LMFDB - Embedded newform 2541.2.a.bl.1.3

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			1.3
Root			$-1.43091$ 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)

$f(q)$	$=$	$q-0.301143 q^{2} +1.00000 q^{3} -1.90931 q^{4} -0.698857 q^{5} -0.301143 q^{6} +1.00000 q^{7} +1.17726 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.301143 q^{2} +1.00000 q^{3} -1.90931 q^{4} -0.698857 q^{5} -0.301143 q^{6} +1.00000 q^{7} +1.17726 q^{8} +1.00000 q^{9} +0.210456 q^{10} -1.90931 q^{12} -4.43091 q^{13} -0.301143 q^{14} -0.698857 q^{15} +3.46410 q^{16} +6.80432 q^{17} -0.301143 q^{18} -1.78954 q^{19} +1.33434 q^{20} +1.00000 q^{21} -9.20204 q^{23} +1.17726 q^{24} -4.51160 q^{25} +1.33434 q^{26} +1.00000 q^{27} -1.90931 q^{28} -7.89932 q^{29} +0.210456 q^{30} +10.4600 q^{31} -3.39771 q^{32} -2.04907 q^{34} -0.698857 q^{35} -1.90931 q^{36} +6.16884 q^{37} +0.538909 q^{38} -4.43091 q^{39} -0.822738 q^{40} -1.33434 q^{41} -0.301143 q^{42} -6.33434 q^{43} -0.698857 q^{45} +2.77113 q^{46} +8.20634 q^{47} +3.46410 q^{48} +1.00000 q^{49} +1.35864 q^{50} +6.80432 q^{51} +8.45999 q^{52} -2.35452 q^{53} -0.301143 q^{54} +1.17726 q^{56} -1.78954 q^{57} +2.37882 q^{58} -4.76524 q^{59} +1.33434 q^{60} +1.69455 q^{61} -3.14995 q^{62} +1.00000 q^{63} -5.90501 q^{64} +3.09657 q^{65} -12.5423 q^{67} -12.9916 q^{68} -9.20204 q^{69} +0.210456 q^{70} +7.58387 q^{71} +1.17726 q^{72} -6.96681 q^{73} -1.85770 q^{74} -4.51160 q^{75} +3.41680 q^{76} +1.33434 q^{78} -8.85751 q^{79} -2.42091 q^{80} +1.00000 q^{81} +0.401826 q^{82} -5.71775 q^{83} -1.90931 q^{84} -4.75525 q^{85} +1.90754 q^{86} -7.89932 q^{87} -2.22935 q^{89} +0.210456 q^{90} -4.43091 q^{91} +17.5696 q^{92} +10.4600 q^{93} -2.47128 q^{94} +1.25064 q^{95} -3.39771 q^{96} -0.171378 q^{97} -0.301143 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.301143	−0.212940	−0.106470	−	0.994316i	$-0.533955\pi$
$2$	−0.301143	−0.212940	−0.106470	+	0.994316i	$0.533955\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.90931	−0.954656
$5$	−0.698857	−0.312538	−0.156269	−	0.987715i	$-0.549947\pi$
$5$	−0.698857	−0.312538	−0.156269	+	0.987715i	$0.549947\pi$
$6$	−0.301143	−0.122941
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.17726	0.416225
$9$	1.00000	0.333333
$10$	0.210456	0.0665520
$11$	0	0
$11$	0	0
$12$	−1.90931	−0.551171
$13$	−4.43091	−1.22891	−0.614456	−	0.788951i	$-0.710625\pi$
$13$	−4.43091	−1.22891	−0.614456	+	0.788951i	$0.710625\pi$
$14$	−0.301143	−0.0804838
$15$	−0.698857	−0.180444
$16$	3.46410	0.866025
$17$	6.80432	1.65029	0.825145	−	0.564921i	$-0.191093\pi$
$17$	6.80432	1.65029	0.825145	+	0.564921i	$0.191093\pi$
$18$	−0.301143	−0.0709801
$19$	−1.78954	−0.410550	−0.205275	−	0.978704i	$-0.565809\pi$
$19$	−1.78954	−0.410550	−0.205275	+	0.978704i	$0.565809\pi$
$20$	1.33434	0.298367
$21$	1.00000	0.218218
$22$	0	0
$23$	−9.20204	−1.91876	−0.959379	−	0.282122i	$-0.908962\pi$
$23$	−9.20204	−1.91876	−0.959379	+	0.282122i	$0.908962\pi$
$24$	1.17726	0.240308
$25$	−4.51160	−0.902320
$26$	1.33434	0.261685
$27$	1.00000	0.192450
$28$	−1.90931	−0.360826
$29$	−7.89932	−1.46687	−0.733433	−	0.679762i	$-0.762083\pi$
$29$	−7.89932	−1.46687	−0.733433	+	0.679762i	$0.762083\pi$
$30$	0.210456	0.0384238
$31$	10.4600	1.87867	0.939335	−	0.343002i	$-0.111444\pi$
$31$	10.4600	1.87867	0.939335	+	0.343002i	$0.111444\pi$
$32$	−3.39771	−0.600637
$33$	0	0
$34$	−2.04907	−0.351413
$35$	−0.698857	−0.118128
$36$	−1.90931	−0.318219
$37$	6.16884	1.01415	0.507076	−	0.861901i	$-0.330726\pi$
$37$	6.16884	1.01415	0.507076	+	0.861901i	$0.330726\pi$
$38$	0.538909	0.0874225
$39$	−4.43091	−0.709513
$40$	−0.822738	−0.130086
$41$	−1.33434	−0.208388	−0.104194	−	0.994557i	$-0.533226\pi$
$41$	−1.33434	−0.208388	−0.104194	+	0.994557i	$0.533226\pi$
$42$	−0.301143	−0.0464674
$43$	−6.33434	−0.965977	−0.482989	−	0.875627i	$-0.660449\pi$
$43$	−6.33434	−0.965977	−0.482989	+	0.875627i	$0.660449\pi$
$44$	0	0
$45$	−0.698857	−0.104179
$46$	2.77113	0.408581
$47$	8.20634	1.19702	0.598509	−	0.801116i	$-0.295760\pi$
$47$	8.20634	1.19702	0.598509	+	0.801116i	$0.295760\pi$
$48$	3.46410	0.500000
$49$	1.00000	0.142857
$50$	1.35864	0.192140
$51$	6.80432	0.952796
$52$	8.45999	1.17319
$53$	−2.35452	−0.323419	−0.161709	−	0.986838i	$-0.551701\pi$
$53$	−2.35452	−0.323419	−0.161709	+	0.986838i	$0.551701\pi$
$54$	−0.301143	−0.0409804
$55$	0	0
$56$	1.17726	0.157318
$57$	−1.78954	−0.237031
$58$	2.37882	0.312355
$59$	−4.76524	−0.620382	−0.310191	−	0.950674i	$-0.600393\pi$
$59$	−4.76524	−0.620382	−0.310191	+	0.950674i	$0.600393\pi$
$60$	1.33434	0.172262
$61$	1.69455	0.216965	0.108482	−	0.994098i	$-0.465401\pi$
$61$	1.69455	0.216965	0.108482	+	0.994098i	$0.465401\pi$
$62$	−3.14995	−0.400044
$63$	1.00000	0.125988
$64$	−5.90501	−0.738126
$65$	3.09657	0.384082
$66$	0	0
$67$	−12.5423	−1.53228	−0.766140	−	0.642673i	$-0.777825\pi$
$67$	−12.5423	−1.53228	−0.766140	+	0.642673i	$0.777825\pi$
$68$	−12.9916	−1.57546
$69$	−9.20204	−1.10780
$70$	0.210456	0.0251543
$71$	7.58387	0.900040	0.450020	−	0.893019i	$-0.351417\pi$
$71$	7.58387	0.900040	0.450020	+	0.893019i	$0.351417\pi$
$72$	1.17726	0.138742
$73$	−6.96681	−0.815403	−0.407701	−	0.913115i	$-0.633670\pi$
$73$	−6.96681	−0.815403	−0.407701	+	0.913115i	$0.633670\pi$
$74$	−1.85770	−0.215954
$75$	−4.51160	−0.520955
$76$	3.41680	0.391934
$77$	0	0
$78$	1.33434	0.151084
$79$	−8.85751	−0.996548	−0.498274	−	0.867020i	$-0.666033\pi$
$79$	−8.85751	−0.996548	−0.498274	+	0.867020i	$0.666033\pi$
$80$	−2.42091	−0.270666
$81$	1.00000	0.111111
$82$	0.401826	0.0443743
$83$	−5.71775	−0.627604	−0.313802	−	0.949488i	$-0.601603\pi$
$83$	−5.71775	−0.627604	−0.313802	+	0.949488i	$0.601603\pi$
$84$	−1.90931	−0.208323
$85$	−4.75525	−0.515779
$86$	1.90754	0.205695
$87$	−7.89932	−0.846896
$88$	0	0
$89$	−2.22935	−0.236310	−0.118155	−	0.992995i	$-0.537698\pi$
$89$	−2.22935	−0.236310	−0.118155	+	0.992995i	$0.537698\pi$
$90$	0.210456	0.0221840
$91$	−4.43091	−0.464485
$92$	17.5696	1.83175
$93$	10.4600	1.08465
$94$	−2.47128	−0.254893
$95$	1.25064	0.128312
$96$	−3.39771	−0.346778
$97$	−0.171378	−0.0174008	−0.00870041	−	0.999962i	$-0.502769\pi$
$97$	−0.171378	−0.0174008	−0.00870041	+	0.999962i	$0.502769\pi$
$98$	−0.301143	−0.0304200
$99$	0	0
$100$	8.61405	0.861405
$101$	−18.0723	−1.79826	−0.899129	−	0.437683i	$-0.855799\pi$
$101$	−18.0723	−1.79826	−0.899129	+	0.437683i	$0.855799\pi$
$102$	−2.04907	−0.202889
$103$	−1.73047	−0.170509	−0.0852543	−	0.996359i	$-0.527170\pi$
$103$	−1.73047	−0.170509	−0.0852543	+	0.996359i	$0.527170\pi$
$104$	−5.21634	−0.511504
$105$	−0.698857	−0.0682015
$106$	0.709048	0.0688689
$107$	6.96982	0.673798	0.336899	−	0.941541i	$-0.390622\pi$
$107$	6.96982	0.673798	0.336899	+	0.941541i	$0.390622\pi$
$108$	−1.90931	−0.183724
$109$	−17.6531	−1.69086	−0.845432	−	0.534084i	$-0.820657\pi$
$109$	−17.6531	−1.69086	−0.845432	+	0.534084i	$0.820657\pi$
$110$	0	0
$111$	6.16884	0.585521
$112$	3.46410	0.327327
$113$	11.7236	1.10287	0.551433	−	0.834219i	$-0.314081\pi$
$113$	11.7236	1.10287	0.551433	+	0.834219i	$0.314081\pi$
$114$	0.538909	0.0504734
$115$	6.43091	0.599685
$116$	15.0823	1.40035
$117$	−4.43091	−0.409638
$118$	1.43502	0.132104
$119$	6.80432	0.623751
$120$	−0.822738	−0.0751054
$121$	0	0
$122$	−0.510302	−0.0462005
$123$	−1.33434	−0.120313
$124$	−19.9714	−1.79348
$125$	6.64725	0.594548
$126$	−0.301143	−0.0268279
$127$	−12.1530	−1.07840	−0.539201	−	0.842177i	$-0.681274\pi$
$127$	−12.1530	−1.07840	−0.539201	+	0.842177i	$0.681274\pi$
$128$	8.57368	0.757813
$129$	−6.33434	−0.557707
$130$	−0.932511	−0.0817866
$131$	−18.9111	−1.65227	−0.826135	−	0.563473i	$-0.809465\pi$
$131$	−18.9111	−1.65227	−0.826135	+	0.563473i	$0.809465\pi$
$132$	0	0
$133$	−1.78954	−0.155173
$134$	3.77701	0.326284
$135$	−0.698857	−0.0601480
$136$	8.01047	0.686892
$137$	−8.37930	−0.715892	−0.357946	−	0.933742i	$-0.616523\pi$
$137$	−8.37930	−0.715892	−0.357946	+	0.933742i	$0.616523\pi$
$138$	2.77113	0.235894
$139$	−9.84039	−0.834651	−0.417325	−	0.908757i	$-0.637032\pi$
$139$	−9.84039	−0.834651	−0.417325	+	0.908757i	$0.637032\pi$
$140$	1.33434	0.112772
$141$	8.20634	0.691099
$142$	−2.28383	−0.191655
$143$	0	0
$144$	3.46410	0.288675
$145$	5.52049	0.458452
$146$	2.09800	0.173632
$147$	1.00000	0.0824786
$148$	−11.7783	−0.968166
$149$	−7.13435	−0.584469	−0.292234	−	0.956347i	$-0.594399\pi$
$149$	−7.13435	−0.584469	−0.292234	+	0.956347i	$0.594399\pi$
$150$	1.35864	0.110932
$151$	−7.83881	−0.637914	−0.318957	−	0.947769i	$-0.603332\pi$
$151$	−7.83881	−0.637914	−0.318957	+	0.947769i	$0.603332\pi$
$152$	−2.10676	−0.170881
$153$	6.80432	0.550097
$154$	0	0
$155$	−7.31004	−0.587156
$156$	8.45999	0.677341
$157$	−18.9959	−1.51604	−0.758018	−	0.652233i	$-0.773832\pi$
$157$	−18.9959	−1.51604	−0.758018	+	0.652233i	$0.773832\pi$
$158$	2.66738	0.212205
$159$	−2.35452	−0.186726
$160$	2.37452	0.187722
$161$	−9.20204	−0.725222
$162$	−0.301143	−0.0236600
$163$	−12.8779	−1.00867	−0.504337	−	0.863507i	$-0.668263\pi$
$163$	−12.8779	−1.00867	−0.504337	+	0.863507i	$0.668263\pi$
$164$	2.54767	0.198939
$165$	0	0
$166$	1.72186	0.133642
$167$	−0.00588400	−0.000455318 0	−0.000227659	−	1.00000i	$-0.500072\pi$
$167$	−0.00588400	−0.000455318 0	−0.000227659		1.00000i	$0.500072\pi$
$168$	1.17726	0.0908277
$169$	6.63294	0.510226
$170$	1.43201	0.109830
$171$	−1.78954	−0.136850
$172$	12.0942	0.922176
$173$	12.9193	0.982237	0.491118	−	0.871093i	$-0.336588\pi$
$173$	12.9193	0.982237	0.491118	+	0.871093i	$0.336588\pi$
$174$	2.37882	0.180338
$175$	−4.51160	−0.341045
$176$	0	0
$177$	−4.76524	−0.358178
$178$	0.671352	0.0503200
$179$	−1.31133	−0.0980137	−0.0490069	−	0.998798i	$-0.515606\pi$
$179$	−1.31133	−0.0980137	−0.0490069	+	0.998798i	$0.515606\pi$
$180$	1.33434	0.0994556
$181$	4.43138	0.329382	0.164691	−	0.986345i	$-0.447337\pi$
$181$	4.43138	0.329382	0.164691	+	0.986345i	$0.447337\pi$
$182$	1.33434	0.0989076
$183$	1.69455	0.125265
$184$	−10.8332	−0.798635
$185$	−4.31114	−0.316961
$186$	−3.14995	−0.230966
$187$	0	0
$188$	−15.6685	−1.14274
$189$	1.00000	0.0727393
$190$	−0.376620	−0.0273229
$191$	5.34563	0.386796	0.193398	−	0.981120i	$-0.438049\pi$
$191$	5.34563	0.386796	0.193398	+	0.981120i	$0.438049\pi$
$192$	−5.90501	−0.426157
$193$	−0.803848	−0.0578622	−0.0289311	−	0.999581i	$-0.509210\pi$
$193$	−0.803848	−0.0578622	−0.0289311	+	0.999581i	$0.509210\pi$
$194$	0.0516093	0.00370533
$195$	3.09657	0.221750
$196$	−1.90931	−0.136379
$197$	23.4082	1.66776	0.833882	−	0.551943i	$-0.186113\pi$
$197$	23.4082	1.66776	0.833882	+	0.551943i	$0.186113\pi$
$198$	0	0
$199$	23.3118	1.65253	0.826265	−	0.563281i	$-0.190461\pi$
$199$	23.3118	1.65253	0.826265	+	0.563281i	$0.190461\pi$
$200$	−5.31133	−0.375568
$201$	−12.5423	−0.884663
$202$	5.44234	0.382922
$203$	−7.89932	−0.554423
$204$	−12.9916	−0.909593
$205$	0.932511	0.0651294
$206$	0.521120	0.0363082
$207$	−9.20204	−0.639586
$208$	−15.3491	−1.06427
$209$	0	0
$210$	0.210456	0.0145228
$211$	−10.1455	−0.698445	−0.349223	−	0.937040i	$-0.613554\pi$
$211$	−10.1455	−0.698445	−0.349223	+	0.937040i	$0.613554\pi$
$212$	4.49552	0.308754
$213$	7.58387	0.519638
$214$	−2.09891	−0.143479
$215$	4.42680	0.301905
$216$	1.17726	0.0801025
$217$	10.4600	0.710070
$218$	5.31612	0.360053
$219$	−6.96681	−0.470773
$220$	0	0
$221$	−30.1493	−2.02806
$222$	−1.85770	−0.124681
$223$	−6.86052	−0.459414	−0.229707	−	0.973260i	$-0.573777\pi$
$223$	−6.86052	−0.459414	−0.229707	+	0.973260i	$0.573777\pi$
$224$	−3.39771	−0.227019
$225$	−4.51160	−0.300773
$226$	−3.53049	−0.234845
$227$	−9.65136	−0.640583	−0.320292	−	0.947319i	$-0.603781\pi$
$227$	−9.65136	−0.640583	−0.320292	+	0.947319i	$0.603781\pi$
$228$	3.41680	0.226283
$229$	2.37452	0.156912	0.0784562	−	0.996918i	$-0.475001\pi$
$229$	2.37452	0.156912	0.0784562	+	0.996918i	$0.475001\pi$
$230$	−1.93662	−0.127697
$231$	0	0
$232$	−9.29957	−0.610546
$233$	−16.2643	−1.06551	−0.532755	−	0.846269i	$-0.678843\pi$
$233$	−16.2643	−1.06551	−0.532755	+	0.846269i	$0.678843\pi$
$234$	1.33434	0.0872283
$235$	−5.73506	−0.374114
$236$	9.09834	0.592252
$237$	−8.85751	−0.575357
$238$	−2.04907	−0.132822
$239$	17.2386	1.11507	0.557535	−	0.830153i	$-0.311747\pi$
$239$	17.2386	1.11507	0.557535	+	0.830153i	$0.311747\pi$
$240$	−2.42091	−0.156269
$241$	−5.41818	−0.349016	−0.174508	−	0.984656i	$-0.555833\pi$
$241$	−5.41818	−0.349016	−0.174508	+	0.984656i	$0.555833\pi$
$242$	0	0
$243$	1.00000	0.0641500
$244$	−3.23543	−0.207127
$245$	−0.698857	−0.0446483
$246$	0.401826	0.0256195
$247$	7.92931	0.504530
$248$	12.3141	0.781949
$249$	−5.71775	−0.362348
$250$	−2.00177	−0.126603
$251$	15.1995	0.959384	0.479692	−	0.877437i	$-0.340748\pi$
$251$	15.1995	0.959384	0.479692	+	0.877437i	$0.340748\pi$
$252$	−1.90931	−0.120275
$253$	0	0
$254$	3.65978	0.229635
$255$	−4.75525	−0.297785
$256$	9.22811	0.576757
$257$	−26.6304	−1.66116	−0.830580	−	0.556900i	$-0.811991\pi$
$257$	−26.6304	−1.66116	−0.830580	+	0.556900i	$0.811991\pi$
$258$	1.90754	0.118758
$259$	6.16884	0.383313
$260$	−5.91232	−0.366667
$261$	−7.89932	−0.488955
$262$	5.69494	0.351835
$263$	5.63979	0.347764	0.173882	−	0.984766i	$-0.444369\pi$
$263$	5.63979	0.347764	0.173882	+	0.984766i	$0.444369\pi$
$264$	0	0
$265$	1.64548	0.101081
$266$	0.538909	0.0330426
$267$	−2.22935	−0.136434
$268$	23.9471	1.46280
$269$	−1.10958	−0.0676521	−0.0338261	−	0.999428i	$-0.510769\pi$
$269$	−1.10958	−0.0676521	−0.0338261	+	0.999428i	$0.510769\pi$
$270$	0.210456	0.0128079
$271$	13.7713	0.836548	0.418274	−	0.908321i	$-0.362635\pi$
$271$	13.7713	0.836548	0.418274	+	0.908321i	$0.362635\pi$
$272$	23.5709	1.42919
$273$	−4.43091	−0.268171
$274$	2.52337	0.152442
$275$	0	0
$276$	17.5696	1.05756
$277$	7.90089	0.474719	0.237359	−	0.971422i	$-0.423718\pi$
$277$	7.90089	0.474719	0.237359	+	0.971422i	$0.423718\pi$
$278$	2.96336	0.177731
$279$	10.4600	0.626223
$280$	−0.822738	−0.0491680
$281$	13.7596	0.820826	0.410413	−	0.911900i	$-0.365384\pi$
$281$	13.7596	0.820826	0.410413	+	0.911900i	$0.365384\pi$
$282$	−2.47128	−0.147163
$283$	−17.8650	−1.06197	−0.530983	−	0.847383i	$-0.678177\pi$
$283$	−17.8650	−1.06197	−0.530983	+	0.847383i	$0.678177\pi$
$284$	−14.4800	−0.859229
$285$	1.25064	0.0740813
$286$	0	0
$287$	−1.33434	−0.0787634
$288$	−3.39771	−0.200212
$289$	29.2988	1.72346
$290$	−1.66246	−0.0976229
$291$	−0.171378	−0.0100464
$292$	13.3018	0.778430
$293$	23.9721	1.40046	0.700231	−	0.713916i	$-0.253080\pi$
$293$	23.9721	1.40046	0.700231	+	0.713916i	$0.253080\pi$
$294$	−0.301143	−0.0175630
$295$	3.33022	0.193893
$296$	7.26234	0.422115
$297$	0	0
$298$	2.14846	0.124457
$299$	40.7734	2.35799
$300$	8.61405	0.497333
$301$	−6.33434	−0.365105
$302$	2.36060	0.135837
$303$	−18.0723	−1.03822
$304$	−6.19916	−0.355546
$305$	−1.18425	−0.0678098
$306$	−2.04907	−0.117138
$307$	24.2718	1.38526	0.692632	−	0.721292i	$-0.256451\pi$
$307$	24.2718	1.38526	0.692632	+	0.721292i	$0.256451\pi$
$308$	0	0
$309$	−1.73047	−0.0984432
$310$	2.20137	0.125029
$311$	−1.97542	−0.112016	−0.0560079	−	0.998430i	$-0.517837\pi$
$311$	−1.97542	−0.112016	−0.0560079	+	0.998430i	$0.517837\pi$
$312$	−5.21634	−0.295317
$313$	3.04189	0.171938	0.0859690	−	0.996298i	$-0.472601\pi$
$313$	3.04189	0.171938	0.0859690	+	0.996298i	$0.472601\pi$
$314$	5.72048	0.322825
$315$	−0.698857	−0.0393761
$316$	16.9118	0.951361
$317$	27.7329	1.55763	0.778816	−	0.627252i	$-0.215820\pi$
$317$	27.7329	1.55763	0.778816	+	0.627252i	$0.215820\pi$
$318$	0.709048	0.0397615
$319$	0	0
$320$	4.12675	0.230693
$321$	6.96982	0.389017
$322$	2.77113	0.154429
$323$	−12.1766	−0.677526
$324$	−1.90931	−0.106073
$325$	19.9905	1.10887
$326$	3.87809	0.214787
$327$	−17.6531	−0.976220
$328$	−1.57086	−0.0867365
$329$	8.20634	0.452430
$330$	0	0
$331$	−13.3502	−0.733794	−0.366897	−	0.930262i	$-0.619580\pi$
$331$	−13.3502	−0.733794	−0.366897	+	0.930262i	$0.619580\pi$
$332$	10.9170	0.599147
$333$	6.16884	0.338050
$334$	0.00177192	9.69554e−5 0
$335$	8.76524	0.478896
$336$	3.46410	0.188982
$337$	−6.41345	−0.349363	−0.174681	−	0.984625i	$-0.555890\pi$
$337$	−6.41345	−0.349363	−0.174681	+	0.984625i	$0.555890\pi$
$338$	−1.99746	−0.108648
$339$	11.7236	0.636740
$340$	9.07926	0.492392
$341$	0	0
$342$	0.538909	0.0291408
$343$	1.00000	0.0539949
$344$	−7.45717	−0.402064
$345$	6.43091	0.346228
$346$	−3.89056	−0.209158
$347$	9.97432	0.535450	0.267725	−	0.963495i	$-0.413728\pi$
$347$	9.97432	0.535450	0.267725	+	0.963495i	$0.413728\pi$
$348$	15.0823	0.808494
$349$	−8.18267	−0.438008	−0.219004	−	0.975724i	$-0.570281\pi$
$349$	−8.18267	−0.438008	−0.219004	+	0.975724i	$0.570281\pi$
$350$	1.35864	0.0726222
$351$	−4.43091	−0.236504
$352$	0	0
$353$	−0.173150	−0.00921585	−0.00460792	−	0.999989i	$-0.501467\pi$
$353$	−0.173150	−0.00921585	−0.00460792	+	0.999989i	$0.501467\pi$
$354$	1.43502	0.0762704
$355$	−5.30004	−0.281297
$356$	4.25652	0.225595
$357$	6.80432	0.360123
$358$	0.394899	0.0208711
$359$	24.9257	1.31553	0.657763	−	0.753225i	$-0.271503\pi$
$359$	24.9257	1.31553	0.657763	+	0.753225i	$0.271503\pi$
$360$	−0.822738	−0.0433621
$361$	−15.7975	−0.831449
$362$	−1.33448	−0.0701387
$363$	0	0
$364$	8.45999	0.443424
$365$	4.86880	0.254845
$366$	−0.510302	−0.0266739
$367$	−34.1736	−1.78385	−0.891924	−	0.452185i	$-0.850645\pi$
$367$	−34.1736	−1.78385	−0.891924	+	0.452185i	$0.850645\pi$
$368$	−31.8768	−1.66169
$369$	−1.33434	−0.0694628
$370$	1.29827	0.0674938
$371$	−2.35452	−0.122241
$372$	−19.9714	−1.03547
$373$	1.51030	0.0782005	0.0391002	−	0.999235i	$-0.487551\pi$
$373$	1.51030	0.0782005	0.0391002	+	0.999235i	$0.487551\pi$
$374$	0	0
$375$	6.64725	0.343262
$376$	9.66102	0.498229
$377$	35.0011	1.80265
$378$	−0.301143	−0.0154891
$379$	−7.46013	−0.383201	−0.191601	−	0.981473i	$-0.561368\pi$
$379$	−7.46013	−0.383201	−0.191601	+	0.981473i	$0.561368\pi$
$380$	−2.38785	−0.122494
$381$	−12.1530	−0.622615
$382$	−1.60980	−0.0823645
$383$	25.7482	1.31567	0.657836	−	0.753161i	$-0.271472\pi$
$383$	25.7482	1.31567	0.657836	+	0.753161i	$0.271472\pi$
$384$	8.57368	0.437524
$385$	0	0
$386$	0.242073	0.0123212
$387$	−6.33434	−0.321992
$388$	0.327214	0.0166118
$389$	−33.6464	−1.70594	−0.852971	−	0.521959i	$-0.825201\pi$
$389$	−33.6464	−1.70594	−0.852971	+	0.521959i	$0.825201\pi$
$390$	−0.932511	−0.0472195
$391$	−62.6136	−3.16651
$392$	1.17726	0.0594607
$393$	−18.9111	−0.953938
$394$	−7.04921	−0.355134
$395$	6.19013	0.311459
$396$	0	0
$397$	−19.6950	−0.988465	−0.494232	−	0.869330i	$-0.664551\pi$
$397$	−19.6950	−0.988465	−0.494232	+	0.869330i	$0.664551\pi$
$398$	−7.02019	−0.351890
$399$	−1.78954	−0.0895893
$400$	−15.6286	−0.781432
$401$	17.4368	0.870752	0.435376	−	0.900249i	$-0.356615\pi$
$401$	17.4368	0.870752	0.435376	+	0.900249i	$0.356615\pi$
$402$	3.77701	0.188380
$403$	−46.3472	−2.30872
$404$	34.5056	1.71672
$405$	−0.698857	−0.0347265
$406$	2.37882	0.118059
$407$	0	0
$408$	8.01047	0.396577
$409$	−7.92547	−0.391889	−0.195945	−	0.980615i	$-0.562777\pi$
$409$	−7.92547	−0.391889	−0.195945	+	0.980615i	$0.562777\pi$
$410$	−0.280819	−0.0138687
$411$	−8.37930	−0.413320
$412$	3.30402	0.162777
$413$	−4.76524	−0.234482
$414$	2.77113	0.136194
$415$	3.99589	0.196150
$416$	15.0550	0.738130
$417$	−9.84039	−0.481886
$418$	0	0
$419$	−12.0302	−0.587713	−0.293856	−	0.955850i	$-0.594939\pi$
$419$	−12.0302	−0.587713	−0.293856	+	0.955850i	$0.594939\pi$
$420$	1.33434	0.0651090
$421$	−1.36314	−0.0664353	−0.0332177	−	0.999448i	$-0.510575\pi$
$421$	−1.36314	−0.0664353	−0.0332177	+	0.999448i	$0.510575\pi$
$422$	3.05525	0.148727
$423$	8.20634	0.399006
$424$	−2.77189	−0.134615
$425$	−30.6984	−1.48909
$426$	−2.28383	−0.110652
$427$	1.69455	0.0820050
$428$	−13.3076	−0.643245
$429$	0	0
$430$	−1.33310	−0.0642877
$431$	8.23954	0.396885	0.198442	−	0.980113i	$-0.436412\pi$
$431$	8.23954	0.396885	0.198442	+	0.980113i	$0.436412\pi$
$432$	3.46410	0.166667
$433$	13.7708	0.661785	0.330892	−	0.943668i	$-0.392650\pi$
$433$	13.7708	0.661785	0.330892	+	0.943668i	$0.392650\pi$
$434$	−3.14995	−0.151203
$435$	5.52049	0.264687
$436$	33.7054	1.61419
$437$	16.4675	0.787745
$438$	2.09800	0.100247
$439$	18.7090	0.892934	0.446467	−	0.894800i	$-0.352682\pi$
$439$	18.7090	0.892934	0.446467	+	0.894800i	$0.352682\pi$
$440$	0	0
$441$	1.00000	0.0476190
$442$	9.07926	0.431856
$443$	33.3148	1.58283	0.791417	−	0.611276i	$-0.209344\pi$
$443$	33.3148	1.58283	0.791417	+	0.611276i	$0.209344\pi$
$444$	−11.7783	−0.558971
$445$	1.55799	0.0738560
$446$	2.06600	0.0978278
$447$	−7.13435	−0.337443
$448$	−5.90501	−0.278985
$449$	−3.74233	−0.176611	−0.0883057	−	0.996093i	$-0.528145\pi$
$449$	−3.74233	−0.176611	−0.0883057	+	0.996093i	$0.528145\pi$
$450$	1.35864	0.0640467
$451$	0	0
$452$	−22.3841	−1.05286
$453$	−7.83881	−0.368300
$454$	2.90644	0.136406
$455$	3.09657	0.145169
$456$	−2.10676	−0.0986582
$457$	−19.9747	−0.934379	−0.467190	−	0.884157i	$-0.654733\pi$
$457$	−19.9747	−0.934379	−0.467190	+	0.884157i	$0.654733\pi$
$458$	−0.715069	−0.0334130
$459$	6.80432	0.317599
$460$	−12.2786	−0.572493
$461$	0.904388	0.0421215	0.0210608	−	0.999778i	$-0.493296\pi$
$461$	0.904388	0.0421215	0.0210608	+	0.999778i	$0.493296\pi$
$462$	0	0
$463$	23.2784	1.08184	0.540920	−	0.841074i	$-0.318076\pi$
$463$	23.2784	1.08184	0.540920	+	0.841074i	$0.318076\pi$
$464$	−27.3640	−1.27034
$465$	−7.31004	−0.338995
$466$	4.89788	0.226890
$467$	3.75018	0.173538	0.0867688	−	0.996228i	$-0.472346\pi$
$467$	3.75018	0.173538	0.0867688	+	0.996228i	$0.472346\pi$
$468$	8.45999	0.391063
$469$	−12.5423	−0.579148
$470$	1.72707	0.0796640
$471$	−18.9959	−0.875284
$472$	−5.60994	−0.258219
$473$	0	0
$474$	2.66738	0.122517
$475$	8.07371	0.370447
$476$	−12.9916	−0.595468
$477$	−2.35452	−0.107806
$478$	−5.19128	−0.237443
$479$	29.0418	1.32695	0.663477	−	0.748197i	$-0.269080\pi$
$479$	29.0418	1.32695	0.663477	+	0.748197i	$0.269080\pi$
$480$	2.37452	0.108381
$481$	−27.3336	−1.24630
$482$	1.63165	0.0743195
$483$	−9.20204	−0.418707
$484$	0	0
$485$	0.119769	0.00543842
$486$	−0.301143	−0.0136601
$487$	−12.4381	−0.563624	−0.281812	−	0.959470i	$-0.590935\pi$
$487$	−12.4381	−0.563624	−0.281812	+	0.959470i	$0.590935\pi$
$488$	1.99493	0.0903062
$489$	−12.8779	−0.582358
$490$	0.210456	0.00950743
$491$	−6.46343	−0.291691	−0.145845	−	0.989307i	$-0.546590\pi$
$491$	−6.46343	−0.291691	−0.145845	+	0.989307i	$0.546590\pi$
$492$	2.54767	0.114858
$493$	−53.7495	−2.42076
$494$	−2.38785	−0.107435
$495$	0	0
$496$	36.2345	1.62698
$497$	7.58387	0.340183
$498$	1.72186	0.0771584
$499$	−13.2848	−0.594708	−0.297354	−	0.954767i	$-0.596104\pi$
$499$	−13.2848	−0.594708	−0.297354	+	0.954767i	$0.596104\pi$
$500$	−12.6917	−0.567589
$501$	−0.00588400	−0.000262878 0
$502$	−4.57722	−0.204291
$503$	−36.5805	−1.63104	−0.815522	−	0.578726i	$-0.803550\pi$
$503$	−36.5805	−1.63104	−0.815522	+	0.578726i	$0.803550\pi$
$504$	1.17726	0.0524394
$505$	12.6299	0.562025
$506$	0	0
$507$	6.63294	0.294579
$508$	23.2038	1.02950
$509$	−4.36993	−0.193694	−0.0968469	−	0.995299i	$-0.530876\pi$
$509$	−4.36993	−0.193694	−0.0968469	+	0.995299i	$0.530876\pi$
$510$	1.43201	0.0634105
$511$	−6.96681	−0.308193
$512$	−19.9263	−0.880628
$513$	−1.78954	−0.0790103
$514$	8.01956	0.353728
$515$	1.20935	0.0532905
$516$	12.0942	0.532419
$517$	0	0
$518$	−1.85770	−0.0816228
$519$	12.9193	0.567095
$520$	3.64548	0.159865
$521$	−36.1430	−1.58345	−0.791726	−	0.610876i	$-0.790817\pi$
$521$	−36.1430	−1.58345	−0.791726	+	0.610876i	$0.790817\pi$
$522$	2.37882	0.104118
$523$	28.5269	1.24739	0.623696	−	0.781667i	$-0.285630\pi$
$523$	28.5269	1.24739	0.623696	+	0.781667i	$0.285630\pi$
$524$	36.1072	1.57735
$525$	−4.51160	−0.196902
$526$	−1.69838	−0.0740530
$527$	71.1731	3.10035
$528$	0	0
$529$	61.6775	2.68163
$530$	−0.495523	−0.0215242
$531$	−4.76524	−0.206794
$532$	3.41680	0.148137
$533$	5.91232	0.256091
$534$	0.671352	0.0290522
$535$	−4.87091	−0.210588
$536$	−14.7655	−0.637774
$537$	−1.31133	−0.0565883
$538$	0.334141	0.0144059
$539$	0	0
$540$	1.33434	0.0574207
$541$	26.3725	1.13384	0.566921	−	0.823772i	$-0.308134\pi$
$541$	26.3725	1.13384	0.566921	+	0.823772i	$0.308134\pi$
$542$	−4.14714	−0.178135
$543$	4.43138	0.190169
$544$	−23.1191	−0.991225
$545$	12.3370	0.528460
$546$	1.33434	0.0571043
$547$	−32.2848	−1.38040	−0.690199	−	0.723620i	$-0.742477\pi$
$547$	−32.2848	−1.38040	−0.690199	+	0.723620i	$0.742477\pi$
$548$	15.9987	0.683431
$549$	1.69455	0.0723216
$550$	0	0
$551$	14.1362	0.602221
$552$	−10.8332	−0.461092
$553$	−8.85751	−0.376660
$554$	−2.37930	−0.101087
$555$	−4.31114	−0.182998
$556$	18.7884	0.796805
$557$	37.4768	1.58794	0.793972	−	0.607954i	$-0.208010\pi$
$557$	37.4768	1.58794	0.793972	+	0.607954i	$0.208010\pi$
$558$	−3.14995	−0.133348
$559$	28.0669	1.18710
$560$	−2.42091	−0.102302
$561$	0	0
$562$	−4.14359	−0.174787
$563$	14.3834	0.606188	0.303094	−	0.952961i	$-0.401980\pi$
$563$	14.3834	0.606188	0.303094	+	0.952961i	$0.401980\pi$
$564$	−15.6685	−0.659762
$565$	−8.19314	−0.344688
$566$	5.37993	0.226135
$567$	1.00000	0.0419961
$568$	8.92820	0.374619
$569$	−29.2888	−1.22785	−0.613925	−	0.789364i	$-0.710410\pi$
$569$	−29.2888	−1.22785	−0.613925	+	0.789364i	$0.710410\pi$
$570$	−0.376620	−0.0157749
$571$	−18.5737	−0.777284	−0.388642	−	0.921389i	$-0.627056\pi$
$571$	−18.5737	−0.777284	−0.388642	+	0.921389i	$0.627056\pi$
$572$	0	0
$573$	5.34563	0.223317
$574$	0.401826	0.0167719
$575$	41.5159	1.73133
$576$	−5.90501	−0.246042
$577$	20.3524	0.847282	0.423641	−	0.905830i	$-0.360752\pi$
$577$	20.3524	0.847282	0.423641	+	0.905830i	$0.360752\pi$
$578$	−8.82313	−0.366994
$579$	−0.803848	−0.0334068
$580$	−10.5403	−0.437664
$581$	−5.71775	−0.237212
$582$	0.0516093	0.00213927
$583$	0	0
$584$	−8.20176	−0.339391
$585$	3.09657	0.128027
$586$	−7.21902	−0.298215
$587$	−30.8643	−1.27391	−0.636954	−	0.770902i	$-0.719806\pi$
$587$	−30.8643	−1.27391	−0.636954	+	0.770902i	$0.719806\pi$
$588$	−1.90931	−0.0787387
$589$	−18.7186	−0.771287
$590$	−1.00287	−0.0412877
$591$	23.4082	0.962884
$592$	21.3695	0.878281
$593$	−4.76749	−0.195777	−0.0978887	−	0.995197i	$-0.531209\pi$
$593$	−4.76749	−0.195777	−0.0978887	+	0.995197i	$0.531209\pi$
$594$	0	0
$595$	−4.75525	−0.194946
$596$	13.6217	0.557967
$597$	23.3118	0.954089
$598$	−12.2786	−0.502110
$599$	31.5423	1.28878	0.644391	−	0.764696i	$-0.277111\pi$
$599$	31.5423	1.28878	0.644391	+	0.764696i	$0.277111\pi$
$600$	−5.31133	−0.216834
$601$	2.59544	0.105870	0.0529352	−	0.998598i	$-0.483142\pi$
$601$	2.59544	0.105870	0.0529352	+	0.998598i	$0.483142\pi$
$602$	1.90754	0.0777456
$603$	−12.5423	−0.510760
$604$	14.9667	0.608988
$605$	0	0
$606$	5.44234	0.221080
$607$	−24.2991	−0.986269	−0.493135	−	0.869953i	$-0.664149\pi$
$607$	−24.2991	−0.986269	−0.493135	+	0.869953i	$0.664149\pi$
$608$	6.08036	0.246591
$609$	−7.89932	−0.320096
$610$	0.356628	0.0144394
$611$	−36.3616	−1.47103
$612$	−12.9916	−0.525154
$613$	4.32611	0.174730	0.0873650	−	0.996176i	$-0.472155\pi$
$613$	4.32611	0.174730	0.0873650	+	0.996176i	$0.472155\pi$
$614$	−7.30927	−0.294978
$615$	0.932511	0.0376025
$616$	0	0
$617$	27.3809	1.10231	0.551156	−	0.834402i	$-0.314187\pi$
$617$	27.3809	1.10231	0.551156	+	0.834402i	$0.314187\pi$
$618$	0.521120	0.0209625
$619$	9.13728	0.367258	0.183629	−	0.982996i	$-0.441215\pi$
$619$	9.13728	0.367258	0.183629	+	0.982996i	$0.441215\pi$
$620$	13.9571	0.560533
$621$	−9.20204	−0.369265
$622$	0.594884	0.0238527
$623$	−2.22935	−0.0893169
$624$	−15.3491	−0.614456
$625$	17.9125	0.716501
$626$	−0.916045	−0.0366125
$627$	0	0
$628$	36.2691	1.44729
$629$	41.9748	1.67364
$630$	0.210456	0.00838476
$631$	29.7629	1.18484	0.592421	−	0.805628i	$-0.298172\pi$
$631$	29.7629	1.18484	0.592421	+	0.805628i	$0.298172\pi$
$632$	−10.4276	−0.414788
$633$	−10.1455	−0.403248
$634$	−8.35156	−0.331683
$635$	8.49318	0.337042
$636$	4.49552	0.178259
$637$	−4.43091	−0.175559
$638$	0	0
$639$	7.58387	0.300013
$640$	−5.99178	−0.236846
$641$	−17.6506	−0.697159	−0.348579	−	0.937279i	$-0.613336\pi$
$641$	−17.6506	−0.697159	−0.348579	+	0.937279i	$0.613336\pi$
$642$	−2.09891	−0.0828374
$643$	6.56451	0.258879	0.129439	−	0.991587i	$-0.458682\pi$
$643$	6.56451	0.258879	0.129439	+	0.991587i	$0.458682\pi$
$644$	17.5696	0.692338
$645$	4.42680	0.174305
$646$	3.66691	0.144273
$647$	28.8178	1.13294	0.566472	−	0.824081i	$-0.308308\pi$
$647$	28.8178	1.13294	0.566472	+	0.824081i	$0.308308\pi$
$648$	1.17726	0.0462472
$649$	0	0
$650$	−6.01999	−0.236124
$651$	10.4600	0.409959
$652$	24.5879	0.962937
$653$	32.3666	1.26660	0.633302	−	0.773905i	$-0.281699\pi$
$653$	32.3666	1.26660	0.633302	+	0.773905i	$0.281699\pi$
$654$	5.31612	0.207877
$655$	13.2161	0.516397
$656$	−4.62228	−0.180470
$657$	−6.96681	−0.271801
$658$	−2.47128	−0.0963406
$659$	3.30435	0.128719	0.0643596	−	0.997927i	$-0.479500\pi$
$659$	3.30435	0.128719	0.0643596	+	0.997927i	$0.479500\pi$
$660$	0	0
$661$	−7.07404	−0.275148	−0.137574	−	0.990491i	$-0.543931\pi$
$661$	−7.07404	−0.275148	−0.137574	+	0.990491i	$0.543931\pi$
$662$	4.02032	0.156254
$663$	−30.1493	−1.17090
$664$	−6.73129	−0.261225
$665$	1.25064	0.0484976
$666$	−1.85770	−0.0719846
$667$	72.6898	2.81456
$668$	0.0112344	0.000434672 0
$669$	−6.86052	−0.265243
$670$	−2.63959	−0.101976
$671$	0	0
$672$	−3.39771	−0.131070
$673$	−21.2582	−0.819445	−0.409722	−	0.912210i	$-0.634374\pi$
$673$	−21.2582	−0.819445	−0.409722	+	0.912210i	$0.634374\pi$
$674$	1.93137	0.0743934
$675$	−4.51160	−0.173652
$676$	−12.6644	−0.487091
$677$	43.2282	1.66140	0.830698	−	0.556723i	$-0.187942\pi$
$677$	43.2282	1.66140	0.830698	+	0.556723i	$0.187942\pi$
$678$	−3.53049	−0.135588
$679$	−0.171378	−0.00657689
$680$	−5.59817	−0.214680
$681$	−9.65136	−0.369841
$682$	0	0
$683$	30.9708	1.18507	0.592533	−	0.805546i	$-0.298128\pi$
$683$	30.9708	1.18507	0.592533	+	0.805546i	$0.298128\pi$
$684$	3.41680	0.130645
$685$	5.85593	0.223744
$686$	−0.301143	−0.0114977
$687$	2.37452	0.0905934
$688$	−21.9428	−0.836561
$689$	10.4327	0.397453
$690$	−1.93662	−0.0737260
$691$	−6.50729	−0.247549	−0.123775	−	0.992310i	$-0.539500\pi$
$691$	−6.50729	−0.247549	−0.123775	+	0.992310i	$0.539500\pi$
$692$	−24.6670	−0.937699
$693$	0	0
$694$	−3.00370	−0.114019
$695$	6.87703	0.260860
$696$	−9.29957	−0.352499
$697$	−9.07926	−0.343901
$698$	2.46415	0.0932696
$699$	−16.2643	−0.615173
$700$	8.61405	0.325581
$701$	13.3174	0.502992	0.251496	−	0.967858i	$-0.419078\pi$
$701$	13.3174	0.502992	0.251496	+	0.967858i	$0.419078\pi$
$702$	1.33434	0.0503613
$703$	−11.0394	−0.416359
$704$	0	0
$705$	−5.73506	−0.215995
$706$	0.0521429	0.00196242
$707$	−18.0723	−0.679678
$708$	9.09834	0.341937
$709$	48.2055	1.81040	0.905198	−	0.424990i	$-0.139722\pi$
$709$	48.2055	1.81040	0.905198	+	0.424990i	$0.139722\pi$
$710$	1.59607	0.0598994
$711$	−8.85751	−0.332183
$712$	−2.62452	−0.0983582
$713$	−96.2532	−3.60471
$714$	−2.04907	−0.0766847
$715$	0	0
$716$	2.50375	0.0935694
$717$	17.2386	0.643787
$718$	−7.50619	−0.280129
$719$	−11.4733	−0.427881	−0.213940	−	0.976847i	$-0.568630\pi$
$719$	−11.4733	−0.427881	−0.213940	+	0.976847i	$0.568630\pi$
$720$	−2.42091	−0.0902221
$721$	−1.73047	−0.0644462
$722$	4.75732	0.177049
$723$	−5.41818	−0.201504
$724$	−8.46090	−0.314447
$725$	35.6385	1.32358
$726$	0	0
$727$	−29.5904	−1.09745	−0.548724	−	0.836004i	$-0.684886\pi$
$727$	−29.5904	−1.09745	−0.548724	+	0.836004i	$0.684886\pi$
$728$	−5.21634	−0.193330
$729$	1.00000	0.0370370
$730$	−1.46621	−0.0542667
$731$	−43.1009	−1.59414
$732$	−3.23543	−0.119585
$733$	−39.1482	−1.44597	−0.722986	−	0.690862i	$-0.757231\pi$
$733$	−39.1482	−1.44597	−0.722986	+	0.690862i	$0.757231\pi$
$734$	10.2911	0.379853
$735$	−0.698857	−0.0257777
$736$	31.2659	1.15248
$737$	0	0
$738$	0.401826	0.0147914
$739$	−15.6126	−0.574317	−0.287159	−	0.957883i	$-0.592711\pi$
$739$	−15.6126	−0.574317	−0.287159	+	0.957883i	$0.592711\pi$
$740$	8.23131	0.302589
$741$	7.92931	0.291290
$742$	0.709048	0.0260300
$743$	−29.8447	−1.09490	−0.547448	−	0.836840i	$-0.684401\pi$
$743$	−29.8447	−1.09490	−0.547448	+	0.836840i	$0.684401\pi$
$744$	12.3141	0.451459
$745$	4.98589	0.182669
$746$	−0.454817	−0.0166520
$747$	−5.71775	−0.209201
$748$	0	0
$749$	6.96982	0.254672
$750$	−2.00177	−0.0730944
$751$	1.52452	0.0556306	0.0278153	−	0.999613i	$-0.491145\pi$
$751$	1.52452	0.0556306	0.0278153	+	0.999613i	$0.491145\pi$
$752$	28.4276	1.03665
$753$	15.1995	0.553901
$754$	−10.5403	−0.383857
$755$	5.47821	0.199372
$756$	−1.90931	−0.0694410
$757$	−13.3841	−0.486453	−0.243226	−	0.969970i	$-0.578206\pi$
$757$	−13.3841	−0.486453	−0.243226	+	0.969970i	$0.578206\pi$
$758$	2.24657	0.0815990
$759$	0	0
$760$	1.47233	0.0534069
$761$	17.1185	0.620544	0.310272	−	0.950648i	$-0.399580\pi$
$761$	17.1185	0.620544	0.310272	+	0.950648i	$0.399580\pi$
$762$	3.65978	0.132580
$763$	−17.6531	−0.639086
$764$	−10.2065	−0.369257
$765$	−4.75525	−0.171926
$766$	−7.75389	−0.280160
$767$	21.1144	0.762395
$768$	9.22811	0.332991
$769$	15.9428	0.574912	0.287456	−	0.957794i	$-0.407191\pi$
$769$	15.9428	0.574912	0.287456	+	0.957794i	$0.407191\pi$
$770$	0	0
$771$	−26.6304	−0.959071
$772$	1.53480	0.0552385
$773$	−11.9350	−0.429274	−0.214637	−	0.976694i	$-0.568857\pi$
$773$	−11.9350	−0.429274	−0.214637	+	0.976694i	$0.568857\pi$
$774$	1.90754	0.0685651
$775$	−47.1913	−1.69516
$776$	−0.201757	−0.00724265
$777$	6.16884	0.221306
$778$	10.1324	0.363264
$779$	2.38785	0.0855538
$780$	−5.91232	−0.211695
$781$	0	0
$782$	18.8557	0.674277
$783$	−7.89932	−0.282299
$784$	3.46410	0.123718
$785$	13.2754	0.473820
$786$	5.69494	0.203132
$787$	2.80275	0.0999071	0.0499535	−	0.998752i	$-0.484093\pi$
$787$	2.80275	0.0999071	0.0499535	+	0.998752i	$0.484093\pi$
$788$	−44.6935	−1.59214
$789$	5.63979	0.200782
$790$	−1.86411	−0.0663222
$791$	11.7236	0.416844
$792$	0	0
$793$	−7.50839	−0.266631
$794$	5.93102	0.210484
$795$	1.64548	0.0583590
$796$	−44.5095	−1.57760
$797$	−13.6873	−0.484828	−0.242414	−	0.970173i	$-0.577939\pi$
$797$	−13.6873	−0.484828	−0.242414	+	0.970173i	$0.577939\pi$
$798$	0.538909	0.0190772
$799$	55.8386	1.97543
$800$	15.3291	0.541966
$801$	−2.22935	−0.0787701
$802$	−5.25097	−0.185418
$803$	0	0
$804$	23.9471	0.844549
$805$	6.43091	0.226660
$806$	13.9571	0.491620
$807$	−1.10958	−0.0390590
$808$	−21.2758	−0.748480
$809$	25.4980	0.896464	0.448232	−	0.893917i	$-0.352054\pi$
$809$	25.4980	0.896464	0.448232	+	0.893917i	$0.352054\pi$
$810$	0.210456	0.00739467
$811$	36.7404	1.29013	0.645065	−	0.764128i	$-0.276830\pi$
$811$	36.7404	1.29013	0.645065	+	0.764128i	$0.276830\pi$
$812$	15.0823	0.529284
$813$	13.7713	0.482981
$814$	0	0
$815$	8.99980	0.315249
$816$	23.5709	0.825145
$817$	11.3356	0.396582
$818$	2.38670	0.0834490
$819$	−4.43091	−0.154828
$820$	−1.78045	−0.0621762
$821$	−13.0737	−0.456274	−0.228137	−	0.973629i	$-0.573263\pi$
$821$	−13.0737	−0.456274	−0.228137	+	0.973629i	$0.573263\pi$
$822$	2.52337	0.0880125
$823$	48.7149	1.69809	0.849047	−	0.528318i	$-0.177177\pi$
$823$	48.7149	1.69809	0.849047	+	0.528318i	$0.177177\pi$
$824$	−2.03722	−0.0709700
$825$	0	0
$826$	1.43502	0.0499307
$827$	−53.8443	−1.87235	−0.936176	−	0.351532i	$-0.885661\pi$
$827$	−53.8443	−1.87235	−0.936176	+	0.351532i	$0.885661\pi$
$828$	17.5696	0.610585
$829$	11.1183	0.386154	0.193077	−	0.981184i	$-0.438153\pi$
$829$	11.1183	0.386154	0.193077	+	0.981184i	$0.438153\pi$
$830$	−1.20333	−0.0417683
$831$	7.90089	0.274079
$832$	26.1645	0.907092
$833$	6.80432	0.235756
$834$	2.96336	0.102613
$835$	0.00411207	0.000142304 0
$836$	0	0
$837$	10.4600	0.361550
$838$	3.62281	0.125148
$839$	26.8372	0.926524	0.463262	−	0.886221i	$-0.346679\pi$
$839$	26.8372	0.926524	0.463262	+	0.886221i	$0.346679\pi$
$840$	−0.822738	−0.0283872
$841$	33.3992	1.15170
$842$	0.410500	0.0141468
$843$	13.7596	0.473904
$844$	19.3709	0.666775
$845$	−4.63548	−0.159465
$846$	−2.47128	−0.0849645
$847$	0	0
$848$	−8.15631	−0.280089
$849$	−17.8650	−0.613126
$850$	9.24460	0.317087
$851$	−56.7659	−1.94591
$852$	−14.4800	−0.496076
$853$	34.8276	1.19247	0.596237	−	0.802809i	$-0.296662\pi$
$853$	34.8276	1.19247	0.596237	+	0.802809i	$0.296662\pi$
$854$	−0.510302	−0.0174622
$855$	1.25064	0.0427708
$856$	8.20530	0.280451
$857$	−38.4741	−1.31425	−0.657126	−	0.753781i	$-0.728228\pi$
$857$	−38.4741	−1.31425	−0.657126	+	0.753781i	$0.728228\pi$
$858$	0	0
$859$	−7.58039	−0.258639	−0.129320	−	0.991603i	$-0.541279\pi$
$859$	−7.58039	−0.258639	−0.129320	+	0.991603i	$0.541279\pi$
$860$	−8.45214	−0.288216
$861$	−1.33434	−0.0454741
$862$	−2.48128	−0.0845127
$863$	−32.4054	−1.10309	−0.551546	−	0.834145i	$-0.685962\pi$
$863$	−32.4054	−1.10309	−0.551546	+	0.834145i	$0.685962\pi$
$864$	−3.39771	−0.115593
$865$	−9.02875	−0.306987
$866$	−4.14699	−0.140921
$867$	29.2988	0.995040
$868$	−19.9714	−0.677873
$869$	0	0
$870$	−1.66246	−0.0563626
$871$	55.5736	1.88304
$872$	−20.7824	−0.703780
$873$	−0.171378	−0.00580027
$874$	−4.95906	−0.167743
$875$	6.64725	0.224718
$876$	13.3018	0.449427
$877$	−11.2438	−0.379676	−0.189838	−	0.981815i	$-0.560796\pi$
$877$	−11.2438	−0.379676	−0.189838	+	0.981815i	$0.560796\pi$
$878$	−5.63410	−0.190142
$879$	23.9721	0.808558
$880$	0	0
$881$	−35.8854	−1.20901	−0.604505	−	0.796601i	$-0.706629\pi$
$881$	−35.8854	−1.20901	−0.604505	+	0.796601i	$0.706629\pi$
$882$	−0.301143	−0.0101400
$883$	−12.8564	−0.432653	−0.216326	−	0.976321i	$-0.569407\pi$
$883$	−12.8564	−0.432653	−0.216326	+	0.976321i	$0.569407\pi$
$884$	57.5645	1.93610
$885$	3.33022	0.111944
$886$	−10.0325	−0.337049
$887$	−44.5324	−1.49525	−0.747627	−	0.664119i	$-0.768807\pi$
$887$	−44.5324	−1.49525	−0.747627	+	0.664119i	$0.768807\pi$
$888$	7.26234	0.243708
$889$	−12.1530	−0.407597
$890$	−0.469179	−0.0157269
$891$	0	0
$892$	13.0989	0.438583
$893$	−14.6856	−0.491435
$894$	2.14846	0.0718552
$895$	0.916435	0.0306331
$896$	8.57368	0.286427
$897$	40.7734	1.36138
$898$	1.12698	0.0376077
$899$	−82.6268	−2.75576
$900$	8.61405	0.287135
$901$	−16.0209	−0.533735
$902$	0	0
$903$	−6.33434	−0.210794
$904$	13.8018	0.459041
$905$	−3.09690	−0.102945
$906$	2.36060	0.0784258
$907$	−0.321610	−0.0106789	−0.00533944	−	0.999986i	$-0.501700\pi$
$907$	−0.321610	−0.0106789	−0.00533944	+	0.999986i	$0.501700\pi$
$908$	18.4275	0.611537
$909$	−18.0723	−0.599419
$910$	−0.932511	−0.0309124
$911$	42.8345	1.41917	0.709585	−	0.704620i	$-0.248882\pi$
$911$	42.8345	1.41917	0.709585	+	0.704620i	$0.248882\pi$
$912$	−6.19916	−0.205275
$913$	0	0
$914$	6.01525	0.198967
$915$	−1.18425	−0.0391500
$916$	−4.53369	−0.149797
$917$	−18.9111	−0.624499
$918$	−2.04907	−0.0676295
$919$	−41.3657	−1.36453	−0.682265	−	0.731105i	$-0.739005\pi$
$919$	−41.3657	−1.36453	−0.682265	+	0.731105i	$0.739005\pi$
$920$	7.57086	0.249604
$921$	24.2718	0.799782
$922$	−0.272350	−0.00896937
$923$	−33.6034	−1.10607
$924$	0	0
$925$	−27.8313	−0.915089
$926$	−7.01013	−0.230367
$927$	−1.73047	−0.0568362
$928$	26.8396	0.881054
$929$	39.4522	1.29439	0.647193	−	0.762326i	$-0.275943\pi$
$929$	39.4522	1.29439	0.647193	+	0.762326i	$0.275943\pi$
$930$	2.20137	0.0721856
$931$	−1.78954	−0.0586499
$932$	31.0537	1.01720
$933$	−1.97542	−0.0646724
$934$	−1.12934	−0.0369531
$935$	0	0
$936$	−5.21634	−0.170501
$937$	−17.9805	−0.587397	−0.293698	−	0.955898i	$-0.594886\pi$
$937$	−17.9805	−0.587397	−0.293698	+	0.955898i	$0.594886\pi$
$938$	3.77701	0.123324
$939$	3.04189	0.0992684
$940$	10.9500	0.357150
$941$	30.5804	0.996892	0.498446	−	0.866921i	$-0.333904\pi$
$941$	30.5804	0.996892	0.498446	+	0.866921i	$0.333904\pi$
$942$	5.72048	0.186383
$943$	12.2786	0.399847
$944$	−16.5073	−0.537267
$945$	−0.698857	−0.0227338
$946$	0	0
$947$	−8.17056	−0.265507	−0.132754	−	0.991149i	$-0.542382\pi$
$947$	−8.17056	−0.265507	−0.132754	+	0.991149i	$0.542382\pi$
$948$	16.9118	0.549268
$949$	30.8693	1.00206
$950$	−2.43134	−0.0788831
$951$	27.7329	0.899300
$952$	8.01047	0.259621
$953$	−8.38538	−0.271629	−0.135815	−	0.990734i	$-0.543365\pi$
$953$	−8.38538	−0.271629	−0.135815	+	0.990734i	$0.543365\pi$
$954$	0.709048	0.0229563
$955$	−3.73583	−0.120889
$956$	−32.9138	−1.06451
$957$	0	0
$958$	−8.74573	−0.282562
$959$	−8.37930	−0.270582
$960$	4.12675	0.133190
$961$	78.4114	2.52940
$962$	8.23131	0.265388
$963$	6.96982	0.224599
$964$	10.3450	0.333190
$965$	0.561775	0.0180842
$966$	2.77113	0.0891596
$967$	−51.4778	−1.65541	−0.827707	−	0.561161i	$-0.810355\pi$
$967$	−51.4778	−1.65541	−0.827707	+	0.561161i	$0.810355\pi$
$968$	0	0
$969$	−12.1766	−0.391170
$970$	−0.0360675	−0.00115806
$971$	−13.5974	−0.436360	−0.218180	−	0.975909i	$-0.570012\pi$
$971$	−13.5974	−0.436360	−0.218180	+	0.975909i	$0.570012\pi$
$972$	−1.90931	−0.0612412
$973$	−9.84039	−0.315468
$974$	3.74564	0.120018
$975$	19.9905	0.640208
$976$	5.87009	0.187897
$977$	19.6433	0.628446	0.314223	−	0.949349i	$-0.398256\pi$
$977$	19.6433	0.628446	0.314223	+	0.949349i	$0.398256\pi$
$978$	3.87809	0.124008
$979$	0	0
$980$	1.33434	0.0426238
$981$	−17.6531	−0.563621
$982$	1.94642	0.0621127
$983$	−57.0855	−1.82074	−0.910372	−	0.413791i	$-0.864204\pi$
$983$	−57.0855	−1.82074	−0.910372	+	0.413791i	$0.864204\pi$
$984$	−1.57086	−0.0500773
$985$	−16.3590	−0.521240
$986$	16.1863	0.515476
$987$	8.20634	0.261211
$988$	−15.1395	−0.481652
$989$	58.2888	1.85348
$990$	0	0
$991$	−32.7803	−1.04130	−0.520650	−	0.853770i	$-0.674310\pi$
$991$	−32.7803	−1.04130	−0.520650	+	0.853770i	$0.674310\pi$
$992$	−35.5401	−1.12840
$993$	−13.3502	−0.423656
$994$	−2.28383	−0.0724387
$995$	−16.2916	−0.516479
$996$	10.9170	0.345917
$997$	−33.3145	−1.05508	−0.527540	−	0.849530i	$-0.676886\pi$
$997$	−33.3145	−1.05508	−0.527540	+	0.849530i	$0.676886\pi$
$998$	4.00062	0.126637
$999$	6.16884	0.195174

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2541.2.a.bl.1.3	✓	4
3.2	odd	2		7623.2.a.cn.1.2		4
11.10	odd	2		2541.2.a.bp.1.2	yes	4
33.32	even	2		7623.2.a.cg.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2541.2.a.bl.1.3	✓	4	1.1	even	1	trivial
2541.2.a.bp.1.2	yes	4	11.10	odd	2
7623.2.a.cg.1.3		4	33.32	even	2
7623.2.a.cn.1.2		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)

\(f(q)\)	\(=\)	\(q-0.301143 q^{2} +1.00000 q^{3} -1.90931 q^{4} -0.698857 q^{5} -0.301143 q^{6} +1.00000 q^{7} +1.17726 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.301143 q^{2} +1.00000 q^{3} -1.90931 q^{4} -0.698857 q^{5} -0.301143 q^{6} +1.00000 q^{7} +1.17726 q^{8} +1.00000 q^{9} +0.210456 q^{10} -1.90931 q^{12} -4.43091 q^{13} -0.301143 q^{14} -0.698857 q^{15} +3.46410 q^{16} +6.80432 q^{17} -0.301143 q^{18} -1.78954 q^{19} +1.33434 q^{20} +1.00000 q^{21} -9.20204 q^{23} +1.17726 q^{24} -4.51160 q^{25} +1.33434 q^{26} +1.00000 q^{27} -1.90931 q^{28} -7.89932 q^{29} +0.210456 q^{30} +10.4600 q^{31} -3.39771 q^{32} -2.04907 q^{34} -0.698857 q^{35} -1.90931 q^{36} +6.16884 q^{37} +0.538909 q^{38} -4.43091 q^{39} -0.822738 q^{40} -1.33434 q^{41} -0.301143 q^{42} -6.33434 q^{43} -0.698857 q^{45} +2.77113 q^{46} +8.20634 q^{47} +3.46410 q^{48} +1.00000 q^{49} +1.35864 q^{50} +6.80432 q^{51} +8.45999 q^{52} -2.35452 q^{53} -0.301143 q^{54} +1.17726 q^{56} -1.78954 q^{57} +2.37882 q^{58} -4.76524 q^{59} +1.33434 q^{60} +1.69455 q^{61} -3.14995 q^{62} +1.00000 q^{63} -5.90501 q^{64} +3.09657 q^{65} -12.5423 q^{67} -12.9916 q^{68} -9.20204 q^{69} +0.210456 q^{70} +7.58387 q^{71} +1.17726 q^{72} -6.96681 q^{73} -1.85770 q^{74} -4.51160 q^{75} +3.41680 q^{76} +1.33434 q^{78} -8.85751 q^{79} -2.42091 q^{80} +1.00000 q^{81} +0.401826 q^{82} -5.71775 q^{83} -1.90931 q^{84} -4.75525 q^{85} +1.90754 q^{86} -7.89932 q^{87} -2.22935 q^{89} +0.210456 q^{90} -4.43091 q^{91} +17.5696 q^{92} +10.4600 q^{93} -2.47128 q^{94} +1.25064 q^{95} -3.39771 q^{96} -0.171378 q^{97} -0.301143 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 4 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} + 4 q^{7} + 4 q^{9}+O(q^{10}) \) 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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