LMFDB - Embedded newform 1305.2.c.f.784.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1305,2,Mod(784,1305)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1305, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1305.784");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1305 = 3^{2} \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1305.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$10.4204774638$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 4x^{2} + 1 $ x^4 + 4*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 145)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			784.2
Root			$-0.517638i$ of defining polynomial
Character	$\chi$	$=$	1305.784
Dual form			1305.2.c.f.784.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-0.517638i q^{2} +1.73205 q^{4} +(1.73205 + 1.41421i) q^{5} -2.44949i q^{7} -1.93185i q^{8} +(0.732051 - 0.896575i) q^{10} +1.26795 q^{11} +1.79315i q^{13} -1.26795 q^{14} +2.46410 q^{16} -1.41421i q^{17} +3.26795 q^{19} +(3.00000 + 2.44949i) q^{20} -0.656339i q^{22} -6.31319i q^{23} +(1.00000 + 4.89898i) q^{25} +0.928203 q^{26} -4.24264i q^{28} +1.00000 q^{29} -8.73205 q^{31} -5.13922i q^{32} -0.732051 q^{34} +(3.46410 - 4.24264i) q^{35} +9.14162i q^{37} -1.69161i q^{38} +(2.73205 - 3.34607i) q^{40} +6.92820 q^{41} -9.14162i q^{43} +2.19615 q^{44} -3.26795 q^{46} -1.41421i q^{47} +1.00000 q^{49} +(2.53590 - 0.517638i) q^{50} +3.10583i q^{52} +5.93426i q^{53} +(2.19615 + 1.79315i) q^{55} -4.73205 q^{56} -0.517638i q^{58} -10.3923 q^{59} +2.92820 q^{61} +4.52004i q^{62} +2.26795 q^{64} +(-2.53590 + 3.10583i) q^{65} +4.24264i q^{67} -2.44949i q^{68} +(-2.19615 - 1.79315i) q^{70} -3.46410 q^{71} +7.34847i q^{73} +4.73205 q^{74} +5.66025 q^{76} -3.10583i q^{77} +4.19615 q^{79} +(4.26795 + 3.48477i) q^{80} -3.58630i q^{82} +10.1769i q^{83} +(2.00000 - 2.44949i) q^{85} -4.73205 q^{86} -2.44949i q^{88} +10.3923 q^{89} +4.39230 q^{91} -10.9348i q^{92} -0.732051 q^{94} +(5.66025 + 4.62158i) q^{95} -10.9348i q^{97} -0.517638i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{10} + 12 q^{11} - 12 q^{14} - 4 q^{16} + 20 q^{19} + 12 q^{20} + 4 q^{25} - 24 q^{26} + 4 q^{29} - 28 q^{31} + 4 q^{34} + 4 q^{40} - 12 q^{44} - 20 q^{46} + 4 q^{49} + 24 q^{50} - 12 q^{55} - 12 q^{56}+ \cdots - 12 q^{95}+O(q^{100}) $ 4 * q - 4 * q^10 + 12 * q^11 - 12 * q^14 - 4 * q^16 + 20 * q^19 + 12 * q^20 + 4 * q^25 - 24 * q^26 + 4 * q^29 - 28 * q^31 + 4 * q^34 + 4 * q^40 - 12 * q^44 - 20 * q^46 + 4 * q^49 + 24 * q^50 - 12 * q^55 - 12 * q^56 - 16 * q^61 + 16 * q^64 - 24 * q^65 + 12 * q^70 + 12 * q^74 - 12 * q^76 - 4 * q^79 + 24 * q^80 + 8 * q^85 - 12 * q^86 - 24 * q^91 + 4 * q^94 - 12 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1305\mathbb{Z}\right)^\times$.

$n$	$146$	$262$	$901$
$\chi(n)$	$1$	$-1$	$1$

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 $

$2$		−	0.517638i		−	0.366025i	−0.983111	−	0.183013i	$-0.941415\pi$
$2$		−	0.517638i		−	0.366025i	0.983111	−	0.183013i	$-0.0585849\pi$
$3$		0			0
$3$		0			0
$4$	1.73205			0.866025
$5$	1.73205	+	1.41421i	0.774597	+	0.632456i
$5$	1.73205	+	1.41421i	0.774597	+	0.632456i
$6$		0			0
$7$		−	2.44949i		−	0.925820i	−0.886405	−	0.462910i	$-0.846805\pi$
$7$		−	2.44949i		−	0.925820i	0.886405	−	0.462910i	$-0.153195\pi$
$8$		−	1.93185i		−	0.683013i
$9$		0			0
$10$	0.732051	−	0.896575i	0.231495	−	0.283522i
$11$	1.26795			0.382301			0.191151	−	0.981561i	$-0.438778\pi$
$11$	1.26795			0.382301			0.191151	+	0.981561i	$0.438778\pi$
$12$		0			0
$13$			1.79315i			0.497331i	0.968589	+	0.248665i	$0.0799919\pi$
$13$			1.79315i			0.497331i	−0.968589	+	0.248665i	$0.920008\pi$
$14$	−1.26795			−0.338874
$15$		0			0
$16$	2.46410			0.616025
$17$		−	1.41421i		−	0.342997i	−0.985184	−	0.171499i	$-0.945139\pi$
$17$		−	1.41421i		−	0.342997i	0.985184	−	0.171499i	$-0.0548609\pi$
$18$		0			0
$19$	3.26795			0.749719			0.374859	−	0.927082i	$-0.377691\pi$
$19$	3.26795			0.749719			0.374859	+	0.927082i	$0.377691\pi$
$20$	3.00000	+	2.44949i	0.670820	+	0.547723i
$21$		0			0
$22$		−	0.656339i		−	0.139932i
$23$		−	6.31319i		−	1.31639i	−0.752847	−	0.658196i	$-0.771320\pi$
$23$		−	6.31319i		−	1.31639i	0.752847	−	0.658196i	$-0.228680\pi$
$24$		0			0
$25$	1.00000	+	4.89898i	0.200000	+	0.979796i
$26$	0.928203			0.182036
$27$		0			0
$28$		−	4.24264i		−	0.801784i
$29$	1.00000			0.185695
$29$	1.00000			0.185695
$30$		0			0
$31$	−8.73205			−1.56832			−0.784161	−	0.620557i	$-0.786907\pi$
$31$	−8.73205			−1.56832			−0.784161	+	0.620557i	$0.786907\pi$
$32$		−	5.13922i		−	0.908494i
$33$		0			0
$34$	−0.732051			−0.125546
$35$	3.46410	−	4.24264i	0.585540	−	0.717137i
$36$		0			0
$37$			9.14162i			1.50287i	0.659805	+	0.751437i	$0.270639\pi$
$37$			9.14162i			1.50287i	−0.659805	+	0.751437i	$0.729361\pi$
$38$		−	1.69161i		−	0.274416i
$39$		0			0
$40$	2.73205	−	3.34607i	0.431975	−	0.529059i
$41$	6.92820			1.08200			0.541002	−	0.841021i	$-0.318045\pi$
$41$	6.92820			1.08200			0.541002	+	0.841021i	$0.318045\pi$
$42$		0			0
$43$		−	9.14162i		−	1.39408i	−0.717030	−	0.697042i	$-0.754499\pi$
$43$		−	9.14162i		−	1.39408i	0.717030	−	0.697042i	$-0.245501\pi$
$44$	2.19615			0.331082
$45$		0			0
$46$	−3.26795			−0.481833
$47$		−	1.41421i		−	0.206284i	−0.994667	−	0.103142i	$-0.967110\pi$
$47$		−	1.41421i		−	0.206284i	0.994667	−	0.103142i	$-0.0328896\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	2.53590	−	0.517638i	0.358630	−	0.0732051i
$51$		0			0
$52$			3.10583i			0.430701i
$53$			5.93426i			0.815133i	0.913176	+	0.407566i	$0.133622\pi$
$53$			5.93426i			0.815133i	−0.913176	+	0.407566i	$0.866378\pi$
$54$		0			0
$55$	2.19615	+	1.79315i	0.296129	+	0.241788i
$56$	−4.73205			−0.632347
$57$		0			0
$58$		−	0.517638i		−	0.0679692i
$59$	−10.3923			−1.35296			−0.676481	−	0.736460i	$-0.736496\pi$
$59$	−10.3923			−1.35296			−0.676481	+	0.736460i	$0.736496\pi$
$60$		0			0
$61$	2.92820			0.374918			0.187459	−	0.982272i	$-0.439975\pi$
$61$	2.92820			0.374918			0.187459	+	0.982272i	$0.439975\pi$
$62$			4.52004i			0.574046i
$63$		0			0
$64$	2.26795			0.283494
$65$	−2.53590	+	3.10583i	−0.314539	+	0.385231i
$66$		0			0
$67$			4.24264i			0.518321i	0.965834	+	0.259161i	$0.0834459\pi$
$67$			4.24264i			0.518321i	−0.965834	+	0.259161i	$0.916554\pi$
$68$		−	2.44949i		−	0.297044i
$69$		0			0
$70$	−2.19615	−	1.79315i	−0.262490	−	0.214323i
$71$	−3.46410			−0.411113			−0.205557	−	0.978645i	$-0.565900\pi$
$71$	−3.46410			−0.411113			−0.205557	+	0.978645i	$0.565900\pi$
$72$		0			0
$73$			7.34847i			0.860073i	0.902811	+	0.430037i	$0.141499\pi$
$73$			7.34847i			0.860073i	−0.902811	+	0.430037i	$0.858501\pi$
$74$	4.73205			0.550090
$75$		0			0
$76$	5.66025			0.649276
$77$		−	3.10583i		−	0.353942i
$78$		0			0
$79$	4.19615			0.472104			0.236052	−	0.971740i	$-0.424146\pi$
$79$	4.19615			0.472104			0.236052	+	0.971740i	$0.424146\pi$
$80$	4.26795	+	3.48477i	0.477171	+	0.389609i
$81$		0			0
$82$		−	3.58630i		−	0.396041i
$83$			10.1769i			1.11706i	0.829484	+	0.558530i	$0.188634\pi$
$83$			10.1769i			1.11706i	−0.829484	+	0.558530i	$0.811366\pi$
$84$		0			0
$85$	2.00000	−	2.44949i	0.216930	−	0.265684i
$86$	−4.73205			−0.510270
$87$		0			0
$88$		−	2.44949i		−	0.261116i
$89$	10.3923			1.10158			0.550791	−	0.834643i	$-0.314326\pi$
$89$	10.3923			1.10158			0.550791	+	0.834643i	$0.314326\pi$
$90$		0			0
$91$	4.39230			0.460439
$92$		−	10.9348i		−	1.14003i
$93$		0			0
$94$	−0.732051			−0.0755053
$95$	5.66025	+	4.62158i	0.580730	+	0.474164i
$96$		0			0
$97$		−	10.9348i		−	1.11026i	−0.831764	−	0.555129i	$-0.812669\pi$
$97$		−	10.9348i		−	1.11026i	0.831764	−	0.555129i	$-0.187331\pi$
$98$		−	0.517638i		−	0.0522893i
$99$		0			0
$100$	1.73205	+	8.48528i	0.173205	+	0.848528i
$101$	6.00000			0.597022			0.298511	−	0.954406i	$-0.403510\pi$
$101$	6.00000			0.597022			0.298511	+	0.954406i	$0.403510\pi$
$102$		0			0
$103$		−	9.14162i		−	0.900751i	−0.892839	−	0.450375i	$-0.851290\pi$
$103$		−	9.14162i		−	0.900751i	0.892839	−	0.450375i	$-0.148710\pi$
$104$	3.46410			0.339683
$105$		0			0
$106$	3.07180			0.298359
$107$			18.6622i			1.80414i	0.431589	+	0.902070i	$0.357953\pi$
$107$			18.6622i			1.80414i	−0.431589	+	0.902070i	$0.642047\pi$
$108$		0			0
$109$	−17.8564			−1.71033			−0.855167	−	0.518353i	$-0.826545\pi$
$109$	−17.8564			−1.71033			−0.855167	+	0.518353i	$0.826545\pi$
$110$	0.928203	−	1.13681i	0.0885007	−	0.108391i
$111$		0			0
$112$		−	6.03579i		−	0.570329i
$113$		−	13.0053i		−	1.22344i	−0.791075	−	0.611719i	$-0.790478\pi$
$113$		−	13.0053i		−	1.22344i	0.791075	−	0.611719i	$-0.209522\pi$
$114$		0			0
$115$	8.92820	−	10.9348i	0.832559	−	1.01967i
$116$	1.73205			0.160817
$117$		0			0
$118$			5.37945i			0.495219i
$119$	−3.46410			−0.317554
$120$		0			0
$121$	−9.39230			−0.853846
$122$		−	1.51575i		−	0.137230i
$123$		0			0
$124$	−15.1244			−1.35821
$125$	−5.19615	+	9.89949i	−0.464758	+	0.885438i
$126$		0			0
$127$			4.24264i			0.376473i	0.982124	+	0.188237i	$0.0602772\pi$
$127$			4.24264i			0.376473i	−0.982124	+	0.188237i	$0.939723\pi$
$128$		−	11.4524i		−	1.01226i
$129$		0			0
$130$	1.60770	+	1.31268i	0.141004	+	0.115129i
$131$	4.73205			0.413441			0.206721	−	0.978400i	$-0.433721\pi$
$131$	4.73205			0.413441			0.206721	+	0.978400i	$0.433721\pi$
$132$		0			0
$133$		−	8.00481i		−	0.694105i
$134$	2.19615			0.189719
$135$		0			0
$136$	−2.73205			−0.234271
$137$		−	14.7985i		−	1.26432i	−0.774838	−	0.632159i	$-0.782169\pi$
$137$		−	14.7985i		−	1.26432i	0.774838	−	0.632159i	$-0.217831\pi$
$138$		0			0
$139$	8.00000			0.678551			0.339276	−	0.940687i	$-0.389818\pi$
$139$	8.00000			0.678551			0.339276	+	0.940687i	$0.389818\pi$
$140$	6.00000	−	7.34847i	0.507093	−	0.621059i
$141$		0			0
$142$			1.79315i			0.150478i
$143$			2.27362i			0.190130i
$144$		0			0
$145$	1.73205	+	1.41421i	0.143839	+	0.117444i
$146$	3.80385			0.314809
$147$		0			0
$148$			15.8338i			1.30153i
$149$	−0.928203			−0.0760414			−0.0380207	−	0.999277i	$-0.512105\pi$
$149$	−0.928203			−0.0760414			−0.0380207	+	0.999277i	$0.512105\pi$
$150$		0			0
$151$	−18.7846			−1.52867			−0.764335	−	0.644819i	$-0.776933\pi$
$151$	−18.7846			−1.52867			−0.764335	+	0.644819i	$0.776933\pi$
$152$		−	6.31319i		−	0.512068i
$153$		0			0
$154$	−1.60770			−0.129552
$155$	−15.1244	−	12.3490i	−1.21482	−	0.991894i
$156$		0			0
$157$			10.9348i			0.872690i	0.899780	+	0.436345i	$0.143727\pi$
$157$			10.9348i			0.872690i	−0.899780	+	0.436345i	$0.856273\pi$
$158$		−	2.17209i		−	0.172802i
$159$		0			0
$160$	7.26795	−	8.90138i	0.574582	−	0.703716i
$161$	−15.4641			−1.21874
$162$		0			0
$163$		−	14.0406i		−	1.09974i	−0.835249	−	0.549872i	$-0.814676\pi$
$163$		−	14.0406i		−	1.09974i	0.835249	−	0.549872i	$-0.185324\pi$
$164$	12.0000			0.937043
$165$		0			0
$166$	5.26795			0.408872
$167$		−	11.2122i		−	0.867624i	−0.901003	−	0.433812i	$-0.857168\pi$
$167$		−	11.2122i		−	0.867624i	0.901003	−	0.433812i	$-0.142832\pi$
$168$		0			0
$169$	9.78461			0.752662
$170$	−1.26795	−	1.03528i	−0.0972473	−	0.0794021i
$171$		0			0
$172$		−	15.8338i		−	1.20731i
$173$			4.62158i			0.351372i	0.984446	+	0.175686i	$0.0562144\pi$
$173$			4.62158i			0.351372i	−0.984446	+	0.175686i	$0.943786\pi$
$174$		0			0
$175$	12.0000	−	2.44949i	0.907115	−	0.185164i
$176$	3.12436			0.235507
$177$		0			0
$178$		−	5.37945i		−	0.403207i
$179$	2.53590			0.189542			0.0947710	−	0.995499i	$-0.469788\pi$
$179$	2.53590			0.189542			0.0947710	+	0.995499i	$0.469788\pi$
$180$		0			0
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$		−	2.27362i		−	0.168532i
$183$		0			0
$184$	−12.1962			−0.899112
$185$	−12.9282	+	15.8338i	−0.950500	+	1.16412i
$186$		0			0
$187$		−	1.79315i		−	0.131128i
$188$		−	2.44949i		−	0.178647i
$189$		0			0
$190$	2.39230	−	2.92996i	0.173556	−	0.212562i
$191$	−15.1244			−1.09436			−0.547180	−	0.837015i	$-0.684299\pi$
$191$	−15.1244			−1.09436			−0.547180	+	0.837015i	$0.684299\pi$
$192$		0			0
$193$			0.656339i			0.0472443i	0.999721	+	0.0236222i	$0.00751986\pi$
$193$			0.656339i			0.0472443i	−0.999721	+	0.0236222i	$0.992480\pi$
$194$	−5.66025			−0.406383
$195$		0			0
$196$	1.73205			0.123718
$197$			22.4243i			1.59767i	0.601551	+	0.798834i	$0.294550\pi$
$197$			22.4243i			1.59767i	−0.601551	+	0.798834i	$0.705450\pi$
$198$		0			0
$199$	14.0000			0.992434			0.496217	−	0.868199i	$-0.334722\pi$
$199$	14.0000			0.992434			0.496217	+	0.868199i	$0.334722\pi$
$200$	9.46410	−	1.93185i	0.669213	−	0.136603i
$201$		0			0
$202$		−	3.10583i		−	0.218525i
$203$		−	2.44949i		−	0.171920i
$204$		0			0
$205$	12.0000	+	9.79796i	0.838116	+	0.684319i
$206$	−4.73205			−0.329698
$207$		0			0
$208$			4.41851i			0.306368i
$209$	4.14359			0.286618
$210$		0			0
$211$	−14.7321			−1.01420			−0.507098	−	0.861888i	$-0.669282\pi$
$211$	−14.7321			−1.01420			−0.507098	+	0.861888i	$0.669282\pi$
$212$			10.2784i			0.705926i
$213$		0			0
$214$	9.66025			0.660361
$215$	12.9282	−	15.8338i	0.881696	−	1.07985i
$216$		0			0
$217$			21.3891i			1.45198i
$218$			9.24316i			0.626026i
$219$		0			0
$220$	3.80385	+	3.10583i	0.256455	+	0.209395i
$221$	2.53590			0.170583
$222$		0			0
$223$			15.3533i			1.02813i	0.857751	+	0.514066i	$0.171861\pi$
$223$			15.3533i			1.02813i	−0.857751	+	0.514066i	$0.828139\pi$
$224$	−12.5885			−0.841102
$225$		0			0
$226$	−6.73205			−0.447809
$227$			20.4553i			1.35767i	0.734292	+	0.678834i	$0.237514\pi$
$227$			20.4553i			1.35767i	−0.734292	+	0.678834i	$0.762486\pi$
$228$		0			0
$229$	−18.7846			−1.24132			−0.620661	−	0.784079i	$-0.713136\pi$
$229$	−18.7846			−1.24132			−0.620661	+	0.784079i	$0.713136\pi$
$230$	−5.66025	−	4.62158i	−0.373226	−	0.304738i
$231$		0			0
$232$		−	1.93185i		−	0.126832i
$233$		−	3.38323i		−	0.221643i	−0.993840	−	0.110821i	$-0.964652\pi$
$233$		−	3.38323i		−	0.221643i	0.993840	−	0.110821i	$-0.0353481\pi$
$234$		0			0
$235$	2.00000	−	2.44949i	0.130466	−	0.159787i
$236$	−18.0000			−1.17170
$237$		0			0
$238$			1.79315i			0.116233i
$239$	10.3923			0.672222			0.336111	−	0.941822i	$-0.390888\pi$
$239$	10.3923			0.672222			0.336111	+	0.941822i	$0.390888\pi$
$240$		0			0
$241$	11.4641			0.738468			0.369234	−	0.929337i	$-0.379620\pi$
$241$	11.4641			0.738468			0.369234	+	0.929337i	$0.379620\pi$
$242$			4.86181i			0.312529i
$243$		0			0
$244$	5.07180			0.324689
$245$	1.73205	+	1.41421i	0.110657	+	0.0903508i
$246$		0			0
$247$			5.85993i			0.372858i
$248$			16.8690i			1.07118i
$249$		0			0
$250$	5.12436	+	2.68973i	0.324093	+	0.170113i
$251$	−15.1244			−0.954641			−0.477320	−	0.878729i	$-0.658392\pi$
$251$	−15.1244			−0.954641			−0.477320	+	0.878729i	$0.658392\pi$
$252$		0			0
$253$		−	8.00481i		−	0.503258i
$254$	2.19615			0.137799
$255$		0			0
$256$	−1.39230			−0.0870191
$257$			9.52056i			0.593876i	0.954897	+	0.296938i	$0.0959655\pi$
$257$			9.52056i			0.593876i	−0.954897	+	0.296938i	$0.904035\pi$
$258$		0			0
$259$	22.3923			1.39139
$260$	−4.39230	+	5.37945i	−0.272399	+	0.333620i
$261$		0			0
$262$		−	2.44949i		−	0.151330i
$263$			4.79744i			0.295823i	0.989001	+	0.147912i	$0.0472551\pi$
$263$			4.79744i			0.295823i	−0.989001	+	0.147912i	$0.952745\pi$
$264$		0			0
$265$	−8.39230	+	10.2784i	−0.515535	+	0.631399i
$266$	−4.14359			−0.254060
$267$		0			0
$268$			7.34847i			0.448879i
$269$	−12.0000			−0.731653			−0.365826	−	0.930683i	$-0.619214\pi$
$269$	−12.0000			−0.731653			−0.365826	+	0.930683i	$0.619214\pi$
$270$		0			0
$271$	−26.7321			−1.62386			−0.811928	−	0.583757i	$-0.801582\pi$
$271$	−26.7321			−1.62386			−0.811928	+	0.583757i	$0.801582\pi$
$272$		−	3.48477i		−	0.211295i
$273$		0			0
$274$	−7.66025			−0.462773
$275$	1.26795	+	6.21166i	0.0764602	+	0.374577i
$276$		0			0
$277$			18.7637i			1.12740i	0.825979	+	0.563701i	$0.190623\pi$
$277$			18.7637i			1.12740i	−0.825979	+	0.563701i	$0.809377\pi$
$278$		−	4.14110i		−	0.248367i
$279$		0			0
$280$	−8.19615	−	6.69213i	−0.489814	−	0.399931i
$281$	−32.7846			−1.95577			−0.977883	−	0.209153i	$-0.932929\pi$
$281$	−32.7846			−1.95577			−0.977883	+	0.209153i	$0.932929\pi$
$282$		0			0
$283$			27.4249i			1.63024i	0.579293	+	0.815119i	$0.303329\pi$
$283$			27.4249i			1.63024i	−0.579293	+	0.815119i	$0.696671\pi$
$284$	−6.00000			−0.356034
$285$		0			0
$286$	1.17691			0.0695924
$287$		−	16.9706i		−	1.00174i
$288$		0			0
$289$	15.0000			0.882353
$290$	0.732051	−	0.896575i	0.0429875	−	0.0526487i
$291$		0			0
$292$			12.7279i			0.744845i
$293$			30.7338i			1.79549i	0.440520	+	0.897743i	$0.354794\pi$
$293$			30.7338i			1.79549i	−0.440520	+	0.897743i	$0.645206\pi$
$294$		0			0
$295$	−18.0000	−	14.6969i	−1.04800	−	0.855689i
$296$	17.6603			1.02648
$297$		0			0
$298$			0.480473i			0.0278331i
$299$	11.3205			0.654682
$300$		0			0
$301$	−22.3923			−1.29067
$302$			9.72363i			0.559532i
$303$		0			0
$304$	8.05256			0.461846
$305$	5.07180	+	4.14110i	0.290410	+	0.237119i
$306$		0			0
$307$			10.4543i			0.596658i	0.954463	+	0.298329i	$0.0964293\pi$
$307$			10.4543i			0.596658i	−0.954463	+	0.298329i	$0.903571\pi$
$308$		−	5.37945i		−	0.306523i
$309$		0			0
$310$	−6.39230	+	7.82894i	−0.363059	+	0.444654i
$311$	6.58846			0.373597			0.186799	−	0.982398i	$-0.440189\pi$
$311$	6.58846			0.373597			0.186799	+	0.982398i	$0.440189\pi$
$312$		0			0
$313$			23.6627i			1.33749i	0.743490	+	0.668747i	$0.233169\pi$
$313$			23.6627i			1.33749i	−0.743490	+	0.668747i	$0.766831\pi$
$314$	5.66025			0.319427
$315$		0			0
$316$	7.26795			0.408854
$317$			5.75839i			0.323423i	0.986838	+	0.161712i	$0.0517015\pi$
$317$			5.75839i			0.323423i	−0.986838	+	0.161712i	$0.948299\pi$
$318$		0			0
$319$	1.26795			0.0709915
$320$	3.92820	+	3.20736i	0.219593	+	0.179297i
$321$		0			0
$322$			8.00481i			0.446091i
$323$		−	4.62158i		−	0.257151i
$324$		0			0
$325$	−8.78461	+	1.79315i	−0.487282	+	0.0994661i
$326$	−7.26795			−0.402534
$327$		0			0
$328$		−	13.3843i		−	0.739022i
$329$	−3.46410			−0.190982
$330$		0			0
$331$	−18.1962			−1.00015			−0.500075	−	0.865982i	$-0.666694\pi$
$331$	−18.1962			−1.00015			−0.500075	+	0.865982i	$0.666694\pi$
$332$			17.6269i			0.967402i
$333$		0			0
$334$	−5.80385			−0.317572
$335$	−6.00000	+	7.34847i	−0.327815	+	0.401490i
$336$		0			0
$337$		−	27.9053i		−	1.52010i	−0.649864	−	0.760050i	$-0.725174\pi$
$337$		−	27.9053i		−	1.52010i	0.649864	−	0.760050i	$-0.274826\pi$
$338$		−	5.06489i		−	0.275494i
$339$		0			0
$340$	3.46410	−	4.24264i	0.187867	−	0.230089i
$341$	−11.0718			−0.599571
$342$		0			0
$343$		−	19.5959i		−	1.05808i
$344$	−17.6603			−0.952177
$345$		0			0
$346$	2.39230			0.128611
$347$		−	21.4906i		−	1.15368i	−0.816859	−	0.576838i	$-0.804286\pi$
$347$		−	21.4906i		−	1.15368i	0.816859	−	0.576838i	$-0.195714\pi$
$348$		0			0
$349$	22.7846			1.21963			0.609816	−	0.792543i	$-0.291243\pi$
$349$	22.7846			1.21963			0.609816	+	0.792543i	$0.291243\pi$
$350$	−1.26795	−	6.21166i	−0.0677747	−	0.332027i
$351$		0			0
$352$		−	6.51626i		−	0.347318i
$353$		−	31.9449i		−	1.70026i	−0.526576	−	0.850128i	$-0.676525\pi$
$353$		−	31.9449i		−	1.70026i	0.526576	−	0.850128i	$-0.323475\pi$
$354$		0			0
$355$	−6.00000	−	4.89898i	−0.318447	−	0.260011i
$356$	18.0000			0.953998
$357$		0			0
$358$		−	1.31268i		−	0.0693772i
$359$	−7.26795			−0.383588			−0.191794	−	0.981435i	$-0.561430\pi$
$359$	−7.26795			−0.383588			−0.191794	+	0.981435i	$0.561430\pi$
$360$		0			0
$361$	−8.32051			−0.437921
$362$			8.28221i			0.435303i
$363$		0			0
$364$	7.60770			0.398752
$365$	−10.3923	+	12.7279i	−0.543958	+	0.666210i
$366$		0			0
$367$		−	33.6365i		−	1.75581i	−0.478833	−	0.877906i	$-0.658940\pi$
$367$		−	33.6365i		−	1.75581i	0.478833	−	0.877906i	$-0.341060\pi$
$368$		−	15.5563i		−	0.810931i
$369$		0			0
$370$	8.19615	+	6.69213i	0.426098	+	0.347907i
$371$	14.5359			0.754666
$372$		0			0
$373$			19.5959i			1.01464i	0.861758	+	0.507319i	$0.169363\pi$
$373$			19.5959i			1.01464i	−0.861758	+	0.507319i	$0.830637\pi$
$374$	−0.928203			−0.0479962
$375$		0			0
$376$	−2.73205			−0.140895
$377$			1.79315i			0.0923520i
$378$		0			0
$379$	16.1962			0.831940			0.415970	−	0.909378i	$-0.363442\pi$
$379$	16.1962			0.831940			0.415970	+	0.909378i	$0.363442\pi$
$380$	9.80385	+	8.00481i	0.502927	+	0.410638i
$381$		0			0
$382$			7.82894i			0.400564i
$383$		−	0.933740i		−	0.0477119i	−0.999715	−	0.0238559i	$-0.992406\pi$
$383$		−	0.933740i		−	0.0477119i	0.999715	−	0.0238559i	$-0.00759430\pi$
$384$		0			0
$385$	4.39230	−	5.37945i	0.223853	−	0.274162i
$386$	0.339746			0.0172926
$387$		0			0
$388$		−	18.9396i		−	0.961511i
$389$	−20.7846			−1.05382			−0.526911	−	0.849921i	$-0.676650\pi$
$389$	−20.7846			−1.05382			−0.526911	+	0.849921i	$0.676650\pi$
$390$		0			0
$391$	−8.92820			−0.451519
$392$		−	1.93185i		−	0.0975732i
$393$		0			0
$394$	11.6077			0.584787
$395$	7.26795	+	5.93426i	0.365690	+	0.298585i
$396$		0			0
$397$			4.89898i			0.245873i	0.992415	+	0.122936i	$0.0392311\pi$
$397$			4.89898i			0.245873i	−0.992415	+	0.122936i	$0.960769\pi$
$398$		−	7.24693i		−	0.363256i
$399$		0			0
$400$	2.46410	+	12.0716i	0.123205	+	0.603579i
$401$	−37.8564			−1.89046			−0.945229	−	0.326407i	$-0.894162\pi$
$401$	−37.8564			−1.89046			−0.945229	+	0.326407i	$0.894162\pi$
$402$		0			0
$403$		−	15.6579i		−	0.779975i
$404$	10.3923			0.517036
$405$		0			0
$406$	−1.26795			−0.0629273
$407$			11.5911i			0.574550i
$408$		0			0
$409$	−9.07180			−0.448571			−0.224286	−	0.974523i	$-0.572005\pi$
$409$	−9.07180			−0.448571			−0.224286	+	0.974523i	$0.572005\pi$
$410$	5.07180	−	6.21166i	0.250478	−	0.306772i
$411$		0			0
$412$		−	15.8338i		−	0.780073i
$413$			25.4558i			1.25260i
$414$		0			0
$415$	−14.3923	+	17.6269i	−0.706490	+	0.865271i
$416$	9.21539			0.451822
$417$		0			0
$418$		−	2.14488i		−	0.104910i
$419$	−6.00000			−0.293119			−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000			−0.293119			−0.146560	+	0.989202i	$0.546820\pi$
$420$		0			0
$421$	5.46410			0.266304			0.133152	−	0.991096i	$-0.457490\pi$
$421$	5.46410			0.266304			0.133152	+	0.991096i	$0.457490\pi$
$422$			7.62587i			0.371222i
$423$		0			0
$424$	11.4641			0.556746
$425$	6.92820	−	1.41421i	0.336067	−	0.0685994i
$426$		0			0
$427$		−	7.17260i		−	0.347107i
$428$			32.3238i			1.56243i
$429$		0			0
$430$	−8.19615	−	6.69213i	−0.395254	−	0.322723i
$431$	37.1769			1.79075			0.895374	−	0.445314i	$-0.146908\pi$
$431$	37.1769			1.79075			0.895374	+	0.445314i	$0.146908\pi$
$432$		0			0
$433$			2.92996i			0.140805i	0.997519	+	0.0704025i	$0.0224284\pi$
$433$			2.92996i			0.140805i	−0.997519	+	0.0704025i	$0.977572\pi$
$434$	11.0718			0.531463
$435$		0			0
$436$	−30.9282			−1.48119
$437$		−	20.6312i		−	0.986924i
$438$		0			0
$439$	7.07180			0.337518			0.168759	−	0.985657i	$-0.446024\pi$
$439$	7.07180			0.337518			0.168759	+	0.985657i	$0.446024\pi$
$440$	3.46410	−	4.24264i	0.165145	−	0.202260i
$441$		0			0
$442$		−	1.31268i		−	0.0624377i
$443$			18.1817i			0.863839i	0.901912	+	0.431919i	$0.142164\pi$
$443$			18.1817i			0.863839i	−0.901912	+	0.431919i	$0.857836\pi$
$444$		0			0
$445$	18.0000	+	14.6969i	0.853282	+	0.696702i
$446$	7.94744			0.376322
$447$		0			0
$448$		−	5.55532i		−	0.262464i
$449$	−25.8564			−1.22024			−0.610120	−	0.792309i	$-0.708879\pi$
$449$	−25.8564			−1.22024			−0.610120	+	0.792309i	$0.708879\pi$
$450$		0			0
$451$	8.78461			0.413651
$452$		−	22.5259i		−	1.05953i
$453$		0			0
$454$	10.5885			0.496941
$455$	7.60770	+	6.21166i	0.356654	+	0.291207i
$456$		0			0
$457$		−	23.6627i		−	1.10689i	−0.832884	−	0.553447i	$-0.813312\pi$
$457$		−	23.6627i		−	1.10689i	0.832884	−	0.553447i	$-0.186688\pi$
$458$			9.72363i			0.454355i
$459$		0			0
$460$	15.4641	−	18.9396i	0.721017	−	0.883062i
$461$	−24.9282			−1.16102			−0.580511	−	0.814252i	$-0.697147\pi$
$461$	−24.9282			−1.16102			−0.580511	+	0.814252i	$0.697147\pi$
$462$		0			0
$463$		−	6.86800i		−	0.319183i	−0.987183	−	0.159591i	$-0.948982\pi$
$463$		−	6.86800i		−	0.319183i	0.987183	−	0.159591i	$-0.0510177\pi$
$464$	2.46410			0.114393
$465$		0			0
$466$	−1.75129			−0.0811269
$467$		−	21.0101i		−	0.972233i	−0.873894	−	0.486116i	$-0.838413\pi$
$467$		−	21.0101i		−	0.972233i	0.873894	−	0.486116i	$-0.161587\pi$
$468$		0			0
$469$	10.3923			0.479872
$470$	−1.26795	−	1.03528i	−0.0584861	−	0.0477537i
$471$		0			0
$472$			20.0764i			0.924091i
$473$		−	11.5911i		−	0.532960i
$474$		0			0
$475$	3.26795	+	16.0096i	0.149944	+	0.734572i
$476$	−6.00000			−0.275010
$477$		0			0
$478$		−	5.37945i		−	0.246050i
$479$	5.66025			0.258624			0.129312	−	0.991604i	$-0.458723\pi$
$479$	5.66025			0.258624			0.129312	+	0.991604i	$0.458723\pi$
$480$		0			0
$481$	−16.3923			−0.747425
$482$		−	5.93426i		−	0.270298i
$483$		0			0
$484$	−16.2679			−0.739452
$485$	15.4641	−	18.9396i	0.702189	−	0.860002i
$486$		0			0
$487$		−	10.9348i		−	0.495502i	−0.968824	−	0.247751i	$-0.920309\pi$
$487$		−	10.9348i		−	0.495502i	0.968824	−	0.247751i	$-0.0796915\pi$
$488$		−	5.65685i		−	0.256074i
$489$		0			0
$490$	0.732051	−	0.896575i	0.0330707	−	0.0405032i
$491$	−7.26795			−0.327998			−0.163999	−	0.986461i	$-0.552439\pi$
$491$	−7.26795			−0.327998			−0.163999	+	0.986461i	$0.552439\pi$
$492$		0			0
$493$		−	1.41421i		−	0.0636930i
$494$	3.03332			0.136476
$495$		0			0
$496$	−21.5167			−0.966127
$497$			8.48528i			0.380617i
$498$		0			0
$499$	1.07180			0.0479802			0.0239901	−	0.999712i	$-0.492363\pi$
$499$	1.07180			0.0479802			0.0239901	+	0.999712i	$0.492363\pi$
$500$	−9.00000	+	17.1464i	−0.402492	+	0.766812i
$501$		0			0
$502$			7.82894i			0.349423i
$503$		−	12.1731i		−	0.542773i	−0.962471	−	0.271386i	$-0.912518\pi$
$503$		−	12.1731i		−	0.542773i	0.962471	−	0.271386i	$-0.0874821\pi$
$504$		0			0
$505$	10.3923	+	8.48528i	0.462451	+	0.377590i
$506$	−4.14359			−0.184205
$507$		0			0
$508$			7.34847i			0.326036i
$509$	33.4641			1.48327			0.741635	−	0.670804i	$-0.234051\pi$
$509$	33.4641			1.48327			0.741635	+	0.670804i	$0.234051\pi$
$510$		0			0
$511$	18.0000			0.796273
$512$		−	22.1841i		−	0.980408i
$513$		0			0
$514$	4.92820			0.217374
$515$	12.9282	−	15.8338i	0.569685	−	0.697718i
$516$		0			0
$517$		−	1.79315i		−	0.0788627i
$518$		−	11.5911i		−	0.509284i
$519$		0			0
$520$	6.00000	+	4.89898i	0.263117	+	0.214834i
$521$	−4.39230			−0.192430			−0.0962152	−	0.995361i	$-0.530674\pi$
$521$	−4.39230			−0.192430			−0.0962152	+	0.995361i	$0.530674\pi$
$522$		0			0
$523$		−	1.61729i		−	0.0707190i	−0.999375	−	0.0353595i	$-0.988742\pi$
$523$		−	1.61729i		−	0.0707190i	0.999375	−	0.0353595i	$-0.0112576\pi$
$524$	8.19615			0.358051
$525$		0			0
$526$	2.48334			0.108279
$527$			12.3490i			0.537930i
$528$		0			0
$529$	−16.8564			−0.732887
$530$	5.32051	+	4.34418i	0.231108	+	0.188699i
$531$		0			0
$532$		−	13.8647i		−	0.601112i
$533$			12.4233i			0.538113i
$534$		0			0
$535$	−26.3923	+	32.3238i	−1.14104	+	1.39748i
$536$	8.19615			0.354020
$537$		0			0
$538$			6.21166i			0.267804i
$539$	1.26795			0.0546144
$540$		0			0
$541$	42.3923			1.82259			0.911294	−	0.411757i	$-0.135085\pi$
$541$	42.3923			1.82259			0.911294	+	0.411757i	$0.135085\pi$
$542$			13.8375i			0.594373i
$543$		0			0
$544$	−7.26795			−0.311611
$545$	−30.9282	−	25.2528i	−1.32482	−	1.08171i
$546$		0			0
$547$		−	2.44949i		−	0.104733i	−0.998628	−	0.0523663i	$-0.983324\pi$
$547$		−	2.44949i		−	0.104733i	0.998628	−	0.0523663i	$-0.0166763\pi$
$548$		−	25.6317i		−	1.09493i
$549$		0			0
$550$	3.21539	−	0.656339i	0.137105	−	0.0279864i
$551$	3.26795			0.139219
$552$		0			0
$553$		−	10.2784i		−	0.437083i
$554$	9.71281			0.412658
$555$		0			0
$556$	13.8564			0.587643
$557$			0.554803i			0.0235078i	0.999931	+	0.0117539i	$0.00374146\pi$
$557$			0.554803i			0.0235078i	−0.999931	+	0.0117539i	$0.996259\pi$
$558$		0			0
$559$	16.3923			0.693321
$560$	8.53590	−	10.4543i	0.360708	−	0.441775i
$561$		0			0
$562$			16.9706i			0.715860i
$563$			13.2827i			0.559800i	0.960029	+	0.279900i	$0.0903013\pi$
$563$			13.2827i			0.559800i	−0.960029	+	0.279900i	$0.909699\pi$
$564$		0			0
$565$	18.3923	−	22.5259i	0.773770	−	0.947671i
$566$	14.1962			0.596709
$567$		0			0
$568$			6.69213i			0.280796i
$569$	21.4641			0.899822			0.449911	−	0.893073i	$-0.351456\pi$
$569$	21.4641			0.899822			0.449911	+	0.893073i	$0.351456\pi$
$570$		0			0
$571$	−39.3205			−1.64551			−0.822756	−	0.568395i	$-0.807565\pi$
$571$	−39.3205			−1.64551			−0.822756	+	0.568395i	$0.807565\pi$
$572$			3.93803i			0.164657i
$573$		0			0
$574$	−8.78461			−0.366663
$575$	30.9282	−	6.31319i	1.28980	−	0.263278i
$576$		0			0
$577$			9.14162i			0.380571i	0.981729	+	0.190285i	$0.0609413\pi$
$577$			9.14162i			0.380571i	−0.981729	+	0.190285i	$0.939059\pi$
$578$		−	7.76457i		−	0.322964i
$579$		0			0
$580$	3.00000	+	2.44949i	0.124568	+	0.101710i
$581$	24.9282			1.03420
$582$		0			0
$583$			7.52433i			0.311626i
$584$	14.1962			0.587441
$585$		0			0
$586$	15.9090			0.657193
$587$			15.5563i			0.642079i	0.947066	+	0.321040i	$0.104032\pi$
$587$			15.5563i			0.642079i	−0.947066	+	0.321040i	$0.895968\pi$
$588$		0			0
$589$	−28.5359			−1.17580
$590$	−7.60770	+	9.31749i	−0.313204	+	0.383595i
$591$		0			0
$592$			22.5259i			0.925808i
$593$			25.5302i			1.04840i	0.851596	+	0.524199i	$0.175635\pi$
$593$			25.5302i			1.04840i	−0.851596	+	0.524199i	$0.824365\pi$
$594$		0			0
$595$	−6.00000	−	4.89898i	−0.245976	−	0.200839i
$596$	−1.60770			−0.0658538
$597$		0			0
$598$		−	5.85993i		−	0.239630i
$599$	1.26795			0.0518070			0.0259035	−	0.999664i	$-0.491754\pi$
$599$	1.26795			0.0518070			0.0259035	+	0.999664i	$0.491754\pi$
$600$		0			0
$601$	16.7846			0.684659			0.342329	−	0.939580i	$-0.388784\pi$
$601$	16.7846			0.684659			0.342329	+	0.939580i	$0.388784\pi$
$602$			11.5911i			0.472418i
$603$		0			0
$604$	−32.5359			−1.32387
$605$	−16.2679	−	13.2827i	−0.661386	−	0.540020i
$606$		0			0
$607$			16.3142i			0.662174i	0.943600	+	0.331087i	$0.107415\pi$
$607$			16.3142i			0.662174i	−0.943600	+	0.331087i	$0.892585\pi$
$608$		−	16.7947i		−	0.681115i
$609$		0			0
$610$	2.14359	−	2.62536i	0.0867916	−	0.106298i
$611$	2.53590			0.102591
$612$		0			0
$613$		−	18.2832i		−	0.738453i	−0.929339	−	0.369227i	$-0.879623\pi$
$613$		−	18.2832i		−	0.738453i	0.929339	−	0.369227i	$-0.120377\pi$
$614$	5.41154			0.218392
$615$		0			0
$616$	−6.00000			−0.241747
$617$			32.0464i			1.29014i	0.764123	+	0.645071i	$0.223172\pi$
$617$			32.0464i			1.29014i	−0.764123	+	0.645071i	$0.776828\pi$
$618$		0			0
$619$	23.8038			0.956757			0.478379	−	0.878154i	$-0.341225\pi$
$619$	23.8038			0.956757			0.478379	+	0.878154i	$0.341225\pi$
$620$	−26.1962	−	21.3891i	−1.05206	−	0.859006i
$621$		0			0
$622$		−	3.41044i		−	0.136746i
$623$		−	25.4558i		−	1.01987i
$624$		0			0
$625$	−23.0000	+	9.79796i	−0.920000	+	0.391918i
$626$	12.2487			0.489557
$627$		0			0
$628$			18.9396i			0.755771i
$629$	12.9282			0.515481
$630$		0			0
$631$	15.6077			0.621333			0.310666	−	0.950519i	$-0.399448\pi$
$631$	15.6077			0.621333			0.310666	+	0.950519i	$0.399448\pi$
$632$		−	8.10634i		−	0.322453i
$633$		0			0
$634$	2.98076			0.118381
$635$	−6.00000	+	7.34847i	−0.238103	+	0.291615i
$636$		0			0
$637$			1.79315i			0.0710472i
$638$		−	0.656339i		−	0.0259847i
$639$		0			0
$640$	16.1962	−	19.8362i	0.640209	−	0.784093i
$641$	−34.6410			−1.36824			−0.684119	−	0.729370i	$-0.739813\pi$
$641$	−34.6410			−1.36824			−0.684119	+	0.729370i	$0.739813\pi$
$642$		0			0
$643$			10.4543i			0.412277i	0.978523	+	0.206139i	$0.0660898\pi$
$643$			10.4543i			0.412277i	−0.978523	+	0.206139i	$0.933910\pi$
$644$	−26.7846			−1.05546
$645$		0			0
$646$	−2.39230			−0.0941240
$647$		−	14.3180i		−	0.562899i	−0.959576	−	0.281449i	$-0.909185\pi$
$647$		−	14.3180i		−	0.562899i	0.959576	−	0.281449i	$-0.0908151\pi$
$648$		0			0
$649$	−13.1769			−0.517239
$650$	0.928203	+	4.54725i	0.0364071	+	0.178358i
$651$		0			0
$652$		−	24.3190i		−	0.952407i
$653$		−	13.0053i		−	0.508938i	−0.967081	−	0.254469i	$-0.918099\pi$
$653$		−	13.0053i		−	0.508938i	0.967081	−	0.254469i	$-0.0819006\pi$
$654$		0			0
$655$	8.19615	+	6.69213i	0.320250	+	0.261483i
$656$	17.0718			0.666542
$657$		0			0
$658$			1.79315i			0.0699043i
$659$	32.4449			1.26387			0.631936	−	0.775020i	$-0.282260\pi$
$659$	32.4449			1.26387			0.631936	+	0.775020i	$0.282260\pi$
$660$		0			0
$661$	−0.784610			−0.0305178			−0.0152589	−	0.999884i	$-0.504857\pi$
$661$	−0.784610			−0.0305178			−0.0152589	+	0.999884i	$0.504857\pi$
$662$			9.41902i			0.366081i
$663$		0			0
$664$	19.6603			0.762966
$665$	11.3205	−	13.8647i	0.438990	−	0.537651i
$666$		0			0
$667$		−	6.31319i		−	0.244448i
$668$		−	19.4201i		−	0.751384i
$669$		0			0
$670$	3.80385	+	3.10583i	0.146955	+	0.119989i
$671$	3.71281			0.143332
$672$		0			0
$673$		−	46.3644i		−	1.78722i	−0.448846	−	0.893609i	$-0.648165\pi$
$673$		−	46.3644i		−	1.78722i	0.448846	−	0.893609i	$-0.351835\pi$
$674$	−14.4449			−0.556395
$675$		0			0
$676$	16.9474			0.651825
$677$		−	32.2495i		−	1.23945i	−0.784819	−	0.619725i	$-0.787244\pi$
$677$		−	32.2495i		−	1.23945i	0.784819	−	0.619725i	$-0.212756\pi$
$678$		0			0
$679$	−26.7846			−1.02790
$680$	−4.73205	−	3.86370i	−0.181466	−	0.148166i
$681$		0			0
$682$			5.73118i			0.219458i
$683$		−	21.9711i		−	0.840700i	−0.907362	−	0.420350i	$-0.861907\pi$
$683$		−	21.9711i		−	0.840700i	0.907362	−	0.420350i	$-0.138093\pi$
$684$		0			0
$685$	20.9282	−	25.6317i	0.799626	−	0.979337i
$686$	−10.1436			−0.387284
$687$		0			0
$688$		−	22.5259i		−	0.858791i
$689$	−10.6410			−0.405390
$690$		0			0
$691$	41.7128			1.58683			0.793415	−	0.608681i	$-0.208301\pi$
$691$	41.7128			1.58683			0.793415	+	0.608681i	$0.208301\pi$
$692$			8.00481i			0.304297i
$693$		0			0
$694$	−11.1244			−0.422275
$695$	13.8564	+	11.3137i	0.525603	+	0.429153i
$696$		0			0
$697$		−	9.79796i		−	0.371124i
$698$		−	11.7942i		−	0.446416i
$699$		0			0
$700$	20.7846	−	4.24264i	0.785584	−	0.160357i
$701$	−27.7128			−1.04670			−0.523349	−	0.852118i	$-0.675318\pi$
$701$	−27.7128			−1.04670			−0.523349	+	0.852118i	$0.675318\pi$
$702$		0			0
$703$			29.8744i			1.12673i
$704$	2.87564			0.108380
$705$		0			0
$706$	−16.5359			−0.622337
$707$		−	14.6969i		−	0.552735i
$708$		0			0
$709$	−20.3923			−0.765849			−0.382925	−	0.923780i	$-0.625083\pi$
$709$	−20.3923			−0.765849			−0.382925	+	0.923780i	$0.625083\pi$
$710$	−2.53590	+	3.10583i	−0.0951706	+	0.116560i
$711$		0			0
$712$		−	20.0764i		−	0.752395i
$713$			55.1271i			2.06453i
$714$		0			0
$715$	−3.21539	+	3.93803i	−0.120249	+	0.147274i
$716$	4.39230			0.164148
$717$		0			0
$718$			3.76217i			0.140403i
$719$	−19.8564			−0.740519			−0.370260	−	0.928928i	$-0.620731\pi$
$719$	−19.8564			−0.740519			−0.370260	+	0.928928i	$0.620731\pi$
$720$		0			0
$721$	−22.3923			−0.833933
$722$			4.30701i			0.160290i
$723$		0			0
$724$	−27.7128			−1.02994
$725$	1.00000	+	4.89898i	0.0371391	+	0.181944i
$726$		0			0
$727$		−	46.6690i		−	1.73086i	−0.501031	−	0.865430i	$-0.667046\pi$
$727$		−	46.6690i		−	1.73086i	0.501031	−	0.865430i	$-0.332954\pi$
$728$		−	8.48528i		−	0.314485i
$729$		0			0
$730$	6.58846	+	5.37945i	0.243850	+	0.199102i
$731$	−12.9282			−0.478167
$732$		0			0
$733$		−	12.7279i		−	0.470117i	−0.971981	−	0.235058i	$-0.924472\pi$
$733$		−	12.7279i		−	0.470117i	0.971981	−	0.235058i	$-0.0755281\pi$
$734$	−17.4115			−0.642672
$735$		0			0
$736$	−32.4449			−1.19593
$737$			5.37945i			0.198155i
$738$		0			0
$739$	18.9808			0.698219			0.349109	−	0.937082i	$-0.386484\pi$
$739$	18.9808			0.698219			0.349109	+	0.937082i	$0.386484\pi$
$740$	−22.3923	+	27.4249i	−0.823157	+	1.00816i
$741$		0			0
$742$		−	7.52433i		−	0.276227i
$743$		−	9.89949i		−	0.363177i	−0.983375	−	0.181589i	$-0.941876\pi$
$743$		−	9.89949i		−	0.363177i	0.983375	−	0.181589i	$-0.0581239\pi$
$744$		0			0
$745$	−1.60770	−	1.31268i	−0.0589014	−	0.0480928i
$746$	10.1436			0.371383
$747$		0			0
$748$		−	3.10583i		−	0.113560i
$749$	45.7128			1.67031
$750$		0			0
$751$	49.9090			1.82120			0.910602	−	0.413284i	$-0.135618\pi$
$751$	49.9090			1.82120			0.910602	+	0.413284i	$0.135618\pi$
$752$		−	3.48477i		−	0.127076i
$753$		0			0
$754$	0.928203			0.0338032
$755$	−32.5359	−	26.5654i	−1.18410	−	0.966816i
$756$		0			0
$757$			10.9348i			0.397431i	0.980057	+	0.198716i	$0.0636770\pi$
$757$			10.9348i			0.397431i	−0.980057	+	0.198716i	$0.936323\pi$
$758$		−	8.38375i		−	0.304511i
$759$		0			0
$760$	8.92820	−	10.9348i	0.323860	−	0.396646i
$761$	35.5692			1.28938			0.644692	−	0.764443i	$-0.276986\pi$
$761$	35.5692			1.28938			0.644692	+	0.764443i	$0.276986\pi$
$762$		0			0
$763$			43.7391i			1.58346i
$764$	−26.1962			−0.947744
$765$		0			0
$766$	−0.483340			−0.0174638
$767$		−	18.6350i		−	0.672870i
$768$		0			0
$769$	19.0718			0.687747			0.343873	−	0.939016i	$-0.388261\pi$
$769$	19.0718			0.687747			0.343873	+	0.939016i	$0.388261\pi$
$770$	−2.78461	−	2.27362i	−0.100350	−	0.0819357i
$771$		0			0
$772$			1.13681i			0.0409148i
$773$		−	11.2122i		−	0.403274i	−0.979460	−	0.201637i	$-0.935374\pi$
$773$		−	11.2122i		−	0.403274i	0.979460	−	0.201637i	$-0.0646261\pi$
$774$		0			0
$775$	−8.73205	−	42.7781i	−0.313665	−	1.53664i
$776$	−21.1244			−0.758320
$777$		0			0
$778$			10.7589i			0.385725i
$779$	22.6410			0.811199
$780$		0			0
$781$	−4.39230			−0.157169
$782$			4.62158i			0.165267i
$783$		0			0
$784$	2.46410			0.0880036
$785$	−15.4641	+	18.9396i	−0.551937	+	0.675983i
$786$		0			0
$787$			35.0779i			1.25039i	0.780467	+	0.625197i	$0.214981\pi$
$787$			35.0779i			1.25039i	−0.780467	+	0.625197i	$0.785019\pi$
$788$			38.8401i			1.38362i
$789$		0			0
$790$	3.07180	−	3.76217i	0.109290	−	0.133852i
$791$	−31.8564			−1.13268
$792$		0			0
$793$			5.25071i			0.186458i
$794$	2.53590			0.0899957
$795$		0			0
$796$	24.2487			0.859473
$797$		−	29.0149i		−	1.02776i	−0.857862	−	0.513881i	$-0.828207\pi$
$797$		−	29.0149i		−	1.02776i	0.857862	−	0.513881i	$-0.171793\pi$
$798$		0			0
$799$	−2.00000			−0.0707549
$800$	25.1769	−	5.13922i	0.890138	−	0.181699i
$801$		0			0
$802$			19.5959i			0.691956i
$803$			9.31749i			0.328807i
$804$		0			0
$805$	−26.7846	−	21.8695i	−0.944033	−	0.770800i
$806$	−8.10512			−0.285491
$807$		0			0
$808$		−	11.5911i		−	0.407774i
$809$	13.6077			0.478421			0.239211	−	0.970968i	$-0.423111\pi$
$809$	13.6077			0.478421			0.239211	+	0.970968i	$0.423111\pi$
$810$		0			0
$811$	−36.7846			−1.29168			−0.645841	−	0.763472i	$-0.723493\pi$
$811$	−36.7846			−1.29168			−0.645841	+	0.763472i	$0.723493\pi$
$812$		−	4.24264i		−	0.148888i
$813$		0			0
$814$	6.00000			0.210300
$815$	19.8564	−	24.3190i	0.695540	−	0.851859i
$816$		0			0
$817$		−	29.8744i		−	1.04517i
$818$			4.69591i			0.164189i
$819$		0			0
$820$	20.7846	+	16.9706i	0.725830	+	0.592638i
$821$	−9.21539			−0.321619			−0.160810	−	0.986985i	$-0.551411\pi$
$821$	−9.21539			−0.321619			−0.160810	+	0.986985i	$0.551411\pi$
$822$		0			0
$823$			40.8091i			1.42252i	0.702931	+	0.711258i	$0.251874\pi$
$823$			40.8091i			1.42252i	−0.702931	+	0.711258i	$0.748126\pi$
$824$	−17.6603			−0.615224
$825$		0			0
$826$	13.1769			0.458483
$827$		−	3.68784i		−	0.128239i	−0.997942	−	0.0641193i	$-0.979576\pi$
$827$		−	3.68784i		−	0.128239i	0.997942	−	0.0641193i	$-0.0204238\pi$
$828$		0			0
$829$	16.7846			0.582954			0.291477	−	0.956578i	$-0.405853\pi$
$829$	16.7846			0.582954			0.291477	+	0.956578i	$0.405853\pi$
$830$	9.12436	+	7.45001i	0.316711	+	0.258593i
$831$		0			0
$832$			4.06678i			0.140990i
$833$		−	1.41421i		−	0.0489996i
$834$		0			0
$835$	15.8564	−	19.4201i	0.548734	−	0.672059i
$836$	7.17691			0.248219
$837$		0			0
$838$			3.10583i			0.107289i
$839$	40.9808			1.41481			0.707407	−	0.706807i	$-0.249865\pi$
$839$	40.9808			1.41481			0.707407	+	0.706807i	$0.249865\pi$
$840$		0			0
$841$	1.00000			0.0344828
$842$		−	2.82843i		−	0.0974740i
$843$		0			0
$844$	−25.5167			−0.878320
$845$	16.9474	+	13.8375i	0.583010	+	0.476025i
$846$		0			0
$847$			23.0064i			0.790508i
$848$			14.6226i			0.502142i
$849$		0			0
$850$	−0.732051	−	3.58630i	−0.0251091	−	0.123009i
$851$	57.7128			1.97837
$852$		0			0
$853$		−	32.3238i		−	1.10675i	−0.832933	−	0.553374i	$-0.813340\pi$
$853$		−	32.3238i		−	1.10675i	0.832933	−	0.553374i	$-0.186660\pi$
$854$	−3.71281			−0.127050
$855$		0			0
$856$	36.0526			1.23225
$857$		−	33.2576i		−	1.13606i	−0.823009	−	0.568029i	$-0.807706\pi$
$857$		−	33.2576i		−	1.13606i	0.823009	−	0.568029i	$-0.192294\pi$
$858$		0			0
$859$	18.7321			0.639129			0.319565	−	0.947564i	$-0.396463\pi$
$859$	18.7321			0.639129			0.319565	+	0.947564i	$0.396463\pi$
$860$	22.3923	−	27.4249i	0.763571	−	0.935180i
$861$		0			0
$862$		−	19.2442i		−	0.655460i
$863$			1.69161i			0.0575832i	0.999585	+	0.0287916i	$0.00916592\pi$
$863$			1.69161i			0.0575832i	−0.999585	+	0.0287916i	$0.990834\pi$
$864$		0			0
$865$	−6.53590	+	8.00481i	−0.222227	+	0.272172i
$866$	1.51666			0.0515382
$867$		0			0
$868$			37.0470i			1.25746i
$869$	5.32051			0.180486
$870$		0			0
$871$	−7.60770			−0.257777
$872$			34.4959i			1.16818i
$873$		0			0
$874$	−10.6795			−0.361239
$875$	24.2487	+	12.7279i	0.819756	+	0.430282i
$876$		0			0
$877$			24.9754i			0.843358i	0.906745	+	0.421679i	$0.138559\pi$
$877$			24.9754i			0.843358i	−0.906745	+	0.421679i	$0.861441\pi$
$878$		−	3.66063i		−	0.123540i
$879$		0			0
$880$	5.41154	+	4.41851i	0.182423	+	0.148948i
$881$	50.5359			1.70260			0.851299	−	0.524681i	$-0.175815\pi$
$881$	50.5359			1.70260			0.851299	+	0.524681i	$0.175815\pi$
$882$		0			0
$883$		−	1.48854i		−	0.0500935i	−0.999686	−	0.0250467i	$-0.992027\pi$
$883$		−	1.48854i		−	0.0500935i	0.999686	−	0.0250467i	$-0.00797346\pi$
$884$	4.39230			0.147729
$885$		0			0
$886$	9.41154			0.316187
$887$		−	21.0101i		−	0.705451i	−0.935727	−	0.352726i	$-0.885255\pi$
$887$		−	21.0101i		−	0.705451i	0.935727	−	0.352726i	$-0.114745\pi$
$888$		0			0
$889$	10.3923			0.348547
$890$	7.60770	−	9.31749i	0.255011	−	0.312323i
$891$		0			0
$892$			26.5927i			0.890388i
$893$		−	4.62158i		−	0.154655i
$894$		0			0
$895$	4.39230	+	3.58630i	0.146819	+	0.119877i
$896$	−28.0526			−0.937170
$897$		0			0
$898$			13.3843i			0.446639i
$899$	−8.73205			−0.291230
$900$		0			0
$901$	8.39230			0.279588
$902$		−	4.54725i		−	0.151407i
$903$		0			0
$904$	−25.1244			−0.835624
$905$	−27.7128	−	22.6274i	−0.921205	−	0.752161i
$906$		0			0
$907$		−	45.7081i		−	1.51771i	−0.651258	−	0.758856i	$-0.725758\pi$
$907$		−	45.7081i		−	1.51771i	0.651258	−	0.758856i	$-0.274242\pi$
$908$			35.4297i			1.17577i
$909$		0			0
$910$	3.21539	−	3.93803i	0.106589	−	0.130545i
$911$	9.80385			0.324816			0.162408	−	0.986724i	$-0.448074\pi$
$911$	9.80385			0.324816			0.162408	+	0.986724i	$0.448074\pi$
$912$		0			0
$913$			12.9038i			0.427053i
$914$	−12.2487			−0.405151
$915$		0			0
$916$	−32.5359			−1.07502
$917$		−	11.5911i		−	0.382772i
$918$		0			0
$919$	−43.9615			−1.45016			−0.725078	−	0.688666i	$-0.758197\pi$
$919$	−43.9615			−1.45016			−0.725078	+	0.688666i	$0.758197\pi$
$920$	−21.1244	−	17.2480i	−0.696449	−	0.568649i
$921$		0			0
$922$			12.9038i			0.424964i
$923$		−	6.21166i		−	0.204459i
$924$		0			0
$925$	−44.7846	+	9.14162i	−1.47251	+	0.300575i
$926$	−3.55514			−0.116829
$927$		0			0
$928$		−	5.13922i		−	0.168703i
$929$	55.8564			1.83259			0.916295	−	0.400505i	$-0.131165\pi$
$929$	55.8564			1.83259			0.916295	+	0.400505i	$0.131165\pi$
$930$		0			0
$931$	3.26795			0.107103
$932$		−	5.85993i		−	0.191948i
$933$		0			0
$934$	−10.8756			−0.355862
$935$	2.53590	−	3.10583i	0.0829327	−	0.101571i
$936$		0			0
$937$			2.75410i			0.0899724i	0.998988	+	0.0449862i	$0.0143244\pi$
$937$			2.75410i			0.0899724i	−0.998988	+	0.0449862i	$0.985676\pi$
$938$		−	5.37945i		−	0.175645i
$939$		0			0
$940$	3.46410	−	4.24264i	0.112987	−	0.138380i
$941$	7.85641			0.256112			0.128056	−	0.991767i	$-0.459126\pi$
$941$	7.85641			0.256112			0.128056	+	0.991767i	$0.459126\pi$
$942$		0			0
$943$		−	43.7391i		−	1.42434i
$944$	−25.6077			−0.833459
$945$		0			0
$946$	−6.00000			−0.195077
$947$			27.9797i			0.909217i	0.890691	+	0.454608i	$0.150221\pi$
$947$			27.9797i			0.909217i	−0.890691	+	0.454608i	$0.849779\pi$
$948$		0			0
$949$	−13.1769			−0.427741
$950$	8.28719	−	1.69161i	0.268872	−	0.0548832i
$951$		0			0
$952$			6.69213i			0.216893i
$953$		−	5.65685i		−	0.183243i	−0.995794	−	0.0916217i	$-0.970795\pi$
$953$		−	5.65685i		−	0.183243i	0.995794	−	0.0916217i	$-0.0292051\pi$
$954$		0			0
$955$	−26.1962	−	21.3891i	−0.847688	−	0.692134i
$956$	18.0000			0.582162
$957$		0			0
$958$		−	2.92996i		−	0.0946628i
$959$	−36.2487			−1.17053
$960$		0			0
$961$	45.2487			1.45964
$962$			8.48528i			0.273576i
$963$		0			0
$964$	19.8564			0.639532
$965$	−0.928203	+	1.13681i	−0.0298799	+	0.0365953i
$966$		0			0
$967$		−	1.96902i		−	0.0633193i	−0.999499	−	0.0316596i	$-0.989921\pi$
$967$		−	1.96902i		−	0.0633193i	0.999499	−	0.0316596i	$-0.0100793\pi$
$968$			18.1445i			0.583188i
$969$		0			0
$970$	−9.80385	−	8.00481i	−0.314783	−	0.257019i
$971$	49.5167			1.58907			0.794533	−	0.607221i	$-0.207716\pi$
$971$	49.5167			1.58907			0.794533	+	0.607221i	$0.207716\pi$
$972$		0			0
$973$		−	19.5959i		−	0.628216i
$974$	−5.66025			−0.181366
$975$		0			0
$976$	7.21539			0.230959
$977$			22.9048i			0.732790i	0.930459	+	0.366395i	$0.119408\pi$
$977$			22.9048i			0.732790i	−0.930459	+	0.366395i	$0.880592\pi$
$978$		0			0
$979$	13.1769			0.421136
$980$	3.00000	+	2.44949i	0.0958315	+	0.0782461i
$981$		0			0
$982$			3.76217i			0.120056i
$983$			30.2533i			0.964930i	0.875915	+	0.482465i	$0.160258\pi$
$983$			30.2533i			0.964930i	−0.875915	+	0.482465i	$0.839742\pi$
$984$		0			0
$985$	−31.7128	+	38.8401i	−1.01045	+	1.23755i
$986$	−0.732051			−0.0233132
$987$		0			0
$988$			10.1497i			0.322905i
$989$	−57.7128			−1.83516
$990$		0			0
$991$	34.7846			1.10497			0.552485	−	0.833523i	$-0.313680\pi$
$991$	34.7846			1.10497			0.552485	+	0.833523i	$0.313680\pi$
$992$			44.8759i			1.42481i
$993$		0			0
$994$	4.39230			0.139315
$995$	24.2487	+	19.7990i	0.768736	+	0.627670i
$996$		0			0
$997$			26.5927i			0.842198i	0.907015	+	0.421099i	$0.138355\pi$
$997$			26.5927i			0.842198i	−0.907015	+	0.421099i	$0.861645\pi$
$998$		−	0.554803i		−	0.0175620i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1305.2.c.f.784.2		4
3.2	odd	2		145.2.b.b.59.3	yes	4
5.2	odd	4		6525.2.a.bj.1.3		4
5.3	odd	4		6525.2.a.bj.1.2		4
5.4	even	2	inner	1305.2.c.f.784.3		4
12.11	even	2		2320.2.d.f.929.3		4
15.2	even	4		725.2.a.f.1.2		4
15.8	even	4		725.2.a.f.1.3		4
15.14	odd	2		145.2.b.b.59.2	✓	4
60.59	even	2		2320.2.d.f.929.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
145.2.b.b.59.2	✓	4	15.14	odd	2
145.2.b.b.59.3	yes	4	3.2	odd	2
725.2.a.f.1.2		4	15.2	even	4
725.2.a.f.1.3		4	15.8	even	4
1305.2.c.f.784.2		4	1.1	even	1	trivial
1305.2.c.f.784.3		4	5.4	even	2	inner
2320.2.d.f.929.1		4	60.59	even	2
2320.2.d.f.929.3		4	12.11	even	2
6525.2.a.bj.1.2		4	5.3	odd	4
6525.2.a.bj.1.3		4	5.2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1305.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.517638i q^{2} +1.73205 q^{4} +(1.73205 + 1.41421i) q^{5} -2.44949i q^{7} -1.93185i q^{8} +(0.732051 - 0.896575i) q^{10} +1.26795 q^{11} +1.79315i q^{13} -1.26795 q^{14} +2.46410 q^{16} -1.41421i q^{17} +3.26795 q^{19} +(3.00000 + 2.44949i) q^{20} -0.656339i q^{22} -6.31319i q^{23} +(1.00000 + 4.89898i) q^{25} +0.928203 q^{26} -4.24264i q^{28} +1.00000 q^{29} -8.73205 q^{31} -5.13922i q^{32} -0.732051 q^{34} +(3.46410 - 4.24264i) q^{35} +9.14162i q^{37} -1.69161i q^{38} +(2.73205 - 3.34607i) q^{40} +6.92820 q^{41} -9.14162i q^{43} +2.19615 q^{44} -3.26795 q^{46} -1.41421i q^{47} +1.00000 q^{49} +(2.53590 - 0.517638i) q^{50} +3.10583i q^{52} +5.93426i q^{53} +(2.19615 + 1.79315i) q^{55} -4.73205 q^{56} -0.517638i q^{58} -10.3923 q^{59} +2.92820 q^{61} +4.52004i q^{62} +2.26795 q^{64} +(-2.53590 + 3.10583i) q^{65} +4.24264i q^{67} -2.44949i q^{68} +(-2.19615 - 1.79315i) q^{70} -3.46410 q^{71} +7.34847i q^{73} +4.73205 q^{74} +5.66025 q^{76} -3.10583i q^{77} +4.19615 q^{79} +(4.26795 + 3.48477i) q^{80} -3.58630i q^{82} +10.1769i q^{83} +(2.00000 - 2.44949i) q^{85} -4.73205 q^{86} -2.44949i q^{88} +10.3923 q^{89} +4.39230 q^{91} -10.9348i q^{92} -0.732051 q^{94} +(5.66025 + 4.62158i) q^{95} -10.9348i q^{97} -0.517638i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{10} + 12 q^{11} - 12 q^{14} - 4 q^{16} + 20 q^{19} + 12 q^{20} + 4 q^{25} - 24 q^{26} + 4 q^{29} - 28 q^{31} + 4 q^{34} + 4 q^{40} - 12 q^{44} - 20 q^{46} + 4 q^{49} + 24 q^{50} - 12 q^{55} - 12 q^{56}+ \cdots - 12 q^{95}+O(q^{100}) \) 4 * q - 4 * q^10 + 12 * q^11 - 12 * q^14 - 4 * q^16 + 20 * q^19 + 12 * q^20 + 4 * q^25 - 24 * q^26 + 4 * q^29 - 28 * q^31 + 4 * q^34 + 4 * q^40 - 12 * q^44 - 20 * q^46 + 4 * q^49 + 24 * q^50 - 12 * q^55 - 12 * q^56 - 16 * q^61 + 16 * q^64 - 24 * q^65 + 12 * q^70 + 12 * q^74 - 12 * q^76 - 4 * q^79 + 24 * q^80 + 8 * q^85 - 12 * q^86 - 24 * q^91 + 4 * q^94 - 12 * q^95

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