LMFDB - Embedded newform 3381.2.a.bd.1.6

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:	$1$
Dimension:	$6$
Coefficient field:	6.6.7997584.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 7x^{4} + 5x^{3} + 12x^{2} - 4x - 2 $ x^6 - x^5 - 7x^4 + 5x^3 + 12x^2 - 4x - 2
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			1.6
Root			$-2.04340$ 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)

$f(q)$	$=$	$q+2.04340 q^{2} +1.00000 q^{3} +2.17548 q^{4} -1.94349 q^{5} +2.04340 q^{6} +0.358585 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.04340 q^{2} +1.00000 q^{3} +2.17548 q^{4} -1.94349 q^{5} +2.04340 q^{6} +0.358585 q^{8} +1.00000 q^{9} -3.97133 q^{10} -5.66529 q^{11} +2.17548 q^{12} +6.17812 q^{13} -1.94349 q^{15} -3.61824 q^{16} -7.23463 q^{17} +2.04340 q^{18} -0.790220 q^{19} -4.22803 q^{20} -11.5765 q^{22} -1.00000 q^{23} +0.358585 q^{24} -1.22285 q^{25} +12.6244 q^{26} +1.00000 q^{27} -5.34085 q^{29} -3.97133 q^{30} -0.911316 q^{31} -8.11067 q^{32} -5.66529 q^{33} -14.7832 q^{34} +2.17548 q^{36} -0.973320 q^{37} -1.61473 q^{38} +6.17812 q^{39} -0.696907 q^{40} +1.51843 q^{41} -2.70342 q^{43} -12.3247 q^{44} -1.94349 q^{45} -2.04340 q^{46} +1.52839 q^{47} -3.61824 q^{48} -2.49877 q^{50} -7.23463 q^{51} +13.4404 q^{52} -8.95803 q^{53} +2.04340 q^{54} +11.0104 q^{55} -0.790220 q^{57} -10.9135 q^{58} +10.8931 q^{59} -4.22803 q^{60} +6.31775 q^{61} -1.86218 q^{62} -9.33688 q^{64} -12.0071 q^{65} -11.5765 q^{66} +7.31833 q^{67} -15.7388 q^{68} -1.00000 q^{69} -8.75692 q^{71} +0.358585 q^{72} +0.875251 q^{73} -1.98888 q^{74} -1.22285 q^{75} -1.71911 q^{76} +12.6244 q^{78} +5.96655 q^{79} +7.03200 q^{80} +1.00000 q^{81} +3.10277 q^{82} +0.273554 q^{83} +14.0604 q^{85} -5.52417 q^{86} -5.34085 q^{87} -2.03149 q^{88} -17.6270 q^{89} -3.97133 q^{90} -2.17548 q^{92} -0.911316 q^{93} +3.12312 q^{94} +1.53578 q^{95} -8.11067 q^{96} -3.09620 q^{97} -5.66529 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} + 6 q^{3} + 3 q^{4} - 3 q^{5} - q^{6} - 3 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q - q^2 + 6 * q^3 + 3 * q^4 - 3 * q^5 - q^6 - 3 * q^8 + 6 * q^9	$ 6 q - q^{2} + 6 q^{3} + 3 q^{4} - 3 q^{5} - q^{6} - 3 q^{8} + 6 q^{9} + 3 q^{10} - 14 q^{11} + 3 q^{12} - 3 q^{15} - 7 q^{16} - 15 q^{17} - q^{18} + q^{19} - 17 q^{20} - 6 q^{22} - 6 q^{23} - 3 q^{24} + 9 q^{25} + 15 q^{26} + 6 q^{27} - 6 q^{29} + 3 q^{30} + 11 q^{31} + 3 q^{32} - 14 q^{33} - 15 q^{34} + 3 q^{36} - 5 q^{37} - 14 q^{38} + 17 q^{40} - 18 q^{41} - 37 q^{43} - 10 q^{44} - 3 q^{45} + q^{46} - 3 q^{47} - 7 q^{48} - 30 q^{50} - 15 q^{51} + 7 q^{52} - 15 q^{53} - q^{54} + 2 q^{55} + q^{57} + 4 q^{58} + 2 q^{59} - 17 q^{60} + 12 q^{61} - 36 q^{62} - 23 q^{64} - 17 q^{65} - 6 q^{66} - 10 q^{67} + q^{68} - 6 q^{69} - 21 q^{71} - 3 q^{72} + 8 q^{73} - 16 q^{74} + 9 q^{75} - 18 q^{76} + 15 q^{78} - 17 q^{79} - 3 q^{80} + 6 q^{81} + 48 q^{82} - 12 q^{83} - 13 q^{85} + 22 q^{86} - 6 q^{87} - 2 q^{88} - 18 q^{89} + 3 q^{90} - 3 q^{92} + 11 q^{93} - 3 q^{94} - 16 q^{95} + 3 q^{96} + 2 q^{97} - 14 q^{99}+O(q^{100}) $ 6 * q - q^2 + 6 * q^3 + 3 * q^4 - 3 * q^5 - q^6 - 3 * q^8 + 6 * q^9 + 3 * q^10 - 14 * q^11 + 3 * q^12 - 3 * q^15 - 7 * q^16 - 15 * q^17 - q^18 + q^19 - 17 * q^20 - 6 * q^22 - 6 * q^23 - 3 * q^24 + 9 * q^25 + 15 * q^26 + 6 * q^27 - 6 * q^29 + 3 * q^30 + 11 * q^31 + 3 * q^32 - 14 * q^33 - 15 * q^34 + 3 * q^36 - 5 * q^37 - 14 * q^38 + 17 * q^40 - 18 * q^41 - 37 * q^43 - 10 * q^44 - 3 * q^45 + q^46 - 3 * q^47 - 7 * q^48 - 30 * q^50 - 15 * q^51 + 7 * q^52 - 15 * q^53 - q^54 + 2 * q^55 + q^57 + 4 * q^58 + 2 * q^59 - 17 * q^60 + 12 * q^61 - 36 * q^62 - 23 * q^64 - 17 * q^65 - 6 * q^66 - 10 * q^67 + q^68 - 6 * q^69 - 21 * q^71 - 3 * q^72 + 8 * q^73 - 16 * q^74 + 9 * q^75 - 18 * q^76 + 15 * q^78 - 17 * q^79 - 3 * q^80 + 6 * q^81 + 48 * q^82 - 12 * q^83 - 13 * q^85 + 22 * q^86 - 6 * q^87 - 2 * q^88 - 18 * q^89 + 3 * q^90 - 3 * q^92 + 11 * q^93 - 3 * q^94 - 16 * q^95 + 3 * q^96 + 2 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.04340	1.44490	0.722451	−	0.691422i	$-0.243015\pi$
$2$	2.04340	1.44490	0.722451	+	0.691422i	$0.243015\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.17548	1.08774
$5$	−1.94349	−0.869155	−0.434577	−	0.900634i	$-0.643102\pi$
$5$	−1.94349	−0.869155	−0.434577	+	0.900634i	$0.643102\pi$
$6$	2.04340	0.834215
$7$	0	0
$7$	0	0
$8$	0.358585	0.126779
$9$	1.00000	0.333333
$10$	−3.97133	−1.25584
$11$	−5.66529	−1.70815	−0.854074	−	0.520151i	$-0.825876\pi$
$11$	−5.66529	−1.70815	−0.854074	+	0.520151i	$0.825876\pi$
$12$	2.17548	0.628008
$13$	6.17812	1.71350	0.856751	−	0.515730i	$-0.172479\pi$
$13$	6.17812	1.71350	0.856751	+	0.515730i	$0.172479\pi$
$14$	0	0
$15$	−1.94349	−0.501807
$16$	−3.61824	−0.904559
$17$	−7.23463	−1.75466	−0.877328	−	0.479892i	$-0.840676\pi$
$17$	−7.23463	−1.75466	−0.877328	+	0.479892i	$0.840676\pi$
$18$	2.04340	0.481634
$19$	−0.790220	−0.181289	−0.0906444	−	0.995883i	$-0.528893\pi$
$19$	−0.790220	−0.181289	−0.0906444	+	0.995883i	$0.528893\pi$
$20$	−4.22803	−0.945417
$21$	0	0
$22$	−11.5765	−2.46811
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	0.358585	0.0731960
$25$	−1.22285	−0.244570
$26$	12.6244	2.47584
$27$	1.00000	0.192450
$28$	0	0
$29$	−5.34085	−0.991770	−0.495885	−	0.868388i	$-0.665156\pi$
$29$	−5.34085	−0.991770	−0.495885	+	0.868388i	$0.665156\pi$
$30$	−3.97133	−0.725062
$31$	−0.911316	−0.163677	−0.0818386	−	0.996646i	$-0.526079\pi$
$31$	−0.911316	−0.163677	−0.0818386	+	0.996646i	$0.526079\pi$
$32$	−8.11067	−1.43378
$33$	−5.66529	−0.986200
$34$	−14.7832	−2.53531
$35$	0	0
$36$	2.17548	0.362581
$37$	−0.973320	−0.160013	−0.0800064	−	0.996794i	$-0.525494\pi$
$37$	−0.973320	−0.160013	−0.0800064	+	0.996794i	$0.525494\pi$
$38$	−1.61473	−0.261945
$39$	6.17812	0.989291
$40$	−0.696907	−0.110191
$41$	1.51843	0.237140	0.118570	−	0.992946i	$-0.462169\pi$
$41$	1.51843	0.237140	0.118570	+	0.992946i	$0.462169\pi$
$42$	0	0
$43$	−2.70342	−0.412268	−0.206134	−	0.978524i	$-0.566088\pi$
$43$	−2.70342	−0.412268	−0.206134	+	0.978524i	$0.566088\pi$
$44$	−12.3247	−1.85803
$45$	−1.94349	−0.289718
$46$	−2.04340	−0.301283
$47$	1.52839	0.222939	0.111470	−	0.993768i	$-0.464444\pi$
$47$	1.52839	0.222939	0.111470	+	0.993768i	$0.464444\pi$
$48$	−3.61824	−0.522247
$49$	0	0
$50$	−2.49877	−0.353379
$51$	−7.23463	−1.01305
$52$	13.4404	1.86385
$53$	−8.95803	−1.23048	−0.615240	−	0.788340i	$-0.710941\pi$
$53$	−8.95803	−1.23048	−0.615240	+	0.788340i	$0.710941\pi$
$54$	2.04340	0.278072
$55$	11.0104	1.48465
$56$	0	0
$57$	−0.790220	−0.104667
$58$	−10.9135	−1.43301
$59$	10.8931	1.41816	0.709081	−	0.705127i	$-0.249110\pi$
$59$	10.8931	1.41816	0.709081	+	0.705127i	$0.249110\pi$
$60$	−4.22803	−0.545837
$61$	6.31775	0.808905	0.404452	−	0.914559i	$-0.367462\pi$
$61$	6.31775	0.808905	0.404452	+	0.914559i	$0.367462\pi$
$62$	−1.86218	−0.236497
$63$	0	0
$64$	−9.33688	−1.16711
$65$	−12.0071	−1.48930
$66$	−11.5765	−1.42496
$67$	7.31833	0.894077	0.447038	−	0.894515i	$-0.352479\pi$
$67$	7.31833	0.894077	0.447038	+	0.894515i	$0.352479\pi$
$68$	−15.7388	−1.90861
$69$	−1.00000	−0.120386
$70$	0	0
$71$	−8.75692	−1.03926	−0.519628	−	0.854393i	$-0.673929\pi$
$71$	−8.75692	−1.03926	−0.519628	+	0.854393i	$0.673929\pi$
$72$	0.358585	0.0422597
$73$	0.875251	0.102440	0.0512202	−	0.998687i	$-0.483689\pi$
$73$	0.875251	0.102440	0.0512202	+	0.998687i	$0.483689\pi$
$74$	−1.98888	−0.231203
$75$	−1.22285	−0.141202
$76$	−1.71911	−0.197196
$77$	0	0
$78$	12.6244	1.42943
$79$	5.96655	0.671289	0.335644	−	0.941989i	$-0.391046\pi$
$79$	5.96655	0.671289	0.335644	+	0.941989i	$0.391046\pi$
$80$	7.03200	0.786202
$81$	1.00000	0.111111
$82$	3.10277	0.342644
$83$	0.273554	0.0300265	0.0150132	−	0.999887i	$-0.495221\pi$
$83$	0.273554	0.0300265	0.0150132	+	0.999887i	$0.495221\pi$
$84$	0	0
$85$	14.0604	1.52507
$86$	−5.52417	−0.595686
$87$	−5.34085	−0.572599
$88$	−2.03149	−0.216558
$89$	−17.6270	−1.86846	−0.934229	−	0.356672i	$-0.883911\pi$
$89$	−17.6270	−1.86846	−0.934229	+	0.356672i	$0.883911\pi$
$90$	−3.97133	−0.418615
$91$	0	0
$92$	−2.17548	−0.226810
$93$	−0.911316	−0.0944991
$94$	3.12312	0.322125
$95$	1.53578	0.157568
$96$	−8.11067	−0.827792
$97$	−3.09620	−0.314372	−0.157186	−	0.987569i	$-0.550242\pi$
$97$	−3.09620	−0.314372	−0.157186	+	0.987569i	$0.550242\pi$
$98$	0	0
$99$	−5.66529	−0.569383
$100$	−2.66029	−0.266029
$101$	−13.4276	−1.33610	−0.668050	−	0.744116i	$-0.732871\pi$
$101$	−13.4276	−1.33610	−0.668050	+	0.744116i	$0.732871\pi$
$102$	−14.7832	−1.46376
$103$	−6.33653	−0.624357	−0.312178	−	0.950023i	$-0.601059\pi$
$103$	−6.33653	−0.624357	−0.312178	+	0.950023i	$0.601059\pi$
$104$	2.21538	0.217236
$105$	0	0
$106$	−18.3049	−1.77792
$107$	15.9609	1.54299	0.771497	−	0.636232i	$-0.219508\pi$
$107$	15.9609	1.54299	0.771497	+	0.636232i	$0.219508\pi$
$108$	2.17548	0.209336
$109$	−0.0470715	−0.00450863	−0.00225431	−	0.999997i	$-0.500718\pi$
$109$	−0.0470715	−0.00450863	−0.00225431	+	0.999997i	$0.500718\pi$
$110$	22.4987	2.14517
$111$	−0.973320	−0.0923835
$112$	0	0
$113$	−6.27141	−0.589965	−0.294982	−	0.955503i	$-0.595314\pi$
$113$	−6.27141	−0.589965	−0.294982	+	0.955503i	$0.595314\pi$
$114$	−1.61473	−0.151234
$115$	1.94349	0.181231
$116$	−11.6189	−1.07879
$117$	6.17812	0.571167
$118$	22.2590	2.04911
$119$	0	0
$120$	−0.696907	−0.0636186
$121$	21.0955	1.91777
$122$	12.9097	1.16879
$123$	1.51843	0.136913
$124$	−1.98255	−0.178039
$125$	12.0940	1.08172
$126$	0	0
$127$	−12.4325	−1.10320	−0.551601	−	0.834108i	$-0.685983\pi$
$127$	−12.4325	−1.10320	−0.551601	+	0.834108i	$0.685983\pi$
$128$	−2.85764	−0.252582
$129$	−2.70342	−0.238023
$130$	−24.5353	−2.15189
$131$	3.31098	0.289281	0.144641	−	0.989484i	$-0.453797\pi$
$131$	3.31098	0.289281	0.144641	+	0.989484i	$0.453797\pi$
$132$	−12.3247	−1.07273
$133$	0	0
$134$	14.9543	1.29185
$135$	−1.94349	−0.167269
$136$	−2.59423	−0.222454
$137$	−13.0442	−1.11444	−0.557220	−	0.830365i	$-0.688132\pi$
$137$	−13.0442	−1.11444	−0.557220	+	0.830365i	$0.688132\pi$
$138$	−2.04340	−0.173946
$139$	11.3674	0.964169	0.482084	−	0.876125i	$-0.339880\pi$
$139$	11.3674	0.964169	0.482084	+	0.876125i	$0.339880\pi$
$140$	0	0
$141$	1.52839	0.128714
$142$	−17.8939	−1.50162
$143$	−35.0008	−2.92692
$144$	−3.61824	−0.301520
$145$	10.3799	0.862002
$146$	1.78849	0.148016
$147$	0	0
$148$	−2.11744	−0.174053
$149$	16.2060	1.32765	0.663824	−	0.747889i	$-0.268932\pi$
$149$	16.2060	1.32765	0.663824	+	0.747889i	$0.268932\pi$
$150$	−2.49877	−0.204024
$151$	−12.9337	−1.05253	−0.526266	−	0.850320i	$-0.676408\pi$
$151$	−12.9337	−1.05253	−0.526266	+	0.850320i	$0.676408\pi$
$152$	−0.283361	−0.0229836
$153$	−7.23463	−0.584885
$154$	0	0
$155$	1.77113	0.142261
$156$	13.4404	1.07609
$157$	9.73442	0.776892	0.388446	−	0.921472i	$-0.373012\pi$
$157$	9.73442	0.776892	0.388446	+	0.921472i	$0.373012\pi$
$158$	12.1920	0.969947
$159$	−8.95803	−0.710418
$160$	15.7630	1.24618
$161$	0	0
$162$	2.04340	0.160545
$163$	−24.0922	−1.88705	−0.943525	−	0.331300i	$-0.892513\pi$
$163$	−24.0922	−1.88705	−0.943525	+	0.331300i	$0.892513\pi$
$164$	3.30333	0.257947
$165$	11.0104	0.857161
$166$	0.558981	0.0433853
$167$	12.2582	0.948566	0.474283	−	0.880373i	$-0.342707\pi$
$167$	12.2582	0.948566	0.474283	+	0.880373i	$0.342707\pi$
$168$	0	0
$169$	25.1692	1.93609
$170$	28.7311	2.20357
$171$	−0.790220	−0.0604296
$172$	−5.88125	−0.448441
$173$	5.88796	0.447653	0.223826	−	0.974629i	$-0.428145\pi$
$173$	5.88796	0.447653	0.223826	+	0.974629i	$0.428145\pi$
$174$	−10.9135	−0.827349
$175$	0	0
$176$	20.4984	1.54512
$177$	10.8931	0.818777
$178$	−36.0190	−2.69974
$179$	−16.9732	−1.26864	−0.634319	−	0.773071i	$-0.718719\pi$
$179$	−16.9732	−1.26864	−0.634319	+	0.773071i	$0.718719\pi$
$180$	−4.22803	−0.315139
$181$	−19.1241	−1.42149	−0.710743	−	0.703452i	$-0.751641\pi$
$181$	−19.1241	−1.42149	−0.710743	+	0.703452i	$0.751641\pi$
$182$	0	0
$183$	6.31775	0.467021
$184$	−0.358585	−0.0264353
$185$	1.89164	0.139076
$186$	−1.86218	−0.136542
$187$	40.9863	2.99721
$188$	3.32500	0.242500
$189$	0	0
$190$	3.13822	0.227670
$191$	−20.6871	−1.49686	−0.748432	−	0.663212i	$-0.769193\pi$
$191$	−20.6871	−1.49686	−0.748432	+	0.663212i	$0.769193\pi$
$192$	−9.33688	−0.673832
$193$	2.22901	0.160447	0.0802237	−	0.996777i	$-0.474437\pi$
$193$	2.22901	0.160447	0.0802237	+	0.996777i	$0.474437\pi$
$194$	−6.32678	−0.454237
$195$	−12.0071	−0.859847
$196$	0	0
$197$	19.3710	1.38013	0.690064	−	0.723748i	$-0.257582\pi$
$197$	19.3710	1.38013	0.690064	+	0.723748i	$0.257582\pi$
$198$	−11.5765	−0.822703
$199$	−24.6840	−1.74980	−0.874902	−	0.484300i	$-0.839074\pi$
$199$	−24.6840	−1.74980	−0.874902	+	0.484300i	$0.839074\pi$
$200$	−0.438496	−0.0310063
$201$	7.31833	0.516195
$202$	−27.4381	−1.93054
$203$	0	0
$204$	−15.7388	−1.10194
$205$	−2.95106	−0.206111
$206$	−12.9481	−0.902135
$207$	−1.00000	−0.0695048
$208$	−22.3539	−1.54996
$209$	4.47682	0.309668
$210$	0	0
$211$	9.90378	0.681804	0.340902	−	0.940099i	$-0.389267\pi$
$211$	9.90378	0.681804	0.340902	+	0.940099i	$0.389267\pi$
$212$	−19.4881	−1.33845
$213$	−8.75692	−0.600014
$214$	32.6144	2.22948
$215$	5.25407	0.358324
$216$	0.358585	0.0243987
$217$	0	0
$218$	−0.0961859	−0.00651453
$219$	0.875251	0.0591440
$220$	23.9530	1.61491
$221$	−44.6964	−3.00661
$222$	−1.98888	−0.133485
$223$	−2.21461	−0.148301	−0.0741507	−	0.997247i	$-0.523625\pi$
$223$	−2.21461	−0.148301	−0.0741507	+	0.997247i	$0.523625\pi$
$224$	0	0
$225$	−1.22285	−0.0815232
$226$	−12.8150	−0.852441
$227$	5.58033	0.370380	0.185190	−	0.982703i	$-0.440710\pi$
$227$	5.58033	0.370380	0.185190	+	0.982703i	$0.440710\pi$
$228$	−1.71911	−0.113851
$229$	−6.97859	−0.461158	−0.230579	−	0.973054i	$-0.574062\pi$
$229$	−6.97859	−0.461158	−0.230579	+	0.973054i	$0.574062\pi$
$230$	3.97133	0.261862
$231$	0	0
$232$	−1.91515	−0.125736
$233$	24.4042	1.59878	0.799388	−	0.600816i	$-0.205157\pi$
$233$	24.4042	1.59878	0.799388	+	0.600816i	$0.205157\pi$
$234$	12.6244	0.825281
$235$	−2.97042	−0.193769
$236$	23.6978	1.54260
$237$	5.96655	0.387569
$238$	0	0
$239$	0.424159	0.0274365	0.0137183	−	0.999906i	$-0.495633\pi$
$239$	0.424159	0.0274365	0.0137183	+	0.999906i	$0.495633\pi$
$240$	7.03200	0.453914
$241$	16.3125	1.05078	0.525389	−	0.850862i	$-0.323920\pi$
$241$	16.3125	1.05078	0.525389	+	0.850862i	$0.323920\pi$
$242$	43.1065	2.77099
$243$	1.00000	0.0641500
$244$	13.7442	0.879880
$245$	0	0
$246$	3.10277	0.197825
$247$	−4.88207	−0.310639
$248$	−0.326785	−0.0207508
$249$	0.273554	0.0173358
$250$	24.7130	1.56299
$251$	15.9242	1.00513	0.502564	−	0.864540i	$-0.332390\pi$
$251$	15.9242	1.00513	0.502564	+	0.864540i	$0.332390\pi$
$252$	0	0
$253$	5.66529	0.356174
$254$	−25.4045	−1.59402
$255$	14.0604	0.880498
$256$	12.8345	0.802154
$257$	30.1569	1.88114	0.940569	−	0.339602i	$-0.110292\pi$
$257$	30.1569	1.88114	0.940569	+	0.339602i	$0.110292\pi$
$258$	−5.52417	−0.343920
$259$	0	0
$260$	−26.1213	−1.61997
$261$	−5.34085	−0.330590
$262$	6.76565	0.417983
$263$	15.1656	0.935153	0.467576	−	0.883953i	$-0.345127\pi$
$263$	15.1656	0.935153	0.467576	+	0.883953i	$0.345127\pi$
$264$	−2.03149	−0.125030
$265$	17.4098	1.06948
$266$	0	0
$267$	−17.6270	−1.07876
$268$	15.9209	0.972525
$269$	−0.470833	−0.0287072	−0.0143536	−	0.999897i	$-0.504569\pi$
$269$	−0.470833	−0.0287072	−0.0143536	+	0.999897i	$0.504569\pi$
$270$	−3.97133	−0.241687
$271$	7.28736	0.442676	0.221338	−	0.975197i	$-0.428958\pi$
$271$	7.28736	0.442676	0.221338	+	0.975197i	$0.428958\pi$
$272$	26.1766	1.58719
$273$	0	0
$274$	−26.6545	−1.61026
$275$	6.92779	0.417761
$276$	−2.17548	−0.130949
$277$	2.96021	0.177862	0.0889310	−	0.996038i	$-0.471655\pi$
$277$	2.96021	0.177862	0.0889310	+	0.996038i	$0.471655\pi$
$278$	23.2281	1.39313
$279$	−0.911316	−0.0545591
$280$	0	0
$281$	7.16141	0.427214	0.213607	−	0.976920i	$-0.431479\pi$
$281$	7.16141	0.427214	0.213607	+	0.976920i	$0.431479\pi$
$282$	3.12312	0.185979
$283$	20.0106	1.18951	0.594753	−	0.803908i	$-0.297250\pi$
$283$	20.0106	1.18951	0.594753	+	0.803908i	$0.297250\pi$
$284$	−19.0505	−1.13044
$285$	1.53578	0.0909720
$286$	−71.5207	−4.22911
$287$	0	0
$288$	−8.11067	−0.477926
$289$	35.3399	2.07882
$290$	21.2103	1.24551
$291$	−3.09620	−0.181503
$292$	1.90409	0.111429
$293$	−6.27910	−0.366829	−0.183414	−	0.983036i	$-0.558715\pi$
$293$	−6.27910	−0.366829	−0.183414	+	0.983036i	$0.558715\pi$
$294$	0	0
$295$	−21.1707	−1.23260
$296$	−0.349019	−0.0202863
$297$	−5.66529	−0.328733
$298$	33.1154	1.91832
$299$	−6.17812	−0.357290
$300$	−2.66029	−0.153592
$301$	0	0
$302$	−26.4288	−1.52081
$303$	−13.4276	−0.771398
$304$	2.85920	0.163986
$305$	−12.2785	−0.703064
$306$	−14.7832	−0.845102
$307$	−25.1923	−1.43780	−0.718900	−	0.695114i	$-0.755354\pi$
$307$	−25.1923	−1.43780	−0.718900	+	0.695114i	$0.755354\pi$
$308$	0	0
$309$	−6.33653	−0.360473
$310$	3.61913	0.205553
$311$	−11.9221	−0.676038	−0.338019	−	0.941139i	$-0.609757\pi$
$311$	−11.9221	−0.676038	−0.338019	+	0.941139i	$0.609757\pi$
$312$	2.21538	0.125421
$313$	−10.0423	−0.567625	−0.283812	−	0.958880i	$-0.591599\pi$
$313$	−10.0423	−0.567625	−0.283812	+	0.958880i	$0.591599\pi$
$314$	19.8913	1.12253
$315$	0	0
$316$	12.9801	0.730189
$317$	−8.86210	−0.497745	−0.248872	−	0.968536i	$-0.580060\pi$
$317$	−8.86210	−0.497745	−0.248872	+	0.968536i	$0.580060\pi$
$318$	−18.3049	−1.02649
$319$	30.2574	1.69409
$320$	18.1461	1.01440
$321$	15.9609	0.890849
$322$	0	0
$323$	5.71695	0.318099
$324$	2.17548	0.120860
$325$	−7.55490	−0.419071
$326$	−49.2301	−2.72660
$327$	−0.0470715	−0.00260306
$328$	0.544489	0.0300644
$329$	0	0
$330$	22.4987	1.23851
$331$	−22.8992	−1.25865	−0.629327	−	0.777141i	$-0.716669\pi$
$331$	−22.8992	−1.25865	−0.629327	+	0.777141i	$0.716669\pi$
$332$	0.595113	0.0326611
$333$	−0.973320	−0.0533376
$334$	25.0483	1.37058
$335$	−14.2231	−0.777091
$336$	0	0
$337$	12.2517	0.667392	0.333696	−	0.942681i	$-0.391704\pi$
$337$	12.2517	0.667392	0.333696	+	0.942681i	$0.391704\pi$
$338$	51.4307	2.79746
$339$	−6.27141	−0.340616
$340$	30.5882	1.65888
$341$	5.16287	0.279585
$342$	−1.61473	−0.0873149
$343$	0	0
$344$	−0.969407	−0.0522669
$345$	1.94349	0.104634
$346$	12.0314	0.646815
$347$	−6.45833	−0.346701	−0.173351	−	0.984860i	$-0.555459\pi$
$347$	−6.45833	−0.346701	−0.173351	+	0.984860i	$0.555459\pi$
$348$	−11.6189	−0.622840
$349$	−20.5047	−1.09759	−0.548795	−	0.835957i	$-0.684913\pi$
$349$	−20.5047	−1.09759	−0.548795	+	0.835957i	$0.684913\pi$
$350$	0	0
$351$	6.17812	0.329764
$352$	45.9493	2.44911
$353$	−14.5113	−0.772357	−0.386178	−	0.922424i	$-0.626205\pi$
$353$	−14.5113	−0.772357	−0.386178	+	0.922424i	$0.626205\pi$
$354$	22.2590	1.18305
$355$	17.0190	0.903274
$356$	−38.3473	−2.03240
$357$	0	0
$358$	−34.6831	−1.83306
$359$	4.67780	0.246885	0.123442	−	0.992352i	$-0.460607\pi$
$359$	4.67780	0.246885	0.123442	+	0.992352i	$0.460607\pi$
$360$	−0.696907	−0.0367302
$361$	−18.3756	−0.967134
$362$	−39.0782	−2.05391
$363$	21.0955	1.10723
$364$	0	0
$365$	−1.70104	−0.0890366
$366$	12.9097	0.674800
$367$	28.0660	1.46503	0.732515	−	0.680750i	$-0.238346\pi$
$367$	28.0660	1.46503	0.732515	+	0.680750i	$0.238346\pi$
$368$	3.61824	0.188614
$369$	1.51843	0.0790465
$370$	3.86537	0.200951
$371$	0	0
$372$	−1.98255	−0.102791
$373$	14.6303	0.757527	0.378763	−	0.925494i	$-0.376349\pi$
$373$	14.6303	0.757527	0.378763	+	0.925494i	$0.376349\pi$
$374$	83.7514	4.33068
$375$	12.0940	0.624534
$376$	0.548060	0.0282640
$377$	−32.9964	−1.69940
$378$	0	0
$379$	−2.44369	−0.125524	−0.0627620	−	0.998029i	$-0.519991\pi$
$379$	−2.44369	−0.125524	−0.0627620	+	0.998029i	$0.519991\pi$
$380$	3.34107	0.171393
$381$	−12.4325	−0.636934
$382$	−42.2720	−2.16282
$383$	−30.7792	−1.57274	−0.786371	−	0.617755i	$-0.788042\pi$
$383$	−30.7792	−1.57274	−0.786371	+	0.617755i	$0.788042\pi$
$384$	−2.85764	−0.145828
$385$	0	0
$386$	4.55475	0.231831
$387$	−2.70342	−0.137423
$388$	−6.73575	−0.341956
$389$	12.1855	0.617830	0.308915	−	0.951090i	$-0.400034\pi$
$389$	12.1855	0.617830	0.308915	+	0.951090i	$0.400034\pi$
$390$	−24.5353	−1.24239
$391$	7.23463	0.365871
$392$	0	0
$393$	3.31098	0.167017
$394$	39.5827	1.99415
$395$	−11.5959	−0.583454
$396$	−12.3247	−0.619342
$397$	−21.3044	−1.06924	−0.534618	−	0.845094i	$-0.679545\pi$
$397$	−21.3044	−1.06924	−0.534618	+	0.845094i	$0.679545\pi$
$398$	−50.4394	−2.52830
$399$	0	0
$400$	4.42455	0.221228
$401$	7.40280	0.369678	0.184839	−	0.982769i	$-0.440824\pi$
$401$	7.40280	0.369678	0.184839	+	0.982769i	$0.440824\pi$
$402$	14.9543	0.745852
$403$	−5.63022	−0.280461
$404$	−29.2116	−1.45333
$405$	−1.94349	−0.0965728
$406$	0	0
$407$	5.51414	0.273326
$408$	−2.59423	−0.128434
$409$	−26.4674	−1.30873	−0.654364	−	0.756180i	$-0.727064\pi$
$409$	−26.4674	−1.30873	−0.654364	+	0.756180i	$0.727064\pi$
$410$	−6.03020	−0.297810
$411$	−13.0442	−0.643423
$412$	−13.7850	−0.679140
$413$	0	0
$414$	−2.04340	−0.100428
$415$	−0.531650	−0.0260977
$416$	−50.1087	−2.45678
$417$	11.3674	0.556663
$418$	9.14794	0.447440
$419$	30.7294	1.50123	0.750614	−	0.660741i	$-0.229758\pi$
$419$	30.7294	1.50123	0.750614	+	0.660741i	$0.229758\pi$
$420$	0	0
$421$	2.65571	0.129432	0.0647158	−	0.997904i	$-0.479386\pi$
$421$	2.65571	0.129432	0.0647158	+	0.997904i	$0.479386\pi$
$422$	20.2374	0.985141
$423$	1.52839	0.0743130
$424$	−3.21222	−0.155999
$425$	8.84685	0.429135
$426$	−17.8939	−0.866962
$427$	0	0
$428$	34.7226	1.67838
$429$	−35.0008	−1.68986
$430$	10.7362	0.517744
$431$	21.2541	1.02377	0.511887	−	0.859053i	$-0.328947\pi$
$431$	21.2541	1.02377	0.511887	+	0.859053i	$0.328947\pi$
$432$	−3.61824	−0.174082
$433$	16.8730	0.810864	0.405432	−	0.914125i	$-0.367121\pi$
$433$	16.8730	0.810864	0.405432	+	0.914125i	$0.367121\pi$
$434$	0	0
$435$	10.3799	0.497677
$436$	−0.102403	−0.00490423
$437$	0.790220	0.0378013
$438$	1.78849	0.0854573
$439$	11.0905	0.529320	0.264660	−	0.964342i	$-0.414740\pi$
$439$	11.0905	0.529320	0.264660	+	0.964342i	$0.414740\pi$
$440$	3.94818	0.188222
$441$	0	0
$442$	−91.3327	−4.34425
$443$	−12.7742	−0.606920	−0.303460	−	0.952844i	$-0.598142\pi$
$443$	−12.7742	−0.606920	−0.303460	+	0.952844i	$0.598142\pi$
$444$	−2.11744	−0.100489
$445$	34.2579	1.62398
$446$	−4.52534	−0.214281
$447$	16.2060	0.766518
$448$	0	0
$449$	38.7094	1.82681	0.913405	−	0.407052i	$-0.133443\pi$
$449$	38.7094	1.82681	0.913405	+	0.407052i	$0.133443\pi$
$450$	−2.49877	−0.117793
$451$	−8.60237	−0.405070
$452$	−13.6434	−0.641729
$453$	−12.9337	−0.607680
$454$	11.4029	0.535162
$455$	0	0
$456$	−0.283361	−0.0132696
$457$	−36.2907	−1.69761	−0.848803	−	0.528709i	$-0.822676\pi$
$457$	−36.2907	−1.69761	−0.848803	+	0.528709i	$0.822676\pi$
$458$	−14.2601	−0.666329
$459$	−7.23463	−0.337684
$460$	4.22803	0.197133
$461$	3.70588	0.172600	0.0862999	−	0.996269i	$-0.472496\pi$
$461$	3.70588	0.172600	0.0862999	+	0.996269i	$0.472496\pi$
$462$	0	0
$463$	−29.9926	−1.39387	−0.696937	−	0.717132i	$-0.745454\pi$
$463$	−29.9926	−1.39387	−0.696937	+	0.717132i	$0.745454\pi$
$464$	19.3244	0.897115
$465$	1.77113	0.0821343
$466$	49.8676	2.31007
$467$	−28.0845	−1.29959	−0.649797	−	0.760108i	$-0.725146\pi$
$467$	−28.0845	−1.29959	−0.649797	+	0.760108i	$0.725146\pi$
$468$	13.4404	0.621283
$469$	0	0
$470$	−6.06975	−0.279977
$471$	9.73442	0.448539
$472$	3.90611	0.179793
$473$	15.3156	0.704214
$474$	12.1920	0.559999
$475$	0.966319	0.0443377
$476$	0	0
$477$	−8.95803	−0.410160
$478$	0.866726	0.0396431
$479$	12.8184	0.585688	0.292844	−	0.956160i	$-0.405398\pi$
$479$	12.8184	0.585688	0.292844	+	0.956160i	$0.405398\pi$
$480$	15.7630	0.719480
$481$	−6.01329	−0.274182
$482$	33.3329	1.51827
$483$	0	0
$484$	45.8929	2.08604
$485$	6.01744	0.273238
$486$	2.04340	0.0926905
$487$	9.33744	0.423120	0.211560	−	0.977365i	$-0.432146\pi$
$487$	9.33744	0.423120	0.211560	+	0.977365i	$0.432146\pi$
$488$	2.26545	0.102552
$489$	−24.0922	−1.08949
$490$	0	0
$491$	−1.98455	−0.0895616	−0.0447808	−	0.998997i	$-0.514259\pi$
$491$	−1.98455	−0.0895616	−0.0447808	+	0.998997i	$0.514259\pi$
$492$	3.30333	0.148926
$493$	38.6391	1.74022
$494$	−9.97603	−0.448843
$495$	11.0104	0.494882
$496$	3.29736	0.148056
$497$	0	0
$498$	0.558981	0.0250485
$499$	−40.8742	−1.82978	−0.914890	−	0.403702i	$-0.867723\pi$
$499$	−40.8742	−1.82978	−0.914890	+	0.403702i	$0.867723\pi$
$500$	26.3104	1.17664
$501$	12.2582	0.547655
$502$	32.5396	1.45231
$503$	2.08575	0.0929989	0.0464994	−	0.998918i	$-0.485193\pi$
$503$	2.08575	0.0929989	0.0464994	+	0.998918i	$0.485193\pi$
$504$	0	0
$505$	26.0965	1.16128
$506$	11.5765	0.514636
$507$	25.1692	1.11780
$508$	−27.0466	−1.20000
$509$	17.4199	0.772123	0.386062	−	0.922473i	$-0.373835\pi$
$509$	17.4199	0.772123	0.386062	+	0.922473i	$0.373835\pi$
$510$	28.7311	1.27223
$511$	0	0
$512$	31.9412	1.41162
$513$	−0.790220	−0.0348890
$514$	61.6227	2.71806
$515$	12.3150	0.542663
$516$	−5.88125	−0.258907
$517$	−8.65879	−0.380813
$518$	0	0
$519$	5.88796	0.258453
$520$	−4.30558	−0.188812
$521$	13.2487	0.580438	0.290219	−	0.956960i	$-0.406272\pi$
$521$	13.2487	0.580438	0.290219	+	0.956960i	$0.406272\pi$
$522$	−10.9135	−0.477670
$523$	−6.49239	−0.283892	−0.141946	−	0.989874i	$-0.545336\pi$
$523$	−6.49239	−0.283892	−0.141946	+	0.989874i	$0.545336\pi$
$524$	7.20298	0.314664
$525$	0	0
$526$	30.9894	1.35120
$527$	6.59303	0.287197
$528$	20.4984	0.892076
$529$	1.00000	0.0434783
$530$	35.5753	1.54529
$531$	10.8931	0.472721
$532$	0	0
$533$	9.38107	0.406339
$534$	−36.0190	−1.55870
$535$	−31.0198	−1.34110
$536$	2.62425	0.113350
$537$	−16.9732	−0.732449
$538$	−0.962101	−0.0414791
$539$	0	0
$540$	−4.22803	−0.181946
$541$	17.0384	0.732536	0.366268	−	0.930509i	$-0.380635\pi$
$541$	17.0384	0.732536	0.366268	+	0.930509i	$0.380635\pi$
$542$	14.8910	0.639623
$543$	−19.1241	−0.820695
$544$	58.6777	2.51579
$545$	0.0914829	0.00391870
$546$	0	0
$547$	−29.4820	−1.26056	−0.630280	−	0.776368i	$-0.717060\pi$
$547$	−29.4820	−1.26056	−0.630280	+	0.776368i	$0.717060\pi$
$548$	−28.3774	−1.21222
$549$	6.31775	0.269635
$550$	14.1562	0.603624
$551$	4.22044	0.179797
$552$	−0.358585	−0.0152624
$553$	0	0
$554$	6.04890	0.256993
$555$	1.89164	0.0802956
$556$	24.7296	1.04877
$557$	−10.2316	−0.433526	−0.216763	−	0.976224i	$-0.569550\pi$
$557$	−10.2316	−0.433526	−0.216763	+	0.976224i	$0.569550\pi$
$558$	−1.86218	−0.0788325
$559$	−16.7020	−0.706421
$560$	0	0
$561$	40.9863	1.73044
$562$	14.6336	0.617282
$563$	−23.2599	−0.980288	−0.490144	−	0.871641i	$-0.663056\pi$
$563$	−23.2599	−0.980288	−0.490144	+	0.871641i	$0.663056\pi$
$564$	3.32500	0.140008
$565$	12.1884	0.512771
$566$	40.8897	1.71872
$567$	0	0
$568$	−3.14010	−0.131756
$569$	19.6402	0.823362	0.411681	−	0.911328i	$-0.364942\pi$
$569$	19.6402	0.823362	0.411681	+	0.911328i	$0.364942\pi$
$570$	3.13822	0.131446
$571$	−41.5761	−1.73991	−0.869953	−	0.493134i	$-0.835851\pi$
$571$	−41.5761	−1.73991	−0.869953	+	0.493134i	$0.835851\pi$
$572$	−76.1438	−3.18373
$573$	−20.6871	−0.864215
$574$	0	0
$575$	1.22285	0.0509963
$576$	−9.33688	−0.389037
$577$	1.41768	0.0590187	0.0295093	−	0.999565i	$-0.490606\pi$
$577$	1.41768	0.0590187	0.0295093	+	0.999565i	$0.490606\pi$
$578$	72.2135	3.00369
$579$	2.22901	0.0926344
$580$	22.5813	0.937636
$581$	0	0
$582$	−6.32678	−0.262254
$583$	50.7499	2.10184
$584$	0.313852	0.0129873
$585$	−12.0071	−0.496433
$586$	−12.8307	−0.530032
$587$	−28.5127	−1.17685	−0.588423	−	0.808553i	$-0.700251\pi$
$587$	−28.5127	−1.17685	−0.588423	+	0.808553i	$0.700251\pi$
$588$	0	0
$589$	0.720140	0.0296728
$590$	−43.2601	−1.78099
$591$	19.3710	0.796817
$592$	3.52170	0.144741
$593$	8.25387	0.338946	0.169473	−	0.985535i	$-0.445794\pi$
$593$	8.25387	0.338946	0.169473	+	0.985535i	$0.445794\pi$
$594$	−11.5765	−0.474988
$595$	0	0
$596$	35.2559	1.44414
$597$	−24.6840	−1.01025
$598$	−12.6244	−0.516249
$599$	25.2430	1.03140	0.515700	−	0.856769i	$-0.327532\pi$
$599$	25.2430	1.03140	0.515700	+	0.856769i	$0.327532\pi$
$600$	−0.438496	−0.0179015
$601$	−19.9481	−0.813702	−0.406851	−	0.913495i	$-0.633373\pi$
$601$	−19.9481	−0.813702	−0.406851	+	0.913495i	$0.633373\pi$
$602$	0	0
$603$	7.31833	0.298026
$604$	−28.1371	−1.14488
$605$	−40.9989	−1.66684
$606$	−27.4381	−1.11459
$607$	−28.0616	−1.13899	−0.569493	−	0.821996i	$-0.692861\pi$
$607$	−28.0616	−1.13899	−0.569493	+	0.821996i	$0.692861\pi$
$608$	6.40921	0.259928
$609$	0	0
$610$	−25.0898	−1.01586
$611$	9.44260	0.382007
$612$	−15.7388	−0.636204
$613$	−34.9865	−1.41309	−0.706545	−	0.707668i	$-0.749747\pi$
$613$	−34.9865	−1.41309	−0.706545	+	0.707668i	$0.749747\pi$
$614$	−51.4779	−2.07748
$615$	−2.95106	−0.118998
$616$	0	0
$617$	−30.9952	−1.24782	−0.623911	−	0.781496i	$-0.714457\pi$
$617$	−30.9952	−1.24782	−0.623911	+	0.781496i	$0.714457\pi$
$618$	−12.9481	−0.520848
$619$	−31.2143	−1.25461	−0.627305	−	0.778774i	$-0.715842\pi$
$619$	−31.2143	−1.25461	−0.627305	+	0.778774i	$0.715842\pi$
$620$	3.85307	0.154743
$621$	−1.00000	−0.0401286
$622$	−24.3615	−0.976809
$623$	0	0
$624$	−22.3539	−0.894872
$625$	−17.3904	−0.695616
$626$	−20.5205	−0.820162
$627$	4.47682	0.178787
$628$	21.1771	0.845058
$629$	7.04161	0.280767
$630$	0	0
$631$	19.1609	0.762782	0.381391	−	0.924414i	$-0.375445\pi$
$631$	19.1609	0.762782	0.381391	+	0.924414i	$0.375445\pi$
$632$	2.13952	0.0851054
$633$	9.90378	0.393640
$634$	−18.1088	−0.719193
$635$	24.1624	0.958854
$636$	−19.4881	−0.772752
$637$	0	0
$638$	61.8281	2.44780
$639$	−8.75692	−0.346418
$640$	5.55380	0.219533
$641$	16.1599	0.638278	0.319139	−	0.947708i	$-0.396606\pi$
$641$	16.1599	0.638278	0.319139	+	0.947708i	$0.396606\pi$
$642$	32.6144	1.28719
$643$	44.7116	1.76325	0.881627	−	0.471947i	$-0.156449\pi$
$643$	44.7116	1.76325	0.881627	+	0.471947i	$0.156449\pi$
$644$	0	0
$645$	5.25407	0.206879
$646$	11.6820	0.459623
$647$	−7.95077	−0.312577	−0.156288	−	0.987711i	$-0.549953\pi$
$647$	−7.95077	−0.312577	−0.156288	+	0.987711i	$0.549953\pi$
$648$	0.358585	0.0140866
$649$	−61.7126	−2.42243
$650$	−15.4377	−0.605516
$651$	0	0
$652$	−52.4123	−2.05262
$653$	−42.7024	−1.67107	−0.835537	−	0.549434i	$-0.814843\pi$
$653$	−42.7024	−1.67107	−0.835537	+	0.549434i	$0.814843\pi$
$654$	−0.0961859	−0.00376117
$655$	−6.43485	−0.251430
$656$	−5.49405	−0.214507
$657$	0.875251	0.0341468
$658$	0	0
$659$	−31.2099	−1.21577	−0.607883	−	0.794027i	$-0.707981\pi$
$659$	−31.2099	−1.21577	−0.607883	+	0.794027i	$0.707981\pi$
$660$	23.9530	0.932370
$661$	−5.89998	−0.229483	−0.114741	−	0.993395i	$-0.536604\pi$
$661$	−5.89998	−0.229483	−0.114741	+	0.993395i	$0.536604\pi$
$662$	−46.7922	−1.81863
$663$	−44.6964	−1.73586
$664$	0.0980926	0.00380673
$665$	0	0
$666$	−1.98888	−0.0770677
$667$	5.34085	0.206798
$668$	26.6675	1.03180
$669$	−2.21461	−0.0856218
$670$	−29.0635	−1.12282
$671$	−35.7919	−1.38173
$672$	0	0
$673$	−6.61159	−0.254858	−0.127429	−	0.991848i	$-0.540673\pi$
$673$	−6.61159	−0.254858	−0.127429	+	0.991848i	$0.540673\pi$
$674$	25.0351	0.964316
$675$	−1.22285	−0.0470675
$676$	54.7551	2.10597
$677$	−3.71673	−0.142845	−0.0714227	−	0.997446i	$-0.522754\pi$
$677$	−3.71673	−0.142845	−0.0714227	+	0.997446i	$0.522754\pi$
$678$	−12.8150	−0.492157
$679$	0	0
$680$	5.04187	0.193347
$681$	5.58033	0.213839
$682$	10.5498	0.403973
$683$	29.5669	1.13135	0.565674	−	0.824629i	$-0.308616\pi$
$683$	29.5669	1.13135	0.565674	+	0.824629i	$0.308616\pi$
$684$	−1.71911	−0.0657318
$685$	25.3513	0.968622
$686$	0	0
$687$	−6.97859	−0.266250
$688$	9.78161	0.372920
$689$	−55.3438	−2.10843
$690$	3.97133	0.151186
$691$	−0.603892	−0.0229731	−0.0114866	−	0.999934i	$-0.503656\pi$
$691$	−0.603892	−0.0229731	−0.0114866	+	0.999934i	$0.503656\pi$
$692$	12.8092	0.486931
$693$	0	0
$694$	−13.1969	−0.500949
$695$	−22.0924	−0.838012
$696$	−1.91515	−0.0725936
$697$	−10.9853	−0.416098
$698$	−41.8992	−1.58591
$699$	24.4042	0.923053
$700$	0	0
$701$	8.15835	0.308136	0.154068	−	0.988060i	$-0.450762\pi$
$701$	8.15835	0.308136	0.154068	+	0.988060i	$0.450762\pi$
$702$	12.6244	0.476476
$703$	0.769137	0.0290085
$704$	52.8961	1.99360
$705$	−2.97042	−0.111872
$706$	−29.6523	−1.11598
$707$	0	0
$708$	23.6978	0.890618
$709$	−24.2270	−0.909863	−0.454932	−	0.890526i	$-0.650336\pi$
$709$	−24.2270	−0.909863	−0.454932	+	0.890526i	$0.650336\pi$
$710$	34.7766	1.30514
$711$	5.96655	0.223763
$712$	−6.32079	−0.236882
$713$	0.911316	0.0341290
$714$	0	0
$715$	68.0238	2.54394
$716$	−36.9250	−1.37995
$717$	0.424159	0.0158405
$718$	9.55861	0.356724
$719$	−2.58504	−0.0964058	−0.0482029	−	0.998838i	$-0.515349\pi$
$719$	−2.58504	−0.0964058	−0.0482029	+	0.998838i	$0.515349\pi$
$720$	7.03200	0.262067
$721$	0	0
$722$	−37.5486	−1.39741
$723$	16.3125	0.606667
$724$	−41.6042	−1.54621
$725$	6.53105	0.242557
$726$	43.1065	1.59983
$727$	1.39574	0.0517650	0.0258825	−	0.999665i	$-0.491760\pi$
$727$	1.39574	0.0517650	0.0258825	+	0.999665i	$0.491760\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−3.47591	−0.128649
$731$	19.5582	0.723388
$732$	13.7442	0.507999
$733$	−20.4900	−0.756815	−0.378408	−	0.925639i	$-0.623528\pi$
$733$	−20.4900	−0.756815	−0.378408	+	0.925639i	$0.623528\pi$
$734$	57.3500	2.11683
$735$	0	0
$736$	8.11067	0.298963
$737$	−41.4605	−1.52722
$738$	3.10277	0.114215
$739$	−47.4816	−1.74664	−0.873320	−	0.487148i	$-0.838037\pi$
$739$	−47.4816	−1.74664	−0.873320	+	0.487148i	$0.838037\pi$
$740$	4.11523	0.151279
$741$	−4.88207	−0.179347
$742$	0	0
$743$	−41.4450	−1.52047	−0.760235	−	0.649648i	$-0.774916\pi$
$743$	−41.4450	−1.52047	−0.760235	+	0.649648i	$0.774916\pi$
$744$	−0.326785	−0.0119805
$745$	−31.4962	−1.15393
$746$	29.8955	1.09455
$747$	0.273554	0.0100088
$748$	89.1650	3.26020
$749$	0	0
$750$	24.7130	0.902390
$751$	11.5886	0.422872	0.211436	−	0.977392i	$-0.432186\pi$
$751$	11.5886	0.422872	0.211436	+	0.977392i	$0.432186\pi$
$752$	−5.53009	−0.201662
$753$	15.9242	0.580311
$754$	−67.4248	−2.45547
$755$	25.1366	0.914814
$756$	0	0
$757$	−11.3101	−0.411073	−0.205536	−	0.978649i	$-0.565894\pi$
$757$	−11.3101	−0.411073	−0.205536	+	0.978649i	$0.565894\pi$
$758$	−4.99344	−0.181370
$759$	5.66529	0.205637
$760$	0.550710	0.0199763
$761$	21.8257	0.791183	0.395591	−	0.918427i	$-0.370540\pi$
$761$	21.8257	0.791183	0.395591	+	0.918427i	$0.370540\pi$
$762$	−25.4045	−0.920308
$763$	0	0
$764$	−45.0044	−1.62820
$765$	14.0604	0.508356
$766$	−62.8941	−2.27246
$767$	67.2990	2.43002
$768$	12.8345	0.463124
$769$	24.1550	0.871052	0.435526	−	0.900176i	$-0.356562\pi$
$769$	24.1550	0.871052	0.435526	+	0.900176i	$0.356562\pi$
$770$	0	0
$771$	30.1569	1.08608
$772$	4.84917	0.174525
$773$	−14.7390	−0.530124	−0.265062	−	0.964231i	$-0.585392\pi$
$773$	−14.7390	−0.530124	−0.265062	+	0.964231i	$0.585392\pi$
$774$	−5.52417	−0.198562
$775$	1.11440	0.0400305
$776$	−1.11025	−0.0398558
$777$	0	0
$778$	24.8999	0.892703
$779$	−1.19990	−0.0429908
$780$	−26.1213	−0.935292
$781$	49.6105	1.77520
$782$	14.7832	0.528648
$783$	−5.34085	−0.190866
$784$	0	0
$785$	−18.9188	−0.675239
$786$	6.76565	0.241323
$787$	−23.8103	−0.848746	−0.424373	−	0.905487i	$-0.639505\pi$
$787$	−23.8103	−0.848746	−0.424373	+	0.905487i	$0.639505\pi$
$788$	42.1414	1.50122
$789$	15.1656	0.539911
$790$	−23.6951	−0.843034
$791$	0	0
$792$	−2.03149	−0.0721859
$793$	39.0318	1.38606
$794$	−43.5334	−1.54494
$795$	17.4098	0.617464
$796$	−53.6997	−1.90334
$797$	−19.8938	−0.704674	−0.352337	−	0.935873i	$-0.614613\pi$
$797$	−19.8938	−0.704674	−0.352337	+	0.935873i	$0.614613\pi$
$798$	0	0
$799$	−11.0574	−0.391181
$800$	9.91812	0.350659
$801$	−17.6270	−0.622820
$802$	15.1269	0.534149
$803$	−4.95855	−0.174983
$804$	15.9209	0.561488
$805$	0	0
$806$	−11.5048	−0.405239
$807$	−0.470833	−0.0165741
$808$	−4.81496	−0.169390
$809$	−47.9127	−1.68452	−0.842260	−	0.539071i	$-0.818775\pi$
$809$	−47.9127	−1.68452	−0.842260	+	0.539071i	$0.818775\pi$
$810$	−3.97133	−0.139538
$811$	48.3843	1.69900	0.849500	−	0.527588i	$-0.176903\pi$
$811$	48.3843	1.69900	0.849500	+	0.527588i	$0.176903\pi$
$812$	0	0
$813$	7.28736	0.255579
$814$	11.2676	0.394929
$815$	46.8230	1.64014
$816$	26.1766	0.916364
$817$	2.13629	0.0747395
$818$	−54.0835	−1.89098
$819$	0	0
$820$	−6.41999	−0.224196
$821$	−8.16367	−0.284914	−0.142457	−	0.989801i	$-0.545500\pi$
$821$	−8.16367	−0.284914	−0.142457	+	0.989801i	$0.545500\pi$
$822$	−26.6545	−0.929683
$823$	−33.2648	−1.15954	−0.579769	−	0.814781i	$-0.696857\pi$
$823$	−33.2648	−1.15954	−0.579769	+	0.814781i	$0.696857\pi$
$824$	−2.27219	−0.0791554
$825$	6.92779	0.241195
$826$	0	0
$827$	31.2711	1.08740	0.543701	−	0.839279i	$-0.317023\pi$
$827$	31.2711	1.08740	0.543701	+	0.839279i	$0.317023\pi$
$828$	−2.17548	−0.0756033
$829$	17.8076	0.618484	0.309242	−	0.950983i	$-0.399925\pi$
$829$	17.8076	0.618484	0.309242	+	0.950983i	$0.399925\pi$
$830$	−1.08637	−0.0377086
$831$	2.96021	0.102689
$832$	−57.6844	−1.99985
$833$	0	0
$834$	23.2281	0.804324
$835$	−23.8236	−0.824451
$836$	9.73926	0.336839
$837$	−0.911316	−0.0314997
$838$	62.7924	2.16913
$839$	−29.7947	−1.02863	−0.514313	−	0.857603i	$-0.671953\pi$
$839$	−29.7947	−1.02863	−0.514313	+	0.857603i	$0.671953\pi$
$840$	0	0
$841$	−0.475352	−0.0163915
$842$	5.42669	0.187016
$843$	7.16141	0.246652
$844$	21.5455	0.741628
$845$	−48.9160	−1.68276
$846$	3.12312	0.107375
$847$	0	0
$848$	32.4123	1.11304
$849$	20.0106	0.686762
$850$	18.0777	0.620059
$851$	0.973320	0.0333650
$852$	−19.0505	−0.652661
$853$	43.0902	1.47538	0.737690	−	0.675140i	$-0.235917\pi$
$853$	43.0902	1.47538	0.737690	+	0.675140i	$0.235917\pi$
$854$	0	0
$855$	1.53578	0.0525227
$856$	5.72333	0.195620
$857$	−48.0096	−1.63998	−0.819988	−	0.572381i	$-0.806020\pi$
$857$	−48.0096	−1.63998	−0.819988	+	0.572381i	$0.806020\pi$
$858$	−71.5207	−2.44168
$859$	−11.7497	−0.400896	−0.200448	−	0.979704i	$-0.564240\pi$
$859$	−11.7497	−0.400896	−0.200448	+	0.979704i	$0.564240\pi$
$860$	11.4301	0.389765
$861$	0	0
$862$	43.4306	1.47925
$863$	−5.60759	−0.190885	−0.0954424	−	0.995435i	$-0.530427\pi$
$863$	−5.60759	−0.190885	−0.0954424	+	0.995435i	$0.530427\pi$
$864$	−8.11067	−0.275931
$865$	−11.4432	−0.389080
$866$	34.4783	1.17162
$867$	35.3399	1.20021
$868$	0	0
$869$	−33.8022	−1.14666
$870$	21.2103	0.719095
$871$	45.2135	1.53200
$872$	−0.0168791	−0.000571600 0
$873$	−3.09620	−0.104791
$874$	1.61473	0.0546192
$875$	0	0
$876$	1.90409	0.0643334
$877$	16.7638	0.566075	0.283037	−	0.959109i	$-0.408658\pi$
$877$	16.7638	0.566075	0.283037	+	0.959109i	$0.408658\pi$
$878$	22.6623	0.764816
$879$	−6.27910	−0.211789
$880$	−39.8383	−1.34295
$881$	39.4239	1.32823	0.664113	−	0.747632i	$-0.268809\pi$
$881$	39.4239	1.32823	0.664113	+	0.747632i	$0.268809\pi$
$882$	0	0
$883$	−17.4928	−0.588679	−0.294339	−	0.955701i	$-0.595100\pi$
$883$	−17.4928	−0.588679	−0.294339	+	0.955701i	$0.595100\pi$
$884$	−97.2364	−3.27041
$885$	−21.1707	−0.711644
$886$	−26.1028	−0.876940
$887$	−2.75212	−0.0924073	−0.0462037	−	0.998932i	$-0.514712\pi$
$887$	−2.75212	−0.0924073	−0.0462037	+	0.998932i	$0.514712\pi$
$888$	−0.349019	−0.0117123
$889$	0	0
$890$	70.0026	2.34649
$891$	−5.66529	−0.189794
$892$	−4.81785	−0.161314
$893$	−1.20777	−0.0404164
$894$	33.1154	1.10754
$895$	32.9873	1.10264
$896$	0	0
$897$	−6.17812	−0.206281
$898$	79.0988	2.63956
$899$	4.86720	0.162330
$900$	−2.66029	−0.0886763
$901$	64.8081	2.15907
$902$	−17.5781	−0.585286
$903$	0	0
$904$	−2.24884	−0.0747952
$905$	37.1675	1.23549
$906$	−26.4288	−0.878038
$907$	−29.1794	−0.968886	−0.484443	−	0.874823i	$-0.660978\pi$
$907$	−29.1794	−0.968886	−0.484443	+	0.874823i	$0.660978\pi$
$908$	12.1399	0.402878
$909$	−13.4276	−0.445367
$910$	0	0
$911$	−6.24020	−0.206747	−0.103374	−	0.994643i	$-0.532964\pi$
$911$	−6.24020	−0.206747	−0.103374	+	0.994643i	$0.532964\pi$
$912$	2.85920	0.0946776
$913$	−1.54976	−0.0512897
$914$	−74.1564	−2.45288
$915$	−12.2785	−0.405914
$916$	−15.1818	−0.501621
$917$	0	0
$918$	−14.7832	−0.487920
$919$	−36.4022	−1.20080	−0.600398	−	0.799701i	$-0.704991\pi$
$919$	−36.4022	−1.20080	−0.600398	+	0.799701i	$0.704991\pi$
$920$	0.696907	0.0229763
$921$	−25.1923	−0.830114
$922$	7.57259	0.249390
$923$	−54.1013	−1.78077
$924$	0	0
$925$	1.19022	0.0391343
$926$	−61.2869	−2.01401
$927$	−6.33653	−0.208119
$928$	43.3179	1.42198
$929$	0.0513202	0.00168376	0.000841881	−	1.00000i	$-0.499732\pi$
$929$	0.0513202	0.00168376	0.000841881		1.00000i	$0.499732\pi$
$930$	3.61913	0.118676
$931$	0	0
$932$	53.0911	1.73906
$933$	−11.9221	−0.390311
$934$	−57.3878	−1.87779
$935$	−79.6564	−2.60504
$936$	2.21538	0.0724121
$937$	8.46139	0.276421	0.138211	−	0.990403i	$-0.455865\pi$
$937$	8.46139	0.276421	0.138211	+	0.990403i	$0.455865\pi$
$938$	0	0
$939$	−10.0423	−0.327718
$940$	−6.46210	−0.210770
$941$	6.94143	0.226284	0.113142	−	0.993579i	$-0.463908\pi$
$941$	6.94143	0.226284	0.113142	+	0.993579i	$0.463908\pi$
$942$	19.8913	0.648094
$943$	−1.51843	−0.0494470
$944$	−39.4139	−1.28281
$945$	0	0
$946$	31.2960	1.01752
$947$	6.05341	0.196709	0.0983547	−	0.995151i	$-0.468642\pi$
$947$	6.05341	0.196709	0.0983547	+	0.995151i	$0.468642\pi$
$948$	12.9801	0.421575
$949$	5.40740	0.175532
$950$	1.97458	0.0640637
$951$	−8.86210	−0.287373
$952$	0	0
$953$	−52.7135	−1.70756	−0.853778	−	0.520637i	$-0.825695\pi$
$953$	−52.7135	−1.70756	−0.853778	+	0.520637i	$0.825695\pi$
$954$	−18.3049	−0.592641
$955$	40.2051	1.30101
$956$	0.922751	0.0298439
$957$	30.2574	0.978084
$958$	26.1931	0.846262
$959$	0	0
$960$	18.1461	0.585664
$961$	−30.1695	−0.973210
$962$	−12.2876	−0.396167
$963$	15.9609	0.514332
$964$	35.4875	1.14298
$965$	−4.33205	−0.139454
$966$	0	0
$967$	−16.9757	−0.545900	−0.272950	−	0.962028i	$-0.587999\pi$
$967$	−16.9757	−0.545900	−0.272950	+	0.962028i	$0.587999\pi$
$968$	7.56454	0.243133
$969$	5.71695	0.183655
$970$	12.2960	0.394802
$971$	29.0124	0.931051	0.465525	−	0.885034i	$-0.345865\pi$
$971$	29.0124	0.931051	0.465525	+	0.885034i	$0.345865\pi$
$972$	2.17548	0.0697787
$973$	0	0
$974$	19.0801	0.611367
$975$	−7.55490	−0.241951
$976$	−22.8591	−0.731702
$977$	−32.1866	−1.02974	−0.514871	−	0.857268i	$-0.672160\pi$
$977$	−32.1866	−1.02974	−0.514871	+	0.857268i	$0.672160\pi$
$978$	−49.2301	−1.57421
$979$	99.8621	3.19161
$980$	0	0
$981$	−0.0470715	−0.00150288
$982$	−4.05523	−0.129408
$983$	−6.03861	−0.192602	−0.0963009	−	0.995352i	$-0.530701\pi$
$983$	−6.03861	−0.192602	−0.0963009	+	0.995352i	$0.530701\pi$
$984$	0.544489	0.0173577
$985$	−37.6474	−1.19955
$986$	78.9551	2.51444
$987$	0	0
$988$	−10.6209	−0.337895
$989$	2.70342	0.0859637
$990$	22.4987	0.715056
$991$	20.8108	0.661075	0.330538	−	0.943793i	$-0.392770\pi$
$991$	20.8108	0.661075	0.330538	+	0.943793i	$0.392770\pi$
$992$	7.39139	0.234677
$993$	−22.8992	−0.726684
$994$	0	0
$995$	47.9732	1.52085
$996$	0.595113	0.0188569
$997$	53.1594	1.68358	0.841788	−	0.539809i	$-0.181504\pi$
$997$	53.1594	1.68358	0.841788	+	0.539809i	$0.181504\pi$
$998$	−83.5224	−2.64385
$999$	−0.973320	−0.0307945

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.bd.1.6		6
7.3	odd	6		483.2.i.f.415.1	yes	12
7.5	odd	6		483.2.i.f.277.1	✓	12
7.6	odd	2		3381.2.a.bc.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.i.f.277.1	✓	12	7.5	odd	6
483.2.i.f.415.1	yes	12	7.3	odd	6
3381.2.a.bc.1.6		6	7.6	odd	2
3381.2.a.bd.1.6		6	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)

\(f(q)\)	\(=\)	\(q+2.04340 q^{2} +1.00000 q^{3} +2.17548 q^{4} -1.94349 q^{5} +2.04340 q^{6} +0.358585 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.04340 q^{2} +1.00000 q^{3} +2.17548 q^{4} -1.94349 q^{5} +2.04340 q^{6} +0.358585 q^{8} +1.00000 q^{9} -3.97133 q^{10} -5.66529 q^{11} +2.17548 q^{12} +6.17812 q^{13} -1.94349 q^{15} -3.61824 q^{16} -7.23463 q^{17} +2.04340 q^{18} -0.790220 q^{19} -4.22803 q^{20} -11.5765 q^{22} -1.00000 q^{23} +0.358585 q^{24} -1.22285 q^{25} +12.6244 q^{26} +1.00000 q^{27} -5.34085 q^{29} -3.97133 q^{30} -0.911316 q^{31} -8.11067 q^{32} -5.66529 q^{33} -14.7832 q^{34} +2.17548 q^{36} -0.973320 q^{37} -1.61473 q^{38} +6.17812 q^{39} -0.696907 q^{40} +1.51843 q^{41} -2.70342 q^{43} -12.3247 q^{44} -1.94349 q^{45} -2.04340 q^{46} +1.52839 q^{47} -3.61824 q^{48} -2.49877 q^{50} -7.23463 q^{51} +13.4404 q^{52} -8.95803 q^{53} +2.04340 q^{54} +11.0104 q^{55} -0.790220 q^{57} -10.9135 q^{58} +10.8931 q^{59} -4.22803 q^{60} +6.31775 q^{61} -1.86218 q^{62} -9.33688 q^{64} -12.0071 q^{65} -11.5765 q^{66} +7.31833 q^{67} -15.7388 q^{68} -1.00000 q^{69} -8.75692 q^{71} +0.358585 q^{72} +0.875251 q^{73} -1.98888 q^{74} -1.22285 q^{75} -1.71911 q^{76} +12.6244 q^{78} +5.96655 q^{79} +7.03200 q^{80} +1.00000 q^{81} +3.10277 q^{82} +0.273554 q^{83} +14.0604 q^{85} -5.52417 q^{86} -5.34085 q^{87} -2.03149 q^{88} -17.6270 q^{89} -3.97133 q^{90} -2.17548 q^{92} -0.911316 q^{93} +3.12312 q^{94} +1.53578 q^{95} -8.11067 q^{96} -3.09620 q^{97} -5.66529 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} + 6 q^{3} + 3 q^{4} - 3 q^{5} - q^{6} - 3 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q - q^2 + 6 * q^3 + 3 * q^4 - 3 * q^5 - q^6 - 3 * q^8 + 6 * q^9	\( 6 q - q^{2} + 6 q^{3} + 3 q^{4} - 3 q^{5} - q^{6} - 3 q^{8} + 6 q^{9} + 3 q^{10} - 14 q^{11} + 3 q^{12} - 3 q^{15} - 7 q^{16} - 15 q^{17} - q^{18} + q^{19} - 17 q^{20} - 6 q^{22} - 6 q^{23} - 3 q^{24} + 9 q^{25} + 15 q^{26} + 6 q^{27} - 6 q^{29} + 3 q^{30} + 11 q^{31} + 3 q^{32} - 14 q^{33} - 15 q^{34} + 3 q^{36} - 5 q^{37} - 14 q^{38} + 17 q^{40} - 18 q^{41} - 37 q^{43} - 10 q^{44} - 3 q^{45} + q^{46} - 3 q^{47} - 7 q^{48} - 30 q^{50} - 15 q^{51} + 7 q^{52} - 15 q^{53} - q^{54} + 2 q^{55} + q^{57} + 4 q^{58} + 2 q^{59} - 17 q^{60} + 12 q^{61} - 36 q^{62} - 23 q^{64} - 17 q^{65} - 6 q^{66} - 10 q^{67} + q^{68} - 6 q^{69} - 21 q^{71} - 3 q^{72} + 8 q^{73} - 16 q^{74} + 9 q^{75} - 18 q^{76} + 15 q^{78} - 17 q^{79} - 3 q^{80} + 6 q^{81} + 48 q^{82} - 12 q^{83} - 13 q^{85} + 22 q^{86} - 6 q^{87} - 2 q^{88} - 18 q^{89} + 3 q^{90} - 3 q^{92} + 11 q^{93} - 3 q^{94} - 16 q^{95} + 3 q^{96} + 2 q^{97} - 14 q^{99}+O(q^{100}) \) 6 * q - q^2 + 6 * q^3 + 3 * q^4 - 3 * q^5 - q^6 - 3 * q^8 + 6 * q^9 + 3 * q^10 - 14 * q^11 + 3 * q^12 - 3 * q^15 - 7 * q^16 - 15 * q^17 - q^18 + q^19 - 17 * q^20 - 6 * q^22 - 6 * q^23 - 3 * q^24 + 9 * q^25 + 15 * q^26 + 6 * q^27 - 6 * q^29 + 3 * q^30 + 11 * q^31 + 3 * q^32 - 14 * q^33 - 15 * q^34 + 3 * q^36 - 5 * q^37 - 14 * q^38 + 17 * q^40 - 18 * q^41 - 37 * q^43 - 10 * q^44 - 3 * q^45 + q^46 - 3 * q^47 - 7 * q^48 - 30 * q^50 - 15 * q^51 + 7 * q^52 - 15 * q^53 - q^54 + 2 * q^55 + q^57 + 4 * q^58 + 2 * q^59 - 17 * q^60 + 12 * q^61 - 36 * q^62 - 23 * q^64 - 17 * q^65 - 6 * q^66 - 10 * q^67 + q^68 - 6 * q^69 - 21 * q^71 - 3 * q^72 + 8 * q^73 - 16 * q^74 + 9 * q^75 - 18 * q^76 + 15 * q^78 - 17 * q^79 - 3 * q^80 + 6 * q^81 + 48 * q^82 - 12 * q^83 - 13 * q^85 + 22 * q^86 - 6 * q^87 - 2 * q^88 - 18 * q^89 + 3 * q^90 - 3 * q^92 + 11 * q^93 - 3 * q^94 - 16 * q^95 + 3 * q^96 + 2 * q^97 - 14 * q^99

Introduction

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