LMFDB - Embedded newform 3381.2.a.bf.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3381,2,Mod(1,3381)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3381, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("3381.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3381 = 3 \cdot 7^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3381.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:	$26.9974209234$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 15x^{6} + 11x^{5} + 75x^{4} - 35x^{3} - 141x^{2} + 37x + 80 $ x^8 - x^7 - 15x^6 + 11x^5 + 75x^4 - 35x^3 - 141x^2 + 37x + 80
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 483)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.19194$ of defining polynomial
Character	$\chi$	$=$	3381.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.19194 q^{2} +1.00000 q^{3} -0.579274 q^{4} -3.78820 q^{5} +1.19194 q^{6} -3.07435 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.19194 q^{2} +1.00000 q^{3} -0.579274 q^{4} -3.78820 q^{5} +1.19194 q^{6} -3.07435 q^{8} +1.00000 q^{9} -4.51532 q^{10} -1.49040 q^{11} -0.579274 q^{12} -0.460711 q^{13} -3.78820 q^{15} -2.50589 q^{16} +6.05928 q^{17} +1.19194 q^{18} -5.90634 q^{19} +2.19441 q^{20} -1.77647 q^{22} -1.00000 q^{23} -3.07435 q^{24} +9.35049 q^{25} -0.549141 q^{26} +1.00000 q^{27} +2.10833 q^{29} -4.51532 q^{30} -8.07148 q^{31} +3.16181 q^{32} -1.49040 q^{33} +7.22231 q^{34} -0.579274 q^{36} +11.3034 q^{37} -7.04002 q^{38} -0.460711 q^{39} +11.6462 q^{40} +5.23193 q^{41} +4.64064 q^{43} +0.863350 q^{44} -3.78820 q^{45} -1.19194 q^{46} -4.60558 q^{47} -2.50589 q^{48} +11.1452 q^{50} +6.05928 q^{51} +0.266878 q^{52} -5.32282 q^{53} +1.19194 q^{54} +5.64594 q^{55} -5.90634 q^{57} +2.51300 q^{58} +12.2909 q^{59} +2.19441 q^{60} +0.411824 q^{61} -9.62074 q^{62} +8.78048 q^{64} +1.74527 q^{65} -1.77647 q^{66} +15.1208 q^{67} -3.50998 q^{68} -1.00000 q^{69} +6.85490 q^{71} -3.07435 q^{72} -12.1424 q^{73} +13.4730 q^{74} +9.35049 q^{75} +3.42139 q^{76} -0.549141 q^{78} +6.47369 q^{79} +9.49284 q^{80} +1.00000 q^{81} +6.23615 q^{82} -4.68019 q^{83} -22.9538 q^{85} +5.53137 q^{86} +2.10833 q^{87} +4.58201 q^{88} +16.2810 q^{89} -4.51532 q^{90} +0.579274 q^{92} -8.07148 q^{93} -5.48958 q^{94} +22.3744 q^{95} +3.16181 q^{96} -6.78248 q^{97} -1.49040 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + 8 q^{3} + 15 q^{4} + 5 q^{5} + q^{6} + 9 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q + q^2 + 8 * q^3 + 15 * q^4 + 5 * q^5 + q^6 + 9 * q^8 + 8 * q^9	$ 8 q + q^{2} + 8 q^{3} + 15 q^{4} + 5 q^{5} + q^{6} + 9 q^{8} + 8 q^{9} - 3 q^{10} + 10 q^{11} + 15 q^{12} - 6 q^{13} + 5 q^{15} + 13 q^{16} + 21 q^{17} + q^{18} + 5 q^{19} - q^{20} + 18 q^{22} - 8 q^{23} + 9 q^{24} + 27 q^{25} + 3 q^{26} + 8 q^{27} + 2 q^{29} - 3 q^{30} - 13 q^{31} + 29 q^{32} + 10 q^{33} - 19 q^{34} + 15 q^{36} + 13 q^{37} - 6 q^{38} - 6 q^{39} + 7 q^{40} + 16 q^{41} + 15 q^{43} + 24 q^{44} + 5 q^{45} - q^{46} - q^{47} + 13 q^{48} + 16 q^{50} + 21 q^{51} - 19 q^{52} + 3 q^{53} + q^{54} - 10 q^{55} + 5 q^{57} - 40 q^{58} + 26 q^{59} - q^{60} - 14 q^{61} - 14 q^{62} + 49 q^{64} - 3 q^{65} + 18 q^{66} + 38 q^{67} + 43 q^{68} - 8 q^{69} + 9 q^{71} + 9 q^{72} - 6 q^{73} + 32 q^{74} + 27 q^{75} - 14 q^{76} + 3 q^{78} + 23 q^{79} - 17 q^{80} + 8 q^{81} + 20 q^{82} + 30 q^{83} - 37 q^{85} - 28 q^{86} + 2 q^{87} + 86 q^{88} + 12 q^{89} - 3 q^{90} - 15 q^{92} - 13 q^{93} - 45 q^{94} + 16 q^{95} + 29 q^{96} + 14 q^{97} + 10 q^{99}+O(q^{100}) $ 8 * q + q^2 + 8 * q^3 + 15 * q^4 + 5 * q^5 + q^6 + 9 * q^8 + 8 * q^9 - 3 * q^10 + 10 * q^11 + 15 * q^12 - 6 * q^13 + 5 * q^15 + 13 * q^16 + 21 * q^17 + q^18 + 5 * q^19 - q^20 + 18 * q^22 - 8 * q^23 + 9 * q^24 + 27 * q^25 + 3 * q^26 + 8 * q^27 + 2 * q^29 - 3 * q^30 - 13 * q^31 + 29 * q^32 + 10 * q^33 - 19 * q^34 + 15 * q^36 + 13 * q^37 - 6 * q^38 - 6 * q^39 + 7 * q^40 + 16 * q^41 + 15 * q^43 + 24 * q^44 + 5 * q^45 - q^46 - q^47 + 13 * q^48 + 16 * q^50 + 21 * q^51 - 19 * q^52 + 3 * q^53 + q^54 - 10 * q^55 + 5 * q^57 - 40 * q^58 + 26 * q^59 - q^60 - 14 * q^61 - 14 * q^62 + 49 * q^64 - 3 * q^65 + 18 * q^66 + 38 * q^67 + 43 * q^68 - 8 * q^69 + 9 * q^71 + 9 * q^72 - 6 * q^73 + 32 * q^74 + 27 * q^75 - 14 * q^76 + 3 * q^78 + 23 * q^79 - 17 * q^80 + 8 * q^81 + 20 * q^82 + 30 * q^83 - 37 * q^85 - 28 * q^86 + 2 * q^87 + 86 * q^88 + 12 * q^89 - 3 * q^90 - 15 * q^92 - 13 * q^93 - 45 * q^94 + 16 * q^95 + 29 * q^96 + 14 * 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 $

$2$	1.19194	0.842830	0.421415	−	0.906868i	$-0.361534\pi$
$2$	1.19194	0.842830	0.421415	+	0.906868i	$0.361534\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.579274	−0.289637
$5$	−3.78820	−1.69414	−0.847068	−	0.531484i	$-0.821634\pi$
$5$	−3.78820	−1.69414	−0.847068	+	0.531484i	$0.821634\pi$
$6$	1.19194	0.486608
$7$	0	0
$7$	0	0
$8$	−3.07435	−1.08695
$9$	1.00000	0.333333
$10$	−4.51532	−1.42787
$11$	−1.49040	−0.449373	−0.224686	−	0.974431i	$-0.572136\pi$
$11$	−1.49040	−0.449373	−0.224686	+	0.974431i	$0.572136\pi$
$12$	−0.579274	−0.167222
$13$	−0.460711	−0.127778	−0.0638892	−	0.997957i	$-0.520350\pi$
$13$	−0.460711	−0.127778	−0.0638892	+	0.997957i	$0.520350\pi$
$14$	0	0
$15$	−3.78820	−0.978110
$16$	−2.50589	−0.626474
$17$	6.05928	1.46959	0.734796	−	0.678289i	$-0.237278\pi$
$17$	6.05928	1.46959	0.734796	+	0.678289i	$0.237278\pi$
$18$	1.19194	0.280943
$19$	−5.90634	−1.35501	−0.677504	−	0.735519i	$-0.736938\pi$
$19$	−5.90634	−1.35501	−0.677504	+	0.735519i	$0.736938\pi$
$20$	2.19441	0.490684
$21$	0	0
$22$	−1.77647	−0.378745
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−3.07435	−0.627548
$25$	9.35049	1.87010
$26$	−0.549141	−0.107695
$27$	1.00000	0.192450
$28$	0	0
$29$	2.10833	0.391506	0.195753	−	0.980653i	$-0.437285\pi$
$29$	2.10833	0.391506	0.195753	+	0.980653i	$0.437285\pi$
$30$	−4.51532	−0.824381
$31$	−8.07148	−1.44968	−0.724841	−	0.688917i	$-0.758087\pi$
$31$	−8.07148	−1.44968	−0.724841	+	0.688917i	$0.758087\pi$
$32$	3.16181	0.558934
$33$	−1.49040	−0.259446
$34$	7.22231	1.23862
$35$	0	0
$36$	−0.579274	−0.0965456
$37$	11.3034	1.85827	0.929135	−	0.369741i	$-0.120554\pi$
$37$	11.3034	1.85827	0.929135	+	0.369741i	$0.120554\pi$
$38$	−7.04002	−1.14204
$39$	−0.460711	−0.0737729
$40$	11.6462	1.84143
$41$	5.23193	0.817090	0.408545	−	0.912738i	$-0.366036\pi$
$41$	5.23193	0.817090	0.408545	+	0.912738i	$0.366036\pi$
$42$	0	0
$43$	4.64064	0.707691	0.353845	−	0.935304i	$-0.384874\pi$
$43$	4.64064	0.707691	0.353845	+	0.935304i	$0.384874\pi$
$44$	0.863350	0.130155
$45$	−3.78820	−0.564712
$46$	−1.19194	−0.175742
$47$	−4.60558	−0.671792	−0.335896	−	0.941899i	$-0.609039\pi$
$47$	−4.60558	−0.671792	−0.335896	+	0.941899i	$0.609039\pi$
$48$	−2.50589	−0.361695
$49$	0	0
$50$	11.1452	1.57618
$51$	6.05928	0.848469
$52$	0.266878	0.0370093
$53$	−5.32282	−0.731146	−0.365573	−	0.930783i	$-0.619127\pi$
$53$	−5.32282	−0.731146	−0.365573	+	0.930783i	$0.619127\pi$
$54$	1.19194	0.162203
$55$	5.64594	0.761299
$56$	0	0
$57$	−5.90634	−0.782314
$58$	2.51300	0.329973
$59$	12.2909	1.60014	0.800071	−	0.599905i	$-0.204795\pi$
$59$	12.2909	1.60014	0.800071	+	0.599905i	$0.204795\pi$
$60$	2.19441	0.283297
$61$	0.411824	0.0527287	0.0263643	−	0.999652i	$-0.491607\pi$
$61$	0.411824	0.0527287	0.0263643	+	0.999652i	$0.491607\pi$
$62$	−9.62074	−1.22184
$63$	0	0
$64$	8.78048	1.09756
$65$	1.74527	0.216474
$66$	−1.77647	−0.218669
$67$	15.1208	1.84730	0.923652	−	0.383232i	$-0.125189\pi$
$67$	15.1208	1.84730	0.923652	+	0.383232i	$0.125189\pi$
$68$	−3.50998	−0.425648
$69$	−1.00000	−0.120386
$70$	0	0
$71$	6.85490	0.813527	0.406764	−	0.913533i	$-0.366657\pi$
$71$	6.85490	0.813527	0.406764	+	0.913533i	$0.366657\pi$
$72$	−3.07435	−0.362315
$73$	−12.1424	−1.42116	−0.710579	−	0.703617i	$-0.751567\pi$
$73$	−12.1424	−1.42116	−0.710579	+	0.703617i	$0.751567\pi$
$74$	13.4730	1.56621
$75$	9.35049	1.07970
$76$	3.42139	0.392460
$77$	0	0
$78$	−0.549141	−0.0621780
$79$	6.47369	0.728347	0.364174	−	0.931331i	$-0.381351\pi$
$79$	6.47369	0.728347	0.364174	+	0.931331i	$0.381351\pi$
$80$	9.49284	1.06133
$81$	1.00000	0.111111
$82$	6.23615	0.688668
$83$	−4.68019	−0.513717	−0.256859	−	0.966449i	$-0.582687\pi$
$83$	−4.68019	−0.513717	−0.256859	+	0.966449i	$0.582687\pi$
$84$	0	0
$85$	−22.9538	−2.48969
$86$	5.53137	0.596463
$87$	2.10833	0.226036
$88$	4.58201	0.488444
$89$	16.2810	1.72578	0.862889	−	0.505394i	$-0.168653\pi$
$89$	16.2810	1.72578	0.862889	+	0.505394i	$0.168653\pi$
$90$	−4.51532	−0.475957
$91$	0	0
$92$	0.579274	0.0603935
$93$	−8.07148	−0.836974
$94$	−5.48958	−0.566207
$95$	22.3744	2.29557
$96$	3.16181	0.322701
$97$	−6.78248	−0.688656	−0.344328	−	0.938849i	$-0.611893\pi$
$97$	−6.78248	−0.688656	−0.344328	+	0.938849i	$0.611893\pi$
$98$	0	0
$99$	−1.49040	−0.149791
$100$	−5.41649	−0.541649
$101$	−2.43744	−0.242535	−0.121267	−	0.992620i	$-0.538696\pi$
$101$	−2.43744	−0.242535	−0.121267	+	0.992620i	$0.538696\pi$
$102$	7.22231	0.715115
$103$	5.80746	0.572226	0.286113	−	0.958196i	$-0.407637\pi$
$103$	5.80746	0.572226	0.286113	+	0.958196i	$0.407637\pi$
$104$	1.41639	0.138888
$105$	0	0
$106$	−6.34450	−0.616232
$107$	12.2582	1.18504	0.592521	−	0.805555i	$-0.298133\pi$
$107$	12.2582	1.18504	0.592521	+	0.805555i	$0.298133\pi$
$108$	−0.579274	−0.0557407
$109$	−8.98838	−0.860931	−0.430465	−	0.902607i	$-0.641651\pi$
$109$	−8.98838	−0.860931	−0.430465	+	0.902607i	$0.641651\pi$
$110$	6.72964	0.641646
$111$	11.3034	1.07287
$112$	0	0
$113$	6.08150	0.572099	0.286050	−	0.958215i	$-0.407658\pi$
$113$	6.08150	0.572099	0.286050	+	0.958215i	$0.407658\pi$
$114$	−7.04002	−0.659358
$115$	3.78820	0.353252
$116$	−1.22130	−0.113395
$117$	−0.460711	−0.0425928
$118$	14.6501	1.34865
$119$	0	0
$120$	11.6462	1.06315
$121$	−8.77870	−0.798064
$122$	0.490870	0.0444413
$123$	5.23193	0.471747
$124$	4.67560	0.419881
$125$	−16.4805	−1.47406
$126$	0	0
$127$	2.84429	0.252390	0.126195	−	0.992005i	$-0.459724\pi$
$127$	2.84429	0.252390	0.126195	+	0.992005i	$0.459724\pi$
$128$	4.14221	0.366123
$129$	4.64064	0.408585
$130$	2.08026	0.182451
$131$	9.92887	0.867489	0.433745	−	0.901036i	$-0.357192\pi$
$131$	9.92887	0.867489	0.433745	+	0.901036i	$0.357192\pi$
$132$	0.863350	0.0751450
$133$	0	0
$134$	18.0232	1.55696
$135$	−3.78820	−0.326037
$136$	−18.6283	−1.59736
$137$	−12.0409	−1.02873	−0.514363	−	0.857573i	$-0.671972\pi$
$137$	−12.0409	−1.02873	−0.514363	+	0.857573i	$0.671972\pi$
$138$	−1.19194	−0.101465
$139$	−1.51537	−0.128532	−0.0642659	−	0.997933i	$-0.520471\pi$
$139$	−1.51537	−0.128532	−0.0642659	+	0.997933i	$0.520471\pi$
$140$	0	0
$141$	−4.60558	−0.387859
$142$	8.17065	0.685665
$143$	0.686645	0.0574201
$144$	−2.50589	−0.208825
$145$	−7.98677	−0.663265
$146$	−14.4730	−1.19780
$147$	0	0
$148$	−6.54777	−0.538223
$149$	18.2521	1.49527	0.747635	−	0.664110i	$-0.231190\pi$
$149$	18.2521	1.49527	0.747635	+	0.664110i	$0.231190\pi$
$150$	11.1452	0.910005
$151$	−2.93165	−0.238575	−0.119287	−	0.992860i	$-0.538061\pi$
$151$	−2.93165	−0.238575	−0.119287	+	0.992860i	$0.538061\pi$
$152$	18.1581	1.47282
$153$	6.05928	0.489864
$154$	0	0
$155$	30.5764	2.45596
$156$	0.266878	0.0213673
$157$	16.7975	1.34059	0.670295	−	0.742095i	$-0.266168\pi$
$157$	16.7975	1.34059	0.670295	+	0.742095i	$0.266168\pi$
$158$	7.71627	0.613873
$159$	−5.32282	−0.422127
$160$	−11.9776	−0.946911
$161$	0	0
$162$	1.19194	0.0936478
$163$	−3.64979	−0.285873	−0.142937	−	0.989732i	$-0.545655\pi$
$163$	−3.64979	−0.285873	−0.142937	+	0.989732i	$0.545655\pi$
$164$	−3.03072	−0.236659
$165$	5.64594	0.439536
$166$	−5.57851	−0.432977
$167$	−15.2399	−1.17930	−0.589649	−	0.807660i	$-0.700734\pi$
$167$	−15.2399	−1.17930	−0.589649	+	0.807660i	$0.700734\pi$
$168$	0	0
$169$	−12.7877	−0.983673
$170$	−27.3596	−2.09838
$171$	−5.90634	−0.451669
$172$	−2.68820	−0.204973
$173$	2.18632	0.166223	0.0831113	−	0.996540i	$-0.473514\pi$
$173$	2.18632	0.166223	0.0831113	+	0.996540i	$0.473514\pi$
$174$	2.51300	0.190510
$175$	0	0
$176$	3.73479	0.281520
$177$	12.2909	0.923842
$178$	19.4060	1.45454
$179$	−1.86104	−0.139101	−0.0695505	−	0.997578i	$-0.522156\pi$
$179$	−1.86104	−0.139101	−0.0695505	+	0.997578i	$0.522156\pi$
$180$	2.19441	0.163561
$181$	−14.4867	−1.07679	−0.538394	−	0.842693i	$-0.680969\pi$
$181$	−14.4867	−1.07679	−0.538394	+	0.842693i	$0.680969\pi$
$182$	0	0
$183$	0.411824	0.0304429
$184$	3.07435	0.226644
$185$	−42.8196	−3.14816
$186$	−9.62074	−0.705427
$187$	−9.03076	−0.660394
$188$	2.66789	0.194576
$189$	0	0
$190$	26.6690	1.93477
$191$	19.8535	1.43655	0.718273	−	0.695761i	$-0.244933\pi$
$191$	19.8535	1.43655	0.718273	+	0.695761i	$0.244933\pi$
$192$	8.78048	0.633677
$193$	1.55889	0.112211	0.0561055	−	0.998425i	$-0.482132\pi$
$193$	1.55889	0.112211	0.0561055	+	0.998425i	$0.482132\pi$
$194$	−8.08432	−0.580420
$195$	1.74527	0.124981
$196$	0	0
$197$	−2.48101	−0.176764	−0.0883822	−	0.996087i	$-0.528170\pi$
$197$	−2.48101	−0.176764	−0.0883822	+	0.996087i	$0.528170\pi$
$198$	−1.77647	−0.126248
$199$	−5.29246	−0.375172	−0.187586	−	0.982248i	$-0.560066\pi$
$199$	−5.29246	−0.375172	−0.187586	+	0.982248i	$0.560066\pi$
$200$	−28.7466	−2.03269
$201$	15.1208	1.06654
$202$	−2.90529	−0.204415
$203$	0	0
$204$	−3.50998	−0.245748
$205$	−19.8196	−1.38426
$206$	6.92215	0.482289
$207$	−1.00000	−0.0695048
$208$	1.15449	0.0800497
$209$	8.80282	0.608904
$210$	0	0
$211$	27.0118	1.85957	0.929784	−	0.368105i	$-0.119993\pi$
$211$	27.0118	1.85957	0.929784	+	0.368105i	$0.119993\pi$
$212$	3.08337	0.211767
$213$	6.85490	0.469690
$214$	14.6110	0.998789
$215$	−17.5797	−1.19892
$216$	−3.07435	−0.209183
$217$	0	0
$218$	−10.7136	−0.725619
$219$	−12.1424	−0.820506
$220$	−3.27055	−0.220500
$221$	−2.79158	−0.187782
$222$	13.4730	0.904249
$223$	−4.93735	−0.330630	−0.165315	−	0.986241i	$-0.552864\pi$
$223$	−4.93735	−0.330630	−0.165315	+	0.986241i	$0.552864\pi$
$224$	0	0
$225$	9.35049	0.623366
$226$	7.24879	0.482182
$227$	11.4573	0.760449	0.380224	−	0.924894i	$-0.375847\pi$
$227$	11.4573	0.760449	0.380224	+	0.924894i	$0.375847\pi$
$228$	3.42139	0.226587
$229$	−9.71293	−0.641848	−0.320924	−	0.947105i	$-0.603993\pi$
$229$	−9.71293	−0.641848	−0.320924	+	0.947105i	$0.603993\pi$
$230$	4.51532	0.297731
$231$	0	0
$232$	−6.48172	−0.425546
$233$	8.92690	0.584821	0.292410	−	0.956293i	$-0.405543\pi$
$233$	8.92690	0.584821	0.292410	+	0.956293i	$0.405543\pi$
$234$	−0.549141	−0.0358985
$235$	17.4469	1.13811
$236$	−7.11981	−0.463460
$237$	6.47369	0.420511
$238$	0	0
$239$	14.7250	0.952480	0.476240	−	0.879315i	$-0.341999\pi$
$239$	14.7250	0.952480	0.476240	+	0.879315i	$0.341999\pi$
$240$	9.49284	0.612760
$241$	−24.4669	−1.57605	−0.788027	−	0.615641i	$-0.788897\pi$
$241$	−24.4669	−1.57605	−0.788027	+	0.615641i	$0.788897\pi$
$242$	−10.4637	−0.672633
$243$	1.00000	0.0641500
$244$	−0.238559	−0.0152722
$245$	0	0
$246$	6.23615	0.397603
$247$	2.72112	0.173141
$248$	24.8145	1.57572
$249$	−4.68019	−0.296595
$250$	−19.6439	−1.24239
$251$	−2.61433	−0.165015	−0.0825076	−	0.996590i	$-0.526293\pi$
$251$	−2.61433	−0.165015	−0.0825076	+	0.996590i	$0.526293\pi$
$252$	0	0
$253$	1.49040	0.0937007
$254$	3.39022	0.212722
$255$	−22.9538	−1.43742
$256$	−12.6237	−0.788981
$257$	−1.01996	−0.0636231	−0.0318116	−	0.999494i	$-0.510128\pi$
$257$	−1.01996	−0.0636231	−0.0318116	+	0.999494i	$0.510128\pi$
$258$	5.53137	0.344368
$259$	0	0
$260$	−1.01099	−0.0626988
$261$	2.10833	0.130502
$262$	11.8346	0.731146
$263$	8.93801	0.551141	0.275571	−	0.961281i	$-0.411133\pi$
$263$	8.93801	0.551141	0.275571	+	0.961281i	$0.411133\pi$
$264$	4.58201	0.282003
$265$	20.1639	1.23866
$266$	0	0
$267$	16.2810	0.996378
$268$	−8.75911	−0.535047
$269$	−13.6811	−0.834152	−0.417076	−	0.908872i	$-0.636945\pi$
$269$	−13.6811	−0.834152	−0.417076	+	0.908872i	$0.636945\pi$
$270$	−4.51532	−0.274794
$271$	−3.97383	−0.241393	−0.120696	−	0.992689i	$-0.538513\pi$
$271$	−3.97383	−0.241393	−0.120696	+	0.992689i	$0.538513\pi$
$272$	−15.1839	−0.920660
$273$	0	0
$274$	−14.3521	−0.867042
$275$	−13.9360	−0.840371
$276$	0.579274	0.0348682
$277$	−10.0146	−0.601716	−0.300858	−	0.953669i	$-0.597273\pi$
$277$	−10.0146	−0.601716	−0.300858	+	0.953669i	$0.597273\pi$
$278$	−1.80623	−0.108330
$279$	−8.07148	−0.483227
$280$	0	0
$281$	−21.3379	−1.27291	−0.636456	−	0.771313i	$-0.719600\pi$
$281$	−21.3379	−1.27291	−0.636456	+	0.771313i	$0.719600\pi$
$282$	−5.48958	−0.326900
$283$	14.4830	0.860927	0.430463	−	0.902608i	$-0.358350\pi$
$283$	14.4830	0.860927	0.430463	+	0.902608i	$0.358350\pi$
$284$	−3.97087	−0.235627
$285$	22.3744	1.32535
$286$	0.818441	0.0483954
$287$	0	0
$288$	3.16181	0.186311
$289$	19.7149	1.15970
$290$	−9.51977	−0.559020
$291$	−6.78248	−0.397596
$292$	7.03376	0.411620
$293$	33.1986	1.93948	0.969741	−	0.244134i	$-0.0785038\pi$
$293$	33.1986	1.93948	0.969741	+	0.244134i	$0.0785038\pi$
$294$	0	0
$295$	−46.5605	−2.71086
$296$	−34.7506	−2.01984
$297$	−1.49040	−0.0864819
$298$	21.7554	1.26026
$299$	0.460711	0.0266436
$300$	−5.41649	−0.312721
$301$	0	0
$302$	−3.49436	−0.201078
$303$	−2.43744	−0.140027
$304$	14.8007	0.848876
$305$	−1.56007	−0.0893295
$306$	7.22231	0.412872
$307$	31.4823	1.79679	0.898396	−	0.439187i	$-0.144733\pi$
$307$	31.4823	1.79679	0.898396	+	0.439187i	$0.144733\pi$
$308$	0	0
$309$	5.80746	0.330375
$310$	36.4453	2.06996
$311$	−18.2076	−1.03246	−0.516229	−	0.856451i	$-0.672665\pi$
$311$	−18.2076	−1.03246	−0.516229	+	0.856451i	$0.672665\pi$
$312$	1.41639	0.0801870
$313$	21.4552	1.21272	0.606359	−	0.795191i	$-0.292629\pi$
$313$	21.4552	1.21272	0.606359	+	0.795191i	$0.292629\pi$
$314$	20.0217	1.12989
$315$	0	0
$316$	−3.75004	−0.210956
$317$	−2.80865	−0.157749	−0.0788747	−	0.996885i	$-0.525133\pi$
$317$	−2.80865	−0.157749	−0.0788747	+	0.996885i	$0.525133\pi$
$318$	−6.34450	−0.355782
$319$	−3.14225	−0.175932
$320$	−33.2623	−1.85942
$321$	12.2582	0.684184
$322$	0	0
$323$	−35.7882	−1.99131
$324$	−0.579274	−0.0321819
$325$	−4.30788	−0.238958
$326$	−4.35034	−0.240943
$327$	−8.98838	−0.497059
$328$	−16.0848	−0.888132
$329$	0	0
$330$	6.72964	0.370454
$331$	−27.0983	−1.48945	−0.744727	−	0.667369i	$-0.767420\pi$
$331$	−27.0983	−1.48945	−0.744727	+	0.667369i	$0.767420\pi$
$332$	2.71111	0.148791
$333$	11.3034	0.619423
$334$	−18.1651	−0.993948
$335$	−57.2808	−3.12959
$336$	0	0
$337$	8.21670	0.447592	0.223796	−	0.974636i	$-0.428155\pi$
$337$	8.21670	0.447592	0.223796	+	0.974636i	$0.428155\pi$
$338$	−15.2423	−0.829069
$339$	6.08150	0.330302
$340$	13.2965	0.721105
$341$	12.0298	0.651448
$342$	−7.04002	−0.380680
$343$	0	0
$344$	−14.2669	−0.769221
$345$	3.78820	0.203950
$346$	2.60596	0.140097
$347$	2.61249	0.140246	0.0701230	−	0.997538i	$-0.477661\pi$
$347$	2.61249	0.140246	0.0701230	+	0.997538i	$0.477661\pi$
$348$	−1.22130	−0.0654684
$349$	−16.3975	−0.877740	−0.438870	−	0.898551i	$-0.644621\pi$
$349$	−16.3975	−0.877740	−0.438870	+	0.898551i	$0.644621\pi$
$350$	0	0
$351$	−0.460711	−0.0245910
$352$	−4.71237	−0.251170
$353$	29.0145	1.54428	0.772142	−	0.635450i	$-0.219186\pi$
$353$	29.0145	1.54428	0.772142	+	0.635450i	$0.219186\pi$
$354$	14.6501	0.778642
$355$	−25.9678	−1.37823
$356$	−9.43113	−0.499849
$357$	0	0
$358$	−2.21826	−0.117239
$359$	−30.1607	−1.59182	−0.795910	−	0.605414i	$-0.793007\pi$
$359$	−30.1607	−1.59182	−0.795910	+	0.605414i	$0.793007\pi$
$360$	11.6462	0.613811
$361$	15.8849	0.836045
$362$	−17.2673	−0.907549
$363$	−8.77870	−0.460762
$364$	0	0
$365$	45.9978	2.40764
$366$	0.490870	0.0256582
$367$	8.71833	0.455093	0.227546	−	0.973767i	$-0.426930\pi$
$367$	8.71833	0.455093	0.227546	+	0.973767i	$0.426930\pi$
$368$	2.50589	0.130629
$369$	5.23193	0.272363
$370$	−51.0385	−2.65337
$371$	0	0
$372$	4.67560	0.242419
$373$	−10.9069	−0.564740	−0.282370	−	0.959306i	$-0.591121\pi$
$373$	−10.9069	−0.564740	−0.282370	+	0.959306i	$0.591121\pi$
$374$	−10.7641	−0.556600
$375$	−16.4805	−0.851052
$376$	14.1591	0.730201
$377$	−0.971330	−0.0500260
$378$	0	0
$379$	−11.5747	−0.594551	−0.297275	−	0.954792i	$-0.596078\pi$
$379$	−11.5747	−0.594551	−0.297275	+	0.954792i	$0.596078\pi$
$380$	−12.9609	−0.664881
$381$	2.84429	0.145717
$382$	23.6642	1.21076
$383$	24.2449	1.23886	0.619428	−	0.785054i	$-0.287365\pi$
$383$	24.2449	1.23886	0.619428	+	0.785054i	$0.287365\pi$
$384$	4.14221	0.211381
$385$	0	0
$386$	1.85810	0.0945748
$387$	4.64064	0.235897
$388$	3.92891	0.199460
$389$	5.80479	0.294315	0.147157	−	0.989113i	$-0.452988\pi$
$389$	5.80479	0.294315	0.147157	+	0.989113i	$0.452988\pi$
$390$	2.08026	0.105338
$391$	−6.05928	−0.306431
$392$	0	0
$393$	9.92887	0.500845
$394$	−2.95722	−0.148982
$395$	−24.5237	−1.23392
$396$	0.863350	0.0433850
$397$	−13.2018	−0.662581	−0.331290	−	0.943529i	$-0.607484\pi$
$397$	−13.2018	−0.662581	−0.331290	+	0.943529i	$0.607484\pi$
$398$	−6.30830	−0.316207
$399$	0	0
$400$	−23.4313	−1.17157
$401$	23.5989	1.17847	0.589236	−	0.807961i	$-0.299429\pi$
$401$	23.5989	1.17847	0.589236	+	0.807961i	$0.299429\pi$
$402$	18.0232	0.898914
$403$	3.71862	0.185238
$404$	1.41195	0.0702470
$405$	−3.78820	−0.188237
$406$	0	0
$407$	−16.8466	−0.835056
$408$	−18.6283	−0.922239
$409$	8.64130	0.427285	0.213642	−	0.976912i	$-0.431467\pi$
$409$	8.64130	0.427285	0.213642	+	0.976912i	$0.431467\pi$
$410$	−23.6238	−1.16670
$411$	−12.0409	−0.593935
$412$	−3.36411	−0.165738
$413$	0	0
$414$	−1.19194	−0.0585808
$415$	17.7295	0.870307
$416$	−1.45668	−0.0714197
$417$	−1.51537	−0.0742079
$418$	10.4924	0.513202
$419$	30.0603	1.46854	0.734270	−	0.678858i	$-0.237525\pi$
$419$	30.0603	1.46854	0.734270	+	0.678858i	$0.237525\pi$
$420$	0	0
$421$	−24.7510	−1.20629	−0.603144	−	0.797632i	$-0.706085\pi$
$421$	−24.7510	−1.20629	−0.603144	+	0.797632i	$0.706085\pi$
$422$	32.1965	1.56730
$423$	−4.60558	−0.223931
$424$	16.3642	0.794716
$425$	56.6572	2.74828
$426$	8.17065	0.395869
$427$	0	0
$428$	−7.10084	−0.343232
$429$	0.686645	0.0331515
$430$	−20.9540	−1.01049
$431$	−15.6538	−0.754019	−0.377010	−	0.926209i	$-0.623048\pi$
$431$	−15.6538	−0.754019	−0.377010	+	0.926209i	$0.623048\pi$
$432$	−2.50589	−0.120565
$433$	−0.941683	−0.0452544	−0.0226272	−	0.999744i	$-0.507203\pi$
$433$	−0.941683	−0.0452544	−0.0226272	+	0.999744i	$0.507203\pi$
$434$	0	0
$435$	−7.98677	−0.382936
$436$	5.20673	0.249357
$437$	5.90634	0.282539
$438$	−14.4730	−0.691548
$439$	−18.8441	−0.899379	−0.449689	−	0.893185i	$-0.648465\pi$
$439$	−18.8441	−0.899379	−0.449689	+	0.893185i	$0.648465\pi$
$440$	−17.3576	−0.827490
$441$	0	0
$442$	−3.32740	−0.158268
$443$	−2.53680	−0.120527	−0.0602634	−	0.998183i	$-0.519194\pi$
$443$	−2.53680	−0.120527	−0.0602634	+	0.998183i	$0.519194\pi$
$444$	−6.54777	−0.310743
$445$	−61.6756	−2.92370
$446$	−5.88504	−0.278665
$447$	18.2521	0.863294
$448$	0	0
$449$	−34.2788	−1.61772	−0.808859	−	0.588003i	$-0.799914\pi$
$449$	−34.2788	−1.61772	−0.808859	+	0.588003i	$0.799914\pi$
$450$	11.1452	0.525392
$451$	−7.79767	−0.367178
$452$	−3.52285	−0.165701
$453$	−2.93165	−0.137741
$454$	13.6565	0.640929
$455$	0	0
$456$	18.1581	0.850332
$457$	−15.0865	−0.705718	−0.352859	−	0.935676i	$-0.614790\pi$
$457$	−15.0865	−0.705718	−0.352859	+	0.935676i	$0.614790\pi$
$458$	−11.5772	−0.540969
$459$	6.05928	0.282823
$460$	−2.19441	−0.102315
$461$	15.6065	0.726865	0.363433	−	0.931621i	$-0.381605\pi$
$461$	15.6065	0.726865	0.363433	+	0.931621i	$0.381605\pi$
$462$	0	0
$463$	6.25815	0.290841	0.145420	−	0.989370i	$-0.453547\pi$
$463$	6.25815	0.290841	0.145420	+	0.989370i	$0.453547\pi$
$464$	−5.28324	−0.245268
$465$	30.5764	1.41795
$466$	10.6404	0.492905
$467$	8.76308	0.405507	0.202753	−	0.979230i	$-0.435011\pi$
$467$	8.76308	0.405507	0.202753	+	0.979230i	$0.435011\pi$
$468$	0.266878	0.0123364
$469$	0	0
$470$	20.7956	0.959232
$471$	16.7975	0.773990
$472$	−37.7865	−1.73927
$473$	−6.91641	−0.318017
$474$	7.71627	0.354420
$475$	−55.2272	−2.53400
$476$	0	0
$477$	−5.32282	−0.243715
$478$	17.5513	0.802779
$479$	−15.7762	−0.720833	−0.360417	−	0.932791i	$-0.617366\pi$
$479$	−15.7762	−0.720833	−0.360417	+	0.932791i	$0.617366\pi$
$480$	−11.9776	−0.546699
$481$	−5.20761	−0.237447
$482$	−29.1632	−1.32835
$483$	0	0
$484$	5.08527	0.231149
$485$	25.6934	1.16668
$486$	1.19194	0.0540676
$487$	40.5754	1.83865	0.919323	−	0.393504i	$-0.128737\pi$
$487$	40.5754	1.83865	0.919323	+	0.393504i	$0.128737\pi$
$488$	−1.26609	−0.0573132
$489$	−3.64979	−0.165049
$490$	0	0
$491$	9.38984	0.423757	0.211879	−	0.977296i	$-0.432042\pi$
$491$	9.38984	0.423757	0.211879	+	0.977296i	$0.432042\pi$
$492$	−3.03072	−0.136635
$493$	12.7749	0.575354
$494$	3.24342	0.145928
$495$	5.64594	0.253766
$496$	20.2263	0.908187
$497$	0	0
$498$	−5.57851	−0.249979
$499$	19.0780	0.854050	0.427025	−	0.904240i	$-0.359562\pi$
$499$	19.0780	0.854050	0.427025	+	0.904240i	$0.359562\pi$
$500$	9.54675	0.426944
$501$	−15.2399	−0.680868
$502$	−3.11613	−0.139080
$503$	30.4559	1.35796	0.678982	−	0.734155i	$-0.262422\pi$
$503$	30.4559	1.35796	0.678982	+	0.734155i	$0.262422\pi$
$504$	0	0
$505$	9.23353	0.410887
$506$	1.77647	0.0789738
$507$	−12.7877	−0.567924
$508$	−1.64762	−0.0731013
$509$	−22.3391	−0.990163	−0.495082	−	0.868847i	$-0.664862\pi$
$509$	−22.3391	−0.990163	−0.495082	+	0.868847i	$0.664862\pi$
$510$	−27.3596	−1.21150
$511$	0	0
$512$	−23.3311	−1.03110
$513$	−5.90634	−0.260771
$514$	−1.21573	−0.0536235
$515$	−21.9998	−0.969428
$516$	−2.68820	−0.118341
$517$	6.86416	0.301885
$518$	0	0
$519$	2.18632	0.0959687
$520$	−5.36556	−0.235295
$521$	−15.8587	−0.694783	−0.347391	−	0.937720i	$-0.612932\pi$
$521$	−15.8587	−0.694783	−0.347391	+	0.937720i	$0.612932\pi$
$522$	2.51300	0.109991
$523$	−18.7311	−0.819053	−0.409527	−	0.912298i	$-0.634306\pi$
$523$	−18.7311	−0.819053	−0.409527	+	0.912298i	$0.634306\pi$
$524$	−5.75153	−0.251257
$525$	0	0
$526$	10.6536	0.464519
$527$	−48.9074	−2.13044
$528$	3.73479	0.162536
$529$	1.00000	0.0434783
$530$	24.0342	1.04398
$531$	12.2909	0.533381
$532$	0	0
$533$	−2.41041	−0.104406
$534$	19.4060	0.839778
$535$	−46.4364	−2.00762
$536$	−46.4867	−2.00792
$537$	−1.86104	−0.0803100
$538$	−16.3071	−0.703049
$539$	0	0
$540$	2.19441	0.0944323
$541$	−20.2458	−0.870433	−0.435217	−	0.900326i	$-0.643328\pi$
$541$	−20.2458	−0.870433	−0.435217	+	0.900326i	$0.643328\pi$
$542$	−4.73657	−0.203453
$543$	−14.4867	−0.621684
$544$	19.1583	0.821405
$545$	34.0498	1.45853
$546$	0	0
$547$	−11.9031	−0.508940	−0.254470	−	0.967081i	$-0.581901\pi$
$547$	−11.9031	−0.508940	−0.254470	+	0.967081i	$0.581901\pi$
$548$	6.97500	0.297957
$549$	0.411824	0.0175762
$550$	−16.6109	−0.708291
$551$	−12.4525	−0.530494
$552$	3.07435	0.130853
$553$	0	0
$554$	−11.9368	−0.507145
$555$	−42.8196	−1.81759
$556$	0.877813	0.0372275
$557$	15.5621	0.659388	0.329694	−	0.944088i	$-0.393054\pi$
$557$	15.5621	0.659388	0.329694	+	0.944088i	$0.393054\pi$
$558$	−9.62074	−0.407278
$559$	−2.13799	−0.0904275
$560$	0	0
$561$	−9.03076	−0.381279
$562$	−25.4335	−1.07285
$563$	20.0861	0.846528	0.423264	−	0.906006i	$-0.360884\pi$
$563$	20.0861	0.846528	0.423264	+	0.906006i	$0.360884\pi$
$564$	2.66789	0.112338
$565$	−23.0379	−0.969214
$566$	17.2629	0.725615
$567$	0	0
$568$	−21.0743	−0.884259
$569$	15.1053	0.633247	0.316623	−	0.948551i	$-0.397451\pi$
$569$	15.1053	0.633247	0.316623	+	0.948551i	$0.397451\pi$
$570$	26.6690	1.11704
$571$	24.2031	1.01287	0.506435	−	0.862278i	$-0.330963\pi$
$571$	24.2031	1.01287	0.506435	+	0.862278i	$0.330963\pi$
$572$	−0.397755	−0.0166310
$573$	19.8535	0.829390
$574$	0	0
$575$	−9.35049	−0.389942
$576$	8.78048	0.365853
$577$	2.35727	0.0981346	0.0490673	−	0.998795i	$-0.484375\pi$
$577$	2.35727	0.0981346	0.0490673	+	0.998795i	$0.484375\pi$
$578$	23.4990	0.977429
$579$	1.55889	0.0647851
$580$	4.62653	0.192106
$581$	0	0
$582$	−8.08432	−0.335106
$583$	7.93314	0.328557
$584$	37.3299	1.54472
$585$	1.74527	0.0721580
$586$	39.5708	1.63466
$587$	−3.74241	−0.154466	−0.0772329	−	0.997013i	$-0.524608\pi$
$587$	−3.74241	−0.154466	−0.0772329	+	0.997013i	$0.524608\pi$
$588$	0	0
$589$	47.6729	1.96433
$590$	−55.4975	−2.28479
$591$	−2.48101	−0.102055
$592$	−28.3252	−1.16416
$593$	4.53729	0.186324	0.0931621	−	0.995651i	$-0.470303\pi$
$593$	4.53729	0.186324	0.0931621	+	0.995651i	$0.470303\pi$
$594$	−1.77647	−0.0728895
$595$	0	0
$596$	−10.5730	−0.433085
$597$	−5.29246	−0.216606
$598$	0.549141	0.0224561
$599$	35.2213	1.43910	0.719551	−	0.694439i	$-0.244347\pi$
$599$	35.2213	1.43910	0.719551	+	0.694439i	$0.244347\pi$
$600$	−28.7466	−1.17358
$601$	29.5802	1.20660	0.603302	−	0.797513i	$-0.293852\pi$
$601$	29.5802	1.20660	0.603302	+	0.797513i	$0.293852\pi$
$602$	0	0
$603$	15.1208	0.615768
$604$	1.69823	0.0691000
$605$	33.2555	1.35203
$606$	−2.90529	−0.118019
$607$	21.6840	0.880125	0.440062	−	0.897967i	$-0.354956\pi$
$607$	21.6840	0.880125	0.440062	+	0.897967i	$0.354956\pi$
$608$	−18.6747	−0.757360
$609$	0	0
$610$	−1.85952	−0.0752896
$611$	2.12184	0.0858405
$612$	−3.50998	−0.141883
$613$	−24.9875	−1.00923	−0.504617	−	0.863343i	$-0.668366\pi$
$613$	−24.9875	−1.00923	−0.504617	+	0.863343i	$0.668366\pi$
$614$	37.5251	1.51439
$615$	−19.8196	−0.799204
$616$	0	0
$617$	−15.3643	−0.618542	−0.309271	−	0.950974i	$-0.600085\pi$
$617$	−15.3643	−0.618542	−0.309271	+	0.950974i	$0.600085\pi$
$618$	6.92215	0.278450
$619$	23.6888	0.952134	0.476067	−	0.879409i	$-0.342062\pi$
$619$	23.6888	0.952134	0.476067	+	0.879409i	$0.342062\pi$
$620$	−17.7121	−0.711336
$621$	−1.00000	−0.0401286
$622$	−21.7024	−0.870187
$623$	0	0
$624$	1.15449	0.0462167
$625$	15.6792	0.627168
$626$	25.5733	1.02212
$627$	8.80282	0.351551
$628$	−9.73037	−0.388284
$629$	68.4905	2.73090
$630$	0	0
$631$	12.2965	0.489515	0.244758	−	0.969584i	$-0.421292\pi$
$631$	12.2965	0.489515	0.244758	+	0.969584i	$0.421292\pi$
$632$	−19.9024	−0.791674
$633$	27.0118	1.07362
$634$	−3.34775	−0.132956
$635$	−10.7747	−0.427582
$636$	3.08337	0.122264
$637$	0	0
$638$	−3.74538	−0.148281
$639$	6.85490	0.271176
$640$	−15.6915	−0.620262
$641$	3.10564	0.122665	0.0613326	−	0.998117i	$-0.480465\pi$
$641$	3.10564	0.122665	0.0613326	+	0.998117i	$0.480465\pi$
$642$	14.6110	0.576651
$643$	44.2523	1.74514	0.872570	−	0.488489i	$-0.162452\pi$
$643$	44.2523	1.74514	0.872570	+	0.488489i	$0.162452\pi$
$644$	0	0
$645$	−17.5797	−0.692199
$646$	−42.6574	−1.67833
$647$	28.5862	1.12384	0.561919	−	0.827192i	$-0.310063\pi$
$647$	28.5862	1.12384	0.561919	+	0.827192i	$0.310063\pi$
$648$	−3.07435	−0.120772
$649$	−18.3184	−0.719060
$650$	−5.13474	−0.201401
$651$	0	0
$652$	2.11423	0.0827995
$653$	9.71942	0.380350	0.190175	−	0.981750i	$-0.439094\pi$
$653$	9.71942	0.380350	0.190175	+	0.981750i	$0.439094\pi$
$654$	−10.7136	−0.418936
$655$	−37.6126	−1.46964
$656$	−13.1107	−0.511885
$657$	−12.1424	−0.473719
$658$	0	0
$659$	29.8923	1.16444	0.582220	−	0.813031i	$-0.302184\pi$
$659$	29.8923	1.16444	0.582220	+	0.813031i	$0.302184\pi$
$660$	−3.27055	−0.127306
$661$	43.1624	1.67882	0.839411	−	0.543498i	$-0.182900\pi$
$661$	43.1624	1.67882	0.839411	+	0.543498i	$0.182900\pi$
$662$	−32.2996	−1.25536
$663$	−2.79158	−0.108416
$664$	14.3885	0.558383
$665$	0	0
$666$	13.4730	0.522069
$667$	−2.10833	−0.0816347
$668$	8.82806	0.341568
$669$	−4.93735	−0.190889
$670$	−68.2754	−2.63771
$671$	−0.613783	−0.0236948
$672$	0	0
$673$	2.93645	0.113192	0.0565959	−	0.998397i	$-0.481975\pi$
$673$	2.93645	0.113192	0.0565959	+	0.998397i	$0.481975\pi$
$674$	9.79383	0.377244
$675$	9.35049	0.359901
$676$	7.40761	0.284908
$677$	38.5619	1.48206	0.741028	−	0.671474i	$-0.234339\pi$
$677$	38.5619	1.48206	0.741028	+	0.671474i	$0.234339\pi$
$678$	7.24879	0.278388
$679$	0	0
$680$	70.5679	2.70615
$681$	11.4573	0.439045
$682$	14.3388	0.549060
$683$	−14.2560	−0.545491	−0.272746	−	0.962086i	$-0.587932\pi$
$683$	−14.2560	−0.545491	−0.272746	+	0.962086i	$0.587932\pi$
$684$	3.42139	0.130820
$685$	45.6135	1.74280
$686$	0	0
$687$	−9.71293	−0.370571
$688$	−11.6289	−0.443350
$689$	2.45228	0.0934246
$690$	4.51532	0.171895
$691$	1.46370	0.0556817	0.0278408	−	0.999612i	$-0.491137\pi$
$691$	1.46370	0.0556817	0.0278408	+	0.999612i	$0.491137\pi$
$692$	−1.26648	−0.0481442
$693$	0	0
$694$	3.11394	0.118204
$695$	5.74052	0.217750
$696$	−6.48172	−0.245689
$697$	31.7017	1.20079
$698$	−19.5449	−0.739786
$699$	8.92690	0.337646
$700$	0	0
$701$	−26.8881	−1.01555	−0.507775	−	0.861490i	$-0.669532\pi$
$701$	−26.8881	−1.01555	−0.507775	+	0.861490i	$0.669532\pi$
$702$	−0.549141	−0.0207260
$703$	−66.7618	−2.51797
$704$	−13.0864	−0.493214
$705$	17.4469	0.657087
$706$	34.5835	1.30157
$707$	0	0
$708$	−7.11981	−0.267579
$709$	3.67152	0.137887	0.0689435	−	0.997621i	$-0.478037\pi$
$709$	3.67152	0.137887	0.0689435	+	0.997621i	$0.478037\pi$
$710$	−30.9521	−1.16161
$711$	6.47369	0.242782
$712$	−50.0533	−1.87583
$713$	8.07148	0.302279
$714$	0	0
$715$	−2.60115	−0.0972775
$716$	1.07805	0.0402888
$717$	14.7250	0.549915
$718$	−35.9498	−1.34163
$719$	−18.5917	−0.693354	−0.346677	−	0.937985i	$-0.612690\pi$
$719$	−18.5917	−0.693354	−0.346677	+	0.937985i	$0.612690\pi$
$720$	9.49284	0.353777
$721$	0	0
$722$	18.9338	0.704644
$723$	−24.4669	−0.909935
$724$	8.39176	0.311877
$725$	19.7139	0.732155
$726$	−10.4637	−0.388345
$727$	16.8322	0.624273	0.312136	−	0.950037i	$-0.398955\pi$
$727$	16.8322	0.624273	0.312136	+	0.950037i	$0.398955\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	54.8267	2.02923
$731$	28.1189	1.04002
$732$	−0.238559	−0.00881739
$733$	18.8588	0.696567	0.348284	−	0.937389i	$-0.386765\pi$
$733$	18.8588	0.696567	0.348284	+	0.937389i	$0.386765\pi$
$734$	10.3917	0.383566
$735$	0	0
$736$	−3.16181	−0.116546
$737$	−22.5361	−0.830128
$738$	6.23615	0.229556
$739$	44.7095	1.64467	0.822333	−	0.569006i	$-0.192672\pi$
$739$	44.7095	1.64467	0.822333	+	0.569006i	$0.192672\pi$
$740$	24.8043	0.911824
$741$	2.72112	0.0999628
$742$	0	0
$743$	49.0083	1.79794	0.898970	−	0.438011i	$-0.144317\pi$
$743$	49.0083	1.79794	0.898970	+	0.438011i	$0.144317\pi$
$744$	24.8145	0.909745
$745$	−69.1426	−2.53319
$746$	−13.0004	−0.475980
$747$	−4.68019	−0.171239
$748$	5.23128	0.191275
$749$	0	0
$750$	−19.6439	−0.717292
$751$	11.7092	0.427276	0.213638	−	0.976913i	$-0.431469\pi$
$751$	11.7092	0.427276	0.213638	+	0.976913i	$0.431469\pi$
$752$	11.5411	0.420860
$753$	−2.61433	−0.0952716
$754$	−1.15777	−0.0421634
$755$	11.1057	0.404178
$756$	0	0
$757$	−24.2422	−0.881096	−0.440548	−	0.897729i	$-0.645216\pi$
$757$	−24.2422	−0.881096	−0.440548	+	0.897729i	$0.645216\pi$
$758$	−13.7963	−0.501106
$759$	1.49040	0.0540981
$760$	−68.7867	−2.49516
$761$	30.7255	1.11380	0.556900	−	0.830580i	$-0.311991\pi$
$761$	30.7255	1.11380	0.556900	+	0.830580i	$0.311991\pi$
$762$	3.39022	0.122815
$763$	0	0
$764$	−11.5006	−0.416077
$765$	−22.9538	−0.829896
$766$	28.8985	1.04414
$767$	−5.66257	−0.204463
$768$	−12.6237	−0.455518
$769$	−39.0901	−1.40963	−0.704813	−	0.709393i	$-0.748969\pi$
$769$	−39.0901	−1.40963	−0.704813	+	0.709393i	$0.748969\pi$
$770$	0	0
$771$	−1.01996	−0.0367328
$772$	−0.903021	−0.0325005
$773$	0.874992	0.0314713	0.0157356	−	0.999876i	$-0.494991\pi$
$773$	0.874992	0.0314713	0.0157356	+	0.999876i	$0.494991\pi$
$774$	5.53137	0.198821
$775$	−75.4723	−2.71105
$776$	20.8517	0.748532
$777$	0	0
$778$	6.91898	0.248057
$779$	−30.9015	−1.10716
$780$	−1.01099	−0.0361992
$781$	−10.2166	−0.365577
$782$	−7.22231	−0.258269
$783$	2.10833	0.0753454
$784$	0	0
$785$	−63.6325	−2.27114
$786$	11.8346	0.422127
$787$	12.3241	0.439308	0.219654	−	0.975578i	$-0.429507\pi$
$787$	12.3241	0.439308	0.219654	+	0.975578i	$0.429507\pi$
$788$	1.43718	0.0511975
$789$	8.93801	0.318202
$790$	−29.2308	−1.03998
$791$	0	0
$792$	4.58201	0.162815
$793$	−0.189732	−0.00673758
$794$	−15.7358	−0.558443
$795$	20.1639	0.715141
$796$	3.06578	0.108664
$797$	−33.6866	−1.19324	−0.596621	−	0.802524i	$-0.703490\pi$
$797$	−33.6866	−1.19324	−0.596621	+	0.802524i	$0.703490\pi$
$798$	0	0
$799$	−27.9065	−0.987260
$800$	29.5645	1.04526
$801$	16.2810	0.575259
$802$	28.1285	0.993252
$803$	18.0970	0.638630
$804$	−8.75911	−0.308910
$805$	0	0
$806$	4.43238	0.156124
$807$	−13.6811	−0.481598
$808$	7.49354	0.263622
$809$	−5.88227	−0.206809	−0.103405	−	0.994639i	$-0.532974\pi$
$809$	−5.88227	−0.206809	−0.103405	+	0.994639i	$0.532974\pi$
$810$	−4.51532	−0.158652
$811$	13.3036	0.467152	0.233576	−	0.972339i	$-0.424957\pi$
$811$	13.3036	0.467152	0.233576	+	0.972339i	$0.424957\pi$
$812$	0	0
$813$	−3.97383	−0.139368
$814$	−20.0802	−0.703811
$815$	13.8261	0.484309
$816$	−15.1839	−0.531543
$817$	−27.4092	−0.958926
$818$	10.2999	0.360128
$819$	0	0
$820$	11.4810	0.400933
$821$	39.0813	1.36395	0.681973	−	0.731377i	$-0.261122\pi$
$821$	39.0813	1.36395	0.681973	+	0.731377i	$0.261122\pi$
$822$	−14.3521	−0.500587
$823$	−19.0070	−0.662543	−0.331272	−	0.943535i	$-0.607478\pi$
$823$	−19.0070	−0.662543	−0.331272	+	0.943535i	$0.607478\pi$
$824$	−17.8541	−0.621978
$825$	−13.9360	−0.485189
$826$	0	0
$827$	35.8180	1.24551	0.622757	−	0.782415i	$-0.286012\pi$
$827$	35.8180	1.24551	0.622757	+	0.782415i	$0.286012\pi$
$828$	0.579274	0.0201312
$829$	−27.1055	−0.941412	−0.470706	−	0.882290i	$-0.656001\pi$
$829$	−27.1055	−0.941412	−0.470706	+	0.882290i	$0.656001\pi$
$830$	21.1325	0.733521
$831$	−10.0146	−0.347401
$832$	−4.04527	−0.140244
$833$	0	0
$834$	−1.80623	−0.0625446
$835$	57.7318	1.99789
$836$	−5.09924	−0.176361
$837$	−8.07148	−0.278991
$838$	35.8301	1.23773
$839$	25.7997	0.890704	0.445352	−	0.895356i	$-0.353079\pi$
$839$	25.7997	0.890704	0.445352	+	0.895356i	$0.353079\pi$
$840$	0	0
$841$	−24.5550	−0.846723
$842$	−29.5017	−1.01670
$843$	−21.3379	−0.734916
$844$	−15.6472	−0.538600
$845$	48.4426	1.66648
$846$	−5.48958	−0.188736
$847$	0	0
$848$	13.3384	0.458044
$849$	14.4830	0.497056
$850$	67.5321	2.31633
$851$	−11.3034	−0.387476
$852$	−3.97087	−0.136040
$853$	−6.24250	−0.213739	−0.106870	−	0.994273i	$-0.534083\pi$
$853$	−6.24250	−0.213739	−0.106870	+	0.994273i	$0.534083\pi$
$854$	0	0
$855$	22.3744	0.765189
$856$	−37.6858	−1.28808
$857$	21.9705	0.750498	0.375249	−	0.926924i	$-0.377557\pi$
$857$	21.9705	0.750498	0.375249	+	0.926924i	$0.377557\pi$
$858$	0.818441	0.0279411
$859$	20.3317	0.693708	0.346854	−	0.937919i	$-0.387250\pi$
$859$	20.3317	0.693708	0.346854	+	0.937919i	$0.387250\pi$
$860$	10.1835	0.347253
$861$	0	0
$862$	−18.6585	−0.635510
$863$	27.7709	0.945334	0.472667	−	0.881241i	$-0.343291\pi$
$863$	27.7709	0.945334	0.472667	+	0.881241i	$0.343291\pi$
$864$	3.16181	0.107567
$865$	−8.28222	−0.281604
$866$	−1.12243	−0.0381418
$867$	19.7149	0.669552
$868$	0	0
$869$	−9.64840	−0.327300
$870$	−9.51977	−0.322750
$871$	−6.96634	−0.236045
$872$	27.6334	0.935784
$873$	−6.78248	−0.229552
$874$	7.04002	0.238132
$875$	0	0
$876$	7.03376	0.237649
$877$	32.5312	1.09850	0.549251	−	0.835657i	$-0.314913\pi$
$877$	32.5312	1.09850	0.549251	+	0.835657i	$0.314913\pi$
$878$	−22.4610	−0.758024
$879$	33.1986	1.11976
$880$	−14.1481	−0.476934
$881$	3.88986	0.131053	0.0655263	−	0.997851i	$-0.479127\pi$
$881$	3.88986	0.131053	0.0655263	+	0.997851i	$0.479127\pi$
$882$	0	0
$883$	−35.6597	−1.20004	−0.600022	−	0.799984i	$-0.704841\pi$
$883$	−35.6597	−1.20004	−0.600022	+	0.799984i	$0.704841\pi$
$884$	1.61709	0.0543886
$885$	−46.5605	−1.56511
$886$	−3.02371	−0.101584
$887$	−47.7271	−1.60252	−0.801259	−	0.598318i	$-0.795836\pi$
$887$	−47.7271	−1.60252	−0.801259	+	0.598318i	$0.795836\pi$
$888$	−34.7506	−1.16615
$889$	0	0
$890$	−73.5137	−2.46419
$891$	−1.49040	−0.0499303
$892$	2.86008	0.0957626
$893$	27.2021	0.910283
$894$	21.7554	0.727610
$895$	7.05002	0.235656
$896$	0	0
$897$	0.460711	0.0153827
$898$	−40.8584	−1.36346
$899$	−17.0173	−0.567559
$900$	−5.41649	−0.180550
$901$	−32.2525	−1.07449
$902$	−9.29437	−0.309469
$903$	0	0
$904$	−18.6966	−0.621840
$905$	54.8786	1.82423
$906$	−3.49436	−0.116092
$907$	−9.88069	−0.328083	−0.164041	−	0.986453i	$-0.552453\pi$
$907$	−9.88069	−0.328083	−0.164041	+	0.986453i	$0.552453\pi$
$908$	−6.63692	−0.220254
$909$	−2.43744	−0.0808448
$910$	0	0
$911$	−22.5568	−0.747339	−0.373669	−	0.927562i	$-0.621901\pi$
$911$	−22.5568	−0.747339	−0.373669	+	0.927562i	$0.621901\pi$
$912$	14.8007	0.490099
$913$	6.97536	0.230851
$914$	−17.9823	−0.594801
$915$	−1.56007	−0.0515744
$916$	5.62644	0.185903
$917$	0	0
$918$	7.22231	0.238372
$919$	35.1020	1.15791	0.578954	−	0.815360i	$-0.303461\pi$
$919$	35.1020	1.15791	0.578954	+	0.815360i	$0.303461\pi$
$920$	−11.6462	−0.383965
$921$	31.4823	1.03738
$922$	18.6020	0.612624
$923$	−3.15813	−0.103951
$924$	0	0
$925$	105.692	3.47515
$926$	7.45935	0.245129
$927$	5.80746	0.190742
$928$	6.66612	0.218826
$929$	−47.7500	−1.56663	−0.783314	−	0.621627i	$-0.786472\pi$
$929$	−47.7500	−1.56663	−0.783314	+	0.621627i	$0.786472\pi$
$930$	36.4453	1.19509
$931$	0	0
$932$	−5.17112	−0.169386
$933$	−18.2076	−0.596090
$934$	10.4451	0.341773
$935$	34.2104	1.11880
$936$	1.41639	0.0462960
$937$	16.1702	0.528258	0.264129	−	0.964487i	$-0.414916\pi$
$937$	16.1702	0.528258	0.264129	+	0.964487i	$0.414916\pi$
$938$	0	0
$939$	21.4552	0.700164
$940$	−10.1065	−0.329638
$941$	−47.7585	−1.55688	−0.778441	−	0.627717i	$-0.783989\pi$
$941$	−47.7585	−1.55688	−0.778441	+	0.627717i	$0.783989\pi$
$942$	20.0217	0.652342
$943$	−5.23193	−0.170375
$944$	−30.7998	−1.00245
$945$	0	0
$946$	−8.24397	−0.268034
$947$	4.88184	0.158638	0.0793192	−	0.996849i	$-0.474725\pi$
$947$	4.88184	0.158638	0.0793192	+	0.996849i	$0.474725\pi$
$948$	−3.75004	−0.121796
$949$	5.59413	0.181593
$950$	−65.8276	−2.13573
$951$	−2.80865	−0.0910767
$952$	0	0
$953$	17.0472	0.552212	0.276106	−	0.961127i	$-0.410956\pi$
$953$	17.0472	0.552212	0.276106	+	0.961127i	$0.410956\pi$
$954$	−6.34450	−0.205411
$955$	−75.2089	−2.43370
$956$	−8.52980	−0.275873
$957$	−3.14225	−0.101575
$958$	−18.8043	−0.607540
$959$	0	0
$960$	−33.2623	−1.07353
$961$	34.1489	1.10158
$962$	−6.20717	−0.200127
$963$	12.2582	0.395014
$964$	14.1731	0.456483
$965$	−5.90538	−0.190101
$966$	0	0
$967$	23.3640	0.751335	0.375667	−	0.926755i	$-0.377413\pi$
$967$	23.3640	0.751335	0.375667	+	0.926755i	$0.377413\pi$
$968$	26.9888	0.867452
$969$	−35.7882	−1.14968
$970$	30.6251	0.983311
$971$	36.9046	1.18432	0.592162	−	0.805819i	$-0.298275\pi$
$971$	36.9046	1.18432	0.592162	+	0.805819i	$0.298275\pi$
$972$	−0.579274	−0.0185802
$973$	0	0
$974$	48.3635	1.54967
$975$	−4.30788	−0.137962
$976$	−1.03199	−0.0330331
$977$	0.548852	0.0175593	0.00877967	−	0.999961i	$-0.497205\pi$
$977$	0.548852	0.0175593	0.00877967	+	0.999961i	$0.497205\pi$
$978$	−4.35034	−0.139108
$979$	−24.2652	−0.775518
$980$	0	0
$981$	−8.98838	−0.286977
$982$	11.1921	0.357156
$983$	6.97354	0.222421	0.111211	−	0.993797i	$-0.464527\pi$
$983$	6.97354	0.222421	0.111211	+	0.993797i	$0.464527\pi$
$984$	−16.0848	−0.512763
$985$	9.39856	0.299463
$986$	15.2270	0.484926
$987$	0	0
$988$	−1.57627	−0.0501479
$989$	−4.64064	−0.147564
$990$	6.72964	0.213882
$991$	−31.3125	−0.994675	−0.497337	−	0.867557i	$-0.665689\pi$
$991$	−31.3125	−0.994675	−0.497337	+	0.867557i	$0.665689\pi$
$992$	−25.5205	−0.810277
$993$	−27.0983	−0.859937
$994$	0	0
$995$	20.0489	0.635593
$996$	2.71111	0.0859048
$997$	45.2125	1.43189	0.715947	−	0.698155i	$-0.245995\pi$
$997$	45.2125	1.43189	0.715947	+	0.698155i	$0.245995\pi$
$998$	22.7399	0.719819
$999$	11.3034	0.357624

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bf.1.5		8
7.2	even	3		483.2.i.g.277.4	✓	16
7.4	even	3		483.2.i.g.415.4	yes	16
7.6	odd	2		3381.2.a.be.1.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.g.277.4	✓	16	7.2	even	3
483.2.i.g.415.4	yes	16	7.4	even	3
3381.2.a.be.1.5		8	7.6	odd	2
3381.2.a.bf.1.5		8	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:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q+1.19194 q^{2} +1.00000 q^{3} -0.579274 q^{4} -3.78820 q^{5} +1.19194 q^{6} -3.07435 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.19194 q^{2} +1.00000 q^{3} -0.579274 q^{4} -3.78820 q^{5} +1.19194 q^{6} -3.07435 q^{8} +1.00000 q^{9} -4.51532 q^{10} -1.49040 q^{11} -0.579274 q^{12} -0.460711 q^{13} -3.78820 q^{15} -2.50589 q^{16} +6.05928 q^{17} +1.19194 q^{18} -5.90634 q^{19} +2.19441 q^{20} -1.77647 q^{22} -1.00000 q^{23} -3.07435 q^{24} +9.35049 q^{25} -0.549141 q^{26} +1.00000 q^{27} +2.10833 q^{29} -4.51532 q^{30} -8.07148 q^{31} +3.16181 q^{32} -1.49040 q^{33} +7.22231 q^{34} -0.579274 q^{36} +11.3034 q^{37} -7.04002 q^{38} -0.460711 q^{39} +11.6462 q^{40} +5.23193 q^{41} +4.64064 q^{43} +0.863350 q^{44} -3.78820 q^{45} -1.19194 q^{46} -4.60558 q^{47} -2.50589 q^{48} +11.1452 q^{50} +6.05928 q^{51} +0.266878 q^{52} -5.32282 q^{53} +1.19194 q^{54} +5.64594 q^{55} -5.90634 q^{57} +2.51300 q^{58} +12.2909 q^{59} +2.19441 q^{60} +0.411824 q^{61} -9.62074 q^{62} +8.78048 q^{64} +1.74527 q^{65} -1.77647 q^{66} +15.1208 q^{67} -3.50998 q^{68} -1.00000 q^{69} +6.85490 q^{71} -3.07435 q^{72} -12.1424 q^{73} +13.4730 q^{74} +9.35049 q^{75} +3.42139 q^{76} -0.549141 q^{78} +6.47369 q^{79} +9.49284 q^{80} +1.00000 q^{81} +6.23615 q^{82} -4.68019 q^{83} -22.9538 q^{85} +5.53137 q^{86} +2.10833 q^{87} +4.58201 q^{88} +16.2810 q^{89} -4.51532 q^{90} +0.579274 q^{92} -8.07148 q^{93} -5.48958 q^{94} +22.3744 q^{95} +3.16181 q^{96} -6.78248 q^{97} -1.49040 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 8 q^{3} + 15 q^{4} + 5 q^{5} + q^{6} + 9 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q + q^2 + 8 * q^3 + 15 * q^4 + 5 * q^5 + q^6 + 9 * q^8 + 8 * q^9	\( 8 q + q^{2} + 8 q^{3} + 15 q^{4} + 5 q^{5} + q^{6} + 9 q^{8} + 8 q^{9} - 3 q^{10} + 10 q^{11} + 15 q^{12} - 6 q^{13} + 5 q^{15} + 13 q^{16} + 21 q^{17} + q^{18} + 5 q^{19} - q^{20} + 18 q^{22} - 8 q^{23} + 9 q^{24} + 27 q^{25} + 3 q^{26} + 8 q^{27} + 2 q^{29} - 3 q^{30} - 13 q^{31} + 29 q^{32} + 10 q^{33} - 19 q^{34} + 15 q^{36} + 13 q^{37} - 6 q^{38} - 6 q^{39} + 7 q^{40} + 16 q^{41} + 15 q^{43} + 24 q^{44} + 5 q^{45} - q^{46} - q^{47} + 13 q^{48} + 16 q^{50} + 21 q^{51} - 19 q^{52} + 3 q^{53} + q^{54} - 10 q^{55} + 5 q^{57} - 40 q^{58} + 26 q^{59} - q^{60} - 14 q^{61} - 14 q^{62} + 49 q^{64} - 3 q^{65} + 18 q^{66} + 38 q^{67} + 43 q^{68} - 8 q^{69} + 9 q^{71} + 9 q^{72} - 6 q^{73} + 32 q^{74} + 27 q^{75} - 14 q^{76} + 3 q^{78} + 23 q^{79} - 17 q^{80} + 8 q^{81} + 20 q^{82} + 30 q^{83} - 37 q^{85} - 28 q^{86} + 2 q^{87} + 86 q^{88} + 12 q^{89} - 3 q^{90} - 15 q^{92} - 13 q^{93} - 45 q^{94} + 16 q^{95} + 29 q^{96} + 14 q^{97} + 10 q^{99}+O(q^{100}) \) 8 * q + q^2 + 8 * q^3 + 15 * q^4 + 5 * q^5 + q^6 + 9 * q^8 + 8 * q^9 - 3 * q^10 + 10 * q^11 + 15 * q^12 - 6 * q^13 + 5 * q^15 + 13 * q^16 + 21 * q^17 + q^18 + 5 * q^19 - q^20 + 18 * q^22 - 8 * q^23 + 9 * q^24 + 27 * q^25 + 3 * q^26 + 8 * q^27 + 2 * q^29 - 3 * q^30 - 13 * q^31 + 29 * q^32 + 10 * q^33 - 19 * q^34 + 15 * q^36 + 13 * q^37 - 6 * q^38 - 6 * q^39 + 7 * q^40 + 16 * q^41 + 15 * q^43 + 24 * q^44 + 5 * q^45 - q^46 - q^47 + 13 * q^48 + 16 * q^50 + 21 * q^51 - 19 * q^52 + 3 * q^53 + q^54 - 10 * q^55 + 5 * q^57 - 40 * q^58 + 26 * q^59 - q^60 - 14 * q^61 - 14 * q^62 + 49 * q^64 - 3 * q^65 + 18 * q^66 + 38 * q^67 + 43 * q^68 - 8 * q^69 + 9 * q^71 + 9 * q^72 - 6 * q^73 + 32 * q^74 + 27 * q^75 - 14 * q^76 + 3 * q^78 + 23 * q^79 - 17 * q^80 + 8 * q^81 + 20 * q^82 + 30 * q^83 - 37 * q^85 - 28 * q^86 + 2 * q^87 + 86 * q^88 + 12 * q^89 - 3 * q^90 - 15 * q^92 - 13 * q^93 - 45 * q^94 + 16 * q^95 + 29 * q^96 + 14 * q^97 + 10 * q^99

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