LMFDB - Embedded newform 8085.2.a.ci.1.4

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:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 4x^{9} - 6x^{8} + 36x^{7} + x^{6} - 104x^{5} + 40x^{4} + 104x^{3} - 48x^{2} - 32x + 14 $ x^10 - 4x^9 - 6x^8 + 36x^7 + x^6 - 104x^5 + 40x^4 + 104x^3 - 48x^2 - 32x + 14
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$1.37094$ 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)

$f(q)$	$=$	$q-1.37094 q^{2} -1.00000 q^{3} -0.120524 q^{4} -1.00000 q^{5} +1.37094 q^{6} +2.90711 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.37094 q^{2} -1.00000 q^{3} -0.120524 q^{4} -1.00000 q^{5} +1.37094 q^{6} +2.90711 q^{8} +1.00000 q^{9} +1.37094 q^{10} -1.00000 q^{11} +0.120524 q^{12} -5.30398 q^{13} +1.00000 q^{15} -3.74443 q^{16} -4.23452 q^{17} -1.37094 q^{18} +4.82031 q^{19} +0.120524 q^{20} +1.37094 q^{22} -3.96605 q^{23} -2.90711 q^{24} +1.00000 q^{25} +7.27144 q^{26} -1.00000 q^{27} +4.34167 q^{29} -1.37094 q^{30} +3.41919 q^{31} -0.680838 q^{32} +1.00000 q^{33} +5.80527 q^{34} -0.120524 q^{36} -0.342381 q^{37} -6.60835 q^{38} +5.30398 q^{39} -2.90711 q^{40} +11.3051 q^{41} -7.36557 q^{43} +0.120524 q^{44} -1.00000 q^{45} +5.43721 q^{46} +12.1720 q^{47} +3.74443 q^{48} -1.37094 q^{50} +4.23452 q^{51} +0.639256 q^{52} -11.4635 q^{53} +1.37094 q^{54} +1.00000 q^{55} -4.82031 q^{57} -5.95217 q^{58} -3.43519 q^{59} -0.120524 q^{60} -0.505406 q^{61} -4.68751 q^{62} +8.42224 q^{64} +5.30398 q^{65} -1.37094 q^{66} -5.09837 q^{67} +0.510361 q^{68} +3.96605 q^{69} -3.51583 q^{71} +2.90711 q^{72} +7.86080 q^{73} +0.469383 q^{74} -1.00000 q^{75} -0.580962 q^{76} -7.27144 q^{78} +4.11465 q^{79} +3.74443 q^{80} +1.00000 q^{81} -15.4987 q^{82} -2.69930 q^{83} +4.23452 q^{85} +10.0978 q^{86} -4.34167 q^{87} -2.90711 q^{88} -0.896400 q^{89} +1.37094 q^{90} +0.478003 q^{92} -3.41919 q^{93} -16.6871 q^{94} -4.82031 q^{95} +0.680838 q^{96} +9.12469 q^{97} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 4 q^{2} - 10 q^{3} + 8 q^{4} - 10 q^{5} + 4 q^{6} - 12 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 4 * q^2 - 10 * q^3 + 8 * q^4 - 10 * q^5 + 4 * q^6 - 12 * q^8 + 10 * q^9	$ 10 q - 4 q^{2} - 10 q^{3} + 8 q^{4} - 10 q^{5} + 4 q^{6} - 12 q^{8} + 10 q^{9} + 4 q^{10} - 10 q^{11} - 8 q^{12} + 8 q^{13} + 10 q^{15} + 4 q^{16} + 2 q^{17} - 4 q^{18} + 18 q^{19} - 8 q^{20} + 4 q^{22} - 18 q^{23} + 12 q^{24} + 10 q^{25} + 4 q^{26} - 10 q^{27} - 10 q^{29} - 4 q^{30} + 20 q^{31} - 28 q^{32} + 10 q^{33} + 16 q^{34} + 8 q^{36} - 4 q^{37} - 24 q^{38} - 8 q^{39} + 12 q^{40} + 16 q^{41} - 30 q^{43} - 8 q^{44} - 10 q^{45} - 12 q^{46} - 16 q^{47} - 4 q^{48} - 4 q^{50} - 2 q^{51} + 36 q^{52} - 14 q^{53} + 4 q^{54} + 10 q^{55} - 18 q^{57} - 4 q^{58} + 10 q^{59} + 8 q^{60} + 38 q^{61} + 20 q^{62} + 20 q^{64} - 8 q^{65} - 4 q^{66} - 16 q^{67} - 32 q^{68} + 18 q^{69} - 4 q^{71} - 12 q^{72} + 16 q^{73} - 4 q^{74} - 10 q^{75} + 48 q^{76} - 4 q^{78} - 28 q^{79} - 4 q^{80} + 10 q^{81} + 4 q^{82} - 2 q^{83} - 2 q^{85} + 16 q^{86} + 10 q^{87} + 12 q^{88} - 26 q^{89} + 4 q^{90} - 20 q^{93} + 36 q^{94} - 18 q^{95} + 28 q^{96} + 26 q^{97} - 10 q^{99}+O(q^{100}) $ 10 * q - 4 * q^2 - 10 * q^3 + 8 * q^4 - 10 * q^5 + 4 * q^6 - 12 * q^8 + 10 * q^9 + 4 * q^10 - 10 * q^11 - 8 * q^12 + 8 * q^13 + 10 * q^15 + 4 * q^16 + 2 * q^17 - 4 * q^18 + 18 * q^19 - 8 * q^20 + 4 * q^22 - 18 * q^23 + 12 * q^24 + 10 * q^25 + 4 * q^26 - 10 * q^27 - 10 * q^29 - 4 * q^30 + 20 * q^31 - 28 * q^32 + 10 * q^33 + 16 * q^34 + 8 * q^36 - 4 * q^37 - 24 * q^38 - 8 * q^39 + 12 * q^40 + 16 * q^41 - 30 * q^43 - 8 * q^44 - 10 * q^45 - 12 * q^46 - 16 * q^47 - 4 * q^48 - 4 * q^50 - 2 * q^51 + 36 * q^52 - 14 * q^53 + 4 * q^54 + 10 * q^55 - 18 * q^57 - 4 * q^58 + 10 * q^59 + 8 * q^60 + 38 * q^61 + 20 * q^62 + 20 * q^64 - 8 * q^65 - 4 * q^66 - 16 * q^67 - 32 * q^68 + 18 * q^69 - 4 * q^71 - 12 * q^72 + 16 * q^73 - 4 * q^74 - 10 * q^75 + 48 * q^76 - 4 * q^78 - 28 * q^79 - 4 * q^80 + 10 * q^81 + 4 * q^82 - 2 * q^83 - 2 * q^85 + 16 * q^86 + 10 * q^87 + 12 * q^88 - 26 * q^89 + 4 * q^90 - 20 * q^93 + 36 * q^94 - 18 * q^95 + 28 * q^96 + 26 * q^97 - 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.37094	−0.969401	−0.484700	−	0.874680i	$-0.661071\pi$
$2$	−1.37094	−0.969401	−0.484700	+	0.874680i	$0.661071\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.120524	−0.0602619
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.37094	0.559684
$7$	0	0
$7$	0	0
$8$	2.90711	1.02782
$9$	1.00000	0.333333
$10$	1.37094	0.433529
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.120524	0.0347923
$13$	−5.30398	−1.47106	−0.735529	−	0.677493i	$-0.763067\pi$
$13$	−5.30398	−1.47106	−0.735529	+	0.677493i	$0.763067\pi$
$14$	0	0
$15$	1.00000	0.258199
$16$	−3.74443	−0.936107
$17$	−4.23452	−1.02702	−0.513511	−	0.858083i	$-0.671655\pi$
$17$	−4.23452	−1.02702	−0.513511	+	0.858083i	$0.671655\pi$
$18$	−1.37094	−0.323134
$19$	4.82031	1.10585	0.552927	−	0.833230i	$-0.313511\pi$
$19$	4.82031	1.10585	0.552927	+	0.833230i	$0.313511\pi$
$20$	0.120524	0.0269500
$21$	0	0
$22$	1.37094	0.292285
$23$	−3.96605	−0.826978	−0.413489	−	0.910509i	$-0.635690\pi$
$23$	−3.96605	−0.826978	−0.413489	+	0.910509i	$0.635690\pi$
$24$	−2.90711	−0.593411
$25$	1.00000	0.200000
$26$	7.27144	1.42605
$27$	−1.00000	−0.192450
$28$	0	0
$29$	4.34167	0.806228	0.403114	−	0.915150i	$-0.367928\pi$
$29$	4.34167	0.806228	0.403114	+	0.915150i	$0.367928\pi$
$30$	−1.37094	−0.250298
$31$	3.41919	0.614105	0.307053	−	0.951693i	$-0.400657\pi$
$31$	3.41919	0.614105	0.307053	+	0.951693i	$0.400657\pi$
$32$	−0.680838	−0.120356
$33$	1.00000	0.174078
$34$	5.80527	0.995596
$35$	0	0
$36$	−0.120524	−0.0200873
$37$	−0.342381	−0.0562870	−0.0281435	−	0.999604i	$-0.508960\pi$
$37$	−0.342381	−0.0562870	−0.0281435	+	0.999604i	$0.508960\pi$
$38$	−6.60835	−1.07202
$39$	5.30398	0.849316
$40$	−2.90711	−0.459655
$41$	11.3051	1.76557	0.882784	−	0.469779i	$-0.155667\pi$
$41$	11.3051	1.76557	0.882784	+	0.469779i	$0.155667\pi$
$42$	0	0
$43$	−7.36557	−1.12324	−0.561619	−	0.827396i	$-0.689821\pi$
$43$	−7.36557	−1.12324	−0.561619	+	0.827396i	$0.689821\pi$
$44$	0.120524	0.0181697
$45$	−1.00000	−0.149071
$46$	5.43721	0.801673
$47$	12.1720	1.77547	0.887735	−	0.460354i	$-0.152278\pi$
$47$	12.1720	1.77547	0.887735	+	0.460354i	$0.152278\pi$
$48$	3.74443	0.540461
$49$	0	0
$50$	−1.37094	−0.193880
$51$	4.23452	0.592951
$52$	0.639256	0.0886489
$53$	−11.4635	−1.57463	−0.787317	−	0.616548i	$-0.788531\pi$
$53$	−11.4635	−1.57463	−0.787317	+	0.616548i	$0.788531\pi$
$54$	1.37094	0.186561
$55$	1.00000	0.134840
$56$	0	0
$57$	−4.82031	−0.638465
$58$	−5.95217	−0.781558
$59$	−3.43519	−0.447224	−0.223612	−	0.974678i	$-0.571785\pi$
$59$	−3.43519	−0.447224	−0.223612	+	0.974678i	$0.571785\pi$
$60$	−0.120524	−0.0155596
$61$	−0.505406	−0.0647105	−0.0323553	−	0.999476i	$-0.510301\pi$
$61$	−0.505406	−0.0647105	−0.0323553	+	0.999476i	$0.510301\pi$
$62$	−4.68751	−0.595314
$63$	0	0
$64$	8.42224	1.05278
$65$	5.30398	0.657878
$66$	−1.37094	−0.168751
$67$	−5.09837	−0.622865	−0.311432	−	0.950268i	$-0.600809\pi$
$67$	−5.09837	−0.622865	−0.311432	+	0.950268i	$0.600809\pi$
$68$	0.510361	0.0618903
$69$	3.96605	0.477456
$70$	0	0
$71$	−3.51583	−0.417252	−0.208626	−	0.977995i	$-0.566899\pi$
$71$	−3.51583	−0.417252	−0.208626	+	0.977995i	$0.566899\pi$
$72$	2.90711	0.342606
$73$	7.86080	0.920037	0.460019	−	0.887909i	$-0.347843\pi$
$73$	7.86080	0.920037	0.460019	+	0.887909i	$0.347843\pi$
$74$	0.469383	0.0545647
$75$	−1.00000	−0.115470
$76$	−0.580962	−0.0666409
$77$	0	0
$78$	−7.27144	−0.823328
$79$	4.11465	0.462934	0.231467	−	0.972843i	$-0.425647\pi$
$79$	4.11465	0.462934	0.231467	+	0.972843i	$0.425647\pi$
$80$	3.74443	0.418640
$81$	1.00000	0.111111
$82$	−15.4987	−1.71154
$83$	−2.69930	−0.296287	−0.148144	−	0.988966i	$-0.547330\pi$
$83$	−2.69930	−0.296287	−0.148144	+	0.988966i	$0.547330\pi$
$84$	0	0
$85$	4.23452	0.459298
$86$	10.0978	1.08887
$87$	−4.34167	−0.465476
$88$	−2.90711	−0.309899
$89$	−0.896400	−0.0950182	−0.0475091	−	0.998871i	$-0.515128\pi$
$89$	−0.896400	−0.0950182	−0.0475091	+	0.998871i	$0.515128\pi$
$90$	1.37094	0.144510
$91$	0	0
$92$	0.478003	0.0498353
$93$	−3.41919	−0.354554
$94$	−16.6871	−1.72114
$95$	−4.82031	−0.494553
$96$	0.680838	0.0694878
$97$	9.12469	0.926472	0.463236	−	0.886235i	$-0.346688\pi$
$97$	9.12469	0.926472	0.463236	+	0.886235i	$0.346688\pi$
$98$	0	0
$99$	−1.00000	−0.100504
$100$	−0.120524	−0.0120524
$101$	−8.75953	−0.871606	−0.435803	−	0.900042i	$-0.643536\pi$
$101$	−8.75953	−0.871606	−0.435803	+	0.900042i	$0.643536\pi$
$102$	−5.80527	−0.574807
$103$	18.6153	1.83422	0.917112	−	0.398630i	$-0.130514\pi$
$103$	18.6153	1.83422	0.917112	+	0.398630i	$0.130514\pi$
$104$	−15.4193	−1.51198
$105$	0	0
$106$	15.7158	1.52645
$107$	−5.79701	−0.560418	−0.280209	−	0.959939i	$-0.590404\pi$
$107$	−5.79701	−0.560418	−0.280209	+	0.959939i	$0.590404\pi$
$108$	0.120524	0.0115974
$109$	−13.8237	−1.32407	−0.662037	−	0.749471i	$-0.730308\pi$
$109$	−13.8237	−1.32407	−0.662037	+	0.749471i	$0.730308\pi$
$110$	−1.37094	−0.130714
$111$	0.342381	0.0324973
$112$	0	0
$113$	5.36262	0.504473	0.252236	−	0.967666i	$-0.418834\pi$
$113$	5.36262	0.504473	0.252236	+	0.967666i	$0.418834\pi$
$114$	6.60835	0.618929
$115$	3.96605	0.369836
$116$	−0.523275	−0.0485849
$117$	−5.30398	−0.490353
$118$	4.70944	0.433540
$119$	0	0
$120$	2.90711	0.265382
$121$	1.00000	0.0909091
$122$	0.692881	0.0627305
$123$	−11.3051	−1.01935
$124$	−0.412095	−0.0370072
$125$	−1.00000	−0.0894427
$126$	0	0
$127$	3.92030	0.347870	0.173935	−	0.984757i	$-0.444352\pi$
$127$	3.92030	0.347870	0.173935	+	0.984757i	$0.444352\pi$
$128$	−10.1847	−0.900210
$129$	7.36557	0.648502
$130$	−7.27144	−0.637747
$131$	5.58647	0.488092	0.244046	−	0.969764i	$-0.421525\pi$
$131$	5.58647	0.488092	0.244046	+	0.969764i	$0.421525\pi$
$132$	−0.120524	−0.0104903
$133$	0	0
$134$	6.98955	0.603805
$135$	1.00000	0.0860663
$136$	−12.3102	−1.05559
$137$	−5.87369	−0.501823	−0.250912	−	0.968010i	$-0.580730\pi$
$137$	−5.87369	−0.501823	−0.250912	+	0.968010i	$0.580730\pi$
$138$	−5.43721	−0.462846
$139$	2.49304	0.211457	0.105728	−	0.994395i	$-0.466283\pi$
$139$	2.49304	0.211457	0.105728	+	0.994395i	$0.466283\pi$
$140$	0	0
$141$	−12.1720	−1.02507
$142$	4.81999	0.404485
$143$	5.30398	0.443541
$144$	−3.74443	−0.312036
$145$	−4.34167	−0.360556
$146$	−10.7767	−0.891885
$147$	0	0
$148$	0.0412650	0.00339196
$149$	−2.39867	−0.196507	−0.0982534	−	0.995161i	$-0.531326\pi$
$149$	−2.39867	−0.196507	−0.0982534	+	0.995161i	$0.531326\pi$
$150$	1.37094	0.111937
$151$	13.4185	1.09198	0.545992	−	0.837790i	$-0.316153\pi$
$151$	13.4185	1.09198	0.545992	+	0.837790i	$0.316153\pi$
$152$	14.0132	1.13662
$153$	−4.23452	−0.342341
$154$	0	0
$155$	−3.41919	−0.274636
$156$	−0.639256	−0.0511815
$157$	−17.7438	−1.41611	−0.708056	−	0.706156i	$-0.750428\pi$
$157$	−17.7438	−1.41611	−0.708056	+	0.706156i	$0.750428\pi$
$158$	−5.64093	−0.448769
$159$	11.4635	0.909115
$160$	0.680838	0.0538250
$161$	0	0
$162$	−1.37094	−0.107711
$163$	8.92616	0.699151	0.349576	−	0.936908i	$-0.386326\pi$
$163$	8.92616	0.699151	0.349576	+	0.936908i	$0.386326\pi$
$164$	−1.36254	−0.106397
$165$	−1.00000	−0.0778499
$166$	3.70058	0.287221
$167$	8.55200	0.661774	0.330887	−	0.943670i	$-0.392652\pi$
$167$	8.55200	0.661774	0.330887	+	0.943670i	$0.392652\pi$
$168$	0	0
$169$	15.1322	1.16401
$170$	−5.80527	−0.445244
$171$	4.82031	0.368618
$172$	0.887727	0.0676886
$173$	15.2821	1.16188	0.580938	−	0.813948i	$-0.302686\pi$
$173$	15.2821	1.16188	0.580938	+	0.813948i	$0.302686\pi$
$174$	5.95217	0.451233
$175$	0	0
$176$	3.74443	0.282247
$177$	3.43519	0.258205
$178$	1.22891	0.0921107
$179$	7.47330	0.558581	0.279290	−	0.960207i	$-0.409901\pi$
$179$	7.47330	0.558581	0.279290	+	0.960207i	$0.409901\pi$
$180$	0.120524	0.00898332
$181$	−8.28778	−0.616026	−0.308013	−	0.951382i	$-0.599664\pi$
$181$	−8.28778	−0.616026	−0.308013	+	0.951382i	$0.599664\pi$
$182$	0	0
$183$	0.505406	0.0373607
$184$	−11.5297	−0.849983
$185$	0.342381	0.0251723
$186$	4.68751	0.343705
$187$	4.23452	0.309659
$188$	−1.46702	−0.106993
$189$	0	0
$190$	6.60835	0.479420
$191$	−9.02925	−0.653334	−0.326667	−	0.945140i	$-0.605925\pi$
$191$	−9.02925	−0.653334	−0.326667	+	0.945140i	$0.605925\pi$
$192$	−8.42224	−0.607823
$193$	8.05778	0.580012	0.290006	−	0.957025i	$-0.406343\pi$
$193$	8.05778	0.580012	0.290006	+	0.957025i	$0.406343\pi$
$194$	−12.5094	−0.898123
$195$	−5.30398	−0.379826
$196$	0	0
$197$	19.2982	1.37494	0.687471	−	0.726211i	$-0.258721\pi$
$197$	19.2982	1.37494	0.687471	+	0.726211i	$0.258721\pi$
$198$	1.37094	0.0974285
$199$	7.25842	0.514535	0.257268	−	0.966340i	$-0.417178\pi$
$199$	7.25842	0.514535	0.257268	+	0.966340i	$0.417178\pi$
$200$	2.90711	0.205564
$201$	5.09837	0.359611
$202$	12.0088	0.844936
$203$	0	0
$204$	−0.510361	−0.0357324
$205$	−11.3051	−0.789586
$206$	−25.5205	−1.77810
$207$	−3.96605	−0.275659
$208$	19.8604	1.37707
$209$	−4.82031	−0.333427
$210$	0	0
$211$	−10.0680	−0.693107	−0.346554	−	0.938030i	$-0.612648\pi$
$211$	−10.0680	−0.693107	−0.346554	+	0.938030i	$0.612648\pi$
$212$	1.38163	0.0948905
$213$	3.51583	0.240901
$214$	7.94735	0.543270
$215$	7.36557	0.502328
$216$	−2.90711	−0.197804
$217$	0	0
$218$	18.9515	1.28356
$219$	−7.86080	−0.531184
$220$	−0.120524	−0.00812572
$221$	22.4598	1.51081
$222$	−0.469383	−0.0315029
$223$	4.04049	0.270571	0.135286	−	0.990807i	$-0.456805\pi$
$223$	4.04049	0.270571	0.135286	+	0.990807i	$0.456805\pi$
$224$	0	0
$225$	1.00000	0.0666667
$226$	−7.35182	−0.489036
$227$	−19.3834	−1.28652	−0.643262	−	0.765646i	$-0.722419\pi$
$227$	−19.3834	−1.28652	−0.643262	+	0.765646i	$0.722419\pi$
$228$	0.580962	0.0384751
$229$	19.0525	1.25902	0.629512	−	0.776991i	$-0.283255\pi$
$229$	19.0525	1.25902	0.629512	+	0.776991i	$0.283255\pi$
$230$	−5.43721	−0.358519
$231$	0	0
$232$	12.6217	0.828656
$233$	7.44917	0.488011	0.244006	−	0.969774i	$-0.421538\pi$
$233$	7.44917	0.488011	0.244006	+	0.969774i	$0.421538\pi$
$234$	7.27144	0.475349
$235$	−12.1720	−0.794015
$236$	0.414023	0.0269506
$237$	−4.11465	−0.267275
$238$	0	0
$239$	16.8581	1.09046	0.545230	−	0.838287i	$-0.316442\pi$
$239$	16.8581	1.09046	0.545230	+	0.838287i	$0.316442\pi$
$240$	−3.74443	−0.241702
$241$	16.7509	1.07902	0.539511	−	0.841979i	$-0.318609\pi$
$241$	16.7509	1.07902	0.539511	+	0.841979i	$0.318609\pi$
$242$	−1.37094	−0.0881274
$243$	−1.00000	−0.0641500
$244$	0.0609134	0.00389958
$245$	0	0
$246$	15.4987	0.988160
$247$	−25.5668	−1.62678
$248$	9.93998	0.631189
$249$	2.69930	0.171061
$250$	1.37094	0.0867058
$251$	−5.21849	−0.329388	−0.164694	−	0.986345i	$-0.552664\pi$
$251$	−5.21849	−0.329388	−0.164694	+	0.986345i	$0.552664\pi$
$252$	0	0
$253$	3.96605	0.249343
$254$	−5.37449	−0.337225
$255$	−4.23452	−0.265176
$256$	−2.88186	−0.180116
$257$	−13.3791	−0.834564	−0.417282	−	0.908777i	$-0.637017\pi$
$257$	−13.3791	−0.834564	−0.417282	+	0.908777i	$0.637017\pi$
$258$	−10.0978	−0.628659
$259$	0	0
$260$	−0.639256	−0.0396450
$261$	4.34167	0.268743
$262$	−7.65871	−0.473157
$263$	3.95861	0.244098	0.122049	−	0.992524i	$-0.461053\pi$
$263$	3.95861	0.244098	0.122049	+	0.992524i	$0.461053\pi$
$264$	2.90711	0.178920
$265$	11.4635	0.704198
$266$	0	0
$267$	0.896400	0.0548588
$268$	0.614475	0.0375350
$269$	19.9409	1.21582	0.607909	−	0.794007i	$-0.292008\pi$
$269$	19.9409	1.21582	0.607909	+	0.794007i	$0.292008\pi$
$270$	−1.37094	−0.0834327
$271$	1.32793	0.0806659	0.0403329	−	0.999186i	$-0.487158\pi$
$271$	1.32793	0.0806659	0.0403329	+	0.999186i	$0.487158\pi$
$272$	15.8558	0.961402
$273$	0	0
$274$	8.05247	0.486468
$275$	−1.00000	−0.0603023
$276$	−0.478003	−0.0287724
$277$	−12.3666	−0.743039	−0.371520	−	0.928425i	$-0.621163\pi$
$277$	−12.3666	−0.743039	−0.371520	+	0.928425i	$0.621163\pi$
$278$	−3.41781	−0.204987
$279$	3.41919	0.204702
$280$	0	0
$281$	−21.1194	−1.25988	−0.629940	−	0.776644i	$-0.716920\pi$
$281$	−21.1194	−1.25988	−0.629940	+	0.776644i	$0.716920\pi$
$282$	16.6871	0.993702
$283$	32.9425	1.95823	0.979115	−	0.203306i	$-0.0651688\pi$
$283$	32.9425	1.95823	0.979115	+	0.203306i	$0.0651688\pi$
$284$	0.423741	0.0251444
$285$	4.82031	0.285530
$286$	−7.27144	−0.429969
$287$	0	0
$288$	−0.680838	−0.0401188
$289$	0.931147	0.0547734
$290$	5.95217	0.349523
$291$	−9.12469	−0.534899
$292$	−0.947414	−0.0554432
$293$	−22.1831	−1.29595	−0.647976	−	0.761661i	$-0.724384\pi$
$293$	−22.1831	−1.29595	−0.647976	+	0.761661i	$0.724384\pi$
$294$	0	0
$295$	3.43519	0.200005
$296$	−0.995338	−0.0578528
$297$	1.00000	0.0580259
$298$	3.28843	0.190494
$299$	21.0358	1.21653
$300$	0.120524	0.00695845
$301$	0	0
$302$	−18.3960	−1.05857
$303$	8.75953	0.503222
$304$	−18.0493	−1.03520
$305$	0.505406	0.0289394
$306$	5.80527	0.331865
$307$	−23.9824	−1.36875	−0.684374	−	0.729131i	$-0.739925\pi$
$307$	−23.9824	−1.36875	−0.684374	+	0.729131i	$0.739925\pi$
$308$	0	0
$309$	−18.6153	−1.05899
$310$	4.68751	0.266233
$311$	−15.4397	−0.875506	−0.437753	−	0.899095i	$-0.644225\pi$
$311$	−15.4397	−0.875506	−0.437753	+	0.899095i	$0.644225\pi$
$312$	15.4193	0.872943
$313$	13.9666	0.789440	0.394720	−	0.918802i	$-0.370842\pi$
$313$	13.9666	0.789440	0.394720	+	0.918802i	$0.370842\pi$
$314$	24.3257	1.37278
$315$	0	0
$316$	−0.495913	−0.0278973
$317$	20.8345	1.17018	0.585091	−	0.810968i	$-0.301059\pi$
$317$	20.8345	1.17018	0.585091	+	0.810968i	$0.301059\pi$
$318$	−15.7158	−0.881297
$319$	−4.34167	−0.243087
$320$	−8.42224	−0.470818
$321$	5.79701	0.323558
$322$	0	0
$323$	−20.4117	−1.13574
$324$	−0.120524	−0.00669577
$325$	−5.30398	−0.294212
$326$	−12.2372	−0.677758
$327$	13.8237	0.764454
$328$	32.8653	1.81468
$329$	0	0
$330$	1.37094	0.0754678
$331$	16.2076	0.890849	0.445425	−	0.895319i	$-0.353053\pi$
$331$	16.2076	0.890849	0.445425	+	0.895319i	$0.353053\pi$
$332$	0.325331	0.0178548
$333$	−0.342381	−0.0187623
$334$	−11.7243	−0.641524
$335$	5.09837	0.278554
$336$	0	0
$337$	4.18167	0.227790	0.113895	−	0.993493i	$-0.463667\pi$
$337$	4.18167	0.227790	0.113895	+	0.993493i	$0.463667\pi$
$338$	−20.7453	−1.12840
$339$	−5.36262	−0.291257
$340$	−0.510361	−0.0276782
$341$	−3.41919	−0.185160
$342$	−6.60835	−0.357339
$343$	0	0
$344$	−21.4125	−1.15449
$345$	−3.96605	−0.213525
$346$	−20.9508	−1.12632
$347$	−12.4862	−0.670295	−0.335148	−	0.942166i	$-0.608786\pi$
$347$	−12.4862	−0.670295	−0.335148	+	0.942166i	$0.608786\pi$
$348$	0.523275	0.0280505
$349$	−0.428929	−0.0229601	−0.0114800	−	0.999934i	$-0.503654\pi$
$349$	−0.428929	−0.0229601	−0.0114800	+	0.999934i	$0.503654\pi$
$350$	0	0
$351$	5.30398	0.283105
$352$	0.680838	0.0362888
$353$	−34.7465	−1.84937	−0.924684	−	0.380736i	$-0.875671\pi$
$353$	−34.7465	−1.84937	−0.924684	+	0.380736i	$0.875671\pi$
$354$	−4.70944	−0.250304
$355$	3.51583	0.186601
$356$	0.108038	0.00572598
$357$	0	0
$358$	−10.2454	−0.541489
$359$	−33.1160	−1.74780	−0.873898	−	0.486109i	$-0.838416\pi$
$359$	−33.1160	−1.74780	−0.873898	+	0.486109i	$0.838416\pi$
$360$	−2.90711	−0.153218
$361$	4.23534	0.222913
$362$	11.3621	0.597176
$363$	−1.00000	−0.0524864
$364$	0	0
$365$	−7.86080	−0.411453
$366$	−0.692881	−0.0362174
$367$	21.9838	1.14754	0.573772	−	0.819015i	$-0.305479\pi$
$367$	21.9838	1.14754	0.573772	+	0.819015i	$0.305479\pi$
$368$	14.8506	0.774139
$369$	11.3051	0.588523
$370$	−0.469383	−0.0244021
$371$	0	0
$372$	0.412095	0.0213661
$373$	−27.5069	−1.42426	−0.712128	−	0.702050i	$-0.752268\pi$
$373$	−27.5069	−1.42426	−0.712128	+	0.702050i	$0.752268\pi$
$374$	−5.80527	−0.300183
$375$	1.00000	0.0516398
$376$	35.3854	1.82486
$377$	−23.0281	−1.18601
$378$	0	0
$379$	7.37164	0.378656	0.189328	−	0.981914i	$-0.439369\pi$
$379$	7.37164	0.378656	0.189328	+	0.981914i	$0.439369\pi$
$380$	0.580962	0.0298027
$381$	−3.92030	−0.200843
$382$	12.3786	0.633342
$383$	−21.0642	−1.07633	−0.538164	−	0.842840i	$-0.680882\pi$
$383$	−21.0642	−1.07633	−0.538164	+	0.842840i	$0.680882\pi$
$384$	10.1847	0.519736
$385$	0	0
$386$	−11.0467	−0.562264
$387$	−7.36557	−0.374413
$388$	−1.09974	−0.0558310
$389$	33.8511	1.71632	0.858159	−	0.513383i	$-0.171608\pi$
$389$	33.8511	1.71632	0.858159	+	0.513383i	$0.171608\pi$
$390$	7.27144	0.368203
$391$	16.7943	0.849324
$392$	0	0
$393$	−5.58647	−0.281800
$394$	−26.4567	−1.33287
$395$	−4.11465	−0.207030
$396$	0.120524	0.00605655
$397$	−25.0109	−1.25526	−0.627630	−	0.778512i	$-0.715975\pi$
$397$	−25.0109	−1.25526	−0.627630	+	0.778512i	$0.715975\pi$
$398$	−9.95085	−0.498791
$399$	0	0
$400$	−3.74443	−0.187221
$401$	−17.8488	−0.891326	−0.445663	−	0.895201i	$-0.647032\pi$
$401$	−17.8488	−0.891326	−0.445663	+	0.895201i	$0.647032\pi$
$402$	−6.98955	−0.348607
$403$	−18.1353	−0.903385
$404$	1.05573	0.0525247
$405$	−1.00000	−0.0496904
$406$	0	0
$407$	0.342381	0.0169712
$408$	12.3102	0.609446
$409$	−22.2174	−1.09858	−0.549291	−	0.835631i	$-0.685102\pi$
$409$	−22.2174	−1.09858	−0.549291	+	0.835631i	$0.685102\pi$
$410$	15.4987	0.765425
$411$	5.87369	0.289728
$412$	−2.24359	−0.110534
$413$	0	0
$414$	5.43721	0.267224
$415$	2.69930	0.132504
$416$	3.61115	0.177051
$417$	−2.49304	−0.122085
$418$	6.60835	0.323225
$419$	31.0991	1.51929	0.759645	−	0.650338i	$-0.225373\pi$
$419$	31.0991	1.51929	0.759645	+	0.650338i	$0.225373\pi$
$420$	0	0
$421$	27.1602	1.32371	0.661853	−	0.749634i	$-0.269770\pi$
$421$	27.1602	1.32371	0.661853	+	0.749634i	$0.269770\pi$
$422$	13.8026	0.671899
$423$	12.1720	0.591824
$424$	−33.3257	−1.61844
$425$	−4.23452	−0.205404
$426$	−4.81999	−0.233529
$427$	0	0
$428$	0.698678	0.0337719
$429$	−5.30398	−0.256078
$430$	−10.0978	−0.486957
$431$	9.16471	0.441448	0.220724	−	0.975336i	$-0.429158\pi$
$431$	9.16471	0.441448	0.220724	+	0.975336i	$0.429158\pi$
$432$	3.74443	0.180154
$433$	12.1106	0.581999	0.291000	−	0.956723i	$-0.406012\pi$
$433$	12.1106	0.581999	0.291000	+	0.956723i	$0.406012\pi$
$434$	0	0
$435$	4.34167	0.208167
$436$	1.66609	0.0797913
$437$	−19.1175	−0.914516
$438$	10.7767	0.514930
$439$	37.7913	1.80368	0.901839	−	0.432072i	$-0.142217\pi$
$439$	37.7913	1.80368	0.901839	+	0.432072i	$0.142217\pi$
$440$	2.90711	0.138591
$441$	0	0
$442$	−30.7910	−1.46458
$443$	−31.2977	−1.48700	−0.743500	−	0.668736i	$-0.766836\pi$
$443$	−31.2977	−1.48700	−0.743500	+	0.668736i	$0.766836\pi$
$444$	−0.0412650	−0.00195835
$445$	0.896400	0.0424934
$446$	−5.53927	−0.262292
$447$	2.39867	0.113453
$448$	0	0
$449$	−14.7262	−0.694974	−0.347487	−	0.937685i	$-0.612965\pi$
$449$	−14.7262	−0.694974	−0.347487	+	0.937685i	$0.612965\pi$
$450$	−1.37094	−0.0646267
$451$	−11.3051	−0.532339
$452$	−0.646323	−0.0304005
$453$	−13.4185	−0.630458
$454$	26.5735	1.24716
$455$	0	0
$456$	−14.0132	−0.656226
$457$	22.5664	1.05561	0.527806	−	0.849365i	$-0.323015\pi$
$457$	22.5664	1.05561	0.527806	+	0.849365i	$0.323015\pi$
$458$	−26.1198	−1.22050
$459$	4.23452	0.197650
$460$	−0.478003	−0.0222870
$461$	−30.1432	−1.40391	−0.701953	−	0.712223i	$-0.747689\pi$
$461$	−30.1432	−1.40391	−0.701953	+	0.712223i	$0.747689\pi$
$462$	0	0
$463$	−23.0353	−1.07054	−0.535272	−	0.844680i	$-0.679791\pi$
$463$	−23.0353	−1.07054	−0.535272	+	0.844680i	$0.679791\pi$
$464$	−16.2571	−0.754715
$465$	3.41919	0.158561
$466$	−10.2124	−0.473079
$467$	−29.6245	−1.37086	−0.685429	−	0.728140i	$-0.740385\pi$
$467$	−29.6245	−1.37086	−0.685429	+	0.728140i	$0.740385\pi$
$468$	0.639256	0.0295496
$469$	0	0
$470$	16.6871	0.769718
$471$	17.7438	0.817593
$472$	−9.98649	−0.459665
$473$	7.36557	0.338669
$474$	5.64093	0.259097
$475$	4.82031	0.221171
$476$	0	0
$477$	−11.4635	−0.524878
$478$	−23.1114	−1.05709
$479$	7.26757	0.332064	0.166032	−	0.986120i	$-0.446905\pi$
$479$	7.26757	0.332064	0.166032	+	0.986120i	$0.446905\pi$
$480$	−0.680838	−0.0310759
$481$	1.81598	0.0828015
$482$	−22.9645	−1.04600
$483$	0	0
$484$	−0.120524	−0.00547836
$485$	−9.12469	−0.414331
$486$	1.37094	0.0621871
$487$	−19.4354	−0.880701	−0.440350	−	0.897826i	$-0.645146\pi$
$487$	−19.4354	−0.880701	−0.440350	+	0.897826i	$0.645146\pi$
$488$	−1.46927	−0.0665107
$489$	−8.92616	−0.403655
$490$	0	0
$491$	−28.8905	−1.30381	−0.651906	−	0.758300i	$-0.726030\pi$
$491$	−28.8905	−1.30381	−0.651906	+	0.758300i	$0.726030\pi$
$492$	1.36254	0.0614281
$493$	−18.3849	−0.828013
$494$	35.0505	1.57700
$495$	1.00000	0.0449467
$496$	−12.8029	−0.574868
$497$	0	0
$498$	−3.70058	−0.165827
$499$	−3.59950	−0.161136	−0.0805679	−	0.996749i	$-0.525673\pi$
$499$	−3.59950	−0.161136	−0.0805679	+	0.996749i	$0.525673\pi$
$500$	0.120524	0.00538999
$501$	−8.55200	−0.382075
$502$	7.15424	0.319309
$503$	9.61468	0.428697	0.214349	−	0.976757i	$-0.431237\pi$
$503$	9.61468	0.428697	0.214349	+	0.976757i	$0.431237\pi$
$504$	0	0
$505$	8.75953	0.389794
$506$	−5.43721	−0.241713
$507$	−15.1322	−0.672044
$508$	−0.472489	−0.0209633
$509$	−36.1351	−1.60166	−0.800829	−	0.598893i	$-0.795607\pi$
$509$	−36.1351	−1.60166	−0.800829	+	0.598893i	$0.795607\pi$
$510$	5.80527	0.257062
$511$	0	0
$512$	24.3203	1.07481
$513$	−4.82031	−0.212822
$514$	18.3419	0.809027
$515$	−18.6153	−0.820290
$516$	−0.887727	−0.0390800
$517$	−12.1720	−0.535325
$518$	0	0
$519$	−15.2821	−0.670809
$520$	15.4193	0.676179
$521$	−39.7699	−1.74235	−0.871175	−	0.490973i	$-0.836641\pi$
$521$	−39.7699	−1.74235	−0.871175	+	0.490973i	$0.836641\pi$
$522$	−5.95217	−0.260519
$523$	−41.2819	−1.80513	−0.902566	−	0.430551i	$-0.858319\pi$
$523$	−41.2819	−1.80513	−0.902566	+	0.430551i	$0.858319\pi$
$524$	−0.673303	−0.0294134
$525$	0	0
$526$	−5.42702	−0.236629
$527$	−14.4786	−0.630699
$528$	−3.74443	−0.162955
$529$	−7.27048	−0.316108
$530$	−15.7158	−0.682650
$531$	−3.43519	−0.149075
$532$	0	0
$533$	−59.9623	−2.59725
$534$	−1.22891	−0.0531801
$535$	5.79701	0.250627
$536$	−14.8215	−0.640192
$537$	−7.47330	−0.322497
$538$	−27.3378	−1.17862
$539$	0	0
$540$	−0.120524	−0.00518652
$541$	−19.0790	−0.820269	−0.410134	−	0.912025i	$-0.634518\pi$
$541$	−19.0790	−0.820269	−0.410134	+	0.912025i	$0.634518\pi$
$542$	−1.82051	−0.0781976
$543$	8.28778	0.355663
$544$	2.88302	0.123609
$545$	13.8237	0.592144
$546$	0	0
$547$	35.7404	1.52815	0.764074	−	0.645129i	$-0.223196\pi$
$547$	35.7404	1.52815	0.764074	+	0.645129i	$0.223196\pi$
$548$	0.707920	0.0302408
$549$	−0.505406	−0.0215702
$550$	1.37094	0.0584571
$551$	20.9282	0.891570
$552$	11.5297	0.490738
$553$	0	0
$554$	16.9539	0.720303
$555$	−0.342381	−0.0145332
$556$	−0.300471	−0.0127428
$557$	−39.8204	−1.68724	−0.843621	−	0.536938i	$-0.819581\pi$
$557$	−39.8204	−1.68724	−0.843621	+	0.536938i	$0.819581\pi$
$558$	−4.68751	−0.198438
$559$	39.0668	1.65235
$560$	0	0
$561$	−4.23452	−0.178782
$562$	28.9535	1.22133
$563$	19.5975	0.825935	0.412968	−	0.910746i	$-0.364492\pi$
$563$	19.5975	0.825935	0.412968	+	0.910746i	$0.364492\pi$
$564$	1.46702	0.0617726
$565$	−5.36262	−0.225607
$566$	−45.1622	−1.89831
$567$	0	0
$568$	−10.2209	−0.428860
$569$	−21.9708	−0.921065	−0.460532	−	0.887643i	$-0.652341\pi$
$569$	−21.9708	−0.921065	−0.460532	+	0.887643i	$0.652341\pi$
$570$	−6.60835	−0.276793
$571$	−35.8538	−1.50044	−0.750218	−	0.661191i	$-0.770051\pi$
$571$	−35.8538	−1.50044	−0.750218	+	0.661191i	$0.770051\pi$
$572$	−0.639256	−0.0267286
$573$	9.02925	0.377202
$574$	0	0
$575$	−3.96605	−0.165396
$576$	8.42224	0.350927
$577$	13.9570	0.581036	0.290518	−	0.956870i	$-0.406172\pi$
$577$	13.9570	0.581036	0.290518	+	0.956870i	$0.406172\pi$
$578$	−1.27655	−0.0530974
$579$	−8.05778	−0.334870
$580$	0.523275	0.0217278
$581$	0	0
$582$	12.5094	0.518531
$583$	11.4635	0.474770
$584$	22.8522	0.945632
$585$	5.30398	0.219293
$586$	30.4117	1.25630
$587$	−37.5266	−1.54889	−0.774444	−	0.632642i	$-0.781970\pi$
$587$	−37.5266	−1.54889	−0.774444	+	0.632642i	$0.781970\pi$
$588$	0	0
$589$	16.4816	0.679111
$590$	−4.70944	−0.193885
$591$	−19.2982	−0.793824
$592$	1.28202	0.0526906
$593$	−28.8617	−1.18521	−0.592604	−	0.805494i	$-0.701900\pi$
$593$	−28.8617	−1.18521	−0.592604	+	0.805494i	$0.701900\pi$
$594$	−1.37094	−0.0562503
$595$	0	0
$596$	0.289097	0.0118419
$597$	−7.25842	−0.297067
$598$	−28.8388	−1.17931
$599$	10.1002	0.412685	0.206342	−	0.978480i	$-0.433844\pi$
$599$	10.1002	0.412685	0.206342	+	0.978480i	$0.433844\pi$
$600$	−2.90711	−0.118682
$601$	7.66520	0.312670	0.156335	−	0.987704i	$-0.450032\pi$
$601$	7.66520	0.312670	0.156335	+	0.987704i	$0.450032\pi$
$602$	0	0
$603$	−5.09837	−0.207622
$604$	−1.61725	−0.0658051
$605$	−1.00000	−0.0406558
$606$	−12.0088	−0.487824
$607$	−2.44658	−0.0993036	−0.0496518	−	0.998767i	$-0.515811\pi$
$607$	−2.44658	−0.0993036	−0.0496518	+	0.998767i	$0.515811\pi$
$608$	−3.28185	−0.133097
$609$	0	0
$610$	−0.692881	−0.0280539
$611$	−64.5601	−2.61182
$612$	0.510361	0.0206301
$613$	−12.6855	−0.512362	−0.256181	−	0.966629i	$-0.582464\pi$
$613$	−12.6855	−0.512362	−0.256181	+	0.966629i	$0.582464\pi$
$614$	32.8784	1.32687
$615$	11.3051	0.455868
$616$	0	0
$617$	32.6891	1.31601	0.658007	−	0.753011i	$-0.271400\pi$
$617$	32.6891	1.31601	0.658007	+	0.753011i	$0.271400\pi$
$618$	25.5205	1.02659
$619$	22.6869	0.911865	0.455933	−	0.890014i	$-0.349306\pi$
$619$	22.6869	0.911865	0.455933	+	0.890014i	$0.349306\pi$
$620$	0.412095	0.0165501
$621$	3.96605	0.159152
$622$	21.1669	0.848716
$623$	0	0
$624$	−19.8604	−0.795050
$625$	1.00000	0.0400000
$626$	−19.1474	−0.765283
$627$	4.82031	0.192504
$628$	2.13856	0.0853377
$629$	1.44982	0.0578080
$630$	0	0
$631$	6.54066	0.260379	0.130190	−	0.991489i	$-0.458441\pi$
$631$	6.54066	0.260379	0.130190	+	0.991489i	$0.458441\pi$
$632$	11.9617	0.475812
$633$	10.0680	0.400166
$634$	−28.5629	−1.13438
$635$	−3.92030	−0.155572
$636$	−1.38163	−0.0547851
$637$	0	0
$638$	5.95217	0.235649
$639$	−3.51583	−0.139084
$640$	10.1847	0.402586
$641$	−26.7346	−1.05595	−0.527977	−	0.849259i	$-0.677049\pi$
$641$	−26.7346	−1.05595	−0.527977	+	0.849259i	$0.677049\pi$
$642$	−7.94735	−0.313657
$643$	44.0091	1.73555	0.867774	−	0.496959i	$-0.165550\pi$
$643$	44.0091	1.73555	0.867774	+	0.496959i	$0.165550\pi$
$644$	0	0
$645$	−7.36557	−0.290019
$646$	27.9832	1.10098
$647$	−42.8806	−1.68581	−0.842905	−	0.538062i	$-0.819157\pi$
$647$	−42.8806	−1.68581	−0.842905	+	0.538062i	$0.819157\pi$
$648$	2.90711	0.114202
$649$	3.43519	0.134843
$650$	7.27144	0.285209
$651$	0	0
$652$	−1.07582	−0.0421322
$653$	10.9827	0.429786	0.214893	−	0.976638i	$-0.431060\pi$
$653$	10.9827	0.429786	0.214893	+	0.976638i	$0.431060\pi$
$654$	−18.9515	−0.741063
$655$	−5.58647	−0.218281
$656$	−42.3313	−1.65276
$657$	7.86080	0.306679
$658$	0	0
$659$	36.5748	1.42475	0.712375	−	0.701799i	$-0.247620\pi$
$659$	36.5748	1.42475	0.712375	+	0.701799i	$0.247620\pi$
$660$	0.120524	0.00469139
$661$	2.19292	0.0852949	0.0426474	−	0.999090i	$-0.486421\pi$
$661$	2.19292	0.0852949	0.0426474	+	0.999090i	$0.486421\pi$
$662$	−22.2196	−0.863590
$663$	−22.4598	−0.872266
$664$	−7.84718	−0.304530
$665$	0	0
$666$	0.469383	0.0181882
$667$	−17.2193	−0.666732
$668$	−1.03072	−0.0398798
$669$	−4.04049	−0.156214
$670$	−6.98955	−0.270030
$671$	0.505406	0.0195110
$672$	0	0
$673$	−20.1166	−0.775439	−0.387720	−	0.921777i	$-0.626737\pi$
$673$	−20.1166	−0.775439	−0.387720	+	0.921777i	$0.626737\pi$
$674$	−5.73281	−0.220820
$675$	−1.00000	−0.0384900
$676$	−1.82379	−0.0701458
$677$	32.7051	1.25696	0.628481	−	0.777825i	$-0.283677\pi$
$677$	32.7051	1.25696	0.628481	+	0.777825i	$0.283677\pi$
$678$	7.35182	0.282345
$679$	0	0
$680$	12.3102	0.472075
$681$	19.3834	0.742775
$682$	4.68751	0.179494
$683$	−19.1604	−0.733150	−0.366575	−	0.930388i	$-0.619470\pi$
$683$	−19.1604	−0.733150	−0.366575	+	0.930388i	$0.619470\pi$
$684$	−0.580962	−0.0222136
$685$	5.87369	0.224422
$686$	0	0
$687$	−19.0525	−0.726898
$688$	27.5798	1.05147
$689$	60.8022	2.31638
$690$	5.43721	0.206991
$691$	−18.4297	−0.701100	−0.350550	−	0.936544i	$-0.614005\pi$
$691$	−18.4297	−0.701100	−0.350550	+	0.936544i	$0.614005\pi$
$692$	−1.84186	−0.0700169
$693$	0	0
$694$	17.1179	0.649785
$695$	−2.49304	−0.0945664
$696$	−12.6217	−0.478425
$697$	−47.8719	−1.81328
$698$	0.588036	0.0222575
$699$	−7.44917	−0.281754
$700$	0	0
$701$	−9.59036	−0.362223	−0.181111	−	0.983463i	$-0.557969\pi$
$701$	−9.59036	−0.362223	−0.181111	+	0.983463i	$0.557969\pi$
$702$	−7.27144	−0.274443
$703$	−1.65038	−0.0622452
$704$	−8.42224	−0.317425
$705$	12.1720	0.458425
$706$	47.6353	1.79278
$707$	0	0
$708$	−0.414023	−0.0155599
$709$	26.2394	0.985440	0.492720	−	0.870188i	$-0.336003\pi$
$709$	26.2394	0.985440	0.492720	+	0.870188i	$0.336003\pi$
$710$	−4.81999	−0.180891
$711$	4.11465	0.154311
$712$	−2.60593	−0.0976615
$713$	−13.5607	−0.507851
$714$	0	0
$715$	−5.30398	−0.198358
$716$	−0.900712	−0.0336612
$717$	−16.8581	−0.629577
$718$	45.4001	1.69431
$719$	−14.2770	−0.532444	−0.266222	−	0.963912i	$-0.585775\pi$
$719$	−14.2770	−0.532444	−0.266222	+	0.963912i	$0.585775\pi$
$720$	3.74443	0.139547
$721$	0	0
$722$	−5.80640	−0.216092
$723$	−16.7509	−0.622973
$724$	0.998876	0.0371229
$725$	4.34167	0.161246
$726$	1.37094	0.0508804
$727$	25.8260	0.957832	0.478916	−	0.877861i	$-0.341030\pi$
$727$	25.8260	0.957832	0.478916	+	0.877861i	$0.341030\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	10.7767	0.398863
$731$	31.1896	1.15359
$732$	−0.0609134	−0.00225143
$733$	42.6670	1.57594	0.787971	−	0.615712i	$-0.211132\pi$
$733$	42.6670	1.57594	0.787971	+	0.615712i	$0.211132\pi$
$734$	−30.1385	−1.11243
$735$	0	0
$736$	2.70024	0.0995320
$737$	5.09837	0.187801
$738$	−15.4987	−0.570514
$739$	22.9227	0.843225	0.421612	−	0.906776i	$-0.361464\pi$
$739$	22.9227	0.843225	0.421612	+	0.906776i	$0.361464\pi$
$740$	−0.0412650	−0.00151693
$741$	25.5668	0.939220
$742$	0	0
$743$	−44.3096	−1.62556	−0.812780	−	0.582570i	$-0.802047\pi$
$743$	−44.3096	−1.62556	−0.812780	+	0.582570i	$0.802047\pi$
$744$	−9.93998	−0.364417
$745$	2.39867	0.0878805
$746$	37.7104	1.38067
$747$	−2.69930	−0.0987624
$748$	−0.510361	−0.0186606
$749$	0	0
$750$	−1.37094	−0.0500596
$751$	−38.0610	−1.38887	−0.694433	−	0.719557i	$-0.744345\pi$
$751$	−38.0610	−1.38887	−0.694433	+	0.719557i	$0.744345\pi$
$752$	−45.5772	−1.66203
$753$	5.21849	0.190172
$754$	31.5702	1.14972
$755$	−13.4185	−0.488350
$756$	0	0
$757$	−31.3503	−1.13945	−0.569723	−	0.821837i	$-0.692949\pi$
$757$	−31.3503	−1.13945	−0.569723	+	0.821837i	$0.692949\pi$
$758$	−10.1061	−0.367069
$759$	−3.96605	−0.143958
$760$	−14.0132	−0.508311
$761$	−36.2067	−1.31249	−0.656246	−	0.754547i	$-0.727857\pi$
$761$	−36.2067	−1.31249	−0.656246	+	0.754547i	$0.727857\pi$
$762$	5.37449	0.194697
$763$	0	0
$764$	1.08824	0.0393712
$765$	4.23452	0.153099
$766$	28.8777	1.04339
$767$	18.2202	0.657893
$768$	2.88186	0.103990
$769$	9.89580	0.356852	0.178426	−	0.983953i	$-0.442900\pi$
$769$	9.89580	0.356852	0.178426	+	0.983953i	$0.442900\pi$
$770$	0	0
$771$	13.3791	0.481836
$772$	−0.971156	−0.0349527
$773$	−33.8623	−1.21794	−0.608972	−	0.793192i	$-0.708418\pi$
$773$	−33.8623	−1.21794	−0.608972	+	0.793192i	$0.708418\pi$
$774$	10.0978	0.362956
$775$	3.41919	0.122821
$776$	26.5265	0.952245
$777$	0	0
$778$	−46.4078	−1.66380
$779$	54.4943	1.95246
$780$	0.639256	0.0228890
$781$	3.51583	0.125806
$782$	−23.0240	−0.823335
$783$	−4.34167	−0.155159
$784$	0	0
$785$	17.7438	0.633305
$786$	7.65871	0.273177
$787$	24.2920	0.865918	0.432959	−	0.901414i	$-0.357470\pi$
$787$	24.2920	0.865918	0.432959	+	0.901414i	$0.357470\pi$
$788$	−2.32590	−0.0828567
$789$	−3.95861	−0.140930
$790$	5.64093	0.200695
$791$	0	0
$792$	−2.90711	−0.103300
$793$	2.68066	0.0951930
$794$	34.2884	1.21685
$795$	−11.4635	−0.406569
$796$	−0.874813	−0.0310069
$797$	−21.0924	−0.747132	−0.373566	−	0.927604i	$-0.621865\pi$
$797$	−21.0924	−0.747132	−0.373566	+	0.927604i	$0.621865\pi$
$798$	0	0
$799$	−51.5426	−1.82345
$800$	−0.680838	−0.0240713
$801$	−0.896400	−0.0316727
$802$	24.4696	0.864052
$803$	−7.86080	−0.277402
$804$	−0.614475	−0.0216709
$805$	0	0
$806$	24.8624	0.875742
$807$	−19.9409	−0.701953
$808$	−25.4649	−0.895853
$809$	42.4781	1.49345	0.746725	−	0.665132i	$-0.231625\pi$
$809$	42.4781	1.49345	0.746725	+	0.665132i	$0.231625\pi$
$810$	1.37094	0.0481699
$811$	−30.3523	−1.06581	−0.532907	−	0.846174i	$-0.678900\pi$
$811$	−30.3523	−1.06581	−0.532907	+	0.846174i	$0.678900\pi$
$812$	0	0
$813$	−1.32793	−0.0465725
$814$	−0.469383	−0.0164519
$815$	−8.92616	−0.312670
$816$	−15.8558	−0.555066
$817$	−35.5043	−1.24214
$818$	30.4588	1.06497
$819$	0	0
$820$	1.36254	0.0475820
$821$	30.2783	1.05672	0.528360	−	0.849020i	$-0.322807\pi$
$821$	30.2783	1.05672	0.528360	+	0.849020i	$0.322807\pi$
$822$	−8.05247	−0.280862
$823$	−4.45091	−0.155149	−0.0775745	−	0.996987i	$-0.524718\pi$
$823$	−4.45091	−0.155149	−0.0775745	+	0.996987i	$0.524718\pi$
$824$	54.1169	1.88525
$825$	1.00000	0.0348155
$826$	0	0
$827$	17.8534	0.620824	0.310412	−	0.950602i	$-0.399533\pi$
$827$	17.8534	0.620824	0.310412	+	0.950602i	$0.399533\pi$
$828$	0.478003	0.0166118
$829$	13.0701	0.453943	0.226972	−	0.973901i	$-0.427118\pi$
$829$	13.0701	0.453943	0.226972	+	0.973901i	$0.427118\pi$
$830$	−3.70058	−0.128449
$831$	12.3666	0.428994
$832$	−44.6714	−1.54870
$833$	0	0
$834$	3.41781	0.118349
$835$	−8.55200	−0.295954
$836$	0.580962	0.0200930
$837$	−3.41919	−0.118185
$838$	−42.6350	−1.47280
$839$	−33.7135	−1.16392	−0.581959	−	0.813218i	$-0.697714\pi$
$839$	−33.7135	−1.16392	−0.581959	+	0.813218i	$0.697714\pi$
$840$	0	0
$841$	−10.1499	−0.349997
$842$	−37.2350	−1.28320
$843$	21.1194	0.727392
$844$	1.21343	0.0417680
$845$	−15.1322	−0.520563
$846$	−16.6871	−0.573714
$847$	0	0
$848$	42.9243	1.47403
$849$	−32.9425	−1.13058
$850$	5.80527	0.199119
$851$	1.35790	0.0465481
$852$	−0.423741	−0.0145171
$853$	14.9184	0.510795	0.255398	−	0.966836i	$-0.417794\pi$
$853$	14.9184	0.510795	0.255398	+	0.966836i	$0.417794\pi$
$854$	0	0
$855$	−4.82031	−0.164851
$856$	−16.8526	−0.576008
$857$	23.0146	0.786164	0.393082	−	0.919503i	$-0.371409\pi$
$857$	23.0146	0.786164	0.393082	+	0.919503i	$0.371409\pi$
$858$	7.27144	0.248243
$859$	−52.7630	−1.80025	−0.900126	−	0.435630i	$-0.856526\pi$
$859$	−52.7630	−1.80025	−0.900126	+	0.435630i	$0.856526\pi$
$860$	−0.887727	−0.0302712
$861$	0	0
$862$	−12.5643	−0.427940
$863$	−34.3206	−1.16829	−0.584144	−	0.811650i	$-0.698570\pi$
$863$	−34.3206	−1.16829	−0.584144	+	0.811650i	$0.698570\pi$
$864$	0.680838	0.0231626
$865$	−15.2821	−0.519607
$866$	−16.6029	−0.564191
$867$	−0.931147	−0.0316234
$868$	0	0
$869$	−4.11465	−0.139580
$870$	−5.95217	−0.201797
$871$	27.0416	0.916270
$872$	−40.1871	−1.36091
$873$	9.12469	0.308824
$874$	26.2090	0.886533
$875$	0	0
$876$	0.947414	0.0320102
$877$	19.7857	0.668117	0.334059	−	0.942552i	$-0.391582\pi$
$877$	19.7857	0.668117	0.334059	+	0.942552i	$0.391582\pi$
$878$	−51.8096	−1.74849
$879$	22.1831	0.748218
$880$	−3.74443	−0.126225
$881$	−8.74671	−0.294684	−0.147342	−	0.989086i	$-0.547072\pi$
$881$	−8.74671	−0.294684	−0.147342	+	0.989086i	$0.547072\pi$
$882$	0	0
$883$	40.1535	1.35127	0.675636	−	0.737235i	$-0.263869\pi$
$883$	40.1535	1.35127	0.675636	+	0.737235i	$0.263869\pi$
$884$	−2.70694	−0.0910443
$885$	−3.43519	−0.115473
$886$	42.9073	1.44150
$887$	16.7128	0.561161	0.280581	−	0.959830i	$-0.409473\pi$
$887$	16.7128	0.561161	0.280581	+	0.959830i	$0.409473\pi$
$888$	0.995338	0.0334014
$889$	0	0
$890$	−1.22891	−0.0411932
$891$	−1.00000	−0.0335013
$892$	−0.486976	−0.0163052
$893$	58.6728	1.96341
$894$	−3.28843	−0.109982
$895$	−7.47330	−0.249805
$896$	0	0
$897$	−21.0358	−0.702366
$898$	20.1888	0.673709
$899$	14.8450	0.495109
$900$	−0.120524	−0.00401746
$901$	48.5424	1.61718
$902$	15.4987	0.516050
$903$	0	0
$904$	15.5897	0.518506
$905$	8.28778	0.275495
$906$	18.3960	0.611166
$907$	−32.3486	−1.07412	−0.537059	−	0.843545i	$-0.680465\pi$
$907$	−32.3486	−1.07412	−0.537059	+	0.843545i	$0.680465\pi$
$908$	2.33617	0.0775285
$909$	−8.75953	−0.290535
$910$	0	0
$911$	−7.83167	−0.259475	−0.129737	−	0.991548i	$-0.541413\pi$
$911$	−7.83167	−0.259475	−0.129737	+	0.991548i	$0.541413\pi$
$912$	18.0493	0.597671
$913$	2.69930	0.0893339
$914$	−30.9372	−1.02331
$915$	−0.505406	−0.0167082
$916$	−2.29628	−0.0758713
$917$	0	0
$918$	−5.80527	−0.191602
$919$	−20.5346	−0.677374	−0.338687	−	0.940899i	$-0.609983\pi$
$919$	−20.5346	−0.677374	−0.338687	+	0.940899i	$0.609983\pi$
$920$	11.5297	0.380124
$921$	23.9824	0.790247
$922$	41.3245	1.36095
$923$	18.6479	0.613803
$924$	0	0
$925$	−0.342381	−0.0112574
$926$	31.5801	1.03779
$927$	18.6153	0.611408
$928$	−2.95598	−0.0970346
$929$	9.11239	0.298968	0.149484	−	0.988764i	$-0.452239\pi$
$929$	9.11239	0.298968	0.149484	+	0.988764i	$0.452239\pi$
$930$	−4.68751	−0.153709
$931$	0	0
$932$	−0.897803	−0.0294085
$933$	15.4397	0.505473
$934$	40.6134	1.32891
$935$	−4.23452	−0.138484
$936$	−15.4193	−0.503994
$937$	38.9277	1.27171	0.635856	−	0.771808i	$-0.280647\pi$
$937$	38.9277	1.27171	0.635856	+	0.771808i	$0.280647\pi$
$938$	0	0
$939$	−13.9666	−0.455783
$940$	1.46702	0.0478489
$941$	19.9779	0.651261	0.325631	−	0.945497i	$-0.394423\pi$
$941$	19.9779	0.651261	0.325631	+	0.945497i	$0.394423\pi$
$942$	−24.3257	−0.792576
$943$	−44.8367	−1.46008
$944$	12.8628	0.418650
$945$	0	0
$946$	−10.0978	−0.328306
$947$	−37.5032	−1.21869	−0.609344	−	0.792906i	$-0.708567\pi$
$947$	−37.5032	−1.21869	−0.609344	+	0.792906i	$0.708567\pi$
$948$	0.495913	0.0161065
$949$	−41.6935	−1.35343
$950$	−6.60835	−0.214403
$951$	−20.8345	−0.675605
$952$	0	0
$953$	−49.1108	−1.59086	−0.795428	−	0.606048i	$-0.792754\pi$
$953$	−49.1108	−1.59086	−0.795428	+	0.606048i	$0.792754\pi$
$954$	15.7158	0.508817
$955$	9.02925	0.292180
$956$	−2.03180	−0.0657132
$957$	4.34167	0.140346
$958$	−9.96340	−0.321903
$959$	0	0
$960$	8.42224	0.271827
$961$	−19.3091	−0.622875
$962$	−2.48960	−0.0802678
$963$	−5.79701	−0.186806
$964$	−2.01889	−0.0650239
$965$	−8.05778	−0.259389
$966$	0	0
$967$	−50.1090	−1.61140	−0.805699	−	0.592325i	$-0.798210\pi$
$967$	−50.1090	−1.61140	−0.805699	+	0.592325i	$0.798210\pi$
$968$	2.90711	0.0934381
$969$	20.4117	0.655717
$970$	12.5094	0.401653
$971$	4.73161	0.151845	0.0759223	−	0.997114i	$-0.475810\pi$
$971$	4.73161	0.151845	0.0759223	+	0.997114i	$0.475810\pi$
$972$	0.120524	0.00386581
$973$	0	0
$974$	26.6447	0.853752
$975$	5.30398	0.169863
$976$	1.89245	0.0605760
$977$	49.2854	1.57678	0.788389	−	0.615177i	$-0.210915\pi$
$977$	49.2854	1.57678	0.788389	+	0.615177i	$0.210915\pi$
$978$	12.2372	0.391304
$979$	0.896400	0.0286491
$980$	0	0
$981$	−13.8237	−0.441358
$982$	39.6072	1.26392
$983$	−17.4922	−0.557916	−0.278958	−	0.960303i	$-0.589989\pi$
$983$	−17.4922	−0.557916	−0.278958	+	0.960303i	$0.589989\pi$
$984$	−32.8653	−1.04771
$985$	−19.2982	−0.614893
$986$	25.2046	0.802677
$987$	0	0
$988$	3.08141	0.0980327
$989$	29.2122	0.928893
$990$	−1.37094	−0.0435713
$991$	−6.44030	−0.204583	−0.102291	−	0.994754i	$-0.532617\pi$
$991$	−6.44030	−0.204583	−0.102291	+	0.994754i	$0.532617\pi$
$992$	−2.32792	−0.0739115
$993$	−16.2076	−0.514332
$994$	0	0
$995$	−7.25842	−0.230107
$996$	−0.325331	−0.0103085
$997$	23.9326	0.757953	0.378976	−	0.925406i	$-0.376276\pi$
$997$	23.9326	0.757953	0.378976	+	0.925406i	$0.376276\pi$
$998$	4.93470	0.156205
$999$	0.342381	0.0108324

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8085.2.a.ci.1.4	✓	10
7.6	odd	2		8085.2.a.cj.1.4	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8085.2.a.ci.1.4	✓	10	1.1	even	1	trivial
8085.2.a.cj.1.4	yes	10	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)

\(f(q)\)	\(=\)	\(q-1.37094 q^{2} -1.00000 q^{3} -0.120524 q^{4} -1.00000 q^{5} +1.37094 q^{6} +2.90711 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.37094 q^{2} -1.00000 q^{3} -0.120524 q^{4} -1.00000 q^{5} +1.37094 q^{6} +2.90711 q^{8} +1.00000 q^{9} +1.37094 q^{10} -1.00000 q^{11} +0.120524 q^{12} -5.30398 q^{13} +1.00000 q^{15} -3.74443 q^{16} -4.23452 q^{17} -1.37094 q^{18} +4.82031 q^{19} +0.120524 q^{20} +1.37094 q^{22} -3.96605 q^{23} -2.90711 q^{24} +1.00000 q^{25} +7.27144 q^{26} -1.00000 q^{27} +4.34167 q^{29} -1.37094 q^{30} +3.41919 q^{31} -0.680838 q^{32} +1.00000 q^{33} +5.80527 q^{34} -0.120524 q^{36} -0.342381 q^{37} -6.60835 q^{38} +5.30398 q^{39} -2.90711 q^{40} +11.3051 q^{41} -7.36557 q^{43} +0.120524 q^{44} -1.00000 q^{45} +5.43721 q^{46} +12.1720 q^{47} +3.74443 q^{48} -1.37094 q^{50} +4.23452 q^{51} +0.639256 q^{52} -11.4635 q^{53} +1.37094 q^{54} +1.00000 q^{55} -4.82031 q^{57} -5.95217 q^{58} -3.43519 q^{59} -0.120524 q^{60} -0.505406 q^{61} -4.68751 q^{62} +8.42224 q^{64} +5.30398 q^{65} -1.37094 q^{66} -5.09837 q^{67} +0.510361 q^{68} +3.96605 q^{69} -3.51583 q^{71} +2.90711 q^{72} +7.86080 q^{73} +0.469383 q^{74} -1.00000 q^{75} -0.580962 q^{76} -7.27144 q^{78} +4.11465 q^{79} +3.74443 q^{80} +1.00000 q^{81} -15.4987 q^{82} -2.69930 q^{83} +4.23452 q^{85} +10.0978 q^{86} -4.34167 q^{87} -2.90711 q^{88} -0.896400 q^{89} +1.37094 q^{90} +0.478003 q^{92} -3.41919 q^{93} -16.6871 q^{94} -4.82031 q^{95} +0.680838 q^{96} +9.12469 q^{97} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 4 q^{2} - 10 q^{3} + 8 q^{4} - 10 q^{5} + 4 q^{6} - 12 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 4 * q^2 - 10 * q^3 + 8 * q^4 - 10 * q^5 + 4 * q^6 - 12 * q^8 + 10 * q^9	\( 10 q - 4 q^{2} - 10 q^{3} + 8 q^{4} - 10 q^{5} + 4 q^{6} - 12 q^{8} + 10 q^{9} + 4 q^{10} - 10 q^{11} - 8 q^{12} + 8 q^{13} + 10 q^{15} + 4 q^{16} + 2 q^{17} - 4 q^{18} + 18 q^{19} - 8 q^{20} + 4 q^{22} - 18 q^{23} + 12 q^{24} + 10 q^{25} + 4 q^{26} - 10 q^{27} - 10 q^{29} - 4 q^{30} + 20 q^{31} - 28 q^{32} + 10 q^{33} + 16 q^{34} + 8 q^{36} - 4 q^{37} - 24 q^{38} - 8 q^{39} + 12 q^{40} + 16 q^{41} - 30 q^{43} - 8 q^{44} - 10 q^{45} - 12 q^{46} - 16 q^{47} - 4 q^{48} - 4 q^{50} - 2 q^{51} + 36 q^{52} - 14 q^{53} + 4 q^{54} + 10 q^{55} - 18 q^{57} - 4 q^{58} + 10 q^{59} + 8 q^{60} + 38 q^{61} + 20 q^{62} + 20 q^{64} - 8 q^{65} - 4 q^{66} - 16 q^{67} - 32 q^{68} + 18 q^{69} - 4 q^{71} - 12 q^{72} + 16 q^{73} - 4 q^{74} - 10 q^{75} + 48 q^{76} - 4 q^{78} - 28 q^{79} - 4 q^{80} + 10 q^{81} + 4 q^{82} - 2 q^{83} - 2 q^{85} + 16 q^{86} + 10 q^{87} + 12 q^{88} - 26 q^{89} + 4 q^{90} - 20 q^{93} + 36 q^{94} - 18 q^{95} + 28 q^{96} + 26 q^{97} - 10 q^{99}+O(q^{100}) \) 10 * q - 4 * q^2 - 10 * q^3 + 8 * q^4 - 10 * q^5 + 4 * q^6 - 12 * q^8 + 10 * q^9 + 4 * q^10 - 10 * q^11 - 8 * q^12 + 8 * q^13 + 10 * q^15 + 4 * q^16 + 2 * q^17 - 4 * q^18 + 18 * q^19 - 8 * q^20 + 4 * q^22 - 18 * q^23 + 12 * q^24 + 10 * q^25 + 4 * q^26 - 10 * q^27 - 10 * q^29 - 4 * q^30 + 20 * q^31 - 28 * q^32 + 10 * q^33 + 16 * q^34 + 8 * q^36 - 4 * q^37 - 24 * q^38 - 8 * q^39 + 12 * q^40 + 16 * q^41 - 30 * q^43 - 8 * q^44 - 10 * q^45 - 12 * q^46 - 16 * q^47 - 4 * q^48 - 4 * q^50 - 2 * q^51 + 36 * q^52 - 14 * q^53 + 4 * q^54 + 10 * q^55 - 18 * q^57 - 4 * q^58 + 10 * q^59 + 8 * q^60 + 38 * q^61 + 20 * q^62 + 20 * q^64 - 8 * q^65 - 4 * q^66 - 16 * q^67 - 32 * q^68 + 18 * q^69 - 4 * q^71 - 12 * q^72 + 16 * q^73 - 4 * q^74 - 10 * q^75 + 48 * q^76 - 4 * q^78 - 28 * q^79 - 4 * q^80 + 10 * q^81 + 4 * q^82 - 2 * q^83 - 2 * q^85 + 16 * q^86 + 10 * q^87 + 12 * q^88 - 26 * q^89 + 4 * q^90 - 20 * q^93 + 36 * q^94 - 18 * q^95 + 28 * q^96 + 26 * q^97 - 10 * q^99

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