LMFDB - Embedded newform 572.2.p.a.309.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(309,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("572.309");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.p (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			309.5
Character	$\chi$	$=$	572.309
Dual form			572.2.p.a.485.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.780208 - 1.35136i) q^{3} -0.661534i q^{5} +(3.95034 + 2.28073i) q^{7} +(0.282552 - 0.489394i) q^{9} +O(q^{10})$	\(q+(-0.780208 - 1.35136i) q^{3} -0.661534i q^{5} +(3.95034 + 2.28073i) q^{7} +(0.282552 - 0.489394i) q^{9} +(0.866025 - 0.500000i) q^{11} +(-0.622136 + 3.55147i) q^{13} +(-0.893971 + 0.516134i) q^{15} +(0.341829 - 0.592065i) q^{17} +(2.99373 + 1.72843i) q^{19} -7.11777i q^{21} +(-1.71192 - 2.96514i) q^{23} +4.56237 q^{25} -5.56304 q^{27} +(2.34444 + 4.06068i) q^{29} -8.47738i q^{31} +(-1.35136 - 0.780208i) q^{33} +(1.50878 - 2.61329i) q^{35} +(7.15315 - 4.12987i) q^{37} +(5.28471 - 1.93016i) q^{39} +(-0.354267 + 0.204536i) q^{41} +(1.98295 - 3.43457i) q^{43} +(-0.323751 - 0.186918i) q^{45} -12.6498i q^{47} +(6.90346 + 11.9571i) q^{49} -1.06679 q^{51} -6.70091 q^{53} +(-0.330767 - 0.572905i) q^{55} -5.39415i q^{57} +(-10.6502 - 6.14888i) q^{59} +(-2.68700 + 4.65402i) q^{61} +(2.23235 - 1.28885i) q^{63} +(2.34942 + 0.411564i) q^{65} +(-11.4160 + 6.59105i) q^{67} +(-2.67131 + 4.62685i) q^{69} +(12.6084 + 7.27944i) q^{71} +12.4460i q^{73} +(-3.55960 - 6.16541i) q^{75} +4.56146 q^{77} -5.02010 q^{79} +(3.49267 + 6.04949i) q^{81} +14.7757i q^{83} +(-0.391671 - 0.226132i) q^{85} +(3.65829 - 6.33635i) q^{87} +(5.65315 - 3.26385i) q^{89} +(-10.5576 + 12.6106i) q^{91} +(-11.4560 + 6.61412i) q^{93} +(1.14342 - 1.98046i) q^{95} +(2.48119 + 1.43252i) q^{97} -0.565103i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{3} + 6 q^{7} - 14 q^{9}+O(q^{10}) $ 24 * q - 2 * q^3 + 6 * q^7 - 14 * q^9	$ 24 q - 2 q^{3} + 6 q^{7} - 14 q^{9} - 2 q^{13} - 6 q^{19} + 10 q^{23} - 40 q^{25} - 8 q^{27} - 8 q^{29} + 8 q^{35} + 18 q^{37} + 36 q^{41} + 10 q^{43} - 30 q^{45} + 14 q^{49} + 44 q^{51} + 16 q^{53} - 24 q^{59} + 6 q^{61} - 6 q^{63} - 24 q^{65} - 54 q^{67} + 10 q^{69} + 18 q^{71} + 6 q^{75} - 16 q^{77} - 32 q^{79} - 4 q^{81} + 52 q^{87} - 18 q^{89} - 18 q^{91} + 30 q^{93} - 12 q^{95} + 42 q^{97}+O(q^{100}) $ 24 * q - 2 * q^3 + 6 * q^7 - 14 * q^9 - 2 * q^13 - 6 * q^19 + 10 * q^23 - 40 * q^25 - 8 * q^27 - 8 * q^29 + 8 * q^35 + 18 * q^37 + 36 * q^41 + 10 * q^43 - 30 * q^45 + 14 * q^49 + 44 * q^51 + 16 * q^53 - 24 * q^59 + 6 * q^61 - 6 * q^63 - 24 * q^65 - 54 * q^67 + 10 * q^69 + 18 * q^71 + 6 * q^75 - 16 * q^77 - 32 * q^79 - 4 * q^81 + 52 * q^87 - 18 * q^89 - 18 * q^91 + 30 * q^93 - 12 * q^95 + 42 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.780208	−	1.35136i	−0.450453	−	0.780208i	0.547961	−	0.836504i	$-0.315404\pi$
$3$	−0.780208	−	1.35136i	−0.450453	−	0.780208i	−0.998414	+	0.0562961i	$0.982071\pi$
$4$		0			0
$5$		−	0.661534i		−	0.295847i	−0.988999	−	0.147924i	$-0.952741\pi$
$5$		−	0.661534i		−	0.295847i	0.988999	−	0.147924i	$-0.0472590\pi$
$6$		0			0
$7$	3.95034	+	2.28073i	1.49309	+	0.862035i	0.999969	−	0.00792621i	$-0.00252302\pi$
$7$	3.95034	+	2.28073i	1.49309	+	0.862035i	0.493120	+	0.869961i	$0.335856\pi$
$8$		0			0
$9$	0.282552	−	0.489394i	0.0941839	−	0.163131i
$10$		0			0
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$11$	0.866025	−	0.500000i	0.261116	−	0.150756i
$12$		0			0
$13$	−0.622136	+	3.55147i	−0.172549	+	0.985001i
$13$	−0.622136	+	3.55147i	−0.172549	+	0.985001i
$14$		0			0
$15$	−0.893971	+	0.516134i	−0.230822	+	0.133265i
$16$		0			0
$17$	0.341829	−	0.592065i	0.0829057	−	0.143597i	−0.821591	−	0.570077i	$-0.806913\pi$
$17$	0.341829	−	0.592065i	0.0829057	−	0.143597i	0.904497	+	0.426480i	$0.140247\pi$
$18$		0			0
$19$	2.99373	+	1.72843i	0.686810	+	0.396530i	0.802416	−	0.596765i	$-0.203548\pi$
$19$	2.99373	+	1.72843i	0.686810	+	0.396530i	−0.115606	+	0.993295i	$0.536881\pi$
$20$		0			0
$21$		−	7.11777i		−	1.55323i
$22$		0			0
$23$	−1.71192	−	2.96514i	−0.356961	−	0.618274i	0.630491	−	0.776197i	$-0.282854\pi$
$23$	−1.71192	−	2.96514i	−0.356961	−	0.618274i	−0.987451	+	0.157923i	$0.949520\pi$
$24$		0			0
$25$	4.56237			0.912474
$26$		0			0
$27$	−5.56304			−1.07061
$28$		0			0
$29$	2.34444	+	4.06068i	0.435351	+	0.754049i	0.997324	−	0.0731058i	$-0.0232911\pi$
$29$	2.34444	+	4.06068i	0.435351	+	0.754049i	−0.561974	+	0.827155i	$0.689958\pi$
$30$		0			0
$31$		−	8.47738i		−	1.52258i	−0.648410	−	0.761291i	$-0.724566\pi$
$31$		−	8.47738i		−	1.52258i	0.648410	−	0.761291i	$-0.275434\pi$
$32$		0			0
$33$	−1.35136	−	0.780208i	−0.235241	−	0.135817i
$34$		0			0
$35$	1.50878	−	2.61329i	0.255031	−	0.441726i
$36$		0			0
$37$	7.15315	−	4.12987i	1.17597	−	0.678947i	0.220891	−	0.975298i	$-0.429103\pi$
$37$	7.15315	−	4.12987i	1.17597	−	0.678947i	0.955079	+	0.296352i	$0.0957701\pi$
$38$		0			0
$39$	5.28471	−	1.93016i	0.846231	−	0.309072i
$40$		0			0
$41$	−0.354267	+	0.204536i	−0.0553272	+	0.0319432i	−0.527408	−	0.849612i	$-0.676836\pi$
$41$	−0.354267	+	0.204536i	−0.0553272	+	0.0319432i	0.472081	+	0.881555i	$0.343503\pi$
$42$		0			0
$43$	1.98295	−	3.43457i	0.302397	−	0.523767i	−0.674282	−	0.738474i	$-0.735547\pi$
$43$	1.98295	−	3.43457i	0.302397	−	0.523767i	0.976678	+	0.214708i	$0.0688799\pi$
$44$		0			0
$45$	−0.323751	−	0.186918i	−0.0482619	−	0.0278640i
$46$		0			0
$47$		−	12.6498i		−	1.84517i	−0.385795	−	0.922585i	$-0.626073\pi$
$47$		−	12.6498i		−	1.84517i	0.385795	−	0.922585i	$-0.373927\pi$
$48$		0			0
$49$	6.90346	+	11.9571i	0.986209	+	1.70816i
$50$		0			0
$51$	−1.06679			−0.149381
$52$		0			0
$53$	−6.70091			−0.920441			−0.460221	−	0.887805i	$-0.652230\pi$
$53$	−6.70091			−0.920441			−0.460221	+	0.887805i	$0.652230\pi$
$54$		0			0
$55$	−0.330767	−	0.572905i	−0.0446006	−	0.0772506i
$56$		0			0
$57$		−	5.39415i		−	0.714472i
$58$		0			0
$59$	−10.6502	−	6.14888i	−1.38653	−	0.800516i	−0.393611	−	0.919277i	$-0.628774\pi$
$59$	−10.6502	−	6.14888i	−1.38653	−	0.800516i	−0.992923	+	0.118762i	$0.962108\pi$
$60$		0			0
$61$	−2.68700	+	4.65402i	−0.344035	+	0.595886i	−0.985178	−	0.171535i	$-0.945127\pi$
$61$	−2.68700	+	4.65402i	−0.344035	+	0.595886i	0.641143	+	0.767421i	$0.278461\pi$
$62$		0			0
$63$	2.23235	−	1.28885i	0.281250	−	0.162380i
$64$		0			0
$65$	2.34942	+	0.411564i	0.291410	+	0.0510482i
$66$		0			0
$67$	−11.4160	+	6.59105i	−1.39469	+	0.805224i	−0.993830	−	0.110915i	$-0.964622\pi$
$67$	−11.4160	+	6.59105i	−1.39469	+	0.805224i	−0.400860	+	0.916139i	$0.631289\pi$
$68$		0			0
$69$	−2.67131	+	4.62685i	−0.321588	+	0.557007i
$70$		0			0
$71$	12.6084	+	7.27944i	1.49634	+	0.863911i	0.999991	−	0.00421351i	$-0.00134121\pi$
$71$	12.6084	+	7.27944i	1.49634	+	0.863911i	0.496347	+	0.868124i	$0.334675\pi$
$72$		0			0
$73$			12.4460i			1.45669i	0.685210	+	0.728346i	$0.259711\pi$
$73$			12.4460i			1.45669i	−0.685210	+	0.728346i	$0.740289\pi$
$74$		0			0
$75$	−3.55960	−	6.16541i	−0.411027	−	0.711920i
$76$		0			0
$77$	4.56146			0.519827
$78$		0			0
$79$	−5.02010			−0.564806			−0.282403	−	0.959296i	$-0.591131\pi$
$79$	−5.02010			−0.564806			−0.282403	+	0.959296i	$0.591131\pi$
$80$		0			0
$81$	3.49267	+	6.04949i	0.388075	+	0.672165i
$82$		0			0
$83$			14.7757i			1.62184i	0.585157	+	0.810920i	$0.301033\pi$
$83$			14.7757i			1.62184i	−0.585157	+	0.810920i	$0.698967\pi$
$84$		0			0
$85$	−0.391671	−	0.226132i	−0.0424827	−	0.0245274i
$86$		0			0
$87$	3.65829	−	6.33635i	0.392210	−	0.679328i
$88$		0			0
$89$	5.65315	−	3.26385i	0.599232	−	0.345967i	−0.169507	−	0.985529i	$-0.554218\pi$
$89$	5.65315	−	3.26385i	0.599232	−	0.345967i	0.768740	+	0.639562i	$0.220884\pi$
$90$		0			0
$91$	−10.5576	+	12.6106i	−1.10674	+	1.32195i
$92$		0			0
$93$	−11.4560	+	6.61412i	−1.18793	+	0.685852i
$94$		0			0
$95$	1.14342	−	1.98046i	0.117312	−	0.203191i
$96$		0			0
$97$	2.48119	+	1.43252i	0.251927	+	0.145450i	0.620646	−	0.784091i	$-0.286870\pi$
$97$	2.48119	+	1.43252i	0.251927	+	0.145450i	−0.368719	+	0.929541i	$0.620204\pi$
$98$		0			0
$99$		−	0.565103i		−	0.0567950i
$100$		0			0
$101$	5.84736	+	10.1279i	0.581834	+	1.00777i	0.995262	+	0.0972295i	$0.0309981\pi$
$101$	5.84736	+	10.1279i	0.581834	+	1.00777i	−0.413428	+	0.910537i	$0.635669\pi$
$102$		0			0
$103$	−1.53775			−0.151519			−0.0757594	−	0.997126i	$-0.524138\pi$
$103$	−1.53775			−0.151519			−0.0757594	+	0.997126i	$0.524138\pi$
$104$		0			0
$105$	−4.70865			−0.459517
$106$		0			0
$107$	−5.31166	−	9.20006i	−0.513497	−	0.889403i	−0.999877	−	0.0156561i	$-0.995016\pi$
$107$	−5.31166	−	9.20006i	−0.513497	−	0.889403i	0.486380	−	0.873747i	$-0.338317\pi$
$108$		0			0
$109$		−	5.64478i		−	0.540672i	−0.962766	−	0.270336i	$-0.912865\pi$
$109$		−	5.64478i		−	0.540672i	0.962766	−	0.270336i	$-0.0871348\pi$
$110$		0			0
$111$	−11.1619	−	6.44432i	−1.05944	−	0.611667i
$112$		0			0
$113$	−3.52678	+	6.10857i	−0.331772	+	0.574645i	−0.982859	−	0.184357i	$-0.940980\pi$
$113$	−3.52678	+	6.10857i	−0.331772	+	0.574645i	0.651088	+	0.759003i	$0.274313\pi$
$114$		0			0
$115$	−1.96154	+	1.13250i	−0.182915	+	0.105606i
$116$		0			0
$117$	1.56228	+	1.30794i	0.144433	+	0.120919i
$118$		0			0
$119$	2.70068	−	1.55924i	0.247571	−	0.142935i
$120$		0			0
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$		0			0
$123$	0.552804	+	0.319161i	0.0498446	+	0.0287778i
$124$		0			0
$125$		−	6.32584i		−	0.565800i
$126$		0			0
$127$	2.82747	+	4.89731i	0.250897	+	0.434566i	0.963773	−	0.266724i	$-0.0859411\pi$
$127$	2.82747	+	4.89731i	0.250897	+	0.434566i	−0.712876	+	0.701290i	$0.752608\pi$
$128$		0			0
$129$	−6.18845			−0.544862
$130$		0			0
$131$	−4.72237			−0.412595			−0.206298	−	0.978489i	$-0.566142\pi$
$131$	−4.72237			−0.412595			−0.206298	+	0.978489i	$0.566142\pi$
$132$		0			0
$133$	7.88418	+	13.6558i	0.683645	+	1.18411i
$134$		0			0
$135$			3.68014i			0.316736i
$136$		0			0
$137$	−1.51000	−	0.871799i	−0.129008	−	0.0744828i	0.434107	−	0.900861i	$-0.357064\pi$
$137$	−1.51000	−	0.871799i	−0.129008	−	0.0744828i	−0.563115	+	0.826378i	$0.690397\pi$
$138$		0			0
$139$	0.959288	−	1.66154i	0.0813657	−	0.140930i	−0.822471	−	0.568807i	$-0.807405\pi$
$139$	0.959288	−	1.66154i	0.0813657	−	0.140930i	0.903837	+	0.427877i	$0.140738\pi$
$140$		0			0
$141$	−17.0945	+	9.86950i	−1.43962	+	0.831162i
$142$		0			0
$143$	1.23695	+	3.38673i	0.103439	+	0.283213i
$144$		0			0
$145$	2.68628	−	1.55092i	0.223083	−	0.128797i
$146$		0			0
$147$	10.7723	−	18.6581i	0.888482	−	1.53890i
$148$		0			0
$149$	−14.9956	−	8.65773i	−1.22849	−	0.709269i	−0.261776	−	0.965129i	$-0.584308\pi$
$149$	−14.9956	−	8.65773i	−1.22849	−	0.709269i	−0.966714	+	0.255860i	$0.917641\pi$
$150$		0			0
$151$		−	2.26030i		−	0.183940i	−0.995762	−	0.0919702i	$-0.970684\pi$
$151$		−	2.26030i		−	0.183940i	0.995762	−	0.0919702i	$-0.0293165\pi$
$152$		0			0
$153$	−0.193169	−	0.334578i	−0.0156168	−	0.0270490i
$154$		0			0
$155$	−5.60808			−0.450451
$156$		0			0
$157$	−0.325028			−0.0259401			−0.0129700	−	0.999916i	$-0.504129\pi$
$157$	−0.325028			−0.0259401			−0.0129700	+	0.999916i	$0.504129\pi$
$158$		0			0
$159$	5.22810	+	9.05534i	0.414616	+	0.718135i
$160$		0			0
$161$		−	15.6177i		−	1.23085i
$162$		0			0
$163$	7.58005	+	4.37634i	0.593715	+	0.342782i	0.766565	−	0.642166i	$-0.221964\pi$
$163$	7.58005	+	4.37634i	0.593715	+	0.342782i	−0.172850	+	0.984948i	$0.555298\pi$
$164$		0			0
$165$	−0.516134	+	0.893971i	−0.0401810	+	0.0695955i
$166$		0			0
$167$	−9.29934	+	5.36898i	−0.719604	+	0.415464i	−0.814607	−	0.580013i	$-0.803047\pi$
$167$	−9.29934	+	5.36898i	−0.719604	+	0.415464i	0.0950027	+	0.995477i	$0.469714\pi$
$168$		0			0
$169$	−12.2259	−	4.41899i	−0.940453	−	0.339923i
$170$		0			0
$171$	1.69177	−	0.976743i	0.129373	−	0.0746934i
$172$		0			0
$173$	−2.60130	+	4.50559i	−0.197773	+	0.342554i	−0.947806	−	0.318847i	$-0.896704\pi$
$173$	−2.60130	+	4.50559i	−0.197773	+	0.342554i	0.750033	+	0.661401i	$0.230038\pi$
$174$		0			0
$175$	18.0229	+	10.4055i	1.36241	+	0.786585i
$176$		0			0
$177$			19.1896i			1.44238i
$178$		0			0
$179$	12.7244	+	22.0393i	0.951065	+	1.64729i	0.743127	+	0.669151i	$0.233342\pi$
$179$	12.7244	+	22.0393i	0.951065	+	1.64729i	0.207938	+	0.978142i	$0.433325\pi$
$180$		0			0
$181$	−10.4039			−0.773319			−0.386660	−	0.922223i	$-0.626371\pi$
$181$	−10.4039			−0.773319			−0.386660	+	0.922223i	$0.626371\pi$
$182$		0			0
$183$	8.38567			0.619887
$184$		0			0
$185$	−2.73205	−	4.73205i	−0.200864	−	0.347907i
$186$		0			0
$187$		−	0.683658i		−	0.0499940i
$188$		0			0
$189$	−21.9759	−	12.6878i	−1.59851	−	0.922902i
$190$		0			0
$191$	11.0707	−	19.1750i	0.801047	−	1.38745i	−0.117881	−	0.993028i	$-0.537610\pi$
$191$	11.0707	−	19.1750i	0.801047	−	1.38745i	0.918928	−	0.394426i	$-0.129057\pi$
$192$		0			0
$193$	−18.5683	+	10.7204i	−1.33657	+	0.771671i	−0.986298	−	0.164976i	$-0.947245\pi$
$193$	−18.5683	+	10.7204i	−1.33657	+	0.771671i	−0.350275	+	0.936647i	$0.613912\pi$
$194$		0			0
$195$	−1.27686	−	3.49602i	−0.0914382	−	0.250355i
$196$		0			0
$197$	−1.08240	+	0.624925i	−0.0771179	+	0.0445241i	−0.538063	−	0.842905i	$-0.680844\pi$
$197$	−1.08240	+	0.624925i	−0.0771179	+	0.0445241i	0.460945	+	0.887429i	$0.347510\pi$
$198$		0			0
$199$	2.39145	−	4.14211i	0.169525	−	0.293626i	−0.768728	−	0.639576i	$-0.779110\pi$
$199$	2.39145	−	4.14211i	0.169525	−	0.293626i	0.938253	+	0.345950i	$0.112443\pi$
$200$		0			0
$201$	17.8137	+	10.2848i	1.25648	+	0.725432i
$202$		0			0
$203$			21.3881i			1.50115i
$204$		0			0
$205$	0.135308	+	0.234360i	0.00945030	+	0.0163684i
$206$		0			0
$207$	−1.93483			−0.134480
$208$		0			0
$209$	3.45687			0.239116
$210$		0			0
$211$	−11.1219	−	19.2638i	−0.765666	−	1.32617i	−0.939894	−	0.341467i	$-0.889076\pi$
$211$	−11.1219	−	19.2638i	−0.765666	−	1.32617i	0.174228	−	0.984705i	$-0.444257\pi$
$212$		0			0
$213$		−	22.7179i		−	1.55661i
$214$		0			0
$215$	−2.27208	−	1.31179i	−0.154955	−	0.0894632i
$216$		0			0
$217$	19.3346	−	33.4885i	1.31252	−	2.27335i
$218$		0			0
$219$	16.8190	−	9.71045i	1.13652	−	0.656171i
$220$		0			0
$221$	1.89004	+	1.58234i	0.127138	+	0.106440i
$222$		0			0
$223$	−17.9777	+	10.3794i	−1.20388	+	0.695059i	−0.961415	−	0.275102i	$-0.911288\pi$
$223$	−17.9777	+	10.3794i	−1.20388	+	0.695059i	−0.242463	+	0.970161i	$0.577955\pi$
$224$		0			0
$225$	1.28911	−	2.23280i	0.0859404	−	0.148853i
$226$		0			0
$227$	−12.3111	−	7.10780i	−0.817114	−	0.471761i	0.0323060	−	0.999478i	$-0.489715\pi$
$227$	−12.3111	−	7.10780i	−0.817114	−	0.471761i	−0.849420	+	0.527717i	$0.823048\pi$
$228$		0			0
$229$			10.8583i			0.717536i	0.933427	+	0.358768i	$0.116803\pi$
$229$			10.8583i			0.717536i	−0.933427	+	0.358768i	$0.883197\pi$
$230$		0			0
$231$	−3.55889	−	6.16417i	−0.234158	−	0.405573i
$232$		0			0
$233$	23.5195			1.54081			0.770406	−	0.637554i	$-0.220054\pi$
$233$	23.5195			1.54081			0.770406	+	0.637554i	$0.220054\pi$
$234$		0			0
$235$	−8.36830			−0.545888
$236$		0			0
$237$	3.91672	+	6.78396i	0.254419	+	0.440666i
$238$		0			0
$239$		−	20.4960i		−	1.32578i	−0.748718	−	0.662889i	$-0.769330\pi$
$239$		−	20.4960i		−	1.32578i	0.748718	−	0.662889i	$-0.230670\pi$
$240$		0			0
$241$	−7.88078	−	4.54997i	−0.507646	−	0.293089i	0.224220	−	0.974539i	$-0.428017\pi$
$241$	−7.88078	−	4.54997i	−0.507646	−	0.293089i	−0.731865	+	0.681449i	$0.761350\pi$
$242$		0			0
$243$	−2.89454	+	5.01349i	−0.185685	+	0.321616i
$244$		0			0
$245$	7.91006	−	4.56688i	0.505355	−	0.291767i
$246$		0			0
$247$	−8.00099	+	9.55684i	−0.509091	+	0.608087i
$248$		0			0
$249$	19.9672	−	11.5281i	1.26537	−	0.730563i
$250$		0			0
$251$	9.25157	−	16.0242i	0.583954	−	1.01144i	−0.411051	−	0.911612i	$-0.634838\pi$
$251$	9.25157	−	16.0242i	0.583954	−	1.01144i	0.995005	−	0.0998255i	$-0.0318285\pi$
$252$		0			0
$253$	−2.96514	−	1.71192i	−0.186417	−	0.107628i
$254$		0			0
$255$			0.705719i			0.0441938i
$256$		0			0
$257$	5.47013	+	9.47454i	0.341217	+	0.591005i	0.984659	−	0.174490i	$-0.0558275\pi$
$257$	5.47013	+	9.47454i	0.341217	+	0.591005i	−0.643442	+	0.765495i	$0.722494\pi$
$258$		0			0
$259$	37.6765			2.34110
$260$		0			0
$261$	2.64970			0.164012
$262$		0			0
$263$	−4.17712	−	7.23498i	−0.257572	−	0.446128i	0.708019	−	0.706194i	$-0.249589\pi$
$263$	−4.17712	−	7.23498i	−0.257572	−	0.446128i	−0.965591	+	0.260066i	$0.916256\pi$
$264$		0			0
$265$			4.43288i			0.272310i
$266$		0			0
$267$	−8.82126	−	5.09296i	−0.539852	−	0.311684i
$268$		0			0
$269$	−1.08425	+	1.87798i	−0.0661080	+	0.114502i	−0.897185	−	0.441655i	$-0.854392\pi$
$269$	−1.08425	+	1.87798i	−0.0661080	+	0.114502i	0.831077	+	0.556157i	$0.187725\pi$
$270$		0			0
$271$	−8.45023	+	4.87874i	−0.513315	+	0.296362i	−0.734195	−	0.678938i	$-0.762440\pi$
$271$	−8.45023	+	4.87874i	−0.513315	+	0.296362i	0.220880	+	0.975301i	$0.429107\pi$
$272$		0			0
$273$	25.2786	+	4.42822i	1.52993	+	0.268008i
$274$		0			0
$275$	3.95113	−	2.28119i	0.238262	−	0.137561i
$276$		0			0
$277$	−0.0251709	+	0.0435972i	−0.00151237	+	0.00261950i	−0.866781	−	0.498690i	$-0.833815\pi$
$277$	−0.0251709	+	0.0435972i	−0.00151237	+	0.00261950i	0.865268	+	0.501309i	$0.167148\pi$
$278$		0			0
$279$	−4.14878	−	2.39530i	−0.248381	−	0.143403i
$280$		0			0
$281$			23.1655i			1.38194i	0.722885	+	0.690968i	$0.242816\pi$
$281$			23.1655i			1.38194i	−0.722885	+	0.690968i	$0.757184\pi$
$282$		0			0
$283$	16.7158	+	28.9527i	0.993654	+	1.72106i	0.594238	+	0.804289i	$0.297454\pi$
$283$	16.7158	+	28.9527i	0.993654	+	1.72106i	0.399416	+	0.916770i	$0.369213\pi$
$284$		0			0
$285$	−3.56841			−0.211375
$286$		0			0
$287$	−1.86597			−0.110145
$288$		0			0
$289$	8.26631	+	14.3177i	0.486253	+	0.842215i
$290$		0			0
$291$		−	4.47064i		−	0.262074i
$292$		0			0
$293$	−26.2140	−	15.1347i	−1.53144	−	0.884177i	−0.999296	−	0.0375223i	$-0.988053\pi$
$293$	−26.2140	−	15.1347i	−1.53144	−	0.884177i	−0.532143	−	0.846654i	$-0.678613\pi$
$294$		0			0
$295$	−4.06769	+	7.04545i	−0.236830	+	0.410202i
$296$		0			0
$297$	−4.81774	+	2.78152i	−0.279553	+	0.161400i
$298$		0			0
$299$	11.5956	−	4.23513i	0.670594	−	0.244924i
$300$		0			0
$301$	15.6666	−	9.04514i	0.903010	−	0.521353i
$302$		0			0
$303$	9.12431	−	15.8038i	0.524178	−	0.907903i
$304$		0			0
$305$	3.07879	+	1.77754i	0.176291	+	0.101782i
$306$		0			0
$307$		−	3.85497i		−	0.220015i	−0.993931	−	0.110007i	$-0.964913\pi$
$307$		−	3.85497i		−	0.220015i	0.993931	−	0.110007i	$-0.0350875\pi$
$308$		0			0
$309$	1.19976	+	2.07805i	0.0682521	+	0.118216i
$310$		0			0
$311$	−28.0824			−1.59241			−0.796203	−	0.605030i	$-0.793161\pi$
$311$	−28.0824			−1.59241			−0.796203	+	0.605030i	$0.793161\pi$
$312$		0			0
$313$	−9.16618			−0.518103			−0.259052	−	0.965863i	$-0.583410\pi$
$313$	−9.16618			−0.518103			−0.259052	+	0.965863i	$0.583410\pi$
$314$		0			0
$315$	−0.852617	−	1.47678i	−0.0480395	−	0.0832069i
$316$		0			0
$317$			2.28144i			0.128139i	0.997945	+	0.0640693i	$0.0204079\pi$
$317$			2.28144i			0.128139i	−0.997945	+	0.0640693i	$0.979592\pi$
$318$		0			0
$319$	4.06068	+	2.34444i	0.227354	+	0.131263i
$320$		0			0
$321$	−8.28839	+	14.3559i	−0.462613	+	0.801269i
$322$		0			0
$323$	2.04669	−	1.18166i	0.113881	−	0.0657492i
$324$		0			0
$325$	−2.83842	+	16.2031i	−0.157447	+	0.898788i
$326$		0			0
$327$	−7.62813	+	4.40410i	−0.421836	+	0.243547i
$328$		0			0
$329$	28.8509	−	49.9712i	1.59060	−	2.75500i
$330$		0			0
$331$	14.8448	+	8.57064i	0.815943	+	0.471085i	0.849016	−	0.528368i	$-0.177196\pi$
$331$	14.8448	+	8.57064i	0.815943	+	0.471085i	−0.0330721	+	0.999453i	$0.510529\pi$
$332$		0			0
$333$		−	4.66761i		−	0.255783i
$334$		0			0
$335$	4.36020	+	7.55209i	0.238223	+	0.412615i
$336$		0			0
$337$	10.0048			0.544994			0.272497	−	0.962157i	$-0.412150\pi$
$337$	10.0048			0.544994			0.272497	+	0.962157i	$0.412150\pi$
$338$		0			0
$339$	11.0065			0.597790
$340$		0			0
$341$	−4.23869	−	7.34162i	−0.229538	−	0.397571i
$342$		0			0
$343$			31.0495i			1.67652i
$344$		0			0
$345$	3.06082	+	1.76716i	0.164789	+	0.0951409i
$346$		0			0
$347$	−9.53438	+	16.5140i	−0.511832	+	0.886519i	0.488074	+	0.872802i	$0.337700\pi$
$347$	−9.53438	+	16.5140i	−0.511832	+	0.886519i	−0.999906	+	0.0137170i	$0.995634\pi$
$348$		0			0
$349$	6.85682	−	3.95879i	0.367037	−	0.211909i	−0.305126	−	0.952312i	$-0.598699\pi$
$349$	6.85682	−	3.95879i	0.367037	−	0.211909i	0.672163	+	0.740403i	$0.265365\pi$
$350$		0			0
$351$	3.46097	−	19.7570i	0.184733	−	1.05455i
$352$		0			0
$353$	−6.16736	+	3.56073i	−0.328255	+	0.189518i	−0.655066	−	0.755571i	$-0.727359\pi$
$353$	−6.16736	+	3.56073i	−0.328255	+	0.189518i	0.326811	+	0.945090i	$0.394026\pi$
$354$		0			0
$355$	4.81560	−	8.34087i	0.255586	−	0.442687i
$356$		0			0
$357$	−4.21419	−	2.43306i	−0.223038	−	0.128771i
$358$		0			0
$359$		−	5.89478i		−	0.311115i	−0.987827	−	0.155557i	$-0.950283\pi$
$359$		−	5.89478i		−	0.311115i	0.987827	−	0.155557i	$-0.0497173\pi$
$360$		0			0
$361$	−3.52504	−	6.10555i	−0.185528	−	0.321345i
$362$		0			0
$363$	−1.56042			−0.0819006
$364$		0			0
$365$	8.23344			0.430958
$366$		0			0
$367$	0.00966434	+	0.0167391i	0.000504474	+	0.000873775i	0.866278	−	0.499563i	$-0.166506\pi$
$367$	0.00966434	+	0.0167391i	0.000504474	+	0.000873775i	−0.865773	+	0.500437i	$0.833173\pi$
$368$		0			0
$369$			0.231168i			0.0120341i
$370$		0			0
$371$	−26.4709	−	15.2830i	−1.37430	−	0.793453i
$372$		0			0
$373$	4.42187	−	7.65890i	0.228956	−	0.396563i	−0.728543	−	0.685000i	$-0.759802\pi$
$373$	4.42187	−	7.65890i	0.228956	−	0.396563i	0.957499	+	0.288437i	$0.0931356\pi$
$374$		0			0
$375$	−8.54848	+	4.93547i	−0.441442	+	0.254866i
$376$		0			0
$377$	−15.8799	+	5.79990i	−0.817859	+	0.298710i
$378$		0			0
$379$	−4.94138	+	2.85291i	−0.253822	+	0.146544i	−0.621513	−	0.783404i	$-0.713482\pi$
$379$	−4.94138	+	2.85291i	−0.253822	+	0.146544i	0.367691	+	0.929948i	$0.380148\pi$
$380$		0			0
$381$	4.41202	−	7.64184i	0.226035	−	0.391504i
$382$		0			0
$383$	−1.00603	−	0.580830i	−0.0514056	−	0.0296790i	0.474077	−	0.880483i	$-0.342782\pi$
$383$	−1.00603	−	0.580830i	−0.0514056	−	0.0296790i	−0.525483	+	0.850804i	$0.676115\pi$
$384$		0			0
$385$		−	3.01756i		−	0.153789i
$386$		0			0
$387$	−1.12057	−	1.94089i	−0.0569618	−	0.0986607i
$388$		0			0
$389$	32.2653			1.63591			0.817957	−	0.575279i	$-0.195107\pi$
$389$	32.2653			1.63591			0.817957	+	0.575279i	$0.195107\pi$
$390$		0			0
$391$	−2.34074			−0.118376
$392$		0			0
$393$	3.68443	+	6.38162i	0.185855	+	0.321910i
$394$		0			0
$395$			3.32097i			0.167096i
$396$		0			0
$397$	15.5572	+	8.98198i	0.780796	+	0.450793i	0.836712	−	0.547643i	$-0.184475\pi$
$397$	15.5572	+	8.98198i	0.780796	+	0.450793i	−0.0559166	+	0.998435i	$0.517808\pi$
$398$		0			0
$399$	12.3026	−	21.3087i	0.615900	−	1.06677i
$400$		0			0
$401$	3.12929	−	1.80670i	0.156269	−	0.0902221i	−0.419826	−	0.907604i	$-0.637909\pi$
$401$	3.12929	−	1.80670i	0.156269	−	0.0902221i	0.576095	+	0.817382i	$0.304576\pi$
$402$		0			0
$403$	30.1072	+	5.27408i	1.49974	+	0.262721i
$404$		0			0
$405$	4.00194	−	2.31052i	0.198858	−	0.114811i
$406$		0			0
$407$	4.12987	−	7.15315i	0.204710	−	0.354568i
$408$		0			0
$409$	−16.4798	−	9.51461i	−0.814873	−	0.470467i	0.0337724	−	0.999430i	$-0.489248\pi$
$409$	−16.4798	−	9.51461i	−0.814873	−	0.470467i	−0.848645	+	0.528963i	$0.822581\pi$
$410$		0			0
$411$			2.72074i			0.134204i
$412$		0			0
$413$	−28.0479	−	48.5803i	−1.38014	−	2.39048i
$414$		0			0
$415$	9.77461			0.479817
$416$		0			0
$417$	−2.99378			−0.146606
$418$		0			0
$419$	−6.27973	−	10.8768i	−0.306785	−	0.531367i	0.670872	−	0.741573i	$-0.265920\pi$
$419$	−6.27973	−	10.8768i	−0.306785	−	0.531367i	−0.977657	+	0.210206i	$0.932586\pi$
$420$		0			0
$421$		−	26.6775i		−	1.30018i	−0.759857	−	0.650091i	$-0.774731\pi$
$421$		−	26.6775i		−	1.30018i	0.759857	−	0.650091i	$-0.225269\pi$
$422$		0			0
$423$	−6.19075	−	3.57423i	−0.301005	−	0.173785i
$424$		0			0
$425$	1.55955	−	2.70122i	0.0756494	−	0.131029i
$426$		0			0
$427$	−21.2291	+	12.2566i	−1.02735	+	0.593140i
$428$		0			0
$429$	3.61161	−	4.31392i	0.174370	−	0.208278i
$430$		0			0
$431$	9.34393	−	5.39472i	0.450081	−	0.259854i	−0.257783	−	0.966203i	$-0.582992\pi$
$431$	9.34393	−	5.39472i	0.450081	−	0.259854i	0.707864	+	0.706348i	$0.249659\pi$
$432$		0			0
$433$	−16.2358	+	28.1212i	−0.780241	+	1.35142i	0.151560	+	0.988448i	$0.451570\pi$
$433$	−16.2358	+	28.1212i	−0.780241	+	1.35142i	−0.931801	+	0.362969i	$0.881763\pi$
$434$		0			0
$435$	−4.19171	−	2.42009i	−0.200977	−	0.116034i
$436$		0			0
$437$		−	11.8358i		−	0.566182i
$438$		0			0
$439$	−13.4100	−	23.2268i	−0.640024	−	1.10855i	−0.985427	−	0.170099i	$-0.945591\pi$
$439$	−13.4100	−	23.2268i	−0.640024	−	1.10855i	0.345403	−	0.938454i	$-0.387742\pi$
$440$		0			0
$441$	7.80234			0.371540
$442$		0			0
$443$	−19.8788			−0.944470			−0.472235	−	0.881473i	$-0.656553\pi$
$443$	−19.8788			−0.944470			−0.472235	+	0.881473i	$0.656553\pi$
$444$		0			0
$445$	−2.15915	−	3.73975i	−0.102353	−	0.177281i
$446$		0			0
$447$			27.0193i			1.27797i
$448$		0			0
$449$	9.34536	+	5.39555i	0.441035	+	0.254632i	0.704036	−	0.710164i	$-0.251379\pi$
$449$	9.34536	+	5.39555i	0.441035	+	0.254632i	−0.263002	+	0.964795i	$0.584712\pi$
$450$		0			0
$451$	−0.204536	+	0.354267i	−0.00963123	+	0.0166818i
$452$		0			0
$453$	−3.05448	+	1.76350i	−0.143512	+	0.0828566i
$454$		0			0
$455$	8.34234	+	6.98421i	0.391095	+	0.327425i
$456$		0			0
$457$	−12.8708	+	7.43094i	−0.602069	+	0.347605i	−0.769855	−	0.638219i	$-0.779672\pi$
$457$	−12.8708	+	7.43094i	−0.602069	+	0.347605i	0.167786	+	0.985823i	$0.446338\pi$
$458$		0			0
$459$	−1.90161	+	3.29368i	−0.0887595	+	0.153736i
$460$		0			0
$461$	−20.8256	−	12.0237i	−0.969946	−	0.559998i	−0.0707260	−	0.997496i	$-0.522532\pi$
$461$	−20.8256	−	12.0237i	−0.969946	−	0.559998i	−0.899220	+	0.437497i	$0.855865\pi$
$462$		0			0
$463$			12.7062i			0.590505i	0.955419	+	0.295253i	$0.0954038\pi$
$463$			12.7062i			0.590505i	−0.955419	+	0.295253i	$0.904596\pi$
$464$		0			0
$465$	4.37546	+	7.57853i	0.202907	+	0.351446i
$466$		0			0
$467$	−0.367599			−0.0170105			−0.00850523	−	0.999964i	$-0.502707\pi$
$467$	−0.367599			−0.0170105			−0.00850523	+	0.999964i	$0.502707\pi$
$468$		0			0
$469$	−60.1296			−2.77653
$470$		0			0
$471$	0.253590	+	0.439230i	0.0116848	+	0.0202387i
$472$		0			0
$473$		−	3.96590i		−	0.182352i
$474$		0			0
$475$	13.6585	+	7.88575i	0.626696	+	0.361823i
$476$		0			0
$477$	−1.89335	+	3.27939i	−0.0866907	+	0.150153i
$478$		0			0
$479$	−28.3322	+	16.3576i	−1.29453	+	0.747398i	−0.979454	−	0.201668i	$-0.935364\pi$
$479$	−28.3322	+	16.3576i	−1.29453	+	0.747398i	−0.315077	+	0.949066i	$0.602030\pi$
$480$		0			0
$481$	10.2169	+	27.9735i	0.465850	+	1.27548i
$482$		0			0
$483$	−21.1052	+	12.1851i	−0.960319	+	0.554440i
$484$		0			0
$485$	0.947659	−	1.64139i	0.0430310	−	0.0745319i
$486$		0			0
$487$	34.0316	+	19.6482i	1.54212	+	0.890343i	0.998705	+	0.0508791i	$0.0162023\pi$
$487$	34.0316	+	19.6482i	1.54212	+	0.890343i	0.543415	+	0.839464i	$0.317131\pi$
$488$		0			0
$489$		−	13.6578i		−	0.617628i
$490$		0			0
$491$	4.49228	+	7.78086i	0.202734	+	0.351145i	0.949408	−	0.314044i	$-0.101684\pi$
$491$	4.49228	+	7.78086i	0.202734	+	0.351145i	−0.746674	+	0.665190i	$0.768351\pi$
$492$		0			0
$493$	3.20558			0.144372
$494$		0			0
$495$	−0.373835			−0.0168026
$496$		0			0
$497$	33.2049	+	57.5126i	1.48944	+	2.57979i
$498$		0			0
$499$		−	26.2822i		−	1.17655i	−0.808660	−	0.588277i	$-0.799807\pi$
$499$		−	26.2822i		−	1.17655i	0.808660	−	0.588277i	$-0.200193\pi$
$500$		0			0
$501$	14.5108	+	8.37783i	0.648296	+	0.374294i
$502$		0			0
$503$	−14.8928	+	25.7952i	−0.664039	+	1.15015i	0.315506	+	0.948924i	$0.397826\pi$
$503$	−14.8928	+	25.7952i	−0.664039	+	1.15015i	−0.979545	+	0.201225i	$0.935508\pi$
$504$		0			0
$505$	6.69997	−	3.86823i	0.298145	−	0.172134i
$506$		0			0
$507$	3.56709	+	19.9693i	0.158420	+	0.886868i
$508$		0			0
$509$	−12.0526	+	6.95859i	−0.534224	+	0.308434i	−0.742735	−	0.669586i	$-0.766472\pi$
$509$	−12.0526	+	6.95859i	−0.534224	+	0.308434i	0.208511	+	0.978020i	$0.433138\pi$
$510$		0			0
$511$	−28.3859	+	49.1659i	−1.25572	+	2.17497i
$512$		0			0
$513$	−16.6543	−	9.61535i	−0.735304	−	0.424528i
$514$		0			0
$515$			1.01727i			0.0448264i
$516$		0			0
$517$	−6.32492	−	10.9551i	−0.278170	−	0.481804i
$518$		0			0
$519$	8.11823			0.356351
$520$		0			0
$521$	3.96635			0.173769			0.0868844	−	0.996218i	$-0.472309\pi$
$521$	3.96635			0.173769			0.0868844	+	0.996218i	$0.472309\pi$
$522$		0			0
$523$	−3.55326	−	6.15442i	−0.155373	−	0.269114i	0.777822	−	0.628485i	$-0.216325\pi$
$523$	−3.55326	−	6.15442i	−0.155373	−	0.269114i	−0.933195	+	0.359371i	$0.882991\pi$
$524$		0			0
$525$		−	32.4739i		−	1.41728i
$526$		0			0
$527$	−5.01916	−	2.89781i	−0.218638	−	0.126231i
$528$		0			0
$529$	5.63864	−	9.76641i	0.245158	−	0.424627i
$530$		0			0
$531$	−6.01844	+	3.47475i	−0.261178	+	0.150791i
$532$		0			0
$533$	−0.506002	−	1.38542i	−0.0219174	−	0.0600091i
$534$		0			0
$535$	−6.08616	+	3.51384i	−0.263127	+	0.151917i
$536$		0			0
$537$	19.8553	−	34.3904i	0.856820	−	1.48406i
$538$		0			0
$539$	11.9571	+	6.90346i	0.515031	+	0.297353i
$540$		0			0
$541$			10.6430i			0.457579i	0.973476	+	0.228790i	$0.0734768\pi$
$541$			10.6430i			0.457579i	−0.973476	+	0.228790i	$0.926523\pi$
$542$		0			0
$543$	8.11724	+	14.0595i	0.348344	+	0.603350i
$544$		0			0
$545$	−3.73421			−0.159956
$546$		0			0
$547$	−20.0320			−0.856507			−0.428254	−	0.903659i	$-0.640871\pi$
$547$	−20.0320			−0.856507			−0.428254	+	0.903659i	$0.640871\pi$
$548$		0			0
$549$	1.51843	+	2.63000i	0.0648051	+	0.112246i
$550$		0			0
$551$			16.2088i			0.690518i
$552$		0			0
$553$	−19.8311	−	11.4495i	−0.843305	−	0.486882i
$554$		0			0
$555$	−4.26314	+	7.38397i	−0.180960	+	0.313432i
$556$		0			0
$557$	−30.6271	+	17.6825i	−1.29771	+	0.749233i	−0.980008	−	0.198957i	$-0.936245\pi$
$557$	−30.6271	+	17.6825i	−1.29771	+	0.749233i	−0.317702	+	0.948191i	$0.602911\pi$
$558$		0			0
$559$	10.9641	+	9.17915i	0.463732	+	0.388237i
$560$		0			0
$561$	−0.923868	+	0.533395i	−0.0390057	+	0.0225200i
$562$		0			0
$563$	−4.46633	+	7.73591i	−0.188233	+	0.326030i	−0.944661	−	0.328047i	$-0.893609\pi$
$563$	−4.46633	+	7.73591i	−0.188233	+	0.326030i	0.756428	+	0.654077i	$0.226943\pi$
$564$		0			0
$565$	4.04103	+	2.33309i	0.170007	+	0.0981537i
$566$		0			0
$567$			31.8634i			1.33814i
$568$		0			0
$569$	7.65485	+	13.2586i	0.320908	+	0.555829i	0.980676	−	0.195641i	$-0.0626786\pi$
$569$	7.65485	+	13.2586i	0.320908	+	0.555829i	−0.659768	+	0.751470i	$0.729345\pi$
$570$		0			0
$571$	23.6589			0.990094			0.495047	−	0.868866i	$-0.335151\pi$
$571$	23.6589			0.990094			0.495047	+	0.868866i	$0.335151\pi$
$572$		0			0
$573$	−34.5497			−1.44334
$574$		0			0
$575$	−7.81043	−	13.5281i	−0.325717	−	0.564159i
$576$		0			0
$577$		−	19.7763i		−	0.823297i	−0.911343	−	0.411648i	$-0.864953\pi$
$577$		−	19.7763i		−	0.823297i	0.911343	−	0.411648i	$-0.135047\pi$
$578$		0			0
$579$	28.9742	+	16.7283i	1.20413	+	0.695203i
$580$		0			0
$581$	−33.6993	+	58.3689i	−1.39808	+	2.42155i
$582$		0			0
$583$	−5.80316	+	3.35046i	−0.240342	+	0.138762i
$584$		0			0
$585$	0.865249	−	1.03350i	0.0357737	−	0.0427301i
$586$		0			0
$587$	−23.4937	+	13.5641i	−0.969688	+	0.559850i	−0.899141	−	0.437659i	$-0.855808\pi$
$587$	−23.4937	+	13.5641i	−0.969688	+	0.559850i	−0.0705468	+	0.997508i	$0.522474\pi$
$588$		0			0
$589$	14.6526	−	25.3790i	0.603749	−	1.04572i
$590$		0			0
$591$	1.68900	+	0.975142i	0.0694760	+	0.0401120i
$592$		0			0
$593$		−	30.8995i		−	1.26889i	−0.772968	−	0.634445i	$-0.781229\pi$
$593$		−	30.8995i		−	1.26889i	0.772968	−	0.634445i	$-0.218771\pi$
$594$		0			0
$595$	−1.03149	−	1.78659i	−0.0422870	−	0.0732432i
$596$		0			0
$597$	−7.46330			−0.305453
$598$		0			0
$599$	1.83304			0.0748958			0.0374479	−	0.999299i	$-0.488077\pi$
$599$	1.83304			0.0748958			0.0374479	+	0.999299i	$0.488077\pi$
$600$		0			0
$601$	−8.98459	−	15.5618i	−0.366489	−	0.634778i	0.622525	−	0.782600i	$-0.286107\pi$
$601$	−8.98459	−	15.5618i	−0.366489	−	0.634778i	−0.989014	+	0.147822i	$0.952774\pi$
$602$		0			0
$603$			7.44924i			0.303357i
$604$		0			0
$605$	−0.572905	−	0.330767i	−0.0232919	−	0.0134476i
$606$		0			0
$607$	14.3576	−	24.8680i	0.582755	−	1.00936i	−0.412396	−	0.911005i	$-0.635308\pi$
$607$	14.3576	−	24.8680i	0.582755	−	1.00936i	0.995151	−	0.0983567i	$-0.0313586\pi$
$608$		0			0
$609$	28.9030	−	16.6872i	1.17121	−	0.676198i
$610$		0			0
$611$	44.9255	+	7.86992i	1.81749	+	0.318383i
$612$		0			0
$613$	7.85760	−	4.53659i	0.317366	−	0.183231i	−0.332852	−	0.942979i	$-0.608011\pi$
$613$	7.85760	−	4.53659i	0.317366	−	0.183231i	0.650218	+	0.759748i	$0.274678\pi$
$614$		0			0
$615$	0.211136	−	0.365699i	0.00851383	−	0.0147464i
$616$		0			0
$617$	−7.59823	−	4.38684i	−0.305893	−	0.176608i	0.339194	−	0.940716i	$-0.389846\pi$
$617$	−7.59823	−	4.38684i	−0.305893	−	0.176608i	−0.645087	+	0.764109i	$0.723179\pi$
$618$		0			0
$619$		−	8.31401i		−	0.334168i	−0.985943	−	0.167084i	$-0.946565\pi$
$619$		−	8.31401i		−	0.334168i	0.985943	−	0.167084i	$-0.0534352\pi$
$620$		0			0
$621$	9.52350	+	16.4952i	0.382165	+	0.661929i
$622$		0			0
$623$	29.7758			1.19294
$624$		0			0
$625$	18.6271			0.745084
$626$		0			0
$627$	−2.69707	−	4.67147i	−0.107711	−	0.186560i
$628$		0			0
$629$		−	5.64684i		−	0.225154i
$630$		0			0
$631$	−13.7080	−	7.91434i	−0.545709	−	0.315065i	0.201681	−	0.979451i	$-0.435360\pi$
$631$	−13.7080	−	7.91434i	−0.545709	−	0.315065i	−0.747389	+	0.664386i	$0.768693\pi$
$632$		0			0
$633$	−17.3549	+	30.0595i	−0.689793	+	1.19476i
$634$		0			0
$635$	3.23974	−	1.87047i	0.128565	−	0.0742271i
$636$		0			0
$637$	−46.7604	+	17.0785i	−1.85271	+	0.676674i
$638$		0			0
$639$	7.12503	−	4.11364i	0.281862	−	0.162733i
$640$		0			0
$641$	9.15342	−	15.8542i	0.361538	−	0.626202i	−0.626676	−	0.779280i	$-0.715585\pi$
$641$	9.15342	−	15.8542i	0.361538	−	0.626202i	0.988214	+	0.153077i	$0.0489184\pi$
$642$		0			0
$643$	−1.99311	−	1.15072i	−0.0786006	−	0.0453801i	0.460185	−	0.887823i	$-0.347783\pi$
$643$	−1.99311	−	1.15072i	−0.0786006	−	0.0453801i	−0.538785	+	0.842443i	$0.681117\pi$
$644$		0			0
$645$			4.09387i			0.161196i
$646$		0			0
$647$	−24.2647	−	42.0277i	−0.953944	−	1.65228i	−0.736766	−	0.676147i	$-0.763648\pi$
$647$	−24.2647	−	42.0277i	−0.953944	−	1.65228i	−0.217177	−	0.976132i	$-0.569685\pi$
$648$		0			0
$649$	−12.2978			−0.482729
$650$		0			0
$651$	−60.3401			−2.36491
$652$		0			0
$653$	0.0543587	+	0.0941521i	0.00212722	+	0.00368446i	0.867087	−	0.498157i	$-0.165990\pi$
$653$	0.0543587	+	0.0941521i	0.00212722	+	0.00368446i	−0.864960	+	0.501841i	$0.832656\pi$
$654$		0			0
$655$			3.12401i			0.122065i
$656$		0			0
$657$	6.09099	+	3.51663i	0.237632	+	0.137197i
$658$		0			0
$659$	7.52002	−	13.0251i	0.292938	−	0.507384i	−0.681565	−	0.731758i	$-0.738700\pi$
$659$	7.52002	−	13.0251i	0.292938	−	0.507384i	0.974503	+	0.224374i	$0.0720336\pi$
$660$		0			0
$661$	−23.2122	+	13.4016i	−0.902849	+	0.521260i	−0.878124	−	0.478434i	$-0.841205\pi$
$661$	−23.2122	+	13.4016i	−0.902849	+	0.521260i	−0.0247259	+	0.999694i	$0.507871\pi$
$662$		0			0
$663$	0.663689	−	3.78868i	0.0257755	−	0.147140i
$664$		0			0
$665$	9.03378	−	5.21565i	0.350315	−	0.202254i
$666$		0			0
$667$	8.02698	−	13.9031i	0.310806	−	0.538332i
$668$		0			0
$669$	28.0527	+	16.1962i	1.08458	+	0.626183i
$670$		0			0
$671$			5.37400i			0.207461i
$672$		0			0
$673$	−10.0683	−	17.4389i	−0.388106	−	0.672219i	0.604089	−	0.796917i	$-0.293537\pi$
$673$	−10.0683	−	17.4389i	−0.388106	−	0.672219i	−0.992195	+	0.124698i	$0.960204\pi$
$674$		0			0
$675$	−25.3807			−0.976903
$676$		0			0
$677$	49.2695			1.89358			0.946791	−	0.321849i	$-0.104304\pi$
$677$	49.2695			1.89358			0.946791	+	0.321849i	$0.104304\pi$
$678$		0			0
$679$	6.53437	+	11.3179i	0.250766	+	0.434340i
$680$		0			0
$681$			22.1822i			0.850025i
$682$		0			0
$683$	−18.0662	−	10.4305i	−0.691284	−	0.399113i	0.112809	−	0.993617i	$-0.464015\pi$
$683$	−18.0662	−	10.4305i	−0.691284	−	0.399113i	−0.804093	+	0.594504i	$0.797349\pi$
$684$		0			0
$685$	−0.576725	+	0.998917i	−0.0220355	+	0.0381666i
$686$		0			0
$687$	14.6734	−	8.47172i	0.559827	−	0.323216i
$688$		0			0
$689$	4.16888	−	23.7981i	0.158822	−	0.906635i
$690$		0			0
$691$	19.4381	−	11.2226i	0.739459	−	0.426927i	−0.0824138	−	0.996598i	$-0.526263\pi$
$691$	19.4381	−	11.2226i	0.739459	−	0.426927i	0.821872	+	0.569672i	$0.192930\pi$
$692$		0			0
$693$	1.28885	−	2.23235i	0.0489593	−	0.0848000i
$694$		0			0
$695$	−1.09916	−	0.634602i	−0.0416936	−	0.0240718i
$696$		0			0
$697$			0.279666i			0.0105931i
$698$		0			0
$699$	−18.3501	−	31.7833i	−0.694063	−	1.20215i
$700$		0			0
$701$	−0.371274			−0.0140228			−0.00701141	−	0.999975i	$-0.502232\pi$
$701$	−0.371274			−0.0140228			−0.00701141	+	0.999975i	$0.502232\pi$
$702$		0			0
$703$	28.5528			1.07689
$704$		0			0
$705$	6.52902	+	11.3086i	0.245897	+	0.425906i
$706$		0			0
$707$			53.3450i			2.00625i
$708$		0			0
$709$	−20.0753	−	11.5905i	−0.753943	−	0.435289i	0.0731736	−	0.997319i	$-0.476687\pi$
$709$	−20.0753	−	11.5905i	−0.753943	−	0.435289i	−0.827117	+	0.562030i	$0.810021\pi$
$710$		0			0
$711$	−1.41844	+	2.45681i	−0.0531956	+	0.0921375i
$712$		0			0
$713$	−25.1366	+	14.5126i	−0.941372	+	0.543502i
$714$		0			0
$715$	2.24044	−	0.818285i	0.0837877	−	0.0306021i
$716$		0			0
$717$	−27.6975	+	15.9912i	−1.03438	+	0.597201i
$718$		0			0
$719$	−14.0127	+	24.2707i	−0.522585	+	0.905143i	0.477070	+	0.878865i	$0.341699\pi$
$719$	−14.0127	+	24.2707i	−0.522585	+	0.905143i	−0.999655	+	0.0262780i	$0.991634\pi$
$720$		0			0
$721$	−6.07462	−	3.50719i	−0.226231	−	0.130614i
$722$		0			0
$723$			14.1997i			0.528092i
$724$		0			0
$725$	10.6962	+	18.5263i	0.397246	+	0.688051i
$726$		0			0
$727$	38.4272			1.42519			0.712593	−	0.701578i	$-0.247521\pi$
$727$	38.4272			1.42519			0.712593	+	0.701578i	$0.247521\pi$
$728$		0			0
$729$	29.9894			1.11072
$730$		0			0
$731$	−1.35566	−	2.34807i	−0.0501408	−	0.0868465i
$732$		0			0
$733$		−	19.6286i		−	0.725000i	−0.931984	−	0.362500i	$-0.881923\pi$
$733$		−	19.6286i		−	0.725000i	0.931984	−	0.362500i	$-0.118077\pi$
$734$		0			0
$735$	−12.3430	−	7.12623i	−0.455278	−	0.262855i
$736$		0			0
$737$	−6.59105	+	11.4160i	−0.242784	+	0.420515i
$738$		0			0
$739$	32.9231	−	19.0082i	1.21110	−	0.699227i	0.248098	−	0.968735i	$-0.420194\pi$
$739$	32.9231	−	19.0082i	1.21110	−	0.699227i	0.962998	+	0.269508i	$0.0868611\pi$
$740$		0			0
$741$	19.1572	+	3.35589i	0.703756	+	0.123282i
$742$		0			0
$743$	−8.06944	+	4.65889i	−0.296039	+	0.170918i	−0.640662	−	0.767823i	$-0.721340\pi$
$743$	−8.06944	+	4.65889i	−0.296039	+	0.170918i	0.344623	+	0.938741i	$0.388007\pi$
$744$		0			0
$745$	−5.72738	+	9.92012i	−0.209835	+	0.363445i
$746$		0			0
$747$	7.23112	+	4.17489i	0.264573	+	0.152751i
$748$		0			0
$749$		−	48.4578i		−	1.77061i
$750$		0			0
$751$	7.51599	+	13.0181i	0.274263	+	0.475037i	0.969949	−	0.243309i	$-0.0782329\pi$
$751$	7.51599	+	13.0181i	0.274263	+	0.475037i	−0.695686	+	0.718346i	$0.744900\pi$
$752$		0			0
$753$	−28.8726			−1.05218
$754$		0			0
$755$	−1.49526			−0.0544183
$756$		0			0
$757$	−20.8150	−	36.0527i	−0.756535	−	1.31036i	−0.944608	−	0.328201i	$-0.893558\pi$
$757$	−20.8150	−	36.0527i	−0.756535	−	1.31036i	0.188073	−	0.982155i	$-0.439776\pi$
$758$		0			0
$759$			5.34262i			0.193925i
$760$		0			0
$761$	35.4321	+	20.4568i	1.28441	+	0.741557i	0.977652	−	0.210229i	$-0.0674211\pi$
$761$	35.4321	+	20.4568i	1.28441	+	0.741557i	0.306762	+	0.951786i	$0.400754\pi$
$762$		0			0
$763$	12.8742	−	22.2988i	0.466078	−	0.807271i
$764$		0			0
$765$	−0.221335	+	0.127788i	−0.00800238	+	0.00462017i
$766$		0			0
$767$	28.4634	−	33.9983i	1.02775	−	1.22761i
$768$		0			0
$769$	−7.68863	+	4.43903i	−0.277259	+	0.160076i	−0.632182	−	0.774820i	$-0.717840\pi$
$769$	−7.68863	+	4.43903i	−0.277259	+	0.160076i	0.354923	+	0.934896i	$0.384507\pi$
$770$		0			0
$771$	8.53567	−	14.7842i	0.307405	−	0.532440i
$772$		0			0
$773$	28.3699	+	16.3794i	1.02040	+	0.589125i	0.914218	−	0.405222i	$-0.132806\pi$
$773$	28.3699	+	16.3794i	1.02040	+	0.589125i	0.106177	+	0.994347i	$0.466139\pi$
$774$		0			0
$775$		−	38.6770i		−	1.38932i
$776$		0			0
$777$	−29.3955	−	50.9145i	−1.05456	−	1.82655i
$778$		0			0
$779$	−1.41411			−0.0506657
$780$		0			0
$781$	14.5589			0.520958
$782$		0			0
$783$	−13.0422	−	22.5897i	−0.466090	−	0.807291i
$784$		0			0
$785$			0.215017i			0.00767430i
$786$		0			0
$787$	−16.5378	−	9.54810i	−0.589509	−	0.340353i	0.175395	−	0.984498i	$-0.443880\pi$
$787$	−16.5378	−	9.54810i	−0.589509	−	0.340353i	−0.764903	+	0.644145i	$0.777213\pi$
$788$		0			0
$789$	−6.51804	+	11.2896i	−0.232048	+	0.401920i
$790$		0			0
$791$	−27.8640	+	16.0873i	−0.990729	+	0.571998i
$792$		0			0
$793$	−14.8569	−	12.4382i	−0.527585	−	0.441694i
$794$		0			0
$795$	5.99042	−	3.45857i	0.212458	−	0.122663i
$796$		0			0
$797$	14.3104	−	24.7864i	0.506901	−	0.877978i	−0.493067	−	0.869991i	$-0.664124\pi$
$797$	14.3104	−	24.7864i	0.506901	−	0.877978i	0.999968	−	0.00798669i	$-0.00254227\pi$
$798$		0			0
$799$	−7.48953	−	4.32408i	−0.264961	−	0.152975i
$800$		0			0
$801$		−	3.68882i		−	0.130338i
$802$		0			0
$803$	6.22299	+	10.7785i	0.219605	+	0.380366i
$804$		0			0
$805$	−10.3317			−0.364143
$806$		0			0
$807$	3.38377			0.119114
$808$		0			0
$809$	4.48881	+	7.77484i	0.157818	+	0.273349i	0.934082	−	0.357060i	$-0.116221\pi$
$809$	4.48881	+	7.77484i	0.157818	+	0.273349i	−0.776264	+	0.630409i	$0.782887\pi$
$810$		0			0
$811$		−	53.7213i		−	1.88641i	−0.332213	−	0.943204i	$-0.607795\pi$
$811$		−	53.7213i		−	1.88641i	0.332213	−	0.943204i	$-0.392205\pi$
$812$		0			0
$813$	13.1859	+	7.61287i	0.462449	+	0.266995i
$814$		0			0
$815$	2.89510	−	5.01446i	0.101411	−	0.175649i
$816$		0			0
$817$	11.8728	−	6.85479i	0.415378	−	0.239819i
$818$		0			0
$819$	3.18848	+	8.72997i	0.111415	+	0.305050i
$820$		0			0
$821$	6.64547	−	3.83676i	0.231928	−	0.133904i	−0.379533	−	0.925178i	$-0.623915\pi$
$821$	6.64547	−	3.83676i	0.231928	−	0.133904i	0.611461	+	0.791274i	$0.290582\pi$
$822$		0			0
$823$	−14.3878	+	24.9203i	−0.501526	+	0.868668i	0.498473	+	0.866905i	$0.333894\pi$
$823$	−14.3878	+	24.9203i	−0.501526	+	0.868668i	−0.999998	+	0.00176288i	$0.999439\pi$
$824$		0			0
$825$	−6.16541	−	3.55960i	−0.214652	−	0.123929i
$826$		0			0
$827$			31.2861i			1.08792i	0.839110	+	0.543962i	$0.183077\pi$
$827$			31.2861i			1.08792i	−0.839110	+	0.543962i	$0.816923\pi$
$828$		0			0
$829$	2.43641	+	4.21999i	0.0846201	+	0.146566i	0.905229	−	0.424923i	$-0.139699\pi$
$829$	2.43641	+	4.21999i	0.0846201	+	0.146566i	−0.820609	+	0.571490i	$0.806366\pi$
$830$		0			0
$831$	0.0785540			0.00272501
$832$		0			0
$833$	9.43922			0.327049
$834$		0			0
$835$	3.55176	+	6.15183i	0.122914	+	0.212893i
$836$		0			0
$837$			47.1600i			1.63009i
$838$		0			0
$839$	27.2315	+	15.7221i	0.940135	+	0.542787i	0.890003	−	0.455956i	$-0.150702\pi$
$839$	27.2315	+	15.7221i	0.940135	+	0.542787i	0.0501322	+	0.998743i	$0.484036\pi$
$840$		0			0
$841$	3.50725	−	6.07473i	0.120940	−	0.209474i
$842$		0			0
$843$	31.3049	−	18.0739i	1.07820	−	0.622498i
$844$		0			0
$845$	−2.92332	+	8.08785i	−0.100565	+	0.278230i
$846$		0			0
$847$	3.95034	−	2.28073i	0.135735	−	0.0783668i
$848$		0			0
$849$	26.0837	−	45.1782i	0.895189	−	1.55051i
$850$		0			0
$851$	−24.4913	−	14.1400i	−0.839550	−	0.484714i
$852$		0			0
$853$		−	14.0443i		−	0.480868i	−0.970665	−	0.240434i	$-0.922710\pi$
$853$		−	14.0443i		−	0.480868i	0.970665	−	0.240434i	$-0.0772898\pi$
$854$		0			0
$855$	−0.646149	−	1.11916i	−0.0220978	−	0.0382746i
$856$		0			0
$857$	45.9965			1.57121			0.785605	−	0.618728i	$-0.212352\pi$
$857$	45.9965			1.57121			0.785605	+	0.618728i	$0.212352\pi$
$858$		0			0
$859$	25.8561			0.882200			0.441100	−	0.897458i	$-0.354588\pi$
$859$	25.8561			0.882200			0.441100	+	0.897458i	$0.354588\pi$
$860$		0			0
$861$	1.45584	+	2.52159i	0.0496150	+	0.0859357i
$862$		0			0
$863$		−	34.6497i		−	1.17949i	−0.807589	−	0.589746i	$-0.799228\pi$
$863$		−	34.6497i		−	1.17949i	0.807589	−	0.589746i	$-0.200772\pi$
$864$		0			0
$865$	2.98060	+	1.72085i	0.101344	+	0.0585107i
$866$		0			0
$867$	12.8989	−	22.3415i	0.438069	−	0.758757i
$868$		0			0
$869$	−4.34754	+	2.51005i	−0.147480	+	0.0851477i
$870$		0			0
$871$	−16.3056	−	44.6442i	−0.552494	−	1.51271i
$872$		0			0
$873$	1.40213	−	0.809520i	0.0474549	−	0.0273981i
$874$		0			0
$875$	14.4275	−	24.9892i	0.487740	−	0.844790i
$876$		0			0
$877$	−23.6503	−	13.6545i	−0.798613	−	0.461080i	0.0443728	−	0.999015i	$-0.485871\pi$
$877$	−23.6503	−	13.6545i	−0.798613	−	0.461080i	−0.842986	+	0.537935i	$0.819204\pi$
$878$		0			0
$879$			47.2327i			1.59312i
$880$		0			0
$881$	6.00132	+	10.3946i	0.202189	+	0.350202i	0.949234	−	0.314572i	$-0.101861\pi$
$881$	6.00132	+	10.3946i	0.202189	+	0.350202i	−0.747044	+	0.664774i	$0.768528\pi$
$882$		0			0
$883$	−20.8851			−0.702840			−0.351420	−	0.936218i	$-0.614301\pi$
$883$	−20.8851			−0.702840			−0.351420	+	0.936218i	$0.614301\pi$
$884$		0			0
$885$	12.6946			0.426724
$886$		0			0
$887$	17.9158	+	31.0310i	0.601552	+	1.04192i	0.992586	+	0.121543i	$0.0387842\pi$
$887$	17.9158	+	31.0310i	0.601552	+	1.04192i	−0.391034	+	0.920376i	$0.627882\pi$
$888$		0			0
$889$			25.7947i			0.865128i
$890$		0			0
$891$	6.04949	+	3.49267i	0.202666	+	0.117009i
$892$		0			0
$893$	21.8644	−	37.8703i	0.731664	−	1.26728i
$894$		0			0
$895$	14.5797	−	8.41761i	0.487347	−	0.281370i
$896$		0			0
$897$	−14.7702	−	12.3656i	−0.493162	−	0.412876i
$898$		0			0
$899$	34.4239	−	19.8747i	1.14810	−	0.662857i
$900$		0			0
$901$	−2.29057	+	3.96738i	−0.0763098	+	0.132172i
$902$		0			0
$903$	−24.4465	−	14.1142i	−0.813528	−	0.469690i
$904$		0			0
$905$			6.88257i			0.228784i
$906$		0			0
$907$	25.7415	+	44.5855i	0.854732	+	1.48044i	0.876894	+	0.480684i	$0.159612\pi$
$907$	25.7415	+	44.5855i	0.854732	+	1.48044i	−0.0221618	+	0.999754i	$0.507055\pi$
$908$		0			0
$909$	6.60873			0.219198
$910$		0			0
$911$	23.6265			0.782780			0.391390	−	0.920225i	$-0.371994\pi$
$911$	23.6265			0.782780			0.391390	+	0.920225i	$0.371994\pi$
$912$		0			0
$913$	7.38783	+	12.7961i	0.244502	+	0.423489i
$914$		0			0
$915$		−	5.54741i		−	0.183392i
$916$		0			0
$917$	−18.6550	−	10.7705i	−0.616041	−	0.355672i
$918$		0			0
$919$	7.99447	−	13.8468i	0.263713	−	0.456765i	−0.703512	−	0.710683i	$-0.748386\pi$
$919$	7.99447	−	13.8468i	0.263713	−	0.456765i	0.967226	+	0.253918i	$0.0817194\pi$
$920$		0			0
$921$	−5.20945	+	3.00768i	−0.171657	+	0.0991064i
$922$		0			0
$923$	−33.6968	+	40.2494i	−1.10915	+	1.32483i
$924$		0			0
$925$	32.6353	−	18.8420i	1.07304	−	0.619521i
$926$		0			0
$927$	−0.434493	+	0.752564i	−0.0142706	+	0.0247174i
$928$		0			0
$929$	16.9139	+	9.76524i	0.554927	+	0.320387i	0.751107	−	0.660181i	$-0.229520\pi$
$929$	16.9139	+	9.76524i	0.554927	+	0.320387i	−0.196180	+	0.980568i	$0.562854\pi$
$930$		0			0
$931$			47.7287i			1.56424i
$932$		0			0
$933$	21.9101	+	37.9494i	0.717304	+	1.24241i
$934$		0			0
$935$	−0.452263			−0.0147906
$936$		0			0
$937$	−12.0215			−0.392726			−0.196363	−	0.980531i	$-0.562913\pi$
$937$	−12.0215			−0.392726			−0.196363	+	0.980531i	$0.562913\pi$
$938$		0			0
$939$	7.15153	+	12.3868i	0.233381	+	0.404228i
$940$		0			0
$941$			9.35219i			0.304873i	0.988313	+	0.152436i	$0.0487119\pi$
$941$			9.35219i			0.304873i	−0.988313	+	0.152436i	$0.951288\pi$
$942$		0			0
$943$	1.21296	+	0.700300i	0.0394993	+	0.0228049i
$944$		0			0
$945$	−8.39341	+	14.5378i	−0.273038	+	0.472915i
$946$		0			0
$947$	34.9537	−	20.1805i	1.13584	−	0.655780i	0.190445	−	0.981698i	$-0.439007\pi$
$947$	34.9537	−	20.1805i	1.13584	−	0.655780i	0.945398	+	0.325918i	$0.105673\pi$
$948$		0			0
$949$	−44.2015	−	7.74309i	−1.43484	−	0.251351i
$950$		0			0
$951$	3.08305	−	1.78000i	0.0999748	−	0.0577205i
$952$		0			0
$953$	−26.9306	+	46.6452i	−0.872369	+	1.51099i	−0.0128289	+	0.999918i	$0.504084\pi$
$953$	−26.9306	+	46.6452i	−0.872369	+	1.51099i	−0.859540	+	0.511069i	$0.829250\pi$
$954$		0			0
$955$	−12.6849	−	7.32364i	−0.410474	−	0.236987i
$956$		0			0
$957$		−	7.31659i		−	0.236512i
$958$		0			0
$959$	−3.97668	−	6.88781i	−0.128414	−	0.222419i
$960$		0			0
$961$	−40.8659			−1.31826
$962$		0			0
$963$	−6.00327			−0.193453
$964$		0			0
$965$	7.09191	+	12.2835i	0.228297	+	0.395421i
$966$		0			0
$967$			51.7187i			1.66316i	0.555404	+	0.831581i	$0.312564\pi$
$967$			51.7187i			1.66316i	−0.555404	+	0.831581i	$0.687436\pi$
$968$		0			0
$969$	−3.19369	−	1.84388i	−0.102596	−	0.0592338i
$970$		0			0
$971$	4.18996	−	7.25723i	0.134462	−	0.232896i	−0.790930	−	0.611907i	$-0.790403\pi$
$971$	4.18996	−	7.25723i	0.134462	−	0.232896i	0.925392	+	0.379012i	$0.123736\pi$
$972$		0			0
$973$	7.57903	−	4.37575i	0.242972	−	0.140280i
$974$		0			0
$975$	24.1108	−	8.80609i	0.772164	−	0.282021i
$976$		0			0
$977$	31.6830	−	18.2922i	1.01363	−	0.585220i	0.101378	−	0.994848i	$-0.467675\pi$
$977$	31.6830	−	18.2922i	1.01363	−	0.585220i	0.912253	+	0.409628i	$0.134342\pi$
$978$		0			0
$979$	3.26385	−	5.65315i	0.104313	−	0.180675i
$980$		0			0
$981$	−2.76252	−	1.59494i	−0.0882005	−	0.0509226i
$982$		0			0
$983$			1.84949i			0.0589896i	0.999565	+	0.0294948i	$0.00938984\pi$
$983$			1.84949i			0.0589896i	−0.999565	+	0.0294948i	$0.990610\pi$
$984$		0			0
$985$	0.413409	+	0.716046i	0.0131723	+	0.0228151i
$986$		0			0
$987$	−90.0387			−2.86596
$988$		0			0
$989$	−13.5786			−0.431775
$990$		0			0
$991$	−8.40934	−	14.5654i	−0.267132	−	0.462685i	0.700988	−	0.713173i	$-0.252743\pi$
$991$	−8.40934	−	14.5654i	−0.267132	−	0.462685i	−0.968120	+	0.250487i	$0.919409\pi$
$992$		0			0
$993$		−	26.7475i		−	0.848807i
$994$		0			0
$995$	−2.74015	−	1.58202i	−0.0868685	−	0.0501535i
$996$		0			0
$997$	13.0014	−	22.5190i	0.411757	−	0.713184i	−0.583325	−	0.812239i	$-0.698249\pi$
$997$	13.0014	−	22.5190i	0.411757	−	0.713184i	0.995082	+	0.0990547i	$0.0315819\pi$
$998$		0			0
$999$	−39.7933	+	22.9746i	−1.25900	+	0.726886i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.p.a.309.5	✓	24
13.2	odd	12		7436.2.a.u.1.8		12
13.4	even	6	inner	572.2.p.a.485.5	yes	24
13.11	odd	12		7436.2.a.v.1.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.p.a.309.5	✓	24	1.1	even	1	trivial
572.2.p.a.485.5	yes	24	13.4	even	6	inner
7436.2.a.u.1.8		12	13.2	odd	12
7436.2.a.v.1.8		12	13.11	odd	12

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.p (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.780208 - 1.35136i) q^{3} -0.661534i q^{5} +(3.95034 + 2.28073i) q^{7} +(0.282552 - 0.489394i) q^{9} +O(q^{10})\)	\(q+(-0.780208 - 1.35136i) q^{3} -0.661534i q^{5} +(3.95034 + 2.28073i) q^{7} +(0.282552 - 0.489394i) q^{9} +(0.866025 - 0.500000i) q^{11} +(-0.622136 + 3.55147i) q^{13} +(-0.893971 + 0.516134i) q^{15} +(0.341829 - 0.592065i) q^{17} +(2.99373 + 1.72843i) q^{19} -7.11777i q^{21} +(-1.71192 - 2.96514i) q^{23} +4.56237 q^{25} -5.56304 q^{27} +(2.34444 + 4.06068i) q^{29} -8.47738i q^{31} +(-1.35136 - 0.780208i) q^{33} +(1.50878 - 2.61329i) q^{35} +(7.15315 - 4.12987i) q^{37} +(5.28471 - 1.93016i) q^{39} +(-0.354267 + 0.204536i) q^{41} +(1.98295 - 3.43457i) q^{43} +(-0.323751 - 0.186918i) q^{45} -12.6498i q^{47} +(6.90346 + 11.9571i) q^{49} -1.06679 q^{51} -6.70091 q^{53} +(-0.330767 - 0.572905i) q^{55} -5.39415i q^{57} +(-10.6502 - 6.14888i) q^{59} +(-2.68700 + 4.65402i) q^{61} +(2.23235 - 1.28885i) q^{63} +(2.34942 + 0.411564i) q^{65} +(-11.4160 + 6.59105i) q^{67} +(-2.67131 + 4.62685i) q^{69} +(12.6084 + 7.27944i) q^{71} +12.4460i q^{73} +(-3.55960 - 6.16541i) q^{75} +4.56146 q^{77} -5.02010 q^{79} +(3.49267 + 6.04949i) q^{81} +14.7757i q^{83} +(-0.391671 - 0.226132i) q^{85} +(3.65829 - 6.33635i) q^{87} +(5.65315 - 3.26385i) q^{89} +(-10.5576 + 12.6106i) q^{91} +(-11.4560 + 6.61412i) q^{93} +(1.14342 - 1.98046i) q^{95} +(2.48119 + 1.43252i) q^{97} -0.565103i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{3} + 6 q^{7} - 14 q^{9}+O(q^{10}) \) 24 * q - 2 * q^3 + 6 * q^7 - 14 * q^9	\( 24 q - 2 q^{3} + 6 q^{7} - 14 q^{9} - 2 q^{13} - 6 q^{19} + 10 q^{23} - 40 q^{25} - 8 q^{27} - 8 q^{29} + 8 q^{35} + 18 q^{37} + 36 q^{41} + 10 q^{43} - 30 q^{45} + 14 q^{49} + 44 q^{51} + 16 q^{53} - 24 q^{59} + 6 q^{61} - 6 q^{63} - 24 q^{65} - 54 q^{67} + 10 q^{69} + 18 q^{71} + 6 q^{75} - 16 q^{77} - 32 q^{79} - 4 q^{81} + 52 q^{87} - 18 q^{89} - 18 q^{91} + 30 q^{93} - 12 q^{95} + 42 q^{97}+O(q^{100}) \) 24 * q - 2 * q^3 + 6 * q^7 - 14 * q^9 - 2 * q^13 - 6 * q^19 + 10 * q^23 - 40 * q^25 - 8 * q^27 - 8 * q^29 + 8 * q^35 + 18 * q^37 + 36 * q^41 + 10 * q^43 - 30 * q^45 + 14 * q^49 + 44 * q^51 + 16 * q^53 - 24 * q^59 + 6 * q^61 - 6 * q^63 - 24 * q^65 - 54 * q^67 + 10 * q^69 + 18 * q^71 + 6 * q^75 - 16 * q^77 - 32 * q^79 - 4 * q^81 + 52 * q^87 - 18 * q^89 - 18 * q^91 + 30 * q^93 - 12 * q^95 + 42 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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