LMFDB - Embedded newform 7098.2.a.ct.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7098,2,Mod(1,7098)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7098, 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("7098.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7098.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:	$56.6778153547$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.48406561.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 17x^{4} + 39x^{3} + 111x^{2} - 131x - 281 $ x^6 - 3x^5 - 17x^4 + 39x^3 + 111x^2 - 131*x - 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			$-2.10863$ of defining polynomial
Character	$\chi$	$=$	7098.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.10863 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.10863 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.10863 q^{10} +1.55496 q^{11} +1.00000 q^{12} +1.00000 q^{14} -2.10863 q^{15} +1.00000 q^{16} -1.24698 q^{17} +1.00000 q^{18} +6.98503 q^{19} -2.10863 q^{20} +1.00000 q^{21} +1.55496 q^{22} -1.97111 q^{23} +1.00000 q^{24} -0.553673 q^{25} +1.00000 q^{27} +1.00000 q^{28} +6.02003 q^{29} -2.10863 q^{30} +2.75174 q^{31} +1.00000 q^{32} +1.55496 q^{33} -1.24698 q^{34} -2.10863 q^{35} +1.00000 q^{36} -2.76545 q^{37} +6.98503 q^{38} -2.10863 q^{40} -7.97320 q^{41} +1.00000 q^{42} -3.66462 q^{43} +1.55496 q^{44} -2.10863 q^{45} -1.97111 q^{46} +5.63759 q^{47} +1.00000 q^{48} +1.00000 q^{49} -0.553673 q^{50} -1.24698 q^{51} +8.81309 q^{53} +1.00000 q^{54} -3.27883 q^{55} +1.00000 q^{56} +6.98503 q^{57} +6.02003 q^{58} +5.40902 q^{59} -2.10863 q^{60} +3.42032 q^{61} +2.75174 q^{62} +1.00000 q^{63} +1.00000 q^{64} +1.55496 q^{66} -1.40756 q^{67} -1.24698 q^{68} -1.97111 q^{69} -2.10863 q^{70} +11.6269 q^{71} +1.00000 q^{72} -7.48979 q^{73} -2.76545 q^{74} -0.553673 q^{75} +6.98503 q^{76} +1.55496 q^{77} -16.4358 q^{79} -2.10863 q^{80} +1.00000 q^{81} -7.97320 q^{82} +16.7237 q^{83} +1.00000 q^{84} +2.62942 q^{85} -3.66462 q^{86} +6.02003 q^{87} +1.55496 q^{88} +10.9813 q^{89} -2.10863 q^{90} -1.97111 q^{92} +2.75174 q^{93} +5.63759 q^{94} -14.7289 q^{95} +1.00000 q^{96} -6.39487 q^{97} +1.00000 q^{98} +1.55496 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9	$ 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} + 3 q^{10} + 10 q^{11} + 6 q^{12} + 6 q^{14} + 3 q^{15} + 6 q^{16} + 2 q^{17} + 6 q^{18} + 2 q^{19} + 3 q^{20} + 6 q^{21} + 10 q^{22} + 4 q^{23} + 6 q^{24} + 13 q^{25} + 6 q^{27} + 6 q^{28} + 2 q^{29} + 3 q^{30} + 9 q^{31} + 6 q^{32} + 10 q^{33} + 2 q^{34} + 3 q^{35} + 6 q^{36} + 7 q^{37} + 2 q^{38} + 3 q^{40} + 11 q^{41} + 6 q^{42} - 5 q^{43} + 10 q^{44} + 3 q^{45} + 4 q^{46} + 5 q^{47} + 6 q^{48} + 6 q^{49} + 13 q^{50} + 2 q^{51} - 6 q^{53} + 6 q^{54} + 5 q^{55} + 6 q^{56} + 2 q^{57} + 2 q^{58} + 28 q^{59} + 3 q^{60} + 23 q^{61} + 9 q^{62} + 6 q^{63} + 6 q^{64} + 10 q^{66} - 10 q^{67} + 2 q^{68} + 4 q^{69} + 3 q^{70} + 21 q^{71} + 6 q^{72} - 7 q^{73} + 7 q^{74} + 13 q^{75} + 2 q^{76} + 10 q^{77} - 14 q^{79} + 3 q^{80} + 6 q^{81} + 11 q^{82} + 17 q^{83} + 6 q^{84} + q^{85} - 5 q^{86} + 2 q^{87} + 10 q^{88} + 17 q^{89} + 3 q^{90} + 4 q^{92} + 9 q^{93} + 5 q^{94} - 22 q^{95} + 6 q^{96} + 6 q^{98} + 10 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9 + 3 * q^10 + 10 * q^11 + 6 * q^12 + 6 * q^14 + 3 * q^15 + 6 * q^16 + 2 * q^17 + 6 * q^18 + 2 * q^19 + 3 * q^20 + 6 * q^21 + 10 * q^22 + 4 * q^23 + 6 * q^24 + 13 * q^25 + 6 * q^27 + 6 * q^28 + 2 * q^29 + 3 * q^30 + 9 * q^31 + 6 * q^32 + 10 * q^33 + 2 * q^34 + 3 * q^35 + 6 * q^36 + 7 * q^37 + 2 * q^38 + 3 * q^40 + 11 * q^41 + 6 * q^42 - 5 * q^43 + 10 * q^44 + 3 * q^45 + 4 * q^46 + 5 * q^47 + 6 * q^48 + 6 * q^49 + 13 * q^50 + 2 * q^51 - 6 * q^53 + 6 * q^54 + 5 * q^55 + 6 * q^56 + 2 * q^57 + 2 * q^58 + 28 * q^59 + 3 * q^60 + 23 * q^61 + 9 * q^62 + 6 * q^63 + 6 * q^64 + 10 * q^66 - 10 * q^67 + 2 * q^68 + 4 * q^69 + 3 * q^70 + 21 * q^71 + 6 * q^72 - 7 * q^73 + 7 * q^74 + 13 * q^75 + 2 * q^76 + 10 * q^77 - 14 * q^79 + 3 * q^80 + 6 * q^81 + 11 * q^82 + 17 * q^83 + 6 * q^84 + q^85 - 5 * q^86 + 2 * q^87 + 10 * q^88 + 17 * q^89 + 3 * q^90 + 4 * q^92 + 9 * q^93 + 5 * q^94 - 22 * q^95 + 6 * q^96 + 6 * q^98 + 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	−2.10863	−0.943009	−0.471504	−	0.881864i	$-0.656289\pi$
$5$	−2.10863	−0.943009	−0.471504	+	0.881864i	$0.656289\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.10863	−0.666808
$11$	1.55496	0.468838	0.234419	−	0.972136i	$-0.424681\pi$
$11$	1.55496	0.468838	0.234419	+	0.972136i	$0.424681\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	−2.10863	−0.544446
$16$	1.00000	0.250000
$17$	−1.24698	−0.302437	−0.151218	−	0.988500i	$-0.548320\pi$
$17$	−1.24698	−0.302437	−0.151218	+	0.988500i	$0.548320\pi$
$18$	1.00000	0.235702
$19$	6.98503	1.60248	0.801238	−	0.598346i	$-0.204175\pi$
$19$	6.98503	1.60248	0.801238	+	0.598346i	$0.204175\pi$
$20$	−2.10863	−0.471504
$21$	1.00000	0.218218
$22$	1.55496	0.331518
$23$	−1.97111	−0.411005	−0.205502	−	0.978657i	$-0.565883\pi$
$23$	−1.97111	−0.411005	−0.205502	+	0.978657i	$0.565883\pi$
$24$	1.00000	0.204124
$25$	−0.553673	−0.110735
$26$	0	0
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	6.02003	1.11789	0.558945	−	0.829204i	$-0.311206\pi$
$29$	6.02003	1.11789	0.558945	+	0.829204i	$0.311206\pi$
$30$	−2.10863	−0.384982
$31$	2.75174	0.494226	0.247113	−	0.968987i	$-0.420518\pi$
$31$	2.75174	0.494226	0.247113	+	0.968987i	$0.420518\pi$
$32$	1.00000	0.176777
$33$	1.55496	0.270683
$34$	−1.24698	−0.213855
$35$	−2.10863	−0.356424
$36$	1.00000	0.166667
$37$	−2.76545	−0.454638	−0.227319	−	0.973820i	$-0.572996\pi$
$37$	−2.76545	−0.454638	−0.227319	+	0.973820i	$0.572996\pi$
$38$	6.98503	1.13312
$39$	0	0
$40$	−2.10863	−0.333404
$41$	−7.97320	−1.24521	−0.622603	−	0.782538i	$-0.713925\pi$
$41$	−7.97320	−1.24521	−0.622603	+	0.782538i	$0.713925\pi$
$42$	1.00000	0.154303
$43$	−3.66462	−0.558849	−0.279425	−	0.960168i	$-0.590144\pi$
$43$	−3.66462	−0.558849	−0.279425	+	0.960168i	$0.590144\pi$
$44$	1.55496	0.234419
$45$	−2.10863	−0.314336
$46$	−1.97111	−0.290624
$47$	5.63759	0.822326	0.411163	−	0.911562i	$-0.365123\pi$
$47$	5.63759	0.822326	0.411163	+	0.911562i	$0.365123\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−0.553673	−0.0783012
$51$	−1.24698	−0.174612
$52$	0	0
$53$	8.81309	1.21057	0.605285	−	0.796009i	$-0.293059\pi$
$53$	8.81309	1.21057	0.605285	+	0.796009i	$0.293059\pi$
$54$	1.00000	0.136083
$55$	−3.27883	−0.442118
$56$	1.00000	0.133631
$57$	6.98503	0.925190
$58$	6.02003	0.790468
$59$	5.40902	0.704194	0.352097	−	0.935964i	$-0.385469\pi$
$59$	5.40902	0.704194	0.352097	+	0.935964i	$0.385469\pi$
$60$	−2.10863	−0.272223
$61$	3.42032	0.437928	0.218964	−	0.975733i	$-0.429732\pi$
$61$	3.42032	0.437928	0.218964	+	0.975733i	$0.429732\pi$
$62$	2.75174	0.349471
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	1.55496	0.191402
$67$	−1.40756	−0.171960	−0.0859802	−	0.996297i	$-0.527402\pi$
$67$	−1.40756	−0.171960	−0.0859802	+	0.996297i	$0.527402\pi$
$68$	−1.24698	−0.151218
$69$	−1.97111	−0.237294
$70$	−2.10863	−0.252030
$71$	11.6269	1.37985	0.689927	−	0.723879i	$-0.257643\pi$
$71$	11.6269	1.37985	0.689927	+	0.723879i	$0.257643\pi$
$72$	1.00000	0.117851
$73$	−7.48979	−0.876613	−0.438307	−	0.898825i	$-0.644422\pi$
$73$	−7.48979	−0.876613	−0.438307	+	0.898825i	$0.644422\pi$
$74$	−2.76545	−0.321477
$75$	−0.553673	−0.0639327
$76$	6.98503	0.801238
$77$	1.55496	0.177204
$78$	0	0
$79$	−16.4358	−1.84918	−0.924589	−	0.380967i	$-0.875591\pi$
$79$	−16.4358	−1.84918	−0.924589	+	0.380967i	$0.875591\pi$
$80$	−2.10863	−0.235752
$81$	1.00000	0.111111
$82$	−7.97320	−0.880493
$83$	16.7237	1.83566	0.917830	−	0.396974i	$-0.129940\pi$
$83$	16.7237	1.83566	0.917830	+	0.396974i	$0.129940\pi$
$84$	1.00000	0.109109
$85$	2.62942	0.285201
$86$	−3.66462	−0.395166
$87$	6.02003	0.645415
$88$	1.55496	0.165759
$89$	10.9813	1.16401	0.582005	−	0.813185i	$-0.302268\pi$
$89$	10.9813	1.16401	0.582005	+	0.813185i	$0.302268\pi$
$90$	−2.10863	−0.222269
$91$	0	0
$92$	−1.97111	−0.205502
$93$	2.75174	0.285342
$94$	5.63759	0.581473
$95$	−14.7289	−1.51115
$96$	1.00000	0.102062
$97$	−6.39487	−0.649301	−0.324651	−	0.945834i	$-0.605247\pi$
$97$	−6.39487	−0.649301	−0.324651	+	0.945834i	$0.605247\pi$
$98$	1.00000	0.101015
$99$	1.55496	0.156279
$100$	−0.553673	−0.0553673
$101$	−1.28670	−0.128032	−0.0640158	−	0.997949i	$-0.520391\pi$
$101$	−1.28670	−0.128032	−0.0640158	+	0.997949i	$0.520391\pi$
$102$	−1.24698	−0.123469
$103$	6.54173	0.644576	0.322288	−	0.946642i	$-0.395548\pi$
$103$	6.54173	0.644576	0.322288	+	0.946642i	$0.395548\pi$
$104$	0	0
$105$	−2.10863	−0.205781
$106$	8.81309	0.856003
$107$	2.66334	0.257474	0.128737	−	0.991679i	$-0.458908\pi$
$107$	2.66334	0.257474	0.128737	+	0.991679i	$0.458908\pi$
$108$	1.00000	0.0962250
$109$	−4.40973	−0.422376	−0.211188	−	0.977446i	$-0.567733\pi$
$109$	−4.40973	−0.422376	−0.211188	+	0.977446i	$0.567733\pi$
$110$	−3.27883	−0.312625
$111$	−2.76545	−0.262485
$112$	1.00000	0.0944911
$113$	−5.81726	−0.547242	−0.273621	−	0.961838i	$-0.588221\pi$
$113$	−5.81726	−0.547242	−0.273621	+	0.961838i	$0.588221\pi$
$114$	6.98503	0.654208
$115$	4.15634	0.387581
$116$	6.02003	0.558945
$117$	0	0
$118$	5.40902	0.497940
$119$	−1.24698	−0.114310
$120$	−2.10863	−0.192491
$121$	−8.58211	−0.780191
$122$	3.42032	0.309662
$123$	−7.97320	−0.718920
$124$	2.75174	0.247113
$125$	11.7107	1.04743
$126$	1.00000	0.0890871
$127$	−3.83276	−0.340103	−0.170051	−	0.985435i	$-0.554393\pi$
$127$	−3.83276	−0.340103	−0.170051	+	0.985435i	$0.554393\pi$
$128$	1.00000	0.0883883
$129$	−3.66462	−0.322652
$130$	0	0
$131$	11.8617	1.03637	0.518183	−	0.855270i	$-0.326609\pi$
$131$	11.8617	1.03637	0.518183	+	0.855270i	$0.326609\pi$
$132$	1.55496	0.135342
$133$	6.98503	0.605679
$134$	−1.40756	−0.121594
$135$	−2.10863	−0.181482
$136$	−1.24698	−0.106928
$137$	2.18760	0.186899	0.0934496	−	0.995624i	$-0.470211\pi$
$137$	2.18760	0.186899	0.0934496	+	0.995624i	$0.470211\pi$
$138$	−1.97111	−0.167792
$139$	4.14041	0.351185	0.175592	−	0.984463i	$-0.443816\pi$
$139$	4.14041	0.351185	0.175592	+	0.984463i	$0.443816\pi$
$140$	−2.10863	−0.178212
$141$	5.63759	0.474770
$142$	11.6269	0.975704
$143$	0	0
$144$	1.00000	0.0833333
$145$	−12.6940	−1.05418
$146$	−7.48979	−0.619859
$147$	1.00000	0.0824786
$148$	−2.76545	−0.227319
$149$	16.1634	1.32416	0.662079	−	0.749434i	$-0.269674\pi$
$149$	16.1634	1.32416	0.662079	+	0.749434i	$0.269674\pi$
$150$	−0.553673	−0.0452072
$151$	14.5820	1.18667	0.593333	−	0.804957i	$-0.297812\pi$
$151$	14.5820	1.18667	0.593333	+	0.804957i	$0.297812\pi$
$152$	6.98503	0.566561
$153$	−1.24698	−0.100812
$154$	1.55496	0.125302
$155$	−5.80240	−0.466060
$156$	0	0
$157$	5.49884	0.438855	0.219428	−	0.975629i	$-0.429581\pi$
$157$	5.49884	0.438855	0.219428	+	0.975629i	$0.429581\pi$
$158$	−16.4358	−1.30757
$159$	8.81309	0.698923
$160$	−2.10863	−0.166702
$161$	−1.97111	−0.155345
$162$	1.00000	0.0785674
$163$	14.1960	1.11192	0.555958	−	0.831211i	$-0.312352\pi$
$163$	14.1960	1.11192	0.555958	+	0.831211i	$0.312352\pi$
$164$	−7.97320	−0.622603
$165$	−3.27883	−0.255257
$166$	16.7237	1.29801
$167$	24.5175	1.89722	0.948612	−	0.316442i	$-0.102488\pi$
$167$	24.5175	1.89722	0.948612	+	0.316442i	$0.102488\pi$
$168$	1.00000	0.0771517
$169$	0	0
$170$	2.62942	0.201667
$171$	6.98503	0.534159
$172$	−3.66462	−0.279425
$173$	−12.5776	−0.956259	−0.478129	−	0.878289i	$-0.658685\pi$
$173$	−12.5776	−0.956259	−0.478129	+	0.878289i	$0.658685\pi$
$174$	6.02003	0.456377
$175$	−0.553673	−0.0418538
$176$	1.55496	0.117209
$177$	5.40902	0.406567
$178$	10.9813	0.823080
$179$	2.52767	0.188927	0.0944635	−	0.995528i	$-0.469886\pi$
$179$	2.52767	0.188927	0.0944635	+	0.995528i	$0.469886\pi$
$180$	−2.10863	−0.157168
$181$	−12.7141	−0.945031	−0.472516	−	0.881322i	$-0.656654\pi$
$181$	−12.7141	−0.945031	−0.472516	+	0.881322i	$0.656654\pi$
$182$	0	0
$183$	3.42032	0.252838
$184$	−1.97111	−0.145312
$185$	5.83132	0.428727
$186$	2.75174	0.201767
$187$	−1.93900	−0.141794
$188$	5.63759	0.411163
$189$	1.00000	0.0727393
$190$	−14.7289	−1.06854
$191$	−2.77016	−0.200442	−0.100221	−	0.994965i	$-0.531955\pi$
$191$	−2.77016	−0.200442	−0.100221	+	0.994965i	$0.531955\pi$
$192$	1.00000	0.0721688
$193$	22.2930	1.60468	0.802341	−	0.596865i	$-0.203587\pi$
$193$	22.2930	1.60468	0.802341	+	0.596865i	$0.203587\pi$
$194$	−6.39487	−0.459125
$195$	0	0
$196$	1.00000	0.0714286
$197$	−8.75440	−0.623725	−0.311863	−	0.950127i	$-0.600953\pi$
$197$	−8.75440	−0.623725	−0.311863	+	0.950127i	$0.600953\pi$
$198$	1.55496	0.110506
$199$	−14.5824	−1.03372	−0.516859	−	0.856070i	$-0.672899\pi$
$199$	−14.5824	−1.03372	−0.516859	+	0.856070i	$0.672899\pi$
$200$	−0.553673	−0.0391506
$201$	−1.40756	−0.0992814
$202$	−1.28670	−0.0905320
$203$	6.02003	0.422523
$204$	−1.24698	−0.0873060
$205$	16.8125	1.17424
$206$	6.54173	0.455784
$207$	−1.97111	−0.137002
$208$	0	0
$209$	10.8614	0.751301
$210$	−2.10863	−0.145509
$211$	13.1688	0.906575	0.453287	−	0.891364i	$-0.350251\pi$
$211$	13.1688	0.906575	0.453287	+	0.891364i	$0.350251\pi$
$212$	8.81309	0.605285
$213$	11.6269	0.796659
$214$	2.66334	0.182062
$215$	7.72733	0.527000
$216$	1.00000	0.0680414
$217$	2.75174	0.186800
$218$	−4.40973	−0.298665
$219$	−7.48979	−0.506113
$220$	−3.27883	−0.221059
$221$	0	0
$222$	−2.76545	−0.185605
$223$	4.36466	0.292280	0.146140	−	0.989264i	$-0.453315\pi$
$223$	4.36466	0.292280	0.146140	+	0.989264i	$0.453315\pi$
$224$	1.00000	0.0668153
$225$	−0.553673	−0.0369116
$226$	−5.81726	−0.386958
$227$	0.618667	0.0410624	0.0205312	−	0.999789i	$-0.493464\pi$
$227$	0.618667	0.0410624	0.0205312	+	0.999789i	$0.493464\pi$
$228$	6.98503	0.462595
$229$	−2.93024	−0.193636	−0.0968180	−	0.995302i	$-0.530866\pi$
$229$	−2.93024	−0.193636	−0.0968180	+	0.995302i	$0.530866\pi$
$230$	4.15634	0.274061
$231$	1.55496	0.102309
$232$	6.02003	0.395234
$233$	−18.7941	−1.23124	−0.615620	−	0.788043i	$-0.711094\pi$
$233$	−18.7941	−1.23124	−0.615620	+	0.788043i	$0.711094\pi$
$234$	0	0
$235$	−11.8876	−0.775461
$236$	5.40902	0.352097
$237$	−16.4358	−1.06762
$238$	−1.24698	−0.0808297
$239$	−19.6751	−1.27267	−0.636337	−	0.771411i	$-0.719551\pi$
$239$	−19.6751	−1.27267	−0.636337	+	0.771411i	$0.719551\pi$
$240$	−2.10863	−0.136112
$241$	−5.57097	−0.358858	−0.179429	−	0.983771i	$-0.557425\pi$
$241$	−5.57097	−0.358858	−0.179429	+	0.983771i	$0.557425\pi$
$242$	−8.58211	−0.551679
$243$	1.00000	0.0641500
$244$	3.42032	0.218964
$245$	−2.10863	−0.134716
$246$	−7.97320	−0.508353
$247$	0	0
$248$	2.75174	0.174735
$249$	16.7237	1.05982
$250$	11.7107	0.740647
$251$	10.6372	0.671413	0.335707	−	0.941967i	$-0.391025\pi$
$251$	10.6372	0.671413	0.335707	+	0.941967i	$0.391025\pi$
$252$	1.00000	0.0629941
$253$	−3.06499	−0.192694
$254$	−3.83276	−0.240489
$255$	2.62942	0.164661
$256$	1.00000	0.0625000
$257$	−2.38334	−0.148669	−0.0743345	−	0.997233i	$-0.523683\pi$
$257$	−2.38334	−0.148669	−0.0743345	+	0.997233i	$0.523683\pi$
$258$	−3.66462	−0.228149
$259$	−2.76545	−0.171837
$260$	0	0
$261$	6.02003	0.372630
$262$	11.8617	0.732821
$263$	7.81509	0.481899	0.240949	−	0.970538i	$-0.422541\pi$
$263$	7.81509	0.481899	0.240949	+	0.970538i	$0.422541\pi$
$264$	1.55496	0.0957011
$265$	−18.5836	−1.14158
$266$	6.98503	0.428280
$267$	10.9813	0.672042
$268$	−1.40756	−0.0859802
$269$	−7.21556	−0.439940	−0.219970	−	0.975507i	$-0.570596\pi$
$269$	−7.21556	−0.439940	−0.219970	+	0.975507i	$0.570596\pi$
$270$	−2.10863	−0.128327
$271$	−4.97552	−0.302241	−0.151121	−	0.988515i	$-0.548288\pi$
$271$	−4.97552	−0.302241	−0.151121	+	0.988515i	$0.548288\pi$
$272$	−1.24698	−0.0756092
$273$	0	0
$274$	2.18760	0.132158
$275$	−0.860939	−0.0519166
$276$	−1.97111	−0.118647
$277$	−13.1229	−0.788479	−0.394240	−	0.919008i	$-0.628992\pi$
$277$	−13.1229	−0.788479	−0.394240	+	0.919008i	$0.628992\pi$
$278$	4.14041	0.248325
$279$	2.75174	0.164742
$280$	−2.10863	−0.126015
$281$	−0.105985	−0.00632254	−0.00316127	−	0.999995i	$-0.501006\pi$
$281$	−0.105985	−0.00632254	−0.00316127	+	0.999995i	$0.501006\pi$
$282$	5.63759	0.335713
$283$	29.5509	1.75662	0.878309	−	0.478094i	$-0.158672\pi$
$283$	29.5509	1.75662	0.878309	+	0.478094i	$0.158672\pi$
$284$	11.6269	0.689927
$285$	−14.7289	−0.872462
$286$	0	0
$287$	−7.97320	−0.470643
$288$	1.00000	0.0589256
$289$	−15.4450	−0.908532
$290$	−12.6940	−0.745418
$291$	−6.39487	−0.374874
$292$	−7.48979	−0.438307
$293$	12.1002	0.706903	0.353451	−	0.935453i	$-0.385008\pi$
$293$	12.1002	0.706903	0.353451	+	0.935453i	$0.385008\pi$
$294$	1.00000	0.0583212
$295$	−11.4056	−0.664061
$296$	−2.76545	−0.160739
$297$	1.55496	0.0902278
$298$	16.1634	0.936322
$299$	0	0
$300$	−0.553673	−0.0319663
$301$	−3.66462	−0.211225
$302$	14.5820	0.839099
$303$	−1.28670	−0.0739190
$304$	6.98503	0.400619
$305$	−7.21220	−0.412969
$306$	−1.24698	−0.0712851
$307$	−11.8071	−0.673867	−0.336934	−	0.941528i	$-0.609390\pi$
$307$	−11.8071	−0.673867	−0.336934	+	0.941528i	$0.609390\pi$
$308$	1.55496	0.0886020
$309$	6.54173	0.372146
$310$	−5.80240	−0.329554
$311$	2.36454	0.134080	0.0670402	−	0.997750i	$-0.478644\pi$
$311$	2.36454	0.134080	0.0670402	+	0.997750i	$0.478644\pi$
$312$	0	0
$313$	−6.67399	−0.377236	−0.188618	−	0.982051i	$-0.560401\pi$
$313$	−6.67399	−0.377236	−0.188618	+	0.982051i	$0.560401\pi$
$314$	5.49884	0.310318
$315$	−2.10863	−0.118808
$316$	−16.4358	−0.924589
$317$	0.860447	0.0483275	0.0241638	−	0.999708i	$-0.492308\pi$
$317$	0.860447	0.0483275	0.0241638	+	0.999708i	$0.492308\pi$
$318$	8.81309	0.494213
$319$	9.36089	0.524109
$320$	−2.10863	−0.117876
$321$	2.66334	0.148653
$322$	−1.97111	−0.109846
$323$	−8.71019	−0.484648
$324$	1.00000	0.0555556
$325$	0	0
$326$	14.1960	0.786243
$327$	−4.40973	−0.243859
$328$	−7.97320	−0.440247
$329$	5.63759	0.310810
$330$	−3.27883	−0.180494
$331$	15.4980	0.851848	0.425924	−	0.904759i	$-0.359949\pi$
$331$	15.4980	0.851848	0.425924	+	0.904759i	$0.359949\pi$
$332$	16.7237	0.917830
$333$	−2.76545	−0.151546
$334$	24.5175	1.34154
$335$	2.96802	0.162160
$336$	1.00000	0.0545545
$337$	−15.6615	−0.853135	−0.426568	−	0.904456i	$-0.640277\pi$
$337$	−15.6615	−0.853135	−0.426568	+	0.904456i	$0.640277\pi$
$338$	0	0
$339$	−5.81726	−0.315950
$340$	2.62942	0.142600
$341$	4.27883	0.231712
$342$	6.98503	0.377707
$343$	1.00000	0.0539949
$344$	−3.66462	−0.197583
$345$	4.15634	0.223770
$346$	−12.5776	−0.676177
$347$	−13.0233	−0.699129	−0.349564	−	0.936912i	$-0.613670\pi$
$347$	−13.0233	−0.699129	−0.349564	+	0.936912i	$0.613670\pi$
$348$	6.02003	0.322707
$349$	26.4749	1.41717	0.708584	−	0.705626i	$-0.249334\pi$
$349$	26.4749	1.41717	0.708584	+	0.705626i	$0.249334\pi$
$350$	−0.553673	−0.0295951
$351$	0	0
$352$	1.55496	0.0828795
$353$	21.5831	1.14875	0.574375	−	0.818592i	$-0.305245\pi$
$353$	21.5831	1.14875	0.574375	+	0.818592i	$0.305245\pi$
$354$	5.40902	0.287486
$355$	−24.5167	−1.30121
$356$	10.9813	0.582005
$357$	−1.24698	−0.0659972
$358$	2.52767	0.133592
$359$	4.67664	0.246824	0.123412	−	0.992356i	$-0.460616\pi$
$359$	4.67664	0.246824	0.123412	+	0.992356i	$0.460616\pi$
$360$	−2.10863	−0.111135
$361$	29.7907	1.56793
$362$	−12.7141	−0.668238
$363$	−8.58211	−0.450444
$364$	0	0
$365$	15.7932	0.826654
$366$	3.42032	0.178783
$367$	31.3614	1.63705	0.818525	−	0.574471i	$-0.194792\pi$
$367$	31.3614	1.63705	0.818525	+	0.574471i	$0.194792\pi$
$368$	−1.97111	−0.102751
$369$	−7.97320	−0.415068
$370$	5.83132	0.303156
$371$	8.81309	0.457553
$372$	2.75174	0.142671
$373$	28.2046	1.46038	0.730190	−	0.683244i	$-0.239432\pi$
$373$	28.2046	1.46038	0.730190	+	0.683244i	$0.239432\pi$
$374$	−1.93900	−0.100263
$375$	11.7107	0.604735
$376$	5.63759	0.290736
$377$	0	0
$378$	1.00000	0.0514344
$379$	−32.5590	−1.67245	−0.836223	−	0.548390i	$-0.815241\pi$
$379$	−32.5590	−1.67245	−0.836223	+	0.548390i	$0.815241\pi$
$380$	−14.7289	−0.755574
$381$	−3.83276	−0.196358
$382$	−2.77016	−0.141734
$383$	8.63110	0.441029	0.220514	−	0.975384i	$-0.429226\pi$
$383$	8.63110	0.441029	0.220514	+	0.975384i	$0.429226\pi$
$384$	1.00000	0.0510310
$385$	−3.27883	−0.167105
$386$	22.2930	1.13468
$387$	−3.66462	−0.186283
$388$	−6.39487	−0.324651
$389$	−26.3682	−1.33692	−0.668460	−	0.743748i	$-0.733046\pi$
$389$	−26.3682	−1.33692	−0.668460	+	0.743748i	$0.733046\pi$
$390$	0	0
$391$	2.45793	0.124303
$392$	1.00000	0.0505076
$393$	11.8617	0.598346
$394$	−8.75440	−0.441040
$395$	34.6571	1.74379
$396$	1.55496	0.0781396
$397$	−12.0701	−0.605779	−0.302889	−	0.953026i	$-0.597951\pi$
$397$	−12.0701	−0.605779	−0.302889	+	0.953026i	$0.597951\pi$
$398$	−14.5824	−0.730949
$399$	6.98503	0.349689
$400$	−0.553673	−0.0276837
$401$	−18.5164	−0.924664	−0.462332	−	0.886707i	$-0.652987\pi$
$401$	−18.5164	−0.924664	−0.462332	+	0.886707i	$0.652987\pi$
$402$	−1.40756	−0.0702025
$403$	0	0
$404$	−1.28670	−0.0640158
$405$	−2.10863	−0.104779
$406$	6.02003	0.298769
$407$	−4.30016	−0.213151
$408$	−1.24698	−0.0617347
$409$	−35.8394	−1.77214	−0.886072	−	0.463547i	$-0.846576\pi$
$409$	−35.8394	−1.77214	−0.886072	+	0.463547i	$0.846576\pi$
$410$	16.8125	0.830313
$411$	2.18760	0.107906
$412$	6.54173	0.322288
$413$	5.40902	0.266160
$414$	−1.97111	−0.0968748
$415$	−35.2640	−1.73104
$416$	0	0
$417$	4.14041	0.202757
$418$	10.8614	0.531250
$419$	27.0079	1.31942	0.659710	−	0.751520i	$-0.270679\pi$
$419$	27.0079	1.31942	0.659710	+	0.751520i	$0.270679\pi$
$420$	−2.10863	−0.102891
$421$	−26.2859	−1.28110	−0.640549	−	0.767918i	$-0.721293\pi$
$421$	−26.2859	−1.28110	−0.640549	+	0.767918i	$0.721293\pi$
$422$	13.1688	0.641045
$423$	5.63759	0.274109
$424$	8.81309	0.428001
$425$	0.690419	0.0334903
$426$	11.6269	0.563323
$427$	3.42032	0.165521
$428$	2.66334	0.128737
$429$	0	0
$430$	7.72733	0.372645
$431$	−6.58585	−0.317229	−0.158615	−	0.987341i	$-0.550703\pi$
$431$	−6.58585	−0.317229	−0.158615	+	0.987341i	$0.550703\pi$
$432$	1.00000	0.0481125
$433$	25.4472	1.22291	0.611457	−	0.791278i	$-0.290584\pi$
$433$	25.4472	1.22291	0.611457	+	0.791278i	$0.290584\pi$
$434$	2.75174	0.132088
$435$	−12.6940	−0.608632
$436$	−4.40973	−0.211188
$437$	−13.7683	−0.658625
$438$	−7.48979	−0.357876
$439$	23.8445	1.13803	0.569017	−	0.822326i	$-0.307324\pi$
$439$	23.8445	1.13803	0.569017	+	0.822326i	$0.307324\pi$
$440$	−3.27883	−0.156312
$441$	1.00000	0.0476190
$442$	0	0
$443$	−0.966959	−0.0459416	−0.0229708	−	0.999736i	$-0.507312\pi$
$443$	−0.966959	−0.0459416	−0.0229708	+	0.999736i	$0.507312\pi$
$444$	−2.76545	−0.131243
$445$	−23.1554	−1.09767
$446$	4.36466	0.206673
$447$	16.1634	0.764503
$448$	1.00000	0.0472456
$449$	−32.7563	−1.54586	−0.772932	−	0.634489i	$-0.781210\pi$
$449$	−32.7563	−1.54586	−0.772932	+	0.634489i	$0.781210\pi$
$450$	−0.553673	−0.0261004
$451$	−12.3980	−0.583799
$452$	−5.81726	−0.273621
$453$	14.5820	0.685122
$454$	0.618667	0.0290355
$455$	0	0
$456$	6.98503	0.327104
$457$	2.38368	0.111504	0.0557520	−	0.998445i	$-0.482244\pi$
$457$	2.38368	0.111504	0.0557520	+	0.998445i	$0.482244\pi$
$458$	−2.93024	−0.136921
$459$	−1.24698	−0.0582040
$460$	4.15634	0.193791
$461$	36.9292	1.71996	0.859982	−	0.510325i	$-0.170475\pi$
$461$	36.9292	1.71996	0.859982	+	0.510325i	$0.170475\pi$
$462$	1.55496	0.0723432
$463$	−29.8161	−1.38567	−0.692836	−	0.721095i	$-0.743639\pi$
$463$	−29.8161	−1.38567	−0.692836	+	0.721095i	$0.743639\pi$
$464$	6.02003	0.279473
$465$	−5.80240	−0.269080
$466$	−18.7941	−0.870618
$467$	9.34853	0.432598	0.216299	−	0.976327i	$-0.430601\pi$
$467$	9.34853	0.432598	0.216299	+	0.976327i	$0.430601\pi$
$468$	0	0
$469$	−1.40756	−0.0649949
$470$	−11.8876	−0.548334
$471$	5.49884	0.253373
$472$	5.40902	0.248970
$473$	−5.69833	−0.262010
$474$	−16.4358	−0.754923
$475$	−3.86743	−0.177450
$476$	−1.24698	−0.0571552
$477$	8.81309	0.403523
$478$	−19.6751	−0.899917
$479$	17.5839	0.803429	0.401715	−	0.915765i	$-0.368414\pi$
$479$	17.5839	0.803429	0.401715	+	0.915765i	$0.368414\pi$
$480$	−2.10863	−0.0962454
$481$	0	0
$482$	−5.57097	−0.253751
$483$	−1.97111	−0.0896886
$484$	−8.58211	−0.390096
$485$	13.4844	0.612297
$486$	1.00000	0.0453609
$487$	35.9216	1.62776	0.813882	−	0.581030i	$-0.197350\pi$
$487$	35.9216	1.62776	0.813882	+	0.581030i	$0.197350\pi$
$488$	3.42032	0.154831
$489$	14.1960	0.641965
$490$	−2.10863	−0.0952583
$491$	−28.4463	−1.28376	−0.641882	−	0.766804i	$-0.721846\pi$
$491$	−28.4463	−1.28376	−0.641882	+	0.766804i	$0.721846\pi$
$492$	−7.97320	−0.359460
$493$	−7.50685	−0.338092
$494$	0	0
$495$	−3.27883	−0.147373
$496$	2.75174	0.123557
$497$	11.6269	0.521536
$498$	16.7237	0.749405
$499$	−41.0934	−1.83960	−0.919798	−	0.392393i	$-0.871647\pi$
$499$	−41.0934	−1.83960	−0.919798	+	0.392393i	$0.871647\pi$
$500$	11.7107	0.523716
$501$	24.5175	1.09536
$502$	10.6372	0.474761
$503$	−39.3325	−1.75375	−0.876874	−	0.480720i	$-0.840375\pi$
$503$	−39.3325	−1.75375	−0.876874	+	0.480720i	$0.840375\pi$
$504$	1.00000	0.0445435
$505$	2.71318	0.120735
$506$	−3.06499	−0.136256
$507$	0	0
$508$	−3.83276	−0.170051
$509$	−39.3970	−1.74624	−0.873121	−	0.487504i	$-0.837907\pi$
$509$	−39.3970	−1.74624	−0.873121	+	0.487504i	$0.837907\pi$
$510$	2.62942	0.116433
$511$	−7.48979	−0.331329
$512$	1.00000	0.0441942
$513$	6.98503	0.308397
$514$	−2.38334	−0.105125
$515$	−13.7941	−0.607841
$516$	−3.66462	−0.161326
$517$	8.76621	0.385537
$518$	−2.76545	−0.121507
$519$	−12.5776	−0.552096
$520$	0	0
$521$	−14.1675	−0.620689	−0.310344	−	0.950624i	$-0.600444\pi$
$521$	−14.1675	−0.620689	−0.310344	+	0.950624i	$0.600444\pi$
$522$	6.02003	0.263489
$523$	−35.5333	−1.55376	−0.776882	−	0.629647i	$-0.783200\pi$
$523$	−35.5333	−1.55376	−0.776882	+	0.629647i	$0.783200\pi$
$524$	11.8617	0.518183
$525$	−0.553673	−0.0241643
$526$	7.81509	0.340754
$527$	−3.43136	−0.149472
$528$	1.55496	0.0676709
$529$	−19.1147	−0.831075
$530$	−18.5836	−0.807218
$531$	5.40902	0.234731
$532$	6.98503	0.302840
$533$	0	0
$534$	10.9813	0.475205
$535$	−5.61599	−0.242801
$536$	−1.40756	−0.0607972
$537$	2.52767	0.109077
$538$	−7.21556	−0.311085
$539$	1.55496	0.0669768
$540$	−2.10863	−0.0907411
$541$	−26.1033	−1.12227	−0.561134	−	0.827725i	$-0.689635\pi$
$541$	−26.1033	−1.12227	−0.561134	+	0.827725i	$0.689635\pi$
$542$	−4.97552	−0.213717
$543$	−12.7141	−0.545614
$544$	−1.24698	−0.0534638
$545$	9.29850	0.398304
$546$	0	0
$547$	30.0222	1.28366	0.641828	−	0.766848i	$-0.278176\pi$
$547$	30.0222	1.28366	0.641828	+	0.766848i	$0.278176\pi$
$548$	2.18760	0.0934496
$549$	3.42032	0.145976
$550$	−0.860939	−0.0367106
$551$	42.0501	1.79139
$552$	−1.97111	−0.0838960
$553$	−16.4358	−0.698923
$554$	−13.1229	−0.557539
$555$	5.83132	0.247526
$556$	4.14041	0.175592
$557$	2.05456	0.0870546	0.0435273	−	0.999052i	$-0.486140\pi$
$557$	2.05456	0.0870546	0.0435273	+	0.999052i	$0.486140\pi$
$558$	2.75174	0.116490
$559$	0	0
$560$	−2.10863	−0.0891059
$561$	−1.93900	−0.0818647
$562$	−0.105985	−0.00447071
$563$	−2.42156	−0.102057	−0.0510283	−	0.998697i	$-0.516250\pi$
$563$	−2.42156	−0.102057	−0.0510283	+	0.998697i	$0.516250\pi$
$564$	5.63759	0.237385
$565$	12.2665	0.516054
$566$	29.5509	1.24212
$567$	1.00000	0.0419961
$568$	11.6269	0.487852
$569$	6.71089	0.281335	0.140668	−	0.990057i	$-0.455075\pi$
$569$	6.71089	0.281335	0.140668	+	0.990057i	$0.455075\pi$
$570$	−14.7289	−0.616924
$571$	2.23277	0.0934384	0.0467192	−	0.998908i	$-0.485123\pi$
$571$	2.23277	0.0934384	0.0467192	+	0.998908i	$0.485123\pi$
$572$	0	0
$573$	−2.77016	−0.115725
$574$	−7.97320	−0.332795
$575$	1.09135	0.0455125
$576$	1.00000	0.0416667
$577$	−38.5277	−1.60393	−0.801964	−	0.597372i	$-0.796212\pi$
$577$	−38.5277	−1.60393	−0.801964	+	0.597372i	$0.796212\pi$
$578$	−15.4450	−0.642429
$579$	22.2930	0.926464
$580$	−12.6940	−0.527090
$581$	16.7237	0.693814
$582$	−6.39487	−0.265076
$583$	13.7040	0.567561
$584$	−7.48979	−0.309930
$585$	0	0
$586$	12.1002	0.499856
$587$	24.0684	0.993409	0.496704	−	0.867920i	$-0.334543\pi$
$587$	24.0684	0.993409	0.496704	+	0.867920i	$0.334543\pi$
$588$	1.00000	0.0412393
$589$	19.2210	0.791986
$590$	−11.4056	−0.469562
$591$	−8.75440	−0.360108
$592$	−2.76545	−0.113659
$593$	18.5679	0.762492	0.381246	−	0.924474i	$-0.375495\pi$
$593$	18.5679	0.762492	0.381246	+	0.924474i	$0.375495\pi$
$594$	1.55496	0.0638007
$595$	2.62942	0.107796
$596$	16.1634	0.662079
$597$	−14.5824	−0.596818
$598$	0	0
$599$	38.4810	1.57229	0.786145	−	0.618042i	$-0.212074\pi$
$599$	38.4810	1.57229	0.786145	+	0.618042i	$0.212074\pi$
$600$	−0.553673	−0.0226036
$601$	−46.5198	−1.89758	−0.948791	−	0.315905i	$-0.897692\pi$
$601$	−46.5198	−1.89758	−0.948791	+	0.315905i	$0.897692\pi$
$602$	−3.66462	−0.149359
$603$	−1.40756	−0.0573201
$604$	14.5820	0.593333
$605$	18.0965	0.735727
$606$	−1.28670	−0.0522687
$607$	−3.32130	−0.134807	−0.0674037	−	0.997726i	$-0.521472\pi$
$607$	−3.32130	−0.134807	−0.0674037	+	0.997726i	$0.521472\pi$
$608$	6.98503	0.283280
$609$	6.02003	0.243944
$610$	−7.21220	−0.292013
$611$	0	0
$612$	−1.24698	−0.0504062
$613$	6.34784	0.256387	0.128193	−	0.991749i	$-0.459082\pi$
$613$	6.34784	0.256387	0.128193	+	0.991749i	$0.459082\pi$
$614$	−11.8071	−0.476496
$615$	16.8125	0.677947
$616$	1.55496	0.0626510
$617$	31.3868	1.26358	0.631792	−	0.775138i	$-0.282320\pi$
$617$	31.3868	1.26358	0.631792	+	0.775138i	$0.282320\pi$
$618$	6.54173	0.263147
$619$	−8.74463	−0.351476	−0.175738	−	0.984437i	$-0.556231\pi$
$619$	−8.74463	−0.351476	−0.175738	+	0.984437i	$0.556231\pi$
$620$	−5.80240	−0.233030
$621$	−1.97111	−0.0790979
$622$	2.36454	0.0948092
$623$	10.9813	0.439955
$624$	0	0
$625$	−21.9251	−0.877003
$626$	−6.67399	−0.266746
$627$	10.8614	0.433764
$628$	5.49884	0.219428
$629$	3.44846	0.137499
$630$	−2.10863	−0.0840099
$631$	−37.0302	−1.47415	−0.737074	−	0.675812i	$-0.763793\pi$
$631$	−37.0302	−1.47415	−0.737074	+	0.675812i	$0.763793\pi$
$632$	−16.4358	−0.653783
$633$	13.1688	0.523411
$634$	0.860447	0.0341727
$635$	8.08188	0.320720
$636$	8.81309	0.349462
$637$	0	0
$638$	9.36089	0.370601
$639$	11.6269	0.459951
$640$	−2.10863	−0.0833510
$641$	−4.96318	−0.196034	−0.0980169	−	0.995185i	$-0.531250\pi$
$641$	−4.96318	−0.196034	−0.0980169	+	0.995185i	$0.531250\pi$
$642$	2.66334	0.105113
$643$	0.0131905	0.000520184 0	0.000260092	−	1.00000i	$-0.499917\pi$
$643$	0.0131905	0.000520184 0	0.000260092		1.00000i	$0.499917\pi$
$644$	−1.97111	−0.0776726
$645$	7.72733	0.304263
$646$	−8.71019	−0.342698
$647$	16.2940	0.640582	0.320291	−	0.947319i	$-0.396219\pi$
$647$	16.2940	0.640582	0.320291	+	0.947319i	$0.396219\pi$
$648$	1.00000	0.0392837
$649$	8.41079	0.330153
$650$	0	0
$651$	2.75174	0.107849
$652$	14.1960	0.555958
$653$	−29.3247	−1.14756	−0.573782	−	0.819008i	$-0.694524\pi$
$653$	−29.3247	−1.14756	−0.573782	+	0.819008i	$0.694524\pi$
$654$	−4.40973	−0.172434
$655$	−25.0121	−0.977302
$656$	−7.97320	−0.311301
$657$	−7.48979	−0.292204
$658$	5.63759	0.219776
$659$	−33.7303	−1.31395	−0.656974	−	0.753914i	$-0.728164\pi$
$659$	−33.7303	−1.31395	−0.656974	+	0.753914i	$0.728164\pi$
$660$	−3.27883	−0.127628
$661$	11.4642	0.445907	0.222953	−	0.974829i	$-0.428430\pi$
$661$	11.4642	0.445907	0.222953	+	0.974829i	$0.428430\pi$
$662$	15.4980	0.602348
$663$	0	0
$664$	16.7237	0.649004
$665$	−14.7289	−0.571161
$666$	−2.76545	−0.107159
$667$	−11.8661	−0.459458
$668$	24.5175	0.948612
$669$	4.36466	0.168748
$670$	2.96802	0.114665
$671$	5.31846	0.205317
$672$	1.00000	0.0385758
$673$	−16.8424	−0.649227	−0.324614	−	0.945847i	$-0.605234\pi$
$673$	−16.8424	−0.649227	−0.324614	+	0.945847i	$0.605234\pi$
$674$	−15.6615	−0.603258
$675$	−0.553673	−0.0213109
$676$	0	0
$677$	−14.5299	−0.558429	−0.279215	−	0.960229i	$-0.590074\pi$
$677$	−14.5299	−0.558429	−0.279215	+	0.960229i	$0.590074\pi$
$678$	−5.81726	−0.223410
$679$	−6.39487	−0.245413
$680$	2.62942	0.100834
$681$	0.618667	0.0237074
$682$	4.27883	0.163845
$683$	−0.888021	−0.0339792	−0.0169896	−	0.999856i	$-0.505408\pi$
$683$	−0.888021	−0.0339792	−0.0169896	+	0.999856i	$0.505408\pi$
$684$	6.98503	0.267079
$685$	−4.61284	−0.176248
$686$	1.00000	0.0381802
$687$	−2.93024	−0.111796
$688$	−3.66462	−0.139712
$689$	0	0
$690$	4.15634	0.158229
$691$	−32.1864	−1.22443	−0.612214	−	0.790692i	$-0.709721\pi$
$691$	−32.1864	−1.22443	−0.612214	+	0.790692i	$0.709721\pi$
$692$	−12.5776	−0.478129
$693$	1.55496	0.0590680
$694$	−13.0233	−0.494359
$695$	−8.73060	−0.331170
$696$	6.02003	0.228189
$697$	9.94242	0.376596
$698$	26.4749	1.00209
$699$	−18.7941	−0.710857
$700$	−0.553673	−0.0209269
$701$	−29.3407	−1.10818	−0.554091	−	0.832456i	$-0.686934\pi$
$701$	−29.3407	−1.10818	−0.554091	+	0.832456i	$0.686934\pi$
$702$	0	0
$703$	−19.3168	−0.728546
$704$	1.55496	0.0586047
$705$	−11.8876	−0.447713
$706$	21.5831	0.812289
$707$	−1.28670	−0.0483914
$708$	5.40902	0.203283
$709$	−34.9450	−1.31239	−0.656194	−	0.754592i	$-0.727835\pi$
$709$	−34.9450	−1.31239	−0.656194	+	0.754592i	$0.727835\pi$
$710$	−24.5167	−0.920097
$711$	−16.4358	−0.616392
$712$	10.9813	0.411540
$713$	−5.42397	−0.203129
$714$	−1.24698	−0.0466670
$715$	0	0
$716$	2.52767	0.0944635
$717$	−19.6751	−0.734779
$718$	4.67664	0.174531
$719$	−39.7736	−1.48331	−0.741653	−	0.670784i	$-0.765958\pi$
$719$	−39.7736	−1.48331	−0.741653	+	0.670784i	$0.765958\pi$
$720$	−2.10863	−0.0785841
$721$	6.54173	0.243627
$722$	29.7907	1.10869
$723$	−5.57097	−0.207187
$724$	−12.7141	−0.472516
$725$	−3.33313	−0.123789
$726$	−8.58211	−0.318512
$727$	28.3096	1.04995	0.524973	−	0.851119i	$-0.324075\pi$
$727$	28.3096	1.04995	0.524973	+	0.851119i	$0.324075\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	15.7932	0.584533
$731$	4.56971	0.169017
$732$	3.42032	0.126419
$733$	15.4937	0.572272	0.286136	−	0.958189i	$-0.407629\pi$
$733$	15.4937	0.572272	0.286136	+	0.958189i	$0.407629\pi$
$734$	31.3614	1.15757
$735$	−2.10863	−0.0777780
$736$	−1.97111	−0.0726561
$737$	−2.18869	−0.0806215
$738$	−7.97320	−0.293498
$739$	46.7102	1.71826	0.859132	−	0.511755i	$-0.171004\pi$
$739$	46.7102	1.71826	0.859132	+	0.511755i	$0.171004\pi$
$740$	5.83132	0.214364
$741$	0	0
$742$	8.81309	0.323539
$743$	37.7024	1.38317	0.691584	−	0.722296i	$-0.256913\pi$
$743$	37.7024	1.38317	0.691584	+	0.722296i	$0.256913\pi$
$744$	2.75174	0.100884
$745$	−34.0827	−1.24869
$746$	28.2046	1.03264
$747$	16.7237	0.611887
$748$	−1.93900	−0.0708969
$749$	2.66334	0.0973161
$750$	11.7107	0.427612
$751$	−30.7925	−1.12364	−0.561818	−	0.827261i	$-0.689898\pi$
$751$	−30.7925	−1.12364	−0.561818	+	0.827261i	$0.689898\pi$
$752$	5.63759	0.205582
$753$	10.6372	0.387641
$754$	0	0
$755$	−30.7480	−1.11904
$756$	1.00000	0.0363696
$757$	8.21818	0.298695	0.149347	−	0.988785i	$-0.452283\pi$
$757$	8.21818	0.298695	0.149347	+	0.988785i	$0.452283\pi$
$758$	−32.5590	−1.18260
$759$	−3.06499	−0.111252
$760$	−14.7289	−0.534272
$761$	−42.8880	−1.55469	−0.777345	−	0.629074i	$-0.783434\pi$
$761$	−42.8880	−1.55469	−0.777345	+	0.629074i	$0.783434\pi$
$762$	−3.83276	−0.138846
$763$	−4.40973	−0.159643
$764$	−2.77016	−0.100221
$765$	2.62942	0.0950669
$766$	8.63110	0.311854
$767$	0	0
$768$	1.00000	0.0360844
$769$	49.1724	1.77320	0.886602	−	0.462534i	$-0.153060\pi$
$769$	49.1724	1.77320	0.886602	+	0.462534i	$0.153060\pi$
$770$	−3.27883	−0.118161
$771$	−2.38334	−0.0858340
$772$	22.2930	0.802341
$773$	−10.3709	−0.373016	−0.186508	−	0.982453i	$-0.559717\pi$
$773$	−10.3709	−0.373016	−0.186508	+	0.982453i	$0.559717\pi$
$774$	−3.66462	−0.131722
$775$	−1.52356	−0.0547280
$776$	−6.39487	−0.229563
$777$	−2.76545	−0.0992101
$778$	−26.3682	−0.945345
$779$	−55.6931	−1.99541
$780$	0	0
$781$	18.0793	0.646927
$782$	2.45793	0.0878955
$783$	6.02003	0.215138
$784$	1.00000	0.0357143
$785$	−11.5950	−0.413844
$786$	11.8617	0.423095
$787$	−23.5512	−0.839509	−0.419754	−	0.907638i	$-0.637884\pi$
$787$	−23.5512	−0.839509	−0.419754	+	0.907638i	$0.637884\pi$
$788$	−8.75440	−0.311863
$789$	7.81509	0.278224
$790$	34.6571	1.23305
$791$	−5.81726	−0.206838
$792$	1.55496	0.0552530
$793$	0	0
$794$	−12.0701	−0.428350
$795$	−18.5836	−0.659091
$796$	−14.5824	−0.516859
$797$	−26.7104	−0.946132	−0.473066	−	0.881027i	$-0.656853\pi$
$797$	−26.7104	−0.946132	−0.473066	+	0.881027i	$0.656853\pi$
$798$	6.98503	0.247267
$799$	−7.02995	−0.248702
$800$	−0.553673	−0.0195753
$801$	10.9813	0.388004
$802$	−18.5164	−0.653836
$803$	−11.6463	−0.410989
$804$	−1.40756	−0.0496407
$805$	4.15634	0.146492
$806$	0	0
$807$	−7.21556	−0.254000
$808$	−1.28670	−0.0452660
$809$	−3.80663	−0.133834	−0.0669169	−	0.997759i	$-0.521316\pi$
$809$	−3.80663	−0.133834	−0.0669169	+	0.997759i	$0.521316\pi$
$810$	−2.10863	−0.0740898
$811$	−0.849234	−0.0298206	−0.0149103	−	0.999889i	$-0.504746\pi$
$811$	−0.849234	−0.0298206	−0.0149103	+	0.999889i	$0.504746\pi$
$812$	6.02003	0.211262
$813$	−4.97552	−0.174499
$814$	−4.30016	−0.150721
$815$	−29.9341	−1.04855
$816$	−1.24698	−0.0436530
$817$	−25.5975	−0.895543
$818$	−35.8394	−1.25310
$819$	0	0
$820$	16.8125	0.587120
$821$	20.0311	0.699090	0.349545	−	0.936919i	$-0.386336\pi$
$821$	20.0311	0.699090	0.349545	+	0.936919i	$0.386336\pi$
$822$	2.18760	0.0763013
$823$	36.6174	1.27640	0.638201	−	0.769870i	$-0.279679\pi$
$823$	36.6174	1.27640	0.638201	+	0.769870i	$0.279679\pi$
$824$	6.54173	0.227892
$825$	−0.860939	−0.0299740
$826$	5.40902	0.188204
$827$	−14.3761	−0.499907	−0.249953	−	0.968258i	$-0.580415\pi$
$827$	−14.3761	−0.499907	−0.249953	+	0.968258i	$0.580415\pi$
$828$	−1.97111	−0.0685008
$829$	−6.10322	−0.211974	−0.105987	−	0.994368i	$-0.533800\pi$
$829$	−6.10322	−0.211974	−0.105987	+	0.994368i	$0.533800\pi$
$830$	−35.2640	−1.22403
$831$	−13.1229	−0.455229
$832$	0	0
$833$	−1.24698	−0.0432053
$834$	4.14041	0.143371
$835$	−51.6984	−1.78910
$836$	10.8614	0.375650
$837$	2.75174	0.0951139
$838$	27.0079	0.932971
$839$	−53.2223	−1.83744	−0.918718	−	0.394914i	$-0.870774\pi$
$839$	−53.2223	−1.83744	−0.918718	+	0.394914i	$0.870774\pi$
$840$	−2.10863	−0.0727547
$841$	7.24072	0.249680
$842$	−26.2859	−0.905873
$843$	−0.105985	−0.00365032
$844$	13.1688	0.453287
$845$	0	0
$846$	5.63759	0.193824
$847$	−8.58211	−0.294885
$848$	8.81309	0.302643
$849$	29.5509	1.01418
$850$	0.690419	0.0236812
$851$	5.45101	0.186858
$852$	11.6269	0.398329
$853$	13.3932	0.458573	0.229287	−	0.973359i	$-0.426361\pi$
$853$	13.3932	0.458573	0.229287	+	0.973359i	$0.426361\pi$
$854$	3.42032	0.117041
$855$	−14.7289	−0.503716
$856$	2.66334	0.0910309
$857$	−3.82155	−0.130541	−0.0652707	−	0.997868i	$-0.520791\pi$
$857$	−3.82155	−0.130541	−0.0652707	+	0.997868i	$0.520791\pi$
$858$	0	0
$859$	−44.8782	−1.53122	−0.765612	−	0.643302i	$-0.777564\pi$
$859$	−44.8782	−1.53122	−0.765612	+	0.643302i	$0.777564\pi$
$860$	7.72733	0.263500
$861$	−7.97320	−0.271726
$862$	−6.58585	−0.224315
$863$	8.69475	0.295973	0.147986	−	0.988989i	$-0.452721\pi$
$863$	8.69475	0.295973	0.147986	+	0.988989i	$0.452721\pi$
$864$	1.00000	0.0340207
$865$	26.5216	0.901760
$866$	25.4472	0.864731
$867$	−15.4450	−0.524541
$868$	2.75174	0.0934000
$869$	−25.5571	−0.866964
$870$	−12.6940	−0.430368
$871$	0	0
$872$	−4.40973	−0.149332
$873$	−6.39487	−0.216434
$874$	−13.7683	−0.465718
$875$	11.7107	0.395892
$876$	−7.48979	−0.253056
$877$	21.9730	0.741976	0.370988	−	0.928638i	$-0.379019\pi$
$877$	21.9730	0.741976	0.370988	+	0.928638i	$0.379019\pi$
$878$	23.8445	0.804712
$879$	12.1002	0.408131
$880$	−3.27883	−0.110529
$881$	−29.7224	−1.00137	−0.500687	−	0.865628i	$-0.666919\pi$
$881$	−29.7224	−1.00137	−0.500687	+	0.865628i	$0.666919\pi$
$882$	1.00000	0.0336718
$883$	35.0900	1.18087	0.590436	−	0.807084i	$-0.298956\pi$
$883$	35.0900	1.18087	0.590436	+	0.807084i	$0.298956\pi$
$884$	0	0
$885$	−11.4056	−0.383396
$886$	−0.966959	−0.0324856
$887$	25.4402	0.854200	0.427100	−	0.904204i	$-0.359535\pi$
$887$	25.4402	0.854200	0.427100	+	0.904204i	$0.359535\pi$
$888$	−2.76545	−0.0928025
$889$	−3.83276	−0.128547
$890$	−23.1554	−0.776172
$891$	1.55496	0.0520931
$892$	4.36466	0.146140
$893$	39.3787	1.31776
$894$	16.1634	0.540586
$895$	−5.32992	−0.178160
$896$	1.00000	0.0334077
$897$	0	0
$898$	−32.7563	−1.09309
$899$	16.5655	0.552491
$900$	−0.553673	−0.0184558
$901$	−10.9897	−0.366121
$902$	−12.3980	−0.412808
$903$	−3.66462	−0.121951
$904$	−5.81726	−0.193479
$905$	26.8093	0.891172
$906$	14.5820	0.484454
$907$	52.5340	1.74436	0.872181	−	0.489183i	$-0.162705\pi$
$907$	52.5340	1.74436	0.872181	+	0.489183i	$0.162705\pi$
$908$	0.618667	0.0205312
$909$	−1.28670	−0.0426772
$910$	0	0
$911$	−15.7819	−0.522879	−0.261439	−	0.965220i	$-0.584197\pi$
$911$	−15.7819	−0.522879	−0.261439	+	0.965220i	$0.584197\pi$
$912$	6.98503	0.231298
$913$	26.0046	0.860626
$914$	2.38368	0.0788452
$915$	−7.21220	−0.238428
$916$	−2.93024	−0.0968180
$917$	11.8617	0.391709
$918$	−1.24698	−0.0411565
$919$	−49.8498	−1.64439	−0.822197	−	0.569203i	$-0.807252\pi$
$919$	−49.8498	−1.64439	−0.822197	+	0.569203i	$0.807252\pi$
$920$	4.15634	0.137031
$921$	−11.8071	−0.389057
$922$	36.9292	1.21620
$923$	0	0
$924$	1.55496	0.0511544
$925$	1.53116	0.0503442
$926$	−29.8161	−0.979818
$927$	6.54173	0.214859
$928$	6.02003	0.197617
$929$	−19.1901	−0.629606	−0.314803	−	0.949157i	$-0.601938\pi$
$929$	−19.1901	−0.629606	−0.314803	+	0.949157i	$0.601938\pi$
$930$	−5.80240	−0.190268
$931$	6.98503	0.228925
$932$	−18.7941	−0.615620
$933$	2.36454	0.0774114
$934$	9.34853	0.305893
$935$	4.08864	0.133713
$936$	0	0
$937$	−23.4063	−0.764650	−0.382325	−	0.924028i	$-0.624876\pi$
$937$	−23.4063	−0.764650	−0.382325	+	0.924028i	$0.624876\pi$
$938$	−1.40756	−0.0459584
$939$	−6.67399	−0.217797
$940$	−11.8876	−0.387730
$941$	3.86671	0.126051	0.0630256	−	0.998012i	$-0.479925\pi$
$941$	3.86671	0.126051	0.0630256	+	0.998012i	$0.479925\pi$
$942$	5.49884	0.179162
$943$	15.7161	0.511785
$944$	5.40902	0.176048
$945$	−2.10863	−0.0685938
$946$	−5.69833	−0.185269
$947$	−48.4114	−1.57316	−0.786579	−	0.617489i	$-0.788150\pi$
$947$	−48.4114	−1.57316	−0.786579	+	0.617489i	$0.788150\pi$
$948$	−16.4358	−0.533811
$949$	0	0
$950$	−3.86743	−0.125476
$951$	0.860447	0.0279019
$952$	−1.24698	−0.0404148
$953$	22.6556	0.733885	0.366943	−	0.930244i	$-0.380405\pi$
$953$	22.6556	0.733885	0.366943	+	0.930244i	$0.380405\pi$
$954$	8.81309	0.285334
$955$	5.84125	0.189018
$956$	−19.6751	−0.636337
$957$	9.36089	0.302595
$958$	17.5839	0.568110
$959$	2.18760	0.0706413
$960$	−2.10863	−0.0680558
$961$	−23.4280	−0.755740
$962$	0	0
$963$	2.66334	0.0858248
$964$	−5.57097	−0.179429
$965$	−47.0077	−1.51323
$966$	−1.97111	−0.0634194
$967$	−19.7448	−0.634950	−0.317475	−	0.948267i	$-0.602835\pi$
$967$	−19.7448	−0.634950	−0.317475	+	0.948267i	$0.602835\pi$
$968$	−8.58211	−0.275839
$969$	−8.71019	−0.279812
$970$	13.4844	0.432959
$971$	−12.7120	−0.407947	−0.203974	−	0.978976i	$-0.565386\pi$
$971$	−12.7120	−0.407947	−0.203974	+	0.978976i	$0.565386\pi$
$972$	1.00000	0.0320750
$973$	4.14041	0.132735
$974$	35.9216	1.15100
$975$	0	0
$976$	3.42032	0.109482
$977$	−41.1062	−1.31510	−0.657552	−	0.753409i	$-0.728408\pi$
$977$	−41.1062	−1.31510	−0.657552	+	0.753409i	$0.728408\pi$
$978$	14.1960	0.453938
$979$	17.0754	0.545732
$980$	−2.10863	−0.0673578
$981$	−4.40973	−0.140792
$982$	−28.4463	−0.907758
$983$	12.6710	0.404144	0.202072	−	0.979371i	$-0.435233\pi$
$983$	12.6710	0.404144	0.202072	+	0.979371i	$0.435233\pi$
$984$	−7.97320	−0.254176
$985$	18.4598	0.588178
$986$	−7.50685	−0.239067
$987$	5.63759	0.179446
$988$	0	0
$989$	7.22337	0.229690
$990$	−3.27883	−0.104208
$991$	42.4770	1.34932	0.674662	−	0.738126i	$-0.264289\pi$
$991$	42.4770	1.34932	0.674662	+	0.738126i	$0.264289\pi$
$992$	2.75174	0.0873677
$993$	15.4980	0.491815
$994$	11.6269	0.368781
$995$	30.7489	0.974806
$996$	16.7237	0.529909
$997$	8.78235	0.278140	0.139070	−	0.990283i	$-0.455589\pi$
$997$	8.78235	0.278140	0.139070	+	0.990283i	$0.455589\pi$
$998$	−41.0934	−1.30079
$999$	−2.76545	−0.0874951

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.ct.1.2	yes	6
13.12	even	2		7098.2.a.cr.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7098.2.a.cr.1.5	✓	6	13.12	even	2
7098.2.a.ct.1.2	yes	6	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:	\( N \)	\(=\)	\( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7098.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.10863 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -2.10863 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.10863 q^{10} +1.55496 q^{11} +1.00000 q^{12} +1.00000 q^{14} -2.10863 q^{15} +1.00000 q^{16} -1.24698 q^{17} +1.00000 q^{18} +6.98503 q^{19} -2.10863 q^{20} +1.00000 q^{21} +1.55496 q^{22} -1.97111 q^{23} +1.00000 q^{24} -0.553673 q^{25} +1.00000 q^{27} +1.00000 q^{28} +6.02003 q^{29} -2.10863 q^{30} +2.75174 q^{31} +1.00000 q^{32} +1.55496 q^{33} -1.24698 q^{34} -2.10863 q^{35} +1.00000 q^{36} -2.76545 q^{37} +6.98503 q^{38} -2.10863 q^{40} -7.97320 q^{41} +1.00000 q^{42} -3.66462 q^{43} +1.55496 q^{44} -2.10863 q^{45} -1.97111 q^{46} +5.63759 q^{47} +1.00000 q^{48} +1.00000 q^{49} -0.553673 q^{50} -1.24698 q^{51} +8.81309 q^{53} +1.00000 q^{54} -3.27883 q^{55} +1.00000 q^{56} +6.98503 q^{57} +6.02003 q^{58} +5.40902 q^{59} -2.10863 q^{60} +3.42032 q^{61} +2.75174 q^{62} +1.00000 q^{63} +1.00000 q^{64} +1.55496 q^{66} -1.40756 q^{67} -1.24698 q^{68} -1.97111 q^{69} -2.10863 q^{70} +11.6269 q^{71} +1.00000 q^{72} -7.48979 q^{73} -2.76545 q^{74} -0.553673 q^{75} +6.98503 q^{76} +1.55496 q^{77} -16.4358 q^{79} -2.10863 q^{80} +1.00000 q^{81} -7.97320 q^{82} +16.7237 q^{83} +1.00000 q^{84} +2.62942 q^{85} -3.66462 q^{86} +6.02003 q^{87} +1.55496 q^{88} +10.9813 q^{89} -2.10863 q^{90} -1.97111 q^{92} +2.75174 q^{93} +5.63759 q^{94} -14.7289 q^{95} +1.00000 q^{96} -6.39487 q^{97} +1.00000 q^{98} +1.55496 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 6 q^{2} + 6 q^{3} + 6 q^{4} + 3 q^{5} + 6 q^{6} + 6 q^{7} + 6 q^{8} + 6 q^{9} + 3 q^{10} + 10 q^{11} + 6 q^{12} + 6 q^{14} + 3 q^{15} + 6 q^{16} + 2 q^{17} + 6 q^{18} + 2 q^{19} + 3 q^{20} + 6 q^{21} + 10 q^{22} + 4 q^{23} + 6 q^{24} + 13 q^{25} + 6 q^{27} + 6 q^{28} + 2 q^{29} + 3 q^{30} + 9 q^{31} + 6 q^{32} + 10 q^{33} + 2 q^{34} + 3 q^{35} + 6 q^{36} + 7 q^{37} + 2 q^{38} + 3 q^{40} + 11 q^{41} + 6 q^{42} - 5 q^{43} + 10 q^{44} + 3 q^{45} + 4 q^{46} + 5 q^{47} + 6 q^{48} + 6 q^{49} + 13 q^{50} + 2 q^{51} - 6 q^{53} + 6 q^{54} + 5 q^{55} + 6 q^{56} + 2 q^{57} + 2 q^{58} + 28 q^{59} + 3 q^{60} + 23 q^{61} + 9 q^{62} + 6 q^{63} + 6 q^{64} + 10 q^{66} - 10 q^{67} + 2 q^{68} + 4 q^{69} + 3 q^{70} + 21 q^{71} + 6 q^{72} - 7 q^{73} + 7 q^{74} + 13 q^{75} + 2 q^{76} + 10 q^{77} - 14 q^{79} + 3 q^{80} + 6 q^{81} + 11 q^{82} + 17 q^{83} + 6 q^{84} + q^{85} - 5 q^{86} + 2 q^{87} + 10 q^{88} + 17 q^{89} + 3 q^{90} + 4 q^{92} + 9 q^{93} + 5 q^{94} - 22 q^{95} + 6 q^{96} + 6 q^{98} + 10 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^3 + 6 * q^4 + 3 * q^5 + 6 * q^6 + 6 * q^7 + 6 * q^8 + 6 * q^9 + 3 * q^10 + 10 * q^11 + 6 * q^12 + 6 * q^14 + 3 * q^15 + 6 * q^16 + 2 * q^17 + 6 * q^18 + 2 * q^19 + 3 * q^20 + 6 * q^21 + 10 * q^22 + 4 * q^23 + 6 * q^24 + 13 * q^25 + 6 * q^27 + 6 * q^28 + 2 * q^29 + 3 * q^30 + 9 * q^31 + 6 * q^32 + 10 * q^33 + 2 * q^34 + 3 * q^35 + 6 * q^36 + 7 * q^37 + 2 * q^38 + 3 * q^40 + 11 * q^41 + 6 * q^42 - 5 * q^43 + 10 * q^44 + 3 * q^45 + 4 * q^46 + 5 * q^47 + 6 * q^48 + 6 * q^49 + 13 * q^50 + 2 * q^51 - 6 * q^53 + 6 * q^54 + 5 * q^55 + 6 * q^56 + 2 * q^57 + 2 * q^58 + 28 * q^59 + 3 * q^60 + 23 * q^61 + 9 * q^62 + 6 * q^63 + 6 * q^64 + 10 * q^66 - 10 * q^67 + 2 * q^68 + 4 * q^69 + 3 * q^70 + 21 * q^71 + 6 * q^72 - 7 * q^73 + 7 * q^74 + 13 * q^75 + 2 * q^76 + 10 * q^77 - 14 * q^79 + 3 * q^80 + 6 * q^81 + 11 * q^82 + 17 * q^83 + 6 * q^84 + q^85 - 5 * q^86 + 2 * q^87 + 10 * q^88 + 17 * q^89 + 3 * q^90 + 4 * q^92 + 9 * q^93 + 5 * q^94 - 22 * q^95 + 6 * q^96 + 6 * q^98 + 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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