LMFDB - Embedded newform 2009.2.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2009,2,Mod(1,2009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2009, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2009 = 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2009.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:	$16.0419457661$
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 287)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	2009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.618034 q^{2} +0.381966 q^{3} -1.61803 q^{4} +1.61803 q^{5} +0.236068 q^{6} -2.23607 q^{8} -2.85410 q^{9} +O(q^{10})$	\(q+0.618034 q^{2} +0.381966 q^{3} -1.61803 q^{4} +1.61803 q^{5} +0.236068 q^{6} -2.23607 q^{8} -2.85410 q^{9} +1.00000 q^{10} -2.23607 q^{11} -0.618034 q^{12} +3.00000 q^{13} +0.618034 q^{15} +1.85410 q^{16} -1.47214 q^{17} -1.76393 q^{18} +4.85410 q^{19} -2.61803 q^{20} -1.38197 q^{22} +0.381966 q^{23} -0.854102 q^{24} -2.38197 q^{25} +1.85410 q^{26} -2.23607 q^{27} +7.85410 q^{29} +0.381966 q^{30} +9.61803 q^{31} +5.61803 q^{32} -0.854102 q^{33} -0.909830 q^{34} +4.61803 q^{36} +7.70820 q^{37} +3.00000 q^{38} +1.14590 q^{39} -3.61803 q^{40} -1.00000 q^{41} +7.94427 q^{43} +3.61803 q^{44} -4.61803 q^{45} +0.236068 q^{46} +3.23607 q^{47} +0.708204 q^{48} -1.47214 q^{50} -0.562306 q^{51} -4.85410 q^{52} -14.0902 q^{53} -1.38197 q^{54} -3.61803 q^{55} +1.85410 q^{57} +4.85410 q^{58} -7.61803 q^{59} -1.00000 q^{60} +11.0000 q^{61} +5.94427 q^{62} -0.236068 q^{64} +4.85410 q^{65} -0.527864 q^{66} +4.38197 q^{67} +2.38197 q^{68} +0.145898 q^{69} +0.236068 q^{71} +6.38197 q^{72} +15.0000 q^{73} +4.76393 q^{74} -0.909830 q^{75} -7.85410 q^{76} +0.708204 q^{78} -7.70820 q^{79} +3.00000 q^{80} +7.70820 q^{81} -0.618034 q^{82} -11.9443 q^{83} -2.38197 q^{85} +4.90983 q^{86} +3.00000 q^{87} +5.00000 q^{88} +14.5623 q^{89} -2.85410 q^{90} -0.618034 q^{92} +3.67376 q^{93} +2.00000 q^{94} +7.85410 q^{95} +2.14590 q^{96} +5.14590 q^{97} +6.38197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 3 q^{3} - q^{4} + q^{5} - 4 q^{6} + q^{9}+O(q^{10}) $ 2 * q - q^2 + 3 * q^3 - q^4 + q^5 - 4 * q^6 + q^9	$ 2 q - q^{2} + 3 q^{3} - q^{4} + q^{5} - 4 q^{6} + q^{9} + 2 q^{10} + q^{12} + 6 q^{13} - q^{15} - 3 q^{16} + 6 q^{17} - 8 q^{18} + 3 q^{19} - 3 q^{20} - 5 q^{22} + 3 q^{23} + 5 q^{24} - 7 q^{25} - 3 q^{26} + 9 q^{29} + 3 q^{30} + 17 q^{31} + 9 q^{32} + 5 q^{33} - 13 q^{34} + 7 q^{36} + 2 q^{37} + 6 q^{38} + 9 q^{39} - 5 q^{40} - 2 q^{41} - 2 q^{43} + 5 q^{44} - 7 q^{45} - 4 q^{46} + 2 q^{47} - 12 q^{48} + 6 q^{50} + 19 q^{51} - 3 q^{52} - 17 q^{53} - 5 q^{54} - 5 q^{55} - 3 q^{57} + 3 q^{58} - 13 q^{59} - 2 q^{60} + 22 q^{61} - 6 q^{62} + 4 q^{64} + 3 q^{65} - 10 q^{66} + 11 q^{67} + 7 q^{68} + 7 q^{69} - 4 q^{71} + 15 q^{72} + 30 q^{73} + 14 q^{74} - 13 q^{75} - 9 q^{76} - 12 q^{78} - 2 q^{79} + 6 q^{80} + 2 q^{81} + q^{82} - 6 q^{83} - 7 q^{85} + 21 q^{86} + 6 q^{87} + 10 q^{88} + 9 q^{89} + q^{90} + q^{92} + 23 q^{93} + 4 q^{94} + 9 q^{95} + 11 q^{96} + 17 q^{97} + 15 q^{99}+O(q^{100}) $ 2 * q - q^2 + 3 * q^3 - q^4 + q^5 - 4 * q^6 + q^9 + 2 * q^10 + q^12 + 6 * q^13 - q^15 - 3 * q^16 + 6 * q^17 - 8 * q^18 + 3 * q^19 - 3 * q^20 - 5 * q^22 + 3 * q^23 + 5 * q^24 - 7 * q^25 - 3 * q^26 + 9 * q^29 + 3 * q^30 + 17 * q^31 + 9 * q^32 + 5 * q^33 - 13 * q^34 + 7 * q^36 + 2 * q^37 + 6 * q^38 + 9 * q^39 - 5 * q^40 - 2 * q^41 - 2 * q^43 + 5 * q^44 - 7 * q^45 - 4 * q^46 + 2 * q^47 - 12 * q^48 + 6 * q^50 + 19 * q^51 - 3 * q^52 - 17 * q^53 - 5 * q^54 - 5 * q^55 - 3 * q^57 + 3 * q^58 - 13 * q^59 - 2 * q^60 + 22 * q^61 - 6 * q^62 + 4 * q^64 + 3 * q^65 - 10 * q^66 + 11 * q^67 + 7 * q^68 + 7 * q^69 - 4 * q^71 + 15 * q^72 + 30 * q^73 + 14 * q^74 - 13 * q^75 - 9 * q^76 - 12 * q^78 - 2 * q^79 + 6 * q^80 + 2 * q^81 + q^82 - 6 * q^83 - 7 * q^85 + 21 * q^86 + 6 * q^87 + 10 * q^88 + 9 * q^89 + q^90 + q^92 + 23 * q^93 + 4 * q^94 + 9 * q^95 + 11 * q^96 + 17 * q^97 + 15 * 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 $

$2$	0.618034	0.437016	0.218508	−	0.975835i	$-0.429881\pi$
$2$	0.618034	0.437016	0.218508	+	0.975835i	$0.429881\pi$
$3$	0.381966	0.220528	0.110264	−	0.993902i	$-0.464830\pi$
$3$	0.381966	0.220528	0.110264	+	0.993902i	$0.464830\pi$
$4$	−1.61803	−0.809017
$5$	1.61803	0.723607	0.361803	−	0.932254i	$-0.382161\pi$
$5$	1.61803	0.723607	0.361803	+	0.932254i	$0.382161\pi$
$6$	0.236068	0.0963743
$7$	0	0
$7$	0	0
$8$	−2.23607	−0.790569
$9$	−2.85410	−0.951367
$10$	1.00000	0.316228
$11$	−2.23607	−0.674200	−0.337100	−	0.941469i	$-0.609446\pi$
$11$	−2.23607	−0.674200	−0.337100	+	0.941469i	$0.609446\pi$
$12$	−0.618034	−0.178411
$13$	3.00000	0.832050	0.416025	−	0.909353i	$-0.363423\pi$
$13$	3.00000	0.832050	0.416025	+	0.909353i	$0.363423\pi$
$14$	0	0
$15$	0.618034	0.159576
$16$	1.85410	0.463525
$17$	−1.47214	−0.357045	−0.178523	−	0.983936i	$-0.557132\pi$
$17$	−1.47214	−0.357045	−0.178523	+	0.983936i	$0.557132\pi$
$18$	−1.76393	−0.415763
$19$	4.85410	1.11361	0.556804	−	0.830644i	$-0.312028\pi$
$19$	4.85410	1.11361	0.556804	+	0.830644i	$0.312028\pi$
$20$	−2.61803	−0.585410
$21$	0	0
$22$	−1.38197	−0.294636
$23$	0.381966	0.0796454	0.0398227	−	0.999207i	$-0.487321\pi$
$23$	0.381966	0.0796454	0.0398227	+	0.999207i	$0.487321\pi$
$24$	−0.854102	−0.174343
$25$	−2.38197	−0.476393
$26$	1.85410	0.363619
$27$	−2.23607	−0.430331
$28$	0	0
$29$	7.85410	1.45847	0.729235	−	0.684263i	$-0.239876\pi$
$29$	7.85410	1.45847	0.729235	+	0.684263i	$0.239876\pi$
$30$	0.381966	0.0697371
$31$	9.61803	1.72745	0.863725	−	0.503964i	$-0.168125\pi$
$31$	9.61803	1.72745	0.863725	+	0.503964i	$0.168125\pi$
$32$	5.61803	0.993137
$33$	−0.854102	−0.148680
$34$	−0.909830	−0.156035
$35$	0	0
$36$	4.61803	0.769672
$37$	7.70820	1.26722	0.633610	−	0.773652i	$-0.281572\pi$
$37$	7.70820	1.26722	0.633610	+	0.773652i	$0.281572\pi$
$38$	3.00000	0.486664
$39$	1.14590	0.183491
$40$	−3.61803	−0.572061
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	7.94427	1.21149	0.605745	−	0.795659i	$-0.292875\pi$
$43$	7.94427	1.21149	0.605745	+	0.795659i	$0.292875\pi$
$44$	3.61803	0.545439
$45$	−4.61803	−0.688416
$46$	0.236068	0.0348063
$47$	3.23607	0.472029	0.236015	−	0.971750i	$-0.424159\pi$
$47$	3.23607	0.472029	0.236015	+	0.971750i	$0.424159\pi$
$48$	0.708204	0.102220
$49$	0	0
$50$	−1.47214	−0.208191
$51$	−0.562306	−0.0787386
$52$	−4.85410	−0.673143
$53$	−14.0902	−1.93543	−0.967717	−	0.252040i	$-0.918899\pi$
$53$	−14.0902	−1.93543	−0.967717	+	0.252040i	$0.918899\pi$
$54$	−1.38197	−0.188062
$55$	−3.61803	−0.487856
$56$	0	0
$57$	1.85410	0.245582
$58$	4.85410	0.637375
$59$	−7.61803	−0.991784	−0.495892	−	0.868384i	$-0.665159\pi$
$59$	−7.61803	−0.991784	−0.495892	+	0.868384i	$0.665159\pi$
$60$	−1.00000	−0.129099
$61$	11.0000	1.40841	0.704203	−	0.709999i	$-0.251305\pi$
$61$	11.0000	1.40841	0.704203	+	0.709999i	$0.251305\pi$
$62$	5.94427	0.754923
$63$	0	0
$64$	−0.236068	−0.0295085
$65$	4.85410	0.602077
$66$	−0.527864	−0.0649756
$67$	4.38197	0.535342	0.267671	−	0.963510i	$-0.413746\pi$
$67$	4.38197	0.535342	0.267671	+	0.963510i	$0.413746\pi$
$68$	2.38197	0.288856
$69$	0.145898	0.0175641
$70$	0	0
$71$	0.236068	0.0280161	0.0140081	−	0.999902i	$-0.495541\pi$
$71$	0.236068	0.0280161	0.0140081	+	0.999902i	$0.495541\pi$
$72$	6.38197	0.752122
$73$	15.0000	1.75562	0.877809	−	0.479012i	$-0.159005\pi$
$73$	15.0000	1.75562	0.877809	+	0.479012i	$0.159005\pi$
$74$	4.76393	0.553796
$75$	−0.909830	−0.105058
$76$	−7.85410	−0.900927
$77$	0	0
$78$	0.708204	0.0801883
$79$	−7.70820	−0.867241	−0.433620	−	0.901096i	$-0.642764\pi$
$79$	−7.70820	−0.867241	−0.433620	+	0.901096i	$0.642764\pi$
$80$	3.00000	0.335410
$81$	7.70820	0.856467
$82$	−0.618034	−0.0682504
$83$	−11.9443	−1.31105	−0.655527	−	0.755172i	$-0.727553\pi$
$83$	−11.9443	−1.31105	−0.655527	+	0.755172i	$0.727553\pi$
$84$	0	0
$85$	−2.38197	−0.258360
$86$	4.90983	0.529441
$87$	3.00000	0.321634
$88$	5.00000	0.533002
$89$	14.5623	1.54360	0.771801	−	0.635865i	$-0.219356\pi$
$89$	14.5623	1.54360	0.771801	+	0.635865i	$0.219356\pi$
$90$	−2.85410	−0.300849
$91$	0	0
$92$	−0.618034	−0.0644345
$93$	3.67376	0.380951
$94$	2.00000	0.206284
$95$	7.85410	0.805814
$96$	2.14590	0.219015
$97$	5.14590	0.522487	0.261243	−	0.965273i	$-0.415867\pi$
$97$	5.14590	0.522487	0.261243	+	0.965273i	$0.415867\pi$
$98$	0	0
$99$	6.38197	0.641412
$100$	3.85410	0.385410
$101$	−1.76393	−0.175518	−0.0877589	−	0.996142i	$-0.527971\pi$
$101$	−1.76393	−0.175518	−0.0877589	+	0.996142i	$0.527971\pi$
$102$	−0.347524	−0.0344100
$103$	−3.56231	−0.351004	−0.175502	−	0.984479i	$-0.556155\pi$
$103$	−3.56231	−0.351004	−0.175502	+	0.984479i	$0.556155\pi$
$104$	−6.70820	−0.657794
$105$	0	0
$106$	−8.70820	−0.845816
$107$	9.70820	0.938527	0.469264	−	0.883058i	$-0.344519\pi$
$107$	9.70820	0.938527	0.469264	+	0.883058i	$0.344519\pi$
$108$	3.61803	0.348145
$109$	−6.94427	−0.665141	−0.332570	−	0.943078i	$-0.607916\pi$
$109$	−6.94427	−0.665141	−0.332570	+	0.943078i	$0.607916\pi$
$110$	−2.23607	−0.213201
$111$	2.94427	0.279458
$112$	0	0
$113$	−9.94427	−0.935478	−0.467739	−	0.883867i	$-0.654931\pi$
$113$	−9.94427	−0.935478	−0.467739	+	0.883867i	$0.654931\pi$
$114$	1.14590	0.107323
$115$	0.618034	0.0576320
$116$	−12.7082	−1.17993
$117$	−8.56231	−0.791585
$118$	−4.70820	−0.433425
$119$	0	0
$120$	−1.38197	−0.126156
$121$	−6.00000	−0.545455
$122$	6.79837	0.615496
$123$	−0.381966	−0.0344407
$124$	−15.5623	−1.39754
$125$	−11.9443	−1.06833
$126$	0	0
$127$	−11.6525	−1.03399	−0.516995	−	0.855988i	$-0.672949\pi$
$127$	−11.6525	−1.03399	−0.516995	+	0.855988i	$0.672949\pi$
$128$	−11.3820	−1.00603
$129$	3.03444	0.267168
$130$	3.00000	0.263117
$131$	8.38197	0.732336	0.366168	−	0.930549i	$-0.380670\pi$
$131$	8.38197	0.732336	0.366168	+	0.930549i	$0.380670\pi$
$132$	1.38197	0.120285
$133$	0	0
$134$	2.70820	0.233953
$135$	−3.61803	−0.311391
$136$	3.29180	0.282269
$137$	−9.61803	−0.821724	−0.410862	−	0.911698i	$-0.634772\pi$
$137$	−9.61803	−0.821724	−0.410862	+	0.911698i	$0.634772\pi$
$138$	0.0901699	0.00767578
$139$	18.4164	1.56206	0.781030	−	0.624494i	$-0.214695\pi$
$139$	18.4164	1.56206	0.781030	+	0.624494i	$0.214695\pi$
$140$	0	0
$141$	1.23607	0.104096
$142$	0.145898	0.0122435
$143$	−6.70820	−0.560968
$144$	−5.29180	−0.440983
$145$	12.7082	1.05536
$146$	9.27051	0.767233
$147$	0	0
$148$	−12.4721	−1.02520
$149$	19.8885	1.62933	0.814666	−	0.579930i	$-0.196920\pi$
$149$	19.8885	1.62933	0.814666	+	0.579930i	$0.196920\pi$
$150$	−0.562306	−0.0459121
$151$	17.6525	1.43654	0.718269	−	0.695765i	$-0.244935\pi$
$151$	17.6525	1.43654	0.718269	+	0.695765i	$0.244935\pi$
$152$	−10.8541	−0.880384
$153$	4.20163	0.339681
$154$	0	0
$155$	15.5623	1.24999
$156$	−1.85410	−0.148447
$157$	7.41641	0.591894	0.295947	−	0.955204i	$-0.404365\pi$
$157$	7.41641	0.591894	0.295947	+	0.955204i	$0.404365\pi$
$158$	−4.76393	−0.378998
$159$	−5.38197	−0.426818
$160$	9.09017	0.718641
$161$	0	0
$162$	4.76393	0.374290
$163$	5.52786	0.432976	0.216488	−	0.976285i	$-0.430540\pi$
$163$	5.52786	0.432976	0.216488	+	0.976285i	$0.430540\pi$
$164$	1.61803	0.126347
$165$	−1.38197	−0.107586
$166$	−7.38197	−0.572952
$167$	−6.70820	−0.519096	−0.259548	−	0.965730i	$-0.583574\pi$
$167$	−6.70820	−0.519096	−0.259548	+	0.965730i	$0.583574\pi$
$168$	0	0
$169$	−4.00000	−0.307692
$170$	−1.47214	−0.112908
$171$	−13.8541	−1.05945
$172$	−12.8541	−0.980116
$173$	0.708204	0.0538437	0.0269219	−	0.999638i	$-0.491429\pi$
$173$	0.708204	0.0538437	0.0269219	+	0.999638i	$0.491429\pi$
$174$	1.85410	0.140559
$175$	0	0
$176$	−4.14590	−0.312509
$177$	−2.90983	−0.218716
$178$	9.00000	0.674579
$179$	4.67376	0.349333	0.174667	−	0.984628i	$-0.444115\pi$
$179$	4.67376	0.349333	0.174667	+	0.984628i	$0.444115\pi$
$180$	7.47214	0.556940
$181$	5.41641	0.402598	0.201299	−	0.979530i	$-0.435484\pi$
$181$	5.41641	0.402598	0.201299	+	0.979530i	$0.435484\pi$
$182$	0	0
$183$	4.20163	0.310593
$184$	−0.854102	−0.0629652
$185$	12.4721	0.916970
$186$	2.27051	0.166482
$187$	3.29180	0.240720
$188$	−5.23607	−0.381880
$189$	0	0
$190$	4.85410	0.352154
$191$	−3.05573	−0.221105	−0.110552	−	0.993870i	$-0.535262\pi$
$191$	−3.05573	−0.221105	−0.110552	+	0.993870i	$0.535262\pi$
$192$	−0.0901699	−0.00650746
$193$	−14.4164	−1.03772	−0.518858	−	0.854861i	$-0.673643\pi$
$193$	−14.4164	−1.03772	−0.518858	+	0.854861i	$0.673643\pi$
$194$	3.18034	0.228335
$195$	1.85410	0.132775
$196$	0	0
$197$	−4.09017	−0.291413	−0.145706	−	0.989328i	$-0.546545\pi$
$197$	−4.09017	−0.291413	−0.145706	+	0.989328i	$0.546545\pi$
$198$	3.94427	0.280307
$199$	−0.708204	−0.0502032	−0.0251016	−	0.999685i	$-0.507991\pi$
$199$	−0.708204	−0.0502032	−0.0251016	+	0.999685i	$0.507991\pi$
$200$	5.32624	0.376622
$201$	1.67376	0.118058
$202$	−1.09017	−0.0767041
$203$	0	0
$204$	0.909830	0.0637008
$205$	−1.61803	−0.113008
$206$	−2.20163	−0.153395
$207$	−1.09017	−0.0757720
$208$	5.56231	0.385677
$209$	−10.8541	−0.750794
$210$	0	0
$211$	1.85410	0.127642	0.0638208	−	0.997961i	$-0.479671\pi$
$211$	1.85410	0.127642	0.0638208	+	0.997961i	$0.479671\pi$
$212$	22.7984	1.56580
$213$	0.0901699	0.00617834
$214$	6.00000	0.410152
$215$	12.8541	0.876642
$216$	5.00000	0.340207
$217$	0	0
$218$	−4.29180	−0.290677
$219$	5.72949	0.387163
$220$	5.85410	0.394683
$221$	−4.41641	−0.297080
$222$	1.81966	0.122128
$223$	5.14590	0.344595	0.172297	−	0.985045i	$-0.444881\pi$
$223$	5.14590	0.344595	0.172297	+	0.985045i	$0.444881\pi$
$224$	0	0
$225$	6.79837	0.453225
$226$	−6.14590	−0.408819
$227$	−0.527864	−0.0350356	−0.0175178	−	0.999847i	$-0.505576\pi$
$227$	−0.527864	−0.0350356	−0.0175178	+	0.999847i	$0.505576\pi$
$228$	−3.00000	−0.198680
$229$	−15.7082	−1.03803	−0.519014	−	0.854766i	$-0.673701\pi$
$229$	−15.7082	−1.03803	−0.519014	+	0.854766i	$0.673701\pi$
$230$	0.381966	0.0251861
$231$	0	0
$232$	−17.5623	−1.15302
$233$	1.85410	0.121466	0.0607331	−	0.998154i	$-0.480656\pi$
$233$	1.85410	0.121466	0.0607331	+	0.998154i	$0.480656\pi$
$234$	−5.29180	−0.345936
$235$	5.23607	0.341563
$236$	12.3262	0.802370
$237$	−2.94427	−0.191251
$238$	0	0
$239$	23.5623	1.52412	0.762059	−	0.647507i	$-0.224188\pi$
$239$	23.5623	1.52412	0.762059	+	0.647507i	$0.224188\pi$
$240$	1.14590	0.0739674
$241$	−13.7082	−0.883023	−0.441512	−	0.897256i	$-0.645558\pi$
$241$	−13.7082	−0.883023	−0.441512	+	0.897256i	$0.645558\pi$
$242$	−3.70820	−0.238372
$243$	9.65248	0.619207
$244$	−17.7984	−1.13942
$245$	0	0
$246$	−0.236068	−0.0150511
$247$	14.5623	0.926577
$248$	−21.5066	−1.36567
$249$	−4.56231	−0.289124
$250$	−7.38197	−0.466877
$251$	19.3607	1.22204	0.611018	−	0.791617i	$-0.290760\pi$
$251$	19.3607	1.22204	0.611018	+	0.791617i	$0.290760\pi$
$252$	0	0
$253$	−0.854102	−0.0536969
$254$	−7.20163	−0.451870
$255$	−0.909830	−0.0569758
$256$	−6.56231	−0.410144
$257$	−3.00000	−0.187135	−0.0935674	−	0.995613i	$-0.529827\pi$
$257$	−3.00000	−0.187135	−0.0935674	+	0.995613i	$0.529827\pi$
$258$	1.87539	0.116757
$259$	0	0
$260$	−7.85410	−0.487091
$261$	−22.4164	−1.38754
$262$	5.18034	0.320042
$263$	−4.41641	−0.272327	−0.136164	−	0.990686i	$-0.543477\pi$
$263$	−4.41641	−0.272327	−0.136164	+	0.990686i	$0.543477\pi$
$264$	1.90983	0.117542
$265$	−22.7984	−1.40049
$266$	0	0
$267$	5.56231	0.340408
$268$	−7.09017	−0.433101
$269$	−20.5066	−1.25031	−0.625154	−	0.780501i	$-0.714964\pi$
$269$	−20.5066	−1.25031	−0.625154	+	0.780501i	$0.714964\pi$
$270$	−2.23607	−0.136083
$271$	−29.6525	−1.80126	−0.900630	−	0.434587i	$-0.856894\pi$
$271$	−29.6525	−1.80126	−0.900630	+	0.434587i	$0.856894\pi$
$272$	−2.72949	−0.165500
$273$	0	0
$274$	−5.94427	−0.359107
$275$	5.32624	0.321184
$276$	−0.236068	−0.0142096
$277$	4.70820	0.282889	0.141444	−	0.989946i	$-0.454825\pi$
$277$	4.70820	0.282889	0.141444	+	0.989946i	$0.454825\pi$
$278$	11.3820	0.682645
$279$	−27.4508	−1.64344
$280$	0	0
$281$	27.0000	1.61068	0.805342	−	0.592810i	$-0.201981\pi$
$281$	27.0000	1.61068	0.805342	+	0.592810i	$0.201981\pi$
$282$	0.763932	0.0454915
$283$	9.88854	0.587813	0.293906	−	0.955834i	$-0.405045\pi$
$283$	9.88854	0.587813	0.293906	+	0.955834i	$0.405045\pi$
$284$	−0.381966	−0.0226655
$285$	3.00000	0.177705
$286$	−4.14590	−0.245152
$287$	0	0
$288$	−16.0344	−0.944839
$289$	−14.8328	−0.872519
$290$	7.85410	0.461209
$291$	1.96556	0.115223
$292$	−24.2705	−1.42032
$293$	0.0557281	0.00325567	0.00162783	−	0.999999i	$-0.499482\pi$
$293$	0.0557281	0.00325567	0.00162783	+	0.999999i	$0.499482\pi$
$294$	0	0
$295$	−12.3262	−0.717661
$296$	−17.2361	−1.00183
$297$	5.00000	0.290129
$298$	12.2918	0.712045
$299$	1.14590	0.0662690
$300$	1.47214	0.0849938
$301$	0	0
$302$	10.9098	0.627790
$303$	−0.673762	−0.0387066
$304$	9.00000	0.516185
$305$	17.7984	1.01913
$306$	2.59675	0.148446
$307$	19.8885	1.13510	0.567550	−	0.823339i	$-0.307892\pi$
$307$	19.8885	1.13510	0.567550	+	0.823339i	$0.307892\pi$
$308$	0	0
$309$	−1.36068	−0.0774064
$310$	9.61803	0.546268
$311$	−18.0344	−1.02264	−0.511320	−	0.859391i	$-0.670843\pi$
$311$	−18.0344	−1.02264	−0.511320	+	0.859391i	$0.670843\pi$
$312$	−2.56231	−0.145062
$313$	−14.1246	−0.798370	−0.399185	−	0.916870i	$-0.630707\pi$
$313$	−14.1246	−0.798370	−0.399185	+	0.916870i	$0.630707\pi$
$314$	4.58359	0.258667
$315$	0	0
$316$	12.4721	0.701612
$317$	−1.58359	−0.0889434	−0.0444717	−	0.999011i	$-0.514160\pi$
$317$	−1.58359	−0.0889434	−0.0444717	+	0.999011i	$0.514160\pi$
$318$	−3.32624	−0.186526
$319$	−17.5623	−0.983300
$320$	−0.381966	−0.0213525
$321$	3.70820	0.206972
$322$	0	0
$323$	−7.14590	−0.397608
$324$	−12.4721	−0.692896
$325$	−7.14590	−0.396383
$326$	3.41641	0.189217
$327$	−2.65248	−0.146682
$328$	2.23607	0.123466
$329$	0	0
$330$	−0.854102	−0.0470168
$331$	9.88854	0.543524	0.271762	−	0.962365i	$-0.412394\pi$
$331$	9.88854	0.543524	0.271762	+	0.962365i	$0.412394\pi$
$332$	19.3262	1.06067
$333$	−22.0000	−1.20559
$334$	−4.14590	−0.226853
$335$	7.09017	0.387377
$336$	0	0
$337$	−5.05573	−0.275403	−0.137702	−	0.990474i	$-0.543971\pi$
$337$	−5.05573	−0.275403	−0.137702	+	0.990474i	$0.543971\pi$
$338$	−2.47214	−0.134466
$339$	−3.79837	−0.206299
$340$	3.85410	0.209018
$341$	−21.5066	−1.16465
$342$	−8.56231	−0.462996
$343$	0	0
$344$	−17.7639	−0.957767
$345$	0.236068	0.0127095
$346$	0.437694	0.0235306
$347$	35.1246	1.88559	0.942794	−	0.333376i	$-0.108188\pi$
$347$	35.1246	1.88559	0.942794	+	0.333376i	$0.108188\pi$
$348$	−4.85410	−0.260207
$349$	−2.70820	−0.144967	−0.0724834	−	0.997370i	$-0.523092\pi$
$349$	−2.70820	−0.144967	−0.0724834	+	0.997370i	$0.523092\pi$
$350$	0	0
$351$	−6.70820	−0.358057
$352$	−12.5623	−0.669573
$353$	11.8885	0.632763	0.316382	−	0.948632i	$-0.397532\pi$
$353$	11.8885	0.632763	0.316382	+	0.948632i	$0.397532\pi$
$354$	−1.79837	−0.0955825
$355$	0.381966	0.0202727
$356$	−23.5623	−1.24880
$357$	0	0
$358$	2.88854	0.152664
$359$	−6.76393	−0.356987	−0.178493	−	0.983941i	$-0.557122\pi$
$359$	−6.76393	−0.356987	−0.178493	+	0.983941i	$0.557122\pi$
$360$	10.3262	0.544241
$361$	4.56231	0.240121
$362$	3.34752	0.175942
$363$	−2.29180	−0.120288
$364$	0	0
$365$	24.2705	1.27038
$366$	2.59675	0.135734
$367$	−33.4508	−1.74612	−0.873060	−	0.487613i	$-0.837868\pi$
$367$	−33.4508	−1.74612	−0.873060	+	0.487613i	$0.837868\pi$
$368$	0.708204	0.0369177
$369$	2.85410	0.148579
$370$	7.70820	0.400730
$371$	0	0
$372$	−5.94427	−0.308196
$373$	−9.50658	−0.492232	−0.246116	−	0.969240i	$-0.579154\pi$
$373$	−9.50658	−0.492232	−0.246116	+	0.969240i	$0.579154\pi$
$374$	2.03444	0.105198
$375$	−4.56231	−0.235596
$376$	−7.23607	−0.373172
$377$	23.5623	1.21352
$378$	0	0
$379$	−19.2361	−0.988090	−0.494045	−	0.869436i	$-0.664482\pi$
$379$	−19.2361	−0.988090	−0.494045	+	0.869436i	$0.664482\pi$
$380$	−12.7082	−0.651917
$381$	−4.45085	−0.228024
$382$	−1.88854	−0.0966263
$383$	4.52786	0.231363	0.115682	−	0.993286i	$-0.463095\pi$
$383$	4.52786	0.231363	0.115682	+	0.993286i	$0.463095\pi$
$384$	−4.34752	−0.221859
$385$	0	0
$386$	−8.90983	−0.453498
$387$	−22.6738	−1.15257
$388$	−8.32624	−0.422701
$389$	−6.32624	−0.320753	−0.160376	−	0.987056i	$-0.551271\pi$
$389$	−6.32624	−0.320753	−0.160376	+	0.987056i	$0.551271\pi$
$390$	1.14590	0.0580248
$391$	−0.562306	−0.0284370
$392$	0	0
$393$	3.20163	0.161501
$394$	−2.52786	−0.127352
$395$	−12.4721	−0.627541
$396$	−10.3262	−0.518913
$397$	30.7426	1.54293	0.771465	−	0.636272i	$-0.219525\pi$
$397$	30.7426	1.54293	0.771465	+	0.636272i	$0.219525\pi$
$398$	−0.437694	−0.0219396
$399$	0	0
$400$	−4.41641	−0.220820
$401$	−38.1803	−1.90664	−0.953318	−	0.301969i	$-0.902356\pi$
$401$	−38.1803	−1.90664	−0.953318	+	0.301969i	$0.902356\pi$
$402$	1.03444	0.0515933
$403$	28.8541	1.43733
$404$	2.85410	0.141997
$405$	12.4721	0.619745
$406$	0	0
$407$	−17.2361	−0.854360
$408$	1.25735	0.0622483
$409$	−26.5967	−1.31512	−0.657562	−	0.753400i	$-0.728412\pi$
$409$	−26.5967	−1.31512	−0.657562	+	0.753400i	$0.728412\pi$
$410$	−1.00000	−0.0493865
$411$	−3.67376	−0.181213
$412$	5.76393	0.283969
$413$	0	0
$414$	−0.673762	−0.0331136
$415$	−19.3262	−0.948688
$416$	16.8541	0.826340
$417$	7.03444	0.344478
$418$	−6.70820	−0.328109
$419$	17.5623	0.857975	0.428987	−	0.903310i	$-0.358870\pi$
$419$	17.5623	0.857975	0.428987	+	0.903310i	$0.358870\pi$
$420$	0	0
$421$	11.5279	0.561834	0.280917	−	0.959732i	$-0.409361\pi$
$421$	11.5279	0.561834	0.280917	+	0.959732i	$0.409361\pi$
$422$	1.14590	0.0557814
$423$	−9.23607	−0.449073
$424$	31.5066	1.53009
$425$	3.50658	0.170094
$426$	0.0557281	0.00270003
$427$	0	0
$428$	−15.7082	−0.759285
$429$	−2.56231	−0.123709
$430$	7.94427	0.383107
$431$	−14.0557	−0.677041	−0.338520	−	0.940959i	$-0.609926\pi$
$431$	−14.0557	−0.677041	−0.338520	+	0.940959i	$0.609926\pi$
$432$	−4.14590	−0.199470
$433$	37.5066	1.80245	0.901226	−	0.433350i	$-0.142669\pi$
$433$	37.5066	1.80245	0.901226	+	0.433350i	$0.142669\pi$
$434$	0	0
$435$	4.85410	0.232736
$436$	11.2361	0.538110
$437$	1.85410	0.0886937
$438$	3.54102	0.169196
$439$	−19.7639	−0.943281	−0.471641	−	0.881791i	$-0.656338\pi$
$439$	−19.7639	−0.943281	−0.471641	+	0.881791i	$0.656338\pi$
$440$	8.09017	0.385684
$441$	0	0
$442$	−2.72949	−0.129829
$443$	−33.6180	−1.59724	−0.798620	−	0.601835i	$-0.794437\pi$
$443$	−33.6180	−1.59724	−0.798620	+	0.601835i	$0.794437\pi$
$444$	−4.76393	−0.226086
$445$	23.5623	1.11696
$446$	3.18034	0.150593
$447$	7.59675	0.359314
$448$	0	0
$449$	−27.8885	−1.31614	−0.658071	−	0.752956i	$-0.728627\pi$
$449$	−27.8885	−1.31614	−0.658071	+	0.752956i	$0.728627\pi$
$450$	4.20163	0.198067
$451$	2.23607	0.105292
$452$	16.0902	0.756818
$453$	6.74265	0.316797
$454$	−0.326238	−0.0153111
$455$	0	0
$456$	−4.14590	−0.194149
$457$	−20.7082	−0.968689	−0.484344	−	0.874877i	$-0.660942\pi$
$457$	−20.7082	−0.968689	−0.484344	+	0.874877i	$0.660942\pi$
$458$	−9.70820	−0.453635
$459$	3.29180	0.153648
$460$	−1.00000	−0.0466252
$461$	8.81966	0.410773	0.205386	−	0.978681i	$-0.434155\pi$
$461$	8.81966	0.410773	0.205386	+	0.978681i	$0.434155\pi$
$462$	0	0
$463$	−38.6869	−1.79793	−0.898967	−	0.438017i	$-0.855681\pi$
$463$	−38.6869	−1.79793	−0.898967	+	0.438017i	$0.855681\pi$
$464$	14.5623	0.676038
$465$	5.94427	0.275659
$466$	1.14590	0.0530827
$467$	18.5967	0.860555	0.430277	−	0.902697i	$-0.358416\pi$
$467$	18.5967	0.860555	0.430277	+	0.902697i	$0.358416\pi$
$468$	13.8541	0.640406
$469$	0	0
$470$	3.23607	0.149269
$471$	2.83282	0.130529
$472$	17.0344	0.784074
$473$	−17.7639	−0.816786
$474$	−1.81966	−0.0835798
$475$	−11.5623	−0.530515
$476$	0	0
$477$	40.2148	1.84131
$478$	14.5623	0.666064
$479$	1.03444	0.0472649	0.0236324	−	0.999721i	$-0.492477\pi$
$479$	1.03444	0.0472649	0.0236324	+	0.999721i	$0.492477\pi$
$480$	3.47214	0.158481
$481$	23.1246	1.05439
$482$	−8.47214	−0.385895
$483$	0	0
$484$	9.70820	0.441282
$485$	8.32624	0.378075
$486$	5.96556	0.270603
$487$	20.2918	0.919509	0.459755	−	0.888046i	$-0.347937\pi$
$487$	20.2918	0.919509	0.459755	+	0.888046i	$0.347937\pi$
$488$	−24.5967	−1.11344
$489$	2.11146	0.0954833
$490$	0	0
$491$	39.1591	1.76722	0.883612	−	0.468220i	$-0.155105\pi$
$491$	39.1591	1.76722	0.883612	+	0.468220i	$0.155105\pi$
$492$	0.618034	0.0278631
$493$	−11.5623	−0.520740
$494$	9.00000	0.404929
$495$	10.3262	0.464130
$496$	17.8328	0.800717
$497$	0	0
$498$	−2.81966	−0.126352
$499$	−1.23607	−0.0553340	−0.0276670	−	0.999617i	$-0.508808\pi$
$499$	−1.23607	−0.0553340	−0.0276670	+	0.999617i	$0.508808\pi$
$500$	19.3262	0.864296
$501$	−2.56231	−0.114475
$502$	11.9656	0.534049
$503$	−1.38197	−0.0616188	−0.0308094	−	0.999525i	$-0.509808\pi$
$503$	−1.38197	−0.0616188	−0.0308094	+	0.999525i	$0.509808\pi$
$504$	0	0
$505$	−2.85410	−0.127006
$506$	−0.527864	−0.0234664
$507$	−1.52786	−0.0678548
$508$	18.8541	0.836516
$509$	−37.0902	−1.64399	−0.821996	−	0.569493i	$-0.807140\pi$
$509$	−37.0902	−1.64399	−0.821996	+	0.569493i	$0.807140\pi$
$510$	−0.562306	−0.0248993
$511$	0	0
$512$	18.7082	0.826794
$513$	−10.8541	−0.479220
$514$	−1.85410	−0.0817809
$515$	−5.76393	−0.253989
$516$	−4.90983	−0.216143
$517$	−7.23607	−0.318242
$518$	0	0
$519$	0.270510	0.0118741
$520$	−10.8541	−0.475984
$521$	−15.4377	−0.676338	−0.338169	−	0.941085i	$-0.609807\pi$
$521$	−15.4377	−0.676338	−0.338169	+	0.941085i	$0.609807\pi$
$522$	−13.8541	−0.606378
$523$	13.8328	0.604867	0.302433	−	0.953171i	$-0.402201\pi$
$523$	13.8328	0.604867	0.302433	+	0.953171i	$0.402201\pi$
$524$	−13.5623	−0.592472
$525$	0	0
$526$	−2.72949	−0.119011
$527$	−14.1591	−0.616778
$528$	−1.58359	−0.0689170
$529$	−22.8541	−0.993657
$530$	−14.0902	−0.612038
$531$	21.7426	0.943550
$532$	0	0
$533$	−3.00000	−0.129944
$534$	3.43769	0.148764
$535$	15.7082	0.679125
$536$	−9.79837	−0.423225
$537$	1.78522	0.0770379
$538$	−12.6738	−0.546405
$539$	0	0
$540$	5.85410	0.251920
$541$	−8.20163	−0.352615	−0.176308	−	0.984335i	$-0.556415\pi$
$541$	−8.20163	−0.352615	−0.176308	+	0.984335i	$0.556415\pi$
$542$	−18.3262	−0.787179
$543$	2.06888	0.0887843
$544$	−8.27051	−0.354595
$545$	−11.2361	−0.481300
$546$	0	0
$547$	15.1803	0.649064	0.324532	−	0.945875i	$-0.394793\pi$
$547$	15.1803	0.649064	0.324532	+	0.945875i	$0.394793\pi$
$548$	15.5623	0.664789
$549$	−31.3951	−1.33991
$550$	3.29180	0.140363
$551$	38.1246	1.62416
$552$	−0.326238	−0.0138856
$553$	0	0
$554$	2.90983	0.123627
$555$	4.76393	0.202218
$556$	−29.7984	−1.26373
$557$	−41.5623	−1.76105	−0.880526	−	0.473998i	$-0.842810\pi$
$557$	−41.5623	−1.76105	−0.880526	+	0.473998i	$0.842810\pi$
$558$	−16.9656	−0.718209
$559$	23.8328	1.00802
$560$	0	0
$561$	1.25735	0.0530855
$562$	16.6869	0.703895
$563$	29.1803	1.22980	0.614902	−	0.788603i	$-0.289195\pi$
$563$	29.1803	1.22980	0.614902	+	0.788603i	$0.289195\pi$
$564$	−2.00000	−0.0842152
$565$	−16.0902	−0.676919
$566$	6.11146	0.256884
$567$	0	0
$568$	−0.527864	−0.0221487
$569$	18.2705	0.765940	0.382970	−	0.923761i	$-0.374901\pi$
$569$	18.2705	0.765940	0.382970	+	0.923761i	$0.374901\pi$
$570$	1.85410	0.0776598
$571$	36.8328	1.54141	0.770703	−	0.637195i	$-0.219905\pi$
$571$	36.8328	1.54141	0.770703	+	0.637195i	$0.219905\pi$
$572$	10.8541	0.453833
$573$	−1.16718	−0.0487598
$574$	0	0
$575$	−0.909830	−0.0379425
$576$	0.673762	0.0280734
$577$	10.8885	0.453296	0.226648	−	0.973977i	$-0.427223\pi$
$577$	10.8885	0.453296	0.226648	+	0.973977i	$0.427223\pi$
$578$	−9.16718	−0.381305
$579$	−5.50658	−0.228846
$580$	−20.5623	−0.853803
$581$	0	0
$582$	1.21478	0.0503543
$583$	31.5066	1.30487
$584$	−33.5410	−1.38794
$585$	−13.8541	−0.572797
$586$	0.0344419	0.00142278
$587$	8.52786	0.351983	0.175991	−	0.984392i	$-0.443687\pi$
$587$	8.52786	0.351983	0.175991	+	0.984392i	$0.443687\pi$
$588$	0	0
$589$	46.6869	1.92370
$590$	−7.61803	−0.313629
$591$	−1.56231	−0.0642647
$592$	14.2918	0.587389
$593$	−36.0000	−1.47834	−0.739171	−	0.673517i	$-0.764783\pi$
$593$	−36.0000	−1.47834	−0.739171	+	0.673517i	$0.764783\pi$
$594$	3.09017	0.126791
$595$	0	0
$596$	−32.1803	−1.31816
$597$	−0.270510	−0.0110712
$598$	0.708204	0.0289606
$599$	−5.12461	−0.209386	−0.104693	−	0.994505i	$-0.533386\pi$
$599$	−5.12461	−0.209386	−0.104693	+	0.994505i	$0.533386\pi$
$600$	2.03444	0.0830557
$601$	23.5623	0.961127	0.480563	−	0.876960i	$-0.340432\pi$
$601$	23.5623	0.961127	0.480563	+	0.876960i	$0.340432\pi$
$602$	0	0
$603$	−12.5066	−0.509307
$604$	−28.5623	−1.16218
$605$	−9.70820	−0.394695
$606$	−0.416408	−0.0169154
$607$	−11.5836	−0.470164	−0.235082	−	0.971976i	$-0.575536\pi$
$607$	−11.5836	−0.470164	−0.235082	+	0.971976i	$0.575536\pi$
$608$	27.2705	1.10597
$609$	0	0
$610$	11.0000	0.445377
$611$	9.70820	0.392752
$612$	−6.79837	−0.274808
$613$	43.3951	1.75271	0.876356	−	0.481664i	$-0.159967\pi$
$613$	43.3951	1.75271	0.876356	+	0.481664i	$0.159967\pi$
$614$	12.2918	0.496057
$615$	−0.618034	−0.0249215
$616$	0	0
$617$	19.7639	0.795666	0.397833	−	0.917458i	$-0.369762\pi$
$617$	19.7639	0.795666	0.397833	+	0.917458i	$0.369762\pi$
$618$	−0.840946	−0.0338278
$619$	−9.09017	−0.365365	−0.182682	−	0.983172i	$-0.558478\pi$
$619$	−9.09017	−0.365365	−0.182682	+	0.983172i	$0.558478\pi$
$620$	−25.1803	−1.01127
$621$	−0.854102	−0.0342739
$622$	−11.1459	−0.446910
$623$	0	0
$624$	2.12461	0.0850525
$625$	−7.41641	−0.296656
$626$	−8.72949	−0.348901
$627$	−4.14590	−0.165571
$628$	−12.0000	−0.478852
$629$	−11.3475	−0.452455
$630$	0	0
$631$	22.7082	0.903999	0.452000	−	0.892018i	$-0.350711\pi$
$631$	22.7082	0.903999	0.452000	+	0.892018i	$0.350711\pi$
$632$	17.2361	0.685614
$633$	0.708204	0.0281486
$634$	−0.978714	−0.0388697
$635$	−18.8541	−0.748202
$636$	8.70820	0.345303
$637$	0	0
$638$	−10.8541	−0.429718
$639$	−0.673762	−0.0266536
$640$	−18.4164	−0.727972
$641$	−8.05573	−0.318182	−0.159091	−	0.987264i	$-0.550856\pi$
$641$	−8.05573	−0.318182	−0.159091	+	0.987264i	$0.550856\pi$
$642$	2.29180	0.0904500
$643$	−19.4508	−0.767067	−0.383533	−	0.923527i	$-0.625293\pi$
$643$	−19.4508	−0.767067	−0.383533	+	0.923527i	$0.625293\pi$
$644$	0	0
$645$	4.90983	0.193324
$646$	−4.41641	−0.173761
$647$	39.7214	1.56161	0.780804	−	0.624776i	$-0.214810\pi$
$647$	39.7214	1.56161	0.780804	+	0.624776i	$0.214810\pi$
$648$	−17.2361	−0.677097
$649$	17.0344	0.668660
$650$	−4.41641	−0.173226
$651$	0	0
$652$	−8.94427	−0.350285
$653$	−31.6869	−1.24000	−0.620002	−	0.784600i	$-0.712868\pi$
$653$	−31.6869	−1.24000	−0.620002	+	0.784600i	$0.712868\pi$
$654$	−1.63932	−0.0641025
$655$	13.5623	0.529923
$656$	−1.85410	−0.0723905
$657$	−42.8115	−1.67024
$658$	0	0
$659$	−33.0000	−1.28550	−0.642749	−	0.766077i	$-0.722206\pi$
$659$	−33.0000	−1.28550	−0.642749	+	0.766077i	$0.722206\pi$
$660$	2.23607	0.0870388
$661$	40.6525	1.58120	0.790599	−	0.612334i	$-0.209769\pi$
$661$	40.6525	1.58120	0.790599	+	0.612334i	$0.209769\pi$
$662$	6.11146	0.237528
$663$	−1.68692	−0.0655145
$664$	26.7082	1.03648
$665$	0	0
$666$	−13.5967	−0.526863
$667$	3.00000	0.116160
$668$	10.8541	0.419958
$669$	1.96556	0.0759929
$670$	4.38197	0.169290
$671$	−24.5967	−0.949547
$672$	0	0
$673$	−38.7082	−1.49209	−0.746046	−	0.665895i	$-0.768050\pi$
$673$	−38.7082	−1.49209	−0.746046	+	0.665895i	$0.768050\pi$
$674$	−3.12461	−0.120356
$675$	5.32624	0.205007
$676$	6.47214	0.248928
$677$	31.3262	1.20397	0.601983	−	0.798509i	$-0.294378\pi$
$677$	31.3262	1.20397	0.601983	+	0.798509i	$0.294378\pi$
$678$	−2.34752	−0.0901561
$679$	0	0
$680$	5.32624	0.204252
$681$	−0.201626	−0.00772633
$682$	−13.2918	−0.508969
$683$	3.87539	0.148288	0.0741438	−	0.997248i	$-0.476378\pi$
$683$	3.87539	0.148288	0.0741438	+	0.997248i	$0.476378\pi$
$684$	22.4164	0.857113
$685$	−15.5623	−0.594605
$686$	0	0
$687$	−6.00000	−0.228914
$688$	14.7295	0.561557
$689$	−42.2705	−1.61038
$690$	0.145898	0.00555424
$691$	−46.5066	−1.76919	−0.884597	−	0.466357i	$-0.845566\pi$
$691$	−46.5066	−1.76919	−0.884597	+	0.466357i	$0.845566\pi$
$692$	−1.14590	−0.0435605
$693$	0	0
$694$	21.7082	0.824032
$695$	29.7984	1.13032
$696$	−6.70820	−0.254274
$697$	1.47214	0.0557611
$698$	−1.67376	−0.0633528
$699$	0.708204	0.0267867
$700$	0	0
$701$	12.2016	0.460849	0.230425	−	0.973090i	$-0.425989\pi$
$701$	12.2016	0.460849	0.230425	+	0.973090i	$0.425989\pi$
$702$	−4.14590	−0.156477
$703$	37.4164	1.41119
$704$	0.527864	0.0198946
$705$	2.00000	0.0753244
$706$	7.34752	0.276528
$707$	0	0
$708$	4.70820	0.176945
$709$	−22.5410	−0.846546	−0.423273	−	0.906002i	$-0.639119\pi$
$709$	−22.5410	−0.846546	−0.423273	+	0.906002i	$0.639119\pi$
$710$	0.236068	0.00885947
$711$	22.0000	0.825064
$712$	−32.5623	−1.22032
$713$	3.67376	0.137583
$714$	0	0
$715$	−10.8541	−0.405920
$716$	−7.56231	−0.282617
$717$	9.00000	0.336111
$718$	−4.18034	−0.156009
$719$	−11.3607	−0.423682	−0.211841	−	0.977304i	$-0.567946\pi$
$719$	−11.3607	−0.423682	−0.211841	+	0.977304i	$0.567946\pi$
$720$	−8.56231	−0.319098
$721$	0	0
$722$	2.81966	0.104937
$723$	−5.23607	−0.194731
$724$	−8.76393	−0.325709
$725$	−18.7082	−0.694805
$726$	−1.41641	−0.0525678
$727$	36.9787	1.37146	0.685732	−	0.727854i	$-0.259482\pi$
$727$	36.9787	1.37146	0.685732	+	0.727854i	$0.259482\pi$
$728$	0	0
$729$	−19.4377	−0.719915
$730$	15.0000	0.555175
$731$	−11.6950	−0.432557
$732$	−6.79837	−0.251275
$733$	28.4164	1.04958	0.524792	−	0.851231i	$-0.324143\pi$
$733$	28.4164	1.04958	0.524792	+	0.851231i	$0.324143\pi$
$734$	−20.6738	−0.763082
$735$	0	0
$736$	2.14590	0.0790989
$737$	−9.79837	−0.360928
$738$	1.76393	0.0649312
$739$	2.14590	0.0789381	0.0394691	−	0.999221i	$-0.487433\pi$
$739$	2.14590	0.0789381	0.0394691	+	0.999221i	$0.487433\pi$
$740$	−20.1803	−0.741844
$741$	5.56231	0.204336
$742$	0	0
$743$	24.4377	0.896532	0.448266	−	0.893900i	$-0.352042\pi$
$743$	24.4377	0.896532	0.448266	+	0.893900i	$0.352042\pi$
$744$	−8.21478	−0.301169
$745$	32.1803	1.17900
$746$	−5.87539	−0.215113
$747$	34.0902	1.24729
$748$	−5.32624	−0.194747
$749$	0	0
$750$	−2.81966	−0.102959
$751$	33.9443	1.23864	0.619322	−	0.785137i	$-0.287408\pi$
$751$	33.9443	1.23864	0.619322	+	0.785137i	$0.287408\pi$
$752$	6.00000	0.218797
$753$	7.39512	0.269493
$754$	14.5623	0.530328
$755$	28.5623	1.03949
$756$	0	0
$757$	3.70820	0.134777	0.0673885	−	0.997727i	$-0.478533\pi$
$757$	3.70820	0.134777	0.0673885	+	0.997727i	$0.478533\pi$
$758$	−11.8885	−0.431811
$759$	−0.326238	−0.0118417
$760$	−17.5623	−0.637052
$761$	38.4721	1.39461	0.697307	−	0.716773i	$-0.254381\pi$
$761$	38.4721	1.39461	0.697307	+	0.716773i	$0.254381\pi$
$762$	−2.75078	−0.0996501
$763$	0	0
$764$	4.94427	0.178877
$765$	6.79837	0.245796
$766$	2.79837	0.101109
$767$	−22.8541	−0.825214
$768$	−2.50658	−0.0904483
$769$	7.34752	0.264958	0.132479	−	0.991186i	$-0.457706\pi$
$769$	7.34752	0.264958	0.132479	+	0.991186i	$0.457706\pi$
$770$	0	0
$771$	−1.14590	−0.0412685
$772$	23.3262	0.839530
$773$	−21.9443	−0.789281	−0.394640	−	0.918836i	$-0.629131\pi$
$773$	−21.9443	−0.789281	−0.394640	+	0.918836i	$0.629131\pi$
$774$	−14.0132	−0.503692
$775$	−22.9098	−0.822945
$776$	−11.5066	−0.413062
$777$	0	0
$778$	−3.90983	−0.140174
$779$	−4.85410	−0.173916
$780$	−3.00000	−0.107417
$781$	−0.527864	−0.0188885
$782$	−0.347524	−0.0124274
$783$	−17.5623	−0.627626
$784$	0	0
$785$	12.0000	0.428298
$786$	1.97871	0.0705784
$787$	−27.7082	−0.987691	−0.493845	−	0.869550i	$-0.664409\pi$
$787$	−27.7082	−0.987691	−0.493845	+	0.869550i	$0.664409\pi$
$788$	6.61803	0.235758
$789$	−1.68692	−0.0600559
$790$	−7.70820	−0.274246
$791$	0	0
$792$	−14.2705	−0.507080
$793$	33.0000	1.17186
$794$	19.0000	0.674285
$795$	−8.70820	−0.308848
$796$	1.14590	0.0406153
$797$	−6.52786	−0.231229	−0.115614	−	0.993294i	$-0.536884\pi$
$797$	−6.52786	−0.231229	−0.115614	+	0.993294i	$0.536884\pi$
$798$	0	0
$799$	−4.76393	−0.168536
$800$	−13.3820	−0.473124
$801$	−41.5623	−1.46853
$802$	−23.5967	−0.833230
$803$	−33.5410	−1.18364
$804$	−2.70820	−0.0955110
$805$	0	0
$806$	17.8328	0.628134
$807$	−7.83282	−0.275728
$808$	3.94427	0.138759
$809$	−12.9656	−0.455845	−0.227922	−	0.973679i	$-0.573193\pi$
$809$	−12.9656	−0.455845	−0.227922	+	0.973679i	$0.573193\pi$
$810$	7.70820	0.270839
$811$	40.2361	1.41288	0.706440	−	0.707773i	$-0.250300\pi$
$811$	40.2361	1.41288	0.706440	+	0.707773i	$0.250300\pi$
$812$	0	0
$813$	−11.3262	−0.397229
$814$	−10.6525	−0.373369
$815$	8.94427	0.313304
$816$	−1.04257	−0.0364973
$817$	38.5623	1.34912
$818$	−16.4377	−0.574730
$819$	0	0
$820$	2.61803	0.0914257
$821$	−0.0557281	−0.00194492	−0.000972462	−	1.00000i	$-0.500310\pi$
$821$	−0.0557281	−0.00194492	−0.000972462		1.00000i	$0.500310\pi$
$822$	−2.27051	−0.0791931
$823$	4.50658	0.157089	0.0785447	−	0.996911i	$-0.474973\pi$
$823$	4.50658	0.157089	0.0785447	+	0.996911i	$0.474973\pi$
$824$	7.96556	0.277493
$825$	2.03444	0.0708302
$826$	0	0
$827$	−50.1246	−1.74300	−0.871502	−	0.490392i	$-0.836853\pi$
$827$	−50.1246	−1.74300	−0.871502	+	0.490392i	$0.836853\pi$
$828$	1.76393	0.0613009
$829$	−12.3050	−0.427369	−0.213684	−	0.976903i	$-0.568546\pi$
$829$	−12.3050	−0.427369	−0.213684	+	0.976903i	$0.568546\pi$
$830$	−11.9443	−0.414592
$831$	1.79837	0.0623849
$832$	−0.708204	−0.0245526
$833$	0	0
$834$	4.34752	0.150542
$835$	−10.8541	−0.375622
$836$	17.5623	0.607405
$837$	−21.5066	−0.743376
$838$	10.8541	0.374949
$839$	−27.5967	−0.952746	−0.476373	−	0.879243i	$-0.658049\pi$
$839$	−27.5967	−0.952746	−0.476373	+	0.879243i	$0.658049\pi$
$840$	0	0
$841$	32.6869	1.12714
$842$	7.12461	0.245530
$843$	10.3131	0.355201
$844$	−3.00000	−0.103264
$845$	−6.47214	−0.222648
$846$	−5.70820	−0.196252
$847$	0	0
$848$	−26.1246	−0.897123
$849$	3.77709	0.129629
$850$	2.16718	0.0743338
$851$	2.94427	0.100928
$852$	−0.145898	−0.00499838
$853$	−26.0000	−0.890223	−0.445112	−	0.895475i	$-0.646836\pi$
$853$	−26.0000	−0.890223	−0.445112	+	0.895475i	$0.646836\pi$
$854$	0	0
$855$	−22.4164	−0.766625
$856$	−21.7082	−0.741971
$857$	11.0902	0.378833	0.189416	−	0.981897i	$-0.439340\pi$
$857$	11.0902	0.378833	0.189416	+	0.981897i	$0.439340\pi$
$858$	−1.58359	−0.0540629
$859$	22.3820	0.763663	0.381831	−	0.924232i	$-0.375293\pi$
$859$	22.3820	0.763663	0.381831	+	0.924232i	$0.375293\pi$
$860$	−20.7984	−0.709219
$861$	0	0
$862$	−8.68692	−0.295878
$863$	−9.87539	−0.336162	−0.168081	−	0.985773i	$-0.553757\pi$
$863$	−9.87539	−0.336162	−0.168081	+	0.985773i	$0.553757\pi$
$864$	−12.5623	−0.427378
$865$	1.14590	0.0389617
$866$	23.1803	0.787700
$867$	−5.66563	−0.192415
$868$	0	0
$869$	17.2361	0.584694
$870$	3.00000	0.101710
$871$	13.1459	0.445432
$872$	15.5279	0.525840
$873$	−14.6869	−0.497077
$874$	1.14590	0.0387606
$875$	0	0
$876$	−9.27051	−0.313222
$877$	32.9787	1.11361	0.556806	−	0.830643i	$-0.312027\pi$
$877$	32.9787	1.11361	0.556806	+	0.830643i	$0.312027\pi$
$878$	−12.2148	−0.412229
$879$	0.0212862	0.000717967 0
$880$	−6.70820	−0.226134
$881$	−18.0000	−0.606435	−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000	−0.606435	−0.303218	+	0.952921i	$0.598061\pi$
$882$	0	0
$883$	20.5623	0.691977	0.345988	−	0.938239i	$-0.387544\pi$
$883$	20.5623	0.691977	0.345988	+	0.938239i	$0.387544\pi$
$884$	7.14590	0.240343
$885$	−4.70820	−0.158265
$886$	−20.7771	−0.698020
$887$	41.3050	1.38688	0.693442	−	0.720512i	$-0.256093\pi$
$887$	41.3050	1.38688	0.693442	+	0.720512i	$0.256093\pi$
$888$	−6.58359	−0.220931
$889$	0	0
$890$	14.5623	0.488130
$891$	−17.2361	−0.577430
$892$	−8.32624	−0.278783
$893$	15.7082	0.525655
$894$	4.69505	0.157026
$895$	7.56231	0.252780
$896$	0	0
$897$	0.437694	0.0146142
$898$	−17.2361	−0.575175
$899$	75.5410	2.51943
$900$	−11.0000	−0.366667
$901$	20.7426	0.691038
$902$	1.38197	0.0460144
$903$	0	0
$904$	22.2361	0.739561
$905$	8.76393	0.291323
$906$	4.16718	0.138445
$907$	−2.54915	−0.0846431	−0.0423216	−	0.999104i	$-0.513475\pi$
$907$	−2.54915	−0.0846431	−0.0423216	+	0.999104i	$0.513475\pi$
$908$	0.854102	0.0283444
$909$	5.03444	0.166982
$910$	0	0
$911$	−21.3050	−0.705865	−0.352932	−	0.935649i	$-0.614815\pi$
$911$	−21.3050	−0.705865	−0.352932	+	0.935649i	$0.614815\pi$
$912$	3.43769	0.113833
$913$	26.7082	0.883913
$914$	−12.7984	−0.423333
$915$	6.79837	0.224747
$916$	25.4164	0.839782
$917$	0	0
$918$	2.03444	0.0671466
$919$	−7.56231	−0.249457	−0.124729	−	0.992191i	$-0.539806\pi$
$919$	−7.56231	−0.249457	−0.124729	+	0.992191i	$0.539806\pi$
$920$	−1.38197	−0.0455621
$921$	7.59675	0.250321
$922$	5.45085	0.179514
$923$	0.708204	0.0233108
$924$	0	0
$925$	−18.3607	−0.603695
$926$	−23.9098	−0.785726
$927$	10.1672	0.333934
$928$	44.1246	1.44846
$929$	16.6869	0.547480	0.273740	−	0.961804i	$-0.411739\pi$
$929$	16.6869	0.547480	0.273740	+	0.961804i	$0.411739\pi$
$930$	3.67376	0.120467
$931$	0	0
$932$	−3.00000	−0.0982683
$933$	−6.88854	−0.225521
$934$	11.4934	0.376076
$935$	5.32624	0.174187
$936$	19.1459	0.625803
$937$	−16.5967	−0.542192	−0.271096	−	0.962552i	$-0.587386\pi$
$937$	−16.5967	−0.542192	−0.271096	+	0.962552i	$0.587386\pi$
$938$	0	0
$939$	−5.39512	−0.176063
$940$	−8.47214	−0.276331
$941$	−2.49342	−0.0812832	−0.0406416	−	0.999174i	$-0.512940\pi$
$941$	−2.49342	−0.0812832	−0.0406416	+	0.999174i	$0.512940\pi$
$942$	1.75078	0.0570434
$943$	−0.381966	−0.0124385
$944$	−14.1246	−0.459717
$945$	0	0
$946$	−10.9787	−0.356949
$947$	19.0902	0.620347	0.310174	−	0.950680i	$-0.399613\pi$
$947$	19.0902	0.620347	0.310174	+	0.950680i	$0.399613\pi$
$948$	4.76393	0.154725
$949$	45.0000	1.46076
$950$	−7.14590	−0.231844
$951$	−0.604878	−0.0196145
$952$	0	0
$953$	6.32624	0.204927	0.102463	−	0.994737i	$-0.467328\pi$
$953$	6.32624	0.204927	0.102463	+	0.994737i	$0.467328\pi$
$954$	24.8541	0.804681
$955$	−4.94427	−0.159993
$956$	−38.1246	−1.23304
$957$	−6.70820	−0.216845
$958$	0.639320	0.0206555
$959$	0	0
$960$	−0.145898	−0.00470884
$961$	61.5066	1.98408
$962$	14.2918	0.460786
$963$	−27.7082	−0.892884
$964$	22.1803	0.714381
$965$	−23.3262	−0.750898
$966$	0	0
$967$	46.2492	1.48727	0.743637	−	0.668583i	$-0.233099\pi$
$967$	46.2492	1.48727	0.743637	+	0.668583i	$0.233099\pi$
$968$	13.4164	0.431220
$969$	−2.72949	−0.0876839
$970$	5.14590	0.165225
$971$	−43.9443	−1.41024	−0.705119	−	0.709089i	$-0.749107\pi$
$971$	−43.9443	−1.41024	−0.705119	+	0.709089i	$0.749107\pi$
$972$	−15.6180	−0.500949
$973$	0	0
$974$	12.5410	0.401840
$975$	−2.72949	−0.0874136
$976$	20.3951	0.652832
$977$	8.32624	0.266380	0.133190	−	0.991091i	$-0.457478\pi$
$977$	8.32624	0.266380	0.133190	+	0.991091i	$0.457478\pi$
$978$	1.30495	0.0417278
$979$	−32.5623	−1.04070
$980$	0	0
$981$	19.8197	0.632793
$982$	24.2016	0.772305
$983$	34.3050	1.09416	0.547079	−	0.837081i	$-0.315740\pi$
$983$	34.3050	1.09416	0.547079	+	0.837081i	$0.315740\pi$
$984$	0.854102	0.0272278
$985$	−6.61803	−0.210868
$986$	−7.14590	−0.227572
$987$	0	0
$988$	−23.5623	−0.749617
$989$	3.03444	0.0964896
$990$	6.38197	0.202832
$991$	1.58359	0.0503045	0.0251522	−	0.999684i	$-0.491993\pi$
$991$	1.58359	0.0503045	0.0251522	+	0.999684i	$0.491993\pi$
$992$	54.0344	1.71560
$993$	3.77709	0.119862
$994$	0	0
$995$	−1.14590	−0.0363274
$996$	7.38197	0.233907
$997$	8.32624	0.263695	0.131847	−	0.991270i	$-0.457909\pi$
$997$	8.32624	0.263695	0.131847	+	0.991270i	$0.457909\pi$
$998$	−0.763932	−0.0241818
$999$	−17.2361	−0.545325

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2009.2.a.b.1.2		2
7.6	odd	2		287.2.a.a.1.2	✓	2
21.20	even	2		2583.2.a.h.1.1		2
28.27	even	2		4592.2.a.p.1.1		2
35.34	odd	2		7175.2.a.h.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.a.a.1.2	✓	2	7.6	odd	2
2009.2.a.b.1.2		2	1.1	even	1	trivial
2583.2.a.h.1.1		2	21.20	even	2
4592.2.a.p.1.1		2	28.27	even	2
7175.2.a.h.1.1		2	35.34	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2009 = 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2009.a (trivial)

\(f(q)\)	\(=\)	\(q+0.618034 q^{2} +0.381966 q^{3} -1.61803 q^{4} +1.61803 q^{5} +0.236068 q^{6} -2.23607 q^{8} -2.85410 q^{9} +O(q^{10})\)	\(q+0.618034 q^{2} +0.381966 q^{3} -1.61803 q^{4} +1.61803 q^{5} +0.236068 q^{6} -2.23607 q^{8} -2.85410 q^{9} +1.00000 q^{10} -2.23607 q^{11} -0.618034 q^{12} +3.00000 q^{13} +0.618034 q^{15} +1.85410 q^{16} -1.47214 q^{17} -1.76393 q^{18} +4.85410 q^{19} -2.61803 q^{20} -1.38197 q^{22} +0.381966 q^{23} -0.854102 q^{24} -2.38197 q^{25} +1.85410 q^{26} -2.23607 q^{27} +7.85410 q^{29} +0.381966 q^{30} +9.61803 q^{31} +5.61803 q^{32} -0.854102 q^{33} -0.909830 q^{34} +4.61803 q^{36} +7.70820 q^{37} +3.00000 q^{38} +1.14590 q^{39} -3.61803 q^{40} -1.00000 q^{41} +7.94427 q^{43} +3.61803 q^{44} -4.61803 q^{45} +0.236068 q^{46} +3.23607 q^{47} +0.708204 q^{48} -1.47214 q^{50} -0.562306 q^{51} -4.85410 q^{52} -14.0902 q^{53} -1.38197 q^{54} -3.61803 q^{55} +1.85410 q^{57} +4.85410 q^{58} -7.61803 q^{59} -1.00000 q^{60} +11.0000 q^{61} +5.94427 q^{62} -0.236068 q^{64} +4.85410 q^{65} -0.527864 q^{66} +4.38197 q^{67} +2.38197 q^{68} +0.145898 q^{69} +0.236068 q^{71} +6.38197 q^{72} +15.0000 q^{73} +4.76393 q^{74} -0.909830 q^{75} -7.85410 q^{76} +0.708204 q^{78} -7.70820 q^{79} +3.00000 q^{80} +7.70820 q^{81} -0.618034 q^{82} -11.9443 q^{83} -2.38197 q^{85} +4.90983 q^{86} +3.00000 q^{87} +5.00000 q^{88} +14.5623 q^{89} -2.85410 q^{90} -0.618034 q^{92} +3.67376 q^{93} +2.00000 q^{94} +7.85410 q^{95} +2.14590 q^{96} +5.14590 q^{97} +6.38197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 3 q^{3} - q^{4} + q^{5} - 4 q^{6} + q^{9}+O(q^{10}) \) 2 * q - q^2 + 3 * q^3 - q^4 + q^5 - 4 * q^6 + q^9	\( 2 q - q^{2} + 3 q^{3} - q^{4} + q^{5} - 4 q^{6} + q^{9} + 2 q^{10} + q^{12} + 6 q^{13} - q^{15} - 3 q^{16} + 6 q^{17} - 8 q^{18} + 3 q^{19} - 3 q^{20} - 5 q^{22} + 3 q^{23} + 5 q^{24} - 7 q^{25} - 3 q^{26} + 9 q^{29} + 3 q^{30} + 17 q^{31} + 9 q^{32} + 5 q^{33} - 13 q^{34} + 7 q^{36} + 2 q^{37} + 6 q^{38} + 9 q^{39} - 5 q^{40} - 2 q^{41} - 2 q^{43} + 5 q^{44} - 7 q^{45} - 4 q^{46} + 2 q^{47} - 12 q^{48} + 6 q^{50} + 19 q^{51} - 3 q^{52} - 17 q^{53} - 5 q^{54} - 5 q^{55} - 3 q^{57} + 3 q^{58} - 13 q^{59} - 2 q^{60} + 22 q^{61} - 6 q^{62} + 4 q^{64} + 3 q^{65} - 10 q^{66} + 11 q^{67} + 7 q^{68} + 7 q^{69} - 4 q^{71} + 15 q^{72} + 30 q^{73} + 14 q^{74} - 13 q^{75} - 9 q^{76} - 12 q^{78} - 2 q^{79} + 6 q^{80} + 2 q^{81} + q^{82} - 6 q^{83} - 7 q^{85} + 21 q^{86} + 6 q^{87} + 10 q^{88} + 9 q^{89} + q^{90} + q^{92} + 23 q^{93} + 4 q^{94} + 9 q^{95} + 11 q^{96} + 17 q^{97} + 15 q^{99}+O(q^{100}) \) 2 * q - q^2 + 3 * q^3 - q^4 + q^5 - 4 * q^6 + q^9 + 2 * q^10 + q^12 + 6 * q^13 - q^15 - 3 * q^16 + 6 * q^17 - 8 * q^18 + 3 * q^19 - 3 * q^20 - 5 * q^22 + 3 * q^23 + 5 * q^24 - 7 * q^25 - 3 * q^26 + 9 * q^29 + 3 * q^30 + 17 * q^31 + 9 * q^32 + 5 * q^33 - 13 * q^34 + 7 * q^36 + 2 * q^37 + 6 * q^38 + 9 * q^39 - 5 * q^40 - 2 * q^41 - 2 * q^43 + 5 * q^44 - 7 * q^45 - 4 * q^46 + 2 * q^47 - 12 * q^48 + 6 * q^50 + 19 * q^51 - 3 * q^52 - 17 * q^53 - 5 * q^54 - 5 * q^55 - 3 * q^57 + 3 * q^58 - 13 * q^59 - 2 * q^60 + 22 * q^61 - 6 * q^62 + 4 * q^64 + 3 * q^65 - 10 * q^66 + 11 * q^67 + 7 * q^68 + 7 * q^69 - 4 * q^71 + 15 * q^72 + 30 * q^73 + 14 * q^74 - 13 * q^75 - 9 * q^76 - 12 * q^78 - 2 * q^79 + 6 * q^80 + 2 * q^81 + q^82 - 6 * q^83 - 7 * q^85 + 21 * q^86 + 6 * q^87 + 10 * q^88 + 9 * q^89 + q^90 + q^92 + 23 * q^93 + 4 * q^94 + 9 * q^95 + 11 * q^96 + 17 * q^97 + 15 * q^99

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