LMFDB - Embedded newform 6027.2.a.bh.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6027,2,Mod(1,6027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6027, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6027 = 3 \cdot 7^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6027.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:	$48.1258372982$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 4 x^{12} - 11 x^{11} + 56 x^{10} + 26 x^{9} - 263 x^{8} + 50 x^{7} + 478 x^{6} - 174 x^{5} + \cdots - 4 $ x^13 - 4x^12 - 11x^11 + 56x^10 + 26x^9 - 263x^8 + 50x^7 + 478x^6 - 174x^5 - 311x^4 + 84x^3 + 69x^2 - 12x - 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 861)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Root			$-1.46649$ of defining polynomial
Character	$\chi$	$=$	6027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.46649 q^{2} -1.00000 q^{3} +0.150578 q^{4} -1.27945 q^{5} -1.46649 q^{6} -2.71215 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.46649 q^{2} -1.00000 q^{3} +0.150578 q^{4} -1.27945 q^{5} -1.46649 q^{6} -2.71215 q^{8} +1.00000 q^{9} -1.87630 q^{10} +4.55512 q^{11} -0.150578 q^{12} +3.82930 q^{13} +1.27945 q^{15} -4.27848 q^{16} +3.03199 q^{17} +1.46649 q^{18} +4.80420 q^{19} -0.192658 q^{20} +6.68002 q^{22} -6.82949 q^{23} +2.71215 q^{24} -3.36300 q^{25} +5.61561 q^{26} -1.00000 q^{27} -8.73574 q^{29} +1.87630 q^{30} -0.252900 q^{31} -0.850033 q^{32} -4.55512 q^{33} +4.44637 q^{34} +0.150578 q^{36} +1.57080 q^{37} +7.04529 q^{38} -3.82930 q^{39} +3.47007 q^{40} -1.00000 q^{41} +3.30779 q^{43} +0.685903 q^{44} -1.27945 q^{45} -10.0153 q^{46} +7.07743 q^{47} +4.27848 q^{48} -4.93178 q^{50} -3.03199 q^{51} +0.576610 q^{52} +3.70905 q^{53} -1.46649 q^{54} -5.82807 q^{55} -4.80420 q^{57} -12.8108 q^{58} -10.7021 q^{59} +0.192658 q^{60} +11.5919 q^{61} -0.370874 q^{62} +7.31041 q^{64} -4.89942 q^{65} -6.68002 q^{66} -9.19482 q^{67} +0.456553 q^{68} +6.82949 q^{69} -6.31030 q^{71} -2.71215 q^{72} -1.54239 q^{73} +2.30356 q^{74} +3.36300 q^{75} +0.723409 q^{76} -5.61561 q^{78} +12.1437 q^{79} +5.47412 q^{80} +1.00000 q^{81} -1.46649 q^{82} +11.4396 q^{83} -3.87930 q^{85} +4.85083 q^{86} +8.73574 q^{87} -12.3542 q^{88} +6.14545 q^{89} -1.87630 q^{90} -1.02837 q^{92} +0.252900 q^{93} +10.3790 q^{94} -6.14675 q^{95} +0.850033 q^{96} +9.51325 q^{97} +4.55512 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 4 q^{2} - 13 q^{3} + 12 q^{4} + 8 q^{5} + 4 q^{6} - 12 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q - 4 * q^2 - 13 * q^3 + 12 * q^4 + 8 * q^5 + 4 * q^6 - 12 * q^8 + 13 * q^9	$ 13 q - 4 q^{2} - 13 q^{3} + 12 q^{4} + 8 q^{5} + 4 q^{6} - 12 q^{8} + 13 q^{9} + q^{10} - 10 q^{11} - 12 q^{12} + 16 q^{13} - 8 q^{15} + 26 q^{16} + 12 q^{17} - 4 q^{18} + 11 q^{19} + 6 q^{20} + q^{22} - 15 q^{23} + 12 q^{24} + 15 q^{25} + 18 q^{26} - 13 q^{27} - 8 q^{29} - q^{30} + 9 q^{31} - 23 q^{32} + 10 q^{33} - 7 q^{34} + 12 q^{36} - 2 q^{37} + 20 q^{38} - 16 q^{39} + 49 q^{40} - 13 q^{41} - 7 q^{43} - 22 q^{44} + 8 q^{45} - 4 q^{46} + 26 q^{47} - 26 q^{48} - 15 q^{50} - 12 q^{51} + 24 q^{52} + 4 q^{53} + 4 q^{54} + q^{55} - 11 q^{57} + 39 q^{58} - 3 q^{59} - 6 q^{60} + 28 q^{61} + 7 q^{62} + 2 q^{64} - 20 q^{65} - q^{66} + 7 q^{67} + 55 q^{68} + 15 q^{69} - 40 q^{71} - 12 q^{72} - 2 q^{73} + q^{74} - 15 q^{75} - 26 q^{76} - 18 q^{78} + 13 q^{79} + 22 q^{80} + 13 q^{81} + 4 q^{82} + 14 q^{83} + 48 q^{85} - 49 q^{86} + 8 q^{87} + 20 q^{88} + 35 q^{89} + q^{90} - 105 q^{92} - 9 q^{93} - 2 q^{94} + 7 q^{95} + 23 q^{96} + 64 q^{97} - 10 q^{99}+O(q^{100}) $ 13 * q - 4 * q^2 - 13 * q^3 + 12 * q^4 + 8 * q^5 + 4 * q^6 - 12 * q^8 + 13 * q^9 + q^10 - 10 * q^11 - 12 * q^12 + 16 * q^13 - 8 * q^15 + 26 * q^16 + 12 * q^17 - 4 * q^18 + 11 * q^19 + 6 * q^20 + q^22 - 15 * q^23 + 12 * q^24 + 15 * q^25 + 18 * q^26 - 13 * q^27 - 8 * q^29 - q^30 + 9 * q^31 - 23 * q^32 + 10 * q^33 - 7 * q^34 + 12 * q^36 - 2 * q^37 + 20 * q^38 - 16 * q^39 + 49 * q^40 - 13 * q^41 - 7 * q^43 - 22 * q^44 + 8 * q^45 - 4 * q^46 + 26 * q^47 - 26 * q^48 - 15 * q^50 - 12 * q^51 + 24 * q^52 + 4 * q^53 + 4 * q^54 + q^55 - 11 * q^57 + 39 * q^58 - 3 * q^59 - 6 * q^60 + 28 * q^61 + 7 * q^62 + 2 * q^64 - 20 * q^65 - q^66 + 7 * q^67 + 55 * q^68 + 15 * q^69 - 40 * q^71 - 12 * q^72 - 2 * q^73 + q^74 - 15 * q^75 - 26 * q^76 - 18 * q^78 + 13 * q^79 + 22 * q^80 + 13 * q^81 + 4 * q^82 + 14 * q^83 + 48 * q^85 - 49 * q^86 + 8 * q^87 + 20 * q^88 + 35 * q^89 + q^90 - 105 * q^92 - 9 * q^93 - 2 * q^94 + 7 * q^95 + 23 * q^96 + 64 * q^97 - 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.46649	1.03696	0.518481	−	0.855089i	$-0.326498\pi$
$2$	1.46649	1.03696	0.518481	+	0.855089i	$0.326498\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.150578	0.0752892
$5$	−1.27945	−0.572189	−0.286095	−	0.958201i	$-0.592357\pi$
$5$	−1.27945	−0.572189	−0.286095	+	0.958201i	$0.592357\pi$
$6$	−1.46649	−0.598690
$7$	0	0
$7$	0	0
$8$	−2.71215	−0.958890
$9$	1.00000	0.333333
$10$	−1.87630	−0.593338
$11$	4.55512	1.37342	0.686710	−	0.726931i	$-0.259054\pi$
$11$	4.55512	1.37342	0.686710	+	0.726931i	$0.259054\pi$
$12$	−0.150578	−0.0434682
$13$	3.82930	1.06206	0.531029	−	0.847354i	$-0.321806\pi$
$13$	3.82930	1.06206	0.531029	+	0.847354i	$0.321806\pi$
$14$	0	0
$15$	1.27945	0.330354
$16$	−4.27848	−1.06962
$17$	3.03199	0.735366	0.367683	−	0.929951i	$-0.380151\pi$
$17$	3.03199	0.735366	0.367683	+	0.929951i	$0.380151\pi$
$18$	1.46649	0.345654
$19$	4.80420	1.10216	0.551080	−	0.834453i	$-0.314216\pi$
$19$	4.80420	1.10216	0.551080	+	0.834453i	$0.314216\pi$
$20$	−0.192658	−0.0430797
$21$	0	0
$22$	6.68002	1.42418
$23$	−6.82949	−1.42405	−0.712023	−	0.702156i	$-0.752221\pi$
$23$	−6.82949	−1.42405	−0.712023	+	0.702156i	$0.752221\pi$
$24$	2.71215	0.553615
$25$	−3.36300	−0.672599
$26$	5.61561	1.10131
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−8.73574	−1.62219	−0.811093	−	0.584917i	$-0.801127\pi$
$29$	−8.73574	−1.62219	−0.811093	+	0.584917i	$0.801127\pi$
$30$	1.87630	0.342564
$31$	−0.252900	−0.0454221	−0.0227111	−	0.999742i	$-0.507230\pi$
$31$	−0.252900	−0.0454221	−0.0227111	+	0.999742i	$0.507230\pi$
$32$	−0.850033	−0.150266
$33$	−4.55512	−0.792945
$34$	4.44637	0.762546
$35$	0	0
$36$	0.150578	0.0250964
$37$	1.57080	0.258238	0.129119	−	0.991629i	$-0.458785\pi$
$37$	1.57080	0.258238	0.129119	+	0.991629i	$0.458785\pi$
$38$	7.04529	1.14290
$39$	−3.82930	−0.613179
$40$	3.47007	0.548666
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	3.30779	0.504434	0.252217	−	0.967671i	$-0.418840\pi$
$43$	3.30779	0.504434	0.252217	+	0.967671i	$0.418840\pi$
$44$	0.685903	0.103404
$45$	−1.27945	−0.190730
$46$	−10.0153	−1.47668
$47$	7.07743	1.03235	0.516175	−	0.856483i	$-0.327355\pi$
$47$	7.07743	1.03235	0.516175	+	0.856483i	$0.327355\pi$
$48$	4.27848	0.617546
$49$	0	0
$50$	−4.93178	−0.697460
$51$	−3.03199	−0.424564
$52$	0.576610	0.0799615
$53$	3.70905	0.509477	0.254738	−	0.967010i	$-0.418011\pi$
$53$	3.70905	0.509477	0.254738	+	0.967010i	$0.418011\pi$
$54$	−1.46649	−0.199563
$55$	−5.82807	−0.785857
$56$	0	0
$57$	−4.80420	−0.636332
$58$	−12.8108	−1.68214
$59$	−10.7021	−1.39329	−0.696645	−	0.717416i	$-0.745325\pi$
$59$	−10.7021	−1.39329	−0.696645	+	0.717416i	$0.745325\pi$
$60$	0.192658	0.0248721
$61$	11.5919	1.48419	0.742096	−	0.670294i	$-0.233832\pi$
$61$	11.5919	1.48419	0.742096	+	0.670294i	$0.233832\pi$
$62$	−0.370874	−0.0471010
$63$	0	0
$64$	7.31041	0.913801
$65$	−4.89942	−0.607698
$66$	−6.68002	−0.822253
$67$	−9.19482	−1.12333	−0.561663	−	0.827366i	$-0.689838\pi$
$67$	−9.19482	−1.12333	−0.561663	+	0.827366i	$0.689838\pi$
$68$	0.456553	0.0553651
$69$	6.82949	0.822174
$70$	0	0
$71$	−6.31030	−0.748894	−0.374447	−	0.927248i	$-0.622168\pi$
$71$	−6.31030	−0.748894	−0.374447	+	0.927248i	$0.622168\pi$
$72$	−2.71215	−0.319630
$73$	−1.54239	−0.180523	−0.0902616	−	0.995918i	$-0.528770\pi$
$73$	−1.54239	−0.180523	−0.0902616	+	0.995918i	$0.528770\pi$
$74$	2.30356	0.267783
$75$	3.36300	0.388325
$76$	0.723409	0.0829807
$77$	0	0
$78$	−5.61561	−0.635843
$79$	12.1437	1.36628	0.683139	−	0.730288i	$-0.260614\pi$
$79$	12.1437	1.36628	0.683139	+	0.730288i	$0.260614\pi$
$80$	5.47412	0.612026
$81$	1.00000	0.111111
$82$	−1.46649	−0.161946
$83$	11.4396	1.25566	0.627830	−	0.778350i	$-0.283943\pi$
$83$	11.4396	1.25566	0.627830	+	0.778350i	$0.283943\pi$
$84$	0	0
$85$	−3.87930	−0.420769
$86$	4.85083	0.523079
$87$	8.73574	0.936569
$88$	−12.3542	−1.31696
$89$	6.14545	0.651416	0.325708	−	0.945470i	$-0.394397\pi$
$89$	6.14545	0.651416	0.325708	+	0.945470i	$0.394397\pi$
$90$	−1.87630	−0.197779
$91$	0	0
$92$	−1.02837	−0.107215
$93$	0.252900	0.0262245
$94$	10.3790	1.07051
$95$	−6.14675	−0.630644
$96$	0.850033	0.0867561
$97$	9.51325	0.965925	0.482962	−	0.875641i	$-0.339561\pi$
$97$	9.51325	0.965925	0.482962	+	0.875641i	$0.339561\pi$
$98$	0	0
$99$	4.55512	0.457807
$100$	−0.506395	−0.0506395
$101$	−18.8292	−1.87358	−0.936788	−	0.349898i	$-0.886216\pi$
$101$	−18.8292	−1.87358	−0.936788	+	0.349898i	$0.886216\pi$
$102$	−4.44637	−0.440256
$103$	9.78428	0.964074	0.482037	−	0.876151i	$-0.339897\pi$
$103$	9.78428	0.964074	0.482037	+	0.876151i	$0.339897\pi$
$104$	−10.3856	−1.01840
$105$	0	0
$106$	5.43926	0.528308
$107$	9.64440	0.932359	0.466180	−	0.884690i	$-0.345630\pi$
$107$	9.64440	0.932359	0.466180	+	0.884690i	$0.345630\pi$
$108$	−0.150578	−0.0144894
$109$	7.19766	0.689411	0.344705	−	0.938711i	$-0.387979\pi$
$109$	7.19766	0.689411	0.344705	+	0.938711i	$0.387979\pi$
$110$	−8.54678	−0.814903
$111$	−1.57080	−0.149094
$112$	0	0
$113$	16.2060	1.52453	0.762265	−	0.647265i	$-0.224087\pi$
$113$	16.2060	1.52453	0.762265	+	0.647265i	$0.224087\pi$
$114$	−7.04529	−0.659852
$115$	8.73802	0.814824
$116$	−1.31541	−0.122133
$117$	3.82930	0.354019
$118$	−15.6944	−1.44479
$119$	0	0
$120$	−3.47007	−0.316773
$121$	9.74912	0.886284
$122$	16.9994	1.53905
$123$	1.00000	0.0901670
$124$	−0.0380812	−0.00341980
$125$	10.7001	0.957044
$126$	0	0
$127$	−9.30123	−0.825350	−0.412675	−	0.910878i	$-0.635406\pi$
$127$	−9.30123	−0.825350	−0.412675	+	0.910878i	$0.635406\pi$
$128$	12.4207	1.09784
$129$	−3.30779	−0.291235
$130$	−7.18492	−0.630159
$131$	−2.36148	−0.206323	−0.103162	−	0.994665i	$-0.532896\pi$
$131$	−2.36148	−0.206323	−0.103162	+	0.994665i	$0.532896\pi$
$132$	−0.685903	−0.0597002
$133$	0	0
$134$	−13.4841	−1.16485
$135$	1.27945	0.110118
$136$	−8.22322	−0.705135
$137$	−8.05057	−0.687807	−0.343903	−	0.939005i	$-0.611749\pi$
$137$	−8.05057	−0.687807	−0.343903	+	0.939005i	$0.611749\pi$
$138$	10.0153	0.852563
$139$	4.36913	0.370585	0.185292	−	0.982683i	$-0.440677\pi$
$139$	4.36913	0.370585	0.185292	+	0.982683i	$0.440677\pi$
$140$	0	0
$141$	−7.07743	−0.596027
$142$	−9.25396	−0.776575
$143$	17.4429	1.45865
$144$	−4.27848	−0.356540
$145$	11.1770	0.928197
$146$	−2.26189	−0.187196
$147$	0	0
$148$	0.236529	0.0194425
$149$	21.7122	1.77873	0.889365	−	0.457198i	$-0.151147\pi$
$149$	21.7122	1.77873	0.889365	+	0.457198i	$0.151147\pi$
$150$	4.93178	0.402679
$151$	8.17544	0.665308	0.332654	−	0.943049i	$-0.392056\pi$
$151$	8.17544	0.665308	0.332654	+	0.943049i	$0.392056\pi$
$152$	−13.0297	−1.05685
$153$	3.03199	0.245122
$154$	0	0
$155$	0.323574	0.0259901
$156$	−0.576610	−0.0461658
$157$	−16.4197	−1.31043	−0.655216	−	0.755442i	$-0.727422\pi$
$157$	−16.4197	−1.31043	−0.655216	+	0.755442i	$0.727422\pi$
$158$	17.8086	1.41678
$159$	−3.70905	−0.294146
$160$	1.08758	0.0859806
$161$	0	0
$162$	1.46649	0.115218
$163$	−7.65254	−0.599393	−0.299697	−	0.954035i	$-0.596885\pi$
$163$	−7.65254	−0.599393	−0.299697	+	0.954035i	$0.596885\pi$
$164$	−0.150578	−0.0117582
$165$	5.82807	0.453715
$166$	16.7760	1.30207
$167$	0.211772	0.0163874	0.00819369	−	0.999966i	$-0.497392\pi$
$167$	0.211772	0.0163874	0.00819369	+	0.999966i	$0.497392\pi$
$168$	0	0
$169$	1.66355	0.127966
$170$	−5.68893	−0.436321
$171$	4.80420	0.367386
$172$	0.498082	0.0379784
$173$	0.100684	0.00765484	0.00382742	−	0.999993i	$-0.498782\pi$
$173$	0.100684	0.00765484	0.00382742	+	0.999993i	$0.498782\pi$
$174$	12.8108	0.971187
$175$	0	0
$176$	−19.4890	−1.46904
$177$	10.7021	0.804416
$178$	9.01221	0.675494
$179$	5.96037	0.445499	0.222750	−	0.974876i	$-0.428497\pi$
$179$	5.96037	0.445499	0.222750	+	0.974876i	$0.428497\pi$
$180$	−0.192658	−0.0143599
$181$	8.73411	0.649201	0.324601	−	0.945851i	$-0.394770\pi$
$181$	8.73411	0.649201	0.324601	+	0.945851i	$0.394770\pi$
$182$	0	0
$183$	−11.5919	−0.856899
$184$	18.5226	1.36550
$185$	−2.00977	−0.147761
$186$	0.370874	0.0271938
$187$	13.8111	1.00997
$188$	1.06571	0.0777248
$189$	0	0
$190$	−9.01412	−0.653953
$191$	21.8499	1.58100	0.790502	−	0.612459i	$-0.209819\pi$
$191$	21.8499	1.58100	0.790502	+	0.612459i	$0.209819\pi$
$192$	−7.31041	−0.527583
$193$	1.99809	0.143826	0.0719129	−	0.997411i	$-0.477090\pi$
$193$	1.99809	0.143826	0.0719129	+	0.997411i	$0.477090\pi$
$194$	13.9510	1.00163
$195$	4.89942	0.350855
$196$	0	0
$197$	−2.78972	−0.198760	−0.0993798	−	0.995050i	$-0.531686\pi$
$197$	−2.78972	−0.198760	−0.0993798	+	0.995050i	$0.531686\pi$
$198$	6.68002	0.474728
$199$	22.1261	1.56848	0.784238	−	0.620460i	$-0.213054\pi$
$199$	22.1261	1.56848	0.784238	+	0.620460i	$0.213054\pi$
$200$	9.12095	0.644948
$201$	9.19482	0.648553
$202$	−27.6127	−1.94283
$203$	0	0
$204$	−0.456553	−0.0319651
$205$	1.27945	0.0893610
$206$	14.3485	0.999708
$207$	−6.82949	−0.474682
$208$	−16.3836	−1.13600
$209$	21.8837	1.51373
$210$	0	0
$211$	−2.11123	−0.145343	−0.0726717	−	0.997356i	$-0.523153\pi$
$211$	−2.11123	−0.145343	−0.0726717	+	0.997356i	$0.523153\pi$
$212$	0.558502	0.0383581
$213$	6.31030	0.432374
$214$	14.1434	0.966820
$215$	−4.23217	−0.288632
$216$	2.71215	0.184538
$217$	0	0
$218$	10.5553	0.714892
$219$	1.54239	0.104225
$220$	−0.877581	−0.0591665
$221$	11.6104	0.781001
$222$	−2.30356	−0.154605
$223$	24.2366	1.62300	0.811501	−	0.584351i	$-0.198651\pi$
$223$	24.2366	1.62300	0.811501	+	0.584351i	$0.198651\pi$
$224$	0	0
$225$	−3.36300	−0.224200
$226$	23.7658	1.58088
$227$	−2.14939	−0.142660	−0.0713301	−	0.997453i	$-0.522724\pi$
$227$	−2.14939	−0.142660	−0.0713301	+	0.997453i	$0.522724\pi$
$228$	−0.723409	−0.0479089
$229$	−3.06900	−0.202805	−0.101402	−	0.994845i	$-0.532333\pi$
$229$	−3.06900	−0.202805	−0.101402	+	0.994845i	$0.532333\pi$
$230$	12.8142	0.844942
$231$	0	0
$232$	23.6926	1.55550
$233$	9.37576	0.614227	0.307113	−	0.951673i	$-0.400637\pi$
$233$	9.37576	0.614227	0.307113	+	0.951673i	$0.400637\pi$
$234$	5.61561	0.367104
$235$	−9.05525	−0.590700
$236$	−1.61150	−0.104900
$237$	−12.1437	−0.788821
$238$	0	0
$239$	15.5926	1.00860	0.504300	−	0.863528i	$-0.331750\pi$
$239$	15.5926	1.00860	0.504300	+	0.863528i	$0.331750\pi$
$240$	−5.47412	−0.353353
$241$	−4.22330	−0.272047	−0.136023	−	0.990706i	$-0.543432\pi$
$241$	−4.22330	−0.272047	−0.136023	+	0.990706i	$0.543432\pi$
$242$	14.2969	0.919042
$243$	−1.00000	−0.0641500
$244$	1.74549	0.111744
$245$	0	0
$246$	1.46649	0.0934997
$247$	18.3967	1.17056
$248$	0.685902	0.0435548
$249$	−11.4396	−0.724956
$250$	15.6915	0.992417
$251$	4.51217	0.284806	0.142403	−	0.989809i	$-0.454517\pi$
$251$	4.51217	0.284806	0.142403	+	0.989809i	$0.454517\pi$
$252$	0	0
$253$	−31.1091	−1.95582
$254$	−13.6401	−0.855857
$255$	3.87930	0.242931
$256$	3.59391	0.224619
$257$	4.76009	0.296927	0.148463	−	0.988918i	$-0.452567\pi$
$257$	4.76009	0.296927	0.148463	+	0.988918i	$0.452567\pi$
$258$	−4.85083	−0.302000
$259$	0	0
$260$	−0.737746	−0.0457531
$261$	−8.73574	−0.540729
$262$	−3.46307	−0.213949
$263$	−28.7541	−1.77305	−0.886527	−	0.462678i	$-0.846889\pi$
$263$	−28.7541	−1.77305	−0.886527	+	0.462678i	$0.846889\pi$
$264$	12.3542	0.760346
$265$	−4.74555	−0.291517
$266$	0	0
$267$	−6.14545	−0.376095
$268$	−1.38454	−0.0845744
$269$	25.0023	1.52442	0.762208	−	0.647332i	$-0.224115\pi$
$269$	25.0023	1.52442	0.762208	+	0.647332i	$0.224115\pi$
$270$	1.87630	0.114188
$271$	25.4980	1.54890	0.774448	−	0.632638i	$-0.218028\pi$
$271$	25.4980	1.54890	0.774448	+	0.632638i	$0.218028\pi$
$272$	−12.9723	−0.786563
$273$	0	0
$274$	−11.8060	−0.713229
$275$	−15.3189	−0.923762
$276$	1.02837	0.0619008
$277$	22.6527	1.36107	0.680535	−	0.732716i	$-0.261748\pi$
$277$	22.6527	1.36107	0.680535	+	0.732716i	$0.261748\pi$
$278$	6.40727	0.384282
$279$	−0.252900	−0.0151407
$280$	0	0
$281$	−26.4784	−1.57957	−0.789784	−	0.613385i	$-0.789807\pi$
$281$	−26.4784	−1.57957	−0.789784	+	0.613385i	$0.789807\pi$
$282$	−10.3790	−0.618058
$283$	19.4386	1.15550	0.577752	−	0.816212i	$-0.303930\pi$
$283$	19.4386	1.15550	0.577752	+	0.816212i	$0.303930\pi$
$284$	−0.950195	−0.0563837
$285$	6.14675	0.364102
$286$	25.5798	1.51257
$287$	0	0
$288$	−0.850033	−0.0500887
$289$	−7.80702	−0.459237
$290$	16.3909	0.962505
$291$	−9.51325	−0.557677
$292$	−0.232251	−0.0135915
$293$	19.8355	1.15880	0.579400	−	0.815043i	$-0.303287\pi$
$293$	19.8355	1.15880	0.579400	+	0.815043i	$0.303287\pi$
$294$	0	0
$295$	13.6928	0.797226
$296$	−4.26025	−0.247622
$297$	−4.55512	−0.264315
$298$	31.8406	1.84447
$299$	−26.1522	−1.51242
$300$	0.506395	0.0292367
$301$	0	0
$302$	11.9892	0.689899
$303$	18.8292	1.08171
$304$	−20.5547	−1.17889
$305$	−14.8313	−0.849239
$306$	4.44637	0.254182
$307$	−18.8959	−1.07845	−0.539223	−	0.842163i	$-0.681282\pi$
$307$	−18.8959	−1.07845	−0.539223	+	0.842163i	$0.681282\pi$
$308$	0	0
$309$	−9.78428	−0.556608
$310$	0.474516	0.0269507
$311$	−22.0458	−1.25011	−0.625053	−	0.780583i	$-0.714923\pi$
$311$	−22.0458	−1.25011	−0.625053	+	0.780583i	$0.714923\pi$
$312$	10.3856	0.587971
$313$	−11.6199	−0.656795	−0.328397	−	0.944540i	$-0.606509\pi$
$313$	−11.6199	−0.656795	−0.328397	+	0.944540i	$0.606509\pi$
$314$	−24.0792	−1.35887
$315$	0	0
$316$	1.82859	0.102866
$317$	−6.76104	−0.379738	−0.189869	−	0.981809i	$-0.560806\pi$
$317$	−6.76104	−0.379738	−0.189869	+	0.981809i	$0.560806\pi$
$318$	−5.43926	−0.305019
$319$	−39.7923	−2.22794
$320$	−9.35333	−0.522867
$321$	−9.64440	−0.538298
$322$	0	0
$323$	14.5663	0.810490
$324$	0.150578	0.00836547
$325$	−12.8779	−0.714339
$326$	−11.2223	−0.621548
$327$	−7.19766	−0.398031
$328$	2.71215	0.149753
$329$	0	0
$330$	8.54678	0.470485
$331$	27.7408	1.52477	0.762387	−	0.647122i	$-0.224028\pi$
$331$	27.7408	1.52477	0.762387	+	0.647122i	$0.224028\pi$
$332$	1.72256	0.0945377
$333$	1.57080	0.0860794
$334$	0.310560	0.0169931
$335$	11.7644	0.642755
$336$	0	0
$337$	16.1071	0.877411	0.438706	−	0.898631i	$-0.355437\pi$
$337$	16.1071	0.877411	0.438706	+	0.898631i	$0.355437\pi$
$338$	2.43958	0.132696
$339$	−16.2060	−0.880188
$340$	−0.584138	−0.0316793
$341$	−1.15199	−0.0623837
$342$	7.04529	0.380966
$343$	0	0
$344$	−8.97123	−0.483696
$345$	−8.73802	−0.470439
$346$	0.147651	0.00793777
$347$	−22.8151	−1.22478	−0.612390	−	0.790556i	$-0.709792\pi$
$347$	−22.8151	−1.22478	−0.612390	+	0.790556i	$0.709792\pi$
$348$	1.31541	0.0705136
$349$	35.0143	1.87427	0.937136	−	0.348965i	$-0.113467\pi$
$349$	35.0143	1.87427	0.937136	+	0.348965i	$0.113467\pi$
$350$	0	0
$351$	−3.82930	−0.204393
$352$	−3.87200	−0.206378
$353$	20.4057	1.08609	0.543044	−	0.839704i	$-0.317272\pi$
$353$	20.4057	1.08609	0.543044	+	0.839704i	$0.317272\pi$
$354$	15.6944	0.834149
$355$	8.07374	0.428509
$356$	0.925372	0.0490446
$357$	0	0
$358$	8.74080	0.461966
$359$	−12.3014	−0.649242	−0.324621	−	0.945844i	$-0.605237\pi$
$359$	−12.3014	−0.649242	−0.324621	+	0.945844i	$0.605237\pi$
$360$	3.47007	0.182889
$361$	4.08034	0.214755
$362$	12.8084	0.673197
$363$	−9.74912	−0.511696
$364$	0	0
$365$	1.97342	0.103293
$366$	−16.9994	−0.888571
$367$	−20.8417	−1.08793	−0.543963	−	0.839109i	$-0.683077\pi$
$367$	−20.8417	−1.08793	−0.543963	+	0.839109i	$0.683077\pi$
$368$	29.2199	1.52319
$369$	−1.00000	−0.0520579
$370$	−2.94730	−0.153223
$371$	0	0
$372$	0.0380812	0.00197442
$373$	−5.74240	−0.297330	−0.148665	−	0.988888i	$-0.547498\pi$
$373$	−5.74240	−0.297330	−0.148665	+	0.988888i	$0.547498\pi$
$374$	20.2538	1.04730
$375$	−10.7001	−0.552549
$376$	−19.1951	−0.989909
$377$	−33.4518	−1.72285
$378$	0	0
$379$	23.9770	1.23162	0.615808	−	0.787896i	$-0.288830\pi$
$379$	23.9770	1.23162	0.615808	+	0.787896i	$0.288830\pi$
$380$	−0.925569	−0.0474807
$381$	9.30123	0.476516
$382$	32.0426	1.63944
$383$	32.3926	1.65518	0.827591	−	0.561331i	$-0.189710\pi$
$383$	32.3926	1.65518	0.827591	+	0.561331i	$0.189710\pi$
$384$	−12.4207	−0.633839
$385$	0	0
$386$	2.93017	0.149142
$387$	3.30779	0.168145
$388$	1.43249	0.0727237
$389$	5.10993	0.259084	0.129542	−	0.991574i	$-0.458649\pi$
$389$	5.10993	0.259084	0.129542	+	0.991574i	$0.458649\pi$
$390$	7.18492	0.363823
$391$	−20.7070	−1.04720
$392$	0	0
$393$	2.36148	0.119121
$394$	−4.09109	−0.206106
$395$	−15.5374	−0.781770
$396$	0.685903	0.0344679
$397$	4.25431	0.213518	0.106759	−	0.994285i	$-0.465953\pi$
$397$	4.25431	0.213518	0.106759	+	0.994285i	$0.465953\pi$
$398$	32.4476	1.62645
$399$	0	0
$400$	14.3885	0.719426
$401$	−22.6592	−1.13155	−0.565774	−	0.824561i	$-0.691422\pi$
$401$	−22.6592	−1.13155	−0.565774	+	0.824561i	$0.691422\pi$
$402$	13.4841	0.672524
$403$	−0.968430	−0.0482409
$404$	−2.83527	−0.141060
$405$	−1.27945	−0.0635766
$406$	0	0
$407$	7.15519	0.354670
$408$	8.22322	0.407110
$409$	−8.95406	−0.442750	−0.221375	−	0.975189i	$-0.571054\pi$
$409$	−8.95406	−0.442750	−0.221375	+	0.975189i	$0.571054\pi$
$410$	1.87630	0.0926639
$411$	8.05057	0.397106
$412$	1.47330	0.0725844
$413$	0	0
$414$	−10.0153	−0.492227
$415$	−14.6365	−0.718475
$416$	−3.25503	−0.159591
$417$	−4.36913	−0.213957
$418$	32.0921	1.56968
$419$	−2.97330	−0.145255	−0.0726276	−	0.997359i	$-0.523138\pi$
$419$	−2.97330	−0.145255	−0.0726276	+	0.997359i	$0.523138\pi$
$420$	0	0
$421$	−28.2554	−1.37708	−0.688541	−	0.725197i	$-0.741749\pi$
$421$	−28.2554	−1.37708	−0.688541	+	0.725197i	$0.741749\pi$
$422$	−3.09609	−0.150715
$423$	7.07743	0.344117
$424$	−10.0595	−0.488532
$425$	−10.1966	−0.494607
$426$	9.25396	0.448356
$427$	0	0
$428$	1.45224	0.0701966
$429$	−17.4429	−0.842153
$430$	−6.20642	−0.299300
$431$	−3.95002	−0.190266	−0.0951330	−	0.995465i	$-0.530328\pi$
$431$	−3.95002	−0.190266	−0.0951330	+	0.995465i	$0.530328\pi$
$432$	4.27848	0.205849
$433$	−26.0349	−1.25116	−0.625578	−	0.780162i	$-0.715137\pi$
$433$	−26.0349	−1.25116	−0.625578	+	0.780162i	$0.715137\pi$
$434$	0	0
$435$	−11.1770	−0.535895
$436$	1.08381	0.0519052
$437$	−32.8102	−1.56953
$438$	2.26189	0.108077
$439$	11.7277	0.559731	0.279865	−	0.960039i	$-0.409710\pi$
$439$	11.7277	0.559731	0.279865	+	0.960039i	$0.409710\pi$
$440$	15.8066	0.753550
$441$	0	0
$442$	17.0265	0.809868
$443$	−19.0476	−0.904979	−0.452490	−	0.891770i	$-0.649464\pi$
$443$	−19.0476	−0.904979	−0.452490	+	0.891770i	$0.649464\pi$
$444$	−0.236529	−0.0112252
$445$	−7.86282	−0.372733
$446$	35.5426	1.68299
$447$	−21.7122	−1.02695
$448$	0	0
$449$	26.3284	1.24252	0.621258	−	0.783606i	$-0.286622\pi$
$449$	26.3284	1.24252	0.621258	+	0.783606i	$0.286622\pi$
$450$	−4.93178	−0.232487
$451$	−4.55512	−0.214492
$452$	2.44027	0.114781
$453$	−8.17544	−0.384116
$454$	−3.15205	−0.147933
$455$	0	0
$456$	13.0297	0.610172
$457$	21.8307	1.02120	0.510598	−	0.859820i	$-0.329424\pi$
$457$	21.8307	1.02120	0.510598	+	0.859820i	$0.329424\pi$
$458$	−4.50064	−0.210301
$459$	−3.03199	−0.141521
$460$	1.31576	0.0613475
$461$	−24.3400	−1.13363	−0.566813	−	0.823847i	$-0.691824\pi$
$461$	−24.3400	−1.13363	−0.566813	+	0.823847i	$0.691824\pi$
$462$	0	0
$463$	−42.6333	−1.98134	−0.990669	−	0.136288i	$-0.956483\pi$
$463$	−42.6333	−1.98134	−0.990669	+	0.136288i	$0.956483\pi$
$464$	37.3757	1.73512
$465$	−0.323574	−0.0150054
$466$	13.7494	0.636929
$467$	−20.2806	−0.938473	−0.469237	−	0.883072i	$-0.655471\pi$
$467$	−20.2806	−0.938473	−0.469237	+	0.883072i	$0.655471\pi$
$468$	0.576610	0.0266538
$469$	0	0
$470$	−13.2794	−0.612533
$471$	16.4197	0.756578
$472$	29.0256	1.33601
$473$	15.0674	0.692800
$474$	−17.8086	−0.817977
$475$	−16.1565	−0.741311
$476$	0	0
$477$	3.70905	0.169826
$478$	22.8663	1.04588
$479$	9.77588	0.446671	0.223336	−	0.974742i	$-0.428305\pi$
$479$	9.77588	0.446671	0.223336	+	0.974742i	$0.428305\pi$
$480$	−1.08758	−0.0496409
$481$	6.01507	0.274264
$482$	−6.19340	−0.282102
$483$	0	0
$484$	1.46801	0.0667276
$485$	−12.1718	−0.552692
$486$	−1.46649	−0.0665211
$487$	41.3316	1.87291	0.936456	−	0.350784i	$-0.114085\pi$
$487$	41.3316	1.87291	0.936456	+	0.350784i	$0.114085\pi$
$488$	−31.4390	−1.42318
$489$	7.65254	0.346060
$490$	0	0
$491$	10.1552	0.458297	0.229149	−	0.973391i	$-0.426406\pi$
$491$	10.1552	0.458297	0.229149	+	0.973391i	$0.426406\pi$
$492$	0.150578	0.00678860
$493$	−26.4867	−1.19290
$494$	26.9785	1.21382
$495$	−5.82807	−0.261952
$496$	1.08203	0.0485845
$497$	0	0
$498$	−16.7760	−0.751751
$499$	−31.2177	−1.39750	−0.698748	−	0.715368i	$-0.746259\pi$
$499$	−31.2177	−1.39750	−0.698748	+	0.715368i	$0.746259\pi$
$500$	1.61120	0.0720551
$501$	−0.211772	−0.00946126
$502$	6.61703	0.295332
$503$	−7.06660	−0.315084	−0.157542	−	0.987512i	$-0.550357\pi$
$503$	−7.06660	−0.315084	−0.157542	+	0.987512i	$0.550357\pi$
$504$	0	0
$505$	24.0911	1.07204
$506$	−45.6211	−2.02811
$507$	−1.66355	−0.0738811
$508$	−1.40056	−0.0621400
$509$	−31.3182	−1.38815	−0.694077	−	0.719901i	$-0.744187\pi$
$509$	−31.3182	−1.38815	−0.694077	+	0.719901i	$0.744187\pi$
$510$	5.68893	0.251910
$511$	0	0
$512$	−19.5709	−0.864920
$513$	−4.80420	−0.212111
$514$	6.98061	0.307901
$515$	−12.5185	−0.551633
$516$	−0.498082	−0.0219269
$517$	32.2386	1.41785
$518$	0	0
$519$	−0.100684	−0.00441952
$520$	13.2879	0.582715
$521$	−31.3657	−1.37415	−0.687077	−	0.726584i	$-0.741107\pi$
$521$	−31.3657	−1.37415	−0.687077	+	0.726584i	$0.741107\pi$
$522$	−12.8108	−0.560715
$523$	1.05298	0.0460435	0.0230217	−	0.999735i	$-0.492671\pi$
$523$	1.05298	0.0460435	0.0230217	+	0.999735i	$0.492671\pi$
$524$	−0.355587	−0.0155339
$525$	0	0
$526$	−42.1674	−1.83859
$527$	−0.766790	−0.0334019
$528$	19.4890	0.848150
$529$	23.6419	1.02791
$530$	−6.95928	−0.302292
$531$	−10.7021	−0.464430
$532$	0	0
$533$	−3.82930	−0.165865
$534$	−9.01221	−0.389996
$535$	−12.3396	−0.533486
$536$	24.9377	1.07715
$537$	−5.96037	−0.257209
$538$	36.6655	1.58076
$539$	0	0
$540$	0.192658	0.00829069
$541$	−29.4388	−1.26567	−0.632836	−	0.774286i	$-0.718109\pi$
$541$	−29.4388	−1.26567	−0.632836	+	0.774286i	$0.718109\pi$
$542$	37.3925	1.60615
$543$	−8.73411	−0.374816
$544$	−2.57729	−0.110501
$545$	−9.20908	−0.394473
$546$	0	0
$547$	−16.9838	−0.726173	−0.363087	−	0.931755i	$-0.618277\pi$
$547$	−16.9838	−0.726173	−0.363087	+	0.931755i	$0.618277\pi$
$548$	−1.21224	−0.0517844
$549$	11.5919	0.494731
$550$	−22.4649	−0.957905
$551$	−41.9682	−1.78791
$552$	−18.5226	−0.788374
$553$	0	0
$554$	33.2199	1.41138
$555$	2.00977	0.0853099
$556$	0.657897	0.0279010
$557$	34.1849	1.44846	0.724231	−	0.689557i	$-0.242195\pi$
$557$	34.1849	1.44846	0.724231	+	0.689557i	$0.242195\pi$
$558$	−0.370874	−0.0157003
$559$	12.6665	0.535738
$560$	0	0
$561$	−13.8111	−0.583105
$562$	−38.8301	−1.63795
$563$	11.3775	0.479505	0.239752	−	0.970834i	$-0.422934\pi$
$563$	11.3775	0.479505	0.239752	+	0.970834i	$0.422934\pi$
$564$	−1.06571	−0.0448744
$565$	−20.7348	−0.872320
$566$	28.5064	1.19821
$567$	0	0
$568$	17.1145	0.718107
$569$	15.5552	0.652108	0.326054	−	0.945351i	$-0.394281\pi$
$569$	15.5552	0.652108	0.326054	+	0.945351i	$0.394281\pi$
$570$	9.01412	0.377560
$571$	−4.44306	−0.185936	−0.0929682	−	0.995669i	$-0.529636\pi$
$571$	−4.44306	−0.185936	−0.0929682	+	0.995669i	$0.529636\pi$
$572$	2.62653	0.109821
$573$	−21.8499	−0.912794
$574$	0	0
$575$	22.9675	0.957813
$576$	7.31041	0.304600
$577$	10.9014	0.453831	0.226916	−	0.973914i	$-0.427136\pi$
$577$	10.9014	0.453831	0.226916	+	0.973914i	$0.427136\pi$
$578$	−11.4489	−0.476211
$579$	−1.99809	−0.0830378
$580$	1.68301	0.0698833
$581$	0	0
$582$	−13.9510	−0.578289
$583$	16.8952	0.699726
$584$	4.18320	0.173102
$585$	−4.89942	−0.202566
$586$	29.0884	1.20163
$587$	−24.0069	−0.990870	−0.495435	−	0.868645i	$-0.664991\pi$
$587$	−24.0069	−0.990870	−0.495435	+	0.868645i	$0.664991\pi$
$588$	0	0
$589$	−1.21498	−0.0500624
$590$	20.0803	0.826692
$591$	2.78972	0.114754
$592$	−6.72065	−0.276217
$593$	22.1604	0.910019	0.455009	−	0.890487i	$-0.349636\pi$
$593$	22.1604	0.910019	0.455009	+	0.890487i	$0.349636\pi$
$594$	−6.68002	−0.274084
$595$	0	0
$596$	3.26938	0.133919
$597$	−22.1261	−0.905560
$598$	−38.3518	−1.56832
$599$	14.8012	0.604760	0.302380	−	0.953188i	$-0.402219\pi$
$599$	14.8012	0.604760	0.302380	+	0.953188i	$0.402219\pi$
$600$	−9.12095	−0.372361
$601$	14.5905	0.595159	0.297580	−	0.954697i	$-0.403821\pi$
$601$	14.5905	0.595159	0.297580	+	0.954697i	$0.403821\pi$
$602$	0	0
$603$	−9.19482	−0.374442
$604$	1.23105	0.0500905
$605$	−12.4736	−0.507122
$606$	27.6127	1.12169
$607$	−27.2613	−1.10650	−0.553252	−	0.833014i	$-0.686613\pi$
$607$	−27.2613	−1.10650	−0.553252	+	0.833014i	$0.686613\pi$
$608$	−4.08373	−0.165617
$609$	0	0
$610$	−21.7499	−0.880628
$611$	27.1016	1.09641
$612$	0.456553	0.0184550
$613$	−15.2639	−0.616505	−0.308252	−	0.951305i	$-0.599744\pi$
$613$	−15.2639	−0.616505	−0.308252	+	0.951305i	$0.599744\pi$
$614$	−27.7106	−1.11831
$615$	−1.27945	−0.0515926
$616$	0	0
$617$	−3.36538	−0.135485	−0.0677425	−	0.997703i	$-0.521580\pi$
$617$	−3.36538	−0.135485	−0.0677425	+	0.997703i	$0.521580\pi$
$618$	−14.3485	−0.577182
$619$	−40.1468	−1.61363	−0.806817	−	0.590801i	$-0.798812\pi$
$619$	−40.1468	−1.61363	−0.806817	+	0.590801i	$0.798812\pi$
$620$	0.0487232	0.00195677
$621$	6.82949	0.274058
$622$	−32.3299	−1.29631
$623$	0	0
$624$	16.3836	0.655869
$625$	3.12473	0.124989
$626$	−17.0404	−0.681071
$627$	−21.8837	−0.873951
$628$	−2.47245	−0.0986613
$629$	4.76266	0.189900
$630$	0	0
$631$	4.02333	0.160166	0.0800832	−	0.996788i	$-0.474481\pi$
$631$	4.02333	0.160166	0.0800832	+	0.996788i	$0.474481\pi$
$632$	−32.9356	−1.31011
$633$	2.11123	0.0839140
$634$	−9.91496	−0.393773
$635$	11.9005	0.472257
$636$	−0.558502	−0.0221461
$637$	0	0
$638$	−58.3549	−2.31029
$639$	−6.31030	−0.249631
$640$	−15.8917	−0.628174
$641$	18.6090	0.735012	0.367506	−	0.930021i	$-0.380212\pi$
$641$	18.6090	0.735012	0.367506	+	0.930021i	$0.380212\pi$
$642$	−14.1434	−0.558194
$643$	−29.4661	−1.16203	−0.581015	−	0.813893i	$-0.697344\pi$
$643$	−29.4661	−1.16203	−0.581015	+	0.813893i	$0.697344\pi$
$644$	0	0
$645$	4.23217	0.166642
$646$	21.3613	0.840447
$647$	24.1937	0.951152	0.475576	−	0.879675i	$-0.342240\pi$
$647$	24.1937	0.951152	0.475576	+	0.879675i	$0.342240\pi$
$648$	−2.71215	−0.106543
$649$	−48.7492	−1.91357
$650$	−18.8853	−0.740742
$651$	0	0
$652$	−1.15231	−0.0451278
$653$	6.14391	0.240430	0.120215	−	0.992748i	$-0.461642\pi$
$653$	6.14391	0.240430	0.120215	+	0.992748i	$0.461642\pi$
$654$	−10.5553	−0.412743
$655$	3.02140	0.118056
$656$	4.27848	0.167047
$657$	−1.54239	−0.0601744
$658$	0	0
$659$	−28.3257	−1.10341	−0.551707	−	0.834038i	$-0.686023\pi$
$659$	−28.3257	−1.10341	−0.551707	+	0.834038i	$0.686023\pi$
$660$	0.877581	0.0341598
$661$	19.0553	0.741164	0.370582	−	0.928800i	$-0.379158\pi$
$661$	19.0553	0.741164	0.370582	+	0.928800i	$0.379158\pi$
$662$	40.6815	1.58113
$663$	−11.6104	−0.450911
$664$	−31.0259	−1.20404
$665$	0	0
$666$	2.30356	0.0892610
$667$	59.6606	2.31007
$668$	0.0318882	0.00123379
$669$	−24.2366	−0.937041
$670$	17.2523	0.666513
$671$	52.8025	2.03842
$672$	0	0
$673$	18.6442	0.718682	0.359341	−	0.933206i	$-0.383001\pi$
$673$	18.6442	0.718682	0.359341	+	0.933206i	$0.383001\pi$
$674$	23.6209	0.909842
$675$	3.36300	0.129442
$676$	0.250495	0.00963444
$677$	−3.36750	−0.129424	−0.0647118	−	0.997904i	$-0.520613\pi$
$677$	−3.36750	−0.129424	−0.0647118	+	0.997904i	$0.520613\pi$
$678$	−23.7658	−0.912721
$679$	0	0
$680$	10.5212	0.403471
$681$	2.14939	0.0823649
$682$	−1.68937	−0.0646895
$683$	19.9474	0.763266	0.381633	−	0.924314i	$-0.375362\pi$
$683$	19.9474	0.763266	0.381633	+	0.924314i	$0.375362\pi$
$684$	0.723409	0.0276602
$685$	10.3003	0.393556
$686$	0	0
$687$	3.06900	0.117089
$688$	−14.1523	−0.539553
$689$	14.2031	0.541093
$690$	−12.8142	−0.487827
$691$	−14.3012	−0.544042	−0.272021	−	0.962291i	$-0.587692\pi$
$691$	−14.3012	−0.544042	−0.272021	+	0.962291i	$0.587692\pi$
$692$	0.0151608	0.000576327 0
$693$	0	0
$694$	−33.4580	−1.27005
$695$	−5.59010	−0.212045
$696$	−23.6926	−0.898067
$697$	−3.03199	−0.114845
$698$	51.3479	1.94355
$699$	−9.37576	−0.354624
$700$	0	0
$701$	0.464844	0.0175569	0.00877846	−	0.999961i	$-0.497206\pi$
$701$	0.464844	0.0175569	0.00877846	+	0.999961i	$0.497206\pi$
$702$	−5.61561	−0.211948
$703$	7.54644	0.284620
$704$	33.2998	1.25503
$705$	9.05525	0.341041
$706$	29.9247	1.12623
$707$	0	0
$708$	1.61150	0.0605639
$709$	13.2728	0.498472	0.249236	−	0.968443i	$-0.419821\pi$
$709$	13.2728	0.498472	0.249236	+	0.968443i	$0.419821\pi$
$710$	11.8400	0.444348
$711$	12.1437	0.455426
$712$	−16.6674	−0.624636
$713$	1.72718	0.0646833
$714$	0	0
$715$	−22.3174	−0.834625
$716$	0.897504	0.0335413
$717$	−15.5926	−0.582316
$718$	−18.0398	−0.673239
$719$	34.4829	1.28600	0.642998	−	0.765868i	$-0.277690\pi$
$719$	34.4829	1.28600	0.642998	+	0.765868i	$0.277690\pi$
$720$	5.47412	0.204009
$721$	0	0
$722$	5.98375	0.222692
$723$	4.22330	0.157066
$724$	1.31517	0.0488778
$725$	29.3783	1.09108
$726$	−14.2969	−0.530609
$727$	21.6773	0.803967	0.401984	−	0.915647i	$-0.368321\pi$
$727$	21.6773	0.803967	0.401984	+	0.915647i	$0.368321\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	2.89399	0.107111
$731$	10.0292	0.370944
$732$	−1.74549	−0.0645152
$733$	22.6515	0.836652	0.418326	−	0.908297i	$-0.362617\pi$
$733$	22.6515	0.836652	0.418326	+	0.908297i	$0.362617\pi$
$734$	−30.5640	−1.12814
$735$	0	0
$736$	5.80529	0.213986
$737$	−41.8835	−1.54280
$738$	−1.46649	−0.0539821
$739$	48.9365	1.80016	0.900079	−	0.435727i	$-0.143509\pi$
$739$	48.9365	1.80016	0.900079	+	0.435727i	$0.143509\pi$
$740$	−0.302628	−0.0111248
$741$	−18.3967	−0.675821
$742$	0	0
$743$	−30.4774	−1.11811	−0.559054	−	0.829131i	$-0.688835\pi$
$743$	−30.4774	−1.11811	−0.559054	+	0.829131i	$0.688835\pi$
$744$	−0.685902	−0.0251464
$745$	−27.7797	−1.01777
$746$	−8.42114	−0.308320
$747$	11.4396	0.418553
$748$	2.07965	0.0760396
$749$	0	0
$750$	−15.6915	−0.572972
$751$	−38.1654	−1.39268	−0.696338	−	0.717714i	$-0.745188\pi$
$751$	−38.1654	−1.39268	−0.696338	+	0.717714i	$0.745188\pi$
$752$	−30.2807	−1.10422
$753$	−4.51217	−0.164433
$754$	−49.0565	−1.78653
$755$	−10.4601	−0.380682
$756$	0	0
$757$	16.1752	0.587898	0.293949	−	0.955821i	$-0.405030\pi$
$757$	16.1752	0.587898	0.293949	+	0.955821i	$0.405030\pi$
$758$	35.1619	1.27714
$759$	31.1091	1.12919
$760$	16.6709	0.604718
$761$	−3.03664	−0.110078	−0.0550391	−	0.998484i	$-0.517528\pi$
$761$	−3.03664	−0.110078	−0.0550391	+	0.998484i	$0.517528\pi$
$762$	13.6401	0.494129
$763$	0	0
$764$	3.29013	0.119033
$765$	−3.87930	−0.140256
$766$	47.5032	1.71636
$767$	−40.9814	−1.47975
$768$	−3.59391	−0.129684
$769$	31.1611	1.12370	0.561848	−	0.827240i	$-0.310091\pi$
$769$	31.1611	1.12370	0.561848	+	0.827240i	$0.310091\pi$
$770$	0	0
$771$	−4.76009	−0.171431
$772$	0.300869	0.0108285
$773$	23.7229	0.853252	0.426626	−	0.904428i	$-0.359702\pi$
$773$	23.7229	0.853252	0.426626	+	0.904428i	$0.359702\pi$
$774$	4.85083	0.174360
$775$	0.850501	0.0305509
$776$	−25.8014	−0.926215
$777$	0	0
$778$	7.49364	0.268660
$779$	−4.80420	−0.172128
$780$	0.737746	0.0264156
$781$	−28.7442	−1.02855
$782$	−30.3664	−1.08590
$783$	8.73574	0.312190
$784$	0	0
$785$	21.0082	0.749815
$786$	3.46307	0.123524
$787$	15.3274	0.546363	0.273182	−	0.961962i	$-0.411924\pi$
$787$	15.3274	0.546363	0.273182	+	0.961962i	$0.411924\pi$
$788$	−0.420072	−0.0149645
$789$	28.7541	1.02367
$790$	−22.7853	−0.810665
$791$	0	0
$792$	−12.3542	−0.438986
$793$	44.3889	1.57630
$794$	6.23889	0.221410
$795$	4.74555	0.168307
$796$	3.33171	0.118089
$797$	−12.7798	−0.452683	−0.226342	−	0.974048i	$-0.572677\pi$
$797$	−12.7798	−0.452683	−0.226342	+	0.974048i	$0.572677\pi$
$798$	0	0
$799$	21.4587	0.759155
$800$	2.85866	0.101069
$801$	6.14545	0.217139
$802$	−33.2294	−1.17337
$803$	−7.02578	−0.247934
$804$	1.38454	0.0488290
$805$	0	0
$806$	−1.42019	−0.0500240
$807$	−25.0023	−0.880122
$808$	51.0676	1.79655
$809$	36.0453	1.26729	0.633643	−	0.773625i	$-0.281559\pi$
$809$	36.0453	1.26729	0.633643	+	0.773625i	$0.281559\pi$
$810$	−1.87630	−0.0659265
$811$	−50.0804	−1.75856	−0.879281	−	0.476304i	$-0.841976\pi$
$811$	−50.0804	−1.75856	−0.879281	+	0.476304i	$0.841976\pi$
$812$	0	0
$813$	−25.4980	−0.894255
$814$	10.4930	0.367779
$815$	9.79108	0.342966
$816$	12.9723	0.454122
$817$	15.8913	0.555966
$818$	−13.1310	−0.459114
$819$	0	0
$820$	0.192658	0.00672792
$821$	6.58081	0.229672	0.114836	−	0.993384i	$-0.463366\pi$
$821$	6.58081	0.229672	0.114836	+	0.993384i	$0.463366\pi$
$822$	11.8060	0.411783
$823$	−47.0271	−1.63926	−0.819630	−	0.572893i	$-0.805821\pi$
$823$	−47.0271	−1.63926	−0.819630	+	0.572893i	$0.805821\pi$
$824$	−26.5364	−0.924441
$825$	15.3189	0.533334
$826$	0	0
$827$	−40.7549	−1.41719	−0.708593	−	0.705617i	$-0.750670\pi$
$827$	−40.7549	−1.41719	−0.708593	+	0.705617i	$0.750670\pi$
$828$	−1.02837	−0.0357385
$829$	3.84526	0.133551	0.0667757	−	0.997768i	$-0.478729\pi$
$829$	3.84526	0.133551	0.0667757	+	0.997768i	$0.478729\pi$
$830$	−21.4641	−0.745031
$831$	−22.6527	−0.785814
$832$	27.9937	0.970509
$833$	0	0
$834$	−6.40727	−0.221865
$835$	−0.270952	−0.00937669
$836$	3.29521	0.113967
$837$	0.252900	0.00874149
$838$	−4.36030	−0.150624
$839$	−6.17902	−0.213323	−0.106662	−	0.994295i	$-0.534016\pi$
$839$	−6.17902	−0.213323	−0.106662	+	0.994295i	$0.534016\pi$
$840$	0	0
$841$	47.3131	1.63149
$842$	−41.4361	−1.42798
$843$	26.4784	0.911964
$844$	−0.317906	−0.0109428
$845$	−2.12844	−0.0732206
$846$	10.3790	0.356836
$847$	0	0
$848$	−15.8691	−0.544947
$849$	−19.4386	−0.667131
$850$	−14.9531	−0.512888
$851$	−10.7278	−0.367743
$852$	0.950195	0.0325531
$853$	46.9552	1.60772	0.803859	−	0.594821i	$-0.202777\pi$
$853$	46.9552	1.60772	0.803859	+	0.594821i	$0.202777\pi$
$854$	0	0
$855$	−6.14675	−0.210215
$856$	−26.1570	−0.894029
$857$	26.3427	0.899851	0.449925	−	0.893066i	$-0.351451\pi$
$857$	26.3427	0.899851	0.449925	+	0.893066i	$0.351451\pi$
$858$	−25.5798	−0.873280
$859$	49.5524	1.69071	0.845354	−	0.534207i	$-0.179390\pi$
$859$	49.5524	1.69071	0.845354	+	0.534207i	$0.179390\pi$
$860$	−0.637274	−0.0217309
$861$	0	0
$862$	−5.79265	−0.197298
$863$	28.2906	0.963024	0.481512	−	0.876439i	$-0.340088\pi$
$863$	28.2906	0.963024	0.481512	+	0.876439i	$0.340088\pi$
$864$	0.850033	0.0289187
$865$	−0.128820	−0.00438002
$866$	−38.1798	−1.29740
$867$	7.80702	0.265140
$868$	0	0
$869$	55.3162	1.87647
$870$	−16.3909	−0.555703
$871$	−35.2098	−1.19304
$872$	−19.5211	−0.661069
$873$	9.51325	0.321975
$874$	−48.1157	−1.62754
$875$	0	0
$876$	0.232251	0.00784703
$877$	30.9380	1.04470	0.522351	−	0.852731i	$-0.325055\pi$
$877$	30.9380	1.04470	0.522351	+	0.852731i	$0.325055\pi$
$878$	17.1984	0.580419
$879$	−19.8355	−0.669033
$880$	24.9353	0.840569
$881$	16.8026	0.566093	0.283046	−	0.959106i	$-0.408655\pi$
$881$	16.8026	0.566093	0.283046	+	0.959106i	$0.408655\pi$
$882$	0	0
$883$	27.2149	0.915853	0.457926	−	0.888990i	$-0.348592\pi$
$883$	27.2149	0.915853	0.457926	+	0.888990i	$0.348592\pi$
$884$	1.74828	0.0588010
$885$	−13.6928	−0.460278
$886$	−27.9330	−0.938428
$887$	−18.8116	−0.631630	−0.315815	−	0.948821i	$-0.602278\pi$
$887$	−18.8116	−0.631630	−0.315815	+	0.948821i	$0.602278\pi$
$888$	4.26025	0.142965
$889$	0	0
$890$	−11.5307	−0.386510
$891$	4.55512	0.152602
$892$	3.64951	0.122195
$893$	34.0014	1.13781
$894$	−31.8406	−1.06491
$895$	−7.62603	−0.254910
$896$	0	0
$897$	26.1522	0.873196
$898$	38.6102	1.28844
$899$	2.20927	0.0736832
$900$	−0.506395	−0.0168798
$901$	11.2458	0.374652
$902$	−6.68002	−0.222420
$903$	0	0
$904$	−43.9530	−1.46186
$905$	−11.1749	−0.371466
$906$	−11.9892	−0.398313
$907$	−9.49673	−0.315334	−0.157667	−	0.987492i	$-0.550397\pi$
$907$	−9.49673	−0.315334	−0.157667	+	0.987492i	$0.550397\pi$
$908$	−0.323652	−0.0107408
$909$	−18.8292	−0.624525
$910$	0	0
$911$	−4.27058	−0.141491	−0.0707454	−	0.997494i	$-0.522538\pi$
$911$	−4.27058	−0.141491	−0.0707454	+	0.997494i	$0.522538\pi$
$912$	20.5547	0.680634
$913$	52.1088	1.72455
$914$	32.0143	1.05894
$915$	14.8313	0.490308
$916$	−0.462125	−0.0152690
$917$	0	0
$918$	−4.44637	−0.146752
$919$	17.0686	0.563040	0.281520	−	0.959555i	$-0.409161\pi$
$919$	17.0686	0.563040	0.281520	+	0.959555i	$0.409161\pi$
$920$	−23.6988	−0.781327
$921$	18.8959	0.622641
$922$	−35.6942	−1.17553
$923$	−24.1640	−0.795369
$924$	0	0
$925$	−5.28260	−0.173691
$926$	−62.5211	−2.05457
$927$	9.78428	0.321358
$928$	7.42567	0.243759
$929$	7.76360	0.254716	0.127358	−	0.991857i	$-0.459350\pi$
$929$	7.76360	0.254716	0.127358	+	0.991857i	$0.459350\pi$
$930$	−0.474516	−0.0155600
$931$	0	0
$932$	1.41179	0.0462446
$933$	22.0458	0.721749
$934$	−29.7412	−0.973161
$935$	−17.6707	−0.577892
$936$	−10.3856	−0.339465
$937$	−15.7893	−0.515815	−0.257907	−	0.966170i	$-0.583033\pi$
$937$	−15.7893	−0.515815	−0.257907	+	0.966170i	$0.583033\pi$
$938$	0	0
$939$	11.6199	0.379201
$940$	−1.36353	−0.0444733
$941$	−4.84076	−0.157804	−0.0789022	−	0.996882i	$-0.525141\pi$
$941$	−4.84076	−0.157804	−0.0789022	+	0.996882i	$0.525141\pi$
$942$	24.0792	0.784542
$943$	6.82949	0.222399
$944$	45.7886	1.49029
$945$	0	0
$946$	22.0961	0.718407
$947$	29.4532	0.957101	0.478550	−	0.878060i	$-0.341162\pi$
$947$	29.4532	0.957101	0.478550	+	0.878060i	$0.341162\pi$
$948$	−1.82859	−0.0593897
$949$	−5.90628	−0.191726
$950$	−23.6933	−0.768711
$951$	6.76104	0.219242
$952$	0	0
$953$	−42.3799	−1.37282	−0.686410	−	0.727215i	$-0.740814\pi$
$953$	−42.3799	−1.37282	−0.686410	+	0.727215i	$0.740814\pi$
$954$	5.43926	0.176103
$955$	−27.9560	−0.904634
$956$	2.34791	0.0759367
$957$	39.7923	1.28630
$958$	14.3362	0.463181
$959$	0	0
$960$	9.35333	0.301877
$961$	−30.9360	−0.997937
$962$	8.82101	0.284401
$963$	9.64440	0.310786
$964$	−0.635938	−0.0204822
$965$	−2.55647	−0.0822956
$966$	0	0
$967$	53.7551	1.72865	0.864324	−	0.502935i	$-0.167747\pi$
$967$	53.7551	1.72865	0.864324	+	0.502935i	$0.167747\pi$
$968$	−26.4411	−0.849848
$969$	−14.5663	−0.467937
$970$	−17.8497	−0.573120
$971$	−59.8654	−1.92117	−0.960586	−	0.277984i	$-0.910334\pi$
$971$	−59.8654	−1.92117	−0.960586	+	0.277984i	$0.910334\pi$
$972$	−0.150578	−0.00482981
$973$	0	0
$974$	60.6121	1.94214
$975$	12.8779	0.412424
$976$	−49.5958	−1.58752
$977$	−40.7952	−1.30515	−0.652577	−	0.757722i	$-0.726312\pi$
$977$	−40.7952	−1.30515	−0.652577	+	0.757722i	$0.726312\pi$
$978$	11.2223	0.358851
$979$	27.9933	0.894669
$980$	0	0
$981$	7.19766	0.229804
$982$	14.8924	0.475237
$983$	−5.14025	−0.163948	−0.0819742	−	0.996634i	$-0.526123\pi$
$983$	−5.14025	−0.163948	−0.0819742	+	0.996634i	$0.526123\pi$
$984$	−2.71215	−0.0864602
$985$	3.56933	0.113728
$986$	−38.8423	−1.23699
$987$	0	0
$988$	2.77015	0.0881302
$989$	−22.5905	−0.718338
$990$	−8.54678	−0.271634
$991$	10.6227	0.337440	0.168720	−	0.985664i	$-0.446037\pi$
$991$	10.6227	0.337440	0.168720	+	0.985664i	$0.446037\pi$
$992$	0.214973	0.00682541
$993$	−27.7408	−0.880328
$994$	0	0
$995$	−28.3093	−0.897465
$996$	−1.72256	−0.0545814
$997$	−33.9535	−1.07532	−0.537659	−	0.843162i	$-0.680691\pi$
$997$	−33.9535	−1.07532	−0.537659	+	0.843162i	$0.680691\pi$
$998$	−45.7803	−1.44915
$999$	−1.57080	−0.0496980

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bh.1.11		13
7.3	odd	6		861.2.i.f.247.3	✓	26
7.5	odd	6		861.2.i.f.739.3	yes	26
7.6	odd	2		6027.2.a.bi.1.11		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.f.247.3	✓	26	7.3	odd	6
861.2.i.f.739.3	yes	26	7.5	odd	6
6027.2.a.bh.1.11		13	1.1	even	1	trivial
6027.2.a.bi.1.11		13	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6027 = 3 \cdot 7^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6027.a (trivial)

\(f(q)\)	\(=\)	\(q+1.46649 q^{2} -1.00000 q^{3} +0.150578 q^{4} -1.27945 q^{5} -1.46649 q^{6} -2.71215 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.46649 q^{2} -1.00000 q^{3} +0.150578 q^{4} -1.27945 q^{5} -1.46649 q^{6} -2.71215 q^{8} +1.00000 q^{9} -1.87630 q^{10} +4.55512 q^{11} -0.150578 q^{12} +3.82930 q^{13} +1.27945 q^{15} -4.27848 q^{16} +3.03199 q^{17} +1.46649 q^{18} +4.80420 q^{19} -0.192658 q^{20} +6.68002 q^{22} -6.82949 q^{23} +2.71215 q^{24} -3.36300 q^{25} +5.61561 q^{26} -1.00000 q^{27} -8.73574 q^{29} +1.87630 q^{30} -0.252900 q^{31} -0.850033 q^{32} -4.55512 q^{33} +4.44637 q^{34} +0.150578 q^{36} +1.57080 q^{37} +7.04529 q^{38} -3.82930 q^{39} +3.47007 q^{40} -1.00000 q^{41} +3.30779 q^{43} +0.685903 q^{44} -1.27945 q^{45} -10.0153 q^{46} +7.07743 q^{47} +4.27848 q^{48} -4.93178 q^{50} -3.03199 q^{51} +0.576610 q^{52} +3.70905 q^{53} -1.46649 q^{54} -5.82807 q^{55} -4.80420 q^{57} -12.8108 q^{58} -10.7021 q^{59} +0.192658 q^{60} +11.5919 q^{61} -0.370874 q^{62} +7.31041 q^{64} -4.89942 q^{65} -6.68002 q^{66} -9.19482 q^{67} +0.456553 q^{68} +6.82949 q^{69} -6.31030 q^{71} -2.71215 q^{72} -1.54239 q^{73} +2.30356 q^{74} +3.36300 q^{75} +0.723409 q^{76} -5.61561 q^{78} +12.1437 q^{79} +5.47412 q^{80} +1.00000 q^{81} -1.46649 q^{82} +11.4396 q^{83} -3.87930 q^{85} +4.85083 q^{86} +8.73574 q^{87} -12.3542 q^{88} +6.14545 q^{89} -1.87630 q^{90} -1.02837 q^{92} +0.252900 q^{93} +10.3790 q^{94} -6.14675 q^{95} +0.850033 q^{96} +9.51325 q^{97} +4.55512 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 4 q^{2} - 13 q^{3} + 12 q^{4} + 8 q^{5} + 4 q^{6} - 12 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q - 4 * q^2 - 13 * q^3 + 12 * q^4 + 8 * q^5 + 4 * q^6 - 12 * q^8 + 13 * q^9	\( 13 q - 4 q^{2} - 13 q^{3} + 12 q^{4} + 8 q^{5} + 4 q^{6} - 12 q^{8} + 13 q^{9} + q^{10} - 10 q^{11} - 12 q^{12} + 16 q^{13} - 8 q^{15} + 26 q^{16} + 12 q^{17} - 4 q^{18} + 11 q^{19} + 6 q^{20} + q^{22} - 15 q^{23} + 12 q^{24} + 15 q^{25} + 18 q^{26} - 13 q^{27} - 8 q^{29} - q^{30} + 9 q^{31} - 23 q^{32} + 10 q^{33} - 7 q^{34} + 12 q^{36} - 2 q^{37} + 20 q^{38} - 16 q^{39} + 49 q^{40} - 13 q^{41} - 7 q^{43} - 22 q^{44} + 8 q^{45} - 4 q^{46} + 26 q^{47} - 26 q^{48} - 15 q^{50} - 12 q^{51} + 24 q^{52} + 4 q^{53} + 4 q^{54} + q^{55} - 11 q^{57} + 39 q^{58} - 3 q^{59} - 6 q^{60} + 28 q^{61} + 7 q^{62} + 2 q^{64} - 20 q^{65} - q^{66} + 7 q^{67} + 55 q^{68} + 15 q^{69} - 40 q^{71} - 12 q^{72} - 2 q^{73} + q^{74} - 15 q^{75} - 26 q^{76} - 18 q^{78} + 13 q^{79} + 22 q^{80} + 13 q^{81} + 4 q^{82} + 14 q^{83} + 48 q^{85} - 49 q^{86} + 8 q^{87} + 20 q^{88} + 35 q^{89} + q^{90} - 105 q^{92} - 9 q^{93} - 2 q^{94} + 7 q^{95} + 23 q^{96} + 64 q^{97} - 10 q^{99}+O(q^{100}) \) 13 * q - 4 * q^2 - 13 * q^3 + 12 * q^4 + 8 * q^5 + 4 * q^6 - 12 * q^8 + 13 * q^9 + q^10 - 10 * q^11 - 12 * q^12 + 16 * q^13 - 8 * q^15 + 26 * q^16 + 12 * q^17 - 4 * q^18 + 11 * q^19 + 6 * q^20 + q^22 - 15 * q^23 + 12 * q^24 + 15 * q^25 + 18 * q^26 - 13 * q^27 - 8 * q^29 - q^30 + 9 * q^31 - 23 * q^32 + 10 * q^33 - 7 * q^34 + 12 * q^36 - 2 * q^37 + 20 * q^38 - 16 * q^39 + 49 * q^40 - 13 * q^41 - 7 * q^43 - 22 * q^44 + 8 * q^45 - 4 * q^46 + 26 * q^47 - 26 * q^48 - 15 * q^50 - 12 * q^51 + 24 * q^52 + 4 * q^53 + 4 * q^54 + q^55 - 11 * q^57 + 39 * q^58 - 3 * q^59 - 6 * q^60 + 28 * q^61 + 7 * q^62 + 2 * q^64 - 20 * q^65 - q^66 + 7 * q^67 + 55 * q^68 + 15 * q^69 - 40 * q^71 - 12 * q^72 - 2 * q^73 + q^74 - 15 * q^75 - 26 * q^76 - 18 * q^78 + 13 * q^79 + 22 * q^80 + 13 * q^81 + 4 * q^82 + 14 * q^83 + 48 * q^85 - 49 * q^86 + 8 * q^87 + 20 * q^88 + 35 * q^89 + q^90 - 105 * q^92 - 9 * q^93 - 2 * q^94 + 7 * q^95 + 23 * q^96 + 64 * q^97 - 10 * q^99

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