LMFDB - Embedded newform 572.2.n.b.313.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(53,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6, 0]))

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

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

chi := DirichletCharacter("572.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.n (of order $5$, degree $4$, 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:	$28$
Relative dimension:	$7$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			313.2
Character	$\chi$	$=$	572.313
Dual form			572.2.n.b.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.94312 - 1.41176i) q^{3} +(0.879947 - 2.70820i) q^{5} +(3.92186 - 2.84939i) q^{7} +(0.855592 + 2.63324i) q^{9} +O(q^{10})$	\(q+(-1.94312 - 1.41176i) q^{3} +(0.879947 - 2.70820i) q^{5} +(3.92186 - 2.84939i) q^{7} +(0.855592 + 2.63324i) q^{9} +(2.96132 + 1.49352i) q^{11} +(-0.309017 - 0.951057i) q^{13} +(-5.53316 + 4.02007i) q^{15} +(0.656171 - 2.01949i) q^{17} +(2.27397 + 1.65213i) q^{19} -11.6433 q^{21} +6.11635 q^{23} +(-2.51495 - 1.82722i) q^{25} +(-0.171632 + 0.528230i) q^{27} +(-6.73510 + 4.89334i) q^{29} +(-2.46308 - 7.58059i) q^{31} +(-3.64571 - 7.08273i) q^{33} +(-4.26570 - 13.1285i) q^{35} +(-4.56216 + 3.31460i) q^{37} +(-0.742204 + 2.28427i) q^{39} +(-6.95695 - 5.05452i) q^{41} +4.16172 q^{43} +7.88422 q^{45} +(0.986841 + 0.716982i) q^{47} +(5.09878 - 15.6924i) q^{49} +(-4.12604 + 2.99774i) q^{51} +(3.81403 + 11.7384i) q^{53} +(6.65054 - 6.70563i) q^{55} +(-2.08617 - 6.42057i) q^{57} +(-6.92832 + 5.03372i) q^{59} +(0.363071 - 1.11742i) q^{61} +(10.8586 + 7.88927i) q^{63} -2.84757 q^{65} +9.43288 q^{67} +(-11.8848 - 8.63479i) q^{69} +(-1.28747 + 3.96241i) q^{71} +(-11.4227 + 8.29905i) q^{73} +(2.30726 + 7.10100i) q^{75} +(15.8695 - 2.58062i) q^{77} +(3.65182 + 11.2391i) q^{79} +(7.79914 - 5.66641i) q^{81} +(-4.31181 + 13.2704i) q^{83} +(-4.89178 - 3.55409i) q^{85} +19.9953 q^{87} -2.42031 q^{89} +(-3.92186 - 2.84939i) q^{91} +(-5.91589 + 18.2072i) q^{93} +(6.47528 - 4.70457i) q^{95} +(-4.02888 - 12.3996i) q^{97} +(-1.39911 + 9.07571i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9}+O(q^{10}) $ 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9	$ 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9} + q^{11} + 7 q^{13} - 24 q^{15} + 7 q^{17} - 7 q^{19} - 12 q^{21} + 34 q^{23} - 26 q^{25} - 11 q^{27} + 8 q^{29} - 17 q^{31} - 2 q^{33} - 6 q^{35} - 15 q^{37} + 4 q^{39} + 29 q^{41} - 8 q^{43} + 62 q^{45} - 27 q^{47} - 4 q^{49} + 69 q^{51} - 32 q^{53} + 19 q^{55} + 9 q^{57} - 37 q^{59} - 19 q^{61} + 46 q^{63} - 18 q^{65} + 10 q^{67} - 32 q^{69} - 27 q^{71} - 79 q^{75} + 13 q^{77} + 21 q^{79} - 18 q^{81} + 27 q^{83} + 7 q^{85} + 56 q^{87} + 82 q^{89} - 11 q^{91} - 53 q^{93} + 51 q^{95} - 88 q^{97} + 86 q^{99}+O(q^{100}) $ 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9 + q^11 + 7 * q^13 - 24 * q^15 + 7 * q^17 - 7 * q^19 - 12 * q^21 + 34 * q^23 - 26 * q^25 - 11 * q^27 + 8 * q^29 - 17 * q^31 - 2 * q^33 - 6 * q^35 - 15 * q^37 + 4 * q^39 + 29 * q^41 - 8 * q^43 + 62 * q^45 - 27 * q^47 - 4 * q^49 + 69 * q^51 - 32 * q^53 + 19 * q^55 + 9 * q^57 - 37 * q^59 - 19 * q^61 + 46 * q^63 - 18 * q^65 + 10 * q^67 - 32 * q^69 - 27 * q^71 - 79 * q^75 + 13 * q^77 + 21 * q^79 - 18 * q^81 + 27 * q^83 + 7 * q^85 + 56 * q^87 + 82 * q^89 - 11 * q^91 - 53 * q^93 + 51 * q^95 - 88 * q^97 + 86 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.94312	−	1.41176i	−1.12186	−	0.815078i	−0.137369	−	0.990520i	$-0.543864\pi$
$3$	−1.94312	−	1.41176i	−1.12186	−	0.815078i	−0.984490	+	0.175442i	$0.943864\pi$
$4$		0			0
$5$	0.879947	−	2.70820i	0.393524	−	1.21114i	−0.536580	−	0.843849i	$-0.680284\pi$
$5$	0.879947	−	2.70820i	0.393524	−	1.21114i	0.930105	−	0.367295i	$-0.119716\pi$
$6$		0			0
$7$	3.92186	−	2.84939i	1.48232	−	1.07697i	0.505523	−	0.862813i	$-0.331300\pi$
$7$	3.92186	−	2.84939i	1.48232	−	1.07697i	0.976799	−	0.214157i	$-0.0687003\pi$
$8$		0			0
$9$	0.855592	+	2.63324i	0.285197	+	0.877747i
$10$		0			0
$11$	2.96132	+	1.49352i	0.892871	+	0.450312i
$11$	2.96132	+	1.49352i	0.892871	+	0.450312i
$12$		0			0
$13$	−0.309017	−	0.951057i	−0.0857059	−	0.263776i
$13$	−0.309017	−	0.951057i	−0.0857059	−	0.263776i
$14$		0			0
$15$	−5.53316	+	4.02007i	−1.42866	+	1.03798i
$16$		0			0
$17$	0.656171	−	2.01949i	0.159145	−	0.489798i	−0.839412	−	0.543495i	$-0.817101\pi$
$17$	0.656171	−	2.01949i	0.159145	−	0.489798i	0.998557	+	0.0536975i	$0.0171007\pi$
$18$		0			0
$19$	2.27397	+	1.65213i	0.521684	+	0.379025i	0.817238	−	0.576301i	$-0.195504\pi$
$19$	2.27397	+	1.65213i	0.521684	+	0.379025i	−0.295554	+	0.955326i	$0.595504\pi$
$20$		0			0
$21$	−11.6433			−2.54077
$22$		0			0
$23$	6.11635			1.27535			0.637673	−	0.770307i	$-0.279897\pi$
$23$	6.11635			1.27535			0.637673	+	0.770307i	$0.279897\pi$
$24$		0			0
$25$	−2.51495	−	1.82722i	−0.502991	−	0.365444i
$26$		0			0
$27$	−0.171632	+	0.528230i	−0.0330307	+	0.101658i
$28$		0			0
$29$	−6.73510	+	4.89334i	−1.25068	+	0.908670i	−0.998261	−	0.0589488i	$-0.981225\pi$
$29$	−6.73510	+	4.89334i	−1.25068	+	0.908670i	−0.252416	+	0.967619i	$0.581225\pi$
$30$		0			0
$31$	−2.46308	−	7.58059i	−0.442383	−	1.36151i	−0.885329	−	0.464965i	$-0.846067\pi$
$31$	−2.46308	−	7.58059i	−0.442383	−	1.36151i	0.442946	−	0.896548i	$-0.353933\pi$
$32$		0			0
$33$	−3.64571	−	7.08273i	−0.634636	−	1.23295i
$34$		0			0
$35$	−4.26570	−	13.1285i	−0.721035	−	2.21912i
$36$		0			0
$37$	−4.56216	+	3.31460i	−0.750015	+	0.544918i	−0.895831	−	0.444394i	$-0.853419\pi$
$37$	−4.56216	+	3.31460i	−0.750015	+	0.544918i	0.145817	+	0.989312i	$0.453419\pi$
$38$		0			0
$39$	−0.742204	+	2.28427i	−0.118848	+	0.365776i
$40$		0			0
$41$	−6.95695	−	5.05452i	−1.08649	−	0.789383i	−0.107689	−	0.994185i	$-0.534345\pi$
$41$	−6.95695	−	5.05452i	−1.08649	−	0.789383i	−0.978803	+	0.204802i	$0.934345\pi$
$42$		0			0
$43$	4.16172			0.634656			0.317328	−	0.948316i	$-0.397214\pi$
$43$	4.16172			0.634656			0.317328	+	0.948316i	$0.397214\pi$
$44$		0			0
$45$	7.88422			1.17531
$46$		0			0
$47$	0.986841	+	0.716982i	0.143946	+	0.104583i	0.657427	−	0.753518i	$-0.271645\pi$
$47$	0.986841	+	0.716982i	0.143946	+	0.104583i	−0.513482	+	0.858100i	$0.671645\pi$
$48$		0			0
$49$	5.09878	−	15.6924i	0.728397	−	2.24178i
$50$		0			0
$51$	−4.12604	+	2.99774i	−0.577761	+	0.419768i
$52$		0			0
$53$	3.81403	+	11.7384i	0.523897	+	1.61239i	0.766486	+	0.642261i	$0.222003\pi$
$53$	3.81403	+	11.7384i	0.523897	+	1.61239i	−0.242589	+	0.970129i	$0.577997\pi$
$54$		0			0
$55$	6.65054	−	6.70563i	0.896759	−	0.904187i
$56$		0			0
$57$	−2.08617	−	6.42057i	−0.276320	−	0.850426i
$58$		0			0
$59$	−6.92832	+	5.03372i	−0.901990	+	0.655334i	−0.938976	−	0.343981i	$-0.888224\pi$
$59$	−6.92832	+	5.03372i	−0.901990	+	0.655334i	0.0369861	+	0.999316i	$0.488224\pi$
$60$		0			0
$61$	0.363071	−	1.11742i	0.0464865	−	0.143071i	−0.925119	−	0.379677i	$-0.876035\pi$
$61$	0.363071	−	1.11742i	0.0464865	−	0.143071i	0.971606	+	0.236606i	$0.0760352\pi$
$62$		0			0
$63$	10.8586	+	7.88927i	1.36806	+	0.993955i
$64$		0			0
$65$	−2.84757			−0.353198
$66$		0			0
$67$	9.43288			1.15241			0.576205	−	0.817305i	$-0.304533\pi$
$67$	9.43288			1.15241			0.576205	+	0.817305i	$0.304533\pi$
$68$		0			0
$69$	−11.8848	−	8.63479i	−1.43076	−	1.03951i
$70$		0			0
$71$	−1.28747	+	3.96241i	−0.152794	+	0.470252i	−0.997931	−	0.0642986i	$-0.979519\pi$
$71$	−1.28747	+	3.96241i	−0.152794	+	0.470252i	0.845137	+	0.534550i	$0.179519\pi$
$72$		0			0
$73$	−11.4227	+	8.29905i	−1.33692	+	0.971331i	−0.337371	+	0.941372i	$0.609538\pi$
$73$	−11.4227	+	8.29905i	−1.33692	+	0.971331i	−0.999551	+	0.0299587i	$0.990462\pi$
$74$		0			0
$75$	2.30726	+	7.10100i	0.266419	+	0.819953i
$76$		0			0
$77$	15.8695	−	2.58062i	1.80850	−	0.294088i
$78$		0			0
$79$	3.65182	+	11.2391i	0.410862	+	1.26450i	0.915900	+	0.401406i	$0.131478\pi$
$79$	3.65182	+	11.2391i	0.410862	+	1.26450i	−0.505039	+	0.863097i	$0.668522\pi$
$80$		0			0
$81$	7.79914	−	5.66641i	0.866571	−	0.629601i
$82$		0			0
$83$	−4.31181	+	13.2704i	−0.473282	+	1.45661i	0.374978	+	0.927034i	$0.377650\pi$
$83$	−4.31181	+	13.2704i	−0.473282	+	1.45661i	−0.848260	+	0.529579i	$0.822350\pi$
$84$		0			0
$85$	−4.89178	−	3.55409i	−0.530588	−	0.385495i
$86$		0			0
$87$	19.9953			2.14372
$88$		0			0
$89$	−2.42031			−0.256552			−0.128276	−	0.991738i	$-0.540944\pi$
$89$	−2.42031			−0.256552			−0.128276	+	0.991738i	$0.540944\pi$
$90$		0			0
$91$	−3.92186	−	2.84939i	−0.411122	−	0.298698i
$92$		0			0
$93$	−5.91589	+	18.2072i	−0.613449	+	1.88800i
$94$		0			0
$95$	6.47528	−	4.70457i	0.664350	−	0.482678i
$96$		0			0
$97$	−4.02888	−	12.3996i	−0.409071	−	1.25899i	−0.917448	−	0.397857i	$-0.869754\pi$
$97$	−4.02888	−	12.3996i	−0.409071	−	1.25899i	0.508376	−	0.861135i	$-0.330246\pi$
$98$		0			0
$99$	−1.39911	+	9.07571i	−0.140615	+	0.912143i
$100$		0			0
$101$	2.02721	+	6.23912i	0.201715	+	0.620816i	0.999832	+	0.0183134i	$0.00582965\pi$
$101$	2.02721	+	6.23912i	0.201715	+	0.620816i	−0.798117	+	0.602503i	$0.794170\pi$
$102$		0			0
$103$	−5.12404	+	3.72283i	−0.504886	+	0.366821i	−0.810880	−	0.585212i	$-0.801011\pi$
$103$	−5.12404	+	3.72283i	−0.504886	+	0.366821i	0.305994	+	0.952033i	$0.401011\pi$
$104$		0			0
$105$	−10.2455	+	31.5323i	−0.999855	+	3.07724i
$106$		0			0
$107$	−3.15689	−	2.29362i	−0.305188	−	0.221732i	0.424641	−	0.905362i	$-0.360400\pi$
$107$	−3.15689	−	2.29362i	−0.305188	−	0.221732i	−0.729829	+	0.683630i	$0.760400\pi$
$108$		0			0
$109$	4.30951			0.412776			0.206388	−	0.978470i	$-0.433829\pi$
$109$	4.30951			0.412776			0.206388	+	0.978470i	$0.433829\pi$
$110$		0			0
$111$	13.5442			1.28556
$112$		0			0
$113$	9.38813	+	6.82088i	0.883161	+	0.641654i	0.934086	−	0.357048i	$-0.116217\pi$
$113$	9.38813	+	6.82088i	0.883161	+	0.641654i	−0.0509246	+	0.998702i	$0.516217\pi$
$114$		0			0
$115$	5.38206	−	16.5643i	0.501880	−	1.54463i
$116$		0			0
$117$	2.23997	−	1.62743i	0.207085	−	0.150456i
$118$		0			0
$119$	−3.18091	−	9.78983i	−0.291593	−	0.897432i
$120$		0			0
$121$	6.53882	+	8.84555i	0.594438	+	0.804141i
$122$		0			0
$123$	6.38240	+	19.6430i	0.575482	+	1.77115i
$124$		0			0
$125$	4.35715	−	3.16566i	0.389716	−	0.283145i
$126$		0			0
$127$	1.53982	−	4.73908i	0.136637	−	0.420526i	−0.859204	−	0.511633i	$-0.829041\pi$
$127$	1.53982	−	4.73908i	0.136637	−	0.420526i	0.995841	+	0.0911075i	$0.0290407\pi$
$128$		0			0
$129$	−8.08670	−	5.87533i	−0.711994	−	0.517294i
$130$		0			0
$131$	−4.61189			−0.402942			−0.201471	−	0.979494i	$-0.564572\pi$
$131$	−4.61189			−0.402942			−0.201471	+	0.979494i	$0.564572\pi$
$132$		0			0
$133$	13.6257			1.18150
$134$		0			0
$135$	1.27953	+	0.929630i	0.110124	+	0.0800098i
$136$		0			0
$137$	3.25304	−	10.0118i	0.277926	−	0.855369i	−0.710504	−	0.703693i	$-0.751533\pi$
$137$	3.25304	−	10.0118i	0.277926	−	0.855369i	0.988430	−	0.151676i	$-0.0484670\pi$
$138$		0			0
$139$	15.7761	−	11.4620i	1.33811	−	0.972192i	0.338596	−	0.940932i	$-0.390048\pi$
$139$	15.7761	−	11.4620i	1.33811	−	0.972192i	0.999511	−	0.0312602i	$-0.00995205\pi$
$140$		0			0
$141$	−0.905343	−	2.78636i	−0.0762436	−	0.234654i
$142$		0			0
$143$	0.505320	−	3.27790i	0.0422570	−	0.274112i
$144$		0			0
$145$	7.32560	+	22.5459i	0.608358	+	1.87233i
$146$		0			0
$147$	−32.0614	+	23.2940i	−2.64438	+	1.92125i
$148$		0			0
$149$	−2.00516	+	6.17126i	−0.164269	+	0.505569i	−0.998982	−	0.0451171i	$-0.985634\pi$
$149$	−2.00516	+	6.17126i	−0.164269	+	0.505569i	0.834712	+	0.550686i	$0.185634\pi$
$150$		0			0
$151$	−3.30640	−	2.40224i	−0.269071	−	0.195492i	0.445065	−	0.895498i	$-0.353180\pi$
$151$	−3.30640	−	2.40224i	−0.269071	−	0.195492i	−0.714137	+	0.700006i	$0.753180\pi$
$152$		0			0
$153$	5.87921			0.475306
$154$		0			0
$155$	−22.6971			−1.82308
$156$		0			0
$157$	−6.22505	−	4.52276i	−0.496813	−	0.360956i	0.310985	−	0.950415i	$-0.399341\pi$
$157$	−6.22505	−	4.52276i	−0.496813	−	0.360956i	−0.807798	+	0.589459i	$0.799341\pi$
$158$		0			0
$159$	9.16062	−	28.1935i	0.726485	−	2.23589i
$160$		0			0
$161$	23.9874	−	17.4279i	1.89047	−	1.37351i
$162$		0			0
$163$	−4.14132	−	12.7457i	−0.324374	−	0.998319i	−0.971723	−	0.236125i	$-0.924122\pi$
$163$	−4.14132	−	12.7457i	−0.324374	−	0.998319i	0.647349	−	0.762194i	$-0.275878\pi$
$164$		0			0
$165$	−22.3895	+	3.64087i	−1.74302	+	0.283441i
$166$		0			0
$167$	3.38061	+	10.4045i	0.261600	+	0.805121i	0.992457	+	0.122591i	$0.0391203\pi$
$167$	3.38061	+	10.4045i	0.261600	+	0.805121i	−0.730858	+	0.682530i	$0.760880\pi$
$168$		0			0
$169$	−0.809017	+	0.587785i	−0.0622321	+	0.0452143i
$170$		0			0
$171$	−2.40488	+	7.40145i	−0.183906	+	0.566003i
$172$		0			0
$173$	3.79647	+	2.75830i	0.288640	+	0.209709i	0.722677	−	0.691186i	$-0.242911\pi$
$173$	3.79647	+	2.75830i	0.288640	+	0.209709i	−0.434037	+	0.900895i	$0.642911\pi$
$174$		0			0
$175$	−15.0698			−1.13917
$176$		0			0
$177$	20.5689			1.54605
$178$		0			0
$179$	−11.1513	−	8.10191i	−0.833489	−	0.605565i	0.0870553	−	0.996203i	$-0.472254\pi$
$179$	−11.1513	−	8.10191i	−0.833489	−	0.605565i	−0.920544	+	0.390638i	$0.872254\pi$
$180$		0			0
$181$	−1.45463	+	4.47688i	−0.108122	+	0.332764i	−0.990450	−	0.137869i	$-0.955975\pi$
$181$	−1.45463	+	4.47688i	−0.108122	+	0.332764i	0.882329	+	0.470633i	$0.155975\pi$
$182$		0			0
$183$	−2.28301	+	1.65870i	−0.168765	+	0.122615i
$184$		0			0
$185$	4.96215	+	15.2719i	0.364824	+	1.12281i
$186$		0			0
$187$	4.95927	−	5.00034i	0.362658	−	0.365661i
$188$		0			0
$189$	0.832019	+	2.56069i	0.0605205	+	0.186263i
$190$		0			0
$191$	−3.63766	+	2.64292i	−0.263212	+	0.191235i	−0.711562	−	0.702623i	$-0.752012\pi$
$191$	−3.63766	+	2.64292i	−0.263212	+	0.191235i	0.448350	+	0.893858i	$0.352012\pi$
$192$		0			0
$193$	2.81270	−	8.65660i	0.202463	−	0.623116i	−0.797345	−	0.603523i	$-0.793763\pi$
$193$	2.81270	−	8.65660i	0.202463	−	0.623116i	0.999808	−	0.0195926i	$-0.00623692\pi$
$194$		0			0
$195$	5.53316	+	4.02007i	0.396238	+	0.287883i
$196$		0			0
$197$	−10.6672			−0.760005			−0.380003	−	0.924985i	$-0.624077\pi$
$197$	−10.6672			−0.760005			−0.380003	+	0.924985i	$0.624077\pi$
$198$		0			0
$199$	4.70718			0.333683			0.166842	−	0.985984i	$-0.446643\pi$
$199$	4.70718			0.333683			0.166842	+	0.985984i	$0.446643\pi$
$200$		0			0
$201$	−18.3292	−	13.3169i	−1.29284	−	0.939304i
$202$		0			0
$203$	−12.4710	+	38.3819i	−0.875296	+	2.69388i
$204$		0			0
$205$	−19.8104	+	14.3931i	−1.38362	+	1.00526i
$206$		0			0
$207$	5.23309	+	16.1058i	0.363725	+	1.11943i
$208$		0			0
$209$	4.26645	+	8.28870i	0.295117	+	0.573341i
$210$		0			0
$211$	−1.52638	−	4.69771i	−0.105080	−	0.323404i	0.884669	−	0.466220i	$-0.154384\pi$
$211$	−1.52638	−	4.69771i	−0.105080	−	0.323404i	−0.989749	+	0.142816i	$0.954384\pi$
$212$		0			0
$213$	8.09565	−	5.88184i	0.554705	−	0.403017i
$214$		0			0
$215$	3.66209	−	11.2708i	0.249753	−	0.768660i
$216$		0			0
$217$	−31.2599	−	22.7117i	−2.12206	−	1.54177i
$218$		0			0
$219$	33.9118			2.29155
$220$		0			0
$221$	−2.12341			−0.142836
$222$		0			0
$223$	19.4844	+	14.1563i	1.30477	+	0.947974i	0.999990	−	0.00444683i	$-0.00141547\pi$
$223$	19.4844	+	14.1563i	1.30477	+	0.947974i	0.304785	+	0.952421i	$0.401415\pi$
$224$		0			0
$225$	2.65974	−	8.18584i	0.177316	−	0.545722i
$226$		0			0
$227$	18.5588	−	13.4838i	1.23179	−	0.894949i	0.234768	−	0.972051i	$-0.424567\pi$
$227$	18.5588	−	13.4838i	1.23179	−	0.894949i	0.997023	+	0.0771024i	$0.0245668\pi$
$228$		0			0
$229$	−6.91371	−	21.2782i	−0.456871	−	1.40610i	−0.868925	−	0.494944i	$-0.835189\pi$
$229$	−6.91371	−	21.2782i	−0.456871	−	1.40610i	0.412054	−	0.911159i	$-0.364811\pi$
$230$		0			0
$231$	−34.4794	−	17.3894i	−2.26858	−	1.14414i
$232$		0			0
$233$	−1.02886	−	3.16651i	−0.0674029	−	0.207445i	0.911682	−	0.410896i	$-0.134784\pi$
$233$	−1.02886	−	3.16651i	−0.0674029	−	0.207445i	−0.979085	+	0.203451i	$0.934784\pi$
$234$		0			0
$235$	2.81010	−	2.04166i	0.183311	−	0.133183i
$236$		0			0
$237$	8.77102	−	26.9944i	0.569739	−	1.75348i
$238$		0			0
$239$	−6.82844	−	4.96115i	−0.441695	−	0.320910i	0.344613	−	0.938745i	$-0.388010\pi$
$239$	−6.82844	−	4.96115i	−0.441695	−	0.320910i	−0.786308	+	0.617835i	$0.788010\pi$
$240$		0			0
$241$	21.6899			1.39717			0.698585	−	0.715527i	$-0.253813\pi$
$241$	21.6899			1.39717			0.698585	+	0.715527i	$0.253813\pi$
$242$		0			0
$243$	−21.4880			−1.37845
$244$		0			0
$245$	−38.0116	−	27.6170i	−2.42847	−	1.76439i
$246$		0			0
$247$	0.868578	−	2.67321i	0.0552663	−	0.170092i
$248$		0			0
$249$	27.1129	−	19.6987i	1.71821	−	1.24835i
$250$		0			0
$251$	−1.15850	−	3.56549i	−0.0731237	−	0.225052i	0.907814	−	0.419372i	$-0.137750\pi$
$251$	−1.15850	−	3.56549i	−0.0731237	−	0.225052i	−0.980938	+	0.194321i	$0.937750\pi$
$252$		0			0
$253$	18.1125	+	9.13486i	1.13872	+	0.574304i
$254$		0			0
$255$	4.48779	+	13.8120i	0.281036	+	0.864941i
$256$		0			0
$257$	−8.18531	+	5.94697i	−0.510585	+	0.370962i	−0.813046	−	0.582200i	$-0.802192\pi$
$257$	−8.18531	+	5.94697i	−0.510585	+	0.370962i	0.302460	+	0.953162i	$0.402192\pi$
$258$		0			0
$259$	−8.44752	+	25.9988i	−0.524903	+	1.61549i
$260$		0			0
$261$	−18.6478	−	13.5484i	−1.15427	−	0.838628i
$262$		0			0
$263$	−2.11231			−0.130251			−0.0651253	−	0.997877i	$-0.520745\pi$
$263$	−2.11231			−0.130251			−0.0651253	+	0.997877i	$0.520745\pi$
$264$		0			0
$265$	35.1460			2.15900
$266$		0			0
$267$	4.70294	+	3.41689i	0.287815	+	0.209110i
$268$		0			0
$269$	−3.93051	+	12.0969i	−0.239647	+	0.737559i	0.756823	+	0.653619i	$0.226750\pi$
$269$	−3.93051	+	12.0969i	−0.239647	+	0.737559i	−0.996471	+	0.0839396i	$0.973250\pi$
$270$		0			0
$271$	−2.31838	+	1.68440i	−0.140832	+	0.102320i	−0.655970	−	0.754787i	$-0.727740\pi$
$271$	−2.31838	+	1.68440i	−0.140832	+	0.102320i	0.515139	+	0.857107i	$0.327740\pi$
$272$		0			0
$273$	3.59797	+	11.0734i	0.217759	+	0.670193i
$274$		0			0
$275$	−4.71860	−	9.16711i	−0.284542	−	0.552797i
$276$		0			0
$277$	0.254729	+	0.783974i	0.0153052	+	0.0471044i	0.958417	−	0.285370i	$-0.0921165\pi$
$277$	0.254729	+	0.783974i	0.0153052	+	0.0471044i	−0.943112	+	0.332474i	$0.892116\pi$
$278$		0			0
$279$	17.8541	−	12.9718i	1.06890	−	0.776600i
$280$		0			0
$281$	−5.00493	+	15.4036i	−0.298569	+	0.918901i	0.683430	+	0.730016i	$0.260487\pi$
$281$	−5.00493	+	15.4036i	−0.298569	+	0.918901i	−0.981999	+	0.188885i	$0.939513\pi$
$282$		0			0
$283$	5.09559	+	3.70216i	0.302901	+	0.220071i	0.728845	−	0.684679i	$-0.240058\pi$
$283$	5.09559	+	3.70216i	0.302901	+	0.220071i	−0.425943	+	0.904750i	$0.640058\pi$
$284$		0			0
$285$	−19.2239			−1.13873
$286$		0			0
$287$	−41.6864			−2.46067
$288$		0			0
$289$	10.1055	+	7.34209i	0.594442	+	0.431888i
$290$		0			0
$291$	−9.67667	+	29.7817i	−0.567256	+	1.74584i
$292$		0			0
$293$	4.19937	−	3.05102i	0.245330	−	0.178242i	−0.458325	−	0.888785i	$-0.651550\pi$
$293$	4.19937	−	3.05102i	0.245330	−	0.178242i	0.703654	+	0.710542i	$0.251550\pi$
$294$		0			0
$295$	7.53576	+	23.1927i	0.438749	+	1.35033i
$296$		0			0
$297$	−1.29718	+	1.30792i	−0.0752699	+	0.0758934i
$298$		0			0
$299$	−1.89005	−	5.81699i	−0.109305	−	0.336405i
$300$		0			0
$301$	16.3217	−	11.8584i	0.940765	−	0.683505i
$302$		0			0
$303$	4.86901	−	14.9853i	0.279717	−	0.860881i
$304$		0			0
$305$	−2.70671	−	1.96654i	−0.154986	−	0.112604i
$306$		0			0
$307$	20.4689			1.16822			0.584112	−	0.811673i	$-0.301443\pi$
$307$	20.4689			1.16822			0.584112	+	0.811673i	$0.301443\pi$
$308$		0			0
$309$	15.2123			0.865399
$310$		0			0
$311$	1.21818	+	0.885057i	0.0690765	+	0.0501870i	0.621788	−	0.783186i	$-0.286407\pi$
$311$	1.21818	+	0.885057i	0.0690765	+	0.0501870i	−0.552711	+	0.833373i	$0.686407\pi$
$312$		0			0
$313$	−5.41721	+	16.6724i	−0.306199	+	0.942382i	0.673029	+	0.739616i	$0.264993\pi$
$313$	−5.41721	+	16.6724i	−0.306199	+	0.942382i	−0.979227	+	0.202766i	$0.935007\pi$
$314$		0			0
$315$	30.9208	−	22.4652i	1.74219	−	1.26577i
$316$		0			0
$317$	−0.173525	−	0.534055i	−0.00974614	−	0.0299955i	0.946065	−	0.323976i	$-0.105020\pi$
$317$	−0.173525	−	0.534055i	−0.00974614	−	0.0299955i	−0.955811	+	0.293981i	$0.905020\pi$
$318$		0			0
$319$	−27.2531	+	4.43176i	−1.52588	+	0.248131i
$320$		0			0
$321$	2.89618	+	8.91352i	0.161649	+	0.497504i
$322$		0			0
$323$	4.82857	−	3.50816i	0.268669	−	0.195199i
$324$		0			0
$325$	−0.960627	+	2.95651i	−0.0532860	+	0.163997i
$326$		0			0
$327$	−8.37387	−	6.08398i	−0.463076	−	0.336445i
$328$		0			0
$329$	5.91321			0.326006
$330$		0			0
$331$	6.34168			0.348570			0.174285	−	0.984695i	$-0.444239\pi$
$331$	6.34168			0.348570			0.174285	+	0.984695i	$0.444239\pi$
$332$		0			0
$333$	−12.6315	−	9.17732i	−0.692202	−	0.502914i
$334$		0			0
$335$	8.30044	−	25.5461i	0.453502	−	1.39573i
$336$		0			0
$337$	13.3541	−	9.70230i	0.727442	−	0.528518i	−0.161311	−	0.986904i	$-0.551572\pi$
$337$	13.3541	−	9.70230i	0.727442	−	0.528518i	0.888753	+	0.458386i	$0.151572\pi$
$338$		0			0
$339$	−8.61281	−	26.5075i	−0.467784	−	1.43969i
$340$		0			0
$341$	4.02775	−	26.1272i	0.218115	−	1.41487i
$342$		0			0
$343$	−14.2311	−	43.7990i	−0.768409	−	2.36492i
$344$		0			0
$345$	−33.8427	+	24.5882i	−1.82203	+	1.32378i
$346$		0			0
$347$	−1.06415	+	3.27511i	−0.0571265	+	0.175817i	−0.975548	−	0.219785i	$-0.929464\pi$
$347$	−1.06415	+	3.27511i	−0.0571265	+	0.175817i	0.918422	+	0.395603i	$0.129464\pi$
$348$		0			0
$349$	−9.25976	−	6.72761i	−0.495663	−	0.360120i	0.311695	−	0.950182i	$-0.399103\pi$
$349$	−9.25976	−	6.72761i	−0.495663	−	0.360120i	−0.807358	+	0.590062i	$0.799103\pi$
$350$		0			0
$351$	0.555414			0.0296458
$352$		0			0
$353$	−5.34753			−0.284620			−0.142310	−	0.989822i	$-0.545453\pi$
$353$	−5.34753			−0.284620			−0.142310	+	0.989822i	$0.545453\pi$
$354$		0			0
$355$	9.59810	+	6.97343i	0.509414	+	0.370111i
$356$		0			0
$357$	−7.63998	+	23.5134i	−0.404350	+	1.24446i
$358$		0			0
$359$	−28.3977	+	20.6321i	−1.49877	+	1.08892i	−0.527907	+	0.849302i	$0.677023\pi$
$359$	−28.3977	+	20.6321i	−1.49877	+	1.08892i	−0.970867	+	0.239620i	$0.922977\pi$
$360$		0			0
$361$	−3.42994	−	10.5563i	−0.180523	−	0.555594i
$362$		0			0
$363$	−0.217926	−	26.4192i	−0.0114382	−	1.38665i
$364$		0			0
$365$	12.4241	+	38.2376i	0.650310	+	2.00145i
$366$		0			0
$367$	−3.07194	+	2.23189i	−0.160354	+	0.116504i	−0.665069	−	0.746782i	$-0.731598\pi$
$367$	−3.07194	+	2.23189i	−0.160354	+	0.116504i	0.504715	+	0.863286i	$0.331598\pi$
$368$		0			0
$369$	7.35745	−	22.6439i	0.383014	−	1.17880i
$370$		0			0
$371$	48.4053	+	35.1685i	2.51308	+	1.82586i
$372$		0			0
$373$	25.2100			1.30532			0.652662	−	0.757650i	$-0.273652\pi$
$373$	25.2100			1.30532			0.652662	+	0.757650i	$0.273652\pi$
$374$		0			0
$375$	−12.9356			−0.667991
$376$		0			0
$377$	6.73510	+	4.89334i	0.346875	+	0.252020i
$378$		0			0
$379$	6.85043	−	21.0834i	0.351883	−	1.08298i	−0.605912	−	0.795532i	$-0.707192\pi$
$379$	6.85043	−	21.0834i	0.351883	−	1.08298i	0.957795	−	0.287452i	$-0.0928083\pi$
$380$		0			0
$381$	−9.68248	+	7.03474i	−0.496049	+	0.360400i
$382$		0			0
$383$	−6.41454	−	19.7419i	−0.327768	−	1.00877i	−0.970176	−	0.242402i	$-0.922065\pi$
$383$	−6.41454	−	19.7419i	−0.327768	−	1.00877i	0.642408	−	0.766363i	$-0.277935\pi$
$384$		0			0
$385$	6.97549	−	45.2485i	0.355504	−	2.30608i
$386$		0			0
$387$	3.56073	+	10.9588i	0.181002	+	0.557067i
$388$		0			0
$389$	−13.8101	+	10.0336i	−0.700200	+	0.508725i	−0.879997	−	0.474979i	$-0.842456\pi$
$389$	−13.8101	+	10.0336i	−0.700200	+	0.508725i	0.179797	+	0.983704i	$0.442456\pi$
$390$		0			0
$391$	4.01337	−	12.3519i	0.202965	−	0.624661i
$392$		0			0
$393$	8.96143	+	6.51086i	0.452044	+	0.328429i
$394$		0			0
$395$	33.6513			1.69318
$396$		0			0
$397$	−28.6322			−1.43701			−0.718506	−	0.695521i	$-0.755174\pi$
$397$	−28.6322			−1.43701			−0.718506	+	0.695521i	$0.755174\pi$
$398$		0			0
$399$	−26.4764	−	19.2362i	−1.32548	−	0.963016i
$400$		0			0
$401$	−1.56879	+	4.82825i	−0.0783419	+	0.241111i	−0.982556	−	0.185969i	$-0.940458\pi$
$401$	−1.56879	+	4.82825i	−0.0783419	+	0.241111i	0.904214	+	0.427080i	$0.140458\pi$
$402$		0			0
$403$	−6.44843	+	4.68506i	−0.321219	+	0.233379i
$404$		0			0
$405$	−8.48293	−	26.1078i	−0.421520	−	1.29731i
$406$		0			0
$407$	−18.4604	+	3.00194i	−0.915049	+	0.148801i
$408$		0			0
$409$	−2.59142	−	7.97556i	−0.128137	−	0.394366i	0.866322	−	0.499485i	$-0.166478\pi$
$409$	−2.59142	−	7.97556i	−0.128137	−	0.394366i	−0.994460	+	0.105119i	$0.966478\pi$
$410$		0			0
$411$	−20.4553	+	14.8616i	−1.00899	+	0.733071i
$412$		0			0
$413$	−12.8288	+	39.4830i	−0.631265	+	1.94283i
$414$		0			0
$415$	32.1447	+	23.3545i	1.57792	+	1.14643i
$416$		0			0
$417$	−46.8362			−2.29358
$418$		0			0
$419$	−1.67520			−0.0818391			−0.0409195	−	0.999162i	$-0.513029\pi$
$419$	−1.67520			−0.0818391			−0.0409195	+	0.999162i	$0.513029\pi$
$420$		0			0
$421$	−27.4976	−	19.9782i	−1.34015	−	0.973678i	−0.999438	−	0.0335106i	$-0.989331\pi$
$421$	−27.4976	−	19.9782i	−1.34015	−	0.973678i	−0.340714	−	0.940167i	$-0.610669\pi$
$422$		0			0
$423$	−1.04365	+	3.21204i	−0.0507442	+	0.156174i
$424$		0			0
$425$	−5.34029	+	3.87995i	−0.259042	+	0.188205i
$426$		0			0
$427$	−1.76005	−	5.41688i	−0.0851749	−	0.262141i
$428$		0			0
$429$	−5.60949	+	5.65596i	−0.270829	+	0.273072i
$430$		0			0
$431$	−2.98906	−	9.19937i	−0.143978	−	0.443118i	0.852900	−	0.522074i	$-0.174841\pi$
$431$	−2.98906	−	9.19937i	−0.143978	−	0.443118i	−0.996878	+	0.0789557i	$0.974841\pi$
$432$		0			0
$433$	−20.6517	+	15.0044i	−0.992459	+	0.721064i	−0.960458	−	0.278424i	$-0.910188\pi$
$433$	−20.6517	+	15.0044i	−0.992459	+	0.721064i	−0.0320007	+	0.999488i	$0.510188\pi$
$434$		0			0
$435$	17.5948	−	54.1512i	0.843606	−	2.59635i
$436$		0			0
$437$	13.9084	+	10.1050i	0.665327	+	0.483389i
$438$		0			0
$439$	−7.77708			−0.371180			−0.185590	−	0.982627i	$-0.559420\pi$
$439$	−7.77708			−0.371180			−0.185590	+	0.982627i	$0.559420\pi$
$440$		0			0
$441$	45.6844			2.17545
$442$		0			0
$443$	−15.0703	−	10.9492i	−0.716010	−	0.520211i	0.169097	−	0.985599i	$-0.445915\pi$
$443$	−15.0703	−	10.9492i	−0.716010	−	0.520211i	−0.885107	+	0.465388i	$0.845915\pi$
$444$		0			0
$445$	−2.12975	+	6.55468i	−0.100960	+	0.310722i
$446$		0			0
$447$	12.6086	−	9.16067i	0.596365	−	0.433285i
$448$		0			0
$449$	−1.11468	−	3.43062i	−0.0526048	−	0.161901i	0.921303	−	0.388846i	$-0.127126\pi$
$449$	−1.11468	−	3.43062i	−0.0526048	−	0.161901i	−0.973908	+	0.226945i	$0.927126\pi$
$450$		0			0
$451$	−13.0527	−	25.3583i	−0.614629	−	1.19408i
$452$		0			0
$453$	3.03334	+	9.33567i	0.142519	+	0.438628i
$454$		0			0
$455$	−11.1678	+	8.11385i	−0.523553	+	0.380383i
$456$		0			0
$457$	−13.0483	+	40.1585i	−0.610373	+	1.87854i	−0.155909	+	0.987771i	$0.549831\pi$
$457$	−13.0483	+	40.1585i	−0.610373	+	1.87854i	−0.454464	+	0.890765i	$0.650169\pi$
$458$		0			0
$459$	0.954134	+	0.693219i	0.0445351	+	0.0323567i
$460$		0			0
$461$	−4.97530			−0.231723			−0.115861	−	0.993265i	$-0.536963\pi$
$461$	−4.97530			−0.231723			−0.115861	+	0.993265i	$0.536963\pi$
$462$		0			0
$463$	29.4563			1.36895			0.684475	−	0.729036i	$-0.260031\pi$
$463$	29.4563			1.36895			0.684475	+	0.729036i	$0.260031\pi$
$464$		0			0
$465$	44.1031	+	32.0428i	2.04523	+	1.48595i
$466$		0			0
$467$	−10.4781	+	32.2482i	−0.484868	+	1.49227i	0.347304	+	0.937752i	$0.387097\pi$
$467$	−10.4781	+	32.2482i	−0.484868	+	1.49227i	−0.832172	+	0.554517i	$0.812903\pi$
$468$		0			0
$469$	36.9944	−	26.8780i	1.70824	−	1.24111i
$470$		0			0
$471$	5.71095	+	17.5765i	0.263147	+	0.809882i
$472$		0			0
$473$	12.3242	+	6.21559i	0.566666	+	0.285793i
$474$		0			0
$475$	−2.70011	−	8.31008i	−0.123890	−	0.381293i
$476$		0			0
$477$	−27.6467	+	20.0865i	−1.26586	+	0.919698i
$478$		0			0
$479$	−3.37339	+	10.3822i	−0.154134	+	0.474376i	−0.998072	−	0.0620645i	$-0.980232\pi$
$479$	−3.37339	+	10.3822i	−0.154134	+	0.474376i	0.843938	+	0.536441i	$0.180232\pi$
$480$		0			0
$481$	4.56216	+	3.31460i	0.208017	+	0.151133i
$482$		0			0
$483$	−71.2142			−3.24036
$484$		0			0
$485$	−37.1259			−1.68580
$486$		0			0
$487$	19.3055	+	14.0262i	0.874814	+	0.635589i	0.931874	−	0.362781i	$-0.118173\pi$
$487$	19.3055	+	14.0262i	0.874814	+	0.635589i	−0.0570604	+	0.998371i	$0.518173\pi$
$488$		0			0
$489$	−9.94673	+	30.6129i	−0.449807	+	1.38436i
$490$		0			0
$491$	17.7955	−	12.9292i	0.803100	−	0.583486i	−0.108722	−	0.994072i	$-0.534676\pi$
$491$	17.7955	−	12.9292i	0.803100	−	0.583486i	0.911822	+	0.410586i	$0.134676\pi$
$492$		0			0
$493$	5.46265	+	16.8123i	0.246026	+	0.757189i
$494$		0			0
$495$	23.3477	+	11.7752i	1.04940	+	0.529256i
$496$		0			0
$497$	6.24122	+	19.2085i	0.279957	+	0.861619i
$498$		0			0
$499$	−0.991094	+	0.720072i	−0.0443675	+	0.0322349i	−0.609748	−	0.792595i	$-0.708729\pi$
$499$	−0.991094	+	0.720072i	−0.0443675	+	0.0322349i	0.565381	+	0.824830i	$0.308729\pi$
$500$		0			0
$501$	8.11963	−	24.9897i	0.362758	−	1.11646i
$502$		0			0
$503$	35.4208	+	25.7347i	1.57933	+	1.14745i	0.917453	+	0.397844i	$0.130241\pi$
$503$	35.4208	+	25.7347i	1.57933	+	1.14745i	0.661881	+	0.749609i	$0.269759\pi$
$504$		0			0
$505$	18.6806			0.831277
$506$		0			0
$507$	2.40182			0.106669
$508$		0			0
$509$	1.66216	+	1.20763i	0.0736737	+	0.0535271i	0.624012	−	0.781414i	$-0.285501\pi$
$509$	1.66216	+	1.20763i	0.0736737	+	0.0535271i	−0.550339	+	0.834941i	$0.685501\pi$
$510$		0			0
$511$	−21.1508	+	65.0954i	−0.935655	+	2.87965i
$512$		0			0
$513$	−1.26299	+	0.917618i	−0.0557625	+	0.0405138i
$514$		0			0
$515$	5.57329	+	17.1528i	0.245588	+	0.755843i
$516$		0			0
$517$	1.85153	+	3.59708i	0.0814301	+	0.158199i
$518$		0			0
$519$	−3.48294	−	10.7194i	−0.152884	−	0.470528i
$520$		0			0
$521$	36.2150	−	26.3118i	1.58661	−	1.15274i	0.678026	−	0.735038i	$-0.262836\pi$
$521$	36.2150	−	26.3118i	1.58661	−	1.15274i	0.908584	−	0.417702i	$-0.137164\pi$
$522$		0			0
$523$	−6.05833	+	18.6456i	−0.264912	+	0.815316i	0.726801	+	0.686848i	$0.241006\pi$
$523$	−6.05833	+	18.6456i	−0.264912	+	0.815316i	−0.991714	+	0.128469i	$0.958994\pi$
$524$		0			0
$525$	29.2823	+	21.2748i	1.27798	+	0.928510i
$526$		0			0
$527$	−16.9251			−0.737269
$528$		0			0
$529$	14.4097			0.626508
$530$		0			0
$531$	−19.1828	−	13.9371i	−0.832463	−	0.604820i
$532$		0			0
$533$	−2.65732	+	8.17838i	−0.115101	+	0.354245i
$534$		0			0
$535$	−8.98947	+	6.53123i	−0.388649	+	0.282370i
$536$		0			0
$537$	10.2304	+	31.4859i	0.441474	+	1.35872i
$538$		0			0
$539$	38.5360	−	38.8552i	1.65986	−	1.67361i
$540$		0			0
$541$	0.557869	+	1.71694i	0.0239847	+	0.0738172i	0.962332	−	0.271876i	$-0.0876439\pi$
$541$	0.557869	+	1.71694i	0.0239847	+	0.0738172i	−0.938348	+	0.345693i	$0.887644\pi$
$542$		0			0
$543$	9.14678	−	6.64552i	0.392526	−	0.285187i
$544$		0			0
$545$	3.79214	−	11.6710i	0.162437	−	0.499931i
$546$		0			0
$547$	−34.4623	−	25.0383i	−1.47350	−	1.07056i	−0.979580	−	0.201056i	$-0.935563\pi$
$547$	−34.4623	−	25.0383i	−1.47350	−	1.07056i	−0.493922	−	0.869506i	$-0.664437\pi$
$548$		0			0
$549$	3.25307			0.138838
$550$		0			0
$551$	−23.3998			−0.996867
$552$		0			0
$553$	46.3467	+	33.6728i	1.97086	+	1.43191i
$554$		0			0
$555$	11.9182	−	36.6805i	0.505899	−	1.55700i
$556$		0			0
$557$	−3.46684	+	2.51881i	−0.146895	+	0.106725i	−0.658805	−	0.752313i	$-0.728938\pi$
$557$	−3.46684	+	2.51881i	−0.146895	+	0.106725i	0.511911	+	0.859039i	$0.328938\pi$
$558$		0			0
$559$	−1.28604	−	3.95803i	−0.0543938	−	0.167407i
$560$		0			0
$561$	−16.6957	+	2.71497i	−0.704893	+	0.114626i
$562$		0			0
$563$	−0.437983	−	1.34797i	−0.0184588	−	0.0568103i	0.941403	−	0.337284i	$-0.109508\pi$
$563$	−0.437983	−	1.34797i	−0.0184588	−	0.0568103i	−0.959862	+	0.280474i	$0.909508\pi$
$564$		0			0
$565$	26.7334	−	19.4229i	1.12468	−	0.817129i
$566$		0			0
$567$	14.4413	−	44.4456i	0.606476	−	1.86654i
$568$		0			0
$569$	15.2268	+	11.0629i	0.638342	+	0.463783i	0.859280	−	0.511505i	$-0.170912\pi$
$569$	15.2268	+	11.0629i	0.638342	+	0.463783i	−0.220938	+	0.975288i	$0.570912\pi$
$570$		0			0
$571$	−11.0266			−0.461450			−0.230725	−	0.973019i	$-0.574110\pi$
$571$	−11.0266			−0.461450			−0.230725	+	0.973019i	$0.574110\pi$
$572$		0			0
$573$	10.7995			0.451158
$574$		0			0
$575$	−15.3823	−	11.1759i	−0.641487	−	0.466068i
$576$		0			0
$577$	8.38287	−	25.7998i	0.348984	−	1.07406i	−0.610433	−	0.792068i	$-0.709004\pi$
$577$	8.38287	−	25.7998i	0.348984	−	1.07406i	0.959416	−	0.281993i	$-0.0909955\pi$
$578$		0			0
$579$	−17.6864	+	12.8499i	−0.735022	+	0.534025i
$580$		0			0
$581$	20.9023	+	64.3305i	0.867172	+	2.66888i
$582$		0			0
$583$	−6.23689	+	40.4574i	−0.258305	+	1.67557i
$584$		0			0
$585$	−2.43636	−	7.49834i	−0.100731	−	0.310018i
$586$		0			0
$587$	28.3520	−	20.5989i	1.17021	−	0.850209i	0.179179	−	0.983817i	$-0.442656\pi$
$587$	28.3520	−	20.5989i	1.17021	−	0.850209i	0.991034	+	0.133607i	$0.0426560\pi$
$588$		0			0
$589$	6.92318	−	21.3073i	0.285264	−	0.877954i
$590$		0			0
$591$	20.7276	+	15.0595i	0.852618	+	0.619463i
$592$		0			0
$593$	−16.6790			−0.684924			−0.342462	−	0.939532i	$-0.611261\pi$
$593$	−16.6790			−0.684924			−0.342462	+	0.939532i	$0.611261\pi$
$594$		0			0
$595$	−29.3118			−1.20167
$596$		0			0
$597$	−9.14659	−	6.64539i	−0.374345	−	0.271978i
$598$		0			0
$599$	8.63326	−	26.5704i	0.352745	−	1.08564i	−0.604560	−	0.796560i	$-0.706651\pi$
$599$	8.63326	−	26.5704i	0.352745	−	1.08564i	0.957305	−	0.289079i	$-0.0933491\pi$
$600$		0			0
$601$	17.1606	−	12.4679i	0.699996	−	0.508577i	−0.179935	−	0.983679i	$-0.557589\pi$
$601$	17.1606	−	12.4679i	0.699996	−	0.508577i	0.879931	+	0.475102i	$0.157589\pi$
$602$		0			0
$603$	8.07070	+	24.8390i	0.328664	+	1.01152i
$604$		0			0
$605$	29.7093	−	9.92482i	1.20786	−	0.403501i
$606$		0			0
$607$	10.6408	+	32.7489i	0.431896	+	1.32924i	0.896234	+	0.443581i	$0.146292\pi$
$607$	10.6408	+	32.7489i	0.431896	+	1.32924i	−0.464339	+	0.885658i	$0.653708\pi$
$608$		0			0
$609$	78.4186	−	56.9744i	3.17768	−	2.30872i
$610$		0			0
$611$	0.376940	−	1.16010i	0.0152494	−	0.0469327i
$612$		0			0
$613$	35.0159	+	25.4406i	1.41428	+	1.02753i	0.992683	+	0.120751i	$0.0385303\pi$
$613$	35.0159	+	25.4406i	1.41428	+	1.02753i	0.421597	+	0.906783i	$0.361470\pi$
$614$		0			0
$615$	58.8134			2.37159
$616$		0			0
$617$	44.0594			1.77376			0.886882	−	0.461995i	$-0.152866\pi$
$617$	44.0594			1.77376			0.886882	+	0.461995i	$0.152866\pi$
$618$		0			0
$619$	−31.4418	−	22.8438i	−1.26375	−	0.918170i	−0.264817	−	0.964299i	$-0.585311\pi$
$619$	−31.4418	−	22.8438i	−1.26375	−	0.918170i	−0.998935	+	0.0461290i	$0.985311\pi$
$620$		0			0
$621$	−1.04976	+	3.23084i	−0.0421255	+	0.129649i
$622$		0			0
$623$	−9.49211	+	6.89642i	−0.380293	+	0.276299i
$624$		0			0
$625$	−9.54230	−	29.3682i	−0.381692	−	1.17473i
$626$		0			0
$627$	3.41141	−	22.1291i	0.136239	−	0.883751i
$628$		0			0
$629$	3.70024	+	11.3882i	0.147538	+	0.454076i
$630$		0			0
$631$	−35.6600	+	25.9085i	−1.41960	+	1.03140i	−0.427767	+	0.903889i	$0.640700\pi$
$631$	−35.6600	+	25.9085i	−1.41960	+	1.03140i	−0.991837	+	0.127513i	$0.959300\pi$
$632$		0			0
$633$	−3.66609	+	11.2831i	−0.145714	+	0.448462i
$634$		0			0
$635$	−11.4794	−	8.34029i	−0.455547	−	0.330974i
$636$		0			0
$637$	−16.5000			−0.653754
$638$		0			0
$639$	−11.5355			−0.456338
$640$		0			0
$641$	−26.1882	−	19.0268i	−1.03437	−	0.751514i	−0.0651916	−	0.997873i	$-0.520766\pi$
$641$	−26.1882	−	19.0268i	−1.03437	−	0.751514i	−0.969179	+	0.246359i	$0.920766\pi$
$642$		0			0
$643$	−1.32945	+	4.09164i	−0.0524285	+	0.161358i	−0.973843	−	0.227224i	$-0.927035\pi$
$643$	−1.32945	+	4.09164i	−0.0524285	+	0.161358i	0.921414	+	0.388582i	$0.127035\pi$
$644$		0			0
$645$	−23.0274	+	16.7304i	−0.906705	+	0.658759i
$646$		0			0
$647$	10.5089	+	32.3430i	0.413146	+	1.27153i	0.913898	+	0.405943i	$0.133057\pi$
$647$	10.5089	+	32.3430i	0.413146	+	1.27153i	−0.500752	+	0.865591i	$0.666943\pi$
$648$		0			0
$649$	−28.0349	+	4.55890i	−1.10047	+	0.178952i
$650$		0			0
$651$	28.6783	+	88.2628i	1.12399	+	3.45929i
$652$		0			0
$653$	−22.6634	+	16.4659i	−0.886889	+	0.644362i	−0.935065	−	0.354477i	$-0.884659\pi$
$653$	−22.6634	+	16.4659i	−0.886889	+	0.644362i	0.0481763	+	0.998839i	$0.484659\pi$
$654$		0			0
$655$	−4.05822	+	12.4899i	−0.158568	+	0.488021i
$656$		0			0
$657$	−31.6265	−	22.9780i	−1.23387	−	0.896458i
$658$		0			0
$659$	26.7454			1.04185			0.520927	−	0.853601i	$-0.325587\pi$
$659$	26.7454			1.04185			0.520927	+	0.853601i	$0.325587\pi$
$660$		0			0
$661$	−20.3199			−0.790352			−0.395176	−	0.918605i	$-0.629316\pi$
$661$	−20.3199			−0.790352			−0.395176	+	0.918605i	$0.629316\pi$
$662$		0			0
$663$	4.12604	+	2.99774i	0.160242	+	0.116423i
$664$		0			0
$665$	11.9899	−	36.9013i	0.464950	−	1.43097i
$666$		0			0
$667$	−41.1942	+	29.9293i	−1.59505	+	1.15887i
$668$		0			0
$669$	−17.8753	−	55.0146i	−0.691100	−	2.12699i
$670$		0			0
$671$	2.74405	−	2.76678i	0.105933	−	0.106810i
$672$		0			0
$673$	1.71883	+	5.29002i	0.0662561	+	0.203915i	0.978704	−	0.205278i	$-0.0658100\pi$
$673$	1.71883	+	5.29002i	0.0662561	+	0.203915i	−0.912448	+	0.409194i	$0.865810\pi$
$674$		0			0
$675$	1.39684	−	1.01486i	0.0537644	−	0.0390621i
$676$		0			0
$677$	−2.63347	+	8.10497i	−0.101212	+	0.311499i	−0.988823	−	0.149095i	$-0.952364\pi$
$677$	−2.63347	+	8.10497i	−0.101212	+	0.311499i	0.887611	+	0.460595i	$0.152364\pi$
$678$		0			0
$679$	−51.1321	−	37.1497i	−1.96227	−	1.42567i
$680$		0			0
$681$	−55.0977			−2.11135
$682$		0			0
$683$	−0.612240			−0.0234267			−0.0117133	−	0.999931i	$-0.503729\pi$
$683$	−0.612240			−0.0234267			−0.0117133	+	0.999931i	$0.503729\pi$
$684$		0			0
$685$	−24.2515	−	17.6198i	−0.926604	−	0.673217i
$686$		0			0
$687$	−16.6055	+	51.1065i	−0.633539	+	1.94983i
$688$		0			0
$689$	9.98526	−	7.25471i	0.380408	−	0.276383i
$690$		0			0
$691$	0.162587	+	0.500390i	0.00618508	+	0.0190357i	0.954101	−	0.299484i	$-0.0968144\pi$
$691$	0.162587	+	0.500390i	0.00618508	+	0.0190357i	−0.947916	+	0.318519i	$0.896814\pi$
$692$		0			0
$693$	20.3732	+	39.5802i	0.773913	+	1.50353i
$694$		0			0
$695$	−17.1592	−	52.8106i	−0.650886	−	2.00322i
$696$		0			0
$697$	−14.7725	+	10.7328i	−0.559548	+	0.406535i
$698$		0			0
$699$	−2.47114	+	7.60539i	−0.0934671	+	0.287662i
$700$		0			0
$701$	−13.0446	−	9.47745i	−0.492687	−	0.357958i	0.313529	−	0.949578i	$-0.398489\pi$
$701$	−13.0446	−	9.47745i	−0.492687	−	0.357958i	−0.806217	+	0.591620i	$0.798489\pi$
$702$		0			0
$703$	−15.8504			−0.597808
$704$		0			0
$705$	−8.34267			−0.314203
$706$		0			0
$707$	25.7282	+	18.6926i	0.967607	+	0.703008i
$708$		0			0
$709$	11.4294	−	35.1761i	0.429240	−	1.32107i	−0.469635	−	0.882861i	$-0.655614\pi$
$709$	11.4294	−	35.1761i	0.429240	−	1.32107i	0.898875	−	0.438205i	$-0.144386\pi$
$710$		0			0
$711$	−26.4709	+	19.2322i	−0.992736	+	0.721265i
$712$		0			0
$713$	−15.0651	−	46.3655i	−0.564191	−	1.73640i
$714$		0			0
$715$	−8.43256	−	4.25289i	−0.315360	−	0.159049i
$716$		0			0
$717$	6.26451	+	19.2802i	0.233953	+	0.720032i
$718$		0			0
$719$	27.1088	−	19.6957i	1.01099	−	0.734525i	0.0465713	−	0.998915i	$-0.485171\pi$
$719$	27.1088	−	19.6957i	1.01099	−	0.734525i	0.964416	+	0.264390i	$0.0851705\pi$
$720$		0			0
$721$	−9.48792	+	29.2008i	−0.353349	+	1.08750i
$722$		0			0
$723$	−42.1460	−	30.6209i	−1.56743	−	1.13880i
$724$		0			0
$725$	25.8797			0.961147
$726$		0			0
$727$	20.8584			0.773596			0.386798	−	0.922164i	$-0.373581\pi$
$727$	20.8584			0.773596			0.386798	+	0.922164i	$0.373581\pi$
$728$		0			0
$729$	18.3562	+	13.3366i	0.679859	+	0.493946i
$730$		0			0
$731$	2.73080	−	8.40454i	0.101002	−	0.310853i
$732$		0			0
$733$	−33.4233	+	24.2835i	−1.23452	+	0.896930i	−0.997221	−	0.0745066i	$-0.976262\pi$
$733$	−33.4233	+	24.2835i	−1.23452	+	0.896930i	−0.237298	+	0.971437i	$0.576262\pi$
$734$		0			0
$735$	34.8724	+	107.326i	1.28629	+	3.95878i
$736$		0			0
$737$	27.9338	+	14.0882i	1.02895	+	0.518944i
$738$		0			0
$739$	12.9568	+	39.8768i	0.476622	+	1.46689i	0.843757	+	0.536725i	$0.180339\pi$
$739$	12.9568	+	39.8768i	0.476622	+	1.46689i	−0.367135	+	0.930168i	$0.619661\pi$
$740$		0			0
$741$	−5.46167	+	3.96813i	−0.200639	+	0.145773i
$742$		0			0
$743$	9.53348	−	29.3410i	0.349749	−	1.07642i	−0.609242	−	0.792984i	$-0.708526\pi$
$743$	9.53348	−	29.3410i	0.349749	−	1.07642i	0.958992	−	0.283434i	$-0.0914737\pi$
$744$		0			0
$745$	14.9486	+	10.8608i	0.547673	+	0.397908i
$746$		0			0
$747$	−38.6332			−1.41352
$748$		0			0
$749$	−18.9163			−0.691186
$750$		0			0
$751$	−30.9204	−	22.4650i	−1.12830	−	0.819759i	−0.142855	−	0.989744i	$-0.545628\pi$
$751$	−30.9204	−	22.4650i	−1.12830	−	0.819759i	−0.985447	+	0.169985i	$0.945628\pi$
$752$		0			0
$753$	−2.78251	+	8.56367i	−0.101400	+	0.312078i
$754$		0			0
$755$	−9.41522	+	6.84055i	−0.342655	+	0.248953i
$756$		0			0
$757$	−14.7016	−	45.2467i	−0.534337	−	1.64452i	−0.745077	−	0.666978i	$-0.767587\pi$
$757$	−14.7016	−	45.2467i	−0.534337	−	1.64452i	0.210740	−	0.977542i	$-0.432413\pi$
$758$		0			0
$759$	−22.2984	−	43.3204i	−0.809381	−	1.57243i
$760$		0			0
$761$	−5.74697	−	17.6874i	−0.208328	−	0.641166i	−0.999560	−	0.0296512i	$-0.990560\pi$
$761$	−5.74697	−	17.6874i	−0.208328	−	0.641166i	0.791233	−	0.611515i	$-0.209440\pi$
$762$		0			0
$763$	16.9013	−	12.2795i	0.611867	−	0.444547i
$764$		0			0
$765$	5.17340	−	15.9221i	0.187045	−	0.575664i
$766$		0			0
$767$	6.92832	+	5.03372i	0.250167	+	0.181757i
$768$		0			0
$769$	9.04252			0.326082			0.163041	−	0.986619i	$-0.447870\pi$
$769$	9.04252			0.326082			0.163041	+	0.986619i	$0.447870\pi$
$770$		0			0
$771$	24.3007			0.875167
$772$		0			0
$773$	−19.4550	−	14.1349i	−0.699746	−	0.508395i	0.180103	−	0.983648i	$-0.442357\pi$
$773$	−19.4550	−	14.1349i	−0.699746	−	0.508395i	−0.879850	+	0.475252i	$0.842357\pi$
$774$		0			0
$775$	−7.65687	+	23.5654i	−0.275043	+	0.846495i
$776$		0			0
$777$	53.1185	−	38.5928i	1.90561	−	1.38451i
$778$		0			0
$779$	−7.46913	−	22.9876i	−0.267609	−	0.823617i
$780$		0			0
$781$	−9.73052	+	9.81111i	−0.348185	+	0.351069i
$782$		0			0
$783$	−1.42885	−	4.39754i	−0.0510628	−	0.157155i
$784$		0			0
$785$	−17.7263	+	12.8789i	−0.632677	+	0.459667i
$786$		0			0
$787$	5.16044	−	15.8822i	0.183950	−	0.566140i	−0.815979	−	0.578082i	$-0.803801\pi$
$787$	5.16044	−	15.8822i	0.183950	−	0.566140i	0.999929	+	0.0119422i	$0.00380140\pi$
$788$		0			0
$789$	4.10446	+	2.98207i	0.146123	+	0.106164i
$790$		0			0
$791$	56.2543			2.00017
$792$		0			0
$793$	−1.17492			−0.0417227
$794$		0			0
$795$	−68.2928	−	49.6176i	−2.42209	−	1.75975i
$796$		0			0
$797$	16.6039	−	51.1014i	0.588139	−	1.81011i	0.00185713	−	0.999998i	$-0.499409\pi$
$797$	16.6039	−	51.1014i	0.588139	−	1.81011i	0.586282	−	0.810107i	$-0.300591\pi$
$798$		0			0
$799$	2.09547	−	1.52245i	0.0741325	−	0.0538604i
$800$		0			0
$801$	−2.07080	−	6.37326i	−0.0731680	−	0.225188i
$802$		0			0
$803$	−46.2209	+	7.51621i	−1.63110	+	0.265241i
$804$		0			0
$805$	−26.0905	−	80.2984i	−0.919570	−	2.83015i
$806$		0			0
$807$	24.7153	−	17.9567i	0.870018	−	0.632105i
$808$		0			0
$809$	−8.24014	+	25.3605i	−0.289708	+	0.891629i	0.695240	+	0.718777i	$0.255298\pi$
$809$	−8.24014	+	25.3605i	−0.289708	+	0.891629i	−0.984948	+	0.172851i	$0.944702\pi$
$810$		0			0
$811$	30.3839	+	22.0752i	1.06692	+	0.775164i	0.975356	−	0.220635i	$-0.0708130\pi$
$811$	30.3839	+	22.0752i	1.06692	+	0.775164i	0.0915653	+	0.995799i	$0.470813\pi$
$812$		0			0
$813$	6.88285			0.241392
$814$		0			0
$815$	−38.1620			−1.33676
$816$		0			0
$817$	9.46361	+	6.87571i	0.331090	+	0.240551i
$818$		0			0
$819$	4.14763	−	12.7651i	0.144930	−	0.446049i
$820$		0			0
$821$	−5.41126	+	3.93151i	−0.188854	+	0.137211i	−0.678195	−	0.734882i	$-0.737237\pi$
$821$	−5.41126	+	3.93151i	−0.188854	+	0.137211i	0.489341	+	0.872093i	$0.337237\pi$
$822$		0			0
$823$	−10.7029	−	32.9400i	−0.373078	−	1.14822i	−0.944766	−	0.327746i	$-0.893711\pi$
$823$	−10.7029	−	32.9400i	−0.373078	−	1.14822i	0.571687	−	0.820471i	$-0.306289\pi$
$824$		0			0
$825$	−3.77294	+	24.4743i	−0.131357	+	0.852084i
$826$		0			0
$827$	−13.0141	−	40.0532i	−0.452543	−	1.39278i	−0.873995	−	0.485934i	$-0.838479\pi$
$827$	−13.0141	−	40.0532i	−0.452543	−	1.39278i	0.421452	−	0.906851i	$-0.361521\pi$
$828$		0			0
$829$	−19.4375	+	14.1221i	−0.675091	+	0.490482i	−0.871726	−	0.489994i	$-0.836999\pi$
$829$	−19.4375	+	14.1221i	−0.675091	+	0.490482i	0.196634	+	0.980477i	$0.436999\pi$
$830$		0			0
$831$	0.611813	−	1.88297i	0.0212235	−	0.0653194i
$832$		0			0
$833$	−28.3450	−	20.5938i	−0.982096	−	0.713534i
$834$		0			0
$835$	31.1521			1.07806
$836$		0			0
$837$	4.42704			0.153021
$838$		0			0
$839$	−20.7617	−	15.0842i	−0.716772	−	0.520765i	0.168579	−	0.985688i	$-0.446082\pi$
$839$	−20.7617	−	15.0842i	−0.716772	−	0.520765i	−0.885351	+	0.464923i	$0.846082\pi$
$840$		0			0
$841$	12.4553	−	38.3336i	0.429495	−	1.32185i
$842$		0			0
$843$	31.4713	−	22.8652i	1.08393	−	0.787520i
$844$		0			0
$845$	0.879947	+	2.70820i	0.0302711	+	0.0931649i
$846$		0			0
$847$	50.8488	+	16.0593i	1.74718	+	0.551804i
$848$		0			0
$849$	−4.67477	−	14.3875i	−0.160438	−	0.493777i
$850$		0			0
$851$	−27.9038	+	20.2733i	−0.956528	+	0.694959i
$852$		0			0
$853$	−8.36709	+	25.7513i	−0.286484	+	0.881707i	0.699466	+	0.714666i	$0.253421\pi$
$853$	−8.36709	+	25.7513i	−0.286484	+	0.881707i	−0.985950	+	0.167041i	$0.946579\pi$
$854$		0			0
$855$	17.9285	+	13.0258i	0.613140	+	0.445472i
$856$		0			0
$857$	−21.9251			−0.748948			−0.374474	−	0.927237i	$-0.622177\pi$
$857$	−21.9251			−0.748948			−0.374474	+	0.927237i	$0.622177\pi$
$858$		0			0
$859$	−26.0558			−0.889012			−0.444506	−	0.895776i	$-0.646621\pi$
$859$	−26.0558			−0.889012			−0.444506	+	0.895776i	$0.646621\pi$
$860$		0			0
$861$	81.0016	+	58.8511i	2.76053	+	2.00564i
$862$		0			0
$863$	13.1655	−	40.5194i	0.448160	−	1.37930i	−0.430820	−	0.902438i	$-0.641776\pi$
$863$	13.1655	−	40.5194i	0.448160	−	1.37930i	0.878980	−	0.476858i	$-0.158224\pi$
$864$		0			0
$865$	10.8107	−	7.85444i	0.367575	−	0.267059i
$866$		0			0
$867$	−9.27095	−	28.5331i	−0.314858	−	0.969034i
$868$		0			0
$869$	−5.97163	+	38.7367i	−0.202574	+	1.31405i
$870$		0			0
$871$	−2.91492	−	8.97120i	−0.0987683	−	0.303978i
$872$		0			0
$873$	29.2041	−	21.2180i	0.988410	−	0.718122i
$874$		0			0
$875$	8.06792	−	24.8305i	0.272745	−	0.839424i
$876$		0			0
$877$	−7.44962	−	5.41247i	−0.251556	−	0.182766i	0.454860	−	0.890563i	$-0.349689\pi$
$877$	−7.44962	−	5.41247i	−0.251556	−	0.182766i	−0.706416	+	0.707797i	$0.749689\pi$
$878$		0			0
$879$	−12.4671			−0.420507
$880$		0			0
$881$	−29.1622			−0.982499			−0.491249	−	0.871019i	$-0.663460\pi$
$881$	−29.1622			−0.982499			−0.491249	+	0.871019i	$0.663460\pi$
$882$		0			0
$883$	25.3727	+	18.4343i	0.853859	+	0.620365i	0.926207	−	0.377015i	$-0.123049\pi$
$883$	25.3727	+	18.4343i	0.853859	+	0.620365i	−0.0723486	+	0.997379i	$0.523049\pi$
$884$		0			0
$885$	18.0996	−	55.7047i	0.608410	−	1.87249i
$886$		0			0
$887$	−7.13054	+	5.18064i	−0.239420	+	0.173949i	−0.701025	−	0.713137i	$-0.747274\pi$
$887$	−7.13054	+	5.18064i	−0.239420	+	0.173949i	0.461605	+	0.887086i	$0.347274\pi$
$888$		0			0
$889$	−7.46456	−	22.9736i	−0.250353	−	0.770509i
$890$		0			0
$891$	31.5586	−	5.13190i	1.05725	−	0.171925i
$892$		0			0
$893$	1.05949	+	3.26079i	0.0354546	+	0.109118i
$894$		0			0
$895$	−31.7542	+	23.0708i	−1.06142	+	0.771170i
$896$		0			0
$897$	−4.53958	+	13.9714i	−0.151572	+	0.466491i
$898$		0			0
$899$	53.6835	+	39.0033i	1.79044	+	1.30083i
$900$		0			0
$901$	26.2082			0.873120
$902$		0			0
$903$	−48.4560			−1.61251
$904$		0			0
$905$	10.8443	+	7.87884i	0.360477	+	0.261902i
$906$		0			0
$907$	6.84129	−	21.0553i	0.227161	−	0.699131i	−0.770904	−	0.636952i	$-0.780195\pi$
$907$	6.84129	−	21.0553i	0.227161	−	0.699131i	0.998065	−	0.0621789i	$-0.0198049\pi$
$908$		0			0
$909$	−14.6946	+	10.6763i	−0.487391	+	0.354110i
$910$		0			0
$911$	4.99023	+	15.3583i	0.165334	+	0.508845i	0.999061	−	0.0433321i	$-0.0137974\pi$
$911$	4.99023	+	15.3583i	0.165334	+	0.508845i	−0.833727	+	0.552177i	$0.813797\pi$
$912$		0			0
$913$	−32.5881	+	32.8581i	−1.07851	+	1.08744i
$914$		0			0
$915$	2.48317	+	7.64242i	0.0820911	+	0.252651i
$916$		0			0
$917$	−18.0872	+	13.1411i	−0.597290	+	0.433957i
$918$		0			0
$919$	−8.06941	+	24.8351i	−0.266185	+	0.819234i	0.725233	+	0.688504i	$0.241732\pi$
$919$	−8.06941	+	24.8351i	−0.266185	+	0.819234i	−0.991418	+	0.130730i	$0.958268\pi$
$920$		0			0
$921$	−39.7735	−	28.8972i	−1.31058	−	0.952194i
$922$		0			0
$923$	4.16633			0.137136
$924$		0			0
$925$	17.5301			0.576388
$926$		0			0
$927$	−14.1872	−	10.3076i	−0.465969	−	0.338546i
$928$		0			0
$929$	−9.37518	+	28.8538i	−0.307590	+	0.946664i	0.671109	+	0.741359i	$0.265818\pi$
$929$	−9.37518	+	28.8538i	−0.307590	+	0.946664i	−0.978698	+	0.205304i	$0.934182\pi$
$930$		0			0
$931$	37.5204	−	27.2602i	1.22968	−	0.893417i
$932$		0			0
$933$	−1.11757	−	3.43954i	−0.0365877	−	0.112605i
$934$		0			0
$935$	−9.17804	−	17.8307i	−0.300154	−	0.583127i
$936$		0			0
$937$	11.2114	+	34.5052i	0.366261	+	1.12723i	0.949188	+	0.314710i	$0.101907\pi$
$937$	11.2114	+	34.5052i	0.366261	+	1.12723i	−0.582927	+	0.812525i	$0.698093\pi$
$938$		0			0
$939$	34.0637	−	24.7487i	1.11163	−	0.807644i
$940$		0			0
$941$	7.03332	−	21.6463i	0.229280	−	0.705651i	−0.768549	−	0.639791i	$-0.779021\pi$
$941$	7.03332	−	21.6463i	0.229280	−	0.705651i	0.997829	−	0.0658598i	$-0.0209790\pi$
$942$		0			0
$943$	−42.5511	−	30.9152i	−1.38565	−	1.00674i
$944$		0			0
$945$	7.66699			0.249407
$946$		0			0
$947$	12.1480			0.394755			0.197378	−	0.980328i	$-0.436757\pi$
$947$	12.1480			0.394755			0.197378	+	0.980328i	$0.436757\pi$
$948$		0			0
$949$	11.4227	+	8.29905i	0.370795	+	0.269399i
$950$		0			0
$951$	−0.416776	+	1.28271i	−0.0135149	+	0.0415946i
$952$		0			0
$953$	−21.2910	+	15.4688i	−0.689684	+	0.501085i	−0.876556	−	0.481300i	$-0.840165\pi$
$953$	−21.2910	+	15.4688i	−0.689684	+	0.501085i	0.186872	+	0.982384i	$0.440165\pi$
$954$		0			0
$955$	3.95659	+	12.1771i	0.128032	+	0.394043i
$956$		0			0
$957$	59.2124	+	29.8633i	1.91407	+	0.965342i
$958$		0			0
$959$	−15.7697	−	48.5342i	−0.509230	−	1.56725i
$960$		0			0
$961$	−26.3190	+	19.1219i	−0.849000	+	0.616834i
$962$		0			0
$963$	3.33863	−	10.2753i	0.107586	−	0.331116i
$964$		0			0
$965$	−20.9688	−	15.2347i	−0.675009	−	0.490423i
$966$		0			0
$967$	−11.8302			−0.380434			−0.190217	−	0.981742i	$-0.560919\pi$
$967$	−11.8302			−0.380434			−0.190217	+	0.981742i	$0.560919\pi$
$968$		0			0
$969$	−14.3351			−0.460511
$970$		0			0
$971$	33.9111	+	24.6378i	1.08826	+	0.790666i	0.979104	−	0.203359i	$-0.0651858\pi$
$971$	33.9111	+	24.6378i	1.08826	+	0.790666i	0.109154	+	0.994025i	$0.465186\pi$
$972$		0			0
$973$	29.2117	−	89.9044i	0.936484	−	2.88220i
$974$		0			0
$975$	6.04047	−	4.38866i	0.193450	−	0.140550i
$976$		0			0
$977$	−4.24843	−	13.0753i	−0.135919	−	0.418316i	0.859813	−	0.510610i	$-0.170580\pi$
$977$	−4.24843	−	13.0753i	−0.135919	−	0.418316i	−0.995732	+	0.0922934i	$0.970580\pi$
$978$		0			0
$979$	−7.16731	−	3.61477i	−0.229068	−	0.115529i
$980$		0			0
$981$	3.68718	+	11.3480i	0.117723	+	0.362313i
$982$		0			0
$983$	42.2270	−	30.6797i	1.34683	−	0.978530i	0.347669	−	0.937617i	$-0.386973\pi$
$983$	42.2270	−	30.6797i	1.34683	−	0.978530i	0.999163	−	0.0409131i	$-0.0130267\pi$
$984$		0			0
$985$	−9.38656	+	28.8889i	−0.299081	+	0.920476i
$986$		0			0
$987$	−11.4901	−	8.34802i	−0.365733	−	0.265720i
$988$		0			0
$989$	25.4545			0.809406
$990$		0			0
$991$	−17.9862			−0.571352			−0.285676	−	0.958326i	$-0.592218\pi$
$991$	−17.9862			−0.571352			−0.285676	+	0.958326i	$0.592218\pi$
$992$		0			0
$993$	−12.3226	−	8.95290i	−0.391046	−	0.284112i
$994$		0			0
$995$	4.14207	−	12.7480i	0.131312	−	0.404138i
$996$		0			0
$997$	−21.6983	+	15.7647i	−0.687192	+	0.499274i	−0.875736	−	0.482791i	$-0.839623\pi$
$997$	−21.6983	+	15.7647i	−0.687192	+	0.499274i	0.188544	+	0.982065i	$0.439623\pi$
$998$		0			0
$999$	−0.967859	−	2.97876i	−0.0306217	−	0.0942439i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.n.b.313.2	yes	28
11.3	even	5		6292.2.a.z.1.11		14
11.8	odd	10		6292.2.a.y.1.11		14
11.9	even	5	inner	572.2.n.b.53.2	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.n.b.53.2	✓	28	11.9	even	5	inner
572.2.n.b.313.2	yes	28	1.1	even	1	trivial
6292.2.a.y.1.11		14	11.8	odd	10
6292.2.a.z.1.11		14	11.3	even	5

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.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.94312 - 1.41176i) q^{3} +(0.879947 - 2.70820i) q^{5} +(3.92186 - 2.84939i) q^{7} +(0.855592 + 2.63324i) q^{9} +O(q^{10})\)	\(q+(-1.94312 - 1.41176i) q^{3} +(0.879947 - 2.70820i) q^{5} +(3.92186 - 2.84939i) q^{7} +(0.855592 + 2.63324i) q^{9} +(2.96132 + 1.49352i) q^{11} +(-0.309017 - 0.951057i) q^{13} +(-5.53316 + 4.02007i) q^{15} +(0.656171 - 2.01949i) q^{17} +(2.27397 + 1.65213i) q^{19} -11.6433 q^{21} +6.11635 q^{23} +(-2.51495 - 1.82722i) q^{25} +(-0.171632 + 0.528230i) q^{27} +(-6.73510 + 4.89334i) q^{29} +(-2.46308 - 7.58059i) q^{31} +(-3.64571 - 7.08273i) q^{33} +(-4.26570 - 13.1285i) q^{35} +(-4.56216 + 3.31460i) q^{37} +(-0.742204 + 2.28427i) q^{39} +(-6.95695 - 5.05452i) q^{41} +4.16172 q^{43} +7.88422 q^{45} +(0.986841 + 0.716982i) q^{47} +(5.09878 - 15.6924i) q^{49} +(-4.12604 + 2.99774i) q^{51} +(3.81403 + 11.7384i) q^{53} +(6.65054 - 6.70563i) q^{55} +(-2.08617 - 6.42057i) q^{57} +(-6.92832 + 5.03372i) q^{59} +(0.363071 - 1.11742i) q^{61} +(10.8586 + 7.88927i) q^{63} -2.84757 q^{65} +9.43288 q^{67} +(-11.8848 - 8.63479i) q^{69} +(-1.28747 + 3.96241i) q^{71} +(-11.4227 + 8.29905i) q^{73} +(2.30726 + 7.10100i) q^{75} +(15.8695 - 2.58062i) q^{77} +(3.65182 + 11.2391i) q^{79} +(7.79914 - 5.66641i) q^{81} +(-4.31181 + 13.2704i) q^{83} +(-4.89178 - 3.55409i) q^{85} +19.9953 q^{87} -2.42031 q^{89} +(-3.92186 - 2.84939i) q^{91} +(-5.91589 + 18.2072i) q^{93} +(6.47528 - 4.70457i) q^{95} +(-4.02888 - 12.3996i) q^{97} +(-1.39911 + 9.07571i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9}+O(q^{10}) \) 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9	\( 28 q + q^{3} - 7 q^{5} + 11 q^{7} - 22 q^{9} + q^{11} + 7 q^{13} - 24 q^{15} + 7 q^{17} - 7 q^{19} - 12 q^{21} + 34 q^{23} - 26 q^{25} - 11 q^{27} + 8 q^{29} - 17 q^{31} - 2 q^{33} - 6 q^{35} - 15 q^{37} + 4 q^{39} + 29 q^{41} - 8 q^{43} + 62 q^{45} - 27 q^{47} - 4 q^{49} + 69 q^{51} - 32 q^{53} + 19 q^{55} + 9 q^{57} - 37 q^{59} - 19 q^{61} + 46 q^{63} - 18 q^{65} + 10 q^{67} - 32 q^{69} - 27 q^{71} - 79 q^{75} + 13 q^{77} + 21 q^{79} - 18 q^{81} + 27 q^{83} + 7 q^{85} + 56 q^{87} + 82 q^{89} - 11 q^{91} - 53 q^{93} + 51 q^{95} - 88 q^{97} + 86 q^{99}+O(q^{100}) \) 28 * q + q^3 - 7 * q^5 + 11 * q^7 - 22 * q^9 + q^11 + 7 * q^13 - 24 * q^15 + 7 * q^17 - 7 * q^19 - 12 * q^21 + 34 * q^23 - 26 * q^25 - 11 * q^27 + 8 * q^29 - 17 * q^31 - 2 * q^33 - 6 * q^35 - 15 * q^37 + 4 * q^39 + 29 * q^41 - 8 * q^43 + 62 * q^45 - 27 * q^47 - 4 * q^49 + 69 * q^51 - 32 * q^53 + 19 * q^55 + 9 * q^57 - 37 * q^59 - 19 * q^61 + 46 * q^63 - 18 * q^65 + 10 * q^67 - 32 * q^69 - 27 * q^71 - 79 * q^75 + 13 * q^77 + 21 * q^79 - 18 * q^81 + 27 * q^83 + 7 * q^85 + 56 * q^87 + 82 * q^89 - 11 * q^91 - 53 * q^93 + 51 * q^95 - 88 * q^97 + 86 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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