LMFDB - Embedded newform 8085.2.a.cb.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8085,2,Mod(1,8085)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8085, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8085.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8085.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:	$64.5590500342$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 12x^{5} + 37x^{3} - 2x^{2} - 26x - 6 $ x^7 - 12x^5 + 37x^3 - 2x^2 - 26x - 6
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-2.02288$ of defining polynomial
Character	$\chi$	$=$	8085.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.02288 q^{2} -1.00000 q^{3} +2.09206 q^{4} +1.00000 q^{5} -2.02288 q^{6} +0.186217 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.02288 q^{2} -1.00000 q^{3} +2.09206 q^{4} +1.00000 q^{5} -2.02288 q^{6} +0.186217 q^{8} +1.00000 q^{9} +2.02288 q^{10} +1.00000 q^{11} -2.09206 q^{12} -0.386126 q^{13} -1.00000 q^{15} -3.80741 q^{16} -4.09593 q^{17} +2.02288 q^{18} +8.07209 q^{19} +2.09206 q^{20} +2.02288 q^{22} +4.54260 q^{23} -0.186217 q^{24} +1.00000 q^{25} -0.781088 q^{26} -1.00000 q^{27} +9.37765 q^{29} -2.02288 q^{30} -3.88243 q^{31} -8.07439 q^{32} -1.00000 q^{33} -8.28560 q^{34} +2.09206 q^{36} +1.42801 q^{37} +16.3289 q^{38} +0.386126 q^{39} +0.186217 q^{40} -4.61775 q^{41} +0.660164 q^{43} +2.09206 q^{44} +1.00000 q^{45} +9.18914 q^{46} -6.42394 q^{47} +3.80741 q^{48} +2.02288 q^{50} +4.09593 q^{51} -0.807797 q^{52} +6.09593 q^{53} -2.02288 q^{54} +1.00000 q^{55} -8.07209 q^{57} +18.9699 q^{58} +0.213503 q^{59} -2.09206 q^{60} +7.06113 q^{61} -7.85370 q^{62} -8.71872 q^{64} -0.386126 q^{65} -2.02288 q^{66} -8.30637 q^{67} -8.56892 q^{68} -4.54260 q^{69} +3.42801 q^{71} +0.186217 q^{72} -11.2338 q^{73} +2.88870 q^{74} -1.00000 q^{75} +16.8873 q^{76} +0.781088 q^{78} +13.4736 q^{79} -3.80741 q^{80} +1.00000 q^{81} -9.34117 q^{82} -8.62704 q^{83} -4.09593 q^{85} +1.33543 q^{86} -9.37765 q^{87} +0.186217 q^{88} +8.66792 q^{89} +2.02288 q^{90} +9.50336 q^{92} +3.88243 q^{93} -12.9949 q^{94} +8.07209 q^{95} +8.07439 q^{96} +7.90876 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 7 q^{3} + 10 q^{4} + 7 q^{5} + 7 q^{9}+O(q^{10}) $ 7 * q - 7 * q^3 + 10 * q^4 + 7 * q^5 + 7 * q^9	$ 7 q - 7 q^{3} + 10 q^{4} + 7 q^{5} + 7 q^{9} + 7 q^{11} - 10 q^{12} - 4 q^{13} - 7 q^{15} + 24 q^{16} + 7 q^{17} - 3 q^{19} + 10 q^{20} + 13 q^{23} + 7 q^{25} + 14 q^{26} - 7 q^{27} + 7 q^{29} + 14 q^{31} - 10 q^{32} - 7 q^{33} - 4 q^{34} + 10 q^{36} + 14 q^{37} + 20 q^{38} + 4 q^{39} + 27 q^{43} + 10 q^{44} + 7 q^{45} - 6 q^{46} - 10 q^{47} - 24 q^{48} - 7 q^{51} - 30 q^{52} + 7 q^{53} + 7 q^{55} + 3 q^{57} - 4 q^{58} + 7 q^{59} - 10 q^{60} - 15 q^{61} - 28 q^{62} + 68 q^{64} - 4 q^{65} + 18 q^{67} - 10 q^{68} - 13 q^{69} + 28 q^{71} - 10 q^{73} + 30 q^{74} - 7 q^{75} - 54 q^{76} - 14 q^{78} + 24 q^{80} + 7 q^{81} - 18 q^{82} - 11 q^{83} + 7 q^{85} - 34 q^{86} - 7 q^{87} + 21 q^{89} + 62 q^{92} - 14 q^{93} + 52 q^{94} - 3 q^{95} + 10 q^{96} - 17 q^{97} + 7 q^{99}+O(q^{100}) $ 7 * q - 7 * q^3 + 10 * q^4 + 7 * q^5 + 7 * q^9 + 7 * q^11 - 10 * q^12 - 4 * q^13 - 7 * q^15 + 24 * q^16 + 7 * q^17 - 3 * q^19 + 10 * q^20 + 13 * q^23 + 7 * q^25 + 14 * q^26 - 7 * q^27 + 7 * q^29 + 14 * q^31 - 10 * q^32 - 7 * q^33 - 4 * q^34 + 10 * q^36 + 14 * q^37 + 20 * q^38 + 4 * q^39 + 27 * q^43 + 10 * q^44 + 7 * q^45 - 6 * q^46 - 10 * q^47 - 24 * q^48 - 7 * q^51 - 30 * q^52 + 7 * q^53 + 7 * q^55 + 3 * q^57 - 4 * q^58 + 7 * q^59 - 10 * q^60 - 15 * q^61 - 28 * q^62 + 68 * q^64 - 4 * q^65 + 18 * q^67 - 10 * q^68 - 13 * q^69 + 28 * q^71 - 10 * q^73 + 30 * q^74 - 7 * q^75 - 54 * q^76 - 14 * q^78 + 24 * q^80 + 7 * q^81 - 18 * q^82 - 11 * q^83 + 7 * q^85 - 34 * q^86 - 7 * q^87 + 21 * q^89 + 62 * q^92 - 14 * q^93 + 52 * q^94 - 3 * q^95 + 10 * q^96 - 17 * q^97 + 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.02288	1.43039	0.715197	−	0.698923i	$-0.246337\pi$
$2$	2.02288	1.43039	0.715197	+	0.698923i	$0.246337\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.09206	1.04603
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.02288	−0.825839
$7$	0	0
$7$	0	0
$8$	0.186217	0.0658378
$9$	1.00000	0.333333
$10$	2.02288	0.639692
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.09206	−0.603924
$13$	−0.386126	−0.107092	−0.0535460	−	0.998565i	$-0.517052\pi$
$13$	−0.386126	−0.107092	−0.0535460	+	0.998565i	$0.517052\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	−3.80741	−0.951854
$17$	−4.09593	−0.993410	−0.496705	−	0.867919i	$-0.665457\pi$
$17$	−4.09593	−0.993410	−0.496705	+	0.867919i	$0.665457\pi$
$18$	2.02288	0.476798
$19$	8.07209	1.85187	0.925933	−	0.377689i	$-0.123281\pi$
$19$	8.07209	1.85187	0.925933	+	0.377689i	$0.123281\pi$
$20$	2.09206	0.467798
$21$	0	0
$22$	2.02288	0.431280
$23$	4.54260	0.947197	0.473598	−	0.880741i	$-0.342955\pi$
$23$	4.54260	0.947197	0.473598	+	0.880741i	$0.342955\pi$
$24$	−0.186217	−0.0380115
$25$	1.00000	0.200000
$26$	−0.781088	−0.153184
$27$	−1.00000	−0.192450
$28$	0	0
$29$	9.37765	1.74139	0.870693	−	0.491827i	$-0.163671\pi$
$29$	9.37765	1.74139	0.870693	+	0.491827i	$0.163671\pi$
$30$	−2.02288	−0.369326
$31$	−3.88243	−0.697305	−0.348653	−	0.937252i	$-0.613361\pi$
$31$	−3.88243	−0.697305	−0.348653	+	0.937252i	$0.613361\pi$
$32$	−8.07439	−1.42736
$33$	−1.00000	−0.174078
$34$	−8.28560	−1.42097
$35$	0	0
$36$	2.09206	0.348676
$37$	1.42801	0.234764	0.117382	−	0.993087i	$-0.462550\pi$
$37$	1.42801	0.234764	0.117382	+	0.993087i	$0.462550\pi$
$38$	16.3289	2.64890
$39$	0.386126	0.0618296
$40$	0.186217	0.0294436
$41$	−4.61775	−0.721172	−0.360586	−	0.932726i	$-0.617423\pi$
$41$	−4.61775	−0.721172	−0.360586	+	0.932726i	$0.617423\pi$
$42$	0	0
$43$	0.660164	0.100674	0.0503370	−	0.998732i	$-0.483970\pi$
$43$	0.660164	0.100674	0.0503370	+	0.998732i	$0.483970\pi$
$44$	2.09206	0.315389
$45$	1.00000	0.149071
$46$	9.18914	1.35486
$47$	−6.42394	−0.937028	−0.468514	−	0.883456i	$-0.655210\pi$
$47$	−6.42394	−0.937028	−0.468514	+	0.883456i	$0.655210\pi$
$48$	3.80741	0.549553
$49$	0	0
$50$	2.02288	0.286079
$51$	4.09593	0.573546
$52$	−0.807797	−0.112021
$53$	6.09593	0.837341	0.418671	−	0.908138i	$-0.362496\pi$
$53$	6.09593	0.837341	0.418671	+	0.908138i	$0.362496\pi$
$54$	−2.02288	−0.275280
$55$	1.00000	0.134840
$56$	0	0
$57$	−8.07209	−1.06917
$58$	18.9699	2.49087
$59$	0.213503	0.0277957	0.0138979	−	0.999903i	$-0.495576\pi$
$59$	0.213503	0.0277957	0.0138979	+	0.999903i	$0.495576\pi$
$60$	−2.09206	−0.270083
$61$	7.06113	0.904085	0.452043	−	0.891996i	$-0.350695\pi$
$61$	7.06113	0.904085	0.452043	+	0.891996i	$0.350695\pi$
$62$	−7.85370	−0.997421
$63$	0	0
$64$	−8.71872	−1.08984
$65$	−0.386126	−0.0478930
$66$	−2.02288	−0.249000
$67$	−8.30637	−1.01478	−0.507392	−	0.861715i	$-0.669391\pi$
$67$	−8.30637	−1.01478	−0.507392	+	0.861715i	$0.669391\pi$
$68$	−8.56892	−1.03913
$69$	−4.54260	−0.546864
$70$	0	0
$71$	3.42801	0.406830	0.203415	−	0.979093i	$-0.434796\pi$
$71$	3.42801	0.406830	0.203415	+	0.979093i	$0.434796\pi$
$72$	0.186217	0.0219459
$73$	−11.2338	−1.31481	−0.657406	−	0.753537i	$-0.728346\pi$
$73$	−11.2338	−1.31481	−0.657406	+	0.753537i	$0.728346\pi$
$74$	2.88870	0.335805
$75$	−1.00000	−0.115470
$76$	16.8873	1.93710
$77$	0	0
$78$	0.781088	0.0884408
$79$	13.4736	1.51590	0.757948	−	0.652314i	$-0.226202\pi$
$79$	13.4736	1.51590	0.757948	+	0.652314i	$0.226202\pi$
$80$	−3.80741	−0.425682
$81$	1.00000	0.111111
$82$	−9.34117	−1.03156
$83$	−8.62704	−0.946941	−0.473470	−	0.880810i	$-0.656999\pi$
$83$	−8.62704	−0.946941	−0.473470	+	0.880810i	$0.656999\pi$
$84$	0	0
$85$	−4.09593	−0.444266
$86$	1.33543	0.144004
$87$	−9.37765	−1.00539
$88$	0.186217	0.0198508
$89$	8.66792	0.918798	0.459399	−	0.888230i	$-0.348065\pi$
$89$	8.66792	0.918798	0.459399	+	0.888230i	$0.348065\pi$
$90$	2.02288	0.213231
$91$	0	0
$92$	9.50336	0.990794
$93$	3.88243	0.402589
$94$	−12.9949	−1.34032
$95$	8.07209	0.828179
$96$	8.07439	0.824089
$97$	7.90876	0.803013	0.401506	−	0.915856i	$-0.368487\pi$
$97$	7.90876	0.803013	0.401506	+	0.915856i	$0.368487\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	2.09206	0.209206
$101$	4.04577	0.402569	0.201284	−	0.979533i	$-0.435488\pi$
$101$	4.04577	0.402569	0.201284	+	0.979533i	$0.435488\pi$
$102$	8.28560	0.820396
$103$	16.5111	1.62688	0.813442	−	0.581646i	$-0.197591\pi$
$103$	16.5111	1.62688	0.813442	+	0.581646i	$0.197591\pi$
$104$	−0.0719034	−0.00705071
$105$	0	0
$106$	12.3314	1.19773
$107$	8.40010	0.812068	0.406034	−	0.913858i	$-0.366911\pi$
$107$	8.40010	0.812068	0.406034	+	0.913858i	$0.366911\pi$
$108$	−2.09206	−0.201308
$109$	12.1473	1.16350	0.581748	−	0.813369i	$-0.302369\pi$
$109$	12.1473	1.16350	0.581748	+	0.813369i	$0.302369\pi$
$110$	2.02288	0.192874
$111$	−1.42801	−0.135541
$112$	0	0
$113$	15.8926	1.49505	0.747525	−	0.664233i	$-0.231242\pi$
$113$	15.8926	1.49505	0.747525	+	0.664233i	$0.231242\pi$
$114$	−16.3289	−1.52934
$115$	4.54260	0.423599
$116$	19.6186	1.82154
$117$	−0.386126	−0.0356974
$118$	0.431892	0.0397589
$119$	0	0
$120$	−0.186217	−0.0169992
$121$	1.00000	0.0909091
$122$	14.2838	1.29320
$123$	4.61775	0.416369
$124$	−8.12226	−0.729401
$125$	1.00000	0.0894427
$126$	0	0
$127$	4.47832	0.397387	0.198693	−	0.980062i	$-0.436330\pi$
$127$	4.47832	0.397387	0.198693	+	0.980062i	$0.436330\pi$
$128$	−1.48816	−0.131536
$129$	−0.660164	−0.0581242
$130$	−0.781088	−0.0685059
$131$	−1.76244	−0.153985	−0.0769925	−	0.997032i	$-0.524532\pi$
$131$	−1.76244	−0.153985	−0.0769925	+	0.997032i	$0.524532\pi$
$132$	−2.09206	−0.182090
$133$	0	0
$134$	−16.8028	−1.45154
$135$	−1.00000	−0.0860663
$136$	−0.762734	−0.0654039
$137$	8.38481	0.716363	0.358181	−	0.933652i	$-0.383397\pi$
$137$	8.38481	0.716363	0.358181	+	0.933652i	$0.383397\pi$
$138$	−9.18914	−0.782231
$139$	−6.82685	−0.579046	−0.289523	−	0.957171i	$-0.593497\pi$
$139$	−6.82685	−0.579046	−0.289523	+	0.957171i	$0.593497\pi$
$140$	0	0
$141$	6.42394	0.540993
$142$	6.93447	0.581928
$143$	−0.386126	−0.0322895
$144$	−3.80741	−0.317285
$145$	9.37765	0.778772
$146$	−22.7246	−1.88070
$147$	0	0
$148$	2.98748	0.245569
$149$	6.04330	0.495087	0.247543	−	0.968877i	$-0.420377\pi$
$149$	6.04330	0.495087	0.247543	+	0.968877i	$0.420377\pi$
$150$	−2.02288	−0.165168
$151$	6.94931	0.565527	0.282763	−	0.959190i	$-0.408749\pi$
$151$	6.94931	0.565527	0.282763	+	0.959190i	$0.408749\pi$
$152$	1.50316	0.121923
$153$	−4.09593	−0.331137
$154$	0	0
$155$	−3.88243	−0.311844
$156$	0.807797	0.0646755
$157$	8.75945	0.699081	0.349540	−	0.936921i	$-0.386338\pi$
$157$	8.75945	0.699081	0.349540	+	0.936921i	$0.386338\pi$
$158$	27.2555	2.16833
$159$	−6.09593	−0.483439
$160$	−8.07439	−0.638337
$161$	0	0
$162$	2.02288	0.158933
$163$	−7.79317	−0.610408	−0.305204	−	0.952287i	$-0.598725\pi$
$163$	−7.79317	−0.610408	−0.305204	+	0.952287i	$0.598725\pi$
$164$	−9.66060	−0.754366
$165$	−1.00000	−0.0778499
$166$	−17.4515	−1.35450
$167$	18.4138	1.42490	0.712451	−	0.701722i	$-0.247585\pi$
$167$	18.4138	1.42490	0.712451	+	0.701722i	$0.247585\pi$
$168$	0	0
$169$	−12.8509	−0.988531
$170$	−8.28560	−0.635476
$171$	8.07209	0.617288
$172$	1.38110	0.105308
$173$	−14.5767	−1.10824	−0.554122	−	0.832435i	$-0.686946\pi$
$173$	−14.5767	−1.10824	−0.554122	+	0.832435i	$0.686946\pi$
$174$	−18.9699	−1.43810
$175$	0	0
$176$	−3.80741	−0.286995
$177$	−0.213503	−0.0160479
$178$	17.5342	1.31424
$179$	17.0088	1.27129	0.635647	−	0.771980i	$-0.280733\pi$
$179$	17.0088	1.27129	0.635647	+	0.771980i	$0.280733\pi$
$180$	2.09206	0.155933
$181$	2.26147	0.168094	0.0840470	−	0.996462i	$-0.473215\pi$
$181$	2.26147	0.168094	0.0840470	+	0.996462i	$0.473215\pi$
$182$	0	0
$183$	−7.06113	−0.521974
$184$	0.845910	0.0623613
$185$	1.42801	0.104990
$186$	7.85370	0.575862
$187$	−4.09593	−0.299524
$188$	−13.4392	−0.980157
$189$	0	0
$190$	16.3289	1.18462
$191$	19.9382	1.44267	0.721337	−	0.692584i	$-0.243528\pi$
$191$	19.9382	1.44267	0.721337	+	0.692584i	$0.243528\pi$
$192$	8.71872	0.629219
$193$	−13.9373	−1.00323	−0.501614	−	0.865092i	$-0.667260\pi$
$193$	−13.9373	−1.00323	−0.501614	+	0.865092i	$0.667260\pi$
$194$	15.9985	1.14862
$195$	0.386126	0.0276511
$196$	0	0
$197$	−18.8172	−1.34067	−0.670333	−	0.742060i	$-0.733849\pi$
$197$	−18.8172	−1.34067	−0.670333	+	0.742060i	$0.733849\pi$
$198$	2.02288	0.143760
$199$	−12.1223	−0.859324	−0.429662	−	0.902990i	$-0.641367\pi$
$199$	−12.1223	−0.859324	−0.429662	+	0.902990i	$0.641367\pi$
$200$	0.186217	0.0131676
$201$	8.30637	0.585886
$202$	8.18411	0.575832
$203$	0	0
$204$	8.56892	0.599945
$205$	−4.61775	−0.322518
$206$	33.4000	2.32709
$207$	4.54260	0.315732
$208$	1.47014	0.101936
$209$	8.07209	0.558358
$210$	0	0
$211$	1.54625	0.106449	0.0532243	−	0.998583i	$-0.483050\pi$
$211$	1.54625	0.106449	0.0532243	+	0.998583i	$0.483050\pi$
$212$	12.7530	0.875882
$213$	−3.42801	−0.234884
$214$	16.9924	1.16158
$215$	0.660164	0.0450228
$216$	−0.186217	−0.0126705
$217$	0	0
$218$	24.5725	1.66426
$219$	11.2338	0.759107
$220$	2.09206	0.141046
$221$	1.58155	0.106386
$222$	−2.88870	−0.193877
$223$	−5.71689	−0.382831	−0.191416	−	0.981509i	$-0.561308\pi$
$223$	−5.71689	−0.382831	−0.191416	+	0.981509i	$0.561308\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	32.1489	2.13851
$227$	17.3801	1.15356	0.576778	−	0.816901i	$-0.304310\pi$
$227$	17.3801	1.15356	0.576778	+	0.816901i	$0.304310\pi$
$228$	−16.8873	−1.11839
$229$	−19.2165	−1.26986	−0.634932	−	0.772568i	$-0.718972\pi$
$229$	−19.2165	−1.26986	−0.634932	+	0.772568i	$0.718972\pi$
$230$	9.18914	0.605914
$231$	0	0
$232$	1.74628	0.114649
$233$	−26.3983	−1.72941	−0.864706	−	0.502278i	$-0.832496\pi$
$233$	−26.3983	−1.72941	−0.864706	+	0.502278i	$0.832496\pi$
$234$	−0.781088	−0.0510613
$235$	−6.42394	−0.419052
$236$	0.446660	0.0290751
$237$	−13.4736	−0.875203
$238$	0	0
$239$	11.4743	0.742208	0.371104	−	0.928591i	$-0.378979\pi$
$239$	11.4743	0.742208	0.371104	+	0.928591i	$0.378979\pi$
$240$	3.80741	0.245768
$241$	20.4375	1.31649	0.658247	−	0.752802i	$-0.271298\pi$
$241$	20.4375	1.31649	0.658247	+	0.752802i	$0.271298\pi$
$242$	2.02288	0.130036
$243$	−1.00000	−0.0641500
$244$	14.7723	0.945698
$245$	0	0
$246$	9.34117	0.595572
$247$	−3.11684	−0.198320
$248$	−0.722976	−0.0459090
$249$	8.62704	0.546717
$250$	2.02288	0.127938
$251$	−17.3205	−1.09326	−0.546629	−	0.837375i	$-0.684089\pi$
$251$	−17.3205	−1.09326	−0.546629	+	0.837375i	$0.684089\pi$
$252$	0	0
$253$	4.54260	0.285591
$254$	9.05912	0.568420
$255$	4.09593	0.256497
$256$	14.4271	0.901691
$257$	8.50130	0.530297	0.265148	−	0.964208i	$-0.414579\pi$
$257$	8.50130	0.530297	0.265148	+	0.964208i	$0.414579\pi$
$258$	−1.33543	−0.0831405
$259$	0	0
$260$	−0.807797	−0.0500974
$261$	9.37765	0.580462
$262$	−3.56521	−0.220259
$263$	−10.9080	−0.672614	−0.336307	−	0.941752i	$-0.609178\pi$
$263$	−10.9080	−0.672614	−0.336307	+	0.941752i	$0.609178\pi$
$264$	−0.186217	−0.0114609
$265$	6.09593	0.374470
$266$	0	0
$267$	−8.66792	−0.530468
$268$	−17.3774	−1.06149
$269$	4.23543	0.258239	0.129119	−	0.991629i	$-0.458785\pi$
$269$	4.23543	0.258239	0.129119	+	0.991629i	$0.458785\pi$
$270$	−2.02288	−0.123109
$271$	14.1843	0.861637	0.430818	−	0.902439i	$-0.358225\pi$
$271$	14.1843	0.861637	0.430818	+	0.902439i	$0.358225\pi$
$272$	15.5949	0.945581
$273$	0	0
$274$	16.9615	1.02468
$275$	1.00000	0.0603023
$276$	−9.50336	−0.572035
$277$	16.0513	0.964426	0.482213	−	0.876054i	$-0.339833\pi$
$277$	16.0513	0.964426	0.482213	+	0.876054i	$0.339833\pi$
$278$	−13.8099	−0.828264
$279$	−3.88243	−0.232435
$280$	0	0
$281$	−21.0857	−1.25787	−0.628934	−	0.777459i	$-0.716508\pi$
$281$	−21.0857	−1.25787	−0.628934	+	0.777459i	$0.716508\pi$
$282$	12.9949	0.773834
$283$	−22.6466	−1.34620	−0.673099	−	0.739552i	$-0.735037\pi$
$283$	−22.6466	−1.34620	−0.673099	+	0.739552i	$0.735037\pi$
$284$	7.17159	0.425556
$285$	−8.07209	−0.478150
$286$	−0.781088	−0.0461867
$287$	0	0
$288$	−8.07439	−0.475788
$289$	−0.223320	−0.0131364
$290$	18.9699	1.11395
$291$	−7.90876	−0.463620
$292$	−23.5016	−1.37533
$293$	19.4124	1.13408	0.567042	−	0.823689i	$-0.308088\pi$
$293$	19.4124	1.13408	0.567042	+	0.823689i	$0.308088\pi$
$294$	0	0
$295$	0.213503	0.0124306
$296$	0.265921	0.0154563
$297$	−1.00000	−0.0580259
$298$	12.2249	0.708169
$299$	−1.75401	−0.101437
$300$	−2.09206	−0.120785
$301$	0	0
$302$	14.0576	0.808926
$303$	−4.04577	−0.232423
$304$	−30.7338	−1.76270
$305$	7.06113	0.404319
$306$	−8.28560	−0.473656
$307$	7.66453	0.437438	0.218719	−	0.975788i	$-0.429812\pi$
$307$	7.66453	0.437438	0.218719	+	0.975788i	$0.429812\pi$
$308$	0	0
$309$	−16.5111	−0.939282
$310$	−7.85370	−0.446060
$311$	24.4709	1.38762	0.693808	−	0.720160i	$-0.255932\pi$
$311$	24.4709	1.38762	0.693808	+	0.720160i	$0.255932\pi$
$312$	0.0719034	0.00407073
$313$	19.3118	1.09157	0.545783	−	0.837926i	$-0.316232\pi$
$313$	19.3118	1.09157	0.545783	+	0.837926i	$0.316232\pi$
$314$	17.7193	0.999961
$315$	0	0
$316$	28.1875	1.58567
$317$	−24.7969	−1.39273	−0.696366	−	0.717687i	$-0.745201\pi$
$317$	−24.7969	−1.39273	−0.696366	+	0.717687i	$0.745201\pi$
$318$	−12.3314	−0.691508
$319$	9.37765	0.525048
$320$	−8.71872	−0.487391
$321$	−8.40010	−0.468848
$322$	0	0
$323$	−33.0628	−1.83966
$324$	2.09206	0.116225
$325$	−0.386126	−0.0214184
$326$	−15.7647	−0.873124
$327$	−12.1473	−0.671745
$328$	−0.859906	−0.0474804
$329$	0	0
$330$	−2.02288	−0.111356
$331$	−20.6976	−1.13764	−0.568822	−	0.822461i	$-0.692601\pi$
$331$	−20.6976	−1.13764	−0.568822	+	0.822461i	$0.692601\pi$
$332$	−18.0482	−0.990526
$333$	1.42801	0.0782546
$334$	37.2490	2.03817
$335$	−8.30637	−0.453826
$336$	0	0
$337$	−10.2257	−0.557031	−0.278515	−	0.960432i	$-0.589842\pi$
$337$	−10.2257	−0.557031	−0.278515	+	0.960432i	$0.589842\pi$
$338$	−25.9959	−1.41399
$339$	−15.8926	−0.863168
$340$	−8.56892	−0.464715
$341$	−3.88243	−0.210245
$342$	16.3289	0.882966
$343$	0	0
$344$	0.122934	0.00662815
$345$	−4.54260	−0.244565
$346$	−29.4869	−1.58523
$347$	3.80085	0.204040	0.102020	−	0.994782i	$-0.467469\pi$
$347$	3.80085	0.204040	0.102020	+	0.994782i	$0.467469\pi$
$348$	−19.6186	−1.05167
$349$	29.3034	1.56857	0.784287	−	0.620398i	$-0.213029\pi$
$349$	29.3034	1.56857	0.784287	+	0.620398i	$0.213029\pi$
$350$	0	0
$351$	0.386126	0.0206099
$352$	−8.07439	−0.430366
$353$	5.86520	0.312173	0.156087	−	0.987743i	$-0.450112\pi$
$353$	5.86520	0.312173	0.156087	+	0.987743i	$0.450112\pi$
$354$	−0.431892	−0.0229548
$355$	3.42801	0.181940
$356$	18.1338	0.961088
$357$	0	0
$358$	34.4067	1.81845
$359$	−26.2739	−1.38668	−0.693342	−	0.720608i	$-0.743863\pi$
$359$	−26.2739	−1.38668	−0.693342	+	0.720608i	$0.743863\pi$
$360$	0.186217	0.00981452
$361$	46.1587	2.42940
$362$	4.57469	0.240441
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	−11.2338	−0.588002
$366$	−14.2838	−0.746629
$367$	−33.0303	−1.72417	−0.862084	−	0.506766i	$-0.830841\pi$
$367$	−33.0303	−1.72417	−0.862084	+	0.506766i	$0.830841\pi$
$368$	−17.2955	−0.901593
$369$	−4.61775	−0.240391
$370$	2.88870	0.150176
$371$	0	0
$372$	8.12226	0.421120
$373$	33.2579	1.72203	0.861014	−	0.508580i	$-0.169830\pi$
$373$	33.2579	1.72203	0.861014	+	0.508580i	$0.169830\pi$
$374$	−8.28560	−0.428438
$375$	−1.00000	−0.0516398
$376$	−1.19625	−0.0616919
$377$	−3.62095	−0.186489
$378$	0	0
$379$	0.631421	0.0324339	0.0162170	−	0.999868i	$-0.494838\pi$
$379$	0.631421	0.0324339	0.0162170	+	0.999868i	$0.494838\pi$
$380$	16.8873	0.866298
$381$	−4.47832	−0.229431
$382$	40.3326	2.06359
$383$	1.16240	0.0593958	0.0296979	−	0.999559i	$-0.490545\pi$
$383$	1.16240	0.0593958	0.0296979	+	0.999559i	$0.490545\pi$
$384$	1.48816	0.0759424
$385$	0	0
$386$	−28.1935	−1.43501
$387$	0.660164	0.0335580
$388$	16.5456	0.839974
$389$	29.6452	1.50307	0.751534	−	0.659694i	$-0.229314\pi$
$389$	29.6452	1.50307	0.751534	+	0.659694i	$0.229314\pi$
$390$	0.781088	0.0395519
$391$	−18.6062	−0.940955
$392$	0	0
$393$	1.76244	0.0889033
$394$	−38.0649	−1.91768
$395$	13.4736	0.677930
$396$	2.09206	0.105130
$397$	−2.60004	−0.130492	−0.0652462	−	0.997869i	$-0.520783\pi$
$397$	−2.60004	−0.130492	−0.0652462	+	0.997869i	$0.520783\pi$
$398$	−24.5219	−1.22917
$399$	0	0
$400$	−3.80741	−0.190371
$401$	8.15274	0.407128	0.203564	−	0.979062i	$-0.434747\pi$
$401$	8.15274	0.407128	0.203564	+	0.979062i	$0.434747\pi$
$402$	16.8028	0.838048
$403$	1.49911	0.0746759
$404$	8.46397	0.421098
$405$	1.00000	0.0496904
$406$	0	0
$407$	1.42801	0.0707840
$408$	0.762734	0.0377610
$409$	−24.7460	−1.22361	−0.611805	−	0.791009i	$-0.709556\pi$
$409$	−24.7460	−1.22361	−0.611805	+	0.791009i	$0.709556\pi$
$410$	−9.34117	−0.461328
$411$	−8.38481	−0.413592
$412$	34.5421	1.70177
$413$	0	0
$414$	9.18914	0.451621
$415$	−8.62704	−0.423485
$416$	3.11773	0.152859
$417$	6.82685	0.334312
$418$	16.3289	0.798673
$419$	−18.8925	−0.922961	−0.461480	−	0.887150i	$-0.652682\pi$
$419$	−18.8925	−0.922961	−0.461480	+	0.887150i	$0.652682\pi$
$420$	0	0
$421$	−35.4963	−1.72999	−0.864993	−	0.501784i	$-0.832677\pi$
$421$	−35.4963	−1.72999	−0.864993	+	0.501784i	$0.832677\pi$
$422$	3.12789	0.152263
$423$	−6.42394	−0.312343
$424$	1.13517	0.0551287
$425$	−4.09593	−0.198682
$426$	−6.93447	−0.335976
$427$	0	0
$428$	17.5735	0.849446
$429$	0.386126	0.0186423
$430$	1.33543	0.0644003
$431$	17.8390	0.859275	0.429637	−	0.903002i	$-0.358641\pi$
$431$	17.8390	0.859275	0.429637	+	0.903002i	$0.358641\pi$
$432$	3.80741	0.183184
$433$	−16.6085	−0.798153	−0.399077	−	0.916918i	$-0.630669\pi$
$433$	−16.6085	−0.798153	−0.399077	+	0.916918i	$0.630669\pi$
$434$	0	0
$435$	−9.37765	−0.449624
$436$	25.4127	1.21705
$437$	36.6683	1.75408
$438$	22.7246	1.08582
$439$	27.5580	1.31527	0.657635	−	0.753337i	$-0.271557\pi$
$439$	27.5580	1.31527	0.657635	+	0.753337i	$0.271557\pi$
$440$	0.186217	0.00887757
$441$	0	0
$442$	3.19928	0.152174
$443$	7.41428	0.352263	0.176132	−	0.984367i	$-0.443642\pi$
$443$	7.41428	0.352263	0.176132	+	0.984367i	$0.443642\pi$
$444$	−2.98748	−0.141780
$445$	8.66792	0.410899
$446$	−11.5646	−0.547600
$447$	−6.04330	−0.285838
$448$	0	0
$449$	−33.2999	−1.57152	−0.785760	−	0.618531i	$-0.787728\pi$
$449$	−33.2999	−1.57152	−0.785760	+	0.618531i	$0.787728\pi$
$450$	2.02288	0.0953596
$451$	−4.61775	−0.217442
$452$	33.2482	1.56386
$453$	−6.94931	−0.326507
$454$	35.1579	1.65004
$455$	0	0
$456$	−1.50316	−0.0703921
$457$	−14.8424	−0.694296	−0.347148	−	0.937810i	$-0.612850\pi$
$457$	−14.8424	−0.694296	−0.347148	+	0.937810i	$0.612850\pi$
$458$	−38.8728	−1.81641
$459$	4.09593	0.191182
$460$	9.50336	0.443096
$461$	−10.5428	−0.491028	−0.245514	−	0.969393i	$-0.578957\pi$
$461$	−10.5428	−0.491028	−0.245514	+	0.969393i	$0.578957\pi$
$462$	0	0
$463$	26.0538	1.21082	0.605412	−	0.795912i	$-0.293008\pi$
$463$	26.0538	1.21082	0.605412	+	0.795912i	$0.293008\pi$
$464$	−35.7046	−1.65754
$465$	3.88243	0.180043
$466$	−53.4008	−2.47374
$467$	−37.2755	−1.72490	−0.862452	−	0.506140i	$-0.831072\pi$
$467$	−37.2755	−1.72490	−0.862452	+	0.506140i	$0.831072\pi$
$468$	−0.807797	−0.0373404
$469$	0	0
$470$	−12.9949	−0.599409
$471$	−8.75945	−0.403614
$472$	0.0397580	0.00183001
$473$	0.660164	0.0303544
$474$	−27.2555	−1.25189
$475$	8.07209	0.370373
$476$	0	0
$477$	6.09593	0.279114
$478$	23.2111	1.06165
$479$	−1.32433	−0.0605103	−0.0302551	−	0.999542i	$-0.509632\pi$
$479$	−1.32433	−0.0605103	−0.0302551	+	0.999542i	$0.509632\pi$
$480$	8.07439	0.368544
$481$	−0.551393	−0.0251413
$482$	41.3426	1.88310
$483$	0	0
$484$	2.09206	0.0950934
$485$	7.90876	0.359118
$486$	−2.02288	−0.0917598
$487$	27.9293	1.26560	0.632800	−	0.774316i	$-0.281906\pi$
$487$	27.9293	1.26560	0.632800	+	0.774316i	$0.281906\pi$
$488$	1.31491	0.0595230
$489$	7.79317	0.352419
$490$	0	0
$491$	33.3568	1.50537	0.752687	−	0.658379i	$-0.228758\pi$
$491$	33.3568	1.50537	0.752687	+	0.658379i	$0.228758\pi$
$492$	9.66060	0.435533
$493$	−38.4102	−1.72991
$494$	−6.30501	−0.283676
$495$	1.00000	0.0449467
$496$	14.7820	0.663733
$497$	0	0
$498$	17.4515	0.782020
$499$	1.26929	0.0568212	0.0284106	−	0.999596i	$-0.490955\pi$
$499$	1.26929	0.0568212	0.0284106	+	0.999596i	$0.490955\pi$
$500$	2.09206	0.0935596
$501$	−18.4138	−0.822668
$502$	−35.0373	−1.56379
$503$	27.8290	1.24083	0.620417	−	0.784272i	$-0.286963\pi$
$503$	27.8290	1.24083	0.620417	+	0.784272i	$0.286963\pi$
$504$	0	0
$505$	4.04577	0.180034
$506$	9.18914	0.408507
$507$	12.8509	0.570729
$508$	9.36890	0.415678
$509$	11.7936	0.522740	0.261370	−	0.965239i	$-0.415826\pi$
$509$	11.7936	0.522740	0.261370	+	0.965239i	$0.415826\pi$
$510$	8.28560	0.366892
$511$	0	0
$512$	32.1606	1.42131
$513$	−8.07209	−0.356392
$514$	17.1971	0.758533
$515$	16.5111	0.727565
$516$	−1.38110	−0.0607995
$517$	−6.42394	−0.282525
$518$	0	0
$519$	14.5767	0.639845
$520$	−0.0719034	−0.00315317
$521$	11.6100	0.508643	0.254321	−	0.967120i	$-0.418148\pi$
$521$	11.6100	0.508643	0.254321	+	0.967120i	$0.418148\pi$
$522$	18.9699	0.830290
$523$	−29.8093	−1.30347	−0.651735	−	0.758446i	$-0.725959\pi$
$523$	−29.8093	−1.30347	−0.651735	+	0.758446i	$0.725959\pi$
$524$	−3.68712	−0.161073
$525$	0	0
$526$	−22.0656	−0.962104
$527$	15.9022	0.692710
$528$	3.80741	0.165696
$529$	−2.36483	−0.102819
$530$	12.3314	0.535640
$531$	0.213503	0.00926525
$532$	0	0
$533$	1.78303	0.0772318
$534$	−17.5342	−0.758779
$535$	8.40010	0.363168
$536$	−1.54679	−0.0668112
$537$	−17.0088	−0.733982
$538$	8.56777	0.369383
$539$	0	0
$540$	−2.09206	−0.0900277
$541$	−20.0404	−0.861602	−0.430801	−	0.902447i	$-0.641769\pi$
$541$	−20.0404	−0.861602	−0.430801	+	0.902447i	$0.641769\pi$
$542$	28.6932	1.23248
$543$	−2.26147	−0.0970491
$544$	33.0722	1.41796
$545$	12.1473	0.520331
$546$	0	0
$547$	16.6021	0.709853	0.354927	−	0.934894i	$-0.384506\pi$
$547$	16.6021	0.709853	0.354927	+	0.934894i	$0.384506\pi$
$548$	17.5415	0.749335
$549$	7.06113	0.301362
$550$	2.02288	0.0862560
$551$	75.6973	3.22481
$552$	−0.845910	−0.0360043
$553$	0	0
$554$	32.4698	1.37951
$555$	−1.42801	−0.0606158
$556$	−14.2822	−0.605698
$557$	−31.8949	−1.35143	−0.675715	−	0.737163i	$-0.736165\pi$
$557$	−31.8949	−1.35143	−0.675715	+	0.737163i	$0.736165\pi$
$558$	−7.85370	−0.332474
$559$	−0.254906	−0.0107814
$560$	0	0
$561$	4.09593	0.172930
$562$	−42.6539	−1.79925
$563$	−25.7304	−1.08441	−0.542205	−	0.840247i	$-0.682410\pi$
$563$	−25.7304	−1.08441	−0.542205	+	0.840247i	$0.682410\pi$
$564$	13.4392	0.565894
$565$	15.8926	0.668607
$566$	−45.8114	−1.92560
$567$	0	0
$568$	0.638356	0.0267848
$569$	−5.95472	−0.249635	−0.124817	−	0.992180i	$-0.539834\pi$
$569$	−5.95472	−0.249635	−0.124817	+	0.992180i	$0.539834\pi$
$570$	−16.3289	−0.683942
$571$	−3.18071	−0.133109	−0.0665543	−	0.997783i	$-0.521201\pi$
$571$	−3.18071	−0.133109	−0.0665543	+	0.997783i	$0.521201\pi$
$572$	−0.807797	−0.0337757
$573$	−19.9382	−0.832928
$574$	0	0
$575$	4.54260	0.189439
$576$	−8.71872	−0.363280
$577$	33.7633	1.40558	0.702792	−	0.711396i	$-0.251937\pi$
$577$	33.7633	1.40558	0.702792	+	0.711396i	$0.251937\pi$
$578$	−0.451749	−0.0187903
$579$	13.9373	0.579214
$580$	19.6186	0.814617
$581$	0	0
$582$	−15.9985	−0.663159
$583$	6.09593	0.252468
$584$	−2.09192	−0.0865643
$585$	−0.386126	−0.0159643
$586$	39.2690	1.62219
$587$	−4.98470	−0.205741	−0.102870	−	0.994695i	$-0.532803\pi$
$587$	−4.98470	−0.205741	−0.102870	+	0.994695i	$0.532803\pi$
$588$	0	0
$589$	−31.3393	−1.29132
$590$	0.431892	0.0177807
$591$	18.8172	0.774034
$592$	−5.43704	−0.223461
$593$	12.9571	0.532082	0.266041	−	0.963962i	$-0.414284\pi$
$593$	12.9571	0.532082	0.266041	+	0.963962i	$0.414284\pi$
$594$	−2.02288	−0.0829999
$595$	0	0
$596$	12.6429	0.517874
$597$	12.1223	0.496131
$598$	−3.54816	−0.145095
$599$	15.3357	0.626599	0.313300	−	0.949654i	$-0.398566\pi$
$599$	15.3357	0.626599	0.313300	+	0.949654i	$0.398566\pi$
$600$	−0.186217	−0.00760229
$601$	26.9092	1.09765	0.548825	−	0.835937i	$-0.315075\pi$
$601$	26.9092	1.09765	0.548825	+	0.835937i	$0.315075\pi$
$602$	0	0
$603$	−8.30637	−0.338262
$604$	14.5383	0.591557
$605$	1.00000	0.0406558
$606$	−8.18411	−0.332457
$607$	28.8501	1.17099	0.585494	−	0.810677i	$-0.300901\pi$
$607$	28.8501	1.17099	0.585494	+	0.810677i	$0.300901\pi$
$608$	−65.1772	−2.64329
$609$	0	0
$610$	14.2838	0.578336
$611$	2.48045	0.100348
$612$	−8.56892	−0.346378
$613$	40.2621	1.62617	0.813085	−	0.582145i	$-0.197786\pi$
$613$	40.2621	1.62617	0.813085	+	0.582145i	$0.197786\pi$
$614$	15.5044	0.625708
$615$	4.61775	0.186206
$616$	0	0
$617$	−14.4867	−0.583214	−0.291607	−	0.956538i	$-0.594190\pi$
$617$	−14.4867	−0.583214	−0.291607	+	0.956538i	$0.594190\pi$
$618$	−33.4000	−1.34354
$619$	−45.9202	−1.84569	−0.922843	−	0.385175i	$-0.874141\pi$
$619$	−45.9202	−1.84569	−0.922843	+	0.385175i	$0.874141\pi$
$620$	−8.12226	−0.326198
$621$	−4.54260	−0.182288
$622$	49.5017	1.98484
$623$	0	0
$624$	−1.47014	−0.0588528
$625$	1.00000	0.0400000
$626$	39.0655	1.56137
$627$	−8.07209	−0.322368
$628$	18.3253	0.731258
$629$	−5.84905	−0.233217
$630$	0	0
$631$	−30.7163	−1.22280	−0.611398	−	0.791323i	$-0.709393\pi$
$631$	−30.7163	−1.22280	−0.611398	+	0.791323i	$0.709393\pi$
$632$	2.50902	0.0998033
$633$	−1.54625	−0.0614581
$634$	−50.1612	−1.99216
$635$	4.47832	0.177717
$636$	−12.7530	−0.505691
$637$	0	0
$638$	18.9699	0.751025
$639$	3.42801	0.135610
$640$	−1.48816	−0.0588247
$641$	−6.46243	−0.255251	−0.127625	−	0.991822i	$-0.540735\pi$
$641$	−6.46243	−0.255251	−0.127625	+	0.991822i	$0.540735\pi$
$642$	−16.9924	−0.670637
$643$	−22.4470	−0.885222	−0.442611	−	0.896714i	$-0.645948\pi$
$643$	−22.4470	−0.885222	−0.442611	+	0.896714i	$0.645948\pi$
$644$	0	0
$645$	−0.660164	−0.0259939
$646$	−66.8821	−2.63144
$647$	2.99874	0.117893	0.0589463	−	0.998261i	$-0.481226\pi$
$647$	2.99874	0.117893	0.0589463	+	0.998261i	$0.481226\pi$
$648$	0.186217	0.00731531
$649$	0.213503	0.00838073
$650$	−0.781088	−0.0306368
$651$	0	0
$652$	−16.3037	−0.638504
$653$	−40.1926	−1.57286	−0.786429	−	0.617681i	$-0.788072\pi$
$653$	−40.1926	−1.57286	−0.786429	+	0.617681i	$0.788072\pi$
$654$	−24.5725	−0.960860
$655$	−1.76244	−0.0688642
$656$	17.5817	0.686450
$657$	−11.2338	−0.438271
$658$	0	0
$659$	−32.5347	−1.26737	−0.633687	−	0.773590i	$-0.718459\pi$
$659$	−32.5347	−1.26737	−0.633687	+	0.773590i	$0.718459\pi$
$660$	−2.09206	−0.0814331
$661$	−13.5625	−0.527518	−0.263759	−	0.964589i	$-0.584962\pi$
$661$	−13.5625	−0.527518	−0.263759	+	0.964589i	$0.584962\pi$
$662$	−41.8688	−1.62728
$663$	−1.58155	−0.0614222
$664$	−1.60651	−0.0623445
$665$	0	0
$666$	2.88870	0.111935
$667$	42.5989	1.64944
$668$	38.5227	1.49049
$669$	5.71689	0.221028
$670$	−16.8028	−0.649150
$671$	7.06113	0.272592
$672$	0	0
$673$	−40.9176	−1.57726	−0.788629	−	0.614870i	$-0.789209\pi$
$673$	−40.9176	−1.57726	−0.788629	+	0.614870i	$0.789209\pi$
$674$	−20.6854	−0.796774
$675$	−1.00000	−0.0384900
$676$	−26.8848	−1.03403
$677$	−8.49383	−0.326445	−0.163222	−	0.986589i	$-0.552189\pi$
$677$	−8.49383	−0.326445	−0.163222	+	0.986589i	$0.552189\pi$
$678$	−32.1489	−1.23467
$679$	0	0
$680$	−0.762734	−0.0292495
$681$	−17.3801	−0.666006
$682$	−7.85370	−0.300734
$683$	1.38248	0.0528989	0.0264495	−	0.999650i	$-0.491580\pi$
$683$	1.38248	0.0528989	0.0264495	+	0.999650i	$0.491580\pi$
$684$	16.8873	0.645701
$685$	8.38481	0.320367
$686$	0	0
$687$	19.2165	0.733157
$688$	−2.51352	−0.0958269
$689$	−2.35380	−0.0896726
$690$	−9.18914	−0.349825
$691$	31.7435	1.20758	0.603790	−	0.797143i	$-0.293657\pi$
$691$	31.7435	1.20758	0.603790	+	0.797143i	$0.293657\pi$
$692$	−30.4952	−1.15925
$693$	0	0
$694$	7.68868	0.291858
$695$	−6.82685	−0.258957
$696$	−1.74628	−0.0661926
$697$	18.9140	0.716419
$698$	59.2773	2.24368
$699$	26.3983	0.998477
$700$	0	0
$701$	50.6871	1.91442	0.957212	−	0.289387i	$-0.0934514\pi$
$701$	50.6871	1.91442	0.957212	+	0.289387i	$0.0934514\pi$
$702$	0.781088	0.0294803
$703$	11.5271	0.434751
$704$	−8.71872	−0.328599
$705$	6.42394	0.241940
$706$	11.8646	0.446531
$707$	0	0
$708$	−0.446660	−0.0167865
$709$	13.0026	0.488323	0.244161	−	0.969735i	$-0.421487\pi$
$709$	13.0026	0.488323	0.244161	+	0.969735i	$0.421487\pi$
$710$	6.93447	0.260246
$711$	13.4736	0.505299
$712$	1.61412	0.0604916
$713$	−17.6363	−0.660485
$714$	0	0
$715$	−0.386126	−0.0144403
$716$	35.5833	1.32981
$717$	−11.4743	−0.428514
$718$	−53.1491	−1.98351
$719$	−21.1857	−0.790092	−0.395046	−	0.918661i	$-0.629271\pi$
$719$	−21.1857	−0.790092	−0.395046	+	0.918661i	$0.629271\pi$
$720$	−3.80741	−0.141894
$721$	0	0
$722$	93.3736	3.47501
$723$	−20.4375	−0.760078
$724$	4.73113	0.175831
$725$	9.37765	0.348277
$726$	−2.02288	−0.0750762
$727$	22.5182	0.835153	0.417577	−	0.908642i	$-0.362880\pi$
$727$	22.5182	0.835153	0.417577	+	0.908642i	$0.362880\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−22.7246	−0.841074
$731$	−2.70399	−0.100011
$732$	−14.7723	−0.545999
$733$	−36.7235	−1.35641	−0.678207	−	0.734870i	$-0.737243\pi$
$733$	−36.7235	−1.35641	−0.678207	+	0.734870i	$0.737243\pi$
$734$	−66.8164	−2.46624
$735$	0	0
$736$	−36.6787	−1.35199
$737$	−8.30637	−0.305969
$738$	−9.34117	−0.343853
$739$	−36.6287	−1.34741	−0.673704	−	0.739002i	$-0.735298\pi$
$739$	−36.6287	−1.34741	−0.673704	+	0.739002i	$0.735298\pi$
$740$	2.98748	0.109822
$741$	3.11684	0.114500
$742$	0	0
$743$	−36.9561	−1.35579	−0.677894	−	0.735160i	$-0.737107\pi$
$743$	−36.9561	−1.35579	−0.677894	+	0.735160i	$0.737107\pi$
$744$	0.722976	0.0265056
$745$	6.04330	0.221410
$746$	67.2768	2.46318
$747$	−8.62704	−0.315647
$748$	−8.56892	−0.313311
$749$	0	0
$750$	−2.02288	−0.0738652
$751$	−47.1515	−1.72058	−0.860292	−	0.509802i	$-0.829719\pi$
$751$	−47.1515	−1.72058	−0.860292	+	0.509802i	$0.829719\pi$
$752$	24.4586	0.891914
$753$	17.3205	0.631193
$754$	−7.32477	−0.266752
$755$	6.94931	0.252911
$756$	0	0
$757$	−16.1523	−0.587066	−0.293533	−	0.955949i	$-0.594831\pi$
$757$	−16.1523	−0.587066	−0.293533	+	0.955949i	$0.594831\pi$
$758$	1.27729	0.0463933
$759$	−4.54260	−0.164886
$760$	1.50316	0.0545255
$761$	15.8451	0.574384	0.287192	−	0.957873i	$-0.407278\pi$
$761$	15.8451	0.574384	0.287192	+	0.957873i	$0.407278\pi$
$762$	−9.05912	−0.328177
$763$	0	0
$764$	41.7117	1.50908
$765$	−4.09593	−0.148089
$766$	2.35140	0.0849594
$767$	−0.0824391	−0.00297670
$768$	−14.4271	−0.520591
$769$	−52.2077	−1.88266	−0.941328	−	0.337492i	$-0.890421\pi$
$769$	−52.2077	−1.88266	−0.941328	+	0.337492i	$0.890421\pi$
$770$	0	0
$771$	−8.50130	−0.306167
$772$	−29.1576	−1.04940
$773$	−6.63128	−0.238510	−0.119255	−	0.992864i	$-0.538051\pi$
$773$	−6.63128	−0.238510	−0.119255	+	0.992864i	$0.538051\pi$
$774$	1.33543	0.0480012
$775$	−3.88243	−0.139461
$776$	1.47275	0.0528686
$777$	0	0
$778$	59.9687	2.14998
$779$	−37.2749	−1.33551
$780$	0.807797	0.0289238
$781$	3.42801	0.122664
$782$	−37.6381	−1.34594
$783$	−9.37765	−0.335130
$784$	0	0
$785$	8.75945	0.312638
$786$	3.56521	0.127167
$787$	9.70580	0.345974	0.172987	−	0.984924i	$-0.444658\pi$
$787$	9.70580	0.345974	0.172987	+	0.984924i	$0.444658\pi$
$788$	−39.3665	−1.40237
$789$	10.9080	0.388334
$790$	27.2555	0.969707
$791$	0	0
$792$	0.186217	0.00661695
$793$	−2.72649	−0.0968204
$794$	−5.25958	−0.186655
$795$	−6.09593	−0.216201
$796$	−25.3604	−0.898877
$797$	22.6472	0.802205	0.401103	−	0.916033i	$-0.368627\pi$
$797$	22.6472	0.802205	0.401103	+	0.916033i	$0.368627\pi$
$798$	0	0
$799$	26.3120	0.930853
$800$	−8.07439	−0.285473
$801$	8.66792	0.306266
$802$	16.4920	0.582354
$803$	−11.2338	−0.396431
$804$	17.3774	0.612853
$805$	0	0
$806$	3.03252	0.106816
$807$	−4.23543	−0.149094
$808$	0.753392	0.0265042
$809$	−52.5485	−1.84751	−0.923754	−	0.382986i	$-0.874896\pi$
$809$	−52.5485	−1.84751	−0.923754	+	0.382986i	$0.874896\pi$
$810$	2.02288	0.0710769
$811$	−14.8262	−0.520619	−0.260309	−	0.965525i	$-0.583825\pi$
$811$	−14.8262	−0.520619	−0.260309	+	0.965525i	$0.583825\pi$
$812$	0	0
$813$	−14.1843	−0.497466
$814$	2.88870	0.101249
$815$	−7.79317	−0.272983
$816$	−15.5949	−0.545931
$817$	5.32890	0.186435
$818$	−50.0582	−1.75024
$819$	0	0
$820$	−9.66060	−0.337363
$821$	30.8277	1.07590	0.537948	−	0.842978i	$-0.319200\pi$
$821$	30.8277	1.07590	0.537948	+	0.842978i	$0.319200\pi$
$822$	−16.9615	−0.591600
$823$	−13.5865	−0.473596	−0.236798	−	0.971559i	$-0.576098\pi$
$823$	−13.5865	−0.473596	−0.236798	+	0.971559i	$0.576098\pi$
$824$	3.07465	0.107110
$825$	−1.00000	−0.0348155
$826$	0	0
$827$	−23.7377	−0.825440	−0.412720	−	0.910858i	$-0.635421\pi$
$827$	−23.7377	−0.825440	−0.412720	+	0.910858i	$0.635421\pi$
$828$	9.50336	0.330265
$829$	−48.8458	−1.69648	−0.848242	−	0.529609i	$-0.822339\pi$
$829$	−48.8458	−1.69648	−0.848242	+	0.529609i	$0.822339\pi$
$830$	−17.4515	−0.605750
$831$	−16.0513	−0.556812
$832$	3.36652	0.116713
$833$	0	0
$834$	13.8099	0.478199
$835$	18.4138	0.637236
$836$	16.8873	0.584058
$837$	3.88243	0.134196
$838$	−38.2174	−1.32020
$839$	−9.14463	−0.315708	−0.157854	−	0.987462i	$-0.550457\pi$
$839$	−9.14463	−0.315708	−0.157854	+	0.987462i	$0.550457\pi$
$840$	0	0
$841$	58.9404	2.03243
$842$	−71.8049	−2.47456
$843$	21.0857	0.726230
$844$	3.23485	0.111348
$845$	−12.8509	−0.442085
$846$	−12.9949	−0.446773
$847$	0	0
$848$	−23.2098	−0.797026
$849$	22.6466	0.777228
$850$	−8.28560	−0.284194
$851$	6.48688	0.222367
$852$	−7.17159	−0.245695
$853$	17.9616	0.614995	0.307498	−	0.951549i	$-0.400508\pi$
$853$	17.9616	0.614995	0.307498	+	0.951549i	$0.400508\pi$
$854$	0	0
$855$	8.07209	0.276060
$856$	1.56424	0.0534648
$857$	39.2608	1.34112	0.670562	−	0.741854i	$-0.266053\pi$
$857$	39.2608	1.34112	0.670562	+	0.741854i	$0.266053\pi$
$858$	0.781088	0.0266659
$859$	−1.66034	−0.0566501	−0.0283251	−	0.999599i	$-0.509017\pi$
$859$	−1.66034	−0.0566501	−0.0283251	+	0.999599i	$0.509017\pi$
$860$	1.38110	0.0470951
$861$	0	0
$862$	36.0862	1.22910
$863$	−35.5245	−1.20927	−0.604634	−	0.796503i	$-0.706681\pi$
$863$	−35.5245	−1.20927	−0.604634	+	0.796503i	$0.706681\pi$
$864$	8.07439	0.274696
$865$	−14.5767	−0.495622
$866$	−33.5970	−1.14167
$867$	0.223320	0.00758433
$868$	0	0
$869$	13.4736	0.457060
$870$	−18.9699	−0.643140
$871$	3.20731	0.108675
$872$	2.26203	0.0766020
$873$	7.90876	0.267671
$874$	74.1756	2.50903
$875$	0	0
$876$	23.5016	0.794047
$877$	−33.0601	−1.11636	−0.558181	−	0.829719i	$-0.688500\pi$
$877$	−33.0601	−1.11636	−0.558181	+	0.829719i	$0.688500\pi$
$878$	55.7465	1.88135
$879$	−19.4124	−0.654764
$880$	−3.80741	−0.128348
$881$	−16.2149	−0.546293	−0.273147	−	0.961972i	$-0.588064\pi$
$881$	−16.2149	−0.546293	−0.273147	+	0.961972i	$0.588064\pi$
$882$	0	0
$883$	22.5135	0.757638	0.378819	−	0.925471i	$-0.376330\pi$
$883$	22.5135	0.757638	0.378819	+	0.925471i	$0.376330\pi$
$884$	3.30868	0.111283
$885$	−0.213503	−0.00717683
$886$	14.9982	0.503875
$887$	−16.0239	−0.538031	−0.269016	−	0.963136i	$-0.586698\pi$
$887$	−16.0239	−0.538031	−0.269016	+	0.963136i	$0.586698\pi$
$888$	−0.265921	−0.00892372
$889$	0	0
$890$	17.5342	0.587747
$891$	1.00000	0.0335013
$892$	−11.9600	−0.400452
$893$	−51.8547	−1.73525
$894$	−12.2249	−0.408862
$895$	17.0088	0.568540
$896$	0	0
$897$	1.75401	0.0585648
$898$	−67.3618	−2.24789
$899$	−36.4081	−1.21428
$900$	2.09206	0.0697352
$901$	−24.9685	−0.831823
$902$	−9.34117	−0.311027
$903$	0	0
$904$	2.95948	0.0984308
$905$	2.26147	0.0751739
$906$	−14.0576	−0.467034
$907$	−3.65837	−0.121474	−0.0607371	−	0.998154i	$-0.519345\pi$
$907$	−3.65837	−0.121474	−0.0607371	+	0.998154i	$0.519345\pi$
$908$	36.3601	1.20665
$909$	4.04577	0.134190
$910$	0	0
$911$	−32.9314	−1.09107	−0.545534	−	0.838089i	$-0.683673\pi$
$911$	−32.9314	−1.09107	−0.545534	+	0.838089i	$0.683673\pi$
$912$	30.7338	1.01770
$913$	−8.62704	−0.285513
$914$	−30.0244	−0.993117
$915$	−7.06113	−0.233434
$916$	−40.2021	−1.32831
$917$	0	0
$918$	8.28560	0.273465
$919$	16.9274	0.558383	0.279191	−	0.960235i	$-0.409934\pi$
$919$	16.9274	0.558383	0.279191	+	0.960235i	$0.409934\pi$
$920$	0.845910	0.0278888
$921$	−7.66453	−0.252555
$922$	−21.3269	−0.702363
$923$	−1.32364	−0.0435683
$924$	0	0
$925$	1.42801	0.0469528
$926$	52.7039	1.73196
$927$	16.5111	0.542295
$928$	−75.7188	−2.48559
$929$	48.9342	1.60548	0.802740	−	0.596329i	$-0.203375\pi$
$929$	48.9342	1.60548	0.802740	+	0.596329i	$0.203375\pi$
$930$	7.85370	0.257533
$931$	0	0
$932$	−55.2268	−1.80901
$933$	−24.4709	−0.801140
$934$	−75.4039	−2.46729
$935$	−4.09593	−0.133951
$936$	−0.0719034	−0.00235024
$937$	18.1950	0.594405	0.297202	−	0.954815i	$-0.403946\pi$
$937$	18.1950	0.594405	0.297202	+	0.954815i	$0.403946\pi$
$938$	0	0
$939$	−19.3118	−0.630216
$940$	−13.4392	−0.438340
$941$	−39.0129	−1.27178	−0.635892	−	0.771778i	$-0.719368\pi$
$941$	−39.0129	−1.27178	−0.635892	+	0.771778i	$0.719368\pi$
$942$	−17.7193	−0.577328
$943$	−20.9766	−0.683092
$944$	−0.812895	−0.0264575
$945$	0	0
$946$	1.33543	0.0434187
$947$	1.69096	0.0549488	0.0274744	−	0.999623i	$-0.491254\pi$
$947$	1.69096	0.0549488	0.0274744	+	0.999623i	$0.491254\pi$
$948$	−28.1875	−0.915487
$949$	4.33764	0.140806
$950$	16.3289	0.529779
$951$	24.7969	0.804094
$952$	0	0
$953$	31.7216	1.02756	0.513782	−	0.857921i	$-0.328244\pi$
$953$	31.7216	1.02756	0.513782	+	0.857921i	$0.328244\pi$
$954$	12.3314	0.399243
$955$	19.9382	0.645184
$956$	24.0048	0.776370
$957$	−9.37765	−0.303136
$958$	−2.67897	−0.0865535
$959$	0	0
$960$	8.71872	0.281395
$961$	−15.9267	−0.513765
$962$	−1.11540	−0.0359620
$963$	8.40010	0.270689
$964$	42.7563	1.37709
$965$	−13.9373	−0.448657
$966$	0	0
$967$	−3.02249	−0.0971968	−0.0485984	−	0.998818i	$-0.515475\pi$
$967$	−3.02249	−0.0971968	−0.0485984	+	0.998818i	$0.515475\pi$
$968$	0.186217	0.00598525
$969$	33.0628	1.06213
$970$	15.9985	0.513681
$971$	31.1369	0.999231	0.499616	−	0.866247i	$-0.333475\pi$
$971$	31.1369	0.999231	0.499616	+	0.866247i	$0.333475\pi$
$972$	−2.09206	−0.0671027
$973$	0	0
$974$	56.4978	1.81031
$975$	0.386126	0.0123659
$976$	−26.8847	−0.860557
$977$	25.7675	0.824376	0.412188	−	0.911099i	$-0.364765\pi$
$977$	25.7675	0.824376	0.412188	+	0.911099i	$0.364765\pi$
$978$	15.7647	0.504099
$979$	8.66792	0.277028
$980$	0	0
$981$	12.1473	0.387832
$982$	67.4770	2.15328
$983$	−0.900491	−0.0287212	−0.0143606	−	0.999897i	$-0.504571\pi$
$983$	−0.900491	−0.0287212	−0.0143606	+	0.999897i	$0.504571\pi$
$984$	0.859906	0.0274128
$985$	−18.8172	−0.599564
$986$	−77.6994	−2.47445
$987$	0	0
$988$	−6.52061	−0.207448
$989$	2.99886	0.0953581
$990$	2.02288	0.0642914
$991$	5.77958	0.183595	0.0917973	−	0.995778i	$-0.470739\pi$
$991$	5.77958	0.183595	0.0917973	+	0.995778i	$0.470739\pi$
$992$	31.3483	0.995308
$993$	20.6976	0.656819
$994$	0	0
$995$	−12.1223	−0.384302
$996$	18.0482	0.571881
$997$	−31.6055	−1.00096	−0.500478	−	0.865749i	$-0.666842\pi$
$997$	−31.6055	−1.00096	−0.500478	+	0.865749i	$0.666842\pi$
$998$	2.56762	0.0812767
$999$	−1.42801	−0.0451803

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8085.2.a.cb.1.6	✓	7
7.6	odd	2		8085.2.a.cd.1.6	yes	7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8085.2.a.cb.1.6	✓	7	1.1	even	1	trivial
8085.2.a.cd.1.6	yes	7	7.6	odd	2

Overview	Random
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Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8085.a (trivial)

\(f(q)\)	\(=\)	\(q+2.02288 q^{2} -1.00000 q^{3} +2.09206 q^{4} +1.00000 q^{5} -2.02288 q^{6} +0.186217 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.02288 q^{2} -1.00000 q^{3} +2.09206 q^{4} +1.00000 q^{5} -2.02288 q^{6} +0.186217 q^{8} +1.00000 q^{9} +2.02288 q^{10} +1.00000 q^{11} -2.09206 q^{12} -0.386126 q^{13} -1.00000 q^{15} -3.80741 q^{16} -4.09593 q^{17} +2.02288 q^{18} +8.07209 q^{19} +2.09206 q^{20} +2.02288 q^{22} +4.54260 q^{23} -0.186217 q^{24} +1.00000 q^{25} -0.781088 q^{26} -1.00000 q^{27} +9.37765 q^{29} -2.02288 q^{30} -3.88243 q^{31} -8.07439 q^{32} -1.00000 q^{33} -8.28560 q^{34} +2.09206 q^{36} +1.42801 q^{37} +16.3289 q^{38} +0.386126 q^{39} +0.186217 q^{40} -4.61775 q^{41} +0.660164 q^{43} +2.09206 q^{44} +1.00000 q^{45} +9.18914 q^{46} -6.42394 q^{47} +3.80741 q^{48} +2.02288 q^{50} +4.09593 q^{51} -0.807797 q^{52} +6.09593 q^{53} -2.02288 q^{54} +1.00000 q^{55} -8.07209 q^{57} +18.9699 q^{58} +0.213503 q^{59} -2.09206 q^{60} +7.06113 q^{61} -7.85370 q^{62} -8.71872 q^{64} -0.386126 q^{65} -2.02288 q^{66} -8.30637 q^{67} -8.56892 q^{68} -4.54260 q^{69} +3.42801 q^{71} +0.186217 q^{72} -11.2338 q^{73} +2.88870 q^{74} -1.00000 q^{75} +16.8873 q^{76} +0.781088 q^{78} +13.4736 q^{79} -3.80741 q^{80} +1.00000 q^{81} -9.34117 q^{82} -8.62704 q^{83} -4.09593 q^{85} +1.33543 q^{86} -9.37765 q^{87} +0.186217 q^{88} +8.66792 q^{89} +2.02288 q^{90} +9.50336 q^{92} +3.88243 q^{93} -12.9949 q^{94} +8.07209 q^{95} +8.07439 q^{96} +7.90876 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 7 q^{3} + 10 q^{4} + 7 q^{5} + 7 q^{9}+O(q^{10}) \) 7 * q - 7 * q^3 + 10 * q^4 + 7 * q^5 + 7 * q^9	\( 7 q - 7 q^{3} + 10 q^{4} + 7 q^{5} + 7 q^{9} + 7 q^{11} - 10 q^{12} - 4 q^{13} - 7 q^{15} + 24 q^{16} + 7 q^{17} - 3 q^{19} + 10 q^{20} + 13 q^{23} + 7 q^{25} + 14 q^{26} - 7 q^{27} + 7 q^{29} + 14 q^{31} - 10 q^{32} - 7 q^{33} - 4 q^{34} + 10 q^{36} + 14 q^{37} + 20 q^{38} + 4 q^{39} + 27 q^{43} + 10 q^{44} + 7 q^{45} - 6 q^{46} - 10 q^{47} - 24 q^{48} - 7 q^{51} - 30 q^{52} + 7 q^{53} + 7 q^{55} + 3 q^{57} - 4 q^{58} + 7 q^{59} - 10 q^{60} - 15 q^{61} - 28 q^{62} + 68 q^{64} - 4 q^{65} + 18 q^{67} - 10 q^{68} - 13 q^{69} + 28 q^{71} - 10 q^{73} + 30 q^{74} - 7 q^{75} - 54 q^{76} - 14 q^{78} + 24 q^{80} + 7 q^{81} - 18 q^{82} - 11 q^{83} + 7 q^{85} - 34 q^{86} - 7 q^{87} + 21 q^{89} + 62 q^{92} - 14 q^{93} + 52 q^{94} - 3 q^{95} + 10 q^{96} - 17 q^{97} + 7 q^{99}+O(q^{100}) \) 7 * q - 7 * q^3 + 10 * q^4 + 7 * q^5 + 7 * q^9 + 7 * q^11 - 10 * q^12 - 4 * q^13 - 7 * q^15 + 24 * q^16 + 7 * q^17 - 3 * q^19 + 10 * q^20 + 13 * q^23 + 7 * q^25 + 14 * q^26 - 7 * q^27 + 7 * q^29 + 14 * q^31 - 10 * q^32 - 7 * q^33 - 4 * q^34 + 10 * q^36 + 14 * q^37 + 20 * q^38 + 4 * q^39 + 27 * q^43 + 10 * q^44 + 7 * q^45 - 6 * q^46 - 10 * q^47 - 24 * q^48 - 7 * q^51 - 30 * q^52 + 7 * q^53 + 7 * q^55 + 3 * q^57 - 4 * q^58 + 7 * q^59 - 10 * q^60 - 15 * q^61 - 28 * q^62 + 68 * q^64 - 4 * q^65 + 18 * q^67 - 10 * q^68 - 13 * q^69 + 28 * q^71 - 10 * q^73 + 30 * q^74 - 7 * q^75 - 54 * q^76 - 14 * q^78 + 24 * q^80 + 7 * q^81 - 18 * q^82 - 11 * q^83 + 7 * q^85 - 34 * q^86 - 7 * q^87 + 21 * q^89 + 62 * q^92 - 14 * q^93 + 52 * q^94 - 3 * q^95 + 10 * q^96 - 17 * q^97 + 7 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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