LMFDB - Embedded newform 3381.2.a.u.1.1

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:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
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			1.1
Root			$-0.618034$ 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)

$f(q)$	$=$	$q-0.618034 q^{2} +1.00000 q^{3} -1.61803 q^{4} +0.381966 q^{5} -0.618034 q^{6} +2.23607 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.618034 q^{2} +1.00000 q^{3} -1.61803 q^{4} +0.381966 q^{5} -0.618034 q^{6} +2.23607 q^{8} +1.00000 q^{9} -0.236068 q^{10} +2.23607 q^{11} -1.61803 q^{12} +0.145898 q^{13} +0.381966 q^{15} +1.85410 q^{16} +5.47214 q^{17} -0.618034 q^{18} +8.23607 q^{19} -0.618034 q^{20} -1.38197 q^{22} +1.00000 q^{23} +2.23607 q^{24} -4.85410 q^{25} -0.0901699 q^{26} +1.00000 q^{27} -2.70820 q^{29} -0.236068 q^{30} +5.00000 q^{31} -5.61803 q^{32} +2.23607 q^{33} -3.38197 q^{34} -1.61803 q^{36} -0.527864 q^{37} -5.09017 q^{38} +0.145898 q^{39} +0.854102 q^{40} -8.70820 q^{41} -8.32624 q^{43} -3.61803 q^{44} +0.381966 q^{45} -0.618034 q^{46} -5.23607 q^{47} +1.85410 q^{48} +3.00000 q^{50} +5.47214 q^{51} -0.236068 q^{52} -3.61803 q^{53} -0.618034 q^{54} +0.854102 q^{55} +8.23607 q^{57} +1.67376 q^{58} +4.85410 q^{59} -0.618034 q^{60} +9.09017 q^{61} -3.09017 q^{62} -0.236068 q^{64} +0.0557281 q^{65} -1.38197 q^{66} -6.85410 q^{67} -8.85410 q^{68} +1.00000 q^{69} +9.38197 q^{71} +2.23607 q^{72} +3.47214 q^{73} +0.326238 q^{74} -4.85410 q^{75} -13.3262 q^{76} -0.0901699 q^{78} +5.94427 q^{79} +0.708204 q^{80} +1.00000 q^{81} +5.38197 q^{82} -7.94427 q^{83} +2.09017 q^{85} +5.14590 q^{86} -2.70820 q^{87} +5.00000 q^{88} +16.3262 q^{89} -0.236068 q^{90} -1.61803 q^{92} +5.00000 q^{93} +3.23607 q^{94} +3.14590 q^{95} -5.61803 q^{96} +17.1803 q^{97} +2.23607 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} + 2 q^{3} - q^{4} + 3 q^{5} + q^{6} + 2 q^{9}+O(q^{10}) $ 2 * q + q^2 + 2 * q^3 - q^4 + 3 * q^5 + q^6 + 2 * q^9	$ 2 q + q^{2} + 2 q^{3} - q^{4} + 3 q^{5} + q^{6} + 2 q^{9} + 4 q^{10} - q^{12} + 7 q^{13} + 3 q^{15} - 3 q^{16} + 2 q^{17} + q^{18} + 12 q^{19} + q^{20} - 5 q^{22} + 2 q^{23} - 3 q^{25} + 11 q^{26} + 2 q^{27} + 8 q^{29} + 4 q^{30} + 10 q^{31} - 9 q^{32} - 9 q^{34} - q^{36} - 10 q^{37} + q^{38} + 7 q^{39} - 5 q^{40} - 4 q^{41} - q^{43} - 5 q^{44} + 3 q^{45} + q^{46} - 6 q^{47} - 3 q^{48} + 6 q^{50} + 2 q^{51} + 4 q^{52} - 5 q^{53} + q^{54} - 5 q^{55} + 12 q^{57} + 19 q^{58} + 3 q^{59} + q^{60} + 7 q^{61} + 5 q^{62} + 4 q^{64} + 18 q^{65} - 5 q^{66} - 7 q^{67} - 11 q^{68} + 2 q^{69} + 21 q^{71} - 2 q^{73} - 15 q^{74} - 3 q^{75} - 11 q^{76} + 11 q^{78} - 6 q^{79} - 12 q^{80} + 2 q^{81} + 13 q^{82} + 2 q^{83} - 7 q^{85} + 17 q^{86} + 8 q^{87} + 10 q^{88} + 17 q^{89} + 4 q^{90} - q^{92} + 10 q^{93} + 2 q^{94} + 13 q^{95} - 9 q^{96} + 12 q^{97}+O(q^{100}) $ 2 * q + q^2 + 2 * q^3 - q^4 + 3 * q^5 + q^6 + 2 * q^9 + 4 * q^10 - q^12 + 7 * q^13 + 3 * q^15 - 3 * q^16 + 2 * q^17 + q^18 + 12 * q^19 + q^20 - 5 * q^22 + 2 * q^23 - 3 * q^25 + 11 * q^26 + 2 * q^27 + 8 * q^29 + 4 * q^30 + 10 * q^31 - 9 * q^32 - 9 * q^34 - q^36 - 10 * q^37 + q^38 + 7 * q^39 - 5 * q^40 - 4 * q^41 - q^43 - 5 * q^44 + 3 * q^45 + q^46 - 6 * q^47 - 3 * q^48 + 6 * q^50 + 2 * q^51 + 4 * q^52 - 5 * q^53 + q^54 - 5 * q^55 + 12 * q^57 + 19 * q^58 + 3 * q^59 + q^60 + 7 * q^61 + 5 * q^62 + 4 * q^64 + 18 * q^65 - 5 * q^66 - 7 * q^67 - 11 * q^68 + 2 * q^69 + 21 * q^71 - 2 * q^73 - 15 * q^74 - 3 * q^75 - 11 * q^76 + 11 * q^78 - 6 * q^79 - 12 * q^80 + 2 * q^81 + 13 * q^82 + 2 * q^83 - 7 * q^85 + 17 * q^86 + 8 * q^87 + 10 * q^88 + 17 * q^89 + 4 * q^90 - q^92 + 10 * q^93 + 2 * q^94 + 13 * q^95 - 9 * q^96 + 12 * q^97

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 $

$2$	−0.618034	−0.437016	−0.218508	−	0.975835i	$-0.570119\pi$
$2$	−0.618034	−0.437016	−0.218508	+	0.975835i	$0.570119\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.61803	−0.809017
$5$	0.381966	0.170820	0.0854102	−	0.996346i	$-0.472780\pi$
$5$	0.381966	0.170820	0.0854102	+	0.996346i	$0.472780\pi$
$6$	−0.618034	−0.252311
$7$	0	0
$7$	0	0
$8$	2.23607	0.790569
$9$	1.00000	0.333333
$10$	−0.236068	−0.0746512
$11$	2.23607	0.674200	0.337100	−	0.941469i	$-0.390554\pi$
$11$	2.23607	0.674200	0.337100	+	0.941469i	$0.390554\pi$
$12$	−1.61803	−0.467086
$13$	0.145898	0.0404648	0.0202324	−	0.999795i	$-0.493559\pi$
$13$	0.145898	0.0404648	0.0202324	+	0.999795i	$0.493559\pi$
$14$	0	0
$15$	0.381966	0.0986232
$16$	1.85410	0.463525
$17$	5.47214	1.32719	0.663594	−	0.748093i	$-0.269030\pi$
$17$	5.47214	1.32719	0.663594	+	0.748093i	$0.269030\pi$
$18$	−0.618034	−0.145672
$19$	8.23607	1.88948	0.944742	−	0.327815i	$-0.106312\pi$
$19$	8.23607	1.88948	0.944742	+	0.327815i	$0.106312\pi$
$20$	−0.618034	−0.138197
$21$	0	0
$22$	−1.38197	−0.294636
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.23607	0.456435
$25$	−4.85410	−0.970820
$26$	−0.0901699	−0.0176838
$27$	1.00000	0.192450
$28$	0	0
$29$	−2.70820	−0.502901	−0.251450	−	0.967870i	$-0.580908\pi$
$29$	−2.70820	−0.502901	−0.251450	+	0.967870i	$0.580908\pi$
$30$	−0.236068	−0.0430999
$31$	5.00000	0.898027	0.449013	−	0.893525i	$-0.351776\pi$
$31$	5.00000	0.898027	0.449013	+	0.893525i	$0.351776\pi$
$32$	−5.61803	−0.993137
$33$	2.23607	0.389249
$34$	−3.38197	−0.580002
$35$	0	0
$36$	−1.61803	−0.269672
$37$	−0.527864	−0.0867803	−0.0433902	−	0.999058i	$-0.513816\pi$
$37$	−0.527864	−0.0867803	−0.0433902	+	0.999058i	$0.513816\pi$
$38$	−5.09017	−0.825735
$39$	0.145898	0.0233624
$40$	0.854102	0.135045
$41$	−8.70820	−1.35999	−0.679996	−	0.733215i	$-0.738019\pi$
$41$	−8.70820	−1.35999	−0.679996	+	0.733215i	$0.738019\pi$
$42$	0	0
$43$	−8.32624	−1.26974	−0.634870	−	0.772619i	$-0.718946\pi$
$43$	−8.32624	−1.26974	−0.634870	+	0.772619i	$0.718946\pi$
$44$	−3.61803	−0.545439
$45$	0.381966	0.0569401
$46$	−0.618034	−0.0911241
$47$	−5.23607	−0.763759	−0.381880	−	0.924212i	$-0.624723\pi$
$47$	−5.23607	−0.763759	−0.381880	+	0.924212i	$0.624723\pi$
$48$	1.85410	0.267617
$49$	0	0
$50$	3.00000	0.424264
$51$	5.47214	0.766252
$52$	−0.236068	−0.0327367
$53$	−3.61803	−0.496975	−0.248488	−	0.968635i	$-0.579934\pi$
$53$	−3.61803	−0.496975	−0.248488	+	0.968635i	$0.579934\pi$
$54$	−0.618034	−0.0841038
$55$	0.854102	0.115167
$56$	0	0
$57$	8.23607	1.09089
$58$	1.67376	0.219776
$59$	4.85410	0.631950	0.315975	−	0.948767i	$-0.397668\pi$
$59$	4.85410	0.631950	0.315975	+	0.948767i	$0.397668\pi$
$60$	−0.618034	−0.0797878
$61$	9.09017	1.16388	0.581938	−	0.813233i	$-0.302294\pi$
$61$	9.09017	1.16388	0.581938	+	0.813233i	$0.302294\pi$
$62$	−3.09017	−0.392452
$63$	0	0
$64$	−0.236068	−0.0295085
$65$	0.0557281	0.00691222
$66$	−1.38197	−0.170108
$67$	−6.85410	−0.837362	−0.418681	−	0.908133i	$-0.637507\pi$
$67$	−6.85410	−0.837362	−0.418681	+	0.908133i	$0.637507\pi$
$68$	−8.85410	−1.07372
$69$	1.00000	0.120386
$70$	0	0
$71$	9.38197	1.11343	0.556717	−	0.830702i	$-0.312061\pi$
$71$	9.38197	1.11343	0.556717	+	0.830702i	$0.312061\pi$
$72$	2.23607	0.263523
$73$	3.47214	0.406383	0.203191	−	0.979139i	$-0.434869\pi$
$73$	3.47214	0.406383	0.203191	+	0.979139i	$0.434869\pi$
$74$	0.326238	0.0379244
$75$	−4.85410	−0.560503
$76$	−13.3262	−1.52862
$77$	0	0
$78$	−0.0901699	−0.0102097
$79$	5.94427	0.668783	0.334391	−	0.942434i	$-0.391469\pi$
$79$	5.94427	0.668783	0.334391	+	0.942434i	$0.391469\pi$
$80$	0.708204	0.0791796
$81$	1.00000	0.111111
$82$	5.38197	0.594339
$83$	−7.94427	−0.871997	−0.435999	−	0.899947i	$-0.643605\pi$
$83$	−7.94427	−0.871997	−0.435999	+	0.899947i	$0.643605\pi$
$84$	0	0
$85$	2.09017	0.226711
$86$	5.14590	0.554896
$87$	−2.70820	−0.290350
$88$	5.00000	0.533002
$89$	16.3262	1.73058	0.865289	−	0.501274i	$-0.167135\pi$
$89$	16.3262	1.73058	0.865289	+	0.501274i	$0.167135\pi$
$90$	−0.236068	−0.0248837
$91$	0	0
$92$	−1.61803	−0.168692
$93$	5.00000	0.518476
$94$	3.23607	0.333775
$95$	3.14590	0.322762
$96$	−5.61803	−0.573388
$97$	17.1803	1.74440	0.872200	−	0.489150i	$-0.162693\pi$
$97$	17.1803	1.74440	0.872200	+	0.489150i	$0.162693\pi$
$98$	0	0
$99$	2.23607	0.224733
$100$	7.85410	0.785410
$101$	16.0902	1.60103	0.800516	−	0.599312i	$-0.204559\pi$
$101$	16.0902	1.60103	0.800516	+	0.599312i	$0.204559\pi$
$102$	−3.38197	−0.334865
$103$	−2.47214	−0.243587	−0.121793	−	0.992555i	$-0.538865\pi$
$103$	−2.47214	−0.243587	−0.121793	+	0.992555i	$0.538865\pi$
$104$	0.326238	0.0319903
$105$	0	0
$106$	2.23607	0.217186
$107$	5.85410	0.565937	0.282969	−	0.959129i	$-0.408681\pi$
$107$	5.85410	0.565937	0.282969	+	0.959129i	$0.408681\pi$
$108$	−1.61803	−0.155695
$109$	15.0344	1.44004	0.720019	−	0.693954i	$-0.244133\pi$
$109$	15.0344	1.44004	0.720019	+	0.693954i	$0.244133\pi$
$110$	−0.527864	−0.0503299
$111$	−0.527864	−0.0501026
$112$	0	0
$113$	4.09017	0.384771	0.192385	−	0.981319i	$-0.438378\pi$
$113$	4.09017	0.384771	0.192385	+	0.981319i	$0.438378\pi$
$114$	−5.09017	−0.476738
$115$	0.381966	0.0356185
$116$	4.38197	0.406855
$117$	0.145898	0.0134883
$118$	−3.00000	−0.276172
$119$	0	0
$120$	0.854102	0.0779685
$121$	−6.00000	−0.545455
$122$	−5.61803	−0.508633
$123$	−8.70820	−0.785192
$124$	−8.09017	−0.726519
$125$	−3.76393	−0.336656
$126$	0	0
$127$	−18.3262	−1.62619	−0.813095	−	0.582131i	$-0.802219\pi$
$127$	−18.3262	−1.62619	−0.813095	+	0.582131i	$0.802219\pi$
$128$	11.3820	1.00603
$129$	−8.32624	−0.733084
$130$	−0.0344419	−0.00302075
$131$	−14.4164	−1.25957	−0.629784	−	0.776771i	$-0.716856\pi$
$131$	−14.4164	−1.25957	−0.629784	+	0.776771i	$0.716856\pi$
$132$	−3.61803	−0.314909
$133$	0	0
$134$	4.23607	0.365941
$135$	0.381966	0.0328744
$136$	12.2361	1.04923
$137$	−2.05573	−0.175633	−0.0878164	−	0.996137i	$-0.527989\pi$
$137$	−2.05573	−0.175633	−0.0878164	+	0.996137i	$0.527989\pi$
$138$	−0.618034	−0.0526105
$139$	−13.1459	−1.11502	−0.557510	−	0.830170i	$-0.688243\pi$
$139$	−13.1459	−1.11502	−0.557510	+	0.830170i	$0.688243\pi$
$140$	0	0
$141$	−5.23607	−0.440956
$142$	−5.79837	−0.486589
$143$	0.326238	0.0272814
$144$	1.85410	0.154508
$145$	−1.03444	−0.0859057
$146$	−2.14590	−0.177596
$147$	0	0
$148$	0.854102	0.0702067
$149$	16.6525	1.36422	0.682112	−	0.731248i	$-0.261062\pi$
$149$	16.6525	1.36422	0.682112	+	0.731248i	$0.261062\pi$
$150$	3.00000	0.244949
$151$	11.7082	0.952800	0.476400	−	0.879229i	$-0.341941\pi$
$151$	11.7082	0.952800	0.476400	+	0.879229i	$0.341941\pi$
$152$	18.4164	1.49377
$153$	5.47214	0.442396
$154$	0	0
$155$	1.90983	0.153401
$156$	−0.236068	−0.0189006
$157$	−8.18034	−0.652862	−0.326431	−	0.945221i	$-0.605846\pi$
$157$	−8.18034	−0.652862	−0.326431	+	0.945221i	$0.605846\pi$
$158$	−3.67376	−0.292269
$159$	−3.61803	−0.286929
$160$	−2.14590	−0.169648
$161$	0	0
$162$	−0.618034	−0.0485573
$163$	15.5066	1.21457	0.607284	−	0.794484i	$-0.292259\pi$
$163$	15.5066	1.21457	0.607284	+	0.794484i	$0.292259\pi$
$164$	14.0902	1.10026
$165$	0.854102	0.0664917
$166$	4.90983	0.381077
$167$	−2.52786	−0.195612	−0.0978060	−	0.995205i	$-0.531182\pi$
$167$	−2.52786	−0.195612	−0.0978060	+	0.995205i	$0.531182\pi$
$168$	0	0
$169$	−12.9787	−0.998363
$170$	−1.29180	−0.0990762
$171$	8.23607	0.629828
$172$	13.4721	1.02724
$173$	24.7082	1.87853	0.939265	−	0.343193i	$-0.111508\pi$
$173$	24.7082	1.87853	0.939265	+	0.343193i	$0.111508\pi$
$174$	1.67376	0.126888
$175$	0	0
$176$	4.14590	0.312509
$177$	4.85410	0.364857
$178$	−10.0902	−0.756290
$179$	−9.03444	−0.675266	−0.337633	−	0.941278i	$-0.609626\pi$
$179$	−9.03444	−0.675266	−0.337633	+	0.941278i	$0.609626\pi$
$180$	−0.618034	−0.0460655
$181$	−7.18034	−0.533710	−0.266855	−	0.963737i	$-0.585985\pi$
$181$	−7.18034	−0.533710	−0.266855	+	0.963737i	$0.585985\pi$
$182$	0	0
$183$	9.09017	0.671965
$184$	2.23607	0.164845
$185$	−0.201626	−0.0148238
$186$	−3.09017	−0.226582
$187$	12.2361	0.894790
$188$	8.47214	0.617894
$189$	0	0
$190$	−1.94427	−0.141052
$191$	8.29180	0.599973	0.299987	−	0.953943i	$-0.403018\pi$
$191$	8.29180	0.599973	0.299987	+	0.953943i	$0.403018\pi$
$192$	−0.236068	−0.0170367
$193$	4.18034	0.300907	0.150454	−	0.988617i	$-0.451927\pi$
$193$	4.18034	0.300907	0.150454	+	0.988617i	$0.451927\pi$
$194$	−10.6180	−0.762330
$195$	0.0557281	0.00399077
$196$	0	0
$197$	−9.67376	−0.689227	−0.344614	−	0.938745i	$-0.611990\pi$
$197$	−9.67376	−0.689227	−0.344614	+	0.938745i	$0.611990\pi$
$198$	−1.38197	−0.0982120
$199$	−10.5623	−0.748742	−0.374371	−	0.927279i	$-0.622141\pi$
$199$	−10.5623	−0.748742	−0.374371	+	0.927279i	$0.622141\pi$
$200$	−10.8541	−0.767501
$201$	−6.85410	−0.483451
$202$	−9.94427	−0.699677
$203$	0	0
$204$	−8.85410	−0.619911
$205$	−3.32624	−0.232315
$206$	1.52786	0.106451
$207$	1.00000	0.0695048
$208$	0.270510	0.0187565
$209$	18.4164	1.27389
$210$	0	0
$211$	15.0000	1.03264	0.516321	−	0.856395i	$-0.327301\pi$
$211$	15.0000	1.03264	0.516321	+	0.856395i	$0.327301\pi$
$212$	5.85410	0.402061
$213$	9.38197	0.642842
$214$	−3.61803	−0.247324
$215$	−3.18034	−0.216897
$216$	2.23607	0.152145
$217$	0	0
$218$	−9.29180	−0.629320
$219$	3.47214	0.234625
$220$	−1.38197	−0.0931721
$221$	0.798374	0.0537044
$222$	0.326238	0.0218957
$223$	−2.67376	−0.179048	−0.0895242	−	0.995985i	$-0.528535\pi$
$223$	−2.67376	−0.179048	−0.0895242	+	0.995985i	$0.528535\pi$
$224$	0	0
$225$	−4.85410	−0.323607
$226$	−2.52786	−0.168151
$227$	18.2705	1.21266	0.606328	−	0.795215i	$-0.292642\pi$
$227$	18.2705	1.21266	0.606328	+	0.795215i	$0.292642\pi$
$228$	−13.3262	−0.882552
$229$	21.3262	1.40928	0.704639	−	0.709566i	$-0.251109\pi$
$229$	21.3262	1.40928	0.704639	+	0.709566i	$0.251109\pi$
$230$	−0.236068	−0.0155659
$231$	0	0
$232$	−6.05573	−0.397578
$233$	−4.09017	−0.267956	−0.133978	−	0.990984i	$-0.542775\pi$
$233$	−4.09017	−0.267956	−0.133978	+	0.990984i	$0.542775\pi$
$234$	−0.0901699	−0.00589459
$235$	−2.00000	−0.130466
$236$	−7.85410	−0.511258
$237$	5.94427	0.386122
$238$	0	0
$239$	−4.38197	−0.283446	−0.141723	−	0.989906i	$-0.545264\pi$
$239$	−4.38197	−0.283446	−0.141723	+	0.989906i	$0.545264\pi$
$240$	0.708204	0.0457144
$241$	−15.2918	−0.985031	−0.492516	−	0.870304i	$-0.663923\pi$
$241$	−15.2918	−0.985031	−0.492516	+	0.870304i	$0.663923\pi$
$242$	3.70820	0.238372
$243$	1.00000	0.0641500
$244$	−14.7082	−0.941596
$245$	0	0
$246$	5.38197	0.343142
$247$	1.20163	0.0764576
$248$	11.1803	0.709952
$249$	−7.94427	−0.503448
$250$	2.32624	0.147124
$251$	25.7082	1.62269	0.811344	−	0.584569i	$-0.198737\pi$
$251$	25.7082	1.62269	0.811344	+	0.584569i	$0.198737\pi$
$252$	0	0
$253$	2.23607	0.140580
$254$	11.3262	0.710671
$255$	2.09017	0.130892
$256$	−6.56231	−0.410144
$257$	−16.2918	−1.01625	−0.508127	−	0.861282i	$-0.669662\pi$
$257$	−16.2918	−1.01625	−0.508127	+	0.861282i	$0.669662\pi$
$258$	5.14590	0.320370
$259$	0	0
$260$	−0.0901699	−0.00559210
$261$	−2.70820	−0.167634
$262$	8.90983	0.550451
$263$	5.00000	0.308313	0.154157	−	0.988046i	$-0.450734\pi$
$263$	5.00000	0.308313	0.154157	+	0.988046i	$0.450734\pi$
$264$	5.00000	0.307729
$265$	−1.38197	−0.0848935
$266$	0	0
$267$	16.3262	0.999150
$268$	11.0902	0.677440
$269$	−3.85410	−0.234989	−0.117494	−	0.993074i	$-0.537486\pi$
$269$	−3.85410	−0.234989	−0.117494	+	0.993074i	$0.537486\pi$
$270$	−0.236068	−0.0143666
$271$	−5.18034	−0.314683	−0.157342	−	0.987544i	$-0.550292\pi$
$271$	−5.18034	−0.314683	−0.157342	+	0.987544i	$0.550292\pi$
$272$	10.1459	0.615185
$273$	0	0
$274$	1.27051	0.0767543
$275$	−10.8541	−0.654527
$276$	−1.61803	−0.0973942
$277$	−30.2148	−1.81543	−0.907715	−	0.419587i	$-0.862175\pi$
$277$	−30.2148	−1.81543	−0.907715	+	0.419587i	$0.862175\pi$
$278$	8.12461	0.487282
$279$	5.00000	0.299342
$280$	0	0
$281$	27.5967	1.64628	0.823142	−	0.567836i	$-0.192219\pi$
$281$	27.5967	1.64628	0.823142	+	0.567836i	$0.192219\pi$
$282$	3.23607	0.192705
$283$	1.32624	0.0788367	0.0394183	−	0.999223i	$-0.487450\pi$
$283$	1.32624	0.0788367	0.0394183	+	0.999223i	$0.487450\pi$
$284$	−15.1803	−0.900787
$285$	3.14590	0.186347
$286$	−0.201626	−0.0119224
$287$	0	0
$288$	−5.61803	−0.331046
$289$	12.9443	0.761428
$290$	0.639320	0.0375422
$291$	17.1803	1.00713
$292$	−5.61803	−0.328771
$293$	18.4721	1.07915	0.539577	−	0.841936i	$-0.318584\pi$
$293$	18.4721	1.07915	0.539577	+	0.841936i	$0.318584\pi$
$294$	0	0
$295$	1.85410	0.107950
$296$	−1.18034	−0.0686059
$297$	2.23607	0.129750
$298$	−10.2918	−0.596188
$299$	0.145898	0.00843750
$300$	7.85410	0.453457
$301$	0	0
$302$	−7.23607	−0.416389
$303$	16.0902	0.924356
$304$	15.2705	0.875824
$305$	3.47214	0.198814
$306$	−3.38197	−0.193334
$307$	−8.05573	−0.459765	−0.229882	−	0.973218i	$-0.573834\pi$
$307$	−8.05573	−0.459765	−0.229882	+	0.973218i	$0.573834\pi$
$308$	0	0
$309$	−2.47214	−0.140635
$310$	−1.18034	−0.0670388
$311$	−5.38197	−0.305183	−0.152592	−	0.988289i	$-0.548762\pi$
$311$	−5.38197	−0.305183	−0.152592	+	0.988289i	$0.548762\pi$
$312$	0.326238	0.0184696
$313$	10.4721	0.591920	0.295960	−	0.955200i	$-0.404360\pi$
$313$	10.4721	0.591920	0.295960	+	0.955200i	$0.404360\pi$
$314$	5.05573	0.285311
$315$	0	0
$316$	−9.61803	−0.541057
$317$	−28.8541	−1.62061	−0.810304	−	0.586010i	$-0.800698\pi$
$317$	−28.8541	−1.62061	−0.810304	+	0.586010i	$0.800698\pi$
$318$	2.23607	0.125392
$319$	−6.05573	−0.339056
$320$	−0.0901699	−0.00504065
$321$	5.85410	0.326744
$322$	0	0
$323$	45.0689	2.50770
$324$	−1.61803	−0.0898908
$325$	−0.708204	−0.0392841
$326$	−9.58359	−0.530786
$327$	15.0344	0.831407
$328$	−19.4721	−1.07517
$329$	0	0
$330$	−0.527864	−0.0290580
$331$	−6.94427	−0.381692	−0.190846	−	0.981620i	$-0.561123\pi$
$331$	−6.94427	−0.381692	−0.190846	+	0.981620i	$0.561123\pi$
$332$	12.8541	0.705460
$333$	−0.527864	−0.0289268
$334$	1.56231	0.0854856
$335$	−2.61803	−0.143038
$336$	0	0
$337$	1.56231	0.0851042	0.0425521	−	0.999094i	$-0.486451\pi$
$337$	1.56231	0.0851042	0.0425521	+	0.999094i	$0.486451\pi$
$338$	8.02129	0.436300
$339$	4.09017	0.222148
$340$	−3.38197	−0.183413
$341$	11.1803	0.605449
$342$	−5.09017	−0.275245
$343$	0	0
$344$	−18.6180	−1.00382
$345$	0.381966	0.0205644
$346$	−15.2705	−0.820948
$347$	27.6525	1.48446	0.742231	−	0.670144i	$-0.233768\pi$
$347$	27.6525	1.48446	0.742231	+	0.670144i	$0.233768\pi$
$348$	4.38197	0.234898
$349$	−31.5066	−1.68651	−0.843254	−	0.537515i	$-0.819363\pi$
$349$	−31.5066	−1.68651	−0.843254	+	0.537515i	$0.819363\pi$
$350$	0	0
$351$	0.145898	0.00778746
$352$	−12.5623	−0.669573
$353$	−22.5967	−1.20270	−0.601352	−	0.798984i	$-0.705371\pi$
$353$	−22.5967	−1.20270	−0.601352	+	0.798984i	$0.705371\pi$
$354$	−3.00000	−0.159448
$355$	3.58359	0.190197
$356$	−26.4164	−1.40007
$357$	0	0
$358$	5.58359	0.295102
$359$	−1.79837	−0.0949145	−0.0474573	−	0.998873i	$-0.515112\pi$
$359$	−1.79837	−0.0949145	−0.0474573	+	0.998873i	$0.515112\pi$
$360$	0.854102	0.0450151
$361$	48.8328	2.57015
$362$	4.43769	0.233240
$363$	−6.00000	−0.314918
$364$	0	0
$365$	1.32624	0.0694185
$366$	−5.61803	−0.293659
$367$	−23.4508	−1.22412	−0.612062	−	0.790810i	$-0.709660\pi$
$367$	−23.4508	−1.22412	−0.612062	+	0.790810i	$0.709660\pi$
$368$	1.85410	0.0966517
$369$	−8.70820	−0.453331
$370$	0.124612	0.00647826
$371$	0	0
$372$	−8.09017	−0.419456
$373$	−32.8885	−1.70290	−0.851452	−	0.524432i	$-0.824278\pi$
$373$	−32.8885	−1.70290	−0.851452	+	0.524432i	$0.824278\pi$
$374$	−7.56231	−0.391038
$375$	−3.76393	−0.194369
$376$	−11.7082	−0.603805
$377$	−0.395122	−0.0203498
$378$	0	0
$379$	−3.05573	−0.156962	−0.0784811	−	0.996916i	$-0.525007\pi$
$379$	−3.05573	−0.156962	−0.0784811	+	0.996916i	$0.525007\pi$
$380$	−5.09017	−0.261120
$381$	−18.3262	−0.938882
$382$	−5.12461	−0.262198
$383$	13.4721	0.688394	0.344197	−	0.938897i	$-0.388151\pi$
$383$	13.4721	0.688394	0.344197	+	0.938897i	$0.388151\pi$
$384$	11.3820	0.580834
$385$	0	0
$386$	−2.58359	−0.131501
$387$	−8.32624	−0.423246
$388$	−27.7984	−1.41125
$389$	−18.1246	−0.918954	−0.459477	−	0.888190i	$-0.651963\pi$
$389$	−18.1246	−0.918954	−0.459477	+	0.888190i	$0.651963\pi$
$390$	−0.0344419	−0.00174403
$391$	5.47214	0.276738
$392$	0	0
$393$	−14.4164	−0.727212
$394$	5.97871	0.301203
$395$	2.27051	0.114242
$396$	−3.61803	−0.181813
$397$	−10.7639	−0.540226	−0.270113	−	0.962829i	$-0.587061\pi$
$397$	−10.7639	−0.540226	−0.270113	+	0.962829i	$0.587061\pi$
$398$	6.52786	0.327212
$399$	0	0
$400$	−9.00000	−0.450000
$401$	29.1803	1.45720	0.728598	−	0.684941i	$-0.240172\pi$
$401$	29.1803	1.45720	0.728598	+	0.684941i	$0.240172\pi$
$402$	4.23607	0.211276
$403$	0.729490	0.0363385
$404$	−26.0344	−1.29526
$405$	0.381966	0.0189800
$406$	0	0
$407$	−1.18034	−0.0585073
$408$	12.2361	0.605776
$409$	7.65248	0.378391	0.189195	−	0.981939i	$-0.439412\pi$
$409$	7.65248	0.378391	0.189195	+	0.981939i	$0.439412\pi$
$410$	2.05573	0.101525
$411$	−2.05573	−0.101402
$412$	4.00000	0.197066
$413$	0	0
$414$	−0.618034	−0.0303747
$415$	−3.03444	−0.148955
$416$	−0.819660	−0.0401871
$417$	−13.1459	−0.643757
$418$	−11.3820	−0.556710
$419$	0.562306	0.0274704	0.0137352	−	0.999906i	$-0.495628\pi$
$419$	0.562306	0.0274704	0.0137352	+	0.999906i	$0.495628\pi$
$420$	0	0
$421$	26.3262	1.28306	0.641531	−	0.767097i	$-0.278300\pi$
$421$	26.3262	1.28306	0.641531	+	0.767097i	$0.278300\pi$
$422$	−9.27051	−0.451281
$423$	−5.23607	−0.254586
$424$	−8.09017	−0.392893
$425$	−26.5623	−1.28846
$426$	−5.79837	−0.280932
$427$	0	0
$428$	−9.47214	−0.457853
$429$	0.326238	0.0157509
$430$	1.96556	0.0947876
$431$	31.0902	1.49756	0.748780	−	0.662818i	$-0.230640\pi$
$431$	31.0902	1.49756	0.748780	+	0.662818i	$0.230640\pi$
$432$	1.85410	0.0892055
$433$	17.1246	0.822956	0.411478	−	0.911420i	$-0.365013\pi$
$433$	17.1246	0.822956	0.411478	+	0.911420i	$0.365013\pi$
$434$	0	0
$435$	−1.03444	−0.0495977
$436$	−24.3262	−1.16502
$437$	8.23607	0.393985
$438$	−2.14590	−0.102535
$439$	0.0557281	0.00265976	0.00132988	−	0.999999i	$-0.499577\pi$
$439$	0.0557281	0.00265976	0.00132988	+	0.999999i	$0.499577\pi$
$440$	1.90983	0.0910476
$441$	0	0
$442$	−0.493422	−0.0234697
$443$	−4.00000	−0.190046	−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000	−0.190046	−0.0950229	+	0.995475i	$0.530292\pi$
$444$	0.854102	0.0405339
$445$	6.23607	0.295618
$446$	1.65248	0.0782470
$447$	16.6525	0.787635
$448$	0	0
$449$	24.0902	1.13689	0.568443	−	0.822723i	$-0.307546\pi$
$449$	24.0902	1.13689	0.568443	+	0.822723i	$0.307546\pi$
$450$	3.00000	0.141421
$451$	−19.4721	−0.916907
$452$	−6.61803	−0.311286
$453$	11.7082	0.550099
$454$	−11.2918	−0.529950
$455$	0	0
$456$	18.4164	0.862427
$457$	−8.20163	−0.383656	−0.191828	−	0.981429i	$-0.561442\pi$
$457$	−8.20163	−0.383656	−0.191828	+	0.981429i	$0.561442\pi$
$458$	−13.1803	−0.615877
$459$	5.47214	0.255417
$460$	−0.618034	−0.0288160
$461$	−12.8541	−0.598675	−0.299338	−	0.954147i	$-0.596766\pi$
$461$	−12.8541	−0.598675	−0.299338	+	0.954147i	$0.596766\pi$
$462$	0	0
$463$	−34.5967	−1.60785	−0.803924	−	0.594733i	$-0.797258\pi$
$463$	−34.5967	−1.60785	−0.803924	+	0.594733i	$0.797258\pi$
$464$	−5.02129	−0.233107
$465$	1.90983	0.0885662
$466$	2.52786	0.117101
$467$	16.8885	0.781509	0.390754	−	0.920495i	$-0.372214\pi$
$467$	16.8885	0.781509	0.390754	+	0.920495i	$0.372214\pi$
$468$	−0.236068	−0.0109122
$469$	0	0
$470$	1.23607	0.0570156
$471$	−8.18034	−0.376930
$472$	10.8541	0.499601
$473$	−18.6180	−0.856058
$474$	−3.67376	−0.168741
$475$	−39.9787	−1.83435
$476$	0	0
$477$	−3.61803	−0.165658
$478$	2.70820	0.123870
$479$	−25.6525	−1.17209	−0.586046	−	0.810278i	$-0.699316\pi$
$479$	−25.6525	−1.17209	−0.586046	+	0.810278i	$0.699316\pi$
$480$	−2.14590	−0.0979464
$481$	−0.0770143	−0.00351155
$482$	9.45085	0.430474
$483$	0	0
$484$	9.70820	0.441282
$485$	6.56231	0.297979
$486$	−0.618034	−0.0280346
$487$	22.2361	1.00761	0.503806	−	0.863817i	$-0.331933\pi$
$487$	22.2361	1.00761	0.503806	+	0.863817i	$0.331933\pi$
$488$	20.3262	0.920126
$489$	15.5066	0.701232
$490$	0	0
$491$	16.9098	0.763130	0.381565	−	0.924342i	$-0.375385\pi$
$491$	16.9098	0.763130	0.381565	+	0.924342i	$0.375385\pi$
$492$	14.0902	0.635234
$493$	−14.8197	−0.667444
$494$	−0.742646	−0.0334132
$495$	0.854102	0.0383890
$496$	9.27051	0.416258
$497$	0	0
$498$	4.90983	0.220015
$499$	−11.7984	−0.528168	−0.264084	−	0.964500i	$-0.585070\pi$
$499$	−11.7984	−0.528168	−0.264084	+	0.964500i	$0.585070\pi$
$500$	6.09017	0.272361
$501$	−2.52786	−0.112937
$502$	−15.8885	−0.709140
$503$	9.90983	0.441857	0.220929	−	0.975290i	$-0.429091\pi$
$503$	9.90983	0.441857	0.220929	+	0.975290i	$0.429091\pi$
$504$	0	0
$505$	6.14590	0.273489
$506$	−1.38197	−0.0614359
$507$	−12.9787	−0.576405
$508$	29.6525	1.31562
$509$	−12.2918	−0.544824	−0.272412	−	0.962181i	$-0.587821\pi$
$509$	−12.2918	−0.544824	−0.272412	+	0.962181i	$0.587821\pi$
$510$	−1.29180	−0.0572017
$511$	0	0
$512$	−18.7082	−0.826794
$513$	8.23607	0.363631
$514$	10.0689	0.444119
$515$	−0.944272	−0.0416096
$516$	13.4721	0.593078
$517$	−11.7082	−0.514926
$518$	0	0
$519$	24.7082	1.08457
$520$	0.124612	0.00546459
$521$	12.4721	0.546414	0.273207	−	0.961955i	$-0.411916\pi$
$521$	12.4721	0.546414	0.273207	+	0.961955i	$0.411916\pi$
$522$	1.67376	0.0732586
$523$	20.8328	0.910955	0.455478	−	0.890247i	$-0.349468\pi$
$523$	20.8328	0.910955	0.455478	+	0.890247i	$0.349468\pi$
$524$	23.3262	1.01901
$525$	0	0
$526$	−3.09017	−0.134738
$527$	27.3607	1.19185
$528$	4.14590	0.180427
$529$	1.00000	0.0434783
$530$	0.854102	0.0370998
$531$	4.85410	0.210650
$532$	0	0
$533$	−1.27051	−0.0550319
$534$	−10.0902	−0.436644
$535$	2.23607	0.0966736
$536$	−15.3262	−0.661993
$537$	−9.03444	−0.389865
$538$	2.38197	0.102694
$539$	0	0
$540$	−0.618034	−0.0265959
$541$	−18.7639	−0.806724	−0.403362	−	0.915040i	$-0.632159\pi$
$541$	−18.7639	−0.806724	−0.403362	+	0.915040i	$0.632159\pi$
$542$	3.20163	0.137522
$543$	−7.18034	−0.308138
$544$	−30.7426	−1.31808
$545$	5.74265	0.245988
$546$	0	0
$547$	−24.3820	−1.04250	−0.521249	−	0.853405i	$-0.674534\pi$
$547$	−24.3820	−1.04250	−0.521249	+	0.853405i	$0.674534\pi$
$548$	3.32624	0.142090
$549$	9.09017	0.387959
$550$	6.70820	0.286039
$551$	−22.3050	−0.950223
$552$	2.23607	0.0951734
$553$	0	0
$554$	18.6738	0.793372
$555$	−0.201626	−0.00855855
$556$	21.2705	0.902071
$557$	−12.7639	−0.540825	−0.270413	−	0.962745i	$-0.587160\pi$
$557$	−12.7639	−0.540825	−0.270413	+	0.962745i	$0.587160\pi$
$558$	−3.09017	−0.130817
$559$	−1.21478	−0.0513798
$560$	0	0
$561$	12.2361	0.516607
$562$	−17.0557	−0.719452
$563$	11.5623	0.487293	0.243647	−	0.969864i	$-0.421656\pi$
$563$	11.5623	0.487293	0.243647	+	0.969864i	$0.421656\pi$
$564$	8.47214	0.356741
$565$	1.56231	0.0657267
$566$	−0.819660	−0.0344529
$567$	0	0
$568$	20.9787	0.880247
$569$	−43.7771	−1.83523	−0.917615	−	0.397469i	$-0.869889\pi$
$569$	−43.7771	−1.83523	−0.917615	+	0.397469i	$0.869889\pi$
$570$	−1.94427	−0.0814366
$571$	26.7771	1.12059	0.560293	−	0.828294i	$-0.310688\pi$
$571$	26.7771	1.12059	0.560293	+	0.828294i	$0.310688\pi$
$572$	−0.527864	−0.0220711
$573$	8.29180	0.346395
$574$	0	0
$575$	−4.85410	−0.202430
$576$	−0.236068	−0.00983617
$577$	−9.41641	−0.392010	−0.196005	−	0.980603i	$-0.562797\pi$
$577$	−9.41641	−0.392010	−0.196005	+	0.980603i	$0.562797\pi$
$578$	−8.00000	−0.332756
$579$	4.18034	0.173729
$580$	1.67376	0.0694992
$581$	0	0
$582$	−10.6180	−0.440132
$583$	−8.09017	−0.335061
$584$	7.76393	0.321274
$585$	0.0557281	0.00230407
$586$	−11.4164	−0.471607
$587$	17.5623	0.724874	0.362437	−	0.932008i	$-0.381945\pi$
$587$	17.5623	0.724874	0.362437	+	0.932008i	$0.381945\pi$
$588$	0	0
$589$	41.1803	1.69681
$590$	−1.14590	−0.0471759
$591$	−9.67376	−0.397925
$592$	−0.978714	−0.0402249
$593$	37.7082	1.54849	0.774245	−	0.632886i	$-0.218130\pi$
$593$	37.7082	1.54849	0.774245	+	0.632886i	$0.218130\pi$
$594$	−1.38197	−0.0567028
$595$	0	0
$596$	−26.9443	−1.10368
$597$	−10.5623	−0.432286
$598$	−0.0901699	−0.00368732
$599$	41.2705	1.68627	0.843134	−	0.537704i	$-0.180708\pi$
$599$	41.2705	1.68627	0.843134	+	0.537704i	$0.180708\pi$
$600$	−10.8541	−0.443117
$601$	25.5066	1.04044	0.520218	−	0.854034i	$-0.325851\pi$
$601$	25.5066	1.04044	0.520218	+	0.854034i	$0.325851\pi$
$602$	0	0
$603$	−6.85410	−0.279121
$604$	−18.9443	−0.770831
$605$	−2.29180	−0.0931748
$606$	−9.94427	−0.403958
$607$	10.6180	0.430973	0.215486	−	0.976507i	$-0.430866\pi$
$607$	10.6180	0.430973	0.215486	+	0.976507i	$0.430866\pi$
$608$	−46.2705	−1.87652
$609$	0	0
$610$	−2.14590	−0.0868849
$611$	−0.763932	−0.0309054
$612$	−8.85410	−0.357906
$613$	−37.6525	−1.52077	−0.760385	−	0.649473i	$-0.774990\pi$
$613$	−37.6525	−1.52077	−0.760385	+	0.649473i	$0.774990\pi$
$614$	4.97871	0.200925
$615$	−3.32624	−0.134127
$616$	0	0
$617$	37.7426	1.51946	0.759731	−	0.650238i	$-0.225331\pi$
$617$	37.7426	1.51946	0.759731	+	0.650238i	$0.225331\pi$
$618$	1.52786	0.0614597
$619$	33.2705	1.33725	0.668627	−	0.743598i	$-0.266882\pi$
$619$	33.2705	1.33725	0.668627	+	0.743598i	$0.266882\pi$
$620$	−3.09017	−0.124104
$621$	1.00000	0.0401286
$622$	3.32624	0.133370
$623$	0	0
$624$	0.270510	0.0108291
$625$	22.8328	0.913313
$626$	−6.47214	−0.258679
$627$	18.4164	0.735480
$628$	13.2361	0.528177
$629$	−2.88854	−0.115174
$630$	0	0
$631$	−38.2361	−1.52215	−0.761077	−	0.648662i	$-0.775329\pi$
$631$	−38.2361	−1.52215	−0.761077	+	0.648662i	$0.775329\pi$
$632$	13.2918	0.528719
$633$	15.0000	0.596196
$634$	17.8328	0.708232
$635$	−7.00000	−0.277787
$636$	5.85410	0.232130
$637$	0	0
$638$	3.74265	0.148173
$639$	9.38197	0.371145
$640$	4.34752	0.171851
$641$	−28.6180	−1.13034	−0.565172	−	0.824973i	$-0.691190\pi$
$641$	−28.6180	−1.13034	−0.565172	+	0.824973i	$0.691190\pi$
$642$	−3.61803	−0.142792
$643$	−2.50658	−0.0988498	−0.0494249	−	0.998778i	$-0.515739\pi$
$643$	−2.50658	−0.0988498	−0.0494249	+	0.998778i	$0.515739\pi$
$644$	0	0
$645$	−3.18034	−0.125226
$646$	−27.8541	−1.09590
$647$	−2.09017	−0.0821731	−0.0410865	−	0.999156i	$-0.513082\pi$
$647$	−2.09017	−0.0821731	−0.0410865	+	0.999156i	$0.513082\pi$
$648$	2.23607	0.0878410
$649$	10.8541	0.426061
$650$	0.437694	0.0171678
$651$	0	0
$652$	−25.0902	−0.982607
$653$	−32.0902	−1.25579	−0.627893	−	0.778300i	$-0.716082\pi$
$653$	−32.0902	−1.25579	−0.627893	+	0.778300i	$0.716082\pi$
$654$	−9.29180	−0.363338
$655$	−5.50658	−0.215160
$656$	−16.1459	−0.630391
$657$	3.47214	0.135461
$658$	0	0
$659$	−28.5967	−1.11397	−0.556986	−	0.830522i	$-0.688042\pi$
$659$	−28.5967	−1.11397	−0.556986	+	0.830522i	$0.688042\pi$
$660$	−1.38197	−0.0537930
$661$	−6.81966	−0.265254	−0.132627	−	0.991166i	$-0.542341\pi$
$661$	−6.81966	−0.265254	−0.132627	+	0.991166i	$0.542341\pi$
$662$	4.29180	0.166805
$663$	0.798374	0.0310063
$664$	−17.7639	−0.689374
$665$	0	0
$666$	0.326238	0.0126415
$667$	−2.70820	−0.104862
$668$	4.09017	0.158253
$669$	−2.67376	−0.103374
$670$	1.61803	0.0625101
$671$	20.3262	0.784686
$672$	0	0
$673$	21.9443	0.845890	0.422945	−	0.906155i	$-0.360996\pi$
$673$	21.9443	0.845890	0.422945	+	0.906155i	$0.360996\pi$
$674$	−0.965558	−0.0371919
$675$	−4.85410	−0.186834
$676$	21.0000	0.807692
$677$	−0.798374	−0.0306840	−0.0153420	−	0.999882i	$-0.504884\pi$
$677$	−0.798374	−0.0306840	−0.0153420	+	0.999882i	$0.504884\pi$
$678$	−2.52786	−0.0970820
$679$	0	0
$680$	4.67376	0.179231
$681$	18.2705	0.700127
$682$	−6.90983	−0.264591
$683$	40.7082	1.55766	0.778828	−	0.627237i	$-0.215814\pi$
$683$	40.7082	1.55766	0.778828	+	0.627237i	$0.215814\pi$
$684$	−13.3262	−0.509541
$685$	−0.785218	−0.0300016
$686$	0	0
$687$	21.3262	0.813647
$688$	−15.4377	−0.588557
$689$	−0.527864	−0.0201100
$690$	−0.236068	−0.00898695
$691$	20.7984	0.791207	0.395604	−	0.918421i	$-0.370535\pi$
$691$	20.7984	0.791207	0.395604	+	0.918421i	$0.370535\pi$
$692$	−39.9787	−1.51976
$693$	0	0
$694$	−17.0902	−0.648734
$695$	−5.02129	−0.190468
$696$	−6.05573	−0.229542
$697$	−47.6525	−1.80497
$698$	19.4721	0.737031
$699$	−4.09017	−0.154704
$700$	0	0
$701$	−31.7984	−1.20101	−0.600504	−	0.799622i	$-0.705033\pi$
$701$	−31.7984	−1.20101	−0.600504	+	0.799622i	$0.705033\pi$
$702$	−0.0901699	−0.00340325
$703$	−4.34752	−0.163970
$704$	−0.527864	−0.0198946
$705$	−2.00000	−0.0753244
$706$	13.9656	0.525601
$707$	0	0
$708$	−7.85410	−0.295175
$709$	−12.3262	−0.462922	−0.231461	−	0.972844i	$-0.574350\pi$
$709$	−12.3262	−0.462922	−0.231461	+	0.972844i	$0.574350\pi$
$710$	−2.21478	−0.0831193
$711$	5.94427	0.222928
$712$	36.5066	1.36814
$713$	5.00000	0.187251
$714$	0	0
$715$	0.124612	0.00466022
$716$	14.6180	0.546302
$717$	−4.38197	−0.163648
$718$	1.11146	0.0414792
$719$	−9.29180	−0.346526	−0.173263	−	0.984876i	$-0.555431\pi$
$719$	−9.29180	−0.346526	−0.173263	+	0.984876i	$0.555431\pi$
$720$	0.708204	0.0263932
$721$	0	0
$722$	−30.1803	−1.12320
$723$	−15.2918	−0.568708
$724$	11.6180	0.431781
$725$	13.1459	0.488226
$726$	3.70820	0.137624
$727$	30.2361	1.12139	0.560697	−	0.828021i	$-0.310533\pi$
$727$	30.2361	1.12139	0.560697	+	0.828021i	$0.310533\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−0.819660	−0.0303370
$731$	−45.5623	−1.68518
$732$	−14.7082	−0.543631
$733$	−28.5410	−1.05419	−0.527093	−	0.849807i	$-0.676718\pi$
$733$	−28.5410	−1.05419	−0.527093	+	0.849807i	$0.676718\pi$
$734$	14.4934	0.534962
$735$	0	0
$736$	−5.61803	−0.207083
$737$	−15.3262	−0.564549
$738$	5.38197	0.198113
$739$	−40.4164	−1.48674	−0.743371	−	0.668880i	$-0.766774\pi$
$739$	−40.4164	−1.48674	−0.743371	+	0.668880i	$0.766774\pi$
$740$	0.326238	0.0119927
$741$	1.20163	0.0441428
$742$	0	0
$743$	25.3951	0.931657	0.465828	−	0.884875i	$-0.345756\pi$
$743$	25.3951	0.931657	0.465828	+	0.884875i	$0.345756\pi$
$744$	11.1803	0.409891
$745$	6.36068	0.233037
$746$	20.3262	0.744196
$747$	−7.94427	−0.290666
$748$	−19.7984	−0.723900
$749$	0	0
$750$	2.32624	0.0849422
$751$	−32.0902	−1.17099	−0.585493	−	0.810677i	$-0.699099\pi$
$751$	−32.0902	−1.17099	−0.585493	+	0.810677i	$0.699099\pi$
$752$	−9.70820	−0.354022
$753$	25.7082	0.936859
$754$	0.244199	0.00889319
$755$	4.47214	0.162758
$756$	0	0
$757$	−32.4164	−1.17819	−0.589097	−	0.808062i	$-0.700516\pi$
$757$	−32.4164	−1.17819	−0.589097	+	0.808062i	$0.700516\pi$
$758$	1.88854	0.0685950
$759$	2.23607	0.0811641
$760$	7.03444	0.255166
$761$	−53.8885	−1.95346	−0.976729	−	0.214477i	$-0.931195\pi$
$761$	−53.8885	−1.95346	−0.976729	+	0.214477i	$0.931195\pi$
$762$	11.3262	0.410306
$763$	0	0
$764$	−13.4164	−0.485389
$765$	2.09017	0.0755703
$766$	−8.32624	−0.300839
$767$	0.708204	0.0255718
$768$	−6.56231	−0.236797
$769$	−47.9574	−1.72939	−0.864695	−	0.502298i	$-0.832488\pi$
$769$	−47.9574	−1.72939	−0.864695	+	0.502298i	$0.832488\pi$
$770$	0	0
$771$	−16.2918	−0.586735
$772$	−6.76393	−0.243439
$773$	36.0132	1.29530	0.647652	−	0.761937i	$-0.275751\pi$
$773$	36.0132	1.29530	0.647652	+	0.761937i	$0.275751\pi$
$774$	5.14590	0.184965
$775$	−24.2705	−0.871822
$776$	38.4164	1.37907
$777$	0	0
$778$	11.2016	0.401598
$779$	−71.7214	−2.56968
$780$	−0.0901699	−0.00322860
$781$	20.9787	0.750677
$782$	−3.38197	−0.120939
$783$	−2.70820	−0.0967833
$784$	0	0
$785$	−3.12461	−0.111522
$786$	8.90983	0.317803
$787$	1.79837	0.0641051	0.0320526	−	0.999486i	$-0.489796\pi$
$787$	1.79837	0.0641051	0.0320526	+	0.999486i	$0.489796\pi$
$788$	15.6525	0.557596
$789$	5.00000	0.178005
$790$	−1.40325	−0.0499255
$791$	0	0
$792$	5.00000	0.177667
$793$	1.32624	0.0470961
$794$	6.65248	0.236088
$795$	−1.38197	−0.0490133
$796$	17.0902	0.605745
$797$	3.70820	0.131351	0.0656757	−	0.997841i	$-0.479080\pi$
$797$	3.70820	0.131351	0.0656757	+	0.997841i	$0.479080\pi$
$798$	0	0
$799$	−28.6525	−1.01365
$800$	27.2705	0.964158
$801$	16.3262	0.576859
$802$	−18.0344	−0.636818
$803$	7.76393	0.273983
$804$	11.0902	0.391120
$805$	0	0
$806$	−0.450850	−0.0158805
$807$	−3.85410	−0.135671
$808$	35.9787	1.26573
$809$	−2.43769	−0.0857048	−0.0428524	−	0.999081i	$-0.513645\pi$
$809$	−2.43769	−0.0857048	−0.0428524	+	0.999081i	$0.513645\pi$
$810$	−0.236068	−0.00829458
$811$	25.5410	0.896867	0.448433	−	0.893816i	$-0.351982\pi$
$811$	25.5410	0.896867	0.448433	+	0.893816i	$0.351982\pi$
$812$	0	0
$813$	−5.18034	−0.181682
$814$	0.729490	0.0255686
$815$	5.92299	0.207473
$816$	10.1459	0.355177
$817$	−68.5755	−2.39915
$818$	−4.72949	−0.165363
$819$	0	0
$820$	5.38197	0.187946
$821$	12.2918	0.428987	0.214493	−	0.976725i	$-0.431190\pi$
$821$	12.2918	0.428987	0.214493	+	0.976725i	$0.431190\pi$
$822$	1.27051	0.0443141
$823$	8.02129	0.279604	0.139802	−	0.990179i	$-0.455353\pi$
$823$	8.02129	0.279604	0.139802	+	0.990179i	$0.455353\pi$
$824$	−5.52786	−0.192572
$825$	−10.8541	−0.377891
$826$	0	0
$827$	−22.8541	−0.794715	−0.397357	−	0.917664i	$-0.630073\pi$
$827$	−22.8541	−0.794715	−0.397357	+	0.917664i	$0.630073\pi$
$828$	−1.61803	−0.0562306
$829$	−35.0689	−1.21799	−0.608996	−	0.793173i	$-0.708428\pi$
$829$	−35.0689	−1.21799	−0.608996	+	0.793173i	$0.708428\pi$
$830$	1.87539	0.0650957
$831$	−30.2148	−1.04814
$832$	−0.0344419	−0.00119406
$833$	0	0
$834$	8.12461	0.281332
$835$	−0.965558	−0.0334145
$836$	−29.7984	−1.03060
$837$	5.00000	0.172825
$838$	−0.347524	−0.0120050
$839$	2.72949	0.0942325	0.0471162	−	0.998889i	$-0.484997\pi$
$839$	2.72949	0.0942325	0.0471162	+	0.998889i	$0.484997\pi$
$840$	0	0
$841$	−21.6656	−0.747091
$842$	−16.2705	−0.560719
$843$	27.5967	0.950482
$844$	−24.2705	−0.835425
$845$	−4.95743	−0.170541
$846$	3.23607	0.111258
$847$	0	0
$848$	−6.70820	−0.230361
$849$	1.32624	0.0455164
$850$	16.4164	0.563078
$851$	−0.527864	−0.0180949
$852$	−15.1803	−0.520070
$853$	42.6525	1.46039	0.730196	−	0.683237i	$-0.239429\pi$
$853$	42.6525	1.46039	0.730196	+	0.683237i	$0.239429\pi$
$854$	0	0
$855$	3.14590	0.107587
$856$	13.0902	0.447413
$857$	−43.9574	−1.50156	−0.750779	−	0.660554i	$-0.770321\pi$
$857$	−43.9574	−1.50156	−0.750779	+	0.660554i	$0.770321\pi$
$858$	−0.201626	−0.00688340
$859$	−1.41641	−0.0483272	−0.0241636	−	0.999708i	$-0.507692\pi$
$859$	−1.41641	−0.0483272	−0.0241636	+	0.999708i	$0.507692\pi$
$860$	5.14590	0.175474
$861$	0	0
$862$	−19.2148	−0.654458
$863$	31.5967	1.07557	0.537783	−	0.843083i	$-0.319262\pi$
$863$	31.5967	1.07557	0.537783	+	0.843083i	$0.319262\pi$
$864$	−5.61803	−0.191129
$865$	9.43769	0.320891
$866$	−10.5836	−0.359645
$867$	12.9443	0.439611
$868$	0	0
$869$	13.2918	0.450893
$870$	0.639320	0.0216750
$871$	−1.00000	−0.0338837
$872$	33.6180	1.13845
$873$	17.1803	0.581466
$874$	−5.09017	−0.172178
$875$	0	0
$876$	−5.61803	−0.189816
$877$	−26.4721	−0.893901	−0.446950	−	0.894559i	$-0.647490\pi$
$877$	−26.4721	−0.893901	−0.446950	+	0.894559i	$0.647490\pi$
$878$	−0.0344419	−0.00116236
$879$	18.4721	0.623050
$880$	1.58359	0.0533829
$881$	40.5410	1.36586	0.682931	−	0.730483i	$-0.260705\pi$
$881$	40.5410	1.36586	0.682931	+	0.730483i	$0.260705\pi$
$882$	0	0
$883$	7.74265	0.260561	0.130280	−	0.991477i	$-0.458412\pi$
$883$	7.74265	0.260561	0.130280	+	0.991477i	$0.458412\pi$
$884$	−1.29180	−0.0434478
$885$	1.85410	0.0623250
$886$	2.47214	0.0830530
$887$	−22.3262	−0.749642	−0.374821	−	0.927097i	$-0.622296\pi$
$887$	−22.3262	−0.749642	−0.374821	+	0.927097i	$0.622296\pi$
$888$	−1.18034	−0.0396096
$889$	0	0
$890$	−3.85410	−0.129190
$891$	2.23607	0.0749111
$892$	4.32624	0.144853
$893$	−43.1246	−1.44311
$894$	−10.2918	−0.344209
$895$	−3.45085	−0.115349
$896$	0	0
$897$	0.145898	0.00487139
$898$	−14.8885	−0.496837
$899$	−13.5410	−0.451618
$900$	7.85410	0.261803
$901$	−19.7984	−0.659579
$902$	12.0344	0.400703
$903$	0	0
$904$	9.14590	0.304188
$905$	−2.74265	−0.0911686
$906$	−7.23607	−0.240402
$907$	−0.673762	−0.0223719	−0.0111860	−	0.999937i	$-0.503561\pi$
$907$	−0.673762	−0.0223719	−0.0111860	+	0.999937i	$0.503561\pi$
$908$	−29.5623	−0.981060
$909$	16.0902	0.533677
$910$	0	0
$911$	−31.7082	−1.05054	−0.525270	−	0.850936i	$-0.676036\pi$
$911$	−31.7082	−1.05054	−0.525270	+	0.850936i	$0.676036\pi$
$912$	15.2705	0.505657
$913$	−17.7639	−0.587900
$914$	5.06888	0.167664
$915$	3.47214	0.114785
$916$	−34.5066	−1.14013
$917$	0	0
$918$	−3.38197	−0.111622
$919$	−48.4853	−1.59938	−0.799691	−	0.600412i	$-0.795003\pi$
$919$	−48.4853	−1.59938	−0.799691	+	0.600412i	$0.795003\pi$
$920$	0.854102	0.0281589
$921$	−8.05573	−0.265445
$922$	7.94427	0.261631
$923$	1.36881	0.0450549
$924$	0	0
$925$	2.56231	0.0842481
$926$	21.3820	0.702655
$927$	−2.47214	−0.0811956
$928$	15.2148	0.499450
$929$	8.74265	0.286837	0.143418	−	0.989662i	$-0.454191\pi$
$929$	8.74265	0.286837	0.143418	+	0.989662i	$0.454191\pi$
$930$	−1.18034	−0.0387049
$931$	0	0
$932$	6.61803	0.216781
$933$	−5.38197	−0.176198
$934$	−10.4377	−0.341532
$935$	4.67376	0.152848
$936$	0.326238	0.0106634
$937$	−11.3607	−0.371137	−0.185569	−	0.982631i	$-0.559413\pi$
$937$	−11.3607	−0.371137	−0.185569	+	0.982631i	$0.559413\pi$
$938$	0	0
$939$	10.4721	0.341745
$940$	3.23607	0.105549
$941$	−18.8328	−0.613932	−0.306966	−	0.951720i	$-0.599314\pi$
$941$	−18.8328	−0.613932	−0.306966	+	0.951720i	$0.599314\pi$
$942$	5.05573	0.164725
$943$	−8.70820	−0.283578
$944$	9.00000	0.292925
$945$	0	0
$946$	11.5066	0.374111
$947$	42.7214	1.38826	0.694129	−	0.719851i	$-0.255790\pi$
$947$	42.7214	1.38826	0.694129	+	0.719851i	$0.255790\pi$
$948$	−9.61803	−0.312379
$949$	0.506578	0.0164442
$950$	24.7082	0.801640
$951$	−28.8541	−0.935658
$952$	0	0
$953$	−15.9230	−0.515796	−0.257898	−	0.966172i	$-0.583030\pi$
$953$	−15.9230	−0.515796	−0.257898	+	0.966172i	$0.583030\pi$
$954$	2.23607	0.0723954
$955$	3.16718	0.102488
$956$	7.09017	0.229312
$957$	−6.05573	−0.195754
$958$	15.8541	0.512223
$959$	0	0
$960$	−0.0901699	−0.00291022
$961$	−6.00000	−0.193548
$962$	0.0475975	0.00153460
$963$	5.85410	0.188646
$964$	24.7426	0.796907
$965$	1.59675	0.0514011
$966$	0	0
$967$	−7.52786	−0.242080	−0.121040	−	0.992648i	$-0.538623\pi$
$967$	−7.52786	−0.242080	−0.121040	+	0.992648i	$0.538623\pi$
$968$	−13.4164	−0.431220
$969$	45.0689	1.44782
$970$	−4.05573	−0.130222
$971$	2.90983	0.0933809	0.0466904	−	0.998909i	$-0.485133\pi$
$971$	2.90983	0.0933809	0.0466904	+	0.998909i	$0.485133\pi$
$972$	−1.61803	−0.0518985
$973$	0	0
$974$	−13.7426	−0.440343
$975$	−0.708204	−0.0226807
$976$	16.8541	0.539487
$977$	7.02129	0.224631	0.112315	−	0.993673i	$-0.464173\pi$
$977$	7.02129	0.224631	0.112315	+	0.993673i	$0.464173\pi$
$978$	−9.58359	−0.306449
$979$	36.5066	1.16676
$980$	0	0
$981$	15.0344	0.480013
$982$	−10.4508	−0.333500
$983$	14.6393	0.466922	0.233461	−	0.972366i	$-0.424995\pi$
$983$	14.6393	0.466922	0.233461	+	0.972366i	$0.424995\pi$
$984$	−19.4721	−0.620749
$985$	−3.69505	−0.117734
$986$	9.15905	0.291684
$987$	0	0
$988$	−1.94427	−0.0618555
$989$	−8.32624	−0.264759
$990$	−0.527864	−0.0167766
$991$	18.3262	0.582152	0.291076	−	0.956700i	$-0.405987\pi$
$991$	18.3262	0.582152	0.291076	+	0.956700i	$0.405987\pi$
$992$	−28.0902	−0.891864
$993$	−6.94427	−0.220370
$994$	0	0
$995$	−4.03444	−0.127900
$996$	12.8541	0.407298
$997$	−41.5410	−1.31562	−0.657809	−	0.753185i	$-0.728516\pi$
$997$	−41.5410	−1.31562	−0.657809	+	0.753185i	$0.728516\pi$
$998$	7.29180	0.230818
$999$	−0.527864	−0.0167009

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3381.2.a.u.1.1		2
7.6	odd	2		483.2.a.g.1.1	✓	2
21.20	even	2		1449.2.a.f.1.2		2
28.27	even	2		7728.2.a.bg.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.a.g.1.1	✓	2	7.6	odd	2
1449.2.a.f.1.2		2	21.20	even	2
3381.2.a.u.1.1		2	1.1	even	1	trivial
7728.2.a.bg.1.2		2	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3381.a (trivial)

\(f(q)\)	\(=\)	\(q-0.618034 q^{2} +1.00000 q^{3} -1.61803 q^{4} +0.381966 q^{5} -0.618034 q^{6} +2.23607 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.618034 q^{2} +1.00000 q^{3} -1.61803 q^{4} +0.381966 q^{5} -0.618034 q^{6} +2.23607 q^{8} +1.00000 q^{9} -0.236068 q^{10} +2.23607 q^{11} -1.61803 q^{12} +0.145898 q^{13} +0.381966 q^{15} +1.85410 q^{16} +5.47214 q^{17} -0.618034 q^{18} +8.23607 q^{19} -0.618034 q^{20} -1.38197 q^{22} +1.00000 q^{23} +2.23607 q^{24} -4.85410 q^{25} -0.0901699 q^{26} +1.00000 q^{27} -2.70820 q^{29} -0.236068 q^{30} +5.00000 q^{31} -5.61803 q^{32} +2.23607 q^{33} -3.38197 q^{34} -1.61803 q^{36} -0.527864 q^{37} -5.09017 q^{38} +0.145898 q^{39} +0.854102 q^{40} -8.70820 q^{41} -8.32624 q^{43} -3.61803 q^{44} +0.381966 q^{45} -0.618034 q^{46} -5.23607 q^{47} +1.85410 q^{48} +3.00000 q^{50} +5.47214 q^{51} -0.236068 q^{52} -3.61803 q^{53} -0.618034 q^{54} +0.854102 q^{55} +8.23607 q^{57} +1.67376 q^{58} +4.85410 q^{59} -0.618034 q^{60} +9.09017 q^{61} -3.09017 q^{62} -0.236068 q^{64} +0.0557281 q^{65} -1.38197 q^{66} -6.85410 q^{67} -8.85410 q^{68} +1.00000 q^{69} +9.38197 q^{71} +2.23607 q^{72} +3.47214 q^{73} +0.326238 q^{74} -4.85410 q^{75} -13.3262 q^{76} -0.0901699 q^{78} +5.94427 q^{79} +0.708204 q^{80} +1.00000 q^{81} +5.38197 q^{82} -7.94427 q^{83} +2.09017 q^{85} +5.14590 q^{86} -2.70820 q^{87} +5.00000 q^{88} +16.3262 q^{89} -0.236068 q^{90} -1.61803 q^{92} +5.00000 q^{93} +3.23607 q^{94} +3.14590 q^{95} -5.61803 q^{96} +17.1803 q^{97} +2.23607 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} + 2 q^{3} - q^{4} + 3 q^{5} + q^{6} + 2 q^{9}+O(q^{10}) \) 2 * q + q^2 + 2 * q^3 - q^4 + 3 * q^5 + q^6 + 2 * q^9	\( 2 q + q^{2} + 2 q^{3} - q^{4} + 3 q^{5} + q^{6} + 2 q^{9} + 4 q^{10} - q^{12} + 7 q^{13} + 3 q^{15} - 3 q^{16} + 2 q^{17} + q^{18} + 12 q^{19} + q^{20} - 5 q^{22} + 2 q^{23} - 3 q^{25} + 11 q^{26} + 2 q^{27} + 8 q^{29} + 4 q^{30} + 10 q^{31} - 9 q^{32} - 9 q^{34} - q^{36} - 10 q^{37} + q^{38} + 7 q^{39} - 5 q^{40} - 4 q^{41} - q^{43} - 5 q^{44} + 3 q^{45} + q^{46} - 6 q^{47} - 3 q^{48} + 6 q^{50} + 2 q^{51} + 4 q^{52} - 5 q^{53} + q^{54} - 5 q^{55} + 12 q^{57} + 19 q^{58} + 3 q^{59} + q^{60} + 7 q^{61} + 5 q^{62} + 4 q^{64} + 18 q^{65} - 5 q^{66} - 7 q^{67} - 11 q^{68} + 2 q^{69} + 21 q^{71} - 2 q^{73} - 15 q^{74} - 3 q^{75} - 11 q^{76} + 11 q^{78} - 6 q^{79} - 12 q^{80} + 2 q^{81} + 13 q^{82} + 2 q^{83} - 7 q^{85} + 17 q^{86} + 8 q^{87} + 10 q^{88} + 17 q^{89} + 4 q^{90} - q^{92} + 10 q^{93} + 2 q^{94} + 13 q^{95} - 9 q^{96} + 12 q^{97}+O(q^{100}) \) 2 * q + q^2 + 2 * q^3 - q^4 + 3 * q^5 + q^6 + 2 * q^9 + 4 * q^10 - q^12 + 7 * q^13 + 3 * q^15 - 3 * q^16 + 2 * q^17 + q^18 + 12 * q^19 + q^20 - 5 * q^22 + 2 * q^23 - 3 * q^25 + 11 * q^26 + 2 * q^27 + 8 * q^29 + 4 * q^30 + 10 * q^31 - 9 * q^32 - 9 * q^34 - q^36 - 10 * q^37 + q^38 + 7 * q^39 - 5 * q^40 - 4 * q^41 - q^43 - 5 * q^44 + 3 * q^45 + q^46 - 6 * q^47 - 3 * q^48 + 6 * q^50 + 2 * q^51 + 4 * q^52 - 5 * q^53 + q^54 - 5 * q^55 + 12 * q^57 + 19 * q^58 + 3 * q^59 + q^60 + 7 * q^61 + 5 * q^62 + 4 * q^64 + 18 * q^65 - 5 * q^66 - 7 * q^67 - 11 * q^68 + 2 * q^69 + 21 * q^71 - 2 * q^73 - 15 * q^74 - 3 * q^75 - 11 * q^76 + 11 * q^78 - 6 * q^79 - 12 * q^80 + 2 * q^81 + 13 * q^82 + 2 * q^83 - 7 * q^85 + 17 * q^86 + 8 * q^87 + 10 * q^88 + 17 * q^89 + 4 * q^90 - q^92 + 10 * q^93 + 2 * q^94 + 13 * q^95 - 9 * q^96 + 12 * q^97

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