LMFDB - Embedded newform 2541.2.a.bp.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2541,2,Mod(1,2541)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2541, 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("2541.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2541 = 3 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2541.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:	$20.2899871536$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.7488.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 2x + 1 $ x^4 - 2x^3 - 4x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-0.326909$ of defining polynomial
Character	$\chi$	$=$	2541.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.05896 q^{2} +1.00000 q^{3} +2.23931 q^{4} -3.05896 q^{5} -2.05896 q^{6} -1.00000 q^{7} -0.492737 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.05896 q^{2} +1.00000 q^{3} +2.23931 q^{4} -3.05896 q^{5} -2.05896 q^{6} -1.00000 q^{7} -0.492737 q^{8} +1.00000 q^{9} +6.29827 q^{10} +2.23931 q^{12} +3.32691 q^{13} +2.05896 q^{14} -3.05896 q^{15} -3.46410 q^{16} +5.37651 q^{17} -2.05896 q^{18} +8.29827 q^{19} -6.84997 q^{20} -1.00000 q^{21} -1.74141 q^{23} -0.492737 q^{24} +4.35723 q^{25} -6.84997 q^{26} +1.00000 q^{27} -2.23931 q^{28} -8.16277 q^{29} +6.29827 q^{30} -5.44999 q^{31} +8.11792 q^{32} -11.0700 q^{34} +3.05896 q^{35} +2.23931 q^{36} +4.53242 q^{37} -17.0858 q^{38} +3.32691 q^{39} +1.50726 q^{40} -6.84997 q^{41} +2.05896 q^{42} -1.84997 q^{43} -3.05896 q^{45} +3.58550 q^{46} -7.28416 q^{47} -3.46410 q^{48} +1.00000 q^{49} -8.97136 q^{50} +5.37651 q^{51} +7.44999 q^{52} -0.985474 q^{53} -2.05896 q^{54} +0.492737 q^{56} +8.29827 q^{57} +16.8068 q^{58} +4.52306 q^{59} -6.84997 q^{60} -12.0845 q^{61} +11.2213 q^{62} -1.00000 q^{63} -9.78626 q^{64} -10.1769 q^{65} +0.170993 q^{67} +12.0397 q^{68} -1.74141 q^{69} -6.29827 q^{70} -10.0017 q^{71} -0.492737 q^{72} +12.7910 q^{73} -9.33207 q^{74} +4.35723 q^{75} +18.5824 q^{76} -6.84997 q^{78} +14.6794 q^{79} +10.5965 q^{80} +1.00000 q^{81} +14.1038 q^{82} -1.62993 q^{83} -2.23931 q^{84} -16.4465 q^{85} +3.80901 q^{86} -8.16277 q^{87} +13.9872 q^{89} +6.29827 q^{90} -3.32691 q^{91} -3.89957 q^{92} -5.44999 q^{93} +14.9978 q^{94} -25.3841 q^{95} +8.11792 q^{96} +3.44483 q^{97} -2.05896 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 4 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} + 4 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 + 4 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 4 * q^7 + 4 * q^9	$ 4 q + 2 q^{2} + 4 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} + 4 q^{9} + 10 q^{10} + 4 q^{12} + 10 q^{13} - 2 q^{14} - 2 q^{15} + 6 q^{17} + 2 q^{18} + 18 q^{19} - 4 q^{21} - 2 q^{23} - 8 q^{25} + 4 q^{27} - 4 q^{28} + 6 q^{29} + 10 q^{30} + 12 q^{32} - 2 q^{34} + 2 q^{35} + 4 q^{36} - 4 q^{37} + 10 q^{39} + 8 q^{40} - 2 q^{42} + 20 q^{43} - 2 q^{45} + 16 q^{46} - 6 q^{47} + 4 q^{49} - 24 q^{50} + 6 q^{51} + 8 q^{52} + 2 q^{54} + 18 q^{57} + 24 q^{58} - 6 q^{59} - 10 q^{61} - 4 q^{63} - 16 q^{64} - 10 q^{65} + 4 q^{67} + 28 q^{68} - 2 q^{69} - 10 q^{70} - 6 q^{71} + 34 q^{73} - 36 q^{74} - 8 q^{75} + 36 q^{76} + 24 q^{79} + 12 q^{80} + 4 q^{81} + 28 q^{82} + 6 q^{83} - 4 q^{84} - 8 q^{85} + 38 q^{86} + 6 q^{87} + 18 q^{89} + 10 q^{90} - 10 q^{91} + 24 q^{92} - 6 q^{94} - 18 q^{95} + 12 q^{96} - 10 q^{97} + 2 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 + 4 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 4 * q^7 + 4 * q^9 + 10 * q^10 + 4 * q^12 + 10 * q^13 - 2 * q^14 - 2 * q^15 + 6 * q^17 + 2 * q^18 + 18 * q^19 - 4 * q^21 - 2 * q^23 - 8 * q^25 + 4 * q^27 - 4 * q^28 + 6 * q^29 + 10 * q^30 + 12 * q^32 - 2 * q^34 + 2 * q^35 + 4 * q^36 - 4 * q^37 + 10 * q^39 + 8 * q^40 - 2 * q^42 + 20 * q^43 - 2 * q^45 + 16 * q^46 - 6 * q^47 + 4 * q^49 - 24 * q^50 + 6 * q^51 + 8 * q^52 + 2 * q^54 + 18 * q^57 + 24 * q^58 - 6 * q^59 - 10 * q^61 - 4 * q^63 - 16 * q^64 - 10 * q^65 + 4 * q^67 + 28 * q^68 - 2 * q^69 - 10 * q^70 - 6 * q^71 + 34 * q^73 - 36 * q^74 - 8 * q^75 + 36 * q^76 + 24 * q^79 + 12 * q^80 + 4 * q^81 + 28 * q^82 + 6 * q^83 - 4 * q^84 - 8 * q^85 + 38 * q^86 + 6 * q^87 + 18 * q^89 + 10 * q^90 - 10 * q^91 + 24 * q^92 - 6 * q^94 - 18 * q^95 + 12 * q^96 - 10 * q^97 + 2 * q^98

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 $

$2$	−2.05896	−1.45590	−0.727952	−	0.685628i	$-0.759528\pi$
$2$	−2.05896	−1.45590	−0.727952	+	0.685628i	$0.759528\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.23931	1.11966
$5$	−3.05896	−1.36801	−0.684004	−	0.729478i	$-0.739763\pi$
$5$	−3.05896	−1.36801	−0.684004	+	0.729478i	$0.739763\pi$
$6$	−2.05896	−0.840567
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.492737	−0.174209
$9$	1.00000	0.333333
$10$	6.29827	1.99169
$11$	0	0
$11$	0	0
$12$	2.23931	0.646434
$13$	3.32691	0.922718	0.461359	−	0.887213i	$-0.347362\pi$
$13$	3.32691	0.922718	0.461359	+	0.887213i	$0.347362\pi$
$14$	2.05896	0.550280
$15$	−3.05896	−0.789820
$16$	−3.46410	−0.866025
$17$	5.37651	1.30399	0.651997	−	0.758221i	$-0.273931\pi$
$17$	5.37651	1.30399	0.651997	+	0.758221i	$0.273931\pi$
$18$	−2.05896	−0.485301
$19$	8.29827	1.90375	0.951877	−	0.306480i	$-0.0991512\pi$
$19$	8.29827	1.90375	0.951877	+	0.306480i	$0.0991512\pi$
$20$	−6.84997	−1.53170
$21$	−1.00000	−0.218218
$22$	0	0
$23$	−1.74141	−0.363110	−0.181555	−	0.983381i	$-0.558113\pi$
$23$	−1.74141	−0.363110	−0.181555	+	0.983381i	$0.558113\pi$
$24$	−0.492737	−0.100580
$25$	4.35723	0.871446
$26$	−6.84997	−1.34339
$27$	1.00000	0.192450
$28$	−2.23931	−0.423191
$29$	−8.16277	−1.51579	−0.757894	−	0.652378i	$-0.773772\pi$
$29$	−8.16277	−1.51579	−0.757894	+	0.652378i	$0.773772\pi$
$30$	6.29827	1.14990
$31$	−5.44999	−0.978847	−0.489424	−	0.872046i	$-0.662793\pi$
$31$	−5.44999	−0.978847	−0.489424	+	0.872046i	$0.662793\pi$
$32$	8.11792	1.43506
$33$	0	0
$34$	−11.0700	−1.89849
$35$	3.05896	0.517059
$36$	2.23931	0.373219
$37$	4.53242	0.745126	0.372563	−	0.928007i	$-0.378479\pi$
$37$	4.53242	0.745126	0.372563	+	0.928007i	$0.378479\pi$
$38$	−17.0858	−2.77168
$39$	3.32691	0.532732
$40$	1.50726	0.238319
$41$	−6.84997	−1.06979	−0.534893	−	0.844920i	$-0.679648\pi$
$41$	−6.84997	−1.06979	−0.534893	+	0.844920i	$0.679648\pi$
$42$	2.05896	0.317704
$43$	−1.84997	−0.282118	−0.141059	−	0.990001i	$-0.545051\pi$
$43$	−1.84997	−0.282118	−0.141059	+	0.990001i	$0.545051\pi$
$44$	0	0
$45$	−3.05896	−0.456003
$46$	3.58550	0.528653
$47$	−7.28416	−1.06250	−0.531252	−	0.847214i	$-0.678278\pi$
$47$	−7.28416	−1.06250	−0.531252	+	0.847214i	$0.678278\pi$
$48$	−3.46410	−0.500000
$49$	1.00000	0.142857
$50$	−8.97136	−1.26874
$51$	5.37651	0.752862
$52$	7.44999	1.03313
$53$	−0.985474	−0.135365	−0.0676827	−	0.997707i	$-0.521561\pi$
$53$	−0.985474	−0.135365	−0.0676827	+	0.997707i	$0.521561\pi$
$54$	−2.05896	−0.280189
$55$	0	0
$56$	0.492737	0.0658448
$57$	8.29827	1.09913
$58$	16.8068	2.20684
$59$	4.52306	0.588852	0.294426	−	0.955674i	$-0.404871\pi$
$59$	4.52306	0.588852	0.294426	+	0.955674i	$0.404871\pi$
$60$	−6.84997	−0.884327
$61$	−12.0845	−1.54727	−0.773633	−	0.633634i	$-0.781563\pi$
$61$	−12.0845	−1.54727	−0.773633	+	0.633634i	$0.781563\pi$
$62$	11.2213	1.42511
$63$	−1.00000	−0.125988
$64$	−9.78626	−1.22328
$65$	−10.1769	−1.26229
$66$	0	0
$67$	0.170993	0.0208901	0.0104451	−	0.999945i	$-0.496675\pi$
$67$	0.170993	0.0208901	0.0104451	+	0.999945i	$0.496675\pi$
$68$	12.0397	1.46003
$69$	−1.74141	−0.209641
$70$	−6.29827	−0.752788
$71$	−10.0017	−1.18698	−0.593491	−	0.804841i	$-0.702251\pi$
$71$	−10.0017	−1.18698	−0.593491	+	0.804841i	$0.702251\pi$
$72$	−0.492737	−0.0580696
$73$	12.7910	1.49707	0.748537	−	0.663093i	$-0.230757\pi$
$73$	12.7910	1.49707	0.748537	+	0.663093i	$0.230757\pi$
$74$	−9.33207	−1.08483
$75$	4.35723	0.503130
$76$	18.5824	2.13155
$77$	0	0
$78$	−6.84997	−0.775606
$79$	14.6794	1.65156	0.825780	−	0.563992i	$-0.190735\pi$
$79$	14.6794	1.65156	0.825780	+	0.563992i	$0.190735\pi$
$80$	10.5965	1.18473
$81$	1.00000	0.111111
$82$	14.1038	1.55751
$83$	−1.62993	−0.178908	−0.0894540	−	0.995991i	$-0.528512\pi$
$83$	−1.62993	−0.178908	−0.0894540	+	0.995991i	$0.528512\pi$
$84$	−2.23931	−0.244329
$85$	−16.4465	−1.78388
$86$	3.80901	0.410736
$87$	−8.16277	−0.875141
$88$	0	0
$89$	13.9872	1.48264	0.741318	−	0.671154i	$-0.234201\pi$
$89$	13.9872	1.48264	0.741318	+	0.671154i	$0.234201\pi$
$90$	6.29827	0.663896
$91$	−3.32691	−0.348755
$92$	−3.89957	−0.406558
$93$	−5.44999	−0.565138
$94$	14.9978	1.54690
$95$	−25.3841	−2.60435
$96$	8.11792	0.828532
$97$	3.44483	0.349769	0.174885	−	0.984589i	$-0.444045\pi$
$97$	3.44483	0.349769	0.174885	+	0.984589i	$0.444045\pi$
$98$	−2.05896	−0.207986
$99$	0	0
$100$	9.75721	0.975721
$101$	9.35554	0.930911	0.465456	−	0.885071i	$-0.345890\pi$
$101$	9.35554	0.930911	0.465456	+	0.885071i	$0.345890\pi$
$102$	−11.0700	−1.09609
$103$	12.6952	1.25089	0.625447	−	0.780267i	$-0.284917\pi$
$103$	12.6952	1.25089	0.625447	+	0.780267i	$0.284917\pi$
$104$	−1.63929	−0.160746
$105$	3.05896	0.298524
$106$	2.02905	0.197079
$107$	11.7589	1.13678	0.568388	−	0.822761i	$-0.307567\pi$
$107$	11.7589	1.13678	0.568388	+	0.822761i	$0.307567\pi$
$108$	2.23931	0.215478
$109$	15.9038	1.52330	0.761652	−	0.647986i	$-0.224389\pi$
$109$	15.9038	1.52330	0.761652	+	0.647986i	$0.224389\pi$
$110$	0	0
$111$	4.53242	0.430198
$112$	3.46410	0.327327
$113$	7.30763	0.687444	0.343722	−	0.939071i	$-0.388312\pi$
$113$	7.30763	0.687444	0.343722	+	0.939071i	$0.388312\pi$
$114$	−17.0858	−1.60023
$115$	5.32691	0.496737
$116$	−18.2790	−1.69716
$117$	3.32691	0.307573
$118$	−9.31280	−0.857313
$119$	−5.37651	−0.492864
$120$	1.50726	0.137594
$121$	0	0
$122$	24.8816	2.25267
$123$	−6.84997	−0.617641
$124$	−12.2042	−1.09597
$125$	1.96620	0.175862
$126$	2.05896	0.183427
$127$	−4.32860	−0.384101	−0.192050	−	0.981385i	$-0.561514\pi$
$127$	−4.32860	−0.384101	−0.192050	+	0.981385i	$0.561514\pi$
$128$	3.91368	0.345923
$129$	−1.84997	−0.162881
$130$	20.9538	1.83777
$131$	8.71236	0.761202	0.380601	−	0.924739i	$-0.375717\pi$
$131$	8.71236	0.761202	0.380601	+	0.924739i	$0.375717\pi$
$132$	0	0
$133$	−8.29827	−0.719552
$134$	−0.352068	−0.0304140
$135$	−3.05896	−0.263273
$136$	−2.64920	−0.227167
$137$	−0.234149	−0.0200047	−0.0100024	−	0.999950i	$-0.503184\pi$
$137$	−0.234149	−0.0200047	−0.0100024	+	0.999950i	$0.503184\pi$
$138$	3.58550	0.305218
$139$	19.3200	1.63870	0.819349	−	0.573296i	$-0.194335\pi$
$139$	19.3200	1.63870	0.819349	+	0.573296i	$0.194335\pi$
$140$	6.84997	0.578928
$141$	−7.28416	−0.613437
$142$	20.5931	1.72813
$143$	0	0
$144$	−3.46410	−0.288675
$145$	24.9696	2.07361
$146$	−26.3362	−2.17960
$147$	1.00000	0.0824786
$148$	10.1495	0.834285
$149$	−5.20090	−0.426074	−0.213037	−	0.977044i	$-0.568336\pi$
$149$	−5.20090	−0.426074	−0.213037	+	0.977044i	$0.568336\pi$
$150$	−8.97136	−0.732509
$151$	6.35682	0.517310	0.258655	−	0.965970i	$-0.416721\pi$
$151$	6.35682	0.517310	0.258655	+	0.965970i	$0.416721\pi$
$152$	−4.08887	−0.331651
$153$	5.37651	0.434665
$154$	0	0
$155$	16.6713	1.33907
$156$	7.44999	0.596477
$157$	−10.0141	−0.799213	−0.399606	−	0.916687i	$-0.630853\pi$
$157$	−10.0141	−0.799213	−0.399606	+	0.916687i	$0.630853\pi$
$158$	−30.2243	−2.40451
$159$	−0.985474	−0.0781532
$160$	−24.8324	−1.96317
$161$	1.74141	0.137242
$162$	−2.05896	−0.161767
$163$	−8.50337	−0.666035	−0.333018	−	0.942921i	$-0.608067\pi$
$163$	−8.50337	−0.666035	−0.333018	+	0.942921i	$0.608067\pi$
$164$	−15.3392	−1.19779
$165$	0	0
$166$	3.35596	0.260473
$167$	2.93756	0.227316	0.113658	−	0.993520i	$-0.463743\pi$
$167$	2.93756	0.227316	0.113658	+	0.993520i	$0.463743\pi$
$168$	0.492737	0.0380155
$169$	−1.93168	−0.148591
$170$	33.8627	2.59715
$171$	8.29827	0.634585
$172$	−4.14266	−0.315875
$173$	−20.6841	−1.57259	−0.786293	−	0.617854i	$-0.788002\pi$
$173$	−20.6841	−1.57259	−0.786293	+	0.617854i	$0.788002\pi$
$174$	16.8068	1.27412
$175$	−4.35723	−0.329376
$176$	0	0
$177$	4.52306	0.339974
$178$	−28.7990	−2.15858
$179$	6.14697	0.459446	0.229723	−	0.973256i	$-0.426218\pi$
$179$	6.14697	0.459446	0.229723	+	0.973256i	$0.426218\pi$
$180$	−6.84997	−0.510567
$181$	−19.2458	−1.43053	−0.715263	−	0.698856i	$-0.753693\pi$
$181$	−19.2458	−1.43053	−0.715263	+	0.698856i	$0.753693\pi$
$182$	6.84997	0.507754
$183$	−12.0845	−0.893315
$184$	0.858058	0.0632569
$185$	−13.8645	−1.01934
$186$	11.2213	0.822786
$187$	0	0
$188$	−16.3115	−1.18964
$189$	−1.00000	−0.0727393
$190$	52.2648	3.79169
$191$	25.5978	1.85219	0.926097	−	0.377287i	$-0.123143\pi$
$191$	25.5978	1.85219	0.926097	+	0.377287i	$0.123143\pi$
$192$	−9.78626	−0.706263
$193$	11.1962	0.805917	0.402958	−	0.915218i	$-0.367982\pi$
$193$	11.1962	0.805917	0.402958	+	0.915218i	$0.367982\pi$
$194$	−7.09276	−0.509230
$195$	−10.1769	−0.728781
$196$	2.23931	0.159951
$197$	−17.4687	−1.24459	−0.622297	−	0.782781i	$-0.713800\pi$
$197$	−17.4687	−1.24459	−0.622297	+	0.782781i	$0.713800\pi$
$198$	0	0
$199$	−6.71963	−0.476342	−0.238171	−	0.971223i	$-0.576548\pi$
$199$	−6.71963	−0.476342	−0.238171	+	0.971223i	$0.576548\pi$
$200$	−2.14697	−0.151814
$201$	0.170993	0.0120609
$202$	−19.2627	−1.35532
$203$	8.16277	0.572914
$204$	12.0397	0.842947
$205$	20.9538	1.46348
$206$	−26.1389	−1.82118
$207$	−1.74141	−0.121037
$208$	−11.5247	−0.799098
$209$	0	0
$210$	−6.29827	−0.434622
$211$	−20.2293	−1.39264	−0.696321	−	0.717730i	$-0.745181\pi$
$211$	−20.2293	−1.39264	−0.696321	+	0.717730i	$0.745181\pi$
$212$	−2.20679	−0.151563
$213$	−10.0017	−0.685304
$214$	−24.2111	−1.65504
$215$	5.65898	0.385939
$216$	−0.492737	−0.0335265
$217$	5.44999	0.369970
$218$	−32.7452	−2.21779
$219$	12.7910	0.864336
$220$	0	0
$221$	17.8871	1.20322
$222$	−9.33207	−0.626328
$223$	11.8705	0.794909	0.397454	−	0.917622i	$-0.369894\pi$
$223$	11.8705	0.794909	0.397454	+	0.917622i	$0.369894\pi$
$224$	−8.11792	−0.542401
$225$	4.35723	0.290482
$226$	−15.0461	−1.00085
$227$	13.9521	0.926033	0.463016	−	0.886350i	$-0.346767\pi$
$227$	13.9521	0.926033	0.463016	+	0.886350i	$0.346767\pi$
$228$	18.5824	1.23065
$229$	24.8324	1.64097	0.820485	−	0.571668i	$-0.193703\pi$
$229$	24.8324	1.64097	0.820485	+	0.571668i	$0.193703\pi$
$230$	−10.9679	−0.723201
$231$	0	0
$232$	4.02210	0.264064
$233$	−11.8265	−0.774780	−0.387390	−	0.921916i	$-0.626623\pi$
$233$	−11.8265	−0.774780	−0.387390	+	0.921916i	$0.626623\pi$
$234$	−6.84997	−0.447797
$235$	22.2820	1.45351
$236$	10.1286	0.659313
$237$	14.6794	0.953529
$238$	11.0700	0.717562
$239$	−8.86522	−0.573443	−0.286722	−	0.958014i	$-0.592565\pi$
$239$	−8.86522	−0.573443	−0.286722	+	0.958014i	$0.592565\pi$
$240$	10.5965	0.684004
$241$	11.3922	0.733834	0.366917	−	0.930254i	$-0.380413\pi$
$241$	11.3922	0.733834	0.366917	+	0.930254i	$0.380413\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	−27.0611	−1.73241
$245$	−3.05896	−0.195430
$246$	14.1038	0.899226
$247$	27.6076	1.75663
$248$	2.68541	0.170524
$249$	−1.62993	−0.103293
$250$	−4.04833	−0.256039
$251$	9.71866	0.613436	0.306718	−	0.951800i	$-0.400769\pi$
$251$	9.71866	0.613436	0.306718	+	0.951800i	$0.400769\pi$
$252$	−2.23931	−0.141064
$253$	0	0
$254$	8.91241	0.559214
$255$	−16.4465	−1.02992
$256$	11.5144	0.719651
$257$	−20.0456	−1.25041	−0.625204	−	0.780461i	$-0.714984\pi$
$257$	−20.0456	−1.25041	−0.625204	+	0.780461i	$0.714984\pi$
$258$	3.80901	0.237139
$259$	−4.53242	−0.281631
$260$	−22.7892	−1.41333
$261$	−8.16277	−0.505263
$262$	−17.9384	−1.10824
$263$	12.9345	0.797576	0.398788	−	0.917043i	$-0.369431\pi$
$263$	12.9345	0.797576	0.398788	+	0.917043i	$0.369431\pi$
$264$	0	0
$265$	3.01453	0.185181
$266$	17.0858	1.04760
$267$	13.9872	0.856000
$268$	0.382907	0.0233898
$269$	4.44958	0.271295	0.135648	−	0.990757i	$-0.456688\pi$
$269$	4.44958	0.271295	0.135648	+	0.990757i	$0.456688\pi$
$270$	6.29827	0.383301
$271$	9.59696	0.582974	0.291487	−	0.956575i	$-0.405850\pi$
$271$	9.59696	0.582974	0.291487	+	0.956575i	$0.405850\pi$
$272$	−18.6248	−1.12929
$273$	−3.32691	−0.201354
$274$	0.482104	0.0291249
$275$	0	0
$276$	−3.89957	−0.234726
$277$	−2.80037	−0.168258	−0.0841290	−	0.996455i	$-0.526811\pi$
$277$	−2.80037	−0.168258	−0.0841290	+	0.996455i	$0.526811\pi$
$278$	−39.7790	−2.38579
$279$	−5.44999	−0.326282
$280$	−1.50726	−0.0900762
$281$	15.4721	0.922988	0.461494	−	0.887143i	$-0.347314\pi$
$281$	15.4721	0.922988	0.461494	+	0.887143i	$0.347314\pi$
$282$	14.9978	0.893106
$283$	−25.9076	−1.54004	−0.770022	−	0.638017i	$-0.779755\pi$
$283$	−25.9076	−1.54004	−0.770022	+	0.638017i	$0.779755\pi$
$284$	−22.3969	−1.32901
$285$	−25.3841	−1.50362
$286$	0	0
$287$	6.84997	0.404341
$288$	8.11792	0.478353
$289$	11.9068	0.700401
$290$	−51.4113	−3.01898
$291$	3.44483	0.201939
$292$	28.6431	1.67621
$293$	23.3799	1.36587	0.682934	−	0.730480i	$-0.260704\pi$
$293$	23.3799	1.36587	0.682934	+	0.730480i	$0.260704\pi$
$294$	−2.05896	−0.120081
$295$	−13.8359	−0.805555
$296$	−2.23329	−0.129808
$297$	0	0
$298$	10.7084	0.620323
$299$	−5.79352	−0.335048
$300$	9.75721	0.563333
$301$	1.84997	0.106630
$302$	−13.0884	−0.753154
$303$	9.35554	0.537462
$304$	−28.7461	−1.64870
$305$	36.9661	2.11667
$306$	−11.0700	−0.632830
$307$	−10.0742	−0.574965	−0.287483	−	0.957786i	$-0.592818\pi$
$307$	−10.0742	−0.574965	−0.287483	+	0.957786i	$0.592818\pi$
$308$	0	0
$309$	12.6952	0.722204
$310$	−34.3255	−1.94956
$311$	8.26014	0.468390	0.234195	−	0.972190i	$-0.424755\pi$
$311$	8.26014	0.468390	0.234195	+	0.972190i	$0.424755\pi$
$312$	−1.63929	−0.0928066
$313$	−7.39189	−0.417814	−0.208907	−	0.977935i	$-0.566991\pi$
$313$	−7.39189	−0.417814	−0.208907	+	0.977935i	$0.566991\pi$
$314$	20.6186	1.16358
$315$	3.05896	0.172353
$316$	32.8718	1.84918
$317$	31.1600	1.75012	0.875060	−	0.484014i	$-0.160822\pi$
$317$	31.1600	1.75012	0.875060	+	0.484014i	$0.160822\pi$
$318$	2.02905	0.113784
$319$	0	0
$320$	29.9358	1.67346
$321$	11.7589	0.656318
$322$	−3.58550	−0.199812
$323$	44.6157	2.48249
$324$	2.23931	0.124406
$325$	14.4961	0.804100
$326$	17.5081	0.969684
$327$	15.9038	0.879480
$328$	3.37523	0.186366
$329$	7.28416	0.401589
$330$	0	0
$331$	−20.0110	−1.09991	−0.549953	−	0.835195i	$-0.685355\pi$
$331$	−20.0110	−1.09991	−0.549953	+	0.835195i	$0.685355\pi$
$332$	−3.64992	−0.200316
$333$	4.53242	0.248375
$334$	−6.04833	−0.330950
$335$	−0.523061	−0.0285779
$336$	3.46410	0.188982
$337$	−20.4973	−1.11656	−0.558278	−	0.829654i	$-0.688538\pi$
$337$	−20.4973	−1.11656	−0.558278	+	0.829654i	$0.688538\pi$
$338$	3.97725	0.216334
$339$	7.30763	0.396896
$340$	−36.8289	−1.99733
$341$	0	0
$342$	−17.0858	−0.923895
$343$	−1.00000	−0.0539949
$344$	0.911549	0.0491474
$345$	5.32691	0.286791
$346$	42.5878	2.28953
$347$	33.7959	1.81426	0.907131	−	0.420849i	$-0.138268\pi$
$347$	33.7959	1.81426	0.907131	+	0.420849i	$0.138268\pi$
$348$	−18.2790	−0.979857
$349$	33.0030	1.76661	0.883304	−	0.468801i	$-0.155314\pi$
$349$	33.0030	1.76661	0.883304	+	0.468801i	$0.155314\pi$
$350$	8.97136	0.479540
$351$	3.32691	0.177577
$352$	0	0
$353$	9.49315	0.505270	0.252635	−	0.967562i	$-0.418703\pi$
$353$	9.49315	0.505270	0.252635	+	0.967562i	$0.418703\pi$
$354$	−9.31280	−0.494970
$355$	30.5948	1.62380
$356$	31.3216	1.66004
$357$	−5.37651	−0.284555
$358$	−12.6564	−0.668910
$359$	−13.0490	−0.688702	−0.344351	−	0.938841i	$-0.611901\pi$
$359$	−13.0490	−0.688702	−0.344351	+	0.938841i	$0.611901\pi$
$360$	1.50726	0.0794397
$361$	49.8613	2.62428
$362$	39.6262	2.08271
$363$	0	0
$364$	−7.44999	−0.390486
$365$	−39.1272	−2.04801
$366$	24.8816	1.30058
$367$	−1.93419	−0.100964	−0.0504819	−	0.998725i	$-0.516076\pi$
$367$	−1.93419	−0.100964	−0.0504819	+	0.998725i	$0.516076\pi$
$368$	6.03243	0.314462
$369$	−6.84997	−0.356595
$370$	28.5464	1.48406
$371$	0.985474	0.0511633
$372$	−12.2042	−0.632760
$373$	23.8816	1.23654	0.618270	−	0.785966i	$-0.287834\pi$
$373$	23.8816	1.23654	0.618270	+	0.785966i	$0.287834\pi$
$374$	0	0
$375$	1.96620	0.101534
$376$	3.58918	0.185098
$377$	−27.1568	−1.39865
$378$	2.05896	0.105901
$379$	−38.0262	−1.95327	−0.976637	−	0.214895i	$-0.931059\pi$
$379$	−38.0262	−1.95327	−0.976637	+	0.214895i	$0.931059\pi$
$380$	−56.8429	−2.91598
$381$	−4.32860	−0.221761
$382$	−52.7049	−2.69662
$383$	31.5678	1.61304	0.806519	−	0.591208i	$-0.201349\pi$
$383$	31.5678	1.61304	0.806519	+	0.591208i	$0.201349\pi$
$384$	3.91368	0.199719
$385$	0	0
$386$	−23.0524	−1.17334
$387$	−1.84997	−0.0940392
$388$	7.71405	0.391621
$389$	10.1308	0.513652	0.256826	−	0.966458i	$-0.417323\pi$
$389$	10.1308	0.513652	0.256826	+	0.966458i	$0.417323\pi$
$390$	20.9538	1.06104
$391$	−9.36271	−0.473493
$392$	−0.492737	−0.0248870
$393$	8.71236	0.439480
$394$	35.9674	1.81201
$395$	−44.9037	−2.25935
$396$	0	0
$397$	−7.51188	−0.377010	−0.188505	−	0.982072i	$-0.560364\pi$
$397$	−7.51188	−0.377010	−0.188505	+	0.982072i	$0.560364\pi$
$398$	13.8354	0.693508
$399$	−8.29827	−0.415433
$400$	−15.0939	−0.754695
$401$	19.2645	0.962022	0.481011	−	0.876715i	$-0.340270\pi$
$401$	19.2645	0.962022	0.481011	+	0.876715i	$0.340270\pi$
$402$	−0.352068	−0.0175595
$403$	−18.1316	−0.903201
$404$	20.9500	1.04230
$405$	−3.05896	−0.152001
$406$	−16.8068	−0.834108
$407$	0	0
$408$	−2.64920	−0.131155
$409$	13.0605	0.645801	0.322900	−	0.946433i	$-0.395342\pi$
$409$	13.0605	0.645801	0.322900	+	0.946433i	$0.395342\pi$
$410$	−43.1430	−2.13068
$411$	−0.234149	−0.0115497
$412$	28.4285	1.40057
$413$	−4.52306	−0.222565
$414$	3.58550	0.176218
$415$	4.98589	0.244748
$416$	27.0076	1.32416
$417$	19.3200	0.946102
$418$	0	0
$419$	−30.7589	−1.50267	−0.751335	−	0.659921i	$-0.770590\pi$
$419$	−30.7589	−1.50267	−0.751335	+	0.659921i	$0.770590\pi$
$420$	6.84997	0.334244
$421$	16.0657	0.782993	0.391497	−	0.920180i	$-0.371957\pi$
$421$	16.0657	0.782993	0.391497	+	0.920180i	$0.371957\pi$
$422$	41.6513	2.02755
$423$	−7.28416	−0.354168
$424$	0.485580	0.0235818
$425$	23.4267	1.13636
$426$	20.5931	0.997737
$427$	12.0845	0.584812
$428$	26.3319	1.27280
$429$	0	0
$430$	−11.6516	−0.561891
$431$	13.0752	0.629809	0.314904	−	0.949123i	$-0.398028\pi$
$431$	13.0752	0.629809	0.314904	+	0.949123i	$0.398028\pi$
$432$	−3.46410	−0.166667
$433$	12.9757	0.623572	0.311786	−	0.950152i	$-0.399073\pi$
$433$	12.9757	0.623572	0.311786	+	0.950152i	$0.399073\pi$
$434$	−11.2213	−0.538640
$435$	24.9696	1.19720
$436$	35.6135	1.70558
$437$	−14.4507	−0.691271
$438$	−26.3362	−1.25839
$439$	−15.9709	−0.762252	−0.381126	−	0.924523i	$-0.624464\pi$
$439$	−15.9709	−0.762252	−0.381126	+	0.924523i	$0.624464\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	−36.8289	−1.75177
$443$	−21.2695	−1.01055	−0.505273	−	0.862959i	$-0.668608\pi$
$443$	−21.2695	−1.01055	−0.505273	+	0.862959i	$0.668608\pi$
$444$	10.1495	0.481675
$445$	−42.7862	−2.02826
$446$	−24.4409	−1.15731
$447$	−5.20090	−0.245994
$448$	9.78626	0.462357
$449$	−6.63021	−0.312899	−0.156449	−	0.987686i	$-0.550005\pi$
$449$	−6.63021	−0.312899	−0.156449	+	0.987686i	$0.550005\pi$
$450$	−8.97136	−0.422914
$451$	0	0
$452$	16.3641	0.769702
$453$	6.35682	0.298669
$454$	−28.7268	−1.34821
$455$	10.1769	0.477099
$456$	−4.08887	−0.191479
$457$	17.1191	0.800796	0.400398	−	0.916341i	$-0.368872\pi$
$457$	17.1191	0.800796	0.400398	+	0.916341i	$0.368872\pi$
$458$	−51.1289	−2.38910
$459$	5.37651	0.250954
$460$	11.9286	0.556175
$461$	19.1173	0.890380	0.445190	−	0.895436i	$-0.353136\pi$
$461$	19.1173	0.890380	0.445190	+	0.895436i	$0.353136\pi$
$462$	0	0
$463$	16.0828	0.747433	0.373717	−	0.927543i	$-0.378083\pi$
$463$	16.0828	0.747433	0.373717	+	0.927543i	$0.378083\pi$
$464$	28.2767	1.31271
$465$	16.6713	0.773113
$466$	24.3503	1.12800
$467$	−13.4920	−0.624336	−0.312168	−	0.950027i	$-0.601055\pi$
$467$	−13.4920	−0.624336	−0.312168	+	0.950027i	$0.601055\pi$
$468$	7.44999	0.344376
$469$	−0.170993	−0.00789573
$470$	−45.8776	−2.11618
$471$	−10.0141	−0.461426
$472$	−2.22868	−0.102583
$473$	0	0
$474$	−30.2243	−1.38825
$475$	36.1575	1.65902
$476$	−12.0397	−0.551838
$477$	−0.985474	−0.0451218
$478$	18.2531	0.834878
$479$	25.0471	1.14443	0.572215	−	0.820103i	$-0.306084\pi$
$479$	25.0471	1.14443	0.572215	+	0.820103i	$0.306084\pi$
$480$	−24.8324	−1.13344
$481$	15.0790	0.687541
$482$	−23.4560	−1.06839
$483$	1.74141	0.0792370
$484$	0	0
$485$	−10.5376	−0.478487
$486$	−2.05896	−0.0933963
$487$	−30.7888	−1.39517	−0.697587	−	0.716500i	$-0.745743\pi$
$487$	−30.7888	−1.39517	−0.697587	+	0.716500i	$0.745743\pi$
$488$	5.95450	0.269548
$489$	−8.50337	−0.384536
$490$	6.29827	0.284527
$491$	39.1200	1.76546	0.882731	−	0.469879i	$-0.155702\pi$
$491$	39.1200	1.76546	0.882731	+	0.469879i	$0.155702\pi$
$492$	−15.3392	−0.691546
$493$	−43.8872	−1.97658
$494$	−56.8429	−2.55748
$495$	0	0
$496$	18.8793	0.847707
$497$	10.0017	0.448637
$498$	3.35596	0.150384
$499$	13.5522	0.606682	0.303341	−	0.952882i	$-0.401898\pi$
$499$	13.5522	0.606682	0.303341	+	0.952882i	$0.401898\pi$
$500$	4.40294	0.196905
$501$	2.93756	0.131241
$502$	−20.0103	−0.893105
$503$	−18.1214	−0.807995	−0.403997	−	0.914760i	$-0.632380\pi$
$503$	−18.1214	−0.807995	−0.403997	+	0.914760i	$0.632380\pi$
$504$	0.492737	0.0219483
$505$	−28.6182	−1.27349
$506$	0	0
$507$	−1.93168	−0.0857889
$508$	−9.69309	−0.430061
$509$	−40.4192	−1.79155	−0.895774	−	0.444510i	$-0.853378\pi$
$509$	−40.4192	−1.79155	−0.895774	+	0.444510i	$0.853378\pi$
$510$	33.8627	1.49947
$511$	−12.7910	−0.565841
$512$	−31.5351	−1.39367
$513$	8.29827	0.366378
$514$	41.2730	1.82047
$515$	−38.8341	−1.71123
$516$	−4.14266	−0.182371
$517$	0	0
$518$	9.33207	0.410028
$519$	−20.6841	−0.907933
$520$	5.01453	0.219902
$521$	−7.74795	−0.339444	−0.169722	−	0.985492i	$-0.554287\pi$
$521$	−7.74795	−0.339444	−0.169722	+	0.985492i	$0.554287\pi$
$522$	16.8068	0.735614
$523$	21.6047	0.944706	0.472353	−	0.881409i	$-0.343405\pi$
$523$	21.6047	0.944706	0.472353	+	0.881409i	$0.343405\pi$
$524$	19.5097	0.852286
$525$	−4.35723	−0.190165
$526$	−26.6316	−1.16119
$527$	−29.3019	−1.27641
$528$	0	0
$529$	−19.9675	−0.868151
$530$	−6.20679	−0.269606
$531$	4.52306	0.196284
$532$	−18.5824	−0.805651
$533$	−22.7892	−0.987111
$534$	−28.7990	−1.24625
$535$	−35.9700	−1.55512
$536$	−0.0842547	−0.00363925
$537$	6.14697	0.265261
$538$	−9.16150	−0.394980
$539$	0	0
$540$	−6.84997	−0.294776
$541$	35.2507	1.51555	0.757773	−	0.652519i	$-0.226288\pi$
$541$	35.2507	1.51555	0.757773	+	0.652519i	$0.226288\pi$
$542$	−19.7598	−0.848754
$543$	−19.2458	−0.825914
$544$	43.6460	1.87131
$545$	−48.6490	−2.08389
$546$	6.84997	0.293152
$547$	5.44775	0.232929	0.116465	−	0.993195i	$-0.462844\pi$
$547$	5.44775	0.232929	0.116465	+	0.993195i	$0.462844\pi$
$548$	−0.524333	−0.0223984
$549$	−12.0845	−0.515755
$550$	0	0
$551$	−67.7369	−2.88569
$552$	0.858058	0.0365214
$553$	−14.6794	−0.624231
$554$	5.76585	0.244968
$555$	−13.8645	−0.588515
$556$	43.2634	1.83478
$557$	8.73429	0.370084	0.185042	−	0.982731i	$-0.440758\pi$
$557$	8.73429	0.370084	0.185042	+	0.982731i	$0.440758\pi$
$558$	11.2213	0.475036
$559$	−6.15468	−0.260315
$560$	−10.5965	−0.447786
$561$	0	0
$562$	−31.8564	−1.34378
$563$	−15.2200	−0.641448	−0.320724	−	0.947173i	$-0.603926\pi$
$563$	−15.2200	−0.641448	−0.320724	+	0.947173i	$0.603926\pi$
$564$	−16.3115	−0.686839
$565$	−22.3538	−0.940430
$566$	53.3426	2.24216
$567$	−1.00000	−0.0419961
$568$	4.92820	0.206783
$569$	−0.0166300	−0.000697167 0	−0.000348583	−	1.00000i	$-0.500111\pi$
$569$	−0.0166300	−0.000697167 0	−0.000348583		1.00000i	$0.500111\pi$
$570$	52.2648	2.18913
$571$	6.08632	0.254705	0.127352	−	0.991858i	$-0.459352\pi$
$571$	6.08632	0.254705	0.127352	+	0.991858i	$0.459352\pi$
$572$	0	0
$573$	25.5978	1.06936
$574$	−14.1038	−0.588682
$575$	−7.58774	−0.316430
$576$	−9.78626	−0.407761
$577$	−36.6359	−1.52517	−0.762585	−	0.646888i	$-0.776070\pi$
$577$	−36.6359	−1.52517	−0.762585	+	0.646888i	$0.776070\pi$
$578$	−24.5157	−1.01972
$579$	11.1962	0.465296
$580$	55.9147	2.32173
$581$	1.62993	0.0676209
$582$	−7.09276	−0.294004
$583$	0	0
$584$	−6.30261	−0.260804
$585$	−10.1769	−0.420762
$586$	−48.1382	−1.98857
$587$	5.52836	0.228180	0.114090	−	0.993470i	$-0.463605\pi$
$587$	5.52836	0.228180	0.114090	+	0.993470i	$0.463605\pi$
$588$	2.23931	0.0923477
$589$	−45.2255	−1.86349
$590$	28.4875	1.17281
$591$	−17.4687	−0.718567
$592$	−15.7008	−0.645298
$593$	−33.1440	−1.36106	−0.680531	−	0.732719i	$-0.738251\pi$
$593$	−33.1440	−1.36106	−0.680531	+	0.732719i	$0.738251\pi$
$594$	0	0
$595$	16.4465	0.674241
$596$	−11.6464	−0.477057
$597$	−6.71963	−0.275016
$598$	11.9286	0.487798
$599$	18.8290	0.769332	0.384666	−	0.923056i	$-0.374317\pi$
$599$	18.8290	0.769332	0.384666	+	0.923056i	$0.374317\pi$
$600$	−2.14697	−0.0876497
$601$	−7.88491	−0.321632	−0.160816	−	0.986984i	$-0.551413\pi$
$601$	−7.88491	−0.321632	−0.160816	+	0.986984i	$0.551413\pi$
$602$	−3.80901	−0.155244
$603$	0.170993	0.00696338
$604$	14.2349	0.579210
$605$	0	0
$606$	−19.2627	−0.782493
$607$	1.34563	0.0546175	0.0273087	−	0.999627i	$-0.491306\pi$
$607$	1.34563	0.0546175	0.0273087	+	0.999627i	$0.491306\pi$
$608$	67.3647	2.73200
$609$	8.16277	0.330772
$610$	−76.1117	−3.08167
$611$	−24.2337	−0.980392
$612$	12.0397	0.486675
$613$	21.8217	0.881372	0.440686	−	0.897661i	$-0.354735\pi$
$613$	21.8217	0.881372	0.440686	+	0.897661i	$0.354735\pi$
$614$	20.7424	0.837094
$615$	20.9538	0.844938
$616$	0	0
$617$	30.1973	1.21570	0.607849	−	0.794053i	$-0.292033\pi$
$617$	30.1973	1.21570	0.607849	+	0.794053i	$0.292033\pi$
$618$	−26.1389	−1.05146
$619$	−39.2011	−1.57562	−0.787812	−	0.615915i	$-0.788786\pi$
$619$	−39.2011	−1.57562	−0.787812	+	0.615915i	$0.788786\pi$
$620$	37.3323	1.49930
$621$	−1.74141	−0.0698805
$622$	−17.0073	−0.681930
$623$	−13.9872	−0.560384
$624$	−11.5247	−0.461359
$625$	−27.8007	−1.11203
$626$	15.2196	0.608298
$627$	0	0
$628$	−22.4247	−0.894844
$629$	24.3686	0.971640
$630$	−6.29827	−0.250929
$631$	5.44272	0.216671	0.108336	−	0.994114i	$-0.465448\pi$
$631$	5.44272	0.216671	0.108336	+	0.994114i	$0.465448\pi$
$632$	−7.23308	−0.287717
$633$	−20.2293	−0.804043
$634$	−64.1572	−2.54801
$635$	13.2410	0.525453
$636$	−2.20679	−0.0875048
$637$	3.32691	0.131817
$638$	0	0
$639$	−10.0017	−0.395661
$640$	−11.9718	−0.473226
$641$	45.6066	1.80135	0.900677	−	0.434489i	$-0.143071\pi$
$641$	45.6066	1.80135	0.900677	+	0.434489i	$0.143071\pi$
$642$	−24.2111	−0.955536
$643$	21.2599	0.838407	0.419204	−	0.907892i	$-0.362309\pi$
$643$	21.2599	0.838407	0.419204	+	0.907892i	$0.362309\pi$
$644$	3.89957	0.153664
$645$	5.65898	0.222822
$646$	−91.8620	−3.61426
$647$	−18.5756	−0.730283	−0.365141	−	0.930952i	$-0.618979\pi$
$647$	−18.5756	−0.730283	−0.365141	+	0.930952i	$0.618979\pi$
$648$	−0.492737	−0.0193565
$649$	0	0
$650$	−29.8469	−1.17069
$651$	5.44999	0.213602
$652$	−19.0417	−0.745731
$653$	−32.1882	−1.25962	−0.629812	−	0.776748i	$-0.716868\pi$
$653$	−32.1882	−1.25962	−0.629812	+	0.776748i	$0.716868\pi$
$654$	−32.7452	−1.28044
$655$	−26.6508	−1.04133
$656$	23.7290	0.926461
$657$	12.7910	0.499025
$658$	−14.9978	−0.584675
$659$	40.6203	1.58234	0.791172	−	0.611594i	$-0.209471\pi$
$659$	40.6203	1.58234	0.791172	+	0.611594i	$0.209471\pi$
$660$	0	0
$661$	7.69278	0.299215	0.149607	−	0.988746i	$-0.452199\pi$
$661$	7.69278	0.299215	0.149607	+	0.988746i	$0.452199\pi$
$662$	41.2019	1.60136
$663$	17.8871	0.694679
$664$	0.803127	0.0311674
$665$	25.3841	0.984352
$666$	−9.33207	−0.361610
$667$	14.2147	0.550397
$668$	6.57813	0.254515
$669$	11.8705	0.458941
$670$	1.07696	0.0416066
$671$	0	0
$672$	−8.11792	−0.313156
$673$	7.24740	0.279367	0.139683	−	0.990196i	$-0.455392\pi$
$673$	7.24740	0.279367	0.139683	+	0.990196i	$0.455392\pi$
$674$	42.2030	1.62560
$675$	4.35723	0.167710
$676$	−4.32564	−0.166371
$677$	6.52296	0.250698	0.125349	−	0.992113i	$-0.459995\pi$
$677$	6.52296	0.250698	0.125349	+	0.992113i	$0.459995\pi$
$678$	−15.0461	−0.577843
$679$	−3.44483	−0.132200
$680$	8.10381	0.310767
$681$	13.9521	0.534645
$682$	0	0
$683$	2.12170	0.0811846	0.0405923	−	0.999176i	$-0.487076\pi$
$683$	2.12170	0.0811846	0.0405923	+	0.999176i	$0.487076\pi$
$684$	18.5824	0.710517
$685$	0.716253	0.0273666
$686$	2.05896	0.0786114
$687$	24.8324	0.947415
$688$	6.40848	0.244321
$689$	−3.27858	−0.124904
$690$	−10.9679	−0.417540
$691$	−5.66834	−0.215634	−0.107817	−	0.994171i	$-0.534386\pi$
$691$	−5.66834	−0.215634	−0.107817	+	0.994171i	$0.534386\pi$
$692$	−46.3183	−1.76076
$693$	0	0
$694$	−69.5845	−2.64139
$695$	−59.0990	−2.24175
$696$	4.02210	0.152457
$697$	−36.8289	−1.39499
$698$	−67.9518	−2.57201
$699$	−11.8265	−0.447319
$700$	−9.75721	−0.368788
$701$	8.22087	0.310498	0.155249	−	0.987875i	$-0.450382\pi$
$701$	8.22087	0.310498	0.155249	+	0.987875i	$0.450382\pi$
$702$	−6.84997	−0.258535
$703$	37.6113	1.41854
$704$	0	0
$705$	22.2820	0.839187
$706$	−19.5460	−0.735624
$707$	−9.35554	−0.351851
$708$	10.1286	0.380654
$709$	−6.38116	−0.239649	−0.119825	−	0.992795i	$-0.538233\pi$
$709$	−6.38116	−0.239649	−0.119825	+	0.992795i	$0.538233\pi$
$710$	−62.9934	−2.36410
$711$	14.6794	0.550520
$712$	−6.89199	−0.258288
$713$	9.49068	0.355429
$714$	11.0700	0.414285
$715$	0	0
$716$	13.7650	0.514422
$717$	−8.86522	−0.331078
$718$	26.8675	1.00268
$719$	22.6376	0.844241	0.422121	−	0.906540i	$-0.361286\pi$
$719$	22.6376	0.844241	0.422121	+	0.906540i	$0.361286\pi$
$720$	10.5965	0.394910
$721$	−12.6952	−0.472794
$722$	−102.662	−3.82070
$723$	11.3922	0.423679
$724$	−43.0973	−1.60170
$725$	−35.5671	−1.32093
$726$	0	0
$727$	24.6482	0.914153	0.457076	−	0.889427i	$-0.348897\pi$
$727$	24.6482	0.914153	0.457076	+	0.889427i	$0.348897\pi$
$728$	1.63929	0.0607562
$729$	1.00000	0.0370370
$730$	80.5613	2.98171
$731$	−9.94637	−0.367880
$732$	−27.0611	−1.00021
$733$	−42.4229	−1.56693	−0.783464	−	0.621438i	$-0.786549\pi$
$733$	−42.4229	−1.56693	−0.783464	+	0.621438i	$0.786549\pi$
$734$	3.98241	0.146994
$735$	−3.05896	−0.112831
$736$	−14.1366	−0.521084
$737$	0	0
$738$	14.1038	0.519168
$739$	17.2443	0.634343	0.317172	−	0.948368i	$-0.397267\pi$
$739$	17.2443	0.634343	0.317172	+	0.948368i	$0.397267\pi$
$740$	−31.0470	−1.14131
$741$	27.6076	1.01419
$742$	−2.02905	−0.0744888
$743$	31.2944	1.14808	0.574040	−	0.818827i	$-0.305375\pi$
$743$	31.2944	1.14808	0.574040	+	0.818827i	$0.305375\pi$
$744$	2.68541	0.0984520
$745$	15.9093	0.582873
$746$	−49.1712	−1.80028
$747$	−1.62993	−0.0596360
$748$	0	0
$749$	−11.7589	−0.429661
$750$	−4.04833	−0.147824
$751$	−31.4340	−1.14704	−0.573521	−	0.819191i	$-0.694423\pi$
$751$	−31.4340	−1.14704	−0.573521	+	0.819191i	$0.694423\pi$
$752$	25.2331	0.920156
$753$	9.71866	0.354168
$754$	55.9147	2.03629
$755$	−19.4452	−0.707685
$756$	−2.23931	−0.0814431
$757$	25.3641	0.921873	0.460937	−	0.887433i	$-0.347514\pi$
$757$	25.3641	0.921873	0.460937	+	0.887433i	$0.347514\pi$
$758$	78.2944	2.84378
$759$	0	0
$760$	12.5077	0.453701
$761$	10.0619	0.364744	0.182372	−	0.983230i	$-0.441622\pi$
$761$	10.0619	0.364744	0.182372	+	0.983230i	$0.441622\pi$
$762$	8.91241	0.322862
$763$	−15.9038	−0.575755
$764$	57.3215	2.07382
$765$	−16.4465	−0.594625
$766$	−64.9968	−2.34843
$767$	15.0478	0.543345
$768$	11.5144	0.415491
$769$	−0.408482	−0.0147303	−0.00736513	−	0.999973i	$-0.502344\pi$
$769$	−0.408482	−0.0147303	−0.00736513	+	0.999973i	$0.502344\pi$
$770$	0	0
$771$	−20.0456	−0.721924
$772$	25.0717	0.902350
$773$	11.9310	0.429129	0.214565	−	0.976710i	$-0.431167\pi$
$773$	11.9310	0.429129	0.214565	+	0.976710i	$0.431167\pi$
$774$	3.80901	0.136912
$775$	−23.7469	−0.853013
$776$	−1.69739	−0.0609329
$777$	−4.53242	−0.162600
$778$	−20.8589	−0.747827
$779$	−56.8429	−2.03661
$780$	−22.7892	−0.815985
$781$	0	0
$782$	19.2774	0.689360
$783$	−8.16277	−0.291714
$784$	−3.46410	−0.123718
$785$	30.6328	1.09333
$786$	−17.9384	−0.639841
$787$	20.3396	0.725030	0.362515	−	0.931978i	$-0.381918\pi$
$787$	20.3396	0.725030	0.362515	+	0.931978i	$0.381918\pi$
$788$	−39.1179	−1.39352
$789$	12.9345	0.460481
$790$	92.4548	3.28939
$791$	−7.30763	−0.259830
$792$	0	0
$793$	−40.2041	−1.42769
$794$	15.4666	0.548891
$795$	3.01453	0.106914
$796$	−15.0474	−0.533339
$797$	6.82763	0.241847	0.120924	−	0.992662i	$-0.461414\pi$
$797$	6.82763	0.241847	0.120924	+	0.992662i	$0.461414\pi$
$798$	17.0858	0.604831
$799$	−39.1634	−1.38550
$800$	35.3717	1.25058
$801$	13.9872	0.494212
$802$	−39.6648	−1.40061
$803$	0	0
$804$	0.382907	0.0135041
$805$	−5.32691	−0.187749
$806$	37.3323	1.31497
$807$	4.44958	0.156632
$808$	−4.60982	−0.162173
$809$	15.3890	0.541047	0.270524	−	0.962713i	$-0.412803\pi$
$809$	15.3890	0.541047	0.270524	+	0.962713i	$0.412803\pi$
$810$	6.29827	0.221299
$811$	9.42694	0.331025	0.165512	−	0.986208i	$-0.447072\pi$
$811$	9.42694	0.331025	0.165512	+	0.986208i	$0.447072\pi$
$812$	18.2790	0.641467
$813$	9.59696	0.336580
$814$	0	0
$815$	26.0115	0.911142
$816$	−18.6248	−0.651997
$817$	−15.3516	−0.537083
$818$	−26.8911	−0.940224
$819$	−3.32691	−0.116252
$820$	46.9221	1.63859
$821$	32.3301	1.12833	0.564165	−	0.825662i	$-0.309198\pi$
$821$	32.3301	1.12833	0.564165	+	0.825662i	$0.309198\pi$
$822$	0.482104	0.0168153
$823$	−18.3223	−0.638676	−0.319338	−	0.947641i	$-0.603461\pi$
$823$	−18.3223	−0.638676	−0.319338	+	0.947641i	$0.603461\pi$
$824$	−6.25539	−0.217917
$825$	0	0
$826$	9.31280	0.324034
$827$	−6.37527	−0.221690	−0.110845	−	0.993838i	$-0.535356\pi$
$827$	−6.37527	−0.221690	−0.110845	+	0.993838i	$0.535356\pi$
$828$	−3.89957	−0.135519
$829$	0.949545	0.0329791	0.0164895	−	0.999864i	$-0.494751\pi$
$829$	0.949545	0.0329791	0.0164895	+	0.999864i	$0.494751\pi$
$830$	−10.2657	−0.356329
$831$	−2.80037	−0.0971438
$832$	−32.5580	−1.12875
$833$	5.37651	0.186285
$834$	−39.7790	−1.37743
$835$	−8.98589	−0.310970
$836$	0	0
$837$	−5.44999	−0.188379
$838$	63.3313	2.18774
$839$	14.3937	0.496925	0.248462	−	0.968642i	$-0.420075\pi$
$839$	14.3937	0.496925	0.248462	+	0.968642i	$0.420075\pi$
$840$	−1.50726	−0.0520055
$841$	37.6308	1.29761
$842$	−33.0786	−1.13996
$843$	15.4721	0.532887
$844$	−45.2998	−1.55928
$845$	5.90893	0.203273
$846$	14.9978	0.515635
$847$	0	0
$848$	3.41378	0.117230
$849$	−25.9076	−0.889145
$850$	−48.2346	−1.65443
$851$	−7.89281	−0.270562
$852$	−22.3969	−0.767306
$853$	−39.9349	−1.36735	−0.683673	−	0.729788i	$-0.739619\pi$
$853$	−39.9349	−1.36735	−0.683673	+	0.729788i	$0.739619\pi$
$854$	−24.8816	−0.851430
$855$	−25.3841	−0.868117
$856$	−5.79405	−0.198036
$857$	−52.2332	−1.78425	−0.892127	−	0.451786i	$-0.850787\pi$
$857$	−52.2332	−1.78425	−0.892127	+	0.451786i	$0.850787\pi$
$858$	0	0
$859$	−37.1209	−1.26655	−0.633274	−	0.773928i	$-0.718289\pi$
$859$	−37.1209	−1.26655	−0.633274	+	0.773928i	$0.718289\pi$
$860$	12.6722	0.432120
$861$	6.84997	0.233446
$862$	−26.9213	−0.916941
$863$	−34.0072	−1.15762	−0.578809	−	0.815463i	$-0.696482\pi$
$863$	−34.0072	−1.15762	−0.578809	+	0.815463i	$0.696482\pi$
$864$	8.11792	0.276177
$865$	63.2719	2.15131
$866$	−26.7164	−0.907861
$867$	11.9068	0.404377
$868$	12.2042	0.414239
$869$	0	0
$870$	−51.4113	−1.74301
$871$	0.568878	0.0192757
$872$	−7.83638	−0.265373
$873$	3.44483	0.116590
$874$	29.7534	1.00642
$875$	−1.96620	−0.0664697
$876$	28.6431	0.967760
$877$	45.3869	1.53261	0.766303	−	0.642479i	$-0.222094\pi$
$877$	45.3869	1.53261	0.766303	+	0.642479i	$0.222094\pi$
$878$	32.8835	1.10977
$879$	23.3799	0.788584
$880$	0	0
$881$	18.0836	0.609251	0.304626	−	0.952472i	$-0.401469\pi$
$881$	18.0836	0.609251	0.304626	+	0.952472i	$0.401469\pi$
$882$	−2.05896	−0.0693288
$883$	14.8564	0.499958	0.249979	−	0.968251i	$-0.419576\pi$
$883$	14.8564	0.499958	0.249979	+	0.968251i	$0.419576\pi$
$884$	40.0549	1.34719
$885$	−13.8359	−0.465087
$886$	43.7931	1.47126
$887$	−29.3108	−0.984162	−0.492081	−	0.870549i	$-0.663764\pi$
$887$	−29.3108	−0.984162	−0.492081	+	0.870549i	$0.663764\pi$
$888$	−2.23329	−0.0749444
$889$	4.32860	0.145176
$890$	88.0950	2.95295
$891$	0	0
$892$	26.5818	0.890025
$893$	−60.4460	−2.02275
$894$	10.7084	0.358144
$895$	−18.8033	−0.628526
$896$	−3.91368	−0.130747
$897$	−5.79352	−0.193440
$898$	13.6513	0.455551
$899$	44.4870	1.48373
$900$	9.75721	0.325240
$901$	−5.29841	−0.176516
$902$	0	0
$903$	1.84997	0.0615631
$904$	−3.60074	−0.119759
$905$	58.8720	1.95697
$906$	−13.0884	−0.434834
$907$	0.784709	0.0260558	0.0130279	−	0.999915i	$-0.495853\pi$
$907$	0.784709	0.0260558	0.0130279	+	0.999915i	$0.495853\pi$
$908$	31.2431	1.03684
$909$	9.35554	0.310304
$910$	−20.9538	−0.694611
$911$	49.3824	1.63611	0.818056	−	0.575139i	$-0.195052\pi$
$911$	49.3824	1.63611	0.818056	+	0.575139i	$0.195052\pi$
$912$	−28.7461	−0.951877
$913$	0	0
$914$	−35.2474	−1.16588
$915$	36.9661	1.22206
$916$	55.6075	1.83732
$917$	−8.71236	−0.287707
$918$	−11.0700	−0.365365
$919$	1.20242	0.0396641	0.0198320	−	0.999803i	$-0.493687\pi$
$919$	1.20242	0.0396641	0.0198320	+	0.999803i	$0.493687\pi$
$920$	−2.62477	−0.0865360
$921$	−10.0742	−0.331956
$922$	−39.3617	−1.29631
$923$	−33.2747	−1.09525
$924$	0	0
$925$	19.7488	0.649337
$926$	−33.1139	−1.08819
$927$	12.6952	0.416965
$928$	−66.2647	−2.17525
$929$	−16.9944	−0.557569	−0.278785	−	0.960354i	$-0.589932\pi$
$929$	−16.9944	−0.557569	−0.278785	+	0.960354i	$0.589932\pi$
$930$	−34.3255	−1.12558
$931$	8.29827	0.271965
$932$	−26.4832	−0.867487
$933$	8.26014	0.270425
$934$	27.7795	0.908973
$935$	0	0
$936$	−1.63929	−0.0535819
$937$	−28.4196	−0.928427	−0.464213	−	0.885723i	$-0.653663\pi$
$937$	−28.4196	−0.928427	−0.464213	+	0.885723i	$0.653663\pi$
$938$	0.352068	0.0114954
$939$	−7.39189	−0.241225
$940$	49.8963	1.62744
$941$	−27.9160	−0.910034	−0.455017	−	0.890483i	$-0.650367\pi$
$941$	−27.9160	−0.910034	−0.455017	+	0.890483i	$0.650367\pi$
$942$	20.6186	0.671792
$943$	11.9286	0.388449
$944$	−15.6683	−0.509961
$945$	3.05896	0.0995080
$946$	0	0
$947$	34.5418	1.12246	0.561229	−	0.827660i	$-0.310329\pi$
$947$	34.5418	1.12246	0.561229	+	0.827660i	$0.310329\pi$
$948$	32.8718	1.06763
$949$	42.5545	1.38138
$950$	−74.4468	−2.41537
$951$	31.1600	1.01043
$952$	2.64920	0.0858612
$953$	−13.8398	−0.448314	−0.224157	−	0.974553i	$-0.571963\pi$
$953$	−13.8398	−0.448314	−0.224157	+	0.974553i	$0.571963\pi$
$954$	2.02905	0.0656930
$955$	−78.3027	−2.53382
$956$	−19.8520	−0.642060
$957$	0	0
$958$	−51.5709	−1.66618
$959$	0.234149	0.00756107
$960$	29.9358	0.966173
$961$	−1.29759	−0.0418577
$962$	−31.0470	−1.00099
$963$	11.7589	0.378925
$964$	25.5106	0.821642
$965$	−34.2486	−1.10250
$966$	−3.58550	−0.115361
$967$	−7.67468	−0.246801	−0.123401	−	0.992357i	$-0.539380\pi$
$967$	−7.67468	−0.246801	−0.123401	+	0.992357i	$0.539380\pi$
$968$	0	0
$969$	44.6157	1.43326
$970$	21.6965	0.696631
$971$	6.99587	0.224508	0.112254	−	0.993680i	$-0.464193\pi$
$971$	6.99587	0.224508	0.112254	+	0.993680i	$0.464193\pi$
$972$	2.23931	0.0718260
$973$	−19.3200	−0.619369
$974$	63.3929	2.03124
$975$	14.4961	0.464247
$976$	41.8621	1.33997
$977$	−11.0312	−0.352918	−0.176459	−	0.984308i	$-0.556464\pi$
$977$	−11.0312	−0.352918	−0.176459	+	0.984308i	$0.556464\pi$
$978$	17.5081	0.559847
$979$	0	0
$980$	−6.84997	−0.218814
$981$	15.9038	0.507768
$982$	−80.5465	−2.57034
$983$	13.4873	0.430178	0.215089	−	0.976594i	$-0.430996\pi$
$983$	13.4873	0.430178	0.215089	+	0.976594i	$0.430996\pi$
$984$	3.37523	0.107599
$985$	53.4361	1.70262
$986$	90.3619	2.87771
$987$	7.28416	0.231857
$988$	61.8221	1.96682
$989$	3.22156	0.102440
$990$	0	0
$991$	0.759034	0.0241115	0.0120558	−	0.999927i	$-0.496162\pi$
$991$	0.759034	0.0241115	0.0120558	+	0.999927i	$0.496162\pi$
$992$	−44.2426	−1.40470
$993$	−20.0110	−0.635031
$994$	−20.5931	−0.653173
$995$	20.5551	0.651640
$996$	−3.64992	−0.115652
$997$	47.7793	1.51319	0.756593	−	0.653886i	$-0.226862\pi$
$997$	47.7793	1.51319	0.756593	+	0.653886i	$0.226862\pi$
$998$	−27.9035	−0.883271
$999$	4.53242	0.143399

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2541.2.a.bp.1.1	yes	4
3.2	odd	2		7623.2.a.cg.1.4		4
11.10	odd	2		2541.2.a.bl.1.4	✓	4
33.32	even	2		7623.2.a.cn.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2541.2.a.bl.1.4	✓	4	11.10	odd	2
2541.2.a.bp.1.1	yes	4	1.1	even	1	trivial
7623.2.a.cg.1.4		4	3.2	odd	2
7623.2.a.cn.1.1		4	33.32	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2541 = 3 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2541.a (trivial)

\(f(q)\)	\(=\)	\(q-2.05896 q^{2} +1.00000 q^{3} +2.23931 q^{4} -3.05896 q^{5} -2.05896 q^{6} -1.00000 q^{7} -0.492737 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.05896 q^{2} +1.00000 q^{3} +2.23931 q^{4} -3.05896 q^{5} -2.05896 q^{6} -1.00000 q^{7} -0.492737 q^{8} +1.00000 q^{9} +6.29827 q^{10} +2.23931 q^{12} +3.32691 q^{13} +2.05896 q^{14} -3.05896 q^{15} -3.46410 q^{16} +5.37651 q^{17} -2.05896 q^{18} +8.29827 q^{19} -6.84997 q^{20} -1.00000 q^{21} -1.74141 q^{23} -0.492737 q^{24} +4.35723 q^{25} -6.84997 q^{26} +1.00000 q^{27} -2.23931 q^{28} -8.16277 q^{29} +6.29827 q^{30} -5.44999 q^{31} +8.11792 q^{32} -11.0700 q^{34} +3.05896 q^{35} +2.23931 q^{36} +4.53242 q^{37} -17.0858 q^{38} +3.32691 q^{39} +1.50726 q^{40} -6.84997 q^{41} +2.05896 q^{42} -1.84997 q^{43} -3.05896 q^{45} +3.58550 q^{46} -7.28416 q^{47} -3.46410 q^{48} +1.00000 q^{49} -8.97136 q^{50} +5.37651 q^{51} +7.44999 q^{52} -0.985474 q^{53} -2.05896 q^{54} +0.492737 q^{56} +8.29827 q^{57} +16.8068 q^{58} +4.52306 q^{59} -6.84997 q^{60} -12.0845 q^{61} +11.2213 q^{62} -1.00000 q^{63} -9.78626 q^{64} -10.1769 q^{65} +0.170993 q^{67} +12.0397 q^{68} -1.74141 q^{69} -6.29827 q^{70} -10.0017 q^{71} -0.492737 q^{72} +12.7910 q^{73} -9.33207 q^{74} +4.35723 q^{75} +18.5824 q^{76} -6.84997 q^{78} +14.6794 q^{79} +10.5965 q^{80} +1.00000 q^{81} +14.1038 q^{82} -1.62993 q^{83} -2.23931 q^{84} -16.4465 q^{85} +3.80901 q^{86} -8.16277 q^{87} +13.9872 q^{89} +6.29827 q^{90} -3.32691 q^{91} -3.89957 q^{92} -5.44999 q^{93} +14.9978 q^{94} -25.3841 q^{95} +8.11792 q^{96} +3.44483 q^{97} -2.05896 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 4 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} + 4 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 + 4 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 4 * q^7 + 4 * q^9	\( 4 q + 2 q^{2} + 4 q^{3} + 4 q^{4} - 2 q^{5} + 2 q^{6} - 4 q^{7} + 4 q^{9} + 10 q^{10} + 4 q^{12} + 10 q^{13} - 2 q^{14} - 2 q^{15} + 6 q^{17} + 2 q^{18} + 18 q^{19} - 4 q^{21} - 2 q^{23} - 8 q^{25} + 4 q^{27} - 4 q^{28} + 6 q^{29} + 10 q^{30} + 12 q^{32} - 2 q^{34} + 2 q^{35} + 4 q^{36} - 4 q^{37} + 10 q^{39} + 8 q^{40} - 2 q^{42} + 20 q^{43} - 2 q^{45} + 16 q^{46} - 6 q^{47} + 4 q^{49} - 24 q^{50} + 6 q^{51} + 8 q^{52} + 2 q^{54} + 18 q^{57} + 24 q^{58} - 6 q^{59} - 10 q^{61} - 4 q^{63} - 16 q^{64} - 10 q^{65} + 4 q^{67} + 28 q^{68} - 2 q^{69} - 10 q^{70} - 6 q^{71} + 34 q^{73} - 36 q^{74} - 8 q^{75} + 36 q^{76} + 24 q^{79} + 12 q^{80} + 4 q^{81} + 28 q^{82} + 6 q^{83} - 4 q^{84} - 8 q^{85} + 38 q^{86} + 6 q^{87} + 18 q^{89} + 10 q^{90} - 10 q^{91} + 24 q^{92} - 6 q^{94} - 18 q^{95} + 12 q^{96} - 10 q^{97} + 2 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 + 4 * q^3 + 4 * q^4 - 2 * q^5 + 2 * q^6 - 4 * q^7 + 4 * q^9 + 10 * q^10 + 4 * q^12 + 10 * q^13 - 2 * q^14 - 2 * q^15 + 6 * q^17 + 2 * q^18 + 18 * q^19 - 4 * q^21 - 2 * q^23 - 8 * q^25 + 4 * q^27 - 4 * q^28 + 6 * q^29 + 10 * q^30 + 12 * q^32 - 2 * q^34 + 2 * q^35 + 4 * q^36 - 4 * q^37 + 10 * q^39 + 8 * q^40 - 2 * q^42 + 20 * q^43 - 2 * q^45 + 16 * q^46 - 6 * q^47 + 4 * q^49 - 24 * q^50 + 6 * q^51 + 8 * q^52 + 2 * q^54 + 18 * q^57 + 24 * q^58 - 6 * q^59 - 10 * q^61 - 4 * q^63 - 16 * q^64 - 10 * q^65 + 4 * q^67 + 28 * q^68 - 2 * q^69 - 10 * q^70 - 6 * q^71 + 34 * q^73 - 36 * q^74 - 8 * q^75 + 36 * q^76 + 24 * q^79 + 12 * q^80 + 4 * q^81 + 28 * q^82 + 6 * q^83 - 4 * q^84 - 8 * q^85 + 38 * q^86 + 6 * q^87 + 18 * q^89 + 10 * q^90 - 10 * q^91 + 24 * q^92 - 6 * q^94 - 18 * q^95 + 12 * q^96 - 10 * q^97 + 2 * q^98

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