LMFDB - Embedded newform 8281.2.a.p.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8281,2,Mod(1,8281)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8281, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8281.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8281 = 7^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8281.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:	$66.1241179138$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 637)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.41421$ of defining polynomial
Character	$\chi$	$=$	8281.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.41421 q^{2} -1.41421 q^{3} +3.82843 q^{4} +3.82843 q^{5} +3.41421 q^{6} -4.41421 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.41421 q^{2} -1.41421 q^{3} +3.82843 q^{4} +3.82843 q^{5} +3.41421 q^{6} -4.41421 q^{8} -1.00000 q^{9} -9.24264 q^{10} +3.41421 q^{11} -5.41421 q^{12} -5.41421 q^{15} +3.00000 q^{16} -0.171573 q^{17} +2.41421 q^{18} +6.00000 q^{19} +14.6569 q^{20} -8.24264 q^{22} +1.41421 q^{23} +6.24264 q^{24} +9.65685 q^{25} +5.65685 q^{27} +9.82843 q^{29} +13.0711 q^{30} +5.41421 q^{31} +1.58579 q^{32} -4.82843 q^{33} +0.414214 q^{34} -3.82843 q^{36} +7.48528 q^{37} -14.4853 q^{38} -16.8995 q^{40} +5.82843 q^{41} +0.585786 q^{43} +13.0711 q^{44} -3.82843 q^{45} -3.41421 q^{46} +7.65685 q^{47} -4.24264 q^{48} -23.3137 q^{50} +0.242641 q^{51} -3.00000 q^{53} -13.6569 q^{54} +13.0711 q^{55} -8.48528 q^{57} -23.7279 q^{58} -1.75736 q^{59} -20.7279 q^{60} +9.82843 q^{61} -13.0711 q^{62} -9.82843 q^{64} +11.6569 q^{66} -4.24264 q^{67} -0.656854 q^{68} -2.00000 q^{69} -0.343146 q^{71} +4.41421 q^{72} +0.656854 q^{73} -18.0711 q^{74} -13.6569 q^{75} +22.9706 q^{76} +10.2426 q^{79} +11.4853 q^{80} -5.00000 q^{81} -14.0711 q^{82} -13.0711 q^{83} -0.656854 q^{85} -1.41421 q^{86} -13.8995 q^{87} -15.0711 q^{88} -7.31371 q^{89} +9.24264 q^{90} +5.41421 q^{92} -7.65685 q^{93} -18.4853 q^{94} +22.9706 q^{95} -2.24264 q^{96} -5.17157 q^{97} -3.41421 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} + 4 q^{6} - 6 q^{8} - 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 2 * q^4 + 2 * q^5 + 4 * q^6 - 6 * q^8 - 2 * q^9	$ 2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} + 4 q^{6} - 6 q^{8} - 2 q^{9} - 10 q^{10} + 4 q^{11} - 8 q^{12} - 8 q^{15} + 6 q^{16} - 6 q^{17} + 2 q^{18} + 12 q^{19} + 18 q^{20} - 8 q^{22} + 4 q^{24} + 8 q^{25} + 14 q^{29} + 12 q^{30} + 8 q^{31} + 6 q^{32} - 4 q^{33} - 2 q^{34} - 2 q^{36} - 2 q^{37} - 12 q^{38} - 14 q^{40} + 6 q^{41} + 4 q^{43} + 12 q^{44} - 2 q^{45} - 4 q^{46} + 4 q^{47} - 24 q^{50} - 8 q^{51} - 6 q^{53} - 16 q^{54} + 12 q^{55} - 22 q^{58} - 12 q^{59} - 16 q^{60} + 14 q^{61} - 12 q^{62} - 14 q^{64} + 12 q^{66} + 10 q^{68} - 4 q^{69} - 12 q^{71} + 6 q^{72} - 10 q^{73} - 22 q^{74} - 16 q^{75} + 12 q^{76} + 12 q^{79} + 6 q^{80} - 10 q^{81} - 14 q^{82} - 12 q^{83} + 10 q^{85} - 8 q^{87} - 16 q^{88} + 8 q^{89} + 10 q^{90} + 8 q^{92} - 4 q^{93} - 20 q^{94} + 12 q^{95} + 4 q^{96} - 16 q^{97} - 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 + 2 * q^5 + 4 * q^6 - 6 * q^8 - 2 * q^9 - 10 * q^10 + 4 * q^11 - 8 * q^12 - 8 * q^15 + 6 * q^16 - 6 * q^17 + 2 * q^18 + 12 * q^19 + 18 * q^20 - 8 * q^22 + 4 * q^24 + 8 * q^25 + 14 * q^29 + 12 * q^30 + 8 * q^31 + 6 * q^32 - 4 * q^33 - 2 * q^34 - 2 * q^36 - 2 * q^37 - 12 * q^38 - 14 * q^40 + 6 * q^41 + 4 * q^43 + 12 * q^44 - 2 * q^45 - 4 * q^46 + 4 * q^47 - 24 * q^50 - 8 * q^51 - 6 * q^53 - 16 * q^54 + 12 * q^55 - 22 * q^58 - 12 * q^59 - 16 * q^60 + 14 * q^61 - 12 * q^62 - 14 * q^64 + 12 * q^66 + 10 * q^68 - 4 * q^69 - 12 * q^71 + 6 * q^72 - 10 * q^73 - 22 * q^74 - 16 * q^75 + 12 * q^76 + 12 * q^79 + 6 * q^80 - 10 * q^81 - 14 * q^82 - 12 * q^83 + 10 * q^85 - 8 * q^87 - 16 * q^88 + 8 * q^89 + 10 * q^90 + 8 * q^92 - 4 * q^93 - 20 * q^94 + 12 * q^95 + 4 * q^96 - 16 * q^97 - 4 * 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 $

$2$	−2.41421	−1.70711	−0.853553	−	0.521005i	$-0.825557\pi$
$2$	−2.41421	−1.70711	−0.853553	+	0.521005i	$0.825557\pi$
$3$	−1.41421	−0.816497	−0.408248	−	0.912871i	$-0.633860\pi$
$3$	−1.41421	−0.816497	−0.408248	+	0.912871i	$0.633860\pi$
$4$	3.82843	1.91421
$5$	3.82843	1.71212	0.856062	−	0.516873i	$-0.172904\pi$
$5$	3.82843	1.71212	0.856062	+	0.516873i	$0.172904\pi$
$6$	3.41421	1.39385
$7$	0	0
$7$	0	0
$8$	−4.41421	−1.56066
$9$	−1.00000	−0.333333
$10$	−9.24264	−2.92278
$11$	3.41421	1.02942	0.514712	−	0.857363i	$-0.327899\pi$
$11$	3.41421	1.02942	0.514712	+	0.857363i	$0.327899\pi$
$12$	−5.41421	−1.56295
$13$	0	0
$13$	0	0
$14$	0	0
$15$	−5.41421	−1.39794
$16$	3.00000	0.750000
$17$	−0.171573	−0.0416125	−0.0208063	−	0.999784i	$-0.506623\pi$
$17$	−0.171573	−0.0416125	−0.0208063	+	0.999784i	$0.506623\pi$
$18$	2.41421	0.569036
$19$	6.00000	1.37649	0.688247	−	0.725476i	$-0.258380\pi$
$19$	6.00000	1.37649	0.688247	+	0.725476i	$0.258380\pi$
$20$	14.6569	3.27737
$21$	0	0
$22$	−8.24264	−1.75734
$23$	1.41421	0.294884	0.147442	−	0.989071i	$-0.452896\pi$
$23$	1.41421	0.294884	0.147442	+	0.989071i	$0.452896\pi$
$24$	6.24264	1.27427
$25$	9.65685	1.93137
$26$	0	0
$27$	5.65685	1.08866
$28$	0	0
$29$	9.82843	1.82509	0.912547	−	0.408973i	$-0.134113\pi$
$29$	9.82843	1.82509	0.912547	+	0.408973i	$0.134113\pi$
$30$	13.0711	2.38644
$31$	5.41421	0.972421	0.486211	−	0.873842i	$-0.338379\pi$
$31$	5.41421	0.972421	0.486211	+	0.873842i	$0.338379\pi$
$32$	1.58579	0.280330
$33$	−4.82843	−0.840521
$34$	0.414214	0.0710370
$35$	0	0
$36$	−3.82843	−0.638071
$37$	7.48528	1.23057	0.615286	−	0.788304i	$-0.289040\pi$
$37$	7.48528	1.23057	0.615286	+	0.788304i	$0.289040\pi$
$38$	−14.4853	−2.34982
$39$	0	0
$40$	−16.8995	−2.67204
$41$	5.82843	0.910247	0.455124	−	0.890428i	$-0.349595\pi$
$41$	5.82843	0.910247	0.455124	+	0.890428i	$0.349595\pi$
$42$	0	0
$43$	0.585786	0.0893316	0.0446658	−	0.999002i	$-0.485778\pi$
$43$	0.585786	0.0893316	0.0446658	+	0.999002i	$0.485778\pi$
$44$	13.0711	1.97054
$45$	−3.82843	−0.570708
$46$	−3.41421	−0.503398
$47$	7.65685	1.11687	0.558433	−	0.829549i	$-0.311403\pi$
$47$	7.65685	1.11687	0.558433	+	0.829549i	$0.311403\pi$
$48$	−4.24264	−0.612372
$49$	0	0
$50$	−23.3137	−3.29706
$51$	0.242641	0.0339765
$52$	0	0
$53$	−3.00000	−0.412082	−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000	−0.412082	−0.206041	+	0.978543i	$0.566058\pi$
$54$	−13.6569	−1.85846
$55$	13.0711	1.76250
$56$	0	0
$57$	−8.48528	−1.12390
$58$	−23.7279	−3.11563
$59$	−1.75736	−0.228789	−0.114394	−	0.993435i	$-0.536493\pi$
$59$	−1.75736	−0.228789	−0.114394	+	0.993435i	$0.536493\pi$
$60$	−20.7279	−2.67596
$61$	9.82843	1.25840	0.629201	−	0.777243i	$-0.283382\pi$
$61$	9.82843	1.25840	0.629201	+	0.777243i	$0.283382\pi$
$62$	−13.0711	−1.66003
$63$	0	0
$64$	−9.82843	−1.22855
$65$	0	0
$66$	11.6569	1.43486
$67$	−4.24264	−0.518321	−0.259161	−	0.965834i	$-0.583446\pi$
$67$	−4.24264	−0.518321	−0.259161	+	0.965834i	$0.583446\pi$
$68$	−0.656854	−0.0796553
$69$	−2.00000	−0.240772
$70$	0	0
$71$	−0.343146	−0.0407239	−0.0203620	−	0.999793i	$-0.506482\pi$
$71$	−0.343146	−0.0407239	−0.0203620	+	0.999793i	$0.506482\pi$
$72$	4.41421	0.520220
$73$	0.656854	0.0768790	0.0384395	−	0.999261i	$-0.487761\pi$
$73$	0.656854	0.0768790	0.0384395	+	0.999261i	$0.487761\pi$
$74$	−18.0711	−2.10072
$75$	−13.6569	−1.57696
$76$	22.9706	2.63490
$77$	0	0
$78$	0	0
$79$	10.2426	1.15239	0.576194	−	0.817313i	$-0.304537\pi$
$79$	10.2426	1.15239	0.576194	+	0.817313i	$0.304537\pi$
$80$	11.4853	1.28409
$81$	−5.00000	−0.555556
$82$	−14.0711	−1.55389
$83$	−13.0711	−1.43474	−0.717368	−	0.696694i	$-0.754653\pi$
$83$	−13.0711	−1.43474	−0.717368	+	0.696694i	$0.754653\pi$
$84$	0	0
$85$	−0.656854	−0.0712458
$86$	−1.41421	−0.152499
$87$	−13.8995	−1.49018
$88$	−15.0711	−1.60658
$89$	−7.31371	−0.775252	−0.387626	−	0.921817i	$-0.626705\pi$
$89$	−7.31371	−0.775252	−0.387626	+	0.921817i	$0.626705\pi$
$90$	9.24264	0.974260
$91$	0	0
$92$	5.41421	0.564471
$93$	−7.65685	−0.793979
$94$	−18.4853	−1.90661
$95$	22.9706	2.35673
$96$	−2.24264	−0.228889
$97$	−5.17157	−0.525094	−0.262547	−	0.964919i	$-0.584562\pi$
$97$	−5.17157	−0.525094	−0.262547	+	0.964919i	$0.584562\pi$
$98$	0	0
$99$	−3.41421	−0.343141
$100$	36.9706	3.69706
$101$	3.34315	0.332655	0.166328	−	0.986071i	$-0.446809\pi$
$101$	3.34315	0.332655	0.166328	+	0.986071i	$0.446809\pi$
$102$	−0.585786	−0.0580015
$103$	14.0000	1.37946	0.689730	−	0.724066i	$-0.257729\pi$
$103$	14.0000	1.37946	0.689730	+	0.724066i	$0.257729\pi$
$104$	0	0
$105$	0	0
$106$	7.24264	0.703467
$107$	−5.31371	−0.513696	−0.256848	−	0.966452i	$-0.582684\pi$
$107$	−5.31371	−0.513696	−0.256848	+	0.966452i	$0.582684\pi$
$108$	21.6569	2.08393
$109$	−2.34315	−0.224433	−0.112216	−	0.993684i	$-0.535795\pi$
$109$	−2.34315	−0.224433	−0.112216	+	0.993684i	$0.535795\pi$
$110$	−31.5563	−3.00878
$111$	−10.5858	−1.00476
$112$	0	0
$113$	−2.31371	−0.217655	−0.108828	−	0.994061i	$-0.534710\pi$
$113$	−2.31371	−0.217655	−0.108828	+	0.994061i	$0.534710\pi$
$114$	20.4853	1.91862
$115$	5.41421	0.504878
$116$	37.6274	3.49362
$117$	0	0
$118$	4.24264	0.390567
$119$	0	0
$120$	23.8995	2.18172
$121$	0.656854	0.0597140
$122$	−23.7279	−2.14823
$123$	−8.24264	−0.743214
$124$	20.7279	1.86142
$125$	17.8284	1.59462
$126$	0	0
$127$	−9.31371	−0.826458	−0.413229	−	0.910627i	$-0.635599\pi$
$127$	−9.31371	−0.826458	−0.413229	+	0.910627i	$0.635599\pi$
$128$	20.5563	1.81694
$129$	−0.828427	−0.0729389
$130$	0	0
$131$	−1.31371	−0.114779	−0.0573896	−	0.998352i	$-0.518278\pi$
$131$	−1.31371	−0.114779	−0.0573896	+	0.998352i	$0.518278\pi$
$132$	−18.4853	−1.60894
$133$	0	0
$134$	10.2426	0.884829
$135$	21.6569	1.86393
$136$	0.757359	0.0649430
$137$	−5.82843	−0.497956	−0.248978	−	0.968509i	$-0.580095\pi$
$137$	−5.82843	−0.497956	−0.248978	+	0.968509i	$0.580095\pi$
$138$	4.82843	0.411023
$139$	7.89949	0.670026	0.335013	−	0.942213i	$-0.391259\pi$
$139$	7.89949	0.670026	0.335013	+	0.942213i	$0.391259\pi$
$140$	0	0
$141$	−10.8284	−0.911918
$142$	0.828427	0.0695201
$143$	0	0
$144$	−3.00000	−0.250000
$145$	37.6274	3.12479
$146$	−1.58579	−0.131241
$147$	0	0
$148$	28.6569	2.35558
$149$	3.00000	0.245770	0.122885	−	0.992421i	$-0.460785\pi$
$149$	3.00000	0.245770	0.122885	+	0.992421i	$0.460785\pi$
$150$	32.9706	2.69204
$151$	−18.9706	−1.54380	−0.771901	−	0.635742i	$-0.780694\pi$
$151$	−18.9706	−1.54380	−0.771901	+	0.635742i	$0.780694\pi$
$152$	−26.4853	−2.14824
$153$	0.171573	0.0138708
$154$	0	0
$155$	20.7279	1.66491
$156$	0	0
$157$	−11.4853	−0.916625	−0.458313	−	0.888791i	$-0.651546\pi$
$157$	−11.4853	−0.916625	−0.458313	+	0.888791i	$0.651546\pi$
$158$	−24.7279	−1.96725
$159$	4.24264	0.336463
$160$	6.07107	0.479960
$161$	0	0
$162$	12.0711	0.948393
$163$	15.4142	1.20733	0.603667	−	0.797236i	$-0.293706\pi$
$163$	15.4142	1.20733	0.603667	+	0.797236i	$0.293706\pi$
$164$	22.3137	1.74241
$165$	−18.4853	−1.43908
$166$	31.5563	2.44925
$167$	−18.7279	−1.44921	−0.724605	−	0.689164i	$-0.757978\pi$
$167$	−18.7279	−1.44921	−0.724605	+	0.689164i	$0.757978\pi$
$168$	0	0
$169$	0	0
$170$	1.58579	0.121624
$171$	−6.00000	−0.458831
$172$	2.24264	0.171000
$173$	18.1421	1.37932	0.689661	−	0.724133i	$-0.257760\pi$
$173$	18.1421	1.37932	0.689661	+	0.724133i	$0.257760\pi$
$174$	33.5563	2.54390
$175$	0	0
$176$	10.2426	0.772068
$177$	2.48528	0.186805
$178$	17.6569	1.32344
$179$	5.65685	0.422813	0.211407	−	0.977398i	$-0.432196\pi$
$179$	5.65685	0.422813	0.211407	+	0.977398i	$0.432196\pi$
$180$	−14.6569	−1.09246
$181$	−19.1421	−1.42282	−0.711412	−	0.702775i	$-0.751944\pi$
$181$	−19.1421	−1.42282	−0.711412	+	0.702775i	$0.751944\pi$
$182$	0	0
$183$	−13.8995	−1.02748
$184$	−6.24264	−0.460214
$185$	28.6569	2.10689
$186$	18.4853	1.35541
$187$	−0.585786	−0.0428369
$188$	29.3137	2.13792
$189$	0	0
$190$	−55.4558	−4.02319
$191$	7.75736	0.561303	0.280651	−	0.959810i	$-0.409450\pi$
$191$	7.75736	0.561303	0.280651	+	0.959810i	$0.409450\pi$
$192$	13.8995	1.00311
$193$	−21.1421	−1.52184	−0.760922	−	0.648843i	$-0.775253\pi$
$193$	−21.1421	−1.52184	−0.760922	+	0.648843i	$0.775253\pi$
$194$	12.4853	0.896391
$195$	0	0
$196$	0	0
$197$	9.17157	0.653448	0.326724	−	0.945120i	$-0.394055\pi$
$197$	9.17157	0.653448	0.326724	+	0.945120i	$0.394055\pi$
$198$	8.24264	0.585779
$199$	18.9706	1.34479	0.672394	−	0.740194i	$-0.265266\pi$
$199$	18.9706	1.34479	0.672394	+	0.740194i	$0.265266\pi$
$200$	−42.6274	−3.01421
$201$	6.00000	0.423207
$202$	−8.07107	−0.567878
$203$	0	0
$204$	0.928932	0.0650383
$205$	22.3137	1.55846
$206$	−33.7990	−2.35489
$207$	−1.41421	−0.0982946
$208$	0	0
$209$	20.4853	1.41700
$210$	0	0
$211$	−0.727922	−0.0501122	−0.0250561	−	0.999686i	$-0.507976\pi$
$211$	−0.727922	−0.0501122	−0.0250561	+	0.999686i	$0.507976\pi$
$212$	−11.4853	−0.788812
$213$	0.485281	0.0332509
$214$	12.8284	0.876933
$215$	2.24264	0.152947
$216$	−24.9706	−1.69903
$217$	0	0
$218$	5.65685	0.383131
$219$	−0.928932	−0.0627714
$220$	50.0416	3.37381
$221$	0	0
$222$	25.5563	1.71523
$223$	2.00000	0.133930	0.0669650	−	0.997755i	$-0.478668\pi$
$223$	2.00000	0.133930	0.0669650	+	0.997755i	$0.478668\pi$
$224$	0	0
$225$	−9.65685	−0.643790
$226$	5.58579	0.371561
$227$	−13.8995	−0.922542	−0.461271	−	0.887259i	$-0.652606\pi$
$227$	−13.8995	−0.922542	−0.461271	+	0.887259i	$0.652606\pi$
$228$	−32.4853	−2.15139
$229$	4.48528	0.296396	0.148198	−	0.988958i	$-0.452653\pi$
$229$	4.48528	0.296396	0.148198	+	0.988958i	$0.452653\pi$
$230$	−13.0711	−0.861881
$231$	0	0
$232$	−43.3848	−2.84835
$233$	−2.82843	−0.185296	−0.0926482	−	0.995699i	$-0.529533\pi$
$233$	−2.82843	−0.185296	−0.0926482	+	0.995699i	$0.529533\pi$
$234$	0	0
$235$	29.3137	1.91222
$236$	−6.72792	−0.437950
$237$	−14.4853	−0.940920
$238$	0	0
$239$	−12.3848	−0.801105	−0.400552	−	0.916274i	$-0.631182\pi$
$239$	−12.3848	−0.801105	−0.400552	+	0.916274i	$0.631182\pi$
$240$	−16.2426	−1.04846
$241$	−1.48528	−0.0956754	−0.0478377	−	0.998855i	$-0.515233\pi$
$241$	−1.48528	−0.0956754	−0.0478377	+	0.998855i	$0.515233\pi$
$242$	−1.58579	−0.101938
$243$	−9.89949	−0.635053
$244$	37.6274	2.40885
$245$	0	0
$246$	19.8995	1.26875
$247$	0	0
$248$	−23.8995	−1.51762
$249$	18.4853	1.17146
$250$	−43.0416	−2.72219
$251$	−10.9706	−0.692456	−0.346228	−	0.938150i	$-0.612538\pi$
$251$	−10.9706	−0.692456	−0.346228	+	0.938150i	$0.612538\pi$
$252$	0	0
$253$	4.82843	0.303561
$254$	22.4853	1.41085
$255$	0.928932	0.0581720
$256$	−29.9706	−1.87316
$257$	15.0000	0.935674	0.467837	−	0.883815i	$-0.345033\pi$
$257$	15.0000	0.935674	0.467837	+	0.883815i	$0.345033\pi$
$258$	2.00000	0.124515
$259$	0	0
$260$	0	0
$261$	−9.82843	−0.608364
$262$	3.17157	0.195940
$263$	18.7279	1.15481	0.577407	−	0.816457i	$-0.304065\pi$
$263$	18.7279	1.15481	0.577407	+	0.816457i	$0.304065\pi$
$264$	21.3137	1.31177
$265$	−11.4853	−0.705535
$266$	0	0
$267$	10.3431	0.632990
$268$	−16.2426	−0.992177
$269$	−18.0000	−1.09748	−0.548740	−	0.835993i	$-0.684892\pi$
$269$	−18.0000	−1.09748	−0.548740	+	0.835993i	$0.684892\pi$
$270$	−52.2843	−3.18192
$271$	−6.92893	−0.420903	−0.210451	−	0.977604i	$-0.567493\pi$
$271$	−6.92893	−0.420903	−0.210451	+	0.977604i	$0.567493\pi$
$272$	−0.514719	−0.0312094
$273$	0	0
$274$	14.0711	0.850064
$275$	32.9706	1.98820
$276$	−7.65685	−0.460888
$277$	−31.9706	−1.92092	−0.960462	−	0.278409i	$-0.910193\pi$
$277$	−31.9706	−1.92092	−0.960462	+	0.278409i	$0.910193\pi$
$278$	−19.0711	−1.14381
$279$	−5.41421	−0.324140
$280$	0	0
$281$	−0.514719	−0.0307055	−0.0153528	−	0.999882i	$-0.504887\pi$
$281$	−0.514719	−0.0307055	−0.0153528	+	0.999882i	$0.504887\pi$
$282$	26.1421	1.55674
$283$	−0.100505	−0.00597441	−0.00298720	−	0.999996i	$-0.500951\pi$
$283$	−0.100505	−0.00597441	−0.00298720	+	0.999996i	$0.500951\pi$
$284$	−1.31371	−0.0779543
$285$	−32.4853	−1.92426
$286$	0	0
$287$	0	0
$288$	−1.58579	−0.0934434
$289$	−16.9706	−0.998268
$290$	−90.8406	−5.33434
$291$	7.31371	0.428737
$292$	2.51472	0.147163
$293$	−22.4558	−1.31188	−0.655942	−	0.754811i	$-0.727729\pi$
$293$	−22.4558	−1.31188	−0.655942	+	0.754811i	$0.727729\pi$
$294$	0	0
$295$	−6.72792	−0.391715
$296$	−33.0416	−1.92051
$297$	19.3137	1.12070
$298$	−7.24264	−0.419555
$299$	0	0
$300$	−52.2843	−3.01863
$301$	0	0
$302$	45.7990	2.63544
$303$	−4.72792	−0.271612
$304$	18.0000	1.03237
$305$	37.6274	2.15454
$306$	−0.414214	−0.0236790
$307$	−7.27208	−0.415039	−0.207520	−	0.978231i	$-0.566539\pi$
$307$	−7.27208	−0.415039	−0.207520	+	0.978231i	$0.566539\pi$
$308$	0	0
$309$	−19.7990	−1.12633
$310$	−50.0416	−2.84217
$311$	−27.0711	−1.53506	−0.767530	−	0.641013i	$-0.778514\pi$
$311$	−27.0711	−1.53506	−0.767530	+	0.641013i	$0.778514\pi$
$312$	0	0
$313$	−14.0000	−0.791327	−0.395663	−	0.918396i	$-0.629485\pi$
$313$	−14.0000	−0.791327	−0.395663	+	0.918396i	$0.629485\pi$
$314$	27.7279	1.56478
$315$	0	0
$316$	39.2132	2.20592
$317$	21.3431	1.19875	0.599375	−	0.800468i	$-0.295416\pi$
$317$	21.3431	1.19875	0.599375	+	0.800468i	$0.295416\pi$
$318$	−10.2426	−0.574379
$319$	33.5563	1.87879
$320$	−37.6274	−2.10344
$321$	7.51472	0.419431
$322$	0	0
$323$	−1.02944	−0.0572794
$324$	−19.1421	−1.06345
$325$	0	0
$326$	−37.2132	−2.06105
$327$	3.31371	0.183248
$328$	−25.7279	−1.42059
$329$	0	0
$330$	44.6274	2.45666
$331$	28.8701	1.58684	0.793421	−	0.608673i	$-0.208298\pi$
$331$	28.8701	1.58684	0.793421	+	0.608673i	$0.208298\pi$
$332$	−50.0416	−2.74639
$333$	−7.48528	−0.410191
$334$	45.2132	2.47396
$335$	−16.2426	−0.887430
$336$	0	0
$337$	13.4853	0.734590	0.367295	−	0.930104i	$-0.380284\pi$
$337$	13.4853	0.734590	0.367295	+	0.930104i	$0.380284\pi$
$338$	0	0
$339$	3.27208	0.177715
$340$	−2.51472	−0.136380
$341$	18.4853	1.00103
$342$	14.4853	0.783274
$343$	0	0
$344$	−2.58579	−0.139416
$345$	−7.65685	−0.412231
$346$	−43.7990	−2.35465
$347$	−25.8995	−1.39036	−0.695179	−	0.718837i	$-0.744675\pi$
$347$	−25.8995	−1.39036	−0.695179	+	0.718837i	$0.744675\pi$
$348$	−53.2132	−2.85253
$349$	−13.3137	−0.712666	−0.356333	−	0.934359i	$-0.615973\pi$
$349$	−13.3137	−0.712666	−0.356333	+	0.934359i	$0.615973\pi$
$350$	0	0
$351$	0	0
$352$	5.41421	0.288579
$353$	0.171573	0.00913190	0.00456595	−	0.999990i	$-0.498547\pi$
$353$	0.171573	0.00913190	0.00456595	+	0.999990i	$0.498547\pi$
$354$	−6.00000	−0.318896
$355$	−1.31371	−0.0697244
$356$	−28.0000	−1.48400
$357$	0	0
$358$	−13.6569	−0.721787
$359$	16.9706	0.895672	0.447836	−	0.894116i	$-0.352195\pi$
$359$	16.9706	0.895672	0.447836	+	0.894116i	$0.352195\pi$
$360$	16.8995	0.890682
$361$	17.0000	0.894737
$362$	46.2132	2.42891
$363$	−0.928932	−0.0487563
$364$	0	0
$365$	2.51472	0.131626
$366$	33.5563	1.75402
$367$	−3.27208	−0.170801	−0.0854005	−	0.996347i	$-0.527217\pi$
$367$	−3.27208	−0.170801	−0.0854005	+	0.996347i	$0.527217\pi$
$368$	4.24264	0.221163
$369$	−5.82843	−0.303416
$370$	−69.1838	−3.59669
$371$	0	0
$372$	−29.3137	−1.51984
$373$	−24.4558	−1.26628	−0.633138	−	0.774039i	$-0.718233\pi$
$373$	−24.4558	−1.26628	−0.633138	+	0.774039i	$0.718233\pi$
$374$	1.41421	0.0731272
$375$	−25.2132	−1.30200
$376$	−33.7990	−1.74305
$377$	0	0
$378$	0	0
$379$	8.24264	0.423396	0.211698	−	0.977335i	$-0.432101\pi$
$379$	8.24264	0.423396	0.211698	+	0.977335i	$0.432101\pi$
$380$	87.9411	4.51128
$381$	13.1716	0.674800
$382$	−18.7279	−0.958204
$383$	14.0416	0.717494	0.358747	−	0.933435i	$-0.383204\pi$
$383$	14.0416	0.717494	0.358747	+	0.933435i	$0.383204\pi$
$384$	−29.0711	−1.48353
$385$	0	0
$386$	51.0416	2.59795
$387$	−0.585786	−0.0297772
$388$	−19.7990	−1.00514
$389$	−1.14214	−0.0579086	−0.0289543	−	0.999581i	$-0.509218\pi$
$389$	−1.14214	−0.0579086	−0.0289543	+	0.999581i	$0.509218\pi$
$390$	0	0
$391$	−0.242641	−0.0122709
$392$	0	0
$393$	1.85786	0.0937169
$394$	−22.1421	−1.11550
$395$	39.2132	1.97303
$396$	−13.0711	−0.656846
$397$	−38.6274	−1.93865	−0.969327	−	0.245774i	$-0.920958\pi$
$397$	−38.6274	−1.93865	−0.969327	+	0.245774i	$0.920958\pi$
$398$	−45.7990	−2.29570
$399$	0	0
$400$	28.9706	1.44853
$401$	−30.7990	−1.53803	−0.769014	−	0.639232i	$-0.779252\pi$
$401$	−30.7990	−1.53803	−0.769014	+	0.639232i	$0.779252\pi$
$402$	−14.4853	−0.722460
$403$	0	0
$404$	12.7990	0.636774
$405$	−19.1421	−0.951180
$406$	0	0
$407$	25.5563	1.26678
$408$	−1.07107	−0.0530258
$409$	11.9706	0.591906	0.295953	−	0.955202i	$-0.404363\pi$
$409$	11.9706	0.591906	0.295953	+	0.955202i	$0.404363\pi$
$410$	−53.8701	−2.66045
$411$	8.24264	0.406579
$412$	53.5980	2.64058
$413$	0	0
$414$	3.41421	0.167799
$415$	−50.0416	−2.45645
$416$	0	0
$417$	−11.1716	−0.547074
$418$	−49.4558	−2.41896
$419$	19.5563	0.955390	0.477695	−	0.878526i	$-0.341472\pi$
$419$	19.5563	0.955390	0.477695	+	0.878526i	$0.341472\pi$
$420$	0	0
$421$	4.51472	0.220034	0.110017	−	0.993930i	$-0.464909\pi$
$421$	4.51472	0.220034	0.110017	+	0.993930i	$0.464909\pi$
$422$	1.75736	0.0855469
$423$	−7.65685	−0.372289
$424$	13.2426	0.643119
$425$	−1.65685	−0.0803692
$426$	−1.17157	−0.0567629
$427$	0	0
$428$	−20.3431	−0.983323
$429$	0	0
$430$	−5.41421	−0.261097
$431$	12.0000	0.578020	0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000	0.578020	0.289010	+	0.957326i	$0.406674\pi$
$432$	16.9706	0.816497
$433$	0.514719	0.0247358	0.0123679	−	0.999924i	$-0.496063\pi$
$433$	0.514719	0.0247358	0.0123679	+	0.999924i	$0.496063\pi$
$434$	0	0
$435$	−53.2132	−2.55138
$436$	−8.97056	−0.429612
$437$	8.48528	0.405906
$438$	2.24264	0.107158
$439$	−26.7279	−1.27565	−0.637827	−	0.770180i	$-0.720167\pi$
$439$	−26.7279	−1.27565	−0.637827	+	0.770180i	$0.720167\pi$
$440$	−57.6985	−2.75067
$441$	0	0
$442$	0	0
$443$	14.3431	0.681463	0.340732	−	0.940161i	$-0.389325\pi$
$443$	14.3431	0.681463	0.340732	+	0.940161i	$0.389325\pi$
$444$	−40.5269	−1.92332
$445$	−28.0000	−1.32733
$446$	−4.82843	−0.228633
$447$	−4.24264	−0.200670
$448$	0	0
$449$	15.5147	0.732185	0.366092	−	0.930578i	$-0.380695\pi$
$449$	15.5147	0.732185	0.366092	+	0.930578i	$0.380695\pi$
$450$	23.3137	1.09902
$451$	19.8995	0.937031
$452$	−8.85786	−0.416639
$453$	26.8284	1.26051
$454$	33.5563	1.57488
$455$	0	0
$456$	37.4558	1.75403
$457$	−25.0000	−1.16945	−0.584725	−	0.811231i	$-0.698798\pi$
$457$	−25.0000	−1.16945	−0.584725	+	0.811231i	$0.698798\pi$
$458$	−10.8284	−0.505979
$459$	−0.970563	−0.0453020
$460$	20.7279	0.966444
$461$	12.6569	0.589488	0.294744	−	0.955576i	$-0.404766\pi$
$461$	12.6569	0.589488	0.294744	+	0.955576i	$0.404766\pi$
$462$	0	0
$463$	−18.7279	−0.870360	−0.435180	−	0.900343i	$-0.643315\pi$
$463$	−18.7279	−0.870360	−0.435180	+	0.900343i	$0.643315\pi$
$464$	29.4853	1.36882
$465$	−29.3137	−1.35939
$466$	6.82843	0.316321
$467$	8.58579	0.397303	0.198651	−	0.980070i	$-0.436344\pi$
$467$	8.58579	0.397303	0.198651	+	0.980070i	$0.436344\pi$
$468$	0	0
$469$	0	0
$470$	−70.7696	−3.26436
$471$	16.2426	0.748421
$472$	7.75736	0.357061
$473$	2.00000	0.0919601
$474$	34.9706	1.60625
$475$	57.9411	2.65852
$476$	0	0
$477$	3.00000	0.137361
$478$	29.8995	1.36757
$479$	−38.3848	−1.75385	−0.876923	−	0.480632i	$-0.840407\pi$
$479$	−38.3848	−1.75385	−0.876923	+	0.480632i	$0.840407\pi$
$480$	−8.58579	−0.391886
$481$	0	0
$482$	3.58579	0.163328
$483$	0	0
$484$	2.51472	0.114305
$485$	−19.7990	−0.899026
$486$	23.8995	1.08410
$487$	20.9706	0.950267	0.475133	−	0.879914i	$-0.342400\pi$
$487$	20.9706	0.950267	0.475133	+	0.879914i	$0.342400\pi$
$488$	−43.3848	−1.96394
$489$	−21.7990	−0.985784
$490$	0	0
$491$	35.3137	1.59369	0.796843	−	0.604187i	$-0.206502\pi$
$491$	35.3137	1.59369	0.796843	+	0.604187i	$0.206502\pi$
$492$	−31.5563	−1.42267
$493$	−1.68629	−0.0759467
$494$	0	0
$495$	−13.0711	−0.587501
$496$	16.2426	0.729316
$497$	0	0
$498$	−44.6274	−1.99980
$499$	−28.0416	−1.25532	−0.627658	−	0.778489i	$-0.715986\pi$
$499$	−28.0416	−1.25532	−0.627658	+	0.778489i	$0.715986\pi$
$500$	68.2548	3.05245
$501$	26.4853	1.18328
$502$	26.4853	1.18210
$503$	−33.5563	−1.49620	−0.748102	−	0.663584i	$-0.769035\pi$
$503$	−33.5563	−1.49620	−0.748102	+	0.663584i	$0.769035\pi$
$504$	0	0
$505$	12.7990	0.569548
$506$	−11.6569	−0.518210
$507$	0	0
$508$	−35.6569	−1.58202
$509$	−6.65685	−0.295060	−0.147530	−	0.989058i	$-0.547132\pi$
$509$	−6.65685	−0.295060	−0.147530	+	0.989058i	$0.547132\pi$
$510$	−2.24264	−0.0993058
$511$	0	0
$512$	31.2426	1.38074
$513$	33.9411	1.49854
$514$	−36.2132	−1.59730
$515$	53.5980	2.36181
$516$	−3.17157	−0.139621
$517$	26.1421	1.14973
$518$	0	0
$519$	−25.6569	−1.12621
$520$	0	0
$521$	−13.3431	−0.584574	−0.292287	−	0.956331i	$-0.594416\pi$
$521$	−13.3431	−0.584574	−0.292287	+	0.956331i	$0.594416\pi$
$522$	23.7279	1.03854
$523$	16.9706	0.742071	0.371035	−	0.928619i	$-0.379003\pi$
$523$	16.9706	0.742071	0.371035	+	0.928619i	$0.379003\pi$
$524$	−5.02944	−0.219712
$525$	0	0
$526$	−45.2132	−1.97139
$527$	−0.928932	−0.0404649
$528$	−14.4853	−0.630391
$529$	−21.0000	−0.913043
$530$	27.7279	1.20442
$531$	1.75736	0.0762629
$532$	0	0
$533$	0	0
$534$	−24.9706	−1.08058
$535$	−20.3431	−0.879511
$536$	18.7279	0.808923
$537$	−8.00000	−0.345225
$538$	43.4558	1.87351
$539$	0	0
$540$	82.9117	3.56795
$541$	5.48528	0.235831	0.117915	−	0.993024i	$-0.462379\pi$
$541$	5.48528	0.235831	0.117915	+	0.993024i	$0.462379\pi$
$542$	16.7279	0.718526
$543$	27.0711	1.16173
$544$	−0.272078	−0.0116652
$545$	−8.97056	−0.384257
$546$	0	0
$547$	15.0711	0.644392	0.322196	−	0.946673i	$-0.395579\pi$
$547$	15.0711	0.644392	0.322196	+	0.946673i	$0.395579\pi$
$548$	−22.3137	−0.953194
$549$	−9.82843	−0.419467
$550$	−79.5980	−3.39407
$551$	58.9706	2.51223
$552$	8.82843	0.375763
$553$	0	0
$554$	77.1838	3.27922
$555$	−40.5269	−1.72027
$556$	30.2426	1.28257
$557$	−10.3137	−0.437006	−0.218503	−	0.975836i	$-0.570117\pi$
$557$	−10.3137	−0.437006	−0.218503	+	0.975836i	$0.570117\pi$
$558$	13.0711	0.553342
$559$	0	0
$560$	0	0
$561$	0.828427	0.0349762
$562$	1.24264	0.0524176
$563$	19.8995	0.838664	0.419332	−	0.907833i	$-0.362264\pi$
$563$	19.8995	0.838664	0.419332	+	0.907833i	$0.362264\pi$
$564$	−41.4558	−1.74561
$565$	−8.85786	−0.372653
$566$	0.242641	0.0101989
$567$	0	0
$568$	1.51472	0.0635562
$569$	13.1716	0.552181	0.276091	−	0.961132i	$-0.410961\pi$
$569$	13.1716	0.552181	0.276091	+	0.961132i	$0.410961\pi$
$570$	78.4264	3.28492
$571$	−4.97056	−0.208012	−0.104006	−	0.994577i	$-0.533166\pi$
$571$	−4.97056	−0.208012	−0.104006	+	0.994577i	$0.533166\pi$
$572$	0	0
$573$	−10.9706	−0.458302
$574$	0	0
$575$	13.6569	0.569530
$576$	9.82843	0.409518
$577$	−36.3137	−1.51176	−0.755880	−	0.654710i	$-0.772791\pi$
$577$	−36.3137	−1.51176	−0.755880	+	0.654710i	$0.772791\pi$
$578$	40.9706	1.70415
$579$	29.8995	1.24258
$580$	144.054	5.98151
$581$	0	0
$582$	−17.6569	−0.731900
$583$	−10.2426	−0.424207
$584$	−2.89949	−0.119982
$585$	0	0
$586$	54.2132	2.23953
$587$	−18.3431	−0.757103	−0.378551	−	0.925580i	$-0.623578\pi$
$587$	−18.3431	−0.757103	−0.378551	+	0.925580i	$0.623578\pi$
$588$	0	0
$589$	32.4853	1.33853
$590$	16.2426	0.668699
$591$	−12.9706	−0.533538
$592$	22.4558	0.922930
$593$	−31.2843	−1.28469	−0.642346	−	0.766415i	$-0.722039\pi$
$593$	−31.2843	−1.28469	−0.642346	+	0.766415i	$0.722039\pi$
$594$	−46.6274	−1.91315
$595$	0	0
$596$	11.4853	0.470455
$597$	−26.8284	−1.09801
$598$	0	0
$599$	39.6569	1.62034	0.810168	−	0.586198i	$-0.199376\pi$
$599$	39.6569	1.62034	0.810168	+	0.586198i	$0.199376\pi$
$600$	60.2843	2.46110
$601$	−36.9411	−1.50686	−0.753430	−	0.657528i	$-0.771602\pi$
$601$	−36.9411	−1.50686	−0.753430	+	0.657528i	$0.771602\pi$
$602$	0	0
$603$	4.24264	0.172774
$604$	−72.6274	−2.95517
$605$	2.51472	0.102238
$606$	11.4142	0.463671
$607$	−43.6569	−1.77198	−0.885989	−	0.463707i	$-0.846519\pi$
$607$	−43.6569	−1.77198	−0.885989	+	0.463707i	$0.846519\pi$
$608$	9.51472	0.385873
$609$	0	0
$610$	−90.8406	−3.67803
$611$	0	0
$612$	0.656854	0.0265518
$613$	24.7990	1.00162	0.500811	−	0.865557i	$-0.333035\pi$
$613$	24.7990	1.00162	0.500811	+	0.865557i	$0.333035\pi$
$614$	17.5563	0.708517
$615$	−31.5563	−1.27247
$616$	0	0
$617$	−2.85786	−0.115053	−0.0575266	−	0.998344i	$-0.518321\pi$
$617$	−2.85786	−0.115053	−0.0575266	+	0.998344i	$0.518321\pi$
$618$	47.7990	1.92276
$619$	10.4437	0.419766	0.209883	−	0.977727i	$-0.432692\pi$
$619$	10.4437	0.419766	0.209883	+	0.977727i	$0.432692\pi$
$620$	79.3553	3.18699
$621$	8.00000	0.321029
$622$	65.3553	2.62051
$623$	0	0
$624$	0	0
$625$	19.9706	0.798823
$626$	33.7990	1.35088
$627$	−28.9706	−1.15697
$628$	−43.9706	−1.75462
$629$	−1.28427	−0.0512072
$630$	0	0
$631$	−32.2843	−1.28522	−0.642608	−	0.766195i	$-0.722148\pi$
$631$	−32.2843	−1.28522	−0.642608	+	0.766195i	$0.722148\pi$
$632$	−45.2132	−1.79848
$633$	1.02944	0.0409165
$634$	−51.5269	−2.04640
$635$	−35.6569	−1.41500
$636$	16.2426	0.644063
$637$	0	0
$638$	−81.0122	−3.20730
$639$	0.343146	0.0135746
$640$	78.6985	3.11083
$641$	24.7990	0.979501	0.489751	−	0.871863i	$-0.337088\pi$
$641$	24.7990	0.979501	0.489751	+	0.871863i	$0.337088\pi$
$642$	−18.1421	−0.716013
$643$	48.9706	1.93121	0.965605	−	0.260013i	$-0.0837267\pi$
$643$	48.9706	1.93121	0.965605	+	0.260013i	$0.0837267\pi$
$644$	0	0
$645$	−3.17157	−0.124881
$646$	2.48528	0.0977821
$647$	5.31371	0.208903	0.104452	−	0.994530i	$-0.466691\pi$
$647$	5.31371	0.208903	0.104452	+	0.994530i	$0.466691\pi$
$648$	22.0711	0.867033
$649$	−6.00000	−0.235521
$650$	0	0
$651$	0	0
$652$	59.0122	2.31110
$653$	−2.14214	−0.0838282	−0.0419141	−	0.999121i	$-0.513346\pi$
$653$	−2.14214	−0.0838282	−0.0419141	+	0.999121i	$0.513346\pi$
$654$	−8.00000	−0.312825
$655$	−5.02944	−0.196516
$656$	17.4853	0.682686
$657$	−0.656854	−0.0256263
$658$	0	0
$659$	7.31371	0.284902	0.142451	−	0.989802i	$-0.454502\pi$
$659$	7.31371	0.284902	0.142451	+	0.989802i	$0.454502\pi$
$660$	−70.7696	−2.75470
$661$	−4.85786	−0.188949	−0.0944745	−	0.995527i	$-0.530117\pi$
$661$	−4.85786	−0.188949	−0.0944745	+	0.995527i	$0.530117\pi$
$662$	−69.6985	−2.70891
$663$	0	0
$664$	57.6985	2.23914
$665$	0	0
$666$	18.0711	0.700240
$667$	13.8995	0.538191
$668$	−71.6985	−2.77410
$669$	−2.82843	−0.109353
$670$	39.2132	1.51494
$671$	33.5563	1.29543
$672$	0	0
$673$	31.4853	1.21367	0.606834	−	0.794828i	$-0.292439\pi$
$673$	31.4853	1.21367	0.606834	+	0.794828i	$0.292439\pi$
$674$	−32.5563	−1.25402
$675$	54.6274	2.10261
$676$	0	0
$677$	−6.34315	−0.243787	−0.121893	−	0.992543i	$-0.538897\pi$
$677$	−6.34315	−0.243787	−0.121893	+	0.992543i	$0.538897\pi$
$678$	−7.89949	−0.303378
$679$	0	0
$680$	2.89949	0.111191
$681$	19.6569	0.753252
$682$	−44.6274	−1.70887
$683$	−17.3137	−0.662491	−0.331245	−	0.943545i	$-0.607469\pi$
$683$	−17.3137	−0.662491	−0.331245	+	0.943545i	$0.607469\pi$
$684$	−22.9706	−0.878301
$685$	−22.3137	−0.852563
$686$	0	0
$687$	−6.34315	−0.242006
$688$	1.75736	0.0669987
$689$	0	0
$690$	18.4853	0.703723
$691$	−37.9411	−1.44335	−0.721674	−	0.692233i	$-0.756627\pi$
$691$	−37.9411	−1.44335	−0.721674	+	0.692233i	$0.756627\pi$
$692$	69.4558	2.64032
$693$	0	0
$694$	62.5269	2.37349
$695$	30.2426	1.14717
$696$	61.3553	2.32567
$697$	−1.00000	−0.0378777
$698$	32.1421	1.21660
$699$	4.00000	0.151294
$700$	0	0
$701$	42.1421	1.59169	0.795843	−	0.605503i	$-0.207028\pi$
$701$	42.1421	1.59169	0.795843	+	0.605503i	$0.207028\pi$
$702$	0	0
$703$	44.9117	1.69388
$704$	−33.5563	−1.26470
$705$	−41.4558	−1.56132
$706$	−0.414214	−0.0155891
$707$	0	0
$708$	9.51472	0.357585
$709$	−27.6274	−1.03757	−0.518785	−	0.854905i	$-0.673615\pi$
$709$	−27.6274	−1.03757	−0.518785	+	0.854905i	$0.673615\pi$
$710$	3.17157	0.119027
$711$	−10.2426	−0.384129
$712$	32.2843	1.20990
$713$	7.65685	0.286751
$714$	0	0
$715$	0	0
$716$	21.6569	0.809355
$717$	17.5147	0.654099
$718$	−40.9706	−1.52901
$719$	−36.3848	−1.35692	−0.678462	−	0.734636i	$-0.737353\pi$
$719$	−36.3848	−1.35692	−0.678462	+	0.734636i	$0.737353\pi$
$720$	−11.4853	−0.428031
$721$	0	0
$722$	−41.0416	−1.52741
$723$	2.10051	0.0781186
$724$	−73.2843	−2.72359
$725$	94.9117	3.52493
$726$	2.24264	0.0832322
$727$	−8.97056	−0.332700	−0.166350	−	0.986067i	$-0.553198\pi$
$727$	−8.97056	−0.332700	−0.166350	+	0.986067i	$0.553198\pi$
$728$	0	0
$729$	29.0000	1.07407
$730$	−6.07107	−0.224700
$731$	−0.100505	−0.00371731
$732$	−53.2132	−1.96682
$733$	−21.0000	−0.775653	−0.387826	−	0.921732i	$-0.626774\pi$
$733$	−21.0000	−0.775653	−0.387826	+	0.921732i	$0.626774\pi$
$734$	7.89949	0.291576
$735$	0	0
$736$	2.24264	0.0826648
$737$	−14.4853	−0.533572
$738$	14.0711	0.517963
$739$	36.2843	1.33474	0.667369	−	0.744727i	$-0.267420\pi$
$739$	36.2843	1.33474	0.667369	+	0.744727i	$0.267420\pi$
$740$	109.711	4.03304
$741$	0	0
$742$	0	0
$743$	−47.5980	−1.74620	−0.873100	−	0.487541i	$-0.837894\pi$
$743$	−47.5980	−1.74620	−0.873100	+	0.487541i	$0.837894\pi$
$744$	33.7990	1.23913
$745$	11.4853	0.420788
$746$	59.0416	2.16167
$747$	13.0711	0.478245
$748$	−2.24264	−0.0819991
$749$	0	0
$750$	60.8701	2.22266
$751$	13.5563	0.494678	0.247339	−	0.968929i	$-0.420444\pi$
$751$	13.5563	0.494678	0.247339	+	0.968929i	$0.420444\pi$
$752$	22.9706	0.837650
$753$	15.5147	0.565388
$754$	0	0
$755$	−72.6274	−2.64318
$756$	0	0
$757$	−21.4558	−0.779826	−0.389913	−	0.920852i	$-0.627495\pi$
$757$	−21.4558	−0.779826	−0.389913	+	0.920852i	$0.627495\pi$
$758$	−19.8995	−0.722782
$759$	−6.82843	−0.247856
$760$	−101.397	−3.67805
$761$	46.1421	1.67265	0.836326	−	0.548233i	$-0.184699\pi$
$761$	46.1421	1.67265	0.836326	+	0.548233i	$0.184699\pi$
$762$	−31.7990	−1.15196
$763$	0	0
$764$	29.6985	1.07445
$765$	0.656854	0.0237486
$766$	−33.8995	−1.22484
$767$	0	0
$768$	42.3848	1.52943
$769$	1.45584	0.0524991	0.0262495	−	0.999655i	$-0.491644\pi$
$769$	1.45584	0.0524991	0.0262495	+	0.999655i	$0.491644\pi$
$770$	0	0
$771$	−21.2132	−0.763975
$772$	−80.9411	−2.91313
$773$	17.6569	0.635073	0.317536	−	0.948246i	$-0.397144\pi$
$773$	17.6569	0.635073	0.317536	+	0.948246i	$0.397144\pi$
$774$	1.41421	0.0508329
$775$	52.2843	1.87811
$776$	22.8284	0.819493
$777$	0	0
$778$	2.75736	0.0988561
$779$	34.9706	1.25295
$780$	0	0
$781$	−1.17157	−0.0419222
$782$	0.585786	0.0209477
$783$	55.5980	1.98691
$784$	0	0
$785$	−43.9706	−1.56938
$786$	−4.48528	−0.159985
$787$	5.89949	0.210294	0.105147	−	0.994457i	$-0.466469\pi$
$787$	5.89949	0.210294	0.105147	+	0.994457i	$0.466469\pi$
$788$	35.1127	1.25084
$789$	−26.4853	−0.942901
$790$	−94.6690	−3.36817
$791$	0	0
$792$	15.0711	0.535527
$793$	0	0
$794$	93.2548	3.30949
$795$	16.2426	0.576067
$796$	72.6274	2.57421
$797$	10.1421	0.359253	0.179626	−	0.983735i	$-0.442511\pi$
$797$	10.1421	0.359253	0.179626	+	0.983735i	$0.442511\pi$
$798$	0	0
$799$	−1.31371	−0.0464757
$800$	15.3137	0.541421
$801$	7.31371	0.258417
$802$	74.3553	2.62558
$803$	2.24264	0.0791411
$804$	22.9706	0.810109
$805$	0	0
$806$	0	0
$807$	25.4558	0.896088
$808$	−14.7574	−0.519162
$809$	6.85786	0.241110	0.120555	−	0.992707i	$-0.461533\pi$
$809$	6.85786	0.241110	0.120555	+	0.992707i	$0.461533\pi$
$810$	46.2132	1.62377
$811$	34.1838	1.20035	0.600177	−	0.799867i	$-0.295097\pi$
$811$	34.1838	1.20035	0.600177	+	0.799867i	$0.295097\pi$
$812$	0	0
$813$	9.79899	0.343666
$814$	−61.6985	−2.16253
$815$	59.0122	2.06711
$816$	0.727922	0.0254824
$817$	3.51472	0.122964
$818$	−28.8995	−1.01045
$819$	0	0
$820$	85.4264	2.98322
$821$	27.9411	0.975152	0.487576	−	0.873081i	$-0.337881\pi$
$821$	27.9411	0.975152	0.487576	+	0.873081i	$0.337881\pi$
$822$	−19.8995	−0.694075
$823$	−3.31371	−0.115509	−0.0577543	−	0.998331i	$-0.518394\pi$
$823$	−3.31371	−0.115509	−0.0577543	+	0.998331i	$0.518394\pi$
$824$	−61.7990	−2.15287
$825$	−46.6274	−1.62336
$826$	0	0
$827$	40.6690	1.41420	0.707101	−	0.707113i	$-0.250003\pi$
$827$	40.6690	1.41420	0.707101	+	0.707113i	$0.250003\pi$
$828$	−5.41421	−0.188157
$829$	23.6863	0.822659	0.411329	−	0.911487i	$-0.365065\pi$
$829$	23.6863	0.822659	0.411329	+	0.911487i	$0.365065\pi$
$830$	120.811	4.19342
$831$	45.2132	1.56843
$832$	0	0
$833$	0	0
$834$	26.9706	0.933914
$835$	−71.6985	−2.48123
$836$	78.4264	2.71243
$837$	30.6274	1.05864
$838$	−47.2132	−1.63095
$839$	37.5980	1.29803	0.649013	−	0.760777i	$-0.275182\pi$
$839$	37.5980	1.29803	0.649013	+	0.760777i	$0.275182\pi$
$840$	0	0
$841$	67.5980	2.33096
$842$	−10.8995	−0.375621
$843$	0.727922	0.0250710
$844$	−2.78680	−0.0959255
$845$	0	0
$846$	18.4853	0.635537
$847$	0	0
$848$	−9.00000	−0.309061
$849$	0.142136	0.00487808
$850$	4.00000	0.137199
$851$	10.5858	0.362876
$852$	1.85786	0.0636494
$853$	−35.0000	−1.19838	−0.599189	−	0.800608i	$-0.704510\pi$
$853$	−35.0000	−1.19838	−0.599189	+	0.800608i	$0.704510\pi$
$854$	0	0
$855$	−22.9706	−0.785577
$856$	23.4558	0.801704
$857$	40.7990	1.39367	0.696833	−	0.717233i	$-0.254592\pi$
$857$	40.7990	1.39367	0.696833	+	0.717233i	$0.254592\pi$
$858$	0	0
$859$	−27.0711	−0.923653	−0.461826	−	0.886970i	$-0.652806\pi$
$859$	−27.0711	−0.923653	−0.461826	+	0.886970i	$0.652806\pi$
$860$	8.58579	0.292773
$861$	0	0
$862$	−28.9706	−0.986741
$863$	56.1838	1.91252	0.956259	−	0.292522i	$-0.0944944\pi$
$863$	56.1838	1.91252	0.956259	+	0.292522i	$0.0944944\pi$
$864$	8.97056	0.305185
$865$	69.4558	2.36157
$866$	−1.24264	−0.0422266
$867$	24.0000	0.815083
$868$	0	0
$869$	34.9706	1.18630
$870$	128.468	4.35547
$871$	0	0
$872$	10.3431	0.350263
$873$	5.17157	0.175031
$874$	−20.4853	−0.692925
$875$	0	0
$876$	−3.55635	−0.120158
$877$	17.0000	0.574049	0.287025	−	0.957923i	$-0.407334\pi$
$877$	17.0000	0.574049	0.287025	+	0.957923i	$0.407334\pi$
$878$	64.5269	2.17768
$879$	31.7574	1.07115
$880$	39.2132	1.32188
$881$	−46.4558	−1.56514	−0.782569	−	0.622564i	$-0.786091\pi$
$881$	−46.4558	−1.56514	−0.782569	+	0.622564i	$0.786091\pi$
$882$	0	0
$883$	7.95837	0.267820	0.133910	−	0.990993i	$-0.457247\pi$
$883$	7.95837	0.267820	0.133910	+	0.990993i	$0.457247\pi$
$884$	0	0
$885$	9.51472	0.319834
$886$	−34.6274	−1.16333
$887$	10.6274	0.356834	0.178417	−	0.983955i	$-0.442902\pi$
$887$	10.6274	0.356834	0.178417	+	0.983955i	$0.442902\pi$
$888$	46.7279	1.56809
$889$	0	0
$890$	67.5980	2.26589
$891$	−17.0711	−0.571902
$892$	7.65685	0.256370
$893$	45.9411	1.53736
$894$	10.2426	0.342565
$895$	21.6569	0.723909
$896$	0	0
$897$	0	0
$898$	−37.4558	−1.24992
$899$	53.2132	1.77476
$900$	−36.9706	−1.23235
$901$	0.514719	0.0171478
$902$	−48.0416	−1.59961
$903$	0	0
$904$	10.2132	0.339686
$905$	−73.2843	−2.43605
$906$	−64.7696	−2.15182
$907$	18.7279	0.621850	0.310925	−	0.950434i	$-0.399361\pi$
$907$	18.7279	0.621850	0.310925	+	0.950434i	$0.399361\pi$
$908$	−53.2132	−1.76594
$909$	−3.34315	−0.110885
$910$	0	0
$911$	−18.3431	−0.607736	−0.303868	−	0.952714i	$-0.598278\pi$
$911$	−18.3431	−0.607736	−0.303868	+	0.952714i	$0.598278\pi$
$912$	−25.4558	−0.842927
$913$	−44.6274	−1.47695
$914$	60.3553	1.99638
$915$	−53.2132	−1.75917
$916$	17.1716	0.567365
$917$	0	0
$918$	2.34315	0.0773353
$919$	25.3137	0.835022	0.417511	−	0.908672i	$-0.362902\pi$
$919$	25.3137	0.835022	0.417511	+	0.908672i	$0.362902\pi$
$920$	−23.8995	−0.787943
$921$	10.2843	0.338878
$922$	−30.5563	−1.00632
$923$	0	0
$924$	0	0
$925$	72.2843	2.37669
$926$	45.2132	1.48580
$927$	−14.0000	−0.459820
$928$	15.5858	0.511629
$929$	−18.9411	−0.621438	−0.310719	−	0.950502i	$-0.600570\pi$
$929$	−18.9411	−0.621438	−0.310719	+	0.950502i	$0.600570\pi$
$930$	70.7696	2.32063
$931$	0	0
$932$	−10.8284	−0.354697
$933$	38.2843	1.25337
$934$	−20.7279	−0.678238
$935$	−2.24264	−0.0733422
$936$	0	0
$937$	−8.85786	−0.289374	−0.144687	−	0.989477i	$-0.546217\pi$
$937$	−8.85786	−0.289374	−0.144687	+	0.989477i	$0.546217\pi$
$938$	0	0
$939$	19.7990	0.646116
$940$	112.225	3.66039
$941$	19.0294	0.620342	0.310171	−	0.950681i	$-0.399614\pi$
$941$	19.0294	0.620342	0.310171	+	0.950681i	$0.399614\pi$
$942$	−39.2132	−1.27764
$943$	8.24264	0.268417
$944$	−5.27208	−0.171592
$945$	0	0
$946$	−4.82843	−0.156986
$947$	18.5858	0.603957	0.301978	−	0.953315i	$-0.402353\pi$
$947$	18.5858	0.603957	0.301978	+	0.953315i	$0.402353\pi$
$948$	−55.4558	−1.80112
$949$	0	0
$950$	−139.882	−4.53838
$951$	−30.1838	−0.978776
$952$	0	0
$953$	−38.6274	−1.25126	−0.625632	−	0.780118i	$-0.715159\pi$
$953$	−38.6274	−1.25126	−0.625632	+	0.780118i	$0.715159\pi$
$954$	−7.24264	−0.234489
$955$	29.6985	0.961020
$956$	−47.4142	−1.53349
$957$	−47.4558	−1.53403
$958$	92.6690	2.99400
$959$	0	0
$960$	53.2132	1.71745
$961$	−1.68629	−0.0543965
$962$	0	0
$963$	5.31371	0.171232
$964$	−5.68629	−0.183143
$965$	−80.9411	−2.60559
$966$	0	0
$967$	−28.2426	−0.908222	−0.454111	−	0.890945i	$-0.650043\pi$
$967$	−28.2426	−0.908222	−0.454111	+	0.890945i	$0.650043\pi$
$968$	−2.89949	−0.0931933
$969$	1.45584	0.0467685
$970$	47.7990	1.53473
$971$	40.3431	1.29467	0.647337	−	0.762204i	$-0.275883\pi$
$971$	40.3431	1.29467	0.647337	+	0.762204i	$0.275883\pi$
$972$	−37.8995	−1.21563
$973$	0	0
$974$	−50.6274	−1.62221
$975$	0	0
$976$	29.4853	0.943801
$977$	−48.5980	−1.55479	−0.777394	−	0.629015i	$-0.783459\pi$
$977$	−48.5980	−1.55479	−0.777394	+	0.629015i	$0.783459\pi$
$978$	52.6274	1.68284
$979$	−24.9706	−0.798063
$980$	0	0
$981$	2.34315	0.0748109
$982$	−85.2548	−2.72059
$983$	−42.0000	−1.33959	−0.669796	−	0.742545i	$-0.733618\pi$
$983$	−42.0000	−1.33959	−0.669796	+	0.742545i	$0.733618\pi$
$984$	36.3848	1.15990
$985$	35.1127	1.11878
$986$	4.07107	0.129649
$987$	0	0
$988$	0	0
$989$	0.828427	0.0263425
$990$	31.5563	1.00293
$991$	28.2426	0.897157	0.448579	−	0.893743i	$-0.351930\pi$
$991$	28.2426	0.897157	0.448579	+	0.893743i	$0.351930\pi$
$992$	8.58579	0.272599
$993$	−40.8284	−1.29565
$994$	0	0
$995$	72.6274	2.30244
$996$	70.7696	2.24242
$997$	−19.9706	−0.632474	−0.316237	−	0.948680i	$-0.602419\pi$
$997$	−19.9706	−0.632474	−0.316237	+	0.948680i	$0.602419\pi$
$998$	67.6985	2.14296
$999$	42.3431	1.33968

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8281.2.a.p.1.1		2
7.6	odd	2		8281.2.a.o.1.1		2
13.3	even	3		637.2.f.f.295.2	yes	4
13.9	even	3		637.2.f.f.393.2	yes	4
13.12	even	2		8281.2.a.x.1.2		2
91.3	odd	6		637.2.g.g.373.2		4
91.9	even	3		637.2.g.f.263.2		4
91.16	even	3		637.2.h.b.165.1		4
91.48	odd	6		637.2.f.e.393.2	yes	4
91.55	odd	6		637.2.f.e.295.2	✓	4
91.61	odd	6		637.2.g.g.263.2		4
91.68	odd	6		637.2.h.c.165.1		4
91.74	even	3		637.2.h.b.471.1		4
91.81	even	3		637.2.g.f.373.2		4
91.87	odd	6		637.2.h.c.471.1		4
91.90	odd	2		8281.2.a.y.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.f.e.295.2	✓	4	91.55	odd	6
637.2.f.e.393.2	yes	4	91.48	odd	6
637.2.f.f.295.2	yes	4	13.3	even	3
637.2.f.f.393.2	yes	4	13.9	even	3
637.2.g.f.263.2		4	91.9	even	3
637.2.g.f.373.2		4	91.81	even	3
637.2.g.g.263.2		4	91.61	odd	6
637.2.g.g.373.2		4	91.3	odd	6
637.2.h.b.165.1		4	91.16	even	3
637.2.h.b.471.1		4	91.74	even	3
637.2.h.c.165.1		4	91.68	odd	6
637.2.h.c.471.1		4	91.87	odd	6
8281.2.a.o.1.1		2	7.6	odd	2
8281.2.a.p.1.1		2	1.1	even	1	trivial
8281.2.a.x.1.2		2	13.12	even	2
8281.2.a.y.1.2		2	91.90	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8281 = 7^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8281.a (trivial)

\(f(q)\)	\(=\)	\(q-2.41421 q^{2} -1.41421 q^{3} +3.82843 q^{4} +3.82843 q^{5} +3.41421 q^{6} -4.41421 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.41421 q^{2} -1.41421 q^{3} +3.82843 q^{4} +3.82843 q^{5} +3.41421 q^{6} -4.41421 q^{8} -1.00000 q^{9} -9.24264 q^{10} +3.41421 q^{11} -5.41421 q^{12} -5.41421 q^{15} +3.00000 q^{16} -0.171573 q^{17} +2.41421 q^{18} +6.00000 q^{19} +14.6569 q^{20} -8.24264 q^{22} +1.41421 q^{23} +6.24264 q^{24} +9.65685 q^{25} +5.65685 q^{27} +9.82843 q^{29} +13.0711 q^{30} +5.41421 q^{31} +1.58579 q^{32} -4.82843 q^{33} +0.414214 q^{34} -3.82843 q^{36} +7.48528 q^{37} -14.4853 q^{38} -16.8995 q^{40} +5.82843 q^{41} +0.585786 q^{43} +13.0711 q^{44} -3.82843 q^{45} -3.41421 q^{46} +7.65685 q^{47} -4.24264 q^{48} -23.3137 q^{50} +0.242641 q^{51} -3.00000 q^{53} -13.6569 q^{54} +13.0711 q^{55} -8.48528 q^{57} -23.7279 q^{58} -1.75736 q^{59} -20.7279 q^{60} +9.82843 q^{61} -13.0711 q^{62} -9.82843 q^{64} +11.6569 q^{66} -4.24264 q^{67} -0.656854 q^{68} -2.00000 q^{69} -0.343146 q^{71} +4.41421 q^{72} +0.656854 q^{73} -18.0711 q^{74} -13.6569 q^{75} +22.9706 q^{76} +10.2426 q^{79} +11.4853 q^{80} -5.00000 q^{81} -14.0711 q^{82} -13.0711 q^{83} -0.656854 q^{85} -1.41421 q^{86} -13.8995 q^{87} -15.0711 q^{88} -7.31371 q^{89} +9.24264 q^{90} +5.41421 q^{92} -7.65685 q^{93} -18.4853 q^{94} +22.9706 q^{95} -2.24264 q^{96} -5.17157 q^{97} -3.41421 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} + 4 q^{6} - 6 q^{8} - 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 2 * q^4 + 2 * q^5 + 4 * q^6 - 6 * q^8 - 2 * q^9	\( 2 q - 2 q^{2} + 2 q^{4} + 2 q^{5} + 4 q^{6} - 6 q^{8} - 2 q^{9} - 10 q^{10} + 4 q^{11} - 8 q^{12} - 8 q^{15} + 6 q^{16} - 6 q^{17} + 2 q^{18} + 12 q^{19} + 18 q^{20} - 8 q^{22} + 4 q^{24} + 8 q^{25} + 14 q^{29} + 12 q^{30} + 8 q^{31} + 6 q^{32} - 4 q^{33} - 2 q^{34} - 2 q^{36} - 2 q^{37} - 12 q^{38} - 14 q^{40} + 6 q^{41} + 4 q^{43} + 12 q^{44} - 2 q^{45} - 4 q^{46} + 4 q^{47} - 24 q^{50} - 8 q^{51} - 6 q^{53} - 16 q^{54} + 12 q^{55} - 22 q^{58} - 12 q^{59} - 16 q^{60} + 14 q^{61} - 12 q^{62} - 14 q^{64} + 12 q^{66} + 10 q^{68} - 4 q^{69} - 12 q^{71} + 6 q^{72} - 10 q^{73} - 22 q^{74} - 16 q^{75} + 12 q^{76} + 12 q^{79} + 6 q^{80} - 10 q^{81} - 14 q^{82} - 12 q^{83} + 10 q^{85} - 8 q^{87} - 16 q^{88} + 8 q^{89} + 10 q^{90} + 8 q^{92} - 4 q^{93} - 20 q^{94} + 12 q^{95} + 4 q^{96} - 16 q^{97} - 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 + 2 * q^5 + 4 * q^6 - 6 * q^8 - 2 * q^9 - 10 * q^10 + 4 * q^11 - 8 * q^12 - 8 * q^15 + 6 * q^16 - 6 * q^17 + 2 * q^18 + 12 * q^19 + 18 * q^20 - 8 * q^22 + 4 * q^24 + 8 * q^25 + 14 * q^29 + 12 * q^30 + 8 * q^31 + 6 * q^32 - 4 * q^33 - 2 * q^34 - 2 * q^36 - 2 * q^37 - 12 * q^38 - 14 * q^40 + 6 * q^41 + 4 * q^43 + 12 * q^44 - 2 * q^45 - 4 * q^46 + 4 * q^47 - 24 * q^50 - 8 * q^51 - 6 * q^53 - 16 * q^54 + 12 * q^55 - 22 * q^58 - 12 * q^59 - 16 * q^60 + 14 * q^61 - 12 * q^62 - 14 * q^64 + 12 * q^66 + 10 * q^68 - 4 * q^69 - 12 * q^71 + 6 * q^72 - 10 * q^73 - 22 * q^74 - 16 * q^75 + 12 * q^76 + 12 * q^79 + 6 * q^80 - 10 * q^81 - 14 * q^82 - 12 * q^83 + 10 * q^85 - 8 * q^87 - 16 * q^88 + 8 * q^89 + 10 * q^90 + 8 * q^92 - 4 * q^93 - 20 * q^94 + 12 * q^95 + 4 * q^96 - 16 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more