LMFDB - Embedded newform 8085.2.a.bv.1.1

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:	5.5.352076.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 8x^{3} + 3x^{2} + 8x - 4 $ x^5 - x^4 - 8x^3 + 3x^2 + 8*x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 1155)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$0.567739$ 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)

$f(q)$	$=$	$q-2.52275 q^{2} -1.00000 q^{3} +4.36426 q^{4} +1.00000 q^{5} +2.52275 q^{6} -5.96443 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.52275 q^{2} -1.00000 q^{3} +4.36426 q^{4} +1.00000 q^{5} +2.52275 q^{6} -5.96443 q^{8} +1.00000 q^{9} -2.52275 q^{10} +1.00000 q^{11} -4.36426 q^{12} -5.44168 q^{13} -1.00000 q^{15} +6.31823 q^{16} -1.41028 q^{17} -2.52275 q^{18} +1.36426 q^{19} +4.36426 q^{20} -2.52275 q^{22} -8.40975 q^{23} +5.96443 q^{24} +1.00000 q^{25} +13.7280 q^{26} -1.00000 q^{27} +8.75991 q^{29} +2.52275 q^{30} -3.60382 q^{31} -4.01045 q^{32} -1.00000 q^{33} +3.55779 q^{34} +4.36426 q^{36} +3.48771 q^{37} -3.44168 q^{38} +5.44168 q^{39} -5.96443 q^{40} -10.4411 q^{41} -11.5345 q^{43} +4.36426 q^{44} +1.00000 q^{45} +21.2157 q^{46} +8.21622 q^{47} -6.31823 q^{48} -2.52275 q^{50} +1.41028 q^{51} -23.7489 q^{52} -5.31823 q^{53} +2.52275 q^{54} +1.00000 q^{55} -1.36426 q^{57} -22.0991 q^{58} -7.07689 q^{59} -4.36426 q^{60} -3.52640 q^{61} +9.09152 q^{62} -2.51910 q^{64} -5.44168 q^{65} +2.52275 q^{66} -1.09152 q^{67} -6.15484 q^{68} +8.40975 q^{69} +4.69534 q^{71} -5.96443 q^{72} -7.31645 q^{73} -8.79860 q^{74} -1.00000 q^{75} +5.95397 q^{76} -13.7280 q^{78} +4.55832 q^{79} +6.31823 q^{80} +1.00000 q^{81} +26.3404 q^{82} +9.51910 q^{83} -1.41028 q^{85} +29.0985 q^{86} -8.75991 q^{87} -5.96443 q^{88} +16.7421 q^{89} -2.52275 q^{90} -36.7023 q^{92} +3.60382 q^{93} -20.7275 q^{94} +1.36426 q^{95} +4.01045 q^{96} -16.2630 q^{97} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} - 5 q^{3} + 9 q^{4} + 5 q^{5} - q^{6} + 3 q^{8} + 5 q^{9}+O(q^{10}) $ 5 * q + q^2 - 5 * q^3 + 9 * q^4 + 5 * q^5 - q^6 + 3 * q^8 + 5 * q^9	$ 5 q + q^{2} - 5 q^{3} + 9 q^{4} + 5 q^{5} - q^{6} + 3 q^{8} + 5 q^{9} + q^{10} + 5 q^{11} - 9 q^{12} - 8 q^{13} - 5 q^{15} + 13 q^{16} + q^{18} - 6 q^{19} + 9 q^{20} + q^{22} - 2 q^{23} - 3 q^{24} + 5 q^{25} + 10 q^{26} - 5 q^{27} + 6 q^{29} - q^{30} - 10 q^{31} + 7 q^{32} - 5 q^{33} + 4 q^{34} + 9 q^{36} + 4 q^{37} + 2 q^{38} + 8 q^{39} + 3 q^{40} + 9 q^{44} + 5 q^{45} + 34 q^{46} + 2 q^{47} - 13 q^{48} + q^{50} - 6 q^{52} - 8 q^{53} - q^{54} + 5 q^{55} + 6 q^{57} + 4 q^{59} - 9 q^{60} - 16 q^{61} + 24 q^{62} + 13 q^{64} - 8 q^{65} - q^{66} + 16 q^{67} - 18 q^{68} + 2 q^{69} - 6 q^{71} + 3 q^{72} - 2 q^{73} - 18 q^{74} - 5 q^{75} + 24 q^{76} - 10 q^{78} + 42 q^{79} + 13 q^{80} + 5 q^{81} + 42 q^{82} + 22 q^{83} + 2 q^{86} - 6 q^{87} + 3 q^{88} + 10 q^{89} + q^{90} - 32 q^{92} + 10 q^{93} - 12 q^{94} - 6 q^{95} - 7 q^{96} + 2 q^{97} + 5 q^{99}+O(q^{100}) $ 5 * q + q^2 - 5 * q^3 + 9 * q^4 + 5 * q^5 - q^6 + 3 * q^8 + 5 * q^9 + q^10 + 5 * q^11 - 9 * q^12 - 8 * q^13 - 5 * q^15 + 13 * q^16 + q^18 - 6 * q^19 + 9 * q^20 + q^22 - 2 * q^23 - 3 * q^24 + 5 * q^25 + 10 * q^26 - 5 * q^27 + 6 * q^29 - q^30 - 10 * q^31 + 7 * q^32 - 5 * q^33 + 4 * q^34 + 9 * q^36 + 4 * q^37 + 2 * q^38 + 8 * q^39 + 3 * q^40 + 9 * q^44 + 5 * q^45 + 34 * q^46 + 2 * q^47 - 13 * q^48 + q^50 - 6 * q^52 - 8 * q^53 - q^54 + 5 * q^55 + 6 * q^57 + 4 * q^59 - 9 * q^60 - 16 * q^61 + 24 * q^62 + 13 * q^64 - 8 * q^65 - q^66 + 16 * q^67 - 18 * q^68 + 2 * q^69 - 6 * q^71 + 3 * q^72 - 2 * q^73 - 18 * q^74 - 5 * q^75 + 24 * q^76 - 10 * q^78 + 42 * q^79 + 13 * q^80 + 5 * q^81 + 42 * q^82 + 22 * q^83 + 2 * q^86 - 6 * q^87 + 3 * q^88 + 10 * q^89 + q^90 - 32 * q^92 + 10 * q^93 - 12 * q^94 - 6 * q^95 - 7 * q^96 + 2 * 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 $

$2$	−2.52275	−1.78385	−0.891926	−	0.452181i	$-0.850646\pi$
$2$	−2.52275	−1.78385	−0.891926	+	0.452181i	$0.850646\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	4.36426	2.18213
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.52275	1.02991
$7$	0	0
$7$	0	0
$8$	−5.96443	−2.10874
$9$	1.00000	0.333333
$10$	−2.52275	−0.797763
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−4.36426	−1.25985
$13$	−5.44168	−1.50925	−0.754625	−	0.656156i	$-0.772181\pi$
$13$	−5.44168	−1.50925	−0.754625	+	0.656156i	$0.772181\pi$
$14$	0	0
$15$	−1.00000	−0.258199
$16$	6.31823	1.57956
$17$	−1.41028	−0.342044	−0.171022	−	0.985267i	$-0.554707\pi$
$17$	−1.41028	−0.342044	−0.171022	+	0.985267i	$0.554707\pi$
$18$	−2.52275	−0.594617
$19$	1.36426	0.312982	0.156491	−	0.987679i	$-0.449982\pi$
$19$	1.36426	0.312982	0.156491	+	0.987679i	$0.449982\pi$
$20$	4.36426	0.975878
$21$	0	0
$22$	−2.52275	−0.537852
$23$	−8.40975	−1.75355	−0.876777	−	0.480896i	$-0.840311\pi$
$23$	−8.40975	−1.75355	−0.876777	+	0.480896i	$0.840311\pi$
$24$	5.96443	1.21748
$25$	1.00000	0.200000
$26$	13.7280	2.69228
$27$	−1.00000	−0.192450
$28$	0	0
$29$	8.75991	1.62667	0.813337	−	0.581792i	$-0.197648\pi$
$29$	8.75991	1.62667	0.813337	+	0.581792i	$0.197648\pi$
$30$	2.52275	0.460589
$31$	−3.60382	−0.647265	−0.323632	−	0.946183i	$-0.604904\pi$
$31$	−3.60382	−0.647265	−0.323632	+	0.946183i	$0.604904\pi$
$32$	−4.01045	−0.708955
$33$	−1.00000	−0.174078
$34$	3.55779	0.610156
$35$	0	0
$36$	4.36426	0.727376
$37$	3.48771	0.573375	0.286688	−	0.958024i	$-0.407446\pi$
$37$	3.48771	0.573375	0.286688	+	0.958024i	$0.407446\pi$
$38$	−3.44168	−0.558314
$39$	5.44168	0.871366
$40$	−5.96443	−0.943059
$41$	−10.4411	−1.63063	−0.815317	−	0.579015i	$-0.803437\pi$
$41$	−10.4411	−1.63063	−0.815317	+	0.579015i	$0.803437\pi$
$42$	0	0
$43$	−11.5345	−1.75899	−0.879494	−	0.475910i	$-0.842119\pi$
$43$	−11.5345	−1.75899	−0.879494	+	0.475910i	$0.842119\pi$
$44$	4.36426	0.657937
$45$	1.00000	0.149071
$46$	21.2157	3.12808
$47$	8.21622	1.19846	0.599230	−	0.800577i	$-0.295474\pi$
$47$	8.21622	1.19846	0.599230	+	0.800577i	$0.295474\pi$
$48$	−6.31823	−0.911958
$49$	0	0
$50$	−2.52275	−0.356770
$51$	1.41028	0.197479
$52$	−23.7489	−3.29338
$53$	−5.31823	−0.730515	−0.365258	−	0.930906i	$-0.619019\pi$
$53$	−5.31823	−0.730515	−0.365258	+	0.930906i	$0.619019\pi$
$54$	2.52275	0.343303
$55$	1.00000	0.134840
$56$	0	0
$57$	−1.36426	−0.180700
$58$	−22.0991	−2.90175
$59$	−7.07689	−0.921333	−0.460666	−	0.887573i	$-0.652390\pi$
$59$	−7.07689	−0.921333	−0.460666	+	0.887573i	$0.652390\pi$
$60$	−4.36426	−0.563423
$61$	−3.52640	−0.451509	−0.225754	−	0.974184i	$-0.572485\pi$
$61$	−3.52640	−0.451509	−0.225754	+	0.974184i	$0.572485\pi$
$62$	9.09152	1.15462
$63$	0	0
$64$	−2.51910	−0.314888
$65$	−5.44168	−0.674957
$66$	2.52275	0.310529
$67$	−1.09152	−0.133351	−0.0666753	−	0.997775i	$-0.521239\pi$
$67$	−1.09152	−0.133351	−0.0666753	+	0.997775i	$0.521239\pi$
$68$	−6.15484	−0.746384
$69$	8.40975	1.01242
$70$	0	0
$71$	4.69534	0.557234	0.278617	−	0.960402i	$-0.410124\pi$
$71$	4.69534	0.557234	0.278617	+	0.960402i	$0.410124\pi$
$72$	−5.96443	−0.702915
$73$	−7.31645	−0.856326	−0.428163	−	0.903702i	$-0.640839\pi$
$73$	−7.31645	−0.856326	−0.428163	+	0.903702i	$0.640839\pi$
$74$	−8.79860	−1.02282
$75$	−1.00000	−0.115470
$76$	5.95397	0.682968
$77$	0	0
$78$	−13.7280	−1.55439
$79$	4.55832	0.512851	0.256426	−	0.966564i	$-0.417455\pi$
$79$	4.55832	0.512851	0.256426	+	0.966564i	$0.417455\pi$
$80$	6.31823	0.706400
$81$	1.00000	0.111111
$82$	26.3404	2.90881
$83$	9.51910	1.04486	0.522429	−	0.852683i	$-0.325026\pi$
$83$	9.51910	1.04486	0.522429	+	0.852683i	$0.325026\pi$
$84$	0	0
$85$	−1.41028	−0.152967
$86$	29.0985	3.13777
$87$	−8.75991	−0.939161
$88$	−5.96443	−0.635810
$89$	16.7421	1.77466	0.887329	−	0.461137i	$-0.152558\pi$
$89$	16.7421	1.77466	0.887329	+	0.461137i	$0.152558\pi$
$90$	−2.52275	−0.265921
$91$	0	0
$92$	−36.7023	−3.82648
$93$	3.60382	0.373698
$94$	−20.7275	−2.13787
$95$	1.36426	0.139970
$96$	4.01045	0.409315
$97$	−16.2630	−1.65125	−0.825627	−	0.564216i	$-0.809179\pi$
$97$	−16.2630	−1.65125	−0.825627	+	0.564216i	$0.809179\pi$
$98$	0	0
$99$	1.00000	0.100504
$100$	4.36426	0.436426
$101$	−14.9816	−1.49073	−0.745365	−	0.666657i	$-0.767725\pi$
$101$	−14.9816	−1.49073	−0.745365	+	0.666657i	$0.767725\pi$
$102$	−3.55779	−0.352274
$103$	−2.07742	−0.204694	−0.102347	−	0.994749i	$-0.532635\pi$
$103$	−2.07742	−0.204694	−0.102347	+	0.994749i	$0.532635\pi$
$104$	32.4565	3.18262
$105$	0	0
$106$	13.4166	1.30313
$107$	13.3778	1.29328	0.646642	−	0.762794i	$-0.276173\pi$
$107$	13.3778	1.29328	0.646642	+	0.762794i	$0.276173\pi$
$108$	−4.36426	−0.419951
$109$	−10.2790	−0.984551	−0.492275	−	0.870439i	$-0.663835\pi$
$109$	−10.2790	−0.984551	−0.492275	+	0.870439i	$0.663835\pi$
$110$	−2.52275	−0.240535
$111$	−3.48771	−0.331038
$112$	0	0
$113$	8.29364	0.780200	0.390100	−	0.920772i	$-0.372440\pi$
$113$	8.29364	0.780200	0.390100	+	0.920772i	$0.372440\pi$
$114$	3.44168	0.322343
$115$	−8.40975	−0.784214
$116$	38.2305	3.54961
$117$	−5.44168	−0.503083
$118$	17.8532	1.64352
$119$	0	0
$120$	5.96443	0.544475
$121$	1.00000	0.0909091
$122$	8.89621	0.805425
$123$	10.4411	0.941447
$124$	−15.7280	−1.41241
$125$	1.00000	0.0894427
$126$	0	0
$127$	12.8687	1.14192	0.570958	−	0.820980i	$-0.306572\pi$
$127$	12.8687	1.14192	0.570958	+	0.820980i	$0.306572\pi$
$128$	14.3760	1.27067
$129$	11.5345	1.01555
$130$	13.7280	1.20402
$131$	−11.4239	−0.998107	−0.499053	−	0.866571i	$-0.666319\pi$
$131$	−11.4239	−0.998107	−0.499053	+	0.866571i	$0.666319\pi$
$132$	−4.36426	−0.379860
$133$	0	0
$134$	2.75364	0.237878
$135$	−1.00000	−0.0860663
$136$	8.41154	0.721283
$137$	7.61187	0.650326	0.325163	−	0.945658i	$-0.394581\pi$
$137$	7.61187	0.650326	0.325163	+	0.945658i	$0.394581\pi$
$138$	−21.2157	−1.80600
$139$	9.31645	0.790211	0.395106	−	0.918636i	$-0.370708\pi$
$139$	9.31645	0.790211	0.395106	+	0.918636i	$0.370708\pi$
$140$	0	0
$141$	−8.21622	−0.691931
$142$	−11.8452	−0.994024
$143$	−5.44168	−0.455056
$144$	6.31823	0.526519
$145$	8.75991	0.727471
$146$	18.4576	1.52756
$147$	0	0
$148$	15.2212	1.25118
$149$	14.1370	1.15815	0.579075	−	0.815274i	$-0.303414\pi$
$149$	14.1370	1.15815	0.579075	+	0.815274i	$0.303414\pi$
$150$	2.52275	0.205982
$151$	−7.56585	−0.615700	−0.307850	−	0.951435i	$-0.599610\pi$
$151$	−7.56585	−0.615700	−0.307850	+	0.951435i	$0.599610\pi$
$152$	−8.13702	−0.659999
$153$	−1.41028	−0.114015
$154$	0	0
$155$	−3.60382	−0.289466
$156$	23.7489	1.90143
$157$	21.5972	1.72365	0.861824	−	0.507208i	$-0.169322\pi$
$157$	21.5972	1.72365	0.861824	+	0.507208i	$0.169322\pi$
$158$	−11.4995	−0.914851
$159$	5.31823	0.421763
$160$	−4.01045	−0.317054
$161$	0	0
$162$	−2.52275	−0.198206
$163$	17.0608	1.33631	0.668154	−	0.744023i	$-0.267085\pi$
$163$	17.0608	1.33631	0.668154	+	0.744023i	$0.267085\pi$
$164$	−45.5679	−3.55825
$165$	−1.00000	−0.0778499
$166$	−24.0143	−1.86387
$167$	−0.866594	−0.0670590	−0.0335295	−	0.999438i	$-0.510675\pi$
$167$	−0.866594	−0.0670590	−0.0335295	+	0.999438i	$0.510675\pi$
$168$	0	0
$169$	16.6119	1.27784
$170$	3.55779	0.272870
$171$	1.36426	0.104327
$172$	−50.3393	−3.83834
$173$	−10.0628	−0.765060	−0.382530	−	0.923943i	$-0.624947\pi$
$173$	−10.0628	−0.765060	−0.382530	+	0.923943i	$0.624947\pi$
$174$	22.0991	1.67532
$175$	0	0
$176$	6.31823	0.476255
$177$	7.07689	0.531932
$178$	−42.2361	−3.16573
$179$	2.42024	0.180897	0.0904487	−	0.995901i	$-0.471170\pi$
$179$	2.42024	0.180897	0.0904487	+	0.995901i	$0.471170\pi$
$180$	4.36426	0.325293
$181$	−2.54191	−0.188939	−0.0944693	−	0.995528i	$-0.530115\pi$
$181$	−2.54191	−0.188939	−0.0944693	+	0.995528i	$0.530115\pi$
$182$	0	0
$183$	3.52640	0.260679
$184$	50.1594	3.69780
$185$	3.48771	0.256421
$186$	−9.09152	−0.666623
$187$	−1.41028	−0.103130
$188$	35.8577	2.61519
$189$	0	0
$190$	−3.44168	−0.249686
$191$	24.0899	1.74309	0.871543	−	0.490319i	$-0.163120\pi$
$191$	24.0899	1.74309	0.871543	+	0.490319i	$0.163120\pi$
$192$	2.51910	0.181800
$193$	7.77401	0.559586	0.279793	−	0.960060i	$-0.409734\pi$
$193$	7.77401	0.559586	0.279793	+	0.960060i	$0.409734\pi$
$194$	41.0274	2.94559
$195$	5.44168	0.389687
$196$	0	0
$197$	−0.425797	−0.0303368	−0.0151684	−	0.999885i	$-0.504828\pi$
$197$	−0.425797	−0.0303368	−0.0151684	+	0.999885i	$0.504828\pi$
$198$	−2.52275	−0.179284
$199$	−11.8200	−0.837900	−0.418950	−	0.908009i	$-0.637602\pi$
$199$	−11.8200	−0.837900	−0.418950	+	0.908009i	$0.637602\pi$
$200$	−5.96443	−0.421749
$201$	1.09152	0.0769900
$202$	37.7949	2.65924
$203$	0	0
$204$	6.15484	0.430925
$205$	−10.4411	−0.729242
$206$	5.24081	0.365145
$207$	−8.40975	−0.584518
$208$	−34.3818	−2.38395
$209$	1.36426	0.0943677
$210$	0	0
$211$	−24.2305	−1.66810	−0.834049	−	0.551691i	$-0.813983\pi$
$211$	−24.2305	−1.66810	−0.834049	+	0.551691i	$0.813983\pi$
$212$	−23.2101	−1.59408
$213$	−4.69534	−0.321719
$214$	−33.7489	−2.30703
$215$	−11.5345	−0.786643
$216$	5.96443	0.405828
$217$	0	0
$218$	25.9314	1.75629
$219$	7.31645	0.494400
$220$	4.36426	0.294238
$221$	7.67431	0.516230
$222$	8.79860	0.590523
$223$	−2.62289	−0.175642	−0.0878210	−	0.996136i	$-0.527990\pi$
$223$	−2.62289	−0.175642	−0.0878210	+	0.996136i	$0.527990\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	−20.9228	−1.39176
$227$	3.02281	0.200631	0.100315	−	0.994956i	$-0.468015\pi$
$227$	3.02281	0.200631	0.100315	+	0.994956i	$0.468015\pi$
$228$	−5.95397	−0.394312
$229$	3.23725	0.213923	0.106962	−	0.994263i	$-0.465888\pi$
$229$	3.23725	0.213923	0.106962	+	0.994263i	$0.465888\pi$
$230$	21.2157	1.39892
$231$	0	0
$232$	−52.2479	−3.43024
$233$	−18.0363	−1.18159	−0.590797	−	0.806820i	$-0.701187\pi$
$233$	−18.0363	−1.18159	−0.590797	+	0.806820i	$0.701187\pi$
$234$	13.7280	0.897427
$235$	8.21622	0.535967
$236$	−30.8854	−2.01047
$237$	−4.55832	−0.296095
$238$	0	0
$239$	9.44346	0.610847	0.305423	−	0.952217i	$-0.401202\pi$
$239$	9.44346	0.610847	0.305423	+	0.952217i	$0.401202\pi$
$240$	−6.31823	−0.407840
$241$	−16.7662	−1.08001	−0.540003	−	0.841663i	$-0.681577\pi$
$241$	−16.7662	−1.08001	−0.540003	+	0.841663i	$0.681577\pi$
$242$	−2.52275	−0.162168
$243$	−1.00000	−0.0641500
$244$	−15.3901	−0.985250
$245$	0	0
$246$	−26.3404	−1.67940
$247$	−7.42385	−0.472369
$248$	21.4947	1.36492
$249$	−9.51910	−0.603249
$250$	−2.52275	−0.159553
$251$	27.8200	1.75599	0.877993	−	0.478674i	$-0.158882\pi$
$251$	27.8200	1.75599	0.877993	+	0.478674i	$0.158882\pi$
$252$	0	0
$253$	−8.40975	−0.528717
$254$	−32.4646	−2.03701
$255$	1.41028	0.0883154
$256$	−31.2287	−1.95180
$257$	13.5159	0.843099	0.421550	−	0.906805i	$-0.361486\pi$
$257$	13.5159	0.843099	0.421550	+	0.906805i	$0.361486\pi$
$258$	−29.0985	−1.81159
$259$	0	0
$260$	−23.7489	−1.47284
$261$	8.75991	0.542225
$262$	28.8195	1.78048
$263$	−1.95397	−0.120487	−0.0602436	−	0.998184i	$-0.519188\pi$
$263$	−1.95397	−0.120487	−0.0602436	+	0.998184i	$0.519188\pi$
$264$	5.96443	0.367085
$265$	−5.31823	−0.326696
$266$	0	0
$267$	−16.7421	−1.02460
$268$	−4.76368	−0.290988
$269$	12.2323	0.745814	0.372907	−	0.927869i	$-0.378361\pi$
$269$	12.2323	0.745814	0.372907	+	0.927869i	$0.378361\pi$
$270$	2.52275	0.153530
$271$	27.8877	1.69406	0.847028	−	0.531548i	$-0.178389\pi$
$271$	27.8877	1.69406	0.847028	+	0.531548i	$0.178389\pi$
$272$	−8.91050	−0.540278
$273$	0	0
$274$	−19.2028	−1.16009
$275$	1.00000	0.0603023
$276$	36.7023	2.20922
$277$	−8.34518	−0.501413	−0.250707	−	0.968063i	$-0.580663\pi$
$277$	−8.34518	−0.501413	−0.250707	+	0.968063i	$0.580663\pi$
$278$	−23.5031	−1.40962
$279$	−3.60382	−0.215755
$280$	0	0
$281$	18.1998	1.08571	0.542855	−	0.839827i	$-0.317343\pi$
$281$	18.1998	1.08571	0.542855	+	0.839827i	$0.317343\pi$
$282$	20.7275	1.23430
$283$	7.49021	0.445247	0.222623	−	0.974905i	$-0.428538\pi$
$283$	7.49021	0.445247	0.222623	+	0.974905i	$0.428538\pi$
$284$	20.4917	1.21596
$285$	−1.36426	−0.0808117
$286$	13.7280	0.811753
$287$	0	0
$288$	−4.01045	−0.236318
$289$	−15.0111	−0.883006
$290$	−22.0991	−1.29770
$291$	16.2630	0.953352
$292$	−31.9309	−1.86861
$293$	5.15983	0.301440	0.150720	−	0.988576i	$-0.451841\pi$
$293$	5.15983	0.301440	0.150720	+	0.988576i	$0.451841\pi$
$294$	0	0
$295$	−7.07689	−0.412033
$296$	−20.8022	−1.20910
$297$	−1.00000	−0.0580259
$298$	−35.6641	−2.06597
$299$	45.7632	2.64655
$300$	−4.36426	−0.251971
$301$	0	0
$302$	19.0867	1.09832
$303$	14.9816	0.860673
$304$	8.61970	0.494374
$305$	−3.52640	−0.201921
$306$	3.55779	0.203385
$307$	−16.8859	−0.963727	−0.481864	−	0.876246i	$-0.660040\pi$
$307$	−16.8859	−0.963727	−0.481864	+	0.876246i	$0.660040\pi$
$308$	0	0
$309$	2.07742	0.118180
$310$	9.09152	0.516364
$311$	15.0633	0.854163	0.427081	−	0.904213i	$-0.359542\pi$
$311$	15.0633	0.854163	0.427081	+	0.904213i	$0.359542\pi$
$312$	−32.4565	−1.83749
$313$	14.8687	0.840430	0.420215	−	0.907425i	$-0.361955\pi$
$313$	14.8687	0.840430	0.420215	+	0.907425i	$0.361955\pi$
$314$	−54.4844	−3.07473
$315$	0	0
$316$	19.8937	1.11911
$317$	31.0015	1.74122	0.870609	−	0.491976i	$-0.163725\pi$
$317$	31.0015	1.74122	0.870609	+	0.491976i	$0.163725\pi$
$318$	−13.4166	−0.752363
$319$	8.75991	0.490461
$320$	−2.51910	−0.140822
$321$	−13.3778	−0.746678
$322$	0	0
$323$	−1.92399	−0.107054
$324$	4.36426	0.242459
$325$	−5.44168	−0.301850
$326$	−43.0402	−2.38378
$327$	10.2790	0.568431
$328$	62.2755	3.43859
$329$	0	0
$330$	2.52275	0.138873
$331$	13.6597	0.750804	0.375402	−	0.926862i	$-0.377505\pi$
$331$	13.6597	0.750804	0.375402	+	0.926862i	$0.377505\pi$
$332$	41.5438	2.28001
$333$	3.48771	0.191125
$334$	2.18620	0.119623
$335$	−1.09152	−0.0596362
$336$	0	0
$337$	−21.3060	−1.16061	−0.580305	−	0.814399i	$-0.697067\pi$
$337$	−21.3060	−1.16061	−0.580305	+	0.814399i	$0.697067\pi$
$338$	−41.9076	−2.27947
$339$	−8.29364	−0.450449
$340$	−6.15484	−0.333793
$341$	−3.60382	−0.195158
$342$	−3.44168	−0.186105
$343$	0	0
$344$	68.7964	3.70925
$345$	8.40975	0.452766
$346$	25.3859	1.36475
$347$	−28.6358	−1.53725	−0.768626	−	0.639699i	$-0.779059\pi$
$347$	−28.6358	−1.53725	−0.768626	+	0.639699i	$0.779059\pi$
$348$	−38.2305	−2.04937
$349$	4.50075	0.240919	0.120460	−	0.992718i	$-0.461563\pi$
$349$	4.50075	0.240919	0.120460	+	0.992718i	$0.461563\pi$
$350$	0	0
$351$	5.44168	0.290455
$352$	−4.01045	−0.213758
$353$	7.51838	0.400163	0.200081	−	0.979779i	$-0.435879\pi$
$353$	7.51838	0.400163	0.200081	+	0.979779i	$0.435879\pi$
$354$	−17.8532	−0.948888
$355$	4.69534	0.249203
$356$	73.0668	3.87253
$357$	0	0
$358$	−6.10566	−0.322694
$359$	−24.7410	−1.30578	−0.652891	−	0.757452i	$-0.726444\pi$
$359$	−24.7410	−1.30578	−0.652891	+	0.757452i	$0.726444\pi$
$360$	−5.96443	−0.314353
$361$	−17.1388	−0.902042
$362$	6.41260	0.337039
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	−7.31645	−0.382961
$366$	−8.89621	−0.465012
$367$	−16.6782	−0.870597	−0.435298	−	0.900286i	$-0.643357\pi$
$367$	−16.6782	−0.870597	−0.435298	+	0.900286i	$0.643357\pi$
$368$	−53.1348	−2.76984
$369$	−10.4411	−0.543545
$370$	−8.79860	−0.457418
$371$	0	0
$372$	15.7280	0.815458
$373$	−18.1757	−0.941103	−0.470551	−	0.882373i	$-0.655945\pi$
$373$	−18.1757	−0.941103	−0.470551	+	0.882373i	$0.655945\pi$
$374$	3.55779	0.183969
$375$	−1.00000	−0.0516398
$376$	−49.0051	−2.52724
$377$	−47.6686	−2.45506
$378$	0	0
$379$	−3.31823	−0.170446	−0.0852231	−	0.996362i	$-0.527160\pi$
$379$	−3.31823	−0.170446	−0.0852231	+	0.996362i	$0.527160\pi$
$380$	5.95397	0.305432
$381$	−12.8687	−0.659285
$382$	−60.7728	−3.10941
$383$	−18.6205	−0.951461	−0.475731	−	0.879591i	$-0.657816\pi$
$383$	−18.6205	−0.951461	−0.475731	+	0.879591i	$0.657816\pi$
$384$	−14.3760	−0.733620
$385$	0	0
$386$	−19.6119	−0.998218
$387$	−11.5345	−0.586329
$388$	−70.9758	−3.60325
$389$	−9.64505	−0.489024	−0.244512	−	0.969646i	$-0.578628\pi$
$389$	−9.64505	−0.489024	−0.244512	+	0.969646i	$0.578628\pi$
$390$	−13.7280	−0.695144
$391$	11.8601	0.599793
$392$	0	0
$393$	11.4239	0.576257
$394$	1.07418	0.0541163
$395$	4.55832	0.229354
$396$	4.36426	0.219312
$397$	22.9451	1.15158	0.575791	−	0.817597i	$-0.304694\pi$
$397$	22.9451	1.15158	0.575791	+	0.817597i	$0.304694\pi$
$398$	29.8190	1.49469
$399$	0	0
$400$	6.31823	0.315912
$401$	17.4239	0.870106	0.435053	−	0.900405i	$-0.356730\pi$
$401$	17.4239	0.870106	0.435053	+	0.900405i	$0.356730\pi$
$402$	−2.75364	−0.137339
$403$	19.6108	0.976884
$404$	−65.3838	−3.25296
$405$	1.00000	0.0496904
$406$	0	0
$407$	3.48771	0.172879
$408$	−8.41154	−0.416433
$409$	1.21816	0.0602343	0.0301172	−	0.999546i	$-0.490412\pi$
$409$	1.21816	0.0602343	0.0301172	+	0.999546i	$0.490412\pi$
$410$	26.3404	1.30086
$411$	−7.61187	−0.375466
$412$	−9.06640	−0.446670
$413$	0	0
$414$	21.2157	1.04269
$415$	9.51910	0.467274
$416$	21.8236	1.06999
$417$	−9.31645	−0.456229
$418$	−3.44168	−0.168338
$419$	−2.35088	−0.114848	−0.0574240	−	0.998350i	$-0.518289\pi$
$419$	−2.35088	−0.114848	−0.0574240	+	0.998350i	$0.518289\pi$
$420$	0	0
$421$	−18.9572	−0.923920	−0.461960	−	0.886901i	$-0.652854\pi$
$421$	−18.9572	−0.923920	−0.461960	+	0.886901i	$0.652854\pi$
$422$	61.1275	2.97564
$423$	8.21622	0.399486
$424$	31.7202	1.54047
$425$	−1.41028	−0.0684088
$426$	11.8452	0.573900
$427$	0	0
$428$	58.3843	2.82211
$429$	5.44168	0.262727
$430$	29.0985	1.40326
$431$	32.8823	1.58388	0.791942	−	0.610596i	$-0.209070\pi$
$431$	32.8823	1.58388	0.791942	+	0.610596i	$0.209070\pi$
$432$	−6.31823	−0.303986
$433$	9.33322	0.448526	0.224263	−	0.974529i	$-0.428003\pi$
$433$	9.33322	0.448526	0.224263	+	0.974529i	$0.428003\pi$
$434$	0	0
$435$	−8.75991	−0.420006
$436$	−44.8603	−2.14842
$437$	−11.4731	−0.548832
$438$	−18.4576	−0.881936
$439$	−16.7010	−0.797097	−0.398549	−	0.917147i	$-0.630486\pi$
$439$	−16.7010	−0.797097	−0.398549	+	0.917147i	$0.630486\pi$
$440$	−5.96443	−0.284343
$441$	0	0
$442$	−19.3604	−0.920878
$443$	−9.79184	−0.465224	−0.232612	−	0.972570i	$-0.574727\pi$
$443$	−9.79184	−0.465224	−0.232612	+	0.972570i	$0.574727\pi$
$444$	−15.2212	−0.722368
$445$	16.7421	0.793651
$446$	6.61690	0.313319
$447$	−14.1370	−0.668658
$448$	0	0
$449$	−36.5556	−1.72516	−0.862582	−	0.505918i	$-0.831154\pi$
$449$	−36.5556	−1.72516	−0.862582	+	0.505918i	$0.831154\pi$
$450$	−2.52275	−0.118923
$451$	−10.4411	−0.491655
$452$	36.1956	1.70250
$453$	7.56585	0.355475
$454$	−7.62578	−0.357896
$455$	0	0
$456$	8.13702	0.381051
$457$	−18.7986	−0.879363	−0.439682	−	0.898154i	$-0.644909\pi$
$457$	−18.7986	−0.879363	−0.439682	+	0.898154i	$0.644909\pi$
$458$	−8.16676	−0.381608
$459$	1.41028	0.0658264
$460$	−36.7023	−1.71126
$461$	−34.0972	−1.58807	−0.794033	−	0.607875i	$-0.792022\pi$
$461$	−34.0972	−1.58807	−0.794033	+	0.607875i	$0.792022\pi$
$462$	0	0
$463$	−6.20816	−0.288518	−0.144259	−	0.989540i	$-0.546080\pi$
$463$	−6.20816	−0.288518	−0.144259	+	0.989540i	$0.546080\pi$
$464$	55.3472	2.56943
$465$	3.60382	0.167123
$466$	45.5009	2.10779
$467$	−3.20763	−0.148432	−0.0742158	−	0.997242i	$-0.523645\pi$
$467$	−3.20763	−0.148432	−0.0742158	+	0.997242i	$0.523645\pi$
$468$	−23.7489	−1.09779
$469$	0	0
$470$	−20.7275	−0.956086
$471$	−21.5972	−0.995149
$472$	42.2096	1.94285
$473$	−11.5345	−0.530355
$474$	11.4995	0.528189
$475$	1.36426	0.0625965
$476$	0	0
$477$	−5.31823	−0.243505
$478$	−23.8235	−1.08966
$479$	10.1252	0.462634	0.231317	−	0.972878i	$-0.425697\pi$
$479$	10.1252	0.462634	0.231317	+	0.972878i	$0.425697\pi$
$480$	4.01045	0.183051
$481$	−18.9790	−0.865367
$482$	42.2969	1.92657
$483$	0	0
$484$	4.36426	0.198375
$485$	−16.2630	−0.738463
$486$	2.52275	0.114434
$487$	−25.5721	−1.15878	−0.579391	−	0.815050i	$-0.696710\pi$
$487$	−25.5721	−1.15878	−0.579391	+	0.815050i	$0.696710\pi$
$488$	21.0329	0.952116
$489$	−17.0608	−0.771518
$490$	0	0
$491$	−15.4681	−0.698066	−0.349033	−	0.937111i	$-0.613490\pi$
$491$	−15.4681	−0.698066	−0.349033	+	0.937111i	$0.613490\pi$
$492$	45.5679	2.05436
$493$	−12.3540	−0.556394
$494$	18.7285	0.842636
$495$	1.00000	0.0449467
$496$	−22.7698	−1.02239
$497$	0	0
$498$	24.0143	1.07611
$499$	−0.712473	−0.0318947	−0.0159473	−	0.999873i	$-0.505076\pi$
$499$	−0.712473	−0.0318947	−0.0159473	+	0.999873i	$0.505076\pi$
$500$	4.36426	0.195176
$501$	0.866594	0.0387165
$502$	−70.1829	−3.13242
$503$	41.8595	1.86642	0.933211	−	0.359328i	$-0.116994\pi$
$503$	41.8595	1.86642	0.933211	+	0.359328i	$0.116994\pi$
$504$	0	0
$505$	−14.9816	−0.666674
$506$	21.2157	0.943153
$507$	−16.6119	−0.737759
$508$	56.1625	2.49181
$509$	−5.35247	−0.237244	−0.118622	−	0.992939i	$-0.537848\pi$
$509$	−5.35247	−0.237244	−0.118622	+	0.992939i	$0.537848\pi$
$510$	−3.55779	−0.157542
$511$	0	0
$512$	50.0303	2.21105
$513$	−1.36426	−0.0602335
$514$	−34.0972	−1.50396
$515$	−2.07742	−0.0915421
$516$	50.3393	2.21607
$517$	8.21622	0.361349
$518$	0	0
$519$	10.0628	0.441708
$520$	32.4565	1.42331
$521$	18.6511	0.817119	0.408560	−	0.912732i	$-0.366031\pi$
$521$	18.6511	0.817119	0.408560	+	0.912732i	$0.366031\pi$
$522$	−22.0991	−0.967249
$523$	26.2494	1.14781	0.573903	−	0.818923i	$-0.305429\pi$
$523$	26.2494	1.14781	0.573903	+	0.818923i	$0.305429\pi$
$524$	−49.8567	−2.17800
$525$	0	0
$526$	4.92938	0.214931
$527$	5.08240	0.221393
$528$	−6.31823	−0.274966
$529$	47.7240	2.07496
$530$	13.4166	0.582778
$531$	−7.07689	−0.307111
$532$	0	0
$533$	56.8174	2.46103
$534$	42.2361	1.82773
$535$	13.3778	0.578374
$536$	6.51030	0.281202
$537$	−2.42024	−0.104441
$538$	−30.8589	−1.33042
$539$	0	0
$540$	−4.36426	−0.187808
$541$	23.0714	0.991916	0.495958	−	0.868346i	$-0.334817\pi$
$541$	23.0714	0.991916	0.495958	+	0.868346i	$0.334817\pi$
$542$	−70.3536	−3.02195
$543$	2.54191	0.109084
$544$	5.65588	0.242494
$545$	−10.2790	−0.440305
$546$	0	0
$547$	43.1117	1.84332	0.921662	−	0.387993i	$-0.126831\pi$
$547$	43.1117	1.84332	0.921662	+	0.387993i	$0.126831\pi$
$548$	33.2202	1.41910
$549$	−3.52640	−0.150503
$550$	−2.52275	−0.107570
$551$	11.9508	0.509120
$552$	−50.1594	−2.13492
$553$	0	0
$554$	21.0528	0.894447
$555$	−3.48771	−0.148045
$556$	40.6594	1.72434
$557$	5.15537	0.218440	0.109220	−	0.994018i	$-0.465165\pi$
$557$	5.15537	0.218440	0.109220	+	0.994018i	$0.465165\pi$
$558$	9.09152	0.384875
$559$	62.7668	2.65475
$560$	0	0
$561$	1.41028	0.0595422
$562$	−45.9135	−1.93675
$563$	31.7624	1.33863	0.669313	−	0.742980i	$-0.266588\pi$
$563$	31.7624	1.33863	0.669313	+	0.742980i	$0.266588\pi$
$564$	−35.8577	−1.50988
$565$	8.29364	0.348916
$566$	−18.8959	−0.794254
$567$	0	0
$568$	−28.0050	−1.17506
$569$	−24.5256	−1.02817	−0.514083	−	0.857741i	$-0.671868\pi$
$569$	−24.5256	−1.02817	−0.514083	+	0.857741i	$0.671868\pi$
$570$	3.44168	0.144156
$571$	14.8077	0.619684	0.309842	−	0.950788i	$-0.399724\pi$
$571$	14.8077	0.619684	0.309842	+	0.950788i	$0.399724\pi$
$572$	−23.7489	−0.992991
$573$	−24.0899	−1.00637
$574$	0	0
$575$	−8.40975	−0.350711
$576$	−2.51910	−0.104963
$577$	17.3304	0.721474	0.360737	−	0.932668i	$-0.382525\pi$
$577$	17.3304	0.721474	0.360737	+	0.932668i	$0.382525\pi$
$578$	37.8692	1.57515
$579$	−7.77401	−0.323077
$580$	38.2305	1.58744
$581$	0	0
$582$	−41.0274	−1.70064
$583$	−5.31823	−0.220259
$584$	43.6384	1.80577
$585$	−5.44168	−0.224986
$586$	−13.0169	−0.537725
$587$	−45.9180	−1.89524	−0.947620	−	0.319400i	$-0.896519\pi$
$587$	−45.9180	−1.89524	−0.947620	+	0.319400i	$0.896519\pi$
$588$	0	0
$589$	−4.91654	−0.202582
$590$	17.8532	0.735005
$591$	0.425797	0.0175150
$592$	22.0361	0.905679
$593$	−1.54658	−0.0635104	−0.0317552	−	0.999496i	$-0.510110\pi$
$593$	−1.54658	−0.0635104	−0.0317552	+	0.999496i	$0.510110\pi$
$594$	2.52275	0.103510
$595$	0	0
$596$	61.6976	2.52723
$597$	11.8200	0.483762
$598$	−115.449	−4.72106
$599$	−18.2604	−0.746101	−0.373050	−	0.927811i	$-0.621688\pi$
$599$	−18.2604	−0.746101	−0.373050	+	0.927811i	$0.621688\pi$
$600$	5.96443	0.243497
$601$	20.0990	0.819856	0.409928	−	0.912118i	$-0.365554\pi$
$601$	20.0990	0.819856	0.409928	+	0.912118i	$0.365554\pi$
$602$	0	0
$603$	−1.09152	−0.0444502
$604$	−33.0193	−1.34354
$605$	1.00000	0.0406558
$606$	−37.7949	−1.53531
$607$	−19.3368	−0.784856	−0.392428	−	0.919783i	$-0.628365\pi$
$607$	−19.3368	−0.784856	−0.392428	+	0.919783i	$0.628365\pi$
$608$	−5.47129	−0.221890
$609$	0	0
$610$	8.89621	0.360197
$611$	−44.7100	−1.80877
$612$	−6.15484	−0.248795
$613$	41.1982	1.66398	0.831990	−	0.554790i	$-0.187202\pi$
$613$	41.1982	1.66398	0.831990	+	0.554790i	$0.187202\pi$
$614$	42.5988	1.71915
$615$	10.4411	0.421028
$616$	0	0
$617$	−3.17943	−0.127999	−0.0639996	−	0.997950i	$-0.520386\pi$
$617$	−3.17943	−0.127999	−0.0639996	+	0.997950i	$0.520386\pi$
$618$	−5.24081	−0.210816
$619$	36.5831	1.47040	0.735200	−	0.677850i	$-0.237088\pi$
$619$	36.5831	1.47040	0.735200	+	0.677850i	$0.237088\pi$
$620$	−15.7280	−0.631651
$621$	8.40975	0.337472
$622$	−38.0010	−1.52370
$623$	0	0
$624$	34.3818	1.37637
$625$	1.00000	0.0400000
$626$	−37.5101	−1.49920
$627$	−1.36426	−0.0544832
$628$	94.2559	3.76122
$629$	−4.91865	−0.196120
$630$	0	0
$631$	26.8209	1.06772	0.533861	−	0.845572i	$-0.320740\pi$
$631$	26.8209	1.06772	0.533861	+	0.845572i	$0.320740\pi$
$632$	−27.1878	−1.08147
$633$	24.2305	0.963077
$634$	−78.2090	−3.10607
$635$	12.8687	0.510680
$636$	23.2101	0.920342
$637$	0	0
$638$	−22.0991	−0.874910
$639$	4.69534	0.185745
$640$	14.3760	0.568260
$641$	10.1841	0.402248	0.201124	−	0.979566i	$-0.435541\pi$
$641$	10.1841	0.402248	0.201124	+	0.979566i	$0.435541\pi$
$642$	33.7489	1.33196
$643$	15.3525	0.605442	0.302721	−	0.953079i	$-0.402105\pi$
$643$	15.3525	0.605442	0.302721	+	0.953079i	$0.402105\pi$
$644$	0	0
$645$	11.5345	0.454169
$646$	4.85374	0.190968
$647$	38.5234	1.51451	0.757256	−	0.653118i	$-0.226539\pi$
$647$	38.5234	1.51451	0.757256	+	0.653118i	$0.226539\pi$
$648$	−5.96443	−0.234305
$649$	−7.07689	−0.277792
$650$	13.7280	0.538456
$651$	0	0
$652$	74.4579	2.91600
$653$	4.17089	0.163219	0.0816097	−	0.996664i	$-0.473994\pi$
$653$	4.17089	0.163219	0.0816097	+	0.996664i	$0.473994\pi$
$654$	−25.9314	−1.01400
$655$	−11.4239	−0.446367
$656$	−65.9696	−2.57568
$657$	−7.31645	−0.285442
$658$	0	0
$659$	−38.1242	−1.48511	−0.742555	−	0.669785i	$-0.766386\pi$
$659$	−38.1242	−1.48511	−0.742555	+	0.669785i	$0.766386\pi$
$660$	−4.36426	−0.169879
$661$	28.4621	1.10705	0.553523	−	0.832834i	$-0.313283\pi$
$661$	28.4621	1.10705	0.553523	+	0.832834i	$0.313283\pi$
$662$	−34.4599	−1.33932
$663$	−7.67431	−0.298046
$664$	−56.7760	−2.20334
$665$	0	0
$666$	−8.79860	−0.340939
$667$	−73.6687	−2.85246
$668$	−3.78204	−0.146331
$669$	2.62289	0.101407
$670$	2.75364	0.106382
$671$	−3.52640	−0.136135
$672$	0	0
$673$	−18.4890	−0.712697	−0.356348	−	0.934353i	$-0.615978\pi$
$673$	−18.4890	−0.712697	−0.356348	+	0.934353i	$0.615978\pi$
$674$	53.7496	2.07036
$675$	−1.00000	−0.0384900
$676$	72.4985	2.78840
$677$	−8.58721	−0.330033	−0.165017	−	0.986291i	$-0.552768\pi$
$677$	−8.58721	−0.330033	−0.165017	+	0.986291i	$0.552768\pi$
$678$	20.9228	0.803534
$679$	0	0
$680$	8.41154	0.322568
$681$	−3.02281	−0.115834
$682$	9.09152	0.348132
$683$	4.05226	0.155055	0.0775277	−	0.996990i	$-0.475297\pi$
$683$	4.05226	0.155055	0.0775277	+	0.996990i	$0.475297\pi$
$684$	5.95397	0.227656
$685$	7.61187	0.290835
$686$	0	0
$687$	−3.23725	−0.123509
$688$	−72.8774	−2.77842
$689$	28.9401	1.10253
$690$	−21.2157	−0.807668
$691$	0.408622	0.0155447	0.00777235	−	0.999970i	$-0.497526\pi$
$691$	0.408622	0.0155447	0.00777235	+	0.999970i	$0.497526\pi$
$692$	−43.9166	−1.66946
$693$	0	0
$694$	72.2409	2.74223
$695$	9.31645	0.353393
$696$	52.2479	1.98045
$697$	14.7250	0.557749
$698$	−11.3543	−0.429765
$699$	18.0363	0.682194
$700$	0	0
$701$	−37.1239	−1.40215	−0.701075	−	0.713088i	$-0.747296\pi$
$701$	−37.1239	−1.40215	−0.701075	+	0.713088i	$0.747296\pi$
$702$	−13.7280	−0.518129
$703$	4.75813	0.179456
$704$	−2.51910	−0.0949422
$705$	−8.21622	−0.309441
$706$	−18.9670	−0.713832
$707$	0	0
$708$	30.8854	1.16074
$709$	−3.88834	−0.146030	−0.0730149	−	0.997331i	$-0.523262\pi$
$709$	−3.88834	−0.146030	−0.0730149	+	0.997331i	$0.523262\pi$
$710$	−11.8452	−0.444541
$711$	4.55832	0.170950
$712$	−99.8570	−3.74230
$713$	30.3072	1.13501
$714$	0	0
$715$	−5.44168	−0.203507
$716$	10.5626	0.394742
$717$	−9.44346	−0.352673
$718$	62.4154	2.32932
$719$	25.8792	0.965132	0.482566	−	0.875860i	$-0.339705\pi$
$719$	25.8792	0.965132	0.482566	+	0.875860i	$0.339705\pi$
$720$	6.31823	0.235467
$721$	0	0
$722$	43.2369	1.60911
$723$	16.7662	0.623541
$724$	−11.0935	−0.412288
$725$	8.75991	0.325335
$726$	2.52275	0.0936280
$727$	12.9315	0.479604	0.239802	−	0.970822i	$-0.422918\pi$
$727$	12.9315	0.479604	0.239802	+	0.970822i	$0.422918\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	18.4576	0.683145
$731$	16.2669	0.601651
$732$	15.3901	0.568834
$733$	−34.2270	−1.26420	−0.632101	−	0.774886i	$-0.717807\pi$
$733$	−34.2270	−1.26420	−0.632101	+	0.774886i	$0.717807\pi$
$734$	42.0750	1.55302
$735$	0	0
$736$	33.7269	1.24319
$737$	−1.09152	−0.0402067
$738$	26.3404	0.969603
$739$	−12.1741	−0.447832	−0.223916	−	0.974608i	$-0.571884\pi$
$739$	−12.1741	−0.447832	−0.223916	+	0.974608i	$0.571884\pi$
$740$	15.2212	0.559544
$741$	7.42385	0.272722
$742$	0	0
$743$	−14.2672	−0.523414	−0.261707	−	0.965147i	$-0.584285\pi$
$743$	−14.2672	−0.523414	−0.261707	+	0.965147i	$0.584285\pi$
$744$	−21.4947	−0.788034
$745$	14.1370	0.517940
$746$	45.8527	1.67879
$747$	9.51910	0.348286
$748$	−6.15484	−0.225043
$749$	0	0
$750$	2.52275	0.0921177
$751$	−31.9793	−1.16694	−0.583471	−	0.812134i	$-0.698306\pi$
$751$	−31.9793	−1.16694	−0.583471	+	0.812134i	$0.698306\pi$
$752$	51.9120	1.89304
$753$	−27.8200	−1.01382
$754$	120.256	4.37946
$755$	−7.56585	−0.275349
$756$	0	0
$757$	14.4681	0.525852	0.262926	−	0.964816i	$-0.415313\pi$
$757$	14.4681	0.525852	0.262926	+	0.964816i	$0.415313\pi$
$758$	8.37106	0.304051
$759$	8.40975	0.305255
$760$	−8.13702	−0.295161
$761$	26.5297	0.961700	0.480850	−	0.876803i	$-0.340328\pi$
$761$	26.5297	0.961700	0.480850	+	0.876803i	$0.340328\pi$
$762$	32.4646	1.17607
$763$	0	0
$764$	105.135	3.80364
$765$	−1.41028	−0.0509889
$766$	46.9747	1.69727
$767$	38.5102	1.39052
$768$	31.2287	1.12687
$769$	36.1744	1.30448	0.652240	−	0.758012i	$-0.273829\pi$
$769$	36.1744	1.30448	0.652240	+	0.758012i	$0.273829\pi$
$770$	0	0
$771$	−13.5159	−0.486763
$772$	33.9278	1.22109
$773$	−4.48162	−0.161193	−0.0805964	−	0.996747i	$-0.525682\pi$
$773$	−4.48162	−0.161193	−0.0805964	+	0.996747i	$0.525682\pi$
$774$	29.0985	1.04592
$775$	−3.60382	−0.129453
$776$	96.9993	3.48207
$777$	0	0
$778$	24.3320	0.872346
$779$	−14.2444	−0.510359
$780$	23.7489	0.850347
$781$	4.69534	0.168012
$782$	−29.9201	−1.06994
$783$	−8.75991	−0.313054
$784$	0	0
$785$	21.5972	0.770839
$786$	−28.8195	−1.02796
$787$	−32.7728	−1.16823	−0.584113	−	0.811673i	$-0.698557\pi$
$787$	−32.7728	−1.16823	−0.584113	+	0.811673i	$0.698557\pi$
$788$	−1.85829	−0.0661988
$789$	1.95397	0.0695633
$790$	−11.4995	−0.409134
$791$	0	0
$792$	−5.96443	−0.211937
$793$	19.1895	0.681440
$794$	−57.8847	−2.05425
$795$	5.31823	0.188618
$796$	−51.5857	−1.82841
$797$	−1.56756	−0.0555257	−0.0277629	−	0.999615i	$-0.508838\pi$
$797$	−1.56756	−0.0555257	−0.0277629	+	0.999615i	$0.508838\pi$
$798$	0	0
$799$	−11.5872	−0.409926
$800$	−4.01045	−0.141791
$801$	16.7421	0.591553
$802$	−43.9560	−1.55214
$803$	−7.31645	−0.258192
$804$	4.76368	0.168002
$805$	0	0
$806$	−49.4731	−1.74262
$807$	−12.2323	−0.430596
$808$	89.3569	3.14357
$809$	48.0083	1.68788	0.843940	−	0.536437i	$-0.180230\pi$
$809$	48.0083	1.68788	0.843940	+	0.536437i	$0.180230\pi$
$810$	−2.52275	−0.0886403
$811$	−23.0204	−0.808355	−0.404177	−	0.914681i	$-0.632442\pi$
$811$	−23.0204	−0.808355	−0.404177	+	0.914681i	$0.632442\pi$
$812$	0	0
$813$	−27.8877	−0.978064
$814$	−8.79860	−0.308391
$815$	17.0608	0.597615
$816$	8.91050	0.311930
$817$	−15.7360	−0.550532
$818$	−3.07312	−0.107449
$819$	0	0
$820$	−45.5679	−1.59130
$821$	47.4418	1.65573	0.827864	−	0.560928i	$-0.189556\pi$
$821$	47.4418	1.65573	0.827864	+	0.560928i	$0.189556\pi$
$822$	19.2028	0.669776
$823$	48.0905	1.67633	0.838165	−	0.545416i	$-0.183628\pi$
$823$	48.0905	1.67633	0.838165	+	0.545416i	$0.183628\pi$
$824$	12.3906	0.431648
$825$	−1.00000	−0.0348155
$826$	0	0
$827$	26.9026	0.935496	0.467748	−	0.883862i	$-0.345065\pi$
$827$	26.9026	0.935496	0.467748	+	0.883862i	$0.345065\pi$
$828$	−36.7023	−1.27549
$829$	−18.0592	−0.627223	−0.313611	−	0.949551i	$-0.601539\pi$
$829$	−18.0592	−0.627223	−0.313611	+	0.949551i	$0.601539\pi$
$830$	−24.0143	−0.833548
$831$	8.34518	0.289491
$832$	13.7081	0.475244
$833$	0	0
$834$	23.5031	0.813844
$835$	−0.866594	−0.0299897
$836$	5.95397	0.205923
$837$	3.60382	0.124566
$838$	5.93068	0.204872
$839$	−6.74623	−0.232906	−0.116453	−	0.993196i	$-0.537152\pi$
$839$	−6.74623	−0.232906	−0.116453	+	0.993196i	$0.537152\pi$
$840$	0	0
$841$	47.7361	1.64607
$842$	47.8244	1.64814
$843$	−18.1998	−0.626835
$844$	−105.748	−3.64000
$845$	16.6119	0.571466
$846$	−20.7275	−0.712625
$847$	0	0
$848$	−33.6018	−1.15389
$849$	−7.49021	−0.257063
$850$	3.55779	0.122031
$851$	−29.3307	−1.00544
$852$	−20.4917	−0.702033
$853$	−9.12097	−0.312296	−0.156148	−	0.987734i	$-0.549908\pi$
$853$	−9.12097	−0.312296	−0.156148	+	0.987734i	$0.549908\pi$
$854$	0	0
$855$	1.36426	0.0466566
$856$	−79.7911	−2.72720
$857$	40.8651	1.39593	0.697963	−	0.716134i	$-0.254090\pi$
$857$	40.8651	1.39593	0.697963	+	0.716134i	$0.254090\pi$
$858$	−13.7280	−0.468666
$859$	6.54852	0.223433	0.111716	−	0.993740i	$-0.464365\pi$
$859$	6.54852	0.223433	0.111716	+	0.993740i	$0.464365\pi$
$860$	−50.3393	−1.71656
$861$	0	0
$862$	−82.9538	−2.82542
$863$	32.9504	1.12164	0.560822	−	0.827937i	$-0.310485\pi$
$863$	32.9504	1.12164	0.560822	+	0.827937i	$0.310485\pi$
$864$	4.01045	0.136438
$865$	−10.0628	−0.342145
$866$	−23.5454	−0.800104
$867$	15.0111	0.509804
$868$	0	0
$869$	4.55832	0.154630
$870$	22.0991	0.749228
$871$	5.93971	0.201260
$872$	61.3084	2.07617
$873$	−16.2630	−0.550418
$874$	28.9437	0.979035
$875$	0	0
$876$	31.9309	1.07884
$877$	44.4377	1.50055	0.750277	−	0.661124i	$-0.229920\pi$
$877$	44.4377	1.50055	0.750277	+	0.661124i	$0.229920\pi$
$878$	42.1325	1.42190
$879$	−5.15983	−0.174037
$880$	6.31823	0.212988
$881$	−48.6954	−1.64059	−0.820295	−	0.571941i	$-0.806191\pi$
$881$	−48.6954	−1.64059	−0.820295	+	0.571941i	$0.806191\pi$
$882$	0	0
$883$	14.7954	0.497906	0.248953	−	0.968516i	$-0.419913\pi$
$883$	14.7954	0.497906	0.248953	+	0.968516i	$0.419913\pi$
$884$	33.4927	1.12648
$885$	7.07689	0.237887
$886$	24.7023	0.829891
$887$	21.0707	0.707484	0.353742	−	0.935343i	$-0.384909\pi$
$887$	21.0707	0.707484	0.353742	+	0.935343i	$0.384909\pi$
$888$	20.8022	0.698075
$889$	0	0
$890$	−42.2361	−1.41576
$891$	1.00000	0.0335013
$892$	−11.4470	−0.383273
$893$	11.2090	0.375096
$894$	35.6641	1.19279
$895$	2.42024	0.0808998
$896$	0	0
$897$	−45.7632	−1.52799
$898$	92.2205	3.07744
$899$	−31.5691	−1.05289
$900$	4.36426	0.145475
$901$	7.50022	0.249868
$902$	26.3404	0.877039
$903$	0	0
$904$	−49.4668	−1.64524
$905$	−2.54191	−0.0844959
$906$	−19.0867	−0.634114
$907$	7.04732	0.234002	0.117001	−	0.993132i	$-0.462672\pi$
$907$	7.04732	0.234002	0.117001	+	0.993132i	$0.462672\pi$
$908$	13.1923	0.437802
$909$	−14.9816	−0.496910
$910$	0	0
$911$	41.7472	1.38315	0.691573	−	0.722307i	$-0.256918\pi$
$911$	41.7472	1.38315	0.691573	+	0.722307i	$0.256918\pi$
$912$	−8.61970	−0.285427
$913$	9.51910	0.315036
$914$	47.4242	1.56865
$915$	3.52640	0.116579
$916$	14.1282	0.466808
$917$	0	0
$918$	−3.55779	−0.117425
$919$	−2.65284	−0.0875092	−0.0437546	−	0.999042i	$-0.513932\pi$
$919$	−2.65284	−0.0875092	−0.0437546	+	0.999042i	$0.513932\pi$
$920$	50.1594	1.65371
$921$	16.8859	0.556408
$922$	86.0187	2.83288
$923$	−25.5505	−0.841006
$924$	0	0
$925$	3.48771	0.114675
$926$	15.6616	0.514673
$927$	−2.07742	−0.0682315
$928$	−35.1312	−1.15324
$929$	33.7286	1.10660	0.553299	−	0.832983i	$-0.313369\pi$
$929$	33.7286	1.10660	0.553299	+	0.832983i	$0.313369\pi$
$930$	−9.09152	−0.298123
$931$	0	0
$932$	−78.7149	−2.57839
$933$	−15.0633	−0.493151
$934$	8.09205	0.264780
$935$	−1.41028	−0.0461212
$936$	32.4565	1.06087
$937$	27.4371	0.896330	0.448165	−	0.893951i	$-0.352078\pi$
$937$	27.4371	0.896330	0.448165	+	0.893951i	$0.352078\pi$
$938$	0	0
$939$	−14.8687	−0.485223
$940$	35.8577	1.16955
$941$	−11.5725	−0.377251	−0.188626	−	0.982049i	$-0.560403\pi$
$941$	−11.5725	−0.377251	−0.188626	+	0.982049i	$0.560403\pi$
$942$	54.4844	1.77520
$943$	87.8075	2.85941
$944$	−44.7134	−1.45530
$945$	0	0
$946$	29.0985	0.946075
$947$	11.0719	0.359789	0.179894	−	0.983686i	$-0.442424\pi$
$947$	11.0719	0.359789	0.179894	+	0.983686i	$0.442424\pi$
$948$	−19.8937	−0.646117
$949$	39.8138	1.29241
$950$	−3.44168	−0.111663
$951$	−31.0015	−1.00529
$952$	0	0
$953$	−48.3609	−1.56656	−0.783281	−	0.621667i	$-0.786456\pi$
$953$	−48.3609	−1.56656	−0.783281	+	0.621667i	$0.786456\pi$
$954$	13.4166	0.434377
$955$	24.0899	0.779532
$956$	41.2137	1.33295
$957$	−8.75991	−0.283168
$958$	−25.5434	−0.825270
$959$	0	0
$960$	2.51910	0.0813036
$961$	−18.0125	−0.581049
$962$	47.8792	1.54369
$963$	13.3778	0.431095
$964$	−73.1720	−2.35671
$965$	7.77401	0.250254
$966$	0	0
$967$	−38.9904	−1.25385	−0.626924	−	0.779081i	$-0.715686\pi$
$967$	−38.9904	−1.25385	−0.626924	+	0.779081i	$0.715686\pi$
$968$	−5.96443	−0.191704
$969$	1.92399	0.0618075
$970$	41.0274	1.31731
$971$	56.7487	1.82115	0.910577	−	0.413340i	$-0.135638\pi$
$971$	56.7487	1.82115	0.910577	+	0.413340i	$0.135638\pi$
$972$	−4.36426	−0.139984
$973$	0	0
$974$	64.5119	2.06710
$975$	5.44168	0.174273
$976$	−22.2806	−0.713184
$977$	−33.9990	−1.08772	−0.543862	−	0.839174i	$-0.683039\pi$
$977$	−33.9990	−1.08772	−0.543862	+	0.839174i	$0.683039\pi$
$978$	43.0402	1.37627
$979$	16.7421	0.535079
$980$	0	0
$981$	−10.2790	−0.328184
$982$	39.0221	1.24525
$983$	3.52088	0.112299	0.0561494	−	0.998422i	$-0.482118\pi$
$983$	3.52088	0.112299	0.0561494	+	0.998422i	$0.482118\pi$
$984$	−62.2755	−1.98527
$985$	−0.425797	−0.0135670
$986$	31.1659	0.992526
$987$	0	0
$988$	−32.3996	−1.03077
$989$	97.0019	3.08448
$990$	−2.52275	−0.0801782
$991$	35.2790	1.12068	0.560338	−	0.828264i	$-0.310671\pi$
$991$	35.2790	1.12068	0.560338	+	0.828264i	$0.310671\pi$
$992$	14.4529	0.458881
$993$	−13.6597	−0.433477
$994$	0	0
$995$	−11.8200	−0.374720
$996$	−41.5438	−1.31637
$997$	−22.6176	−0.716306	−0.358153	−	0.933663i	$-0.616593\pi$
$997$	−22.6176	−0.716306	−0.358153	+	0.933663i	$0.616593\pi$
$998$	1.79739	0.0568954
$999$	−3.48771	−0.110346

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8085.2.a.bv.1.1		5
7.6	odd	2		1155.2.a.w.1.1	✓	5
21.20	even	2		3465.2.a.bm.1.5		5
35.34	odd	2		5775.2.a.cg.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.a.w.1.1	✓	5	7.6	odd	2
3465.2.a.bm.1.5		5	21.20	even	2
5775.2.a.cg.1.5		5	35.34	odd	2
8085.2.a.bv.1.1		5	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)

\(f(q)\)	\(=\)	\(q-2.52275 q^{2} -1.00000 q^{3} +4.36426 q^{4} +1.00000 q^{5} +2.52275 q^{6} -5.96443 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.52275 q^{2} -1.00000 q^{3} +4.36426 q^{4} +1.00000 q^{5} +2.52275 q^{6} -5.96443 q^{8} +1.00000 q^{9} -2.52275 q^{10} +1.00000 q^{11} -4.36426 q^{12} -5.44168 q^{13} -1.00000 q^{15} +6.31823 q^{16} -1.41028 q^{17} -2.52275 q^{18} +1.36426 q^{19} +4.36426 q^{20} -2.52275 q^{22} -8.40975 q^{23} +5.96443 q^{24} +1.00000 q^{25} +13.7280 q^{26} -1.00000 q^{27} +8.75991 q^{29} +2.52275 q^{30} -3.60382 q^{31} -4.01045 q^{32} -1.00000 q^{33} +3.55779 q^{34} +4.36426 q^{36} +3.48771 q^{37} -3.44168 q^{38} +5.44168 q^{39} -5.96443 q^{40} -10.4411 q^{41} -11.5345 q^{43} +4.36426 q^{44} +1.00000 q^{45} +21.2157 q^{46} +8.21622 q^{47} -6.31823 q^{48} -2.52275 q^{50} +1.41028 q^{51} -23.7489 q^{52} -5.31823 q^{53} +2.52275 q^{54} +1.00000 q^{55} -1.36426 q^{57} -22.0991 q^{58} -7.07689 q^{59} -4.36426 q^{60} -3.52640 q^{61} +9.09152 q^{62} -2.51910 q^{64} -5.44168 q^{65} +2.52275 q^{66} -1.09152 q^{67} -6.15484 q^{68} +8.40975 q^{69} +4.69534 q^{71} -5.96443 q^{72} -7.31645 q^{73} -8.79860 q^{74} -1.00000 q^{75} +5.95397 q^{76} -13.7280 q^{78} +4.55832 q^{79} +6.31823 q^{80} +1.00000 q^{81} +26.3404 q^{82} +9.51910 q^{83} -1.41028 q^{85} +29.0985 q^{86} -8.75991 q^{87} -5.96443 q^{88} +16.7421 q^{89} -2.52275 q^{90} -36.7023 q^{92} +3.60382 q^{93} -20.7275 q^{94} +1.36426 q^{95} +4.01045 q^{96} -16.2630 q^{97} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} - 5 q^{3} + 9 q^{4} + 5 q^{5} - q^{6} + 3 q^{8} + 5 q^{9}+O(q^{10}) \) 5 * q + q^2 - 5 * q^3 + 9 * q^4 + 5 * q^5 - q^6 + 3 * q^8 + 5 * q^9	\( 5 q + q^{2} - 5 q^{3} + 9 q^{4} + 5 q^{5} - q^{6} + 3 q^{8} + 5 q^{9} + q^{10} + 5 q^{11} - 9 q^{12} - 8 q^{13} - 5 q^{15} + 13 q^{16} + q^{18} - 6 q^{19} + 9 q^{20} + q^{22} - 2 q^{23} - 3 q^{24} + 5 q^{25} + 10 q^{26} - 5 q^{27} + 6 q^{29} - q^{30} - 10 q^{31} + 7 q^{32} - 5 q^{33} + 4 q^{34} + 9 q^{36} + 4 q^{37} + 2 q^{38} + 8 q^{39} + 3 q^{40} + 9 q^{44} + 5 q^{45} + 34 q^{46} + 2 q^{47} - 13 q^{48} + q^{50} - 6 q^{52} - 8 q^{53} - q^{54} + 5 q^{55} + 6 q^{57} + 4 q^{59} - 9 q^{60} - 16 q^{61} + 24 q^{62} + 13 q^{64} - 8 q^{65} - q^{66} + 16 q^{67} - 18 q^{68} + 2 q^{69} - 6 q^{71} + 3 q^{72} - 2 q^{73} - 18 q^{74} - 5 q^{75} + 24 q^{76} - 10 q^{78} + 42 q^{79} + 13 q^{80} + 5 q^{81} + 42 q^{82} + 22 q^{83} + 2 q^{86} - 6 q^{87} + 3 q^{88} + 10 q^{89} + q^{90} - 32 q^{92} + 10 q^{93} - 12 q^{94} - 6 q^{95} - 7 q^{96} + 2 q^{97} + 5 q^{99}+O(q^{100}) \) 5 * q + q^2 - 5 * q^3 + 9 * q^4 + 5 * q^5 - q^6 + 3 * q^8 + 5 * q^9 + q^10 + 5 * q^11 - 9 * q^12 - 8 * q^13 - 5 * q^15 + 13 * q^16 + q^18 - 6 * q^19 + 9 * q^20 + q^22 - 2 * q^23 - 3 * q^24 + 5 * q^25 + 10 * q^26 - 5 * q^27 + 6 * q^29 - q^30 - 10 * q^31 + 7 * q^32 - 5 * q^33 + 4 * q^34 + 9 * q^36 + 4 * q^37 + 2 * q^38 + 8 * q^39 + 3 * q^40 + 9 * q^44 + 5 * q^45 + 34 * q^46 + 2 * q^47 - 13 * q^48 + q^50 - 6 * q^52 - 8 * q^53 - q^54 + 5 * q^55 + 6 * q^57 + 4 * q^59 - 9 * q^60 - 16 * q^61 + 24 * q^62 + 13 * q^64 - 8 * q^65 - q^66 + 16 * q^67 - 18 * q^68 + 2 * q^69 - 6 * q^71 + 3 * q^72 - 2 * q^73 - 18 * q^74 - 5 * q^75 + 24 * q^76 - 10 * q^78 + 42 * q^79 + 13 * q^80 + 5 * q^81 + 42 * q^82 + 22 * q^83 + 2 * q^86 - 6 * q^87 + 3 * q^88 + 10 * q^89 + q^90 - 32 * q^92 + 10 * q^93 - 12 * q^94 - 6 * q^95 - 7 * q^96 + 2 * q^97 + 5 * q^99

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