LMFDB - Embedded newform 8085.2.a.cn.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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 16x^{8} + 84x^{6} - 2x^{5} - 169x^{4} + 8x^{3} + 128x^{2} - 4x - 32 $ x^10 - 16x^8 + 84x^6 - 2x^5 - 169x^4 + 8x^3 + 128x^2 - 4*x - 32
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 1155)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.743153$ 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)

$f(q)$	$=$	$q+0.743153 q^{2} +1.00000 q^{3} -1.44772 q^{4} +1.00000 q^{5} +0.743153 q^{6} -2.56219 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.743153 q^{2} +1.00000 q^{3} -1.44772 q^{4} +1.00000 q^{5} +0.743153 q^{6} -2.56219 q^{8} +1.00000 q^{9} +0.743153 q^{10} +1.00000 q^{11} -1.44772 q^{12} +5.58271 q^{13} +1.00000 q^{15} +0.991352 q^{16} +1.35387 q^{17} +0.743153 q^{18} +3.31409 q^{19} -1.44772 q^{20} +0.743153 q^{22} +8.23470 q^{23} -2.56219 q^{24} +1.00000 q^{25} +4.14881 q^{26} +1.00000 q^{27} +7.38204 q^{29} +0.743153 q^{30} -4.86060 q^{31} +5.86110 q^{32} +1.00000 q^{33} +1.00613 q^{34} -1.44772 q^{36} -9.66129 q^{37} +2.46288 q^{38} +5.58271 q^{39} -2.56219 q^{40} -11.5930 q^{41} -9.98321 q^{43} -1.44772 q^{44} +1.00000 q^{45} +6.11964 q^{46} +1.51330 q^{47} +0.991352 q^{48} +0.743153 q^{50} +1.35387 q^{51} -8.08223 q^{52} +9.25338 q^{53} +0.743153 q^{54} +1.00000 q^{55} +3.31409 q^{57} +5.48599 q^{58} -11.1270 q^{59} -1.44772 q^{60} +9.77360 q^{61} -3.61217 q^{62} +2.37299 q^{64} +5.58271 q^{65} +0.743153 q^{66} -3.06310 q^{67} -1.96003 q^{68} +8.23470 q^{69} +1.75406 q^{71} -2.56219 q^{72} +4.83400 q^{73} -7.17982 q^{74} +1.00000 q^{75} -4.79789 q^{76} +4.14881 q^{78} +6.75643 q^{79} +0.991352 q^{80} +1.00000 q^{81} -8.61539 q^{82} +8.59334 q^{83} +1.35387 q^{85} -7.41905 q^{86} +7.38204 q^{87} -2.56219 q^{88} +4.30128 q^{89} +0.743153 q^{90} -11.9216 q^{92} -4.86060 q^{93} +1.12461 q^{94} +3.31409 q^{95} +5.86110 q^{96} -8.64891 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 10 q^{3} + 12 q^{4} + 10 q^{5} + 10 q^{9}+O(q^{10}) $ 10 * q + 10 * q^3 + 12 * q^4 + 10 * q^5 + 10 * q^9	$ 10 q + 10 q^{3} + 12 q^{4} + 10 q^{5} + 10 q^{9} + 10 q^{11} + 12 q^{12} + 4 q^{13} + 10 q^{15} + 24 q^{16} + 12 q^{17} + 9 q^{19} + 12 q^{20} - q^{23} + 10 q^{25} + 6 q^{26} + 10 q^{27} + 3 q^{29} + 9 q^{31} - 10 q^{32} + 10 q^{33} + 6 q^{34} + 12 q^{36} + 3 q^{37} + 42 q^{38} + 4 q^{39} + 3 q^{41} + 12 q^{44} + 10 q^{45} - 22 q^{46} + 21 q^{47} + 24 q^{48} + 12 q^{51} + 24 q^{52} - 5 q^{53} + 10 q^{55} + 9 q^{57} - 26 q^{58} + 16 q^{59} + 12 q^{60} + 20 q^{61} - 18 q^{62} + 70 q^{64} + 4 q^{65} - q^{67} + 30 q^{68} - q^{69} + 22 q^{71} - q^{73} - 34 q^{74} + 10 q^{75} - 28 q^{76} + 6 q^{78} + 19 q^{79} + 24 q^{80} + 10 q^{81} + 32 q^{82} + 20 q^{83} + 12 q^{85} + 3 q^{87} + 18 q^{89} - 8 q^{92} + 9 q^{93} - 6 q^{94} + 9 q^{95} - 10 q^{96} + 6 q^{97} + 10 q^{99}+O(q^{100}) $ 10 * q + 10 * q^3 + 12 * q^4 + 10 * q^5 + 10 * q^9 + 10 * q^11 + 12 * q^12 + 4 * q^13 + 10 * q^15 + 24 * q^16 + 12 * q^17 + 9 * q^19 + 12 * q^20 - q^23 + 10 * q^25 + 6 * q^26 + 10 * q^27 + 3 * q^29 + 9 * q^31 - 10 * q^32 + 10 * q^33 + 6 * q^34 + 12 * q^36 + 3 * q^37 + 42 * q^38 + 4 * q^39 + 3 * q^41 + 12 * q^44 + 10 * q^45 - 22 * q^46 + 21 * q^47 + 24 * q^48 + 12 * q^51 + 24 * q^52 - 5 * q^53 + 10 * q^55 + 9 * q^57 - 26 * q^58 + 16 * q^59 + 12 * q^60 + 20 * q^61 - 18 * q^62 + 70 * q^64 + 4 * q^65 - q^67 + 30 * q^68 - q^69 + 22 * q^71 - q^73 - 34 * q^74 + 10 * q^75 - 28 * q^76 + 6 * q^78 + 19 * q^79 + 24 * q^80 + 10 * q^81 + 32 * q^82 + 20 * q^83 + 12 * q^85 + 3 * q^87 + 18 * q^89 - 8 * q^92 + 9 * q^93 - 6 * q^94 + 9 * q^95 - 10 * q^96 + 6 * q^97 + 10 * 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 $

$2$	0.743153	0.525488	0.262744	−	0.964866i	$-0.415372\pi$
$2$	0.743153	0.525488	0.262744	+	0.964866i	$0.415372\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.44772	−0.723862
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.743153	0.303391
$7$	0	0
$7$	0	0
$8$	−2.56219	−0.905870
$9$	1.00000	0.333333
$10$	0.743153	0.235006
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.44772	−0.417922
$13$	5.58271	1.54837	0.774183	−	0.632962i	$-0.218161\pi$
$13$	5.58271	1.54837	0.774183	+	0.632962i	$0.218161\pi$
$14$	0	0
$15$	1.00000	0.258199
$16$	0.991352	0.247838
$17$	1.35387	0.328361	0.164180	−	0.986430i	$-0.447502\pi$
$17$	1.35387	0.328361	0.164180	+	0.986430i	$0.447502\pi$
$18$	0.743153	0.175163
$19$	3.31409	0.760305	0.380153	−	0.924924i	$-0.375871\pi$
$19$	3.31409	0.760305	0.380153	+	0.924924i	$0.375871\pi$
$20$	−1.44772	−0.323721
$21$	0	0
$22$	0.743153	0.158441
$23$	8.23470	1.71705	0.858527	−	0.512769i	$-0.171380\pi$
$23$	8.23470	1.71705	0.858527	+	0.512769i	$0.171380\pi$
$24$	−2.56219	−0.523004
$25$	1.00000	0.200000
$26$	4.14881	0.813648
$27$	1.00000	0.192450
$28$	0	0
$29$	7.38204	1.37081	0.685406	−	0.728161i	$-0.259625\pi$
$29$	7.38204	1.37081	0.685406	+	0.728161i	$0.259625\pi$
$30$	0.743153	0.135681
$31$	−4.86060	−0.872990	−0.436495	−	0.899707i	$-0.643780\pi$
$31$	−4.86060	−0.872990	−0.436495	+	0.899707i	$0.643780\pi$
$32$	5.86110	1.03611
$33$	1.00000	0.174078
$34$	1.00613	0.172550
$35$	0	0
$36$	−1.44772	−0.241287
$37$	−9.66129	−1.58831	−0.794153	−	0.607717i	$-0.792085\pi$
$37$	−9.66129	−1.58831	−0.794153	+	0.607717i	$0.792085\pi$
$38$	2.46288	0.399532
$39$	5.58271	0.893950
$40$	−2.56219	−0.405117
$41$	−11.5930	−1.81053	−0.905263	−	0.424851i	$-0.860326\pi$
$41$	−11.5930	−1.81053	−0.905263	+	0.424851i	$0.860326\pi$
$42$	0	0
$43$	−9.98321	−1.52243	−0.761213	−	0.648502i	$-0.775396\pi$
$43$	−9.98321	−1.52243	−0.761213	+	0.648502i	$0.775396\pi$
$44$	−1.44772	−0.218253
$45$	1.00000	0.149071
$46$	6.11964	0.902292
$47$	1.51330	0.220737	0.110369	−	0.993891i	$-0.464797\pi$
$47$	1.51330	0.220737	0.110369	+	0.993891i	$0.464797\pi$
$48$	0.991352	0.143089
$49$	0	0
$50$	0.743153	0.105098
$51$	1.35387	0.189579
$52$	−8.08223	−1.12080
$53$	9.25338	1.27105	0.635525	−	0.772081i	$-0.280784\pi$
$53$	9.25338	1.27105	0.635525	+	0.772081i	$0.280784\pi$
$54$	0.743153	0.101130
$55$	1.00000	0.134840
$56$	0	0
$57$	3.31409	0.438963
$58$	5.48599	0.720345
$59$	−11.1270	−1.44861	−0.724303	−	0.689482i	$-0.757838\pi$
$59$	−11.1270	−1.44861	−0.724303	+	0.689482i	$0.757838\pi$
$60$	−1.44772	−0.186900
$61$	9.77360	1.25138	0.625691	−	0.780071i	$-0.284817\pi$
$61$	9.77360	1.25138	0.625691	+	0.780071i	$0.284817\pi$
$62$	−3.61217	−0.458746
$63$	0	0
$64$	2.37299	0.296624
$65$	5.58271	0.692450
$66$	0.743153	0.0914758
$67$	−3.06310	−0.374217	−0.187108	−	0.982339i	$-0.559912\pi$
$67$	−3.06310	−0.374217	−0.187108	+	0.982339i	$0.559912\pi$
$68$	−1.96003	−0.237688
$69$	8.23470	0.991341
$70$	0	0
$71$	1.75406	0.208168	0.104084	−	0.994568i	$-0.466809\pi$
$71$	1.75406	0.208168	0.104084	+	0.994568i	$0.466809\pi$
$72$	−2.56219	−0.301957
$73$	4.83400	0.565777	0.282889	−	0.959153i	$-0.408707\pi$
$73$	4.83400	0.565777	0.282889	+	0.959153i	$0.408707\pi$
$74$	−7.17982	−0.834637
$75$	1.00000	0.115470
$76$	−4.79789	−0.550356
$77$	0	0
$78$	4.14881	0.469760
$79$	6.75643	0.760157	0.380079	−	0.924954i	$-0.375897\pi$
$79$	6.75643	0.760157	0.380079	+	0.924954i	$0.375897\pi$
$80$	0.991352	0.110836
$81$	1.00000	0.111111
$82$	−8.61539	−0.951411
$83$	8.59334	0.943241	0.471621	−	0.881802i	$-0.343669\pi$
$83$	8.59334	0.943241	0.471621	+	0.881802i	$0.343669\pi$
$84$	0	0
$85$	1.35387	0.146847
$86$	−7.41905	−0.800017
$87$	7.38204	0.791438
$88$	−2.56219	−0.273130
$89$	4.30128	0.455934	0.227967	−	0.973669i	$-0.426792\pi$
$89$	4.30128	0.455934	0.227967	+	0.973669i	$0.426792\pi$
$90$	0.743153	0.0783352
$91$	0	0
$92$	−11.9216	−1.24291
$93$	−4.86060	−0.504021
$94$	1.12461	0.115995
$95$	3.31409	0.340019
$96$	5.86110	0.598196
$97$	−8.64891	−0.878164	−0.439082	−	0.898447i	$-0.644696\pi$
$97$	−8.64891	−0.878164	−0.439082	+	0.898447i	$0.644696\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	−1.44772	−0.144772
$101$	−9.47467	−0.942765	−0.471383	−	0.881929i	$-0.656245\pi$
$101$	−9.47467	−0.942765	−0.471383	+	0.881929i	$0.656245\pi$
$102$	1.00613	0.0996217
$103$	−0.661565	−0.0651860	−0.0325930	−	0.999469i	$-0.510377\pi$
$103$	−0.661565	−0.0651860	−0.0325930	+	0.999469i	$0.510377\pi$
$104$	−14.3039	−1.40262
$105$	0	0
$106$	6.87668	0.667922
$107$	0.895448	0.0865662	0.0432831	−	0.999063i	$-0.486218\pi$
$107$	0.895448	0.0865662	0.0432831	+	0.999063i	$0.486218\pi$
$108$	−1.44772	−0.139307
$109$	−12.5168	−1.19889	−0.599447	−	0.800414i	$-0.704613\pi$
$109$	−12.5168	−1.19889	−0.599447	+	0.800414i	$0.704613\pi$
$110$	0.743153	0.0708568
$111$	−9.66129	−0.917009
$112$	0	0
$113$	−12.9043	−1.21394	−0.606968	−	0.794726i	$-0.707615\pi$
$113$	−12.9043	−1.21394	−0.606968	+	0.794726i	$0.707615\pi$
$114$	2.46288	0.230670
$115$	8.23470	0.767890
$116$	−10.6872	−0.992278
$117$	5.58271	0.516122
$118$	−8.26903	−0.761226
$119$	0	0
$120$	−2.56219	−0.233895
$121$	1.00000	0.0909091
$122$	7.26328	0.657586
$123$	−11.5930	−1.04531
$124$	7.03681	0.631924
$125$	1.00000	0.0894427
$126$	0	0
$127$	20.1125	1.78470	0.892350	−	0.451345i	$-0.149056\pi$
$127$	20.1125	1.78470	0.892350	+	0.451345i	$0.149056\pi$
$128$	−9.95870	−0.880233
$129$	−9.98321	−0.878973
$130$	4.14881	0.363875
$131$	4.25914	0.372123	0.186061	−	0.982538i	$-0.440428\pi$
$131$	4.25914	0.372123	0.186061	+	0.982538i	$0.440428\pi$
$132$	−1.44772	−0.126008
$133$	0	0
$134$	−2.27635	−0.196647
$135$	1.00000	0.0860663
$136$	−3.46886	−0.297452
$137$	15.3615	1.31242	0.656210	−	0.754578i	$-0.272159\pi$
$137$	15.3615	1.31242	0.656210	+	0.754578i	$0.272159\pi$
$138$	6.11964	0.520938
$139$	−2.06062	−0.174780	−0.0873898	−	0.996174i	$-0.527853\pi$
$139$	−2.06062	−0.174780	−0.0873898	+	0.996174i	$0.527853\pi$
$140$	0	0
$141$	1.51330	0.127443
$142$	1.30353	0.109390
$143$	5.58271	0.466850
$144$	0.991352	0.0826126
$145$	7.38204	0.613045
$146$	3.59240	0.297309
$147$	0	0
$148$	13.9869	1.14971
$149$	0.0425686	0.00348735	0.00174368	−	0.999998i	$-0.499445\pi$
$149$	0.0425686	0.00348735	0.00174368	+	0.999998i	$0.499445\pi$
$150$	0.743153	0.0606782
$151$	7.14937	0.581807	0.290904	−	0.956752i	$-0.406044\pi$
$151$	7.14937	0.581807	0.290904	+	0.956752i	$0.406044\pi$
$152$	−8.49133	−0.688737
$153$	1.35387	0.109454
$154$	0	0
$155$	−4.86060	−0.390413
$156$	−8.08223	−0.647096
$157$	15.1647	1.21028	0.605138	−	0.796120i	$-0.293118\pi$
$157$	15.1647	1.21028	0.605138	+	0.796120i	$0.293118\pi$
$158$	5.02106	0.399454
$159$	9.25338	0.733841
$160$	5.86110	0.463360
$161$	0	0
$162$	0.743153	0.0583876
$163$	1.45506	0.113969	0.0569847	−	0.998375i	$-0.481851\pi$
$163$	1.45506	0.113969	0.0569847	+	0.998375i	$0.481851\pi$
$164$	16.7835	1.31057
$165$	1.00000	0.0778499
$166$	6.38616	0.495662
$167$	20.1987	1.56302	0.781509	−	0.623894i	$-0.214450\pi$
$167$	20.1987	1.56302	0.781509	+	0.623894i	$0.214450\pi$
$168$	0	0
$169$	18.1667	1.39744
$170$	1.00613	0.0771667
$171$	3.31409	0.253435
$172$	14.4529	1.10203
$173$	15.7000	1.19365	0.596824	−	0.802372i	$-0.296429\pi$
$173$	15.7000	1.19365	0.596824	+	0.802372i	$0.296429\pi$
$174$	5.48599	0.415892
$175$	0	0
$176$	0.991352	0.0747259
$177$	−11.1270	−0.836353
$178$	3.19651	0.239588
$179$	4.44126	0.331956	0.165978	−	0.986129i	$-0.446922\pi$
$179$	4.44126	0.331956	0.165978	+	0.986129i	$0.446922\pi$
$180$	−1.44772	−0.107907
$181$	11.8535	0.881064	0.440532	−	0.897737i	$-0.354790\pi$
$181$	11.8535	0.881064	0.440532	+	0.897737i	$0.354790\pi$
$182$	0	0
$183$	9.77360	0.722485
$184$	−21.0988	−1.55543
$185$	−9.66129	−0.710312
$186$	−3.61217	−0.264857
$187$	1.35387	0.0990046
$188$	−2.19084	−0.159783
$189$	0	0
$190$	2.46288	0.178676
$191$	−15.1166	−1.09380	−0.546899	−	0.837198i	$-0.684192\pi$
$191$	−15.1166	−1.09380	−0.546899	+	0.837198i	$0.684192\pi$
$192$	2.37299	0.171256
$193$	−22.6853	−1.63292	−0.816461	−	0.577400i	$-0.804067\pi$
$193$	−22.6853	−1.63292	−0.816461	+	0.577400i	$0.804067\pi$
$194$	−6.42746	−0.461465
$195$	5.58271	0.399786
$196$	0	0
$197$	21.9089	1.56094	0.780472	−	0.625191i	$-0.214979\pi$
$197$	21.9089	1.56094	0.780472	+	0.625191i	$0.214979\pi$
$198$	0.743153	0.0528136
$199$	24.0441	1.70444	0.852221	−	0.523182i	$-0.175255\pi$
$199$	24.0441	1.70444	0.852221	+	0.523182i	$0.175255\pi$
$200$	−2.56219	−0.181174
$201$	−3.06310	−0.216054
$202$	−7.04113	−0.495412
$203$	0	0
$204$	−1.96003	−0.137229
$205$	−11.5930	−0.809692
$206$	−0.491644	−0.0342545
$207$	8.23470	0.572351
$208$	5.53443	0.383744
$209$	3.31409	0.229241
$210$	0	0
$211$	24.8038	1.70757	0.853783	−	0.520629i	$-0.174303\pi$
$211$	24.8038	1.70757	0.853783	+	0.520629i	$0.174303\pi$
$212$	−13.3963	−0.920064
$213$	1.75406	0.120186
$214$	0.665454	0.0454895
$215$	−9.98321	−0.680850
$216$	−2.56219	−0.174335
$217$	0	0
$218$	−9.30192	−0.630005
$219$	4.83400	0.326652
$220$	−1.44772	−0.0976055
$221$	7.55825	0.508423
$222$	−7.17982	−0.481878
$223$	25.5502	1.71097	0.855485	−	0.517827i	$-0.173259\pi$
$223$	25.5502	1.71097	0.855485	+	0.517827i	$0.173259\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	−9.58989	−0.637910
$227$	0.560594	0.0372079	0.0186040	−	0.999827i	$-0.494078\pi$
$227$	0.560594	0.0372079	0.0186040	+	0.999827i	$0.494078\pi$
$228$	−4.79789	−0.317748
$229$	13.3061	0.879294	0.439647	−	0.898171i	$-0.355104\pi$
$229$	13.3061	0.879294	0.439647	+	0.898171i	$0.355104\pi$
$230$	6.11964	0.403517
$231$	0	0
$232$	−18.9142	−1.24178
$233$	−15.5264	−1.01717	−0.508583	−	0.861013i	$-0.669830\pi$
$233$	−15.5264	−1.01717	−0.508583	+	0.861013i	$0.669830\pi$
$234$	4.14881	0.271216
$235$	1.51330	0.0987168
$236$	16.1088	1.04859
$237$	6.75643	0.438877
$238$	0	0
$239$	15.3493	0.992867	0.496433	−	0.868075i	$-0.334643\pi$
$239$	15.3493	0.992867	0.496433	+	0.868075i	$0.334643\pi$
$240$	0.991352	0.0639915
$241$	−6.01915	−0.387728	−0.193864	−	0.981028i	$-0.562102\pi$
$241$	−6.01915	−0.387728	−0.193864	+	0.981028i	$0.562102\pi$
$242$	0.743153	0.0477717
$243$	1.00000	0.0641500
$244$	−14.1495	−0.905827
$245$	0	0
$246$	−8.61539	−0.549297
$247$	18.5016	1.17723
$248$	12.4538	0.790815
$249$	8.59334	0.544580
$250$	0.743153	0.0470011
$251$	13.2467	0.836125	0.418062	−	0.908418i	$-0.362709\pi$
$251$	13.2467	0.836125	0.418062	+	0.908418i	$0.362709\pi$
$252$	0	0
$253$	8.23470	0.517711
$254$	14.9467	0.937839
$255$	1.35387	0.0847824
$256$	−12.1468	−0.759176
$257$	6.37900	0.397911	0.198955	−	0.980009i	$-0.436245\pi$
$257$	6.37900	0.397911	0.198955	+	0.980009i	$0.436245\pi$
$258$	−7.41905	−0.461890
$259$	0	0
$260$	−8.08223	−0.501238
$261$	7.38204	0.456937
$262$	3.16519	0.195546
$263$	−15.6515	−0.965110	−0.482555	−	0.875866i	$-0.660291\pi$
$263$	−15.6515	−0.965110	−0.482555	+	0.875866i	$0.660291\pi$
$264$	−2.56219	−0.157692
$265$	9.25338	0.568431
$266$	0	0
$267$	4.30128	0.263234
$268$	4.43452	0.270881
$269$	5.15244	0.314150	0.157075	−	0.987587i	$-0.449794\pi$
$269$	5.15244	0.314150	0.157075	+	0.987587i	$0.449794\pi$
$270$	0.743153	0.0452268
$271$	−17.6751	−1.07368	−0.536842	−	0.843683i	$-0.680383\pi$
$271$	−17.6751	−1.07368	−0.536842	+	0.843683i	$0.680383\pi$
$272$	1.34216	0.0813803
$273$	0	0
$274$	11.4159	0.689661
$275$	1.00000	0.0603023
$276$	−11.9216	−0.717594
$277$	12.2000	0.733026	0.366513	−	0.930413i	$-0.380552\pi$
$277$	12.2000	0.733026	0.366513	+	0.930413i	$0.380552\pi$
$278$	−1.53136	−0.0918447
$279$	−4.86060	−0.290997
$280$	0	0
$281$	−16.8809	−1.00703	−0.503514	−	0.863987i	$-0.667960\pi$
$281$	−16.8809	−1.00703	−0.503514	+	0.863987i	$0.667960\pi$
$282$	1.12461	0.0669697
$283$	−13.7943	−0.819987	−0.409993	−	0.912089i	$-0.634469\pi$
$283$	−13.7943	−0.819987	−0.409993	+	0.912089i	$0.634469\pi$
$284$	−2.53939	−0.150685
$285$	3.31409	0.196310
$286$	4.14881	0.245324
$287$	0	0
$288$	5.86110	0.345368
$289$	−15.1670	−0.892179
$290$	5.48599	0.322148
$291$	−8.64891	−0.507008
$292$	−6.99830	−0.409545
$293$	−8.48052	−0.495438	−0.247719	−	0.968832i	$-0.579681\pi$
$293$	−8.48052	−0.495438	−0.247719	+	0.968832i	$0.579681\pi$
$294$	0	0
$295$	−11.1270	−0.647836
$296$	24.7540	1.43880
$297$	1.00000	0.0580259
$298$	0.0316350	0.00183256
$299$	45.9720	2.65863
$300$	−1.44772	−0.0835844
$301$	0	0
$302$	5.31307	0.305733
$303$	−9.47467	−0.544306
$304$	3.28543	0.188432
$305$	9.77360	0.559635
$306$	1.00613	0.0575166
$307$	−26.0487	−1.48668	−0.743340	−	0.668914i	$-0.766760\pi$
$307$	−26.0487	−1.48668	−0.743340	+	0.668914i	$0.766760\pi$
$308$	0	0
$309$	−0.661565	−0.0376351
$310$	−3.61217	−0.205157
$311$	−21.8397	−1.23842	−0.619209	−	0.785227i	$-0.712546\pi$
$311$	−21.8397	−1.23842	−0.619209	+	0.785227i	$0.712546\pi$
$312$	−14.3039	−0.809802
$313$	−1.89738	−0.107247	−0.0536233	−	0.998561i	$-0.517077\pi$
$313$	−1.89738	−0.107247	−0.0536233	+	0.998561i	$0.517077\pi$
$314$	11.2697	0.635987
$315$	0	0
$316$	−9.78144	−0.550249
$317$	−20.1839	−1.13364	−0.566820	−	0.823842i	$-0.691826\pi$
$317$	−20.1839	−1.13364	−0.566820	+	0.823842i	$0.691826\pi$
$318$	6.87668	0.385625
$319$	7.38204	0.413315
$320$	2.37299	0.132654
$321$	0.895448	0.0499790
$322$	0	0
$323$	4.48684	0.249655
$324$	−1.44772	−0.0804291
$325$	5.58271	0.309673
$326$	1.08134	0.0598896
$327$	−12.5168	−0.692182
$328$	29.7035	1.64010
$329$	0	0
$330$	0.743153	0.0409092
$331$	−28.4757	−1.56517	−0.782584	−	0.622545i	$-0.786099\pi$
$331$	−28.4757	−1.56517	−0.782584	+	0.622545i	$0.786099\pi$
$332$	−12.4408	−0.682776
$333$	−9.66129	−0.529436
$334$	15.0107	0.821348
$335$	−3.06310	−0.167355
$336$	0	0
$337$	28.8270	1.57031	0.785154	−	0.619300i	$-0.212584\pi$
$337$	28.8270	1.57031	0.785154	+	0.619300i	$0.212584\pi$
$338$	13.5006	0.734337
$339$	−12.9043	−0.700867
$340$	−1.96003	−0.106297
$341$	−4.86060	−0.263216
$342$	2.46288	0.133177
$343$	0	0
$344$	25.5789	1.37912
$345$	8.23470	0.443341
$346$	11.6675	0.627248
$347$	5.22941	0.280730	0.140365	−	0.990100i	$-0.455172\pi$
$347$	5.22941	0.280730	0.140365	+	0.990100i	$0.455172\pi$
$348$	−10.6872	−0.572892
$349$	5.01221	0.268297	0.134149	−	0.990961i	$-0.457170\pi$
$349$	5.01221	0.268297	0.134149	+	0.990961i	$0.457170\pi$
$350$	0	0
$351$	5.58271	0.297983
$352$	5.86110	0.312398
$353$	−3.13386	−0.166798	−0.0833992	−	0.996516i	$-0.526578\pi$
$353$	−3.13386	−0.166798	−0.0833992	+	0.996516i	$0.526578\pi$
$354$	−8.26903	−0.439494
$355$	1.75406	0.0930957
$356$	−6.22706	−0.330034
$357$	0	0
$358$	3.30054	0.174439
$359$	24.7234	1.30485	0.652425	−	0.757853i	$-0.273752\pi$
$359$	24.7234	1.30485	0.652425	+	0.757853i	$0.273752\pi$
$360$	−2.56219	−0.135039
$361$	−8.01678	−0.421936
$362$	8.80897	0.462989
$363$	1.00000	0.0524864
$364$	0	0
$365$	4.83400	0.253023
$366$	7.26328	0.379658
$367$	−9.63216	−0.502795	−0.251397	−	0.967884i	$-0.580890\pi$
$367$	−9.63216	−0.502795	−0.251397	+	0.967884i	$0.580890\pi$
$368$	8.16348	0.425551
$369$	−11.5930	−0.603509
$370$	−7.17982	−0.373261
$371$	0	0
$372$	7.03681	0.364842
$373$	−26.6097	−1.37780	−0.688900	−	0.724857i	$-0.741906\pi$
$373$	−26.6097	−1.37780	−0.688900	+	0.724857i	$0.741906\pi$
$374$	1.00613	0.0520258
$375$	1.00000	0.0516398
$376$	−3.87736	−0.199959
$377$	41.2118	2.12252
$378$	0	0
$379$	−27.3224	−1.40346	−0.701728	−	0.712445i	$-0.747588\pi$
$379$	−27.3224	−1.40346	−0.701728	+	0.712445i	$0.747588\pi$
$380$	−4.79789	−0.246127
$381$	20.1125	1.03040
$382$	−11.2339	−0.574779
$383$	8.57281	0.438050	0.219025	−	0.975719i	$-0.429712\pi$
$383$	8.57281	0.438050	0.219025	+	0.975719i	$0.429712\pi$
$384$	−9.95870	−0.508203
$385$	0	0
$386$	−16.8586	−0.858082
$387$	−9.98321	−0.507475
$388$	12.5212	0.635669
$389$	−6.92511	−0.351117	−0.175558	−	0.984469i	$-0.556173\pi$
$389$	−6.92511	−0.351117	−0.175558	+	0.984469i	$0.556173\pi$
$390$	4.14881	0.210083
$391$	11.1487	0.563813
$392$	0	0
$393$	4.25914	0.214845
$394$	16.2817	0.820258
$395$	6.75643	0.339953
$396$	−1.44772	−0.0727509
$397$	−1.80506	−0.0905934	−0.0452967	−	0.998974i	$-0.514423\pi$
$397$	−1.80506	−0.0905934	−0.0452967	+	0.998974i	$0.514423\pi$
$398$	17.8685	0.895665
$399$	0	0
$400$	0.991352	0.0495676
$401$	−6.22060	−0.310642	−0.155321	−	0.987864i	$-0.549641\pi$
$401$	−6.22060	−0.310642	−0.155321	+	0.987864i	$0.549641\pi$
$402$	−2.27635	−0.113534
$403$	−27.1353	−1.35171
$404$	13.7167	0.682432
$405$	1.00000	0.0496904
$406$	0	0
$407$	−9.66129	−0.478892
$408$	−3.46886	−0.171734
$409$	−13.6690	−0.675888	−0.337944	−	0.941166i	$-0.609731\pi$
$409$	−13.6690	−0.675888	−0.337944	+	0.941166i	$0.609731\pi$
$410$	−8.61539	−0.425484
$411$	15.3615	0.757726
$412$	0.957764	0.0471856
$413$	0	0
$414$	6.11964	0.300764
$415$	8.59334	0.421830
$416$	32.7208	1.60427
$417$	−2.06062	−0.100909
$418$	2.46288	0.120463
$419$	25.4761	1.24459	0.622295	−	0.782783i	$-0.286200\pi$
$419$	25.4761	1.24459	0.622295	+	0.782783i	$0.286200\pi$
$420$	0	0
$421$	−5.46155	−0.266180	−0.133090	−	0.991104i	$-0.542490\pi$
$421$	−5.46155	−0.266180	−0.133090	+	0.991104i	$0.542490\pi$
$422$	18.4330	0.897306
$423$	1.51330	0.0735792
$424$	−23.7089	−1.15140
$425$	1.35387	0.0656722
$426$	1.30353	0.0631564
$427$	0	0
$428$	−1.29636	−0.0626620
$429$	5.58271	0.269536
$430$	−7.41905	−0.357779
$431$	−10.1578	−0.489285	−0.244642	−	0.969613i	$-0.578671\pi$
$431$	−10.1578	−0.489285	−0.244642	+	0.969613i	$0.578671\pi$
$432$	0.991352	0.0476964
$433$	−3.79390	−0.182323	−0.0911615	−	0.995836i	$-0.529058\pi$
$433$	−3.79390	−0.182323	−0.0911615	+	0.995836i	$0.529058\pi$
$434$	0	0
$435$	7.38204	0.353942
$436$	18.1209	0.867834
$437$	27.2906	1.30548
$438$	3.59240	0.171652
$439$	3.22973	0.154147	0.0770734	−	0.997025i	$-0.475442\pi$
$439$	3.22973	0.154147	0.0770734	+	0.997025i	$0.475442\pi$
$440$	−2.56219	−0.122147
$441$	0	0
$442$	5.61694	0.267170
$443$	−32.3136	−1.53527	−0.767633	−	0.640890i	$-0.778565\pi$
$443$	−32.3136	−1.53527	−0.767633	+	0.640890i	$0.778565\pi$
$444$	13.9869	0.663788
$445$	4.30128	0.203900
$446$	18.9877	0.899095
$447$	0.0425686	0.00201342
$448$	0	0
$449$	−26.5723	−1.25402	−0.627012	−	0.779010i	$-0.715722\pi$
$449$	−26.5723	−1.25402	−0.627012	+	0.779010i	$0.715722\pi$
$450$	0.743153	0.0350326
$451$	−11.5930	−0.545894
$452$	18.6819	0.878722
$453$	7.14937	0.335907
$454$	0.416607	0.0195523
$455$	0	0
$456$	−8.49133	−0.397643
$457$	19.6266	0.918092	0.459046	−	0.888413i	$-0.348191\pi$
$457$	19.6266	0.918092	0.459046	+	0.888413i	$0.348191\pi$
$458$	9.88849	0.462059
$459$	1.35387	0.0631931
$460$	−11.9216	−0.555846
$461$	15.7047	0.731442	0.365721	−	0.930725i	$-0.380822\pi$
$461$	15.7047	0.731442	0.365721	+	0.930725i	$0.380822\pi$
$462$	0	0
$463$	−24.6064	−1.14355	−0.571777	−	0.820409i	$-0.693746\pi$
$463$	−24.6064	−1.14355	−0.571777	+	0.820409i	$0.693746\pi$
$464$	7.31820	0.339739
$465$	−4.86060	−0.225405
$466$	−11.5385	−0.534509
$467$	19.8307	0.917655	0.458828	−	0.888525i	$-0.348270\pi$
$467$	19.8307	0.917655	0.458828	+	0.888525i	$0.348270\pi$
$468$	−8.08223	−0.373601
$469$	0	0
$470$	1.12461	0.0518745
$471$	15.1647	0.698754
$472$	28.5093	1.31225
$473$	−9.98321	−0.459029
$474$	5.02106	0.230625
$475$	3.31409	0.152061
$476$	0	0
$477$	9.25338	0.423683
$478$	11.4069	0.521740
$479$	−27.2795	−1.24643	−0.623215	−	0.782050i	$-0.714174\pi$
$479$	−27.2795	−1.24643	−0.623215	+	0.782050i	$0.714174\pi$
$480$	5.86110	0.267521
$481$	−53.9362	−2.45928
$482$	−4.47315	−0.203746
$483$	0	0
$484$	−1.44772	−0.0658056
$485$	−8.64891	−0.392727
$486$	0.743153	0.0337101
$487$	−4.38013	−0.198483	−0.0992413	−	0.995063i	$-0.531642\pi$
$487$	−4.38013	−0.198483	−0.0992413	+	0.995063i	$0.531642\pi$
$488$	−25.0418	−1.13359
$489$	1.45506	0.0658003
$490$	0	0
$491$	8.64377	0.390088	0.195044	−	0.980794i	$-0.437515\pi$
$491$	8.64377	0.390088	0.195044	+	0.980794i	$0.437515\pi$
$492$	16.7835	0.756658
$493$	9.99431	0.450121
$494$	13.7495	0.618621
$495$	1.00000	0.0449467
$496$	−4.81857	−0.216360
$497$	0	0
$498$	6.38616	0.286171
$499$	−14.8914	−0.666630	−0.333315	−	0.942816i	$-0.608167\pi$
$499$	−14.8914	−0.666630	−0.333315	+	0.942816i	$0.608167\pi$
$500$	−1.44772	−0.0647442
$501$	20.1987	0.902409
$502$	9.84433	0.439374
$503$	10.6588	0.475253	0.237627	−	0.971357i	$-0.423631\pi$
$503$	10.6588	0.475253	0.237627	+	0.971357i	$0.423631\pi$
$504$	0	0
$505$	−9.47467	−0.421617
$506$	6.11964	0.272051
$507$	18.1667	0.806811
$508$	−29.1174	−1.29188
$509$	24.8153	1.09992	0.549959	−	0.835192i	$-0.314643\pi$
$509$	24.8153	1.09992	0.549959	+	0.835192i	$0.314643\pi$
$510$	1.00613	0.0445522
$511$	0	0
$512$	10.8905	0.481295
$513$	3.31409	0.146321
$514$	4.74057	0.209098
$515$	−0.661565	−0.0291520
$516$	14.4529	0.636255
$517$	1.51330	0.0665549
$518$	0	0
$519$	15.7000	0.689153
$520$	−14.3039	−0.627270
$521$	−31.3416	−1.37310	−0.686549	−	0.727083i	$-0.740875\pi$
$521$	−31.3416	−1.37310	−0.686549	+	0.727083i	$0.740875\pi$
$522$	5.48599	0.240115
$523$	40.7920	1.78371	0.891855	−	0.452322i	$-0.149404\pi$
$523$	40.7920	1.78371	0.891855	+	0.452322i	$0.149404\pi$
$524$	−6.16606	−0.269366
$525$	0	0
$526$	−11.6314	−0.507154
$527$	−6.58061	−0.286656
$528$	0.991352	0.0431430
$529$	44.8103	1.94827
$530$	6.87668	0.298704
$531$	−11.1270	−0.482869
$532$	0	0
$533$	−64.7205	−2.80336
$534$	3.19651	0.138326
$535$	0.895448	0.0387136
$536$	7.84822	0.338992
$537$	4.44126	0.191655
$538$	3.82905	0.165082
$539$	0	0
$540$	−1.44772	−0.0623001
$541$	−7.03400	−0.302415	−0.151208	−	0.988502i	$-0.548316\pi$
$541$	−7.03400	−0.302415	−0.151208	+	0.988502i	$0.548316\pi$
$542$	−13.1353	−0.564208
$543$	11.8535	0.508683
$544$	7.93515	0.340217
$545$	−12.5168	−0.536162
$546$	0	0
$547$	−31.9539	−1.36625	−0.683125	−	0.730301i	$-0.739380\pi$
$547$	−31.9539	−1.36625	−0.683125	+	0.730301i	$0.739380\pi$
$548$	−22.2392	−0.950011
$549$	9.77360	0.417127
$550$	0.743153	0.0316881
$551$	24.4648	1.04224
$552$	−21.0988	−0.898026
$553$	0	0
$554$	9.06646	0.385197
$555$	−9.66129	−0.410099
$556$	2.98321	0.126516
$557$	−20.3960	−0.864205	−0.432103	−	0.901824i	$-0.642228\pi$
$557$	−20.3960	−0.864205	−0.432103	+	0.901824i	$0.642228\pi$
$558$	−3.61217	−0.152915
$559$	−55.7334	−2.35727
$560$	0	0
$561$	1.35387	0.0571603
$562$	−12.5451	−0.529182
$563$	−31.6914	−1.33563	−0.667816	−	0.744326i	$-0.732771\pi$
$563$	−31.6914	−1.33563	−0.667816	+	0.744326i	$0.732771\pi$
$564$	−2.19084	−0.0922510
$565$	−12.9043	−0.542889
$566$	−10.2513	−0.430893
$567$	0	0
$568$	−4.49422	−0.188573
$569$	−15.0649	−0.631554	−0.315777	−	0.948833i	$-0.602265\pi$
$569$	−15.0649	−0.631554	−0.315777	+	0.948833i	$0.602265\pi$
$570$	2.46288	0.103159
$571$	20.1344	0.842600	0.421300	−	0.906921i	$-0.361574\pi$
$571$	20.1344	0.842600	0.421300	+	0.906921i	$0.361574\pi$
$572$	−8.08223	−0.337935
$573$	−15.1166	−0.631505
$574$	0	0
$575$	8.23470	0.343411
$576$	2.37299	0.0988745
$577$	42.8727	1.78481	0.892406	−	0.451234i	$-0.149016\pi$
$577$	42.8727	1.78481	0.892406	+	0.451234i	$0.149016\pi$
$578$	−11.2714	−0.468830
$579$	−22.6853	−0.942768
$580$	−10.6872	−0.443760
$581$	0	0
$582$	−6.42746	−0.266427
$583$	9.25338	0.383236
$584$	−12.3856	−0.512520
$585$	5.58271	0.230817
$586$	−6.30233	−0.260347
$587$	−23.1597	−0.955903	−0.477952	−	0.878386i	$-0.658621\pi$
$587$	−23.1597	−0.955903	−0.477952	+	0.878386i	$0.658621\pi$
$588$	0	0
$589$	−16.1085	−0.663739
$590$	−8.26903	−0.340431
$591$	21.9089	0.901212
$592$	−9.57774	−0.393643
$593$	−14.5663	−0.598166	−0.299083	−	0.954227i	$-0.596681\pi$
$593$	−14.5663	−0.598166	−0.299083	+	0.954227i	$0.596681\pi$
$594$	0.743153	0.0304919
$595$	0	0
$596$	−0.0616275	−0.00252436
$597$	24.0441	0.984060
$598$	34.1642	1.39708
$599$	−8.57026	−0.350171	−0.175086	−	0.984553i	$-0.556020\pi$
$599$	−8.57026	−0.350171	−0.175086	+	0.984553i	$0.556020\pi$
$600$	−2.56219	−0.104601
$601$	12.2389	0.499234	0.249617	−	0.968345i	$-0.419695\pi$
$601$	12.2389	0.499234	0.249617	+	0.968345i	$0.419695\pi$
$602$	0	0
$603$	−3.06310	−0.124739
$604$	−10.3503	−0.421148
$605$	1.00000	0.0406558
$606$	−7.04113	−0.286026
$607$	−5.82778	−0.236542	−0.118271	−	0.992981i	$-0.537735\pi$
$607$	−5.82778	−0.236542	−0.118271	+	0.992981i	$0.537735\pi$
$608$	19.4242	0.787757
$609$	0	0
$610$	7.26328	0.294082
$611$	8.44832	0.341782
$612$	−1.96003	−0.0792293
$613$	−15.3176	−0.618671	−0.309335	−	0.950953i	$-0.600107\pi$
$613$	−15.3176	−0.618671	−0.309335	+	0.950953i	$0.600107\pi$
$614$	−19.3582	−0.781233
$615$	−11.5930	−0.467476
$616$	0	0
$617$	15.5710	0.626866	0.313433	−	0.949610i	$-0.398521\pi$
$617$	15.5710	0.626866	0.313433	+	0.949610i	$0.398521\pi$
$618$	−0.491644	−0.0197768
$619$	3.07153	0.123455	0.0617276	−	0.998093i	$-0.480339\pi$
$619$	3.07153	0.123455	0.0617276	+	0.998093i	$0.480339\pi$
$620$	7.03681	0.282605
$621$	8.23470	0.330447
$622$	−16.2303	−0.650774
$623$	0	0
$624$	5.53443	0.221555
$625$	1.00000	0.0400000
$626$	−1.41005	−0.0563568
$627$	3.31409	0.132352
$628$	−21.9543	−0.876073
$629$	−13.0801	−0.521538
$630$	0	0
$631$	6.93667	0.276145	0.138072	−	0.990422i	$-0.455909\pi$
$631$	6.93667	0.276145	0.138072	+	0.990422i	$0.455909\pi$
$632$	−17.3112	−0.688603
$633$	24.8038	0.985864
$634$	−14.9997	−0.595715
$635$	20.1125	0.798142
$636$	−13.3963	−0.531199
$637$	0	0
$638$	5.48599	0.217192
$639$	1.75406	0.0693894
$640$	−9.95870	−0.393652
$641$	−36.3121	−1.43424	−0.717121	−	0.696948i	$-0.754541\pi$
$641$	−36.3121	−1.43424	−0.717121	+	0.696948i	$0.754541\pi$
$642$	0.665454	0.0262634
$643$	19.2129	0.757684	0.378842	−	0.925461i	$-0.376322\pi$
$643$	19.2129	0.757684	0.378842	+	0.925461i	$0.376322\pi$
$644$	0	0
$645$	−9.98321	−0.393089
$646$	3.33441	0.131191
$647$	−11.3341	−0.445589	−0.222795	−	0.974865i	$-0.571518\pi$
$647$	−11.3341	−0.445589	−0.222795	+	0.974865i	$0.571518\pi$
$648$	−2.56219	−0.100652
$649$	−11.1270	−0.436771
$650$	4.14881	0.162730
$651$	0	0
$652$	−2.10653	−0.0824982
$653$	9.47057	0.370612	0.185306	−	0.982681i	$-0.440672\pi$
$653$	9.47057	0.370612	0.185306	+	0.982681i	$0.440672\pi$
$654$	−9.30192	−0.363734
$655$	4.25914	0.166418
$656$	−11.4928	−0.448717
$657$	4.83400	0.188592
$658$	0	0
$659$	−4.83655	−0.188405	−0.0942026	−	0.995553i	$-0.530030\pi$
$659$	−4.83655	−0.188405	−0.0942026	+	0.995553i	$0.530030\pi$
$660$	−1.44772	−0.0563526
$661$	42.1256	1.63850	0.819248	−	0.573439i	$-0.194391\pi$
$661$	42.1256	1.63850	0.819248	+	0.573439i	$0.194391\pi$
$662$	−21.1618	−0.822478
$663$	7.55825	0.293538
$664$	−22.0177	−0.854453
$665$	0	0
$666$	−7.17982	−0.278212
$667$	60.7889	2.35376
$668$	−29.2421	−1.13141
$669$	25.5502	0.987829
$670$	−2.27635	−0.0879430
$671$	9.77360	0.377306
$672$	0	0
$673$	21.3328	0.822317	0.411159	−	0.911564i	$-0.365124\pi$
$673$	21.3328	0.822317	0.411159	+	0.911564i	$0.365124\pi$
$674$	21.4229	0.825179
$675$	1.00000	0.0384900
$676$	−26.3003	−1.01155
$677$	−27.3581	−1.05146	−0.525729	−	0.850652i	$-0.676207\pi$
$677$	−27.3581	−1.05146	−0.525729	+	0.850652i	$0.676207\pi$
$678$	−9.58989	−0.368297
$679$	0	0
$680$	−3.46886	−0.133025
$681$	0.560594	0.0214820
$682$	−3.61217	−0.138317
$683$	39.1915	1.49962	0.749811	−	0.661652i	$-0.230145\pi$
$683$	39.1915	1.49962	0.749811	+	0.661652i	$0.230145\pi$
$684$	−4.79789	−0.183452
$685$	15.3615	0.586932
$686$	0	0
$687$	13.3061	0.507660
$688$	−9.89688	−0.377315
$689$	51.6590	1.96805
$690$	6.11964	0.232971
$691$	12.5304	0.476678	0.238339	−	0.971182i	$-0.423397\pi$
$691$	12.5304	0.476678	0.238339	+	0.971182i	$0.423397\pi$
$692$	−22.7292	−0.864036
$693$	0	0
$694$	3.88625	0.147520
$695$	−2.06062	−0.0781638
$696$	−18.9142	−0.716940
$697$	−15.6954	−0.594506
$698$	3.72484	0.140987
$699$	−15.5264	−0.587261
$700$	0	0
$701$	−16.0392	−0.605791	−0.302895	−	0.953024i	$-0.597953\pi$
$701$	−16.0392	−0.605791	−0.302895	+	0.953024i	$0.597953\pi$
$702$	4.14881	0.156587
$703$	−32.0184	−1.20760
$704$	2.37299	0.0894354
$705$	1.51330	0.0569942
$706$	−2.32894	−0.0876507
$707$	0	0
$708$	16.1088	0.605404
$709$	−0.826702	−0.0310474	−0.0155237	−	0.999879i	$-0.504942\pi$
$709$	−0.826702	−0.0310474	−0.0155237	+	0.999879i	$0.504942\pi$
$710$	1.30353	0.0489207
$711$	6.75643	0.253386
$712$	−11.0207	−0.413017
$713$	−40.0256	−1.49897
$714$	0	0
$715$	5.58271	0.208782
$716$	−6.42972	−0.240290
$717$	15.3493	0.573232
$718$	18.3733	0.685684
$719$	14.9452	0.557360	0.278680	−	0.960384i	$-0.410103\pi$
$719$	14.9452	0.557360	0.278680	+	0.960384i	$0.410103\pi$
$720$	0.991352	0.0369455
$721$	0	0
$722$	−5.95769	−0.221722
$723$	−6.01915	−0.223855
$724$	−17.1606	−0.637769
$725$	7.38204	0.274162
$726$	0.743153	0.0275810
$727$	44.4822	1.64976	0.824878	−	0.565311i	$-0.191244\pi$
$727$	44.4822	1.64976	0.824878	+	0.565311i	$0.191244\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	3.59240	0.132961
$731$	−13.5159	−0.499905
$732$	−14.1495	−0.522979
$733$	30.8331	1.13885	0.569424	−	0.822044i	$-0.307166\pi$
$733$	30.8331	1.13885	0.569424	+	0.822044i	$0.307166\pi$
$734$	−7.15817	−0.264213
$735$	0	0
$736$	48.2644	1.77905
$737$	−3.06310	−0.112831
$738$	−8.61539	−0.317137
$739$	−15.6625	−0.576155	−0.288077	−	0.957607i	$-0.593016\pi$
$739$	−15.6625	−0.576155	−0.288077	+	0.957607i	$0.593016\pi$
$740$	13.9869	0.514168
$741$	18.5016	0.679675
$742$	0	0
$743$	27.3070	1.00180	0.500899	−	0.865506i	$-0.333003\pi$
$743$	27.3070	1.00180	0.500899	+	0.865506i	$0.333003\pi$
$744$	12.4538	0.456577
$745$	0.0425686	0.00155959
$746$	−19.7751	−0.724017
$747$	8.59334	0.314414
$748$	−1.96003	−0.0716656
$749$	0	0
$750$	0.743153	0.0271361
$751$	−36.6692	−1.33808	−0.669040	−	0.743227i	$-0.733294\pi$
$751$	−36.6692	−1.33808	−0.669040	+	0.743227i	$0.733294\pi$
$752$	1.50021	0.0547071
$753$	13.2467	0.482737
$754$	30.6267	1.11536
$755$	7.14937	0.260192
$756$	0	0
$757$	−33.3164	−1.21091	−0.605453	−	0.795881i	$-0.707008\pi$
$757$	−33.3164	−1.21091	−0.605453	+	0.795881i	$0.707008\pi$
$758$	−20.3047	−0.737500
$759$	8.23470	0.298901
$760$	−8.49133	−0.308013
$761$	−47.1657	−1.70975	−0.854877	−	0.518830i	$-0.826368\pi$
$761$	−47.1657	−1.70975	−0.854877	+	0.518830i	$0.826368\pi$
$762$	14.9467	0.541461
$763$	0	0
$764$	21.8847	0.791759
$765$	1.35387	0.0489492
$766$	6.37091	0.230190
$767$	−62.1186	−2.24297
$768$	−12.1468	−0.438310
$769$	−23.4127	−0.844285	−0.422143	−	0.906529i	$-0.638722\pi$
$769$	−23.4127	−0.844285	−0.422143	+	0.906529i	$0.638722\pi$
$770$	0	0
$771$	6.37900	0.229734
$772$	32.8420	1.18201
$773$	−22.4654	−0.808024	−0.404012	−	0.914754i	$-0.632385\pi$
$773$	−22.4654	−0.808024	−0.404012	+	0.914754i	$0.632385\pi$
$774$	−7.41905	−0.266672
$775$	−4.86060	−0.174598
$776$	22.1601	0.795502
$777$	0	0
$778$	−5.14642	−0.184508
$779$	−38.4204	−1.37655
$780$	−8.08223	−0.289390
$781$	1.75406	0.0627651
$782$	8.28518	0.296277
$783$	7.38204	0.263813
$784$	0	0
$785$	15.1647	0.541252
$786$	3.16519	0.112899
$787$	−9.09094	−0.324057	−0.162028	−	0.986786i	$-0.551804\pi$
$787$	−9.09094	−0.324057	−0.162028	+	0.986786i	$0.551804\pi$
$788$	−31.7180	−1.12991
$789$	−15.6515	−0.557207
$790$	5.02106	0.178641
$791$	0	0
$792$	−2.56219	−0.0910433
$793$	54.5632	1.93760
$794$	−1.34144	−0.0476058
$795$	9.25338	0.328184
$796$	−34.8092	−1.23378
$797$	24.7414	0.876386	0.438193	−	0.898881i	$-0.355619\pi$
$797$	24.7414	0.876386	0.438193	+	0.898881i	$0.355619\pi$
$798$	0	0
$799$	2.04881	0.0724816
$800$	5.86110	0.207221
$801$	4.30128	0.151978
$802$	−4.62286	−0.163239
$803$	4.83400	0.170588
$804$	4.43452	0.156393
$805$	0	0
$806$	−20.1657	−0.710307
$807$	5.15244	0.181375
$808$	24.2759	0.854022
$809$	5.80153	0.203971	0.101986	−	0.994786i	$-0.467480\pi$
$809$	5.80153	0.203971	0.101986	+	0.994786i	$0.467480\pi$
$810$	0.743153	0.0261117
$811$	9.57738	0.336307	0.168154	−	0.985761i	$-0.446220\pi$
$811$	9.57738	0.336307	0.168154	+	0.985761i	$0.446220\pi$
$812$	0	0
$813$	−17.6751	−0.619891
$814$	−7.17982	−0.251652
$815$	1.45506	0.0509687
$816$	1.34216	0.0469849
$817$	−33.0853	−1.15751
$818$	−10.1581	−0.355171
$819$	0	0
$820$	16.7835	0.586105
$821$	43.0070	1.50095	0.750477	−	0.660896i	$-0.229824\pi$
$821$	43.0070	1.50095	0.750477	+	0.660896i	$0.229824\pi$
$822$	11.4159	0.398176
$823$	42.1677	1.46987	0.734937	−	0.678135i	$-0.237212\pi$
$823$	42.1677	1.46987	0.734937	+	0.678135i	$0.237212\pi$
$824$	1.69505	0.0590500
$825$	1.00000	0.0348155
$826$	0	0
$827$	18.0673	0.628262	0.314131	−	0.949380i	$-0.398287\pi$
$827$	18.0673	0.628262	0.314131	+	0.949380i	$0.398287\pi$
$828$	−11.9216	−0.414303
$829$	2.27225	0.0789187	0.0394593	−	0.999221i	$-0.487436\pi$
$829$	2.27225	0.0789187	0.0394593	+	0.999221i	$0.487436\pi$
$830$	6.38616	0.221667
$831$	12.2000	0.423213
$832$	13.2477	0.459282
$833$	0	0
$834$	−1.53136	−0.0530266
$835$	20.1987	0.699003
$836$	−4.79789	−0.165939
$837$	−4.86060	−0.168007
$838$	18.9327	0.654018
$839$	10.8975	0.376223	0.188112	−	0.982148i	$-0.439763\pi$
$839$	10.8975	0.376223	0.188112	+	0.982148i	$0.439763\pi$
$840$	0	0
$841$	25.4946	0.879123
$842$	−4.05877	−0.139874
$843$	−16.8809	−0.581408
$844$	−35.9091	−1.23604
$845$	18.1667	0.624953
$846$	1.12461	0.0386650
$847$	0	0
$848$	9.17335	0.315014
$849$	−13.7943	−0.473419
$850$	1.00613	0.0345100
$851$	−79.5578	−2.72721
$852$	−2.53939	−0.0869981
$853$	−17.8277	−0.610409	−0.305204	−	0.952287i	$-0.598725\pi$
$853$	−17.8277	−0.610409	−0.305204	+	0.952287i	$0.598725\pi$
$854$	0	0
$855$	3.31409	0.113340
$856$	−2.29430	−0.0784177
$857$	1.46488	0.0500393	0.0250196	−	0.999687i	$-0.492035\pi$
$857$	1.46488	0.0500393	0.0250196	+	0.999687i	$0.492035\pi$
$858$	4.14881	0.141638
$859$	44.6859	1.52466	0.762332	−	0.647186i	$-0.224054\pi$
$859$	44.6859	1.52466	0.762332	+	0.647186i	$0.224054\pi$
$860$	14.4529	0.492841
$861$	0	0
$862$	−7.54881	−0.257114
$863$	39.1099	1.33132	0.665659	−	0.746256i	$-0.268151\pi$
$863$	39.1099	1.33132	0.665659	+	0.746256i	$0.268151\pi$
$864$	5.86110	0.199399
$865$	15.7000	0.533815
$866$	−2.81945	−0.0958087
$867$	−15.1670	−0.515100
$868$	0	0
$869$	6.75643	0.229196
$870$	5.48599	0.185992
$871$	−17.1004	−0.579424
$872$	32.0704	1.08604
$873$	−8.64891	−0.292721
$874$	20.2811	0.686017
$875$	0	0
$876$	−6.99830	−0.236451
$877$	−7.48838	−0.252865	−0.126432	−	0.991975i	$-0.540353\pi$
$877$	−7.48838	−0.252865	−0.126432	+	0.991975i	$0.540353\pi$
$878$	2.40018	0.0810023
$879$	−8.48052	−0.286041
$880$	0.991352	0.0334185
$881$	−19.5729	−0.659429	−0.329714	−	0.944081i	$-0.606952\pi$
$881$	−19.5729	−0.659429	−0.329714	+	0.944081i	$0.606952\pi$
$882$	0	0
$883$	−8.51002	−0.286385	−0.143193	−	0.989695i	$-0.545737\pi$
$883$	−8.51002	−0.286385	−0.143193	+	0.989695i	$0.545737\pi$
$884$	−10.9423	−0.368028
$885$	−11.1270	−0.374028
$886$	−24.0139	−0.806764
$887$	17.7654	0.596505	0.298253	−	0.954487i	$-0.403596\pi$
$887$	17.7654	0.596505	0.298253	+	0.954487i	$0.403596\pi$
$888$	24.7540	0.830691
$889$	0	0
$890$	3.19651	0.107147
$891$	1.00000	0.0335013
$892$	−36.9897	−1.23851
$893$	5.01522	0.167828
$894$	0.0316350	0.00105803
$895$	4.44126	0.148455
$896$	0	0
$897$	45.9720	1.53496
$898$	−19.7473	−0.658975
$899$	−35.8812	−1.19670
$900$	−1.44772	−0.0482575
$901$	12.5278	0.417363
$902$	−8.61539	−0.286861
$903$	0	0
$904$	33.0633	1.09967
$905$	11.8535	0.394024
$906$	5.31307	0.176515
$907$	43.4073	1.44132	0.720658	−	0.693291i	$-0.243840\pi$
$907$	43.4073	1.44132	0.720658	+	0.693291i	$0.243840\pi$
$908$	−0.811585	−0.0269334
$909$	−9.47467	−0.314255
$910$	0	0
$911$	14.0291	0.464803	0.232402	−	0.972620i	$-0.425342\pi$
$911$	14.0291	0.464803	0.232402	+	0.972620i	$0.425342\pi$
$912$	3.28543	0.108792
$913$	8.59334	0.284398
$914$	14.5855	0.482447
$915$	9.77360	0.323105
$916$	−19.2636	−0.636487
$917$	0	0
$918$	1.00613	0.0332072
$919$	55.1345	1.81872	0.909359	−	0.416012i	$-0.136572\pi$
$919$	55.1345	1.81872	0.909359	+	0.416012i	$0.136572\pi$
$920$	−21.0988	−0.695608
$921$	−26.0487	−0.858335
$922$	11.6710	0.384364
$923$	9.79240	0.322321
$924$	0	0
$925$	−9.66129	−0.317661
$926$	−18.2863	−0.600925
$927$	−0.661565	−0.0217287
$928$	43.2669	1.42031
$929$	−10.2516	−0.336343	−0.168172	−	0.985758i	$-0.553786\pi$
$929$	−10.2516	−0.336343	−0.168172	+	0.985758i	$0.553786\pi$
$930$	−3.61217	−0.118448
$931$	0	0
$932$	22.4779	0.736287
$933$	−21.8397	−0.715001
$934$	14.7372	0.482217
$935$	1.35387	0.0442762
$936$	−14.3039	−0.467539
$937$	−9.62346	−0.314385	−0.157192	−	0.987568i	$-0.550244\pi$
$937$	−9.62346	−0.314385	−0.157192	+	0.987568i	$0.550244\pi$
$938$	0	0
$939$	−1.89738	−0.0619188
$940$	−2.19084	−0.0714573
$941$	−8.30753	−0.270818	−0.135409	−	0.990790i	$-0.543235\pi$
$941$	−8.30753	−0.270818	−0.135409	+	0.990790i	$0.543235\pi$
$942$	11.2697	0.367187
$943$	−95.4651	−3.10877
$944$	−11.0307	−0.359020
$945$	0	0
$946$	−7.41905	−0.241214
$947$	7.73025	0.251199	0.125600	−	0.992081i	$-0.459915\pi$
$947$	7.73025	0.251199	0.125600	+	0.992081i	$0.459915\pi$
$948$	−9.78144	−0.317686
$949$	26.9869	0.876030
$950$	2.46288	0.0799063
$951$	−20.1839	−0.654507
$952$	0	0
$953$	−21.0114	−0.680627	−0.340313	−	0.940312i	$-0.610533\pi$
$953$	−21.0114	−0.680627	−0.340313	+	0.940312i	$0.610533\pi$
$954$	6.87668	0.222641
$955$	−15.1166	−0.489162
$956$	−22.2216	−0.718698
$957$	7.38204	0.238628
$958$	−20.2728	−0.654985
$959$	0	0
$960$	2.37299	0.0765879
$961$	−7.37455	−0.237889
$962$	−40.0829	−1.29232
$963$	0.895448	0.0288554
$964$	8.71407	0.280661
$965$	−22.6853	−0.730265
$966$	0	0
$967$	−27.3064	−0.878115	−0.439057	−	0.898459i	$-0.644688\pi$
$967$	−27.3064	−0.878115	−0.439057	+	0.898459i	$0.644688\pi$
$968$	−2.56219	−0.0823518
$969$	4.48684	0.144138
$970$	−6.42746	−0.206373
$971$	−36.5971	−1.17446	−0.587228	−	0.809422i	$-0.699781\pi$
$971$	−36.5971	−1.17446	−0.587228	+	0.809422i	$0.699781\pi$
$972$	−1.44772	−0.0464358
$973$	0	0
$974$	−3.25511	−0.104300
$975$	5.58271	0.178790
$976$	9.68907	0.310140
$977$	19.1629	0.613074	0.306537	−	0.951859i	$-0.400830\pi$
$977$	19.1629	0.613074	0.306537	+	0.951859i	$0.400830\pi$
$978$	1.08134	0.0345773
$979$	4.30128	0.137469
$980$	0	0
$981$	−12.5168	−0.399631
$982$	6.42364	0.204987
$983$	19.3604	0.617502	0.308751	−	0.951143i	$-0.400089\pi$
$983$	19.3604	0.617502	0.308751	+	0.951143i	$0.400089\pi$
$984$	29.7035	0.946912
$985$	21.9089	0.698075
$986$	7.42730	0.236533
$987$	0	0
$988$	−26.7853	−0.852153
$989$	−82.2088	−2.61409
$990$	0.743153	0.0236189
$991$	12.4409	0.395198	0.197599	−	0.980283i	$-0.436686\pi$
$991$	12.4409	0.395198	0.197599	+	0.980283i	$0.436686\pi$
$992$	−28.4885	−0.904509
$993$	−28.4757	−0.903651
$994$	0	0
$995$	24.0441	0.762250
$996$	−12.4408	−0.394201
$997$	−54.6196	−1.72982	−0.864911	−	0.501926i	$-0.832625\pi$
$997$	−54.6196	−1.72982	−0.864911	+	0.501926i	$0.832625\pi$
$998$	−11.0666	−0.350306
$999$	−9.66129	−0.305670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8085.2.a.cn.1.6		10
7.2	even	3		1155.2.q.l.991.5	yes	20
7.4	even	3		1155.2.q.l.331.5	✓	20
7.6	odd	2		8085.2.a.ck.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.q.l.331.5	✓	20	7.4	even	3
1155.2.q.l.991.5	yes	20	7.2	even	3
8085.2.a.ck.1.6		10	7.6	odd	2
8085.2.a.cn.1.6		10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.743153 q^{2} +1.00000 q^{3} -1.44772 q^{4} +1.00000 q^{5} +0.743153 q^{6} -2.56219 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.743153 q^{2} +1.00000 q^{3} -1.44772 q^{4} +1.00000 q^{5} +0.743153 q^{6} -2.56219 q^{8} +1.00000 q^{9} +0.743153 q^{10} +1.00000 q^{11} -1.44772 q^{12} +5.58271 q^{13} +1.00000 q^{15} +0.991352 q^{16} +1.35387 q^{17} +0.743153 q^{18} +3.31409 q^{19} -1.44772 q^{20} +0.743153 q^{22} +8.23470 q^{23} -2.56219 q^{24} +1.00000 q^{25} +4.14881 q^{26} +1.00000 q^{27} +7.38204 q^{29} +0.743153 q^{30} -4.86060 q^{31} +5.86110 q^{32} +1.00000 q^{33} +1.00613 q^{34} -1.44772 q^{36} -9.66129 q^{37} +2.46288 q^{38} +5.58271 q^{39} -2.56219 q^{40} -11.5930 q^{41} -9.98321 q^{43} -1.44772 q^{44} +1.00000 q^{45} +6.11964 q^{46} +1.51330 q^{47} +0.991352 q^{48} +0.743153 q^{50} +1.35387 q^{51} -8.08223 q^{52} +9.25338 q^{53} +0.743153 q^{54} +1.00000 q^{55} +3.31409 q^{57} +5.48599 q^{58} -11.1270 q^{59} -1.44772 q^{60} +9.77360 q^{61} -3.61217 q^{62} +2.37299 q^{64} +5.58271 q^{65} +0.743153 q^{66} -3.06310 q^{67} -1.96003 q^{68} +8.23470 q^{69} +1.75406 q^{71} -2.56219 q^{72} +4.83400 q^{73} -7.17982 q^{74} +1.00000 q^{75} -4.79789 q^{76} +4.14881 q^{78} +6.75643 q^{79} +0.991352 q^{80} +1.00000 q^{81} -8.61539 q^{82} +8.59334 q^{83} +1.35387 q^{85} -7.41905 q^{86} +7.38204 q^{87} -2.56219 q^{88} +4.30128 q^{89} +0.743153 q^{90} -11.9216 q^{92} -4.86060 q^{93} +1.12461 q^{94} +3.31409 q^{95} +5.86110 q^{96} -8.64891 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 10 q^{3} + 12 q^{4} + 10 q^{5} + 10 q^{9}+O(q^{10}) \) 10 * q + 10 * q^3 + 12 * q^4 + 10 * q^5 + 10 * q^9	\( 10 q + 10 q^{3} + 12 q^{4} + 10 q^{5} + 10 q^{9} + 10 q^{11} + 12 q^{12} + 4 q^{13} + 10 q^{15} + 24 q^{16} + 12 q^{17} + 9 q^{19} + 12 q^{20} - q^{23} + 10 q^{25} + 6 q^{26} + 10 q^{27} + 3 q^{29} + 9 q^{31} - 10 q^{32} + 10 q^{33} + 6 q^{34} + 12 q^{36} + 3 q^{37} + 42 q^{38} + 4 q^{39} + 3 q^{41} + 12 q^{44} + 10 q^{45} - 22 q^{46} + 21 q^{47} + 24 q^{48} + 12 q^{51} + 24 q^{52} - 5 q^{53} + 10 q^{55} + 9 q^{57} - 26 q^{58} + 16 q^{59} + 12 q^{60} + 20 q^{61} - 18 q^{62} + 70 q^{64} + 4 q^{65} - q^{67} + 30 q^{68} - q^{69} + 22 q^{71} - q^{73} - 34 q^{74} + 10 q^{75} - 28 q^{76} + 6 q^{78} + 19 q^{79} + 24 q^{80} + 10 q^{81} + 32 q^{82} + 20 q^{83} + 12 q^{85} + 3 q^{87} + 18 q^{89} - 8 q^{92} + 9 q^{93} - 6 q^{94} + 9 q^{95} - 10 q^{96} + 6 q^{97} + 10 q^{99}+O(q^{100}) \) 10 * q + 10 * q^3 + 12 * q^4 + 10 * q^5 + 10 * q^9 + 10 * q^11 + 12 * q^12 + 4 * q^13 + 10 * q^15 + 24 * q^16 + 12 * q^17 + 9 * q^19 + 12 * q^20 - q^23 + 10 * q^25 + 6 * q^26 + 10 * q^27 + 3 * q^29 + 9 * q^31 - 10 * q^32 + 10 * q^33 + 6 * q^34 + 12 * q^36 + 3 * q^37 + 42 * q^38 + 4 * q^39 + 3 * q^41 + 12 * q^44 + 10 * q^45 - 22 * q^46 + 21 * q^47 + 24 * q^48 + 12 * q^51 + 24 * q^52 - 5 * q^53 + 10 * q^55 + 9 * q^57 - 26 * q^58 + 16 * q^59 + 12 * q^60 + 20 * q^61 - 18 * q^62 + 70 * q^64 + 4 * q^65 - q^67 + 30 * q^68 - q^69 + 22 * q^71 - q^73 - 34 * q^74 + 10 * q^75 - 28 * q^76 + 6 * q^78 + 19 * q^79 + 24 * q^80 + 10 * q^81 + 32 * q^82 + 20 * q^83 + 12 * q^85 + 3 * q^87 + 18 * q^89 - 8 * q^92 + 9 * q^93 - 6 * q^94 + 9 * q^95 - 10 * q^96 + 6 * q^97 + 10 * q^99

Introduction

L-functions

Modular forms

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Database

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