LMFDB - Embedded newform 7098.2.a.bu.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("7098.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$56.6778153547$
Analytic rank:	$0$
Dimension:	$2$
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			1.2
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.27492 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.27492 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.27492 q^{10} +2.27492 q^{11} -1.00000 q^{12} -1.00000 q^{14} -4.27492 q^{15} +1.00000 q^{16} +0.274917 q^{17} +1.00000 q^{18} +2.27492 q^{19} +4.27492 q^{20} +1.00000 q^{21} +2.27492 q^{22} +2.27492 q^{23} -1.00000 q^{24} +13.2749 q^{25} -1.00000 q^{27} -1.00000 q^{28} +8.27492 q^{29} -4.27492 q^{30} -8.00000 q^{31} +1.00000 q^{32} -2.27492 q^{33} +0.274917 q^{34} -4.27492 q^{35} +1.00000 q^{36} +4.27492 q^{37} +2.27492 q^{38} +4.27492 q^{40} -6.54983 q^{41} +1.00000 q^{42} -2.27492 q^{43} +2.27492 q^{44} +4.27492 q^{45} +2.27492 q^{46} -1.00000 q^{48} +1.00000 q^{49} +13.2749 q^{50} -0.274917 q^{51} +10.0000 q^{53} -1.00000 q^{54} +9.72508 q^{55} -1.00000 q^{56} -2.27492 q^{57} +8.27492 q^{58} -8.00000 q^{59} -4.27492 q^{60} -12.2749 q^{61} -8.00000 q^{62} -1.00000 q^{63} +1.00000 q^{64} -2.27492 q^{66} -12.5498 q^{67} +0.274917 q^{68} -2.27492 q^{69} -4.27492 q^{70} +1.00000 q^{72} +12.8248 q^{73} +4.27492 q^{74} -13.2749 q^{75} +2.27492 q^{76} -2.27492 q^{77} +12.5498 q^{79} +4.27492 q^{80} +1.00000 q^{81} -6.54983 q^{82} +4.54983 q^{83} +1.00000 q^{84} +1.17525 q^{85} -2.27492 q^{86} -8.27492 q^{87} +2.27492 q^{88} +14.0000 q^{89} +4.27492 q^{90} +2.27492 q^{92} +8.00000 q^{93} +9.72508 q^{95} -1.00000 q^{96} -15.0997 q^{97} +1.00000 q^{98} +2.27492 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 3 q^{11} - 2 q^{12} - 2 q^{14} - q^{15} + 2 q^{16} - 7 q^{17} + 2 q^{18} - 3 q^{19} + q^{20} + 2 q^{21} - 3 q^{22} - 3 q^{23} - 2 q^{24} + 19 q^{25} - 2 q^{27} - 2 q^{28} + 9 q^{29} - q^{30} - 16 q^{31} + 2 q^{32} + 3 q^{33} - 7 q^{34} - q^{35} + 2 q^{36} + q^{37} - 3 q^{38} + q^{40} + 2 q^{41} + 2 q^{42} + 3 q^{43} - 3 q^{44} + q^{45} - 3 q^{46} - 2 q^{48} + 2 q^{49} + 19 q^{50} + 7 q^{51} + 20 q^{53} - 2 q^{54} + 27 q^{55} - 2 q^{56} + 3 q^{57} + 9 q^{58} - 16 q^{59} - q^{60} - 17 q^{61} - 16 q^{62} - 2 q^{63} + 2 q^{64} + 3 q^{66} - 10 q^{67} - 7 q^{68} + 3 q^{69} - q^{70} + 2 q^{72} + 3 q^{73} + q^{74} - 19 q^{75} - 3 q^{76} + 3 q^{77} + 10 q^{79} + q^{80} + 2 q^{81} + 2 q^{82} - 6 q^{83} + 2 q^{84} + 25 q^{85} + 3 q^{86} - 9 q^{87} - 3 q^{88} + 28 q^{89} + q^{90} - 3 q^{92} + 16 q^{93} + 27 q^{95} - 2 q^{96} + 2 q^{98} - 3 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 - 3 * q^11 - 2 * q^12 - 2 * q^14 - q^15 + 2 * q^16 - 7 * q^17 + 2 * q^18 - 3 * q^19 + q^20 + 2 * q^21 - 3 * q^22 - 3 * q^23 - 2 * q^24 + 19 * q^25 - 2 * q^27 - 2 * q^28 + 9 * q^29 - q^30 - 16 * q^31 + 2 * q^32 + 3 * q^33 - 7 * q^34 - q^35 + 2 * q^36 + q^37 - 3 * q^38 + q^40 + 2 * q^41 + 2 * q^42 + 3 * q^43 - 3 * q^44 + q^45 - 3 * q^46 - 2 * q^48 + 2 * q^49 + 19 * q^50 + 7 * q^51 + 20 * q^53 - 2 * q^54 + 27 * q^55 - 2 * q^56 + 3 * q^57 + 9 * q^58 - 16 * q^59 - q^60 - 17 * q^61 - 16 * q^62 - 2 * q^63 + 2 * q^64 + 3 * q^66 - 10 * q^67 - 7 * q^68 + 3 * q^69 - q^70 + 2 * q^72 + 3 * q^73 + q^74 - 19 * q^75 - 3 * q^76 + 3 * q^77 + 10 * q^79 + q^80 + 2 * q^81 + 2 * q^82 - 6 * q^83 + 2 * q^84 + 25 * q^85 + 3 * q^86 - 9 * q^87 - 3 * q^88 + 28 * q^89 + q^90 - 3 * q^92 + 16 * q^93 + 27 * q^95 - 2 * q^96 + 2 * q^98 - 3 * 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	$-0.0948835\pi$
$5$	4.27492	1.91180	0.955901	+	0.293691i	$0.0948835\pi$
$6$	−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
$11$	2.27492	0.685913	0.342957	−	0.939351i	$-0.388572\pi$
$11$	2.27492	0.685913	0.342957	+	0.939351i	$0.388572\pi$
$12$	−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
$17$	0.274917	0.0666772	0.0333386	−	0.999444i	$-0.489386\pi$
$17$	0.274917	0.0666772	0.0333386	+	0.999444i	$0.489386\pi$
$18$	1.00000	0.235702
$19$	2.27492	0.521902	0.260951	−	0.965352i	$-0.415964\pi$
$19$	2.27492	0.521902	0.260951	+	0.965352i	$0.415964\pi$
$20$	4.27492	0.955901
$21$	1.00000	0.218218
$22$	2.27492	0.485014
$23$	2.27492	0.474353	0.237177	−	0.971467i	$-0.423778\pi$
$23$	2.27492	0.474353	0.237177	+	0.971467i	$0.423778\pi$
$24$	−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
$31$	−8.00000	−1.43684	−0.718421	−	0.695608i	$-0.755135\pi$
$31$	−8.00000	−1.43684	−0.718421	+	0.695608i	$0.755135\pi$
$32$	1.00000	0.176777
$33$	−2.27492	−0.396012
$34$	0.274917	0.0471479
$35$	−4.27492	−0.722593
$36$	1.00000	0.166667
$37$	4.27492	0.702792	0.351396	−	0.936227i	$-0.385707\pi$
$37$	4.27492	0.702792	0.351396	+	0.936227i	$0.385707\pi$
$38$	2.27492	0.369040
$39$	0	0
$40$	4.27492	0.675924
$41$	−6.54983	−1.02291	−0.511456	−	0.859309i	$-0.670894\pi$
$41$	−6.54983	−1.02291	−0.511456	+	0.859309i	$0.670894\pi$
$42$	1.00000	0.154303
$43$	−2.27492	−0.346922	−0.173461	−	0.984841i	$-0.555495\pi$
$43$	−2.27492	−0.346922	−0.173461	+	0.984841i	$0.555495\pi$
$44$	2.27492	0.342957
$45$	4.27492	0.637267
$46$	2.27492	0.335418
$47$	0	0		−	1.00000i	$-0.5\pi$
$47$	0	0			1.00000i	$0.5\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	13.2749	1.87736
$51$	−0.274917	−0.0384961
$52$	0	0
$53$	10.0000	1.37361	0.686803	−	0.726844i	$-0.259014\pi$
$53$	10.0000	1.37361	0.686803	+	0.726844i	$0.259014\pi$
$54$	−1.00000	−0.136083
$55$	9.72508	1.31133
$56$	−1.00000	−0.133631
$57$	−2.27492	−0.301320
$58$	8.27492	1.08655
$59$	−8.00000	−1.04151	−0.520756	−	0.853706i	$-0.674350\pi$
$59$	−8.00000	−1.04151	−0.520756	+	0.853706i	$0.674350\pi$
$60$	−4.27492	−0.551889
$61$	−12.2749	−1.57164	−0.785821	−	0.618454i	$-0.787759\pi$
$61$	−12.2749	−1.57164	−0.785821	+	0.618454i	$0.787759\pi$
$62$	−8.00000	−1.01600
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	0	0
$66$	−2.27492	−0.280023
$67$	−12.5498	−1.53321	−0.766603	−	0.642121i	$-0.778055\pi$
$67$	−12.5498	−1.53321	−0.766603	+	0.642121i	$0.778055\pi$
$68$	0.274917	0.0333386
$69$	−2.27492	−0.273868
$70$	−4.27492	−0.510950
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	1.00000	0.117851
$73$	12.8248	1.50102	0.750512	−	0.660857i	$-0.229807\pi$
$73$	12.8248	1.50102	0.750512	+	0.660857i	$0.229807\pi$
$74$	4.27492	0.496949
$75$	−13.2749	−1.53286
$76$	2.27492	0.260951
$77$	−2.27492	−0.259251
$78$	0	0
$79$	12.5498	1.41197	0.705983	−	0.708228i	$-0.250505\pi$
$79$	12.5498	1.41197	0.705983	+	0.708228i	$0.250505\pi$
$80$	4.27492	0.477950
$81$	1.00000	0.111111
$82$	−6.54983	−0.723308
$83$	4.54983	0.499409	0.249705	−	0.968322i	$-0.419666\pi$
$83$	4.54983	0.499409	0.249705	+	0.968322i	$0.419666\pi$
$84$	1.00000	0.109109
$85$	1.17525	0.127474
$86$	−2.27492	−0.245311
$87$	−8.27492	−0.887164
$88$	2.27492	0.242507
$89$	14.0000	1.48400	0.741999	−	0.670402i	$-0.233878\pi$
$89$	14.0000	1.48400	0.741999	+	0.670402i	$0.233878\pi$
$90$	4.27492	0.450616
$91$	0	0
$92$	2.27492	0.237177
$93$	8.00000	0.829561
$94$	0	0
$95$	9.72508	0.997772
$96$	−1.00000	−0.102062
$97$	−15.0997	−1.53314	−0.766570	−	0.642161i	$-0.778038\pi$
$97$	−15.0997	−1.53314	−0.766570	+	0.642161i	$0.778038\pi$
$98$	1.00000	0.101015
$99$	2.27492	0.228638
$100$	13.2749	1.32749
$101$	2.54983	0.253718	0.126859	−	0.991921i	$-0.459510\pi$
$101$	2.54983	0.253718	0.126859	+	0.991921i	$0.459510\pi$
$102$	−0.274917	−0.0272209
$103$	10.2749	1.01242	0.506209	−	0.862411i	$-0.331046\pi$
$103$	10.2749	1.01242	0.506209	+	0.862411i	$0.331046\pi$
$104$	0	0
$105$	4.27492	0.417189
$106$	10.0000	0.971286
$107$	0.549834	0.0531545	0.0265773	−	0.999647i	$-0.491539\pi$
$107$	0.549834	0.0531545	0.0265773	+	0.999647i	$0.491539\pi$
$108$	−1.00000	−0.0962250
$109$	−0.274917	−0.0263323	−0.0131661	−	0.999913i	$-0.504191\pi$
$109$	−0.274917	−0.0263323	−0.0131661	+	0.999913i	$0.504191\pi$
$110$	9.72508	0.927250
$111$	−4.27492	−0.405757
$112$	−1.00000	−0.0944911
$113$	−6.00000	−0.564433	−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000	−0.564433	−0.282216	+	0.959351i	$0.591070\pi$
$114$	−2.27492	−0.213066
$115$	9.72508	0.906869
$116$	8.27492	0.768307
$117$	0	0
$118$	−8.00000	−0.736460
$119$	−0.274917	−0.0252016
$120$	−4.27492	−0.390245
$121$	−5.82475	−0.529523
$122$	−12.2749	−1.11132
$123$	6.54983	0.590579
$124$	−8.00000	−0.718421
$125$	35.3746	3.16400
$126$	−1.00000	−0.0890871
$127$	−20.5498	−1.82350	−0.911751	−	0.410742i	$-0.865270\pi$
$127$	−20.5498	−1.82350	−0.911751	+	0.410742i	$0.865270\pi$
$128$	1.00000	0.0883883
$129$	2.27492	0.200295
$130$	0	0
$131$	6.82475	0.596281	0.298141	−	0.954522i	$-0.403634\pi$
$131$	6.82475	0.596281	0.298141	+	0.954522i	$0.403634\pi$
$132$	−2.27492	−0.198006
$133$	−2.27492	−0.197260
$134$	−12.5498	−1.08414
$135$	−4.27492	−0.367926
$136$	0.274917	0.0235740
$137$	17.3746	1.48441	0.742206	−	0.670172i	$-0.233780\pi$
$137$	17.3746	1.48441	0.742206	+	0.670172i	$0.233780\pi$
$138$	−2.27492	−0.193654
$139$	4.00000	0.339276	0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000	0.339276	0.169638	+	0.985506i	$0.445740\pi$
$140$	−4.27492	−0.361296
$141$	0	0
$142$	0	0
$143$	0	0
$144$	1.00000	0.0833333
$145$	35.3746	2.93770
$146$	12.8248	1.06138
$147$	−1.00000	−0.0824786
$148$	4.27492	0.351396
$149$	−22.5498	−1.84735	−0.923677	−	0.383172i	$-0.874832\pi$
$149$	−22.5498	−1.84735	−0.923677	+	0.383172i	$0.874832\pi$
$150$	−13.2749	−1.08389
$151$	−6.27492	−0.510646	−0.255323	−	0.966856i	$-0.582182\pi$
$151$	−6.27492	−0.510646	−0.255323	+	0.966856i	$0.582182\pi$
$152$	2.27492	0.184520
$153$	0.274917	0.0222257
$154$	−2.27492	−0.183318
$155$	−34.1993	−2.74696
$156$	0	0
$157$	−13.3746	−1.06741	−0.533704	−	0.845671i	$-0.679200\pi$
$157$	−13.3746	−1.06741	−0.533704	+	0.845671i	$0.679200\pi$
$158$	12.5498	0.998411
$159$	−10.0000	−0.793052
$160$	4.27492	0.337962
$161$	−2.27492	−0.179289
$162$	1.00000	0.0785674
$163$	−12.5498	−0.982979	−0.491489	−	0.870884i	$-0.663547\pi$
$163$	−12.5498	−0.982979	−0.491489	+	0.870884i	$0.663547\pi$
$164$	−6.54983	−0.511456
$165$	−9.72508	−0.757097
$166$	4.54983	0.353136
$167$	1.72508	0.133491	0.0667455	−	0.997770i	$-0.478738\pi$
$167$	1.72508	0.133491	0.0667455	+	0.997770i	$0.478738\pi$
$168$	1.00000	0.0771517
$169$	0	0
$170$	1.17525	0.0901374
$171$	2.27492	0.173967
$172$	−2.27492	−0.173461
$173$	7.09967	0.539778	0.269889	−	0.962891i	$-0.413013\pi$
$173$	7.09967	0.539778	0.269889	+	0.962891i	$0.413013\pi$
$174$	−8.27492	−0.627320
$175$	−13.2749	−1.00349
$176$	2.27492	0.171478
$177$	8.00000	0.601317
$178$	14.0000	1.04934
$179$	12.0000	0.896922	0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000	0.896922	0.448461	+	0.893802i	$0.351972\pi$
$180$	4.27492	0.318634
$181$	19.0997	1.41967	0.709834	−	0.704369i	$-0.248770\pi$
$181$	19.0997	1.41967	0.709834	+	0.704369i	$0.248770\pi$
$182$	0	0
$183$	12.2749	0.907388
$184$	2.27492	0.167709
$185$	18.2749	1.34360
$186$	8.00000	0.586588
$187$	0.625414	0.0457348
$188$	0	0
$189$	1.00000	0.0727393
$190$	9.72508	0.705532
$191$	2.27492	0.164607	0.0823036	−	0.996607i	$-0.473772\pi$
$191$	2.27492	0.164607	0.0823036	+	0.996607i	$0.473772\pi$
$192$	−1.00000	−0.0721688
$193$	18.5498	1.33525	0.667623	−	0.744499i	$-0.267312\pi$
$193$	18.5498	1.33525	0.667623	+	0.744499i	$0.267312\pi$
$194$	−15.0997	−1.08409
$195$	0	0
$196$	1.00000	0.0714286
$197$	2.54983	0.181668	0.0908341	−	0.995866i	$-0.471047\pi$
$197$	2.54983	0.181668	0.0908341	+	0.995866i	$0.471047\pi$
$198$	2.27492	0.161671
$199$	6.82475	0.483794	0.241897	−	0.970302i	$-0.422230\pi$
$199$	6.82475	0.483794	0.241897	+	0.970302i	$0.422230\pi$
$200$	13.2749	0.938678
$201$	12.5498	0.885197
$202$	2.54983	0.179406
$203$	−8.27492	−0.580785
$204$	−0.274917	−0.0192481
$205$	−28.0000	−1.95560
$206$	10.2749	0.715887
$207$	2.27492	0.158118
$208$	0	0
$209$	5.17525	0.357979
$210$	4.27492	0.294997
$211$	1.17525	0.0809074	0.0404537	−	0.999181i	$-0.487120\pi$
$211$	1.17525	0.0809074	0.0404537	+	0.999181i	$0.487120\pi$
$212$	10.0000	0.686803
$213$	0	0
$214$	0.549834	0.0375859
$215$	−9.72508	−0.663245
$216$	−1.00000	−0.0680414
$217$	8.00000	0.543075
$218$	−0.274917	−0.0186197
$219$	−12.8248	−0.866616
$220$	9.72508	0.655665
$221$	0	0
$222$	−4.27492	−0.286914
$223$	−21.6495	−1.44976	−0.724879	−	0.688876i	$-0.758104\pi$
$223$	−21.6495	−1.44976	−0.724879	+	0.688876i	$0.758104\pi$
$224$	−1.00000	−0.0668153
$225$	13.2749	0.884994
$226$	−6.00000	−0.399114
$227$	20.5498	1.36394	0.681970	−	0.731380i	$-0.261123\pi$
$227$	20.5498	1.36394	0.681970	+	0.731380i	$0.261123\pi$
$228$	−2.27492	−0.150660
$229$	−19.0997	−1.26214	−0.631071	−	0.775725i	$-0.717384\pi$
$229$	−19.0997	−1.26214	−0.631071	+	0.775725i	$0.717384\pi$
$230$	9.72508	0.641253
$231$	2.27492	0.149679
$232$	8.27492	0.543275
$233$	5.45017	0.357052	0.178526	−	0.983935i	$-0.442867\pi$
$233$	5.45017	0.357052	0.178526	+	0.983935i	$0.442867\pi$
$234$	0	0
$235$	0	0
$236$	−8.00000	−0.520756
$237$	−12.5498	−0.815199
$238$	−0.274917	−0.0178202
$239$	−25.0997	−1.62356	−0.811781	−	0.583962i	$-0.801502\pi$
$239$	−25.0997	−1.62356	−0.811781	+	0.583962i	$0.801502\pi$
$240$	−4.27492	−0.275945
$241$	−15.0997	−0.972655	−0.486328	−	0.873777i	$-0.661664\pi$
$241$	−15.0997	−0.972655	−0.486328	+	0.873777i	$0.661664\pi$
$242$	−5.82475	−0.374429
$243$	−1.00000	−0.0641500
$244$	−12.2749	−0.785821
$245$	4.27492	0.273114
$246$	6.54983	0.417602
$247$	0	0
$248$	−8.00000	−0.508001
$249$	−4.54983	−0.288334
$250$	35.3746	2.23729
$251$	23.9244	1.51010	0.755048	−	0.655669i	$-0.227614\pi$
$251$	23.9244	1.51010	0.755048	+	0.655669i	$0.227614\pi$
$252$	−1.00000	−0.0629941
$253$	5.17525	0.325365
$254$	−20.5498	−1.28941
$255$	−1.17525	−0.0735969
$256$	1.00000	0.0625000
$257$	−14.0000	−0.873296	−0.436648	−	0.899632i	$-0.643834\pi$
$257$	−14.0000	−0.873296	−0.436648	+	0.899632i	$0.643834\pi$
$258$	2.27492	0.141630
$259$	−4.27492	−0.265630
$260$	0	0
$261$	8.27492	0.512205
$262$	6.82475	0.421635
$263$	28.0000	1.72655	0.863277	−	0.504730i	$-0.168408\pi$
$263$	28.0000	1.72655	0.863277	+	0.504730i	$0.168408\pi$
$264$	−2.27492	−0.140011
$265$	42.7492	2.62606
$266$	−2.27492	−0.139484
$267$	−14.0000	−0.856786
$268$	−12.5498	−0.766603
$269$	6.00000	0.365826	0.182913	−	0.983129i	$-0.441447\pi$
$269$	6.00000	0.365826	0.182913	+	0.983129i	$0.441447\pi$
$270$	−4.27492	−0.260163
$271$	−28.5498	−1.73428	−0.867139	−	0.498065i	$-0.834044\pi$
$271$	−28.5498	−1.73428	−0.867139	+	0.498065i	$0.834044\pi$
$272$	0.274917	0.0166693
$273$	0	0
$274$	17.3746	1.04964
$275$	30.1993	1.82109
$276$	−2.27492	−0.136934
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	4.00000	0.239904
$279$	−8.00000	−0.478947
$280$	−4.27492	−0.255475
$281$	−15.0997	−0.900771	−0.450385	−	0.892834i	$-0.648713\pi$
$281$	−15.0997	−0.900771	−0.450385	+	0.892834i	$0.648713\pi$
$282$	0	0
$283$	−4.00000	−0.237775	−0.118888	−	0.992908i	$-0.537933\pi$
$283$	−4.00000	−0.237775	−0.118888	+	0.992908i	$0.537933\pi$
$284$	0	0
$285$	−9.72508	−0.576064
$286$	0	0
$287$	6.54983	0.386625
$288$	1.00000	0.0589256
$289$	−16.9244	−0.995554
$290$	35.3746	2.07727
$291$	15.0997	0.885158
$292$	12.8248	0.750512
$293$	6.00000	0.350524	0.175262	−	0.984522i	$-0.443923\pi$
$293$	6.00000	0.350524	0.175262	+	0.984522i	$0.443923\pi$
$294$	−1.00000	−0.0583212
$295$	−34.1993	−1.99116
$296$	4.27492	0.248475
$297$	−2.27492	−0.132004
$298$	−22.5498	−1.30628
$299$	0	0
$300$	−13.2749	−0.766428
$301$	2.27492	0.131124
$302$	−6.27492	−0.361081
$303$	−2.54983	−0.146484
$304$	2.27492	0.130475
$305$	−52.4743	−3.00467
$306$	0.274917	0.0157160
$307$	−21.0997	−1.20422	−0.602111	−	0.798412i	$-0.705673\pi$
$307$	−21.0997	−1.20422	−0.602111	+	0.798412i	$0.705673\pi$
$308$	−2.27492	−0.129625
$309$	−10.2749	−0.584520
$310$	−34.1993	−1.94239
$311$	3.45017	0.195641	0.0978205	−	0.995204i	$-0.468813\pi$
$311$	3.45017	0.195641	0.0978205	+	0.995204i	$0.468813\pi$
$312$	0	0
$313$	−27.6495	−1.56284	−0.781421	−	0.624004i	$-0.785505\pi$
$313$	−27.6495	−1.56284	−0.781421	+	0.624004i	$0.785505\pi$
$314$	−13.3746	−0.754772
$315$	−4.27492	−0.240864
$316$	12.5498	0.705983
$317$	1.45017	0.0814494	0.0407247	−	0.999170i	$-0.487033\pi$
$317$	1.45017	0.0814494	0.0407247	+	0.999170i	$0.487033\pi$
$318$	−10.0000	−0.560772
$319$	18.8248	1.05398
$320$	4.27492	0.238975
$321$	−0.549834	−0.0306888
$322$	−2.27492	−0.126776
$323$	0.625414	0.0347990
$324$	1.00000	0.0555556
$325$	0	0
$326$	−12.5498	−0.695071
$327$	0.274917	0.0152030
$328$	−6.54983	−0.361654
$329$	0	0
$330$	−9.72508	−0.535348
$331$	29.6495	1.62968	0.814842	−	0.579683i	$-0.196824\pi$
$331$	29.6495	1.62968	0.814842	+	0.579683i	$0.196824\pi$
$332$	4.54983	0.249705
$333$	4.27492	0.234264
$334$	1.72508	0.0943923
$335$	−53.6495	−2.93119
$336$	1.00000	0.0545545
$337$	9.37459	0.510666	0.255333	−	0.966853i	$-0.417815\pi$
$337$	9.37459	0.510666	0.255333	+	0.966853i	$0.417815\pi$
$338$	0	0
$339$	6.00000	0.325875
$340$	1.17525	0.0637368
$341$	−18.1993	−0.985549
$342$	2.27492	0.123013
$343$	−1.00000	−0.0539949
$344$	−2.27492	−0.122655
$345$	−9.72508	−0.523581
$346$	7.09967	0.381681
$347$	5.09967	0.273765	0.136882	−	0.990587i	$-0.456292\pi$
$347$	5.09967	0.273765	0.136882	+	0.990587i	$0.456292\pi$
$348$	−8.27492	−0.443582
$349$	−2.00000	−0.107058	−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000	−0.107058	−0.0535288	+	0.998566i	$0.517047\pi$
$350$	−13.2749	−0.709574
$351$	0	0
$352$	2.27492	0.121253
$353$	−27.0997	−1.44237	−0.721185	−	0.692743i	$-0.756402\pi$
$353$	−27.0997	−1.44237	−0.721185	+	0.692743i	$0.756402\pi$
$354$	8.00000	0.425195
$355$	0	0
$356$	14.0000	0.741999
$357$	0.274917	0.0145502
$358$	12.0000	0.634220
$359$	32.0000	1.68890	0.844448	−	0.535638i	$-0.179929\pi$
$359$	32.0000	1.68890	0.844448	+	0.535638i	$0.179929\pi$
$360$	4.27492	0.225308
$361$	−13.8248	−0.727619
$362$	19.0997	1.00386
$363$	5.82475	0.305720
$364$	0	0
$365$	54.8248	2.86966
$366$	12.2749	0.641620
$367$	−2.90033	−0.151396	−0.0756980	−	0.997131i	$-0.524119\pi$
$367$	−2.90033	−0.151396	−0.0756980	+	0.997131i	$0.524119\pi$
$368$	2.27492	0.118588
$369$	−6.54983	−0.340971
$370$	18.2749	0.950068
$371$	−10.0000	−0.519174
$372$	8.00000	0.414781
$373$	26.5498	1.37470	0.687349	−	0.726327i	$-0.258774\pi$
$373$	26.5498	1.37470	0.687349	+	0.726327i	$0.258774\pi$
$374$	0.625414	0.0323394
$375$	−35.3746	−1.82674
$376$	0	0
$377$	0	0
$378$	1.00000	0.0514344
$379$	33.0997	1.70022	0.850108	−	0.526609i	$-0.176537\pi$
$379$	33.0997	1.70022	0.850108	+	0.526609i	$0.176537\pi$
$380$	9.72508	0.498886
$381$	20.5498	1.05280
$382$	2.27492	0.116395
$383$	−30.2749	−1.54698	−0.773488	−	0.633811i	$-0.781490\pi$
$383$	−30.2749	−1.54698	−0.773488	+	0.633811i	$0.781490\pi$
$384$	−1.00000	−0.0510310
$385$	−9.72508	−0.495636
$386$	18.5498	0.944162
$387$	−2.27492	−0.115641
$388$	−15.0997	−0.766570
$389$	28.1993	1.42976	0.714882	−	0.699246i	$-0.246481\pi$
$389$	28.1993	1.42976	0.714882	+	0.699246i	$0.246481\pi$
$390$	0	0
$391$	0.625414	0.0316285
$392$	1.00000	0.0505076
$393$	−6.82475	−0.344263
$394$	2.54983	0.128459
$395$	53.6495	2.69940
$396$	2.27492	0.114319
$397$	14.0000	0.702640	0.351320	−	0.936255i	$-0.385733\pi$
$397$	14.0000	0.702640	0.351320	+	0.936255i	$0.385733\pi$
$398$	6.82475	0.342094
$399$	2.27492	0.113888
$400$	13.2749	0.663746
$401$	3.09967	0.154790	0.0773950	−	0.997001i	$-0.475340\pi$
$401$	3.09967	0.154790	0.0773950	+	0.997001i	$0.475340\pi$
$402$	12.5498	0.625929
$403$	0	0
$404$	2.54983	0.126859
$405$	4.27492	0.212422
$406$	−8.27492	−0.410677
$407$	9.72508	0.482054
$408$	−0.274917	−0.0136104
$409$	7.17525	0.354793	0.177397	−	0.984139i	$-0.443232\pi$
$409$	7.17525	0.354793	0.177397	+	0.984139i	$0.443232\pi$
$410$	−28.0000	−1.38282
$411$	−17.3746	−0.857025
$412$	10.2749	0.506209
$413$	8.00000	0.393654
$414$	2.27492	0.111806
$415$	19.4502	0.954771
$416$	0	0
$417$	−4.00000	−0.195881
$418$	5.17525	0.253130
$419$	2.27492	0.111137	0.0555685	−	0.998455i	$-0.482303\pi$
$419$	2.27492	0.111137	0.0555685	+	0.998455i	$0.482303\pi$
$420$	4.27492	0.208595
$421$	−3.09967	−0.151069	−0.0755343	−	0.997143i	$-0.524066\pi$
$421$	−3.09967	−0.151069	−0.0755343	+	0.997143i	$0.524066\pi$
$422$	1.17525	0.0572102
$423$	0	0
$424$	10.0000	0.485643
$425$	3.64950	0.177027
$426$	0	0
$427$	12.2749	0.594025
$428$	0.549834	0.0265773
$429$	0	0
$430$	−9.72508	−0.468985
$431$	11.4502	0.551535	0.275768	−	0.961224i	$-0.411068\pi$
$431$	11.4502	0.551535	0.275768	+	0.961224i	$0.411068\pi$
$432$	−1.00000	−0.0481125
$433$	23.6495	1.13652	0.568261	−	0.822848i	$-0.307616\pi$
$433$	23.6495	1.13652	0.568261	+	0.822848i	$0.307616\pi$
$434$	8.00000	0.384012
$435$	−35.3746	−1.69608
$436$	−0.274917	−0.0131661
$437$	5.17525	0.247566
$438$	−12.8248	−0.612790
$439$	−14.8248	−0.707547	−0.353773	−	0.935331i	$-0.615102\pi$
$439$	−14.8248	−0.707547	−0.353773	+	0.935331i	$0.615102\pi$
$440$	9.72508	0.463625
$441$	1.00000	0.0476190
$442$	0	0
$443$	7.45017	0.353968	0.176984	−	0.984214i	$-0.443366\pi$
$443$	7.45017	0.353968	0.176984	+	0.984214i	$0.443366\pi$
$444$	−4.27492	−0.202879
$445$	59.8488	2.83711
$446$	−21.6495	−1.02513
$447$	22.5498	1.06657
$448$	−1.00000	−0.0472456
$449$	0.274917	0.0129741	0.00648707	−	0.999979i	$-0.497935\pi$
$449$	0.274917	0.0129741	0.00648707	+	0.999979i	$0.497935\pi$
$450$	13.2749	0.625786
$451$	−14.9003	−0.701629
$452$	−6.00000	−0.282216
$453$	6.27492	0.294821
$454$	20.5498	0.964452
$455$	0	0
$456$	−2.27492	−0.106533
$457$	18.5498	0.867725	0.433862	−	0.900979i	$-0.357150\pi$
$457$	18.5498	0.867725	0.433862	+	0.900979i	$0.357150\pi$
$458$	−19.0997	−0.892469
$459$	−0.274917	−0.0128320
$460$	9.72508	0.453434
$461$	17.9244	0.834823	0.417412	−	0.908717i	$-0.362937\pi$
$461$	17.9244	0.834823	0.417412	+	0.908717i	$0.362937\pi$
$462$	2.27492	0.105839
$463$	−30.2749	−1.40699	−0.703497	−	0.710698i	$-0.748379\pi$
$463$	−30.2749	−1.40699	−0.703497	+	0.710698i	$0.748379\pi$
$464$	8.27492	0.384153
$465$	34.1993	1.58596
$466$	5.45017	0.252474
$467$	−26.2749	−1.21586	−0.607929	−	0.793991i	$-0.708000\pi$
$467$	−26.2749	−1.21586	−0.607929	+	0.793991i	$0.708000\pi$
$468$	0	0
$469$	12.5498	0.579498
$470$	0	0
$471$	13.3746	0.616268
$472$	−8.00000	−0.368230
$473$	−5.17525	−0.237958
$474$	−12.5498	−0.576433
$475$	30.1993	1.38564
$476$	−0.274917	−0.0126008
$477$	10.0000	0.457869
$478$	−25.0997	−1.14803
$479$	23.3746	1.06801	0.534006	−	0.845481i	$-0.320686\pi$
$479$	23.3746	1.06801	0.534006	+	0.845481i	$0.320686\pi$
$480$	−4.27492	−0.195122
$481$	0	0
$482$	−15.0997	−0.687771
$483$	2.27492	0.103512
$484$	−5.82475	−0.264761
$485$	−64.5498	−2.93106
$486$	−1.00000	−0.0453609
$487$	18.1993	0.824691	0.412345	−	0.911028i	$-0.364710\pi$
$487$	18.1993	0.824691	0.412345	+	0.911028i	$0.364710\pi$
$488$	−12.2749	−0.555659
$489$	12.5498	0.567523
$490$	4.27492	0.193121
$491$	8.54983	0.385849	0.192924	−	0.981214i	$-0.438203\pi$
$491$	8.54983	0.385849	0.192924	+	0.981214i	$0.438203\pi$
$492$	6.54983	0.295289
$493$	2.27492	0.102457
$494$	0	0
$495$	9.72508	0.437110
$496$	−8.00000	−0.359211
$497$	0	0
$498$	−4.54983	−0.203883
$499$	−25.0997	−1.12362	−0.561808	−	0.827268i	$-0.689894\pi$
$499$	−25.0997	−1.12362	−0.561808	+	0.827268i	$0.689894\pi$
$500$	35.3746	1.58200
$501$	−1.72508	−0.0770710
$502$	23.9244	1.06780
$503$	−3.45017	−0.153835	−0.0769176	−	0.997037i	$-0.524508\pi$
$503$	−3.45017	−0.153835	−0.0769176	+	0.997037i	$0.524508\pi$
$504$	−1.00000	−0.0445435
$505$	10.9003	0.485058
$506$	5.17525	0.230068
$507$	0	0
$508$	−20.5498	−0.911751
$509$	9.92442	0.439892	0.219946	−	0.975512i	$-0.429412\pi$
$509$	9.92442	0.439892	0.219946	+	0.975512i	$0.429412\pi$
$510$	−1.17525	−0.0520409
$511$	−12.8248	−0.567334
$512$	1.00000	0.0441942
$513$	−2.27492	−0.100440
$514$	−14.0000	−0.617514
$515$	43.9244	1.93554
$516$	2.27492	0.100148
$517$	0	0
$518$	−4.27492	−0.187829
$519$	−7.09967	−0.311641
$520$	0	0
$521$	−4.27492	−0.187288	−0.0936438	−	0.995606i	$-0.529851\pi$
$521$	−4.27492	−0.187288	−0.0936438	+	0.995606i	$0.529851\pi$
$522$	8.27492	0.362183
$523$	36.0000	1.57417	0.787085	−	0.616844i	$-0.211589\pi$
$523$	36.0000	1.57417	0.787085	+	0.616844i	$0.211589\pi$
$524$	6.82475	0.298141
$525$	13.2749	0.579365
$526$	28.0000	1.22086
$527$	−2.19934	−0.0958047
$528$	−2.27492	−0.0990031
$529$	−17.8248	−0.774989
$530$	42.7492	1.85691
$531$	−8.00000	−0.347170
$532$	−2.27492	−0.0986302
$533$	0	0
$534$	−14.0000	−0.605839
$535$	2.35050	0.101621
$536$	−12.5498	−0.542070
$537$	−12.0000	−0.517838
$538$	6.00000	0.258678
$539$	2.27492	0.0979876
$540$	−4.27492	−0.183963
$541$	−42.4743	−1.82611	−0.913055	−	0.407835i	$-0.866284\pi$
$541$	−42.4743	−1.82611	−0.913055	+	0.407835i	$0.866284\pi$
$542$	−28.5498	−1.22632
$543$	−19.0997	−0.819645
$544$	0.274917	0.0117870
$545$	−1.17525	−0.0503421
$546$	0	0
$547$	−4.00000	−0.171028	−0.0855138	−	0.996337i	$-0.527253\pi$
$547$	−4.00000	−0.171028	−0.0855138	+	0.996337i	$0.527253\pi$
$548$	17.3746	0.742206
$549$	−12.2749	−0.523881
$550$	30.1993	1.28770
$551$	18.8248	0.801961
$552$	−2.27492	−0.0968269
$553$	−12.5498	−0.533673
$554$	−10.0000	−0.424859
$555$	−18.2749	−0.775727
$556$	4.00000	0.169638
$557$	44.7492	1.89608	0.948042	−	0.318146i	$-0.103060\pi$
$557$	44.7492	1.89608	0.948042	+	0.318146i	$0.103060\pi$
$558$	−8.00000	−0.338667
$559$	0	0
$560$	−4.27492	−0.180648
$561$	−0.625414	−0.0264050
$562$	−15.0997	−0.636941
$563$	−35.3746	−1.49086	−0.745431	−	0.666583i	$-0.767756\pi$
$563$	−35.3746	−1.49086	−0.745431	+	0.666583i	$0.767756\pi$
$564$	0	0
$565$	−25.6495	−1.07908
$566$	−4.00000	−0.168133
$567$	−1.00000	−0.0419961
$568$	0	0
$569$	3.09967	0.129945	0.0649724	−	0.997887i	$-0.479304\pi$
$569$	3.09967	0.129945	0.0649724	+	0.997887i	$0.479304\pi$
$570$	−9.72508	−0.407339
$571$	−37.0997	−1.55257	−0.776286	−	0.630380i	$-0.782899\pi$
$571$	−37.0997	−1.55257	−0.776286	+	0.630380i	$0.782899\pi$
$572$	0	0
$573$	−2.27492	−0.0950360
$574$	6.54983	0.273385
$575$	30.1993	1.25940
$576$	1.00000	0.0416667
$577$	8.90033	0.370526	0.185263	−	0.982689i	$-0.440686\pi$
$577$	8.90033	0.370526	0.185263	+	0.982689i	$0.440686\pi$
$578$	−16.9244	−0.703963
$579$	−18.5498	−0.770905
$580$	35.3746	1.46885
$581$	−4.54983	−0.188759
$582$	15.0997	0.625901
$583$	22.7492	0.942174
$584$	12.8248	0.530692
$585$	0	0
$586$	6.00000	0.247858
$587$	−46.7492	−1.92954	−0.964772	−	0.263086i	$-0.915260\pi$
$587$	−46.7492	−1.92954	−0.964772	+	0.263086i	$0.915260\pi$
$588$	−1.00000	−0.0412393
$589$	−18.1993	−0.749891
$590$	−34.1993	−1.40796
$591$	−2.54983	−0.104886
$592$	4.27492	0.175698
$593$	7.09967	0.291548	0.145774	−	0.989318i	$-0.453433\pi$
$593$	7.09967	0.291548	0.145774	+	0.989318i	$0.453433\pi$
$594$	−2.27492	−0.0933410
$595$	−1.17525	−0.0481805
$596$	−22.5498	−0.923677
$597$	−6.82475	−0.279318
$598$	0	0
$599$	21.7251	0.887663	0.443831	−	0.896110i	$-0.353619\pi$
$599$	21.7251	0.887663	0.443831	+	0.896110i	$0.353619\pi$
$600$	−13.2749	−0.541946
$601$	23.6495	0.964683	0.482342	−	0.875983i	$-0.339786\pi$
$601$	23.6495	0.964683	0.482342	+	0.875983i	$0.339786\pi$
$602$	2.27492	0.0927187
$603$	−12.5498	−0.511069
$604$	−6.27492	−0.255323
$605$	−24.9003	−1.01234
$606$	−2.54983	−0.103580
$607$	9.17525	0.372412	0.186206	−	0.982511i	$-0.440381\pi$
$607$	9.17525	0.372412	0.186206	+	0.982511i	$0.440381\pi$
$608$	2.27492	0.0922601
$609$	8.27492	0.335317
$610$	−52.4743	−2.12462
$611$	0	0
$612$	0.274917	0.0111129
$613$	−16.2749	−0.657338	−0.328669	−	0.944445i	$-0.606600\pi$
$613$	−16.2749	−0.657338	−0.328669	+	0.944445i	$0.606600\pi$
$614$	−21.0997	−0.851513
$615$	28.0000	1.12907
$616$	−2.27492	−0.0916590
$617$	20.8248	0.838373	0.419186	−	0.907900i	$-0.362315\pi$
$617$	20.8248	0.838373	0.419186	+	0.907900i	$0.362315\pi$
$618$	−10.2749	−0.413318
$619$	−29.7251	−1.19475	−0.597376	−	0.801961i	$-0.703790\pi$
$619$	−29.7251	−1.19475	−0.597376	+	0.801961i	$0.703790\pi$
$620$	−34.1993	−1.37348
$621$	−2.27492	−0.0912893
$622$	3.45017	0.138339
$623$	−14.0000	−0.560898
$624$	0	0
$625$	84.8488	3.39395
$626$	−27.6495	−1.10510
$627$	−5.17525	−0.206680
$628$	−13.3746	−0.533704
$629$	1.17525	0.0468602
$630$	−4.27492	−0.170317
$631$	10.8248	0.430927	0.215463	−	0.976512i	$-0.430874\pi$
$631$	10.8248	0.430927	0.215463	+	0.976512i	$0.430874\pi$
$632$	12.5498	0.499206
$633$	−1.17525	−0.0467119
$634$	1.45017	0.0575934
$635$	−87.8488	−3.48617
$636$	−10.0000	−0.396526
$637$	0	0
$638$	18.8248	0.745279
$639$	0	0
$640$	4.27492	0.168981
$641$	−15.0997	−0.596401	−0.298201	−	0.954503i	$-0.596386\pi$
$641$	−15.0997	−0.596401	−0.298201	+	0.954503i	$0.596386\pi$
$642$	−0.549834	−0.0217002
$643$	23.9244	0.943487	0.471744	−	0.881736i	$-0.343625\pi$
$643$	23.9244	0.943487	0.471744	+	0.881736i	$0.343625\pi$
$644$	−2.27492	−0.0896443
$645$	9.72508	0.382925
$646$	0.625414	0.0246066
$647$	−18.1993	−0.715490	−0.357745	−	0.933819i	$-0.616454\pi$
$647$	−18.1993	−0.715490	−0.357745	+	0.933819i	$0.616454\pi$
$648$	1.00000	0.0392837
$649$	−18.1993	−0.714386
$650$	0	0
$651$	−8.00000	−0.313545
$652$	−12.5498	−0.491489
$653$	−5.37459	−0.210324	−0.105162	−	0.994455i	$-0.533536\pi$
$653$	−5.37459	−0.210324	−0.105162	+	0.994455i	$0.533536\pi$
$654$	0.274917	0.0107501
$655$	29.1752	1.13997
$656$	−6.54983	−0.255728
$657$	12.8248	0.500341
$658$	0	0
$659$	−7.45017	−0.290217	−0.145109	−	0.989416i	$-0.546353\pi$
$659$	−7.45017	−0.290217	−0.145109	+	0.989416i	$0.546353\pi$
$660$	−9.72508	−0.378548
$661$	40.1993	1.56357	0.781787	−	0.623546i	$-0.214309\pi$
$661$	40.1993	1.56357	0.781787	+	0.623546i	$0.214309\pi$
$662$	29.6495	1.15236
$663$	0	0
$664$	4.54983	0.176568
$665$	−9.72508	−0.377123
$666$	4.27492	0.165650
$667$	18.8248	0.728897
$668$	1.72508	0.0667455
$669$	21.6495	0.837018
$670$	−53.6495	−2.07266
$671$	−27.9244	−1.07801
$672$	1.00000	0.0385758
$673$	16.2749	0.627352	0.313676	−	0.949530i	$-0.398439\pi$
$673$	16.2749	0.627352	0.313676	+	0.949530i	$0.398439\pi$
$674$	9.37459	0.361096
$675$	−13.2749	−0.510952
$676$	0	0
$677$	16.1993	0.622591	0.311296	−	0.950313i	$-0.399237\pi$
$677$	16.1993	0.622591	0.311296	+	0.950313i	$0.399237\pi$
$678$	6.00000	0.230429
$679$	15.0997	0.579472
$680$	1.17525	0.0450687
$681$	−20.5498	−0.787471
$682$	−18.1993	−0.696889
$683$	−3.37459	−0.129125	−0.0645625	−	0.997914i	$-0.520565\pi$
$683$	−3.37459	−0.129125	−0.0645625	+	0.997914i	$0.520565\pi$
$684$	2.27492	0.0869836
$685$	74.2749	2.83790
$686$	−1.00000	−0.0381802
$687$	19.0997	0.728698
$688$	−2.27492	−0.0867304
$689$	0	0
$690$	−9.72508	−0.370228
$691$	−20.0000	−0.760836	−0.380418	−	0.924815i	$-0.624220\pi$
$691$	−20.0000	−0.760836	−0.380418	+	0.924815i	$0.624220\pi$
$692$	7.09967	0.269889
$693$	−2.27492	−0.0864170
$694$	5.09967	0.193581
$695$	17.0997	0.648627
$696$	−8.27492	−0.313660
$697$	−1.80066	−0.0682049
$698$	−2.00000	−0.0757011
$699$	−5.45017	−0.206144
$700$	−13.2749	−0.501745
$701$	−15.0997	−0.570307	−0.285153	−	0.958482i	$-0.592045\pi$
$701$	−15.0997	−0.570307	−0.285153	+	0.958482i	$0.592045\pi$
$702$	0	0
$703$	9.72508	0.366788
$704$	2.27492	0.0857392
$705$	0	0
$706$	−27.0997	−1.01991
$707$	−2.54983	−0.0958964
$708$	8.00000	0.300658
$709$	23.0997	0.867526	0.433763	−	0.901027i	$-0.357185\pi$
$709$	23.0997	0.867526	0.433763	+	0.901027i	$0.357185\pi$
$710$	0	0
$711$	12.5498	0.470656
$712$	14.0000	0.524672
$713$	−18.1993	−0.681571
$714$	0.274917	0.0102885
$715$	0	0
$716$	12.0000	0.448461
$717$	25.0997	0.937364
$718$	32.0000	1.19423
$719$	−29.6495	−1.10574	−0.552870	−	0.833268i	$-0.686467\pi$
$719$	−29.6495	−1.10574	−0.552870	+	0.833268i	$0.686467\pi$
$720$	4.27492	0.159317
$721$	−10.2749	−0.382658
$722$	−13.8248	−0.514504
$723$	15.0997	0.561563
$724$	19.0997	0.709834
$725$	109.849	4.07968
$726$	5.82475	0.216177
$727$	35.3746	1.31197	0.655985	−	0.754774i	$-0.272253\pi$
$727$	35.3746	1.31197	0.655985	+	0.754774i	$0.272253\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	54.8248	2.02916
$731$	−0.625414	−0.0231318
$732$	12.2749	0.453694
$733$	−14.5498	−0.537410	−0.268705	−	0.963222i	$-0.586596\pi$
$733$	−14.5498	−0.537410	−0.268705	+	0.963222i	$0.586596\pi$
$734$	−2.90033	−0.107053
$735$	−4.27492	−0.157683
$736$	2.27492	0.0838546
$737$	−28.5498	−1.05165
$738$	−6.54983	−0.241103
$739$	−37.6495	−1.38496	−0.692480	−	0.721437i	$-0.743482\pi$
$739$	−37.6495	−1.38496	−0.692480	+	0.721437i	$0.743482\pi$
$740$	18.2749	0.671799
$741$	0	0
$742$	−10.0000	−0.367112
$743$	−11.4502	−0.420066	−0.210033	−	0.977694i	$-0.567357\pi$
$743$	−11.4502	−0.420066	−0.210033	+	0.977694i	$0.567357\pi$
$744$	8.00000	0.293294
$745$	−96.3987	−3.53177
$746$	26.5498	0.972059
$747$	4.54983	0.166470
$748$	0.625414	0.0228674
$749$	−0.549834	−0.0200905
$750$	−35.3746	−1.29170
$751$	10.1993	0.372179	0.186090	−	0.982533i	$-0.440419\pi$
$751$	10.1993	0.372179	0.186090	+	0.982533i	$0.440419\pi$
$752$	0	0
$753$	−23.9244	−0.871854
$754$	0	0
$755$	−26.8248	−0.976253
$756$	1.00000	0.0363696
$757$	−35.0997	−1.27572	−0.637860	−	0.770153i	$-0.720180\pi$
$757$	−35.0997	−1.27572	−0.637860	+	0.770153i	$0.720180\pi$
$758$	33.0997	1.20223
$759$	−5.17525	−0.187850
$760$	9.72508	0.352766
$761$	−38.5498	−1.39743	−0.698715	−	0.715400i	$-0.746245\pi$
$761$	−38.5498	−1.39743	−0.698715	+	0.715400i	$0.746245\pi$
$762$	20.5498	0.744442
$763$	0.274917	0.00995267
$764$	2.27492	0.0823036
$765$	1.17525	0.0424912
$766$	−30.2749	−1.09388
$767$	0	0
$768$	−1.00000	−0.0360844
$769$	−32.8248	−1.18369	−0.591845	−	0.806051i	$-0.701600\pi$
$769$	−32.8248	−1.18369	−0.591845	+	0.806051i	$0.701600\pi$
$770$	−9.72508	−0.350468
$771$	14.0000	0.504198
$772$	18.5498	0.667623
$773$	9.92442	0.356957	0.178478	−	0.983944i	$-0.442883\pi$
$773$	9.92442	0.356957	0.178478	+	0.983944i	$0.442883\pi$
$774$	−2.27492	−0.0817702
$775$	−106.199	−3.81479
$776$	−15.0997	−0.542047
$777$	4.27492	0.153362
$778$	28.1993	1.01100
$779$	−14.9003	−0.533860
$780$	0	0
$781$	0	0
$782$	0.625414	0.0223648
$783$	−8.27492	−0.295721
$784$	1.00000	0.0357143
$785$	−57.1752	−2.04067
$786$	−6.82475	−0.243431
$787$	10.2749	0.366261	0.183131	−	0.983089i	$-0.441377\pi$
$787$	10.2749	0.366261	0.183131	+	0.983089i	$0.441377\pi$
$788$	2.54983	0.0908341
$789$	−28.0000	−0.996826
$790$	53.6495	1.90876
$791$	6.00000	0.213335
$792$	2.27492	0.0808357
$793$	0	0
$794$	14.0000	0.496841
$795$	−42.7492	−1.51616
$796$	6.82475	0.241897
$797$	−15.6495	−0.554334	−0.277167	−	0.960822i	$-0.589396\pi$
$797$	−15.6495	−0.554334	−0.277167	+	0.960822i	$0.589396\pi$
$798$	2.27492	0.0805312
$799$	0	0
$800$	13.2749	0.469339
$801$	14.0000	0.494666
$802$	3.09967	0.109453
$803$	29.1752	1.02957
$804$	12.5498	0.442599
$805$	−9.72508	−0.342764
$806$	0	0
$807$	−6.00000	−0.211210
$808$	2.54983	0.0897029
$809$	−56.1993	−1.97586	−0.987932	−	0.154890i	$-0.950498\pi$
$809$	−56.1993	−1.97586	−0.987932	+	0.154890i	$0.950498\pi$
$810$	4.27492	0.150205
$811$	11.3746	0.399416	0.199708	−	0.979855i	$-0.436001\pi$
$811$	11.3746	0.399416	0.199708	+	0.979855i	$0.436001\pi$
$812$	−8.27492	−0.290393
$813$	28.5498	1.00129
$814$	9.72508	0.340864
$815$	−53.6495	−1.87926
$816$	−0.274917	−0.00962403
$817$	−5.17525	−0.181059
$818$	7.17525	0.250877
$819$	0	0
$820$	−28.0000	−0.977802
$821$	−31.6495	−1.10458	−0.552288	−	0.833654i	$-0.686245\pi$
$821$	−31.6495	−1.10458	−0.552288	+	0.833654i	$0.686245\pi$
$822$	−17.3746	−0.606008
$823$	−25.0997	−0.874919	−0.437460	−	0.899238i	$-0.644122\pi$
$823$	−25.0997	−0.874919	−0.437460	+	0.899238i	$0.644122\pi$
$824$	10.2749	0.357944
$825$	−30.1993	−1.05141
$826$	8.00000	0.278356
$827$	26.2749	0.913668	0.456834	−	0.889552i	$-0.348983\pi$
$827$	26.2749	0.913668	0.456834	+	0.889552i	$0.348983\pi$
$828$	2.27492	0.0790588
$829$	11.7251	0.407229	0.203614	−	0.979051i	$-0.434731\pi$
$829$	11.7251	0.407229	0.203614	+	0.979051i	$0.434731\pi$
$830$	19.4502	0.675125
$831$	10.0000	0.346896
$832$	0	0
$833$	0.274917	0.00952532
$834$	−4.00000	−0.138509
$835$	7.37459	0.255208
$836$	5.17525	0.178990
$837$	8.00000	0.276520
$838$	2.27492	0.0785857
$839$	−22.9003	−0.790607	−0.395304	−	0.918551i	$-0.629361\pi$
$839$	−22.9003	−0.790607	−0.395304	+	0.918551i	$0.629361\pi$
$840$	4.27492	0.147499
$841$	39.4743	1.36118
$842$	−3.09967	−0.106822
$843$	15.0997	0.520060
$844$	1.17525	0.0404537
$845$	0	0
$846$	0	0
$847$	5.82475	0.200141
$848$	10.0000	0.343401
$849$	4.00000	0.137280
$850$	3.64950	0.125177
$851$	9.72508	0.333372
$852$	0	0
$853$	27.6495	0.946701	0.473350	−	0.880874i	$-0.343044\pi$
$853$	27.6495	0.946701	0.473350	+	0.880874i	$0.343044\pi$
$854$	12.2749	0.420039
$855$	9.72508	0.332591
$856$	0.549834	0.0187930
$857$	19.0997	0.652432	0.326216	−	0.945295i	$-0.394226\pi$
$857$	19.0997	0.652432	0.326216	+	0.945295i	$0.394226\pi$
$858$	0	0
$859$	−20.0000	−0.682391	−0.341196	−	0.939992i	$-0.610832\pi$
$859$	−20.0000	−0.682391	−0.341196	+	0.939992i	$0.610832\pi$
$860$	−9.72508	−0.331623
$861$	−6.54983	−0.223218
$862$	11.4502	0.389994
$863$	−29.6495	−1.00928	−0.504640	−	0.863330i	$-0.668375\pi$
$863$	−29.6495	−1.00928	−0.504640	+	0.863330i	$0.668375\pi$
$864$	−1.00000	−0.0340207
$865$	30.3505	1.03195
$866$	23.6495	0.803643
$867$	16.9244	0.574783
$868$	8.00000	0.271538
$869$	28.5498	0.968487
$870$	−35.3746	−1.19931
$871$	0	0
$872$	−0.274917	−0.00930987
$873$	−15.0997	−0.511046
$874$	5.17525	0.175055
$875$	−35.3746	−1.19588
$876$	−12.8248	−0.433308
$877$	−51.0997	−1.72551	−0.862757	−	0.505619i	$-0.831264\pi$
$877$	−51.0997	−1.72551	−0.862757	+	0.505619i	$0.831264\pi$
$878$	−14.8248	−0.500311
$879$	−6.00000	−0.202375
$880$	9.72508	0.327832
$881$	−31.7251	−1.06885	−0.534423	−	0.845217i	$-0.679471\pi$
$881$	−31.7251	−1.06885	−0.534423	+	0.845217i	$0.679471\pi$
$882$	1.00000	0.0336718
$883$	31.9244	1.07434	0.537171	−	0.843473i	$-0.319493\pi$
$883$	31.9244	1.07434	0.537171	+	0.843473i	$0.319493\pi$
$884$	0	0
$885$	34.1993	1.14960
$886$	7.45017	0.250293
$887$	−33.0997	−1.11138	−0.555689	−	0.831390i	$-0.687545\pi$
$887$	−33.0997	−1.11138	−0.555689	+	0.831390i	$0.687545\pi$
$888$	−4.27492	−0.143457
$889$	20.5498	0.689219
$890$	59.8488	2.00614
$891$	2.27492	0.0762126
$892$	−21.6495	−0.724879
$893$	0	0
$894$	22.5498	0.754179
$895$	51.2990	1.71474
$896$	−1.00000	−0.0334077
$897$	0	0
$898$	0.274917	0.00917411
$899$	−66.1993	−2.20787
$900$	13.2749	0.442497
$901$	2.74917	0.0915882
$902$	−14.9003	−0.496127
$903$	−2.27492	−0.0757045
$904$	−6.00000	−0.199557
$905$	81.6495	2.71412
$906$	6.27492	0.208470
$907$	28.0000	0.929725	0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000	0.929725	0.464862	+	0.885383i	$0.346104\pi$
$908$	20.5498	0.681970
$909$	2.54983	0.0845727
$910$	0	0
$911$	−52.4743	−1.73855	−0.869275	−	0.494329i	$-0.835414\pi$
$911$	−52.4743	−1.73855	−0.869275	+	0.494329i	$0.835414\pi$
$912$	−2.27492	−0.0753300
$913$	10.3505	0.342551
$914$	18.5498	0.613574
$915$	52.4743	1.73475
$916$	−19.0997	−0.631071
$917$	−6.82475	−0.225373
$918$	−0.274917	−0.00907362
$919$	−12.5498	−0.413981	−0.206990	−	0.978343i	$-0.566367\pi$
$919$	−12.5498	−0.413981	−0.206990	+	0.978343i	$0.566367\pi$
$920$	9.72508	0.320626
$921$	21.0997	0.695258
$922$	17.9244	0.590309
$923$	0	0
$924$	2.27492	0.0748393
$925$	56.7492	1.86590
$926$	−30.2749	−0.994896
$927$	10.2749	0.337473
$928$	8.27492	0.271637
$929$	−14.5498	−0.477365	−0.238682	−	0.971098i	$-0.576715\pi$
$929$	−14.5498	−0.477365	−0.238682	+	0.971098i	$0.576715\pi$
$930$	34.1993	1.12144
$931$	2.27492	0.0745574
$932$	5.45017	0.178526
$933$	−3.45017	−0.112953
$934$	−26.2749	−0.859742
$935$	2.67359	0.0874358
$936$	0	0
$937$	16.9003	0.552110	0.276055	−	0.961142i	$-0.410973\pi$
$937$	16.9003	0.552110	0.276055	+	0.961142i	$0.410973\pi$
$938$	12.5498	0.409767
$939$	27.6495	0.902307
$940$	0	0
$941$	−51.0997	−1.66580	−0.832901	−	0.553422i	$-0.813322\pi$
$941$	−51.0997	−1.66580	−0.832901	+	0.553422i	$0.813322\pi$
$942$	13.3746	0.435768
$943$	−14.9003	−0.485222
$944$	−8.00000	−0.260378
$945$	4.27492	0.139063
$946$	−5.17525	−0.168262
$947$	17.1752	0.558121	0.279060	−	0.960274i	$-0.409977\pi$
$947$	17.1752	0.558121	0.279060	+	0.960274i	$0.409977\pi$
$948$	−12.5498	−0.407600
$949$	0	0
$950$	30.1993	0.979796
$951$	−1.45017	−0.0470248
$952$	−0.274917	−0.00891012
$953$	31.6495	1.02523	0.512614	−	0.858619i	$-0.328677\pi$
$953$	31.6495	1.02523	0.512614	+	0.858619i	$0.328677\pi$
$954$	10.0000	0.323762
$955$	9.72508	0.314696
$956$	−25.0997	−0.811781
$957$	−18.8248	−0.608518
$958$	23.3746	0.755199
$959$	−17.3746	−0.561055
$960$	−4.27492	−0.137972
$961$	33.0000	1.06452
$962$	0	0
$963$	0.549834	0.0177182
$964$	−15.0997	−0.486328
$965$	79.2990	2.55273
$966$	2.27492	0.0731943
$967$	−42.8248	−1.37715	−0.688576	−	0.725165i	$-0.741764\pi$
$967$	−42.8248	−1.37715	−0.688576	+	0.725165i	$0.741764\pi$
$968$	−5.82475	−0.187215
$969$	−0.625414	−0.0200912
$970$	−64.5498	−2.07257
$971$	−29.0997	−0.933853	−0.466926	−	0.884296i	$-0.654639\pi$
$971$	−29.0997	−0.933853	−0.466926	+	0.884296i	$0.654639\pi$
$972$	−1.00000	−0.0320750
$973$	−4.00000	−0.128234
$974$	18.1993	0.583144
$975$	0	0
$976$	−12.2749	−0.392911
$977$	13.9244	0.445482	0.222741	−	0.974878i	$-0.428500\pi$
$977$	13.9244	0.445482	0.222741	+	0.974878i	$0.428500\pi$
$978$	12.5498	0.401299
$979$	31.8488	1.01789
$980$	4.27492	0.136557
$981$	−0.274917	−0.00877743
$982$	8.54983	0.272836
$983$	−61.0241	−1.94637	−0.973183	−	0.230032i	$-0.926117\pi$
$983$	−61.0241	−1.94637	−0.973183	+	0.230032i	$0.926117\pi$
$984$	6.54983	0.208801
$985$	10.9003	0.347313
$986$	2.27492	0.0724481
$987$	0	0
$988$	0	0
$989$	−5.17525	−0.164563
$990$	9.72508	0.309083
$991$	−46.7492	−1.48504	−0.742518	−	0.669826i	$-0.766369\pi$
$991$	−46.7492	−1.48504	−0.742518	+	0.669826i	$0.766369\pi$
$992$	−8.00000	−0.254000
$993$	−29.6495	−0.940899
$994$	0	0
$995$	29.1752	0.924918
$996$	−4.54983	−0.144167
$997$	−12.9003	−0.408558	−0.204279	−	0.978913i	$-0.565485\pi$
$997$	−12.9003	−0.408558	−0.204279	+	0.978913i	$0.565485\pi$
$998$	−25.0997	−0.794516
$999$	−4.27492	−0.135252

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7098.2.a.bu.1.2		2
13.12	even	2		546.2.a.h.1.1	✓	2
39.38	odd	2		1638.2.a.y.1.2		2
52.51	odd	2		4368.2.a.bh.1.1		2
91.90	odd	2		3822.2.a.bm.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.a.h.1.1	✓	2	13.12	even	2
1638.2.a.y.1.2		2	39.38	odd	2
3822.2.a.bm.1.2		2	91.90	odd	2
4368.2.a.bh.1.1		2	52.51	odd	2
7098.2.a.bu.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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.27492 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +4.27492 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +4.27492 q^{10} +2.27492 q^{11} -1.00000 q^{12} -1.00000 q^{14} -4.27492 q^{15} +1.00000 q^{16} +0.274917 q^{17} +1.00000 q^{18} +2.27492 q^{19} +4.27492 q^{20} +1.00000 q^{21} +2.27492 q^{22} +2.27492 q^{23} -1.00000 q^{24} +13.2749 q^{25} -1.00000 q^{27} -1.00000 q^{28} +8.27492 q^{29} -4.27492 q^{30} -8.00000 q^{31} +1.00000 q^{32} -2.27492 q^{33} +0.274917 q^{34} -4.27492 q^{35} +1.00000 q^{36} +4.27492 q^{37} +2.27492 q^{38} +4.27492 q^{40} -6.54983 q^{41} +1.00000 q^{42} -2.27492 q^{43} +2.27492 q^{44} +4.27492 q^{45} +2.27492 q^{46} -1.00000 q^{48} +1.00000 q^{49} +13.2749 q^{50} -0.274917 q^{51} +10.0000 q^{53} -1.00000 q^{54} +9.72508 q^{55} -1.00000 q^{56} -2.27492 q^{57} +8.27492 q^{58} -8.00000 q^{59} -4.27492 q^{60} -12.2749 q^{61} -8.00000 q^{62} -1.00000 q^{63} +1.00000 q^{64} -2.27492 q^{66} -12.5498 q^{67} +0.274917 q^{68} -2.27492 q^{69} -4.27492 q^{70} +1.00000 q^{72} +12.8248 q^{73} +4.27492 q^{74} -13.2749 q^{75} +2.27492 q^{76} -2.27492 q^{77} +12.5498 q^{79} +4.27492 q^{80} +1.00000 q^{81} -6.54983 q^{82} +4.54983 q^{83} +1.00000 q^{84} +1.17525 q^{85} -2.27492 q^{86} -8.27492 q^{87} +2.27492 q^{88} +14.0000 q^{89} +4.27492 q^{90} +2.27492 q^{92} +8.00000 q^{93} +9.72508 q^{95} -1.00000 q^{96} -15.0997 q^{97} +1.00000 q^{98} +2.27492 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} + q^{10} - 3 q^{11} - 2 q^{12} - 2 q^{14} - q^{15} + 2 q^{16} - 7 q^{17} + 2 q^{18} - 3 q^{19} + q^{20} + 2 q^{21} - 3 q^{22} - 3 q^{23} - 2 q^{24} + 19 q^{25} - 2 q^{27} - 2 q^{28} + 9 q^{29} - q^{30} - 16 q^{31} + 2 q^{32} + 3 q^{33} - 7 q^{34} - q^{35} + 2 q^{36} + q^{37} - 3 q^{38} + q^{40} + 2 q^{41} + 2 q^{42} + 3 q^{43} - 3 q^{44} + q^{45} - 3 q^{46} - 2 q^{48} + 2 q^{49} + 19 q^{50} + 7 q^{51} + 20 q^{53} - 2 q^{54} + 27 q^{55} - 2 q^{56} + 3 q^{57} + 9 q^{58} - 16 q^{59} - q^{60} - 17 q^{61} - 16 q^{62} - 2 q^{63} + 2 q^{64} + 3 q^{66} - 10 q^{67} - 7 q^{68} + 3 q^{69} - q^{70} + 2 q^{72} + 3 q^{73} + q^{74} - 19 q^{75} - 3 q^{76} + 3 q^{77} + 10 q^{79} + q^{80} + 2 q^{81} + 2 q^{82} - 6 q^{83} + 2 q^{84} + 25 q^{85} + 3 q^{86} - 9 q^{87} - 3 q^{88} + 28 q^{89} + q^{90} - 3 q^{92} + 16 q^{93} + 27 q^{95} - 2 q^{96} + 2 q^{98} - 3 q^{99}+O(q^{100}) \) 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 - 3 * q^11 - 2 * q^12 - 2 * q^14 - q^15 + 2 * q^16 - 7 * q^17 + 2 * q^18 - 3 * q^19 + q^20 + 2 * q^21 - 3 * q^22 - 3 * q^23 - 2 * q^24 + 19 * q^25 - 2 * q^27 - 2 * q^28 + 9 * q^29 - q^30 - 16 * q^31 + 2 * q^32 + 3 * q^33 - 7 * q^34 - q^35 + 2 * q^36 + q^37 - 3 * q^38 + q^40 + 2 * q^41 + 2 * q^42 + 3 * q^43 - 3 * q^44 + q^45 - 3 * q^46 - 2 * q^48 + 2 * q^49 + 19 * q^50 + 7 * q^51 + 20 * q^53 - 2 * q^54 + 27 * q^55 - 2 * q^56 + 3 * q^57 + 9 * q^58 - 16 * q^59 - q^60 - 17 * q^61 - 16 * q^62 - 2 * q^63 + 2 * q^64 + 3 * q^66 - 10 * q^67 - 7 * q^68 + 3 * q^69 - q^70 + 2 * q^72 + 3 * q^73 + q^74 - 19 * q^75 - 3 * q^76 + 3 * q^77 + 10 * q^79 + q^80 + 2 * q^81 + 2 * q^82 - 6 * q^83 + 2 * q^84 + 25 * q^85 + 3 * q^86 - 9 * q^87 - 3 * q^88 + 28 * q^89 + q^90 - 3 * q^92 + 16 * q^93 + 27 * q^95 - 2 * q^96 + 2 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

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Database

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