LMFDB - Embedded newform 7098.2.a.bm.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{57}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 14 $ x^2 - x - 14
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
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			$4.27492$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.27492 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.27492 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +4.27492 q^{10} +4.00000 q^{11} +1.00000 q^{12} +1.00000 q^{14} -4.27492 q^{15} +1.00000 q^{16} +3.00000 q^{17} -1.00000 q^{18} -6.54983 q^{19} -4.27492 q^{20} -1.00000 q^{21} -4.00000 q^{22} -5.27492 q^{23} -1.00000 q^{24} +13.2749 q^{25} +1.00000 q^{27} -1.00000 q^{28} +8.27492 q^{29} +4.27492 q^{30} +1.27492 q^{31} -1.00000 q^{32} +4.00000 q^{33} -3.00000 q^{34} +4.27492 q^{35} +1.00000 q^{36} -0.274917 q^{37} +6.54983 q^{38} +4.27492 q^{40} -8.27492 q^{41} +1.00000 q^{42} -11.8248 q^{43} +4.00000 q^{44} -4.27492 q^{45} +5.27492 q^{46} +6.54983 q^{47} +1.00000 q^{48} +1.00000 q^{49} -13.2749 q^{50} +3.00000 q^{51} -3.54983 q^{53} -1.00000 q^{54} -17.0997 q^{55} +1.00000 q^{56} -6.54983 q^{57} -8.27492 q^{58} +11.8248 q^{59} -4.27492 q^{60} -9.00000 q^{61} -1.27492 q^{62} -1.00000 q^{63} +1.00000 q^{64} -4.00000 q^{66} +2.72508 q^{67} +3.00000 q^{68} -5.27492 q^{69} -4.27492 q^{70} -5.27492 q^{71} -1.00000 q^{72} -5.72508 q^{73} +0.274917 q^{74} +13.2749 q^{75} -6.54983 q^{76} -4.00000 q^{77} -8.00000 q^{79} -4.27492 q^{80} +1.00000 q^{81} +8.27492 q^{82} +11.8248 q^{83} -1.00000 q^{84} -12.8248 q^{85} +11.8248 q^{86} +8.27492 q^{87} -4.00000 q^{88} -0.725083 q^{89} +4.27492 q^{90} -5.27492 q^{92} +1.27492 q^{93} -6.54983 q^{94} +28.0000 q^{95} -1.00000 q^{96} +0.549834 q^{97} -1.00000 q^{98} +4.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{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 - 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} - q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} + q^{10} + 8 q^{11} + 2 q^{12} + 2 q^{14} - q^{15} + 2 q^{16} + 6 q^{17} - 2 q^{18} + 2 q^{19} - q^{20} - 2 q^{21} - 8 q^{22} - 3 q^{23} - 2 q^{24} + 19 q^{25} + 2 q^{27} - 2 q^{28} + 9 q^{29} + q^{30} - 5 q^{31} - 2 q^{32} + 8 q^{33} - 6 q^{34} + q^{35} + 2 q^{36} + 7 q^{37} - 2 q^{38} + q^{40} - 9 q^{41} + 2 q^{42} - q^{43} + 8 q^{44} - q^{45} + 3 q^{46} - 2 q^{47} + 2 q^{48} + 2 q^{49} - 19 q^{50} + 6 q^{51} + 8 q^{53} - 2 q^{54} - 4 q^{55} + 2 q^{56} + 2 q^{57} - 9 q^{58} + q^{59} - q^{60} - 18 q^{61} + 5 q^{62} - 2 q^{63} + 2 q^{64} - 8 q^{66} + 13 q^{67} + 6 q^{68} - 3 q^{69} - q^{70} - 3 q^{71} - 2 q^{72} - 19 q^{73} - 7 q^{74} + 19 q^{75} + 2 q^{76} - 8 q^{77} - 16 q^{79} - q^{80} + 2 q^{81} + 9 q^{82} + q^{83} - 2 q^{84} - 3 q^{85} + q^{86} + 9 q^{87} - 8 q^{88} - 9 q^{89} + q^{90} - 3 q^{92} - 5 q^{93} + 2 q^{94} + 56 q^{95} - 2 q^{96} - 14 q^{97} - 2 q^{98} + 8 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 + q^10 + 8 * q^11 + 2 * q^12 + 2 * q^14 - q^15 + 2 * q^16 + 6 * q^17 - 2 * q^18 + 2 * q^19 - q^20 - 2 * q^21 - 8 * q^22 - 3 * q^23 - 2 * q^24 + 19 * q^25 + 2 * q^27 - 2 * q^28 + 9 * q^29 + q^30 - 5 * q^31 - 2 * q^32 + 8 * q^33 - 6 * q^34 + q^35 + 2 * q^36 + 7 * q^37 - 2 * q^38 + q^40 - 9 * q^41 + 2 * q^42 - q^43 + 8 * q^44 - q^45 + 3 * q^46 - 2 * q^47 + 2 * q^48 + 2 * q^49 - 19 * q^50 + 6 * q^51 + 8 * q^53 - 2 * q^54 - 4 * q^55 + 2 * q^56 + 2 * q^57 - 9 * q^58 + q^59 - q^60 - 18 * q^61 + 5 * q^62 - 2 * q^63 + 2 * q^64 - 8 * q^66 + 13 * q^67 + 6 * q^68 - 3 * q^69 - q^70 - 3 * q^71 - 2 * q^72 - 19 * q^73 - 7 * q^74 + 19 * q^75 + 2 * q^76 - 8 * q^77 - 16 * q^79 - q^80 + 2 * q^81 + 9 * q^82 + q^83 - 2 * q^84 - 3 * q^85 + q^86 + 9 * q^87 - 8 * q^88 - 9 * q^89 + q^90 - 3 * q^92 - 5 * q^93 + 2 * q^94 + 56 * q^95 - 2 * q^96 - 14 * q^97 - 2 * q^98 + 8 * 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
$5$	−4.27492	−1.91180	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−4.27492	−1.91180	−0.955901	+	0.293691i	$0.905116\pi$
$6$	−1.00000	−0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	4.27492	1.35185
$11$	4.00000	1.20605	0.603023	−	0.797724i	$-0.293963\pi$
$11$	4.00000	1.20605	0.603023	+	0.797724i	$0.293963\pi$
$12$	1.00000	0.288675
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	−4.27492	−1.10378
$16$	1.00000	0.250000
$17$	3.00000	0.727607	0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000	0.727607	0.363803	+	0.931476i	$0.381478\pi$
$18$	−1.00000	−0.235702
$19$	−6.54983	−1.50264	−0.751318	−	0.659941i	$-0.770581\pi$
$19$	−6.54983	−1.50264	−0.751318	+	0.659941i	$0.770581\pi$
$20$	−4.27492	−0.955901
$21$	−1.00000	−0.218218
$22$	−4.00000	−0.852803
$23$	−5.27492	−1.09990	−0.549948	−	0.835199i	$-0.685353\pi$
$23$	−5.27492	−1.09990	−0.549948	+	0.835199i	$0.685353\pi$
$24$	−1.00000	−0.204124
$25$	13.2749	2.65498
$26$	0	0
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	8.27492	1.53661	0.768307	−	0.640082i	$-0.221100\pi$
$29$	8.27492	1.53661	0.768307	+	0.640082i	$0.221100\pi$
$30$	4.27492	0.780490
$31$	1.27492	0.228982	0.114491	−	0.993424i	$-0.463476\pi$
$31$	1.27492	0.228982	0.114491	+	0.993424i	$0.463476\pi$
$32$	−1.00000	−0.176777
$33$	4.00000	0.696311
$34$	−3.00000	−0.514496
$35$	4.27492	0.722593
$36$	1.00000	0.166667
$37$	−0.274917	−0.0451961	−0.0225981	−	0.999745i	$-0.507194\pi$
$37$	−0.274917	−0.0451961	−0.0225981	+	0.999745i	$0.507194\pi$
$38$	6.54983	1.06252
$39$	0	0
$40$	4.27492	0.675924
$41$	−8.27492	−1.29232	−0.646162	−	0.763200i	$-0.723627\pi$
$41$	−8.27492	−1.29232	−0.646162	+	0.763200i	$0.723627\pi$
$42$	1.00000	0.154303
$43$	−11.8248	−1.80326	−0.901629	−	0.432511i	$-0.857628\pi$
$43$	−11.8248	−1.80326	−0.901629	+	0.432511i	$0.857628\pi$
$44$	4.00000	0.603023
$45$	−4.27492	−0.637267
$46$	5.27492	0.777744
$47$	6.54983	0.955392	0.477696	−	0.878525i	$-0.341472\pi$
$47$	6.54983	0.955392	0.477696	+	0.878525i	$0.341472\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−13.2749	−1.87736
$51$	3.00000	0.420084
$52$	0	0
$53$	−3.54983	−0.487607	−0.243804	−	0.969825i	$-0.578395\pi$
$53$	−3.54983	−0.487607	−0.243804	+	0.969825i	$0.578395\pi$
$54$	−1.00000	−0.136083
$55$	−17.0997	−2.30572
$56$	1.00000	0.133631
$57$	−6.54983	−0.867547
$58$	−8.27492	−1.08655
$59$	11.8248	1.53945	0.769726	−	0.638375i	$-0.220393\pi$
$59$	11.8248	1.53945	0.769726	+	0.638375i	$0.220393\pi$
$60$	−4.27492	−0.551889
$61$	−9.00000	−1.15233	−0.576166	−	0.817333i	$-0.695452\pi$
$61$	−9.00000	−1.15233	−0.576166	+	0.817333i	$0.695452\pi$
$62$	−1.27492	−0.161915
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−4.00000	−0.492366
$67$	2.72508	0.332922	0.166461	−	0.986048i	$-0.446766\pi$
$67$	2.72508	0.332922	0.166461	+	0.986048i	$0.446766\pi$
$68$	3.00000	0.363803
$69$	−5.27492	−0.635025
$70$	−4.27492	−0.510950
$71$	−5.27492	−0.626018	−0.313009	−	0.949750i	$-0.601337\pi$
$71$	−5.27492	−0.626018	−0.313009	+	0.949750i	$0.601337\pi$
$72$	−1.00000	−0.117851
$73$	−5.72508	−0.670070	−0.335035	−	0.942206i	$-0.608748\pi$
$73$	−5.72508	−0.670070	−0.335035	+	0.942206i	$0.608748\pi$
$74$	0.274917	0.0319585
$75$	13.2749	1.53286
$76$	−6.54983	−0.751318
$77$	−4.00000	−0.455842
$78$	0	0
$79$	−8.00000	−0.900070	−0.450035	−	0.893011i	$-0.648589\pi$
$79$	−8.00000	−0.900070	−0.450035	+	0.893011i	$0.648589\pi$
$80$	−4.27492	−0.477950
$81$	1.00000	0.111111
$82$	8.27492	0.913812
$83$	11.8248	1.29794	0.648968	−	0.760816i	$-0.275201\pi$
$83$	11.8248	1.29794	0.648968	+	0.760816i	$0.275201\pi$
$84$	−1.00000	−0.109109
$85$	−12.8248	−1.39104
$86$	11.8248	1.27510
$87$	8.27492	0.887164
$88$	−4.00000	−0.426401
$89$	−0.725083	−0.0768586	−0.0384293	−	0.999261i	$-0.512235\pi$
$89$	−0.725083	−0.0768586	−0.0384293	+	0.999261i	$0.512235\pi$
$90$	4.27492	0.450616
$91$	0	0
$92$	−5.27492	−0.549948
$93$	1.27492	0.132203
$94$	−6.54983	−0.675564
$95$	28.0000	2.87274
$96$	−1.00000	−0.102062
$97$	0.549834	0.0558272	0.0279136	−	0.999610i	$-0.491114\pi$
$97$	0.549834	0.0558272	0.0279136	+	0.999610i	$0.491114\pi$
$98$	−1.00000	−0.101015
$99$	4.00000	0.402015
$100$	13.2749	1.32749
$101$	1.72508	0.171652	0.0858261	−	0.996310i	$-0.472647\pi$
$101$	1.72508	0.171652	0.0858261	+	0.996310i	$0.472647\pi$
$102$	−3.00000	−0.297044
$103$	5.27492	0.519753	0.259877	−	0.965642i	$-0.416318\pi$
$103$	5.27492	0.519753	0.259877	+	0.965642i	$0.416318\pi$
$104$	0	0
$105$	4.27492	0.417189
$106$	3.54983	0.344790
$107$	2.54983	0.246502	0.123251	−	0.992376i	$-0.460668\pi$
$107$	2.54983	0.246502	0.123251	+	0.992376i	$0.460668\pi$
$108$	1.00000	0.0962250
$109$	4.54983	0.435795	0.217898	−	0.975972i	$-0.430080\pi$
$109$	4.54983	0.435795	0.217898	+	0.975972i	$0.430080\pi$
$110$	17.0997	1.63039
$111$	−0.274917	−0.0260940
$112$	−1.00000	−0.0944911
$113$	14.8248	1.39460	0.697298	−	0.716782i	$-0.254386\pi$
$113$	14.8248	1.39460	0.697298	+	0.716782i	$0.254386\pi$
$114$	6.54983	0.613448
$115$	22.5498	2.10278
$116$	8.27492	0.768307
$117$	0	0
$118$	−11.8248	−1.08856
$119$	−3.00000	−0.275010
$120$	4.27492	0.390245
$121$	5.00000	0.454545
$122$	9.00000	0.814822
$123$	−8.27492	−0.746124
$124$	1.27492	0.114491
$125$	−35.3746	−3.16400
$126$	1.00000	0.0890871
$127$	8.00000	0.709885	0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000	0.709885	0.354943	+	0.934888i	$0.384500\pi$
$128$	−1.00000	−0.0883883
$129$	−11.8248	−1.04111
$130$	0	0
$131$	−2.72508	−0.238092	−0.119046	−	0.992889i	$-0.537984\pi$
$131$	−2.72508	−0.238092	−0.119046	+	0.992889i	$0.537984\pi$
$132$	4.00000	0.348155
$133$	6.54983	0.567943
$134$	−2.72508	−0.235411
$135$	−4.27492	−0.367926
$136$	−3.00000	−0.257248
$137$	−22.8248	−1.95005	−0.975025	−	0.222095i	$-0.928711\pi$
$137$	−22.8248	−1.95005	−0.975025	+	0.222095i	$0.928711\pi$
$138$	5.27492	0.449031
$139$	−9.09967	−0.771824	−0.385912	−	0.922536i	$-0.626113\pi$
$139$	−9.09967	−0.771824	−0.385912	+	0.922536i	$0.626113\pi$
$140$	4.27492	0.361296
$141$	6.54983	0.551596
$142$	5.27492	0.442661
$143$	0	0
$144$	1.00000	0.0833333
$145$	−35.3746	−2.93770
$146$	5.72508	0.473811
$147$	1.00000	0.0824786
$148$	−0.274917	−0.0225981
$149$	1.00000	0.0819232	0.0409616	−	0.999161i	$-0.486958\pi$
$149$	1.00000	0.0819232	0.0409616	+	0.999161i	$0.486958\pi$
$150$	−13.2749	−1.08389
$151$	−13.0997	−1.06604	−0.533018	−	0.846104i	$-0.678942\pi$
$151$	−13.0997	−1.06604	−0.533018	+	0.846104i	$0.678942\pi$
$152$	6.54983	0.531262
$153$	3.00000	0.242536
$154$	4.00000	0.322329
$155$	−5.45017	−0.437768
$156$	0	0
$157$	−3.72508	−0.297294	−0.148647	−	0.988890i	$-0.547492\pi$
$157$	−3.72508	−0.297294	−0.148647	+	0.988890i	$0.547492\pi$
$158$	8.00000	0.636446
$159$	−3.54983	−0.281520
$160$	4.27492	0.337962
$161$	5.27492	0.415722
$162$	−1.00000	−0.0785674
$163$	13.2749	1.03977	0.519886	−	0.854236i	$-0.325974\pi$
$163$	13.2749	1.03977	0.519886	+	0.854236i	$0.325974\pi$
$164$	−8.27492	−0.646162
$165$	−17.0997	−1.33121
$166$	−11.8248	−0.917779
$167$	0	0		−	1.00000i	$-0.5\pi$
$167$	0	0			1.00000i	$0.5\pi$
$168$	1.00000	0.0771517
$169$	0	0
$170$	12.8248	0.983614
$171$	−6.54983	−0.500878
$172$	−11.8248	−0.901629
$173$	−4.54983	−0.345918	−0.172959	−	0.984929i	$-0.555333\pi$
$173$	−4.54983	−0.345918	−0.172959	+	0.984929i	$0.555333\pi$
$174$	−8.27492	−0.627320
$175$	−13.2749	−1.00349
$176$	4.00000	0.301511
$177$	11.8248	0.888803
$178$	0.725083	0.0543473
$179$	1.45017	0.108390	0.0541952	−	0.998530i	$-0.482741\pi$
$179$	1.45017	0.108390	0.0541952	+	0.998530i	$0.482741\pi$
$180$	−4.27492	−0.318634
$181$	−16.8248	−1.25057	−0.625287	−	0.780395i	$-0.715018\pi$
$181$	−16.8248	−1.25057	−0.625287	+	0.780395i	$0.715018\pi$
$182$	0	0
$183$	−9.00000	−0.665299
$184$	5.27492	0.388872
$185$	1.17525	0.0864060
$186$	−1.27492	−0.0934815
$187$	12.0000	0.877527
$188$	6.54983	0.477696
$189$	−1.00000	−0.0727393
$190$	−28.0000	−2.03133
$191$	6.72508	0.486610	0.243305	−	0.969950i	$-0.421768\pi$
$191$	6.72508	0.486610	0.243305	+	0.969950i	$0.421768\pi$
$192$	1.00000	0.0721688
$193$	24.8248	1.78692	0.893462	−	0.449138i	$-0.148269\pi$
$193$	24.8248	1.78692	0.893462	+	0.449138i	$0.148269\pi$
$194$	−0.549834	−0.0394758
$195$	0	0
$196$	1.00000	0.0714286
$197$	21.8248	1.55495	0.777475	−	0.628914i	$-0.216500\pi$
$197$	21.8248	1.55495	0.777475	+	0.628914i	$0.216500\pi$
$198$	−4.00000	−0.284268
$199$	11.8248	0.838234	0.419117	−	0.907932i	$-0.362340\pi$
$199$	11.8248	0.838234	0.419117	+	0.907932i	$0.362340\pi$
$200$	−13.2749	−0.938678
$201$	2.72508	0.192213
$202$	−1.72508	−0.121376
$203$	−8.27492	−0.580785
$204$	3.00000	0.210042
$205$	35.3746	2.47067
$206$	−5.27492	−0.367521
$207$	−5.27492	−0.366632
$208$	0	0
$209$	−26.1993	−1.81225
$210$	−4.27492	−0.294997
$211$	21.0997	1.45256	0.726281	−	0.687398i	$-0.241247\pi$
$211$	21.0997	1.45256	0.726281	+	0.687398i	$0.241247\pi$
$212$	−3.54983	−0.243804
$213$	−5.27492	−0.361431
$214$	−2.54983	−0.174303
$215$	50.5498	3.44747
$216$	−1.00000	−0.0680414
$217$	−1.27492	−0.0865470
$218$	−4.54983	−0.308154
$219$	−5.72508	−0.386865
$220$	−17.0997	−1.15286
$221$	0	0
$222$	0.274917	0.0184512
$223$	−10.7251	−0.718205	−0.359102	−	0.933298i	$-0.616917\pi$
$223$	−10.7251	−0.718205	−0.359102	+	0.933298i	$0.616917\pi$
$224$	1.00000	0.0668153
$225$	13.2749	0.884994
$226$	−14.8248	−0.986128
$227$	21.0997	1.40043	0.700217	−	0.713930i	$-0.253087\pi$
$227$	21.0997	1.40043	0.700217	+	0.713930i	$0.253087\pi$
$228$	−6.54983	−0.433773
$229$	−12.7251	−0.840897	−0.420449	−	0.907316i	$-0.638127\pi$
$229$	−12.7251	−0.840897	−0.420449	+	0.907316i	$0.638127\pi$
$230$	−22.5498	−1.48689
$231$	−4.00000	−0.263181
$232$	−8.27492	−0.543275
$233$	7.45017	0.488077	0.244038	−	0.969766i	$-0.421528\pi$
$233$	7.45017	0.488077	0.244038	+	0.969766i	$0.421528\pi$
$234$	0	0
$235$	−28.0000	−1.82652
$236$	11.8248	0.769726
$237$	−8.00000	−0.519656
$238$	3.00000	0.194461
$239$	5.27492	0.341206	0.170603	−	0.985340i	$-0.445428\pi$
$239$	5.27492	0.341206	0.170603	+	0.985340i	$0.445428\pi$
$240$	−4.27492	−0.275945
$241$	15.7251	1.01294	0.506471	−	0.862257i	$-0.330950\pi$
$241$	15.7251	1.01294	0.506471	+	0.862257i	$0.330950\pi$
$242$	−5.00000	−0.321412
$243$	1.00000	0.0641500
$244$	−9.00000	−0.576166
$245$	−4.27492	−0.273114
$246$	8.27492	0.527589
$247$	0	0
$248$	−1.27492	−0.0809573
$249$	11.8248	0.749363
$250$	35.3746	2.23729
$251$	13.2749	0.837905	0.418953	−	0.908008i	$-0.362397\pi$
$251$	13.2749	0.837905	0.418953	+	0.908008i	$0.362397\pi$
$252$	−1.00000	−0.0629941
$253$	−21.0997	−1.32652
$254$	−8.00000	−0.501965
$255$	−12.8248	−0.803117
$256$	1.00000	0.0625000
$257$	15.0000	0.935674	0.467837	−	0.883815i	$-0.345033\pi$
$257$	15.0000	0.935674	0.467837	+	0.883815i	$0.345033\pi$
$258$	11.8248	0.736177
$259$	0.274917	0.0170825
$260$	0	0
$261$	8.27492	0.512205
$262$	2.72508	0.168356
$263$	21.0997	1.30106	0.650531	−	0.759480i	$-0.274547\pi$
$263$	21.0997	1.30106	0.650531	+	0.759480i	$0.274547\pi$
$264$	−4.00000	−0.246183
$265$	15.1752	0.932208
$266$	−6.54983	−0.401596
$267$	−0.725083	−0.0443743
$268$	2.72508	0.166461
$269$	−18.0000	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$270$	4.27492	0.260163
$271$	−25.2749	−1.53534	−0.767671	−	0.640844i	$-0.778584\pi$
$271$	−25.2749	−1.53534	−0.767671	+	0.640844i	$0.778584\pi$
$272$	3.00000	0.181902
$273$	0	0
$274$	22.8248	1.37889
$275$	53.0997	3.20203
$276$	−5.27492	−0.317513
$277$	14.8248	0.890733	0.445366	−	0.895348i	$-0.353073\pi$
$277$	14.8248	0.890733	0.445366	+	0.895348i	$0.353073\pi$
$278$	9.09967	0.545762
$279$	1.27492	0.0763273
$280$	−4.27492	−0.255475
$281$	20.8248	1.24230	0.621150	−	0.783691i	$-0.286666\pi$
$281$	20.8248	1.24230	0.621150	+	0.783691i	$0.286666\pi$
$282$	−6.54983	−0.390037
$283$	−9.45017	−0.561754	−0.280877	−	0.959744i	$-0.590625\pi$
$283$	−9.45017	−0.561754	−0.280877	+	0.959744i	$0.590625\pi$
$284$	−5.27492	−0.313009
$285$	28.0000	1.65858
$286$	0	0
$287$	8.27492	0.488453
$288$	−1.00000	−0.0589256
$289$	−8.00000	−0.470588
$290$	35.3746	2.07727
$291$	0.549834	0.0322319
$292$	−5.72508	−0.335035
$293$	18.2749	1.06763	0.533816	−	0.845601i	$-0.320757\pi$
$293$	18.2749	1.06763	0.533816	+	0.845601i	$0.320757\pi$
$294$	−1.00000	−0.0583212
$295$	−50.5498	−2.94313
$296$	0.274917	0.0159792
$297$	4.00000	0.232104
$298$	−1.00000	−0.0579284
$299$	0	0
$300$	13.2749	0.766428
$301$	11.8248	0.681567
$302$	13.0997	0.753801
$303$	1.72508	0.0991034
$304$	−6.54983	−0.375659
$305$	38.4743	2.20303
$306$	−3.00000	−0.171499
$307$	1.45017	0.0827653	0.0413827	−	0.999143i	$-0.486824\pi$
$307$	1.45017	0.0827653	0.0413827	+	0.999143i	$0.486824\pi$
$308$	−4.00000	−0.227921
$309$	5.27492	0.300080
$310$	5.45017	0.309549
$311$	−2.54983	−0.144588	−0.0722939	−	0.997383i	$-0.523032\pi$
$311$	−2.54983	−0.144588	−0.0722939	+	0.997383i	$0.523032\pi$
$312$	0	0
$313$	17.6495	0.997609	0.498804	−	0.866715i	$-0.333773\pi$
$313$	17.6495	0.997609	0.498804	+	0.866715i	$0.333773\pi$
$314$	3.72508	0.210219
$315$	4.27492	0.240864
$316$	−8.00000	−0.450035
$317$	7.54983	0.424041	0.212020	−	0.977265i	$-0.431996\pi$
$317$	7.54983	0.424041	0.212020	+	0.977265i	$0.431996\pi$
$318$	3.54983	0.199065
$319$	33.0997	1.85323
$320$	−4.27492	−0.238975
$321$	2.54983	0.142318
$322$	−5.27492	−0.293960
$323$	−19.6495	−1.09333
$324$	1.00000	0.0555556
$325$	0	0
$326$	−13.2749	−0.735230
$327$	4.54983	0.251606
$328$	8.27492	0.456906
$329$	−6.54983	−0.361104
$330$	17.0997	0.941306
$331$	−4.00000	−0.219860	−0.109930	−	0.993939i	$-0.535063\pi$
$331$	−4.00000	−0.219860	−0.109930	+	0.993939i	$0.535063\pi$
$332$	11.8248	0.648968
$333$	−0.274917	−0.0150654
$334$	0	0
$335$	−11.6495	−0.636480
$336$	−1.00000	−0.0545545
$337$	0.274917	0.0149757	0.00748785	−	0.999972i	$-0.497617\pi$
$337$	0.274917	0.0149757	0.00748785	+	0.999972i	$0.497617\pi$
$338$	0	0
$339$	14.8248	0.805170
$340$	−12.8248	−0.695520
$341$	5.09967	0.276163
$342$	6.54983	0.354174
$343$	−1.00000	−0.0539949
$344$	11.8248	0.637548
$345$	22.5498	1.21404
$346$	4.54983	0.244601
$347$	30.5498	1.64000	0.820001	−	0.572363i	$-0.193973\pi$
$347$	30.5498	1.64000	0.820001	+	0.572363i	$0.193973\pi$
$348$	8.27492	0.443582
$349$	34.9244	1.86946	0.934731	−	0.355357i	$-0.115641\pi$
$349$	34.9244	1.86946	0.934731	+	0.355357i	$0.115641\pi$
$350$	13.2749	0.709574
$351$	0	0
$352$	−4.00000	−0.213201
$353$	19.5498	1.04053	0.520266	−	0.854004i	$-0.325833\pi$
$353$	19.5498	1.04053	0.520266	+	0.854004i	$0.325833\pi$
$354$	−11.8248	−0.628478
$355$	22.5498	1.19682
$356$	−0.725083	−0.0384293
$357$	−3.00000	−0.158777
$358$	−1.45017	−0.0766436
$359$	1.09967	0.0580383	0.0290192	−	0.999579i	$-0.490762\pi$
$359$	1.09967	0.0580383	0.0290192	+	0.999579i	$0.490762\pi$
$360$	4.27492	0.225308
$361$	23.9003	1.25791
$362$	16.8248	0.884289
$363$	5.00000	0.262432
$364$	0	0
$365$	24.4743	1.28104
$366$	9.00000	0.470438
$367$	13.2749	0.692945	0.346473	−	0.938060i	$-0.387379\pi$
$367$	13.2749	0.692945	0.346473	+	0.938060i	$0.387379\pi$
$368$	−5.27492	−0.274974
$369$	−8.27492	−0.430775
$370$	−1.17525	−0.0610983
$371$	3.54983	0.184298
$372$	1.27492	0.0661014
$373$	26.8248	1.38893	0.694466	−	0.719525i	$-0.255640\pi$
$373$	26.8248	1.38893	0.694466	+	0.719525i	$0.255640\pi$
$374$	−12.0000	−0.620505
$375$	−35.3746	−1.82674
$376$	−6.54983	−0.337782
$377$	0	0
$378$	1.00000	0.0514344
$379$	20.0000	1.02733	0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000	1.02733	0.513665	+	0.857991i	$0.328287\pi$
$380$	28.0000	1.43637
$381$	8.00000	0.409852
$382$	−6.72508	−0.344085
$383$	−22.1993	−1.13433	−0.567167	−	0.823603i	$-0.691960\pi$
$383$	−22.1993	−1.13433	−0.567167	+	0.823603i	$0.691960\pi$
$384$	−1.00000	−0.0510310
$385$	17.0997	0.871480
$386$	−24.8248	−1.26355
$387$	−11.8248	−0.601086
$388$	0.549834	0.0279136
$389$	−24.6495	−1.24978	−0.624890	−	0.780713i	$-0.714856\pi$
$389$	−24.6495	−1.24978	−0.624890	+	0.780713i	$0.714856\pi$
$390$	0	0
$391$	−15.8248	−0.800292
$392$	−1.00000	−0.0505076
$393$	−2.72508	−0.137462
$394$	−21.8248	−1.09952
$395$	34.1993	1.72076
$396$	4.00000	0.201008
$397$	−23.2749	−1.16813	−0.584067	−	0.811705i	$-0.698540\pi$
$397$	−23.2749	−1.16813	−0.584067	+	0.811705i	$0.698540\pi$
$398$	−11.8248	−0.592721
$399$	6.54983	0.327902
$400$	13.2749	0.663746
$401$	2.27492	0.113604	0.0568020	−	0.998385i	$-0.481910\pi$
$401$	2.27492	0.113604	0.0568020	+	0.998385i	$0.481910\pi$
$402$	−2.72508	−0.135915
$403$	0	0
$404$	1.72508	0.0858261
$405$	−4.27492	−0.212422
$406$	8.27492	0.410677
$407$	−1.09967	−0.0545086
$408$	−3.00000	−0.148522
$409$	29.9244	1.47967	0.739834	−	0.672790i	$-0.234904\pi$
$409$	29.9244	1.47967	0.739834	+	0.672790i	$0.234904\pi$
$410$	−35.3746	−1.74703
$411$	−22.8248	−1.12586
$412$	5.27492	0.259877
$413$	−11.8248	−0.581858
$414$	5.27492	0.259248
$415$	−50.5498	−2.48139
$416$	0	0
$417$	−9.09967	−0.445613
$418$	26.1993	1.28145
$419$	−22.3746	−1.09307	−0.546535	−	0.837436i	$-0.684053\pi$
$419$	−22.3746	−1.09307	−0.546535	+	0.837436i	$0.684053\pi$
$420$	4.27492	0.208595
$421$	−8.27492	−0.403295	−0.201647	−	0.979458i	$-0.564630\pi$
$421$	−8.27492	−0.403295	−0.201647	+	0.979458i	$0.564630\pi$
$422$	−21.0997	−1.02712
$423$	6.54983	0.318464
$424$	3.54983	0.172395
$425$	39.8248	1.93178
$426$	5.27492	0.255571
$427$	9.00000	0.435541
$428$	2.54983	0.123251
$429$	0	0
$430$	−50.5498	−2.43773
$431$	13.2749	0.639430	0.319715	−	0.947514i	$-0.396413\pi$
$431$	13.2749	0.639430	0.319715	+	0.947514i	$0.396413\pi$
$432$	1.00000	0.0481125
$433$	−10.2749	−0.493781	−0.246891	−	0.969043i	$-0.579409\pi$
$433$	−10.2749	−0.493781	−0.246891	+	0.969043i	$0.579409\pi$
$434$	1.27492	0.0611980
$435$	−35.3746	−1.69608
$436$	4.54983	0.217898
$437$	34.5498	1.65274
$438$	5.72508	0.273555
$439$	13.0997	0.625213	0.312607	−	0.949883i	$-0.398798\pi$
$439$	13.0997	0.625213	0.312607	+	0.949883i	$0.398798\pi$
$440$	17.0997	0.815195
$441$	1.00000	0.0476190
$442$	0	0
$443$	34.5498	1.64151	0.820756	−	0.571279i	$-0.193552\pi$
$443$	34.5498	1.64151	0.820756	+	0.571279i	$0.193552\pi$
$444$	−0.274917	−0.0130470
$445$	3.09967	0.146938
$446$	10.7251	0.507847
$447$	1.00000	0.0472984
$448$	−1.00000	−0.0472456
$449$	19.0997	0.901369	0.450685	−	0.892683i	$-0.351180\pi$
$449$	19.0997	0.901369	0.450685	+	0.892683i	$0.351180\pi$
$450$	−13.2749	−0.625786
$451$	−33.0997	−1.55860
$452$	14.8248	0.697298
$453$	−13.0997	−0.615476
$454$	−21.0997	−0.990257
$455$	0	0
$456$	6.54983	0.306724
$457$	17.0000	0.795226	0.397613	−	0.917553i	$-0.369839\pi$
$457$	17.0000	0.795226	0.397613	+	0.917553i	$0.369839\pi$
$458$	12.7251	0.594604
$459$	3.00000	0.140028
$460$	22.5498	1.05139
$461$	19.3746	0.902364	0.451182	−	0.892432i	$-0.351002\pi$
$461$	19.3746	0.902364	0.451182	+	0.892432i	$0.351002\pi$
$462$	4.00000	0.186097
$463$	10.5498	0.490292	0.245146	−	0.969486i	$-0.421164\pi$
$463$	10.5498	0.490292	0.245146	+	0.969486i	$0.421164\pi$
$464$	8.27492	0.384153
$465$	−5.45017	−0.252745
$466$	−7.45017	−0.345122
$467$	−8.17525	−0.378305	−0.189153	−	0.981948i	$-0.560574\pi$
$467$	−8.17525	−0.378305	−0.189153	+	0.981948i	$0.560574\pi$
$468$	0	0
$469$	−2.72508	−0.125833
$470$	28.0000	1.29154
$471$	−3.72508	−0.171643
$472$	−11.8248	−0.544278
$473$	−47.2990	−2.17481
$474$	8.00000	0.367452
$475$	−86.9485	−3.98947
$476$	−3.00000	−0.137505
$477$	−3.54983	−0.162536
$478$	−5.27492	−0.241269
$479$	−20.0000	−0.913823	−0.456912	−	0.889512i	$-0.651044\pi$
$479$	−20.0000	−0.913823	−0.456912	+	0.889512i	$0.651044\pi$
$480$	4.27492	0.195122
$481$	0	0
$482$	−15.7251	−0.716258
$483$	5.27492	0.240017
$484$	5.00000	0.227273
$485$	−2.35050	−0.106731
$486$	−1.00000	−0.0453609
$487$	1.09967	0.0498308	0.0249154	−	0.999690i	$-0.492068\pi$
$487$	1.09967	0.0498308	0.0249154	+	0.999690i	$0.492068\pi$
$488$	9.00000	0.407411
$489$	13.2749	0.600313
$490$	4.27492	0.193121
$491$	25.0997	1.13273	0.566366	−	0.824154i	$-0.308349\pi$
$491$	25.0997	1.13273	0.566366	+	0.824154i	$0.308349\pi$
$492$	−8.27492	−0.373062
$493$	24.8248	1.11805
$494$	0	0
$495$	−17.0997	−0.768573
$496$	1.27492	0.0572455
$497$	5.27492	0.236612
$498$	−11.8248	−0.529880
$499$	31.8248	1.42467	0.712336	−	0.701839i	$-0.247637\pi$
$499$	31.8248	1.42467	0.712336	+	0.701839i	$0.247637\pi$
$500$	−35.3746	−1.58200
$501$	0	0
$502$	−13.2749	−0.592489
$503$	−21.0997	−0.940788	−0.470394	−	0.882457i	$-0.655888\pi$
$503$	−21.0997	−0.940788	−0.470394	+	0.882457i	$0.655888\pi$
$504$	1.00000	0.0445435
$505$	−7.37459	−0.328165
$506$	21.0997	0.937995
$507$	0	0
$508$	8.00000	0.354943
$509$	13.1752	0.583983	0.291991	−	0.956421i	$-0.405682\pi$
$509$	13.1752	0.583983	0.291991	+	0.956421i	$0.405682\pi$
$510$	12.8248	0.567890
$511$	5.72508	0.253263
$512$	−1.00000	−0.0441942
$513$	−6.54983	−0.289182
$514$	−15.0000	−0.661622
$515$	−22.5498	−0.993664
$516$	−11.8248	−0.520556
$517$	26.1993	1.15225
$518$	−0.274917	−0.0120792
$519$	−4.54983	−0.199716
$520$	0	0
$521$	−20.8248	−0.912349	−0.456174	−	0.889890i	$-0.650781\pi$
$521$	−20.8248	−0.912349	−0.456174	+	0.889890i	$0.650781\pi$
$522$	−8.27492	−0.362183
$523$	−26.1993	−1.14562	−0.572809	−	0.819689i	$-0.694146\pi$
$523$	−26.1993	−1.14562	−0.572809	+	0.819689i	$0.694146\pi$
$524$	−2.72508	−0.119046
$525$	−13.2749	−0.579365
$526$	−21.0997	−0.919989
$527$	3.82475	0.166609
$528$	4.00000	0.174078
$529$	4.82475	0.209772
$530$	−15.1752	−0.659171
$531$	11.8248	0.513151
$532$	6.54983	0.283971
$533$	0	0
$534$	0.725083	0.0313774
$535$	−10.9003	−0.471262
$536$	−2.72508	−0.117706
$537$	1.45017	0.0625793
$538$	18.0000	0.776035
$539$	4.00000	0.172292
$540$	−4.27492	−0.183963
$541$	−25.3746	−1.09094	−0.545469	−	0.838131i	$-0.683649\pi$
$541$	−25.3746	−1.09094	−0.545469	+	0.838131i	$0.683649\pi$
$542$	25.2749	1.08565
$543$	−16.8248	−0.722019
$544$	−3.00000	−0.128624
$545$	−19.4502	−0.833154
$546$	0	0
$547$	2.90033	0.124009	0.0620046	−	0.998076i	$-0.480251\pi$
$547$	2.90033	0.124009	0.0620046	+	0.998076i	$0.480251\pi$
$548$	−22.8248	−0.975025
$549$	−9.00000	−0.384111
$550$	−53.0997	−2.26418
$551$	−54.1993	−2.30897
$552$	5.27492	0.224515
$553$	8.00000	0.340195
$554$	−14.8248	−0.629843
$555$	1.17525	0.0498865
$556$	−9.09967	−0.385912
$557$	35.1993	1.49144	0.745722	−	0.666257i	$-0.232105\pi$
$557$	35.1993	1.49144	0.745722	+	0.666257i	$0.232105\pi$
$558$	−1.27492	−0.0539715
$559$	0	0
$560$	4.27492	0.180648
$561$	12.0000	0.506640
$562$	−20.8248	−0.878439
$563$	24.0000	1.01148	0.505740	−	0.862686i	$-0.331220\pi$
$563$	24.0000	1.01148	0.505740	+	0.862686i	$0.331220\pi$
$564$	6.54983	0.275798
$565$	−63.3746	−2.66619
$566$	9.45017	0.397220
$567$	−1.00000	−0.0419961
$568$	5.27492	0.221331
$569$	4.90033	0.205433	0.102716	−	0.994711i	$-0.467247\pi$
$569$	4.90033	0.205433	0.102716	+	0.994711i	$0.467247\pi$
$570$	−28.0000	−1.17279
$571$	−14.7251	−0.616226	−0.308113	−	0.951350i	$-0.599697\pi$
$571$	−14.7251	−0.616226	−0.308113	+	0.951350i	$0.599697\pi$
$572$	0	0
$573$	6.72508	0.280944
$574$	−8.27492	−0.345388
$575$	−70.0241	−2.92021
$576$	1.00000	0.0416667
$577$	−9.37459	−0.390269	−0.195135	−	0.980776i	$-0.562514\pi$
$577$	−9.37459	−0.390269	−0.195135	+	0.980776i	$0.562514\pi$
$578$	8.00000	0.332756
$579$	24.8248	1.03168
$580$	−35.3746	−1.46885
$581$	−11.8248	−0.490573
$582$	−0.549834	−0.0227914
$583$	−14.1993	−0.588076
$584$	5.72508	0.236906
$585$	0	0
$586$	−18.2749	−0.754930
$587$	−8.92442	−0.368350	−0.184175	−	0.982893i	$-0.558961\pi$
$587$	−8.92442	−0.368350	−0.184175	+	0.982893i	$0.558961\pi$
$588$	1.00000	0.0412393
$589$	−8.35050	−0.344076
$590$	50.5498	2.08110
$591$	21.8248	0.897750
$592$	−0.274917	−0.0112990
$593$	−4.45017	−0.182746	−0.0913732	−	0.995817i	$-0.529126\pi$
$593$	−4.45017	−0.182746	−0.0913732	+	0.995817i	$0.529126\pi$
$594$	−4.00000	−0.164122
$595$	12.8248	0.525764
$596$	1.00000	0.0409616
$597$	11.8248	0.483955
$598$	0	0
$599$	−10.7251	−0.438215	−0.219108	−	0.975701i	$-0.570315\pi$
$599$	−10.7251	−0.438215	−0.219108	+	0.975701i	$0.570315\pi$
$600$	−13.2749	−0.541946
$601$	−7.72508	−0.315113	−0.157556	−	0.987510i	$-0.550362\pi$
$601$	−7.72508	−0.315113	−0.157556	+	0.987510i	$0.550362\pi$
$602$	−11.8248	−0.481941
$603$	2.72508	0.110974
$604$	−13.0997	−0.533018
$605$	−21.3746	−0.869000
$606$	−1.72508	−0.0700767
$607$	14.7251	0.597673	0.298836	−	0.954304i	$-0.403402\pi$
$607$	14.7251	0.597673	0.298836	+	0.954304i	$0.403402\pi$
$608$	6.54983	0.265631
$609$	−8.27492	−0.335317
$610$	−38.4743	−1.55778
$611$	0	0
$612$	3.00000	0.121268
$613$	−29.3746	−1.18643	−0.593214	−	0.805045i	$-0.702141\pi$
$613$	−29.3746	−1.18643	−0.593214	+	0.805045i	$0.702141\pi$
$614$	−1.45017	−0.0585239
$615$	35.3746	1.42644
$616$	4.00000	0.161165
$617$	−39.9244	−1.60730	−0.803648	−	0.595105i	$-0.797111\pi$
$617$	−39.9244	−1.60730	−0.803648	+	0.595105i	$0.797111\pi$
$618$	−5.27492	−0.212188
$619$	15.6495	0.629007	0.314503	−	0.949256i	$-0.398162\pi$
$619$	15.6495	0.629007	0.314503	+	0.949256i	$0.398162\pi$
$620$	−5.45017	−0.218884
$621$	−5.27492	−0.211675
$622$	2.54983	0.102239
$623$	0.725083	0.0290498
$624$	0	0
$625$	84.8488	3.39395
$626$	−17.6495	−0.705416
$627$	−26.1993	−1.04630
$628$	−3.72508	−0.148647
$629$	−0.824752	−0.0328850
$630$	−4.27492	−0.170317
$631$	29.0997	1.15844	0.579220	−	0.815171i	$-0.303357\pi$
$631$	29.0997	1.15844	0.579220	+	0.815171i	$0.303357\pi$
$632$	8.00000	0.318223
$633$	21.0997	0.838637
$634$	−7.54983	−0.299842
$635$	−34.1993	−1.35716
$636$	−3.54983	−0.140760
$637$	0	0
$638$	−33.0997	−1.31043
$639$	−5.27492	−0.208673
$640$	4.27492	0.168981
$641$	18.8248	0.743533	0.371766	−	0.928326i	$-0.378752\pi$
$641$	18.8248	0.743533	0.371766	+	0.928326i	$0.378752\pi$
$642$	−2.54983	−0.100634
$643$	32.7492	1.29150	0.645751	−	0.763548i	$-0.276545\pi$
$643$	32.7492	1.29150	0.645751	+	0.763548i	$0.276545\pi$
$644$	5.27492	0.207861
$645$	50.5498	1.99040
$646$	19.6495	0.773099
$647$	9.45017	0.371524	0.185762	−	0.982595i	$-0.440525\pi$
$647$	9.45017	0.371524	0.185762	+	0.982595i	$0.440525\pi$
$648$	−1.00000	−0.0392837
$649$	47.2990	1.85665
$650$	0	0
$651$	−1.27492	−0.0499679
$652$	13.2749	0.519886
$653$	33.4743	1.30995	0.654974	−	0.755651i	$-0.272679\pi$
$653$	33.4743	1.30995	0.654974	+	0.755651i	$0.272679\pi$
$654$	−4.54983	−0.177913
$655$	11.6495	0.455184
$656$	−8.27492	−0.323081
$657$	−5.72508	−0.223357
$658$	6.54983	0.255339
$659$	−13.4502	−0.523944	−0.261972	−	0.965075i	$-0.584373\pi$
$659$	−13.4502	−0.523944	−0.261972	+	0.965075i	$0.584373\pi$
$660$	−17.0997	−0.665604
$661$	−9.90033	−0.385078	−0.192539	−	0.981289i	$-0.561672\pi$
$661$	−9.90033	−0.385078	−0.192539	+	0.981289i	$0.561672\pi$
$662$	4.00000	0.155464
$663$	0	0
$664$	−11.8248	−0.458889
$665$	−28.0000	−1.08579
$666$	0.274917	0.0106528
$667$	−43.6495	−1.69012
$668$	0	0
$669$	−10.7251	−0.414656
$670$	11.6495	0.450060
$671$	−36.0000	−1.38976
$672$	1.00000	0.0385758
$673$	−18.0997	−0.697691	−0.348845	−	0.937180i	$-0.613426\pi$
$673$	−18.0997	−0.697691	−0.348845	+	0.937180i	$0.613426\pi$
$674$	−0.274917	−0.0105894
$675$	13.2749	0.510952
$676$	0	0
$677$	−33.6495	−1.29326	−0.646628	−	0.762806i	$-0.723821\pi$
$677$	−33.6495	−1.29326	−0.646628	+	0.762806i	$0.723821\pi$
$678$	−14.8248	−0.569341
$679$	−0.549834	−0.0211007
$680$	12.8248	0.491807
$681$	21.0997	0.808541
$682$	−5.09967	−0.195276
$683$	4.35050	0.166467	0.0832336	−	0.996530i	$-0.473475\pi$
$683$	4.35050	0.166467	0.0832336	+	0.996530i	$0.473475\pi$
$684$	−6.54983	−0.250439
$685$	97.5739	3.72811
$686$	1.00000	0.0381802
$687$	−12.7251	−0.485492
$688$	−11.8248	−0.450814
$689$	0	0
$690$	−22.5498	−0.858458
$691$	−8.00000	−0.304334	−0.152167	−	0.988355i	$-0.548625\pi$
$691$	−8.00000	−0.304334	−0.152167	+	0.988355i	$0.548625\pi$
$692$	−4.54983	−0.172959
$693$	−4.00000	−0.151947
$694$	−30.5498	−1.15966
$695$	38.9003	1.47557
$696$	−8.27492	−0.313660
$697$	−24.8248	−0.940305
$698$	−34.9244	−1.32191
$699$	7.45017	0.281791
$700$	−13.2749	−0.501745
$701$	14.9244	0.563688	0.281844	−	0.959460i	$-0.409054\pi$
$701$	14.9244	0.563688	0.281844	+	0.959460i	$0.409054\pi$
$702$	0	0
$703$	1.80066	0.0679133
$704$	4.00000	0.150756
$705$	−28.0000	−1.05454
$706$	−19.5498	−0.735768
$707$	−1.72508	−0.0648784
$708$	11.8248	0.444401
$709$	47.3746	1.77919	0.889595	−	0.456750i	$-0.150987\pi$
$709$	47.3746	1.77919	0.889595	+	0.456750i	$0.150987\pi$
$710$	−22.5498	−0.846280
$711$	−8.00000	−0.300023
$712$	0.725083	0.0271736
$713$	−6.72508	−0.251856
$714$	3.00000	0.112272
$715$	0	0
$716$	1.45017	0.0541952
$717$	5.27492	0.196995
$718$	−1.09967	−0.0410393
$719$	−8.00000	−0.298350	−0.149175	−	0.988811i	$-0.547662\pi$
$719$	−8.00000	−0.298350	−0.149175	+	0.988811i	$0.547662\pi$
$720$	−4.27492	−0.159317
$721$	−5.27492	−0.196448
$722$	−23.9003	−0.889478
$723$	15.7251	0.584822
$724$	−16.8248	−0.625287
$725$	109.849	4.07968
$726$	−5.00000	−0.185567
$727$	19.8248	0.735259	0.367630	−	0.929972i	$-0.380169\pi$
$727$	19.8248	0.735259	0.367630	+	0.929972i	$0.380169\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−24.4743	−0.905833
$731$	−35.4743	−1.31206
$732$	−9.00000	−0.332650
$733$	32.6495	1.20594	0.602968	−	0.797765i	$-0.293984\pi$
$733$	32.6495	1.20594	0.602968	+	0.797765i	$0.293984\pi$
$734$	−13.2749	−0.489986
$735$	−4.27492	−0.157683
$736$	5.27492	0.194436
$737$	10.9003	0.401519
$738$	8.27492	0.304604
$739$	49.2749	1.81261	0.906304	−	0.422627i	$-0.138892\pi$
$739$	49.2749	1.81261	0.906304	+	0.422627i	$0.138892\pi$
$740$	1.17525	0.0432030
$741$	0	0
$742$	−3.54983	−0.130319
$743$	4.17525	0.153175	0.0765875	−	0.997063i	$-0.475598\pi$
$743$	4.17525	0.153175	0.0765875	+	0.997063i	$0.475598\pi$
$744$	−1.27492	−0.0467407
$745$	−4.27492	−0.156621
$746$	−26.8248	−0.982124
$747$	11.8248	0.432645
$748$	12.0000	0.438763
$749$	−2.54983	−0.0931689
$750$	35.3746	1.29170
$751$	−18.5498	−0.676893	−0.338447	−	0.940986i	$-0.609901\pi$
$751$	−18.5498	−0.676893	−0.338447	+	0.940986i	$0.609901\pi$
$752$	6.54983	0.238848
$753$	13.2749	0.483765
$754$	0	0
$755$	56.0000	2.03805
$756$	−1.00000	−0.0363696
$757$	−26.0000	−0.944986	−0.472493	−	0.881334i	$-0.656646\pi$
$757$	−26.0000	−0.944986	−0.472493	+	0.881334i	$0.656646\pi$
$758$	−20.0000	−0.726433
$759$	−21.0997	−0.765869
$760$	−28.0000	−1.01567
$761$	−20.1993	−0.732225	−0.366113	−	0.930571i	$-0.619312\pi$
$761$	−20.1993	−0.732225	−0.366113	+	0.930571i	$0.619312\pi$
$762$	−8.00000	−0.289809
$763$	−4.54983	−0.164715
$764$	6.72508	0.243305
$765$	−12.8248	−0.463680
$766$	22.1993	0.802095
$767$	0	0
$768$	1.00000	0.0360844
$769$	−41.6495	−1.50192	−0.750960	−	0.660348i	$-0.770409\pi$
$769$	−41.6495	−1.50192	−0.750960	+	0.660348i	$0.770409\pi$
$770$	−17.0997	−0.616229
$771$	15.0000	0.540212
$772$	24.8248	0.893462
$773$	20.9003	0.751733	0.375866	−	0.926674i	$-0.377345\pi$
$773$	20.9003	0.751733	0.375866	+	0.926674i	$0.377345\pi$
$774$	11.8248	0.425032
$775$	16.9244	0.607943
$776$	−0.549834	−0.0197379
$777$	0.274917	0.00986260
$778$	24.6495	0.883728
$779$	54.1993	1.94189
$780$	0	0
$781$	−21.0997	−0.755006
$782$	15.8248	0.565892
$783$	8.27492	0.295721
$784$	1.00000	0.0357143
$785$	15.9244	0.568367
$786$	2.72508	0.0972005
$787$	−21.0997	−0.752122	−0.376061	−	0.926595i	$-0.622722\pi$
$787$	−21.0997	−0.752122	−0.376061	+	0.926595i	$0.622722\pi$
$788$	21.8248	0.777475
$789$	21.0997	0.751168
$790$	−34.1993	−1.21676
$791$	−14.8248	−0.527107
$792$	−4.00000	−0.142134
$793$	0	0
$794$	23.2749	0.825996
$795$	15.1752	0.538211
$796$	11.8248	0.419117
$797$	16.5498	0.586225	0.293113	−	0.956078i	$-0.405309\pi$
$797$	16.5498	0.586225	0.293113	+	0.956078i	$0.405309\pi$
$798$	−6.54983	−0.231862
$799$	19.6495	0.695149
$800$	−13.2749	−0.469339
$801$	−0.725083	−0.0256195
$802$	−2.27492	−0.0803301
$803$	−22.9003	−0.808135
$804$	2.72508	0.0961063
$805$	−22.5498	−0.794777
$806$	0	0
$807$	−18.0000	−0.633630
$808$	−1.72508	−0.0606882
$809$	9.72508	0.341916	0.170958	−	0.985278i	$-0.445314\pi$
$809$	9.72508	0.341916	0.170958	+	0.985278i	$0.445314\pi$
$810$	4.27492	0.150205
$811$	−5.09967	−0.179074	−0.0895368	−	0.995984i	$-0.528539\pi$
$811$	−5.09967	−0.179074	−0.0895368	+	0.995984i	$0.528539\pi$
$812$	−8.27492	−0.290393
$813$	−25.2749	−0.886430
$814$	1.09967	0.0385434
$815$	−56.7492	−1.98784
$816$	3.00000	0.105021
$817$	77.4502	2.70964
$818$	−29.9244	−1.04628
$819$	0	0
$820$	35.3746	1.23533
$821$	−15.2749	−0.533098	−0.266549	−	0.963821i	$-0.585883\pi$
$821$	−15.2749	−0.533098	−0.266549	+	0.963821i	$0.585883\pi$
$822$	22.8248	0.796105
$823$	−6.90033	−0.240530	−0.120265	−	0.992742i	$-0.538374\pi$
$823$	−6.90033	−0.240530	−0.120265	+	0.992742i	$0.538374\pi$
$824$	−5.27492	−0.183760
$825$	53.0997	1.84869
$826$	11.8248	0.411436
$827$	−5.09967	−0.177333	−0.0886664	−	0.996061i	$-0.528261\pi$
$827$	−5.09967	−0.177333	−0.0886664	+	0.996061i	$0.528261\pi$
$828$	−5.27492	−0.183316
$829$	−44.8248	−1.55683	−0.778414	−	0.627751i	$-0.783976\pi$
$829$	−44.8248	−1.55683	−0.778414	+	0.627751i	$0.783976\pi$
$830$	50.5498	1.75461
$831$	14.8248	0.514265
$832$	0	0
$833$	3.00000	0.103944
$834$	9.09967	0.315096
$835$	0	0
$836$	−26.1993	−0.906123
$837$	1.27492	0.0440676
$838$	22.3746	0.772917
$839$	20.7492	0.716341	0.358170	−	0.933656i	$-0.383401\pi$
$839$	20.7492	0.716341	0.358170	+	0.933656i	$0.383401\pi$
$840$	−4.27492	−0.147499
$841$	39.4743	1.36118
$842$	8.27492	0.285172
$843$	20.8248	0.717243
$844$	21.0997	0.726281
$845$	0	0
$846$	−6.54983	−0.225188
$847$	−5.00000	−0.171802
$848$	−3.54983	−0.121902
$849$	−9.45017	−0.324329
$850$	−39.8248	−1.36598
$851$	1.45017	0.0497110
$852$	−5.27492	−0.180716
$853$	14.4502	0.494764	0.247382	−	0.968918i	$-0.420430\pi$
$853$	14.4502	0.494764	0.247382	+	0.968918i	$0.420430\pi$
$854$	−9.00000	−0.307974
$855$	28.0000	0.957580
$856$	−2.54983	−0.0871515
$857$	−36.8248	−1.25791	−0.628955	−	0.777442i	$-0.716517\pi$
$857$	−36.8248	−1.25791	−0.628955	+	0.777442i	$0.716517\pi$
$858$	0	0
$859$	−27.6495	−0.943389	−0.471694	−	0.881762i	$-0.656357\pi$
$859$	−27.6495	−0.943389	−0.471694	+	0.881762i	$0.656357\pi$
$860$	50.5498	1.72374
$861$	8.27492	0.282008
$862$	−13.2749	−0.452145
$863$	−35.2990	−1.20159	−0.600796	−	0.799402i	$-0.705150\pi$
$863$	−35.2990	−1.20159	−0.600796	+	0.799402i	$0.705150\pi$
$864$	−1.00000	−0.0340207
$865$	19.4502	0.661325
$866$	10.2749	0.349156
$867$	−8.00000	−0.271694
$868$	−1.27492	−0.0432735
$869$	−32.0000	−1.08553
$870$	35.3746	1.19931
$871$	0	0
$872$	−4.54983	−0.154077
$873$	0.549834	0.0186091
$874$	−34.5498	−1.16867
$875$	35.3746	1.19588
$876$	−5.72508	−0.193433
$877$	3.72508	0.125787	0.0628936	−	0.998020i	$-0.479967\pi$
$877$	3.72508	0.125787	0.0628936	+	0.998020i	$0.479967\pi$
$878$	−13.0997	−0.442092
$879$	18.2749	0.616398
$880$	−17.0997	−0.576430
$881$	1.54983	0.0522152	0.0261076	−	0.999659i	$-0.491689\pi$
$881$	1.54983	0.0522152	0.0261076	+	0.999659i	$0.491689\pi$
$882$	−1.00000	−0.0336718
$883$	58.0241	1.95267	0.976333	−	0.216273i	$-0.0693900\pi$
$883$	58.0241	1.95267	0.976333	+	0.216273i	$0.0693900\pi$
$884$	0	0
$885$	−50.5498	−1.69921
$886$	−34.5498	−1.16072
$887$	46.5498	1.56299	0.781495	−	0.623911i	$-0.214457\pi$
$887$	46.5498	1.56299	0.781495	+	0.623911i	$0.214457\pi$
$888$	0.274917	0.00922562
$889$	−8.00000	−0.268311
$890$	−3.09967	−0.103901
$891$	4.00000	0.134005
$892$	−10.7251	−0.359102
$893$	−42.9003	−1.43560
$894$	−1.00000	−0.0334450
$895$	−6.19934	−0.207221
$896$	1.00000	0.0334077
$897$	0	0
$898$	−19.0997	−0.637364
$899$	10.5498	0.351857
$900$	13.2749	0.442497
$901$	−10.6495	−0.354786
$902$	33.0997	1.10210
$903$	11.8248	0.393503
$904$	−14.8248	−0.493064
$905$	71.9244	2.39085
$906$	13.0997	0.435207
$907$	−39.8248	−1.32236	−0.661180	−	0.750228i	$-0.729944\pi$
$907$	−39.8248	−1.32236	−0.661180	+	0.750228i	$0.729944\pi$
$908$	21.0997	0.700217
$909$	1.72508	0.0572174
$910$	0	0
$911$	−25.0997	−0.831589	−0.415795	−	0.909459i	$-0.636496\pi$
$911$	−25.0997	−0.831589	−0.415795	+	0.909459i	$0.636496\pi$
$912$	−6.54983	−0.216887
$913$	47.2990	1.56537
$914$	−17.0000	−0.562310
$915$	38.4743	1.27192
$916$	−12.7251	−0.420449
$917$	2.72508	0.0899902
$918$	−3.00000	−0.0990148
$919$	39.6495	1.30792	0.653958	−	0.756531i	$-0.273107\pi$
$919$	39.6495	1.30792	0.653958	+	0.756531i	$0.273107\pi$
$920$	−22.5498	−0.743446
$921$	1.45017	0.0477846
$922$	−19.3746	−0.638068
$923$	0	0
$924$	−4.00000	−0.131590
$925$	−3.64950	−0.119995
$926$	−10.5498	−0.346689
$927$	5.27492	0.173251
$928$	−8.27492	−0.271637
$929$	−53.5498	−1.75691	−0.878457	−	0.477822i	$-0.841426\pi$
$929$	−53.5498	−1.75691	−0.878457	+	0.477822i	$0.841426\pi$
$930$	5.45017	0.178718
$931$	−6.54983	−0.214662
$932$	7.45017	0.244038
$933$	−2.54983	−0.0834778
$934$	8.17525	0.267502
$935$	−51.2990	−1.67766
$936$	0	0
$937$	19.1752	0.626428	0.313214	−	0.949683i	$-0.398594\pi$
$937$	19.1752	0.626428	0.313214	+	0.949683i	$0.398594\pi$
$938$	2.72508	0.0889771
$939$	17.6495	0.575970
$940$	−28.0000	−0.913259
$941$	−37.6495	−1.22734	−0.613669	−	0.789563i	$-0.710307\pi$
$941$	−37.6495	−1.22734	−0.613669	+	0.789563i	$0.710307\pi$
$942$	3.72508	0.121370
$943$	43.6495	1.42142
$944$	11.8248	0.384863
$945$	4.27492	0.139063
$946$	47.2990	1.53782
$947$	9.09967	0.295700	0.147850	−	0.989010i	$-0.452765\pi$
$947$	9.09967	0.295700	0.147850	+	0.989010i	$0.452765\pi$
$948$	−8.00000	−0.259828
$949$	0	0
$950$	86.9485	2.82098
$951$	7.54983	0.244820
$952$	3.00000	0.0972306
$953$	−11.0997	−0.359554	−0.179777	−	0.983707i	$-0.557538\pi$
$953$	−11.0997	−0.359554	−0.179777	+	0.983707i	$0.557538\pi$
$954$	3.54983	0.114930
$955$	−28.7492	−0.930301
$956$	5.27492	0.170603
$957$	33.0997	1.06996
$958$	20.0000	0.646171
$959$	22.8248	0.737050
$960$	−4.27492	−0.137972
$961$	−29.3746	−0.947567
$962$	0	0
$963$	2.54983	0.0821673
$964$	15.7251	0.506471
$965$	−106.124	−3.41624
$966$	−5.27492	−0.169718
$967$	18.5498	0.596522	0.298261	−	0.954484i	$-0.403593\pi$
$967$	18.5498	0.596522	0.298261	+	0.954484i	$0.403593\pi$
$968$	−5.00000	−0.160706
$969$	−19.6495	−0.631233
$970$	2.35050	0.0754699
$971$	48.5739	1.55881	0.779406	−	0.626520i	$-0.215521\pi$
$971$	48.5739	1.55881	0.779406	+	0.626520i	$0.215521\pi$
$972$	1.00000	0.0320750
$973$	9.09967	0.291722
$974$	−1.09967	−0.0352357
$975$	0	0
$976$	−9.00000	−0.288083
$977$	−24.6254	−0.787837	−0.393918	−	0.919145i	$-0.628881\pi$
$977$	−24.6254	−0.787837	−0.393918	+	0.919145i	$0.628881\pi$
$978$	−13.2749	−0.424485
$979$	−2.90033	−0.0926950
$980$	−4.27492	−0.136557
$981$	4.54983	0.145265
$982$	−25.0997	−0.800963
$983$	−53.8488	−1.71751	−0.858756	−	0.512385i	$-0.828762\pi$
$983$	−53.8488	−1.71751	−0.858756	+	0.512385i	$0.828762\pi$
$984$	8.27492	0.263795
$985$	−93.2990	−2.97275
$986$	−24.8248	−0.790581
$987$	−6.54983	−0.208484
$988$	0	0
$989$	62.3746	1.98340
$990$	17.0997	0.543463
$991$	−36.7492	−1.16738	−0.583688	−	0.811978i	$-0.698391\pi$
$991$	−36.7492	−1.16738	−0.583688	+	0.811978i	$0.698391\pi$
$992$	−1.27492	−0.0404787
$993$	−4.00000	−0.126936
$994$	−5.27492	−0.167310
$995$	−50.5498	−1.60254
$996$	11.8248	0.374682
$997$	−3.90033	−0.123525	−0.0617624	−	0.998091i	$-0.519672\pi$
$997$	−3.90033	−0.123525	−0.0617624	+	0.998091i	$0.519672\pi$
$998$	−31.8248	−1.00739
$999$	−0.274917	−0.00869800

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.bm.1.1		2
13.4	even	6		546.2.l.j.211.2	✓	4
13.10	even	6		546.2.l.j.295.2	yes	4
13.12	even	2		7098.2.a.ca.1.2		2
39.17	odd	6		1638.2.r.x.757.1		4
39.23	odd	6		1638.2.r.x.1387.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.j.211.2	✓	4	13.4	even	6
546.2.l.j.295.2	yes	4	13.10	even	6
1638.2.r.x.757.1		4	39.17	odd	6
1638.2.r.x.1387.1		4	39.23	odd	6
7098.2.a.bm.1.1		2	1.1	even	1	trivial
7098.2.a.ca.1.2		2	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7098 = 2 \cdot 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7098.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.27492 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -4.27492 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +4.27492 q^{10} +4.00000 q^{11} +1.00000 q^{12} +1.00000 q^{14} -4.27492 q^{15} +1.00000 q^{16} +3.00000 q^{17} -1.00000 q^{18} -6.54983 q^{19} -4.27492 q^{20} -1.00000 q^{21} -4.00000 q^{22} -5.27492 q^{23} -1.00000 q^{24} +13.2749 q^{25} +1.00000 q^{27} -1.00000 q^{28} +8.27492 q^{29} +4.27492 q^{30} +1.27492 q^{31} -1.00000 q^{32} +4.00000 q^{33} -3.00000 q^{34} +4.27492 q^{35} +1.00000 q^{36} -0.274917 q^{37} +6.54983 q^{38} +4.27492 q^{40} -8.27492 q^{41} +1.00000 q^{42} -11.8248 q^{43} +4.00000 q^{44} -4.27492 q^{45} +5.27492 q^{46} +6.54983 q^{47} +1.00000 q^{48} +1.00000 q^{49} -13.2749 q^{50} +3.00000 q^{51} -3.54983 q^{53} -1.00000 q^{54} -17.0997 q^{55} +1.00000 q^{56} -6.54983 q^{57} -8.27492 q^{58} +11.8248 q^{59} -4.27492 q^{60} -9.00000 q^{61} -1.27492 q^{62} -1.00000 q^{63} +1.00000 q^{64} -4.00000 q^{66} +2.72508 q^{67} +3.00000 q^{68} -5.27492 q^{69} -4.27492 q^{70} -5.27492 q^{71} -1.00000 q^{72} -5.72508 q^{73} +0.274917 q^{74} +13.2749 q^{75} -6.54983 q^{76} -4.00000 q^{77} -8.00000 q^{79} -4.27492 q^{80} +1.00000 q^{81} +8.27492 q^{82} +11.8248 q^{83} -1.00000 q^{84} -12.8248 q^{85} +11.8248 q^{86} +8.27492 q^{87} -4.00000 q^{88} -0.725083 q^{89} +4.27492 q^{90} -5.27492 q^{92} +1.27492 q^{93} -6.54983 q^{94} +28.0000 q^{95} -1.00000 q^{96} +0.549834 q^{97} -1.00000 q^{98} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - q^{5} - 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} + q^{10} + 8 q^{11} + 2 q^{12} + 2 q^{14} - q^{15} + 2 q^{16} + 6 q^{17} - 2 q^{18} + 2 q^{19} - q^{20} - 2 q^{21} - 8 q^{22} - 3 q^{23} - 2 q^{24} + 19 q^{25} + 2 q^{27} - 2 q^{28} + 9 q^{29} + q^{30} - 5 q^{31} - 2 q^{32} + 8 q^{33} - 6 q^{34} + q^{35} + 2 q^{36} + 7 q^{37} - 2 q^{38} + q^{40} - 9 q^{41} + 2 q^{42} - q^{43} + 8 q^{44} - q^{45} + 3 q^{46} - 2 q^{47} + 2 q^{48} + 2 q^{49} - 19 q^{50} + 6 q^{51} + 8 q^{53} - 2 q^{54} - 4 q^{55} + 2 q^{56} + 2 q^{57} - 9 q^{58} + q^{59} - q^{60} - 18 q^{61} + 5 q^{62} - 2 q^{63} + 2 q^{64} - 8 q^{66} + 13 q^{67} + 6 q^{68} - 3 q^{69} - q^{70} - 3 q^{71} - 2 q^{72} - 19 q^{73} - 7 q^{74} + 19 q^{75} + 2 q^{76} - 8 q^{77} - 16 q^{79} - q^{80} + 2 q^{81} + 9 q^{82} + q^{83} - 2 q^{84} - 3 q^{85} + q^{86} + 9 q^{87} - 8 q^{88} - 9 q^{89} + q^{90} - 3 q^{92} - 5 q^{93} + 2 q^{94} + 56 q^{95} - 2 q^{96} - 14 q^{97} - 2 q^{98} + 8 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - q^5 - 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 + q^10 + 8 * q^11 + 2 * q^12 + 2 * q^14 - q^15 + 2 * q^16 + 6 * q^17 - 2 * q^18 + 2 * q^19 - q^20 - 2 * q^21 - 8 * q^22 - 3 * q^23 - 2 * q^24 + 19 * q^25 + 2 * q^27 - 2 * q^28 + 9 * q^29 + q^30 - 5 * q^31 - 2 * q^32 + 8 * q^33 - 6 * q^34 + q^35 + 2 * q^36 + 7 * q^37 - 2 * q^38 + q^40 - 9 * q^41 + 2 * q^42 - q^43 + 8 * q^44 - q^45 + 3 * q^46 - 2 * q^47 + 2 * q^48 + 2 * q^49 - 19 * q^50 + 6 * q^51 + 8 * q^53 - 2 * q^54 - 4 * q^55 + 2 * q^56 + 2 * q^57 - 9 * q^58 + q^59 - q^60 - 18 * q^61 + 5 * q^62 - 2 * q^63 + 2 * q^64 - 8 * q^66 + 13 * q^67 + 6 * q^68 - 3 * q^69 - q^70 - 3 * q^71 - 2 * q^72 - 19 * q^73 - 7 * q^74 + 19 * q^75 + 2 * q^76 - 8 * q^77 - 16 * q^79 - q^80 + 2 * q^81 + 9 * q^82 + q^83 - 2 * q^84 - 3 * q^85 + q^86 + 9 * q^87 - 8 * q^88 - 9 * q^89 + q^90 - 3 * q^92 - 5 * q^93 + 2 * q^94 + 56 * q^95 - 2 * q^96 - 14 * q^97 - 2 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

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Database

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