LMFDB - Embedded newform 8470.2.a.cz.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8470,2,Mod(1,8470)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8470, 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("8470.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8470.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:	$67.6332905120$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.10784448.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 11x^{4} - 4x^{3} + 31x^{2} + 22x - 2 $ x^6 - 11x^4 - 4x^3 + 31x^2 + 22x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.40765$ of defining polynomial
Character	$\chi$	$=$	8470.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.34292 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.34292 q^{6} -1.00000 q^{7} -1.00000 q^{8} -1.19656 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.34292 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.34292 q^{6} -1.00000 q^{7} -1.00000 q^{8} -1.19656 q^{9} -1.00000 q^{10} -1.34292 q^{12} +4.31157 q^{13} +1.00000 q^{14} -1.34292 q^{15} +1.00000 q^{16} +2.63565 q^{17} +1.19656 q^{18} +6.54735 q^{19} +1.00000 q^{20} +1.34292 q^{21} -3.16521 q^{23} +1.34292 q^{24} +1.00000 q^{25} -4.31157 q^{26} +5.63565 q^{27} -1.00000 q^{28} +1.13193 q^{29} +1.34292 q^{30} +1.14637 q^{31} -1.00000 q^{32} -2.63565 q^{34} -1.00000 q^{35} -1.19656 q^{36} +3.13193 q^{37} -6.54735 q^{38} -5.79011 q^{39} -1.00000 q^{40} -0.521462 q^{41} -1.34292 q^{42} +4.96783 q^{43} -1.19656 q^{45} +3.16521 q^{46} +11.8090 q^{47} -1.34292 q^{48} +1.00000 q^{49} -1.00000 q^{50} -3.53948 q^{51} +4.31157 q^{52} +2.59396 q^{53} -5.63565 q^{54} +1.00000 q^{56} -8.79259 q^{57} -1.13193 q^{58} +10.9472 q^{59} -1.34292 q^{60} -5.82933 q^{61} -1.14637 q^{62} +1.19656 q^{63} +1.00000 q^{64} +4.31157 q^{65} -9.72249 q^{67} +2.63565 q^{68} +4.25063 q^{69} +1.00000 q^{70} -4.50169 q^{71} +1.19656 q^{72} -12.1269 q^{73} -3.13193 q^{74} -1.34292 q^{75} +6.54735 q^{76} +5.79011 q^{78} -17.0893 q^{79} +1.00000 q^{80} -3.97858 q^{81} +0.521462 q^{82} -9.06142 q^{83} +1.34292 q^{84} +2.63565 q^{85} -4.96783 q^{86} -1.52009 q^{87} +7.17843 q^{89} +1.19656 q^{90} -4.31157 q^{91} -3.16521 q^{92} -1.53948 q^{93} -11.8090 q^{94} +6.54735 q^{95} +1.34292 q^{96} +9.85645 q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{2} + 4 q^{3} + 6 q^{4} + 6 q^{5} - 4 q^{6} - 6 q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10}) $ 6 * q - 6 * q^2 + 4 * q^3 + 6 * q^4 + 6 * q^5 - 4 * q^6 - 6 * q^7 - 6 * q^8 + 2 * q^9	$ 6 q - 6 q^{2} + 4 q^{3} + 6 q^{4} + 6 q^{5} - 4 q^{6} - 6 q^{7} - 6 q^{8} + 2 q^{9} - 6 q^{10} + 4 q^{12} + 6 q^{14} + 4 q^{15} + 6 q^{16} - 2 q^{17} - 2 q^{18} + 6 q^{20} - 4 q^{21} + 4 q^{23} - 4 q^{24} + 6 q^{25} + 16 q^{27} - 6 q^{28} - 8 q^{29} - 4 q^{30} + 4 q^{31} - 6 q^{32} + 2 q^{34} - 6 q^{35} + 2 q^{36} + 4 q^{37} - 6 q^{40} - 12 q^{41} + 4 q^{42} + 6 q^{43} + 2 q^{45} - 4 q^{46} + 16 q^{47} + 4 q^{48} + 6 q^{49} - 6 q^{50} + 12 q^{53} - 16 q^{54} + 6 q^{56} - 8 q^{57} + 8 q^{58} + 22 q^{59} + 4 q^{60} + 4 q^{61} - 4 q^{62} - 2 q^{63} + 6 q^{64} + 20 q^{67} - 2 q^{68} + 12 q^{69} + 6 q^{70} + 14 q^{71} - 2 q^{72} - 18 q^{73} - 4 q^{74} + 4 q^{75} - 32 q^{79} + 6 q^{80} + 6 q^{81} + 12 q^{82} + 16 q^{83} - 4 q^{84} - 2 q^{85} - 6 q^{86} + 4 q^{87} + 4 q^{89} - 2 q^{90} + 4 q^{92} + 12 q^{93} - 16 q^{94} - 4 q^{96} + 4 q^{97} - 6 q^{98}+O(q^{100}) $ 6 * q - 6 * q^2 + 4 * q^3 + 6 * q^4 + 6 * q^5 - 4 * q^6 - 6 * q^7 - 6 * q^8 + 2 * q^9 - 6 * q^10 + 4 * q^12 + 6 * q^14 + 4 * q^15 + 6 * q^16 - 2 * q^17 - 2 * q^18 + 6 * q^20 - 4 * q^21 + 4 * q^23 - 4 * q^24 + 6 * q^25 + 16 * q^27 - 6 * q^28 - 8 * q^29 - 4 * q^30 + 4 * q^31 - 6 * q^32 + 2 * q^34 - 6 * q^35 + 2 * q^36 + 4 * q^37 - 6 * q^40 - 12 * q^41 + 4 * q^42 + 6 * q^43 + 2 * q^45 - 4 * q^46 + 16 * q^47 + 4 * q^48 + 6 * q^49 - 6 * q^50 + 12 * q^53 - 16 * q^54 + 6 * q^56 - 8 * q^57 + 8 * q^58 + 22 * q^59 + 4 * q^60 + 4 * q^61 - 4 * q^62 - 2 * q^63 + 6 * q^64 + 20 * q^67 - 2 * q^68 + 12 * q^69 + 6 * q^70 + 14 * q^71 - 2 * q^72 - 18 * q^73 - 4 * q^74 + 4 * q^75 - 32 * q^79 + 6 * q^80 + 6 * q^81 + 12 * q^82 + 16 * q^83 - 4 * q^84 - 2 * q^85 - 6 * q^86 + 4 * q^87 + 4 * q^89 - 2 * q^90 + 4 * q^92 + 12 * q^93 - 16 * q^94 - 4 * q^96 + 4 * q^97 - 6 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.34292	−0.775337	−0.387669	−	0.921799i	$-0.626719\pi$
$3$	−1.34292	−0.775337	−0.387669	+	0.921799i	$0.626719\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.34292	0.548246
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−1.19656	−0.398853
$10$	−1.00000	−0.316228
$11$	0	0
$11$	0	0
$12$	−1.34292	−0.387669
$13$	4.31157	1.19582	0.597908	−	0.801565i	$-0.295999\pi$
$13$	4.31157	1.19582	0.597908	+	0.801565i	$0.295999\pi$
$14$	1.00000	0.267261
$15$	−1.34292	−0.346741
$16$	1.00000	0.250000
$17$	2.63565	0.639240	0.319620	−	0.947546i	$-0.396445\pi$
$17$	2.63565	0.639240	0.319620	+	0.947546i	$0.396445\pi$
$18$	1.19656	0.282031
$19$	6.54735	1.50207	0.751033	−	0.660265i	$-0.229556\pi$
$19$	6.54735	1.50207	0.751033	+	0.660265i	$0.229556\pi$
$20$	1.00000	0.223607
$21$	1.34292	0.293050
$22$	0	0
$23$	−3.16521	−0.659992	−0.329996	−	0.943982i	$-0.607047\pi$
$23$	−3.16521	−0.659992	−0.329996	+	0.943982i	$0.607047\pi$
$24$	1.34292	0.274123
$25$	1.00000	0.200000
$26$	−4.31157	−0.845569
$27$	5.63565	1.08458
$28$	−1.00000	−0.188982
$29$	1.13193	0.210194	0.105097	−	0.994462i	$-0.466485\pi$
$29$	1.13193	0.210194	0.105097	+	0.994462i	$0.466485\pi$
$30$	1.34292	0.245183
$31$	1.14637	0.205893	0.102947	−	0.994687i	$-0.467173\pi$
$31$	1.14637	0.205893	0.102947	+	0.994687i	$0.467173\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	−2.63565	−0.452011
$35$	−1.00000	−0.169031
$36$	−1.19656	−0.199426
$37$	3.13193	0.514886	0.257443	−	0.966293i	$-0.417120\pi$
$37$	3.13193	0.514886	0.257443	+	0.966293i	$0.417120\pi$
$38$	−6.54735	−1.06212
$39$	−5.79011	−0.927160
$40$	−1.00000	−0.158114
$41$	−0.521462	−0.0814386	−0.0407193	−	0.999171i	$-0.512965\pi$
$41$	−0.521462	−0.0814386	−0.0407193	+	0.999171i	$0.512965\pi$
$42$	−1.34292	−0.207218
$43$	4.96783	0.757587	0.378793	−	0.925481i	$-0.376339\pi$
$43$	4.96783	0.757587	0.378793	+	0.925481i	$0.376339\pi$
$44$	0	0
$45$	−1.19656	−0.178372
$46$	3.16521	0.466685
$47$	11.8090	1.72251	0.861257	−	0.508170i	$-0.169678\pi$
$47$	11.8090	1.72251	0.861257	+	0.508170i	$0.169678\pi$
$48$	−1.34292	−0.193834
$49$	1.00000	0.142857
$50$	−1.00000	−0.141421
$51$	−3.53948	−0.495626
$52$	4.31157	0.597908
$53$	2.59396	0.356308	0.178154	−	0.984003i	$-0.442988\pi$
$53$	2.59396	0.356308	0.178154	+	0.984003i	$0.442988\pi$
$54$	−5.63565	−0.766915
$55$	0	0
$56$	1.00000	0.133631
$57$	−8.79259	−1.16461
$58$	−1.13193	−0.148630
$59$	10.9472	1.42521	0.712604	−	0.701567i	$-0.247516\pi$
$59$	10.9472	1.42521	0.712604	+	0.701567i	$0.247516\pi$
$60$	−1.34292	−0.173371
$61$	−5.82933	−0.746369	−0.373185	−	0.927757i	$-0.621734\pi$
$61$	−5.82933	−0.746369	−0.373185	+	0.927757i	$0.621734\pi$
$62$	−1.14637	−0.145589
$63$	1.19656	0.150752
$64$	1.00000	0.125000
$65$	4.31157	0.534785
$66$	0	0
$67$	−9.72249	−1.18779	−0.593895	−	0.804542i	$-0.702411\pi$
$67$	−9.72249	−1.18779	−0.593895	+	0.804542i	$0.702411\pi$
$68$	2.63565	0.319620
$69$	4.25063	0.511716
$70$	1.00000	0.119523
$71$	−4.50169	−0.534252	−0.267126	−	0.963662i	$-0.586074\pi$
$71$	−4.50169	−0.534252	−0.267126	+	0.963662i	$0.586074\pi$
$72$	1.19656	0.141016
$73$	−12.1269	−1.41934	−0.709672	−	0.704533i	$-0.751157\pi$
$73$	−12.1269	−1.41934	−0.709672	+	0.704533i	$0.751157\pi$
$74$	−3.13193	−0.364079
$75$	−1.34292	−0.155067
$76$	6.54735	0.751033
$77$	0	0
$78$	5.79011	0.655601
$79$	−17.0893	−1.92270	−0.961349	−	0.275334i	$-0.911212\pi$
$79$	−17.0893	−1.92270	−0.961349	+	0.275334i	$0.911212\pi$
$80$	1.00000	0.111803
$81$	−3.97858	−0.442064
$82$	0.521462	0.0575858
$83$	−9.06142	−0.994620	−0.497310	−	0.867573i	$-0.665679\pi$
$83$	−9.06142	−0.994620	−0.497310	+	0.867573i	$0.665679\pi$
$84$	1.34292	0.146525
$85$	2.63565	0.285877
$86$	−4.96783	−0.535695
$87$	−1.52009	−0.162971
$88$	0	0
$89$	7.17843	0.760913	0.380456	−	0.924799i	$-0.375767\pi$
$89$	7.17843	0.760913	0.380456	+	0.924799i	$0.375767\pi$
$90$	1.19656	0.126128
$91$	−4.31157	−0.451976
$92$	−3.16521	−0.329996
$93$	−1.53948	−0.159637
$94$	−11.8090	−1.21800
$95$	6.54735	0.671744
$96$	1.34292	0.137062
$97$	9.85645	1.00077	0.500385	−	0.865803i	$-0.333192\pi$
$97$	9.85645	1.00077	0.500385	+	0.865803i	$0.333192\pi$
$98$	−1.00000	−0.101015
$99$	0	0
$100$	1.00000	0.100000
$101$	−4.36976	−0.434807	−0.217404	−	0.976082i	$-0.569759\pi$
$101$	−4.36976	−0.434807	−0.217404	+	0.976082i	$0.569759\pi$
$102$	3.53948	0.350461
$103$	14.2978	1.40881	0.704403	−	0.709800i	$-0.251215\pi$
$103$	14.2978	1.40881	0.704403	+	0.709800i	$0.251215\pi$
$104$	−4.31157	−0.422785
$105$	1.34292	0.131056
$106$	−2.59396	−0.251948
$107$	4.78019	0.462118	0.231059	−	0.972940i	$-0.425781\pi$
$107$	4.78019	0.462118	0.231059	+	0.972940i	$0.425781\pi$
$108$	5.63565	0.542291
$109$	−2.58240	−0.247349	−0.123675	−	0.992323i	$-0.539468\pi$
$109$	−2.58240	−0.247349	−0.123675	+	0.992323i	$0.539468\pi$
$110$	0	0
$111$	−4.20594	−0.399210
$112$	−1.00000	−0.0944911
$113$	12.9414	1.21743	0.608714	−	0.793390i	$-0.291686\pi$
$113$	12.9414	1.21743	0.608714	+	0.793390i	$0.291686\pi$
$114$	8.79259	0.823501
$115$	−3.16521	−0.295157
$116$	1.13193	0.105097
$117$	−5.15905	−0.476954
$118$	−10.9472	−1.00777
$119$	−2.63565	−0.241610
$120$	1.34292	0.122592
$121$	0	0
$122$	5.82933	0.527763
$123$	0.700283	0.0631424
$124$	1.14637	0.102947
$125$	1.00000	0.0894427
$126$	−1.19656	−0.106598
$127$	−10.9841	−0.974680	−0.487340	−	0.873212i	$-0.662033\pi$
$127$	−10.9841	−0.974680	−0.487340	+	0.873212i	$0.662033\pi$
$128$	−1.00000	−0.0883883
$129$	−6.67141	−0.587385
$130$	−4.31157	−0.378150
$131$	11.9717	1.04597	0.522986	−	0.852341i	$-0.324818\pi$
$131$	11.9717	1.04597	0.522986	+	0.852341i	$0.324818\pi$
$132$	0	0
$133$	−6.54735	−0.567727
$134$	9.72249	0.839895
$135$	5.63565	0.485040
$136$	−2.63565	−0.226005
$137$	−9.37916	−0.801315	−0.400658	−	0.916228i	$-0.631218\pi$
$137$	−9.37916	−0.801315	−0.400658	+	0.916228i	$0.631218\pi$
$138$	−4.25063	−0.361838
$139$	−11.1498	−0.945714	−0.472857	−	0.881139i	$-0.656777\pi$
$139$	−11.1498	−0.945714	−0.472857	+	0.881139i	$0.656777\pi$
$140$	−1.00000	−0.0845154
$141$	−15.8585	−1.33553
$142$	4.50169	0.377773
$143$	0	0
$144$	−1.19656	−0.0997131
$145$	1.13193	0.0940016
$146$	12.1269	1.00363
$147$	−1.34292	−0.110762
$148$	3.13193	0.257443
$149$	−5.51928	−0.452157	−0.226079	−	0.974109i	$-0.572591\pi$
$149$	−5.51928	−0.452157	−0.226079	+	0.974109i	$0.572591\pi$
$150$	1.34292	0.109649
$151$	−9.66388	−0.786435	−0.393218	−	0.919445i	$-0.628638\pi$
$151$	−9.66388	−0.786435	−0.393218	+	0.919445i	$0.628638\pi$
$152$	−6.54735	−0.531060
$153$	−3.15371	−0.254962
$154$	0	0
$155$	1.14637	0.0920783
$156$	−5.79011	−0.463580
$157$	16.8181	1.34223	0.671114	−	0.741355i	$-0.265816\pi$
$157$	16.8181	1.34223	0.671114	+	0.741355i	$0.265816\pi$
$158$	17.0893	1.35955
$159$	−3.48349	−0.276259
$160$	−1.00000	−0.0790569
$161$	3.16521	0.249453
$162$	3.97858	0.312587
$163$	−22.8952	−1.79329	−0.896644	−	0.442753i	$-0.854002\pi$
$163$	−22.8952	−1.79329	−0.896644	+	0.442753i	$0.854002\pi$
$164$	−0.521462	−0.0407193
$165$	0	0
$166$	9.06142	0.703303
$167$	8.29513	0.641896	0.320948	−	0.947097i	$-0.395998\pi$
$167$	8.29513	0.641896	0.320948	+	0.947097i	$0.395998\pi$
$168$	−1.34292	−0.103609
$169$	5.58967	0.429975
$170$	−2.63565	−0.202145
$171$	−7.83428	−0.599103
$172$	4.96783	0.378793
$173$	21.9024	1.66521	0.832606	−	0.553866i	$-0.186848\pi$
$173$	21.9024	1.66521	0.832606	+	0.553866i	$0.186848\pi$
$174$	1.52009	0.115238
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	−14.7013	−1.10502
$178$	−7.17843	−0.538046
$179$	−3.11079	−0.232511	−0.116256	−	0.993219i	$-0.537089\pi$
$179$	−3.11079	−0.232511	−0.116256	+	0.993219i	$0.537089\pi$
$180$	−1.19656	−0.0891861
$181$	4.58252	0.340616	0.170308	−	0.985391i	$-0.445524\pi$
$181$	4.58252	0.340616	0.170308	+	0.985391i	$0.445524\pi$
$182$	4.31157	0.319595
$183$	7.82834	0.578688
$184$	3.16521	0.233342
$185$	3.13193	0.230264
$186$	1.53948	0.112880
$187$	0	0
$188$	11.8090	0.861257
$189$	−5.63565	−0.409934
$190$	−6.54735	−0.474995
$191$	4.33382	0.313584	0.156792	−	0.987632i	$-0.449885\pi$
$191$	4.33382	0.313584	0.156792	+	0.987632i	$0.449885\pi$
$192$	−1.34292	−0.0969171
$193$	13.4284	0.966599	0.483300	−	0.875455i	$-0.339438\pi$
$193$	13.4284	0.966599	0.483300	+	0.875455i	$0.339438\pi$
$194$	−9.85645	−0.707652
$195$	−5.79011	−0.414639
$196$	1.00000	0.0714286
$197$	−11.8667	−0.845466	−0.422733	−	0.906254i	$-0.638929\pi$
$197$	−11.8667	−0.845466	−0.422733	+	0.906254i	$0.638929\pi$
$198$	0	0
$199$	−14.5672	−1.03264	−0.516319	−	0.856396i	$-0.672698\pi$
$199$	−14.5672	−1.03264	−0.516319	+	0.856396i	$0.672698\pi$
$200$	−1.00000	−0.0707107
$201$	13.0565	0.920938
$202$	4.36976	0.307455
$203$	−1.13193	−0.0794458
$204$	−3.53948	−0.247813
$205$	−0.521462	−0.0364205
$206$	−14.2978	−0.996177
$207$	3.78735	0.263239
$208$	4.31157	0.298954
$209$	0	0
$210$	−1.34292	−0.0926705
$211$	2.79716	0.192565	0.0962823	−	0.995354i	$-0.469305\pi$
$211$	2.79716	0.192565	0.0962823	+	0.995354i	$0.469305\pi$
$212$	2.59396	0.178154
$213$	6.04542	0.414226
$214$	−4.78019	−0.326767
$215$	4.96783	0.338803
$216$	−5.63565	−0.383458
$217$	−1.14637	−0.0778204
$218$	2.58240	0.174902
$219$	16.2855	1.10047
$220$	0	0
$221$	11.3638	0.764413
$222$	4.20594	0.282284
$223$	19.6450	1.31553	0.657763	−	0.753225i	$-0.271503\pi$
$223$	19.6450	1.31553	0.657763	+	0.753225i	$0.271503\pi$
$224$	1.00000	0.0668153
$225$	−1.19656	−0.0797705
$226$	−12.9414	−0.860851
$227$	−7.63636	−0.506843	−0.253422	−	0.967356i	$-0.581556\pi$
$227$	−7.63636	−0.506843	−0.253422	+	0.967356i	$0.581556\pi$
$228$	−8.79259	−0.582303
$229$	−1.56937	−0.103707	−0.0518536	−	0.998655i	$-0.516513\pi$
$229$	−1.56937	−0.103707	−0.0518536	+	0.998655i	$0.516513\pi$
$230$	3.16521	0.208708
$231$	0	0
$232$	−1.13193	−0.0743148
$233$	22.2894	1.46023	0.730114	−	0.683325i	$-0.239467\pi$
$233$	22.2894	1.46023	0.730114	+	0.683325i	$0.239467\pi$
$234$	5.15905	0.337257
$235$	11.8090	0.770331
$236$	10.9472	0.712604
$237$	22.9496	1.49074
$238$	2.63565	0.170844
$239$	5.92057	0.382970	0.191485	−	0.981496i	$-0.438670\pi$
$239$	5.92057	0.382970	0.191485	+	0.981496i	$0.438670\pi$
$240$	−1.34292	−0.0866853
$241$	26.9422	1.73550	0.867749	−	0.497002i	$-0.165566\pi$
$241$	26.9422	1.73550	0.867749	+	0.497002i	$0.165566\pi$
$242$	0	0
$243$	−11.5640	−0.741833
$244$	−5.82933	−0.373185
$245$	1.00000	0.0638877
$246$	−0.700283	−0.0446484
$247$	28.2294	1.79619
$248$	−1.14637	−0.0727943
$249$	12.1688	0.771166
$250$	−1.00000	−0.0632456
$251$	−10.5437	−0.665514	−0.332757	−	0.943013i	$-0.607979\pi$
$251$	−10.5437	−0.665514	−0.332757	+	0.943013i	$0.607979\pi$
$252$	1.19656	0.0753760
$253$	0	0
$254$	10.9841	0.689203
$255$	−3.53948	−0.221651
$256$	1.00000	0.0625000
$257$	19.8973	1.24116	0.620581	−	0.784142i	$-0.286897\pi$
$257$	19.8973	1.24116	0.620581	+	0.784142i	$0.286897\pi$
$258$	6.67141	0.415344
$259$	−3.13193	−0.194609
$260$	4.31157	0.267392
$261$	−1.35442	−0.0838364
$262$	−11.9717	−0.739613
$263$	12.5871	0.776155	0.388077	−	0.921627i	$-0.373139\pi$
$263$	12.5871	0.776155	0.388077	+	0.921627i	$0.373139\pi$
$264$	0	0
$265$	2.59396	0.159346
$266$	6.54735	0.401444
$267$	−9.64009	−0.589964
$268$	−9.72249	−0.593895
$269$	−6.90634	−0.421087	−0.210544	−	0.977584i	$-0.567523\pi$
$269$	−6.90634	−0.421087	−0.210544	+	0.977584i	$0.567523\pi$
$270$	−5.63565	−0.342975
$271$	7.59420	0.461315	0.230657	−	0.973035i	$-0.425912\pi$
$271$	7.59420	0.461315	0.230657	+	0.973035i	$0.425912\pi$
$272$	2.63565	0.159810
$273$	5.79011	0.350434
$274$	9.37916	0.566616
$275$	0	0
$276$	4.25063	0.255858
$277$	−16.8832	−1.01442	−0.507208	−	0.861824i	$-0.669322\pi$
$277$	−16.8832	−1.01442	−0.507208	+	0.861824i	$0.669322\pi$
$278$	11.1498	0.668721
$279$	−1.37169	−0.0821211
$280$	1.00000	0.0597614
$281$	−9.62695	−0.574296	−0.287148	−	0.957886i	$-0.592707\pi$
$281$	−9.62695	−0.574296	−0.287148	+	0.957886i	$0.592707\pi$
$282$	15.8585	0.944361
$283$	−22.5755	−1.34198	−0.670988	−	0.741468i	$-0.734130\pi$
$283$	−22.5755	−1.34198	−0.670988	+	0.741468i	$0.734130\pi$
$284$	−4.50169	−0.267126
$285$	−8.79259	−0.520828
$286$	0	0
$287$	0.521462	0.0307809
$288$	1.19656	0.0705078
$289$	−10.0533	−0.591372
$290$	−1.13193	−0.0664691
$291$	−13.2365	−0.775935
$292$	−12.1269	−0.709672
$293$	21.6239	1.26328	0.631640	−	0.775262i	$-0.282382\pi$
$293$	21.6239	1.26328	0.631640	+	0.775262i	$0.282382\pi$
$294$	1.34292	0.0783209
$295$	10.9472	0.637372
$296$	−3.13193	−0.182040
$297$	0	0
$298$	5.51928	0.319723
$299$	−13.6470	−0.789228
$300$	−1.34292	−0.0775337
$301$	−4.96783	−0.286341
$302$	9.66388	0.556094
$303$	5.86825	0.337122
$304$	6.54735	0.375516
$305$	−5.82933	−0.333787
$306$	3.15371	0.180286
$307$	−9.26120	−0.528565	−0.264282	−	0.964445i	$-0.585135\pi$
$307$	−9.26120	−0.528565	−0.264282	+	0.964445i	$0.585135\pi$
$308$	0	0
$309$	−19.2009	−1.09230
$310$	−1.14637	−0.0651092
$311$	6.38689	0.362167	0.181084	−	0.983468i	$-0.442040\pi$
$311$	6.38689	0.362167	0.181084	+	0.983468i	$0.442040\pi$
$312$	5.79011	0.327801
$313$	−1.93070	−0.109130	−0.0545649	−	0.998510i	$-0.517377\pi$
$313$	−1.93070	−0.109130	−0.0545649	+	0.998510i	$0.517377\pi$
$314$	−16.8181	−0.949098
$315$	1.19656	0.0674184
$316$	−17.0893	−0.961349
$317$	−11.8763	−0.667039	−0.333519	−	0.942743i	$-0.608236\pi$
$317$	−11.8763	−0.667039	−0.333519	+	0.942743i	$0.608236\pi$
$318$	3.48349	0.195344
$319$	0	0
$320$	1.00000	0.0559017
$321$	−6.41942	−0.358297
$322$	−3.16521	−0.176390
$323$	17.2566	0.960180
$324$	−3.97858	−0.221032
$325$	4.31157	0.239163
$326$	22.8952	1.26805
$327$	3.46797	0.191779
$328$	0.521462	0.0287929
$329$	−11.8090	−0.651049
$330$	0	0
$331$	−28.5755	−1.57065	−0.785324	−	0.619084i	$-0.787504\pi$
$331$	−28.5755	−1.57065	−0.785324	+	0.619084i	$0.787504\pi$
$332$	−9.06142	−0.497310
$333$	−3.74753	−0.205364
$334$	−8.29513	−0.453889
$335$	−9.72249	−0.531196
$336$	1.34292	0.0732625
$337$	8.38514	0.456768	0.228384	−	0.973571i	$-0.426656\pi$
$337$	8.38514	0.456768	0.228384	+	0.973571i	$0.426656\pi$
$338$	−5.58967	−0.304038
$339$	−17.3793	−0.943916
$340$	2.63565	0.142938
$341$	0	0
$342$	7.83428	0.423629
$343$	−1.00000	−0.0539949
$344$	−4.96783	−0.267847
$345$	4.25063	0.228846
$346$	−21.9024	−1.17748
$347$	−23.5535	−1.26442	−0.632210	−	0.774797i	$-0.717852\pi$
$347$	−23.5535	−1.26442	−0.632210	+	0.774797i	$0.717852\pi$
$348$	−1.52009	−0.0814856
$349$	25.2540	1.35182	0.675909	−	0.736985i	$-0.263751\pi$
$349$	25.2540	1.35182	0.675909	+	0.736985i	$0.263751\pi$
$350$	1.00000	0.0534522
$351$	24.2985	1.29696
$352$	0	0
$353$	20.9078	1.11281	0.556406	−	0.830911i	$-0.312180\pi$
$353$	20.9078	1.11281	0.556406	+	0.830911i	$0.312180\pi$
$354$	14.7013	0.781365
$355$	−4.50169	−0.238925
$356$	7.17843	0.380456
$357$	3.53948	0.187329
$358$	3.11079	0.164410
$359$	−25.9084	−1.36739	−0.683696	−	0.729767i	$-0.739628\pi$
$359$	−25.9084	−1.36739	−0.683696	+	0.729767i	$0.739628\pi$
$360$	1.19656	0.0630641
$361$	23.8678	1.25620
$362$	−4.58252	−0.240852
$363$	0	0
$364$	−4.31157	−0.225988
$365$	−12.1269	−0.634750
$366$	−7.82834	−0.409194
$367$	−20.8650	−1.08914	−0.544572	−	0.838714i	$-0.683308\pi$
$367$	−20.8650	−1.08914	−0.544572	+	0.838714i	$0.683308\pi$
$368$	−3.16521	−0.164998
$369$	0.623959	0.0324820
$370$	−3.13193	−0.162821
$371$	−2.59396	−0.134672
$372$	−1.53948	−0.0798184
$373$	10.1570	0.525911	0.262956	−	0.964808i	$-0.415303\pi$
$373$	10.1570	0.525911	0.262956	+	0.964808i	$0.415303\pi$
$374$	0	0
$375$	−1.34292	−0.0693482
$376$	−11.8090	−0.609000
$377$	4.88039	0.251353
$378$	5.63565	0.289867
$379$	29.5378	1.51726	0.758628	−	0.651524i	$-0.225870\pi$
$379$	29.5378	1.51726	0.758628	+	0.651524i	$0.225870\pi$
$380$	6.54735	0.335872
$381$	14.7508	0.755706
$382$	−4.33382	−0.221738
$383$	26.2888	1.34330	0.671648	−	0.740871i	$-0.265587\pi$
$383$	26.2888	1.34330	0.671648	+	0.740871i	$0.265587\pi$
$384$	1.34292	0.0685308
$385$	0	0
$386$	−13.4284	−0.683489
$387$	−5.94429	−0.302165
$388$	9.85645	0.500385
$389$	−8.64078	−0.438105	−0.219052	−	0.975713i	$-0.570297\pi$
$389$	−8.64078	−0.438105	−0.219052	+	0.975713i	$0.570297\pi$
$390$	5.79011	0.293194
$391$	−8.34240	−0.421893
$392$	−1.00000	−0.0505076
$393$	−16.0771	−0.810980
$394$	11.8667	0.597835
$395$	−17.0893	−0.859856
$396$	0	0
$397$	35.1598	1.76462	0.882309	−	0.470670i	$-0.155988\pi$
$397$	35.1598	1.76462	0.882309	+	0.470670i	$0.155988\pi$
$398$	14.5672	0.730186
$399$	8.79259	0.440180
$400$	1.00000	0.0500000
$401$	−7.99484	−0.399243	−0.199622	−	0.979873i	$-0.563971\pi$
$401$	−7.99484	−0.399243	−0.199622	+	0.979873i	$0.563971\pi$
$402$	−13.0565	−0.651202
$403$	4.94264	0.246210
$404$	−4.36976	−0.217404
$405$	−3.97858	−0.197697
$406$	1.13193	0.0561767
$407$	0	0
$408$	3.53948	0.175230
$409$	−1.92553	−0.0952114	−0.0476057	−	0.998866i	$-0.515159\pi$
$409$	−1.92553	−0.0952114	−0.0476057	+	0.998866i	$0.515159\pi$
$410$	0.521462	0.0257532
$411$	12.5955	0.621290
$412$	14.2978	0.704403
$413$	−10.9472	−0.538678
$414$	−3.78735	−0.186138
$415$	−9.06142	−0.444808
$416$	−4.31157	−0.211392
$417$	14.9733	0.733247
$418$	0	0
$419$	−22.4861	−1.09852	−0.549259	−	0.835652i	$-0.685090\pi$
$419$	−22.4861	−1.09852	−0.549259	+	0.835652i	$0.685090\pi$
$420$	1.34292	0.0655279
$421$	−23.3112	−1.13612	−0.568059	−	0.822988i	$-0.692306\pi$
$421$	−23.3112	−1.13612	−0.568059	+	0.822988i	$0.692306\pi$
$422$	−2.79716	−0.136164
$423$	−14.1301	−0.687029
$424$	−2.59396	−0.125974
$425$	2.63565	0.127848
$426$	−6.04542	−0.292902
$427$	5.82933	0.282101
$428$	4.78019	0.231059
$429$	0	0
$430$	−4.96783	−0.239570
$431$	−15.2591	−0.735003	−0.367502	−	0.930023i	$-0.619787\pi$
$431$	−15.2591	−0.735003	−0.367502	+	0.930023i	$0.619787\pi$
$432$	5.63565	0.271146
$433$	−0.722365	−0.0347146	−0.0173573	−	0.999849i	$-0.505525\pi$
$433$	−0.722365	−0.0347146	−0.0173573	+	0.999849i	$0.505525\pi$
$434$	1.14637	0.0550273
$435$	−1.52009	−0.0728829
$436$	−2.58240	−0.123675
$437$	−20.7237	−0.991350
$438$	−16.2855	−0.778149
$439$	−31.7894	−1.51722	−0.758612	−	0.651543i	$-0.774122\pi$
$439$	−31.7894	−1.51722	−0.758612	+	0.651543i	$0.774122\pi$
$440$	0	0
$441$	−1.19656	−0.0569789
$442$	−11.3638	−0.540522
$443$	29.1789	1.38633	0.693166	−	0.720778i	$-0.256215\pi$
$443$	29.1789	1.38633	0.693166	+	0.720778i	$0.256215\pi$
$444$	−4.20594	−0.199605
$445$	7.17843	0.340290
$446$	−19.6450	−0.930217
$447$	7.41197	0.350574
$448$	−1.00000	−0.0472456
$449$	18.6378	0.879570	0.439785	−	0.898103i	$-0.355055\pi$
$449$	18.6378	0.879570	0.439785	+	0.898103i	$0.355055\pi$
$450$	1.19656	0.0564063
$451$	0	0
$452$	12.9414	0.608714
$453$	12.9778	0.609752
$454$	7.63636	0.358392
$455$	−4.31157	−0.202130
$456$	8.79259	0.411751
$457$	−3.01602	−0.141084	−0.0705418	−	0.997509i	$-0.522473\pi$
$457$	−3.01602	−0.141084	−0.0705418	+	0.997509i	$0.522473\pi$
$458$	1.56937	0.0733320
$459$	14.8536	0.693308
$460$	−3.16521	−0.147579
$461$	16.8872	0.786513	0.393257	−	0.919429i	$-0.371348\pi$
$461$	16.8872	0.786513	0.393257	+	0.919429i	$0.371348\pi$
$462$	0	0
$463$	0.180188	0.00837403	0.00418701	−	0.999991i	$-0.498667\pi$
$463$	0.180188	0.00837403	0.00418701	+	0.999991i	$0.498667\pi$
$464$	1.13193	0.0525485
$465$	−1.53948	−0.0713917
$466$	−22.2894	−1.03254
$467$	12.4723	0.577147	0.288574	−	0.957458i	$-0.406819\pi$
$467$	12.4723	0.577147	0.288574	+	0.957458i	$0.406819\pi$
$468$	−5.15905	−0.238477
$469$	9.72249	0.448943
$470$	−11.8090	−0.544707
$471$	−22.5854	−1.04068
$472$	−10.9472	−0.503887
$473$	0	0
$474$	−22.9496	−1.05411
$475$	6.54735	0.300413
$476$	−2.63565	−0.120805
$477$	−3.10382	−0.142114
$478$	−5.92057	−0.270801
$479$	1.55428	0.0710166	0.0355083	−	0.999369i	$-0.488695\pi$
$479$	1.55428	0.0710166	0.0355083	+	0.999369i	$0.488695\pi$
$480$	1.34292	0.0612958
$481$	13.5035	0.615709
$482$	−26.9422	−1.22718
$483$	−4.25063	−0.193410
$484$	0	0
$485$	9.85645	0.447558
$486$	11.5640	0.524555
$487$	29.2641	1.32608	0.663042	−	0.748582i	$-0.269265\pi$
$487$	29.2641	1.32608	0.663042	+	0.748582i	$0.269265\pi$
$488$	5.82933	0.263881
$489$	30.7464	1.39040
$490$	−1.00000	−0.0451754
$491$	2.35553	0.106304	0.0531518	−	0.998586i	$-0.483073\pi$
$491$	2.35553	0.106304	0.0531518	+	0.998586i	$0.483073\pi$
$492$	0.700283	0.0315712
$493$	2.98337	0.134364
$494$	−28.2294	−1.27010
$495$	0	0
$496$	1.14637	0.0514733
$497$	4.50169	0.201928
$498$	−12.1688	−0.545297
$499$	25.2783	1.13161	0.565807	−	0.824538i	$-0.308565\pi$
$499$	25.2783	1.13161	0.565807	+	0.824538i	$0.308565\pi$
$500$	1.00000	0.0447214
$501$	−11.1397	−0.497686
$502$	10.5437	0.470589
$503$	3.23636	0.144302	0.0721510	−	0.997394i	$-0.477014\pi$
$503$	3.23636	0.144302	0.0721510	+	0.997394i	$0.477014\pi$
$504$	−1.19656	−0.0532989
$505$	−4.36976	−0.194452
$506$	0	0
$507$	−7.50650	−0.333375
$508$	−10.9841	−0.487340
$509$	39.5692	1.75387	0.876937	−	0.480606i	$-0.159583\pi$
$509$	39.5692	1.75387	0.876937	+	0.480606i	$0.159583\pi$
$510$	3.53948	0.156731
$511$	12.1269	0.536461
$512$	−1.00000	−0.0441942
$513$	36.8986	1.62911
$514$	−19.8973	−0.877634
$515$	14.2978	0.630037
$516$	−6.67141	−0.293692
$517$	0	0
$518$	3.13193	0.137609
$519$	−29.4133	−1.29110
$520$	−4.31157	−0.189075
$521$	−0.586854	−0.0257105	−0.0128553	−	0.999917i	$-0.504092\pi$
$521$	−0.586854	−0.0257105	−0.0128553	+	0.999917i	$0.504092\pi$
$522$	1.35442	0.0592813
$523$	22.7742	0.995846	0.497923	−	0.867221i	$-0.334096\pi$
$523$	22.7742	0.995846	0.497923	+	0.867221i	$0.334096\pi$
$524$	11.9717	0.522986
$525$	1.34292	0.0586100
$526$	−12.5871	−0.548824
$527$	3.02142	0.131615
$528$	0	0
$529$	−12.9815	−0.564411
$530$	−2.59396	−0.112674
$531$	−13.0990	−0.568448
$532$	−6.54735	−0.283864
$533$	−2.24832	−0.0973856
$534$	9.64009	0.417167
$535$	4.78019	0.206665
$536$	9.72249	0.419947
$537$	4.17755	0.180274
$538$	6.90634	0.297753
$539$	0	0
$540$	5.63565	0.242520
$541$	−36.2359	−1.55790	−0.778952	−	0.627084i	$-0.784248\pi$
$541$	−36.2359	−1.55790	−0.778952	+	0.627084i	$0.784248\pi$
$542$	−7.59420	−0.326199
$543$	−6.15397	−0.264092
$544$	−2.63565	−0.113003
$545$	−2.58240	−0.110618
$546$	−5.79011	−0.247794
$547$	−17.1863	−0.734831	−0.367416	−	0.930057i	$-0.619757\pi$
$547$	−17.1863	−0.734831	−0.367416	+	0.930057i	$0.619757\pi$
$548$	−9.37916	−0.400658
$549$	6.97513	0.297691
$550$	0	0
$551$	7.41113	0.315725
$552$	−4.25063	−0.180919
$553$	17.0893	0.726711
$554$	16.8832	0.717300
$555$	−4.20594	−0.178532
$556$	−11.1498	−0.472857
$557$	31.6410	1.34067	0.670335	−	0.742058i	$-0.266150\pi$
$557$	31.6410	1.34067	0.670335	+	0.742058i	$0.266150\pi$
$558$	1.37169	0.0580684
$559$	21.4192	0.905934
$560$	−1.00000	−0.0422577
$561$	0	0
$562$	9.62695	0.406089
$563$	−28.5238	−1.20213	−0.601066	−	0.799199i	$-0.705257\pi$
$563$	−28.5238	−1.20213	−0.601066	+	0.799199i	$0.705257\pi$
$564$	−15.8585	−0.667764
$565$	12.9414	0.544450
$566$	22.5755	0.948920
$567$	3.97858	0.167085
$568$	4.50169	0.188887
$569$	17.6880	0.741520	0.370760	−	0.928729i	$-0.379097\pi$
$569$	17.6880	0.741520	0.370760	+	0.928729i	$0.379097\pi$
$570$	8.79259	0.368281
$571$	−11.2551	−0.471012	−0.235506	−	0.971873i	$-0.575675\pi$
$571$	−11.2551	−0.471012	−0.235506	+	0.971873i	$0.575675\pi$
$572$	0	0
$573$	−5.81999	−0.243134
$574$	−0.521462	−0.0217654
$575$	−3.16521	−0.131998
$576$	−1.19656	−0.0498566
$577$	3.75289	0.156235	0.0781175	−	0.996944i	$-0.475109\pi$
$577$	3.75289	0.156235	0.0781175	+	0.996944i	$0.475109\pi$
$578$	10.0533	0.418163
$579$	−18.0333	−0.749440
$580$	1.13193	0.0470008
$581$	9.06142	0.375931
$582$	13.2365	0.548669
$583$	0	0
$584$	12.1269	0.501814
$585$	−5.15905	−0.213300
$586$	−21.6239	−0.893274
$587$	−31.3692	−1.29475	−0.647374	−	0.762173i	$-0.724133\pi$
$587$	−31.3692	−1.29475	−0.647374	+	0.762173i	$0.724133\pi$
$588$	−1.34292	−0.0553812
$589$	7.50566	0.309265
$590$	−10.9472	−0.450690
$591$	15.9360	0.655521
$592$	3.13193	0.128721
$593$	−4.02015	−0.165088	−0.0825439	−	0.996587i	$-0.526304\pi$
$593$	−4.02015	−0.165088	−0.0825439	+	0.996587i	$0.526304\pi$
$594$	0	0
$595$	−2.63565	−0.108051
$596$	−5.51928	−0.226079
$597$	19.5626	0.800643
$598$	13.6470	0.558069
$599$	−15.0102	−0.613301	−0.306651	−	0.951822i	$-0.599208\pi$
$599$	−15.0102	−0.613301	−0.306651	+	0.951822i	$0.599208\pi$
$600$	1.34292	0.0548246
$601$	20.0520	0.817939	0.408970	−	0.912548i	$-0.365888\pi$
$601$	20.0520	0.817939	0.408970	+	0.912548i	$0.365888\pi$
$602$	4.96783	0.202474
$603$	11.6335	0.473753
$604$	−9.66388	−0.393218
$605$	0	0
$606$	−5.86825	−0.238381
$607$	−17.0030	−0.690129	−0.345064	−	0.938579i	$-0.612143\pi$
$607$	−17.0030	−0.690129	−0.345064	+	0.938579i	$0.612143\pi$
$608$	−6.54735	−0.265530
$609$	1.52009	0.0615973
$610$	5.82933	0.236023
$611$	50.9152	2.05981
$612$	−3.15371	−0.127481
$613$	17.2655	0.697347	0.348673	−	0.937244i	$-0.386632\pi$
$613$	17.2655	0.697347	0.348673	+	0.937244i	$0.386632\pi$
$614$	9.26120	0.373752
$615$	0.700283	0.0282381
$616$	0	0
$617$	−18.0616	−0.727134	−0.363567	−	0.931568i	$-0.618441\pi$
$617$	−18.0616	−0.727134	−0.363567	+	0.931568i	$0.618441\pi$
$618$	19.2009	0.772373
$619$	32.2086	1.29457	0.647287	−	0.762247i	$-0.275904\pi$
$619$	32.2086	1.29457	0.647287	+	0.762247i	$0.275904\pi$
$620$	1.14637	0.0460391
$621$	−17.8380	−0.715815
$622$	−6.38689	−0.256091
$623$	−7.17843	−0.287598
$624$	−5.79011	−0.231790
$625$	1.00000	0.0400000
$626$	1.93070	0.0771664
$627$	0	0
$628$	16.8181	0.671114
$629$	8.25468	0.329136
$630$	−1.19656	−0.0476720
$631$	10.0492	0.400052	0.200026	−	0.979791i	$-0.435897\pi$
$631$	10.0492	0.400052	0.200026	+	0.979791i	$0.435897\pi$
$632$	17.0893	0.679776
$633$	−3.75637	−0.149302
$634$	11.8763	0.471667
$635$	−10.9841	−0.435890
$636$	−3.48349	−0.138129
$637$	4.31157	0.170831
$638$	0	0
$639$	5.38653	0.213088
$640$	−1.00000	−0.0395285
$641$	−22.0387	−0.870476	−0.435238	−	0.900315i	$-0.643336\pi$
$641$	−22.0387	−0.870476	−0.435238	+	0.900315i	$0.643336\pi$
$642$	6.41942	0.253354
$643$	−18.2425	−0.719414	−0.359707	−	0.933065i	$-0.617123\pi$
$643$	−18.2425	−0.719414	−0.359707	+	0.933065i	$0.617123\pi$
$644$	3.16521	0.124727
$645$	−6.67141	−0.262686
$646$	−17.2566	−0.678950
$647$	−10.5244	−0.413755	−0.206878	−	0.978367i	$-0.566330\pi$
$647$	−10.5244	−0.413755	−0.206878	+	0.978367i	$0.566330\pi$
$648$	3.97858	0.156293
$649$	0	0
$650$	−4.31157	−0.169114
$651$	1.53948	0.0603370
$652$	−22.8952	−0.896644
$653$	30.1567	1.18012	0.590061	−	0.807358i	$-0.299104\pi$
$653$	30.1567	1.18012	0.590061	+	0.807358i	$0.299104\pi$
$654$	−3.46797	−0.135608
$655$	11.9717	0.467773
$656$	−0.521462	−0.0203597
$657$	14.5105	0.566109
$658$	11.8090	0.460361
$659$	37.5753	1.46373	0.731863	−	0.681451i	$-0.238651\pi$
$659$	37.5753	1.46373	0.731863	+	0.681451i	$0.238651\pi$
$660$	0	0
$661$	−24.1822	−0.940579	−0.470290	−	0.882512i	$-0.655851\pi$
$661$	−24.1822	−0.940579	−0.470290	+	0.882512i	$0.655851\pi$
$662$	28.5755	1.11062
$663$	−15.2607	−0.592678
$664$	9.06142	0.351651
$665$	−6.54735	−0.253895
$666$	3.74753	0.145214
$667$	−3.58279	−0.138726
$668$	8.29513	0.320948
$669$	−26.3817	−1.01998
$670$	9.72249	0.375612
$671$	0	0
$672$	−1.34292	−0.0518044
$673$	38.4279	1.48129	0.740643	−	0.671899i	$-0.234521\pi$
$673$	38.4279	1.48129	0.740643	+	0.671899i	$0.234521\pi$
$674$	−8.38514	−0.322983
$675$	5.63565	0.216916
$676$	5.58967	0.214987
$677$	−47.8223	−1.83796	−0.918980	−	0.394304i	$-0.870986\pi$
$677$	−47.8223	−1.83796	−0.918980	+	0.394304i	$0.870986\pi$
$678$	17.3793	0.667450
$679$	−9.85645	−0.378256
$680$	−2.63565	−0.101073
$681$	10.2550	0.392974
$682$	0	0
$683$	4.96235	0.189879	0.0949395	−	0.995483i	$-0.469734\pi$
$683$	4.96235	0.189879	0.0949395	+	0.995483i	$0.469734\pi$
$684$	−7.83428	−0.299551
$685$	−9.37916	−0.358359
$686$	1.00000	0.0381802
$687$	2.10755	0.0804080
$688$	4.96783	0.189397
$689$	11.1841	0.426078
$690$	−4.25063	−0.161819
$691$	28.2052	1.07298	0.536488	−	0.843908i	$-0.319751\pi$
$691$	28.2052	1.07298	0.536488	+	0.843908i	$0.319751\pi$
$692$	21.9024	0.832606
$693$	0	0
$694$	23.5535	0.894080
$695$	−11.1498	−0.422936
$696$	1.52009	0.0576190
$697$	−1.37439	−0.0520588
$698$	−25.2540	−0.955879
$699$	−29.9330	−1.13217
$700$	−1.00000	−0.0377964
$701$	16.4276	0.620461	0.310230	−	0.950661i	$-0.399594\pi$
$701$	16.4276	0.620461	0.310230	+	0.950661i	$0.399594\pi$
$702$	−24.2985	−0.917089
$703$	20.5058	0.773392
$704$	0	0
$705$	−15.8585	−0.597266
$706$	−20.9078	−0.786877
$707$	4.36976	0.164342
$708$	−14.7013	−0.552508
$709$	26.0841	0.979610	0.489805	−	0.871832i	$-0.337068\pi$
$709$	26.0841	0.979610	0.489805	+	0.871832i	$0.337068\pi$
$710$	4.50169	0.168945
$711$	20.4483	0.766873
$712$	−7.17843	−0.269023
$713$	−3.62849	−0.135888
$714$	−3.53948	−0.132462
$715$	0	0
$716$	−3.11079	−0.116256
$717$	−7.95087	−0.296931
$718$	25.9084	0.966892
$719$	16.7246	0.623723	0.311862	−	0.950128i	$-0.399047\pi$
$719$	16.7246	0.623723	0.311862	+	0.950128i	$0.399047\pi$
$720$	−1.19656	−0.0445931
$721$	−14.2978	−0.532479
$722$	−23.8678	−0.888267
$723$	−36.1813	−1.34560
$724$	4.58252	0.170308
$725$	1.13193	0.0420388
$726$	0	0
$727$	30.1587	1.11853	0.559263	−	0.828990i	$-0.311084\pi$
$727$	30.1587	1.11853	0.559263	+	0.828990i	$0.311084\pi$
$728$	4.31157	0.159798
$729$	27.4653	1.01724
$730$	12.1269	0.448836
$731$	13.0935	0.484280
$732$	7.82834	0.289344
$733$	−29.3635	−1.08456	−0.542282	−	0.840197i	$-0.682440\pi$
$733$	−29.3635	−1.08456	−0.542282	+	0.840197i	$0.682440\pi$
$734$	20.8650	0.770141
$735$	−1.34292	−0.0495345
$736$	3.16521	0.116671
$737$	0	0
$738$	−0.623959	−0.0229682
$739$	17.5186	0.644432	0.322216	−	0.946666i	$-0.395572\pi$
$739$	17.5186	0.644432	0.322216	+	0.946666i	$0.395572\pi$
$740$	3.13193	0.115132
$741$	−37.9099	−1.39265
$742$	2.59396	0.0952273
$743$	21.7292	0.797169	0.398584	−	0.917132i	$-0.369502\pi$
$743$	21.7292	0.797169	0.398584	+	0.917132i	$0.369502\pi$
$744$	1.53948	0.0564401
$745$	−5.51928	−0.202211
$746$	−10.1570	−0.371876
$747$	10.8425	0.396707
$748$	0	0
$749$	−4.78019	−0.174664
$750$	1.34292	0.0490366
$751$	37.8166	1.37995	0.689974	−	0.723835i	$-0.257622\pi$
$751$	37.8166	1.37995	0.689974	+	0.723835i	$0.257622\pi$
$752$	11.8090	0.430628
$753$	14.1594	0.515998
$754$	−4.88039	−0.177734
$755$	−9.66388	−0.351705
$756$	−5.63565	−0.204967
$757$	45.5840	1.65678	0.828390	−	0.560152i	$-0.189257\pi$
$757$	45.5840	1.65678	0.828390	+	0.560152i	$0.189257\pi$
$758$	−29.5378	−1.07286
$759$	0	0
$760$	−6.54735	−0.237497
$761$	−36.0860	−1.30812	−0.654058	−	0.756445i	$-0.726935\pi$
$761$	−36.0860	−1.30812	−0.654058	+	0.756445i	$0.726935\pi$
$762$	−14.7508	−0.534365
$763$	2.58240	0.0934893
$764$	4.33382	0.156792
$765$	−3.15371	−0.114023
$766$	−26.2888	−0.949853
$767$	47.1998	1.70429
$768$	−1.34292	−0.0484586
$769$	28.8806	1.04146	0.520730	−	0.853722i	$-0.325660\pi$
$769$	28.8806	1.04146	0.520730	+	0.853722i	$0.325660\pi$
$770$	0	0
$771$	−26.7206	−0.962319
$772$	13.4284	0.483300
$773$	41.6626	1.49850	0.749250	−	0.662287i	$-0.230414\pi$
$773$	41.6626	1.49850	0.749250	+	0.662287i	$0.230414\pi$
$774$	5.94429	0.213663
$775$	1.14637	0.0411787
$776$	−9.85645	−0.353826
$777$	4.20594	0.150887
$778$	8.64078	0.309787
$779$	−3.41419	−0.122326
$780$	−5.79011	−0.207319
$781$	0	0
$782$	8.34240	0.298323
$783$	6.37916	0.227973
$784$	1.00000	0.0357143
$785$	16.8181	0.600262
$786$	16.0771	0.573450
$787$	13.3405	0.475537	0.237768	−	0.971322i	$-0.423584\pi$
$787$	13.3405	0.475537	0.237768	+	0.971322i	$0.423584\pi$
$788$	−11.8667	−0.422733
$789$	−16.9035	−0.601781
$790$	17.0893	0.608010
$791$	−12.9414	−0.460144
$792$	0	0
$793$	−25.1336	−0.892520
$794$	−35.1598	−1.24777
$795$	−3.48349	−0.123547
$796$	−14.5672	−0.516319
$797$	32.9064	1.16560	0.582802	−	0.812614i	$-0.301956\pi$
$797$	32.9064	1.16560	0.582802	+	0.812614i	$0.301956\pi$
$798$	−8.79259	−0.311254
$799$	31.1243	1.10110
$800$	−1.00000	−0.0353553
$801$	−8.58941	−0.303492
$802$	7.99484	0.282308
$803$	0	0
$804$	13.0565	0.460469
$805$	3.16521	0.111559
$806$	−4.94264	−0.174097
$807$	9.27468	0.326484
$808$	4.36976	0.153728
$809$	27.0311	0.950363	0.475182	−	0.879888i	$-0.342382\pi$
$809$	27.0311	0.950363	0.475182	+	0.879888i	$0.342382\pi$
$810$	3.97858	0.139793
$811$	18.8842	0.663112	0.331556	−	0.943435i	$-0.392426\pi$
$811$	18.8842	0.663112	0.331556	+	0.943435i	$0.392426\pi$
$812$	−1.13193	−0.0397229
$813$	−10.1984	−0.357674
$814$	0	0
$815$	−22.8952	−0.801982
$816$	−3.53948	−0.123907
$817$	32.5261	1.13794
$818$	1.92553	0.0673247
$819$	5.15905	0.180272
$820$	−0.521462	−0.0182102
$821$	18.9968	0.662992	0.331496	−	0.943457i	$-0.392447\pi$
$821$	18.9968	0.662992	0.331496	+	0.943457i	$0.392447\pi$
$822$	−12.5955	−0.439318
$823$	32.5539	1.13476	0.567378	−	0.823457i	$-0.307958\pi$
$823$	32.5539	1.13476	0.567378	+	0.823457i	$0.307958\pi$
$824$	−14.2978	−0.498088
$825$	0	0
$826$	10.9472	0.380903
$827$	10.3868	0.361183	0.180592	−	0.983558i	$-0.442199\pi$
$827$	10.3868	0.361183	0.180592	+	0.983558i	$0.442199\pi$
$828$	3.78735	0.131620
$829$	−13.1965	−0.458332	−0.229166	−	0.973387i	$-0.573600\pi$
$829$	−13.1965	−0.458332	−0.229166	+	0.973387i	$0.573600\pi$
$830$	9.06142	0.314527
$831$	22.6729	0.786514
$832$	4.31157	0.149477
$833$	2.63565	0.0913200
$834$	−14.9733	−0.518484
$835$	8.29513	0.287065
$836$	0	0
$837$	6.46052	0.223308
$838$	22.4861	0.776769
$839$	−20.4534	−0.706128	−0.353064	−	0.935599i	$-0.614860\pi$
$839$	−20.4534	−0.706128	−0.353064	+	0.935599i	$0.614860\pi$
$840$	−1.34292	−0.0463352
$841$	−27.7187	−0.955819
$842$	23.3112	0.803357
$843$	12.9283	0.445273
$844$	2.79716	0.0962823
$845$	5.58967	0.192291
$846$	14.1301	0.485803
$847$	0	0
$848$	2.59396	0.0890770
$849$	30.3172	1.04048
$850$	−2.63565	−0.0904022
$851$	−9.91321	−0.339820
$852$	6.04542	0.207113
$853$	39.8363	1.36397	0.681984	−	0.731367i	$-0.261117\pi$
$853$	39.8363	1.36397	0.681984	+	0.731367i	$0.261117\pi$
$854$	−5.82933	−0.199476
$855$	−7.83428	−0.267927
$856$	−4.78019	−0.163383
$857$	−50.5306	−1.72609	−0.863047	−	0.505124i	$-0.831447\pi$
$857$	−50.5306	−1.72609	−0.863047	+	0.505124i	$0.831447\pi$
$858$	0	0
$859$	−34.2746	−1.16943	−0.584717	−	0.811238i	$-0.698794\pi$
$859$	−34.2746	−1.16943	−0.584717	+	0.811238i	$0.698794\pi$
$860$	4.96783	0.169401
$861$	−0.700283	−0.0238656
$862$	15.2591	0.519726
$863$	50.1602	1.70747	0.853736	−	0.520706i	$-0.174331\pi$
$863$	50.1602	1.70747	0.853736	+	0.520706i	$0.174331\pi$
$864$	−5.63565	−0.191729
$865$	21.9024	0.744705
$866$	0.722365	0.0245470
$867$	13.5008	0.458513
$868$	−1.14637	−0.0389102
$869$	0	0
$870$	1.52009	0.0515360
$871$	−41.9192	−1.42038
$872$	2.58240	0.0874512
$873$	−11.7938	−0.399160
$874$	20.7237	0.700991
$875$	−1.00000	−0.0338062
$876$	16.2855	0.550235
$877$	42.9675	1.45091	0.725454	−	0.688270i	$-0.241630\pi$
$877$	42.9675	1.45091	0.725454	+	0.688270i	$0.241630\pi$
$878$	31.7894	1.07284
$879$	−29.0392	−0.979468
$880$	0	0
$881$	7.10467	0.239362	0.119681	−	0.992812i	$-0.461813\pi$
$881$	7.10467	0.239362	0.119681	+	0.992812i	$0.461813\pi$
$882$	1.19656	0.0402902
$883$	−41.1823	−1.38589	−0.692947	−	0.720989i	$-0.743688\pi$
$883$	−41.1823	−1.38589	−0.692947	+	0.720989i	$0.743688\pi$
$884$	11.3638	0.382207
$885$	−14.7013	−0.494178
$886$	−29.1789	−0.980284
$887$	31.0647	1.04305	0.521525	−	0.853236i	$-0.325363\pi$
$887$	31.0647	1.04305	0.521525	+	0.853236i	$0.325363\pi$
$888$	4.20594	0.141142
$889$	10.9841	0.368395
$890$	−7.17843	−0.240622
$891$	0	0
$892$	19.6450	0.657763
$893$	77.3174	2.58733
$894$	−7.41197	−0.247893
$895$	−3.11079	−0.103982
$896$	1.00000	0.0334077
$897$	18.3269	0.611918
$898$	−18.6378	−0.621950
$899$	1.29760	0.0432775
$900$	−1.19656	−0.0398853
$901$	6.83678	0.227766
$902$	0	0
$903$	6.67141	0.222011
$904$	−12.9414	−0.430426
$905$	4.58252	0.152328
$906$	−12.9778	−0.431160
$907$	17.7502	0.589386	0.294693	−	0.955592i	$-0.404783\pi$
$907$	17.7502	0.589386	0.294693	+	0.955592i	$0.404783\pi$
$908$	−7.63636	−0.253422
$909$	5.22867	0.173424
$910$	4.31157	0.142927
$911$	27.0043	0.894694	0.447347	−	0.894361i	$-0.352369\pi$
$911$	27.0043	0.894694	0.447347	+	0.894361i	$0.352369\pi$
$912$	−8.79259	−0.291152
$913$	0	0
$914$	3.01602	0.0997611
$915$	7.82834	0.258797
$916$	−1.56937	−0.0518536
$917$	−11.9717	−0.395340
$918$	−14.8536	−0.490243
$919$	−1.75332	−0.0578368	−0.0289184	−	0.999582i	$-0.509206\pi$
$919$	−1.75332	−0.0578368	−0.0289184	+	0.999582i	$0.509206\pi$
$920$	3.16521	0.104354
$921$	12.4371	0.409816
$922$	−16.8872	−0.556149
$923$	−19.4094	−0.638867
$924$	0	0
$925$	3.13193	0.102977
$926$	−0.180188	−0.00592133
$927$	−17.1082	−0.561906
$928$	−1.13193	−0.0371574
$929$	1.51606	0.0497403	0.0248702	−	0.999691i	$-0.492083\pi$
$929$	1.51606	0.0497403	0.0248702	+	0.999691i	$0.492083\pi$
$930$	1.53948	0.0504816
$931$	6.54735	0.214581
$932$	22.2894	0.730114
$933$	−8.57710	−0.280802
$934$	−12.4723	−0.408105
$935$	0	0
$936$	5.15905	0.168629
$937$	31.6995	1.03558	0.517789	−	0.855508i	$-0.326755\pi$
$937$	31.6995	1.03558	0.517789	+	0.855508i	$0.326755\pi$
$938$	−9.72249	−0.317450
$939$	2.59279	0.0846124
$940$	11.8090	0.385166
$941$	−15.4489	−0.503619	−0.251810	−	0.967777i	$-0.581026\pi$
$941$	−15.4489	−0.503619	−0.251810	+	0.967777i	$0.581026\pi$
$942$	22.5854	0.735871
$943$	1.65054	0.0537488
$944$	10.9472	0.356302
$945$	−5.63565	−0.183328
$946$	0	0
$947$	10.0390	0.326222	0.163111	−	0.986608i	$-0.447847\pi$
$947$	10.0390	0.326222	0.163111	+	0.986608i	$0.447847\pi$
$948$	22.9496	0.745369
$949$	−52.2859	−1.69727
$950$	−6.54735	−0.212424
$951$	15.9489	0.517180
$952$	2.63565	0.0854220
$953$	41.2604	1.33656	0.668278	−	0.743912i	$-0.267032\pi$
$953$	41.2604	1.33656	0.668278	+	0.743912i	$0.267032\pi$
$954$	3.10382	0.100490
$955$	4.33382	0.140239
$956$	5.92057	0.191485
$957$	0	0
$958$	−1.55428	−0.0502164
$959$	9.37916	0.302869
$960$	−1.34292	−0.0433427
$961$	−29.6858	−0.957608
$962$	−13.5035	−0.435372
$963$	−5.71977	−0.184317
$964$	26.9422	0.867749
$965$	13.4284	0.432276
$966$	4.25063	0.136762
$967$	18.8930	0.607557	0.303778	−	0.952743i	$-0.401752\pi$
$967$	18.8930	0.607557	0.303778	+	0.952743i	$0.401752\pi$
$968$	0	0
$969$	−23.1742	−0.744463
$970$	−9.85645	−0.316472
$971$	13.6882	0.439277	0.219638	−	0.975581i	$-0.429512\pi$
$971$	13.6882	0.439277	0.219638	+	0.975581i	$0.429512\pi$
$972$	−11.5640	−0.370917
$973$	11.1498	0.357446
$974$	−29.2641	−0.937683
$975$	−5.79011	−0.185432
$976$	−5.82933	−0.186592
$977$	34.5173	1.10431	0.552153	−	0.833743i	$-0.313807\pi$
$977$	34.5173	1.10431	0.552153	+	0.833743i	$0.313807\pi$
$978$	−30.7464	−0.983163
$979$	0	0
$980$	1.00000	0.0319438
$981$	3.09000	0.0986560
$982$	−2.35553	−0.0751680
$983$	−29.7951	−0.950316	−0.475158	−	0.879900i	$-0.657609\pi$
$983$	−29.7951	−0.950316	−0.475158	+	0.879900i	$0.657609\pi$
$984$	−0.700283	−0.0223242
$985$	−11.8667	−0.378104
$986$	−2.98337	−0.0950099
$987$	15.8585	0.504782
$988$	28.2294	0.898096
$989$	−15.7242	−0.500001
$990$	0	0
$991$	39.5393	1.25601	0.628004	−	0.778210i	$-0.283872\pi$
$991$	39.5393	1.25601	0.628004	+	0.778210i	$0.283872\pi$
$992$	−1.14637	−0.0363971
$993$	38.3746	1.21778
$994$	−4.50169	−0.142785
$995$	−14.5672	−0.461810
$996$	12.1688	0.385583
$997$	−8.24240	−0.261040	−0.130520	−	0.991446i	$-0.541665\pi$
$997$	−8.24240	−0.261040	−0.130520	+	0.991446i	$0.541665\pi$
$998$	−25.2783	−0.800172
$999$	17.6505	0.558436

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8470.2.a.cz.1.2	✓	6
11.10	odd	2		8470.2.a.df.1.1	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8470.2.a.cz.1.2	✓	6	1.1	even	1	trivial
8470.2.a.df.1.1	yes	6	11.10	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:	\( N \)	\(=\)	\( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8470.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.34292 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.34292 q^{6} -1.00000 q^{7} -1.00000 q^{8} -1.19656 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.34292 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.34292 q^{6} -1.00000 q^{7} -1.00000 q^{8} -1.19656 q^{9} -1.00000 q^{10} -1.34292 q^{12} +4.31157 q^{13} +1.00000 q^{14} -1.34292 q^{15} +1.00000 q^{16} +2.63565 q^{17} +1.19656 q^{18} +6.54735 q^{19} +1.00000 q^{20} +1.34292 q^{21} -3.16521 q^{23} +1.34292 q^{24} +1.00000 q^{25} -4.31157 q^{26} +5.63565 q^{27} -1.00000 q^{28} +1.13193 q^{29} +1.34292 q^{30} +1.14637 q^{31} -1.00000 q^{32} -2.63565 q^{34} -1.00000 q^{35} -1.19656 q^{36} +3.13193 q^{37} -6.54735 q^{38} -5.79011 q^{39} -1.00000 q^{40} -0.521462 q^{41} -1.34292 q^{42} +4.96783 q^{43} -1.19656 q^{45} +3.16521 q^{46} +11.8090 q^{47} -1.34292 q^{48} +1.00000 q^{49} -1.00000 q^{50} -3.53948 q^{51} +4.31157 q^{52} +2.59396 q^{53} -5.63565 q^{54} +1.00000 q^{56} -8.79259 q^{57} -1.13193 q^{58} +10.9472 q^{59} -1.34292 q^{60} -5.82933 q^{61} -1.14637 q^{62} +1.19656 q^{63} +1.00000 q^{64} +4.31157 q^{65} -9.72249 q^{67} +2.63565 q^{68} +4.25063 q^{69} +1.00000 q^{70} -4.50169 q^{71} +1.19656 q^{72} -12.1269 q^{73} -3.13193 q^{74} -1.34292 q^{75} +6.54735 q^{76} +5.79011 q^{78} -17.0893 q^{79} +1.00000 q^{80} -3.97858 q^{81} +0.521462 q^{82} -9.06142 q^{83} +1.34292 q^{84} +2.63565 q^{85} -4.96783 q^{86} -1.52009 q^{87} +7.17843 q^{89} +1.19656 q^{90} -4.31157 q^{91} -3.16521 q^{92} -1.53948 q^{93} -11.8090 q^{94} +6.54735 q^{95} +1.34292 q^{96} +9.85645 q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{2} + 4 q^{3} + 6 q^{4} + 6 q^{5} - 4 q^{6} - 6 q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10}) \) 6 * q - 6 * q^2 + 4 * q^3 + 6 * q^4 + 6 * q^5 - 4 * q^6 - 6 * q^7 - 6 * q^8 + 2 * q^9	\( 6 q - 6 q^{2} + 4 q^{3} + 6 q^{4} + 6 q^{5} - 4 q^{6} - 6 q^{7} - 6 q^{8} + 2 q^{9} - 6 q^{10} + 4 q^{12} + 6 q^{14} + 4 q^{15} + 6 q^{16} - 2 q^{17} - 2 q^{18} + 6 q^{20} - 4 q^{21} + 4 q^{23} - 4 q^{24} + 6 q^{25} + 16 q^{27} - 6 q^{28} - 8 q^{29} - 4 q^{30} + 4 q^{31} - 6 q^{32} + 2 q^{34} - 6 q^{35} + 2 q^{36} + 4 q^{37} - 6 q^{40} - 12 q^{41} + 4 q^{42} + 6 q^{43} + 2 q^{45} - 4 q^{46} + 16 q^{47} + 4 q^{48} + 6 q^{49} - 6 q^{50} + 12 q^{53} - 16 q^{54} + 6 q^{56} - 8 q^{57} + 8 q^{58} + 22 q^{59} + 4 q^{60} + 4 q^{61} - 4 q^{62} - 2 q^{63} + 6 q^{64} + 20 q^{67} - 2 q^{68} + 12 q^{69} + 6 q^{70} + 14 q^{71} - 2 q^{72} - 18 q^{73} - 4 q^{74} + 4 q^{75} - 32 q^{79} + 6 q^{80} + 6 q^{81} + 12 q^{82} + 16 q^{83} - 4 q^{84} - 2 q^{85} - 6 q^{86} + 4 q^{87} + 4 q^{89} - 2 q^{90} + 4 q^{92} + 12 q^{93} - 16 q^{94} - 4 q^{96} + 4 q^{97} - 6 q^{98}+O(q^{100}) \) 6 * q - 6 * q^2 + 4 * q^3 + 6 * q^4 + 6 * q^5 - 4 * q^6 - 6 * q^7 - 6 * q^8 + 2 * q^9 - 6 * q^10 + 4 * q^12 + 6 * q^14 + 4 * q^15 + 6 * q^16 - 2 * q^17 - 2 * q^18 + 6 * q^20 - 4 * q^21 + 4 * q^23 - 4 * q^24 + 6 * q^25 + 16 * q^27 - 6 * q^28 - 8 * q^29 - 4 * q^30 + 4 * q^31 - 6 * q^32 + 2 * q^34 - 6 * q^35 + 2 * q^36 + 4 * q^37 - 6 * q^40 - 12 * q^41 + 4 * q^42 + 6 * q^43 + 2 * q^45 - 4 * q^46 + 16 * q^47 + 4 * q^48 + 6 * q^49 - 6 * q^50 + 12 * q^53 - 16 * q^54 + 6 * q^56 - 8 * q^57 + 8 * q^58 + 22 * q^59 + 4 * q^60 + 4 * q^61 - 4 * q^62 - 2 * q^63 + 6 * q^64 + 20 * q^67 - 2 * q^68 + 12 * q^69 + 6 * q^70 + 14 * q^71 - 2 * q^72 - 18 * q^73 - 4 * q^74 + 4 * q^75 - 32 * q^79 + 6 * q^80 + 6 * q^81 + 12 * q^82 + 16 * q^83 - 4 * q^84 - 2 * q^85 - 6 * q^86 + 4 * q^87 + 4 * q^89 - 2 * q^90 + 4 * q^92 + 12 * q^93 - 16 * q^94 - 4 * q^96 + 4 * q^97 - 6 * q^98

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