LMFDB - Embedded newform 1450.2.d.b.1449.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1450,2,Mod(1449,1450)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1450.1449"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1450, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1450.d (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,-2,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.5783082931$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 58)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1449.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	1450.1449
Dual form			1450.2.d.b.1449.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -2.00000i q^{7} -1.00000 q^{8} -2.00000 q^{9} -5.00000i q^{11} +1.00000 q^{12} +1.00000i q^{13} +2.00000i q^{14} +1.00000 q^{16} +2.00000 q^{17} +2.00000 q^{18} -4.00000i q^{19} -2.00000i q^{21} +5.00000i q^{22} +6.00000i q^{23} -1.00000 q^{24} -1.00000i q^{26} -5.00000 q^{27} -2.00000i q^{28} +(-5.00000 - 2.00000i) q^{29} +5.00000i q^{31} -1.00000 q^{32} -5.00000i q^{33} -2.00000 q^{34} -2.00000 q^{36} -8.00000 q^{37} +4.00000i q^{38} +1.00000i q^{39} -10.0000i q^{41} +2.00000i q^{42} -9.00000 q^{43} -5.00000i q^{44} -6.00000i q^{46} -3.00000 q^{47} +1.00000 q^{48} +3.00000 q^{49} +2.00000 q^{51} +1.00000i q^{52} +1.00000i q^{53} +5.00000 q^{54} +2.00000i q^{56} -4.00000i q^{57} +(5.00000 + 2.00000i) q^{58} -10.0000 q^{59} -10.0000i q^{61} -5.00000i q^{62} +4.00000i q^{63} +1.00000 q^{64} +5.00000i q^{66} +8.00000i q^{67} +2.00000 q^{68} +6.00000i q^{69} -8.00000 q^{71} +2.00000 q^{72} +16.0000 q^{73} +8.00000 q^{74} -4.00000i q^{76} -10.0000 q^{77} -1.00000i q^{78} +1.00000i q^{79} +1.00000 q^{81} +10.0000i q^{82} -14.0000i q^{83} -2.00000i q^{84} +9.00000 q^{86} +(-5.00000 - 2.00000i) q^{87} +5.00000i q^{88} -14.0000i q^{89} +2.00000 q^{91} +6.00000i q^{92} +5.00000i q^{93} +3.00000 q^{94} -1.00000 q^{96} +2.00000 q^{97} -3.00000 q^{98} +10.0000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} - 2 q^{8} - 4 q^{9} + 2 q^{12} + 2 q^{16} + 4 q^{17} + 4 q^{18} - 2 q^{24} - 10 q^{27} - 10 q^{29} - 2 q^{32} - 4 q^{34} - 4 q^{36} - 16 q^{37} - 18 q^{43} - 6 q^{47}+ \cdots - 6 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 - 2 * q^8 - 4 * q^9 + 2 * q^12 + 2 * q^16 + 4 * q^17 + 4 * q^18 - 2 * q^24 - 10 * q^27 - 10 * q^29 - 2 * q^32 - 4 * q^34 - 4 * q^36 - 16 * q^37 - 18 * q^43 - 6 * q^47 + 2 * q^48 + 6 * q^49 + 4 * q^51 + 10 * q^54 + 10 * q^58 - 20 * q^59 + 2 * q^64 + 4 * q^68 - 16 * q^71 + 4 * q^72 + 32 * q^73 + 16 * q^74 - 20 * q^77 + 2 * q^81 + 18 * q^86 - 10 * q^87 + 4 * q^91 + 6 * q^94 - 2 * q^96 + 4 * q^97 - 6 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1450\mathbb{Z}\right)^\times$.

$n$	$901$	$1277$
$\chi(n)$	$-1$	$-1$

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			0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000			0.577350			0.288675	+	0.957427i	$0.406785\pi$
$4$	1.00000			0.500000
$5$		0			0
$5$		0			0
$6$	−1.00000			−0.408248
$7$		−	2.00000i		−	0.755929i	−0.925820	−	0.377964i	$-0.876624\pi$
$7$		−	2.00000i		−	0.755929i	0.925820	−	0.377964i	$-0.123376\pi$
$8$	−1.00000			−0.353553
$9$	−2.00000			−0.666667
$10$		0			0
$11$		−	5.00000i		−	1.50756i	−0.657129	−	0.753778i	$-0.728229\pi$
$11$		−	5.00000i		−	1.50756i	0.657129	−	0.753778i	$-0.271771\pi$
$12$	1.00000			0.288675
$13$			1.00000i			0.277350i	0.990338	+	0.138675i	$0.0442844\pi$
$13$			1.00000i			0.277350i	−0.990338	+	0.138675i	$0.955716\pi$
$14$			2.00000i			0.534522i
$15$		0			0
$16$	1.00000			0.250000
$17$	2.00000			0.485071			0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000			0.485071			0.242536	+	0.970143i	$0.422021\pi$
$18$	2.00000			0.471405
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$		0			0
$21$		−	2.00000i		−	0.436436i
$22$			5.00000i			1.06600i
$23$			6.00000i			1.25109i	0.780189	+	0.625543i	$0.215123\pi$
$23$			6.00000i			1.25109i	−0.780189	+	0.625543i	$0.784877\pi$
$24$	−1.00000			−0.204124
$25$		0			0
$26$		−	1.00000i		−	0.196116i
$27$	−5.00000			−0.962250
$28$		−	2.00000i		−	0.377964i
$29$	−5.00000	−	2.00000i	−0.928477	−	0.371391i
$29$	−5.00000	−	2.00000i	−0.928477	−	0.371391i
$30$		0			0
$31$			5.00000i			0.898027i	0.893525	+	0.449013i	$0.148224\pi$
$31$			5.00000i			0.898027i	−0.893525	+	0.449013i	$0.851776\pi$
$32$	−1.00000			−0.176777
$33$		−	5.00000i		−	0.870388i
$34$	−2.00000			−0.342997
$35$		0			0
$36$	−2.00000			−0.333333
$37$	−8.00000			−1.31519			−0.657596	−	0.753371i	$-0.728427\pi$
$37$	−8.00000			−1.31519			−0.657596	+	0.753371i	$0.728427\pi$
$38$			4.00000i			0.648886i
$39$			1.00000i			0.160128i
$40$		0			0
$41$		−	10.0000i		−	1.56174i	−0.624695	−	0.780869i	$-0.714777\pi$
$41$		−	10.0000i		−	1.56174i	0.624695	−	0.780869i	$-0.285223\pi$
$42$			2.00000i			0.308607i
$43$	−9.00000			−1.37249			−0.686244	−	0.727372i	$-0.740742\pi$
$43$	−9.00000			−1.37249			−0.686244	+	0.727372i	$0.740742\pi$
$44$		−	5.00000i		−	0.753778i
$45$		0			0
$46$		−	6.00000i		−	0.884652i
$47$	−3.00000			−0.437595			−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000			−0.437595			−0.218797	+	0.975770i	$0.570213\pi$
$48$	1.00000			0.144338
$49$	3.00000			0.428571
$50$		0			0
$51$	2.00000			0.280056
$52$			1.00000i			0.138675i
$53$			1.00000i			0.137361i	0.997639	+	0.0686803i	$0.0218788\pi$
$53$			1.00000i			0.137361i	−0.997639	+	0.0686803i	$0.978121\pi$
$54$	5.00000			0.680414
$55$		0			0
$56$			2.00000i			0.267261i
$57$		−	4.00000i		−	0.529813i
$58$	5.00000	+	2.00000i	0.656532	+	0.262613i
$59$	−10.0000			−1.30189			−0.650945	−	0.759125i	$-0.725627\pi$
$59$	−10.0000			−1.30189			−0.650945	+	0.759125i	$0.725627\pi$
$60$		0			0
$61$		−	10.0000i		−	1.28037i	−0.768221	−	0.640184i	$-0.778858\pi$
$61$		−	10.0000i		−	1.28037i	0.768221	−	0.640184i	$-0.221142\pi$
$62$		−	5.00000i		−	0.635001i
$63$			4.00000i			0.503953i
$64$	1.00000			0.125000
$65$		0			0
$66$			5.00000i			0.615457i
$67$			8.00000i			0.977356i	0.872464	+	0.488678i	$0.162521\pi$
$67$			8.00000i			0.977356i	−0.872464	+	0.488678i	$0.837479\pi$
$68$	2.00000			0.242536
$69$			6.00000i			0.722315i
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$	2.00000			0.235702
$73$	16.0000			1.87266			0.936329	−	0.351123i	$-0.114200\pi$
$73$	16.0000			1.87266			0.936329	+	0.351123i	$0.114200\pi$
$74$	8.00000			0.929981
$75$		0			0
$76$		−	4.00000i		−	0.458831i
$77$	−10.0000			−1.13961
$78$		−	1.00000i		−	0.113228i
$79$			1.00000i			0.112509i	0.998416	+	0.0562544i	$0.0179158\pi$
$79$			1.00000i			0.112509i	−0.998416	+	0.0562544i	$0.982084\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$			10.0000i			1.10432i
$83$		−	14.0000i		−	1.53670i	−0.640030	−	0.768350i	$-0.721078\pi$
$83$		−	14.0000i		−	1.53670i	0.640030	−	0.768350i	$-0.278922\pi$
$84$		−	2.00000i		−	0.218218i
$85$		0			0
$86$	9.00000			0.970495
$87$	−5.00000	−	2.00000i	−0.536056	−	0.214423i
$88$			5.00000i			0.533002i
$89$		−	14.0000i		−	1.48400i	−0.670402	−	0.741999i	$-0.733878\pi$
$89$		−	14.0000i		−	1.48400i	0.670402	−	0.741999i	$-0.266122\pi$
$90$		0			0
$91$	2.00000			0.209657
$92$			6.00000i			0.625543i
$93$			5.00000i			0.518476i
$94$	3.00000			0.309426
$95$		0			0
$96$	−1.00000			−0.102062
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$	−3.00000			−0.303046
$99$			10.0000i			1.00504i
$100$		0			0
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$	−2.00000			−0.198030
$103$		−	4.00000i		−	0.394132i	−0.980390	−	0.197066i	$-0.936859\pi$
$103$		−	4.00000i		−	0.394132i	0.980390	−	0.197066i	$-0.0631413\pi$
$104$		−	1.00000i		−	0.0980581i
$105$		0			0
$106$		−	1.00000i		−	0.0971286i
$107$		−	2.00000i		−	0.193347i	−0.995316	−	0.0966736i	$-0.969180\pi$
$107$		−	2.00000i		−	0.193347i	0.995316	−	0.0966736i	$-0.0308203\pi$
$108$	−5.00000			−0.481125
$109$	15.0000			1.43674			0.718370	−	0.695662i	$-0.244889\pi$
$109$	15.0000			1.43674			0.718370	+	0.695662i	$0.244889\pi$
$110$		0			0
$111$	−8.00000			−0.759326
$112$		−	2.00000i		−	0.188982i
$113$	−4.00000			−0.376288			−0.188144	−	0.982141i	$-0.560247\pi$
$113$	−4.00000			−0.376288			−0.188144	+	0.982141i	$0.560247\pi$
$114$			4.00000i			0.374634i
$115$		0			0
$116$	−5.00000	−	2.00000i	−0.464238	−	0.185695i
$117$		−	2.00000i		−	0.184900i
$118$	10.0000			0.920575
$119$		−	4.00000i		−	0.366679i
$120$		0			0
$121$	−14.0000			−1.27273
$122$			10.0000i			0.905357i
$123$		−	10.0000i		−	0.901670i
$124$			5.00000i			0.449013i
$125$		0			0
$126$		−	4.00000i		−	0.356348i
$127$	12.0000			1.06483			0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000			1.06483			0.532414	+	0.846484i	$0.321285\pi$
$128$	−1.00000			−0.0883883
$129$	−9.00000			−0.792406
$130$		0			0
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$		−	5.00000i		−	0.435194i
$133$	−8.00000			−0.693688
$134$		−	8.00000i		−	0.691095i
$135$		0			0
$136$	−2.00000			−0.171499
$137$	12.0000			1.02523			0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000			1.02523			0.512615	+	0.858619i	$0.328677\pi$
$138$		−	6.00000i		−	0.510754i
$139$	−10.0000			−0.848189			−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000			−0.848189			−0.424094	+	0.905618i	$0.639408\pi$
$140$		0			0
$141$	−3.00000			−0.252646
$142$	8.00000			0.671345
$143$	5.00000			0.418121
$144$	−2.00000			−0.166667
$145$		0			0
$146$	−16.0000			−1.32417
$147$	3.00000			0.247436
$148$	−8.00000			−0.657596
$149$	−15.0000			−1.22885			−0.614424	−	0.788976i	$-0.710612\pi$
$149$	−15.0000			−1.22885			−0.614424	+	0.788976i	$0.710612\pi$
$150$		0			0
$151$	2.00000			0.162758			0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000			0.162758			0.0813788	+	0.996683i	$0.474068\pi$
$152$			4.00000i			0.324443i
$153$	−4.00000			−0.323381
$154$	10.0000			0.805823
$155$		0			0
$156$			1.00000i			0.0800641i
$157$	−18.0000			−1.43656			−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000			−1.43656			−0.718278	+	0.695756i	$0.755069\pi$
$158$		−	1.00000i		−	0.0795557i
$159$			1.00000i			0.0793052i
$160$		0			0
$161$	12.0000			0.945732
$162$	−1.00000			−0.0785674
$163$	1.00000			0.0783260			0.0391630	−	0.999233i	$-0.487531\pi$
$163$	1.00000			0.0783260			0.0391630	+	0.999233i	$0.487531\pi$
$164$		−	10.0000i		−	0.780869i
$165$		0			0
$166$			14.0000i			1.08661i
$167$		−	12.0000i		−	0.928588i	−0.885681	−	0.464294i	$-0.846308\pi$
$167$		−	12.0000i		−	0.928588i	0.885681	−	0.464294i	$-0.153692\pi$
$168$			2.00000i			0.154303i
$169$	12.0000			0.923077
$170$		0			0
$171$			8.00000i			0.611775i
$172$	−9.00000			−0.686244
$173$			6.00000i			0.456172i	0.973641	+	0.228086i	$0.0732467\pi$
$173$			6.00000i			0.456172i	−0.973641	+	0.228086i	$0.926753\pi$
$174$	5.00000	+	2.00000i	0.379049	+	0.151620i
$175$		0			0
$176$		−	5.00000i		−	0.376889i
$177$	−10.0000			−0.751646
$178$			14.0000i			1.04934i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$		0			0
$181$	17.0000			1.26360			0.631800	−	0.775131i	$-0.282316\pi$
$181$	17.0000			1.26360			0.631800	+	0.775131i	$0.282316\pi$
$182$	−2.00000			−0.148250
$183$		−	10.0000i		−	0.739221i
$184$		−	6.00000i		−	0.442326i
$185$		0			0
$186$		−	5.00000i		−	0.366618i
$187$		−	10.0000i		−	0.731272i
$188$	−3.00000			−0.218797
$189$			10.0000i			0.727393i
$190$		0			0
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$	1.00000			0.0721688
$193$	−14.0000			−1.00774			−0.503871	−	0.863779i	$-0.668091\pi$
$193$	−14.0000			−1.00774			−0.503871	+	0.863779i	$0.668091\pi$
$194$	−2.00000			−0.143592
$195$		0			0
$196$	3.00000			0.214286
$197$		−	2.00000i		−	0.142494i	−0.997459	−	0.0712470i	$-0.977302\pi$
$197$		−	2.00000i		−	0.142494i	0.997459	−	0.0712470i	$-0.0226979\pi$
$198$		−	10.0000i		−	0.710669i
$199$	−10.0000			−0.708881			−0.354441	−	0.935079i	$-0.615329\pi$
$199$	−10.0000			−0.708881			−0.354441	+	0.935079i	$0.615329\pi$
$200$		0			0
$201$			8.00000i			0.564276i
$202$		0			0
$203$	−4.00000	+	10.0000i	−0.280745	+	0.701862i
$204$	2.00000			0.140028
$205$		0			0
$206$			4.00000i			0.278693i
$207$		−	12.0000i		−	0.834058i
$208$			1.00000i			0.0693375i
$209$	−20.0000			−1.38343
$210$		0			0
$211$			5.00000i			0.344214i	0.985078	+	0.172107i	$0.0550575\pi$
$211$			5.00000i			0.344214i	−0.985078	+	0.172107i	$0.944942\pi$
$212$			1.00000i			0.0686803i
$213$	−8.00000			−0.548151
$214$			2.00000i			0.136717i
$215$		0			0
$216$	5.00000			0.340207
$217$	10.0000			0.678844
$218$	−15.0000			−1.01593
$219$	16.0000			1.08118
$220$		0			0
$221$			2.00000i			0.134535i
$222$	8.00000			0.536925
$223$		−	24.0000i		−	1.60716i	−0.595198	−	0.803579i	$-0.702926\pi$
$223$		−	24.0000i		−	1.60716i	0.595198	−	0.803579i	$-0.297074\pi$
$224$			2.00000i			0.133631i
$225$		0			0
$226$	4.00000			0.266076
$227$		−	12.0000i		−	0.796468i	−0.917284	−	0.398234i	$-0.869623\pi$
$227$		−	12.0000i		−	0.796468i	0.917284	−	0.398234i	$-0.130377\pi$
$228$		−	4.00000i		−	0.264906i
$229$			6.00000i			0.396491i	0.980152	+	0.198246i	$0.0635244\pi$
$229$			6.00000i			0.396491i	−0.980152	+	0.198246i	$0.936476\pi$
$230$		0			0
$231$	−10.0000			−0.657952
$232$	5.00000	+	2.00000i	0.328266	+	0.131306i
$233$			1.00000i			0.0655122i	0.999463	+	0.0327561i	$0.0104285\pi$
$233$			1.00000i			0.0655122i	−0.999463	+	0.0327561i	$0.989572\pi$
$234$			2.00000i			0.130744i
$235$		0			0
$236$	−10.0000			−0.650945
$237$			1.00000i			0.0649570i
$238$			4.00000i			0.259281i
$239$	30.0000			1.94054			0.970269	−	0.242028i	$-0.0778125\pi$
$239$	30.0000			1.94054			0.970269	+	0.242028i	$0.0778125\pi$
$240$		0			0
$241$	7.00000			0.450910			0.225455	−	0.974254i	$-0.427613\pi$
$241$	7.00000			0.450910			0.225455	+	0.974254i	$0.427613\pi$
$242$	14.0000			0.899954
$243$	16.0000			1.02640
$244$		−	10.0000i		−	0.640184i
$245$		0			0
$246$			10.0000i			0.637577i
$247$	4.00000			0.254514
$248$		−	5.00000i		−	0.317500i
$249$		−	14.0000i		−	0.887214i
$250$		0			0
$251$		−	15.0000i		−	0.946792i	−0.880850	−	0.473396i	$-0.843028\pi$
$251$		−	15.0000i		−	0.946792i	0.880850	−	0.473396i	$-0.156972\pi$
$252$			4.00000i			0.251976i
$253$	30.0000			1.88608
$254$	−12.0000			−0.752947
$255$		0			0
$256$	1.00000			0.0625000
$257$		−	7.00000i		−	0.436648i	−0.975876	−	0.218324i	$-0.929941\pi$
$257$		−	7.00000i		−	0.436648i	0.975876	−	0.218324i	$-0.0700590\pi$
$258$	9.00000			0.560316
$259$			16.0000i			0.994192i
$260$		0			0
$261$	10.0000	+	4.00000i	0.618984	+	0.247594i
$262$		0			0
$263$	−19.0000			−1.17159			−0.585795	−	0.810459i	$-0.699218\pi$
$263$	−19.0000			−1.17159			−0.585795	+	0.810459i	$0.699218\pi$
$264$			5.00000i			0.307729i
$265$		0			0
$266$	8.00000			0.490511
$267$		−	14.0000i		−	0.856786i
$268$			8.00000i			0.488678i
$269$			26.0000i			1.58525i	0.609711	+	0.792624i	$0.291286\pi$
$269$			26.0000i			1.58525i	−0.609711	+	0.792624i	$0.708714\pi$
$270$		0			0
$271$			25.0000i			1.51864i	0.650716	+	0.759321i	$0.274469\pi$
$271$			25.0000i			1.51864i	−0.650716	+	0.759321i	$0.725531\pi$
$272$	2.00000			0.121268
$273$	2.00000			0.121046
$274$	−12.0000			−0.724947
$275$		0			0
$276$			6.00000i			0.361158i
$277$			18.0000i			1.08152i	0.841178	+	0.540758i	$0.181862\pi$
$277$			18.0000i			1.08152i	−0.841178	+	0.540758i	$0.818138\pi$
$278$	10.0000			0.599760
$279$		−	10.0000i		−	0.598684i
$280$		0			0
$281$	−13.0000			−0.775515			−0.387757	−	0.921761i	$-0.626750\pi$
$281$	−13.0000			−0.775515			−0.387757	+	0.921761i	$0.626750\pi$
$282$	3.00000			0.178647
$283$			6.00000i			0.356663i	0.983970	+	0.178331i	$0.0570699\pi$
$283$			6.00000i			0.356663i	−0.983970	+	0.178331i	$0.942930\pi$
$284$	−8.00000			−0.474713
$285$		0			0
$286$	−5.00000			−0.295656
$287$	−20.0000			−1.18056
$288$	2.00000			0.117851
$289$	−13.0000			−0.764706
$290$		0			0
$291$	2.00000			0.117242
$292$	16.0000			0.936329
$293$	−4.00000			−0.233682			−0.116841	−	0.993151i	$-0.537277\pi$
$293$	−4.00000			−0.233682			−0.116841	+	0.993151i	$0.537277\pi$
$294$	−3.00000			−0.174964
$295$		0			0
$296$	8.00000			0.464991
$297$			25.0000i			1.45065i
$298$	15.0000			0.868927
$299$	−6.00000			−0.346989
$300$		0			0
$301$			18.0000i			1.03750i
$302$	−2.00000			−0.115087
$303$		0			0
$304$		−	4.00000i		−	0.229416i
$305$		0			0
$306$	4.00000			0.228665
$307$	−3.00000			−0.171219			−0.0856095	−	0.996329i	$-0.527284\pi$
$307$	−3.00000			−0.171219			−0.0856095	+	0.996329i	$0.527284\pi$
$308$	−10.0000			−0.569803
$309$		−	4.00000i		−	0.227552i
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$		−	1.00000i		−	0.0566139i
$313$			31.0000i			1.75222i	0.482108	+	0.876112i	$0.339871\pi$
$313$			31.0000i			1.75222i	−0.482108	+	0.876112i	$0.660129\pi$
$314$	18.0000			1.01580
$315$		0			0
$316$			1.00000i			0.0562544i
$317$	22.0000			1.23564			0.617822	−	0.786318i	$-0.288015\pi$
$317$	22.0000			1.23564			0.617822	+	0.786318i	$0.288015\pi$
$318$		−	1.00000i		−	0.0560772i
$319$	−10.0000	+	25.0000i	−0.559893	+	1.39973i
$320$		0			0
$321$		−	2.00000i		−	0.111629i
$322$	−12.0000			−0.668734
$323$		−	8.00000i		−	0.445132i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−1.00000			−0.0553849
$327$	15.0000			0.829502
$328$			10.0000i			0.552158i
$329$			6.00000i			0.330791i
$330$		0			0
$331$			25.0000i			1.37412i	0.726599	+	0.687062i	$0.241100\pi$
$331$			25.0000i			1.37412i	−0.726599	+	0.687062i	$0.758900\pi$
$332$		−	14.0000i		−	0.768350i
$333$	16.0000			0.876795
$334$			12.0000i			0.656611i
$335$		0			0
$336$		−	2.00000i		−	0.109109i
$337$	22.0000			1.19842			0.599208	−	0.800593i	$-0.295482\pi$
$337$	22.0000			1.19842			0.599208	+	0.800593i	$0.295482\pi$
$338$	−12.0000			−0.652714
$339$	−4.00000			−0.217250
$340$		0			0
$341$	25.0000			1.35383
$342$		−	8.00000i		−	0.432590i
$343$		−	20.0000i		−	1.07990i
$344$	9.00000			0.485247
$345$		0			0
$346$		−	6.00000i		−	0.322562i
$347$		−	12.0000i		−	0.644194i	−0.946707	−	0.322097i	$-0.895612\pi$
$347$		−	12.0000i		−	0.644194i	0.946707	−	0.322097i	$-0.104388\pi$
$348$	−5.00000	−	2.00000i	−0.268028	−	0.107211i
$349$	25.0000			1.33822			0.669110	−	0.743164i	$-0.266676\pi$
$349$	25.0000			1.33822			0.669110	+	0.743164i	$0.266676\pi$
$350$		0			0
$351$		−	5.00000i		−	0.266880i
$352$			5.00000i			0.266501i
$353$			6.00000i			0.319348i	0.987170	+	0.159674i	$0.0510443\pi$
$353$			6.00000i			0.319348i	−0.987170	+	0.159674i	$0.948956\pi$
$354$	10.0000			0.531494
$355$		0			0
$356$		−	14.0000i		−	0.741999i
$357$		−	4.00000i		−	0.211702i
$358$		0			0
$359$		−	19.0000i		−	1.00278i	−0.865221	−	0.501391i	$-0.832822\pi$
$359$		−	19.0000i		−	1.00278i	0.865221	−	0.501391i	$-0.167178\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	−17.0000			−0.893500
$363$	−14.0000			−0.734809
$364$	2.00000			0.104828
$365$		0			0
$366$			10.0000i			0.522708i
$367$	32.0000			1.67039			0.835193	−	0.549957i	$-0.185356\pi$
$367$	32.0000			1.67039			0.835193	+	0.549957i	$0.185356\pi$
$368$			6.00000i			0.312772i
$369$			20.0000i			1.04116i
$370$		0			0
$371$	2.00000			0.103835
$372$			5.00000i			0.259238i
$373$			11.0000i			0.569558i	0.958593	+	0.284779i	$0.0919203\pi$
$373$			11.0000i			0.569558i	−0.958593	+	0.284779i	$0.908080\pi$
$374$			10.0000i			0.517088i
$375$		0			0
$376$	3.00000			0.154713
$377$	2.00000	−	5.00000i	0.103005	−	0.257513i
$378$		−	10.0000i		−	0.514344i
$379$		−	4.00000i		−	0.205466i	−0.994709	−	0.102733i	$-0.967241\pi$
$379$		−	4.00000i		−	0.205466i	0.994709	−	0.102733i	$-0.0327588\pi$
$380$		0			0
$381$	12.0000			0.614779
$382$		0			0
$383$			6.00000i			0.306586i	0.988181	+	0.153293i	$0.0489878\pi$
$383$			6.00000i			0.306586i	−0.988181	+	0.153293i	$0.951012\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	14.0000			0.712581
$387$	18.0000			0.914991
$388$	2.00000			0.101535
$389$		−	24.0000i		−	1.21685i	−0.793612	−	0.608424i	$-0.791802\pi$
$389$		−	24.0000i		−	1.21685i	0.793612	−	0.608424i	$-0.208198\pi$
$390$		0			0
$391$			12.0000i			0.606866i
$392$	−3.00000			−0.151523
$393$		0			0
$394$			2.00000i			0.100759i
$395$		0			0
$396$			10.0000i			0.502519i
$397$		−	27.0000i		−	1.35509i	−0.735481	−	0.677546i	$-0.763044\pi$
$397$		−	27.0000i		−	1.35509i	0.735481	−	0.677546i	$-0.236956\pi$
$398$	10.0000			0.501255
$399$	−8.00000			−0.400501
$400$		0			0
$401$	7.00000			0.349563			0.174782	−	0.984607i	$-0.444078\pi$
$401$	7.00000			0.349563			0.174782	+	0.984607i	$0.444078\pi$
$402$		−	8.00000i		−	0.399004i
$403$	−5.00000			−0.249068
$404$		0			0
$405$		0			0
$406$	4.00000	−	10.0000i	0.198517	−	0.496292i
$407$			40.0000i			1.98273i
$408$	−2.00000			−0.0990148
$409$		−	4.00000i		−	0.197787i	−0.995098	−	0.0988936i	$-0.968470\pi$
$409$		−	4.00000i		−	0.197787i	0.995098	−	0.0988936i	$-0.0315304\pi$
$410$		0			0
$411$	12.0000			0.591916
$412$		−	4.00000i		−	0.197066i
$413$			20.0000i			0.984136i
$414$			12.0000i			0.589768i
$415$		0			0
$416$		−	1.00000i		−	0.0490290i
$417$	−10.0000			−0.489702
$418$	20.0000			0.978232
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$		−	10.0000i		−	0.487370i	−0.969854	−	0.243685i	$-0.921644\pi$
$421$		−	10.0000i		−	0.487370i	0.969854	−	0.243685i	$-0.0783563\pi$
$422$		−	5.00000i		−	0.243396i
$423$	6.00000			0.291730
$424$		−	1.00000i		−	0.0485643i
$425$		0			0
$426$	8.00000			0.387601
$427$	−20.0000			−0.967868
$428$		−	2.00000i		−	0.0966736i
$429$	5.00000			0.241402
$430$		0			0
$431$	22.0000			1.05970			0.529851	−	0.848091i	$-0.322248\pi$
$431$	22.0000			1.05970			0.529851	+	0.848091i	$0.322248\pi$
$432$	−5.00000			−0.240563
$433$	16.0000			0.768911			0.384455	−	0.923144i	$-0.374389\pi$
$433$	16.0000			0.768911			0.384455	+	0.923144i	$0.374389\pi$
$434$	−10.0000			−0.480015
$435$		0			0
$436$	15.0000			0.718370
$437$	24.0000			1.14808
$438$	−16.0000			−0.764510
$439$	30.0000			1.43182			0.715911	−	0.698192i	$-0.246012\pi$
$439$	30.0000			1.43182			0.715911	+	0.698192i	$0.246012\pi$
$440$		0			0
$441$	−6.00000			−0.285714
$442$		−	2.00000i		−	0.0951303i
$443$	−4.00000			−0.190046			−0.0950229	−	0.995475i	$-0.530292\pi$
$443$	−4.00000			−0.190046			−0.0950229	+	0.995475i	$0.530292\pi$
$444$	−8.00000			−0.379663
$445$		0			0
$446$			24.0000i			1.13643i
$447$	−15.0000			−0.709476
$448$		−	2.00000i		−	0.0944911i
$449$		−	24.0000i		−	1.13263i	−0.824189	−	0.566315i	$-0.808369\pi$
$449$		−	24.0000i		−	1.13263i	0.824189	−	0.566315i	$-0.191631\pi$
$450$		0			0
$451$	−50.0000			−2.35441
$452$	−4.00000			−0.188144
$453$	2.00000			0.0939682
$454$			12.0000i			0.563188i
$455$		0			0
$456$			4.00000i			0.187317i
$457$			18.0000i			0.842004i	0.907060	+	0.421002i	$0.138322\pi$
$457$			18.0000i			0.842004i	−0.907060	+	0.421002i	$0.861678\pi$
$458$		−	6.00000i		−	0.280362i
$459$	−10.0000			−0.466760
$460$		0			0
$461$			20.0000i			0.931493i	0.884918	+	0.465746i	$0.154214\pi$
$461$			20.0000i			0.931493i	−0.884918	+	0.465746i	$0.845786\pi$
$462$	10.0000			0.465242
$463$		−	14.0000i		−	0.650635i	−0.945605	−	0.325318i	$-0.894529\pi$
$463$		−	14.0000i		−	0.650635i	0.945605	−	0.325318i	$-0.105471\pi$
$464$	−5.00000	−	2.00000i	−0.232119	−	0.0928477i
$465$		0			0
$466$		−	1.00000i		−	0.0463241i
$467$	−3.00000			−0.138823			−0.0694117	−	0.997588i	$-0.522112\pi$
$467$	−3.00000			−0.138823			−0.0694117	+	0.997588i	$0.522112\pi$
$468$		−	2.00000i		−	0.0924500i
$469$	16.0000			0.738811
$470$		0			0
$471$	−18.0000			−0.829396
$472$	10.0000			0.460287
$473$			45.0000i			2.06910i
$474$		−	1.00000i		−	0.0459315i
$475$		0			0
$476$		−	4.00000i		−	0.183340i
$477$		−	2.00000i		−	0.0915737i
$478$	−30.0000			−1.37217
$479$			11.0000i			0.502603i	0.967909	+	0.251301i	$0.0808585\pi$
$479$			11.0000i			0.502603i	−0.967909	+	0.251301i	$0.919141\pi$
$480$		0			0
$481$		−	8.00000i		−	0.364769i
$482$	−7.00000			−0.318841
$483$	12.0000			0.546019
$484$	−14.0000			−0.636364
$485$		0			0
$486$	−16.0000			−0.725775
$487$			38.0000i			1.72194i	0.508652	+	0.860972i	$0.330144\pi$
$487$			38.0000i			1.72194i	−0.508652	+	0.860972i	$0.669856\pi$
$488$			10.0000i			0.452679i
$489$	1.00000			0.0452216
$490$		0			0
$491$			15.0000i			0.676941i	0.940977	+	0.338470i	$0.109909\pi$
$491$			15.0000i			0.676941i	−0.940977	+	0.338470i	$0.890091\pi$
$492$		−	10.0000i		−	0.450835i
$493$	−10.0000	−	4.00000i	−0.450377	−	0.180151i
$494$	−4.00000			−0.179969
$495$		0			0
$496$			5.00000i			0.224507i
$497$			16.0000i			0.717698i
$498$			14.0000i			0.627355i
$499$	30.0000			1.34298			0.671492	−	0.741012i	$-0.265654\pi$
$499$	30.0000			1.34298			0.671492	+	0.741012i	$0.265654\pi$
$500$		0			0
$501$		−	12.0000i		−	0.536120i
$502$			15.0000i			0.669483i
$503$	−39.0000			−1.73892			−0.869462	−	0.494000i	$-0.835534\pi$
$503$	−39.0000			−1.73892			−0.869462	+	0.494000i	$0.835534\pi$
$504$		−	4.00000i		−	0.178174i
$505$		0			0
$506$	−30.0000			−1.33366
$507$	12.0000			0.532939
$508$	12.0000			0.532414
$509$	−15.0000			−0.664863			−0.332432	−	0.943127i	$-0.607869\pi$
$509$	−15.0000			−0.664863			−0.332432	+	0.943127i	$0.607869\pi$
$510$		0			0
$511$		−	32.0000i		−	1.41560i
$512$	−1.00000			−0.0441942
$513$			20.0000i			0.883022i
$514$			7.00000i			0.308757i
$515$		0			0
$516$	−9.00000			−0.396203
$517$			15.0000i			0.659699i
$518$		−	16.0000i		−	0.703000i
$519$			6.00000i			0.263371i
$520$		0			0
$521$	17.0000			0.744784			0.372392	−	0.928076i	$-0.378538\pi$
$521$	17.0000			0.744784			0.372392	+	0.928076i	$0.378538\pi$
$522$	−10.0000	−	4.00000i	−0.437688	−	0.175075i
$523$		−	4.00000i		−	0.174908i	−0.996169	−	0.0874539i	$-0.972127\pi$
$523$		−	4.00000i		−	0.174908i	0.996169	−	0.0874539i	$-0.0278730\pi$
$524$		0			0
$525$		0			0
$526$	19.0000			0.828439
$527$			10.0000i			0.435607i
$528$		−	5.00000i		−	0.217597i
$529$	−13.0000			−0.565217
$530$		0			0
$531$	20.0000			0.867926
$532$	−8.00000			−0.346844
$533$	10.0000			0.433148
$534$			14.0000i			0.605839i
$535$		0			0
$536$		−	8.00000i		−	0.345547i
$537$		0			0
$538$		−	26.0000i		−	1.12094i
$539$		−	15.0000i		−	0.646096i
$540$		0			0
$541$		−	40.0000i		−	1.71973i	−0.510518	−	0.859867i	$-0.670546\pi$
$541$		−	40.0000i		−	1.71973i	0.510518	−	0.859867i	$-0.329454\pi$
$542$		−	25.0000i		−	1.07384i
$543$	17.0000			0.729540
$544$	−2.00000			−0.0857493
$545$		0			0
$546$	−2.00000			−0.0855921
$547$		−	22.0000i		−	0.940652i	−0.882493	−	0.470326i	$-0.844136\pi$
$547$		−	22.0000i		−	0.940652i	0.882493	−	0.470326i	$-0.155864\pi$
$548$	12.0000			0.512615
$549$			20.0000i			0.853579i
$550$		0			0
$551$	−8.00000	+	20.0000i	−0.340811	+	0.852029i
$552$		−	6.00000i		−	0.255377i
$553$	2.00000			0.0850487
$554$		−	18.0000i		−	0.764747i
$555$		0			0
$556$	−10.0000			−0.424094
$557$			18.0000i			0.762684i	0.924434	+	0.381342i	$0.124538\pi$
$557$			18.0000i			0.762684i	−0.924434	+	0.381342i	$0.875462\pi$
$558$			10.0000i			0.423334i
$559$		−	9.00000i		−	0.380659i
$560$		0			0
$561$		−	10.0000i		−	0.422200i
$562$	13.0000			0.548372
$563$	−19.0000			−0.800755			−0.400377	−	0.916350i	$-0.631121\pi$
$563$	−19.0000			−0.800755			−0.400377	+	0.916350i	$0.631121\pi$
$564$	−3.00000			−0.126323
$565$		0			0
$566$		−	6.00000i		−	0.252199i
$567$		−	2.00000i		−	0.0839921i
$568$	8.00000			0.335673
$569$		−	24.0000i		−	1.00613i	−0.864248	−	0.503066i	$-0.832205\pi$
$569$		−	24.0000i		−	1.00613i	0.864248	−	0.503066i	$-0.167795\pi$
$570$		0			0
$571$	−8.00000			−0.334790			−0.167395	−	0.985890i	$-0.553535\pi$
$571$	−8.00000			−0.334790			−0.167395	+	0.985890i	$0.553535\pi$
$572$	5.00000			0.209061
$573$		0			0
$574$	20.0000			0.834784
$575$		0			0
$576$	−2.00000			−0.0833333
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$	13.0000			0.540729
$579$	−14.0000			−0.581820
$580$		0			0
$581$	−28.0000			−1.16164
$582$	−2.00000			−0.0829027
$583$	5.00000			0.207079
$584$	−16.0000			−0.662085
$585$		0			0
$586$	4.00000			0.165238
$587$			18.0000i			0.742940i	0.928445	+	0.371470i	$0.121146\pi$
$587$			18.0000i			0.742940i	−0.928445	+	0.371470i	$0.878854\pi$
$588$	3.00000			0.123718
$589$	20.0000			0.824086
$590$		0			0
$591$		−	2.00000i		−	0.0822690i
$592$	−8.00000			−0.328798
$593$		−	29.0000i		−	1.19089i	−0.803397	−	0.595444i	$-0.796976\pi$
$593$		−	29.0000i		−	1.19089i	0.803397	−	0.595444i	$-0.203024\pi$
$594$		−	25.0000i		−	1.02576i
$595$		0			0
$596$	−15.0000			−0.614424
$597$	−10.0000			−0.409273
$598$	6.00000			0.245358
$599$		−	39.0000i		−	1.59350i	−0.604311	−	0.796748i	$-0.706552\pi$
$599$		−	39.0000i		−	1.59350i	0.604311	−	0.796748i	$-0.293448\pi$
$600$		0			0
$601$			30.0000i			1.22373i	0.790964	+	0.611863i	$0.209580\pi$
$601$			30.0000i			1.22373i	−0.790964	+	0.611863i	$0.790420\pi$
$602$		−	18.0000i		−	0.733625i
$603$		−	16.0000i		−	0.651570i
$604$	2.00000			0.0813788
$605$		0			0
$606$		0			0
$607$	−13.0000			−0.527654			−0.263827	−	0.964570i	$-0.584985\pi$
$607$	−13.0000			−0.527654			−0.263827	+	0.964570i	$0.584985\pi$
$608$			4.00000i			0.162221i
$609$	−4.00000	+	10.0000i	−0.162088	+	0.405220i
$610$		0			0
$611$		−	3.00000i		−	0.121367i
$612$	−4.00000			−0.161690
$613$		−	29.0000i		−	1.17130i	−0.810564	−	0.585649i	$-0.800840\pi$
$613$		−	29.0000i		−	1.17130i	0.810564	−	0.585649i	$-0.199160\pi$
$614$	3.00000			0.121070
$615$		0			0
$616$	10.0000			0.402911
$617$	−28.0000			−1.12724			−0.563619	−	0.826035i	$-0.690591\pi$
$617$	−28.0000			−1.12724			−0.563619	+	0.826035i	$0.690591\pi$
$618$			4.00000i			0.160904i
$619$		−	49.0000i		−	1.96948i	−0.174042	−	0.984738i	$-0.555683\pi$
$619$		−	49.0000i		−	1.96948i	0.174042	−	0.984738i	$-0.444317\pi$
$620$		0			0
$621$		−	30.0000i		−	1.20386i
$622$		0			0
$623$	−28.0000			−1.12180
$624$			1.00000i			0.0400320i
$625$		0			0
$626$		−	31.0000i		−	1.23901i
$627$	−20.0000			−0.798723
$628$	−18.0000			−0.718278
$629$	−16.0000			−0.637962
$630$		0			0
$631$	−8.00000			−0.318475			−0.159237	−	0.987240i	$-0.550904\pi$
$631$	−8.00000			−0.318475			−0.159237	+	0.987240i	$0.550904\pi$
$632$		−	1.00000i		−	0.0397779i
$633$			5.00000i			0.198732i
$634$	−22.0000			−0.873732
$635$		0			0
$636$			1.00000i			0.0396526i
$637$			3.00000i			0.118864i
$638$	10.0000	−	25.0000i	0.395904	−	0.989759i
$639$	16.0000			0.632950
$640$		0			0
$641$		−	30.0000i		−	1.18493i	−0.805597	−	0.592464i	$-0.798155\pi$
$641$		−	30.0000i		−	1.18493i	0.805597	−	0.592464i	$-0.201845\pi$
$642$			2.00000i			0.0789337i
$643$		−	14.0000i		−	0.552106i	−0.961142	−	0.276053i	$-0.910973\pi$
$643$		−	14.0000i		−	0.552106i	0.961142	−	0.276053i	$-0.0890266\pi$
$644$	12.0000			0.472866
$645$		0			0
$646$			8.00000i			0.314756i
$647$		−	22.0000i		−	0.864909i	−0.901656	−	0.432455i	$-0.857648\pi$
$647$		−	22.0000i		−	0.864909i	0.901656	−	0.432455i	$-0.142352\pi$
$648$	−1.00000			−0.0392837
$649$			50.0000i			1.96267i
$650$		0			0
$651$	10.0000			0.391931
$652$	1.00000			0.0391630
$653$	6.00000			0.234798			0.117399	−	0.993085i	$-0.462544\pi$
$653$	6.00000			0.234798			0.117399	+	0.993085i	$0.462544\pi$
$654$	−15.0000			−0.586546
$655$		0			0
$656$		−	10.0000i		−	0.390434i
$657$	−32.0000			−1.24844
$658$		−	6.00000i		−	0.233904i
$659$			31.0000i			1.20759i	0.797140	+	0.603794i	$0.206345\pi$
$659$			31.0000i			1.20759i	−0.797140	+	0.603794i	$0.793655\pi$
$660$		0			0
$661$	22.0000			0.855701			0.427850	−	0.903850i	$-0.359271\pi$
$661$	22.0000			0.855701			0.427850	+	0.903850i	$0.359271\pi$
$662$		−	25.0000i		−	0.971653i
$663$			2.00000i			0.0776736i
$664$			14.0000i			0.543305i
$665$		0			0
$666$	−16.0000			−0.619987
$667$	12.0000	−	30.0000i	0.464642	−	1.16160i
$668$		−	12.0000i		−	0.464294i
$669$		−	24.0000i		−	0.927894i
$670$		0			0
$671$	−50.0000			−1.93023
$672$			2.00000i			0.0771517i
$673$		−	19.0000i		−	0.732396i	−0.930537	−	0.366198i	$-0.880659\pi$
$673$		−	19.0000i		−	0.732396i	0.930537	−	0.366198i	$-0.119341\pi$
$674$	−22.0000			−0.847408
$675$		0			0
$676$	12.0000			0.461538
$677$	−8.00000			−0.307465			−0.153732	−	0.988113i	$-0.549129\pi$
$677$	−8.00000			−0.307465			−0.153732	+	0.988113i	$0.549129\pi$
$678$	4.00000			0.153619
$679$		−	4.00000i		−	0.153506i
$680$		0			0
$681$		−	12.0000i		−	0.459841i
$682$	−25.0000			−0.957299
$683$			36.0000i			1.37750i	0.724998	+	0.688751i	$0.241841\pi$
$683$			36.0000i			1.37750i	−0.724998	+	0.688751i	$0.758159\pi$
$684$			8.00000i			0.305888i
$685$		0			0
$686$			20.0000i			0.763604i
$687$			6.00000i			0.228914i
$688$	−9.00000			−0.343122
$689$	−1.00000			−0.0380970
$690$		0			0
$691$	−28.0000			−1.06517			−0.532585	−	0.846376i	$-0.678779\pi$
$691$	−28.0000			−1.06517			−0.532585	+	0.846376i	$0.678779\pi$
$692$			6.00000i			0.228086i
$693$	20.0000			0.759737
$694$			12.0000i			0.455514i
$695$		0			0
$696$	5.00000	+	2.00000i	0.189525	+	0.0758098i
$697$		−	20.0000i		−	0.757554i
$698$	−25.0000			−0.946264
$699$			1.00000i			0.0378235i
$700$		0			0
$701$	27.0000			1.01978			0.509888	−	0.860241i	$-0.329687\pi$
$701$	27.0000			1.01978			0.509888	+	0.860241i	$0.329687\pi$
$702$			5.00000i			0.188713i
$703$			32.0000i			1.20690i
$704$		−	5.00000i		−	0.188445i
$705$		0			0
$706$		−	6.00000i		−	0.225813i
$707$		0			0
$708$	−10.0000			−0.375823
$709$	5.00000			0.187779			0.0938895	−	0.995583i	$-0.470070\pi$
$709$	5.00000			0.187779			0.0938895	+	0.995583i	$0.470070\pi$
$710$		0			0
$711$		−	2.00000i		−	0.0750059i
$712$			14.0000i			0.524672i
$713$	−30.0000			−1.12351
$714$			4.00000i			0.149696i
$715$		0			0
$716$		0			0
$717$	30.0000			1.12037
$718$			19.0000i			0.709074i
$719$	20.0000			0.745874			0.372937	−	0.927857i	$-0.378351\pi$
$719$	20.0000			0.745874			0.372937	+	0.927857i	$0.378351\pi$
$720$		0			0
$721$	−8.00000			−0.297936
$722$	−3.00000			−0.111648
$723$	7.00000			0.260333
$724$	17.0000			0.631800
$725$		0			0
$726$	14.0000			0.519589
$727$	−48.0000			−1.78022			−0.890111	−	0.455744i	$-0.849373\pi$
$727$	−48.0000			−1.78022			−0.890111	+	0.455744i	$0.849373\pi$
$728$	−2.00000			−0.0741249
$729$	13.0000			0.481481
$730$		0			0
$731$	−18.0000			−0.665754
$732$		−	10.0000i		−	0.369611i
$733$	36.0000			1.32969			0.664845	−	0.746981i	$-0.268498\pi$
$733$	36.0000			1.32969			0.664845	+	0.746981i	$0.268498\pi$
$734$	−32.0000			−1.18114
$735$		0			0
$736$		−	6.00000i		−	0.221163i
$737$	40.0000			1.47342
$738$		−	20.0000i		−	0.736210i
$739$		−	9.00000i		−	0.331070i	−0.986204	−	0.165535i	$-0.947065\pi$
$739$		−	9.00000i		−	0.331070i	0.986204	−	0.165535i	$-0.0529351\pi$
$740$		0			0
$741$	4.00000			0.146944
$742$	−2.00000			−0.0734223
$743$	16.0000			0.586983			0.293492	−	0.955962i	$-0.405183\pi$
$743$	16.0000			0.586983			0.293492	+	0.955962i	$0.405183\pi$
$744$		−	5.00000i		−	0.183309i
$745$		0			0
$746$		−	11.0000i		−	0.402739i
$747$			28.0000i			1.02447i
$748$		−	10.0000i		−	0.365636i
$749$	−4.00000			−0.146157
$750$		0			0
$751$		−	40.0000i		−	1.45962i	−0.683650	−	0.729810i	$-0.739608\pi$
$751$		−	40.0000i		−	1.45962i	0.683650	−	0.729810i	$-0.260392\pi$
$752$	−3.00000			−0.109399
$753$		−	15.0000i		−	0.546630i
$754$	−2.00000	+	5.00000i	−0.0728357	+	0.182089i
$755$		0			0
$756$			10.0000i			0.363696i
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$			4.00000i			0.145287i
$759$	30.0000			1.08893
$760$		0			0
$761$	2.00000			0.0724999			0.0362500	−	0.999343i	$-0.488459\pi$
$761$	2.00000			0.0724999			0.0362500	+	0.999343i	$0.488459\pi$
$762$	−12.0000			−0.434714
$763$		−	30.0000i		−	1.08607i
$764$		0			0
$765$		0			0
$766$		−	6.00000i		−	0.216789i
$767$		−	10.0000i		−	0.361079i
$768$	1.00000			0.0360844
$769$		−	34.0000i		−	1.22607i	−0.790055	−	0.613036i	$-0.789948\pi$
$769$		−	34.0000i		−	1.22607i	0.790055	−	0.613036i	$-0.210052\pi$
$770$		0			0
$771$		−	7.00000i		−	0.252099i
$772$	−14.0000			−0.503871
$773$	−14.0000			−0.503545			−0.251773	−	0.967786i	$-0.581013\pi$
$773$	−14.0000			−0.503545			−0.251773	+	0.967786i	$0.581013\pi$
$774$	−18.0000			−0.646997
$775$		0			0
$776$	−2.00000			−0.0717958
$777$			16.0000i			0.573997i
$778$			24.0000i			0.860442i
$779$	−40.0000			−1.43315
$780$		0			0
$781$			40.0000i			1.43131i
$782$		−	12.0000i		−	0.429119i
$783$	25.0000	+	10.0000i	0.893427	+	0.357371i
$784$	3.00000			0.107143
$785$		0			0
$786$		0			0
$787$		−	32.0000i		−	1.14068i	−0.821410	−	0.570338i	$-0.806812\pi$
$787$		−	32.0000i		−	1.14068i	0.821410	−	0.570338i	$-0.193188\pi$
$788$		−	2.00000i		−	0.0712470i
$789$	−19.0000			−0.676418
$790$		0			0
$791$			8.00000i			0.284447i
$792$		−	10.0000i		−	0.355335i
$793$	10.0000			0.355110
$794$			27.0000i			0.958194i
$795$		0			0
$796$	−10.0000			−0.354441
$797$	2.00000			0.0708436			0.0354218	−	0.999372i	$-0.488723\pi$
$797$	2.00000			0.0708436			0.0354218	+	0.999372i	$0.488723\pi$
$798$	8.00000			0.283197
$799$	−6.00000			−0.212265
$800$		0			0
$801$			28.0000i			0.989331i
$802$	−7.00000			−0.247179
$803$		−	80.0000i		−	2.82314i
$804$			8.00000i			0.282138i
$805$		0			0
$806$	5.00000			0.176117
$807$			26.0000i			0.915243i
$808$		0			0
$809$		−	4.00000i		−	0.140633i	−0.997525	−	0.0703163i	$-0.977599\pi$
$809$		−	4.00000i		−	0.140633i	0.997525	−	0.0703163i	$-0.0224008\pi$
$810$		0			0
$811$	−18.0000			−0.632065			−0.316033	−	0.948748i	$-0.602351\pi$
$811$	−18.0000			−0.632065			−0.316033	+	0.948748i	$0.602351\pi$
$812$	−4.00000	+	10.0000i	−0.140372	+	0.350931i
$813$			25.0000i			0.876788i
$814$		−	40.0000i		−	1.40200i
$815$		0			0
$816$	2.00000			0.0700140
$817$			36.0000i			1.25948i
$818$			4.00000i			0.139857i
$819$	−4.00000			−0.139771
$820$		0			0
$821$	−33.0000			−1.15171			−0.575854	−	0.817553i	$-0.695330\pi$
$821$	−33.0000			−1.15171			−0.575854	+	0.817553i	$0.695330\pi$
$822$	−12.0000			−0.418548
$823$	−4.00000			−0.139431			−0.0697156	−	0.997567i	$-0.522209\pi$
$823$	−4.00000			−0.139431			−0.0697156	+	0.997567i	$0.522209\pi$
$824$			4.00000i			0.139347i
$825$		0			0
$826$		−	20.0000i		−	0.695889i
$827$	−33.0000			−1.14752			−0.573761	−	0.819023i	$-0.694516\pi$
$827$	−33.0000			−1.14752			−0.573761	+	0.819023i	$0.694516\pi$
$828$		−	12.0000i		−	0.417029i
$829$			26.0000i			0.903017i	0.892267	+	0.451509i	$0.149114\pi$
$829$			26.0000i			0.903017i	−0.892267	+	0.451509i	$0.850886\pi$
$830$		0			0
$831$			18.0000i			0.624413i
$832$			1.00000i			0.0346688i
$833$	6.00000			0.207888
$834$	10.0000			0.346272
$835$		0			0
$836$	−20.0000			−0.691714
$837$		−	25.0000i		−	0.864126i
$838$		0			0
$839$			21.0000i			0.725001i	0.931984	+	0.362500i	$0.118077\pi$
$839$			21.0000i			0.725001i	−0.931984	+	0.362500i	$0.881923\pi$
$840$		0			0
$841$	21.0000	+	20.0000i	0.724138	+	0.689655i
$842$			10.0000i			0.344623i
$843$	−13.0000			−0.447744
$844$			5.00000i			0.172107i
$845$		0			0
$846$	−6.00000			−0.206284
$847$			28.0000i			0.962091i
$848$			1.00000i			0.0343401i
$849$			6.00000i			0.205919i
$850$		0			0
$851$		−	48.0000i		−	1.64542i
$852$	−8.00000			−0.274075
$853$	−4.00000			−0.136957			−0.0684787	−	0.997653i	$-0.521815\pi$
$853$	−4.00000			−0.136957			−0.0684787	+	0.997653i	$0.521815\pi$
$854$	20.0000			0.684386
$855$		0			0
$856$			2.00000i			0.0683586i
$857$			13.0000i			0.444072i	0.975039	+	0.222036i	$0.0712702\pi$
$857$			13.0000i			0.444072i	−0.975039	+	0.222036i	$0.928730\pi$
$858$	−5.00000			−0.170697
$859$			41.0000i			1.39890i	0.714681	+	0.699451i	$0.246572\pi$
$859$			41.0000i			1.39890i	−0.714681	+	0.699451i	$0.753428\pi$
$860$		0			0
$861$	−20.0000			−0.681598
$862$	−22.0000			−0.749323
$863$			36.0000i			1.22545i	0.790295	+	0.612727i	$0.209928\pi$
$863$			36.0000i			1.22545i	−0.790295	+	0.612727i	$0.790072\pi$
$864$	5.00000			0.170103
$865$		0			0
$866$	−16.0000			−0.543702
$867$	−13.0000			−0.441503
$868$	10.0000			0.339422
$869$	5.00000			0.169613
$870$		0			0
$871$	−8.00000			−0.271070
$872$	−15.0000			−0.507964
$873$	−4.00000			−0.135379
$874$	−24.0000			−0.811812
$875$		0			0
$876$	16.0000			0.540590
$877$			43.0000i			1.45201i	0.687691	+	0.726003i	$0.258624\pi$
$877$			43.0000i			1.45201i	−0.687691	+	0.726003i	$0.741376\pi$
$878$	−30.0000			−1.01245
$879$	−4.00000			−0.134917
$880$		0			0
$881$		−	40.0000i		−	1.34763i	−0.738898	−	0.673817i	$-0.764654\pi$
$881$		−	40.0000i		−	1.34763i	0.738898	−	0.673817i	$-0.235346\pi$
$882$	6.00000			0.202031
$883$		−	34.0000i		−	1.14419i	−0.820187	−	0.572096i	$-0.806131\pi$
$883$		−	34.0000i		−	1.14419i	0.820187	−	0.572096i	$-0.193869\pi$
$884$			2.00000i			0.0672673i
$885$		0			0
$886$	4.00000			0.134383
$887$	27.0000			0.906571			0.453286	−	0.891365i	$-0.350252\pi$
$887$	27.0000			0.906571			0.453286	+	0.891365i	$0.350252\pi$
$888$	8.00000			0.268462
$889$		−	24.0000i		−	0.804934i
$890$		0			0
$891$		−	5.00000i		−	0.167506i
$892$		−	24.0000i		−	0.803579i
$893$			12.0000i			0.401565i
$894$	15.0000			0.501675
$895$		0			0
$896$			2.00000i			0.0668153i
$897$	−6.00000			−0.200334
$898$			24.0000i			0.800890i
$899$	10.0000	−	25.0000i	0.333519	−	0.833797i
$900$		0			0
$901$			2.00000i			0.0666297i
$902$	50.0000			1.66482
$903$			18.0000i			0.599002i
$904$	4.00000			0.133038
$905$		0			0
$906$	−2.00000			−0.0664455
$907$	−28.0000			−0.929725			−0.464862	−	0.885383i	$-0.653896\pi$
$907$	−28.0000			−0.929725			−0.464862	+	0.885383i	$0.653896\pi$
$908$		−	12.0000i		−	0.398234i
$909$		0			0
$910$		0			0
$911$		−	15.0000i		−	0.496972i	−0.968635	−	0.248486i	$-0.920067\pi$
$911$		−	15.0000i		−	0.496972i	0.968635	−	0.248486i	$-0.0799330\pi$
$912$		−	4.00000i		−	0.132453i
$913$	−70.0000			−2.31666
$914$		−	18.0000i		−	0.595387i
$915$		0			0
$916$			6.00000i			0.198246i
$917$		0			0
$918$	10.0000			0.330049
$919$	20.0000			0.659739			0.329870	−	0.944027i	$-0.392995\pi$
$919$	20.0000			0.659739			0.329870	+	0.944027i	$0.392995\pi$
$920$		0			0
$921$	−3.00000			−0.0988534
$922$		−	20.0000i		−	0.658665i
$923$		−	8.00000i		−	0.263323i
$924$	−10.0000			−0.328976
$925$		0			0
$926$			14.0000i			0.460069i
$927$			8.00000i			0.262754i
$928$	5.00000	+	2.00000i	0.164133	+	0.0656532i
$929$	50.0000			1.64045			0.820223	−	0.572043i	$-0.193849\pi$
$929$	50.0000			1.64045			0.820223	+	0.572043i	$0.193849\pi$
$930$		0			0
$931$		−	12.0000i		−	0.393284i
$932$			1.00000i			0.0327561i
$933$		0			0
$934$	3.00000			0.0981630
$935$		0			0
$936$			2.00000i			0.0653720i
$937$		−	22.0000i		−	0.718709i	−0.933201	−	0.359354i	$-0.882997\pi$
$937$		−	22.0000i		−	0.718709i	0.933201	−	0.359354i	$-0.117003\pi$
$938$	−16.0000			−0.522419
$939$			31.0000i			1.01165i
$940$		0			0
$941$	57.0000			1.85815			0.929073	−	0.369895i	$-0.120606\pi$
$941$	57.0000			1.85815			0.929073	+	0.369895i	$0.120606\pi$
$942$	18.0000			0.586472
$943$	60.0000			1.95387
$944$	−10.0000			−0.325472
$945$		0			0
$946$		−	45.0000i		−	1.46308i
$947$	−3.00000			−0.0974869			−0.0487435	−	0.998811i	$-0.515522\pi$
$947$	−3.00000			−0.0974869			−0.0487435	+	0.998811i	$0.515522\pi$
$948$			1.00000i			0.0324785i
$949$			16.0000i			0.519382i
$950$		0			0
$951$	22.0000			0.713399
$952$			4.00000i			0.129641i
$953$			41.0000i			1.32812i	0.747679	+	0.664060i	$0.231168\pi$
$953$			41.0000i			1.32812i	−0.747679	+	0.664060i	$0.768832\pi$
$954$			2.00000i			0.0647524i
$955$		0			0
$956$	30.0000			0.970269
$957$	−10.0000	+	25.0000i	−0.323254	+	0.808135i
$958$		−	11.0000i		−	0.355394i
$959$		−	24.0000i		−	0.775000i
$960$		0			0
$961$	6.00000			0.193548
$962$			8.00000i			0.257930i
$963$			4.00000i			0.128898i
$964$	7.00000			0.225455
$965$		0			0
$966$	−12.0000			−0.386094
$967$	17.0000			0.546683			0.273342	−	0.961917i	$-0.411871\pi$
$967$	17.0000			0.546683			0.273342	+	0.961917i	$0.411871\pi$
$968$	14.0000			0.449977
$969$		−	8.00000i		−	0.256997i
$970$		0			0
$971$		−	20.0000i		−	0.641831i	−0.947108	−	0.320915i	$-0.896010\pi$
$971$		−	20.0000i		−	0.641831i	0.947108	−	0.320915i	$-0.103990\pi$
$972$	16.0000			0.513200
$973$			20.0000i			0.641171i
$974$		−	38.0000i		−	1.21760i
$975$		0			0
$976$		−	10.0000i		−	0.320092i
$977$		−	27.0000i		−	0.863807i	−0.901920	−	0.431903i	$-0.857842\pi$
$977$		−	27.0000i		−	0.863807i	0.901920	−	0.431903i	$-0.142158\pi$
$978$	−1.00000			−0.0319765
$979$	−70.0000			−2.23721
$980$		0			0
$981$	−30.0000			−0.957826
$982$		−	15.0000i		−	0.478669i
$983$	31.0000			0.988746			0.494373	−	0.869250i	$-0.335398\pi$
$983$	31.0000			0.988746			0.494373	+	0.869250i	$0.335398\pi$
$984$			10.0000i			0.318788i
$985$		0			0
$986$	10.0000	+	4.00000i	0.318465	+	0.127386i
$987$			6.00000i			0.190982i
$988$	4.00000			0.127257
$989$		−	54.0000i		−	1.71710i
$990$		0			0
$991$	−8.00000			−0.254128			−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000			−0.254128			−0.127064	+	0.991894i	$0.540555\pi$
$992$		−	5.00000i		−	0.158750i
$993$			25.0000i			0.793351i
$994$		−	16.0000i		−	0.507489i
$995$		0			0
$996$		−	14.0000i		−	0.443607i
$997$	−28.0000			−0.886769			−0.443384	−	0.896332i	$-0.646222\pi$
$997$	−28.0000			−0.886769			−0.443384	+	0.896332i	$0.646222\pi$
$998$	−30.0000			−0.949633
$999$	40.0000			1.26554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.d.b.1449.1		2
5.2	odd	4		1450.2.c.a.1101.1		2
5.3	odd	4		58.2.b.a.57.2	yes	2
5.4	even	2		1450.2.d.c.1449.2		2
15.8	even	4		522.2.d.a.289.1		2
20.3	even	4		464.2.e.c.289.1		2
29.28	even	2		1450.2.d.c.1449.1		2
40.3	even	4		1856.2.e.d.1217.2		2
40.13	odd	4		1856.2.e.b.1217.1		2
60.23	odd	4		4176.2.o.d.289.1		2
145.28	odd	4		58.2.b.a.57.1	✓	2
145.57	odd	4		1450.2.c.a.1101.2		2
145.128	even	4		1682.2.a.c.1.1		1
145.133	even	4		1682.2.a.g.1.1		1
145.144	even	2	inner	1450.2.d.b.1449.2		2
435.173	even	4		522.2.d.a.289.2		2
580.463	even	4		464.2.e.c.289.2		2
1160.173	odd	4		1856.2.e.b.1217.2		2
1160.1043	even	4		1856.2.e.d.1217.1		2
1740.1043	odd	4		4176.2.o.d.289.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.2.b.a.57.1	✓	2	145.28	odd	4
58.2.b.a.57.2	yes	2	5.3	odd	4
464.2.e.c.289.1		2	20.3	even	4
464.2.e.c.289.2		2	580.463	even	4
522.2.d.a.289.1		2	15.8	even	4
522.2.d.a.289.2		2	435.173	even	4
1450.2.c.a.1101.1		2	5.2	odd	4
1450.2.c.a.1101.2		2	145.57	odd	4
1450.2.d.b.1449.1		2	1.1	even	1	trivial
1450.2.d.b.1449.2		2	145.144	even	2	inner
1450.2.d.c.1449.1		2	29.28	even	2
1450.2.d.c.1449.2		2	5.4	even	2
1682.2.a.c.1.1		1	145.128	even	4
1682.2.a.g.1.1		1	145.133	even	4
1856.2.e.b.1217.1		2	40.13	odd	4
1856.2.e.b.1217.2		2	1160.173	odd	4
1856.2.e.d.1217.1		2	1160.1043	even	4
1856.2.e.d.1217.2		2	40.3	even	4
4176.2.o.d.289.1		2	60.23	odd	4
4176.2.o.d.289.2		2	1740.1043	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{6} -2.00000i q^{7} -1.00000 q^{8} -2.00000 q^{9} -5.00000i q^{11} +1.00000 q^{12} +1.00000i q^{13} +2.00000i q^{14} +1.00000 q^{16} +2.00000 q^{17} +2.00000 q^{18} -4.00000i q^{19} -2.00000i q^{21} +5.00000i q^{22} +6.00000i q^{23} -1.00000 q^{24} -1.00000i q^{26} -5.00000 q^{27} -2.00000i q^{28} +(-5.00000 - 2.00000i) q^{29} +5.00000i q^{31} -1.00000 q^{32} -5.00000i q^{33} -2.00000 q^{34} -2.00000 q^{36} -8.00000 q^{37} +4.00000i q^{38} +1.00000i q^{39} -10.0000i q^{41} +2.00000i q^{42} -9.00000 q^{43} -5.00000i q^{44} -6.00000i q^{46} -3.00000 q^{47} +1.00000 q^{48} +3.00000 q^{49} +2.00000 q^{51} +1.00000i q^{52} +1.00000i q^{53} +5.00000 q^{54} +2.00000i q^{56} -4.00000i q^{57} +(5.00000 + 2.00000i) q^{58} -10.0000 q^{59} -10.0000i q^{61} -5.00000i q^{62} +4.00000i q^{63} +1.00000 q^{64} +5.00000i q^{66} +8.00000i q^{67} +2.00000 q^{68} +6.00000i q^{69} -8.00000 q^{71} +2.00000 q^{72} +16.0000 q^{73} +8.00000 q^{74} -4.00000i q^{76} -10.0000 q^{77} -1.00000i q^{78} +1.00000i q^{79} +1.00000 q^{81} +10.0000i q^{82} -14.0000i q^{83} -2.00000i q^{84} +9.00000 q^{86} +(-5.00000 - 2.00000i) q^{87} +5.00000i q^{88} -14.0000i q^{89} +2.00000 q^{91} +6.00000i q^{92} +5.00000i q^{93} +3.00000 q^{94} -1.00000 q^{96} +2.00000 q^{97} -3.00000 q^{98} +10.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{3} + 2 q^{4} - 2 q^{6} - 2 q^{8} - 4 q^{9} + 2 q^{12} + 2 q^{16} + 4 q^{17} + 4 q^{18} - 2 q^{24} - 10 q^{27} - 10 q^{29} - 2 q^{32} - 4 q^{34} - 4 q^{36} - 16 q^{37} - 18 q^{43} - 6 q^{47}+ \cdots - 6 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^3 + 2 * q^4 - 2 * q^6 - 2 * q^8 - 4 * q^9 + 2 * q^12 + 2 * q^16 + 4 * q^17 + 4 * q^18 - 2 * q^24 - 10 * q^27 - 10 * q^29 - 2 * q^32 - 4 * q^34 - 4 * q^36 - 16 * q^37 - 18 * q^43 - 6 * q^47 + 2 * q^48 + 6 * q^49 + 4 * q^51 + 10 * q^54 + 10 * q^58 - 20 * q^59 + 2 * q^64 + 4 * q^68 - 16 * q^71 + 4 * q^72 + 32 * q^73 + 16 * q^74 - 20 * q^77 + 2 * q^81 + 18 * q^86 - 10 * q^87 + 4 * q^91 + 6 * q^94 - 2 * q^96 + 4 * q^97 - 6 * q^98

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