LMFDB - Embedded newform 1450.2.c.a.1101.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1450,2,Mod(1101,1450)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1450, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1450.1101"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1450.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,0,-2,0,-2,4,0,4,0,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == 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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 58)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1101.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	1450.1101
Dual form			1450.2.c.a.1101.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		−	1.00000i		−	0.577350i	−0.957427	−	0.288675i	$-0.906785\pi$
$3$		−	1.00000i		−	0.577350i	0.957427	−	0.288675i	$-0.0932147\pi$
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$	−1.00000			−0.408248
$7$	2.00000			0.755929			0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000			0.755929			0.377964	+	0.925820i	$0.376624\pi$
$8$			1.00000i			0.353553i
$9$	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	$-0.271771\pi$
$12$			1.00000i			0.288675i
$13$	1.00000			0.277350			0.138675	−	0.990338i	$-0.455716\pi$
$13$	1.00000			0.277350			0.138675	+	0.990338i	$0.455716\pi$
$14$		−	2.00000i		−	0.534522i
$15$		0			0
$16$	1.00000			0.250000
$17$			2.00000i			0.485071i	0.970143	+	0.242536i	$0.0779791\pi$
$17$			2.00000i			0.485071i	−0.970143	+	0.242536i	$0.922021\pi$
$18$		−	2.00000i		−	0.471405i
$19$			4.00000i			0.917663i	0.888523	+	0.458831i	$0.151732\pi$
$19$			4.00000i			0.917663i	−0.888523	+	0.458831i	$0.848268\pi$
$20$		0			0
$21$		−	2.00000i		−	0.436436i
$22$	−5.00000			−1.06600
$23$	6.00000			1.25109			0.625543	−	0.780189i	$-0.284877\pi$
$23$	6.00000			1.25109			0.625543	+	0.780189i	$0.284877\pi$
$24$	1.00000			0.204124
$25$		0			0
$26$		−	1.00000i		−	0.196116i
$27$		−	5.00000i		−	0.962250i
$28$	−2.00000			−0.377964
$29$	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	$0.851776\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−5.00000			−0.870388
$34$	2.00000			0.342997
$35$		0			0
$36$	−2.00000			−0.333333
$37$		−	8.00000i		−	1.31519i	−0.753371	−	0.657596i	$-0.771573\pi$
$37$		−	8.00000i		−	1.31519i	0.753371	−	0.657596i	$-0.228427\pi$
$38$	4.00000			0.648886
$39$		−	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	$-0.285223\pi$
$42$	−2.00000			−0.308607
$43$			9.00000i			1.37249i	0.727372	+	0.686244i	$0.240742\pi$
$43$			9.00000i			1.37249i	−0.727372	+	0.686244i	$0.759258\pi$
$44$			5.00000i			0.753778i
$45$		0			0
$46$		−	6.00000i		−	0.884652i
$47$		−	3.00000i		−	0.437595i	−0.975770	−	0.218797i	$-0.929787\pi$
$47$		−	3.00000i		−	0.437595i	0.975770	−	0.218797i	$-0.0702134\pi$
$48$		−	1.00000i		−	0.144338i
$49$	−3.00000			−0.428571
$50$		0			0
$51$	2.00000			0.280056
$52$	−1.00000			−0.138675
$53$	1.00000			0.137361			0.0686803	−	0.997639i	$-0.478121\pi$
$53$	1.00000			0.137361			0.0686803	+	0.997639i	$0.478121\pi$
$54$	−5.00000			−0.680414
$55$		0			0
$56$			2.00000i			0.267261i
$57$	4.00000			0.529813
$58$	2.00000	−	5.00000i	0.262613	−	0.656532i
$59$	10.0000			1.30189			0.650945	−	0.759125i	$-0.274373\pi$
$59$	10.0000			1.30189			0.650945	+	0.759125i	$0.274373\pi$
$60$		0			0
$61$		−	10.0000i		−	1.28037i	−0.768221	−	0.640184i	$-0.778858\pi$
$61$		−	10.0000i		−	1.28037i	0.768221	−	0.640184i	$-0.221142\pi$
$62$	5.00000			0.635001
$63$	4.00000			0.503953
$64$	−1.00000			−0.125000
$65$		0			0
$66$			5.00000i			0.615457i
$67$	−8.00000			−0.977356			−0.488678	−	0.872464i	$-0.662521\pi$
$67$	−8.00000			−0.977356			−0.488678	+	0.872464i	$0.662521\pi$
$68$		−	2.00000i		−	0.242536i
$69$		−	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	$0.657448\pi$
$72$			2.00000i			0.235702i
$73$		−	16.0000i		−	1.87266i	−0.351123	−	0.936329i	$-0.614200\pi$
$73$		−	16.0000i		−	1.87266i	0.351123	−	0.936329i	$-0.385800\pi$
$74$	−8.00000			−0.929981
$75$		0			0
$76$		−	4.00000i		−	0.458831i
$77$		−	10.0000i		−	1.13961i
$78$	−1.00000			−0.113228
$79$		−	1.00000i		−	0.112509i	−0.998416	−	0.0562544i	$-0.982084\pi$
$79$		−	1.00000i		−	0.112509i	0.998416	−	0.0562544i	$-0.0179158\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$	−10.0000			−1.10432
$83$	−14.0000			−1.53670			−0.768350	−	0.640030i	$-0.778922\pi$
$83$	−14.0000			−1.53670			−0.768350	+	0.640030i	$0.778922\pi$
$84$			2.00000i			0.218218i
$85$		0			0
$86$	9.00000			0.970495
$87$	2.00000	−	5.00000i	0.214423	−	0.536056i
$88$	5.00000			0.533002
$89$			14.0000i			1.48400i	0.670402	+	0.741999i	$0.266122\pi$
$89$			14.0000i			1.48400i	−0.670402	+	0.741999i	$0.733878\pi$
$90$		0			0
$91$	2.00000			0.209657
$92$	−6.00000			−0.625543
$93$	5.00000			0.518476
$94$	−3.00000			−0.309426
$95$		0			0
$96$	−1.00000			−0.102062
$97$			2.00000i			0.203069i	0.994832	+	0.101535i	$0.0323753\pi$
$97$			2.00000i			0.203069i	−0.994832	+	0.101535i	$0.967625\pi$
$98$			3.00000i			0.303046i
$99$		−	10.0000i		−	1.00504i
$100$		0			0
$101$		0			0		1.00000			$0$
$101$		0			0		−1.00000			$\pi$
$102$		−	2.00000i		−	0.198030i
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$			1.00000i			0.0980581i
$105$		0			0
$106$		−	1.00000i		−	0.0971286i
$107$	2.00000			0.193347			0.0966736	−	0.995316i	$-0.469180\pi$
$107$	2.00000			0.193347			0.0966736	+	0.995316i	$0.469180\pi$
$108$			5.00000i			0.481125i
$109$	−15.0000			−1.43674			−0.718370	−	0.695662i	$-0.755111\pi$
$109$	−15.0000			−1.43674			−0.718370	+	0.695662i	$0.755111\pi$
$110$		0			0
$111$	−8.00000			−0.759326
$112$	2.00000			0.188982
$113$			4.00000i			0.376288i	0.982141	+	0.188144i	$0.0602472\pi$
$113$			4.00000i			0.376288i	−0.982141	+	0.188144i	$0.939753\pi$
$114$		−	4.00000i		−	0.374634i
$115$		0			0
$116$	−5.00000	−	2.00000i	−0.464238	−	0.185695i
$117$	2.00000			0.184900
$118$		−	10.0000i		−	0.920575i
$119$			4.00000i			0.366679i
$120$		0			0
$121$	−14.0000			−1.27273
$122$	−10.0000			−0.905357
$123$	−10.0000			−0.901670
$124$		−	5.00000i		−	0.449013i
$125$		0			0
$126$		−	4.00000i		−	0.356348i
$127$			12.0000i			1.06483i	0.846484	+	0.532414i	$0.178715\pi$
$127$			12.0000i			1.06483i	−0.846484	+	0.532414i	$0.821285\pi$
$128$			1.00000i			0.0883883i
$129$	9.00000			0.792406
$130$		0			0
$131$		0			0		1.00000			$0$
$131$		0			0		−1.00000			$\pi$
$132$	5.00000			0.435194
$133$			8.00000i			0.693688i
$134$			8.00000i			0.691095i
$135$		0			0
$136$	−2.00000			−0.171499
$137$			12.0000i			1.02523i	0.858619	+	0.512615i	$0.171323\pi$
$137$			12.0000i			1.02523i	−0.858619	+	0.512615i	$0.828677\pi$
$138$	−6.00000			−0.510754
$139$	10.0000			0.848189			0.424094	−	0.905618i	$-0.360592\pi$
$139$	10.0000			0.848189			0.424094	+	0.905618i	$0.360592\pi$
$140$		0			0
$141$	−3.00000			−0.252646
$142$			8.00000i			0.671345i
$143$		−	5.00000i		−	0.418121i
$144$	2.00000			0.166667
$145$		0			0
$146$	−16.0000			−1.32417
$147$			3.00000i			0.247436i
$148$			8.00000i			0.657596i
$149$	15.0000			1.22885			0.614424	−	0.788976i	$-0.289388\pi$
$149$	15.0000			1.22885			0.614424	+	0.788976i	$0.289388\pi$
$150$		0			0
$151$	2.00000			0.162758			0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000			0.162758			0.0813788	+	0.996683i	$0.474068\pi$
$152$	−4.00000			−0.324443
$153$			4.00000i			0.323381i
$154$	−10.0000			−0.805823
$155$		0			0
$156$			1.00000i			0.0800641i
$157$		−	18.0000i		−	1.43656i	−0.695756	−	0.718278i	$-0.744931\pi$
$157$		−	18.0000i		−	1.43656i	0.695756	−	0.718278i	$-0.255069\pi$
$158$	−1.00000			−0.0795557
$159$		−	1.00000i		−	0.0793052i
$160$		0			0
$161$	12.0000			0.945732
$162$		−	1.00000i		−	0.0785674i
$163$		−	1.00000i		−	0.0783260i	−0.999233	−	0.0391630i	$-0.987531\pi$
$163$		−	1.00000i		−	0.0783260i	0.999233	−	0.0391630i	$-0.0124692\pi$
$164$			10.0000i			0.780869i
$165$		0			0
$166$			14.0000i			1.08661i
$167$	12.0000			0.928588			0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000			0.928588			0.464294	+	0.885681i	$0.346308\pi$
$168$	2.00000			0.154303
$169$	−12.0000			−0.923077
$170$		0			0
$171$			8.00000i			0.611775i
$172$		−	9.00000i		−	0.686244i
$173$	6.00000			0.456172			0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000			0.456172			0.228086	+	0.973641i	$0.426753\pi$
$174$	−5.00000	−	2.00000i	−0.379049	−	0.151620i
$175$		0			0
$176$		−	5.00000i		−	0.376889i
$177$		−	10.0000i		−	0.751646i
$178$	14.0000			1.04934
$179$		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	$0.282316\pi$
$182$		−	2.00000i		−	0.148250i
$183$	−10.0000			−0.739221
$184$			6.00000i			0.442326i
$185$		0			0
$186$		−	5.00000i		−	0.366618i
$187$	10.0000			0.731272
$188$			3.00000i			0.218797i
$189$		−	10.0000i		−	0.727393i
$190$		0			0
$191$		0			0		1.00000			$0$
$191$		0			0		−1.00000			$\pi$
$192$			1.00000i			0.0721688i
$193$			14.0000i			1.00774i	0.863779	+	0.503871i	$0.168091\pi$
$193$			14.0000i			1.00774i	−0.863779	+	0.503871i	$0.831909\pi$
$194$	2.00000			0.143592
$195$		0			0
$196$	3.00000			0.214286
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$	−10.0000			−0.710669
$199$	10.0000			0.708881			0.354441	−	0.935079i	$-0.384671\pi$
$199$	10.0000			0.708881			0.354441	+	0.935079i	$0.384671\pi$
$200$		0			0
$201$			8.00000i			0.564276i
$202$		0			0
$203$	10.0000	+	4.00000i	0.701862	+	0.280745i
$204$	−2.00000			−0.140028
$205$		0			0
$206$			4.00000i			0.278693i
$207$	12.0000			0.834058
$208$	1.00000			0.0693375
$209$	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	$0.944942\pi$
$212$	−1.00000			−0.0686803
$213$			8.00000i			0.548151i
$214$		−	2.00000i		−	0.136717i
$215$		0			0
$216$	5.00000			0.340207
$217$			10.0000i			0.678844i
$218$			15.0000i			1.01593i
$219$	−16.0000			−1.08118
$220$		0			0
$221$			2.00000i			0.134535i
$222$			8.00000i			0.536925i
$223$	−24.0000			−1.60716			−0.803579	−	0.595198i	$-0.797074\pi$
$223$	−24.0000			−1.60716			−0.803579	+	0.595198i	$0.797074\pi$
$224$		−	2.00000i		−	0.133631i
$225$		0			0
$226$	4.00000			0.266076
$227$	12.0000			0.796468			0.398234	−	0.917284i	$-0.369623\pi$
$227$	12.0000			0.796468			0.398234	+	0.917284i	$0.369623\pi$
$228$	−4.00000			−0.264906
$229$		−	6.00000i		−	0.396491i	−0.980152	−	0.198246i	$-0.936476\pi$
$229$		−	6.00000i		−	0.396491i	0.980152	−	0.198246i	$-0.0635244\pi$
$230$		0			0
$231$	−10.0000			−0.657952
$232$	−2.00000	+	5.00000i	−0.131306	+	0.328266i
$233$	1.00000			0.0655122			0.0327561	−	0.999463i	$-0.489572\pi$
$233$	1.00000			0.0655122			0.0327561	+	0.999463i	$0.489572\pi$
$234$		−	2.00000i		−	0.130744i
$235$		0			0
$236$	−10.0000			−0.650945
$237$	−1.00000			−0.0649570
$238$	4.00000			0.259281
$239$	−30.0000			−1.94054			−0.970269	−	0.242028i	$-0.922188\pi$
$239$	−30.0000			−1.94054			−0.970269	+	0.242028i	$0.922188\pi$
$240$		0			0
$241$	7.00000			0.450910			0.225455	−	0.974254i	$-0.427613\pi$
$241$	7.00000			0.450910			0.225455	+	0.974254i	$0.427613\pi$
$242$			14.0000i			0.899954i
$243$		−	16.0000i		−	1.02640i
$244$			10.0000i			0.640184i
$245$		0			0
$246$			10.0000i			0.637577i
$247$			4.00000i			0.254514i
$248$	−5.00000			−0.317500
$249$			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	$-0.156972\pi$
$252$	−4.00000			−0.251976
$253$		−	30.0000i		−	1.88608i
$254$	12.0000			0.752947
$255$		0			0
$256$	1.00000			0.0625000
$257$	7.00000			0.436648			0.218324	−	0.975876i	$-0.429941\pi$
$257$	7.00000			0.436648			0.218324	+	0.975876i	$0.429941\pi$
$258$		−	9.00000i		−	0.560316i
$259$		−	16.0000i		−	0.994192i
$260$		0			0
$261$	10.0000	+	4.00000i	0.618984	+	0.247594i
$262$		0			0
$263$			19.0000i			1.17159i	0.810459	+	0.585795i	$0.199218\pi$
$263$			19.0000i			1.17159i	−0.810459	+	0.585795i	$0.800782\pi$
$264$		−	5.00000i		−	0.307729i
$265$		0			0
$266$	8.00000			0.490511
$267$	14.0000			0.856786
$268$	8.00000			0.488678
$269$		−	26.0000i		−	1.58525i	−0.609711	−	0.792624i	$-0.708714\pi$
$269$		−	26.0000i		−	1.58525i	0.609711	−	0.792624i	$-0.291286\pi$
$270$		0			0
$271$			25.0000i			1.51864i	0.650716	+	0.759321i	$0.274469\pi$
$271$			25.0000i			1.51864i	−0.650716	+	0.759321i	$0.725531\pi$
$272$			2.00000i			0.121268i
$273$		−	2.00000i		−	0.121046i
$274$	12.0000			0.724947
$275$		0			0
$276$			6.00000i			0.361158i
$277$	−18.0000			−1.08152			−0.540758	−	0.841178i	$-0.681862\pi$
$277$	−18.0000			−1.08152			−0.540758	+	0.841178i	$0.681862\pi$
$278$		−	10.0000i		−	0.599760i
$279$			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	$0.626750\pi$
$282$			3.00000i			0.178647i
$283$	6.00000			0.356663			0.178331	−	0.983970i	$-0.442930\pi$
$283$	6.00000			0.356663			0.178331	+	0.983970i	$0.442930\pi$
$284$	8.00000			0.474713
$285$		0			0
$286$	−5.00000			−0.295656
$287$		−	20.0000i		−	1.18056i
$288$		−	2.00000i		−	0.117851i
$289$	13.0000			0.764706
$290$		0			0
$291$	2.00000			0.117242
$292$			16.0000i			0.936329i
$293$			4.00000i			0.233682i	0.993151	+	0.116841i	$0.0372769\pi$
$293$			4.00000i			0.233682i	−0.993151	+	0.116841i	$0.962723\pi$
$294$	3.00000			0.174964
$295$		0			0
$296$	8.00000			0.464991
$297$	−25.0000			−1.45065
$298$		−	15.0000i		−	0.868927i
$299$	6.00000			0.346989
$300$		0			0
$301$			18.0000i			1.03750i
$302$		−	2.00000i		−	0.115087i
$303$		0			0
$304$			4.00000i			0.229416i
$305$		0			0
$306$	4.00000			0.228665
$307$		−	3.00000i		−	0.171219i	−0.996329	−	0.0856095i	$-0.972716\pi$
$307$		−	3.00000i		−	0.171219i	0.996329	−	0.0856095i	$-0.0272838\pi$
$308$			10.0000i			0.569803i
$309$			4.00000i			0.227552i
$310$		0			0
$311$		0			0		1.00000			$0$
$311$		0			0		−1.00000			$\pi$
$312$	1.00000			0.0566139
$313$	31.0000			1.75222			0.876112	−	0.482108i	$-0.160129\pi$
$313$	31.0000			1.75222			0.876112	+	0.482108i	$0.160129\pi$
$314$	−18.0000			−1.01580
$315$		0			0
$316$			1.00000i			0.0562544i
$317$			22.0000i			1.23564i	0.786318	+	0.617822i	$0.211985\pi$
$317$			22.0000i			1.23564i	−0.786318	+	0.617822i	$0.788015\pi$
$318$	−1.00000			−0.0560772
$319$	10.0000	−	25.0000i	0.559893	−	1.39973i
$320$		0			0
$321$		−	2.00000i		−	0.111629i
$322$		−	12.0000i		−	0.668734i
$323$	−8.00000			−0.445132
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−1.00000			−0.0553849
$327$			15.0000i			0.829502i
$328$	10.0000			0.552158
$329$		−	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	$0.758900\pi$
$332$	14.0000			0.768350
$333$		−	16.0000i		−	0.876795i
$334$		−	12.0000i		−	0.656611i
$335$		0			0
$336$		−	2.00000i		−	0.109109i
$337$			22.0000i			1.19842i	0.800593	+	0.599208i	$0.204518\pi$
$337$			22.0000i			1.19842i	−0.800593	+	0.599208i	$0.795482\pi$
$338$			12.0000i			0.652714i
$339$	4.00000			0.217250
$340$		0			0
$341$	25.0000			1.35383
$342$	8.00000			0.432590
$343$	−20.0000			−1.07990
$344$	−9.00000			−0.485247
$345$		0			0
$346$		−	6.00000i		−	0.322562i
$347$	12.0000			0.644194			0.322097	−	0.946707i	$-0.395612\pi$
$347$	12.0000			0.644194			0.322097	+	0.946707i	$0.395612\pi$
$348$	−2.00000	+	5.00000i	−0.107211	+	0.268028i
$349$	−25.0000			−1.33822			−0.669110	−	0.743164i	$-0.733324\pi$
$349$	−25.0000			−1.33822			−0.669110	+	0.743164i	$0.733324\pi$
$350$		0			0
$351$		−	5.00000i		−	0.266880i
$352$	−5.00000			−0.266501
$353$	6.00000			0.319348			0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000			0.319348			0.159674	+	0.987170i	$0.448956\pi$
$354$	−10.0000			−0.531494
$355$		0			0
$356$		−	14.0000i		−	0.741999i
$357$	4.00000			0.211702
$358$		0			0
$359$			19.0000i			1.00278i	0.865221	+	0.501391i	$0.167178\pi$
$359$			19.0000i			1.00278i	−0.865221	+	0.501391i	$0.832822\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$		−	17.0000i		−	0.893500i
$363$			14.0000i			0.734809i
$364$	−2.00000			−0.104828
$365$		0			0
$366$			10.0000i			0.522708i
$367$			32.0000i			1.67039i	0.549957	+	0.835193i	$0.314644\pi$
$367$			32.0000i			1.67039i	−0.549957	+	0.835193i	$0.685356\pi$
$368$	6.00000			0.312772
$369$		−	20.0000i		−	1.04116i
$370$		0			0
$371$	2.00000			0.103835
$372$	−5.00000			−0.259238
$373$	11.0000			0.569558			0.284779	−	0.958593i	$-0.408080\pi$
$373$	11.0000			0.569558			0.284779	+	0.958593i	$0.408080\pi$
$374$		−	10.0000i		−	0.517088i
$375$		0			0
$376$	3.00000			0.154713
$377$	5.00000	+	2.00000i	0.257513	+	0.103005i
$378$	−10.0000			−0.514344
$379$			4.00000i			0.205466i	0.994709	+	0.102733i	$0.0327588\pi$
$379$			4.00000i			0.205466i	−0.994709	+	0.102733i	$0.967241\pi$
$380$		0			0
$381$	12.0000			0.614779
$382$		0			0
$383$	6.00000			0.306586			0.153293	−	0.988181i	$-0.451012\pi$
$383$	6.00000			0.306586			0.153293	+	0.988181i	$0.451012\pi$
$384$	1.00000			0.0510310
$385$		0			0
$386$	14.0000			0.712581
$387$			18.0000i			0.914991i
$388$		−	2.00000i		−	0.101535i
$389$			24.0000i			1.21685i	0.793612	+	0.608424i	$0.208198\pi$
$389$			24.0000i			1.21685i	−0.793612	+	0.608424i	$0.791802\pi$
$390$		0			0
$391$			12.0000i			0.606866i
$392$		−	3.00000i		−	0.151523i
$393$		0			0
$394$		−	2.00000i		−	0.100759i
$395$		0			0
$396$			10.0000i			0.502519i
$397$	27.0000			1.35509			0.677546	−	0.735481i	$-0.263044\pi$
$397$	27.0000			1.35509			0.677546	+	0.735481i	$0.263044\pi$
$398$		−	10.0000i		−	0.501255i
$399$	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	$0.444078\pi$
$402$	8.00000			0.399004
$403$			5.00000i			0.249068i
$404$		0			0
$405$		0			0
$406$	4.00000	−	10.0000i	0.198517	−	0.496292i
$407$	−40.0000			−1.98273
$408$			2.00000i			0.0990148i
$409$			4.00000i			0.197787i	0.995098	+	0.0988936i	$0.0315304\pi$
$409$			4.00000i			0.197787i	−0.995098	+	0.0988936i	$0.968470\pi$
$410$		0			0
$411$	12.0000			0.591916
$412$	4.00000			0.197066
$413$	20.0000			0.984136
$414$		−	12.0000i		−	0.589768i
$415$		0			0
$416$		−	1.00000i		−	0.0490290i
$417$		−	10.0000i		−	0.489702i
$418$		−	20.0000i		−	0.978232i
$419$		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	$-0.0783563\pi$
$422$	5.00000			0.243396
$423$		−	6.00000i		−	0.291730i
$424$			1.00000i			0.0485643i
$425$		0			0
$426$	8.00000			0.387601
$427$		−	20.0000i		−	0.967868i
$428$	−2.00000			−0.0966736
$429$	−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	$0.322248\pi$
$432$		−	5.00000i		−	0.240563i
$433$		−	16.0000i		−	0.768911i	−0.923144	−	0.384455i	$-0.874389\pi$
$433$		−	16.0000i		−	0.768911i	0.923144	−	0.384455i	$-0.125611\pi$
$434$	10.0000			0.480015
$435$		0			0
$436$	15.0000			0.718370
$437$			24.0000i			1.14808i
$438$			16.0000i			0.764510i
$439$	−30.0000			−1.43182			−0.715911	−	0.698192i	$-0.753988\pi$
$439$	−30.0000			−1.43182			−0.715911	+	0.698192i	$0.753988\pi$
$440$		0			0
$441$	−6.00000			−0.285714
$442$	2.00000			0.0951303
$443$			4.00000i			0.190046i	0.995475	+	0.0950229i	$0.0302924\pi$
$443$			4.00000i			0.190046i	−0.995475	+	0.0950229i	$0.969708\pi$
$444$	8.00000			0.379663
$445$		0			0
$446$			24.0000i			1.13643i
$447$		−	15.0000i		−	0.709476i
$448$	−2.00000			−0.0944911
$449$			24.0000i			1.13263i	0.824189	+	0.566315i	$0.191631\pi$
$449$			24.0000i			1.13263i	−0.824189	+	0.566315i	$0.808369\pi$
$450$		0			0
$451$	−50.0000			−2.35441
$452$		−	4.00000i		−	0.188144i
$453$		−	2.00000i		−	0.0939682i
$454$		−	12.0000i		−	0.563188i
$455$		0			0
$456$			4.00000i			0.187317i
$457$	−18.0000			−0.842004			−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000			−0.842004			−0.421002	+	0.907060i	$0.638322\pi$
$458$	−6.00000			−0.280362
$459$	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	$0.845786\pi$
$462$			10.0000i			0.465242i
$463$	−14.0000			−0.650635			−0.325318	−	0.945605i	$-0.605471\pi$
$463$	−14.0000			−0.650635			−0.325318	+	0.945605i	$0.605471\pi$
$464$	5.00000	+	2.00000i	0.232119	+	0.0928477i
$465$		0			0
$466$		−	1.00000i		−	0.0463241i
$467$		−	3.00000i		−	0.138823i	−0.997588	−	0.0694117i	$-0.977888\pi$
$467$		−	3.00000i		−	0.138823i	0.997588	−	0.0694117i	$-0.0221122\pi$
$468$	−2.00000			−0.0924500
$469$	−16.0000			−0.738811
$470$		0			0
$471$	−18.0000			−0.829396
$472$			10.0000i			0.460287i
$473$	45.0000			2.06910
$474$			1.00000i			0.0459315i
$475$		0			0
$476$		−	4.00000i		−	0.183340i
$477$	2.00000			0.0915737
$478$			30.0000i			1.37217i
$479$		−	11.0000i		−	0.502603i	−0.967909	−	0.251301i	$-0.919141\pi$
$479$		−	11.0000i		−	0.502603i	0.967909	−	0.251301i	$-0.0808585\pi$
$480$		0			0
$481$		−	8.00000i		−	0.364769i
$482$		−	7.00000i		−	0.318841i
$483$		−	12.0000i		−	0.546019i
$484$	14.0000			0.636364
$485$		0			0
$486$	−16.0000			−0.725775
$487$	−38.0000			−1.72194			−0.860972	−	0.508652i	$-0.830144\pi$
$487$	−38.0000			−1.72194			−0.860972	+	0.508652i	$0.830144\pi$
$488$	10.0000			0.452679
$489$	−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	$0.890091\pi$
$492$	10.0000			0.450835
$493$	−4.00000	+	10.0000i	−0.180151	+	0.450377i
$494$	4.00000			0.179969
$495$		0			0
$496$			5.00000i			0.224507i
$497$	−16.0000			−0.717698
$498$	14.0000			0.627355
$499$	−30.0000			−1.34298			−0.671492	−	0.741012i	$-0.734346\pi$
$499$	−30.0000			−1.34298			−0.671492	+	0.741012i	$0.734346\pi$
$500$		0			0
$501$		−	12.0000i		−	0.536120i
$502$	−15.0000			−0.669483
$503$			39.0000i			1.73892i	0.494000	+	0.869462i	$0.335534\pi$
$503$			39.0000i			1.73892i	−0.494000	+	0.869462i	$0.664466\pi$
$504$			4.00000i			0.178174i
$505$		0			0
$506$	−30.0000			−1.33366
$507$			12.0000i			0.532939i
$508$		−	12.0000i		−	0.532414i
$509$	15.0000			0.664863			0.332432	−	0.943127i	$-0.392131\pi$
$509$	15.0000			0.664863			0.332432	+	0.943127i	$0.392131\pi$
$510$		0			0
$511$		−	32.0000i		−	1.41560i
$512$		−	1.00000i		−	0.0441942i
$513$	20.0000			0.883022
$514$		−	7.00000i		−	0.308757i
$515$		0			0
$516$	−9.00000			−0.396203
$517$	−15.0000			−0.659699
$518$	−16.0000			−0.703000
$519$		−	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	$0.378538\pi$
$522$	4.00000	−	10.0000i	0.175075	−	0.437688i
$523$	−4.00000			−0.174908			−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000			−0.174908			−0.0874539	+	0.996169i	$0.527873\pi$
$524$		0			0
$525$		0			0
$526$	19.0000			0.828439
$527$	−10.0000			−0.435607
$528$	−5.00000			−0.217597
$529$	13.0000			0.565217
$530$		0			0
$531$	20.0000			0.867926
$532$		−	8.00000i		−	0.346844i
$533$		−	10.0000i		−	0.433148i
$534$		−	14.0000i		−	0.605839i
$535$		0			0
$536$		−	8.00000i		−	0.345547i
$537$		0			0
$538$	−26.0000			−1.12094
$539$			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	$-0.329454\pi$
$542$	25.0000			1.07384
$543$		−	17.0000i		−	0.729540i
$544$	2.00000			0.0857493
$545$		0			0
$546$	−2.00000			−0.0855921
$547$	22.0000			0.940652			0.470326	−	0.882493i	$-0.344136\pi$
$547$	22.0000			0.940652			0.470326	+	0.882493i	$0.344136\pi$
$548$		−	12.0000i		−	0.512615i
$549$		−	20.0000i		−	0.853579i
$550$		0			0
$551$	−8.00000	+	20.0000i	−0.340811	+	0.852029i
$552$	6.00000			0.255377
$553$		−	2.00000i		−	0.0850487i
$554$			18.0000i			0.764747i
$555$		0			0
$556$	−10.0000			−0.424094
$557$	−18.0000			−0.762684			−0.381342	−	0.924434i	$-0.624538\pi$
$557$	−18.0000			−0.762684			−0.381342	+	0.924434i	$0.624538\pi$
$558$	10.0000			0.423334
$559$			9.00000i			0.380659i
$560$		0			0
$561$		−	10.0000i		−	0.422200i
$562$			13.0000i			0.548372i
$563$			19.0000i			0.800755i	0.916350	+	0.400377i	$0.131121\pi$
$563$			19.0000i			0.800755i	−0.916350	+	0.400377i	$0.868879\pi$
$564$	3.00000			0.126323
$565$		0			0
$566$		−	6.00000i		−	0.252199i
$567$	2.00000			0.0839921
$568$		−	8.00000i		−	0.335673i
$569$			24.0000i			1.00613i	0.864248	+	0.503066i	$0.167795\pi$
$569$			24.0000i			1.00613i	−0.864248	+	0.503066i	$0.832205\pi$
$570$		0			0
$571$	−8.00000			−0.334790			−0.167395	−	0.985890i	$-0.553535\pi$
$571$	−8.00000			−0.334790			−0.167395	+	0.985890i	$0.553535\pi$
$572$			5.00000i			0.209061i
$573$		0			0
$574$	−20.0000			−0.834784
$575$		0			0
$576$	−2.00000			−0.0833333
$577$			2.00000i			0.0832611i	0.999133	+	0.0416305i	$0.0132552\pi$
$577$			2.00000i			0.0832611i	−0.999133	+	0.0416305i	$0.986745\pi$
$578$		−	13.0000i		−	0.540729i
$579$	14.0000			0.581820
$580$		0			0
$581$	−28.0000			−1.16164
$582$		−	2.00000i		−	0.0829027i
$583$		−	5.00000i		−	0.207079i
$584$	16.0000			0.662085
$585$		0			0
$586$	4.00000			0.165238
$587$	−18.0000			−0.742940			−0.371470	−	0.928445i	$-0.621146\pi$
$587$	−18.0000			−0.742940			−0.371470	+	0.928445i	$0.621146\pi$
$588$		−	3.00000i		−	0.123718i
$589$	−20.0000			−0.824086
$590$		0			0
$591$		−	2.00000i		−	0.0822690i
$592$		−	8.00000i		−	0.328798i
$593$	−29.0000			−1.19089			−0.595444	−	0.803397i	$-0.703024\pi$
$593$	−29.0000			−1.19089			−0.595444	+	0.803397i	$0.703024\pi$
$594$			25.0000i			1.02576i
$595$		0			0
$596$	−15.0000			−0.614424
$597$		−	10.0000i		−	0.409273i
$598$		−	6.00000i		−	0.245358i
$599$			39.0000i			1.59350i	0.604311	+	0.796748i	$0.293448\pi$
$599$			39.0000i			1.59350i	−0.604311	+	0.796748i	$0.706552\pi$
$600$		0			0
$601$			30.0000i			1.22373i	0.790964	+	0.611863i	$0.209580\pi$
$601$			30.0000i			1.22373i	−0.790964	+	0.611863i	$0.790420\pi$
$602$	18.0000			0.733625
$603$	−16.0000			−0.651570
$604$	−2.00000			−0.0813788
$605$		0			0
$606$		0			0
$607$		−	13.0000i		−	0.527654i	−0.964570	−	0.263827i	$-0.915015\pi$
$607$		−	13.0000i		−	0.527654i	0.964570	−	0.263827i	$-0.0849848\pi$
$608$	4.00000			0.162221
$609$	4.00000	−	10.0000i	0.162088	−	0.405220i
$610$		0			0
$611$		−	3.00000i		−	0.121367i
$612$		−	4.00000i		−	0.161690i
$613$	−29.0000			−1.17130			−0.585649	−	0.810564i	$-0.699160\pi$
$613$	−29.0000			−1.17130			−0.585649	+	0.810564i	$0.699160\pi$
$614$	−3.00000			−0.121070
$615$		0			0
$616$	10.0000			0.402911
$617$		−	28.0000i		−	1.12724i	−0.826035	−	0.563619i	$-0.809409\pi$
$617$		−	28.0000i		−	1.12724i	0.826035	−	0.563619i	$-0.190591\pi$
$618$	4.00000			0.160904
$619$			49.0000i			1.96948i	0.174042	+	0.984738i	$0.444317\pi$
$619$			49.0000i			1.96948i	−0.174042	+	0.984738i	$0.555683\pi$
$620$		0			0
$621$		−	30.0000i		−	1.20386i
$622$		0			0
$623$			28.0000i			1.12180i
$624$		−	1.00000i		−	0.0400320i
$625$		0			0
$626$		−	31.0000i		−	1.23901i
$627$		−	20.0000i		−	0.798723i
$628$			18.0000i			0.718278i
$629$	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	$0.550904\pi$
$632$	1.00000			0.0397779
$633$	5.00000			0.198732
$634$	22.0000			0.873732
$635$		0			0
$636$			1.00000i			0.0396526i
$637$	−3.00000			−0.118864
$638$	−25.0000	−	10.0000i	−0.989759	−	0.395904i
$639$	−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	$-0.201845\pi$
$642$	−2.00000			−0.0789337
$643$	−14.0000			−0.552106			−0.276053	−	0.961142i	$-0.589027\pi$
$643$	−14.0000			−0.552106			−0.276053	+	0.961142i	$0.589027\pi$
$644$	−12.0000			−0.472866
$645$		0			0
$646$			8.00000i			0.314756i
$647$	22.0000			0.864909			0.432455	−	0.901656i	$-0.357648\pi$
$647$	22.0000			0.864909			0.432455	+	0.901656i	$0.357648\pi$
$648$			1.00000i			0.0392837i
$649$		−	50.0000i		−	1.96267i
$650$		0			0
$651$	10.0000			0.391931
$652$			1.00000i			0.0391630i
$653$		−	6.00000i		−	0.234798i	−0.993085	−	0.117399i	$-0.962544\pi$
$653$		−	6.00000i		−	0.234798i	0.993085	−	0.117399i	$-0.0374557\pi$
$654$	15.0000			0.586546
$655$		0			0
$656$		−	10.0000i		−	0.390434i
$657$		−	32.0000i		−	1.24844i
$658$	−6.00000			−0.233904
$659$		−	31.0000i		−	1.20759i	−0.797140	−	0.603794i	$-0.793655\pi$
$659$		−	31.0000i		−	1.20759i	0.797140	−	0.603794i	$-0.206345\pi$
$660$		0			0
$661$	22.0000			0.855701			0.427850	−	0.903850i	$-0.359271\pi$
$661$	22.0000			0.855701			0.427850	+	0.903850i	$0.359271\pi$
$662$	25.0000			0.971653
$663$	2.00000			0.0776736
$664$		−	14.0000i		−	0.543305i
$665$		0			0
$666$	−16.0000			−0.619987
$667$	30.0000	+	12.0000i	1.16160	+	0.464642i
$668$	−12.0000			−0.464294
$669$			24.0000i			0.927894i
$670$		0			0
$671$	−50.0000			−1.93023
$672$	−2.00000			−0.0771517
$673$	−19.0000			−0.732396			−0.366198	−	0.930537i	$-0.619341\pi$
$673$	−19.0000			−0.732396			−0.366198	+	0.930537i	$0.619341\pi$
$674$	22.0000			0.847408
$675$		0			0
$676$	12.0000			0.461538
$677$		−	8.00000i		−	0.307465i	−0.988113	−	0.153732i	$-0.950871\pi$
$677$		−	8.00000i		−	0.307465i	0.988113	−	0.153732i	$-0.0491294\pi$
$678$		−	4.00000i		−	0.153619i
$679$			4.00000i			0.153506i
$680$		0			0
$681$		−	12.0000i		−	0.459841i
$682$		−	25.0000i		−	0.957299i
$683$	36.0000			1.37750			0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000			1.37750			0.688751	+	0.724998i	$0.258159\pi$
$684$		−	8.00000i		−	0.305888i
$685$		0			0
$686$			20.0000i			0.763604i
$687$	−6.00000			−0.228914
$688$			9.00000i			0.343122i
$689$	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	$0.678779\pi$
$692$	−6.00000			−0.228086
$693$		−	20.0000i		−	0.759737i
$694$		−	12.0000i		−	0.455514i
$695$		0			0
$696$	5.00000	+	2.00000i	0.189525	+	0.0758098i
$697$	20.0000			0.757554
$698$			25.0000i			0.946264i
$699$		−	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	$0.329687\pi$
$702$	−5.00000			−0.188713
$703$	32.0000			1.20690
$704$			5.00000i			0.188445i
$705$		0			0
$706$		−	6.00000i		−	0.225813i
$707$		0			0
$708$			10.0000i			0.375823i
$709$	−5.00000			−0.187779			−0.0938895	−	0.995583i	$-0.529930\pi$
$709$	−5.00000			−0.187779			−0.0938895	+	0.995583i	$0.529930\pi$
$710$		0			0
$711$		−	2.00000i		−	0.0750059i
$712$	−14.0000			−0.524672
$713$			30.0000i			1.12351i
$714$		−	4.00000i		−	0.149696i
$715$		0			0
$716$		0			0
$717$			30.0000i			1.12037i
$718$	19.0000			0.709074
$719$	−20.0000			−0.745874			−0.372937	−	0.927857i	$-0.621649\pi$
$719$	−20.0000			−0.745874			−0.372937	+	0.927857i	$0.621649\pi$
$720$		0			0
$721$	−8.00000			−0.297936
$722$		−	3.00000i		−	0.111648i
$723$		−	7.00000i		−	0.260333i
$724$	−17.0000			−0.631800
$725$		0			0
$726$	14.0000			0.519589
$727$		−	48.0000i		−	1.78022i	−0.455744	−	0.890111i	$-0.650627\pi$
$727$		−	48.0000i		−	1.78022i	0.455744	−	0.890111i	$-0.349373\pi$
$728$			2.00000i			0.0741249i
$729$	−13.0000			−0.481481
$730$		0			0
$731$	−18.0000			−0.665754
$732$	10.0000			0.369611
$733$		−	36.0000i		−	1.32969i	−0.746981	−	0.664845i	$-0.768498\pi$
$733$		−	36.0000i		−	1.32969i	0.746981	−	0.664845i	$-0.231502\pi$
$734$	32.0000			1.18114
$735$		0			0
$736$		−	6.00000i		−	0.221163i
$737$			40.0000i			1.47342i
$738$	−20.0000			−0.736210
$739$			9.00000i			0.331070i	0.986204	+	0.165535i	$0.0529351\pi$
$739$			9.00000i			0.331070i	−0.986204	+	0.165535i	$0.947065\pi$
$740$		0			0
$741$	4.00000			0.146944
$742$		−	2.00000i		−	0.0734223i
$743$		−	16.0000i		−	0.586983i	−0.955962	−	0.293492i	$-0.905183\pi$
$743$		−	16.0000i		−	0.586983i	0.955962	−	0.293492i	$-0.0948173\pi$
$744$			5.00000i			0.183309i
$745$		0			0
$746$		−	11.0000i		−	0.402739i
$747$	−28.0000			−1.02447
$748$	−10.0000			−0.365636
$749$	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	$-0.260392\pi$
$752$		−	3.00000i		−	0.109399i
$753$	−15.0000			−0.546630
$754$	2.00000	−	5.00000i	0.0728357	−	0.182089i
$755$		0			0
$756$			10.0000i			0.363696i
$757$			2.00000i			0.0726912i	0.999339	+	0.0363456i	$0.0115717\pi$
$757$			2.00000i			0.0726912i	−0.999339	+	0.0363456i	$0.988428\pi$
$758$	4.00000			0.145287
$759$	−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	$0.488459\pi$
$762$		−	12.0000i		−	0.434714i
$763$	−30.0000			−1.08607
$764$		0			0
$765$		0			0
$766$		−	6.00000i		−	0.216789i
$767$	10.0000			0.361079
$768$		−	1.00000i		−	0.0360844i
$769$			34.0000i			1.22607i	0.790055	+	0.613036i	$0.210052\pi$
$769$			34.0000i			1.22607i	−0.790055	+	0.613036i	$0.789948\pi$
$770$		0			0
$771$		−	7.00000i		−	0.252099i
$772$		−	14.0000i		−	0.503871i
$773$			14.0000i			0.503545i	0.967786	+	0.251773i	$0.0810135\pi$
$773$			14.0000i			0.503545i	−0.967786	+	0.251773i	$0.918987\pi$
$774$	18.0000			0.646997
$775$		0			0
$776$	−2.00000			−0.0717958
$777$	−16.0000			−0.573997
$778$	24.0000			0.860442
$779$	40.0000			1.43315
$780$		0			0
$781$			40.0000i			1.43131i
$782$	12.0000			0.429119
$783$	10.0000	−	25.0000i	0.357371	−	0.893427i
$784$	−3.00000			−0.107143
$785$		0			0
$786$		0			0
$787$	32.0000			1.14068			0.570338	−	0.821410i	$-0.306812\pi$
$787$	32.0000			1.14068			0.570338	+	0.821410i	$0.306812\pi$
$788$	−2.00000			−0.0712470
$789$	19.0000			0.676418
$790$		0			0
$791$			8.00000i			0.284447i
$792$	10.0000			0.355335
$793$		−	10.0000i		−	0.355110i
$794$		−	27.0000i		−	0.958194i
$795$		0			0
$796$	−10.0000			−0.354441
$797$			2.00000i			0.0708436i	0.999372	+	0.0354218i	$0.0112775\pi$
$797$			2.00000i			0.0708436i	−0.999372	+	0.0354218i	$0.988723\pi$
$798$		−	8.00000i		−	0.283197i
$799$	6.00000			0.212265
$800$		0			0
$801$			28.0000i			0.989331i
$802$		−	7.00000i		−	0.247179i
$803$	−80.0000			−2.82314
$804$		−	8.00000i		−	0.282138i
$805$		0			0
$806$	5.00000			0.176117
$807$	−26.0000			−0.915243
$808$		0			0
$809$			4.00000i			0.140633i	0.997525	+	0.0703163i	$0.0224008\pi$
$809$			4.00000i			0.140633i	−0.997525	+	0.0703163i	$0.977599\pi$
$810$		0			0
$811$	−18.0000			−0.632065			−0.316033	−	0.948748i	$-0.602351\pi$
$811$	−18.0000			−0.632065			−0.316033	+	0.948748i	$0.602351\pi$
$812$	−10.0000	−	4.00000i	−0.350931	−	0.140372i
$813$	25.0000			0.876788
$814$			40.0000i			1.40200i
$815$		0			0
$816$	2.00000			0.0700140
$817$	−36.0000			−1.25948
$818$	4.00000			0.139857
$819$	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	$0.695330\pi$
$822$		−	12.0000i		−	0.418548i
$823$			4.00000i			0.139431i	0.997567	+	0.0697156i	$0.0222092\pi$
$823$			4.00000i			0.139431i	−0.997567	+	0.0697156i	$0.977791\pi$
$824$		−	4.00000i		−	0.139347i
$825$		0			0
$826$		−	20.0000i		−	0.695889i
$827$		−	33.0000i		−	1.14752i	−0.819023	−	0.573761i	$-0.805484\pi$
$827$		−	33.0000i		−	1.14752i	0.819023	−	0.573761i	$-0.194516\pi$
$828$	−12.0000			−0.417029
$829$		−	26.0000i		−	0.903017i	−0.892267	−	0.451509i	$-0.850886\pi$
$829$		−	26.0000i		−	0.903017i	0.892267	−	0.451509i	$-0.149114\pi$
$830$		0			0
$831$			18.0000i			0.624413i
$832$	−1.00000			−0.0346688
$833$		−	6.00000i		−	0.207888i
$834$	−10.0000			−0.346272
$835$		0			0
$836$	−20.0000			−0.691714
$837$	25.0000			0.864126
$838$		0			0
$839$		−	21.0000i		−	0.725001i	−0.931984	−	0.362500i	$-0.881923\pi$
$839$		−	21.0000i		−	0.725001i	0.931984	−	0.362500i	$-0.118077\pi$
$840$		0			0
$841$	21.0000	+	20.0000i	0.724138	+	0.689655i
$842$	−10.0000			−0.344623
$843$			13.0000i			0.447744i
$844$		−	5.00000i		−	0.172107i
$845$		0			0
$846$	−6.00000			−0.206284
$847$	−28.0000			−0.962091
$848$	1.00000			0.0343401
$849$		−	6.00000i		−	0.205919i
$850$		0			0
$851$		−	48.0000i		−	1.64542i
$852$		−	8.00000i		−	0.274075i
$853$			4.00000i			0.136957i	0.997653	+	0.0684787i	$0.0218145\pi$
$853$			4.00000i			0.136957i	−0.997653	+	0.0684787i	$0.978185\pi$
$854$	−20.0000			−0.684386
$855$		0			0
$856$			2.00000i			0.0683586i
$857$	−13.0000			−0.444072			−0.222036	−	0.975039i	$-0.571270\pi$
$857$	−13.0000			−0.444072			−0.222036	+	0.975039i	$0.571270\pi$
$858$			5.00000i			0.170697i
$859$		−	41.0000i		−	1.39890i	−0.714681	−	0.699451i	$-0.753428\pi$
$859$		−	41.0000i		−	1.39890i	0.714681	−	0.699451i	$-0.246572\pi$
$860$		0			0
$861$	−20.0000			−0.681598
$862$		−	22.0000i		−	0.749323i
$863$	36.0000			1.22545			0.612727	−	0.790295i	$-0.290072\pi$
$863$	36.0000			1.22545			0.612727	+	0.790295i	$0.290072\pi$
$864$	−5.00000			−0.170103
$865$		0			0
$866$	−16.0000			−0.543702
$867$		−	13.0000i		−	0.441503i
$868$		−	10.0000i		−	0.339422i
$869$	−5.00000			−0.169613
$870$		0			0
$871$	−8.00000			−0.271070
$872$		−	15.0000i		−	0.507964i
$873$			4.00000i			0.135379i
$874$	24.0000			0.811812
$875$		0			0
$876$	16.0000			0.540590
$877$	−43.0000			−1.45201			−0.726003	−	0.687691i	$-0.758624\pi$
$877$	−43.0000			−1.45201			−0.726003	+	0.687691i	$0.758624\pi$
$878$			30.0000i			1.01245i
$879$	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	$-0.235346\pi$
$882$			6.00000i			0.202031i
$883$	−34.0000			−1.14419			−0.572096	−	0.820187i	$-0.693869\pi$
$883$	−34.0000			−1.14419			−0.572096	+	0.820187i	$0.693869\pi$
$884$		−	2.00000i		−	0.0672673i
$885$		0			0
$886$	4.00000			0.134383
$887$			27.0000i			0.906571i	0.891365	+	0.453286i	$0.149748\pi$
$887$			27.0000i			0.906571i	−0.891365	+	0.453286i	$0.850252\pi$
$888$		−	8.00000i		−	0.268462i
$889$			24.0000i			0.804934i
$890$		0			0
$891$		−	5.00000i		−	0.167506i
$892$	24.0000			0.803579
$893$	12.0000			0.401565
$894$	−15.0000			−0.501675
$895$		0			0
$896$			2.00000i			0.0668153i
$897$		−	6.00000i		−	0.200334i
$898$	24.0000			0.800890
$899$	−10.0000	+	25.0000i	−0.333519	+	0.833797i
$900$		0			0
$901$			2.00000i			0.0666297i
$902$			50.0000i			1.66482i
$903$	18.0000			0.599002
$904$	−4.00000			−0.133038
$905$		0			0
$906$	−2.00000			−0.0664455
$907$		−	28.0000i		−	0.929725i	−0.885383	−	0.464862i	$-0.846104\pi$
$907$		−	28.0000i		−	0.929725i	0.885383	−	0.464862i	$-0.153896\pi$
$908$	−12.0000			−0.398234
$909$		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	$-0.0799330\pi$
$912$	4.00000			0.132453
$913$			70.0000i			2.31666i
$914$			18.0000i			0.595387i
$915$		0			0
$916$			6.00000i			0.198246i
$917$		0			0
$918$		−	10.0000i		−	0.330049i
$919$	−20.0000			−0.659739			−0.329870	−	0.944027i	$-0.607005\pi$
$919$	−20.0000			−0.659739			−0.329870	+	0.944027i	$0.607005\pi$
$920$		0			0
$921$	−3.00000			−0.0988534
$922$	20.0000			0.658665
$923$	−8.00000			−0.263323
$924$	10.0000			0.328976
$925$		0			0
$926$			14.0000i			0.460069i
$927$	−8.00000			−0.262754
$928$	2.00000	−	5.00000i	0.0656532	−	0.164133i
$929$	−50.0000			−1.64045			−0.820223	−	0.572043i	$-0.806151\pi$
$929$	−50.0000			−1.64045			−0.820223	+	0.572043i	$0.806151\pi$
$930$		0			0
$931$		−	12.0000i		−	0.393284i
$932$	−1.00000			−0.0327561
$933$		0			0
$934$	−3.00000			−0.0981630
$935$		0			0
$936$			2.00000i			0.0653720i
$937$	22.0000			0.718709			0.359354	−	0.933201i	$-0.382997\pi$
$937$	22.0000			0.718709			0.359354	+	0.933201i	$0.382997\pi$
$938$			16.0000i			0.522419i
$939$		−	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	$0.120606\pi$
$942$			18.0000i			0.586472i
$943$		−	60.0000i		−	1.95387i
$944$	10.0000			0.325472
$945$		0			0
$946$		−	45.0000i		−	1.46308i
$947$		−	3.00000i		−	0.0974869i	−0.998811	−	0.0487435i	$-0.984478\pi$
$947$		−	3.00000i		−	0.0974869i	0.998811	−	0.0487435i	$-0.0155217\pi$
$948$	1.00000			0.0324785
$949$		−	16.0000i		−	0.519382i
$950$		0			0
$951$	22.0000			0.713399
$952$	−4.00000			−0.129641
$953$	41.0000			1.32812			0.664060	−	0.747679i	$-0.268832\pi$
$953$	41.0000			1.32812			0.664060	+	0.747679i	$0.268832\pi$
$954$		−	2.00000i		−	0.0647524i
$955$		0			0
$956$	30.0000			0.970269
$957$	−25.0000	−	10.0000i	−0.808135	−	0.323254i
$958$	−11.0000			−0.355394
$959$			24.0000i			0.775000i
$960$		0			0
$961$	6.00000			0.193548
$962$	−8.00000			−0.257930
$963$	4.00000			0.128898
$964$	−7.00000			−0.225455
$965$		0			0
$966$	−12.0000			−0.386094
$967$			17.0000i			0.546683i	0.961917	+	0.273342i	$0.0881289\pi$
$967$			17.0000i			0.546683i	−0.961917	+	0.273342i	$0.911871\pi$
$968$		−	14.0000i		−	0.449977i
$969$			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	$-0.103990\pi$
$972$			16.0000i			0.513200i
$973$	20.0000			0.641171
$974$			38.0000i			1.21760i
$975$		0			0
$976$		−	10.0000i		−	0.320092i
$977$	27.0000			0.863807			0.431903	−	0.901920i	$-0.357842\pi$
$977$	27.0000			0.863807			0.431903	+	0.901920i	$0.357842\pi$
$978$			1.00000i			0.0319765i
$979$	70.0000			2.23721
$980$		0			0
$981$	−30.0000			−0.957826
$982$	15.0000			0.478669
$983$		−	31.0000i		−	0.988746i	−0.869250	−	0.494373i	$-0.835398\pi$
$983$		−	31.0000i		−	0.988746i	0.869250	−	0.494373i	$-0.164602\pi$
$984$		−	10.0000i		−	0.318788i
$985$		0			0
$986$	10.0000	+	4.00000i	0.318465	+	0.127386i
$987$	−6.00000			−0.190982
$988$		−	4.00000i		−	0.127257i
$989$			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	$0.540555\pi$
$992$	5.00000			0.158750
$993$	25.0000			0.793351
$994$			16.0000i			0.507489i
$995$		0			0
$996$		−	14.0000i		−	0.443607i
$997$		−	28.0000i		−	0.886769i	−0.896332	−	0.443384i	$-0.853778\pi$
$997$		−	28.0000i		−	0.886769i	0.896332	−	0.443384i	$-0.146222\pi$
$998$			30.0000i			0.949633i
$999$	−40.0000			−1.26554

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.c.a.1101.1		2
5.2	odd	4		1450.2.d.c.1449.2		2
5.3	odd	4		1450.2.d.b.1449.1		2
5.4	even	2		58.2.b.a.57.2	yes	2
15.14	odd	2		522.2.d.a.289.1		2
20.19	odd	2		464.2.e.c.289.1		2
29.28	even	2	inner	1450.2.c.a.1101.2		2
40.19	odd	2		1856.2.e.d.1217.2		2
40.29	even	2		1856.2.e.b.1217.1		2
60.59	even	2		4176.2.o.d.289.1		2
145.28	odd	4		1450.2.d.c.1449.1		2
145.57	odd	4		1450.2.d.b.1449.2		2
145.99	odd	4		1682.2.a.c.1.1		1
145.104	odd	4		1682.2.a.g.1.1		1
145.144	even	2		58.2.b.a.57.1	✓	2
435.434	odd	2		522.2.d.a.289.2		2
580.579	odd	2		464.2.e.c.289.2		2
1160.579	odd	2		1856.2.e.d.1217.1		2
1160.869	even	2		1856.2.e.b.1217.2		2
1740.1739	even	2		4176.2.o.d.289.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.2.b.a.57.1	✓	2	145.144	even	2
58.2.b.a.57.2	yes	2	5.4	even	2
464.2.e.c.289.1		2	20.19	odd	2
464.2.e.c.289.2		2	580.579	odd	2
522.2.d.a.289.1		2	15.14	odd	2
522.2.d.a.289.2		2	435.434	odd	2
1450.2.c.a.1101.1		2	1.1	even	1	trivial
1450.2.c.a.1101.2		2	29.28	even	2	inner
1450.2.d.b.1449.1		2	5.3	odd	4
1450.2.d.b.1449.2		2	145.57	odd	4
1450.2.d.c.1449.1		2	145.28	odd	4
1450.2.d.c.1449.2		2	5.2	odd	4
1682.2.a.c.1.1		1	145.99	odd	4
1682.2.a.g.1.1		1	145.104	odd	4
1856.2.e.b.1217.1		2	40.29	even	2
1856.2.e.b.1217.2		2	1160.869	even	2
1856.2.e.d.1217.1		2	1160.579	odd	2
1856.2.e.d.1217.2		2	40.19	odd	2
4176.2.o.d.289.1		2	60.59	even	2
4176.2.o.d.289.2		2	1740.1739	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.c (of order \(2\), degree \(1\), minimal)

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

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