971492	0.485746	+	0.874100i	$0.338548\pi$
$542$	−9.28866	−0.398982
$543$	26.5739	1.14040
$544$	71.5397	3.06724
$545$	−5.92454	−0.253780
$546$	0	0
$547$	−24.9820	−1.06815	−0.534076	−	0.845436i	$-0.679340\pi$
$547$	−24.9820	−1.06815	−0.534076	+	0.845436i	$0.679340\pi$
$548$	42.8644	1.83107
$549$	5.82817	0.248740
$550$	26.2733	1.12030
$551$	5.45148	0.232241
$552$	−71.8090	−3.05639
$553$	−1.46368	−0.0622420
$554$	−18.0901	−0.768577
$555$	15.0234	0.637709
$556$	46.4321	1.96916
$557$	11.7270	0.496891	0.248445	−	0.968646i	$-0.420080\pi$
$557$	11.7270	0.496891	0.248445	+	0.968646i	$0.420080\pi$
$558$	2.68746	0.113769
$559$	0	0
$560$	16.1033	0.680487
$561$	13.8398	0.584315
$562$	11.1865	0.471872
$563$	−6.86242	−0.289216	−0.144608	−	0.989489i	$-0.546192\pi$
$563$	−6.86242	−0.289216	−0.144608	+	0.989489i	$0.546192\pi$
$564$	−65.9254	−2.77596
$565$	8.73817	0.367618
$566$	13.9487	0.586309
$567$	−1.00000	−0.0419961
$568$	−50.7287	−2.12853
$569$	−13.4308	−0.563049	−0.281525	−	0.959554i	$-0.590840\pi$
$569$	−13.4308	−0.563049	−0.281525	+	0.959554i	$0.590840\pi$
$570$	3.33033	0.139492
$571$	−18.8819	−0.790185	−0.395092	−	0.918641i	$-0.629287\pi$
$571$	−18.8819	−0.790185	−0.395092	+	0.918641i	$0.629287\pi$
$572$	0	0
$573$	0.582610	0.0243389
$574$	20.6051	0.860039
$575$	−27.7418	−1.15691
$576$	17.5894	0.732891
$577$	−31.9538	−1.33025	−0.665126	−	0.746731i	$-0.731622\pi$
$577$	−31.9538	−1.33025	−0.665126	+	0.746731i	$0.731622\pi$
$578$	10.2436	0.426076
$579$	4.20527	0.174765
$580$	−39.5207	−1.64101
$581$	−4.31767	−0.179127
$582$	14.7445	0.611179
$583$	−15.9579	−0.660907
$584$	−103.034	−4.26356
$585$	0	0
$586$	26.7392	1.10459
$587$	−14.8277	−0.612005	−0.306002	−	0.952031i	$-0.598992\pi$
$587$	−14.8277	−0.612005	−0.306002	+	0.952031i	$0.598992\pi$
$588$	−5.14091	−0.212008
$589$	0.945444	0.0389563
$590$	46.7031	1.92274
$591$	−20.0883	−0.826322
$592$	137.658	5.65772
$593$	14.1339	0.580411	0.290205	−	0.956964i	$-0.406276\pi$
$593$	14.1339	0.580411	0.290205	+	0.956964i	$0.406276\pi$
$594$	8.10263	0.332455
$595$	6.05089	0.248062
$596$	−59.5125	−2.43773
$597$	26.6158	1.08931
$598$	0	0
$599$	−6.24004	−0.254961	−0.127481	−	0.991841i	$-0.540689\pi$
$599$	−6.24004	−0.254961	−0.127481	+	0.991841i	$0.540689\pi$
$600$	27.2157	1.11108
$601$	−38.1259	−1.55519	−0.777594	−	0.628767i	$-0.783560\pi$
$601$	−38.1259	−1.55519	−0.777594	+	0.628767i	$0.783560\pi$
$602$	−19.2515	−0.784633
$603$	3.02297	0.123105
$604$	65.8392	2.67896
$605$	2.39435	0.0973443
$606$	41.7402	1.69558
$607$	6.64697	0.269792	0.134896	−	0.990860i	$-0.456930\pi$
$607$	6.64697	0.269792	0.134896	+	0.990860i	$0.456930\pi$
$608$	14.7346	0.597567
$609$	5.79888	0.234982
$610$	−20.6466	−0.835958
$611$	0	0
$612$	23.4649	0.948513
$613$	−5.39777	−0.218014	−0.109007	−	0.994041i	$-0.534767\pi$
$613$	−5.39777	−0.218014	−0.109007	+	0.994041i	$0.534767\pi$
$614$	−1.27253	−0.0513551
$615$	−10.2220	−0.412192
$616$	25.4496	1.02539
$617$	−15.6769	−0.631127	−0.315563	−	0.948904i	$-0.602193\pi$
$617$	−15.6769	−0.631127	−0.315563	+	0.948904i	$0.602193\pi$
$618$	−9.74915	−0.392168
$619$	−4.62364	−0.185840	−0.0929199	−	0.995674i	$-0.529620\pi$
$619$	−4.62364	−0.185840	−0.0929199	+	0.995674i	$0.529620\pi$
$620$	−6.85402	−0.275264
$621$	−8.55552	−0.343321
$622$	58.9697	2.36447
$623$	3.22598	0.129246
$624$	0	0
$625$	1.72700	0.0690799
$626$	−16.4980	−0.659393
$627$	2.85049	0.113838
$628$	109.150	4.35557
$629$	51.7259	2.06245
$630$	3.54256	0.141139
$631$	−22.5825	−0.898997	−0.449498	−	0.893281i	$-0.648397\pi$
$631$	−22.5825	−0.898997	−0.449498	+	0.893281i	$0.648397\pi$
$632$	12.2851	0.488675
$633$	22.5261	0.895330
$634$	32.5876	1.29422
$635$	4.43329	0.175930
$636$	−27.0561	−1.07284
$637$	0	0
$638$	−46.9862	−1.86020
$639$	−6.04396	−0.239095
$640$	−20.7550	−0.820415
$641$	0.836649	0.0330456	0.0165228	−	0.999863i	$-0.494740\pi$
$641$	0.836649	0.0330456	0.0165228	+	0.999863i	$0.494740\pi$
$642$	37.0674	1.46293
$643$	−19.3772	−0.764161	−0.382081	−	0.924129i	$-0.624792\pi$
$643$	−19.3772	−0.764161	−0.382081	+	0.924129i	$0.624792\pi$
$644$	−43.9832	−1.73318
$645$	9.55054	0.376052
$646$	11.4664	0.451139
$647$	34.6544	1.36240	0.681202	−	0.732095i	$-0.261457\pi$
$647$	34.6544	1.36240	0.681202	+	0.732095i	$0.261457\pi$
$648$	8.39329	0.329719
$649$	39.9740	1.56912
$650$	0	0
$651$	1.00569	0.0394162
$652$	−49.3009	−1.93077
$653$	−23.7620	−0.929878	−0.464939	−	0.885343i	$-0.653924\pi$
$653$	−23.7620	−0.929878	−0.464939	+	0.885343i	$0.653924\pi$
$654$	−11.9424	−0.466984
$655$	−23.3010	−0.910445
$656$	−93.6636	−3.65695
$657$	−12.2757	−0.478921
$658$	−34.2681	−1.33591
$659$	−15.1656	−0.590767	−0.295384	−	0.955379i	$-0.595447\pi$
$659$	−15.1656	−0.590767	−0.295384	+	0.955379i	$0.595447\pi$
$660$	−20.6647	−0.804373
$661$	6.98694	0.271760	0.135880	−	0.990725i	$-0.456614\pi$
$661$	6.98694	0.271760	0.135880	+	0.990725i	$0.456614\pi$
$662$	−58.5641	−2.27616
$663$	0	0
$664$	36.2395	1.40636
$665$	1.24627	0.0483281
$666$	30.2835	1.17346
$667$	49.6124	1.92100
$668$	94.1065	3.64109
$669$	−9.50381	−0.367439
$670$	−10.7090	−0.413727
$671$	−17.6718	−0.682214
$672$	15.6736	0.604621
$673$	−29.9128	−1.15305	−0.576527	−	0.817078i	$-0.695592\pi$
$673$	−29.9128	−1.15305	−0.576527	+	0.817078i	$0.695592\pi$
$674$	−24.4927	−0.943424
$675$	3.24256	0.124806
$676$	0	0
$677$	12.5395	0.481934	0.240967	−	0.970533i	$-0.422535\pi$
$677$	12.5395	0.481934	0.240967	+	0.970533i	$0.422535\pi$
$678$	17.6140	0.676460
$679$	5.51764	0.211748
$680$	−50.7869	−1.94759
$681$	14.9121	0.571432
$682$	−8.14875	−0.312032
$683$	38.3070	1.46578	0.732888	−	0.680349i	$-0.238172\pi$
$683$	38.3070	1.46578	0.732888	+	0.680349i	$0.238172\pi$
$684$	4.83293	0.184792
$685$	−11.0534	−0.422329
$686$	−2.67225	−0.102027
$687$	14.1266	0.538964
$688$	87.5108	3.33632
$689$	0	0
$690$	30.3084	1.15382
$691$	13.5321	0.514786	0.257393	−	0.966307i	$-0.417137\pi$
$691$	13.5321	0.514786	0.257393	+	0.966307i	$0.417137\pi$
$692$	−73.9811	−2.81234
$693$	3.03214	0.115181
$694$	30.1027	1.14268
$695$	−11.9734	−0.454178
$696$	−48.6717	−1.84489
$697$	−35.1946	−1.33309
$698$	28.4359	1.07632
$699$	15.0580	0.569545
$700$	16.6697	0.630056
$701$	−33.0151	−1.24696	−0.623482	−	0.781838i	$-0.714282\pi$
$701$	−33.0151	−1.24696	−0.623482	+	0.781838i	$0.714282\pi$
$702$	0	0
$703$	10.6537	0.401811
$704$	−53.3335	−2.01008
$705$	17.0002	0.640263
$706$	−24.1509	−0.908932
$707$	15.6199	0.587446
$708$	67.7749	2.54714
$709$	−18.2760	−0.686370	−0.343185	−	0.939268i	$-0.611506\pi$
$709$	−18.2760	−0.686370	−0.343185	+	0.939268i	$0.611506\pi$
$710$	21.4111	0.803543
$711$	1.46368	0.0548923
$712$	−27.0765	−1.01474
$713$	8.60422	0.322231
$714$	12.1971	0.456464
$715$	0	0
$716$	59.0246	2.20585
$717$	−4.14971	−0.154974
$718$	−6.27249	−0.234087
$719$	3.47453	0.129578	0.0647891	−	0.997899i	$-0.479363\pi$
$719$	3.47453	0.129578	0.0647891	+	0.997899i	$0.479363\pi$
$720$	−16.1033	−0.600133
$721$	−3.64829	−0.135870
$722$	−48.4110	−1.80167
$723$	18.1010	0.673185
$724$	−136.614	−5.07722
$725$	−18.8032	−0.698334
$726$	4.82642	0.179125
$727$	17.5710	0.651674	0.325837	−	0.945426i	$-0.394354\pi$
$727$	17.5710	0.651674	0.325837	+	0.945426i	$0.394354\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	43.4874	1.60954
$731$	32.8827	1.21621
$732$	−29.9621	−1.10743
$733$	9.61436	0.355114	0.177557	−	0.984110i	$-0.443181\pi$
$733$	9.61436	0.355114	0.177557	+	0.984110i	$0.443181\pi$
$734$	80.5391	2.97275
$735$	1.32568	0.0488986
$736$	134.096	4.94283
$737$	−9.16607	−0.337637
$738$	−20.6051	−0.758483
$739$	26.3610	0.969705	0.484853	−	0.874596i	$-0.338873\pi$
$739$	26.3610	0.969705	0.484853	+	0.874596i	$0.338873\pi$
$740$	−77.2341	−2.83918
$741$	0	0
$742$	−14.0638	−0.516298
$743$	−22.0239	−0.807980	−0.403990	−	0.914764i	$-0.632377\pi$
$743$	−22.0239	−0.807980	−0.403990	+	0.914764i	$0.632377\pi$
$744$	−8.44106	−0.309464
$745$	15.3465	0.562251
$746$	−4.99180	−0.182763
$747$	4.31767	0.157975
$748$	−71.1489	−2.60146
$749$	13.8712	0.506844
$750$	−29.1997	−1.06622
$751$	−12.4993	−0.456105	−0.228052	−	0.973649i	$-0.573236\pi$
$751$	−12.4993	−0.456105	−0.228052	+	0.973649i	$0.573236\pi$
$752$	155.771	5.68038
$753$	−4.22142	−0.153837
$754$	0	0
$755$	−16.9779	−0.617891
$756$	5.14091	0.186973
$757$	−6.58820	−0.239452	−0.119726	−	0.992807i	$-0.538202\pi$
$757$	−6.58820	−0.239452	−0.119726	+	0.992807i	$0.538202\pi$
$758$	−83.5575	−3.03494
$759$	25.9415	0.941618
$760$	−10.4603	−0.379434
$761$	45.9690	1.66637	0.833187	−	0.552991i	$-0.186514\pi$
$761$	45.9690	1.66637	0.833187	+	0.552991i	$0.186514\pi$
$762$	8.93641	0.323732
$763$	−4.46904	−0.161790
$764$	−2.99514	−0.108361
$765$	−6.05089	−0.218770
$766$	−14.0948	−0.509266
$767$	0	0
$768$	−6.65816	−0.240256
$769$	−26.8238	−0.967291	−0.483645	−	0.875264i	$-0.660688\pi$
$769$	−26.8238	−0.967291	−0.483645	+	0.875264i	$0.660688\pi$
$770$	−10.7415	−0.387098
$771$	−11.8550	−0.426947
$772$	−21.6189	−0.778082
$773$	−16.6180	−0.597708	−0.298854	−	0.954299i	$-0.596604\pi$
$773$	−16.6180	−0.597708	−0.298854	+	0.954299i	$0.596604\pi$
$774$	19.2515	0.691981
$775$	−3.26102	−0.117139
$776$	−46.3111	−1.66247
$777$	11.3326	0.406554
$778$	85.3834	3.06114
$779$	−7.24883	−0.259716
$780$	0	0
$781$	18.3261	0.655760
$782$	104.352	3.73163
$783$	−5.79888	−0.207235
$784$	12.1471	0.433826
$785$	−28.1466	−1.00459
$786$	−46.9690	−1.67533
$787$	−53.2069	−1.89662	−0.948311	−	0.317342i	$-0.897210\pi$
$787$	−53.2069	−1.89662	−0.948311	+	0.317342i	$0.897210\pi$
$788$	103.272	3.67892
$789$	−12.5753	−0.447692
$790$	−5.18517	−0.184480
$791$	6.59144	0.234365
$792$	−25.4496	−0.904313
$793$	0	0
$794$	0.309408	0.0109805
$795$	6.97695	0.247447
$796$	−136.830	−4.84980
$797$	−8.69215	−0.307892	−0.153946	−	0.988079i	$-0.549198\pi$
$797$	−8.69215	−0.307892	−0.153946	+	0.988079i	$0.549198\pi$
$798$	2.51216	0.0889295
$799$	58.5318	2.07071
$800$	−50.8225	−1.79685
$801$	−3.22598	−0.113984
$802$	−47.3437	−1.67176
$803$	37.2217	1.31352
$804$	−15.5408	−0.548082
$805$	11.3419	0.399750
$806$	0	0
$807$	−12.5342	−0.441223
$808$	−131.102	−4.61215
$809$	9.92301	0.348875	0.174437	−	0.984668i	$-0.444189\pi$
$809$	9.92301	0.348875	0.174437	+	0.984668i	$0.444189\pi$
$810$	−3.54256	−0.124473
$811$	−5.95089	−0.208964	−0.104482	−	0.994527i	$-0.533318\pi$
$811$	−5.95089	−0.208964	−0.104482	+	0.994527i	$0.533318\pi$
$812$	−29.8115	−1.04618
$813$	3.47597	0.121908
$814$	−91.8237	−3.21842
$815$	12.7132	0.445324
$816$	−55.4438	−1.94092
$817$	6.77265	0.236945
$818$	49.5415	1.73218
$819$	0	0
$820$	52.5506	1.83515
$821$	−52.7490	−1.84095	−0.920476	−	0.390800i	$-0.872198\pi$
$821$	−52.7490	−1.84095	−0.920476	+	0.390800i	$0.872198\pi$
$822$	−22.2809	−0.777136
$823$	−9.92502	−0.345964	−0.172982	−	0.984925i	$-0.555340\pi$
$823$	−9.92502	−0.345964	−0.172982	+	0.984925i	$0.555340\pi$
$824$	30.6212	1.06674
$825$	−9.83190	−0.342303
$826$	35.2294	1.22579
$827$	18.6645	0.649028	0.324514	−	0.945881i	$-0.394799\pi$
$827$	18.6645	0.649028	0.324514	+	0.945881i	$0.394799\pi$
$828$	43.9832	1.52852
$829$	12.8111	0.444947	0.222473	−	0.974939i	$-0.428587\pi$
$829$	12.8111	0.444947	0.222473	+	0.974939i	$0.428587\pi$
$830$	−15.2956	−0.530918
$831$	6.76964	0.234836
$832$	0	0
$833$	4.56435	0.158145
$834$	−24.1354	−0.835741
$835$	−24.2672	−0.839801
$836$	−14.6541	−0.506823
$837$	−1.00569	−0.0347618
$838$	54.1584	1.87087
$839$	2.50652	0.0865348	0.0432674	−	0.999064i	$-0.486223\pi$
$839$	2.50652	0.0865348	0.0432674	+	0.999064i	$0.486223\pi$
$840$	−11.1269	−0.383913
$841$	4.62700	0.159552
$842$	−103.357	−3.56191
$843$	−4.18616	−0.144179
$844$	−115.804	−3.98615
$845$	0	0
$846$	34.2681	1.17816
$847$	1.80613	0.0620592
$848$	63.9292	2.19534
$849$	−5.21985	−0.179145
$850$	−39.5498	−1.35655
$851$	96.9562	3.32361
$852$	31.0714	1.06449
$853$	35.0626	1.20052	0.600261	−	0.799804i	$-0.295064\pi$
$853$	35.0626	1.20052	0.600261	+	0.799804i	$0.295064\pi$
$854$	−15.5743	−0.532943
$855$	−1.24627	−0.0426214
$856$	−116.425	−3.97933
$857$	21.1331	0.721894	0.360947	−	0.932586i	$-0.382453\pi$
$857$	21.1331	0.721894	0.360947	+	0.932586i	$0.382453\pi$
$858$	0	0
$859$	46.4000	1.58315	0.791574	−	0.611074i	$-0.209262\pi$
$859$	46.4000	1.58315	0.791574	+	0.611074i	$0.209262\pi$
$860$	−49.0985	−1.67424
$861$	−7.71076	−0.262782
$862$	−73.4307	−2.50106
$863$	−15.6094	−0.531349	−0.265675	−	0.964063i	$-0.585595\pi$
$863$	−15.6094	−0.531349	−0.265675	+	0.964063i	$0.585595\pi$
$864$	−15.6736	−0.533225
$865$	19.0775	0.648653
$866$	−95.8838	−3.25826
$867$	−3.83331	−0.130186
$868$	−5.17017	−0.175487
$869$	−4.43808	−0.150552
$870$	20.5429	0.696468
$871$	0	0
$872$	37.5100	1.27025
$873$	−5.51764	−0.186744
$874$	21.4928	0.727006
$875$	−10.9270	−0.369401
$876$	63.1083	2.13223
$877$	24.5637	0.829459	0.414729	−	0.909945i	$-0.363876\pi$
$877$	24.5637	0.829459	0.414729	+	0.909945i	$0.363876\pi$
$878$	−33.7723	−1.13976
$879$	−10.0063	−0.337503
$880$	48.8273	1.64597
$881$	40.3246	1.35857	0.679285	−	0.733874i	$-0.262290\pi$
$881$	40.3246	1.35857	0.679285	+	0.733874i	$0.262290\pi$
$882$	2.67225	0.0899793
$883$	3.76928	0.126846	0.0634232	−	0.997987i	$-0.479798\pi$
$883$	3.76928	0.126846	0.0634232	+	0.997987i	$0.479798\pi$
$884$	0	0
$885$	−17.4771	−0.587486
$886$	12.9912	0.436448
$887$	7.71311	0.258981	0.129490	−	0.991581i	$-0.458666\pi$
$887$	7.71311	0.258981	0.129490	+	0.991581i	$0.458666\pi$
$888$	−95.1176	−3.19194
$889$	3.34415	0.112159
$890$	11.4282	0.383074
$891$	−3.03214	−0.101581
$892$	48.8582	1.63590
$893$	12.0555	0.403420
$894$	30.9346	1.03461
$895$	−15.2206	−0.508770
$896$	−15.6561	−0.523033
$897$	0	0
$898$	−69.6607	−2.32461
$899$	5.83189	0.194504
$900$	−16.6697	−0.555657
$901$	24.0217	0.800280
$902$	62.4775	2.08027
$903$	7.20423	0.239742
$904$	−55.3238	−1.84004
$905$	35.2286	1.17104
$906$	−34.2233	−1.13699
$907$	−6.02488	−0.200053	−0.100026	−	0.994985i	$-0.531893\pi$
$907$	−6.02488	−0.200053	−0.100026	+	0.994985i	$0.531893\pi$
$908$	−76.6616	−2.54410
$909$	−15.6199	−0.518078
$910$	0	0
$911$	−44.1545	−1.46290	−0.731452	−	0.681893i	$-0.761157\pi$
$911$	−44.1545	−1.46290	−0.731452	+	0.681893i	$0.761157\pi$
$912$	−11.4194	−0.378135
$913$	−13.0918	−0.433275
$914$	6.22449	0.205888
$915$	7.72632	0.255424
$916$	−72.6237	−2.39955
$917$	−17.5766	−0.580430
$918$	−12.1971	−0.402564
$919$	2.47103	0.0815119	0.0407559	−	0.999169i	$-0.487023\pi$
$919$	2.47103	0.0815119	0.0407559	+	0.999169i	$0.487023\pi$
$920$	−95.1960	−3.13852
$921$	0.476202	0.0156914
$922$	−31.2317	−1.02856
$923$	0	0
$924$	−15.5880	−0.512806
$925$	−36.7466	−1.20822
$926$	67.6785	2.22405
$927$	3.64829	0.119826
$928$	90.8891	2.98358
$929$	−27.4089	−0.899257	−0.449628	−	0.893216i	$-0.648444\pi$
$929$	−27.4089	−0.899257	−0.449628	+	0.893216i	$0.648444\pi$
$930$	3.56272	0.116826
$931$	0.940093	0.0308103
$932$	−77.4117	−2.53571
$933$	−22.0675	−0.722456
$934$	12.5535	0.410764
$935$	18.3472	0.600016
$936$	0	0
$937$	12.7270	0.415772	0.207886	−	0.978153i	$-0.433342\pi$
$937$	12.7270	0.415772	0.207886	+	0.978153i	$0.433342\pi$
$938$	−8.07813	−0.263760
$939$	6.17383	0.201475
$940$	−87.3963	−2.85055
$941$	3.02848	0.0987256	0.0493628	−	0.998781i	$-0.484281\pi$
$941$	3.02848	0.0987256	0.0493628	+	0.998781i	$0.484281\pi$
$942$	−56.7364	−1.84857
$943$	−65.9696	−2.14827
$944$	−160.141	−5.21214
$945$	−1.32568	−0.0431245
$946$	−58.3732	−1.89788
$947$	4.41915	0.143603	0.0718015	−	0.997419i	$-0.477125\pi$
$947$	4.41915	0.143603	0.0718015	+	0.997419i	$0.477125\pi$
$948$	−7.52465	−0.244389
$949$	0	0
$950$	−8.14583	−0.264286
$951$	−12.1948	−0.395445
$952$	−38.3099	−1.24163
$953$	−11.6151	−0.376250	−0.188125	−	0.982145i	$-0.560241\pi$
$953$	−11.6151	−0.376250	−0.188125	+	0.982145i	$0.560241\pi$
$954$	14.0638	0.455332
$955$	0.772357	0.0249929
$956$	21.3333	0.689968
$957$	17.5830	0.568378
$958$	−68.7871	−2.22241
$959$	−8.33789	−0.269245
$960$	23.3180	0.752585
$961$	−29.9886	−0.967374
$962$	0	0
$963$	−13.8712	−0.446994
$964$	−93.0558	−2.99712
$965$	5.57487	0.179461
$966$	22.8625	0.735588
$967$	14.3606	0.461807	0.230903	−	0.972977i	$-0.425832\pi$
$967$	14.3606	0.461807	0.230903	+	0.972977i	$0.425832\pi$
$968$	−15.1593	−0.487240
$969$	−4.29091	−0.137844
$970$	19.5466	0.627602
$971$	27.3485	0.877656	0.438828	−	0.898571i	$-0.355394\pi$
$971$	27.3485	0.877656	0.438828	+	0.898571i	$0.355394\pi$
$972$	−5.14091	−0.164895
$973$	−9.03188	−0.289549
$974$	−23.4577	−0.751632
$975$	0	0
$976$	70.7956	2.26611
$977$	31.1899	0.997852	0.498926	−	0.866644i	$-0.333728\pi$
$977$	31.1899	0.997852	0.498926	+	0.866644i	$0.333728\pi$
$978$	25.6266	0.819450
$979$	9.78161	0.312622
$980$	−6.81522	−0.217704
$981$	4.46904	0.142686
$982$	92.5720	2.95409
$983$	−33.6418	−1.07301	−0.536504	−	0.843898i	$-0.680255\pi$
$983$	−33.6418	−1.07301	−0.536504	+	0.843898i	$0.680255\pi$
$984$	64.7187	2.06316
$985$	−26.6307	−0.848526
$986$	70.7294	2.25248
$987$	12.8237	0.408182
$988$	0	0
$989$	61.6360	1.95991
$990$	10.7415	0.341388
$991$	47.5698	1.51110	0.755552	−	0.655089i	$-0.227369\pi$
$991$	47.5698	1.51110	0.755552	+	0.655089i	$0.227369\pi$
$992$	15.7628	0.500469
$993$	21.9157	0.695473
$994$	16.1509	0.512277
$995$	35.2842	1.11859
$996$	−22.1968	−0.703331
$997$	−43.7979	−1.38709	−0.693547	−	0.720411i	$-0.743953\pi$
$997$	−43.7979	−1.38709	−0.693547	+	0.720411i	$0.743953\pi$
$998$	40.8669	1.29362
$999$	−11.3326	−0.358547

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bf.1.9	yes	9
13.12	even	2		3549.2.a.be.1.1	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3549.2.a.be.1.1	✓	9	13.12	even	2
3549.2.a.bf.1.9	yes	9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.67225 q^{2} -1.00000 q^{3} +5.14091 q^{4} -1.32568 q^{5} -2.67225 q^{6} -1.00000 q^{7} +8.39329 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.67225 q^{2} -1.00000 q^{3} +5.14091 q^{4} -1.32568 q^{5} -2.67225 q^{6} -1.00000 q^{7} +8.39329 q^{8} +1.00000 q^{9} -3.54256 q^{10} -3.03214 q^{11} -5.14091 q^{12} -2.67225 q^{14} +1.32568 q^{15} +12.1471 q^{16} +4.56435 q^{17} +2.67225 q^{18} +0.940093 q^{19} -6.81522 q^{20} +1.00000 q^{21} -8.10263 q^{22} +8.55552 q^{23} -8.39329 q^{24} -3.24256 q^{25} -1.00000 q^{27} -5.14091 q^{28} +5.79888 q^{29} +3.54256 q^{30} +1.00569 q^{31} +15.6736 q^{32} +3.03214 q^{33} +12.1971 q^{34} +1.32568 q^{35} +5.14091 q^{36} +11.3326 q^{37} +2.51216 q^{38} -11.1269 q^{40} -7.71076 q^{41} +2.67225 q^{42} +7.20423 q^{43} -15.5880 q^{44} -1.32568 q^{45} +22.8625 q^{46} +12.8237 q^{47} -12.1471 q^{48} +1.00000 q^{49} -8.66492 q^{50} -4.56435 q^{51} +5.26290 q^{53} -2.67225 q^{54} +4.01966 q^{55} -8.39329 q^{56} -0.940093 q^{57} +15.4960 q^{58} -13.1834 q^{59} +6.81522 q^{60} +5.82817 q^{61} +2.68746 q^{62} -1.00000 q^{63} +17.5894 q^{64} +8.10263 q^{66} +3.02297 q^{67} +23.4649 q^{68} -8.55552 q^{69} +3.54256 q^{70} -6.04396 q^{71} +8.39329 q^{72} -12.2757 q^{73} +30.2835 q^{74} +3.24256 q^{75} +4.83293 q^{76} +3.03214 q^{77} +1.46368 q^{79} -16.1033 q^{80} +1.00000 q^{81} -20.6051 q^{82} +4.31767 q^{83} +5.14091 q^{84} -6.05089 q^{85} +19.2515 q^{86} -5.79888 q^{87} -25.4496 q^{88} -3.22598 q^{89} -3.54256 q^{90} +43.9832 q^{92} -1.00569 q^{93} +34.2681 q^{94} -1.24627 q^{95} -15.6736 q^{96} -5.51764 q^{97} +2.67225 q^{98} -3.03214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + q^{2} - 9 q^{3} + 5 q^{4} - 9 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 9 q^{9}+O(q^{10}) \) 9 * q + q^2 - 9 * q^3 + 5 * q^4 - 9 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 9 * q^9	\( 9 q + q^{2} - 9 q^{3} + 5 q^{4} - 9 q^{5} - q^{6} - 9 q^{7} + 6 q^{8} + 9 q^{9} + q^{10} + q^{11} - 5 q^{12} - q^{14} + 9 q^{15} + 5 q^{16} + 11 q^{17} + q^{18} - 7 q^{19} - 23 q^{20} + 9 q^{21} - 3 q^{22} + 22 q^{23} - 6 q^{24} - 8 q^{25} - 9 q^{27} - 5 q^{28} + 11 q^{29} - q^{30} - 7 q^{31} + 18 q^{32} - q^{33} + 6 q^{34} + 9 q^{35} + 5 q^{36} + q^{37} - 6 q^{38} - 14 q^{40} - 16 q^{41} + q^{42} + 32 q^{43} - 18 q^{44} - 9 q^{45} + 9 q^{46} + 12 q^{47} - 5 q^{48} + 9 q^{49} - 10 q^{50} - 11 q^{51} + 13 q^{53} - q^{54} + 9 q^{55} - 6 q^{56} + 7 q^{57} - 4 q^{58} - 29 q^{59} + 23 q^{60} - 12 q^{61} + 30 q^{62} - 9 q^{63} + 6 q^{64} + 3 q^{66} + 20 q^{67} + 34 q^{68} - 22 q^{69} - q^{70} + 2 q^{71} + 6 q^{72} - q^{73} + 43 q^{74} + 8 q^{75} - 13 q^{76} - q^{77} + 3 q^{79} + 39 q^{80} + 9 q^{81} - 19 q^{82} - 24 q^{83} + 5 q^{84} - 15 q^{85} + 28 q^{86} - 11 q^{87} - 19 q^{88} - 11 q^{89} + q^{90} + 73 q^{92} + 7 q^{93} + 15 q^{94} + 39 q^{95} - 18 q^{96} - 20 q^{97} + q^{98} + q^{99}+O(q^{100}) \) 9 * q + q^2 - 9 * q^3 + 5 * q^4 - 9 * q^5 - q^6 - 9 * q^7 + 6 * q^8 + 9 * q^9 + q^10 + q^11 - 5 * q^12 - q^14 + 9 * q^15 + 5 * q^16 + 11 * q^17 + q^18 - 7 * q^19 - 23 * q^20 + 9 * q^21 - 3 * q^22 + 22 * q^23 - 6 * q^24 - 8 * q^25 - 9 * q^27 - 5 * q^28 + 11 * q^29 - q^30 - 7 * q^31 + 18 * q^32 - q^33 + 6 * q^34 + 9 * q^35 + 5 * q^36 + q^37 - 6 * q^38 - 14 * q^40 - 16 * q^41 + q^42 + 32 * q^43 - 18 * q^44 - 9 * q^45 + 9 * q^46 + 12 * q^47 - 5 * q^48 + 9 * q^49 - 10 * q^50 - 11 * q^51 + 13 * q^53 - q^54 + 9 * q^55 - 6 * q^56 + 7 * q^57 - 4 * q^58 - 29 * q^59 + 23 * q^60 - 12 * q^61 + 30 * q^62 - 9 * q^63 + 6 * q^64 + 3 * q^66 + 20 * q^67 + 34 * q^68 - 22 * q^69 - q^70 + 2 * q^71 + 6 * q^72 - q^73 + 43 * q^74 + 8 * q^75 - 13 * q^76 - q^77 + 3 * q^79 + 39 * q^80 + 9 * q^81 - 19 * q^82 - 24 * q^83 + 5 * q^84 - 15 * q^85 + 28 * q^86 - 11 * q^87 - 19 * q^88 - 11 * q^89 + q^90 + 73 * q^92 + 7 * q^93 + 15 * q^94 + 39 * q^95 - 18 * q^96 - 20 * q^97 + q^98 + q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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