LMFDB - Embedded newform 2541.2.a.bl.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:	$1$
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			$0.698857$ 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)

$f(q)$	$=$	$q-2.43091 q^{2} +1.00000 q^{3} +3.90931 q^{4} +1.43091 q^{5} -2.43091 q^{6} +1.00000 q^{7} -4.64136 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.43091 q^{2} +1.00000 q^{3} +3.90931 q^{4} +1.43091 q^{5} -2.43091 q^{6} +1.00000 q^{7} -4.64136 q^{8} +1.00000 q^{9} -3.47841 q^{10} +3.90931 q^{12} -2.30114 q^{13} -2.43091 q^{14} +1.43091 q^{15} +3.46410 q^{16} -1.14407 q^{17} -2.43091 q^{18} -5.47841 q^{19} +5.59387 q^{20} +1.00000 q^{21} +3.00588 q^{23} -4.64136 q^{24} -2.95250 q^{25} +5.59387 q^{26} +1.00000 q^{27} +3.90931 q^{28} +3.16727 q^{29} -3.47841 q^{30} -6.99589 q^{31} +0.861816 q^{32} +2.78112 q^{34} +1.43091 q^{35} +3.90931 q^{36} -8.16884 q^{37} +13.3175 q^{38} -2.30114 q^{39} -6.64136 q^{40} -5.59387 q^{41} -2.43091 q^{42} -10.5939 q^{43} +1.43091 q^{45} -7.30703 q^{46} -12.9384 q^{47} +3.46410 q^{48} +1.00000 q^{49} +7.17726 q^{50} -1.14407 q^{51} -8.99589 q^{52} +9.28273 q^{53} -2.43091 q^{54} -4.64136 q^{56} -5.47841 q^{57} -7.69933 q^{58} -6.89501 q^{59} +5.59387 q^{60} +8.50160 q^{61} +17.0064 q^{62} +1.00000 q^{63} -9.02320 q^{64} -3.29272 q^{65} +7.61405 q^{67} -4.47252 q^{68} +3.00588 q^{69} -3.47841 q^{70} -1.92362 q^{71} -4.64136 q^{72} -4.83704 q^{73} +19.8577 q^{74} -2.95250 q^{75} -21.4168 q^{76} +5.59387 q^{78} -13.5348 q^{79} +4.95681 q^{80} +1.00000 q^{81} +13.5982 q^{82} -9.40661 q^{83} +3.90931 q^{84} -1.63706 q^{85} +25.7527 q^{86} +3.16727 q^{87} -4.35911 q^{89} -3.47841 q^{90} -2.30114 q^{91} +11.7509 q^{92} -6.99589 q^{93} +31.4520 q^{94} -7.83909 q^{95} +0.861816 q^{96} -6.56067 q^{97} -2.43091 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.43091	−1.71891	−0.859456	−	0.511210i	$-0.829197\pi$
$2$	−2.43091	−1.71891	−0.859456	+	0.511210i	$0.829197\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.90931	1.95466
$5$	1.43091	0.639921	0.319961	−	0.947431i	$-0.396330\pi$
$5$	1.43091	0.639921	0.319961	+	0.947431i	$0.396330\pi$
$6$	−2.43091	−0.992414
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−4.64136	−1.64097
$9$	1.00000	0.333333
$10$	−3.47841	−1.09997
$11$	0	0
$11$	0	0
$12$	3.90931	1.12852
$13$	−2.30114	−0.638222	−0.319111	−	0.947717i	$-0.603384\pi$
$13$	−2.30114	−0.638222	−0.319111	+	0.947717i	$0.603384\pi$
$14$	−2.43091	−0.649687
$15$	1.43091	0.369459
$16$	3.46410	0.866025
$17$	−1.14407	−0.277477	−0.138739	−	0.990329i	$-0.544305\pi$
$17$	−1.14407	−0.277477	−0.138739	+	0.990329i	$0.544305\pi$
$18$	−2.43091	−0.572970
$19$	−5.47841	−1.25683	−0.628416	−	0.777877i	$-0.716296\pi$
$19$	−5.47841	−1.25683	−0.628416	+	0.777877i	$0.716296\pi$
$20$	5.59387	1.25083
$21$	1.00000	0.218218
$22$	0	0
$23$	3.00588	0.626770	0.313385	−	0.949626i	$-0.398537\pi$
$23$	3.00588	0.626770	0.313385	+	0.949626i	$0.398537\pi$
$24$	−4.64136	−0.947414
$25$	−2.95250	−0.590501
$26$	5.59387	1.09705
$27$	1.00000	0.192450
$28$	3.90931	0.738791
$29$	3.16727	0.588147	0.294073	−	0.955783i	$-0.404989\pi$
$29$	3.16727	0.588147	0.294073	+	0.955783i	$0.404989\pi$
$30$	−3.47841	−0.635067
$31$	−6.99589	−1.25650	−0.628249	−	0.778012i	$-0.716228\pi$
$31$	−6.99589	−1.25650	−0.628249	+	0.778012i	$0.716228\pi$
$32$	0.861816	0.152349
$33$	0	0
$34$	2.78112	0.476959
$35$	1.43091	0.241868
$36$	3.90931	0.651552
$37$	−8.16884	−1.34295	−0.671475	−	0.741027i	$-0.734339\pi$
$37$	−8.16884	−1.34295	−0.671475	+	0.741027i	$0.734339\pi$
$38$	13.3175	2.16038
$39$	−2.30114	−0.368478
$40$	−6.64136	−1.05009
$41$	−5.59387	−0.873615	−0.436808	−	0.899555i	$-0.643891\pi$
$41$	−5.59387	−0.873615	−0.436808	+	0.899555i	$0.643891\pi$
$42$	−2.43091	−0.375097
$43$	−10.5939	−1.61555	−0.807775	−	0.589491i	$-0.799328\pi$
$43$	−10.5939	−1.61555	−0.807775	+	0.589491i	$0.799328\pi$
$44$	0	0
$45$	1.43091	0.213307
$46$	−7.30703	−1.07736
$47$	−12.9384	−1.88726	−0.943629	−	0.331004i	$-0.892613\pi$
$47$	−12.9384	−1.88726	−0.943629	+	0.331004i	$0.892613\pi$
$48$	3.46410	0.500000
$49$	1.00000	0.142857
$50$	7.17726	1.01502
$51$	−1.14407	−0.160202
$52$	−8.99589	−1.24751
$53$	9.28273	1.27508	0.637540	−	0.770417i	$-0.279952\pi$
$53$	9.28273	1.27508	0.637540	+	0.770417i	$0.279952\pi$
$54$	−2.43091	−0.330805
$55$	0	0
$56$	−4.64136	−0.620228
$57$	−5.47841	−0.725632
$58$	−7.69933	−1.01097
$59$	−6.89501	−0.897654	−0.448827	−	0.893619i	$-0.648158\pi$
$59$	−6.89501	−0.897654	−0.448827	+	0.893619i	$0.648158\pi$
$60$	5.59387	0.722165
$61$	8.50160	1.08852	0.544259	−	0.838917i	$-0.316811\pi$
$61$	8.50160	1.08852	0.544259	+	0.838917i	$0.316811\pi$
$62$	17.0064	2.15981
$63$	1.00000	0.125988
$64$	−9.02320	−1.12790
$65$	−3.29272	−0.408412
$66$	0	0
$67$	7.61405	0.930205	0.465102	−	0.885257i	$-0.346018\pi$
$67$	7.61405	0.930205	0.465102	+	0.885257i	$0.346018\pi$
$68$	−4.47252	−0.542373
$69$	3.00588	0.361866
$70$	−3.47841	−0.415749
$71$	−1.92362	−0.228291	−0.114146	−	0.993464i	$-0.536413\pi$
$71$	−1.92362	−0.228291	−0.114146	+	0.993464i	$0.536413\pi$
$72$	−4.64136	−0.546990
$73$	−4.83704	−0.566133	−0.283066	−	0.959100i	$-0.591352\pi$
$73$	−4.83704	−0.566133	−0.283066	+	0.959100i	$0.591352\pi$
$74$	19.8577	2.30841
$75$	−2.95250	−0.340926
$76$	−21.4168	−2.45668
$77$	0	0
$78$	5.59387	0.633381
$79$	−13.5348	−1.52278	−0.761392	−	0.648292i	$-0.775484\pi$
$79$	−13.5348	−1.52278	−0.761392	+	0.648292i	$0.775484\pi$
$80$	4.95681	0.554188
$81$	1.00000	0.111111
$82$	13.5982	1.50167
$83$	−9.40661	−1.03251	−0.516255	−	0.856435i	$-0.672674\pi$
$83$	−9.40661	−1.03251	−0.516255	+	0.856435i	$0.672674\pi$
$84$	3.90931	0.426541
$85$	−1.63706	−0.177564
$86$	25.7527	2.77699
$87$	3.16727	0.339567
$88$	0	0
$89$	−4.35911	−0.462065	−0.231032	−	0.972946i	$-0.574210\pi$
$89$	−4.35911	−0.462065	−0.231032	+	0.972946i	$0.574210\pi$
$90$	−3.47841	−0.366656
$91$	−2.30114	−0.241225
$92$	11.7509	1.22512
$93$	−6.99589	−0.725440
$94$	31.4520	3.24403
$95$	−7.83909	−0.804274
$96$	0.861816	0.0879587
$97$	−6.56067	−0.666135	−0.333068	−	0.942903i	$-0.608084\pi$
$97$	−6.56067	−0.666135	−0.333068	+	0.942903i	$0.608084\pi$
$98$	−2.43091	−0.245559
$99$	0	0
$100$	−11.5423	−1.15423
$101$	−10.1239	−1.00736	−0.503682	−	0.863889i	$-0.668022\pi$
$101$	−10.1239	−1.00736	−0.503682	+	0.863889i	$0.668022\pi$
$102$	2.78112	0.275372
$103$	−5.00158	−0.492820	−0.246410	−	0.969166i	$-0.579251\pi$
$103$	−5.00158	−0.492820	−0.246410	+	0.969166i	$0.579251\pi$
$104$	10.6804	1.04730
$105$	1.43091	0.139642
$106$	−22.5655	−2.19175
$107$	17.6186	1.70326	0.851629	−	0.524145i	$-0.175615\pi$
$107$	17.6186	1.70326	0.851629	+	0.524145i	$0.175615\pi$
$108$	3.90931	0.376174
$109$	12.5813	1.20507	0.602537	−	0.798091i	$-0.294157\pi$
$109$	12.5813	1.20507	0.602537	+	0.798091i	$0.294157\pi$
$110$	0	0
$111$	−8.16884	−0.775352
$112$	3.46410	0.327327
$113$	3.20457	0.301461	0.150730	−	0.988575i	$-0.451837\pi$
$113$	3.20457	0.301461	0.150730	+	0.988575i	$0.451837\pi$
$114$	13.3175	1.24730
$115$	4.30114	0.401084
$116$	12.3818	1.14962
$117$	−2.30114	−0.212741
$118$	16.7611	1.54299
$119$	−1.14407	−0.104877
$120$	−6.64136	−0.606271
$121$	0	0
$122$	−20.6666	−1.87107
$123$	−5.59387	−0.504382
$124$	−27.3491	−2.45602
$125$	−11.3793	−1.01780
$126$	−2.43091	−0.216562
$127$	−4.77524	−0.423734	−0.211867	−	0.977298i	$-0.567954\pi$
$127$	−4.77524	−0.423734	−0.211867	+	0.977298i	$0.567954\pi$
$128$	20.2109	1.78641
$129$	−10.5939	−0.932738
$130$	8.00431	0.702024
$131$	16.5713	1.44784	0.723922	−	0.689882i	$-0.242337\pi$
$131$	16.5713	1.44784	0.723922	+	0.689882i	$0.242337\pi$
$132$	0	0
$133$	−5.47841	−0.475038
$134$	−18.5091	−1.59894
$135$	1.43091	0.123153
$136$	5.31004	0.455332
$137$	9.64725	0.824220	0.412110	−	0.911134i	$-0.364792\pi$
$137$	9.64725	0.824220	0.412110	+	0.911134i	$0.364792\pi$
$138$	−7.30703	−0.622015
$139$	20.9647	1.77821	0.889103	−	0.457707i	$-0.151329\pi$
$139$	20.9647	1.77821	0.889103	+	0.457707i	$0.151329\pi$
$140$	5.59387	0.472768
$141$	−12.9384	−1.08961
$142$	4.67613	0.392412
$143$	0	0
$144$	3.46410	0.288675
$145$	4.53207	0.376368
$146$	11.7584	0.973132
$147$	1.00000	0.0824786
$148$	−31.9346	−2.62500
$149$	−12.3823	−1.01440	−0.507199	−	0.861829i	$-0.669319\pi$
$149$	−12.3823	−1.01440	−0.507199	+	0.861829i	$0.669319\pi$
$150$	7.17726	0.586021
$151$	19.6952	1.60277	0.801387	−	0.598146i	$-0.204096\pi$
$151$	19.6952	1.60277	0.801387	+	0.598146i	$0.204096\pi$
$152$	25.4273	2.06242
$153$	−1.14407	−0.0924924
$154$	0	0
$155$	−10.0105	−0.804060
$156$	−8.99589	−0.720247
$157$	−1.54001	−0.122906	−0.0614531	−	0.998110i	$-0.519573\pi$
$157$	−1.54001	−0.122906	−0.0614531	+	0.998110i	$0.519573\pi$
$158$	32.9018	2.61753
$159$	9.28273	0.736168
$160$	1.23318	0.0974913
$161$	3.00588	0.236897
$162$	−2.43091	−0.190990
$163$	24.7343	1.93734	0.968670	−	0.248352i	$-0.0798890\pi$
$163$	24.7343	1.93734	0.968670	+	0.248352i	$0.0798890\pi$
$164$	−21.8682	−1.70762
$165$	0	0
$166$	22.8666	1.77479
$167$	12.2020	0.944222	0.472111	−	0.881539i	$-0.343492\pi$
$167$	12.2020	0.944222	0.472111	+	0.881539i	$0.343492\pi$
$168$	−4.64136	−0.358089
$169$	−7.70474	−0.592672
$170$	3.97953	0.305216
$171$	−5.47841	−0.418944
$172$	−41.4147	−3.15784
$173$	12.3486	0.938850	0.469425	−	0.882972i	$-0.344461\pi$
$173$	12.3486	0.938850	0.469425	+	0.882972i	$0.344461\pi$
$174$	−7.69933	−0.583685
$175$	−2.95250	−0.223188
$176$	0	0
$177$	−6.89501	−0.518261
$178$	10.5966	0.794249
$179$	17.7036	1.32323	0.661616	−	0.749843i	$-0.269871\pi$
$179$	17.7036	1.32323	0.661616	+	0.749843i	$0.269871\pi$
$180$	5.59387	0.416942
$181$	−5.64677	−0.419721	−0.209861	−	0.977731i	$-0.567301\pi$
$181$	−5.64677	−0.419721	−0.209861	+	0.977731i	$0.567301\pi$
$182$	5.59387	0.414645
$183$	8.50160	0.628457
$184$	−13.9514	−1.02851
$185$	−11.6889	−0.859382
$186$	17.0064	1.24697
$187$	0	0
$188$	−50.5802	−3.68894
$189$	1.00000	0.0727393
$190$	19.0561	1.38248
$191$	−6.86229	−0.496538	−0.248269	−	0.968691i	$-0.579862\pi$
$191$	−6.86229	−0.496538	−0.248269	+	0.968691i	$0.579862\pi$
$192$	−9.02320	−0.651193
$193$	−0.803848	−0.0578622	−0.0289311	−	0.999581i	$-0.509210\pi$
$193$	−0.803848	−0.0578622	−0.0289311	+	0.999581i	$0.509210\pi$
$194$	15.9484	1.14503
$195$	−3.29272	−0.235797
$196$	3.90931	0.279237
$197$	16.4482	1.17189	0.585944	−	0.810352i	$-0.300724\pi$
$197$	16.4482	1.17189	0.585944	+	0.810352i	$0.300724\pi$
$198$	0	0
$199$	−3.65156	−0.258852	−0.129426	−	0.991589i	$-0.541313\pi$
$199$	−3.65156	−0.258852	−0.129426	+	0.991589i	$0.541313\pi$
$200$	13.7036	0.968994
$201$	7.61405	0.537054
$202$	24.6102	1.73157
$203$	3.16727	0.222298
$204$	−4.47252	−0.313139
$205$	−8.00431	−0.559045
$206$	12.1584	0.847114
$207$	3.00588	0.208923
$208$	−7.97139	−0.552717
$209$	0	0
$210$	−3.47841	−0.240033
$211$	−18.2468	−1.25616	−0.628081	−	0.778148i	$-0.716159\pi$
$211$	−18.2468	−1.25616	−0.628081	+	0.778148i	$0.716159\pi$
$212$	36.2891	2.49234
$213$	−1.92362	−0.131804
$214$	−42.8293	−2.92775
$215$	−15.1588	−1.03382
$216$	−4.64136	−0.315805
$217$	−6.99589	−0.474912
$218$	−30.5841	−2.07141
$219$	−4.83704	−0.326857
$220$	0	0
$221$	2.63266	0.177092
$222$	19.8577	1.33276
$223$	−24.3164	−1.62835	−0.814173	−	0.580622i	$-0.802809\pi$
$223$	−24.3164	−1.62835	−0.814173	+	0.580622i	$0.802809\pi$
$224$	0.861816	0.0575825
$225$	−2.95250	−0.196834
$226$	−7.79002	−0.518184
$227$	−9.08069	−0.602707	−0.301353	−	0.953513i	$-0.597438\pi$
$227$	−9.08069	−0.602707	−0.301353	+	0.953513i	$0.597438\pi$
$228$	−21.4168	−1.41836
$229$	1.23318	0.0814907	0.0407454	−	0.999170i	$-0.487027\pi$
$229$	1.23318	0.0814907	0.0407454	+	0.999170i	$0.487027\pi$
$230$	−10.4557	−0.689427
$231$	0	0
$232$	−14.7004	−0.965131
$233$	9.13996	0.598778	0.299389	−	0.954131i	$-0.403217\pi$
$233$	9.13996	0.598778	0.299389	+	0.954131i	$0.403217\pi$
$234$	5.59387	0.365682
$235$	−18.5137	−1.20770
$236$	−26.9547	−1.75460
$237$	−13.5348	−0.879180
$238$	2.78112	0.180274
$239$	−25.7745	−1.66721	−0.833606	−	0.552359i	$-0.813728\pi$
$239$	−25.7745	−1.66721	−0.833606	+	0.552359i	$0.813728\pi$
$240$	4.95681	0.319961
$241$	−3.70617	−0.238736	−0.119368	−	0.992850i	$-0.538087\pi$
$241$	−3.70617	−0.238736	−0.119368	+	0.992850i	$0.538087\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	33.2354	2.12768
$245$	1.43091	0.0914173
$246$	13.5982	0.866988
$247$	12.6066	0.802138
$248$	32.4705	2.06188
$249$	−9.40661	−0.596120
$250$	27.6620	1.74950
$251$	−17.7354	−1.11945	−0.559724	−	0.828679i	$-0.689093\pi$
$251$	−17.7354	−1.11945	−0.559724	+	0.828679i	$0.689093\pi$
$252$	3.90931	0.246264
$253$	0	0
$254$	11.6082	0.728361
$255$	−1.63706	−0.102516
$256$	−31.0845	−1.94278
$257$	8.43426	0.526114	0.263057	−	0.964780i	$-0.415269\pi$
$257$	8.43426	0.526114	0.263057	+	0.964780i	$0.415269\pi$
$258$	25.7527	1.60329
$259$	−8.16884	−0.507587
$260$	−12.8723	−0.798305
$261$	3.16727	0.196049
$262$	−40.2834	−2.48872
$263$	3.09226	0.190677	0.0953386	−	0.995445i	$-0.469607\pi$
$263$	3.09226	0.190677	0.0953386	+	0.995445i	$0.469607\pi$
$264$	0	0
$265$	13.2827	0.815951
$266$	13.3175	0.816548
$267$	−4.35911	−0.266773
$268$	29.7657	1.81823
$269$	−12.7468	−0.777188	−0.388594	−	0.921409i	$-0.627039\pi$
$269$	−12.7468	−0.777188	−0.388594	+	0.921409i	$0.627039\pi$
$270$	−3.47841	−0.211689
$271$	−22.6995	−1.37890	−0.689449	−	0.724334i	$-0.742147\pi$
$271$	−22.6995	−1.37890	−0.689449	+	0.724334i	$0.742147\pi$
$272$	−3.96317	−0.240302
$273$	−2.30114	−0.139272
$274$	−23.4516	−1.41676
$275$	0	0
$276$	11.7509	0.707324
$277$	−6.43679	−0.386749	−0.193375	−	0.981125i	$-0.561943\pi$
$277$	−6.43679	−0.386749	−0.193375	+	0.981125i	$0.561943\pi$
$278$	−50.9634	−3.05658
$279$	−6.99589	−0.418833
$280$	−6.64136	−0.396897
$281$	1.70455	0.101685	0.0508423	−	0.998707i	$-0.483809\pi$
$281$	1.70455	0.101685	0.0508423	+	0.998707i	$0.483809\pi$
$282$	31.4520	1.87294
$283$	0.00861477	0.000512095 0	0.000256048	−	1.00000i	$-0.499918\pi$
$283$	0.00861477	0.000512095 0	0.000256048		1.00000i	$0.499918\pi$
$284$	−7.52002	−0.446231
$285$	−7.83909	−0.464348
$286$	0	0
$287$	−5.59387	−0.330195
$288$	0.861816	0.0507830
$289$	−15.6911	−0.923006
$290$	−11.0170	−0.646943
$291$	−6.56067	−0.384593
$292$	−18.9095	−1.10660
$293$	−2.99130	−0.174754	−0.0873768	−	0.996175i	$-0.527848\pi$
$293$	−2.99130	−0.174754	−0.0873768	+	0.996175i	$0.527848\pi$
$294$	−2.43091	−0.141773
$295$	−9.86612	−0.574428
$296$	37.9146	2.20374
$297$	0	0
$298$	30.1003	1.74366
$299$	−6.91697	−0.400019
$300$	−11.5423	−0.666393
$301$	−10.5939	−0.610620
$302$	−47.8773	−2.75503
$303$	−10.1239	−0.581602
$304$	−18.9778	−1.08845
$305$	12.1650	0.696566
$306$	2.78112	0.158986
$307$	−16.6115	−0.948069	−0.474035	−	0.880506i	$-0.657203\pi$
$307$	−16.6115	−0.948069	−0.474035	+	0.880506i	$0.657203\pi$
$308$	0	0
$309$	−5.00158	−0.284530
$310$	24.3345	1.38211
$311$	18.0280	1.02227	0.511136	−	0.859500i	$-0.329225\pi$
$311$	18.0280	1.02227	0.511136	+	0.859500i	$0.329225\pi$
$312$	10.6804	0.604661
$313$	32.1350	1.81638	0.908189	−	0.418559i	$-0.137465\pi$
$313$	32.1350	1.81638	0.908189	+	0.418559i	$0.137465\pi$
$314$	3.74362	0.211265
$315$	1.43091	0.0806225
$316$	−52.9118	−2.97652
$317$	−25.9290	−1.45632	−0.728159	−	0.685408i	$-0.759624\pi$
$317$	−25.9290	−1.45632	−0.728159	+	0.685408i	$0.759624\pi$
$318$	−22.5655	−1.26541
$319$	0	0
$320$	−12.9114	−0.721767
$321$	17.6186	0.983377
$322$	−7.30703	−0.407205
$323$	6.26767	0.348742
$324$	3.90931	0.217184
$325$	6.79413	0.376871
$326$	−60.1268	−3.33012
$327$	12.5813	0.695749
$328$	25.9632	1.43358
$329$	−12.9384	−0.713317
$330$	0	0
$331$	−10.6498	−0.585365	−0.292683	−	0.956210i	$-0.594548\pi$
$331$	−10.6498	−0.585365	−0.292683	+	0.956210i	$0.594548\pi$
$332$	−36.7734	−2.01820
$333$	−8.16884	−0.447650
$334$	−29.6620	−1.62303
$335$	10.8950	0.595258
$336$	3.46410	0.188982
$337$	−14.5148	−0.790669	−0.395334	−	0.918537i	$-0.629371\pi$
$337$	−14.5148	−0.790669	−0.395334	+	0.918537i	$0.629371\pi$
$338$	18.7295	1.01875
$339$	3.20457	0.174048
$340$	−6.39977	−0.347076
$341$	0	0
$342$	13.3175	0.720128
$343$	1.00000	0.0539949
$344$	49.1700	2.65107
$345$	4.30114	0.231566
$346$	−30.0184	−1.61380
$347$	−14.7064	−0.789479	−0.394740	−	0.918793i	$-0.629165\pi$
$347$	−14.7064	−0.789479	−0.394740	+	0.918793i	$0.629165\pi$
$348$	12.3818	0.663736
$349$	1.89548	0.101463	0.0507315	−	0.998712i	$-0.483845\pi$
$349$	1.89548	0.101463	0.0507315	+	0.998712i	$0.483845\pi$
$350$	7.17726	0.383641
$351$	−2.30114	−0.122826
$352$	0	0
$353$	23.1014	1.22956	0.614780	−	0.788698i	$-0.289245\pi$
$353$	23.1014	1.22956	0.614780	+	0.788698i	$0.289245\pi$
$354$	16.7611	0.890844
$355$	−2.75252	−0.146088
$356$	−17.0411	−0.903178
$357$	−1.14407	−0.0605505
$358$	−43.0359	−2.27452
$359$	4.19869	0.221598	0.110799	−	0.993843i	$-0.464659\pi$
$359$	4.19869	0.221598	0.110799	+	0.993843i	$0.464659\pi$
$360$	−6.64136	−0.350031
$361$	11.0129	0.579627
$362$	13.7268	0.721464
$363$	0	0
$364$	−8.99589	−0.471513
$365$	−6.92136	−0.362281
$366$	−20.6666	−1.08026
$367$	−2.95073	−0.154027	−0.0770134	−	0.997030i	$-0.524538\pi$
$367$	−2.95073	−0.154027	−0.0770134	+	0.997030i	$0.524538\pi$
$368$	10.4127	0.542799
$369$	−5.59387	−0.291205
$370$	28.4145	1.47720
$371$	9.28273	0.481935
$372$	−27.3491	−1.41799
$373$	21.6666	1.12185	0.560927	−	0.827865i	$-0.310445\pi$
$373$	21.6666	1.12185	0.560927	+	0.827865i	$0.310445\pi$
$374$	0	0
$375$	−11.3793	−0.587624
$376$	60.0518	3.09693
$377$	−7.28833	−0.375368
$378$	−2.43091	−0.125032
$379$	29.3165	1.50589	0.752945	−	0.658084i	$-0.228633\pi$
$379$	29.3165	1.50589	0.752945	+	0.658084i	$0.228633\pi$
$380$	−30.6455	−1.57208
$381$	−4.77524	−0.244643
$382$	16.6816	0.853505
$383$	37.2326	1.90249	0.951247	−	0.308429i	$-0.0998033\pi$
$383$	37.2326	1.90249	0.951247	+	0.308429i	$0.0998033\pi$
$384$	20.2109	1.03138
$385$	0	0
$386$	1.95408	0.0994600
$387$	−10.5939	−0.538516
$388$	−25.6477	−1.30207
$389$	−29.3869	−1.48997	−0.744987	−	0.667079i	$-0.767545\pi$
$389$	−29.3869	−1.48997	−0.744987	+	0.667079i	$0.767545\pi$
$390$	8.00431	0.405314
$391$	−3.43894	−0.173915
$392$	−4.64136	−0.234424
$393$	16.5713	0.835913
$394$	−39.9841	−2.01437
$395$	−19.3670	−0.974462
$396$	0	0
$397$	−18.5537	−0.931183	−0.465591	−	0.885000i	$-0.654158\pi$
$397$	−18.5537	−0.931183	−0.465591	+	0.885000i	$0.654158\pi$
$398$	8.87659	0.444943
$399$	−5.47841	−0.274263
$400$	−10.2278	−0.511388
$401$	3.09911	0.154762	0.0773810	−	0.997002i	$-0.475344\pi$
$401$	3.09911	0.154762	0.0773810	+	0.997002i	$0.475344\pi$
$402$	−18.5091	−0.923148
$403$	16.0985	0.801925
$404$	−39.5774	−1.96905
$405$	1.43091	0.0711024
$406$	−7.69933	−0.382111
$407$	0	0
$408$	5.31004	0.262886
$409$	−13.5912	−0.672041	−0.336020	−	0.941855i	$-0.609081\pi$
$409$	−13.5912	−0.672041	−0.336020	+	0.941855i	$0.609081\pi$
$410$	19.4577	0.960949
$411$	9.64725	0.475864
$412$	−19.5527	−0.963294
$413$	−6.89501	−0.339281
$414$	−7.30703	−0.359121
$415$	−13.4600	−0.660725
$416$	−1.98316	−0.0972325
$417$	20.9647	1.02665
$418$	0	0
$419$	−1.38136	−0.0674838	−0.0337419	−	0.999431i	$-0.510742\pi$
$419$	−1.38136	−0.0674838	−0.0337419	+	0.999431i	$0.510742\pi$
$420$	5.59387	0.272953
$421$	28.1477	1.37184	0.685919	−	0.727678i	$-0.259401\pi$
$421$	28.1477	1.37184	0.685919	+	0.727678i	$0.259401\pi$
$422$	44.3563	2.15923
$423$	−12.9384	−0.629086
$424$	−43.0845	−2.09237
$425$	3.37786	0.163851
$426$	4.67613	0.226559
$427$	8.50160	0.411421
$428$	68.8768	3.32928
$429$	0	0
$430$	36.8498	1.77705
$431$	−10.7754	−0.519034	−0.259517	−	0.965738i	$-0.583563\pi$
$431$	−10.7754	−0.519034	−0.259517	+	0.965738i	$0.583563\pi$
$432$	3.46410	0.166667
$433$	−14.7516	−0.708917	−0.354459	−	0.935072i	$-0.615335\pi$
$433$	−14.7516	−0.708917	−0.354459	+	0.935072i	$0.615335\pi$
$434$	17.0064	0.816331
$435$	4.53207	0.217296
$436$	49.1844	2.35550
$437$	−16.4675	−0.787745
$438$	11.7584	0.561838
$439$	−4.56545	−0.217897	−0.108949	−	0.994047i	$-0.534748\pi$
$439$	−4.56545	−0.217897	−0.108949	+	0.994047i	$0.534748\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	−6.39977	−0.304406
$443$	19.1300	0.908896	0.454448	−	0.890773i	$-0.349837\pi$
$443$	19.1300	0.908896	0.454448	+	0.890773i	$0.349837\pi$
$444$	−31.9346	−1.51555
$445$	−6.23749	−0.295685
$446$	59.1109	2.79898
$447$	−12.3823	−0.585663
$448$	−9.02320	−0.426306
$449$	−27.4346	−1.29472	−0.647359	−	0.762185i	$-0.724127\pi$
$449$	−27.4346	−1.29472	−0.647359	+	0.762185i	$0.724127\pi$
$450$	7.17726	0.338339
$451$	0	0
$452$	12.5277	0.589252
$453$	19.6952	0.925362
$454$	22.0743	1.03600
$455$	−3.29272	−0.154365
$456$	25.4273	1.19074
$457$	5.58244	0.261135	0.130568	−	0.991439i	$-0.458320\pi$
$457$	5.58244	0.261135	0.130568	+	0.991439i	$0.458320\pi$
$458$	−2.99774	−0.140075
$459$	−1.14407	−0.0534005
$460$	16.8145	0.783981
$461$	31.2918	1.45740	0.728701	−	0.684832i	$-0.240124\pi$
$461$	31.2918	1.45740	0.728701	+	0.684832i	$0.240124\pi$
$462$	0	0
$463$	20.5780	0.956340	0.478170	−	0.878267i	$-0.341300\pi$
$463$	20.5780	0.956340	0.478170	+	0.878267i	$0.341300\pi$
$464$	10.9717	0.509350
$465$	−10.0105	−0.464224
$466$	−22.2184	−1.02925
$467$	−40.8220	−1.88902	−0.944508	−	0.328489i	$-0.893461\pi$
$467$	−40.8220	−1.88902	−0.944508	+	0.328489i	$0.893461\pi$
$468$	−8.99589	−0.415835
$469$	7.61405	0.351584
$470$	45.0050	2.07592
$471$	−1.54001	−0.0709599
$472$	32.0022	1.47302
$473$	0	0
$474$	32.9018	1.51123
$475$	16.1750	0.742160
$476$	−4.47252	−0.204998
$477$	9.28273	0.425027
$478$	62.6554	2.86579
$479$	−26.5969	−1.21525	−0.607623	−	0.794226i	$-0.707877\pi$
$479$	−26.5969	−1.21525	−0.607623	+	0.794226i	$0.707877\pi$
$480$	1.23318	0.0562867
$481$	18.7977	0.857100
$482$	9.00937	0.410366
$483$	3.00588	0.136772
$484$	0	0
$485$	−9.38772	−0.426274
$486$	−2.43091	−0.110268
$487$	23.6150	1.07010	0.535049	−	0.844821i	$-0.320293\pi$
$487$	23.6150	1.07010	0.535049	+	0.844821i	$0.320293\pi$
$488$	−39.4590	−1.78623
$489$	24.7343	1.11852
$490$	−3.47841	−0.157138
$491$	−40.8045	−1.84148	−0.920741	−	0.390174i	$-0.872415\pi$
$491$	−40.8045	−1.84148	−0.920741	+	0.390174i	$0.872415\pi$
$492$	−21.8682	−0.985893
$493$	−3.62357	−0.163197
$494$	−30.6455	−1.37880
$495$	0	0
$496$	−24.2345	−1.08816
$497$	−1.92362	−0.0862860
$498$	22.8666	1.02468
$499$	9.57197	0.428500	0.214250	−	0.976779i	$-0.431269\pi$
$499$	9.57197	0.428500	0.214250	+	0.976779i	$0.431269\pi$
$500$	−44.4852	−1.98944
$501$	12.2020	0.545147
$502$	43.1131	1.92423
$503$	−20.1131	−0.896797	−0.448399	−	0.893834i	$-0.648005\pi$
$503$	−20.1131	−0.896797	−0.448399	+	0.893834i	$0.648005\pi$
$504$	−4.64136	−0.206743
$505$	−14.4863	−0.644634
$506$	0	0
$507$	−7.70474	−0.342180
$508$	−18.6679	−0.828255
$509$	6.27889	0.278307	0.139154	−	0.990271i	$-0.455562\pi$
$509$	6.27889	0.278307	0.139154	+	0.990271i	$0.455562\pi$
$510$	3.97953	0.176217
$511$	−4.83704	−0.213978
$512$	35.1417	1.55306
$513$	−5.47841	−0.241877
$514$	−20.5029	−0.904344
$515$	−7.15680	−0.315366
$516$	−41.4147	−1.82318
$517$	0	0
$518$	19.8577	0.872497
$519$	12.3486	0.542045
$520$	15.2827	0.670192
$521$	−23.5173	−1.03031	−0.515156	−	0.857097i	$-0.672266\pi$
$521$	−23.5173	−1.03031	−0.515156	+	0.857097i	$0.672266\pi$
$522$	−7.69933	−0.336991
$523$	7.38211	0.322797	0.161399	−	0.986889i	$-0.448400\pi$
$523$	7.38211	0.322797	0.161399	+	0.986889i	$0.448400\pi$
$524$	64.7825	2.83004
$525$	−2.95250	−0.128858
$526$	−7.51701	−0.327757
$527$	8.00377	0.348650
$528$	0	0
$529$	−13.9647	−0.607159
$530$	−32.2891	−1.40255
$531$	−6.89501	−0.299218
$532$	−21.4168	−0.928536
$533$	12.8723	0.557561
$534$	10.5966	0.458560
$535$	25.2107	1.08995
$536$	−35.3396	−1.52644
$537$	17.7036	0.763968
$538$	30.9864	1.33592
$539$	0	0
$540$	5.59387	0.240722
$541$	−10.5161	−0.452123	−0.226061	−	0.974113i	$-0.572585\pi$
$541$	−10.5161	−0.452123	−0.226061	+	0.974113i	$0.572585\pi$
$542$	55.1805	2.37020
$543$	−5.64677	−0.242326
$544$	−0.985976	−0.0422734
$545$	18.0027	0.771152
$546$	5.59387	0.239395
$547$	−9.42803	−0.403114	−0.201557	−	0.979477i	$-0.564600\pi$
$547$	−9.42803	−0.403114	−0.201557	+	0.979477i	$0.564600\pi$
$548$	37.7141	1.61107
$549$	8.50160	0.362840
$550$	0	0
$551$	−17.3516	−0.739202
$552$	−13.9514	−0.593811
$553$	−13.5348	−0.575558
$554$	15.6472	0.664788
$555$	−11.6889	−0.496165
$556$	81.9578	3.47578
$557$	−2.83580	−0.120157	−0.0600784	−	0.998194i	$-0.519135\pi$
$557$	−2.83580	−0.120157	−0.0600784	+	0.998194i	$0.519135\pi$
$558$	17.0064	0.719937
$559$	24.3780	1.03108
$560$	4.95681	0.209463
$561$	0	0
$562$	−4.14359	−0.174787
$563$	13.8127	0.582138	0.291069	−	0.956702i	$-0.405989\pi$
$563$	13.8127	0.582138	0.291069	+	0.956702i	$0.405989\pi$
$564$	−50.5802	−2.12981
$565$	4.58545	0.192911
$566$	−0.0209417	−0.000880246 0
$567$	1.00000	0.0419961
$568$	8.92820	0.374619
$569$	20.9491	0.878230	0.439115	−	0.898431i	$-0.355292\pi$
$569$	20.9491	0.878230	0.439115	+	0.898431i	$0.355292\pi$
$570$	19.0561	0.798173
$571$	−30.2109	−1.26429	−0.632144	−	0.774851i	$-0.717825\pi$
$571$	−30.2109	−1.26429	−0.632144	+	0.774851i	$0.717825\pi$
$572$	0	0
$573$	−6.86229	−0.286676
$574$	13.5982	0.567577
$575$	−8.87488	−0.370108
$576$	−9.02320	−0.375967
$577$	44.1976	1.83997	0.919985	−	0.391955i	$-0.128201\pi$
$577$	44.1976	1.83997	0.919985	+	0.391955i	$0.128201\pi$
$578$	38.1436	1.58657
$579$	−0.803848	−0.0334068
$580$	17.7173	0.735669
$581$	−9.40661	−0.390252
$582$	15.9484	0.661082
$583$	0	0
$584$	22.4505	0.929007
$585$	−3.29272	−0.136137
$586$	7.27158	0.300386
$587$	−7.43693	−0.306955	−0.153477	−	0.988152i	$-0.549047\pi$
$587$	−7.43693	−0.306955	−0.153477	+	0.988152i	$0.549047\pi$
$588$	3.90931	0.161217
$589$	38.3263	1.57921
$590$	23.9836	0.987391
$591$	16.4482	0.676589
$592$	−28.2977	−1.16303
$593$	30.7149	1.26131	0.630656	−	0.776063i	$-0.282786\pi$
$593$	30.7149	1.26131	0.630656	+	0.776063i	$0.282786\pi$
$594$	0	0
$595$	−1.63706	−0.0671128
$596$	−48.4063	−1.98280
$597$	−3.65156	−0.149448
$598$	16.8145	0.687597
$599$	11.3859	0.465217	0.232609	−	0.972570i	$-0.425274\pi$
$599$	11.3859	0.465217	0.232609	+	0.972570i	$0.425274\pi$
$600$	13.7036	0.559449
$601$	−4.93519	−0.201311	−0.100655	−	0.994921i	$-0.532094\pi$
$601$	−4.93519	−0.201311	−0.100655	+	0.994921i	$0.532094\pi$
$602$	25.7527	1.04960
$603$	7.61405	0.310068
$604$	76.9948	3.13287
$605$	0	0
$606$	24.6102	0.999722
$607$	2.24652	0.0911836	0.0455918	−	0.998960i	$-0.485483\pi$
$607$	2.24652	0.0911836	0.0455918	+	0.998960i	$0.485483\pi$
$608$	−4.72138	−0.191477
$609$	3.16727	0.128344
$610$	−29.5720	−1.19734
$611$	29.7731	1.20449
$612$	−4.47252	−0.180791
$613$	−26.3261	−1.06330	−0.531651	−	0.846964i	$-0.678428\pi$
$613$	−26.3261	−1.06330	−0.531651	+	0.846964i	$0.678428\pi$
$614$	40.3811	1.62965
$615$	−8.00431	−0.322765
$616$	0	0
$617$	6.08323	0.244901	0.122451	−	0.992475i	$-0.460925\pi$
$617$	6.08323	0.244901	0.122451	+	0.992475i	$0.460925\pi$
$618$	12.1584	0.489081
$619$	−17.6732	−0.710345	−0.355172	−	0.934801i	$-0.615578\pi$
$619$	−17.6732	−0.710345	−0.355172	+	0.934801i	$0.615578\pi$
$620$	−39.1341	−1.57166
$621$	3.00588	0.120622
$622$	−43.8244	−1.75720
$623$	−4.35911	−0.174644
$624$	−7.97139	−0.319111
$625$	−1.52021	−0.0608085
$626$	−78.1173	−3.12219
$627$	0	0
$628$	−6.02038	−0.240239
$629$	9.34571	0.372638
$630$	−3.47841	−0.138583
$631$	−15.2270	−0.606178	−0.303089	−	0.952962i	$-0.598018\pi$
$631$	−15.2270	−0.606178	−0.303089	+	0.952962i	$0.598018\pi$
$632$	62.8199	2.49884
$633$	−18.2468	−0.725245
$634$	63.0310	2.50328
$635$	−6.83293	−0.271157
$636$	36.2891	1.43896
$637$	−2.30114	−0.0911746
$638$	0	0
$639$	−1.92362	−0.0760971
$640$	28.9200	1.14316
$641$	40.3827	1.59502	0.797510	−	0.603305i	$-0.206150\pi$
$641$	40.3827	1.59502	0.797510	+	0.603305i	$0.206150\pi$
$642$	−42.8293	−1.69034
$643$	−0.813217	−0.0320701	−0.0160351	−	0.999871i	$-0.505104\pi$
$643$	−0.813217	−0.0320701	−0.0160351	+	0.999871i	$0.505104\pi$
$644$	11.7509	0.463052
$645$	−15.1588	−0.596879
$646$	−15.2361	−0.599457
$647$	30.9476	1.21667	0.608337	−	0.793679i	$-0.291837\pi$
$647$	30.9476	1.21667	0.608337	+	0.793679i	$0.291837\pi$
$648$	−4.64136	−0.182330
$649$	0	0
$650$	−16.5159	−0.647807
$651$	−6.99589	−0.274190
$652$	96.6941	3.78683
$653$	7.68593	0.300774	0.150387	−	0.988627i	$-0.451948\pi$
$653$	7.68593	0.300774	0.150387	+	0.988627i	$0.451948\pi$
$654$	−30.5841	−1.19593
$655$	23.7121	0.926507
$656$	−19.3777	−0.756573
$657$	−4.83704	−0.188711
$658$	31.4520	1.22613
$659$	−8.17999	−0.318647	−0.159324	−	0.987226i	$-0.550931\pi$
$659$	−8.17999	−0.318647	−0.159324	+	0.987226i	$0.550931\pi$
$660$	0	0
$661$	30.5381	1.18780	0.593898	−	0.804540i	$-0.297588\pi$
$661$	30.5381	1.18780	0.593898	+	0.804540i	$0.297588\pi$
$662$	25.8886	1.00619
$663$	2.63266	0.102244
$664$	43.6595	1.69432
$665$	−7.83909	−0.303987
$666$	19.8577	0.769470
$667$	9.52043	0.368633
$668$	47.7016	1.84563
$669$	−24.3164	−0.940126
$670$	−26.4848	−1.02320
$671$	0	0
$672$	0.861816	0.0332453
$673$	−34.4546	−1.32813	−0.664063	−	0.747676i	$-0.731169\pi$
$673$	−34.4546	−1.32813	−0.664063	+	0.747676i	$0.731169\pi$
$674$	35.2840	1.35909
$675$	−2.95250	−0.113642
$676$	−30.1202	−1.15847
$677$	40.6807	1.56349	0.781744	−	0.623600i	$-0.214331\pi$
$677$	40.6807	1.56349	0.781744	+	0.623600i	$0.214331\pi$
$678$	−7.79002	−0.299174
$679$	−6.56067	−0.251776
$680$	7.59817	0.291377
$681$	−9.08069	−0.347973
$682$	0	0
$683$	−38.4349	−1.47067	−0.735336	−	0.677703i	$-0.762976\pi$
$683$	−38.4349	−1.47067	−0.735336	+	0.677703i	$0.762976\pi$
$684$	−21.4168	−0.818892
$685$	13.8043	0.527436
$686$	−2.43091	−0.0928125
$687$	1.23318	0.0470487
$688$	−36.6982	−1.39911
$689$	−21.3609	−0.813785
$690$	−10.4557	−0.398041
$691$	−13.8850	−0.528211	−0.264105	−	0.964494i	$-0.585077\pi$
$691$	−13.8850	−0.528211	−0.264105	+	0.964494i	$0.585077\pi$
$692$	48.2747	1.83513
$693$	0	0
$694$	35.7498	1.35704
$695$	29.9986	1.13791
$696$	−14.7004	−0.557218
$697$	6.39977	0.242408
$698$	−4.60775	−0.174406
$699$	9.13996	0.345705
$700$	−11.5423	−0.436256
$701$	−44.2982	−1.67312	−0.836560	−	0.547876i	$-0.815437\pi$
$701$	−44.2982	−1.67312	−0.836560	+	0.547876i	$0.815437\pi$
$702$	5.59387	0.211127
$703$	44.7522	1.68786
$704$	0	0
$705$	−18.5137	−0.697264
$706$	−56.1573	−2.11351
$707$	−10.1239	−0.380748
$708$	−26.9547	−1.01302
$709$	40.8278	1.53332	0.766660	−	0.642053i	$-0.221917\pi$
$709$	40.8278	1.53332	0.766660	+	0.642053i	$0.221917\pi$
$710$	6.69112	0.251113
$711$	−13.5348	−0.507595
$712$	20.2322	0.758234
$713$	−21.0288	−0.787536
$714$	2.78112	0.104081
$715$	0	0
$716$	69.2091	2.58646
$717$	−25.7745	−0.962565
$718$	−10.2066	−0.380908
$719$	−30.4882	−1.13702	−0.568510	−	0.822676i	$-0.692480\pi$
$719$	−30.4882	−1.13702	−0.568510	+	0.822676i	$0.692480\pi$
$720$	4.95681	0.184729
$721$	−5.00158	−0.186268
$722$	−26.7714	−0.996328
$723$	−3.70617	−0.137834
$724$	−22.0750	−0.820411
$725$	−9.35136	−0.347301
$726$	0	0
$727$	26.4661	0.981572	0.490786	−	0.871280i	$-0.336710\pi$
$727$	26.4661	0.981572	0.490786	+	0.871280i	$0.336710\pi$
$728$	10.6804	0.395843
$729$	1.00000	0.0370370
$730$	16.8252	0.622728
$731$	12.1201	0.448278
$732$	33.2354	1.22842
$733$	−1.68895	−0.0623826	−0.0311913	−	0.999513i	$-0.509930\pi$
$733$	−1.68895	−0.0623826	−0.0311913	+	0.999513i	$0.509930\pi$
$734$	7.17295	0.264759
$735$	1.43091	0.0527798
$736$	2.59052	0.0954878
$737$	0	0
$738$	13.5982	0.500556
$739$	−43.5644	−1.60254	−0.801270	−	0.598302i	$-0.795842\pi$
$739$	−43.5644	−1.60254	−0.801270	+	0.598302i	$0.795842\pi$
$740$	−45.6954	−1.67980
$741$	12.6066	0.463115
$742$	−22.5655	−0.828404
$743$	9.89726	0.363095	0.181548	−	0.983382i	$-0.441889\pi$
$743$	9.89726	0.363095	0.181548	+	0.983382i	$0.441889\pi$
$744$	32.4705	1.19042
$745$	−17.7179	−0.649135
$746$	−52.6695	−1.92837
$747$	−9.40661	−0.344170
$748$	0	0
$749$	17.6186	0.643771
$750$	27.6620	1.01007
$751$	−26.8450	−0.979589	−0.489795	−	0.871838i	$-0.662928\pi$
$751$	−26.8450	−0.979589	−0.489795	+	0.871838i	$0.662928\pi$
$752$	−44.8199	−1.63441
$753$	−17.7354	−0.646314
$754$	17.7173	0.645225
$755$	28.1820	1.02565
$756$	3.90931	0.142180
$757$	21.5277	0.782437	0.391218	−	0.920298i	$-0.372054\pi$
$757$	21.5277	0.782437	0.391218	+	0.920298i	$0.372054\pi$
$758$	−71.2658	−2.58849
$759$	0	0
$760$	36.3841	1.31979
$761$	29.3264	1.06308	0.531540	−	0.847033i	$-0.321613\pi$
$761$	29.3264	1.06308	0.531540	+	0.847033i	$0.321613\pi$
$762$	11.6082	0.420520
$763$	12.5813	0.455475
$764$	−26.8268	−0.970561
$765$	−1.63706	−0.0591879
$766$	−90.5089	−3.27022
$767$	15.8664	0.572903
$768$	−31.0845	−1.12167
$769$	30.6982	1.10701	0.553503	−	0.832847i	$-0.313291\pi$
$769$	30.6982	1.10701	0.553503	+	0.832847i	$0.313291\pi$
$770$	0	0
$771$	8.43426	0.303752
$772$	−3.14249	−0.113101
$773$	−23.7252	−0.853336	−0.426668	−	0.904408i	$-0.640313\pi$
$773$	−23.7252	−0.853336	−0.426668	+	0.904408i	$0.640313\pi$
$774$	25.7527	0.925662
$775$	20.6554	0.741963
$776$	30.4505	1.09311
$777$	−8.16884	−0.293056
$778$	71.4368	2.56113
$779$	30.6455	1.09799
$780$	−12.8723	−0.460902
$781$	0	0
$782$	8.35974	0.298944
$783$	3.16727	0.113189
$784$	3.46410	0.123718
$785$	−2.20361	−0.0786503
$786$	−40.2834	−1.43686
$787$	−1.87454	−0.0668202	−0.0334101	−	0.999442i	$-0.510637\pi$
$787$	−1.87454	−0.0668202	−0.0334101	+	0.999442i	$0.510637\pi$
$788$	64.3012	2.29064
$789$	3.09226	0.110088
$790$	47.0795	1.67501
$791$	3.20457	0.113941
$792$	0	0
$793$	−19.5634	−0.694717
$794$	45.1023	1.60062
$795$	13.2827	0.471090
$796$	−14.2751	−0.505966
$797$	−9.58066	−0.339365	−0.169682	−	0.985499i	$-0.554274\pi$
$797$	−9.58066	−0.339365	−0.169682	+	0.985499i	$0.554274\pi$
$798$	13.3175	0.471434
$799$	14.8024	0.523672
$800$	−2.54451	−0.0899621
$801$	−4.35911	−0.154022
$802$	−7.53364	−0.266022
$803$	0	0
$804$	29.7657	1.04976
$805$	4.30114	0.151595
$806$	−39.1341	−1.37844
$807$	−12.7468	−0.448710
$808$	46.9886	1.65305
$809$	38.1237	1.34036	0.670179	−	0.742199i	$-0.266217\pi$
$809$	38.1237	1.34036	0.670179	+	0.742199i	$0.266217\pi$
$810$	−3.47841	−0.122219
$811$	−39.4724	−1.38606	−0.693032	−	0.720907i	$-0.743726\pi$
$811$	−39.4724	−1.38606	−0.693032	+	0.720907i	$0.743726\pi$
$812$	12.3818	0.434517
$813$	−22.6995	−0.796107
$814$	0	0
$815$	35.3925	1.23975
$816$	−3.96317	−0.138739
$817$	58.0375	2.03047
$818$	33.0389	1.15518
$819$	−2.30114	−0.0804084
$820$	−31.2913	−1.09274
$821$	−28.2469	−0.985822	−0.492911	−	0.870080i	$-0.664067\pi$
$821$	−28.2469	−0.985822	−0.492911	+	0.870080i	$0.664067\pi$
$822$	−23.4516	−0.817967
$823$	37.4954	1.30701	0.653503	−	0.756924i	$-0.273299\pi$
$823$	37.4954	1.30701	0.653503	+	0.756924i	$0.273299\pi$
$824$	23.2141	0.808703
$825$	0	0
$826$	16.7611	0.583194
$827$	−19.9210	−0.692722	−0.346361	−	0.938101i	$-0.612583\pi$
$827$	−19.9210	−0.692722	−0.346361	+	0.938101i	$0.612583\pi$
$828$	11.7509	0.408373
$829$	49.7189	1.72681	0.863404	−	0.504513i	$-0.168328\pi$
$829$	49.7189	1.72681	0.863404	+	0.504513i	$0.168328\pi$
$830$	32.7200	1.13573
$831$	−6.43679	−0.223290
$832$	20.7637	0.719851
$833$	−1.14407	−0.0396396
$834$	−50.9634	−1.76472
$835$	17.4600	0.604228
$836$	0	0
$837$	−6.99589	−0.241813
$838$	3.35796	0.115999
$839$	2.57431	0.0888749	0.0444375	−	0.999012i	$-0.485850\pi$
$839$	2.57431	0.0888749	0.0444375	+	0.999012i	$0.485850\pi$
$840$	−6.64136	−0.229149
$841$	−18.9684	−0.654084
$842$	−68.4246	−2.35807
$843$	1.70455	0.0587077
$844$	−71.3325	−2.45536
$845$	−11.0248	−0.379264
$846$	31.4520	1.08134
$847$	0	0
$848$	32.1563	1.10425
$849$	0.00861477	0.000295658 0
$850$	−8.21128	−0.281645
$851$	−24.5546	−0.841721
$852$	−7.52002	−0.257632
$853$	−40.3968	−1.38316	−0.691580	−	0.722300i	$-0.743085\pi$
$853$	−40.3968	−1.38316	−0.691580	+	0.722300i	$0.743085\pi$
$854$	−20.6666	−0.707197
$855$	−7.83909	−0.268091
$856$	−81.7745	−2.79500
$857$	3.24467	0.110836	0.0554179	−	0.998463i	$-0.482351\pi$
$857$	3.24467	0.110836	0.0554179	+	0.998463i	$0.482351\pi$
$858$	0	0
$859$	6.75730	0.230556	0.115278	−	0.993333i	$-0.463224\pi$
$859$	6.75730	0.230556	0.115278	+	0.993333i	$0.463224\pi$
$860$	−59.2607	−2.02077
$861$	−5.59387	−0.190638
$862$	26.1941	0.892174
$863$	13.7259	0.467234	0.233617	−	0.972329i	$-0.424944\pi$
$863$	13.7259	0.467234	0.233617	+	0.972329i	$0.424944\pi$
$864$	0.861816	0.0293196
$865$	17.6698	0.600790
$866$	35.8598	1.21857
$867$	−15.6911	−0.532898
$868$	−27.3491	−0.928289
$869$	0	0
$870$	−11.0170	−0.373512
$871$	−17.5210	−0.593677
$872$	−58.3946	−1.97749
$873$	−6.56067	−0.222045
$874$	40.0309	1.35406
$875$	−11.3793	−0.384691
$876$	−18.9095	−0.638893
$877$	9.63610	0.325388	0.162694	−	0.986677i	$-0.447982\pi$
$877$	9.63610	0.325388	0.162694	+	0.986677i	$0.447982\pi$
$878$	11.0982	0.374546
$879$	−2.99130	−0.100894
$880$	0	0
$881$	24.2777	0.817937	0.408968	−	0.912549i	$-0.365889\pi$
$881$	24.2777	0.817937	0.408968	+	0.912549i	$0.365889\pi$
$882$	−2.43091	−0.0818529
$883$	−12.8564	−0.432653	−0.216326	−	0.976321i	$-0.569407\pi$
$883$	−12.8564	−0.432653	−0.216326	+	0.976321i	$0.569407\pi$
$884$	10.2919	0.346154
$885$	−9.86612	−0.331646
$886$	−46.5034	−1.56231
$887$	47.1594	1.58346	0.791729	−	0.610873i	$-0.209181\pi$
$887$	47.1594	1.58346	0.791729	+	0.610873i	$0.209181\pi$
$888$	37.9146	1.27233
$889$	−4.77524	−0.160156
$890$	15.1628	0.508257
$891$	0	0
$892$	−95.0604	−3.18286
$893$	70.8818	2.37197
$894$	30.1003	1.00670
$895$	25.3323	0.846765
$896$	20.2109	0.675200
$897$	−6.91697	−0.230951
$898$	66.6910	2.22551
$899$	−22.1578	−0.739005
$900$	−11.5423	−0.384742
$901$	−10.6201	−0.353806
$902$	0	0
$903$	−10.5939	−0.352542
$904$	−14.8736	−0.494688
$905$	−8.08001	−0.268589
$906$	−47.8773	−1.59062
$907$	−4.99890	−0.165986	−0.0829928	−	0.996550i	$-0.526448\pi$
$907$	−4.99890	−0.165986	−0.0829928	+	0.996550i	$0.526448\pi$
$908$	−35.4993	−1.17808
$909$	−10.1239	−0.335788
$910$	8.00431	0.265340
$911$	24.2373	0.803017	0.401509	−	0.915855i	$-0.368486\pi$
$911$	24.2373	0.803017	0.401509	+	0.915855i	$0.368486\pi$
$912$	−18.9778	−0.628416
$913$	0	0
$914$	−13.5704	−0.448869
$915$	12.1650	0.402163
$916$	4.82088	0.159286
$917$	16.5713	0.547234
$918$	2.78112	0.0917908
$919$	−37.5240	−1.23780	−0.618901	−	0.785469i	$-0.712422\pi$
$919$	−37.5240	−1.23780	−0.618901	+	0.785469i	$0.712422\pi$
$920$	−19.9632	−0.658166
$921$	−16.6115	−0.547368
$922$	−76.0674	−2.50515
$923$	4.42652	0.145701
$924$	0	0
$925$	24.1185	0.793012
$926$	−50.0232	−1.64386
$927$	−5.00158	−0.164273
$928$	2.72960	0.0896035
$929$	−20.8638	−0.684519	−0.342259	−	0.939606i	$-0.611192\pi$
$929$	−20.8638	−0.684519	−0.342259	+	0.939606i	$0.611192\pi$
$930$	24.3345	0.797961
$931$	−5.47841	−0.179547
$932$	35.7309	1.17041
$933$	18.0280	0.590210
$934$	99.2345	3.24705
$935$	0	0
$936$	10.6804	0.349101
$937$	0.463822	0.0151524	0.00757620	−	0.999971i	$-0.497588\pi$
$937$	0.463822	0.0151524	0.00757620	+	0.999971i	$0.497588\pi$
$938$	−18.5091	−0.604342
$939$	32.1350	1.04869
$940$	−72.3757	−2.36063
$941$	−23.6522	−0.771039	−0.385519	−	0.922700i	$-0.625978\pi$
$941$	−23.6522	−0.771039	−0.385519	+	0.922700i	$0.625978\pi$
$942$	3.74362	0.121974
$943$	−16.8145	−0.547556
$944$	−23.8850	−0.777391
$945$	1.43091	0.0465474
$946$	0	0
$947$	−28.3269	−0.920499	−0.460250	−	0.887789i	$-0.652240\pi$
$947$	−28.3269	−0.920499	−0.460250	+	0.887789i	$0.652240\pi$
$948$	−52.9118	−1.71849
$949$	11.1307	0.361319
$950$	−39.3199	−1.27571
$951$	−25.9290	−0.840806
$952$	5.31004	0.172099
$953$	48.2418	1.56270	0.781352	−	0.624090i	$-0.214530\pi$
$953$	48.2418	1.56270	0.781352	+	0.624090i	$0.214530\pi$
$954$	−22.5655	−0.730584
$955$	−9.81931	−0.317745
$956$	−100.760	−3.25883
$957$	0	0
$958$	64.6547	2.08890
$959$	9.64725	0.311526
$960$	−12.9114	−0.416712
$961$	17.9424	0.578789
$962$	−45.6954	−1.47328
$963$	17.6186	0.567753
$964$	−14.4886	−0.466646
$965$	−1.15023	−0.0370273
$966$	−7.30703	−0.235100
$967$	−35.1632	−1.13077	−0.565387	−	0.824826i	$-0.691273\pi$
$967$	−35.1632	−1.13077	−0.565387	+	0.824826i	$0.691273\pi$
$968$	0	0
$969$	6.26767	0.201347
$970$	22.8207	0.732728
$971$	−54.0629	−1.73496	−0.867480	−	0.497471i	$-0.834262\pi$
$971$	−54.0629	−1.73496	−0.867480	+	0.497471i	$0.834262\pi$
$972$	3.90931	0.125391
$973$	20.9647	0.672099
$974$	−57.4059	−1.83940
$975$	6.79413	0.217586
$976$	29.4504	0.942685
$977$	−42.2318	−1.35111	−0.675557	−	0.737307i	$-0.736097\pi$
$977$	−42.2318	−1.35111	−0.675557	+	0.737307i	$0.736097\pi$
$978$	−60.1268	−1.92264
$979$	0	0
$980$	5.59387	0.178690
$981$	12.5813	0.401691
$982$	99.1920	3.16534
$983$	−0.876060	−0.0279420	−0.0139710	−	0.999902i	$-0.504447\pi$
$983$	−0.876060	−0.0279420	−0.0139710	+	0.999902i	$0.504447\pi$
$984$	25.9632	0.827676
$985$	23.5359	0.749916
$986$	8.80856	0.280522
$987$	−12.9384	−0.411834
$988$	49.2831	1.56790
$989$	−31.8439	−1.01258
$990$	0	0
$991$	−41.7171	−1.32519	−0.662594	−	0.748979i	$-0.730544\pi$
$991$	−41.7171	−1.32519	−0.662594	+	0.748979i	$0.730544\pi$
$992$	−6.02917	−0.191426
$993$	−10.6498	−0.337961
$994$	4.67613	0.148318
$995$	−5.22504	−0.165645
$996$	−36.7734	−1.16521
$997$	−7.75731	−0.245676	−0.122838	−	0.992427i	$-0.539200\pi$
$997$	−7.75731	−0.245676	−0.122838	+	0.992427i	$0.539200\pi$
$998$	−23.2686	−0.736554
$999$	−8.16884	−0.258451

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2541.2.a.bl.1.1	✓	4	1.1	even	1	trivial
2541.2.a.bp.1.4	yes	4	11.10	odd	2
7623.2.a.cg.1.1		4	33.32	even	2
7623.2.a.cn.1.4		4	3.2	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:	\( N \)	\(=\)	\( 2541 = 3 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2541.a (trivial)

\(f(q)\)	\(=\)	\(q-2.43091 q^{2} +1.00000 q^{3} +3.90931 q^{4} +1.43091 q^{5} -2.43091 q^{6} +1.00000 q^{7} -4.64136 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.43091 q^{2} +1.00000 q^{3} +3.90931 q^{4} +1.43091 q^{5} -2.43091 q^{6} +1.00000 q^{7} -4.64136 q^{8} +1.00000 q^{9} -3.47841 q^{10} +3.90931 q^{12} -2.30114 q^{13} -2.43091 q^{14} +1.43091 q^{15} +3.46410 q^{16} -1.14407 q^{17} -2.43091 q^{18} -5.47841 q^{19} +5.59387 q^{20} +1.00000 q^{21} +3.00588 q^{23} -4.64136 q^{24} -2.95250 q^{25} +5.59387 q^{26} +1.00000 q^{27} +3.90931 q^{28} +3.16727 q^{29} -3.47841 q^{30} -6.99589 q^{31} +0.861816 q^{32} +2.78112 q^{34} +1.43091 q^{35} +3.90931 q^{36} -8.16884 q^{37} +13.3175 q^{38} -2.30114 q^{39} -6.64136 q^{40} -5.59387 q^{41} -2.43091 q^{42} -10.5939 q^{43} +1.43091 q^{45} -7.30703 q^{46} -12.9384 q^{47} +3.46410 q^{48} +1.00000 q^{49} +7.17726 q^{50} -1.14407 q^{51} -8.99589 q^{52} +9.28273 q^{53} -2.43091 q^{54} -4.64136 q^{56} -5.47841 q^{57} -7.69933 q^{58} -6.89501 q^{59} +5.59387 q^{60} +8.50160 q^{61} +17.0064 q^{62} +1.00000 q^{63} -9.02320 q^{64} -3.29272 q^{65} +7.61405 q^{67} -4.47252 q^{68} +3.00588 q^{69} -3.47841 q^{70} -1.92362 q^{71} -4.64136 q^{72} -4.83704 q^{73} +19.8577 q^{74} -2.95250 q^{75} -21.4168 q^{76} +5.59387 q^{78} -13.5348 q^{79} +4.95681 q^{80} +1.00000 q^{81} +13.5982 q^{82} -9.40661 q^{83} +3.90931 q^{84} -1.63706 q^{85} +25.7527 q^{86} +3.16727 q^{87} -4.35911 q^{89} -3.47841 q^{90} -2.30114 q^{91} +11.7509 q^{92} -6.99589 q^{93} +31.4520 q^{94} -7.83909 q^{95} +0.861816 q^{96} -6.56067 q^{97} -2.43091 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 4 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} + 4 q^{7} + 4 q^{9}+O(q^{10}) \) 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

Introduction

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