LMFDB - Embedded newform 572.2.bh.a.57.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(57,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 2, 15]))

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

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

chi := DirichletCharacter("572.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bh (of order $20$, 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 $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			57.11
Character	$\chi$	$=$	572.57
Dual form			572.2.bh.a.281.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.76806 - 1.28457i) q^{3} +(3.38384 + 1.72415i) q^{5} +(-2.59890 + 0.411625i) q^{7} +(0.548857 - 1.68921i) q^{9} +O(q^{10})$	\(q+(1.76806 - 1.28457i) q^{3} +(3.38384 + 1.72415i) q^{5} +(-2.59890 + 0.411625i) q^{7} +(0.548857 - 1.68921i) q^{9} +(-0.101219 - 3.31508i) q^{11} +(2.29223 - 2.78311i) q^{13} +(8.19760 - 1.29837i) q^{15} +(0.923428 + 2.84202i) q^{17} +(1.00893 + 0.159798i) q^{19} +(-4.06624 + 4.06624i) q^{21} -3.48596i q^{23} +(5.53872 + 7.62340i) q^{25} +(0.826520 + 2.54377i) q^{27} +(0.452715 - 0.623108i) q^{29} +(0.326349 + 0.640496i) q^{31} +(-4.43741 - 5.73123i) q^{33} +(-9.50394 - 3.08802i) q^{35} +(1.54584 + 9.76007i) q^{37} +(0.477704 - 7.86521i) q^{39} +(-6.55526 - 1.03825i) q^{41} -7.49699 q^{43} +(4.76969 - 4.76969i) q^{45} +(-6.10280 - 0.966589i) q^{47} +(-0.0725646 + 0.0235777i) q^{49} +(5.28344 + 3.83864i) q^{51} +(3.80660 - 11.7155i) q^{53} +(5.37319 - 11.3922i) q^{55} +(1.98911 - 1.01350i) q^{57} +(1.80988 + 11.4271i) q^{59} +(3.82727 - 1.24355i) q^{61} +(-0.731102 + 4.61600i) q^{63} +(12.5550 - 5.46542i) q^{65} +(4.67217 - 4.67217i) q^{67} +(-4.47796 - 6.16338i) q^{69} +(-4.01923 - 2.04790i) q^{71} +(-12.4091 + 1.96540i) q^{73} +(19.5855 + 6.36373i) q^{75} +(1.62763 + 8.57389i) q^{77} +(-16.4221 - 5.33586i) q^{79} +(9.03975 + 6.56776i) q^{81} +(-7.17277 + 14.0774i) q^{83} +(-1.77534 + 11.2091i) q^{85} -1.68323i q^{87} +(-6.62508 - 6.62508i) q^{89} +(-4.81168 + 8.17654i) q^{91} +(1.39976 + 0.713215i) q^{93} +(3.13853 + 2.28028i) q^{95} +(-1.70151 - 3.33941i) q^{97} +(-5.65541 - 1.64852i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 28 q^{9}+O(q^{10}) $ 112 * q - 28 * q^9	$ 112 q - 28 q^{9} + 8 q^{11} - 10 q^{13} + 4 q^{15} - 24 q^{27} - 20 q^{29} - 16 q^{31} - 54 q^{33} + 100 q^{35} - 12 q^{37} + 40 q^{39} - 20 q^{41} - 4 q^{45} - 10 q^{47} - 76 q^{53} - 20 q^{55} + 18 q^{59} + 40 q^{61} + 80 q^{63} + 92 q^{67} + 8 q^{71} - 30 q^{73} - 80 q^{79} + 12 q^{81} + 40 q^{85} + 32 q^{89} - 12 q^{91} - 114 q^{93} + 54 q^{97} - 90 q^{99}+O(q^{100}) $ 112 * q - 28 * q^9 + 8 * q^11 - 10 * q^13 + 4 * q^15 - 24 * q^27 - 20 * q^29 - 16 * q^31 - 54 * q^33 + 100 * q^35 - 12 * q^37 + 40 * q^39 - 20 * q^41 - 4 * q^45 - 10 * q^47 - 76 * q^53 - 20 * q^55 + 18 * q^59 + 40 * q^61 + 80 * q^63 + 92 * q^67 + 8 * q^71 - 30 * q^73 - 80 * q^79 + 12 * q^81 + 40 * q^85 + 32 * q^89 - 12 * q^91 - 114 * q^93 + 54 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{10}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.76806	−	1.28457i	1.02079	−	0.741646i	0.0543435	−	0.998522i	$-0.482693\pi$
$3$	1.76806	−	1.28457i	1.02079	−	0.741646i	0.966444	+	0.256877i	$0.0826934\pi$
$4$		0			0
$5$	3.38384	+	1.72415i	1.51330	+	0.771063i	0.996383	−	0.0849739i	$-0.0270807\pi$
$5$	3.38384	+	1.72415i	1.51330	+	0.771063i	0.516914	+	0.856037i	$0.327081\pi$
$6$		0			0
$7$	−2.59890	+	0.411625i	−0.982291	+	0.155580i	−0.626867	−	0.779126i	$-0.715663\pi$
$7$	−2.59890	+	0.411625i	−0.982291	+	0.155580i	−0.355423	+	0.934705i	$0.615663\pi$
$8$		0			0
$9$	0.548857	−	1.68921i	0.182952	−	0.563069i
$10$		0			0
$11$	−0.101219	−	3.31508i	−0.0305186	−	0.999534i
$11$	−0.101219	−	3.31508i	−0.0305186	−	0.999534i
$12$		0			0
$13$	2.29223	−	2.78311i	0.635750	−	0.771895i
$13$	2.29223	−	2.78311i	0.635750	−	0.771895i
$14$		0			0
$15$	8.19760	−	1.29837i	2.11661	−	0.335238i
$16$		0			0
$17$	0.923428	+	2.84202i	0.223964	+	0.689291i	0.998395	+	0.0566323i	$0.0180363\pi$
$17$	0.923428	+	2.84202i	0.223964	+	0.689291i	−0.774431	+	0.632658i	$0.781964\pi$
$18$		0			0
$19$	1.00893	+	0.159798i	0.231464	+	0.0366603i	0.271089	−	0.962554i	$-0.412616\pi$
$19$	1.00893	+	0.159798i	0.231464	+	0.0366603i	−0.0396249	+	0.999215i	$0.512616\pi$
$20$		0			0
$21$	−4.06624	+	4.06624i	−0.887325	+	0.887325i
$22$		0			0
$23$		−	3.48596i		−	0.726874i	−0.931619	−	0.363437i	$-0.881603\pi$
$23$		−	3.48596i		−	0.726874i	0.931619	−	0.363437i	$-0.118397\pi$
$24$		0			0
$25$	5.53872	+	7.62340i	1.10774	+	1.52468i
$26$		0			0
$27$	0.826520	+	2.54377i	0.159064	+	0.489548i
$28$		0			0
$29$	0.452715	−	0.623108i	0.0840670	−	0.115708i	−0.764912	−	0.644135i	$-0.777218\pi$
$29$	0.452715	−	0.623108i	0.0840670	−	0.115708i	0.848979	+	0.528426i	$0.177218\pi$
$30$		0			0
$31$	0.326349	+	0.640496i	0.0586140	+	0.115036i	0.918455	−	0.395525i	$-0.129437\pi$
$31$	0.326349	+	0.640496i	0.0586140	+	0.115036i	−0.859841	+	0.510562i	$0.829437\pi$
$32$		0			0
$33$	−4.43741	−	5.73123i	−0.772453	−	0.997678i
$34$		0			0
$35$	−9.50394	−	3.08802i	−1.60646	−	0.521970i
$36$		0			0
$37$	1.54584	+	9.76007i	0.254135	+	1.60455i	0.703164	+	0.711028i	$0.251770\pi$
$37$	1.54584	+	9.76007i	0.254135	+	1.60455i	−0.449029	+	0.893517i	$0.648230\pi$
$38$		0			0
$39$	0.477704	−	7.86521i	0.0764939	−	1.25944i
$40$		0			0
$41$	−6.55526	−	1.03825i	−1.02376	−	0.162147i	−0.378093	−	0.925768i	$-0.623420\pi$
$41$	−6.55526	−	1.03825i	−1.02376	−	0.162147i	−0.645666	+	0.763620i	$0.723420\pi$
$42$		0			0
$43$	−7.49699			−1.14328			−0.571640	−	0.820505i	$-0.693693\pi$
$43$	−7.49699			−1.14328			−0.571640	+	0.820505i	$0.693693\pi$
$44$		0			0
$45$	4.76969	−	4.76969i	0.711023	−	0.711023i
$46$		0			0
$47$	−6.10280	−	0.966589i	−0.890186	−	0.140992i	−0.305443	−	0.952210i	$-0.598805\pi$
$47$	−6.10280	−	0.966589i	−0.890186	−	0.140992i	−0.584743	+	0.811219i	$0.698805\pi$
$48$		0			0
$49$	−0.0725646	+	0.0235777i	−0.0103664	+	0.00336824i
$50$		0			0
$51$	5.28344	+	3.83864i	0.739829	+	0.537517i
$52$		0			0
$53$	3.80660	−	11.7155i	0.522877	−	1.60925i	−0.245600	−	0.969371i	$-0.578985\pi$
$53$	3.80660	−	11.7155i	0.522877	−	1.60925i	0.768477	−	0.639878i	$-0.221015\pi$
$54$		0			0
$55$	5.37319	−	11.3922i	0.724521	−	1.53612i
$56$		0			0
$57$	1.98911	−	1.01350i	0.263464	−	0.134242i
$58$		0			0
$59$	1.80988	+	11.4271i	0.235627	+	1.48769i	0.767601	+	0.640928i	$0.221450\pi$
$59$	1.80988	+	11.4271i	0.235627	+	1.48769i	−0.531975	+	0.846760i	$0.678550\pi$
$60$		0			0
$61$	3.82727	−	1.24355i	0.490031	−	0.159221i	−0.0535704	−	0.998564i	$-0.517060\pi$
$61$	3.82727	−	1.24355i	0.490031	−	0.159221i	0.543602	+	0.839343i	$0.317060\pi$
$62$		0			0
$63$	−0.731102	+	4.61600i	−0.0921102	+	0.581561i
$64$		0			0
$65$	12.5550	−	5.46542i	1.55726	−	0.677902i
$66$		0			0
$67$	4.67217	−	4.67217i	0.570796	−	0.570796i	−0.361555	−	0.932351i	$-0.617754\pi$
$67$	4.67217	−	4.67217i	0.570796	−	0.570796i	0.932351	+	0.361555i	$0.117754\pi$
$68$		0			0
$69$	−4.47796	−	6.16338i	−0.539083	−	0.741984i
$70$		0			0
$71$	−4.01923	−	2.04790i	−0.476995	−	0.243041i	0.198927	−	0.980014i	$-0.436254\pi$
$71$	−4.01923	−	2.04790i	−0.476995	−	0.243041i	−0.675922	+	0.736973i	$0.736254\pi$
$72$		0			0
$73$	−12.4091	+	1.96540i	−1.45237	+	0.230033i	−0.832219	−	0.554447i	$-0.812930\pi$
$73$	−12.4091	+	1.96540i	−1.45237	+	0.230033i	−0.620154	+	0.784480i	$0.712930\pi$
$74$		0			0
$75$	19.5855	+	6.36373i	2.26154	+	0.734820i
$76$		0			0
$77$	1.62763	+	8.57389i	0.185485	+	0.977085i
$78$		0			0
$79$	−16.4221	−	5.33586i	−1.84763	−	0.600331i	−0.997246	−	0.0741688i	$-0.976370\pi$
$79$	−16.4221	−	5.33586i	−1.84763	−	0.600331i	−0.850384	−	0.526162i	$-0.823630\pi$
$80$		0			0
$81$	9.03975	+	6.56776i	1.00442	+	0.729752i
$82$		0			0
$83$	−7.17277	+	14.0774i	−0.787314	+	1.54519i	0.0501775	+	0.998740i	$0.484021\pi$
$83$	−7.17277	+	14.0774i	−0.787314	+	1.54519i	−0.837491	+	0.546450i	$0.815979\pi$
$84$		0			0
$85$	−1.77534	+	11.2091i	−0.192563	+	1.21579i
$86$		0			0
$87$		−	1.68323i		−	0.180462i
$88$		0			0
$89$	−6.62508	−	6.62508i	−0.702257	−	0.702257i	0.262638	−	0.964894i	$-0.415408\pi$
$89$	−6.62508	−	6.62508i	−0.702257	−	0.702257i	−0.964894	+	0.262638i	$0.915408\pi$
$90$		0			0
$91$	−4.81168	+	8.17654i	−0.504401	+	0.857135i
$92$		0			0
$93$	1.39976	+	0.713215i	0.145149	+	0.0739570i
$94$		0			0
$95$	3.13853	+	2.28028i	0.322006	+	0.233951i
$96$		0			0
$97$	−1.70151	−	3.33941i	−0.172762	−	0.339065i	0.788348	−	0.615229i	$-0.210937\pi$
$97$	−1.70151	−	3.33941i	−0.172762	−	0.339065i	−0.961110	+	0.276164i	$0.910937\pi$
$98$		0			0
$99$	−5.65541	−	1.64852i	−0.568390	−	0.165683i
$100$		0			0
$101$	1.23126	−	3.78942i	0.122515	−	0.377061i	−0.870925	−	0.491415i	$-0.836480\pi$
$101$	1.23126	−	3.78942i	0.122515	−	0.377061i	0.993440	+	0.114354i	$0.0364798\pi$
$102$		0			0
$103$	8.81582	−	12.1339i	0.868648	−	1.19559i	−0.110789	−	0.993844i	$-0.535338\pi$
$103$	8.81582	−	12.1339i	0.868648	−	1.19559i	0.979437	−	0.201748i	$-0.0646621\pi$
$104$		0			0
$105$	−20.7703	+	6.74867i	−2.02697	+	0.658603i
$106$		0			0
$107$	4.52401	+	6.22676i	0.437352	+	0.601964i	0.969621	−	0.244612i	$-0.0786605\pi$
$107$	4.52401	+	6.22676i	0.437352	+	0.601964i	−0.532269	+	0.846575i	$0.678661\pi$
$108$		0			0
$109$	4.05579	+	4.05579i	0.388474	+	0.388474i	0.874143	−	0.485669i	$-0.161424\pi$
$109$	4.05579	+	4.05579i	0.388474	+	0.388474i	−0.485669	+	0.874143i	$0.661424\pi$
$110$		0			0
$111$	15.2706	+	15.2706i	1.44942	+	1.44942i
$112$		0			0
$113$	−6.02177	+	4.37507i	−0.566481	+	0.411572i	−0.833825	−	0.552029i	$-0.813854\pi$
$113$	−6.02177	+	4.37507i	−0.566481	+	0.411572i	0.267344	+	0.963601i	$0.413854\pi$
$114$		0			0
$115$	6.01033	−	11.7959i	0.560466	−	1.09998i
$116$		0			0
$117$	−3.44314	−	5.39958i	−0.318318	−	0.499191i
$118$		0			0
$119$	−3.56974	−	7.00601i	−0.327237	−	0.642240i
$120$		0			0
$121$	−10.9795	+	0.671096i	−0.998137	+	0.0610087i
$122$		0			0
$123$	−12.9238	+	6.58499i	−1.16530	+	0.593748i
$124$		0			0
$125$	2.62773	+	16.5909i	0.235032	+	1.48393i
$126$		0			0
$127$	−1.32603	−	4.08109i	−0.117666	−	0.362138i	0.874828	−	0.484434i	$-0.160974\pi$
$127$	−1.32603	−	4.08109i	−0.117666	−	0.362138i	−0.992494	+	0.122296i	$0.960974\pi$
$128$		0			0
$129$	−13.2551	+	9.63039i	−1.16705	+	0.847908i
$130$		0			0
$131$		−	8.70501i		−	0.760561i	−0.924871	−	0.380280i	$-0.875828\pi$
$131$		−	8.70501i		−	0.760561i	0.924871	−	0.380280i	$-0.124172\pi$
$132$		0			0
$133$	−2.68788			−0.233068
$134$		0			0
$135$	−1.58903	+	10.0327i	−0.136762	+	0.863480i
$136$		0			0
$137$	−5.98608	+	11.7484i	−0.511426	+	1.00373i	0.480510	+	0.876989i	$0.340451\pi$
$137$	−5.98608	+	11.7484i	−0.511426	+	1.00373i	−0.991936	+	0.126740i	$0.959549\pi$
$138$		0			0
$139$	4.94369	−	6.80440i	0.419318	−	0.577142i	−0.546142	−	0.837693i	$-0.683904\pi$
$139$	4.94369	−	6.80440i	0.419318	−	0.577142i	0.965460	+	0.260551i	$0.0839041\pi$
$140$		0			0
$141$	−12.0318	+	6.13048i	−1.01326	+	0.516280i
$142$		0			0
$143$	−9.45823	−	7.31723i	−0.790937	−	0.611897i
$144$		0			0
$145$	2.60624	−	1.32795i	0.216437	−	0.110280i
$146$		0			0
$147$	−0.0980112	+	0.134901i	−0.00808383	+	0.0111264i
$148$		0			0
$149$	−6.02075	+	11.8164i	−0.493239	+	0.968036i	0.501458	+	0.865182i	$0.332797\pi$
$149$	−6.02075	+	11.8164i	−0.493239	+	0.968036i	−0.994697	+	0.102854i	$0.967203\pi$
$150$		0			0
$151$	1.11843	−	7.06150i	0.0910167	−	0.574657i	−0.899463	−	0.436997i	$-0.856042\pi$
$151$	1.11843	−	7.06150i	0.0910167	−	0.574657i	0.990480	−	0.137660i	$-0.0439580\pi$
$152$		0			0
$153$	5.30759			0.429093
$154$		0			0
$155$			2.73001i			0.219280i
$156$		0			0
$157$	8.68931	−	6.31315i	0.693482	−	0.503844i	−0.184321	−	0.982866i	$-0.559009\pi$
$157$	8.68931	−	6.31315i	0.693482	−	0.503844i	0.877803	+	0.479022i	$0.159009\pi$
$158$		0			0
$159$	−8.31909	−	25.6035i	−0.659746	−	2.03049i
$160$		0			0
$161$	1.43491	+	9.05966i	0.113087	+	0.714001i
$162$		0			0
$163$	2.16733	−	1.10431i	0.169758	−	0.0864962i	−0.367047	−	0.930203i	$-0.619631\pi$
$163$	2.16733	−	1.10431i	0.169758	−	0.0864962i	0.536805	+	0.843706i	$0.319631\pi$
$164$		0			0
$165$	−5.13396	−	27.0443i	−0.399678	−	2.10539i
$166$		0			0
$167$	1.74760	+	3.42986i	0.135233	+	0.265410i	0.948685	−	0.316222i	$-0.102414\pi$
$167$	1.74760	+	3.42986i	0.135233	+	0.265410i	−0.813452	+	0.581632i	$0.802414\pi$
$168$		0			0
$169$	−2.49136	−	12.7590i	−0.191643	−	0.981465i
$170$		0			0
$171$	0.823690	−	1.61658i	0.0629891	−	0.123623i
$172$		0			0
$173$	13.0236	−	9.46223i	0.990169	−	0.719400i	0.0302112	−	0.999544i	$-0.490382\pi$
$173$	13.0236	−	9.46223i	0.990169	−	0.719400i	0.959958	+	0.280143i	$0.0903820\pi$
$174$		0			0
$175$	−17.5325	−	17.5325i	−1.32534	−	1.32534i
$176$		0			0
$177$	17.8789	+	17.8789i	1.34386	+	1.34386i
$178$		0			0
$179$	4.47653	+	6.16141i	0.334591	+	0.460525i	0.942852	−	0.333212i	$-0.108132\pi$
$179$	4.47653	+	6.16141i	0.334591	+	0.460525i	−0.608261	+	0.793737i	$0.708132\pi$
$180$		0			0
$181$	−21.5197	+	6.99216i	−1.59954	+	0.519723i	−0.966995	−	0.254796i	$-0.917992\pi$
$181$	−21.5197	+	6.99216i	−1.59954	+	0.519723i	−0.632550	+	0.774520i	$0.717992\pi$
$182$		0			0
$183$	5.16939	−	7.11506i	0.382133	−	0.525960i
$184$		0			0
$185$	−11.5969	+	35.6917i	−0.852625	+	2.62411i
$186$		0			0
$187$	9.32805	−	3.34890i	0.682135	−	0.244896i
$188$		0			0
$189$	−3.19512	−	6.27077i	−0.232411	−	0.456132i
$190$		0			0
$191$	13.3984	+	9.73450i	0.969474	+	0.704364i	0.955332	−	0.295536i	$-0.0954982\pi$
$191$	13.3984	+	9.73450i	0.969474	+	0.704364i	0.0141423	+	0.999900i	$0.495498\pi$
$192$		0			0
$193$	21.1177	+	10.7600i	1.52008	+	0.774521i	0.996973	−	0.0777440i	$-0.0247717\pi$
$193$	21.1177	+	10.7600i	1.52008	+	0.774521i	0.523110	+	0.852265i	$0.324772\pi$
$194$		0			0
$195$	15.1773	−	25.7910i	1.08687	−	1.84693i
$196$		0			0
$197$	−0.967825	−	0.967825i	−0.0689547	−	0.0689547i	0.671788	−	0.740743i	$-0.265526\pi$
$197$	−0.967825	−	0.967825i	−0.0689547	−	0.0689547i	−0.740743	+	0.671788i	$0.765526\pi$
$198$		0			0
$199$			6.16708i			0.437173i	0.975818	+	0.218586i	$0.0701445\pi$
$199$			6.16708i			0.437173i	−0.975818	+	0.218586i	$0.929855\pi$
$200$		0			0
$201$	2.25894	−	14.2624i	0.159333	−	1.00599i
$202$		0			0
$203$	−0.920072	+	1.80574i	−0.0645764	+	0.126738i
$204$		0			0
$205$	−20.3918	−	14.8155i	−1.42423	−	1.03476i
$206$		0			0
$207$	−5.88852	−	1.91329i	−0.409280	−	0.132983i
$208$		0			0
$209$	0.427622	−	3.36085i	0.0295793	−	0.232475i
$210$		0			0
$211$	13.6751	+	4.44332i	0.941435	+	0.305891i	0.739230	−	0.673453i	$-0.235189\pi$
$211$	13.6751	+	4.44332i	0.941435	+	0.305891i	0.202204	+	0.979343i	$0.435189\pi$
$212$		0			0
$213$	−9.73688	+	1.54217i	−0.667160	+	0.105668i
$214$		0			0
$215$	−25.3686	−	12.9259i	−1.73012	−	0.881541i
$216$		0			0
$217$	−1.11179	−	1.53025i	−0.0754733	−	0.103880i
$218$		0			0
$219$	−19.4152	+	19.4152i	−1.31196	+	1.31196i
$220$		0			0
$221$	10.0263	+	3.94457i	0.674445	+	0.265340i
$222$		0			0
$223$	2.06229	−	13.0208i	0.138101	−	0.871938i	−0.817211	−	0.576339i	$-0.804481\pi$
$223$	2.06229	−	13.0208i	0.138101	−	0.871938i	0.955312	−	0.295599i	$-0.0955192\pi$
$224$		0			0
$225$	15.9175	−	5.17190i	1.06116	−	0.344793i
$226$		0			0
$227$	3.61425	+	22.8195i	0.239886	+	1.51458i	0.754008	+	0.656865i	$0.228118\pi$
$227$	3.61425	+	22.8195i	0.239886	+	1.51458i	−0.514121	+	0.857717i	$0.671882\pi$
$228$		0			0
$229$	−7.60063	+	3.87272i	−0.502264	+	0.255916i	−0.686717	−	0.726925i	$-0.740949\pi$
$229$	−7.60063	+	3.87272i	−0.502264	+	0.255916i	0.184453	+	0.982841i	$0.440949\pi$
$230$		0			0
$231$	13.8915	+	13.0683i	0.913992	+	0.859832i
$232$		0			0
$233$	−1.15616	+	3.55828i	−0.0757423	+	0.233111i	−0.981759	−	0.190132i	$-0.939108\pi$
$233$	−1.15616	+	3.55828i	−0.0757423	+	0.233111i	0.906016	+	0.423243i	$0.139108\pi$
$234$		0			0
$235$	−18.9843	−	13.7929i	−1.23840	−	0.899752i
$236$		0			0
$237$	−35.8895	+	11.6612i	−2.33127	+	0.757476i
$238$		0			0
$239$	18.5586	+	2.93940i	1.20046	+	0.190134i	0.724463	−	0.689314i	$-0.242088\pi$
$239$	18.5586	+	2.93940i	1.20046	+	0.190134i	0.475995	+	0.879448i	$0.342088\pi$
$240$		0			0
$241$	11.6952	−	11.6952i	0.753354	−	0.753354i	−0.221750	−	0.975104i	$-0.571177\pi$
$241$	11.6952	−	11.6952i	0.753354	−	0.753354i	0.975104	+	0.221750i	$0.0711767\pi$
$242$		0			0
$243$	16.3955			1.05177
$244$		0			0
$245$	−0.286198	−	0.0453294i	−0.0182845	−	0.00289599i
$246$		0			0
$247$	2.75743	−	2.44166i	0.175451	−	0.155359i
$248$		0			0
$249$	5.40146	+	34.1035i	0.342304	+	2.16122i
$250$		0			0
$251$	−1.48853	−	0.483652i	−0.0939551	−	0.0305279i	0.261662	−	0.965160i	$-0.415729\pi$
$251$	−1.48853	−	0.483652i	−0.0939551	−	0.0305279i	−0.355617	+	0.934632i	$0.615729\pi$
$252$		0			0
$253$	−11.5562	+	0.352844i	−0.726535	+	0.0221831i
$254$		0			0
$255$	11.2599	+	22.0988i	0.705122	+	1.38388i
$256$		0			0
$257$	3.16940	−	4.36231i	0.197702	−	0.272114i	−0.698643	−	0.715470i	$-0.746213\pi$
$257$	3.16940	−	4.36231i	0.197702	−	0.272114i	0.896345	+	0.443357i	$0.146213\pi$
$258$		0			0
$259$	−8.03497	−	24.7291i	−0.499269	−	1.53659i
$260$		0			0
$261$	−0.804083	−	1.10673i	−0.0497715	−	0.0685046i
$262$		0			0
$263$			4.79868i			0.295899i	0.988995	+	0.147950i	$0.0472674\pi$
$263$			4.79868i			0.295899i	−0.988995	+	0.147950i	$0.952733\pi$
$264$		0			0
$265$	33.0802	−	33.0802i	2.03210	−	2.03210i
$266$		0			0
$267$	−20.2239	−	3.20315i	−1.23768	−	0.196029i
$268$		0			0
$269$	4.79343	+	14.7526i	0.292260	+	0.899485i	0.984128	+	0.177460i	$0.0567882\pi$
$269$	4.79343	+	14.7526i	0.292260	+	0.899485i	−0.691868	+	0.722024i	$0.743212\pi$
$270$		0			0
$271$	−11.4491	+	1.81335i	−0.695480	+	0.110153i	−0.494158	−	0.869372i	$-0.664524\pi$
$271$	−11.4491	+	1.81335i	−0.695480	+	0.110153i	−0.201322	+	0.979525i	$0.564524\pi$
$272$		0			0
$273$	1.99601	+	20.6375i	0.120804	+	1.24904i
$274$		0			0
$275$	24.7115	−	19.1329i	1.49016	−	1.15376i
$276$		0			0
$277$	−2.53497	+	7.80185i	−0.152312	+	0.468768i	−0.997879	−	0.0651020i	$-0.979263\pi$
$277$	−2.53497	+	7.80185i	−0.152312	+	0.468768i	0.845567	+	0.533870i	$0.179263\pi$
$278$		0			0
$279$	1.26105	−	0.199731i	0.0754971	−	0.0119576i
$280$		0			0
$281$	16.6233	+	8.46998i	0.991661	+	0.505277i	0.873033	−	0.487662i	$-0.162150\pi$
$281$	16.6233	+	8.46998i	0.991661	+	0.505277i	0.118629	+	0.992939i	$0.462150\pi$
$282$		0			0
$283$	12.0716	−	8.77056i	0.717584	−	0.521356i	−0.168027	−	0.985782i	$-0.553740\pi$
$283$	12.0716	−	8.77056i	0.717584	−	0.521356i	0.885612	+	0.464427i	$0.153740\pi$
$284$		0			0
$285$	8.47826			0.502209
$286$		0			0
$287$	17.4638			1.03086
$288$		0			0
$289$	6.52894	−	4.74355i	0.384055	−	0.279032i
$290$		0			0
$291$	−7.29806	−	3.71855i	−0.427820	−	0.217985i
$292$		0			0
$293$	31.2851	−	4.95508i	1.82770	−	0.289479i	0.854499	−	0.519452i	$-0.173864\pi$
$293$	31.2851	−	4.95508i	1.82770	−	0.289479i	0.973197	+	0.229974i	$0.0738640\pi$
$294$		0			0
$295$	−13.5778	+	41.7881i	−0.790529	+	2.43300i
$296$		0			0
$297$	8.34913	−	2.99746i	0.484466	−	0.173930i
$298$		0			0
$299$	−9.70181	−	7.99063i	−0.561070	−	0.462110i
$300$		0			0
$301$	19.4839	−	3.08595i	1.12303	−	0.177871i
$302$		0			0
$303$	−2.69084	−	8.28154i	−0.154585	−	0.475762i
$304$		0			0
$305$	15.0949	+	2.39080i	0.864333	+	0.136897i
$306$		0			0
$307$	23.3335	−	23.3335i	1.33171	−	1.33171i	0.427873	−	0.903839i	$-0.359263\pi$
$307$	23.3335	−	23.3335i	1.33171	−	1.33171i	0.903839	−	0.427873i	$-0.140737\pi$
$308$		0			0
$309$		−	32.7780i		−	1.86467i
$310$		0			0
$311$	0.368330	+	0.506963i	0.0208861	+	0.0287472i	0.819332	−	0.573319i	$-0.194344\pi$
$311$	0.368330	+	0.506963i	0.0208861	+	0.0287472i	−0.798446	+	0.602066i	$0.794344\pi$
$312$		0			0
$313$	−2.30004	−	7.07879i	−0.130006	−	0.400117i	0.864774	−	0.502161i	$-0.167462\pi$
$313$	−2.30004	−	7.07879i	−0.130006	−	0.400117i	−0.994780	+	0.102044i	$0.967462\pi$
$314$		0			0
$315$	−10.4326	+	14.3592i	−0.587811	+	0.809052i
$316$		0			0
$317$	−15.6138	−	30.6438i	−0.876957	−	1.72112i	−0.669401	−	0.742901i	$-0.733449\pi$
$317$	−15.6138	−	30.6438i	−0.876957	−	1.72112i	−0.207556	−	0.978223i	$-0.566551\pi$
$318$		0			0
$319$	−2.11148	−	1.43771i	−0.118220	−	0.0804966i
$320$		0			0
$321$	15.9974	+	5.19787i	0.892887	+	0.290117i
$322$		0			0
$323$	0.477522	+	3.01495i	0.0265700	+	0.167757i
$324$		0			0
$325$	33.9127	+	2.05974i	1.88114	+	0.114254i
$326$		0			0
$327$	12.3808	+	1.96093i	0.684660	+	0.108439i
$328$		0			0
$329$	16.2584			0.896356
$330$		0			0
$331$	−21.7365	+	21.7365i	−1.19474	+	1.19474i	−0.219025	+	0.975719i	$0.570288\pi$
$331$	−21.7365	+	21.7365i	−1.19474	+	1.19474i	−0.975719	+	0.219025i	$0.929712\pi$
$332$		0			0
$333$	17.3352	+	2.74563i	0.949965	+	0.150460i
$334$		0			0
$335$	23.8654	−	7.75432i	1.30390	−	0.423664i
$336$		0			0
$337$	−6.34247	−	4.60808i	−0.345497	−	0.251018i	0.401481	−	0.915867i	$-0.368496\pi$
$337$	−6.34247	−	4.60808i	−0.345497	−	0.251018i	−0.746977	+	0.664849i	$0.768496\pi$
$338$		0			0
$339$	−5.02675	+	15.4708i	−0.273016	+	0.840256i
$340$		0			0
$341$	2.09026	−	1.14670i	0.113194	−	0.0620975i
$342$		0			0
$343$	16.5904	−	8.45322i	0.895796	−	0.456431i
$344$		0			0
$345$	−4.52608	−	28.5765i	−0.243676	−	1.53851i
$346$		0			0
$347$	32.3954	−	10.5259i	1.73907	−	0.565060i	0.744364	−	0.667775i	$-0.232753\pi$
$347$	32.3954	−	10.5259i	1.73907	−	0.565060i	0.994711	+	0.102715i	$0.0327530\pi$
$348$		0			0
$349$	−0.488919	+	3.08691i	−0.0261712	+	0.165239i	−0.997312	−	0.0732669i	$-0.976658\pi$
$349$	−0.488919	+	3.08691i	−0.0261712	+	0.165239i	0.971141	+	0.238505i	$0.0766575\pi$
$350$		0			0
$351$	8.97415	+	3.53061i	0.479005	+	0.188450i
$352$		0			0
$353$	3.50230	−	3.50230i	0.186409	−	0.186409i	−0.607733	−	0.794142i	$-0.707921\pi$
$353$	3.50230	−	3.50230i	0.186409	−	0.186409i	0.794142	+	0.607733i	$0.207921\pi$
$354$		0			0
$355$	−10.0695	−	13.8595i	−0.534435	−	0.735586i
$356$		0			0
$357$	−15.3112	−	7.80144i	−0.810354	−	0.412896i
$358$		0			0
$359$	−20.7605	+	3.28815i	−1.09570	+	0.173542i	−0.678013	−	0.735050i	$-0.737159\pi$
$359$	−20.7605	+	3.28815i	−1.09570	+	0.173542i	−0.417686	+	0.908591i	$0.637159\pi$
$360$		0			0
$361$	−17.0777	−	5.54887i	−0.898825	−	0.292046i
$362$		0			0
$363$	−18.5503	+	15.2905i	−0.973639	+	0.802541i
$364$		0			0
$365$	−45.3789	−	14.7445i	−2.37524	−	0.771763i
$366$		0			0
$367$	−7.98083	−	5.79841i	−0.416596	−	0.302675i	0.359671	−	0.933079i	$-0.382889\pi$
$367$	−7.98083	−	5.79841i	−0.416596	−	0.302675i	−0.776267	+	0.630405i	$0.782889\pi$
$368$		0			0
$369$	−5.35172	+	10.5033i	−0.278599	+	0.546782i
$370$		0			0
$371$	−5.07057	+	32.0143i	−0.263251	+	1.66210i
$372$		0			0
$373$		−	33.6076i		−	1.74014i	−0.492932	−	0.870068i	$-0.664075\pi$
$373$		−	33.6076i		−	1.74014i	0.492932	−	0.870068i	$-0.335925\pi$
$374$		0			0
$375$	25.9581	+	25.9581i	1.34047	+	1.34047i
$376$		0			0
$377$	−0.696450	−	2.68826i	−0.0358690	−	0.138452i
$378$		0			0
$379$	−2.30218	−	1.17302i	−0.118255	−	0.0602540i	0.393862	−	0.919170i	$-0.371139\pi$
$379$	−2.30218	−	1.17302i	−0.118255	−	0.0602540i	−0.512117	+	0.858915i	$0.671139\pi$
$380$		0			0
$381$	−7.58693	−	5.51223i	−0.388690	−	0.282400i
$382$		0			0
$383$	2.50510	+	4.91654i	0.128005	+	0.251224i	0.946110	−	0.323845i	$-0.104976\pi$
$383$	2.50510	+	4.91654i	0.128005	+	0.251224i	−0.818105	+	0.575068i	$0.804976\pi$
$384$		0			0
$385$	−9.27505	+	31.8189i	−0.472700	+	1.62164i
$386$		0			0
$387$	−4.11477	+	12.6640i	−0.209166	+	0.643745i
$388$		0			0
$389$	4.79952	−	6.60597i	0.243345	−	0.334936i	−0.669821	−	0.742522i	$-0.733629\pi$
$389$	4.79952	−	6.60597i	0.243345	−	0.334936i	0.913167	+	0.407586i	$0.133629\pi$
$390$		0			0
$391$	9.90717	−	3.21904i	0.501027	−	0.162794i
$392$		0			0
$393$	−11.1822	−	15.3910i	−0.564066	−	0.776371i
$394$		0			0
$395$	−46.3698	−	46.3698i	−2.33312	−	2.33312i
$396$		0			0
$397$	−1.18851	−	1.18851i	−0.0596495	−	0.0596495i	0.676653	−	0.736302i	$-0.263430\pi$
$397$	−1.18851	−	1.18851i	−0.0596495	−	0.0596495i	−0.736302	+	0.676653i	$0.763430\pi$
$398$		0			0
$399$	−4.75232	+	3.45276i	−0.237913	+	0.172854i
$400$		0			0
$401$	10.9669	−	21.5237i	0.547659	−	1.07484i	−0.436854	−	0.899532i	$-0.643907\pi$
$401$	10.9669	−	21.5237i	0.547659	−	1.07484i	0.984513	−	0.175309i	$-0.0560925\pi$
$402$		0			0
$403$	2.53064	+	0.559901i	0.126060	+	0.0278906i
$404$		0			0
$405$	19.2652	+	37.8101i	0.957297	+	1.87880i
$406$		0			0
$407$	32.1989	−	6.11249i	1.59604	−	0.302985i
$408$		0			0
$409$	19.6691	−	10.0219i	0.972577	−	0.495553i	0.105875	−	0.994379i	$-0.466236\pi$
$409$	19.6691	−	10.0219i	0.972577	−	0.495553i	0.866702	+	0.498827i	$0.166236\pi$
$410$		0			0
$411$	4.50782	+	28.4613i	0.222355	+	1.40389i
$412$		0			0
$413$	−9.40740	−	28.9530i	−0.462908	−	1.42468i
$414$		0			0
$415$	−48.5430	+	35.2685i	−2.38288	+	1.73126i
$416$		0			0
$417$		−	18.3811i		−	0.900125i
$418$		0			0
$419$	−9.99770			−0.488420			−0.244210	−	0.969722i	$-0.578529\pi$
$419$	−9.99770			−0.488420			−0.244210	+	0.969722i	$0.578529\pi$
$420$		0			0
$421$	−0.804653	+	5.08038i	−0.0392164	+	0.247602i	−0.999507	−	0.0313995i	$-0.990004\pi$
$421$	−0.804653	+	5.08038i	−0.0392164	+	0.247602i	0.960291	+	0.279002i	$0.0900036\pi$
$422$		0			0
$423$	−4.98233	+	9.77838i	−0.242249	+	0.475441i
$424$		0			0
$425$	−16.5512	+	22.7808i	−0.802852	+	1.10503i
$426$		0			0
$427$	−9.43480	+	4.80727i	−0.456582	+	0.232640i
$428$		0			0
$429$	−26.1222	−	0.787521i	−1.26119	−	0.0380219i
$430$		0			0
$431$	−22.8452	+	11.6402i	−1.10042	+	0.560690i	−0.907299	−	0.420486i	$-0.861860\pi$
$431$	−22.8452	+	11.6402i	−1.10042	+	0.560690i	−0.193117	+	0.981176i	$0.561860\pi$
$432$		0			0
$433$	18.1965	−	25.0453i	0.874466	−	1.20360i	−0.103457	−	0.994634i	$-0.532990\pi$
$433$	18.1965	−	25.0453i	0.874466	−	1.20360i	0.977923	−	0.208965i	$-0.0670096\pi$
$434$		0			0
$435$	2.90215	−	5.69578i	0.139147	−	0.273092i
$436$		0			0
$437$	0.557052	−	3.51709i	0.0266474	−	0.168245i
$438$		0			0
$439$	−0.402842			−0.0192266			−0.00961329	−	0.999954i	$-0.503060\pi$
$439$	−0.402842			−0.0192266			−0.00961329	+	0.999954i	$0.503060\pi$
$440$		0			0
$441$			0.135518i			0.00645321i
$442$		0			0
$443$	−17.8101	+	12.9398i	−0.846184	+	0.614789i	−0.924091	−	0.382172i	$-0.875176\pi$
$443$	−17.8101	+	12.9398i	−0.846184	+	0.614789i	0.0779074	+	0.996961i	$0.475176\pi$
$444$		0			0
$445$	−10.9955	−	33.8408i	−0.521239	−	1.60421i
$446$		0			0
$447$	4.53393	+	28.6261i	0.214447	+	1.35397i
$448$		0			0
$449$	−14.5258	+	7.40125i	−0.685513	+	0.349287i	−0.761812	−	0.647799i	$-0.775690\pi$
$449$	−14.5258	+	7.40125i	−0.685513	+	0.349287i	0.0762983	+	0.997085i	$0.475690\pi$
$450$		0			0
$451$	−2.77837	+	21.8363i	−0.130828	+	1.02823i
$452$		0			0
$453$	−7.09353	−	13.9218i	−0.333283	−	0.654105i
$454$		0			0
$455$	−30.3795	+	19.3720i	−1.42421	+	0.908175i
$456$		0			0
$457$	−11.2933	+	22.1643i	−0.528278	+	1.03680i	0.460535	+	0.887641i	$0.347658\pi$
$457$	−11.2933	+	22.1643i	−0.528278	+	1.03680i	−0.988813	+	0.149162i	$0.952342\pi$
$458$		0			0
$459$	−6.46620	+	4.69797i	−0.301816	+	0.219282i
$460$		0			0
$461$	−2.00685	−	2.00685i	−0.0934683	−	0.0934683i	0.658827	−	0.752295i	$-0.271053\pi$
$461$	−2.00685	−	2.00685i	−0.0934683	−	0.0934683i	−0.752295	+	0.658827i	$0.771053\pi$
$462$		0			0
$463$	14.5209	+	14.5209i	0.674844	+	0.674844i	0.958829	−	0.283984i	$-0.0916564\pi$
$463$	14.5209	+	14.5209i	0.674844	+	0.674844i	−0.283984	+	0.958829i	$0.591656\pi$
$464$		0			0
$465$	3.50688	+	4.82681i	0.162628	+	0.223838i
$466$		0			0
$467$	−23.1276	+	7.51461i	−1.07022	+	0.347734i	−0.790572	−	0.612369i	$-0.790217\pi$
$467$	−23.1276	+	7.51461i	−1.07022	+	0.347734i	−0.279645	+	0.960104i	$0.590217\pi$
$468$		0			0
$469$	−10.2193	+	14.0657i	−0.471883	+	0.649492i
$470$		0			0
$471$	7.25351	−	22.3240i	0.334224	−	1.02864i
$472$		0			0
$473$	0.758834	+	24.8531i	0.0348912	+	1.14275i
$474$		0			0
$475$	4.36996	+	8.57654i	0.200508	+	0.393519i
$476$		0			0
$477$	−17.7006	−	12.8603i	−0.810457	−	0.588831i
$478$		0			0
$479$	−13.8639	−	7.06403i	−0.633460	−	0.322764i	0.107609	−	0.994193i	$-0.465681\pi$
$479$	−13.8639	−	7.06403i	−0.633460	−	0.322764i	−0.741068	+	0.671429i	$0.765681\pi$
$480$		0			0
$481$	30.7067	+	18.0701i	1.40011	+	0.823925i
$482$		0			0
$483$	14.1748	+	14.1748i	0.644974	+	0.644974i
$484$		0			0
$485$		−	14.2337i		−	0.646317i
$486$		0			0
$487$	−0.199567	+	1.26001i	−0.00904322	+	0.0570967i	−0.991797	−	0.127821i	$-0.959202\pi$
$487$	−0.199567	+	1.26001i	−0.00904322	+	0.0570967i	0.982754	+	0.184917i	$0.0592018\pi$
$488$		0			0
$489$	2.41340	−	4.73656i	0.109138	−	0.214195i
$490$		0			0
$491$	−19.4872	−	14.1583i	−0.879443	−	0.638953i	0.0536608	−	0.998559i	$-0.482911\pi$
$491$	−19.4872	−	14.1583i	−0.879443	−	0.638953i	−0.933104	+	0.359606i	$0.882911\pi$
$492$		0			0
$493$	2.18893	+	0.711228i	0.0985846	+	0.0320321i
$494$		0			0
$495$	−16.2947	−	15.3291i	−0.732391	−	0.688992i
$496$		0			0
$497$	11.2885	+	3.66786i	0.506359	+	0.164526i
$498$		0			0
$499$	4.84874	−	0.767965i	0.217060	−	0.0343789i	−0.0469574	−	0.998897i	$-0.514953\pi$
$499$	4.84874	−	0.767965i	0.217060	−	0.0343789i	0.264017	+	0.964518i	$0.414953\pi$
$500$		0			0
$501$	7.49574	+	3.81927i	0.334885	+	0.170632i
$502$		0			0
$503$	6.86243	+	9.44532i	0.305980	+	0.421146i	0.934122	−	0.356953i	$-0.116184\pi$
$503$	6.86243	+	9.44532i	0.305980	+	0.421146i	−0.628142	+	0.778099i	$0.716184\pi$
$504$		0			0
$505$	10.6999	−	10.6999i	0.476139	−	0.476139i
$506$		0			0
$507$	−20.7947	−	19.3584i	−0.923526	−	0.859736i
$508$		0			0
$509$	3.92426	−	24.7768i	0.173940	−	1.09821i	−0.734011	−	0.679137i	$-0.762354\pi$
$509$	3.92426	−	24.7768i	0.173940	−	1.09821i	0.907951	−	0.419076i	$-0.137646\pi$
$510$		0			0
$511$	31.4409	−	10.2158i	1.39086	−	0.451919i
$512$		0			0
$513$	0.427409	+	2.69855i	0.0188706	+	0.119144i
$514$		0			0
$515$	50.7520	−	25.8594i	2.23640	−	1.13950i
$516$		0			0
$517$	−2.58660	+	20.3291i	−0.113759	+	0.894074i
$518$		0			0
$519$	10.8717	−	33.4595i	0.477213	−	1.46871i
$520$		0			0
$521$	−20.1947	−	14.6723i	−0.884747	−	0.642807i	0.0497557	−	0.998761i	$-0.484156\pi$
$521$	−20.1947	−	14.6723i	−0.884747	−	0.642807i	−0.934503	+	0.355955i	$0.884156\pi$
$522$		0			0
$523$	25.8824	−	8.40971i	1.13176	−	0.367731i	0.317515	−	0.948253i	$-0.397152\pi$
$523$	25.8824	−	8.40971i	1.13176	−	0.367731i	0.814244	+	0.580522i	$0.197152\pi$
$524$		0			0
$525$	−53.5203	−	8.47678i	−2.33582	−	0.369957i
$526$		0			0
$527$	−1.51894	+	1.51894i	−0.0661661	+	0.0661661i
$528$		0			0
$529$	10.8481			0.471655
$530$		0			0
$531$	20.2962	+	3.21460i	0.880779	+	0.139502i
$532$		0			0
$533$	−17.9157	+	15.8641i	−0.776016	+	0.687149i
$534$		0			0
$535$	4.57262	+	28.8704i	0.197692	+	1.24818i
$536$		0			0
$537$	15.8295	+	5.14332i	0.683093	+	0.221950i
$538$		0			0
$539$	0.0855068	+	0.238171i	0.00368304	+	0.0102588i
$540$		0			0
$541$	−1.58052	−	3.10195i	−0.0679519	−	0.133363i	0.854532	−	0.519399i	$-0.173844\pi$
$541$	−1.58052	−	3.10195i	−0.0679519	−	0.133363i	−0.922484	+	0.386036i	$0.873844\pi$
$542$		0			0
$543$	−29.0661	+	40.0060i	−1.24734	+	1.71682i
$544$		0			0
$545$	6.73133	+	20.7169i	0.288339	+	0.887415i
$546$		0			0
$547$	3.44624	+	4.74334i	0.147350	+	0.202811i	0.876312	−	0.481744i	$-0.159997\pi$
$547$	3.44624	+	4.74334i	0.147350	+	0.202811i	−0.728961	+	0.684555i	$0.759997\pi$
$548$		0			0
$549$		−	7.14758i		−	0.305051i
$550$		0			0
$551$	0.556328	−	0.556328i	0.0237004	−	0.0237004i
$552$		0			0
$553$	44.8757	+	7.10761i	1.90831	+	0.302246i
$554$		0			0
$555$	25.3444	+	78.0021i	1.07581	+	3.31100i
$556$		0			0
$557$	3.55280	−	0.562708i	0.150537	−	0.0238427i	−0.0807112	−	0.996738i	$-0.525719\pi$
$557$	3.55280	−	0.562708i	0.150537	−	0.0238427i	0.231248	+	0.972895i	$0.425719\pi$
$558$		0			0
$559$	−17.1848	+	20.8649i	−0.726840	+	0.882491i
$560$		0			0
$561$	12.1906	−	17.9036i	0.514689	−	0.755889i
$562$		0			0
$563$	−4.73965	+	14.5871i	−0.199753	+	0.614775i	0.800136	+	0.599819i	$0.204761\pi$
$563$	−4.73965	+	14.5871i	−0.199753	+	0.614775i	−0.999888	+	0.0149559i	$0.995239\pi$
$564$		0			0
$565$	−27.9200	+	4.42209i	−1.17460	+	0.186039i
$566$		0			0
$567$	−26.1968	−	13.3480i	−1.10016	−	0.560561i
$568$		0			0
$569$	11.9288	−	8.66675i	0.500079	−	0.363329i	−0.308968	−	0.951072i	$-0.599984\pi$
$569$	11.9288	−	8.66675i	0.500079	−	0.363329i	0.809047	+	0.587744i	$0.199984\pi$
$570$		0			0
$571$	−13.7460			−0.575253			−0.287626	−	0.957743i	$-0.592866\pi$
$571$	−13.7460			−0.575253			−0.287626	+	0.957743i	$0.592866\pi$
$572$		0			0
$573$	36.1938			1.51202
$574$		0			0
$575$	26.5749	−	19.3078i	1.10825	−	0.805190i
$576$		0			0
$577$	−32.6603	−	16.6412i	−1.35966	−	0.692784i	−0.386370	−	0.922344i	$-0.626271\pi$
$577$	−32.6603	−	16.6412i	−1.35966	−	0.692784i	−0.973294	+	0.229560i	$0.926271\pi$
$578$		0			0
$579$	51.1592	−	8.10282i	2.12610	−	0.336742i
$580$		0			0
$581$	12.8467	−	39.5381i	0.532971	−	1.64032i
$582$		0			0
$583$	−39.2231	−	11.4334i	−1.62446	−	0.473521i
$584$		0			0
$585$	−2.34132	−	24.2078i	−0.0968017	−	1.00087i
$586$		0			0
$587$	22.4883	−	3.56180i	0.928191	−	0.147011i	0.326006	−	0.945368i	$-0.394297\pi$
$587$	22.4883	−	3.56180i	0.928191	−	0.147011i	0.602185	+	0.798357i	$0.294297\pi$
$588$		0			0
$589$	0.226912	+	0.698364i	0.00934976	+	0.0287756i
$590$		0			0
$591$	−2.95441	−	0.467932i	−0.121528	−	0.0192482i
$592$		0			0
$593$	−31.1909	+	31.1909i	−1.28086	+	1.28086i	−0.340676	+	0.940181i	$0.610656\pi$
$593$	−31.1909	+	31.1909i	−1.28086	+	1.28086i	−0.940181	+	0.340676i	$0.889344\pi$
$594$		0			0
$595$		−	29.8619i		−	1.22422i
$596$		0			0
$597$	7.92203	+	10.9037i	0.324227	+	0.446260i
$598$		0			0
$599$	−14.7259	−	45.3215i	−0.601682	−	1.85179i	−0.518165	−	0.855281i	$-0.673385\pi$
$599$	−14.7259	−	45.3215i	−0.601682	−	1.85179i	−0.0835169	−	0.996506i	$-0.526615\pi$
$600$		0			0
$601$	−11.1420	+	15.3356i	−0.454492	+	0.625554i	−0.973355	−	0.229303i	$-0.926355\pi$
$601$	−11.1420	+	15.3356i	−0.454492	+	0.625554i	0.518863	+	0.854857i	$0.326355\pi$
$602$		0			0
$603$	−5.32791	−	10.4566i	−0.216969	−	0.425826i
$604$		0			0
$605$	−38.3099	−	16.6594i	−1.55752	−	0.677303i
$606$		0			0
$607$	−15.2537	−	4.95624i	−0.619131	−	0.201168i	−0.0173763	−	0.999849i	$-0.505531\pi$
$607$	−15.2537	−	4.95624i	−0.619131	−	0.201168i	−0.601754	+	0.798681i	$0.705531\pi$
$608$		0			0
$609$	0.692860	+	4.37455i	0.0280761	+	0.177266i
$610$		0			0
$611$	−16.6792	+	14.7691i	−0.674766	+	0.597494i
$612$		0			0
$613$	47.3997	+	7.50737i	1.91445	+	0.303220i	0.995778	−	0.0917911i	$-0.0292592\pi$
$613$	47.3997	+	7.50737i	1.91445	+	0.303220i	0.918676	+	0.395011i	$0.129259\pi$
$614$		0			0
$615$	−55.0854			−2.22126
$616$		0			0
$617$	−27.0368	+	27.0368i	−1.08846	+	1.08846i	−0.0927740	+	0.995687i	$0.529573\pi$
$617$	−27.0368	+	27.0368i	−1.08846	+	1.08846i	−0.995687	+	0.0927740i	$0.970427\pi$
$618$		0			0
$619$	−15.9763	−	2.53040i	−0.642143	−	0.101706i	−0.173133	−	0.984898i	$-0.555389\pi$
$619$	−15.9763	−	2.53040i	−0.642143	−	0.101706i	−0.469010	+	0.883193i	$0.655389\pi$
$620$		0			0
$621$	8.86748	−	2.88122i	0.355840	−	0.115619i
$622$		0			0
$623$	19.9449	+	14.4908i	0.799077	+	0.580563i
$624$		0			0
$625$	−5.15392	+	15.8621i	−0.206157	+	0.634485i
$626$		0			0
$627$	−3.56118	−	6.49148i	−0.142220	−	0.259245i
$628$		0			0
$629$	−26.3108	+	13.4060i	−1.04908	+	0.534534i
$630$		0			0
$631$	−4.61505	−	29.1383i	−0.183722	−	1.15998i	−0.891325	−	0.453365i	$-0.850223\pi$
$631$	−4.61505	−	29.1383i	−0.183722	−	1.15998i	0.707603	−	0.706610i	$-0.249777\pi$
$632$		0			0
$633$	29.8861	−	9.71060i	1.18787	−	0.385962i
$634$		0			0
$635$	2.54936	−	16.0960i	0.101168	−	0.638751i
$636$		0			0
$637$	−0.100716	+	0.256001i	−0.00399050	+	0.0101431i
$638$		0			0
$639$	−5.66530	+	5.66530i	−0.224116	+	0.224116i
$640$		0			0
$641$	22.7291	+	31.2840i	0.897747	+	1.23564i	0.971181	+	0.238343i	$0.0766043\pi$
$641$	22.7291	+	31.2840i	0.897747	+	1.23564i	−0.0734335	+	0.997300i	$0.523396\pi$
$642$		0			0
$643$	−17.5127	−	8.92318i	−0.690634	−	0.351896i	0.0731918	−	0.997318i	$-0.476681\pi$
$643$	−17.5127	−	8.92318i	−0.690634	−	0.351896i	−0.763826	+	0.645422i	$0.776681\pi$
$644$		0			0
$645$	−61.4573	+	9.73388i	−2.41988	+	0.383271i
$646$		0			0
$647$	34.3957	+	11.1759i	1.35224	+	0.439368i	0.893444	−	0.449176i	$-0.148282\pi$
$647$	34.3957	+	11.1759i	1.35224	+	0.439368i	0.458792	+	0.888544i	$0.348282\pi$
$648$		0			0
$649$	37.6987	−	7.15654i	1.47980	−	0.280919i
$650$		0			0
$651$	−3.93142	−	1.27740i	−0.154084	−	0.0500651i
$652$		0			0
$653$	37.5050	+	27.2490i	1.46768	+	1.06633i	0.981277	+	0.192603i	$0.0616929\pi$
$653$	37.5050	+	27.2490i	1.46768	+	1.06633i	0.486407	+	0.873732i	$0.338307\pi$
$654$		0			0
$655$	15.0088	−	29.4563i	0.586440	−	1.15095i
$656$		0			0
$657$	−3.49083	+	22.0402i	−0.136190	+	0.859871i
$658$		0			0
$659$			14.9305i			0.581610i	0.956782	+	0.290805i	$0.0939230\pi$
$659$			14.9305i			0.581610i	−0.956782	+	0.290805i	$0.906077\pi$
$660$		0			0
$661$	16.3940	+	16.3940i	0.637652	+	0.637652i	0.949976	−	0.312324i	$-0.101107\pi$
$661$	16.3940	+	16.3940i	0.637652	+	0.637652i	−0.312324	+	0.949976i	$0.601107\pi$
$662$		0			0
$663$	22.7942	−	5.90531i	0.885254	−	0.229343i
$664$		0			0
$665$	−9.09533	−	4.63430i	−0.352702	−	0.179711i
$666$		0			0
$667$	−2.17213	−	1.57815i	−0.0841053	−	0.0611061i
$668$		0			0
$669$	−13.0799	−	25.6707i	−0.505697	−	0.992486i
$670$		0			0
$671$	−4.50987	−	12.5618i	−0.174102	−	0.484944i
$672$		0			0
$673$	−15.5089	+	47.7315i	−0.597824	+	1.83991i	−0.0576915	+	0.998334i	$0.518374\pi$
$673$	−15.5089	+	47.7315i	−0.597824	+	1.83991i	−0.540133	+	0.841580i	$0.681626\pi$
$674$		0			0
$675$	−14.8143	+	20.3901i	−0.570202	+	0.784816i
$676$		0			0
$677$	30.4337	−	9.88852i	1.16966	−	0.380047i	0.341146	−	0.940010i	$-0.389185\pi$
$677$	30.4337	−	9.88852i	1.16966	−	0.380047i	0.828517	+	0.559964i	$0.189185\pi$
$678$		0			0
$679$	5.79664	+	7.97839i	0.222454	+	0.306182i
$680$		0			0
$681$	35.7034	+	35.7034i	1.36816	+	1.36816i
$682$		0			0
$683$	−4.44579	−	4.44579i	−0.170113	−	0.170113i	0.616916	−	0.787029i	$-0.288382\pi$
$683$	−4.44579	−	4.44579i	−0.170113	−	0.170113i	−0.787029	+	0.616916i	$0.788382\pi$
$684$		0			0
$685$	−40.5118	+	29.4336i	−1.54788	+	1.12460i
$686$		0			0
$687$	−8.46358	+	16.6107i	−0.322906	+	0.633738i
$688$		0			0
$689$	−23.8799	−	37.4488i	−0.909752	−	1.42669i
$690$		0			0
$691$	1.43166	+	2.80980i	0.0544630	+	0.106890i	0.916634	−	0.399728i	$-0.130895\pi$
$691$	1.43166	+	2.80980i	0.0544630	+	0.106890i	−0.862171	+	0.506618i	$0.830895\pi$
$692$		0			0
$693$	15.3764	+	1.95644i	0.584101	+	0.0743189i
$694$		0			0
$695$	28.4604	−	14.5013i	1.07957	−	0.550066i
$696$		0			0
$697$	−3.10258	−	19.5889i	−0.117519	−	0.741983i
$698$		0			0
$699$	2.52671	+	7.77641i	0.0955688	+	0.294131i
$700$		0			0
$701$	−7.04112	+	5.11567i	−0.265939	+	0.193216i	−0.712761	−	0.701407i	$-0.752556\pi$
$701$	−7.04112	+	5.11567i	−0.265939	+	0.193216i	0.446822	+	0.894623i	$0.352556\pi$
$702$		0			0
$703$			10.0942i			0.380711i
$704$		0			0
$705$	−51.2833			−1.93144
$706$		0			0
$707$	−1.64009	+	10.3551i	−0.0616820	+	0.389445i
$708$		0			0
$709$	20.2419	−	39.7270i	0.760201	−	1.49198i	−0.107128	−	0.994245i	$-0.534166\pi$
$709$	20.2419	−	39.7270i	0.760201	−	1.49198i	0.867330	−	0.497734i	$-0.165834\pi$
$710$		0			0
$711$	−18.0268	+	24.8117i	−0.676056	+	0.930511i
$712$		0			0
$713$	2.23275	−	1.13764i	0.0836170	−	0.0426050i
$714$		0			0
$715$	−19.3891	−	41.0677i	−0.725112	−	1.53585i
$716$		0			0
$717$	36.5886	−	18.6428i	1.36642	−	0.696228i
$718$		0			0
$719$	−20.4664	+	28.1695i	−0.763266	+	1.05055i	0.233669	+	0.972316i	$0.424927\pi$
$719$	−20.4664	+	28.1695i	−0.763266	+	1.05055i	−0.996935	+	0.0782300i	$0.975073\pi$
$720$		0			0
$721$	−17.9168	+	35.1636i	−0.667256	+	1.30956i
$722$		0			0
$723$	5.65449	−	35.7011i	0.210293	−	1.32774i
$724$		0			0
$725$	7.25766			0.269543
$726$		0			0
$727$		−	9.11914i		−	0.338210i	−0.985598	−	0.169105i	$-0.945912\pi$
$727$		−	9.11914i		−	0.338210i	0.985598	−	0.169105i	$-0.0540877\pi$
$728$		0			0
$729$	1.86892	−	1.35785i	0.0692191	−	0.0502907i
$730$		0			0
$731$	−6.92292	−	21.3066i	−0.256054	−	0.788052i
$732$		0			0
$733$	−0.933696	−	5.89512i	−0.0344868	−	0.217741i	0.964426	−	0.264352i	$-0.0851580\pi$
$733$	−0.933696	−	5.89512i	−0.0344868	−	0.217741i	−0.998913	+	0.0466106i	$0.985158\pi$
$734$		0			0
$735$	−0.564243	+	0.287496i	−0.0208124	+	0.0106045i
$736$		0			0
$737$	−15.9615	−	15.0157i	−0.587950	−	0.553110i
$738$		0			0
$739$	−6.21217	−	12.1921i	−0.228518	−	0.448492i	0.748067	−	0.663623i	$-0.230982\pi$
$739$	−6.21217	−	12.1921i	−0.228518	−	0.448492i	−0.976585	+	0.215131i	$0.930982\pi$
$740$		0			0
$741$	1.73882	−	7.85910i	0.0638771	−	0.288711i
$742$		0			0
$743$	−17.0364	+	33.4359i	−0.625006	+	1.22664i	0.333817	+	0.942638i	$0.391663\pi$
$743$	−17.0364	+	33.4359i	−0.625006	+	1.22664i	−0.958823	+	0.284005i	$0.908337\pi$
$744$		0			0
$745$	−40.7464	+	29.6040i	−1.49283	+	1.08461i
$746$		0			0
$747$	19.8428	+	19.8428i	0.726008	+	0.726008i
$748$		0			0
$749$	−14.3205	−	14.3205i	−0.523260	−	0.523260i
$750$		0			0
$751$	8.74766	+	12.0401i	0.319207	+	0.439350i	0.938225	−	0.346026i	$-0.112469\pi$
$751$	8.74766	+	12.0401i	0.319207	+	0.439350i	−0.619018	+	0.785377i	$0.712469\pi$
$752$		0			0
$753$	−3.25309	+	1.05699i	−0.118549	+	0.0385189i
$754$		0			0
$755$	15.9597	−	21.9666i	0.580832	−	0.799447i
$756$		0			0
$757$	11.0803	−	34.1018i	0.402722	−	1.23945i	−0.520061	−	0.854129i	$-0.674091\pi$
$757$	11.0803	−	34.1018i	0.402722	−	1.23945i	0.922783	−	0.385321i	$-0.125909\pi$
$758$		0			0
$759$	−19.9788	+	15.4686i	−0.725186	+	0.561476i
$760$		0			0
$761$	−5.46088	−	10.7176i	−0.197957	−	0.388512i	0.770595	−	0.637326i	$-0.219959\pi$
$761$	−5.46088	−	10.7176i	−0.197957	−	0.388512i	−0.968551	+	0.248814i	$0.919959\pi$
$762$		0			0
$763$	−12.2100	−	8.87111i	−0.442033	−	0.321156i
$764$		0			0
$765$	17.9600	+	9.15108i	0.649345	+	0.330858i
$766$		0			0
$767$	35.9516	+	21.1566i	1.29814	+	0.763919i
$768$		0			0
$769$	4.27430	+	4.27430i	0.154135	+	0.154135i	0.779962	−	0.625827i	$-0.215238\pi$
$769$	4.27430	+	4.27430i	0.154135	+	0.154135i	−0.625827	+	0.779962i	$0.715238\pi$
$770$		0			0
$771$		−	11.7841i		−	0.424395i
$772$		0			0
$773$	−0.278342	+	1.75738i	−0.0100113	+	0.0632087i	−0.992188	−	0.124750i	$-0.960187\pi$
$773$	−0.278342	+	1.75738i	−0.0100113	+	0.0632087i	0.982177	+	0.187959i	$0.0601871\pi$
$774$		0			0
$775$	−3.07520	+	6.03542i	−0.110464	+	0.216799i
$776$		0			0
$777$	−45.9725	−	33.4010i	−1.64925	−	1.19825i
$778$		0			0
$779$	−6.44787	−	2.09504i	−0.231019	−	0.0750626i
$780$		0			0
$781$	−6.38213	+	13.5313i	−0.228370	+	0.484190i
$782$		0			0
$783$	1.95922	+	0.636589i	0.0700168	+	0.0227498i
$784$		0			0
$785$	40.2880	−	6.38099i	1.43794	−	0.227747i
$786$		0			0
$787$	16.9874	+	8.65550i	0.605535	+	0.308535i	0.729744	−	0.683721i	$-0.239639\pi$
$787$	16.9874	+	8.65550i	0.605535	+	0.308535i	−0.124209	+	0.992256i	$0.539639\pi$
$788$		0			0
$789$	6.16423	+	8.48434i	0.219453	+	0.302050i
$790$		0			0
$791$	13.8491	−	13.8491i	0.492417	−	0.492417i
$792$		0			0
$793$	5.31204	−	13.5022i	0.188636	−	0.479477i
$794$		0			0
$795$	15.9939	−	100.981i	0.567245	−	3.58144i
$796$		0			0
$797$	33.4917	−	10.8821i	1.18634	−	0.385465i	0.351620	−	0.936143i	$-0.385631\pi$
$797$	33.4917	−	10.8821i	1.18634	−	0.385465i	0.834718	+	0.550678i	$0.185631\pi$
$798$		0			0
$799$	−2.88843	−	18.2369i	−0.102185	−	0.645174i
$800$		0			0
$801$	−14.8273	+	7.55491i	−0.523898	+	0.266940i
$802$		0			0
$803$	7.77150	+	40.9381i	0.274250	+	1.44468i
$804$		0			0
$805$	−10.7647	+	33.1304i	−0.379407	+	1.16769i
$806$		0			0
$807$	27.4258	+	19.9260i	0.965435	+	0.701430i
$808$		0			0
$809$	−12.9731	+	4.21522i	−0.456111	+	0.148199i	−0.528057	−	0.849209i	$-0.677079\pi$
$809$	−12.9731	+	4.21522i	−0.456111	+	0.148199i	0.0719458	+	0.997409i	$0.477079\pi$
$810$		0			0
$811$	−10.7628	−	1.70466i	−0.377933	−	0.0598588i	−0.0354220	−	0.999372i	$-0.511278\pi$
$811$	−10.7628	−	1.70466i	−0.377933	−	0.0598588i	−0.342511	+	0.939514i	$0.611278\pi$
$812$		0			0
$813$	−17.9132	+	17.9132i	−0.628243	+	0.628243i
$814$		0			0
$815$	9.23788			0.323589
$816$		0			0
$817$	−7.56392	−	1.19801i	−0.264628	−	0.0419130i
$818$		0			0
$819$	11.1710	+	12.6157i	0.390345	+	0.440827i
$820$		0			0
$821$	−7.16352	−	45.2287i	−0.250009	−	1.57849i	−0.718821	−	0.695195i	$-0.755318\pi$
$821$	−7.16352	−	45.2287i	−0.250009	−	1.57849i	0.468813	−	0.883298i	$-0.344682\pi$
$822$		0			0
$823$	30.8596	+	10.0269i	1.07570	+	0.349516i	0.792704	−	0.609606i	$-0.208672\pi$
$823$	30.8596	+	10.0269i	1.07570	+	0.349516i	0.282994	+	0.959122i	$0.408672\pi$
$824$		0			0
$825$	19.1138	−	65.5718i	0.665459	−	2.28292i
$826$		0			0
$827$	14.0548	+	27.5841i	0.488733	+	0.959193i	0.995286	+	0.0969840i	$0.0309196\pi$
$827$	14.0548	+	27.5841i	0.488733	+	0.959193i	−0.506553	+	0.862209i	$0.669080\pi$
$828$		0			0
$829$	12.4008	−	17.0683i	0.430698	−	0.592805i	−0.537415	−	0.843318i	$-0.680599\pi$
$829$	12.4008	−	17.0683i	0.430698	−	0.592805i	0.968113	+	0.250512i	$0.0805991\pi$
$830$		0			0
$831$	5.54003	+	17.0505i	0.192181	+	0.591474i
$832$		0			0
$833$	−0.134016	−	0.184458i	−0.00464339	−	0.00639108i
$834$		0			0
$835$			14.6192i			0.505918i
$836$		0			0
$837$	−1.35954	+	1.35954i	−0.0469925	+	0.0469925i
$838$		0			0
$839$	−49.8113	−	7.88933i	−1.71968	−	0.272370i	−0.782861	−	0.622197i	$-0.786240\pi$
$839$	−49.8113	−	7.88933i	−1.71968	−	0.272370i	−0.936814	+	0.349827i	$0.886240\pi$
$840$		0			0
$841$	8.77818	+	27.0165i	0.302696	+	0.931602i
$842$		0			0
$843$	40.2711	−	6.37832i	1.38701	−	0.219681i
$844$		0			0
$845$	13.5682	−	47.4700i	0.466759	−	1.63302i
$846$		0			0
$847$	28.2584	−	6.26355i	0.970969	−	0.215218i
$848$		0			0
$849$	10.0770	−	31.0137i	0.345840	−	1.06439i
$850$		0			0
$851$	34.0232	−	5.38875i	1.16630	−	0.184724i
$852$		0			0
$853$	19.4223	+	9.89618i	0.665008	+	0.338839i	0.753698	−	0.657221i	$-0.228268\pi$
$853$	19.4223	+	9.89618i	0.665008	+	0.338839i	−0.0886899	+	0.996059i	$0.528268\pi$
$854$		0			0
$855$	5.57446	−	4.05008i	0.190643	−	0.138510i
$856$		0			0
$857$	−25.4503			−0.869365			−0.434682	−	0.900584i	$-0.643139\pi$
$857$	−25.4503			−0.869365			−0.434682	+	0.900584i	$0.643139\pi$
$858$		0			0
$859$	−41.1380			−1.40361			−0.701805	−	0.712369i	$-0.747622\pi$
$859$	−41.1380			−1.40361			−0.701805	+	0.712369i	$0.747622\pi$
$860$		0			0
$861$	30.8770	−	22.4334i	1.05228	−	0.764530i
$862$		0			0
$863$	7.60715	+	3.87604i	0.258950	+	0.131942i	0.578647	−	0.815578i	$-0.303581\pi$
$863$	7.60715	+	3.87604i	0.258950	+	0.131942i	−0.319697	+	0.947520i	$0.603581\pi$
$864$		0			0
$865$	60.3842	−	9.56391i	2.05312	−	0.325183i
$866$		0			0
$867$	5.45012	−	16.7737i	0.185096	−	0.569666i
$868$		0			0
$869$	−16.0266	+	54.9806i	−0.543665	+	1.86509i
$870$		0			0
$871$	−2.29345	−	23.7128i	−0.0777106	−	0.803478i
$872$		0			0
$873$	−6.57483	+	1.04135i	−0.222524	+	0.0352444i
$874$		0			0
$875$	−13.6584	−	42.0363i	−0.461739	−	1.42109i
$876$		0			0
$877$	−15.9117	−	2.52017i	−0.537301	−	0.0851000i	−0.118114	−	0.993000i	$-0.537685\pi$
$877$	−15.9117	−	2.52017i	−0.537301	−	0.0851000i	−0.419187	+	0.907900i	$0.637685\pi$
$878$		0			0
$879$	48.9487	−	48.9487i	1.65100	−	1.65100i
$880$		0			0
$881$			16.0588i			0.541035i	0.962715	+	0.270518i	$0.0871948\pi$
$881$			16.0588i			0.541035i	−0.962715	+	0.270518i	$0.912805\pi$
$882$		0			0
$883$	1.52318	+	2.09648i	0.0512591	+	0.0705520i	0.833877	−	0.551950i	$-0.186116\pi$
$883$	1.52318	+	2.09648i	0.0512591	+	0.0705520i	−0.782618	+	0.622502i	$0.786116\pi$
$884$		0			0
$885$	29.6734	+	91.3253i	0.997460	+	3.06987i
$886$		0			0
$887$	−3.84370	+	5.29039i	−0.129059	+	0.177634i	−0.868656	−	0.495415i	$-0.835016\pi$
$887$	−3.84370	+	5.29039i	−0.129059	+	0.177634i	0.739598	+	0.673049i	$0.235016\pi$
$888$		0			0
$889$	5.12609	+	10.0605i	0.171924	+	0.337419i
$890$		0			0
$891$	20.8577	−	30.6323i	0.698758	−	1.02622i
$892$		0			0
$893$	−6.00283	−	1.95044i	−0.200877	−	0.0652689i
$894$		0			0
$895$	4.52463	+	28.5674i	0.151242	+	0.954903i
$896$		0			0
$897$	−27.4179	−	1.66526i	−0.915455	−	0.0556014i
$898$		0			0
$899$	0.546841	+	0.0866111i	0.0182382	+	0.00288864i
$900$		0			0
$901$	36.8108			1.22635
$902$		0			0
$903$	30.4845	−	30.4845i	1.01446	−	1.01446i
$904$		0			0
$905$	−84.8746	−	13.4428i	−2.82133	−	0.446854i
$906$		0			0
$907$	45.5565	−	14.8022i	1.51268	−	0.491500i	0.568994	−	0.822342i	$-0.307333\pi$
$907$	45.5565	−	14.8022i	1.51268	−	0.491500i	0.943686	+	0.330842i	$0.107333\pi$
$908$		0			0
$909$	−5.72533	−	4.15970i	−0.189897	−	0.137968i
$910$		0			0
$911$	−1.16838	+	3.59591i	−0.0387102	+	0.119138i	−0.968544	−	0.248841i	$-0.919950\pi$
$911$	−1.16838	+	3.59591i	−0.0387102	+	0.119138i	0.929834	+	0.367979i	$0.119950\pi$
$912$		0			0
$913$	47.3936	+	22.3534i	1.56850	+	0.739790i
$914$		0			0
$915$	29.7598	−	15.1634i	0.983829	−	0.501286i
$916$		0			0
$917$	3.58320	+	22.6234i	0.118328	+	0.747092i
$918$		0			0
$919$	−31.6052	+	10.2692i	−1.04256	+	0.338748i	−0.779744	−	0.626098i	$-0.784651\pi$
$919$	−31.6052	+	10.2692i	−1.04256	+	0.338748i	−0.262815	+	0.964846i	$0.584651\pi$
$920$		0			0
$921$	11.2815	−	71.2283i	0.371737	−	2.34705i
$922$		0			0
$923$	−14.9125	+	6.49168i	−0.490851	+	0.213676i
$924$		0			0
$925$	−65.8429	+	65.8429i	−2.16490	+	2.16490i
$926$		0			0
$927$	−15.6581	−	21.5515i	−0.514280	−	0.707845i
$928$		0			0
$929$	9.00565	+	4.58861i	0.295466	+	0.150547i	0.595440	−	0.803400i	$-0.296978\pi$
$929$	9.00565	+	4.58861i	0.295466	+	0.150547i	−0.299974	+	0.953947i	$0.596978\pi$
$930$		0			0
$931$	−0.0769802	+	0.0121925i	−0.00252292	+	0.000399592i
$932$		0			0
$933$	1.30246	+	0.423194i	0.0426405	+	0.0138547i
$934$		0			0
$935$	37.3386	+	4.75083i	1.22110	+	0.155369i
$936$		0			0
$937$	9.64319	+	3.13326i	0.315029	+	0.102359i	0.462264	−	0.886742i	$-0.347037\pi$
$937$	9.64319	+	3.13326i	0.315029	+	0.102359i	−0.147235	+	0.989102i	$0.547037\pi$
$938$		0			0
$939$	−13.1598	−	9.56115i	−0.429454	−	0.312016i
$940$		0			0
$941$	4.80759	−	9.43543i	0.156723	−	0.307586i	−0.799272	−	0.600970i	$-0.794781\pi$
$941$	4.80759	−	9.43543i	0.156723	−	0.307586i	0.955995	+	0.293383i	$0.0947812\pi$
$942$		0			0
$943$	−3.61930	+	22.8514i	−0.117861	+	0.744143i
$944$		0			0
$945$		−	26.7281i		−	0.869466i
$946$		0			0
$947$	−6.35504	−	6.35504i	−0.206511	−	0.206511i	0.596272	−	0.802783i	$-0.296648\pi$
$947$	−6.35504	−	6.35504i	−0.206511	−	0.206511i	−0.802783	+	0.596272i	$0.796648\pi$
$948$		0			0
$949$	−22.9745	+	39.0409i	−0.745785	+	1.26732i
$950$		0			0
$951$	−66.9700	−	34.1229i	−2.17165	−	1.10651i
$952$		0			0
$953$	27.7323	+	20.1487i	0.898339	+	0.652681i	0.938039	−	0.346530i	$-0.112640\pi$
$953$	27.7323	+	20.1487i	0.898339	+	0.652681i	−0.0397000	+	0.999212i	$0.512640\pi$
$954$		0			0
$955$	28.5542	+	56.0408i	0.923993	+	1.81344i
$956$		0			0
$957$	−5.58005	+	0.170374i	−0.180377	+	0.00550742i
$958$		0			0
$959$	10.7213	−	32.9968i	0.346209	−	1.06552i
$960$		0			0
$961$	17.9176	−	24.6615i	0.577987	−	0.795531i
$962$		0			0
$963$	13.0013	−	4.22438i	0.418962	−	0.136129i
$964$		0			0
$965$	52.9069	+	72.8201i	1.70313	+	2.34416i
$966$		0			0
$967$	35.6555	+	35.6555i	1.14660	+	1.14660i	0.987216	+	0.159388i	$0.0509521\pi$
$967$	35.6555	+	35.6555i	1.14660	+	1.14660i	0.159388	+	0.987216i	$0.449048\pi$
$968$		0			0
$969$	4.71720	+	4.71720i	0.151538	+	0.151538i
$970$		0			0
$971$	2.32705	−	1.69070i	0.0746785	−	0.0542571i	−0.549820	−	0.835283i	$-0.685304\pi$
$971$	2.32705	−	1.69070i	0.0746785	−	0.0542571i	0.624498	+	0.781026i	$0.285304\pi$
$972$		0			0
$973$	−10.0473	+	19.7189i	−0.322101	+	0.632158i
$974$		0			0
$975$	62.6055	−	39.9215i	2.00498	−	1.27851i
$976$		0			0
$977$	−1.86865	−	3.66744i	−0.0597835	−	0.117332i	0.859181	−	0.511671i	$-0.170973\pi$
$977$	−1.86865	−	3.66744i	−0.0597835	−	0.117332i	−0.918965	+	0.394340i	$0.870973\pi$
$978$		0			0
$979$	−21.2921	+	22.6332i	−0.680498	+	0.723361i
$980$		0			0
$981$	9.07711	−	4.62502i	0.289810	−	0.147666i
$982$		0			0
$983$	8.44169	+	53.2987i	0.269248	+	1.69996i	0.637673	+	0.770307i	$0.279897\pi$
$983$	8.44169	+	53.2987i	0.269248	+	1.69996i	−0.368425	+	0.929658i	$0.620103\pi$
$984$		0			0
$985$	−1.60629	−	4.94364i	−0.0511805	−	0.157517i
$986$		0			0
$987$	28.7458	−	20.8851i	0.914990	−	0.664779i
$988$		0			0
$989$			26.1342i			0.831020i
$990$		0			0
$991$	−5.90113			−0.187456			−0.0937278	−	0.995598i	$-0.529878\pi$
$991$	−5.90113			−0.187456			−0.0937278	+	0.995598i	$0.529878\pi$
$992$		0			0
$993$	−10.5093	+	66.3533i	−0.333503	+	2.10566i
$994$		0			0
$995$	−10.6330	+	20.8684i	−0.337088	+	0.661572i
$996$		0			0
$997$	3.71898	−	5.11873i	0.117781	−	0.162112i	−0.746056	−	0.665884i	$-0.768055\pi$
$997$	3.71898	−	5.11873i	0.117781	−	0.162112i	0.863837	+	0.503772i	$0.168055\pi$
$998$		0			0
$999$	−23.5497	+	11.9992i	−0.745079	+	0.379637i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bh.a.57.11	✓	112
11.6	odd	10	inner	572.2.bh.a.369.11	yes	112
13.8	odd	4	inner	572.2.bh.a.541.11	yes	112
143.138	even	20	inner	572.2.bh.a.281.11	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bh.a.57.11	✓	112	1.1	even	1	trivial
572.2.bh.a.281.11	yes	112	143.138	even	20	inner
572.2.bh.a.369.11	yes	112	11.6	odd	10	inner
572.2.bh.a.541.11	yes	112	13.8	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bh (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.76806 - 1.28457i) q^{3} +(3.38384 + 1.72415i) q^{5} +(-2.59890 + 0.411625i) q^{7} +(0.548857 - 1.68921i) q^{9} +O(q^{10})\)	\(q+(1.76806 - 1.28457i) q^{3} +(3.38384 + 1.72415i) q^{5} +(-2.59890 + 0.411625i) q^{7} +(0.548857 - 1.68921i) q^{9} +(-0.101219 - 3.31508i) q^{11} +(2.29223 - 2.78311i) q^{13} +(8.19760 - 1.29837i) q^{15} +(0.923428 + 2.84202i) q^{17} +(1.00893 + 0.159798i) q^{19} +(-4.06624 + 4.06624i) q^{21} -3.48596i q^{23} +(5.53872 + 7.62340i) q^{25} +(0.826520 + 2.54377i) q^{27} +(0.452715 - 0.623108i) q^{29} +(0.326349 + 0.640496i) q^{31} +(-4.43741 - 5.73123i) q^{33} +(-9.50394 - 3.08802i) q^{35} +(1.54584 + 9.76007i) q^{37} +(0.477704 - 7.86521i) q^{39} +(-6.55526 - 1.03825i) q^{41} -7.49699 q^{43} +(4.76969 - 4.76969i) q^{45} +(-6.10280 - 0.966589i) q^{47} +(-0.0725646 + 0.0235777i) q^{49} +(5.28344 + 3.83864i) q^{51} +(3.80660 - 11.7155i) q^{53} +(5.37319 - 11.3922i) q^{55} +(1.98911 - 1.01350i) q^{57} +(1.80988 + 11.4271i) q^{59} +(3.82727 - 1.24355i) q^{61} +(-0.731102 + 4.61600i) q^{63} +(12.5550 - 5.46542i) q^{65} +(4.67217 - 4.67217i) q^{67} +(-4.47796 - 6.16338i) q^{69} +(-4.01923 - 2.04790i) q^{71} +(-12.4091 + 1.96540i) q^{73} +(19.5855 + 6.36373i) q^{75} +(1.62763 + 8.57389i) q^{77} +(-16.4221 - 5.33586i) q^{79} +(9.03975 + 6.56776i) q^{81} +(-7.17277 + 14.0774i) q^{83} +(-1.77534 + 11.2091i) q^{85} -1.68323i q^{87} +(-6.62508 - 6.62508i) q^{89} +(-4.81168 + 8.17654i) q^{91} +(1.39976 + 0.713215i) q^{93} +(3.13853 + 2.28028i) q^{95} +(-1.70151 - 3.33941i) q^{97} +(-5.65541 - 1.64852i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 28 q^{9}+O(q^{10}) \) 112 * q - 28 * q^9	\( 112 q - 28 q^{9} + 8 q^{11} - 10 q^{13} + 4 q^{15} - 24 q^{27} - 20 q^{29} - 16 q^{31} - 54 q^{33} + 100 q^{35} - 12 q^{37} + 40 q^{39} - 20 q^{41} - 4 q^{45} - 10 q^{47} - 76 q^{53} - 20 q^{55} + 18 q^{59} + 40 q^{61} + 80 q^{63} + 92 q^{67} + 8 q^{71} - 30 q^{73} - 80 q^{79} + 12 q^{81} + 40 q^{85} + 32 q^{89} - 12 q^{91} - 114 q^{93} + 54 q^{97} - 90 q^{99}+O(q^{100}) \) 112 * q - 28 * q^9 + 8 * q^11 - 10 * q^13 + 4 * q^15 - 24 * q^27 - 20 * q^29 - 16 * q^31 - 54 * q^33 + 100 * q^35 - 12 * q^37 + 40 * q^39 - 20 * q^41 - 4 * q^45 - 10 * q^47 - 76 * q^53 - 20 * q^55 + 18 * q^59 + 40 * q^61 + 80 * q^63 + 92 * q^67 + 8 * q^71 - 30 * q^73 - 80 * q^79 + 12 * q^81 + 40 * q^85 + 32 * q^89 - 12 * q^91 - 114 * q^93 + 54 * q^97 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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