LMFDB - Embedded newform 8670.2.a.bs.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [8670,2,Mod(1,8670)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("8670.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8670, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8670.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,3,3,3,3,3,-6,3,3,3,-12,3,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	yes
Analytic conductor:	$69.2302985525$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
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			1.2
Root			$-0.347296$ of defining polynomial
Character	$\chi$	$=$	8670.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -2.34730 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -2.12061 q^{11} +1.00000 q^{12} -5.29086 q^{13} -2.34730 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{18} +8.51754 q^{19} +1.00000 q^{20} -2.34730 q^{21} -2.12061 q^{22} -2.83750 q^{23} +1.00000 q^{24} +1.00000 q^{25} -5.29086 q^{26} +1.00000 q^{27} -2.34730 q^{28} -2.69459 q^{29} +1.00000 q^{30} -2.24123 q^{31} +1.00000 q^{32} -2.12061 q^{33} -2.34730 q^{35} +1.00000 q^{36} -6.06418 q^{37} +8.51754 q^{38} -5.29086 q^{39} +1.00000 q^{40} -1.24123 q^{41} -2.34730 q^{42} -5.75877 q^{43} -2.12061 q^{44} +1.00000 q^{45} -2.83750 q^{46} -11.1702 q^{47} +1.00000 q^{48} -1.49020 q^{49} +1.00000 q^{50} -5.29086 q^{52} +0.573978 q^{53} +1.00000 q^{54} -2.12061 q^{55} -2.34730 q^{56} +8.51754 q^{57} -2.69459 q^{58} +3.26857 q^{59} +1.00000 q^{60} -4.61081 q^{61} -2.24123 q^{62} -2.34730 q^{63} +1.00000 q^{64} -5.29086 q^{65} -2.12061 q^{66} -14.4534 q^{67} -2.83750 q^{69} -2.34730 q^{70} -4.77837 q^{71} +1.00000 q^{72} -0.0837781 q^{73} -6.06418 q^{74} +1.00000 q^{75} +8.51754 q^{76} +4.97771 q^{77} -5.29086 q^{78} +4.36959 q^{79} +1.00000 q^{80} +1.00000 q^{81} -1.24123 q^{82} +1.87164 q^{83} -2.34730 q^{84} -5.75877 q^{86} -2.69459 q^{87} -2.12061 q^{88} +13.2148 q^{89} +1.00000 q^{90} +12.4192 q^{91} -2.83750 q^{92} -2.24123 q^{93} -11.1702 q^{94} +8.51754 q^{95} +1.00000 q^{96} +4.08378 q^{97} -1.49020 q^{98} -2.12061 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} - 6 q^{7} + 3 q^{8} + 3 q^{9} + 3 q^{10} - 12 q^{11} + 3 q^{12} - 6 q^{14} + 3 q^{15} + 3 q^{16} + 3 q^{18} + 3 q^{19} + 3 q^{20} - 6 q^{21} - 12 q^{22}+ \cdots - 12 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 - 6 * q^7 + 3 * q^8 + 3 * q^9 + 3 * q^10 - 12 * q^11 + 3 * q^12 - 6 * q^14 + 3 * q^15 + 3 * q^16 + 3 * q^18 + 3 * q^19 + 3 * q^20 - 6 * q^21 - 12 * q^22 - 6 * q^23 + 3 * q^24 + 3 * q^25 + 3 * q^27 - 6 * q^28 - 6 * q^29 + 3 * q^30 - 18 * q^31 + 3 * q^32 - 12 * q^33 - 6 * q^35 + 3 * q^36 - 9 * q^37 + 3 * q^38 + 3 * q^40 - 15 * q^41 - 6 * q^42 - 6 * q^43 - 12 * q^44 + 3 * q^45 - 6 * q^46 - 12 * q^47 + 3 * q^48 - 3 * q^49 + 3 * q^50 - 6 * q^53 + 3 * q^54 - 12 * q^55 - 6 * q^56 + 3 * q^57 - 6 * q^58 + 3 * q^60 - 18 * q^61 - 18 * q^62 - 6 * q^63 + 3 * q^64 - 12 * q^66 - 30 * q^67 - 6 * q^69 - 6 * q^70 - 6 * q^71 + 3 * q^72 + 6 * q^73 - 9 * q^74 + 3 * q^75 + 3 * q^76 + 21 * q^77 + 6 * q^79 + 3 * q^80 + 3 * q^81 - 15 * q^82 + 24 * q^83 - 6 * q^84 - 6 * q^86 - 6 * q^87 - 12 * q^88 + 6 * q^89 + 3 * q^90 + 3 * q^91 - 6 * q^92 - 18 * q^93 - 12 * q^94 + 3 * q^95 + 3 * q^96 + 6 * q^97 - 3 * q^98 - 12 * 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
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	−2.34730	−0.887195	−0.443597	−	0.896226i	$-0.646298\pi$
$7$	−2.34730	−0.887195	−0.443597	+	0.896226i	$0.646298\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−2.12061	−0.639389	−0.319695	−	0.947521i	$-0.603580\pi$
$11$	−2.12061	−0.639389	−0.319695	+	0.947521i	$0.603580\pi$
$12$	1.00000	0.288675
$13$	−5.29086	−1.46742	−0.733710	−	0.679463i	$-0.762213\pi$
$13$	−5.29086	−1.46742	−0.733710	+	0.679463i	$0.762213\pi$
$14$	−2.34730	−0.627341
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	0	0
$17$	0	0
$18$	1.00000	0.235702
$19$	8.51754	1.95406	0.977029	−	0.213107i	$-0.0683582\pi$
$19$	8.51754	1.95406	0.977029	+	0.213107i	$0.0683582\pi$
$20$	1.00000	0.223607
$21$	−2.34730	−0.512222
$22$	−2.12061	−0.452117
$23$	−2.83750	−0.591659	−0.295829	−	0.955241i	$-0.595596\pi$
$23$	−2.83750	−0.591659	−0.295829	+	0.955241i	$0.595596\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−5.29086	−1.03762
$27$	1.00000	0.192450
$28$	−2.34730	−0.443597
$29$	−2.69459	−0.500373	−0.250187	−	0.968198i	$-0.580492\pi$
$29$	−2.69459	−0.500373	−0.250187	+	0.968198i	$0.580492\pi$
$30$	1.00000	0.182574
$31$	−2.24123	−0.402537	−0.201268	−	0.979536i	$-0.564506\pi$
$31$	−2.24123	−0.402537	−0.201268	+	0.979536i	$0.564506\pi$
$32$	1.00000	0.176777
$33$	−2.12061	−0.369152
$34$	0	0
$35$	−2.34730	−0.396766
$36$	1.00000	0.166667
$37$	−6.06418	−0.996945	−0.498472	−	0.866906i	$-0.666105\pi$
$37$	−6.06418	−0.996945	−0.498472	+	0.866906i	$0.666105\pi$
$38$	8.51754	1.38173
$39$	−5.29086	−0.847216
$40$	1.00000	0.158114
$41$	−1.24123	−0.193847	−0.0969237	−	0.995292i	$-0.530900\pi$
$41$	−1.24123	−0.193847	−0.0969237	+	0.995292i	$0.530900\pi$
$42$	−2.34730	−0.362196
$43$	−5.75877	−0.878204	−0.439102	−	0.898437i	$-0.644703\pi$
$43$	−5.75877	−0.878204	−0.439102	+	0.898437i	$0.644703\pi$
$44$	−2.12061	−0.319695
$45$	1.00000	0.149071
$46$	−2.83750	−0.418366
$47$	−11.1702	−1.62935	−0.814674	−	0.579919i	$-0.803084\pi$
$47$	−11.1702	−1.62935	−0.814674	+	0.579919i	$0.803084\pi$
$48$	1.00000	0.144338
$49$	−1.49020	−0.212886
$50$	1.00000	0.141421
$51$	0	0
$52$	−5.29086	−0.733710
$53$	0.573978	0.0788419	0.0394210	−	0.999223i	$-0.487449\pi$
$53$	0.573978	0.0788419	0.0394210	+	0.999223i	$0.487449\pi$
$54$	1.00000	0.136083
$55$	−2.12061	−0.285944
$56$	−2.34730	−0.313671
$57$	8.51754	1.12818
$58$	−2.69459	−0.353817
$59$	3.26857	0.425532	0.212766	−	0.977103i	$-0.431753\pi$
$59$	3.26857	0.425532	0.212766	+	0.977103i	$0.431753\pi$
$60$	1.00000	0.129099
$61$	−4.61081	−0.590354	−0.295177	−	0.955443i	$-0.595379\pi$
$61$	−4.61081	−0.590354	−0.295177	+	0.955443i	$0.595379\pi$
$62$	−2.24123	−0.284636
$63$	−2.34730	−0.295732
$64$	1.00000	0.125000
$65$	−5.29086	−0.656250
$66$	−2.12061	−0.261030
$67$	−14.4534	−1.76576	−0.882880	−	0.469599i	$-0.844398\pi$
$67$	−14.4534	−1.76576	−0.882880	+	0.469599i	$0.844398\pi$
$68$	0	0
$69$	−2.83750	−0.341594
$70$	−2.34730	−0.280556
$71$	−4.77837	−0.567088	−0.283544	−	0.958959i	$-0.591510\pi$
$71$	−4.77837	−0.567088	−0.283544	+	0.958959i	$0.591510\pi$
$72$	1.00000	0.117851
$73$	−0.0837781	−0.00980549	−0.00490274	−	0.999988i	$-0.501561\pi$
$73$	−0.0837781	−0.00980549	−0.00490274	+	0.999988i	$0.501561\pi$
$74$	−6.06418	−0.704946
$75$	1.00000	0.115470
$76$	8.51754	0.977029
$77$	4.97771	0.567263
$78$	−5.29086	−0.599072
$79$	4.36959	0.491617	0.245808	−	0.969318i	$-0.420947\pi$
$79$	4.36959	0.491617	0.245808	+	0.969318i	$0.420947\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−1.24123	−0.137071
$83$	1.87164	0.205440	0.102720	−	0.994710i	$-0.467245\pi$
$83$	1.87164	0.205440	0.102720	+	0.994710i	$0.467245\pi$
$84$	−2.34730	−0.256111
$85$	0	0
$86$	−5.75877	−0.620984
$87$	−2.69459	−0.288891
$88$	−2.12061	−0.226058
$89$	13.2148	1.40077	0.700384	−	0.713766i	$-0.253012\pi$
$89$	13.2148	1.40077	0.700384	+	0.713766i	$0.253012\pi$
$90$	1.00000	0.105409
$91$	12.4192	1.30189
$92$	−2.83750	−0.295829
$93$	−2.24123	−0.232405
$94$	−11.1702	−1.15212
$95$	8.51754	0.873881
$96$	1.00000	0.102062
$97$	4.08378	0.414645	0.207322	−	0.978273i	$-0.433525\pi$
$97$	4.08378	0.414645	0.207322	+	0.978273i	$0.433525\pi$
$98$	−1.49020	−0.150533
$99$	−2.12061	−0.213130
$100$	1.00000	0.100000
$101$	13.6459	1.35782	0.678909	−	0.734223i	$-0.262453\pi$
$101$	13.6459	1.35782	0.678909	+	0.734223i	$0.262453\pi$
$102$	0	0
$103$	18.9317	1.86540	0.932698	−	0.360658i	$-0.117448\pi$
$103$	18.9317	1.86540	0.932698	+	0.360658i	$0.117448\pi$
$104$	−5.29086	−0.518811
$105$	−2.34730	−0.229073
$106$	0.573978	0.0557497
$107$	0.935822	0.0904693	0.0452347	−	0.998976i	$-0.485596\pi$
$107$	0.935822	0.0904693	0.0452347	+	0.998976i	$0.485596\pi$
$108$	1.00000	0.0962250
$109$	−2.73917	−0.262365	−0.131182	−	0.991358i	$-0.541877\pi$
$109$	−2.73917	−0.262365	−0.131182	+	0.991358i	$0.541877\pi$
$110$	−2.12061	−0.202193
$111$	−6.06418	−0.575586
$112$	−2.34730	−0.221799
$113$	−3.84255	−0.361477	−0.180738	−	0.983531i	$-0.557849\pi$
$113$	−3.84255	−0.361477	−0.180738	+	0.983531i	$0.557849\pi$
$114$	8.51754	0.797741
$115$	−2.83750	−0.264598
$116$	−2.69459	−0.250187
$117$	−5.29086	−0.489140
$118$	3.26857	0.300896
$119$	0	0
$120$	1.00000	0.0912871
$121$	−6.50299	−0.591181
$122$	−4.61081	−0.417444
$123$	−1.24123	−0.111918
$124$	−2.24123	−0.201268
$125$	1.00000	0.0894427
$126$	−2.34730	−0.209114
$127$	−17.4534	−1.54874	−0.774368	−	0.632736i	$-0.781932\pi$
$127$	−17.4534	−1.54874	−0.774368	+	0.632736i	$0.781932\pi$
$128$	1.00000	0.0883883
$129$	−5.75877	−0.507031
$130$	−5.29086	−0.464039
$131$	−20.7246	−1.81072	−0.905359	−	0.424646i	$-0.860398\pi$
$131$	−20.7246	−1.81072	−0.905359	+	0.424646i	$0.860398\pi$
$132$	−2.12061	−0.184576
$133$	−19.9932	−1.73363
$134$	−14.4534	−1.24858
$135$	1.00000	0.0860663
$136$	0	0
$137$	−10.6655	−0.911215	−0.455607	−	0.890181i	$-0.650578\pi$
$137$	−10.6655	−0.911215	−0.455607	+	0.890181i	$0.650578\pi$
$138$	−2.83750	−0.241544
$139$	−1.61081	−0.136628	−0.0683138	−	0.997664i	$-0.521762\pi$
$139$	−1.61081	−0.136628	−0.0683138	+	0.997664i	$0.521762\pi$
$140$	−2.34730	−0.198383
$141$	−11.1702	−0.940704
$142$	−4.77837	−0.400992
$143$	11.2199	0.938253
$144$	1.00000	0.0833333
$145$	−2.69459	−0.223774
$146$	−0.0837781	−0.00693353
$147$	−1.49020	−0.122910
$148$	−6.06418	−0.498472
$149$	−1.75877	−0.144084	−0.0720420	−	0.997402i	$-0.522952\pi$
$149$	−1.75877	−0.144084	−0.0720420	+	0.997402i	$0.522952\pi$
$150$	1.00000	0.0816497
$151$	10.5817	0.861128	0.430564	−	0.902560i	$-0.358315\pi$
$151$	10.5817	0.861128	0.430564	+	0.902560i	$0.358315\pi$
$152$	8.51754	0.690864
$153$	0	0
$154$	4.97771	0.401115
$155$	−2.24123	−0.180020
$156$	−5.29086	−0.423608
$157$	0.672304	0.0536557	0.0268279	−	0.999640i	$-0.491459\pi$
$157$	0.672304	0.0536557	0.0268279	+	0.999640i	$0.491459\pi$
$158$	4.36959	0.347626
$159$	0.573978	0.0455194
$160$	1.00000	0.0790569
$161$	6.66044	0.524917
$162$	1.00000	0.0785674
$163$	−17.9317	−1.40452	−0.702260	−	0.711921i	$-0.747825\pi$
$163$	−17.9317	−1.40452	−0.702260	+	0.711921i	$0.747825\pi$
$164$	−1.24123	−0.0969237
$165$	−2.12061	−0.165090
$166$	1.87164	0.145268
$167$	−21.0428	−1.62834	−0.814171	−	0.580625i	$-0.802808\pi$
$167$	−21.0428	−1.62834	−0.814171	+	0.580625i	$0.802808\pi$
$168$	−2.34730	−0.181098
$169$	14.9932	1.15332
$170$	0	0
$171$	8.51754	0.651353
$172$	−5.75877	−0.439102
$173$	16.6955	1.26934	0.634669	−	0.772784i	$-0.281137\pi$
$173$	16.6955	1.26934	0.634669	+	0.772784i	$0.281137\pi$
$174$	−2.69459	−0.204277
$175$	−2.34730	−0.177439
$176$	−2.12061	−0.159847
$177$	3.26857	0.245681
$178$	13.2148	0.990493
$179$	−3.33544	−0.249302	−0.124651	−	0.992201i	$-0.539781\pi$
$179$	−3.33544	−0.249302	−0.124651	+	0.992201i	$0.539781\pi$
$180$	1.00000	0.0745356
$181$	−11.7588	−0.874023	−0.437011	−	0.899456i	$-0.643963\pi$
$181$	−11.7588	−0.874023	−0.437011	+	0.899456i	$0.643963\pi$
$182$	12.4192	0.920573
$183$	−4.61081	−0.340841
$184$	−2.83750	−0.209183
$185$	−6.06418	−0.445847
$186$	−2.24123	−0.164335
$187$	0	0
$188$	−11.1702	−0.814674
$189$	−2.34730	−0.170741
$190$	8.51754	0.617927
$191$	−12.8229	−0.927836	−0.463918	−	0.885878i	$-0.653557\pi$
$191$	−12.8229	−0.927836	−0.463918	+	0.885878i	$0.653557\pi$
$192$	1.00000	0.0721688
$193$	−22.4243	−1.61413	−0.807067	−	0.590460i	$-0.798946\pi$
$193$	−22.4243	−1.61413	−0.807067	+	0.590460i	$0.798946\pi$
$194$	4.08378	0.293198
$195$	−5.29086	−0.378886
$196$	−1.49020	−0.106443
$197$	−19.6091	−1.39709	−0.698544	−	0.715567i	$-0.746168\pi$
$197$	−19.6091	−1.39709	−0.698544	+	0.715567i	$0.746168\pi$
$198$	−2.12061	−0.150706
$199$	22.7547	1.61303	0.806517	−	0.591211i	$-0.201350\pi$
$199$	22.7547	1.61303	0.806517	+	0.591211i	$0.201350\pi$
$200$	1.00000	0.0707107
$201$	−14.4534	−1.01946
$202$	13.6459	0.960122
$203$	6.32501	0.443929
$204$	0	0
$205$	−1.24123	−0.0866912
$206$	18.9317	1.31903
$207$	−2.83750	−0.197220
$208$	−5.29086	−0.366855
$209$	−18.0624	−1.24940
$210$	−2.34730	−0.161979
$211$	25.2695	1.73962	0.869812	−	0.493383i	$-0.164240\pi$
$211$	25.2695	1.73962	0.869812	+	0.493383i	$0.164240\pi$
$212$	0.573978	0.0394210
$213$	−4.77837	−0.327409
$214$	0.935822	0.0639715
$215$	−5.75877	−0.392745
$216$	1.00000	0.0680414
$217$	5.26083	0.357128
$218$	−2.73917	−0.185520
$219$	−0.0837781	−0.00566120
$220$	−2.12061	−0.142972
$221$	0	0
$222$	−6.06418	−0.407001
$223$	21.2172	1.42081	0.710404	−	0.703794i	$-0.248512\pi$
$223$	21.2172	1.42081	0.710404	+	0.703794i	$0.248512\pi$
$224$	−2.34730	−0.156835
$225$	1.00000	0.0666667
$226$	−3.84255	−0.255603
$227$	23.7743	1.57795	0.788976	−	0.614424i	$-0.210611\pi$
$227$	23.7743	1.57795	0.788976	+	0.614424i	$0.210611\pi$
$228$	8.51754	0.564088
$229$	−17.3601	−1.14719	−0.573594	−	0.819140i	$-0.694451\pi$
$229$	−17.3601	−1.14719	−0.573594	+	0.819140i	$0.694451\pi$
$230$	−2.83750	−0.187099
$231$	4.97771	0.327509
$232$	−2.69459	−0.176909
$233$	−15.8425	−1.03788	−0.518940	−	0.854811i	$-0.673673\pi$
$233$	−15.8425	−1.03788	−0.518940	+	0.854811i	$0.673673\pi$
$234$	−5.29086	−0.345874
$235$	−11.1702	−0.728666
$236$	3.26857	0.212766
$237$	4.36959	0.283835
$238$	0	0
$239$	1.10876	0.0717194	0.0358597	−	0.999357i	$-0.488583\pi$
$239$	1.10876	0.0717194	0.0358597	+	0.999357i	$0.488583\pi$
$240$	1.00000	0.0645497
$241$	3.86484	0.248956	0.124478	−	0.992222i	$-0.460274\pi$
$241$	3.86484	0.248956	0.124478	+	0.992222i	$0.460274\pi$
$242$	−6.50299	−0.418028
$243$	1.00000	0.0641500
$244$	−4.61081	−0.295177
$245$	−1.49020	−0.0952054
$246$	−1.24123	−0.0791379
$247$	−45.0651	−2.86742
$248$	−2.24123	−0.142318
$249$	1.87164	0.118611
$250$	1.00000	0.0632456
$251$	−7.50980	−0.474014	−0.237007	−	0.971508i	$-0.576166\pi$
$251$	−7.50980	−0.474014	−0.237007	+	0.971508i	$0.576166\pi$
$252$	−2.34730	−0.147866
$253$	6.01724	0.378300
$254$	−17.4534	−1.09512
$255$	0	0
$256$	1.00000	0.0625000
$257$	27.1925	1.69622	0.848112	−	0.529817i	$-0.177740\pi$
$257$	27.1925	1.69622	0.848112	+	0.529817i	$0.177740\pi$
$258$	−5.75877	−0.358525
$259$	14.2344	0.884484
$260$	−5.29086	−0.328125
$261$	−2.69459	−0.166791
$262$	−20.7246	−1.28037
$263$	−31.4293	−1.93801	−0.969007	−	0.247032i	$-0.920545\pi$
$263$	−31.4293	−1.93801	−0.969007	+	0.247032i	$0.920545\pi$
$264$	−2.12061	−0.130515
$265$	0.573978	0.0352592
$266$	−19.9932	−1.22586
$267$	13.2148	0.808734
$268$	−14.4534	−0.882880
$269$	−32.1438	−1.95984	−0.979922	−	0.199380i	$-0.936107\pi$
$269$	−32.1438	−1.95984	−0.979922	+	0.199380i	$0.936107\pi$
$270$	1.00000	0.0608581
$271$	7.27631	0.442004	0.221002	−	0.975273i	$-0.429067\pi$
$271$	7.27631	0.442004	0.221002	+	0.975273i	$0.429067\pi$
$272$	0	0
$273$	12.4192	0.751645
$274$	−10.6655	−0.644326
$275$	−2.12061	−0.127878
$276$	−2.83750	−0.170797
$277$	15.9017	0.955439	0.477719	−	0.878512i	$-0.341464\pi$
$277$	15.9017	0.955439	0.477719	+	0.878512i	$0.341464\pi$
$278$	−1.61081	−0.0966102
$279$	−2.24123	−0.134179
$280$	−2.34730	−0.140278
$281$	−4.70233	−0.280518	−0.140259	−	0.990115i	$-0.544793\pi$
$281$	−4.70233	−0.280518	−0.140259	+	0.990115i	$0.544793\pi$
$282$	−11.1702	−0.665178
$283$	−27.0642	−1.60880	−0.804399	−	0.594089i	$-0.797513\pi$
$283$	−27.0642	−1.60880	−0.804399	+	0.594089i	$0.797513\pi$
$284$	−4.77837	−0.283544
$285$	8.51754	0.504536
$286$	11.2199	0.663445
$287$	2.91353	0.171980
$288$	1.00000	0.0589256
$289$	0	0
$290$	−2.69459	−0.158232
$291$	4.08378	0.239395
$292$	−0.0837781	−0.00490274
$293$	−13.5699	−0.792760	−0.396380	−	0.918087i	$-0.629734\pi$
$293$	−13.5699	−0.792760	−0.396380	+	0.918087i	$0.629734\pi$
$294$	−1.49020	−0.0869102
$295$	3.26857	0.190304
$296$	−6.06418	−0.352473
$297$	−2.12061	−0.123051
$298$	−1.75877	−0.101883
$299$	15.0128	0.868212
$300$	1.00000	0.0577350
$301$	13.5175	0.779138
$302$	10.5817	0.608909
$303$	13.6459	0.783936
$304$	8.51754	0.488514
$305$	−4.61081	−0.264014
$306$	0	0
$307$	9.93170	0.566832	0.283416	−	0.958997i	$-0.408532\pi$
$307$	9.93170	0.566832	0.283416	+	0.958997i	$0.408532\pi$
$308$	4.97771	0.283631
$309$	18.9317	1.07699
$310$	−2.24123	−0.127293
$311$	−11.1771	−0.633792	−0.316896	−	0.948460i	$-0.602641\pi$
$311$	−11.1771	−0.633792	−0.316896	+	0.948460i	$0.602641\pi$
$312$	−5.29086	−0.299536
$313$	−1.84255	−0.104147	−0.0520735	−	0.998643i	$-0.516583\pi$
$313$	−1.84255	−0.104147	−0.0520735	+	0.998643i	$0.516583\pi$
$314$	0.672304	0.0379403
$315$	−2.34730	−0.132255
$316$	4.36959	0.245808
$317$	−13.3405	−0.749277	−0.374638	−	0.927171i	$-0.622233\pi$
$317$	−13.3405	−0.749277	−0.374638	+	0.927171i	$0.622233\pi$
$318$	0.573978	0.0321871
$319$	5.71419	0.319933
$320$	1.00000	0.0559017
$321$	0.935822	0.0522325
$322$	6.66044	0.371172
$323$	0	0
$324$	1.00000	0.0555556
$325$	−5.29086	−0.293484
$326$	−17.9317	−0.993145
$327$	−2.73917	−0.151476
$328$	−1.24123	−0.0685354
$329$	26.2199	1.44555
$330$	−2.12061	−0.116736
$331$	28.7870	1.58228	0.791140	−	0.611636i	$-0.209488\pi$
$331$	28.7870	1.58228	0.791140	+	0.611636i	$0.209488\pi$
$332$	1.87164	0.102720
$333$	−6.06418	−0.332315
$334$	−21.0428	−1.15141
$335$	−14.4534	−0.789672
$336$	−2.34730	−0.128056
$337$	9.36009	0.509877	0.254938	−	0.966957i	$-0.417945\pi$
$337$	9.36009	0.509877	0.254938	+	0.966957i	$0.417945\pi$
$338$	14.9932	0.815522
$339$	−3.84255	−0.208699
$340$	0	0
$341$	4.75278	0.257378
$342$	8.51754	0.460576
$343$	19.9290	1.07607
$344$	−5.75877	−0.310492
$345$	−2.83750	−0.152766
$346$	16.6955	0.897557
$347$	26.0702	1.39952	0.699760	−	0.714378i	$-0.253290\pi$
$347$	26.0702	1.39952	0.699760	+	0.714378i	$0.253290\pi$
$348$	−2.69459	−0.144445
$349$	14.0000	0.749403	0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000	0.749403	0.374701	+	0.927146i	$0.377745\pi$
$350$	−2.34730	−0.125468
$351$	−5.29086	−0.282405
$352$	−2.12061	−0.113029
$353$	17.9263	0.954122	0.477061	−	0.878870i	$-0.341702\pi$
$353$	17.9263	0.954122	0.477061	+	0.878870i	$0.341702\pi$
$354$	3.26857	0.173723
$355$	−4.77837	−0.253610
$356$	13.2148	0.700384
$357$	0	0
$358$	−3.33544	−0.176283
$359$	13.6851	0.722272	0.361136	−	0.932513i	$-0.382389\pi$
$359$	13.6851	0.722272	0.361136	+	0.932513i	$0.382389\pi$
$360$	1.00000	0.0527046
$361$	53.5485	2.81834
$362$	−11.7588	−0.618027
$363$	−6.50299	−0.341319
$364$	12.4192	0.650944
$365$	−0.0837781	−0.00438515
$366$	−4.61081	−0.241011
$367$	−10.4611	−0.546065	−0.273033	−	0.962005i	$-0.588027\pi$
$367$	−10.4611	−0.546065	−0.273033	+	0.962005i	$0.588027\pi$
$368$	−2.83750	−0.147915
$369$	−1.24123	−0.0646158
$370$	−6.06418	−0.315262
$371$	−1.34730	−0.0699481
$372$	−2.24123	−0.116202
$373$	−17.7128	−0.917132	−0.458566	−	0.888660i	$-0.651637\pi$
$373$	−17.7128	−0.917132	−0.458566	+	0.888660i	$0.651637\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	−11.1702	−0.576061
$377$	14.2567	0.734258
$378$	−2.34730	−0.120732
$379$	5.70409	0.292999	0.146500	−	0.989211i	$-0.453199\pi$
$379$	5.70409	0.292999	0.146500	+	0.989211i	$0.453199\pi$
$380$	8.51754	0.436941
$381$	−17.4534	−0.894163
$382$	−12.8229	−0.656079
$383$	−0.344608	−0.0176086	−0.00880432	−	0.999961i	$-0.502803\pi$
$383$	−0.344608	−0.0176086	−0.00880432	+	0.999961i	$0.502803\pi$
$384$	1.00000	0.0510310
$385$	4.97771	0.253688
$386$	−22.4243	−1.14137
$387$	−5.75877	−0.292735
$388$	4.08378	0.207322
$389$	28.6655	1.45340	0.726699	−	0.686956i	$-0.241053\pi$
$389$	28.6655	1.45340	0.726699	+	0.686956i	$0.241053\pi$
$390$	−5.29086	−0.267913
$391$	0	0
$392$	−1.49020	−0.0752665
$393$	−20.7246	−1.04542
$394$	−19.6091	−0.987890
$395$	4.36959	0.219858
$396$	−2.12061	−0.106565
$397$	−12.6117	−0.632965	−0.316483	−	0.948598i	$-0.602502\pi$
$397$	−12.6117	−0.632965	−0.316483	+	0.948598i	$0.602502\pi$
$398$	22.7547	1.14059
$399$	−19.9932	−1.00091
$400$	1.00000	0.0500000
$401$	−13.1848	−0.658417	−0.329209	−	0.944257i	$-0.606782\pi$
$401$	−13.1848	−0.658417	−0.329209	+	0.944257i	$0.606782\pi$
$402$	−14.4534	−0.720868
$403$	11.8580	0.590691
$404$	13.6459	0.678909
$405$	1.00000	0.0496904
$406$	6.32501	0.313905
$407$	12.8598	0.637436
$408$	0	0
$409$	−12.8239	−0.634100	−0.317050	−	0.948409i	$-0.602692\pi$
$409$	−12.8239	−0.634100	−0.317050	+	0.948409i	$0.602692\pi$
$410$	−1.24123	−0.0613000
$411$	−10.6655	−0.526090
$412$	18.9317	0.932698
$413$	−7.67230	−0.377529
$414$	−2.83750	−0.139455
$415$	1.87164	0.0918754
$416$	−5.29086	−0.259406
$417$	−1.61081	−0.0788819
$418$	−18.0624	−0.883462
$419$	−6.36865	−0.311129	−0.155564	−	0.987826i	$-0.549720\pi$
$419$	−6.36865	−0.311129	−0.155564	+	0.987826i	$0.549720\pi$
$420$	−2.34730	−0.114536
$421$	−22.2722	−1.08548	−0.542740	−	0.839901i	$-0.682613\pi$
$421$	−22.2722	−1.08548	−0.542740	+	0.839901i	$0.682613\pi$
$422$	25.2695	1.23010
$423$	−11.1702	−0.543116
$424$	0.573978	0.0278748
$425$	0	0
$426$	−4.77837	−0.231513
$427$	10.8229	0.523759
$428$	0.935822	0.0452347
$429$	11.2199	0.541701
$430$	−5.75877	−0.277713
$431$	−9.47834	−0.456556	−0.228278	−	0.973596i	$-0.573309\pi$
$431$	−9.47834	−0.456556	−0.228278	+	0.973596i	$0.573309\pi$
$432$	1.00000	0.0481125
$433$	−15.5621	−0.747868	−0.373934	−	0.927455i	$-0.621991\pi$
$433$	−15.5621	−0.747868	−0.373934	+	0.927455i	$0.621991\pi$
$434$	5.26083	0.252528
$435$	−2.69459	−0.129196
$436$	−2.73917	−0.131182
$437$	−24.1685	−1.15614
$438$	−0.0837781	−0.00400307
$439$	−21.5229	−1.02723	−0.513616	−	0.858020i	$-0.671695\pi$
$439$	−21.5229	−1.02723	−0.513616	+	0.858020i	$0.671695\pi$
$440$	−2.12061	−0.101096
$441$	−1.49020	−0.0709619
$442$	0	0
$443$	25.6067	1.21661	0.608305	−	0.793703i	$-0.291850\pi$
$443$	25.6067	1.21661	0.608305	+	0.793703i	$0.291850\pi$
$444$	−6.06418	−0.287793
$445$	13.2148	0.626443
$446$	21.2172	1.00466
$447$	−1.75877	−0.0831870
$448$	−2.34730	−0.110899
$449$	27.3310	1.28983	0.644915	−	0.764255i	$-0.276893\pi$
$449$	27.3310	1.28983	0.644915	+	0.764255i	$0.276893\pi$
$450$	1.00000	0.0471405
$451$	2.63217	0.123944
$452$	−3.84255	−0.180738
$453$	10.5817	0.497173
$454$	23.7743	1.11578
$455$	12.4192	0.582222
$456$	8.51754	0.398870
$457$	7.02498	0.328615	0.164307	−	0.986409i	$-0.447461\pi$
$457$	7.02498	0.328615	0.164307	+	0.986409i	$0.447461\pi$
$458$	−17.3601	−0.811184
$459$	0	0
$460$	−2.83750	−0.132299
$461$	7.04870	0.328291	0.164145	−	0.986436i	$-0.447513\pi$
$461$	7.04870	0.328291	0.164145	+	0.986436i	$0.447513\pi$
$462$	4.97771	0.231584
$463$	−7.08647	−0.329336	−0.164668	−	0.986349i	$-0.552655\pi$
$463$	−7.08647	−0.329336	−0.164668	+	0.986349i	$0.552655\pi$
$464$	−2.69459	−0.125093
$465$	−2.24123	−0.103935
$466$	−15.8425	−0.733892
$467$	5.46286	0.252791	0.126395	−	0.991980i	$-0.459659\pi$
$467$	5.46286	0.252791	0.126395	+	0.991980i	$0.459659\pi$
$468$	−5.29086	−0.244570
$469$	33.9263	1.56657
$470$	−11.1702	−0.515245
$471$	0.672304	0.0309781
$472$	3.26857	0.150448
$473$	12.2121	0.561515
$474$	4.36959	0.200702
$475$	8.51754	0.390812
$476$	0	0
$477$	0.573978	0.0262806
$478$	1.10876	0.0507133
$479$	−22.0892	−1.00928	−0.504640	−	0.863330i	$-0.668375\pi$
$479$	−22.0892	−1.00928	−0.504640	+	0.863330i	$0.668375\pi$
$480$	1.00000	0.0456435
$481$	32.0847	1.46294
$482$	3.86484	0.176039
$483$	6.66044	0.303061
$484$	−6.50299	−0.295591
$485$	4.08378	0.185435
$486$	1.00000	0.0453609
$487$	39.7992	1.80348	0.901738	−	0.432284i	$-0.142292\pi$
$487$	39.7992	1.80348	0.901738	+	0.432284i	$0.142292\pi$
$488$	−4.61081	−0.208722
$489$	−17.9317	−0.810900
$490$	−1.49020	−0.0673204
$491$	13.1548	0.593666	0.296833	−	0.954929i	$-0.404070\pi$
$491$	13.1548	0.593666	0.296833	+	0.954929i	$0.404070\pi$
$492$	−1.24123	−0.0559589
$493$	0	0
$494$	−45.0651	−2.02758
$495$	−2.12061	−0.0953145
$496$	−2.24123	−0.100634
$497$	11.2163	0.503118
$498$	1.87164	0.0838704
$499$	−5.97771	−0.267599	−0.133800	−	0.991008i	$-0.542718\pi$
$499$	−5.97771	−0.267599	−0.133800	+	0.991008i	$0.542718\pi$
$500$	1.00000	0.0447214
$501$	−21.0428	−0.940124
$502$	−7.50980	−0.335179
$503$	−6.71925	−0.299596	−0.149798	−	0.988717i	$-0.547862\pi$
$503$	−6.71925	−0.299596	−0.149798	+	0.988717i	$0.547862\pi$
$504$	−2.34730	−0.104557
$505$	13.6459	0.607234
$506$	6.01724	0.267499
$507$	14.9932	0.665871
$508$	−17.4534	−0.774368
$509$	40.0019	1.77305	0.886526	−	0.462679i	$-0.153112\pi$
$509$	40.0019	1.77305	0.886526	+	0.462679i	$0.153112\pi$
$510$	0	0
$511$	0.196652	0.00869938
$512$	1.00000	0.0441942
$513$	8.51754	0.376059
$514$	27.1925	1.19941
$515$	18.9317	0.834231
$516$	−5.75877	−0.253516
$517$	23.6878	1.04179
$518$	14.2344	0.625425
$519$	16.6955	0.732852
$520$	−5.29086	−0.232020
$521$	21.9222	0.960429	0.480215	−	0.877151i	$-0.340559\pi$
$521$	21.9222	0.960429	0.480215	+	0.877151i	$0.340559\pi$
$522$	−2.69459	−0.117939
$523$	3.26083	0.142586	0.0712931	−	0.997455i	$-0.477287\pi$
$523$	3.26083	0.142586	0.0712931	+	0.997455i	$0.477287\pi$
$524$	−20.7246	−0.905359
$525$	−2.34730	−0.102444
$526$	−31.4293	−1.37038
$527$	0	0
$528$	−2.12061	−0.0922879
$529$	−14.9486	−0.649940
$530$	0.573978	0.0249320
$531$	3.26857	0.141844
$532$	−19.9932	−0.866815
$533$	6.56717	0.284456
$534$	13.2148	0.571861
$535$	0.935822	0.0404591
$536$	−14.4534	−0.624290
$537$	−3.33544	−0.143935
$538$	−32.1438	−1.38582
$539$	3.16014	0.136117
$540$	1.00000	0.0430331
$541$	−27.0898	−1.16468	−0.582340	−	0.812945i	$-0.697863\pi$
$541$	−27.0898	−1.16468	−0.582340	+	0.812945i	$0.697863\pi$
$542$	7.27631	0.312544
$543$	−11.7588	−0.504617
$544$	0	0
$545$	−2.73917	−0.117333
$546$	12.4192	0.531493
$547$	−4.11287	−0.175854	−0.0879269	−	0.996127i	$-0.528024\pi$
$547$	−4.11287	−0.175854	−0.0879269	+	0.996127i	$0.528024\pi$
$548$	−10.6655	−0.455607
$549$	−4.61081	−0.196785
$550$	−2.12061	−0.0904233
$551$	−22.9513	−0.977758
$552$	−2.83750	−0.120772
$553$	−10.2567	−0.436160
$554$	15.9017	0.675597
$555$	−6.06418	−0.257410
$556$	−1.61081	−0.0683138
$557$	39.8221	1.68732	0.843659	−	0.536880i	$-0.180397\pi$
$557$	39.8221	1.68732	0.843659	+	0.536880i	$0.180397\pi$
$558$	−2.24123	−0.0948788
$559$	30.4688	1.28869
$560$	−2.34730	−0.0991914
$561$	0	0
$562$	−4.70233	−0.198356
$563$	−6.82295	−0.287553	−0.143776	−	0.989610i	$-0.545925\pi$
$563$	−6.82295	−0.287553	−0.143776	+	0.989610i	$0.545925\pi$
$564$	−11.1702	−0.470352
$565$	−3.84255	−0.161657
$566$	−27.0642	−1.13759
$567$	−2.34730	−0.0985772
$568$	−4.77837	−0.200496
$569$	−25.6263	−1.07431	−0.537155	−	0.843483i	$-0.680501\pi$
$569$	−25.6263	−1.07431	−0.537155	+	0.843483i	$0.680501\pi$
$570$	8.51754	0.356761
$571$	−24.8976	−1.04193	−0.520965	−	0.853578i	$-0.674428\pi$
$571$	−24.8976	−1.04193	−0.520965	+	0.853578i	$0.674428\pi$
$572$	11.2199	0.469127
$573$	−12.8229	−0.535686
$574$	2.91353	0.121609
$575$	−2.83750	−0.118332
$576$	1.00000	0.0416667
$577$	32.4107	1.34927	0.674637	−	0.738150i	$-0.264300\pi$
$577$	32.4107	1.34927	0.674637	+	0.738150i	$0.264300\pi$
$578$	0	0
$579$	−22.4243	−0.931921
$580$	−2.69459	−0.111887
$581$	−4.39330	−0.182265
$582$	4.08378	0.169278
$583$	−1.21719	−0.0504107
$584$	−0.0837781	−0.00346676
$585$	−5.29086	−0.218750
$586$	−13.5699	−0.560566
$587$	27.6560	1.14149	0.570743	−	0.821129i	$-0.306655\pi$
$587$	27.6560	1.14149	0.570743	+	0.821129i	$0.306655\pi$
$588$	−1.49020	−0.0614548
$589$	−19.0898	−0.786580
$590$	3.26857	0.134565
$591$	−19.6091	−0.806609
$592$	−6.06418	−0.249236
$593$	39.2918	1.61352	0.806760	−	0.590879i	$-0.201219\pi$
$593$	39.2918	1.61352	0.806760	+	0.590879i	$0.201219\pi$
$594$	−2.12061	−0.0870099
$595$	0	0
$596$	−1.75877	−0.0720420
$597$	22.7547	0.931286
$598$	15.0128	0.613919
$599$	−16.6655	−0.680934	−0.340467	−	0.940257i	$-0.610585\pi$
$599$	−16.6655	−0.680934	−0.340467	+	0.940257i	$0.610585\pi$
$600$	1.00000	0.0408248
$601$	30.9537	1.26263	0.631313	−	0.775528i	$-0.282516\pi$
$601$	30.9537	1.26263	0.631313	+	0.775528i	$0.282516\pi$
$602$	13.5175	0.550934
$603$	−14.4534	−0.588586
$604$	10.5817	0.430564
$605$	−6.50299	−0.264384
$606$	13.6459	0.554327
$607$	−31.8590	−1.29312	−0.646558	−	0.762865i	$-0.723792\pi$
$607$	−31.8590	−1.29312	−0.646558	+	0.762865i	$0.723792\pi$
$608$	8.51754	0.345432
$609$	6.32501	0.256302
$610$	−4.61081	−0.186686
$611$	59.1002	2.39094
$612$	0	0
$613$	−8.24804	−0.333135	−0.166568	−	0.986030i	$-0.553268\pi$
$613$	−8.24804	−0.333135	−0.166568	+	0.986030i	$0.553268\pi$
$614$	9.93170	0.400811
$615$	−1.24123	−0.0500512
$616$	4.97771	0.200558
$617$	24.8621	1.00091	0.500456	−	0.865762i	$-0.333166\pi$
$617$	24.8621	1.00091	0.500456	+	0.865762i	$0.333166\pi$
$618$	18.9317	0.761545
$619$	27.5790	1.10849	0.554247	−	0.832352i	$-0.313006\pi$
$619$	27.5790	1.10849	0.554247	+	0.832352i	$0.313006\pi$
$620$	−2.24123	−0.0900099
$621$	−2.83750	−0.113865
$622$	−11.1771	−0.448159
$623$	−31.0191	−1.24275
$624$	−5.29086	−0.211804
$625$	1.00000	0.0400000
$626$	−1.84255	−0.0736431
$627$	−18.0624	−0.721344
$628$	0.672304	0.0268279
$629$	0	0
$630$	−2.34730	−0.0935185
$631$	−30.1830	−1.20157	−0.600784	−	0.799411i	$-0.705145\pi$
$631$	−30.1830	−1.20157	−0.600784	+	0.799411i	$0.705145\pi$
$632$	4.36959	0.173813
$633$	25.2695	1.00437
$634$	−13.3405	−0.529819
$635$	−17.4534	−0.692616
$636$	0.573978	0.0227597
$637$	7.88444	0.312393
$638$	5.71419	0.226227
$639$	−4.77837	−0.189029
$640$	1.00000	0.0395285
$641$	15.5243	0.613175	0.306587	−	0.951842i	$-0.400813\pi$
$641$	15.5243	0.613175	0.306587	+	0.951842i	$0.400813\pi$
$642$	0.935822	0.0369340
$643$	−39.4492	−1.55573	−0.777863	−	0.628434i	$-0.783696\pi$
$643$	−39.4492	−1.55573	−0.777863	+	0.628434i	$0.783696\pi$
$644$	6.66044	0.262458
$645$	−5.75877	−0.226751
$646$	0	0
$647$	−19.1712	−0.753697	−0.376848	−	0.926275i	$-0.622992\pi$
$647$	−19.1712	−0.753697	−0.376848	+	0.926275i	$0.622992\pi$
$648$	1.00000	0.0392837
$649$	−6.93138	−0.272080
$650$	−5.29086	−0.207525
$651$	5.26083	0.206188
$652$	−17.9317	−0.702260
$653$	−24.0925	−0.942811	−0.471405	−	0.881917i	$-0.656253\pi$
$653$	−24.0925	−0.942811	−0.471405	+	0.881917i	$0.656253\pi$
$654$	−2.73917	−0.107110
$655$	−20.7246	−0.809778
$656$	−1.24123	−0.0484619
$657$	−0.0837781	−0.00326850
$658$	26.2199	1.02216
$659$	−19.0547	−0.742265	−0.371133	−	0.928580i	$-0.621030\pi$
$659$	−19.0547	−0.742265	−0.371133	+	0.928580i	$0.621030\pi$
$660$	−2.12061	−0.0825448
$661$	−34.4107	−1.33842	−0.669210	−	0.743074i	$-0.733367\pi$
$661$	−34.4107	−1.33842	−0.669210	+	0.743074i	$0.733367\pi$
$662$	28.7870	1.11884
$663$	0	0
$664$	1.87164	0.0726339
$665$	−19.9932	−0.775303
$666$	−6.06418	−0.234982
$667$	7.64590	0.296050
$668$	−21.0428	−0.814171
$669$	21.2172	0.820304
$670$	−14.4534	−0.558382
$671$	9.77776	0.377466
$672$	−2.34730	−0.0905489
$673$	−11.6459	−0.448916	−0.224458	−	0.974484i	$-0.572061\pi$
$673$	−11.6459	−0.448916	−0.224458	+	0.974484i	$0.572061\pi$
$674$	9.36009	0.360537
$675$	1.00000	0.0384900
$676$	14.9932	0.576661
$677$	6.94263	0.266827	0.133413	−	0.991060i	$-0.457406\pi$
$677$	6.94263	0.266827	0.133413	+	0.991060i	$0.457406\pi$
$678$	−3.84255	−0.147572
$679$	−9.58584	−0.367871
$680$	0	0
$681$	23.7743	0.911031
$682$	4.75278	0.181994
$683$	−5.67499	−0.217148	−0.108574	−	0.994088i	$-0.534628\pi$
$683$	−5.67499	−0.217148	−0.108574	+	0.994088i	$0.534628\pi$
$684$	8.51754	0.325676
$685$	−10.6655	−0.407508
$686$	19.9290	0.760893
$687$	−17.3601	−0.662329
$688$	−5.75877	−0.219551
$689$	−3.03684	−0.115694
$690$	−2.83750	−0.108022
$691$	29.1834	1.11019	0.555094	−	0.831788i	$-0.312682\pi$
$691$	29.1834	1.11019	0.555094	+	0.831788i	$0.312682\pi$
$692$	16.6955	0.634669
$693$	4.97771	0.189088
$694$	26.0702	0.989610
$695$	−1.61081	−0.0611017
$696$	−2.69459	−0.102138
$697$	0	0
$698$	14.0000	0.529908
$699$	−15.8425	−0.599220
$700$	−2.34730	−0.0887195
$701$	35.0642	1.32436	0.662178	−	0.749347i	$-0.269632\pi$
$701$	35.0642	1.32436	0.662178	+	0.749347i	$0.269632\pi$
$702$	−5.29086	−0.199691
$703$	−51.6519	−1.94809
$704$	−2.12061	−0.0799237
$705$	−11.1702	−0.420696
$706$	17.9263	0.674666
$707$	−32.0310	−1.20465
$708$	3.26857	0.122840
$709$	20.8621	0.783494	0.391747	−	0.920073i	$-0.371871\pi$
$709$	20.8621	0.783494	0.391747	+	0.920073i	$0.371871\pi$
$710$	−4.77837	−0.179329
$711$	4.36959	0.163872
$712$	13.2148	0.495246
$713$	6.35948	0.238164
$714$	0	0
$715$	11.2199	0.419600
$716$	−3.33544	−0.124651
$717$	1.10876	0.0414072
$718$	13.6851	0.510723
$719$	−22.2412	−0.829458	−0.414729	−	0.909945i	$-0.636124\pi$
$719$	−22.2412	−0.829458	−0.414729	+	0.909945i	$0.636124\pi$
$720$	1.00000	0.0372678
$721$	−44.4383	−1.65497
$722$	53.5485	1.99287
$723$	3.86484	0.143735
$724$	−11.7588	−0.437011
$725$	−2.69459	−0.100075
$726$	−6.50299	−0.241349
$727$	−26.2713	−0.974347	−0.487174	−	0.873305i	$-0.661972\pi$
$727$	−26.2713	−0.974347	−0.487174	+	0.873305i	$0.661972\pi$
$728$	12.4192	0.460287
$729$	1.00000	0.0370370
$730$	−0.0837781	−0.00310077
$731$	0	0
$732$	−4.61081	−0.170421
$733$	1.54252	0.0569742	0.0284871	−	0.999594i	$-0.490931\pi$
$733$	1.54252	0.0569742	0.0284871	+	0.999594i	$0.490931\pi$
$734$	−10.4611	−0.386126
$735$	−1.49020	−0.0549668
$736$	−2.83750	−0.104591
$737$	30.6500	1.12901
$738$	−1.24123	−0.0456903
$739$	−42.6049	−1.56725	−0.783624	−	0.621235i	$-0.786631\pi$
$739$	−42.6049	−1.56725	−0.783624	+	0.621235i	$0.786631\pi$
$740$	−6.06418	−0.222924
$741$	−45.0651	−1.65551
$742$	−1.34730	−0.0494608
$743$	−39.7273	−1.45745	−0.728727	−	0.684804i	$-0.759888\pi$
$743$	−39.7273	−1.45745	−0.728727	+	0.684804i	$0.759888\pi$
$744$	−2.24123	−0.0821675
$745$	−1.75877	−0.0644364
$746$	−17.7128	−0.648510
$747$	1.87164	0.0684799
$748$	0	0
$749$	−2.19665	−0.0802639
$750$	1.00000	0.0365148
$751$	−17.6851	−0.645338	−0.322669	−	0.946512i	$-0.604580\pi$
$751$	−17.6851	−0.645338	−0.322669	+	0.946512i	$0.604580\pi$
$752$	−11.1702	−0.407337
$753$	−7.50980	−0.273672
$754$	14.2567	0.519199
$755$	10.5817	0.385108
$756$	−2.34730	−0.0853703
$757$	−6.23349	−0.226560	−0.113280	−	0.993563i	$-0.536136\pi$
$757$	−6.23349	−0.226560	−0.113280	+	0.993563i	$0.536136\pi$
$758$	5.70409	0.207182
$759$	6.01724	0.218412
$760$	8.51754	0.308964
$761$	−0.578421	−0.0209677	−0.0104839	−	0.999945i	$-0.503337\pi$
$761$	−0.578421	−0.0209677	−0.0104839	+	0.999945i	$0.503337\pi$
$762$	−17.4534	−0.632269
$763$	6.42964	0.232769
$764$	−12.8229	−0.463918
$765$	0	0
$766$	−0.344608	−0.0124512
$767$	−17.2935	−0.624434
$768$	1.00000	0.0360844
$769$	−23.4270	−0.844798	−0.422399	−	0.906410i	$-0.638812\pi$
$769$	−23.4270	−0.844798	−0.422399	+	0.906410i	$0.638812\pi$
$770$	4.97771	0.179384
$771$	27.1925	0.979315
$772$	−22.4243	−0.807067
$773$	17.0446	0.613051	0.306525	−	0.951862i	$-0.400834\pi$
$773$	17.0446	0.613051	0.306525	+	0.951862i	$0.400834\pi$
$774$	−5.75877	−0.206995
$775$	−2.24123	−0.0805073
$776$	4.08378	0.146599
$777$	14.2344	0.510657
$778$	28.6655	1.02771
$779$	−10.5722	−0.378789
$780$	−5.29086	−0.189443
$781$	10.1331	0.362590
$782$	0	0
$783$	−2.69459	−0.0962969
$784$	−1.49020	−0.0532214
$785$	0.672304	0.0239956
$786$	−20.7246	−0.739223
$787$	13.8735	0.494537	0.247269	−	0.968947i	$-0.420467\pi$
$787$	13.8735	0.494537	0.247269	+	0.968947i	$0.420467\pi$
$788$	−19.6091	−0.698544
$789$	−31.4293	−1.11891
$790$	4.36959	0.155463
$791$	9.01960	0.320700
$792$	−2.12061	−0.0753528
$793$	24.3952	0.866298
$794$	−12.6117	−0.447574
$795$	0.573978	0.0203569
$796$	22.7547	0.806517
$797$	23.6682	0.838370	0.419185	−	0.907901i	$-0.362316\pi$
$797$	23.6682	0.838370	0.419185	+	0.907901i	$0.362316\pi$
$798$	−19.9932	−0.707751
$799$	0	0
$800$	1.00000	0.0353553
$801$	13.2148	0.466923
$802$	−13.1848	−0.465571
$803$	0.177661	0.00626953
$804$	−14.4534	−0.509731
$805$	6.66044	0.234750
$806$	11.8580	0.417681
$807$	−32.1438	−1.13152
$808$	13.6459	0.480061
$809$	48.1789	1.69388	0.846940	−	0.531688i	$-0.178442\pi$
$809$	48.1789	1.69388	0.846940	+	0.531688i	$0.178442\pi$
$810$	1.00000	0.0351364
$811$	−42.3884	−1.48846	−0.744228	−	0.667925i	$-0.767183\pi$
$811$	−42.3884	−1.48846	−0.744228	+	0.667925i	$0.767183\pi$
$812$	6.32501	0.221964
$813$	7.27631	0.255191
$814$	12.8598	0.450735
$815$	−17.9317	−0.628120
$816$	0	0
$817$	−49.0506	−1.71606
$818$	−12.8239	−0.448377
$819$	12.4192	0.433962
$820$	−1.24123	−0.0433456
$821$	24.4587	0.853616	0.426808	−	0.904342i	$-0.359638\pi$
$821$	24.4587	0.853616	0.426808	+	0.904342i	$0.359638\pi$
$822$	−10.6655	−0.372002
$823$	20.3459	0.709212	0.354606	−	0.935016i	$-0.384615\pi$
$823$	20.3459	0.709212	0.354606	+	0.935016i	$0.384615\pi$
$824$	18.9317	0.659517
$825$	−2.12061	−0.0738303
$826$	−7.67230	−0.266954
$827$	−8.86753	−0.308354	−0.154177	−	0.988043i	$-0.549273\pi$
$827$	−8.86753	−0.308354	−0.154177	+	0.988043i	$0.549273\pi$
$828$	−2.83750	−0.0986098
$829$	−14.5662	−0.505906	−0.252953	−	0.967479i	$-0.581402\pi$
$829$	−14.5662	−0.505906	−0.252953	+	0.967479i	$0.581402\pi$
$830$	1.87164	0.0649657
$831$	15.9017	0.551623
$832$	−5.29086	−0.183428
$833$	0	0
$834$	−1.61081	−0.0557779
$835$	−21.0428	−0.728217
$836$	−18.0624	−0.624702
$837$	−2.24123	−0.0774682
$838$	−6.36865	−0.220001
$839$	−33.5912	−1.15970	−0.579849	−	0.814724i	$-0.696888\pi$
$839$	−33.5912	−1.15970	−0.579849	+	0.814724i	$0.696888\pi$
$840$	−2.34730	−0.0809894
$841$	−21.7392	−0.749627
$842$	−22.2722	−0.767550
$843$	−4.70233	−0.161957
$844$	25.2695	0.869812
$845$	14.9932	0.515782
$846$	−11.1702	−0.384041
$847$	15.2645	0.524493
$848$	0.573978	0.0197105
$849$	−27.0642	−0.928840
$850$	0	0
$851$	17.2071	0.589851
$852$	−4.77837	−0.163704
$853$	40.9691	1.40276	0.701378	−	0.712789i	$-0.252568\pi$
$853$	40.9691	1.40276	0.701378	+	0.712789i	$0.252568\pi$
$854$	10.8229	0.370354
$855$	8.51754	0.291294
$856$	0.935822	0.0319857
$857$	49.9709	1.70697	0.853487	−	0.521114i	$-0.174484\pi$
$857$	49.9709	1.70697	0.853487	+	0.521114i	$0.174484\pi$
$858$	11.2199	0.383040
$859$	−7.22575	−0.246539	−0.123270	−	0.992373i	$-0.539338\pi$
$859$	−7.22575	−0.246539	−0.123270	+	0.992373i	$0.539338\pi$
$860$	−5.75877	−0.196372
$861$	2.91353	0.0992930
$862$	−9.47834	−0.322834
$863$	35.3387	1.20294	0.601472	−	0.798894i	$-0.294581\pi$
$863$	35.3387	1.20294	0.601472	+	0.798894i	$0.294581\pi$
$864$	1.00000	0.0340207
$865$	16.6955	0.567665
$866$	−15.5621	−0.528822
$867$	0	0
$868$	5.26083	0.178564
$869$	−9.26621	−0.314335
$870$	−2.69459	−0.0913552
$871$	76.4707	2.59111
$872$	−2.73917	−0.0927600
$873$	4.08378	0.138215
$874$	−24.1685	−0.817511
$875$	−2.34730	−0.0793531
$876$	−0.0837781	−0.00283060
$877$	15.9641	0.539069	0.269535	−	0.962991i	$-0.413130\pi$
$877$	15.9641	0.539069	0.269535	+	0.962991i	$0.413130\pi$
$878$	−21.5229	−0.726363
$879$	−13.5699	−0.457700
$880$	−2.12061	−0.0714859
$881$	22.6699	0.763770	0.381885	−	0.924210i	$-0.375275\pi$
$881$	22.6699	0.763770	0.381885	+	0.924210i	$0.375275\pi$
$882$	−1.49020	−0.0501776
$883$	−27.8479	−0.937157	−0.468579	−	0.883422i	$-0.655234\pi$
$883$	−27.8479	−0.937157	−0.468579	+	0.883422i	$0.655234\pi$
$884$	0	0
$885$	3.26857	0.109872
$886$	25.6067	0.860274
$887$	13.9121	0.467123	0.233561	−	0.972342i	$-0.424962\pi$
$887$	13.9121	0.467123	0.233561	+	0.972342i	$0.424962\pi$
$888$	−6.06418	−0.203500
$889$	40.9682	1.37403
$890$	13.2148	0.442962
$891$	−2.12061	−0.0710433
$892$	21.2172	0.710404
$893$	−95.1430	−3.18384
$894$	−1.75877	−0.0588221
$895$	−3.33544	−0.111491
$896$	−2.34730	−0.0784177
$897$	15.0128	0.501263
$898$	27.3310	0.912047
$899$	6.03920	0.201419
$900$	1.00000	0.0333333
$901$	0	0
$902$	2.63217	0.0876417
$903$	13.5175	0.449836
$904$	−3.84255	−0.127801
$905$	−11.7588	−0.390875
$906$	10.5817	0.351554
$907$	13.7879	0.457819	0.228909	−	0.973448i	$-0.426484\pi$
$907$	13.7879	0.457819	0.228909	+	0.973448i	$0.426484\pi$
$908$	23.7743	0.788976
$909$	13.6459	0.452606
$910$	12.4192	0.411693
$911$	55.8836	1.85151	0.925753	−	0.378128i	$-0.123432\pi$
$911$	55.8836	1.85151	0.925753	+	0.378128i	$0.123432\pi$
$912$	8.51754	0.282044
$913$	−3.96904	−0.131356
$914$	7.02498	0.232366
$915$	−4.61081	−0.152429
$916$	−17.3601	−0.573594
$917$	48.6468	1.60646
$918$	0	0
$919$	46.3816	1.52999	0.764993	−	0.644038i	$-0.222742\pi$
$919$	46.3816	1.52999	0.764993	+	0.644038i	$0.222742\pi$
$920$	−2.83750	−0.0935495
$921$	9.93170	0.327261
$922$	7.04870	0.232136
$923$	25.2817	0.832157
$924$	4.97771	0.163755
$925$	−6.06418	−0.199389
$926$	−7.08647	−0.232876
$927$	18.9317	0.621799
$928$	−2.69459	−0.0884543
$929$	−0.809334	−0.0265534	−0.0132767	−	0.999912i	$-0.504226\pi$
$929$	−0.809334	−0.0265534	−0.0132767	+	0.999912i	$0.504226\pi$
$930$	−2.24123	−0.0734928
$931$	−12.6928	−0.415991
$932$	−15.8425	−0.518940
$933$	−11.1771	−0.365920
$934$	5.46286	0.178750
$935$	0	0
$936$	−5.29086	−0.172937
$937$	−40.3851	−1.31932	−0.659661	−	0.751563i	$-0.729300\pi$
$937$	−40.3851	−1.31932	−0.659661	+	0.751563i	$0.729300\pi$
$938$	33.9263	1.10773
$939$	−1.84255	−0.0601293
$940$	−11.1702	−0.364333
$941$	55.1735	1.79861	0.899303	−	0.437326i	$-0.144074\pi$
$941$	55.1735	1.79861	0.899303	+	0.437326i	$0.144074\pi$
$942$	0.672304	0.0219048
$943$	3.52198	0.114692
$944$	3.26857	0.106383
$945$	−2.34730	−0.0763576
$946$	12.2121	0.397051
$947$	−35.8735	−1.16573	−0.582866	−	0.812568i	$-0.698069\pi$
$947$	−35.8735	−1.16573	−0.582866	+	0.812568i	$0.698069\pi$
$948$	4.36959	0.141918
$949$	0.443258	0.0143888
$950$	8.51754	0.276346
$951$	−13.3405	−0.432595
$952$	0	0
$953$	34.0411	1.10270	0.551349	−	0.834275i	$-0.314113\pi$
$953$	34.0411	1.10270	0.551349	+	0.834275i	$0.314113\pi$
$954$	0.573978	0.0185832
$955$	−12.8229	−0.414941
$956$	1.10876	0.0358597
$957$	5.71419	0.184714
$958$	−22.0892	−0.713668
$959$	25.0351	0.808425
$960$	1.00000	0.0322749
$961$	−25.9769	−0.837964
$962$	32.0847	1.03445
$963$	0.935822	0.0301564
$964$	3.86484	0.124478
$965$	−22.4243	−0.721863
$966$	6.66044	0.214296
$967$	29.0993	0.935769	0.467885	−	0.883790i	$-0.345016\pi$
$967$	29.0993	0.935769	0.467885	+	0.883790i	$0.345016\pi$
$968$	−6.50299	−0.209014
$969$	0	0
$970$	4.08378	0.131122
$971$	10.3345	0.331650	0.165825	−	0.986155i	$-0.446971\pi$
$971$	10.3345	0.331650	0.165825	+	0.986155i	$0.446971\pi$
$972$	1.00000	0.0320750
$973$	3.78106	0.121215
$974$	39.7992	1.27525
$975$	−5.29086	−0.169443
$976$	−4.61081	−0.147589
$977$	−54.0993	−1.73079	−0.865394	−	0.501091i	$-0.832932\pi$
$977$	−54.0993	−1.73079	−0.865394	+	0.501091i	$0.832932\pi$
$978$	−17.9317	−0.573393
$979$	−28.0235	−0.895636
$980$	−1.49020	−0.0476027
$981$	−2.73917	−0.0874550
$982$	13.1548	0.419785
$983$	55.4593	1.76888	0.884439	−	0.466655i	$-0.154541\pi$
$983$	55.4593	1.76888	0.884439	+	0.466655i	$0.154541\pi$
$984$	−1.24123	−0.0395690
$985$	−19.6091	−0.624797
$986$	0	0
$987$	26.2199	0.834588
$988$	−45.0651	−1.43371
$989$	16.3405	0.519597
$990$	−2.12061	−0.0673976
$991$	18.1147	0.575434	0.287717	−	0.957716i	$-0.407104\pi$
$991$	18.1147	0.575434	0.287717	+	0.957716i	$0.407104\pi$
$992$	−2.24123	−0.0711591
$993$	28.7870	0.913529
$994$	11.2163	0.355758
$995$	22.7547	0.721371
$996$	1.87164	0.0593053
$997$	39.5954	1.25400	0.627000	−	0.779019i	$-0.284283\pi$
$997$	39.5954	1.25400	0.627000	+	0.779019i	$0.284283\pi$
$998$	−5.97771	−0.189221
$999$	−6.06418	−0.191862

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8670.2.a.bs.1.2	yes	3
17.16	even	2		8670.2.a.bp.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8670.2.a.bp.1.2	✓	3	17.16	even	2
8670.2.a.bs.1.2	yes	3	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8670.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -2.34730 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -2.12061 q^{11} +1.00000 q^{12} -5.29086 q^{13} -2.34730 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{18} +8.51754 q^{19} +1.00000 q^{20} -2.34730 q^{21} -2.12061 q^{22} -2.83750 q^{23} +1.00000 q^{24} +1.00000 q^{25} -5.29086 q^{26} +1.00000 q^{27} -2.34730 q^{28} -2.69459 q^{29} +1.00000 q^{30} -2.24123 q^{31} +1.00000 q^{32} -2.12061 q^{33} -2.34730 q^{35} +1.00000 q^{36} -6.06418 q^{37} +8.51754 q^{38} -5.29086 q^{39} +1.00000 q^{40} -1.24123 q^{41} -2.34730 q^{42} -5.75877 q^{43} -2.12061 q^{44} +1.00000 q^{45} -2.83750 q^{46} -11.1702 q^{47} +1.00000 q^{48} -1.49020 q^{49} +1.00000 q^{50} -5.29086 q^{52} +0.573978 q^{53} +1.00000 q^{54} -2.12061 q^{55} -2.34730 q^{56} +8.51754 q^{57} -2.69459 q^{58} +3.26857 q^{59} +1.00000 q^{60} -4.61081 q^{61} -2.24123 q^{62} -2.34730 q^{63} +1.00000 q^{64} -5.29086 q^{65} -2.12061 q^{66} -14.4534 q^{67} -2.83750 q^{69} -2.34730 q^{70} -4.77837 q^{71} +1.00000 q^{72} -0.0837781 q^{73} -6.06418 q^{74} +1.00000 q^{75} +8.51754 q^{76} +4.97771 q^{77} -5.29086 q^{78} +4.36959 q^{79} +1.00000 q^{80} +1.00000 q^{81} -1.24123 q^{82} +1.87164 q^{83} -2.34730 q^{84} -5.75877 q^{86} -2.69459 q^{87} -2.12061 q^{88} +13.2148 q^{89} +1.00000 q^{90} +12.4192 q^{91} -2.83750 q^{92} -2.24123 q^{93} -11.1702 q^{94} +8.51754 q^{95} +1.00000 q^{96} +4.08378 q^{97} -1.49020 q^{98} -2.12061 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} - 6 q^{7} + 3 q^{8} + 3 q^{9} + 3 q^{10} - 12 q^{11} + 3 q^{12} - 6 q^{14} + 3 q^{15} + 3 q^{16} + 3 q^{18} + 3 q^{19} + 3 q^{20} - 6 q^{21} - 12 q^{22}+ \cdots - 12 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 - 6 * q^7 + 3 * q^8 + 3 * q^9 + 3 * q^10 - 12 * q^11 + 3 * q^12 - 6 * q^14 + 3 * q^15 + 3 * q^16 + 3 * q^18 + 3 * q^19 + 3 * q^20 - 6 * q^21 - 12 * q^22 - 6 * q^23 + 3 * q^24 + 3 * q^25 + 3 * q^27 - 6 * q^28 - 6 * q^29 + 3 * q^30 - 18 * q^31 + 3 * q^32 - 12 * q^33 - 6 * q^35 + 3 * q^36 - 9 * q^37 + 3 * q^38 + 3 * q^40 - 15 * q^41 - 6 * q^42 - 6 * q^43 - 12 * q^44 + 3 * q^45 - 6 * q^46 - 12 * q^47 + 3 * q^48 - 3 * q^49 + 3 * q^50 - 6 * q^53 + 3 * q^54 - 12 * q^55 - 6 * q^56 + 3 * q^57 - 6 * q^58 + 3 * q^60 - 18 * q^61 - 18 * q^62 - 6 * q^63 + 3 * q^64 - 12 * q^66 - 30 * q^67 - 6 * q^69 - 6 * q^70 - 6 * q^71 + 3 * q^72 + 6 * q^73 - 9 * q^74 + 3 * q^75 + 3 * q^76 + 21 * q^77 + 6 * q^79 + 3 * q^80 + 3 * q^81 - 15 * q^82 + 24 * q^83 - 6 * q^84 - 6 * q^86 - 6 * q^87 - 12 * q^88 + 6 * q^89 + 3 * q^90 + 3 * q^91 - 6 * q^92 - 18 * q^93 - 12 * q^94 + 3 * q^95 + 3 * q^96 + 6 * q^97 - 3 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more