LMFDB - Embedded newform 1400.2.x.b.993.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1400,2,Mod(657,1400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))

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

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

chi := DirichletCharacter("1400.657");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1400 = 2^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1400.x (of order $4$, degree $2$, 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:	$11.1790562830$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			993.4
Character	$\chi$	$=$	1400.993
Dual form			1400.2.x.b.657.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.03893 + 1.03893i) q^{3} +(-1.58883 + 2.11557i) q^{7} +0.841261i q^{9} +O(q^{10})$	$q+(-1.03893 + 1.03893i) q^{3} +(-1.58883 + 2.11557i) q^{7} +0.841261i q^{9} -2.34687 q^{11} +(-1.96436 + 1.96436i) q^{13} +(5.15858 + 5.15858i) q^{17} +3.74821 q^{19} +(-0.547244 - 3.84860i) q^{21} +(-6.08007 - 6.08007i) q^{23} +(-3.99079 - 3.99079i) q^{27} -5.89034i q^{29} +1.56648i q^{31} +(2.43823 - 2.43823i) q^{33} +(-1.53441 + 1.53441i) q^{37} -4.08166i q^{39} +9.51977i q^{41} +(-1.86313 - 1.86313i) q^{43} +(-4.59474 - 4.59474i) q^{47} +(-1.95125 - 6.72254i) q^{49} -10.7188 q^{51} +(-3.88128 - 3.88128i) q^{53} +(-3.89412 + 3.89412i) q^{57} -4.62061 q^{59} +2.00065i q^{61} +(-1.77974 - 1.33662i) q^{63} +(-2.69156 + 2.69156i) q^{67} +12.6335 q^{69} -0.392229 q^{71} +(7.08543 - 7.08543i) q^{73} +(3.72878 - 4.96497i) q^{77} +4.98717i q^{79} +5.76850 q^{81} +(9.36651 - 9.36651i) q^{83} +(6.11964 + 6.11964i) q^{87} -9.83200 q^{89} +(-1.03471 - 7.27677i) q^{91} +(-1.62746 - 1.62746i) q^{93} +(-11.8576 - 11.8576i) q^{97} -1.97433i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{7}+O(q^{10}) $ 24 * q - 4 * q^7	$ 24 q - 4 q^{7} + 8 q^{11} + 16 q^{21} + 32 q^{23} + 8 q^{37} - 16 q^{43} - 24 q^{51} + 16 q^{53} - 20 q^{63} + 32 q^{67} - 32 q^{71} + 40 q^{77} - 72 q^{81} - 64 q^{91} - 72 q^{93}+O(q^{100}) $ 24 * q - 4 * q^7 + 8 * q^11 + 16 * q^21 + 32 * q^23 + 8 * q^37 - 16 * q^43 - 24 * q^51 + 16 * q^53 - 20 * q^63 + 32 * q^67 - 32 * q^71 + 40 * q^77 - 72 * q^81 - 64 * q^91 - 72 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times$.

$n$	$351$	$701$	$801$	$1177$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	−1.03893	+	1.03893i	−0.599825	+	0.599825i	−0.940266	−	0.340441i	$-0.889424\pi$
$3$	−1.03893	+	1.03893i	−0.599825	+	0.599825i	0.340441	+	0.940266i	$0.389424\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−1.58883	+	2.11557i	−0.600520	+	0.799609i
$7$	−1.58883	+	2.11557i	−0.600520	+	0.799609i
$8$		0			0
$9$			0.841261i			0.280420i
$10$		0			0
$11$	−2.34687			−0.707609			−0.353804	−	0.935319i	$-0.615112\pi$
$11$	−2.34687			−0.707609			−0.353804	+	0.935319i	$0.615112\pi$
$12$		0			0
$13$	−1.96436	+	1.96436i	−0.544816	+	0.544816i	−0.924937	−	0.380121i	$-0.875882\pi$
$13$	−1.96436	+	1.96436i	−0.544816	+	0.544816i	0.380121	+	0.924937i	$0.375882\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	5.15858	+	5.15858i	1.25114	+	1.25114i	0.955210	+	0.295929i	$0.0956291\pi$
$17$	5.15858	+	5.15858i	1.25114	+	1.25114i	0.295929	+	0.955210i	$0.404371\pi$
$18$		0			0
$19$	3.74821			0.859899			0.429949	−	0.902853i	$-0.358531\pi$
$19$	3.74821			0.859899			0.429949	+	0.902853i	$0.358531\pi$
$20$		0			0
$21$	−0.547244	−	3.84860i	−0.119419	−	0.839833i
$22$		0			0
$23$	−6.08007	−	6.08007i	−1.26778	−	1.26778i	−0.947232	−	0.320550i	$-0.896132\pi$
$23$	−6.08007	−	6.08007i	−1.26778	−	1.26778i	−0.320550	−	0.947232i	$-0.603868\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−3.99079	−	3.99079i	−0.768028	−	0.768028i
$28$		0			0
$29$		−	5.89034i		−	1.09381i	−0.837195	−	0.546905i	$-0.815806\pi$
$29$		−	5.89034i		−	1.09381i	0.837195	−	0.546905i	$-0.184194\pi$
$30$		0			0
$31$			1.56648i			0.281348i	0.990056	+	0.140674i	$0.0449270\pi$
$31$			1.56648i			0.281348i	−0.990056	+	0.140674i	$0.955073\pi$
$32$		0			0
$33$	2.43823	−	2.43823i	0.424441	−	0.424441i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.53441	+	1.53441i	−0.252256	+	0.252256i	−0.821895	−	0.569639i	$-0.807083\pi$
$37$	−1.53441	+	1.53441i	−0.252256	+	0.252256i	0.569639	+	0.821895i	$0.307083\pi$
$38$		0			0
$39$		−	4.08166i		−	0.653588i
$40$		0			0
$41$			9.51977i			1.48674i	0.668882	+	0.743369i	$0.266773\pi$
$41$			9.51977i			1.48674i	−0.668882	+	0.743369i	$0.733227\pi$
$42$		0			0
$43$	−1.86313	−	1.86313i	−0.284125	−	0.284125i	0.550626	−	0.834752i	$-0.314389\pi$
$43$	−1.86313	−	1.86313i	−0.284125	−	0.284125i	−0.834752	+	0.550626i	$0.814389\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.59474	−	4.59474i	−0.670212	−	0.670212i	0.287553	−	0.957765i	$-0.407158\pi$
$47$	−4.59474	−	4.59474i	−0.670212	−	0.670212i	−0.957765	+	0.287553i	$0.907158\pi$
$48$		0			0
$49$	−1.95125	−	6.72254i	−0.278750	−	0.960364i
$50$		0			0
$51$	−10.7188			−1.50093
$52$		0			0
$53$	−3.88128	−	3.88128i	−0.533135	−	0.533135i	0.388369	−	0.921504i	$-0.373039\pi$
$53$	−3.88128	−	3.88128i	−0.533135	−	0.533135i	−0.921504	+	0.388369i	$0.873039\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−3.89412	+	3.89412i	−0.515789	+	0.515789i
$58$		0			0
$59$	−4.62061			−0.601552			−0.300776	−	0.953695i	$-0.597246\pi$
$59$	−4.62061			−0.601552			−0.300776	+	0.953695i	$0.597246\pi$
$60$		0			0
$61$			2.00065i			0.256156i	0.991764	+	0.128078i	$0.0408808\pi$
$61$			2.00065i			0.256156i	−0.991764	+	0.128078i	$0.959119\pi$
$62$		0			0
$63$	−1.77974	−	1.33662i	−0.224227	−	0.168398i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2.69156	+	2.69156i	−0.328827	+	0.328827i	−0.852140	−	0.523314i	$-0.824696\pi$
$67$	−2.69156	+	2.69156i	−0.328827	+	0.328827i	0.523314	+	0.852140i	$0.324696\pi$
$68$		0			0
$69$	12.6335			1.52089
$70$		0			0
$71$	−0.392229			−0.0465491			−0.0232745	−	0.999729i	$-0.507409\pi$
$71$	−0.392229			−0.0465491			−0.0232745	+	0.999729i	$0.507409\pi$
$72$		0			0
$73$	7.08543	−	7.08543i	0.829287	−	0.829287i	−0.158131	−	0.987418i	$-0.550547\pi$
$73$	7.08543	−	7.08543i	0.829287	−	0.829287i	0.987418	+	0.158131i	$0.0505468\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.72878	−	4.96497i	0.424934	−	0.565811i
$78$		0			0
$79$			4.98717i			0.561100i	0.959839	+	0.280550i	$0.0905169\pi$
$79$			4.98717i			0.561100i	−0.959839	+	0.280550i	$0.909483\pi$
$80$		0			0
$81$	5.76850			0.640944
$82$		0			0
$83$	9.36651	−	9.36651i	1.02811	−	1.02811i	0.0285148	−	0.999593i	$-0.490922\pi$
$83$	9.36651	−	9.36651i	1.02811	−	1.02811i	0.999593	−	0.0285148i	$-0.00907776\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	6.11964	+	6.11964i	0.656094	+	0.656094i
$88$		0			0
$89$	−9.83200			−1.04219			−0.521095	−	0.853499i	$-0.674476\pi$
$89$	−9.83200			−1.04219			−0.521095	+	0.853499i	$0.674476\pi$
$90$		0			0
$91$	−1.03471	−	7.27677i	−0.108467	−	0.762813i
$92$		0			0
$93$	−1.62746	−	1.62746i	−0.168760	−	0.168760i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−11.8576	−	11.8576i	−1.20396	−	1.20396i	−0.972952	−	0.231006i	$-0.925798\pi$
$97$	−11.8576	−	11.8576i	−1.20396	−	1.20396i	−0.231006	−	0.972952i	$-0.574202\pi$
$98$		0			0
$99$		−	1.97433i		−	0.198428i
$100$		0			0
$101$		−	8.41529i		−	0.837353i	−0.908135	−	0.418676i	$-0.862494\pi$
$101$		−	8.41529i		−	0.837353i	0.908135	−	0.418676i	$-0.137506\pi$
$102$		0			0
$103$	−8.77874	+	8.77874i	−0.864995	+	0.864995i	−0.991913	−	0.126918i	$-0.959491\pi$
$103$	−8.77874	+	8.77874i	−0.864995	+	0.864995i	0.126918	+	0.991913i	$0.459491\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−10.3741	+	10.3741i	−1.00290	+	1.00290i	−0.00290471	+	0.999996i	$0.500925\pi$
$107$	−10.3741	+	10.3741i	−1.00290	+	1.00290i	−0.999996	+	0.00290471i	$0.999075\pi$
$108$		0			0
$109$		−	4.92724i		−	0.471944i	−0.971760	−	0.235972i	$-0.924173\pi$
$109$		−	4.92724i		−	0.471944i	0.971760	−	0.235972i	$-0.0758273\pi$
$110$		0			0
$111$		−	3.18828i		−	0.302618i
$112$		0			0
$113$	3.79963	+	3.79963i	0.357439	+	0.357439i	0.862868	−	0.505429i	$-0.168666\pi$
$113$	3.79963	+	3.79963i	0.357439	+	0.357439i	−0.505429	+	0.862868i	$0.668666\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.65254	−	1.65254i	−0.152777	−	0.152777i
$118$		0			0
$119$	−19.1094	+	2.71723i	−1.75176	+	0.249088i
$120$		0			0
$121$	−5.49219			−0.499290
$122$		0			0
$123$	−9.89034	−	9.89034i	−0.891782	−	0.891782i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	0.777755	−	0.777755i	0.0690146	−	0.0690146i	−0.671757	−	0.740772i	$-0.734460\pi$
$127$	0.777755	−	0.777755i	0.0690146	−	0.0690146i	0.740772	+	0.671757i	$0.234460\pi$
$128$		0			0
$129$	3.87132			0.340851
$130$		0			0
$131$		−	11.0373i		−	0.964336i	−0.876079	−	0.482168i	$-0.839849\pi$
$131$		−	11.0373i		−	0.964336i	0.876079	−	0.482168i	$-0.160151\pi$
$132$		0			0
$133$	−5.95526	+	7.92959i	−0.516387	+	0.687583i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.65313	+	2.65313i	−0.226672	+	0.226672i	−0.811301	−	0.584629i	$-0.801240\pi$
$137$	−2.65313	+	2.65313i	−0.226672	+	0.226672i	0.584629	+	0.811301i	$0.301240\pi$
$138$		0			0
$139$	7.15451			0.606838			0.303419	−	0.952857i	$-0.401872\pi$
$139$	7.15451			0.606838			0.303419	+	0.952857i	$0.401872\pi$
$140$		0			0
$141$	9.54720			0.804019
$142$		0			0
$143$	4.61011	−	4.61011i	0.385516	−	0.385516i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	9.01144	+	4.95702i	0.743251	+	0.408848i
$148$		0			0
$149$		−	12.2552i		−	1.00399i	−0.864872	−	0.501993i	$-0.832600\pi$
$149$		−	12.2552i		−	1.00399i	0.864872	−	0.501993i	$-0.167400\pi$
$150$		0			0
$151$	−13.2221			−1.07600			−0.537998	−	0.842946i	$-0.680819\pi$
$151$	−13.2221			−1.07600			−0.537998	+	0.842946i	$0.680819\pi$
$152$		0			0
$153$	−4.33971	+	4.33971i	−0.350845	+	0.350845i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	8.35401	+	8.35401i	0.666723	+	0.666723i	0.956956	−	0.290233i	$-0.0937329\pi$
$157$	8.35401	+	8.35401i	0.666723	+	0.666723i	−0.290233	+	0.956956i	$0.593733\pi$
$158$		0			0
$159$	8.06474			0.639576
$160$		0			0
$161$	22.5230	−	3.20261i	1.77506	−	0.252401i
$162$		0			0
$163$	−2.21768	−	2.21768i	−0.173702	−	0.173702i	0.614902	−	0.788604i	$-0.289196\pi$
$163$	−2.21768	−	2.21768i	−0.173702	−	0.173702i	−0.788604	+	0.614902i	$0.789196\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	15.1934	+	15.1934i	1.17570	+	1.17570i	0.980829	+	0.194871i	$0.0624288\pi$
$167$	15.1934	+	15.1934i	1.17570	+	1.17570i	0.194871	+	0.980829i	$0.437571\pi$
$168$		0			0
$169$			5.28257i			0.406352i
$170$		0			0
$171$			3.15322i			0.241133i
$172$		0			0
$173$	−4.60458	+	4.60458i	−0.350080	+	0.350080i	−0.860139	−	0.510059i	$-0.829623\pi$
$173$	−4.60458	+	4.60458i	−0.350080	+	0.350080i	0.510059	+	0.860139i	$0.329623\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	4.80047	−	4.80047i	0.360826	−	0.360826i
$178$		0			0
$179$			11.5721i			0.864939i	0.901648	+	0.432470i	$0.142358\pi$
$179$			11.5721i			0.864939i	−0.901648	+	0.432470i	$0.857642\pi$
$180$		0			0
$181$			5.28640i			0.392935i	0.980510	+	0.196467i	$0.0629470\pi$
$181$			5.28640i			0.392935i	−0.980510	+	0.196467i	$0.937053\pi$
$182$		0			0
$183$	−2.07852	−	2.07852i	−0.153649	−	0.153649i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−12.1065	−	12.1065i	−0.885317	−	0.885317i
$188$		0			0
$189$	14.7835	−	2.10211i	1.07534	−	0.152906i
$190$		0			0
$191$	−11.6115			−0.840179			−0.420089	−	0.907483i	$-0.638001\pi$
$191$	−11.6115			−0.840179			−0.420089	+	0.907483i	$0.638001\pi$
$192$		0			0
$193$	17.6369	+	17.6369i	1.26954	+	1.26954i	0.946328	+	0.323207i	$0.104761\pi$
$193$	17.6369	+	17.6369i	1.26954	+	1.26954i	0.323207	+	0.946328i	$0.395239\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	17.2130	−	17.2130i	1.22637	−	1.22637i	0.261049	−	0.965325i	$-0.415931\pi$
$197$	17.2130	−	17.2130i	1.22637	−	1.22637i	0.965325	−	0.261049i	$-0.0840685\pi$
$198$		0			0
$199$	6.95883			0.493299			0.246649	−	0.969105i	$-0.420670\pi$
$199$	6.95883			0.493299			0.246649	+	0.969105i	$0.420670\pi$
$200$		0			0
$201$		−	5.59267i		−	0.394477i
$202$		0			0
$203$	12.4614	+	9.35874i	0.874620	+	0.656855i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	5.11492	−	5.11492i	0.355512	−	0.355512i
$208$		0			0
$209$	−8.79658			−0.608472
$210$		0			0
$211$	9.28431			0.639159			0.319579	−	0.947560i	$-0.396458\pi$
$211$	9.28431			0.639159			0.319579	+	0.947560i	$0.396458\pi$
$212$		0			0
$213$	0.407498	−	0.407498i	0.0279213	−	0.0279213i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−3.31400	−	2.48887i	−0.224969	−	0.168955i
$218$		0			0
$219$			14.7225i			0.994854i
$220$		0			0
$221$	−20.2666			−1.36328
$222$		0			0
$223$	−4.77582	+	4.77582i	−0.319813	+	0.319813i	−0.848695	−	0.528882i	$-0.822611\pi$
$223$	−4.77582	+	4.77582i	−0.319813	+	0.319813i	0.528882	+	0.848695i	$0.322611\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−2.49990	−	2.49990i	−0.165925	−	0.165925i	0.619261	−	0.785185i	$-0.287432\pi$
$227$	−2.49990	−	2.49990i	−0.165925	−	0.165925i	−0.785185	+	0.619261i	$0.787432\pi$
$228$		0			0
$229$	−18.0694			−1.19406			−0.597031	−	0.802218i	$-0.703653\pi$
$229$	−18.0694			−1.19406			−0.597031	+	0.802218i	$0.703653\pi$
$230$		0			0
$231$	1.28431	+	9.03217i	0.0845016	+	0.594273i
$232$		0			0
$233$	−9.14278	−	9.14278i	−0.598963	−	0.598963i	0.341073	−	0.940037i	$-0.389210\pi$
$233$	−9.14278	−	9.14278i	−0.598963	−	0.598963i	−0.940037	+	0.341073i	$0.889210\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−5.18130	−	5.18130i	−0.336562	−	0.336562i
$238$		0			0
$239$		−	11.3719i		−	0.735590i	−0.929907	−	0.367795i	$-0.880113\pi$
$239$		−	11.3719i		−	0.735590i	0.929907	−	0.367795i	$-0.119887\pi$
$240$		0			0
$241$			19.6361i			1.26488i	0.774611	+	0.632438i	$0.217946\pi$
$241$			19.6361i			1.26488i	−0.774611	+	0.632438i	$0.782054\pi$
$242$		0			0
$243$	5.97932	−	5.97932i	0.383574	−	0.383574i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−7.36284	+	7.36284i	−0.468486	+	0.468486i
$248$		0			0
$249$			19.4622i			1.23337i
$250$		0			0
$251$			26.2420i			1.65638i	0.560447	+	0.828190i	$0.310629\pi$
$251$			26.2420i			1.65638i	−0.560447	+	0.828190i	$0.689371\pi$
$252$		0			0
$253$	14.2691	+	14.2691i	0.897094	+	0.897094i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	1.93157	+	1.93157i	0.120488	+	0.120488i	0.764780	−	0.644292i	$-0.222848\pi$
$257$	1.93157	+	1.93157i	0.120488	+	0.120488i	−0.644292	+	0.764780i	$0.722848\pi$
$258$		0			0
$259$	−0.808236	−	5.68406i	−0.0502213	−	0.353191i
$260$		0			0
$261$	4.95532			0.306726
$262$		0			0
$263$	−2.64248	−	2.64248i	−0.162942	−	0.162942i	0.620927	−	0.783869i	$-0.286757\pi$
$263$	−2.64248	−	2.64248i	−0.162942	−	0.162942i	−0.783869	+	0.620927i	$0.786757\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	10.2147	−	10.2147i	0.625131	−	0.625131i
$268$		0			0
$269$	1.17948			0.0719143			0.0359572	−	0.999353i	$-0.488552\pi$
$269$	1.17948			0.0719143			0.0359572	+	0.999353i	$0.488552\pi$
$270$		0			0
$271$			14.7880i			0.898306i	0.893455	+	0.449153i	$0.148274\pi$
$271$			14.7880i			0.898306i	−0.893455	+	0.449153i	$0.851726\pi$
$272$		0			0
$273$	8.63502	+	6.48505i	0.522615	+	0.392493i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−11.6478	+	11.6478i	−0.699848	+	0.699848i	−0.964378	−	0.264529i	$-0.914783\pi$
$277$	−11.6478	+	11.6478i	−0.699848	+	0.699848i	0.264529	+	0.964378i	$0.414783\pi$
$278$		0			0
$279$	−1.31782			−0.0788957
$280$		0			0
$281$	20.2153			1.20594			0.602971	−	0.797763i	$-0.293983\pi$
$281$	20.2153			1.20594			0.602971	+	0.797763i	$0.293983\pi$
$282$		0			0
$283$	−5.53654	+	5.53654i	−0.329113	+	0.329113i	−0.852249	−	0.523136i	$-0.824762\pi$
$283$	−5.53654	+	5.53654i	−0.329113	+	0.329113i	0.523136	+	0.852249i	$0.324762\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−20.1397	−	15.1253i	−1.18881	−	0.892816i
$288$		0			0
$289$			36.2218i			2.13070i
$290$		0			0
$291$	24.6384			1.44433
$292$		0			0
$293$	1.12050	−	1.12050i	0.0654601	−	0.0654601i	−0.673619	−	0.739079i	$-0.735261\pi$
$293$	1.12050	−	1.12050i	0.0654601	−	0.0654601i	0.739079	+	0.673619i	$0.235261\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	9.36588	+	9.36588i	0.543463	+	0.543463i
$298$		0			0
$299$	23.8869			1.38141
$300$		0			0
$301$	6.90179	−	0.981388i	0.397812	−	0.0565662i
$302$		0			0
$303$	8.74288	+	8.74288i	0.502265	+	0.502265i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	9.43044	+	9.43044i	0.538224	+	0.538224i	0.923007	−	0.384783i	$-0.125724\pi$
$307$	9.43044	+	9.43044i	0.538224	+	0.538224i	−0.384783	+	0.923007i	$0.625724\pi$
$308$		0			0
$309$		−	18.2409i		−	1.03769i
$310$		0			0
$311$			14.6035i			0.828090i	0.910256	+	0.414045i	$0.135884\pi$
$311$			14.6035i			0.828090i	−0.910256	+	0.414045i	$0.864116\pi$
$312$		0			0
$313$	7.05535	−	7.05535i	0.398792	−	0.398792i	−0.479015	−	0.877807i	$-0.659006\pi$
$313$	7.05535	−	7.05535i	0.398792	−	0.398792i	0.877807	+	0.479015i	$0.159006\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	11.2538	−	11.2538i	0.632075	−	0.632075i	−0.316513	−	0.948588i	$-0.602512\pi$
$317$	11.2538	−	11.2538i	0.632075	−	0.632075i	0.948588	+	0.316513i	$0.102512\pi$
$318$		0			0
$319$			13.8239i			0.773989i
$320$		0			0
$321$		−	21.5558i		−	1.20313i
$322$		0			0
$323$	19.3354	+	19.3354i	1.07585	+	1.07585i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	5.11904	+	5.11904i	0.283084	+	0.283084i
$328$		0			0
$329$	17.0207	−	2.42023i	0.938383	−	0.133432i
$330$		0			0
$331$	−33.6643			−1.85036			−0.925179	−	0.379531i	$-0.876085\pi$
$331$	−33.6643			−1.85036			−0.925179	+	0.379531i	$0.876085\pi$
$332$		0			0
$333$	−1.29084	−	1.29084i	−0.0707376	−	0.0707376i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−12.8298	+	12.8298i	−0.698885	+	0.698885i	−0.964170	−	0.265285i	$-0.914534\pi$
$337$	−12.8298	+	12.8298i	−0.698885	+	0.698885i	0.265285	+	0.964170i	$0.414534\pi$
$338$		0			0
$339$	−7.89507			−0.428802
$340$		0			0
$341$		−	3.67633i		−	0.199085i
$342$		0			0
$343$	17.3222	+	6.55296i	0.935311	+	0.353826i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	20.6439	−	20.6439i	1.10822	−	1.10822i	0.114837	−	0.993384i	$-0.463365\pi$
$347$	20.6439	−	20.6439i	1.10822	−	1.10822i	0.993384	−	0.114837i	$-0.0366345\pi$
$348$		0			0
$349$	−29.3356			−1.57030			−0.785150	−	0.619306i	$-0.787414\pi$
$349$	−29.3356			−1.57030			−0.785150	+	0.619306i	$0.787414\pi$
$350$		0			0
$351$	15.6787			0.836867
$352$		0			0
$353$	−16.5837	+	16.5837i	−0.882662	+	0.882662i	−0.993805	−	0.111142i	$-0.964549\pi$
$353$	−16.5837	+	16.5837i	−0.882662	+	0.882662i	0.111142	+	0.993805i	$0.464549\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	17.0303	−	22.6763i	0.901338	−	1.20016i
$358$		0			0
$359$			30.4050i			1.60472i	0.596843	+	0.802358i	$0.296421\pi$
$359$			30.4050i			1.60472i	−0.596843	+	0.802358i	$0.703579\pi$
$360$		0			0
$361$	−4.95092			−0.260575
$362$		0			0
$363$	5.70598	−	5.70598i	0.299486	−	0.299486i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−13.6007	−	13.6007i	−0.709950	−	0.709950i	0.256574	−	0.966525i	$-0.417406\pi$
$367$	−13.6007	−	13.6007i	−0.709950	−	0.709950i	−0.966525	+	0.256574i	$0.917406\pi$
$368$		0			0
$369$	−8.00861			−0.416911
$370$		0			0
$371$	14.3778	−	2.04443i	0.746459	−	0.106141i
$372$		0			0
$373$	−13.8626	−	13.8626i	−0.717776	−	0.717776i	0.250373	−	0.968149i	$-0.419447\pi$
$373$	−13.8626	−	13.8626i	−0.717776	−	0.717776i	−0.968149	+	0.250373i	$0.919447\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	11.5708	+	11.5708i	0.595925	+	0.595925i
$378$		0			0
$379$			11.8896i			0.610727i	0.952236	+	0.305363i	$0.0987779\pi$
$379$			11.8896i			0.610727i	−0.952236	+	0.305363i	$0.901222\pi$
$380$		0			0
$381$			1.61606i			0.0827934i
$382$		0			0
$383$	−16.5186	+	16.5186i	−0.844059	+	0.844059i	−0.989384	−	0.145325i	$-0.953577\pi$
$383$	−16.5186	+	16.5186i	−0.844059	+	0.844059i	0.145325	+	0.989384i	$0.453577\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	1.56738	−	1.56738i	0.0796745	−	0.0796745i
$388$		0			0
$389$		−	9.62098i		−	0.487803i	−0.969800	−	0.243902i	$-0.921573\pi$
$389$		−	9.62098i		−	0.487803i	0.969800	−	0.243902i	$-0.0784274\pi$
$390$		0			0
$391$		−	62.7290i		−	3.17234i
$392$		0			0
$393$	11.4670	+	11.4670i	0.578433	+	0.578433i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	17.5393	+	17.5393i	0.880270	+	0.880270i	0.993562	−	0.113292i	$-0.0361394\pi$
$397$	17.5393	+	17.5393i	0.880270	+	0.880270i	−0.113292	+	0.993562i	$0.536139\pi$
$398$		0			0
$399$	−2.05119	−	14.4254i	−0.102688	−	0.722171i
$400$		0			0
$401$	−14.2238			−0.710302			−0.355151	−	0.934809i	$-0.615571\pi$
$401$	−14.2238			−0.710302			−0.355151	+	0.934809i	$0.615571\pi$
$402$		0			0
$403$	−3.07713	−	3.07713i	−0.153283	−	0.153283i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	3.60107	−	3.60107i	0.178498	−	0.178498i
$408$		0			0
$409$	14.2602			0.705123			0.352562	−	0.935789i	$-0.385311\pi$
$409$	14.2602			0.705123			0.352562	+	0.935789i	$0.385311\pi$
$410$		0			0
$411$		−	5.51281i		−	0.271927i
$412$		0			0
$413$	7.34135	−	9.77520i	0.361244	−	0.481006i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−7.43302	+	7.43302i	−0.363996	+	0.363996i
$418$		0			0
$419$	−13.5802			−0.663434			−0.331717	−	0.943379i	$-0.607628\pi$
$419$	−13.5802			−0.663434			−0.331717	+	0.943379i	$0.607628\pi$
$420$		0			0
$421$	−12.7805			−0.622884			−0.311442	−	0.950265i	$-0.600812\pi$
$421$	−12.7805			−0.622884			−0.311442	+	0.950265i	$0.600812\pi$
$422$		0			0
$423$	3.86537	−	3.86537i	0.187941	−	0.187941i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−4.23250	−	3.17868i	−0.204825	−	0.153827i
$428$		0			0
$429$			9.57913i			0.462485i
$430$		0			0
$431$	37.7947			1.82051			0.910254	−	0.414049i	$-0.135886\pi$
$431$	37.7947			1.82051			0.910254	+	0.414049i	$0.135886\pi$
$432$		0			0
$433$	−14.2122	+	14.2122i	−0.682996	+	0.682996i	−0.960674	−	0.277678i	$-0.910435\pi$
$433$	−14.2122	+	14.2122i	−0.682996	+	0.682996i	0.277678	+	0.960674i	$0.410435\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−22.7894	−	22.7894i	−1.09016	−	1.09016i
$438$		0			0
$439$	−27.7697			−1.32538			−0.662688	−	0.748896i	$-0.730584\pi$
$439$	−27.7697			−1.32538			−0.662688	+	0.748896i	$0.730584\pi$
$440$		0			0
$441$	5.65541	−	1.64151i	0.269305	−	0.0781673i
$442$		0			0
$443$	−11.8951	−	11.8951i	−0.565152	−	0.565152i	0.365615	−	0.930766i	$-0.380859\pi$
$443$	−11.8951	−	11.8951i	−0.565152	−	0.565152i	−0.930766	+	0.365615i	$0.880859\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	12.7323	+	12.7323i	0.602216	+	0.602216i
$448$		0			0
$449$		−	3.92227i		−	0.185104i	−0.995708	−	0.0925518i	$-0.970498\pi$
$449$		−	3.92227i		−	0.185104i	0.995708	−	0.0925518i	$-0.0295024\pi$
$450$		0			0
$451$		−	22.3417i		−	1.05203i
$452$		0			0
$453$	13.7367	−	13.7367i	0.645409	−	0.645409i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−17.6596	+	17.6596i	−0.826083	+	0.826083i	−0.986972	−	0.160889i	$-0.948564\pi$
$457$	−17.6596	+	17.6596i	−0.826083	+	0.826083i	0.160889	+	0.986972i	$0.448564\pi$
$458$		0			0
$459$		−	41.1736i		−	1.92182i
$460$		0			0
$461$			0.616064i			0.0286930i	0.999897	+	0.0143465i	$0.00456678\pi$
$461$			0.616064i			0.0286930i	−0.999897	+	0.0143465i	$0.995433\pi$
$462$		0			0
$463$	11.9726	+	11.9726i	0.556413	+	0.556413i	0.928284	−	0.371871i	$-0.121284\pi$
$463$	11.9726	+	11.9726i	0.556413	+	0.556413i	−0.371871	+	0.928284i	$0.621284\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	12.8767	+	12.8767i	0.595861	+	0.595861i	0.939208	−	0.343348i	$-0.111561\pi$
$467$	12.8767	+	12.8767i	0.595861	+	0.595861i	−0.343348	+	0.939208i	$0.611561\pi$
$468$		0			0
$469$	−1.41775	−	9.97061i	−0.0654658	−	0.460400i
$470$		0			0
$471$	−17.3584			−0.799834
$472$		0			0
$473$	4.37254	+	4.37254i	0.201050	+	0.201050i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	3.26517	−	3.26517i	0.149502	−	0.149502i
$478$		0			0
$479$	8.34016			0.381072			0.190536	−	0.981680i	$-0.438977\pi$
$479$	8.34016			0.381072			0.190536	+	0.981680i	$0.438977\pi$
$480$		0			0
$481$		−	6.02827i		−	0.274866i
$482$		0			0
$483$	−20.0724	+	26.7270i	−0.913328	+	1.21612i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	6.90541	−	6.90541i	0.312914	−	0.312914i	−0.533123	−	0.846037i	$-0.678982\pi$
$487$	6.90541	−	6.90541i	0.312914	−	0.312914i	0.846037	+	0.533123i	$0.178982\pi$
$488$		0			0
$489$	4.60801			0.208381
$490$		0			0
$491$	25.1783			1.13628			0.568140	−	0.822932i	$-0.307663\pi$
$491$	25.1783			1.13628			0.568140	+	0.822932i	$0.307663\pi$
$492$		0			0
$493$	30.3858	−	30.3858i	1.36851	−	1.36851i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.623185	−	0.829788i	0.0279537	−	0.0372211i
$498$		0			0
$499$		−	20.8907i		−	0.935197i	−0.883941	−	0.467599i	$-0.845119\pi$
$499$		−	20.8907i		−	0.935197i	0.883941	−	0.467599i	$-0.154881\pi$
$500$		0			0
$501$	−31.5696			−1.41043
$502$		0			0
$503$	0.585795	−	0.585795i	0.0261193	−	0.0261193i	−0.693927	−	0.720046i	$-0.744121\pi$
$503$	0.585795	−	0.585795i	0.0261193	−	0.0261193i	0.720046	+	0.693927i	$0.244121\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−5.48821	−	5.48821i	−0.243740	−	0.243740i
$508$		0			0
$509$	38.2153			1.69386			0.846932	−	0.531701i	$-0.178447\pi$
$509$	38.2153			1.69386			0.846932	+	0.531701i	$0.178447\pi$
$510$		0			0
$511$	3.73218	+	26.2472i	0.165102	+	1.16111i
$512$		0			0
$513$	−14.9583	−	14.9583i	−0.660426	−	0.660426i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	10.7833	+	10.7833i	0.474248	+	0.474248i
$518$		0			0
$519$		−	9.56765i		−	0.419973i
$520$		0			0
$521$		−	8.40522i		−	0.368239i	−0.982904	−	0.184120i	$-0.941057\pi$
$521$		−	8.40522i		−	0.368239i	0.982904	−	0.184120i	$-0.0589434\pi$
$522$		0			0
$523$	14.1989	−	14.1989i	0.620876	−	0.620876i	−0.324879	−	0.945755i	$-0.605324\pi$
$523$	14.1989	−	14.1989i	0.620876	−	0.620876i	0.945755	+	0.324879i	$0.105324\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−8.08081	+	8.08081i	−0.352006	+	0.352006i
$528$		0			0
$529$			50.9344i			2.21454i
$530$		0			0
$531$		−	3.88713i		−	0.168687i
$532$		0			0
$533$	−18.7003	−	18.7003i	−0.809998	−	0.809998i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−12.0226	−	12.0226i	−0.518812	−	0.518812i
$538$		0			0
$539$	4.57934	+	15.7770i	0.197246	+	0.679562i
$540$		0			0
$541$	−38.9363			−1.67400			−0.837001	−	0.547202i	$-0.815693\pi$
$541$	−38.9363			−1.67400			−0.837001	+	0.547202i	$0.815693\pi$
$542$		0			0
$543$	−5.49218	−	5.49218i	−0.235692	−	0.235692i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−2.30390	+	2.30390i	−0.0985078	+	0.0985078i	−0.754643	−	0.656135i	$-0.772190\pi$
$547$	−2.30390	+	2.30390i	−0.0985078	+	0.0985078i	0.656135	+	0.754643i	$0.272190\pi$
$548$		0			0
$549$	−1.68306			−0.0718314
$550$		0			0
$551$		−	22.0783i		−	0.940565i
$552$		0			0
$553$	−10.5507	−	7.92375i	−0.448661	−	0.336952i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−7.69913	+	7.69913i	−0.326223	+	0.326223i	−0.851148	−	0.524926i	$-0.824093\pi$
$557$	−7.69913	+	7.69913i	−0.326223	+	0.326223i	0.524926	+	0.851148i	$0.324093\pi$
$558$		0			0
$559$	7.31974			0.309592
$560$		0			0
$561$	25.1556			1.06207
$562$		0			0
$563$	−11.8855	+	11.8855i	−0.500914	+	0.500914i	−0.911722	−	0.410808i	$-0.865247\pi$
$563$	−11.8855	+	11.8855i	−0.500914	+	0.500914i	0.410808	+	0.911722i	$0.365247\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−9.16515	+	12.2036i	−0.384900	+	0.512505i
$568$		0			0
$569$		−	3.16924i		−	0.132861i	−0.997791	−	0.0664307i	$-0.978839\pi$
$569$		−	3.16924i		−	0.132861i	0.997791	−	0.0664307i	$-0.0211611\pi$
$570$		0			0
$571$	−24.8492			−1.03991			−0.519953	−	0.854195i	$-0.674050\pi$
$571$	−24.8492			−1.03991			−0.519953	+	0.854195i	$0.674050\pi$
$572$		0			0
$573$	12.0635	−	12.0635i	0.503960	−	0.503960i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−29.2688	−	29.2688i	−1.21848	−	1.21848i	−0.968166	−	0.250309i	$-0.919468\pi$
$577$	−29.2688	−	29.2688i	−1.21848	−	1.21848i	−0.250309	−	0.968166i	$-0.580532\pi$
$578$		0			0
$579$	−36.6470			−1.52300
$580$		0			0
$581$	4.93372	+	34.6973i	0.204685	+	1.43948i
$582$		0			0
$583$	9.10888	+	9.10888i	0.377251	+	0.377251i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−16.3313	−	16.3313i	−0.674065	−	0.674065i	0.284586	−	0.958651i	$-0.408144\pi$
$587$	−16.3313	−	16.3313i	−0.674065	−	0.674065i	−0.958651	+	0.284586i	$0.908144\pi$
$588$		0			0
$589$			5.87150i			0.241931i
$590$		0			0
$591$			35.7661i			1.47122i
$592$		0			0
$593$	−17.5540	+	17.5540i	−0.720858	+	0.720858i	−0.968780	−	0.247922i	$-0.920252\pi$
$593$	−17.5540	+	17.5540i	−0.720858	+	0.720858i	0.247922	+	0.968780i	$0.420252\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−7.22972	+	7.22972i	−0.295893	+	0.295893i
$598$		0			0
$599$		−	21.4754i		−	0.877461i	−0.898619	−	0.438731i	$-0.855428\pi$
$599$		−	21.4754i		−	0.877461i	0.898619	−	0.438731i	$-0.144572\pi$
$600$		0			0
$601$			32.4373i			1.32314i	0.749882	+	0.661572i	$0.230110\pi$
$601$			32.4373i			1.32314i	−0.749882	+	0.661572i	$0.769890\pi$
$602$		0			0
$603$	−2.26431	−	2.26431i	−0.0922096	−	0.0922096i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	13.4507	+	13.4507i	0.545947	+	0.545947i	0.925266	−	0.379319i	$-0.123842\pi$
$607$	13.4507	+	13.4507i	0.545947	+	0.545947i	−0.379319	+	0.925266i	$0.623842\pi$
$608$		0			0
$609$	−22.6696	+	3.22346i	−0.918617	+	0.130621i
$610$		0			0
$611$	18.0515			0.730284
$612$		0			0
$613$	1.66986	+	1.66986i	0.0674449	+	0.0674449i	0.740025	−	0.672580i	$-0.234814\pi$
$613$	1.66986	+	1.66986i	0.0674449	+	0.0674449i	−0.672580	+	0.740025i	$0.734814\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	16.0944	−	16.0944i	0.647938	−	0.647938i	−0.304556	−	0.952494i	$-0.598508\pi$
$617$	16.0944	−	16.0944i	0.647938	−	0.647938i	0.952494	+	0.304556i	$0.0985082\pi$
$618$		0			0
$619$	−0.973019			−0.0391089			−0.0195545	−	0.999809i	$-0.506225\pi$
$619$	−0.973019			−0.0391089			−0.0195545	+	0.999809i	$0.506225\pi$
$620$		0			0
$621$			48.5285i			1.94738i
$622$		0			0
$623$	15.6213	−	20.8003i	0.625856	−	0.833345i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	9.13900	−	9.13900i	0.364977	−	0.364977i
$628$		0			0
$629$	−15.8308			−0.631213
$630$		0			0
$631$	17.4830			0.695987			0.347994	−	0.937497i	$-0.386863\pi$
$631$	17.4830			0.695987			0.347994	+	0.937497i	$0.386863\pi$
$632$		0			0
$633$	−9.64573	+	9.64573i	−0.383383	+	0.383383i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	17.0385	+	9.37254i	0.675089	+	0.371353i
$638$		0			0
$639$		−	0.329967i		−	0.0130533i
$640$		0			0
$641$	−25.0710			−0.990244			−0.495122	−	0.868823i	$-0.664877\pi$
$641$	−25.0710			−0.990244			−0.495122	+	0.868823i	$0.664877\pi$
$642$		0			0
$643$	3.86619	−	3.86619i	0.152468	−	0.152468i	−0.626752	−	0.779219i	$-0.715616\pi$
$643$	3.86619	−	3.86619i	0.152468	−	0.152468i	0.779219	+	0.626752i	$0.215616\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−24.4727	−	24.4727i	−0.962119	−	0.962119i	0.0371889	−	0.999308i	$-0.488160\pi$
$647$	−24.4727	−	24.4727i	−0.962119	−	0.962119i	−0.999308	+	0.0371889i	$0.988160\pi$
$648$		0			0
$649$	10.8440			0.425663
$650$		0			0
$651$	6.02875	−	0.857248i	0.236285	−	0.0335982i
$652$		0			0
$653$	−23.1478	−	23.1478i	−0.905845	−	0.905845i	0.0900885	−	0.995934i	$-0.471285\pi$
$653$	−23.1478	−	23.1478i	−0.905845	−	0.905845i	−0.995934	+	0.0900885i	$0.971285\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	5.96070	+	5.96070i	0.232549	+	0.232549i
$658$		0			0
$659$		−	36.1548i		−	1.40839i	−0.710006	−	0.704195i	$-0.751308\pi$
$659$		−	36.1548i		−	1.40839i	0.710006	−	0.704195i	$-0.248692\pi$
$660$		0			0
$661$		−	33.4541i		−	1.30121i	−0.759415	−	0.650606i	$-0.774515\pi$
$661$		−	33.4541i		−	1.30121i	0.759415	−	0.650606i	$-0.225485\pi$
$662$		0			0
$663$	21.0555	−	21.0555i	0.817729	−	0.817729i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−35.8137	+	35.8137i	−1.38671	+	1.38671i
$668$		0			0
$669$		−	9.92347i		−	0.383663i
$670$		0			0
$671$		−	4.69526i		−	0.181259i
$672$		0			0
$673$	6.30998	+	6.30998i	0.243232	+	0.243232i	0.818186	−	0.574954i	$-0.194980\pi$
$673$	6.30998	+	6.30998i	0.243232	+	0.243232i	−0.574954	+	0.818186i	$0.694980\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−6.88730	−	6.88730i	−0.264700	−	0.264700i	0.562260	−	0.826960i	$-0.309932\pi$
$677$	−6.88730	−	6.88730i	−0.264700	−	0.264700i	−0.826960	+	0.562260i	$0.809932\pi$
$678$		0			0
$679$	43.9253	−	6.24588i	1.68570	−	0.239695i
$680$		0			0
$681$	5.19444			0.199051
$682$		0			0
$683$	−1.06740	−	1.06740i	−0.0408430	−	0.0408430i	0.686390	−	0.727233i	$-0.259194\pi$
$683$	−1.06740	−	1.06740i	−0.0408430	−	0.0408430i	−0.727233	+	0.686390i	$0.759194\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	18.7728	−	18.7728i	0.716228	−	0.716228i
$688$		0			0
$689$	15.2485			0.580921
$690$		0			0
$691$			43.8638i			1.66866i	0.551267	+	0.834329i	$0.314145\pi$
$691$			43.8638i			1.66866i	−0.551267	+	0.834329i	$0.685855\pi$
$692$		0			0
$693$	4.17683	+	3.13687i	0.158665	+	0.119160i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−49.1085	+	49.1085i	−1.86012	+	1.86012i
$698$		0			0
$699$	18.9974			0.718546
$700$		0			0
$701$	−36.6200			−1.38312			−0.691559	−	0.722320i	$-0.743076\pi$
$701$	−36.6200			−1.38312			−0.691559	+	0.722320i	$0.743076\pi$
$702$		0			0
$703$	−5.75130	+	5.75130i	−0.216914	+	0.216914i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	17.8031	+	13.3705i	0.669555	+	0.502848i
$708$		0			0
$709$		−	30.7975i		−	1.15662i	−0.815816	−	0.578311i	$-0.803712\pi$
$709$		−	30.7975i		−	1.15662i	0.815816	−	0.578311i	$-0.196288\pi$
$710$		0			0
$711$	−4.19551			−0.157344
$712$		0			0
$713$	9.52431	−	9.52431i	0.356688	−	0.356688i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	11.8146	+	11.8146i	0.441225	+	0.441225i
$718$		0			0
$719$	36.9703			1.37876			0.689379	−	0.724401i	$-0.257883\pi$
$719$	36.9703			1.37876			0.689379	+	0.724401i	$0.257883\pi$
$720$		0			0
$721$	−4.62411	−	32.5199i	−0.172211	−	1.21111i
$722$		0			0
$723$	−20.4005	−	20.4005i	−0.758704	−	0.758704i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−4.99011	−	4.99011i	−0.185073	−	0.185073i	0.608489	−	0.793562i	$-0.291776\pi$
$727$	−4.99011	−	4.99011i	−0.185073	−	0.185073i	−0.793562	+	0.608489i	$0.791776\pi$
$728$		0			0
$729$			29.7297i			1.10110i
$730$		0			0
$731$		−	19.2222i		−	0.710960i
$732$		0			0
$733$	−18.9857	+	18.9857i	−0.701252	+	0.701252i	−0.964679	−	0.263427i	$-0.915147\pi$
$733$	−18.9857	+	18.9857i	−0.701252	+	0.701252i	0.263427	+	0.964679i	$0.415147\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6.31675	−	6.31675i	0.232681	−	0.232681i
$738$		0			0
$739$		−	4.09135i		−	0.150503i	−0.997165	−	0.0752515i	$-0.976024\pi$
$739$		−	4.09135i		−	0.150503i	0.997165	−	0.0752515i	$-0.0239759\pi$
$740$		0			0
$741$		−	15.2989i		−	0.562019i
$742$		0			0
$743$	−37.7330	−	37.7330i	−1.38429	−	1.38429i	−0.836838	−	0.547451i	$-0.815598\pi$
$743$	−37.7330	−	37.7330i	−1.38429	−	1.38429i	−0.547451	−	0.836838i	$-0.684402\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	7.87968	+	7.87968i	0.288302	+	0.288302i
$748$		0			0
$749$	−5.46444	−	38.4297i	−0.199666	−	1.40419i
$750$		0			0
$751$	−21.3975			−0.780805			−0.390403	−	0.920644i	$-0.627664\pi$
$751$	−21.3975			−0.780805			−0.390403	+	0.920644i	$0.627664\pi$
$752$		0			0
$753$	−27.2635	−	27.2635i	−0.993538	−	0.993538i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−24.8160	+	24.8160i	−0.901952	+	0.901952i	−0.995605	−	0.0936529i	$-0.970146\pi$
$757$	−24.8160	+	24.8160i	−0.901952	+	0.901952i	0.0936529	+	0.995605i	$0.470146\pi$
$758$		0			0
$759$	−29.6492			−1.07620
$760$		0			0
$761$		−	20.4451i		−	0.741135i	−0.928806	−	0.370567i	$-0.879163\pi$
$761$		−	20.4451i		−	0.741135i	0.928806	−	0.370567i	$-0.120837\pi$
$762$		0			0
$763$	10.4239	+	7.82853i	0.377371	+	0.283412i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	9.07654	−	9.07654i	0.327735	−	0.327735i
$768$		0			0
$769$	6.20785			0.223861			0.111930	−	0.993716i	$-0.464297\pi$
$769$	6.20785			0.223861			0.111930	+	0.993716i	$0.464297\pi$
$770$		0			0
$771$	−4.01351			−0.144543
$772$		0			0
$773$	−12.7179	+	12.7179i	−0.457430	+	0.457430i	−0.897811	−	0.440381i	$-0.854843\pi$
$773$	−12.7179	+	12.7179i	−0.457430	+	0.457430i	0.440381	+	0.897811i	$0.354843\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	6.74503	+	5.06563i	0.241976	+	0.181728i
$778$		0			0
$779$			35.6821i			1.27844i
$780$		0			0
$781$	0.920513			0.0329385
$782$		0			0
$783$	−23.5071	+	23.5071i	−0.840076	+	0.840076i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	32.6842	+	32.6842i	1.16506	+	1.16506i	0.983352	+	0.181713i	$0.0581642\pi$
$787$	32.6842	+	32.6842i	1.16506	+	1.16506i	0.181713	+	0.983352i	$0.441836\pi$
$788$		0			0
$789$	5.49068			0.195474
$790$		0			0
$791$	−14.0753	+	2.00142i	−0.500461	+	0.0711622i
$792$		0			0
$793$	−3.92999	−	3.92999i	−0.139558	−	0.139558i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−8.76878	−	8.76878i	−0.310606	−	0.310606i	0.534538	−	0.845144i	$-0.320486\pi$
$797$	−8.76878	−	8.76878i	−0.310606	−	0.310606i	−0.845144	+	0.534538i	$0.820486\pi$
$798$		0			0
$799$		−	47.4046i		−	1.67706i
$800$		0			0
$801$		−	8.27127i		−	0.292251i
$802$		0			0
$803$	−16.6286	+	16.6286i	−0.586811	+	0.586811i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	−1.22540	+	1.22540i	−0.0431360	+	0.0431360i
$808$		0			0
$809$		−	15.9362i		−	0.560287i	−0.959958	−	0.280144i	$-0.909618\pi$
$809$		−	15.9362i		−	0.560287i	0.959958	−	0.280144i	$-0.0903821\pi$
$810$		0			0
$811$			49.6560i			1.74366i	0.489812	+	0.871828i	$0.337065\pi$
$811$			49.6560i			1.74366i	−0.489812	+	0.871828i	$0.662935\pi$
$812$		0			0
$813$	−15.3636	−	15.3636i	−0.538826	−	0.538826i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−6.98342	−	6.98342i	−0.244319	−	0.244319i
$818$		0			0
$819$	6.12166	−	0.870459i	0.213908	−	0.0304163i
$820$		0			0
$821$	−30.1755			−1.05313			−0.526566	−	0.850135i	$-0.676521\pi$
$821$	−30.1755			−1.05313			−0.526566	+	0.850135i	$0.676521\pi$
$822$		0			0
$823$	−17.2900	−	17.2900i	−0.602693	−	0.602693i	0.338333	−	0.941026i	$-0.390137\pi$
$823$	−17.2900	−	17.2900i	−0.602693	−	0.602693i	−0.941026	+	0.338333i	$0.890137\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−1.93183	+	1.93183i	−0.0671761	+	0.0671761i	−0.739897	−	0.672721i	$-0.765126\pi$
$827$	−1.93183	+	1.93183i	−0.0671761	+	0.0671761i	0.672721	+	0.739897i	$0.265126\pi$
$828$		0			0
$829$	−31.2032			−1.08373			−0.541865	−	0.840465i	$-0.682282\pi$
$829$	−31.2032			−1.08373			−0.541865	+	0.840465i	$0.682282\pi$
$830$		0			0
$831$		−	24.2024i		−	0.839573i
$832$		0			0
$833$	24.6131	−	44.7445i	0.852793	−	1.55030i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	6.25150	−	6.25150i	0.216083	−	0.216083i
$838$		0			0
$839$	7.79348			0.269061			0.134530	−	0.990909i	$-0.457047\pi$
$839$	7.79348			0.269061			0.134530	+	0.990909i	$0.457047\pi$
$840$		0			0
$841$	−5.69616			−0.196419
$842$		0			0
$843$	−21.0022	+	21.0022i	−0.723354	+	0.723354i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	8.72614	−	11.6191i	0.299834	−	0.399237i
$848$		0			0
$849$		−	11.5041i		−	0.394821i
$850$		0			0
$851$	18.6586			0.639610
$852$		0			0
$853$	−16.5954	+	16.5954i	−0.568215	+	0.568215i	−0.931628	−	0.363413i	$-0.881611\pi$
$853$	−16.5954	+	16.5954i	−0.568215	+	0.568215i	0.363413	+	0.931628i	$0.381611\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	29.2133	+	29.2133i	0.997909	+	0.997909i	0.999998	−	0.00208912i	$-0.000664987\pi$
$857$	29.2133	+	29.2133i	0.997909	+	0.997909i	−0.00208912	+	0.999998i	$0.500665\pi$
$858$		0			0
$859$	−18.3754			−0.626962			−0.313481	−	0.949594i	$-0.601495\pi$
$859$	−18.3754			−0.626962			−0.313481	+	0.949594i	$0.601495\pi$
$860$		0			0
$861$	36.6377	−	5.20964i	1.24861	−	0.177544i
$862$		0			0
$863$	31.7261	+	31.7261i	1.07997	+	1.07997i	0.996511	+	0.0834585i	$0.0265966\pi$
$863$	31.7261	+	31.7261i	1.07997	+	1.07997i	0.0834585	+	0.996511i	$0.473403\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−37.6318	−	37.6318i	−1.27804	−	1.27804i
$868$		0			0
$869$		−	11.7042i		−	0.397039i
$870$		0			0
$871$		−	10.5744i		−	0.358300i
$872$		0			0
$873$	9.97534	−	9.97534i	0.337614	−	0.337614i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	32.2606	−	32.2606i	1.08936	−	1.08936i	0.0937674	−	0.995594i	$-0.470109\pi$
$877$	32.2606	−	32.2606i	1.08936	−	1.08936i	0.995594	−	0.0937674i	$-0.0298910\pi$
$878$		0			0
$879$			2.32823i			0.0785292i
$880$		0			0
$881$		−	9.96766i		−	0.335819i	−0.985802	−	0.167909i	$-0.946298\pi$
$881$		−	9.96766i		−	0.335819i	0.985802	−	0.167909i	$-0.0537016\pi$
$882$		0			0
$883$	36.7464	+	36.7464i	1.23662	+	1.23662i	0.961376	+	0.275239i	$0.0887571\pi$
$883$	36.7464	+	36.7464i	1.23662	+	1.23662i	0.275239	+	0.961376i	$0.411243\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	9.82975	+	9.82975i	0.330051	+	0.330051i	0.852606	−	0.522555i	$-0.175021\pi$
$887$	9.82975	+	9.82975i	0.330051	+	0.330051i	−0.522555	+	0.852606i	$0.675021\pi$
$888$		0			0
$889$	0.409675	+	2.88111i	0.0137401	+	0.0966294i
$890$		0			0
$891$	−13.5379			−0.453538
$892$		0			0
$893$	−17.2221	−	17.2221i	−0.576314	−	0.576314i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−24.8167	+	24.8167i	−0.828607	+	0.828607i
$898$		0			0
$899$	9.22711			0.307741
$900$		0			0
$901$		−	40.0438i		−	1.33405i
$902$		0			0
$903$	−6.15086	+	8.19004i	−0.204688	+	0.272548i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−10.4096	+	10.4096i	−0.345646	+	0.345646i	−0.858485	−	0.512839i	$-0.828594\pi$
$907$	−10.4096	+	10.4096i	−0.345646	+	0.345646i	0.512839	+	0.858485i	$0.328594\pi$
$908$		0			0
$909$	7.07946			0.234811
$910$		0			0
$911$	16.5150			0.547167			0.273583	−	0.961848i	$-0.411791\pi$
$911$	16.5150			0.547167			0.273583	+	0.961848i	$0.411791\pi$
$912$		0			0
$913$	−21.9820	+	21.9820i	−0.727498	+	0.727498i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	23.3502	+	17.5364i	0.771092	+	0.579104i
$918$		0			0
$919$			14.9494i			0.493134i	0.969126	+	0.246567i	$0.0793026\pi$
$919$			14.9494i			0.493134i	−0.969126	+	0.246567i	$0.920697\pi$
$920$		0			0
$921$	−19.5951			−0.645680
$922$		0			0
$923$	0.770480	−	0.770480i	0.0253607	−	0.0253607i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−7.38521	−	7.38521i	−0.242562	−	0.242562i
$928$		0			0
$929$	−2.36098			−0.0774611			−0.0387306	−	0.999250i	$-0.512331\pi$
$929$	−2.36098			−0.0774611			−0.0387306	+	0.999250i	$0.512331\pi$
$930$		0			0
$931$	−7.31371	−	25.1975i	−0.239697	−	0.825815i
$932$		0			0
$933$	−15.1720	−	15.1720i	−0.496709	−	0.496709i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−2.28379	−	2.28379i	−0.0746081	−	0.0746081i	0.668818	−	0.743426i	$-0.266801\pi$
$937$	−2.28379	−	2.28379i	−0.0746081	−	0.0746081i	−0.743426	+	0.668818i	$0.766801\pi$
$938$		0			0
$939$			14.6600i			0.478410i
$940$		0			0
$941$		−	30.1034i		−	0.981344i	−0.871344	−	0.490672i	$-0.836751\pi$
$941$		−	30.1034i		−	0.981344i	0.871344	−	0.490672i	$-0.163249\pi$
$942$		0			0
$943$	57.8808	−	57.8808i	1.88486	−	1.88486i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−9.50072	+	9.50072i	−0.308732	+	0.308732i	−0.844417	−	0.535686i	$-0.820053\pi$
$947$	−9.50072	+	9.50072i	−0.308732	+	0.308732i	0.535686	+	0.844417i	$0.320053\pi$
$948$		0			0
$949$			27.8367i			0.903617i
$950$		0			0
$951$			23.3837i			0.758269i
$952$		0			0
$953$	21.9629	+	21.9629i	0.711448	+	0.711448i	0.966838	−	0.255390i	$-0.0822039\pi$
$953$	21.9629	+	21.9629i	0.711448	+	0.711448i	−0.255390	+	0.966838i	$0.582204\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−14.3620	−	14.3620i	−0.464258	−	0.464258i
$958$		0			0
$959$	−1.39751	−	9.82823i	−0.0451279	−	0.317370i
$960$		0			0
$961$	28.5461			0.920843
$962$		0			0
$963$	−8.72731	−	8.72731i	−0.281234	−	0.281234i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−14.6279	+	14.6279i	−0.470400	+	0.470400i	−0.902044	−	0.431644i	$-0.857934\pi$
$967$	−14.6279	+	14.6279i	−0.470400	+	0.470400i	0.431644	+	0.902044i	$0.357934\pi$
$968$		0			0
$969$	−40.1762			−1.29065
$970$		0			0
$971$			14.5120i			0.465712i	0.972511	+	0.232856i	$0.0748071\pi$
$971$			14.5120i			0.465712i	−0.972511	+	0.232856i	$0.925193\pi$
$972$		0			0
$973$	−11.3673	+	15.1359i	−0.364419	+	0.485233i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−3.07281	+	3.07281i	−0.0983080	+	0.0983080i	−0.754550	−	0.656242i	$-0.772145\pi$
$977$	−3.07281	+	3.07281i	−0.0983080	+	0.0983080i	0.656242	+	0.754550i	$0.272145\pi$
$978$		0			0
$979$	23.0744			0.737463
$980$		0			0
$981$	4.14509			0.132343
$982$		0			0
$983$	38.2010	−	38.2010i	1.21842	−	1.21842i	0.250238	−	0.968184i	$-0.419491\pi$
$983$	38.2010	−	38.2010i	1.21842	−	1.21842i	0.968184	−	0.250238i	$-0.0805088\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−15.1689	+	20.1977i	−0.482830	+	0.642901i
$988$		0			0
$989$			22.6560i			0.720418i
$990$		0			0
$991$	42.3300			1.34466			0.672328	−	0.740253i	$-0.265294\pi$
$991$	42.3300			1.34466			0.672328	+	0.740253i	$0.265294\pi$
$992$		0			0
$993$	34.9748	−	34.9748i	1.10989	−	1.10989i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−24.3987	−	24.3987i	−0.772713	−	0.772713i	0.205867	−	0.978580i	$-0.433999\pi$
$997$	−24.3987	−	24.3987i	−0.772713	−	0.772713i	−0.978580	+	0.205867i	$0.933999\pi$
$998$		0			0
$999$	12.2470			0.387479

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.2.x.b.993.4		24
5.2	odd	4	inner	1400.2.x.b.657.9		24
5.3	odd	4		280.2.x.a.97.4	✓	24
5.4	even	2		280.2.x.a.153.9	yes	24
7.6	odd	2	inner	1400.2.x.b.993.9		24
20.3	even	4		560.2.bj.d.97.9		24
20.19	odd	2		560.2.bj.d.433.4		24
35.13	even	4		280.2.x.a.97.9	yes	24
35.27	even	4	inner	1400.2.x.b.657.4		24
35.34	odd	2		280.2.x.a.153.4	yes	24
140.83	odd	4		560.2.bj.d.97.4		24
140.139	even	2		560.2.bj.d.433.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.x.a.97.4	✓	24	5.3	odd	4
280.2.x.a.97.9	yes	24	35.13	even	4
280.2.x.a.153.4	yes	24	35.34	odd	2
280.2.x.a.153.9	yes	24	5.4	even	2
560.2.bj.d.97.4		24	140.83	odd	4
560.2.bj.d.97.9		24	20.3	even	4
560.2.bj.d.433.4		24	20.19	odd	2
560.2.bj.d.433.9		24	140.139	even	2
1400.2.x.b.657.4		24	35.27	even	4	inner
1400.2.x.b.657.9		24	5.2	odd	4	inner
1400.2.x.b.993.4		24	1.1	even	1	trivial
1400.2.x.b.993.9		24	7.6	odd	2	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:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1400.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.03893 + 1.03893i) q^{3} +(-1.58883 + 2.11557i) q^{7} +0.841261i q^{9} +O(q^{10})\)	\(q+(-1.03893 + 1.03893i) q^{3} +(-1.58883 + 2.11557i) q^{7} +0.841261i q^{9} -2.34687 q^{11} +(-1.96436 + 1.96436i) q^{13} +(5.15858 + 5.15858i) q^{17} +3.74821 q^{19} +(-0.547244 - 3.84860i) q^{21} +(-6.08007 - 6.08007i) q^{23} +(-3.99079 - 3.99079i) q^{27} -5.89034i q^{29} +1.56648i q^{31} +(2.43823 - 2.43823i) q^{33} +(-1.53441 + 1.53441i) q^{37} -4.08166i q^{39} +9.51977i q^{41} +(-1.86313 - 1.86313i) q^{43} +(-4.59474 - 4.59474i) q^{47} +(-1.95125 - 6.72254i) q^{49} -10.7188 q^{51} +(-3.88128 - 3.88128i) q^{53} +(-3.89412 + 3.89412i) q^{57} -4.62061 q^{59} +2.00065i q^{61} +(-1.77974 - 1.33662i) q^{63} +(-2.69156 + 2.69156i) q^{67} +12.6335 q^{69} -0.392229 q^{71} +(7.08543 - 7.08543i) q^{73} +(3.72878 - 4.96497i) q^{77} +4.98717i q^{79} +5.76850 q^{81} +(9.36651 - 9.36651i) q^{83} +(6.11964 + 6.11964i) q^{87} -9.83200 q^{89} +(-1.03471 - 7.27677i) q^{91} +(-1.62746 - 1.62746i) q^{93} +(-11.8576 - 11.8576i) q^{97} -1.97433i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{7}+O(q^{10}) \) 24 * q - 4 * q^7	\( 24 q - 4 q^{7} + 8 q^{11} + 16 q^{21} + 32 q^{23} + 8 q^{37} - 16 q^{43} - 24 q^{51} + 16 q^{53} - 20 q^{63} + 32 q^{67} - 32 q^{71} + 40 q^{77} - 72 q^{81} - 64 q^{91} - 72 q^{93}+O(q^{100}) \) 24 * q - 4 * q^7 + 8 * q^11 + 16 * q^21 + 32 * q^23 + 8 * q^37 - 16 * q^43 - 24 * q^51 + 16 * q^53 - 20 * q^63 + 32 * q^67 - 32 * q^71 + 40 * q^77 - 72 * q^81 - 64 * q^91 - 72 * q^93

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