LMFDB - Embedded newform 2009.2.a.a.1.1

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:	$1$
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			1.1
Root			$1.61803$ 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)

$f(q)$	$=$	$q-1.61803 q^{2} -0.618034 q^{3} +0.618034 q^{4} +0.618034 q^{5} +1.00000 q^{6} +2.23607 q^{8} -2.61803 q^{9} +O(q^{10})$	\(q-1.61803 q^{2} -0.618034 q^{3} +0.618034 q^{4} +0.618034 q^{5} +1.00000 q^{6} +2.23607 q^{8} -2.61803 q^{9} -1.00000 q^{10} -1.00000 q^{11} -0.381966 q^{12} +1.76393 q^{13} -0.381966 q^{15} -4.85410 q^{16} -0.236068 q^{17} +4.23607 q^{18} +3.85410 q^{19} +0.381966 q^{20} +1.61803 q^{22} -1.38197 q^{23} -1.38197 q^{24} -4.61803 q^{25} -2.85410 q^{26} +3.47214 q^{27} +0.854102 q^{29} +0.618034 q^{30} +3.09017 q^{31} +3.38197 q^{32} +0.618034 q^{33} +0.381966 q^{34} -1.61803 q^{36} -7.23607 q^{37} -6.23607 q^{38} -1.09017 q^{39} +1.38197 q^{40} +1.00000 q^{41} -1.00000 q^{43} -0.618034 q^{44} -1.61803 q^{45} +2.23607 q^{46} +3.70820 q^{47} +3.00000 q^{48} +7.47214 q^{50} +0.145898 q^{51} +1.09017 q^{52} +4.61803 q^{53} -5.61803 q^{54} -0.618034 q^{55} -2.38197 q^{57} -1.38197 q^{58} -10.6180 q^{59} -0.236068 q^{60} -0.527864 q^{61} -5.00000 q^{62} +4.23607 q^{64} +1.09017 q^{65} -1.00000 q^{66} -0.909830 q^{67} -0.145898 q^{68} +0.854102 q^{69} +11.9443 q^{71} -5.85410 q^{72} -7.94427 q^{73} +11.7082 q^{74} +2.85410 q^{75} +2.38197 q^{76} +1.76393 q^{78} +1.70820 q^{79} -3.00000 q^{80} +5.70820 q^{81} -1.61803 q^{82} -3.47214 q^{83} -0.145898 q^{85} +1.61803 q^{86} -0.527864 q^{87} -2.23607 q^{88} -6.32624 q^{89} +2.61803 q^{90} -0.854102 q^{92} -1.90983 q^{93} -6.00000 q^{94} +2.38197 q^{95} -2.09017 q^{96} +17.5623 q^{97} +2.61803 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - 3 q^{9}+O(q^{10}) $ 2 * q - q^2 + q^3 - q^4 - q^5 + 2 * q^6 - 3 * q^9	$ 2 q - q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - 3 q^{9} - 2 q^{10} - 2 q^{11} - 3 q^{12} + 8 q^{13} - 3 q^{15} - 3 q^{16} + 4 q^{17} + 4 q^{18} + q^{19} + 3 q^{20} + q^{22} - 5 q^{23} - 5 q^{24} - 7 q^{25} + q^{26} - 2 q^{27} - 5 q^{29} - q^{30} - 5 q^{31} + 9 q^{32} - q^{33} + 3 q^{34} - q^{36} - 10 q^{37} - 8 q^{38} + 9 q^{39} + 5 q^{40} + 2 q^{41} - 2 q^{43} + q^{44} - q^{45} - 6 q^{47} + 6 q^{48} + 6 q^{50} + 7 q^{51} - 9 q^{52} + 7 q^{53} - 9 q^{54} + q^{55} - 7 q^{57} - 5 q^{58} - 19 q^{59} + 4 q^{60} - 10 q^{61} - 10 q^{62} + 4 q^{64} - 9 q^{65} - 2 q^{66} - 13 q^{67} - 7 q^{68} - 5 q^{69} + 6 q^{71} - 5 q^{72} + 2 q^{73} + 10 q^{74} - q^{75} + 7 q^{76} + 8 q^{78} - 10 q^{79} - 6 q^{80} - 2 q^{81} - q^{82} + 2 q^{83} - 7 q^{85} + q^{86} - 10 q^{87} + 3 q^{89} + 3 q^{90} + 5 q^{92} - 15 q^{93} - 12 q^{94} + 7 q^{95} + 7 q^{96} + 15 q^{97} + 3 q^{99}+O(q^{100}) $ 2 * q - q^2 + q^3 - q^4 - q^5 + 2 * q^6 - 3 * q^9 - 2 * q^10 - 2 * q^11 - 3 * q^12 + 8 * q^13 - 3 * q^15 - 3 * q^16 + 4 * q^17 + 4 * q^18 + q^19 + 3 * q^20 + q^22 - 5 * q^23 - 5 * q^24 - 7 * q^25 + q^26 - 2 * q^27 - 5 * q^29 - q^30 - 5 * q^31 + 9 * q^32 - q^33 + 3 * q^34 - q^36 - 10 * q^37 - 8 * q^38 + 9 * q^39 + 5 * q^40 + 2 * q^41 - 2 * q^43 + q^44 - q^45 - 6 * q^47 + 6 * q^48 + 6 * q^50 + 7 * q^51 - 9 * q^52 + 7 * q^53 - 9 * q^54 + q^55 - 7 * q^57 - 5 * q^58 - 19 * q^59 + 4 * q^60 - 10 * q^61 - 10 * q^62 + 4 * q^64 - 9 * q^65 - 2 * q^66 - 13 * q^67 - 7 * q^68 - 5 * q^69 + 6 * q^71 - 5 * q^72 + 2 * q^73 + 10 * q^74 - q^75 + 7 * q^76 + 8 * q^78 - 10 * q^79 - 6 * q^80 - 2 * q^81 - q^82 + 2 * q^83 - 7 * q^85 + q^86 - 10 * q^87 + 3 * q^89 + 3 * q^90 + 5 * q^92 - 15 * q^93 - 12 * q^94 + 7 * q^95 + 7 * q^96 + 15 * q^97 + 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.61803	−1.14412	−0.572061	−	0.820211i	$-0.693856\pi$
$2$	−1.61803	−1.14412	−0.572061	+	0.820211i	$0.693856\pi$
$3$	−0.618034	−0.356822	−0.178411	−	0.983956i	$-0.557096\pi$
$3$	−0.618034	−0.356822	−0.178411	+	0.983956i	$0.557096\pi$
$4$	0.618034	0.309017
$5$	0.618034	0.276393	0.138197	−	0.990405i	$-0.455869\pi$
$5$	0.618034	0.276393	0.138197	+	0.990405i	$0.455869\pi$
$6$	1.00000	0.408248
$7$	0	0
$7$	0	0
$8$	2.23607	0.790569
$9$	−2.61803	−0.872678
$10$	−1.00000	−0.316228
$11$	−1.00000	−0.301511	−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000	−0.301511	−0.150756	+	0.988571i	$0.548171\pi$
$12$	−0.381966	−0.110264
$13$	1.76393	0.489227	0.244613	−	0.969621i	$-0.421339\pi$
$13$	1.76393	0.489227	0.244613	+	0.969621i	$0.421339\pi$
$14$	0	0
$15$	−0.381966	−0.0986232
$16$	−4.85410	−1.21353
$17$	−0.236068	−0.0572549	−0.0286274	−	0.999590i	$-0.509114\pi$
$17$	−0.236068	−0.0572549	−0.0286274	+	0.999590i	$0.509114\pi$
$18$	4.23607	0.998451
$19$	3.85410	0.884192	0.442096	−	0.896968i	$-0.354235\pi$
$19$	3.85410	0.884192	0.442096	+	0.896968i	$0.354235\pi$
$20$	0.381966	0.0854102
$21$	0	0
$22$	1.61803	0.344966
$23$	−1.38197	−0.288160	−0.144080	−	0.989566i	$-0.546022\pi$
$23$	−1.38197	−0.288160	−0.144080	+	0.989566i	$0.546022\pi$
$24$	−1.38197	−0.282093
$25$	−4.61803	−0.923607
$26$	−2.85410	−0.559735
$27$	3.47214	0.668213
$28$	0	0
$29$	0.854102	0.158603	0.0793014	−	0.996851i	$-0.474731\pi$
$29$	0.854102	0.158603	0.0793014	+	0.996851i	$0.474731\pi$
$30$	0.618034	0.112837
$31$	3.09017	0.555011	0.277505	−	0.960724i	$-0.410492\pi$
$31$	3.09017	0.555011	0.277505	+	0.960724i	$0.410492\pi$
$32$	3.38197	0.597853
$33$	0.618034	0.107586
$34$	0.381966	0.0655066
$35$	0	0
$36$	−1.61803	−0.269672
$37$	−7.23607	−1.18960	−0.594801	−	0.803873i	$-0.702769\pi$
$37$	−7.23607	−1.18960	−0.594801	+	0.803873i	$0.702769\pi$
$38$	−6.23607	−1.01162
$39$	−1.09017	−0.174567
$40$	1.38197	0.218508
$41$	1.00000	0.156174
$41$	1.00000	0.156174
$42$	0	0
$43$	−1.00000	−0.152499	−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000	−0.152499	−0.0762493	+	0.997089i	$0.524294\pi$
$44$	−0.618034	−0.0931721
$45$	−1.61803	−0.241202
$46$	2.23607	0.329690
$47$	3.70820	0.540897	0.270449	−	0.962734i	$-0.412828\pi$
$47$	3.70820	0.540897	0.270449	+	0.962734i	$0.412828\pi$
$48$	3.00000	0.433013
$49$	0	0
$50$	7.47214	1.05672
$51$	0.145898	0.0204298
$52$	1.09017	0.151179
$53$	4.61803	0.634336	0.317168	−	0.948369i	$-0.397268\pi$
$53$	4.61803	0.634336	0.317168	+	0.948369i	$0.397268\pi$
$54$	−5.61803	−0.764518
$55$	−0.618034	−0.0833357
$56$	0	0
$57$	−2.38197	−0.315499
$58$	−1.38197	−0.181461
$59$	−10.6180	−1.38235	−0.691175	−	0.722687i	$-0.742907\pi$
$59$	−10.6180	−1.38235	−0.691175	+	0.722687i	$0.742907\pi$
$60$	−0.236068	−0.0304762
$61$	−0.527864	−0.0675861	−0.0337930	−	0.999429i	$-0.510759\pi$
$61$	−0.527864	−0.0675861	−0.0337930	+	0.999429i	$0.510759\pi$
$62$	−5.00000	−0.635001
$63$	0	0
$64$	4.23607	0.529508
$65$	1.09017	0.135219
$66$	−1.00000	−0.123091
$67$	−0.909830	−0.111153	−0.0555767	−	0.998454i	$-0.517700\pi$
$67$	−0.909830	−0.111153	−0.0555767	+	0.998454i	$0.517700\pi$
$68$	−0.145898	−0.0176927
$69$	0.854102	0.102822
$70$	0	0
$71$	11.9443	1.41752	0.708762	−	0.705448i	$-0.249254\pi$
$71$	11.9443	1.41752	0.708762	+	0.705448i	$0.249254\pi$
$72$	−5.85410	−0.689913
$73$	−7.94427	−0.929807	−0.464903	−	0.885361i	$-0.653911\pi$
$73$	−7.94427	−0.929807	−0.464903	+	0.885361i	$0.653911\pi$
$74$	11.7082	1.36105
$75$	2.85410	0.329563
$76$	2.38197	0.273230
$77$	0	0
$78$	1.76393	0.199726
$79$	1.70820	0.192188	0.0960940	−	0.995372i	$-0.469365\pi$
$79$	1.70820	0.192188	0.0960940	+	0.995372i	$0.469365\pi$
$80$	−3.00000	−0.335410
$81$	5.70820	0.634245
$82$	−1.61803	−0.178682
$83$	−3.47214	−0.381116	−0.190558	−	0.981676i	$-0.561030\pi$
$83$	−3.47214	−0.381116	−0.190558	+	0.981676i	$0.561030\pi$
$84$	0	0
$85$	−0.145898	−0.0158249
$86$	1.61803	0.174477
$87$	−0.527864	−0.0565930
$88$	−2.23607	−0.238366
$89$	−6.32624	−0.670580	−0.335290	−	0.942115i	$-0.608834\pi$
$89$	−6.32624	−0.670580	−0.335290	+	0.942115i	$0.608834\pi$
$90$	2.61803	0.275965
$91$	0	0
$92$	−0.854102	−0.0890463
$93$	−1.90983	−0.198040
$94$	−6.00000	−0.618853
$95$	2.38197	0.244385
$96$	−2.09017	−0.213327
$97$	17.5623	1.78318	0.891591	−	0.452842i	$-0.149590\pi$
$97$	17.5623	1.78318	0.891591	+	0.452842i	$0.149590\pi$
$98$	0	0
$99$	2.61803	0.263122
$100$	−2.85410	−0.285410
$101$	8.52786	0.848554	0.424277	−	0.905532i	$-0.360528\pi$
$101$	8.52786	0.848554	0.424277	+	0.905532i	$0.360528\pi$
$102$	−0.236068	−0.0233742
$103$	−10.0902	−0.994214	−0.497107	−	0.867689i	$-0.665604\pi$
$103$	−10.0902	−0.994214	−0.497107	+	0.867689i	$0.665604\pi$
$104$	3.94427	0.386768
$105$	0	0
$106$	−7.47214	−0.725758
$107$	−5.23607	−0.506190	−0.253095	−	0.967441i	$-0.581448\pi$
$107$	−5.23607	−0.506190	−0.253095	+	0.967441i	$0.581448\pi$
$108$	2.14590	0.206489
$109$	−0.472136	−0.0452224	−0.0226112	−	0.999744i	$-0.507198\pi$
$109$	−0.472136	−0.0452224	−0.0226112	+	0.999744i	$0.507198\pi$
$110$	1.00000	0.0953463
$111$	4.47214	0.424476
$112$	0	0
$113$	−12.4164	−1.16804	−0.584019	−	0.811740i	$-0.698521\pi$
$113$	−12.4164	−1.16804	−0.584019	+	0.811740i	$0.698521\pi$
$114$	3.85410	0.360970
$115$	−0.854102	−0.0796454
$116$	0.527864	0.0490109
$117$	−4.61803	−0.426937
$118$	17.1803	1.58158
$119$	0	0
$120$	−0.854102	−0.0779685
$121$	−10.0000	−0.909091
$122$	0.854102	0.0773268
$123$	−0.618034	−0.0557262
$124$	1.90983	0.171508
$125$	−5.94427	−0.531672
$126$	0	0
$127$	−16.7082	−1.48261	−0.741307	−	0.671166i	$-0.765794\pi$
$127$	−16.7082	−1.48261	−0.741307	+	0.671166i	$0.765794\pi$
$128$	−13.6180	−1.20368
$129$	0.618034	0.0544149
$130$	−1.76393	−0.154707
$131$	−4.14590	−0.362229	−0.181114	−	0.983462i	$-0.557970\pi$
$131$	−4.14590	−0.362229	−0.181114	+	0.983462i	$0.557970\pi$
$132$	0.381966	0.0332459
$133$	0	0
$134$	1.47214	0.127173
$135$	2.14590	0.184689
$136$	−0.527864	−0.0452640
$137$	−8.79837	−0.751696	−0.375848	−	0.926681i	$-0.622648\pi$
$137$	−8.79837	−0.751696	−0.375848	+	0.926681i	$0.622648\pi$
$138$	−1.38197	−0.117641
$139$	−11.9443	−1.01310	−0.506550	−	0.862211i	$-0.669079\pi$
$139$	−11.9443	−1.01310	−0.506550	+	0.862211i	$0.669079\pi$
$140$	0	0
$141$	−2.29180	−0.193004
$142$	−19.3262	−1.62182
$143$	−1.76393	−0.147507
$144$	12.7082	1.05902
$145$	0.527864	0.0438367
$146$	12.8541	1.06381
$147$	0	0
$148$	−4.47214	−0.367607
$149$	1.05573	0.0864886	0.0432443	−	0.999065i	$-0.486231\pi$
$149$	1.05573	0.0864886	0.0432443	+	0.999065i	$0.486231\pi$
$150$	−4.61803	−0.377061
$151$	−2.05573	−0.167293	−0.0836464	−	0.996495i	$-0.526657\pi$
$151$	−2.05573	−0.167293	−0.0836464	+	0.996495i	$0.526657\pi$
$152$	8.61803	0.699015
$153$	0.618034	0.0499651
$154$	0	0
$155$	1.90983	0.153401
$156$	−0.673762	−0.0539441
$157$	8.00000	0.638470	0.319235	−	0.947676i	$-0.396574\pi$
$157$	8.00000	0.638470	0.319235	+	0.947676i	$0.396574\pi$
$158$	−2.76393	−0.219887
$159$	−2.85410	−0.226345
$160$	2.09017	0.165242
$161$	0	0
$162$	−9.23607	−0.725654
$163$	0.944272	0.0739611	0.0369805	−	0.999316i	$-0.488226\pi$
$163$	0.944272	0.0739611	0.0369805	+	0.999316i	$0.488226\pi$
$164$	0.618034	0.0482603
$165$	0.381966	0.0297360
$166$	5.61803	0.436044
$167$	−16.4164	−1.27034	−0.635170	−	0.772372i	$-0.719070\pi$
$167$	−16.4164	−1.27034	−0.635170	+	0.772372i	$0.719070\pi$
$168$	0	0
$169$	−9.88854	−0.760657
$170$	0.236068	0.0181056
$171$	−10.0902	−0.771615
$172$	−0.618034	−0.0471246
$173$	8.70820	0.662072	0.331036	−	0.943618i	$-0.392602\pi$
$173$	8.70820	0.662072	0.331036	+	0.943618i	$0.392602\pi$
$174$	0.854102	0.0647493
$175$	0	0
$176$	4.85410	0.365892
$177$	6.56231	0.493253
$178$	10.2361	0.767226
$179$	−26.0344	−1.94591	−0.972953	−	0.231004i	$-0.925799\pi$
$179$	−26.0344	−1.94591	−0.972953	+	0.231004i	$0.925799\pi$
$180$	−1.00000	−0.0745356
$181$	−14.9443	−1.11080	−0.555399	−	0.831584i	$-0.687435\pi$
$181$	−14.9443	−1.11080	−0.555399	+	0.831584i	$0.687435\pi$
$182$	0	0
$183$	0.326238	0.0241162
$184$	−3.09017	−0.227810
$185$	−4.47214	−0.328798
$186$	3.09017	0.226582
$187$	0.236068	0.0172630
$188$	2.29180	0.167146
$189$	0	0
$190$	−3.85410	−0.279606
$191$	13.5279	0.978842	0.489421	−	0.872048i	$-0.337208\pi$
$191$	13.5279	0.978842	0.489421	+	0.872048i	$0.337208\pi$
$192$	−2.61803	−0.188940
$193$	−9.29180	−0.668838	−0.334419	−	0.942424i	$-0.608540\pi$
$193$	−9.29180	−0.668838	−0.334419	+	0.942424i	$0.608540\pi$
$194$	−28.4164	−2.04018
$195$	−0.673762	−0.0482491
$196$	0	0
$197$	−7.38197	−0.525943	−0.262972	−	0.964804i	$-0.584703\pi$
$197$	−7.38197	−0.525943	−0.262972	+	0.964804i	$0.584703\pi$
$198$	−4.23607	−0.301044
$199$	−23.3607	−1.65599	−0.827997	−	0.560732i	$-0.810520\pi$
$199$	−23.3607	−1.65599	−0.827997	+	0.560732i	$0.810520\pi$
$200$	−10.3262	−0.730175
$201$	0.562306	0.0396620
$202$	−13.7984	−0.970850
$203$	0	0
$204$	0.0901699	0.00631316
$205$	0.618034	0.0431654
$206$	16.3262	1.13750
$207$	3.61803	0.251471
$208$	−8.56231	−0.593689
$209$	−3.85410	−0.266594
$210$	0	0
$211$	−15.0344	−1.03501	−0.517507	−	0.855679i	$-0.673140\pi$
$211$	−15.0344	−1.03501	−0.517507	+	0.855679i	$0.673140\pi$
$212$	2.85410	0.196021
$213$	−7.38197	−0.505804
$214$	8.47214	0.579143
$215$	−0.618034	−0.0421496
$216$	7.76393	0.528269
$217$	0	0
$218$	0.763932	0.0517400
$219$	4.90983	0.331776
$220$	−0.381966	−0.0257521
$221$	−0.416408	−0.0280106
$222$	−7.23607	−0.485653
$223$	−14.3262	−0.959356	−0.479678	−	0.877445i	$-0.659246\pi$
$223$	−14.3262	−0.959356	−0.479678	+	0.877445i	$0.659246\pi$
$224$	0	0
$225$	12.0902	0.806011
$226$	20.0902	1.33638
$227$	25.6525	1.70261	0.851307	−	0.524667i	$-0.175810\pi$
$227$	25.6525	1.70261	0.851307	+	0.524667i	$0.175810\pi$
$228$	−1.47214	−0.0974946
$229$	−16.7639	−1.10779	−0.553896	−	0.832586i	$-0.686859\pi$
$229$	−16.7639	−1.10779	−0.553896	+	0.832586i	$0.686859\pi$
$230$	1.38197	0.0911241
$231$	0	0
$232$	1.90983	0.125386
$233$	9.32624	0.610982	0.305491	−	0.952195i	$-0.401179\pi$
$233$	9.32624	0.610982	0.305491	+	0.952195i	$0.401179\pi$
$234$	7.47214	0.488469
$235$	2.29180	0.149500
$236$	−6.56231	−0.427170
$237$	−1.05573	−0.0685769
$238$	0	0
$239$	−12.8541	−0.831463	−0.415731	−	0.909487i	$-0.636474\pi$
$239$	−12.8541	−0.831463	−0.415731	+	0.909487i	$0.636474\pi$
$240$	1.85410	0.119682
$241$	9.23607	0.594947	0.297474	−	0.954730i	$-0.403856\pi$
$241$	9.23607	0.594947	0.297474	+	0.954730i	$0.403856\pi$
$242$	16.1803	1.04011
$243$	−13.9443	−0.894525
$244$	−0.326238	−0.0208852
$245$	0	0
$246$	1.00000	0.0637577
$247$	6.79837	0.432570
$248$	6.90983	0.438775
$249$	2.14590	0.135991
$250$	9.61803	0.608298
$251$	−19.9443	−1.25887	−0.629436	−	0.777053i	$-0.716714\pi$
$251$	−19.9443	−1.25887	−0.629436	+	0.777053i	$0.716714\pi$
$252$	0	0
$253$	1.38197	0.0868835
$254$	27.0344	1.69629
$255$	0.0901699	0.00564666
$256$	13.5623	0.847644
$257$	16.1246	1.00583	0.502913	−	0.864337i	$-0.332262\pi$
$257$	16.1246	1.00583	0.502913	+	0.864337i	$0.332262\pi$
$258$	−1.00000	−0.0622573
$259$	0	0
$260$	0.673762	0.0417850
$261$	−2.23607	−0.138409
$262$	6.70820	0.414434
$263$	0.708204	0.0436697	0.0218349	−	0.999762i	$-0.493049\pi$
$263$	0.708204	0.0436697	0.0218349	+	0.999762i	$0.493049\pi$
$264$	1.38197	0.0850541
$265$	2.85410	0.175326
$266$	0	0
$267$	3.90983	0.239278
$268$	−0.562306	−0.0343483
$269$	10.2705	0.626204	0.313102	−	0.949719i	$-0.398632\pi$
$269$	10.2705	0.626204	0.313102	+	0.949719i	$0.398632\pi$
$270$	−3.47214	−0.211307
$271$	0.236068	0.0143401	0.00717005	−	0.999974i	$-0.497718\pi$
$271$	0.236068	0.0143401	0.00717005	+	0.999974i	$0.497718\pi$
$272$	1.14590	0.0694803
$273$	0	0
$274$	14.2361	0.860032
$275$	4.61803	0.278478
$276$	0.527864	0.0317737
$277$	−23.1803	−1.39277	−0.696386	−	0.717668i	$-0.745210\pi$
$277$	−23.1803	−1.39277	−0.696386	+	0.717668i	$0.745210\pi$
$278$	19.3262	1.15911
$279$	−8.09017	−0.484346
$280$	0	0
$281$	−11.2918	−0.673612	−0.336806	−	0.941574i	$-0.609347\pi$
$281$	−11.2918	−0.673612	−0.336806	+	0.941574i	$0.609347\pi$
$282$	3.70820	0.220820
$283$	0	0		−	1.00000i	$-0.5\pi$
$283$	0	0			1.00000i	$0.5\pi$
$284$	7.38197	0.438039
$285$	−1.47214	−0.0872018
$286$	2.85410	0.168767
$287$	0	0
$288$	−8.85410	−0.521733
$289$	−16.9443	−0.996722
$290$	−0.854102	−0.0501546
$291$	−10.8541	−0.636279
$292$	−4.90983	−0.287326
$293$	7.76393	0.453574	0.226787	−	0.973944i	$-0.427178\pi$
$293$	7.76393	0.453574	0.226787	+	0.973944i	$0.427178\pi$
$294$	0	0
$295$	−6.56231	−0.382072
$296$	−16.1803	−0.940463
$297$	−3.47214	−0.201474
$298$	−1.70820	−0.0989536
$299$	−2.43769	−0.140975
$300$	1.76393	0.101841
$301$	0	0
$302$	3.32624	0.191403
$303$	−5.27051	−0.302783
$304$	−18.7082	−1.07299
$305$	−0.326238	−0.0186803
$306$	−1.00000	−0.0571662
$307$	−32.4721	−1.85328	−0.926641	−	0.375947i	$-0.877318\pi$
$307$	−32.4721	−1.85328	−0.926641	+	0.375947i	$0.877318\pi$
$308$	0	0
$309$	6.23607	0.354758
$310$	−3.09017	−0.175510
$311$	1.61803	0.0917503	0.0458751	−	0.998947i	$-0.485392\pi$
$311$	1.61803	0.0917503	0.0458751	+	0.998947i	$0.485392\pi$
$312$	−2.43769	−0.138007
$313$	20.5279	1.16030	0.580152	−	0.814508i	$-0.302993\pi$
$313$	20.5279	1.16030	0.580152	+	0.814508i	$0.302993\pi$
$314$	−12.9443	−0.730488
$315$	0	0
$316$	1.05573	0.0593893
$317$	32.1246	1.80430	0.902149	−	0.431425i	$-0.141989\pi$
$317$	32.1246	1.80430	0.902149	+	0.431425i	$0.141989\pi$
$318$	4.61803	0.258966
$319$	−0.854102	−0.0478205
$320$	2.61803	0.146353
$321$	3.23607	0.180620
$322$	0	0
$323$	−0.909830	−0.0506243
$324$	3.52786	0.195992
$325$	−8.14590	−0.451853
$326$	−1.52786	−0.0846206
$327$	0.291796	0.0161364
$328$	2.23607	0.123466
$329$	0	0
$330$	−0.618034	−0.0340217
$331$	−1.88854	−0.103804	−0.0519019	−	0.998652i	$-0.516528\pi$
$331$	−1.88854	−0.103804	−0.0519019	+	0.998652i	$0.516528\pi$
$332$	−2.14590	−0.117771
$333$	18.9443	1.03814
$334$	26.5623	1.45342
$335$	−0.562306	−0.0307221
$336$	0	0
$337$	−11.5279	−0.627963	−0.313981	−	0.949429i	$-0.601663\pi$
$337$	−11.5279	−0.627963	−0.313981	+	0.949429i	$0.601663\pi$
$338$	16.0000	0.870285
$339$	7.67376	0.416782
$340$	−0.0901699	−0.00489015
$341$	−3.09017	−0.167342
$342$	16.3262	0.882822
$343$	0	0
$344$	−2.23607	−0.120561
$345$	0.527864	0.0284192
$346$	−14.0902	−0.757492
$347$	−17.7082	−0.950626	−0.475313	−	0.879817i	$-0.657665\pi$
$347$	−17.7082	−0.950626	−0.475313	+	0.879817i	$0.657665\pi$
$348$	−0.326238	−0.0174882
$349$	−3.29180	−0.176206	−0.0881029	−	0.996111i	$-0.528080\pi$
$349$	−3.29180	−0.176206	−0.0881029	+	0.996111i	$0.528080\pi$
$350$	0	0
$351$	6.12461	0.326908
$352$	−3.38197	−0.180259
$353$	34.3607	1.82883	0.914417	−	0.404773i	$-0.132649\pi$
$353$	34.3607	1.82883	0.914417	+	0.404773i	$0.132649\pi$
$354$	−10.6180	−0.564342
$355$	7.38197	0.391794
$356$	−3.90983	−0.207221
$357$	0	0
$358$	42.1246	2.22635
$359$	−0.180340	−0.00951798	−0.00475899	−	0.999989i	$-0.501515\pi$
$359$	−0.180340	−0.00951798	−0.00475899	+	0.999989i	$0.501515\pi$
$360$	−3.61803	−0.190687
$361$	−4.14590	−0.218205
$362$	24.1803	1.27089
$363$	6.18034	0.324384
$364$	0	0
$365$	−4.90983	−0.256992
$366$	−0.527864	−0.0275919
$367$	6.27051	0.327318	0.163659	−	0.986517i	$-0.447670\pi$
$367$	6.27051	0.327318	0.163659	+	0.986517i	$0.447670\pi$
$368$	6.70820	0.349689
$369$	−2.61803	−0.136289
$370$	7.23607	0.376185
$371$	0	0
$372$	−1.18034	−0.0611978
$373$	−29.7426	−1.54002	−0.770008	−	0.638034i	$-0.779748\pi$
$373$	−29.7426	−1.54002	−0.770008	+	0.638034i	$0.779748\pi$
$374$	−0.381966	−0.0197510
$375$	3.67376	0.189712
$376$	8.29180	0.427617
$377$	1.50658	0.0775927
$378$	0	0
$379$	20.6525	1.06085	0.530423	−	0.847733i	$-0.322033\pi$
$379$	20.6525	1.06085	0.530423	+	0.847733i	$0.322033\pi$
$380$	1.47214	0.0755190
$381$	10.3262	0.529029
$382$	−21.8885	−1.11992
$383$	0.819660	0.0418827	0.0209413	−	0.999781i	$-0.493334\pi$
$383$	0.819660	0.0418827	0.0209413	+	0.999781i	$0.493334\pi$
$384$	8.41641	0.429498
$385$	0	0
$386$	15.0344	0.765233
$387$	2.61803	0.133082
$388$	10.8541	0.551034
$389$	29.6869	1.50519	0.752593	−	0.658486i	$-0.228803\pi$
$389$	29.6869	1.50519	0.752593	+	0.658486i	$0.228803\pi$
$390$	1.09017	0.0552029
$391$	0.326238	0.0164986
$392$	0	0
$393$	2.56231	0.129251
$394$	11.9443	0.601744
$395$	1.05573	0.0531194
$396$	1.61803	0.0813093
$397$	−21.4508	−1.07659	−0.538294	−	0.842757i	$-0.680931\pi$
$397$	−21.4508	−1.07659	−0.538294	+	0.842757i	$0.680931\pi$
$398$	37.7984	1.89466
$399$	0	0
$400$	22.4164	1.12082
$401$	16.7639	0.837151	0.418575	−	0.908182i	$-0.362530\pi$
$401$	16.7639	0.837151	0.418575	+	0.908182i	$0.362530\pi$
$402$	−0.909830	−0.0453782
$403$	5.45085	0.271526
$404$	5.27051	0.262218
$405$	3.52786	0.175301
$406$	0	0
$407$	7.23607	0.358679
$408$	0.326238	0.0161512
$409$	−5.65248	−0.279497	−0.139748	−	0.990187i	$-0.544629\pi$
$409$	−5.65248	−0.279497	−0.139748	+	0.990187i	$0.544629\pi$
$410$	−1.00000	−0.0493865
$411$	5.43769	0.268222
$412$	−6.23607	−0.307229
$413$	0	0
$414$	−5.85410	−0.287713
$415$	−2.14590	−0.105338
$416$	5.96556	0.292486
$417$	7.38197	0.361496
$418$	6.23607	0.305016
$419$	−24.2705	−1.18569	−0.592846	−	0.805316i	$-0.701996\pi$
$419$	−24.2705	−1.18569	−0.592846	+	0.805316i	$0.701996\pi$
$420$	0	0
$421$	−11.5279	−0.561834	−0.280917	−	0.959732i	$-0.590639\pi$
$421$	−11.5279	−0.561834	−0.280917	+	0.959732i	$0.590639\pi$
$422$	24.3262	1.18418
$423$	−9.70820	−0.472029
$424$	10.3262	0.501486
$425$	1.09017	0.0528810
$426$	11.9443	0.578702
$427$	0	0
$428$	−3.23607	−0.156421
$429$	1.09017	0.0526339
$430$	1.00000	0.0482243
$431$	−0.527864	−0.0254263	−0.0127132	−	0.999919i	$-0.504047\pi$
$431$	−0.527864	−0.0254263	−0.0127132	+	0.999919i	$0.504047\pi$
$432$	−16.8541	−0.810893
$433$	30.0344	1.44336	0.721682	−	0.692225i	$-0.243369\pi$
$433$	30.0344	1.44336	0.721682	+	0.692225i	$0.243369\pi$
$434$	0	0
$435$	−0.326238	−0.0156419
$436$	−0.291796	−0.0139745
$437$	−5.32624	−0.254789
$438$	−7.94427	−0.379592
$439$	−3.94427	−0.188250	−0.0941249	−	0.995560i	$-0.530005\pi$
$439$	−3.94427	−0.188250	−0.0941249	+	0.995560i	$0.530005\pi$
$440$	−1.38197	−0.0658826
$441$	0	0
$442$	0.673762	0.0320476
$443$	10.1459	0.482046	0.241023	−	0.970519i	$-0.422517\pi$
$443$	10.1459	0.482046	0.241023	+	0.970519i	$0.422517\pi$
$444$	2.76393	0.131170
$445$	−3.90983	−0.185344
$446$	23.1803	1.09762
$447$	−0.652476	−0.0308610
$448$	0	0
$449$	−6.00000	−0.283158	−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000	−0.283158	−0.141579	+	0.989927i	$0.545218\pi$
$450$	−19.5623	−0.922176
$451$	−1.00000	−0.0470882
$452$	−7.67376	−0.360943
$453$	1.27051	0.0596938
$454$	−41.5066	−1.94800
$455$	0	0
$456$	−5.32624	−0.249424
$457$	10.4164	0.487259	0.243630	−	0.969868i	$-0.421662\pi$
$457$	10.4164	0.487259	0.243630	+	0.969868i	$0.421662\pi$
$458$	27.1246	1.26745
$459$	−0.819660	−0.0382585
$460$	−0.527864	−0.0246118
$461$	7.65248	0.356411	0.178206	−	0.983993i	$-0.442971\pi$
$461$	7.65248	0.356411	0.178206	+	0.983993i	$0.442971\pi$
$462$	0	0
$463$	33.6180	1.56236	0.781181	−	0.624304i	$-0.214617\pi$
$463$	33.6180	1.56236	0.781181	+	0.624304i	$0.214617\pi$
$464$	−4.14590	−0.192468
$465$	−1.18034	−0.0547370
$466$	−15.0902	−0.699039
$467$	−0.236068	−0.0109239	−0.00546196	−	0.999985i	$-0.501739\pi$
$467$	−0.236068	−0.0109239	−0.00546196	+	0.999985i	$0.501739\pi$
$468$	−2.85410	−0.131931
$469$	0	0
$470$	−3.70820	−0.171047
$471$	−4.94427	−0.227820
$472$	−23.7426	−1.09284
$473$	1.00000	0.0459800
$474$	1.70820	0.0784604
$475$	−17.7984	−0.816645
$476$	0	0
$477$	−12.0902	−0.553571
$478$	20.7984	0.951295
$479$	19.5623	0.893825	0.446912	−	0.894578i	$-0.352524\pi$
$479$	19.5623	0.893825	0.446912	+	0.894578i	$0.352524\pi$
$480$	−1.29180	−0.0589622
$481$	−12.7639	−0.581985
$482$	−14.9443	−0.680693
$483$	0	0
$484$	−6.18034	−0.280925
$485$	10.8541	0.492859
$486$	22.5623	1.02345
$487$	−15.2361	−0.690412	−0.345206	−	0.938527i	$-0.612191\pi$
$487$	−15.2361	−0.690412	−0.345206	+	0.938527i	$0.612191\pi$
$488$	−1.18034	−0.0534315
$489$	−0.583592	−0.0263909
$490$	0	0
$491$	−12.2705	−0.553760	−0.276880	−	0.960904i	$-0.589301\pi$
$491$	−12.2705	−0.553760	−0.276880	+	0.960904i	$0.589301\pi$
$492$	−0.381966	−0.0172204
$493$	−0.201626	−0.00908078
$494$	−11.0000	−0.494913
$495$	1.61803	0.0727252
$496$	−15.0000	−0.673520
$497$	0	0
$498$	−3.47214	−0.155590
$499$	−6.65248	−0.297806	−0.148903	−	0.988852i	$-0.547574\pi$
$499$	−6.65248	−0.297806	−0.148903	+	0.988852i	$0.547574\pi$
$500$	−3.67376	−0.164296
$501$	10.1459	0.453285
$502$	32.2705	1.44030
$503$	35.6869	1.59120	0.795601	−	0.605822i	$-0.207155\pi$
$503$	35.6869	1.59120	0.795601	+	0.605822i	$0.207155\pi$
$504$	0	0
$505$	5.27051	0.234535
$506$	−2.23607	−0.0994053
$507$	6.11146	0.271419
$508$	−10.3262	−0.458153
$509$	13.0344	0.577741	0.288871	−	0.957368i	$-0.406720\pi$
$509$	13.0344	0.577741	0.288871	+	0.957368i	$0.406720\pi$
$510$	−0.145898	−0.00646047
$511$	0	0
$512$	5.29180	0.233867
$513$	13.3820	0.590828
$514$	−26.0902	−1.15079
$515$	−6.23607	−0.274794
$516$	0.381966	0.0168151
$517$	−3.70820	−0.163087
$518$	0	0
$519$	−5.38197	−0.236242
$520$	2.43769	0.106900
$521$	35.0902	1.53733	0.768664	−	0.639653i	$-0.220922\pi$
$521$	35.0902	1.53733	0.768664	+	0.639653i	$0.220922\pi$
$522$	3.61803	0.158357
$523$	−8.52786	−0.372897	−0.186449	−	0.982465i	$-0.559698\pi$
$523$	−8.52786	−0.372897	−0.186449	+	0.982465i	$0.559698\pi$
$524$	−2.56231	−0.111935
$525$	0	0
$526$	−1.14590	−0.0499635
$527$	−0.729490	−0.0317771
$528$	−3.00000	−0.130558
$529$	−21.0902	−0.916964
$530$	−4.61803	−0.200595
$531$	27.7984	1.20635
$532$	0	0
$533$	1.76393	0.0764044
$534$	−6.32624	−0.273763
$535$	−3.23607	−0.139907
$536$	−2.03444	−0.0878745
$537$	16.0902	0.694342
$538$	−16.6180	−0.716454
$539$	0	0
$540$	1.32624	0.0570722
$541$	−1.74265	−0.0749222	−0.0374611	−	0.999298i	$-0.511927\pi$
$541$	−1.74265	−0.0749222	−0.0374611	+	0.999298i	$0.511927\pi$
$542$	−0.381966	−0.0164068
$543$	9.23607	0.396358
$544$	−0.798374	−0.0342300
$545$	−0.291796	−0.0124992
$546$	0	0
$547$	−15.0000	−0.641354	−0.320677	−	0.947189i	$-0.603910\pi$
$547$	−15.0000	−0.641354	−0.320677	+	0.947189i	$0.603910\pi$
$548$	−5.43769	−0.232287
$549$	1.38197	0.0589809
$550$	−7.47214	−0.318613
$551$	3.29180	0.140235
$552$	1.90983	0.0812878
$553$	0	0
$554$	37.5066	1.59350
$555$	2.76393	0.117322
$556$	−7.38197	−0.313065
$557$	23.2148	0.983642	0.491821	−	0.870696i	$-0.336331\pi$
$557$	23.2148	0.983642	0.491821	+	0.870696i	$0.336331\pi$
$558$	13.0902	0.554151
$559$	−1.76393	−0.0746064
$560$	0	0
$561$	−0.145898	−0.00615982
$562$	18.2705	0.770695
$563$	−0.527864	−0.0222468	−0.0111234	−	0.999938i	$-0.503541\pi$
$563$	−0.527864	−0.0222468	−0.0111234	+	0.999938i	$0.503541\pi$
$564$	−1.41641	−0.0596415
$565$	−7.67376	−0.322838
$566$	0	0
$567$	0	0
$568$	26.7082	1.12065
$569$	2.61803	0.109754	0.0548768	−	0.998493i	$-0.482523\pi$
$569$	2.61803	0.109754	0.0548768	+	0.998493i	$0.482523\pi$
$570$	2.38197	0.0997696
$571$	−15.8885	−0.664915	−0.332457	−	0.943118i	$-0.607878\pi$
$571$	−15.8885	−0.664915	−0.332457	+	0.943118i	$0.607878\pi$
$572$	−1.09017	−0.0455823
$573$	−8.36068	−0.349272
$574$	0	0
$575$	6.38197	0.266146
$576$	−11.0902	−0.462090
$577$	−1.18034	−0.0491382	−0.0245691	−	0.999698i	$-0.507821\pi$
$577$	−1.18034	−0.0491382	−0.0245691	+	0.999698i	$0.507821\pi$
$578$	27.4164	1.14037
$579$	5.74265	0.238656
$580$	0.326238	0.0135463
$581$	0	0
$582$	17.5623	0.727981
$583$	−4.61803	−0.191259
$584$	−17.7639	−0.735077
$585$	−2.85410	−0.118003
$586$	−12.5623	−0.518944
$587$	−21.0689	−0.869606	−0.434803	−	0.900526i	$-0.643182\pi$
$587$	−21.0689	−0.869606	−0.434803	+	0.900526i	$0.643182\pi$
$588$	0	0
$589$	11.9098	0.490736
$590$	10.6180	0.437138
$591$	4.56231	0.187668
$592$	35.1246	1.44361
$593$	−18.8328	−0.773371	−0.386686	−	0.922212i	$-0.626380\pi$
$593$	−18.8328	−0.773371	−0.386686	+	0.922212i	$0.626380\pi$
$594$	5.61803	0.230511
$595$	0	0
$596$	0.652476	0.0267265
$597$	14.4377	0.590895
$598$	3.94427	0.161293
$599$	−4.65248	−0.190095	−0.0950475	−	0.995473i	$-0.530300\pi$
$599$	−4.65248	−0.190095	−0.0950475	+	0.995473i	$0.530300\pi$
$600$	6.38197	0.260543
$601$	−6.56231	−0.267682	−0.133841	−	0.991003i	$-0.542731\pi$
$601$	−6.56231	−0.267682	−0.133841	+	0.991003i	$0.542731\pi$
$602$	0	0
$603$	2.38197	0.0970012
$604$	−1.27051	−0.0516963
$605$	−6.18034	−0.251267
$606$	8.52786	0.346421
$607$	41.8328	1.69794	0.848971	−	0.528440i	$-0.177223\pi$
$607$	41.8328	1.69794	0.848971	+	0.528440i	$0.177223\pi$
$608$	13.0344	0.528616
$609$	0	0
$610$	0.527864	0.0213726
$611$	6.54102	0.264621
$612$	0.381966	0.0154401
$613$	27.2705	1.10145	0.550723	−	0.834688i	$-0.314352\pi$
$613$	27.2705	1.10145	0.550723	+	0.834688i	$0.314352\pi$
$614$	52.5410	2.12038
$615$	−0.381966	−0.0154024
$616$	0	0
$617$	16.5967	0.668160	0.334080	−	0.942545i	$-0.391574\pi$
$617$	16.5967	0.668160	0.334080	+	0.942545i	$0.391574\pi$
$618$	−10.0902	−0.405886
$619$	21.3262	0.857174	0.428587	−	0.903501i	$-0.359012\pi$
$619$	21.3262	0.857174	0.428587	+	0.903501i	$0.359012\pi$
$620$	1.18034	0.0474036
$621$	−4.79837	−0.192552
$622$	−2.61803	−0.104974
$623$	0	0
$624$	5.29180	0.211841
$625$	19.4164	0.776656
$626$	−33.2148	−1.32753
$627$	2.38197	0.0951266
$628$	4.94427	0.197298
$629$	1.70820	0.0681106
$630$	0	0
$631$	44.4853	1.77093	0.885466	−	0.464705i	$-0.153839\pi$
$631$	44.4853	1.77093	0.885466	+	0.464705i	$0.153839\pi$
$632$	3.81966	0.151938
$633$	9.29180	0.369316
$634$	−51.9787	−2.06434
$635$	−10.3262	−0.409784
$636$	−1.76393	−0.0699445
$637$	0	0
$638$	1.38197	0.0547126
$639$	−31.2705	−1.23704
$640$	−8.41641	−0.332688
$641$	−5.18034	−0.204611	−0.102306	−	0.994753i	$-0.532622\pi$
$641$	−5.18034	−0.204611	−0.102306	+	0.994753i	$0.532622\pi$
$642$	−5.23607	−0.206651
$643$	36.9230	1.45610	0.728050	−	0.685524i	$-0.240427\pi$
$643$	36.9230	1.45610	0.728050	+	0.685524i	$0.240427\pi$
$644$	0	0
$645$	0.381966	0.0150399
$646$	1.47214	0.0579204
$647$	−23.3607	−0.918403	−0.459202	−	0.888332i	$-0.651864\pi$
$647$	−23.3607	−0.918403	−0.459202	+	0.888332i	$0.651864\pi$
$648$	12.7639	0.501415
$649$	10.6180	0.416794
$650$	13.1803	0.516975
$651$	0	0
$652$	0.583592	0.0228552
$653$	25.3820	0.993273	0.496637	−	0.867959i	$-0.334568\pi$
$653$	25.3820	0.993273	0.496637	+	0.867959i	$0.334568\pi$
$654$	−0.472136	−0.0184620
$655$	−2.56231	−0.100118
$656$	−4.85410	−0.189521
$657$	20.7984	0.811422
$658$	0	0
$659$	−19.0689	−0.742818	−0.371409	−	0.928469i	$-0.621125\pi$
$659$	−19.0689	−0.742818	−0.371409	+	0.928469i	$0.621125\pi$
$660$	0.236068	0.00918893
$661$	−35.2361	−1.37052	−0.685262	−	0.728297i	$-0.740312\pi$
$661$	−35.2361	−1.37052	−0.685262	+	0.728297i	$0.740312\pi$
$662$	3.05573	0.118764
$663$	0.257354	0.00999481
$664$	−7.76393	−0.301299
$665$	0	0
$666$	−30.6525	−1.18776
$667$	−1.18034	−0.0457029
$668$	−10.1459	−0.392557
$669$	8.85410	0.342319
$670$	0.909830	0.0351498
$671$	0.527864	0.0203780
$672$	0	0
$673$	−33.8328	−1.30416	−0.652080	−	0.758151i	$-0.726103\pi$
$673$	−33.8328	−1.30416	−0.652080	+	0.758151i	$0.726103\pi$
$674$	18.6525	0.718467
$675$	−16.0344	−0.617166
$676$	−6.11146	−0.235056
$677$	−43.0902	−1.65609	−0.828045	−	0.560662i	$-0.810547\pi$
$677$	−43.0902	−1.65609	−0.828045	+	0.560662i	$0.810547\pi$
$678$	−12.4164	−0.476849
$679$	0	0
$680$	−0.326238	−0.0125107
$681$	−15.8541	−0.607531
$682$	5.00000	0.191460
$683$	35.9443	1.37537	0.687685	−	0.726009i	$-0.258627\pi$
$683$	35.9443	1.37537	0.687685	+	0.726009i	$0.258627\pi$
$684$	−6.23607	−0.238442
$685$	−5.43769	−0.207764
$686$	0	0
$687$	10.3607	0.395285
$688$	4.85410	0.185061
$689$	8.14590	0.310334
$690$	−0.854102	−0.0325151
$691$	−21.3262	−0.811288	−0.405644	−	0.914031i	$-0.632953\pi$
$691$	−21.3262	−0.811288	−0.405644	+	0.914031i	$0.632953\pi$
$692$	5.38197	0.204592
$693$	0	0
$694$	28.6525	1.08763
$695$	−7.38197	−0.280014
$696$	−1.18034	−0.0447407
$697$	−0.236068	−0.00894171
$698$	5.32624	0.201601
$699$	−5.76393	−0.218012
$700$	0	0
$701$	5.38197	0.203274	0.101637	−	0.994822i	$-0.467592\pi$
$701$	5.38197	0.203274	0.101637	+	0.994822i	$0.467592\pi$
$702$	−9.90983	−0.374022
$703$	−27.8885	−1.05184
$704$	−4.23607	−0.159653
$705$	−1.41641	−0.0533450
$706$	−55.5967	−2.09241
$707$	0	0
$708$	4.05573	0.152424
$709$	9.12461	0.342682	0.171341	−	0.985212i	$-0.445190\pi$
$709$	9.12461	0.342682	0.171341	+	0.985212i	$0.445190\pi$
$710$	−11.9443	−0.448261
$711$	−4.47214	−0.167718
$712$	−14.1459	−0.530140
$713$	−4.27051	−0.159932
$714$	0	0
$715$	−1.09017	−0.0407700
$716$	−16.0902	−0.601318
$717$	7.94427	0.296684
$718$	0.291796	0.0108897
$719$	23.1803	0.864481	0.432240	−	0.901758i	$-0.357723\pi$
$719$	23.1803	0.864481	0.432240	+	0.901758i	$0.357723\pi$
$720$	7.85410	0.292705
$721$	0	0
$722$	6.70820	0.249653
$723$	−5.70820	−0.212290
$724$	−9.23607	−0.343256
$725$	−3.94427	−0.146487
$726$	−10.0000	−0.371135
$727$	28.1591	1.04436	0.522181	−	0.852835i	$-0.325119\pi$
$727$	28.1591	1.04436	0.522181	+	0.852835i	$0.325119\pi$
$728$	0	0
$729$	−8.50658	−0.315058
$730$	7.94427	0.294031
$731$	0.236068	0.00873129
$732$	0.201626	0.00745232
$733$	19.9443	0.736658	0.368329	−	0.929695i	$-0.379930\pi$
$733$	19.9443	0.736658	0.368329	+	0.929695i	$0.379930\pi$
$734$	−10.1459	−0.374492
$735$	0	0
$736$	−4.67376	−0.172277
$737$	0.909830	0.0335140
$738$	4.23607	0.155932
$739$	−32.6738	−1.20192	−0.600962	−	0.799278i	$-0.705216\pi$
$739$	−32.6738	−1.20192	−0.600962	+	0.799278i	$0.705216\pi$
$740$	−2.76393	−0.101604
$741$	−4.20163	−0.154351
$742$	0	0
$743$	−9.68692	−0.355379	−0.177689	−	0.984087i	$-0.556862\pi$
$743$	−9.68692	−0.355379	−0.177689	+	0.984087i	$0.556862\pi$
$744$	−4.27051	−0.156564
$745$	0.652476	0.0239049
$746$	48.1246	1.76197
$747$	9.09017	0.332592
$748$	0.145898	0.00533456
$749$	0	0
$750$	−5.94427	−0.217054
$751$	−31.5410	−1.15095	−0.575474	−	0.817820i	$-0.695182\pi$
$751$	−31.5410	−1.15095	−0.575474	+	0.817820i	$0.695182\pi$
$752$	−18.0000	−0.656392
$753$	12.3262	0.449193
$754$	−2.43769	−0.0887756
$755$	−1.27051	−0.0462386
$756$	0	0
$757$	−26.6525	−0.968701	−0.484350	−	0.874874i	$-0.660944\pi$
$757$	−26.6525	−0.968701	−0.484350	+	0.874874i	$0.660944\pi$
$758$	−33.4164	−1.21374
$759$	−0.854102	−0.0310019
$760$	5.32624	0.193203
$761$	−39.7771	−1.44192	−0.720959	−	0.692978i	$-0.756298\pi$
$761$	−39.7771	−1.44192	−0.720959	+	0.692978i	$0.756298\pi$
$762$	−16.7082	−0.605274
$763$	0	0
$764$	8.36068	0.302479
$765$	0.381966	0.0138100
$766$	−1.32624	−0.0479189
$767$	−18.7295	−0.676283
$768$	−8.38197	−0.302458
$769$	23.8197	0.858959	0.429479	−	0.903077i	$-0.358697\pi$
$769$	23.8197	0.858959	0.429479	+	0.903077i	$0.358697\pi$
$770$	0	0
$771$	−9.96556	−0.358901
$772$	−5.74265	−0.206682
$773$	33.1803	1.19341	0.596707	−	0.802459i	$-0.296475\pi$
$773$	33.1803	1.19341	0.596707	+	0.802459i	$0.296475\pi$
$774$	−4.23607	−0.152262
$775$	−14.2705	−0.512612
$776$	39.2705	1.40973
$777$	0	0
$778$	−48.0344	−1.72212
$779$	3.85410	0.138088
$780$	−0.416408	−0.0149098
$781$	−11.9443	−0.427400
$782$	−0.527864	−0.0188764
$783$	2.96556	0.105980
$784$	0	0
$785$	4.94427	0.176469
$786$	−4.14590	−0.147879
$787$	4.18034	0.149013	0.0745065	−	0.997221i	$-0.476262\pi$
$787$	4.18034	0.149013	0.0745065	+	0.997221i	$0.476262\pi$
$788$	−4.56231	−0.162525
$789$	−0.437694	−0.0155823
$790$	−1.70820	−0.0607752
$791$	0	0
$792$	5.85410	0.208016
$793$	−0.931116	−0.0330649
$794$	34.7082	1.23175
$795$	−1.76393	−0.0625602
$796$	−14.4377	−0.511730
$797$	−29.8328	−1.05673	−0.528366	−	0.849017i	$-0.677195\pi$
$797$	−29.8328	−1.05673	−0.528366	+	0.849017i	$0.677195\pi$
$798$	0	0
$799$	−0.875388	−0.0309690
$800$	−15.6180	−0.552181
$801$	16.5623	0.585200
$802$	−27.1246	−0.957803
$803$	7.94427	0.280347
$804$	0.347524	0.0122562
$805$	0	0
$806$	−8.81966	−0.310659
$807$	−6.34752	−0.223443
$808$	19.0689	0.670841
$809$	−47.8115	−1.68096	−0.840482	−	0.541840i	$-0.817728\pi$
$809$	−47.8115	−1.68096	−0.840482	+	0.541840i	$0.817728\pi$
$810$	−5.70820	−0.200566
$811$	−49.0689	−1.72304	−0.861521	−	0.507722i	$-0.830488\pi$
$811$	−49.0689	−1.72304	−0.861521	+	0.507722i	$0.830488\pi$
$812$	0	0
$813$	−0.145898	−0.00511687
$814$	−11.7082	−0.410372
$815$	0.583592	0.0204423
$816$	−0.708204	−0.0247921
$817$	−3.85410	−0.134838
$818$	9.14590	0.319779
$819$	0	0
$820$	0.381966	0.0133388
$821$	50.7771	1.77213	0.886066	−	0.463559i	$-0.153428\pi$
$821$	50.7771	1.77213	0.886066	+	0.463559i	$0.153428\pi$
$822$	−8.79837	−0.306879
$823$	−6.96556	−0.242804	−0.121402	−	0.992603i	$-0.538739\pi$
$823$	−6.96556	−0.242804	−0.121402	+	0.992603i	$0.538739\pi$
$824$	−22.5623	−0.785995
$825$	−2.85410	−0.0993671
$826$	0	0
$827$	−45.2492	−1.57347	−0.786735	−	0.617291i	$-0.788230\pi$
$827$	−45.2492	−1.57347	−0.786735	+	0.617291i	$0.788230\pi$
$828$	2.23607	0.0777087
$829$	−37.3607	−1.29759	−0.648795	−	0.760963i	$-0.724727\pi$
$829$	−37.3607	−1.29759	−0.648795	+	0.760963i	$0.724727\pi$
$830$	3.47214	0.120520
$831$	14.3262	0.496972
$832$	7.47214	0.259050
$833$	0	0
$834$	−11.9443	−0.413596
$835$	−10.1459	−0.351113
$836$	−2.38197	−0.0823820
$837$	10.7295	0.370865
$838$	39.2705	1.35658
$839$	−1.23607	−0.0426738	−0.0213369	−	0.999772i	$-0.506792\pi$
$839$	−1.23607	−0.0426738	−0.0213369	+	0.999772i	$0.506792\pi$
$840$	0	0
$841$	−28.2705	−0.974845
$842$	18.6525	0.642807
$843$	6.97871	0.240360
$844$	−9.29180	−0.319837
$845$	−6.11146	−0.210240
$846$	15.7082	0.540059
$847$	0	0
$848$	−22.4164	−0.769783
$849$	0	0
$850$	−1.76393	−0.0605024
$851$	10.0000	0.342796
$852$	−4.56231	−0.156302
$853$	52.2492	1.78898	0.894490	−	0.447089i	$-0.147539\pi$
$853$	52.2492	1.78898	0.894490	+	0.447089i	$0.147539\pi$
$854$	0	0
$855$	−6.23607	−0.213269
$856$	−11.7082	−0.400178
$857$	−2.38197	−0.0813664	−0.0406832	−	0.999172i	$-0.512953\pi$
$857$	−2.38197	−0.0813664	−0.0406832	+	0.999172i	$0.512953\pi$
$858$	−1.76393	−0.0602196
$859$	19.9656	0.681216	0.340608	−	0.940205i	$-0.389367\pi$
$859$	19.9656	0.681216	0.340608	+	0.940205i	$0.389367\pi$
$860$	−0.381966	−0.0130249
$861$	0	0
$862$	0.854102	0.0290908
$863$	−29.7639	−1.01318	−0.506588	−	0.862188i	$-0.669093\pi$
$863$	−29.7639	−1.01318	−0.506588	+	0.862188i	$0.669093\pi$
$864$	11.7426	0.399493
$865$	5.38197	0.182992
$866$	−48.5967	−1.65138
$867$	10.4721	0.355652
$868$	0	0
$869$	−1.70820	−0.0579468
$870$	0.527864	0.0178963
$871$	−1.60488	−0.0543792
$872$	−1.05573	−0.0357515
$873$	−45.9787	−1.55614
$874$	8.61803	0.291509
$875$	0	0
$876$	3.03444	0.102524
$877$	8.85410	0.298982	0.149491	−	0.988763i	$-0.452237\pi$
$877$	8.85410	0.298982	0.149491	+	0.988763i	$0.452237\pi$
$878$	6.38197	0.215381
$879$	−4.79837	−0.161845
$880$	3.00000	0.101130
$881$	−29.4164	−0.991064	−0.495532	−	0.868590i	$-0.665027\pi$
$881$	−29.4164	−0.991064	−0.495532	+	0.868590i	$0.665027\pi$
$882$	0	0
$883$	3.38197	0.113812	0.0569061	−	0.998380i	$-0.481876\pi$
$883$	3.38197	0.113812	0.0569061	+	0.998380i	$0.481876\pi$
$884$	−0.257354	−0.00865576
$885$	4.05573	0.136332
$886$	−16.4164	−0.551520
$887$	−10.1115	−0.339509	−0.169755	−	0.985486i	$-0.554298\pi$
$887$	−10.1115	−0.339509	−0.169755	+	0.985486i	$0.554298\pi$
$888$	10.0000	0.335578
$889$	0	0
$890$	6.32624	0.212056
$891$	−5.70820	−0.191232
$892$	−8.85410	−0.296457
$893$	14.2918	0.478257
$894$	1.05573	0.0353088
$895$	−16.0902	−0.537835
$896$	0	0
$897$	1.50658	0.0503032
$898$	9.70820	0.323967
$899$	2.63932	0.0880263
$900$	7.47214	0.249071
$901$	−1.09017	−0.0363188
$902$	1.61803	0.0538746
$903$	0	0
$904$	−27.7639	−0.923415
$905$	−9.23607	−0.307017
$906$	−2.05573	−0.0682970
$907$	12.1591	0.403735	0.201867	−	0.979413i	$-0.435299\pi$
$907$	12.1591	0.403735	0.201867	+	0.979413i	$0.435299\pi$
$908$	15.8541	0.526137
$909$	−22.3262	−0.740515
$910$	0	0
$911$	−56.3607	−1.86731	−0.933656	−	0.358170i	$-0.883401\pi$
$911$	−56.3607	−1.86731	−0.933656	+	0.358170i	$0.883401\pi$
$912$	11.5623	0.382866
$913$	3.47214	0.114911
$914$	−16.8541	−0.557484
$915$	0.201626	0.00666555
$916$	−10.3607	−0.342326
$917$	0	0
$918$	1.32624	0.0437724
$919$	−56.4508	−1.86214	−0.931071	−	0.364838i	$-0.881124\pi$
$919$	−56.4508	−1.86214	−0.931071	+	0.364838i	$0.881124\pi$
$920$	−1.90983	−0.0629652
$921$	20.0689	0.661292
$922$	−12.3820	−0.407778
$923$	21.0689	0.693491
$924$	0	0
$925$	33.4164	1.09872
$926$	−54.3951	−1.78753
$927$	26.4164	0.867629
$928$	2.88854	0.0948211
$929$	24.5623	0.805863	0.402932	−	0.915230i	$-0.367991\pi$
$929$	24.5623	0.805863	0.402932	+	0.915230i	$0.367991\pi$
$930$	1.90983	0.0626258
$931$	0	0
$932$	5.76393	0.188804
$933$	−1.00000	−0.0327385
$934$	0.381966	0.0124983
$935$	0.145898	0.00477138
$936$	−10.3262	−0.337524
$937$	50.4164	1.64703	0.823516	−	0.567293i	$-0.192009\pi$
$937$	50.4164	1.64703	0.823516	+	0.567293i	$0.192009\pi$
$938$	0	0
$939$	−12.6869	−0.414022
$940$	1.41641	0.0461981
$941$	36.8673	1.20184	0.600919	−	0.799310i	$-0.294801\pi$
$941$	36.8673	1.20184	0.600919	+	0.799310i	$0.294801\pi$
$942$	8.00000	0.260654
$943$	−1.38197	−0.0450030
$944$	51.5410	1.67752
$945$	0	0
$946$	−1.61803	−0.0526068
$947$	12.2705	0.398738	0.199369	−	0.979924i	$-0.436111\pi$
$947$	12.2705	0.398738	0.199369	+	0.979924i	$0.436111\pi$
$948$	−0.652476	−0.0211914
$949$	−14.0132	−0.454886
$950$	28.7984	0.934343
$951$	−19.8541	−0.643813
$952$	0	0
$953$	10.0902	0.326853	0.163426	−	0.986556i	$-0.447745\pi$
$953$	10.0902	0.326853	0.163426	+	0.986556i	$0.447745\pi$
$954$	19.5623	0.633353
$955$	8.36068	0.270545
$956$	−7.94427	−0.256936
$957$	0.527864	0.0170634
$958$	−31.6525	−1.02265
$959$	0	0
$960$	−1.61803	−0.0522218
$961$	−21.4508	−0.691963
$962$	20.6525	0.665863
$963$	13.7082	0.441741
$964$	5.70820	0.183849
$965$	−5.74265	−0.184862
$966$	0	0
$967$	−5.88854	−0.189363	−0.0946814	−	0.995508i	$-0.530183\pi$
$967$	−5.88854	−0.189363	−0.0946814	+	0.995508i	$0.530183\pi$
$968$	−22.3607	−0.718699
$969$	0.562306	0.0180639
$970$	−17.5623	−0.563892
$971$	−4.59675	−0.147517	−0.0737583	−	0.997276i	$-0.523499\pi$
$971$	−4.59675	−0.147517	−0.0737583	+	0.997276i	$0.523499\pi$
$972$	−8.61803	−0.276424
$973$	0	0
$974$	24.6525	0.789916
$975$	5.03444	0.161231
$976$	2.56231	0.0820174
$977$	51.7984	1.65718	0.828588	−	0.559858i	$-0.189144\pi$
$977$	51.7984	1.65718	0.828588	+	0.559858i	$0.189144\pi$
$978$	0.944272	0.0301945
$979$	6.32624	0.202187
$980$	0	0
$981$	1.23607	0.0394646
$982$	19.8541	0.633570
$983$	−34.5279	−1.10127	−0.550634	−	0.834747i	$-0.685614\pi$
$983$	−34.5279	−1.10127	−0.550634	+	0.834747i	$0.685614\pi$
$984$	−1.38197	−0.0440555
$985$	−4.56231	−0.145367
$986$	0.326238	0.0103895
$987$	0	0
$988$	4.20163	0.133672
$989$	1.38197	0.0439440
$990$	−2.61803	−0.0832066
$991$	16.8197	0.534294	0.267147	−	0.963656i	$-0.413919\pi$
$991$	16.8197	0.534294	0.267147	+	0.963656i	$0.413919\pi$
$992$	10.4508	0.331815
$993$	1.16718	0.0370395
$994$	0	0
$995$	−14.4377	−0.457706
$996$	1.32624	0.0420235
$997$	55.3951	1.75438	0.877191	−	0.480142i	$-0.159415\pi$
$997$	55.3951	1.75438	0.877191	+	0.480142i	$0.159415\pi$
$998$	10.7639	0.340726
$999$	−25.1246	−0.794908

Twists

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

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

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q-1.61803 q^{2} -0.618034 q^{3} +0.618034 q^{4} +0.618034 q^{5} +1.00000 q^{6} +2.23607 q^{8} -2.61803 q^{9} +O(q^{10})\)	\(q-1.61803 q^{2} -0.618034 q^{3} +0.618034 q^{4} +0.618034 q^{5} +1.00000 q^{6} +2.23607 q^{8} -2.61803 q^{9} -1.00000 q^{10} -1.00000 q^{11} -0.381966 q^{12} +1.76393 q^{13} -0.381966 q^{15} -4.85410 q^{16} -0.236068 q^{17} +4.23607 q^{18} +3.85410 q^{19} +0.381966 q^{20} +1.61803 q^{22} -1.38197 q^{23} -1.38197 q^{24} -4.61803 q^{25} -2.85410 q^{26} +3.47214 q^{27} +0.854102 q^{29} +0.618034 q^{30} +3.09017 q^{31} +3.38197 q^{32} +0.618034 q^{33} +0.381966 q^{34} -1.61803 q^{36} -7.23607 q^{37} -6.23607 q^{38} -1.09017 q^{39} +1.38197 q^{40} +1.00000 q^{41} -1.00000 q^{43} -0.618034 q^{44} -1.61803 q^{45} +2.23607 q^{46} +3.70820 q^{47} +3.00000 q^{48} +7.47214 q^{50} +0.145898 q^{51} +1.09017 q^{52} +4.61803 q^{53} -5.61803 q^{54} -0.618034 q^{55} -2.38197 q^{57} -1.38197 q^{58} -10.6180 q^{59} -0.236068 q^{60} -0.527864 q^{61} -5.00000 q^{62} +4.23607 q^{64} +1.09017 q^{65} -1.00000 q^{66} -0.909830 q^{67} -0.145898 q^{68} +0.854102 q^{69} +11.9443 q^{71} -5.85410 q^{72} -7.94427 q^{73} +11.7082 q^{74} +2.85410 q^{75} +2.38197 q^{76} +1.76393 q^{78} +1.70820 q^{79} -3.00000 q^{80} +5.70820 q^{81} -1.61803 q^{82} -3.47214 q^{83} -0.145898 q^{85} +1.61803 q^{86} -0.527864 q^{87} -2.23607 q^{88} -6.32624 q^{89} +2.61803 q^{90} -0.854102 q^{92} -1.90983 q^{93} -6.00000 q^{94} +2.38197 q^{95} -2.09017 q^{96} +17.5623 q^{97} +2.61803 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - 3 q^{9}+O(q^{10}) \) 2 * q - q^2 + q^3 - q^4 - q^5 + 2 * q^6 - 3 * q^9	\( 2 q - q^{2} + q^{3} - q^{4} - q^{5} + 2 q^{6} - 3 q^{9} - 2 q^{10} - 2 q^{11} - 3 q^{12} + 8 q^{13} - 3 q^{15} - 3 q^{16} + 4 q^{17} + 4 q^{18} + q^{19} + 3 q^{20} + q^{22} - 5 q^{23} - 5 q^{24} - 7 q^{25} + q^{26} - 2 q^{27} - 5 q^{29} - q^{30} - 5 q^{31} + 9 q^{32} - q^{33} + 3 q^{34} - q^{36} - 10 q^{37} - 8 q^{38} + 9 q^{39} + 5 q^{40} + 2 q^{41} - 2 q^{43} + q^{44} - q^{45} - 6 q^{47} + 6 q^{48} + 6 q^{50} + 7 q^{51} - 9 q^{52} + 7 q^{53} - 9 q^{54} + q^{55} - 7 q^{57} - 5 q^{58} - 19 q^{59} + 4 q^{60} - 10 q^{61} - 10 q^{62} + 4 q^{64} - 9 q^{65} - 2 q^{66} - 13 q^{67} - 7 q^{68} - 5 q^{69} + 6 q^{71} - 5 q^{72} + 2 q^{73} + 10 q^{74} - q^{75} + 7 q^{76} + 8 q^{78} - 10 q^{79} - 6 q^{80} - 2 q^{81} - q^{82} + 2 q^{83} - 7 q^{85} + q^{86} - 10 q^{87} + 3 q^{89} + 3 q^{90} + 5 q^{92} - 15 q^{93} - 12 q^{94} + 7 q^{95} + 7 q^{96} + 15 q^{97} + 3 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 - q^5 + 2 * q^6 - 3 * q^9 - 2 * q^10 - 2 * q^11 - 3 * q^12 + 8 * q^13 - 3 * q^15 - 3 * q^16 + 4 * q^17 + 4 * q^18 + q^19 + 3 * q^20 + q^22 - 5 * q^23 - 5 * q^24 - 7 * q^25 + q^26 - 2 * q^27 - 5 * q^29 - q^30 - 5 * q^31 + 9 * q^32 - q^33 + 3 * q^34 - q^36 - 10 * q^37 - 8 * q^38 + 9 * q^39 + 5 * q^40 + 2 * q^41 - 2 * q^43 + q^44 - q^45 - 6 * q^47 + 6 * q^48 + 6 * q^50 + 7 * q^51 - 9 * q^52 + 7 * q^53 - 9 * q^54 + q^55 - 7 * q^57 - 5 * q^58 - 19 * q^59 + 4 * q^60 - 10 * q^61 - 10 * q^62 + 4 * q^64 - 9 * q^65 - 2 * q^66 - 13 * q^67 - 7 * q^68 - 5 * q^69 + 6 * q^71 - 5 * q^72 + 2 * q^73 + 10 * q^74 - q^75 + 7 * q^76 + 8 * q^78 - 10 * q^79 - 6 * q^80 - 2 * q^81 - q^82 + 2 * q^83 - 7 * q^85 + q^86 - 10 * q^87 + 3 * q^89 + 3 * q^90 + 5 * q^92 - 15 * q^93 - 12 * q^94 + 7 * q^95 + 7 * q^96 + 15 * q^97 + 3 * q^99

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