LMFDB - Embedded newform 572.2.n.a.313.3

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:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 22 x^{18} - 72 x^{17} + 236 x^{16} - 556 x^{15} + 1232 x^{14} - 1981 x^{13} + \cdots + 400 $ x^20 - 4x^19 + 22x^18 - 72x^17 + 236x^16 - 556x^15 + 1232x^14 - 1981x^13 + 3407x^12 - 4130x^11 + 5358x^10 - 6093x^9 + 10112x^8 - 14136x^7 + 17259x^6 - 10035x^5 + 2921x^4 + 440x^3 + 560x^2 - 200*x + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			313.3
Root			$0.170304 + 0.524141i$ of defining polynomial
Character	$\chi$	$=$	572.313
Dual form			572.2.n.a.53.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.445861 + 0.323937i) q^{3} +(0.710005 - 2.18517i) q^{5} +(3.17229 - 2.30481i) q^{7} +(-0.833194 - 2.56431i) q^{9} +O(q^{10})$	\(q+(0.445861 + 0.323937i) q^{3} +(0.710005 - 2.18517i) q^{5} +(3.17229 - 2.30481i) q^{7} +(-0.833194 - 2.56431i) q^{9} +(-3.07538 + 1.24179i) q^{11} +(0.309017 + 0.951057i) q^{13} +(1.02442 - 0.744286i) q^{15} +(0.370358 - 1.13985i) q^{17} +(-5.34361 - 3.88236i) q^{19} +2.16101 q^{21} -4.07991 q^{23} +(-0.225784 - 0.164041i) q^{25} +(0.970096 - 2.98565i) q^{27} +(0.649571 - 0.471941i) q^{29} +(2.37682 + 7.31510i) q^{31} +(-1.77345 - 0.442564i) q^{33} +(-2.78405 - 8.56843i) q^{35} +(5.68378 - 4.12951i) q^{37} +(-0.170304 + 0.524141i) q^{39} +(3.10461 + 2.25563i) q^{41} +12.3660 q^{43} -6.19503 q^{45} +(9.33005 + 6.77868i) q^{47} +(2.58819 - 7.96564i) q^{49} +(0.534366 - 0.388240i) q^{51} +(-2.21636 - 6.82125i) q^{53} +(0.529988 + 7.60191i) q^{55} +(-1.12487 - 3.46199i) q^{57} +(-3.45262 + 2.50847i) q^{59} +(1.52592 - 4.69631i) q^{61} +(-8.55337 - 6.21438i) q^{63} +2.29763 q^{65} +4.27348 q^{67} +(-1.81907 - 1.32163i) q^{69} +(-3.32834 + 10.2436i) q^{71} +(-4.82278 + 3.50395i) q^{73} +(-0.0475291 - 0.146279i) q^{75} +(-6.89392 + 11.0275i) q^{77} +(2.82591 + 8.69726i) q^{79} +(-5.14430 + 3.73755i) q^{81} +(-0.235272 + 0.724094i) q^{83} +(-2.22780 - 1.61859i) q^{85} +0.442497 q^{87} +1.79022 q^{89} +(3.17229 + 2.30481i) q^{91} +(-1.30990 + 4.03146i) q^{93} +(-12.2776 + 8.92022i) q^{95} +(-2.14160 - 6.59118i) q^{97} +(5.74672 + 6.85157i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9}+O(q^{10}) $ 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9	$ 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9} - q^{11} - 5 q^{13} + 14 q^{15} - 3 q^{17} - 7 q^{19} - 32 q^{21} - 30 q^{23} - 12 q^{25} + 13 q^{27} - 14 q^{29} + 11 q^{31} - 10 q^{33} - 10 q^{35} + 45 q^{37} - 4 q^{39} + 9 q^{41} - 8 q^{43} - 34 q^{45} + 39 q^{47} + 30 q^{49} - 55 q^{51} + 36 q^{53} + 11 q^{55} - 31 q^{57} - 31 q^{59} - 7 q^{61} + 14 q^{63} - 14 q^{65} + 26 q^{67} + 32 q^{69} + 33 q^{71} - 44 q^{73} + 37 q^{75} - 73 q^{77} + 21 q^{79} + 16 q^{81} - 25 q^{83} + 15 q^{85} + 32 q^{87} - 2 q^{89} + 3 q^{91} + 33 q^{93} - 37 q^{95} + 52 q^{97} - 8 q^{99}+O(q^{100}) $ 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9 - q^11 - 5 * q^13 + 14 * q^15 - 3 * q^17 - 7 * q^19 - 32 * q^21 - 30 * q^23 - 12 * q^25 + 13 * q^27 - 14 * q^29 + 11 * q^31 - 10 * q^33 - 10 * q^35 + 45 * q^37 - 4 * q^39 + 9 * q^41 - 8 * q^43 - 34 * q^45 + 39 * q^47 + 30 * q^49 - 55 * q^51 + 36 * q^53 + 11 * q^55 - 31 * q^57 - 31 * q^59 - 7 * q^61 + 14 * q^63 - 14 * q^65 + 26 * q^67 + 32 * q^69 + 33 * q^71 - 44 * q^73 + 37 * q^75 - 73 * q^77 + 21 * q^79 + 16 * q^81 - 25 * q^83 + 15 * q^85 + 32 * q^87 - 2 * q^89 + 3 * q^91 + 33 * q^93 - 37 * q^95 + 52 * q^97 - 8 * 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
$3$	0.445861	+	0.323937i	0.257418	+	0.187025i	0.709008	−	0.705200i	$-0.249143\pi$
$3$	0.445861	+	0.323937i	0.257418	+	0.187025i	−0.451590	+	0.892226i	$0.649143\pi$
$4$		0			0
$5$	0.710005	−	2.18517i	0.317524	−	0.977239i	−0.657179	−	0.753735i	$-0.728250\pi$
$5$	0.710005	−	2.18517i	0.317524	−	0.977239i	0.974703	−	0.223504i	$-0.0717496\pi$
$6$		0			0
$7$	3.17229	−	2.30481i	1.19901	−	0.871135i	0.204826	−	0.978798i	$-0.434337\pi$
$7$	3.17229	−	2.30481i	1.19901	−	0.871135i	0.994187	+	0.107664i	$0.0343370\pi$
$8$		0			0
$9$	−0.833194	−	2.56431i	−0.277731	−	0.854769i
$10$		0			0
$11$	−3.07538	+	1.24179i	−0.927262	+	0.374414i
$11$	−3.07538	+	1.24179i	−0.927262	+	0.374414i
$12$		0			0
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$14$		0			0
$15$	1.02442	−	0.744286i	0.264505	−	0.192174i
$16$		0			0
$17$	0.370358	−	1.13985i	0.0898251	−	0.276453i	−0.896045	−	0.443962i	$-0.853572\pi$
$17$	0.370358	−	1.13985i	0.0898251	−	0.276453i	0.985871	+	0.167509i	$0.0535724\pi$
$18$		0			0
$19$	−5.34361	−	3.88236i	−1.22591	−	0.890675i	−0.229332	−	0.973348i	$-0.573654\pi$
$19$	−5.34361	−	3.88236i	−1.22591	−	0.890675i	−0.996577	+	0.0826732i	$0.973654\pi$
$20$		0			0
$21$	2.16101			0.471572
$22$		0			0
$23$	−4.07991			−0.850721			−0.425360	−	0.905024i	$-0.639853\pi$
$23$	−4.07991			−0.850721			−0.425360	+	0.905024i	$0.639853\pi$
$24$		0			0
$25$	−0.225784	−	0.164041i	−0.0451567	−	0.0328083i
$26$		0			0
$27$	0.970096	−	2.98565i	0.186695	−	0.574589i
$28$		0			0
$29$	0.649571	−	0.471941i	0.120622	−	0.0876372i	−0.525839	−	0.850584i	$-0.676248\pi$
$29$	0.649571	−	0.471941i	0.120622	−	0.0876372i	0.646461	+	0.762947i	$0.276248\pi$
$30$		0			0
$31$	2.37682	+	7.31510i	0.426889	+	1.31383i	0.901173	+	0.433459i	$0.142707\pi$
$31$	2.37682	+	7.31510i	0.426889	+	1.31383i	−0.474284	+	0.880372i	$0.657293\pi$
$32$		0			0
$33$	−1.77345	−	0.442564i	−0.308719	−	0.0770404i
$34$		0			0
$35$	−2.78405	−	8.56843i	−0.470591	−	1.44833i
$36$		0			0
$37$	5.68378	−	4.12951i	0.934408	−	0.678887i	−0.0126601	−	0.999920i	$-0.504030\pi$
$37$	5.68378	−	4.12951i	0.934408	−	0.678887i	0.947068	+	0.321033i	$0.104030\pi$
$38$		0			0
$39$	−0.170304	+	0.524141i	−0.0272704	+	0.0839297i
$40$		0			0
$41$	3.10461	+	2.25563i	0.484858	+	0.352270i	0.803204	−	0.595705i	$-0.203127\pi$
$41$	3.10461	+	2.25563i	0.484858	+	0.352270i	−0.318345	+	0.947975i	$0.603127\pi$
$42$		0			0
$43$	12.3660			1.88580			0.942898	−	0.333082i	$-0.108089\pi$
$43$	12.3660			1.88580			0.942898	+	0.333082i	$0.108089\pi$
$44$		0			0
$45$	−6.19503			−0.923500
$46$		0			0
$47$	9.33005	+	6.77868i	1.36093	+	0.988772i	0.998385	+	0.0568053i	$0.0180914\pi$
$47$	9.33005	+	6.77868i	1.36093	+	0.988772i	0.362543	+	0.931967i	$0.381909\pi$
$48$		0			0
$49$	2.58819	−	7.96564i	0.369742	−	1.13795i
$50$		0			0
$51$	0.534366	−	0.388240i	0.0748262	−	0.0543645i
$52$		0			0
$53$	−2.21636	−	6.82125i	−0.304440	−	0.936970i	−0.979886	−	0.199560i	$-0.936049\pi$
$53$	−2.21636	−	6.82125i	−0.304440	−	0.936970i	0.675445	−	0.737410i	$-0.263951\pi$
$54$		0			0
$55$	0.529988	+	7.60191i	0.0714635	+	1.02504i
$56$		0			0
$57$	−1.12487	−	3.46199i	−0.148992	−	0.458551i
$58$		0			0
$59$	−3.45262	+	2.50847i	−0.449492	+	0.326575i	−0.789395	−	0.613885i	$-0.789606\pi$
$59$	−3.45262	+	2.50847i	−0.449492	+	0.326575i	0.339903	+	0.940460i	$0.389606\pi$
$60$		0			0
$61$	1.52592	−	4.69631i	0.195374	−	0.601300i	−0.804598	−	0.593820i	$-0.797619\pi$
$61$	1.52592	−	4.69631i	0.195374	−	0.601300i	0.999972	−	0.00748002i	$-0.00238099\pi$
$62$		0			0
$63$	−8.55337	−	6.21438i	−1.07762	−	0.782939i
$64$		0			0
$65$	2.29763			0.284985
$66$		0			0
$67$	4.27348			0.522089			0.261044	−	0.965327i	$-0.415933\pi$
$67$	4.27348			0.522089			0.261044	+	0.965327i	$0.415933\pi$
$68$		0			0
$69$	−1.81907	−	1.32163i	−0.218991	−	0.159106i
$70$		0			0
$71$	−3.32834	+	10.2436i	−0.395001	+	1.21569i	0.533960	+	0.845510i	$0.320703\pi$
$71$	−3.32834	+	10.2436i	−0.395001	+	1.21569i	−0.928961	+	0.370178i	$0.879297\pi$
$72$		0			0
$73$	−4.82278	+	3.50395i	−0.564463	+	0.410106i	−0.833090	−	0.553138i	$-0.813430\pi$
$73$	−4.82278	+	3.50395i	−0.564463	+	0.410106i	0.268627	+	0.963244i	$0.413430\pi$
$74$		0			0
$75$	−0.0475291	−	0.146279i	−0.00548818	−	0.0168909i
$76$		0			0
$77$	−6.89392	+	11.0275i	−0.785635	+	1.25670i
$78$		0			0
$79$	2.82591	+	8.69726i	0.317940	+	0.978518i	0.974527	+	0.224268i	$0.0719991\pi$
$79$	2.82591	+	8.69726i	0.317940	+	0.978518i	−0.656588	+	0.754250i	$0.728001\pi$
$80$		0			0
$81$	−5.14430	+	3.73755i	−0.571589	+	0.415284i
$82$		0			0
$83$	−0.235272	+	0.724094i	−0.0258245	+	0.0794796i	−0.963138	−	0.269007i	$-0.913304\pi$
$83$	−0.235272	+	0.724094i	−0.0258245	+	0.0794796i	0.937314	+	0.348487i	$0.113304\pi$
$84$		0			0
$85$	−2.22780	−	1.61859i	−0.241639	−	0.175561i
$86$		0			0
$87$	0.442497			0.0474407
$88$		0			0
$89$	1.79022			0.189763			0.0948816	−	0.995489i	$-0.469753\pi$
$89$	1.79022			0.189763			0.0948816	+	0.995489i	$0.469753\pi$
$90$		0			0
$91$	3.17229	+	2.30481i	0.332547	+	0.241609i
$92$		0			0
$93$	−1.30990	+	4.03146i	−0.135830	+	0.418043i
$94$		0			0
$95$	−12.2776	+	8.92022i	−1.25966	+	0.915195i
$96$		0			0
$97$	−2.14160	−	6.59118i	−0.217447	−	0.669233i	−0.998971	−	0.0453575i	$-0.985557\pi$
$97$	−2.14160	−	6.59118i	−0.217447	−	0.669233i	0.781524	−	0.623875i	$-0.214443\pi$
$98$		0			0
$99$	5.74672	+	6.85157i	0.577567	+	0.688608i
$100$		0			0
$101$	−1.82370	−	5.61278i	−0.181465	−	0.558493i	0.818404	−	0.574643i	$-0.194859\pi$
$101$	−1.82370	−	5.61278i	−0.181465	−	0.558493i	−0.999870	+	0.0161502i	$0.994859\pi$
$102$		0			0
$103$	8.48359	−	6.16369i	0.835913	−	0.607326i	−0.0853131	−	0.996354i	$-0.527189\pi$
$103$	8.48359	−	6.16369i	0.835913	−	0.607326i	0.921226	+	0.389028i	$0.127189\pi$
$104$		0			0
$105$	1.53433	−	4.72218i	0.149735	−	0.460838i
$106$		0			0
$107$	−1.90575	−	1.38461i	−0.184236	−	0.133855i	0.491844	−	0.870683i	$-0.336323\pi$
$107$	−1.90575	−	1.38461i	−0.184236	−	0.133855i	−0.676080	+	0.736828i	$0.736323\pi$
$108$		0			0
$109$	−16.9879			−1.62715			−0.813573	−	0.581462i	$-0.802481\pi$
$109$	−16.9879			−1.62715			−0.813573	+	0.581462i	$0.802481\pi$
$110$		0			0
$111$	3.87188			0.367502
$112$		0			0
$113$	13.1199	+	9.53216i	1.23422	+	0.896710i	0.997199	−	0.0747958i	$-0.0238305\pi$
$113$	13.1199	+	9.53216i	1.23422	+	0.896710i	0.237016	+	0.971506i	$0.423831\pi$
$114$		0			0
$115$	−2.89676	+	8.91531i	−0.270124	+	0.831357i
$116$		0			0
$117$	2.18133	−	1.58483i	0.201664	−	0.146518i
$118$		0			0
$119$	−1.45224	−	4.46953i	−0.133126	−	0.409721i
$120$		0			0
$121$	7.91592	−	7.63795i	0.719629	−	0.694359i
$122$		0			0
$123$	0.653542	+	2.01139i	0.0589279	+	0.181361i
$124$		0			0
$125$	8.77532	−	6.37565i	0.784889	−	0.570255i
$126$		0			0
$127$	−2.16252	+	6.65555i	−0.191893	+	0.590585i	0.808106	+	0.589037i	$0.200493\pi$
$127$	−2.16252	+	6.65555i	−0.191893	+	0.590585i	−0.999999	+	0.00154797i	$0.999507\pi$
$128$		0			0
$129$	5.51351	+	4.00580i	0.485438	+	0.352691i
$130$		0			0
$131$	−13.3090			−1.16282			−0.581408	−	0.813612i	$-0.697498\pi$
$131$	−13.3090			−1.16282			−0.581408	+	0.813612i	$0.697498\pi$
$132$		0			0
$133$	−25.8996			−2.24578
$134$		0			0
$135$	−5.83538	−	4.23966i	−0.502230	−	0.364891i
$136$		0			0
$137$	−0.988089	+	3.04103i	−0.0844181	+	0.259812i	−0.984352	−	0.176215i	$-0.943615\pi$
$137$	−0.988089	+	3.04103i	−0.0844181	+	0.259812i	0.899934	+	0.436027i	$0.143615\pi$
$138$		0			0
$139$	−3.39492	+	2.46655i	−0.287953	+	0.209210i	−0.722379	−	0.691497i	$-0.756951\pi$
$139$	−3.39492	+	2.46655i	−0.287953	+	0.209210i	0.434426	+	0.900708i	$0.356951\pi$
$140$		0			0
$141$	1.96404	+	6.04470i	0.165402	+	0.509055i
$142$		0			0
$143$	−2.13136	−	2.54113i	−0.178233	−	0.212500i
$144$		0			0
$145$	−0.570073	−	1.75450i	−0.0473420	−	0.145704i
$146$		0			0
$147$	3.73434	−	2.71316i	0.308003	−	0.223777i
$148$		0			0
$149$	−3.27933	+	10.0927i	−0.268653	+	0.826830i	0.722176	+	0.691710i	$0.243142\pi$
$149$	−3.27933	+	10.0927i	−0.268653	+	0.826830i	−0.990829	+	0.135121i	$0.956858\pi$
$150$		0			0
$151$	5.77954	+	4.19908i	0.470332	+	0.341716i	0.797571	−	0.603225i	$-0.206118\pi$
$151$	5.77954	+	4.19908i	0.470332	+	0.341716i	−0.327238	+	0.944942i	$0.606118\pi$
$152$		0			0
$153$	−3.23149			−0.261251
$154$		0			0
$155$	17.6723			1.41947
$156$		0			0
$157$	15.8479	+	11.5142i	1.26480	+	0.918931i	0.998983	−	0.0450922i	$-0.0143581\pi$
$157$	15.8479	+	11.5142i	1.26480	+	0.918931i	0.265817	+	0.964023i	$0.414358\pi$
$158$		0			0
$159$	1.22147	−	3.75929i	0.0968686	−	0.298131i
$160$		0			0
$161$	−12.9427	+	9.40341i	−1.02003	+	0.741092i
$162$		0			0
$163$	7.09245	+	21.8283i	0.555523	+	1.70973i	0.694557	+	0.719437i	$0.255600\pi$
$163$	7.09245	+	21.8283i	0.555523	+	1.70973i	−0.139034	+	0.990288i	$0.544400\pi$
$164$		0			0
$165$	−2.22624	+	3.56108i	−0.173312	+	0.277229i
$166$		0			0
$167$	−4.16927	−	12.8317i	−0.322628	−	0.992946i	−0.972500	−	0.232903i	$-0.925178\pi$
$167$	−4.16927	−	12.8317i	−0.322628	−	0.992946i	0.649872	−	0.760043i	$-0.274822\pi$
$168$		0			0
$169$	−0.809017	+	0.587785i	−0.0622321	+	0.0452143i
$170$		0			0
$171$	−5.50330	+	16.9374i	−0.420848	+	1.29524i
$172$		0			0
$173$	2.11337	+	1.53546i	0.160677	+	0.116739i	0.665218	−	0.746649i	$-0.268338\pi$
$173$	2.11337	+	1.53546i	0.160677	+	0.116739i	−0.504542	+	0.863387i	$0.668338\pi$
$174$		0			0
$175$	−1.09434			−0.0827240
$176$		0			0
$177$	−2.35197			−0.176785
$178$		0			0
$179$	12.5765	+	9.13734i	0.940010	+	0.682957i	0.948423	−	0.317008i	$-0.102678\pi$
$179$	12.5765	+	9.13734i	0.940010	+	0.682957i	−0.00841345	+	0.999965i	$0.502678\pi$
$180$		0			0
$181$	1.44652	−	4.45192i	0.107519	−	0.330909i	−0.882795	−	0.469759i	$-0.844341\pi$
$181$	1.44652	−	4.45192i	0.107519	−	0.330909i	0.990313	+	0.138850i	$0.0443407\pi$
$182$		0			0
$183$	2.20166	−	1.59960i	0.162751	−	0.118246i
$184$		0			0
$185$	−4.98817	−	15.3520i	−0.366738	−	1.12870i
$186$		0			0
$187$	0.276456	+	3.96536i	0.0202165	+	0.289976i
$188$		0			0
$189$	−3.80391	−	11.7072i	−0.276694	−	0.851576i
$190$		0			0
$191$	−6.61955	+	4.80939i	−0.478974	+	0.347995i	−0.800928	−	0.598760i	$-0.795660\pi$
$191$	−6.61955	+	4.80939i	−0.478974	+	0.347995i	0.321954	+	0.946755i	$0.395660\pi$
$192$		0			0
$193$	2.00483	−	6.17024i	0.144311	−	0.444144i	−0.852611	−	0.522547i	$-0.824982\pi$
$193$	2.00483	−	6.17024i	0.144311	−	0.444144i	0.996922	+	0.0784030i	$0.0249821\pi$
$194$		0			0
$195$	1.02442	+	0.744286i	0.0733604	+	0.0532994i
$196$		0			0
$197$	−22.5295			−1.60516			−0.802581	−	0.596544i	$-0.796540\pi$
$197$	−22.5295			−1.60516			−0.802581	+	0.596544i	$0.796540\pi$
$198$		0			0
$199$	10.7674			0.763283			0.381642	−	0.924310i	$-0.375359\pi$
$199$	10.7674			0.763283			0.381642	+	0.924310i	$0.375359\pi$
$200$		0			0
$201$	1.90538	+	1.38434i	0.134395	+	0.0976437i
$202$		0			0
$203$	0.972896	−	2.99427i	0.0682839	−	0.210156i
$204$		0			0
$205$	7.13323	−	5.18259i	0.498206	−	0.361968i
$206$		0			0
$207$	3.39936	+	10.4622i	0.236272	+	0.727170i
$208$		0			0
$209$	21.2547	+	5.30409i	1.47022	+	0.366892i
$210$		0			0
$211$	−7.21958	−	22.2196i	−0.497017	−	1.52966i	−0.813790	−	0.581159i	$-0.802600\pi$
$211$	−7.21958	−	22.2196i	−0.497017	−	1.52966i	0.316774	−	0.948501i	$-0.397400\pi$
$212$		0			0
$213$	−4.80225	+	3.48904i	−0.329045	+	0.239065i
$214$		0			0
$215$	8.77992	−	27.0218i	0.598785	−	1.84287i
$216$		0			0
$217$	24.3998	+	17.7275i	1.65637	+	1.20342i
$218$		0			0
$219$	−3.28535			−0.222003
$220$		0			0
$221$	1.19850			0.0806201
$222$		0			0
$223$	−3.84841	−	2.79604i	−0.257709	−	0.187236i	0.451428	−	0.892308i	$-0.350915\pi$
$223$	−3.84841	−	2.79604i	−0.257709	−	0.187236i	−0.709136	+	0.705071i	$0.750915\pi$
$224$		0			0
$225$	−0.232531	+	0.715657i	−0.0155021	+	0.0477105i
$226$		0			0
$227$	−18.0389	+	13.1060i	−1.19728	+	0.869877i	−0.994015	−	0.109246i	$-0.965156\pi$
$227$	−18.0389	+	13.1060i	−1.19728	+	0.869877i	−0.203268	+	0.979123i	$0.565156\pi$
$228$		0			0
$229$	−2.85778	−	8.79535i	−0.188847	−	0.581213i	0.811146	−	0.584844i	$-0.198844\pi$
$229$	−2.85778	−	8.79535i	−0.188847	−	0.581213i	−0.999993	+	0.00363102i	$0.998844\pi$
$230$		0			0
$231$	−6.64593	+	2.68352i	−0.437270	+	0.176563i
$232$		0			0
$233$	−0.240837	−	0.741221i	−0.0157778	−	0.0485590i	0.942858	−	0.333196i	$-0.108127\pi$
$233$	−0.240837	−	0.741221i	−0.0157778	−	0.0485590i	−0.958635	+	0.284637i	$0.908127\pi$
$234$		0			0
$235$	21.4370	−	15.5749i	1.39839	−	1.01599i
$236$		0			0
$237$	−1.55740	+	4.79318i	−0.101164	+	0.311351i
$238$		0			0
$239$	−12.7579	−	9.26915i	−0.825239	−	0.599571i	0.0929692	−	0.995669i	$-0.470364\pi$
$239$	−12.7579	−	9.26915i	−0.825239	−	0.599571i	−0.918208	+	0.396098i	$0.870364\pi$
$240$		0			0
$241$	8.37811			0.539681			0.269841	−	0.962905i	$-0.413029\pi$
$241$	8.37811			0.539681			0.269841	+	0.962905i	$0.413029\pi$
$242$		0			0
$243$	−12.9223			−0.828964
$244$		0			0
$245$	−15.5687	−	11.3113i	−0.994645	−	0.722652i
$246$		0			0
$247$	2.04108	−	6.28179i	0.129871	−	0.399701i
$248$		0			0
$249$	−0.339459	+	0.246632i	−0.0215124	+	0.0156296i
$250$		0			0
$251$	1.88492	+	5.80119i	0.118975	+	0.366168i	0.992755	−	0.120153i	$-0.0383386\pi$
$251$	1.88492	+	5.80119i	0.118975	+	0.366168i	−0.873780	+	0.486321i	$0.838339\pi$
$252$		0			0
$253$	12.5473	−	5.06639i	0.788841	−	0.318522i
$254$		0			0
$255$	−0.468968	−	1.44333i	−0.0293679	−	0.0903851i
$256$		0			0
$257$	−0.566228	+	0.411389i	−0.0353203	+	0.0256617i	−0.605305	−	0.795993i	$-0.706949\pi$
$257$	−0.566228	+	0.411389i	−0.0353203	+	0.0256617i	0.569985	+	0.821655i	$0.306949\pi$
$258$		0			0
$259$	8.51290	−	26.2000i	0.528966	−	1.62799i
$260$		0			0
$261$	−1.75142	−	1.27248i	−0.108410	−	0.0787646i
$262$		0			0
$263$	−27.6342			−1.70400			−0.852000	−	0.523542i	$-0.824610\pi$
$263$	−27.6342			−1.70400			−0.852000	+	0.523542i	$0.824610\pi$
$264$		0			0
$265$	−16.4792			−1.01231
$266$		0			0
$267$	0.798190	+	0.579919i	0.0488485	+	0.0354905i
$268$		0			0
$269$	7.33610	−	22.5782i	0.447290	−	1.37662i	−0.432663	−	0.901556i	$-0.642426\pi$
$269$	7.33610	−	22.5782i	0.447290	−	1.37662i	0.879953	−	0.475061i	$-0.157574\pi$
$270$		0			0
$271$	−14.3388	+	10.4178i	−0.871021	+	0.632834i	−0.930861	−	0.365374i	$-0.880941\pi$
$271$	−14.3388	+	10.4178i	−0.871021	+	0.632834i	0.0598399	+	0.998208i	$0.480941\pi$
$272$		0			0
$273$	0.667790	+	2.05525i	0.0404165	+	0.124389i
$274$		0			0
$275$	0.898076	+	0.224114i	0.0541560	+	0.0135146i
$276$		0			0
$277$	−6.06240	−	18.6581i	−0.364254	−	1.12106i	−0.950447	−	0.310887i	$-0.899374\pi$
$277$	−6.06240	−	18.6581i	−0.364254	−	1.12106i	0.586193	−	0.810172i	$-0.300626\pi$
$278$		0			0
$279$	16.7778	−	12.1898i	1.00446	−	0.729784i
$280$		0			0
$281$	8.11026	−	24.9608i	0.483818	−	1.48904i	−0.349869	−	0.936799i	$-0.613774\pi$
$281$	8.11026	−	24.9608i	0.483818	−	1.48904i	0.833686	−	0.552239i	$-0.186226\pi$
$282$		0			0
$283$	21.3641	+	15.5220i	1.26997	+	0.922685i	0.999201	−	0.0399605i	$-0.0127232\pi$
$283$	21.3641	+	15.5220i	1.26997	+	0.922685i	0.270766	+	0.962645i	$0.412723\pi$
$284$		0			0
$285$	−8.36370			−0.495423
$286$		0			0
$287$	15.0475			0.888226
$288$		0			0
$289$	12.5912	+	9.14805i	0.740659	+	0.538120i
$290$		0			0
$291$	1.18027	−	3.63249i	0.0691886	−	0.212941i
$292$		0			0
$293$	−21.8074	+	15.8440i	−1.27400	+	0.925617i	−0.999354	−	0.0359279i	$-0.988561\pi$
$293$	−21.8074	+	15.8440i	−1.27400	+	0.925617i	−0.274648	+	0.961545i	$0.588561\pi$
$294$		0			0
$295$	3.03007	+	9.32559i	0.176417	+	0.542957i
$296$		0			0
$297$	0.724134	+	10.3867i	0.0420185	+	0.602695i
$298$		0			0
$299$	−1.26076	−	3.88023i	−0.0729118	−	0.224399i
$300$		0			0
$301$	39.2285	−	28.5012i	2.26109	−	1.64278i
$302$		0			0
$303$	1.00507	−	3.09328i	0.0577397	−	0.177705i
$304$		0			0
$305$	−9.17882	−	6.66880i	−0.525578	−	0.381855i
$306$		0			0
$307$	4.05292			0.231312			0.115656	−	0.993289i	$-0.463103\pi$
$307$	4.05292			0.231312			0.115656	+	0.993289i	$0.463103\pi$
$308$		0			0
$309$	5.77915			0.328764
$310$		0			0
$311$	11.6251	+	8.44614i	0.659200	+	0.478937i	0.866393	−	0.499363i	$-0.166433\pi$
$311$	11.6251	+	8.44614i	0.659200	+	0.478937i	−0.207193	+	0.978300i	$0.566433\pi$
$312$		0			0
$313$	−5.68174	+	17.4866i	−0.321151	+	0.988401i	0.651997	+	0.758221i	$0.273931\pi$
$313$	−5.68174	+	17.4866i	−0.321151	+	0.988401i	−0.973148	+	0.230180i	$0.926069\pi$
$314$		0			0
$315$	−19.6524	+	14.2783i	−1.10729	+	0.804493i
$316$		0			0
$317$	−6.60427	−	20.3258i	−0.370933	−	1.14161i	−0.946182	−	0.323635i	$-0.895095\pi$
$317$	−6.60427	−	20.3258i	−0.370933	−	1.14161i	0.575249	−	0.817978i	$-0.304905\pi$
$318$		0			0
$319$	−1.41163	+	2.25803i	−0.0790358	+	0.126425i
$320$		0			0
$321$	−0.401174	−	1.23469i	−0.0223914	−	0.0689135i
$322$		0			0
$323$	−6.40434	+	4.65303i	−0.356347	+	0.258901i
$324$		0			0
$325$	0.0862417	−	0.265425i	0.00478383	−	0.0147231i
$326$		0			0
$327$	−7.57425	−	5.50301i	−0.418857	−	0.304317i
$328$		0			0
$329$	45.2212			2.49313
$330$		0			0
$331$	−28.4233			−1.56228			−0.781142	−	0.624353i	$-0.785363\pi$
$331$	−28.4233			−1.56228			−0.781142	+	0.624353i	$0.785363\pi$
$332$		0			0
$333$	−15.3250	−	11.1343i	−0.839806	−	0.610155i
$334$		0			0
$335$	3.03419	−	9.33829i	0.165776	−	0.510205i
$336$		0			0
$337$	10.9892	−	7.98410i	0.598618	−	0.434922i	−0.246770	−	0.969074i	$-0.579369\pi$
$337$	10.9892	−	7.98410i	0.598618	−	0.434922i	0.845388	+	0.534152i	$0.179369\pi$
$338$		0			0
$339$	2.76183	+	8.50003i	0.150002	+	0.461658i
$340$		0			0
$341$	−16.3934	−	19.5452i	−0.887754	−	1.05843i
$342$		0			0
$343$	−1.66678	−	5.12984i	−0.0899979	−	0.276985i
$344$		0			0
$345$	−4.17955	+	3.03662i	−0.225020	+	0.163486i
$346$		0			0
$347$	−0.310593	+	0.955908i	−0.0166735	+	0.0513158i	−0.959047	−	0.283247i	$-0.908589\pi$
$347$	−0.310593	+	0.955908i	−0.0166735	+	0.0513158i	0.942374	+	0.334562i	$0.108589\pi$
$348$		0			0
$349$	21.7797	+	15.8239i	1.16584	+	0.847034i	0.990505	−	0.137474i	$-0.0438983\pi$
$349$	21.7797	+	15.8239i	1.16584	+	0.847034i	0.175338	+	0.984508i	$0.443898\pi$
$350$		0			0
$351$	3.13930			0.167563
$352$		0			0
$353$	−16.1634			−0.860293			−0.430147	−	0.902759i	$-0.641538\pi$
$353$	−16.1634			−0.860293			−0.430147	+	0.902759i	$0.641538\pi$
$354$		0			0
$355$	20.0208	+	14.5460i	1.06260	+	0.772021i
$356$		0			0
$357$	0.800349	−	2.46322i	0.0423590	−	0.130367i
$358$		0			0
$359$	29.0994	−	21.1420i	1.53581	−	1.11583i	0.582914	−	0.812534i	$-0.301912\pi$
$359$	29.0994	−	21.1420i	1.53581	−	1.11583i	0.952896	−	0.303298i	$-0.0980877\pi$
$360$		0			0
$361$	7.61014	+	23.4216i	0.400534	+	1.23272i
$362$		0			0
$363$	6.00361	−	0.841205i	0.315108	−	0.0441518i
$364$		0			0
$365$	4.23254	+	13.0264i	0.221541	+	0.681834i
$366$		0			0
$367$	−19.4040	+	14.0978i	−1.01288	+	0.735899i	−0.964811	−	0.262945i	$-0.915306\pi$
$367$	−19.4040	+	14.0978i	−1.01288	+	0.735899i	−0.0480676	+	0.998844i	$0.515306\pi$
$368$		0			0
$369$	3.19739	−	9.84055i	0.166449	−	0.512278i
$370$		0			0
$371$	−22.7526	−	16.5307i	−1.18126	−	0.858232i
$372$		0			0
$373$	15.5226			0.803728			0.401864	−	0.915699i	$-0.368363\pi$
$373$	15.5226			0.803728			0.401864	+	0.915699i	$0.368363\pi$
$374$		0			0
$375$	5.97788			0.308696
$376$		0			0
$377$	0.649571	+	0.471941i	0.0334546	+	0.0243062i
$378$		0			0
$379$	9.83468	−	30.2680i	0.505173	−	1.55476i	−0.295305	−	0.955403i	$-0.595421\pi$
$379$	9.83468	−	30.2680i	0.505173	−	1.55476i	0.800479	−	0.599361i	$-0.204579\pi$
$380$		0			0
$381$	−3.12016	+	2.26693i	−0.159851	+	0.116138i
$382$		0			0
$383$	−8.79040	−	27.0541i	−0.449168	−	1.38240i	−0.877847	−	0.478941i	$-0.841021\pi$
$383$	−8.79040	−	27.0541i	−0.449168	−	1.38240i	0.428679	−	0.903457i	$-0.358979\pi$
$384$		0			0
$385$	19.2022	+	22.8940i	0.978635	+	1.16678i
$386$		0			0
$387$	−10.3033	−	31.7102i	−0.523745	−	1.61192i
$388$		0			0
$389$	−0.528146	+	0.383721i	−0.0267781	+	0.0194554i	−0.601094	−	0.799178i	$-0.705268\pi$
$389$	−0.528146	+	0.383721i	−0.0267781	+	0.0194554i	0.574316	+	0.818634i	$0.305268\pi$
$390$		0			0
$391$	−1.51103	+	4.65047i	−0.0764161	+	0.235184i
$392$		0			0
$393$	−5.93398	−	4.31129i	−0.299330	−	0.217476i
$394$		0			0
$395$	21.0114			1.05720
$396$		0			0
$397$	−20.2508			−1.01636			−0.508180	−	0.861251i	$-0.669681\pi$
$397$	−20.2508			−1.01636			−0.508180	+	0.861251i	$0.669681\pi$
$398$		0			0
$399$	−11.5476	−	8.38983i	−0.578104	−	0.420017i
$400$		0			0
$401$	−7.99498	+	24.6060i	−0.399250	+	1.22877i	0.526351	+	0.850267i	$0.323560\pi$
$401$	−7.99498	+	24.6060i	−0.399250	+	1.22877i	−0.925602	+	0.378499i	$0.876440\pi$
$402$		0			0
$403$	−6.22259	+	4.52098i	−0.309970	+	0.225206i
$404$		0			0
$405$	4.51472	+	13.8949i	0.224338	+	0.690441i
$406$		0			0
$407$	−12.3518	+	19.7579i	−0.612256	+	0.979361i
$408$		0			0
$409$	2.31490	+	7.12452i	0.114464	+	0.352285i	0.991835	−	0.127528i	$-0.0407044\pi$
$409$	2.31490	+	7.12452i	0.114464	+	0.352285i	−0.877371	+	0.479813i	$0.840704\pi$
$410$		0			0
$411$	−1.42565	+	1.03580i	−0.0703222	+	0.0510920i
$412$		0			0
$413$	−5.17117	+	15.9152i	−0.254456	+	0.783136i
$414$		0			0
$415$	1.41522	+	1.02822i	0.0694706	+	0.0504734i
$416$		0			0
$417$	−2.31267			−0.113252
$418$		0			0
$419$	−6.25748			−0.305698			−0.152849	−	0.988250i	$-0.548845\pi$
$419$	−6.25748			−0.305698			−0.152849	+	0.988250i	$0.548845\pi$
$420$		0			0
$421$	1.16258	+	0.844666i	0.0566609	+	0.0411665i	0.615755	−	0.787938i	$-0.288851\pi$
$421$	1.16258	+	0.844666i	0.0566609	+	0.0411665i	−0.559094	+	0.829104i	$0.688851\pi$
$422$		0			0
$423$	9.60888	−	29.5731i	0.467200	−	1.43789i
$424$		0			0
$425$	−0.270603	+	0.196604i	−0.0131262	+	0.00953672i
$426$		0			0
$427$	−5.98340	−	18.4150i	−0.289557	−	0.891165i
$428$		0			0
$429$	−0.127124	−	1.82341i	−0.00613761	−	0.0880352i
$430$		0			0
$431$	5.94439	+	18.2949i	0.286331	+	0.881236i	0.985997	+	0.166766i	$0.0533323\pi$
$431$	5.94439	+	18.2949i	0.286331	+	0.881236i	−0.699666	+	0.714470i	$0.746668\pi$
$432$		0			0
$433$	1.03362	−	0.750966i	0.0496724	−	0.0360891i	−0.562672	−	0.826680i	$-0.690227\pi$
$433$	1.03362	−	0.750966i	0.0496724	−	0.0360891i	0.612344	+	0.790591i	$0.290227\pi$
$434$		0			0
$435$	0.314175	−	0.966932i	0.0150636	−	0.0463609i
$436$		0			0
$437$	21.8015	+	15.8397i	1.04291	+	0.757716i
$438$		0			0
$439$	−3.18226			−0.151881			−0.0759404	−	0.997112i	$-0.524196\pi$
$439$	−3.18226			−0.151881			−0.0759404	+	0.997112i	$0.524196\pi$
$440$		0			0
$441$	−22.5828			−1.07537
$442$		0			0
$443$	18.3886	+	13.3601i	0.873668	+	0.634757i	0.931569	−	0.363565i	$-0.118441\pi$
$443$	18.3886	+	13.3601i	0.873668	+	0.634757i	−0.0579008	+	0.998322i	$0.518441\pi$
$444$		0			0
$445$	1.27107	−	3.91194i	0.0602544	−	0.185444i
$446$		0			0
$447$	−4.73154	+	3.43767i	−0.223794	+	0.162596i
$448$		0			0
$449$	12.8139	+	39.4371i	0.604725	+	1.86115i	0.498668	+	0.866793i	$0.333823\pi$
$449$	12.8139	+	39.4371i	0.604725	+	1.86115i	0.106057	+	0.994360i	$0.466177\pi$
$450$		0			0
$451$	−12.3489	−	3.08165i	−0.581485	−	0.145109i
$452$		0			0
$453$	1.21663	+	3.74441i	0.0571624	+	0.175928i
$454$		0			0
$455$	7.28874	−	5.29558i	0.341701	−	0.248261i
$456$		0			0
$457$	−1.74096	+	5.35811i	−0.0814384	+	0.250642i	−0.983483	−	0.181002i	$-0.942066\pi$
$457$	−1.74096	+	5.35811i	−0.0814384	+	0.250642i	0.902044	+	0.431643i	$0.142066\pi$
$458$		0			0
$459$	−3.04390	−	2.21152i	−0.142077	−	0.103225i
$460$		0			0
$461$	−32.1106			−1.49554			−0.747769	−	0.663959i	$-0.768875\pi$
$461$	−32.1106			−1.49554			−0.747769	+	0.663959i	$0.768875\pi$
$462$		0			0
$463$	8.41875			0.391253			0.195626	−	0.980679i	$-0.437326\pi$
$463$	8.41875			0.391253			0.195626	+	0.980679i	$0.437326\pi$
$464$		0			0
$465$	7.87939	+	5.72471i	0.365398	+	0.265477i
$466$		0			0
$467$	4.86783	−	14.9816i	0.225256	−	0.693267i	−0.773009	−	0.634395i	$-0.781249\pi$
$467$	4.86783	−	14.9816i	0.225256	−	0.693267i	0.998266	−	0.0588726i	$-0.0187506\pi$
$468$		0			0
$469$	13.5567	−	9.84954i	0.625991	−	0.454809i
$470$		0			0
$471$	3.33609	+	10.2674i	0.153719	+	0.473099i
$472$		0			0
$473$	−38.0301	+	15.3560i	−1.74863	+	0.706068i
$474$		0			0
$475$	0.569632	+	1.75315i	0.0261365	+	0.0804400i
$476$		0			0
$477$	−15.6451	+	11.3668i	−0.716341	+	0.520452i
$478$		0			0
$479$	4.03026	−	12.4039i	0.184147	−	0.566747i	−0.815785	−	0.578355i	$-0.803695\pi$
$479$	4.03026	−	12.4039i	0.184147	−	0.566747i	0.999933	+	0.0116080i	$0.00369501\pi$
$480$		0			0
$481$	5.68378	+	4.12951i	0.259158	+	0.188289i
$482$		0			0
$483$	−8.81675			−0.401176
$484$		0			0
$485$	−15.9234			−0.723045
$486$		0			0
$487$	−34.8394	−	25.3123i	−1.57872	−	1.14701i	−0.918139	−	0.396259i	$-0.870308\pi$
$487$	−34.8394	−	25.3123i	−1.57872	−	1.14701i	−0.660585	−	0.750751i	$-0.729692\pi$
$488$		0			0
$489$	−3.90875	+	12.0299i	−0.176760	+	0.544011i
$490$		0			0
$491$	−7.40743	+	5.38181i	−0.334292	+	0.242878i	−0.742250	−	0.670123i	$-0.766241\pi$
$491$	−7.40743	+	5.38181i	−0.334292	+	0.242878i	0.407957	+	0.913001i	$0.366241\pi$
$492$		0			0
$493$	−0.297366	−	0.915197i	−0.0133927	−	0.0412184i
$494$		0			0
$495$	19.0521	−	7.69292i	0.856326	−	0.345771i
$496$		0			0
$497$	13.0510	+	40.1668i	0.585416	+	1.80173i
$498$		0			0
$499$	−4.28785	+	3.11530i	−0.191950	+	0.139460i	−0.679610	−	0.733574i	$-0.737851\pi$
$499$	−4.28785	+	3.11530i	−0.191950	+	0.139460i	0.487659	+	0.873034i	$0.337851\pi$
$500$		0			0
$501$	2.29774	−	7.07173i	0.102656	−	0.315942i
$502$		0			0
$503$	11.7504	+	8.53716i	0.523924	+	0.380653i	0.818080	−	0.575104i	$-0.195039\pi$
$503$	11.7504	+	8.53716i	0.523924	+	0.380653i	−0.294156	+	0.955757i	$0.595039\pi$
$504$		0			0
$505$	−13.5597			−0.603400
$506$		0			0
$507$	−0.551114			−0.0244759
$508$		0			0
$509$	31.4899	+	22.8787i	1.39576	+	1.01408i	0.995205	+	0.0978109i	$0.0311840\pi$
$509$	31.4899	+	22.8787i	1.39576	+	1.01408i	0.400559	+	0.916271i	$0.368816\pi$
$510$		0			0
$511$	−7.22333	+	22.2311i	−0.319541	+	0.983447i
$512$		0			0
$513$	−16.7752	+	12.1879i	−0.740643	+	0.538109i
$514$		0			0
$515$	−7.44532	−	22.9144i	−0.328080	−	1.00973i
$516$		0			0
$517$	−37.1112	−	9.26105i	−1.63215	−	0.407301i
$518$		0			0
$519$	0.444880	+	1.36920i	0.0195281	+	0.0601012i
$520$		0			0
$521$	28.4180	−	20.6469i	1.24502	−	0.904558i	0.247095	−	0.968991i	$-0.420524\pi$
$521$	28.4180	−	20.6469i	1.24502	−	0.904558i	0.997922	+	0.0644335i	$0.0205240\pi$
$522$		0			0
$523$	−0.601303	+	1.85062i	−0.0262931	+	0.0809220i	−0.963342	−	0.268276i	$-0.913546\pi$
$523$	−0.601303	+	1.85062i	−0.0262931	+	0.0809220i	0.937049	+	0.349198i	$0.113546\pi$
$524$		0			0
$525$	−0.487922	−	0.354496i	−0.0212946	−	0.0154715i
$526$		0			0
$527$	9.21836			0.401558
$528$		0			0
$529$	−6.35430			−0.276274
$530$		0			0
$531$	9.30919	+	6.76352i	0.403985	+	0.293512i
$532$		0			0
$533$	−1.18585	+	3.64969i	−0.0513651	+	0.158085i
$534$		0			0
$535$	−4.37871	+	3.18132i	−0.189308	+	0.137540i
$536$		0			0
$537$	2.64743	+	8.14797i	0.114245	+	0.351611i
$538$		0			0
$539$	1.93197	+	27.7113i	0.0832159	+	1.19361i
$540$		0			0
$541$	8.58493	+	26.4217i	0.369095	+	1.13596i	0.947377	+	0.320120i	$0.103723\pi$
$541$	8.58493	+	26.4217i	0.369095	+	1.13596i	−0.578282	+	0.815837i	$0.696277\pi$
$542$		0			0
$543$	2.08709	−	1.51636i	0.0895655	−	0.0650731i
$544$		0			0
$545$	−12.0615	+	37.1215i	−0.516658	+	1.59011i
$546$		0			0
$547$	−15.5767	−	11.3171i	−0.666011	−	0.483885i	0.202677	−	0.979246i	$-0.435036\pi$
$547$	−15.5767	−	11.3171i	−0.666011	−	0.483885i	−0.868687	+	0.495361i	$0.835036\pi$
$548$		0			0
$549$	−13.3142			−0.568235
$550$		0			0
$551$	−5.30330			−0.225928
$552$		0			0
$553$	29.0101	+	21.0771i	1.23363	+	0.896288i
$554$		0			0
$555$	2.74905	−	8.46072i	0.116691	−	0.359137i
$556$		0			0
$557$	−19.5570	+	14.2090i	−0.828659	+	0.602056i	−0.919180	−	0.393839i	$-0.871147\pi$
$557$	−19.5570	+	14.2090i	−0.828659	+	0.602056i	0.0905208	+	0.995895i	$0.471147\pi$
$558$		0			0
$559$	3.82130	+	11.7608i	0.161624	+	0.497427i
$560$		0			0
$561$	−1.16127	+	1.85756i	−0.0490287	+	0.0784260i
$562$		0			0
$563$	−5.36535	−	16.5129i	−0.226123	−	0.695934i	−0.998176	−	0.0603760i	$-0.980770\pi$
$563$	−5.36535	−	16.5129i	−0.226123	−	0.695934i	0.772053	−	0.635558i	$-0.219230\pi$
$564$		0			0
$565$	30.1446	−	21.9013i	1.26819	−	0.921396i
$566$		0			0
$567$	−7.70489	+	23.7132i	−0.323575	+	0.995862i
$568$		0			0
$569$	−28.5551	−	20.7465i	−1.19709	−	0.869739i	−0.203098	−	0.979158i	$-0.565101\pi$
$569$	−28.5551	−	20.7465i	−1.19709	−	0.869739i	−0.993996	+	0.109419i	$0.965101\pi$
$570$		0			0
$571$	3.83418			0.160456			0.0802278	−	0.996777i	$-0.474435\pi$
$571$	3.83418			0.160456			0.0802278	+	0.996777i	$0.474435\pi$
$572$		0			0
$573$	−4.50934			−0.188380
$574$		0			0
$575$	0.921178	+	0.669275i	0.0384158	+	0.0279107i
$576$		0			0
$577$	−6.06269	+	18.6590i	−0.252393	+	0.776786i	0.741939	+	0.670467i	$0.233906\pi$
$577$	−6.06269	+	18.6590i	−0.252393	+	0.776786i	−0.994332	+	0.106319i	$0.966094\pi$
$578$		0			0
$579$	2.89264	−	2.10163i	0.120214	−	0.0873407i
$580$		0			0
$581$	0.922542	+	2.83929i	0.0382735	+	0.117794i
$582$		0			0
$583$	15.2867	+	18.2257i	0.633110	+	0.754830i
$584$		0			0
$585$	−1.91437	−	5.89182i	−0.0791494	−	0.243597i
$586$		0			0
$587$	26.1479	−	18.9976i	1.07924	−	0.784114i	0.101689	−	0.994816i	$-0.467575\pi$
$587$	26.1479	−	18.9976i	1.07924	−	0.784114i	0.977550	+	0.210703i	$0.0675752\pi$
$588$		0			0
$589$	15.6991	−	48.3167i	0.646868	−	1.99086i
$590$		0			0
$591$	−10.0450	−	7.29814i	−0.413197	−	0.300205i
$592$		0			0
$593$	28.7043			1.17874			0.589372	−	0.807862i	$-0.299375\pi$
$593$	28.7043			1.17874			0.589372	+	0.807862i	$0.299375\pi$
$594$		0			0
$595$	−10.7978			−0.442666
$596$		0			0
$597$	4.80078	+	3.48797i	0.196483	+	0.142753i
$598$		0			0
$599$	2.24226	−	6.90098i	0.0916164	−	0.281966i	−0.894741	−	0.446586i	$-0.852640\pi$
$599$	2.24226	−	6.90098i	0.0916164	−	0.281966i	0.986357	+	0.164620i	$0.0526397\pi$
$600$		0			0
$601$	22.3406	−	16.2314i	0.911293	−	0.662093i	−0.0300484	−	0.999548i	$-0.509566\pi$
$601$	22.3406	−	16.2314i	0.911293	−	0.662093i	0.941342	+	0.337455i	$0.109566\pi$
$602$		0			0
$603$	−3.56064	−	10.9585i	−0.145000	−	0.446265i
$604$		0			0
$605$	−11.0699	−	22.7206i	−0.450055	−	0.923725i
$606$		0			0
$607$	−3.17191	−	9.76213i	−0.128744	−	0.396233i	0.865821	−	0.500354i	$-0.166797\pi$
$607$	−3.17191	−	9.76213i	−0.128744	−	0.396233i	−0.994565	+	0.104122i	$0.966797\pi$
$608$		0			0
$609$	1.40373	−	1.01987i	0.0568820	−	0.0413272i
$610$		0			0
$611$	−3.56376	+	10.9681i	−0.144174	+	0.443723i
$612$		0			0
$613$	−21.3554	−	15.5156i	−0.862538	−	0.626671i	0.0660361	−	0.997817i	$-0.478965\pi$
$613$	−21.3554	−	15.5156i	−0.862538	−	0.626671i	−0.928574	+	0.371147i	$0.878965\pi$
$614$		0			0
$615$	4.85926			0.195944
$616$		0			0
$617$	27.8864			1.12267			0.561333	−	0.827590i	$-0.310289\pi$
$617$	27.8864			1.12267			0.561333	+	0.827590i	$0.310289\pi$
$618$		0			0
$619$	−4.93321	−	3.58419i	−0.198282	−	0.144061i	0.484214	−	0.874950i	$-0.339106\pi$
$619$	−4.93321	−	3.58419i	−0.198282	−	0.144061i	−0.682496	+	0.730889i	$0.739106\pi$
$620$		0			0
$621$	−3.95791	+	12.1812i	−0.158825	+	0.488815i
$622$		0			0
$623$	5.67911	−	4.12611i	0.227529	−	0.165309i
$624$		0			0
$625$	−8.13256	−	25.0295i	−0.325303	−	1.00118i
$626$		0			0
$627$	7.75846	+	9.25008i	0.309843	+	0.369412i
$628$		0			0
$629$	−2.60197	−	8.00803i	−0.103747	−	0.319301i
$630$		0			0
$631$	−14.1996	+	10.3166i	−0.565276	+	0.410697i	−0.833386	−	0.552691i	$-0.813601\pi$
$631$	−14.1996	+	10.3166i	−0.565276	+	0.410697i	0.268110	+	0.963388i	$0.413601\pi$
$632$		0			0
$633$	3.97882	−	12.2455i	0.158144	−	0.486716i
$634$		0			0
$635$	13.0081	+	9.45096i	0.516212	+	0.375050i
$636$		0			0
$637$	8.37557			0.331852
$638$		0			0
$639$	29.0408			1.14884
$640$		0			0
$641$	−14.2425	−	10.3478i	−0.562544	−	0.408712i	0.269845	−	0.962904i	$-0.413027\pi$
$641$	−14.2425	−	10.3478i	−0.562544	−	0.408712i	−0.832389	+	0.554192i	$0.813027\pi$
$642$		0			0
$643$	−12.1469	+	37.3844i	−0.479029	+	1.47430i	0.361418	+	0.932404i	$0.382293\pi$
$643$	−12.1469	+	37.3844i	−0.479029	+	1.47430i	−0.840446	+	0.541895i	$0.817707\pi$
$644$		0			0
$645$	12.6680	−	9.20383i	0.498801	−	0.362400i
$646$		0			0
$647$	0.257265	+	0.791781i	0.0101141	+	0.0311281i	0.955986	−	0.293412i	$-0.0947906\pi$
$647$	0.257265	+	0.791781i	0.0101141	+	0.0311281i	−0.945872	+	0.324540i	$0.894791\pi$
$648$		0			0
$649$	7.50311	−	12.0019i	0.294523	−	0.471117i
$650$		0			0
$651$	5.13634	+	15.8080i	0.201309	+	0.619565i
$652$		0			0
$653$	−14.1284	+	10.2649i	−0.552886	+	0.401695i	−0.828848	−	0.559473i	$-0.811004\pi$
$653$	−14.1284	+	10.2649i	−0.552886	+	0.401695i	0.275962	+	0.961168i	$0.411004\pi$
$654$		0			0
$655$	−9.44949	+	29.0825i	−0.369222	+	1.13635i
$656$		0			0
$657$	13.0035	+	9.44761i	0.507316	+	0.368586i
$658$		0			0
$659$	6.34626			0.247215			0.123608	−	0.992331i	$-0.460554\pi$
$659$	6.34626			0.247215			0.123608	+	0.992331i	$0.460554\pi$
$660$		0			0
$661$	−3.68612			−0.143374			−0.0716868	−	0.997427i	$-0.522838\pi$
$661$	−3.68612			−0.143374			−0.0716868	+	0.997427i	$0.522838\pi$
$662$		0			0
$663$	0.534366	+	0.388240i	0.0207531	+	0.0150780i
$664$		0			0
$665$	−18.3889	+	56.5951i	−0.713089	+	2.19466i
$666$		0			0
$667$	−2.65019	+	1.92548i	−0.102616	+	0.0745548i
$668$		0			0
$669$	−0.810118	−	2.49329i	−0.0313210	−	0.0963960i
$670$		0			0
$671$	1.13903	+	16.3378i	0.0439719	+	0.630714i
$672$		0			0
$673$	−1.17669	−	3.62148i	−0.0453581	−	0.139598i	0.925813	−	0.377983i	$-0.123382\pi$
$673$	−1.17669	−	3.62148i	−0.0453581	−	0.139598i	−0.971171	+	0.238385i	$0.923382\pi$
$674$		0			0
$675$	−0.708802	+	0.514975i	−0.0272818	+	0.0198214i
$676$		0			0
$677$	−4.71386	+	14.5078i	−0.181168	+	0.557579i	−0.999861	−	0.0166525i	$-0.994699\pi$
$677$	−4.71386	+	14.5078i	−0.181168	+	0.557579i	0.818693	+	0.574232i	$0.194699\pi$
$678$		0			0
$679$	−21.9852	−	15.9732i	−0.843714	−	0.612994i
$680$		0			0
$681$	−12.2884			−0.470891
$682$		0			0
$683$	−16.0356			−0.613584			−0.306792	−	0.951777i	$-0.599256\pi$
$683$	−16.0356			−0.613584			−0.306792	+	0.951777i	$0.599256\pi$
$684$		0			0
$685$	5.94361	+	4.31829i	0.227094	+	0.164993i
$686$		0			0
$687$	1.57496	−	4.84724i	0.0600886	−	0.184934i
$688$		0			0
$689$	5.80250	−	4.21576i	0.221058	−	0.160608i
$690$		0			0
$691$	−1.40423	−	4.32179i	−0.0534196	−	0.164409i	0.920787	−	0.390065i	$-0.127547\pi$
$691$	−1.40423	−	4.32179i	−0.0534196	−	0.164409i	−0.974207	+	0.225656i	$0.927547\pi$
$692$		0			0
$693$	34.0218	+	8.49011i	1.29238	+	0.322513i
$694$		0			0
$695$	2.97943	+	9.16975i	0.113016	+	0.347829i
$696$		0			0
$697$	3.72089	−	2.70338i	0.140939	−	0.102398i
$698$		0			0
$699$	0.132729	−	0.408498i	0.00502027	−	0.0154508i
$700$		0			0
$701$	−10.8517	−	7.88419i	−0.409862	−	0.297782i	0.363684	−	0.931522i	$-0.381519\pi$
$701$	−10.8517	−	7.88419i	−0.409862	−	0.297782i	−0.773546	+	0.633740i	$0.781519\pi$
$702$		0			0
$703$	−46.4042			−1.75017
$704$		0			0
$705$	14.6032			0.549988
$706$		0			0
$707$	−18.7217	−	13.6021i	−0.704102	−	0.511560i
$708$		0			0
$709$	−6.34005	+	19.5127i	−0.238106	+	0.732814i	0.758589	+	0.651570i	$0.225889\pi$
$709$	−6.34005	+	19.5127i	−0.238106	+	0.732814i	−0.996694	+	0.0812438i	$0.974111\pi$
$710$		0			0
$711$	19.9479	−	14.4930i	0.748105	−	0.543530i
$712$		0			0
$713$	−9.69722	−	29.8450i	−0.363164	−	1.11770i
$714$		0			0
$715$	−7.06607	+	2.85317i	−0.264256	+	0.106702i
$716$		0			0
$717$	−2.68562	−	8.26550i	−0.100296	−	0.308681i
$718$		0			0
$719$	−40.8516	+	29.6805i	−1.52351	+	1.10689i	−0.563795	+	0.825915i	$0.690659\pi$
$719$	−40.8516	+	29.6805i	−1.52351	+	1.10689i	−0.959714	+	0.280979i	$0.909341\pi$
$720$		0			0
$721$	12.7063	−	39.1060i	0.473208	−	1.45638i
$722$		0			0
$723$	3.73547	+	2.71398i	0.138924	+	0.100934i
$724$		0			0
$725$	−0.224080			−0.00832213
$726$		0			0
$727$	−6.74389			−0.250117			−0.125058	−	0.992149i	$-0.539912\pi$
$727$	−6.74389			−0.250117			−0.125058	+	0.992149i	$0.539912\pi$
$728$		0			0
$729$	9.67137	+	7.02666i	0.358199	+	0.260247i
$730$		0			0
$731$	4.57985	−	14.0953i	0.169392	−	0.521334i
$732$		0			0
$733$	−13.5023	+	9.80997i	−0.498718	+	0.362340i	−0.808527	−	0.588459i	$-0.799735\pi$
$733$	−13.5023	+	9.80997i	−0.498718	+	0.362340i	0.309809	+	0.950799i	$0.399735\pi$
$734$		0			0
$735$	−3.27731	−	10.0865i	−0.120885	−	0.372047i
$736$		0			0
$737$	−13.1426	+	5.30676i	−0.484113	+	0.195477i
$738$		0			0
$739$	−16.4539	−	50.6400i	−0.605267	−	1.86282i	−0.494942	−	0.868926i	$-0.664811\pi$
$739$	−16.4539	−	50.6400i	−0.605267	−	1.86282i	−0.110326	−	0.993896i	$-0.535189\pi$
$740$		0			0
$741$	2.94494	−	2.13963i	0.108185	−	0.0786011i
$742$		0			0
$743$	−8.08786	+	24.8919i	−0.296715	+	0.913194i	0.685925	+	0.727672i	$0.259398\pi$
$743$	−8.08786	+	24.8919i	−0.296715	+	0.913194i	−0.982640	+	0.185522i	$0.940602\pi$
$744$		0			0
$745$	19.7260	+	14.3318i	0.722707	+	0.525077i
$746$		0			0
$747$	2.05283			0.0751090
$748$		0			0
$749$	−9.23686			−0.337507
$750$		0			0
$751$	−21.0117	−	15.2659i	−0.766729	−	0.557061i	0.134238	−	0.990949i	$-0.457141\pi$
$751$	−21.0117	−	15.2659i	−0.766729	−	0.557061i	−0.900967	+	0.433888i	$0.857141\pi$
$752$		0			0
$753$	−1.03881	+	3.19712i	−0.0378562	+	0.116509i
$754$		0			0
$755$	13.2792	−	9.64792i	0.483280	−	0.351124i
$756$		0			0
$757$	6.31713	+	19.4421i	0.229600	+	0.706636i	0.997792	+	0.0664165i	$0.0211566\pi$
$757$	6.31713	+	19.4421i	0.229600	+	0.706636i	−0.768192	+	0.640220i	$0.778843\pi$
$758$		0			0
$759$	7.23554	+	1.80562i	0.262633	+	0.0655399i
$760$		0			0
$761$	−6.83845	−	21.0466i	−0.247894	−	0.762938i	−0.995147	−	0.0983988i	$-0.968628\pi$
$761$	−6.83845	−	21.0466i	−0.247894	−	0.762938i	0.747254	−	0.664539i	$-0.231372\pi$
$762$		0			0
$763$	−53.8906	+	39.1538i	−1.95097	+	1.41746i
$764$		0			0
$765$	−2.29438	+	7.06137i	−0.0829534	+	0.255304i
$766$		0			0
$767$	−3.45262	−	2.50847i	−0.124667	−	0.0905757i
$768$		0			0
$769$	6.43027			0.231881			0.115941	−	0.993256i	$-0.463012\pi$
$769$	6.43027			0.231881			0.115941	+	0.993256i	$0.463012\pi$
$770$		0			0
$771$	−0.385723			−0.0138915
$772$		0			0
$773$	22.4555	+	16.3149i	0.807669	+	0.586806i	0.913154	−	0.407615i	$-0.133640\pi$
$773$	22.4555	+	16.3149i	0.807669	+	0.586806i	−0.105485	+	0.994421i	$0.533640\pi$
$774$		0			0
$775$	0.663332	−	2.04153i	0.0238276	−	0.0733338i
$776$		0			0
$777$	12.2827	−	8.92392i	0.440640	−	0.320144i
$778$		0			0
$779$	−7.83265	−	24.1064i	−0.280634	−	0.863702i
$780$		0			0
$781$	−2.48446	−	35.6360i	−0.0889009	−	1.27516i
$782$		0			0
$783$	−0.778903	−	2.39722i	−0.0278357	−	0.0856696i
$784$		0			0
$785$	36.4125	−	26.4553i	1.29962	−	0.944229i
$786$		0			0
$787$	−4.46972	+	13.7564i	−0.159328	+	0.490362i	−0.998574	−	0.0533907i	$-0.982997\pi$
$787$	−4.46972	+	13.7564i	−0.159328	+	0.490362i	0.839245	+	0.543753i	$0.182997\pi$
$788$		0			0
$789$	−12.3210	−	8.95175i	−0.438640	−	0.318691i
$790$		0			0
$791$	63.5899			2.26100
$792$		0			0
$793$	4.93799			0.175353
$794$		0			0
$795$	−7.34744	−	5.33823i	−0.260587	−	0.189327i
$796$		0			0
$797$	1.40789	−	4.33305i	0.0498701	−	0.153484i	−0.923020	−	0.384752i	$-0.874287\pi$
$797$	1.40789	−	4.33305i	0.0498701	−	0.153484i	0.972890	+	0.231267i	$0.0742871\pi$
$798$		0			0
$799$	11.1821	−	8.12428i	0.395595	−	0.287416i
$800$		0			0
$801$	−1.49160	−	4.59068i	−0.0527032	−	0.162204i
$802$		0			0
$803$	10.4807	−	16.7649i	0.369856	−	0.591619i
$804$		0			0
$805$	11.3587	+	34.9585i	0.400341	+	1.23212i
$806$		0			0
$807$	10.5848	−	7.69030i	0.372602	−	0.270712i
$808$		0			0
$809$	16.2109	−	49.8921i	0.569946	−	1.75411i	−0.0828330	−	0.996563i	$-0.526397\pi$
$809$	16.2109	−	49.8921i	0.569946	−	1.75411i	0.652779	−	0.757549i	$-0.273603\pi$
$810$		0			0
$811$	22.5800	+	16.4053i	0.792890	+	0.576068i	0.908820	−	0.417189i	$-0.136985\pi$
$811$	22.5800	+	16.4053i	0.792890	+	0.576068i	−0.115930	+	0.993257i	$0.536985\pi$
$812$		0			0
$813$	−9.76781			−0.342572
$814$		0			0
$815$	52.7343			1.84720
$816$		0			0
$817$	−66.0791	−	48.0092i	−2.31181	−	1.67963i
$818$		0			0
$819$	3.26710	−	10.0551i	0.114162	−	0.351353i
$820$		0			0
$821$	7.44381	−	5.40824i	0.259791	−	0.188749i	−0.450264	−	0.892895i	$-0.648670\pi$
$821$	7.44381	−	5.40824i	0.259791	−	0.188749i	0.710055	+	0.704146i	$0.248670\pi$
$822$		0			0
$823$	−0.687880	−	2.11708i	−0.0239780	−	0.0737967i	0.938351	−	0.345683i	$-0.112353\pi$
$823$	−0.687880	−	2.11708i	−0.0239780	−	0.0737967i	−0.962329	+	0.271886i	$0.912353\pi$
$824$		0			0
$825$	0.327818	+	0.390844i	0.0114132	+	0.0136074i
$826$		0			0
$827$	0.260729	+	0.802442i	0.00906645	+	0.0279037i	0.955487	−	0.295032i	$-0.0953303\pi$
$827$	0.260729	+	0.802442i	0.00906645	+	0.0279037i	−0.946421	+	0.322936i	$0.895330\pi$
$828$		0			0
$829$	21.1474	−	15.3645i	0.734479	−	0.533630i	−0.156498	−	0.987678i	$-0.550021\pi$
$829$	21.1474	−	15.3645i	0.734479	−	0.533630i	0.890977	+	0.454048i	$0.150021\pi$
$830$		0			0
$831$	3.34107	−	10.2828i	0.115901	−	0.356705i
$832$		0			0
$833$	−8.12104	−	5.90028i	−0.281377	−	0.204433i
$834$		0			0
$835$	−30.9997			−1.07279
$836$		0			0
$837$	24.1461			0.834610
$838$		0			0
$839$	38.3197	+	27.8409i	1.32294	+	0.961173i	0.999891	+	0.0147919i	$0.00470857\pi$
$839$	38.3197	+	27.8409i	1.32294	+	0.961173i	0.323051	+	0.946382i	$0.395291\pi$
$840$		0			0
$841$	−8.76228	+	26.9675i	−0.302148	+	0.929915i
$842$		0			0
$843$	11.7018	−	8.50184i	0.403031	−	0.292819i
$844$		0			0
$845$	0.710005	+	2.18517i	0.0244249	+	0.0751722i
$846$		0			0
$847$	7.50762	−	42.4745i	0.257965	−	1.45944i
$848$		0			0
$849$	4.49730	+	13.8413i	0.154347	+	0.475031i
$850$		0			0
$851$	−23.1893	+	16.8480i	−0.794920	+	0.577544i
$852$		0			0
$853$	4.08705	−	12.5787i	0.139938	−	0.430685i	−0.856387	−	0.516334i	$-0.827296\pi$
$853$	4.08705	−	12.5787i	0.139938	−	0.430685i	0.996325	+	0.0856490i	$0.0272964\pi$
$854$		0			0
$855$	33.1038	+	24.0513i	1.13213	+	0.822538i
$856$		0			0
$857$	43.7977			1.49610			0.748050	−	0.663642i	$-0.230990\pi$
$857$	43.7977			1.49610			0.748050	+	0.663642i	$0.230990\pi$
$858$		0			0
$859$	12.3519			0.421441			0.210720	−	0.977546i	$-0.432419\pi$
$859$	12.3519			0.421441			0.210720	+	0.977546i	$0.432419\pi$
$860$		0			0
$861$	6.70910	+	4.87444i	0.228645	+	0.166121i
$862$		0			0
$863$	0.0983231	−	0.302607i	0.00334696	−	0.0103009i	−0.949369	−	0.314163i	$-0.898276\pi$
$863$	0.0983231	−	0.302607i	0.00334696	−	0.0103009i	0.952716	+	0.303862i	$0.0982762\pi$
$864$		0			0
$865$	4.85574	−	3.52790i	0.165100	−	0.119952i
$866$		0			0
$867$	2.65054	+	8.15751i	0.0900170	+	0.277044i
$868$		0			0
$869$	−19.4909	−	23.2382i	−0.661184	−	0.788301i
$870$		0			0
$871$	1.32058	+	4.06432i	0.0447461	+	0.137714i
$872$		0			0
$873$	−15.1174	+	10.9835i	−0.511648	+	0.371734i
$874$		0			0
$875$	13.1433	−	40.4508i	0.444324	−	1.36749i
$876$		0			0
$877$	−6.76113	−	4.91225i	−0.228307	−	0.165875i	0.467751	−	0.883860i	$-0.345064\pi$
$877$	−6.76113	−	4.91225i	−0.228307	−	0.165875i	−0.696058	+	0.717985i	$0.745064\pi$
$878$		0			0
$879$	−14.8555			−0.501065
$880$		0			0
$881$	40.0240			1.34844			0.674221	−	0.738530i	$-0.264480\pi$
$881$	40.0240			1.34844			0.674221	+	0.738530i	$0.264480\pi$
$882$		0			0
$883$	19.3048	+	14.0258i	0.649660	+	0.472006i	0.863155	−	0.504939i	$-0.168485\pi$
$883$	19.3048	+	14.0258i	0.649660	+	0.472006i	−0.213495	+	0.976944i	$0.568485\pi$
$884$		0			0
$885$	−1.66991	+	5.13946i	−0.0561335	+	0.172761i
$886$		0			0
$887$	23.9864	−	17.4271i	0.805384	−	0.585146i	−0.107104	−	0.994248i	$-0.534158\pi$
$887$	23.9864	−	17.4271i	0.805384	−	0.585146i	0.912489	+	0.409102i	$0.134158\pi$
$888$		0			0
$889$	8.47961	+	26.0975i	0.284397	+	0.875284i
$890$		0			0
$891$	11.1794	−	17.8825i	0.374525	−	0.599087i
$892$		0			0
$893$	−23.5389	−	72.4453i	−0.787699	−	2.42429i
$894$		0			0
$895$	28.8960	−	20.9942i	0.965887	−	0.701758i
$896$		0			0
$897$	0.694825	−	2.13845i	0.0231995	−	0.0714008i
$898$		0			0
$899$	4.99620	+	3.62995i	0.166633	+	0.121066i
$900$		0			0
$901$	−8.59601			−0.286375
$902$		0			0
$903$	26.7231			0.889288
$904$		0			0
$905$	−8.70118	−	6.32178i	−0.289237	−	0.210143i
$906$		0			0
$907$	17.7704	−	54.6916i	0.590056	−	1.81601i	0.0121150	−	0.999927i	$-0.496144\pi$
$907$	17.7704	−	54.6916i	0.590056	−	1.81601i	0.577941	−	0.816079i	$-0.303856\pi$
$908$		0			0
$909$	−12.8734	+	9.35307i	−0.426984	+	0.310222i
$910$		0			0
$911$	−4.86140	−	14.9619i	−0.161065	−	0.495708i	0.837659	−	0.546193i	$-0.183923\pi$
$911$	−4.86140	−	14.9619i	−0.161065	−	0.495708i	−0.998725	+	0.0504845i	$0.983923\pi$
$912$		0			0
$913$	−0.175620	−	2.51902i	−0.00581218	−	0.0833674i
$914$		0			0
$915$	−1.93221	−	5.94672i	−0.0638768	−	0.196592i
$916$		0			0
$917$	−42.2202	+	30.6747i	−1.39423	+	1.01297i
$918$		0			0
$919$	−0.608621	+	1.87314i	−0.0200766	+	0.0617893i	−0.960593	−	0.277959i	$-0.910342\pi$
$919$	−0.608621	+	1.87314i	−0.0200766	+	0.0617893i	0.940516	+	0.339749i	$0.110342\pi$
$920$		0			0
$921$	1.80704	+	1.31289i	0.0595439	+	0.0432612i
$922$		0			0
$923$	−10.7707			−0.354523
$924$		0			0
$925$	−1.96072			−0.0644680
$926$		0			0
$927$	−22.8741	−	16.6190i	−0.751283	−	0.545839i
$928$		0			0
$929$	4.82890	−	14.8618i	0.158431	−	0.487600i	−0.840061	−	0.542491i	$-0.817481\pi$
$929$	4.82890	−	14.8618i	0.158431	−	0.487600i	0.998492	+	0.0548910i	$0.0174811\pi$
$930$		0			0
$931$	−44.7558	+	32.5170i	−1.46681	+	1.06570i
$932$		0			0
$933$	2.44717	+	7.53161i	0.0801167	+	0.246574i
$934$		0			0
$935$	8.86129	+	2.21133i	0.289795	+	0.0723181i
$936$		0			0
$937$	−2.55561	−	7.86537i	−0.0834882	−	0.256950i	0.900595	−	0.434660i	$-0.143131\pi$
$937$	−2.55561	−	7.86537i	−0.0834882	−	0.256950i	−0.984083	+	0.177709i	$0.943131\pi$
$938$		0			0
$939$	−8.19782	+	5.95607i	−0.267526	+	0.194369i
$940$		0			0
$941$	−10.2883	+	31.6643i	−0.335390	+	1.03223i	0.631139	+	0.775670i	$0.282588\pi$
$941$	−10.2883	+	31.6643i	−0.335390	+	1.03223i	−0.966529	+	0.256556i	$0.917412\pi$
$942$		0			0
$943$	−12.6665	−	9.20278i	−0.412479	−	0.299684i
$944$		0			0
$945$	−28.2831			−0.920050
$946$		0			0
$947$	20.7911			0.675621			0.337811	−	0.941214i	$-0.390314\pi$
$947$	20.7911			0.675621			0.337811	+	0.941214i	$0.390314\pi$
$948$		0			0
$949$	−4.82278	−	3.50395i	−0.156554	−	0.113743i
$950$		0			0
$951$	3.63971	−	11.2019i	0.118026	−	0.363245i
$952$		0			0
$953$	−7.85864	+	5.70964i	−0.254566	+	0.184953i	−0.707748	−	0.706465i	$-0.750289\pi$
$953$	−7.85864	+	5.70964i	−0.254566	+	0.184953i	0.453182	+	0.891418i	$0.350289\pi$
$954$		0			0
$955$	5.80942	+	17.8795i	0.187988	+	0.578569i
$956$		0			0
$957$	−1.36085	+	0.549488i	−0.0439899	+	0.0177624i
$958$		0			0
$959$	3.87446	+	11.9244i	0.125113	+	0.385058i
$960$		0			0
$961$	−22.7819	+	16.5520i	−0.734899	+	0.533935i
$962$		0			0
$963$	−1.96270	+	6.04058i	−0.0632473	+	0.194655i
$964$		0			0
$965$	−12.0596	−	8.76181i	−0.388212	−	0.282053i
$966$		0			0
$967$	3.67076			0.118044			0.0590219	−	0.998257i	$-0.481202\pi$
$967$	3.67076			0.118044			0.0590219	+	0.998257i	$0.481202\pi$
$968$		0			0
$969$	−4.36273			−0.140151
$970$		0			0
$971$	16.1936	+	11.7653i	0.519677	+	0.377567i	0.816482	−	0.577371i	$-0.195921\pi$
$971$	16.1936	+	11.7653i	0.519677	+	0.377567i	−0.296805	+	0.954938i	$0.595921\pi$
$972$		0			0
$973$	−5.08475	+	15.6493i	−0.163010	+	0.501692i
$974$		0			0
$975$	0.124433	−	0.0904056i	0.00398503	−	0.00289530i
$976$		0			0
$977$	−11.9964	−	36.9212i	−0.383800	−	1.18121i	−0.937347	−	0.348397i	$-0.886726\pi$
$977$	−11.9964	−	36.9212i	−0.383800	−	1.18121i	0.553547	−	0.832818i	$-0.313274\pi$
$978$		0			0
$979$	−5.50561	+	2.22308i	−0.175960	+	0.0710499i
$980$		0			0
$981$	14.1542	+	43.5622i	0.451910	+	1.39084i
$982$		0			0
$983$	−16.9525	+	12.3167i	−0.540701	+	0.392842i	−0.824345	−	0.566087i	$-0.808456\pi$
$983$	−16.9525	+	12.3167i	−0.540701	+	0.392842i	0.283644	+	0.958930i	$0.408456\pi$
$984$		0			0
$985$	−15.9961	+	49.2309i	−0.509677	+	1.56863i
$986$		0			0
$987$	20.1624	+	14.6488i	0.641775	+	0.466277i
$988$		0			0
$989$	−50.4522			−1.60429
$990$		0			0
$991$	−44.1472			−1.40238			−0.701191	−	0.712973i	$-0.747348\pi$
$991$	−44.1472			−1.40238			−0.701191	+	0.712973i	$0.747348\pi$
$992$		0			0
$993$	−12.6728	−	9.20735i	−0.402160	−	0.292186i
$994$		0			0
$995$	7.64494	−	23.5287i	0.242361	−	0.745910i
$996$		0			0
$997$	14.9649	−	10.8726i	0.473943	−	0.344340i	−0.325033	−	0.945703i	$-0.605375\pi$
$997$	14.9649	−	10.8726i	0.473943	−	0.344340i	0.798976	+	0.601363i	$0.205375\pi$
$998$		0			0
$999$	−6.81545	−	20.9758i	−0.215631	−	0.663645i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.n.a.313.3	yes	20
11.3	even	5		6292.2.a.w.1.4		10
11.8	odd	10		6292.2.a.x.1.4		10
11.9	even	5	inner	572.2.n.a.53.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.n.a.53.3	✓	20	11.9	even	5	inner
572.2.n.a.313.3	yes	20	1.1	even	1	trivial
6292.2.a.w.1.4		10	11.3	even	5
6292.2.a.x.1.4		10	11.8	odd	10

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)

\(f(q)\)	\(=\)	\(q+(0.445861 + 0.323937i) q^{3} +(0.710005 - 2.18517i) q^{5} +(3.17229 - 2.30481i) q^{7} +(-0.833194 - 2.56431i) q^{9} +O(q^{10})\)	\(q+(0.445861 + 0.323937i) q^{3} +(0.710005 - 2.18517i) q^{5} +(3.17229 - 2.30481i) q^{7} +(-0.833194 - 2.56431i) q^{9} +(-3.07538 + 1.24179i) q^{11} +(0.309017 + 0.951057i) q^{13} +(1.02442 - 0.744286i) q^{15} +(0.370358 - 1.13985i) q^{17} +(-5.34361 - 3.88236i) q^{19} +2.16101 q^{21} -4.07991 q^{23} +(-0.225784 - 0.164041i) q^{25} +(0.970096 - 2.98565i) q^{27} +(0.649571 - 0.471941i) q^{29} +(2.37682 + 7.31510i) q^{31} +(-1.77345 - 0.442564i) q^{33} +(-2.78405 - 8.56843i) q^{35} +(5.68378 - 4.12951i) q^{37} +(-0.170304 + 0.524141i) q^{39} +(3.10461 + 2.25563i) q^{41} +12.3660 q^{43} -6.19503 q^{45} +(9.33005 + 6.77868i) q^{47} +(2.58819 - 7.96564i) q^{49} +(0.534366 - 0.388240i) q^{51} +(-2.21636 - 6.82125i) q^{53} +(0.529988 + 7.60191i) q^{55} +(-1.12487 - 3.46199i) q^{57} +(-3.45262 + 2.50847i) q^{59} +(1.52592 - 4.69631i) q^{61} +(-8.55337 - 6.21438i) q^{63} +2.29763 q^{65} +4.27348 q^{67} +(-1.81907 - 1.32163i) q^{69} +(-3.32834 + 10.2436i) q^{71} +(-4.82278 + 3.50395i) q^{73} +(-0.0475291 - 0.146279i) q^{75} +(-6.89392 + 11.0275i) q^{77} +(2.82591 + 8.69726i) q^{79} +(-5.14430 + 3.73755i) q^{81} +(-0.235272 + 0.724094i) q^{83} +(-2.22780 - 1.61859i) q^{85} +0.442497 q^{87} +1.79022 q^{89} +(3.17229 + 2.30481i) q^{91} +(-1.30990 + 4.03146i) q^{93} +(-12.2776 + 8.92022i) q^{95} +(-2.14160 - 6.59118i) q^{97} +(5.74672 + 6.85157i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9}+O(q^{10}) \) 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9	\( 20 q + q^{3} + q^{5} + 3 q^{7} + 12 q^{9} - q^{11} - 5 q^{13} + 14 q^{15} - 3 q^{17} - 7 q^{19} - 32 q^{21} - 30 q^{23} - 12 q^{25} + 13 q^{27} - 14 q^{29} + 11 q^{31} - 10 q^{33} - 10 q^{35} + 45 q^{37} - 4 q^{39} + 9 q^{41} - 8 q^{43} - 34 q^{45} + 39 q^{47} + 30 q^{49} - 55 q^{51} + 36 q^{53} + 11 q^{55} - 31 q^{57} - 31 q^{59} - 7 q^{61} + 14 q^{63} - 14 q^{65} + 26 q^{67} + 32 q^{69} + 33 q^{71} - 44 q^{73} + 37 q^{75} - 73 q^{77} + 21 q^{79} + 16 q^{81} - 25 q^{83} + 15 q^{85} + 32 q^{87} - 2 q^{89} + 3 q^{91} + 33 q^{93} - 37 q^{95} + 52 q^{97} - 8 q^{99}+O(q^{100}) \) 20 * q + q^3 + q^5 + 3 * q^7 + 12 * q^9 - q^11 - 5 * q^13 + 14 * q^15 - 3 * q^17 - 7 * q^19 - 32 * q^21 - 30 * q^23 - 12 * q^25 + 13 * q^27 - 14 * q^29 + 11 * q^31 - 10 * q^33 - 10 * q^35 + 45 * q^37 - 4 * q^39 + 9 * q^41 - 8 * q^43 - 34 * q^45 + 39 * q^47 + 30 * q^49 - 55 * q^51 + 36 * q^53 + 11 * q^55 - 31 * q^57 - 31 * q^59 - 7 * q^61 + 14 * q^63 - 14 * q^65 + 26 * q^67 + 32 * q^69 + 33 * q^71 - 44 * q^73 + 37 * q^75 - 73 * q^77 + 21 * q^79 + 16 * q^81 - 25 * q^83 + 15 * q^85 + 32 * q^87 - 2 * q^89 + 3 * q^91 + 33 * q^93 - 37 * q^95 + 52 * q^97 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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