LMFDB - Embedded newform 8085.2.a.br.1.5

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:	$5$
Coefficient field:	5.5.833376.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 7x^{3} + 10x - 2 $ x^5 - 7x^3 + 10x - 2
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 1155)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-2.15639$ 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)

$f(q)$	$=$	$q+2.15639 q^{2} -1.00000 q^{3} +2.65001 q^{4} +1.00000 q^{5} -2.15639 q^{6} +1.40167 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.15639 q^{2} -1.00000 q^{3} +2.65001 q^{4} +1.00000 q^{5} -2.15639 q^{6} +1.40167 q^{8} +1.00000 q^{9} +2.15639 q^{10} -1.00000 q^{11} -2.65001 q^{12} -3.03531 q^{13} -1.00000 q^{15} -2.27747 q^{16} +1.40167 q^{17} +2.15639 q^{18} +7.71445 q^{19} +2.65001 q^{20} -2.15639 q^{22} -7.61593 q^{23} -1.40167 q^{24} +1.00000 q^{25} -6.54531 q^{26} -1.00000 q^{27} +0.878922 q^{29} -2.15639 q^{30} +6.68532 q^{31} -7.71445 q^{32} +1.00000 q^{33} +3.02255 q^{34} +2.65001 q^{36} -2.84979 q^{37} +16.6354 q^{38} +3.03531 q^{39} +1.40167 q^{40} +9.58062 q^{41} +5.48249 q^{43} -2.65001 q^{44} +1.00000 q^{45} -16.4229 q^{46} -2.12726 q^{47} +2.27747 q^{48} +2.15639 q^{50} -1.40167 q^{51} -8.04360 q^{52} +11.3114 q^{53} -2.15639 q^{54} -1.00000 q^{55} -7.71445 q^{57} +1.89530 q^{58} +4.27747 q^{59} -2.65001 q^{60} +4.00000 q^{61} +14.4161 q^{62} -12.0804 q^{64} -3.03531 q^{65} +2.15639 q^{66} +8.24338 q^{67} +3.71445 q^{68} +7.61593 q^{69} +11.0712 q^{71} +1.40167 q^{72} +13.0308 q^{73} -6.14526 q^{74} -1.00000 q^{75} +20.4434 q^{76} +6.54531 q^{78} -9.18049 q^{79} -2.27747 q^{80} +1.00000 q^{81} +20.6595 q^{82} -1.00313 q^{83} +1.40167 q^{85} +11.8224 q^{86} -0.878922 q^{87} -1.40167 q^{88} +3.27690 q^{89} +2.15639 q^{90} -20.1823 q^{92} -6.68532 q^{93} -4.58719 q^{94} +7.71445 q^{95} +7.71445 q^{96} -10.9859 q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 5 q^{3} + 4 q^{4} + 5 q^{5} + 5 q^{9}+O(q^{10}) $ 5 * q - 5 * q^3 + 4 * q^4 + 5 * q^5 + 5 * q^9	$ 5 q - 5 q^{3} + 4 q^{4} + 5 q^{5} + 5 q^{9} - 5 q^{11} - 4 q^{12} + q^{13} - 5 q^{15} - 6 q^{16} + 10 q^{19} + 4 q^{20} + 9 q^{23} + 5 q^{25} - 18 q^{26} - 5 q^{27} - q^{29} + 8 q^{31} - 10 q^{32} + 5 q^{33} + 2 q^{34} + 4 q^{36} - 12 q^{37} + 30 q^{38} - q^{39} + 17 q^{41} + q^{43} - 4 q^{44} + 5 q^{45} - 24 q^{46} - 3 q^{47} + 6 q^{48} + 10 q^{52} - 3 q^{53} - 5 q^{55} - 10 q^{57} + 4 q^{58} + 16 q^{59} - 4 q^{60} + 20 q^{61} + 18 q^{62} - 18 q^{64} + q^{65} - 2 q^{67} - 10 q^{68} - 9 q^{69} + 32 q^{71} + 18 q^{73} + 8 q^{74} - 5 q^{75} - 2 q^{76} + 18 q^{78} + 8 q^{79} - 6 q^{80} + 5 q^{81} + 6 q^{82} + 2 q^{83} + 16 q^{86} + q^{87} + 2 q^{89} - 2 q^{92} - 8 q^{93} - 2 q^{94} + 10 q^{95} + 10 q^{96} - 20 q^{97} - 5 q^{99}+O(q^{100}) $ 5 * q - 5 * q^3 + 4 * q^4 + 5 * q^5 + 5 * q^9 - 5 * q^11 - 4 * q^12 + q^13 - 5 * q^15 - 6 * q^16 + 10 * q^19 + 4 * q^20 + 9 * q^23 + 5 * q^25 - 18 * q^26 - 5 * q^27 - q^29 + 8 * q^31 - 10 * q^32 + 5 * q^33 + 2 * q^34 + 4 * q^36 - 12 * q^37 + 30 * q^38 - q^39 + 17 * q^41 + q^43 - 4 * q^44 + 5 * q^45 - 24 * q^46 - 3 * q^47 + 6 * q^48 + 10 * q^52 - 3 * q^53 - 5 * q^55 - 10 * q^57 + 4 * q^58 + 16 * q^59 - 4 * q^60 + 20 * q^61 + 18 * q^62 - 18 * q^64 + q^65 - 2 * q^67 - 10 * q^68 - 9 * q^69 + 32 * q^71 + 18 * q^73 + 8 * q^74 - 5 * q^75 - 2 * q^76 + 18 * q^78 + 8 * q^79 - 6 * q^80 + 5 * q^81 + 6 * q^82 + 2 * q^83 + 16 * q^86 + q^87 + 2 * q^89 - 2 * q^92 - 8 * q^93 - 2 * q^94 + 10 * q^95 + 10 * q^96 - 20 * q^97 - 5 * 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 $

$2$	2.15639	1.52480	0.762398	−	0.647108i	$-0.224022\pi$
$2$	2.15639	1.52480	0.762398	+	0.647108i	$0.224022\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.65001	1.32501
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.15639	−0.880342
$7$	0	0
$7$	0	0
$8$	1.40167	0.495567
$9$	1.00000	0.333333
$10$	2.15639	0.681910
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−2.65001	−0.764992
$13$	−3.03531	−0.841843	−0.420922	−	0.907097i	$-0.638293\pi$
$13$	−3.03531	−0.841843	−0.420922	+	0.907097i	$0.638293\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	−2.27747	−0.569367
$17$	1.40167	0.339956	0.169978	−	0.985448i	$-0.445630\pi$
$17$	1.40167	0.339956	0.169978	+	0.985448i	$0.445630\pi$
$18$	2.15639	0.508266
$19$	7.71445	1.76982	0.884908	−	0.465766i	$-0.154221\pi$
$19$	7.71445	1.76982	0.884908	+	0.465766i	$0.154221\pi$
$20$	2.65001	0.592560
$21$	0	0
$22$	−2.15639	−0.459744
$23$	−7.61593	−1.58803	−0.794015	−	0.607898i	$-0.792013\pi$
$23$	−7.61593	−1.58803	−0.794015	+	0.607898i	$0.792013\pi$
$24$	−1.40167	−0.286116
$25$	1.00000	0.200000
$26$	−6.54531	−1.28364
$27$	−1.00000	−0.192450
$28$	0	0
$29$	0.878922	0.163212	0.0816058	−	0.996665i	$-0.473995\pi$
$29$	0.878922	0.163212	0.0816058	+	0.996665i	$0.473995\pi$
$30$	−2.15639	−0.393701
$31$	6.68532	1.20072	0.600359	−	0.799730i	$-0.295024\pi$
$31$	6.68532	1.20072	0.600359	+	0.799730i	$0.295024\pi$
$32$	−7.71445	−1.36374
$33$	1.00000	0.174078
$34$	3.02255	0.518364
$35$	0	0
$36$	2.65001	0.441668
$37$	−2.84979	−0.468503	−0.234251	−	0.972176i	$-0.575264\pi$
$37$	−2.84979	−0.468503	−0.234251	+	0.972176i	$0.575264\pi$
$38$	16.6354	2.69861
$39$	3.03531	0.486039
$40$	1.40167	0.221624
$41$	9.58062	1.49624	0.748120	−	0.663563i	$-0.230957\pi$
$41$	9.58062	1.49624	0.748120	+	0.663563i	$0.230957\pi$
$42$	0	0
$43$	5.48249	0.836072	0.418036	−	0.908431i	$-0.362719\pi$
$43$	5.48249	0.836072	0.418036	+	0.908431i	$0.362719\pi$
$44$	−2.65001	−0.399504
$45$	1.00000	0.149071
$46$	−16.4229	−2.42142
$47$	−2.12726	−0.310292	−0.155146	−	0.987892i	$-0.549585\pi$
$47$	−2.12726	−0.310292	−0.155146	+	0.987892i	$0.549585\pi$
$48$	2.27747	0.328724
$49$	0	0
$50$	2.15639	0.304959
$51$	−1.40167	−0.196274
$52$	−8.04360	−1.11545
$53$	11.3114	1.55375	0.776873	−	0.629657i	$-0.216805\pi$
$53$	11.3114	1.55375	0.776873	+	0.629657i	$0.216805\pi$
$54$	−2.15639	−0.293447
$55$	−1.00000	−0.134840
$56$	0	0
$57$	−7.71445	−1.02180
$58$	1.89530	0.248865
$59$	4.27747	0.556879	0.278439	−	0.960454i	$-0.410183\pi$
$59$	4.27747	0.556879	0.278439	+	0.960454i	$0.410183\pi$
$60$	−2.65001	−0.342115
$61$	4.00000	0.512148	0.256074	−	0.966657i	$-0.417571\pi$
$61$	4.00000	0.512148	0.256074	+	0.966657i	$0.417571\pi$
$62$	14.4161	1.83085
$63$	0	0
$64$	−12.0804	−1.51005
$65$	−3.03531	−0.376484
$66$	2.15639	0.265433
$67$	8.24338	1.00709	0.503545	−	0.863969i	$-0.332029\pi$
$67$	8.24338	1.00709	0.503545	+	0.863969i	$0.332029\pi$
$68$	3.71445	0.450443
$69$	7.61593	0.916850
$70$	0	0
$71$	11.0712	1.31391	0.656954	−	0.753931i	$-0.271845\pi$
$71$	11.0712	1.31391	0.656954	+	0.753931i	$0.271845\pi$
$72$	1.40167	0.165189
$73$	13.0308	1.52515	0.762573	−	0.646903i	$-0.223936\pi$
$73$	13.0308	1.52515	0.762573	+	0.646903i	$0.223936\pi$
$74$	−6.14526	−0.714371
$75$	−1.00000	−0.115470
$76$	20.4434	2.34502
$77$	0	0
$78$	6.54531	0.741110
$79$	−9.18049	−1.03289	−0.516443	−	0.856322i	$-0.672744\pi$
$79$	−9.18049	−1.03289	−0.516443	+	0.856322i	$0.672744\pi$
$80$	−2.27747	−0.254629
$81$	1.00000	0.111111
$82$	20.6595	2.28146
$83$	−1.00313	−0.110108	−0.0550539	−	0.998483i	$-0.517533\pi$
$83$	−1.00313	−0.110108	−0.0550539	+	0.998483i	$0.517533\pi$
$84$	0	0
$85$	1.40167	0.152033
$86$	11.8224	1.27484
$87$	−0.878922	−0.0942303
$88$	−1.40167	−0.149419
$89$	3.27690	0.347351	0.173675	−	0.984803i	$-0.444436\pi$
$89$	3.27690	0.347351	0.173675	+	0.984803i	$0.444436\pi$
$90$	2.15639	0.227303
$91$	0	0
$92$	−20.1823	−2.10415
$93$	−6.68532	−0.693235
$94$	−4.58719	−0.473133
$95$	7.71445	0.791486
$96$	7.71445	0.787353
$97$	−10.9859	−1.11545	−0.557725	−	0.830026i	$-0.688326\pi$
$97$	−10.9859	−1.11545	−0.557725	+	0.830026i	$0.688326\pi$
$98$	0	0
$99$	−1.00000	−0.100504
$100$	2.65001	0.265001
$101$	7.30347	0.726722	0.363361	−	0.931648i	$-0.381629\pi$
$101$	7.30347	0.726722	0.363361	+	0.931648i	$0.381629\pi$
$102$	−3.02255	−0.299277
$103$	−0.803348	−0.0791563	−0.0395781	−	0.999216i	$-0.512601\pi$
$103$	−0.803348	−0.0791563	−0.0395781	+	0.999216i	$0.512601\pi$
$104$	−4.25452	−0.417190
$105$	0	0
$106$	24.3919	2.36915
$107$	4.04511	0.391055	0.195528	−	0.980698i	$-0.437358\pi$
$107$	4.04511	0.391055	0.195528	+	0.980698i	$0.437358\pi$
$108$	−2.65001	−0.254997
$109$	−11.4084	−1.09273	−0.546364	−	0.837548i	$-0.683989\pi$
$109$	−11.4084	−1.09273	−0.546364	+	0.837548i	$0.683989\pi$
$110$	−2.15639	−0.205604
$111$	2.84979	0.270490
$112$	0	0
$113$	−1.73082	−0.162822	−0.0814112	−	0.996681i	$-0.525943\pi$
$113$	−1.73082	−0.162822	−0.0814112	+	0.996681i	$0.525943\pi$
$114$	−16.6354	−1.55804
$115$	−7.61593	−0.710189
$116$	2.32915	0.216256
$117$	−3.03531	−0.280614
$118$	9.22388	0.849127
$119$	0	0
$120$	−1.40167	−0.127955
$121$	1.00000	0.0909091
$122$	8.62555	0.780921
$123$	−9.58062	−0.863855
$124$	17.7162	1.59096
$125$	1.00000	0.0894427
$126$	0	0
$127$	−16.5855	−1.47172	−0.735861	−	0.677133i	$-0.763222\pi$
$127$	−16.5855	−1.47172	−0.735861	+	0.677133i	$0.763222\pi$
$128$	−10.6212	−0.938787
$129$	−5.48249	−0.482706
$130$	−6.54531	−0.574061
$131$	13.9593	1.21963	0.609813	−	0.792545i	$-0.291245\pi$
$131$	13.9593	1.21963	0.609813	+	0.792545i	$0.291245\pi$
$132$	2.65001	0.230654
$133$	0	0
$134$	17.7759	1.53561
$135$	−1.00000	−0.0860663
$136$	1.96469	0.168471
$137$	7.52085	0.642549	0.321275	−	0.946986i	$-0.395889\pi$
$137$	7.52085	0.642549	0.321275	+	0.946986i	$0.395889\pi$
$138$	16.4229	1.39801
$139$	−3.15448	−0.267560	−0.133780	−	0.991011i	$-0.542712\pi$
$139$	−3.15448	−0.267560	−0.133780	+	0.991011i	$0.542712\pi$
$140$	0	0
$141$	2.12726	0.179147
$142$	23.8738	2.00344
$143$	3.03531	0.253825
$144$	−2.27747	−0.189789
$145$	0.878922	0.0729905
$146$	28.0996	2.32554
$147$	0	0
$148$	−7.55197	−0.620768
$149$	12.5966	1.03195	0.515977	−	0.856603i	$-0.327429\pi$
$149$	12.5966	1.03195	0.515977	+	0.856603i	$0.327429\pi$
$150$	−2.15639	−0.176068
$151$	11.3711	0.925369	0.462685	−	0.886523i	$-0.346886\pi$
$151$	11.3711	0.925369	0.462685	+	0.886523i	$0.346886\pi$
$152$	10.8131	0.877062
$153$	1.40167	0.113319
$154$	0	0
$155$	6.68532	0.536978
$156$	8.04360	0.644004
$157$	−16.6886	−1.33189	−0.665947	−	0.745999i	$-0.731972\pi$
$157$	−16.6886	−1.33189	−0.665947	+	0.745999i	$0.731972\pi$
$158$	−19.7967	−1.57494
$159$	−11.3114	−0.897056
$160$	−7.71445	−0.609881
$161$	0	0
$162$	2.15639	0.169422
$163$	12.7401	0.997878	0.498939	−	0.866637i	$-0.333723\pi$
$163$	12.7401	0.997878	0.498939	+	0.866637i	$0.333723\pi$
$164$	25.3887	1.98253
$165$	1.00000	0.0778499
$166$	−2.16314	−0.167892
$167$	14.9224	1.15473	0.577367	−	0.816485i	$-0.304080\pi$
$167$	14.9224	1.15473	0.577367	+	0.816485i	$0.304080\pi$
$168$	0	0
$169$	−3.78689	−0.291300
$170$	3.02255	0.231819
$171$	7.71445	0.589939
$172$	14.5287	1.10780
$173$	−21.8195	−1.65891	−0.829454	−	0.558575i	$-0.811348\pi$
$173$	−21.8195	−1.65891	−0.829454	+	0.558575i	$0.811348\pi$
$174$	−1.89530	−0.143682
$175$	0	0
$176$	2.27747	0.171671
$177$	−4.27747	−0.321514
$178$	7.06627	0.529639
$179$	17.6809	1.32153	0.660765	−	0.750593i	$-0.270232\pi$
$179$	17.6809	1.32153	0.660765	+	0.750593i	$0.270232\pi$
$180$	2.65001	0.197520
$181$	5.85332	0.435074	0.217537	−	0.976052i	$-0.430198\pi$
$181$	5.85332	0.435074	0.217537	+	0.976052i	$0.430198\pi$
$182$	0	0
$183$	−4.00000	−0.295689
$184$	−10.6750	−0.786975
$185$	−2.84979	−0.209521
$186$	−14.4161	−1.05704
$187$	−1.40167	−0.102501
$188$	−5.63725	−0.411139
$189$	0	0
$190$	16.6354	1.20686
$191$	−8.37730	−0.606160	−0.303080	−	0.952965i	$-0.598015\pi$
$191$	−8.37730	−0.606160	−0.303080	+	0.952965i	$0.598015\pi$
$192$	12.0804	0.871829
$193$	−4.81505	−0.346595	−0.173297	−	0.984870i	$-0.555442\pi$
$193$	−4.81505	−0.346595	−0.173297	+	0.984870i	$0.555442\pi$
$194$	−23.6899	−1.70083
$195$	3.03531	0.217363
$196$	0	0
$197$	−26.5116	−1.88887	−0.944437	−	0.328693i	$-0.893392\pi$
$197$	−26.5116	−1.88887	−0.944437	+	0.328693i	$0.893392\pi$
$198$	−2.15639	−0.153248
$199$	23.5278	1.66784	0.833921	−	0.551884i	$-0.186091\pi$
$199$	23.5278	1.66784	0.833921	+	0.551884i	$0.186091\pi$
$200$	1.40167	0.0991133
$201$	−8.24338	−0.581443
$202$	15.7491	1.10810
$203$	0	0
$204$	−3.71445	−0.260064
$205$	9.58062	0.669139
$206$	−1.73233	−0.120697
$207$	−7.61593	−0.529343
$208$	6.91282	0.479318
$209$	−7.71445	−0.533620
$210$	0	0
$211$	−3.33057	−0.229286	−0.114643	−	0.993407i	$-0.536572\pi$
$211$	−3.33057	−0.229286	−0.114643	+	0.993407i	$0.536572\pi$
$212$	29.9754	2.05872
$213$	−11.0712	−0.758585
$214$	8.72282	0.596280
$215$	5.48249	0.373903
$216$	−1.40167	−0.0953718
$217$	0	0
$218$	−24.6010	−1.66619
$219$	−13.0308	−0.880543
$220$	−2.65001	−0.178664
$221$	−4.25452	−0.286190
$222$	6.14526	0.412443
$223$	3.72120	0.249190	0.124595	−	0.992208i	$-0.460237\pi$
$223$	3.72120	0.249190	0.124595	+	0.992208i	$0.460237\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	−3.73233	−0.248271
$227$	−13.2097	−0.876759	−0.438380	−	0.898790i	$-0.644447\pi$
$227$	−13.2097	−0.876759	−0.438380	+	0.898790i	$0.644447\pi$
$228$	−20.4434	−1.35390
$229$	7.82667	0.517201	0.258600	−	0.965984i	$-0.416739\pi$
$229$	7.82667	0.517201	0.258600	+	0.965984i	$0.416739\pi$
$230$	−16.4229	−1.08289
$231$	0	0
$232$	1.23196	0.0808822
$233$	−4.04612	−0.265070	−0.132535	−	0.991178i	$-0.542312\pi$
$233$	−4.04612	−0.265070	−0.132535	+	0.991178i	$0.542312\pi$
$234$	−6.54531	−0.427880
$235$	−2.12726	−0.138767
$236$	11.3353	0.737867
$237$	9.18049	0.596337
$238$	0	0
$239$	11.3194	0.732193	0.366097	−	0.930577i	$-0.380694\pi$
$239$	11.3194	0.732193	0.366097	+	0.930577i	$0.380694\pi$
$240$	2.27747	0.147010
$241$	25.3464	1.63270	0.816351	−	0.577556i	$-0.195994\pi$
$241$	25.3464	1.63270	0.816351	+	0.577556i	$0.195994\pi$
$242$	2.15639	0.138618
$243$	−1.00000	−0.0641500
$244$	10.6000	0.678598
$245$	0	0
$246$	−20.6595	−1.31720
$247$	−23.4157	−1.48991
$248$	9.37064	0.595036
$249$	1.00313	0.0635707
$250$	2.15639	0.136382
$251$	0.653906	0.0412742	0.0206371	−	0.999787i	$-0.493431\pi$
$251$	0.653906	0.0412742	0.0206371	+	0.999787i	$0.493431\pi$
$252$	0	0
$253$	7.61593	0.478809
$254$	−35.7647	−2.24408
$255$	−1.40167	−0.0877762
$256$	1.25747	0.0785921
$257$	−8.30611	−0.518121	−0.259060	−	0.965861i	$-0.583413\pi$
$257$	−8.30611	−0.518121	−0.259060	+	0.965861i	$0.583413\pi$
$258$	−11.8224	−0.736029
$259$	0	0
$260$	−8.04360	−0.498843
$261$	0.878922	0.0544039
$262$	30.1016	1.85968
$263$	14.9810	0.923771	0.461885	−	0.886940i	$-0.347173\pi$
$263$	14.9810	0.923771	0.461885	+	0.886940i	$0.347173\pi$
$264$	1.40167	0.0862671
$265$	11.3114	0.694856
$266$	0	0
$267$	−3.27690	−0.200543
$268$	21.8450	1.33440
$269$	−11.2025	−0.683027	−0.341513	−	0.939877i	$-0.610939\pi$
$269$	−11.2025	−0.683027	−0.341513	+	0.939877i	$0.610939\pi$
$270$	−2.15639	−0.131234
$271$	−16.1118	−0.978724	−0.489362	−	0.872081i	$-0.662770\pi$
$271$	−16.1118	−0.978724	−0.489362	+	0.872081i	$0.662770\pi$
$272$	−3.19227	−0.193560
$273$	0	0
$274$	16.2179	0.979757
$275$	−1.00000	−0.0603023
$276$	20.1823	1.21483
$277$	26.7701	1.60846	0.804229	−	0.594319i	$-0.202578\pi$
$277$	26.7701	1.60846	0.804229	+	0.594319i	$0.202578\pi$
$278$	−6.80229	−0.407974
$279$	6.68532	0.400240
$280$	0	0
$281$	9.82565	0.586149	0.293075	−	0.956090i	$-0.405322\pi$
$281$	9.82565	0.586149	0.293075	+	0.956090i	$0.405322\pi$
$282$	4.58719	0.273163
$283$	13.6143	0.809286	0.404643	−	0.914475i	$-0.367396\pi$
$283$	13.6143	0.809286	0.404643	+	0.914475i	$0.367396\pi$
$284$	29.3388	1.74094
$285$	−7.71445	−0.456965
$286$	6.54531	0.387032
$287$	0	0
$288$	−7.71445	−0.454578
$289$	−15.0353	−0.884430
$290$	1.89530	0.111296
$291$	10.9859	0.644005
$292$	34.5319	2.02082
$293$	−8.06350	−0.471075	−0.235537	−	0.971865i	$-0.575685\pi$
$293$	−8.06350	−0.471075	−0.235537	+	0.971865i	$0.575685\pi$
$294$	0	0
$295$	4.27747	0.249044
$296$	−3.99448	−0.232174
$297$	1.00000	0.0580259
$298$	27.1631	1.57352
$299$	23.1167	1.33687
$300$	−2.65001	−0.152998
$301$	0	0
$302$	24.5206	1.41100
$303$	−7.30347	−0.419573
$304$	−17.5694	−1.00767
$305$	4.00000	0.229039
$306$	3.02255	0.172788
$307$	−24.8861	−1.42032	−0.710162	−	0.704038i	$-0.751378\pi$
$307$	−24.8861	−1.42032	−0.710162	+	0.704038i	$0.751378\pi$
$308$	0	0
$309$	0.803348	0.0457009
$310$	14.4161	0.818782
$311$	31.7542	1.80062	0.900308	−	0.435254i	$-0.143341\pi$
$311$	31.7542	1.80062	0.900308	+	0.435254i	$0.143341\pi$
$312$	4.25452	0.240864
$313$	19.2374	1.08736	0.543681	−	0.839292i	$-0.317030\pi$
$313$	19.2374	1.08736	0.543681	+	0.839292i	$0.317030\pi$
$314$	−35.9871	−2.03087
$315$	0	0
$316$	−24.3284	−1.36858
$317$	17.1382	0.962579	0.481290	−	0.876562i	$-0.340168\pi$
$317$	17.1382	0.962579	0.481290	+	0.876562i	$0.340168\pi$
$318$	−24.3919	−1.36783
$319$	−0.878922	−0.0492102
$320$	−12.0804	−0.675316
$321$	−4.04511	−0.225776
$322$	0	0
$323$	10.8131	0.601660
$324$	2.65001	0.147223
$325$	−3.03531	−0.168369
$326$	27.4725	1.52156
$327$	11.4084	0.630887
$328$	13.4289	0.741487
$329$	0	0
$330$	2.15639	0.118705
$331$	−32.3435	−1.77776	−0.888880	−	0.458140i	$-0.848516\pi$
$331$	−32.3435	−1.77776	−0.888880	+	0.458140i	$0.848516\pi$
$332$	−2.65830	−0.145893
$333$	−2.84979	−0.156168
$334$	32.1786	1.76073
$335$	8.24338	0.450384
$336$	0	0
$337$	14.9970	0.816936	0.408468	−	0.912773i	$-0.366063\pi$
$337$	14.9970	0.816936	0.408468	+	0.912773i	$0.366063\pi$
$338$	−8.16602	−0.444173
$339$	1.73082	0.0940055
$340$	3.71445	0.201444
$341$	−6.68532	−0.362030
$342$	16.6354	0.899537
$343$	0	0
$344$	7.68466	0.414329
$345$	7.61593	0.410028
$346$	−47.0514	−2.52950
$347$	−12.7424	−0.684049	−0.342024	−	0.939691i	$-0.611113\pi$
$347$	−12.7424	−0.684049	−0.342024	+	0.939691i	$0.611113\pi$
$348$	−2.32915	−0.124856
$349$	−28.8558	−1.54461	−0.772307	−	0.635249i	$-0.780897\pi$
$349$	−28.8558	−1.54461	−0.772307	+	0.635249i	$0.780897\pi$
$350$	0	0
$351$	3.03531	0.162013
$352$	7.71445	0.411182
$353$	−4.42548	−0.235545	−0.117772	−	0.993041i	$-0.537575\pi$
$353$	−4.42548	−0.235545	−0.117772	+	0.993041i	$0.537575\pi$
$354$	−9.22388	−0.490244
$355$	11.0712	0.587598
$356$	8.68381	0.460241
$357$	0	0
$358$	38.1268	2.01506
$359$	−23.9686	−1.26501	−0.632507	−	0.774554i	$-0.717974\pi$
$359$	−23.9686	−1.26501	−0.632507	+	0.774554i	$0.717974\pi$
$360$	1.40167	0.0738747
$361$	40.5127	2.13225
$362$	12.6220	0.663399
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	13.0308	0.682066
$366$	−8.62555	−0.450865
$367$	−2.07046	−0.108077	−0.0540386	−	0.998539i	$-0.517209\pi$
$367$	−2.07046	−0.108077	−0.0540386	+	0.998539i	$0.517209\pi$
$368$	17.3450	0.904171
$369$	9.58062	0.498747
$370$	−6.14526	−0.319477
$371$	0	0
$372$	−17.7162	−0.918540
$373$	−34.2276	−1.77224	−0.886120	−	0.463456i	$-0.846609\pi$
$373$	−34.2276	−1.77224	−0.886120	+	0.463456i	$0.846609\pi$
$374$	−3.02255	−0.156293
$375$	−1.00000	−0.0516398
$376$	−2.98172	−0.153771
$377$	−2.66780	−0.137399
$378$	0	0
$379$	−33.7462	−1.73343	−0.866714	−	0.498805i	$-0.833772\pi$
$379$	−33.7462	−1.73343	−0.866714	+	0.498805i	$0.833772\pi$
$380$	20.4434	1.04872
$381$	16.5855	0.849699
$382$	−18.0647	−0.924271
$383$	11.5495	0.590151	0.295076	−	0.955474i	$-0.404655\pi$
$383$	11.5495	0.590151	0.295076	+	0.955474i	$0.404655\pi$
$384$	10.6212	0.542009
$385$	0	0
$386$	−10.3831	−0.528487
$387$	5.48249	0.278691
$388$	−29.1128	−1.47798
$389$	−23.1902	−1.17579	−0.587894	−	0.808938i	$-0.700043\pi$
$389$	−23.1902	−1.17579	−0.587894	+	0.808938i	$0.700043\pi$
$390$	6.54531	0.331434
$391$	−10.6750	−0.539860
$392$	0	0
$393$	−13.9593	−0.704151
$394$	−57.1693	−2.88015
$395$	−9.18049	−0.461920
$396$	−2.65001	−0.133168
$397$	34.4903	1.73102	0.865509	−	0.500893i	$-0.166995\pi$
$397$	34.4903	1.73102	0.865509	+	0.500893i	$0.166995\pi$
$398$	50.7351	2.54312
$399$	0	0
$400$	−2.27747	−0.113873
$401$	24.3031	1.21364	0.606818	−	0.794841i	$-0.292446\pi$
$401$	24.3031	1.21364	0.606818	+	0.794841i	$0.292446\pi$
$402$	−17.7759	−0.886583
$403$	−20.2920	−1.01082
$404$	19.3543	0.962911
$405$	1.00000	0.0496904
$406$	0	0
$407$	2.84979	0.141259
$408$	−1.96469	−0.0972667
$409$	−4.59272	−0.227095	−0.113548	−	0.993533i	$-0.536221\pi$
$409$	−4.59272	−0.227095	−0.113548	+	0.993533i	$0.536221\pi$
$410$	20.6595	1.02030
$411$	−7.52085	−0.370976
$412$	−2.12888	−0.104882
$413$	0	0
$414$	−16.4229	−0.807141
$415$	−1.00313	−0.0492417
$416$	23.4157	1.14805
$417$	3.15448	0.154476
$418$	−16.6354	−0.813662
$419$	29.0297	1.41819	0.709096	−	0.705112i	$-0.249103\pi$
$419$	29.0297	1.41819	0.709096	+	0.705112i	$0.249103\pi$
$420$	0	0
$421$	2.14003	0.104298	0.0521492	−	0.998639i	$-0.483393\pi$
$421$	2.14003	0.104298	0.0521492	+	0.998639i	$0.483393\pi$
$422$	−7.18199	−0.349614
$423$	−2.12726	−0.103431
$424$	15.8550	0.769985
$425$	1.40167	0.0679912
$426$	−23.8738	−1.15669
$427$	0	0
$428$	10.7196	0.518150
$429$	−3.03531	−0.146546
$430$	11.8224	0.570126
$431$	−28.0211	−1.34973	−0.674865	−	0.737942i	$-0.735798\pi$
$431$	−28.0211	−1.34973	−0.674865	+	0.737942i	$0.735798\pi$
$432$	2.27747	0.109575
$433$	7.93804	0.381478	0.190739	−	0.981641i	$-0.438912\pi$
$433$	7.93804	0.381478	0.190739	+	0.981641i	$0.438912\pi$
$434$	0	0
$435$	−0.878922	−0.0421411
$436$	−30.2324	−1.44787
$437$	−58.7527	−2.81052
$438$	−28.0996	−1.34265
$439$	8.01049	0.382320	0.191160	−	0.981559i	$-0.438775\pi$
$439$	8.01049	0.382320	0.191160	+	0.981559i	$0.438775\pi$
$440$	−1.40167	−0.0668222
$441$	0	0
$442$	−9.17439	−0.436381
$443$	1.03587	0.0492155	0.0246077	−	0.999697i	$-0.492166\pi$
$443$	1.03587	0.0492155	0.0246077	+	0.999697i	$0.492166\pi$
$444$	7.55197	0.358401
$445$	3.27690	0.155340
$446$	8.02435	0.379964
$447$	−12.5966	−0.595798
$448$	0	0
$449$	5.99629	0.282982	0.141491	−	0.989940i	$-0.454810\pi$
$449$	5.99629	0.282982	0.141491	+	0.989940i	$0.454810\pi$
$450$	2.15639	0.101653
$451$	−9.58062	−0.451134
$452$	−4.58670	−0.215740
$453$	−11.3711	−0.534262
$454$	−28.4853	−1.33688
$455$	0	0
$456$	−10.8131	−0.506372
$457$	−12.2794	−0.574405	−0.287202	−	0.957870i	$-0.592725\pi$
$457$	−12.2794	−0.574405	−0.287202	+	0.957870i	$0.592725\pi$
$458$	16.8773	0.788626
$459$	−1.40167	−0.0654245
$460$	−20.1823	−0.941004
$461$	−40.4587	−1.88435	−0.942176	−	0.335119i	$-0.891224\pi$
$461$	−40.4587	−1.88435	−0.942176	+	0.335119i	$0.891224\pi$
$462$	0	0
$463$	21.7942	1.01286	0.506431	−	0.862281i	$-0.330965\pi$
$463$	21.7942	1.01286	0.506431	+	0.862281i	$0.330965\pi$
$464$	−2.00171	−0.0929273
$465$	−6.68532	−0.310024
$466$	−8.72501	−0.404178
$467$	−37.1126	−1.71737	−0.858684	−	0.512506i	$-0.828717\pi$
$467$	−37.1126	−1.71737	−0.858684	+	0.512506i	$0.828717\pi$
$468$	−8.04360	−0.371816
$469$	0	0
$470$	−4.58719	−0.211591
$471$	16.6886	0.768969
$472$	5.99561	0.275971
$473$	−5.48249	−0.252085
$474$	19.7967	0.909292
$475$	7.71445	0.353963
$476$	0	0
$477$	11.3114	0.517915
$478$	24.4091	1.11645
$479$	−22.3282	−1.02020	−0.510101	−	0.860115i	$-0.670392\pi$
$479$	−22.3282	−1.02020	−0.510101	+	0.860115i	$0.670392\pi$
$480$	7.71445	0.352115
$481$	8.65000	0.394406
$482$	54.6566	2.48954
$483$	0	0
$484$	2.65001	0.120455
$485$	−10.9859	−0.498844
$486$	−2.15639	−0.0978158
$487$	−29.6981	−1.34575	−0.672875	−	0.739756i	$-0.734941\pi$
$487$	−29.6981	−1.34575	−0.672875	+	0.739756i	$0.734941\pi$
$488$	5.60670	0.253803
$489$	−12.7401	−0.576125
$490$	0	0
$491$	20.3023	0.916230	0.458115	−	0.888893i	$-0.348525\pi$
$491$	20.3023	0.916230	0.458115	+	0.888893i	$0.348525\pi$
$492$	−25.3887	−1.14461
$493$	1.23196	0.0554848
$494$	−50.4934	−2.27181
$495$	−1.00000	−0.0449467
$496$	−15.2256	−0.683649
$497$	0	0
$498$	2.16314	0.0969324
$499$	−7.87141	−0.352373	−0.176186	−	0.984357i	$-0.556376\pi$
$499$	−7.87141	−0.352373	−0.176186	+	0.984357i	$0.556376\pi$
$500$	2.65001	0.118512
$501$	−14.9224	−0.666686
$502$	1.41008	0.0629348
$503$	9.54929	0.425782	0.212891	−	0.977076i	$-0.431712\pi$
$503$	9.54929	0.425782	0.212891	+	0.977076i	$0.431712\pi$
$504$	0	0
$505$	7.30347	0.325000
$506$	16.4229	0.730087
$507$	3.78689	0.168182
$508$	−43.9516	−1.95004
$509$	33.7298	1.49505	0.747524	−	0.664235i	$-0.231243\pi$
$509$	33.7298	1.49505	0.747524	+	0.664235i	$0.231243\pi$
$510$	−3.02255	−0.133841
$511$	0	0
$512$	23.9539	1.05862
$513$	−7.71445	−0.340601
$514$	−17.9112	−0.790029
$515$	−0.803348	−0.0353998
$516$	−14.5287	−0.639588
$517$	2.12726	0.0935567
$518$	0	0
$519$	21.8195	0.957771
$520$	−4.25452	−0.186573
$521$	−17.9090	−0.784610	−0.392305	−	0.919835i	$-0.628322\pi$
$521$	−17.9090	−0.784610	−0.392305	+	0.919835i	$0.628322\pi$
$522$	1.89530	0.0829549
$523$	28.0334	1.22582	0.612908	−	0.790155i	$-0.290000\pi$
$523$	28.0334	1.22582	0.612908	+	0.790155i	$0.290000\pi$
$524$	36.9922	1.61601
$525$	0	0
$526$	32.3049	1.40856
$527$	9.37064	0.408191
$528$	−2.27747	−0.0991140
$529$	35.0023	1.52184
$530$	24.3919	1.05951
$531$	4.27747	0.185626
$532$	0	0
$533$	−29.0801	−1.25960
$534$	−7.06627	−0.305787
$535$	4.04511	0.174885
$536$	11.5545	0.499080
$537$	−17.6809	−0.762985
$538$	−24.1569	−1.04148
$539$	0	0
$540$	−2.65001	−0.114038
$541$	6.70243	0.288160	0.144080	−	0.989566i	$-0.453978\pi$
$541$	6.70243	0.288160	0.144080	+	0.989566i	$0.453978\pi$
$542$	−34.7434	−1.49236
$543$	−5.85332	−0.251190
$544$	−10.8131	−0.463610
$545$	−11.4084	−0.488683
$546$	0	0
$547$	−17.5461	−0.750215	−0.375108	−	0.926981i	$-0.622394\pi$
$547$	−17.5461	−0.750215	−0.375108	+	0.926981i	$0.622394\pi$
$548$	19.9303	0.851381
$549$	4.00000	0.170716
$550$	−2.15639	−0.0919487
$551$	6.78040	0.288855
$552$	10.6750	0.454360
$553$	0	0
$554$	57.7267	2.45257
$555$	2.84979	0.120967
$556$	−8.35942	−0.354518
$557$	29.1691	1.23594	0.617968	−	0.786203i	$-0.287956\pi$
$557$	29.1691	1.23594	0.617968	+	0.786203i	$0.287956\pi$
$558$	14.4161	0.610284
$559$	−16.6411	−0.703842
$560$	0	0
$561$	1.40167	0.0591787
$562$	21.1879	0.893759
$563$	15.0605	0.634726	0.317363	−	0.948304i	$-0.397203\pi$
$563$	15.0605	0.634726	0.317363	+	0.948304i	$0.397203\pi$
$564$	5.63725	0.237371
$565$	−1.73082	−0.0728164
$566$	29.3577	1.23400
$567$	0	0
$568$	15.5182	0.651129
$569$	−6.19669	−0.259779	−0.129889	−	0.991528i	$-0.541462\pi$
$569$	−6.19669	−0.259779	−0.129889	+	0.991528i	$0.541462\pi$
$570$	−16.6354	−0.696778
$571$	5.37113	0.224775	0.112387	−	0.993664i	$-0.464150\pi$
$571$	5.37113	0.224775	0.112387	+	0.993664i	$0.464150\pi$
$572$	8.04360	0.336320
$573$	8.37730	0.349967
$574$	0	0
$575$	−7.61593	−0.317606
$576$	−12.0804	−0.503351
$577$	−34.8445	−1.45060	−0.725298	−	0.688436i	$-0.758298\pi$
$577$	−34.8445	−1.45060	−0.725298	+	0.688436i	$0.758298\pi$
$578$	−32.4220	−1.34858
$579$	4.81505	0.200107
$580$	2.32915	0.0967127
$581$	0	0
$582$	23.6899	0.981977
$583$	−11.3114	−0.468472
$584$	18.2650	0.755811
$585$	−3.03531	−0.125495
$586$	−17.3880	−0.718293
$587$	21.1475	0.872851	0.436426	−	0.899740i	$-0.356244\pi$
$587$	21.1475	0.872851	0.436426	+	0.899740i	$0.356244\pi$
$588$	0	0
$589$	51.5736	2.12505
$590$	9.22388	0.379741
$591$	26.5116	1.09054
$592$	6.49030	0.266750
$593$	5.89322	0.242006	0.121003	−	0.992652i	$-0.461389\pi$
$593$	5.89322	0.242006	0.121003	+	0.992652i	$0.461389\pi$
$594$	2.15639	0.0884777
$595$	0	0
$596$	33.3811	1.36734
$597$	−23.5278	−0.962929
$598$	49.8486	2.03846
$599$	−30.8870	−1.26201	−0.631005	−	0.775779i	$-0.717357\pi$
$599$	−30.8870	−1.26201	−0.631005	+	0.775779i	$0.717357\pi$
$600$	−1.40167	−0.0572231
$601$	−38.9939	−1.59059	−0.795296	−	0.606221i	$-0.792685\pi$
$601$	−38.9939	−1.59059	−0.795296	+	0.606221i	$0.792685\pi$
$602$	0	0
$603$	8.24338	0.335696
$604$	30.1336	1.22612
$605$	1.00000	0.0406558
$606$	−15.7491	−0.639764
$607$	0.977845	0.0396895	0.0198447	−	0.999803i	$-0.493683\pi$
$607$	0.977845	0.0396895	0.0198447	+	0.999803i	$0.493683\pi$
$608$	−59.5127	−2.41356
$609$	0	0
$610$	8.62555	0.349238
$611$	6.45689	0.261218
$612$	3.71445	0.150148
$613$	22.4402	0.906351	0.453176	−	0.891421i	$-0.350291\pi$
$613$	22.4402	0.906351	0.453176	+	0.891421i	$0.350291\pi$
$614$	−53.6641	−2.16571
$615$	−9.58062	−0.386328
$616$	0	0
$617$	29.1949	1.17534	0.587672	−	0.809100i	$-0.300045\pi$
$617$	29.1949	1.17534	0.587672	+	0.809100i	$0.300045\pi$
$618$	1.73233	0.0696846
$619$	−7.29162	−0.293075	−0.146537	−	0.989205i	$-0.546813\pi$
$619$	−7.29162	−0.293075	−0.146537	+	0.989205i	$0.546813\pi$
$620$	17.7162	0.711498
$621$	7.61593	0.305617
$622$	68.4744	2.74557
$623$	0	0
$624$	−6.91282	−0.276734
$625$	1.00000	0.0400000
$626$	41.4833	1.65801
$627$	7.71445	0.308085
$628$	−44.2249	−1.76477
$629$	−3.99448	−0.159270
$630$	0	0
$631$	34.3697	1.36823	0.684117	−	0.729372i	$-0.260188\pi$
$631$	34.3697	1.36823	0.684117	+	0.729372i	$0.260188\pi$
$632$	−12.8680	−0.511864
$633$	3.33057	0.132378
$634$	36.9567	1.46774
$635$	−16.5855	−0.658174
$636$	−29.9754	−1.18860
$637$	0	0
$638$	−1.89530	−0.0750355
$639$	11.0712	0.437969
$640$	−10.6212	−0.419838
$641$	20.1247	0.794878	0.397439	−	0.917628i	$-0.369899\pi$
$641$	20.1247	0.794878	0.397439	+	0.917628i	$0.369899\pi$
$642$	−8.72282	−0.344262
$643$	25.1624	0.992307	0.496153	−	0.868235i	$-0.334745\pi$
$643$	25.1624	0.992307	0.496153	+	0.868235i	$0.334745\pi$
$644$	0	0
$645$	−5.48249	−0.215873
$646$	23.3173	0.917408
$647$	19.0839	0.750267	0.375134	−	0.926971i	$-0.377597\pi$
$647$	19.0839	0.750267	0.375134	+	0.926971i	$0.377597\pi$
$648$	1.40167	0.0550630
$649$	−4.27747	−0.167905
$650$	−6.54531	−0.256728
$651$	0	0
$652$	33.7613	1.32219
$653$	34.7481	1.35980	0.679899	−	0.733306i	$-0.262024\pi$
$653$	34.7481	1.35980	0.679899	+	0.733306i	$0.262024\pi$
$654$	24.6010	0.961975
$655$	13.9593	0.545433
$656$	−21.8195	−0.851910
$657$	13.0308	0.508382
$658$	0	0
$659$	19.6971	0.767292	0.383646	−	0.923480i	$-0.374668\pi$
$659$	19.6971	0.767292	0.383646	+	0.923480i	$0.374668\pi$
$660$	2.65001	0.103152
$661$	−19.4371	−0.756014	−0.378007	−	0.925803i	$-0.623390\pi$
$661$	−19.4371	−0.756014	−0.378007	+	0.925803i	$0.623390\pi$
$662$	−69.7452	−2.71072
$663$	4.25452	0.165232
$664$	−1.40606	−0.0545657
$665$	0	0
$666$	−6.14526	−0.238124
$667$	−6.69380	−0.259185
$668$	39.5446	1.53003
$669$	−3.72120	−0.143870
$670$	17.7759	0.686744
$671$	−4.00000	−0.154418
$672$	0	0
$673$	−48.1626	−1.85653	−0.928266	−	0.371916i	$-0.878701\pi$
$673$	−48.1626	−1.85653	−0.928266	+	0.371916i	$0.878701\pi$
$674$	32.3393	1.24566
$675$	−1.00000	−0.0384900
$676$	−10.0353	−0.385973
$677$	2.06765	0.0794663	0.0397331	−	0.999210i	$-0.487349\pi$
$677$	2.06765	0.0794663	0.0397331	+	0.999210i	$0.487349\pi$
$678$	3.73233	0.143339
$679$	0	0
$680$	1.96469	0.0753424
$681$	13.2097	0.506197
$682$	−14.4161	−0.552023
$683$	28.4773	1.08965	0.544827	−	0.838549i	$-0.316595\pi$
$683$	28.4773	1.08965	0.544827	+	0.838549i	$0.316595\pi$
$684$	20.4434	0.781672
$685$	7.52085	0.287357
$686$	0	0
$687$	−7.82667	−0.298606
$688$	−12.4862	−0.476031
$689$	−34.3337	−1.30801
$690$	16.4229	0.625209
$691$	−22.0632	−0.839324	−0.419662	−	0.907681i	$-0.637851\pi$
$691$	−22.0632	−0.839324	−0.419662	+	0.907681i	$0.637851\pi$
$692$	−57.8220	−2.19806
$693$	0	0
$694$	−27.4776	−1.04304
$695$	−3.15448	−0.119656
$696$	−1.23196	−0.0466974
$697$	13.4289	0.508656
$698$	−62.2243	−2.35522
$699$	4.04612	0.153038
$700$	0	0
$701$	−36.3358	−1.37239	−0.686193	−	0.727420i	$-0.740719\pi$
$701$	−36.3358	−1.37239	−0.686193	+	0.727420i	$0.740719\pi$
$702$	6.54531	0.247037
$703$	−21.9846	−0.829164
$704$	12.0804	0.455298
$705$	2.12726	0.0801172
$706$	−9.54306	−0.359158
$707$	0	0
$708$	−11.3353	−0.426008
$709$	−49.3785	−1.85445	−0.927223	−	0.374509i	$-0.877811\pi$
$709$	−49.3785	−1.85445	−0.927223	+	0.374509i	$0.877811\pi$
$710$	23.8738	0.895967
$711$	−9.18049	−0.344295
$712$	4.59314	0.172135
$713$	−50.9149	−1.90678
$714$	0	0
$715$	3.03531	0.113514
$716$	46.8544	1.75103
$717$	−11.3194	−0.422732
$718$	−51.6856	−1.92889
$719$	−27.3322	−1.01932	−0.509660	−	0.860376i	$-0.670229\pi$
$719$	−27.3322	−1.01932	−0.509660	+	0.860376i	$0.670229\pi$
$720$	−2.27747	−0.0848762
$721$	0	0
$722$	87.3612	3.25125
$723$	−25.3464	−0.942641
$724$	15.5114	0.576475
$725$	0.878922	0.0326423
$726$	−2.15639	−0.0800311
$727$	10.7532	0.398814	0.199407	−	0.979917i	$-0.436098\pi$
$727$	10.7532	0.398814	0.199407	+	0.979917i	$0.436098\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	28.0996	1.04001
$731$	7.68466	0.284228
$732$	−10.6000	−0.391789
$733$	31.3655	1.15851	0.579255	−	0.815146i	$-0.303343\pi$
$733$	31.3655	1.15851	0.579255	+	0.815146i	$0.303343\pi$
$734$	−4.46472	−0.164796
$735$	0	0
$736$	58.7527	2.16565
$737$	−8.24338	−0.303649
$738$	20.6595	0.760488
$739$	41.4231	1.52377	0.761887	−	0.647709i	$-0.224273\pi$
$739$	41.4231	1.52377	0.761887	+	0.647709i	$0.224273\pi$
$740$	−7.55197	−0.277616
$741$	23.4157	0.860199
$742$	0	0
$743$	35.5631	1.30468	0.652342	−	0.757925i	$-0.273787\pi$
$743$	35.5631	1.30468	0.652342	+	0.757925i	$0.273787\pi$
$744$	−9.37064	−0.343544
$745$	12.5966	0.461503
$746$	−73.8081	−2.70230
$747$	−1.00313	−0.0367026
$748$	−3.71445	−0.135814
$749$	0	0
$750$	−2.15639	−0.0787402
$751$	10.3347	0.377118	0.188559	−	0.982062i	$-0.439618\pi$
$751$	10.3347	0.377118	0.188559	+	0.982062i	$0.439618\pi$
$752$	4.84476	0.176670
$753$	−0.653906	−0.0238297
$754$	−5.75281	−0.209505
$755$	11.3711	0.413838
$756$	0	0
$757$	5.19434	0.188791	0.0943957	−	0.995535i	$-0.469908\pi$
$757$	5.19434	0.188791	0.0943957	+	0.995535i	$0.469908\pi$
$758$	−72.7700	−2.64313
$759$	−7.61593	−0.276441
$760$	10.8131	0.392234
$761$	25.8776	0.938061	0.469031	−	0.883182i	$-0.344603\pi$
$761$	25.8776	0.938061	0.469031	+	0.883182i	$0.344603\pi$
$762$	35.7647	1.29562
$763$	0	0
$764$	−22.1999	−0.803165
$765$	1.40167	0.0506776
$766$	24.9052	0.899861
$767$	−12.9834	−0.468805
$768$	−1.25747	−0.0453752
$769$	15.7481	0.567892	0.283946	−	0.958840i	$-0.408356\pi$
$769$	15.7481	0.567892	0.283946	+	0.958840i	$0.408356\pi$
$770$	0	0
$771$	8.30611	0.299137
$772$	−12.7599	−0.459240
$773$	−48.7828	−1.75460	−0.877299	−	0.479945i	$-0.840657\pi$
$773$	−48.7828	−1.75460	−0.877299	+	0.479945i	$0.840657\pi$
$774$	11.8224	0.424946
$775$	6.68532	0.240144
$776$	−15.3987	−0.552780
$777$	0	0
$778$	−50.0070	−1.79284
$779$	73.9092	2.64807
$780$	8.04360	0.288007
$781$	−11.0712	−0.396158
$782$	−23.0195	−0.823177
$783$	−0.878922	−0.0314101
$784$	0	0
$785$	−16.6886	−0.595641
$786$	−30.1016	−1.07369
$787$	−1.66110	−0.0592118	−0.0296059	−	0.999562i	$-0.509425\pi$
$787$	−1.66110	−0.0592118	−0.0296059	+	0.999562i	$0.509425\pi$
$788$	−70.2560	−2.50277
$789$	−14.9810	−0.533339
$790$	−19.7967	−0.704335
$791$	0	0
$792$	−1.40167	−0.0498063
$793$	−12.1412	−0.431148
$794$	74.3745	2.63945
$795$	−11.3114	−0.401175
$796$	62.3489	2.20990
$797$	−30.1974	−1.06965	−0.534824	−	0.844964i	$-0.679622\pi$
$797$	−30.1974	−1.06965	−0.534824	+	0.844964i	$0.679622\pi$
$798$	0	0
$799$	−2.98172	−0.105486
$800$	−7.71445	−0.272747
$801$	3.27690	0.115784
$802$	52.4068	1.85055
$803$	−13.0308	−0.459849
$804$	−21.8450	−0.770415
$805$	0	0
$806$	−43.7575	−1.54129
$807$	11.2025	0.394346
$808$	10.2371	0.360139
$809$	−33.3929	−1.17403	−0.587017	−	0.809575i	$-0.699698\pi$
$809$	−33.3929	−1.17403	−0.587017	+	0.809575i	$0.699698\pi$
$810$	2.15639	0.0757678
$811$	−54.5879	−1.91684	−0.958420	−	0.285362i	$-0.907886\pi$
$811$	−54.5879	−1.91684	−0.958420	+	0.285362i	$0.907886\pi$
$812$	0	0
$813$	16.1118	0.565067
$814$	6.14526	0.215391
$815$	12.7401	0.446265
$816$	3.19227	0.111752
$817$	42.2944	1.47969
$818$	−9.90368	−0.346274
$819$	0	0
$820$	25.3887	0.886613
$821$	−14.4763	−0.505226	−0.252613	−	0.967567i	$-0.581290\pi$
$821$	−14.4763	−0.505226	−0.252613	+	0.967567i	$0.581290\pi$
$822$	−16.2179	−0.565663
$823$	−25.3194	−0.882580	−0.441290	−	0.897365i	$-0.645479\pi$
$823$	−25.3194	−0.882580	−0.441290	+	0.897365i	$0.645479\pi$
$824$	−1.12603	−0.0392272
$825$	1.00000	0.0348155
$826$	0	0
$827$	−11.2759	−0.392102	−0.196051	−	0.980594i	$-0.562812\pi$
$827$	−11.2759	−0.392102	−0.196051	+	0.980594i	$0.562812\pi$
$828$	−20.1823	−0.701383
$829$	−22.7948	−0.791697	−0.395848	−	0.918316i	$-0.629549\pi$
$829$	−22.7948	−0.791697	−0.395848	+	0.918316i	$0.629549\pi$
$830$	−2.16314	−0.0750835
$831$	−26.7701	−0.928644
$832$	36.6678	1.27123
$833$	0	0
$834$	6.80229	0.235544
$835$	14.9224	0.516412
$836$	−20.4434	−0.707049
$837$	−6.68532	−0.231078
$838$	62.5992	2.16245
$839$	−45.1089	−1.55733	−0.778667	−	0.627438i	$-0.784104\pi$
$839$	−45.1089	−1.55733	−0.778667	+	0.627438i	$0.784104\pi$
$840$	0	0
$841$	−28.2275	−0.973362
$842$	4.61473	0.159034
$843$	−9.82565	−0.338413
$844$	−8.82603	−0.303805
$845$	−3.78689	−0.130273
$846$	−4.58719	−0.157711
$847$	0	0
$848$	−25.7614	−0.884651
$849$	−13.6143	−0.467242
$850$	3.02255	0.103673
$851$	21.7038	0.743996
$852$	−29.3388	−1.00513
$853$	−15.2857	−0.523372	−0.261686	−	0.965153i	$-0.584278\pi$
$853$	−15.2857	−0.523372	−0.261686	+	0.965153i	$0.584278\pi$
$854$	0	0
$855$	7.71445	0.263829
$856$	5.66992	0.193794
$857$	18.4094	0.628852	0.314426	−	0.949282i	$-0.398188\pi$
$857$	18.4094	0.628852	0.314426	+	0.949282i	$0.398188\pi$
$858$	−6.54531	−0.223453
$859$	12.3793	0.422376	0.211188	−	0.977445i	$-0.432267\pi$
$859$	12.3793	0.422376	0.211188	+	0.977445i	$0.432267\pi$
$860$	14.5287	0.495423
$861$	0	0
$862$	−60.4244	−2.05806
$863$	−28.8104	−0.980719	−0.490359	−	0.871520i	$-0.663134\pi$
$863$	−28.8104	−0.980719	−0.490359	+	0.871520i	$0.663134\pi$
$864$	7.71445	0.262451
$865$	−21.8195	−0.741886
$866$	17.1175	0.581676
$867$	15.0353	0.510626
$868$	0	0
$869$	9.18049	0.311427
$870$	−1.89530	−0.0642566
$871$	−25.0212	−0.847812
$872$	−15.9909	−0.541520
$873$	−10.9859	−0.371817
$874$	−126.694	−4.28547
$875$	0	0
$876$	−34.5319	−1.16672
$877$	51.9929	1.75567	0.877837	−	0.478960i	$-0.158986\pi$
$877$	51.9929	1.75567	0.877837	+	0.478960i	$0.158986\pi$
$878$	17.2737	0.582960
$879$	8.06350	0.271975
$880$	2.27747	0.0767734
$881$	2.53096	0.0852701	0.0426350	−	0.999091i	$-0.486425\pi$
$881$	2.53096	0.0852701	0.0426350	+	0.999091i	$0.486425\pi$
$882$	0	0
$883$	−25.5088	−0.858439	−0.429219	−	0.903200i	$-0.641211\pi$
$883$	−25.5088	−0.858439	−0.429219	+	0.903200i	$0.641211\pi$
$884$	−11.2745	−0.379203
$885$	−4.27747	−0.143785
$886$	2.23373	0.0750436
$887$	10.7913	0.362337	0.181169	−	0.983452i	$-0.442012\pi$
$887$	10.7913	0.362337	0.181169	+	0.983452i	$0.442012\pi$
$888$	3.99448	0.134046
$889$	0	0
$890$	7.06627	0.236862
$891$	−1.00000	−0.0335013
$892$	9.86121	0.330178
$893$	−16.4106	−0.549161
$894$	−27.1631	−0.908471
$895$	17.6809	0.591006
$896$	0	0
$897$	−23.1167	−0.771844
$898$	12.9303	0.431491
$899$	5.87587	0.195971
$900$	2.65001	0.0883337
$901$	15.8550	0.528205
$902$	−20.6595	−0.687887
$903$	0	0
$904$	−2.42605	−0.0806893
$905$	5.85332	0.194571
$906$	−24.5206	−0.814641
$907$	32.7652	1.08795	0.543975	−	0.839101i	$-0.316919\pi$
$907$	32.7652	1.08795	0.543975	+	0.839101i	$0.316919\pi$
$908$	−35.0059	−1.16171
$909$	7.30347	0.242241
$910$	0	0
$911$	−21.5369	−0.713551	−0.356775	−	0.934190i	$-0.616124\pi$
$911$	−21.5369	−0.713551	−0.356775	+	0.934190i	$0.616124\pi$
$912$	17.5694	0.581781
$913$	1.00313	0.0331987
$914$	−26.4791	−0.875850
$915$	−4.00000	−0.132236
$916$	20.7408	0.685294
$917$	0	0
$918$	−3.02255	−0.0997591
$919$	−26.9793	−0.889965	−0.444982	−	0.895539i	$-0.646790\pi$
$919$	−26.9793	−0.889965	−0.444982	+	0.895539i	$0.646790\pi$
$920$	−10.6750	−0.351946
$921$	24.8861	0.820024
$922$	−87.2448	−2.87325
$923$	−33.6045	−1.10611
$924$	0	0
$925$	−2.84979	−0.0937005
$926$	46.9967	1.54441
$927$	−0.803348	−0.0263854
$928$	−6.78040	−0.222577
$929$	37.7240	1.23768	0.618842	−	0.785516i	$-0.287602\pi$
$929$	37.7240	1.23768	0.618842	+	0.785516i	$0.287602\pi$
$930$	−14.4161	−0.472724
$931$	0	0
$932$	−10.7223	−0.351220
$933$	−31.7542	−1.03959
$934$	−80.0292	−2.61864
$935$	−1.40167	−0.0458396
$936$	−4.25452	−0.139063
$937$	0.213873	0.00698691	0.00349346	−	0.999994i	$-0.498888\pi$
$937$	0.213873	0.00698691	0.00349346	+	0.999994i	$0.498888\pi$
$938$	0	0
$939$	−19.2374	−0.627789
$940$	−5.63725	−0.183867
$941$	28.5968	0.932230	0.466115	−	0.884724i	$-0.345653\pi$
$941$	28.5968	0.932230	0.466115	+	0.884724i	$0.345653\pi$
$942$	35.9871	1.17252
$943$	−72.9653	−2.37608
$944$	−9.74179	−0.317068
$945$	0	0
$946$	−11.8224	−0.384379
$947$	26.6852	0.867154	0.433577	−	0.901117i	$-0.357251\pi$
$947$	26.6852	0.867154	0.433577	+	0.901117i	$0.357251\pi$
$948$	24.3284	0.790149
$949$	−39.5527	−1.28393
$950$	16.6354	0.539722
$951$	−17.1382	−0.555746
$952$	0	0
$953$	−13.7056	−0.443967	−0.221983	−	0.975050i	$-0.571253\pi$
$953$	−13.7056	−0.443967	−0.221983	+	0.975050i	$0.571253\pi$
$954$	24.3919	0.789716
$955$	−8.37730	−0.271083
$956$	29.9966	0.970160
$957$	0.878922	0.0284115
$958$	−48.1483	−1.55560
$959$	0	0
$960$	12.0804	0.389894
$961$	13.6935	0.441726
$962$	18.6528	0.601389
$963$	4.04511	0.130352
$964$	67.1681	2.16334
$965$	−4.81505	−0.155002
$966$	0	0
$967$	2.47306	0.0795283	0.0397641	−	0.999209i	$-0.487339\pi$
$967$	2.47306	0.0795283	0.0397641	+	0.999209i	$0.487339\pi$
$968$	1.40167	0.0450515
$969$	−10.8131	−0.347368
$970$	−23.6899	−0.760636
$971$	−1.58932	−0.0510036	−0.0255018	−	0.999675i	$-0.508118\pi$
$971$	−1.58932	−0.0510036	−0.0255018	+	0.999675i	$0.508118\pi$
$972$	−2.65001	−0.0849991
$973$	0	0
$974$	−64.0407	−2.05200
$975$	3.03531	0.0972077
$976$	−9.10987	−0.291600
$977$	10.2324	0.327364	0.163682	−	0.986513i	$-0.447663\pi$
$977$	10.2324	0.327364	0.163682	+	0.986513i	$0.447663\pi$
$978$	−27.4725	−0.878474
$979$	−3.27690	−0.104730
$980$	0	0
$981$	−11.4084	−0.364243
$982$	43.7796	1.39706
$983$	31.8604	1.01619	0.508094	−	0.861302i	$-0.330350\pi$
$983$	31.8604	1.01619	0.508094	+	0.861302i	$0.330350\pi$
$984$	−13.4289	−0.428098
$985$	−26.5116	−0.844730
$986$	2.65659	0.0846030
$987$	0	0
$988$	−62.0520	−1.97414
$989$	−41.7542	−1.32771
$990$	−2.15639	−0.0685345
$991$	−24.6017	−0.781498	−0.390749	−	0.920497i	$-0.627784\pi$
$991$	−24.6017	−0.781498	−0.390749	+	0.920497i	$0.627784\pi$
$992$	−51.5736	−1.63746
$993$	32.3435	1.02639
$994$	0	0
$995$	23.5278	0.745882
$996$	2.65830	0.0842315
$997$	−39.0616	−1.23709	−0.618547	−	0.785748i	$-0.712278\pi$
$997$	−39.0616	−1.23709	−0.618547	+	0.785748i	$0.712278\pi$
$998$	−16.9738	−0.537297
$999$	2.84979	0.0901634

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8085.2.a.br.1.5		5
7.2	even	3		1155.2.q.g.991.1	yes	10
7.4	even	3		1155.2.q.g.331.1	✓	10
7.6	odd	2		8085.2.a.bu.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.q.g.331.1	✓	10	7.4	even	3
1155.2.q.g.991.1	yes	10	7.2	even	3
8085.2.a.br.1.5		5	1.1	even	1	trivial
8085.2.a.bu.1.5		5	7.6	odd	2

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)

\(f(q)\)	\(=\)	\(q+2.15639 q^{2} -1.00000 q^{3} +2.65001 q^{4} +1.00000 q^{5} -2.15639 q^{6} +1.40167 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.15639 q^{2} -1.00000 q^{3} +2.65001 q^{4} +1.00000 q^{5} -2.15639 q^{6} +1.40167 q^{8} +1.00000 q^{9} +2.15639 q^{10} -1.00000 q^{11} -2.65001 q^{12} -3.03531 q^{13} -1.00000 q^{15} -2.27747 q^{16} +1.40167 q^{17} +2.15639 q^{18} +7.71445 q^{19} +2.65001 q^{20} -2.15639 q^{22} -7.61593 q^{23} -1.40167 q^{24} +1.00000 q^{25} -6.54531 q^{26} -1.00000 q^{27} +0.878922 q^{29} -2.15639 q^{30} +6.68532 q^{31} -7.71445 q^{32} +1.00000 q^{33} +3.02255 q^{34} +2.65001 q^{36} -2.84979 q^{37} +16.6354 q^{38} +3.03531 q^{39} +1.40167 q^{40} +9.58062 q^{41} +5.48249 q^{43} -2.65001 q^{44} +1.00000 q^{45} -16.4229 q^{46} -2.12726 q^{47} +2.27747 q^{48} +2.15639 q^{50} -1.40167 q^{51} -8.04360 q^{52} +11.3114 q^{53} -2.15639 q^{54} -1.00000 q^{55} -7.71445 q^{57} +1.89530 q^{58} +4.27747 q^{59} -2.65001 q^{60} +4.00000 q^{61} +14.4161 q^{62} -12.0804 q^{64} -3.03531 q^{65} +2.15639 q^{66} +8.24338 q^{67} +3.71445 q^{68} +7.61593 q^{69} +11.0712 q^{71} +1.40167 q^{72} +13.0308 q^{73} -6.14526 q^{74} -1.00000 q^{75} +20.4434 q^{76} +6.54531 q^{78} -9.18049 q^{79} -2.27747 q^{80} +1.00000 q^{81} +20.6595 q^{82} -1.00313 q^{83} +1.40167 q^{85} +11.8224 q^{86} -0.878922 q^{87} -1.40167 q^{88} +3.27690 q^{89} +2.15639 q^{90} -20.1823 q^{92} -6.68532 q^{93} -4.58719 q^{94} +7.71445 q^{95} +7.71445 q^{96} -10.9859 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 5 q^{3} + 4 q^{4} + 5 q^{5} + 5 q^{9}+O(q^{10}) \) 5 * q - 5 * q^3 + 4 * q^4 + 5 * q^5 + 5 * q^9	\( 5 q - 5 q^{3} + 4 q^{4} + 5 q^{5} + 5 q^{9} - 5 q^{11} - 4 q^{12} + q^{13} - 5 q^{15} - 6 q^{16} + 10 q^{19} + 4 q^{20} + 9 q^{23} + 5 q^{25} - 18 q^{26} - 5 q^{27} - q^{29} + 8 q^{31} - 10 q^{32} + 5 q^{33} + 2 q^{34} + 4 q^{36} - 12 q^{37} + 30 q^{38} - q^{39} + 17 q^{41} + q^{43} - 4 q^{44} + 5 q^{45} - 24 q^{46} - 3 q^{47} + 6 q^{48} + 10 q^{52} - 3 q^{53} - 5 q^{55} - 10 q^{57} + 4 q^{58} + 16 q^{59} - 4 q^{60} + 20 q^{61} + 18 q^{62} - 18 q^{64} + q^{65} - 2 q^{67} - 10 q^{68} - 9 q^{69} + 32 q^{71} + 18 q^{73} + 8 q^{74} - 5 q^{75} - 2 q^{76} + 18 q^{78} + 8 q^{79} - 6 q^{80} + 5 q^{81} + 6 q^{82} + 2 q^{83} + 16 q^{86} + q^{87} + 2 q^{89} - 2 q^{92} - 8 q^{93} - 2 q^{94} + 10 q^{95} + 10 q^{96} - 20 q^{97} - 5 q^{99}+O(q^{100}) \) 5 * q - 5 * q^3 + 4 * q^4 + 5 * q^5 + 5 * q^9 - 5 * q^11 - 4 * q^12 + q^13 - 5 * q^15 - 6 * q^16 + 10 * q^19 + 4 * q^20 + 9 * q^23 + 5 * q^25 - 18 * q^26 - 5 * q^27 - q^29 + 8 * q^31 - 10 * q^32 + 5 * q^33 + 2 * q^34 + 4 * q^36 - 12 * q^37 + 30 * q^38 - q^39 + 17 * q^41 + q^43 - 4 * q^44 + 5 * q^45 - 24 * q^46 - 3 * q^47 + 6 * q^48 + 10 * q^52 - 3 * q^53 - 5 * q^55 - 10 * q^57 + 4 * q^58 + 16 * q^59 - 4 * q^60 + 20 * q^61 + 18 * q^62 - 18 * q^64 + q^65 - 2 * q^67 - 10 * q^68 - 9 * q^69 + 32 * q^71 + 18 * q^73 + 8 * q^74 - 5 * q^75 - 2 * q^76 + 18 * q^78 + 8 * q^79 - 6 * q^80 + 5 * q^81 + 6 * q^82 + 2 * q^83 + 16 * q^86 + q^87 + 2 * q^89 - 2 * q^92 - 8 * q^93 - 2 * q^94 + 10 * q^95 + 10 * q^96 - 20 * q^97 - 5 * q^99

Introduction

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