LMFDB - Embedded newform 8281.2.a.bt.1.4

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:	$4$
Coefficient field:	4.4.27004.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 6x^{2} + 3x + 1 $ x^4 - x^3 - 6x^2 + 3x + 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			1.4
Root			$2.74108$ 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)

$f(q)$	$=$	$q+2.74108 q^{2} -1.36482 q^{3} +5.51353 q^{4} +0.741082 q^{5} -3.74108 q^{6} +9.63087 q^{8} -1.13727 q^{9} +O(q^{10})$	\(q+2.74108 q^{2} -1.36482 q^{3} +5.51353 q^{4} +0.741082 q^{5} -3.74108 q^{6} +9.63087 q^{8} -1.13727 q^{9} +2.03137 q^{10} +1.36482 q^{11} -7.52497 q^{12} -1.01144 q^{15} +15.3720 q^{16} +4.14871 q^{17} -3.11734 q^{18} +7.26606 q^{19} +4.08598 q^{20} +3.74108 q^{22} -2.33345 q^{23} -13.1444 q^{24} -4.45080 q^{25} +5.64662 q^{27} -0.407629 q^{29} -2.77245 q^{30} -2.77245 q^{31} +22.8740 q^{32} -1.86273 q^{33} +11.3720 q^{34} -6.27036 q^{36} +6.10590 q^{37} +19.9169 q^{38} +7.13727 q^{40} +1.25461 q^{41} -1.74108 q^{43} +7.52497 q^{44} -0.842809 q^{45} -6.39619 q^{46} -5.85843 q^{47} -20.9799 q^{48} -12.2000 q^{50} -5.66224 q^{51} +4.56778 q^{53} +15.4779 q^{54} +1.01144 q^{55} -9.91685 q^{57} -1.11734 q^{58} -10.9843 q^{59} -5.57662 q^{60} -6.52497 q^{61} -7.59951 q^{62} +31.9557 q^{64} -5.10590 q^{66} +13.7597 q^{67} +22.8740 q^{68} +3.18474 q^{69} +4.81526 q^{71} -10.9529 q^{72} +6.06987 q^{73} +16.7368 q^{74} +6.07453 q^{75} +40.0616 q^{76} -9.12582 q^{79} +11.3919 q^{80} -4.29482 q^{81} +3.43900 q^{82} +11.7368 q^{83} +3.07453 q^{85} -4.77245 q^{86} +0.556340 q^{87} +13.1444 q^{88} -1.76101 q^{89} -2.31021 q^{90} -12.8656 q^{92} +3.78389 q^{93} -16.0584 q^{94} +5.38474 q^{95} -31.2189 q^{96} +9.53381 q^{97} -1.55217 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - q^{3} + 5 q^{4} - 7 q^{5} - 5 q^{6} + 6 q^{8} + 7 q^{9}+O(q^{10}) $ 4 * q + q^2 - q^3 + 5 * q^4 - 7 * q^5 - 5 * q^6 + 6 * q^8 + 7 * q^9	$ 4 q + q^{2} - q^{3} + 5 q^{4} - 7 q^{5} - 5 q^{6} + 6 q^{8} + 7 q^{9} + 11 q^{10} + q^{11} - 12 q^{12} - 3 q^{15} + 19 q^{16} + 4 q^{17} + 3 q^{18} + q^{19} - 2 q^{20} + 5 q^{22} - 2 q^{23} - 3 q^{24} + 5 q^{25} + 26 q^{27} + q^{29} - 4 q^{30} - 4 q^{31} + 33 q^{32} - 19 q^{33} + 3 q^{34} - 34 q^{36} + 10 q^{37} + 23 q^{38} + 17 q^{40} - 22 q^{41} + 3 q^{43} + 12 q^{44} - 11 q^{45} - 24 q^{46} + 2 q^{47} - 11 q^{48} - 43 q^{50} + 7 q^{51} + 2 q^{53} + 5 q^{54} + 3 q^{55} + 17 q^{57} + 11 q^{58} - 8 q^{59} + 11 q^{60} - 8 q^{61} + 5 q^{62} + 14 q^{64} - 6 q^{66} + 6 q^{67} + 33 q^{68} + 18 q^{69} + 14 q^{71} - 5 q^{72} - 8 q^{73} + 20 q^{74} + 7 q^{75} + 32 q^{76} - 26 q^{79} + 7 q^{80} + 24 q^{81} + 14 q^{82} - 5 q^{85} - 12 q^{86} - 13 q^{87} + 3 q^{88} - q^{89} - 26 q^{90} + 12 q^{92} + 7 q^{93} - 33 q^{94} + 21 q^{95} - 58 q^{96} + 3 q^{97} - 23 q^{99}+O(q^{100}) $ 4 * q + q^2 - q^3 + 5 * q^4 - 7 * q^5 - 5 * q^6 + 6 * q^8 + 7 * q^9 + 11 * q^10 + q^11 - 12 * q^12 - 3 * q^15 + 19 * q^16 + 4 * q^17 + 3 * q^18 + q^19 - 2 * q^20 + 5 * q^22 - 2 * q^23 - 3 * q^24 + 5 * q^25 + 26 * q^27 + q^29 - 4 * q^30 - 4 * q^31 + 33 * q^32 - 19 * q^33 + 3 * q^34 - 34 * q^36 + 10 * q^37 + 23 * q^38 + 17 * q^40 - 22 * q^41 + 3 * q^43 + 12 * q^44 - 11 * q^45 - 24 * q^46 + 2 * q^47 - 11 * q^48 - 43 * q^50 + 7 * q^51 + 2 * q^53 + 5 * q^54 + 3 * q^55 + 17 * q^57 + 11 * q^58 - 8 * q^59 + 11 * q^60 - 8 * q^61 + 5 * q^62 + 14 * q^64 - 6 * q^66 + 6 * q^67 + 33 * q^68 + 18 * q^69 + 14 * q^71 - 5 * q^72 - 8 * q^73 + 20 * q^74 + 7 * q^75 + 32 * q^76 - 26 * q^79 + 7 * q^80 + 24 * q^81 + 14 * q^82 - 5 * q^85 - 12 * q^86 - 13 * q^87 + 3 * q^88 - q^89 - 26 * q^90 + 12 * q^92 + 7 * q^93 - 33 * q^94 + 21 * q^95 - 58 * q^96 + 3 * q^97 - 23 * 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 $

$2$	2.74108	1.93824	0.969119	−	0.246594i	$-0.0793115\pi$
$2$	2.74108	1.93824	0.969119	+	0.246594i	$0.0793115\pi$
$3$	−1.36482	−0.787979	−0.393989	−	0.919115i	$-0.628905\pi$
$3$	−1.36482	−0.787979	−0.393989	+	0.919115i	$0.628905\pi$
$4$	5.51353	2.75677
$5$	0.741082	0.331422	0.165711	−	0.986174i	$-0.447008\pi$
$5$	0.741082	0.331422	0.165711	+	0.986174i	$0.447008\pi$
$6$	−3.74108	−1.52729
$7$	0	0
$7$	0	0
$8$	9.63087	3.40503
$9$	−1.13727	−0.379089
$10$	2.03137	0.642374
$11$	1.36482	0.411509	0.205754	−	0.978604i	$-0.434035\pi$
$11$	1.36482	0.411509	0.205754	+	0.978604i	$0.434035\pi$
$12$	−7.52497	−2.17227
$13$	0	0
$13$	0	0
$14$	0	0
$15$	−1.01144	−0.261153
$16$	15.3720	3.84299
$17$	4.14871	1.00621	0.503105	−	0.864225i	$-0.332191\pi$
$17$	4.14871	1.00621	0.503105	+	0.864225i	$0.332191\pi$
$18$	−3.11734	−0.734765
$19$	7.26606	1.66695	0.833474	−	0.552559i	$-0.186349\pi$
$19$	7.26606	1.66695	0.833474	+	0.552559i	$0.186349\pi$
$20$	4.08598	0.913652
$21$	0	0
$22$	3.74108	0.797601
$23$	−2.33345	−0.486559	−0.243279	−	0.969956i	$-0.578223\pi$
$23$	−2.33345	−0.486559	−0.243279	+	0.969956i	$0.578223\pi$
$24$	−13.1444	−2.68309
$25$	−4.45080	−0.890159
$26$	0	0
$27$	5.64662	1.08669
$28$	0	0
$29$	−0.407629	−0.0756948	−0.0378474	−	0.999284i	$-0.512050\pi$
$29$	−0.407629	−0.0756948	−0.0378474	+	0.999284i	$0.512050\pi$
$30$	−2.77245	−0.506178
$31$	−2.77245	−0.497946	−0.248973	−	0.968510i	$-0.580093\pi$
$31$	−2.77245	−0.497946	−0.248973	+	0.968510i	$0.580093\pi$
$32$	22.8740	4.04360
$33$	−1.86273	−0.324260
$34$	11.3720	1.95027
$35$	0	0
$36$	−6.27036	−1.04506
$37$	6.10590	1.00380	0.501902	−	0.864924i	$-0.332634\pi$
$37$	6.10590	1.00380	0.501902	+	0.864924i	$0.332634\pi$
$38$	19.9169	3.23094
$39$	0	0
$40$	7.13727	1.12850
$41$	1.25461	0.195938	0.0979688	−	0.995189i	$-0.468765\pi$
$41$	1.25461	0.195938	0.0979688	+	0.995189i	$0.468765\pi$
$42$	0	0
$43$	−1.74108	−0.265513	−0.132756	−	0.991149i	$-0.542383\pi$
$43$	−1.74108	−0.265513	−0.132756	+	0.991149i	$0.542383\pi$
$44$	7.52497	1.13443
$45$	−0.842809	−0.125639
$46$	−6.39619	−0.943066
$47$	−5.85843	−0.854539	−0.427270	−	0.904124i	$-0.640525\pi$
$47$	−5.85843	−0.854539	−0.427270	+	0.904124i	$0.640525\pi$
$48$	−20.9799	−3.02819
$49$	0	0
$50$	−12.2000	−1.72534
$51$	−5.66224	−0.792872
$52$	0	0
$53$	4.56778	0.627433	0.313717	−	0.949517i	$-0.398426\pi$
$53$	4.56778	0.627433	0.313717	+	0.949517i	$0.398426\pi$
$54$	15.4779	2.10627
$55$	1.01144	0.136383
$56$	0	0
$57$	−9.91685	−1.31352
$58$	−1.11734	−0.146715
$59$	−10.9843	−1.43003	−0.715014	−	0.699110i	$-0.753580\pi$
$59$	−10.9843	−1.43003	−0.715014	+	0.699110i	$0.753580\pi$
$60$	−5.57662	−0.719939
$61$	−6.52497	−0.835437	−0.417719	−	0.908576i	$-0.637170\pi$
$61$	−6.52497	−0.835437	−0.417719	+	0.908576i	$0.637170\pi$
$62$	−7.59951	−0.965139
$63$	0	0
$64$	31.9557	3.99446
$65$	0	0
$66$	−5.10590	−0.628493
$67$	13.7597	1.68101	0.840505	−	0.541804i	$-0.182258\pi$
$67$	13.7597	1.68101	0.840505	+	0.541804i	$0.182258\pi$
$68$	22.8740	2.77389
$69$	3.18474	0.383398
$70$	0	0
$71$	4.81526	0.571466	0.285733	−	0.958309i	$-0.407763\pi$
$71$	4.81526	0.571466	0.285733	+	0.958309i	$0.407763\pi$
$72$	−10.9529	−1.29081
$73$	6.06987	0.710425	0.355212	−	0.934786i	$-0.384409\pi$
$73$	6.06987	0.710425	0.355212	+	0.934786i	$0.384409\pi$
$74$	16.7368	1.94561
$75$	6.07453	0.701427
$76$	40.0616	4.59538
$77$	0	0
$78$	0	0
$79$	−9.12582	−1.02674	−0.513368	−	0.858169i	$-0.671602\pi$
$79$	−9.12582	−1.02674	−0.513368	+	0.858169i	$0.671602\pi$
$80$	11.3919	1.27365
$81$	−4.29482	−0.477202
$82$	3.43900	0.379774
$83$	11.7368	1.28828	0.644139	−	0.764908i	$-0.277216\pi$
$83$	11.7368	1.28828	0.644139	+	0.764908i	$0.277216\pi$
$84$	0	0
$85$	3.07453	0.333480
$86$	−4.77245	−0.514626
$87$	0.556340	0.0596459
$88$	13.1444	1.40120
$89$	−1.76101	−0.186666	−0.0933331	−	0.995635i	$-0.529752\pi$
$89$	−1.76101	−0.186666	−0.0933331	+	0.995635i	$0.529752\pi$
$90$	−2.31021	−0.243517
$91$	0	0
$92$	−12.8656	−1.34133
$93$	3.78389	0.392371
$94$	−16.0584	−1.65630
$95$	5.38474	0.552463
$96$	−31.2189	−3.18627
$97$	9.53381	0.968012	0.484006	−	0.875065i	$-0.339181\pi$
$97$	9.53381	0.968012	0.484006	+	0.875065i	$0.339181\pi$
$98$	0	0
$99$	−1.55217	−0.155998
$100$	−24.5396	−2.45396
$101$	7.49361	0.745642	0.372821	−	0.927903i	$-0.378391\pi$
$101$	7.49361	0.745642	0.372821	+	0.927903i	$0.378391\pi$
$102$	−15.5207	−1.53678
$103$	−2.80848	−0.276728	−0.138364	−	0.990381i	$-0.544184\pi$
$103$	−2.80848	−0.276728	−0.138364	+	0.990381i	$0.544184\pi$
$104$	0	0
$105$	0	0
$106$	12.5207	1.21611
$107$	1.48647	0.143702	0.0718512	−	0.997415i	$-0.477109\pi$
$107$	1.48647	0.143702	0.0718512	+	0.997415i	$0.477109\pi$
$108$	31.1328	2.99576
$109$	−2.87121	−0.275012	−0.137506	−	0.990501i	$-0.543909\pi$
$109$	−2.87121	−0.275012	−0.137506	+	0.990501i	$0.543909\pi$
$110$	2.77245	0.264343
$111$	−8.33345	−0.790976
$112$	0	0
$113$	−12.4194	−1.16832	−0.584161	−	0.811638i	$-0.698576\pi$
$113$	−12.4194	−1.16832	−0.584161	+	0.811638i	$0.698576\pi$
$114$	−27.1829	−2.54591
$115$	−1.72928	−0.161256
$116$	−2.24747	−0.208673
$117$	0	0
$118$	−30.1087	−2.77173
$119$	0	0
$120$	−9.74108	−0.889235
$121$	−9.13727	−0.830661
$122$	−17.8855	−1.61928
$123$	−1.71232	−0.154395
$124$	−15.2860	−1.37272
$125$	−7.00382	−0.626440
$126$	0	0
$127$	5.43052	0.481880	0.240940	−	0.970540i	$-0.422544\pi$
$127$	5.43052	0.481880	0.240940	+	0.970540i	$0.422544\pi$
$128$	41.8452	3.69862
$129$	2.37626	0.209218
$130$	0	0
$131$	11.3220	0.989209	0.494604	−	0.869118i	$-0.335313\pi$
$131$	11.3220	0.989209	0.494604	+	0.869118i	$0.335313\pi$
$132$	−10.2702	−0.893909
$133$	0	0
$134$	37.7164	3.25820
$135$	4.18461	0.360154
$136$	39.9557	3.42617
$137$	13.9754	1.19400	0.597000	−	0.802241i	$-0.296359\pi$
$137$	13.9754	1.19400	0.597000	+	0.802241i	$0.296359\pi$
$138$	8.72964	0.743116
$139$	−10.4309	−0.884735	−0.442368	−	0.896834i	$-0.645861\pi$
$139$	−10.4309	−0.884735	−0.442368	+	0.896834i	$0.645861\pi$
$140$	0	0
$141$	7.99569	0.673359
$142$	13.1990	1.10764
$143$	0	0
$144$	−17.4820	−1.45684
$145$	−0.302087	−0.0250869
$146$	16.6380	1.37697
$147$	0	0
$148$	33.6651	2.76725
$149$	−8.16433	−0.668848	−0.334424	−	0.942423i	$-0.608542\pi$
$149$	−8.16433	−0.668848	−0.334424	+	0.942423i	$0.608542\pi$
$150$	16.6508	1.35953
$151$	2.46188	0.200345	0.100173	−	0.994970i	$-0.468061\pi$
$151$	2.46188	0.200345	0.100173	+	0.994970i	$0.468061\pi$
$152$	69.9785	5.67600
$153$	−4.71820	−0.381444
$154$	0	0
$155$	−2.05461	−0.165030
$156$	0	0
$157$	12.9198	1.03111	0.515557	−	0.856855i	$-0.327585\pi$
$157$	12.9198	1.03111	0.515557	+	0.856855i	$0.327585\pi$
$158$	−25.0146	−1.99006
$159$	−6.23420	−0.494404
$160$	16.9515	1.34014
$161$	0	0
$162$	−11.7724	−0.924931
$163$	6.02742	0.472104	0.236052	−	0.971740i	$-0.424146\pi$
$163$	6.02742	0.472104	0.236052	+	0.971740i	$0.424146\pi$
$164$	6.91734	0.540154
$165$	−1.38044	−0.107467
$166$	32.1715	2.49699
$167$	7.65116	0.592064	0.296032	−	0.955178i	$-0.404336\pi$
$167$	7.65116	0.592064	0.296032	+	0.955178i	$0.404336\pi$
$168$	0	0
$169$	0	0
$170$	8.42755	0.646364
$171$	−8.26345	−0.631922
$172$	−9.59951	−0.731956
$173$	0.164460	0.0125036	0.00625182	−	0.999980i	$-0.498010\pi$
$173$	0.164460	0.0125036	0.00625182	+	0.999980i	$0.498010\pi$
$174$	1.52497	0.115608
$175$	0	0
$176$	20.9799	1.58142
$177$	14.9915	1.12683
$178$	−4.82706	−0.361803
$179$	0.768633	0.0574503	0.0287252	−	0.999587i	$-0.490855\pi$
$179$	0.768633	0.0574503	0.0287252	+	0.999587i	$0.490855\pi$
$180$	−4.64685	−0.346356
$181$	9.92152	0.737461	0.368730	−	0.929536i	$-0.379793\pi$
$181$	9.92152	0.737461	0.368730	+	0.929536i	$0.379793\pi$
$182$	0	0
$183$	8.90541	0.658307
$184$	−22.4732	−1.65675
$185$	4.52497	0.332683
$186$	10.3720	0.760509
$187$	5.66224	0.414064
$188$	−32.3006	−2.35576
$189$	0	0
$190$	14.7600	1.07080
$191$	9.89693	0.716117	0.358058	−	0.933699i	$-0.383439\pi$
$191$	9.89693	0.716117	0.358058	+	0.933699i	$0.383439\pi$
$192$	−43.6138	−3.14755
$193$	−8.70075	−0.626293	−0.313147	−	0.949705i	$-0.601383\pi$
$193$	−8.70075	−0.626293	−0.313147	+	0.949705i	$0.601383\pi$
$194$	26.1330	1.87624
$195$	0	0
$196$	0	0
$197$	26.0186	1.85375	0.926874	−	0.375374i	$-0.122486\pi$
$197$	26.0186	1.85375	0.926874	+	0.375374i	$0.122486\pi$
$198$	−4.25461	−0.302362
$199$	−10.1330	−0.718307	−0.359153	−	0.933279i	$-0.616934\pi$
$199$	−10.1330	−0.718307	−0.359153	+	0.933279i	$0.616934\pi$
$200$	−42.8651	−3.03102
$201$	−18.7795	−1.32460
$202$	20.5406	1.44523
$203$	0	0
$204$	−31.2189	−2.18576
$205$	0.929771	0.0649380
$206$	−7.69827	−0.536364
$207$	2.65376	0.184449
$208$	0	0
$209$	9.91685	0.685963
$210$	0	0
$211$	16.6782	1.14818	0.574088	−	0.818794i	$-0.305357\pi$
$211$	16.6782	1.14818	0.574088	+	0.818794i	$0.305357\pi$
$212$	25.1846	1.72969
$213$	−6.57196	−0.450303
$214$	4.07453	0.278529
$215$	−1.29028	−0.0879967
$216$	54.3819	3.70022
$217$	0	0
$218$	−7.87023	−0.533039
$219$	−8.28428	−0.559800
$220$	5.57662	0.375976
$221$	0	0
$222$	−22.8427	−1.53310
$223$	1.07036	0.0716766	0.0358383	−	0.999358i	$-0.488590\pi$
$223$	1.07036	0.0716766	0.0358383	+	0.999358i	$0.488590\pi$
$224$	0	0
$225$	5.06175	0.337450
$226$	−34.0427	−2.26449
$227$	−24.4664	−1.62389	−0.811947	−	0.583732i	$-0.801592\pi$
$227$	−24.4664	−1.62389	−0.811947	+	0.583732i	$0.801592\pi$
$228$	−54.6769	−3.62106
$229$	4.72964	0.312543	0.156272	−	0.987714i	$-0.450052\pi$
$229$	4.72964	0.312543	0.156272	+	0.987714i	$0.450052\pi$
$230$	−4.74010	−0.312553
$231$	0	0
$232$	−3.92582	−0.257743
$233$	20.5507	1.34632	0.673160	−	0.739497i	$-0.264936\pi$
$233$	20.5507	1.34632	0.673160	+	0.739497i	$0.264936\pi$
$234$	0	0
$235$	−4.34157	−0.283213
$236$	−60.5620	−3.94225
$237$	12.4551	0.809046
$238$	0	0
$239$	−6.25461	−0.404577	−0.202289	−	0.979326i	$-0.564838\pi$
$239$	−6.25461	−0.404577	−0.202289	+	0.979326i	$0.564838\pi$
$240$	−15.5479	−1.00361
$241$	−12.1444	−0.782290	−0.391145	−	0.920329i	$-0.627921\pi$
$241$	−12.1444	−0.782290	−0.391145	+	0.920329i	$0.627921\pi$
$242$	−25.0460	−1.61002
$243$	−11.0782	−0.710668
$244$	−35.9756	−2.30310
$245$	0	0
$246$	−4.69361	−0.299254
$247$	0	0
$248$	−26.7011	−1.69552
$249$	−16.0186	−1.01514
$250$	−19.1980	−1.21419
$251$	6.31438	0.398560	0.199280	−	0.979943i	$-0.436140\pi$
$251$	6.31438	0.398560	0.199280	+	0.979943i	$0.436140\pi$
$252$	0	0
$253$	−3.18474	−0.200223
$254$	14.8855	0.933999
$255$	−4.19619	−0.262775
$256$	50.7896	3.17435
$257$	−24.3562	−1.51930	−0.759649	−	0.650333i	$-0.774629\pi$
$257$	−24.3562	−1.51930	−0.759649	+	0.650333i	$0.774629\pi$
$258$	6.51353	0.405515
$259$	0	0
$260$	0	0
$261$	0.463583	0.0286951
$262$	31.0346	1.91732
$263$	−9.57910	−0.590672	−0.295336	−	0.955393i	$-0.595432\pi$
$263$	−9.57910	−0.590672	−0.295336	+	0.955393i	$0.595432\pi$
$264$	−17.9397	−1.10411
$265$	3.38510	0.207945
$266$	0	0
$267$	2.40345	0.147089
$268$	75.8643	4.63415
$269$	−29.3990	−1.79249	−0.896245	−	0.443560i	$-0.853715\pi$
$269$	−29.3990	−1.79249	−0.896245	+	0.443560i	$0.853715\pi$
$270$	11.4704	0.698064
$271$	−0.300385	−0.0182471	−0.00912354	−	0.999958i	$-0.502904\pi$
$271$	−0.300385	−0.0182471	−0.00912354	+	0.999958i	$0.502904\pi$
$272$	63.7738	3.86686
$273$	0	0
$274$	38.3078	2.31426
$275$	−6.07453	−0.366308
$276$	17.5592	1.05694
$277$	−32.7710	−1.96902	−0.984509	−	0.175337i	$-0.943899\pi$
$277$	−32.7710	−1.96902	−0.984509	+	0.175337i	$0.943899\pi$
$278$	−28.5919	−1.71483
$279$	3.15302	0.188766
$280$	0	0
$281$	−4.29482	−0.256207	−0.128104	−	0.991761i	$-0.540889\pi$
$281$	−4.29482	−0.256207	−0.128104	+	0.991761i	$0.540889\pi$
$282$	21.9169	1.30513
$283$	21.1003	1.25428	0.627140	−	0.778907i	$-0.284225\pi$
$283$	21.1003	1.25428	0.627140	+	0.778907i	$0.284225\pi$
$284$	26.5491	1.57540
$285$	−7.34920	−0.435329
$286$	0	0
$287$	0	0
$288$	−26.0139	−1.53288
$289$	0.211803	0.0124590
$290$	−0.828044	−0.0486244
$291$	−13.0119	−0.762773
$292$	33.4664	1.95847
$293$	17.7638	1.03777	0.518887	−	0.854843i	$-0.326346\pi$
$293$	17.7638	1.03777	0.518887	+	0.854843i	$0.326346\pi$
$294$	0	0
$295$	−8.14023	−0.473943
$296$	58.8052	3.41798
$297$	7.70662	0.447184
$298$	−22.3791	−1.29639
$299$	0	0
$300$	33.4921	1.93367
$301$	0	0
$302$	6.74822	0.388316
$303$	−10.2274	−0.587550
$304$	111.693	6.40606
$305$	−4.83554	−0.276882
$306$	−12.9330	−0.739328
$307$	18.0156	1.02821	0.514103	−	0.857729i	$-0.328125\pi$
$307$	18.0156	1.02821	0.514103	+	0.857729i	$0.328125\pi$
$308$	0	0
$309$	3.83307	0.218056
$310$	−5.63186	−0.319868
$311$	−17.2545	−0.978412	−0.489206	−	0.872168i	$-0.662713\pi$
$311$	−17.2545	−0.978412	−0.489206	+	0.872168i	$0.662713\pi$
$312$	0	0
$313$	−6.81526	−0.385221	−0.192611	−	0.981275i	$-0.561695\pi$
$313$	−6.81526	−0.385221	−0.192611	+	0.981275i	$0.561695\pi$
$314$	35.4143	1.99854
$315$	0	0
$316$	−50.3155	−2.83047
$317$	25.0770	1.40847	0.704233	−	0.709969i	$-0.251291\pi$
$317$	25.0770	1.40847	0.704233	+	0.709969i	$0.251291\pi$
$318$	−17.0885	−0.958273
$319$	−0.556340	−0.0311491
$320$	23.6818	1.32385
$321$	−2.02876	−0.113234
$322$	0	0
$323$	30.1448	1.67730
$324$	−23.6796	−1.31553
$325$	0	0
$326$	16.5217	0.915050
$327$	3.91869	0.216704
$328$	12.0830	0.667173
$329$	0	0
$330$	−3.78389	−0.208296
$331$	2.99534	0.164639	0.0823193	−	0.996606i	$-0.473767\pi$
$331$	2.99534	0.164639	0.0823193	+	0.996606i	$0.473767\pi$
$332$	64.7111	3.55148
$333$	−6.94405	−0.380531
$334$	20.9724	1.14756
$335$	10.1970	0.557124
$336$	0	0
$337$	−29.4888	−1.60636	−0.803179	−	0.595738i	$-0.796860\pi$
$337$	−29.4888	−1.60636	−0.803179	+	0.595738i	$0.796860\pi$
$338$	0	0
$339$	16.9503	0.920613
$340$	16.9515	0.919326
$341$	−3.78389	−0.204909
$342$	−22.6508	−1.22481
$343$	0	0
$344$	−16.7681	−0.904078
$345$	2.36015	0.127066
$346$	0.450797	0.0242350
$347$	−5.98686	−0.321391	−0.160696	−	0.987004i	$-0.551374\pi$
$347$	−5.98686	−0.321391	−0.160696	+	0.987004i	$0.551374\pi$
$348$	3.06740	0.164430
$349$	−30.3362	−1.62386	−0.811929	−	0.583757i	$-0.801582\pi$
$349$	−30.3362	−1.62386	−0.811929	+	0.583757i	$0.801582\pi$
$350$	0	0
$351$	0	0
$352$	31.2189	1.66398
$353$	−28.6063	−1.52256	−0.761280	−	0.648424i	$-0.775428\pi$
$353$	−28.6063	−1.52256	−0.761280	+	0.648424i	$0.775428\pi$
$354$	41.0930	2.18407
$355$	3.56850	0.189396
$356$	−9.70936	−0.514595
$357$	0	0
$358$	2.10689	0.111352
$359$	−23.4618	−1.23826	−0.619132	−	0.785287i	$-0.712515\pi$
$359$	−23.4618	−1.23826	−0.619132	+	0.785287i	$0.712515\pi$
$360$	−8.11699	−0.427803
$361$	33.7956	1.77871
$362$	27.1957	1.42937
$363$	12.4707	0.654543
$364$	0	0
$365$	4.49827	0.235450
$366$	24.4105	1.27596
$367$	−36.5197	−1.90631	−0.953156	−	0.302479i	$-0.902186\pi$
$367$	−36.5197	−1.90631	−0.953156	+	0.302479i	$0.902186\pi$
$368$	−35.8697	−1.86984
$369$	−1.42683	−0.0742778
$370$	12.4033	0.644818
$371$	0	0
$372$	20.8626	1.08168
$373$	−13.0498	−0.675694	−0.337847	−	0.941201i	$-0.609699\pi$
$373$	−13.0498	−0.675694	−0.337847	+	0.941201i	$0.609699\pi$
$374$	15.5207	0.802555
$375$	9.55894	0.493622
$376$	−56.4218	−2.90973
$377$	0	0
$378$	0	0
$379$	−30.6037	−1.57201	−0.786003	−	0.618223i	$-0.787853\pi$
$379$	−30.6037	−1.57201	−0.786003	+	0.618223i	$0.787853\pi$
$380$	29.6889	1.52301
$381$	−7.41167	−0.379711
$382$	27.1283	1.38800
$383$	−4.88598	−0.249662	−0.124831	−	0.992178i	$-0.539839\pi$
$383$	−4.88598	−0.249662	−0.124831	+	0.992178i	$0.539839\pi$
$384$	−57.1111	−2.91444
$385$	0	0
$386$	−23.8495	−1.21391
$387$	1.98008	0.100653
$388$	52.5650	2.66858
$389$	−1.85425	−0.0940143	−0.0470072	−	0.998895i	$-0.514968\pi$
$389$	−1.85425	−0.0940143	−0.0470072	+	0.998895i	$0.514968\pi$
$390$	0	0
$391$	−9.68082	−0.489580
$392$	0	0
$393$	−15.4525	−0.779475
$394$	71.3191	3.59300
$395$	−6.76298	−0.340283
$396$	−8.55791	−0.430051
$397$	21.5134	1.07973	0.539863	−	0.841753i	$-0.318476\pi$
$397$	21.5134	1.07973	0.539863	+	0.841753i	$0.318476\pi$
$398$	−27.7753	−1.39225
$399$	0	0
$400$	−68.4175	−3.42087
$401$	14.5653	0.727357	0.363678	−	0.931525i	$-0.381521\pi$
$401$	14.5653	0.727357	0.363678	+	0.931525i	$0.381521\pi$
$402$	−51.4760	−2.56739
$403$	0	0
$404$	41.3162	2.05556
$405$	−3.18281	−0.158155
$406$	0	0
$407$	8.33345	0.413074
$408$	−54.5323	−2.69975
$409$	−22.1290	−1.09421	−0.547105	−	0.837064i	$-0.684270\pi$
$409$	−22.1290	−1.09421	−0.547105	+	0.837064i	$0.684270\pi$
$410$	2.54858	0.125865
$411$	−19.0739	−0.940847
$412$	−15.4846	−0.762873
$413$	0	0
$414$	7.27418	0.357506
$415$	8.69791	0.426964
$416$	0	0
$417$	14.2363	0.697153
$418$	27.1829	1.32956
$419$	−3.37590	−0.164924	−0.0824618	−	0.996594i	$-0.526278\pi$
$419$	−3.37590	−0.164924	−0.0824618	+	0.996594i	$0.526278\pi$
$420$	0	0
$421$	25.1101	1.22379	0.611895	−	0.790939i	$-0.290407\pi$
$421$	25.1101	1.22379	0.611895	+	0.790939i	$0.290407\pi$
$422$	45.7164	2.22544
$423$	6.66260	0.323947
$424$	43.9917	2.13643
$425$	−18.4651	−0.895688
$426$	−18.0143	−0.872794
$427$	0	0
$428$	8.19570	0.396154
$429$	0	0
$430$	−3.53678	−0.170558
$431$	−10.7948	−0.519969	−0.259985	−	0.965613i	$-0.583718\pi$
$431$	−10.7948	−0.519969	−0.259985	+	0.965613i	$0.583718\pi$
$432$	86.7997	4.17615
$433$	14.5182	0.697700	0.348850	−	0.937179i	$-0.386572\pi$
$433$	14.5182	0.697700	0.348850	+	0.937179i	$0.386572\pi$
$434$	0	0
$435$	0.412294	0.0197680
$436$	−15.8305	−0.758144
$437$	−16.9550	−0.811068
$438$	−22.7079	−1.08502
$439$	14.4309	0.688748	0.344374	−	0.938833i	$-0.388091\pi$
$439$	14.4309	0.688748	0.344374	+	0.938833i	$0.388091\pi$
$440$	9.74108	0.464388
$441$	0	0
$442$	0	0
$443$	−30.2430	−1.43689	−0.718445	−	0.695584i	$-0.755146\pi$
$443$	−30.2430	−1.43689	−0.718445	+	0.695584i	$0.755146\pi$
$444$	−45.9467	−2.18054
$445$	−1.30505	−0.0618653
$446$	2.93395	0.138926
$447$	11.1428	0.527038
$448$	0	0
$449$	−31.2760	−1.47601	−0.738003	−	0.674797i	$-0.764231\pi$
$449$	−31.2760	−1.47601	−0.738003	+	0.674797i	$0.764231\pi$
$450$	13.8747	0.654058
$451$	1.71232	0.0806300
$452$	−68.4749	−3.22079
$453$	−3.36002	−0.157868
$454$	−67.0645	−3.14749
$455$	0	0
$456$	−95.5080	−4.47257
$457$	−20.6466	−0.965808	−0.482904	−	0.875673i	$-0.660418\pi$
$457$	−20.6466	−0.965808	−0.482904	+	0.875673i	$0.660418\pi$
$458$	12.9643	0.605783
$459$	23.4262	1.09344
$460$	−9.53444	−0.444545
$461$	27.2961	1.27131	0.635653	−	0.771975i	$-0.280731\pi$
$461$	27.2961	1.27131	0.635653	+	0.771975i	$0.280731\pi$
$462$	0	0
$463$	−5.65977	−0.263032	−0.131516	−	0.991314i	$-0.541984\pi$
$463$	−5.65977	−0.263032	−0.131516	+	0.991314i	$0.541984\pi$
$464$	−6.26606	−0.290894
$465$	2.80417	0.130040
$466$	56.3311	2.60949
$467$	−42.2145	−1.95345	−0.976727	−	0.214486i	$-0.931192\pi$
$467$	−42.2145	−1.95345	−0.976727	+	0.214486i	$0.931192\pi$
$468$	0	0
$469$	0	0
$470$	−11.9006	−0.548934
$471$	−17.6332	−0.812496
$472$	−105.788	−4.86929
$473$	−2.37626	−0.109261
$474$	34.1405	1.56812
$475$	−32.3397	−1.48385
$476$	0	0
$477$	−5.19479	−0.237853
$478$	−17.1444	−0.784167
$479$	32.5316	1.48641	0.743204	−	0.669065i	$-0.233305\pi$
$479$	32.5316	1.48641	0.743204	+	0.669065i	$0.233305\pi$
$480$	−23.1358	−1.05600
$481$	0	0
$482$	−33.2888	−1.51626
$483$	0	0
$484$	−50.3786	−2.28994
$485$	7.06534	0.320820
$486$	−30.3663	−1.37744
$487$	−26.8583	−1.21707	−0.608533	−	0.793529i	$-0.708242\pi$
$487$	−26.8583	−1.21707	−0.608533	+	0.793529i	$0.708242\pi$
$488$	−62.8412	−2.84469
$489$	−8.22634	−0.372008
$490$	0	0
$491$	43.6878	1.97160	0.985802	−	0.167912i	$-0.0537023\pi$
$491$	43.6878	1.97160	0.985802	+	0.167912i	$0.0537023\pi$
$492$	−9.44093	−0.425630
$493$	−1.69113	−0.0761649
$494$	0	0
$495$	−1.15028	−0.0517013
$496$	−42.6180	−1.91360
$497$	0	0
$498$	−43.9082	−1.96758
$499$	18.1020	0.810355	0.405177	−	0.914238i	$-0.367210\pi$
$499$	18.1020	0.810355	0.405177	+	0.914238i	$0.367210\pi$
$500$	−38.6158	−1.72695
$501$	−10.4424	−0.466534
$502$	17.3082	0.772505
$503$	28.4155	1.26698	0.633492	−	0.773749i	$-0.281621\pi$
$503$	28.4155	1.26698	0.633492	+	0.773749i	$0.281621\pi$
$504$	0	0
$505$	5.55338	0.247122
$506$	−8.72964	−0.388080
$507$	0	0
$508$	29.9413	1.32843
$509$	17.4791	0.774748	0.387374	−	0.921923i	$-0.373382\pi$
$509$	17.4791	0.774748	0.387374	+	0.921923i	$0.373382\pi$
$510$	−11.5021	−0.509321
$511$	0	0
$512$	55.5280	2.45402
$513$	41.0287	1.81146
$514$	−66.7624	−2.94476
$515$	−2.08131	−0.0917136
$516$	13.1016	0.576766
$517$	−7.99569	−0.351650
$518$	0	0
$519$	−0.224458	−0.00985260
$520$	0	0
$521$	−19.3087	−0.845931	−0.422966	−	0.906146i	$-0.639011\pi$
$521$	−19.3087	−0.845931	−0.422966	+	0.906146i	$0.639011\pi$
$522$	1.27072	0.0556179
$523$	10.0229	0.438270	0.219135	−	0.975695i	$-0.429676\pi$
$523$	10.0229	0.438270	0.219135	+	0.975695i	$0.429676\pi$
$524$	62.4242	2.72702
$525$	0	0
$526$	−26.2571	−1.14486
$527$	−11.5021	−0.501039
$528$	−28.6338	−1.24613
$529$	−17.5550	−0.763261
$530$	9.27884	0.403047
$531$	12.4920	0.542108
$532$	0	0
$533$	0	0
$534$	6.58807	0.285093
$535$	1.10160	0.0476261
$536$	132.518	5.72389
$537$	−1.04904	−0.0452696
$538$	−80.5851	−3.47427
$539$	0	0
$540$	23.0720	0.992860
$541$	−17.6153	−0.757339	−0.378670	−	0.925532i	$-0.623618\pi$
$541$	−17.6153	−0.757339	−0.378670	+	0.925532i	$0.623618\pi$
$542$	−0.823379	−0.0353672
$543$	−13.5411	−0.581103
$544$	94.8978	4.06871
$545$	−2.12780	−0.0911451
$546$	0	0
$547$	2.98425	0.127597	0.0637987	−	0.997963i	$-0.479678\pi$
$547$	2.98425	0.127597	0.0637987	+	0.997963i	$0.479678\pi$
$548$	77.0539	3.29158
$549$	7.42064	0.316705
$550$	−16.6508	−0.709992
$551$	−2.96185	−0.126179
$552$	30.6719	1.30548
$553$	0	0
$554$	−89.8279	−3.81642
$555$	−6.17577	−0.262147
$556$	−57.5109	−2.43901
$557$	−7.25596	−0.307445	−0.153722	−	0.988114i	$-0.549126\pi$
$557$	−7.25596	−0.307445	−0.153722	+	0.988114i	$0.549126\pi$
$558$	8.64268	0.365874
$559$	0	0
$560$	0	0
$561$	−7.72794	−0.326274
$562$	−11.7724	−0.496591
$563$	−4.27933	−0.180352	−0.0901762	−	0.995926i	$-0.528743\pi$
$563$	−4.27933	−0.180352	−0.0901762	+	0.995926i	$0.528743\pi$
$564$	44.0845	1.85629
$565$	−9.20382	−0.387207
$566$	57.8375	2.43109
$567$	0	0
$568$	46.3751	1.94586
$569$	−19.7626	−0.828492	−0.414246	−	0.910165i	$-0.635955\pi$
$569$	−19.7626	−0.828492	−0.414246	+	0.910165i	$0.635955\pi$
$570$	−20.1448	−0.843771
$571$	−19.9236	−0.833778	−0.416889	−	0.908957i	$-0.636880\pi$
$571$	−19.9236	−0.833778	−0.416889	+	0.908957i	$0.636880\pi$
$572$	0	0
$573$	−13.5075	−0.564285
$574$	0	0
$575$	10.3857	0.433115
$576$	−36.3422	−1.51426
$577$	−28.7300	−1.19605	−0.598023	−	0.801479i	$-0.704047\pi$
$577$	−28.7300	−1.19605	−0.598023	+	0.801479i	$0.704047\pi$
$578$	0.580569	0.0241485
$579$	11.8749	0.493506
$580$	−1.66556	−0.0691587
$581$	0	0
$582$	−35.6668	−1.47844
$583$	6.23420	0.258194
$584$	58.4582	2.41902
$585$	0	0
$586$	48.6921	2.01145
$587$	31.5388	1.30174	0.650872	−	0.759188i	$-0.274403\pi$
$587$	31.5388	1.30174	0.650872	+	0.759188i	$0.274403\pi$
$588$	0	0
$589$	−20.1448	−0.830051
$590$	−22.3130	−0.918613
$591$	−35.5107	−1.46071
$592$	93.8597	3.85761
$593$	−11.1181	−0.456564	−0.228282	−	0.973595i	$-0.573311\pi$
$593$	−11.1181	−0.456564	−0.228282	+	0.973595i	$0.573311\pi$
$594$	21.1245	0.866748
$595$	0	0
$596$	−45.0143	−1.84386
$597$	13.8297	0.566010
$598$	0	0
$599$	−7.29572	−0.298095	−0.149048	−	0.988830i	$-0.547621\pi$
$599$	−7.29572	−0.298095	−0.149048	+	0.988830i	$0.547621\pi$
$600$	58.5031	2.38838
$601$	1.17258	0.0478306	0.0239153	−	0.999714i	$-0.492387\pi$
$601$	1.17258	0.0478306	0.0239153	+	0.999714i	$0.492387\pi$
$602$	0	0
$603$	−15.6484	−0.637253
$604$	13.5737	0.552304
$605$	−6.77146	−0.275299
$606$	−28.0342	−1.13881
$607$	−0.633838	−0.0257267	−0.0128633	−	0.999917i	$-0.504095\pi$
$607$	−0.633838	−0.0257267	−0.0128633	+	0.999917i	$0.504095\pi$
$608$	166.204	6.74047
$609$	0	0
$610$	−13.2546	−0.536664
$611$	0	0
$612$	−26.0139	−1.05155
$613$	30.8550	1.24622	0.623110	−	0.782134i	$-0.285869\pi$
$613$	30.8550	1.24622	0.623110	+	0.782134i	$0.285869\pi$
$614$	49.3823	1.99291
$615$	−1.26897	−0.0511698
$616$	0	0
$617$	−33.8209	−1.36158	−0.680790	−	0.732479i	$-0.738363\pi$
$617$	−33.8209	−1.36158	−0.680790	+	0.732479i	$0.738363\pi$
$618$	10.5068	0.422644
$619$	−0.404797	−0.0162702	−0.00813509	−	0.999967i	$-0.502590\pi$
$619$	−0.404797	−0.0162702	−0.00813509	+	0.999967i	$0.502590\pi$
$620$	−11.3282	−0.454950
$621$	−13.1761	−0.528740
$622$	−47.2959	−1.89639
$623$	0	0
$624$	0	0
$625$	17.0636	0.682543
$626$	−18.6812	−0.746650
$627$	−13.5347	−0.540524
$628$	71.2338	2.84254
$629$	25.3316	1.01004
$630$	0	0
$631$	−30.4508	−1.21223	−0.606114	−	0.795378i	$-0.707272\pi$
$631$	−30.4508	−1.21223	−0.606114	+	0.795378i	$0.707272\pi$
$632$	−87.8897	−3.49606
$633$	−22.7628	−0.904738
$634$	68.7381	2.72994
$635$	4.02446	0.159706
$636$	−34.3724	−1.36296
$637$	0	0
$638$	−1.52497	−0.0603743
$639$	−5.47624	−0.216637
$640$	31.0107	1.22581
$641$	9.64564	0.380980	0.190490	−	0.981689i	$-0.438992\pi$
$641$	9.64564	0.380980	0.190490	+	0.981689i	$0.438992\pi$
$642$	−5.56100	−0.219475
$643$	8.13296	0.320733	0.160366	−	0.987058i	$-0.448732\pi$
$643$	8.13296	0.320733	0.160366	+	0.987058i	$0.448732\pi$
$644$	0	0
$645$	1.76101	0.0693395
$646$	82.6293	3.25101
$647$	11.5227	0.453005	0.226503	−	0.974011i	$-0.427271\pi$
$647$	11.5227	0.453005	0.226503	+	0.974011i	$0.427271\pi$
$648$	−41.3629	−1.62489
$649$	−14.9915	−0.588469
$650$	0	0
$651$	0	0
$652$	33.2324	1.30148
$653$	42.4039	1.65939	0.829697	−	0.558215i	$-0.188513\pi$
$653$	42.4039	1.65939	0.829697	+	0.558215i	$0.188513\pi$
$654$	10.7414	0.420024
$655$	8.39054	0.327845
$656$	19.2858	0.752986
$657$	−6.90307	−0.269314
$658$	0	0
$659$	−2.50088	−0.0974203	−0.0487101	−	0.998813i	$-0.515511\pi$
$659$	−2.50088	−0.0974203	−0.0487101	+	0.998813i	$0.515511\pi$
$660$	−7.61108	−0.296261
$661$	14.8394	0.577184	0.288592	−	0.957452i	$-0.406813\pi$
$661$	14.8394	0.577184	0.288592	+	0.957452i	$0.406813\pi$
$662$	8.21046	0.319109
$663$	0	0
$664$	113.035	4.38663
$665$	0	0
$666$	−19.0342	−0.737560
$667$	0.951183	0.0368300
$668$	42.1849	1.63218
$669$	−1.46085	−0.0564797
$670$	27.9509	1.07984
$671$	−8.90541	−0.343790
$672$	0	0
$673$	39.6091	1.52682	0.763410	−	0.645915i	$-0.223524\pi$
$673$	39.6091	1.52682	0.763410	+	0.645915i	$0.223524\pi$
$674$	−80.8313	−3.11350
$675$	−25.1320	−0.967330
$676$	0	0
$677$	−17.0321	−0.654596	−0.327298	−	0.944921i	$-0.606138\pi$
$677$	−17.0321	−0.654596	−0.327298	+	0.944921i	$0.606138\pi$
$678$	46.4621	1.78437
$679$	0	0
$680$	29.6105	1.13551
$681$	33.3922	1.27959
$682$	−10.3720	−0.397163
$683$	−32.8912	−1.25854	−0.629272	−	0.777185i	$-0.716647\pi$
$683$	−32.8912	−1.25854	−0.629272	+	0.777185i	$0.716647\pi$
$684$	−45.5608	−1.74206
$685$	10.3569	0.395718
$686$	0	0
$687$	−6.45510	−0.246278
$688$	−26.7638	−1.02036
$689$	0	0
$690$	6.46938	0.246285
$691$	−23.7922	−0.905099	−0.452550	−	0.891739i	$-0.649486\pi$
$691$	−23.7922	−0.905099	−0.452550	+	0.891739i	$0.649486\pi$
$692$	0.906754	0.0344696
$693$	0	0
$694$	−16.4105	−0.622933
$695$	−7.73013	−0.293221
$696$	5.35804	0.203096
$697$	5.20502	0.197154
$698$	−83.1539	−3.14742
$699$	−28.0480	−1.06087
$700$	0	0
$701$	29.7796	1.12476	0.562380	−	0.826879i	$-0.309886\pi$
$701$	29.7796	1.12476	0.562380	+	0.826879i	$0.309886\pi$
$702$	0	0
$703$	44.3658	1.67329
$704$	43.6138	1.64376
$705$	5.92547	0.223166
$706$	−78.4122	−2.95108
$707$	0	0
$708$	82.6562	3.10641
$709$	−11.9304	−0.448054	−0.224027	−	0.974583i	$-0.571920\pi$
$709$	−11.9304	−0.448054	−0.224027	+	0.974583i	$0.571920\pi$
$710$	9.78155	0.367095
$711$	10.3785	0.389224
$712$	−16.9600	−0.635604
$713$	6.46938	0.242280
$714$	0	0
$715$	0	0
$716$	4.23788	0.158377
$717$	8.53642	0.318798
$718$	−64.3106	−2.40005
$719$	−32.3638	−1.20697	−0.603484	−	0.797375i	$-0.706221\pi$
$719$	−32.3638	−1.20697	−0.603484	+	0.797375i	$0.706221\pi$
$720$	−12.9556	−0.482827
$721$	0	0
$722$	92.6364	3.44757
$723$	16.5749	0.616428
$724$	54.7026	2.03301
$725$	1.81427	0.0673805
$726$	34.1833	1.26866
$727$	31.4897	1.16789	0.583943	−	0.811794i	$-0.301509\pi$
$727$	31.4897	1.16789	0.583943	+	0.811794i	$0.301509\pi$
$728$	0	0
$729$	28.0042	1.03719
$730$	12.3301	0.456359
$731$	−7.22325	−0.267161
$732$	49.1003	1.81480
$733$	2.66224	0.0983321	0.0491661	−	0.998791i	$-0.484344\pi$
$733$	2.66224	0.0983321	0.0491661	+	0.998791i	$0.484344\pi$
$734$	−100.103	−3.69489
$735$	0	0
$736$	−53.3755	−1.96745
$737$	18.7795	0.691750
$738$	−3.91106	−0.143968
$739$	35.5828	1.30893	0.654467	−	0.756091i	$-0.272893\pi$
$739$	35.5828	1.30893	0.654467	+	0.756091i	$0.272893\pi$
$740$	24.9486	0.917128
$741$	0	0
$742$	0	0
$743$	−24.2406	−0.889300	−0.444650	−	0.895704i	$-0.646672\pi$
$743$	−24.2406	−0.889300	−0.444650	+	0.895704i	$0.646672\pi$
$744$	36.4422	1.33604
$745$	−6.05044	−0.221671
$746$	−35.7706	−1.30966
$747$	−13.3479	−0.488373
$748$	31.2189	1.14148
$749$	0	0
$750$	26.2018	0.956756
$751$	−29.1410	−1.06337	−0.531684	−	0.846943i	$-0.678441\pi$
$751$	−29.1410	−1.06337	−0.531684	+	0.846943i	$0.678441\pi$
$752$	−90.0555	−3.28399
$753$	−8.61799	−0.314057
$754$	0	0
$755$	1.82446	0.0663988
$756$	0	0
$757$	−4.98990	−0.181361	−0.0906805	−	0.995880i	$-0.528904\pi$
$757$	−4.98990	−0.181361	−0.0906805	+	0.995880i	$0.528904\pi$
$758$	−83.8872	−3.04692
$759$	4.34660	0.157772
$760$	51.8598	1.88115
$761$	−11.8372	−0.429097	−0.214548	−	0.976713i	$-0.568828\pi$
$761$	−11.8372	−0.429097	−0.214548	+	0.976713i	$0.568828\pi$
$762$	−20.3160	−0.735971
$763$	0	0
$764$	54.5670	1.97417
$765$	−3.49657	−0.126419
$766$	−13.3929	−0.483904
$767$	0	0
$768$	−69.3186	−2.50132
$769$	−35.8183	−1.29164	−0.645821	−	0.763489i	$-0.723485\pi$
$769$	−35.8183	−1.29164	−0.645821	+	0.763489i	$0.723485\pi$
$770$	0	0
$771$	33.2418	1.19718
$772$	−47.9718	−1.72654
$773$	−19.9534	−0.717673	−0.358837	−	0.933400i	$-0.616826\pi$
$773$	−19.9534	−0.717673	−0.358837	+	0.933400i	$0.616826\pi$
$774$	5.42755	0.195089
$775$	12.3396	0.443252
$776$	91.8190	3.29611
$777$	0	0
$778$	−5.08266	−0.182222
$779$	9.11608	0.326618
$780$	0	0
$781$	6.57196	0.235163
$782$	−26.5359	−0.948923
$783$	−2.30173	−0.0822570
$784$	0	0
$785$	9.57464	0.341734
$786$	−42.3566	−1.51081
$787$	2.79619	0.0996733	0.0498367	−	0.998757i	$-0.484130\pi$
$787$	2.79619	0.0996733	0.0498367	+	0.998757i	$0.484130\pi$
$788$	143.454	5.11035
$789$	13.0737	0.465437
$790$	−18.5379	−0.659549
$791$	0	0
$792$	−14.9487	−0.531179
$793$	0	0
$794$	58.9700	2.09277
$795$	−4.62005	−0.163856
$796$	−55.8684	−1.98020
$797$	−1.68562	−0.0597076	−0.0298538	−	0.999554i	$-0.509504\pi$
$797$	−1.68562	−0.0597076	−0.0298538	+	0.999554i	$0.509504\pi$
$798$	0	0
$799$	−24.3049	−0.859846
$800$	−101.808	−3.59945
$801$	2.00273	0.0707632
$802$	39.9247	1.40979
$803$	8.28428	0.292346
$804$	−103.541	−3.65161
$805$	0	0
$806$	0	0
$807$	40.1244	1.41244
$808$	72.1700	2.53893
$809$	−43.4372	−1.52717	−0.763585	−	0.645708i	$-0.776562\pi$
$809$	−43.4372	−1.52717	−0.763585	+	0.645708i	$0.776562\pi$
$810$	−8.72435	−0.306542
$811$	5.60812	0.196928	0.0984639	−	0.995141i	$-0.468607\pi$
$811$	5.60812	0.196928	0.0984639	+	0.995141i	$0.468607\pi$
$812$	0	0
$813$	0.409971	0.0143783
$814$	22.8427	0.800635
$815$	4.46681	0.156466
$816$	−87.0397	−3.04700
$817$	−12.6508	−0.442595
$818$	−60.6574	−2.12084
$819$	0	0
$820$	5.12632	0.179019
$821$	23.9448	0.835678	0.417839	−	0.908521i	$-0.362788\pi$
$821$	23.9448	0.835678	0.417839	+	0.908521i	$0.362788\pi$
$822$	−52.2832	−1.82358
$823$	35.4117	1.23437	0.617187	−	0.786817i	$-0.288272\pi$
$823$	35.4117	1.23437	0.617187	+	0.786817i	$0.288272\pi$
$824$	−27.0481	−0.942266
$825$	8.29064	0.288643
$826$	0	0
$827$	16.1563	0.561811	0.280905	−	0.959735i	$-0.409365\pi$
$827$	16.1563	0.561811	0.280905	+	0.959735i	$0.409365\pi$
$828$	14.6316	0.508483
$829$	52.7010	1.83038	0.915190	−	0.403022i	$-0.132040\pi$
$829$	52.7010	1.83038	0.915190	+	0.403022i	$0.132040\pi$
$830$	23.8417	0.827557
$831$	44.7265	1.55154
$832$	0	0
$833$	0	0
$834$	39.0228	1.35125
$835$	5.67013	0.196223
$836$	54.6769	1.89104
$837$	−15.6550	−0.541115
$838$	−9.25363	−0.319661
$839$	−22.4338	−0.774502	−0.387251	−	0.921974i	$-0.626575\pi$
$839$	−22.4338	−0.774502	−0.387251	+	0.921974i	$0.626575\pi$
$840$	0	0
$841$	−28.8338	−0.994270
$842$	68.8288	2.37200
$843$	5.86165	0.201886
$844$	91.9559	3.16525
$845$	0	0
$846$	18.2627	0.627886
$847$	0	0
$848$	70.2158	2.41122
$849$	−28.7980	−0.988346
$850$	−50.6143	−1.73606
$851$	−14.2478	−0.488409
$852$	−36.2347	−1.24138
$853$	30.8521	1.05635	0.528177	−	0.849134i	$-0.322876\pi$
$853$	30.8521	1.05635	0.528177	+	0.849134i	$0.322876\pi$
$854$	0	0
$855$	−6.12390	−0.209433
$856$	14.3160	0.489311
$857$	−26.7400	−0.913420	−0.456710	−	0.889616i	$-0.650972\pi$
$857$	−26.7400	−0.913420	−0.456710	+	0.889616i	$0.650972\pi$
$858$	0	0
$859$	5.15804	0.175990	0.0879950	−	0.996121i	$-0.471954\pi$
$859$	5.15804	0.175990	0.0879950	+	0.996121i	$0.471954\pi$
$860$	−7.11402	−0.242586
$861$	0	0
$862$	−29.5896	−1.00782
$863$	−8.16814	−0.278047	−0.139023	−	0.990289i	$-0.544396\pi$
$863$	−8.16814	−0.278047	−0.139023	+	0.990289i	$0.544396\pi$
$864$	129.161	4.39415
$865$	0.121878	0.00414398
$866$	39.7956	1.35231
$867$	−0.289073	−0.00981742
$868$	0	0
$869$	−12.4551	−0.422510
$870$	1.13013	0.0383150
$871$	0	0
$872$	−27.6523	−0.936425
$873$	−10.8425	−0.366963
$874$	−46.4750	−1.57204
$875$	0	0
$876$	−45.6756	−1.54324
$877$	−15.6184	−0.527398	−0.263699	−	0.964605i	$-0.584942\pi$
$877$	−15.6184	−0.527398	−0.263699	+	0.964605i	$0.584942\pi$
$878$	39.5562	1.33496
$879$	−24.2444	−0.817744
$880$	15.5479	0.524118
$881$	46.4375	1.56452	0.782260	−	0.622952i	$-0.214067\pi$
$881$	46.4375	1.56452	0.782260	+	0.622952i	$0.214067\pi$
$882$	0	0
$883$	15.6588	0.526960	0.263480	−	0.964665i	$-0.415130\pi$
$883$	15.6588	0.526960	0.263480	+	0.964665i	$0.415130\pi$
$884$	0	0
$885$	11.1099	0.373457
$886$	−82.8986	−2.78503
$887$	−31.5107	−1.05803	−0.529013	−	0.848614i	$-0.677438\pi$
$887$	−31.5107	−1.05803	−0.529013	+	0.848614i	$0.677438\pi$
$888$	−80.2584	−2.69330
$889$	0	0
$890$	−3.57725	−0.119910
$891$	−5.86165	−0.196373
$892$	5.90146	0.197596
$893$	−42.5677	−1.42447
$894$	30.5434	1.02152
$895$	0.569620	0.0190403
$896$	0	0
$897$	0	0
$898$	−85.7301	−2.86085
$899$	1.13013	0.0376920
$900$	27.9081	0.930270
$901$	18.9504	0.631330
$902$	4.69361	0.156280
$903$	0	0
$904$	−119.610	−3.97817
$905$	7.35266	0.244411
$906$	−9.21010	−0.305985
$907$	−0.747991	−0.0248366	−0.0124183	−	0.999923i	$-0.503953\pi$
$907$	−0.747991	−0.0248366	−0.0124183	+	0.999923i	$0.503953\pi$
$908$	−134.896	−4.47669
$909$	−8.52224	−0.282665
$910$	0	0
$911$	24.9000	0.824973	0.412486	−	0.910964i	$-0.364660\pi$
$911$	24.9000	0.824973	0.412486	+	0.910964i	$0.364660\pi$
$912$	−152.441	−5.04784
$913$	16.0186	0.530138
$914$	−56.5941	−1.87197
$915$	6.59964	0.218177
$916$	26.0770	0.861609
$917$	0	0
$918$	64.2132	2.11935
$919$	0.586495	0.0193467	0.00967334	−	0.999953i	$-0.496921\pi$
$919$	0.586495	0.0193467	0.00967334	+	0.999953i	$0.496921\pi$
$920$	−16.6545	−0.549082
$921$	−24.5881	−0.810204
$922$	74.8208	2.46409
$923$	0	0
$924$	0	0
$925$	−27.1761	−0.893546
$926$	−15.5139	−0.509818
$927$	3.19399	0.104905
$928$	−9.32412	−0.306079
$929$	−50.1949	−1.64684	−0.823421	−	0.567431i	$-0.807938\pi$
$929$	−50.1949	−1.64684	−0.823421	+	0.567431i	$0.807938\pi$
$930$	7.68647	0.252049
$931$	0	0
$932$	113.307	3.71149
$933$	23.5493	0.770968
$934$	−115.713	−3.78626
$935$	4.19619	0.137230
$936$	0	0
$937$	−22.7130	−0.742003	−0.371001	−	0.928632i	$-0.620985\pi$
$937$	−22.7130	−0.742003	−0.371001	+	0.928632i	$0.620985\pi$
$938$	0	0
$939$	9.30160	0.303546
$940$	−23.9374	−0.780752
$941$	−49.8734	−1.62583	−0.812914	−	0.582384i	$-0.802120\pi$
$941$	−49.8734	−1.62583	−0.812914	+	0.582384i	$0.802120\pi$
$942$	−48.3341	−1.57481
$943$	−2.92758	−0.0953351
$944$	−168.849	−5.49558
$945$	0	0
$946$	−6.51353	−0.211773
$947$	−0.266414	−0.00865731	−0.00432865	−	0.999991i	$-0.501378\pi$
$947$	−0.266414	−0.00865731	−0.00432865	+	0.999991i	$0.501378\pi$
$948$	68.6716	2.23035
$949$	0	0
$950$	−88.6459	−2.87605
$951$	−34.2256	−1.10984
$952$	0	0
$953$	7.82029	0.253324	0.126662	−	0.991946i	$-0.459574\pi$
$953$	7.82029	0.253324	0.126662	+	0.991946i	$0.459574\pi$
$954$	−14.2394	−0.461016
$955$	7.33444	0.237337
$956$	−34.4850	−1.11532
$957$	0.759304	0.0245448
$958$	89.1718	2.88101
$959$	0	0
$960$	−32.3214	−1.04317
$961$	−23.3135	−0.752049
$962$	0	0
$963$	−1.69051	−0.0544761
$964$	−66.9585	−2.15659
$965$	−6.44797	−0.207567
$966$	0	0
$967$	−39.8224	−1.28060	−0.640301	−	0.768124i	$-0.721190\pi$
$967$	−39.8224	−1.28060	−0.640301	+	0.768124i	$0.721190\pi$
$968$	−87.9999	−2.82842
$969$	−41.1422	−1.32168
$970$	19.3667	0.621826
$971$	45.9295	1.47395	0.736974	−	0.675921i	$-0.236254\pi$
$971$	45.9295	1.47395	0.736974	+	0.675921i	$0.236254\pi$
$972$	−61.0801	−1.95915
$973$	0	0
$974$	−73.6208	−2.35896
$975$	0	0
$976$	−100.302	−3.21058
$977$	28.6627	0.917002	0.458501	−	0.888694i	$-0.348387\pi$
$977$	28.6627	0.917002	0.458501	+	0.888694i	$0.348387\pi$
$978$	−22.5491	−0.721040
$979$	−2.40345	−0.0768147
$980$	0	0
$981$	3.26534	0.104254
$982$	119.752	3.82144
$983$	−46.1200	−1.47100	−0.735500	−	0.677524i	$-0.763053\pi$
$983$	−46.1200	−1.47100	−0.735500	+	0.677524i	$0.763053\pi$
$984$	−16.4911	−0.525718
$985$	19.2819	0.614372
$986$	−4.63554	−0.147626
$987$	0	0
$988$	0	0
$989$	4.06273	0.129187
$990$	−3.15302	−0.100209
$991$	37.8249	1.20155	0.600773	−	0.799419i	$-0.294859\pi$
$991$	37.8249	1.20155	0.600773	+	0.799419i	$0.294859\pi$
$992$	−63.4171	−2.01350
$993$	−4.08809	−0.129732
$994$	0	0
$995$	−7.50936	−0.238063
$996$	−88.3189	−2.79849
$997$	−38.3748	−1.21534	−0.607671	−	0.794189i	$-0.707896\pi$
$997$	−38.3748	−1.21534	−0.607671	+	0.794189i	$0.707896\pi$
$998$	49.6189	1.57066
$999$	34.4777	1.09083

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8281.2.a.bt.1.4		4
7.6	odd	2		1183.2.a.l.1.4		4
13.4	even	6		637.2.f.i.393.4		8
13.10	even	6		637.2.f.i.295.4		8
13.12	even	2		8281.2.a.bp.1.1		4
91.4	even	6		637.2.h.i.471.1		8
91.10	odd	6		637.2.g.k.373.4		8
91.17	odd	6		637.2.h.h.471.1		8
91.23	even	6		637.2.h.i.165.1		8
91.30	even	6		637.2.g.j.263.4		8
91.34	even	4		1183.2.c.g.337.8		8
91.62	odd	6		91.2.f.c.22.4	✓	8
91.69	odd	6		91.2.f.c.29.4	yes	8
91.75	odd	6		637.2.h.h.165.1		8
91.82	odd	6		637.2.g.k.263.4		8
91.83	even	4		1183.2.c.g.337.1		8
91.88	even	6		637.2.g.j.373.4		8
91.90	odd	2		1183.2.a.k.1.1		4
273.62	even	6		819.2.o.h.568.1		8
273.251	even	6		819.2.o.h.757.1		8
364.251	even	6		1456.2.s.q.1121.3		8
364.335	even	6		1456.2.s.q.113.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.f.c.22.4	✓	8	91.62	odd	6
91.2.f.c.29.4	yes	8	91.69	odd	6
637.2.f.i.295.4		8	13.10	even	6
637.2.f.i.393.4		8	13.4	even	6
637.2.g.j.263.4		8	91.30	even	6
637.2.g.j.373.4		8	91.88	even	6
637.2.g.k.263.4		8	91.82	odd	6
637.2.g.k.373.4		8	91.10	odd	6
637.2.h.h.165.1		8	91.75	odd	6
637.2.h.h.471.1		8	91.17	odd	6
637.2.h.i.165.1		8	91.23	even	6
637.2.h.i.471.1		8	91.4	even	6
819.2.o.h.568.1		8	273.62	even	6
819.2.o.h.757.1		8	273.251	even	6
1183.2.a.k.1.1		4	91.90	odd	2
1183.2.a.l.1.4		4	7.6	odd	2
1183.2.c.g.337.1		8	91.83	even	4
1183.2.c.g.337.8		8	91.34	even	4
1456.2.s.q.113.3		8	364.335	even	6
1456.2.s.q.1121.3		8	364.251	even	6
8281.2.a.bp.1.1		4	13.12	even	2
8281.2.a.bt.1.4		4	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)

\(f(q)\)	\(=\)	\(q+2.74108 q^{2} -1.36482 q^{3} +5.51353 q^{4} +0.741082 q^{5} -3.74108 q^{6} +9.63087 q^{8} -1.13727 q^{9} +O(q^{10})\)	\(q+2.74108 q^{2} -1.36482 q^{3} +5.51353 q^{4} +0.741082 q^{5} -3.74108 q^{6} +9.63087 q^{8} -1.13727 q^{9} +2.03137 q^{10} +1.36482 q^{11} -7.52497 q^{12} -1.01144 q^{15} +15.3720 q^{16} +4.14871 q^{17} -3.11734 q^{18} +7.26606 q^{19} +4.08598 q^{20} +3.74108 q^{22} -2.33345 q^{23} -13.1444 q^{24} -4.45080 q^{25} +5.64662 q^{27} -0.407629 q^{29} -2.77245 q^{30} -2.77245 q^{31} +22.8740 q^{32} -1.86273 q^{33} +11.3720 q^{34} -6.27036 q^{36} +6.10590 q^{37} +19.9169 q^{38} +7.13727 q^{40} +1.25461 q^{41} -1.74108 q^{43} +7.52497 q^{44} -0.842809 q^{45} -6.39619 q^{46} -5.85843 q^{47} -20.9799 q^{48} -12.2000 q^{50} -5.66224 q^{51} +4.56778 q^{53} +15.4779 q^{54} +1.01144 q^{55} -9.91685 q^{57} -1.11734 q^{58} -10.9843 q^{59} -5.57662 q^{60} -6.52497 q^{61} -7.59951 q^{62} +31.9557 q^{64} -5.10590 q^{66} +13.7597 q^{67} +22.8740 q^{68} +3.18474 q^{69} +4.81526 q^{71} -10.9529 q^{72} +6.06987 q^{73} +16.7368 q^{74} +6.07453 q^{75} +40.0616 q^{76} -9.12582 q^{79} +11.3919 q^{80} -4.29482 q^{81} +3.43900 q^{82} +11.7368 q^{83} +3.07453 q^{85} -4.77245 q^{86} +0.556340 q^{87} +13.1444 q^{88} -1.76101 q^{89} -2.31021 q^{90} -12.8656 q^{92} +3.78389 q^{93} -16.0584 q^{94} +5.38474 q^{95} -31.2189 q^{96} +9.53381 q^{97} -1.55217 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - q^{3} + 5 q^{4} - 7 q^{5} - 5 q^{6} + 6 q^{8} + 7 q^{9}+O(q^{10}) \) 4 * q + q^2 - q^3 + 5 * q^4 - 7 * q^5 - 5 * q^6 + 6 * q^8 + 7 * q^9	\( 4 q + q^{2} - q^{3} + 5 q^{4} - 7 q^{5} - 5 q^{6} + 6 q^{8} + 7 q^{9} + 11 q^{10} + q^{11} - 12 q^{12} - 3 q^{15} + 19 q^{16} + 4 q^{17} + 3 q^{18} + q^{19} - 2 q^{20} + 5 q^{22} - 2 q^{23} - 3 q^{24} + 5 q^{25} + 26 q^{27} + q^{29} - 4 q^{30} - 4 q^{31} + 33 q^{32} - 19 q^{33} + 3 q^{34} - 34 q^{36} + 10 q^{37} + 23 q^{38} + 17 q^{40} - 22 q^{41} + 3 q^{43} + 12 q^{44} - 11 q^{45} - 24 q^{46} + 2 q^{47} - 11 q^{48} - 43 q^{50} + 7 q^{51} + 2 q^{53} + 5 q^{54} + 3 q^{55} + 17 q^{57} + 11 q^{58} - 8 q^{59} + 11 q^{60} - 8 q^{61} + 5 q^{62} + 14 q^{64} - 6 q^{66} + 6 q^{67} + 33 q^{68} + 18 q^{69} + 14 q^{71} - 5 q^{72} - 8 q^{73} + 20 q^{74} + 7 q^{75} + 32 q^{76} - 26 q^{79} + 7 q^{80} + 24 q^{81} + 14 q^{82} - 5 q^{85} - 12 q^{86} - 13 q^{87} + 3 q^{88} - q^{89} - 26 q^{90} + 12 q^{92} + 7 q^{93} - 33 q^{94} + 21 q^{95} - 58 q^{96} + 3 q^{97} - 23 q^{99}+O(q^{100}) \) 4 * q + q^2 - q^3 + 5 * q^4 - 7 * q^5 - 5 * q^6 + 6 * q^8 + 7 * q^9 + 11 * q^10 + q^11 - 12 * q^12 - 3 * q^15 + 19 * q^16 + 4 * q^17 + 3 * q^18 + q^19 - 2 * q^20 + 5 * q^22 - 2 * q^23 - 3 * q^24 + 5 * q^25 + 26 * q^27 + q^29 - 4 * q^30 - 4 * q^31 + 33 * q^32 - 19 * q^33 + 3 * q^34 - 34 * q^36 + 10 * q^37 + 23 * q^38 + 17 * q^40 - 22 * q^41 + 3 * q^43 + 12 * q^44 - 11 * q^45 - 24 * q^46 + 2 * q^47 - 11 * q^48 - 43 * q^50 + 7 * q^51 + 2 * q^53 + 5 * q^54 + 3 * q^55 + 17 * q^57 + 11 * q^58 - 8 * q^59 + 11 * q^60 - 8 * q^61 + 5 * q^62 + 14 * q^64 - 6 * q^66 + 6 * q^67 + 33 * q^68 + 18 * q^69 + 14 * q^71 - 5 * q^72 - 8 * q^73 + 20 * q^74 + 7 * q^75 + 32 * q^76 - 26 * q^79 + 7 * q^80 + 24 * q^81 + 14 * q^82 - 5 * q^85 - 12 * q^86 - 13 * q^87 + 3 * q^88 - q^89 - 26 * q^90 + 12 * q^92 + 7 * q^93 - 33 * q^94 + 21 * q^95 - 58 * q^96 + 3 * q^97 - 23 * q^99

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