LMFDB - Embedded newform 572.2.bv.a.41.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(41,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([0, 18, 5]))

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

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

chi := DirichletCharacter("572.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bv (of order $60$, degree $16$, 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:	$224$
Relative dimension:	$14$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			41.8
Character	$\chi$	$=$	572.41
Dual form			572.2.bv.a.293.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.183828 - 0.204162i) q^{3} +(2.17308 - 0.344183i) q^{5} +(-2.74555 - 0.143888i) q^{7} +(0.305696 + 2.90850i) q^{9} +O(q^{10})$	\(q+(0.183828 - 0.204162i) q^{3} +(2.17308 - 0.344183i) q^{5} +(-2.74555 - 0.143888i) q^{7} +(0.305696 + 2.90850i) q^{9} +(-0.106522 + 3.31491i) q^{11} +(3.56919 - 0.510766i) q^{13} +(0.329205 - 0.506931i) q^{15} +(6.11274 - 2.72157i) q^{17} +(3.48299 + 5.36333i) q^{19} +(-0.534086 + 0.534086i) q^{21} +(-0.621252 + 0.358680i) q^{23} +(-0.151451 + 0.0492093i) q^{25} +(1.31678 + 0.956694i) q^{27} +(-1.85630 - 8.73321i) q^{29} +(0.300126 - 1.89492i) q^{31} +(0.657196 + 0.631122i) q^{33} +(-6.01584 + 0.632291i) q^{35} +(-0.143632 - 0.0932755i) q^{37} +(0.551838 - 0.822585i) q^{39} +(6.05892 - 0.317535i) q^{41} +(1.37772 - 2.38628i) q^{43} +(1.66536 + 6.21521i) q^{45} +(2.28006 - 4.47487i) q^{47} +(0.555711 + 0.0584076i) q^{49} +(0.568053 - 1.74829i) q^{51} +(-9.40668 + 6.83435i) q^{53} +(0.909454 + 7.24025i) q^{55} +(1.73526 + 0.274838i) q^{57} +(-0.559874 + 10.6830i) q^{59} +(3.92137 + 8.80754i) q^{61} +(-0.420805 - 8.02944i) q^{63} +(7.58035 - 2.33839i) q^{65} +(2.58450 + 0.692516i) q^{67} +(-0.0409748 + 0.192771i) q^{69} +(-0.975040 + 2.54007i) q^{71} +(-3.36296 - 6.60017i) q^{73} +(-0.0177942 + 0.0399664i) q^{75} +(0.769441 - 9.08595i) q^{77} +(-5.15446 - 7.09450i) q^{79} +(-8.14447 + 1.73116i) q^{81} +(-0.972825 - 6.14217i) q^{83} +(12.3468 - 8.01809i) q^{85} +(-2.12423 - 1.22642i) q^{87} +(-1.18236 + 4.41262i) q^{89} +(-9.87290 + 0.888770i) q^{91} +(-0.331698 - 0.409613i) q^{93} +(9.41478 + 10.4562i) q^{95} +(-1.28714 - 1.04230i) q^{97} +(-9.67400 + 0.703535i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q + 28 q^{9}+O(q^{10}) $ 224 * q + 28 * q^9	$ 224 q + 28 q^{9} + 16 q^{11} + 10 q^{13} - 28 q^{15} - 48 q^{23} + 24 q^{27} + 20 q^{29} + 4 q^{31} + 60 q^{33} + 50 q^{35} + 12 q^{37} - 40 q^{39} + 20 q^{41} + 64 q^{45} - 62 q^{47} + 100 q^{53} - 22 q^{55} + 12 q^{59} - 40 q^{61} - 80 q^{63} - 44 q^{67} - 152 q^{71} + 30 q^{73} - 120 q^{75} + 80 q^{79} + 72 q^{81} + 90 q^{83} - 40 q^{85} - 8 q^{89} - 36 q^{91} - 90 q^{93} - 42 q^{97} + 144 q^{99}+O(q^{100}) $ 224 * q + 28 * q^9 + 16 * q^11 + 10 * q^13 - 28 * q^15 - 48 * q^23 + 24 * q^27 + 20 * q^29 + 4 * q^31 + 60 * q^33 + 50 * q^35 + 12 * q^37 - 40 * q^39 + 20 * q^41 + 64 * q^45 - 62 * q^47 + 100 * q^53 - 22 * q^55 + 12 * q^59 - 40 * q^61 - 80 * q^63 - 44 * q^67 - 152 * q^71 + 30 * q^73 - 120 * q^75 + 80 * q^79 + 72 * q^81 + 90 * q^83 - 40 * q^85 - 8 * q^89 - 36 * q^91 - 90 * q^93 - 42 * q^97 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{3}{10}\right)$

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
$3$	0.183828	−	0.204162i	0.106133	−	0.117873i	−0.687738	−	0.725959i	$-0.741396\pi$
$3$	0.183828	−	0.204162i	0.106133	−	0.117873i	0.793871	+	0.608087i	$0.208063\pi$
$4$		0			0
$5$	2.17308	−	0.344183i	0.971833	−	0.153923i	0.349723	−	0.936853i	$-0.386276\pi$
$5$	2.17308	−	0.344183i	0.971833	−	0.153923i	0.622110	+	0.782930i	$0.286276\pi$
$6$		0			0
$7$	−2.74555	−	0.143888i	−1.03772	−	0.0543847i	−0.474144	−	0.880447i	$-0.657242\pi$
$7$	−2.74555	−	0.143888i	−1.03772	−	0.0543847i	−0.563578	+	0.826063i	$0.690576\pi$
$8$		0			0
$9$	0.305696	+	2.90850i	0.101899	+	0.969501i
$10$		0			0
$11$	−0.106522	+	3.31491i	−0.0321177	+	0.999484i
$11$	−0.106522	+	3.31491i	−0.0321177	+	0.999484i
$12$		0			0
$13$	3.56919	−	0.510766i	0.989915	−	0.141661i
$13$	3.56919	−	0.510766i	0.989915	−	0.141661i
$14$		0			0
$15$	0.329205	−	0.506931i	0.0850003	−	0.130889i
$16$		0			0
$17$	6.11274	−	2.72157i	1.48256	−	0.660077i	0.503562	−	0.863959i	$-0.332023\pi$
$17$	6.11274	−	2.72157i	1.48256	−	0.660077i	0.978995	+	0.203882i	$0.0653560\pi$
$18$		0			0
$19$	3.48299	+	5.36333i	0.799052	+	1.23043i	0.969506	+	0.245066i	$0.0788097\pi$
$19$	3.48299	+	5.36333i	0.799052	+	1.23043i	−0.170455	+	0.985366i	$0.554524\pi$
$20$		0			0
$21$	−0.534086	+	0.534086i	−0.116547	+	0.116547i
$22$		0			0
$23$	−0.621252	+	0.358680i	−0.129540	+	0.0747899i	−0.563370	−	0.826205i	$-0.690495\pi$
$23$	−0.621252	+	0.358680i	−0.129540	+	0.0747899i	0.433830	+	0.900995i	$0.357162\pi$
$24$		0			0
$25$	−0.151451	+	0.0492093i	−0.0302901	+	0.00984185i
$26$		0			0
$27$	1.31678	+	0.956694i	0.253414	+	0.184116i
$28$		0			0
$29$	−1.85630	−	8.73321i	−0.344707	−	1.62172i	−0.719419	−	0.694576i	$-0.755592\pi$
$29$	−1.85630	−	8.73321i	−0.344707	−	1.62172i	0.374713	−	0.927141i	$-0.377741\pi$
$30$		0			0
$31$	0.300126	−	1.89492i	0.0539041	−	0.340337i	−0.945967	−	0.324264i	$-0.894883\pi$
$31$	0.300126	−	1.89492i	0.0539041	−	0.340337i	0.999871	−	0.0160735i	$-0.00511657\pi$
$32$		0			0
$33$	0.657196	+	0.631122i	0.114403	+	0.109864i
$34$		0			0
$35$	−6.01584	+	0.632291i	−1.01686	+	0.106877i
$36$		0			0
$37$	−0.143632	−	0.0932755i	−0.0236129	−	0.0153344i	0.532779	−	0.846255i	$-0.321148\pi$
$37$	−0.143632	−	0.0932755i	−0.0236129	−	0.0153344i	−0.556392	+	0.830920i	$0.687815\pi$
$38$		0			0
$39$	0.551838	−	0.822585i	0.0883648	−	0.131719i
$40$		0			0
$41$	6.05892	−	0.317535i	0.946245	−	0.0495906i	0.427033	−	0.904236i	$-0.359559\pi$
$41$	6.05892	−	0.317535i	0.946245	−	0.0495906i	0.519212	+	0.854645i	$0.326226\pi$
$42$		0			0
$43$	1.37772	−	2.38628i	0.210100	−	0.363904i	−0.741646	−	0.670792i	$-0.765954\pi$
$43$	1.37772	−	2.38628i	0.210100	−	0.363904i	0.951746	+	0.306888i	$0.0992877\pi$
$44$		0			0
$45$	1.66536	+	6.21521i	0.248257	+	0.926509i
$46$		0			0
$47$	2.28006	−	4.47487i	0.332581	−	0.652726i	−0.662793	−	0.748802i	$-0.730629\pi$
$47$	2.28006	−	4.47487i	0.332581	−	0.652726i	0.995374	+	0.0960761i	$0.0306292\pi$
$48$		0			0
$49$	0.555711	+	0.0584076i	0.0793873	+	0.00834394i
$50$		0			0
$51$	0.568053	−	1.74829i	0.0795433	−	0.244809i
$52$		0			0
$53$	−9.40668	+	6.83435i	−1.29211	+	0.938771i	−0.999846	−	0.0175676i	$-0.994408\pi$
$53$	−9.40668	+	6.83435i	−1.29211	+	0.938771i	−0.292262	+	0.956338i	$0.594408\pi$
$54$		0			0
$55$	0.909454	+	7.24025i	0.122631	+	0.976275i
$56$		0			0
$57$	1.73526	+	0.274838i	0.229840	+	0.0364031i
$58$		0			0
$59$	−0.559874	+	10.6830i	−0.0728894	+	1.39081i	0.680263	+	0.732968i	$0.261865\pi$
$59$	−0.559874	+	10.6830i	−0.0728894	+	1.39081i	−0.753153	+	0.657846i	$0.771468\pi$
$60$		0			0
$61$	3.92137	+	8.80754i	0.502080	+	1.12769i	0.969820	+	0.243823i	$0.0784017\pi$
$61$	3.92137	+	8.80754i	0.502080	+	1.12769i	−0.467740	+	0.883866i	$0.654932\pi$
$62$		0			0
$63$	−0.420805	−	8.02944i	−0.0530165	−	1.01161i
$64$		0			0
$65$	7.58035	−	2.33839i	0.940227	−	0.290042i
$66$		0			0
$67$	2.58450	+	0.692516i	0.315747	+	0.0846043i	0.413212	−	0.910635i	$-0.364407\pi$
$67$	2.58450	+	0.692516i	0.315747	+	0.0846043i	−0.0974649	+	0.995239i	$0.531073\pi$
$68$		0			0
$69$	−0.0409748	+	0.192771i	−0.00493278	+	0.0232069i
$70$		0			0
$71$	−0.975040	+	2.54007i	−0.115716	+	0.301450i	−0.979191	−	0.202941i	$-0.934950\pi$
$71$	−0.975040	+	2.54007i	−0.115716	+	0.301450i	0.863475	+	0.504392i	$0.168283\pi$
$72$		0			0
$73$	−3.36296	−	6.60017i	−0.393604	−	0.772492i	0.606134	−	0.795362i	$-0.292719\pi$
$73$	−3.36296	−	6.60017i	−0.393604	−	0.772492i	−0.999738	+	0.0228704i	$0.992719\pi$
$74$		0			0
$75$	−0.0177942	+	0.0399664i	−0.00205470	+	0.00461492i
$76$		0			0
$77$	0.769441	−	9.08595i	0.0876859	−	1.03544i
$78$		0			0
$79$	−5.15446	−	7.09450i	−0.579922	−	0.798194i	0.413765	−	0.910384i	$-0.364213\pi$
$79$	−5.15446	−	7.09450i	−0.579922	−	0.798194i	−0.993687	+	0.112190i	$0.964213\pi$
$80$		0			0
$81$	−8.14447	+	1.73116i	−0.904941	+	0.192351i
$82$		0			0
$83$	−0.972825	−	6.14217i	−0.106781	−	0.674191i	−0.981774	−	0.190054i	$-0.939134\pi$
$83$	−0.972825	−	6.14217i	−0.106781	−	0.674191i	0.874992	−	0.484137i	$-0.160866\pi$
$84$		0			0
$85$	12.3468	−	8.01809i	1.33920	−	0.869684i
$86$		0			0
$87$	−2.12423	−	1.22642i	−0.227741	−	0.131486i
$88$		0			0
$89$	−1.18236	+	4.41262i	−0.125330	+	0.467737i	−0.999851	−	0.0172498i	$-0.994509\pi$
$89$	−1.18236	+	4.41262i	−0.125330	+	0.467737i	0.874521	+	0.484987i	$0.161176\pi$
$90$		0			0
$91$	−9.87290	+	0.888770i	−1.03496	+	0.0931684i
$92$		0			0
$93$	−0.331698	−	0.409613i	−0.0343955	−	0.0424749i
$94$		0			0
$95$	9.41478	+	10.4562i	0.965936	+	1.07278i
$96$		0			0
$97$	−1.28714	−	1.04230i	−0.130689	−	0.105830i	0.561747	−	0.827309i	$-0.310129\pi$
$97$	−1.28714	−	1.04230i	−0.130689	−	0.105830i	−0.692436	+	0.721479i	$0.743463\pi$
$98$		0			0
$99$	−9.67400	+	0.703535i	−0.972274	+	0.0707080i
$100$		0			0
$101$	4.50529	+	2.00588i	0.448293	+	0.199593i	0.618450	−	0.785824i	$-0.287761\pi$
$101$	4.50529	+	2.00588i	0.448293	+	0.199593i	−0.170157	+	0.985417i	$0.554428\pi$
$102$		0			0
$103$	−4.56085	−	1.48191i	−0.449394	−	0.146017i	0.0755716	−	0.997140i	$-0.475922\pi$
$103$	−4.56085	−	1.48191i	−0.449394	−	0.146017i	−0.524966	+	0.851123i	$0.675922\pi$
$104$		0			0
$105$	−0.976791	+	1.34444i	−0.0953250	+	0.131204i
$106$		0			0
$107$	−9.77574	−	8.80212i	−0.945056	−	0.850933i	0.0439156	−	0.999035i	$-0.486017\pi$
$107$	−9.77574	−	8.80212i	−0.945056	−	0.850933i	−0.988972	+	0.148103i	$0.952683\pi$
$108$		0			0
$109$	−12.2190	−	12.2190i	−1.17037	−	1.17037i	−0.982121	−	0.188250i	$-0.939718\pi$
$109$	−12.2190	−	12.2190i	−1.17037	−	1.17037i	−0.188250	−	0.982121i	$-0.560282\pi$
$110$		0			0
$111$	−0.0454468	+	0.0121774i	−0.00431362	+	0.00115583i
$112$		0			0
$113$	−4.36330	−	0.927449i	−0.410465	−	0.0872471i	−0.00194888	−	0.999998i	$-0.500620\pi$
$113$	−4.36330	−	0.927449i	−0.410465	−	0.0872471i	−0.408516	+	0.912751i	$0.633954\pi$
$114$		0			0
$115$	−1.22658	+	0.993266i	−0.114379	+	0.0926225i
$116$		0			0
$117$	2.57665	+	10.2249i	0.238212	+	0.945289i
$118$		0			0
$119$	−17.1745	+	6.59266i	−1.57438	+	0.604348i
$120$		0			0
$121$	−10.9773	−	0.706225i	−0.997937	−	0.0642023i
$122$		0			0
$123$	1.04897	−	1.29537i	0.0945825	−	0.116800i
$124$		0			0
$125$	−10.1140	+	5.15335i	−0.904625	+	0.460929i
$126$		0			0
$127$	0.939635	−	8.94003i	0.0833791	−	0.793299i	−0.870310	−	0.492505i	$-0.836082\pi$
$127$	0.939635	−	8.94003i	0.0833791	−	0.793299i	0.953689	−	0.300795i	$-0.0972518\pi$
$128$		0			0
$129$	−0.233923	−	0.719942i	−0.0205958	−	0.0633873i
$130$		0			0
$131$		−	4.30916i		−	0.376493i	−0.982122	−	0.188246i	$-0.939720\pi$
$131$		−	4.30916i		−	0.376493i	0.982122	−	0.188246i	$-0.0602804\pi$
$132$		0			0
$133$	−8.79100	−	15.2265i	−0.762277	−	1.32030i
$134$		0			0
$135$	3.19074	+	1.62576i	0.274615	+	0.139924i
$136$		0			0
$137$	14.0254	+	5.38384i	1.19827	+	0.459972i	0.873969	−	0.485982i	$-0.161538\pi$
$137$	14.0254	+	5.38384i	1.19827	+	0.459972i	0.324300	+	0.945954i	$0.394871\pi$
$138$		0			0
$139$	−5.68279	+	5.11681i	−0.482008	+	0.434002i	−0.873970	−	0.485979i	$-0.838463\pi$
$139$	−5.68279	+	5.11681i	−0.482008	+	0.434002i	0.391962	+	0.919981i	$0.371796\pi$
$140$		0			0
$141$	−0.494457	−	1.28811i	−0.0416408	−	0.108478i
$142$		0			0
$143$	1.31295	+	11.8860i	0.109794	+	0.993954i
$144$		0			0
$145$	−7.03972	−	18.3391i	−0.584617	−	1.52298i
$146$		0			0
$147$	0.114080	−	0.102718i	0.00940914	−	0.00847203i
$148$		0			0
$149$	−5.18308	−	1.98960i	−0.424615	−	0.162994i	0.136671	−	0.990616i	$-0.456360\pi$
$149$	−5.18308	−	1.98960i	−0.424615	−	0.162994i	−0.561285	+	0.827622i	$0.689693\pi$
$150$		0			0
$151$	9.27463	+	4.72566i	0.754759	+	0.384569i	0.788639	−	0.614857i	$-0.210786\pi$
$151$	9.27463	+	4.72566i	0.754759	+	0.384569i	−0.0338797	+	0.999426i	$0.510786\pi$
$152$		0			0
$153$	9.78433	+	16.9470i	0.791016	+	1.37008i
$154$		0			0
$155$		−	4.22111i		−	0.339048i
$156$		0			0
$157$	−1.93818	−	5.96509i	−0.154683	−	0.476066i	0.843445	−	0.537215i	$-0.180524\pi$
$157$	−1.93818	−	5.96509i	−0.154683	−	0.476066i	−0.998129	+	0.0611488i	$0.980524\pi$
$158$		0			0
$159$	−0.333898	+	3.17683i	−0.0264798	+	0.251939i
$160$		0			0
$161$	1.75729	−	0.895384i	0.138494	−	0.0705662i
$162$		0			0
$163$	9.64048	−	11.9050i	0.755101	−	0.932472i	−0.244205	−	0.969724i	$-0.578527\pi$
$163$	9.64048	−	11.9050i	0.755101	−	0.932472i	0.999306	+	0.0372520i	$0.0118604\pi$
$164$		0			0
$165$	1.64536	+	1.14528i	0.128091	+	0.0891603i
$166$		0			0
$167$	−4.80996	+	1.84637i	−0.372206	+	0.142876i	−0.537278	−	0.843405i	$-0.680547\pi$
$167$	−4.80996	+	1.84637i	−0.372206	+	0.142876i	0.165073	+	0.986281i	$0.447214\pi$
$168$		0			0
$169$	12.4782	−	3.64604i	0.959864	−	0.280465i
$170$		0			0
$171$	−14.5345	+	11.7698i	−1.11148	+	0.900061i
$172$		0			0
$173$	14.4452	+	3.07042i	1.09825	+	0.233440i	0.721181	−	0.692746i	$-0.243600\pi$
$173$	14.4452	+	3.07042i	1.09825	+	0.233440i	0.377066	+	0.926186i	$0.376933\pi$
$174$		0			0
$175$	0.422896	−	0.113315i	0.0319680	−	0.00856579i
$176$		0			0
$177$	2.07815	+	2.07815i	0.156203	+	0.156203i
$178$		0			0
$179$	−18.6016	−	16.7490i	−1.39035	−	1.25188i	−0.931684	−	0.363271i	$-0.881660\pi$
$179$	−18.6016	−	16.7490i	−1.39035	−	1.25188i	−0.458668	−	0.888608i	$-0.651673\pi$
$180$		0			0
$181$	12.9109	−	17.7703i	0.959659	−	1.32086i	0.0125576	−	0.999921i	$-0.496003\pi$
$181$	12.9109	−	17.7703i	0.959659	−	1.32086i	0.947101	−	0.320936i	$-0.103997\pi$
$182$		0			0
$183$	2.51902	+	0.818478i	0.186211	+	0.0605037i
$184$		0			0
$185$	−0.344227	−	0.153260i	−0.0253081	−	0.0112679i
$186$		0			0
$187$	8.37062	+	20.5531i	0.612120	+	1.50299i
$188$		0			0
$189$	−3.47762	−	2.81612i	−0.252960	−	0.204843i
$190$		0			0
$191$	4.71598	+	5.23762i	0.341236	+	0.378981i	0.889198	−	0.457522i	$-0.151263\pi$
$191$	4.71598	+	5.23762i	0.341236	+	0.378981i	−0.547962	+	0.836503i	$0.684596\pi$
$192$		0			0
$193$	5.45977	+	6.74226i	0.393003	+	0.485318i	0.934792	−	0.355196i	$-0.115586\pi$
$193$	5.45977	+	6.74226i	0.393003	+	0.485318i	−0.541789	+	0.840515i	$0.682253\pi$
$194$		0			0
$195$	0.916071	−	1.97748i	0.0656012	−	0.141610i
$196$		0			0
$197$	−2.47576	+	9.23968i	−0.176391	+	0.658300i	0.819920	+	0.572479i	$0.194018\pi$
$197$	−2.47576	+	9.23968i	−0.176391	+	0.658300i	−0.996311	+	0.0858211i	$0.972649\pi$
$198$		0			0
$199$	−23.1463	−	13.3635i	−1.64080	−	0.947314i	−0.980551	−	0.196264i	$-0.937119\pi$
$199$	−23.1463	−	13.3635i	−1.64080	−	0.947314i	−0.660245	−	0.751050i	$-0.729548\pi$
$200$		0			0
$201$	0.616489	−	0.400353i	0.0434838	−	0.0282387i
$202$		0			0
$203$	3.83997	+	24.2446i	0.269513	+	1.70164i
$204$		0			0
$205$	13.0573	−	2.77541i	0.911959	−	0.193843i
$206$		0			0
$207$	−1.23314	−	1.69727i	−0.0857089	−	0.117968i
$208$		0			0
$209$	−18.1500	+	10.9745i	−1.25546	+	0.759121i
$210$		0			0
$211$	5.10131	−	11.4577i	0.351189	−	0.788783i	−0.648433	−	0.761272i	$-0.724575\pi$
$211$	5.10131	−	11.4577i	0.351189	−	0.788783i	0.999622	−	0.0275110i	$-0.00875812\pi$
$212$		0			0
$213$	0.339345	+	0.666001i	0.0232515	+	0.0456336i
$214$		0			0
$215$	2.17258	−	5.65977i	0.148169	−	0.385993i
$216$		0			0
$217$	−1.09667	+	5.15942i	−0.0744467	+	0.350244i
$218$		0			0
$219$	−1.96571	−	0.526710i	−0.132830	−	0.0355918i
$220$		0			0
$221$	20.4274	−	12.8360i	1.37410	−	0.863441i
$222$		0			0
$223$	−1.18117	−	22.5380i	−0.0790969	−	1.50926i	−0.693609	−	0.720351i	$-0.743981\pi$
$223$	−1.18117	−	22.5380i	−0.0790969	−	1.50926i	0.614513	−	0.788907i	$-0.289353\pi$
$224$		0			0
$225$	−0.189423	−	0.425451i	−0.0126282	−	0.0283634i
$226$		0			0
$227$	−0.304931	+	5.81843i	−0.0202390	+	0.386183i	0.969665	+	0.244440i	$0.0786040\pi$
$227$	−0.304931	+	5.81843i	−0.0202390	+	0.386183i	−0.989903	+	0.141743i	$0.954729\pi$
$228$		0			0
$229$	22.9311	+	3.63194i	1.51533	+	0.240005i	0.858021	−	0.513614i	$-0.171694\pi$
$229$	22.9311	+	3.63194i	1.51533	+	0.240005i	0.657311	+	0.753619i	$0.271694\pi$
$230$		0			0
$231$	−1.71356	−	1.82734i	−0.112744	−	0.120230i
$232$		0			0
$233$	−20.7713	+	15.0912i	−1.36077	+	0.988660i	−0.362379	+	0.932031i	$0.618035\pi$
$233$	−20.7713	+	15.0912i	−1.36077	+	0.988660i	−0.998395	+	0.0566293i	$0.981965\pi$
$234$		0			0
$235$	3.41459	−	10.5090i	0.222743	−	0.685533i
$236$		0			0
$237$	−2.39596	−	0.251825i	−0.155634	−	0.0163578i
$238$		0			0
$239$	−4.95159	+	9.71805i	−0.320292	+	0.628608i	−0.993876	−	0.110503i	$-0.964754\pi$
$239$	−4.95159	+	9.71805i	−0.320292	+	0.628608i	0.673584	+	0.739111i	$0.264754\pi$
$240$		0			0
$241$	−4.49588	−	16.7789i	−0.289605	−	1.08082i	−0.945408	−	0.325889i	$-0.894336\pi$
$241$	−4.49588	−	16.7789i	−0.289605	−	1.08082i	0.655803	−	0.754932i	$-0.272330\pi$
$242$		0			0
$243$	−3.58518	+	6.20972i	−0.229990	+	0.398354i
$244$		0			0
$245$	1.22771	−	0.0643415i	0.0784355	−	0.00411063i
$246$		0			0
$247$	15.1708	+	17.3637i	0.965297	+	1.10483i
$248$		0			0
$249$	−1.43283	−	0.930490i	−0.0908018	−	0.0589674i
$250$		0			0
$251$	−9.96847	+	1.04773i	−0.629204	+	0.0661320i	−0.413763	−	0.910385i	$-0.635786\pi$
$251$	−9.96847	+	1.04773i	−0.629204	+	0.0661320i	−0.215441	+	0.976517i	$0.569119\pi$
$252$		0			0
$253$	−1.12282	−	2.09760i	−0.0705908	−	0.131875i
$254$		0			0
$255$	0.632696	−	3.99469i	0.0396210	−	0.250157i
$256$		0			0
$257$	2.57720	+	12.1248i	0.160761	+	0.756323i	0.982471	+	0.186416i	$0.0596873\pi$
$257$	2.57720	+	12.1248i	0.160761	+	0.756323i	−0.821710	+	0.569907i	$0.806979\pi$
$258$		0			0
$259$	0.380927	+	0.276760i	0.0236697	+	0.0171970i
$260$		0			0
$261$	24.8331	−	8.06877i	1.53713	−	0.499444i
$262$		0			0
$263$	3.45242	−	1.99326i	0.212885	−	0.122909i	−0.389766	−	0.920914i	$-0.627444\pi$
$263$	3.45242	−	1.99326i	0.212885	−	0.122909i	0.602652	+	0.798004i	$0.294111\pi$
$264$		0			0
$265$	−18.0892	+	18.0892i	−1.11121	+	1.11121i
$266$		0			0
$267$	0.683538	+	1.05256i	0.0418318	+	0.0644154i
$268$		0			0
$269$	−6.46155	+	2.87687i	−0.393968	+	0.175406i	−0.594152	−	0.804352i	$-0.702512\pi$
$269$	−6.46155	+	2.87687i	−0.393968	+	0.175406i	0.200185	+	0.979758i	$0.435846\pi$
$270$		0			0
$271$	−10.0379	+	15.4570i	−0.609757	+	0.938944i	0.390078	+	0.920782i	$0.372448\pi$
$271$	−10.0379	+	15.4570i	−0.609757	+	0.938944i	−0.999835	+	0.0181622i	$0.994218\pi$
$272$		0			0
$273$	−1.63346	+	2.17905i	−0.0988616	+	0.131882i
$274$		0			0
$275$	−0.146992	−	0.507287i	−0.00886392	−	0.0305906i
$276$		0			0
$277$	−1.25516	−	11.9421i	−0.0754154	−	0.717529i	−0.965265	−	0.261274i	$-0.915857\pi$
$277$	−1.25516	−	11.9421i	−0.0754154	−	0.717529i	0.889849	−	0.456255i	$-0.150809\pi$
$278$		0			0
$279$	5.60313	+	0.293647i	0.335450	+	0.0175802i
$280$		0			0
$281$	−21.1993	+	3.35764i	−1.26464	+	0.200300i	−0.752496	−	0.658597i	$-0.771150\pi$
$281$	−21.1993	+	3.35764i	−1.26464	+	0.200300i	−0.512148	+	0.858897i	$0.671150\pi$
$282$		0			0
$283$	21.6739	−	24.0713i	1.28838	−	1.43089i	0.443183	−	0.896431i	$-0.353849\pi$
$283$	21.6739	−	24.0713i	1.28838	−	1.43089i	0.845195	−	0.534458i	$-0.179484\pi$
$284$		0			0
$285$	3.86545			0.228970
$286$		0			0
$287$	−16.6808			−0.984636
$288$		0			0
$289$	18.5834	−	20.6390i	1.09314	−	1.21406i
$290$		0			0
$291$	−0.449410	+	0.0711796i	−0.0263449	+	0.00417262i
$292$		0			0
$293$	26.8596	+	1.40765i	1.56915	+	0.0822358i	0.816955	−	0.576702i	$-0.195661\pi$
$293$	26.8596	+	1.40765i	1.56915	+	0.0822358i	0.752198	+	0.658938i	$0.228994\pi$
$294$		0			0
$295$	2.46026	+	23.4078i	0.143242	+	1.36286i
$296$		0			0
$297$	−3.31162	+	4.26309i	−0.192160	+	0.247370i
$298$		0			0
$299$	−2.03416	+	1.59751i	−0.117639	+	0.0923864i
$300$		0			0
$301$	−4.12596	+	6.35342i	−0.237816	+	0.366205i
$302$		0			0
$303$	1.23772	−	0.551069i	0.0711052	−	0.0316581i
$304$		0			0
$305$	11.5529	+	17.7898i	0.661515	+	1.01864i
$306$		0			0
$307$	20.8913	−	20.8913i	1.19233	−	1.19233i	0.215915	−	0.976412i	$-0.430726\pi$
$307$	20.8913	−	20.8913i	1.19233	−	1.19233i	0.976412	−	0.215915i	$-0.0692735\pi$
$308$		0			0
$309$	−1.14096	+	0.658734i	−0.0649070	+	0.0374741i
$310$		0			0
$311$	30.4228	−	9.88498i	1.72512	−	0.560526i	0.732390	−	0.680885i	$-0.238405\pi$
$311$	30.4228	−	9.88498i	1.72512	−	0.560526i	0.992730	+	0.120359i	$0.0384046\pi$
$312$		0			0
$313$	6.37712	+	4.63325i	0.360456	+	0.261887i	0.753242	−	0.657743i	$-0.228489\pi$
$313$	6.37712	+	4.63325i	0.360456	+	0.261887i	−0.392786	+	0.919630i	$0.628489\pi$
$314$		0			0
$315$	−3.67804	−	17.3038i	−0.207234	−	0.974960i
$316$		0			0
$317$	−0.357245	+	2.25556i	−0.0200649	+	0.126685i	−0.995688	−	0.0927701i	$-0.970428\pi$
$317$	−0.357245	+	2.25556i	−0.0200649	+	0.126685i	0.975623	+	0.219455i	$0.0704278\pi$
$318$		0			0
$319$	29.1476	−	5.22320i	1.63195	−	0.292443i
$320$		0			0
$321$	−3.59411	+	0.377756i	−0.200604	+	0.0210843i
$322$		0			0
$323$	35.8872	+	23.3054i	1.99682	+	1.29675i
$324$		0			0
$325$	−0.515421	+	0.252993i	−0.0285904	+	0.0140335i
$326$		0			0
$327$	−4.74086	+	0.248458i	−0.262170	+	0.0137398i
$328$		0			0
$329$	−6.90390	+	11.9579i	−0.380625	+	0.659261i
$330$		0			0
$331$	5.03246	+	18.7814i	0.276609	+	1.03232i	0.954755	+	0.297392i	$0.0961169\pi$
$331$	5.03246	+	18.7814i	0.276609	+	1.03232i	−0.678146	+	0.734927i	$0.737216\pi$
$332$		0			0
$333$	0.227384	−	0.446267i	0.0124606	−	0.0244553i
$334$		0			0
$335$	5.85470	+	0.615354i	0.319876	+	0.0336204i
$336$		0			0
$337$	−5.15599	+	15.8685i	−0.280865	+	0.864412i	0.706743	+	0.707470i	$0.250164\pi$
$337$	−5.15599	+	15.8685i	−0.280865	+	0.864412i	−0.987608	+	0.156942i	$0.949836\pi$
$338$		0			0
$339$	−0.991447	+	0.720328i	−0.0538480	+	0.0391229i
$340$		0			0
$341$	6.24952	+	1.19674i	0.338431	+	0.0648072i
$342$		0			0
$343$	17.4910	+	2.77030i	0.944424	+	0.149582i
$344$		0			0
$345$	−0.0226931	+	0.433011i	−0.00122176	+	0.0233125i
$346$		0			0
$347$	1.69118	+	3.79846i	0.0907874	+	0.203912i	0.953232	−	0.302240i	$-0.0977343\pi$
$347$	1.69118	+	3.79846i	0.0907874	+	0.203912i	−0.862445	+	0.506152i	$0.831068\pi$
$348$		0			0
$349$	0.283476	+	5.40905i	0.0151741	+	0.289540i	0.995667	+	0.0929868i	$0.0296414\pi$
$349$	0.283476	+	5.40905i	0.0151741	+	0.289540i	−0.980493	+	0.196553i	$0.937025\pi$
$350$		0			0
$351$	5.18847	+	2.74206i	0.276940	+	0.146360i
$352$		0			0
$353$	6.32868	+	1.69577i	0.336842	+	0.0902565i	0.423275	−	0.906001i	$-0.360880\pi$
$353$	6.32868	+	1.69577i	0.336842	+	0.0902565i	−0.0864335	+	0.996258i	$0.527547\pi$
$354$		0			0
$355$	−1.24460	+	5.85537i	−0.0660564	+	0.310771i
$356$		0			0
$357$	−1.81118	+	4.71828i	−0.0958577	+	0.249718i
$358$		0			0
$359$	−12.9398	−	25.3957i	−0.682935	−	1.34033i	−0.928637	−	0.370989i	$-0.879019\pi$
$359$	−12.9398	−	25.3957i	−0.682935	−	1.34033i	0.245702	−	0.969345i	$-0.420981\pi$
$360$		0			0
$361$	−8.90610	+	20.0034i	−0.468742	+	1.05281i
$362$		0			0
$363$	−2.16212	+	2.11132i	−0.113482	+	0.110816i
$364$		0			0
$365$	−9.57965	−	13.1853i	−0.501422	−	0.690148i
$366$		0			0
$367$	−33.4364	+	7.10713i	−1.74537	+	0.370989i	−0.966593	−	0.256316i	$-0.917491\pi$
$367$	−33.4364	+	7.10713i	−1.74537	+	0.370989i	−0.778773	+	0.627305i	$0.784158\pi$
$368$		0			0
$369$	2.77574	+	17.5253i	0.144499	+	0.912333i
$370$		0			0
$371$	26.8099	−	17.4106i	1.39190	−	0.903912i
$372$		0			0
$373$	−19.8874	−	11.4820i	−1.02973	−	0.594514i	−0.112821	−	0.993615i	$-0.535989\pi$
$373$	−19.8874	−	11.4820i	−1.02973	−	0.594514i	−0.916907	+	0.399102i	$0.869322\pi$
$374$		0			0
$375$	−0.807123	+	3.01222i	−0.0416796	+	0.155551i
$376$		0			0
$377$	−11.0861	−	30.2224i	−0.570964	−	1.55653i
$378$		0			0
$379$	8.50173	+	10.4988i	0.436704	+	0.539285i	0.947220	−	0.320583i	$-0.103879\pi$
$379$	8.50173	+	10.4988i	0.436704	+	0.539285i	−0.510516	+	0.859868i	$0.670546\pi$
$380$		0			0
$381$	−1.65248	−	1.83526i	−0.0846591	−	0.0940234i
$382$		0			0
$383$	14.9359	+	12.0948i	0.763186	+	0.618016i	0.929825	−	0.368002i	$-0.119958\pi$
$383$	14.9359	+	12.0948i	0.763186	+	0.618016i	−0.166639	+	0.986018i	$0.553291\pi$
$384$		0			0
$385$	−1.45517	−	20.0094i	−0.0741622	−	1.01977i
$386$		0			0
$387$	7.36166	+	3.27762i	0.374214	+	0.166611i
$388$		0			0
$389$	1.00878	+	0.327772i	0.0511471	+	0.0166187i	0.334479	−	0.942403i	$-0.391440\pi$
$389$	1.00878	+	0.327772i	0.0511471	+	0.0166187i	−0.283332	+	0.959022i	$0.591440\pi$
$390$		0			0
$391$	−2.82138	+	3.88329i	−0.142683	+	0.196387i
$392$		0			0
$393$	−0.879765	−	0.792144i	−0.0443783	−	0.0399584i
$394$		0			0
$395$	−13.6429	−	13.6429i	−0.686447	−	0.686447i
$396$		0			0
$397$	4.09132	−	1.09627i	0.205338	−	0.0550200i	−0.154684	−	0.987964i	$-0.549436\pi$
$397$	4.09132	−	1.09627i	0.205338	−	0.0550200i	0.360022	+	0.932944i	$0.382769\pi$
$398$		0			0
$399$	−4.72469	−	1.00426i	−0.236530	−	0.0502761i
$400$		0			0
$401$	−13.6286	+	11.0362i	−0.680578	+	0.551121i	−0.906072	−	0.423123i	$-0.860934\pi$
$401$	−13.6286	+	11.0362i	−0.680578	+	0.551121i	0.225494	+	0.974244i	$0.427600\pi$
$402$		0			0
$403$	0.103346	−	6.91662i	0.00514803	−	0.344541i
$404$		0			0
$405$	−17.1028	+	6.56514i	−0.849844	+	0.326225i
$406$		0			0
$407$	0.324500	−	0.466190i	0.0160849	−	0.0231082i
$408$		0			0
$409$	−11.8287	+	14.6072i	−0.584890	+	0.722278i	−0.980583	−	0.196104i	$-0.937171\pi$
$409$	−11.8287	+	14.6072i	−0.584890	+	0.722278i	0.395693	+	0.918383i	$0.370504\pi$
$410$		0			0
$411$	3.67743	−	1.87374i	0.181394	−	0.0924249i
$412$		0			0
$413$	3.07433	−	29.2503i	0.151278	−	1.43931i
$414$		0			0
$415$	−4.22806	−	13.0126i	−0.207547	−	0.638765i
$416$		0			0
$417$			2.10082i			0.102878i
$418$		0			0
$419$	−14.3944	−	24.9318i	−0.703210	−	1.21800i	−0.967334	−	0.253507i	$-0.918416\pi$
$419$	−14.3944	−	24.9318i	−0.703210	−	1.21800i	0.264123	−	0.964489i	$-0.414917\pi$
$420$		0			0
$421$	−26.8412	−	13.6763i	−1.30816	−	0.666542i	−0.345799	−	0.938309i	$-0.612392\pi$
$421$	−26.8412	−	13.6763i	−1.30816	−	0.666542i	−0.962363	+	0.271767i	$0.912392\pi$
$422$		0			0
$423$	13.7122	+	5.26361i	0.666709	+	0.255925i
$424$		0			0
$425$	−0.791851	+	0.712986i	−0.0384104	+	0.0345849i
$426$		0			0
$427$	−9.49902	−	24.7458i	−0.459690	−	1.19753i
$428$		0			0
$429$	2.66801	+	1.91692i	0.128813	+	0.0925498i
$430$		0			0
$431$	−1.29092	−	3.36297i	−0.0621817	−	0.161989i	0.898970	−	0.438011i	$-0.144317\pi$
$431$	−1.29092	−	3.36297i	−0.0621817	−	0.161989i	−0.961151	+	0.276022i	$0.910984\pi$
$432$		0			0
$433$	−13.1962	+	11.8819i	−0.634167	+	0.571007i	−0.922248	−	0.386599i	$-0.873650\pi$
$433$	−13.1962	+	11.8819i	−0.634167	+	0.571007i	0.288080	+	0.957606i	$0.406983\pi$
$434$		0			0
$435$	−5.03824	−	1.93400i	−0.241565	−	0.0927281i
$436$		0			0
$437$	−4.08753	−	2.08270i	−0.195533	−	0.0996290i
$438$		0			0
$439$	−8.38190	−	14.5179i	−0.400046	−	0.692900i	0.593685	−	0.804698i	$-0.297673\pi$
$439$	−8.38190	−	14.5179i	−0.400046	−	0.692900i	−0.993731	+	0.111797i	$0.964339\pi$
$440$		0			0
$441$			1.63414i			0.0778163i
$442$		0			0
$443$	11.9995	+	36.9307i	0.570114	+	1.75463i	0.652244	+	0.758009i	$0.273828\pi$
$443$	11.9995	+	36.9307i	0.570114	+	1.75463i	−0.0821300	+	0.996622i	$0.526172\pi$
$444$		0			0
$445$	−1.05062	+	9.99595i	−0.0498040	+	0.473853i
$446$		0			0
$447$	−1.35899	+	0.692442i	−0.0642782	+	0.0327514i
$448$		0			0
$449$	−8.12440	+	10.0328i	−0.383414	+	0.473477i	−0.931917	−	0.362672i	$-0.881865\pi$
$449$	−8.12440	+	10.0328i	−0.383414	+	0.473477i	0.548503	+	0.836149i	$0.315198\pi$
$450$		0			0
$451$	0.407189	+	20.1186i	0.0191738	+	0.947349i
$452$		0			0
$453$	2.66974	−	1.02482i	0.125435	−	0.0481500i
$454$		0			0
$455$	−21.1487	+	5.32945i	−0.991468	+	0.249849i
$456$		0			0
$457$	7.54904	−	6.11309i	0.353129	−	0.285958i	−0.436299	−	0.899802i	$-0.643711\pi$
$457$	7.54904	−	6.11309i	0.353129	−	0.285958i	0.789428	+	0.613844i	$0.210378\pi$
$458$		0			0
$459$	10.6528	+	2.26433i	0.497231	+	0.105690i
$460$		0			0
$461$	7.61264	−	2.03980i	0.354556	−	0.0950030i	−0.0771447	−	0.997020i	$-0.524580\pi$
$461$	7.61264	−	2.03980i	0.354556	−	0.0950030i	0.431701	+	0.902017i	$0.357914\pi$
$462$		0			0
$463$	10.6331	+	10.6331i	0.494163	+	0.494163i	0.909615	−	0.415452i	$-0.136377\pi$
$463$	10.6331	+	10.6331i	0.494163	+	0.494163i	−0.415452	+	0.909615i	$0.636377\pi$
$464$		0			0
$465$	−0.861790	−	0.775959i	−0.0399645	−	0.0359842i
$466$		0			0
$467$	9.15556	−	12.6016i	0.423669	−	0.583130i	−0.542817	−	0.839851i	$-0.682642\pi$
$467$	9.15556	−	12.6016i	0.423669	−	0.583130i	0.966486	+	0.256721i	$0.0826421\pi$
$468$		0			0
$469$	−6.99625	−	2.27322i	−0.323057	−	0.104968i
$470$		0			0
$471$	−1.57413	−	0.700849i	−0.0725322	−	0.0322934i
$472$		0			0
$473$	7.76355	+	4.82121i	0.356968	+	0.221679i
$474$		0			0
$475$	−0.791425	−	0.640884i	−0.0363131	−	0.0294058i
$476$		0			0
$477$	−22.7533	−	25.2701i	−1.04180	−	1.15704i
$478$		0			0
$479$	15.7533	+	19.4537i	0.719787	+	0.888863i	0.997417	−	0.0718248i	$-0.0228822\pi$
$479$	15.7533	+	19.4537i	0.719787	+	0.888863i	−0.277630	+	0.960688i	$0.589549\pi$
$480$		0			0
$481$	−0.560290	−	0.259556i	−0.0255470	−	0.0118347i
$482$		0			0
$483$	0.140236	−	0.523368i	0.00638096	−	0.0238141i
$484$		0			0
$485$	−3.15580	−	1.82200i	−0.143298	−	0.0827329i
$486$		0			0
$487$	−2.30327	+	1.49576i	−0.104371	+	0.0677795i	−0.595769	−	0.803156i	$-0.703153\pi$
$487$	−2.30327	+	1.49576i	−0.104371	+	0.0677795i	0.491398	+	0.870935i	$0.336486\pi$
$488$		0			0
$489$	−0.658355	−	4.15669i	−0.0297718	−	0.187972i
$490$		0			0
$491$	16.4890	−	3.50484i	0.744137	−	0.158171i	0.179786	−	0.983706i	$-0.442460\pi$
$491$	16.4890	−	3.50484i	0.744137	−	0.158171i	0.564352	+	0.825534i	$0.309126\pi$
$492$		0			0
$493$	−35.1151	−	48.3318i	−1.58151	−	2.17676i
$494$		0			0
$495$	−20.7803	+	4.85847i	−0.934004	+	0.218372i
$496$		0			0
$497$	3.04251	−	6.83359i	0.136475	−	0.306529i
$498$		0			0
$499$	−1.34233	−	2.63447i	−0.0600909	−	0.117935i	0.859008	−	0.511963i	$-0.171081\pi$
$499$	−1.34233	−	2.63447i	−0.0600909	−	0.117935i	−0.919099	+	0.394028i	$0.871081\pi$
$500$		0			0
$501$	−0.507247	+	1.32142i	−0.0226621	+	0.0590368i
$502$		0			0
$503$	−0.769093	+	3.61830i	−0.0342922	+	0.161332i	−0.991962	−	0.126537i	$-0.959614\pi$
$503$	−0.769093	+	3.61830i	−0.0342922	+	0.161332i	0.957670	+	0.287869i	$0.0929469\pi$
$504$		0			0
$505$	10.4808	+	2.80831i	0.466387	+	0.124968i
$506$		0			0
$507$	1.54947	−	3.21782i	0.0688143	−	0.142908i
$508$		0			0
$509$	−0.790033	−	15.0747i	−0.0350176	−	0.668176i	−0.958597	−	0.284767i	$-0.908084\pi$
$509$	−0.790033	−	15.0747i	−0.0350176	−	0.668176i	0.923579	−	0.383408i	$-0.125250\pi$
$510$		0			0
$511$	8.28349	+	18.6050i	0.366440	+	0.823038i
$512$		0			0
$513$	−0.544750	+	10.3945i	−0.0240513	+	0.458926i
$514$		0			0
$515$	−10.4212	−	1.65055i	−0.459211	−	0.0727319i
$516$		0			0
$517$	14.5909	+	8.03487i	0.641708	+	0.353373i
$518$		0			0
$519$	3.28229	−	2.38472i	0.144077	−	0.104678i
$520$		0			0
$521$	1.96319	−	6.04206i	0.0860087	−	0.264708i	−0.898798	−	0.438364i	$-0.855558\pi$
$521$	1.96319	−	6.04206i	0.0860087	−	0.264708i	0.984806	+	0.173656i	$0.0555582\pi$
$522$		0			0
$523$	11.8653	+	1.24710i	0.518835	+	0.0545318i	0.360327	−	0.932826i	$-0.382665\pi$
$523$	11.8653	+	1.24710i	0.518835	+	0.0545318i	0.158508	+	0.987358i	$0.449332\pi$
$524$		0			0
$525$	0.0546056	−	0.107170i	0.00238319	−	0.00467726i
$526$		0			0
$527$	−3.32256	−	12.4000i	−0.144733	−	0.540150i
$528$		0			0
$529$	−11.2427	+	19.4729i	−0.488813	+	0.846649i
$530$		0			0
$531$	−31.2428	+	1.63737i	−1.35582	+	0.0710557i
$532$		0			0
$533$	21.4633	−	4.22803i	0.929677	−	0.183136i
$534$		0			0
$535$	−24.2730	−	15.7631i	−1.04941	−	0.681498i
$536$		0			0
$537$	−6.83900	+	0.718808i	−0.295125	+	0.0310189i
$538$		0			0
$539$	−0.252812	+	1.83591i	−0.0108894	+	0.0790783i
$540$		0			0
$541$	−2.21205	+	13.9663i	−0.0951033	+	0.600459i	0.893400	+	0.449261i	$0.148313\pi$
$541$	−2.21205	+	13.9663i	−0.0951033	+	0.600459i	−0.988504	+	0.151197i	$0.951687\pi$
$542$		0			0
$543$	−1.25463	−	5.90259i	−0.0538415	−	0.253304i
$544$		0			0
$545$	−30.7586	−	22.3474i	−1.31755	−	0.957258i
$546$		0			0
$547$	−37.2367	+	12.0989i	−1.59213	+	0.517313i	−0.965144	−	0.261721i	$-0.915710\pi$
$547$	−37.2367	+	12.0989i	−1.59213	+	0.517313i	−0.626982	+	0.779034i	$0.715710\pi$
$548$		0			0
$549$	−24.4180	+	14.0977i	−1.04214	+	0.601677i
$550$		0			0
$551$	40.3736	−	40.3736i	1.71997	−	1.71997i
$552$		0			0
$553$	13.1310	+	20.2200i	0.558388	+	0.859842i
$554$		0			0
$555$	−0.0945684	+	0.0421046i	−0.00401420	+	0.00178724i
$556$		0			0
$557$	−18.7284	+	28.8391i	−0.793546	+	1.22195i	0.177749	+	0.984076i	$0.443118\pi$
$557$	−18.7284	+	28.8391i	−0.793546	+	1.22195i	−0.971295	+	0.237878i	$0.923548\pi$
$558$		0			0
$559$	3.69851	−	9.22077i	0.156430	−	0.389997i
$560$		0			0
$561$	5.73491	+	2.06928i	0.242128	+	0.0873650i
$562$		0			0
$563$	−4.20378	−	39.9963i	−0.177168	−	1.68564i	−0.616530	−	0.787331i	$-0.711462\pi$
$563$	−4.20378	−	39.9963i	−0.177168	−	1.68564i	0.439362	−	0.898310i	$-0.355204\pi$
$564$		0			0
$565$	−9.80104	−	0.513651i	−0.412333	−	0.0216094i
$566$		0			0
$567$	22.6102	−	3.58110i	0.949538	−	0.150392i
$568$		0			0
$569$	−2.81423	+	3.12552i	−0.117979	+	0.131029i	−0.799241	−	0.601011i	$-0.794765\pi$
$569$	−2.81423	+	3.12552i	−0.117979	+	0.131029i	0.681262	+	0.732040i	$0.261431\pi$
$570$		0			0
$571$	45.3904			1.89953			0.949764	−	0.312966i	$-0.101323\pi$
$571$	45.3904			1.89953			0.949764	+	0.312966i	$0.101323\pi$
$572$		0			0
$573$	1.93625			0.0808880
$574$		0			0
$575$	0.0764385	−	0.0848936i	0.00318771	−	0.00354031i
$576$		0			0
$577$	27.2395	−	4.31432i	1.13400	−	0.179607i	0.438908	−	0.898532i	$-0.355365\pi$
$577$	27.2395	−	4.31432i	1.13400	−	0.179607i	0.695088	+	0.718924i	$0.255365\pi$
$578$		0			0
$579$	2.38017	+	0.124739i	0.0989164	+	0.00518399i
$580$		0			0
$581$	1.78716	+	17.0037i	0.0741437	+	0.705430i
$582$		0			0
$583$	−21.6533	−	31.9104i	−0.896787	−	1.32159i
$584$		0			0
$585$	9.11850	+	21.3327i	0.377004	+	0.881997i
$586$		0			0
$587$	−21.0153	+	32.3608i	−0.867396	+	1.33567i	0.0736117	+	0.997287i	$0.476547\pi$
$587$	−21.0153	+	32.3608i	−0.867396	+	1.33567i	−0.941008	+	0.338386i	$0.890119\pi$
$588$		0			0
$589$	11.2084	−	4.99030i	0.461834	−	0.205622i
$590$		0			0
$591$	1.43127	+	2.20397i	0.0588747	+	0.0906591i
$592$		0			0
$593$	−27.6937	+	27.6937i	−1.13725	+	1.13725i	−0.148303	+	0.988942i	$0.547381\pi$
$593$	−27.6937	+	27.6937i	−1.13725	+	1.13725i	−0.988942	+	0.148303i	$0.952619\pi$
$594$		0			0
$595$	−35.0525	+	20.2375i	−1.43701	+	0.829659i
$596$		0			0
$597$	−6.98325	+	2.26900i	−0.285805	+	0.0928638i
$598$		0			0
$599$	−5.17689	−	3.76123i	−0.211522	−	0.153680i	0.476980	−	0.878914i	$-0.341731\pi$
$599$	−5.17689	−	3.76123i	−0.211522	−	0.153680i	−0.688502	+	0.725234i	$0.741731\pi$
$600$		0			0
$601$	−2.25439	−	10.6061i	−0.0919583	−	0.432630i	−0.999908	−	0.0135511i	$-0.995686\pi$
$601$	−2.25439	−	10.6061i	−0.0919583	−	0.432630i	0.907950	−	0.419079i	$-0.137647\pi$
$602$		0			0
$603$	−1.22411	+	7.72874i	−0.0498497	+	0.314739i
$604$		0			0
$605$	−24.0977	+	2.24351i	−0.979710	+	0.0912117i
$606$		0			0
$607$	10.9980	−	1.15593i	0.446394	−	0.0469178i	0.121335	−	0.992612i	$-0.461283\pi$
$607$	10.9980	−	1.15593i	0.446394	−	0.0469178i	0.325059	+	0.945694i	$0.394616\pi$
$608$		0			0
$609$	5.65571	+	3.67286i	0.229181	+	0.148832i
$610$		0			0
$611$	5.85235	−	17.1362i	0.236761	−	0.693257i
$612$		0			0
$613$	28.4961	−	1.49342i	1.15095	−	0.0603186i	0.532701	−	0.846303i	$-0.321177\pi$
$613$	28.4961	−	1.49342i	1.15095	−	0.0603186i	0.618246	+	0.785985i	$0.287844\pi$
$614$		0			0
$615$	1.83366	−	3.17599i	0.0739402	−	0.128068i
$616$		0			0
$617$	4.28268	+	15.9832i	0.172414	+	0.643458i	0.996978	+	0.0776887i	$0.0247540\pi$
$617$	4.28268	+	15.9832i	0.172414	+	0.643458i	−0.824564	+	0.565769i	$0.808579\pi$
$618$		0			0
$619$	−12.1112	+	23.7696i	−0.486791	+	0.955381i	0.508738	+	0.860921i	$0.330112\pi$
$619$	−12.1112	+	23.7696i	−0.486791	+	0.955381i	−0.995529	+	0.0944593i	$0.969888\pi$
$620$		0			0
$621$	−1.16120	−	0.122047i	−0.0465972	−	0.00489756i
$622$		0			0
$623$	3.88115	−	11.9450i	0.155495	−	0.478565i
$624$		0			0
$625$	−19.5608	+	14.2117i	−0.782430	+	0.568469i
$626$		0			0
$627$	−1.09591	+	5.72295i	−0.0437663	+	0.228552i
$628$		0			0
$629$	−1.13184	−	0.179266i	−0.0451293	−	0.00714778i
$630$		0			0
$631$	−0.101861	+	1.94363i	−0.00405504	+	0.0773748i	−0.999907	−	0.0136093i	$-0.995668\pi$
$631$	−0.101861	+	1.94363i	−0.00405504	+	0.0773748i	0.995852	+	0.0909841i	$0.0290012\pi$
$632$		0			0
$633$	−1.40147	−	3.14774i	−0.0557033	−	0.125112i
$634$		0			0
$635$	−1.03510	−	19.7508i	−0.0410766	−	0.783788i
$636$		0			0
$637$	2.01327	−	0.0753704i	0.0797687	−	0.00298628i
$638$		0			0
$639$	−7.68586	−	2.05942i	−0.304048	−	0.0814694i
$640$		0			0
$641$	−5.12306	+	24.1021i	−0.202349	+	0.951977i	0.753348	+	0.657623i	$0.228438\pi$
$641$	−5.12306	+	24.1021i	−0.202349	+	0.951977i	−0.955696	+	0.294354i	$0.904896\pi$
$642$		0			0
$643$	7.29436	−	19.0025i	0.287661	−	0.749384i	−0.711259	−	0.702930i	$-0.751875\pi$
$643$	7.29436	−	19.0025i	0.287661	−	0.749384i	0.998920	−	0.0464536i	$-0.0147920\pi$
$644$		0			0
$645$	−0.756126	−	1.48398i	−0.0297724	−	0.0584317i
$646$		0			0
$647$	0.759473	−	1.70580i	0.0298580	−	0.0670621i	−0.898001	−	0.439994i	$-0.854981\pi$
$647$	0.759473	−	1.70580i	0.0298580	−	0.0670621i	0.927859	+	0.372932i	$0.121647\pi$
$648$		0			0
$649$	−35.3537	−	2.99392i	−1.38775	−	0.117522i
$650$		0			0
$651$	0.851757	+	1.17234i	0.0333830	+	0.0459477i
$652$		0			0
$653$	22.0678	−	4.69066i	0.863581	−	0.183560i	0.245233	−	0.969464i	$-0.421136\pi$
$653$	22.0678	−	4.69066i	0.863581	−	0.183560i	0.618348	+	0.785904i	$0.287802\pi$
$654$		0			0
$655$	−1.48314	−	9.36416i	−0.0579510	−	0.365888i
$656$		0			0
$657$	18.1686	−	11.7988i	0.708824	−	0.460316i
$658$		0			0
$659$	−14.2662	−	8.23658i	−0.555731	−	0.320852i	0.195699	−	0.980664i	$-0.437302\pi$
$659$	−14.2662	−	8.23658i	−0.555731	−	0.320852i	−0.751430	+	0.659812i	$0.770636\pi$
$660$		0			0
$661$	9.18662	−	34.2849i	0.357318	−	1.33353i	−0.520224	−	0.854030i	$-0.674152\pi$
$661$	9.18662	−	34.2849i	0.357318	−	1.33353i	0.877542	−	0.479499i	$-0.159182\pi$
$662$		0			0
$663$	1.13452	−	6.53011i	0.0440612	−	0.253608i
$664$		0			0
$665$	−24.3443	−	30.0627i	−0.944031	−	1.16578i
$666$		0			0
$667$	4.28566	+	4.75971i	0.165941	+	0.184297i
$668$		0			0
$669$	−4.81853	−	3.90197i	−0.186295	−	0.150859i
$670$		0			0
$671$	−29.6139	+	12.0608i	−1.14323	+	0.465602i
$672$		0			0
$673$	−12.5072	−	5.56856i	−0.482117	−	0.214652i	0.151262	−	0.988494i	$-0.451666\pi$
$673$	−12.5072	−	5.56856i	−0.482117	−	0.214652i	−0.633380	+	0.773841i	$0.718333\pi$
$674$		0			0
$675$	−0.246505	−	0.0800942i	−0.00948797	−	0.00308283i
$676$		0			0
$677$	15.1297	−	20.8243i	0.581483	−	0.800343i	−0.412374	−	0.911015i	$-0.635300\pi$
$677$	15.1297	−	20.8243i	0.581483	−	0.800343i	0.993857	+	0.110672i	$0.0353003\pi$
$678$		0			0
$679$	3.38393	+	3.04690i	0.129863	+	0.116929i
$680$		0			0
$681$	1.13185	+	1.13185i	0.0433724	+	0.0433724i
$682$		0			0
$683$	−11.1821	+	2.99624i	−0.427873	+	0.114648i	−0.466327	−	0.884612i	$-0.654423\pi$
$683$	−11.1821	+	2.99624i	−0.427873	+	0.114648i	0.0384548	+	0.999260i	$0.487756\pi$
$684$		0			0
$685$	32.3313	+	6.87224i	1.23532	+	0.262575i
$686$		0			0
$687$	4.95689	−	4.01401i	0.189117	−	0.153144i
$688$		0			0
$689$	−30.0835	+	29.1977i	−1.14609	+	1.11234i
$690$		0			0
$691$	45.6362	−	17.5181i	1.73608	−	0.666420i	0.736137	−	0.676833i	$-0.236648\pi$
$691$	45.6362	−	17.5181i	1.73608	−	0.666420i	0.999946	+	0.0104129i	$0.00331460\pi$
$692$		0			0
$693$	26.6617	−	0.539618i	1.01280	−	0.0204984i
$694$		0			0
$695$	−10.5881	+	13.0752i	−0.401628	+	0.495970i
$696$		0			0
$697$	36.1724	−	18.4308i	1.37013	−	0.698115i
$698$		0			0
$699$	−0.737295	+	7.01490i	−0.0278871	+	0.265328i
$700$		0			0
$701$	−2.83010	−	8.71015i	−0.106891	−	0.328978i	0.883278	−	0.468849i	$-0.155331\pi$
$701$	−2.83010	−	8.71015i	−0.106891	−	0.328978i	−0.990170	+	0.139871i	$0.955331\pi$
$702$		0			0
$703$		−	1.09522i		−	0.0413070i
$704$		0			0
$705$	−1.51784	−	2.62898i	−0.0571652	−	0.0990131i
$706$		0			0
$707$	−12.0809	−	6.15552i	−0.454348	−	0.231502i
$708$		0			0
$709$	−46.4004	−	17.8114i	−1.74260	−	0.668923i	−0.742604	−	0.669731i	$-0.766409\pi$
$709$	−46.4004	−	17.8114i	−1.74260	−	0.668923i	−1.00000		0.000808477i	$0.999743\pi$
$710$		0			0
$711$	19.0587	−	17.1605i	0.714757	−	0.643570i
$712$		0			0
$713$	0.493216	+	1.28487i	0.0184711	+	0.0481188i
$714$		0			0
$715$	6.94408	+	25.3773i	0.259694	+	0.949057i
$716$		0			0
$717$	1.07381	+	2.79737i	0.0401022	+	0.104470i
$718$		0			0
$719$	17.4490	−	15.7112i	0.650739	−	0.585928i	−0.276218	−	0.961095i	$-0.589081\pi$
$719$	17.4490	−	15.7112i	0.650739	−	0.585928i	0.926957	+	0.375167i	$0.122415\pi$
$720$		0			0
$721$	12.3088	+	4.72492i	0.458405	+	0.175965i
$722$		0			0
$723$	−4.25207	−	2.16654i	−0.158136	−	0.0805744i
$724$		0			0
$725$	0.710893	+	1.23130i	0.0264019	+	0.0457294i
$726$		0			0
$727$			32.8105i			1.21688i	0.793601	+	0.608438i	$0.208204\pi$
$727$			32.8105i			1.21688i	−0.793601	+	0.608438i	$0.791796\pi$
$728$		0			0
$729$	−7.11029	−	21.8832i	−0.263344	−	0.810490i
$730$		0			0
$731$	1.92722	−	18.3362i	0.0712807	−	0.678190i
$732$		0			0
$733$	20.7743	−	10.5850i	0.767317	−	0.390968i	−0.0260896	−	0.999660i	$-0.508306\pi$
$733$	20.7743	−	10.5850i	0.767317	−	0.390968i	0.793407	+	0.608692i	$0.208306\pi$
$734$		0			0
$735$	0.212551	−	0.262479i	0.00784007	−	0.00968168i
$736$		0			0
$737$	−2.57094	+	8.49364i	−0.0947017	+	0.312867i
$738$		0			0
$739$	−33.0782	+	12.6975i	−1.21680	+	0.467087i	−0.880219	−	0.474567i	$-0.842605\pi$
$739$	−33.0782	+	12.6975i	−1.21680	+	0.467087i	−0.336583	+	0.941654i	$0.609271\pi$
$740$		0			0
$741$	6.33384	+	0.0946382i	0.232679	+	0.00347662i
$742$		0			0
$743$	−27.7695	+	22.4873i	−1.01876	+	0.824978i	−0.984668	−	0.174441i	$-0.944188\pi$
$743$	−27.7695	+	22.4873i	−1.01876	+	0.824978i	−0.0340952	+	0.999419i	$0.510855\pi$
$744$		0			0
$745$	−11.9481	−	2.53964i	−0.437743	−	0.0930451i
$746$		0			0
$747$	17.5672	−	4.70710i	0.642749	−	0.172224i
$748$		0			0
$749$	25.5733	+	25.5733i	0.934428	+	0.934428i
$750$		0			0
$751$	7.23596	+	6.51529i	0.264044	+	0.237746i	0.790509	−	0.612451i	$-0.209816\pi$
$751$	7.23596	+	6.51529i	0.264044	+	0.237746i	−0.526465	+	0.850197i	$0.676483\pi$
$752$		0			0
$753$	−1.61858	+	2.22778i	−0.0589842	+	0.0811848i
$754$		0			0
$755$	21.7810	+	7.07709i	0.792693	+	0.257562i
$756$		0			0
$757$	−32.4222	−	14.4353i	−1.17841	−	0.524660i	−0.278369	−	0.960474i	$-0.589794\pi$
$757$	−32.4222	−	14.4353i	−1.17841	−	0.524660i	−0.900037	+	0.435814i	$0.856461\pi$
$758$		0			0
$759$	−0.634655	−	0.156362i	−0.0230365	−	0.00567559i
$760$		0			0
$761$	7.86681	+	6.37042i	0.285172	+	0.230928i	0.761223	−	0.648490i	$-0.224599\pi$
$761$	7.86681	+	6.37042i	0.285172	+	0.230928i	−0.476052	+	0.879417i	$0.657932\pi$
$762$		0			0
$763$	31.7898	+	35.3062i	1.15087	+	1.27817i
$764$		0			0
$765$	27.0950	+	33.4596i	0.979623	+	1.20973i
$766$		0			0
$767$	3.45823	+	38.4158i	0.124870	+	1.38711i
$768$		0			0
$769$	5.17170	−	19.3010i	0.186496	−	0.696014i	−0.807809	−	0.589444i	$-0.799347\pi$
$769$	5.17170	−	19.3010i	0.186496	−	0.696014i	0.994305	−	0.106569i	$-0.0339866\pi$
$770$		0			0
$771$	2.94918	+	1.70271i	0.106212	+	0.0613215i
$772$		0			0
$773$	−0.771591	+	0.501077i	−0.0277522	+	0.0180225i	−0.558441	−	0.829545i	$-0.688600\pi$
$773$	−0.771591	+	0.501077i	−0.0277522	+	0.0180225i	0.530688	+	0.847567i	$0.321933\pi$
$774$		0			0
$775$	0.0477933	+	0.301755i	0.00171679	+	0.0108394i
$776$		0			0
$777$	0.126529	−	0.0268945i	0.00453919	−	0.000964836i
$778$		0			0
$779$	22.8062	+	31.3900i	0.817116	+	1.12466i
$780$		0			0
$781$	−8.31624	−	3.50275i	−0.297578	−	0.125338i
$782$		0			0
$783$	5.91068	−	13.2756i	0.211230	−	0.474431i
$784$		0			0
$785$	−6.26490	−	12.2956i	−0.223604	−	0.438847i
$786$		0			0
$787$	−10.7224	+	27.9329i	−0.382213	+	0.995700i	0.598652	+	0.801010i	$0.295703\pi$
$787$	−10.7224	+	27.9329i	−0.382213	+	0.995700i	−0.980865	+	0.194690i	$0.937630\pi$
$788$		0			0
$789$	0.227705	−	1.07127i	0.00810651	−	0.0381381i
$790$		0			0
$791$	11.8462	+	3.17419i	0.421204	+	0.112861i
$792$		0			0
$793$	18.4947	+	29.4329i	0.656766	+	1.04519i
$794$		0			0
$795$	0.367821	+	7.01844i	0.0130453	+	0.248918i
$796$		0			0
$797$	−3.00264	−	6.74404i	−0.106359	−	0.238886i	0.852524	−	0.522688i	$-0.175071\pi$
$797$	−3.00264	−	6.74404i	−0.106359	−	0.238886i	−0.958883	+	0.283802i	$0.908404\pi$
$798$		0			0
$799$	1.75875	−	33.5590i	0.0622202	−	1.18723i
$800$		0			0
$801$	−13.1956	−	2.08997i	−0.466243	−	0.0738456i
$802$		0			0
$803$	22.2372	−	10.4448i	0.784735	−	0.368591i
$804$		0			0
$805$	3.51056	−	2.55057i	0.123731	−	0.0898959i
$806$		0			0
$807$	−0.600467	+	1.84805i	−0.0211375	+	0.0650544i
$808$		0			0
$809$	2.01469	+	0.211752i	0.0708326	+	0.00744481i	0.139878	−	0.990169i	$-0.455329\pi$
$809$	2.01469	+	0.211752i	0.0708326	+	0.00744481i	−0.0690458	+	0.997613i	$0.521995\pi$
$810$		0			0
$811$	−9.21691	+	18.0892i	−0.323649	+	0.635198i	−0.994305	−	0.106571i	$-0.966013\pi$
$811$	−9.21691	+	18.0892i	−0.323649	+	0.635198i	0.670656	+	0.741769i	$0.266013\pi$
$812$		0			0
$813$	1.31048	+	4.89077i	0.0459605	+	0.171527i
$814$		0			0
$815$	16.8521	−	29.1887i	0.590302	−	1.02243i
$816$		0			0
$817$	17.5970	−	0.922217i	0.615640	−	0.0322643i
$818$		0			0
$819$	−5.60310	−	28.4437i	−0.195788	−	0.993902i
$820$		0			0
$821$	0.167561	+	0.108815i	0.00584792	+	0.00379768i	0.547560	−	0.836767i	$-0.315557\pi$
$821$	0.167561	+	0.108815i	0.00584792	+	0.00379768i	−0.541712	+	0.840564i	$0.682224\pi$
$822$		0			0
$823$	54.0410	−	5.67994i	1.88375	−	0.197990i	0.908316	−	0.418284i	$-0.137368\pi$
$823$	54.0410	−	5.67994i	1.88375	−	0.197990i	0.975434	+	0.220294i	$0.0707015\pi$
$824$		0			0
$825$	−0.130590	−	0.0632435i	−0.00454655	−	0.00220186i
$826$		0			0
$827$	3.27014	−	20.6468i	0.113714	−	0.717961i	−0.863285	−	0.504717i	$-0.831597\pi$
$827$	3.27014	−	20.6468i	0.113714	−	0.717961i	0.976999	−	0.213244i	$-0.0684031\pi$
$828$		0			0
$829$	1.94895	+	9.16908i	0.0676898	+	0.318455i	0.998946	−	0.0459108i	$-0.0146190\pi$
$829$	1.94895	+	9.16908i	0.0676898	+	0.318455i	−0.931256	+	0.364366i	$0.881286\pi$
$830$		0			0
$831$	−2.66885	−	1.93903i	−0.0925812	−	0.0672642i
$832$		0			0
$833$	3.55588	−	1.15537i	0.123204	−	0.0400313i
$834$		0			0
$835$	−9.81695	+	5.66782i	−0.339730	+	0.196143i
$836$		0			0
$837$	2.20805	−	2.20805i	0.0763215	−	0.0763215i
$838$		0			0
$839$	15.8562	+	24.4164i	0.547418	+	0.842949i	0.998779	−	0.0493917i	$-0.0157283\pi$
$839$	15.8562	+	24.4164i	0.547418	+	0.842949i	−0.451362	+	0.892341i	$0.649062\pi$
$840$		0			0
$841$	−46.3304	+	20.6276i	−1.59760	+	0.711297i
$842$		0			0
$843$	−3.21152	+	4.94531i	−0.110611	+	0.170325i
$844$		0			0
$845$	25.8614	−	12.2179i	0.889658	−	0.420310i
$846$		0			0
$847$	30.0372	+	3.51849i	1.03209	+	0.120897i
$848$		0			0
$849$	−0.930167	−	8.84995i	−0.0319232	−	0.303729i
$850$		0			0
$851$	0.122687	+	0.00642978i	0.00420567	+	0.000220410i
$852$		0			0
$853$	−13.8357	+	2.19136i	−0.473726	+	0.0750308i	−0.388733	−	0.921351i	$-0.627087\pi$
$853$	−13.8357	+	2.19136i	−0.473726	+	0.0750308i	−0.0849936	+	0.996381i	$0.527087\pi$
$854$		0			0
$855$	−27.5338	+	30.5794i	−0.941635	+	1.04579i
$856$		0			0
$857$	36.8874			1.26005			0.630024	−	0.776576i	$-0.283045\pi$
$857$	36.8874			1.26005			0.630024	+	0.776576i	$0.283045\pi$
$858$		0			0
$859$	−44.2797			−1.51080			−0.755402	−	0.655261i	$-0.772559\pi$
$859$	−44.2797			−1.51080			−0.755402	+	0.655261i	$0.772559\pi$
$860$		0			0
$861$	−3.06640	+	3.40558i	−0.104503	+	0.116062i
$862$		0			0
$863$	−50.7927	+	8.04477i	−1.72900	+	0.273847i	−0.940157	−	0.340743i	$-0.889321\pi$
$863$	−50.7927	+	8.04477i	−1.72900	+	0.273847i	−0.788847	+	0.614590i	$0.789321\pi$
$864$		0			0
$865$	32.4474	+	1.70050i	1.10324	+	0.0578186i
$866$		0			0
$867$	−0.797536	−	7.58805i	−0.0270857	−	0.257704i
$868$		0			0
$869$	24.0667	−	16.3309i	0.816408	−	0.553986i
$870$		0			0
$871$	9.57830	+	1.15164i	0.324548	+	0.0390220i
$872$		0			0
$873$	2.63807	−	4.06227i	0.0892852	−	0.137487i
$874$		0			0
$875$	28.5101	−	12.6935i	0.963817	−	0.429119i
$876$		0			0
$877$	−4.81950	−	7.42138i	−0.162743	−	0.250602i	0.747886	−	0.663827i	$-0.231069\pi$
$877$	−4.81950	−	7.42138i	−0.162743	−	0.250602i	−0.910629	+	0.413225i	$0.864402\pi$
$878$		0			0
$879$	5.22493	−	5.22493i	0.176232	−	0.176232i
$880$		0			0
$881$	19.5275	−	11.2742i	0.657899	−	0.379838i	−0.133577	−	0.991038i	$-0.542646\pi$
$881$	19.5275	−	11.2742i	0.657899	−	0.379838i	0.791476	+	0.611200i	$0.209313\pi$
$882$		0			0
$883$	−23.0549	+	7.49098i	−0.775858	+	0.252092i	−0.670071	−	0.742297i	$-0.733736\pi$
$883$	−23.0549	+	7.49098i	−0.775858	+	0.252092i	−0.105788	+	0.994389i	$0.533736\pi$
$884$		0			0
$885$	5.23125	+	3.80072i	0.175846	+	0.127760i
$886$		0			0
$887$	3.87710	+	18.2403i	0.130180	+	0.612449i	0.994068	+	0.108764i	$0.0346894\pi$
$887$	3.87710	+	18.2403i	0.130180	+	0.612449i	−0.863887	+	0.503685i	$0.831977\pi$
$888$		0			0
$889$	−3.86618	+	24.4101i	−0.129668	+	0.818689i
$890$		0			0
$891$	−4.87108	−	27.1826i	−0.163187	−	0.910652i
$892$		0			0
$893$	31.9416	−	3.35720i	1.06888	−	0.112344i
$894$		0			0
$895$	−46.1876	−	29.9946i	−1.54388	−	1.00261i
$896$		0			0
$897$	−0.0477859	+	0.708965i	−0.00159552	+	0.0236717i
$898$		0			0
$899$	−17.1059	+	0.896480i	−0.570512	+	0.0298993i
$900$		0			0
$901$	−38.9004	+	67.3775i	−1.29596	+	2.24467i
$902$		0			0
$903$	0.538658	+	2.01030i	0.0179254	+	0.0668985i
$904$		0			0
$905$	21.9402	−	43.0601i	0.729317	−	1.43137i
$906$		0			0
$907$	41.1926	+	4.32951i	1.36778	+	0.143759i	0.759780	−	0.650180i	$-0.225307\pi$
$907$	41.1926	+	4.32951i	1.36778	+	0.143759i	0.607997	+	0.793939i	$0.291973\pi$
$908$		0			0
$909$	−4.45687	+	13.7168i	−0.147825	+	0.454959i
$910$		0			0
$911$	33.7625	−	24.5299i	1.11860	−	0.812712i	0.134605	−	0.990899i	$-0.457023\pi$
$911$	33.7625	−	24.5299i	1.11860	−	0.812712i	0.983997	+	0.178188i	$0.0570234\pi$
$912$		0			0
$913$	20.4644	−	2.57055i	0.677273	−	0.0850728i
$914$		0			0
$915$	5.75574	+	0.911620i	0.190279	+	0.0301372i
$916$		0			0
$917$	−0.620038	+	11.8310i	−0.0204755	+	0.390695i
$918$		0			0
$919$	14.3591	+	32.2511i	0.473663	+	1.06386i	0.979538	+	0.201258i	$0.0645029\pi$
$919$	14.3591	+	32.2511i	0.473663	+	1.06386i	−0.505875	+	0.862607i	$0.668830\pi$
$920$		0			0
$921$	−0.424796	−	8.10559i	−0.0139975	−	0.267088i
$922$		0			0
$923$	−2.18273	+	9.56400i	−0.0718453	+	0.314803i
$924$		0			0
$925$	0.0263431	+	0.00705861i	0.000866156	+	0.000232086i
$926$		0			0
$927$	2.91591	−	13.7183i	0.0957710	−	0.450567i
$928$		0			0
$929$	−4.84525	+	12.6223i	−0.158967	+	0.414124i	−0.989812	−	0.142380i	$-0.954524\pi$
$929$	−4.84525	+	12.6223i	−0.158967	+	0.414124i	0.830845	+	0.556505i	$0.187858\pi$
$930$		0			0
$931$	1.62227	+	3.18389i	0.0531679	+	0.104348i
$932$		0			0
$933$	3.57443	−	8.02831i	0.117022	−	0.262835i
$934$		0			0
$935$	25.2641	+	41.7826i	0.826224	+	1.36644i
$936$		0			0
$937$	7.02745	+	9.67246i	0.229577	+	0.315985i	0.908228	−	0.418475i	$-0.137435\pi$
$937$	7.02745	+	9.67246i	0.229577	+	0.315985i	−0.678651	+	0.734461i	$0.737435\pi$
$938$		0			0
$939$	2.11822	−	0.450242i	0.0691256	−	0.0146931i
$940$		0			0
$941$	3.80657	+	24.0338i	0.124091	+	0.783478i	0.968725	+	0.248135i	$0.0798177\pi$
$941$	3.80657	+	24.0338i	0.124091	+	0.783478i	−0.844635	+	0.535343i	$0.820182\pi$
$942$		0			0
$943$	−3.65022	+	2.37048i	−0.118868	+	0.0771936i
$944$		0			0
$945$	−8.52643	−	4.92273i	−0.277365	−	0.160137i
$946$		0			0
$947$	7.10362	−	26.5111i	0.230837	−	0.861494i	−0.749145	−	0.662406i	$-0.769535\pi$
$947$	7.10362	−	26.5111i	0.230837	−	0.861494i	0.979982	−	0.199088i	$-0.0637979\pi$
$948$		0			0
$949$	−15.3742	−	21.8396i	−0.499067	−	0.708943i
$950$		0			0
$951$	0.394827	+	0.487570i	0.0128031	+	0.0158105i
$952$		0			0
$953$	6.29050	+	6.98631i	0.203769	+	0.226309i	0.836364	−	0.548174i	$-0.184677\pi$
$953$	6.29050	+	6.98631i	0.203769	+	0.226309i	−0.632595	+	0.774483i	$0.718010\pi$
$954$		0			0
$955$	12.0509	+	9.75864i	0.389958	+	0.315782i
$956$		0			0
$957$	4.29177	−	6.91099i	0.138733	−	0.223401i
$958$		0			0
$959$	−37.7328	−	16.7997i	−1.21845	−	0.542491i
$960$		0			0
$961$	25.9821	+	8.44210i	0.838133	+	0.272326i
$962$		0			0
$963$	22.6126	−	31.1236i	0.728680	−	1.00294i
$964$		0			0
$965$	14.1851	+	12.7723i	0.456635	+	0.411156i
$966$		0			0
$967$	−3.02861	−	3.02861i	−0.0973936	−	0.0973936i	0.656731	−	0.754125i	$-0.271939\pi$
$967$	−3.02861	−	3.02861i	−0.0973936	−	0.0973936i	−0.754125	+	0.656731i	$0.771939\pi$
$968$		0			0
$969$	11.3552	−	3.04260i	0.364780	−	0.0977425i
$970$		0			0
$971$	−22.2731	−	4.73430i	−0.714779	−	0.151931i	−0.163852	−	0.986485i	$-0.552392\pi$
$971$	−22.2731	−	4.73430i	−0.714779	−	0.151931i	−0.550926	+	0.834554i	$0.685725\pi$
$972$		0			0
$973$	16.3387	−	13.2308i	0.523794	−	0.424160i
$974$		0			0
$975$	−0.0430974	+	0.151736i	−0.00138022	+	0.00485945i
$976$		0			0
$977$	37.1230	−	14.2502i	1.18767	−	0.455904i	0.317311	−	0.948322i	$-0.397220\pi$
$977$	37.1230	−	14.2502i	1.18767	−	0.455904i	0.870359	+	0.492418i	$0.163887\pi$
$978$		0			0
$979$	−14.5015	−	4.38946i	−0.463470	−	0.140288i
$980$		0			0
$981$	31.8038	−	39.2744i	1.01542	−	1.25394i
$982$		0			0
$983$	−1.93774	+	0.987328i	−0.0618043	+	0.0314909i	−0.484620	−	0.874725i	$-0.661042\pi$
$983$	−1.93774	+	0.987328i	−0.0618043	+	0.0314909i	0.422815	+	0.906216i	$0.361042\pi$
$984$		0			0
$985$	−2.19991	+	20.9307i	−0.0700948	+	0.666908i
$986$		0			0
$987$	1.17222	+	3.60771i	0.0373121	+	0.114835i
$988$		0			0
$989$			1.97664i			0.0628535i
$990$		0			0
$991$	23.2518	+	40.2732i	0.738617	+	1.27932i	0.953118	+	0.302598i	$0.0978539\pi$
$991$	23.2518	+	40.2732i	0.738617	+	1.27932i	−0.214502	+	0.976724i	$0.568813\pi$
$992$		0			0
$993$	4.75955	+	2.42511i	0.151040	+	0.0769586i
$994$		0			0
$995$	−54.8983	−	21.0735i	−1.74039	−	0.668074i
$996$		0			0
$997$	7.02366	−	6.32413i	0.222442	−	0.200287i	−0.550373	−	0.834919i	$-0.685515\pi$
$997$	7.02366	−	6.32413i	0.222442	−	0.200287i	0.772815	+	0.634631i	$0.218848\pi$
$998$		0			0
$999$	−0.0998946	−	0.260234i	−0.00316053	−	0.00823345i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bv.a.41.8	✓	224
11.7	odd	10	inner	572.2.bv.a.249.7	yes	224
13.7	odd	12	inner	572.2.bv.a.85.7	yes	224
143.7	even	60	inner	572.2.bv.a.293.8	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bv.a.41.8	✓	224	1.1	even	1	trivial
572.2.bv.a.85.7	yes	224	13.7	odd	12	inner
572.2.bv.a.249.7	yes	224	11.7	odd	10	inner
572.2.bv.a.293.8	yes	224	143.7	even	60	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.bv (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.183828 - 0.204162i) q^{3} +(2.17308 - 0.344183i) q^{5} +(-2.74555 - 0.143888i) q^{7} +(0.305696 + 2.90850i) q^{9} +O(q^{10})\)	\(q+(0.183828 - 0.204162i) q^{3} +(2.17308 - 0.344183i) q^{5} +(-2.74555 - 0.143888i) q^{7} +(0.305696 + 2.90850i) q^{9} +(-0.106522 + 3.31491i) q^{11} +(3.56919 - 0.510766i) q^{13} +(0.329205 - 0.506931i) q^{15} +(6.11274 - 2.72157i) q^{17} +(3.48299 + 5.36333i) q^{19} +(-0.534086 + 0.534086i) q^{21} +(-0.621252 + 0.358680i) q^{23} +(-0.151451 + 0.0492093i) q^{25} +(1.31678 + 0.956694i) q^{27} +(-1.85630 - 8.73321i) q^{29} +(0.300126 - 1.89492i) q^{31} +(0.657196 + 0.631122i) q^{33} +(-6.01584 + 0.632291i) q^{35} +(-0.143632 - 0.0932755i) q^{37} +(0.551838 - 0.822585i) q^{39} +(6.05892 - 0.317535i) q^{41} +(1.37772 - 2.38628i) q^{43} +(1.66536 + 6.21521i) q^{45} +(2.28006 - 4.47487i) q^{47} +(0.555711 + 0.0584076i) q^{49} +(0.568053 - 1.74829i) q^{51} +(-9.40668 + 6.83435i) q^{53} +(0.909454 + 7.24025i) q^{55} +(1.73526 + 0.274838i) q^{57} +(-0.559874 + 10.6830i) q^{59} +(3.92137 + 8.80754i) q^{61} +(-0.420805 - 8.02944i) q^{63} +(7.58035 - 2.33839i) q^{65} +(2.58450 + 0.692516i) q^{67} +(-0.0409748 + 0.192771i) q^{69} +(-0.975040 + 2.54007i) q^{71} +(-3.36296 - 6.60017i) q^{73} +(-0.0177942 + 0.0399664i) q^{75} +(0.769441 - 9.08595i) q^{77} +(-5.15446 - 7.09450i) q^{79} +(-8.14447 + 1.73116i) q^{81} +(-0.972825 - 6.14217i) q^{83} +(12.3468 - 8.01809i) q^{85} +(-2.12423 - 1.22642i) q^{87} +(-1.18236 + 4.41262i) q^{89} +(-9.87290 + 0.888770i) q^{91} +(-0.331698 - 0.409613i) q^{93} +(9.41478 + 10.4562i) q^{95} +(-1.28714 - 1.04230i) q^{97} +(-9.67400 + 0.703535i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q + 28 q^{9}+O(q^{10}) \) 224 * q + 28 * q^9	\( 224 q + 28 q^{9} + 16 q^{11} + 10 q^{13} - 28 q^{15} - 48 q^{23} + 24 q^{27} + 20 q^{29} + 4 q^{31} + 60 q^{33} + 50 q^{35} + 12 q^{37} - 40 q^{39} + 20 q^{41} + 64 q^{45} - 62 q^{47} + 100 q^{53} - 22 q^{55} + 12 q^{59} - 40 q^{61} - 80 q^{63} - 44 q^{67} - 152 q^{71} + 30 q^{73} - 120 q^{75} + 80 q^{79} + 72 q^{81} + 90 q^{83} - 40 q^{85} - 8 q^{89} - 36 q^{91} - 90 q^{93} - 42 q^{97} + 144 q^{99}+O(q^{100}) \) 224 * q + 28 * q^9 + 16 * q^11 + 10 * q^13 - 28 * q^15 - 48 * q^23 + 24 * q^27 + 20 * q^29 + 4 * q^31 + 60 * q^33 + 50 * q^35 + 12 * q^37 - 40 * q^39 + 20 * q^41 + 64 * q^45 - 62 * q^47 + 100 * q^53 - 22 * q^55 + 12 * q^59 - 40 * q^61 - 80 * q^63 - 44 * q^67 - 152 * q^71 + 30 * q^73 - 120 * q^75 + 80 * q^79 + 72 * q^81 + 90 * q^83 - 40 * q^85 - 8 * q^89 - 36 * q^91 - 90 * q^93 - 42 * q^97 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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