LMFDB - Embedded newform 366.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [366,2,Mod(1,366)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(366, 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("366.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 366 = 2 \cdot 3 \cdot 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	366.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:	$2.92252471398$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{17}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4 $ x^2 - x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.56155$ of defining polynomial
Character	$\chi$	$=$	366.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.12311 q^{5} +1.00000 q^{6} -3.56155 q^{7} -1.00000 q^{8} +1.00000 q^{9} +4.12311 q^{10} +3.56155 q^{11} -1.00000 q^{12} +5.56155 q^{13} +3.56155 q^{14} +4.12311 q^{15} +1.00000 q^{16} +0.561553 q^{17} -1.00000 q^{18} +4.00000 q^{19} -4.12311 q^{20} +3.56155 q^{21} -3.56155 q^{22} -5.00000 q^{23} +1.00000 q^{24} +12.0000 q^{25} -5.56155 q^{26} -1.00000 q^{27} -3.56155 q^{28} -5.12311 q^{29} -4.12311 q^{30} +4.00000 q^{31} -1.00000 q^{32} -3.56155 q^{33} -0.561553 q^{34} +14.6847 q^{35} +1.00000 q^{36} -3.68466 q^{37} -4.00000 q^{38} -5.56155 q^{39} +4.12311 q^{40} +9.56155 q^{41} -3.56155 q^{42} -2.56155 q^{43} +3.56155 q^{44} -4.12311 q^{45} +5.00000 q^{46} +7.12311 q^{47} -1.00000 q^{48} +5.68466 q^{49} -12.0000 q^{50} -0.561553 q^{51} +5.56155 q^{52} +9.12311 q^{53} +1.00000 q^{54} -14.6847 q^{55} +3.56155 q^{56} -4.00000 q^{57} +5.12311 q^{58} -6.43845 q^{59} +4.12311 q^{60} +1.00000 q^{61} -4.00000 q^{62} -3.56155 q^{63} +1.00000 q^{64} -22.9309 q^{65} +3.56155 q^{66} -3.31534 q^{67} +0.561553 q^{68} +5.00000 q^{69} -14.6847 q^{70} +13.9309 q^{71} -1.00000 q^{72} +16.3693 q^{73} +3.68466 q^{74} -12.0000 q^{75} +4.00000 q^{76} -12.6847 q^{77} +5.56155 q^{78} -12.9309 q^{79} -4.12311 q^{80} +1.00000 q^{81} -9.56155 q^{82} -10.8078 q^{83} +3.56155 q^{84} -2.31534 q^{85} +2.56155 q^{86} +5.12311 q^{87} -3.56155 q^{88} +15.6847 q^{89} +4.12311 q^{90} -19.8078 q^{91} -5.00000 q^{92} -4.00000 q^{93} -7.12311 q^{94} -16.4924 q^{95} +1.00000 q^{96} -3.43845 q^{97} -5.68466 q^{98} +3.56155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 3 q^{7} - 2 q^{8} + 2 q^{9} + 3 q^{11} - 2 q^{12} + 7 q^{13} + 3 q^{14} + 2 q^{16} - 3 q^{17} - 2 q^{18} + 8 q^{19} + 3 q^{21} - 3 q^{22} - 10 q^{23} + 2 q^{24}+ \cdots + 3 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 3 * q^7 - 2 * q^8 + 2 * q^9 + 3 * q^11 - 2 * q^12 + 7 * q^13 + 3 * q^14 + 2 * q^16 - 3 * q^17 - 2 * q^18 + 8 * q^19 + 3 * q^21 - 3 * q^22 - 10 * q^23 + 2 * q^24 + 24 * q^25 - 7 * q^26 - 2 * q^27 - 3 * q^28 - 2 * q^29 + 8 * q^31 - 2 * q^32 - 3 * q^33 + 3 * q^34 + 17 * q^35 + 2 * q^36 + 5 * q^37 - 8 * q^38 - 7 * q^39 + 15 * q^41 - 3 * q^42 - q^43 + 3 * q^44 + 10 * q^46 + 6 * q^47 - 2 * q^48 - q^49 - 24 * q^50 + 3 * q^51 + 7 * q^52 + 10 * q^53 + 2 * q^54 - 17 * q^55 + 3 * q^56 - 8 * q^57 + 2 * q^58 - 17 * q^59 + 2 * q^61 - 8 * q^62 - 3 * q^63 + 2 * q^64 - 17 * q^65 + 3 * q^66 - 19 * q^67 - 3 * q^68 + 10 * q^69 - 17 * q^70 - q^71 - 2 * q^72 + 8 * q^73 - 5 * q^74 - 24 * q^75 + 8 * q^76 - 13 * q^77 + 7 * q^78 + 3 * q^79 + 2 * q^81 - 15 * q^82 - q^83 + 3 * q^84 - 17 * q^85 + q^86 + 2 * q^87 - 3 * q^88 + 19 * q^89 - 19 * q^91 - 10 * q^92 - 8 * q^93 - 6 * q^94 + 2 * q^96 - 11 * q^97 + q^98 + 3 * q^99

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
$5$	−4.12311	−1.84391	−0.921954	−	0.387298i	$-0.873408\pi$
$5$	−4.12311	−1.84391	−0.921954	+	0.387298i	$0.873408\pi$
$6$	1.00000	0.408248
$7$	−3.56155	−1.34614	−0.673070	−	0.739579i	$-0.735025\pi$
$7$	−3.56155	−1.34614	−0.673070	+	0.739579i	$0.735025\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	4.12311	1.30384
$11$	3.56155	1.07385	0.536924	−	0.843630i	$-0.319586\pi$
$11$	3.56155	1.07385	0.536924	+	0.843630i	$0.319586\pi$
$12$	−1.00000	−0.288675
$13$	5.56155	1.54250	0.771249	−	0.636534i	$-0.219633\pi$
$13$	5.56155	1.54250	0.771249	+	0.636534i	$0.219633\pi$
$14$	3.56155	0.951865
$15$	4.12311	1.06458
$16$	1.00000	0.250000
$17$	0.561553	0.136197	0.0680983	−	0.997679i	$-0.478307\pi$
$17$	0.561553	0.136197	0.0680983	+	0.997679i	$0.478307\pi$
$18$	−1.00000	−0.235702
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	−4.12311	−0.921954
$21$	3.56155	0.777195
$22$	−3.56155	−0.759326
$23$	−5.00000	−1.04257	−0.521286	−	0.853382i	$-0.674548\pi$
$23$	−5.00000	−1.04257	−0.521286	+	0.853382i	$0.674548\pi$
$24$	1.00000	0.204124
$25$	12.0000	2.40000
$26$	−5.56155	−1.09071
$27$	−1.00000	−0.192450
$28$	−3.56155	−0.673070
$29$	−5.12311	−0.951337	−0.475668	−	0.879625i	$-0.657794\pi$
$29$	−5.12311	−0.951337	−0.475668	+	0.879625i	$0.657794\pi$
$30$	−4.12311	−0.752773
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	−1.00000	−0.176777
$33$	−3.56155	−0.619987
$34$	−0.561553	−0.0963055
$35$	14.6847	2.48216
$36$	1.00000	0.166667
$37$	−3.68466	−0.605754	−0.302877	−	0.953030i	$-0.597947\pi$
$37$	−3.68466	−0.605754	−0.302877	+	0.953030i	$0.597947\pi$
$38$	−4.00000	−0.648886
$39$	−5.56155	−0.890561
$40$	4.12311	0.651920
$41$	9.56155	1.49326	0.746632	−	0.665237i	$-0.231670\pi$
$41$	9.56155	1.49326	0.746632	+	0.665237i	$0.231670\pi$
$42$	−3.56155	−0.549560
$43$	−2.56155	−0.390633	−0.195317	−	0.980740i	$-0.562573\pi$
$43$	−2.56155	−0.390633	−0.195317	+	0.980740i	$0.562573\pi$
$44$	3.56155	0.536924
$45$	−4.12311	−0.614636
$46$	5.00000	0.737210
$47$	7.12311	1.03901	0.519506	−	0.854467i	$-0.326116\pi$
$47$	7.12311	1.03901	0.519506	+	0.854467i	$0.326116\pi$
$48$	−1.00000	−0.144338
$49$	5.68466	0.812094
$50$	−12.0000	−1.69706
$51$	−0.561553	−0.0786331
$52$	5.56155	0.771249
$53$	9.12311	1.25315	0.626577	−	0.779359i	$-0.284455\pi$
$53$	9.12311	1.25315	0.626577	+	0.779359i	$0.284455\pi$
$54$	1.00000	0.136083
$55$	−14.6847	−1.98008
$56$	3.56155	0.475933
$57$	−4.00000	−0.529813
$58$	5.12311	0.672697
$59$	−6.43845	−0.838214	−0.419107	−	0.907937i	$-0.637657\pi$
$59$	−6.43845	−0.838214	−0.419107	+	0.907937i	$0.637657\pi$
$60$	4.12311	0.532291
$61$	1.00000	0.128037
$61$	1.00000	0.128037
$62$	−4.00000	−0.508001
$63$	−3.56155	−0.448713
$64$	1.00000	0.125000
$65$	−22.9309	−2.84422
$66$	3.56155	0.438397
$67$	−3.31534	−0.405033	−0.202517	−	0.979279i	$-0.564912\pi$
$67$	−3.31534	−0.405033	−0.202517	+	0.979279i	$0.564912\pi$
$68$	0.561553	0.0680983
$69$	5.00000	0.601929
$70$	−14.6847	−1.75515
$71$	13.9309	1.65329	0.826645	−	0.562724i	$-0.190247\pi$
$71$	13.9309	1.65329	0.826645	+	0.562724i	$0.190247\pi$
$72$	−1.00000	−0.117851
$73$	16.3693	1.91588	0.957942	−	0.286963i	$-0.0926455\pi$
$73$	16.3693	1.91588	0.957942	+	0.286963i	$0.0926455\pi$
$74$	3.68466	0.428333
$75$	−12.0000	−1.38564
$76$	4.00000	0.458831
$77$	−12.6847	−1.44555
$78$	5.56155	0.629722
$79$	−12.9309	−1.45484	−0.727418	−	0.686194i	$-0.759280\pi$
$79$	−12.9309	−1.45484	−0.727418	+	0.686194i	$0.759280\pi$
$80$	−4.12311	−0.460977
$81$	1.00000	0.111111
$82$	−9.56155	−1.05590
$83$	−10.8078	−1.18631	−0.593153	−	0.805090i	$-0.702117\pi$
$83$	−10.8078	−1.18631	−0.593153	+	0.805090i	$0.702117\pi$
$84$	3.56155	0.388597
$85$	−2.31534	−0.251134
$86$	2.56155	0.276219
$87$	5.12311	0.549255
$88$	−3.56155	−0.379663
$89$	15.6847	1.66257	0.831285	−	0.555846i	$-0.187606\pi$
$89$	15.6847	1.66257	0.831285	+	0.555846i	$0.187606\pi$
$90$	4.12311	0.434613
$91$	−19.8078	−2.07642
$92$	−5.00000	−0.521286
$93$	−4.00000	−0.414781
$94$	−7.12311	−0.734692
$95$	−16.4924	−1.69209
$96$	1.00000	0.102062
$97$	−3.43845	−0.349121	−0.174561	−	0.984646i	$-0.555851\pi$
$97$	−3.43845	−0.349121	−0.174561	+	0.984646i	$0.555851\pi$
$98$	−5.68466	−0.574237
$99$	3.56155	0.357950
$100$	12.0000	1.20000
$101$	6.24621	0.621521	0.310761	−	0.950488i	$-0.399416\pi$
$101$	6.24621	0.621521	0.310761	+	0.950488i	$0.399416\pi$
$102$	0.561553	0.0556020
$103$	4.56155	0.449463	0.224732	−	0.974421i	$-0.427849\pi$
$103$	4.56155	0.449463	0.224732	+	0.974421i	$0.427849\pi$
$104$	−5.56155	−0.545355
$105$	−14.6847	−1.43308
$106$	−9.12311	−0.886114
$107$	8.56155	0.827677	0.413838	−	0.910350i	$-0.364188\pi$
$107$	8.56155	0.827677	0.413838	+	0.910350i	$0.364188\pi$
$108$	−1.00000	−0.0962250
$109$	6.43845	0.616691	0.308346	−	0.951274i	$-0.400225\pi$
$109$	6.43845	0.616691	0.308346	+	0.951274i	$0.400225\pi$
$110$	14.6847	1.40013
$111$	3.68466	0.349732
$112$	−3.56155	−0.336535
$113$	1.56155	0.146899	0.0734493	−	0.997299i	$-0.476599\pi$
$113$	1.56155	0.146899	0.0734493	+	0.997299i	$0.476599\pi$
$114$	4.00000	0.374634
$115$	20.6155	1.92241
$116$	−5.12311	−0.475668
$117$	5.56155	0.514166
$118$	6.43845	0.592707
$119$	−2.00000	−0.183340
$120$	−4.12311	−0.376386
$121$	1.68466	0.153151
$122$	−1.00000	−0.0905357
$123$	−9.56155	−0.862136
$124$	4.00000	0.359211
$125$	−28.8617	−2.58147
$126$	3.56155	0.317288
$127$	−14.8078	−1.31398	−0.656988	−	0.753901i	$-0.728170\pi$
$127$	−14.8078	−1.31398	−0.656988	+	0.753901i	$0.728170\pi$
$128$	−1.00000	−0.0883883
$129$	2.56155	0.225532
$130$	22.9309	2.01117
$131$	−5.68466	−0.496671	−0.248335	−	0.968674i	$-0.579884\pi$
$131$	−5.68466	−0.496671	−0.248335	+	0.968674i	$0.579884\pi$
$132$	−3.56155	−0.309993
$133$	−14.2462	−1.23530
$134$	3.31534	0.286402
$135$	4.12311	0.354860
$136$	−0.561553	−0.0481528
$137$	18.0540	1.54246	0.771228	−	0.636559i	$-0.219643\pi$
$137$	18.0540	1.54246	0.771228	+	0.636559i	$0.219643\pi$
$138$	−5.00000	−0.425628
$139$	13.4924	1.14441	0.572206	−	0.820110i	$-0.306088\pi$
$139$	13.4924	1.14441	0.572206	+	0.820110i	$0.306088\pi$
$140$	14.6847	1.24108
$141$	−7.12311	−0.599874
$142$	−13.9309	−1.16905
$143$	19.8078	1.65641
$144$	1.00000	0.0833333
$145$	21.1231	1.75418
$146$	−16.3693	−1.35473
$147$	−5.68466	−0.468863
$148$	−3.68466	−0.302877
$149$	8.43845	0.691305	0.345652	−	0.938363i	$-0.387658\pi$
$149$	8.43845	0.691305	0.345652	+	0.938363i	$0.387658\pi$
$150$	12.0000	0.979796
$151$	−2.68466	−0.218474	−0.109237	−	0.994016i	$-0.534841\pi$
$151$	−2.68466	−0.218474	−0.109237	+	0.994016i	$0.534841\pi$
$152$	−4.00000	−0.324443
$153$	0.561553	0.0453989
$154$	12.6847	1.02216
$155$	−16.4924	−1.32470
$156$	−5.56155	−0.445281
$157$	−7.75379	−0.618820	−0.309410	−	0.950929i	$-0.600131\pi$
$157$	−7.75379	−0.618820	−0.309410	+	0.950929i	$0.600131\pi$
$158$	12.9309	1.02872
$159$	−9.12311	−0.723509
$160$	4.12311	0.325960
$161$	17.8078	1.40345
$162$	−1.00000	−0.0785674
$163$	−1.75379	−0.137367	−0.0686837	−	0.997638i	$-0.521880\pi$
$163$	−1.75379	−0.137367	−0.0686837	+	0.997638i	$0.521880\pi$
$164$	9.56155	0.746632
$165$	14.6847	1.14320
$166$	10.8078	0.838845
$167$	4.24621	0.328582	0.164291	−	0.986412i	$-0.447466\pi$
$167$	4.24621	0.328582	0.164291	+	0.986412i	$0.447466\pi$
$168$	−3.56155	−0.274780
$169$	17.9309	1.37930
$170$	2.31534	0.177579
$171$	4.00000	0.305888
$172$	−2.56155	−0.195317
$173$	−3.75379	−0.285395	−0.142698	−	0.989766i	$-0.545578\pi$
$173$	−3.75379	−0.285395	−0.142698	+	0.989766i	$0.545578\pi$
$174$	−5.12311	−0.388382
$175$	−42.7386	−3.23074
$176$	3.56155	0.268462
$177$	6.43845	0.483943
$178$	−15.6847	−1.17561
$179$	−15.6847	−1.17233	−0.586163	−	0.810193i	$-0.699362\pi$
$179$	−15.6847	−1.17233	−0.586163	+	0.810193i	$0.699362\pi$
$180$	−4.12311	−0.307318
$181$	22.8078	1.69529	0.847644	−	0.530566i	$-0.178020\pi$
$181$	22.8078	1.69529	0.847644	+	0.530566i	$0.178020\pi$
$182$	19.8078	1.46825
$183$	−1.00000	−0.0739221
$184$	5.00000	0.368605
$185$	15.1922	1.11696
$186$	4.00000	0.293294
$187$	2.00000	0.146254
$188$	7.12311	0.519506
$189$	3.56155	0.259065
$190$	16.4924	1.19649
$191$	3.31534	0.239890	0.119945	−	0.992781i	$-0.461728\pi$
$191$	3.31534	0.239890	0.119945	+	0.992781i	$0.461728\pi$
$192$	−1.00000	−0.0721688
$193$	12.8769	0.926899	0.463450	−	0.886123i	$-0.346612\pi$
$193$	12.8769	0.926899	0.463450	+	0.886123i	$0.346612\pi$
$194$	3.43845	0.246866
$195$	22.9309	1.64211
$196$	5.68466	0.406047
$197$	−6.19224	−0.441179	−0.220589	−	0.975367i	$-0.570798\pi$
$197$	−6.19224	−0.441179	−0.220589	+	0.975367i	$0.570798\pi$
$198$	−3.56155	−0.253109
$199$	7.43845	0.527298	0.263649	−	0.964619i	$-0.415074\pi$
$199$	7.43845	0.527298	0.263649	+	0.964619i	$0.415074\pi$
$200$	−12.0000	−0.848528
$201$	3.31534	0.233846
$202$	−6.24621	−0.439482
$203$	18.2462	1.28063
$204$	−0.561553	−0.0393166
$205$	−39.4233	−2.75344
$206$	−4.56155	−0.317818
$207$	−5.00000	−0.347524
$208$	5.56155	0.385624
$209$	14.2462	0.985431
$210$	14.6847	1.01334
$211$	−24.4924	−1.68613	−0.843064	−	0.537813i	$-0.819251\pi$
$211$	−24.4924	−1.68613	−0.843064	+	0.537813i	$0.819251\pi$
$212$	9.12311	0.626577
$213$	−13.9309	−0.954527
$214$	−8.56155	−0.585256
$215$	10.5616	0.720292
$216$	1.00000	0.0680414
$217$	−14.2462	−0.967096
$218$	−6.43845	−0.436067
$219$	−16.3693	−1.10614
$220$	−14.6847	−0.990039
$221$	3.12311	0.210083
$222$	−3.68466	−0.247298
$223$	3.56155	0.238499	0.119250	−	0.992864i	$-0.461951\pi$
$223$	3.56155	0.238499	0.119250	+	0.992864i	$0.461951\pi$
$224$	3.56155	0.237966
$225$	12.0000	0.800000
$226$	−1.56155	−0.103873
$227$	−11.5616	−0.767367	−0.383684	−	0.923465i	$-0.625345\pi$
$227$	−11.5616	−0.767367	−0.383684	+	0.923465i	$0.625345\pi$
$228$	−4.00000	−0.264906
$229$	−21.8078	−1.44110	−0.720549	−	0.693404i	$-0.756110\pi$
$229$	−21.8078	−1.44110	−0.720549	+	0.693404i	$0.756110\pi$
$230$	−20.6155	−1.35935
$231$	12.6847	0.834589
$232$	5.12311	0.336348
$233$	5.12311	0.335626	0.167813	−	0.985819i	$-0.446330\pi$
$233$	5.12311	0.335626	0.167813	+	0.985819i	$0.446330\pi$
$234$	−5.56155	−0.363570
$235$	−29.3693	−1.91584
$236$	−6.43845	−0.419107
$237$	12.9309	0.839950
$238$	2.00000	0.129641
$239$	11.3693	0.735420	0.367710	−	0.929941i	$-0.380142\pi$
$239$	11.3693	0.735420	0.367710	+	0.929941i	$0.380142\pi$
$240$	4.12311	0.266145
$241$	−19.4924	−1.25562	−0.627809	−	0.778368i	$-0.716048\pi$
$241$	−19.4924	−1.25562	−0.627809	+	0.778368i	$0.716048\pi$
$242$	−1.68466	−0.108294
$243$	−1.00000	−0.0641500
$244$	1.00000	0.0640184
$245$	−23.4384	−1.49743
$246$	9.56155	0.609622
$247$	22.2462	1.41549
$248$	−4.00000	−0.254000
$249$	10.8078	0.684914
$250$	28.8617	1.82538
$251$	−7.36932	−0.465147	−0.232574	−	0.972579i	$-0.574715\pi$
$251$	−7.36932	−0.465147	−0.232574	+	0.972579i	$0.574715\pi$
$252$	−3.56155	−0.224357
$253$	−17.8078	−1.11956
$254$	14.8078	0.929122
$255$	2.31534	0.144992
$256$	1.00000	0.0625000
$257$	13.3693	0.833955	0.416978	−	0.908917i	$-0.363089\pi$
$257$	13.3693	0.833955	0.416978	+	0.908917i	$0.363089\pi$
$258$	−2.56155	−0.159475
$259$	13.1231	0.815430
$260$	−22.9309	−1.42211
$261$	−5.12311	−0.317112
$262$	5.68466	0.351199
$263$	28.0000	1.72655	0.863277	−	0.504730i	$-0.168408\pi$
$263$	28.0000	1.72655	0.863277	+	0.504730i	$0.168408\pi$
$264$	3.56155	0.219198
$265$	−37.6155	−2.31070
$266$	14.2462	0.873491
$267$	−15.6847	−0.959886
$268$	−3.31534	−0.202517
$269$	22.0000	1.34136	0.670682	−	0.741745i	$-0.266002\pi$
$269$	22.0000	1.34136	0.670682	+	0.741745i	$0.266002\pi$
$270$	−4.12311	−0.250924
$271$	16.1771	0.982688	0.491344	−	0.870966i	$-0.336506\pi$
$271$	16.1771	0.982688	0.491344	+	0.870966i	$0.336506\pi$
$272$	0.561553	0.0340491
$273$	19.8078	1.19882
$274$	−18.0540	−1.09068
$275$	42.7386	2.57724
$276$	5.00000	0.300965
$277$	6.49242	0.390092	0.195046	−	0.980794i	$-0.437514\pi$
$277$	6.49242	0.390092	0.195046	+	0.980794i	$0.437514\pi$
$278$	−13.4924	−0.809222
$279$	4.00000	0.239474
$280$	−14.6847	−0.877576
$281$	−2.87689	−0.171621	−0.0858106	−	0.996311i	$-0.527348\pi$
$281$	−2.87689	−0.171621	−0.0858106	+	0.996311i	$0.527348\pi$
$282$	7.12311	0.424175
$283$	27.6155	1.64157	0.820786	−	0.571235i	$-0.193536\pi$
$283$	27.6155	1.64157	0.820786	+	0.571235i	$0.193536\pi$
$284$	13.9309	0.826645
$285$	16.4924	0.976927
$286$	−19.8078	−1.17126
$287$	−34.0540	−2.01014
$288$	−1.00000	−0.0589256
$289$	−16.6847	−0.981450
$290$	−21.1231	−1.24039
$291$	3.43845	0.201565
$292$	16.3693	0.957942
$293$	−22.1771	−1.29560	−0.647799	−	0.761811i	$-0.724311\pi$
$293$	−22.1771	−1.29560	−0.647799	+	0.761811i	$0.724311\pi$
$294$	5.68466	0.331536
$295$	26.5464	1.54559
$296$	3.68466	0.214166
$297$	−3.56155	−0.206662
$298$	−8.43845	−0.488826
$299$	−27.8078	−1.60816
$300$	−12.0000	−0.692820
$301$	9.12311	0.525847
$302$	2.68466	0.154485
$303$	−6.24621	−0.358835
$304$	4.00000	0.229416
$305$	−4.12311	−0.236088
$306$	−0.561553	−0.0321018
$307$	29.4924	1.68322	0.841611	−	0.540085i	$-0.181608\pi$
$307$	29.4924	1.68322	0.841611	+	0.540085i	$0.181608\pi$
$308$	−12.6847	−0.722775
$309$	−4.56155	−0.259498
$310$	16.4924	0.936707
$311$	−11.8078	−0.669557	−0.334778	−	0.942297i	$-0.608661\pi$
$311$	−11.8078	−0.669557	−0.334778	+	0.942297i	$0.608661\pi$
$312$	5.56155	0.314861
$313$	−13.6155	−0.769595	−0.384798	−	0.923001i	$-0.625729\pi$
$313$	−13.6155	−0.769595	−0.384798	+	0.923001i	$0.625729\pi$
$314$	7.75379	0.437572
$315$	14.6847	0.827387
$316$	−12.9309	−0.727418
$317$	−23.4384	−1.31643	−0.658217	−	0.752828i	$-0.728689\pi$
$317$	−23.4384	−1.31643	−0.658217	+	0.752828i	$0.728689\pi$
$318$	9.12311	0.511598
$319$	−18.2462	−1.02159
$320$	−4.12311	−0.230489
$321$	−8.56155	−0.477859
$322$	−17.8078	−0.992388
$323$	2.24621	0.124983
$324$	1.00000	0.0555556
$325$	66.7386	3.70199
$326$	1.75379	0.0971334
$327$	−6.43845	−0.356047
$328$	−9.56155	−0.527948
$329$	−25.3693	−1.39866
$330$	−14.6847	−0.808364
$331$	−5.00000	−0.274825	−0.137412	−	0.990514i	$-0.543879\pi$
$331$	−5.00000	−0.274825	−0.137412	+	0.990514i	$0.543879\pi$
$332$	−10.8078	−0.593153
$333$	−3.68466	−0.201918
$334$	−4.24621	−0.232342
$335$	13.6695	0.746845
$336$	3.56155	0.194299
$337$	−29.6155	−1.61326	−0.806630	−	0.591056i	$-0.798711\pi$
$337$	−29.6155	−1.61326	−0.806630	+	0.591056i	$0.798711\pi$
$338$	−17.9309	−0.975311
$339$	−1.56155	−0.0848119
$340$	−2.31534	−0.125567
$341$	14.2462	0.771476
$342$	−4.00000	−0.216295
$343$	4.68466	0.252948
$344$	2.56155	0.138110
$345$	−20.6155	−1.10990
$346$	3.75379	0.201805
$347$	−29.3002	−1.57292	−0.786458	−	0.617643i	$-0.788087\pi$
$347$	−29.3002	−1.57292	−0.786458	+	0.617643i	$0.788087\pi$
$348$	5.12311	0.274627
$349$	21.0540	1.12699	0.563497	−	0.826118i	$-0.309456\pi$
$349$	21.0540	1.12699	0.563497	+	0.826118i	$0.309456\pi$
$350$	42.7386	2.28448
$351$	−5.56155	−0.296854
$352$	−3.56155	−0.189831
$353$	21.3153	1.13450	0.567251	−	0.823545i	$-0.308007\pi$
$353$	21.3153	1.13450	0.567251	+	0.823545i	$0.308007\pi$
$354$	−6.43845	−0.342200
$355$	−57.4384	−3.04852
$356$	15.6847	0.831285
$357$	2.00000	0.105851
$358$	15.6847	0.828960
$359$	2.56155	0.135194	0.0675968	−	0.997713i	$-0.478467\pi$
$359$	2.56155	0.135194	0.0675968	+	0.997713i	$0.478467\pi$
$360$	4.12311	0.217307
$361$	−3.00000	−0.157895
$362$	−22.8078	−1.19875
$363$	−1.68466	−0.0884216
$364$	−19.8078	−1.03821
$365$	−67.4924	−3.53271
$366$	1.00000	0.0522708
$367$	−8.00000	−0.417597	−0.208798	−	0.977959i	$-0.566955\pi$
$367$	−8.00000	−0.417597	−0.208798	+	0.977959i	$0.566955\pi$
$368$	−5.00000	−0.260643
$369$	9.56155	0.497755
$370$	−15.1922	−0.789807
$371$	−32.4924	−1.68692
$372$	−4.00000	−0.207390
$373$	10.5616	0.546856	0.273428	−	0.961892i	$-0.411842\pi$
$373$	10.5616	0.546856	0.273428	+	0.961892i	$0.411842\pi$
$374$	−2.00000	−0.103418
$375$	28.8617	1.49041
$376$	−7.12311	−0.367346
$377$	−28.4924	−1.46743
$378$	−3.56155	−0.183187
$379$	−2.24621	−0.115380	−0.0576901	−	0.998335i	$-0.518374\pi$
$379$	−2.24621	−0.115380	−0.0576901	+	0.998335i	$0.518374\pi$
$380$	−16.4924	−0.846043
$381$	14.8078	0.758625
$382$	−3.31534	−0.169628
$383$	2.43845	0.124599	0.0622994	−	0.998058i	$-0.480157\pi$
$383$	2.43845	0.124599	0.0622994	+	0.998058i	$0.480157\pi$
$384$	1.00000	0.0510310
$385$	52.3002	2.66546
$386$	−12.8769	−0.655417
$387$	−2.56155	−0.130211
$388$	−3.43845	−0.174561
$389$	−8.24621	−0.418100	−0.209050	−	0.977905i	$-0.567037\pi$
$389$	−8.24621	−0.418100	−0.209050	+	0.977905i	$0.567037\pi$
$390$	−22.9309	−1.16115
$391$	−2.80776	−0.141995
$392$	−5.68466	−0.287119
$393$	5.68466	0.286753
$394$	6.19224	0.311960
$395$	53.3153	2.68259
$396$	3.56155	0.178975
$397$	−10.1771	−0.510773	−0.255387	−	0.966839i	$-0.582203\pi$
$397$	−10.1771	−0.510773	−0.255387	+	0.966839i	$0.582203\pi$
$398$	−7.43845	−0.372856
$399$	14.2462	0.713203
$400$	12.0000	0.600000
$401$	0.561553	0.0280426	0.0140213	−	0.999902i	$-0.495537\pi$
$401$	0.561553	0.0280426	0.0140213	+	0.999902i	$0.495537\pi$
$402$	−3.31534	−0.165354
$403$	22.2462	1.10816
$404$	6.24621	0.310761
$405$	−4.12311	−0.204879
$406$	−18.2462	−0.905544
$407$	−13.1231	−0.650488
$408$	0.561553	0.0278010
$409$	8.00000	0.395575	0.197787	−	0.980245i	$-0.436624\pi$
$409$	8.00000	0.395575	0.197787	+	0.980245i	$0.436624\pi$
$410$	39.4233	1.94698
$411$	−18.0540	−0.890537
$412$	4.56155	0.224732
$413$	22.9309	1.12835
$414$	5.00000	0.245737
$415$	44.5616	2.18744
$416$	−5.56155	−0.272678
$417$	−13.4924	−0.660727
$418$	−14.2462	−0.696805
$419$	−4.00000	−0.195413	−0.0977064	−	0.995215i	$-0.531151\pi$
$419$	−4.00000	−0.195413	−0.0977064	+	0.995215i	$0.531151\pi$
$420$	−14.6847	−0.716538
$421$	−2.31534	−0.112843	−0.0564214	−	0.998407i	$-0.517969\pi$
$421$	−2.31534	−0.112843	−0.0564214	+	0.998407i	$0.517969\pi$
$422$	24.4924	1.19227
$423$	7.12311	0.346337
$424$	−9.12311	−0.443057
$425$	6.73863	0.326872
$426$	13.9309	0.674953
$427$	−3.56155	−0.172356
$428$	8.56155	0.413838
$429$	−19.8078	−0.956328
$430$	−10.5616	−0.509323
$431$	−12.7386	−0.613598	−0.306799	−	0.951774i	$-0.599258\pi$
$431$	−12.7386	−0.613598	−0.306799	+	0.951774i	$0.599258\pi$
$432$	−1.00000	−0.0481125
$433$	12.8769	0.618824	0.309412	−	0.950928i	$-0.399868\pi$
$433$	12.8769	0.618824	0.309412	+	0.950928i	$0.399868\pi$
$434$	14.2462	0.683840
$435$	−21.1231	−1.01278
$436$	6.43845	0.308346
$437$	−20.0000	−0.956730
$438$	16.3693	0.782156
$439$	−22.5616	−1.07680	−0.538402	−	0.842688i	$-0.680972\pi$
$439$	−22.5616	−1.07680	−0.538402	+	0.842688i	$0.680972\pi$
$440$	14.6847	0.700064
$441$	5.68466	0.270698
$442$	−3.12311	−0.148551
$443$	4.31534	0.205028	0.102514	−	0.994732i	$-0.467311\pi$
$443$	4.31534	0.205028	0.102514	+	0.994732i	$0.467311\pi$
$444$	3.68466	0.174866
$445$	−64.6695	−3.06563
$446$	−3.56155	−0.168644
$447$	−8.43845	−0.399125
$448$	−3.56155	−0.168268
$449$	−23.5616	−1.11194	−0.555969	−	0.831203i	$-0.687653\pi$
$449$	−23.5616	−1.11194	−0.555969	+	0.831203i	$0.687653\pi$
$450$	−12.0000	−0.565685
$451$	34.0540	1.60354
$452$	1.56155	0.0734493
$453$	2.68466	0.126136
$454$	11.5616	0.542611
$455$	81.6695	3.82873
$456$	4.00000	0.187317
$457$	33.1231	1.54943	0.774717	−	0.632308i	$-0.217892\pi$
$457$	33.1231	1.54943	0.774717	+	0.632308i	$0.217892\pi$
$458$	21.8078	1.01901
$459$	−0.561553	−0.0262110
$460$	20.6155	0.961204
$461$	26.1771	1.21919	0.609594	−	0.792714i	$-0.291332\pi$
$461$	26.1771	1.21919	0.609594	+	0.792714i	$0.291332\pi$
$462$	−12.6847	−0.590144
$463$	25.4384	1.18222	0.591112	−	0.806589i	$-0.298689\pi$
$463$	25.4384	1.18222	0.591112	+	0.806589i	$0.298689\pi$
$464$	−5.12311	−0.237834
$465$	16.4924	0.764818
$466$	−5.12311	−0.237323
$467$	39.4233	1.82429	0.912146	−	0.409865i	$-0.134424\pi$
$467$	39.4233	1.82429	0.912146	+	0.409865i	$0.134424\pi$
$468$	5.56155	0.257083
$469$	11.8078	0.545232
$470$	29.3693	1.35471
$471$	7.75379	0.357276
$472$	6.43845	0.296354
$473$	−9.12311	−0.419481
$474$	−12.9309	−0.593935
$475$	48.0000	2.20239
$476$	−2.00000	−0.0916698
$477$	9.12311	0.417718
$478$	−11.3693	−0.520020
$479$	−7.36932	−0.336713	−0.168356	−	0.985726i	$-0.553846\pi$
$479$	−7.36932	−0.336713	−0.168356	+	0.985726i	$0.553846\pi$
$480$	−4.12311	−0.188193
$481$	−20.4924	−0.934374
$482$	19.4924	0.887856
$483$	−17.8078	−0.810281
$484$	1.68466	0.0765754
$485$	14.1771	0.643748
$486$	1.00000	0.0453609
$487$	14.2462	0.645557	0.322779	−	0.946474i	$-0.395383\pi$
$487$	14.2462	0.645557	0.322779	+	0.946474i	$0.395383\pi$
$488$	−1.00000	−0.0452679
$489$	1.75379	0.0793091
$490$	23.4384	1.05884
$491$	20.4924	0.924810	0.462405	−	0.886669i	$-0.346987\pi$
$491$	20.4924	0.924810	0.462405	+	0.886669i	$0.346987\pi$
$492$	−9.56155	−0.431068
$493$	−2.87689	−0.129569
$494$	−22.2462	−1.00090
$495$	−14.6847	−0.660026
$496$	4.00000	0.179605
$497$	−49.6155	−2.22556
$498$	−10.8078	−0.484307
$499$	16.3693	0.732791	0.366396	−	0.930459i	$-0.380592\pi$
$499$	16.3693	0.732791	0.366396	+	0.930459i	$0.380592\pi$
$500$	−28.8617	−1.29074
$501$	−4.24621	−0.189707
$502$	7.36932	0.328909
$503$	6.63068	0.295648	0.147824	−	0.989014i	$-0.452773\pi$
$503$	6.63068	0.295648	0.147824	+	0.989014i	$0.452773\pi$
$504$	3.56155	0.158644
$505$	−25.7538	−1.14603
$506$	17.8078	0.791652
$507$	−17.9309	−0.796338
$508$	−14.8078	−0.656988
$509$	31.6155	1.40133	0.700667	−	0.713489i	$-0.252886\pi$
$509$	31.6155	1.40133	0.700667	+	0.713489i	$0.252886\pi$
$510$	−2.31534	−0.102525
$511$	−58.3002	−2.57905
$512$	−1.00000	−0.0441942
$513$	−4.00000	−0.176604
$514$	−13.3693	−0.589695
$515$	−18.8078	−0.828769
$516$	2.56155	0.112766
$517$	25.3693	1.11574
$518$	−13.1231	−0.576596
$519$	3.75379	0.164773
$520$	22.9309	1.00559
$521$	−18.4924	−0.810168	−0.405084	−	0.914280i	$-0.632758\pi$
$521$	−18.4924	−0.810168	−0.405084	+	0.914280i	$0.632758\pi$
$522$	5.12311	0.224232
$523$	−44.2311	−1.93409	−0.967045	−	0.254607i	$-0.918054\pi$
$523$	−44.2311	−1.93409	−0.967045	+	0.254607i	$0.918054\pi$
$524$	−5.68466	−0.248335
$525$	42.7386	1.86527
$526$	−28.0000	−1.22086
$527$	2.24621	0.0978465
$528$	−3.56155	−0.154997
$529$	2.00000	0.0869565
$530$	37.6155	1.63391
$531$	−6.43845	−0.279405
$532$	−14.2462	−0.617652
$533$	53.1771	2.30336
$534$	15.6847	0.678742
$535$	−35.3002	−1.52616
$536$	3.31534	0.143201
$537$	15.6847	0.676843
$538$	−22.0000	−0.948487
$539$	20.2462	0.872066
$540$	4.12311	0.177430
$541$	8.80776	0.378675	0.189338	−	0.981912i	$-0.439366\pi$
$541$	8.80776	0.378675	0.189338	+	0.981912i	$0.439366\pi$
$542$	−16.1771	−0.694865
$543$	−22.8078	−0.978775
$544$	−0.561553	−0.0240764
$545$	−26.5464	−1.13712
$546$	−19.8078	−0.847694
$547$	−4.68466	−0.200302	−0.100151	−	0.994972i	$-0.531933\pi$
$547$	−4.68466	−0.200302	−0.100151	+	0.994972i	$0.531933\pi$
$548$	18.0540	0.771228
$549$	1.00000	0.0426790
$550$	−42.7386	−1.82238
$551$	−20.4924	−0.873007
$552$	−5.00000	−0.212814
$553$	46.0540	1.95841
$554$	−6.49242	−0.275837
$555$	−15.1922	−0.644875
$556$	13.4924	0.572206
$557$	−45.6155	−1.93279	−0.966396	−	0.257058i	$-0.917247\pi$
$557$	−45.6155	−1.93279	−0.966396	+	0.257058i	$0.917247\pi$
$558$	−4.00000	−0.169334
$559$	−14.2462	−0.602551
$560$	14.6847	0.620540
$561$	−2.00000	−0.0844401
$562$	2.87689	0.121354
$563$	−17.3693	−0.732029	−0.366015	−	0.930609i	$-0.619278\pi$
$563$	−17.3693	−0.732029	−0.366015	+	0.930609i	$0.619278\pi$
$564$	−7.12311	−0.299937
$565$	−6.43845	−0.270868
$566$	−27.6155	−1.16077
$567$	−3.56155	−0.149571
$568$	−13.9309	−0.584526
$569$	23.8078	0.998073	0.499037	−	0.866581i	$-0.333687\pi$
$569$	23.8078	0.998073	0.499037	+	0.866581i	$0.333687\pi$
$570$	−16.4924	−0.690792
$571$	11.6155	0.486095	0.243047	−	0.970014i	$-0.421853\pi$
$571$	11.6155	0.486095	0.243047	+	0.970014i	$0.421853\pi$
$572$	19.8078	0.828204
$573$	−3.31534	−0.138500
$574$	34.0540	1.42139
$575$	−60.0000	−2.50217
$576$	1.00000	0.0416667
$577$	−1.36932	−0.0570054	−0.0285027	−	0.999594i	$-0.509074\pi$
$577$	−1.36932	−0.0570054	−0.0285027	+	0.999594i	$0.509074\pi$
$578$	16.6847	0.693990
$579$	−12.8769	−0.535145
$580$	21.1231	0.877089
$581$	38.4924	1.59693
$582$	−3.43845	−0.142528
$583$	32.4924	1.34570
$584$	−16.3693	−0.677367
$585$	−22.9309	−0.948075
$586$	22.1771	0.916127
$587$	−39.8617	−1.64527	−0.822635	−	0.568570i	$-0.807497\pi$
$587$	−39.8617	−1.64527	−0.822635	+	0.568570i	$0.807497\pi$
$588$	−5.68466	−0.234431
$589$	16.0000	0.659269
$590$	−26.5464	−1.09290
$591$	6.19224	0.254715
$592$	−3.68466	−0.151439
$593$	−2.80776	−0.115301	−0.0576505	−	0.998337i	$-0.518361\pi$
$593$	−2.80776	−0.115301	−0.0576505	+	0.998337i	$0.518361\pi$
$594$	3.56155	0.146132
$595$	8.24621	0.338062
$596$	8.43845	0.345652
$597$	−7.43845	−0.304435
$598$	27.8078	1.13714
$599$	19.2462	0.786379	0.393189	−	0.919457i	$-0.371372\pi$
$599$	19.2462	0.786379	0.393189	+	0.919457i	$0.371372\pi$
$600$	12.0000	0.489898
$601$	25.4924	1.03986	0.519929	−	0.854210i	$-0.325958\pi$
$601$	25.4924	1.03986	0.519929	+	0.854210i	$0.325958\pi$
$602$	−9.12311	−0.371830
$603$	−3.31534	−0.135011
$604$	−2.68466	−0.109237
$605$	−6.94602	−0.282396
$606$	6.24621	0.253735
$607$	9.43845	0.383095	0.191547	−	0.981483i	$-0.438649\pi$
$607$	9.43845	0.383095	0.191547	+	0.981483i	$0.438649\pi$
$608$	−4.00000	−0.162221
$609$	−18.2462	−0.739374
$610$	4.12311	0.166940
$611$	39.6155	1.60267
$612$	0.561553	0.0226994
$613$	13.8617	0.559870	0.279935	−	0.960019i	$-0.409687\pi$
$613$	13.8617	0.559870	0.279935	+	0.960019i	$0.409687\pi$
$614$	−29.4924	−1.19022
$615$	39.4233	1.58970
$616$	12.6847	0.511079
$617$	−25.6847	−1.03403	−0.517013	−	0.855978i	$-0.672956\pi$
$617$	−25.6847	−1.03403	−0.517013	+	0.855978i	$0.672956\pi$
$618$	4.56155	0.183493
$619$	22.4924	0.904047	0.452023	−	0.892006i	$-0.350702\pi$
$619$	22.4924	0.904047	0.452023	+	0.892006i	$0.350702\pi$
$620$	−16.4924	−0.662352
$621$	5.00000	0.200643
$622$	11.8078	0.473448
$623$	−55.8617	−2.23805
$624$	−5.56155	−0.222640
$625$	59.0000	2.36000
$626$	13.6155	0.544186
$627$	−14.2462	−0.568939
$628$	−7.75379	−0.309410
$629$	−2.06913	−0.0825016
$630$	−14.6847	−0.585051
$631$	−4.05398	−0.161386	−0.0806931	−	0.996739i	$-0.525713\pi$
$631$	−4.05398	−0.161386	−0.0806931	+	0.996739i	$0.525713\pi$
$632$	12.9309	0.514362
$633$	24.4924	0.973486
$634$	23.4384	0.930860
$635$	61.0540	2.42285
$636$	−9.12311	−0.361755
$637$	31.6155	1.25265
$638$	18.2462	0.722374
$639$	13.9309	0.551097
$640$	4.12311	0.162980
$641$	−33.4384	−1.32074	−0.660370	−	0.750941i	$-0.729600\pi$
$641$	−33.4384	−1.32074	−0.660370	+	0.750941i	$0.729600\pi$
$642$	8.56155	0.337898
$643$	−2.06913	−0.0815985	−0.0407993	−	0.999167i	$-0.512990\pi$
$643$	−2.06913	−0.0815985	−0.0407993	+	0.999167i	$0.512990\pi$
$644$	17.8078	0.701724
$645$	−10.5616	−0.415861
$646$	−2.24621	−0.0883760
$647$	−10.1231	−0.397980	−0.198990	−	0.980001i	$-0.563766\pi$
$647$	−10.1231	−0.397980	−0.198990	+	0.980001i	$0.563766\pi$
$648$	−1.00000	−0.0392837
$649$	−22.9309	−0.900115
$650$	−66.7386	−2.61770
$651$	14.2462	0.558353
$652$	−1.75379	−0.0686837
$653$	−19.1231	−0.748345	−0.374172	−	0.927359i	$-0.622073\pi$
$653$	−19.1231	−0.748345	−0.374172	+	0.927359i	$0.622073\pi$
$654$	6.43845	0.251763
$655$	23.4384	0.915816
$656$	9.56155	0.373316
$657$	16.3693	0.638628
$658$	25.3693	0.988999
$659$	−15.3002	−0.596011	−0.298005	−	0.954564i	$-0.596321\pi$
$659$	−15.3002	−0.596011	−0.298005	+	0.954564i	$0.596321\pi$
$660$	14.6847	0.571600
$661$	−26.8769	−1.04539	−0.522695	−	0.852520i	$-0.675073\pi$
$661$	−26.8769	−1.04539	−0.522695	+	0.852520i	$0.675073\pi$
$662$	5.00000	0.194331
$663$	−3.12311	−0.121291
$664$	10.8078	0.419423
$665$	58.7386	2.27779
$666$	3.68466	0.142778
$667$	25.6155	0.991837
$668$	4.24621	0.164291
$669$	−3.56155	−0.137698
$670$	−13.6695	−0.528099
$671$	3.56155	0.137492
$672$	−3.56155	−0.137390
$673$	−4.73863	−0.182661	−0.0913305	−	0.995821i	$-0.529112\pi$
$673$	−4.73863	−0.182661	−0.0913305	+	0.995821i	$0.529112\pi$
$674$	29.6155	1.14075
$675$	−12.0000	−0.461880
$676$	17.9309	0.689649
$677$	−41.8617	−1.60888	−0.804439	−	0.594036i	$-0.797534\pi$
$677$	−41.8617	−1.60888	−0.804439	+	0.594036i	$0.797534\pi$
$678$	1.56155	0.0599711
$679$	12.2462	0.469966
$680$	2.31534	0.0887893
$681$	11.5616	0.443040
$682$	−14.2462	−0.545516
$683$	43.6847	1.67155	0.835774	−	0.549074i	$-0.185020\pi$
$683$	43.6847	1.67155	0.835774	+	0.549074i	$0.185020\pi$
$684$	4.00000	0.152944
$685$	−74.4384	−2.84415
$686$	−4.68466	−0.178861
$687$	21.8078	0.832018
$688$	−2.56155	−0.0976583
$689$	50.7386	1.93299
$690$	20.6155	0.784820
$691$	8.63068	0.328327	0.164163	−	0.986433i	$-0.447508\pi$
$691$	8.63068	0.328327	0.164163	+	0.986433i	$0.447508\pi$
$692$	−3.75379	−0.142698
$693$	−12.6847	−0.481850
$694$	29.3002	1.11222
$695$	−55.6307	−2.11019
$696$	−5.12311	−0.194191
$697$	5.36932	0.203377
$698$	−21.0540	−0.796905
$699$	−5.12311	−0.193774
$700$	−42.7386	−1.61537
$701$	22.9848	0.868126	0.434063	−	0.900883i	$-0.357080\pi$
$701$	22.9848	0.868126	0.434063	+	0.900883i	$0.357080\pi$
$702$	5.56155	0.209907
$703$	−14.7386	−0.555878
$704$	3.56155	0.134231
$705$	29.3693	1.10611
$706$	−21.3153	−0.802213
$707$	−22.2462	−0.836655
$708$	6.43845	0.241972
$709$	−15.9309	−0.598296	−0.299148	−	0.954207i	$-0.596702\pi$
$709$	−15.9309	−0.598296	−0.299148	+	0.954207i	$0.596702\pi$
$710$	57.4384	2.15563
$711$	−12.9309	−0.484946
$712$	−15.6847	−0.587807
$713$	−20.0000	−0.749006
$714$	−2.00000	−0.0748481
$715$	−81.6695	−3.05427
$716$	−15.6847	−0.586163
$717$	−11.3693	−0.424595
$718$	−2.56155	−0.0955963
$719$	−8.49242	−0.316714	−0.158357	−	0.987382i	$-0.550620\pi$
$719$	−8.49242	−0.316714	−0.158357	+	0.987382i	$0.550620\pi$
$720$	−4.12311	−0.153659
$721$	−16.2462	−0.605041
$722$	3.00000	0.111648
$723$	19.4924	0.724931
$724$	22.8078	0.847644
$725$	−61.4773	−2.28321
$726$	1.68466	0.0625235
$727$	−52.1080	−1.93258	−0.966288	−	0.257462i	$-0.917114\pi$
$727$	−52.1080	−1.93258	−0.966288	+	0.257462i	$0.917114\pi$
$728$	19.8078	0.734125
$729$	1.00000	0.0370370
$730$	67.4924	2.49801
$731$	−1.43845	−0.0532029
$732$	−1.00000	−0.0369611
$733$	−19.5616	−0.722522	−0.361261	−	0.932465i	$-0.617654\pi$
$733$	−19.5616	−0.722522	−0.361261	+	0.932465i	$0.617654\pi$
$734$	8.00000	0.295285
$735$	23.4384	0.864540
$736$	5.00000	0.184302
$737$	−11.8078	−0.434945
$738$	−9.56155	−0.351966
$739$	−24.6155	−0.905497	−0.452748	−	0.891638i	$-0.649556\pi$
$739$	−24.6155	−0.905497	−0.452748	+	0.891638i	$0.649556\pi$
$740$	15.1922	0.558478
$741$	−22.2462	−0.817235
$742$	32.4924	1.19283
$743$	−17.6307	−0.646807	−0.323404	−	0.946261i	$-0.604827\pi$
$743$	−17.6307	−0.646807	−0.323404	+	0.946261i	$0.604827\pi$
$744$	4.00000	0.146647
$745$	−34.7926	−1.27470
$746$	−10.5616	−0.386686
$747$	−10.8078	−0.395435
$748$	2.00000	0.0731272
$749$	−30.4924	−1.11417
$750$	−28.8617	−1.05388
$751$	11.0540	0.403365	0.201683	−	0.979451i	$-0.435359\pi$
$751$	11.0540	0.403365	0.201683	+	0.979451i	$0.435359\pi$
$752$	7.12311	0.259753
$753$	7.36932	0.268553
$754$	28.4924	1.03763
$755$	11.0691	0.402847
$756$	3.56155	0.129532
$757$	3.56155	0.129447	0.0647234	−	0.997903i	$-0.479383\pi$
$757$	3.56155	0.129447	0.0647234	+	0.997903i	$0.479383\pi$
$758$	2.24621	0.0815861
$759$	17.8078	0.646381
$760$	16.4924	0.598243
$761$	13.5076	0.489649	0.244825	−	0.969567i	$-0.421270\pi$
$761$	13.5076	0.489649	0.244825	+	0.969567i	$0.421270\pi$
$762$	−14.8078	−0.536429
$763$	−22.9309	−0.830153
$764$	3.31534	0.119945
$765$	−2.31534	−0.0837114
$766$	−2.43845	−0.0881047
$767$	−35.8078	−1.29294
$768$	−1.00000	−0.0360844
$769$	−51.6155	−1.86130	−0.930652	−	0.365906i	$-0.880759\pi$
$769$	−51.6155	−1.86130	−0.930652	+	0.365906i	$0.880759\pi$
$770$	−52.3002	−1.88477
$771$	−13.3693	−0.481484
$772$	12.8769	0.463450
$773$	−26.6695	−0.959235	−0.479618	−	0.877478i	$-0.659225\pi$
$773$	−26.6695	−0.959235	−0.479618	+	0.877478i	$0.659225\pi$
$774$	2.56155	0.0920731
$775$	48.0000	1.72421
$776$	3.43845	0.123433
$777$	−13.1231	−0.470789
$778$	8.24621	0.295641
$779$	38.2462	1.37031
$780$	22.9309	0.821057
$781$	49.6155	1.77538
$782$	2.80776	0.100405
$783$	5.12311	0.183085
$784$	5.68466	0.203024
$785$	31.9697	1.14105
$786$	−5.68466	−0.202765
$787$	54.7386	1.95122	0.975611	−	0.219508i	$-0.0704451\pi$
$787$	54.7386	1.95122	0.975611	+	0.219508i	$0.0704451\pi$
$788$	−6.19224	−0.220589
$789$	−28.0000	−0.996826
$790$	−53.3153	−1.89687
$791$	−5.56155	−0.197746
$792$	−3.56155	−0.126554
$793$	5.56155	0.197497
$794$	10.1771	0.361171
$795$	37.6155	1.33409
$796$	7.43845	0.263649
$797$	24.5464	0.869478	0.434739	−	0.900556i	$-0.356841\pi$
$797$	24.5464	0.869478	0.434739	+	0.900556i	$0.356841\pi$
$798$	−14.2462	−0.504310
$799$	4.00000	0.141510
$800$	−12.0000	−0.424264
$801$	15.6847	0.554190
$802$	−0.561553	−0.0198291
$803$	58.3002	2.05737
$804$	3.31534	0.116923
$805$	−73.4233	−2.58783
$806$	−22.2462	−0.783589
$807$	−22.0000	−0.774437
$808$	−6.24621	−0.219741
$809$	−44.0540	−1.54886	−0.774428	−	0.632662i	$-0.781962\pi$
$809$	−44.0540	−1.54886	−0.774428	+	0.632662i	$0.781962\pi$
$810$	4.12311	0.144871
$811$	7.49242	0.263095	0.131547	−	0.991310i	$-0.458005\pi$
$811$	7.49242	0.263095	0.131547	+	0.991310i	$0.458005\pi$
$812$	18.2462	0.640316
$813$	−16.1771	−0.567355
$814$	13.1231	0.459965
$815$	7.23106	0.253293
$816$	−0.561553	−0.0196583
$817$	−10.2462	−0.358470
$818$	−8.00000	−0.279713
$819$	−19.8078	−0.692139
$820$	−39.4233	−1.37672
$821$	−20.2462	−0.706598	−0.353299	−	0.935511i	$-0.614940\pi$
$821$	−20.2462	−0.706598	−0.353299	+	0.935511i	$0.614940\pi$
$822$	18.0540	0.629705
$823$	15.3693	0.535741	0.267870	−	0.963455i	$-0.413680\pi$
$823$	15.3693	0.535741	0.267870	+	0.963455i	$0.413680\pi$
$824$	−4.56155	−0.158909
$825$	−42.7386	−1.48797
$826$	−22.9309	−0.797867
$827$	15.0540	0.523478	0.261739	−	0.965139i	$-0.415704\pi$
$827$	15.0540	0.523478	0.261739	+	0.965139i	$0.415704\pi$
$828$	−5.00000	−0.173762
$829$	−10.1922	−0.353991	−0.176995	−	0.984212i	$-0.556638\pi$
$829$	−10.1922	−0.353991	−0.176995	+	0.984212i	$0.556638\pi$
$830$	−44.5616	−1.54675
$831$	−6.49242	−0.225220
$832$	5.56155	0.192812
$833$	3.19224	0.110604
$834$	13.4924	0.467204
$835$	−17.5076	−0.605875
$836$	14.2462	0.492716
$837$	−4.00000	−0.138260
$838$	4.00000	0.138178
$839$	−3.50758	−0.121095	−0.0605475	−	0.998165i	$-0.519285\pi$
$839$	−3.50758	−0.121095	−0.0605475	+	0.998165i	$0.519285\pi$
$840$	14.6847	0.506669
$841$	−2.75379	−0.0949582
$842$	2.31534	0.0797919
$843$	2.87689	0.0990855
$844$	−24.4924	−0.843064
$845$	−73.9309	−2.54330
$846$	−7.12311	−0.244897
$847$	−6.00000	−0.206162
$848$	9.12311	0.313289
$849$	−27.6155	−0.947762
$850$	−6.73863	−0.231133
$851$	18.4233	0.631542
$852$	−13.9309	−0.477264
$853$	−11.5616	−0.395860	−0.197930	−	0.980216i	$-0.563422\pi$
$853$	−11.5616	−0.395860	−0.197930	+	0.980216i	$0.563422\pi$
$854$	3.56155	0.121874
$855$	−16.4924	−0.564029
$856$	−8.56155	−0.292628
$857$	36.4384	1.24471	0.622357	−	0.782734i	$-0.286175\pi$
$857$	36.4384	1.24471	0.622357	+	0.782734i	$0.286175\pi$
$858$	19.8078	0.676226
$859$	−54.3542	−1.85454	−0.927270	−	0.374393i	$-0.877851\pi$
$859$	−54.3542	−1.85454	−0.927270	+	0.374393i	$0.877851\pi$
$860$	10.5616	0.360146
$861$	34.0540	1.16056
$862$	12.7386	0.433880
$863$	24.0000	0.816970	0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000	0.816970	0.408485	+	0.912765i	$0.366057\pi$
$864$	1.00000	0.0340207
$865$	15.4773	0.526243
$866$	−12.8769	−0.437575
$867$	16.6847	0.566641
$868$	−14.2462	−0.483548
$869$	−46.0540	−1.56227
$870$	21.1231	0.716140
$871$	−18.4384	−0.624763
$872$	−6.43845	−0.218033
$873$	−3.43845	−0.116374
$874$	20.0000	0.676510
$875$	102.793	3.47502
$876$	−16.3693	−0.553068
$877$	55.5464	1.87567	0.937834	−	0.347083i	$-0.112828\pi$
$877$	55.5464	1.87567	0.937834	+	0.347083i	$0.112828\pi$
$878$	22.5616	0.761416
$879$	22.1771	0.748014
$880$	−14.6847	−0.495020
$881$	−13.4233	−0.452242	−0.226121	−	0.974099i	$-0.572605\pi$
$881$	−13.4233	−0.452242	−0.226121	+	0.974099i	$0.572605\pi$
$882$	−5.68466	−0.191412
$883$	42.4773	1.42947	0.714737	−	0.699393i	$-0.246546\pi$
$883$	42.4773	1.42947	0.714737	+	0.699393i	$0.246546\pi$
$884$	3.12311	0.105041
$885$	−26.5464	−0.892347
$886$	−4.31534	−0.144977
$887$	6.56155	0.220315	0.110158	−	0.993914i	$-0.464864\pi$
$887$	6.56155	0.220315	0.110158	+	0.993914i	$0.464864\pi$
$888$	−3.68466	−0.123649
$889$	52.7386	1.76880
$890$	64.6695	2.16773
$891$	3.56155	0.119317
$892$	3.56155	0.119250
$893$	28.4924	0.953463
$894$	8.43845	0.282224
$895$	64.6695	2.16166
$896$	3.56155	0.118983
$897$	27.8078	0.928474
$898$	23.5616	0.786259
$899$	−20.4924	−0.683461
$900$	12.0000	0.400000
$901$	5.12311	0.170675
$902$	−34.0540	−1.13387
$903$	−9.12311	−0.303598
$904$	−1.56155	−0.0519365
$905$	−94.0388	−3.12596
$906$	−2.68466	−0.0891918
$907$	−46.4233	−1.54146	−0.770730	−	0.637162i	$-0.780108\pi$
$907$	−46.4233	−1.54146	−0.770730	+	0.637162i	$0.780108\pi$
$908$	−11.5616	−0.383684
$909$	6.24621	0.207174
$910$	−81.6695	−2.70732
$911$	34.7386	1.15094	0.575471	−	0.817822i	$-0.304819\pi$
$911$	34.7386	1.15094	0.575471	+	0.817822i	$0.304819\pi$
$912$	−4.00000	−0.132453
$913$	−38.4924	−1.27391
$914$	−33.1231	−1.09561
$915$	4.12311	0.136306
$916$	−21.8078	−0.720549
$917$	20.2462	0.668589
$918$	0.561553	0.0185340
$919$	−16.9460	−0.558998	−0.279499	−	0.960146i	$-0.590168\pi$
$919$	−16.9460	−0.558998	−0.279499	+	0.960146i	$0.590168\pi$
$920$	−20.6155	−0.679674
$921$	−29.4924	−0.971808
$922$	−26.1771	−0.862096
$923$	77.4773	2.55020
$924$	12.6847	0.417295
$925$	−44.2159	−1.45381
$926$	−25.4384	−0.835959
$927$	4.56155	0.149821
$928$	5.12311	0.168174
$929$	40.3002	1.32221	0.661103	−	0.750295i	$-0.270089\pi$
$929$	40.3002	1.32221	0.661103	+	0.750295i	$0.270089\pi$
$930$	−16.4924	−0.540808
$931$	22.7386	0.745229
$932$	5.12311	0.167813
$933$	11.8078	0.386569
$934$	−39.4233	−1.28997
$935$	−8.24621	−0.269680
$936$	−5.56155	−0.181785
$937$	35.4924	1.15949	0.579743	−	0.814799i	$-0.303153\pi$
$937$	35.4924	1.15949	0.579743	+	0.814799i	$0.303153\pi$
$938$	−11.8078	−0.385537
$939$	13.6155	0.444326
$940$	−29.3693	−0.957921
$941$	−8.00000	−0.260793	−0.130396	−	0.991462i	$-0.541625\pi$
$941$	−8.00000	−0.260793	−0.130396	+	0.991462i	$0.541625\pi$
$942$	−7.75379	−0.252632
$943$	−47.8078	−1.55683
$944$	−6.43845	−0.209554
$945$	−14.6847	−0.477692
$946$	9.12311	0.296618
$947$	19.4233	0.631172	0.315586	−	0.948897i	$-0.397799\pi$
$947$	19.4233	0.631172	0.315586	+	0.948897i	$0.397799\pi$
$948$	12.9309	0.419975
$949$	91.0388	2.95525
$950$	−48.0000	−1.55733
$951$	23.4384	0.760044
$952$	2.00000	0.0648204
$953$	28.5616	0.925199	0.462600	−	0.886567i	$-0.346917\pi$
$953$	28.5616	0.925199	0.462600	+	0.886567i	$0.346917\pi$
$954$	−9.12311	−0.295371
$955$	−13.6695	−0.442335
$956$	11.3693	0.367710
$957$	18.2462	0.589816
$958$	7.36932	0.238092
$959$	−64.3002	−2.07636
$960$	4.12311	0.133073
$961$	−15.0000	−0.483871
$962$	20.4924	0.660702
$963$	8.56155	0.275892
$964$	−19.4924	−0.627809
$965$	−53.0928	−1.70912
$966$	17.8078	0.572955
$967$	50.1771	1.61359	0.806793	−	0.590834i	$-0.201201\pi$
$967$	50.1771	1.61359	0.806793	+	0.590834i	$0.201201\pi$
$968$	−1.68466	−0.0541470
$969$	−2.24621	−0.0721587
$970$	−14.1771	−0.455199
$971$	−20.4233	−0.655415	−0.327707	−	0.944779i	$-0.606276\pi$
$971$	−20.4233	−0.655415	−0.327707	+	0.944779i	$0.606276\pi$
$972$	−1.00000	−0.0320750
$973$	−48.0540	−1.54054
$974$	−14.2462	−0.456478
$975$	−66.7386	−2.13735
$976$	1.00000	0.0320092
$977$	1.36932	0.0438083	0.0219042	−	0.999760i	$-0.493027\pi$
$977$	1.36932	0.0438083	0.0219042	+	0.999760i	$0.493027\pi$
$978$	−1.75379	−0.0560800
$979$	55.8617	1.78535
$980$	−23.4384	−0.748714
$981$	6.43845	0.205564
$982$	−20.4924	−0.653939
$983$	−31.2311	−0.996116	−0.498058	−	0.867144i	$-0.665953\pi$
$983$	−31.2311	−0.996116	−0.498058	+	0.867144i	$0.665953\pi$
$984$	9.56155	0.304811
$985$	25.5312	0.813493
$986$	2.87689	0.0916190
$987$	25.3693	0.807514
$988$	22.2462	0.707746
$989$	12.8078	0.407263
$990$	14.6847	0.466709
$991$	13.7538	0.436903	0.218452	−	0.975848i	$-0.429899\pi$
$991$	13.7538	0.436903	0.218452	+	0.975848i	$0.429899\pi$
$992$	−4.00000	−0.127000
$993$	5.00000	0.158670
$994$	49.6155	1.57371
$995$	−30.6695	−0.972289
$996$	10.8078	0.342457
$997$	39.9309	1.26462	0.632312	−	0.774714i	$-0.282106\pi$
$997$	39.9309	1.26462	0.632312	+	0.774714i	$0.282106\pi$
$998$	−16.3693	−0.518162
$999$	3.68466	0.116577

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	366.2.a.h.1.1	✓	2
3.2	odd	2		1098.2.a.m.1.2		2
4.3	odd	2		2928.2.a.u.1.1		2
5.4	even	2		9150.2.a.bh.1.2		2
12.11	even	2		8784.2.a.bg.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
366.2.a.h.1.1	✓	2	1.1	even	1	trivial
1098.2.a.m.1.2		2	3.2	odd	2
2928.2.a.u.1.1		2	4.3	odd	2
8784.2.a.bg.1.2		2	12.11	even	2
9150.2.a.bh.1.2		2	5.4	even	2

Overview	Random
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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:	\( N \)	\(=\)	\( 366 = 2 \cdot 3 \cdot 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	366.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -4.12311 q^{5} +1.00000 q^{6} -3.56155 q^{7} -1.00000 q^{8} +1.00000 q^{9} +4.12311 q^{10} +3.56155 q^{11} -1.00000 q^{12} +5.56155 q^{13} +3.56155 q^{14} +4.12311 q^{15} +1.00000 q^{16} +0.561553 q^{17} -1.00000 q^{18} +4.00000 q^{19} -4.12311 q^{20} +3.56155 q^{21} -3.56155 q^{22} -5.00000 q^{23} +1.00000 q^{24} +12.0000 q^{25} -5.56155 q^{26} -1.00000 q^{27} -3.56155 q^{28} -5.12311 q^{29} -4.12311 q^{30} +4.00000 q^{31} -1.00000 q^{32} -3.56155 q^{33} -0.561553 q^{34} +14.6847 q^{35} +1.00000 q^{36} -3.68466 q^{37} -4.00000 q^{38} -5.56155 q^{39} +4.12311 q^{40} +9.56155 q^{41} -3.56155 q^{42} -2.56155 q^{43} +3.56155 q^{44} -4.12311 q^{45} +5.00000 q^{46} +7.12311 q^{47} -1.00000 q^{48} +5.68466 q^{49} -12.0000 q^{50} -0.561553 q^{51} +5.56155 q^{52} +9.12311 q^{53} +1.00000 q^{54} -14.6847 q^{55} +3.56155 q^{56} -4.00000 q^{57} +5.12311 q^{58} -6.43845 q^{59} +4.12311 q^{60} +1.00000 q^{61} -4.00000 q^{62} -3.56155 q^{63} +1.00000 q^{64} -22.9309 q^{65} +3.56155 q^{66} -3.31534 q^{67} +0.561553 q^{68} +5.00000 q^{69} -14.6847 q^{70} +13.9309 q^{71} -1.00000 q^{72} +16.3693 q^{73} +3.68466 q^{74} -12.0000 q^{75} +4.00000 q^{76} -12.6847 q^{77} +5.56155 q^{78} -12.9309 q^{79} -4.12311 q^{80} +1.00000 q^{81} -9.56155 q^{82} -10.8078 q^{83} +3.56155 q^{84} -2.31534 q^{85} +2.56155 q^{86} +5.12311 q^{87} -3.56155 q^{88} +15.6847 q^{89} +4.12311 q^{90} -19.8078 q^{91} -5.00000 q^{92} -4.00000 q^{93} -7.12311 q^{94} -16.4924 q^{95} +1.00000 q^{96} -3.43845 q^{97} -5.68466 q^{98} +3.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 3 q^{7} - 2 q^{8} + 2 q^{9} + 3 q^{11} - 2 q^{12} + 7 q^{13} + 3 q^{14} + 2 q^{16} - 3 q^{17} - 2 q^{18} + 8 q^{19} + 3 q^{21} - 3 q^{22} - 10 q^{23} + 2 q^{24}+ \cdots + 3 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 3 * q^7 - 2 * q^8 + 2 * q^9 + 3 * q^11 - 2 * q^12 + 7 * q^13 + 3 * q^14 + 2 * q^16 - 3 * q^17 - 2 * q^18 + 8 * q^19 + 3 * q^21 - 3 * q^22 - 10 * q^23 + 2 * q^24 + 24 * q^25 - 7 * q^26 - 2 * q^27 - 3 * q^28 - 2 * q^29 + 8 * q^31 - 2 * q^32 - 3 * q^33 + 3 * q^34 + 17 * q^35 + 2 * q^36 + 5 * q^37 - 8 * q^38 - 7 * q^39 + 15 * q^41 - 3 * q^42 - q^43 + 3 * q^44 + 10 * q^46 + 6 * q^47 - 2 * q^48 - q^49 - 24 * q^50 + 3 * q^51 + 7 * q^52 + 10 * q^53 + 2 * q^54 - 17 * q^55 + 3 * q^56 - 8 * q^57 + 2 * q^58 - 17 * q^59 + 2 * q^61 - 8 * q^62 - 3 * q^63 + 2 * q^64 - 17 * q^65 + 3 * q^66 - 19 * q^67 - 3 * q^68 + 10 * q^69 - 17 * q^70 - q^71 - 2 * q^72 + 8 * q^73 - 5 * q^74 - 24 * q^75 + 8 * q^76 - 13 * q^77 + 7 * q^78 + 3 * q^79 + 2 * q^81 - 15 * q^82 - q^83 + 3 * q^84 - 17 * q^85 + q^86 + 2 * q^87 - 3 * q^88 + 19 * q^89 - 19 * q^91 - 10 * q^92 - 8 * q^93 - 6 * q^94 + 2 * q^96 - 11 * q^97 + q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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