LMFDB - Embedded newform 7098.2.a.br.1.1

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:	$2$
Coefficient field:	$\Q(\sqrt{129}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 32 $ x^2 - x - 32
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$6.17891$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.00000 q^{10} -5.17891 q^{11} -1.00000 q^{12} -1.00000 q^{14} +2.00000 q^{15} +1.00000 q^{16} +5.00000 q^{17} +1.00000 q^{18} +3.17891 q^{19} -2.00000 q^{20} +1.00000 q^{21} -5.17891 q^{22} -8.17891 q^{23} -1.00000 q^{24} -1.00000 q^{25} -1.00000 q^{27} -1.00000 q^{28} -3.17891 q^{29} +2.00000 q^{30} +4.17891 q^{31} +1.00000 q^{32} +5.17891 q^{33} +5.00000 q^{34} +2.00000 q^{35} +1.00000 q^{36} +2.00000 q^{37} +3.17891 q^{38} -2.00000 q^{40} -7.17891 q^{41} +1.00000 q^{42} +12.1789 q^{43} -5.17891 q^{44} -2.00000 q^{45} -8.17891 q^{46} -7.17891 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} -5.00000 q^{51} -3.00000 q^{53} -1.00000 q^{54} +10.3578 q^{55} -1.00000 q^{56} -3.17891 q^{57} -3.17891 q^{58} -12.1789 q^{59} +2.00000 q^{60} -3.00000 q^{61} +4.17891 q^{62} -1.00000 q^{63} +1.00000 q^{64} +5.17891 q^{66} -3.82109 q^{67} +5.00000 q^{68} +8.17891 q^{69} +2.00000 q^{70} -2.17891 q^{71} +1.00000 q^{72} +4.00000 q^{73} +2.00000 q^{74} +1.00000 q^{75} +3.17891 q^{76} +5.17891 q^{77} +13.1789 q^{79} -2.00000 q^{80} +1.00000 q^{81} -7.17891 q^{82} +6.17891 q^{83} +1.00000 q^{84} -10.0000 q^{85} +12.1789 q^{86} +3.17891 q^{87} -5.17891 q^{88} +9.00000 q^{89} -2.00000 q^{90} -8.17891 q^{92} -4.17891 q^{93} -7.17891 q^{94} -6.35782 q^{95} -1.00000 q^{96} -10.3578 q^{97} +1.00000 q^{98} -5.17891 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} - 4 q^{10} + q^{11} - 2 q^{12} - 2 q^{14} + 4 q^{15} + 2 q^{16} + 10 q^{17} + 2 q^{18} - 5 q^{19} - 4 q^{20} + 2 q^{21} + q^{22} - 5 q^{23} - 2 q^{24} - 2 q^{25} - 2 q^{27} - 2 q^{28} + 5 q^{29} + 4 q^{30} - 3 q^{31} + 2 q^{32} - q^{33} + 10 q^{34} + 4 q^{35} + 2 q^{36} + 4 q^{37} - 5 q^{38} - 4 q^{40} - 3 q^{41} + 2 q^{42} + 13 q^{43} + q^{44} - 4 q^{45} - 5 q^{46} - 3 q^{47} - 2 q^{48} + 2 q^{49} - 2 q^{50} - 10 q^{51} - 6 q^{53} - 2 q^{54} - 2 q^{55} - 2 q^{56} + 5 q^{57} + 5 q^{58} - 13 q^{59} + 4 q^{60} - 6 q^{61} - 3 q^{62} - 2 q^{63} + 2 q^{64} - q^{66} - 19 q^{67} + 10 q^{68} + 5 q^{69} + 4 q^{70} + 7 q^{71} + 2 q^{72} + 8 q^{73} + 4 q^{74} + 2 q^{75} - 5 q^{76} - q^{77} + 15 q^{79} - 4 q^{80} + 2 q^{81} - 3 q^{82} + q^{83} + 2 q^{84} - 20 q^{85} + 13 q^{86} - 5 q^{87} + q^{88} + 18 q^{89} - 4 q^{90} - 5 q^{92} + 3 q^{93} - 3 q^{94} + 10 q^{95} - 2 q^{96} + 2 q^{97} + 2 q^{98} + q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9 - 4 * q^10 + q^11 - 2 * q^12 - 2 * q^14 + 4 * q^15 + 2 * q^16 + 10 * q^17 + 2 * q^18 - 5 * q^19 - 4 * q^20 + 2 * q^21 + q^22 - 5 * q^23 - 2 * q^24 - 2 * q^25 - 2 * q^27 - 2 * q^28 + 5 * q^29 + 4 * q^30 - 3 * q^31 + 2 * q^32 - q^33 + 10 * q^34 + 4 * q^35 + 2 * q^36 + 4 * q^37 - 5 * q^38 - 4 * q^40 - 3 * q^41 + 2 * q^42 + 13 * q^43 + q^44 - 4 * q^45 - 5 * q^46 - 3 * q^47 - 2 * q^48 + 2 * q^49 - 2 * q^50 - 10 * q^51 - 6 * q^53 - 2 * q^54 - 2 * q^55 - 2 * q^56 + 5 * q^57 + 5 * q^58 - 13 * q^59 + 4 * q^60 - 6 * q^61 - 3 * q^62 - 2 * q^63 + 2 * q^64 - q^66 - 19 * q^67 + 10 * q^68 + 5 * q^69 + 4 * q^70 + 7 * q^71 + 2 * q^72 + 8 * q^73 + 4 * q^74 + 2 * q^75 - 5 * q^76 - q^77 + 15 * q^79 - 4 * q^80 + 2 * q^81 - 3 * q^82 + q^83 + 2 * q^84 - 20 * q^85 + 13 * q^86 - 5 * q^87 + q^88 + 18 * q^89 - 4 * q^90 - 5 * q^92 + 3 * q^93 - 3 * q^94 + 10 * q^95 - 2 * q^96 + 2 * q^97 + 2 * q^98 + q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−2.00000	−0.894427	−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000	−0.894427	−0.447214	+	0.894427i	$0.647584\pi$
$6$	−1.00000	−0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−2.00000	−0.632456
$11$	−5.17891	−1.56150	−0.780750	−	0.624844i	$-0.785163\pi$
$11$	−5.17891	−1.56150	−0.780750	+	0.624844i	$0.785163\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	−1.00000	−0.267261
$15$	2.00000	0.516398
$16$	1.00000	0.250000
$17$	5.00000	1.21268	0.606339	−	0.795206i	$-0.292637\pi$
$17$	5.00000	1.21268	0.606339	+	0.795206i	$0.292637\pi$
$18$	1.00000	0.235702
$19$	3.17891	0.729292	0.364646	−	0.931146i	$-0.381190\pi$
$19$	3.17891	0.729292	0.364646	+	0.931146i	$0.381190\pi$
$20$	−2.00000	−0.447214
$21$	1.00000	0.218218
$22$	−5.17891	−1.10415
$23$	−8.17891	−1.70542	−0.852710	−	0.522384i	$-0.825043\pi$
$23$	−8.17891	−1.70542	−0.852710	+	0.522384i	$0.825043\pi$
$24$	−1.00000	−0.204124
$25$	−1.00000	−0.200000
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	−3.17891	−0.590308	−0.295154	−	0.955450i	$-0.595371\pi$
$29$	−3.17891	−0.590308	−0.295154	+	0.955450i	$0.595371\pi$
$30$	2.00000	0.365148
$31$	4.17891	0.750554	0.375277	−	0.926913i	$-0.377548\pi$
$31$	4.17891	0.750554	0.375277	+	0.926913i	$0.377548\pi$
$32$	1.00000	0.176777
$33$	5.17891	0.901532
$34$	5.00000	0.857493
$35$	2.00000	0.338062
$36$	1.00000	0.166667
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	3.17891	0.515687
$39$	0	0
$40$	−2.00000	−0.316228
$41$	−7.17891	−1.12116	−0.560579	−	0.828101i	$-0.689421\pi$
$41$	−7.17891	−1.12116	−0.560579	+	0.828101i	$0.689421\pi$
$42$	1.00000	0.154303
$43$	12.1789	1.85727	0.928633	−	0.371000i	$-0.120985\pi$
$43$	12.1789	1.85727	0.928633	+	0.371000i	$0.120985\pi$
$44$	−5.17891	−0.780750
$45$	−2.00000	−0.298142
$46$	−8.17891	−1.20591
$47$	−7.17891	−1.04715	−0.523576	−	0.851979i	$-0.675402\pi$
$47$	−7.17891	−1.04715	−0.523576	+	0.851979i	$0.675402\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	−5.00000	−0.700140
$52$	0	0
$53$	−3.00000	−0.412082	−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000	−0.412082	−0.206041	+	0.978543i	$0.566058\pi$
$54$	−1.00000	−0.136083
$55$	10.3578	1.39665
$56$	−1.00000	−0.133631
$57$	−3.17891	−0.421057
$58$	−3.17891	−0.417411
$59$	−12.1789	−1.58556	−0.792779	−	0.609509i	$-0.791367\pi$
$59$	−12.1789	−1.58556	−0.792779	+	0.609509i	$0.791367\pi$
$60$	2.00000	0.258199
$61$	−3.00000	−0.384111	−0.192055	−	0.981384i	$-0.561515\pi$
$61$	−3.00000	−0.384111	−0.192055	+	0.981384i	$0.561515\pi$
$62$	4.17891	0.530722
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	5.17891	0.637480
$67$	−3.82109	−0.466821	−0.233410	−	0.972378i	$-0.574989\pi$
$67$	−3.82109	−0.466821	−0.233410	+	0.972378i	$0.574989\pi$
$68$	5.00000	0.606339
$69$	8.17891	0.984625
$70$	2.00000	0.239046
$71$	−2.17891	−0.258589	−0.129294	−	0.991606i	$-0.541271\pi$
$71$	−2.17891	−0.258589	−0.129294	+	0.991606i	$0.541271\pi$
$72$	1.00000	0.117851
$73$	4.00000	0.468165	0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000	0.468165	0.234082	+	0.972217i	$0.424791\pi$
$74$	2.00000	0.232495
$75$	1.00000	0.115470
$76$	3.17891	0.364646
$77$	5.17891	0.590191
$78$	0	0
$79$	13.1789	1.48274	0.741372	−	0.671095i	$-0.234176\pi$
$79$	13.1789	1.48274	0.741372	+	0.671095i	$0.234176\pi$
$80$	−2.00000	−0.223607
$81$	1.00000	0.111111
$82$	−7.17891	−0.792778
$83$	6.17891	0.678223	0.339112	−	0.940746i	$-0.389874\pi$
$83$	6.17891	0.678223	0.339112	+	0.940746i	$0.389874\pi$
$84$	1.00000	0.109109
$85$	−10.0000	−1.08465
$86$	12.1789	1.31329
$87$	3.17891	0.340815
$88$	−5.17891	−0.552073
$89$	9.00000	0.953998	0.476999	−	0.878904i	$-0.341725\pi$
$89$	9.00000	0.953998	0.476999	+	0.878904i	$0.341725\pi$
$90$	−2.00000	−0.210819
$91$	0	0
$92$	−8.17891	−0.852710
$93$	−4.17891	−0.433333
$94$	−7.17891	−0.740448
$95$	−6.35782	−0.652298
$96$	−1.00000	−0.102062
$97$	−10.3578	−1.05168	−0.525838	−	0.850584i	$-0.676248\pi$
$97$	−10.3578	−1.05168	−0.525838	+	0.850584i	$0.676248\pi$
$98$	1.00000	0.101015
$99$	−5.17891	−0.520500
$100$	−1.00000	−0.100000
$101$	6.35782	0.632626	0.316313	−	0.948655i	$-0.397555\pi$
$101$	6.35782	0.632626	0.316313	+	0.948655i	$0.397555\pi$
$102$	−5.00000	−0.495074
$103$	−8.17891	−0.805892	−0.402946	−	0.915224i	$-0.632014\pi$
$103$	−8.17891	−0.805892	−0.402946	+	0.915224i	$0.632014\pi$
$104$	0	0
$105$	−2.00000	−0.195180
$106$	−3.00000	−0.291386
$107$	19.1789	1.85410	0.927048	−	0.374944i	$-0.122338\pi$
$107$	19.1789	1.85410	0.927048	+	0.374944i	$0.122338\pi$
$108$	−1.00000	−0.0962250
$109$	4.00000	0.383131	0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000	0.383131	0.191565	+	0.981480i	$0.438644\pi$
$110$	10.3578	0.987579
$111$	−2.00000	−0.189832
$112$	−1.00000	−0.0944911
$113$	18.3578	1.72696	0.863479	−	0.504385i	$-0.168281\pi$
$113$	18.3578	1.72696	0.863479	+	0.504385i	$0.168281\pi$
$114$	−3.17891	−0.297732
$115$	16.3578	1.52537
$116$	−3.17891	−0.295154
$117$	0	0
$118$	−12.1789	−1.12116
$119$	−5.00000	−0.458349
$120$	2.00000	0.182574
$121$	15.8211	1.43828
$122$	−3.00000	−0.271607
$123$	7.17891	0.647300
$124$	4.17891	0.375277
$125$	12.0000	1.07331
$126$	−1.00000	−0.0890871
$127$	12.0000	1.06483	0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000	1.06483	0.532414	+	0.846484i	$0.321285\pi$
$128$	1.00000	0.0883883
$129$	−12.1789	−1.07229
$130$	0	0
$131$	−14.5367	−1.27008	−0.635040	−	0.772479i	$-0.719016\pi$
$131$	−14.5367	−1.27008	−0.635040	+	0.772479i	$0.719016\pi$
$132$	5.17891	0.450766
$133$	−3.17891	−0.275646
$134$	−3.82109	−0.330092
$135$	2.00000	0.172133
$136$	5.00000	0.428746
$137$	6.35782	0.543185	0.271592	−	0.962412i	$-0.412450\pi$
$137$	6.35782	0.543185	0.271592	+	0.962412i	$0.412450\pi$
$138$	8.17891	0.696235
$139$	−6.82109	−0.578557	−0.289279	−	0.957245i	$-0.593415\pi$
$139$	−6.82109	−0.578557	−0.289279	+	0.957245i	$0.593415\pi$
$140$	2.00000	0.169031
$141$	7.17891	0.604573
$142$	−2.17891	−0.182850
$143$	0	0
$144$	1.00000	0.0833333
$145$	6.35782	0.527988
$146$	4.00000	0.331042
$147$	−1.00000	−0.0824786
$148$	2.00000	0.164399
$149$	16.1789	1.32543	0.662714	−	0.748873i	$-0.269405\pi$
$149$	16.1789	1.32543	0.662714	+	0.748873i	$0.269405\pi$
$150$	1.00000	0.0816497
$151$	19.5367	1.58988	0.794938	−	0.606691i	$-0.207503\pi$
$151$	19.5367	1.58988	0.794938	+	0.606691i	$0.207503\pi$
$152$	3.17891	0.257844
$153$	5.00000	0.404226
$154$	5.17891	0.417328
$155$	−8.35782	−0.671316
$156$	0	0
$157$	2.00000	0.159617	0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000	0.159617	0.0798087	+	0.996810i	$0.474569\pi$
$158$	13.1789	1.04846
$159$	3.00000	0.237915
$160$	−2.00000	−0.158114
$161$	8.17891	0.644588
$162$	1.00000	0.0785674
$163$	−20.1789	−1.58053	−0.790267	−	0.612763i	$-0.790058\pi$
$163$	−20.1789	−1.58053	−0.790267	+	0.612763i	$0.790058\pi$
$164$	−7.17891	−0.560579
$165$	−10.3578	−0.806355
$166$	6.17891	0.479576
$167$	−8.00000	−0.619059	−0.309529	−	0.950890i	$-0.600171\pi$
$167$	−8.00000	−0.619059	−0.309529	+	0.950890i	$0.600171\pi$
$168$	1.00000	0.0771517
$169$	0	0
$170$	−10.0000	−0.766965
$171$	3.17891	0.243097
$172$	12.1789	0.928633
$173$	4.00000	0.304114	0.152057	−	0.988372i	$-0.451410\pi$
$173$	4.00000	0.304114	0.152057	+	0.988372i	$0.451410\pi$
$174$	3.17891	0.240992
$175$	1.00000	0.0755929
$176$	−5.17891	−0.390375
$177$	12.1789	0.915423
$178$	9.00000	0.674579
$179$	8.35782	0.624693	0.312346	−	0.949968i	$-0.398885\pi$
$179$	8.35782	0.624693	0.312346	+	0.949968i	$0.398885\pi$
$180$	−2.00000	−0.149071
$181$	19.1789	1.42556	0.712779	−	0.701389i	$-0.247436\pi$
$181$	19.1789	1.42556	0.712779	+	0.701389i	$0.247436\pi$
$182$	0	0
$183$	3.00000	0.221766
$184$	−8.17891	−0.602957
$185$	−4.00000	−0.294086
$186$	−4.17891	−0.306412
$187$	−25.8945	−1.89360
$188$	−7.17891	−0.523576
$189$	1.00000	0.0727393
$190$	−6.35782	−0.461245
$191$	−6.53673	−0.472981	−0.236490	−	0.971634i	$-0.575997\pi$
$191$	−6.53673	−0.472981	−0.236490	+	0.971634i	$0.575997\pi$
$192$	−1.00000	−0.0721688
$193$	−13.5367	−0.974395	−0.487197	−	0.873292i	$-0.661981\pi$
$193$	−13.5367	−0.974395	−0.487197	+	0.873292i	$0.661981\pi$
$194$	−10.3578	−0.743648
$195$	0	0
$196$	1.00000	0.0714286
$197$	17.0000	1.21120	0.605600	−	0.795769i	$-0.292933\pi$
$197$	17.0000	1.21120	0.605600	+	0.795769i	$0.292933\pi$
$198$	−5.17891	−0.368049
$199$	24.1789	1.71400	0.856999	−	0.515319i	$-0.172326\pi$
$199$	24.1789	1.71400	0.856999	+	0.515319i	$0.172326\pi$
$200$	−1.00000	−0.0707107
$201$	3.82109	0.269519
$202$	6.35782	0.447334
$203$	3.17891	0.223116
$204$	−5.00000	−0.350070
$205$	14.3578	1.00279
$206$	−8.17891	−0.569852
$207$	−8.17891	−0.568473
$208$	0	0
$209$	−16.4633	−1.13879
$210$	−2.00000	−0.138013
$211$	−6.35782	−0.437690	−0.218845	−	0.975760i	$-0.570229\pi$
$211$	−6.35782	−0.437690	−0.218845	+	0.975760i	$0.570229\pi$
$212$	−3.00000	−0.206041
$213$	2.17891	0.149296
$214$	19.1789	1.31104
$215$	−24.3578	−1.66119
$216$	−1.00000	−0.0680414
$217$	−4.17891	−0.283683
$218$	4.00000	0.270914
$219$	−4.00000	−0.270295
$220$	10.3578	0.698324
$221$	0	0
$222$	−2.00000	−0.134231
$223$	−2.17891	−0.145910	−0.0729552	−	0.997335i	$-0.523243\pi$
$223$	−2.17891	−0.145910	−0.0729552	+	0.997335i	$0.523243\pi$
$224$	−1.00000	−0.0668153
$225$	−1.00000	−0.0666667
$226$	18.3578	1.22114
$227$	−14.3578	−0.952962	−0.476481	−	0.879185i	$-0.658088\pi$
$227$	−14.3578	−0.952962	−0.476481	+	0.879185i	$0.658088\pi$
$228$	−3.17891	−0.210528
$229$	1.00000	0.0660819	0.0330409	−	0.999454i	$-0.489481\pi$
$229$	1.00000	0.0660819	0.0330409	+	0.999454i	$0.489481\pi$
$230$	16.3578	1.07860
$231$	−5.17891	−0.340747
$232$	−3.17891	−0.208706
$233$	22.3578	1.46471	0.732355	−	0.680923i	$-0.238421\pi$
$233$	22.3578	1.46471	0.732355	+	0.680923i	$0.238421\pi$
$234$	0	0
$235$	14.3578	0.936601
$236$	−12.1789	−0.792779
$237$	−13.1789	−0.856062
$238$	−5.00000	−0.324102
$239$	10.1789	0.658419	0.329209	−	0.944257i	$-0.393218\pi$
$239$	10.1789	0.658419	0.329209	+	0.944257i	$0.393218\pi$
$240$	2.00000	0.129099
$241$	4.35782	0.280712	0.140356	−	0.990101i	$-0.455175\pi$
$241$	4.35782	0.280712	0.140356	+	0.990101i	$0.455175\pi$
$242$	15.8211	1.01702
$243$	−1.00000	−0.0641500
$244$	−3.00000	−0.192055
$245$	−2.00000	−0.127775
$246$	7.17891	0.457710
$247$	0	0
$248$	4.17891	0.265361
$249$	−6.17891	−0.391572
$250$	12.0000	0.758947
$251$	22.1789	1.39992	0.699960	−	0.714182i	$-0.253201\pi$
$251$	22.1789	1.39992	0.699960	+	0.714182i	$0.253201\pi$
$252$	−1.00000	−0.0629941
$253$	42.3578	2.66301
$254$	12.0000	0.752947
$255$	10.0000	0.626224
$256$	1.00000	0.0625000
$257$	−19.7156	−1.22983	−0.614914	−	0.788594i	$-0.710809\pi$
$257$	−19.7156	−1.22983	−0.614914	+	0.788594i	$0.710809\pi$
$258$	−12.1789	−0.758226
$259$	−2.00000	−0.124274
$260$	0	0
$261$	−3.17891	−0.196769
$262$	−14.5367	−0.898082
$263$	−12.0000	−0.739952	−0.369976	−	0.929041i	$-0.620634\pi$
$263$	−12.0000	−0.739952	−0.369976	+	0.929041i	$0.620634\pi$
$264$	5.17891	0.318740
$265$	6.00000	0.368577
$266$	−3.17891	−0.194911
$267$	−9.00000	−0.550791
$268$	−3.82109	−0.233410
$269$	−4.35782	−0.265701	−0.132850	−	0.991136i	$-0.542413\pi$
$269$	−4.35782	−0.265701	−0.132850	+	0.991136i	$0.542413\pi$
$270$	2.00000	0.121716
$271$	19.8211	1.20405	0.602023	−	0.798479i	$-0.294362\pi$
$271$	19.8211	1.20405	0.602023	+	0.798479i	$0.294362\pi$
$272$	5.00000	0.303170
$273$	0	0
$274$	6.35782	0.384090
$275$	5.17891	0.312300
$276$	8.17891	0.492312
$277$	5.64218	0.339006	0.169503	−	0.985530i	$-0.445784\pi$
$277$	5.64218	0.339006	0.169503	+	0.985530i	$0.445784\pi$
$278$	−6.82109	−0.409102
$279$	4.17891	0.250185
$280$	2.00000	0.119523
$281$	28.3578	1.69169	0.845843	−	0.533432i	$-0.179098\pi$
$281$	28.3578	1.69169	0.845843	+	0.533432i	$0.179098\pi$
$282$	7.17891	0.427498
$283$	7.64218	0.454281	0.227140	−	0.973862i	$-0.427062\pi$
$283$	7.64218	0.454281	0.227140	+	0.973862i	$0.427062\pi$
$284$	−2.17891	−0.129294
$285$	6.35782	0.376605
$286$	0	0
$287$	7.17891	0.423758
$288$	1.00000	0.0589256
$289$	8.00000	0.470588
$290$	6.35782	0.373344
$291$	10.3578	0.607186
$292$	4.00000	0.234082
$293$	12.0000	0.701047	0.350524	−	0.936554i	$-0.386004\pi$
$293$	12.0000	0.701047	0.350524	+	0.936554i	$0.386004\pi$
$294$	−1.00000	−0.0583212
$295$	24.3578	1.41817
$296$	2.00000	0.116248
$297$	5.17891	0.300511
$298$	16.1789	0.937219
$299$	0	0
$300$	1.00000	0.0577350
$301$	−12.1789	−0.701981
$302$	19.5367	1.12421
$303$	−6.35782	−0.365247
$304$	3.17891	0.182323
$305$	6.00000	0.343559
$306$	5.00000	0.285831
$307$	−31.8945	−1.82032	−0.910159	−	0.414259i	$-0.864041\pi$
$307$	−31.8945	−1.82032	−0.910159	+	0.414259i	$0.864041\pi$
$308$	5.17891	0.295096
$309$	8.17891	0.465282
$310$	−8.35782	−0.474692
$311$	25.5367	1.44805	0.724027	−	0.689771i	$-0.242289\pi$
$311$	25.5367	1.44805	0.724027	+	0.689771i	$0.242289\pi$
$312$	0	0
$313$	4.00000	0.226093	0.113047	−	0.993590i	$-0.463939\pi$
$313$	4.00000	0.226093	0.113047	+	0.993590i	$0.463939\pi$
$314$	2.00000	0.112867
$315$	2.00000	0.112687
$316$	13.1789	0.741372
$317$	−4.17891	−0.234711	−0.117355	−	0.993090i	$-0.537442\pi$
$317$	−4.17891	−0.234711	−0.117355	+	0.993090i	$0.537442\pi$
$318$	3.00000	0.168232
$319$	16.4633	0.921766
$320$	−2.00000	−0.111803
$321$	−19.1789	−1.07046
$322$	8.17891	0.455793
$323$	15.8945	0.884396
$324$	1.00000	0.0555556
$325$	0	0
$326$	−20.1789	−1.11761
$327$	−4.00000	−0.221201
$328$	−7.17891	−0.396389
$329$	7.17891	0.395786
$330$	−10.3578	−0.570179
$331$	−1.64218	−0.0902626	−0.0451313	−	0.998981i	$-0.514371\pi$
$331$	−1.64218	−0.0902626	−0.0451313	+	0.998981i	$0.514371\pi$
$332$	6.17891	0.339112
$333$	2.00000	0.109599
$334$	−8.00000	−0.437741
$335$	7.64218	0.417537
$336$	1.00000	0.0545545
$337$	33.5367	1.82686	0.913431	−	0.406994i	$-0.133423\pi$
$337$	33.5367	1.82686	0.913431	+	0.406994i	$0.133423\pi$
$338$	0	0
$339$	−18.3578	−0.997060
$340$	−10.0000	−0.542326
$341$	−21.6422	−1.17199
$342$	3.17891	0.171896
$343$	−1.00000	−0.0539949
$344$	12.1789	0.656643
$345$	−16.3578	−0.880675
$346$	4.00000	0.215041
$347$	−19.1789	−1.02958	−0.514789	−	0.857317i	$-0.672130\pi$
$347$	−19.1789	−1.02958	−0.514789	+	0.857317i	$0.672130\pi$
$348$	3.17891	0.170407
$349$	8.17891	0.437807	0.218903	−	0.975747i	$-0.429752\pi$
$349$	8.17891	0.437807	0.218903	+	0.975747i	$0.429752\pi$
$350$	1.00000	0.0534522
$351$	0	0
$352$	−5.17891	−0.276037
$353$	4.17891	0.222421	0.111210	−	0.993797i	$-0.464527\pi$
$353$	4.17891	0.222421	0.111210	+	0.993797i	$0.464527\pi$
$354$	12.1789	0.647302
$355$	4.35782	0.231289
$356$	9.00000	0.476999
$357$	5.00000	0.264628
$358$	8.35782	0.441724
$359$	−10.3578	−0.546665	−0.273332	−	0.961920i	$-0.588126\pi$
$359$	−10.3578	−0.546665	−0.273332	+	0.961920i	$0.588126\pi$
$360$	−2.00000	−0.105409
$361$	−8.89454	−0.468134
$362$	19.1789	1.00802
$363$	−15.8211	−0.830392
$364$	0	0
$365$	−8.00000	−0.418739
$366$	3.00000	0.156813
$367$	−8.17891	−0.426936	−0.213468	−	0.976950i	$-0.568476\pi$
$367$	−8.17891	−0.426936	−0.213468	+	0.976950i	$0.568476\pi$
$368$	−8.17891	−0.426355
$369$	−7.17891	−0.373719
$370$	−4.00000	−0.207950
$371$	3.00000	0.155752
$372$	−4.17891	−0.216666
$373$	−20.0000	−1.03556	−0.517780	−	0.855514i	$-0.673242\pi$
$373$	−20.0000	−1.03556	−0.517780	+	0.855514i	$0.673242\pi$
$374$	−25.8945	−1.33897
$375$	−12.0000	−0.619677
$376$	−7.17891	−0.370224
$377$	0	0
$378$	1.00000	0.0514344
$379$	−24.7156	−1.26956	−0.634778	−	0.772694i	$-0.718909\pi$
$379$	−24.7156	−1.26956	−0.634778	+	0.772694i	$0.718909\pi$
$380$	−6.35782	−0.326149
$381$	−12.0000	−0.614779
$382$	−6.53673	−0.334448
$383$	21.1789	1.08219	0.541096	−	0.840961i	$-0.318010\pi$
$383$	21.1789	1.08219	0.541096	+	0.840961i	$0.318010\pi$
$384$	−1.00000	−0.0510310
$385$	−10.3578	−0.527883
$386$	−13.5367	−0.689001
$387$	12.1789	0.619089
$388$	−10.3578	−0.525838
$389$	−12.1789	−0.617495	−0.308748	−	0.951144i	$-0.599910\pi$
$389$	−12.1789	−0.617495	−0.308748	+	0.951144i	$0.599910\pi$
$390$	0	0
$391$	−40.8945	−2.06813
$392$	1.00000	0.0505076
$393$	14.5367	0.733281
$394$	17.0000	0.856448
$395$	−26.3578	−1.32621
$396$	−5.17891	−0.260250
$397$	3.00000	0.150566	0.0752828	−	0.997162i	$-0.476014\pi$
$397$	3.00000	0.150566	0.0752828	+	0.997162i	$0.476014\pi$
$398$	24.1789	1.21198
$399$	3.17891	0.159144
$400$	−1.00000	−0.0500000
$401$	9.64218	0.481508	0.240754	−	0.970586i	$-0.422605\pi$
$401$	9.64218	0.481508	0.240754	+	0.970586i	$0.422605\pi$
$402$	3.82109	0.190579
$403$	0	0
$404$	6.35782	0.316313
$405$	−2.00000	−0.0993808
$406$	3.17891	0.157767
$407$	−10.3578	−0.513418
$408$	−5.00000	−0.247537
$409$	−36.3578	−1.79778	−0.898889	−	0.438176i	$-0.855625\pi$
$409$	−36.3578	−1.79778	−0.898889	+	0.438176i	$0.855625\pi$
$410$	14.3578	0.709082
$411$	−6.35782	−0.313608
$412$	−8.17891	−0.402946
$413$	12.1789	0.599285
$414$	−8.17891	−0.401971
$415$	−12.3578	−0.606621
$416$	0	0
$417$	6.82109	0.334030
$418$	−16.4633	−0.805245
$419$	−26.8945	−1.31388	−0.656942	−	0.753941i	$-0.728150\pi$
$419$	−26.8945	−1.31388	−0.656942	+	0.753941i	$0.728150\pi$
$420$	−2.00000	−0.0975900
$421$	10.7156	0.522248	0.261124	−	0.965305i	$-0.415907\pi$
$421$	10.7156	0.522248	0.261124	+	0.965305i	$0.415907\pi$
$422$	−6.35782	−0.309494
$423$	−7.17891	−0.349050
$424$	−3.00000	−0.145693
$425$	−5.00000	−0.242536
$426$	2.17891	0.105568
$427$	3.00000	0.145180
$428$	19.1789	0.927048
$429$	0	0
$430$	−24.3578	−1.17464
$431$	10.1789	0.490301	0.245150	−	0.969485i	$-0.421163\pi$
$431$	10.1789	0.490301	0.245150	+	0.969485i	$0.421163\pi$
$432$	−1.00000	−0.0481125
$433$	34.3578	1.65113	0.825566	−	0.564306i	$-0.190856\pi$
$433$	34.3578	1.65113	0.825566	+	0.564306i	$0.190856\pi$
$434$	−4.17891	−0.200594
$435$	−6.35782	−0.304834
$436$	4.00000	0.191565
$437$	−26.0000	−1.24375
$438$	−4.00000	−0.191127
$439$	40.7156	1.94325	0.971626	−	0.236524i	$-0.0760083\pi$
$439$	40.7156	1.94325	0.971626	+	0.236524i	$0.0760083\pi$
$440$	10.3578	0.493790
$441$	1.00000	0.0476190
$442$	0	0
$443$	3.17891	0.151034	0.0755172	−	0.997144i	$-0.475939\pi$
$443$	3.17891	0.151034	0.0755172	+	0.997144i	$0.475939\pi$
$444$	−2.00000	−0.0949158
$445$	−18.0000	−0.853282
$446$	−2.17891	−0.103174
$447$	−16.1789	−0.765236
$448$	−1.00000	−0.0472456
$449$	−14.0000	−0.660701	−0.330350	−	0.943858i	$-0.607167\pi$
$449$	−14.0000	−0.660701	−0.330350	+	0.943858i	$0.607167\pi$
$450$	−1.00000	−0.0471405
$451$	37.1789	1.75069
$452$	18.3578	0.863479
$453$	−19.5367	−0.917915
$454$	−14.3578	−0.673846
$455$	0	0
$456$	−3.17891	−0.148866
$457$	24.8945	1.16452	0.582259	−	0.813004i	$-0.302169\pi$
$457$	24.8945	1.16452	0.582259	+	0.813004i	$0.302169\pi$
$458$	1.00000	0.0467269
$459$	−5.00000	−0.233380
$460$	16.3578	0.762687
$461$	20.7156	0.964823	0.482412	−	0.875945i	$-0.339761\pi$
$461$	20.7156	0.964823	0.482412	+	0.875945i	$0.339761\pi$
$462$	−5.17891	−0.240945
$463$	27.8945	1.29637	0.648185	−	0.761483i	$-0.275528\pi$
$463$	27.8945	1.29637	0.648185	+	0.761483i	$0.275528\pi$
$464$	−3.17891	−0.147577
$465$	8.35782	0.387584
$466$	22.3578	1.03571
$467$	−22.8945	−1.05943	−0.529717	−	0.848175i	$-0.677702\pi$
$467$	−22.8945	−1.05943	−0.529717	+	0.848175i	$0.677702\pi$
$468$	0	0
$469$	3.82109	0.176442
$470$	14.3578	0.662277
$471$	−2.00000	−0.0921551
$472$	−12.1789	−0.560580
$473$	−63.0735	−2.90012
$474$	−13.1789	−0.605327
$475$	−3.17891	−0.145858
$476$	−5.00000	−0.229175
$477$	−3.00000	−0.137361
$478$	10.1789	0.465572
$479$	−41.1789	−1.88151	−0.940756	−	0.339084i	$-0.889883\pi$
$479$	−41.1789	−1.88151	−0.940756	+	0.339084i	$0.889883\pi$
$480$	2.00000	0.0912871
$481$	0	0
$482$	4.35782	0.198493
$483$	−8.17891	−0.372153
$484$	15.8211	0.719141
$485$	20.7156	0.940648
$486$	−1.00000	−0.0453609
$487$	−26.8211	−1.21538	−0.607690	−	0.794174i	$-0.707904\pi$
$487$	−26.8211	−1.21538	−0.607690	+	0.794174i	$0.707904\pi$
$488$	−3.00000	−0.135804
$489$	20.1789	0.912522
$490$	−2.00000	−0.0903508
$491$	0	0		−	1.00000i	$-0.5\pi$
$491$	0	0			1.00000i	$0.5\pi$
$492$	7.17891	0.323650
$493$	−15.8945	−0.715854
$494$	0	0
$495$	10.3578	0.465549
$496$	4.17891	0.187639
$497$	2.17891	0.0977374
$498$	−6.17891	−0.276884
$499$	8.17891	0.366138	0.183069	−	0.983100i	$-0.441397\pi$
$499$	8.17891	0.366138	0.183069	+	0.983100i	$0.441397\pi$
$500$	12.0000	0.536656
$501$	8.00000	0.357414
$502$	22.1789	0.989893
$503$	−24.0000	−1.07011	−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000	−1.07011	−0.535054	+	0.844818i	$0.679709\pi$
$504$	−1.00000	−0.0445435
$505$	−12.7156	−0.565838
$506$	42.3578	1.88303
$507$	0	0
$508$	12.0000	0.532414
$509$	−16.7156	−0.740907	−0.370454	−	0.928851i	$-0.620798\pi$
$509$	−16.7156	−0.740907	−0.370454	+	0.928851i	$0.620798\pi$
$510$	10.0000	0.442807
$511$	−4.00000	−0.176950
$512$	1.00000	0.0441942
$513$	−3.17891	−0.140352
$514$	−19.7156	−0.869619
$515$	16.3578	0.720812
$516$	−12.1789	−0.536147
$517$	37.1789	1.63513
$518$	−2.00000	−0.0878750
$519$	−4.00000	−0.175581
$520$	0	0
$521$	7.17891	0.314514	0.157257	−	0.987558i	$-0.449735\pi$
$521$	7.17891	0.314514	0.157257	+	0.987558i	$0.449735\pi$
$522$	−3.17891	−0.139137
$523$	11.5367	0.504466	0.252233	−	0.967667i	$-0.418835\pi$
$523$	11.5367	0.504466	0.252233	+	0.967667i	$0.418835\pi$
$524$	−14.5367	−0.635040
$525$	−1.00000	−0.0436436
$526$	−12.0000	−0.523225
$527$	20.8945	0.910181
$528$	5.17891	0.225383
$529$	43.8945	1.90846
$530$	6.00000	0.260623
$531$	−12.1789	−0.528520
$532$	−3.17891	−0.137823
$533$	0	0
$534$	−9.00000	−0.389468
$535$	−38.3578	−1.65835
$536$	−3.82109	−0.165046
$537$	−8.35782	−0.360666
$538$	−4.35782	−0.187879
$539$	−5.17891	−0.223071
$540$	2.00000	0.0860663
$541$	−20.3578	−0.875251	−0.437625	−	0.899157i	$-0.644180\pi$
$541$	−20.3578	−0.875251	−0.437625	+	0.899157i	$0.644180\pi$
$542$	19.8211	0.851389
$543$	−19.1789	−0.823046
$544$	5.00000	0.214373
$545$	−8.00000	−0.342682
$546$	0	0
$547$	36.0000	1.53925	0.769624	−	0.638497i	$-0.220443\pi$
$547$	36.0000	1.53925	0.769624	+	0.638497i	$0.220443\pi$
$548$	6.35782	0.271592
$549$	−3.00000	−0.128037
$550$	5.17891	0.220829
$551$	−10.1055	−0.430507
$552$	8.17891	0.348117
$553$	−13.1789	−0.560424
$554$	5.64218	0.239713
$555$	4.00000	0.169791
$556$	−6.82109	−0.289279
$557$	23.7156	1.00486	0.502432	−	0.864617i	$-0.332439\pi$
$557$	23.7156	1.00486	0.502432	+	0.864617i	$0.332439\pi$
$558$	4.17891	0.176907
$559$	0	0
$560$	2.00000	0.0845154
$561$	25.8945	1.09327
$562$	28.3578	1.19620
$563$	−18.3578	−0.773690	−0.386845	−	0.922145i	$-0.626435\pi$
$563$	−18.3578	−0.773690	−0.386845	+	0.922145i	$0.626435\pi$
$564$	7.17891	0.302287
$565$	−36.7156	−1.54464
$566$	7.64218	0.321225
$567$	−1.00000	−0.0419961
$568$	−2.17891	−0.0914250
$569$	−3.64218	−0.152688	−0.0763441	−	0.997082i	$-0.524325\pi$
$569$	−3.64218	−0.152688	−0.0763441	+	0.997082i	$0.524325\pi$
$570$	6.35782	0.266300
$571$	−34.1789	−1.43034	−0.715171	−	0.698949i	$-0.753651\pi$
$571$	−34.1789	−1.43034	−0.715171	+	0.698949i	$0.753651\pi$
$572$	0	0
$573$	6.53673	0.273076
$574$	7.17891	0.299642
$575$	8.17891	0.341084
$576$	1.00000	0.0416667
$577$	−28.3578	−1.18055	−0.590276	−	0.807202i	$-0.700981\pi$
$577$	−28.3578	−1.18055	−0.590276	+	0.807202i	$0.700981\pi$
$578$	8.00000	0.332756
$579$	13.5367	0.562567
$580$	6.35782	0.263994
$581$	−6.17891	−0.256344
$582$	10.3578	0.429345
$583$	15.5367	0.643465
$584$	4.00000	0.165521
$585$	0	0
$586$	12.0000	0.495715
$587$	0.178908	0.00738434	0.00369217	−	0.999993i	$-0.498825\pi$
$587$	0.178908	0.00738434	0.00369217	+	0.999993i	$0.498825\pi$
$588$	−1.00000	−0.0412393
$589$	13.2844	0.547373
$590$	24.3578	1.00280
$591$	−17.0000	−0.699287
$592$	2.00000	0.0821995
$593$	−33.0000	−1.35515	−0.677574	−	0.735455i	$-0.736969\pi$
$593$	−33.0000	−1.35515	−0.677574	+	0.735455i	$0.736969\pi$
$594$	5.17891	0.212493
$595$	10.0000	0.409960
$596$	16.1789	0.662714
$597$	−24.1789	−0.989577
$598$	0	0
$599$	40.1789	1.64167	0.820833	−	0.571168i	$-0.193510\pi$
$599$	40.1789	1.64167	0.820833	+	0.571168i	$0.193510\pi$
$600$	1.00000	0.0408248
$601$	−22.0000	−0.897399	−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000	−0.897399	−0.448699	+	0.893683i	$0.648113\pi$
$602$	−12.1789	−0.496375
$603$	−3.82109	−0.155607
$604$	19.5367	0.794938
$605$	−31.6422	−1.28644
$606$	−6.35782	−0.258269
$607$	−0.536725	−0.0217850	−0.0108925	−	0.999941i	$-0.503467\pi$
$607$	−0.536725	−0.0217850	−0.0108925	+	0.999941i	$0.503467\pi$
$608$	3.17891	0.128922
$609$	−3.17891	−0.128816
$610$	6.00000	0.242933
$611$	0	0
$612$	5.00000	0.202113
$613$	15.6422	0.631782	0.315891	−	0.948796i	$-0.397697\pi$
$613$	15.6422	0.631782	0.315891	+	0.948796i	$0.397697\pi$
$614$	−31.8945	−1.28716
$615$	−14.3578	−0.578963
$616$	5.17891	0.208664
$617$	32.0000	1.28827	0.644136	−	0.764911i	$-0.277217\pi$
$617$	32.0000	1.28827	0.644136	+	0.764911i	$0.277217\pi$
$618$	8.17891	0.329004
$619$	25.5367	1.02641	0.513204	−	0.858267i	$-0.328458\pi$
$619$	25.5367	1.02641	0.513204	+	0.858267i	$0.328458\pi$
$620$	−8.35782	−0.335658
$621$	8.17891	0.328208
$622$	25.5367	1.02393
$623$	−9.00000	−0.360577
$624$	0	0
$625$	−19.0000	−0.760000
$626$	4.00000	0.159872
$627$	16.4633	0.657480
$628$	2.00000	0.0798087
$629$	10.0000	0.398726
$630$	2.00000	0.0796819
$631$	25.8945	1.03085	0.515423	−	0.856936i	$-0.327635\pi$
$631$	25.8945	1.03085	0.515423	+	0.856936i	$0.327635\pi$
$632$	13.1789	0.524229
$633$	6.35782	0.252701
$634$	−4.17891	−0.165966
$635$	−24.0000	−0.952411
$636$	3.00000	0.118958
$637$	0	0
$638$	16.4633	0.651787
$639$	−2.17891	−0.0861963
$640$	−2.00000	−0.0790569
$641$	27.0735	1.06934	0.534668	−	0.845062i	$-0.320436\pi$
$641$	27.0735	1.06934	0.534668	+	0.845062i	$0.320436\pi$
$642$	−19.1789	−0.756931
$643$	−8.82109	−0.347870	−0.173935	−	0.984757i	$-0.555648\pi$
$643$	−8.82109	−0.347870	−0.173935	+	0.984757i	$0.555648\pi$
$644$	8.17891	0.322294
$645$	24.3578	0.959088
$646$	15.8945	0.625362
$647$	47.8945	1.88293	0.941464	−	0.337113i	$-0.109450\pi$
$647$	47.8945	1.88293	0.941464	+	0.337113i	$0.109450\pi$
$648$	1.00000	0.0392837
$649$	63.0735	2.47585
$650$	0	0
$651$	4.17891	0.163784
$652$	−20.1789	−0.790267
$653$	21.0000	0.821794	0.410897	−	0.911682i	$-0.365216\pi$
$653$	21.0000	0.821794	0.410897	+	0.911682i	$0.365216\pi$
$654$	−4.00000	−0.156412
$655$	29.0735	1.13599
$656$	−7.17891	−0.280289
$657$	4.00000	0.156055
$658$	7.17891	0.279863
$659$	17.5367	0.683134	0.341567	−	0.939857i	$-0.389042\pi$
$659$	17.5367	0.683134	0.341567	+	0.939857i	$0.389042\pi$
$660$	−10.3578	−0.403177
$661$	16.5367	0.643204	0.321602	−	0.946875i	$-0.395779\pi$
$661$	16.5367	0.643204	0.321602	+	0.946875i	$0.395779\pi$
$662$	−1.64218	−0.0638253
$663$	0	0
$664$	6.17891	0.239788
$665$	6.35782	0.246546
$666$	2.00000	0.0774984
$667$	26.0000	1.00672
$668$	−8.00000	−0.309529
$669$	2.17891	0.0842415
$670$	7.64218	0.295243
$671$	15.5367	0.599789
$672$	1.00000	0.0385758
$673$	−1.00000	−0.0385472	−0.0192736	−	0.999814i	$-0.506135\pi$
$673$	−1.00000	−0.0385472	−0.0192736	+	0.999814i	$0.506135\pi$
$674$	33.5367	1.29179
$675$	1.00000	0.0384900
$676$	0	0
$677$	12.0000	0.461197	0.230599	−	0.973049i	$-0.425932\pi$
$677$	12.0000	0.461197	0.230599	+	0.973049i	$0.425932\pi$
$678$	−18.3578	−0.705028
$679$	10.3578	0.397497
$680$	−10.0000	−0.383482
$681$	14.3578	0.550193
$682$	−21.6422	−0.828722
$683$	8.35782	0.319803	0.159901	−	0.987133i	$-0.448882\pi$
$683$	8.35782	0.319803	0.159901	+	0.987133i	$0.448882\pi$
$684$	3.17891	0.121549
$685$	−12.7156	−0.485839
$686$	−1.00000	−0.0381802
$687$	−1.00000	−0.0381524
$688$	12.1789	0.464317
$689$	0	0
$690$	−16.3578	−0.622731
$691$	−40.0000	−1.52167	−0.760836	−	0.648944i	$-0.775211\pi$
$691$	−40.0000	−1.52167	−0.760836	+	0.648944i	$0.775211\pi$
$692$	4.00000	0.152057
$693$	5.17891	0.196730
$694$	−19.1789	−0.728021
$695$	13.6422	0.517478
$696$	3.17891	0.120496
$697$	−35.8945	−1.35960
$698$	8.17891	0.309576
$699$	−22.3578	−0.845650
$700$	1.00000	0.0377964
$701$	−21.7156	−0.820188	−0.410094	−	0.912043i	$-0.634504\pi$
$701$	−21.7156	−0.820188	−0.410094	+	0.912043i	$0.634504\pi$
$702$	0	0
$703$	6.35782	0.239790
$704$	−5.17891	−0.195187
$705$	−14.3578	−0.540747
$706$	4.17891	0.157275
$707$	−6.35782	−0.239110
$708$	12.1789	0.457711
$709$	−16.0000	−0.600893	−0.300446	−	0.953799i	$-0.597136\pi$
$709$	−16.0000	−0.600893	−0.300446	+	0.953799i	$0.597136\pi$
$710$	4.35782	0.163546
$711$	13.1789	0.494248
$712$	9.00000	0.337289
$713$	−34.1789	−1.28001
$714$	5.00000	0.187120
$715$	0	0
$716$	8.35782	0.312346
$717$	−10.1789	−0.380138
$718$	−10.3578	−0.386550
$719$	−37.1789	−1.38654	−0.693270	−	0.720678i	$-0.743831\pi$
$719$	−37.1789	−1.38654	−0.693270	+	0.720678i	$0.743831\pi$
$720$	−2.00000	−0.0745356
$721$	8.17891	0.304598
$722$	−8.89454	−0.331021
$723$	−4.35782	−0.162069
$724$	19.1789	0.712779
$725$	3.17891	0.118062
$726$	−15.8211	−0.587176
$727$	34.5367	1.28090	0.640448	−	0.768001i	$-0.278749\pi$
$727$	34.5367	1.28090	0.640448	+	0.768001i	$0.278749\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−8.00000	−0.296093
$731$	60.8945	2.25227
$732$	3.00000	0.110883
$733$	19.7156	0.728214	0.364107	−	0.931357i	$-0.381374\pi$
$733$	19.7156	0.728214	0.364107	+	0.931357i	$0.381374\pi$
$734$	−8.17891	−0.301889
$735$	2.00000	0.0737711
$736$	−8.17891	−0.301479
$737$	19.7891	0.728940
$738$	−7.17891	−0.264259
$739$	−16.1789	−0.595151	−0.297575	−	0.954698i	$-0.596178\pi$
$739$	−16.1789	−0.595151	−0.297575	+	0.954698i	$0.596178\pi$
$740$	−4.00000	−0.147043
$741$	0	0
$742$	3.00000	0.110133
$743$	31.8211	1.16740	0.583701	−	0.811968i	$-0.301604\pi$
$743$	31.8211	1.16740	0.583701	+	0.811968i	$0.301604\pi$
$744$	−4.17891	−0.153206
$745$	−32.3578	−1.18550
$746$	−20.0000	−0.732252
$747$	6.17891	0.226074
$748$	−25.8945	−0.946798
$749$	−19.1789	−0.700782
$750$	−12.0000	−0.438178
$751$	−35.8945	−1.30981	−0.654905	−	0.755711i	$-0.727291\pi$
$751$	−35.8945	−1.30981	−0.654905	+	0.755711i	$0.727291\pi$
$752$	−7.17891	−0.261788
$753$	−22.1789	−0.808244
$754$	0	0
$755$	−39.0735	−1.42203
$756$	1.00000	0.0363696
$757$	−20.3578	−0.739917	−0.369959	−	0.929048i	$-0.620628\pi$
$757$	−20.3578	−0.739917	−0.369959	+	0.929048i	$0.620628\pi$
$758$	−24.7156	−0.897712
$759$	−42.3578	−1.53749
$760$	−6.35782	−0.230622
$761$	−43.4313	−1.57438	−0.787191	−	0.616709i	$-0.788465\pi$
$761$	−43.4313	−1.57438	−0.787191	+	0.616709i	$0.788465\pi$
$762$	−12.0000	−0.434714
$763$	−4.00000	−0.144810
$764$	−6.53673	−0.236490
$765$	−10.0000	−0.361551
$766$	21.1789	0.765225
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	18.3578	0.662000	0.331000	−	0.943631i	$-0.392614\pi$
$769$	18.3578	0.662000	0.331000	+	0.943631i	$0.392614\pi$
$770$	−10.3578	−0.373270
$771$	19.7156	0.710041
$772$	−13.5367	−0.487197
$773$	14.7156	0.529285	0.264642	−	0.964347i	$-0.414746\pi$
$773$	14.7156	0.529285	0.264642	+	0.964347i	$0.414746\pi$
$774$	12.1789	0.437762
$775$	−4.17891	−0.150111
$776$	−10.3578	−0.371824
$777$	2.00000	0.0717496
$778$	−12.1789	−0.436635
$779$	−22.8211	−0.817650
$780$	0	0
$781$	11.2844	0.403786
$782$	−40.8945	−1.46239
$783$	3.17891	0.113605
$784$	1.00000	0.0357143
$785$	−4.00000	−0.142766
$786$	14.5367	0.518508
$787$	−10.8211	−0.385730	−0.192865	−	0.981225i	$-0.561778\pi$
$787$	−10.8211	−0.385730	−0.192865	+	0.981225i	$0.561778\pi$
$788$	17.0000	0.605600
$789$	12.0000	0.427211
$790$	−26.3578	−0.937769
$791$	−18.3578	−0.652729
$792$	−5.17891	−0.184024
$793$	0	0
$794$	3.00000	0.106466
$795$	−6.00000	−0.212798
$796$	24.1789	0.856999
$797$	0	0		−	1.00000i	$-0.5\pi$
$797$	0	0			1.00000i	$0.5\pi$
$798$	3.17891	0.112532
$799$	−35.8945	−1.26986
$800$	−1.00000	−0.0353553
$801$	9.00000	0.317999
$802$	9.64218	0.340477
$803$	−20.7156	−0.731039
$804$	3.82109	0.134760
$805$	−16.3578	−0.576537
$806$	0	0
$807$	4.35782	0.153402
$808$	6.35782	0.223667
$809$	−20.0000	−0.703163	−0.351581	−	0.936157i	$-0.614356\pi$
$809$	−20.0000	−0.703163	−0.351581	+	0.936157i	$0.614356\pi$
$810$	−2.00000	−0.0702728
$811$	−12.7156	−0.446506	−0.223253	−	0.974761i	$-0.571668\pi$
$811$	−12.7156	−0.446506	−0.223253	+	0.974761i	$0.571668\pi$
$812$	3.17891	0.111558
$813$	−19.8211	−0.695156
$814$	−10.3578	−0.363041
$815$	40.3578	1.41367
$816$	−5.00000	−0.175035
$817$	38.7156	1.35449
$818$	−36.3578	−1.27122
$819$	0	0
$820$	14.3578	0.501397
$821$	0.284367	0.00992446	0.00496223	−	0.999988i	$-0.498420\pi$
$821$	0.284367	0.00992446	0.00496223	+	0.999988i	$0.498420\pi$
$822$	−6.35782	−0.221754
$823$	32.7156	1.14040	0.570198	−	0.821508i	$-0.306867\pi$
$823$	32.7156	1.14040	0.570198	+	0.821508i	$0.306867\pi$
$824$	−8.17891	−0.284926
$825$	−5.17891	−0.180306
$826$	12.1789	0.423758
$827$	−40.7156	−1.41582	−0.707911	−	0.706302i	$-0.750362\pi$
$827$	−40.7156	−1.41582	−0.707911	+	0.706302i	$0.750362\pi$
$828$	−8.17891	−0.284237
$829$	−3.17891	−0.110408	−0.0552040	−	0.998475i	$-0.517581\pi$
$829$	−3.17891	−0.110408	−0.0552040	+	0.998475i	$0.517581\pi$
$830$	−12.3578	−0.428946
$831$	−5.64218	−0.195725
$832$	0	0
$833$	5.00000	0.173240
$834$	6.82109	0.236195
$835$	16.0000	0.553703
$836$	−16.4633	−0.569394
$837$	−4.17891	−0.144444
$838$	−26.8945	−0.929057
$839$	11.6422	0.401933	0.200966	−	0.979598i	$-0.435592\pi$
$839$	11.6422	0.401933	0.200966	+	0.979598i	$0.435592\pi$
$840$	−2.00000	−0.0690066
$841$	−18.8945	−0.651536
$842$	10.7156	0.369285
$843$	−28.3578	−0.976695
$844$	−6.35782	−0.218845
$845$	0	0
$846$	−7.17891	−0.246816
$847$	−15.8211	−0.543619
$848$	−3.00000	−0.103020
$849$	−7.64218	−0.262279
$850$	−5.00000	−0.171499
$851$	−16.3578	−0.560739
$852$	2.17891	0.0746482
$853$	27.7156	0.948965	0.474483	−	0.880265i	$-0.342635\pi$
$853$	27.7156	0.948965	0.474483	+	0.880265i	$0.342635\pi$
$854$	3.00000	0.102658
$855$	−6.35782	−0.217433
$856$	19.1789	0.655522
$857$	−10.7156	−0.366039	−0.183020	−	0.983109i	$-0.558587\pi$
$857$	−10.7156	−0.366039	−0.183020	+	0.983109i	$0.558587\pi$
$858$	0	0
$859$	19.8945	0.678793	0.339397	−	0.940643i	$-0.389777\pi$
$859$	19.8945	0.678793	0.339397	+	0.940643i	$0.389777\pi$
$860$	−24.3578	−0.830595
$861$	−7.17891	−0.244657
$862$	10.1789	0.346695
$863$	13.6422	0.464385	0.232193	−	0.972670i	$-0.425410\pi$
$863$	13.6422	0.464385	0.232193	+	0.972670i	$0.425410\pi$
$864$	−1.00000	−0.0340207
$865$	−8.00000	−0.272008
$866$	34.3578	1.16753
$867$	−8.00000	−0.271694
$868$	−4.17891	−0.141841
$869$	−68.2524	−2.31530
$870$	−6.35782	−0.215550
$871$	0	0
$872$	4.00000	0.135457
$873$	−10.3578	−0.350559
$874$	−26.0000	−0.879463
$875$	−12.0000	−0.405674
$876$	−4.00000	−0.135147
$877$	−40.3578	−1.36279	−0.681393	−	0.731917i	$-0.738626\pi$
$877$	−40.3578	−1.36279	−0.681393	+	0.731917i	$0.738626\pi$
$878$	40.7156	1.37409
$879$	−12.0000	−0.404750
$880$	10.3578	0.349162
$881$	11.4633	0.386208	0.193104	−	0.981178i	$-0.438145\pi$
$881$	11.4633	0.386208	0.193104	+	0.981178i	$0.438145\pi$
$882$	1.00000	0.0336718
$883$	−3.46327	−0.116548	−0.0582742	−	0.998301i	$-0.518560\pi$
$883$	−3.46327	−0.116548	−0.0582742	+	0.998301i	$0.518560\pi$
$884$	0	0
$885$	−24.3578	−0.818779
$886$	3.17891	0.106798
$887$	−45.5367	−1.52897	−0.764487	−	0.644639i	$-0.777008\pi$
$887$	−45.5367	−1.52897	−0.764487	+	0.644639i	$0.777008\pi$
$888$	−2.00000	−0.0671156
$889$	−12.0000	−0.402467
$890$	−18.0000	−0.603361
$891$	−5.17891	−0.173500
$892$	−2.17891	−0.0729552
$893$	−22.8211	−0.763679
$894$	−16.1789	−0.541104
$895$	−16.7156	−0.558742
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	−14.0000	−0.467186
$899$	−13.2844	−0.443058
$900$	−1.00000	−0.0333333
$901$	−15.0000	−0.499722
$902$	37.1789	1.23792
$903$	12.1789	0.405289
$904$	18.3578	0.610572
$905$	−38.3578	−1.27506
$906$	−19.5367	−0.649064
$907$	49.6102	1.64728	0.823639	−	0.567114i	$-0.191940\pi$
$907$	49.6102	1.64728	0.823639	+	0.567114i	$0.191940\pi$
$908$	−14.3578	−0.476481
$909$	6.35782	0.210875
$910$	0	0
$911$	28.7156	0.951391	0.475696	−	0.879610i	$-0.342196\pi$
$911$	28.7156	0.951391	0.475696	+	0.879610i	$0.342196\pi$
$912$	−3.17891	−0.105264
$913$	−32.0000	−1.05905
$914$	24.8945	0.823438
$915$	−6.00000	−0.198354
$916$	1.00000	0.0330409
$917$	14.5367	0.480045
$918$	−5.00000	−0.165025
$919$	−58.2524	−1.92157	−0.960784	−	0.277298i	$-0.910561\pi$
$919$	−58.2524	−1.92157	−0.960784	+	0.277298i	$0.910561\pi$
$920$	16.3578	0.539301
$921$	31.8945	1.05096
$922$	20.7156	0.682233
$923$	0	0
$924$	−5.17891	−0.170374
$925$	−2.00000	−0.0657596
$926$	27.8945	0.916672
$927$	−8.17891	−0.268631
$928$	−3.17891	−0.104353
$929$	39.0000	1.27955	0.639774	−	0.768563i	$-0.279028\pi$
$929$	39.0000	1.27955	0.639774	+	0.768563i	$0.279028\pi$
$930$	8.35782	0.274064
$931$	3.17891	0.104185
$932$	22.3578	0.732355
$933$	−25.5367	−0.836035
$934$	−22.8945	−0.749132
$935$	51.7891	1.69368
$936$	0	0
$937$	21.0735	0.688440	0.344220	−	0.938889i	$-0.388143\pi$
$937$	21.0735	0.688440	0.344220	+	0.938889i	$0.388143\pi$
$938$	3.82109	0.124763
$939$	−4.00000	−0.130535
$940$	14.3578	0.468300
$941$	−20.0000	−0.651981	−0.325991	−	0.945373i	$-0.605698\pi$
$941$	−20.0000	−0.651981	−0.325991	+	0.945373i	$0.605698\pi$
$942$	−2.00000	−0.0651635
$943$	58.7156	1.91204
$944$	−12.1789	−0.396390
$945$	−2.00000	−0.0650600
$946$	−63.0735	−2.05069
$947$	−40.2524	−1.30803	−0.654013	−	0.756483i	$-0.726916\pi$
$947$	−40.2524	−1.30803	−0.654013	+	0.756483i	$0.726916\pi$
$948$	−13.1789	−0.428031
$949$	0	0
$950$	−3.17891	−0.103137
$951$	4.17891	0.135510
$952$	−5.00000	−0.162051
$953$	−2.71563	−0.0879680	−0.0439840	−	0.999032i	$-0.514005\pi$
$953$	−2.71563	−0.0879680	−0.0439840	+	0.999032i	$0.514005\pi$
$954$	−3.00000	−0.0971286
$955$	13.0735	0.423047
$956$	10.1789	0.329209
$957$	−16.4633	−0.532182
$958$	−41.1789	−1.33043
$959$	−6.35782	−0.205305
$960$	2.00000	0.0645497
$961$	−13.5367	−0.436669
$962$	0	0
$963$	19.1789	0.618032
$964$	4.35782	0.140356
$965$	27.0735	0.871525
$966$	−8.17891	−0.263152
$967$	11.6422	0.374387	0.187194	−	0.982323i	$-0.440061\pi$
$967$	11.6422	0.374387	0.187194	+	0.982323i	$0.440061\pi$
$968$	15.8211	0.508509
$969$	−15.8945	−0.510606
$970$	20.7156	0.665139
$971$	−28.1789	−0.904304	−0.452152	−	0.891941i	$-0.649344\pi$
$971$	−28.1789	−0.904304	−0.452152	+	0.891941i	$0.649344\pi$
$972$	−1.00000	−0.0320750
$973$	6.82109	0.218674
$974$	−26.8211	−0.859403
$975$	0	0
$976$	−3.00000	−0.0960277
$977$	12.0000	0.383914	0.191957	−	0.981403i	$-0.438517\pi$
$977$	12.0000	0.383914	0.191957	+	0.981403i	$0.438517\pi$
$978$	20.1789	0.645250
$979$	−46.6102	−1.48967
$980$	−2.00000	−0.0638877
$981$	4.00000	0.127710
$982$	0	0
$983$	−13.0735	−0.416978	−0.208489	−	0.978025i	$-0.566855\pi$
$983$	−13.0735	−0.416978	−0.208489	+	0.978025i	$0.566855\pi$
$984$	7.17891	0.228855
$985$	−34.0000	−1.08333
$986$	−15.8945	−0.506185
$987$	−7.17891	−0.228507
$988$	0	0
$989$	−99.6102	−3.16742
$990$	10.3578	0.329193
$991$	−49.5367	−1.57359	−0.786793	−	0.617217i	$-0.788260\pi$
$991$	−49.5367	−1.57359	−0.786793	+	0.617217i	$0.788260\pi$
$992$	4.17891	0.132680
$993$	1.64218	0.0521131
$994$	2.17891	0.0691108
$995$	−48.3578	−1.53305
$996$	−6.17891	−0.195786
$997$	12.2844	0.389050	0.194525	−	0.980898i	$-0.437683\pi$
$997$	12.2844	0.389050	0.194525	+	0.980898i	$0.437683\pi$
$998$	8.17891	0.258899
$999$	−2.00000	−0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.br.1.1		2
13.3	even	3		546.2.l.k.295.2	yes	4
13.9	even	3		546.2.l.k.211.2	✓	4
13.12	even	2		7098.2.a.bk.1.2		2
39.29	odd	6		1638.2.r.ba.1387.1		4
39.35	odd	6		1638.2.r.ba.757.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.k.211.2	✓	4	13.9	even	3
546.2.l.k.295.2	yes	4	13.3	even	3
1638.2.r.ba.757.1		4	39.35	odd	6
1638.2.r.ba.1387.1		4	39.29	odd	6
7098.2.a.bk.1.2		2	13.12	even	2
7098.2.a.br.1.1		2	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -2.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.00000 q^{10} -5.17891 q^{11} -1.00000 q^{12} -1.00000 q^{14} +2.00000 q^{15} +1.00000 q^{16} +5.00000 q^{17} +1.00000 q^{18} +3.17891 q^{19} -2.00000 q^{20} +1.00000 q^{21} -5.17891 q^{22} -8.17891 q^{23} -1.00000 q^{24} -1.00000 q^{25} -1.00000 q^{27} -1.00000 q^{28} -3.17891 q^{29} +2.00000 q^{30} +4.17891 q^{31} +1.00000 q^{32} +5.17891 q^{33} +5.00000 q^{34} +2.00000 q^{35} +1.00000 q^{36} +2.00000 q^{37} +3.17891 q^{38} -2.00000 q^{40} -7.17891 q^{41} +1.00000 q^{42} +12.1789 q^{43} -5.17891 q^{44} -2.00000 q^{45} -8.17891 q^{46} -7.17891 q^{47} -1.00000 q^{48} +1.00000 q^{49} -1.00000 q^{50} -5.00000 q^{51} -3.00000 q^{53} -1.00000 q^{54} +10.3578 q^{55} -1.00000 q^{56} -3.17891 q^{57} -3.17891 q^{58} -12.1789 q^{59} +2.00000 q^{60} -3.00000 q^{61} +4.17891 q^{62} -1.00000 q^{63} +1.00000 q^{64} +5.17891 q^{66} -3.82109 q^{67} +5.00000 q^{68} +8.17891 q^{69} +2.00000 q^{70} -2.17891 q^{71} +1.00000 q^{72} +4.00000 q^{73} +2.00000 q^{74} +1.00000 q^{75} +3.17891 q^{76} +5.17891 q^{77} +13.1789 q^{79} -2.00000 q^{80} +1.00000 q^{81} -7.17891 q^{82} +6.17891 q^{83} +1.00000 q^{84} -10.0000 q^{85} +12.1789 q^{86} +3.17891 q^{87} -5.17891 q^{88} +9.00000 q^{89} -2.00000 q^{90} -8.17891 q^{92} -4.17891 q^{93} -7.17891 q^{94} -6.35782 q^{95} -1.00000 q^{96} -10.3578 q^{97} +1.00000 q^{98} -5.17891 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 4 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} - 4 q^{10} + q^{11} - 2 q^{12} - 2 q^{14} + 4 q^{15} + 2 q^{16} + 10 q^{17} + 2 q^{18} - 5 q^{19} - 4 q^{20} + 2 q^{21} + q^{22} - 5 q^{23} - 2 q^{24} - 2 q^{25} - 2 q^{27} - 2 q^{28} + 5 q^{29} + 4 q^{30} - 3 q^{31} + 2 q^{32} - q^{33} + 10 q^{34} + 4 q^{35} + 2 q^{36} + 4 q^{37} - 5 q^{38} - 4 q^{40} - 3 q^{41} + 2 q^{42} + 13 q^{43} + q^{44} - 4 q^{45} - 5 q^{46} - 3 q^{47} - 2 q^{48} + 2 q^{49} - 2 q^{50} - 10 q^{51} - 6 q^{53} - 2 q^{54} - 2 q^{55} - 2 q^{56} + 5 q^{57} + 5 q^{58} - 13 q^{59} + 4 q^{60} - 6 q^{61} - 3 q^{62} - 2 q^{63} + 2 q^{64} - q^{66} - 19 q^{67} + 10 q^{68} + 5 q^{69} + 4 q^{70} + 7 q^{71} + 2 q^{72} + 8 q^{73} + 4 q^{74} + 2 q^{75} - 5 q^{76} - q^{77} + 15 q^{79} - 4 q^{80} + 2 q^{81} - 3 q^{82} + q^{83} + 2 q^{84} - 20 q^{85} + 13 q^{86} - 5 q^{87} + q^{88} + 18 q^{89} - 4 q^{90} - 5 q^{92} + 3 q^{93} - 3 q^{94} + 10 q^{95} - 2 q^{96} + 2 q^{97} + 2 q^{98} + q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 4 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9 - 4 * q^10 + q^11 - 2 * q^12 - 2 * q^14 + 4 * q^15 + 2 * q^16 + 10 * q^17 + 2 * q^18 - 5 * q^19 - 4 * q^20 + 2 * q^21 + q^22 - 5 * q^23 - 2 * q^24 - 2 * q^25 - 2 * q^27 - 2 * q^28 + 5 * q^29 + 4 * q^30 - 3 * q^31 + 2 * q^32 - q^33 + 10 * q^34 + 4 * q^35 + 2 * q^36 + 4 * q^37 - 5 * q^38 - 4 * q^40 - 3 * q^41 + 2 * q^42 + 13 * q^43 + q^44 - 4 * q^45 - 5 * q^46 - 3 * q^47 - 2 * q^48 + 2 * q^49 - 2 * q^50 - 10 * q^51 - 6 * q^53 - 2 * q^54 - 2 * q^55 - 2 * q^56 + 5 * q^57 + 5 * q^58 - 13 * q^59 + 4 * q^60 - 6 * q^61 - 3 * q^62 - 2 * q^63 + 2 * q^64 - q^66 - 19 * q^67 + 10 * q^68 + 5 * q^69 + 4 * q^70 + 7 * q^71 + 2 * q^72 + 8 * q^73 + 4 * q^74 + 2 * q^75 - 5 * q^76 - q^77 + 15 * q^79 - 4 * q^80 + 2 * q^81 - 3 * q^82 + q^83 + 2 * q^84 - 20 * q^85 + 13 * q^86 - 5 * q^87 + q^88 + 18 * q^89 - 4 * q^90 - 5 * q^92 + 3 * q^93 - 3 * q^94 + 10 * q^95 - 2 * q^96 + 2 * q^97 + 2 * q^98 + q^99

Introduction

L-functions

Modular forms

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Database

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