LMFDB - Embedded newform 510.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [510,2,Mod(1,510)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(510, 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("510.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.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:	$4.07237050309$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{6}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 6 $ x^2 - 6
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.44949$ of defining polynomial
Character	$\chi$	$=$	510.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -4.89898 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -4.89898 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{12} +6.89898 q^{13} +4.89898 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +4.00000 q^{19} +1.00000 q^{20} +4.89898 q^{21} -4.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -6.89898 q^{26} -1.00000 q^{27} -4.89898 q^{28} +6.00000 q^{29} +1.00000 q^{30} +4.00000 q^{31} -1.00000 q^{32} +1.00000 q^{34} -4.89898 q^{35} +1.00000 q^{36} +6.00000 q^{37} -4.00000 q^{38} -6.89898 q^{39} -1.00000 q^{40} -2.89898 q^{41} -4.89898 q^{42} +8.89898 q^{43} +1.00000 q^{45} +4.00000 q^{46} +9.79796 q^{47} -1.00000 q^{48} +17.0000 q^{49} -1.00000 q^{50} +1.00000 q^{51} +6.89898 q^{52} -7.79796 q^{53} +1.00000 q^{54} +4.89898 q^{56} -4.00000 q^{57} -6.00000 q^{58} +4.89898 q^{59} -1.00000 q^{60} +11.7980 q^{61} -4.00000 q^{62} -4.89898 q^{63} +1.00000 q^{64} +6.89898 q^{65} +0.898979 q^{67} -1.00000 q^{68} +4.00000 q^{69} +4.89898 q^{70} -8.89898 q^{71} -1.00000 q^{72} -10.8990 q^{73} -6.00000 q^{74} -1.00000 q^{75} +4.00000 q^{76} +6.89898 q^{78} -5.79796 q^{79} +1.00000 q^{80} +1.00000 q^{81} +2.89898 q^{82} +13.7980 q^{83} +4.89898 q^{84} -1.00000 q^{85} -8.89898 q^{86} -6.00000 q^{87} -7.79796 q^{89} -1.00000 q^{90} -33.7980 q^{91} -4.00000 q^{92} -4.00000 q^{93} -9.79796 q^{94} +4.00000 q^{95} +1.00000 q^{96} -12.6969 q^{97} -17.0000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{12} + 4 q^{13} - 2 q^{15} + 2 q^{16} - 2 q^{17} - 2 q^{18} + 8 q^{19} + 2 q^{20} - 8 q^{23} + 2 q^{24} + 2 q^{25} - 4 q^{26} - 2 q^{27} + 12 q^{29} + 2 q^{30} + 8 q^{31} - 2 q^{32} + 2 q^{34} + 2 q^{36} + 12 q^{37} - 8 q^{38} - 4 q^{39} - 2 q^{40} + 4 q^{41} + 8 q^{43} + 2 q^{45} + 8 q^{46} - 2 q^{48} + 34 q^{49} - 2 q^{50} + 2 q^{51} + 4 q^{52} + 4 q^{53} + 2 q^{54} - 8 q^{57} - 12 q^{58} - 2 q^{60} + 4 q^{61} - 8 q^{62} + 2 q^{64} + 4 q^{65} - 8 q^{67} - 2 q^{68} + 8 q^{69} - 8 q^{71} - 2 q^{72} - 12 q^{73} - 12 q^{74} - 2 q^{75} + 8 q^{76} + 4 q^{78} + 8 q^{79} + 2 q^{80} + 2 q^{81} - 4 q^{82} + 8 q^{83} - 2 q^{85} - 8 q^{86} - 12 q^{87} + 4 q^{89} - 2 q^{90} - 48 q^{91} - 8 q^{92} - 8 q^{93} + 8 q^{95} + 2 q^{96} + 4 q^{97} - 34 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9 - 2 * q^10 - 2 * q^12 + 4 * q^13 - 2 * q^15 + 2 * q^16 - 2 * q^17 - 2 * q^18 + 8 * q^19 + 2 * q^20 - 8 * q^23 + 2 * q^24 + 2 * q^25 - 4 * q^26 - 2 * q^27 + 12 * q^29 + 2 * q^30 + 8 * q^31 - 2 * q^32 + 2 * q^34 + 2 * q^36 + 12 * q^37 - 8 * q^38 - 4 * q^39 - 2 * q^40 + 4 * q^41 + 8 * q^43 + 2 * q^45 + 8 * q^46 - 2 * q^48 + 34 * q^49 - 2 * q^50 + 2 * q^51 + 4 * q^52 + 4 * q^53 + 2 * q^54 - 8 * q^57 - 12 * q^58 - 2 * q^60 + 4 * q^61 - 8 * q^62 + 2 * q^64 + 4 * q^65 - 8 * q^67 - 2 * q^68 + 8 * q^69 - 8 * q^71 - 2 * q^72 - 12 * q^73 - 12 * q^74 - 2 * q^75 + 8 * q^76 + 4 * q^78 + 8 * q^79 + 2 * q^80 + 2 * q^81 - 4 * q^82 + 8 * q^83 - 2 * q^85 - 8 * q^86 - 12 * q^87 + 4 * q^89 - 2 * q^90 - 48 * q^91 - 8 * q^92 - 8 * q^93 + 8 * q^95 + 2 * q^96 + 4 * q^97 - 34 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	−4.89898	−1.85164	−0.925820	−	0.377964i	$-0.876624\pi$
$7$	−4.89898	−1.85164	−0.925820	+	0.377964i	$0.876624\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	0	0		−	1.00000i	$-0.5\pi$
$11$	0	0			1.00000i	$0.5\pi$
$12$	−1.00000	−0.288675
$13$	6.89898	1.91343	0.956716	−	0.291022i	$-0.0939953\pi$
$13$	6.89898	1.91343	0.956716	+	0.291022i	$0.0939953\pi$
$14$	4.89898	1.30931
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−1.00000	−0.235702
$19$	4.00000	0.917663	0.458831	−	0.888523i	$-0.348268\pi$
$19$	4.00000	0.917663	0.458831	+	0.888523i	$0.348268\pi$
$20$	1.00000	0.223607
$21$	4.89898	1.06904
$22$	0	0
$23$	−4.00000	−0.834058	−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000	−0.834058	−0.417029	+	0.908893i	$0.636929\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−6.89898	−1.35300
$27$	−1.00000	−0.192450
$28$	−4.89898	−0.925820
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	1.00000	0.182574
$31$	4.00000	0.718421	0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000	0.718421	0.359211	+	0.933257i	$0.383046\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	1.00000	0.171499
$35$	−4.89898	−0.828079
$36$	1.00000	0.166667
$37$	6.00000	0.986394	0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000	0.986394	0.493197	+	0.869918i	$0.335828\pi$
$38$	−4.00000	−0.648886
$39$	−6.89898	−1.10472
$40$	−1.00000	−0.158114
$41$	−2.89898	−0.452745	−0.226372	−	0.974041i	$-0.572687\pi$
$41$	−2.89898	−0.452745	−0.226372	+	0.974041i	$0.572687\pi$
$42$	−4.89898	−0.755929
$43$	8.89898	1.35708	0.678541	−	0.734563i	$-0.262613\pi$
$43$	8.89898	1.35708	0.678541	+	0.734563i	$0.262613\pi$
$44$	0	0
$45$	1.00000	0.149071
$46$	4.00000	0.589768
$47$	9.79796	1.42918	0.714590	−	0.699544i	$-0.246613\pi$
$47$	9.79796	1.42918	0.714590	+	0.699544i	$0.246613\pi$
$48$	−1.00000	−0.144338
$49$	17.0000	2.42857
$50$	−1.00000	−0.141421
$51$	1.00000	0.140028
$52$	6.89898	0.956716
$53$	−7.79796	−1.07113	−0.535566	−	0.844493i	$-0.679902\pi$
$53$	−7.79796	−1.07113	−0.535566	+	0.844493i	$0.679902\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	4.89898	0.654654
$57$	−4.00000	−0.529813
$58$	−6.00000	−0.787839
$59$	4.89898	0.637793	0.318896	−	0.947790i	$-0.396688\pi$
$59$	4.89898	0.637793	0.318896	+	0.947790i	$0.396688\pi$
$60$	−1.00000	−0.129099
$61$	11.7980	1.51057	0.755287	−	0.655394i	$-0.227498\pi$
$61$	11.7980	1.51057	0.755287	+	0.655394i	$0.227498\pi$
$62$	−4.00000	−0.508001
$63$	−4.89898	−0.617213
$64$	1.00000	0.125000
$65$	6.89898	0.855713
$66$	0	0
$67$	0.898979	0.109828	0.0549139	−	0.998491i	$-0.482512\pi$
$67$	0.898979	0.109828	0.0549139	+	0.998491i	$0.482512\pi$
$68$	−1.00000	−0.121268
$69$	4.00000	0.481543
$70$	4.89898	0.585540
$71$	−8.89898	−1.05611	−0.528057	−	0.849209i	$-0.677079\pi$
$71$	−8.89898	−1.05611	−0.528057	+	0.849209i	$0.677079\pi$
$72$	−1.00000	−0.117851
$73$	−10.8990	−1.27563	−0.637815	−	0.770190i	$-0.720161\pi$
$73$	−10.8990	−1.27563	−0.637815	+	0.770190i	$0.720161\pi$
$74$	−6.00000	−0.697486
$75$	−1.00000	−0.115470
$76$	4.00000	0.458831
$77$	0	0
$78$	6.89898	0.781156
$79$	−5.79796	−0.652321	−0.326161	−	0.945314i	$-0.605755\pi$
$79$	−5.79796	−0.652321	−0.326161	+	0.945314i	$0.605755\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	2.89898	0.320139
$83$	13.7980	1.51452	0.757261	−	0.653112i	$-0.226537\pi$
$83$	13.7980	1.51452	0.757261	+	0.653112i	$0.226537\pi$
$84$	4.89898	0.534522
$85$	−1.00000	−0.108465
$86$	−8.89898	−0.959602
$87$	−6.00000	−0.643268
$88$	0	0
$89$	−7.79796	−0.826582	−0.413291	−	0.910599i	$-0.635621\pi$
$89$	−7.79796	−0.826582	−0.413291	+	0.910599i	$0.635621\pi$
$90$	−1.00000	−0.105409
$91$	−33.7980	−3.54299
$92$	−4.00000	−0.417029
$93$	−4.00000	−0.414781
$94$	−9.79796	−1.01058
$95$	4.00000	0.410391
$96$	1.00000	0.102062
$97$	−12.6969	−1.28918	−0.644589	−	0.764529i	$-0.722972\pi$
$97$	−12.6969	−1.28918	−0.644589	+	0.764529i	$0.722972\pi$
$98$	−17.0000	−1.71726
$99$	0	0
$100$	1.00000	0.100000
$101$	−18.8990	−1.88052	−0.940259	−	0.340459i	$-0.889418\pi$
$101$	−18.8990	−1.88052	−0.940259	+	0.340459i	$0.889418\pi$
$102$	−1.00000	−0.0990148
$103$	4.00000	0.394132	0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000	0.394132	0.197066	+	0.980390i	$0.436859\pi$
$104$	−6.89898	−0.676501
$105$	4.89898	0.478091
$106$	7.79796	0.757405
$107$	5.79796	0.560510	0.280255	−	0.959926i	$-0.409581\pi$
$107$	5.79796	0.560510	0.280255	+	0.959926i	$0.409581\pi$
$108$	−1.00000	−0.0962250
$109$	11.7980	1.13004	0.565020	−	0.825077i	$-0.308869\pi$
$109$	11.7980	1.13004	0.565020	+	0.825077i	$0.308869\pi$
$110$	0	0
$111$	−6.00000	−0.569495
$112$	−4.89898	−0.462910
$113$	7.79796	0.733570	0.366785	−	0.930306i	$-0.380458\pi$
$113$	7.79796	0.733570	0.366785	+	0.930306i	$0.380458\pi$
$114$	4.00000	0.374634
$115$	−4.00000	−0.373002
$116$	6.00000	0.557086
$117$	6.89898	0.637811
$118$	−4.89898	−0.450988
$119$	4.89898	0.449089
$120$	1.00000	0.0912871
$121$	−11.0000	−1.00000
$122$	−11.7980	−1.06814
$123$	2.89898	0.261392
$124$	4.00000	0.359211
$125$	1.00000	0.0894427
$126$	4.89898	0.436436
$127$	−12.0000	−1.06483	−0.532414	−	0.846484i	$-0.678715\pi$
$127$	−12.0000	−1.06483	−0.532414	+	0.846484i	$0.678715\pi$
$128$	−1.00000	−0.0883883
$129$	−8.89898	−0.783511
$130$	−6.89898	−0.605081
$131$	9.79796	0.856052	0.428026	−	0.903767i	$-0.359209\pi$
$131$	9.79796	0.856052	0.428026	+	0.903767i	$0.359209\pi$
$132$	0	0
$133$	−19.5959	−1.69918
$134$	−0.898979	−0.0776600
$135$	−1.00000	−0.0860663
$136$	1.00000	0.0857493
$137$	14.0000	1.19610	0.598050	−	0.801459i	$-0.295942\pi$
$137$	14.0000	1.19610	0.598050	+	0.801459i	$0.295942\pi$
$138$	−4.00000	−0.340503
$139$	13.7980	1.17033	0.585164	−	0.810915i	$-0.301030\pi$
$139$	13.7980	1.17033	0.585164	+	0.810915i	$0.301030\pi$
$140$	−4.89898	−0.414039
$141$	−9.79796	−0.825137
$142$	8.89898	0.746786
$143$	0	0
$144$	1.00000	0.0833333
$145$	6.00000	0.498273
$146$	10.8990	0.902006
$147$	−17.0000	−1.40214
$148$	6.00000	0.493197
$149$	−18.8990	−1.54826	−0.774132	−	0.633024i	$-0.781814\pi$
$149$	−18.8990	−1.54826	−0.774132	+	0.633024i	$0.781814\pi$
$150$	1.00000	0.0816497
$151$	−9.79796	−0.797347	−0.398673	−	0.917093i	$-0.630529\pi$
$151$	−9.79796	−0.797347	−0.398673	+	0.917093i	$0.630529\pi$
$152$	−4.00000	−0.324443
$153$	−1.00000	−0.0808452
$154$	0	0
$155$	4.00000	0.321288
$156$	−6.89898	−0.552360
$157$	−1.10102	−0.0878710	−0.0439355	−	0.999034i	$-0.513990\pi$
$157$	−1.10102	−0.0878710	−0.0439355	+	0.999034i	$0.513990\pi$
$158$	5.79796	0.461261
$159$	7.79796	0.618418
$160$	−1.00000	−0.0790569
$161$	19.5959	1.54437
$162$	−1.00000	−0.0785674
$163$	−2.20204	−0.172477	−0.0862386	−	0.996275i	$-0.527485\pi$
$163$	−2.20204	−0.172477	−0.0862386	+	0.996275i	$0.527485\pi$
$164$	−2.89898	−0.226372
$165$	0	0
$166$	−13.7980	−1.07093
$167$	2.20204	0.170399	0.0851995	−	0.996364i	$-0.472847\pi$
$167$	2.20204	0.170399	0.0851995	+	0.996364i	$0.472847\pi$
$168$	−4.89898	−0.377964
$169$	34.5959	2.66122
$170$	1.00000	0.0766965
$171$	4.00000	0.305888
$172$	8.89898	0.678541
$173$	6.00000	0.456172	0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000	0.456172	0.228086	+	0.973641i	$0.426753\pi$
$174$	6.00000	0.454859
$175$	−4.89898	−0.370328
$176$	0	0
$177$	−4.89898	−0.368230
$178$	7.79796	0.584482
$179$	−4.89898	−0.366167	−0.183083	−	0.983097i	$-0.558608\pi$
$179$	−4.89898	−0.366167	−0.183083	+	0.983097i	$0.558608\pi$
$180$	1.00000	0.0745356
$181$	−4.20204	−0.312335	−0.156168	−	0.987731i	$-0.549914\pi$
$181$	−4.20204	−0.312335	−0.156168	+	0.987731i	$0.549914\pi$
$182$	33.7980	2.50527
$183$	−11.7980	−0.872130
$184$	4.00000	0.294884
$185$	6.00000	0.441129
$186$	4.00000	0.293294
$187$	0	0
$188$	9.79796	0.714590
$189$	4.89898	0.356348
$190$	−4.00000	−0.290191
$191$	−9.79796	−0.708955	−0.354478	−	0.935064i	$-0.615341\pi$
$191$	−9.79796	−0.708955	−0.354478	+	0.935064i	$0.615341\pi$
$192$	−1.00000	−0.0721688
$193$	−1.10102	−0.0792532	−0.0396266	−	0.999215i	$-0.512617\pi$
$193$	−1.10102	−0.0792532	−0.0396266	+	0.999215i	$0.512617\pi$
$194$	12.6969	0.911587
$195$	−6.89898	−0.494046
$196$	17.0000	1.21429
$197$	−13.5959	−0.968669	−0.484335	−	0.874883i	$-0.660938\pi$
$197$	−13.5959	−0.968669	−0.484335	+	0.874883i	$0.660938\pi$
$198$	0	0
$199$	15.5959	1.10557	0.552783	−	0.833325i	$-0.313566\pi$
$199$	15.5959	1.10557	0.552783	+	0.833325i	$0.313566\pi$
$200$	−1.00000	−0.0707107
$201$	−0.898979	−0.0634091
$202$	18.8990	1.32973
$203$	−29.3939	−2.06305
$204$	1.00000	0.0700140
$205$	−2.89898	−0.202474
$206$	−4.00000	−0.278693
$207$	−4.00000	−0.278019
$208$	6.89898	0.478358
$209$	0	0
$210$	−4.89898	−0.338062
$211$	−12.0000	−0.826114	−0.413057	−	0.910705i	$-0.635539\pi$
$211$	−12.0000	−0.826114	−0.413057	+	0.910705i	$0.635539\pi$
$212$	−7.79796	−0.535566
$213$	8.89898	0.609748
$214$	−5.79796	−0.396340
$215$	8.89898	0.606905
$216$	1.00000	0.0680414
$217$	−19.5959	−1.33026
$218$	−11.7980	−0.799059
$219$	10.8990	0.736485
$220$	0	0
$221$	−6.89898	−0.464076
$222$	6.00000	0.402694
$223$	−4.00000	−0.267860	−0.133930	−	0.990991i	$-0.542760\pi$
$223$	−4.00000	−0.267860	−0.133930	+	0.990991i	$0.542760\pi$
$224$	4.89898	0.327327
$225$	1.00000	0.0666667
$226$	−7.79796	−0.518713
$227$	−21.7980	−1.44678	−0.723391	−	0.690439i	$-0.757417\pi$
$227$	−21.7980	−1.44678	−0.723391	+	0.690439i	$0.757417\pi$
$228$	−4.00000	−0.264906
$229$	−13.5959	−0.898444	−0.449222	−	0.893420i	$-0.648299\pi$
$229$	−13.5959	−0.898444	−0.449222	+	0.893420i	$0.648299\pi$
$230$	4.00000	0.263752
$231$	0	0
$232$	−6.00000	−0.393919
$233$	14.0000	0.917170	0.458585	−	0.888650i	$-0.348356\pi$
$233$	14.0000	0.917170	0.458585	+	0.888650i	$0.348356\pi$
$234$	−6.89898	−0.451000
$235$	9.79796	0.639148
$236$	4.89898	0.318896
$237$	5.79796	0.376618
$238$	−4.89898	−0.317554
$239$	0	0		−	1.00000i	$-0.5\pi$
$239$	0	0			1.00000i	$0.5\pi$
$240$	−1.00000	−0.0645497
$241$	13.5959	0.875790	0.437895	−	0.899026i	$-0.355724\pi$
$241$	13.5959	0.875790	0.437895	+	0.899026i	$0.355724\pi$
$242$	11.0000	0.707107
$243$	−1.00000	−0.0641500
$244$	11.7980	0.755287
$245$	17.0000	1.08609
$246$	−2.89898	−0.184832
$247$	27.5959	1.75589
$248$	−4.00000	−0.254000
$249$	−13.7980	−0.874410
$250$	−1.00000	−0.0632456
$251$	4.89898	0.309221	0.154610	−	0.987976i	$-0.450588\pi$
$251$	4.89898	0.309221	0.154610	+	0.987976i	$0.450588\pi$
$252$	−4.89898	−0.308607
$253$	0	0
$254$	12.0000	0.752947
$255$	1.00000	0.0626224
$256$	1.00000	0.0625000
$257$	−2.00000	−0.124757	−0.0623783	−	0.998053i	$-0.519869\pi$
$257$	−2.00000	−0.124757	−0.0623783	+	0.998053i	$0.519869\pi$
$258$	8.89898	0.554026
$259$	−29.3939	−1.82645
$260$	6.89898	0.427857
$261$	6.00000	0.371391
$262$	−9.79796	−0.605320
$263$	8.00000	0.493301	0.246651	−	0.969104i	$-0.420670\pi$
$263$	8.00000	0.493301	0.246651	+	0.969104i	$0.420670\pi$
$264$	0	0
$265$	−7.79796	−0.479025
$266$	19.5959	1.20150
$267$	7.79796	0.477227
$268$	0.898979	0.0549139
$269$	9.59592	0.585073	0.292537	−	0.956254i	$-0.405501\pi$
$269$	9.59592	0.585073	0.292537	+	0.956254i	$0.405501\pi$
$270$	1.00000	0.0608581
$271$	−1.79796	−0.109218	−0.0546091	−	0.998508i	$-0.517391\pi$
$271$	−1.79796	−0.109218	−0.0546091	+	0.998508i	$0.517391\pi$
$272$	−1.00000	−0.0606339
$273$	33.7980	2.04555
$274$	−14.0000	−0.845771
$275$	0	0
$276$	4.00000	0.240772
$277$	7.79796	0.468534	0.234267	−	0.972172i	$-0.424731\pi$
$277$	7.79796	0.468534	0.234267	+	0.972172i	$0.424731\pi$
$278$	−13.7980	−0.827547
$279$	4.00000	0.239474
$280$	4.89898	0.292770
$281$	27.7980	1.65829	0.829144	−	0.559036i	$-0.188829\pi$
$281$	27.7980	1.65829	0.829144	+	0.559036i	$0.188829\pi$
$282$	9.79796	0.583460
$283$	23.5959	1.40263	0.701316	−	0.712851i	$-0.252596\pi$
$283$	23.5959	1.40263	0.701316	+	0.712851i	$0.252596\pi$
$284$	−8.89898	−0.528057
$285$	−4.00000	−0.236940
$286$	0	0
$287$	14.2020	0.838320
$288$	−1.00000	−0.0589256
$289$	1.00000	0.0588235
$290$	−6.00000	−0.352332
$291$	12.6969	0.744308
$292$	−10.8990	−0.637815
$293$	13.5959	0.794282	0.397141	−	0.917758i	$-0.370002\pi$
$293$	13.5959	0.794282	0.397141	+	0.917758i	$0.370002\pi$
$294$	17.0000	0.991460
$295$	4.89898	0.285230
$296$	−6.00000	−0.348743
$297$	0	0
$298$	18.8990	1.09479
$299$	−27.5959	−1.59591
$300$	−1.00000	−0.0577350
$301$	−43.5959	−2.51283
$302$	9.79796	0.563809
$303$	18.8990	1.08572
$304$	4.00000	0.229416
$305$	11.7980	0.675549
$306$	1.00000	0.0571662
$307$	0.898979	0.0513075	0.0256537	−	0.999671i	$-0.491833\pi$
$307$	0.898979	0.0513075	0.0256537	+	0.999671i	$0.491833\pi$
$308$	0	0
$309$	−4.00000	−0.227552
$310$	−4.00000	−0.227185
$311$	−7.10102	−0.402662	−0.201331	−	0.979523i	$-0.564527\pi$
$311$	−7.10102	−0.402662	−0.201331	+	0.979523i	$0.564527\pi$
$312$	6.89898	0.390578
$313$	6.89898	0.389953	0.194977	−	0.980808i	$-0.437537\pi$
$313$	6.89898	0.389953	0.194977	+	0.980808i	$0.437537\pi$
$314$	1.10102	0.0621342
$315$	−4.89898	−0.276026
$316$	−5.79796	−0.326161
$317$	14.0000	0.786318	0.393159	−	0.919470i	$-0.371382\pi$
$317$	14.0000	0.786318	0.393159	+	0.919470i	$0.371382\pi$
$318$	−7.79796	−0.437288
$319$	0	0
$320$	1.00000	0.0559017
$321$	−5.79796	−0.323611
$322$	−19.5959	−1.09204
$323$	−4.00000	−0.222566
$324$	1.00000	0.0555556
$325$	6.89898	0.382687
$326$	2.20204	0.121960
$327$	−11.7980	−0.652429
$328$	2.89898	0.160069
$329$	−48.0000	−2.64633
$330$	0	0
$331$	−5.79796	−0.318685	−0.159342	−	0.987223i	$-0.550937\pi$
$331$	−5.79796	−0.318685	−0.159342	+	0.987223i	$0.550937\pi$
$332$	13.7980	0.757261
$333$	6.00000	0.328798
$334$	−2.20204	−0.120490
$335$	0.898979	0.0491165
$336$	4.89898	0.267261
$337$	32.6969	1.78112	0.890558	−	0.454870i	$-0.150314\pi$
$337$	32.6969	1.78112	0.890558	+	0.454870i	$0.150314\pi$
$338$	−34.5959	−1.88177
$339$	−7.79796	−0.423527
$340$	−1.00000	−0.0542326
$341$	0	0
$342$	−4.00000	−0.216295
$343$	−48.9898	−2.64520
$344$	−8.89898	−0.479801
$345$	4.00000	0.215353
$346$	−6.00000	−0.322562
$347$	21.7980	1.17018	0.585088	−	0.810970i	$-0.301060\pi$
$347$	21.7980	1.17018	0.585088	+	0.810970i	$0.301060\pi$
$348$	−6.00000	−0.321634
$349$	4.20204	0.224930	0.112465	−	0.993656i	$-0.464125\pi$
$349$	4.20204	0.224930	0.112465	+	0.993656i	$0.464125\pi$
$350$	4.89898	0.261861
$351$	−6.89898	−0.368240
$352$	0	0
$353$	−26.0000	−1.38384	−0.691920	−	0.721974i	$-0.743235\pi$
$353$	−26.0000	−1.38384	−0.691920	+	0.721974i	$0.743235\pi$
$354$	4.89898	0.260378
$355$	−8.89898	−0.472309
$356$	−7.79796	−0.413291
$357$	−4.89898	−0.259281
$358$	4.89898	0.258919
$359$	37.3939	1.97357	0.986787	−	0.162025i	$-0.0518025\pi$
$359$	37.3939	1.97357	0.986787	+	0.162025i	$0.0518025\pi$
$360$	−1.00000	−0.0527046
$361$	−3.00000	−0.157895
$362$	4.20204	0.220854
$363$	11.0000	0.577350
$364$	−33.7980	−1.77149
$365$	−10.8990	−0.570479
$366$	11.7980	0.616689
$367$	−27.1010	−1.41466	−0.707331	−	0.706883i	$-0.750101\pi$
$367$	−27.1010	−1.41466	−0.707331	+	0.706883i	$0.750101\pi$
$368$	−4.00000	−0.208514
$369$	−2.89898	−0.150915
$370$	−6.00000	−0.311925
$371$	38.2020	1.98335
$372$	−4.00000	−0.207390
$373$	24.6969	1.27876	0.639380	−	0.768891i	$-0.279191\pi$
$373$	24.6969	1.27876	0.639380	+	0.768891i	$0.279191\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	−9.79796	−0.505291
$377$	41.3939	2.13189
$378$	−4.89898	−0.251976
$379$	−29.7980	−1.53062	−0.765309	−	0.643663i	$-0.777414\pi$
$379$	−29.7980	−1.53062	−0.765309	+	0.643663i	$0.777414\pi$
$380$	4.00000	0.205196
$381$	12.0000	0.614779
$382$	9.79796	0.501307
$383$	8.00000	0.408781	0.204390	−	0.978889i	$-0.434479\pi$
$383$	8.00000	0.408781	0.204390	+	0.978889i	$0.434479\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	1.10102	0.0560405
$387$	8.89898	0.452361
$388$	−12.6969	−0.644589
$389$	−38.4949	−1.95177	−0.975884	−	0.218288i	$-0.929953\pi$
$389$	−38.4949	−1.95177	−0.975884	+	0.218288i	$0.929953\pi$
$390$	6.89898	0.349343
$391$	4.00000	0.202289
$392$	−17.0000	−0.858630
$393$	−9.79796	−0.494242
$394$	13.5959	0.684952
$395$	−5.79796	−0.291727
$396$	0	0
$397$	1.59592	0.0800968	0.0400484	−	0.999198i	$-0.487249\pi$
$397$	1.59592	0.0800968	0.0400484	+	0.999198i	$0.487249\pi$
$398$	−15.5959	−0.781753
$399$	19.5959	0.981023
$400$	1.00000	0.0500000
$401$	22.8990	1.14352	0.571760	−	0.820421i	$-0.306261\pi$
$401$	22.8990	1.14352	0.571760	+	0.820421i	$0.306261\pi$
$402$	0.898979	0.0448370
$403$	27.5959	1.37465
$404$	−18.8990	−0.940259
$405$	1.00000	0.0496904
$406$	29.3939	1.45879
$407$	0	0
$408$	−1.00000	−0.0495074
$409$	−17.5959	−0.870062	−0.435031	−	0.900415i	$-0.643263\pi$
$409$	−17.5959	−0.870062	−0.435031	+	0.900415i	$0.643263\pi$
$410$	2.89898	0.143170
$411$	−14.0000	−0.690569
$412$	4.00000	0.197066
$413$	−24.0000	−1.18096
$414$	4.00000	0.196589
$415$	13.7980	0.677315
$416$	−6.89898	−0.338250
$417$	−13.7980	−0.675689
$418$	0	0
$419$	−17.7980	−0.869487	−0.434744	−	0.900554i	$-0.643161\pi$
$419$	−17.7980	−0.869487	−0.434744	+	0.900554i	$0.643161\pi$
$420$	4.89898	0.239046
$421$	14.0000	0.682318	0.341159	−	0.940006i	$-0.389181\pi$
$421$	14.0000	0.682318	0.341159	+	0.940006i	$0.389181\pi$
$422$	12.0000	0.584151
$423$	9.79796	0.476393
$424$	7.79796	0.378702
$425$	−1.00000	−0.0485071
$426$	−8.89898	−0.431157
$427$	−57.7980	−2.79704
$428$	5.79796	0.280255
$429$	0	0
$430$	−8.89898	−0.429147
$431$	−23.1010	−1.11274	−0.556369	−	0.830936i	$-0.687806\pi$
$431$	−23.1010	−1.11274	−0.556369	+	0.830936i	$0.687806\pi$
$432$	−1.00000	−0.0481125
$433$	−35.3939	−1.70092	−0.850461	−	0.526039i	$-0.823677\pi$
$433$	−35.3939	−1.70092	−0.850461	+	0.526039i	$0.823677\pi$
$434$	19.5959	0.940634
$435$	−6.00000	−0.287678
$436$	11.7980	0.565020
$437$	−16.0000	−0.765384
$438$	−10.8990	−0.520773
$439$	5.79796	0.276721	0.138361	−	0.990382i	$-0.455817\pi$
$439$	5.79796	0.276721	0.138361	+	0.990382i	$0.455817\pi$
$440$	0	0
$441$	17.0000	0.809524
$442$	6.89898	0.328151
$443$	37.7980	1.79584	0.897918	−	0.440164i	$-0.145080\pi$
$443$	37.7980	1.79584	0.897918	+	0.440164i	$0.145080\pi$
$444$	−6.00000	−0.284747
$445$	−7.79796	−0.369659
$446$	4.00000	0.189405
$447$	18.8990	0.893891
$448$	−4.89898	−0.231455
$449$	6.89898	0.325583	0.162791	−	0.986660i	$-0.447950\pi$
$449$	6.89898	0.325583	0.162791	+	0.986660i	$0.447950\pi$
$450$	−1.00000	−0.0471405
$451$	0	0
$452$	7.79796	0.366785
$453$	9.79796	0.460348
$454$	21.7980	1.02303
$455$	−33.7980	−1.58447
$456$	4.00000	0.187317
$457$	16.2020	0.757900	0.378950	−	0.925417i	$-0.376285\pi$
$457$	16.2020	0.757900	0.378950	+	0.925417i	$0.376285\pi$
$458$	13.5959	0.635296
$459$	1.00000	0.0466760
$460$	−4.00000	−0.186501
$461$	−28.6969	−1.33655	−0.668275	−	0.743914i	$-0.732967\pi$
$461$	−28.6969	−1.33655	−0.668275	+	0.743914i	$0.732967\pi$
$462$	0	0
$463$	7.59592	0.353012	0.176506	−	0.984300i	$-0.443520\pi$
$463$	7.59592	0.353012	0.176506	+	0.984300i	$0.443520\pi$
$464$	6.00000	0.278543
$465$	−4.00000	−0.185496
$466$	−14.0000	−0.648537
$467$	−7.59592	−0.351497	−0.175749	−	0.984435i	$-0.556235\pi$
$467$	−7.59592	−0.351497	−0.175749	+	0.984435i	$0.556235\pi$
$468$	6.89898	0.318905
$469$	−4.40408	−0.203362
$470$	−9.79796	−0.451946
$471$	1.10102	0.0507323
$472$	−4.89898	−0.225494
$473$	0	0
$474$	−5.79796	−0.266309
$475$	4.00000	0.183533
$476$	4.89898	0.224544
$477$	−7.79796	−0.357044
$478$	0	0
$479$	−32.8990	−1.50319	−0.751596	−	0.659623i	$-0.770716\pi$
$479$	−32.8990	−1.50319	−0.751596	+	0.659623i	$0.770716\pi$
$480$	1.00000	0.0456435
$481$	41.3939	1.88740
$482$	−13.5959	−0.619277
$483$	−19.5959	−0.891645
$484$	−11.0000	−0.500000
$485$	−12.6969	−0.576538
$486$	1.00000	0.0453609
$487$	−20.8990	−0.947023	−0.473512	−	0.880788i	$-0.657014\pi$
$487$	−20.8990	−0.947023	−0.473512	+	0.880788i	$0.657014\pi$
$488$	−11.7980	−0.534069
$489$	2.20204	0.0995797
$490$	−17.0000	−0.767982
$491$	−1.30306	−0.0588063	−0.0294032	−	0.999568i	$-0.509361\pi$
$491$	−1.30306	−0.0588063	−0.0294032	+	0.999568i	$0.509361\pi$
$492$	2.89898	0.130696
$493$	−6.00000	−0.270226
$494$	−27.5959	−1.24160
$495$	0	0
$496$	4.00000	0.179605
$497$	43.5959	1.95554
$498$	13.7980	0.618301
$499$	−39.5959	−1.77256	−0.886278	−	0.463153i	$-0.846718\pi$
$499$	−39.5959	−1.77256	−0.886278	+	0.463153i	$0.846718\pi$
$500$	1.00000	0.0447214
$501$	−2.20204	−0.0983799
$502$	−4.89898	−0.218652
$503$	4.00000	0.178351	0.0891756	−	0.996016i	$-0.471577\pi$
$503$	4.00000	0.178351	0.0891756	+	0.996016i	$0.471577\pi$
$504$	4.89898	0.218218
$505$	−18.8990	−0.840994
$506$	0	0
$507$	−34.5959	−1.53646
$508$	−12.0000	−0.532414
$509$	−15.3031	−0.678296	−0.339148	−	0.940733i	$-0.610139\pi$
$509$	−15.3031	−0.678296	−0.339148	+	0.940733i	$0.610139\pi$
$510$	−1.00000	−0.0442807
$511$	53.3939	2.36201
$512$	−1.00000	−0.0441942
$513$	−4.00000	−0.176604
$514$	2.00000	0.0882162
$515$	4.00000	0.176261
$516$	−8.89898	−0.391756
$517$	0	0
$518$	29.3939	1.29149
$519$	−6.00000	−0.263371
$520$	−6.89898	−0.302540
$521$	−40.2929	−1.76526	−0.882631	−	0.470066i	$-0.844230\pi$
$521$	−40.2929	−1.76526	−0.882631	+	0.470066i	$0.844230\pi$
$522$	−6.00000	−0.262613
$523$	18.6969	0.817560	0.408780	−	0.912633i	$-0.365954\pi$
$523$	18.6969	0.817560	0.408780	+	0.912633i	$0.365954\pi$
$524$	9.79796	0.428026
$525$	4.89898	0.213809
$526$	−8.00000	−0.348817
$527$	−4.00000	−0.174243
$528$	0	0
$529$	−7.00000	−0.304348
$530$	7.79796	0.338722
$531$	4.89898	0.212598
$532$	−19.5959	−0.849591
$533$	−20.0000	−0.866296
$534$	−7.79796	−0.337451
$535$	5.79796	0.250668
$536$	−0.898979	−0.0388300
$537$	4.89898	0.211407
$538$	−9.59592	−0.413709
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	−7.79796	−0.335260	−0.167630	−	0.985850i	$-0.553611\pi$
$541$	−7.79796	−0.335260	−0.167630	+	0.985850i	$0.553611\pi$
$542$	1.79796	0.0772290
$543$	4.20204	0.180327
$544$	1.00000	0.0428746
$545$	11.7980	0.505369
$546$	−33.7980	−1.44642
$547$	0.404082	0.0172773	0.00863865	−	0.999963i	$-0.497250\pi$
$547$	0.404082	0.0172773	0.00863865	+	0.999963i	$0.497250\pi$
$548$	14.0000	0.598050
$549$	11.7980	0.503525
$550$	0	0
$551$	24.0000	1.02243
$552$	−4.00000	−0.170251
$553$	28.4041	1.20786
$554$	−7.79796	−0.331304
$555$	−6.00000	−0.254686
$556$	13.7980	0.585164
$557$	19.7980	0.838866	0.419433	−	0.907786i	$-0.362229\pi$
$557$	19.7980	0.838866	0.419433	+	0.907786i	$0.362229\pi$
$558$	−4.00000	−0.169334
$559$	61.3939	2.59668
$560$	−4.89898	−0.207020
$561$	0	0
$562$	−27.7980	−1.17259
$563$	21.7980	0.918674	0.459337	−	0.888262i	$-0.348087\pi$
$563$	21.7980	0.918674	0.459337	+	0.888262i	$0.348087\pi$
$564$	−9.79796	−0.412568
$565$	7.79796	0.328063
$566$	−23.5959	−0.991810
$567$	−4.89898	−0.205738
$568$	8.89898	0.373393
$569$	34.0000	1.42535	0.712677	−	0.701492i	$-0.247483\pi$
$569$	34.0000	1.42535	0.712677	+	0.701492i	$0.247483\pi$
$570$	4.00000	0.167542
$571$	29.7980	1.24701	0.623503	−	0.781821i	$-0.285709\pi$
$571$	29.7980	1.24701	0.623503	+	0.781821i	$0.285709\pi$
$572$	0	0
$573$	9.79796	0.409316
$574$	−14.2020	−0.592782
$575$	−4.00000	−0.166812
$576$	1.00000	0.0416667
$577$	−27.3939	−1.14042	−0.570211	−	0.821498i	$-0.693139\pi$
$577$	−27.3939	−1.14042	−0.570211	+	0.821498i	$0.693139\pi$
$578$	−1.00000	−0.0415945
$579$	1.10102	0.0457569
$580$	6.00000	0.249136
$581$	−67.5959	−2.80435
$582$	−12.6969	−0.526305
$583$	0	0
$584$	10.8990	0.451003
$585$	6.89898	0.285238
$586$	−13.5959	−0.561642
$587$	−41.3939	−1.70851	−0.854254	−	0.519856i	$-0.825986\pi$
$587$	−41.3939	−1.70851	−0.854254	+	0.519856i	$0.825986\pi$
$588$	−17.0000	−0.701068
$589$	16.0000	0.659269
$590$	−4.89898	−0.201688
$591$	13.5959	0.559261
$592$	6.00000	0.246598
$593$	1.59592	0.0655365	0.0327682	−	0.999463i	$-0.489568\pi$
$593$	1.59592	0.0655365	0.0327682	+	0.999463i	$0.489568\pi$
$594$	0	0
$595$	4.89898	0.200839
$596$	−18.8990	−0.774132
$597$	−15.5959	−0.638298
$598$	27.5959	1.12848
$599$	21.3939	0.874130	0.437065	−	0.899430i	$-0.356018\pi$
$599$	21.3939	0.874130	0.437065	+	0.899430i	$0.356018\pi$
$600$	1.00000	0.0408248
$601$	16.2020	0.660895	0.330448	−	0.943824i	$-0.392800\pi$
$601$	16.2020	0.660895	0.330448	+	0.943824i	$0.392800\pi$
$602$	43.5959	1.77684
$603$	0.898979	0.0366093
$604$	−9.79796	−0.398673
$605$	−11.0000	−0.447214
$606$	−18.8990	−0.767719
$607$	−32.4949	−1.31893	−0.659464	−	0.751736i	$-0.729217\pi$
$607$	−32.4949	−1.31893	−0.659464	+	0.751736i	$0.729217\pi$
$608$	−4.00000	−0.162221
$609$	29.3939	1.19110
$610$	−11.7980	−0.477685
$611$	67.5959	2.73464
$612$	−1.00000	−0.0404226
$613$	−14.4949	−0.585443	−0.292722	−	0.956198i	$-0.594561\pi$
$613$	−14.4949	−0.585443	−0.292722	+	0.956198i	$0.594561\pi$
$614$	−0.898979	−0.0362799
$615$	2.89898	0.116898
$616$	0	0
$617$	−37.5959	−1.51355	−0.756777	−	0.653673i	$-0.773227\pi$
$617$	−37.5959	−1.51355	−0.756777	+	0.653673i	$0.773227\pi$
$618$	4.00000	0.160904
$619$	20.0000	0.803868	0.401934	−	0.915669i	$-0.368338\pi$
$619$	20.0000	0.803868	0.401934	+	0.915669i	$0.368338\pi$
$620$	4.00000	0.160644
$621$	4.00000	0.160514
$622$	7.10102	0.284725
$623$	38.2020	1.53053
$624$	−6.89898	−0.276180
$625$	1.00000	0.0400000
$626$	−6.89898	−0.275739
$627$	0	0
$628$	−1.10102	−0.0439355
$629$	−6.00000	−0.239236
$630$	4.89898	0.195180
$631$	−40.0000	−1.59237	−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000	−1.59237	−0.796187	+	0.605050i	$0.793153\pi$
$632$	5.79796	0.230630
$633$	12.0000	0.476957
$634$	−14.0000	−0.556011
$635$	−12.0000	−0.476205
$636$	7.79796	0.309209
$637$	117.283	4.64691
$638$	0	0
$639$	−8.89898	−0.352038
$640$	−1.00000	−0.0395285
$641$	−20.6969	−0.817480	−0.408740	−	0.912651i	$-0.634032\pi$
$641$	−20.6969	−0.817480	−0.408740	+	0.912651i	$0.634032\pi$
$642$	5.79796	0.228827
$643$	29.7980	1.17512	0.587558	−	0.809182i	$-0.300089\pi$
$643$	29.7980	1.17512	0.587558	+	0.809182i	$0.300089\pi$
$644$	19.5959	0.772187
$645$	−8.89898	−0.350397
$646$	4.00000	0.157378
$647$	−32.0000	−1.25805	−0.629025	−	0.777385i	$-0.716546\pi$
$647$	−32.0000	−1.25805	−0.629025	+	0.777385i	$0.716546\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	−6.89898	−0.270600
$651$	19.5959	0.768025
$652$	−2.20204	−0.0862386
$653$	30.0000	1.17399	0.586995	−	0.809590i	$-0.300311\pi$
$653$	30.0000	1.17399	0.586995	+	0.809590i	$0.300311\pi$
$654$	11.7980	0.461337
$655$	9.79796	0.382838
$656$	−2.89898	−0.113186
$657$	−10.8990	−0.425210
$658$	48.0000	1.87123
$659$	30.6969	1.19578	0.597891	−	0.801577i	$-0.296005\pi$
$659$	30.6969	1.19578	0.597891	+	0.801577i	$0.296005\pi$
$660$	0	0
$661$	−19.7980	−0.770051	−0.385026	−	0.922906i	$-0.625807\pi$
$661$	−19.7980	−0.770051	−0.385026	+	0.922906i	$0.625807\pi$
$662$	5.79796	0.225344
$663$	6.89898	0.267934
$664$	−13.7980	−0.535465
$665$	−19.5959	−0.759897
$666$	−6.00000	−0.232495
$667$	−24.0000	−0.929284
$668$	2.20204	0.0851995
$669$	4.00000	0.154649
$670$	−0.898979	−0.0347306
$671$	0	0
$672$	−4.89898	−0.188982
$673$	−33.1010	−1.27595	−0.637975	−	0.770057i	$-0.720228\pi$
$673$	−33.1010	−1.27595	−0.637975	+	0.770057i	$0.720228\pi$
$674$	−32.6969	−1.25944
$675$	−1.00000	−0.0384900
$676$	34.5959	1.33061
$677$	−13.5959	−0.522534	−0.261267	−	0.965267i	$-0.584140\pi$
$677$	−13.5959	−0.522534	−0.261267	+	0.965267i	$0.584140\pi$
$678$	7.79796	0.299479
$679$	62.2020	2.38710
$680$	1.00000	0.0383482
$681$	21.7980	0.835300
$682$	0	0
$683$	12.0000	0.459167	0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000	0.459167	0.229584	+	0.973289i	$0.426264\pi$
$684$	4.00000	0.152944
$685$	14.0000	0.534913
$686$	48.9898	1.87044
$687$	13.5959	0.518717
$688$	8.89898	0.339270
$689$	−53.7980	−2.04954
$690$	−4.00000	−0.152277
$691$	−27.1918	−1.03443	−0.517213	−	0.855857i	$-0.673031\pi$
$691$	−27.1918	−1.03443	−0.517213	+	0.855857i	$0.673031\pi$
$692$	6.00000	0.228086
$693$	0	0
$694$	−21.7980	−0.827439
$695$	13.7980	0.523386
$696$	6.00000	0.227429
$697$	2.89898	0.109807
$698$	−4.20204	−0.159050
$699$	−14.0000	−0.529529
$700$	−4.89898	−0.185164
$701$	14.8990	0.562727	0.281363	−	0.959601i	$-0.409213\pi$
$701$	14.8990	0.562727	0.281363	+	0.959601i	$0.409213\pi$
$702$	6.89898	0.260385
$703$	24.0000	0.905177
$704$	0	0
$705$	−9.79796	−0.369012
$706$	26.0000	0.978523
$707$	92.5857	3.48204
$708$	−4.89898	−0.184115
$709$	−31.7980	−1.19420	−0.597099	−	0.802168i	$-0.703680\pi$
$709$	−31.7980	−1.19420	−0.597099	+	0.802168i	$0.703680\pi$
$710$	8.89898	0.333973
$711$	−5.79796	−0.217440
$712$	7.79796	0.292241
$713$	−16.0000	−0.599205
$714$	4.89898	0.183340
$715$	0	0
$716$	−4.89898	−0.183083
$717$	0	0
$718$	−37.3939	−1.39553
$719$	−12.4949	−0.465981	−0.232991	−	0.972479i	$-0.574851\pi$
$719$	−12.4949	−0.465981	−0.232991	+	0.972479i	$0.574851\pi$
$720$	1.00000	0.0372678
$721$	−19.5959	−0.729790
$722$	3.00000	0.111648
$723$	−13.5959	−0.505638
$724$	−4.20204	−0.156168
$725$	6.00000	0.222834
$726$	−11.0000	−0.408248
$727$	0.404082	0.0149866	0.00749329	−	0.999972i	$-0.497615\pi$
$727$	0.404082	0.0149866	0.00749329	+	0.999972i	$0.497615\pi$
$728$	33.7980	1.25264
$729$	1.00000	0.0370370
$730$	10.8990	0.403389
$731$	−8.89898	−0.329141
$732$	−11.7980	−0.436065
$733$	−46.4949	−1.71733	−0.858664	−	0.512539i	$-0.828705\pi$
$733$	−46.4949	−1.71733	−0.858664	+	0.512539i	$0.828705\pi$
$734$	27.1010	1.00032
$735$	−17.0000	−0.627054
$736$	4.00000	0.147442
$737$	0	0
$738$	2.89898	0.106713
$739$	−9.39388	−0.345559	−0.172780	−	0.984960i	$-0.555275\pi$
$739$	−9.39388	−0.345559	−0.172780	+	0.984960i	$0.555275\pi$
$740$	6.00000	0.220564
$741$	−27.5959	−1.01376
$742$	−38.2020	−1.40244
$743$	−9.39388	−0.344628	−0.172314	−	0.985042i	$-0.555124\pi$
$743$	−9.39388	−0.344628	−0.172314	+	0.985042i	$0.555124\pi$
$744$	4.00000	0.146647
$745$	−18.8990	−0.692405
$746$	−24.6969	−0.904219
$747$	13.7980	0.504841
$748$	0	0
$749$	−28.4041	−1.03786
$750$	1.00000	0.0365148
$751$	21.7980	0.795419	0.397709	−	0.917511i	$-0.369805\pi$
$751$	21.7980	0.795419	0.397709	+	0.917511i	$0.369805\pi$
$752$	9.79796	0.357295
$753$	−4.89898	−0.178529
$754$	−41.3939	−1.50748
$755$	−9.79796	−0.356584
$756$	4.89898	0.178174
$757$	−4.69694	−0.170713	−0.0853566	−	0.996350i	$-0.527203\pi$
$757$	−4.69694	−0.170713	−0.0853566	+	0.996350i	$0.527203\pi$
$758$	29.7980	1.08231
$759$	0	0
$760$	−4.00000	−0.145095
$761$	−1.59592	−0.0578520	−0.0289260	−	0.999582i	$-0.509209\pi$
$761$	−1.59592	−0.0578520	−0.0289260	+	0.999582i	$0.509209\pi$
$762$	−12.0000	−0.434714
$763$	−57.7980	−2.09243
$764$	−9.79796	−0.354478
$765$	−1.00000	−0.0361551
$766$	−8.00000	−0.289052
$767$	33.7980	1.22037
$768$	−1.00000	−0.0360844
$769$	26.0000	0.937584	0.468792	−	0.883309i	$-0.344689\pi$
$769$	26.0000	0.937584	0.468792	+	0.883309i	$0.344689\pi$
$770$	0	0
$771$	2.00000	0.0720282
$772$	−1.10102	−0.0396266
$773$	−35.3939	−1.27303	−0.636515	−	0.771265i	$-0.719625\pi$
$773$	−35.3939	−1.27303	−0.636515	+	0.771265i	$0.719625\pi$
$774$	−8.89898	−0.319867
$775$	4.00000	0.143684
$776$	12.6969	0.455794
$777$	29.3939	1.05450
$778$	38.4949	1.38011
$779$	−11.5959	−0.415467
$780$	−6.89898	−0.247023
$781$	0	0
$782$	−4.00000	−0.143040
$783$	−6.00000	−0.214423
$784$	17.0000	0.607143
$785$	−1.10102	−0.0392971
$786$	9.79796	0.349482
$787$	−45.7980	−1.63252	−0.816260	−	0.577684i	$-0.803957\pi$
$787$	−45.7980	−1.63252	−0.816260	+	0.577684i	$0.803957\pi$
$788$	−13.5959	−0.484335
$789$	−8.00000	−0.284808
$790$	5.79796	0.206282
$791$	−38.2020	−1.35831
$792$	0	0
$793$	81.3939	2.89038
$794$	−1.59592	−0.0566370
$795$	7.79796	0.276565
$796$	15.5959	0.552783
$797$	26.0000	0.920967	0.460484	−	0.887668i	$-0.347676\pi$
$797$	26.0000	0.920967	0.460484	+	0.887668i	$0.347676\pi$
$798$	−19.5959	−0.693688
$799$	−9.79796	−0.346627
$800$	−1.00000	−0.0353553
$801$	−7.79796	−0.275527
$802$	−22.8990	−0.808591
$803$	0	0
$804$	−0.898979	−0.0317046
$805$	19.5959	0.690665
$806$	−27.5959	−0.972025
$807$	−9.59592	−0.337792
$808$	18.8990	0.664864
$809$	32.6969	1.14956	0.574782	−	0.818307i	$-0.305087\pi$
$809$	32.6969	1.14956	0.574782	+	0.818307i	$0.305087\pi$
$810$	−1.00000	−0.0351364
$811$	25.3939	0.891700	0.445850	−	0.895108i	$-0.352902\pi$
$811$	25.3939	0.891700	0.445850	+	0.895108i	$0.352902\pi$
$812$	−29.3939	−1.03152
$813$	1.79796	0.0630572
$814$	0	0
$815$	−2.20204	−0.0771341
$816$	1.00000	0.0350070
$817$	35.5959	1.24534
$818$	17.5959	0.615227
$819$	−33.7980	−1.18100
$820$	−2.89898	−0.101237
$821$	15.7980	0.551353	0.275676	−	0.961251i	$-0.411098\pi$
$821$	15.7980	0.551353	0.275676	+	0.961251i	$0.411098\pi$
$822$	14.0000	0.488306
$823$	20.8990	0.728493	0.364246	−	0.931303i	$-0.381327\pi$
$823$	20.8990	0.728493	0.364246	+	0.931303i	$0.381327\pi$
$824$	−4.00000	−0.139347
$825$	0	0
$826$	24.0000	0.835067
$827$	−4.00000	−0.139094	−0.0695468	−	0.997579i	$-0.522155\pi$
$827$	−4.00000	−0.139094	−0.0695468	+	0.997579i	$0.522155\pi$
$828$	−4.00000	−0.139010
$829$	3.39388	0.117874	0.0589371	−	0.998262i	$-0.481229\pi$
$829$	3.39388	0.117874	0.0589371	+	0.998262i	$0.481229\pi$
$830$	−13.7980	−0.478934
$831$	−7.79796	−0.270508
$832$	6.89898	0.239179
$833$	−17.0000	−0.589015
$834$	13.7980	0.477784
$835$	2.20204	0.0762048
$836$	0	0
$837$	−4.00000	−0.138260
$838$	17.7980	0.614820
$839$	−7.10102	−0.245154	−0.122577	−	0.992459i	$-0.539116\pi$
$839$	−7.10102	−0.245154	−0.122577	+	0.992459i	$0.539116\pi$
$840$	−4.89898	−0.169031
$841$	7.00000	0.241379
$842$	−14.0000	−0.482472
$843$	−27.7980	−0.957413
$844$	−12.0000	−0.413057
$845$	34.5959	1.19014
$846$	−9.79796	−0.336861
$847$	53.8888	1.85164
$848$	−7.79796	−0.267783
$849$	−23.5959	−0.809810
$850$	1.00000	0.0342997
$851$	−24.0000	−0.822709
$852$	8.89898	0.304874
$853$	11.3939	0.390119	0.195059	−	0.980791i	$-0.437510\pi$
$853$	11.3939	0.390119	0.195059	+	0.980791i	$0.437510\pi$
$854$	57.7980	1.97781
$855$	4.00000	0.136797
$856$	−5.79796	−0.198170
$857$	−10.0000	−0.341593	−0.170797	−	0.985306i	$-0.554634\pi$
$857$	−10.0000	−0.341593	−0.170797	+	0.985306i	$0.554634\pi$
$858$	0	0
$859$	5.79796	0.197824	0.0989119	−	0.995096i	$-0.468464\pi$
$859$	5.79796	0.197824	0.0989119	+	0.995096i	$0.468464\pi$
$860$	8.89898	0.303453
$861$	−14.2020	−0.484004
$862$	23.1010	0.786824
$863$	−45.3939	−1.54523	−0.772613	−	0.634878i	$-0.781051\pi$
$863$	−45.3939	−1.54523	−0.772613	+	0.634878i	$0.781051\pi$
$864$	1.00000	0.0340207
$865$	6.00000	0.204006
$866$	35.3939	1.20273
$867$	−1.00000	−0.0339618
$868$	−19.5959	−0.665129
$869$	0	0
$870$	6.00000	0.203419
$871$	6.20204	0.210148
$872$	−11.7980	−0.399529
$873$	−12.6969	−0.429726
$874$	16.0000	0.541208
$875$	−4.89898	−0.165616
$876$	10.8990	0.368242
$877$	−31.3939	−1.06010	−0.530048	−	0.847968i	$-0.677826\pi$
$877$	−31.3939	−1.06010	−0.530048	+	0.847968i	$0.677826\pi$
$878$	−5.79796	−0.195672
$879$	−13.5959	−0.458579
$880$	0	0
$881$	34.4949	1.16216	0.581081	−	0.813846i	$-0.302630\pi$
$881$	34.4949	1.16216	0.581081	+	0.813846i	$0.302630\pi$
$882$	−17.0000	−0.572420
$883$	26.6969	0.898424	0.449212	−	0.893425i	$-0.351705\pi$
$883$	26.6969	0.898424	0.449212	+	0.893425i	$0.351705\pi$
$884$	−6.89898	−0.232038
$885$	−4.89898	−0.164677
$886$	−37.7980	−1.26985
$887$	−12.0000	−0.402921	−0.201460	−	0.979497i	$-0.564569\pi$
$887$	−12.0000	−0.402921	−0.201460	+	0.979497i	$0.564569\pi$
$888$	6.00000	0.201347
$889$	58.7878	1.97168
$890$	7.79796	0.261388
$891$	0	0
$892$	−4.00000	−0.133930
$893$	39.1918	1.31150
$894$	−18.8990	−0.632076
$895$	−4.89898	−0.163755
$896$	4.89898	0.163663
$897$	27.5959	0.921401
$898$	−6.89898	−0.230222
$899$	24.0000	0.800445
$900$	1.00000	0.0333333
$901$	7.79796	0.259788
$902$	0	0
$903$	43.5959	1.45078
$904$	−7.79796	−0.259356
$905$	−4.20204	−0.139681
$906$	−9.79796	−0.325515
$907$	−33.3939	−1.10883	−0.554413	−	0.832242i	$-0.687057\pi$
$907$	−33.3939	−1.10883	−0.554413	+	0.832242i	$0.687057\pi$
$908$	−21.7980	−0.723391
$909$	−18.8990	−0.626840
$910$	33.7980	1.12039
$911$	23.1010	0.765371	0.382685	−	0.923879i	$-0.374999\pi$
$911$	23.1010	0.765371	0.382685	+	0.923879i	$0.374999\pi$
$912$	−4.00000	−0.132453
$913$	0	0
$914$	−16.2020	−0.535916
$915$	−11.7980	−0.390028
$916$	−13.5959	−0.449222
$917$	−48.0000	−1.58510
$918$	−1.00000	−0.0330049
$919$	1.79796	0.0593092	0.0296546	−	0.999560i	$-0.490559\pi$
$919$	1.79796	0.0593092	0.0296546	+	0.999560i	$0.490559\pi$
$920$	4.00000	0.131876
$921$	−0.898979	−0.0296224
$922$	28.6969	0.945083
$923$	−61.3939	−2.02080
$924$	0	0
$925$	6.00000	0.197279
$926$	−7.59592	−0.249617
$927$	4.00000	0.131377
$928$	−6.00000	−0.196960
$929$	36.2929	1.19073	0.595365	−	0.803455i	$-0.297007\pi$
$929$	36.2929	1.19073	0.595365	+	0.803455i	$0.297007\pi$
$930$	4.00000	0.131165
$931$	68.0000	2.22861
$932$	14.0000	0.458585
$933$	7.10102	0.232477
$934$	7.59592	0.248546
$935$	0	0
$936$	−6.89898	−0.225500
$937$	39.3939	1.28694	0.643471	−	0.765471i	$-0.277494\pi$
$937$	39.3939	1.28694	0.643471	+	0.765471i	$0.277494\pi$
$938$	4.40408	0.143798
$939$	−6.89898	−0.225140
$940$	9.79796	0.319574
$941$	−16.2020	−0.528171	−0.264086	−	0.964499i	$-0.585070\pi$
$941$	−16.2020	−0.528171	−0.264086	+	0.964499i	$0.585070\pi$
$942$	−1.10102	−0.0358732
$943$	11.5959	0.377615
$944$	4.89898	0.159448
$945$	4.89898	0.159364
$946$	0	0
$947$	21.7980	0.708338	0.354169	−	0.935181i	$-0.384764\pi$
$947$	21.7980	0.708338	0.354169	+	0.935181i	$0.384764\pi$
$948$	5.79796	0.188309
$949$	−75.1918	−2.44083
$950$	−4.00000	−0.129777
$951$	−14.0000	−0.453981
$952$	−4.89898	−0.158777
$953$	−41.1918	−1.33433	−0.667167	−	0.744908i	$-0.732493\pi$
$953$	−41.1918	−1.33433	−0.667167	+	0.744908i	$0.732493\pi$
$954$	7.79796	0.252468
$955$	−9.79796	−0.317055
$956$	0	0
$957$	0	0
$958$	32.8990	1.06292
$959$	−68.5857	−2.21475
$960$	−1.00000	−0.0322749
$961$	−15.0000	−0.483871
$962$	−41.3939	−1.33459
$963$	5.79796	0.186837
$964$	13.5959	0.437895
$965$	−1.10102	−0.0354431
$966$	19.5959	0.630488
$967$	−41.3939	−1.33114	−0.665569	−	0.746337i	$-0.731811\pi$
$967$	−41.3939	−1.33114	−0.665569	+	0.746337i	$0.731811\pi$
$968$	11.0000	0.353553
$969$	4.00000	0.128499
$970$	12.6969	0.407674
$971$	38.6969	1.24184	0.620922	−	0.783872i	$-0.286758\pi$
$971$	38.6969	1.24184	0.620922	+	0.783872i	$0.286758\pi$
$972$	−1.00000	−0.0320750
$973$	−67.5959	−2.16703
$974$	20.8990	0.669646
$975$	−6.89898	−0.220944
$976$	11.7980	0.377643
$977$	−29.5959	−0.946857	−0.473429	−	0.880832i	$-0.656984\pi$
$977$	−29.5959	−0.946857	−0.473429	+	0.880832i	$0.656984\pi$
$978$	−2.20204	−0.0704135
$979$	0	0
$980$	17.0000	0.543045
$981$	11.7980	0.376680
$982$	1.30306	0.0415824
$983$	9.39388	0.299618	0.149809	−	0.988715i	$-0.452134\pi$
$983$	9.39388	0.299618	0.149809	+	0.988715i	$0.452134\pi$
$984$	−2.89898	−0.0924161
$985$	−13.5959	−0.433202
$986$	6.00000	0.191079
$987$	48.0000	1.52786
$988$	27.5959	0.877943
$989$	−35.5959	−1.13188
$990$	0	0
$991$	−15.5959	−0.495421	−0.247710	−	0.968834i	$-0.579678\pi$
$991$	−15.5959	−0.495421	−0.247710	+	0.968834i	$0.579678\pi$
$992$	−4.00000	−0.127000
$993$	5.79796	0.183993
$994$	−43.5959	−1.38278
$995$	15.5959	0.494424
$996$	−13.7980	−0.437205
$997$	−21.5959	−0.683950	−0.341975	−	0.939709i	$-0.611096\pi$
$997$	−21.5959	−0.683950	−0.341975	+	0.939709i	$0.611096\pi$
$998$	39.5959	1.25339
$999$	−6.00000	−0.189832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.a.h.1.1	✓	2
3.2	odd	2		1530.2.a.s.1.1		2
4.3	odd	2		4080.2.a.bq.1.2		2
5.2	odd	4		2550.2.d.u.2449.1		4
5.3	odd	4		2550.2.d.u.2449.4		4
5.4	even	2		2550.2.a.bl.1.2		2
15.14	odd	2		7650.2.a.cu.1.2		2
17.16	even	2		8670.2.a.be.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.a.h.1.1	✓	2	1.1	even	1	trivial
1530.2.a.s.1.1		2	3.2	odd	2
2550.2.a.bl.1.2		2	5.4	even	2
2550.2.d.u.2449.1		4	5.2	odd	4
2550.2.d.u.2449.4		4	5.3	odd	4
4080.2.a.bq.1.2		2	4.3	odd	2
7650.2.a.cu.1.2		2	15.14	odd	2
8670.2.a.be.1.2		2	17.16	even	2

Overview	Random
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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:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -4.89898 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -4.89898 q^{7} -1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{12} +6.89898 q^{13} +4.89898 q^{14} -1.00000 q^{15} +1.00000 q^{16} -1.00000 q^{17} -1.00000 q^{18} +4.00000 q^{19} +1.00000 q^{20} +4.89898 q^{21} -4.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} -6.89898 q^{26} -1.00000 q^{27} -4.89898 q^{28} +6.00000 q^{29} +1.00000 q^{30} +4.00000 q^{31} -1.00000 q^{32} +1.00000 q^{34} -4.89898 q^{35} +1.00000 q^{36} +6.00000 q^{37} -4.00000 q^{38} -6.89898 q^{39} -1.00000 q^{40} -2.89898 q^{41} -4.89898 q^{42} +8.89898 q^{43} +1.00000 q^{45} +4.00000 q^{46} +9.79796 q^{47} -1.00000 q^{48} +17.0000 q^{49} -1.00000 q^{50} +1.00000 q^{51} +6.89898 q^{52} -7.79796 q^{53} +1.00000 q^{54} +4.89898 q^{56} -4.00000 q^{57} -6.00000 q^{58} +4.89898 q^{59} -1.00000 q^{60} +11.7980 q^{61} -4.00000 q^{62} -4.89898 q^{63} +1.00000 q^{64} +6.89898 q^{65} +0.898979 q^{67} -1.00000 q^{68} +4.00000 q^{69} +4.89898 q^{70} -8.89898 q^{71} -1.00000 q^{72} -10.8990 q^{73} -6.00000 q^{74} -1.00000 q^{75} +4.00000 q^{76} +6.89898 q^{78} -5.79796 q^{79} +1.00000 q^{80} +1.00000 q^{81} +2.89898 q^{82} +13.7980 q^{83} +4.89898 q^{84} -1.00000 q^{85} -8.89898 q^{86} -6.00000 q^{87} -7.79796 q^{89} -1.00000 q^{90} -33.7980 q^{91} -4.00000 q^{92} -4.00000 q^{93} -9.79796 q^{94} +4.00000 q^{95} +1.00000 q^{96} -12.6969 q^{97} -17.0000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} + 2 q^{6} - 2 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{12} + 4 q^{13} - 2 q^{15} + 2 q^{16} - 2 q^{17} - 2 q^{18} + 8 q^{19} + 2 q^{20} - 8 q^{23} + 2 q^{24} + 2 q^{25} - 4 q^{26} - 2 q^{27} + 12 q^{29} + 2 q^{30} + 8 q^{31} - 2 q^{32} + 2 q^{34} + 2 q^{36} + 12 q^{37} - 8 q^{38} - 4 q^{39} - 2 q^{40} + 4 q^{41} + 8 q^{43} + 2 q^{45} + 8 q^{46} - 2 q^{48} + 34 q^{49} - 2 q^{50} + 2 q^{51} + 4 q^{52} + 4 q^{53} + 2 q^{54} - 8 q^{57} - 12 q^{58} - 2 q^{60} + 4 q^{61} - 8 q^{62} + 2 q^{64} + 4 q^{65} - 8 q^{67} - 2 q^{68} + 8 q^{69} - 8 q^{71} - 2 q^{72} - 12 q^{73} - 12 q^{74} - 2 q^{75} + 8 q^{76} + 4 q^{78} + 8 q^{79} + 2 q^{80} + 2 q^{81} - 4 q^{82} + 8 q^{83} - 2 q^{85} - 8 q^{86} - 12 q^{87} + 4 q^{89} - 2 q^{90} - 48 q^{91} - 8 q^{92} - 8 q^{93} + 8 q^{95} + 2 q^{96} + 4 q^{97} - 34 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 + 2 * q^6 - 2 * q^8 + 2 * q^9 - 2 * q^10 - 2 * q^12 + 4 * q^13 - 2 * q^15 + 2 * q^16 - 2 * q^17 - 2 * q^18 + 8 * q^19 + 2 * q^20 - 8 * q^23 + 2 * q^24 + 2 * q^25 - 4 * q^26 - 2 * q^27 + 12 * q^29 + 2 * q^30 + 8 * q^31 - 2 * q^32 + 2 * q^34 + 2 * q^36 + 12 * q^37 - 8 * q^38 - 4 * q^39 - 2 * q^40 + 4 * q^41 + 8 * q^43 + 2 * q^45 + 8 * q^46 - 2 * q^48 + 34 * q^49 - 2 * q^50 + 2 * q^51 + 4 * q^52 + 4 * q^53 + 2 * q^54 - 8 * q^57 - 12 * q^58 - 2 * q^60 + 4 * q^61 - 8 * q^62 + 2 * q^64 + 4 * q^65 - 8 * q^67 - 2 * q^68 + 8 * q^69 - 8 * q^71 - 2 * q^72 - 12 * q^73 - 12 * q^74 - 2 * q^75 + 8 * q^76 + 4 * q^78 + 8 * q^79 + 2 * q^80 + 2 * q^81 - 4 * q^82 + 8 * q^83 - 2 * q^85 - 8 * q^86 - 12 * q^87 + 4 * q^89 - 2 * q^90 - 48 * q^91 - 8 * q^92 - 8 * q^93 + 8 * q^95 + 2 * q^96 + 4 * q^97 - 34 * q^98

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