LMFDB - Embedded newform 7098.2.a.bt.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7098, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("7098.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$56.6778153547$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
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			1.2
Root			$-1.56155$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.56155 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.56155 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.56155 q^{10} -2.56155 q^{11} -1.00000 q^{12} +1.00000 q^{14} -1.56155 q^{15} +1.00000 q^{16} +0.123106 q^{17} +1.00000 q^{18} -2.56155 q^{19} +1.56155 q^{20} -1.00000 q^{21} -2.56155 q^{22} -1.12311 q^{23} -1.00000 q^{24} -2.56155 q^{25} -1.00000 q^{27} +1.00000 q^{28} -6.12311 q^{29} -1.56155 q^{30} +1.00000 q^{32} +2.56155 q^{33} +0.123106 q^{34} +1.56155 q^{35} +1.00000 q^{36} -2.43845 q^{37} -2.56155 q^{38} +1.56155 q^{40} -11.2462 q^{41} -1.00000 q^{42} -8.00000 q^{43} -2.56155 q^{44} +1.56155 q^{45} -1.12311 q^{46} -0.315342 q^{47} -1.00000 q^{48} +1.00000 q^{49} -2.56155 q^{50} -0.123106 q^{51} +7.00000 q^{53} -1.00000 q^{54} -4.00000 q^{55} +1.00000 q^{56} +2.56155 q^{57} -6.12311 q^{58} +5.12311 q^{59} -1.56155 q^{60} -11.2462 q^{61} +1.00000 q^{63} +1.00000 q^{64} +2.56155 q^{66} +9.12311 q^{67} +0.123106 q^{68} +1.12311 q^{69} +1.56155 q^{70} -11.3693 q^{71} +1.00000 q^{72} -2.43845 q^{73} -2.43845 q^{74} +2.56155 q^{75} -2.56155 q^{76} -2.56155 q^{77} -6.56155 q^{79} +1.56155 q^{80} +1.00000 q^{81} -11.2462 q^{82} -5.12311 q^{83} -1.00000 q^{84} +0.192236 q^{85} -8.00000 q^{86} +6.12311 q^{87} -2.56155 q^{88} +3.43845 q^{89} +1.56155 q^{90} -1.12311 q^{92} -0.315342 q^{94} -4.00000 q^{95} -1.00000 q^{96} -0.876894 q^{97} +1.00000 q^{98} -2.56155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - q^{11} - 2 q^{12} + 2 q^{14} + q^{15} + 2 q^{16} - 8 q^{17} + 2 q^{18} - q^{19} - q^{20} - 2 q^{21} - q^{22} + 6 q^{23} - 2 q^{24} - q^{25} - 2 q^{27} + 2 q^{28} - 4 q^{29} + q^{30} + 2 q^{32} + q^{33} - 8 q^{34} - q^{35} + 2 q^{36} - 9 q^{37} - q^{38} - q^{40} - 6 q^{41} - 2 q^{42} - 16 q^{43} - q^{44} - q^{45} + 6 q^{46} - 13 q^{47} - 2 q^{48} + 2 q^{49} - q^{50} + 8 q^{51} + 14 q^{53} - 2 q^{54} - 8 q^{55} + 2 q^{56} + q^{57} - 4 q^{58} + 2 q^{59} + q^{60} - 6 q^{61} + 2 q^{63} + 2 q^{64} + q^{66} + 10 q^{67} - 8 q^{68} - 6 q^{69} - q^{70} + 2 q^{71} + 2 q^{72} - 9 q^{73} - 9 q^{74} + q^{75} - q^{76} - q^{77} - 9 q^{79} - q^{80} + 2 q^{81} - 6 q^{82} - 2 q^{83} - 2 q^{84} + 21 q^{85} - 16 q^{86} + 4 q^{87} - q^{88} + 11 q^{89} - q^{90} + 6 q^{92} - 13 q^{94} - 8 q^{95} - 2 q^{96} - 10 q^{97} + 2 q^{98} - 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 - q^11 - 2 * q^12 + 2 * q^14 + q^15 + 2 * q^16 - 8 * q^17 + 2 * q^18 - q^19 - q^20 - 2 * q^21 - q^22 + 6 * q^23 - 2 * q^24 - q^25 - 2 * q^27 + 2 * q^28 - 4 * q^29 + q^30 + 2 * q^32 + q^33 - 8 * q^34 - q^35 + 2 * q^36 - 9 * q^37 - q^38 - q^40 - 6 * q^41 - 2 * q^42 - 16 * q^43 - q^44 - q^45 + 6 * q^46 - 13 * q^47 - 2 * q^48 + 2 * q^49 - q^50 + 8 * q^51 + 14 * q^53 - 2 * q^54 - 8 * q^55 + 2 * q^56 + q^57 - 4 * q^58 + 2 * q^59 + q^60 - 6 * q^61 + 2 * q^63 + 2 * q^64 + q^66 + 10 * q^67 - 8 * q^68 - 6 * q^69 - q^70 + 2 * q^71 + 2 * q^72 - 9 * q^73 - 9 * q^74 + q^75 - q^76 - q^77 - 9 * q^79 - q^80 + 2 * q^81 - 6 * q^82 - 2 * q^83 - 2 * q^84 + 21 * q^85 - 16 * q^86 + 4 * q^87 - q^88 + 11 * q^89 - q^90 + 6 * q^92 - 13 * q^94 - 8 * q^95 - 2 * q^96 - 10 * 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
$5$	1.56155	0.698348	0.349174	−	0.937058i	$-0.386462\pi$
$5$	1.56155	0.698348	0.349174	+	0.937058i	$0.386462\pi$
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.56155	0.493806
$11$	−2.56155	−0.772337	−0.386169	−	0.922428i	$-0.626202\pi$
$11$	−2.56155	−0.772337	−0.386169	+	0.922428i	$0.626202\pi$
$12$	−1.00000	−0.288675
$13$	0	0
$13$	0	0
$14$	1.00000	0.267261
$15$	−1.56155	−0.403191
$16$	1.00000	0.250000
$17$	0.123106	0.0298575	0.0149287	−	0.999889i	$-0.495248\pi$
$17$	0.123106	0.0298575	0.0149287	+	0.999889i	$0.495248\pi$
$18$	1.00000	0.235702
$19$	−2.56155	−0.587661	−0.293830	−	0.955858i	$-0.594930\pi$
$19$	−2.56155	−0.587661	−0.293830	+	0.955858i	$0.594930\pi$
$20$	1.56155	0.349174
$21$	−1.00000	−0.218218
$22$	−2.56155	−0.546125
$23$	−1.12311	−0.234184	−0.117092	−	0.993121i	$-0.537357\pi$
$23$	−1.12311	−0.234184	−0.117092	+	0.993121i	$0.537357\pi$
$24$	−1.00000	−0.204124
$25$	−2.56155	−0.512311
$26$	0	0
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	−6.12311	−1.13703	−0.568516	−	0.822672i	$-0.692482\pi$
$29$	−6.12311	−1.13703	−0.568516	+	0.822672i	$0.692482\pi$
$30$	−1.56155	−0.285099
$31$	0	0		−	1.00000i	$-0.5\pi$
$31$	0	0			1.00000i	$0.5\pi$
$32$	1.00000	0.176777
$33$	2.56155	0.445909
$34$	0.123106	0.0211124
$35$	1.56155	0.263951
$36$	1.00000	0.166667
$37$	−2.43845	−0.400878	−0.200439	−	0.979706i	$-0.564237\pi$
$37$	−2.43845	−0.400878	−0.200439	+	0.979706i	$0.564237\pi$
$38$	−2.56155	−0.415539
$39$	0	0
$40$	1.56155	0.246903
$41$	−11.2462	−1.75636	−0.878182	−	0.478327i	$-0.841243\pi$
$41$	−11.2462	−1.75636	−0.878182	+	0.478327i	$0.841243\pi$
$42$	−1.00000	−0.154303
$43$	−8.00000	−1.21999	−0.609994	−	0.792406i	$-0.708828\pi$
$43$	−8.00000	−1.21999	−0.609994	+	0.792406i	$0.708828\pi$
$44$	−2.56155	−0.386169
$45$	1.56155	0.232783
$46$	−1.12311	−0.165593
$47$	−0.315342	−0.0459973	−0.0229986	−	0.999735i	$-0.507321\pi$
$47$	−0.315342	−0.0459973	−0.0229986	+	0.999735i	$0.507321\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−2.56155	−0.362258
$51$	−0.123106	−0.0172382
$52$	0	0
$53$	7.00000	0.961524	0.480762	−	0.876851i	$-0.340360\pi$
$53$	7.00000	0.961524	0.480762	+	0.876851i	$0.340360\pi$
$54$	−1.00000	−0.136083
$55$	−4.00000	−0.539360
$56$	1.00000	0.133631
$57$	2.56155	0.339286
$58$	−6.12311	−0.804003
$59$	5.12311	0.666972	0.333486	−	0.942755i	$-0.391775\pi$
$59$	5.12311	0.666972	0.333486	+	0.942755i	$0.391775\pi$
$60$	−1.56155	−0.201596
$61$	−11.2462	−1.43993	−0.719965	−	0.694010i	$-0.755842\pi$
$61$	−11.2462	−1.43993	−0.719965	+	0.694010i	$0.755842\pi$
$62$	0	0
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	2.56155	0.315305
$67$	9.12311	1.11456	0.557282	−	0.830323i	$-0.311844\pi$
$67$	9.12311	1.11456	0.557282	+	0.830323i	$0.311844\pi$
$68$	0.123106	0.0149287
$69$	1.12311	0.135206
$70$	1.56155	0.186641
$71$	−11.3693	−1.34929	−0.674645	−	0.738142i	$-0.735703\pi$
$71$	−11.3693	−1.34929	−0.674645	+	0.738142i	$0.735703\pi$
$72$	1.00000	0.117851
$73$	−2.43845	−0.285399	−0.142699	−	0.989766i	$-0.545578\pi$
$73$	−2.43845	−0.285399	−0.142699	+	0.989766i	$0.545578\pi$
$74$	−2.43845	−0.283464
$75$	2.56155	0.295783
$76$	−2.56155	−0.293830
$77$	−2.56155	−0.291916
$78$	0	0
$79$	−6.56155	−0.738232	−0.369116	−	0.929383i	$-0.620340\pi$
$79$	−6.56155	−0.738232	−0.369116	+	0.929383i	$0.620340\pi$
$80$	1.56155	0.174587
$81$	1.00000	0.111111
$82$	−11.2462	−1.24194
$83$	−5.12311	−0.562334	−0.281167	−	0.959659i	$-0.590721\pi$
$83$	−5.12311	−0.562334	−0.281167	+	0.959659i	$0.590721\pi$
$84$	−1.00000	−0.109109
$85$	0.192236	0.0208509
$86$	−8.00000	−0.862662
$87$	6.12311	0.656466
$88$	−2.56155	−0.273062
$89$	3.43845	0.364475	0.182237	−	0.983255i	$-0.441666\pi$
$89$	3.43845	0.364475	0.182237	+	0.983255i	$0.441666\pi$
$90$	1.56155	0.164602
$91$	0	0
$92$	−1.12311	−0.117092
$93$	0	0
$94$	−0.315342	−0.0325250
$95$	−4.00000	−0.410391
$96$	−1.00000	−0.102062
$97$	−0.876894	−0.0890351	−0.0445176	−	0.999009i	$-0.514175\pi$
$97$	−0.876894	−0.0890351	−0.0445176	+	0.999009i	$0.514175\pi$
$98$	1.00000	0.101015
$99$	−2.56155	−0.257446
$100$	−2.56155	−0.256155
$101$	−5.80776	−0.577894	−0.288947	−	0.957345i	$-0.593305\pi$
$101$	−5.80776	−0.577894	−0.288947	+	0.957345i	$0.593305\pi$
$102$	−0.123106	−0.0121893
$103$	6.24621	0.615457	0.307729	−	0.951474i	$-0.400431\pi$
$103$	6.24621	0.615457	0.307729	+	0.951474i	$0.400431\pi$
$104$	0	0
$105$	−1.56155	−0.152392
$106$	7.00000	0.679900
$107$	13.9309	1.34675	0.673374	−	0.739302i	$-0.264844\pi$
$107$	13.9309	1.34675	0.673374	+	0.739302i	$0.264844\pi$
$108$	−1.00000	−0.0962250
$109$	−12.2462	−1.17297	−0.586487	−	0.809959i	$-0.699490\pi$
$109$	−12.2462	−1.17297	−0.586487	+	0.809959i	$0.699490\pi$
$110$	−4.00000	−0.381385
$111$	2.43845	0.231447
$112$	1.00000	0.0944911
$113$	1.56155	0.146899	0.0734493	−	0.997299i	$-0.476599\pi$
$113$	1.56155	0.146899	0.0734493	+	0.997299i	$0.476599\pi$
$114$	2.56155	0.239911
$115$	−1.75379	−0.163542
$116$	−6.12311	−0.568516
$117$	0	0
$118$	5.12311	0.471620
$119$	0.123106	0.0112851
$120$	−1.56155	−0.142550
$121$	−4.43845	−0.403495
$122$	−11.2462	−1.01818
$123$	11.2462	1.01404
$124$	0	0
$125$	−11.8078	−1.05612
$126$	1.00000	0.0890871
$127$	12.4924	1.10852	0.554262	−	0.832343i	$-0.313001\pi$
$127$	12.4924	1.10852	0.554262	+	0.832343i	$0.313001\pi$
$128$	1.00000	0.0883883
$129$	8.00000	0.704361
$130$	0	0
$131$	14.2462	1.24470	0.622349	−	0.782740i	$-0.286179\pi$
$131$	14.2462	1.24470	0.622349	+	0.782740i	$0.286179\pi$
$132$	2.56155	0.222955
$133$	−2.56155	−0.222115
$134$	9.12311	0.788116
$135$	−1.56155	−0.134397
$136$	0.123106	0.0105562
$137$	12.4384	1.06269	0.531344	−	0.847156i	$-0.321687\pi$
$137$	12.4384	1.06269	0.531344	+	0.847156i	$0.321687\pi$
$138$	1.12311	0.0956051
$139$	−5.43845	−0.461283	−0.230642	−	0.973039i	$-0.574082\pi$
$139$	−5.43845	−0.461283	−0.230642	+	0.973039i	$0.574082\pi$
$140$	1.56155	0.131975
$141$	0.315342	0.0265566
$142$	−11.3693	−0.954092
$143$	0	0
$144$	1.00000	0.0833333
$145$	−9.56155	−0.794044
$146$	−2.43845	−0.201807
$147$	−1.00000	−0.0824786
$148$	−2.43845	−0.200439
$149$	−15.5616	−1.27485	−0.637426	−	0.770512i	$-0.720001\pi$
$149$	−15.5616	−1.27485	−0.637426	+	0.770512i	$0.720001\pi$
$150$	2.56155	0.209150
$151$	−21.9309	−1.78471	−0.892354	−	0.451335i	$-0.850948\pi$
$151$	−21.9309	−1.78471	−0.892354	+	0.451335i	$0.850948\pi$
$152$	−2.56155	−0.207769
$153$	0.123106	0.00995250
$154$	−2.56155	−0.206416
$155$	0	0
$156$	0	0
$157$	−1.31534	−0.104976	−0.0524878	−	0.998622i	$-0.516715\pi$
$157$	−1.31534	−0.104976	−0.0524878	+	0.998622i	$0.516715\pi$
$158$	−6.56155	−0.522009
$159$	−7.00000	−0.555136
$160$	1.56155	0.123452
$161$	−1.12311	−0.0885131
$162$	1.00000	0.0785674
$163$	24.4924	1.91839	0.959197	−	0.282738i	$-0.0912426\pi$
$163$	24.4924	1.91839	0.959197	+	0.282738i	$0.0912426\pi$
$164$	−11.2462	−0.878182
$165$	4.00000	0.311400
$166$	−5.12311	−0.397630
$167$	12.4924	0.966693	0.483346	−	0.875429i	$-0.339421\pi$
$167$	12.4924	0.966693	0.483346	+	0.875429i	$0.339421\pi$
$168$	−1.00000	−0.0771517
$169$	0	0
$170$	0.192236	0.0147438
$171$	−2.56155	−0.195887
$172$	−8.00000	−0.609994
$173$	−18.0000	−1.36851	−0.684257	−	0.729241i	$-0.739873\pi$
$173$	−18.0000	−1.36851	−0.684257	+	0.729241i	$0.739873\pi$
$174$	6.12311	0.464191
$175$	−2.56155	−0.193635
$176$	−2.56155	−0.193084
$177$	−5.12311	−0.385076
$178$	3.43845	0.257723
$179$	−1.75379	−0.131084	−0.0655422	−	0.997850i	$-0.520878\pi$
$179$	−1.75379	−0.131084	−0.0655422	+	0.997850i	$0.520878\pi$
$180$	1.56155	0.116391
$181$	13.2462	0.984583	0.492292	−	0.870430i	$-0.336159\pi$
$181$	13.2462	0.984583	0.492292	+	0.870430i	$0.336159\pi$
$182$	0	0
$183$	11.2462	0.831344
$184$	−1.12311	−0.0827964
$185$	−3.80776	−0.279952
$186$	0	0
$187$	−0.315342	−0.0230601
$188$	−0.315342	−0.0229986
$189$	−1.00000	−0.0727393
$190$	−4.00000	−0.290191
$191$	−5.12311	−0.370695	−0.185347	−	0.982673i	$-0.559341\pi$
$191$	−5.12311	−0.370695	−0.185347	+	0.982673i	$0.559341\pi$
$192$	−1.00000	−0.0721688
$193$	0.123106	0.00886134	0.00443067	−	0.999990i	$-0.498590\pi$
$193$	0.123106	0.00886134	0.00443067	+	0.999990i	$0.498590\pi$
$194$	−0.876894	−0.0629573
$195$	0	0
$196$	1.00000	0.0714286
$197$	12.5616	0.894974	0.447487	−	0.894291i	$-0.352319\pi$
$197$	12.5616	0.894974	0.447487	+	0.894291i	$0.352319\pi$
$198$	−2.56155	−0.182042
$199$	−16.0000	−1.13421	−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000	−1.13421	−0.567105	+	0.823646i	$0.691937\pi$
$200$	−2.56155	−0.181129
$201$	−9.12311	−0.643494
$202$	−5.80776	−0.408633
$203$	−6.12311	−0.429758
$204$	−0.123106	−0.00861912
$205$	−17.5616	−1.22655
$206$	6.24621	0.435194
$207$	−1.12311	−0.0780612
$208$	0	0
$209$	6.56155	0.453872
$210$	−1.56155	−0.107757
$211$	5.12311	0.352689	0.176345	−	0.984328i	$-0.443573\pi$
$211$	5.12311	0.352689	0.176345	+	0.984328i	$0.443573\pi$
$212$	7.00000	0.480762
$213$	11.3693	0.779013
$214$	13.9309	0.952295
$215$	−12.4924	−0.851976
$216$	−1.00000	−0.0680414
$217$	0	0
$218$	−12.2462	−0.829418
$219$	2.43845	0.164775
$220$	−4.00000	−0.269680
$221$	0	0
$222$	2.43845	0.163658
$223$	9.75379	0.653162	0.326581	−	0.945169i	$-0.394103\pi$
$223$	9.75379	0.653162	0.326581	+	0.945169i	$0.394103\pi$
$224$	1.00000	0.0668153
$225$	−2.56155	−0.170770
$226$	1.56155	0.103873
$227$	−10.8769	−0.721925	−0.360962	−	0.932580i	$-0.617552\pi$
$227$	−10.8769	−0.721925	−0.360962	+	0.932580i	$0.617552\pi$
$228$	2.56155	0.169643
$229$	17.0540	1.12696	0.563479	−	0.826130i	$-0.309462\pi$
$229$	17.0540	1.12696	0.563479	+	0.826130i	$0.309462\pi$
$230$	−1.75379	−0.115641
$231$	2.56155	0.168538
$232$	−6.12311	−0.402002
$233$	1.36932	0.0897069	0.0448535	−	0.998994i	$-0.485718\pi$
$233$	1.36932	0.0897069	0.0448535	+	0.998994i	$0.485718\pi$
$234$	0	0
$235$	−0.492423	−0.0321221
$236$	5.12311	0.333486
$237$	6.56155	0.426219
$238$	0.123106	0.00797975
$239$	19.3693	1.25290	0.626448	−	0.779463i	$-0.284508\pi$
$239$	19.3693	1.25290	0.626448	+	0.779463i	$0.284508\pi$
$240$	−1.56155	−0.100798
$241$	−0.192236	−0.0123830	−0.00619150	−	0.999981i	$-0.501971\pi$
$241$	−0.192236	−0.0123830	−0.00619150	+	0.999981i	$0.501971\pi$
$242$	−4.43845	−0.285314
$243$	−1.00000	−0.0641500
$244$	−11.2462	−0.719965
$245$	1.56155	0.0997639
$246$	11.2462	0.717032
$247$	0	0
$248$	0	0
$249$	5.12311	0.324664
$250$	−11.8078	−0.746789
$251$	−13.6155	−0.859405	−0.429702	−	0.902971i	$-0.641381\pi$
$251$	−13.6155	−0.859405	−0.429702	+	0.902971i	$0.641381\pi$
$252$	1.00000	0.0629941
$253$	2.87689	0.180869
$254$	12.4924	0.783844
$255$	−0.192236	−0.0120383
$256$	1.00000	0.0625000
$257$	−24.3693	−1.52012	−0.760058	−	0.649855i	$-0.774830\pi$
$257$	−24.3693	−1.52012	−0.760058	+	0.649855i	$0.774830\pi$
$258$	8.00000	0.498058
$259$	−2.43845	−0.151518
$260$	0	0
$261$	−6.12311	−0.379011
$262$	14.2462	0.880134
$263$	5.12311	0.315904	0.157952	−	0.987447i	$-0.449511\pi$
$263$	5.12311	0.315904	0.157952	+	0.987447i	$0.449511\pi$
$264$	2.56155	0.157653
$265$	10.9309	0.671478
$266$	−2.56155	−0.157059
$267$	−3.43845	−0.210430
$268$	9.12311	0.557282
$269$	27.1231	1.65372	0.826862	−	0.562404i	$-0.190123\pi$
$269$	27.1231	1.65372	0.826862	+	0.562404i	$0.190123\pi$
$270$	−1.56155	−0.0950331
$271$	−22.7386	−1.38127	−0.690637	−	0.723202i	$-0.742670\pi$
$271$	−22.7386	−1.38127	−0.690637	+	0.723202i	$0.742670\pi$
$272$	0.123106	0.00746437
$273$	0	0
$274$	12.4384	0.751434
$275$	6.56155	0.395677
$276$	1.12311	0.0676030
$277$	−19.5616	−1.17534	−0.587670	−	0.809101i	$-0.699955\pi$
$277$	−19.5616	−1.17534	−0.587670	+	0.809101i	$0.699955\pi$
$278$	−5.43845	−0.326176
$279$	0	0
$280$	1.56155	0.0933206
$281$	12.9309	0.771391	0.385696	−	0.922626i	$-0.373962\pi$
$281$	12.9309	0.771391	0.385696	+	0.922626i	$0.373962\pi$
$282$	0.315342	0.0187783
$283$	−20.0000	−1.18888	−0.594438	−	0.804141i	$-0.702626\pi$
$283$	−20.0000	−1.18888	−0.594438	+	0.804141i	$0.702626\pi$
$284$	−11.3693	−0.674645
$285$	4.00000	0.236940
$286$	0	0
$287$	−11.2462	−0.663843
$288$	1.00000	0.0589256
$289$	−16.9848	−0.999109
$290$	−9.56155	−0.561474
$291$	0.876894	0.0514045
$292$	−2.43845	−0.142699
$293$	−6.93087	−0.404906	−0.202453	−	0.979292i	$-0.564891\pi$
$293$	−6.93087	−0.404906	−0.202453	+	0.979292i	$0.564891\pi$
$294$	−1.00000	−0.0583212
$295$	8.00000	0.465778
$296$	−2.43845	−0.141732
$297$	2.56155	0.148636
$298$	−15.5616	−0.901457
$299$	0	0
$300$	2.56155	0.147891
$301$	−8.00000	−0.461112
$302$	−21.9309	−1.26198
$303$	5.80776	0.333647
$304$	−2.56155	−0.146915
$305$	−17.5616	−1.00557
$306$	0.123106	0.00703748
$307$	−9.93087	−0.566785	−0.283392	−	0.959004i	$-0.591460\pi$
$307$	−9.93087	−0.566785	−0.283392	+	0.959004i	$0.591460\pi$
$308$	−2.56155	−0.145958
$309$	−6.24621	−0.355335
$310$	0	0
$311$	21.9309	1.24359	0.621793	−	0.783182i	$-0.286405\pi$
$311$	21.9309	1.24359	0.621793	+	0.783182i	$0.286405\pi$
$312$	0	0
$313$	−6.00000	−0.339140	−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000	−0.339140	−0.169570	+	0.985518i	$0.554238\pi$
$314$	−1.31534	−0.0742290
$315$	1.56155	0.0879835
$316$	−6.56155	−0.369116
$317$	12.4384	0.698613	0.349306	−	0.937009i	$-0.386417\pi$
$317$	12.4384	0.698613	0.349306	+	0.937009i	$0.386417\pi$
$318$	−7.00000	−0.392541
$319$	15.6847	0.878172
$320$	1.56155	0.0872935
$321$	−13.9309	−0.777545
$322$	−1.12311	−0.0625882
$323$	−0.315342	−0.0175461
$324$	1.00000	0.0555556
$325$	0	0
$326$	24.4924	1.35651
$327$	12.2462	0.677217
$328$	−11.2462	−0.620968
$329$	−0.315342	−0.0173853
$330$	4.00000	0.220193
$331$	19.3693	1.06463	0.532317	−	0.846545i	$-0.321321\pi$
$331$	19.3693	1.06463	0.532317	+	0.846545i	$0.321321\pi$
$332$	−5.12311	−0.281167
$333$	−2.43845	−0.133626
$334$	12.4924	0.683555
$335$	14.2462	0.778354
$336$	−1.00000	−0.0545545
$337$	−13.4924	−0.734979	−0.367490	−	0.930028i	$-0.619783\pi$
$337$	−13.4924	−0.734979	−0.367490	+	0.930028i	$0.619783\pi$
$338$	0	0
$339$	−1.56155	−0.0848119
$340$	0.192236	0.0104255
$341$	0	0
$342$	−2.56155	−0.138513
$343$	1.00000	0.0539949
$344$	−8.00000	−0.431331
$345$	1.75379	0.0944208
$346$	−18.0000	−0.967686
$347$	15.0540	0.808140	0.404070	−	0.914728i	$-0.367595\pi$
$347$	15.0540	0.808140	0.404070	+	0.914728i	$0.367595\pi$
$348$	6.12311	0.328233
$349$	−18.0000	−0.963518	−0.481759	−	0.876304i	$-0.660002\pi$
$349$	−18.0000	−0.963518	−0.481759	+	0.876304i	$0.660002\pi$
$350$	−2.56155	−0.136921
$351$	0	0
$352$	−2.56155	−0.136531
$353$	−33.8078	−1.79941	−0.899703	−	0.436503i	$-0.856217\pi$
$353$	−33.8078	−1.79941	−0.899703	+	0.436503i	$0.856217\pi$
$354$	−5.12311	−0.272290
$355$	−17.7538	−0.942273
$356$	3.43845	0.182237
$357$	−0.123106	−0.00651544
$358$	−1.75379	−0.0926906
$359$	−1.75379	−0.0925614	−0.0462807	−	0.998928i	$-0.514737\pi$
$359$	−1.75379	−0.0925614	−0.0462807	+	0.998928i	$0.514737\pi$
$360$	1.56155	0.0823011
$361$	−12.4384	−0.654655
$362$	13.2462	0.696205
$363$	4.43845	0.232958
$364$	0	0
$365$	−3.80776	−0.199307
$366$	11.2462	0.587849
$367$	13.6155	0.710725	0.355362	−	0.934729i	$-0.384357\pi$
$367$	13.6155	0.710725	0.355362	+	0.934729i	$0.384357\pi$
$368$	−1.12311	−0.0585459
$369$	−11.2462	−0.585454
$370$	−3.80776	−0.197956
$371$	7.00000	0.363422
$372$	0	0
$373$	−3.06913	−0.158914	−0.0794568	−	0.996838i	$-0.525319\pi$
$373$	−3.06913	−0.158914	−0.0794568	+	0.996838i	$0.525319\pi$
$374$	−0.315342	−0.0163059
$375$	11.8078	0.609750
$376$	−0.315342	−0.0162625
$377$	0	0
$378$	−1.00000	−0.0514344
$379$	37.6155	1.93218	0.966090	−	0.258206i	$-0.0831312\pi$
$379$	37.6155	1.93218	0.966090	+	0.258206i	$0.0831312\pi$
$380$	−4.00000	−0.205196
$381$	−12.4924	−0.640006
$382$	−5.12311	−0.262121
$383$	−12.8078	−0.654446	−0.327223	−	0.944947i	$-0.606113\pi$
$383$	−12.8078	−0.654446	−0.327223	+	0.944947i	$0.606113\pi$
$384$	−1.00000	−0.0510310
$385$	−4.00000	−0.203859
$386$	0.123106	0.00626591
$387$	−8.00000	−0.406663
$388$	−0.876894	−0.0445176
$389$	−5.31534	−0.269499	−0.134749	−	0.990880i	$-0.543023\pi$
$389$	−5.31534	−0.269499	−0.134749	+	0.990880i	$0.543023\pi$
$390$	0	0
$391$	−0.138261	−0.00699214
$392$	1.00000	0.0505076
$393$	−14.2462	−0.718626
$394$	12.5616	0.632842
$395$	−10.2462	−0.515543
$396$	−2.56155	−0.128723
$397$	27.9309	1.40181	0.700905	−	0.713255i	$-0.252780\pi$
$397$	27.9309	1.40181	0.700905	+	0.713255i	$0.252780\pi$
$398$	−16.0000	−0.802008
$399$	2.56155	0.128238
$400$	−2.56155	−0.128078
$401$	−1.80776	−0.0902754	−0.0451377	−	0.998981i	$-0.514373\pi$
$401$	−1.80776	−0.0902754	−0.0451377	+	0.998981i	$0.514373\pi$
$402$	−9.12311	−0.455019
$403$	0	0
$404$	−5.80776	−0.288947
$405$	1.56155	0.0775942
$406$	−6.12311	−0.303885
$407$	6.24621	0.309613
$408$	−0.123106	−0.00609464
$409$	−11.5616	−0.571682	−0.285841	−	0.958277i	$-0.592273\pi$
$409$	−11.5616	−0.571682	−0.285841	+	0.958277i	$0.592273\pi$
$410$	−17.5616	−0.867303
$411$	−12.4384	−0.613543
$412$	6.24621	0.307729
$413$	5.12311	0.252092
$414$	−1.12311	−0.0551976
$415$	−8.00000	−0.392705
$416$	0	0
$417$	5.43845	0.266322
$418$	6.56155	0.320936
$419$	23.3693	1.14167	0.570833	−	0.821066i	$-0.306620\pi$
$419$	23.3693	1.14167	0.570833	+	0.821066i	$0.306620\pi$
$420$	−1.56155	−0.0761960
$421$	−22.3002	−1.08684	−0.543422	−	0.839459i	$-0.682872\pi$
$421$	−22.3002	−1.08684	−0.543422	+	0.839459i	$0.682872\pi$
$422$	5.12311	0.249389
$423$	−0.315342	−0.0153324
$424$	7.00000	0.339950
$425$	−0.315342	−0.0152963
$426$	11.3693	0.550845
$427$	−11.2462	−0.544242
$428$	13.9309	0.673374
$429$	0	0
$430$	−12.4924	−0.602438
$431$	19.3693	0.932987	0.466494	−	0.884525i	$-0.345517\pi$
$431$	19.3693	0.932987	0.466494	+	0.884525i	$0.345517\pi$
$432$	−1.00000	−0.0481125
$433$	−21.3153	−1.02435	−0.512175	−	0.858881i	$-0.671160\pi$
$433$	−21.3153	−1.02435	−0.512175	+	0.858881i	$0.671160\pi$
$434$	0	0
$435$	9.56155	0.458441
$436$	−12.2462	−0.586487
$437$	2.87689	0.137621
$438$	2.43845	0.116514
$439$	−26.2462	−1.25266	−0.626332	−	0.779557i	$-0.715444\pi$
$439$	−26.2462	−1.25266	−0.626332	+	0.779557i	$0.715444\pi$
$440$	−4.00000	−0.190693
$441$	1.00000	0.0476190
$442$	0	0
$443$	−27.0540	−1.28537	−0.642687	−	0.766129i	$-0.722180\pi$
$443$	−27.0540	−1.28537	−0.642687	+	0.766129i	$0.722180\pi$
$444$	2.43845	0.115724
$445$	5.36932	0.254530
$446$	9.75379	0.461855
$447$	15.5616	0.736036
$448$	1.00000	0.0472456
$449$	−6.63068	−0.312921	−0.156461	−	0.987684i	$-0.550008\pi$
$449$	−6.63068	−0.312921	−0.156461	+	0.987684i	$0.550008\pi$
$450$	−2.56155	−0.120753
$451$	28.8078	1.35650
$452$	1.56155	0.0734493
$453$	21.9309	1.03040
$454$	−10.8769	−0.510478
$455$	0	0
$456$	2.56155	0.119956
$457$	28.9309	1.35333	0.676665	−	0.736291i	$-0.263425\pi$
$457$	28.9309	1.35333	0.676665	+	0.736291i	$0.263425\pi$
$458$	17.0540	0.796880
$459$	−0.123106	−0.00574608
$460$	−1.75379	−0.0817708
$461$	6.05398	0.281962	0.140981	−	0.990012i	$-0.454974\pi$
$461$	6.05398	0.281962	0.140981	+	0.990012i	$0.454974\pi$
$462$	2.56155	0.119174
$463$	12.3153	0.572342	0.286171	−	0.958178i	$-0.407617\pi$
$463$	12.3153	0.572342	0.286171	+	0.958178i	$0.407617\pi$
$464$	−6.12311	−0.284258
$465$	0	0
$466$	1.36932	0.0634324
$467$	−36.9848	−1.71145	−0.855727	−	0.517427i	$-0.826890\pi$
$467$	−36.9848	−1.71145	−0.855727	+	0.517427i	$0.826890\pi$
$468$	0	0
$469$	9.12311	0.421266
$470$	−0.492423	−0.0227138
$471$	1.31534	0.0606077
$472$	5.12311	0.235810
$473$	20.4924	0.942243
$474$	6.56155	0.301382
$475$	6.56155	0.301065
$476$	0.123106	0.00564254
$477$	7.00000	0.320508
$478$	19.3693	0.885932
$479$	−1.93087	−0.0882237	−0.0441118	−	0.999027i	$-0.514046\pi$
$479$	−1.93087	−0.0882237	−0.0441118	+	0.999027i	$0.514046\pi$
$480$	−1.56155	−0.0712748
$481$	0	0
$482$	−0.192236	−0.00875611
$483$	1.12311	0.0511031
$484$	−4.43845	−0.201748
$485$	−1.36932	−0.0621775
$486$	−1.00000	−0.0453609
$487$	23.6847	1.07325	0.536627	−	0.843819i	$-0.319698\pi$
$487$	23.6847	1.07325	0.536627	+	0.843819i	$0.319698\pi$
$488$	−11.2462	−0.509092
$489$	−24.4924	−1.10759
$490$	1.56155	0.0705438
$491$	−16.4924	−0.744293	−0.372146	−	0.928174i	$-0.621378\pi$
$491$	−16.4924	−0.744293	−0.372146	+	0.928174i	$0.621378\pi$
$492$	11.2462	0.507018
$493$	−0.753789	−0.0339489
$494$	0	0
$495$	−4.00000	−0.179787
$496$	0	0
$497$	−11.3693	−0.509984
$498$	5.12311	0.229572
$499$	30.2462	1.35401	0.677003	−	0.735980i	$-0.263278\pi$
$499$	30.2462	1.35401	0.677003	+	0.735980i	$0.263278\pi$
$500$	−11.8078	−0.528059
$501$	−12.4924	−0.558120
$502$	−13.6155	−0.607691
$503$	−28.4924	−1.27041	−0.635207	−	0.772342i	$-0.719085\pi$
$503$	−28.4924	−1.27041	−0.635207	+	0.772342i	$0.719085\pi$
$504$	1.00000	0.0445435
$505$	−9.06913	−0.403571
$506$	2.87689	0.127894
$507$	0	0
$508$	12.4924	0.554262
$509$	−41.8078	−1.85310	−0.926548	−	0.376176i	$-0.877239\pi$
$509$	−41.8078	−1.85310	−0.926548	+	0.376176i	$0.877239\pi$
$510$	−0.192236	−0.00851235
$511$	−2.43845	−0.107871
$512$	1.00000	0.0441942
$513$	2.56155	0.113095
$514$	−24.3693	−1.07488
$515$	9.75379	0.429803
$516$	8.00000	0.352180
$517$	0.807764	0.0355254
$518$	−2.43845	−0.107139
$519$	18.0000	0.790112
$520$	0	0
$521$	25.8769	1.13369	0.566844	−	0.823825i	$-0.308164\pi$
$521$	25.8769	1.13369	0.566844	+	0.823825i	$0.308164\pi$
$522$	−6.12311	−0.268001
$523$	−16.8078	−0.734952	−0.367476	−	0.930033i	$-0.619778\pi$
$523$	−16.8078	−0.734952	−0.367476	+	0.930033i	$0.619778\pi$
$524$	14.2462	0.622349
$525$	2.56155	0.111795
$526$	5.12311	0.223378
$527$	0	0
$528$	2.56155	0.111477
$529$	−21.7386	−0.945158
$530$	10.9309	0.474807
$531$	5.12311	0.222324
$532$	−2.56155	−0.111057
$533$	0	0
$534$	−3.43845	−0.148796
$535$	21.7538	0.940498
$536$	9.12311	0.394058
$537$	1.75379	0.0756816
$538$	27.1231	1.16936
$539$	−2.56155	−0.110334
$540$	−1.56155	−0.0671985
$541$	19.1771	0.824487	0.412244	−	0.911074i	$-0.364745\pi$
$541$	19.1771	0.824487	0.412244	+	0.911074i	$0.364745\pi$
$542$	−22.7386	−0.976708
$543$	−13.2462	−0.568449
$544$	0.123106	0.00527811
$545$	−19.1231	−0.819144
$546$	0	0
$547$	−33.6155	−1.43730	−0.718648	−	0.695374i	$-0.755239\pi$
$547$	−33.6155	−1.43730	−0.718648	+	0.695374i	$0.755239\pi$
$548$	12.4384	0.531344
$549$	−11.2462	−0.479977
$550$	6.56155	0.279786
$551$	15.6847	0.668189
$552$	1.12311	0.0478025
$553$	−6.56155	−0.279026
$554$	−19.5616	−0.831091
$555$	3.80776	0.161631
$556$	−5.43845	−0.230642
$557$	12.1231	0.513672	0.256836	−	0.966455i	$-0.417320\pi$
$557$	12.1231	0.513672	0.256836	+	0.966455i	$0.417320\pi$
$558$	0	0
$559$	0	0
$560$	1.56155	0.0659877
$561$	0.315342	0.0133137
$562$	12.9309	0.545456
$563$	−5.75379	−0.242493	−0.121247	−	0.992622i	$-0.538689\pi$
$563$	−5.75379	−0.242493	−0.121247	+	0.992622i	$0.538689\pi$
$564$	0.315342	0.0132783
$565$	2.43845	0.102586
$566$	−20.0000	−0.840663
$567$	1.00000	0.0419961
$568$	−11.3693	−0.477046
$569$	−22.0000	−0.922288	−0.461144	−	0.887325i	$-0.652561\pi$
$569$	−22.0000	−0.922288	−0.461144	+	0.887325i	$0.652561\pi$
$570$	4.00000	0.167542
$571$	−21.1231	−0.883974	−0.441987	−	0.897021i	$-0.645726\pi$
$571$	−21.1231	−0.883974	−0.441987	+	0.897021i	$0.645726\pi$
$572$	0	0
$573$	5.12311	0.214021
$574$	−11.2462	−0.469408
$575$	2.87689	0.119975
$576$	1.00000	0.0416667
$577$	−35.5616	−1.48045	−0.740223	−	0.672361i	$-0.765280\pi$
$577$	−35.5616	−1.48045	−0.740223	+	0.672361i	$0.765280\pi$
$578$	−16.9848	−0.706476
$579$	−0.123106	−0.00511610
$580$	−9.56155	−0.397022
$581$	−5.12311	−0.212542
$582$	0.876894	0.0363484
$583$	−17.9309	−0.742621
$584$	−2.43845	−0.100904
$585$	0	0
$586$	−6.93087	−0.286312
$587$	2.24621	0.0927111	0.0463555	−	0.998925i	$-0.485239\pi$
$587$	2.24621	0.0927111	0.0463555	+	0.998925i	$0.485239\pi$
$588$	−1.00000	−0.0412393
$589$	0	0
$590$	8.00000	0.329355
$591$	−12.5616	−0.516713
$592$	−2.43845	−0.100220
$593$	−33.9848	−1.39559	−0.697795	−	0.716297i	$-0.745835\pi$
$593$	−33.9848	−1.39559	−0.697795	+	0.716297i	$0.745835\pi$
$594$	2.56155	0.105102
$595$	0.192236	0.00788091
$596$	−15.5616	−0.637426
$597$	16.0000	0.654836
$598$	0	0
$599$	23.8617	0.974964	0.487482	−	0.873133i	$-0.337915\pi$
$599$	23.8617	0.974964	0.487482	+	0.873133i	$0.337915\pi$
$600$	2.56155	0.104575
$601$	28.3002	1.15439	0.577194	−	0.816607i	$-0.304148\pi$
$601$	28.3002	1.15439	0.577194	+	0.816607i	$0.304148\pi$
$602$	−8.00000	−0.326056
$603$	9.12311	0.371522
$604$	−21.9309	−0.892354
$605$	−6.93087	−0.281780
$606$	5.80776	0.235924
$607$	−48.9848	−1.98823	−0.994117	−	0.108314i	$-0.965455\pi$
$607$	−48.9848	−1.98823	−0.994117	+	0.108314i	$0.965455\pi$
$608$	−2.56155	−0.103885
$609$	6.12311	0.248121
$610$	−17.5616	−0.711046
$611$	0	0
$612$	0.123106	0.00497625
$613$	21.5616	0.870863	0.435431	−	0.900222i	$-0.356596\pi$
$613$	21.5616	0.870863	0.435431	+	0.900222i	$0.356596\pi$
$614$	−9.93087	−0.400777
$615$	17.5616	0.708150
$616$	−2.56155	−0.103208
$617$	23.1771	0.933074	0.466537	−	0.884502i	$-0.345501\pi$
$617$	23.1771	0.933074	0.466537	+	0.884502i	$0.345501\pi$
$618$	−6.24621	−0.251259
$619$	2.06913	0.0831654	0.0415827	−	0.999135i	$-0.486760\pi$
$619$	2.06913	0.0831654	0.0415827	+	0.999135i	$0.486760\pi$
$620$	0	0
$621$	1.12311	0.0450687
$622$	21.9309	0.879348
$623$	3.43845	0.137758
$624$	0	0
$625$	−5.63068	−0.225227
$626$	−6.00000	−0.239808
$627$	−6.56155	−0.262043
$628$	−1.31534	−0.0524878
$629$	−0.300187	−0.0119692
$630$	1.56155	0.0622138
$631$	−10.0691	−0.400846	−0.200423	−	0.979709i	$-0.564232\pi$
$631$	−10.0691	−0.400846	−0.200423	+	0.979709i	$0.564232\pi$
$632$	−6.56155	−0.261005
$633$	−5.12311	−0.203625
$634$	12.4384	0.493994
$635$	19.5076	0.774135
$636$	−7.00000	−0.277568
$637$	0	0
$638$	15.6847	0.620962
$639$	−11.3693	−0.449763
$640$	1.56155	0.0617258
$641$	8.43845	0.333299	0.166649	−	0.986016i	$-0.446705\pi$
$641$	8.43845	0.333299	0.166649	+	0.986016i	$0.446705\pi$
$642$	−13.9309	−0.549808
$643$	47.6847	1.88050	0.940250	−	0.340486i	$-0.110592\pi$
$643$	47.6847	1.88050	0.940250	+	0.340486i	$0.110592\pi$
$644$	−1.12311	−0.0442566
$645$	12.4924	0.491889
$646$	−0.315342	−0.0124069
$647$	−8.94602	−0.351705	−0.175852	−	0.984417i	$-0.556268\pi$
$647$	−8.94602	−0.351705	−0.175852	+	0.984417i	$0.556268\pi$
$648$	1.00000	0.0392837
$649$	−13.1231	−0.515127
$650$	0	0
$651$	0	0
$652$	24.4924	0.959197
$653$	20.5616	0.804636	0.402318	−	0.915500i	$-0.368205\pi$
$653$	20.5616	0.804636	0.402318	+	0.915500i	$0.368205\pi$
$654$	12.2462	0.478865
$655$	22.2462	0.869231
$656$	−11.2462	−0.439091
$657$	−2.43845	−0.0951329
$658$	−0.315342	−0.0122933
$659$	2.06913	0.0806019	0.0403009	−	0.999188i	$-0.487168\pi$
$659$	2.06913	0.0806019	0.0403009	+	0.999188i	$0.487168\pi$
$660$	4.00000	0.155700
$661$	−20.0540	−0.780009	−0.390005	−	0.920813i	$-0.627527\pi$
$661$	−20.0540	−0.780009	−0.390005	+	0.920813i	$0.627527\pi$
$662$	19.3693	0.752810
$663$	0	0
$664$	−5.12311	−0.198815
$665$	−4.00000	−0.155113
$666$	−2.43845	−0.0944879
$667$	6.87689	0.266274
$668$	12.4924	0.483346
$669$	−9.75379	−0.377103
$670$	14.2462	0.550379
$671$	28.8078	1.11211
$672$	−1.00000	−0.0385758
$673$	−2.75379	−0.106151	−0.0530754	−	0.998591i	$-0.516902\pi$
$673$	−2.75379	−0.106151	−0.0530754	+	0.998591i	$0.516902\pi$
$674$	−13.4924	−0.519709
$675$	2.56155	0.0985942
$676$	0	0
$677$	−24.7386	−0.950783	−0.475391	−	0.879774i	$-0.657694\pi$
$677$	−24.7386	−0.950783	−0.475391	+	0.879774i	$0.657694\pi$
$678$	−1.56155	−0.0599711
$679$	−0.876894	−0.0336521
$680$	0.192236	0.00737191
$681$	10.8769	0.416803
$682$	0	0
$683$	40.4924	1.54940	0.774700	−	0.632329i	$-0.217901\pi$
$683$	40.4924	1.54940	0.774700	+	0.632329i	$0.217901\pi$
$684$	−2.56155	−0.0979434
$685$	19.4233	0.742126
$686$	1.00000	0.0381802
$687$	−17.0540	−0.650650
$688$	−8.00000	−0.304997
$689$	0	0
$690$	1.75379	0.0667656
$691$	−32.9848	−1.25480	−0.627401	−	0.778696i	$-0.715881\pi$
$691$	−32.9848	−1.25480	−0.627401	+	0.778696i	$0.715881\pi$
$692$	−18.0000	−0.684257
$693$	−2.56155	−0.0973053
$694$	15.0540	0.571441
$695$	−8.49242	−0.322136
$696$	6.12311	0.232096
$697$	−1.38447	−0.0524406
$698$	−18.0000	−0.681310
$699$	−1.36932	−0.0517923
$700$	−2.56155	−0.0968176
$701$	−39.3002	−1.48435	−0.742174	−	0.670207i	$-0.766205\pi$
$701$	−39.3002	−1.48435	−0.742174	+	0.670207i	$0.766205\pi$
$702$	0	0
$703$	6.24621	0.235580
$704$	−2.56155	−0.0965422
$705$	0.492423	0.0185457
$706$	−33.8078	−1.27237
$707$	−5.80776	−0.218423
$708$	−5.12311	−0.192538
$709$	−38.3002	−1.43839	−0.719197	−	0.694806i	$-0.755490\pi$
$709$	−38.3002	−1.43839	−0.719197	+	0.694806i	$0.755490\pi$
$710$	−17.7538	−0.666288
$711$	−6.56155	−0.246077
$712$	3.43845	0.128861
$713$	0	0
$714$	−0.123106	−0.00460711
$715$	0	0
$716$	−1.75379	−0.0655422
$717$	−19.3693	−0.723360
$718$	−1.75379	−0.0654508
$719$	0.807764	0.0301245	0.0150623	−	0.999887i	$-0.495205\pi$
$719$	0.807764	0.0301245	0.0150623	+	0.999887i	$0.495205\pi$
$720$	1.56155	0.0581956
$721$	6.24621	0.232621
$722$	−12.4384	−0.462911
$723$	0.192236	0.00714933
$724$	13.2462	0.492292
$725$	15.6847	0.582514
$726$	4.43845	0.164726
$727$	40.0000	1.48352	0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000	1.48352	0.741759	+	0.670667i	$0.233992\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−3.80776	−0.140932
$731$	−0.984845	−0.0364258
$732$	11.2462	0.415672
$733$	−28.8617	−1.06603	−0.533016	−	0.846105i	$-0.678942\pi$
$733$	−28.8617	−1.06603	−0.533016	+	0.846105i	$0.678942\pi$
$734$	13.6155	0.502558
$735$	−1.56155	−0.0575987
$736$	−1.12311	−0.0413982
$737$	−23.3693	−0.860820
$738$	−11.2462	−0.413979
$739$	15.3693	0.565369	0.282685	−	0.959213i	$-0.408775\pi$
$739$	15.3693	0.565369	0.282685	+	0.959213i	$0.408775\pi$
$740$	−3.80776	−0.139976
$741$	0	0
$742$	7.00000	0.256978
$743$	−4.49242	−0.164811	−0.0824055	−	0.996599i	$-0.526260\pi$
$743$	−4.49242	−0.164811	−0.0824055	+	0.996599i	$0.526260\pi$
$744$	0	0
$745$	−24.3002	−0.890290
$746$	−3.06913	−0.112369
$747$	−5.12311	−0.187445
$748$	−0.315342	−0.0115300
$749$	13.9309	0.509023
$750$	11.8078	0.431159
$751$	−40.8078	−1.48910	−0.744548	−	0.667569i	$-0.767335\pi$
$751$	−40.8078	−1.48910	−0.744548	+	0.667569i	$0.767335\pi$
$752$	−0.315342	−0.0114993
$753$	13.6155	0.496177
$754$	0	0
$755$	−34.2462	−1.24635
$756$	−1.00000	−0.0363696
$757$	52.7386	1.91682	0.958409	−	0.285398i	$-0.0921257\pi$
$757$	52.7386	1.91682	0.958409	+	0.285398i	$0.0921257\pi$
$758$	37.6155	1.36626
$759$	−2.87689	−0.104425
$760$	−4.00000	−0.145095
$761$	50.9848	1.84820	0.924100	−	0.382152i	$-0.124817\pi$
$761$	50.9848	1.84820	0.924100	+	0.382152i	$0.124817\pi$
$762$	−12.4924	−0.452553
$763$	−12.2462	−0.443343
$764$	−5.12311	−0.185347
$765$	0.192236	0.00695030
$766$	−12.8078	−0.462763
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	4.87689	0.175865	0.0879327	−	0.996126i	$-0.471974\pi$
$769$	4.87689	0.175865	0.0879327	+	0.996126i	$0.471974\pi$
$770$	−4.00000	−0.144150
$771$	24.3693	0.877640
$772$	0.123106	0.00443067
$773$	20.7386	0.745917	0.372958	−	0.927848i	$-0.378343\pi$
$773$	20.7386	0.745917	0.372958	+	0.927848i	$0.378343\pi$
$774$	−8.00000	−0.287554
$775$	0	0
$776$	−0.876894	−0.0314787
$777$	2.43845	0.0874788
$778$	−5.31534	−0.190564
$779$	28.8078	1.03215
$780$	0	0
$781$	29.1231	1.04211
$782$	−0.138261	−0.00494419
$783$	6.12311	0.218822
$784$	1.00000	0.0357143
$785$	−2.05398	−0.0733095
$786$	−14.2462	−0.508146
$787$	−0.177081	−0.00631225	−0.00315613	−	0.999995i	$-0.501005\pi$
$787$	−0.177081	−0.00631225	−0.00315613	+	0.999995i	$0.501005\pi$
$788$	12.5616	0.447487
$789$	−5.12311	−0.182387
$790$	−10.2462	−0.364544
$791$	1.56155	0.0555224
$792$	−2.56155	−0.0910208
$793$	0	0
$794$	27.9309	0.991229
$795$	−10.9309	−0.387678
$796$	−16.0000	−0.567105
$797$	50.4924	1.78853	0.894267	−	0.447534i	$-0.147698\pi$
$797$	50.4924	1.78853	0.894267	+	0.447534i	$0.147698\pi$
$798$	2.56155	0.0906780
$799$	−0.0388203	−0.00137336
$800$	−2.56155	−0.0905646
$801$	3.43845	0.121492
$802$	−1.80776	−0.0638344
$803$	6.24621	0.220424
$804$	−9.12311	−0.321747
$805$	−1.75379	−0.0618129
$806$	0	0
$807$	−27.1231	−0.954779
$808$	−5.80776	−0.204316
$809$	8.93087	0.313993	0.156996	−	0.987599i	$-0.449819\pi$
$809$	8.93087	0.313993	0.156996	+	0.987599i	$0.449819\pi$
$810$	1.56155	0.0548674
$811$	24.0000	0.842754	0.421377	−	0.906886i	$-0.361547\pi$
$811$	24.0000	0.842754	0.421377	+	0.906886i	$0.361547\pi$
$812$	−6.12311	−0.214879
$813$	22.7386	0.797479
$814$	6.24621	0.218930
$815$	38.2462	1.33971
$816$	−0.123106	−0.00430956
$817$	20.4924	0.716939
$818$	−11.5616	−0.404240
$819$	0	0
$820$	−17.5616	−0.613276
$821$	27.3002	0.952783	0.476392	−	0.879233i	$-0.341944\pi$
$821$	27.3002	0.952783	0.476392	+	0.879233i	$0.341944\pi$
$822$	−12.4384	−0.433841
$823$	−38.2462	−1.33318	−0.666590	−	0.745425i	$-0.732247\pi$
$823$	−38.2462	−1.33318	−0.666590	+	0.745425i	$0.732247\pi$
$824$	6.24621	0.217597
$825$	−6.56155	−0.228444
$826$	5.12311	0.178256
$827$	34.2462	1.19086	0.595429	−	0.803408i	$-0.296982\pi$
$827$	34.2462	1.19086	0.595429	+	0.803408i	$0.296982\pi$
$828$	−1.12311	−0.0390306
$829$	−0.369317	−0.0128269	−0.00641345	−	0.999979i	$-0.502041\pi$
$829$	−0.369317	−0.0128269	−0.00641345	+	0.999979i	$0.502041\pi$
$830$	−8.00000	−0.277684
$831$	19.5616	0.678583
$832$	0	0
$833$	0.123106	0.00426536
$834$	5.43845	0.188318
$835$	19.5076	0.675088
$836$	6.56155	0.226936
$837$	0	0
$838$	23.3693	0.807280
$839$	18.2462	0.629929	0.314965	−	0.949103i	$-0.398007\pi$
$839$	18.2462	0.629929	0.314965	+	0.949103i	$0.398007\pi$
$840$	−1.56155	−0.0538787
$841$	8.49242	0.292842
$842$	−22.3002	−0.768515
$843$	−12.9309	−0.445363
$844$	5.12311	0.176345
$845$	0	0
$846$	−0.315342	−0.0108417
$847$	−4.43845	−0.152507
$848$	7.00000	0.240381
$849$	20.0000	0.686398
$850$	−0.315342	−0.0108161
$851$	2.73863	0.0938792
$852$	11.3693	0.389506
$853$	30.3693	1.03983	0.519913	−	0.854219i	$-0.325964\pi$
$853$	30.3693	1.03983	0.519913	+	0.854219i	$0.325964\pi$
$854$	−11.2462	−0.384837
$855$	−4.00000	−0.136797
$856$	13.9309	0.476147
$857$	16.4384	0.561527	0.280763	−	0.959777i	$-0.409412\pi$
$857$	16.4384	0.561527	0.280763	+	0.959777i	$0.409412\pi$
$858$	0	0
$859$	17.9309	0.611793	0.305897	−	0.952065i	$-0.401044\pi$
$859$	17.9309	0.611793	0.305897	+	0.952065i	$0.401044\pi$
$860$	−12.4924	−0.425988
$861$	11.2462	0.383270
$862$	19.3693	0.659722
$863$	41.1231	1.39985	0.699923	−	0.714218i	$-0.253217\pi$
$863$	41.1231	1.39985	0.699923	+	0.714218i	$0.253217\pi$
$864$	−1.00000	−0.0340207
$865$	−28.1080	−0.955699
$866$	−21.3153	−0.724325
$867$	16.9848	0.576836
$868$	0	0
$869$	16.8078	0.570164
$870$	9.56155	0.324167
$871$	0	0
$872$	−12.2462	−0.414709
$873$	−0.876894	−0.0296784
$874$	2.87689	0.0973124
$875$	−11.8078	−0.399175
$876$	2.43845	0.0823875
$877$	−28.5464	−0.963943	−0.481972	−	0.876187i	$-0.660079\pi$
$877$	−28.5464	−0.963943	−0.481972	+	0.876187i	$0.660079\pi$
$878$	−26.2462	−0.885767
$879$	6.93087	0.233772
$880$	−4.00000	−0.134840
$881$	19.9460	0.671999	0.335999	−	0.941862i	$-0.390926\pi$
$881$	19.9460	0.671999	0.335999	+	0.941862i	$0.390926\pi$
$882$	1.00000	0.0336718
$883$	−20.0000	−0.673054	−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000	−0.673054	−0.336527	+	0.941674i	$0.609252\pi$
$884$	0	0
$885$	−8.00000	−0.268917
$886$	−27.0540	−0.908896
$887$	−8.94602	−0.300378	−0.150189	−	0.988657i	$-0.547988\pi$
$887$	−8.94602	−0.300378	−0.150189	+	0.988657i	$0.547988\pi$
$888$	2.43845	0.0818289
$889$	12.4924	0.418982
$890$	5.36932	0.179980
$891$	−2.56155	−0.0858152
$892$	9.75379	0.326581
$893$	0.807764	0.0270308
$894$	15.5616	0.520456
$895$	−2.73863	−0.0915424
$896$	1.00000	0.0334077
$897$	0	0
$898$	−6.63068	−0.221269
$899$	0	0
$900$	−2.56155	−0.0853851
$901$	0.861739	0.0287087
$902$	28.8078	0.959194
$903$	8.00000	0.266223
$904$	1.56155	0.0519365
$905$	20.6847	0.687581
$906$	21.9309	0.728604
$907$	−1.12311	−0.0372921	−0.0186461	−	0.999826i	$-0.505936\pi$
$907$	−1.12311	−0.0372921	−0.0186461	+	0.999826i	$0.505936\pi$
$908$	−10.8769	−0.360962
$909$	−5.80776	−0.192631
$910$	0	0
$911$	13.6155	0.451103	0.225551	−	0.974231i	$-0.427582\pi$
$911$	13.6155	0.451103	0.225551	+	0.974231i	$0.427582\pi$
$912$	2.56155	0.0848215
$913$	13.1231	0.434311
$914$	28.9309	0.956948
$915$	17.5616	0.580567
$916$	17.0540	0.563479
$917$	14.2462	0.470451
$918$	−0.123106	−0.00406309
$919$	−45.9309	−1.51512	−0.757560	−	0.652766i	$-0.773609\pi$
$919$	−45.9309	−1.51512	−0.757560	+	0.652766i	$0.773609\pi$
$920$	−1.75379	−0.0578207
$921$	9.93087	0.327233
$922$	6.05398	0.199377
$923$	0	0
$924$	2.56155	0.0842689
$925$	6.24621	0.205374
$926$	12.3153	0.404707
$927$	6.24621	0.205152
$928$	−6.12311	−0.201001
$929$	−2.75379	−0.0903489	−0.0451744	−	0.998979i	$-0.514384\pi$
$929$	−2.75379	−0.0903489	−0.0451744	+	0.998979i	$0.514384\pi$
$930$	0	0
$931$	−2.56155	−0.0839515
$932$	1.36932	0.0448535
$933$	−21.9309	−0.717984
$934$	−36.9848	−1.21018
$935$	−0.492423	−0.0161039
$936$	0	0
$937$	−34.4384	−1.12506	−0.562528	−	0.826779i	$-0.690171\pi$
$937$	−34.4384	−1.12506	−0.562528	+	0.826779i	$0.690171\pi$
$938$	9.12311	0.297880
$939$	6.00000	0.195803
$940$	−0.492423	−0.0160611
$941$	−10.6307	−0.346550	−0.173275	−	0.984873i	$-0.555435\pi$
$941$	−10.6307	−0.346550	−0.173275	+	0.984873i	$0.555435\pi$
$942$	1.31534	0.0428561
$943$	12.6307	0.411312
$944$	5.12311	0.166743
$945$	−1.56155	−0.0507973
$946$	20.4924	0.666266
$947$	58.5616	1.90299	0.951497	−	0.307657i	$-0.0995449\pi$
$947$	58.5616	1.90299	0.951497	+	0.307657i	$0.0995449\pi$
$948$	6.56155	0.213109
$949$	0	0
$950$	6.56155	0.212885
$951$	−12.4384	−0.403344
$952$	0.123106	0.00398988
$953$	12.8769	0.417124	0.208562	−	0.978009i	$-0.433122\pi$
$953$	12.8769	0.417124	0.208562	+	0.978009i	$0.433122\pi$
$954$	7.00000	0.226633
$955$	−8.00000	−0.258874
$956$	19.3693	0.626448
$957$	−15.6847	−0.507013
$958$	−1.93087	−0.0623836
$959$	12.4384	0.401658
$960$	−1.56155	−0.0503989
$961$	−31.0000	−1.00000
$962$	0	0
$963$	13.9309	0.448916
$964$	−0.192236	−0.00619150
$965$	0.192236	0.00618829
$966$	1.12311	0.0361353
$967$	−28.4924	−0.916255	−0.458127	−	0.888887i	$-0.651480\pi$
$967$	−28.4924	−0.916255	−0.458127	+	0.888887i	$0.651480\pi$
$968$	−4.43845	−0.142657
$969$	0.315342	0.0101302
$970$	−1.36932	−0.0439661
$971$	41.6155	1.33551	0.667753	−	0.744383i	$-0.267256\pi$
$971$	41.6155	1.33551	0.667753	+	0.744383i	$0.267256\pi$
$972$	−1.00000	−0.0320750
$973$	−5.43845	−0.174349
$974$	23.6847	0.758905
$975$	0	0
$976$	−11.2462	−0.359982
$977$	−41.1771	−1.31737	−0.658686	−	0.752418i	$-0.728887\pi$
$977$	−41.1771	−1.31737	−0.658686	+	0.752418i	$0.728887\pi$
$978$	−24.4924	−0.783181
$979$	−8.80776	−0.281497
$980$	1.56155	0.0498820
$981$	−12.2462	−0.390991
$982$	−16.4924	−0.526294
$983$	18.7386	0.597670	0.298835	−	0.954305i	$-0.403402\pi$
$983$	18.7386	0.597670	0.298835	+	0.954305i	$0.403402\pi$
$984$	11.2462	0.358516
$985$	19.6155	0.625003
$986$	−0.753789	−0.0240055
$987$	0.315342	0.0100374
$988$	0	0
$989$	8.98485	0.285701
$990$	−4.00000	−0.127128
$991$	−28.6695	−0.910717	−0.455358	−	0.890308i	$-0.650489\pi$
$991$	−28.6695	−0.910717	−0.455358	+	0.890308i	$0.650489\pi$
$992$	0	0
$993$	−19.3693	−0.614667
$994$	−11.3693	−0.360613
$995$	−24.9848	−0.792073
$996$	5.12311	0.162332
$997$	−41.9848	−1.32967	−0.664837	−	0.746989i	$-0.731499\pi$
$997$	−41.9848	−1.32967	−0.664837	+	0.746989i	$0.731499\pi$
$998$	30.2462	0.957427
$999$	2.43845	0.0771491

Twists

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.56155 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.56155 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.56155 q^{10} -2.56155 q^{11} -1.00000 q^{12} +1.00000 q^{14} -1.56155 q^{15} +1.00000 q^{16} +0.123106 q^{17} +1.00000 q^{18} -2.56155 q^{19} +1.56155 q^{20} -1.00000 q^{21} -2.56155 q^{22} -1.12311 q^{23} -1.00000 q^{24} -2.56155 q^{25} -1.00000 q^{27} +1.00000 q^{28} -6.12311 q^{29} -1.56155 q^{30} +1.00000 q^{32} +2.56155 q^{33} +0.123106 q^{34} +1.56155 q^{35} +1.00000 q^{36} -2.43845 q^{37} -2.56155 q^{38} +1.56155 q^{40} -11.2462 q^{41} -1.00000 q^{42} -8.00000 q^{43} -2.56155 q^{44} +1.56155 q^{45} -1.12311 q^{46} -0.315342 q^{47} -1.00000 q^{48} +1.00000 q^{49} -2.56155 q^{50} -0.123106 q^{51} +7.00000 q^{53} -1.00000 q^{54} -4.00000 q^{55} +1.00000 q^{56} +2.56155 q^{57} -6.12311 q^{58} +5.12311 q^{59} -1.56155 q^{60} -11.2462 q^{61} +1.00000 q^{63} +1.00000 q^{64} +2.56155 q^{66} +9.12311 q^{67} +0.123106 q^{68} +1.12311 q^{69} +1.56155 q^{70} -11.3693 q^{71} +1.00000 q^{72} -2.43845 q^{73} -2.43845 q^{74} +2.56155 q^{75} -2.56155 q^{76} -2.56155 q^{77} -6.56155 q^{79} +1.56155 q^{80} +1.00000 q^{81} -11.2462 q^{82} -5.12311 q^{83} -1.00000 q^{84} +0.192236 q^{85} -8.00000 q^{86} +6.12311 q^{87} -2.56155 q^{88} +3.43845 q^{89} +1.56155 q^{90} -1.12311 q^{92} -0.315342 q^{94} -4.00000 q^{95} -1.00000 q^{96} -0.876894 q^{97} +1.00000 q^{98} -2.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - q^{5} - 2 q^{6} + 2 q^{7} + 2 q^{8} + 2 q^{9} - q^{10} - q^{11} - 2 q^{12} + 2 q^{14} + q^{15} + 2 q^{16} - 8 q^{17} + 2 q^{18} - q^{19} - q^{20} - 2 q^{21} - q^{22} + 6 q^{23} - 2 q^{24} - q^{25} - 2 q^{27} + 2 q^{28} - 4 q^{29} + q^{30} + 2 q^{32} + q^{33} - 8 q^{34} - q^{35} + 2 q^{36} - 9 q^{37} - q^{38} - q^{40} - 6 q^{41} - 2 q^{42} - 16 q^{43} - q^{44} - q^{45} + 6 q^{46} - 13 q^{47} - 2 q^{48} + 2 q^{49} - q^{50} + 8 q^{51} + 14 q^{53} - 2 q^{54} - 8 q^{55} + 2 q^{56} + q^{57} - 4 q^{58} + 2 q^{59} + q^{60} - 6 q^{61} + 2 q^{63} + 2 q^{64} + q^{66} + 10 q^{67} - 8 q^{68} - 6 q^{69} - q^{70} + 2 q^{71} + 2 q^{72} - 9 q^{73} - 9 q^{74} + q^{75} - q^{76} - q^{77} - 9 q^{79} - q^{80} + 2 q^{81} - 6 q^{82} - 2 q^{83} - 2 q^{84} + 21 q^{85} - 16 q^{86} + 4 q^{87} - q^{88} + 11 q^{89} - q^{90} + 6 q^{92} - 13 q^{94} - 8 q^{95} - 2 q^{96} - 10 q^{97} + 2 q^{98} - q^{99}+O(q^{100}) \) 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 - q^11 - 2 * q^12 + 2 * q^14 + q^15 + 2 * q^16 - 8 * q^17 + 2 * q^18 - q^19 - q^20 - 2 * q^21 - q^22 + 6 * q^23 - 2 * q^24 - q^25 - 2 * q^27 + 2 * q^28 - 4 * q^29 + q^30 + 2 * q^32 + q^33 - 8 * q^34 - q^35 + 2 * q^36 - 9 * q^37 - q^38 - q^40 - 6 * q^41 - 2 * q^42 - 16 * q^43 - q^44 - q^45 + 6 * q^46 - 13 * q^47 - 2 * q^48 + 2 * q^49 - q^50 + 8 * q^51 + 14 * q^53 - 2 * q^54 - 8 * q^55 + 2 * q^56 + q^57 - 4 * q^58 + 2 * q^59 + q^60 - 6 * q^61 + 2 * q^63 + 2 * q^64 + q^66 + 10 * q^67 - 8 * q^68 - 6 * q^69 - q^70 + 2 * q^71 + 2 * q^72 - 9 * q^73 - 9 * q^74 + q^75 - q^76 - q^77 - 9 * q^79 - q^80 + 2 * q^81 - 6 * q^82 - 2 * q^83 - 2 * q^84 + 21 * q^85 - 16 * q^86 + 4 * q^87 - q^88 + 11 * q^89 - q^90 + 6 * q^92 - 13 * q^94 - 8 * q^95 - 2 * q^96 - 10 * q^97 + 2 * q^98 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more