LMFDB - Embedded newform 980.3.l.c.393.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [980,3,Mod(197,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.197"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 980 = 2^{2} \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	980.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,8,0,-20] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$26.7030659073$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.1218533392384.32
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 78x^{4} + 121 $ x^8 + 78*x^4 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			393.2
Root			$2.09065 + 2.09065i$ of defining polynomial
Character	$\chi$	$=$	980.393
Dual form			980.3.l.c.197.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.21982 + 1.21982i) q^{3} +(-4.10078 - 2.86071i) q^{5} -6.02406i q^{9} +5.08021 q^{11} +(-14.6059 - 14.6059i) q^{13} +(-1.51267 - 8.49178i) q^{15} +(-16.7461 + 16.7461i) q^{17} +31.6925i q^{19} +(4.92296 + 4.92296i) q^{23} +(8.63273 + 23.4622i) q^{25} +(18.3267 - 18.3267i) q^{27} +21.9203i q^{29} +32.5294 q^{31} +(6.19696 + 6.19696i) q^{33} +(-45.7885 + 45.7885i) q^{37} -35.6331i q^{39} +36.3364 q^{41} +(23.2691 + 23.2691i) q^{43} +(-17.2331 + 24.7033i) q^{45} +(17.4139 - 17.4139i) q^{47} -40.8546 q^{51} +(-23.6722 - 23.6722i) q^{53} +(-20.8328 - 14.5330i) q^{55} +(-38.6593 + 38.6593i) q^{57} +104.467i q^{59} -57.0140 q^{61} +(18.1123 + 101.678i) q^{65} +(12.2596 - 12.2596i) q^{67} +12.0103i q^{69} -88.5489 q^{71} +(-39.7353 - 39.7353i) q^{73} +(-18.0894 + 39.1502i) q^{75} +134.383i q^{79} -9.50581 q^{81} +(27.7461 + 27.7461i) q^{83} +(116.578 - 20.7664i) q^{85} +(-26.7389 + 26.7389i) q^{87} +116.214i q^{89} +(39.6801 + 39.6801i) q^{93} +(90.6629 - 129.964i) q^{95} +(56.9445 - 56.9445i) q^{97} -30.6035i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} - 20 q^{5} + 32 q^{11} + 16 q^{13} + 56 q^{15} + 16 q^{17} - 24 q^{23} + 32 q^{25} + 8 q^{27} + 32 q^{31} + 80 q^{33} - 208 q^{37} - 48 q^{43} + 92 q^{45} - 176 q^{47} - 176 q^{51} + 96 q^{53}+ \cdots + 400 q^{97}+O(q^{100}) $ 8 * q + 8 * q^3 - 20 * q^5 + 32 * q^11 + 16 * q^13 + 56 * q^15 + 16 * q^17 - 24 * q^23 + 32 * q^25 + 8 * q^27 + 32 * q^31 + 80 * q^33 - 208 * q^37 - 48 * q^43 + 92 * q^45 - 176 * q^47 - 176 * q^51 + 96 * q^53 + 72 * q^55 + 24 * q^57 - 72 * q^61 - 344 * q^65 + 80 * q^67 - 400 * q^71 - 432 * q^73 - 72 * q^75 + 152 * q^81 + 16 * q^83 + 56 * q^85 - 704 * q^87 + 272 * q^93 + 72 * q^95 + 400 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/980\mathbb{Z}\right)^\times$.

$n$	$101$	$197$	$491$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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
$3$	1.21982	+	1.21982i	0.406608	+	0.406608i	0.880554	−	0.473946i	$-0.157171\pi$
$3$	1.21982	+	1.21982i	0.406608	+	0.406608i	−0.473946	+	0.880554i	$0.657171\pi$
$4$		0			0
$5$	−4.10078	−	2.86071i	−0.820155	−	0.572141i
$5$	−4.10078	−	2.86071i	−0.820155	−	0.572141i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$		−	6.02406i		−	0.669340i
$10$		0			0
$11$	5.08021			0.461837			0.230919	−	0.972973i	$-0.425827\pi$
$11$	5.08021			0.461837			0.230919	+	0.972973i	$0.425827\pi$
$12$		0			0
$13$	−14.6059	−	14.6059i	−1.12353	−	1.12353i	−0.991207	−	0.132320i	$-0.957757\pi$
$13$	−14.6059	−	14.6059i	−1.12353	−	1.12353i	−0.132320	−	0.991207i	$-0.542243\pi$
$14$		0			0
$15$	−1.51267	−	8.49178i	−0.100845	−	0.566119i
$16$		0			0
$17$	−16.7461	+	16.7461i	−0.985065	+	0.985065i	−0.999890	−	0.0148249i	$-0.995281\pi$
$17$	−16.7461	+	16.7461i	−0.985065	+	0.985065i	0.0148249	+	0.999890i	$0.495281\pi$
$18$		0			0
$19$			31.6925i			1.66803i	0.551745	+	0.834013i	$0.313962\pi$
$19$			31.6925i			1.66803i	−0.551745	+	0.834013i	$0.686038\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.92296	+	4.92296i	0.214042	+	0.214042i	0.805982	−	0.591940i	$-0.201638\pi$
$23$	4.92296	+	4.92296i	0.214042	+	0.214042i	−0.591940	+	0.805982i	$0.701638\pi$
$24$		0			0
$25$	8.63273	+	23.4622i	0.345309	+	0.938489i
$26$		0			0
$27$	18.3267	−	18.3267i	0.678767	−	0.678767i
$28$		0			0
$29$			21.9203i			0.755872i	0.925832	+	0.377936i	$0.123366\pi$
$29$			21.9203i			0.755872i	−0.925832	+	0.377936i	$0.876634\pi$
$30$		0			0
$31$	32.5294			1.04933			0.524667	−	0.851307i	$-0.324190\pi$
$31$	32.5294			1.04933			0.524667	+	0.851307i	$0.324190\pi$
$32$		0			0
$33$	6.19696	+	6.19696i	0.187787	+	0.187787i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−45.7885	+	45.7885i	−1.23753	+	1.23753i	−0.276518	+	0.961009i	$0.589181\pi$
$37$	−45.7885	+	45.7885i	−1.23753	+	1.23753i	−0.961009	+	0.276518i	$0.910819\pi$
$38$		0			0
$39$		−	35.6331i		−	0.913670i
$40$		0			0
$41$	36.3364			0.886253			0.443126	−	0.896459i	$-0.353869\pi$
$41$	36.3364			0.886253			0.443126	+	0.896459i	$0.353869\pi$
$42$		0			0
$43$	23.2691	+	23.2691i	0.541143	+	0.541143i	0.923864	−	0.382721i	$-0.125013\pi$
$43$	23.2691	+	23.2691i	0.541143	+	0.541143i	−0.382721	+	0.923864i	$0.625013\pi$
$44$		0			0
$45$	−17.2331	+	24.7033i	−0.382957	+	0.548963i
$46$		0			0
$47$	17.4139	−	17.4139i	0.370509	−	0.370509i	−0.497154	−	0.867662i	$-0.665622\pi$
$47$	17.4139	−	17.4139i	0.370509	−	0.370509i	0.867662	+	0.497154i	$0.165622\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	−40.8546			−0.801071
$52$		0			0
$53$	−23.6722	−	23.6722i	−0.446646	−	0.446646i	0.447592	−	0.894238i	$-0.352282\pi$
$53$	−23.6722	−	23.6722i	−0.446646	−	0.446646i	−0.894238	+	0.447592i	$0.852282\pi$
$54$		0			0
$55$	−20.8328	−	14.5330i	−0.378778	−	0.264236i
$56$		0			0
$57$	−38.6593	+	38.6593i	−0.678233	+	0.678233i
$58$		0			0
$59$			104.467i			1.77063i	0.464991	+	0.885315i	$0.346058\pi$
$59$			104.467i			1.77063i	−0.464991	+	0.885315i	$0.653942\pi$
$60$		0			0
$61$	−57.0140			−0.934656			−0.467328	−	0.884084i	$-0.654783\pi$
$61$	−57.0140			−0.934656			−0.467328	+	0.884084i	$0.654783\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	18.1123	+	101.678i	0.278651	+	1.56428i
$66$		0			0
$67$	12.2596	−	12.2596i	0.182979	−	0.182979i	−0.609673	−	0.792653i	$-0.708699\pi$
$67$	12.2596	−	12.2596i	0.182979	−	0.182979i	0.792653	+	0.609673i	$0.208699\pi$
$68$		0			0
$69$			12.0103i			0.174062i
$70$		0			0
$71$	−88.5489			−1.24717			−0.623584	−	0.781757i	$-0.714324\pi$
$71$	−88.5489			−1.24717			−0.623584	+	0.781757i	$0.714324\pi$
$72$		0			0
$73$	−39.7353	−	39.7353i	−0.544319	−	0.544319i	0.380473	−	0.924792i	$-0.375761\pi$
$73$	−39.7353	−	39.7353i	−0.544319	−	0.544319i	−0.924792	+	0.380473i	$0.875761\pi$
$74$		0			0
$75$	−18.0894	+	39.1502i	−0.241192	+	0.522003i
$76$		0			0
$77$		0			0
$78$		0			0
$79$			134.383i			1.70104i	0.525939	+	0.850522i	$0.323714\pi$
$79$			134.383i			1.70104i	−0.525939	+	0.850522i	$0.676286\pi$
$80$		0			0
$81$	−9.50581			−0.117356
$82$		0			0
$83$	27.7461	+	27.7461i	0.334290	+	0.334290i	0.854213	−	0.519923i	$-0.174039\pi$
$83$	27.7461	+	27.7461i	0.334290	+	0.334290i	−0.519923	+	0.854213i	$0.674039\pi$
$84$		0			0
$85$	116.578	−	20.7664i	1.37150	−	0.244310i
$86$		0			0
$87$	−26.7389	+	26.7389i	−0.307344	+	0.307344i
$88$		0			0
$89$			116.214i			1.30577i	0.757457	+	0.652885i	$0.226442\pi$
$89$			116.214i			1.30577i	−0.757457	+	0.652885i	$0.773558\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	39.6801	+	39.6801i	0.426668	+	0.426668i
$94$		0			0
$95$	90.6629	−	129.964i	0.954346	−	1.36804i
$96$		0			0
$97$	56.9445	−	56.9445i	0.587056	−	0.587056i	−0.349777	−	0.936833i	$-0.613743\pi$
$97$	56.9445	−	56.9445i	0.587056	−	0.587056i	0.936833	+	0.349777i	$0.113743\pi$
$98$		0			0
$99$		−	30.6035i		−	0.309126i
$100$		0			0
$101$	−55.5034			−0.549538			−0.274769	−	0.961510i	$-0.588601\pi$
$101$	−55.5034			−0.549538			−0.274769	+	0.961510i	$0.588601\pi$
$102$		0			0
$103$	−27.8918	−	27.8918i	−0.270794	−	0.270794i	0.558626	−	0.829420i	$-0.311329\pi$
$103$	−27.8918	−	27.8918i	−0.270794	−	0.270794i	−0.829420	+	0.558626i	$0.811329\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−19.7040	+	19.7040i	−0.184150	+	0.184150i	−0.793161	−	0.609012i	$-0.791566\pi$
$107$	−19.7040	+	19.7040i	−0.184150	+	0.184150i	0.609012	+	0.793161i	$0.291566\pi$
$108$		0			0
$109$		−	27.9789i		−	0.256687i	−0.991730	−	0.128343i	$-0.959034\pi$
$109$		−	27.9789i		−	0.256687i	0.991730	−	0.128343i	$-0.0409660\pi$
$110$		0			0
$111$	−111.708			−1.00638
$112$		0			0
$113$	−20.1003	−	20.1003i	−0.177879	−	0.177879i	0.612552	−	0.790431i	$-0.290143\pi$
$113$	−20.1003	−	20.1003i	−0.177879	−	0.177879i	−0.790431	+	0.612552i	$0.790143\pi$
$114$		0			0
$115$	−6.10482	−	34.2711i	−0.0530854	−	0.298010i
$116$		0			0
$117$	−87.9865	+	87.9865i	−0.752022	+	0.752022i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−95.1915			−0.786706
$122$		0			0
$123$	44.3240	+	44.3240i	0.360357	+	0.360357i
$124$		0			0
$125$	31.7176	−	120.909i	0.253741	−	0.967272i
$126$		0			0
$127$	−24.8723	+	24.8723i	−0.195845	+	0.195845i	−0.798216	−	0.602371i	$-0.794223\pi$
$127$	−24.8723	+	24.8723i	−0.195845	+	0.195845i	0.602371	+	0.798216i	$0.294223\pi$
$128$		0			0
$129$			56.7685i			0.440066i
$130$		0			0
$131$	40.7823			0.311315			0.155658	−	0.987811i	$-0.450250\pi$
$131$	40.7823			0.311315			0.155658	+	0.987811i	$0.450250\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−127.581	+	22.7264i	−0.945045	+	0.168344i
$136$		0			0
$137$	−11.1477	+	11.1477i	−0.0813703	+	0.0813703i	−0.746620	−	0.665250i	$-0.768325\pi$
$137$	−11.1477	+	11.1477i	−0.0813703	+	0.0813703i	0.665250	+	0.746620i	$0.268325\pi$
$138$		0			0
$139$		−	155.615i		−	1.11953i	−0.828650	−	0.559767i	$-0.810891\pi$
$139$		−	155.615i		−	1.11953i	0.828650	−	0.559767i	$-0.189109\pi$
$140$		0			0
$141$	42.4838			0.301303
$142$		0			0
$143$	−74.2008	−	74.2008i	−0.518887	−	0.518887i
$144$		0			0
$145$	62.7075	−	89.8902i	0.432465	−	0.619932i
$146$		0			0
$147$		0			0
$148$		0			0
$149$		−	139.674i		−	0.937411i	−0.883355	−	0.468705i	$-0.844721\pi$
$149$		−	139.674i		−	0.937411i	0.883355	−	0.468705i	$-0.155279\pi$
$150$		0			0
$151$	−136.288			−0.902572			−0.451286	−	0.892379i	$-0.649035\pi$
$151$	−136.288			−0.902572			−0.451286	+	0.892379i	$0.649035\pi$
$152$		0			0
$153$	100.880	+	100.880i	0.659343	+	0.659343i
$154$		0			0
$155$	−133.396	−	93.0569i	−0.860617	−	0.600367i
$156$		0			0
$157$	−119.702	+	119.702i	−0.762433	+	0.762433i	−0.976762	−	0.214329i	$-0.931244\pi$
$157$	−119.702	+	119.702i	−0.762433	+	0.762433i	0.214329	+	0.976762i	$0.431244\pi$
$158$		0			0
$159$		−	57.7519i		−	0.363220i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	137.477	+	137.477i	0.843418	+	0.843418i	0.989302	−	0.145884i	$-0.0466025\pi$
$163$	137.477	+	137.477i	0.843418	+	0.843418i	−0.145884	+	0.989302i	$0.546603\pi$
$164$		0			0
$165$	−7.68467	−	43.1400i	−0.0465738	−	0.261455i
$166$		0			0
$167$	97.0825	−	97.0825i	0.581332	−	0.581332i	−0.353937	−	0.935269i	$-0.615157\pi$
$167$	97.0825	−	97.0825i	0.581332	−	0.581332i	0.935269	+	0.353937i	$0.115157\pi$
$168$		0			0
$169$			257.662i			1.52463i
$170$		0			0
$171$	190.917			1.11648
$172$		0			0
$173$	130.770	+	130.770i	0.755897	+	0.755897i	0.975573	−	0.219676i	$-0.0705000\pi$
$173$	130.770	+	130.770i	0.755897	+	0.755897i	−0.219676	+	0.975573i	$0.570500\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−127.432	+	127.432i	−0.719953	+	0.719953i
$178$		0			0
$179$			293.263i			1.63834i	0.573552	+	0.819169i	$0.305565\pi$
$179$			293.263i			1.63834i	−0.573552	+	0.819169i	$0.694435\pi$
$180$		0			0
$181$	−59.6174			−0.329378			−0.164689	−	0.986346i	$-0.552662\pi$
$181$	−59.6174			−0.329378			−0.164689	+	0.986346i	$0.552662\pi$
$182$		0			0
$183$	−69.5470	−	69.5470i	−0.380038	−	0.380038i
$184$		0			0
$185$	318.756	−	56.7810i	1.72300	−	0.306924i
$186$		0			0
$187$	−85.0737	+	85.0737i	−0.454940	+	0.454940i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	217.142			1.13687			0.568435	−	0.822728i	$-0.307549\pi$
$191$	217.142			1.13687			0.568435	+	0.822728i	$0.307549\pi$
$192$		0			0
$193$	−129.689	−	129.689i	−0.671965	−	0.671965i	0.286204	−	0.958169i	$-0.407606\pi$
$193$	−129.689	−	129.689i	−0.671965	−	0.671965i	−0.958169	+	0.286204i	$0.907606\pi$
$194$		0			0
$195$	−101.936	+	146.124i	−0.522748	+	0.749352i
$196$		0			0
$197$	164.544	−	164.544i	0.835248	−	0.835248i	−0.152982	−	0.988229i	$-0.548887\pi$
$197$	164.544	−	164.544i	0.835248	−	0.835248i	0.988229	+	0.152982i	$0.0488875\pi$
$198$		0			0
$199$			27.5216i			0.138300i	0.997606	+	0.0691498i	$0.0220286\pi$
$199$			27.5216i			0.138300i	−0.997606	+	0.0691498i	$0.977971\pi$
$200$		0			0
$201$	29.9092			0.148802
$202$		0			0
$203$		0			0
$204$		0			0
$205$	−149.007	−	103.948i	−0.726865	−	0.507062i
$206$		0			0
$207$	29.6562	−	29.6562i	0.143267	−	0.143267i
$208$		0			0
$209$			161.004i			0.770356i
$210$		0			0
$211$	−107.167			−0.507903			−0.253951	−	0.967217i	$-0.581730\pi$
$211$	−107.167			−0.507903			−0.253951	+	0.967217i	$0.581730\pi$
$212$		0			0
$213$	−108.014	−	108.014i	−0.507108	−	0.507108i
$214$		0			0
$215$	−28.8554	−	161.988i	−0.134211	−	0.753431i
$216$		0			0
$217$		0			0
$218$		0			0
$219$		−	96.9402i		−	0.442649i
$220$		0			0
$221$	489.182			2.21350
$222$		0			0
$223$	−12.6151	−	12.6151i	−0.0565701	−	0.0565701i	0.678256	−	0.734826i	$-0.262736\pi$
$223$	−12.6151	−	12.6151i	−0.0565701	−	0.0565701i	−0.734826	+	0.678256i	$0.762736\pi$
$224$		0			0
$225$	141.338	−	52.0041i	0.628168	−	0.231129i
$226$		0			0
$227$	−170.439	+	170.439i	−0.750834	+	0.750834i	−0.974635	−	0.223801i	$-0.928153\pi$
$227$	−170.439	+	170.439i	−0.750834	+	0.750834i	0.223801	+	0.974635i	$0.428153\pi$
$228$		0			0
$229$		−	3.22979i		−	0.0141039i	−0.999975	−	0.00705195i	$-0.997755\pi$
$229$		−	3.22979i		−	0.0141039i	0.999975	−	0.00705195i	$-0.00224473\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−135.391	−	135.391i	−0.581077	−	0.581077i	0.354122	−	0.935199i	$-0.384780\pi$
$233$	−135.391	−	135.391i	−0.581077	−	0.581077i	−0.935199	+	0.354122i	$0.884780\pi$
$234$		0			0
$235$	−121.227	+	21.5945i	−0.515858	+	0.0918914i
$236$		0			0
$237$	−163.923	+	163.923i	−0.691658	+	0.691658i
$238$		0			0
$239$			380.792i			1.59327i	0.604460	+	0.796636i	$0.293389\pi$
$239$			380.792i			1.59327i	−0.604460	+	0.796636i	$0.706611\pi$
$240$		0			0
$241$	−10.8181			−0.0448883			−0.0224441	−	0.999748i	$-0.507145\pi$
$241$	−10.8181			−0.0448883			−0.0224441	+	0.999748i	$0.507145\pi$
$242$		0			0
$243$	−176.536	−	176.536i	−0.726485	−	0.726485i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	462.896	−	462.896i	1.87407	−	1.87407i
$248$		0			0
$249$			67.6906i			0.271850i
$250$		0			0
$251$	−25.0435			−0.0997747			−0.0498874	−	0.998755i	$-0.515886\pi$
$251$	−25.0435			−0.0997747			−0.0498874	+	0.998755i	$0.515886\pi$
$252$		0			0
$253$	25.0097	+	25.0097i	0.0988525	+	0.0988525i
$254$		0			0
$255$	167.536	+	116.873i	0.657002	+	0.458325i
$256$		0			0
$257$	178.978	−	178.978i	0.696412	−	0.696412i	−0.267223	−	0.963635i	$-0.586106\pi$
$257$	178.978	−	178.978i	0.696412	−	0.696412i	0.963635	+	0.267223i	$0.0861059\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	132.049			0.505935
$262$		0			0
$263$	−278.905	−	278.905i	−1.06047	−	1.06047i	−0.998050	−	0.0624240i	$-0.980117\pi$
$263$	−278.905	−	278.905i	−1.06047	−	1.06047i	−0.0624240	−	0.998050i	$-0.519883\pi$
$264$		0			0
$265$	29.3553	+	164.794i	0.110775	+	0.621864i
$266$		0			0
$267$	−141.760	+	141.760i	−0.530937	+	0.530937i
$268$		0			0
$269$		−	19.1253i		−	0.0710976i	−0.999368	−	0.0355488i	$-0.988682\pi$
$269$		−	19.1253i		−	0.0710976i	0.999368	−	0.0355488i	$-0.0113179\pi$
$270$		0			0
$271$	−208.660			−0.769964			−0.384982	−	0.922924i	$-0.625792\pi$
$271$	−208.660			−0.769964			−0.384982	+	0.922924i	$0.625792\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	43.8561	+	119.193i	0.159477	+	0.433429i
$276$		0			0
$277$	−278.584	+	278.584i	−1.00572	+	1.00572i	−0.00573597	+	0.999984i	$0.501826\pi$
$277$	−278.584	+	278.584i	−1.00572	+	1.00572i	−0.999984	+	0.00573597i	$0.998174\pi$
$278$		0			0
$279$		−	195.959i		−	0.702362i
$280$		0			0
$281$	537.591			1.91314			0.956568	−	0.291509i	$-0.0941574\pi$
$281$	537.591			1.91314			0.956568	+	0.291509i	$0.0941574\pi$
$282$		0			0
$283$	−283.002	−	283.002i	−1.00001	−	1.00001i	−1.00000		6.62573e-6i	$-0.999998\pi$
$283$	−283.002	−	283.002i	−1.00001	−	1.00001i	−6.62573e−6	−	1.00000i	$-0.500002\pi$
$284$		0			0
$285$	269.126	−	47.9402i	0.944301	−	0.168211i
$286$		0			0
$287$		0			0
$288$		0			0
$289$		−	271.864i		−	0.940707i
$290$		0			0
$291$	138.924			0.477404
$292$		0			0
$293$	233.614	+	233.614i	0.797319	+	0.797319i	0.982672	−	0.185353i	$-0.0593430\pi$
$293$	233.614	+	233.614i	0.797319	+	0.797319i	−0.185353	+	0.982672i	$0.559343\pi$
$294$		0			0
$295$	298.850	−	428.397i	1.01305	−	1.45219i
$296$		0			0
$297$	93.1035	−	93.1035i	0.313480	−	0.313480i
$298$		0			0
$299$		−	143.808i		−	0.480964i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−67.7044	−	67.7044i	−0.223447	−	0.223447i
$304$		0			0
$305$	233.802	+	163.100i	0.766563	+	0.534755i
$306$		0			0
$307$	−265.195	+	265.195i	−0.863827	+	0.863827i	−0.991780	−	0.127954i	$-0.959159\pi$
$307$	−265.195	+	265.195i	−0.863827	+	0.863827i	0.127954	+	0.991780i	$0.459159\pi$
$308$		0			0
$309$		−	68.0461i		−	0.220214i
$310$		0			0
$311$	510.439			1.64128			0.820642	−	0.571442i	$-0.193616\pi$
$311$	510.439			1.64128			0.820642	+	0.571442i	$0.193616\pi$
$312$		0			0
$313$	117.747	+	117.747i	0.376188	+	0.376188i	0.869725	−	0.493537i	$-0.164296\pi$
$313$	117.747	+	117.747i	0.376188	+	0.376188i	−0.493537	+	0.869725i	$0.664296\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	310.879	−	310.879i	0.980689	−	0.980689i	−0.0191277	−	0.999817i	$-0.506089\pi$
$317$	310.879	−	310.879i	0.980689	−	0.980689i	0.999817	+	0.0191277i	$0.00608892\pi$
$318$		0			0
$319$			111.360i			0.349090i
$320$		0			0
$321$	−48.0708			−0.149753
$322$		0			0
$323$	−530.726	−	530.726i	−1.64311	−	1.64311i
$324$		0			0
$325$	216.597	−	468.774i	0.666453	−	1.44238i
$326$		0			0
$327$	34.1293	−	34.1293i	0.104371	−	0.104371i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−350.310			−1.05834			−0.529169	−	0.848516i	$-0.677496\pi$
$331$	−350.310			−1.05834			−0.529169	+	0.848516i	$0.677496\pi$
$332$		0			0
$333$	275.833	+	275.833i	0.828326	+	0.828326i
$334$		0			0
$335$	−85.3451	+	15.2028i	−0.254762	+	0.0453815i
$336$		0			0
$337$	−97.4127	+	97.4127i	−0.289058	+	0.289058i	−0.836708	−	0.547650i	$-0.815523\pi$
$337$	−97.4127	+	97.4127i	−0.289058	+	0.289058i	0.547650	+	0.836708i	$0.315523\pi$
$338$		0			0
$339$		−	49.0377i		−	0.144654i
$340$		0			0
$341$	165.256			0.484622
$342$		0			0
$343$		0			0
$344$		0			0
$345$	34.3579	−	49.2515i	0.0995882	−	0.142758i
$346$		0			0
$347$	−232.771	+	232.771i	−0.670810	+	0.670810i	−0.957903	−	0.287093i	$-0.907311\pi$
$347$	−232.771	+	232.771i	−0.670810	+	0.670810i	0.287093	+	0.957903i	$0.407311\pi$
$348$		0			0
$349$		−	318.627i		−	0.912971i	−0.889731	−	0.456485i	$-0.849108\pi$
$349$		−	318.627i		−	0.912971i	0.889731	−	0.456485i	$-0.150892\pi$
$350$		0			0
$351$	−535.354			−1.52523
$352$		0			0
$353$	−489.810	−	489.810i	−1.38756	−	1.38756i	−0.830407	−	0.557157i	$-0.811892\pi$
$353$	−489.810	−	489.810i	−1.38756	−	1.38756i	−0.557157	−	0.830407i	$-0.688108\pi$
$354$		0			0
$355$	363.119	+	253.312i	1.02287	+	0.713555i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	388.155i		−	1.08121i	−0.841276	−	0.540606i	$-0.818195\pi$
$359$		−	388.155i		−	1.08121i	0.841276	−	0.540606i	$-0.181805\pi$
$360$		0			0
$361$	−643.414			−1.78231
$362$		0			0
$363$	−116.117	−	116.117i	−0.319881	−	0.319881i
$364$		0			0
$365$	49.2746	+	276.617i	0.134999	+	0.757854i
$366$		0			0
$367$	63.7979	−	63.7979i	0.173836	−	0.173836i	−0.614826	−	0.788663i	$-0.710774\pi$
$367$	63.7979	−	63.7979i	0.173836	−	0.173836i	0.788663	+	0.614826i	$0.210774\pi$
$368$		0			0
$369$		−	218.892i		−	0.593204i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−10.1310	−	10.1310i	−0.0271608	−	0.0271608i	0.693396	−	0.720557i	$-0.256114\pi$
$373$	−10.1310	−	10.1310i	−0.0271608	−	0.0271608i	−0.720557	+	0.693396i	$0.756114\pi$
$374$		0			0
$375$	186.178	−	108.798i	0.496474	−	0.290128i
$376$		0			0
$377$	320.165	−	320.165i	0.849243	−	0.849243i
$378$		0			0
$379$		−	630.917i		−	1.66469i	−0.554259	−	0.832344i	$-0.686998\pi$
$379$		−	630.917i		−	1.66469i	0.554259	−	0.832344i	$-0.313002\pi$
$380$		0			0
$381$	−60.6796			−0.159264
$382$		0			0
$383$	−452.761	−	452.761i	−1.18214	−	1.18214i	−0.979188	−	0.202954i	$-0.934946\pi$
$383$	−452.761	−	452.761i	−1.18214	−	1.18214i	−0.202954	−	0.979188i	$-0.565054\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	140.175	−	140.175i	0.362208	−	0.362208i
$388$		0			0
$389$			123.424i			0.317284i	0.987336	+	0.158642i	$0.0507116\pi$
$389$			123.424i			0.317284i	−0.987336	+	0.158642i	$0.949288\pi$
$390$		0			0
$391$	−164.881			−0.421690
$392$		0			0
$393$	49.7472	+	49.7472i	0.126583	+	0.126583i
$394$		0			0
$395$	384.429	−	551.073i	0.973237	−	1.39512i
$396$		0			0
$397$	218.938	−	218.938i	0.551481	−	0.551481i	−0.375387	−	0.926868i	$-0.622490\pi$
$397$	218.938	−	218.938i	0.551481	−	0.551481i	0.926868	+	0.375387i	$0.122490\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	192.905			0.481059			0.240530	−	0.970642i	$-0.422679\pi$
$401$	192.905			0.481059			0.240530	+	0.970642i	$0.422679\pi$
$402$		0			0
$403$	−475.119	−	475.119i	−1.17896	−	1.17896i
$404$		0			0
$405$	38.9812	+	27.1933i	0.0962499	+	0.0671440i
$406$		0			0
$407$	−232.615	+	232.615i	−0.571536	+	0.571536i
$408$		0			0
$409$			558.827i			1.36632i	0.730267	+	0.683162i	$0.239396\pi$
$409$			558.827i			1.36632i	−0.730267	+	0.683162i	$0.760604\pi$
$410$		0			0
$411$	−27.1965			−0.0661716
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−34.4071	−	193.154i	−0.0829086	−	0.465430i
$416$		0			0
$417$	189.823	−	189.823i	0.455211	−	0.455211i
$418$		0			0
$419$			705.379i			1.68348i	0.539881	+	0.841741i	$0.318469\pi$
$419$			705.379i			1.68348i	−0.539881	+	0.841741i	$0.681531\pi$
$420$		0			0
$421$	626.873			1.48901			0.744505	−	0.667617i	$-0.232686\pi$
$421$	626.873			1.48901			0.744505	+	0.667617i	$0.232686\pi$
$422$		0			0
$423$	−104.902	−	104.902i	−0.247996	−	0.247996i
$424$		0			0
$425$	−537.466	−	248.336i	−1.26462	−	0.584321i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		−	181.024i		−	0.421967i
$430$		0			0
$431$	72.0558			0.167183			0.0835914	−	0.996500i	$-0.473361\pi$
$431$	72.0558			0.167183			0.0835914	+	0.996500i	$0.473361\pi$
$432$		0			0
$433$	256.051	+	256.051i	0.591341	+	0.591341i	0.937994	−	0.346653i	$-0.112682\pi$
$433$	256.051	+	256.051i	0.591341	+	0.591341i	−0.346653	+	0.937994i	$0.612682\pi$
$434$		0			0
$435$	186.142	−	33.1581i	0.427913	−	0.0762256i
$436$		0			0
$437$	−156.021	+	156.021i	−0.357027	+	0.357027i
$438$		0			0
$439$			281.392i			0.640984i	0.947251	+	0.320492i	$0.103848\pi$
$439$			281.392i			0.640984i	−0.947251	+	0.320492i	$0.896152\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	585.310	+	585.310i	1.32124	+	1.32124i	0.912773	+	0.408468i	$0.133937\pi$
$443$	585.310	+	585.310i	1.32124	+	1.32124i	0.408468	+	0.912773i	$0.366063\pi$
$444$		0			0
$445$	332.453	−	476.566i	0.747085	−	1.07093i
$446$		0			0
$447$	170.378	−	170.378i	0.381159	−	0.381159i
$448$		0			0
$449$			99.5968i			0.221819i	0.993831	+	0.110910i	$0.0353764\pi$
$449$			99.5968i			0.221819i	−0.993831	+	0.110910i	$0.964624\pi$
$450$		0			0
$451$	184.596			0.409305
$452$		0			0
$453$	−166.248	−	166.248i	−0.366993	−	0.366993i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−4.95652	+	4.95652i	−0.0108458	+	0.0108458i	−0.712509	−	0.701663i	$-0.752441\pi$
$457$	−4.95652	+	4.95652i	−0.0108458	+	0.0108458i	0.701663	+	0.712509i	$0.252441\pi$
$458$		0			0
$459$			613.802i			1.33726i
$460$		0			0
$461$	−205.805			−0.446432			−0.223216	−	0.974769i	$-0.571656\pi$
$461$	−205.805			−0.446432			−0.223216	+	0.974769i	$0.571656\pi$
$462$		0			0
$463$	−95.3578	−	95.3578i	−0.205956	−	0.205956i	0.596590	−	0.802546i	$-0.296522\pi$
$463$	−95.3578	−	95.3578i	−0.205956	−	0.205956i	−0.802546	+	0.596590i	$0.796522\pi$
$464$		0			0
$465$	−49.2062	−	276.232i	−0.105820	−	0.594048i
$466$		0			0
$467$	−241.992	+	241.992i	−0.518184	+	0.518184i	−0.917022	−	0.398838i	$-0.869414\pi$
$467$	−241.992	+	241.992i	−0.518184	+	0.518184i	0.398838	+	0.917022i	$0.369414\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−292.031			−0.620023
$472$		0			0
$473$	118.212	+	118.212i	0.249920	+	0.249920i
$474$		0			0
$475$	−743.576	+	273.593i	−1.56542	+	0.575985i
$476$		0			0
$477$	−142.603	+	142.603i	−0.298958	+	0.298958i
$478$		0			0
$479$			676.492i			1.41230i	0.708062	+	0.706150i	$0.249570\pi$
$479$			676.492i			1.41230i	−0.708062	+	0.706150i	$0.750430\pi$
$480$		0			0
$481$	1337.56			2.78079
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−396.418	+	70.6152i	−0.817356	+	0.145598i
$486$		0			0
$487$	221.449	−	221.449i	0.454720	−	0.454720i	−0.442197	−	0.896918i	$-0.645801\pi$
$487$	221.449	−	221.449i	0.454720	−	0.454720i	0.896918	+	0.442197i	$0.145801\pi$
$488$		0			0
$489$			335.396i			0.685881i
$490$		0			0
$491$	753.534			1.53469			0.767346	−	0.641233i	$-0.221577\pi$
$491$	753.534			1.53469			0.767346	+	0.641233i	$0.221577\pi$
$492$		0			0
$493$	−367.080	−	367.080i	−0.744583	−	0.744583i
$494$		0			0
$495$	−87.5475	+	125.498i	−0.176864	+	0.253531i
$496$		0			0
$497$		0			0
$498$		0			0
$499$		−	152.060i		−	0.304729i	−0.988324	−	0.152364i	$-0.951311\pi$
$499$		−	152.060i		−	0.304729i	0.988324	−	0.152364i	$-0.0486887\pi$
$500$		0			0
$501$	236.847			0.472749
$502$		0			0
$503$	−52.9338	−	52.9338i	−0.105236	−	0.105236i	0.652528	−	0.757764i	$-0.273708\pi$
$503$	−52.9338	−	52.9338i	−0.105236	−	0.105236i	−0.757764	+	0.652528i	$0.773708\pi$
$504$		0			0
$505$	227.607	+	158.779i	0.450707	+	0.314413i
$506$		0			0
$507$	−314.302	+	314.302i	−0.619926	+	0.619926i
$508$		0			0
$509$			601.859i			1.18244i	0.806512	+	0.591218i	$0.201353\pi$
$509$			601.859i			1.18244i	−0.806512	+	0.591218i	$0.798647\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	580.819	+	580.819i	1.13220	+	1.13220i
$514$		0			0
$515$	34.5878	+	194.168i	0.0671607	+	0.377025i
$516$		0			0
$517$	88.4663	−	88.4663i	0.171115	−	0.171115i
$518$		0			0
$519$			319.033i			0.614707i
$520$		0			0
$521$	−164.616			−0.315962			−0.157981	−	0.987442i	$-0.550498\pi$
$521$	−164.616			−0.315962			−0.157981	+	0.987442i	$0.550498\pi$
$522$		0			0
$523$	−232.695	−	232.695i	−0.444923	−	0.444923i	0.448740	−	0.893663i	$-0.351873\pi$
$523$	−232.695	−	232.695i	−0.444923	−	0.444923i	−0.893663	+	0.448740i	$0.851873\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−544.740	+	544.740i	−1.03366	+	1.03366i
$528$		0			0
$529$		−	480.529i		−	0.908372i
$530$		0			0
$531$	629.317			1.18515
$532$		0			0
$533$	−530.724	−	530.724i	−0.995729	−	0.995729i
$534$		0			0
$535$	137.169	−	24.4344i	0.256391	−	0.0456717i
$536$		0			0
$537$	−357.729	+	357.729i	−0.666162	+	0.666162i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	−476.597			−0.880956			−0.440478	−	0.897763i	$-0.645191\pi$
$541$	−476.597			−0.880956			−0.440478	+	0.897763i	$0.645191\pi$
$542$		0			0
$543$	−72.7227	−	72.7227i	−0.133928	−	0.133928i
$544$		0			0
$545$	−80.0393	+	114.735i	−0.146861	+	0.210523i
$546$		0			0
$547$	−348.383	+	348.383i	−0.636897	+	0.636897i	−0.949789	−	0.312892i	$-0.898702\pi$
$547$	−348.383	+	348.383i	−0.636897	+	0.636897i	0.312892	+	0.949789i	$0.398702\pi$
$548$		0			0
$549$			343.456i			0.625602i
$550$		0			0
$551$	−694.709			−1.26081
$552$		0			0
$553$		0			0
$554$		0			0
$555$	458.089	+	319.563i	0.825385	+	0.575789i
$556$		0			0
$557$	−675.728	+	675.728i	−1.21316	+	1.21316i	−0.243173	+	0.969983i	$0.578188\pi$
$557$	−675.728	+	675.728i	−1.21316	+	1.21316i	−0.969983	+	0.243173i	$0.921812\pi$
$558$		0			0
$559$		−	679.731i		−	1.21598i
$560$		0			0
$561$	−207.550			−0.369964
$562$		0			0
$563$	517.108	+	517.108i	0.918486	+	0.918486i	0.996919	−	0.0784334i	$-0.0249918\pi$
$563$	517.108	+	517.108i	0.918486	+	0.918486i	−0.0784334	+	0.996919i	$0.524992\pi$
$564$		0			0
$565$	24.9258	+	139.928i	0.0441165	+	0.247660i
$566$		0			0
$567$		0			0
$568$		0			0
$569$		−	43.5644i		−	0.0765631i	−0.999267	−	0.0382816i	$-0.987812\pi$
$569$		−	43.5644i		−	0.0765631i	0.999267	−	0.0382816i	$-0.0121884\pi$
$570$		0			0
$571$	−120.877			−0.211694			−0.105847	−	0.994382i	$-0.533755\pi$
$571$	−120.877			−0.211694			−0.105847	+	0.994382i	$0.533755\pi$
$572$		0			0
$573$	264.875	+	264.875i	0.462261	+	0.462261i
$574$		0			0
$575$	−73.0050	+	158.002i	−0.126965	+	0.274787i
$576$		0			0
$577$	−509.383	+	509.383i	−0.882812	+	0.882812i	−0.993820	−	0.111008i	$-0.964592\pi$
$577$	−509.383	+	509.383i	−0.882812	+	0.882812i	0.111008	+	0.993820i	$0.464592\pi$
$578$		0			0
$579$		−	316.396i		−	0.546452i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−120.260	−	120.260i	−0.206278	−	0.206278i
$584$		0			0
$585$	612.517	−	109.110i	1.04704	−	0.186512i
$586$		0			0
$587$	456.597	−	456.597i	0.777848	−	0.777848i	−0.201617	−	0.979465i	$-0.564619\pi$
$587$	456.597	−	456.597i	0.777848	−	0.777848i	0.979465	+	0.201617i	$0.0646195\pi$
$588$		0			0
$589$			1030.94i			1.75032i
$590$		0			0
$591$	401.429			0.679237
$592$		0			0
$593$	76.0087	+	76.0087i	0.128177	+	0.128177i	0.768285	−	0.640108i	$-0.221110\pi$
$593$	76.0087	+	76.0087i	0.128177	+	0.128177i	−0.640108	+	0.768285i	$0.721110\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−33.5715	+	33.5715i	−0.0562337	+	0.0562337i
$598$		0			0
$599$		−	401.296i		−	0.669944i	−0.942228	−	0.334972i	$-0.891273\pi$
$599$		−	401.296i		−	0.669944i	0.942228	−	0.334972i	$-0.108727\pi$
$600$		0			0
$601$	199.864			0.332552			0.166276	−	0.986079i	$-0.446826\pi$
$601$	199.864			0.332552			0.166276	+	0.986079i	$0.446826\pi$
$602$		0			0
$603$	−73.8527	−	73.8527i	−0.122475	−	0.122475i
$604$		0			0
$605$	390.359	+	272.315i	0.645221	+	0.450107i
$606$		0			0
$607$	202.502	−	202.502i	0.333612	−	0.333612i	−0.520344	−	0.853956i	$-0.674196\pi$
$607$	202.502	−	202.502i	0.333612	−	0.333612i	0.853956	+	0.520344i	$0.174196\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−508.690			−0.832553
$612$		0			0
$613$	−693.477	−	693.477i	−1.13128	−	1.13128i	−0.989964	−	0.141320i	$-0.954865\pi$
$613$	−693.477	−	693.477i	−1.13128	−	1.13128i	−0.141320	−	0.989964i	$-0.545135\pi$
$614$		0			0
$615$	−54.9649	−	308.560i	−0.0893738	−	0.501724i
$616$		0			0
$617$	−90.4270	+	90.4270i	−0.146559	+	0.146559i	−0.776579	−	0.630020i	$-0.783047\pi$
$617$	−90.4270	+	90.4270i	−0.146559	+	0.146559i	0.630020	+	0.776579i	$0.283047\pi$
$618$		0			0
$619$			650.515i			1.05091i	0.850820	+	0.525457i	$0.176105\pi$
$619$			650.515i			1.05091i	−0.850820	+	0.525457i	$0.823895\pi$
$620$		0			0
$621$	180.443			0.290569
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−475.952	+	405.086i	−0.761523	+	0.648138i
$626$		0			0
$627$	−196.397	+	196.397i	−0.313233	+	0.313233i
$628$		0			0
$629$		−	1533.56i		−	2.43809i
$630$		0			0
$631$	−51.8964			−0.0822448			−0.0411224	−	0.999154i	$-0.513093\pi$
$631$	−51.8964			−0.0822448			−0.0411224	+	0.999154i	$0.513093\pi$
$632$		0			0
$633$	−130.725	−	130.725i	−0.206517	−	0.206517i
$634$		0			0
$635$	173.148	−	30.8434i	0.272674	−	0.0485723i
$636$		0			0
$637$		0			0
$638$		0			0
$639$			533.424i			0.834779i
$640$		0			0
$641$	1182.56			1.84487			0.922436	−	0.386151i	$-0.126196\pi$
$641$	1182.56			1.84487			0.922436	+	0.386151i	$0.126196\pi$
$642$		0			0
$643$	−634.733	−	634.733i	−0.987143	−	0.987143i	0.0127759	−	0.999918i	$-0.495933\pi$
$643$	−634.733	−	634.733i	−0.987143	−	0.987143i	−0.999918	+	0.0127759i	$0.995933\pi$
$644$		0			0
$645$	162.398	−	232.795i	0.251780	−	0.360922i
$646$		0			0
$647$	390.821	−	390.821i	0.604052	−	0.604052i	−0.337333	−	0.941385i	$-0.609525\pi$
$647$	390.821	−	390.821i	0.604052	−	0.604052i	0.941385	+	0.337333i	$0.109525\pi$
$648$		0			0
$649$			530.715i			0.817743i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−259.786	−	259.786i	−0.397835	−	0.397835i	0.479634	−	0.877469i	$-0.340769\pi$
$653$	−259.786	−	259.786i	−0.397835	−	0.397835i	−0.877469	+	0.479634i	$0.840769\pi$
$654$		0			0
$655$	−167.239	−	116.666i	−0.255327	−	0.178116i
$656$		0			0
$657$	−239.368	+	239.368i	−0.364335	+	0.364335i
$658$		0			0
$659$		−	587.969i		−	0.892213i	−0.894980	−	0.446107i	$-0.852810\pi$
$659$		−	587.969i		−	0.892213i	0.894980	−	0.446107i	$-0.147190\pi$
$660$		0			0
$661$	−24.6995			−0.0373668			−0.0186834	−	0.999825i	$-0.505947\pi$
$661$	−24.6995			−0.0373668			−0.0186834	+	0.999825i	$0.505947\pi$
$662$		0			0
$663$	596.716	+	596.716i	0.900025	+	0.900025i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−107.913	+	107.913i	−0.161788	+	0.161788i
$668$		0			0
$669$		−	30.7765i		−	0.0460037i
$670$		0			0
$671$	−289.643			−0.431659
$672$		0			0
$673$	38.4321	+	38.4321i	0.0571056	+	0.0571056i	0.735083	−	0.677977i	$-0.237143\pi$
$673$	38.4321	+	38.4321i	0.0571056	+	0.0571056i	−0.677977	+	0.735083i	$0.737143\pi$
$674$		0			0
$675$	588.195	+	271.776i	0.871400	+	0.402631i
$676$		0			0
$677$	−791.550	+	791.550i	−1.16920	+	1.16920i	−0.186805	+	0.982397i	$0.559813\pi$
$677$	−791.550	+	791.550i	−1.16920	+	1.16920i	−0.982397	+	0.186805i	$0.940187\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	−415.812			−0.610590
$682$		0			0
$683$	297.386	+	297.386i	0.435411	+	0.435411i	0.890464	−	0.455053i	$-0.150380\pi$
$683$	297.386	+	297.386i	0.435411	+	0.435411i	−0.455053	+	0.890464i	$0.650380\pi$
$684$		0			0
$685$	77.6047	−	13.8240i	0.113292	−	0.0201810i
$686$		0			0
$687$	3.93978	−	3.93978i	0.00573476	−	0.00573476i
$688$		0			0
$689$			691.507i			1.00364i
$690$		0			0
$691$	−132.747			−0.192109			−0.0960544	−	0.995376i	$-0.530622\pi$
$691$	−132.747			−0.192109			−0.0960544	+	0.995376i	$0.530622\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−445.169	+	638.143i	−0.640531	+	0.918191i
$696$		0			0
$697$	−608.493	+	608.493i	−0.873017	+	0.873017i
$698$		0			0
$699$		−	330.306i		−	0.472541i
$700$		0			0
$701$	−600.972			−0.857307			−0.428654	−	0.903469i	$-0.641012\pi$
$701$	−600.972			−0.857307			−0.428654	+	0.903469i	$0.641012\pi$
$702$		0			0
$703$	−1451.15	−	1451.15i	−2.06423	−	2.06423i
$704$		0			0
$705$	−174.217	−	121.534i	−0.247116	−	0.172388i
$706$		0			0
$707$		0			0
$708$		0			0
$709$			908.125i			1.28085i	0.768019	+	0.640427i	$0.221243\pi$
$709$			908.125i			1.28085i	−0.768019	+	0.640427i	$0.778757\pi$
$710$		0			0
$711$	809.528			1.13858
$712$		0			0
$713$	160.141	+	160.141i	0.224602	+	0.224602i
$714$		0			0
$715$	92.0143	+	516.547i	0.128691	+	0.722444i
$716$		0			0
$717$	−464.499	+	464.499i	−0.647837	+	0.647837i
$718$		0			0
$719$			543.447i			0.755837i	0.925839	+	0.377919i	$0.123360\pi$
$719$			543.447i			0.755837i	−0.925839	+	0.377919i	$0.876640\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−13.1962	−	13.1962i	−0.0182519	−	0.0182519i
$724$		0			0
$725$	−514.299	+	189.232i	−0.709378	+	0.261010i
$726$		0			0
$727$	−29.3887	+	29.3887i	−0.0404246	+	0.0404246i	−0.727030	−	0.686606i	$-0.759100\pi$
$727$	−29.3887	+	29.3887i	−0.0404246	+	0.0404246i	0.686606	+	0.727030i	$0.259100\pi$
$728$		0			0
$729$		−	345.133i		−	0.473433i
$730$		0			0
$731$	−779.335			−1.06612
$732$		0			0
$733$	131.090	+	131.090i	0.178841	+	0.178841i	0.790850	−	0.612010i	$-0.209639\pi$
$733$	131.090	+	131.090i	0.178841	+	0.178841i	−0.612010	+	0.790850i	$0.709639\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	62.2814	−	62.2814i	0.0845067	−	0.0845067i
$738$		0			0
$739$			383.346i			0.518736i	0.965779	+	0.259368i	$0.0835142\pi$
$739$			383.346i			0.518736i	−0.965779	+	0.259368i	$0.916486\pi$
$740$		0			0
$741$	1129.30			1.52403
$742$		0			0
$743$	−13.2772	−	13.2772i	−0.0178697	−	0.0178697i	0.698116	−	0.715985i	$-0.254022\pi$
$743$	−13.2772	−	13.2772i	−0.0178697	−	0.0178697i	−0.715985	+	0.698116i	$0.754022\pi$
$744$		0			0
$745$	−399.567	+	572.773i	−0.536331	+	0.768822i
$746$		0			0
$747$	167.144	−	167.144i	0.223753	−	0.223753i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	1026.15			1.36638			0.683191	−	0.730240i	$-0.260592\pi$
$751$	1026.15			1.36638			0.683191	+	0.730240i	$0.260592\pi$
$752$		0			0
$753$	−30.5486	−	30.5486i	−0.0405692	−	0.0405692i
$754$		0			0
$755$	558.888	+	389.881i	0.740249	+	0.516398i
$756$		0			0
$757$	386.485	−	386.485i	0.510548	−	0.510548i	−0.404146	−	0.914694i	$-0.632431\pi$
$757$	386.485	−	386.485i	0.510548	−	0.510548i	0.914694	+	0.404146i	$0.132431\pi$
$758$		0			0
$759$			61.0148i			0.0803884i
$760$		0			0
$761$	−732.604			−0.962686			−0.481343	−	0.876532i	$-0.659851\pi$
$761$	−732.604			−0.962686			−0.481343	+	0.876532i	$0.659851\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−125.098	−	702.271i	−0.163527	−	0.918001i
$766$		0			0
$767$	1525.83	−	1525.83i	1.98935	−	1.98935i
$768$		0			0
$769$		−	158.129i		−	0.205630i	−0.994701	−	0.102815i	$-0.967215\pi$
$769$		−	158.129i		−	0.205630i	0.994701	−	0.102815i	$-0.0327849\pi$
$770$		0			0
$771$	436.643			0.566334
$772$		0			0
$773$	417.689	+	417.689i	0.540348	+	0.540348i	0.923631	−	0.383283i	$-0.125207\pi$
$773$	417.689	+	417.689i	0.540348	+	0.540348i	−0.383283	+	0.923631i	$0.625207\pi$
$774$		0			0
$775$	280.817	+	763.211i	0.362345	+	0.984789i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			1151.59i			1.47829i
$780$		0			0
$781$	−449.847			−0.575988
$782$		0			0
$783$	401.727	+	401.727i	0.513061	+	0.513061i
$784$		0			0
$785$	833.303	−	148.439i	1.06153	−	0.189094i
$786$		0			0
$787$	−1002.23	+	1002.23i	−1.27348	+	1.27348i	−0.329230	+	0.944250i	$0.606789\pi$
$787$	−1002.23	+	1002.23i	−1.27348	+	1.27348i	−0.944250	+	0.329230i	$0.893211\pi$
$788$		0			0
$789$		−	680.429i		−	0.862394i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	832.738	+	832.738i	1.05011	+	1.05011i
$794$		0			0
$795$	−165.211	+	236.828i	−0.207813	+	0.297897i
$796$		0			0
$797$	−434.483	+	434.483i	−0.545148	+	0.545148i	−0.925034	−	0.379885i	$-0.875963\pi$
$797$	−434.483	+	434.483i	−0.545148	+	0.545148i	0.379885	+	0.925034i	$0.375963\pi$
$798$		0			0
$799$			583.230i			0.729950i
$800$		0			0
$801$	700.078			0.874004
$802$		0			0
$803$	−201.864	−	201.864i	−0.251387	−	0.251387i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	23.3294	−	23.3294i	0.0289089	−	0.0289089i
$808$		0			0
$809$		−	756.499i		−	0.935104i	−0.883966	−	0.467552i	$-0.845136\pi$
$809$		−	756.499i		−	0.935104i	0.883966	−	0.467552i	$-0.154864\pi$
$810$		0			0
$811$	−1254.32			−1.54663			−0.773315	−	0.634022i	$-0.781403\pi$
$811$	−1254.32			−1.54663			−0.773315	+	0.634022i	$0.781403\pi$
$812$		0			0
$813$	−254.529	−	254.529i	−0.313074	−	0.313074i
$814$		0			0
$815$	−170.481	−	957.045i	−0.209180	−	1.17429i
$816$		0			0
$817$	−737.457	+	737.457i	−0.902640	+	0.902640i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	116.895			0.142381			0.0711906	−	0.997463i	$-0.477320\pi$
$821$	116.895			0.142381			0.0711906	+	0.997463i	$0.477320\pi$
$822$		0			0
$823$	−883.464	−	883.464i	−1.07347	−	1.07347i	−0.997078	−	0.0763897i	$-0.975661\pi$
$823$	−883.464	−	883.464i	−1.07347	−	1.07347i	−0.0763897	−	0.997078i	$-0.524339\pi$
$824$		0			0
$825$	−91.8978	+	198.891i	−0.111391	+	0.241080i
$826$		0			0
$827$	−667.120	+	667.120i	−0.806675	+	0.806675i	−0.984129	−	0.177454i	$-0.943214\pi$
$827$	−667.120	+	667.120i	−0.806675	+	0.806675i	0.177454	+	0.984129i	$0.443214\pi$
$828$		0			0
$829$		−	1418.50i		−	1.71110i	−0.517720	−	0.855550i	$-0.673219\pi$
$829$		−	1418.50i		−	1.71110i	0.517720	−	0.855550i	$-0.326781\pi$
$830$		0			0
$831$	−679.648			−0.817867
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−675.838	+	120.389i	−0.809387	+	0.144179i
$836$		0			0
$837$	596.156	−	596.156i	0.712254	−	0.712254i
$838$		0			0
$839$			1080.06i			1.28731i	0.765315	+	0.643656i	$0.222583\pi$
$839$			1080.06i			1.28731i	−0.765315	+	0.643656i	$0.777417\pi$
$840$		0			0
$841$	360.501			0.428657
$842$		0			0
$843$	655.767	+	655.767i	0.777896	+	0.777896i
$844$		0			0
$845$	737.095	−	1056.61i	0.872302	−	1.25043i
$846$		0			0
$847$		0			0
$848$		0			0
$849$		−	690.425i		−	0.813221i
$850$		0			0
$851$	−450.830			−0.529765
$852$		0			0
$853$	−718.095	−	718.095i	−0.841846	−	0.841846i	0.147253	−	0.989099i	$-0.452957\pi$
$853$	−718.095	−	718.095i	−0.841846	−	0.841846i	−0.989099	+	0.147253i	$0.952957\pi$
$854$		0			0
$855$	−782.910	−	546.158i	−0.915684	−	0.638782i
$856$		0			0
$857$	580.587	−	580.587i	0.677464	−	0.677464i	−0.281962	−	0.959426i	$-0.590985\pi$
$857$	580.587	−	580.587i	0.677464	−	0.677464i	0.959426	+	0.281962i	$0.0909851\pi$
$858$		0			0
$859$		−	863.738i		−	1.00552i	−0.864427	−	0.502758i	$-0.832319\pi$
$859$		−	863.738i		−	1.00552i	0.864427	−	0.502758i	$-0.167681\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−240.532	−	240.532i	−0.278716	−	0.278716i	0.553880	−	0.832596i	$-0.313146\pi$
$863$	−240.532	−	240.532i	−0.278716	−	0.278716i	−0.832596	+	0.553880i	$0.813146\pi$
$864$		0			0
$865$	−162.164	−	910.354i	−0.187473	−	1.05243i
$866$		0			0
$867$	331.627	−	331.627i	0.382499	−	0.382499i
$868$		0			0
$869$			682.691i			0.785606i
$870$		0			0
$871$	−358.124			−0.411165
$872$		0			0
$873$	−343.037	−	343.037i	−0.392940	−	0.392940i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−1233.55	+	1233.55i	−1.40655	+	1.40655i	−0.629772	+	0.776780i	$0.716852\pi$
$877$	−1233.55	+	1233.55i	−1.40655	+	1.40655i	−0.776780	+	0.629772i	$0.783148\pi$
$878$		0			0
$879$			569.937i			0.648392i
$880$		0			0
$881$	−556.908			−0.632132			−0.316066	−	0.948737i	$-0.602362\pi$
$881$	−556.908			−0.632132			−0.316066	+	0.948737i	$0.602362\pi$
$882$		0			0
$883$	137.269	+	137.269i	0.155458	+	0.155458i	0.780551	−	0.625093i	$-0.214939\pi$
$883$	137.269	+	137.269i	0.155458	+	0.155458i	−0.625093	+	0.780551i	$0.714939\pi$
$884$		0			0
$885$	887.113	−	158.024i	1.00239	−	0.178559i
$886$		0			0
$887$	324.611	−	324.611i	0.365965	−	0.365965i	−0.500038	−	0.866003i	$-0.666681\pi$
$887$	324.611	−	324.611i	0.365965	−	0.365965i	0.866003	+	0.500038i	$0.166681\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−48.2915			−0.0541992
$892$		0			0
$893$	551.890	+	551.890i	0.618018	+	0.618018i
$894$		0			0
$895$	838.938	−	1202.60i	0.937361	−	1.34369i
$896$		0			0
$897$	175.421	−	175.421i	0.195564	−	0.195564i
$898$		0			0
$899$			713.053i			0.793163i
$900$		0			0
$901$	792.836			0.879951
$902$		0			0
$903$		0			0
$904$		0			0
$905$	244.478	+	170.548i	0.270141	+	0.188451i
$906$		0			0
$907$	−376.844	+	376.844i	−0.415484	+	0.415484i	−0.883644	−	0.468160i	$-0.844917\pi$
$907$	−376.844	+	376.844i	−0.415484	+	0.415484i	0.468160	+	0.883644i	$0.344917\pi$
$908$		0			0
$909$			334.356i			0.367828i
$910$		0			0
$911$	72.2584			0.0793177			0.0396588	−	0.999213i	$-0.487373\pi$
$911$	72.2584			0.0793177			0.0396588	+	0.999213i	$0.487373\pi$
$912$		0			0
$913$	140.956	+	140.956i	0.154387	+	0.154387i
$914$		0			0
$915$	86.2433	+	484.150i	0.0942550	+	0.529126i
$916$		0			0
$917$		0			0
$918$		0			0
$919$		−	323.949i		−	0.352502i	−0.984345	−	0.176251i	$-0.943603\pi$
$919$		−	323.949i		−	0.352502i	0.984345	−	0.176251i	$-0.0563970\pi$
$920$		0			0
$921$	−646.982			−0.702478
$922$		0			0
$923$	1293.33	+	1293.33i	1.40123	+	1.40123i
$924$		0			0
$925$	−1469.58	−	679.020i	−1.58873	−	0.734076i
$926$		0			0
$927$	−168.022	+	168.022i	−0.181253	+	0.181253i
$928$		0			0
$929$		−	711.664i		−	0.766054i	−0.923737	−	0.383027i	$-0.874882\pi$
$929$		−	711.664i		−	0.766054i	0.923737	−	0.383027i	$-0.125118\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	622.646	+	622.646i	0.667359	+	0.667359i
$934$		0			0
$935$	592.239	−	105.497i	0.633411	−	0.112832i
$936$		0			0
$937$	−313.108	+	313.108i	−0.334160	+	0.334160i	−0.854164	−	0.520004i	$-0.825930\pi$
$937$	−313.108	+	313.108i	−0.334160	+	0.334160i	0.520004	+	0.854164i	$0.325930\pi$
$938$		0			0
$939$			287.261i			0.305922i
$940$		0			0
$941$	−60.1873			−0.0639610			−0.0319805	−	0.999488i	$-0.510181\pi$
$941$	−60.1873			−0.0639610			−0.0319805	+	0.999488i	$0.510181\pi$
$942$		0			0
$943$	178.883	+	178.883i	0.189695	+	0.189695i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	1255.69	−	1255.69i	1.32596	−	1.32596i	0.417107	−	0.908858i	$-0.363044\pi$
$947$	1255.69	−	1255.69i	1.32596	−	1.32596i	0.908858	−	0.417107i	$-0.136956\pi$
$948$		0			0
$949$			1160.74i			1.22312i
$950$		0			0
$951$	758.434			0.797512
$952$		0			0
$953$	−118.550	−	118.550i	−0.124396	−	0.124396i	0.642168	−	0.766564i	$-0.278035\pi$
$953$	−118.550	−	118.550i	−0.124396	−	0.124396i	−0.766564	+	0.642168i	$0.778035\pi$
$954$		0			0
$955$	−890.452	−	621.180i	−0.932411	−	0.650450i
$956$		0			0
$957$	−135.839	+	135.839i	−0.141943	+	0.141943i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	97.1602			0.101103
$962$		0			0
$963$	118.698	+	118.698i	0.123259	+	0.123259i
$964$		0			0
$965$	160.824	+	902.829i	0.166657	+	0.935574i
$966$		0			0
$967$	194.361	−	194.361i	0.200994	−	0.200994i	−0.599432	−	0.800426i	$-0.704607\pi$
$967$	194.361	−	194.361i	0.200994	−	0.200994i	0.800426	+	0.599432i	$0.204607\pi$
$968$		0			0
$969$		−	1294.78i		−	1.33621i
$970$		0			0
$971$	849.517			0.874888			0.437444	−	0.899246i	$-0.355884\pi$
$971$	849.517			0.874888			0.437444	+	0.899246i	$0.355884\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	836.033	−	307.611i	0.857469	−	0.315499i
$976$		0			0
$977$	−609.749	+	609.749i	−0.624104	+	0.624104i	−0.946578	−	0.322474i	$-0.895485\pi$
$977$	−609.749	+	609.749i	−0.624104	+	0.624104i	0.322474	+	0.946578i	$0.395485\pi$
$978$		0			0
$979$			590.389i			0.603054i
$980$		0			0
$981$	−168.546			−0.171811
$982$		0			0
$983$	404.149	+	404.149i	0.411138	+	0.411138i	0.882135	−	0.470997i	$-0.156106\pi$
$983$	404.149	+	404.149i	0.411138	+	0.411138i	−0.470997	+	0.882135i	$0.656106\pi$
$984$		0			0
$985$	−1145.47	+	204.046i	−1.16291	+	0.207153i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			229.106i			0.231654i
$990$		0			0
$991$	−1539.16			−1.55314			−0.776570	−	0.630030i	$-0.783042\pi$
$991$	−1539.16			−1.55314			−0.776570	+	0.630030i	$0.783042\pi$
$992$		0			0
$993$	−427.317	−	427.317i	−0.430329	−	0.430329i
$994$		0			0
$995$	78.7312	−	112.860i	0.0791268	−	0.113427i
$996$		0			0
$997$	461.996	−	461.996i	0.463386	−	0.463386i	−0.436378	−	0.899764i	$-0.643739\pi$
$997$	461.996	−	461.996i	0.463386	−	0.463386i	0.899764	+	0.436378i	$0.143739\pi$
$998$		0			0
$999$			1678.30i			1.67998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	980.3.l.c.393.2		8
5.2	odd	4	inner	980.3.l.c.197.2		8
7.6	odd	2		140.3.l.b.113.3	yes	8
21.20	even	2		1260.3.y.b.253.2		8
28.27	even	2		560.3.bh.d.113.2		8
35.13	even	4		700.3.l.c.57.2		8
35.27	even	4		140.3.l.b.57.3	✓	8
35.34	odd	2		700.3.l.c.393.2		8
105.62	odd	4		1260.3.y.b.757.2		8
140.27	odd	4		560.3.bh.d.337.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.3.l.b.57.3	✓	8	35.27	even	4
140.3.l.b.113.3	yes	8	7.6	odd	2
560.3.bh.d.113.2		8	28.27	even	2
560.3.bh.d.337.2		8	140.27	odd	4
700.3.l.c.57.2		8	35.13	even	4
700.3.l.c.393.2		8	35.34	odd	2
980.3.l.c.197.2		8	5.2	odd	4	inner
980.3.l.c.393.2		8	1.1	even	1	trivial
1260.3.y.b.253.2		8	21.20	even	2
1260.3.y.b.757.2		8	105.62	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	980.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.21982 + 1.21982i) q^{3} +(-4.10078 - 2.86071i) q^{5} -6.02406i q^{9} +5.08021 q^{11} +(-14.6059 - 14.6059i) q^{13} +(-1.51267 - 8.49178i) q^{15} +(-16.7461 + 16.7461i) q^{17} +31.6925i q^{19} +(4.92296 + 4.92296i) q^{23} +(8.63273 + 23.4622i) q^{25} +(18.3267 - 18.3267i) q^{27} +21.9203i q^{29} +32.5294 q^{31} +(6.19696 + 6.19696i) q^{33} +(-45.7885 + 45.7885i) q^{37} -35.6331i q^{39} +36.3364 q^{41} +(23.2691 + 23.2691i) q^{43} +(-17.2331 + 24.7033i) q^{45} +(17.4139 - 17.4139i) q^{47} -40.8546 q^{51} +(-23.6722 - 23.6722i) q^{53} +(-20.8328 - 14.5330i) q^{55} +(-38.6593 + 38.6593i) q^{57} +104.467i q^{59} -57.0140 q^{61} +(18.1123 + 101.678i) q^{65} +(12.2596 - 12.2596i) q^{67} +12.0103i q^{69} -88.5489 q^{71} +(-39.7353 - 39.7353i) q^{73} +(-18.0894 + 39.1502i) q^{75} +134.383i q^{79} -9.50581 q^{81} +(27.7461 + 27.7461i) q^{83} +(116.578 - 20.7664i) q^{85} +(-26.7389 + 26.7389i) q^{87} +116.214i q^{89} +(39.6801 + 39.6801i) q^{93} +(90.6629 - 129.964i) q^{95} +(56.9445 - 56.9445i) q^{97} -30.6035i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} - 20 q^{5} + 32 q^{11} + 16 q^{13} + 56 q^{15} + 16 q^{17} - 24 q^{23} + 32 q^{25} + 8 q^{27} + 32 q^{31} + 80 q^{33} - 208 q^{37} - 48 q^{43} + 92 q^{45} - 176 q^{47} - 176 q^{51} + 96 q^{53}+ \cdots + 400 q^{97}+O(q^{100}) \) 8 * q + 8 * q^3 - 20 * q^5 + 32 * q^11 + 16 * q^13 + 56 * q^15 + 16 * q^17 - 24 * q^23 + 32 * q^25 + 8 * q^27 + 32 * q^31 + 80 * q^33 - 208 * q^37 - 48 * q^43 + 92 * q^45 - 176 * q^47 - 176 * q^51 + 96 * q^53 + 72 * q^55 + 24 * q^57 - 72 * q^61 - 344 * q^65 + 80 * q^67 - 400 * q^71 - 432 * q^73 - 72 * q^75 + 152 * q^81 + 16 * q^83 + 56 * q^85 - 704 * q^87 + 272 * q^93 + 72 * q^95 + 400 * q^97

Introduction

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