LMFDB - Embedded newform 572.2.bg.a.81.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(9,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 18, 20]))

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

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

chi := DirichletCharacter("572.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bg (of order $15$, degree $8$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			81.6
Character	$\chi$	$=$	572.81
Dual form			572.2.bg.a.113.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.807770 + 0.171697i) q^{3} +(0.437086 - 0.317562i) q^{5} +(-2.23753 - 0.475601i) q^{7} +(-2.11762 + 0.942827i) q^{9} +O(q^{10})$	\(q+(-0.807770 + 0.171697i) q^{3} +(0.437086 - 0.317562i) q^{5} +(-2.23753 - 0.475601i) q^{7} +(-2.11762 + 0.942827i) q^{9} +(3.31194 + 0.176210i) q^{11} +(2.14084 + 2.90117i) q^{13} +(-0.298541 + 0.331563i) q^{15} +(0.598752 + 5.69674i) q^{17} +(-0.899848 - 0.999382i) q^{19} +1.88907 q^{21} +(1.79858 + 3.11523i) q^{23} +(-1.45489 + 4.47768i) q^{25} +(3.55297 - 2.58138i) q^{27} +(-2.56550 + 2.84927i) q^{29} +(3.15989 + 2.29579i) q^{31} +(-2.70554 + 0.426313i) q^{33} +(-1.12902 + 0.502674i) q^{35} +(-0.191711 + 0.212916i) q^{37} +(-2.22743 - 1.97590i) q^{39} +(-0.983809 + 0.209115i) q^{41} +(1.24754 - 2.16080i) q^{43} +(-0.626178 + 1.08457i) q^{45} +(-0.636874 + 1.96010i) q^{47} +(-1.61449 - 0.718816i) q^{49} +(-1.46177 - 4.49885i) q^{51} +(4.33179 + 3.14723i) q^{53} +(1.50356 - 0.974726i) q^{55} +(0.898461 + 0.652770i) q^{57} +(-6.04441 - 1.28478i) q^{59} +(1.23803 + 11.7790i) q^{61} +(5.18665 - 1.10246i) q^{63} +(1.85703 + 0.588211i) q^{65} +(0.157813 + 0.273341i) q^{67} +(-1.98771 - 2.20758i) q^{69} +(-0.104799 - 0.997095i) q^{71} +(3.57135 + 10.9915i) q^{73} +(0.406410 - 3.86673i) q^{75} +(-7.32675 - 1.96944i) q^{77} +(-2.66930 - 1.93936i) q^{79} +(2.22642 - 2.47269i) q^{81} +(1.95382 - 1.41954i) q^{83} +(2.07077 + 2.29983i) q^{85} +(1.58312 - 2.74204i) q^{87} +(-4.74947 - 8.22632i) q^{89} +(-3.41040 - 7.50963i) q^{91} +(-2.94664 - 1.31193i) q^{93} +(-0.710676 - 0.151059i) q^{95} +(13.4003 - 5.96619i) q^{97} +(-7.17958 + 2.74944i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 8 q^{9}+O(q^{10}) $ 112 * q + 8 * q^9	$ 112 q + 8 q^{9} - 10 q^{11} + 11 q^{13} - 2 q^{15} + 4 q^{17} - 12 q^{19} - 40 q^{21} + 10 q^{23} - 16 q^{25} - 12 q^{27} + q^{29} + 4 q^{31} + 35 q^{33} - 5 q^{35} - 12 q^{37} + 21 q^{39} - 10 q^{41} - 32 q^{43} + 34 q^{45} + 70 q^{47} + 16 q^{49} - 48 q^{51} - 26 q^{53} + 10 q^{55} - 12 q^{57} - 5 q^{59} + 28 q^{61} + 34 q^{63} + 22 q^{65} - 68 q^{67} - 58 q^{69} + 44 q^{71} + 42 q^{73} - 24 q^{75} + 46 q^{77} - 24 q^{79} + 64 q^{81} - 114 q^{83} + 4 q^{85} - 30 q^{87} - 6 q^{89} + 77 q^{91} - 5 q^{93} - 36 q^{95} - 15 q^{97} - 40 q^{99}+O(q^{100}) $ 112 * q + 8 * q^9 - 10 * q^11 + 11 * q^13 - 2 * q^15 + 4 * q^17 - 12 * q^19 - 40 * q^21 + 10 * q^23 - 16 * q^25 - 12 * q^27 + q^29 + 4 * q^31 + 35 * q^33 - 5 * q^35 - 12 * q^37 + 21 * q^39 - 10 * q^41 - 32 * q^43 + 34 * q^45 + 70 * q^47 + 16 * q^49 - 48 * q^51 - 26 * q^53 + 10 * q^55 - 12 * q^57 - 5 * q^59 + 28 * q^61 + 34 * q^63 + 22 * q^65 - 68 * q^67 - 58 * q^69 + 44 * q^71 + 42 * q^73 - 24 * q^75 + 46 * q^77 - 24 * q^79 + 64 * q^81 - 114 * q^83 + 4 * q^85 - 30 * q^87 - 6 * q^89 + 77 * q^91 - 5 * q^93 - 36 * q^95 - 15 * q^97 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−0.807770	+	0.171697i	−0.466366	+	0.0991292i	−0.435100	−	0.900382i	$-0.643287\pi$
$3$	−0.807770	+	0.171697i	−0.466366	+	0.0991292i	−0.0312658	+	0.999511i	$0.509954\pi$
$4$		0			0
$5$	0.437086	−	0.317562i	0.195471	−	0.142018i	−0.485745	−	0.874101i	$-0.661452\pi$
$5$	0.437086	−	0.317562i	0.195471	−	0.142018i	0.681216	+	0.732083i	$0.261452\pi$
$6$		0			0
$7$	−2.23753	−	0.475601i	−0.845706	−	0.179760i	−0.235373	−	0.971905i	$-0.575631\pi$
$7$	−2.23753	−	0.475601i	−0.845706	−	0.179760i	−0.610333	+	0.792145i	$0.708964\pi$
$8$		0			0
$9$	−2.11762	+	0.942827i	−0.705875	+	0.314276i
$10$		0			0
$11$	3.31194	+	0.176210i	0.998588	+	0.0531293i
$11$	3.31194	+	0.176210i	0.998588	+	0.0531293i
$12$		0			0
$13$	2.14084	+	2.90117i	0.593763	+	0.804640i
$13$	2.14084	+	2.90117i	0.593763	+	0.804640i
$14$		0			0
$15$	−0.298541	+	0.331563i	−0.0770829	+	0.0856092i
$16$		0			0
$17$	0.598752	+	5.69674i	0.145219	+	1.38166i	0.788029	+	0.615638i	$0.211102\pi$
$17$	0.598752	+	5.69674i	0.145219	+	1.38166i	−0.642810	+	0.766025i	$0.722232\pi$
$18$		0			0
$19$	−0.899848	−	0.999382i	−0.206439	−	0.229274i	0.631030	−	0.775758i	$-0.282632\pi$
$19$	−0.899848	−	0.999382i	−0.206439	−	0.229274i	−0.837469	+	0.546484i	$0.815966\pi$
$20$		0			0
$21$	1.88907			0.412228
$22$		0			0
$23$	1.79858	+	3.11523i	0.375030	+	0.649570i	0.990331	−	0.138721i	$-0.0442992\pi$
$23$	1.79858	+	3.11523i	0.375030	+	0.649570i	−0.615302	+	0.788292i	$0.710966\pi$
$24$		0			0
$25$	−1.45489	+	4.47768i	−0.290977	+	0.895536i
$26$		0			0
$27$	3.55297	−	2.58138i	0.683769	−	0.496788i
$28$		0			0
$29$	−2.56550	+	2.84927i	−0.476401	+	0.529097i	−0.932663	−	0.360749i	$-0.882521\pi$
$29$	−2.56550	+	2.84927i	−0.476401	+	0.529097i	0.456262	+	0.889845i	$0.349188\pi$
$30$		0			0
$31$	3.15989	+	2.29579i	0.567533	+	0.412337i	0.834208	−	0.551450i	$-0.185925\pi$
$31$	3.15989	+	2.29579i	0.567533	+	0.412337i	−0.266675	+	0.963786i	$0.585925\pi$
$32$		0			0
$33$	−2.70554	+	0.426313i	−0.470974	+	0.0742115i
$34$		0			0
$35$	−1.12902	+	0.502674i	−0.190840	+	0.0849674i
$36$		0			0
$37$	−0.191711	+	0.212916i	−0.0315171	+	0.0350032i	−0.758697	−	0.651443i	$-0.774164\pi$
$37$	−0.191711	+	0.212916i	−0.0315171	+	0.0350032i	0.727180	+	0.686447i	$0.240830\pi$
$38$		0			0
$39$	−2.22743	−	1.97590i	−0.356675	−	0.316398i
$40$		0			0
$41$	−0.983809	+	0.209115i	−0.153645	+	0.0326583i	−0.284092	−	0.958797i	$-0.591692\pi$
$41$	−0.983809	+	0.209115i	−0.153645	+	0.0326583i	0.130447	+	0.991455i	$0.458359\pi$
$42$		0			0
$43$	1.24754	−	2.16080i	0.190248	−	0.329519i	−0.755084	−	0.655628i	$-0.772404\pi$
$43$	1.24754	−	2.16080i	0.190248	−	0.329519i	0.945332	+	0.326108i	$0.105737\pi$
$44$		0			0
$45$	−0.626178	+	1.08457i	−0.0933451	+	0.161678i
$46$		0			0
$47$	−0.636874	+	1.96010i	−0.0928977	+	0.285910i	−0.986700	−	0.162551i	$-0.948028\pi$
$47$	−0.636874	+	1.96010i	−0.0928977	+	0.285910i	0.893802	+	0.448461i	$0.148028\pi$
$48$		0			0
$49$	−1.61449	−	0.718816i	−0.230641	−	0.102688i
$50$		0			0
$51$	−1.46177	−	4.49885i	−0.204688	−	0.629966i
$52$		0			0
$53$	4.33179	+	3.14723i	0.595017	+	0.432305i	0.844107	−	0.536176i	$-0.180131\pi$
$53$	4.33179	+	3.14723i	0.595017	+	0.432305i	−0.249090	+	0.968480i	$0.580131\pi$
$54$		0			0
$55$	1.50356	−	0.974726i	0.202740	−	0.131432i
$56$		0			0
$57$	0.898461	+	0.652770i	0.119004	+	0.0864615i
$58$		0			0
$59$	−6.04441	−	1.28478i	−0.786915	−	0.167264i	−0.203108	−	0.979156i	$-0.565104\pi$
$59$	−6.04441	−	1.28478i	−0.786915	−	0.167264i	−0.583807	+	0.811892i	$0.698438\pi$
$60$		0			0
$61$	1.23803	+	11.7790i	0.158513	+	1.50815i	0.727673	+	0.685924i	$0.240602\pi$
$61$	1.23803	+	11.7790i	0.158513	+	1.50815i	−0.569160	+	0.822227i	$0.692731\pi$
$62$		0			0
$63$	5.18665	−	1.10246i	0.653456	−	0.138896i
$64$		0			0
$65$	1.85703	+	0.588211i	0.230337	+	0.0729586i
$66$		0			0
$67$	0.157813	+	0.273341i	0.0192800	+	0.0333939i	0.875504	−	0.483210i	$-0.160529\pi$
$67$	0.157813	+	0.273341i	0.0192800	+	0.0333939i	−0.856224	+	0.516604i	$0.827196\pi$
$68$		0			0
$69$	−1.98771	−	2.20758i	−0.239293	−	0.265761i
$70$		0			0
$71$	−0.104799	−	0.997095i	−0.0124373	−	0.118333i	0.986542	−	0.163510i	$-0.0522816\pi$
$71$	−0.104799	−	0.997095i	−0.0124373	−	0.118333i	−0.998979	+	0.0451766i	$0.985615\pi$
$72$		0			0
$73$	3.57135	+	10.9915i	0.417995	+	1.28646i	0.909545	+	0.415606i	$0.136431\pi$
$73$	3.57135	+	10.9915i	0.417995	+	1.28646i	−0.491550	+	0.870849i	$0.663569\pi$
$74$		0			0
$75$	0.406410	−	3.86673i	0.0469282	−	0.446492i
$76$		0			0
$77$	−7.32675	−	1.96944i	−0.834961	−	0.224438i
$78$		0			0
$79$	−2.66930	−	1.93936i	−0.300320	−	0.218195i	0.427412	−	0.904057i	$-0.359425\pi$
$79$	−2.66930	−	1.93936i	−0.300320	−	0.218195i	−0.727732	+	0.685862i	$0.759425\pi$
$80$		0			0
$81$	2.22642	−	2.47269i	0.247380	−	0.274744i
$82$		0			0
$83$	1.95382	−	1.41954i	0.214460	−	0.155814i	−0.475369	−	0.879786i	$-0.657686\pi$
$83$	1.95382	−	1.41954i	0.214460	−	0.155814i	0.689829	+	0.723972i	$0.257686\pi$
$84$		0			0
$85$	2.07077	+	2.29983i	0.224607	+	0.249451i
$86$		0			0
$87$	1.58312	−	2.74204i	0.169728	−	0.293978i
$88$		0			0
$89$	−4.74947	−	8.22632i	−0.503443	−	0.871989i	−0.999992	−	0.00398007i	$-0.998733\pi$
$89$	−4.74947	−	8.22632i	−0.503443	−	0.871989i	0.496549	−	0.868009i	$-0.334600\pi$
$90$		0			0
$91$	−3.41040	−	7.50963i	−0.357507	−	0.787223i
$92$		0			0
$93$	−2.94664	−	1.31193i	−0.305553	−	0.136041i
$94$		0			0
$95$	−0.710676	−	0.151059i	−0.0729138	−	0.0154983i
$96$		0			0
$97$	13.4003	−	5.96619i	1.36059	−	0.605774i	0.408829	−	0.912611i	$-0.365937\pi$
$97$	13.4003	−	5.96619i	1.36059	−	0.605774i	0.951762	+	0.306836i	$0.0992705\pi$
$98$		0			0
$99$	−7.17958	+	2.74944i	−0.721575	+	0.276329i
$100$		0			0
$101$	1.67197	−	15.9078i	0.166367	−	1.58288i	−0.519059	−	0.854738i	$-0.673718\pi$
$101$	1.67197	−	15.9078i	0.166367	−	1.58288i	0.685426	−	0.728142i	$-0.259616\pi$
$102$		0			0
$103$	−3.53221	−	10.8710i	−0.348039	−	1.07116i	−0.959936	−	0.280218i	$-0.909593\pi$
$103$	−3.53221	−	10.8710i	−0.348039	−	1.07116i	0.611897	−	0.790937i	$-0.290407\pi$
$104$		0			0
$105$	0.825684	−	0.599895i	0.0805786	−	0.0585437i
$106$		0			0
$107$	6.99922	−	1.48773i	0.676640	−	0.143824i	0.143241	−	0.989688i	$-0.454248\pi$
$107$	6.99922	−	1.48773i	0.676640	−	0.143824i	0.533399	+	0.845864i	$0.320914\pi$
$108$		0			0
$109$	−2.00250			−0.191804			−0.0959022	−	0.995391i	$-0.530574\pi$
$109$	−2.00250			−0.191804			−0.0959022	+	0.995391i	$0.530574\pi$
$110$		0			0
$111$	0.118301	−	0.204904i	0.0112287	−	0.0194486i
$112$		0			0
$113$	−12.2767	−	13.6347i	−1.15490	−	1.28264i	−0.952910	−	0.303254i	$-0.901927\pi$
$113$	−12.2767	−	13.6347i	−1.15490	−	1.28264i	−0.201987	−	0.979388i	$-0.564740\pi$
$114$		0			0
$115$	1.77541	+	0.790464i	0.165558	+	0.0737111i
$116$		0			0
$117$	−7.26880	−	4.12514i	−0.672001	−	0.381369i
$118$		0			0
$119$	1.36965	−	13.0314i	0.125556	−	1.19458i
$120$		0			0
$121$	10.9379	+	1.16719i	0.994355	+	0.106109i
$122$		0			0
$123$	0.758787	−	0.337834i	0.0684175	−	0.0304614i
$124$		0			0
$125$	1.62079	+	4.98827i	0.144968	+	0.446165i
$126$		0			0
$127$	2.96131	+	1.31846i	0.262774	+	0.116994i	0.533895	−	0.845551i	$-0.320728\pi$
$127$	2.96131	+	1.31846i	0.262774	+	0.116994i	−0.271121	+	0.962545i	$0.587394\pi$
$128$		0			0
$129$	−0.636722	+	1.95963i	−0.0560603	+	0.172536i
$130$		0			0
$131$	−8.97896			−0.784495			−0.392247	−	0.919860i	$-0.628302\pi$
$131$	−8.97896			−0.784495			−0.392247	+	0.919860i	$0.628302\pi$
$132$		0			0
$133$	1.53813	+	2.66411i	0.133372	+	0.231008i
$134$		0			0
$135$	0.733205	−	2.25657i	0.0631043	−	0.194215i
$136$		0			0
$137$	−1.26761	−	12.0605i	−0.108299	−	1.03040i	−0.904822	−	0.425791i	$-0.859996\pi$
$137$	−1.26761	−	12.0605i	−0.108299	−	1.03040i	0.796522	−	0.604609i	$-0.206671\pi$
$138$		0			0
$139$	−11.4432	−	2.43234i	−0.970603	−	0.206308i	−0.304784	−	0.952421i	$-0.598584\pi$
$139$	−11.4432	−	2.43234i	−0.970603	−	0.206308i	−0.665819	+	0.746113i	$0.731918\pi$
$140$		0			0
$141$	0.177905	−	1.69266i	0.0149823	−	0.142547i
$142$		0			0
$143$	6.57913	+	9.98574i	0.550175	+	0.835049i
$144$		0			0
$145$	−0.216523	+	2.06008i	−0.0179813	+	0.171080i
$146$		0			0
$147$	1.42755	+	0.303436i	0.117743	+	0.0250270i
$148$		0			0
$149$	1.10432	+	10.5069i	0.0904694	+	0.860759i	0.941810	+	0.336146i	$0.109123\pi$
$149$	1.10432	+	10.5069i	0.0904694	+	0.860759i	−0.851341	+	0.524613i	$0.824210\pi$
$150$		0			0
$151$	−4.82737	+	14.8571i	−0.392846	+	1.20905i	0.537781	+	0.843085i	$0.319263\pi$
$151$	−4.82737	+	14.8571i	−0.392846	+	1.20905i	−0.930627	+	0.365970i	$0.880737\pi$
$152$		0			0
$153$	−6.63897	−	11.4990i	−0.536729	−	0.929642i
$154$		0			0
$155$	2.11020			0.169495
$156$		0			0
$157$	−4.62752	+	14.2420i	−0.369316	+	1.13664i	0.577917	+	0.816095i	$0.303866\pi$
$157$	−4.62752	+	14.2420i	−0.369316	+	1.13664i	−0.947234	+	0.320544i	$0.896134\pi$
$158$		0			0
$159$	−4.03946	−	1.79848i	−0.320350	−	0.142629i
$160$		0			0
$161$	−2.54276	−	7.82582i	−0.200398	−	0.616761i
$162$		0			0
$163$	12.2431	−	5.45098i	0.958953	−	0.426954i	0.133265	−	0.991080i	$-0.457454\pi$
$163$	12.2431	−	5.45098i	0.958953	−	0.426954i	0.825688	+	0.564127i	$0.190787\pi$
$164$		0			0
$165$	−1.04717	+	1.04551i	−0.0815224	+	0.0813929i
$166$		0			0
$167$	2.27080	−	21.6052i	0.175720	−	1.67186i	−0.450929	−	0.892560i	$-0.648907\pi$
$167$	2.27080	−	21.6052i	0.175720	−	1.67186i	0.626648	−	0.779302i	$-0.284426\pi$
$168$		0			0
$169$	−3.83357	+	12.4219i	−0.294890	+	0.955531i
$170$		0			0
$171$	2.84778	+	1.26791i	0.217775	+	0.0969599i
$172$		0			0
$173$	12.8538	+	14.2756i	0.977257	+	1.08535i	0.996335	+	0.0855362i	$0.0272603\pi$
$173$	12.8538	+	14.2756i	0.977257	+	1.08535i	−0.0190778	+	0.999818i	$0.506073\pi$
$174$		0			0
$175$	5.38494	−	9.32698i	0.407063	−	0.705054i
$176$		0			0
$177$	5.10308			0.383571
$178$		0			0
$179$	1.19785	−	0.254611i	0.0895314	−	0.0190305i	−0.162928	−	0.986638i	$-0.552094\pi$
$179$	1.19785	−	0.254611i	0.0895314	−	0.0190305i	0.252460	+	0.967607i	$0.418761\pi$
$180$		0			0
$181$	−0.966967	+	0.702543i	−0.0718741	+	0.0522196i	−0.623142	−	0.782109i	$-0.714144\pi$
$181$	−0.966967	+	0.702543i	−0.0718741	+	0.0522196i	0.551268	+	0.834328i	$0.314144\pi$
$182$		0			0
$183$	−3.02246	−	9.30219i	−0.223427	−	0.687638i
$184$		0			0
$185$	−0.0161800	+	0.153943i	−0.00118958	+	0.0113181i
$186$		0			0
$187$	0.979208	+	18.9728i	0.0716068	+	1.38743i
$188$		0			0
$189$	−9.17758	+	4.08612i	−0.667570	+	0.297222i
$190$		0			0
$191$	−19.8558	−	4.22049i	−1.43672	−	0.305384i	−0.577247	−	0.816569i	$-0.695873\pi$
$191$	−19.8558	−	4.22049i	−1.43672	−	0.305384i	−0.859470	+	0.511185i	$0.829207\pi$
$192$		0			0
$193$	12.2701	+	5.46300i	0.883222	+	0.393236i	0.797667	−	0.603098i	$-0.206067\pi$
$193$	12.2701	+	5.46300i	0.883222	+	0.393236i	0.0855545	+	0.996333i	$0.472734\pi$
$194$		0			0
$195$	−1.60105	−	0.156292i	−0.114654	−	0.0111923i
$196$		0			0
$197$	1.43591	+	2.48706i	0.102304	+	0.177196i	0.912634	−	0.408779i	$-0.134045\pi$
$197$	1.43591	+	2.48706i	0.102304	+	0.177196i	−0.810329	+	0.585975i	$0.800712\pi$
$198$		0			0
$199$	5.74631	−	9.95290i	0.407345	−	0.705542i	−0.587246	−	0.809408i	$-0.699788\pi$
$199$	5.74631	−	9.95290i	0.407345	−	0.705542i	0.994591	+	0.103866i	$0.0331213\pi$
$200$		0			0
$201$	−0.174409	−	0.193700i	−0.0123018	−	0.0136626i
$202$		0			0
$203$	7.09548	−	5.15517i	0.498005	−	0.361822i
$204$		0			0
$205$	−0.363602	+	0.403821i	−0.0253951	+	0.0282041i
$206$		0			0
$207$	−6.74584	−	4.90114i	−0.468868	−	0.340653i
$208$		0			0
$209$	−2.80414	−	3.46846i	−0.193967	−	0.239918i
$210$		0			0
$211$	−2.72642	+	25.9402i	−0.187695	+	1.78579i	0.344112	+	0.938929i	$0.388180\pi$
$211$	−2.72642	+	25.9402i	−0.187695	+	1.78579i	−0.531806	+	0.846866i	$0.678487\pi$
$212$		0			0
$213$	0.255851	+	0.787430i	0.0175307	+	0.0539538i
$214$		0			0
$215$	−0.140906	−	1.34063i	−0.00960968	−	0.0914300i
$216$		0			0
$217$	−5.97845	−	6.63975i	−0.405844	−	0.450735i
$218$		0			0
$219$	−4.77203	−	8.26540i	−0.322464	−	0.558524i
$220$		0			0
$221$	−15.2454	+	13.9329i	−1.02552	+	0.937230i
$222$		0			0
$223$	19.8996	−	4.22979i	1.33258	−	0.283248i	0.514072	−	0.857747i	$-0.328136\pi$
$223$	19.8996	−	4.22979i	1.33258	−	0.283248i	0.818505	+	0.574499i	$0.194803\pi$
$224$		0			0
$225$	−1.14077	−	10.8537i	−0.0760516	−	0.723583i
$226$		0			0
$227$	−14.7991	−	3.14565i	−0.982252	−	0.208784i	−0.311322	−	0.950305i	$-0.600772\pi$
$227$	−14.7991	−	3.14565i	−0.982252	−	0.208784i	−0.670930	+	0.741521i	$0.734105\pi$
$228$		0			0
$229$	22.7695	+	16.5430i	1.50465	+	1.09319i	0.968483	+	0.249081i	$0.0801285\pi$
$229$	22.7695	+	16.5430i	1.50465	+	1.09319i	0.536168	+	0.844112i	$0.319872\pi$
$230$		0			0
$231$	6.25648	+	0.332872i	0.411646	+	0.0219014i
$232$		0			0
$233$	0.687877	+	0.499772i	0.0450643	+	0.0327412i	0.610089	−	0.792333i	$-0.291134\pi$
$233$	0.687877	+	0.499772i	0.0450643	+	0.0327412i	−0.565025	+	0.825074i	$0.691134\pi$
$234$		0			0
$235$	0.344083	+	1.05898i	0.0224455	+	0.0690801i
$236$		0			0
$237$	2.48917	+	1.10825i	0.161689	+	0.0719885i
$238$		0			0
$239$	−4.26856	+	13.1373i	−0.276110	+	0.849780i	0.712813	+	0.701354i	$0.247421\pi$
$239$	−4.26856	+	13.1373i	−0.276110	+	0.849780i	−0.988924	+	0.148426i	$0.952579\pi$
$240$		0			0
$241$	3.46404	−	5.99989i	0.223138	−	0.386487i	−0.732621	−	0.680637i	$-0.761703\pi$
$241$	3.46404	−	5.99989i	0.223138	−	0.386487i	0.955759	+	0.294150i	$0.0950365\pi$
$242$		0			0
$243$	−7.96145	+	13.7896i	−0.510727	+	0.884606i
$244$		0			0
$245$	−0.933938	+	0.198515i	−0.0596671	+	0.0126826i
$246$		0			0
$247$	0.972943	−	4.75013i	0.0619069	−	0.302244i
$248$		0			0
$249$	−1.33451	+	1.48212i	−0.0845711	+	0.0939257i
$250$		0			0
$251$	14.9322	−	6.64825i	0.942513	−	0.419634i	0.122815	−	0.992430i	$-0.460808\pi$
$251$	14.9322	−	6.64825i	0.942513	−	0.419634i	0.819698	+	0.572796i	$0.194141\pi$
$252$		0			0
$253$	5.40785	+	10.6344i	0.339989	+	0.668578i
$254$		0			0
$255$	−2.06758	−	1.50219i	−0.129477	−	0.0940705i
$256$		0			0
$257$	0.121070	−	0.134462i	0.00755216	−	0.00838753i	−0.739357	−	0.673314i	$-0.764870\pi$
$257$	0.121070	−	0.134462i	0.00755216	−	0.00838753i	0.746909	+	0.664926i	$0.231537\pi$
$258$		0			0
$259$	0.530221	−	0.385228i	0.0329464	−	0.0239369i
$260$		0			0
$261$	2.74639	−	8.45251i	0.169997	−	0.523197i
$262$		0			0
$263$	7.22708	+	12.5177i	0.445641	+	0.771872i	0.998097	−	0.0616699i	$-0.0196426\pi$
$263$	7.22708	+	12.5177i	0.445641	+	0.771872i	−0.552456	+	0.833542i	$0.686309\pi$
$264$		0			0
$265$	2.89280			0.177703
$266$		0			0
$267$	5.24891	+	5.82951i	0.321228	+	0.356760i
$268$		0			0
$269$	−1.28783	−	12.2529i	−0.0785202	−	0.747069i	−0.960968	−	0.276659i	$-0.910773\pi$
$269$	−1.28783	−	12.2529i	−0.0785202	−	0.747069i	0.882448	−	0.470410i	$-0.155894\pi$
$270$		0			0
$271$	−5.28797	+	5.87288i	−0.321221	+	0.356752i	−0.882030	−	0.471193i	$-0.843824\pi$
$271$	−5.28797	+	5.87288i	−0.321221	+	0.356752i	0.560809	+	0.827945i	$0.310490\pi$
$272$		0			0
$273$	4.04420	+	5.48050i	0.244766	+	0.331695i
$274$		0			0
$275$	−5.60751	+	14.5734i	−0.338145	+	0.878812i
$276$		0			0
$277$	−12.9606	+	5.77042i	−0.778725	+	0.346711i	−0.757306	−	0.653060i	$-0.773485\pi$
$277$	−12.9606	+	5.77042i	−0.778725	+	0.346711i	−0.0214187	+	0.999771i	$0.506818\pi$
$278$		0			0
$279$	−8.85599	−	1.88240i	−0.530194	−	0.112696i
$280$		0			0
$281$	1.59887	−	1.16165i	0.0953809	−	0.0692982i	−0.539073	−	0.842259i	$-0.681225\pi$
$281$	1.59887	−	1.16165i	0.0953809	−	0.0692982i	0.634454	+	0.772961i	$0.281225\pi$
$282$		0			0
$283$	11.5400	−	2.45291i	0.685984	−	0.145810i	0.148282	−	0.988945i	$-0.452626\pi$
$283$	11.5400	−	2.45291i	0.685984	−	0.145810i	0.537702	+	0.843135i	$0.319292\pi$
$284$		0			0
$285$	0.599999			0.0355409
$286$		0			0
$287$	2.30075			0.135809
$288$		0			0
$289$	−15.4659	+	3.28737i	−0.909757	+	0.193375i
$290$		0			0
$291$	−9.79996	+	7.12009i	−0.574484	+	0.417387i
$292$		0			0
$293$	−17.3244	−	3.68243i	−1.01211	−	0.215130i	−0.328128	−	0.944633i	$-0.606418\pi$
$293$	−17.3244	−	3.68243i	−1.01211	−	0.215130i	−0.683977	+	0.729504i	$0.739751\pi$
$294$		0			0
$295$	−3.04992	+	1.35791i	−0.177573	+	0.0790607i
$296$		0			0
$297$	12.2221	−	7.92332i	0.709198	−	0.459758i
$298$		0			0
$299$	−5.18733	+	11.8872i	−0.299991	+	0.687455i
$300$		0			0
$301$	−3.81908	+	4.24152i	−0.220128	+	0.244477i
$302$		0			0
$303$	1.38074	+	13.1369i	0.0793215	+	0.754694i
$304$		0			0
$305$	4.28169	+	4.75530i	0.245169	+	0.272288i
$306$		0			0
$307$	16.4108			0.936616			0.468308	−	0.883565i	$-0.344864\pi$
$307$	16.4108			0.936616			0.468308	+	0.883565i	$0.344864\pi$
$308$		0			0
$309$	4.71974	+	8.17483i	0.268497	+	0.465050i
$310$		0			0
$311$	6.76598	−	20.8235i	0.383663	−	1.18079i	−0.553782	−	0.832662i	$-0.686816\pi$
$311$	6.76598	−	20.8235i	0.383663	−	1.18079i	0.937445	−	0.348133i	$-0.113184\pi$
$312$		0			0
$313$	13.4087	−	9.74200i	0.757905	−	0.550650i	−0.140362	−	0.990100i	$-0.544827\pi$
$313$	13.4087	−	9.74200i	0.757905	−	0.550650i	0.898267	+	0.439450i	$0.144827\pi$
$314$		0			0
$315$	1.91691	−	2.12895i	0.108006	−	0.119953i
$316$		0			0
$317$	3.80185	+	2.76220i	0.213533	+	0.155141i	0.689411	−	0.724371i	$-0.257870\pi$
$317$	3.80185	+	2.76220i	0.213533	+	0.155141i	−0.475878	+	0.879511i	$0.657870\pi$
$318$		0			0
$319$	−8.99884	+	8.98455i	−0.503838	+	0.503038i
$320$		0			0
$321$	−5.39832	+	2.40349i	−0.301305	+	0.134150i
$322$		0			0
$323$	5.15444	−	5.72458i	0.286801	−	0.318524i
$324$		0			0
$325$	−16.1052	+	5.36514i	−0.893355	+	0.297605i
$326$		0			0
$327$	1.61756	−	0.343822i	0.0894511	−	0.0190134i
$328$		0			0
$329$	2.35725	−	4.08287i	0.129959	−	0.225096i
$330$		0			0
$331$	2.49055	−	4.31376i	0.136893	−	0.237106i	−0.789426	−	0.613846i	$-0.789622\pi$
$331$	2.49055	−	4.31376i	0.136893	−	0.237106i	0.926319	+	0.376740i	$0.122955\pi$
$332$		0			0
$333$	0.205228	−	0.631627i	0.0112464	−	0.0346129i
$334$		0			0
$335$	0.155780	+	0.0693579i	0.00851119	+	0.00378943i
$336$		0			0
$337$	−3.98238	−	12.2565i	−0.216934	−	0.667654i	−0.999011	−	0.0444716i	$-0.985840\pi$
$337$	−3.98238	−	12.2565i	−0.216934	−	0.667654i	0.782077	−	0.623182i	$-0.214160\pi$
$338$		0			0
$339$	12.2578	+	8.90581i	0.665752	+	0.483697i
$340$		0			0
$341$	10.0608	+	8.16033i	0.544824	+	0.441907i
$342$		0			0
$343$	16.2251	+	11.7882i	0.876071	+	0.636503i
$344$		0			0
$345$	−1.56984	−	0.333681i	−0.0845175	−	0.0179648i
$346$		0			0
$347$	2.56761	+	24.4292i	0.137836	+	1.31143i	0.816658	+	0.577122i	$0.195824\pi$
$347$	2.56761	+	24.4292i	0.137836	+	1.31143i	−0.678821	+	0.734304i	$0.737509\pi$
$348$		0			0
$349$	10.4586	−	2.22304i	0.559835	−	0.118997i	0.0807012	−	0.996738i	$-0.474284\pi$
$349$	10.4586	−	2.22304i	0.559835	−	0.118997i	0.479134	+	0.877742i	$0.340951\pi$
$350$		0			0
$351$	15.0954	+	4.78143i	0.805732	+	0.255214i
$352$		0			0
$353$	−4.50059	−	7.79524i	−0.239542	−	0.414899i	0.721041	−	0.692892i	$-0.243664\pi$
$353$	−4.50059	−	7.79524i	−0.239542	−	0.414899i	−0.960583	+	0.277994i	$0.910331\pi$
$354$		0			0
$355$	−0.362445	−	0.402536i	−0.0192366	−	0.0213644i
$356$		0			0
$357$	1.13108	+	10.7615i	0.0598632	+	0.569560i
$358$		0			0
$359$	11.3400	+	34.9010i	0.598504	+	1.84201i	0.536447	+	0.843934i	$0.319766\pi$
$359$	11.3400	+	34.9010i	0.598504	+	1.84201i	0.0620572	+	0.998073i	$0.480234\pi$
$360$		0			0
$361$	1.79700	−	17.0973i	0.0945791	−	0.899860i
$362$		0			0
$363$	−9.03571	+	0.935179i	−0.474252	+	0.0490842i
$364$		0			0
$365$	5.05146	+	3.67010i	0.264405	+	0.192102i
$366$		0			0
$367$	−20.4734	+	22.7380i	−1.06870	+	1.18691i	−0.0870567	+	0.996203i	$0.527746\pi$
$367$	−20.4734	+	22.7380i	−1.06870	+	1.18691i	−0.981646	+	0.190711i	$0.938921\pi$
$368$		0			0
$369$	1.88618	−	1.37039i	0.0981905	−	0.0713396i
$370$		0			0
$371$	−8.19566	−	9.10221i	−0.425498	−	0.472563i
$372$		0			0
$373$	−0.130603	+	0.226211i	−0.00676236	+	0.0117128i	−0.869387	−	0.494132i	$-0.835486\pi$
$373$	−0.130603	+	0.226211i	−0.00676236	+	0.0117128i	0.862624	+	0.505845i	$0.168819\pi$
$374$		0			0
$375$	−2.16569	−	3.75109i	−0.111836	−	0.193706i
$376$		0			0
$377$	−13.7586	−	1.34309i	−0.708601	−	0.0691727i
$378$		0			0
$379$	−30.9242	−	13.7683i	−1.58847	−	0.707232i	−0.593261	−	0.805010i	$-0.702160\pi$
$379$	−30.9242	−	13.7683i	−1.58847	−	0.707232i	−0.995208	+	0.0977783i	$0.968826\pi$
$380$		0			0
$381$	−2.61843	−	0.556565i	−0.134146	−	0.0285137i
$382$		0			0
$383$	8.90921	−	3.96664i	0.455239	−	0.202686i	−0.166289	−	0.986077i	$-0.553179\pi$
$383$	8.90921	−	3.96664i	0.455239	−	0.202686i	0.621529	+	0.783391i	$0.286512\pi$
$384$		0			0
$385$	−3.82784	+	1.46588i	−0.195085	+	0.0747082i
$386$		0			0
$387$	−0.604557	+	5.75198i	−0.0307314	+	0.292390i
$388$		0			0
$389$	−10.7805	−	33.1788i	−0.546591	−	1.68223i	−0.717178	−	0.696890i	$-0.754566\pi$
$389$	−10.7805	−	33.1788i	−0.546591	−	1.68223i	0.170587	−	0.985343i	$-0.445434\pi$
$390$		0			0
$391$	−16.6698	+	12.1113i	−0.843026	+	0.612494i
$392$		0			0
$393$	7.25293	−	1.54166i	0.365862	−	0.0777664i
$394$		0			0
$395$	−1.78258			−0.0896914
$396$		0			0
$397$	−19.2853	+	33.4031i	−0.967901	+	1.67645i	−0.266290	+	0.963893i	$0.585798\pi$
$397$	−19.2853	+	33.4031i	−0.967901	+	1.67645i	−0.701611	+	0.712560i	$0.747536\pi$
$398$		0			0
$399$	−1.69987	−	1.88790i	−0.0851001	−	0.0945132i
$400$		0			0
$401$	13.6694	+	6.08603i	0.682619	+	0.303922i	0.718593	−	0.695431i	$-0.244787\pi$
$401$	13.6694	+	6.08603i	0.682619	+	0.303922i	−0.0359735	+	0.999353i	$0.511453\pi$
$402$		0			0
$403$	0.104344	+	14.0823i	0.00519773	+	0.701490i
$404$		0			0
$405$	0.187906	−	1.78781i	0.00933712	−	0.0888367i
$406$		0			0
$407$	−0.672453	+	0.671385i	−0.0333322	+	0.0332793i
$408$		0			0
$409$	26.8527	−	11.9556i	1.32778	−	0.591167i	0.384490	−	0.923129i	$-0.374377\pi$
$409$	26.8527	−	11.9556i	1.32778	−	0.591167i	0.943293	+	0.331963i	$0.107711\pi$
$410$		0			0
$411$	3.09469	+	9.52449i	0.152650	+	0.469808i
$412$		0			0
$413$	12.9135	+	5.74945i	0.635431	+	0.282912i
$414$		0			0
$415$	0.403199	−	1.24092i	0.0197922	−	0.0609143i
$416$		0			0
$417$	9.66113			0.473108
$418$		0			0
$419$	−14.9837	−	25.9526i	−0.732003	−	1.26787i	−0.956026	−	0.293282i	$-0.905253\pi$
$419$	−14.9837	−	25.9526i	−0.732003	−	1.26787i	0.224023	−	0.974584i	$-0.428081\pi$
$420$		0			0
$421$	1.53903	−	4.73665i	0.0750077	−	0.230850i	−0.906522	−	0.422158i	$-0.861273\pi$
$421$	1.53903	−	4.73665i	0.0750077	−	0.230850i	0.981530	+	0.191308i	$0.0612728\pi$
$422$		0			0
$423$	−0.499372	−	4.75121i	−0.0242803	−	0.231012i
$424$		0			0
$425$	−26.3793	−	5.60709i	−1.27958	−	0.271984i
$426$		0			0
$427$	2.83200	−	26.9447i	0.137050	−	1.30395i
$428$		0			0
$429$	−7.02895	−	6.93656i	−0.339361	−	0.334901i
$430$		0			0
$431$	−0.568945	+	5.41315i	−0.0274051	+	0.260742i	0.972237	+	0.233998i	$0.0751808\pi$
$431$	−0.568945	+	5.41315i	−0.0274051	+	0.260742i	−0.999642	+	0.0267447i	$0.991486\pi$
$432$		0			0
$433$	4.54628	+	0.966343i	0.218480	+	0.0464395i	0.315851	−	0.948809i	$-0.397710\pi$
$433$	4.54628	+	0.966343i	0.218480	+	0.0464395i	−0.0973708	+	0.995248i	$0.531043\pi$
$434$		0			0
$435$	−0.178808	−	1.70125i	−0.00857320	−	0.0815686i
$436$		0			0
$437$	1.49486	−	4.60070i	0.0715088	−	0.220081i
$438$		0			0
$439$	−5.23926	−	9.07466i	−0.250056	−	0.433110i	0.713485	−	0.700671i	$-0.247116\pi$
$439$	−5.23926	−	9.07466i	−0.250056	−	0.433110i	−0.963541	+	0.267561i	$0.913782\pi$
$440$		0			0
$441$	4.09660			0.195076
$442$		0			0
$443$	−0.969429	+	2.98360i	−0.0460590	+	0.141755i	−0.971441	−	0.237280i	$-0.923744\pi$
$443$	−0.969429	+	2.98360i	−0.0460590	+	0.141755i	0.925382	+	0.379035i	$0.123744\pi$
$444$		0			0
$445$	−4.68829	−	2.08736i	−0.222246	−	0.0989504i
$446$		0			0
$447$	−2.69604	−	8.29755i	−0.127518	−	0.392461i
$448$		0			0
$449$	30.8043	−	13.7149i	1.45374	−	0.647248i	0.480493	−	0.876998i	$-0.340458\pi$
$449$	30.8043	−	13.7149i	1.45374	−	0.647248i	0.973250	+	0.229750i	$0.0737909\pi$
$450$		0			0
$451$	−3.29516	+	0.519220i	−0.155163	+	0.0244491i
$452$		0			0
$453$	1.34848	−	12.8300i	0.0633573	−	0.602805i
$454$		0			0
$455$	−3.87541	−	2.19934i	−0.181682	−	0.103107i
$456$		0			0
$457$	3.26590	+	1.45407i	0.152772	+	0.0680185i	0.481698	−	0.876337i	$-0.340020\pi$
$457$	3.26590	+	1.45407i	0.152772	+	0.0680185i	−0.328926	+	0.944356i	$0.606687\pi$
$458$		0			0
$459$	16.8328	+	18.6948i	0.785689	+	0.872596i
$460$		0			0
$461$	−2.93924	+	5.09091i	−0.136894	+	0.237107i	−0.926319	−	0.376739i	$-0.877045\pi$
$461$	−2.93924	+	5.09091i	−0.136894	+	0.237107i	0.789425	+	0.613846i	$0.210379\pi$
$462$		0			0
$463$	16.4537			0.764666			0.382333	−	0.924025i	$-0.375121\pi$
$463$	16.4537			0.764666			0.382333	+	0.924025i	$0.375121\pi$
$464$		0			0
$465$	−1.70456	+	0.362314i	−0.0790469	+	0.0168019i
$466$		0			0
$467$	4.09310	−	2.97381i	0.189406	−	0.137612i	−0.489041	−	0.872261i	$-0.662653\pi$
$467$	4.09310	−	2.97381i	0.189406	−	0.137612i	0.678447	+	0.734649i	$0.262653\pi$
$468$		0			0
$469$	−0.223110	−	0.686663i	−0.0103023	−	0.0317072i
$470$		0			0
$471$	1.29266	−	12.2988i	0.0595626	−	0.566700i
$472$		0			0
$473$	4.51253	−	6.93662i	0.207486	−	0.318946i
$474$		0			0
$475$	5.78409	−	2.57524i	0.265392	−	0.118160i
$476$		0			0
$477$	−12.1404	−	2.58052i	−0.555870	−	0.118154i
$478$		0			0
$479$	−31.0683	−	13.8325i	−1.41955	−	0.632024i	−0.453705	−	0.891152i	$-0.649898\pi$
$479$	−31.0683	−	13.8325i	−1.41955	−	0.632024i	−0.965843	+	0.259128i	$0.916565\pi$
$480$		0			0
$481$	−1.02813	−	0.100365i	−0.0468787	−	0.00457623i
$482$		0			0
$483$	3.39763	+	5.88488i	0.154598	+	0.267771i
$484$		0			0
$485$	3.96244	−	6.86315i	0.179925	−	0.311639i
$486$		0			0
$487$	19.3014	+	21.4363i	0.874629	+	0.971373i	0.999784	−	0.0207637i	$-0.00660975\pi$
$487$	19.3014	+	21.4363i	0.874629	+	0.971373i	−0.125156	+	0.992137i	$0.539943\pi$
$488$		0			0
$489$	−8.95369	+	6.50524i	−0.404900	+	0.294177i
$490$		0			0
$491$	26.4553	−	29.3816i	1.19391	−	1.32597i	0.261230	−	0.965277i	$-0.415872\pi$
$491$	26.4553	−	29.3816i	1.19391	−	1.32597i	0.932683	−	0.360698i	$-0.117461\pi$
$492$		0			0
$493$	−17.7677	−	12.9090i	−0.800216	−	0.581391i
$494$		0			0
$495$	−2.26498	+	3.48170i	−0.101803	+	0.156491i
$496$		0			0
$497$	−0.239729	+	2.28087i	−0.0107533	+	0.102311i
$498$		0			0
$499$	−0.511522	−	1.57430i	−0.0228989	−	0.0704754i	0.938954	−	0.344043i	$-0.111796\pi$
$499$	−0.511522	−	1.57430i	−0.0228989	−	0.0704754i	−0.961853	+	0.273567i	$0.911796\pi$
$500$		0			0
$501$	1.87526	+	17.8419i	0.0837806	+	0.797119i
$502$		0			0
$503$	7.95725	+	8.83742i	0.354796	+	0.394041i	0.893950	−	0.448166i	$-0.147923\pi$
$503$	7.95725	+	8.83742i	0.354796	+	0.394041i	−0.539154	+	0.842207i	$0.681256\pi$
$504$		0			0
$505$	−4.32089	−	7.48401i	−0.192277	−	0.333034i
$506$		0			0
$507$	0.963842	−	10.6923i	0.0428057	−	0.474860i
$508$		0			0
$509$	−1.51560	+	0.322151i	−0.0671779	+	0.0142791i	−0.241378	−	0.970431i	$-0.577599\pi$
$509$	−1.51560	+	0.322151i	−0.0671779	+	0.0142791i	0.174200	+	0.984710i	$0.444266\pi$
$510$		0			0
$511$	−2.76343	−	26.2923i	−0.122247	−	1.16310i
$512$		0			0
$513$	−5.77692	−	1.22792i	−0.255057	−	0.0542141i
$514$		0			0
$515$	−4.99610	−	3.62988i	−0.220155	−	0.159952i
$516$		0			0
$517$	−2.45468	+	6.37950i	−0.107957	+	0.280570i
$518$		0			0
$519$	−12.8340	−	9.32445i	−0.563350	−	0.409298i
$520$		0			0
$521$	−5.32409	−	16.3859i	−0.233253	−	0.717878i	−0.997348	−	0.0727748i	$-0.976815\pi$
$521$	−5.32409	−	16.3859i	−0.233253	−	0.717878i	0.764096	−	0.645103i	$-0.223185\pi$
$522$		0			0
$523$	−14.0089	−	6.23715i	−0.612566	−	0.272732i	0.0769131	−	0.997038i	$-0.475494\pi$
$523$	−14.0089	−	6.23715i	−0.612566	−	0.272732i	−0.689479	+	0.724306i	$0.742160\pi$
$524$		0			0
$525$	−2.74838	+	8.45863i	−0.119949	+	0.369165i
$526$		0			0
$527$	−11.1866	+	19.3757i	−0.487294	+	0.844018i
$528$		0			0
$529$	5.03023	−	8.71261i	0.218706	−	0.378809i
$530$		0			0
$531$	14.0111	−	2.97815i	0.608030	−	0.129241i
$532$		0			0
$533$	−2.71286	−	2.40651i	−0.117507	−	0.104238i
$534$		0			0
$535$	2.58681	−	2.87295i	0.111838	−	0.124208i
$536$		0			0
$537$	−0.923871	+	0.411334i	−0.0398680	+	0.0177504i
$538$		0			0
$539$	−5.22042	−	2.66517i	−0.224860	−	0.114797i
$540$		0			0
$541$	−4.86511	−	3.53471i	−0.209168	−	0.151969i	0.478269	−	0.878213i	$-0.341264\pi$
$541$	−4.86511	−	3.53471i	−0.209168	−	0.151969i	−0.687437	+	0.726244i	$0.741264\pi$
$542$		0			0
$543$	0.660463	−	0.733518i	0.0283432	−	0.0314783i
$544$		0			0
$545$	−0.875263	+	0.635916i	−0.0374922	+	0.0272396i
$546$		0			0
$547$	−4.32988	+	13.3260i	−0.185132	+	0.569778i	−0.999951	−	0.00993787i	$-0.996837\pi$
$547$	−4.32988	+	13.3260i	−0.185132	+	0.569778i	0.814818	+	0.579716i	$0.196837\pi$
$548$		0			0
$549$	−13.7273	−	23.7763i	−0.585866	−	1.01475i
$550$		0			0
$551$	5.15607			0.219656
$552$		0			0
$553$	5.05028	+	5.60890i	0.214760	+	0.238515i
$554$		0			0
$555$	−0.0133617	−	0.127128i	−0.000567174	−	0.00539630i
$556$		0			0
$557$	12.5046	−	13.8878i	0.529837	−	0.588444i	−0.417502	−	0.908676i	$-0.637094\pi$
$557$	12.5046	−	13.8878i	0.529837	−	0.588444i	0.947339	+	0.320232i	$0.103761\pi$
$558$		0			0
$559$	8.93964	−	1.00662i	0.378106	−	0.0425754i
$560$		0			0
$561$	−4.04854	−	15.1575i	−0.170930	−	0.639951i
$562$		0			0
$563$	1.70991	−	0.761303i	0.0720643	−	0.0320851i	−0.370388	−	0.928877i	$-0.620775\pi$
$563$	1.70991	−	0.761303i	0.0720643	−	0.0320851i	0.442452	+	0.896792i	$0.354109\pi$
$564$		0			0
$565$	−9.69583	−	2.06091i	−0.407907	−	0.0867032i
$566$		0			0
$567$	−6.15769	+	4.47383i	−0.258599	+	0.187883i
$568$		0			0
$569$	−39.9056	+	8.48219i	−1.67293	+	0.355592i	−0.944241	−	0.329254i	$-0.893203\pi$
$569$	−39.9056	+	8.48219i	−1.67293	+	0.355592i	−0.728687	+	0.684846i	$0.759869\pi$
$570$		0			0
$571$	4.87168			0.203873			0.101937	−	0.994791i	$-0.467496\pi$
$571$	4.87168			0.203873			0.101937	+	0.994791i	$0.467496\pi$
$572$		0			0
$573$	16.7636			0.700309
$574$		0			0
$575$	−16.5657	+	3.52115i	−0.690839	+	0.146842i
$576$		0			0
$577$	25.9303	−	18.8395i	1.07949	−	0.784297i	0.101898	−	0.994795i	$-0.467509\pi$
$577$	25.9303	−	18.8395i	1.07949	−	0.784297i	0.977594	+	0.210498i	$0.0675086\pi$
$578$		0			0
$579$	−10.8494	−	2.30611i	−0.450886	−	0.0958388i
$580$		0			0
$581$	−5.04686	+	2.24701i	−0.209379	+	0.0932216i
$582$		0			0
$583$	13.7920	+	11.1867i	0.571208	+	0.463307i
$584$		0			0
$585$	−4.48708	+	0.505252i	−0.185518	+	0.0208896i
$586$		0			0
$587$	21.8382	−	24.2538i	0.901359	−	1.00106i	−0.0986236	−	0.995125i	$-0.531444\pi$
$587$	21.8382	−	24.2538i	0.901359	−	1.00106i	0.999982	−	0.00593549i	$-0.00188934\pi$
$588$		0			0
$589$	−0.549044	−	5.22380i	−0.0226229	−	0.215243i
$590$		0			0
$591$	−1.58690	−	1.76244i	−0.0652765	−	0.0724969i
$592$		0			0
$593$	2.73898			0.112476			0.0562381	−	0.998417i	$-0.482089\pi$
$593$	2.73898			0.112476			0.0562381	+	0.998417i	$0.482089\pi$
$594$		0			0
$595$	−3.53961	−	6.13078i	−0.145110	−	0.251338i
$596$		0			0
$597$	−2.93281	+	9.02627i	−0.120032	+	0.369421i
$598$		0			0
$599$	−25.6906	+	18.6653i	−1.04969	+	0.762644i	−0.972153	−	0.234346i	$-0.924705\pi$
$599$	−25.6906	+	18.6653i	−1.04969	+	0.762644i	−0.0775361	+	0.996990i	$0.524705\pi$
$600$		0			0
$601$	10.0520	−	11.1639i	0.410031	−	0.455386i	−0.502388	−	0.864642i	$-0.667545\pi$
$601$	10.0520	−	11.1639i	0.410031	−	0.455386i	0.912419	+	0.409256i	$0.134212\pi$
$602$		0			0
$603$	−0.591902	−	0.430042i	−0.0241041	−	0.0175127i
$604$		0			0
$605$	5.15146	−	2.96329i	0.209437	−	0.120475i
$606$		0			0
$607$	−24.9766	+	11.1203i	−1.01377	+	0.451358i	−0.845268	−	0.534343i	$-0.820559\pi$
$607$	−24.9766	+	11.1203i	−1.01377	+	0.451358i	−0.168500	+	0.985702i	$0.553892\pi$
$608$		0			0
$609$	−4.84639	+	5.38246i	−0.196386	+	0.218108i
$610$		0			0
$611$	−7.05002	+	2.34858i	−0.285213	+	0.0950135i
$612$		0			0
$613$	47.7053	−	10.1401i	1.92680	−	0.409554i	0.927433	−	0.373989i	$-0.122010\pi$
$613$	47.7053	−	10.1401i	1.92680	−	0.409554i	0.999367	−	0.0355650i	$-0.0113231\pi$
$614$		0			0
$615$	0.224372	−	0.388624i	0.00904756	−	0.0156708i
$616$		0			0
$617$	15.5643	−	26.9582i	0.626597	−	1.08530i	−0.361633	−	0.932320i	$-0.617781\pi$
$617$	15.5643	−	26.9582i	0.626597	−	1.08530i	0.988230	−	0.152977i	$-0.0488859\pi$
$618$		0			0
$619$	12.0718	−	37.1533i	0.485208	−	1.49332i	−0.346472	−	0.938060i	$-0.612620\pi$
$619$	12.0718	−	37.1533i	0.485208	−	1.49332i	0.831680	−	0.555256i	$-0.187380\pi$
$620$		0			0
$621$	14.4319	+	6.42550i	0.579132	+	0.257846i
$622$		0			0
$623$	6.71462	+	20.6655i	0.269016	+	0.827945i
$624$		0			0
$625$	−16.7522	−	12.1712i	−0.670088	−	0.486847i
$626$		0			0
$627$	2.86062	+	2.32025i	0.114242	+	0.0926620i
$628$		0			0
$629$	−1.32772	−	0.964643i	−0.0529396	−	0.0384628i
$630$		0			0
$631$	24.0460	+	5.11114i	0.957256	+	0.203471i	0.659949	−	0.751311i	$-0.270578\pi$
$631$	24.0460	+	5.11114i	0.957256	+	0.203471i	0.297308	+	0.954782i	$0.403911\pi$
$632$		0			0
$633$	−2.25152	−	21.4218i	−0.0894900	−	0.851440i
$634$		0			0
$635$	1.71304	−	0.364118i	0.0679799	−	0.0144496i
$636$		0			0
$637$	−1.37096	−	6.22278i	−0.0543194	−	0.246555i
$638$		0			0
$639$	1.16201	+	2.01266i	0.0459685	+	0.0796198i
$640$		0			0
$641$	−12.9915	−	14.4286i	−0.513135	−	0.569894i	0.429778	−	0.902935i	$-0.358592\pi$
$641$	−12.9915	−	14.4286i	−0.513135	−	0.569894i	−0.942912	+	0.333041i	$0.891925\pi$
$642$		0			0
$643$	−3.14322	−	29.9058i	−0.123957	−	1.17937i	−0.862819	−	0.505512i	$-0.831304\pi$
$643$	−3.14322	−	29.9058i	−0.123957	−	1.17937i	0.738863	−	0.673856i	$-0.235363\pi$
$644$		0			0
$645$	0.344001	+	1.05873i	0.0135450	+	0.0416873i
$646$		0			0
$647$	2.03434	−	19.3554i	0.0799781	−	0.760941i	−0.878878	−	0.477047i	$-0.841707\pi$
$647$	2.03434	−	19.3554i	0.0799781	−	0.760941i	0.958856	−	0.283894i	$-0.0916263\pi$
$648$		0			0
$649$	−19.7923	−	5.32020i	−0.776917	−	0.208836i
$650$		0			0
$651$	5.96924	+	4.33691i	0.233953	+	0.169977i
$652$		0			0
$653$	3.37656	−	3.75005i	0.132135	−	0.146751i	−0.673446	−	0.739236i	$-0.735187\pi$
$653$	3.37656	−	3.75005i	0.132135	−	0.146751i	0.805581	+	0.592486i	$0.201853\pi$
$654$		0			0
$655$	−3.92458	+	2.85137i	−0.153346	+	0.111412i
$656$		0			0
$657$	−17.9258	−	19.9087i	−0.699353	−	0.776711i
$658$		0			0
$659$	−8.51455	+	14.7476i	−0.331680	+	0.574486i	−0.982841	−	0.184453i	$-0.940949\pi$
$659$	−8.51455	+	14.7476i	−0.331680	+	0.574486i	0.651162	+	0.758939i	$0.274282\pi$
$660$		0			0
$661$	3.14089	+	5.44018i	0.122166	+	0.211599i	0.920622	−	0.390456i	$-0.127682\pi$
$661$	3.14089	+	5.44018i	0.122166	+	0.211599i	−0.798455	+	0.602054i	$0.794349\pi$
$662$		0			0
$663$	9.92253	−	13.8722i	0.385359	−	0.538751i
$664$		0			0
$665$	1.51831	+	0.675997i	0.0588777	+	0.0262140i
$666$		0			0
$667$	−13.4904	−	2.86747i	−0.522350	−	0.111029i
$668$		0			0
$669$	−15.3481	+	6.83340i	−0.593391	+	0.264195i
$670$		0			0
$671$	2.02469	+	39.2296i	0.0781622	+	1.51444i
$672$		0			0
$673$	2.82940	−	26.9200i	0.109065	−	1.03769i	−0.793921	−	0.608020i	$-0.791964\pi$
$673$	2.82940	−	26.9200i	0.109065	−	1.03769i	0.902987	−	0.429668i	$-0.141369\pi$
$674$		0			0
$675$	6.38944	+	19.6647i	0.245930	+	0.756894i
$676$		0			0
$677$	12.5311	−	9.10441i	0.481611	−	0.349911i	−0.320338	−	0.947303i	$-0.603797\pi$
$677$	12.5311	−	9.10441i	0.481611	−	0.349911i	0.801949	+	0.597393i	$0.203797\pi$
$678$		0			0
$679$	−32.8210	+	6.97632i	−1.25955	+	0.267727i
$680$		0			0
$681$	12.4944			0.478786
$682$		0			0
$683$	−16.9638	+	29.3821i	−0.649101	+	1.12428i	0.334236	+	0.942489i	$0.391522\pi$
$683$	−16.9638	+	29.3821i	−0.649101	+	1.12428i	−0.983338	+	0.181787i	$0.941812\pi$
$684$		0			0
$685$	−4.38402	−	4.86894i	−0.167505	−	0.186033i
$686$		0			0
$687$	−21.2329	−	9.45349i	−0.810085	−	0.360673i
$688$		0			0
$689$	0.143041	+	19.3050i	0.00544943	+	0.735461i
$690$		0			0
$691$	−2.11446	+	20.1178i	−0.0804379	+	0.765315i	0.877739	+	0.479139i	$0.159051\pi$
$691$	−2.11446	+	20.1178i	−0.0804379	+	0.765315i	−0.958177	+	0.286176i	$0.907616\pi$
$692$		0			0
$693$	17.3721	−	2.73733i	0.659913	−	0.103983i
$694$		0			0
$695$	−5.77410	+	2.57079i	−0.219024	+	0.0975158i
$696$		0			0
$697$	−1.78033	−	5.47930i	−0.0674349	−	0.207543i
$698$		0			0
$699$	−0.641456	−	0.285595i	−0.0242621	−	0.0108022i
$700$		0			0
$701$	−1.08502	+	3.33935i	−0.0409807	+	0.126126i	−0.969454	−	0.245274i	$-0.921122\pi$
$701$	−1.08502	+	3.33935i	−0.0409807	+	0.126126i	0.928473	+	0.371400i	$0.121122\pi$
$702$		0			0
$703$	0.385295			0.0145317
$704$		0			0
$705$	−0.459763	−	0.796333i	−0.0173157	−	0.0299916i
$706$		0			0
$707$	−11.3068	+	34.7988i	−0.425237	+	1.30874i
$708$		0			0
$709$	4.10192	+	39.0271i	0.154051	+	1.46569i	0.749341	+	0.662184i	$0.230370\pi$
$709$	4.10192	+	39.0271i	0.154051	+	1.46569i	−0.595291	+	0.803511i	$0.702963\pi$
$710$		0			0
$711$	7.48106	+	1.59015i	0.280562	+	0.0596353i
$712$		0			0
$713$	−1.46862	+	13.9729i	−0.0550001	+	0.523291i
$714$		0			0
$715$	6.04673	+	2.27535i	0.226135	+	0.0850931i
$716$		0			0
$717$	1.19239	−	11.3448i	0.0445305	−	0.423679i
$718$		0			0
$719$	29.2811	+	6.22389i	1.09200	+	0.232112i	0.718507	−	0.695520i	$-0.244826\pi$
$719$	29.2811	+	6.22389i	1.09200	+	0.232112i	0.373495	+	0.927632i	$0.378159\pi$
$720$		0			0
$721$	2.73315	+	26.0042i	0.101788	+	0.968446i
$722$		0			0
$723$	−1.76798	+	5.44129i	−0.0657520	+	0.202364i
$724$		0			0
$725$	−9.02562	−	15.6328i	−0.335203	−	0.580589i
$726$		0			0
$727$	29.0034			1.07568			0.537839	−	0.843048i	$-0.319241\pi$
$727$	29.0034			1.07568			0.537839	+	0.843048i	$0.319241\pi$
$728$		0			0
$729$	0.978776	−	3.01236i	0.0362510	−	0.111569i
$730$		0			0
$731$	13.0565	+	5.81313i	0.482912	+	0.215006i
$732$		0			0
$733$	0.0427309	+	0.131512i	0.00157830	+	0.00485751i	0.951843	−	0.306587i	$-0.0991871\pi$
$733$	0.0427309	+	0.131512i	0.00157830	+	0.00485751i	−0.950264	+	0.311445i	$0.899187\pi$
$734$		0			0
$735$	0.720323	−	0.320708i	0.0265695	−	0.0118295i
$736$		0			0
$737$	0.474503	+	0.933096i	0.0174785	+	0.0343710i
$738$		0			0
$739$	−3.39581	+	32.3090i	−0.124917	+	1.18851i	0.734998	+	0.678069i	$0.237183\pi$
$739$	−3.39581	+	32.3090i	−0.124917	+	1.18851i	−0.859915	+	0.510437i	$0.829484\pi$
$740$		0			0
$741$	0.0296683	+	4.00407i	0.00108989	+	0.147093i
$742$		0			0
$743$	43.1698	+	19.2204i	1.58375	+	0.705129i	0.994686	−	0.102959i	$-0.0328311\pi$
$743$	43.1698	+	19.2204i	1.58375	+	0.705129i	0.589061	+	0.808089i	$0.299498\pi$
$744$		0			0
$745$	3.81927	+	4.24173i	0.139927	+	0.155405i
$746$		0			0
$747$	−2.79909	+	4.84816i	−0.102413	+	0.177385i
$748$		0			0
$749$	−16.3685			−0.598092
$750$		0			0
$751$	26.6851	−	5.67209i	0.973753	−	0.206978i	0.306551	−	0.951854i	$-0.400825\pi$
$751$	26.6851	−	5.67209i	0.973753	−	0.206978i	0.667202	+	0.744877i	$0.267492\pi$
$752$		0			0
$753$	−10.9203	+	7.93407i	−0.397958	+	0.289134i
$754$		0			0
$755$	2.60807	+	8.02682i	0.0949175	+	0.292126i
$756$		0			0
$757$	−4.75360	+	45.2275i	−0.172772	+	1.64382i	0.473558	+	0.880763i	$0.342969\pi$
$757$	−4.75360	+	45.2275i	−0.172772	+	1.64382i	−0.646331	+	0.763057i	$0.723697\pi$
$758$		0			0
$759$	−6.19419	−	7.66163i	−0.224835	−	0.278099i
$760$		0			0
$761$	23.0517	−	10.2633i	0.835625	−	0.372044i	0.0561077	−	0.998425i	$-0.482131\pi$
$761$	23.0517	−	10.2633i	0.835625	−	0.372044i	0.779518	+	0.626380i	$0.215464\pi$
$762$		0			0
$763$	4.48064	+	0.952390i	0.162210	+	0.0344788i
$764$		0			0
$765$	−6.55345	−	2.91779i	−0.236941	−	0.105493i
$766$		0			0
$767$	−9.21278	−	20.2864i	−0.332654	−	0.732498i
$768$		0			0
$769$	−8.84390	−	15.3181i	−0.318919	−	0.552384i	0.661344	−	0.750083i	$-0.269987\pi$
$769$	−8.84390	−	15.3181i	−0.318919	−	0.552384i	−0.980263	+	0.197699i	$0.936653\pi$
$770$		0			0
$771$	−0.0747103	+	0.129402i	−0.00269062	+	0.00466030i
$772$		0			0
$773$	14.9394	+	16.5919i	0.537332	+	0.596768i	0.949277	−	0.314441i	$-0.101817\pi$
$773$	14.9394	+	16.5919i	0.537332	+	0.596768i	−0.411945	+	0.911209i	$0.635150\pi$
$774$		0			0
$775$	−14.8771	+	10.8088i	−0.534401	+	0.388265i
$776$		0			0
$777$	−0.362154	+	0.402213i	−0.0129922	+	0.0144293i
$778$		0			0
$779$	1.09426	+	0.795029i	0.0392061	+	0.0284849i
$780$		0			0
$781$	−0.171390	−	3.32079i	−0.00613280	−	0.118827i
$782$		0			0
$783$	−1.76007	+	16.7459i	−0.0628996	+	0.598450i
$784$		0			0
$785$	2.50010	+	7.69452i	0.0892325	+	0.274629i
$786$		0			0
$787$	−4.03799	−	38.4189i	−0.143939	−	1.36948i	−0.793220	−	0.608936i	$-0.791597\pi$
$787$	−4.03799	−	38.4189i	−0.143939	−	1.36948i	0.649281	−	0.760549i	$-0.275070\pi$
$788$		0			0
$789$	−7.98706	−	8.87053i	−0.284347	−	0.315799i
$790$		0			0
$791$	20.9848	+	36.3468i	0.746134	+	1.29234i
$792$		0			0
$793$	−31.5226	+	28.8088i	−1.11940	+	1.02303i
$794$		0			0
$795$	−2.33672	+	0.496685i	−0.0828748	+	0.0176156i
$796$		0			0
$797$	−1.59931	−	15.2164i	−0.0566503	−	0.538992i	−0.985637	−	0.168878i	$-0.945985\pi$
$797$	−1.59931	−	15.2164i	−0.0566503	−	0.538992i	0.928987	−	0.370114i	$-0.120681\pi$
$798$		0			0
$799$	−11.5475	−	2.45450i	−0.408521	−	0.0868339i
$800$		0			0
$801$	17.8136	+	12.9423i	0.629412	+	0.457295i
$802$		0			0
$803$	9.89129	+	37.0324i	0.349056	+	1.30685i
$804$		0			0
$805$	−3.59658	−	2.61307i	−0.126763	−	0.0920987i
$806$		0			0
$807$	3.14404	+	9.67637i	0.110676	+	0.340624i
$808$		0			0
$809$	28.8591	+	12.8489i	1.01463	+	0.451744i	0.845572	−	0.533862i	$-0.179260\pi$
$809$	28.8591	+	12.8489i	1.01463	+	0.451744i	0.169061	+	0.985606i	$0.445927\pi$
$810$		0			0
$811$	7.66026	−	23.5759i	0.268988	−	0.827860i	−0.721760	−	0.692144i	$-0.756666\pi$
$811$	7.66026	−	23.5759i	0.268988	−	0.827860i	0.990748	−	0.135716i	$-0.0433336\pi$
$812$		0			0
$813$	3.26311	−	5.65186i	0.114442	−	0.198220i
$814$		0			0
$815$	3.62026	−	6.27048i	0.126812	−	0.219645i
$816$		0			0
$817$	−3.28206	+	0.697624i	−0.114825	+	0.0244068i
$818$		0			0
$819$	14.3022	+	12.6872i	0.499760	+	0.443325i
$820$		0			0
$821$	−28.1968	+	31.3157i	−0.984074	+	1.09293i	0.0115924	+	0.999933i	$0.496310\pi$
$821$	−28.1968	+	31.3157i	−0.984074	+	1.09293i	−0.995667	+	0.0929925i	$0.970357\pi$
$822$		0			0
$823$	−33.0714	+	14.7243i	−1.15280	+	0.513258i	−0.891956	−	0.452123i	$-0.850667\pi$
$823$	−33.0714	+	14.7243i	−1.15280	+	0.513258i	−0.260842	+	0.965382i	$0.584000\pi$
$824$		0			0
$825$	2.02736	−	12.7348i	0.0705837	−	0.443368i
$826$		0			0
$827$	−9.24838	−	6.71934i	−0.321598	−	0.233654i	0.415259	−	0.909703i	$-0.363691\pi$
$827$	−9.24838	−	6.71934i	−0.321598	−	0.233654i	−0.736857	+	0.676049i	$0.763691\pi$
$828$		0			0
$829$	−18.0786	+	20.0783i	−0.627895	+	0.697348i	−0.970218	−	0.242235i	$-0.922120\pi$
$829$	−18.0786	+	20.0783i	−0.627895	+	0.697348i	0.342323	+	0.939582i	$0.388786\pi$
$830$		0			0
$831$	9.47840	−	6.88646i	0.328802	−	0.238889i
$832$		0			0
$833$	3.12823	−	9.62771i	0.108387	−	0.333581i
$834$		0			0
$835$	−5.86845	−	10.1645i	−0.203086	−	0.351756i
$836$		0			0
$837$	17.1533			0.592905
$838$		0			0
$839$	−34.0942	−	37.8654i	−1.17706	−	1.30726i	−0.942130	−	0.335247i	$-0.891180\pi$
$839$	−34.0942	−	37.8654i	−1.17706	−	1.30726i	−0.234931	−	0.972012i	$-0.575486\pi$
$840$		0			0
$841$	1.49474	+	14.2215i	0.0515429	+	0.490398i
$842$		0			0
$843$	−1.09207	+	1.21287i	−0.0376129	+	0.0417734i
$844$		0			0
$845$	2.26912	+	6.64683i	0.0780601	+	0.228658i
$846$		0			0
$847$	−23.9187	−	7.81370i	−0.821857	−	0.268482i
$848$		0			0
$849$	−8.90054	+	3.96278i	−0.305466	+	0.136002i
$850$		0			0
$851$	−1.00809	−	0.214276i	−0.0345569	−	0.00734530i
$852$		0			0
$853$	21.7188	−	15.7796i	0.743636	−	0.540283i	−0.150212	−	0.988654i	$-0.547996\pi$
$853$	21.7188	−	15.7796i	0.743636	−	0.540283i	0.893848	+	0.448371i	$0.147996\pi$
$854$		0			0
$855$	1.64737	−	0.350159i	0.0563388	−	0.0119752i
$856$		0			0
$857$	16.9662			0.579553			0.289776	−	0.957094i	$-0.406419\pi$
$857$	16.9662			0.579553			0.289776	+	0.957094i	$0.406419\pi$
$858$		0			0
$859$	−41.8067			−1.42643			−0.713213	−	0.700947i	$-0.752761\pi$
$859$	−41.8067			−1.42643			−0.713213	+	0.700947i	$0.752761\pi$
$860$		0			0
$861$	−1.85848	+	0.395032i	−0.0633368	+	0.0134627i
$862$		0			0
$863$	−9.37875	+	6.81406i	−0.319256	+	0.231953i	−0.735858	−	0.677136i	$-0.763221\pi$
$863$	−9.37875	+	6.81406i	−0.319256	+	0.231953i	0.416602	+	0.909089i	$0.363221\pi$
$864$		0			0
$865$	10.1516	+	2.15779i	0.345165	+	0.0733671i
$866$		0			0
$867$	11.9284	−	5.31088i	0.405111	−	0.180367i
$868$		0			0
$869$	−8.49884	−	6.89341i	−0.288303	−	0.233843i
$870$		0			0
$871$	−0.455154	+	1.04302i	−0.0154223	+	0.0353415i
$872$		0			0
$873$	−22.7517	+	25.2683i	−0.770027	+	0.855201i
$874$		0			0
$875$	−1.25413	−	11.9322i	−0.0423973	−	0.403383i
$876$		0			0
$877$	17.7220	+	19.6823i	0.598430	+	0.664624i	0.963920	−	0.266191i	$-0.0857653\pi$
$877$	17.7220	+	19.6823i	0.598430	+	0.664624i	−0.365490	+	0.930815i	$0.619099\pi$
$878$		0			0
$879$	14.6264			0.493337
$880$		0			0
$881$	−0.778258	−	1.34798i	−0.0262202	−	0.0454147i	0.852618	−	0.522535i	$-0.175014\pi$
$881$	−0.778258	−	1.34798i	−0.0262202	−	0.0454147i	−0.878838	+	0.477121i	$0.841680\pi$
$882$		0			0
$883$	12.1162	−	37.2898i	0.407742	−	1.25490i	−0.510842	−	0.859675i	$-0.670666\pi$
$883$	12.1162	−	37.2898i	0.407742	−	1.25490i	0.918584	−	0.395226i	$-0.129334\pi$
$884$		0			0
$885$	2.23049	−	1.62054i	0.0749770	−	0.0544740i
$886$		0			0
$887$	24.7041	−	27.4367i	0.829483	−	0.921234i	−0.168436	−	0.985713i	$-0.553872\pi$
$887$	24.7041	−	27.4367i	0.829483	−	0.921234i	0.997919	+	0.0644785i	$0.0205384\pi$
$888$		0			0
$889$	−5.99895	−	4.35849i	−0.201198	−	0.146179i
$890$		0			0
$891$	7.80949	−	7.79709i	0.261628	−	0.261212i
$892$		0			0
$893$	2.53198	−	1.12731i	0.0847294	−	0.0377239i
$894$		0			0
$895$	0.442708	−	0.491677i	0.0147981	−	0.0164350i
$896$		0			0
$897$	2.14918	−	10.4928i	0.0717589	−	0.350344i
$898$		0			0
$899$	−14.6480	+	3.11353i	−0.488539	+	0.103842i
$900$		0			0
$901$	−15.3353	+	26.5615i	−0.510892	+	0.884891i
$902$		0			0
$903$	2.35669	−	4.08190i	0.0784256	−	0.135837i
$904$		0			0
$905$	−0.199547	+	0.614143i	−0.00663317	+	0.0204148i
$906$		0			0
$907$	34.0164	+	15.1451i	1.12950	+	0.502884i	0.884453	−	0.466629i	$-0.154532\pi$
$907$	34.0164	+	15.1451i	1.12950	+	0.502884i	0.245042	+	0.969512i	$0.421198\pi$
$908$		0			0
$909$	11.4576	+	35.2630i	0.380026	+	1.16960i
$910$		0			0
$911$	−3.71010	−	2.69554i	−0.122921	−	0.0893073i	0.524626	−	0.851333i	$-0.324205\pi$
$911$	−3.71010	−	2.69554i	−0.122921	−	0.0893073i	−0.647547	+	0.762025i	$0.724205\pi$
$912$		0			0
$913$	6.72108	−	4.35713i	0.222435	−	0.144200i
$914$		0			0
$915$	−4.27509	−	3.10604i	−0.141330	−	0.102682i
$916$		0			0
$917$	20.0907	+	4.27040i	0.663452	+	0.141021i
$918$		0			0
$919$	−2.71856	−	25.8654i	−0.0896770	−	0.853220i	−0.943214	−	0.332187i	$-0.892214\pi$
$919$	−2.71856	−	25.8654i	−0.0896770	−	0.853220i	0.853537	−	0.521033i	$-0.174453\pi$
$920$		0			0
$921$	−13.2562	+	2.81769i	−0.436806	+	0.0928460i
$922$		0			0
$923$	2.66838	−	2.43866i	0.0878309	−	0.0802696i
$924$		0			0
$925$	−0.674454	−	1.16819i	−0.0221759	−	0.0384098i
$926$		0			0
$927$	17.7294	+	19.6905i	0.582310	+	0.646721i
$928$		0			0
$929$	0.723669	+	6.88525i	0.0237428	+	0.225898i	0.999959	+	0.00909673i	$0.00289562\pi$
$929$	0.723669	+	6.88525i	0.0237428	+	0.225898i	−0.976216	+	0.216801i	$0.930438\pi$
$930$		0			0
$931$	0.734421	+	2.26032i	0.0240697	+	0.0740788i
$932$		0			0
$933$	−1.89002	+	17.9823i	−0.0618764	+	0.588715i
$934$		0			0
$935$	6.45302	+	7.98178i	0.211036	+	0.261032i
$936$		0			0
$937$	14.3920	+	10.4564i	0.470165	+	0.341595i	0.797506	−	0.603312i	$-0.206152\pi$
$937$	14.3920	+	10.4564i	0.470165	+	0.341595i	−0.327341	+	0.944906i	$0.606152\pi$
$938$		0			0
$939$	−9.15849	+	10.1715i	−0.298876	+	0.331935i
$940$		0			0
$941$	29.1113	−	21.1506i	0.949001	−	0.689489i	−0.00156951	−	0.999999i	$-0.500500\pi$
$941$	29.1113	−	21.1506i	0.949001	−	0.689489i	0.950570	+	0.310509i	$0.100500\pi$
$942$		0			0
$943$	−2.42090	−	2.68868i	−0.0788353	−	0.0875555i
$944$		0			0
$945$	−2.71380	+	4.70043i	−0.0882798	+	0.152905i
$946$		0			0
$947$	5.40733	+	9.36577i	0.175715	+	0.304347i	0.940408	−	0.340047i	$-0.110443\pi$
$947$	5.40733	+	9.36577i	0.175715	+	0.304347i	−0.764694	+	0.644394i	$0.777110\pi$
$948$		0			0
$949$	−24.2424	+	33.8921i	−0.786943	+	1.10019i
$950$		0			0
$951$	−3.54528	−	1.57846i	−0.114964	−	0.0511851i
$952$		0			0
$953$	5.02745	+	1.06862i	0.162855	+	0.0346159i	0.288618	−	0.957444i	$-0.406804\pi$
$953$	5.02745	+	1.06862i	0.162855	+	0.0346159i	−0.125762	+	0.992060i	$0.540138\pi$
$954$		0			0
$955$	−10.0190	+	4.46073i	−0.324206	+	0.144346i
$956$		0			0
$957$	5.72638	−	8.80253i	0.185107	−	0.284545i
$958$		0			0
$959$	−2.89968	+	27.5886i	−0.0936356	+	0.890884i
$960$		0			0
$961$	−4.86530	−	14.9738i	−0.156945	−	0.483027i
$962$		0			0
$963$	−13.4190	+	9.74950i	−0.432422	+	0.314173i
$964$		0			0
$965$	7.09793	−	1.50871i	0.228491	−	0.0485672i
$966$		0			0
$967$	−52.6532			−1.69321			−0.846606	−	0.532221i	$-0.821358\pi$
$967$	−52.6532			−1.69321			−0.846606	+	0.532221i	$0.821358\pi$
$968$		0			0
$969$	−3.18071	+	5.50915i	−0.102179	+	0.176979i
$970$		0			0
$971$	38.5595	+	42.8247i	1.23743	+	1.37431i	0.901705	+	0.432352i	$0.142316\pi$
$971$	38.5595	+	42.8247i	1.23743	+	1.37431i	0.335730	+	0.941958i	$0.391017\pi$
$972$		0			0
$973$	24.4477	+	10.8848i	0.783759	+	0.348952i
$974$		0			0
$975$	12.0881	−	7.09901i	0.387129	−	0.227350i
$976$		0			0
$977$	−6.41773	+	61.0606i	−0.205321	+	1.95350i	0.0845084	+	0.996423i	$0.473068\pi$
$977$	−6.41773	+	61.0606i	−0.205321	+	1.95350i	−0.289830	+	0.957078i	$0.593599\pi$
$978$		0			0
$979$	−14.2804	−	28.0820i	−0.456404	−	0.897505i
$980$		0			0
$981$	4.24054	−	1.88801i	0.135390	−	0.0602795i
$982$		0			0
$983$	−7.76124	−	23.8866i	−0.247545	−	0.761866i	−0.995207	−	0.0977865i	$-0.968824\pi$
$983$	−7.76124	−	23.8866i	−0.247545	−	0.761866i	0.747662	−	0.664079i	$-0.231176\pi$
$984$		0			0
$985$	1.41741	+	0.631072i	0.0451625	+	0.0201076i
$986$		0			0
$987$	−1.20310	+	3.70275i	−0.0382950	+	0.117860i
$988$		0			0
$989$	8.97519			0.285395
$990$		0			0
$991$	11.6478	+	20.1746i	0.370004	+	0.640866i	0.989566	−	0.144082i	$-0.0460229\pi$
$991$	11.6478	+	20.1746i	0.370004	+	0.640866i	−0.619562	+	0.784948i	$0.712690\pi$
$992$		0			0
$993$	−1.27113	+	3.91214i	−0.0403382	+	0.124148i
$994$		0			0
$995$	−0.649027	−	6.17508i	−0.0205755	−	0.195763i
$996$		0			0
$997$	15.8505	+	3.36914i	0.501992	+	0.106702i	0.451946	−	0.892045i	$-0.350730\pi$
$997$	15.8505	+	3.36914i	0.501992	+	0.106702i	0.0500457	+	0.998747i	$0.484063\pi$
$998$		0			0
$999$	−0.131524	+	1.25137i	−0.00416123	+	0.0395914i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bg.a.81.6	✓	112
11.3	even	5	inner	572.2.bg.a.289.9	yes	112
13.9	even	3	inner	572.2.bg.a.477.9	yes	112
143.113	even	15	inner	572.2.bg.a.113.6	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bg.a.81.6	✓	112	1.1	even	1	trivial
572.2.bg.a.113.6	yes	112	143.113	even	15	inner
572.2.bg.a.289.9	yes	112	11.3	even	5	inner
572.2.bg.a.477.9	yes	112	13.9	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.807770 + 0.171697i) q^{3} +(0.437086 - 0.317562i) q^{5} +(-2.23753 - 0.475601i) q^{7} +(-2.11762 + 0.942827i) q^{9} +O(q^{10})\)	\(q+(-0.807770 + 0.171697i) q^{3} +(0.437086 - 0.317562i) q^{5} +(-2.23753 - 0.475601i) q^{7} +(-2.11762 + 0.942827i) q^{9} +(3.31194 + 0.176210i) q^{11} +(2.14084 + 2.90117i) q^{13} +(-0.298541 + 0.331563i) q^{15} +(0.598752 + 5.69674i) q^{17} +(-0.899848 - 0.999382i) q^{19} +1.88907 q^{21} +(1.79858 + 3.11523i) q^{23} +(-1.45489 + 4.47768i) q^{25} +(3.55297 - 2.58138i) q^{27} +(-2.56550 + 2.84927i) q^{29} +(3.15989 + 2.29579i) q^{31} +(-2.70554 + 0.426313i) q^{33} +(-1.12902 + 0.502674i) q^{35} +(-0.191711 + 0.212916i) q^{37} +(-2.22743 - 1.97590i) q^{39} +(-0.983809 + 0.209115i) q^{41} +(1.24754 - 2.16080i) q^{43} +(-0.626178 + 1.08457i) q^{45} +(-0.636874 + 1.96010i) q^{47} +(-1.61449 - 0.718816i) q^{49} +(-1.46177 - 4.49885i) q^{51} +(4.33179 + 3.14723i) q^{53} +(1.50356 - 0.974726i) q^{55} +(0.898461 + 0.652770i) q^{57} +(-6.04441 - 1.28478i) q^{59} +(1.23803 + 11.7790i) q^{61} +(5.18665 - 1.10246i) q^{63} +(1.85703 + 0.588211i) q^{65} +(0.157813 + 0.273341i) q^{67} +(-1.98771 - 2.20758i) q^{69} +(-0.104799 - 0.997095i) q^{71} +(3.57135 + 10.9915i) q^{73} +(0.406410 - 3.86673i) q^{75} +(-7.32675 - 1.96944i) q^{77} +(-2.66930 - 1.93936i) q^{79} +(2.22642 - 2.47269i) q^{81} +(1.95382 - 1.41954i) q^{83} +(2.07077 + 2.29983i) q^{85} +(1.58312 - 2.74204i) q^{87} +(-4.74947 - 8.22632i) q^{89} +(-3.41040 - 7.50963i) q^{91} +(-2.94664 - 1.31193i) q^{93} +(-0.710676 - 0.151059i) q^{95} +(13.4003 - 5.96619i) q^{97} +(-7.17958 + 2.74944i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 8 q^{9}+O(q^{10}) \) 112 * q + 8 * q^9	\( 112 q + 8 q^{9} - 10 q^{11} + 11 q^{13} - 2 q^{15} + 4 q^{17} - 12 q^{19} - 40 q^{21} + 10 q^{23} - 16 q^{25} - 12 q^{27} + q^{29} + 4 q^{31} + 35 q^{33} - 5 q^{35} - 12 q^{37} + 21 q^{39} - 10 q^{41} - 32 q^{43} + 34 q^{45} + 70 q^{47} + 16 q^{49} - 48 q^{51} - 26 q^{53} + 10 q^{55} - 12 q^{57} - 5 q^{59} + 28 q^{61} + 34 q^{63} + 22 q^{65} - 68 q^{67} - 58 q^{69} + 44 q^{71} + 42 q^{73} - 24 q^{75} + 46 q^{77} - 24 q^{79} + 64 q^{81} - 114 q^{83} + 4 q^{85} - 30 q^{87} - 6 q^{89} + 77 q^{91} - 5 q^{93} - 36 q^{95} - 15 q^{97} - 40 q^{99}+O(q^{100}) \) 112 * q + 8 * q^9 - 10 * q^11 + 11 * q^13 - 2 * q^15 + 4 * q^17 - 12 * q^19 - 40 * q^21 + 10 * q^23 - 16 * q^25 - 12 * q^27 + q^29 + 4 * q^31 + 35 * q^33 - 5 * q^35 - 12 * q^37 + 21 * q^39 - 10 * q^41 - 32 * q^43 + 34 * q^45 + 70 * q^47 + 16 * q^49 - 48 * q^51 - 26 * q^53 + 10 * q^55 - 12 * q^57 - 5 * q^59 + 28 * q^61 + 34 * q^63 + 22 * q^65 - 68 * q^67 - 58 * q^69 + 44 * q^71 + 42 * q^73 - 24 * q^75 + 46 * q^77 - 24 * q^79 + 64 * q^81 - 114 * q^83 + 4 * q^85 - 30 * q^87 - 6 * q^89 + 77 * q^91 - 5 * q^93 - 36 * q^95 - 15 * q^97 - 40 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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