LMFDB - Embedded newform 6027.2.a.bh.1.3

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			1.3
Root			$2.20098$ 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)

$f(q)$	$=$	$q-2.20098 q^{2} -1.00000 q^{3} +2.84432 q^{4} -2.77621 q^{5} +2.20098 q^{6} -1.85834 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.20098 q^{2} -1.00000 q^{3} +2.84432 q^{4} -2.77621 q^{5} +2.20098 q^{6} -1.85834 q^{8} +1.00000 q^{9} +6.11039 q^{10} -1.68076 q^{11} -2.84432 q^{12} -1.26732 q^{13} +2.77621 q^{15} -1.59848 q^{16} +5.32090 q^{17} -2.20098 q^{18} +0.141922 q^{19} -7.89643 q^{20} +3.69932 q^{22} -3.48122 q^{23} +1.85834 q^{24} +2.70734 q^{25} +2.78934 q^{26} -1.00000 q^{27} -2.99377 q^{29} -6.11039 q^{30} +5.66199 q^{31} +7.23490 q^{32} +1.68076 q^{33} -11.7112 q^{34} +2.84432 q^{36} +0.881374 q^{37} -0.312369 q^{38} +1.26732 q^{39} +5.15913 q^{40} -1.00000 q^{41} +4.77245 q^{43} -4.78062 q^{44} -2.77621 q^{45} +7.66210 q^{46} -6.78607 q^{47} +1.59848 q^{48} -5.95881 q^{50} -5.32090 q^{51} -3.60466 q^{52} -9.07358 q^{53} +2.20098 q^{54} +4.66614 q^{55} -0.141922 q^{57} +6.58924 q^{58} +3.92073 q^{59} +7.89643 q^{60} +9.47100 q^{61} -12.4619 q^{62} -12.7269 q^{64} +3.51834 q^{65} -3.69932 q^{66} +5.95186 q^{67} +15.1343 q^{68} +3.48122 q^{69} -2.01895 q^{71} -1.85834 q^{72} +1.94237 q^{73} -1.93989 q^{74} -2.70734 q^{75} +0.403673 q^{76} -2.78934 q^{78} -9.24032 q^{79} +4.43772 q^{80} +1.00000 q^{81} +2.20098 q^{82} +0.172587 q^{83} -14.7719 q^{85} -10.5041 q^{86} +2.99377 q^{87} +3.12341 q^{88} -11.9751 q^{89} +6.11039 q^{90} -9.90171 q^{92} -5.66199 q^{93} +14.9360 q^{94} -0.394007 q^{95} -7.23490 q^{96} -5.03657 q^{97} -1.68076 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.20098	−1.55633	−0.778165	−	0.628060i	$-0.783849\pi$
$2$	−2.20098	−1.55633	−0.778165	+	0.628060i	$0.783849\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.84432	1.42216
$5$	−2.77621	−1.24156	−0.620779	−	0.783985i	$-0.713184\pi$
$5$	−2.77621	−1.24156	−0.620779	+	0.783985i	$0.713184\pi$
$6$	2.20098	0.898547
$7$	0	0
$7$	0	0
$8$	−1.85834	−0.657021
$9$	1.00000	0.333333
$10$	6.11039	1.93227
$11$	−1.68076	−0.506768	−0.253384	−	0.967366i	$-0.581544\pi$
$11$	−1.68076	−0.506768	−0.253384	+	0.967366i	$0.581544\pi$
$12$	−2.84432	−0.821085
$13$	−1.26732	−0.351491	−0.175745	−	0.984436i	$-0.556234\pi$
$13$	−1.26732	−0.351491	−0.175745	+	0.984436i	$0.556234\pi$
$14$	0	0
$15$	2.77621	0.716814
$16$	−1.59848	−0.399620
$17$	5.32090	1.29051	0.645254	−	0.763968i	$-0.276752\pi$
$17$	5.32090	1.29051	0.645254	+	0.763968i	$0.276752\pi$
$18$	−2.20098	−0.518776
$19$	0.141922	0.0325593	0.0162796	−	0.999867i	$-0.494818\pi$
$19$	0.141922	0.0325593	0.0162796	+	0.999867i	$0.494818\pi$
$20$	−7.89643	−1.76570
$21$	0	0
$22$	3.69932	0.788698
$23$	−3.48122	−0.725884	−0.362942	−	0.931812i	$-0.618228\pi$
$23$	−3.48122	−0.725884	−0.362942	+	0.931812i	$0.618228\pi$
$24$	1.85834	0.379331
$25$	2.70734	0.541469
$26$	2.78934	0.547035
$27$	−1.00000	−0.192450
$28$	0	0
$29$	−2.99377	−0.555929	−0.277965	−	0.960591i	$-0.589660\pi$
$29$	−2.99377	−0.555929	−0.277965	+	0.960591i	$0.589660\pi$
$30$	−6.11039	−1.11560
$31$	5.66199	1.01692	0.508462	−	0.861084i	$-0.330214\pi$
$31$	5.66199	1.01692	0.508462	+	0.861084i	$0.330214\pi$
$32$	7.23490	1.27896
$33$	1.68076	0.292583
$34$	−11.7112	−2.00846
$35$	0	0
$36$	2.84432	0.474054
$37$	0.881374	0.144897	0.0724485	−	0.997372i	$-0.476919\pi$
$37$	0.881374	0.144897	0.0724485	+	0.997372i	$0.476919\pi$
$38$	−0.312369	−0.0506729
$39$	1.26732	0.202933
$40$	5.15913	0.815730
$41$	−1.00000	−0.156174
$41$	−1.00000	−0.156174
$42$	0	0
$43$	4.77245	0.727792	0.363896	−	0.931440i	$-0.381446\pi$
$43$	4.77245	0.727792	0.363896	+	0.931440i	$0.381446\pi$
$44$	−4.78062	−0.720705
$45$	−2.77621	−0.413853
$46$	7.66210	1.12972
$47$	−6.78607	−0.989851	−0.494925	−	0.868936i	$-0.664805\pi$
$47$	−6.78607	−0.989851	−0.494925	+	0.868936i	$0.664805\pi$
$48$	1.59848	0.230721
$49$	0	0
$50$	−5.95881	−0.842703
$51$	−5.32090	−0.745075
$52$	−3.60466	−0.499876
$53$	−9.07358	−1.24635	−0.623176	−	0.782082i	$-0.714158\pi$
$53$	−9.07358	−1.24635	−0.623176	+	0.782082i	$0.714158\pi$
$54$	2.20098	0.299516
$55$	4.66614	0.629182
$56$	0	0
$57$	−0.141922	−0.0187981
$58$	6.58924	0.865209
$59$	3.92073	0.510436	0.255218	−	0.966884i	$-0.417853\pi$
$59$	3.92073	0.510436	0.255218	+	0.966884i	$0.417853\pi$
$60$	7.89643	1.01943
$61$	9.47100	1.21264	0.606319	−	0.795222i	$-0.292646\pi$
$61$	9.47100	1.21264	0.606319	+	0.795222i	$0.292646\pi$
$62$	−12.4619	−1.58267
$63$	0	0
$64$	−12.7269	−1.59086
$65$	3.51834	0.436396
$66$	−3.69932	−0.455355
$67$	5.95186	0.727135	0.363568	−	0.931568i	$-0.381559\pi$
$67$	5.95186	0.727135	0.363568	+	0.931568i	$0.381559\pi$
$68$	15.1343	1.83531
$69$	3.48122	0.419090
$70$	0	0
$71$	−2.01895	−0.239606	−0.119803	−	0.992798i	$-0.538226\pi$
$71$	−2.01895	−0.239606	−0.119803	+	0.992798i	$0.538226\pi$
$72$	−1.85834	−0.219007
$73$	1.94237	0.227337	0.113669	−	0.993519i	$-0.463740\pi$
$73$	1.94237	0.227337	0.113669	+	0.993519i	$0.463740\pi$
$74$	−1.93989	−0.225508
$75$	−2.70734	−0.312617
$76$	0.403673	0.0463045
$77$	0	0
$78$	−2.78934	−0.315831
$79$	−9.24032	−1.03962	−0.519809	−	0.854283i	$-0.673997\pi$
$79$	−9.24032	−1.03962	−0.519809	+	0.854283i	$0.673997\pi$
$80$	4.43772	0.496152
$81$	1.00000	0.111111
$82$	2.20098	0.243058
$83$	0.172587	0.0189439	0.00947197	−	0.999955i	$-0.496985\pi$
$83$	0.172587	0.0189439	0.00947197	+	0.999955i	$0.496985\pi$
$84$	0	0
$85$	−14.7719	−1.60224
$86$	−10.5041	−1.13268
$87$	2.99377	0.320966
$88$	3.12341	0.332957
$89$	−11.9751	−1.26936	−0.634680	−	0.772775i	$-0.718868\pi$
$89$	−11.9751	−1.26936	−0.634680	+	0.772775i	$0.718868\pi$
$90$	6.11039	0.644091
$91$	0	0
$92$	−9.90171	−1.03232
$93$	−5.66199	−0.587121
$94$	14.9360	1.54053
$95$	−0.394007	−0.0404242
$96$	−7.23490	−0.738408
$97$	−5.03657	−0.511386	−0.255693	−	0.966758i	$-0.582304\pi$
$97$	−5.03657	−0.511386	−0.255693	+	0.966758i	$0.582304\pi$
$98$	0	0
$99$	−1.68076	−0.168923
$100$	7.70055	0.770055
$101$	1.59733	0.158940	0.0794701	−	0.996837i	$-0.474677\pi$
$101$	1.59733	0.158940	0.0794701	+	0.996837i	$0.474677\pi$
$102$	11.7112	1.15958
$103$	6.42012	0.632594	0.316297	−	0.948660i	$-0.397560\pi$
$103$	6.42012	0.632594	0.316297	+	0.948660i	$0.397560\pi$
$104$	2.35510	0.230937
$105$	0	0
$106$	19.9708	1.93973
$107$	−4.09410	−0.395792	−0.197896	−	0.980223i	$-0.563411\pi$
$107$	−4.09410	−0.395792	−0.197896	+	0.980223i	$0.563411\pi$
$108$	−2.84432	−0.273695
$109$	19.1231	1.83167	0.915833	−	0.401560i	$-0.131532\pi$
$109$	19.1231	1.83167	0.915833	+	0.401560i	$0.131532\pi$
$110$	−10.2701	−0.979215
$111$	−0.881374	−0.0836564
$112$	0	0
$113$	−16.6729	−1.56845	−0.784227	−	0.620474i	$-0.786940\pi$
$113$	−16.6729	−1.56845	−0.784227	+	0.620474i	$0.786940\pi$
$114$	0.312369	0.0292560
$115$	9.66460	0.901228
$116$	−8.51525	−0.790621
$117$	−1.26732	−0.117164
$118$	−8.62946	−0.794407
$119$	0	0
$120$	−5.15913	−0.470962
$121$	−8.17505	−0.743186
$122$	−20.8455	−1.88726
$123$	1.00000	0.0901670
$124$	16.1045	1.44623
$125$	6.36490	0.569294
$126$	0	0
$127$	4.34746	0.385775	0.192887	−	0.981221i	$-0.438215\pi$
$127$	4.34746	0.385775	0.192887	+	0.981221i	$0.438215\pi$
$128$	13.5419	1.19695
$129$	−4.77245	−0.420191
$130$	−7.74380	−0.679176
$131$	1.07778	0.0941661	0.0470831	−	0.998891i	$-0.485007\pi$
$131$	1.07778	0.0941661	0.0470831	+	0.998891i	$0.485007\pi$
$132$	4.78062	0.416099
$133$	0	0
$134$	−13.0999	−1.13166
$135$	2.77621	0.238938
$136$	−9.88802	−0.847890
$137$	−11.2392	−0.960226	−0.480113	−	0.877207i	$-0.659404\pi$
$137$	−11.2392	−0.960226	−0.480113	+	0.877207i	$0.659404\pi$
$138$	−7.66210	−0.652241
$139$	−4.02098	−0.341055	−0.170528	−	0.985353i	$-0.554547\pi$
$139$	−4.02098	−0.341055	−0.170528	+	0.985353i	$0.554547\pi$
$140$	0	0
$141$	6.78607	0.571491
$142$	4.44368	0.372905
$143$	2.13006	0.178124
$144$	−1.59848	−0.133207
$145$	8.31134	0.690219
$146$	−4.27512	−0.353812
$147$	0	0
$148$	2.50691	0.206067
$149$	−14.6463	−1.19987	−0.599934	−	0.800049i	$-0.704807\pi$
$149$	−14.6463	−1.19987	−0.599934	+	0.800049i	$0.704807\pi$
$150$	5.95881	0.486535
$151$	−11.3142	−0.920734	−0.460367	−	0.887729i	$-0.652282\pi$
$151$	−11.3142	−0.920734	−0.460367	+	0.887729i	$0.652282\pi$
$152$	−0.263740	−0.0213921
$153$	5.32090	0.430169
$154$	0	0
$155$	−15.7189	−1.26257
$156$	3.60466	0.288604
$157$	7.93305	0.633127	0.316563	−	0.948571i	$-0.397471\pi$
$157$	7.93305	0.633127	0.316563	+	0.948571i	$0.397471\pi$
$158$	20.3378	1.61799
$159$	9.07358	0.719582
$160$	−20.0856	−1.58791
$161$	0	0
$162$	−2.20098	−0.172925
$163$	−8.61646	−0.674893	−0.337447	−	0.941345i	$-0.609563\pi$
$163$	−8.61646	−0.674893	−0.337447	+	0.941345i	$0.609563\pi$
$164$	−2.84432	−0.222104
$165$	−4.66614	−0.363259
$166$	−0.379862	−0.0294830
$167$	18.8593	1.45937	0.729687	−	0.683781i	$-0.239666\pi$
$167$	18.8593	1.45937	0.729687	+	0.683781i	$0.239666\pi$
$168$	0	0
$169$	−11.3939	−0.876454
$170$	32.5128	2.49362
$171$	0.141922	0.0108531
$172$	13.5744	1.03504
$173$	8.08980	0.615056	0.307528	−	0.951539i	$-0.400498\pi$
$173$	8.08980	0.615056	0.307528	+	0.951539i	$0.400498\pi$
$174$	−6.58924	−0.499529
$175$	0	0
$176$	2.68666	0.202515
$177$	−3.92073	−0.294700
$178$	26.3570	1.97554
$179$	−24.8321	−1.85604	−0.928021	−	0.372529i	$-0.878491\pi$
$179$	−24.8321	−1.85604	−0.928021	+	0.372529i	$0.878491\pi$
$180$	−7.89643	−0.588565
$181$	1.27932	0.0950910	0.0475455	−	0.998869i	$-0.484860\pi$
$181$	1.27932	0.0950910	0.0475455	+	0.998869i	$0.484860\pi$
$182$	0	0
$183$	−9.47100	−0.700117
$184$	6.46927	0.476921
$185$	−2.44688	−0.179898
$186$	12.4619	0.913754
$187$	−8.94315	−0.653988
$188$	−19.3018	−1.40773
$189$	0	0
$190$	0.867202	0.0629134
$191$	−13.0880	−0.947016	−0.473508	−	0.880790i	$-0.657012\pi$
$191$	−13.0880	−0.947016	−0.473508	+	0.880790i	$0.657012\pi$
$192$	12.7269	0.918486
$193$	14.5967	1.05069	0.525345	−	0.850889i	$-0.323936\pi$
$193$	14.5967	1.05069	0.525345	+	0.850889i	$0.323936\pi$
$194$	11.0854	0.795885
$195$	−3.51834	−0.251954
$196$	0	0
$197$	−4.38705	−0.312565	−0.156282	−	0.987712i	$-0.549951\pi$
$197$	−4.38705	−0.312565	−0.156282	+	0.987712i	$0.549951\pi$
$198$	3.69932	0.262899
$199$	−15.7383	−1.11566	−0.557828	−	0.829956i	$-0.688365\pi$
$199$	−15.7383	−1.11566	−0.557828	+	0.829956i	$0.688365\pi$
$200$	−5.03115	−0.355756
$201$	−5.95186	−0.419812
$202$	−3.51569	−0.247363
$203$	0	0
$204$	−15.1343	−1.05962
$205$	2.77621	0.193899
$206$	−14.1306	−0.984524
$207$	−3.48122	−0.241961
$208$	2.02578	0.140463
$209$	−0.238538	−0.0165000
$210$	0	0
$211$	19.1506	1.31838	0.659191	−	0.751976i	$-0.270899\pi$
$211$	19.1506	1.31838	0.659191	+	0.751976i	$0.270899\pi$
$212$	−25.8082	−1.77251
$213$	2.01895	0.138336
$214$	9.01104	0.615982
$215$	−13.2493	−0.903597
$216$	1.85834	0.126444
$217$	0	0
$218$	−42.0897	−2.85067
$219$	−1.94237	−0.131253
$220$	13.2720	0.894798
$221$	−6.74327	−0.453601
$222$	1.93989	0.130197
$223$	−12.6193	−0.845050	−0.422525	−	0.906351i	$-0.638856\pi$
$223$	−12.6193	−0.845050	−0.422525	+	0.906351i	$0.638856\pi$
$224$	0	0
$225$	2.70734	0.180490
$226$	36.6968	2.44103
$227$	−22.1670	−1.47128	−0.735638	−	0.677375i	$-0.763117\pi$
$227$	−22.1670	−1.47128	−0.735638	+	0.677375i	$0.763117\pi$
$228$	−0.403673	−0.0267339
$229$	9.97602	0.659234	0.329617	−	0.944115i	$-0.393080\pi$
$229$	9.97602	0.659234	0.329617	+	0.944115i	$0.393080\pi$
$230$	−21.2716	−1.40261
$231$	0	0
$232$	5.56343	0.365257
$233$	21.0690	1.38028	0.690138	−	0.723678i	$-0.257550\pi$
$233$	21.0690	1.38028	0.690138	+	0.723678i	$0.257550\pi$
$234$	2.78934	0.182345
$235$	18.8396	1.22896
$236$	11.1518	0.725922
$237$	9.24032	0.600224
$238$	0	0
$239$	−18.5783	−1.20173	−0.600865	−	0.799351i	$-0.705177\pi$
$239$	−18.5783	−1.20173	−0.600865	+	0.799351i	$0.705177\pi$
$240$	−4.43772	−0.286453
$241$	−17.3118	−1.11515	−0.557574	−	0.830127i	$-0.688268\pi$
$241$	−17.3118	−1.11515	−0.557574	+	0.830127i	$0.688268\pi$
$242$	17.9931	1.15664
$243$	−1.00000	−0.0641500
$244$	26.9386	1.72457
$245$	0	0
$246$	−2.20098	−0.140329
$247$	−0.179861	−0.0114443
$248$	−10.5219	−0.668140
$249$	−0.172587	−0.0109373
$250$	−14.0090	−0.886008
$251$	10.9914	0.693773	0.346886	−	0.937907i	$-0.387239\pi$
$251$	10.9914	0.693773	0.346886	+	0.937907i	$0.387239\pi$
$252$	0	0
$253$	5.85109	0.367855
$254$	−9.56868	−0.600393
$255$	14.7719	0.925055
$256$	−4.35168	−0.271980
$257$	29.6313	1.84835	0.924173	−	0.381973i	$-0.124755\pi$
$257$	29.6313	1.84835	0.924173	+	0.381973i	$0.124755\pi$
$258$	10.5041	0.653956
$259$	0	0
$260$	10.0073	0.620626
$261$	−2.99377	−0.185310
$262$	−2.37218	−0.146553
$263$	−11.8050	−0.727930	−0.363965	−	0.931413i	$-0.618577\pi$
$263$	−11.8050	−0.727930	−0.363965	+	0.931413i	$0.618577\pi$
$264$	−3.12341	−0.192233
$265$	25.1902	1.54742
$266$	0	0
$267$	11.9751	0.732865
$268$	16.9290	1.03410
$269$	−15.9048	−0.969733	−0.484866	−	0.874588i	$-0.661132\pi$
$269$	−15.9048	−0.969733	−0.484866	+	0.874588i	$0.661132\pi$
$270$	−6.11039	−0.371866
$271$	−24.7648	−1.50436	−0.752178	−	0.658959i	$-0.770997\pi$
$271$	−24.7648	−1.50436	−0.752178	+	0.658959i	$0.770997\pi$
$272$	−8.50535	−0.515713
$273$	0	0
$274$	24.7372	1.49443
$275$	−4.55039	−0.274399
$276$	9.90171	0.596013
$277$	6.15817	0.370009	0.185004	−	0.982738i	$-0.440770\pi$
$277$	6.15817	0.370009	0.185004	+	0.982738i	$0.440770\pi$
$278$	8.85010	0.530794
$279$	5.66199	0.338975
$280$	0	0
$281$	21.5548	1.28585	0.642925	−	0.765929i	$-0.277721\pi$
$281$	21.5548	1.28585	0.642925	+	0.765929i	$0.277721\pi$
$282$	−14.9360	−0.889427
$283$	22.2222	1.32097	0.660486	−	0.750838i	$-0.270350\pi$
$283$	22.2222	1.32097	0.660486	+	0.750838i	$0.270350\pi$
$284$	−5.74255	−0.340758
$285$	0.394007	0.0233389
$286$	−4.68821	−0.277220
$287$	0	0
$288$	7.23490	0.426320
$289$	11.3120	0.665411
$290$	−18.2931	−1.07421
$291$	5.03657	0.295249
$292$	5.52473	0.323310
$293$	27.7559	1.62151	0.810757	−	0.585383i	$-0.199056\pi$
$293$	27.7559	1.62151	0.810757	+	0.585383i	$0.199056\pi$
$294$	0	0
$295$	−10.8848	−0.633736
$296$	−1.63789	−0.0952004
$297$	1.68076	0.0975275
$298$	32.2362	1.86739
$299$	4.41181	0.255142
$300$	−7.70055	−0.444592
$301$	0	0
$302$	24.9023	1.43297
$303$	−1.59733	−0.0917642
$304$	−0.226860	−0.0130113
$305$	−26.2935	−1.50556
$306$	−11.7112	−0.669485
$307$	−28.8875	−1.64870	−0.824348	−	0.566083i	$-0.808458\pi$
$307$	−28.8875	−1.64870	−0.824348	+	0.566083i	$0.808458\pi$
$308$	0	0
$309$	−6.42012	−0.365228
$310$	34.5970	1.96498
$311$	28.5330	1.61796	0.808979	−	0.587838i	$-0.200021\pi$
$311$	28.5330	1.61796	0.808979	+	0.587838i	$0.200021\pi$
$312$	−2.35510	−0.133331
$313$	−13.2617	−0.749595	−0.374798	−	0.927107i	$-0.622288\pi$
$313$	−13.2617	−0.749595	−0.374798	+	0.927107i	$0.622288\pi$
$314$	−17.4605	−0.985353
$315$	0	0
$316$	−26.2824	−1.47850
$317$	−15.3817	−0.863922	−0.431961	−	0.901892i	$-0.642178\pi$
$317$	−15.3817	−0.863922	−0.431961	+	0.901892i	$0.642178\pi$
$318$	−19.9708	−1.11991
$319$	5.03181	0.281727
$320$	35.3326	1.97515
$321$	4.09410	0.228510
$322$	0	0
$323$	0.755155	0.0420180
$324$	2.84432	0.158018
$325$	−3.43106	−0.190321
$326$	18.9647	1.05036
$327$	−19.1231	−1.05751
$328$	1.85834	0.102609
$329$	0	0
$330$	10.2701	0.565350
$331$	13.2085	0.726003	0.363001	−	0.931789i	$-0.381752\pi$
$331$	13.2085	0.726003	0.363001	+	0.931789i	$0.381752\pi$
$332$	0.490894	0.0269413
$333$	0.881374	0.0482990
$334$	−41.5089	−2.27127
$335$	−16.5236	−0.902781
$336$	0	0
$337$	−8.13494	−0.443138	−0.221569	−	0.975145i	$-0.571118\pi$
$337$	−8.13494	−0.443138	−0.221569	+	0.975145i	$0.571118\pi$
$338$	25.0778	1.36405
$339$	16.6729	0.905548
$340$	−42.0161	−2.27864
$341$	−9.51645	−0.515345
$342$	−0.312369	−0.0168910
$343$	0	0
$344$	−8.86882	−0.478175
$345$	−9.66460	−0.520324
$346$	−17.8055	−0.957230
$347$	25.6878	1.37899	0.689497	−	0.724289i	$-0.257832\pi$
$347$	25.6878	1.37899	0.689497	+	0.724289i	$0.257832\pi$
$348$	8.51525	0.456465
$349$	21.3702	1.14392	0.571960	−	0.820282i	$-0.306183\pi$
$349$	21.3702	1.14392	0.571960	+	0.820282i	$0.306183\pi$
$350$	0	0
$351$	1.26732	0.0676444
$352$	−12.1601	−0.648136
$353$	−18.1309	−0.965012	−0.482506	−	0.875893i	$-0.660273\pi$
$353$	−18.1309	−0.965012	−0.482506	+	0.875893i	$0.660273\pi$
$354$	8.62946	0.458651
$355$	5.60504	0.297485
$356$	−34.0611	−1.80523
$357$	0	0
$358$	54.6551	2.88861
$359$	37.0107	1.95335	0.976675	−	0.214722i	$-0.0688844\pi$
$359$	37.0107	1.95335	0.976675	+	0.214722i	$0.0688844\pi$
$360$	5.15913	0.271910
$361$	−18.9799	−0.998940
$362$	−2.81576	−0.147993
$363$	8.17505	0.429079
$364$	0	0
$365$	−5.39243	−0.282253
$366$	20.8455	1.08961
$367$	−22.5758	−1.17845	−0.589224	−	0.807969i	$-0.700567\pi$
$367$	−22.5758	−1.17845	−0.589224	+	0.807969i	$0.700567\pi$
$368$	5.56466	0.290078
$369$	−1.00000	−0.0520579
$370$	5.38554	0.279981
$371$	0	0
$372$	−16.1045	−0.834981
$373$	−15.8413	−0.820230	−0.410115	−	0.912034i	$-0.634511\pi$
$373$	−15.8413	−0.820230	−0.410115	+	0.912034i	$0.634511\pi$
$374$	19.6837	1.01782
$375$	−6.36490	−0.328682
$376$	12.6108	0.650352
$377$	3.79406	0.195404
$378$	0	0
$379$	−24.3793	−1.25228	−0.626140	−	0.779711i	$-0.715366\pi$
$379$	−24.3793	−1.25228	−0.626140	+	0.779711i	$0.715366\pi$
$380$	−1.12068	−0.0574897
$381$	−4.34746	−0.222727
$382$	28.8065	1.47387
$383$	13.4064	0.685035	0.342517	−	0.939511i	$-0.388720\pi$
$383$	13.4064	0.685035	0.342517	+	0.939511i	$0.388720\pi$
$384$	−13.5419	−0.691058
$385$	0	0
$386$	−32.1270	−1.63522
$387$	4.77245	0.242597
$388$	−14.3256	−0.727273
$389$	22.1503	1.12306	0.561531	−	0.827456i	$-0.310212\pi$
$389$	22.1503	1.12306	0.561531	+	0.827456i	$0.310212\pi$
$390$	7.74380	0.392123
$391$	−18.5232	−0.936760
$392$	0	0
$393$	−1.07778	−0.0543668
$394$	9.65583	0.486454
$395$	25.6531	1.29075
$396$	−4.78062	−0.240235
$397$	−2.97442	−0.149282	−0.0746408	−	0.997210i	$-0.523781\pi$
$397$	−2.97442	−0.149282	−0.0746408	+	0.997210i	$0.523781\pi$
$398$	34.6397	1.73633
$399$	0	0
$400$	−4.32763	−0.216382
$401$	−16.9346	−0.845673	−0.422836	−	0.906206i	$-0.638965\pi$
$401$	−16.9346	−0.845673	−0.422836	+	0.906206i	$0.638965\pi$
$402$	13.0999	0.653365
$403$	−7.17554	−0.357439
$404$	4.54332	0.226038
$405$	−2.77621	−0.137951
$406$	0	0
$407$	−1.48138	−0.0734292
$408$	9.88802	0.489530
$409$	−36.9109	−1.82513	−0.912563	−	0.408937i	$-0.865900\pi$
$409$	−36.9109	−1.82513	−0.912563	+	0.408937i	$0.865900\pi$
$410$	−6.11039	−0.301771
$411$	11.2392	0.554387
$412$	18.2609	0.899650
$413$	0	0
$414$	7.66210	0.376572
$415$	−0.479139	−0.0235200
$416$	−9.16891	−0.449543
$417$	4.02098	0.196908
$418$	0.525017	0.0256794
$419$	−37.7151	−1.84250	−0.921252	−	0.388967i	$-0.872832\pi$
$419$	−37.7151	−1.84250	−0.921252	+	0.388967i	$0.872832\pi$
$420$	0	0
$421$	30.8690	1.50446	0.752232	−	0.658898i	$-0.228977\pi$
$421$	30.8690	1.50446	0.752232	+	0.658898i	$0.228977\pi$
$422$	−42.1501	−2.05184
$423$	−6.78607	−0.329950
$424$	16.8618	0.818879
$425$	14.4055	0.698770
$426$	−4.44368	−0.215297
$427$	0	0
$428$	−11.6449	−0.562879
$429$	−2.13006	−0.102840
$430$	29.1615	1.40629
$431$	9.74950	0.469617	0.234808	−	0.972042i	$-0.424554\pi$
$431$	9.74950	0.469617	0.234808	+	0.972042i	$0.424554\pi$
$432$	1.59848	0.0769069
$433$	22.5435	1.08337	0.541686	−	0.840581i	$-0.317786\pi$
$433$	22.5435	1.08337	0.541686	+	0.840581i	$0.317786\pi$
$434$	0	0
$435$	−8.31134	−0.398498
$436$	54.3924	2.60492
$437$	−0.494063	−0.0236343
$438$	4.27512	0.204273
$439$	31.5537	1.50598	0.752989	−	0.658034i	$-0.228612\pi$
$439$	31.5537	1.50598	0.752989	+	0.658034i	$0.228612\pi$
$440$	−8.67125	−0.413386
$441$	0	0
$442$	14.8418	0.705953
$443$	−12.2210	−0.580637	−0.290319	−	0.956930i	$-0.593761\pi$
$443$	−12.2210	−0.580637	−0.290319	+	0.956930i	$0.593761\pi$
$444$	−2.50691	−0.118973
$445$	33.2454	1.57599
$446$	27.7748	1.31518
$447$	14.6463	0.692745
$448$	0	0
$449$	15.8619	0.748571	0.374286	−	0.927313i	$-0.377888\pi$
$449$	15.8619	0.748571	0.374286	+	0.927313i	$0.377888\pi$
$450$	−5.95881	−0.280901
$451$	1.68076	0.0791439
$452$	−47.4231	−2.23059
$453$	11.3142	0.531586
$454$	48.7892	2.28979
$455$	0	0
$456$	0.263740	0.0123507
$457$	−38.2429	−1.78893	−0.894464	−	0.447140i	$-0.852443\pi$
$457$	−38.2429	−1.78893	−0.894464	+	0.447140i	$0.852443\pi$
$458$	−21.9570	−1.02599
$459$	−5.32090	−0.248358
$460$	27.4892	1.28169
$461$	21.4857	1.00069	0.500344	−	0.865826i	$-0.333207\pi$
$461$	21.4857	1.00069	0.500344	+	0.865826i	$0.333207\pi$
$462$	0	0
$463$	42.5313	1.97660	0.988298	−	0.152533i	$-0.0487430\pi$
$463$	42.5313	1.97660	0.988298	+	0.152533i	$0.0487430\pi$
$464$	4.78548	0.222161
$465$	15.7189	0.728946
$466$	−46.3725	−2.14816
$467$	23.1182	1.06978	0.534891	−	0.844921i	$-0.320353\pi$
$467$	23.1182	1.06978	0.534891	+	0.844921i	$0.320353\pi$
$468$	−3.60466	−0.166625
$469$	0	0
$470$	−41.4655	−1.91266
$471$	−7.93305	−0.365536
$472$	−7.28604	−0.335367
$473$	−8.02134	−0.368822
$474$	−20.3378	−0.934145
$475$	0.384233	0.0176298
$476$	0	0
$477$	−9.07358	−0.415451
$478$	40.8905	1.87029
$479$	1.05824	0.0483523	0.0241762	−	0.999708i	$-0.492304\pi$
$479$	1.05824	0.0483523	0.0241762	+	0.999708i	$0.492304\pi$
$480$	20.0856	0.916778
$481$	−1.11698	−0.0509300
$482$	38.1029	1.73554
$483$	0	0
$484$	−23.2525	−1.05693
$485$	13.9826	0.634916
$486$	2.20098	0.0998386
$487$	13.8878	0.629317	0.314658	−	0.949205i	$-0.398110\pi$
$487$	13.8878	0.629317	0.314658	+	0.949205i	$0.398110\pi$
$488$	−17.6003	−0.796728
$489$	8.61646	0.389650
$490$	0	0
$491$	25.1078	1.13310	0.566551	−	0.824027i	$-0.308278\pi$
$491$	25.1078	1.13310	0.566551	+	0.824027i	$0.308278\pi$
$492$	2.84432	0.128232
$493$	−15.9296	−0.717431
$494$	0.395870	0.0178111
$495$	4.66614	0.209727
$496$	−9.05058	−0.406383
$497$	0	0
$498$	0.379862	0.0170220
$499$	13.3400	0.597182	0.298591	−	0.954381i	$-0.403483\pi$
$499$	13.3400	0.597182	0.298591	+	0.954381i	$0.403483\pi$
$500$	18.1038	0.809627
$501$	−18.8593	−0.842570
$502$	−24.1919	−1.07974
$503$	18.1652	0.809947	0.404974	−	0.914328i	$-0.367281\pi$
$503$	18.1652	0.809947	0.404974	+	0.914328i	$0.367281\pi$
$504$	0	0
$505$	−4.43452	−0.197334
$506$	−12.8781	−0.572503
$507$	11.3939	0.506021
$508$	12.3656	0.548634
$509$	17.3945	0.770997	0.385499	−	0.922708i	$-0.374029\pi$
$509$	17.3945	0.770997	0.385499	+	0.922708i	$0.374029\pi$
$510$	−32.5128	−1.43969
$511$	0	0
$512$	−17.5059	−0.773657
$513$	−0.141922	−0.00626603
$514$	−65.2178	−2.87664
$515$	−17.8236	−0.785402
$516$	−13.5744	−0.597579
$517$	11.4058	0.501625
$518$	0	0
$519$	−8.08980	−0.355103
$520$	−6.53825	−0.286721
$521$	−1.13722	−0.0498225	−0.0249112	−	0.999690i	$-0.507930\pi$
$521$	−1.13722	−0.0498225	−0.0249112	+	0.999690i	$0.507930\pi$
$522$	6.58924	0.288403
$523$	−4.02160	−0.175852	−0.0879262	−	0.996127i	$-0.528024\pi$
$523$	−4.02160	−0.175852	−0.0879262	+	0.996127i	$0.528024\pi$
$524$	3.06555	0.133919
$525$	0	0
$526$	25.9827	1.13290
$527$	30.1269	1.31235
$528$	−2.68666	−0.116922
$529$	−10.8811	−0.473092
$530$	−55.4431	−2.40829
$531$	3.92073	0.170145
$532$	0	0
$533$	1.26732	0.0548936
$534$	−26.3570	−1.14058
$535$	11.3661	0.491399
$536$	−11.0606	−0.477743
$537$	24.8321	1.07159
$538$	35.0062	1.50922
$539$	0	0
$540$	7.89643	0.339808
$541$	8.17405	0.351430	0.175715	−	0.984441i	$-0.443776\pi$
$541$	8.17405	0.351430	0.175715	+	0.984441i	$0.443776\pi$
$542$	54.5070	2.34127
$543$	−1.27932	−0.0549008
$544$	38.4962	1.65051
$545$	−53.0899	−2.27412
$546$	0	0
$547$	2.23302	0.0954770	0.0477385	−	0.998860i	$-0.484799\pi$
$547$	2.23302	0.0954770	0.0477385	+	0.998860i	$0.484799\pi$
$548$	−31.9678	−1.36560
$549$	9.47100	0.404213
$550$	10.0153	0.427055
$551$	−0.424884	−0.0181006
$552$	−6.46927	−0.275351
$553$	0	0
$554$	−13.5540	−0.575855
$555$	2.44688	0.103864
$556$	−11.4370	−0.485035
$557$	9.79030	0.414828	0.207414	−	0.978253i	$-0.433495\pi$
$557$	9.79030	0.414828	0.207414	+	0.978253i	$0.433495\pi$
$558$	−12.4619	−0.527556
$559$	−6.04821	−0.255812
$560$	0	0
$561$	8.94315	0.377580
$562$	−47.4417	−2.00121
$563$	27.8923	1.17552	0.587759	−	0.809036i	$-0.300010\pi$
$563$	27.8923	1.17552	0.587759	+	0.809036i	$0.300010\pi$
$564$	19.3018	0.812751
$565$	46.2875	1.94733
$566$	−48.9107	−2.05587
$567$	0	0
$568$	3.75189	0.157426
$569$	12.7526	0.534618	0.267309	−	0.963611i	$-0.413866\pi$
$569$	12.7526	0.534618	0.267309	+	0.963611i	$0.413866\pi$
$570$	−0.867202	−0.0363231
$571$	−10.8170	−0.452677	−0.226339	−	0.974049i	$-0.572676\pi$
$571$	−10.8170	−0.452677	−0.226339	+	0.974049i	$0.572676\pi$
$572$	6.05856	0.253321
$573$	13.0880	0.546760
$574$	0	0
$575$	−9.42486	−0.393044
$576$	−12.7269	−0.530288
$577$	44.3003	1.84424	0.922122	−	0.386899i	$-0.126454\pi$
$577$	44.3003	1.84424	0.922122	+	0.386899i	$0.126454\pi$
$578$	−24.8975	−1.03560
$579$	−14.5967	−0.606616
$580$	23.6401	0.981602
$581$	0	0
$582$	−11.0854	−0.459504
$583$	15.2505	0.631611
$584$	−3.60958	−0.149365
$585$	3.51834	0.145465
$586$	−61.0901	−2.52361
$587$	−1.39567	−0.0576056	−0.0288028	−	0.999585i	$-0.509169\pi$
$587$	−1.39567	−0.0576056	−0.0288028	+	0.999585i	$0.509169\pi$
$588$	0	0
$589$	0.803564	0.0331103
$590$	23.9572	0.986303
$591$	4.38705	0.180459
$592$	−1.40886	−0.0579038
$593$	33.3985	1.37151	0.685757	−	0.727831i	$-0.259471\pi$
$593$	33.3985	1.37151	0.685757	+	0.727831i	$0.259471\pi$
$594$	−3.69932	−0.151785
$595$	0	0
$596$	−41.6587	−1.70641
$597$	15.7383	0.644125
$598$	−9.71031	−0.397084
$599$	−14.3153	−0.584907	−0.292454	−	0.956280i	$-0.594472\pi$
$599$	−14.3153	−0.584907	−0.292454	+	0.956280i	$0.594472\pi$
$600$	5.03115	0.205396
$601$	1.70356	0.0694898	0.0347449	−	0.999396i	$-0.488938\pi$
$601$	1.70356	0.0694898	0.0347449	+	0.999396i	$0.488938\pi$
$602$	0	0
$603$	5.95186	0.242378
$604$	−32.1811	−1.30943
$605$	22.6957	0.922710
$606$	3.51569	0.142815
$607$	10.5203	0.427005	0.213502	−	0.976943i	$-0.431513\pi$
$607$	10.5203	0.427005	0.213502	+	0.976943i	$0.431513\pi$
$608$	1.02679	0.0416420
$609$	0	0
$610$	57.8715	2.34315
$611$	8.60011	0.347923
$612$	15.1343	0.611770
$613$	33.3563	1.34725	0.673623	−	0.739075i	$-0.264737\pi$
$613$	33.3563	1.34725	0.673623	+	0.739075i	$0.264737\pi$
$614$	63.5809	2.56591
$615$	−2.77621	−0.111948
$616$	0	0
$617$	10.1418	0.408294	0.204147	−	0.978940i	$-0.434558\pi$
$617$	10.1418	0.408294	0.204147	+	0.978940i	$0.434558\pi$
$618$	14.1306	0.568415
$619$	42.6281	1.71337	0.856684	−	0.515841i	$-0.172521\pi$
$619$	42.6281	1.71337	0.856684	+	0.515841i	$0.172521\pi$
$620$	−44.7096	−1.79558
$621$	3.48122	0.139697
$622$	−62.8006	−2.51808
$623$	0	0
$624$	−2.02578	−0.0810962
$625$	−31.2070	−1.24828
$626$	29.1888	1.16662
$627$	0.238538	0.00952627
$628$	22.5641	0.900408
$629$	4.68971	0.186991
$630$	0	0
$631$	−14.4149	−0.573847	−0.286924	−	0.957953i	$-0.592633\pi$
$631$	−14.4149	−0.573847	−0.286924	+	0.957953i	$0.592633\pi$
$632$	17.1716	0.683050
$633$	−19.1506	−0.761168
$634$	33.8548	1.34455
$635$	−12.0695	−0.478962
$636$	25.8082	1.02336
$637$	0	0
$638$	−11.0749	−0.438460
$639$	−2.01895	−0.0798686
$640$	−37.5952	−1.48608
$641$	−37.7765	−1.49208	−0.746041	−	0.665900i	$-0.768048\pi$
$641$	−37.7765	−1.49208	−0.746041	+	0.665900i	$0.768048\pi$
$642$	−9.01104	−0.355637
$643$	−16.7736	−0.661487	−0.330744	−	0.943721i	$-0.607300\pi$
$643$	−16.7736	−0.661487	−0.330744	+	0.943721i	$0.607300\pi$
$644$	0	0
$645$	13.2493	0.521692
$646$	−1.66208	−0.0653938
$647$	8.87132	0.348768	0.174384	−	0.984678i	$-0.444207\pi$
$647$	8.87132	0.348768	0.174384	+	0.984678i	$0.444207\pi$
$648$	−1.85834	−0.0730023
$649$	−6.58981	−0.258673
$650$	7.55171	0.296202
$651$	0	0
$652$	−24.5080	−0.959806
$653$	−18.5160	−0.724587	−0.362293	−	0.932064i	$-0.618006\pi$
$653$	−18.5160	−0.724587	−0.362293	+	0.932064i	$0.618006\pi$
$654$	42.0897	1.64584
$655$	−2.99214	−0.116913
$656$	1.59848	0.0624102
$657$	1.94237	0.0757791
$658$	0	0
$659$	30.8220	1.20065	0.600327	−	0.799755i	$-0.295037\pi$
$659$	30.8220	1.20065	0.600327	+	0.799755i	$0.295037\pi$
$660$	−13.2720	−0.516612
$661$	−20.6052	−0.801451	−0.400726	−	0.916198i	$-0.631242\pi$
$661$	−20.6052	−0.801451	−0.400726	+	0.916198i	$0.631242\pi$
$662$	−29.0716	−1.12990
$663$	6.74327	0.261887
$664$	−0.320725	−0.0124466
$665$	0	0
$666$	−1.93989	−0.0751692
$667$	10.4220	0.403541
$668$	53.6418	2.07546
$669$	12.6193	0.487890
$670$	36.3682	1.40503
$671$	−15.9185	−0.614526
$672$	0	0
$673$	36.8522	1.42055	0.710274	−	0.703925i	$-0.248571\pi$
$673$	36.8522	1.42055	0.710274	+	0.703925i	$0.248571\pi$
$674$	17.9048	0.689669
$675$	−2.70734	−0.104206
$676$	−32.4079	−1.24646
$677$	37.3335	1.43484	0.717422	−	0.696639i	$-0.245322\pi$
$677$	37.3335	1.43484	0.717422	+	0.696639i	$0.245322\pi$
$678$	−36.6968	−1.40933
$679$	0	0
$680$	27.4512	1.05271
$681$	22.1670	0.849441
$682$	20.9455	0.802046
$683$	6.82622	0.261198	0.130599	−	0.991435i	$-0.458310\pi$
$683$	6.82622	0.261198	0.130599	+	0.991435i	$0.458310\pi$
$684$	0.403673	0.0154348
$685$	31.2023	1.19218
$686$	0	0
$687$	−9.97602	−0.380609
$688$	−7.62867	−0.290840
$689$	11.4991	0.438081
$690$	21.2716	0.809796
$691$	−29.8021	−1.13372	−0.566862	−	0.823813i	$-0.691843\pi$
$691$	−29.8021	−1.13372	−0.566862	+	0.823813i	$0.691843\pi$
$692$	23.0100	0.874709
$693$	0	0
$694$	−56.5384	−2.14617
$695$	11.1631	0.423440
$696$	−5.56343	−0.210881
$697$	−5.32090	−0.201543
$698$	−47.0354	−1.78032
$699$	−21.0690	−0.796903
$700$	0	0
$701$	26.7515	1.01039	0.505194	−	0.863006i	$-0.331421\pi$
$701$	26.7515	1.01039	0.505194	+	0.863006i	$0.331421\pi$
$702$	−2.78934	−0.105277
$703$	0.125087	0.00471774
$704$	21.3909	0.806199
$705$	−18.8396	−0.709539
$706$	39.9059	1.50188
$707$	0	0
$708$	−11.1518	−0.419111
$709$	−9.26049	−0.347785	−0.173892	−	0.984765i	$-0.555635\pi$
$709$	−9.26049	−0.347785	−0.173892	+	0.984765i	$0.555635\pi$
$710$	−12.3366	−0.462984
$711$	−9.24032	−0.346539
$712$	22.2538	0.833996
$713$	−19.7106	−0.738169
$714$	0	0
$715$	−5.91348	−0.221152
$716$	−70.6306	−2.63959
$717$	18.5783	0.693819
$718$	−81.4599	−3.04006
$719$	−27.5504	−1.02746	−0.513728	−	0.857953i	$-0.671736\pi$
$719$	−27.5504	−1.02746	−0.513728	+	0.857953i	$0.671736\pi$
$720$	4.43772	0.165384
$721$	0	0
$722$	41.7743	1.55468
$723$	17.3118	0.643831
$724$	3.63879	0.135235
$725$	−8.10517	−0.301018
$726$	−17.9931	−0.667788
$727$	44.4745	1.64947	0.824733	−	0.565522i	$-0.191325\pi$
$727$	44.4745	1.64947	0.824733	+	0.565522i	$0.191325\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	11.8686	0.439278
$731$	25.3937	0.939222
$732$	−26.9386	−0.995678
$733$	0.734001	0.0271109	0.0135555	−	0.999908i	$-0.495685\pi$
$733$	0.734001	0.0271109	0.0135555	+	0.999908i	$0.495685\pi$
$734$	49.6890	1.83405
$735$	0	0
$736$	−25.1863	−0.928378
$737$	−10.0036	−0.368489
$738$	2.20098	0.0810193
$739$	−4.64598	−0.170905	−0.0854526	−	0.996342i	$-0.527234\pi$
$739$	−4.64598	−0.170905	−0.0854526	+	0.996342i	$0.527234\pi$
$740$	−6.95971	−0.255844
$741$	0.179861	0.00660735
$742$	0	0
$743$	11.3522	0.416473	0.208237	−	0.978078i	$-0.433228\pi$
$743$	11.3522	0.416473	0.208237	+	0.978078i	$0.433228\pi$
$744$	10.5219	0.385751
$745$	40.6611	1.48971
$746$	34.8663	1.27655
$747$	0.172587	0.00631464
$748$	−25.4372	−0.930076
$749$	0	0
$750$	14.0090	0.511537
$751$	6.44376	0.235136	0.117568	−	0.993065i	$-0.462490\pi$
$751$	6.44376	0.235136	0.117568	+	0.993065i	$0.462490\pi$
$752$	10.8474	0.395564
$753$	−10.9914	−0.400550
$754$	−8.35065	−0.304113
$755$	31.4105	1.14315
$756$	0	0
$757$	20.7231	0.753192	0.376596	−	0.926378i	$-0.377094\pi$
$757$	20.7231	0.753192	0.376596	+	0.926378i	$0.377094\pi$
$758$	53.6584	1.94896
$759$	−5.85109	−0.212381
$760$	0.732196	0.0265596
$761$	−16.1646	−0.585966	−0.292983	−	0.956118i	$-0.594648\pi$
$761$	−16.1646	−0.585966	−0.292983	+	0.956118i	$0.594648\pi$
$762$	9.56868	0.346637
$763$	0	0
$764$	−37.2265	−1.34681
$765$	−14.7719	−0.534081
$766$	−29.5072	−1.06614
$767$	−4.96881	−0.179413
$768$	4.35168	0.157028
$769$	17.0644	0.615357	0.307679	−	0.951490i	$-0.400448\pi$
$769$	17.0644	0.615357	0.307679	+	0.951490i	$0.400448\pi$
$770$	0	0
$771$	−29.6313	−1.06714
$772$	41.5176	1.49425
$773$	26.9356	0.968807	0.484404	−	0.874845i	$-0.339037\pi$
$773$	26.9356	0.968807	0.484404	+	0.874845i	$0.339037\pi$
$774$	−10.5041	−0.377561
$775$	15.3290	0.550633
$776$	9.35963	0.335991
$777$	0	0
$778$	−48.7523	−1.74786
$779$	−0.141922	−0.00508490
$780$	−10.0073	−0.358318
$781$	3.39337	0.121424
$782$	40.7693	1.45791
$783$	2.99377	0.106989
$784$	0	0
$785$	−22.0238	−0.786064
$786$	2.37218	0.0846127
$787$	1.66602	0.0593870	0.0296935	−	0.999559i	$-0.490547\pi$
$787$	1.66602	0.0593870	0.0296935	+	0.999559i	$0.490547\pi$
$788$	−12.4782	−0.444517
$789$	11.8050	0.420271
$790$	−56.4620	−2.00883
$791$	0	0
$792$	3.12341	0.110986
$793$	−12.0028	−0.426231
$794$	6.54664	0.232331
$795$	−25.1902	−0.893403
$796$	−44.7647	−1.58664
$797$	29.9784	1.06189	0.530944	−	0.847407i	$-0.321837\pi$
$797$	29.9784	1.06189	0.530944	+	0.847407i	$0.321837\pi$
$798$	0	0
$799$	−36.1080	−1.27741
$800$	19.5873	0.692517
$801$	−11.9751	−0.423120
$802$	37.2727	1.31614
$803$	−3.26466	−0.115207
$804$	−16.9290	−0.597040
$805$	0	0
$806$	15.7932	0.556293
$807$	15.9048	0.559875
$808$	−2.96837	−0.104427
$809$	−29.0232	−1.02040	−0.510202	−	0.860055i	$-0.670429\pi$
$809$	−29.0232	−1.02040	−0.510202	+	0.860055i	$0.670429\pi$
$810$	6.11039	0.214697
$811$	32.0798	1.12648	0.563238	−	0.826295i	$-0.309556\pi$
$811$	32.0798	1.12648	0.563238	+	0.826295i	$0.309556\pi$
$812$	0	0
$813$	24.7648	0.868541
$814$	3.26049	0.114280
$815$	23.9211	0.837920
$816$	8.50535	0.297747
$817$	0.677318	0.0236964
$818$	81.2402	2.84050
$819$	0	0
$820$	7.89643	0.275755
$821$	11.7235	0.409153	0.204577	−	0.978851i	$-0.434418\pi$
$821$	11.7235	0.409153	0.204577	+	0.978851i	$0.434418\pi$
$822$	−24.7372	−0.862808
$823$	−6.04947	−0.210871	−0.105436	−	0.994426i	$-0.533624\pi$
$823$	−6.04947	−0.210871	−0.105436	+	0.994426i	$0.533624\pi$
$824$	−11.9307	−0.415627
$825$	4.55039	0.158424
$826$	0	0
$827$	33.7991	1.17531	0.587655	−	0.809112i	$-0.300051\pi$
$827$	33.7991	1.17531	0.587655	+	0.809112i	$0.300051\pi$
$828$	−9.90171	−0.344108
$829$	10.0690	0.349711	0.174855	−	0.984594i	$-0.444054\pi$
$829$	10.0690	0.349711	0.174855	+	0.984594i	$0.444054\pi$
$830$	1.05458	0.0366049
$831$	−6.15817	−0.213625
$832$	16.1290	0.559174
$833$	0	0
$834$	−8.85010	−0.306454
$835$	−52.3573	−1.81190
$836$	−0.678477	−0.0234656
$837$	−5.66199	−0.195707
$838$	83.0102	2.86754
$839$	39.0487	1.34811	0.674055	−	0.738681i	$-0.264551\pi$
$839$	39.0487	1.34811	0.674055	+	0.738681i	$0.264551\pi$
$840$	0	0
$841$	−20.0373	−0.690942
$842$	−67.9422	−2.34144
$843$	−21.5548	−0.742386
$844$	54.4705	1.87495
$845$	31.6319	1.08817
$846$	14.9360	0.513511
$847$	0	0
$848$	14.5039	0.498067
$849$	−22.2222	−0.762664
$850$	−31.7063	−1.08752
$851$	−3.06826	−0.105179
$852$	5.74255	0.196737
$853$	47.2452	1.61764	0.808822	−	0.588053i	$-0.200105\pi$
$853$	47.2452	1.61764	0.808822	+	0.588053i	$0.200105\pi$
$854$	0	0
$855$	−0.394007	−0.0134747
$856$	7.60821	0.260043
$857$	−1.31443	−0.0449002	−0.0224501	−	0.999748i	$-0.507147\pi$
$857$	−1.31443	−0.0449002	−0.0224501	+	0.999748i	$0.507147\pi$
$858$	4.68821	0.160053
$859$	−18.9148	−0.645365	−0.322682	−	0.946507i	$-0.604585\pi$
$859$	−18.9148	−0.645365	−0.322682	+	0.946507i	$0.604585\pi$
$860$	−37.6854	−1.28506
$861$	0	0
$862$	−21.4585	−0.730879
$863$	36.1765	1.23146	0.615732	−	0.787956i	$-0.288860\pi$
$863$	36.1765	1.23146	0.615732	+	0.787956i	$0.288860\pi$
$864$	−7.23490	−0.246136
$865$	−22.4590	−0.763629
$866$	−49.6179	−1.68608
$867$	−11.3120	−0.384175
$868$	0	0
$869$	15.5308	0.526845
$870$	18.2931	0.620194
$871$	−7.54289	−0.255581
$872$	−35.5372	−1.20344
$873$	−5.03657	−0.170462
$874$	1.08742	0.0367827
$875$	0	0
$876$	−5.52473	−0.186663
$877$	0.653186	0.0220565	0.0110283	−	0.999939i	$-0.496490\pi$
$877$	0.653186	0.0220565	0.0110283	+	0.999939i	$0.496490\pi$
$878$	−69.4492	−2.34380
$879$	−27.7559	−0.936182
$880$	−7.45873	−0.251434
$881$	−24.9292	−0.839886	−0.419943	−	0.907550i	$-0.637950\pi$
$881$	−24.9292	−0.839886	−0.419943	+	0.907550i	$0.637950\pi$
$882$	0	0
$883$	20.6768	0.695828	0.347914	−	0.937526i	$-0.386890\pi$
$883$	20.6768	0.695828	0.347914	+	0.937526i	$0.386890\pi$
$884$	−19.1800	−0.645094
$885$	10.8848	0.365888
$886$	26.8982	0.903663
$887$	34.9460	1.17337	0.586686	−	0.809815i	$-0.300432\pi$
$887$	34.9460	1.17337	0.586686	+	0.809815i	$0.300432\pi$
$888$	1.63789	0.0549640
$889$	0	0
$890$	−73.1726	−2.45275
$891$	−1.68076	−0.0563076
$892$	−35.8933	−1.20180
$893$	−0.963097	−0.0322288
$894$	−32.2362	−1.07814
$895$	68.9392	2.30438
$896$	0	0
$897$	−4.41181	−0.147306
$898$	−34.9118	−1.16502
$899$	−16.9507	−0.565338
$900$	7.70055	0.256685
$901$	−48.2796	−1.60843
$902$	−3.69932	−0.123174
$903$	0	0
$904$	30.9838	1.03051
$905$	−3.55166	−0.118061
$906$	−24.9023	−0.827323
$907$	18.3204	0.608320	0.304160	−	0.952621i	$-0.401624\pi$
$907$	18.3204	0.608320	0.304160	+	0.952621i	$0.401624\pi$
$908$	−63.0501	−2.09239
$909$	1.59733	0.0529801
$910$	0	0
$911$	−36.0342	−1.19387	−0.596933	−	0.802291i	$-0.703614\pi$
$911$	−36.0342	−1.19387	−0.596933	+	0.802291i	$0.703614\pi$
$912$	0.226860	0.00751209
$913$	−0.290078	−0.00960018
$914$	84.1719	2.78416
$915$	26.2935	0.869236
$916$	28.3750	0.937537
$917$	0	0
$918$	11.7112	0.386527
$919$	23.0264	0.759572	0.379786	−	0.925074i	$-0.375998\pi$
$919$	23.0264	0.759572	0.379786	+	0.925074i	$0.375998\pi$
$920$	−17.9601	−0.592126
$921$	28.8875	0.951876
$922$	−47.2896	−1.55740
$923$	2.55865	0.0842191
$924$	0	0
$925$	2.38618	0.0784572
$926$	−93.6106	−3.07624
$927$	6.42012	0.210865
$928$	−21.6596	−0.711012
$929$	−23.9754	−0.786606	−0.393303	−	0.919409i	$-0.628668\pi$
$929$	−23.9754	−0.786606	−0.393303	+	0.919409i	$0.628668\pi$
$930$	−34.5970	−1.13448
$931$	0	0
$932$	59.9270	1.96297
$933$	−28.5330	−0.934128
$934$	−50.8827	−1.66493
$935$	24.8281	0.811965
$936$	2.35510	0.0769789
$937$	43.5758	1.42356	0.711779	−	0.702403i	$-0.247890\pi$
$937$	43.5758	1.42356	0.711779	+	0.702403i	$0.247890\pi$
$938$	0	0
$939$	13.2617	0.432779
$940$	53.5858	1.74778
$941$	20.8056	0.678243	0.339122	−	0.940743i	$-0.389870\pi$
$941$	20.8056	0.678243	0.339122	+	0.940743i	$0.389870\pi$
$942$	17.4605	0.568894
$943$	3.48122	0.113364
$944$	−6.26721	−0.203980
$945$	0	0
$946$	17.6548	0.574008
$947$	−28.0596	−0.911814	−0.455907	−	0.890027i	$-0.650685\pi$
$947$	−28.0596	−0.911814	−0.455907	+	0.890027i	$0.650685\pi$
$948$	26.2824	0.853614
$949$	−2.46160	−0.0799069
$950$	−0.845690	−0.0274378
$951$	15.3817	0.498786
$952$	0	0
$953$	38.8678	1.25905	0.629526	−	0.776980i	$-0.283249\pi$
$953$	38.8678	1.25905	0.629526	+	0.776980i	$0.283249\pi$
$954$	19.9708	0.646578
$955$	36.3351	1.17578
$956$	−52.8426	−1.70905
$957$	−5.03181	−0.162655
$958$	−2.32917	−0.0752522
$959$	0	0
$960$	−35.3326	−1.14035
$961$	1.05817	0.0341346
$962$	2.45846	0.0792638
$963$	−4.09410	−0.131931
$964$	−49.2402	−1.58592
$965$	−40.5234	−1.30449
$966$	0	0
$967$	7.10903	0.228611	0.114305	−	0.993446i	$-0.463536\pi$
$967$	7.10903	0.228611	0.114305	+	0.993446i	$0.463536\pi$
$968$	15.1920	0.488289
$969$	−0.755155	−0.0242591
$970$	−30.7754	−0.988138
$971$	−47.1332	−1.51258	−0.756288	−	0.654238i	$-0.772989\pi$
$971$	−47.1332	−1.51258	−0.756288	+	0.654238i	$0.772989\pi$
$972$	−2.84432	−0.0912316
$973$	0	0
$974$	−30.5668	−0.979424
$975$	3.43106	0.109882
$976$	−15.1392	−0.484594
$977$	4.22880	0.135291	0.0676456	−	0.997709i	$-0.478451\pi$
$977$	4.22880	0.135291	0.0676456	+	0.997709i	$0.478451\pi$
$978$	−18.9647	−0.606423
$979$	20.1273	0.643271
$980$	0	0
$981$	19.1231	0.610555
$982$	−55.2619	−1.76348
$983$	−19.1192	−0.609807	−0.304904	−	0.952383i	$-0.598624\pi$
$983$	−19.1192	−0.609807	−0.304904	+	0.952383i	$0.598624\pi$
$984$	−1.85834	−0.0592416
$985$	12.1794	0.388068
$986$	35.0607	1.11656
$987$	0	0
$988$	−0.511582	−0.0162756
$989$	−16.6140	−0.528293
$990$	−10.2701	−0.326405
$991$	−46.5883	−1.47993	−0.739963	−	0.672648i	$-0.765157\pi$
$991$	−46.5883	−1.47993	−0.739963	+	0.672648i	$0.765157\pi$
$992$	40.9639	1.30061
$993$	−13.2085	−0.419158
$994$	0	0
$995$	43.6928	1.38515
$996$	−0.490894	−0.0155546
$997$	28.3345	0.897362	0.448681	−	0.893692i	$-0.351894\pi$
$997$	28.3345	0.897362	0.448681	+	0.893692i	$0.351894\pi$
$998$	−29.3612	−0.929412
$999$	−0.881374	−0.0278855

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6027.2.a.bh.1.3		13
7.3	odd	6		861.2.i.f.247.11	✓	26
7.5	odd	6		861.2.i.f.739.11	yes	26
7.6	odd	2		6027.2.a.bi.1.3		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
861.2.i.f.247.11	✓	26	7.3	odd	6
861.2.i.f.739.11	yes	26	7.5	odd	6
6027.2.a.bh.1.3		13	1.1	even	1	trivial
6027.2.a.bi.1.3		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)

\(f(q)\)	\(=\)	\(q-2.20098 q^{2} -1.00000 q^{3} +2.84432 q^{4} -2.77621 q^{5} +2.20098 q^{6} -1.85834 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.20098 q^{2} -1.00000 q^{3} +2.84432 q^{4} -2.77621 q^{5} +2.20098 q^{6} -1.85834 q^{8} +1.00000 q^{9} +6.11039 q^{10} -1.68076 q^{11} -2.84432 q^{12} -1.26732 q^{13} +2.77621 q^{15} -1.59848 q^{16} +5.32090 q^{17} -2.20098 q^{18} +0.141922 q^{19} -7.89643 q^{20} +3.69932 q^{22} -3.48122 q^{23} +1.85834 q^{24} +2.70734 q^{25} +2.78934 q^{26} -1.00000 q^{27} -2.99377 q^{29} -6.11039 q^{30} +5.66199 q^{31} +7.23490 q^{32} +1.68076 q^{33} -11.7112 q^{34} +2.84432 q^{36} +0.881374 q^{37} -0.312369 q^{38} +1.26732 q^{39} +5.15913 q^{40} -1.00000 q^{41} +4.77245 q^{43} -4.78062 q^{44} -2.77621 q^{45} +7.66210 q^{46} -6.78607 q^{47} +1.59848 q^{48} -5.95881 q^{50} -5.32090 q^{51} -3.60466 q^{52} -9.07358 q^{53} +2.20098 q^{54} +4.66614 q^{55} -0.141922 q^{57} +6.58924 q^{58} +3.92073 q^{59} +7.89643 q^{60} +9.47100 q^{61} -12.4619 q^{62} -12.7269 q^{64} +3.51834 q^{65} -3.69932 q^{66} +5.95186 q^{67} +15.1343 q^{68} +3.48122 q^{69} -2.01895 q^{71} -1.85834 q^{72} +1.94237 q^{73} -1.93989 q^{74} -2.70734 q^{75} +0.403673 q^{76} -2.78934 q^{78} -9.24032 q^{79} +4.43772 q^{80} +1.00000 q^{81} +2.20098 q^{82} +0.172587 q^{83} -14.7719 q^{85} -10.5041 q^{86} +2.99377 q^{87} +3.12341 q^{88} -11.9751 q^{89} +6.11039 q^{90} -9.90171 q^{92} -5.66199 q^{93} +14.9360 q^{94} -0.394007 q^{95} -7.23490 q^{96} -5.03657 q^{97} -1.68076 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 4 q^{2} - 13 q^{3} + 12 q^{4} + 8 q^{5} + 4 q^{6} - 12 q^{8} + 13 q^{9}+O(q^{10}) \) 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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