LMFDB - Embedded newform 3626.2.a.s.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3626,2,Mod(1,3626)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3626, 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("3626.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3626 = 2 \cdot 7^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3626.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:	$28.9537557729$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	3626.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} +2.85410 q^{5} -0.618034 q^{6} +1.00000 q^{8} -2.61803 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} +2.85410 q^{5} -0.618034 q^{6} +1.00000 q^{8} -2.61803 q^{9} +2.85410 q^{10} -3.61803 q^{11} -0.618034 q^{12} -3.85410 q^{13} -1.76393 q^{15} +1.00000 q^{16} -4.47214 q^{17} -2.61803 q^{18} +4.47214 q^{19} +2.85410 q^{20} -3.61803 q^{22} -3.85410 q^{23} -0.618034 q^{24} +3.14590 q^{25} -3.85410 q^{26} +3.47214 q^{27} +6.32624 q^{29} -1.76393 q^{30} -9.61803 q^{31} +1.00000 q^{32} +2.23607 q^{33} -4.47214 q^{34} -2.61803 q^{36} -1.00000 q^{37} +4.47214 q^{38} +2.38197 q^{39} +2.85410 q^{40} -7.38197 q^{41} -0.763932 q^{43} -3.61803 q^{44} -7.47214 q^{45} -3.85410 q^{46} -3.23607 q^{47} -0.618034 q^{48} +3.14590 q^{50} +2.76393 q^{51} -3.85410 q^{52} -8.47214 q^{53} +3.47214 q^{54} -10.3262 q^{55} -2.76393 q^{57} +6.32624 q^{58} +9.23607 q^{59} -1.76393 q^{60} -8.38197 q^{61} -9.61803 q^{62} +1.00000 q^{64} -11.0000 q^{65} +2.23607 q^{66} -10.0902 q^{67} -4.47214 q^{68} +2.38197 q^{69} -14.9443 q^{71} -2.61803 q^{72} +4.09017 q^{73} -1.00000 q^{74} -1.94427 q^{75} +4.47214 q^{76} +2.38197 q^{78} +11.5623 q^{79} +2.85410 q^{80} +5.70820 q^{81} -7.38197 q^{82} +5.52786 q^{83} -12.7639 q^{85} -0.763932 q^{86} -3.90983 q^{87} -3.61803 q^{88} +10.4721 q^{89} -7.47214 q^{90} -3.85410 q^{92} +5.94427 q^{93} -3.23607 q^{94} +12.7639 q^{95} -0.618034 q^{96} -8.47214 q^{97} +9.47214 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + q^{3} + 2 q^{4} - q^{5} + q^{6} + 2 q^{8} - 3 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + q^3 + 2 * q^4 - q^5 + q^6 + 2 * q^8 - 3 * q^9	$ 2 q + 2 q^{2} + q^{3} + 2 q^{4} - q^{5} + q^{6} + 2 q^{8} - 3 q^{9} - q^{10} - 5 q^{11} + q^{12} - q^{13} - 8 q^{15} + 2 q^{16} - 3 q^{18} - q^{20} - 5 q^{22} - q^{23} + q^{24} + 13 q^{25} - q^{26} - 2 q^{27} - 3 q^{29} - 8 q^{30} - 17 q^{31} + 2 q^{32} - 3 q^{36} - 2 q^{37} + 7 q^{39} - q^{40} - 17 q^{41} - 6 q^{43} - 5 q^{44} - 6 q^{45} - q^{46} - 2 q^{47} + q^{48} + 13 q^{50} + 10 q^{51} - q^{52} - 8 q^{53} - 2 q^{54} - 5 q^{55} - 10 q^{57} - 3 q^{58} + 14 q^{59} - 8 q^{60} - 19 q^{61} - 17 q^{62} + 2 q^{64} - 22 q^{65} - 9 q^{67} + 7 q^{69} - 12 q^{71} - 3 q^{72} - 3 q^{73} - 2 q^{74} + 14 q^{75} + 7 q^{78} + 3 q^{79} - q^{80} - 2 q^{81} - 17 q^{82} + 20 q^{83} - 30 q^{85} - 6 q^{86} - 19 q^{87} - 5 q^{88} + 12 q^{89} - 6 q^{90} - q^{92} - 6 q^{93} - 2 q^{94} + 30 q^{95} + q^{96} - 8 q^{97} + 10 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + q^3 + 2 * q^4 - q^5 + q^6 + 2 * q^8 - 3 * q^9 - q^10 - 5 * q^11 + q^12 - q^13 - 8 * q^15 + 2 * q^16 - 3 * q^18 - q^20 - 5 * q^22 - q^23 + q^24 + 13 * q^25 - q^26 - 2 * q^27 - 3 * q^29 - 8 * q^30 - 17 * q^31 + 2 * q^32 - 3 * q^36 - 2 * q^37 + 7 * q^39 - q^40 - 17 * q^41 - 6 * q^43 - 5 * q^44 - 6 * q^45 - q^46 - 2 * q^47 + q^48 + 13 * q^50 + 10 * q^51 - q^52 - 8 * q^53 - 2 * q^54 - 5 * q^55 - 10 * q^57 - 3 * q^58 + 14 * q^59 - 8 * q^60 - 19 * q^61 - 17 * q^62 + 2 * q^64 - 22 * q^65 - 9 * q^67 + 7 * q^69 - 12 * q^71 - 3 * q^72 - 3 * q^73 - 2 * q^74 + 14 * q^75 + 7 * q^78 + 3 * q^79 - q^80 - 2 * q^81 - 17 * q^82 + 20 * q^83 - 30 * q^85 - 6 * q^86 - 19 * q^87 - 5 * q^88 + 12 * q^89 - 6 * q^90 - q^92 - 6 * q^93 - 2 * q^94 + 30 * q^95 + q^96 - 8 * q^97 + 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.618034	−0.356822	−0.178411	−	0.983956i	$-0.557096\pi$
$3$	−0.618034	−0.356822	−0.178411	+	0.983956i	$0.557096\pi$
$4$	1.00000	0.500000
$5$	2.85410	1.27639	0.638197	−	0.769873i	$-0.279681\pi$
$5$	2.85410	1.27639	0.638197	+	0.769873i	$0.279681\pi$
$6$	−0.618034	−0.252311
$7$	0	0
$7$	0	0
$8$	1.00000	0.353553
$9$	−2.61803	−0.872678
$10$	2.85410	0.902546
$11$	−3.61803	−1.09088	−0.545439	−	0.838150i	$-0.683637\pi$
$11$	−3.61803	−1.09088	−0.545439	+	0.838150i	$0.683637\pi$
$12$	−0.618034	−0.178411
$13$	−3.85410	−1.06894	−0.534468	−	0.845189i	$-0.679488\pi$
$13$	−3.85410	−1.06894	−0.534468	+	0.845189i	$0.679488\pi$
$14$	0	0
$15$	−1.76393	−0.455445
$16$	1.00000	0.250000
$17$	−4.47214	−1.08465	−0.542326	−	0.840168i	$-0.682456\pi$
$17$	−4.47214	−1.08465	−0.542326	+	0.840168i	$0.682456\pi$
$18$	−2.61803	−0.617077
$19$	4.47214	1.02598	0.512989	−	0.858395i	$-0.328538\pi$
$19$	4.47214	1.02598	0.512989	+	0.858395i	$0.328538\pi$
$20$	2.85410	0.638197
$21$	0	0
$22$	−3.61803	−0.771367
$23$	−3.85410	−0.803636	−0.401818	−	0.915720i	$-0.631622\pi$
$23$	−3.85410	−0.803636	−0.401818	+	0.915720i	$0.631622\pi$
$24$	−0.618034	−0.126156
$25$	3.14590	0.629180
$26$	−3.85410	−0.755852
$27$	3.47214	0.668213
$28$	0	0
$29$	6.32624	1.17475	0.587376	−	0.809314i	$-0.300161\pi$
$29$	6.32624	1.17475	0.587376	+	0.809314i	$0.300161\pi$
$30$	−1.76393	−0.322048
$31$	−9.61803	−1.72745	−0.863725	−	0.503964i	$-0.831875\pi$
$31$	−9.61803	−1.72745	−0.863725	+	0.503964i	$0.831875\pi$
$32$	1.00000	0.176777
$33$	2.23607	0.389249
$34$	−4.47214	−0.766965
$35$	0	0
$36$	−2.61803	−0.436339
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	4.47214	0.725476
$39$	2.38197	0.381420
$40$	2.85410	0.451273
$41$	−7.38197	−1.15287	−0.576435	−	0.817143i	$-0.695556\pi$
$41$	−7.38197	−1.15287	−0.576435	+	0.817143i	$0.695556\pi$
$42$	0	0
$43$	−0.763932	−0.116499	−0.0582493	−	0.998302i	$-0.518552\pi$
$43$	−0.763932	−0.116499	−0.0582493	+	0.998302i	$0.518552\pi$
$44$	−3.61803	−0.545439
$45$	−7.47214	−1.11388
$46$	−3.85410	−0.568256
$47$	−3.23607	−0.472029	−0.236015	−	0.971750i	$-0.575841\pi$
$47$	−3.23607	−0.472029	−0.236015	+	0.971750i	$0.575841\pi$
$48$	−0.618034	−0.0892055
$49$	0	0
$50$	3.14590	0.444897
$51$	2.76393	0.387028
$52$	−3.85410	−0.534468
$53$	−8.47214	−1.16374	−0.581869	−	0.813283i	$-0.697678\pi$
$53$	−8.47214	−1.16374	−0.581869	+	0.813283i	$0.697678\pi$
$54$	3.47214	0.472498
$55$	−10.3262	−1.39239
$56$	0	0
$57$	−2.76393	−0.366092
$58$	6.32624	0.830676
$59$	9.23607	1.20243	0.601217	−	0.799086i	$-0.294683\pi$
$59$	9.23607	1.20243	0.601217	+	0.799086i	$0.294683\pi$
$60$	−1.76393	−0.227723
$61$	−8.38197	−1.07320	−0.536600	−	0.843836i	$-0.680292\pi$
$61$	−8.38197	−1.07320	−0.536600	+	0.843836i	$0.680292\pi$
$62$	−9.61803	−1.22149
$63$	0	0
$64$	1.00000	0.125000
$65$	−11.0000	−1.36438
$66$	2.23607	0.275241
$67$	−10.0902	−1.23271	−0.616355	−	0.787468i	$-0.711391\pi$
$67$	−10.0902	−1.23271	−0.616355	+	0.787468i	$0.711391\pi$
$68$	−4.47214	−0.542326
$69$	2.38197	0.286755
$70$	0	0
$71$	−14.9443	−1.77356	−0.886779	−	0.462193i	$-0.847063\pi$
$71$	−14.9443	−1.77356	−0.886779	+	0.462193i	$0.847063\pi$
$72$	−2.61803	−0.308538
$73$	4.09017	0.478718	0.239359	−	0.970931i	$-0.423063\pi$
$73$	4.09017	0.478718	0.239359	+	0.970931i	$0.423063\pi$
$74$	−1.00000	−0.116248
$75$	−1.94427	−0.224505
$76$	4.47214	0.512989
$77$	0	0
$78$	2.38197	0.269705
$79$	11.5623	1.30086	0.650431	−	0.759566i	$-0.274589\pi$
$79$	11.5623	1.30086	0.650431	+	0.759566i	$0.274589\pi$
$80$	2.85410	0.319098
$81$	5.70820	0.634245
$82$	−7.38197	−0.815202
$83$	5.52786	0.606762	0.303381	−	0.952869i	$-0.401885\pi$
$83$	5.52786	0.606762	0.303381	+	0.952869i	$0.401885\pi$
$84$	0	0
$85$	−12.7639	−1.38444
$86$	−0.763932	−0.0823769
$87$	−3.90983	−0.419178
$88$	−3.61803	−0.385684
$89$	10.4721	1.11004	0.555022	−	0.831836i	$-0.312710\pi$
$89$	10.4721	1.11004	0.555022	+	0.831836i	$0.312710\pi$
$90$	−7.47214	−0.787632
$91$	0	0
$92$	−3.85410	−0.401818
$93$	5.94427	0.616392
$94$	−3.23607	−0.333775
$95$	12.7639	1.30955
$96$	−0.618034	−0.0630778
$97$	−8.47214	−0.860215	−0.430108	−	0.902778i	$-0.641524\pi$
$97$	−8.47214	−0.860215	−0.430108	+	0.902778i	$0.641524\pi$
$98$	0	0
$99$	9.47214	0.951985
$100$	3.14590	0.314590
$101$	−12.4721	−1.24102	−0.620512	−	0.784197i	$-0.713075\pi$
$101$	−12.4721	−1.24102	−0.620512	+	0.784197i	$0.713075\pi$
$102$	2.76393	0.273670
$103$	16.2705	1.60318	0.801590	−	0.597873i	$-0.203987\pi$
$103$	16.2705	1.60318	0.801590	+	0.597873i	$0.203987\pi$
$104$	−3.85410	−0.377926
$105$	0	0
$106$	−8.47214	−0.822887
$107$	8.32624	0.804928	0.402464	−	0.915436i	$-0.368154\pi$
$107$	8.32624	0.804928	0.402464	+	0.915436i	$0.368154\pi$
$108$	3.47214	0.334106
$109$	−14.9443	−1.43140	−0.715701	−	0.698407i	$-0.753893\pi$
$109$	−14.9443	−1.43140	−0.715701	+	0.698407i	$0.753893\pi$
$110$	−10.3262	−0.984568
$111$	0.618034	0.0586612
$112$	0	0
$113$	10.9443	1.02955	0.514775	−	0.857325i	$-0.327875\pi$
$113$	10.9443	1.02955	0.514775	+	0.857325i	$0.327875\pi$
$114$	−2.76393	−0.258866
$115$	−11.0000	−1.02576
$116$	6.32624	0.587376
$117$	10.0902	0.932837
$118$	9.23607	0.850249
$119$	0	0
$120$	−1.76393	−0.161024
$121$	2.09017	0.190015
$122$	−8.38197	−0.758868
$123$	4.56231	0.411369
$124$	−9.61803	−0.863725
$125$	−5.29180	−0.473313
$126$	0	0
$127$	0.472136	0.0418953	0.0209476	−	0.999781i	$-0.493332\pi$
$127$	0.472136	0.0418953	0.0209476	+	0.999781i	$0.493332\pi$
$128$	1.00000	0.0883883
$129$	0.472136	0.0415693
$130$	−11.0000	−0.964764
$131$	−8.65248	−0.755970	−0.377985	−	0.925812i	$-0.623383\pi$
$131$	−8.65248	−0.755970	−0.377985	+	0.925812i	$0.623383\pi$
$132$	2.23607	0.194625
$133$	0	0
$134$	−10.0902	−0.871658
$135$	9.90983	0.852902
$136$	−4.47214	−0.383482
$137$	19.3262	1.65115	0.825576	−	0.564291i	$-0.190850\pi$
$137$	19.3262	1.65115	0.825576	+	0.564291i	$0.190850\pi$
$138$	2.38197	0.202766
$139$	1.85410	0.157263	0.0786314	−	0.996904i	$-0.474945\pi$
$139$	1.85410	0.157263	0.0786314	+	0.996904i	$0.474945\pi$
$140$	0	0
$141$	2.00000	0.168430
$142$	−14.9443	−1.25410
$143$	13.9443	1.16608
$144$	−2.61803	−0.218169
$145$	18.0557	1.49945
$146$	4.09017	0.338505
$147$	0	0
$148$	−1.00000	−0.0821995
$149$	−6.18034	−0.506313	−0.253157	−	0.967425i	$-0.581469\pi$
$149$	−6.18034	−0.506313	−0.253157	+	0.967425i	$0.581469\pi$
$150$	−1.94427	−0.158749
$151$	17.7082	1.44107	0.720537	−	0.693417i	$-0.243896\pi$
$151$	17.7082	1.44107	0.720537	+	0.693417i	$0.243896\pi$
$152$	4.47214	0.362738
$153$	11.7082	0.946552
$154$	0	0
$155$	−27.4508	−2.20491
$156$	2.38197	0.190710
$157$	7.52786	0.600789	0.300394	−	0.953815i	$-0.402882\pi$
$157$	7.52786	0.600789	0.300394	+	0.953815i	$0.402882\pi$
$158$	11.5623	0.919848
$159$	5.23607	0.415247
$160$	2.85410	0.225637
$161$	0	0
$162$	5.70820	0.448479
$163$	−12.4721	−0.976893	−0.488447	−	0.872594i	$-0.662436\pi$
$163$	−12.4721	−0.976893	−0.488447	+	0.872594i	$0.662436\pi$
$164$	−7.38197	−0.576435
$165$	6.38197	0.496835
$166$	5.52786	0.429045
$167$	−7.14590	−0.552966	−0.276483	−	0.961019i	$-0.589169\pi$
$167$	−7.14590	−0.552966	−0.276483	+	0.961019i	$0.589169\pi$
$168$	0	0
$169$	1.85410	0.142623
$170$	−12.7639	−0.978949
$171$	−11.7082	−0.895349
$172$	−0.763932	−0.0582493
$173$	−8.47214	−0.644125	−0.322062	−	0.946718i	$-0.604376\pi$
$173$	−8.47214	−0.644125	−0.322062	+	0.946718i	$0.604376\pi$
$174$	−3.90983	−0.296403
$175$	0	0
$176$	−3.61803	−0.272720
$177$	−5.70820	−0.429055
$178$	10.4721	0.784920
$179$	18.6525	1.39415	0.697076	−	0.716997i	$-0.254484\pi$
$179$	18.6525	1.39415	0.697076	+	0.716997i	$0.254484\pi$
$180$	−7.47214	−0.556940
$181$	−5.52786	−0.410883	−0.205441	−	0.978669i	$-0.565863\pi$
$181$	−5.52786	−0.410883	−0.205441	+	0.978669i	$0.565863\pi$
$182$	0	0
$183$	5.18034	0.382942
$184$	−3.85410	−0.284128
$185$	−2.85410	−0.209838
$186$	5.94427	0.435855
$187$	16.1803	1.18322
$188$	−3.23607	−0.236015
$189$	0	0
$190$	12.7639	0.925993
$191$	4.09017	0.295954	0.147977	−	0.988991i	$-0.452724\pi$
$191$	4.09017	0.295954	0.147977	+	0.988991i	$0.452724\pi$
$192$	−0.618034	−0.0446028
$193$	4.00000	0.287926	0.143963	−	0.989583i	$-0.454015\pi$
$193$	4.00000	0.287926	0.143963	+	0.989583i	$0.454015\pi$
$194$	−8.47214	−0.608264
$195$	6.79837	0.486842
$196$	0	0
$197$	−16.4721	−1.17359	−0.586796	−	0.809735i	$-0.699611\pi$
$197$	−16.4721	−1.17359	−0.586796	+	0.809735i	$0.699611\pi$
$198$	9.47214	0.673155
$199$	−20.9443	−1.48470	−0.742350	−	0.670012i	$-0.766289\pi$
$199$	−20.9443	−1.48470	−0.742350	+	0.670012i	$0.766289\pi$
$200$	3.14590	0.222449
$201$	6.23607	0.439858
$202$	−12.4721	−0.877536
$203$	0	0
$204$	2.76393	0.193514
$205$	−21.0689	−1.47151
$206$	16.2705	1.13362
$207$	10.0902	0.701315
$208$	−3.85410	−0.267234
$209$	−16.1803	−1.11922
$210$	0	0
$211$	−22.2705	−1.53317	−0.766583	−	0.642146i	$-0.778044\pi$
$211$	−22.2705	−1.53317	−0.766583	+	0.642146i	$0.778044\pi$
$212$	−8.47214	−0.581869
$213$	9.23607	0.632845
$214$	8.32624	0.569170
$215$	−2.18034	−0.148698
$216$	3.47214	0.236249
$217$	0	0
$218$	−14.9443	−1.01215
$219$	−2.52786	−0.170817
$220$	−10.3262	−0.696195
$221$	17.2361	1.15942
$222$	0.618034	0.0414797
$223$	8.18034	0.547796	0.273898	−	0.961759i	$-0.411687\pi$
$223$	8.18034	0.547796	0.273898	+	0.961759i	$0.411687\pi$
$224$	0	0
$225$	−8.23607	−0.549071
$226$	10.9443	0.728002
$227$	17.7082	1.17533	0.587667	−	0.809103i	$-0.300046\pi$
$227$	17.7082	1.17533	0.587667	+	0.809103i	$0.300046\pi$
$228$	−2.76393	−0.183046
$229$	−17.1246	−1.13163	−0.565813	−	0.824534i	$-0.691438\pi$
$229$	−17.1246	−1.13163	−0.565813	+	0.824534i	$0.691438\pi$
$230$	−11.0000	−0.725319
$231$	0	0
$232$	6.32624	0.415338
$233$	13.5623	0.888496	0.444248	−	0.895904i	$-0.353471\pi$
$233$	13.5623	0.888496	0.444248	+	0.895904i	$0.353471\pi$
$234$	10.0902	0.659615
$235$	−9.23607	−0.602495
$236$	9.23607	0.601217
$237$	−7.14590	−0.464176
$238$	0	0
$239$	3.14590	0.203491	0.101746	−	0.994810i	$-0.467557\pi$
$239$	3.14590	0.203491	0.101746	+	0.994810i	$0.467557\pi$
$240$	−1.76393	−0.113861
$241$	10.4721	0.674570	0.337285	−	0.941403i	$-0.390491\pi$
$241$	10.4721	0.674570	0.337285	+	0.941403i	$0.390491\pi$
$242$	2.09017	0.134361
$243$	−13.9443	−0.894525
$244$	−8.38197	−0.536600
$245$	0	0
$246$	4.56231	0.290882
$247$	−17.2361	−1.09670
$248$	−9.61803	−0.610746
$249$	−3.41641	−0.216506
$250$	−5.29180	−0.334683
$251$	3.05573	0.192876	0.0964379	−	0.995339i	$-0.469255\pi$
$251$	3.05573	0.192876	0.0964379	+	0.995339i	$0.469255\pi$
$252$	0	0
$253$	13.9443	0.876669
$254$	0.472136	0.0296244
$255$	7.88854	0.494000
$256$	1.00000	0.0625000
$257$	18.9443	1.18171	0.590856	−	0.806777i	$-0.298790\pi$
$257$	18.9443	1.18171	0.590856	+	0.806777i	$0.298790\pi$
$258$	0.472136	0.0293939
$259$	0	0
$260$	−11.0000	−0.682191
$261$	−16.5623	−1.02518
$262$	−8.65248	−0.534552
$263$	−8.76393	−0.540407	−0.270204	−	0.962803i	$-0.587091\pi$
$263$	−8.76393	−0.540407	−0.270204	+	0.962803i	$0.587091\pi$
$264$	2.23607	0.137620
$265$	−24.1803	−1.48539
$266$	0	0
$267$	−6.47214	−0.396088
$268$	−10.0902	−0.616355
$269$	−4.00000	−0.243884	−0.121942	−	0.992537i	$-0.538912\pi$
$269$	−4.00000	−0.243884	−0.121942	+	0.992537i	$0.538912\pi$
$270$	9.90983	0.603093
$271$	4.94427	0.300343	0.150172	−	0.988660i	$-0.452017\pi$
$271$	4.94427	0.300343	0.150172	+	0.988660i	$0.452017\pi$
$272$	−4.47214	−0.271163
$273$	0	0
$274$	19.3262	1.16754
$275$	−11.3820	−0.686358
$276$	2.38197	0.143378
$277$	−7.79837	−0.468559	−0.234279	−	0.972169i	$-0.575273\pi$
$277$	−7.79837	−0.468559	−0.234279	+	0.972169i	$0.575273\pi$
$278$	1.85410	0.111202
$279$	25.1803	1.50751
$280$	0	0
$281$	−5.88854	−0.351281	−0.175641	−	0.984454i	$-0.556200\pi$
$281$	−5.88854	−0.351281	−0.175641	+	0.984454i	$0.556200\pi$
$282$	2.00000	0.119098
$283$	−11.2361	−0.667915	−0.333957	−	0.942588i	$-0.608384\pi$
$283$	−11.2361	−0.667915	−0.333957	+	0.942588i	$0.608384\pi$
$284$	−14.9443	−0.886779
$285$	−7.88854	−0.467277
$286$	13.9443	0.824542
$287$	0	0
$288$	−2.61803	−0.154269
$289$	3.00000	0.176471
$290$	18.0557	1.06027
$291$	5.23607	0.306944
$292$	4.09017	0.239359
$293$	−18.6525	−1.08969	−0.544845	−	0.838537i	$-0.683411\pi$
$293$	−18.6525	−1.08969	−0.544845	+	0.838537i	$0.683411\pi$
$294$	0	0
$295$	26.3607	1.53478
$296$	−1.00000	−0.0581238
$297$	−12.5623	−0.728939
$298$	−6.18034	−0.358017
$299$	14.8541	0.859035
$300$	−1.94427	−0.112253
$301$	0	0
$302$	17.7082	1.01899
$303$	7.70820	0.442825
$304$	4.47214	0.256495
$305$	−23.9230	−1.36983
$306$	11.7082	0.669313
$307$	6.14590	0.350765	0.175382	−	0.984500i	$-0.443884\pi$
$307$	6.14590	0.350765	0.175382	+	0.984500i	$0.443884\pi$
$308$	0	0
$309$	−10.0557	−0.572050
$310$	−27.4508	−1.55910
$311$	−2.03444	−0.115363	−0.0576813	−	0.998335i	$-0.518371\pi$
$311$	−2.03444	−0.115363	−0.0576813	+	0.998335i	$0.518371\pi$
$312$	2.38197	0.134852
$313$	−5.81966	−0.328947	−0.164473	−	0.986382i	$-0.552592\pi$
$313$	−5.81966	−0.328947	−0.164473	+	0.986382i	$0.552592\pi$
$314$	7.52786	0.424822
$315$	0	0
$316$	11.5623	0.650431
$317$	3.05573	0.171627	0.0858134	−	0.996311i	$-0.472651\pi$
$317$	3.05573	0.171627	0.0858134	+	0.996311i	$0.472651\pi$
$318$	5.23607	0.293624
$319$	−22.8885	−1.28151
$320$	2.85410	0.159549
$321$	−5.14590	−0.287216
$322$	0	0
$323$	−20.0000	−1.11283
$324$	5.70820	0.317122
$325$	−12.1246	−0.672552
$326$	−12.4721	−0.690768
$327$	9.23607	0.510756
$328$	−7.38197	−0.407601
$329$	0	0
$330$	6.38197	0.351316
$331$	28.0000	1.53902	0.769510	−	0.638635i	$-0.220501\pi$
$331$	28.0000	1.53902	0.769510	+	0.638635i	$0.220501\pi$
$332$	5.52786	0.303381
$333$	2.61803	0.143467
$334$	−7.14590	−0.391006
$335$	−28.7984	−1.57342
$336$	0	0
$337$	−17.0344	−0.927925	−0.463963	−	0.885855i	$-0.653573\pi$
$337$	−17.0344	−0.927925	−0.463963	+	0.885855i	$0.653573\pi$
$338$	1.85410	0.100850
$339$	−6.76393	−0.367366
$340$	−12.7639	−0.692221
$341$	34.7984	1.88444
$342$	−11.7082	−0.633107
$343$	0	0
$344$	−0.763932	−0.0411885
$345$	6.79837	0.366012
$346$	−8.47214	−0.455465
$347$	12.7639	0.685204	0.342602	−	0.939481i	$-0.388692\pi$
$347$	12.7639	0.685204	0.342602	+	0.939481i	$0.388692\pi$
$348$	−3.90983	−0.209589
$349$	−12.1803	−0.651999	−0.325999	−	0.945370i	$-0.605701\pi$
$349$	−12.1803	−0.651999	−0.325999	+	0.945370i	$0.605701\pi$
$350$	0	0
$351$	−13.3820	−0.714277
$352$	−3.61803	−0.192842
$353$	−29.7082	−1.58121	−0.790604	−	0.612328i	$-0.790233\pi$
$353$	−29.7082	−1.58121	−0.790604	+	0.612328i	$0.790233\pi$
$354$	−5.70820	−0.303388
$355$	−42.6525	−2.26376
$356$	10.4721	0.555022
$357$	0	0
$358$	18.6525	0.985814
$359$	4.47214	0.236030	0.118015	−	0.993012i	$-0.462347\pi$
$359$	4.47214	0.236030	0.118015	+	0.993012i	$0.462347\pi$
$360$	−7.47214	−0.393816
$361$	1.00000	0.0526316
$362$	−5.52786	−0.290538
$363$	−1.29180	−0.0678017
$364$	0	0
$365$	11.6738	0.611033
$366$	5.18034	0.270781
$367$	27.1246	1.41589	0.707947	−	0.706266i	$-0.249622\pi$
$367$	27.1246	1.41589	0.707947	+	0.706266i	$0.249622\pi$
$368$	−3.85410	−0.200909
$369$	19.3262	1.00608
$370$	−2.85410	−0.148378
$371$	0	0
$372$	5.94427	0.308196
$373$	14.2918	0.740001	0.370001	−	0.929032i	$-0.379357\pi$
$373$	14.2918	0.740001	0.370001	+	0.929032i	$0.379357\pi$
$374$	16.1803	0.836665
$375$	3.27051	0.168888
$376$	−3.23607	−0.166887
$377$	−24.3820	−1.25574
$378$	0	0
$379$	16.9098	0.868600	0.434300	−	0.900768i	$-0.356996\pi$
$379$	16.9098	0.868600	0.434300	+	0.900768i	$0.356996\pi$
$380$	12.7639	0.654776
$381$	−0.291796	−0.0149492
$382$	4.09017	0.209271
$383$	17.8885	0.914062	0.457031	−	0.889451i	$-0.348913\pi$
$383$	17.8885	0.914062	0.457031	+	0.889451i	$0.348913\pi$
$384$	−0.618034	−0.0315389
$385$	0	0
$386$	4.00000	0.203595
$387$	2.00000	0.101666
$388$	−8.47214	−0.430108
$389$	−0.145898	−0.00739732	−0.00369866	−	0.999993i	$-0.501177\pi$
$389$	−0.145898	−0.00739732	−0.00369866	+	0.999993i	$0.501177\pi$
$390$	6.79837	0.344249
$391$	17.2361	0.871665
$392$	0	0
$393$	5.34752	0.269747
$394$	−16.4721	−0.829854
$395$	33.0000	1.66041
$396$	9.47214	0.475993
$397$	10.6525	0.534632	0.267316	−	0.963609i	$-0.413863\pi$
$397$	10.6525	0.534632	0.267316	+	0.963609i	$0.413863\pi$
$398$	−20.9443	−1.04984
$399$	0	0
$400$	3.14590	0.157295
$401$	−9.23607	−0.461227	−0.230614	−	0.973045i	$-0.574073\pi$
$401$	−9.23607	−0.461227	−0.230614	+	0.973045i	$0.574073\pi$
$402$	6.23607	0.311027
$403$	37.0689	1.84653
$404$	−12.4721	−0.620512
$405$	16.2918	0.809546
$406$	0	0
$407$	3.61803	0.179339
$408$	2.76393	0.136835
$409$	3.81966	0.188870	0.0944350	−	0.995531i	$-0.469896\pi$
$409$	3.81966	0.188870	0.0944350	+	0.995531i	$0.469896\pi$
$410$	−21.0689	−1.04052
$411$	−11.9443	−0.589167
$412$	16.2705	0.801590
$413$	0	0
$414$	10.0902	0.495905
$415$	15.7771	0.774467
$416$	−3.85410	−0.188963
$417$	−1.14590	−0.0561149
$418$	−16.1803	−0.791406
$419$	−9.56231	−0.467149	−0.233575	−	0.972339i	$-0.575042\pi$
$419$	−9.56231	−0.467149	−0.233575	+	0.972339i	$0.575042\pi$
$420$	0	0
$421$	−1.96556	−0.0957954	−0.0478977	−	0.998852i	$-0.515252\pi$
$421$	−1.96556	−0.0957954	−0.0478977	+	0.998852i	$0.515252\pi$
$422$	−22.2705	−1.08411
$423$	8.47214	0.411929
$424$	−8.47214	−0.411443
$425$	−14.0689	−0.682441
$426$	9.23607	0.447489
$427$	0	0
$428$	8.32624	0.402464
$429$	−8.61803	−0.416083
$430$	−2.18034	−0.105145
$431$	−32.3607	−1.55876	−0.779380	−	0.626552i	$-0.784466\pi$
$431$	−32.3607	−1.55876	−0.779380	+	0.626552i	$0.784466\pi$
$432$	3.47214	0.167053
$433$	36.3262	1.74573	0.872864	−	0.487964i	$-0.162260\pi$
$433$	36.3262	1.74573	0.872864	+	0.487964i	$0.162260\pi$
$434$	0	0
$435$	−11.1591	−0.535036
$436$	−14.9443	−0.715701
$437$	−17.2361	−0.824513
$438$	−2.52786	−0.120786
$439$	16.7984	0.801743	0.400871	−	0.916134i	$-0.368707\pi$
$439$	16.7984	0.801743	0.400871	+	0.916134i	$0.368707\pi$
$440$	−10.3262	−0.492284
$441$	0	0
$442$	17.2361	0.819836
$443$	−18.2705	−0.868058	−0.434029	−	0.900899i	$-0.642908\pi$
$443$	−18.2705	−0.868058	−0.434029	+	0.900899i	$0.642908\pi$
$444$	0.618034	0.0293306
$445$	29.8885	1.41685
$446$	8.18034	0.387350
$447$	3.81966	0.180664
$448$	0	0
$449$	−19.5279	−0.921577	−0.460788	−	0.887510i	$-0.652433\pi$
$449$	−19.5279	−0.921577	−0.460788	+	0.887510i	$0.652433\pi$
$450$	−8.23607	−0.388252
$451$	26.7082	1.25764
$452$	10.9443	0.514775
$453$	−10.9443	−0.514207
$454$	17.7082	0.831087
$455$	0	0
$456$	−2.76393	−0.129433
$457$	−29.2361	−1.36761	−0.683803	−	0.729667i	$-0.739675\pi$
$457$	−29.2361	−1.36761	−0.683803	+	0.729667i	$0.739675\pi$
$458$	−17.1246	−0.800181
$459$	−15.5279	−0.724779
$460$	−11.0000	−0.512878
$461$	21.0557	0.980663	0.490332	−	0.871536i	$-0.336876\pi$
$461$	21.0557	0.980663	0.490332	+	0.871536i	$0.336876\pi$
$462$	0	0
$463$	15.5623	0.723242	0.361621	−	0.932325i	$-0.382223\pi$
$463$	15.5623	0.723242	0.361621	+	0.932325i	$0.382223\pi$
$464$	6.32624	0.293688
$465$	16.9656	0.786759
$466$	13.5623	0.628262
$467$	−20.3607	−0.942180	−0.471090	−	0.882085i	$-0.656139\pi$
$467$	−20.3607	−0.942180	−0.471090	+	0.882085i	$0.656139\pi$
$468$	10.0902	0.466418
$469$	0	0
$470$	−9.23607	−0.426028
$471$	−4.65248	−0.214375
$472$	9.23607	0.425124
$473$	2.76393	0.127086
$474$	−7.14590	−0.328222
$475$	14.0689	0.645525
$476$	0	0
$477$	22.1803	1.01557
$478$	3.14590	0.143890
$479$	−16.4377	−0.751057	−0.375529	−	0.926811i	$-0.622539\pi$
$479$	−16.4377	−0.751057	−0.375529	+	0.926811i	$0.622539\pi$
$480$	−1.76393	−0.0805121
$481$	3.85410	0.175732
$482$	10.4721	0.476993
$483$	0	0
$484$	2.09017	0.0950077
$485$	−24.1803	−1.09797
$486$	−13.9443	−0.632525
$487$	−25.3050	−1.14668	−0.573338	−	0.819319i	$-0.694352\pi$
$487$	−25.3050	−1.14668	−0.573338	+	0.819319i	$0.694352\pi$
$488$	−8.38197	−0.379434
$489$	7.70820	0.348577
$490$	0	0
$491$	27.4508	1.23884	0.619420	−	0.785060i	$-0.287368\pi$
$491$	27.4508	1.23884	0.619420	+	0.785060i	$0.287368\pi$
$492$	4.56231	0.205685
$493$	−28.2918	−1.27420
$494$	−17.2361	−0.775487
$495$	27.0344	1.21511
$496$	−9.61803	−0.431862
$497$	0	0
$498$	−3.41641	−0.153093
$499$	23.7082	1.06132	0.530662	−	0.847583i	$-0.321943\pi$
$499$	23.7082	1.06132	0.530662	+	0.847583i	$0.321943\pi$
$500$	−5.29180	−0.236656
$501$	4.41641	0.197311
$502$	3.05573	0.136384
$503$	−7.90983	−0.352682	−0.176341	−	0.984329i	$-0.556426\pi$
$503$	−7.90983	−0.352682	−0.176341	+	0.984329i	$0.556426\pi$
$504$	0	0
$505$	−35.5967	−1.58403
$506$	13.9443	0.619898
$507$	−1.14590	−0.0508911
$508$	0.472136	0.0209476
$509$	4.29180	0.190231	0.0951153	−	0.995466i	$-0.469678\pi$
$509$	4.29180	0.190231	0.0951153	+	0.995466i	$0.469678\pi$
$510$	7.88854	0.349311
$511$	0	0
$512$	1.00000	0.0441942
$513$	15.5279	0.685572
$514$	18.9443	0.835596
$515$	46.4377	2.04629
$516$	0.472136	0.0207846
$517$	11.7082	0.514926
$518$	0	0
$519$	5.23607	0.229838
$520$	−11.0000	−0.482382
$521$	−25.4164	−1.11351	−0.556757	−	0.830676i	$-0.687954\pi$
$521$	−25.4164	−1.11351	−0.556757	+	0.830676i	$0.687954\pi$
$522$	−16.5623	−0.724912
$523$	−34.1803	−1.49460	−0.747301	−	0.664486i	$-0.768651\pi$
$523$	−34.1803	−1.49460	−0.747301	+	0.664486i	$0.768651\pi$
$524$	−8.65248	−0.377985
$525$	0	0
$526$	−8.76393	−0.382126
$527$	43.0132	1.87368
$528$	2.23607	0.0973124
$529$	−8.14590	−0.354169
$530$	−24.1803	−1.05033
$531$	−24.1803	−1.04934
$532$	0	0
$533$	28.4508	1.23234
$534$	−6.47214	−0.280077
$535$	23.7639	1.02740
$536$	−10.0902	−0.435829
$537$	−11.5279	−0.497464
$538$	−4.00000	−0.172452
$539$	0	0
$540$	9.90983	0.426451
$541$	5.32624	0.228993	0.114496	−	0.993424i	$-0.463475\pi$
$541$	5.32624	0.228993	0.114496	+	0.993424i	$0.463475\pi$
$542$	4.94427	0.212375
$543$	3.41641	0.146612
$544$	−4.47214	−0.191741
$545$	−42.6525	−1.82703
$546$	0	0
$547$	42.0689	1.79874	0.899368	−	0.437193i	$-0.144027\pi$
$547$	42.0689	1.79874	0.899368	+	0.437193i	$0.144027\pi$
$548$	19.3262	0.825576
$549$	21.9443	0.936559
$550$	−11.3820	−0.485329
$551$	28.2918	1.20527
$552$	2.38197	0.101383
$553$	0	0
$554$	−7.79837	−0.331321
$555$	1.76393	0.0748747
$556$	1.85410	0.0786314
$557$	−0.562306	−0.0238257	−0.0119128	−	0.999929i	$-0.503792\pi$
$557$	−0.562306	−0.0238257	−0.0119128	+	0.999929i	$0.503792\pi$
$558$	25.1803	1.06597
$559$	2.94427	0.124529
$560$	0	0
$561$	−10.0000	−0.422200
$562$	−5.88854	−0.248393
$563$	27.8885	1.17536	0.587681	−	0.809093i	$-0.300041\pi$
$563$	27.8885	1.17536	0.587681	+	0.809093i	$0.300041\pi$
$564$	2.00000	0.0842152
$565$	31.2361	1.31411
$566$	−11.2361	−0.472287
$567$	0	0
$568$	−14.9443	−0.627048
$569$	−21.8885	−0.917615	−0.458808	−	0.888536i	$-0.651723\pi$
$569$	−21.8885	−0.917615	−0.458808	+	0.888536i	$0.651723\pi$
$570$	−7.88854	−0.330415
$571$	9.56231	0.400170	0.200085	−	0.979779i	$-0.435878\pi$
$571$	9.56231	0.400170	0.200085	+	0.979779i	$0.435878\pi$
$572$	13.9443	0.583039
$573$	−2.52786	−0.105603
$574$	0	0
$575$	−12.1246	−0.505631
$576$	−2.61803	−0.109085
$577$	20.6525	0.859774	0.429887	−	0.902883i	$-0.358553\pi$
$577$	20.6525	0.859774	0.429887	+	0.902883i	$0.358553\pi$
$578$	3.00000	0.124784
$579$	−2.47214	−0.102738
$580$	18.0557	0.749723
$581$	0	0
$582$	5.23607	0.217042
$583$	30.6525	1.26950
$584$	4.09017	0.169252
$585$	28.7984	1.19067
$586$	−18.6525	−0.770527
$587$	30.9443	1.27721	0.638603	−	0.769536i	$-0.279512\pi$
$587$	30.9443	1.27721	0.638603	+	0.769536i	$0.279512\pi$
$588$	0	0
$589$	−43.0132	−1.77233
$590$	26.3607	1.08525
$591$	10.1803	0.418763
$592$	−1.00000	−0.0410997
$593$	2.56231	0.105221	0.0526106	−	0.998615i	$-0.483246\pi$
$593$	2.56231	0.105221	0.0526106	+	0.998615i	$0.483246\pi$
$594$	−12.5623	−0.515438
$595$	0	0
$596$	−6.18034	−0.253157
$597$	12.9443	0.529774
$598$	14.8541	0.607429
$599$	38.3607	1.56737	0.783687	−	0.621155i	$-0.213336\pi$
$599$	38.3607	1.56737	0.783687	+	0.621155i	$0.213336\pi$
$600$	−1.94427	−0.0793746
$601$	−35.6869	−1.45570	−0.727850	−	0.685737i	$-0.759480\pi$
$601$	−35.6869	−1.45570	−0.727850	+	0.685737i	$0.759480\pi$
$602$	0	0
$603$	26.4164	1.07576
$604$	17.7082	0.720537
$605$	5.96556	0.242534
$606$	7.70820	0.313124
$607$	−5.96556	−0.242135	−0.121067	−	0.992644i	$-0.538632\pi$
$607$	−5.96556	−0.242135	−0.121067	+	0.992644i	$0.538632\pi$
$608$	4.47214	0.181369
$609$	0	0
$610$	−23.9230	−0.968613
$611$	12.4721	0.504569
$612$	11.7082	0.473276
$613$	−36.1803	−1.46131	−0.730655	−	0.682747i	$-0.760785\pi$
$613$	−36.1803	−1.46131	−0.730655	+	0.682747i	$0.760785\pi$
$614$	6.14590	0.248028
$615$	13.0213	0.525069
$616$	0	0
$617$	−11.0902	−0.446473	−0.223237	−	0.974764i	$-0.571662\pi$
$617$	−11.0902	−0.446473	−0.223237	+	0.974764i	$0.571662\pi$
$618$	−10.0557	−0.404501
$619$	−18.2705	−0.734354	−0.367177	−	0.930151i	$-0.619676\pi$
$619$	−18.2705	−0.734354	−0.367177	+	0.930151i	$0.619676\pi$
$620$	−27.4508	−1.10245
$621$	−13.3820	−0.537000
$622$	−2.03444	−0.0815737
$623$	0	0
$624$	2.38197	0.0953550
$625$	−30.8328	−1.23331
$626$	−5.81966	−0.232600
$627$	10.0000	0.399362
$628$	7.52786	0.300394
$629$	4.47214	0.178316
$630$	0	0
$631$	26.3951	1.05077	0.525387	−	0.850864i	$-0.323921\pi$
$631$	26.3951	1.05077	0.525387	+	0.850864i	$0.323921\pi$
$632$	11.5623	0.459924
$633$	13.7639	0.547067
$634$	3.05573	0.121358
$635$	1.34752	0.0534749
$636$	5.23607	0.207624
$637$	0	0
$638$	−22.8885	−0.906166
$639$	39.1246	1.54775
$640$	2.85410	0.112818
$641$	−22.5066	−0.888956	−0.444478	−	0.895790i	$-0.646611\pi$
$641$	−22.5066	−0.888956	−0.444478	+	0.895790i	$0.646611\pi$
$642$	−5.14590	−0.203092
$643$	33.2361	1.31070	0.655351	−	0.755324i	$-0.272521\pi$
$643$	33.2361	1.31070	0.655351	+	0.755324i	$0.272521\pi$
$644$	0	0
$645$	1.34752	0.0530587
$646$	−20.0000	−0.786889
$647$	−18.9098	−0.743422	−0.371711	−	0.928348i	$-0.621229\pi$
$647$	−18.9098	−0.743422	−0.371711	+	0.928348i	$0.621229\pi$
$648$	5.70820	0.224239
$649$	−33.4164	−1.31171
$650$	−12.1246	−0.475566
$651$	0	0
$652$	−12.4721	−0.488447
$653$	−4.72949	−0.185079	−0.0925396	−	0.995709i	$-0.529498\pi$
$653$	−4.72949	−0.185079	−0.0925396	+	0.995709i	$0.529498\pi$
$654$	9.23607	0.361159
$655$	−24.6950	−0.964915
$656$	−7.38197	−0.288217
$657$	−10.7082	−0.417767
$658$	0	0
$659$	−15.4508	−0.601880	−0.300940	−	0.953643i	$-0.597300\pi$
$659$	−15.4508	−0.601880	−0.300940	+	0.953643i	$0.597300\pi$
$660$	6.38197	0.248418
$661$	−1.67376	−0.0651018	−0.0325509	−	0.999470i	$-0.510363\pi$
$661$	−1.67376	−0.0651018	−0.0325509	+	0.999470i	$0.510363\pi$
$662$	28.0000	1.08825
$663$	−10.6525	−0.413708
$664$	5.52786	0.214523
$665$	0	0
$666$	2.61803	0.101447
$667$	−24.3820	−0.944073
$668$	−7.14590	−0.276483
$669$	−5.05573	−0.195466
$670$	−28.7984	−1.11258
$671$	30.3262	1.17073
$672$	0	0
$673$	17.8541	0.688225	0.344113	−	0.938928i	$-0.388180\pi$
$673$	17.8541	0.688225	0.344113	+	0.938928i	$0.388180\pi$
$674$	−17.0344	−0.656142
$675$	10.9230	0.420426
$676$	1.85410	0.0713116
$677$	−3.34752	−0.128656	−0.0643279	−	0.997929i	$-0.520490\pi$
$677$	−3.34752	−0.128656	−0.0643279	+	0.997929i	$0.520490\pi$
$678$	−6.76393	−0.259767
$679$	0	0
$680$	−12.7639	−0.489474
$681$	−10.9443	−0.419385
$682$	34.7984	1.33250
$683$	−35.4164	−1.35517	−0.677586	−	0.735444i	$-0.736974\pi$
$683$	−35.4164	−1.35517	−0.677586	+	0.735444i	$0.736974\pi$
$684$	−11.7082	−0.447674
$685$	55.1591	2.10752
$686$	0	0
$687$	10.5836	0.403789
$688$	−0.763932	−0.0291246
$689$	32.6525	1.24396
$690$	6.79837	0.258810
$691$	35.7771	1.36102	0.680512	−	0.732737i	$-0.261757\pi$
$691$	35.7771	1.36102	0.680512	+	0.732737i	$0.261757\pi$
$692$	−8.47214	−0.322062
$693$	0	0
$694$	12.7639	0.484512
$695$	5.29180	0.200729
$696$	−3.90983	−0.148202
$697$	33.0132	1.25046
$698$	−12.1803	−0.461033
$699$	−8.38197	−0.317035
$700$	0	0
$701$	3.97871	0.150274	0.0751370	−	0.997173i	$-0.476061\pi$
$701$	3.97871	0.150274	0.0751370	+	0.997173i	$0.476061\pi$
$702$	−13.3820	−0.505070
$703$	−4.47214	−0.168670
$704$	−3.61803	−0.136360
$705$	5.70820	0.214983
$706$	−29.7082	−1.11808
$707$	0	0
$708$	−5.70820	−0.214527
$709$	43.2148	1.62297	0.811483	−	0.584377i	$-0.198661\pi$
$709$	43.2148	1.62297	0.811483	+	0.584377i	$0.198661\pi$
$710$	−42.6525	−1.60072
$711$	−30.2705	−1.13523
$712$	10.4721	0.392460
$713$	37.0689	1.38824
$714$	0	0
$715$	39.7984	1.48837
$716$	18.6525	0.697076
$717$	−1.94427	−0.0726102
$718$	4.47214	0.166899
$719$	−0.583592	−0.0217643	−0.0108822	−	0.999941i	$-0.503464\pi$
$719$	−0.583592	−0.0217643	−0.0108822	+	0.999941i	$0.503464\pi$
$720$	−7.47214	−0.278470
$721$	0	0
$722$	1.00000	0.0372161
$723$	−6.47214	−0.240701
$724$	−5.52786	−0.205441
$725$	19.9017	0.739131
$726$	−1.29180	−0.0479430
$727$	23.1459	0.858434	0.429217	−	0.903201i	$-0.358790\pi$
$727$	23.1459	0.858434	0.429217	+	0.903201i	$0.358790\pi$
$728$	0	0
$729$	−8.50658	−0.315058
$730$	11.6738	0.432065
$731$	3.41641	0.126360
$732$	5.18034	0.191471
$733$	−36.4721	−1.34713	−0.673565	−	0.739128i	$-0.735238\pi$
$733$	−36.4721	−1.34713	−0.673565	+	0.739128i	$0.735238\pi$
$734$	27.1246	1.00119
$735$	0	0
$736$	−3.85410	−0.142064
$737$	36.5066	1.34474
$738$	19.3262	0.711409
$739$	−22.0902	−0.812600	−0.406300	−	0.913740i	$-0.633181\pi$
$739$	−22.0902	−0.812600	−0.406300	+	0.913740i	$0.633181\pi$
$740$	−2.85410	−0.104919
$741$	10.6525	0.391328
$742$	0	0
$743$	10.0689	0.369392	0.184696	−	0.982796i	$-0.440870\pi$
$743$	10.0689	0.369392	0.184696	+	0.982796i	$0.440870\pi$
$744$	5.94427	0.217928
$745$	−17.6393	−0.646255
$746$	14.2918	0.523260
$747$	−14.4721	−0.529508
$748$	16.1803	0.591612
$749$	0	0
$750$	3.27051	0.119422
$751$	−18.9443	−0.691286	−0.345643	−	0.938366i	$-0.612339\pi$
$751$	−18.9443	−0.691286	−0.345643	+	0.938366i	$0.612339\pi$
$752$	−3.23607	−0.118007
$753$	−1.88854	−0.0688224
$754$	−24.3820	−0.887939
$755$	50.5410	1.83938
$756$	0	0
$757$	−10.8541	−0.394499	−0.197250	−	0.980353i	$-0.563201\pi$
$757$	−10.8541	−0.394499	−0.197250	+	0.980353i	$0.563201\pi$
$758$	16.9098	0.614193
$759$	−8.61803	−0.312815
$760$	12.7639	0.462996
$761$	25.8541	0.937210	0.468605	−	0.883408i	$-0.344757\pi$
$761$	25.8541	0.937210	0.468605	+	0.883408i	$0.344757\pi$
$762$	−0.291796	−0.0105707
$763$	0	0
$764$	4.09017	0.147977
$765$	33.4164	1.20817
$766$	17.8885	0.646339
$767$	−35.5967	−1.28532
$768$	−0.618034	−0.0223014
$769$	11.8885	0.428712	0.214356	−	0.976756i	$-0.431235\pi$
$769$	11.8885	0.428712	0.214356	+	0.976756i	$0.431235\pi$
$770$	0	0
$771$	−11.7082	−0.421661
$772$	4.00000	0.143963
$773$	24.0000	0.863220	0.431610	−	0.902060i	$-0.357946\pi$
$773$	24.0000	0.863220	0.431610	+	0.902060i	$0.357946\pi$
$774$	2.00000	0.0718885
$775$	−30.2574	−1.08688
$776$	−8.47214	−0.304132
$777$	0	0
$778$	−0.145898	−0.00523070
$779$	−33.0132	−1.18282
$780$	6.79837	0.243421
$781$	54.0689	1.93474
$782$	17.2361	0.616361
$783$	21.9656	0.784985
$784$	0	0
$785$	21.4853	0.766843
$786$	5.34752	0.190740
$787$	34.4721	1.22880	0.614399	−	0.788995i	$-0.289398\pi$
$787$	34.4721	1.22880	0.614399	+	0.788995i	$0.289398\pi$
$788$	−16.4721	−0.586796
$789$	5.41641	0.192829
$790$	33.0000	1.17409
$791$	0	0
$792$	9.47214	0.336578
$793$	32.3050	1.14718
$794$	10.6525	0.378042
$795$	14.9443	0.530019
$796$	−20.9443	−0.742350
$797$	−12.7295	−0.450902	−0.225451	−	0.974255i	$-0.572386\pi$
$797$	−12.7295	−0.450902	−0.225451	+	0.974255i	$0.572386\pi$
$798$	0	0
$799$	14.4721	0.511987
$800$	3.14590	0.111224
$801$	−27.4164	−0.968711
$802$	−9.23607	−0.326137
$803$	−14.7984	−0.522223
$804$	6.23607	0.219929
$805$	0	0
$806$	37.0689	1.30570
$807$	2.47214	0.0870233
$808$	−12.4721	−0.438768
$809$	27.1246	0.953651	0.476825	−	0.878998i	$-0.341787\pi$
$809$	27.1246	0.953651	0.476825	+	0.878998i	$0.341787\pi$
$810$	16.2918	0.572435
$811$	−53.1033	−1.86471	−0.932355	−	0.361544i	$-0.882250\pi$
$811$	−53.1033	−1.86471	−0.932355	+	0.361544i	$0.882250\pi$
$812$	0	0
$813$	−3.05573	−0.107169
$814$	3.61803	0.126812
$815$	−35.5967	−1.24690
$816$	2.76393	0.0967570
$817$	−3.41641	−0.119525
$818$	3.81966	0.133551
$819$	0	0
$820$	−21.0689	−0.735757
$821$	21.4164	0.747438	0.373719	−	0.927542i	$-0.378082\pi$
$821$	21.4164	0.747438	0.373719	+	0.927542i	$0.378082\pi$
$822$	−11.9443	−0.416604
$823$	−33.8885	−1.18128	−0.590640	−	0.806935i	$-0.701125\pi$
$823$	−33.8885	−1.18128	−0.590640	+	0.806935i	$0.701125\pi$
$824$	16.2705	0.566810
$825$	7.03444	0.244908
$826$	0	0
$827$	56.0689	1.94971	0.974853	−	0.222849i	$-0.0715356\pi$
$827$	56.0689	1.94971	0.974853	+	0.222849i	$0.0715356\pi$
$828$	10.0902	0.350658
$829$	−31.2016	−1.08368	−0.541839	−	0.840483i	$-0.682272\pi$
$829$	−31.2016	−1.08368	−0.541839	+	0.840483i	$0.682272\pi$
$830$	15.7771	0.547631
$831$	4.81966	0.167192
$832$	−3.85410	−0.133617
$833$	0	0
$834$	−1.14590	−0.0396792
$835$	−20.3951	−0.705802
$836$	−16.1803	−0.559609
$837$	−33.3951	−1.15430
$838$	−9.56231	−0.330324
$839$	5.34752	0.184617	0.0923085	−	0.995730i	$-0.470575\pi$
$839$	5.34752	0.184617	0.0923085	+	0.995730i	$0.470575\pi$
$840$	0	0
$841$	11.0213	0.380044
$842$	−1.96556	−0.0677376
$843$	3.63932	0.125345
$844$	−22.2705	−0.766583
$845$	5.29180	0.182043
$846$	8.47214	0.291278
$847$	0	0
$848$	−8.47214	−0.290934
$849$	6.94427	0.238327
$850$	−14.0689	−0.482559
$851$	3.85410	0.132117
$852$	9.23607	0.316422
$853$	12.7426	0.436300	0.218150	−	0.975915i	$-0.429998\pi$
$853$	12.7426	0.436300	0.218150	+	0.975915i	$0.429998\pi$
$854$	0	0
$855$	−33.4164	−1.14282
$856$	8.32624	0.284585
$857$	26.9443	0.920399	0.460199	−	0.887816i	$-0.347778\pi$
$857$	26.9443	0.920399	0.460199	+	0.887816i	$0.347778\pi$
$858$	−8.61803	−0.294215
$859$	−26.5836	−0.907020	−0.453510	−	0.891251i	$-0.649828\pi$
$859$	−26.5836	−0.907020	−0.453510	+	0.891251i	$0.649828\pi$
$860$	−2.18034	−0.0743490
$861$	0	0
$862$	−32.3607	−1.10221
$863$	−7.41641	−0.252457	−0.126229	−	0.992001i	$-0.540287\pi$
$863$	−7.41641	−0.252457	−0.126229	+	0.992001i	$0.540287\pi$
$864$	3.47214	0.118124
$865$	−24.1803	−0.822156
$866$	36.3262	1.23442
$867$	−1.85410	−0.0629686
$868$	0	0
$869$	−41.8328	−1.41908
$870$	−11.1591	−0.378327
$871$	38.8885	1.31769
$872$	−14.9443	−0.506077
$873$	22.1803	0.750691
$874$	−17.2361	−0.583019
$875$	0	0
$876$	−2.52786	−0.0854086
$877$	36.8328	1.24376	0.621878	−	0.783114i	$-0.286370\pi$
$877$	36.8328	1.24376	0.621878	+	0.783114i	$0.286370\pi$
$878$	16.7984	0.566918
$879$	11.5279	0.388825
$880$	−10.3262	−0.348097
$881$	22.7426	0.766219	0.383110	−	0.923703i	$-0.374853\pi$
$881$	22.7426	0.766219	0.383110	+	0.923703i	$0.374853\pi$
$882$	0	0
$883$	29.3050	0.986190	0.493095	−	0.869975i	$-0.335865\pi$
$883$	29.3050	0.986190	0.493095	+	0.869975i	$0.335865\pi$
$884$	17.2361	0.579712
$885$	−16.2918	−0.547643
$886$	−18.2705	−0.613810
$887$	7.88854	0.264871	0.132436	−	0.991192i	$-0.457720\pi$
$887$	7.88854	0.264871	0.132436	+	0.991192i	$0.457720\pi$
$888$	0.618034	0.0207399
$889$	0	0
$890$	29.8885	1.00187
$891$	−20.6525	−0.691884
$892$	8.18034	0.273898
$893$	−14.4721	−0.484292
$894$	3.81966	0.127749
$895$	53.2361	1.77949
$896$	0	0
$897$	−9.18034	−0.306523
$898$	−19.5279	−0.651653
$899$	−60.8460	−2.02933
$900$	−8.23607	−0.274536
$901$	37.8885	1.26225
$902$	26.7082	0.889286
$903$	0	0
$904$	10.9443	0.364001
$905$	−15.7771	−0.524448
$906$	−10.9443	−0.363599
$907$	−20.1115	−0.667790	−0.333895	−	0.942610i	$-0.608363\pi$
$907$	−20.1115	−0.667790	−0.333895	+	0.942610i	$0.608363\pi$
$908$	17.7082	0.587667
$909$	32.6525	1.08301
$910$	0	0
$911$	−21.8885	−0.725200	−0.362600	−	0.931945i	$-0.618111\pi$
$911$	−21.8885	−0.725200	−0.362600	+	0.931945i	$0.618111\pi$
$912$	−2.76393	−0.0915229
$913$	−20.0000	−0.661903
$914$	−29.2361	−0.967043
$915$	14.7852	0.488784
$916$	−17.1246	−0.565813
$917$	0	0
$918$	−15.5279	−0.512496
$919$	29.8885	0.985932	0.492966	−	0.870049i	$-0.335913\pi$
$919$	29.8885	0.985932	0.492966	+	0.870049i	$0.335913\pi$
$920$	−11.0000	−0.362659
$921$	−3.79837	−0.125161
$922$	21.0557	0.693433
$923$	57.5967	1.89582
$924$	0	0
$925$	−3.14590	−0.103436
$926$	15.5623	0.511409
$927$	−42.5967	−1.39906
$928$	6.32624	0.207669
$929$	−28.4508	−0.933442	−0.466721	−	0.884405i	$-0.654565\pi$
$929$	−28.4508	−0.933442	−0.466721	+	0.884405i	$0.654565\pi$
$930$	16.9656	0.556323
$931$	0	0
$932$	13.5623	0.444248
$933$	1.25735	0.0411639
$934$	−20.3607	−0.666222
$935$	46.1803	1.51026
$936$	10.0902	0.329808
$937$	−57.0476	−1.86366	−0.931832	−	0.362890i	$-0.881790\pi$
$937$	−57.0476	−1.86366	−0.931832	+	0.362890i	$0.881790\pi$
$938$	0	0
$939$	3.59675	0.117375
$940$	−9.23607	−0.301247
$941$	3.81966	0.124517	0.0622587	−	0.998060i	$-0.480170\pi$
$941$	3.81966	0.124517	0.0622587	+	0.998060i	$0.480170\pi$
$942$	−4.65248	−0.151586
$943$	28.4508	0.926487
$944$	9.23607	0.300608
$945$	0	0
$946$	2.76393	0.0898632
$947$	−34.8328	−1.13191	−0.565957	−	0.824435i	$-0.691493\pi$
$947$	−34.8328	−1.13191	−0.565957	+	0.824435i	$0.691493\pi$
$948$	−7.14590	−0.232088
$949$	−15.7639	−0.511719
$950$	14.0689	0.456455
$951$	−1.88854	−0.0612402
$952$	0	0
$953$	−44.4508	−1.43990	−0.719952	−	0.694024i	$-0.755836\pi$
$953$	−44.4508	−1.43990	−0.719952	+	0.694024i	$0.755836\pi$
$954$	22.1803	0.718115
$955$	11.6738	0.377754
$956$	3.14590	0.101746
$957$	14.1459	0.457272
$958$	−16.4377	−0.531078
$959$	0	0
$960$	−1.76393	−0.0569307
$961$	61.5066	1.98408
$962$	3.85410	0.124261
$963$	−21.7984	−0.702443
$964$	10.4721	0.337285
$965$	11.4164	0.367507
$966$	0	0
$967$	11.7295	0.377195	0.188597	−	0.982054i	$-0.439606\pi$
$967$	11.7295	0.377195	0.188597	+	0.982054i	$0.439606\pi$
$968$	2.09017	0.0671806
$969$	12.3607	0.397082
$970$	−24.1803	−0.776384
$971$	−26.6738	−0.856002	−0.428001	−	0.903778i	$-0.640782\pi$
$971$	−26.6738	−0.856002	−0.428001	+	0.903778i	$0.640782\pi$
$972$	−13.9443	−0.447263
$973$	0	0
$974$	−25.3050	−0.810823
$975$	7.49342	0.239982
$976$	−8.38197	−0.268300
$977$	52.4721	1.67873	0.839366	−	0.543566i	$-0.182926\pi$
$977$	52.4721	1.67873	0.839366	+	0.543566i	$0.182926\pi$
$978$	7.70820	0.246481
$979$	−37.8885	−1.21092
$980$	0	0
$981$	39.1246	1.24915
$982$	27.4508	0.875992
$983$	−39.7771	−1.26869	−0.634346	−	0.773049i	$-0.718731\pi$
$983$	−39.7771	−1.26869	−0.634346	+	0.773049i	$0.718731\pi$
$984$	4.56231	0.145441
$985$	−47.0132	−1.49796
$986$	−28.2918	−0.900994
$987$	0	0
$988$	−17.2361	−0.548352
$989$	2.94427	0.0936224
$990$	27.0344	0.859211
$991$	−54.1033	−1.71865	−0.859324	−	0.511431i	$-0.829116\pi$
$991$	−54.1033	−1.71865	−0.859324	+	0.511431i	$0.829116\pi$
$992$	−9.61803	−0.305373
$993$	−17.3050	−0.549156
$994$	0	0
$995$	−59.7771	−1.89506
$996$	−3.41641	−0.108253
$997$	−53.7771	−1.70314	−0.851569	−	0.524243i	$-0.824348\pi$
$997$	−53.7771	−1.70314	−0.851569	+	0.524243i	$0.824348\pi$
$998$	23.7082	0.750470
$999$	−3.47214	−0.109854

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3626.2.a.s.1.1		2
7.6	odd	2		74.2.a.b.1.2	✓	2
21.20	even	2		666.2.a.i.1.2		2
28.27	even	2		592.2.a.g.1.1		2
35.13	even	4		1850.2.b.j.149.2		4
35.27	even	4		1850.2.b.j.149.3		4
35.34	odd	2		1850.2.a.t.1.1		2
56.13	odd	2		2368.2.a.y.1.1		2
56.27	even	2		2368.2.a.u.1.2		2
77.76	even	2		8954.2.a.j.1.2		2
84.83	odd	2		5328.2.a.bc.1.2		2
259.258	odd	2		2738.2.a.g.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.a.b.1.2	✓	2	7.6	odd	2
592.2.a.g.1.1		2	28.27	even	2
666.2.a.i.1.2		2	21.20	even	2
1850.2.a.t.1.1		2	35.34	odd	2
1850.2.b.j.149.2		4	35.13	even	4
1850.2.b.j.149.3		4	35.27	even	4
2368.2.a.u.1.2		2	56.27	even	2
2368.2.a.y.1.1		2	56.13	odd	2
2738.2.a.g.1.2		2	259.258	odd	2
3626.2.a.s.1.1		2	1.1	even	1	trivial
5328.2.a.bc.1.2		2	84.83	odd	2
8954.2.a.j.1.2		2	77.76	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3626 = 2 \cdot 7^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3626.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} +2.85410 q^{5} -0.618034 q^{6} +1.00000 q^{8} -2.61803 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.618034 q^{3} +1.00000 q^{4} +2.85410 q^{5} -0.618034 q^{6} +1.00000 q^{8} -2.61803 q^{9} +2.85410 q^{10} -3.61803 q^{11} -0.618034 q^{12} -3.85410 q^{13} -1.76393 q^{15} +1.00000 q^{16} -4.47214 q^{17} -2.61803 q^{18} +4.47214 q^{19} +2.85410 q^{20} -3.61803 q^{22} -3.85410 q^{23} -0.618034 q^{24} +3.14590 q^{25} -3.85410 q^{26} +3.47214 q^{27} +6.32624 q^{29} -1.76393 q^{30} -9.61803 q^{31} +1.00000 q^{32} +2.23607 q^{33} -4.47214 q^{34} -2.61803 q^{36} -1.00000 q^{37} +4.47214 q^{38} +2.38197 q^{39} +2.85410 q^{40} -7.38197 q^{41} -0.763932 q^{43} -3.61803 q^{44} -7.47214 q^{45} -3.85410 q^{46} -3.23607 q^{47} -0.618034 q^{48} +3.14590 q^{50} +2.76393 q^{51} -3.85410 q^{52} -8.47214 q^{53} +3.47214 q^{54} -10.3262 q^{55} -2.76393 q^{57} +6.32624 q^{58} +9.23607 q^{59} -1.76393 q^{60} -8.38197 q^{61} -9.61803 q^{62} +1.00000 q^{64} -11.0000 q^{65} +2.23607 q^{66} -10.0902 q^{67} -4.47214 q^{68} +2.38197 q^{69} -14.9443 q^{71} -2.61803 q^{72} +4.09017 q^{73} -1.00000 q^{74} -1.94427 q^{75} +4.47214 q^{76} +2.38197 q^{78} +11.5623 q^{79} +2.85410 q^{80} +5.70820 q^{81} -7.38197 q^{82} +5.52786 q^{83} -12.7639 q^{85} -0.763932 q^{86} -3.90983 q^{87} -3.61803 q^{88} +10.4721 q^{89} -7.47214 q^{90} -3.85410 q^{92} +5.94427 q^{93} -3.23607 q^{94} +12.7639 q^{95} -0.618034 q^{96} -8.47214 q^{97} +9.47214 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} - q^{5} + q^{6} + 2 q^{8} - 3 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 - q^5 + q^6 + 2 * q^8 - 3 * q^9	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} - q^{5} + q^{6} + 2 q^{8} - 3 q^{9} - q^{10} - 5 q^{11} + q^{12} - q^{13} - 8 q^{15} + 2 q^{16} - 3 q^{18} - q^{20} - 5 q^{22} - q^{23} + q^{24} + 13 q^{25} - q^{26} - 2 q^{27} - 3 q^{29} - 8 q^{30} - 17 q^{31} + 2 q^{32} - 3 q^{36} - 2 q^{37} + 7 q^{39} - q^{40} - 17 q^{41} - 6 q^{43} - 5 q^{44} - 6 q^{45} - q^{46} - 2 q^{47} + q^{48} + 13 q^{50} + 10 q^{51} - q^{52} - 8 q^{53} - 2 q^{54} - 5 q^{55} - 10 q^{57} - 3 q^{58} + 14 q^{59} - 8 q^{60} - 19 q^{61} - 17 q^{62} + 2 q^{64} - 22 q^{65} - 9 q^{67} + 7 q^{69} - 12 q^{71} - 3 q^{72} - 3 q^{73} - 2 q^{74} + 14 q^{75} + 7 q^{78} + 3 q^{79} - q^{80} - 2 q^{81} - 17 q^{82} + 20 q^{83} - 30 q^{85} - 6 q^{86} - 19 q^{87} - 5 q^{88} + 12 q^{89} - 6 q^{90} - q^{92} - 6 q^{93} - 2 q^{94} + 30 q^{95} + q^{96} - 8 q^{97} + 10 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 - q^5 + q^6 + 2 * q^8 - 3 * q^9 - q^10 - 5 * q^11 + q^12 - q^13 - 8 * q^15 + 2 * q^16 - 3 * q^18 - q^20 - 5 * q^22 - q^23 + q^24 + 13 * q^25 - q^26 - 2 * q^27 - 3 * q^29 - 8 * q^30 - 17 * q^31 + 2 * q^32 - 3 * q^36 - 2 * q^37 + 7 * q^39 - q^40 - 17 * q^41 - 6 * q^43 - 5 * q^44 - 6 * q^45 - q^46 - 2 * q^47 + q^48 + 13 * q^50 + 10 * q^51 - q^52 - 8 * q^53 - 2 * q^54 - 5 * q^55 - 10 * q^57 - 3 * q^58 + 14 * q^59 - 8 * q^60 - 19 * q^61 - 17 * q^62 + 2 * q^64 - 22 * q^65 - 9 * q^67 + 7 * q^69 - 12 * q^71 - 3 * q^72 - 3 * q^73 - 2 * q^74 + 14 * q^75 + 7 * q^78 + 3 * q^79 - q^80 - 2 * q^81 - 17 * q^82 + 20 * q^83 - 30 * q^85 - 6 * q^86 - 19 * q^87 - 5 * q^88 + 12 * q^89 - 6 * q^90 - q^92 - 6 * q^93 - 2 * q^94 + 30 * q^95 + q^96 - 8 * q^97 + 10 * q^99

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