LMFDB - Embedded newform 1152.2.r.g.193.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1152,2,Mod(193,1152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1152, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1152.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1152 = 2^{7} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1152.r (of order $6$, 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:	$9.19876631285$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			193.4
Character	$\chi$	$=$	1152.193
Dual form			1152.2.r.g.961.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37296 + 1.05593i) q^{3} +(3.35903 + 1.93934i) q^{5} +(-1.14978 - 1.99147i) q^{7} +(0.770012 - 2.89950i) q^{9} +O(q^{10})$	\(q+(-1.37296 + 1.05593i) q^{3} +(3.35903 + 1.93934i) q^{5} +(-1.14978 - 1.99147i) q^{7} +(0.770012 - 2.89950i) q^{9} +(-3.60542 + 2.08159i) q^{11} +(-0.846691 - 0.488838i) q^{13} +(-6.65962 + 0.884289i) q^{15} -6.79209 q^{17} -0.729224i q^{19} +(3.68146 + 1.52012i) q^{21} +(-2.94585 + 5.10236i) q^{23} +(5.02208 + 8.69849i) q^{25} +(2.00448 + 4.79396i) q^{27} +(-4.32630 + 2.49779i) q^{29} +(-1.53163 + 2.65287i) q^{31} +(2.75206 - 6.66502i) q^{33} -8.91924i q^{35} -1.11690i q^{37} +(1.67865 - 0.222897i) q^{39} +(-3.12603 + 5.41445i) q^{41} +(4.80283 - 2.77291i) q^{43} +(8.20961 - 8.24620i) q^{45} +(-4.86355 - 8.42391i) q^{47} +(0.856020 - 1.48267i) q^{49} +(9.32523 - 7.17199i) q^{51} +6.81170i q^{53} -16.1477 q^{55} +(0.770012 + 1.00119i) q^{57} +(10.6458 + 6.14633i) q^{59} +(-10.8032 + 6.23724i) q^{61} +(-6.65962 + 1.80032i) q^{63} +(-1.89604 - 3.28404i) q^{65} +(-0.0524343 - 0.0302730i) q^{67} +(-1.34323 - 10.1159i) q^{69} -12.7904 q^{71} -1.71204 q^{73} +(-16.0801 - 6.63966i) q^{75} +(8.29088 + 4.78674i) q^{77} +(5.77427 + 10.0013i) q^{79} +(-7.81416 - 4.46529i) q^{81} +(-6.35637 + 3.66985i) q^{83} +(-22.8149 - 13.1722i) q^{85} +(3.30232 - 7.99764i) q^{87} +10.3321 q^{89} +2.24822i q^{91} +(-0.698385 - 5.25957i) q^{93} +(1.41421 - 2.44949i) q^{95} +(-4.66606 - 8.08185i) q^{97} +(3.25935 + 12.0568i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{9}+O(q^{10}) $ 24 * q + 4 * q^9	$ 24 q + 4 q^{9} - 40 q^{17} + 12 q^{25} - 28 q^{33} - 28 q^{41} - 12 q^{49} + 4 q^{57} + 16 q^{65} + 24 q^{73} + 44 q^{81} + 96 q^{89} - 36 q^{97}+O(q^{100}) $ 24 * q + 4 * q^9 - 40 * q^17 + 12 * q^25 - 28 * q^33 - 28 * q^41 - 12 * q^49 + 4 * q^57 + 16 * q^65 + 24 * q^73 + 44 * q^81 + 96 * q^89 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times$.

$n$	$127$	$641$	$901$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

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
$3$	−1.37296	+	1.05593i	−0.792676	+	0.609643i
$3$	−1.37296	+	1.05593i	−0.792676	+	0.609643i
$4$		0			0
$5$	3.35903	+	1.93934i	1.50221	+	0.867299i	0.999997	+	0.00255286i	$0.000812602\pi$
$5$	3.35903	+	1.93934i	1.50221	+	0.867299i	0.502209	+	0.864746i	$0.332521\pi$
$6$		0			0
$7$	−1.14978	−	1.99147i	−0.434575	−	0.752707i	0.562686	−	0.826671i	$-0.309768\pi$
$7$	−1.14978	−	1.99147i	−0.434575	−	0.752707i	−0.997261	+	0.0739645i	$0.976435\pi$
$8$		0			0
$9$	0.770012	−	2.89950i	0.256671	−	0.966499i
$10$		0			0
$11$	−3.60542	+	2.08159i	−1.08708	+	0.627624i	−0.932797	−	0.360403i	$-0.882639\pi$
$11$	−3.60542	+	2.08159i	−1.08708	+	0.627624i	−0.154280	+	0.988027i	$0.549306\pi$
$12$		0			0
$13$	−0.846691	−	0.488838i	−0.234830	−	0.135579i	0.377968	−	0.925819i	$-0.376623\pi$
$13$	−0.846691	−	0.488838i	−0.234830	−	0.135579i	−0.612798	+	0.790239i	$0.709956\pi$
$14$		0			0
$15$	−6.65962	+	0.884289i	−1.71951	+	0.228322i
$16$		0			0
$17$	−6.79209			−1.64732			−0.823662	−	0.567082i	$-0.808072\pi$
$17$	−6.79209			−1.64732			−0.823662	+	0.567082i	$0.808072\pi$
$18$		0			0
$19$		−	0.729224i		−	0.167296i	−0.996495	−	0.0836478i	$-0.973343\pi$
$19$		−	0.729224i		−	0.167296i	0.996495	−	0.0836478i	$-0.0266571\pi$
$20$		0			0
$21$	3.68146	+	1.52012i	0.803360	+	0.331717i
$22$		0			0
$23$	−2.94585	+	5.10236i	−0.614251	+	1.06391i	0.376264	+	0.926513i	$0.377209\pi$
$23$	−2.94585	+	5.10236i	−0.614251	+	1.06391i	−0.990515	+	0.137402i	$0.956125\pi$
$24$		0			0
$25$	5.02208	+	8.69849i	1.00442	+	1.73970i
$26$		0			0
$27$	2.00448	+	4.79396i	0.385763	+	0.922598i
$28$		0			0
$29$	−4.32630	+	2.49779i	−0.803374	+	0.463828i	−0.844650	−	0.535320i	$-0.820191\pi$
$29$	−4.32630	+	2.49779i	−0.803374	+	0.463828i	0.0412755	+	0.999148i	$0.486858\pi$
$30$		0			0
$31$	−1.53163	+	2.65287i	−0.275089	+	0.476469i	−0.970158	−	0.242475i	$-0.922041\pi$
$31$	−1.53163	+	2.65287i	−0.275089	+	0.476469i	0.695068	+	0.718944i	$0.255374\pi$
$32$		0			0
$33$	2.75206	−	6.66502i	0.479073	−	1.16023i
$34$		0			0
$35$		−	8.91924i		−	1.50763i
$36$		0			0
$37$		−	1.11690i		−	0.183618i	−0.995777	−	0.0918089i	$-0.970735\pi$
$37$		−	1.11690i		−	0.183618i	0.995777	−	0.0918089i	$-0.0292649\pi$
$38$		0			0
$39$	1.67865	−	0.222897i	0.268799	−	0.0356921i
$40$		0			0
$41$	−3.12603	+	5.41445i	−0.488204	+	0.845594i	−0.999908	−	0.0135675i	$-0.995681\pi$
$41$	−3.12603	+	5.41445i	−0.488204	+	0.845594i	0.511704	+	0.859162i	$0.329015\pi$
$42$		0			0
$43$	4.80283	−	2.77291i	0.732424	−	0.422865i	−0.0868842	−	0.996218i	$-0.527691\pi$
$43$	4.80283	−	2.77291i	0.732424	−	0.422865i	0.819308	+	0.573353i	$0.194358\pi$
$44$		0			0
$45$	8.20961	−	8.24620i	1.22382	−	1.22927i
$46$		0			0
$47$	−4.86355	−	8.42391i	−0.709421	−	1.22875i	−0.965072	−	0.261985i	$-0.915623\pi$
$47$	−4.86355	−	8.42391i	−0.709421	−	1.22875i	0.255651	−	0.966769i	$-0.417710\pi$
$48$		0			0
$49$	0.856020	−	1.48267i	0.122289	−	0.211810i
$50$		0			0
$51$	9.32523	−	7.17199i	1.30579	−	1.00428i
$52$		0			0
$53$			6.81170i			0.935660i	0.883819	+	0.467830i	$0.154964\pi$
$53$			6.81170i			0.935660i	−0.883819	+	0.467830i	$0.845036\pi$
$54$		0			0
$55$	−16.1477			−2.17735
$56$		0			0
$57$	0.770012	+	1.00119i	0.101991	+	0.132611i
$58$		0			0
$59$	10.6458	+	6.14633i	1.38596	+	0.800184i	0.992857	−	0.119311i	$-0.0380686\pi$
$59$	10.6458	+	6.14633i	1.38596	+	0.800184i	0.393102	+	0.919495i	$0.371402\pi$
$60$		0			0
$61$	−10.8032	+	6.23724i	−1.38321	+	0.798597i	−0.992538	−	0.121933i	$-0.961091\pi$
$61$	−10.8032	+	6.23724i	−1.38321	+	0.798597i	−0.390672	+	0.920530i	$0.627757\pi$
$62$		0			0
$63$	−6.65962	+	1.80032i	−0.839033	+	0.226819i
$64$		0			0
$65$	−1.89604	−	3.28404i	−0.235175	−	0.407336i
$66$		0			0
$67$	−0.0524343	−	0.0302730i	−0.00640587	−	0.00369843i	0.496794	−	0.867869i	$-0.334511\pi$
$67$	−0.0524343	−	0.0302730i	−0.00640587	−	0.00369843i	−0.503200	+	0.864170i	$0.667844\pi$
$68$		0			0
$69$	−1.34323	−	10.1159i	−0.161706	−	1.21781i
$70$		0			0
$71$	−12.7904			−1.51794			−0.758968	−	0.651128i	$-0.774296\pi$
$71$	−12.7904			−1.51794			−0.758968	+	0.651128i	$0.774296\pi$
$72$		0			0
$73$	−1.71204			−0.200379			−0.100190	−	0.994968i	$-0.531945\pi$
$73$	−1.71204			−0.200379			−0.100190	+	0.994968i	$0.531945\pi$
$74$		0			0
$75$	−16.0801	−	6.63966i	−1.85677	−	0.766682i
$76$		0			0
$77$	8.29088	+	4.78674i	0.944833	+	0.545500i
$78$		0			0
$79$	5.77427	+	10.0013i	0.649657	+	1.12524i	0.983205	+	0.182505i	$0.0584206\pi$
$79$	5.77427	+	10.0013i	0.649657	+	1.12524i	−0.333548	+	0.942733i	$0.608246\pi$
$80$		0			0
$81$	−7.81416	−	4.46529i	−0.868240	−	0.496144i
$82$		0			0
$83$	−6.35637	+	3.66985i	−0.697702	+	0.402818i	−0.806491	−	0.591246i	$-0.798636\pi$
$83$	−6.35637	+	3.66985i	−0.697702	+	0.402818i	0.108789	+	0.994065i	$0.465303\pi$
$84$		0			0
$85$	−22.8149	−	13.1722i	−2.47462	−	1.42872i
$86$		0			0
$87$	3.30232	−	7.99764i	0.354046	−	0.857437i
$88$		0			0
$89$	10.3321			1.09520			0.547601	−	0.836740i	$-0.315541\pi$
$89$	10.3321			1.09520			0.547601	+	0.836740i	$0.315541\pi$
$90$		0			0
$91$			2.24822i			0.235677i
$92$		0			0
$93$	−0.698385	−	5.25957i	−0.0724191	−	0.545392i
$94$		0			0
$95$	1.41421	−	2.44949i	0.145095	−	0.251312i
$96$		0			0
$97$	−4.66606	−	8.08185i	−0.473766	−	0.820587i	0.525783	−	0.850619i	$-0.323772\pi$
$97$	−4.66606	−	8.08185i	−0.473766	−	0.820587i	−0.999549	+	0.0300318i	$0.990439\pi$
$98$		0			0
$99$	3.25935	+	12.0568i	0.327577	+	1.21175i
$100$		0			0
$101$	−5.29357	+	3.05624i	−0.526730	+	0.304108i	−0.739684	−	0.672955i	$-0.765025\pi$
$101$	−5.29357	+	3.05624i	−0.526730	+	0.304108i	0.212954	+	0.977062i	$0.431692\pi$
$102$		0			0
$103$	5.39242	−	9.33994i	0.531331	−	0.920292i	−0.468000	−	0.883728i	$-0.655025\pi$
$103$	5.39242	−	9.33994i	0.531331	−	0.920292i	0.999331	−	0.0365638i	$-0.0116412\pi$
$104$		0			0
$105$	9.41812	+	12.2457i	0.919114	+	1.19506i
$106$		0			0
$107$		−	0.608132i		−	0.0587904i	−0.999568	−	0.0293952i	$-0.990642\pi$
$107$		−	0.608132i		−	0.0587904i	0.999568	−	0.0293952i	$-0.00935813\pi$
$108$		0			0
$109$		−	14.8475i		−	1.42213i	−0.703124	−	0.711067i	$-0.748212\pi$
$109$		−	14.8475i		−	1.42213i	0.703124	−	0.711067i	$-0.251788\pi$
$110$		0			0
$111$	1.17938	+	1.53346i	0.111941	+	0.145549i
$112$		0			0
$113$	5.98205	−	10.3612i	0.562744	−	0.974701i	−0.434512	−	0.900666i	$-0.643079\pi$
$113$	5.98205	−	10.3612i	0.562744	−	0.974701i	0.997256	−	0.0740351i	$-0.0235877\pi$
$114$		0			0
$115$	−19.7904	+	11.4260i	−1.84546	+	1.06548i
$116$		0			0
$117$	−2.06935	+	2.07857i	−0.191311	+	0.192164i
$118$		0			0
$119$	7.80939	+	13.5263i	0.715886	+	1.23995i
$120$		0			0
$121$	3.16606	−	5.48377i	0.287823	−	0.498524i
$122$		0			0
$123$	−1.42539	−	10.7347i	−0.128523	−	0.967913i
$124$		0			0
$125$			19.5646i			1.74992i
$126$		0			0
$127$	−8.48528			−0.752947			−0.376473	−	0.926427i	$-0.622863\pi$
$127$	−8.48528			−0.752947			−0.376473	+	0.926427i	$0.622863\pi$
$128$		0			0
$129$	−3.66606	+	8.87855i	−0.322778	+	0.781713i
$130$		0			0
$131$	6.69741	+	3.86675i	0.585155	+	0.337839i	0.763179	−	0.646187i	$-0.223637\pi$
$131$	6.69741	+	3.86675i	0.585155	+	0.337839i	−0.178024	+	0.984026i	$0.556971\pi$
$132$		0			0
$133$	−1.45223	+	0.838446i	−0.125924	+	0.0727025i
$134$		0			0
$135$	−2.56399	+	19.9904i	−0.220673	+	1.72050i
$136$		0			0
$137$	3.91812	+	6.78638i	0.334748	+	0.579800i	0.983436	−	0.181254i	$-0.0580156\pi$
$137$	3.91812	+	6.78638i	0.334748	+	0.579800i	−0.648689	+	0.761054i	$0.724682\pi$
$138$		0			0
$139$	−3.33004	−	1.92260i	−0.282450	−	0.163073i	0.352082	−	0.935969i	$-0.385474\pi$
$139$	−3.33004	−	1.92260i	−0.282450	−	0.163073i	−0.634532	+	0.772897i	$0.718807\pi$
$140$		0			0
$141$	15.5725	+	6.43007i	1.31144	+	0.541510i
$142$		0			0
$143$	4.07024			0.340371
$144$		0			0
$145$	−19.3763			−1.60911
$146$		0			0
$147$	0.390323	+	2.93954i	0.0321933	+	0.242449i
$148$		0			0
$149$	7.32361	+	4.22829i	0.599973	+	0.346395i	0.769031	−	0.639211i	$-0.220739\pi$
$149$	7.32361	+	4.22829i	0.599973	+	0.346395i	−0.169058	+	0.985606i	$0.554072\pi$
$150$		0			0
$151$	2.71101	+	4.69560i	0.220619	+	0.382123i	0.954996	−	0.296619i	$-0.0958590\pi$
$151$	2.71101	+	4.69560i	0.220619	+	0.382123i	−0.734377	+	0.678741i	$0.762526\pi$
$152$		0			0
$153$	−5.22999	+	19.6936i	−0.422819	+	1.59214i
$154$		0			0
$155$	−10.2896	+	5.94071i	−0.826482	+	0.477169i
$156$		0			0
$157$	−3.50734	−	2.02496i	−0.279916	−	0.161610i	0.353469	−	0.935446i	$-0.385002\pi$
$157$	−3.50734	−	2.02496i	−0.279916	−	0.161610i	−0.633386	+	0.773836i	$0.718335\pi$
$158$		0			0
$159$	−7.19270	−	9.35216i	−0.570418	−	0.741675i
$160$		0			0
$161$	13.5483			1.06775
$162$		0			0
$163$			9.39102i			0.735562i	0.929913	+	0.367781i	$0.119882\pi$
$163$			9.39102i			0.735562i	−0.929913	+	0.367781i	$0.880118\pi$
$164$		0			0
$165$	22.1700	−	17.0508i	1.72593	−	1.32741i
$166$		0			0
$167$	7.92681	−	13.7296i	0.613395	−	1.06243i	−0.377269	−	0.926104i	$-0.623137\pi$
$167$	7.92681	−	13.7296i	0.613395	−	1.06243i	0.990664	−	0.136328i	$-0.0435300\pi$
$168$		0			0
$169$	−6.02208	−	10.4305i	−0.463237	−	0.802349i
$170$		0			0
$171$	−2.11438	−	0.561511i	−0.161691	−	0.0429398i
$172$		0			0
$173$	3.21073	−	1.85371i	0.244107	−	0.140935i	−0.372956	−	0.927849i	$-0.621656\pi$
$173$	3.21073	−	1.85371i	0.244107	−	0.140935i	0.617063	+	0.786914i	$0.288322\pi$
$174$		0			0
$175$	11.5485	−	20.0027i	0.872988	−	1.51206i
$176$		0			0
$177$	−21.1063	+	2.80257i	−1.58644	+	0.210654i
$178$		0			0
$179$		−	22.1833i		−	1.65806i	−0.559206	−	0.829029i	$-0.688894\pi$
$179$		−	22.1833i		−	1.65806i	0.559206	−	0.829029i	$-0.311106\pi$
$180$		0			0
$181$			20.1998i			1.50144i	0.660620	+	0.750720i	$0.270293\pi$
$181$			20.1998i			1.50144i	−0.660620	+	0.750720i	$0.729707\pi$
$182$		0			0
$183$	8.24623	−	19.9709i	0.609579	−	1.47629i
$184$		0			0
$185$	2.16606	−	3.75172i	0.159252	−	0.275832i
$186$		0			0
$187$	24.4884	−	14.1384i	1.79077	−	1.03390i
$188$		0			0
$189$	7.24234	−	9.50387i	0.526803	−	0.691304i
$190$		0			0
$191$	6.27776	+	10.8734i	0.454243	+	0.786772i	0.998644	−	0.0520530i	$-0.0165765\pi$
$191$	6.27776	+	10.8734i	0.454243	+	0.786772i	−0.544401	+	0.838825i	$0.683243\pi$
$192$		0			0
$193$	3.66606	−	6.34979i	0.263888	−	0.457068i	−0.703383	−	0.710811i	$-0.748328\pi$
$193$	3.66606	−	6.34979i	0.263888	−	0.457068i	0.967272	+	0.253742i	$0.0816616\pi$
$194$		0			0
$195$	6.07091	+	2.50675i	0.434747	+	0.179512i
$196$		0			0
$197$			25.5059i			1.81722i	0.417647	+	0.908609i	$0.362855\pi$
$197$			25.5059i			1.81722i	−0.417647	+	0.908609i	$0.637145\pi$
$198$		0			0
$199$	20.6876			1.46650			0.733252	−	0.679957i	$-0.238002\pi$
$199$	20.6876			1.46650			0.733252	+	0.679957i	$0.238002\pi$
$200$		0			0
$201$	0.103956	−	0.0138037i	0.00733250	−	0.000973637i
$202$		0			0
$203$	9.94857	+	5.74381i	0.698253	+	0.403137i
$204$		0			0
$205$	−21.0009	+	12.1249i	−1.46677	+	0.846838i
$206$		0			0
$207$	12.5259	+	12.4703i	0.870612	+	0.866749i
$208$		0			0
$209$	1.51795	+	2.62916i	0.104999	+	0.181863i
$210$		0			0
$211$	6.18585	+	3.57140i	0.425851	+	0.245865i	0.697578	−	0.716509i	$-0.254261\pi$
$211$	6.18585	+	3.57140i	0.425851	+	0.245865i	−0.271726	+	0.962375i	$0.587595\pi$
$212$		0			0
$213$	17.5606	−	13.5058i	1.20323	−	0.925400i
$214$		0			0
$215$	21.5105			1.46700
$216$		0			0
$217$	7.04415			0.478188
$218$		0			0
$219$	2.35055	−	1.80780i	0.158836	−	0.122160i
$220$		0			0
$221$	5.75080	+	3.32023i	0.386841	+	0.223343i
$222$		0			0
$223$	2.32915	+	4.03421i	0.155972	+	0.270151i	0.933412	−	0.358805i	$-0.116816\pi$
$223$	2.32915	+	4.03421i	0.155972	+	0.270151i	−0.777441	+	0.628956i	$0.783482\pi$
$224$		0			0
$225$	29.0883	−	7.86355i	1.93922	−	0.524237i
$226$		0			0
$227$	8.39503	−	4.84688i	0.557198	−	0.321698i	−0.194822	−	0.980839i	$-0.562413\pi$
$227$	8.39503	−	4.84688i	0.557198	−	0.321698i	0.752020	+	0.659140i	$0.229080\pi$
$228$		0			0
$229$	−3.26619	−	1.88574i	−0.215836	−	0.124613i	0.388185	−	0.921582i	$-0.373102\pi$
$229$	−3.26619	−	1.88574i	−0.215836	−	0.124613i	−0.604021	+	0.796969i	$0.706436\pi$
$230$		0			0
$231$	−16.4375	+	2.18263i	−1.08151	+	0.143606i
$232$		0			0
$233$	1.95585			0.128132			0.0640659	−	0.997946i	$-0.479593\pi$
$233$	1.95585			0.128132			0.0640659	+	0.997946i	$0.479593\pi$
$234$		0			0
$235$		−	37.7283i		−	2.46112i
$236$		0			0
$237$	−18.4886	−	7.63414i	−1.20096	−	0.495891i
$238$		0			0
$239$	−6.78125	+	11.7455i	−0.438643	+	0.759751i	−0.997585	−	0.0694552i	$-0.977874\pi$
$239$	−6.78125	+	11.7455i	−0.438643	+	0.759751i	0.558942	+	0.829206i	$0.311207\pi$
$240$		0			0
$241$	−1.21204	−	2.09932i	−0.0780744	−	0.135229i	0.824345	−	0.566088i	$-0.191544\pi$
$241$	−1.21204	−	2.09932i	−0.0780744	−	0.135229i	−0.902419	+	0.430859i	$0.858210\pi$
$242$		0			0
$243$	15.4435	−	2.12058i	0.990704	−	0.136035i
$244$		0			0
$245$	5.75080	−	3.32023i	0.367405	−	0.212122i
$246$		0			0
$247$	−0.356472	+	0.617428i	−0.0226818	+	0.0392860i
$248$		0			0
$249$	4.85189	−	11.7504i	0.307476	−	0.744654i
$250$		0			0
$251$			22.7914i			1.43858i	0.694708	+	0.719291i	$0.255533\pi$
$251$			22.7914i			1.43858i	−0.694708	+	0.719291i	$0.744467\pi$
$252$		0			0
$253$		−	24.5282i		−	1.54208i
$254$		0			0
$255$	45.2327	−	6.00617i	2.83258	−	0.376121i
$256$		0			0
$257$	1.78796	−	3.09684i	0.111530	−	0.193175i	−0.804857	−	0.593468i	$-0.797758\pi$
$257$	1.78796	−	3.09684i	0.111530	−	0.193175i	0.916387	+	0.400293i	$0.131092\pi$
$258$		0			0
$259$	−2.22429	+	1.28419i	−0.138210	+	0.0797958i
$260$		0			0
$261$	3.91103	+	14.4674i	0.242087	+	0.895511i
$262$		0			0
$263$	−13.0802	−	22.6555i	−0.806558	−	1.39700i	−0.915234	−	0.402923i	$-0.867994\pi$
$263$	−13.0802	−	22.6555i	−0.806558	−	1.39700i	0.108676	−	0.994077i	$-0.465339\pi$
$264$		0			0
$265$	−13.2102	+	22.8808i	−0.811497	+	1.40555i
$266$		0			0
$267$	−14.1855	+	10.9100i	−0.868140	+	0.667682i
$268$		0			0
$269$			14.5691i			0.888291i	0.895955	+	0.444146i	$0.146493\pi$
$269$			14.5691i			0.888291i	−0.895955	+	0.444146i	$0.853507\pi$
$270$		0			0
$271$	−12.3714			−0.751512			−0.375756	−	0.926719i	$-0.622617\pi$
$271$	−12.3714			−0.751512			−0.375756	+	0.926719i	$0.622617\pi$
$272$		0			0
$273$	−2.37397	−	3.08670i	−0.143679	−	0.186816i
$274$		0			0
$275$	−36.2134	−	20.9078i	−2.18375	−	1.26079i
$276$		0			0
$277$	10.0771	−	5.81802i	0.605474	−	0.349571i	−0.165718	−	0.986173i	$-0.552994\pi$
$277$	10.0771	−	5.81802i	0.605474	−	0.349571i	0.771192	+	0.636602i	$0.219661\pi$
$278$		0			0
$279$	6.51260	+	6.48370i	0.389899	+	0.388169i
$280$		0			0
$281$	−4.89604	−	8.48020i	−0.292073	−	0.505886i	0.682226	−	0.731141i	$-0.261012\pi$
$281$	−4.89604	−	8.48020i	−0.292073	−	0.505886i	−0.974300	+	0.225255i	$0.927679\pi$
$282$		0			0
$283$	15.0400	+	8.68335i	0.894036	+	0.516172i	0.875260	−	0.483652i	$-0.160690\pi$
$283$	15.0400	+	8.68335i	0.894036	+	0.516172i	0.0187752	+	0.999824i	$0.494023\pi$
$284$		0			0
$285$	0.644845	+	4.85635i	0.0381973	+	0.287666i
$286$		0			0
$287$	14.3770			0.848646
$288$		0			0
$289$	29.1325			1.71367
$290$		0			0
$291$	14.9402	+	6.16897i	0.875808	+	0.361631i
$292$		0			0
$293$	−5.14526	−	2.97062i	−0.300589	−	0.173545i	0.342118	−	0.939657i	$-0.388856\pi$
$293$	−5.14526	−	2.97062i	−0.300589	−	0.173545i	−0.642708	+	0.766112i	$0.722189\pi$
$294$		0			0
$295$	23.8396	+	41.2915i	1.38800	+	2.40408i
$296$		0			0
$297$	−17.2061	−	13.1117i	−0.998398	−	0.760821i
$298$		0			0
$299$	4.98845	−	2.88008i	0.288489	−	0.166559i
$300$		0			0
$301$	−11.0444	−	6.37647i	−0.636587	−	0.367534i
$302$		0			0
$303$	4.04065	−	9.78574i	0.232129	−	0.562176i
$304$		0			0
$305$	−48.3845			−2.77049
$306$		0			0
$307$			29.3867i			1.67718i	0.544759	+	0.838592i	$0.316621\pi$
$307$			29.3867i			1.67718i	−0.544759	+	0.838592i	$0.683379\pi$
$308$		0			0
$309$	2.45880	+	18.5174i	0.139876	+	1.05342i
$310$		0			0
$311$	7.18849	−	12.4508i	0.407622	−	0.706021i	−0.587001	−	0.809586i	$-0.699692\pi$
$311$	7.18849	−	12.4508i	0.407622	−	0.706021i	0.994623	+	0.103565i	$0.0330249\pi$
$312$		0			0
$313$	2.50000	+	4.33013i	0.141308	+	0.244753i	0.927990	−	0.372606i	$-0.121536\pi$
$313$	2.50000	+	4.33013i	0.141308	+	0.244753i	−0.786681	+	0.617359i	$0.788202\pi$
$314$		0			0
$315$	−25.8613	−	6.86792i	−1.45712	−	0.386964i
$316$		0			0
$317$	2.54007	−	1.46651i	0.142665	−	0.0823675i	−0.426969	−	0.904266i	$-0.640419\pi$
$317$	2.54007	−	1.46651i	0.142665	−	0.0823675i	0.569633	+	0.821899i	$0.307085\pi$
$318$		0			0
$319$	10.3988	−	18.0112i	0.582219	−	1.00843i
$320$		0			0
$321$	0.642147	+	0.834939i	0.0358412	+	0.0466017i
$322$		0			0
$323$			4.95296i			0.275590i
$324$		0			0
$325$		−	9.81992i		−	0.544711i
$326$		0			0
$327$	15.6780	+	20.3850i	0.866994	+	1.12729i
$328$		0			0
$329$	−11.1840	+	19.3713i	−0.616594	+	1.06797i
$330$		0			0
$331$	−11.2381	+	6.48830i	−0.617700	+	0.356629i	−0.775973	−	0.630766i	$-0.782741\pi$
$331$	−11.2381	+	6.48830i	−0.617700	+	0.356629i	0.158273	+	0.987395i	$0.449407\pi$
$332$		0			0
$333$	−3.23846	−	0.860029i	−0.177466	−	0.0471293i
$334$		0			0
$335$	−0.117419	−	0.203376i	−0.00641529	−	0.0111116i
$336$		0			0
$337$	−6.54415	+	11.3348i	−0.356483	+	0.617446i	−0.987371	−	0.158428i	$-0.949357\pi$
$337$	−6.54415	+	11.3348i	−0.356483	+	0.617446i	0.630888	+	0.775874i	$0.282691\pi$
$338$		0			0
$339$	2.72766	+	20.5421i	0.148146	+	1.11570i
$340$		0			0
$341$		−	12.7529i		−	0.690610i
$342$		0			0
$343$	−20.0338			−1.08173
$344$		0			0
$345$	15.1063	−	36.5847i	0.813293	−	1.96965i
$346$		0			0
$347$	−12.1842	−	7.03455i	−0.654082	−	0.377634i	0.135936	−	0.990718i	$-0.456596\pi$
$347$	−12.1842	−	7.03455i	−0.654082	−	0.377634i	−0.790018	+	0.613083i	$0.789929\pi$
$348$		0			0
$349$	1.81396	−	1.04729i	0.0970990	−	0.0560601i	−0.450664	−	0.892694i	$-0.648813\pi$
$349$	1.81396	−	1.04729i	0.0970990	−	0.0560601i	0.547763	+	0.836633i	$0.315479\pi$
$350$		0			0
$351$	0.646290	−	5.03887i	0.0344964	−	0.268955i
$352$		0			0
$353$	12.0901	+	20.9407i	0.643493	+	1.11456i	0.984647	+	0.174555i	$0.0558488\pi$
$353$	12.0901	+	20.9407i	0.643493	+	1.11456i	−0.341154	+	0.940007i	$0.610818\pi$
$354$		0			0
$355$	−42.9633	−	24.8049i	−2.28025	−	1.31650i
$356$		0			0
$357$	−25.0048	−	10.3248i	−1.32339	−	0.546444i
$358$		0			0
$359$	0.469676			0.0247886			0.0123943	−	0.999923i	$-0.496055\pi$
$359$	0.469676			0.0247886			0.0123943	+	0.999923i	$0.496055\pi$
$360$		0			0
$361$	18.4682			0.972012
$362$		0			0
$363$	1.44364	+	10.8721i	0.0757714	+	0.570638i
$364$		0			0
$365$	−5.75080	−	3.32023i	−0.301011	−	0.173789i
$366$		0			0
$367$	2.71101	+	4.69560i	0.141513	+	0.245109i	0.928067	−	0.372414i	$-0.121470\pi$
$367$	2.71101	+	4.69560i	0.141513	+	0.245109i	−0.786553	+	0.617522i	$0.788136\pi$
$368$		0			0
$369$	13.2921	+	13.2331i	0.691958	+	0.688888i
$370$		0			0
$371$	13.5653	−	7.83195i	0.704277	−	0.406615i
$372$		0			0
$373$	−17.6141	−	10.1695i	−0.912025	−	0.526558i	−0.0309430	−	0.999521i	$-0.509851\pi$
$373$	−17.6141	−	10.1695i	−0.912025	−	0.526558i	−0.881082	+	0.472963i	$0.843184\pi$
$374$		0			0
$375$	−20.6590	−	26.8614i	−1.06682	−	1.38712i
$376$		0			0
$377$	4.88406			0.251542
$378$		0			0
$379$			18.7646i			0.963873i	0.876206	+	0.481937i	$0.160066\pi$
$379$			18.7646i			0.963873i	−0.876206	+	0.481937i	$0.839934\pi$
$380$		0			0
$381$	11.6499	−	8.95989i	0.596843	−	0.459029i
$382$		0			0
$383$	−6.68500	+	11.5788i	−0.341587	+	0.591647i	−0.984728	−	0.174102i	$-0.944298\pi$
$383$	−6.68500	+	11.5788i	−0.341587	+	0.591647i	0.643140	+	0.765748i	$0.277631\pi$
$384$		0			0
$385$	18.5662	+	32.1576i	0.946223	+	1.63891i
$386$		0			0
$387$	−4.34182	−	16.0610i	−0.220707	−	0.816424i
$388$		0			0
$389$	−15.0089	+	8.66542i	−0.760984	+	0.439354i	−0.829649	−	0.558286i	$-0.811459\pi$
$389$	−15.0089	+	8.66542i	−0.760984	+	0.439354i	0.0686651	+	0.997640i	$0.478126\pi$
$390$		0			0
$391$	20.0084	−	34.6556i	1.01187	−	1.75261i
$392$		0			0
$393$	−13.2783	+	1.76314i	−0.669800	+	0.0889385i
$394$		0			0
$395$			44.7931i			2.25379i
$396$		0			0
$397$			26.6228i			1.33616i	0.744090	+	0.668080i	$0.232883\pi$
$397$			26.6228i			1.33616i	−0.744090	+	0.668080i	$0.767117\pi$
$398$		0			0
$399$	1.10851	−	2.68461i	0.0554947	−	0.134399i
$400$		0			0
$401$	−7.71021	+	13.3545i	−0.385029	+	0.666890i	−0.991773	−	0.128007i	$-0.959142\pi$
$401$	−7.71021	+	13.3545i	−0.385029	+	0.666890i	0.606744	+	0.794897i	$0.292475\pi$
$402$		0			0
$403$	2.59364	−	1.49744i	0.129198	−	0.0745927i
$404$		0			0
$405$	−17.5883	−	30.1534i	−0.873971	−	1.49833i
$406$		0			0
$407$	2.32494	+	4.02691i	0.115243	+	0.199607i
$408$		0			0
$409$	2.50000	−	4.33013i	0.123617	−	0.214111i	−0.797574	−	0.603220i	$-0.793884\pi$
$409$	2.50000	−	4.33013i	0.123617	−	0.214111i	0.921192	+	0.389109i	$0.127217\pi$
$410$		0			0
$411$	−12.5454	−	5.18013i	−0.618817	−	0.255517i
$412$		0			0
$413$		−	28.2677i		−	1.39096i
$414$		0			0
$415$	−28.4683			−1.39746
$416$		0			0
$417$	6.60212	−	0.876654i	0.323307	−	0.0429300i
$418$		0			0
$419$	−1.39624	−	0.806118i	−0.0682107	−	0.0393815i	0.465507	−	0.885044i	$-0.345872\pi$
$419$	−1.39624	−	0.806118i	−0.0682107	−	0.0393815i	−0.533717	+	0.845663i	$0.679205\pi$
$420$		0			0
$421$	−19.5487	+	11.2864i	−0.952744	+	0.550067i	−0.893932	−	0.448202i	$-0.852064\pi$
$421$	−19.5487	+	11.2864i	−0.952744	+	0.550067i	−0.0588116	+	0.998269i	$0.518731\pi$
$422$		0			0
$423$	−28.1701	+	7.61533i	−1.36968	+	0.370270i
$424$		0			0
$425$	−34.1104	−	59.0809i	−1.65460	−	2.86585i
$426$		0			0
$427$	24.8426	+	14.3429i	1.20222	+	0.694101i
$428$		0			0
$429$	−5.58826	+	4.29790i	−0.269804	+	0.207505i
$430$		0			0
$431$	−11.7834			−0.567586			−0.283793	−	0.958886i	$-0.591593\pi$
$431$	−11.7834			−0.567586			−0.283793	+	0.958886i	$0.591593\pi$
$432$		0			0
$433$	2.28796			0.109952			0.0549762	−	0.998488i	$-0.482492\pi$
$433$	2.28796			0.109952			0.0549762	+	0.998488i	$0.482492\pi$
$434$		0			0
$435$	26.6027	−	20.4600i	1.27550	−	0.980983i
$436$		0			0
$437$	3.72076	+	2.14818i	0.177988	+	0.102762i
$438$		0			0
$439$	7.71736	+	13.3669i	0.368329	+	0.637965i	0.989304	−	0.145865i	$-0.0465965\pi$
$439$	7.71736	+	13.3669i	0.368329	+	0.637965i	−0.620975	+	0.783830i	$0.713263\pi$
$440$		0			0
$441$	−3.63985	−	3.62370i	−0.173326	−	0.172557i
$442$		0			0
$443$	17.8566	−	10.3095i	0.848393	−	0.489820i	−0.0117155	−	0.999931i	$-0.503729\pi$
$443$	17.8566	−	10.3095i	0.848393	−	0.489820i	0.860108	+	0.510112i	$0.170396\pi$
$444$		0			0
$445$	34.7059	+	20.0375i	1.64522	+	0.949867i
$446$		0			0
$447$	−14.5198	+	1.92799i	−0.686762	+	0.0911908i
$448$		0			0
$449$	2.95218			0.139322			0.0696611	−	0.997571i	$-0.477808\pi$
$449$	2.95218			0.139322			0.0696611	+	0.997571i	$0.477808\pi$
$450$		0			0
$451$		−	26.0285i		−	1.22563i
$452$		0			0
$453$	−8.68033	−	3.58421i	−0.407838	−	0.168401i
$454$		0			0
$455$	−4.36006	+	7.55185i	−0.204403	+	0.354036i
$456$		0			0
$457$	−6.37810	−	11.0472i	−0.298355	−	0.516766i	0.677405	−	0.735610i	$-0.263105\pi$
$457$	−6.37810	−	11.0472i	−0.298355	−	0.516766i	−0.975760	+	0.218845i	$0.929771\pi$
$458$		0			0
$459$	−13.6146	−	32.5610i	−0.635476	−	1.51982i
$460$		0			0
$461$	−17.6141	+	10.1695i	−0.820372	+	0.473642i	−0.850545	−	0.525903i	$-0.823728\pi$
$461$	−17.6141	+	10.1695i	−0.820372	+	0.473642i	0.0301727	+	0.999545i	$0.490394\pi$
$462$		0			0
$463$	4.24686	−	7.35577i	0.197368	−	0.341852i	−0.750306	−	0.661091i	$-0.770094\pi$
$463$	4.24686	−	7.35577i	0.197368	−	0.341852i	0.947674	+	0.319239i	$0.103427\pi$
$464$		0			0
$465$	7.85419	−	19.0215i	0.364229	−	0.882100i
$466$		0			0
$467$		−	10.8773i		−	0.503342i	−0.967813	−	0.251671i	$-0.919020\pi$
$467$		−	10.8773i		−	0.503342i	0.967813	−	0.251671i	$-0.0809801\pi$
$468$		0			0
$469$			0.139229i			0.00642899i
$470$		0			0
$471$	6.95365	−	0.923331i	0.320407	−	0.0425449i
$472$		0			0
$473$	−11.5442	+	19.9951i	−0.530801	+	0.919374i
$474$		0			0
$475$	6.34315	−	3.66222i	0.291044	−	0.168034i
$476$		0			0
$477$	19.7505	+	5.24509i	0.904314	+	0.240156i
$478$		0			0
$479$	8.66514	+	15.0085i	0.395920	+	0.685754i	0.993218	−	0.116265i	$-0.0370923\pi$
$479$	8.66514	+	15.0085i	0.395920	+	0.685754i	−0.597298	+	0.802020i	$0.703759\pi$
$480$		0			0
$481$	−0.545984	+	0.945673i	−0.0248947	+	0.0431190i
$482$		0			0
$483$	−18.6012	+	14.3061i	−0.846383	+	0.650949i
$484$		0			0
$485$		−	36.1963i		−	1.64359i
$486$		0			0
$487$	−32.2953			−1.46344			−0.731720	−	0.681605i	$-0.761282\pi$
$487$	−32.2953			−1.46344			−0.731720	+	0.681605i	$0.761282\pi$
$488$		0			0
$489$	−9.91629	−	12.8935i	−0.448430	−	0.583062i
$490$		0			0
$491$	19.2245	+	11.0993i	0.867591	+	0.500904i	0.866547	−	0.499096i	$-0.166334\pi$
$491$	19.2245	+	11.0993i	0.867591	+	0.500904i	0.00104378	+	0.999999i	$0.499668\pi$
$492$		0			0
$493$	29.3846	−	16.9652i	1.32342	−	0.764075i
$494$		0			0
$495$	−12.4339	+	46.8201i	−0.558862	+	2.10441i
$496$		0			0
$497$	14.7061	+	25.4717i	0.659658	+	1.14256i
$498$		0			0
$499$	21.0686	+	12.1639i	0.943158	+	0.544532i	0.890949	−	0.454104i	$-0.150040\pi$
$499$	21.0686	+	12.1639i	0.943158	+	0.544532i	0.0522091	+	0.998636i	$0.483374\pi$
$500$		0			0
$501$	3.61442	+	27.2204i	0.161480	+	1.21612i
$502$		0			0
$503$	3.36573			0.150070			0.0750352	−	0.997181i	$-0.476093\pi$
$503$	3.36573			0.150070			0.0750352	+	0.997181i	$0.476093\pi$
$504$		0			0
$505$	−23.7084			−1.05501
$506$		0			0
$507$	19.2820	+	7.96176i	0.856343	+	0.353594i
$508$		0			0
$509$	−0.753847	−	0.435234i	−0.0334137	−	0.0192914i	0.483200	−	0.875510i	$-0.339474\pi$
$509$	−0.753847	−	0.435234i	−0.0334137	−	0.0192914i	−0.516614	+	0.856219i	$0.672808\pi$
$510$		0			0
$511$	1.96847	+	3.40948i	0.0870798	+	0.150827i
$512$		0			0
$513$	3.49587	−	1.46172i	0.154347	−	0.0645364i
$514$		0			0
$515$	36.2266	−	20.9155i	1.59634	−	0.921645i
$516$		0			0
$517$	35.0703	+	20.2479i	1.54239	+	0.890500i
$518$		0			0
$519$	−2.45079	+	5.93538i	−0.107578	+	0.260534i
$520$		0			0
$521$	19.9558			0.874282			0.437141	−	0.899393i	$-0.355991\pi$
$521$	19.9558			0.874282			0.437141	+	0.899393i	$0.355991\pi$
$522$		0			0
$523$		−	15.1185i		−	0.661085i	−0.943791	−	0.330543i	$-0.892768\pi$
$523$		−	15.1185i		−	0.661085i	0.943791	−	0.330543i	$-0.107232\pi$
$524$		0			0
$525$	5.26584	+	39.6573i	0.229820	+	1.73078i
$526$		0			0
$527$	10.4030	−	18.0185i	0.453161	−	0.784898i
$528$		0			0
$529$	−5.85602	−	10.1429i	−0.254610	−	0.440997i
$530$		0			0
$531$	26.0186	−	26.1346i	1.12911	−	1.13414i
$532$		0			0
$533$	5.29357	−	3.05624i	0.229290	−	0.132381i
$534$		0			0
$535$	1.17938	−	2.04274i	0.0509888	−	0.0883153i
$536$		0			0
$537$	23.4241	+	30.4567i	1.01082	+	1.31430i
$538$		0			0
$539$			7.12754i			0.307005i
$540$		0			0
$541$			12.0537i			0.518230i	0.965846	+	0.259115i	$0.0834309\pi$
$541$			12.0537i			0.518230i	−0.965846	+	0.259115i	$0.916569\pi$
$542$		0			0
$543$	−21.3297	−	27.7334i	−0.915343	−	1.19016i
$544$		0			0
$545$	28.7944	−	49.8733i	1.23342	−	2.13634i
$546$		0			0
$547$	−24.4510	+	14.1168i	−1.04545	+	0.603591i	−0.921372	−	0.388682i	$-0.872931\pi$
$547$	−24.4510	+	14.1168i	−1.04545	+	0.603591i	−0.124078	+	0.992272i	$0.539597\pi$
$548$		0			0
$549$	9.76626	+	36.1267i	0.416814	+	1.54185i
$550$		0			0
$551$	1.82145	+	3.15484i	0.0775964	+	0.134401i
$552$		0			0
$553$	13.2783	−	22.9986i	0.564649	−	0.978001i
$554$		0			0
$555$	0.987665	+	7.43815i	0.0419241	+	0.315732i
$556$		0			0
$557$		−	20.4351i		−	0.865864i	−0.901427	−	0.432932i	$-0.857479\pi$
$557$		−	20.4351i		−	0.865864i	0.901427	−	0.432932i	$-0.142521\pi$
$558$		0			0
$559$	−5.42202			−0.229327
$560$		0			0
$561$	−18.6923	+	45.2694i	−0.789188	+	1.91128i
$562$		0			0
$563$	−23.8436	−	13.7661i	−1.00489	−	0.580173i	−0.0951975	−	0.995458i	$-0.530348\pi$
$563$	−23.8436	−	13.7661i	−1.00489	−	0.580173i	−0.909691	+	0.415286i	$0.863682\pi$
$564$		0			0
$565$	40.1878	−	23.2025i	1.69072	−	0.976135i
$566$		0			0
$567$	0.0920369	+	20.6958i	0.00386518	+	0.869142i
$568$		0			0
$569$	8.25619	+	14.3001i	0.346118	+	0.599493i	0.985556	−	0.169349i	$-0.0541665\pi$
$569$	8.25619	+	14.3001i	0.346118	+	0.599493i	−0.639439	+	0.768842i	$0.720833\pi$
$570$		0			0
$571$	−40.5817	−	23.4298i	−1.69829	−	0.980508i	−0.947384	−	0.320100i	$-0.896283\pi$
$571$	−40.5817	−	23.4298i	−1.69829	−	0.980508i	−0.750907	−	0.660408i	$-0.770383\pi$
$572$		0			0
$573$	−20.1007	−	8.29980i	−0.839717	−	0.346729i
$574$		0			0
$575$	−59.1771			−2.46785
$576$		0			0
$577$	4.95218			0.206162			0.103081	−	0.994673i	$-0.467130\pi$
$577$	4.95218			0.206162			0.103081	+	0.994673i	$0.467130\pi$
$578$		0			0
$579$	1.67163	+	12.5891i	0.0694704	+	0.523185i
$580$		0			0
$581$	14.6168	+	8.43903i	0.606408	+	0.350110i
$582$		0			0
$583$	−14.1792	−	24.5591i	−0.587242	−	1.01713i
$584$		0			0
$585$	−10.9821	+	2.96882i	−0.454052	+	0.122746i
$586$		0			0
$587$	2.06698	−	1.19337i	0.0853135	−	0.0492558i	−0.456736	−	0.889602i	$-0.650982\pi$
$587$	2.06698	−	1.19337i	0.0853135	−	0.0492558i	0.542050	+	0.840346i	$0.317648\pi$
$588$		0			0
$589$	1.93453	+	1.11690i	0.0797111	+	0.0460212i
$590$		0			0
$591$	−26.9325	−	35.0184i	−1.10785	−	1.44047i
$592$		0			0
$593$	25.4287			1.04423			0.522115	−	0.852875i	$-0.325143\pi$
$593$	25.4287			1.04423			0.522115	+	0.852875i	$0.325143\pi$
$594$		0			0
$595$			60.5803i			2.48355i
$596$		0			0
$597$	−28.4031	+	21.8447i	−1.16246	+	0.894044i
$598$		0			0
$599$	−23.3108	+	40.3754i	−0.952452	+	1.64970i	−0.212358	+	0.977192i	$0.568114\pi$
$599$	−23.3108	+	40.3754i	−0.952452	+	1.64970i	−0.740094	+	0.672503i	$0.765219\pi$
$600$		0			0
$601$	−17.7102	−	30.6750i	−0.722414	−	1.25126i	−0.960029	−	0.279899i	$-0.909699\pi$
$601$	−17.7102	−	30.6750i	−0.722414	−	1.25126i	0.237615	−	0.971359i	$-0.423634\pi$
$602$		0			0
$603$	−0.128151	+	0.128723i	−0.00521873	+	0.00524199i
$604$		0			0
$605$	21.2698	−	12.2801i	0.864740	−	0.499258i
$606$		0			0
$607$	−11.8754	+	20.5688i	−0.482009	+	0.834863i	−0.999787	−	0.0206517i	$-0.993426\pi$
$607$	−11.8754	+	20.5688i	−0.482009	+	0.834863i	0.517778	+	0.855515i	$0.326759\pi$
$608$		0			0
$609$	−19.7240	+	2.61903i	−0.799258	+	0.106128i
$610$		0			0
$611$			9.50994i			0.384731i
$612$		0			0
$613$		−	21.5983i		−	0.872345i	−0.899863	−	0.436173i	$-0.856334\pi$
$613$		−	21.5983i		−	0.872345i	0.899863	−	0.436173i	$-0.143666\pi$
$614$		0			0
$615$	16.0302	−	38.8224i	0.646402	−	1.56547i
$616$		0			0
$617$	4.17018	−	7.22297i	0.167885	−	0.290786i	−0.769791	−	0.638296i	$-0.779640\pi$
$617$	4.17018	−	7.22297i	0.167885	−	0.290786i	0.937676	+	0.347510i	$0.112973\pi$
$618$		0			0
$619$	31.0809	−	17.9446i	1.24925	−	0.721253i	0.278287	−	0.960498i	$-0.410233\pi$
$619$	31.0809	−	17.9446i	1.24925	−	0.721253i	0.970959	+	0.239245i	$0.0768999\pi$
$620$		0			0
$621$	−30.3654	−	3.89469i	−1.21852	−	0.156289i
$622$		0			0
$623$	−11.8796	−	20.5761i	−0.475948	−	0.824365i
$624$		0			0
$625$	−12.8321	+	22.2259i	−0.513284	+	0.889035i
$626$		0			0
$627$	−4.86029	−	2.00687i	−0.194101	−	0.0801467i
$628$		0			0
$629$			7.58611i			0.302478i
$630$		0			0
$631$	−31.5824			−1.25727			−0.628637	−	0.777699i	$-0.716387\pi$
$631$	−31.5824			−1.25727			−0.628637	+	0.777699i	$0.716387\pi$
$632$		0			0
$633$	−12.2641	+	1.62847i	−0.487452	+	0.0647257i
$634$		0			0
$635$	−28.5024	−	16.4558i	−1.13108	−	0.653030i
$636$		0			0
$637$	−1.44957	+	0.836909i	−0.0574340	+	0.0331596i
$638$		0			0
$639$	−9.84873	+	37.0856i	−0.389610	+	1.46708i
$640$		0			0
$641$	21.6242	+	37.4542i	0.854105	+	1.47935i	0.877473	+	0.479625i	$0.159227\pi$
$641$	21.6242	+	37.4542i	0.854105	+	1.47935i	−0.0233688	+	0.999727i	$0.507439\pi$
$642$		0			0
$643$	10.9211	+	6.30532i	0.430688	+	0.248658i	0.699640	−	0.714496i	$-0.253344\pi$
$643$	10.9211	+	6.30532i	0.430688	+	0.248658i	−0.268952	+	0.963154i	$0.586677\pi$
$644$		0			0
$645$	−29.5329	+	22.7136i	−1.16286	+	0.894348i
$646$		0			0
$647$	−37.3641			−1.46893			−0.734467	−	0.678644i	$-0.762568\pi$
$647$	−37.3641			−1.46893			−0.734467	+	0.678644i	$0.762568\pi$
$648$		0			0
$649$	−51.1766			−2.00886
$650$		0			0
$651$	−9.67130	+	7.43815i	−0.379048	+	0.291524i
$652$		0			0
$653$	−21.7270	−	12.5441i	−0.850244	−	0.490888i	0.0104893	−	0.999945i	$-0.496661\pi$
$653$	−21.7270	−	12.5441i	−0.850244	−	0.490888i	−0.860733	+	0.509057i	$0.829994\pi$
$654$		0			0
$655$	14.9979	+	25.9771i	0.586016	+	1.01501i
$656$		0			0
$657$	−1.31829	+	4.96405i	−0.0514314	+	0.193666i
$658$		0			0
$659$	−35.0292	+	20.2241i	−1.36455	+	0.787821i	−0.990225	−	0.139479i	$-0.955457\pi$
$659$	−35.0292	+	20.2241i	−1.36455	+	0.787821i	−0.374320	+	0.927299i	$0.622124\pi$
$660$		0			0
$661$	33.8592	+	19.5486i	1.31697	+	0.760354i	0.983240	−	0.182315i	$-0.0583589\pi$
$661$	33.8592	+	19.5486i	1.31697	+	0.760354i	0.333731	+	0.942668i	$0.391692\pi$
$662$		0			0
$663$	−11.4015	+	1.51394i	−0.442799	+	0.0587965i
$664$		0			0
$665$	−6.50413			−0.252219
$666$		0			0
$667$		−	29.4324i		−	1.13963i
$668$		0			0
$669$	−7.45768	−	3.07936i	−0.288331	−	0.119055i
$670$		0			0
$671$	25.9668	−	44.9758i	1.00244	−	1.73627i
$672$		0			0
$673$	−7.26405	−	12.5817i	−0.280009	−	0.484989i	0.691378	−	0.722493i	$-0.257004\pi$
$673$	−7.26405	−	12.5817i	−0.280009	−	0.484989i	−0.971387	+	0.237504i	$0.923671\pi$
$674$		0			0
$675$	−31.6336	+	41.5116i	−1.21758	+	1.59778i
$676$		0			0
$677$	40.9668	−	23.6522i	1.57448	−	0.909027i	0.578871	−	0.815419i	$-0.303493\pi$
$677$	40.9668	−	23.6522i	1.57448	−	0.909027i	0.995609	−	0.0936076i	$-0.0298399\pi$
$678$		0			0
$679$	−10.7299	+	18.5847i	−0.411774	+	0.713214i
$680$		0			0
$681$	−6.40803	+	15.5191i	−0.245556	+	0.594695i
$682$		0			0
$683$		−	2.97962i		−	0.114012i	−0.998374	−	0.0570059i	$-0.981845\pi$
$683$		−	2.97962i		−	0.114012i	0.998374	−	0.0570059i	$-0.0181554\pi$
$684$		0			0
$685$			30.3943i			1.16130i
$686$		0			0
$687$	6.47554	−	0.859847i	0.247057	−	0.0328052i
$688$		0			0
$689$	3.32982	−	5.76741i	0.126856	−	0.219721i
$690$		0			0
$691$	−8.27507	+	4.77761i	−0.314798	+	0.181749i	−0.649072	−	0.760727i	$-0.724842\pi$
$691$	−8.27507	+	4.77761i	−0.314798	+	0.181749i	0.334273	+	0.942476i	$0.391509\pi$
$692$		0			0
$693$	20.2632	−	20.3535i	0.769736	−	0.773166i
$694$		0			0
$695$	−7.45714	−	12.9161i	−0.282865	−	0.489937i
$696$		0			0
$697$	21.2323	−	36.7754i	0.804230	−	1.39297i
$698$		0			0
$699$	−2.68529	+	2.06524i	−0.101567	+	0.0781147i
$700$		0			0
$701$		−	14.7403i		−	0.556734i	−0.960475	−	0.278367i	$-0.910207\pi$
$701$		−	14.7403i		−	0.556734i	0.960475	−	0.278367i	$-0.0897931\pi$
$702$		0			0
$703$	−0.814473			−0.0307184
$704$		0			0
$705$	39.8385	+	51.7992i	1.50041	+	1.95087i
$706$		0			0
$707$	12.1729	+	7.02800i	0.457808	+	0.264315i
$708$		0			0
$709$	−13.5013	+	7.79495i	−0.507050	+	0.292746i	−0.731620	−	0.681712i	$-0.761236\pi$
$709$	−13.5013	+	7.79495i	−0.507050	+	0.292746i	0.224570	+	0.974458i	$0.427902\pi$
$710$		0			0
$711$	33.4451	−	9.04134i	1.25429	−	0.339077i
$712$		0			0
$713$	−9.02391	−	15.6299i	−0.337948	−	0.585343i
$714$		0			0
$715$	13.6721	+	7.89358i	0.511307	+	0.295203i
$716$		0			0
$717$	−3.09207	−	23.2865i	−0.115476	−	0.869652i
$718$		0			0
$719$	37.7089			1.40630			0.703152	−	0.711039i	$-0.251775\pi$
$719$	37.7089			1.40630			0.703152	+	0.711039i	$0.251775\pi$
$720$		0			0
$721$	−24.8003			−0.923613
$722$		0			0
$723$	3.88081	+	1.60243i	0.144329	+	0.0595951i
$724$		0			0
$725$	−43.4540	−	25.0882i	−1.61384	−	0.931752i
$726$		0			0
$727$	−8.83754	−	15.3071i	−0.327766	−	0.567708i	0.654302	−	0.756233i	$-0.272962\pi$
$727$	−8.83754	−	15.3071i	−0.327766	−	0.567708i	−0.982068	+	0.188526i	$0.939629\pi$
$728$		0			0
$729$	−18.9641	+	19.2188i	−0.702374	+	0.711808i
$730$		0			0
$731$	−32.6212	+	18.8339i	−1.20654	+	0.696596i
$732$		0			0
$733$	−4.02969	−	2.32654i	−0.148840	−	0.0859328i	0.423730	−	0.905788i	$-0.360720\pi$
$733$	−4.02969	−	2.32654i	−0.148840	−	0.0859328i	−0.572570	+	0.819856i	$0.694054\pi$
$734$		0			0
$735$	−4.38966	+	10.6310i	−0.161915	+	0.392130i
$736$		0			0
$737$	0.252064			0.00928489
$738$		0			0
$739$		−	41.1901i		−	1.51520i	−0.652718	−	0.757601i	$-0.726371\pi$
$739$		−	41.1901i		−	1.51520i	0.652718	−	0.757601i	$-0.273629\pi$
$740$		0			0
$741$	−0.162542	−	1.22411i	−0.00597113	−	0.0449689i
$742$		0			0
$743$	−3.91901	+	6.78793i	−0.143775	+	0.249025i	−0.928915	−	0.370293i	$-0.879257\pi$
$743$	−3.91901	+	6.78793i	−0.143775	+	0.249025i	0.785141	+	0.619318i	$0.212591\pi$
$744$		0			0
$745$	16.4002	+	28.4059i	0.600856	+	1.04071i
$746$		0			0
$747$	5.74624	+	21.2561i	0.210244	+	0.777720i
$748$		0			0
$749$	−1.21108	+	0.699217i	−0.0442519	+	0.0255489i
$750$		0			0
$751$	0.0295971	−	0.0512637i	0.00108001	−	0.00187064i	−0.865485	−	0.500935i	$-0.832990\pi$
$751$	0.0295971	−	0.0512637i	0.00108001	−	0.00187064i	0.866565	+	0.499064i	$0.166323\pi$
$752$		0			0
$753$	−24.0662	−	31.2916i	−0.877022	−	1.14033i
$754$		0			0
$755$			21.0303i			0.765370i
$756$		0			0
$757$			35.2826i			1.28237i	0.767387	+	0.641185i	$0.221557\pi$
$757$			35.2826i			1.28237i	−0.767387	+	0.641185i	$0.778443\pi$
$758$		0			0
$759$	25.9001	+	33.6761i	0.940115	+	1.22237i
$760$		0			0
$761$	18.4443	−	31.9465i	0.668606	−	1.15806i	−0.309688	−	0.950838i	$-0.600225\pi$
$761$	18.4443	−	31.9465i	0.668606	−	1.15806i	0.978294	−	0.207222i	$-0.0664421\pi$
$762$		0			0
$763$	−29.5685	+	17.0714i	−1.07045	+	0.618025i
$764$		0			0
$765$	−55.7604	+	56.0089i	−2.01602	+	2.02501i
$766$		0			0
$767$	−6.00911	−	10.4081i	−0.216976	−	0.375814i
$768$		0			0
$769$	8.52208	−	14.7607i	0.307314	−	0.532283i	−0.670460	−	0.741946i	$-0.733903\pi$
$769$	8.52208	−	14.7607i	0.307314	−	0.532283i	0.977774	+	0.209662i	$0.0672365\pi$
$770$		0			0
$771$	0.815263	+	6.13978i	0.0293610	+	0.221119i
$772$		0			0
$773$		−	32.1463i		−	1.15622i	−0.815958	−	0.578112i	$-0.803790\pi$
$773$		−	32.1463i		−	1.15622i	0.815958	−	0.578112i	$-0.196210\pi$
$774$		0			0
$775$	−30.7679			−1.10522
$776$		0			0
$777$	1.69782	−	4.11183i	0.0609091	−	0.147511i
$778$		0			0
$779$	3.94835	+	2.27958i	0.141464	+	0.0816744i
$780$		0			0
$781$	46.1147	−	26.6243i	1.65011	−	0.952693i
$782$		0			0
$783$	−20.6463	−	15.7333i	−0.737839	−	0.562264i
$784$		0			0
$785$	−7.85419	−	13.6039i	−0.280328	−	0.485542i
$786$		0			0
$787$	−7.85559	−	4.53543i	−0.280022	−	0.161671i	0.353412	−	0.935468i	$-0.385022\pi$
$787$	−7.85559	−	4.53543i	−0.280022	−	0.161671i	−0.633433	+	0.773797i	$0.718355\pi$
$788$		0			0
$789$	41.8812	+	17.2932i	1.49101	+	0.615656i
$790$		0			0
$791$	−27.5121			−0.978219
$792$		0			0
$793$	12.1960			0.433092
$794$		0			0
$795$	−6.02351	−	45.3633i	−0.213632	−	1.60887i
$796$		0			0
$797$	−42.5519	−	24.5673i	−1.50726	−	0.870220i	−0.999964	−	0.00845051i	$-0.997310\pi$
$797$	−42.5519	−	24.5673i	−1.50726	−	0.870220i	−0.507301	−	0.861769i	$-0.669357\pi$
$798$		0			0
$799$	33.0336	+	57.2160i	1.16865	+	2.02415i
$800$		0			0
$801$	7.95585	−	29.9579i	0.281106	−	1.05851i
$802$		0			0
$803$	6.17263	−	3.56377i	0.217827	−	0.125763i
$804$		0			0
$805$	45.5091	+	26.2747i	1.60399	+	0.926062i
$806$		0			0
$807$	−15.3840	−	20.0027i	−0.541541	−	0.704127i
$808$		0			0
$809$	42.7203			1.50197			0.750983	−	0.660322i	$-0.229580\pi$
$809$	42.7203			1.50197			0.750983	+	0.660322i	$0.229580\pi$
$810$		0			0
$811$			20.9697i			0.736346i	0.929757	+	0.368173i	$0.120017\pi$
$811$			20.9697i			0.736346i	−0.929757	+	0.368173i	$0.879983\pi$
$812$		0			0
$813$	16.9854	−	13.0634i	0.595706	−	0.458154i
$814$		0			0
$815$	−18.2124	+	31.5448i	−0.637952	+	1.10496i
$816$		0			0
$817$	−2.02208	−	3.50234i	−0.0707435	−	0.122531i
$818$		0			0
$819$	6.51870	+	1.73116i	0.227782	+	0.0604915i
$820$		0			0
$821$	−30.9020	+	17.8413i	−1.07849	+	0.622664i	−0.930488	−	0.366323i	$-0.880616\pi$
$821$	−30.9020	+	17.8413i	−1.07849	+	0.622664i	−0.147998	+	0.988988i	$0.547283\pi$
$822$		0			0
$823$	17.2721	−	29.9161i	0.602066	−	1.04281i	−0.390442	−	0.920628i	$-0.627678\pi$
$823$	17.2721	−	29.9161i	0.602066	−	1.04281i	0.992508	−	0.122181i	$-0.0389889\pi$
$824$		0			0
$825$	71.7967	−	9.53343i	2.49964	−	0.331911i
$826$		0			0
$827$		−	55.0950i		−	1.91584i	−0.287034	−	0.957920i	$-0.592669\pi$
$827$		−	55.0950i		−	1.91584i	0.287034	−	0.957920i	$-0.407331\pi$
$828$		0			0
$829$		−	8.70301i		−	0.302268i	−0.988513	−	0.151134i	$-0.951707\pi$
$829$		−	8.70301i		−	0.302268i	0.988513	−	0.151134i	$-0.0482925\pi$
$830$		0			0
$831$	−7.69198	+	18.6286i	−0.266832	+	0.646220i
$832$		0			0
$833$	−5.81416	+	10.0704i	−0.201449	+	0.348920i
$834$		0			0
$835$	53.2529	−	30.7456i	1.84289	−	1.06399i
$836$		0			0
$837$	−15.7879	−	2.02496i	−0.545708	−	0.0699930i
$838$		0			0
$839$	21.6617	+	37.5192i	0.747845	+	1.29531i	0.948854	+	0.315717i	$0.102245\pi$
$839$	21.6617	+	37.5192i	0.747845	+	1.29531i	−0.201008	+	0.979590i	$0.564422\pi$
$840$		0			0
$841$	−2.02208	+	3.50234i	−0.0697268	+	0.120770i
$842$		0			0
$843$	15.6766	+	6.47304i	0.539930	+	0.222943i
$844$		0			0
$845$		−	46.7154i		−	1.60706i
$846$		0			0
$847$	−14.5610			−0.500324
$848$		0			0
$849$	−29.8183	+	3.95938i	−1.02336	+	0.135886i
$850$		0			0
$851$	5.69884	+	3.29023i	0.195354	+	0.112788i
$852$		0			0
$853$	0.846691	−	0.488838i	0.0289902	−	0.0167375i	−0.485435	−	0.874273i	$-0.661339\pi$
$853$	0.846691	−	0.488838i	0.0289902	−	0.0167375i	0.514425	+	0.857535i	$0.328005\pi$
$854$		0			0
$855$	−6.01333	−	5.98664i	−0.205651	−	0.204739i
$856$		0			0
$857$	1.64398	+	2.84746i	0.0561573	+	0.0972673i	0.892737	−	0.450577i	$-0.148782\pi$
$857$	1.64398	+	2.84746i	0.0561573	+	0.0972673i	−0.836580	+	0.547845i	$0.815449\pi$
$858$		0			0
$859$	34.2664	+	19.7837i	1.16915	+	0.675012i	0.953481	−	0.301454i	$-0.0974718\pi$
$859$	34.2664	+	19.7837i	1.16915	+	0.675012i	0.215674	+	0.976465i	$0.430805\pi$
$860$		0			0
$861$	−19.7389	+	15.1811i	−0.672701	+	0.517371i
$862$		0			0
$863$	20.2687			0.689953			0.344977	−	0.938611i	$-0.387887\pi$
$863$	20.2687			0.689953			0.344977	+	0.938611i	$0.387887\pi$
$864$		0			0
$865$	14.3799			0.488932
$866$		0			0
$867$	−39.9976	+	30.7619i	−1.35839	+	1.04473i
$868$		0			0
$869$	−41.6374	−	24.0394i	−1.41245	−	0.815480i
$870$		0			0
$871$	0.0295971	+	0.0512637i	0.00100286	+	0.00173700i
$872$		0			0
$873$	−27.0262	+	7.30610i	−0.914698	+	0.247274i
$874$		0			0
$875$	38.9625	−	22.4950i	1.31717	−	0.760470i
$876$		0			0
$877$	−2.57746	−	1.48810i	−0.0870345	−	0.0502494i	0.455851	−	0.890056i	$-0.349335\pi$
$877$	−2.57746	−	1.48810i	−0.0870345	−	0.0502494i	−0.542886	+	0.839807i	$0.682668\pi$
$878$		0			0
$879$	10.2010	−	1.35452i	0.344071	−	0.0456870i
$880$		0			0
$881$	−47.3404			−1.59494			−0.797469	−	0.603360i	$-0.793828\pi$
$881$	−47.3404			−1.59494			−0.797469	+	0.603360i	$0.793828\pi$
$882$		0			0
$883$		−	31.9403i		−	1.07488i	−0.843303	−	0.537438i	$-0.819392\pi$
$883$		−	31.9403i		−	1.07488i	0.843303	−	0.537438i	$-0.180608\pi$
$884$		0			0
$885$	−76.3318	−	31.5183i	−2.56586	−	1.05948i
$886$		0			0
$887$	−2.71101	+	4.69560i	−0.0910267	+	0.157663i	−0.907943	−	0.419093i	$-0.862348\pi$
$887$	−2.71101	+	4.69560i	−0.0910267	+	0.157663i	0.816917	+	0.576756i	$0.195682\pi$
$888$		0			0
$889$	9.75619	+	16.8982i	0.327212	+	0.566748i
$890$		0			0
$891$	37.4683	−	0.166626i	1.25524	−	0.00558219i
$892$		0			0
$893$	−6.14292	+	3.54662i	−0.205565	+	0.118683i
$894$		0			0
$895$	43.0210	−	74.5145i	1.43803	−	2.49074i
$896$		0			0
$897$	−3.80774	+	9.22168i	−0.127137	+	0.307903i
$898$		0			0
$899$		−	15.3028i		−	0.510377i
$900$		0			0
$901$		−	46.2657i		−	1.54133i
$902$		0			0
$903$	21.8966	−	2.90751i	0.728672	−	0.0967557i
$904$		0			0
$905$	−39.1743	+	67.8519i	−1.30220	+	2.25547i
$906$		0			0
$907$	6.06588	−	3.50214i	0.201414	−	0.116287i	−0.395901	−	0.918293i	$-0.629568\pi$
$907$	6.06588	−	3.50214i	0.201414	−	0.116287i	0.597315	+	0.802007i	$0.296234\pi$
$908$		0			0
$909$	4.78546	+	17.7020i	0.158724	+	0.587139i
$910$		0			0
$911$	−2.88341	−	4.99421i	−0.0955315	−	0.165465i	0.814299	−	0.580446i	$-0.197122\pi$
$911$	−2.88341	−	4.99421i	−0.0955315	−	0.165465i	−0.909830	+	0.414980i	$0.863788\pi$
$912$		0			0
$913$	15.2783	−	26.4627i	0.505637	−	0.875789i
$914$		0			0
$915$	66.4298	−	51.0908i	2.19610	−	1.68901i
$916$		0			0
$917$		−	17.7836i		−	0.587267i
$918$		0			0
$919$	45.3629			1.49638			0.748191	−	0.663483i	$-0.230923\pi$
$919$	45.3629			1.49638			0.748191	+	0.663483i	$0.230923\pi$
$920$		0			0
$921$	−31.0303	−	40.3466i	−1.02248	−	1.32946i
$922$		0			0
$923$	10.8295	+	6.25241i	0.356457	+	0.205801i
$924$		0			0
$925$	9.71538	−	5.60918i	0.319440	−	0.184429i
$926$		0			0
$927$	−22.9289	−	22.8272i	−0.753084	−	0.749743i
$928$		0			0
$929$	−13.0202	−	22.5517i	−0.427180	−	0.739898i	0.569441	−	0.822032i	$-0.307160\pi$
$929$	−13.0202	−	22.5517i	−0.427180	−	0.739898i	−0.996621	+	0.0821342i	$0.973826\pi$
$930$		0			0
$931$	−1.08120	−	0.624231i	−0.0354349	−	0.0204583i
$932$		0			0
$933$	3.27776	+	24.6850i	0.107309	+	0.808150i
$934$		0			0
$935$	109.676			3.58680
$936$		0			0
$937$	15.7562			0.514732			0.257366	−	0.966314i	$-0.417145\pi$
$937$	15.7562			0.514732			0.257366	+	0.966314i	$0.417145\pi$
$938$		0			0
$939$	−8.00471	−	3.30524i	−0.261224	−	0.107862i
$940$		0			0
$941$	33.9521	+	19.6022i	1.10681	+	0.639015i	0.938000	−	0.346635i	$-0.112676\pi$
$941$	33.9521	+	19.6022i	1.10681	+	0.639015i	0.168806	+	0.985649i	$0.446009\pi$
$942$		0			0
$943$	−18.4176	−	31.9003i	−0.599760	−	1.03882i
$944$		0			0
$945$	42.7585	−	17.8785i	1.39093	−	0.581586i
$946$		0			0
$947$	−35.5295	+	20.5129i	−1.15455	+	0.666581i	−0.949992	−	0.312273i	$-0.898910\pi$
$947$	−35.5295	+	20.5129i	−1.15455	+	0.666581i	−0.204560	+	0.978854i	$0.565576\pi$
$948$		0			0
$949$	1.44957	+	0.836909i	0.0470550	+	0.0271672i
$950$		0			0
$951$	−1.93887	+	4.69560i	−0.0628721	+	0.152265i
$952$		0			0
$953$	−5.13612			−0.166375			−0.0831876	−	0.996534i	$-0.526510\pi$
$953$	−5.13612			−0.166375			−0.0831876	+	0.996534i	$0.526510\pi$
$954$		0			0
$955$			48.6988i			1.57586i
$956$		0			0
$957$	4.74157	+	35.7090i	0.153273	+	1.15431i
$958$		0			0
$959$	9.00994	−	15.6057i	0.290946	−	0.503933i
$960$		0			0
$961$	10.8082	+	18.7204i	0.348652	+	0.603882i
$962$		0			0
$963$	−1.76328	−	0.468269i	−0.0568208	−	0.0150898i
$964$		0			0
$965$	24.6288	−	14.2195i	0.792830	−	0.457740i
$966$		0			0
$967$	6.89445	−	11.9415i	0.221711	−	0.384014i	−0.733617	−	0.679563i	$-0.762169\pi$
$967$	6.89445	−	11.9415i	0.221711	−	0.384014i	0.955328	+	0.295549i	$0.0955026\pi$
$968$		0			0
$969$	−5.22999	−	6.80019i	−0.168011	−	0.218453i
$970$		0			0
$971$		−	37.0596i		−	1.18930i	−0.803985	−	0.594650i	$-0.797291\pi$
$971$		−	37.0596i		−	1.18930i	0.803985	−	0.594650i	$-0.202709\pi$
$972$		0			0
$973$			8.84224i			0.283469i
$974$		0			0
$975$	10.3692	+	13.4823i	0.332079	+	0.431779i
$976$		0			0
$977$	0.419953	−	0.727379i	0.0134355	−	0.0232709i	−0.859230	−	0.511590i	$-0.829057\pi$
$977$	0.419953	−	0.727379i	0.0134355	−	0.0232709i	0.872665	+	0.488319i	$0.162390\pi$
$978$		0			0
$979$	−37.2516	+	21.5072i	−1.19057	+	0.687375i
$980$		0			0
$981$	−43.0503	−	11.4328i	−1.37449	−	0.365020i
$982$		0			0
$983$	−21.8627	−	37.8674i	−0.697313	−	1.20778i	−0.969395	−	0.245507i	$-0.921045\pi$
$983$	−21.8627	−	37.8674i	−0.697313	−	1.20778i	0.272082	−	0.962274i	$-0.412288\pi$
$984$		0			0
$985$	−49.4646	+	85.6751i	−1.57607	+	2.72984i
$986$		0			0
$987$	−5.09962	−	38.4054i	−0.162323	−	1.22246i
$988$		0			0
$989$			32.6743i			1.03898i
$990$		0			0
$991$	13.7973			0.438287			0.219143	−	0.975693i	$-0.429674\pi$
$991$	13.7973			0.438287			0.219143	+	0.975693i	$0.429674\pi$
$992$		0			0
$993$	8.57815	−	20.7748i	0.272219	−	0.659268i
$994$		0			0
$995$	69.4903	+	40.1202i	2.20299	+	1.27190i
$996$		0			0
$997$	−47.6848	+	27.5308i	−1.51019	+	0.871911i	−0.510264	+	0.860018i	$0.670452\pi$
$997$	−47.6848	+	27.5308i	−1.51019	+	0.871911i	−0.999929	+	0.0118930i	$0.996214\pi$
$998$		0			0
$999$	5.35439	−	2.23881i	0.169405	−	0.0708329i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1152.2.r.g.193.4	yes	24
3.2	odd	2		3456.2.r.h.577.2		24
4.3	odd	2	inner	1152.2.r.g.193.10	yes	24
8.3	odd	2	inner	1152.2.r.g.193.3	✓	24
8.5	even	2	inner	1152.2.r.g.193.9	yes	24
9.2	odd	6		3456.2.r.h.2881.12		24
9.7	even	3	inner	1152.2.r.g.961.9	yes	24
12.11	even	2		3456.2.r.h.577.1		24
24.5	odd	2		3456.2.r.h.577.12		24
24.11	even	2		3456.2.r.h.577.11		24
36.7	odd	6	inner	1152.2.r.g.961.3	yes	24
36.11	even	6		3456.2.r.h.2881.11		24
72.11	even	6		3456.2.r.h.2881.1		24
72.29	odd	6		3456.2.r.h.2881.2		24
72.43	odd	6	inner	1152.2.r.g.961.10	yes	24
72.61	even	6	inner	1152.2.r.g.961.4	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1152.2.r.g.193.3	✓	24	8.3	odd	2	inner
1152.2.r.g.193.4	yes	24	1.1	even	1	trivial
1152.2.r.g.193.9	yes	24	8.5	even	2	inner
1152.2.r.g.193.10	yes	24	4.3	odd	2	inner
1152.2.r.g.961.3	yes	24	36.7	odd	6	inner
1152.2.r.g.961.4	yes	24	72.61	even	6	inner
1152.2.r.g.961.9	yes	24	9.7	even	3	inner
1152.2.r.g.961.10	yes	24	72.43	odd	6	inner
3456.2.r.h.577.1		24	12.11	even	2
3456.2.r.h.577.2		24	3.2	odd	2
3456.2.r.h.577.11		24	24.11	even	2
3456.2.r.h.577.12		24	24.5	odd	2
3456.2.r.h.2881.1		24	72.11	even	6
3456.2.r.h.2881.2		24	72.29	odd	6
3456.2.r.h.2881.11		24	36.11	even	6
3456.2.r.h.2881.12		24	9.2	odd	6

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:	\( N \)	\(=\)	\( 1152 = 2^{7} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1152.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37296 + 1.05593i) q^{3} +(3.35903 + 1.93934i) q^{5} +(-1.14978 - 1.99147i) q^{7} +(0.770012 - 2.89950i) q^{9} +O(q^{10})\)	\(q+(-1.37296 + 1.05593i) q^{3} +(3.35903 + 1.93934i) q^{5} +(-1.14978 - 1.99147i) q^{7} +(0.770012 - 2.89950i) q^{9} +(-3.60542 + 2.08159i) q^{11} +(-0.846691 - 0.488838i) q^{13} +(-6.65962 + 0.884289i) q^{15} -6.79209 q^{17} -0.729224i q^{19} +(3.68146 + 1.52012i) q^{21} +(-2.94585 + 5.10236i) q^{23} +(5.02208 + 8.69849i) q^{25} +(2.00448 + 4.79396i) q^{27} +(-4.32630 + 2.49779i) q^{29} +(-1.53163 + 2.65287i) q^{31} +(2.75206 - 6.66502i) q^{33} -8.91924i q^{35} -1.11690i q^{37} +(1.67865 - 0.222897i) q^{39} +(-3.12603 + 5.41445i) q^{41} +(4.80283 - 2.77291i) q^{43} +(8.20961 - 8.24620i) q^{45} +(-4.86355 - 8.42391i) q^{47} +(0.856020 - 1.48267i) q^{49} +(9.32523 - 7.17199i) q^{51} +6.81170i q^{53} -16.1477 q^{55} +(0.770012 + 1.00119i) q^{57} +(10.6458 + 6.14633i) q^{59} +(-10.8032 + 6.23724i) q^{61} +(-6.65962 + 1.80032i) q^{63} +(-1.89604 - 3.28404i) q^{65} +(-0.0524343 - 0.0302730i) q^{67} +(-1.34323 - 10.1159i) q^{69} -12.7904 q^{71} -1.71204 q^{73} +(-16.0801 - 6.63966i) q^{75} +(8.29088 + 4.78674i) q^{77} +(5.77427 + 10.0013i) q^{79} +(-7.81416 - 4.46529i) q^{81} +(-6.35637 + 3.66985i) q^{83} +(-22.8149 - 13.1722i) q^{85} +(3.30232 - 7.99764i) q^{87} +10.3321 q^{89} +2.24822i q^{91} +(-0.698385 - 5.25957i) q^{93} +(1.41421 - 2.44949i) q^{95} +(-4.66606 - 8.08185i) q^{97} +(3.25935 + 12.0568i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{9}+O(q^{10}) \) 24 * q + 4 * q^9	\( 24 q + 4 q^{9} - 40 q^{17} + 12 q^{25} - 28 q^{33} - 28 q^{41} - 12 q^{49} + 4 q^{57} + 16 q^{65} + 24 q^{73} + 44 q^{81} + 96 q^{89} - 36 q^{97}+O(q^{100}) \) 24 * q + 4 * q^9 - 40 * q^17 + 12 * q^25 - 28 * q^33 - 28 * q^41 - 12 * q^49 + 4 * q^57 + 16 * q^65 + 24 * q^73 + 44 * q^81 + 96 * q^89 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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