LMFDB - Embedded newform 8281.2.a.bb.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8281,2,Mod(1,8281)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8281, 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("8281.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8281 = 7^{2} \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8281.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:	$66.1241179138$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	8281.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.381966 q^{2} +0.381966 q^{3} -1.85410 q^{4} -0.381966 q^{5} +0.145898 q^{6} -1.47214 q^{8} -2.85410 q^{9} +O(q^{10})$	\(q+0.381966 q^{2} +0.381966 q^{3} -1.85410 q^{4} -0.381966 q^{5} +0.145898 q^{6} -1.47214 q^{8} -2.85410 q^{9} -0.145898 q^{10} -4.85410 q^{11} -0.708204 q^{12} -0.145898 q^{15} +3.14590 q^{16} -7.47214 q^{17} -1.09017 q^{18} -4.85410 q^{19} +0.708204 q^{20} -1.85410 q^{22} +4.47214 q^{23} -0.562306 q^{24} -4.85410 q^{25} -2.23607 q^{27} -4.09017 q^{29} -0.0557281 q^{30} -8.70820 q^{31} +4.14590 q^{32} -1.85410 q^{33} -2.85410 q^{34} +5.29180 q^{36} +4.00000 q^{37} -1.85410 q^{38} +0.562306 q^{40} -5.23607 q^{41} -7.56231 q^{43} +9.00000 q^{44} +1.09017 q^{45} +1.70820 q^{46} -2.23607 q^{47} +1.20163 q^{48} -1.85410 q^{50} -2.85410 q^{51} +8.23607 q^{53} -0.854102 q^{54} +1.85410 q^{55} -1.85410 q^{57} -1.56231 q^{58} -2.23607 q^{59} +0.270510 q^{60} +6.00000 q^{61} -3.32624 q^{62} -4.70820 q^{64} -0.708204 q^{66} +0.708204 q^{67} +13.8541 q^{68} +1.70820 q^{69} +8.18034 q^{71} +4.20163 q^{72} +2.00000 q^{73} +1.52786 q^{74} -1.85410 q^{75} +9.00000 q^{76} +4.00000 q^{79} -1.20163 q^{80} +7.70820 q^{81} -2.00000 q^{82} +6.70820 q^{83} +2.85410 q^{85} -2.88854 q^{86} -1.56231 q^{87} +7.14590 q^{88} -16.0902 q^{89} +0.416408 q^{90} -8.29180 q^{92} -3.32624 q^{93} -0.854102 q^{94} +1.85410 q^{95} +1.58359 q^{96} -12.1459 q^{97} +13.8541 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 7 q^{6} + 6 q^{8} + q^{9}+O(q^{10}) $ 2 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 7 * q^6 + 6 * q^8 + q^9	$ 2 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 7 q^{6} + 6 q^{8} + q^{9} - 7 q^{10} - 3 q^{11} + 12 q^{12} - 7 q^{15} + 13 q^{16} - 6 q^{17} + 9 q^{18} - 3 q^{19} - 12 q^{20} + 3 q^{22} + 19 q^{24} - 3 q^{25} + 3 q^{29} - 18 q^{30} - 4 q^{31} + 15 q^{32} + 3 q^{33} + q^{34} + 24 q^{36} + 8 q^{37} + 3 q^{38} - 19 q^{40} - 6 q^{41} + 5 q^{43} + 18 q^{44} - 9 q^{45} - 10 q^{46} + 27 q^{48} + 3 q^{50} + q^{51} + 12 q^{53} + 5 q^{54} - 3 q^{55} + 3 q^{57} + 17 q^{58} - 33 q^{60} + 12 q^{61} + 9 q^{62} + 4 q^{64} + 12 q^{66} - 12 q^{67} + 21 q^{68} - 10 q^{69} - 6 q^{71} + 33 q^{72} + 4 q^{73} + 12 q^{74} + 3 q^{75} + 18 q^{76} + 8 q^{79} - 27 q^{80} + 2 q^{81} - 4 q^{82} - q^{85} + 30 q^{86} + 17 q^{87} + 21 q^{88} - 21 q^{89} - 26 q^{90} - 30 q^{92} + 9 q^{93} + 5 q^{94} - 3 q^{95} + 30 q^{96} - 31 q^{97} + 21 q^{99}+O(q^{100}) $ 2 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 7 * q^6 + 6 * q^8 + q^9 - 7 * q^10 - 3 * q^11 + 12 * q^12 - 7 * q^15 + 13 * q^16 - 6 * q^17 + 9 * q^18 - 3 * q^19 - 12 * q^20 + 3 * q^22 + 19 * q^24 - 3 * q^25 + 3 * q^29 - 18 * q^30 - 4 * q^31 + 15 * q^32 + 3 * q^33 + q^34 + 24 * q^36 + 8 * q^37 + 3 * q^38 - 19 * q^40 - 6 * q^41 + 5 * q^43 + 18 * q^44 - 9 * q^45 - 10 * q^46 + 27 * q^48 + 3 * q^50 + q^51 + 12 * q^53 + 5 * q^54 - 3 * q^55 + 3 * q^57 + 17 * q^58 - 33 * q^60 + 12 * q^61 + 9 * q^62 + 4 * q^64 + 12 * q^66 - 12 * q^67 + 21 * q^68 - 10 * q^69 - 6 * q^71 + 33 * q^72 + 4 * q^73 + 12 * q^74 + 3 * q^75 + 18 * q^76 + 8 * q^79 - 27 * q^80 + 2 * q^81 - 4 * q^82 - q^85 + 30 * q^86 + 17 * q^87 + 21 * q^88 - 21 * q^89 - 26 * q^90 - 30 * q^92 + 9 * q^93 + 5 * q^94 - 3 * q^95 + 30 * q^96 - 31 * q^97 + 21 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.381966	0.270091	0.135045	−	0.990839i	$-0.456882\pi$
$2$	0.381966	0.270091	0.135045	+	0.990839i	$0.456882\pi$
$3$	0.381966	0.220528	0.110264	−	0.993902i	$-0.464830\pi$
$3$	0.381966	0.220528	0.110264	+	0.993902i	$0.464830\pi$
$4$	−1.85410	−0.927051
$5$	−0.381966	−0.170820	−0.0854102	−	0.996346i	$-0.527220\pi$
$5$	−0.381966	−0.170820	−0.0854102	+	0.996346i	$0.527220\pi$
$6$	0.145898	0.0595626
$7$	0	0
$7$	0	0
$8$	−1.47214	−0.520479
$9$	−2.85410	−0.951367
$10$	−0.145898	−0.0461370
$11$	−4.85410	−1.46357	−0.731783	−	0.681537i	$-0.761312\pi$
$11$	−4.85410	−1.46357	−0.731783	+	0.681537i	$0.761312\pi$
$12$	−0.708204	−0.204441
$13$	0	0
$13$	0	0
$14$	0	0
$15$	−0.145898	−0.0376707
$16$	3.14590	0.786475
$17$	−7.47214	−1.81226	−0.906130	−	0.423000i	$-0.860977\pi$
$17$	−7.47214	−1.81226	−0.906130	+	0.423000i	$0.860977\pi$
$18$	−1.09017	−0.256956
$19$	−4.85410	−1.11361	−0.556804	−	0.830644i	$-0.687972\pi$
$19$	−4.85410	−1.11361	−0.556804	+	0.830644i	$0.687972\pi$
$20$	0.708204	0.158359
$21$	0	0
$22$	−1.85410	−0.395296
$23$	4.47214	0.932505	0.466252	−	0.884652i	$-0.345604\pi$
$23$	4.47214	0.932505	0.466252	+	0.884652i	$0.345604\pi$
$24$	−0.562306	−0.114780
$25$	−4.85410	−0.970820
$26$	0	0
$27$	−2.23607	−0.430331
$28$	0	0
$29$	−4.09017	−0.759525	−0.379763	−	0.925084i	$-0.623994\pi$
$29$	−4.09017	−0.759525	−0.379763	+	0.925084i	$0.623994\pi$
$30$	−0.0557281	−0.0101745
$31$	−8.70820	−1.56404	−0.782020	−	0.623254i	$-0.785810\pi$
$31$	−8.70820	−1.56404	−0.782020	+	0.623254i	$0.785810\pi$
$32$	4.14590	0.732898
$33$	−1.85410	−0.322758
$34$	−2.85410	−0.489474
$35$	0	0
$36$	5.29180	0.881966
$37$	4.00000	0.657596	0.328798	−	0.944400i	$-0.393356\pi$
$37$	4.00000	0.657596	0.328798	+	0.944400i	$0.393356\pi$
$38$	−1.85410	−0.300775
$39$	0	0
$40$	0.562306	0.0889084
$41$	−5.23607	−0.817736	−0.408868	−	0.912593i	$-0.634076\pi$
$41$	−5.23607	−0.817736	−0.408868	+	0.912593i	$0.634076\pi$
$42$	0	0
$43$	−7.56231	−1.15324	−0.576620	−	0.817012i	$-0.695629\pi$
$43$	−7.56231	−1.15324	−0.576620	+	0.817012i	$0.695629\pi$
$44$	9.00000	1.35680
$45$	1.09017	0.162513
$46$	1.70820	0.251861
$47$	−2.23607	−0.326164	−0.163082	−	0.986613i	$-0.552144\pi$
$47$	−2.23607	−0.326164	−0.163082	+	0.986613i	$0.552144\pi$
$48$	1.20163	0.173440
$49$	0	0
$50$	−1.85410	−0.262210
$51$	−2.85410	−0.399654
$52$	0	0
$53$	8.23607	1.13131	0.565655	−	0.824642i	$-0.308623\pi$
$53$	8.23607	1.13131	0.565655	+	0.824642i	$0.308623\pi$
$54$	−0.854102	−0.116229
$55$	1.85410	0.250007
$56$	0	0
$57$	−1.85410	−0.245582
$58$	−1.56231	−0.205141
$59$	−2.23607	−0.291111	−0.145556	−	0.989350i	$-0.546497\pi$
$59$	−2.23607	−0.291111	−0.145556	+	0.989350i	$0.546497\pi$
$60$	0.270510	0.0349227
$61$	6.00000	0.768221	0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000	0.768221	0.384111	+	0.923287i	$0.374508\pi$
$62$	−3.32624	−0.422433
$63$	0	0
$64$	−4.70820	−0.588525
$65$	0	0
$66$	−0.708204	−0.0871739
$67$	0.708204	0.0865209	0.0432604	−	0.999064i	$-0.486225\pi$
$67$	0.708204	0.0865209	0.0432604	+	0.999064i	$0.486225\pi$
$68$	13.8541	1.68006
$69$	1.70820	0.205644
$70$	0	0
$71$	8.18034	0.970828	0.485414	−	0.874284i	$-0.338669\pi$
$71$	8.18034	0.970828	0.485414	+	0.874284i	$0.338669\pi$
$72$	4.20163	0.495166
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	1.52786	0.177611
$75$	−1.85410	−0.214093
$76$	9.00000	1.03237
$77$	0	0
$78$	0	0
$79$	4.00000	0.450035	0.225018	−	0.974355i	$-0.427756\pi$
$79$	4.00000	0.450035	0.225018	+	0.974355i	$0.427756\pi$
$80$	−1.20163	−0.134346
$81$	7.70820	0.856467
$82$	−2.00000	−0.220863
$83$	6.70820	0.736321	0.368161	−	0.929762i	$-0.379988\pi$
$83$	6.70820	0.736321	0.368161	+	0.929762i	$0.379988\pi$
$84$	0	0
$85$	2.85410	0.309571
$86$	−2.88854	−0.311480
$87$	−1.56231	−0.167497
$88$	7.14590	0.761755
$89$	−16.0902	−1.70555	−0.852777	−	0.522275i	$-0.825084\pi$
$89$	−16.0902	−1.70555	−0.852777	+	0.522275i	$0.825084\pi$
$90$	0.416408	0.0438932
$91$	0	0
$92$	−8.29180	−0.864479
$93$	−3.32624	−0.344915
$94$	−0.854102	−0.0880939
$95$	1.85410	0.190227
$96$	1.58359	0.161625
$97$	−12.1459	−1.23323	−0.616615	−	0.787265i	$-0.711496\pi$
$97$	−12.1459	−1.23323	−0.616615	+	0.787265i	$0.711496\pi$
$98$	0	0
$99$	13.8541	1.39239
$100$	9.00000	0.900000
$101$	−8.56231	−0.851981	−0.425991	−	0.904728i	$-0.640074\pi$
$101$	−8.56231	−0.851981	−0.425991	+	0.904728i	$0.640074\pi$
$102$	−1.09017	−0.107943
$103$	−4.70820	−0.463913	−0.231957	−	0.972726i	$-0.574513\pi$
$103$	−4.70820	−0.463913	−0.231957	+	0.972726i	$0.574513\pi$
$104$	0	0
$105$	0	0
$106$	3.14590	0.305557
$107$	−5.61803	−0.543116	−0.271558	−	0.962422i	$-0.587539\pi$
$107$	−5.61803	−0.543116	−0.271558	+	0.962422i	$0.587539\pi$
$108$	4.14590	0.398939
$109$	10.7082	1.02566	0.512830	−	0.858490i	$-0.328597\pi$
$109$	10.7082	1.02566	0.512830	+	0.858490i	$0.328597\pi$
$110$	0.708204	0.0675246
$111$	1.52786	0.145018
$112$	0	0
$113$	−7.47214	−0.702919	−0.351460	−	0.936203i	$-0.614315\pi$
$113$	−7.47214	−0.702919	−0.351460	+	0.936203i	$0.614315\pi$
$114$	−0.708204	−0.0663294
$115$	−1.70820	−0.159291
$116$	7.58359	0.704119
$117$	0	0
$118$	−0.854102	−0.0786265
$119$	0	0
$120$	0.214782	0.0196068
$121$	12.5623	1.14203
$122$	2.29180	0.207489
$123$	−2.00000	−0.180334
$124$	16.1459	1.44994
$125$	3.76393	0.336656
$126$	0	0
$127$	−14.1459	−1.25525	−0.627623	−	0.778518i	$-0.715972\pi$
$127$	−14.1459	−1.25525	−0.627623	+	0.778518i	$0.715972\pi$
$128$	−10.0902	−0.891853
$129$	−2.88854	−0.254322
$130$	0	0
$131$	−0.326238	−0.0285035	−0.0142518	−	0.999898i	$-0.504537\pi$
$131$	−0.326238	−0.0285035	−0.0142518	+	0.999898i	$0.504537\pi$
$132$	3.43769	0.299213
$133$	0	0
$134$	0.270510	0.0233685
$135$	0.854102	0.0735094
$136$	11.0000	0.943242
$137$	−0.381966	−0.0326336	−0.0163168	−	0.999867i	$-0.505194\pi$
$137$	−0.381966	−0.0326336	−0.0163168	+	0.999867i	$0.505194\pi$
$138$	0.652476	0.0555424
$139$	15.5623	1.31998	0.659989	−	0.751275i	$-0.270561\pi$
$139$	15.5623	1.31998	0.659989	+	0.751275i	$0.270561\pi$
$140$	0	0
$141$	−0.854102	−0.0719284
$142$	3.12461	0.262212
$143$	0	0
$144$	−8.97871	−0.748226
$145$	1.56231	0.129742
$146$	0.763932	0.0632235
$147$	0	0
$148$	−7.41641	−0.609625
$149$	−4.85410	−0.397664	−0.198832	−	0.980034i	$-0.563715\pi$
$149$	−4.85410	−0.397664	−0.198832	+	0.980034i	$0.563715\pi$
$150$	−0.708204	−0.0578246
$151$	−14.7082	−1.19694	−0.598468	−	0.801146i	$-0.704224\pi$
$151$	−14.7082	−1.19694	−0.598468	+	0.801146i	$0.704224\pi$
$152$	7.14590	0.579609
$153$	21.3262	1.72412
$154$	0	0
$155$	3.32624	0.267170
$156$	0	0
$157$	−8.14590	−0.650113	−0.325057	−	0.945695i	$-0.605383\pi$
$157$	−8.14590	−0.650113	−0.325057	+	0.945695i	$0.605383\pi$
$158$	1.52786	0.121550
$159$	3.14590	0.249486
$160$	−1.58359	−0.125194
$161$	0	0
$162$	2.94427	0.231324
$163$	9.70820	0.760405	0.380203	−	0.924903i	$-0.375854\pi$
$163$	9.70820	0.760405	0.380203	+	0.924903i	$0.375854\pi$
$164$	9.70820	0.758083
$165$	0.708204	0.0551336
$166$	2.56231	0.198874
$167$	−9.76393	−0.755556	−0.377778	−	0.925896i	$-0.623312\pi$
$167$	−9.76393	−0.755556	−0.377778	+	0.925896i	$0.623312\pi$
$168$	0	0
$169$	0	0
$170$	1.09017	0.0836122
$171$	13.8541	1.05945
$172$	14.0213	1.06911
$173$	9.00000	0.684257	0.342129	−	0.939653i	$-0.388852\pi$
$173$	9.00000	0.684257	0.342129	+	0.939653i	$0.388852\pi$
$174$	−0.596748	−0.0452393
$175$	0	0
$176$	−15.2705	−1.15106
$177$	−0.854102	−0.0641982
$178$	−6.14590	−0.460655
$179$	−9.00000	−0.672692	−0.336346	−	0.941739i	$-0.609191\pi$
$179$	−9.00000	−0.672692	−0.336346	+	0.941739i	$0.609191\pi$
$180$	−2.02129	−0.150658
$181$	3.70820	0.275629	0.137814	−	0.990458i	$-0.455992\pi$
$181$	3.70820	0.275629	0.137814	+	0.990458i	$0.455992\pi$
$182$	0	0
$183$	2.29180	0.169414
$184$	−6.58359	−0.485349
$185$	−1.52786	−0.112331
$186$	−1.27051	−0.0931583
$187$	36.2705	2.65236
$188$	4.14590	0.302371
$189$	0	0
$190$	0.708204	0.0513785
$191$	23.6180	1.70894	0.854470	−	0.519500i	$-0.173882\pi$
$191$	23.6180	1.70894	0.854470	+	0.519500i	$0.173882\pi$
$192$	−1.79837	−0.129786
$193$	−6.00000	−0.431889	−0.215945	−	0.976406i	$-0.569283\pi$
$193$	−6.00000	−0.431889	−0.215945	+	0.976406i	$0.569283\pi$
$194$	−4.63932	−0.333084
$195$	0	0
$196$	0	0
$197$	7.79837	0.555611	0.277806	−	0.960637i	$-0.410393\pi$
$197$	7.79837	0.555611	0.277806	+	0.960637i	$0.410393\pi$
$198$	5.29180	0.376072
$199$	−2.41641	−0.171295	−0.0856473	−	0.996326i	$-0.527296\pi$
$199$	−2.41641	−0.171295	−0.0856473	+	0.996326i	$0.527296\pi$
$200$	7.14590	0.505291
$201$	0.270510	0.0190803
$202$	−3.27051	−0.230112
$203$	0	0
$204$	5.29180	0.370500
$205$	2.00000	0.139686
$206$	−1.79837	−0.125299
$207$	−12.7639	−0.887155
$208$	0	0
$209$	23.5623	1.62984
$210$	0	0
$211$	−8.70820	−0.599497	−0.299749	−	0.954018i	$-0.596903\pi$
$211$	−8.70820	−0.599497	−0.299749	+	0.954018i	$0.596903\pi$
$212$	−15.2705	−1.04878
$213$	3.12461	0.214095
$214$	−2.14590	−0.146691
$215$	2.88854	0.196997
$216$	3.29180	0.223978
$217$	0	0
$218$	4.09017	0.277021
$219$	0.763932	0.0516217
$220$	−3.43769	−0.231769
$221$	0	0
$222$	0.583592	0.0391681
$223$	13.2705	0.888659	0.444330	−	0.895863i	$-0.353442\pi$
$223$	13.2705	0.888659	0.444330	+	0.895863i	$0.353442\pi$
$224$	0	0
$225$	13.8541	0.923607
$226$	−2.85410	−0.189852
$227$	7.47214	0.495943	0.247972	−	0.968767i	$-0.420236\pi$
$227$	7.47214	0.495943	0.247972	+	0.968767i	$0.420236\pi$
$228$	3.43769	0.227667
$229$	−27.1246	−1.79244	−0.896222	−	0.443605i	$-0.853699\pi$
$229$	−27.1246	−1.79244	−0.896222	+	0.443605i	$0.853699\pi$
$230$	−0.652476	−0.0430230
$231$	0	0
$232$	6.02129	0.395317
$233$	0.381966	0.0250234	0.0125117	−	0.999922i	$-0.496017\pi$
$233$	0.381966	0.0250234	0.0125117	+	0.999922i	$0.496017\pi$
$234$	0	0
$235$	0.854102	0.0557155
$236$	4.14590	0.269875
$237$	1.52786	0.0992454
$238$	0	0
$239$	−11.2918	−0.730406	−0.365203	−	0.930928i	$-0.619000\pi$
$239$	−11.2918	−0.730406	−0.365203	+	0.930928i	$0.619000\pi$
$240$	−0.458980	−0.0296271
$241$	−4.43769	−0.285857	−0.142929	−	0.989733i	$-0.545652\pi$
$241$	−4.43769	−0.285857	−0.142929	+	0.989733i	$0.545652\pi$
$242$	4.79837	0.308451
$243$	9.65248	0.619207
$244$	−11.1246	−0.712180
$245$	0	0
$246$	−0.763932	−0.0487065
$247$	0	0
$248$	12.8197	0.814049
$249$	2.56231	0.162380
$250$	1.43769	0.0909278
$251$	−5.23607	−0.330498	−0.165249	−	0.986252i	$-0.552843\pi$
$251$	−5.23607	−0.330498	−0.165249	+	0.986252i	$0.552843\pi$
$252$	0	0
$253$	−21.7082	−1.36478
$254$	−5.40325	−0.339030
$255$	1.09017	0.0682691
$256$	5.56231	0.347644
$257$	25.7426	1.60578	0.802891	−	0.596126i	$-0.203294\pi$
$257$	25.7426	1.60578	0.802891	+	0.596126i	$0.203294\pi$
$258$	−1.10333	−0.0686900
$259$	0	0
$260$	0	0
$261$	11.6738	0.722588
$262$	−0.124612	−0.00769854
$263$	9.00000	0.554964	0.277482	−	0.960731i	$-0.410500\pi$
$263$	9.00000	0.554964	0.277482	+	0.960731i	$0.410500\pi$
$264$	2.72949	0.167989
$265$	−3.14590	−0.193251
$266$	0	0
$267$	−6.14590	−0.376123
$268$	−1.31308	−0.0802093
$269$	−13.7426	−0.837904	−0.418952	−	0.908008i	$-0.637602\pi$
$269$	−13.7426	−0.837904	−0.418952	+	0.908008i	$0.637602\pi$
$270$	0.326238	0.0198542
$271$	−18.4164	−1.11872	−0.559359	−	0.828926i	$-0.688952\pi$
$271$	−18.4164	−1.11872	−0.559359	+	0.828926i	$0.688952\pi$
$272$	−23.5066	−1.42530
$273$	0	0
$274$	−0.145898	−0.00881402
$275$	23.5623	1.42086
$276$	−3.16718	−0.190642
$277$	−5.00000	−0.300421	−0.150210	−	0.988654i	$-0.547995\pi$
$277$	−5.00000	−0.300421	−0.150210	+	0.988654i	$0.547995\pi$
$278$	5.94427	0.356514
$279$	24.8541	1.48798
$280$	0	0
$281$	−2.18034	−0.130068	−0.0650341	−	0.997883i	$-0.520716\pi$
$281$	−2.18034	−0.130068	−0.0650341	+	0.997883i	$0.520716\pi$
$282$	−0.326238	−0.0194272
$283$	13.4164	0.797523	0.398761	−	0.917055i	$-0.369440\pi$
$283$	13.4164	0.797523	0.398761	+	0.917055i	$0.369440\pi$
$284$	−15.1672	−0.900007
$285$	0.708204	0.0419504
$286$	0	0
$287$	0	0
$288$	−11.8328	−0.697255
$289$	38.8328	2.28428
$290$	0.596748	0.0350422
$291$	−4.63932	−0.271962
$292$	−3.70820	−0.217006
$293$	11.2361	0.656418	0.328209	−	0.944605i	$-0.393555\pi$
$293$	11.2361	0.656418	0.328209	+	0.944605i	$0.393555\pi$
$294$	0	0
$295$	0.854102	0.0497277
$296$	−5.88854	−0.342265
$297$	10.8541	0.629819
$298$	−1.85410	−0.107405
$299$	0	0
$300$	3.43769	0.198475
$301$	0	0
$302$	−5.61803	−0.323282
$303$	−3.27051	−0.187886
$304$	−15.2705	−0.875824
$305$	−2.29180	−0.131228
$306$	8.14590	0.465670
$307$	−1.85410	−0.105819	−0.0529096	−	0.998599i	$-0.516850\pi$
$307$	−1.85410	−0.105819	−0.0529096	+	0.998599i	$0.516850\pi$
$308$	0	0
$309$	−1.79837	−0.102306
$310$	1.27051	0.0721601
$311$	12.3262	0.698957	0.349478	−	0.936944i	$-0.386359\pi$
$311$	12.3262	0.698957	0.349478	+	0.936944i	$0.386359\pi$
$312$	0	0
$313$	15.1246	0.854894	0.427447	−	0.904041i	$-0.359413\pi$
$313$	15.1246	0.854894	0.427447	+	0.904041i	$0.359413\pi$
$314$	−3.11146	−0.175590
$315$	0	0
$316$	−7.41641	−0.417206
$317$	21.7639	1.22238	0.611192	−	0.791482i	$-0.290690\pi$
$317$	21.7639	1.22238	0.611192	+	0.791482i	$0.290690\pi$
$318$	1.20163	0.0673838
$319$	19.8541	1.11162
$320$	1.79837	0.100532
$321$	−2.14590	−0.119772
$322$	0	0
$323$	36.2705	2.01815
$324$	−14.2918	−0.793989
$325$	0	0
$326$	3.70820	0.205378
$327$	4.09017	0.226187
$328$	7.70820	0.425614
$329$	0	0
$330$	0.270510	0.0148911
$331$	−16.8541	−0.926385	−0.463193	−	0.886258i	$-0.653296\pi$
$331$	−16.8541	−0.926385	−0.463193	+	0.886258i	$0.653296\pi$
$332$	−12.4377	−0.682607
$333$	−11.4164	−0.625615
$334$	−3.72949	−0.204069
$335$	−0.270510	−0.0147795
$336$	0	0
$337$	8.56231	0.466419	0.233209	−	0.972427i	$-0.425077\pi$
$337$	8.56231	0.466419	0.233209	+	0.972427i	$0.425077\pi$
$338$	0	0
$339$	−2.85410	−0.155014
$340$	−5.29180	−0.286988
$341$	42.2705	2.28908
$342$	5.29180	0.286148
$343$	0	0
$344$	11.1327	0.600237
$345$	−0.652476	−0.0351281
$346$	3.43769	0.184812
$347$	35.2361	1.89157	0.945786	−	0.324792i	$-0.105294\pi$
$347$	35.2361	1.89157	0.945786	+	0.324792i	$0.105294\pi$
$348$	2.89667	0.155278
$349$	−7.29180	−0.390321	−0.195160	−	0.980771i	$-0.562523\pi$
$349$	−7.29180	−0.390321	−0.195160	+	0.980771i	$0.562523\pi$
$350$	0	0
$351$	0	0
$352$	−20.1246	−1.07265
$353$	−28.8541	−1.53575	−0.767874	−	0.640600i	$-0.778686\pi$
$353$	−28.8541	−1.53575	−0.767874	+	0.640600i	$0.778686\pi$
$354$	−0.326238	−0.0173393
$355$	−3.12461	−0.165837
$356$	29.8328	1.58114
$357$	0	0
$358$	−3.43769	−0.181688
$359$	−10.9098	−0.575799	−0.287899	−	0.957661i	$-0.592957\pi$
$359$	−10.9098	−0.575799	−0.287899	+	0.957661i	$0.592957\pi$
$360$	−1.60488	−0.0845845
$361$	4.56231	0.240121
$362$	1.41641	0.0744447
$363$	4.79837	0.251849
$364$	0	0
$365$	−0.763932	−0.0399860
$366$	0.875388	0.0457573
$367$	−25.4164	−1.32673	−0.663363	−	0.748298i	$-0.730871\pi$
$367$	−25.4164	−1.32673	−0.663363	+	0.748298i	$0.730871\pi$
$368$	14.0689	0.733391
$369$	14.9443	0.777968
$370$	−0.583592	−0.0303395
$371$	0	0
$372$	6.16718	0.319754
$373$	−0.437694	−0.0226629	−0.0113315	−	0.999936i	$-0.503607\pi$
$373$	−0.437694	−0.0226629	−0.0113315	+	0.999936i	$0.503607\pi$
$374$	13.8541	0.716379
$375$	1.43769	0.0742422
$376$	3.29180	0.169761
$377$	0	0
$378$	0	0
$379$	−12.8541	−0.660271	−0.330135	−	0.943934i	$-0.607094\pi$
$379$	−12.8541	−0.660271	−0.330135	+	0.943934i	$0.607094\pi$
$380$	−3.43769	−0.176350
$381$	−5.40325	−0.276817
$382$	9.02129	0.461569
$383$	−24.9787	−1.27635	−0.638176	−	0.769890i	$-0.720311\pi$
$383$	−24.9787	−1.27635	−0.638176	+	0.769890i	$0.720311\pi$
$384$	−3.85410	−0.196679
$385$	0	0
$386$	−2.29180	−0.116649
$387$	21.5836	1.09716
$388$	22.5197	1.14327
$389$	23.8885	1.21120	0.605599	−	0.795770i	$-0.292934\pi$
$389$	23.8885	1.21120	0.605599	+	0.795770i	$0.292934\pi$
$390$	0	0
$391$	−33.4164	−1.68994
$392$	0	0
$393$	−0.124612	−0.00628583
$394$	2.97871	0.150065
$395$	−1.52786	−0.0768752
$396$	−25.6869	−1.29082
$397$	25.4164	1.27561	0.637806	−	0.770197i	$-0.279842\pi$
$397$	25.4164	1.27561	0.637806	+	0.770197i	$0.279842\pi$
$398$	−0.922986	−0.0462651
$399$	0	0
$400$	−15.2705	−0.763525
$401$	−20.4508	−1.02127	−0.510633	−	0.859799i	$-0.670589\pi$
$401$	−20.4508	−1.02127	−0.510633	+	0.859799i	$0.670589\pi$
$402$	0.103326	0.00515341
$403$	0	0
$404$	15.8754	0.789830
$405$	−2.94427	−0.146302
$406$	0	0
$407$	−19.4164	−0.962436
$408$	4.20163	0.208011
$409$	−34.5623	−1.70900	−0.854498	−	0.519455i	$-0.826135\pi$
$409$	−34.5623	−1.70900	−0.854498	+	0.519455i	$0.826135\pi$
$410$	0.763932	0.0377279
$411$	−0.145898	−0.00719662
$412$	8.72949	0.430071
$413$	0	0
$414$	−4.87539	−0.239612
$415$	−2.56231	−0.125779
$416$	0	0
$417$	5.94427	0.291092
$418$	9.00000	0.440204
$419$	−5.94427	−0.290397	−0.145198	−	0.989403i	$-0.546382\pi$
$419$	−5.94427	−0.290397	−0.145198	+	0.989403i	$0.546382\pi$
$420$	0	0
$421$	−25.4164	−1.23872	−0.619360	−	0.785107i	$-0.712608\pi$
$421$	−25.4164	−1.23872	−0.619360	+	0.785107i	$0.712608\pi$
$422$	−3.32624	−0.161919
$423$	6.38197	0.310302
$424$	−12.1246	−0.588823
$425$	36.2705	1.75938
$426$	1.19350	0.0578250
$427$	0	0
$428$	10.4164	0.503496
$429$	0	0
$430$	1.10333	0.0532071
$431$	−16.7984	−0.809149	−0.404575	−	0.914505i	$-0.632580\pi$
$431$	−16.7984	−0.809149	−0.404575	+	0.914505i	$0.632580\pi$
$432$	−7.03444	−0.338445
$433$	−1.00000	−0.0480569	−0.0240285	−	0.999711i	$-0.507649\pi$
$433$	−1.00000	−0.0480569	−0.0240285	+	0.999711i	$0.507649\pi$
$434$	0	0
$435$	0.596748	0.0286119
$436$	−19.8541	−0.950839
$437$	−21.7082	−1.03844
$438$	0.291796	0.0139426
$439$	−8.14590	−0.388783	−0.194391	−	0.980924i	$-0.562273\pi$
$439$	−8.14590	−0.388783	−0.194391	+	0.980924i	$0.562273\pi$
$440$	−2.72949	−0.130123
$441$	0	0
$442$	0	0
$443$	−0.763932	−0.0362955	−0.0181478	−	0.999835i	$-0.505777\pi$
$443$	−0.763932	−0.0362955	−0.0181478	+	0.999835i	$0.505777\pi$
$444$	−2.83282	−0.134439
$445$	6.14590	0.291344
$446$	5.06888	0.240019
$447$	−1.85410	−0.0876960
$448$	0	0
$449$	28.4721	1.34368	0.671842	−	0.740695i	$-0.265504\pi$
$449$	28.4721	1.34368	0.671842	+	0.740695i	$0.265504\pi$
$450$	5.29180	0.249458
$451$	25.4164	1.19681
$452$	13.8541	0.651642
$453$	−5.61803	−0.263958
$454$	2.85410	0.133950
$455$	0	0
$456$	2.72949	0.127820
$457$	−11.4164	−0.534037	−0.267019	−	0.963691i	$-0.586038\pi$
$457$	−11.4164	−0.534037	−0.267019	+	0.963691i	$0.586038\pi$
$458$	−10.3607	−0.484123
$459$	16.7082	0.779872
$460$	3.16718	0.147671
$461$	−39.2148	−1.82641	−0.913207	−	0.407495i	$-0.866402\pi$
$461$	−39.2148	−1.82641	−0.913207	+	0.407495i	$0.866402\pi$
$462$	0	0
$463$	−6.70820	−0.311757	−0.155878	−	0.987776i	$-0.549821\pi$
$463$	−6.70820	−0.311757	−0.155878	+	0.987776i	$0.549821\pi$
$464$	−12.8673	−0.597347
$465$	1.27051	0.0589185
$466$	0.145898	0.00675860
$467$	−33.6525	−1.55725	−0.778625	−	0.627489i	$-0.784083\pi$
$467$	−33.6525	−1.55725	−0.778625	+	0.627489i	$0.784083\pi$
$468$	0	0
$469$	0	0
$470$	0.326238	0.0150482
$471$	−3.11146	−0.143368
$472$	3.29180	0.151517
$473$	36.7082	1.68785
$474$	0.583592	0.0268053
$475$	23.5623	1.08111
$476$	0	0
$477$	−23.5066	−1.07629
$478$	−4.31308	−0.197276
$479$	21.9787	1.00423	0.502117	−	0.864800i	$-0.332555\pi$
$479$	21.9787	1.00423	0.502117	+	0.864800i	$0.332555\pi$
$480$	−0.604878	−0.0276088
$481$	0	0
$482$	−1.69505	−0.0772073
$483$	0	0
$484$	−23.2918	−1.05872
$485$	4.63932	0.210661
$486$	3.68692	0.167242
$487$	−16.9787	−0.769379	−0.384689	−	0.923046i	$-0.625691\pi$
$487$	−16.9787	−0.769379	−0.384689	+	0.923046i	$0.625691\pi$
$488$	−8.83282	−0.399843
$489$	3.70820	0.167691
$490$	0	0
$491$	14.6180	0.659703	0.329851	−	0.944033i	$-0.393001\pi$
$491$	14.6180	0.659703	0.329851	+	0.944033i	$0.393001\pi$
$492$	3.70820	0.167179
$493$	30.5623	1.37646
$494$	0	0
$495$	−5.29180	−0.237849
$496$	−27.3951	−1.23008
$497$	0	0
$498$	0.978714	0.0438572
$499$	8.14590	0.364660	0.182330	−	0.983237i	$-0.441636\pi$
$499$	8.14590	0.364660	0.182330	+	0.983237i	$0.441636\pi$
$500$	−6.97871	−0.312098
$501$	−3.72949	−0.166621
$502$	−2.00000	−0.0892644
$503$	−24.3820	−1.08714	−0.543569	−	0.839364i	$-0.682927\pi$
$503$	−24.3820	−1.08714	−0.543569	+	0.839364i	$0.682927\pi$
$504$	0	0
$505$	3.27051	0.145536
$506$	−8.29180	−0.368615
$507$	0	0
$508$	26.2279	1.16368
$509$	−30.5967	−1.35618	−0.678089	−	0.734980i	$-0.737191\pi$
$509$	−30.5967	−1.35618	−0.678089	+	0.734980i	$0.737191\pi$
$510$	0.416408	0.0184389
$511$	0	0
$512$	22.3050	0.985749
$513$	10.8541	0.479220
$514$	9.83282	0.433707
$515$	1.79837	0.0792458
$516$	5.35565	0.235770
$517$	10.8541	0.477363
$518$	0	0
$519$	3.43769	0.150898
$520$	0	0
$521$	12.6525	0.554315	0.277158	−	0.960824i	$-0.410608\pi$
$521$	12.6525	0.554315	0.277158	+	0.960824i	$0.410608\pi$
$522$	4.45898	0.195164
$523$	39.1246	1.71080	0.855400	−	0.517968i	$-0.173311\pi$
$523$	39.1246	1.71080	0.855400	+	0.517968i	$0.173311\pi$
$524$	0.604878	0.0264242
$525$	0	0
$526$	3.43769	0.149891
$527$	65.0689	2.83445
$528$	−5.83282	−0.253841
$529$	−3.00000	−0.130435
$530$	−1.20163	−0.0521953
$531$	6.38197	0.276954
$532$	0	0
$533$	0	0
$534$	−2.34752	−0.101587
$535$	2.14590	0.0927753
$536$	−1.04257	−0.0450323
$537$	−3.43769	−0.148347
$538$	−5.24922	−0.226310
$539$	0	0
$540$	−1.58359	−0.0681470
$541$	1.72949	0.0743566	0.0371783	−	0.999309i	$-0.488163\pi$
$541$	1.72949	0.0743566	0.0371783	+	0.999309i	$0.488163\pi$
$542$	−7.03444	−0.302155
$543$	1.41641	0.0607839
$544$	−30.9787	−1.32820
$545$	−4.09017	−0.175204
$546$	0	0
$547$	−3.00000	−0.128271	−0.0641354	−	0.997941i	$-0.520429\pi$
$547$	−3.00000	−0.128271	−0.0641354	+	0.997941i	$0.520429\pi$
$548$	0.708204	0.0302530
$549$	−17.1246	−0.730861
$550$	9.00000	0.383761
$551$	19.8541	0.845813
$552$	−2.51471	−0.107033
$553$	0	0
$554$	−1.90983	−0.0811409
$555$	−0.583592	−0.0247721
$556$	−28.8541	−1.22369
$557$	18.9787	0.804154	0.402077	−	0.915606i	$-0.368288\pi$
$557$	18.9787	0.804154	0.402077	+	0.915606i	$0.368288\pi$
$558$	9.49342	0.401889
$559$	0	0
$560$	0	0
$561$	13.8541	0.584921
$562$	−0.832816	−0.0351302
$563$	38.9443	1.64131	0.820653	−	0.571427i	$-0.193610\pi$
$563$	38.9443	1.64131	0.820653	+	0.571427i	$0.193610\pi$
$564$	1.58359	0.0666813
$565$	2.85410	0.120073
$566$	5.12461	0.215404
$567$	0	0
$568$	−12.0426	−0.505295
$569$	−2.94427	−0.123430	−0.0617151	−	0.998094i	$-0.519657\pi$
$569$	−2.94427	−0.123430	−0.0617151	+	0.998094i	$0.519657\pi$
$570$	0.270510	0.0113304
$571$	−35.6869	−1.49345	−0.746726	−	0.665132i	$-0.768375\pi$
$571$	−35.6869	−1.49345	−0.746726	+	0.665132i	$0.768375\pi$
$572$	0	0
$573$	9.02129	0.376870
$574$	0	0
$575$	−21.7082	−0.905295
$576$	13.4377	0.559904
$577$	−9.83282	−0.409345	−0.204673	−	0.978830i	$-0.565613\pi$
$577$	−9.83282	−0.409345	−0.204673	+	0.978830i	$0.565613\pi$
$578$	14.8328	0.616964
$579$	−2.29180	−0.0952438
$580$	−2.89667	−0.120278
$581$	0	0
$582$	−1.77206	−0.0734544
$583$	−39.9787	−1.65575
$584$	−2.94427	−0.121835
$585$	0	0
$586$	4.29180	0.177292
$587$	31.0902	1.28323	0.641614	−	0.767027i	$-0.278265\pi$
$587$	31.0902	1.28323	0.641614	+	0.767027i	$0.278265\pi$
$588$	0	0
$589$	42.2705	1.74173
$590$	0.326238	0.0134310
$591$	2.97871	0.122528
$592$	12.5836	0.517182
$593$	−19.2016	−0.788516	−0.394258	−	0.919000i	$-0.628998\pi$
$593$	−19.2016	−0.788516	−0.394258	+	0.919000i	$0.628998\pi$
$594$	4.14590	0.170108
$595$	0	0
$596$	9.00000	0.368654
$597$	−0.922986	−0.0377753
$598$	0	0
$599$	−8.50658	−0.347569	−0.173785	−	0.984784i	$-0.555600\pi$
$599$	−8.50658	−0.347569	−0.173785	+	0.984784i	$0.555600\pi$
$600$	2.72949	0.111431
$601$	33.3951	1.36222	0.681108	−	0.732183i	$-0.261499\pi$
$601$	33.3951	1.36222	0.681108	+	0.732183i	$0.261499\pi$
$602$	0	0
$603$	−2.02129	−0.0823131
$604$	27.2705	1.10962
$605$	−4.79837	−0.195082
$606$	−1.24922	−0.0507462
$607$	23.0000	0.933541	0.466771	−	0.884378i	$-0.345417\pi$
$607$	23.0000	0.933541	0.466771	+	0.884378i	$0.345417\pi$
$608$	−20.1246	−0.816161
$609$	0	0
$610$	−0.875388	−0.0354434
$611$	0	0
$612$	−39.5410	−1.59835
$613$	14.4377	0.583133	0.291566	−	0.956551i	$-0.405824\pi$
$613$	14.4377	0.583133	0.291566	+	0.956551i	$0.405824\pi$
$614$	−0.708204	−0.0285808
$615$	0.763932	0.0308047
$616$	0	0
$617$	17.9443	0.722409	0.361205	−	0.932487i	$-0.382366\pi$
$617$	17.9443	0.722409	0.361205	+	0.932487i	$0.382366\pi$
$618$	−0.686918	−0.0276319
$619$	17.4164	0.700025	0.350012	−	0.936745i	$-0.386177\pi$
$619$	17.4164	0.700025	0.350012	+	0.936745i	$0.386177\pi$
$620$	−6.16718	−0.247680
$621$	−10.0000	−0.401286
$622$	4.70820	0.188782
$623$	0	0
$624$	0	0
$625$	22.8328	0.913313
$626$	5.77709	0.230899
$627$	9.00000	0.359425
$628$	15.1033	0.602688
$629$	−29.8885	−1.19173
$630$	0	0
$631$	−39.3951	−1.56830	−0.784148	−	0.620574i	$-0.786899\pi$
$631$	−39.3951	−1.56830	−0.784148	+	0.620574i	$0.786899\pi$
$632$	−5.88854	−0.234234
$633$	−3.32624	−0.132206
$634$	8.31308	0.330155
$635$	5.40325	0.214422
$636$	−5.83282	−0.231286
$637$	0	0
$638$	7.58359	0.300237
$639$	−23.3475	−0.923614
$640$	3.85410	0.152347
$641$	−9.49342	−0.374968	−0.187484	−	0.982268i	$-0.560033\pi$
$641$	−9.49342	−0.374968	−0.187484	+	0.982268i	$0.560033\pi$
$642$	−0.819660	−0.0323494
$643$	7.00000	0.276053	0.138027	−	0.990429i	$-0.455924\pi$
$643$	7.00000	0.276053	0.138027	+	0.990429i	$0.455924\pi$
$644$	0	0
$645$	1.10333	0.0434434
$646$	13.8541	0.545082
$647$	−29.2361	−1.14939	−0.574694	−	0.818368i	$-0.694879\pi$
$647$	−29.2361	−1.14939	−0.574694	+	0.818368i	$0.694879\pi$
$648$	−11.3475	−0.445773
$649$	10.8541	0.426061
$650$	0	0
$651$	0	0
$652$	−18.0000	−0.704934
$653$	−2.61803	−0.102452	−0.0512258	−	0.998687i	$-0.516313\pi$
$653$	−2.61803	−0.102452	−0.0512258	+	0.998687i	$0.516313\pi$
$654$	1.56231	0.0610910
$655$	0.124612	0.00486899
$656$	−16.4721	−0.643129
$657$	−5.70820	−0.222698
$658$	0	0
$659$	11.8885	0.463112	0.231556	−	0.972822i	$-0.425618\pi$
$659$	11.8885	0.463112	0.231556	+	0.972822i	$0.425618\pi$
$660$	−1.31308	−0.0511117
$661$	−18.5410	−0.721162	−0.360581	−	0.932728i	$-0.617422\pi$
$661$	−18.5410	−0.721162	−0.360581	+	0.932728i	$0.617422\pi$
$662$	−6.43769	−0.250208
$663$	0	0
$664$	−9.87539	−0.383239
$665$	0	0
$666$	−4.36068	−0.168973
$667$	−18.2918	−0.708261
$668$	18.1033	0.700439
$669$	5.06888	0.195974
$670$	−0.103326	−0.00399181
$671$	−29.1246	−1.12434
$672$	0	0
$673$	41.2492	1.59004	0.795020	−	0.606583i	$-0.207460\pi$
$673$	41.2492	1.59004	0.795020	+	0.606583i	$0.207460\pi$
$674$	3.27051	0.125975
$675$	10.8541	0.417775
$676$	0	0
$677$	−1.25735	−0.0483240	−0.0241620	−	0.999708i	$-0.507692\pi$
$677$	−1.25735	−0.0483240	−0.0241620	+	0.999708i	$0.507692\pi$
$678$	−1.09017	−0.0418677
$679$	0	0
$680$	−4.20163	−0.161125
$681$	2.85410	0.109369
$682$	16.1459	0.618258
$683$	−7.47214	−0.285913	−0.142957	−	0.989729i	$-0.545661\pi$
$683$	−7.47214	−0.285913	−0.142957	+	0.989729i	$0.545661\pi$
$684$	−25.6869	−0.982164
$685$	0.145898	0.00557448
$686$	0	0
$687$	−10.3607	−0.395285
$688$	−23.7902	−0.906995
$689$	0	0
$690$	−0.249224	−0.00948778
$691$	−0.854102	−0.0324916	−0.0162458	−	0.999868i	$-0.505171\pi$
$691$	−0.854102	−0.0324916	−0.0162458	+	0.999868i	$0.505171\pi$
$692$	−16.6869	−0.634341
$693$	0	0
$694$	13.4590	0.510896
$695$	−5.94427	−0.225479
$696$	2.29993	0.0871785
$697$	39.1246	1.48195
$698$	−2.78522	−0.105422
$699$	0.145898	0.00551837
$700$	0	0
$701$	6.76393	0.255470	0.127735	−	0.991808i	$-0.459229\pi$
$701$	6.76393	0.255470	0.127735	+	0.991808i	$0.459229\pi$
$702$	0	0
$703$	−19.4164	−0.732304
$704$	22.8541	0.861346
$705$	0.326238	0.0122868
$706$	−11.0213	−0.414792
$707$	0	0
$708$	1.58359	0.0595150
$709$	3.43769	0.129105	0.0645527	−	0.997914i	$-0.479438\pi$
$709$	3.43769	0.129105	0.0645527	+	0.997914i	$0.479438\pi$
$710$	−1.19350	−0.0447911
$711$	−11.4164	−0.428149
$712$	23.6869	0.887705
$713$	−38.9443	−1.45847
$714$	0	0
$715$	0	0
$716$	16.6869	0.623619
$717$	−4.31308	−0.161075
$718$	−4.16718	−0.155518
$719$	32.1246	1.19805	0.599023	−	0.800732i	$-0.295556\pi$
$719$	32.1246	1.19805	0.599023	+	0.800732i	$0.295556\pi$
$720$	3.42956	0.127812
$721$	0	0
$722$	1.74265	0.0648546
$723$	−1.69505	−0.0630395
$724$	−6.87539	−0.255522
$725$	19.8541	0.737363
$726$	1.83282	0.0680222
$727$	17.2918	0.641317	0.320659	−	0.947195i	$-0.396096\pi$
$727$	17.2918	0.641317	0.320659	+	0.947195i	$0.396096\pi$
$728$	0	0
$729$	−19.4377	−0.719915
$730$	−0.291796	−0.0107999
$731$	56.5066	2.08997
$732$	−4.24922	−0.157056
$733$	−1.27051	−0.0469274	−0.0234637	−	0.999725i	$-0.507469\pi$
$733$	−1.27051	−0.0469274	−0.0234637	+	0.999725i	$0.507469\pi$
$734$	−9.70820	−0.358336
$735$	0	0
$736$	18.5410	0.683431
$737$	−3.43769	−0.126629
$738$	5.70820	0.210122
$739$	−47.1246	−1.73351	−0.866753	−	0.498737i	$-0.833797\pi$
$739$	−47.1246	−1.73351	−0.866753	+	0.498737i	$0.833797\pi$
$740$	2.83282	0.104136
$741$	0	0
$742$	0	0
$743$	23.6738	0.868506	0.434253	−	0.900791i	$-0.357012\pi$
$743$	23.6738	0.868506	0.434253	+	0.900791i	$0.357012\pi$
$744$	4.89667	0.179521
$745$	1.85410	0.0679290
$746$	−0.167184	−0.00612105
$747$	−19.1459	−0.700512
$748$	−67.2492	−2.45888
$749$	0	0
$750$	0.549150	0.0200521
$751$	9.29180	0.339062	0.169531	−	0.985525i	$-0.445775\pi$
$751$	9.29180	0.339062	0.169531	+	0.985525i	$0.445775\pi$
$752$	−7.03444	−0.256520
$753$	−2.00000	−0.0728841
$754$	0	0
$755$	5.61803	0.204461
$756$	0	0
$757$	28.0000	1.01768	0.508839	−	0.860862i	$-0.330075\pi$
$757$	28.0000	1.01768	0.508839	+	0.860862i	$0.330075\pi$
$758$	−4.90983	−0.178333
$759$	−8.29180	−0.300973
$760$	−2.72949	−0.0990090
$761$	22.1459	0.802788	0.401394	−	0.915905i	$-0.368526\pi$
$761$	22.1459	0.802788	0.401394	+	0.915905i	$0.368526\pi$
$762$	−2.06386	−0.0747657
$763$	0	0
$764$	−43.7902	−1.58428
$765$	−8.14590	−0.294516
$766$	−9.54102	−0.344731
$767$	0	0
$768$	2.12461	0.0766653
$769$	−8.41641	−0.303503	−0.151752	−	0.988419i	$-0.548491\pi$
$769$	−8.41641	−0.303503	−0.151752	+	0.988419i	$0.548491\pi$
$770$	0	0
$771$	9.83282	0.354120
$772$	11.1246	0.400384
$773$	19.3607	0.696355	0.348178	−	0.937429i	$-0.386801\pi$
$773$	19.3607	0.696355	0.348178	+	0.937429i	$0.386801\pi$
$774$	8.24420	0.296332
$775$	42.2705	1.51840
$776$	17.8804	0.641869
$777$	0	0
$778$	9.12461	0.327133
$779$	25.4164	0.910637
$780$	0	0
$781$	−39.7082	−1.42087
$782$	−12.7639	−0.456437
$783$	9.14590	0.326848
$784$	0	0
$785$	3.11146	0.111053
$786$	−0.0475975	−0.00169775
$787$	−29.4164	−1.04858	−0.524291	−	0.851539i	$-0.675670\pi$
$787$	−29.4164	−1.04858	−0.524291	+	0.851539i	$0.675670\pi$
$788$	−14.4590	−0.515080
$789$	3.43769	0.122385
$790$	−0.583592	−0.0207633
$791$	0	0
$792$	−20.3951	−0.724709
$793$	0	0
$794$	9.70820	0.344531
$795$	−1.20163	−0.0426173
$796$	4.48027	0.158799
$797$	−14.1803	−0.502293	−0.251147	−	0.967949i	$-0.580808\pi$
$797$	−14.1803	−0.502293	−0.251147	+	0.967949i	$0.580808\pi$
$798$	0	0
$799$	16.7082	0.591094
$800$	−20.1246	−0.711512
$801$	45.9230	1.62261
$802$	−7.81153	−0.275835
$803$	−9.70820	−0.342595
$804$	−0.501553	−0.0176884
$805$	0	0
$806$	0	0
$807$	−5.24922	−0.184781
$808$	12.6049	0.443438
$809$	22.4164	0.788119	0.394059	−	0.919085i	$-0.371070\pi$
$809$	22.4164	0.788119	0.394059	+	0.919085i	$0.371070\pi$
$810$	−1.12461	−0.0395148
$811$	−5.72949	−0.201190	−0.100595	−	0.994927i	$-0.532075\pi$
$811$	−5.72949	−0.201190	−0.100595	+	0.994927i	$0.532075\pi$
$812$	0	0
$813$	−7.03444	−0.246709
$814$	−7.41641	−0.259945
$815$	−3.70820	−0.129893
$816$	−8.97871	−0.314318
$817$	36.7082	1.28426
$818$	−13.2016	−0.461584
$819$	0	0
$820$	−3.70820	−0.129496
$821$	37.3607	1.30390	0.651948	−	0.758263i	$-0.273952\pi$
$821$	37.3607	1.30390	0.651948	+	0.758263i	$0.273952\pi$
$822$	−0.0557281	−0.00194374
$823$	−11.5836	−0.403779	−0.201889	−	0.979408i	$-0.564708\pi$
$823$	−11.5836	−0.403779	−0.201889	+	0.979408i	$0.564708\pi$
$824$	6.93112	0.241457
$825$	9.00000	0.313340
$826$	0	0
$827$	−30.9787	−1.07724	−0.538618	−	0.842550i	$-0.681053\pi$
$827$	−30.9787	−1.07724	−0.538618	+	0.842550i	$0.681053\pi$
$828$	23.6656	0.822438
$829$	12.5623	0.436307	0.218153	−	0.975914i	$-0.429997\pi$
$829$	12.5623	0.436307	0.218153	+	0.975914i	$0.429997\pi$
$830$	−0.978714	−0.0339717
$831$	−1.90983	−0.0662513
$832$	0	0
$833$	0	0
$834$	2.27051	0.0786213
$835$	3.72949	0.129064
$836$	−43.6869	−1.51094
$837$	19.4721	0.673055
$838$	−2.27051	−0.0784335
$839$	28.7426	0.992306	0.496153	−	0.868235i	$-0.334745\pi$
$839$	28.7426	0.992306	0.496153	+	0.868235i	$0.334745\pi$
$840$	0	0
$841$	−12.2705	−0.423121
$842$	−9.70820	−0.334567
$843$	−0.832816	−0.0286837
$844$	16.1459	0.555765
$845$	0	0
$846$	2.43769	0.0838096
$847$	0	0
$848$	25.9098	0.889747
$849$	5.12461	0.175876
$850$	13.8541	0.475192
$851$	17.8885	0.613211
$852$	−5.79335	−0.198477
$853$	26.1246	0.894490	0.447245	−	0.894412i	$-0.352405\pi$
$853$	26.1246	0.894490	0.447245	+	0.894412i	$0.352405\pi$
$854$	0	0
$855$	−5.29180	−0.180976
$856$	8.27051	0.282680
$857$	−29.4508	−1.00602	−0.503011	−	0.864280i	$-0.667774\pi$
$857$	−29.4508	−1.00602	−0.503011	+	0.864280i	$0.667774\pi$
$858$	0	0
$859$	−36.2492	−1.23681	−0.618404	−	0.785861i	$-0.712220\pi$
$859$	−36.2492	−1.23681	−0.618404	+	0.785861i	$0.712220\pi$
$860$	−5.35565	−0.182626
$861$	0	0
$862$	−6.41641	−0.218544
$863$	−23.8885	−0.813175	−0.406588	−	0.913612i	$-0.633281\pi$
$863$	−23.8885	−0.813175	−0.406588	+	0.913612i	$0.633281\pi$
$864$	−9.27051	−0.315389
$865$	−3.43769	−0.116885
$866$	−0.381966	−0.0129797
$867$	14.8328	0.503749
$868$	0	0
$869$	−19.4164	−0.658657
$870$	0.227937	0.00772780
$871$	0	0
$872$	−15.7639	−0.533834
$873$	34.6656	1.17325
$874$	−8.29180	−0.280474
$875$	0	0
$876$	−1.41641	−0.0478560
$877$	−12.7082	−0.429126	−0.214563	−	0.976710i	$-0.568833\pi$
$877$	−12.7082	−0.429126	−0.214563	+	0.976710i	$0.568833\pi$
$878$	−3.11146	−0.105007
$879$	4.29180	0.144759
$880$	5.83282	0.196624
$881$	−12.5967	−0.424395	−0.212198	−	0.977227i	$-0.568062\pi$
$881$	−12.5967	−0.424395	−0.212198	+	0.977227i	$0.568062\pi$
$882$	0	0
$883$	29.0000	0.975928	0.487964	−	0.872864i	$-0.337740\pi$
$883$	29.0000	0.975928	0.487964	+	0.872864i	$0.337740\pi$
$884$	0	0
$885$	0.326238	0.0109664
$886$	−0.291796	−0.00980308
$887$	−23.3475	−0.783933	−0.391967	−	0.919979i	$-0.628205\pi$
$887$	−23.3475	−0.783933	−0.391967	+	0.919979i	$0.628205\pi$
$888$	−2.24922	−0.0754790
$889$	0	0
$890$	2.34752	0.0786892
$891$	−37.4164	−1.25350
$892$	−24.6049	−0.823832
$893$	10.8541	0.363219
$894$	−0.708204	−0.0236859
$895$	3.43769	0.114909
$896$	0	0
$897$	0	0
$898$	10.8754	0.362916
$899$	35.6180	1.18793
$900$	−25.6869	−0.856231
$901$	−61.5410	−2.05023
$902$	9.70820	0.323248
$903$	0	0
$904$	11.0000	0.365855
$905$	−1.41641	−0.0470830
$906$	−2.14590	−0.0712927
$907$	−24.0000	−0.796907	−0.398453	−	0.917189i	$-0.630453\pi$
$907$	−24.0000	−0.796907	−0.398453	+	0.917189i	$0.630453\pi$
$908$	−13.8541	−0.459765
$909$	24.4377	0.810547
$910$	0	0
$911$	37.6869	1.24862	0.624312	−	0.781175i	$-0.285380\pi$
$911$	37.6869	1.24862	0.624312	+	0.781175i	$0.285380\pi$
$912$	−5.83282	−0.193144
$913$	−32.5623	−1.07766
$914$	−4.36068	−0.144238
$915$	−0.875388	−0.0289394
$916$	50.2918	1.66169
$917$	0	0
$918$	6.38197	0.210636
$919$	−30.0000	−0.989609	−0.494804	−	0.869004i	$-0.664760\pi$
$919$	−30.0000	−0.989609	−0.494804	+	0.869004i	$0.664760\pi$
$920$	2.51471	0.0829075
$921$	−0.708204	−0.0233361
$922$	−14.9787	−0.493298
$923$	0	0
$924$	0	0
$925$	−19.4164	−0.638408
$926$	−2.56231	−0.0842026
$927$	13.4377	0.441352
$928$	−16.9574	−0.556655
$929$	47.0689	1.54428	0.772140	−	0.635452i	$-0.219186\pi$
$929$	47.0689	1.54428	0.772140	+	0.635452i	$0.219186\pi$
$930$	0.485292	0.0159133
$931$	0	0
$932$	−0.708204	−0.0231980
$933$	4.70820	0.154140
$934$	−12.8541	−0.420599
$935$	−13.8541	−0.453078
$936$	0	0
$937$	56.1246	1.83351	0.916756	−	0.399449i	$-0.130798\pi$
$937$	56.1246	1.83351	0.916756	+	0.399449i	$0.130798\pi$
$938$	0	0
$939$	5.77709	0.188528
$940$	−1.58359	−0.0516511
$941$	−51.6525	−1.68382	−0.841911	−	0.539616i	$-0.818569\pi$
$941$	−51.6525	−1.68382	−0.841911	+	0.539616i	$0.818569\pi$
$942$	−1.18847	−0.0387225
$943$	−23.4164	−0.762543
$944$	−7.03444	−0.228952
$945$	0	0
$946$	14.0213	0.455871
$947$	45.8673	1.49049	0.745243	−	0.666793i	$-0.232334\pi$
$947$	45.8673	1.49049	0.745243	+	0.666793i	$0.232334\pi$
$948$	−2.83282	−0.0920056
$949$	0	0
$950$	9.00000	0.291999
$951$	8.31308	0.269570
$952$	0	0
$953$	−44.7771	−1.45047	−0.725236	−	0.688500i	$-0.758269\pi$
$953$	−44.7771	−1.45047	−0.725236	+	0.688500i	$0.758269\pi$
$954$	−8.97871	−0.290697
$955$	−9.02129	−0.291922
$956$	20.9361	0.677123
$957$	7.58359	0.245143
$958$	8.39512	0.271234
$959$	0	0
$960$	0.686918	0.0221702
$961$	44.8328	1.44622
$962$	0	0
$963$	16.0344	0.516703
$964$	8.22794	0.265004
$965$	2.29180	0.0737755
$966$	0	0
$967$	−39.0000	−1.25416	−0.627078	−	0.778957i	$-0.715749\pi$
$967$	−39.0000	−1.25416	−0.627078	+	0.778957i	$0.715749\pi$
$968$	−18.4934	−0.594401
$969$	13.8541	0.445058
$970$	1.77206	0.0568975
$971$	−58.4164	−1.87467	−0.937336	−	0.348427i	$-0.886716\pi$
$971$	−58.4164	−1.87467	−0.937336	+	0.348427i	$0.886716\pi$
$972$	−17.8967	−0.574036
$973$	0	0
$974$	−6.48529	−0.207802
$975$	0	0
$976$	18.8754	0.604186
$977$	−31.4721	−1.00688	−0.503441	−	0.864029i	$-0.667933\pi$
$977$	−31.4721	−1.00688	−0.503441	+	0.864029i	$0.667933\pi$
$978$	1.41641	0.0452917
$979$	78.1033	2.49619
$980$	0	0
$981$	−30.5623	−0.975779
$982$	5.58359	0.178180
$983$	−20.6180	−0.657613	−0.328807	−	0.944397i	$-0.606646\pi$
$983$	−20.6180	−0.657613	−0.328807	+	0.944397i	$0.606646\pi$
$984$	2.94427	0.0938600
$985$	−2.97871	−0.0949097
$986$	11.6738	0.371768
$987$	0	0
$988$	0	0
$989$	−33.8197	−1.07540
$990$	−2.02129	−0.0642407
$991$	−22.8541	−0.725984	−0.362992	−	0.931792i	$-0.618245\pi$
$991$	−22.8541	−0.725984	−0.362992	+	0.931792i	$0.618245\pi$
$992$	−36.1033	−1.14628
$993$	−6.43769	−0.204294
$994$	0	0
$995$	0.922986	0.0292606
$996$	−4.75078	−0.150534
$997$	−49.0000	−1.55185	−0.775923	−	0.630828i	$-0.782715\pi$
$997$	−49.0000	−1.55185	−0.775923	+	0.630828i	$0.782715\pi$
$998$	3.11146	0.0984914
$999$	−8.94427	−0.282984

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8281.2.a.bb.1.1		2
7.6	odd	2		1183.2.a.g.1.1		2
13.3	even	3		637.2.f.c.295.2		4
13.9	even	3		637.2.f.c.393.2		4
13.12	even	2		8281.2.a.n.1.2		2
91.3	odd	6		637.2.g.b.373.2		4
91.9	even	3		637.2.g.c.263.2		4
91.16	even	3		637.2.h.f.165.1		4
91.34	even	4		1183.2.c.c.337.3		4
91.48	odd	6		91.2.f.a.29.2	yes	4
91.55	odd	6		91.2.f.a.22.2	✓	4
91.61	odd	6		637.2.g.b.263.2		4
91.68	odd	6		637.2.h.g.165.1		4
91.74	even	3		637.2.h.f.471.1		4
91.81	even	3		637.2.g.c.373.2		4
91.83	even	4		1183.2.c.c.337.2		4
91.87	odd	6		637.2.h.g.471.1		4
91.90	odd	2		1183.2.a.c.1.2		2
273.146	even	6		819.2.o.c.568.1		4
273.230	even	6		819.2.o.c.757.1		4
364.55	even	6		1456.2.s.h.113.2		4
364.139	even	6		1456.2.s.h.1121.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.a.22.2	✓	4	91.55	odd	6
91.2.f.a.29.2	yes	4	91.48	odd	6
637.2.f.c.295.2		4	13.3	even	3
637.2.f.c.393.2		4	13.9	even	3
637.2.g.b.263.2		4	91.61	odd	6
637.2.g.b.373.2		4	91.3	odd	6
637.2.g.c.263.2		4	91.9	even	3
637.2.g.c.373.2		4	91.81	even	3
637.2.h.f.165.1		4	91.16	even	3
637.2.h.f.471.1		4	91.74	even	3
637.2.h.g.165.1		4	91.68	odd	6
637.2.h.g.471.1		4	91.87	odd	6
819.2.o.c.568.1		4	273.146	even	6
819.2.o.c.757.1		4	273.230	even	6
1183.2.a.c.1.2		2	91.90	odd	2
1183.2.a.g.1.1		2	7.6	odd	2
1183.2.c.c.337.2		4	91.83	even	4
1183.2.c.c.337.3		4	91.34	even	4
1456.2.s.h.113.2		4	364.55	even	6
1456.2.s.h.1121.2		4	364.139	even	6
8281.2.a.n.1.2		2	13.12	even	2
8281.2.a.bb.1.1		2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8281 = 7^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8281.a (trivial)

\(f(q)\)	\(=\)	\(q+0.381966 q^{2} +0.381966 q^{3} -1.85410 q^{4} -0.381966 q^{5} +0.145898 q^{6} -1.47214 q^{8} -2.85410 q^{9} +O(q^{10})\)	\(q+0.381966 q^{2} +0.381966 q^{3} -1.85410 q^{4} -0.381966 q^{5} +0.145898 q^{6} -1.47214 q^{8} -2.85410 q^{9} -0.145898 q^{10} -4.85410 q^{11} -0.708204 q^{12} -0.145898 q^{15} +3.14590 q^{16} -7.47214 q^{17} -1.09017 q^{18} -4.85410 q^{19} +0.708204 q^{20} -1.85410 q^{22} +4.47214 q^{23} -0.562306 q^{24} -4.85410 q^{25} -2.23607 q^{27} -4.09017 q^{29} -0.0557281 q^{30} -8.70820 q^{31} +4.14590 q^{32} -1.85410 q^{33} -2.85410 q^{34} +5.29180 q^{36} +4.00000 q^{37} -1.85410 q^{38} +0.562306 q^{40} -5.23607 q^{41} -7.56231 q^{43} +9.00000 q^{44} +1.09017 q^{45} +1.70820 q^{46} -2.23607 q^{47} +1.20163 q^{48} -1.85410 q^{50} -2.85410 q^{51} +8.23607 q^{53} -0.854102 q^{54} +1.85410 q^{55} -1.85410 q^{57} -1.56231 q^{58} -2.23607 q^{59} +0.270510 q^{60} +6.00000 q^{61} -3.32624 q^{62} -4.70820 q^{64} -0.708204 q^{66} +0.708204 q^{67} +13.8541 q^{68} +1.70820 q^{69} +8.18034 q^{71} +4.20163 q^{72} +2.00000 q^{73} +1.52786 q^{74} -1.85410 q^{75} +9.00000 q^{76} +4.00000 q^{79} -1.20163 q^{80} +7.70820 q^{81} -2.00000 q^{82} +6.70820 q^{83} +2.85410 q^{85} -2.88854 q^{86} -1.56231 q^{87} +7.14590 q^{88} -16.0902 q^{89} +0.416408 q^{90} -8.29180 q^{92} -3.32624 q^{93} -0.854102 q^{94} +1.85410 q^{95} +1.58359 q^{96} -12.1459 q^{97} +13.8541 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 7 q^{6} + 6 q^{8} + q^{9}+O(q^{10}) \) 2 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 7 * q^6 + 6 * q^8 + q^9	\( 2 q + 3 q^{2} + 3 q^{3} + 3 q^{4} - 3 q^{5} + 7 q^{6} + 6 q^{8} + q^{9} - 7 q^{10} - 3 q^{11} + 12 q^{12} - 7 q^{15} + 13 q^{16} - 6 q^{17} + 9 q^{18} - 3 q^{19} - 12 q^{20} + 3 q^{22} + 19 q^{24} - 3 q^{25} + 3 q^{29} - 18 q^{30} - 4 q^{31} + 15 q^{32} + 3 q^{33} + q^{34} + 24 q^{36} + 8 q^{37} + 3 q^{38} - 19 q^{40} - 6 q^{41} + 5 q^{43} + 18 q^{44} - 9 q^{45} - 10 q^{46} + 27 q^{48} + 3 q^{50} + q^{51} + 12 q^{53} + 5 q^{54} - 3 q^{55} + 3 q^{57} + 17 q^{58} - 33 q^{60} + 12 q^{61} + 9 q^{62} + 4 q^{64} + 12 q^{66} - 12 q^{67} + 21 q^{68} - 10 q^{69} - 6 q^{71} + 33 q^{72} + 4 q^{73} + 12 q^{74} + 3 q^{75} + 18 q^{76} + 8 q^{79} - 27 q^{80} + 2 q^{81} - 4 q^{82} - q^{85} + 30 q^{86} + 17 q^{87} + 21 q^{88} - 21 q^{89} - 26 q^{90} - 30 q^{92} + 9 q^{93} + 5 q^{94} - 3 q^{95} + 30 q^{96} - 31 q^{97} + 21 q^{99}+O(q^{100}) \) 2 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 - 3 * q^5 + 7 * q^6 + 6 * q^8 + q^9 - 7 * q^10 - 3 * q^11 + 12 * q^12 - 7 * q^15 + 13 * q^16 - 6 * q^17 + 9 * q^18 - 3 * q^19 - 12 * q^20 + 3 * q^22 + 19 * q^24 - 3 * q^25 + 3 * q^29 - 18 * q^30 - 4 * q^31 + 15 * q^32 + 3 * q^33 + q^34 + 24 * q^36 + 8 * q^37 + 3 * q^38 - 19 * q^40 - 6 * q^41 + 5 * q^43 + 18 * q^44 - 9 * q^45 - 10 * q^46 + 27 * q^48 + 3 * q^50 + q^51 + 12 * q^53 + 5 * q^54 - 3 * q^55 + 3 * q^57 + 17 * q^58 - 33 * q^60 + 12 * q^61 + 9 * q^62 + 4 * q^64 + 12 * q^66 - 12 * q^67 + 21 * q^68 - 10 * q^69 - 6 * q^71 + 33 * q^72 + 4 * q^73 + 12 * q^74 + 3 * q^75 + 18 * q^76 + 8 * q^79 - 27 * q^80 + 2 * q^81 - 4 * q^82 - q^85 + 30 * q^86 + 17 * q^87 + 21 * q^88 - 21 * q^89 - 26 * q^90 - 30 * q^92 + 9 * q^93 + 5 * q^94 - 3 * q^95 + 30 * q^96 - 31 * q^97 + 21 * q^99

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