LMFDB - Embedded newform 2400.2.bh.b.943.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2400,2,Mod(943,2400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 2, 0, 3]))

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

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

chi := DirichletCharacter("2400.943");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2400 = 2^{5} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2400.bh (of order $4$, degree $2$, not 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:	$19.1640964851$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			943.9
Character	$\chi$	$=$	2400.943
Dual form			2400.2.bh.b.1807.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{3} +(-1.21782 - 1.21782i) q^{7} +1.00000i q^{9} +O(q^{10})$	$q+(0.707107 + 0.707107i) q^{3} +(-1.21782 - 1.21782i) q^{7} +1.00000i q^{9} -5.23822 q^{11} +(0.361752 - 0.361752i) q^{13} +(1.66215 - 1.66215i) q^{17} +3.72919i q^{19} -1.72226i q^{21} +(3.17802 - 3.17802i) q^{23} +(-0.707107 + 0.707107i) q^{27} +6.70849 q^{29} +2.74770i q^{31} +(-3.70398 - 3.70398i) q^{33} +(-4.13265 - 4.13265i) q^{37} +0.511595 q^{39} -7.40796 q^{41} +(-5.67877 - 5.67877i) q^{43} +(-7.31149 - 7.31149i) q^{47} -4.03382i q^{49} +2.35063 q^{51} +(10.0364 - 10.0364i) q^{53} +(-2.63694 + 2.63694i) q^{57} -11.3219i q^{59} -13.3665i q^{61} +(1.21782 - 1.21782i) q^{63} +(-5.40796 + 5.40796i) q^{67} +4.49440 q^{69} -2.63276i q^{71} +(-2.67877 - 2.67877i) q^{73} +(6.37922 + 6.37922i) q^{77} -5.91346 q^{79} -1.00000 q^{81} +(-0.742352 - 0.742352i) q^{83} +(4.74362 + 4.74362i) q^{87} -1.75111i q^{89} -0.881100 q^{91} +(-1.94292 + 1.94292i) q^{93} +(-6.64801 + 6.64801i) q^{97} -5.23822i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q+O(q^{10}) $ 24 * q	$ 24 q - 8 q^{17} - 32 q^{43} + 16 q^{51} + 48 q^{67} + 40 q^{73} - 24 q^{81} + 80 q^{83} - 64 q^{91} + 24 q^{97}+O(q^{100}) $ 24 * q - 8 * q^17 - 32 * q^43 + 16 * q^51 + 48 * q^67 + 40 * q^73 - 24 * q^81 + 80 * q^83 - 64 * q^91 + 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2400\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1601$	$1951$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$	$-1$

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			0
$2$		0			0
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.21782	−	1.21782i	−0.460293	−	0.460293i	0.438458	−	0.898752i	$-0.355525\pi$
$7$	−1.21782	−	1.21782i	−0.460293	−	0.460293i	−0.898752	+	0.438458i	$0.855525\pi$
$8$		0			0
$9$			1.00000i			0.333333i
$10$		0			0
$11$	−5.23822			−1.57938			−0.789692	−	0.613504i	$-0.789759\pi$
$11$	−5.23822			−1.57938			−0.789692	+	0.613504i	$0.789759\pi$
$12$		0			0
$13$	0.361752	−	0.361752i	0.100332	−	0.100332i	−0.655159	−	0.755491i	$-0.727398\pi$
$13$	0.361752	−	0.361752i	0.100332	−	0.100332i	0.755491	+	0.655159i	$0.227398\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	1.66215	−	1.66215i	0.403130	−	0.403130i	−0.476204	−	0.879335i	$-0.657988\pi$
$17$	1.66215	−	1.66215i	0.403130	−	0.403130i	0.879335	+	0.476204i	$0.157988\pi$
$18$		0			0
$19$			3.72919i			0.855535i	0.903889	+	0.427768i	$0.140700\pi$
$19$			3.72919i			0.855535i	−0.903889	+	0.427768i	$0.859300\pi$
$20$		0			0
$21$		−	1.72226i		−	0.375828i
$22$		0			0
$23$	3.17802	−	3.17802i	0.662663	−	0.662663i	−0.293344	−	0.956007i	$-0.594768\pi$
$23$	3.17802	−	3.17802i	0.662663	−	0.662663i	0.956007	+	0.293344i	$0.0947681\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$		0			0
$29$	6.70849			1.24574			0.622868	−	0.782327i	$-0.285967\pi$
$29$	6.70849			1.24574			0.622868	+	0.782327i	$0.285967\pi$
$30$		0			0
$31$			2.74770i			0.493502i	0.969079	+	0.246751i	$0.0793630\pi$
$31$			2.74770i			0.493502i	−0.969079	+	0.246751i	$0.920637\pi$
$32$		0			0
$33$	−3.70398	−	3.70398i	−0.644780	−	0.644780i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−4.13265	−	4.13265i	−0.679403	−	0.679403i	0.280462	−	0.959865i	$-0.409512\pi$
$37$	−4.13265	−	4.13265i	−0.679403	−	0.679403i	−0.959865	+	0.280462i	$0.909512\pi$
$38$		0			0
$39$	0.511595			0.0819208
$40$		0			0
$41$	−7.40796			−1.15693			−0.578465	−	0.815707i	$-0.696348\pi$
$41$	−7.40796			−1.15693			−0.578465	+	0.815707i	$0.696348\pi$
$42$		0			0
$43$	−5.67877	−	5.67877i	−0.866004	−	0.866004i	0.126023	−	0.992027i	$-0.459779\pi$
$43$	−5.67877	−	5.67877i	−0.866004	−	0.866004i	−0.992027	+	0.126023i	$0.959779\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−7.31149	−	7.31149i	−1.06649	−	1.06649i	−0.997626	−	0.0688638i	$-0.978063\pi$
$47$	−7.31149	−	7.31149i	−1.06649	−	1.06649i	−0.0688638	−	0.997626i	$-0.521937\pi$
$48$		0			0
$49$		−	4.03382i		−	0.576260i
$50$		0			0
$51$	2.35063			0.329154
$52$		0			0
$53$	10.0364	−	10.0364i	1.37860	−	1.37860i	0.531610	−	0.846989i	$-0.321587\pi$
$53$	10.0364	−	10.0364i	1.37860	−	1.37860i	0.846989	−	0.531610i	$-0.178413\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−2.63694	+	2.63694i	−0.349271	+	0.349271i
$58$		0			0
$59$		−	11.3219i		−	1.47398i	−0.675901	−	0.736992i	$-0.736245\pi$
$59$		−	11.3219i		−	1.47398i	0.675901	−	0.736992i	$-0.263755\pi$
$60$		0			0
$61$		−	13.3665i		−	1.71140i	−0.517471	−	0.855701i	$-0.673127\pi$
$61$		−	13.3665i		−	1.71140i	0.517471	−	0.855701i	$-0.326873\pi$
$62$		0			0
$63$	1.21782	−	1.21782i	0.153431	−	0.153431i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−5.40796	+	5.40796i	−0.660688	+	0.660688i	−0.955542	−	0.294854i	$-0.904729\pi$
$67$	−5.40796	+	5.40796i	−0.660688	+	0.660688i	0.294854	+	0.955542i	$0.404729\pi$
$68$		0			0
$69$	4.49440			0.541062
$70$		0			0
$71$		−	2.63276i		−	0.312451i	−0.987721	−	0.156225i	$-0.950067\pi$
$71$		−	2.63276i		−	0.312451i	0.987721	−	0.156225i	$-0.0499326\pi$
$72$		0			0
$73$	−2.67877	−	2.67877i	−0.313526	−	0.313526i	0.532748	−	0.846274i	$-0.321159\pi$
$73$	−2.67877	−	2.67877i	−0.313526	−	0.313526i	−0.846274	+	0.532748i	$0.821159\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	6.37922	+	6.37922i	0.726979	+	0.726979i
$78$		0			0
$79$	−5.91346			−0.665316			−0.332658	−	0.943048i	$-0.607945\pi$
$79$	−5.91346			−0.665316			−0.332658	+	0.943048i	$0.607945\pi$
$80$		0			0
$81$	−1.00000			−0.111111
$82$		0			0
$83$	−0.742352	−	0.742352i	−0.0814837	−	0.0814837i	0.665190	−	0.746674i	$-0.268350\pi$
$83$	−0.742352	−	0.742352i	−0.0814837	−	0.0814837i	−0.746674	+	0.665190i	$0.768350\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	4.74362	+	4.74362i	0.508569	+	0.508569i
$88$		0			0
$89$		−	1.75111i		−	0.185617i	−0.995684	−	0.0928086i	$-0.970416\pi$
$89$		−	1.75111i		−	0.185617i	0.995684	−	0.0928086i	$-0.0295845\pi$
$90$		0			0
$91$	−0.881100			−0.0923643
$92$		0			0
$93$	−1.94292	+	1.94292i	−0.201471	+	0.201471i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−6.64801	+	6.64801i	−0.675004	+	0.675004i	−0.958865	−	0.283862i	$-0.908384\pi$
$97$	−6.64801	+	6.64801i	−0.675004	+	0.675004i	0.283862	+	0.958865i	$0.408384\pi$
$98$		0			0
$99$		−	5.23822i		−	0.526461i
$100$		0			0
$101$			7.63230i			0.759442i	0.925101	+	0.379721i	$0.123980\pi$
$101$			7.63230i			0.759442i	−0.925101	+	0.379721i	$0.876020\pi$
$102$		0			0
$103$	−1.72700	+	1.72700i	−0.170166	+	0.170166i	−0.787052	−	0.616886i	$-0.788394\pi$
$103$	−1.72700	+	1.72700i	−0.170166	+	0.170166i	0.616886	+	0.787052i	$0.288394\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	2.79277	−	2.79277i	0.269988	−	0.269988i	−0.559108	−	0.829095i	$-0.688856\pi$
$107$	2.79277	−	2.79277i	0.269988	−	0.269988i	0.829095	+	0.559108i	$0.188856\pi$
$108$		0			0
$109$	−0.115468			−0.0110598			−0.00552990	−	0.999985i	$-0.501760\pi$
$109$	−0.115468			−0.0110598			−0.00552990	+	0.999985i	$0.501760\pi$
$110$		0			0
$111$		−	5.84445i		−	0.554730i
$112$		0			0
$113$	−1.61173	−	1.61173i	−0.151618	−	0.151618i	0.627222	−	0.778840i	$-0.284192\pi$
$113$	−1.61173	−	1.61173i	−0.151618	−	0.151618i	−0.778840	+	0.627222i	$0.784192\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.361752	+	0.361752i	0.0334440	+	0.0334440i
$118$		0			0
$119$	−4.04840			−0.371116
$120$		0			0
$121$	16.4390			1.49445
$122$		0			0
$123$	−5.23822	−	5.23822i	−0.472314	−	0.472314i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−2.39052	−	2.39052i	−0.212124	−	0.212124i	0.593045	−	0.805169i	$-0.297926\pi$
$127$	−2.39052	−	2.39052i	−0.212124	−	0.212124i	−0.805169	+	0.593045i	$0.797926\pi$
$128$		0			0
$129$		−	8.03099i		−	0.707090i
$130$		0			0
$131$	5.62120			0.491127			0.245563	−	0.969381i	$-0.421027\pi$
$131$	5.62120			0.491127			0.245563	+	0.969381i	$0.421027\pi$
$132$		0			0
$133$	4.54149	−	4.54149i	0.393797	−	0.393797i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−11.4027	+	11.4027i	−0.974196	+	0.974196i	−0.999675	−	0.0254796i	$-0.991889\pi$
$137$	−11.4027	+	11.4027i	−0.974196	+	0.974196i	0.0254796	+	0.999675i	$0.491889\pi$
$138$		0			0
$139$		−	3.80050i		−	0.322354i	−0.986926	−	0.161177i	$-0.948471\pi$
$139$		−	3.80050i		−	0.322354i	0.986926	−	0.161177i	$-0.0515290\pi$
$140$		0			0
$141$		−	10.3400i		−	0.870785i
$142$		0			0
$143$	−1.89494	+	1.89494i	−0.158463	+	0.158463i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	2.85234	−	2.85234i	0.235257	−	0.235257i
$148$		0			0
$149$	10.0554			0.823771			0.411886	−	0.911236i	$-0.364870\pi$
$149$	10.0554			0.823771			0.411886	+	0.911236i	$0.364870\pi$
$150$		0			0
$151$			3.24792i			0.264312i	0.991229	+	0.132156i	$0.0421900\pi$
$151$			3.24792i			0.264312i	−0.991229	+	0.132156i	$0.957810\pi$
$152$		0			0
$153$	1.66215	+	1.66215i	0.134377	+	0.134377i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−4.18316	−	4.18316i	−0.333852	−	0.333852i	0.520195	−	0.854047i	$-0.325859\pi$
$157$	−4.18316	−	4.18316i	−0.333852	−	0.333852i	−0.854047	+	0.520195i	$0.825859\pi$
$158$		0			0
$159$	14.1935			1.12562
$160$		0			0
$161$	−7.74052			−0.610039
$162$		0			0
$163$	3.02793	+	3.02793i	0.237166	+	0.237166i	0.815675	−	0.578510i	$-0.196366\pi$
$163$	3.02793	+	3.02793i	0.237166	+	0.237166i	−0.578510	+	0.815675i	$0.696366\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−5.13436	−	5.13436i	−0.397309	−	0.397309i	0.479974	−	0.877283i	$-0.340646\pi$
$167$	−5.13436	−	5.13436i	−0.397309	−	0.397309i	−0.877283	+	0.479974i	$0.840646\pi$
$168$		0			0
$169$			12.7383i			0.979867i
$170$		0			0
$171$	−3.72919			−0.285178
$172$		0			0
$173$	−0.375176	+	0.375176i	−0.0285241	+	0.0285241i	−0.721225	−	0.692701i	$-0.756421\pi$
$173$	−0.375176	+	0.375176i	−0.0285241	+	0.0285241i	0.692701	+	0.721225i	$0.256421\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	8.00578	−	8.00578i	0.601752	−	0.601752i
$178$		0			0
$179$			8.03565i			0.600613i	0.953843	+	0.300306i	$0.0970890\pi$
$179$			8.03565i			0.600613i	−0.953843	+	0.300306i	$0.902911\pi$
$180$		0			0
$181$			21.3530i			1.58716i	0.608469	+	0.793578i	$0.291784\pi$
$181$			21.3530i			1.58716i	−0.608469	+	0.793578i	$0.708216\pi$
$182$		0			0
$183$	9.45152	−	9.45152i	0.698677	−	0.698677i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−8.70670	+	8.70670i	−0.636697	+	0.636697i
$188$		0			0
$189$	1.72226			0.125276
$190$		0			0
$191$		−	19.5320i		−	1.41329i	−0.707570	−	0.706643i	$-0.750209\pi$
$191$		−	19.5320i		−	1.41329i	0.707570	−	0.706643i	$-0.249791\pi$
$192$		0			0
$193$	2.96924	+	2.96924i	0.213731	+	0.213731i	0.805850	−	0.592119i	$-0.201709\pi$
$193$	2.96924	+	2.96924i	0.213731	+	0.213731i	−0.592119	+	0.805850i	$0.701709\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.63229	−	1.63229i	−0.116296	−	0.116296i	0.646564	−	0.762860i	$-0.276205\pi$
$197$	−1.63229	−	1.63229i	−0.116296	−	0.116296i	−0.762860	+	0.646564i	$0.776205\pi$
$198$		0			0
$199$	21.2220			1.50438			0.752192	−	0.658944i	$-0.228996\pi$
$199$	21.2220			1.50438			0.752192	+	0.658944i	$0.228996\pi$
$200$		0			0
$201$	−7.64801			−0.539449
$202$		0			0
$203$	−8.16974	−	8.16974i	−0.573403	−	0.573403i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	3.17802	+	3.17802i	0.220888	+	0.220888i
$208$		0			0
$209$		−	19.5343i		−	1.35122i
$210$		0			0
$211$	−1.45735			−0.100328			−0.0501642	−	0.998741i	$-0.515974\pi$
$211$	−1.45735			−0.100328			−0.0501642	+	0.998741i	$0.515974\pi$
$212$		0			0
$213$	1.86164	−	1.86164i	0.127558	−	0.127558i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	3.34621	−	3.34621i	0.227156	−	0.227156i
$218$		0			0
$219$		−	3.78835i		−	0.255993i
$220$		0			0
$221$		−	1.20257i		−	0.0808938i
$222$		0			0
$223$	13.1842	−	13.1842i	0.882880	−	0.882880i	−0.110946	−	0.993826i	$-0.535388\pi$
$223$	13.1842	−	13.1842i	0.882880	−	0.882880i	0.993826	+	0.110946i	$0.0353881\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.96252	−	2.96252i	0.196629	−	0.196629i	−0.601924	−	0.798553i	$-0.705599\pi$
$227$	2.96252	−	2.96252i	0.196629	−	0.196629i	0.798553	+	0.601924i	$0.205599\pi$
$228$		0			0
$229$	−23.7000			−1.56614			−0.783071	−	0.621932i	$-0.786348\pi$
$229$	−23.7000			−1.56614			−0.783071	+	0.621932i	$0.786348\pi$
$230$		0			0
$231$			9.02157i			0.593576i
$232$		0			0
$233$	−5.41326	−	5.41326i	−0.354634	−	0.354634i	0.507196	−	0.861831i	$-0.330682\pi$
$233$	−5.41326	−	5.41326i	−0.354634	−	0.354634i	−0.861831	+	0.507196i	$0.830682\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−4.18145	−	4.18145i	−0.271614	−	0.271614i
$238$		0			0
$239$	18.4415			1.19288			0.596440	−	0.802658i	$-0.296581\pi$
$239$	18.4415			1.19288			0.596440	+	0.802658i	$0.296581\pi$
$240$		0			0
$241$	−20.2046			−1.30149			−0.650746	−	0.759295i	$-0.725544\pi$
$241$	−20.2046			−1.30149			−0.650746	+	0.759295i	$0.725544\pi$
$242$		0			0
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	1.34904	+	1.34904i	0.0858376	+	0.0858376i
$248$		0			0
$249$		−	1.04984i		−	0.0665312i
$250$		0			0
$251$	6.11932			0.386248			0.193124	−	0.981174i	$-0.438138\pi$
$251$	6.11932			0.386248			0.193124	+	0.981174i	$0.438138\pi$
$252$		0			0
$253$	−16.6472	+	16.6472i	−1.04660	+	1.04660i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	16.2658	−	16.2658i	1.01463	−	1.01463i	0.0147384	−	0.999891i	$-0.495308\pi$
$257$	16.2658	−	16.2658i	1.01463	−	1.01463i	0.999891	−	0.0147384i	$-0.00469154\pi$
$258$		0			0
$259$			10.0657i			0.625449i
$260$		0			0
$261$			6.70849i			0.415245i
$262$		0			0
$263$	−0.0331870	+	0.0331870i	−0.00204640	+	0.00204640i	−0.708129	−	0.706083i	$-0.750461\pi$
$263$	−0.0331870	+	0.0331870i	−0.00204640	+	0.00204640i	0.706083	+	0.708129i	$0.250461\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	1.23822	−	1.23822i	0.0757779	−	0.0757779i
$268$		0			0
$269$	4.14553			0.252757			0.126379	−	0.991982i	$-0.459665\pi$
$269$	4.14553			0.252757			0.126379	+	0.991982i	$0.459665\pi$
$270$		0			0
$271$			20.1717i			1.22534i	0.790337	+	0.612672i	$0.209905\pi$
$271$			20.1717i			1.22534i	−0.790337	+	0.612672i	$0.790095\pi$
$272$		0			0
$273$	−0.623031	−	0.623031i	−0.0377076	−	0.0377076i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−20.8477	−	20.8477i	−1.25262	−	1.25262i	−0.954543	−	0.298072i	$-0.903656\pi$
$277$	−20.8477	−	20.8477i	−1.25262	−	1.25262i	−0.298072	−	0.954543i	$-0.596344\pi$
$278$		0			0
$279$	−2.74770			−0.164501
$280$		0			0
$281$	15.3919			0.918206			0.459103	−	0.888383i	$-0.348171\pi$
$281$	15.3919			0.918206			0.459103	+	0.888383i	$0.348171\pi$
$282$		0			0
$283$	15.8844	+	15.8844i	0.944230	+	0.944230i	0.998525	−	0.0542951i	$-0.0172912\pi$
$283$	15.8844	+	15.8844i	0.944230	+	0.944230i	−0.0542951	+	0.998525i	$0.517291\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	9.02157	+	9.02157i	0.532527	+	0.532527i
$288$		0			0
$289$			11.4745i			0.674972i
$290$		0			0
$291$	−9.40171			−0.551138
$292$		0			0
$293$	1.84536	−	1.84536i	0.107807	−	0.107807i	−0.651146	−	0.758953i	$-0.725711\pi$
$293$	1.84536	−	1.84536i	0.107807	−	0.107807i	0.758953	+	0.651146i	$0.225711\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	3.70398	−	3.70398i	0.214927	−	0.214927i
$298$		0			0
$299$		−	2.29931i		−	0.132973i
$300$		0			0
$301$			13.8315i			0.797232i
$302$		0			0
$303$	−5.39685	+	5.39685i	−0.310041	+	0.310041i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	9.31156	−	9.31156i	0.531439	−	0.531439i	−0.389562	−	0.921000i	$-0.627374\pi$
$307$	9.31156	−	9.31156i	0.531439	−	0.531439i	0.921000	+	0.389562i	$0.127374\pi$
$308$		0			0
$309$	−2.44234			−0.138940
$310$		0			0
$311$		−	5.01005i		−	0.284094i	−0.989860	−	0.142047i	$-0.954632\pi$
$311$		−	5.01005i		−	0.284094i	0.989860	−	0.142047i	$-0.0453684\pi$
$312$		0			0
$313$	8.46971	+	8.46971i	0.478737	+	0.478737i	0.904727	−	0.425991i	$-0.140074\pi$
$313$	8.46971	+	8.46971i	0.478737	+	0.478737i	−0.425991	+	0.904727i	$0.640074\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	10.6205	+	10.6205i	0.596505	+	0.596505i	0.939381	−	0.342875i	$-0.111401\pi$
$317$	10.6205	+	10.6205i	0.596505	+	0.596505i	−0.342875	+	0.939381i	$0.611401\pi$
$318$		0			0
$319$	−35.1406			−1.96749
$320$		0			0
$321$	3.94958			0.220444
$322$		0			0
$323$	6.19847	+	6.19847i	0.344892	+	0.344892i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−0.0816480	−	0.0816480i	−0.00451514	−	0.00451514i
$328$		0			0
$329$			17.8082i			0.981796i
$330$		0			0
$331$	7.08673			0.389522			0.194761	−	0.980851i	$-0.437607\pi$
$331$	7.08673			0.389522			0.194761	+	0.980851i	$0.437607\pi$
$332$		0			0
$333$	4.13265	−	4.13265i	0.226468	−	0.226468i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−5.44648	+	5.44648i	−0.296689	+	0.296689i	−0.839715	−	0.543027i	$-0.817278\pi$
$337$	−5.44648	+	5.44648i	−0.296689	+	0.296689i	0.543027	+	0.839715i	$0.317278\pi$
$338$		0			0
$339$		−	2.27933i		−	0.123796i
$340$		0			0
$341$		−	14.3931i		−	0.779429i
$342$		0			0
$343$	−13.4372	+	13.4372i	−0.725542	+	0.725542i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−2.15272	+	2.15272i	−0.115564	+	0.115564i	−0.762524	−	0.646960i	$-0.776040\pi$
$347$	−2.15272	+	2.15272i	−0.115564	+	0.115564i	0.646960	+	0.762524i	$0.276040\pi$
$348$		0			0
$349$	−21.4726			−1.14940			−0.574702	−	0.818363i	$-0.694882\pi$
$349$	−21.4726			−1.14940			−0.574702	+	0.818363i	$0.694882\pi$
$350$		0			0
$351$			0.511595i			0.0273069i
$352$		0			0
$353$	−16.3162	−	16.3162i	−0.868422	−	0.868422i	0.123875	−	0.992298i	$-0.460468\pi$
$353$	−16.3162	−	16.3162i	−0.868422	−	0.868422i	−0.992298	+	0.123875i	$0.960468\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−2.86265	−	2.86265i	−0.151508	−	0.151508i
$358$		0			0
$359$	16.2275			0.856454			0.428227	−	0.903671i	$-0.359138\pi$
$359$	16.2275			0.856454			0.428227	+	0.903671i	$0.359138\pi$
$360$		0			0
$361$	5.09312			0.268059
$362$		0			0
$363$	11.6241	+	11.6241i	0.610107	+	0.610107i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	2.14505	+	2.14505i	0.111971	+	0.111971i	0.760872	−	0.648902i	$-0.224771\pi$
$367$	2.14505	+	2.14505i	0.111971	+	0.111971i	−0.648902	+	0.760872i	$0.724771\pi$
$368$		0			0
$369$		−	7.40796i		−	0.385643i
$370$		0			0
$371$	−24.4450			−1.26912
$372$		0			0
$373$	−5.83818	+	5.83818i	−0.302289	+	0.302289i	−0.841909	−	0.539620i	$-0.818568\pi$
$373$	−5.83818	+	5.83818i	−0.302289	+	0.302289i	0.539620	+	0.841909i	$0.318568\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	2.42681	−	2.42681i	0.124987	−	0.124987i
$378$		0			0
$379$			33.6252i			1.72721i	0.504170	+	0.863604i	$0.331798\pi$
$379$			33.6252i			1.72721i	−0.504170	+	0.863604i	$0.668202\pi$
$380$		0			0
$381$		−	3.38070i		−	0.173198i
$382$		0			0
$383$	−17.0709	+	17.0709i	−0.872281	+	0.872281i	−0.992721	−	0.120439i	$-0.961570\pi$
$383$	−17.0709	+	17.0709i	−0.872281	+	0.872281i	0.120439	+	0.992721i	$0.461570\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	5.67877	−	5.67877i	0.288668	−	0.288668i
$388$		0			0
$389$	−16.7710			−0.850323			−0.425161	−	0.905118i	$-0.639783\pi$
$389$	−16.7710			−0.850323			−0.425161	+	0.905118i	$0.639783\pi$
$390$		0			0
$391$		−	10.5647i		−	0.534279i
$392$		0			0
$393$	3.97479	+	3.97479i	0.200502	+	0.200502i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−2.59093	−	2.59093i	−0.130035	−	0.130035i	0.639094	−	0.769129i	$-0.279310\pi$
$397$	−2.59093	−	2.59093i	−0.130035	−	0.130035i	−0.769129	+	0.639094i	$0.779310\pi$
$398$		0			0
$399$	6.42264			0.321534
$400$		0			0
$401$	14.1336			0.705800			0.352900	−	0.935661i	$-0.385196\pi$
$401$	14.1336			0.705800			0.352900	+	0.935661i	$0.385196\pi$
$402$		0			0
$403$	0.993989	+	0.993989i	0.0495141	+	0.0495141i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	21.6477	+	21.6477i	1.07304	+	1.07304i
$408$		0			0
$409$			3.28815i			0.162588i	0.996690	+	0.0812942i	$0.0259053\pi$
$409$			3.28815i			0.162588i	−0.996690	+	0.0812942i	$0.974095\pi$
$410$		0			0
$411$	−16.1258			−0.795428
$412$		0			0
$413$	−13.7880	+	13.7880i	−0.678465	+	0.678465i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	2.68736	−	2.68736i	0.131601	−	0.131601i
$418$		0			0
$419$		−	20.8299i		−	1.01761i	−0.860883	−	0.508804i	$-0.830088\pi$
$419$		−	20.8299i		−	1.01761i	0.860883	−	0.508804i	$-0.169912\pi$
$420$		0			0
$421$			0.378145i			0.0184297i	0.999958	+	0.00921484i	$0.00293322\pi$
$421$			0.378145i			0.0184297i	−0.999958	+	0.00921484i	$0.997067\pi$
$422$		0			0
$423$	7.31149	−	7.31149i	0.355497	−	0.355497i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−16.2780	+	16.2780i	−0.787746	+	0.787746i
$428$		0			0
$429$	−2.67985			−0.129384
$430$		0			0
$431$		−	12.2457i		−	0.589854i	−0.955520	−	0.294927i	$-0.904705\pi$
$431$		−	12.2457i		−	0.589854i	0.955520	−	0.294927i	$-0.0952953\pi$
$432$		0			0
$433$	1.66686	+	1.66686i	0.0801044	+	0.0801044i	0.746024	−	0.665919i	$-0.231961\pi$
$433$	1.66686	+	1.66686i	0.0801044	+	0.0801044i	−0.665919	+	0.746024i	$0.731961\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	11.8514	+	11.8514i	0.566932	+	0.566932i
$438$		0			0
$439$	−37.0618			−1.76886			−0.884432	−	0.466669i	$-0.845454\pi$
$439$	−37.0618			−1.76886			−0.884432	+	0.466669i	$0.845454\pi$
$440$		0			0
$441$	4.03382			0.192087
$442$		0			0
$443$	−21.0995	−	21.0995i	−1.00247	−	1.00247i	−0.999997	−	0.00246927i	$-0.999214\pi$
$443$	−21.0995	−	21.0995i	−1.00247	−	1.00247i	−0.00246927	−	0.999997i	$-0.500786\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	7.11025	+	7.11025i	0.336303	+	0.336303i
$448$		0			0
$449$		−	17.8253i		−	0.841230i	−0.907239	−	0.420615i	$-0.861814\pi$
$449$		−	17.8253i		−	0.841230i	0.907239	−	0.420615i	$-0.138186\pi$
$450$		0			0
$451$	38.8045			1.82723
$452$		0			0
$453$	−2.29663	+	2.29663i	−0.107905	+	0.107905i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−17.4395	+	17.4395i	−0.815787	+	0.815787i	−0.985494	−	0.169707i	$-0.945718\pi$
$457$	−17.4395	+	17.4395i	−0.815787	+	0.815787i	0.169707	+	0.985494i	$0.445718\pi$
$458$		0			0
$459$			2.35063i			0.109718i
$460$		0			0
$461$		−	14.8981i		−	0.693872i	−0.937889	−	0.346936i	$-0.887222\pi$
$461$		−	14.8981i		−	0.693872i	0.937889	−	0.346936i	$-0.112778\pi$
$462$		0			0
$463$	7.47612	−	7.47612i	0.347445	−	0.347445i	−0.511712	−	0.859157i	$-0.670989\pi$
$463$	7.47612	−	7.47612i	0.347445	−	0.347445i	0.859157	+	0.511712i	$0.170989\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−13.2540	+	13.2540i	−0.613321	+	0.613321i	−0.943810	−	0.330489i	$-0.892786\pi$
$467$	−13.2540	+	13.2540i	−0.613321	+	0.613321i	0.330489	+	0.943810i	$0.392786\pi$
$468$		0			0
$469$	13.1719			0.608220
$470$		0			0
$471$		−	5.91588i		−	0.272589i
$472$		0			0
$473$	29.7467	+	29.7467i	1.36775	+	1.36775i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	10.0364	+	10.0364i	0.459533	+	0.459533i
$478$		0			0
$479$	−15.9629			−0.729363			−0.364682	−	0.931132i	$-0.618822\pi$
$479$	−15.9629			−0.729363			−0.364682	+	0.931132i	$0.618822\pi$
$480$		0			0
$481$	−2.98999			−0.136332
$482$		0			0
$483$	−5.47337	−	5.47337i	−0.249047	−	0.249047i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−27.8490	−	27.8490i	−1.26196	−	1.26196i	−0.950142	−	0.311818i	$-0.899062\pi$
$487$	−27.8490	−	27.8490i	−1.26196	−	1.26196i	−0.311818	−	0.950142i	$-0.600938\pi$
$488$		0			0
$489$			4.28214i			0.193645i
$490$		0			0
$491$	23.2165			1.04775			0.523874	−	0.851796i	$-0.324486\pi$
$491$	23.2165			1.04775			0.523874	+	0.851796i	$0.324486\pi$
$492$		0			0
$493$	11.1505	−	11.1505i	0.502193	−	0.502193i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−3.20623	+	3.20623i	−0.143819	+	0.143819i
$498$		0			0
$499$		−	5.26255i		−	0.235584i	−0.993038	−	0.117792i	$-0.962418\pi$
$499$		−	5.26255i		−	0.235584i	0.993038	−	0.117792i	$-0.0375816\pi$
$500$		0			0
$501$		−	7.26109i		−	0.324401i
$502$		0			0
$503$	14.3869	−	14.3869i	0.641479	−	0.641479i	−0.309440	−	0.950919i	$-0.600142\pi$
$503$	14.3869	−	14.3869i	0.641479	−	0.641479i	0.950919	+	0.309440i	$0.100142\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−9.00732	+	9.00732i	−0.400029	+	0.400029i
$508$		0			0
$509$	11.1825			0.495655			0.247828	−	0.968804i	$-0.420283\pi$
$509$	11.1825			0.495655			0.247828	+	0.968804i	$0.420283\pi$
$510$		0			0
$511$			6.52453i			0.288628i
$512$		0			0
$513$	−2.63694	−	2.63694i	−0.116424	−	0.116424i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	38.2992	+	38.2992i	1.68440	+	1.68440i
$518$		0			0
$519$	−0.530579			−0.0232898
$520$		0			0
$521$	4.32197			0.189349			0.0946745	−	0.995508i	$-0.469819\pi$
$521$	4.32197			0.189349			0.0946745	+	0.995508i	$0.469819\pi$
$522$		0			0
$523$	0.519319	+	0.519319i	0.0227082	+	0.0227082i	0.718370	−	0.695661i	$-0.244889\pi$
$523$	0.519319	+	0.519319i	0.0227082	+	0.0227082i	−0.695661	+	0.718370i	$0.744889\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	4.56709	+	4.56709i	0.198946	+	0.198946i
$528$		0			0
$529$			2.80038i			0.121755i
$530$		0			0
$531$	11.3219			0.491328
$532$		0			0
$533$	−2.67985	+	2.67985i	−0.116077	+	0.116077i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−5.68207	+	5.68207i	−0.245199	+	0.245199i
$538$		0			0
$539$			21.1301i			0.910136i
$540$		0			0
$541$			10.4911i			0.451046i	0.974238	+	0.225523i	$0.0724090\pi$
$541$			10.4911i			0.451046i	−0.974238	+	0.225523i	$0.927591\pi$
$542$		0			0
$543$	−15.0989	+	15.0989i	−0.647954	+	0.647954i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	22.3537	−	22.3537i	0.955774	−	0.955774i	−0.0432882	−	0.999063i	$-0.513783\pi$
$547$	22.3537	−	22.3537i	0.955774	−	0.955774i	0.999063	+	0.0432882i	$0.0137834\pi$
$548$		0			0
$549$	13.3665			0.570467
$550$		0			0
$551$			25.0173i			1.06577i
$552$		0			0
$553$	7.20154	+	7.20154i	0.306240	+	0.306240i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−6.93719	−	6.93719i	−0.293938	−	0.293938i	0.544696	−	0.838634i	$-0.316645\pi$
$557$	−6.93719	−	6.93719i	−0.293938	−	0.293938i	−0.838634	+	0.544696i	$0.816645\pi$
$558$		0			0
$559$	−4.10862			−0.173776
$560$		0			0
$561$	−12.3131			−0.519861
$562$		0			0
$563$	19.6100	+	19.6100i	0.826461	+	0.826461i	0.987025	−	0.160564i	$-0.0513314\pi$
$563$	19.6100	+	19.6100i	0.826461	+	0.826461i	−0.160564	+	0.987025i	$0.551331\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	1.21782	+	1.21782i	0.0511437	+	0.0511437i
$568$		0			0
$569$			37.8398i			1.58633i	0.609009	+	0.793163i	$0.291567\pi$
$569$			37.8398i			1.58633i	−0.609009	+	0.793163i	$0.708433\pi$
$570$		0			0
$571$	2.23967			0.0937273			0.0468637	−	0.998901i	$-0.485077\pi$
$571$	2.23967			0.0937273			0.0468637	+	0.998901i	$0.485077\pi$
$572$		0			0
$573$	13.8112	−	13.8112i	0.576972	−	0.576972i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	23.0369	−	23.0369i	0.959038	−	0.959038i	−0.0401552	−	0.999193i	$-0.512785\pi$
$577$	23.0369	−	23.0369i	0.959038	−	0.959038i	0.999193	+	0.0401552i	$0.0127852\pi$
$578$		0			0
$579$			4.19914i			0.174511i
$580$		0			0
$581$			1.80810i			0.0750128i
$582$		0			0
$583$	−52.5726	+	52.5726i	−2.17734	+	2.17734i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	23.2134	−	23.2134i	0.958118	−	0.958118i	−0.0410396	−	0.999158i	$-0.513067\pi$
$587$	23.2134	−	23.2134i	0.958118	−	0.958118i	0.999158	+	0.0410396i	$0.0130670\pi$
$588$		0			0
$589$	−10.2467			−0.422209
$590$		0			0
$591$		−	2.30841i		−	0.0949554i
$592$		0			0
$593$	12.1755	+	12.1755i	0.499988	+	0.499988i	0.911434	−	0.411446i	$-0.134976\pi$
$593$	12.1755	+	12.1755i	0.499988	+	0.499988i	−0.411446	+	0.911434i	$0.634976\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	15.0062	+	15.0062i	0.614163	+	0.614163i
$598$		0			0
$599$	−42.9318			−1.75415			−0.877073	−	0.480357i	$-0.840507\pi$
$599$	−42.9318			−1.75415			−0.877073	+	0.480357i	$0.840507\pi$
$600$		0			0
$601$	24.0032			0.979112			0.489556	−	0.871972i	$-0.337159\pi$
$601$	24.0032			0.979112			0.489556	+	0.871972i	$0.337159\pi$
$602$		0			0
$603$	−5.40796	−	5.40796i	−0.220229	−	0.220229i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	3.98935	+	3.98935i	0.161923	+	0.161923i	0.783418	−	0.621495i	$-0.213475\pi$
$607$	3.98935	+	3.98935i	0.161923	+	0.161923i	−0.621495	+	0.783418i	$0.713475\pi$
$608$		0			0
$609$		−	11.5538i		−	0.468182i
$610$		0			0
$611$	−5.28990			−0.214006
$612$		0			0
$613$	−31.8671	+	31.8671i	−1.28710	+	1.28710i	−0.350563	+	0.936539i	$0.614010\pi$
$613$	−31.8671	+	31.8671i	−1.28710	+	1.28710i	−0.936539	+	0.350563i	$0.885990\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−6.45265	+	6.45265i	−0.259774	+	0.259774i	−0.824962	−	0.565188i	$-0.808804\pi$
$617$	−6.45265	+	6.45265i	−0.259774	+	0.259774i	0.565188	+	0.824962i	$0.308804\pi$
$618$		0			0
$619$		−	27.4744i		−	1.10429i	−0.833749	−	0.552144i	$-0.813810\pi$
$619$		−	27.4744i		−	1.10429i	0.833749	−	0.552144i	$-0.186190\pi$
$620$		0			0
$621$			4.49440i			0.180354i
$622$		0			0
$623$	−2.13254	+	2.13254i	−0.0854383	+	0.0854383i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	13.8129	−	13.8129i	0.551632	−	0.551632i
$628$		0			0
$629$	−13.7381			−0.547776
$630$		0			0
$631$		−	13.1266i		−	0.522560i	−0.965263	−	0.261280i	$-0.915855\pi$
$631$		−	13.1266i		−	0.522560i	0.965263	−	0.261280i	$-0.0841447\pi$
$632$		0			0
$633$	−1.03050	−	1.03050i	−0.0409589	−	0.0409589i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−1.45925	−	1.45925i	−0.0578174	−	0.0578174i
$638$		0			0
$639$	2.63276			0.104150
$640$		0			0
$641$	−44.4068			−1.75396			−0.876982	−	0.480524i	$-0.840447\pi$
$641$	−44.4068			−1.75396			−0.876982	+	0.480524i	$0.840447\pi$
$642$		0			0
$643$	18.2206	+	18.2206i	0.718551	+	0.718551i	0.968308	−	0.249758i	$-0.0803510\pi$
$643$	18.2206	+	18.2206i	0.718551	+	0.718551i	−0.249758	+	0.968308i	$0.580351\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−18.3745	−	18.3745i	−0.722375	−	0.722375i	0.246713	−	0.969088i	$-0.420649\pi$
$647$	−18.3745	−	18.3745i	−0.722375	−	0.722375i	−0.969088	+	0.246713i	$0.920649\pi$
$648$		0			0
$649$			59.3065i			2.32799i
$650$		0			0
$651$	4.73226			0.185472
$652$		0			0
$653$	1.11550	−	1.11550i	0.0436531	−	0.0436531i	−0.684943	−	0.728596i	$-0.740173\pi$
$653$	1.11550	−	1.11550i	0.0436531	−	0.0436531i	0.728596	+	0.684943i	$0.240173\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	2.67877	−	2.67877i	0.104509	−	0.104509i
$658$		0			0
$659$			25.3850i			0.988860i	0.869217	+	0.494430i	$0.164623\pi$
$659$			25.3850i			0.988860i	−0.869217	+	0.494430i	$0.835377\pi$
$660$		0			0
$661$		−	7.30922i		−	0.284296i	−0.989845	−	0.142148i	$-0.954599\pi$
$661$		−	7.30922i		−	0.284296i	0.989845	−	0.142148i	$-0.0454008\pi$
$662$		0			0
$663$	0.850347	−	0.850347i	0.0330247	−	0.0330247i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	21.3197	−	21.3197i	0.825503	−	0.825503i
$668$		0			0
$669$	18.6453			0.720869
$670$		0			0
$671$			70.0165i			2.70296i
$672$		0			0
$673$	−10.1902	−	10.1902i	−0.392804	−	0.392804i	0.482882	−	0.875686i	$-0.339590\pi$
$673$	−10.1902	−	10.1902i	−0.392804	−	0.392804i	−0.875686	+	0.482882i	$0.839590\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−14.0161	−	14.0161i	−0.538683	−	0.538683i	0.384459	−	0.923142i	$-0.374388\pi$
$677$	−14.0161	−	14.0161i	−0.538683	−	0.538683i	−0.923142	+	0.384459i	$0.874388\pi$
$678$		0			0
$679$	16.1922			0.621399
$680$		0			0
$681$	4.18963			0.160547
$682$		0			0
$683$	19.0880	+	19.0880i	0.730381	+	0.730381i	0.970695	−	0.240314i	$-0.0772505\pi$
$683$	19.0880	+	19.0880i	0.730381	+	0.730381i	−0.240314	+	0.970695i	$0.577251\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	−16.7584	−	16.7584i	−0.639375	−	0.639375i
$688$		0			0
$689$		−	7.26135i		−	0.276635i
$690$		0			0
$691$	−9.95032			−0.378528			−0.189264	−	0.981926i	$-0.560610\pi$
$691$	−9.95032			−0.378528			−0.189264	+	0.981926i	$0.560610\pi$
$692$		0			0
$693$	−6.37922	+	6.37922i	−0.242326	+	0.242326i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−12.3131	+	12.3131i	−0.466393	+	0.466393i
$698$		0			0
$699$		−	7.65550i		−	0.289558i
$700$		0			0
$701$			45.3620i			1.71330i	0.515899	+	0.856649i	$0.327458\pi$
$701$			45.3620i			1.71330i	−0.515899	+	0.856649i	$0.672542\pi$
$702$		0			0
$703$	15.4114	−	15.4114i	0.581253	−	0.581253i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	9.29478	−	9.29478i	0.349566	−	0.349566i
$708$		0			0
$709$	23.5307			0.883713			0.441856	−	0.897086i	$-0.354320\pi$
$709$	23.5307			0.883713			0.441856	+	0.897086i	$0.354320\pi$
$710$		0			0
$711$		−	5.91346i		−	0.221772i
$712$		0			0
$713$	8.73226	+	8.73226i	0.327026	+	0.327026i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	13.0401	+	13.0401i	0.486991	+	0.486991i
$718$		0			0
$719$	28.7704			1.07296			0.536478	−	0.843914i	$-0.319754\pi$
$719$	28.7704			1.07296			0.536478	+	0.843914i	$0.319754\pi$
$720$		0			0
$721$	4.20635			0.156653
$722$		0			0
$723$	−14.2868	−	14.2868i	−0.531332	−	0.531332i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	16.9689	+	16.9689i	0.629342	+	0.629342i	0.947902	−	0.318561i	$-0.103199\pi$
$727$	16.9689	+	16.9689i	0.629342	+	0.629342i	−0.318561	+	0.947902i	$0.603199\pi$
$728$		0			0
$729$		−	1.00000i		−	0.0370370i
$730$		0			0
$731$	−18.8779			−0.698225
$732$		0			0
$733$	15.4998	−	15.4998i	0.572499	−	0.572499i	−0.360327	−	0.932826i	$-0.617335\pi$
$733$	15.4998	−	15.4998i	0.572499	−	0.572499i	0.932826	+	0.360327i	$0.117335\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	28.3281	−	28.3281i	1.04348	−	1.04348i
$738$		0			0
$739$			9.34289i			0.343684i	0.985125	+	0.171842i	$0.0549718\pi$
$739$			9.34289i			0.343684i	−0.985125	+	0.171842i	$0.945028\pi$
$740$		0			0
$741$			1.90784i			0.0700861i
$742$		0			0
$743$	−6.89738	+	6.89738i	−0.253040	+	0.253040i	−0.822216	−	0.569176i	$-0.807262\pi$
$743$	−6.89738	+	6.89738i	−0.253040	+	0.253040i	0.569176	+	0.822216i	$0.307262\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	0.742352	−	0.742352i	0.0271612	−	0.0271612i
$748$		0			0
$749$	−6.80220			−0.248547
$750$		0			0
$751$			23.0607i			0.841499i	0.907177	+	0.420749i	$0.138233\pi$
$751$			23.0607i			0.841499i	−0.907177	+	0.420749i	$0.861767\pi$
$752$		0			0
$753$	4.32701	+	4.32701i	0.157685	+	0.157685i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−4.92349	−	4.92349i	−0.178947	−	0.178947i	0.611950	−	0.790897i	$-0.290386\pi$
$757$	−4.92349	−	4.92349i	−0.178947	−	0.178947i	−0.790897	+	0.611950i	$0.790386\pi$
$758$		0			0
$759$	−23.5427			−0.854544
$760$		0			0
$761$	22.4172			0.812621			0.406311	−	0.913735i	$-0.366815\pi$
$761$	22.4172			0.812621			0.406311	+	0.913735i	$0.366815\pi$
$762$		0			0
$763$	0.140619	+	0.140619i	0.00509075	+	0.00509075i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−4.09572	−	4.09572i	−0.147888	−	0.147888i
$768$		0			0
$769$		−	50.3148i		−	1.81440i	−0.420701	−	0.907199i	$-0.638216\pi$
$769$		−	50.3148i		−	1.81440i	0.420701	−	0.907199i	$-0.361784\pi$
$770$		0			0
$771$	23.0032			0.828442
$772$		0			0
$773$	−12.8067	+	12.8067i	−0.460625	+	0.460625i	−0.898860	−	0.438235i	$-0.855604\pi$
$773$	−12.8067	+	12.8067i	−0.460625	+	0.460625i	0.438235	+	0.898860i	$0.355604\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−7.11749	+	7.11749i	−0.255339	+	0.255339i
$778$		0			0
$779$		−	27.6257i		−	0.989794i
$780$		0			0
$781$			13.7910i			0.493480i
$782$		0			0
$783$	−4.74362	+	4.74362i	−0.169523	+	0.169523i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−28.1921	+	28.1921i	−1.00494	+	1.00494i	−0.00495215	+	0.999988i	$0.501576\pi$
$787$	−28.1921	+	28.1921i	−1.00494	+	1.00494i	−0.999988	+	0.00495215i	$0.998424\pi$
$788$		0			0
$789$	−0.0469336			−0.00167088
$790$		0			0
$791$			3.92559i			0.139578i
$792$		0			0
$793$	−4.83535	−	4.83535i	−0.171708	−	0.171708i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−15.1514	−	15.1514i	−0.536689	−	0.536689i	0.385866	−	0.922555i	$-0.373903\pi$
$797$	−15.1514	−	15.1514i	−0.536689	−	0.536689i	−0.922555	+	0.385866i	$0.873903\pi$
$798$		0			0
$799$	−24.3055			−0.859868
$800$		0			0
$801$	1.75111			0.0618724
$802$		0			0
$803$	14.0320	+	14.0320i	0.495178	+	0.495178i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	2.93133	+	2.93133i	0.103188	+	0.103188i
$808$		0			0
$809$		−	25.8847i		−	0.910059i	−0.890476	−	0.455030i	$-0.849629\pi$
$809$		−	25.8847i		−	0.910059i	0.890476	−	0.455030i	$-0.150371\pi$
$810$		0			0
$811$	−40.2556			−1.41357			−0.706783	−	0.707431i	$-0.749854\pi$
$811$	−40.2556			−1.41357			−0.706783	+	0.707431i	$0.749854\pi$
$812$		0			0
$813$	−14.2635	+	14.2635i	−0.500244	+	0.500244i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	21.1772	−	21.1772i	0.740897	−	0.740897i
$818$		0			0
$819$		−	0.881100i		−	0.0307881i
$820$		0			0
$821$		−	46.6073i		−	1.62661i	−0.581840	−	0.813303i	$-0.697667\pi$
$821$		−	46.6073i		−	1.62661i	0.581840	−	0.813303i	$-0.302333\pi$
$822$		0			0
$823$	6.40117	−	6.40117i	0.223131	−	0.223131i	−0.586685	−	0.809815i	$-0.699567\pi$
$823$	6.40117	−	6.40117i	0.223131	−	0.223131i	0.809815	+	0.586685i	$0.199567\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	12.3618	−	12.3618i	0.429861	−	0.429861i	−0.458720	−	0.888581i	$-0.651692\pi$
$827$	12.3618	−	12.3618i	0.429861	−	0.429861i	0.888581	+	0.458720i	$0.151692\pi$
$828$		0			0
$829$	−5.60983			−0.194838			−0.0974188	−	0.995243i	$-0.531059\pi$
$829$	−5.60983			−0.194838			−0.0974188	+	0.995243i	$0.531059\pi$
$830$		0			0
$831$		−	29.4831i		−	1.02276i
$832$		0			0
$833$	−6.70481	−	6.70481i	−0.232308	−	0.232308i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−1.94292	−	1.94292i	−0.0671571	−	0.0671571i
$838$		0			0
$839$	3.22857			0.111462			0.0557312	−	0.998446i	$-0.482251\pi$
$839$	3.22857			0.111462			0.0557312	+	0.998446i	$0.482251\pi$
$840$		0			0
$841$	16.0038			0.551857
$842$		0			0
$843$	10.8837	+	10.8837i	0.374856	+	0.374856i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−20.0197	−	20.0197i	−0.687885	−	0.687885i
$848$		0			0
$849$			22.4639i			0.770960i
$850$		0			0
$851$	−26.2673			−0.900430
$852$		0			0
$853$	23.8817	−	23.8817i	0.817692	−	0.817692i	−0.168081	−	0.985773i	$-0.553757\pi$
$853$	23.8817	−	23.8817i	0.817692	−	0.817692i	0.985773	+	0.168081i	$0.0537569\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	10.9520	−	10.9520i	0.374115	−	0.374115i	−0.494859	−	0.868973i	$-0.664780\pi$
$857$	10.9520	−	10.9520i	0.374115	−	0.374115i	0.868973	+	0.494859i	$0.164780\pi$
$858$		0			0
$859$			11.8875i			0.405596i	0.979221	+	0.202798i	$0.0650035\pi$
$859$			11.8875i			0.405596i	−0.979221	+	0.202798i	$0.934997\pi$
$860$		0			0
$861$			12.7584i			0.434806i
$862$		0			0
$863$	22.9476	−	22.9476i	0.781146	−	0.781146i	−0.198878	−	0.980024i	$-0.563730\pi$
$863$	22.9476	−	22.9476i	0.781146	−	0.781146i	0.980024	+	0.198878i	$0.0637298\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−8.11372	+	8.11372i	−0.275556	+	0.275556i
$868$		0			0
$869$	30.9760			1.05079
$870$		0			0
$871$			3.91269i			0.132576i
$872$		0			0
$873$	−6.64801	−	6.64801i	−0.225001	−	0.225001i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−7.53116	−	7.53116i	−0.254309	−	0.254309i	0.568425	−	0.822735i	$-0.307553\pi$
$877$	−7.53116	−	7.53116i	−0.254309	−	0.254309i	−0.822735	+	0.568425i	$0.807553\pi$
$878$		0			0
$879$	2.60974			0.0880242
$880$		0			0
$881$	−30.4673			−1.02647			−0.513235	−	0.858248i	$-0.671553\pi$
$881$	−30.4673			−1.02647			−0.513235	+	0.858248i	$0.671553\pi$
$882$		0			0
$883$	−39.9926	−	39.9926i	−1.34586	−	1.34586i	−0.890107	−	0.455751i	$-0.849371\pi$
$883$	−39.9926	−	39.9926i	−1.34586	−	1.34586i	−0.455751	−	0.890107i	$-0.650629\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	26.9715	+	26.9715i	0.905614	+	0.905614i	0.995915	−	0.0903006i	$-0.0287828\pi$
$887$	26.9715	+	26.9715i	0.905614	+	0.905614i	−0.0903006	+	0.995915i	$0.528783\pi$
$888$		0			0
$889$			5.82244i			0.195278i
$890$		0			0
$891$	5.23822			0.175487
$892$		0			0
$893$	27.2659	−	27.2659i	0.912420	−	0.912420i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	1.62586	−	1.62586i	0.0542859	−	0.0542859i
$898$		0			0
$899$			18.4329i			0.614773i
$900$		0			0
$901$		−	33.3638i		−	1.11151i
$902$		0			0
$903$	−9.78032	+	9.78032i	−0.325469	+	0.325469i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−29.0296	+	29.0296i	−0.963913	+	0.963913i	−0.999371	−	0.0354583i	$-0.988711\pi$
$907$	−29.0296	+	29.0296i	−0.963913	+	0.963913i	0.0354583	+	0.999371i	$0.488711\pi$
$908$		0			0
$909$	−7.63230			−0.253147
$910$		0			0
$911$		−	23.8639i		−	0.790647i	−0.918542	−	0.395323i	$-0.870633\pi$
$911$		−	23.8639i		−	0.790647i	0.918542	−	0.395323i	$-0.129367\pi$
$912$		0			0
$913$	3.88860	+	3.88860i	0.128694	+	0.128694i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−6.84562	−	6.84562i	−0.226062	−	0.226062i
$918$		0			0
$919$	45.2701			1.49332			0.746661	−	0.665204i	$-0.231656\pi$
$919$	45.2701			1.49332			0.746661	+	0.665204i	$0.231656\pi$
$920$		0			0
$921$	13.1685			0.433918
$922$		0			0
$923$	−0.952407	−	0.952407i	−0.0313488	−	0.0313488i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−1.72700	−	1.72700i	−0.0567221	−	0.0567221i
$928$		0			0
$929$		−	26.7024i		−	0.876077i	−0.898956	−	0.438038i	$-0.855673\pi$
$929$		−	26.7024i		−	0.876077i	0.898956	−	0.438038i	$-0.144327\pi$
$930$		0			0
$931$	15.0429			0.493011
$932$		0			0
$933$	3.54264	−	3.54264i	0.115981	−	0.115981i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−14.5936	+	14.5936i	−0.476752	+	0.476752i	−0.904091	−	0.427339i	$-0.859451\pi$
$937$	−14.5936	+	14.5936i	−0.476752	+	0.476752i	0.427339	+	0.904091i	$0.359451\pi$
$938$		0			0
$939$			11.9780i			0.390887i
$940$		0			0
$941$			16.6141i			0.541603i	0.962635	+	0.270802i	$0.0872887\pi$
$941$			16.6141i			0.541603i	−0.962635	+	0.270802i	$0.912711\pi$
$942$		0			0
$943$	−23.5427	+	23.5427i	−0.766654	+	0.766654i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−42.3488	+	42.3488i	−1.37615	+	1.37615i	−0.525128	+	0.851023i	$0.675982\pi$
$947$	−42.3488	+	42.3488i	−1.37615	+	1.37615i	−0.851023	+	0.525128i	$0.824018\pi$
$948$		0			0
$949$	−1.93810			−0.0629135
$950$		0			0
$951$			15.0196i			0.487045i
$952$		0			0
$953$	−24.6483	−	24.6483i	−0.798436	−	0.798436i	0.184413	−	0.982849i	$-0.440962\pi$
$953$	−24.6483	−	24.6483i	−0.798436	−	0.798436i	−0.982849	+	0.184413i	$0.940962\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−24.8481	−	24.8481i	−0.803226	−	0.803226i
$958$		0			0
$959$	27.7728			0.896831
$960$		0			0
$961$	23.4501			0.756456
$962$		0			0
$963$	2.79277	+	2.79277i	0.0899959	+	0.0899959i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	0.316328	+	0.316328i	0.0101724	+	0.0101724i	0.712175	−	0.702002i	$-0.247710\pi$
$967$	0.316328	+	0.316328i	0.0101724	+	0.0101724i	−0.702002	+	0.712175i	$0.747710\pi$
$968$		0			0
$969$			8.76596i			0.281603i
$970$		0			0
$971$	36.8392			1.18223			0.591113	−	0.806588i	$-0.298689\pi$
$971$	36.8392			1.18223			0.591113	+	0.806588i	$0.298689\pi$
$972$		0			0
$973$	−4.62833	+	4.62833i	−0.148377	+	0.148377i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−18.8490	+	18.8490i	−0.603034	+	0.603034i	−0.941116	−	0.338083i	$-0.890222\pi$
$977$	−18.8490	+	18.8490i	−0.603034	+	0.603034i	0.338083	+	0.941116i	$0.390222\pi$
$978$		0			0
$979$			9.17269i			0.293161i
$980$		0			0
$981$		−	0.115468i		−	0.00368660i
$982$		0			0
$983$	28.1727	−	28.1727i	0.898568	−	0.898568i	−0.0967414	−	0.995310i	$-0.530842\pi$
$983$	28.1727	−	28.1727i	0.898568	−	0.898568i	0.995310	+	0.0967414i	$0.0308420\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−12.5923	+	12.5923i	−0.400817	+	0.400817i
$988$		0			0
$989$	−36.0945			−1.14774
$990$		0			0
$991$		−	29.4982i		−	0.937043i	−0.883452	−	0.468521i	$-0.844787\pi$
$991$		−	29.4982i		−	0.937043i	0.883452	−	0.468521i	$-0.155213\pi$
$992$		0			0
$993$	5.01108	+	5.01108i	0.159022	+	0.159022i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	23.9484	+	23.9484i	0.758455	+	0.758455i	0.976041	−	0.217586i	$-0.0698183\pi$
$997$	23.9484	+	23.9484i	0.758455	+	0.758455i	−0.217586	+	0.976041i	$0.569818\pi$
$998$		0			0
$999$	5.84445			0.184910

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2400.2.bh.b.943.9		24
4.3	odd	2		600.2.v.b.43.7		24
5.2	odd	4	inner	2400.2.bh.b.1807.10		24
5.3	odd	4		480.2.bh.a.367.4		24
5.4	even	2		480.2.bh.a.463.3		24
8.3	odd	2	inner	2400.2.bh.b.943.10		24
8.5	even	2		600.2.v.b.43.12		24
15.8	even	4		1440.2.bi.e.847.6		24
15.14	odd	2		1440.2.bi.e.1423.7		24
20.3	even	4		120.2.v.a.67.1	yes	24
20.7	even	4		600.2.v.b.307.12		24
20.19	odd	2		120.2.v.a.43.6	yes	24
40.3	even	4		480.2.bh.a.367.3		24
40.13	odd	4		120.2.v.a.67.6	yes	24
40.19	odd	2		480.2.bh.a.463.4		24
40.27	even	4	inner	2400.2.bh.b.1807.9		24
40.29	even	2		120.2.v.a.43.1	✓	24
40.37	odd	4		600.2.v.b.307.7		24
60.23	odd	4		360.2.w.e.307.12		24
60.59	even	2		360.2.w.e.163.7		24
120.29	odd	2		360.2.w.e.163.12		24
120.53	even	4		360.2.w.e.307.7		24
120.59	even	2		1440.2.bi.e.1423.6		24
120.83	odd	4		1440.2.bi.e.847.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.v.a.43.1	✓	24	40.29	even	2
120.2.v.a.43.6	yes	24	20.19	odd	2
120.2.v.a.67.1	yes	24	20.3	even	4
120.2.v.a.67.6	yes	24	40.13	odd	4
360.2.w.e.163.7		24	60.59	even	2
360.2.w.e.163.12		24	120.29	odd	2
360.2.w.e.307.7		24	120.53	even	4
360.2.w.e.307.12		24	60.23	odd	4
480.2.bh.a.367.3		24	40.3	even	4
480.2.bh.a.367.4		24	5.3	odd	4
480.2.bh.a.463.3		24	5.4	even	2
480.2.bh.a.463.4		24	40.19	odd	2
600.2.v.b.43.7		24	4.3	odd	2
600.2.v.b.43.12		24	8.5	even	2
600.2.v.b.307.7		24	40.37	odd	4
600.2.v.b.307.12		24	20.7	even	4
1440.2.bi.e.847.6		24	15.8	even	4
1440.2.bi.e.847.7		24	120.83	odd	4
1440.2.bi.e.1423.6		24	120.59	even	2
1440.2.bi.e.1423.7		24	15.14	odd	2
2400.2.bh.b.943.9		24	1.1	even	1	trivial
2400.2.bh.b.943.10		24	8.3	odd	2	inner
2400.2.bh.b.1807.9		24	40.27	even	4	inner
2400.2.bh.b.1807.10		24	5.2	odd	4	inner

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:	\( N \)	\(=\)	\( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2400.bh (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{3} +(-1.21782 - 1.21782i) q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{3} +(-1.21782 - 1.21782i) q^{7} +1.00000i q^{9} -5.23822 q^{11} +(0.361752 - 0.361752i) q^{13} +(1.66215 - 1.66215i) q^{17} +3.72919i q^{19} -1.72226i q^{21} +(3.17802 - 3.17802i) q^{23} +(-0.707107 + 0.707107i) q^{27} +6.70849 q^{29} +2.74770i q^{31} +(-3.70398 - 3.70398i) q^{33} +(-4.13265 - 4.13265i) q^{37} +0.511595 q^{39} -7.40796 q^{41} +(-5.67877 - 5.67877i) q^{43} +(-7.31149 - 7.31149i) q^{47} -4.03382i q^{49} +2.35063 q^{51} +(10.0364 - 10.0364i) q^{53} +(-2.63694 + 2.63694i) q^{57} -11.3219i q^{59} -13.3665i q^{61} +(1.21782 - 1.21782i) q^{63} +(-5.40796 + 5.40796i) q^{67} +4.49440 q^{69} -2.63276i q^{71} +(-2.67877 - 2.67877i) q^{73} +(6.37922 + 6.37922i) q^{77} -5.91346 q^{79} -1.00000 q^{81} +(-0.742352 - 0.742352i) q^{83} +(4.74362 + 4.74362i) q^{87} -1.75111i q^{89} -0.881100 q^{91} +(-1.94292 + 1.94292i) q^{93} +(-6.64801 + 6.64801i) q^{97} -5.23822i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q+O(q^{10}) \) 24 * q	\( 24 q - 8 q^{17} - 32 q^{43} + 16 q^{51} + 48 q^{67} + 40 q^{73} - 24 q^{81} + 80 q^{83} - 64 q^{91} + 24 q^{97}+O(q^{100}) \) 24 * q - 8 * q^17 - 32 * q^43 + 16 * q^51 + 48 * q^67 + 40 * q^73 - 24 * q^81 + 80 * q^83 - 64 * q^91 + 24 * q^97

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