LMFDB - Embedded newform 3381.2.a.bf.1.2

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			1.2
Root			$-1.87992$ 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)

$f(q)$	$=$	$q-1.87992 q^{2} +1.00000 q^{3} +1.53408 q^{4} -2.65555 q^{5} -1.87992 q^{6} +0.875886 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.87992 q^{2} +1.00000 q^{3} +1.53408 q^{4} -2.65555 q^{5} -1.87992 q^{6} +0.875886 q^{8} +1.00000 q^{9} +4.99220 q^{10} +6.05086 q^{11} +1.53408 q^{12} +2.90301 q^{13} -2.65555 q^{15} -4.71476 q^{16} +5.61986 q^{17} -1.87992 q^{18} +7.23689 q^{19} -4.07383 q^{20} -11.3751 q^{22} -1.00000 q^{23} +0.875886 q^{24} +2.05192 q^{25} -5.45740 q^{26} +1.00000 q^{27} +8.39241 q^{29} +4.99220 q^{30} -6.09849 q^{31} +7.11157 q^{32} +6.05086 q^{33} -10.5649 q^{34} +1.53408 q^{36} +0.781491 q^{37} -13.6047 q^{38} +2.90301 q^{39} -2.32595 q^{40} -3.31700 q^{41} +7.59896 q^{43} +9.28251 q^{44} -2.65555 q^{45} +1.87992 q^{46} +5.05335 q^{47} -4.71476 q^{48} -3.85744 q^{50} +5.61986 q^{51} +4.45345 q^{52} -1.84950 q^{53} -1.87992 q^{54} -16.0683 q^{55} +7.23689 q^{57} -15.7770 q^{58} +1.96518 q^{59} -4.07383 q^{60} -13.8569 q^{61} +11.4647 q^{62} -3.93964 q^{64} -7.70906 q^{65} -11.3751 q^{66} -7.77980 q^{67} +8.62133 q^{68} -1.00000 q^{69} +9.12822 q^{71} +0.875886 q^{72} +0.883056 q^{73} -1.46914 q^{74} +2.05192 q^{75} +11.1020 q^{76} -5.45740 q^{78} -5.91193 q^{79} +12.5202 q^{80} +1.00000 q^{81} +6.23569 q^{82} -8.51343 q^{83} -14.9238 q^{85} -14.2854 q^{86} +8.39241 q^{87} +5.29986 q^{88} +8.53165 q^{89} +4.99220 q^{90} -1.53408 q^{92} -6.09849 q^{93} -9.49987 q^{94} -19.2179 q^{95} +7.11157 q^{96} -0.669718 q^{97} +6.05086 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.87992	−1.32930	−0.664651	−	0.747154i	$-0.731420\pi$
$2$	−1.87992	−1.32930	−0.664651	+	0.747154i	$0.731420\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.53408	0.767041
$5$	−2.65555	−1.18760	−0.593798	−	0.804614i	$-0.702372\pi$
$5$	−2.65555	−1.18760	−0.593798	+	0.804614i	$0.702372\pi$
$6$	−1.87992	−0.767472
$7$	0	0
$7$	0	0
$8$	0.875886	0.309672
$9$	1.00000	0.333333
$10$	4.99220	1.57867
$11$	6.05086	1.82440	0.912201	−	0.409743i	$-0.134382\pi$
$11$	6.05086	1.82440	0.912201	+	0.409743i	$0.134382\pi$
$12$	1.53408	0.442851
$13$	2.90301	0.805149	0.402574	−	0.915387i	$-0.368115\pi$
$13$	2.90301	0.805149	0.402574	+	0.915387i	$0.368115\pi$
$14$	0	0
$15$	−2.65555	−0.685659
$16$	−4.71476	−1.17869
$17$	5.61986	1.36302	0.681508	−	0.731811i	$-0.261325\pi$
$17$	5.61986	1.36302	0.681508	+	0.731811i	$0.261325\pi$
$18$	−1.87992	−0.443100
$19$	7.23689	1.66026	0.830128	−	0.557573i	$-0.188267\pi$
$19$	7.23689	1.66026	0.830128	+	0.557573i	$0.188267\pi$
$20$	−4.07383	−0.910935
$21$	0	0
$22$	−11.3751	−2.42518
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0.875886	0.178789
$25$	2.05192	0.410384
$26$	−5.45740	−1.07029
$27$	1.00000	0.192450
$28$	0	0
$29$	8.39241	1.55843	0.779215	−	0.626756i	$-0.215618\pi$
$29$	8.39241	1.55843	0.779215	+	0.626756i	$0.215618\pi$
$30$	4.99220	0.911447
$31$	−6.09849	−1.09532	−0.547661	−	0.836700i	$-0.684482\pi$
$31$	−6.09849	−1.09532	−0.547661	+	0.836700i	$0.684482\pi$
$32$	7.11157	1.25716
$33$	6.05086	1.05332
$34$	−10.5649	−1.81186
$35$	0	0
$36$	1.53408	0.255680
$37$	0.781491	0.128476	0.0642381	−	0.997935i	$-0.479538\pi$
$37$	0.781491	0.128476	0.0642381	+	0.997935i	$0.479538\pi$
$38$	−13.6047	−2.20698
$39$	2.90301	0.464853
$40$	−2.32595	−0.367766
$41$	−3.31700	−0.518029	−0.259014	−	0.965873i	$-0.583398\pi$
$41$	−3.31700	−0.518029	−0.259014	+	0.965873i	$0.583398\pi$
$42$	0	0
$43$	7.59896	1.15883	0.579415	−	0.815033i	$-0.303281\pi$
$43$	7.59896	1.15883	0.579415	+	0.815033i	$0.303281\pi$
$44$	9.28251	1.39939
$45$	−2.65555	−0.395865
$46$	1.87992	0.277178
$47$	5.05335	0.737107	0.368553	−	0.929607i	$-0.379853\pi$
$47$	5.05335	0.737107	0.368553	+	0.929607i	$0.379853\pi$
$48$	−4.71476	−0.680516
$49$	0	0
$50$	−3.85744	−0.545524
$51$	5.61986	0.786938
$52$	4.45345	0.617582
$53$	−1.84950	−0.254048	−0.127024	−	0.991900i	$-0.540543\pi$
$53$	−1.84950	−0.254048	−0.127024	+	0.991900i	$0.540543\pi$
$54$	−1.87992	−0.255824
$55$	−16.0683	−2.16665
$56$	0	0
$57$	7.23689	0.958549
$58$	−15.7770	−2.07162
$59$	1.96518	0.255844	0.127922	−	0.991784i	$-0.459169\pi$
$59$	1.96518	0.255844	0.127922	+	0.991784i	$0.459169\pi$
$60$	−4.07383	−0.525929
$61$	−13.8569	−1.77419	−0.887095	−	0.461587i	$-0.847280\pi$
$61$	−13.8569	−1.77419	−0.887095	+	0.461587i	$0.847280\pi$
$62$	11.4647	1.45601
$63$	0	0
$64$	−3.93964	−0.492455
$65$	−7.70906	−0.956191
$66$	−11.3751	−1.40018
$67$	−7.77980	−0.950454	−0.475227	−	0.879863i	$-0.657634\pi$
$67$	−7.77980	−0.950454	−0.475227	+	0.879863i	$0.657634\pi$
$68$	8.62133	1.04549
$69$	−1.00000	−0.120386
$70$	0	0
$71$	9.12822	1.08332	0.541660	−	0.840597i	$-0.317796\pi$
$71$	9.12822	1.08332	0.541660	+	0.840597i	$0.317796\pi$
$72$	0.875886	0.103224
$73$	0.883056	0.103354	0.0516769	−	0.998664i	$-0.483543\pi$
$73$	0.883056	0.103354	0.0516769	+	0.998664i	$0.483543\pi$
$74$	−1.46914	−0.170784
$75$	2.05192	0.236935
$76$	11.1020	1.27348
$77$	0	0
$78$	−5.45740	−0.617929
$79$	−5.91193	−0.665144	−0.332572	−	0.943078i	$-0.607916\pi$
$79$	−5.91193	−0.665144	−0.332572	+	0.943078i	$0.607916\pi$
$80$	12.5202	1.39981
$81$	1.00000	0.111111
$82$	6.23569	0.688616
$83$	−8.51343	−0.934471	−0.467235	−	0.884133i	$-0.654750\pi$
$83$	−8.51343	−0.934471	−0.467235	+	0.884133i	$0.654750\pi$
$84$	0	0
$85$	−14.9238	−1.61871
$86$	−14.2854	−1.54043
$87$	8.39241	0.899761
$88$	5.29986	0.564967
$89$	8.53165	0.904354	0.452177	−	0.891928i	$-0.350648\pi$
$89$	8.53165	0.904354	0.452177	+	0.891928i	$0.350648\pi$
$90$	4.99220	0.526224
$91$	0	0
$92$	−1.53408	−0.159939
$93$	−6.09849	−0.632384
$94$	−9.49987	−0.979837
$95$	−19.2179	−1.97171
$96$	7.11157	0.725822
$97$	−0.669718	−0.0679996	−0.0339998	−	0.999422i	$-0.510825\pi$
$97$	−0.669718	−0.0679996	−0.0339998	+	0.999422i	$0.510825\pi$
$98$	0	0
$99$	6.05086	0.608134
$100$	3.14781	0.314781
$101$	−12.9031	−1.28390	−0.641952	−	0.766744i	$-0.721875\pi$
$101$	−12.9031	−1.28390	−0.641952	+	0.766744i	$0.721875\pi$
$102$	−10.5649	−1.04608
$103$	−10.1267	−0.997818	−0.498909	−	0.866654i	$-0.666266\pi$
$103$	−10.1267	−0.997818	−0.498909	+	0.866654i	$0.666266\pi$
$104$	2.54270	0.249332
$105$	0	0
$106$	3.47690	0.337706
$107$	−7.57052	−0.731870	−0.365935	−	0.930640i	$-0.619251\pi$
$107$	−7.57052	−0.731870	−0.365935	+	0.930640i	$0.619251\pi$
$108$	1.53408	0.147617
$109$	−6.50711	−0.623268	−0.311634	−	0.950202i	$-0.600876\pi$
$109$	−6.50711	−0.623268	−0.311634	+	0.950202i	$0.600876\pi$
$110$	30.2071	2.88013
$111$	0.781491	0.0741758
$112$	0	0
$113$	1.47158	0.138435	0.0692174	−	0.997602i	$-0.477950\pi$
$113$	1.47158	0.138435	0.0692174	+	0.997602i	$0.477950\pi$
$114$	−13.6047	−1.27420
$115$	2.65555	0.247631
$116$	12.8746	1.19538
$117$	2.90301	0.268383
$118$	−3.69437	−0.340094
$119$	0	0
$120$	−2.32595	−0.212330
$121$	25.6129	2.32844
$122$	26.0497	2.35843
$123$	−3.31700	−0.299084
$124$	−9.35559	−0.840157
$125$	7.82876	0.700226
$126$	0	0
$127$	18.8588	1.67345	0.836724	−	0.547625i	$-0.184468\pi$
$127$	18.8588	1.67345	0.836724	+	0.547625i	$0.184468\pi$
$128$	−6.81695	−0.602539
$129$	7.59896	0.669051
$130$	14.4924	1.27107
$131$	16.9594	1.48175	0.740876	−	0.671642i	$-0.234411\pi$
$131$	16.9594	1.48175	0.740876	+	0.671642i	$0.234411\pi$
$132$	9.28251	0.807939
$133$	0	0
$134$	14.6254	1.26344
$135$	−2.65555	−0.228553
$136$	4.92235	0.422088
$137$	12.5631	1.07334	0.536670	−	0.843792i	$-0.319682\pi$
$137$	12.5631	1.07334	0.536670	+	0.843792i	$0.319682\pi$
$138$	1.87992	0.160029
$139$	−13.9762	−1.18545	−0.592725	−	0.805405i	$-0.701948\pi$
$139$	−13.9762	−1.18545	−0.592725	+	0.805405i	$0.701948\pi$
$140$	0	0
$141$	5.05335	0.425569
$142$	−17.1603	−1.44006
$143$	17.5657	1.46891
$144$	−4.71476	−0.392896
$145$	−22.2864	−1.85079
$146$	−1.66007	−0.137388
$147$	0	0
$148$	1.19887	0.0985466
$149$	9.93416	0.813838	0.406919	−	0.913464i	$-0.366603\pi$
$149$	9.93416	0.813838	0.406919	+	0.913464i	$0.366603\pi$
$150$	−3.85744	−0.314958
$151$	10.9587	0.891807	0.445903	−	0.895081i	$-0.352883\pi$
$151$	10.9587	0.891807	0.445903	+	0.895081i	$0.352883\pi$
$152$	6.33869	0.514135
$153$	5.61986	0.454339
$154$	0	0
$155$	16.1948	1.30080
$156$	4.45345	0.356561
$157$	−8.04953	−0.642422	−0.321211	−	0.947008i	$-0.604090\pi$
$157$	−8.04953	−0.642422	−0.321211	+	0.947008i	$0.604090\pi$
$158$	11.1139	0.884177
$159$	−1.84950	−0.146675
$160$	−18.8851	−1.49300
$161$	0	0
$162$	−1.87992	−0.147700
$163$	2.93775	0.230102	0.115051	−	0.993360i	$-0.463297\pi$
$163$	2.93775	0.230102	0.115051	+	0.993360i	$0.463297\pi$
$164$	−5.08856	−0.397350
$165$	−16.0683	−1.25092
$166$	16.0045	1.24219
$167$	−8.45552	−0.654308	−0.327154	−	0.944971i	$-0.606090\pi$
$167$	−8.45552	−0.654308	−0.327154	+	0.944971i	$0.606090\pi$
$168$	0	0
$169$	−4.57256	−0.351735
$170$	28.0555	2.15176
$171$	7.23689	0.553419
$172$	11.6574	0.888870
$173$	6.11837	0.465171	0.232586	−	0.972576i	$-0.425281\pi$
$173$	6.11837	0.465171	0.232586	+	0.972576i	$0.425281\pi$
$174$	−15.7770	−1.19605
$175$	0	0
$176$	−28.5283	−2.15040
$177$	1.96518	0.147712
$178$	−16.0388	−1.20216
$179$	16.7365	1.25094	0.625472	−	0.780246i	$-0.284906\pi$
$179$	16.7365	1.25094	0.625472	+	0.780246i	$0.284906\pi$
$180$	−4.07383	−0.303645
$181$	−1.61304	−0.119897	−0.0599483	−	0.998201i	$-0.519094\pi$
$181$	−1.61304	−0.119897	−0.0599483	+	0.998201i	$0.519094\pi$
$182$	0	0
$183$	−13.8569	−1.02433
$184$	−0.875886	−0.0645711
$185$	−2.07528	−0.152578
$186$	11.4647	0.840629
$187$	34.0050	2.48669
$188$	7.75226	0.565391
$189$	0	0
$190$	36.1280	2.62100
$191$	14.9563	1.08220	0.541100	−	0.840958i	$-0.318008\pi$
$191$	14.9563	1.08220	0.541100	+	0.840958i	$0.318008\pi$
$192$	−3.93964	−0.284319
$193$	−15.7725	−1.13533	−0.567663	−	0.823261i	$-0.692152\pi$
$193$	−15.7725	−1.13533	−0.567663	+	0.823261i	$0.692152\pi$
$194$	1.25901	0.0903919
$195$	−7.70906	−0.552057
$196$	0	0
$197$	−7.28311	−0.518900	−0.259450	−	0.965757i	$-0.583541\pi$
$197$	−7.28311	−0.518900	−0.259450	+	0.965757i	$0.583541\pi$
$198$	−11.3751	−0.808393
$199$	−17.9132	−1.26983	−0.634915	−	0.772582i	$-0.718965\pi$
$199$	−17.9132	−1.26983	−0.634915	+	0.772582i	$0.718965\pi$
$200$	1.79725	0.127085
$201$	−7.77980	−0.548745
$202$	24.2567	1.70670
$203$	0	0
$204$	8.62133	0.603614
$205$	8.80845	0.615209
$206$	19.0374	1.32640
$207$	−1.00000	−0.0695048
$208$	−13.6870	−0.949020
$209$	43.7894	3.02897
$210$	0	0
$211$	−2.02819	−0.139626	−0.0698132	−	0.997560i	$-0.522240\pi$
$211$	−2.02819	−0.139626	−0.0698132	+	0.997560i	$0.522240\pi$
$212$	−2.83728	−0.194865
$213$	9.12822	0.625456
$214$	14.2319	0.972875
$215$	−20.1794	−1.37622
$216$	0.875886	0.0595965
$217$	0	0
$218$	12.2328	0.828511
$219$	0.883056	0.0596714
$220$	−24.6501	−1.66191
$221$	16.3145	1.09743
$222$	−1.46914	−0.0986020
$223$	−2.98676	−0.200008	−0.100004	−	0.994987i	$-0.531886\pi$
$223$	−2.98676	−0.200008	−0.100004	+	0.994987i	$0.531886\pi$
$224$	0	0
$225$	2.05192	0.136795
$226$	−2.76645	−0.184021
$227$	−22.7607	−1.51068	−0.755342	−	0.655331i	$-0.772529\pi$
$227$	−22.7607	−1.51068	−0.755342	+	0.655331i	$0.772529\pi$
$228$	11.1020	0.735247
$229$	23.6494	1.56280	0.781399	−	0.624032i	$-0.214506\pi$
$229$	23.6494	1.56280	0.781399	+	0.624032i	$0.214506\pi$
$230$	−4.99220	−0.329176
$231$	0	0
$232$	7.35079	0.482603
$233$	1.49222	0.0977584	0.0488792	−	0.998805i	$-0.484435\pi$
$233$	1.49222	0.0977584	0.0488792	+	0.998805i	$0.484435\pi$
$234$	−5.45740	−0.356762
$235$	−13.4194	−0.875385
$236$	3.01475	0.196243
$237$	−5.91193	−0.384021
$238$	0	0
$239$	−29.9342	−1.93628	−0.968141	−	0.250407i	$-0.919436\pi$
$239$	−29.9342	−1.93628	−0.968141	+	0.250407i	$0.919436\pi$
$240$	12.5202	0.808178
$241$	10.0993	0.650550	0.325275	−	0.945619i	$-0.394543\pi$
$241$	10.0993	0.650550	0.325275	+	0.945619i	$0.394543\pi$
$242$	−48.1500	−3.09520
$243$	1.00000	0.0641500
$244$	−21.2576	−1.36088
$245$	0	0
$246$	6.23569	0.397573
$247$	21.0087	1.33675
$248$	−5.34158	−0.339191
$249$	−8.51343	−0.539517
$250$	−14.7174	−0.930811
$251$	2.58608	0.163232	0.0816160	−	0.996664i	$-0.473992\pi$
$251$	2.58608	0.163232	0.0816160	+	0.996664i	$0.473992\pi$
$252$	0	0
$253$	−6.05086	−0.380414
$254$	−35.4529	−2.22452
$255$	−14.9238	−0.934564
$256$	20.6946	1.29341
$257$	1.31247	0.0818696	0.0409348	−	0.999162i	$-0.486966\pi$
$257$	1.31247	0.0818696	0.0409348	+	0.999162i	$0.486966\pi$
$258$	−14.2854	−0.889370
$259$	0	0
$260$	−11.8263	−0.733438
$261$	8.39241	0.519477
$262$	−31.8823	−1.96969
$263$	2.91480	0.179734	0.0898670	−	0.995954i	$-0.471356\pi$
$263$	2.91480	0.179734	0.0898670	+	0.995954i	$0.471356\pi$
$264$	5.29986	0.326184
$265$	4.91142	0.301706
$266$	0	0
$267$	8.53165	0.522129
$268$	−11.9349	−0.729037
$269$	−2.33663	−0.142467	−0.0712335	−	0.997460i	$-0.522694\pi$
$269$	−2.33663	−0.142467	−0.0712335	+	0.997460i	$0.522694\pi$
$270$	4.99220	0.303816
$271$	−2.10151	−0.127658	−0.0638288	−	0.997961i	$-0.520331\pi$
$271$	−2.10151	−0.127658	−0.0638288	+	0.997961i	$0.520331\pi$
$272$	−26.4963	−1.60657
$273$	0	0
$274$	−23.6176	−1.42679
$275$	12.4159	0.748705
$276$	−1.53408	−0.0923409
$277$	−3.27367	−0.196695	−0.0983477	−	0.995152i	$-0.531356\pi$
$277$	−3.27367	−0.196695	−0.0983477	+	0.995152i	$0.531356\pi$
$278$	26.2742	1.57582
$279$	−6.09849	−0.365107
$280$	0	0
$281$	0.869751	0.0518850	0.0259425	−	0.999663i	$-0.491741\pi$
$281$	0.869751	0.0518850	0.0259425	+	0.999663i	$0.491741\pi$
$282$	−9.49987	−0.565709
$283$	0.411878	0.0244836	0.0122418	−	0.999925i	$-0.496103\pi$
$283$	0.411878	0.0244836	0.0122418	+	0.999925i	$0.496103\pi$
$284$	14.0034	0.830952
$285$	−19.2179	−1.13837
$286$	−33.0220	−1.95263
$287$	0	0
$288$	7.11157	0.419053
$289$	14.5828	0.857812
$290$	41.8966	2.46025
$291$	−0.669718	−0.0392596
$292$	1.35468	0.0792767
$293$	−4.88076	−0.285137	−0.142569	−	0.989785i	$-0.545536\pi$
$293$	−4.88076	−0.285137	−0.142569	+	0.989785i	$0.545536\pi$
$294$	0	0
$295$	−5.21862	−0.303840
$296$	0.684496	0.0397855
$297$	6.05086	0.351106
$298$	−18.6754	−1.08184
$299$	−2.90301	−0.167885
$300$	3.14781	0.181739
$301$	0	0
$302$	−20.6014	−1.18548
$303$	−12.9031	−0.741263
$304$	−34.1202	−1.95693
$305$	36.7975	2.10702
$306$	−10.5649	−0.603953
$307$	16.5174	0.942699	0.471350	−	0.881946i	$-0.343767\pi$
$307$	16.5174	0.942699	0.471350	+	0.881946i	$0.343767\pi$
$308$	0	0
$309$	−10.1267	−0.576091
$310$	−30.4449	−1.72915
$311$	−5.48088	−0.310792	−0.155396	−	0.987852i	$-0.549665\pi$
$311$	−5.48088	−0.310792	−0.155396	+	0.987852i	$0.549665\pi$
$312$	2.54270	0.143952
$313$	−14.4355	−0.815944	−0.407972	−	0.912994i	$-0.633764\pi$
$313$	−14.4355	−0.815944	−0.407972	+	0.912994i	$0.633764\pi$
$314$	15.1324	0.853973
$315$	0	0
$316$	−9.06939	−0.510193
$317$	−17.0892	−0.959823	−0.479912	−	0.877317i	$-0.659331\pi$
$317$	−17.0892	−0.959823	−0.479912	+	0.877317i	$0.659331\pi$
$318$	3.47690	0.194975
$319$	50.7813	2.84320
$320$	10.4619	0.584838
$321$	−7.57052	−0.422545
$322$	0	0
$323$	40.6703	2.26296
$324$	1.53408	0.0852268
$325$	5.95673	0.330420
$326$	−5.52272	−0.305875
$327$	−6.50711	−0.359844
$328$	−2.90532	−0.160419
$329$	0	0
$330$	30.2071	1.66285
$331$	10.2642	0.564171	0.282086	−	0.959389i	$-0.408974\pi$
$331$	10.2642	0.564171	0.282086	+	0.959389i	$0.408974\pi$
$332$	−13.0603	−0.716777
$333$	0.781491	0.0428254
$334$	15.8957	0.869772
$335$	20.6596	1.12875
$336$	0	0
$337$	7.36005	0.400928	0.200464	−	0.979701i	$-0.435755\pi$
$337$	7.36005	0.400928	0.200464	+	0.979701i	$0.435755\pi$
$338$	8.59603	0.467562
$339$	1.47158	0.0799253
$340$	−22.8943	−1.24162
$341$	−36.9011	−1.99831
$342$	−13.6047	−0.735660
$343$	0	0
$344$	6.65582	0.358858
$345$	2.65555	0.142970
$346$	−11.5020	−0.618353
$347$	−8.73624	−0.468986	−0.234493	−	0.972118i	$-0.575343\pi$
$347$	−8.73624	−0.468986	−0.234493	+	0.972118i	$0.575343\pi$
$348$	12.8746	0.690153
$349$	−19.9554	−1.06819	−0.534095	−	0.845425i	$-0.679347\pi$
$349$	−19.9554	−1.06819	−0.534095	+	0.845425i	$0.679347\pi$
$350$	0	0
$351$	2.90301	0.154951
$352$	43.0311	2.29357
$353$	17.0949	0.909871	0.454936	−	0.890524i	$-0.349662\pi$
$353$	17.0949	0.909871	0.454936	+	0.890524i	$0.349662\pi$
$354$	−3.69437	−0.196354
$355$	−24.2404	−1.28655
$356$	13.0883	0.693676
$357$	0	0
$358$	−31.4632	−1.66288
$359$	35.3511	1.86576	0.932881	−	0.360186i	$-0.117287\pi$
$359$	35.3511	1.86576	0.932881	+	0.360186i	$0.117287\pi$
$360$	−2.32595	−0.122589
$361$	33.3725	1.75645
$362$	3.03239	0.159379
$363$	25.6129	1.34433
$364$	0	0
$365$	−2.34499	−0.122743
$366$	26.0497	1.36164
$367$	15.1577	0.791223	0.395612	−	0.918418i	$-0.370533\pi$
$367$	15.1577	0.791223	0.395612	+	0.918418i	$0.370533\pi$
$368$	4.71476	0.245774
$369$	−3.31700	−0.172676
$370$	3.90136	0.202822
$371$	0	0
$372$	−9.35559	−0.485065
$373$	38.1364	1.97463	0.987315	−	0.158776i	$-0.0507548\pi$
$373$	38.1364	1.97463	0.987315	+	0.158776i	$0.0507548\pi$
$374$	−63.9264	−3.30556
$375$	7.82876	0.404275
$376$	4.42616	0.228262
$377$	24.3632	1.25477
$378$	0	0
$379$	−33.5087	−1.72123	−0.860614	−	0.509258i	$-0.829920\pi$
$379$	−33.5087	−1.72123	−0.860614	+	0.509258i	$0.829920\pi$
$380$	−29.4818	−1.51239
$381$	18.8588	0.966165
$382$	−28.1166	−1.43857
$383$	−31.5563	−1.61245	−0.806227	−	0.591606i	$-0.798494\pi$
$383$	−31.5563	−1.61245	−0.806227	+	0.591606i	$0.798494\pi$
$384$	−6.81695	−0.347876
$385$	0	0
$386$	29.6509	1.50919
$387$	7.59896	0.386277
$388$	−1.02740	−0.0521585
$389$	18.4706	0.936499	0.468250	−	0.883596i	$-0.344885\pi$
$389$	18.4706	0.936499	0.468250	+	0.883596i	$0.344885\pi$
$390$	14.4924	0.733850
$391$	−5.61986	−0.284208
$392$	0	0
$393$	16.9594	0.855490
$394$	13.6916	0.689774
$395$	15.6994	0.789922
$396$	9.28251	0.466464
$397$	−25.0950	−1.25948	−0.629742	−	0.776805i	$-0.716839\pi$
$397$	−25.0950	−1.25948	−0.629742	+	0.776805i	$0.716839\pi$
$398$	33.6752	1.68799
$399$	0	0
$400$	−9.67430	−0.483715
$401$	−26.3245	−1.31458	−0.657292	−	0.753636i	$-0.728298\pi$
$401$	−26.3245	−1.31458	−0.657292	+	0.753636i	$0.728298\pi$
$402$	14.6254	0.729447
$403$	−17.7040	−0.881897
$404$	−19.7944	−0.984808
$405$	−2.65555	−0.131955
$406$	0	0
$407$	4.72869	0.234392
$408$	4.92235	0.243693
$409$	8.90571	0.440359	0.220180	−	0.975459i	$-0.429336\pi$
$409$	8.90571	0.440359	0.220180	+	0.975459i	$0.429336\pi$
$410$	−16.5591	−0.817798
$411$	12.5631	0.619693
$412$	−15.5353	−0.765368
$413$	0	0
$414$	1.87992	0.0923928
$415$	22.6078	1.10977
$416$	20.6449	1.01220
$417$	−13.9762	−0.684420
$418$	−82.3203	−4.02642
$419$	−14.4300	−0.704951	−0.352475	−	0.935821i	$-0.614660\pi$
$419$	−14.4300	−0.704951	−0.352475	+	0.935821i	$0.614660\pi$
$420$	0	0
$421$	19.5884	0.954678	0.477339	−	0.878719i	$-0.341601\pi$
$421$	19.5884	0.954678	0.477339	+	0.878719i	$0.341601\pi$
$422$	3.81283	0.185606
$423$	5.05335	0.245702
$424$	−1.61995	−0.0786716
$425$	11.5315	0.559360
$426$	−17.1603	−0.831419
$427$	0	0
$428$	−11.6138	−0.561374
$429$	17.5657	0.848078
$430$	37.9355	1.82941
$431$	5.90084	0.284233	0.142117	−	0.989850i	$-0.454609\pi$
$431$	5.90084	0.284233	0.142117	+	0.989850i	$0.454609\pi$
$432$	−4.71476	−0.226839
$433$	31.6906	1.52295	0.761477	−	0.648192i	$-0.224475\pi$
$433$	31.6906	1.52295	0.761477	+	0.648192i	$0.224475\pi$
$434$	0	0
$435$	−22.2864	−1.06855
$436$	−9.98244	−0.478072
$437$	−7.23689	−0.346187
$438$	−1.66007	−0.0793212
$439$	−21.0744	−1.00583	−0.502913	−	0.864337i	$-0.667738\pi$
$439$	−21.0744	−1.00583	−0.502913	+	0.864337i	$0.667738\pi$
$440$	−14.0740	−0.670952
$441$	0	0
$442$	−30.6698	−1.45882
$443$	−29.6673	−1.40954	−0.704768	−	0.709438i	$-0.748949\pi$
$443$	−29.6673	−1.40954	−0.704768	+	0.709438i	$0.748949\pi$
$444$	1.19887	0.0568959
$445$	−22.6562	−1.07401
$446$	5.61485	0.265871
$447$	9.93416	0.469870
$448$	0	0
$449$	9.75478	0.460357	0.230178	−	0.973148i	$-0.426069\pi$
$449$	9.75478	0.460357	0.230178	+	0.973148i	$0.426069\pi$
$450$	−3.85744	−0.181841
$451$	−20.0707	−0.945093
$452$	2.25753	0.106185
$453$	10.9587	0.514885
$454$	42.7883	2.00815
$455$	0	0
$456$	6.33869	0.296836
$457$	26.9622	1.26124	0.630619	−	0.776092i	$-0.282801\pi$
$457$	26.9622	1.26124	0.630619	+	0.776092i	$0.282801\pi$
$458$	−44.4589	−2.07743
$459$	5.61986	0.262313
$460$	4.07383	0.189943
$461$	18.7043	0.871148	0.435574	−	0.900153i	$-0.356545\pi$
$461$	18.7043	0.871148	0.435574	+	0.900153i	$0.356545\pi$
$462$	0	0
$463$	29.7340	1.38186	0.690929	−	0.722923i	$-0.257202\pi$
$463$	29.7340	1.38186	0.690929	+	0.722923i	$0.257202\pi$
$464$	−39.5682	−1.83691
$465$	16.1948	0.751017
$466$	−2.80524	−0.129950
$467$	15.4874	0.716671	0.358335	−	0.933593i	$-0.383344\pi$
$467$	15.4874	0.716671	0.358335	+	0.933593i	$0.383344\pi$
$468$	4.45345	0.205861
$469$	0	0
$470$	25.2273	1.16365
$471$	−8.04953	−0.370903
$472$	1.72127	0.0792280
$473$	45.9802	2.11417
$474$	11.1139	0.510480
$475$	14.8495	0.681342
$476$	0	0
$477$	−1.84950	−0.0846827
$478$	56.2737	2.57390
$479$	−25.0155	−1.14299	−0.571493	−	0.820607i	$-0.693635\pi$
$479$	−25.0155	−1.14299	−0.571493	+	0.820607i	$0.693635\pi$
$480$	−18.8851	−0.861983
$481$	2.26867	0.103443
$482$	−18.9857	−0.864777
$483$	0	0
$484$	39.2922	1.78601
$485$	1.77847	0.0807560
$486$	−1.87992	−0.0852747
$487$	−14.7641	−0.669024	−0.334512	−	0.942391i	$-0.608572\pi$
$487$	−14.7641	−0.669024	−0.334512	+	0.942391i	$0.608572\pi$
$488$	−12.1370	−0.549418
$489$	2.93775	0.132850
$490$	0	0
$491$	1.18432	0.0534478	0.0267239	−	0.999643i	$-0.491492\pi$
$491$	1.18432	0.0534478	0.0267239	+	0.999643i	$0.491492\pi$
$492$	−5.08856	−0.229410
$493$	47.1641	2.12417
$494$	−39.4946	−1.77695
$495$	−16.0683	−0.722217
$496$	28.7529	1.29104
$497$	0	0
$498$	16.0045	0.717180
$499$	−7.20580	−0.322576	−0.161288	−	0.986907i	$-0.551565\pi$
$499$	−7.20580	−0.322576	−0.161288	+	0.986907i	$0.551565\pi$
$500$	12.0100	0.537102
$501$	−8.45552	−0.377765
$502$	−4.86161	−0.216984
$503$	−33.8008	−1.50710	−0.753552	−	0.657389i	$-0.771661\pi$
$503$	−33.8008	−1.50710	−0.753552	+	0.657389i	$0.771661\pi$
$504$	0	0
$505$	34.2647	1.52476
$506$	11.3751	0.505685
$507$	−4.57256	−0.203075
$508$	28.9310	1.28360
$509$	31.4793	1.39530	0.697649	−	0.716440i	$-0.254230\pi$
$509$	31.4793	1.39530	0.697649	+	0.716440i	$0.254230\pi$
$510$	28.0555	1.24232
$511$	0	0
$512$	−25.2702	−1.11679
$513$	7.23689	0.319516
$514$	−2.46733	−0.108829
$515$	26.8920	1.18500
$516$	11.6574	0.513190
$517$	30.5771	1.34478
$518$	0	0
$519$	6.11837	0.268567
$520$	−6.75226	−0.296106
$521$	32.9387	1.44307	0.721536	−	0.692377i	$-0.243436\pi$
$521$	32.9387	1.44307	0.721536	+	0.692377i	$0.243436\pi$
$522$	−15.7770	−0.690541
$523$	−19.9689	−0.873180	−0.436590	−	0.899660i	$-0.643814\pi$
$523$	−19.9689	−0.873180	−0.436590	+	0.899660i	$0.643814\pi$
$524$	26.0172	1.13656
$525$	0	0
$526$	−5.47957	−0.238921
$527$	−34.2727	−1.49294
$528$	−28.5283	−1.24154
$529$	1.00000	0.0434783
$530$	−9.23306	−0.401059
$531$	1.96518	0.0852815
$532$	0	0
$533$	−9.62928	−0.417090
$534$	−16.0388	−0.694066
$535$	20.1039	0.869165
$536$	−6.81421	−0.294329
$537$	16.7365	0.722233
$538$	4.39267	0.189382
$539$	0	0
$540$	−4.07383	−0.175310
$541$	−1.03596	−0.0445395	−0.0222698	−	0.999752i	$-0.507089\pi$
$541$	−1.03596	−0.0445395	−0.0222698	+	0.999752i	$0.507089\pi$
$542$	3.95066	0.169695
$543$	−1.61304	−0.0692223
$544$	39.9660	1.71353
$545$	17.2799	0.740191
$546$	0	0
$547$	−0.720769	−0.0308179	−0.0154089	−	0.999881i	$-0.504905\pi$
$547$	−0.720769	−0.0308179	−0.0154089	+	0.999881i	$0.504905\pi$
$548$	19.2729	0.823296
$549$	−13.8569	−0.591397
$550$	−23.3408	−0.995255
$551$	60.7349	2.58739
$552$	−0.875886	−0.0372802
$553$	0	0
$554$	6.15421	0.261468
$555$	−2.07528	−0.0880909
$556$	−21.4407	−0.909289
$557$	−25.1475	−1.06554	−0.532768	−	0.846262i	$-0.678848\pi$
$557$	−25.1475	−1.06554	−0.532768	+	0.846262i	$0.678848\pi$
$558$	11.4647	0.485337
$559$	22.0598	0.933031
$560$	0	0
$561$	34.0050	1.43569
$562$	−1.63506	−0.0689708
$563$	4.35209	0.183419	0.0917093	−	0.995786i	$-0.470767\pi$
$563$	4.35209	0.183419	0.0917093	+	0.995786i	$0.470767\pi$
$564$	7.75226	0.326429
$565$	−3.90785	−0.164404
$566$	−0.774296	−0.0325461
$567$	0	0
$568$	7.99528	0.335474
$569$	23.2897	0.976354	0.488177	−	0.872745i	$-0.337662\pi$
$569$	23.2897	0.976354	0.488177	+	0.872745i	$0.337662\pi$
$570$	36.1280	1.51324
$571$	20.9490	0.876686	0.438343	−	0.898808i	$-0.355565\pi$
$571$	20.9490	0.876686	0.438343	+	0.898808i	$0.355565\pi$
$572$	26.9472	1.12672
$573$	14.9563	0.624809
$574$	0	0
$575$	−2.05192	−0.0855710
$576$	−3.93964	−0.164152
$577$	−19.2064	−0.799574	−0.399787	−	0.916608i	$-0.630916\pi$
$577$	−19.2064	−0.799574	−0.399787	+	0.916608i	$0.630916\pi$
$578$	−27.4144	−1.14029
$579$	−15.7725	−0.655481
$580$	−34.1892	−1.41963
$581$	0	0
$582$	1.25901	0.0521878
$583$	−11.1910	−0.463486
$584$	0.773456	0.0320058
$585$	−7.70906	−0.318730
$586$	9.17542	0.379033
$587$	−15.2668	−0.630127	−0.315064	−	0.949071i	$-0.602026\pi$
$587$	−15.2668	−0.630127	−0.315064	+	0.949071i	$0.602026\pi$
$588$	0	0
$589$	−44.1341	−1.81851
$590$	9.81057	0.403895
$591$	−7.28311	−0.299587
$592$	−3.68454	−0.151434
$593$	29.1310	1.19627	0.598133	−	0.801397i	$-0.295909\pi$
$593$	29.1310	1.19627	0.598133	+	0.801397i	$0.295909\pi$
$594$	−11.3751	−0.466726
$595$	0	0
$596$	15.2398	0.624247
$597$	−17.9132	−0.733137
$598$	5.45740	0.223170
$599$	33.0339	1.34973	0.674865	−	0.737942i	$-0.264202\pi$
$599$	33.0339	1.34973	0.674865	+	0.737942i	$0.264202\pi$
$600$	1.79725	0.0733723
$601$	−7.74804	−0.316049	−0.158025	−	0.987435i	$-0.550513\pi$
$601$	−7.74804	−0.316049	−0.158025	+	0.987435i	$0.550513\pi$
$602$	0	0
$603$	−7.77980	−0.316818
$604$	16.8116	0.684052
$605$	−68.0161	−2.76525
$606$	24.2567	0.985361
$607$	0.197084	0.00799939	0.00399970	−	0.999992i	$-0.498727\pi$
$607$	0.197084	0.00799939	0.00399970	+	0.999992i	$0.498727\pi$
$608$	51.4656	2.08721
$609$	0	0
$610$	−69.1763	−2.80086
$611$	14.6699	0.593481
$612$	8.62133	0.348496
$613$	−11.4624	−0.462961	−0.231481	−	0.972840i	$-0.574357\pi$
$613$	−11.4624	−0.462961	−0.231481	+	0.972840i	$0.574357\pi$
$614$	−31.0514	−1.25313
$615$	8.80845	0.355191
$616$	0	0
$617$	44.3195	1.78423	0.892117	−	0.451804i	$-0.149219\pi$
$617$	44.3195	1.78423	0.892117	+	0.451804i	$0.149219\pi$
$618$	19.0374	0.765798
$619$	9.10900	0.366122	0.183061	−	0.983102i	$-0.441399\pi$
$619$	9.10900	0.366122	0.183061	+	0.983102i	$0.441399\pi$
$620$	24.8442	0.997767
$621$	−1.00000	−0.0401286
$622$	10.3036	0.413136
$623$	0	0
$624$	−13.6870	−0.547917
$625$	−31.0492	−1.24197
$626$	27.1376	1.08464
$627$	43.7894	1.74878
$628$	−12.3486	−0.492765
$629$	4.39187	0.175115
$630$	0	0
$631$	−16.5648	−0.659433	−0.329717	−	0.944080i	$-0.606953\pi$
$631$	−16.5648	−0.659433	−0.329717	+	0.944080i	$0.606953\pi$
$632$	−5.17817	−0.205977
$633$	−2.02819	−0.0806134
$634$	32.1262	1.27589
$635$	−50.0804	−1.98738
$636$	−2.83728	−0.112506
$637$	0	0
$638$	−95.4645	−3.77947
$639$	9.12822	0.361107
$640$	18.1027	0.715573
$641$	−47.8207	−1.88880	−0.944401	−	0.328796i	$-0.893357\pi$
$641$	−47.8207	−1.88880	−0.944401	+	0.328796i	$0.893357\pi$
$642$	14.2319	0.561690
$643$	−11.9619	−0.471733	−0.235867	−	0.971785i	$-0.575793\pi$
$643$	−11.9619	−0.471733	−0.235867	+	0.971785i	$0.575793\pi$
$644$	0	0
$645$	−20.1794	−0.794562
$646$	−76.4567	−3.00815
$647$	−4.38333	−0.172327	−0.0861633	−	0.996281i	$-0.527461\pi$
$647$	−4.38333	−0.172327	−0.0861633	+	0.996281i	$0.527461\pi$
$648$	0.875886	0.0344080
$649$	11.8910	0.466763
$650$	−11.1982	−0.439228
$651$	0	0
$652$	4.50675	0.176498
$653$	−5.83797	−0.228457	−0.114229	−	0.993454i	$-0.536440\pi$
$653$	−5.83797	−0.228457	−0.114229	+	0.993454i	$0.536440\pi$
$654$	12.2328	0.478341
$655$	−45.0365	−1.75972
$656$	15.6389	0.610595
$657$	0.883056	0.0344513
$658$	0	0
$659$	−12.2904	−0.478766	−0.239383	−	0.970925i	$-0.576945\pi$
$659$	−12.2904	−0.478766	−0.239383	+	0.970925i	$0.576945\pi$
$660$	−24.6501	−0.959505
$661$	2.62499	0.102100	0.0510500	−	0.998696i	$-0.483743\pi$
$661$	2.62499	0.102100	0.0510500	+	0.998696i	$0.483743\pi$
$662$	−19.2958	−0.749954
$663$	16.3145	0.633602
$664$	−7.45679	−0.289380
$665$	0	0
$666$	−1.46914	−0.0569279
$667$	−8.39241	−0.324955
$668$	−12.9715	−0.501881
$669$	−2.98676	−0.115475
$670$	−38.8383	−1.50045
$671$	−83.8459	−3.23684
$672$	0	0
$673$	−10.0580	−0.387706	−0.193853	−	0.981031i	$-0.562099\pi$
$673$	−10.0580	−0.387706	−0.193853	+	0.981031i	$0.562099\pi$
$674$	−13.8363	−0.532953
$675$	2.05192	0.0789784
$676$	−7.01468	−0.269796
$677$	−11.1900	−0.430067	−0.215033	−	0.976607i	$-0.568986\pi$
$677$	−11.1900	−0.430067	−0.215033	+	0.976607i	$0.568986\pi$
$678$	−2.76645	−0.106245
$679$	0	0
$680$	−13.0715	−0.501270
$681$	−22.7607	−0.872193
$682$	69.3710	2.65635
$683$	−0.612543	−0.0234383	−0.0117191	−	0.999931i	$-0.503730\pi$
$683$	−0.612543	−0.0234383	−0.0117191	+	0.999931i	$0.503730\pi$
$684$	11.1020	0.424495
$685$	−33.3619	−1.27469
$686$	0	0
$687$	23.6494	0.902282
$688$	−35.8272	−1.36590
$689$	−5.36910	−0.204546
$690$	−4.99220	−0.190050
$691$	−15.4244	−0.586770	−0.293385	−	0.955994i	$-0.594782\pi$
$691$	−15.4244	−0.586770	−0.293385	+	0.955994i	$0.594782\pi$
$692$	9.38609	0.356806
$693$	0	0
$694$	16.4234	0.623424
$695$	37.1146	1.40784
$696$	7.35079	0.278631
$697$	−18.6411	−0.706082
$698$	37.5145	1.41995
$699$	1.49222	0.0564408
$700$	0	0
$701$	13.7197	0.518186	0.259093	−	0.965852i	$-0.416576\pi$
$701$	13.7197	0.518186	0.259093	+	0.965852i	$0.416576\pi$
$702$	−5.45740	−0.205976
$703$	5.65556	0.213303
$704$	−23.8382	−0.898436
$705$	−13.4194	−0.505404
$706$	−32.1370	−1.20949
$707$	0	0
$708$	3.01475	0.113301
$709$	−33.2862	−1.25009	−0.625046	−	0.780588i	$-0.714920\pi$
$709$	−33.2862	−1.25009	−0.625046	+	0.780588i	$0.714920\pi$
$710$	45.5699	1.71021
$711$	−5.91193	−0.221715
$712$	7.47275	0.280053
$713$	6.09849	0.228390
$714$	0	0
$715$	−46.6464	−1.74448
$716$	25.6752	0.959526
$717$	−29.9342	−1.11791
$718$	−66.4571	−2.48016
$719$	−3.74317	−0.139597	−0.0697984	−	0.997561i	$-0.522236\pi$
$719$	−3.74317	−0.139597	−0.0697984	+	0.997561i	$0.522236\pi$
$720$	12.5202	0.466602
$721$	0	0
$722$	−62.7376	−2.33485
$723$	10.0993	0.375595
$724$	−2.47454	−0.0919656
$725$	17.2205	0.639555
$726$	−48.1500	−1.78701
$727$	34.5883	1.28281	0.641404	−	0.767203i	$-0.278352\pi$
$727$	34.5883	1.28281	0.641404	+	0.767203i	$0.278352\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	4.40839	0.163162
$731$	42.7051	1.57950
$732$	−21.2576	−0.785703
$733$	−20.3550	−0.751831	−0.375915	−	0.926654i	$-0.622672\pi$
$733$	−20.3550	−0.751831	−0.375915	+	0.926654i	$0.622672\pi$
$734$	−28.4951	−1.05177
$735$	0	0
$736$	−7.11157	−0.262136
$737$	−47.0744	−1.73401
$738$	6.23569	0.229539
$739$	11.7571	0.432493	0.216246	−	0.976339i	$-0.430619\pi$
$739$	11.7571	0.432493	0.216246	+	0.976339i	$0.430619\pi$
$740$	−3.18366	−0.117034
$741$	21.0087	0.771775
$742$	0	0
$743$	−34.9259	−1.28131	−0.640653	−	0.767831i	$-0.721336\pi$
$743$	−34.9259	−1.28131	−0.640653	+	0.767831i	$0.721336\pi$
$744$	−5.34158	−0.195832
$745$	−26.3806	−0.966510
$746$	−71.6933	−2.62488
$747$	−8.51343	−0.311490
$748$	52.1664	1.90739
$749$	0	0
$750$	−14.7174	−0.537404
$751$	26.7121	0.974739	0.487369	−	0.873196i	$-0.337957\pi$
$751$	26.7121	0.974739	0.487369	+	0.873196i	$0.337957\pi$
$752$	−23.8253	−0.868820
$753$	2.58608	0.0942420
$754$	−45.8008	−1.66797
$755$	−29.1013	−1.05911
$756$	0	0
$757$	−38.4969	−1.39919	−0.699596	−	0.714539i	$-0.746637\pi$
$757$	−38.4969	−1.39919	−0.699596	+	0.714539i	$0.746637\pi$
$758$	62.9936	2.28803
$759$	−6.05086	−0.219632
$760$	−16.8327	−0.610585
$761$	−8.24814	−0.298995	−0.149497	−	0.988762i	$-0.547766\pi$
$761$	−8.24814	−0.298995	−0.149497	+	0.988762i	$0.547766\pi$
$762$	−35.4529	−1.28432
$763$	0	0
$764$	22.9442	0.830093
$765$	−14.9238	−0.539571
$766$	59.3233	2.14344
$767$	5.70492	0.205993
$768$	20.6946	0.746751
$769$	−23.0830	−0.832394	−0.416197	−	0.909274i	$-0.636637\pi$
$769$	−23.0830	−0.832394	−0.416197	+	0.909274i	$0.636637\pi$
$770$	0	0
$771$	1.31247	0.0472674
$772$	−24.1962	−0.870842
$773$	−12.5680	−0.452040	−0.226020	−	0.974123i	$-0.572571\pi$
$773$	−12.5680	−0.452040	−0.226020	+	0.974123i	$0.572571\pi$
$774$	−14.2854	−0.513478
$775$	−12.5136	−0.449502
$776$	−0.586596	−0.0210576
$777$	0	0
$778$	−34.7233	−1.24489
$779$	−24.0048	−0.860061
$780$	−11.8263	−0.423451
$781$	55.2336	1.97641
$782$	10.5649	0.377799
$783$	8.39241	0.299920
$784$	0	0
$785$	21.3759	0.762938
$786$	−31.8823	−1.13720
$787$	−6.38657	−0.227656	−0.113828	−	0.993500i	$-0.536311\pi$
$787$	−6.38657	−0.227656	−0.113828	+	0.993500i	$0.536311\pi$
$788$	−11.1729	−0.398018
$789$	2.91480	0.103769
$790$	−29.5135	−1.05004
$791$	0	0
$792$	5.29986	0.188322
$793$	−40.2266	−1.42849
$794$	47.1765	1.67423
$795$	4.91142	0.174190
$796$	−27.4803	−0.974012
$797$	−5.52987	−0.195878	−0.0979390	−	0.995192i	$-0.531225\pi$
$797$	−5.52987	−0.195878	−0.0979390	+	0.995192i	$0.531225\pi$
$798$	0	0
$799$	28.3991	1.00469
$800$	14.5924	0.515918
$801$	8.53165	0.301451
$802$	49.4879	1.74748
$803$	5.34324	0.188559
$804$	−11.9349	−0.420910
$805$	0	0
$806$	33.2819	1.17231
$807$	−2.33663	−0.0822534
$808$	−11.3016	−0.397590
$809$	−34.8923	−1.22675	−0.613373	−	0.789793i	$-0.710188\pi$
$809$	−34.8923	−1.22675	−0.613373	+	0.789793i	$0.710188\pi$
$810$	4.99220	0.175408
$811$	−6.11632	−0.214773	−0.107386	−	0.994217i	$-0.534248\pi$
$811$	−6.11632	−0.214773	−0.107386	+	0.994217i	$0.534248\pi$
$812$	0	0
$813$	−2.10151	−0.0737031
$814$	−8.88953	−0.311578
$815$	−7.80132	−0.273268
$816$	−26.4963	−0.927555
$817$	54.9928	1.92395
$818$	−16.7420	−0.585370
$819$	0	0
$820$	13.5129	0.471891
$821$	5.23890	0.182839	0.0914194	−	0.995812i	$-0.470860\pi$
$821$	5.23890	0.182839	0.0914194	+	0.995812i	$0.470860\pi$
$822$	−23.6176	−0.823759
$823$	35.0383	1.22136	0.610679	−	0.791878i	$-0.290896\pi$
$823$	35.0383	1.22136	0.610679	+	0.791878i	$0.290896\pi$
$824$	−8.86987	−0.308997
$825$	12.4159	0.432265
$826$	0	0
$827$	37.2117	1.29398	0.646989	−	0.762499i	$-0.276028\pi$
$827$	37.2117	1.29398	0.646989	+	0.762499i	$0.276028\pi$
$828$	−1.53408	−0.0533131
$829$	−1.90908	−0.0663052	−0.0331526	−	0.999450i	$-0.510555\pi$
$829$	−1.90908	−0.0663052	−0.0331526	+	0.999450i	$0.510555\pi$
$830$	−42.5008	−1.47522
$831$	−3.27367	−0.113562
$832$	−11.4368	−0.396500
$833$	0	0
$834$	26.2742	0.909800
$835$	22.4540	0.777053
$836$	67.1765	2.32335
$837$	−6.09849	−0.210795
$838$	27.1272	0.937092
$839$	11.5455	0.398597	0.199298	−	0.979939i	$-0.436134\pi$
$839$	11.5455	0.398597	0.199298	+	0.979939i	$0.436134\pi$
$840$	0	0
$841$	41.4325	1.42871
$842$	−36.8245	−1.26905
$843$	0.869751	0.0299558
$844$	−3.11141	−0.107099
$845$	12.1426	0.417720
$846$	−9.49987	−0.326612
$847$	0	0
$848$	8.71993	0.299444
$849$	0.411878	0.0141356
$850$	−21.6782	−0.743557
$851$	−0.781491	−0.0267892
$852$	14.0034	0.479750
$853$	3.27460	0.112120	0.0560601	−	0.998427i	$-0.482146\pi$
$853$	3.27460	0.112120	0.0560601	+	0.998427i	$0.482146\pi$
$854$	0	0
$855$	−19.2179	−0.657238
$856$	−6.63091	−0.226640
$857$	−42.6260	−1.45608	−0.728038	−	0.685537i	$-0.759567\pi$
$857$	−42.6260	−1.45608	−0.728038	+	0.685537i	$0.759567\pi$
$858$	−33.0220	−1.12735
$859$	−8.61061	−0.293790	−0.146895	−	0.989152i	$-0.546928\pi$
$859$	−8.61061	−0.293790	−0.146895	+	0.989152i	$0.546928\pi$
$860$	−30.9568	−1.05562
$861$	0	0
$862$	−11.0931	−0.377832
$863$	−30.7614	−1.04713	−0.523565	−	0.851986i	$-0.675398\pi$
$863$	−30.7614	−1.04713	−0.523565	+	0.851986i	$0.675398\pi$
$864$	7.11157	0.241941
$865$	−16.2476	−0.552436
$866$	−59.5757	−2.02446
$867$	14.5828	0.495258
$868$	0	0
$869$	−35.7722	−1.21349
$870$	41.8966	1.42043
$871$	−22.5848	−0.765257
$872$	−5.69948	−0.193009
$873$	−0.669718	−0.0226665
$874$	13.6047	0.460187
$875$	0	0
$876$	1.35468	0.0457704
$877$	12.3523	0.417107	0.208554	−	0.978011i	$-0.433124\pi$
$877$	12.3523	0.417107	0.208554	+	0.978011i	$0.433124\pi$
$878$	39.6181	1.33705
$879$	−4.88076	−0.164624
$880$	75.7582	2.55381
$881$	−2.72679	−0.0918680	−0.0459340	−	0.998944i	$-0.514626\pi$
$881$	−2.72679	−0.0918680	−0.0459340	+	0.998944i	$0.514626\pi$
$882$	0	0
$883$	19.6643	0.661755	0.330878	−	0.943674i	$-0.392655\pi$
$883$	19.6643	0.661755	0.330878	+	0.943674i	$0.392655\pi$
$884$	25.0278	0.841774
$885$	−5.21862	−0.175422
$886$	55.7720	1.87370
$887$	−11.3957	−0.382630	−0.191315	−	0.981529i	$-0.561275\pi$
$887$	−11.3957	−0.382630	−0.191315	+	0.981529i	$0.561275\pi$
$888$	0.684496	0.0229702
$889$	0	0
$890$	42.5917	1.42768
$891$	6.05086	0.202711
$892$	−4.58193	−0.153414
$893$	36.5705	1.22379
$894$	−18.6754	−0.624598
$895$	−44.4445	−1.48562
$896$	0	0
$897$	−2.90301	−0.0969285
$898$	−18.3382	−0.611953
$899$	−51.1810	−1.70698
$900$	3.14781	0.104927
$901$	−10.3939	−0.346271
$902$	37.7312	1.25631
$903$	0	0
$904$	1.28894	0.0428694
$905$	4.28351	0.142389
$906$	−20.6014	−0.684437
$907$	−27.5181	−0.913723	−0.456862	−	0.889538i	$-0.651027\pi$
$907$	−27.5181	−0.913723	−0.456862	+	0.889538i	$0.651027\pi$
$908$	−34.9169	−1.15876
$909$	−12.9031	−0.427968
$910$	0	0
$911$	−12.0557	−0.399425	−0.199712	−	0.979855i	$-0.564001\pi$
$911$	−12.0557	−0.399425	−0.199712	+	0.979855i	$0.564001\pi$
$912$	−34.1202	−1.12983
$913$	−51.5136	−1.70485
$914$	−50.6866	−1.67657
$915$	36.7975	1.21649
$916$	36.2802	1.19873
$917$	0	0
$918$	−10.5649	−0.348692
$919$	41.2883	1.36198	0.680988	−	0.732295i	$-0.261551\pi$
$919$	41.2883	1.36198	0.680988	+	0.732295i	$0.261551\pi$
$920$	2.32595	0.0766844
$921$	16.5174	0.544268
$922$	−35.1626	−1.15802
$923$	26.4993	0.872234
$924$	0	0
$925$	1.60356	0.0527246
$926$	−55.8975	−1.83690
$927$	−10.1267	−0.332606
$928$	59.6832	1.95920
$929$	15.1294	0.496379	0.248190	−	0.968711i	$-0.420164\pi$
$929$	15.1294	0.496379	0.248190	+	0.968711i	$0.420164\pi$
$930$	−30.4449	−0.998328
$931$	0	0
$932$	2.28918	0.0749847
$933$	−5.48088	−0.179436
$934$	−29.1150	−0.952671
$935$	−90.3017	−2.95318
$936$	2.54270	0.0831108
$937$	−20.4861	−0.669253	−0.334626	−	0.942351i	$-0.608610\pi$
$937$	−20.4861	−0.669253	−0.334626	+	0.942351i	$0.608610\pi$
$938$	0	0
$939$	−14.4355	−0.471086
$940$	−20.5865	−0.671456
$941$	10.3514	0.337446	0.168723	−	0.985664i	$-0.446036\pi$
$941$	10.3514	0.337446	0.168723	+	0.985664i	$0.446036\pi$
$942$	15.1324	0.493041
$943$	3.31700	0.108016
$944$	−9.26534	−0.301561
$945$	0	0
$946$	−86.4389	−2.81037
$947$	30.6264	0.995223	0.497612	−	0.867400i	$-0.334210\pi$
$947$	30.6264	0.995223	0.497612	+	0.867400i	$0.334210\pi$
$948$	−9.06939	−0.294560
$949$	2.56352	0.0832153
$950$	−27.9158	−0.905709
$951$	−17.0892	−0.554154
$952$	0	0
$953$	−5.88206	−0.190539	−0.0952693	−	0.995452i	$-0.530371\pi$
$953$	−5.88206	−0.190539	−0.0952693	+	0.995452i	$0.530371\pi$
$954$	3.47690	0.112569
$955$	−39.7172	−1.28522
$956$	−45.9215	−1.48521
$957$	50.7813	1.64152
$958$	47.0269	1.51937
$959$	0	0
$960$	10.4619	0.337656
$961$	6.19163	0.199730
$962$	−4.26491	−0.137506
$963$	−7.57052	−0.243957
$964$	15.4931	0.498999
$965$	41.8845	1.34831
$966$	0	0
$967$	−24.6570	−0.792914	−0.396457	−	0.918053i	$-0.629760\pi$
$967$	−24.6570	−0.792914	−0.396457	+	0.918053i	$0.629760\pi$
$968$	22.4339	0.721054
$969$	40.6703	1.30652
$970$	−3.34337	−0.107349
$971$	−24.8492	−0.797448	−0.398724	−	0.917071i	$-0.630547\pi$
$971$	−24.8492	−0.797448	−0.398724	+	0.917071i	$0.630547\pi$
$972$	1.53408	0.0492057
$973$	0	0
$974$	27.7552	0.889335
$975$	5.95673	0.190768
$976$	65.3317	2.09122
$977$	−26.8392	−0.858661	−0.429330	−	0.903148i	$-0.641250\pi$
$977$	−26.8392	−0.858661	−0.429330	+	0.903148i	$0.641250\pi$
$978$	−5.52272	−0.176597
$979$	51.6238	1.64990
$980$	0	0
$981$	−6.50711	−0.207756
$982$	−2.22643	−0.0710483
$983$	17.8380	0.568945	0.284472	−	0.958684i	$-0.408182\pi$
$983$	17.8380	0.568945	0.284472	+	0.958684i	$0.408182\pi$
$984$	−2.90532	−0.0926181
$985$	19.3406	0.616243
$986$	−88.6646	−2.82366
$987$	0	0
$988$	32.2291	1.02534
$989$	−7.59896	−0.241633
$990$	30.2071	0.960044
$991$	−4.69389	−0.149106	−0.0745531	−	0.997217i	$-0.523753\pi$
$991$	−4.69389	−0.149106	−0.0745531	+	0.997217i	$0.523753\pi$
$992$	−43.3699	−1.37699
$993$	10.2642	0.325725
$994$	0	0
$995$	47.5692	1.50805
$996$	−13.0603	−0.413832
$997$	49.4684	1.56668	0.783340	−	0.621594i	$-0.213515\pi$
$997$	49.4684	1.56668	0.783340	+	0.621594i	$0.213515\pi$
$998$	13.5463	0.428801
$999$	0.781491	0.0247253

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bf.1.2		8
7.2	even	3		483.2.i.g.277.7	✓	16
7.4	even	3		483.2.i.g.415.7	yes	16
7.6	odd	2		3381.2.a.be.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.g.277.7	✓	16	7.2	even	3
483.2.i.g.415.7	yes	16	7.4	even	3
3381.2.a.be.1.2		8	7.6	odd	2
3381.2.a.bf.1.2		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)

\(f(q)\)	\(=\)	\(q-1.87992 q^{2} +1.00000 q^{3} +1.53408 q^{4} -2.65555 q^{5} -1.87992 q^{6} +0.875886 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.87992 q^{2} +1.00000 q^{3} +1.53408 q^{4} -2.65555 q^{5} -1.87992 q^{6} +0.875886 q^{8} +1.00000 q^{9} +4.99220 q^{10} +6.05086 q^{11} +1.53408 q^{12} +2.90301 q^{13} -2.65555 q^{15} -4.71476 q^{16} +5.61986 q^{17} -1.87992 q^{18} +7.23689 q^{19} -4.07383 q^{20} -11.3751 q^{22} -1.00000 q^{23} +0.875886 q^{24} +2.05192 q^{25} -5.45740 q^{26} +1.00000 q^{27} +8.39241 q^{29} +4.99220 q^{30} -6.09849 q^{31} +7.11157 q^{32} +6.05086 q^{33} -10.5649 q^{34} +1.53408 q^{36} +0.781491 q^{37} -13.6047 q^{38} +2.90301 q^{39} -2.32595 q^{40} -3.31700 q^{41} +7.59896 q^{43} +9.28251 q^{44} -2.65555 q^{45} +1.87992 q^{46} +5.05335 q^{47} -4.71476 q^{48} -3.85744 q^{50} +5.61986 q^{51} +4.45345 q^{52} -1.84950 q^{53} -1.87992 q^{54} -16.0683 q^{55} +7.23689 q^{57} -15.7770 q^{58} +1.96518 q^{59} -4.07383 q^{60} -13.8569 q^{61} +11.4647 q^{62} -3.93964 q^{64} -7.70906 q^{65} -11.3751 q^{66} -7.77980 q^{67} +8.62133 q^{68} -1.00000 q^{69} +9.12822 q^{71} +0.875886 q^{72} +0.883056 q^{73} -1.46914 q^{74} +2.05192 q^{75} +11.1020 q^{76} -5.45740 q^{78} -5.91193 q^{79} +12.5202 q^{80} +1.00000 q^{81} +6.23569 q^{82} -8.51343 q^{83} -14.9238 q^{85} -14.2854 q^{86} +8.39241 q^{87} +5.29986 q^{88} +8.53165 q^{89} +4.99220 q^{90} -1.53408 q^{92} -6.09849 q^{93} -9.49987 q^{94} -19.2179 q^{95} +7.11157 q^{96} -0.669718 q^{97} +6.05086 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + 8 q^{3} + 15 q^{4} + 5 q^{5} + q^{6} + 9 q^{8} + 8 q^{9}+O(q^{10}) \) 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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