LMFDB - Embedded newform 8619.2.a.bn.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8619,2,Mod(1,8619)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8619, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8619.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8619 = 3 \cdot 13^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8619.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:	$68.8230615021$
Analytic rank:	$1$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 20x^{14} + 156x^{12} - 602x^{10} + 1212x^{8} - 1259x^{6} + 665x^{4} - 168x^{2} + 16 $ x^16 - 20x^14 + 156x^12 - 602x^10 + 1212x^8 - 1259x^6 + 665x^4 - 168*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 663)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Root			$2.45691$ of defining polynomial
Character	$\chi$	$=$	8619.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.45691 q^{2} +1.00000 q^{3} +4.03639 q^{4} +0.284332 q^{5} +2.45691 q^{6} -4.70317 q^{7} +5.00321 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.45691 q^{2} +1.00000 q^{3} +4.03639 q^{4} +0.284332 q^{5} +2.45691 q^{6} -4.70317 q^{7} +5.00321 q^{8} +1.00000 q^{9} +0.698577 q^{10} -0.470529 q^{11} +4.03639 q^{12} -11.5552 q^{14} +0.284332 q^{15} +4.21965 q^{16} -1.00000 q^{17} +2.45691 q^{18} -0.136054 q^{19} +1.14767 q^{20} -4.70317 q^{21} -1.15605 q^{22} -8.62876 q^{23} +5.00321 q^{24} -4.91916 q^{25} +1.00000 q^{27} -18.9838 q^{28} -6.53128 q^{29} +0.698577 q^{30} +3.60080 q^{31} +0.360854 q^{32} -0.470529 q^{33} -2.45691 q^{34} -1.33726 q^{35} +4.03639 q^{36} -5.88371 q^{37} -0.334273 q^{38} +1.42257 q^{40} +2.54407 q^{41} -11.5552 q^{42} +6.60053 q^{43} -1.89924 q^{44} +0.284332 q^{45} -21.2001 q^{46} -1.30120 q^{47} +4.21965 q^{48} +15.1198 q^{49} -12.0859 q^{50} -1.00000 q^{51} -7.22455 q^{53} +2.45691 q^{54} -0.133786 q^{55} -23.5309 q^{56} -0.136054 q^{57} -16.0467 q^{58} +2.10046 q^{59} +1.14767 q^{60} -3.21547 q^{61} +8.84682 q^{62} -4.70317 q^{63} -7.55271 q^{64} -1.15605 q^{66} +9.66976 q^{67} -4.03639 q^{68} -8.62876 q^{69} -3.28552 q^{70} -13.7845 q^{71} +5.00321 q^{72} -0.728230 q^{73} -14.4557 q^{74} -4.91916 q^{75} -0.549168 q^{76} +2.21298 q^{77} -15.1655 q^{79} +1.19978 q^{80} +1.00000 q^{81} +6.25053 q^{82} +13.0056 q^{83} -18.9838 q^{84} -0.284332 q^{85} +16.2169 q^{86} -6.53128 q^{87} -2.35416 q^{88} -4.39696 q^{89} +0.698577 q^{90} -34.8290 q^{92} +3.60080 q^{93} -3.19692 q^{94} -0.0386846 q^{95} +0.360854 q^{96} +12.2190 q^{97} +37.1479 q^{98} -0.470529 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{3} + 8 q^{4} + 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^3 + 8 * q^4 + 16 * q^9	$ 16 q + 16 q^{3} + 8 q^{4} + 16 q^{9} + 2 q^{10} + 8 q^{12} - 26 q^{14} - 16 q^{17} - 2 q^{22} - 42 q^{23} - 14 q^{25} + 16 q^{27} - 58 q^{29} + 2 q^{30} - 30 q^{35} + 8 q^{36} - 62 q^{38} + 4 q^{40} - 26 q^{42} - 6 q^{43} + 4 q^{49} - 16 q^{51} - 26 q^{53} - 18 q^{55} - 74 q^{56} - 58 q^{61} - 40 q^{62} - 36 q^{64} - 2 q^{66} - 8 q^{68} - 42 q^{69} - 34 q^{74} - 14 q^{75} + 8 q^{77} - 14 q^{79} + 16 q^{81} - 6 q^{82} - 58 q^{87} - 10 q^{88} + 2 q^{90} - 64 q^{92} + 50 q^{94} - 54 q^{95}+O(q^{100}) $ 16 * q + 16 * q^3 + 8 * q^4 + 16 * q^9 + 2 * q^10 + 8 * q^12 - 26 * q^14 - 16 * q^17 - 2 * q^22 - 42 * q^23 - 14 * q^25 + 16 * q^27 - 58 * q^29 + 2 * q^30 - 30 * q^35 + 8 * q^36 - 62 * q^38 + 4 * q^40 - 26 * q^42 - 6 * q^43 + 4 * q^49 - 16 * q^51 - 26 * q^53 - 18 * q^55 - 74 * q^56 - 58 * q^61 - 40 * q^62 - 36 * q^64 - 2 * q^66 - 8 * q^68 - 42 * q^69 - 34 * q^74 - 14 * q^75 + 8 * q^77 - 14 * q^79 + 16 * q^81 - 6 * q^82 - 58 * q^87 - 10 * q^88 + 2 * q^90 - 64 * q^92 + 50 * q^94 - 54 * q^95

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 $

$2$	2.45691	1.73729	0.868647	−	0.495431i	$-0.164990\pi$
$2$	2.45691	1.73729	0.868647	+	0.495431i	$0.164990\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.03639	2.01819
$5$	0.284332	0.127157	0.0635786	−	0.997977i	$-0.479749\pi$
$5$	0.284332	0.127157	0.0635786	+	0.997977i	$0.479749\pi$
$6$	2.45691	1.00303
$7$	−4.70317	−1.77763	−0.888815	−	0.458266i	$-0.848471\pi$
$7$	−4.70317	−1.77763	−0.888815	+	0.458266i	$0.848471\pi$
$8$	5.00321	1.76890
$9$	1.00000	0.333333
$10$	0.698577	0.220909
$11$	−0.470529	−0.141870	−0.0709349	−	0.997481i	$-0.522598\pi$
$11$	−0.470529	−0.141870	−0.0709349	+	0.997481i	$0.522598\pi$
$12$	4.03639	1.16520
$13$	0	0
$13$	0	0
$14$	−11.5552	−3.08827
$15$	0.284332	0.0734142
$16$	4.21965	1.05491
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	2.45691	0.579098
$19$	−0.136054	−0.0312130	−0.0156065	−	0.999878i	$-0.504968\pi$
$19$	−0.136054	−0.0312130	−0.0156065	+	0.999878i	$0.504968\pi$
$20$	1.14767	0.256628
$21$	−4.70317	−1.02632
$22$	−1.15605	−0.246470
$23$	−8.62876	−1.79922	−0.899611	−	0.436693i	$-0.856150\pi$
$23$	−8.62876	−1.79922	−0.899611	+	0.436693i	$0.856150\pi$
$24$	5.00321	1.02128
$25$	−4.91916	−0.983831
$26$	0	0
$27$	1.00000	0.192450
$28$	−18.9838	−3.58760
$29$	−6.53128	−1.21283	−0.606414	−	0.795149i	$-0.707393\pi$
$29$	−6.53128	−1.21283	−0.606414	+	0.795149i	$0.707393\pi$
$30$	0.698577	0.127542
$31$	3.60080	0.646723	0.323361	−	0.946276i	$-0.395187\pi$
$31$	3.60080	0.646723	0.323361	+	0.946276i	$0.395187\pi$
$32$	0.360854	0.0637906
$33$	−0.470529	−0.0819086
$34$	−2.45691	−0.421356
$35$	−1.33726	−0.226038
$36$	4.03639	0.672731
$37$	−5.88371	−0.967277	−0.483638	−	0.875268i	$-0.660685\pi$
$37$	−5.88371	−0.967277	−0.483638	+	0.875268i	$0.660685\pi$
$38$	−0.334273	−0.0542262
$39$	0	0
$40$	1.42257	0.224929
$41$	2.54407	0.397316	0.198658	−	0.980069i	$-0.436342\pi$
$41$	2.54407	0.397316	0.198658	+	0.980069i	$0.436342\pi$
$42$	−11.5552	−1.78301
$43$	6.60053	1.00657	0.503286	−	0.864120i	$-0.332124\pi$
$43$	6.60053	1.00657	0.503286	+	0.864120i	$0.332124\pi$
$44$	−1.89924	−0.286321
$45$	0.284332	0.0423857
$46$	−21.2001	−3.12578
$47$	−1.30120	−0.189799	−0.0948997	−	0.995487i	$-0.530253\pi$
$47$	−1.30120	−0.189799	−0.0948997	+	0.995487i	$0.530253\pi$
$48$	4.21965	0.609054
$49$	15.1198	2.15997
$50$	−12.0859	−1.70920
$51$	−1.00000	−0.140028
$52$	0	0
$53$	−7.22455	−0.992369	−0.496184	−	0.868217i	$-0.665266\pi$
$53$	−7.22455	−0.992369	−0.496184	+	0.868217i	$0.665266\pi$
$54$	2.45691	0.334343
$55$	−0.133786	−0.0180398
$56$	−23.5309	−3.14446
$57$	−0.136054	−0.0180208
$58$	−16.0467	−2.10704
$59$	2.10046	0.273457	0.136728	−	0.990609i	$-0.456341\pi$
$59$	2.10046	0.273457	0.136728	+	0.990609i	$0.456341\pi$
$60$	1.14767	0.148164
$61$	−3.21547	−0.411698	−0.205849	−	0.978584i	$-0.565996\pi$
$61$	−3.21547	−0.411698	−0.205849	+	0.978584i	$0.565996\pi$
$62$	8.84682	1.12355
$63$	−4.70317	−0.592543
$64$	−7.55271	−0.944089
$65$	0	0
$66$	−1.15605	−0.142299
$67$	9.66976	1.18135	0.590675	−	0.806910i	$-0.298862\pi$
$67$	9.66976	1.18135	0.590675	+	0.806910i	$0.298862\pi$
$68$	−4.03639	−0.489484
$69$	−8.62876	−1.03878
$70$	−3.28552	−0.392695
$71$	−13.7845	−1.63592	−0.817962	−	0.575272i	$-0.804896\pi$
$71$	−13.7845	−1.63592	−0.817962	+	0.575272i	$0.804896\pi$
$72$	5.00321	0.589634
$73$	−0.728230	−0.0852329	−0.0426165	−	0.999092i	$-0.513569\pi$
$73$	−0.728230	−0.0852329	−0.0426165	+	0.999092i	$0.513569\pi$
$74$	−14.4557	−1.68044
$75$	−4.91916	−0.568015
$76$	−0.549168	−0.0629939
$77$	2.21298	0.252192
$78$	0	0
$79$	−15.1655	−1.70625	−0.853127	−	0.521704i	$-0.825297\pi$
$79$	−15.1655	−1.70625	−0.853127	+	0.521704i	$0.825297\pi$
$80$	1.19978	0.134140
$81$	1.00000	0.111111
$82$	6.25053	0.690256
$83$	13.0056	1.42755	0.713773	−	0.700377i	$-0.246985\pi$
$83$	13.0056	1.42755	0.713773	+	0.700377i	$0.246985\pi$
$84$	−18.9838	−2.07130
$85$	−0.284332	−0.0308401
$86$	16.2169	1.74871
$87$	−6.53128	−0.700227
$88$	−2.35416	−0.250954
$89$	−4.39696	−0.466077	−0.233039	−	0.972468i	$-0.574867\pi$
$89$	−4.39696	−0.466077	−0.233039	+	0.972468i	$0.574867\pi$
$90$	0.698577	0.0736365
$91$	0	0
$92$	−34.8290	−3.63118
$93$	3.60080	0.373385
$94$	−3.19692	−0.329737
$95$	−0.0386846	−0.00396896
$96$	0.360854	0.0368295
$97$	12.2190	1.24065	0.620327	−	0.784343i	$-0.287000\pi$
$97$	12.2190	1.24065	0.620327	+	0.784343i	$0.287000\pi$
$98$	37.1479	3.75250
$99$	−0.470529	−0.0472899
$100$	−19.8556	−1.98556
$101$	3.16138	0.314569	0.157284	−	0.987553i	$-0.449726\pi$
$101$	3.16138	0.314569	0.157284	+	0.987553i	$0.449726\pi$
$102$	−2.45691	−0.243270
$103$	17.7088	1.74490	0.872448	−	0.488706i	$-0.162531\pi$
$103$	17.7088	1.74490	0.872448	+	0.488706i	$0.162531\pi$
$104$	0	0
$105$	−1.33726	−0.130503
$106$	−17.7500	−1.72404
$107$	−3.01037	−0.291024	−0.145512	−	0.989356i	$-0.546483\pi$
$107$	−3.01037	−0.291024	−0.145512	+	0.989356i	$0.546483\pi$
$108$	4.03639	0.388402
$109$	6.53766	0.626194	0.313097	−	0.949721i	$-0.398633\pi$
$109$	6.53766	0.626194	0.313097	+	0.949721i	$0.398633\pi$
$110$	−0.328701	−0.0313404
$111$	−5.88371	−0.558457
$112$	−19.8457	−1.87524
$113$	−12.5670	−1.18220	−0.591102	−	0.806597i	$-0.701307\pi$
$113$	−12.5670	−1.18220	−0.591102	+	0.806597i	$0.701307\pi$
$114$	−0.334273	−0.0313075
$115$	−2.45343	−0.228784
$116$	−26.3628	−2.44772
$117$	0	0
$118$	5.16063	0.475075
$119$	4.70317	0.431139
$120$	1.42257	0.129863
$121$	−10.7786	−0.979873
$122$	−7.90010	−0.715241
$123$	2.54407	0.229391
$124$	14.5342	1.30521
$125$	−2.82033	−0.252258
$126$	−11.5552	−1.02942
$127$	−15.6041	−1.38464	−0.692320	−	0.721591i	$-0.743411\pi$
$127$	−15.6041	−1.38464	−0.692320	+	0.721591i	$0.743411\pi$
$128$	−19.2780	−1.70395
$129$	6.60053	0.581145
$130$	0	0
$131$	8.88619	0.776390	0.388195	−	0.921577i	$-0.373099\pi$
$131$	8.88619	0.776390	0.388195	+	0.921577i	$0.373099\pi$
$132$	−1.89924	−0.165307
$133$	0.639887	0.0554852
$134$	23.7577	2.05235
$135$	0.284332	0.0244714
$136$	−5.00321	−0.429022
$137$	6.99873	0.597941	0.298971	−	0.954262i	$-0.403357\pi$
$137$	6.99873	0.597941	0.298971	+	0.954262i	$0.403357\pi$
$138$	−21.2001	−1.80467
$139$	−4.24002	−0.359633	−0.179817	−	0.983700i	$-0.557550\pi$
$139$	−4.24002	−0.359633	−0.179817	+	0.983700i	$0.557550\pi$
$140$	−5.39770	−0.456189
$141$	−1.30120	−0.109581
$142$	−33.8673	−2.84208
$143$	0	0
$144$	4.21965	0.351637
$145$	−1.85705	−0.154220
$146$	−1.78919	−0.148075
$147$	15.1198	1.24706
$148$	−23.7489	−1.95215
$149$	−11.1279	−0.911632	−0.455816	−	0.890074i	$-0.650653\pi$
$149$	−11.1279	−0.911632	−0.455816	+	0.890074i	$0.650653\pi$
$150$	−12.0859	−0.986810
$151$	−7.59663	−0.618205	−0.309102	−	0.951029i	$-0.600029\pi$
$151$	−7.59663	−0.618205	−0.309102	+	0.951029i	$0.600029\pi$
$152$	−0.680709	−0.0552128
$153$	−1.00000	−0.0808452
$154$	5.43708	0.438132
$155$	1.02382	0.0822354
$156$	0	0
$157$	14.2471	1.13705	0.568523	−	0.822668i	$-0.307515\pi$
$157$	14.2471	1.13705	0.568523	+	0.822668i	$0.307515\pi$
$158$	−37.2602	−2.96427
$159$	−7.22455	−0.572944
$160$	0.102602	0.00811143
$161$	40.5825	3.19835
$162$	2.45691	0.193033
$163$	16.5719	1.29801	0.649005	−	0.760784i	$-0.275185\pi$
$163$	16.5719	1.29801	0.649005	+	0.760784i	$0.275185\pi$
$164$	10.2688	0.801861
$165$	−0.133786	−0.0104153
$166$	31.9534	2.48007
$167$	7.50352	0.580640	0.290320	−	0.956930i	$-0.406238\pi$
$167$	7.50352	0.580640	0.290320	+	0.956930i	$0.406238\pi$
$168$	−23.5309	−1.81545
$169$	0	0
$170$	−0.698577	−0.0535784
$171$	−0.136054	−0.0104043
$172$	26.6423	2.03146
$173$	−25.6628	−1.95111	−0.975555	−	0.219756i	$-0.929474\pi$
$173$	−25.6628	−1.95111	−0.975555	+	0.219756i	$0.929474\pi$
$174$	−16.0467	−1.21650
$175$	23.1356	1.74889
$176$	−1.98547	−0.149660
$177$	2.10046	0.157880
$178$	−10.8029	−0.809713
$179$	−14.2533	−1.06534	−0.532672	−	0.846322i	$-0.678812\pi$
$179$	−14.2533	−1.06534	−0.532672	+	0.846322i	$0.678812\pi$
$180$	1.14767	0.0855426
$181$	3.84190	0.285566	0.142783	−	0.989754i	$-0.454395\pi$
$181$	3.84190	0.285566	0.142783	+	0.989754i	$0.454395\pi$
$182$	0	0
$183$	−3.21547	−0.237694
$184$	−43.1715	−3.18265
$185$	−1.67293	−0.122996
$186$	8.84682	0.648681
$187$	0.470529	0.0344085
$188$	−5.25214	−0.383052
$189$	−4.70317	−0.342105
$190$	−0.0950445	−0.00689525
$191$	−7.45189	−0.539200	−0.269600	−	0.962972i	$-0.586891\pi$
$191$	−7.45189	−0.539200	−0.269600	+	0.962972i	$0.586891\pi$
$192$	−7.55271	−0.545070
$193$	3.34522	0.240794	0.120397	−	0.992726i	$-0.461583\pi$
$193$	3.34522	0.240794	0.120397	+	0.992726i	$0.461583\pi$
$194$	30.0210	2.15538
$195$	0	0
$196$	61.0293	4.35924
$197$	13.7432	0.979165	0.489583	−	0.871957i	$-0.337149\pi$
$197$	13.7432	0.979165	0.489583	+	0.871957i	$0.337149\pi$
$198$	−1.15605	−0.0821566
$199$	−8.13323	−0.576549	−0.288275	−	0.957548i	$-0.593082\pi$
$199$	−8.13323	−0.576549	−0.288275	+	0.957548i	$0.593082\pi$
$200$	−24.6116	−1.74030
$201$	9.66976	0.682052
$202$	7.76721	0.546499
$203$	30.7177	2.15596
$204$	−4.03639	−0.282604
$205$	0.723359	0.0505216
$206$	43.5088	3.03140
$207$	−8.62876	−0.599741
$208$	0	0
$209$	0.0640175	0.00442819
$210$	−3.28552	−0.226723
$211$	15.9267	1.09644	0.548220	−	0.836334i	$-0.315306\pi$
$211$	15.9267	1.09644	0.548220	+	0.836334i	$0.315306\pi$
$212$	−29.1611	−2.00279
$213$	−13.7845	−0.944502
$214$	−7.39621	−0.505594
$215$	1.87674	0.127993
$216$	5.00321	0.340425
$217$	−16.9352	−1.14963
$218$	16.0624	1.08788
$219$	−0.728230	−0.0492092
$220$	−0.540014	−0.0364077
$221$	0	0
$222$	−14.4557	−0.970205
$223$	−28.2978	−1.89496	−0.947479	−	0.319818i	$-0.896378\pi$
$223$	−28.2978	−1.89496	−0.947479	+	0.319818i	$0.896378\pi$
$224$	−1.69716	−0.113396
$225$	−4.91916	−0.327944
$226$	−30.8759	−2.05384
$227$	−8.48348	−0.563068	−0.281534	−	0.959551i	$-0.590843\pi$
$227$	−8.48348	−0.563068	−0.281534	+	0.959551i	$0.590843\pi$
$228$	−0.549168	−0.0363696
$229$	22.6533	1.49697	0.748486	−	0.663150i	$-0.230781\pi$
$229$	22.6533	1.49697	0.748486	+	0.663150i	$0.230781\pi$
$230$	−6.02786	−0.397465
$231$	2.21298	0.145603
$232$	−32.6774	−2.14538
$233$	17.6416	1.15574	0.577870	−	0.816129i	$-0.303884\pi$
$233$	17.6416	1.15574	0.577870	+	0.816129i	$0.303884\pi$
$234$	0	0
$235$	−0.369972	−0.0241343
$236$	8.47827	0.551889
$237$	−15.1655	−0.985106
$238$	11.5552	0.749015
$239$	13.7518	0.889529	0.444765	−	0.895647i	$-0.353287\pi$
$239$	13.7518	0.889529	0.444765	+	0.895647i	$0.353287\pi$
$240$	1.19978	0.0774455
$241$	1.31425	0.0846580	0.0423290	−	0.999104i	$-0.486522\pi$
$241$	1.31425	0.0846580	0.0423290	+	0.999104i	$0.486522\pi$
$242$	−26.4820	−1.70233
$243$	1.00000	0.0641500
$244$	−12.9789	−0.830887
$245$	4.29904	0.274656
$246$	6.25053	0.398519
$247$	0	0
$248$	18.0156	1.14399
$249$	13.0056	0.824194
$250$	−6.92929	−0.438247
$251$	−13.9251	−0.878946	−0.439473	−	0.898256i	$-0.644835\pi$
$251$	−13.9251	−0.878946	−0.439473	+	0.898256i	$0.644835\pi$
$252$	−18.9838	−1.19587
$253$	4.06008	0.255255
$254$	−38.3378	−2.40553
$255$	−0.284332	−0.0178056
$256$	−32.2588	−2.01618
$257$	23.0951	1.44063	0.720315	−	0.693647i	$-0.243997\pi$
$257$	23.0951	1.44063	0.720315	+	0.693647i	$0.243997\pi$
$258$	16.2169	1.00962
$259$	27.6721	1.71946
$260$	0	0
$261$	−6.53128	−0.404276
$262$	21.8325	1.34882
$263$	−6.57477	−0.405418	−0.202709	−	0.979239i	$-0.564975\pi$
$263$	−6.57477	−0.405418	−0.202709	+	0.979239i	$0.564975\pi$
$264$	−2.35416	−0.144888
$265$	−2.05417	−0.126187
$266$	1.57214	0.0963942
$267$	−4.39696	−0.269090
$268$	39.0309	2.38419
$269$	9.90841	0.604126	0.302063	−	0.953288i	$-0.402325\pi$
$269$	9.90841	0.604126	0.302063	+	0.953288i	$0.402325\pi$
$270$	0.698577	0.0425140
$271$	−6.02642	−0.366079	−0.183039	−	0.983106i	$-0.558594\pi$
$271$	−6.02642	−0.366079	−0.183039	+	0.983106i	$0.558594\pi$
$272$	−4.21965	−0.255854
$273$	0	0
$274$	17.1952	1.03880
$275$	2.31460	0.139576
$276$	−34.8290	−2.09646
$277$	3.72271	0.223676	0.111838	−	0.993726i	$-0.464326\pi$
$277$	3.72271	0.223676	0.111838	+	0.993726i	$0.464326\pi$
$278$	−10.4173	−0.624789
$279$	3.60080	0.215574
$280$	−6.69060	−0.399840
$281$	−1.41750	−0.0845611	−0.0422806	−	0.999106i	$-0.513462\pi$
$281$	−1.41750	−0.0845611	−0.0422806	+	0.999106i	$0.513462\pi$
$282$	−3.19692	−0.190374
$283$	20.5587	1.22209	0.611044	−	0.791597i	$-0.290750\pi$
$283$	20.5587	1.22209	0.611044	+	0.791597i	$0.290750\pi$
$284$	−55.6398	−3.30161
$285$	−0.0386846	−0.00229148
$286$	0	0
$287$	−11.9652	−0.706281
$288$	0.360854	0.0212635
$289$	1.00000	0.0588235
$290$	−4.56260	−0.267925
$291$	12.2190	0.716292
$292$	−2.93942	−0.172017
$293$	−26.5455	−1.55080	−0.775402	−	0.631468i	$-0.782453\pi$
$293$	−26.5455	−1.55080	−0.775402	+	0.631468i	$0.782453\pi$
$294$	37.1479	2.16651
$295$	0.597228	0.0347720
$296$	−29.4375	−1.71102
$297$	−0.470529	−0.0273029
$298$	−27.3402	−1.58377
$299$	0	0
$300$	−19.8556	−1.14636
$301$	−31.0434	−1.78931
$302$	−18.6642	−1.07400
$303$	3.16138	0.181616
$304$	−0.574102	−0.0329270
$305$	−0.914260	−0.0523504
$306$	−2.45691	−0.140452
$307$	−13.5305	−0.772225	−0.386113	−	0.922452i	$-0.626182\pi$
$307$	−13.5305	−0.772225	−0.386113	+	0.922452i	$0.626182\pi$
$308$	8.93243	0.508972
$309$	17.7088	1.00742
$310$	2.51544	0.142867
$311$	2.88225	0.163437	0.0817187	−	0.996655i	$-0.473959\pi$
$311$	2.88225	0.163437	0.0817187	+	0.996655i	$0.473959\pi$
$312$	0	0
$313$	−24.4829	−1.38385	−0.691927	−	0.721967i	$-0.743238\pi$
$313$	−24.4829	−1.38385	−0.691927	+	0.721967i	$0.743238\pi$
$314$	35.0039	1.97538
$315$	−1.33726	−0.0753461
$316$	−61.2139	−3.44355
$317$	30.7367	1.72634	0.863172	−	0.504911i	$-0.168475\pi$
$317$	30.7367	1.72634	0.863172	+	0.504911i	$0.168475\pi$
$318$	−17.7500	−0.995373
$319$	3.07316	0.172064
$320$	−2.14748	−0.120048
$321$	−3.01037	−0.168023
$322$	99.7074	5.55648
$323$	0.136054	0.00757027
$324$	4.03639	0.224244
$325$	0	0
$326$	40.7156	2.25503
$327$	6.53766	0.361533
$328$	12.7285	0.702814
$329$	6.11976	0.337393
$330$	−0.328701	−0.0180944
$331$	−7.77974	−0.427613	−0.213806	−	0.976876i	$-0.568586\pi$
$331$	−7.77974	−0.427613	−0.213806	+	0.976876i	$0.568586\pi$
$332$	52.4955	2.88106
$333$	−5.88371	−0.322426
$334$	18.4354	1.00874
$335$	2.74942	0.150217
$336$	−19.8457	−1.08267
$337$	−20.1777	−1.09915	−0.549574	−	0.835445i	$-0.685210\pi$
$337$	−20.1777	−1.09915	−0.549574	+	0.835445i	$0.685210\pi$
$338$	0	0
$339$	−12.5670	−0.682546
$340$	−1.14767	−0.0622414
$341$	−1.69428	−0.0917504
$342$	−0.334273	−0.0180754
$343$	−38.1887	−2.06200
$344$	33.0239	1.78053
$345$	−2.45343	−0.132088
$346$	−63.0512	−3.38965
$347$	−26.6508	−1.43069	−0.715344	−	0.698772i	$-0.753730\pi$
$347$	−26.6508	−1.43069	−0.715344	+	0.698772i	$0.753730\pi$
$348$	−26.3628	−1.41319
$349$	24.5393	1.31356	0.656780	−	0.754082i	$-0.271918\pi$
$349$	24.5393	1.31356	0.656780	+	0.754082i	$0.271918\pi$
$350$	56.8420	3.03833
$351$	0	0
$352$	−0.169792	−0.00904996
$353$	−21.2353	−1.13024	−0.565121	−	0.825008i	$-0.691171\pi$
$353$	−21.2353	−1.13024	−0.565121	+	0.825008i	$0.691171\pi$
$354$	5.16063	0.274285
$355$	−3.91939	−0.208020
$356$	−17.7478	−0.940634
$357$	4.70317	0.248918
$358$	−35.0191	−1.85082
$359$	30.7675	1.62385	0.811923	−	0.583764i	$-0.198421\pi$
$359$	30.7675	1.62385	0.811923	+	0.583764i	$0.198421\pi$
$360$	1.42257	0.0749762
$361$	−18.9815	−0.999026
$362$	9.43919	0.496113
$363$	−10.7786	−0.565730
$364$	0	0
$365$	−0.207059	−0.0108380
$366$	−7.90010	−0.412945
$367$	−33.7643	−1.76248	−0.881240	−	0.472669i	$-0.843291\pi$
$367$	−33.7643	−1.76248	−0.881240	+	0.472669i	$0.843291\pi$
$368$	−36.4103	−1.89802
$369$	2.54407	0.132439
$370$	−4.11023	−0.213681
$371$	33.9783	1.76406
$372$	14.5342	0.753564
$373$	−7.12954	−0.369154	−0.184577	−	0.982818i	$-0.559091\pi$
$373$	−7.12954	−0.369154	−0.184577	+	0.982818i	$0.559091\pi$
$374$	1.15605	0.0597777
$375$	−2.82033	−0.145641
$376$	−6.51017	−0.335737
$377$	0	0
$378$	−11.5552	−0.594337
$379$	3.38300	0.173773	0.0868866	−	0.996218i	$-0.472308\pi$
$379$	3.38300	0.173773	0.0868866	+	0.996218i	$0.472308\pi$
$380$	−0.156146	−0.00801013
$381$	−15.6041	−0.799422
$382$	−18.3086	−0.936749
$383$	−11.8259	−0.604274	−0.302137	−	0.953264i	$-0.597700\pi$
$383$	−11.8259	−0.604274	−0.302137	+	0.953264i	$0.597700\pi$
$384$	−19.2780	−0.983777
$385$	0.629220	0.0320680
$386$	8.21889	0.418331
$387$	6.60053	0.335524
$388$	49.3208	2.50388
$389$	2.26895	0.115040	0.0575201	−	0.998344i	$-0.481681\pi$
$389$	2.26895	0.115040	0.0575201	+	0.998344i	$0.481681\pi$
$390$	0	0
$391$	8.62876	0.436375
$392$	75.6475	3.82078
$393$	8.88619	0.448249
$394$	33.7658	1.70110
$395$	−4.31204	−0.216962
$396$	−1.89924	−0.0954403
$397$	−23.4403	−1.17644	−0.588218	−	0.808703i	$-0.700170\pi$
$397$	−23.4403	−1.17644	−0.588218	+	0.808703i	$0.700170\pi$
$398$	−19.9826	−1.00164
$399$	0.639887	0.0320344
$400$	−20.7571	−1.03786
$401$	−8.74465	−0.436687	−0.218343	−	0.975872i	$-0.570065\pi$
$401$	−8.74465	−0.436687	−0.218343	+	0.975872i	$0.570065\pi$
$402$	23.7577	1.18493
$403$	0	0
$404$	12.7605	0.634861
$405$	0.284332	0.0141286
$406$	75.4705	3.74554
$407$	2.76846	0.137227
$408$	−5.00321	−0.247696
$409$	−31.2754	−1.54647	−0.773235	−	0.634120i	$-0.781363\pi$
$409$	−31.2754	−1.54647	−0.773235	+	0.634120i	$0.781363\pi$
$410$	1.77723	0.0877709
$411$	6.99873	0.345222
$412$	71.4794	3.52154
$413$	−9.87882	−0.486105
$414$	−21.2001	−1.04193
$415$	3.69790	0.181523
$416$	0	0
$417$	−4.24002	−0.207634
$418$	0.157285	0.00769306
$419$	17.1726	0.838937	0.419469	−	0.907770i	$-0.362216\pi$
$419$	17.1726	0.838937	0.419469	+	0.907770i	$0.362216\pi$
$420$	−5.39770	−0.263381
$421$	−13.2245	−0.644522	−0.322261	−	0.946651i	$-0.604443\pi$
$421$	−13.2245	−0.644522	−0.322261	+	0.946651i	$0.604443\pi$
$422$	39.1304	1.90484
$423$	−1.30120	−0.0632665
$424$	−36.1460	−1.75540
$425$	4.91916	0.238614
$426$	−33.8673	−1.64088
$427$	15.1229	0.731847
$428$	−12.1510	−0.587343
$429$	0	0
$430$	4.61098	0.222361
$431$	17.8866	0.861565	0.430783	−	0.902456i	$-0.358238\pi$
$431$	17.8866	0.861565	0.430783	+	0.902456i	$0.358238\pi$
$432$	4.21965	0.203018
$433$	21.4964	1.03305	0.516526	−	0.856272i	$-0.327225\pi$
$433$	21.4964	1.03305	0.516526	+	0.856272i	$0.327225\pi$
$434$	−41.6081	−1.99725
$435$	−1.85705	−0.0890388
$436$	26.3885	1.26378
$437$	1.17398	0.0561591
$438$	−1.78919	−0.0854910
$439$	−5.91380	−0.282250	−0.141125	−	0.989992i	$-0.545072\pi$
$439$	−5.91380	−0.282250	−0.141125	+	0.989992i	$0.545072\pi$
$440$	−0.669362	−0.0319106
$441$	15.1198	0.719990
$442$	0	0
$443$	3.56976	0.169605	0.0848023	−	0.996398i	$-0.472974\pi$
$443$	3.56976	0.169605	0.0848023	+	0.996398i	$0.472974\pi$
$444$	−23.7489	−1.12708
$445$	−1.25020	−0.0592650
$446$	−69.5249	−3.29210
$447$	−11.1279	−0.526331
$448$	35.5217	1.67824
$449$	24.5324	1.15776	0.578878	−	0.815414i	$-0.303491\pi$
$449$	24.5324	1.15776	0.578878	+	0.815414i	$0.303491\pi$
$450$	−12.0859	−0.569735
$451$	−1.19706	−0.0563672
$452$	−50.7253	−2.38592
$453$	−7.59663	−0.356921
$454$	−20.8431	−0.978216
$455$	0	0
$456$	−0.680709	−0.0318771
$457$	3.78524	0.177066	0.0885331	−	0.996073i	$-0.471782\pi$
$457$	3.78524	0.177066	0.0885331	+	0.996073i	$0.471782\pi$
$458$	55.6570	2.60068
$459$	−1.00000	−0.0466760
$460$	−9.90301	−0.461730
$461$	4.09394	0.190674	0.0953369	−	0.995445i	$-0.469607\pi$
$461$	4.09394	0.190674	0.0953369	+	0.995445i	$0.469607\pi$
$462$	5.43708	0.252956
$463$	20.9704	0.974577	0.487289	−	0.873241i	$-0.337986\pi$
$463$	20.9704	0.974577	0.487289	+	0.873241i	$0.337986\pi$
$464$	−27.5597	−1.27943
$465$	1.02382	0.0474786
$466$	43.3438	2.00786
$467$	−11.4563	−0.530132	−0.265066	−	0.964230i	$-0.585394\pi$
$467$	−11.4563	−0.530132	−0.265066	+	0.964230i	$0.585394\pi$
$468$	0	0
$469$	−45.4785	−2.10000
$470$	−0.908988	−0.0419285
$471$	14.2471	0.656474
$472$	10.5091	0.483718
$473$	−3.10574	−0.142802
$474$	−37.2602	−1.71142
$475$	0.669273	0.0307083
$476$	18.9838	0.870121
$477$	−7.22455	−0.330790
$478$	33.7869	1.54537
$479$	−38.2882	−1.74943	−0.874717	−	0.484633i	$-0.838953\pi$
$479$	−38.2882	−1.74943	−0.874717	+	0.484633i	$0.838953\pi$
$480$	0.102602	0.00468314
$481$	0	0
$482$	3.22898	0.147076
$483$	40.5825	1.84657
$484$	−43.5066	−1.97757
$485$	3.47426	0.157758
$486$	2.45691	0.111448
$487$	−1.54113	−0.0698353	−0.0349176	−	0.999390i	$-0.511117\pi$
$487$	−1.54113	−0.0698353	−0.0349176	+	0.999390i	$0.511117\pi$
$488$	−16.0877	−0.728254
$489$	16.5719	0.749407
$490$	10.5623	0.477158
$491$	21.8095	0.984249	0.492125	−	0.870525i	$-0.336220\pi$
$491$	21.8095	0.984249	0.492125	+	0.870525i	$0.336220\pi$
$492$	10.2688	0.462955
$493$	6.53128	0.294154
$494$	0	0
$495$	−0.133786	−0.00601325
$496$	15.1941	0.682235
$497$	64.8310	2.90807
$498$	31.9534	1.43187
$499$	−0.502152	−0.0224794	−0.0112397	−	0.999937i	$-0.503578\pi$
$499$	−0.502152	−0.0224794	−0.0112397	+	0.999937i	$0.503578\pi$
$500$	−11.3840	−0.509106
$501$	7.50352	0.335233
$502$	−34.2127	−1.52699
$503$	14.9899	0.668368	0.334184	−	0.942508i	$-0.391539\pi$
$503$	14.9899	0.668368	0.334184	+	0.942508i	$0.391539\pi$
$504$	−23.5309	−1.04815
$505$	0.898881	0.0399997
$506$	9.97524	0.443454
$507$	0	0
$508$	−62.9842	−2.79447
$509$	−12.1005	−0.536344	−0.268172	−	0.963371i	$-0.586420\pi$
$509$	−12.1005	−0.536344	−0.268172	+	0.963371i	$0.586420\pi$
$510$	−0.698577	−0.0309335
$511$	3.42499	0.151513
$512$	−40.7009	−1.79874
$513$	−0.136054	−0.00600695
$514$	56.7424	2.50280
$515$	5.03517	0.221876
$516$	26.6423	1.17286
$517$	0.612252	0.0269268
$518$	67.9877	2.98721
$519$	−25.6628	−1.12647
$520$	0	0
$521$	43.3795	1.90049	0.950246	−	0.311501i	$-0.100832\pi$
$521$	43.3795	1.90049	0.950246	+	0.311501i	$0.100832\pi$
$522$	−16.0467	−0.702347
$523$	24.9614	1.09149	0.545743	−	0.837953i	$-0.316247\pi$
$523$	24.9614	1.09149	0.545743	+	0.837953i	$0.316247\pi$
$524$	35.8681	1.56691
$525$	23.1356	1.00972
$526$	−16.1536	−0.704330
$527$	−3.60080	−0.156853
$528$	−1.98547	−0.0864063
$529$	51.4556	2.23720
$530$	−5.04691	−0.219224
$531$	2.10046	0.0911522
$532$	2.58283	0.111980
$533$	0	0
$534$	−10.8029	−0.467488
$535$	−0.855946	−0.0370058
$536$	48.3799	2.08969
$537$	−14.2533	−0.615077
$538$	24.3440	1.04955
$539$	−7.11430	−0.306434
$540$	1.14767	0.0493880
$541$	−13.1990	−0.567471	−0.283735	−	0.958903i	$-0.591574\pi$
$541$	−13.1990	−0.567471	−0.283735	+	0.958903i	$0.591574\pi$
$542$	−14.8063	−0.635987
$543$	3.84190	0.164872
$544$	−0.360854	−0.0154715
$545$	1.85887	0.0796250
$546$	0	0
$547$	−28.7221	−1.22807	−0.614033	−	0.789280i	$-0.710454\pi$
$547$	−28.7221	−1.22807	−0.614033	+	0.789280i	$0.710454\pi$
$548$	28.2496	1.20676
$549$	−3.21547	−0.137233
$550$	5.68677	0.242485
$551$	0.888610	0.0378560
$552$	−43.1715	−1.83750
$553$	71.3260	3.03309
$554$	9.14635	0.388591
$555$	−1.67293	−0.0710118
$556$	−17.1143	−0.725810
$557$	10.5107	0.445351	0.222676	−	0.974893i	$-0.428521\pi$
$557$	10.5107	0.445351	0.222676	+	0.974893i	$0.428521\pi$
$558$	8.84682	0.374516
$559$	0	0
$560$	−5.64277	−0.238451
$561$	0.470529	0.0198657
$562$	−3.48267	−0.146908
$563$	16.6073	0.699914	0.349957	−	0.936766i	$-0.386196\pi$
$563$	16.6073	0.699914	0.349957	+	0.936766i	$0.386196\pi$
$564$	−5.25214	−0.221155
$565$	−3.57320	−0.150326
$566$	50.5108	2.12313
$567$	−4.70317	−0.197514
$568$	−68.9670	−2.89379
$569$	−41.5498	−1.74186	−0.870929	−	0.491408i	$-0.836482\pi$
$569$	−41.5498	−1.74186	−0.870929	+	0.491408i	$0.836482\pi$
$570$	−0.0950445	−0.00398098
$571$	−14.1358	−0.591564	−0.295782	−	0.955255i	$-0.595580\pi$
$571$	−14.1358	−0.591564	−0.295782	+	0.955255i	$0.595580\pi$
$572$	0	0
$573$	−7.45189	−0.311307
$574$	−29.3973	−1.22702
$575$	42.4462	1.77013
$576$	−7.55271	−0.314696
$577$	−0.447505	−0.0186299	−0.00931495	−	0.999957i	$-0.502965\pi$
$577$	−0.447505	−0.0186299	−0.00931495	+	0.999957i	$0.502965\pi$
$578$	2.45691	0.102194
$579$	3.34522	0.139023
$580$	−7.49578	−0.311245
$581$	−61.1673	−2.53765
$582$	30.0210	1.24441
$583$	3.39936	0.140787
$584$	−3.64349	−0.150769
$585$	0	0
$586$	−65.2198	−2.69420
$587$	12.3246	0.508689	0.254345	−	0.967114i	$-0.418140\pi$
$587$	12.3246	0.508689	0.254345	+	0.967114i	$0.418140\pi$
$588$	61.0293	2.51681
$589$	−0.489905	−0.0201862
$590$	1.46733	0.0604092
$591$	13.7432	0.565321
$592$	−24.8272	−1.02039
$593$	−32.0563	−1.31639	−0.658196	−	0.752846i	$-0.728680\pi$
$593$	−32.0563	−1.31639	−0.658196	+	0.752846i	$0.728680\pi$
$594$	−1.15605	−0.0474331
$595$	1.33726	0.0548224
$596$	−44.9165	−1.83985
$597$	−8.13323	−0.332871
$598$	0	0
$599$	27.0434	1.10496	0.552481	−	0.833525i	$-0.313681\pi$
$599$	27.0434	1.10496	0.552481	+	0.833525i	$0.313681\pi$
$600$	−24.6116	−1.00476
$601$	7.95165	0.324354	0.162177	−	0.986762i	$-0.448148\pi$
$601$	7.95165	0.324354	0.162177	+	0.986762i	$0.448148\pi$
$602$	−76.2708	−3.10856
$603$	9.66976	0.393783
$604$	−30.6629	−1.24766
$605$	−3.06470	−0.124598
$606$	7.76721	0.315521
$607$	−41.6720	−1.69142	−0.845708	−	0.533646i	$-0.820821\pi$
$607$	−41.6720	−1.69142	−0.845708	+	0.533646i	$0.820821\pi$
$608$	−0.0490958	−0.00199110
$609$	30.7177	1.24474
$610$	−2.24625	−0.0909480
$611$	0	0
$612$	−4.03639	−0.163161
$613$	9.82308	0.396751	0.198375	−	0.980126i	$-0.436434\pi$
$613$	9.82308	0.396751	0.198375	+	0.980126i	$0.436434\pi$
$614$	−33.2431	−1.34158
$615$	0.723359	0.0291687
$616$	11.0720	0.446103
$617$	−26.6301	−1.07209	−0.536044	−	0.844190i	$-0.680082\pi$
$617$	−26.6301	−1.07209	−0.536044	+	0.844190i	$0.680082\pi$
$618$	43.5088	1.75018
$619$	−18.1787	−0.730665	−0.365333	−	0.930877i	$-0.619045\pi$
$619$	−18.1787	−0.730665	−0.365333	+	0.930877i	$0.619045\pi$
$620$	4.13254	0.165967
$621$	−8.62876	−0.346260
$622$	7.08142	0.283939
$623$	20.6797	0.828513
$624$	0	0
$625$	23.7939	0.951755
$626$	−60.1522	−2.40416
$627$	0.0640175	0.00255661
$628$	57.5070	2.29478
$629$	5.88371	0.234599
$630$	−3.28552	−0.130898
$631$	−2.05111	−0.0816536	−0.0408268	−	0.999166i	$-0.512999\pi$
$631$	−2.05111	−0.0816536	−0.0408268	+	0.999166i	$0.512999\pi$
$632$	−75.8763	−3.01820
$633$	15.9267	0.633030
$634$	75.5171	2.99917
$635$	−4.43674	−0.176067
$636$	−29.1611	−1.15631
$637$	0	0
$638$	7.55046	0.298925
$639$	−13.7845	−0.545308
$640$	−5.48136	−0.216670
$641$	−32.7902	−1.29513	−0.647567	−	0.762009i	$-0.724213\pi$
$641$	−32.7902	−1.29513	−0.647567	+	0.762009i	$0.724213\pi$
$642$	−7.39621	−0.291905
$643$	30.0347	1.18445	0.592226	−	0.805772i	$-0.298249\pi$
$643$	30.0347	1.18445	0.592226	+	0.805772i	$0.298249\pi$
$644$	163.807	6.45489
$645$	1.87674	0.0738967
$646$	0.334273	0.0131518
$647$	3.82467	0.150363	0.0751817	−	0.997170i	$-0.476046\pi$
$647$	3.82467	0.150363	0.0751817	+	0.997170i	$0.476046\pi$
$648$	5.00321	0.196545
$649$	−0.988328	−0.0387953
$650$	0	0
$651$	−16.9352	−0.663741
$652$	66.8905	2.61964
$653$	3.64930	0.142808	0.0714040	−	0.997447i	$-0.477252\pi$
$653$	3.64930	0.142808	0.0714040	+	0.997447i	$0.477252\pi$
$654$	16.0624	0.628090
$655$	2.52663	0.0987236
$656$	10.7351	0.419134
$657$	−0.728230	−0.0284110
$658$	15.0357	0.586151
$659$	34.4025	1.34013	0.670066	−	0.742301i	$-0.266266\pi$
$659$	34.4025	1.34013	0.670066	+	0.742301i	$0.266266\pi$
$660$	−0.540014	−0.0210200
$661$	−33.7412	−1.31238	−0.656191	−	0.754595i	$-0.727833\pi$
$661$	−33.7412	−1.31238	−0.656191	+	0.754595i	$0.727833\pi$
$662$	−19.1141	−0.742890
$663$	0	0
$664$	65.0696	2.52519
$665$	0.181940	0.00705534
$666$	−14.4557	−0.560148
$667$	56.3569	2.18215
$668$	30.2871	1.17184
$669$	−28.2978	−1.09405
$670$	6.75507	0.260971
$671$	1.51297	0.0584076
$672$	−1.69716	−0.0654693
$673$	50.5519	1.94863	0.974316	−	0.225186i	$-0.0722989\pi$
$673$	50.5519	1.94863	0.974316	+	0.225186i	$0.0722989\pi$
$674$	−49.5746	−1.90954
$675$	−4.91916	−0.189338
$676$	0	0
$677$	15.3060	0.588259	0.294130	−	0.955766i	$-0.404970\pi$
$677$	15.3060	0.588259	0.294130	+	0.955766i	$0.404970\pi$
$678$	−30.8759	−1.18578
$679$	−57.4682	−2.20543
$680$	−1.42257	−0.0545532
$681$	−8.48348	−0.325088
$682$	−4.16269	−0.159398
$683$	−38.7347	−1.48214	−0.741070	−	0.671427i	$-0.765682\pi$
$683$	−38.7347	−1.48214	−0.741070	+	0.671427i	$0.765682\pi$
$684$	−0.549168	−0.0209980
$685$	1.98996	0.0760325
$686$	−93.8261	−3.58230
$687$	22.6533	0.864278
$688$	27.8519	1.06184
$689$	0	0
$690$	−6.02786	−0.229477
$691$	25.6438	0.975537	0.487768	−	0.872973i	$-0.337811\pi$
$691$	25.6438	0.975537	0.487768	+	0.872973i	$0.337811\pi$
$692$	−103.585	−3.93772
$693$	2.21298	0.0840640
$694$	−65.4784	−2.48553
$695$	−1.20557	−0.0457300
$696$	−32.6774	−1.23863
$697$	−2.54407	−0.0963633
$698$	60.2909	2.28204
$699$	17.6416	0.667267
$700$	93.3843	3.52959
$701$	−1.06049	−0.0400540	−0.0200270	−	0.999799i	$-0.506375\pi$
$701$	−1.06049	−0.0400540	−0.0200270	+	0.999799i	$0.506375\pi$
$702$	0	0
$703$	0.800505	0.0301916
$704$	3.55377	0.133938
$705$	−0.369972	−0.0139340
$706$	−52.1732	−1.96356
$707$	−14.8685	−0.559187
$708$	8.47827	0.318633
$709$	−31.1919	−1.17144	−0.585718	−	0.810515i	$-0.699187\pi$
$709$	−31.1919	−1.17144	−0.585718	+	0.810515i	$0.699187\pi$
$710$	−9.62957	−0.361391
$711$	−15.1655	−0.568751
$712$	−21.9989	−0.824445
$713$	−31.0704	−1.16360
$714$	11.5552	0.432444
$715$	0	0
$716$	−57.5320	−2.15007
$717$	13.7518	0.513570
$718$	75.5929	2.82110
$719$	−10.9699	−0.409108	−0.204554	−	0.978855i	$-0.565574\pi$
$719$	−10.9699	−0.409108	−0.204554	+	0.978855i	$0.565574\pi$
$720$	1.19978	0.0447132
$721$	−83.2873	−3.10178
$722$	−46.6357	−1.73560
$723$	1.31425	0.0488773
$724$	15.5074	0.576328
$725$	32.1284	1.19322
$726$	−26.4820	−0.982840
$727$	24.7789	0.919000	0.459500	−	0.888178i	$-0.348029\pi$
$727$	24.7789	0.919000	0.459500	+	0.888178i	$0.348029\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−0.508725	−0.0188288
$731$	−6.60053	−0.244130
$732$	−12.9789	−0.479713
$733$	27.5830	1.01880	0.509401	−	0.860529i	$-0.329867\pi$
$733$	27.5830	1.01880	0.509401	+	0.860529i	$0.329867\pi$
$734$	−82.9556	−3.06195
$735$	4.29904	0.158572
$736$	−3.11373	−0.114773
$737$	−4.54990	−0.167598
$738$	6.25053	0.230085
$739$	47.2733	1.73898	0.869488	−	0.493955i	$-0.164449\pi$
$739$	47.2733	1.73898	0.869488	+	0.493955i	$0.164449\pi$
$740$	−6.75259	−0.248230
$741$	0	0
$742$	83.4815	3.06470
$743$	35.2037	1.29150	0.645749	−	0.763549i	$-0.276545\pi$
$743$	35.2037	1.29150	0.645749	+	0.763549i	$0.276545\pi$
$744$	18.0156	0.660483
$745$	−3.16401	−0.115921
$746$	−17.5166	−0.641329
$747$	13.0056	0.475849
$748$	1.89924	0.0694430
$749$	14.1583	0.517333
$750$	−6.92929	−0.253022
$751$	−5.04387	−0.184053	−0.0920267	−	0.995757i	$-0.529335\pi$
$751$	−5.04387	−0.184053	−0.0920267	+	0.995757i	$0.529335\pi$
$752$	−5.49060	−0.200222
$753$	−13.9251	−0.507460
$754$	0	0
$755$	−2.15996	−0.0786091
$756$	−18.9838	−0.690434
$757$	17.7873	0.646491	0.323245	−	0.946315i	$-0.395226\pi$
$757$	17.7873	0.646491	0.323245	+	0.946315i	$0.395226\pi$
$758$	8.31172	0.301895
$759$	4.06008	0.147372
$760$	−0.193547	−0.00702070
$761$	−10.5993	−0.384225	−0.192112	−	0.981373i	$-0.561534\pi$
$761$	−10.5993	−0.384225	−0.192112	+	0.981373i	$0.561534\pi$
$762$	−38.3378	−1.38883
$763$	−30.7477	−1.11314
$764$	−30.0787	−1.08821
$765$	−0.284332	−0.0102800
$766$	−29.0551	−1.04980
$767$	0	0
$768$	−32.2588	−1.16404
$769$	8.64455	0.311730	0.155865	−	0.987778i	$-0.450183\pi$
$769$	8.64455	0.311730	0.155865	+	0.987778i	$0.450183\pi$
$770$	1.54593	0.0557116
$771$	23.0951	0.831749
$772$	13.5026	0.485969
$773$	−4.90710	−0.176496	−0.0882480	−	0.996099i	$-0.528127\pi$
$773$	−4.90710	−0.176496	−0.0882480	+	0.996099i	$0.528127\pi$
$774$	16.2169	0.582904
$775$	−17.7129	−0.636266
$776$	61.1344	2.19460
$777$	27.6721	0.992731
$778$	5.57459	0.199859
$779$	−0.346131	−0.0124014
$780$	0	0
$781$	6.48603	0.232088
$782$	21.2001	0.758113
$783$	−6.53128	−0.233409
$784$	63.8002	2.27858
$785$	4.05092	0.144583
$786$	21.8325	0.778741
$787$	40.2953	1.43637	0.718186	−	0.695851i	$-0.244972\pi$
$787$	40.2953	1.43637	0.718186	+	0.695851i	$0.244972\pi$
$788$	55.4730	1.97615
$789$	−6.57477	−0.234068
$790$	−10.5943	−0.376928
$791$	59.1047	2.10152
$792$	−2.35416	−0.0836513
$793$	0	0
$794$	−57.5906	−2.04382
$795$	−2.05417	−0.0728540
$796$	−32.8288	−1.16359
$797$	6.50647	0.230471	0.115236	−	0.993338i	$-0.463238\pi$
$797$	6.50647	0.230471	0.115236	+	0.993338i	$0.463238\pi$
$798$	1.57214	0.0556532
$799$	1.30120	0.0460331
$800$	−1.77510	−0.0627592
$801$	−4.39696	−0.155359
$802$	−21.4848	−0.758654
$803$	0.342653	0.0120920
$804$	39.0309	1.37651
$805$	11.5389	0.406693
$806$	0	0
$807$	9.90841	0.348793
$808$	15.8171	0.556442
$809$	−22.9730	−0.807689	−0.403844	−	0.914828i	$-0.632326\pi$
$809$	−22.9730	−0.807689	−0.403844	+	0.914828i	$0.632326\pi$
$810$	0.698577	0.0245455
$811$	37.2329	1.30742	0.653712	−	0.756743i	$-0.273211\pi$
$811$	37.2329	1.30742	0.653712	+	0.756743i	$0.273211\pi$
$812$	123.989	4.35115
$813$	−6.02642	−0.211356
$814$	6.80184	0.238404
$815$	4.71192	0.165051
$816$	−4.21965	−0.147717
$817$	−0.898032	−0.0314182
$818$	−76.8408	−2.68667
$819$	0	0
$820$	2.91976	0.101962
$821$	−15.9766	−0.557588	−0.278794	−	0.960351i	$-0.589935\pi$
$821$	−15.9766	−0.557588	−0.278794	+	0.960351i	$0.589935\pi$
$822$	17.1952	0.599752
$823$	50.0895	1.74601	0.873006	−	0.487710i	$-0.162168\pi$
$823$	50.0895	1.74601	0.873006	+	0.487710i	$0.162168\pi$
$824$	88.6007	3.08655
$825$	2.31460	0.0805842
$826$	−24.2713	−0.844508
$827$	−10.4238	−0.362471	−0.181235	−	0.983440i	$-0.558010\pi$
$827$	−10.4238	−0.362471	−0.181235	+	0.983440i	$0.558010\pi$
$828$	−34.8290	−1.21039
$829$	−57.4721	−1.99609	−0.998045	−	0.0625028i	$-0.980092\pi$
$829$	−57.4721	−1.99609	−0.998045	+	0.0625028i	$0.980092\pi$
$830$	9.08538	0.315358
$831$	3.72271	0.129139
$832$	0	0
$833$	−15.1198	−0.523870
$834$	−10.4173	−0.360722
$835$	2.13349	0.0738325
$836$	0.258400	0.00893694
$837$	3.60080	0.124462
$838$	42.1915	1.45748
$839$	41.2454	1.42395	0.711975	−	0.702205i	$-0.247801\pi$
$839$	41.2454	1.42395	0.711975	+	0.702205i	$0.247801\pi$
$840$	−6.69060	−0.230848
$841$	13.6576	0.470953
$842$	−32.4913	−1.11972
$843$	−1.41750	−0.0488214
$844$	64.2864	2.21283
$845$	0	0
$846$	−3.19692	−0.109912
$847$	50.6936	1.74185
$848$	−30.4851	−1.04686
$849$	20.5587	0.705573
$850$	12.0859	0.414543
$851$	50.7692	1.74035
$852$	−55.6398	−1.90619
$853$	32.0321	1.09676	0.548380	−	0.836229i	$-0.315245\pi$
$853$	32.0321	1.09676	0.548380	+	0.836229i	$0.315245\pi$
$854$	37.1555	1.27143
$855$	−0.0386846	−0.00132299
$856$	−15.0615	−0.514793
$857$	−15.8691	−0.542078	−0.271039	−	0.962568i	$-0.587367\pi$
$857$	−15.8691	−0.542078	−0.271039	+	0.962568i	$0.587367\pi$
$858$	0	0
$859$	−28.0067	−0.955578	−0.477789	−	0.878475i	$-0.658562\pi$
$859$	−28.0067	−0.955578	−0.477789	+	0.878475i	$0.658562\pi$
$860$	7.57526	0.258314
$861$	−11.9652	−0.407772
$862$	43.9456	1.49679
$863$	−41.9771	−1.42892	−0.714459	−	0.699677i	$-0.753327\pi$
$863$	−41.9771	−1.42892	−0.714459	+	0.699677i	$0.753327\pi$
$864$	0.360854	0.0122765
$865$	−7.29677	−0.248098
$866$	52.8147	1.79472
$867$	1.00000	0.0339618
$868$	−68.3569	−2.32018
$869$	7.13581	0.242066
$870$	−4.56260	−0.154687
$871$	0	0
$872$	32.7093	1.10768
$873$	12.2190	0.413552
$874$	2.88436	0.0975650
$875$	13.2645	0.448422
$876$	−2.93942	−0.0993138
$877$	−8.11830	−0.274135	−0.137068	−	0.990562i	$-0.543768\pi$
$877$	−8.11830	−0.274135	−0.137068	+	0.990562i	$0.543768\pi$
$878$	−14.5297	−0.490352
$879$	−26.5455	−0.895357
$880$	−0.564532	−0.0190304
$881$	−46.9811	−1.58283	−0.791416	−	0.611278i	$-0.790656\pi$
$881$	−46.9811	−1.58283	−0.791416	+	0.611278i	$0.790656\pi$
$882$	37.1479	1.25083
$883$	8.72799	0.293720	0.146860	−	0.989157i	$-0.453083\pi$
$883$	8.72799	0.293720	0.146860	+	0.989157i	$0.453083\pi$
$884$	0	0
$885$	0.597228	0.0200756
$886$	8.77057	0.294653
$887$	−7.43713	−0.249714	−0.124857	−	0.992175i	$-0.539847\pi$
$887$	−7.43713	−0.249714	−0.124857	+	0.992175i	$0.539847\pi$
$888$	−29.4375	−0.987857
$889$	73.3887	2.46138
$890$	−3.07162	−0.102961
$891$	−0.470529	−0.0157633
$892$	−114.221	−3.82439
$893$	0.177034	0.00592421
$894$	−27.3402	−0.914392
$895$	−4.05268	−0.135466
$896$	90.6677	3.02900
$897$	0	0
$898$	60.2738	2.01136
$899$	−23.5178	−0.784364
$900$	−19.8556	−0.661854
$901$	7.22455	0.240685
$902$	−2.94106	−0.0979264
$903$	−31.0434	−1.03306
$904$	−62.8754	−2.09120
$905$	1.09238	0.0363118
$906$	−18.6642	−0.620076
$907$	−8.88629	−0.295064	−0.147532	−	0.989057i	$-0.547133\pi$
$907$	−8.88629	−0.295064	−0.147532	+	0.989057i	$0.547133\pi$
$908$	−34.2426	−1.13638
$909$	3.16138	0.104856
$910$	0	0
$911$	−29.9919	−0.993677	−0.496839	−	0.867843i	$-0.665506\pi$
$911$	−29.9919	−0.993677	−0.496839	+	0.867843i	$0.665506\pi$
$912$	−0.574102	−0.0190104
$913$	−6.11949	−0.202526
$914$	9.29999	0.307616
$915$	−0.914260	−0.0302245
$916$	91.4375	3.02118
$917$	−41.7933	−1.38013
$918$	−2.45691	−0.0810900
$919$	33.3777	1.10103	0.550514	−	0.834826i	$-0.314432\pi$
$919$	33.3777	1.10103	0.550514	+	0.834826i	$0.314432\pi$
$920$	−12.2750	−0.404696
$921$	−13.5305	−0.445845
$922$	10.0584	0.331257
$923$	0	0
$924$	8.93243	0.293855
$925$	28.9429	0.951637
$926$	51.5223	1.69313
$927$	17.7088	0.581632
$928$	−2.35684	−0.0773671
$929$	49.3776	1.62003	0.810013	−	0.586411i	$-0.199460\pi$
$929$	49.3776	1.62003	0.810013	+	0.586411i	$0.199460\pi$
$930$	2.51544	0.0824844
$931$	−2.05711	−0.0674192
$932$	71.2083	2.33251
$933$	2.88225	0.0943606
$934$	−28.1469	−0.920996
$935$	0.133786	0.00437528
$936$	0	0
$937$	−35.3443	−1.15465	−0.577325	−	0.816515i	$-0.695903\pi$
$937$	−35.3443	−1.15465	−0.577325	+	0.816515i	$0.695903\pi$
$938$	−111.736	−3.64832
$939$	−24.4829	−0.798969
$940$	−1.49335	−0.0487078
$941$	35.7349	1.16493	0.582463	−	0.812857i	$-0.302089\pi$
$941$	35.7349	1.16493	0.582463	+	0.812857i	$0.302089\pi$
$942$	35.0039	1.14049
$943$	−21.9521	−0.714860
$944$	8.86321	0.288473
$945$	−1.33726	−0.0435011
$946$	−7.63052	−0.248089
$947$	−20.8840	−0.678639	−0.339320	−	0.940671i	$-0.610197\pi$
$947$	−20.8840	−0.678639	−0.339320	+	0.940671i	$0.610197\pi$
$948$	−61.2139	−1.98813
$949$	0	0
$950$	1.64434	0.0533494
$951$	30.7367	0.996705
$952$	23.5309	0.762642
$953$	−21.7319	−0.703965	−0.351983	−	0.936007i	$-0.614492\pi$
$953$	−21.7319	−0.703965	−0.351983	+	0.936007i	$0.614492\pi$
$954$	−17.7500	−0.574679
$955$	−2.11881	−0.0685631
$956$	55.5075	1.79524
$957$	3.07316	0.0993411
$958$	−94.0706	−3.03928
$959$	−32.9162	−1.06292
$960$	−2.14748	−0.0693095
$961$	−18.0342	−0.581750
$962$	0	0
$963$	−3.01037	−0.0970080
$964$	5.30480	0.170856
$965$	0.951153	0.0306187
$966$	99.7074	3.20803
$967$	31.1613	1.00208	0.501040	−	0.865424i	$-0.332951\pi$
$967$	31.1613	1.00208	0.501040	+	0.865424i	$0.332951\pi$
$968$	−53.9276	−1.73330
$969$	0.136054	0.00437070
$970$	8.53594	0.274072
$971$	36.9457	1.18564	0.592822	−	0.805333i	$-0.298014\pi$
$971$	36.9457	1.18564	0.592822	+	0.805333i	$0.298014\pi$
$972$	4.03639	0.129467
$973$	19.9415	0.639295
$974$	−3.78641	−0.121324
$975$	0	0
$976$	−13.5681	−0.434305
$977$	−47.3399	−1.51454	−0.757269	−	0.653103i	$-0.773467\pi$
$977$	−47.3399	−1.51454	−0.757269	+	0.653103i	$0.773467\pi$
$978$	40.7156	1.30194
$979$	2.06890	0.0661223
$980$	17.3526	0.554308
$981$	6.53766	0.208731
$982$	53.5839	1.70993
$983$	−35.2475	−1.12422	−0.562110	−	0.827063i	$-0.690010\pi$
$983$	−35.2475	−1.12422	−0.562110	+	0.827063i	$0.690010\pi$
$984$	12.7285	0.405770
$985$	3.90764	0.124508
$986$	16.0467	0.511032
$987$	6.11976	0.194794
$988$	0	0
$989$	−56.9544	−1.81105
$990$	−0.328701	−0.0104468
$991$	−34.5143	−1.09638	−0.548191	−	0.836353i	$-0.684683\pi$
$991$	−34.5143	−1.09638	−0.548191	+	0.836353i	$0.684683\pi$
$992$	1.29936	0.0412548
$993$	−7.77974	−0.246882
$994$	159.284	5.05217
$995$	−2.31254	−0.0733123
$996$	52.4955	1.66338
$997$	6.56163	0.207809	0.103904	−	0.994587i	$-0.466866\pi$
$997$	6.56163	0.207809	0.103904	+	0.994587i	$0.466866\pi$
$998$	−1.23374	−0.0390533
$999$	−5.88371	−0.186152

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8619.2.a.bn.1.16		16
13.2	odd	12		663.2.z.d.511.8	yes	16
13.7	odd	12		663.2.z.d.205.8	✓	16
13.12	even	2	inner	8619.2.a.bn.1.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
663.2.z.d.205.8	✓	16	13.7	odd	12
663.2.z.d.511.8	yes	16	13.2	odd	12
8619.2.a.bn.1.1		16	13.12	even	2	inner
8619.2.a.bn.1.16		16	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8619 = 3 \cdot 13^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8619.a (trivial)

\(f(q)\)	\(=\)	\(q+2.45691 q^{2} +1.00000 q^{3} +4.03639 q^{4} +0.284332 q^{5} +2.45691 q^{6} -4.70317 q^{7} +5.00321 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.45691 q^{2} +1.00000 q^{3} +4.03639 q^{4} +0.284332 q^{5} +2.45691 q^{6} -4.70317 q^{7} +5.00321 q^{8} +1.00000 q^{9} +0.698577 q^{10} -0.470529 q^{11} +4.03639 q^{12} -11.5552 q^{14} +0.284332 q^{15} +4.21965 q^{16} -1.00000 q^{17} +2.45691 q^{18} -0.136054 q^{19} +1.14767 q^{20} -4.70317 q^{21} -1.15605 q^{22} -8.62876 q^{23} +5.00321 q^{24} -4.91916 q^{25} +1.00000 q^{27} -18.9838 q^{28} -6.53128 q^{29} +0.698577 q^{30} +3.60080 q^{31} +0.360854 q^{32} -0.470529 q^{33} -2.45691 q^{34} -1.33726 q^{35} +4.03639 q^{36} -5.88371 q^{37} -0.334273 q^{38} +1.42257 q^{40} +2.54407 q^{41} -11.5552 q^{42} +6.60053 q^{43} -1.89924 q^{44} +0.284332 q^{45} -21.2001 q^{46} -1.30120 q^{47} +4.21965 q^{48} +15.1198 q^{49} -12.0859 q^{50} -1.00000 q^{51} -7.22455 q^{53} +2.45691 q^{54} -0.133786 q^{55} -23.5309 q^{56} -0.136054 q^{57} -16.0467 q^{58} +2.10046 q^{59} +1.14767 q^{60} -3.21547 q^{61} +8.84682 q^{62} -4.70317 q^{63} -7.55271 q^{64} -1.15605 q^{66} +9.66976 q^{67} -4.03639 q^{68} -8.62876 q^{69} -3.28552 q^{70} -13.7845 q^{71} +5.00321 q^{72} -0.728230 q^{73} -14.4557 q^{74} -4.91916 q^{75} -0.549168 q^{76} +2.21298 q^{77} -15.1655 q^{79} +1.19978 q^{80} +1.00000 q^{81} +6.25053 q^{82} +13.0056 q^{83} -18.9838 q^{84} -0.284332 q^{85} +16.2169 q^{86} -6.53128 q^{87} -2.35416 q^{88} -4.39696 q^{89} +0.698577 q^{90} -34.8290 q^{92} +3.60080 q^{93} -3.19692 q^{94} -0.0386846 q^{95} +0.360854 q^{96} +12.2190 q^{97} +37.1479 q^{98} -0.470529 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{3} + 8 q^{4} + 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^3 + 8 * q^4 + 16 * q^9	\( 16 q + 16 q^{3} + 8 q^{4} + 16 q^{9} + 2 q^{10} + 8 q^{12} - 26 q^{14} - 16 q^{17} - 2 q^{22} - 42 q^{23} - 14 q^{25} + 16 q^{27} - 58 q^{29} + 2 q^{30} - 30 q^{35} + 8 q^{36} - 62 q^{38} + 4 q^{40} - 26 q^{42} - 6 q^{43} + 4 q^{49} - 16 q^{51} - 26 q^{53} - 18 q^{55} - 74 q^{56} - 58 q^{61} - 40 q^{62} - 36 q^{64} - 2 q^{66} - 8 q^{68} - 42 q^{69} - 34 q^{74} - 14 q^{75} + 8 q^{77} - 14 q^{79} + 16 q^{81} - 6 q^{82} - 58 q^{87} - 10 q^{88} + 2 q^{90} - 64 q^{92} + 50 q^{94} - 54 q^{95}+O(q^{100}) \) 16 * q + 16 * q^3 + 8 * q^4 + 16 * q^9 + 2 * q^10 + 8 * q^12 - 26 * q^14 - 16 * q^17 - 2 * q^22 - 42 * q^23 - 14 * q^25 + 16 * q^27 - 58 * q^29 + 2 * q^30 - 30 * q^35 + 8 * q^36 - 62 * q^38 + 4 * q^40 - 26 * q^42 - 6 * q^43 + 4 * q^49 - 16 * q^51 - 26 * q^53 - 18 * q^55 - 74 * q^56 - 58 * q^61 - 40 * q^62 - 36 * q^64 - 2 * q^66 - 8 * q^68 - 42 * q^69 - 34 * q^74 - 14 * q^75 + 8 * q^77 - 14 * q^79 + 16 * q^81 - 6 * q^82 - 58 * q^87 - 10 * q^88 + 2 * q^90 - 64 * q^92 + 50 * q^94 - 54 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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