LMFDB - Embedded newform 572.2.bh.a.73.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("572.57");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			73.6
Character	$\chi$	$=$	572.73
Dual form			572.2.bh.a.525.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.269308 + 0.828844i) q^{3} +(-2.25685 - 0.357450i) q^{5} +(-0.534177 + 1.04838i) q^{7} +(1.81260 + 1.31693i) q^{9} +O(q^{10})$	\(q+(-0.269308 + 0.828844i) q^{3} +(-2.25685 - 0.357450i) q^{5} +(-0.534177 + 1.04838i) q^{7} +(1.81260 + 1.31693i) q^{9} +(-2.72514 - 1.89040i) q^{11} +(-3.52015 - 0.780108i) q^{13} +(0.904059 - 1.77432i) q^{15} +(2.33710 - 1.69800i) q^{17} +(-2.57739 - 5.05842i) q^{19} +(-0.725086 - 0.725086i) q^{21} -3.64514i q^{23} +(0.210334 + 0.0683418i) q^{25} +(-3.69484 + 2.68446i) q^{27} +(-9.53203 + 3.09714i) q^{29} +(0.0368962 + 0.232953i) q^{31} +(2.30075 - 1.74961i) q^{33} +(1.58030 - 2.17510i) q^{35} +(0.451545 + 0.230073i) q^{37} +(1.59459 - 2.70756i) q^{39} +(-1.25022 - 2.45369i) q^{41} -3.08016 q^{43} +(-3.62003 - 3.62003i) q^{45} +(-5.27766 - 10.3580i) q^{47} +(3.30074 + 4.54308i) q^{49} +(0.777980 + 2.39438i) q^{51} +(1.43649 + 1.04367i) q^{53} +(5.47451 + 5.24047i) q^{55} +(4.88675 - 0.773986i) q^{57} +(-4.14039 - 2.10963i) q^{59} +(5.52681 + 7.60700i) q^{61} +(-2.34889 + 1.19682i) q^{63} +(7.66561 + 3.01887i) q^{65} +(6.38758 + 6.38758i) q^{67} +(3.02126 + 0.981665i) q^{69} +(-4.34658 - 0.688430i) q^{71} +(4.48783 - 8.80785i) q^{73} +(-0.113289 + 0.155930i) q^{75} +(3.43757 - 1.84717i) q^{77} +(-5.07553 + 6.98586i) q^{79} +(0.847099 + 2.60710i) q^{81} +(0.308955 - 1.95066i) q^{83} +(-5.88144 + 2.99675i) q^{85} -8.73465i q^{87} +(2.48837 - 2.48837i) q^{89} +(2.69823 - 3.27374i) q^{91} +(-0.203019 - 0.0321550i) q^{93} +(4.00867 + 12.3374i) q^{95} +(2.72960 + 17.2340i) q^{97} +(-2.45004 - 7.01535i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 28 q^{9}+O(q^{10}) $ 112 * q - 28 * q^9	$ 112 q - 28 q^{9} + 8 q^{11} - 10 q^{13} + 4 q^{15} - 24 q^{27} - 20 q^{29} - 16 q^{31} - 54 q^{33} + 100 q^{35} - 12 q^{37} + 40 q^{39} - 20 q^{41} - 4 q^{45} - 10 q^{47} - 76 q^{53} - 20 q^{55} + 18 q^{59} + 40 q^{61} + 80 q^{63} + 92 q^{67} + 8 q^{71} - 30 q^{73} - 80 q^{79} + 12 q^{81} + 40 q^{85} + 32 q^{89} - 12 q^{91} - 114 q^{93} + 54 q^{97} - 90 q^{99}+O(q^{100}) $ 112 * q - 28 * q^9 + 8 * q^11 - 10 * q^13 + 4 * q^15 - 24 * q^27 - 20 * q^29 - 16 * q^31 - 54 * q^33 + 100 * q^35 - 12 * q^37 + 40 * q^39 - 20 * q^41 - 4 * q^45 - 10 * q^47 - 76 * q^53 - 20 * q^55 + 18 * q^59 + 40 * q^61 + 80 * q^63 + 92 * q^67 + 8 * q^71 - 30 * q^73 - 80 * q^79 + 12 * q^81 + 40 * q^85 + 32 * q^89 - 12 * q^91 - 114 * q^93 + 54 * q^97 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.269308	+	0.828844i	−0.155485	+	0.478533i	−0.998210	−	0.0598113i	$-0.980950\pi$
$3$	−0.269308	+	0.828844i	−0.155485	+	0.478533i	0.842725	+	0.538345i	$0.180950\pi$
$4$		0			0
$5$	−2.25685	−	0.357450i	−1.00930	−	0.159857i	−0.370174	−	0.928962i	$-0.620702\pi$
$5$	−2.25685	−	0.357450i	−1.00930	−	0.159857i	−0.639122	+	0.769106i	$0.720702\pi$
$6$		0			0
$7$	−0.534177	+	1.04838i	−0.201900	+	0.396251i	−0.969649	−	0.244499i	$-0.921376\pi$
$7$	−0.534177	+	1.04838i	−0.201900	+	0.396251i	0.767750	+	0.640750i	$0.221376\pi$
$8$		0			0
$9$	1.81260	+	1.31693i	0.604198	+	0.438976i
$10$		0			0
$11$	−2.72514	−	1.89040i	−0.821660	−	0.569978i
$11$	−2.72514	−	1.89040i	−0.821660	−	0.569978i
$12$		0			0
$13$	−3.52015	−	0.780108i	−0.976313	−	0.216363i
$13$	−3.52015	−	0.780108i	−0.976313	−	0.216363i
$14$		0			0
$15$	0.904059	−	1.77432i	0.233427	−	0.458126i
$16$		0			0
$17$	2.33710	−	1.69800i	0.566830	−	0.411826i	−0.267122	−	0.963663i	$-0.586073\pi$
$17$	2.33710	−	1.69800i	0.566830	−	0.411826i	0.833952	+	0.551837i	$0.186073\pi$
$18$		0			0
$19$	−2.57739	−	5.05842i	−0.591295	−	1.16048i	−0.971823	−	0.235712i	$-0.924258\pi$
$19$	−2.57739	−	5.05842i	−0.591295	−	1.16048i	0.380528	−	0.924769i	$-0.375742\pi$
$20$		0			0
$21$	−0.725086	−	0.725086i	−0.158227	−	0.158227i
$22$		0			0
$23$		−	3.64514i		−	0.760065i	−0.924973	−	0.380032i	$-0.875913\pi$
$23$		−	3.64514i		−	0.760065i	0.924973	−	0.380032i	$-0.124087\pi$
$24$		0			0
$25$	0.210334	+	0.0683418i	0.0420669	+	0.0136684i
$26$		0			0
$27$	−3.69484	+	2.68446i	−0.711073	+	0.516625i
$28$		0			0
$29$	−9.53203	+	3.09714i	−1.77005	+	0.575125i	−0.998161	−	0.0606267i	$-0.980690\pi$
$29$	−9.53203	+	3.09714i	−1.77005	+	0.575125i	−0.771893	+	0.635752i	$0.780690\pi$
$30$		0			0
$31$	0.0368962	+	0.232953i	0.00662675	+	0.0418397i	0.990780	−	0.135480i	$-0.0432575\pi$
$31$	0.0368962	+	0.232953i	0.00662675	+	0.0418397i	−0.984153	+	0.177319i	$0.943258\pi$
$32$		0			0
$33$	2.30075	−	1.74961i	0.400509	−	0.304569i
$34$		0			0
$35$	1.58030	−	2.17510i	0.267120	−	0.367659i
$36$		0			0
$37$	0.451545	+	0.230073i	0.0742335	+	0.0378238i	0.490713	−	0.871321i	$-0.336736\pi$
$37$	0.451545	+	0.230073i	0.0742335	+	0.0378238i	−0.416480	+	0.909145i	$0.636736\pi$
$38$		0			0
$39$	1.59459	−	2.70756i	0.255339	−	0.433557i
$40$		0			0
$41$	−1.25022	−	2.45369i	−0.195252	−	0.383203i	0.772536	−	0.634971i	$-0.218988\pi$
$41$	−1.25022	−	2.45369i	−0.195252	−	0.383203i	−0.967788	+	0.251768i	$0.918988\pi$
$42$		0			0
$43$	−3.08016			−0.469720			−0.234860	−	0.972029i	$-0.575463\pi$
$43$	−3.08016			−0.469720			−0.234860	+	0.972029i	$0.575463\pi$
$44$		0			0
$45$	−3.62003	−	3.62003i	−0.539642	−	0.539642i
$46$		0			0
$47$	−5.27766	−	10.3580i	−0.769826	−	1.51087i	−0.857365	−	0.514708i	$-0.827900\pi$
$47$	−5.27766	−	10.3580i	−0.769826	−	1.51087i	0.0875392	−	0.996161i	$-0.472100\pi$
$48$		0			0
$49$	3.30074	+	4.54308i	0.471534	+	0.649011i
$50$		0			0
$51$	0.777980	+	2.39438i	0.108939	+	0.335280i
$52$		0			0
$53$	1.43649	+	1.04367i	0.197317	+	0.143359i	0.682057	−	0.731299i	$-0.261086\pi$
$53$	1.43649	+	1.04367i	0.197317	+	0.143359i	−0.484740	+	0.874659i	$0.661086\pi$
$54$		0			0
$55$	5.47451	+	5.24047i	0.738183	+	0.706624i
$56$		0			0
$57$	4.88675	−	0.773986i	0.647266	−	0.102517i
$58$		0			0
$59$	−4.14039	−	2.10963i	−0.539032	−	0.274651i	0.163207	−	0.986592i	$-0.447816\pi$
$59$	−4.14039	−	2.10963i	−0.539032	−	0.274651i	−0.702239	+	0.711941i	$0.747816\pi$
$60$		0			0
$61$	5.52681	+	7.60700i	0.707635	+	0.973976i	0.999845	+	0.0176219i	$0.00560950\pi$
$61$	5.52681	+	7.60700i	0.707635	+	0.973976i	−0.292210	+	0.956354i	$0.594390\pi$
$62$		0			0
$63$	−2.34889	+	1.19682i	−0.295932	+	0.150785i
$64$		0			0
$65$	7.66561	+	3.01887i	0.950801	+	0.374444i
$66$		0			0
$67$	6.38758	+	6.38758i	0.780367	+	0.780367i	0.979893	−	0.199525i	$-0.0639400\pi$
$67$	6.38758	+	6.38758i	0.780367	+	0.780367i	−0.199525	+	0.979893i	$0.563940\pi$
$68$		0			0
$69$	3.02126	+	0.981665i	0.363716	+	0.118179i
$70$		0			0
$71$	−4.34658	−	0.688430i	−0.515844	−	0.0817017i	−0.106915	−	0.994268i	$-0.534097\pi$
$71$	−4.34658	−	0.688430i	−0.515844	−	0.0817017i	−0.408928	+	0.912566i	$0.634097\pi$
$72$		0			0
$73$	4.48783	−	8.80785i	0.525260	−	1.03088i	−0.464153	−	0.885755i	$-0.653641\pi$
$73$	4.48783	−	8.80785i	0.525260	−	1.03088i	0.989413	−	0.145126i	$-0.0463588\pi$
$74$		0			0
$75$	−0.113289	+	0.155930i	−0.0130815	+	0.0180052i
$76$		0			0
$77$	3.43757	−	1.84717i	0.391747	−	0.210505i
$78$		0			0
$79$	−5.07553	+	6.98586i	−0.571041	+	0.785971i	−0.992678	−	0.120794i	$-0.961456\pi$
$79$	−5.07553	+	6.98586i	−0.571041	+	0.785971i	0.421636	+	0.906765i	$0.361456\pi$
$80$		0			0
$81$	0.847099	+	2.60710i	0.0941222	+	0.289678i
$82$		0			0
$83$	0.308955	−	1.95066i	0.0339122	−	0.214113i	−0.964913	−	0.262569i	$-0.915430\pi$
$83$	0.308955	−	1.95066i	0.0339122	−	0.214113i	0.998825	+	0.0484562i	$0.0154301\pi$
$84$		0			0
$85$	−5.88144	+	2.99675i	−0.637932	+	0.325043i
$86$		0			0
$87$		−	8.73465i		−	0.936453i
$88$		0			0
$89$	2.48837	−	2.48837i	0.263766	−	0.263766i	−0.562816	−	0.826582i	$-0.690282\pi$
$89$	2.48837	−	2.48837i	0.263766	−	0.263766i	0.826582	+	0.562816i	$0.190282\pi$
$90$		0			0
$91$	2.69823	−	3.27374i	0.282851	−	0.343181i
$92$		0			0
$93$	−0.203019	−	0.0321550i	−0.0210520	−	0.00333432i
$94$		0			0
$95$	4.00867	+	12.3374i	0.411280	+	1.26579i
$96$		0			0
$97$	2.72960	+	17.2340i	0.277149	+	1.74985i	0.596872	+	0.802337i	$0.296410\pi$
$97$	2.72960	+	17.2340i	0.277149	+	1.74985i	−0.319723	+	0.947511i	$0.603590\pi$
$98$		0			0
$99$	−2.45004	−	7.01535i	−0.246239	−	0.705069i
$100$		0			0
$101$	4.69469	+	3.41089i	0.467139	+	0.339396i	0.796325	−	0.604869i	$-0.206774\pi$
$101$	4.69469	+	3.41089i	0.467139	+	0.339396i	−0.329186	+	0.944265i	$0.606774\pi$
$102$		0			0
$103$	−13.7311	+	4.46152i	−1.35297	+	0.439607i	−0.893690	−	0.448685i	$-0.851893\pi$
$103$	−13.7311	+	4.46152i	−1.35297	+	0.439607i	−0.459280	+	0.888291i	$0.651893\pi$
$104$		0			0
$105$	1.37723	+	1.89560i	0.134404	+	0.184991i
$106$		0			0
$107$	−13.1009	−	4.25673i	−1.26651	−	0.411514i	−0.402700	−	0.915332i	$-0.631928\pi$
$107$	−13.1009	−	4.25673i	−1.26651	−	0.411514i	−0.863810	+	0.503818i	$0.831928\pi$
$108$		0			0
$109$	−4.47221	+	4.47221i	−0.428360	+	0.428360i	−0.888069	−	0.459709i	$-0.847954\pi$
$109$	−4.47221	+	4.47221i	−0.428360	+	0.428360i	0.459709	+	0.888069i	$0.347954\pi$
$110$		0			0
$111$	−0.312299	+	0.312299i	−0.0296422	+	0.0296422i
$112$		0			0
$113$	5.78713	−	17.8110i	0.544408	−	1.67551i	−0.177986	−	0.984033i	$-0.556958\pi$
$113$	5.78713	−	17.8110i	0.544408	−	1.67551i	0.722394	−	0.691482i	$-0.243042\pi$
$114$		0			0
$115$	−1.30296	+	8.22655i	−0.121501	+	0.767130i
$116$		0			0
$117$	−5.35326	−	6.04980i	−0.494909	−	0.559304i
$118$		0			0
$119$	0.531729	+	3.35720i	0.0487435	+	0.307754i
$120$		0			0
$121$	3.85274	+	10.3032i	0.350249	+	0.936656i
$122$		0			0
$123$	2.37042	−	0.375438i	0.213734	−	0.0338521i
$124$		0			0
$125$	9.72942	+	4.95739i	0.870226	+	0.443402i
$126$		0			0
$127$	−2.13658	+	1.55231i	−0.189591	+	0.137746i	−0.678532	−	0.734571i	$-0.737383\pi$
$127$	−2.13658	+	1.55231i	−0.189591	+	0.137746i	0.488941	+	0.872317i	$0.337383\pi$
$128$		0			0
$129$	0.829510	−	2.55297i	0.0730343	−	0.224777i
$130$		0			0
$131$			6.59347i			0.576074i	0.957619	+	0.288037i	$0.0930026\pi$
$131$			6.59347i			0.576074i	−0.957619	+	0.288037i	$0.906997\pi$
$132$		0			0
$133$	6.67994			0.579224
$134$		0			0
$135$	9.29828	−	4.73771i	0.800269	−	0.407757i
$136$		0			0
$137$	−1.75466	+	11.0785i	−0.149911	+	0.946501i	0.791971	+	0.610558i	$0.209055\pi$
$137$	−1.75466	+	11.0785i	−0.149911	+	0.946501i	−0.941882	+	0.335943i	$0.890945\pi$
$138$		0			0
$139$	12.9596	−	4.21082i	1.09922	−	0.357157i	0.297416	−	0.954748i	$-0.403875\pi$
$139$	12.9596	−	4.21082i	1.09922	−	0.357157i	0.801801	+	0.597591i	$0.203875\pi$
$140$		0			0
$141$	10.0065	−	1.58487i	0.842698	−	0.133470i
$142$		0			0
$143$	8.11816	+	8.78040i	0.678875	+	0.734254i
$144$		0			0
$145$	22.6195	−	3.58257i	1.87845	−	0.297516i
$146$		0			0
$147$	−4.65442	+	1.51231i	−0.383890	+	0.124733i
$148$		0			0
$149$	−2.17171	+	13.7116i	−0.177913	+	1.12330i	0.723494	+	0.690330i	$0.242535\pi$
$149$	−2.17171	+	13.7116i	−0.177913	+	1.12330i	−0.901408	+	0.432971i	$0.857465\pi$
$150$		0			0
$151$	−14.6639	+	7.47161i	−1.19333	+	0.608031i	−0.933832	−	0.357713i	$-0.883557\pi$
$151$	−14.6639	+	7.47161i	−1.19333	+	0.608031i	−0.259497	+	0.965744i	$0.583557\pi$
$152$		0			0
$153$	6.47236			0.523260
$154$		0			0
$155$		−	0.538930i		−	0.0432879i
$156$		0			0
$157$	1.19253	−	3.67023i	0.0951743	−	0.292916i	−0.892125	−	0.451789i	$-0.850786\pi$
$157$	1.19253	−	3.67023i	0.0951743	−	0.292916i	0.987299	+	0.158873i	$0.0507859\pi$
$158$		0			0
$159$	−1.25190	+	0.909559i	−0.0992821	+	0.0721327i
$160$		0			0
$161$	3.82150	+	1.94715i	0.301176	+	0.153457i
$162$		0			0
$163$	−0.803823	+	0.127313i	−0.0629603	+	0.00997192i	−0.187835	−	0.982201i	$-0.560147\pi$
$163$	−0.803823	+	0.127313i	−0.0629603	+	0.00997192i	0.124875	+	0.992172i	$0.460147\pi$
$164$		0			0
$165$	−5.81786	+	3.12622i	−0.452920	+	0.243376i
$166$		0			0
$167$	−2.83068	−	17.8722i	−0.219045	−	1.38299i	−0.814760	−	0.579798i	$-0.803131\pi$
$167$	−2.83068	−	17.8722i	−0.219045	−	1.38299i	0.595715	−	0.803196i	$-0.296869\pi$
$168$		0			0
$169$	11.7829	+	5.49219i	0.906374	+	0.422476i
$170$		0			0
$171$	1.98980	−	12.5631i	0.152164	−	0.960725i
$172$		0			0
$173$	3.34353	−	10.2903i	0.254204	−	0.782360i	−0.739781	−	0.672848i	$-0.765071\pi$
$173$	3.34353	−	10.2903i	0.254204	−	0.782360i	0.993985	−	0.109513i	$-0.0349290\pi$
$174$		0			0
$175$	−0.184004	+	0.184004i	−0.0139094	+	0.0139094i
$176$		0			0
$177$	2.86359	−	2.86359i	0.215241	−	0.215241i
$178$		0			0
$179$	12.0807	+	3.92526i	0.902954	+	0.293387i	0.723456	−	0.690371i	$-0.242553\pi$
$179$	12.0807	+	3.92526i	0.902954	+	0.293387i	0.179498	+	0.983758i	$0.442553\pi$
$180$		0			0
$181$	−13.1303	−	18.0723i	−0.975969	−	1.34331i	−0.938973	−	0.343991i	$-0.888221\pi$
$181$	−13.1303	−	18.0723i	−0.975969	−	1.34331i	−0.0369964	−	0.999315i	$-0.511779\pi$
$182$		0			0
$183$	−7.79343	+	2.53224i	−0.576107	+	0.187188i
$184$		0			0
$185$	−0.936830	−	0.680647i	−0.0688771	−	0.0500422i
$186$		0			0
$187$	−9.57883	+	0.209225i	−0.700473	+	0.0153001i
$188$		0			0
$189$	−0.840638	−	5.30758i	−0.0611474	−	0.386070i
$190$		0			0
$191$	3.03005	+	9.32553i	0.219247	+	0.674772i	0.998825	+	0.0484668i	$0.0154335\pi$
$191$	3.03005	+	9.32553i	0.219247	+	0.674772i	−0.779578	+	0.626305i	$0.784566\pi$
$192$		0			0
$193$	−14.0410	−	2.22388i	−1.01069	−	0.160078i	−0.370939	−	0.928657i	$-0.620964\pi$
$193$	−14.0410	−	2.22388i	−1.01069	−	0.160078i	−0.639755	+	0.768579i	$0.720964\pi$
$194$		0			0
$195$	−4.56658	+	5.54059i	−0.327019	+	0.396770i
$196$		0			0
$197$	−0.196474	+	0.196474i	−0.0139982	+	0.0139982i	−0.714071	−	0.700073i	$-0.753151\pi$
$197$	−0.196474	+	0.196474i	−0.0139982	+	0.0139982i	0.700073	+	0.714071i	$0.253151\pi$
$198$		0			0
$199$			13.6684i			0.968930i	0.874811	+	0.484465i	$0.160986\pi$
$199$			13.6684i			0.968930i	−0.874811	+	0.484465i	$0.839014\pi$
$200$		0			0
$201$	−7.01453	+	3.57408i	−0.494767	+	0.252096i
$202$		0			0
$203$	1.84480	−	11.6476i	0.129480	−	0.817503i
$204$		0			0
$205$	1.94449	+	5.98452i	0.135809	+	0.417977i
$206$		0			0
$207$	4.80039	−	6.60717i	0.333650	−	0.459230i
$208$		0			0
$209$	−2.53871	+	18.6572i	−0.175606	+	1.29055i
$210$		0			0
$211$	11.1287	−	15.3174i	0.766132	−	1.05449i	−0.230547	−	0.973061i	$-0.574052\pi$
$211$	11.1287	−	15.3174i	0.766132	−	1.05449i	0.996679	−	0.0814293i	$-0.0259485\pi$
$212$		0			0
$213$	1.74117	−	3.41724i	0.119303	−	0.234145i
$214$		0			0
$215$	6.95147	+	1.10100i	0.474086	+	0.0750878i
$216$		0			0
$217$	−0.263933	−	0.0857570i	−0.0179169	−	0.00582157i
$218$		0			0
$219$	6.09173	+	6.09173i	0.411641	+	0.411641i
$220$		0			0
$221$	−9.55156	+	4.15403i	−0.642507	+	0.279430i
$222$		0			0
$223$	14.1895	−	7.22992i	0.950200	−	0.484151i	0.0910340	−	0.995848i	$-0.470983\pi$
$223$	14.1895	−	7.22992i	0.950200	−	0.484151i	0.859166	+	0.511697i	$0.170983\pi$
$224$		0			0
$225$	0.291250	+	0.400871i	0.0194167	+	0.0267248i
$226$		0			0
$227$	−19.4279	−	9.89902i	−1.28948	−	0.657021i	−0.331388	−	0.943495i	$-0.607517\pi$
$227$	−19.4279	−	9.89902i	−1.28948	−	0.657021i	−0.958088	+	0.286474i	$0.907517\pi$
$228$		0			0
$229$	−2.36771	+	0.375008i	−0.156462	+	0.0247812i	−0.234174	−	0.972195i	$-0.575239\pi$
$229$	−2.36771	+	0.375008i	−0.156462	+	0.0247812i	0.0777117	+	0.996976i	$0.475239\pi$
$230$		0			0
$231$	0.605253	+	3.34667i	0.0398227	+	0.220194i
$232$		0			0
$233$	−7.99615	−	5.80955i	−0.523845	−	0.380596i	0.294205	−	0.955742i	$-0.404945\pi$
$233$	−7.99615	−	5.80955i	−0.523845	−	0.380596i	−0.818051	+	0.575146i	$0.804945\pi$
$234$		0			0
$235$	8.20844	+	25.2630i	0.535460	+	1.64798i
$236$		0			0
$237$	−4.42331	−	6.08817i	−0.287325	−	0.395469i
$238$		0			0
$239$	−7.22127	−	14.1725i	−0.467105	−	0.916745i	−0.997612	−	0.0690646i	$-0.977999\pi$
$239$	−7.22127	−	14.1725i	−0.467105	−	0.916745i	0.530507	−	0.847680i	$-0.322001\pi$
$240$		0			0
$241$	−20.8804	−	20.8804i	−1.34502	−	1.34502i	−0.890980	−	0.454042i	$-0.849982\pi$
$241$	−20.8804	−	20.8804i	−1.34502	−	1.34502i	−0.454042	−	0.890980i	$-0.650018\pi$
$242$		0			0
$243$	−16.0902			−1.03219
$244$		0			0
$245$	−5.82536	−	11.4329i	−0.372169	−	0.730422i
$246$		0			0
$247$	5.12669	+	19.8170i	0.326204	+	1.26093i
$248$		0			0
$249$	1.53359	+	0.781405i	0.0971875	+	0.0495195i
$250$		0			0
$251$	14.1813	−	19.5189i	0.895114	−	1.23202i	−0.0768861	−	0.997040i	$-0.524498\pi$
$251$	14.1813	−	19.5189i	0.895114	−	1.23202i	0.972000	−	0.234979i	$-0.0755022\pi$
$252$		0			0
$253$	−6.89079	+	9.93351i	−0.433221	+	0.624515i
$254$		0			0
$255$	−0.899916	−	5.68185i	−0.0563549	−	0.355811i
$256$		0			0
$257$	15.1192	−	4.91252i	0.943108	−	0.306434i	0.203196	−	0.979138i	$-0.434867\pi$
$257$	15.1192	−	4.91252i	0.943108	−	0.306434i	0.739912	+	0.672704i	$0.234867\pi$
$258$		0			0
$259$	−0.482409	+	0.350491i	−0.0299754	+	0.0217784i
$260$		0			0
$261$	−21.3564	−	6.93912i	−1.32193	−	0.429521i
$262$		0			0
$263$		−	6.82415i		−	0.420795i	−0.977616	−	0.210398i	$-0.932524\pi$
$263$		−	6.82415i		−	0.420795i	0.977616	−	0.210398i	$-0.0674758\pi$
$264$		0			0
$265$	−2.86889	−	2.86889i	−0.176235	−	0.176235i
$266$		0			0
$267$	1.39233	+	2.73260i	0.0852093	+	0.167233i
$268$		0			0
$269$	−12.8829	+	9.36000i	−0.785486	+	0.570689i	−0.906620	−	0.421947i	$-0.861347\pi$
$269$	−12.8829	+	9.36000i	−0.785486	+	0.570689i	0.121134	+	0.992636i	$0.461347\pi$
$270$		0			0
$271$	−0.933505	+	1.83211i	−0.0567064	+	0.111293i	−0.917620	−	0.397458i	$-0.869892\pi$
$271$	−0.933505	+	1.83211i	−0.0567064	+	0.111293i	0.860914	+	0.508751i	$0.169892\pi$
$272$		0			0
$273$	1.98676	+	3.11806i	0.120244	+	0.188713i
$274$		0			0
$275$	−0.443997	−	0.583858i	−0.0267740	−	0.0352080i
$276$		0			0
$277$	−0.300772	−	0.218524i	−0.0180717	−	0.0131298i	0.578713	−	0.815531i	$-0.303555\pi$
$277$	−0.300772	−	0.218524i	−0.0180717	−	0.0131298i	−0.596784	+	0.802402i	$0.703555\pi$
$278$		0			0
$279$	−0.239905	+	0.470840i	−0.0143627	+	0.0281884i
$280$		0			0
$281$	−15.3541	−	2.43185i	−0.915948	−	0.145072i	−0.319373	−	0.947629i	$-0.603472\pi$
$281$	−15.3541	−	2.43185i	−0.915948	−	0.145072i	−0.596575	+	0.802557i	$0.703472\pi$
$282$		0			0
$283$	0.486835	−	1.49832i	0.0289393	−	0.0890661i	−0.935544	−	0.353211i	$-0.885090\pi$
$283$	0.486835	−	1.49832i	0.0289393	−	0.0890661i	0.964483	+	0.264145i	$0.0850897\pi$
$284$		0			0
$285$	−11.3054			−0.669671
$286$		0			0
$287$	3.24024			0.191266
$288$		0			0
$289$	−2.67446	+	8.23116i	−0.157321	+	0.484186i
$290$		0			0
$291$	−15.0194	−	2.37884i	−0.880453	−	0.139450i
$292$		0			0
$293$	5.80105	−	11.3852i	0.338901	−	0.665131i	−0.657165	−	0.753747i	$-0.728244\pi$
$293$	5.80105	−	11.3852i	0.338901	−	0.665131i	0.996066	+	0.0886161i	$0.0282444\pi$
$294$		0			0
$295$	8.59015	+	6.24111i	0.500138	+	0.363372i
$296$		0			0
$297$	15.1437	−	0.330776i	0.878725	−	0.0191935i
$298$		0			0
$299$	−2.84360	+	12.8314i	−0.164450	+	0.742061i
$300$		0			0
$301$	1.64535	−	3.22918i	0.0948363	−	0.186127i
$302$		0			0
$303$	−4.09141	+	2.97258i	−0.235045	+	0.170770i
$304$		0			0
$305$	−9.75407	−	19.1434i	−0.558516	−	1.09615i
$306$		0			0
$307$	−6.81300	−	6.81300i	−0.388839	−	0.388839i	0.485435	−	0.874273i	$-0.338661\pi$
$307$	−6.81300	−	6.81300i	−0.388839	−	0.388839i	−0.874273	+	0.485435i	$0.838661\pi$
$308$		0			0
$309$		−	12.5825i		−	0.715794i
$310$		0			0
$311$	−32.3211	−	10.5018i	−1.83276	−	0.595501i	−0.999063	−	0.0432826i	$-0.986218\pi$
$311$	−32.3211	−	10.5018i	−1.83276	−	0.595501i	−0.833700	−	0.552218i	$-0.813782\pi$
$312$		0			0
$313$	−15.6250	+	11.3522i	−0.883175	+	0.641664i	−0.934089	−	0.357039i	$-0.883786\pi$
$313$	−15.6250	+	11.3522i	−0.883175	+	0.641664i	0.0509147	+	0.998703i	$0.483786\pi$
$314$		0			0
$315$	5.72890	−	1.86143i	0.322787	−	0.104880i
$316$		0			0
$317$	4.04977	+	25.5692i	0.227458	+	1.43611i	0.791906	+	0.610643i	$0.209089\pi$
$317$	4.04977	+	25.5692i	0.227458	+	1.43611i	−0.564449	+	0.825468i	$0.690911\pi$
$318$		0			0
$319$	31.8309	+	9.57925i	1.78219	+	0.536335i
$320$		0			0
$321$	7.05634	−	9.71222i	0.393846	−	0.542083i
$322$		0			0
$323$	−14.6128	−	7.44561i	−0.813080	−	0.414285i
$324$		0			0
$325$	−0.687094	−	0.404657i	−0.0381131	−	0.0224463i
$326$		0			0
$327$	−2.50236	−	4.91116i	−0.138381	−	0.271588i
$328$		0			0
$329$	13.6783			0.754111
$330$		0			0
$331$	1.90252	+	1.90252i	0.104572	+	0.104572i	0.757457	−	0.652885i	$-0.226442\pi$
$331$	1.90252	+	1.90252i	0.104572	+	0.104572i	−0.652885	+	0.757457i	$0.726442\pi$
$332$		0			0
$333$	0.515477	+	1.01168i	0.0282480	+	0.0554398i
$334$		0			0
$335$	−12.1326	−	16.6991i	−0.662874	−	0.912368i
$336$		0			0
$337$	−5.87300	−	18.0752i	−0.319923	−	0.984621i	−0.973681	−	0.227917i	$-0.926809\pi$
$337$	−5.87300	−	18.0752i	−0.319923	−	0.984621i	0.653758	−	0.756704i	$-0.273191\pi$
$338$		0			0
$339$	13.2040	+	9.59326i	0.717143	+	0.521035i
$340$		0			0
$341$	0.339829	−	0.704579i	0.0184028	−	0.0381551i
$342$		0			0
$343$	−14.6610	+	2.32208i	−0.791621	+	0.125380i
$344$		0			0
$345$	−6.46763	−	3.29542i	−0.348206	−	0.177420i
$346$		0			0
$347$	−1.69880	−	2.33819i	−0.0911962	−	0.125521i	0.760981	−	0.648774i	$-0.224718\pi$
$347$	−1.69880	−	2.33819i	−0.0911962	−	0.125521i	−0.852177	+	0.523254i	$0.824718\pi$
$348$		0			0
$349$	11.8373	−	6.03142i	0.633638	−	0.322855i	−0.107502	−	0.994205i	$-0.534285\pi$
$349$	11.8373	−	6.03142i	0.633638	−	0.322855i	0.741140	+	0.671350i	$0.234285\pi$
$350$		0			0
$351$	15.1006	−	6.56732i	0.806008	−	0.350538i
$352$		0			0
$353$	18.2427	+	18.2427i	0.970960	+	0.970960i	0.999590	−	0.0286298i	$-0.00911441\pi$
$353$	18.2427	+	18.2427i	0.970960	+	0.970960i	−0.0286298	+	0.999590i	$0.509114\pi$
$354$		0			0
$355$	9.56351	+	3.10737i	0.507578	+	0.164922i
$356$		0			0
$357$	−2.92580	−	0.463401i	−0.154850	−	0.0245258i
$358$		0			0
$359$	−4.81890	+	9.45763i	−0.254332	+	0.499155i	−0.982504	−	0.186239i	$-0.940370\pi$
$359$	−4.81890	+	9.45763i	−0.254332	+	0.499155i	0.728172	+	0.685394i	$0.240370\pi$
$360$		0			0
$361$	−7.77674	+	10.7038i	−0.409302	+	0.563356i
$362$		0			0
$363$	−9.57734	+	0.418586i	−0.502680	+	0.0219700i
$364$		0			0
$365$	−13.2767	+	18.2739i	−0.694936	+	0.956498i
$366$		0			0
$367$	9.82708	+	30.2447i	0.512970	+	1.57876i	0.786946	+	0.617022i	$0.211661\pi$
$367$	9.82708	+	30.2447i	0.512970	+	1.57876i	−0.273977	+	0.961736i	$0.588339\pi$
$368$		0			0
$369$	0.965195	−	6.09400i	0.0502461	−	0.317241i
$370$		0			0
$371$	−1.86151	+	0.948485i	−0.0966446	+	0.0492429i
$372$		0			0
$373$		−	35.8683i		−	1.85719i	−0.371096	−	0.928594i	$-0.621018\pi$
$373$		−	35.8683i		−	1.85719i	0.371096	−	0.928594i	$-0.378982\pi$
$374$		0			0
$375$	−6.72911	+	6.72911i	−0.347490	+	0.347490i
$376$		0			0
$377$	35.9703	−	3.46639i	1.85256	−	0.178528i
$378$		0			0
$379$	−2.02702	−	0.321048i	−0.104121	−	0.0164911i	0.104157	−	0.994561i	$-0.466786\pi$
$379$	−2.02702	−	0.321048i	−0.104121	−	0.0164911i	−0.208278	+	0.978070i	$0.566786\pi$
$380$		0			0
$381$	−0.711229	−	2.18894i	−0.0364374	−	0.112143i
$382$		0			0
$383$	−4.31431	−	27.2395i	−0.220451	−	1.39187i	−0.811083	−	0.584931i	$-0.801122\pi$
$383$	−4.31431	−	27.2395i	−0.220451	−	1.39187i	0.590633	−	0.806941i	$-0.298878\pi$
$384$		0			0
$385$	−8.41836	+	2.94003i	−0.429039	+	0.149838i
$386$		0			0
$387$	−5.58308	−	4.05634i	−0.283804	−	0.206196i
$388$		0			0
$389$	4.20306	−	1.36566i	0.213103	−	0.0692415i	−0.200520	−	0.979690i	$-0.564263\pi$
$389$	4.20306	−	1.36566i	0.213103	−	0.0692415i	0.413623	+	0.910448i	$0.364263\pi$
$390$		0			0
$391$	−6.18946	−	8.51906i	−0.313015	−	0.430828i
$392$		0			0
$393$	−5.46495	−	1.77567i	−0.275671	−	0.0895708i
$394$		0			0
$395$	13.9518	−	13.9518i	0.701992	−	0.701992i
$396$		0			0
$397$	−0.521108	+	0.521108i	−0.0261536	+	0.0261536i	−0.720063	−	0.693909i	$-0.755887\pi$
$397$	−0.521108	+	0.521108i	−0.0261536	+	0.0261536i	0.693909	+	0.720063i	$0.255887\pi$
$398$		0			0
$399$	−1.79896	+	5.53663i	−0.0900606	+	0.277178i
$400$		0			0
$401$	−3.17401	+	20.0399i	−0.158502	+	1.00074i	0.772310	+	0.635246i	$0.219101\pi$
$401$	−3.17401	+	20.0399i	−0.158502	+	1.00074i	−0.930812	+	0.365498i	$0.880899\pi$
$402$		0			0
$403$	0.0518487	−	0.848813i	0.00258277	−	0.0422824i
$404$		0			0
$405$	−0.979869	−	6.18665i	−0.0486901	−	0.307417i
$406$		0			0
$407$	−0.795589	−	1.48058i	−0.0394359	−	0.0733898i
$408$		0			0
$409$	27.5527	−	4.36392i	1.36239	−	0.215782i	0.567922	−	0.823082i	$-0.307747\pi$
$409$	27.5527	−	4.36392i	1.36239	−	0.215782i	0.794473	+	0.607300i	$0.207747\pi$
$410$		0			0
$411$	−8.70982	−	4.43787i	−0.429624	−	0.218904i
$412$		0			0
$413$	4.42339	−	3.21378i	0.217661	−	0.158140i
$414$		0			0
$415$	−1.39453	+	4.29193i	−0.0684549	+	0.210683i
$416$		0			0
$417$			11.8755i			0.581544i
$418$		0			0
$419$	25.1322			1.22779			0.613895	−	0.789388i	$-0.289602\pi$
$419$	25.1322			1.22779			0.613895	+	0.789388i	$0.289602\pi$
$420$		0			0
$421$	−12.8654	+	6.55527i	−0.627023	+	0.319484i	−0.738470	−	0.674286i	$-0.764451\pi$
$421$	−12.8654	+	6.55527i	−0.627023	+	0.319484i	0.111447	+	0.993770i	$0.464451\pi$
$422$		0			0
$423$	4.07446	−	25.7252i	0.198107	−	1.25080i
$424$		0			0
$425$	0.607617	−	0.197427i	0.0294738	−	0.00957661i
$426$		0			0
$427$	−10.9273	+	1.73072i	−0.528810	+	0.0837553i
$428$		0			0
$429$	−9.46387	+	4.36406i	−0.456920	+	0.210699i
$430$		0			0
$431$	23.1496	−	3.66653i	1.11508	−	0.176611i	0.428410	−	0.903584i	$-0.359074\pi$
$431$	23.1496	−	3.66653i	1.11508	−	0.176611i	0.686665	+	0.726974i	$0.259074\pi$
$432$		0			0
$433$	0.839885	−	0.272895i	0.0403623	−	0.0131145i	−0.288766	−	0.957400i	$-0.593245\pi$
$433$	0.839885	−	0.272895i	0.0403623	−	0.0131145i	0.329129	+	0.944285i	$0.393245\pi$
$434$		0			0
$435$	−3.12221	+	19.7128i	−0.149698	+	0.945158i
$436$		0			0
$437$	−18.4387	+	9.39497i	−0.882041	+	0.449422i
$438$		0			0
$439$	24.4890			1.16880			0.584399	−	0.811466i	$-0.301330\pi$
$439$	24.4890			1.16880			0.584399	+	0.811466i	$0.301330\pi$
$440$		0			0
$441$			12.5816i			0.599124i
$442$		0			0
$443$	3.11983	−	9.60186i	0.148228	−	0.456198i	−0.849184	−	0.528097i	$-0.822906\pi$
$443$	3.11983	−	9.60186i	0.148228	−	0.456198i	0.997412	+	0.0718987i	$0.0229058\pi$
$444$		0			0
$445$	−6.50535	+	4.72641i	−0.308383	+	0.224053i
$446$		0			0
$447$	−10.7800	−	5.49266i	−0.509874	−	0.259794i
$448$		0			0
$449$	−18.9717	+	3.00482i	−0.895329	+	0.141806i	−0.587108	−	0.809509i	$-0.699734\pi$
$449$	−18.9717	+	3.00482i	−0.895329	+	0.141806i	−0.308221	+	0.951315i	$0.599734\pi$
$450$		0			0
$451$	−1.23145	+	9.05007i	−0.0579869	+	0.426151i
$452$		0			0
$453$	−2.24371	−	14.1662i	−0.105419	−	0.665587i
$454$		0			0
$455$	−7.25971	+	6.42387i	−0.340340	+	0.301155i
$456$		0			0
$457$	2.70418	−	17.0735i	0.126496	−	0.798666i	−0.840113	−	0.542411i	$-0.817511\pi$
$457$	2.70418	−	17.0735i	0.126496	−	0.798666i	0.966609	−	0.256255i	$-0.0824886\pi$
$458$		0			0
$459$	−4.07700	+	12.5477i	−0.190298	+	0.585677i
$460$		0			0
$461$	−14.8693	+	14.8693i	−0.692531	+	0.692531i	−0.962788	−	0.270257i	$-0.912891\pi$
$461$	−14.8693	+	14.8693i	−0.692531	+	0.692531i	0.270257	+	0.962788i	$0.412891\pi$
$462$		0			0
$463$	26.7540	−	26.7540i	1.24337	−	1.24337i	0.284770	−	0.958596i	$-0.408083\pi$
$463$	26.7540	−	26.7540i	1.24337	−	1.24337i	0.958596	−	0.284770i	$-0.0919171\pi$
$464$		0			0
$465$	0.446689	+	0.145138i	0.0207147	+	0.00673062i
$466$		0			0
$467$	0.144473	+	0.198851i	0.00668543	+	0.00920171i	0.812347	−	0.583175i	$-0.198190\pi$
$467$	0.144473	+	0.198851i	0.00668543	+	0.00920171i	−0.805661	+	0.592377i	$0.798190\pi$
$468$		0			0
$469$	−10.1087	+	3.28452i	−0.466777	+	0.151665i
$470$		0			0
$471$	2.72089	+	1.97684i	0.125372	+	0.0910882i
$472$		0			0
$473$	8.39385	+	5.82274i	0.385950	+	0.267730i
$474$		0			0
$475$	−0.196413	−	1.24010i	−0.00901205	−	0.0568999i
$476$		0			0
$477$	1.22934	+	3.78351i	0.0562875	+	0.173235i
$478$		0			0
$479$	0.185053	+	0.0293094i	0.00845526	+	0.00133918i	0.160661	−	0.987010i	$-0.448638\pi$
$479$	0.185053	+	0.0293094i	0.00845526	+	0.00133918i	−0.152205	+	0.988349i	$0.548638\pi$
$480$		0			0
$481$	−1.41002	−	1.16215i	−0.0642914	−	0.0529893i
$482$		0			0
$483$	−2.64304	+	2.64304i	−0.120263	+	0.120263i
$484$		0			0
$485$		−	39.8703i		−	1.81042i
$486$		0			0
$487$	−2.48416	+	1.26574i	−0.112568	+	0.0573562i	−0.509368	−	0.860549i	$-0.670121\pi$
$487$	−2.48416	+	1.26574i	−0.112568	+	0.0573562i	0.396800	+	0.917905i	$0.370121\pi$
$488$		0			0
$489$	0.110953	−	0.700530i	0.00501747	−	0.0316791i
$490$		0			0
$491$	8.04428	+	24.7578i	0.363033	+	1.11730i	0.951203	+	0.308564i	$0.0998486\pi$
$491$	8.04428	+	24.7578i	0.363033	+	1.11730i	−0.588170	+	0.808737i	$0.700151\pi$
$492$		0			0
$493$	−17.0184	+	23.4238i	−0.766468	+	1.05495i
$494$		0			0
$495$	3.02175	+	16.7084i	0.135818	+	0.750986i
$496$		0			0
$497$	3.04358	−	4.18913i	0.136523	−	0.187908i
$498$		0			0
$499$	−2.04924	+	4.02187i	−0.0917367	+	0.180043i	−0.932316	−	0.361646i	$-0.882215\pi$
$499$	−2.04924	+	4.02187i	−0.0917367	+	0.180043i	0.840579	+	0.541689i	$0.182215\pi$
$500$		0			0
$501$	15.5756	+	2.46693i	0.695867	+	0.110215i
$502$		0			0
$503$	−26.5910	−	8.63993i	−1.18563	−	0.385236i	−0.351176	−	0.936309i	$-0.614218\pi$
$503$	−26.5910	−	8.63993i	−1.18563	−	0.385236i	−0.834457	+	0.551074i	$0.814218\pi$
$504$		0			0
$505$	−9.37599	−	9.37599i	−0.417226	−	0.417226i
$506$		0			0
$507$	−7.72538	+	8.28707i	−0.343096	+	0.368042i
$508$		0			0
$509$	17.2997	−	8.81463i	0.766795	−	0.390702i	−0.0264140	−	0.999651i	$-0.508409\pi$
$509$	17.2997	−	8.81463i	0.766795	−	0.390702i	0.793209	+	0.608950i	$0.208409\pi$
$510$		0			0
$511$	6.83669	+	9.40990i	0.302437	+	0.416270i
$512$		0			0
$513$	23.1022	+	11.7712i	1.01999	+	0.519709i
$514$		0			0
$515$	32.5840	−	5.16079i	1.43582	−	0.227412i
$516$		0			0
$517$	−5.19845	+	38.2039i	−0.228627	+	1.68020i
$518$		0			0
$519$	7.62865	+	5.54254i	0.334861	+	0.243290i
$520$		0			0
$521$	−6.45630	−	19.8704i	−0.282856	−	0.870540i	−0.987033	−	0.160516i	$-0.948684\pi$
$521$	−6.45630	−	19.8704i	−0.282856	−	0.870540i	0.704178	−	0.710024i	$-0.251316\pi$
$522$		0			0
$523$	4.79959	+	6.60607i	0.209872	+	0.288863i	0.900956	−	0.433911i	$-0.142867\pi$
$523$	4.79959	+	6.60607i	0.209872	+	0.288863i	−0.691084	+	0.722774i	$0.742867\pi$
$524$		0			0
$525$	−0.102957	−	0.202064i	−0.00449341	−	0.00881881i
$526$		0			0
$527$	0.481786	+	0.481786i	0.0209869	+	0.0209869i
$528$		0			0
$529$	9.71293			0.422301
$530$		0			0
$531$	−4.72661	−	9.27649i	−0.205117	−	0.402566i
$532$		0			0
$533$	2.48681	+	9.61267i	0.107716	+	0.416371i
$534$		0			0
$535$	28.0452	+	14.2897i	1.21250	+	0.617799i
$536$		0			0
$537$	−6.50685	+	8.95591i	−0.280791	+	0.386476i
$538$		0			0
$539$	−0.406712	−	18.6202i	−0.0175183	−	0.802031i
$540$		0			0
$541$	−3.35413	−	21.1771i	−0.144205	−	0.910475i	−0.948622	−	0.316411i	$-0.897522\pi$
$541$	−3.35413	−	21.1771i	−0.144205	−	0.910475i	0.804417	−	0.594065i	$-0.202478\pi$
$542$		0			0
$543$	18.5153	−	6.01597i	0.794566	−	0.258170i
$544$		0			0
$545$	11.6917	−	8.49453i	0.500818	−	0.363866i
$546$		0			0
$547$	38.6060	+	12.5439i	1.65067	+	0.536337i	0.978886	−	0.204406i	$-0.0655264\pi$
$547$	38.6060	+	12.5439i	1.65067	+	0.536337i	0.671788	+	0.740743i	$0.265526\pi$
$548$		0			0
$549$			21.0668i			0.899109i
$550$		0			0
$551$	40.2345	+	40.2345i	1.71405	+	1.71405i
$552$		0			0
$553$	−4.61262	−	9.05277i	−0.196148	−	0.384963i
$554$		0			0
$555$	0.816446	−	0.593183i	0.0346562	−	0.0251792i
$556$		0			0
$557$	4.33807	−	8.51394i	0.183810	−	0.360747i	−0.780653	−	0.624964i	$-0.785114\pi$
$557$	4.33807	−	8.51394i	0.183810	−	0.360747i	0.964463	+	0.264217i	$0.0851135\pi$
$558$		0			0
$559$	10.8426	+	2.40285i	0.458593	+	0.101630i
$560$		0			0
$561$	2.40624	−	7.99570i	0.101591	−	0.337579i
$562$		0			0
$563$	5.37578	+	3.90573i	0.226562	+	0.164607i	0.695276	−	0.718743i	$-0.255282\pi$
$563$	5.37578	+	3.90573i	0.226562	+	0.164607i	−0.468713	+	0.883350i	$0.655282\pi$
$564$		0			0
$565$	−19.4273	+	38.1281i	−0.817311	+	1.60406i
$566$		0			0
$567$	−3.18574	−	0.504571i	−0.133788	−	0.0211900i
$568$		0			0
$569$	−10.5960	+	32.6111i	−0.444206	+	1.36713i	0.439145	+	0.898416i	$0.355281\pi$
$569$	−10.5960	+	32.6111i	−0.444206	+	1.36713i	−0.883352	+	0.468711i	$0.844719\pi$
$570$		0			0
$571$	20.5543			0.860171			0.430085	−	0.902788i	$-0.358483\pi$
$571$	20.5543			0.860171			0.430085	+	0.902788i	$0.358483\pi$
$572$		0			0
$573$	−8.54543			−0.356990
$574$		0			0
$575$	0.249116	−	0.766699i	0.0103888	−	0.0319736i
$576$		0			0
$577$	19.1856	+	3.03870i	0.798706	+	0.126503i	0.542430	−	0.840101i	$-0.317504\pi$
$577$	19.1856	+	3.03870i	0.798706	+	0.126503i	0.256276	+	0.966604i	$0.417504\pi$
$578$		0			0
$579$	5.62460	−	11.0389i	0.233751	−	0.458761i
$580$		0			0
$581$	1.88000	+	1.36590i	0.0779957	+	0.0566672i
$582$		0			0
$583$	−1.94167	−	5.55970i	−0.0804159	−	0.230259i
$584$		0			0
$585$	9.91901	+	15.5670i	0.410101	+	0.643617i
$586$		0			0
$587$	0.853508	−	1.67510i	0.0352280	−	0.0691389i	−0.872722	−	0.488218i	$-0.837647\pi$
$587$	0.853508	−	1.67510i	0.0352280	−	0.0691389i	0.907950	+	0.419079i	$0.137647\pi$
$588$		0			0
$589$	1.08328	−	0.787049i	0.0446358	−	0.0324298i
$590$		0			0
$591$	−0.109935	−	0.215759i	−0.00452210	−	0.00887512i
$592$		0			0
$593$	−20.2783	−	20.2783i	−0.832728	−	0.832728i	0.155161	−	0.987889i	$-0.450410\pi$
$593$	−20.2783	−	20.2783i	−0.832728	−	0.832728i	−0.987889	+	0.155161i	$0.950410\pi$
$594$		0			0
$595$		−	7.76679i		−	0.318407i
$596$		0			0
$597$	−11.3290	−	3.68102i	−0.463665	−	0.150654i
$598$		0			0
$599$	−34.0973	+	24.7731i	−1.39318	+	1.01220i	−0.397669	+	0.917529i	$0.630181\pi$
$599$	−34.0973	+	24.7731i	−1.39318	+	1.01220i	−0.995508	+	0.0946740i	$0.969819\pi$
$600$		0			0
$601$	1.58301	−	0.514350i	0.0645722	−	0.0209808i	−0.276553	−	0.960999i	$-0.589192\pi$
$601$	1.58301	−	0.514350i	0.0645722	−	0.0209808i	0.341125	+	0.940018i	$0.389192\pi$
$602$		0			0
$603$	3.16612	+	19.9901i	0.128934	+	0.814059i
$604$		0			0
$605$	−5.01218	−	24.6300i	−0.203774	−	1.00135i
$606$		0			0
$607$	−11.4369	+	15.7415i	−0.464208	+	0.638928i	−0.975375	−	0.220554i	$-0.929214\pi$
$607$	−11.4369	+	15.7415i	−0.464208	+	0.638928i	0.511166	+	0.859482i	$0.329214\pi$
$608$		0			0
$609$	9.15724	+	4.66585i	0.371070	+	0.189070i
$610$		0			0
$611$	10.4978	+	40.5788i	0.424695	+	1.64164i
$612$		0			0
$613$	3.17694	+	6.23510i	0.128315	+	0.251833i	0.946222	−	0.323518i	$-0.104866\pi$
$613$	3.17694	+	6.23510i	0.128315	+	0.251833i	−0.817907	+	0.575351i	$0.804866\pi$
$614$		0			0
$615$	−5.48390			−0.221132
$616$		0			0
$617$	5.39619	+	5.39619i	0.217242	+	0.217242i	0.807335	−	0.590093i	$-0.200909\pi$
$617$	5.39619	+	5.39619i	0.217242	+	0.217242i	−0.590093	+	0.807335i	$0.700909\pi$
$618$		0			0
$619$	6.75212	+	13.2518i	0.271391	+	0.532634i	0.985970	−	0.166920i	$-0.0533821\pi$
$619$	6.75212	+	13.2518i	0.271391	+	0.532634i	−0.714580	+	0.699554i	$0.753382\pi$
$620$		0			0
$621$	9.78525	+	13.4682i	0.392668	+	0.540462i
$622$		0			0
$623$	1.27953	+	3.93798i	0.0512632	+	0.157772i
$624$		0			0
$625$	−21.0805	−	15.3159i	−0.843218	−	0.612634i
$626$		0			0
$627$	−14.7802	−	7.12872i	−0.590265	−	0.284694i
$628$		0			0
$629$	1.44597	−	0.229019i	0.0576546	−	0.00913159i
$630$		0			0
$631$	−3.07258	−	1.56556i	−0.122318	−	0.0623240i	0.391761	−	0.920067i	$-0.371866\pi$
$631$	−3.07258	−	1.56556i	−0.122318	−	0.0623240i	−0.514079	+	0.857743i	$0.671866\pi$
$632$		0			0
$633$	9.69865	+	13.3491i	0.385487	+	0.530577i
$634$		0			0
$635$	5.37682	−	2.73962i	0.213372	−	0.108719i
$636$		0			0
$637$	−8.07500	−	18.5672i	−0.319943	−	0.735660i
$638$		0			0
$639$	−6.97197	−	6.97197i	−0.275807	−	0.275807i
$640$		0			0
$641$	−11.9638	−	3.88727i	−0.472541	−	0.153538i	0.0630588	−	0.998010i	$-0.479914\pi$
$641$	−11.9638	−	3.88727i	−0.472541	−	0.153538i	−0.535600	+	0.844472i	$0.679914\pi$
$642$		0			0
$643$	−7.16855	−	1.13539i	−0.282700	−	0.0447753i	0.0134742	−	0.999909i	$-0.495711\pi$
$643$	−7.16855	−	1.13539i	−0.282700	−	0.0447753i	−0.296174	+	0.955134i	$0.595711\pi$
$644$		0			0
$645$	−2.78464	+	5.46517i	−0.109645	+	0.215191i
$646$		0			0
$647$	7.84802	−	10.8019i	0.308537	−	0.424665i	−0.626387	−	0.779512i	$-0.715467\pi$
$647$	7.84802	−	10.8019i	0.308537	−	0.424665i	0.934924	+	0.354847i	$0.115467\pi$
$648$		0			0
$649$	7.29506	+	13.5760i	0.286356	+	0.532906i
$650$		0			0
$651$	0.142158	−	0.195664i	0.00557163	−	0.00766869i
$652$		0			0
$653$	−5.61239	−	17.2732i	−0.219630	−	0.675951i	−0.998792	−	0.0491292i	$-0.984355\pi$
$653$	−5.61239	−	17.2732i	−0.219630	−	0.675951i	0.779163	−	0.626822i	$-0.215645\pi$
$654$		0			0
$655$	2.35684	−	14.8805i	0.0920893	−	0.581429i
$656$		0			0
$657$	19.7339	−	10.0549i	0.769893	−	0.392280i
$658$		0			0
$659$		−	4.40663i		−	0.171658i	−0.996310	−	0.0858290i	$-0.972646\pi$
$659$		−	4.40663i		−	0.171658i	0.996310	−	0.0858290i	$-0.0273539\pi$
$660$		0			0
$661$	15.8190	−	15.8190i	0.615289	−	0.615289i	−0.329031	−	0.944319i	$-0.606722\pi$
$661$	15.8190	−	15.8190i	0.615289	−	0.615289i	0.944319	+	0.329031i	$0.106722\pi$
$662$		0			0
$663$	−0.870733	−	9.03547i	−0.0338165	−	0.350908i
$664$		0			0
$665$	−15.0756	−	2.38775i	−0.584608	−	0.0925928i
$666$		0			0
$667$	11.2895	+	34.7456i	0.437133	+	1.34536i
$668$		0			0
$669$	2.17113	+	13.7080i	0.0839407	+	0.529981i
$670$		0			0
$671$	−0.681005	−	31.1780i	−0.0262899	−	1.20361i
$672$		0			0
$673$	−20.6502	−	15.0033i	−0.796007	−	0.578333i	0.113733	−	0.993511i	$-0.463719\pi$
$673$	−20.6502	−	15.0033i	−0.796007	−	0.578333i	−0.909740	+	0.415178i	$0.863719\pi$
$674$		0			0
$675$	−0.960614	+	0.312122i	−0.0369741	+	0.0120136i
$676$		0			0
$677$	10.1617	+	13.9864i	0.390545	+	0.537540i	0.958340	−	0.285631i	$-0.0922031\pi$
$677$	10.1617	+	13.9864i	0.390545	+	0.537540i	−0.567794	+	0.823170i	$0.692203\pi$
$678$		0			0
$679$	−19.5259	−	6.34435i	−0.749335	−	0.243474i
$680$		0			0
$681$	13.4368	−	13.4368i	0.514901	−	0.514901i
$682$		0			0
$683$	−36.2925	+	36.2925i	−1.38870	+	1.38870i	−0.560628	+	0.828068i	$0.689440\pi$
$683$	−36.2925	+	36.2925i	−1.38870	+	1.38870i	−0.828068	+	0.560628i	$0.810560\pi$
$684$		0			0
$685$	7.92004	−	24.3754i	0.302609	−	0.931335i
$686$		0			0
$687$	0.326819	−	2.06345i	0.0124689	−	0.0787256i
$688$		0			0
$689$	−4.24248	−	4.79450i	−0.161626	−	0.182656i
$690$		0			0
$691$	−7.08216	−	44.7150i	−0.269418	−	1.70104i	−0.636850	−	0.770988i	$-0.719763\pi$
$691$	−7.08216	−	44.7150i	−0.269418	−	1.70104i	0.367432	−	0.930050i	$-0.380237\pi$
$692$		0			0
$693$	8.66351	+	1.17885i	0.329100	+	0.0447810i
$694$		0			0
$695$	−30.7530	+	4.87080i	−1.16653	+	0.184760i
$696$		0			0
$697$	−7.08827	−	3.61165i	−0.268487	−	0.136801i
$698$		0			0
$699$	6.96863	−	5.06301i	0.263578	−	0.191501i
$700$		0			0
$701$	5.98809	−	18.4294i	0.226167	−	0.696070i	−0.772004	−	0.635618i	$-0.780746\pi$
$701$	5.98809	−	18.4294i	0.226167	−	0.696070i	0.998171	−	0.0604528i	$-0.0192545\pi$
$702$		0			0
$703$		−	2.87709i		−	0.108512i
$704$		0			0
$705$	−23.1497			−0.871867
$706$		0			0
$707$	−6.08370	+	3.09980i	−0.228801	+	0.116580i
$708$		0			0
$709$	−5.01526	+	31.6651i	−0.188352	+	1.18921i	0.694478	+	0.719514i	$0.255636\pi$
$709$	−5.01526	+	31.6651i	−0.188352	+	1.18921i	−0.882830	+	0.469693i	$0.844364\pi$
$710$		0			0
$711$	−18.3997	+	5.97844i	−0.690044	+	0.224209i
$712$		0			0
$713$	0.849149	−	0.134492i	0.0318009	−	0.00503676i
$714$		0			0
$715$	−15.1829	−	22.7179i	−0.567810	−	0.849602i
$716$		0			0
$717$	13.6916	−	2.16853i	0.511321	−	0.0809853i
$718$		0			0
$719$	22.7062	−	7.37770i	0.846800	−	0.275142i	0.146695	−	0.989182i	$-0.453136\pi$
$719$	22.7062	−	7.37770i	0.846800	−	0.275142i	0.700105	+	0.714040i	$0.253136\pi$
$720$		0			0
$721$	2.65749	−	16.7787i	0.0989700	−	0.624872i
$722$		0			0
$723$	22.9298	−	11.6833i	0.852769	−	0.434507i
$724$		0			0
$725$	−2.21658			−0.0823217
$726$		0			0
$727$		−	10.9628i		−	0.406587i	−0.979118	−	0.203293i	$-0.934836\pi$
$727$		−	10.9628i		−	0.406587i	0.979118	−	0.203293i	$-0.0651645\pi$
$728$		0			0
$729$	1.79193	−	5.51500i	0.0663678	−	0.204259i
$730$		0			0
$731$	−7.19864	+	5.23012i	−0.266251	+	0.193443i
$732$		0			0
$733$	−25.3662	−	12.9247i	−0.936923	−	0.477386i	−0.0822843	−	0.996609i	$-0.526222\pi$
$733$	−25.3662	−	12.9247i	−0.936923	−	0.477386i	−0.854639	+	0.519223i	$0.826222\pi$
$734$		0			0
$735$	11.0449	−	1.74934i	0.407398	−	0.0645255i
$736$		0			0
$737$	−5.33192	−	29.4821i	−0.196404	−	1.08599i
$738$		0			0
$739$	7.43039	+	46.9137i	0.273331	+	1.72575i	0.617267	+	0.786754i	$0.288240\pi$
$739$	7.43039	+	46.9137i	0.273331	+	1.72575i	−0.343936	+	0.938993i	$0.611760\pi$
$740$		0			0
$741$	−17.8059	−	1.08765i	−0.654115	−	0.0399559i
$742$		0			0
$743$	1.08970	−	6.88011i	0.0399773	−	0.252407i	−0.959604	−	0.281356i	$-0.909216\pi$
$743$	1.08970	−	6.88011i	0.0399773	−	0.252407i	0.999581	+	0.0289488i	$0.00921599\pi$
$744$		0			0
$745$	9.80246	−	30.1689i	0.359134	−	1.10530i
$746$		0			0
$747$	3.12889	−	3.12889i	0.114480	−	0.114480i
$748$		0			0
$749$	11.4609	−	11.4609i	0.418771	−	0.418771i
$750$		0			0
$751$	2.58467	+	0.839809i	0.0943158	+	0.0306451i	0.355795	−	0.934564i	$-0.384210\pi$
$751$	2.58467	+	0.839809i	0.0943158	+	0.0306451i	−0.261479	+	0.965209i	$0.584210\pi$
$752$		0			0
$753$	12.3590	+	17.0106i	0.450386	+	0.619902i
$754$		0			0
$755$	35.7649	−	11.6207i	1.30162	−	0.422922i
$756$		0			0
$757$	−31.2933	−	22.7359i	−1.13737	−	0.826350i	−0.150622	−	0.988592i	$-0.548127\pi$
$757$	−31.2933	−	22.7359i	−1.13737	−	0.826350i	−0.986751	+	0.162242i	$0.948127\pi$
$758$		0			0
$759$	−6.37759	−	8.38657i	−0.231492	−	0.304413i
$760$		0			0
$761$	3.27127	+	20.6540i	0.118583	+	0.748705i	0.973287	+	0.229590i	$0.0737385\pi$
$761$	3.27127	+	20.6540i	0.118583	+	0.748705i	−0.854704	+	0.519115i	$0.826261\pi$
$762$		0			0
$763$	−2.29963	−	7.07753i	−0.0832521	−	0.256224i
$764$		0			0
$765$	−14.6072	−	2.31355i	−0.528124	−	0.0836465i
$766$		0			0
$767$	12.9290	+	10.6562i	0.466840	+	0.384772i
$768$		0			0
$769$	−36.2996	+	36.2996i	−1.30900	+	1.30900i	−0.386857	+	0.922140i	$0.626439\pi$
$769$	−36.2996	+	36.2996i	−1.30900	+	1.30900i	−0.922140	+	0.386857i	$0.873561\pi$
$770$		0			0
$771$			13.8544i			0.498955i
$772$		0			0
$773$	−6.10469	+	3.11050i	−0.219571	+	0.111877i	−0.560316	−	0.828279i	$-0.689320\pi$
$773$	−6.10469	+	3.11050i	−0.219571	+	0.111877i	0.340746	+	0.940155i	$0.389320\pi$
$774$		0			0
$775$	−0.00815992	+	0.0515197i	−0.000293113	+	0.00185064i
$776$		0			0
$777$	−0.160586	−	0.494232i	−0.00576098	−	0.0177305i
$778$		0			0
$779$	−9.18951	+	12.6483i	−0.329248	+	0.453171i
$780$		0			0
$781$	10.5436	+	10.0929i	0.377280	+	0.361151i
$782$		0			0
$783$	26.9052	−	37.0318i	0.961514	−	1.32341i
$784$		0			0
$785$	−4.00329	+	7.85691i	−0.142884	+	0.280425i
$786$		0			0
$787$	22.6743	+	3.59126i	0.808251	+	0.128014i	0.546866	−	0.837220i	$-0.315821\pi$
$787$	22.6743	+	3.59126i	0.808251	+	0.128014i	0.261385	+	0.965235i	$0.415821\pi$
$788$		0			0
$789$	5.65616	+	1.83780i	0.201365	+	0.0654273i
$790$		0			0
$791$	15.5813	+	15.5813i	0.554008	+	0.554008i
$792$		0			0
$793$	−13.5209	−	31.0892i	−0.480141	−	1.10401i
$794$		0			0
$795$	3.15048	−	1.60525i	0.111736	−	0.0569323i
$796$		0			0
$797$	−21.5165	−	29.6150i	−0.762155	−	1.04902i	−0.997032	−	0.0769909i	$-0.975469\pi$
$797$	−21.5165	−	29.6150i	−0.762155	−	1.04902i	0.234877	−	0.972025i	$-0.424531\pi$
$798$		0			0
$799$	−29.9223	−	15.2462i	−1.05858	−	0.539371i
$800$		0			0
$801$	7.78740	−	1.23340i	0.275154	−	0.0435801i
$802$		0			0
$803$	−28.8803	+	15.5188i	−1.01917	+	0.547647i
$804$		0			0
$805$	−7.92855	−	5.76043i	−0.279445	−	0.203028i
$806$		0			0
$807$	−4.28850	−	13.1987i	−0.150962	−	0.464615i
$808$		0			0
$809$	17.2921	+	23.8006i	0.607960	+	0.836785i	0.996408	−	0.0846860i	$-0.0269887\pi$
$809$	17.2921	+	23.8006i	0.607960	+	0.836785i	−0.388448	+	0.921471i	$0.626989\pi$
$810$		0			0
$811$	−3.98104	−	7.81323i	−0.139793	−	0.274359i	0.810487	−	0.585757i	$-0.199203\pi$
$811$	−3.98104	−	7.81323i	−0.139793	−	0.274359i	−0.950280	+	0.311398i	$0.899203\pi$
$812$		0			0
$813$	−1.26713	−	1.26713i	−0.0444402	−	0.0444402i
$814$		0			0
$815$	1.85962			0.0651396
$816$		0			0
$817$	7.93878	+	15.5807i	0.277743	+	0.545101i
$818$		0			0
$819$	9.20208	−	2.38059i	0.321547	−	0.0831845i
$820$		0			0
$821$	−33.3929	−	17.0145i	−1.16542	−	0.593811i	−0.239265	−	0.970954i	$-0.576907\pi$
$821$	−33.3929	−	17.0145i	−1.16542	−	0.593811i	−0.926155	+	0.377143i	$0.876907\pi$
$822$		0			0
$823$	−7.65322	+	10.5338i	−0.266774	+	0.367184i	−0.921297	−	0.388859i	$-0.872869\pi$
$823$	−7.65322	+	10.5338i	−0.266774	+	0.367184i	0.654523	+	0.756042i	$0.272869\pi$
$824$		0			0
$825$	0.603499	−	0.210766i	0.0210111	−	0.00733795i
$826$		0			0
$827$	0.0200438	+	0.126552i	0.000696993	+	0.00440064i	0.988034	−	0.154234i	$-0.0492909\pi$
$827$	0.0200438	+	0.126552i	0.000696993	+	0.00440064i	−0.987337	+	0.158634i	$0.949291\pi$
$828$		0			0
$829$	40.4931	−	13.1570i	1.40638	−	0.456962i	0.495134	−	0.868816i	$-0.335119\pi$
$829$	40.4931	−	13.1570i	1.40638	−	0.456962i	0.911250	+	0.411854i	$0.135119\pi$
$830$		0			0
$831$	0.262123	−	0.190443i	0.00909293	−	0.00660640i
$832$		0			0
$833$	15.4283	+	5.01296i	0.534559	+	0.173689i
$834$		0			0
$835$			41.3468i			1.43087i
$836$		0			0
$837$	−0.761680	−	0.761680i	−0.0263275	−	0.0263275i
$838$		0			0
$839$	−6.17059	−	12.1105i	−0.213032	−	0.418100i	0.759619	−	0.650368i	$-0.225385\pi$
$839$	−6.17059	−	12.1105i	−0.213032	−	0.418100i	−0.972652	+	0.232268i	$0.925385\pi$
$840$		0			0
$841$	57.8058	−	41.9984i	1.99330	−	1.44822i
$842$		0			0
$843$	6.15060	−	12.0712i	0.211838	−	0.415755i
$844$		0			0
$845$	−24.6290	−	16.6069i	−0.847264	−	0.571293i
$846$		0			0
$847$	−12.8597	−	1.46460i	−0.441866	−	0.0503242i
$848$		0			0
$849$	1.11077	+	0.807020i	0.0381215	+	0.0276969i
$850$		0			0
$851$	0.838651	−	1.64594i	0.0287486	−	0.0564223i
$852$		0			0
$853$	−21.8139	−	3.45498i	−0.746893	−	0.118296i	−0.228625	−	0.973515i	$-0.573423\pi$
$853$	−21.8139	−	3.45498i	−0.746893	−	0.118296i	−0.518268	+	0.855218i	$0.673423\pi$
$854$		0			0
$855$	−8.98138	+	27.6418i	−0.307157	+	0.945331i
$856$		0			0
$857$	−25.9236			−0.885534			−0.442767	−	0.896637i	$-0.646003\pi$
$857$	−25.9236			−0.885534			−0.442767	+	0.896637i	$0.646003\pi$
$858$		0			0
$859$	−45.6174			−1.55644			−0.778222	−	0.627989i	$-0.783878\pi$
$859$	−45.6174			−1.55644			−0.778222	+	0.627989i	$0.783878\pi$
$860$		0			0
$861$	−0.872623	+	2.68566i	−0.0297389	+	0.0915270i
$862$		0			0
$863$	31.8928	+	5.05132i	1.08564	+	0.171949i	0.673513	−	0.739176i	$-0.264785\pi$
$863$	31.8928	+	5.05132i	1.08564	+	0.171949i	0.412131	+	0.911125i	$0.364785\pi$
$864$		0			0
$865$	−11.2242	+	22.0286i	−0.381633	+	0.748996i
$866$		0			0
$867$	−6.10209	−	4.43343i	−0.207238	−	0.150567i
$868$		0			0
$869$	27.0376	−	9.44264i	0.917188	−	0.320319i
$870$		0			0
$871$	−17.5022	−	27.4682i	−0.593040	−	0.930725i
$872$		0			0
$873$	−17.7483	+	34.8330i	−0.600688	+	1.17892i
$874$		0			0
$875$	−10.3945	+	7.55202i	−0.351397	+	0.255305i
$876$		0			0
$877$	−12.3820	−	24.3009i	−0.418109	−	0.820585i	−0.999973	−	0.00729903i	$-0.997677\pi$
$877$	−12.3820	−	24.3009i	−0.418109	−	0.820585i	0.581865	−	0.813286i	$-0.302323\pi$
$878$		0			0
$879$	7.87429	+	7.87429i	0.265593	+	0.265593i
$880$		0			0
$881$		−	35.1702i		−	1.18492i	−0.805601	−	0.592458i	$-0.798158\pi$
$881$		−	35.1702i		−	1.18492i	0.805601	−	0.592458i	$-0.201842\pi$
$882$		0			0
$883$	−2.10364	−	0.683513i	−0.0707930	−	0.0230020i	0.273406	−	0.961899i	$-0.411850\pi$
$883$	−2.10364	−	0.683513i	−0.0707930	−	0.0230020i	−0.344199	+	0.938897i	$0.611850\pi$
$884$		0			0
$885$	−7.48630	+	5.43912i	−0.251649	+	0.182834i
$886$		0			0
$887$	−45.8074	+	14.8837i	−1.53806	+	0.499746i	−0.950841	−	0.309680i	$-0.899778\pi$
$887$	−45.8074	+	14.8837i	−1.53806	+	0.499746i	−0.587221	+	0.809427i	$0.699778\pi$
$888$		0			0
$889$	−0.486107	−	3.06916i	−0.0163035	−	0.102936i
$890$		0			0
$891$	2.62002	−	8.70608i	0.0877739	−	0.291664i
$892$		0			0
$893$	−38.7925	+	53.3933i	−1.29814	+	1.78674i
$894$		0			0
$895$	−25.8613	−	13.1770i	−0.864447	−	0.440458i
$896$		0			0
$897$	−9.86946	−	5.81251i	−0.329532	−	0.194074i
$898$		0			0
$899$	−1.07319	−	2.10625i	−0.0357928	−	0.0702473i
$900$		0			0
$901$	5.12938			0.170885
$902$		0			0
$903$	2.23338	+	2.23338i	0.0743223	+	0.0743223i
$904$		0			0
$905$	23.1733	+	45.4801i	0.770305	+	1.51181i
$906$		0			0
$907$	−29.9040	−	41.1593i	−0.992945	−	1.36667i	−0.929555	−	0.368683i	$-0.879809\pi$
$907$	−29.9040	−	41.1593i	−0.992945	−	1.36667i	−0.0633898	−	0.997989i	$-0.520191\pi$
$908$		0			0
$909$	4.01767	+	12.3651i	0.133258	+	0.410125i
$910$		0			0
$911$	17.3829	+	12.6294i	0.575921	+	0.418431i	0.837251	−	0.546818i	$-0.184161\pi$
$911$	17.3829	+	12.6294i	0.575921	+	0.418431i	−0.261330	+	0.965249i	$0.584161\pi$
$912$		0			0
$913$	−4.52949	+	4.73178i	−0.149904	+	0.156599i
$914$		0			0
$915$	18.4938	−	2.92913i	0.611385	−	0.0968339i
$916$		0			0
$917$	−6.91246	−	3.52208i	−0.228270	−	0.116309i
$918$		0			0
$919$	−5.36706	−	7.38712i	−0.177043	−	0.243679i	0.711268	−	0.702921i	$-0.248121\pi$
$919$	−5.36706	−	7.38712i	−0.177043	−	0.243679i	−0.888311	+	0.459242i	$0.848121\pi$
$920$		0			0
$921$	7.48171	−	3.81212i	0.246531	−	0.125614i
$922$		0			0
$923$	14.7635	+	5.81417i	0.485948	+	0.191376i
$924$		0			0
$925$	0.0792518	+	0.0792518i	0.00260578	+	0.00260578i
$926$		0			0
$927$	−30.7645	−	9.99600i	−1.01044	−	0.328312i
$928$		0			0
$929$	56.6042	+	8.96523i	1.85712	+	0.294140i	0.981875	−	0.189531i	$-0.0606968\pi$
$929$	56.6042	+	8.96523i	1.85712	+	0.294140i	0.875250	+	0.483671i	$0.160697\pi$
$930$		0			0
$931$	14.4735	−	28.4058i	0.474350	−	0.930963i
$932$		0			0
$933$	17.4087	−	23.9610i	0.569934	−	0.784447i
$934$		0			0
$935$	21.6928	+	2.95177i	0.709431	+	0.0965331i
$936$		0			0
$937$	3.83047	−	5.27219i	0.125136	−	0.172235i	−0.741852	−	0.670563i	$-0.766053\pi$
$937$	3.83047	−	5.27219i	0.125136	−	0.172235i	0.866988	+	0.498328i	$0.166053\pi$
$938$		0			0
$939$	−5.20128	−	16.0079i	−0.169737	−	0.522398i
$940$		0			0
$941$	−1.91303	+	12.0784i	−0.0623631	+	0.393745i	0.936687	+	0.350168i	$0.113875\pi$
$941$	−1.91303	+	12.0784i	−0.0623631	+	0.393745i	−0.999050	+	0.0435772i	$0.986125\pi$
$942$		0			0
$943$	−8.94407	+	4.55723i	−0.291259	+	0.148404i
$944$		0			0
$945$			12.2789i			0.399433i
$946$		0			0
$947$	3.62726	−	3.62726i	0.117870	−	0.117870i	−0.645711	−	0.763581i	$-0.723439\pi$
$947$	3.62726	−	3.62726i	0.117870	−	0.117870i	0.763581	+	0.645711i	$0.223439\pi$
$948$		0			0
$949$	−22.6689	+	27.5039i	−0.735863	+	0.892816i
$950$		0			0
$951$	−22.2835	−	3.52937i	−0.722593	−	0.114448i
$952$		0			0
$953$	−5.95359	−	18.3233i	−0.192856	−	0.593549i	−0.999995	−	0.00318793i	$-0.998985\pi$
$953$	−5.95359	−	18.3233i	−0.192856	−	0.593549i	0.807139	−	0.590361i	$-0.201015\pi$
$954$		0			0
$955$	−3.50496	−	22.1295i	−0.113418	−	0.716092i
$956$		0			0
$957$	−16.5120	+	23.8031i	−0.533758	+	0.769446i
$958$		0			0
$959$	−10.6772	−	7.75744i	−0.344785	−	0.250501i
$960$		0			0
$961$	29.4298	−	9.56234i	0.949350	−	0.308462i
$962$		0			0
$963$	−18.1408	−	24.9686i	−0.584579	−	0.804603i
$964$		0			0
$965$	30.8936	+	10.0379i	0.994500	+	0.323133i
$966$		0			0
$967$	4.63539	−	4.63539i	0.149064	−	0.149064i	−0.628636	−	0.777700i	$-0.716386\pi$
$967$	4.63539	−	4.63539i	0.149064	−	0.149064i	0.777700	+	0.628636i	$0.216386\pi$
$968$		0			0
$969$	10.1066	−	10.1066i	0.324671	−	0.324671i
$970$		0			0
$971$	−1.18383	+	3.64345i	−0.0379908	+	0.116924i	−0.968253	−	0.249971i	$-0.919579\pi$
$971$	−1.18383	+	3.64345i	−0.0379908	+	0.116924i	0.930263	+	0.366894i	$0.119579\pi$
$972$		0			0
$973$	−2.50816	+	15.8359i	−0.0804079	+	0.507675i
$974$		0			0
$975$	0.520437	−	0.460517i	0.0166673	−	0.0147483i
$976$		0			0
$977$	2.31117	+	14.5921i	0.0739408	+	0.466844i	0.996680	+	0.0814189i	$0.0259452\pi$
$977$	2.31117	+	14.5921i	0.0739408	+	0.466844i	−0.922739	+	0.385425i	$0.874055\pi$
$978$		0			0
$979$	−11.4852	+	2.07712i	−0.367067	+	0.0663851i
$980$		0			0
$981$	−13.9959	+	2.21673i	−0.446854	+	0.0707747i
$982$		0			0
$983$	−29.0826	−	14.8183i	−0.927592	−	0.472632i	−0.0761596	−	0.997096i	$-0.524266\pi$
$983$	−29.0826	−	14.8183i	−0.927592	−	0.472632i	−0.851433	+	0.524464i	$0.824266\pi$
$984$		0			0
$985$	0.513644	−	0.373184i	0.0163660	−	0.0118906i
$986$		0			0
$987$	−3.68368	+	11.3372i	−0.117253	+	0.360867i
$988$		0			0
$989$			11.2276i			0.357017i
$990$		0			0
$991$	12.9001			0.409786			0.204893	−	0.978784i	$-0.434315\pi$
$991$	12.9001			0.409786			0.204893	+	0.978784i	$0.434315\pi$
$992$		0			0
$993$	−2.08925	+	1.06453i	−0.0663004	+	0.0337818i
$994$		0			0
$995$	4.88579	−	30.8477i	0.154890	−	0.977937i
$996$		0			0
$997$	28.6628	−	9.31311i	0.907760	−	0.294949i	0.182324	−	0.983239i	$-0.441638\pi$
$997$	28.6628	−	9.31311i	0.907760	−	0.294949i	0.725436	+	0.688289i	$0.241638\pi$
$998$		0			0
$999$	−2.28601	+	0.362068i	−0.0723262	+	0.0114553i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bh.a.73.6	✓	112
11.8	odd	10	inner	572.2.bh.a.437.6	yes	112
13.5	odd	4	inner	572.2.bh.a.161.6	yes	112
143.96	even	20	inner	572.2.bh.a.525.6	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bh.a.73.6	✓	112	1.1	even	1	trivial
572.2.bh.a.161.6	yes	112	13.5	odd	4	inner
572.2.bh.a.437.6	yes	112	11.8	odd	10	inner
572.2.bh.a.525.6	yes	112	143.96	even	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.269308 + 0.828844i) q^{3} +(-2.25685 - 0.357450i) q^{5} +(-0.534177 + 1.04838i) q^{7} +(1.81260 + 1.31693i) q^{9} +O(q^{10})\)	\(q+(-0.269308 + 0.828844i) q^{3} +(-2.25685 - 0.357450i) q^{5} +(-0.534177 + 1.04838i) q^{7} +(1.81260 + 1.31693i) q^{9} +(-2.72514 - 1.89040i) q^{11} +(-3.52015 - 0.780108i) q^{13} +(0.904059 - 1.77432i) q^{15} +(2.33710 - 1.69800i) q^{17} +(-2.57739 - 5.05842i) q^{19} +(-0.725086 - 0.725086i) q^{21} -3.64514i q^{23} +(0.210334 + 0.0683418i) q^{25} +(-3.69484 + 2.68446i) q^{27} +(-9.53203 + 3.09714i) q^{29} +(0.0368962 + 0.232953i) q^{31} +(2.30075 - 1.74961i) q^{33} +(1.58030 - 2.17510i) q^{35} +(0.451545 + 0.230073i) q^{37} +(1.59459 - 2.70756i) q^{39} +(-1.25022 - 2.45369i) q^{41} -3.08016 q^{43} +(-3.62003 - 3.62003i) q^{45} +(-5.27766 - 10.3580i) q^{47} +(3.30074 + 4.54308i) q^{49} +(0.777980 + 2.39438i) q^{51} +(1.43649 + 1.04367i) q^{53} +(5.47451 + 5.24047i) q^{55} +(4.88675 - 0.773986i) q^{57} +(-4.14039 - 2.10963i) q^{59} +(5.52681 + 7.60700i) q^{61} +(-2.34889 + 1.19682i) q^{63} +(7.66561 + 3.01887i) q^{65} +(6.38758 + 6.38758i) q^{67} +(3.02126 + 0.981665i) q^{69} +(-4.34658 - 0.688430i) q^{71} +(4.48783 - 8.80785i) q^{73} +(-0.113289 + 0.155930i) q^{75} +(3.43757 - 1.84717i) q^{77} +(-5.07553 + 6.98586i) q^{79} +(0.847099 + 2.60710i) q^{81} +(0.308955 - 1.95066i) q^{83} +(-5.88144 + 2.99675i) q^{85} -8.73465i q^{87} +(2.48837 - 2.48837i) q^{89} +(2.69823 - 3.27374i) q^{91} +(-0.203019 - 0.0321550i) q^{93} +(4.00867 + 12.3374i) q^{95} +(2.72960 + 17.2340i) q^{97} +(-2.45004 - 7.01535i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 28 q^{9}+O(q^{10}) \) 112 * q - 28 * q^9	\( 112 q - 28 q^{9} + 8 q^{11} - 10 q^{13} + 4 q^{15} - 24 q^{27} - 20 q^{29} - 16 q^{31} - 54 q^{33} + 100 q^{35} - 12 q^{37} + 40 q^{39} - 20 q^{41} - 4 q^{45} - 10 q^{47} - 76 q^{53} - 20 q^{55} + 18 q^{59} + 40 q^{61} + 80 q^{63} + 92 q^{67} + 8 q^{71} - 30 q^{73} - 80 q^{79} + 12 q^{81} + 40 q^{85} + 32 q^{89} - 12 q^{91} - 114 q^{93} + 54 q^{97} - 90 q^{99}+O(q^{100}) \) 112 * q - 28 * q^9 + 8 * q^11 - 10 * q^13 + 4 * q^15 - 24 * q^27 - 20 * q^29 - 16 * q^31 - 54 * q^33 + 100 * q^35 - 12 * q^37 + 40 * q^39 - 20 * q^41 - 4 * q^45 - 10 * q^47 - 76 * q^53 - 20 * q^55 + 18 * q^59 + 40 * q^61 + 80 * q^63 + 92 * q^67 + 8 * q^71 - 30 * q^73 - 80 * q^79 + 12 * q^81 + 40 * q^85 + 32 * q^89 - 12 * q^91 - 114 * q^93 + 54 * q^97 - 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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