LMFDB - Embedded newform 507.2.e.d.22.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(22,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("507.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.e (of order $3$, degree $2$, not 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 39)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			22.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	507.22
Dual form			507.2.e.d.484.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.20711 + 2.09077i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.91421 - 3.31552i) q^{4} -2.82843 q^{5} +(-1.20711 - 2.09077i) q^{6} +(-1.41421 - 2.44949i) q^{7} +4.41421 q^{8} +(-0.500000 - 0.866025i) q^{9} +(3.41421 - 5.91359i) q^{10} +(-1.00000 + 1.73205i) q^{11} +3.82843 q^{12} +6.82843 q^{14} +(1.41421 - 2.44949i) q^{15} +(-1.50000 + 2.59808i) q^{16} +(1.82843 + 3.16693i) q^{17} +2.41421 q^{18} +(1.41421 + 2.44949i) q^{19} +(5.41421 + 9.37769i) q^{20} +2.82843 q^{21} +(-2.41421 - 4.18154i) q^{22} +(2.00000 - 3.46410i) q^{23} +(-2.20711 + 3.82282i) q^{24} +3.00000 q^{25} +1.00000 q^{27} +(-5.41421 + 9.37769i) q^{28} +(-1.00000 + 1.73205i) q^{29} +(3.41421 + 5.91359i) q^{30} +6.82843 q^{31} +(0.792893 + 1.37333i) q^{32} +(-1.00000 - 1.73205i) q^{33} -8.82843 q^{34} +(4.00000 + 6.92820i) q^{35} +(-1.91421 + 3.31552i) q^{36} +(1.82843 - 3.16693i) q^{37} -6.82843 q^{38} -12.4853 q^{40} +(5.41421 - 9.37769i) q^{41} +(-3.41421 + 5.91359i) q^{42} +(-4.82843 - 8.36308i) q^{43} +7.65685 q^{44} +(1.41421 + 2.44949i) q^{45} +(4.82843 + 8.36308i) q^{46} +0.343146 q^{47} +(-1.50000 - 2.59808i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-3.62132 + 6.27231i) q^{50} -3.65685 q^{51} -2.00000 q^{53} +(-1.20711 + 2.09077i) q^{54} +(2.82843 - 4.89898i) q^{55} +(-6.24264 - 10.8126i) q^{56} -2.82843 q^{57} +(-2.41421 - 4.18154i) q^{58} +(-1.82843 - 3.16693i) q^{59} -10.8284 q^{60} +(4.65685 + 8.06591i) q^{61} +(-8.24264 + 14.2767i) q^{62} +(-1.41421 + 2.44949i) q^{63} -9.82843 q^{64} +4.82843 q^{66} +(0.585786 - 1.01461i) q^{67} +(7.00000 - 12.1244i) q^{68} +(2.00000 + 3.46410i) q^{69} -19.3137 q^{70} +(1.00000 + 1.73205i) q^{71} +(-2.20711 - 3.82282i) q^{72} -11.6569 q^{73} +(4.41421 + 7.64564i) q^{74} +(-1.50000 + 2.59808i) q^{75} +(5.41421 - 9.37769i) q^{76} +5.65685 q^{77} +11.3137 q^{79} +(4.24264 - 7.34847i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(13.0711 + 22.6398i) q^{82} +7.65685 q^{83} +(-5.41421 - 9.37769i) q^{84} +(-5.17157 - 8.95743i) q^{85} +23.3137 q^{86} +(-1.00000 - 1.73205i) q^{87} +(-4.41421 + 7.64564i) q^{88} +(4.58579 - 7.94282i) q^{89} -6.82843 q^{90} -15.3137 q^{92} +(-3.41421 + 5.91359i) q^{93} +(-0.414214 + 0.717439i) q^{94} +(-4.00000 - 6.92820i) q^{95} -1.58579 q^{96} +(-3.82843 - 6.63103i) q^{97} +(-1.20711 - 2.09077i) q^{98} +2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{6} + 12 q^{8} - 2 q^{9} + 8 q^{10} - 4 q^{11} + 4 q^{12} + 16 q^{14} - 6 q^{16} - 4 q^{17} + 4 q^{18} + 16 q^{20} - 4 q^{22} + 8 q^{23} - 6 q^{24} + 12 q^{25} + 4 q^{27}+ \cdots + 8 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^6 + 12 * q^8 - 2 * q^9 + 8 * q^10 - 4 * q^11 + 4 * q^12 + 16 * q^14 - 6 * q^16 - 4 * q^17 + 4 * q^18 + 16 * q^20 - 4 * q^22 + 8 * q^23 - 6 * q^24 + 12 * q^25 + 4 * q^27 - 16 * q^28 - 4 * q^29 + 8 * q^30 + 16 * q^31 + 6 * q^32 - 4 * q^33 - 24 * q^34 + 16 * q^35 - 2 * q^36 - 4 * q^37 - 16 * q^38 - 16 * q^40 + 16 * q^41 - 8 * q^42 - 8 * q^43 + 8 * q^44 + 8 * q^46 + 24 * q^47 - 6 * q^48 - 2 * q^49 - 6 * q^50 + 8 * q^51 - 8 * q^53 - 2 * q^54 - 8 * q^56 - 4 * q^58 + 4 * q^59 - 32 * q^60 - 4 * q^61 - 16 * q^62 - 28 * q^64 + 8 * q^66 + 8 * q^67 + 28 * q^68 + 8 * q^69 - 32 * q^70 + 4 * q^71 - 6 * q^72 - 24 * q^73 + 12 * q^74 - 6 * q^75 + 16 * q^76 - 2 * q^81 + 24 * q^82 + 8 * q^83 - 16 * q^84 - 32 * q^85 + 48 * q^86 - 4 * q^87 - 12 * q^88 + 24 * q^89 - 16 * q^90 - 16 * q^92 - 8 * q^93 + 4 * q^94 - 16 * q^95 - 12 * q^96 - 4 * q^97 - 2 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−1.20711	+	2.09077i	−0.853553	+	1.47840i	0.0244272	+	0.999702i	$0.492224\pi$
$2$	−1.20711	+	2.09077i	−0.853553	+	1.47840i	−0.877981	+	0.478696i	$0.841110\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−1.91421	−	3.31552i	−0.957107	−	1.65776i
$5$	−2.82843			−1.26491			−0.632456	−	0.774597i	$-0.717953\pi$
$5$	−2.82843			−1.26491			−0.632456	+	0.774597i	$0.717953\pi$
$6$	−1.20711	−	2.09077i	−0.492799	−	0.853553i
$7$	−1.41421	−	2.44949i	−0.534522	−	0.925820i	−0.999186	−	0.0403329i	$-0.987158\pi$
$7$	−1.41421	−	2.44949i	−0.534522	−	0.925820i	0.464664	−	0.885487i	$-0.346175\pi$
$8$	4.41421			1.56066
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	3.41421	−	5.91359i	1.07967	−	1.87004i
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$	3.82843			1.10517
$13$		0			0
$13$		0			0
$14$	6.82843			1.82497
$15$	1.41421	−	2.44949i	0.365148	−	0.632456i
$16$	−1.50000	+	2.59808i	−0.375000	+	0.649519i
$17$	1.82843	+	3.16693i	0.443459	+	0.768093i	0.997943	−	0.0641009i	$-0.0204179\pi$
$17$	1.82843	+	3.16693i	0.443459	+	0.768093i	−0.554485	+	0.832194i	$0.687085\pi$
$18$	2.41421			0.569036
$19$	1.41421	+	2.44949i	0.324443	+	0.561951i	0.981399	−	0.191977i	$-0.0614899\pi$
$19$	1.41421	+	2.44949i	0.324443	+	0.561951i	−0.656957	+	0.753928i	$0.728157\pi$
$20$	5.41421	+	9.37769i	1.21065	+	2.09692i
$21$	2.82843			0.617213
$22$	−2.41421	−	4.18154i	−0.514712	−	0.891507i
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	−0.578610	−	0.815604i	$-0.696405\pi$
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	0.995639	+	0.0932891i	$0.0297381\pi$
$24$	−2.20711	+	3.82282i	−0.450524	+	0.780330i
$25$	3.00000			0.600000
$26$		0			0
$27$	1.00000			0.192450
$28$	−5.41421	+	9.37769i	−1.02319	+	1.77222i
$29$	−1.00000	+	1.73205i	−0.185695	+	0.321634i	−0.943811	−	0.330487i	$-0.892787\pi$
$29$	−1.00000	+	1.73205i	−0.185695	+	0.321634i	0.758115	+	0.652121i	$0.226120\pi$
$30$	3.41421	+	5.91359i	0.623347	+	1.07967i
$31$	6.82843			1.22642			0.613211	−	0.789919i	$-0.289878\pi$
$31$	6.82843			1.22642			0.613211	+	0.789919i	$0.289878\pi$
$32$	0.792893	+	1.37333i	0.140165	+	0.242773i
$33$	−1.00000	−	1.73205i	−0.174078	−	0.301511i
$34$	−8.82843			−1.51406
$35$	4.00000	+	6.92820i	0.676123	+	1.17108i
$36$	−1.91421	+	3.31552i	−0.319036	+	0.552586i
$37$	1.82843	−	3.16693i	0.300592	−	0.520640i	−0.675679	−	0.737196i	$-0.736149\pi$
$37$	1.82843	−	3.16693i	0.300592	−	0.520640i	0.976270	+	0.216557i	$0.0694826\pi$
$38$	−6.82843			−1.10772
$39$		0			0
$40$	−12.4853			−1.97410
$41$	5.41421	−	9.37769i	0.845558	−	1.46455i	−0.0395775	−	0.999217i	$-0.512601\pi$
$41$	5.41421	−	9.37769i	0.845558	−	1.46455i	0.885136	−	0.465333i	$-0.154065\pi$
$42$	−3.41421	+	5.91359i	−0.526825	+	0.912487i
$43$	−4.82843	−	8.36308i	−0.736328	−	1.27536i	−0.954138	−	0.299367i	$-0.903225\pi$
$43$	−4.82843	−	8.36308i	−0.736328	−	1.27536i	0.217810	−	0.975991i	$-0.430109\pi$
$44$	7.65685			1.15431
$45$	1.41421	+	2.44949i	0.210819	+	0.365148i
$46$	4.82843	+	8.36308i	0.711913	+	1.23307i
$47$	0.343146			0.0500530			0.0250265	−	0.999687i	$-0.492033\pi$
$47$	0.343146			0.0500530			0.0250265	+	0.999687i	$0.492033\pi$
$48$	−1.50000	−	2.59808i	−0.216506	−	0.375000i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−3.62132	+	6.27231i	−0.512132	+	0.887039i
$51$	−3.65685			−0.512062
$52$		0			0
$53$	−2.00000			−0.274721			−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000			−0.274721			−0.137361	+	0.990521i	$0.543862\pi$
$54$	−1.20711	+	2.09077i	−0.164266	+	0.284518i
$55$	2.82843	−	4.89898i	0.381385	−	0.660578i
$56$	−6.24264	−	10.8126i	−0.834208	−	1.44489i
$57$	−2.82843			−0.374634
$58$	−2.41421	−	4.18154i	−0.317002	−	0.549063i
$59$	−1.82843	−	3.16693i	−0.238041	−	0.412299i	0.722111	−	0.691777i	$-0.243172\pi$
$59$	−1.82843	−	3.16693i	−0.238041	−	0.412299i	−0.960152	+	0.279478i	$0.909839\pi$
$60$	−10.8284			−1.39794
$61$	4.65685	+	8.06591i	0.596249	+	1.03273i	0.993369	+	0.114967i	$0.0366763\pi$
$61$	4.65685	+	8.06591i	0.596249	+	1.03273i	−0.397120	+	0.917767i	$0.629990\pi$
$62$	−8.24264	+	14.2767i	−1.04682	+	1.81314i
$63$	−1.41421	+	2.44949i	−0.178174	+	0.308607i
$64$	−9.82843			−1.22855
$65$		0			0
$66$	4.82843			0.594338
$67$	0.585786	−	1.01461i	0.0715652	−	0.123955i	−0.828022	−	0.560695i	$-0.810534\pi$
$67$	0.585786	−	1.01461i	0.0715652	−	0.123955i	0.899587	+	0.436741i	$0.143867\pi$
$68$	7.00000	−	12.1244i	0.848875	−	1.47029i
$69$	2.00000	+	3.46410i	0.240772	+	0.417029i
$70$	−19.3137			−2.30843
$71$	1.00000	+	1.73205i	0.118678	+	0.205557i	0.919244	−	0.393688i	$-0.128801\pi$
$71$	1.00000	+	1.73205i	0.118678	+	0.205557i	−0.800566	+	0.599245i	$0.795468\pi$
$72$	−2.20711	−	3.82282i	−0.260110	−	0.450524i
$73$	−11.6569			−1.36433			−0.682166	−	0.731198i	$-0.738962\pi$
$73$	−11.6569			−1.36433			−0.682166	+	0.731198i	$0.738962\pi$
$74$	4.41421	+	7.64564i	0.513142	+	0.888788i
$75$	−1.50000	+	2.59808i	−0.173205	+	0.300000i
$76$	5.41421	−	9.37769i	0.621053	−	1.07570i
$77$	5.65685			0.644658
$78$		0			0
$79$	11.3137			1.27289			0.636446	−	0.771321i	$-0.280404\pi$
$79$	11.3137			1.27289			0.636446	+	0.771321i	$0.280404\pi$
$80$	4.24264	−	7.34847i	0.474342	−	0.821584i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	13.0711	+	22.6398i	1.44346	+	2.50014i
$83$	7.65685			0.840449			0.420224	−	0.907420i	$-0.361951\pi$
$83$	7.65685			0.840449			0.420224	+	0.907420i	$0.361951\pi$
$84$	−5.41421	−	9.37769i	−0.590739	−	1.02319i
$85$	−5.17157	−	8.95743i	−0.560936	−	0.971569i
$86$	23.3137			2.51398
$87$	−1.00000	−	1.73205i	−0.107211	−	0.185695i
$88$	−4.41421	+	7.64564i	−0.470557	+	0.815028i
$89$	4.58579	−	7.94282i	0.486092	−	0.841937i	−0.513780	−	0.857922i	$-0.671755\pi$
$89$	4.58579	−	7.94282i	0.486092	−	0.841937i	0.999872	+	0.0159854i	$0.00508851\pi$
$90$	−6.82843			−0.719779
$91$		0			0
$92$	−15.3137			−1.59656
$93$	−3.41421	+	5.91359i	−0.354037	+	0.613211i
$94$	−0.414214	+	0.717439i	−0.0427229	+	0.0739982i
$95$	−4.00000	−	6.92820i	−0.410391	−	0.710819i
$96$	−1.58579			−0.161849
$97$	−3.82843	−	6.63103i	−0.388718	−	0.673279i	0.603559	−	0.797318i	$-0.293749\pi$
$97$	−3.82843	−	6.63103i	−0.388718	−	0.673279i	−0.992277	+	0.124039i	$0.960415\pi$
$98$	−1.20711	−	2.09077i	−0.121936	−	0.211200i
$99$	2.00000			0.201008
$100$	−5.74264	−	9.94655i	−0.574264	−	0.994655i
$101$	1.82843	−	3.16693i	0.181935	−	0.315121i	−0.760604	−	0.649216i	$-0.775097\pi$
$101$	1.82843	−	3.16693i	0.181935	−	0.315121i	0.942540	+	0.334095i	$0.108431\pi$
$102$	4.41421	−	7.64564i	0.437072	−	0.757031i
$103$	13.6569			1.34565			0.672825	−	0.739802i	$-0.265081\pi$
$103$	13.6569			1.34565			0.672825	+	0.739802i	$0.265081\pi$
$104$		0			0
$105$	−8.00000			−0.780720
$106$	2.41421	−	4.18154i	0.234489	−	0.406147i
$107$	−5.65685	+	9.79796i	−0.546869	+	0.947204i	0.451618	+	0.892211i	$0.350847\pi$
$107$	−5.65685	+	9.79796i	−0.546869	+	0.947204i	−0.998487	+	0.0549930i	$0.982486\pi$
$108$	−1.91421	−	3.31552i	−0.184195	−	0.319036i
$109$	17.3137			1.65835			0.829176	−	0.558987i	$-0.188810\pi$
$109$	17.3137			1.65835			0.829176	+	0.558987i	$0.188810\pi$
$110$	6.82843	+	11.8272i	0.651065	+	1.12768i
$111$	1.82843	+	3.16693i	0.173547	+	0.300592i
$112$	8.48528			0.801784
$113$	−8.65685	−	14.9941i	−0.814368	−	1.41053i	−0.909781	−	0.415090i	$-0.863750\pi$
$113$	−8.65685	−	14.9941i	−0.814368	−	1.41053i	0.0954122	−	0.995438i	$-0.469583\pi$
$114$	3.41421	−	5.91359i	0.319770	−	0.553859i
$115$	−5.65685	+	9.79796i	−0.527504	+	0.913664i
$116$	7.65685			0.710921
$117$		0			0
$118$	8.82843			0.812723
$119$	5.17157	−	8.95743i	0.474077	−	0.821126i
$120$	6.24264	−	10.8126i	0.569873	−	0.987048i
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−22.4853			−2.03572
$123$	5.41421	+	9.37769i	0.488183	+	0.845558i
$124$	−13.0711	−	22.6398i	−1.17382	−	2.03311i
$125$	5.65685			0.505964
$126$	−3.41421	−	5.91359i	−0.304162	−	0.526825i
$127$	2.82843	−	4.89898i	0.250982	−	0.434714i	−0.712814	−	0.701353i	$-0.752580\pi$
$127$	2.82843	−	4.89898i	0.250982	−	0.434714i	0.963797	+	0.266639i	$0.0859131\pi$
$128$	10.2782	−	17.8023i	0.908471	−	1.57352i
$129$	9.65685			0.850239
$130$		0			0
$131$	−8.00000			−0.698963			−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000			−0.698963			−0.349482	+	0.936943i	$0.613642\pi$
$132$	−3.82843	+	6.63103i	−0.333222	+	0.577157i
$133$	4.00000	−	6.92820i	0.346844	−	0.600751i
$134$	1.41421	+	2.44949i	0.122169	+	0.211604i
$135$	−2.82843			−0.243432
$136$	8.07107	+	13.9795i	0.692088	+	1.19873i
$137$	−2.58579	−	4.47871i	−0.220919	−	0.382642i	0.734169	−	0.678967i	$-0.237572\pi$
$137$	−2.58579	−	4.47871i	−0.220919	−	0.382642i	−0.955087	+	0.296325i	$0.904239\pi$
$138$	−9.65685			−0.822046
$139$	−7.65685	−	13.2621i	−0.649446	−	1.12487i	−0.983255	−	0.182233i	$-0.941668\pi$
$139$	−7.65685	−	13.2621i	−0.649446	−	1.12487i	0.333810	−	0.942641i	$-0.391666\pi$
$140$	15.3137	−	26.5241i	1.29424	−	2.24170i
$141$	−0.171573	+	0.297173i	−0.0144490	+	0.0250265i
$142$	−4.82843			−0.405193
$143$		0			0
$144$	3.00000			0.250000
$145$	2.82843	−	4.89898i	0.234888	−	0.406838i
$146$	14.0711	−	24.3718i	1.16453	−	2.01702i
$147$	−0.500000	−	0.866025i	−0.0412393	−	0.0714286i
$148$	−14.0000			−1.15079
$149$	−7.41421	−	12.8418i	−0.607396	−	1.05204i	−0.991668	−	0.128821i	$-0.958881\pi$
$149$	−7.41421	−	12.8418i	−0.607396	−	1.05204i	0.384272	−	0.923220i	$-0.374453\pi$
$150$	−3.62132	−	6.27231i	−0.295680	−	0.512132i
$151$	20.4853			1.66707			0.833534	−	0.552468i	$-0.186314\pi$
$151$	20.4853			1.66707			0.833534	+	0.552468i	$0.186314\pi$
$152$	6.24264	+	10.8126i	0.506345	+	0.877015i
$153$	1.82843	−	3.16693i	0.147820	−	0.256031i
$154$	−6.82843	+	11.8272i	−0.550250	+	0.953062i
$155$	−19.3137			−1.55131
$156$		0			0
$157$	−10.0000			−0.798087			−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000			−0.798087			−0.399043	+	0.916932i	$0.630658\pi$
$158$	−13.6569	+	23.6544i	−1.08648	+	1.88184i
$159$	1.00000	−	1.73205i	0.0793052	−	0.137361i
$160$	−2.24264	−	3.88437i	−0.177296	−	0.307086i
$161$	−11.3137			−0.891645
$162$	−1.20711	−	2.09077i	−0.0948393	−	0.164266i
$163$	6.58579	+	11.4069i	0.515839	+	0.893459i	0.999831	+	0.0183864i	$0.00585292\pi$
$163$	6.58579	+	11.4069i	0.515839	+	0.893459i	−0.483992	+	0.875072i	$0.660814\pi$
$164$	−41.4558			−3.23716
$165$	2.82843	+	4.89898i	0.220193	+	0.381385i
$166$	−9.24264	+	16.0087i	−0.717368	+	1.24252i
$167$	3.82843	−	6.63103i	0.296253	−	0.513125i	−0.679023	−	0.734117i	$-0.737596\pi$
$167$	3.82843	−	6.63103i	0.296253	−	0.513125i	0.975275	+	0.220993i	$0.0709296\pi$
$168$	12.4853			0.963260
$169$		0			0
$170$	24.9706			1.91515
$171$	1.41421	−	2.44949i	0.108148	−	0.187317i
$172$	−18.4853	+	32.0174i	−1.40949	+	2.44131i
$173$	0.171573	+	0.297173i	0.0130444	+	0.0225936i	0.872474	−	0.488661i	$-0.162514\pi$
$173$	0.171573	+	0.297173i	0.0130444	+	0.0225936i	−0.859429	+	0.511254i	$0.829181\pi$
$174$	4.82843			0.366042
$175$	−4.24264	−	7.34847i	−0.320713	−	0.555492i
$176$	−3.00000	−	5.19615i	−0.226134	−	0.391675i
$177$	3.65685			0.274866
$178$	11.0711	+	19.1757i	0.829812	+	1.43728i
$179$	0.343146	−	0.594346i	0.0256479	−	0.0444235i	−0.852917	−	0.522047i	$-0.825168\pi$
$179$	0.343146	−	0.594346i	0.0256479	−	0.0444235i	0.878564	+	0.477624i	$0.158502\pi$
$180$	5.41421	−	9.37769i	0.403552	−	0.698972i
$181$	14.0000			1.04061			0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000			1.04061			0.520306	+	0.853980i	$0.325818\pi$
$182$		0			0
$183$	−9.31371			−0.688489
$184$	8.82843	−	15.2913i	0.650840	−	1.12729i
$185$	−5.17157	+	8.95743i	−0.380222	+	0.658563i
$186$	−8.24264	−	14.2767i	−0.604380	−	1.04682i
$187$	−7.31371			−0.534831
$188$	−0.656854	−	1.13770i	−0.0479060	−	0.0829757i
$189$	−1.41421	−	2.44949i	−0.102869	−	0.178174i
$190$	19.3137			1.40116
$191$	9.65685	+	16.7262i	0.698745	+	1.21026i	0.968902	+	0.247446i	$0.0795913\pi$
$191$	9.65685	+	16.7262i	0.698745	+	1.21026i	−0.270156	+	0.962817i	$0.587075\pi$
$192$	4.91421	−	8.51167i	0.354653	−	0.614277i
$193$	−8.65685	+	14.9941i	−0.623134	+	1.07930i	0.365765	+	0.930707i	$0.380808\pi$
$193$	−8.65685	+	14.9941i	−0.623134	+	1.07930i	−0.988899	+	0.148592i	$0.952526\pi$
$194$	18.4853			1.32717
$195$		0			0
$196$	3.82843			0.273459
$197$	−8.24264	+	14.2767i	−0.587264	+	1.01717i	0.407325	+	0.913283i	$0.366462\pi$
$197$	−8.24264	+	14.2767i	−0.587264	+	1.01717i	−0.994589	+	0.103888i	$0.966872\pi$
$198$	−2.41421	+	4.18154i	−0.171571	+	0.297169i
$199$	−5.17157	−	8.95743i	−0.366603	−	0.634975i	0.622429	−	0.782676i	$-0.286146\pi$
$199$	−5.17157	−	8.95743i	−0.366603	−	0.634975i	−0.989032	+	0.147701i	$0.952813\pi$
$200$	13.2426			0.936396
$201$	0.585786	+	1.01461i	0.0413182	+	0.0715652i
$202$	4.41421	+	7.64564i	0.310583	+	0.537946i
$203$	5.65685			0.397033
$204$	7.00000	+	12.1244i	0.490098	+	0.848875i
$205$	−15.3137	+	26.5241i	−1.06956	+	1.85252i
$206$	−16.4853	+	28.5533i	−1.14858	+	1.98941i
$207$	−4.00000			−0.278019
$208$		0			0
$209$	−5.65685			−0.391293
$210$	9.65685	−	16.7262i	0.666386	−	1.15421i
$211$	6.00000	−	10.3923i	0.413057	−	0.715436i	−0.582165	−	0.813070i	$-0.697794\pi$
$211$	6.00000	−	10.3923i	0.413057	−	0.715436i	0.995222	+	0.0976347i	$0.0311277\pi$
$212$	3.82843	+	6.63103i	0.262937	+	0.455421i
$213$	−2.00000			−0.137038
$214$	−13.6569	−	23.6544i	−0.933563	−	1.61698i
$215$	13.6569	+	23.6544i	0.931390	+	1.61321i
$216$	4.41421			0.300349
$217$	−9.65685	−	16.7262i	−0.655550	−	1.13545i
$218$	−20.8995	+	36.1990i	−1.41549	+	2.45170i
$219$	5.82843	−	10.0951i	0.393849	−	0.682166i
$220$	−21.6569			−1.46010
$221$		0			0
$222$	−8.82843			−0.592525
$223$	2.24264	−	3.88437i	0.150178	−	0.260116i	−0.781115	−	0.624388i	$-0.785349\pi$
$223$	2.24264	−	3.88437i	0.150178	−	0.260116i	0.931293	+	0.364271i	$0.118682\pi$
$224$	2.24264	−	3.88437i	0.149843	−	0.259535i
$225$	−1.50000	−	2.59808i	−0.100000	−	0.173205i
$226$	41.7990			2.78043
$227$	2.65685	+	4.60181i	0.176342	+	0.305433i	0.940625	−	0.339448i	$-0.110240\pi$
$227$	2.65685	+	4.60181i	0.176342	+	0.305433i	−0.764283	+	0.644881i	$0.776907\pi$
$228$	5.41421	+	9.37769i	0.358565	+	0.621053i
$229$	−21.3137			−1.40845			−0.704225	−	0.709977i	$-0.748705\pi$
$229$	−21.3137			−1.40845			−0.704225	+	0.709977i	$0.748705\pi$
$230$	−13.6569	−	23.6544i	−0.900506	−	1.55972i
$231$	−2.82843	+	4.89898i	−0.186097	+	0.322329i
$232$	−4.41421	+	7.64564i	−0.289807	+	0.501961i
$233$	−26.9706			−1.76690			−0.883450	−	0.468525i	$-0.844786\pi$
$233$	−26.9706			−1.76690			−0.883450	+	0.468525i	$0.844786\pi$
$234$		0			0
$235$	−0.970563			−0.0633125
$236$	−7.00000	+	12.1244i	−0.455661	+	0.789228i
$237$	−5.65685	+	9.79796i	−0.367452	+	0.636446i
$238$	12.4853	+	21.6251i	0.809301	+	1.40175i
$239$	−2.00000			−0.129369			−0.0646846	−	0.997906i	$-0.520604\pi$
$239$	−2.00000			−0.129369			−0.0646846	+	0.997906i	$0.520604\pi$
$240$	4.24264	+	7.34847i	0.273861	+	0.474342i
$241$	5.82843	+	10.0951i	0.375442	+	0.650285i	0.990393	−	0.138281i	$-0.0441576\pi$
$241$	5.82843	+	10.0951i	0.375442	+	0.650285i	−0.614951	+	0.788565i	$0.710824\pi$
$242$	−16.8995			−1.08634
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	17.8284	−	30.8797i	1.14135	−	1.97687i
$245$	1.41421	−	2.44949i	0.0903508	−	0.156492i
$246$	−26.1421			−1.66676
$247$		0			0
$248$	30.1421			1.91403
$249$	−3.82843	+	6.63103i	−0.242617	+	0.420224i
$250$	−6.82843	+	11.8272i	−0.431868	+	0.748017i
$251$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$251$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$252$	10.8284			0.682127
$253$	4.00000	+	6.92820i	0.251478	+	0.435572i
$254$	6.82843	+	11.8272i	0.428454	+	0.742103i
$255$	10.3431			0.647713
$256$	14.9853	+	25.9553i	0.936580	+	1.62220i
$257$	7.82843	−	13.5592i	0.488324	−	0.845802i	−0.511586	−	0.859232i	$-0.670942\pi$
$257$	7.82843	−	13.5592i	0.488324	−	0.845802i	0.999910	+	0.0134304i	$0.00427515\pi$
$258$	−11.6569	+	20.1903i	−0.725724	+	1.25699i
$259$	−10.3431			−0.642692
$260$		0			0
$261$	2.00000			0.123797
$262$	9.65685	−	16.7262i	0.596602	−	1.03335i
$263$	−6.00000	+	10.3923i	−0.369976	+	0.640817i	−0.989561	−	0.144112i	$-0.953967\pi$
$263$	−6.00000	+	10.3923i	−0.369976	+	0.640817i	0.619586	+	0.784929i	$0.287301\pi$
$264$	−4.41421	−	7.64564i	−0.271676	−	0.470557i
$265$	5.65685			0.347498
$266$	9.65685	+	16.7262i	0.592100	+	1.02555i
$267$	4.58579	+	7.94282i	0.280646	+	0.486092i
$268$	−4.48528			−0.273982
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	−0.998361	−	0.0572259i	$-0.981774\pi$
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	0.449622	−	0.893219i	$-0.351559\pi$
$270$	3.41421	−	5.91359i	0.207782	−	0.359890i
$271$	5.89949	−	10.2182i	0.358369	−	0.620713i	−0.629320	−	0.777147i	$-0.716666\pi$
$271$	5.89949	−	10.2182i	0.358369	−	0.620713i	0.987688	+	0.156434i	$0.0499997\pi$
$272$	−10.9706			−0.665188
$273$		0			0
$274$	12.4853			0.754263
$275$	−3.00000	+	5.19615i	−0.180907	+	0.313340i
$276$	7.65685	−	13.2621i	0.460888	−	0.798282i
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	0.894503	−	0.447062i	$-0.147530\pi$
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	−0.834419	+	0.551131i	$0.814196\pi$
$278$	36.9706			2.21735
$279$	−3.41421	−	5.91359i	−0.204404	−	0.354037i
$280$	17.6569	+	30.5826i	1.05520	+	1.82766i
$281$	−26.8284			−1.60045			−0.800225	−	0.599700i	$-0.795287\pi$
$281$	−26.8284			−1.60045			−0.800225	+	0.599700i	$0.795287\pi$
$282$	−0.414214	−	0.717439i	−0.0246661	−	0.0427229i
$283$	2.48528	−	4.30463i	0.147735	−	0.255884i	−0.782655	−	0.622455i	$-0.786135\pi$
$283$	2.48528	−	4.30463i	0.147735	−	0.255884i	0.930390	+	0.366572i	$0.119469\pi$
$284$	3.82843	−	6.63103i	0.227175	−	0.393479i
$285$	8.00000			0.473879
$286$		0			0
$287$	−30.6274			−1.80788
$288$	0.792893	−	1.37333i	0.0467217	−	0.0809243i
$289$	1.81371	−	3.14144i	0.106689	−	0.184790i
$290$	6.82843	+	11.8272i	0.400979	+	0.694516i
$291$	7.65685			0.448853
$292$	22.3137	+	38.6485i	1.30581	+	2.26173i
$293$	−13.0711	−	22.6398i	−0.763620	−	1.32263i	−0.940973	−	0.338481i	$-0.890087\pi$
$293$	−13.0711	−	22.6398i	−0.763620	−	1.32263i	0.177353	−	0.984147i	$-0.443247\pi$
$294$	2.41421			0.140800
$295$	5.17157	+	8.95743i	0.301101	+	0.521522i
$296$	8.07107	−	13.9795i	0.469121	−	0.812542i
$297$	−1.00000	+	1.73205i	−0.0580259	+	0.100504i
$298$	35.7990			2.07378
$299$		0			0
$300$	11.4853			0.663103
$301$	−13.6569	+	23.6544i	−0.787168	+	1.36341i
$302$	−24.7279	+	42.8300i	−1.42293	+	2.46459i
$303$	1.82843	+	3.16693i	0.105040	+	0.181935i
$304$	−8.48528			−0.486664
$305$	−13.1716	−	22.8138i	−0.754202	−	1.30632i
$306$	4.41421	+	7.64564i	0.252344	+	0.437072i
$307$	17.1716			0.980033			0.490017	−	0.871713i	$-0.336991\pi$
$307$	17.1716			0.980033			0.490017	+	0.871713i	$0.336991\pi$
$308$	−10.8284	−	18.7554i	−0.617007	−	1.06869i
$309$	−6.82843	+	11.8272i	−0.388456	+	0.672825i
$310$	23.3137	−	40.3805i	1.32413	−	2.29346i
$311$	34.6274			1.96354			0.981770	−	0.190071i	$-0.0608718\pi$
$311$	34.6274			1.96354			0.981770	+	0.190071i	$0.0608718\pi$
$312$		0			0
$313$	6.00000			0.339140			0.169570	−	0.985518i	$-0.445762\pi$
$313$	6.00000			0.339140			0.169570	+	0.985518i	$0.445762\pi$
$314$	12.0711	−	20.9077i	0.681210	−	1.17989i
$315$	4.00000	−	6.92820i	0.225374	−	0.390360i
$316$	−21.6569	−	37.5108i	−1.21829	−	2.11015i
$317$	8.48528			0.476581			0.238290	−	0.971194i	$-0.423413\pi$
$317$	8.48528			0.476581			0.238290	+	0.971194i	$0.423413\pi$
$318$	2.41421	+	4.18154i	0.135382	+	0.234489i
$319$	−2.00000	−	3.46410i	−0.111979	−	0.193952i
$320$	27.7990			1.55401
$321$	−5.65685	−	9.79796i	−0.315735	−	0.546869i
$322$	13.6569	−	23.6544i	0.761067	−	1.31821i
$323$	−5.17157	+	8.95743i	−0.287754	+	0.498405i
$324$	3.82843			0.212690
$325$		0			0
$326$	−31.7990			−1.76118
$327$	−8.65685	+	14.9941i	−0.478725	+	0.829176i
$328$	23.8995	−	41.3951i	1.31963	−	2.28566i
$329$	−0.485281	−	0.840532i	−0.0267544	−	0.0463400i
$330$	−13.6569			−0.751785
$331$	−1.07107	−	1.85514i	−0.0588712	−	0.101968i	0.835088	−	0.550117i	$-0.185417\pi$
$331$	−1.07107	−	1.85514i	−0.0588712	−	0.101968i	−0.893959	+	0.448149i	$0.852083\pi$
$332$	−14.6569	−	25.3864i	−0.804399	−	1.39326i
$333$	−3.65685			−0.200394
$334$	9.24264	+	16.0087i	0.505735	+	0.875958i
$335$	−1.65685	+	2.86976i	−0.0905236	+	0.156792i
$336$	−4.24264	+	7.34847i	−0.231455	+	0.400892i
$337$	−13.3137			−0.725244			−0.362622	−	0.931936i	$-0.618118\pi$
$337$	−13.3137			−0.725244			−0.362622	+	0.931936i	$0.618118\pi$
$338$		0			0
$339$	17.3137			0.940352
$340$	−19.7990	+	34.2929i	−1.07375	+	1.85979i
$341$	−6.82843	+	11.8272i	−0.369780	+	0.640478i
$342$	3.41421	+	5.91359i	0.184620	+	0.319770i
$343$	−16.9706			−0.916324
$344$	−21.3137	−	36.9164i	−1.14916	−	1.99040i
$345$	−5.65685	−	9.79796i	−0.304555	−	0.527504i
$346$	−0.828427			−0.0445365
$347$	15.6569	+	27.1185i	0.840504	+	1.45580i	0.889469	+	0.456995i	$0.151074\pi$
$347$	15.6569	+	27.1185i	0.840504	+	1.45580i	−0.0489652	+	0.998800i	$0.515592\pi$
$348$	−3.82843	+	6.63103i	−0.205225	+	0.355461i
$349$	−3.82843	+	6.63103i	−0.204931	+	0.354951i	−0.950111	−	0.311913i	$-0.899030\pi$
$349$	−3.82843	+	6.63103i	−0.204931	+	0.354951i	0.745180	+	0.666864i	$0.232364\pi$
$350$	20.4853			1.09498
$351$		0			0
$352$	−3.17157			−0.169045
$353$	8.72792	−	15.1172i	0.464540	−	0.804608i	−0.534640	−	0.845080i	$-0.679553\pi$
$353$	8.72792	−	15.1172i	0.464540	−	0.804608i	0.999181	+	0.0404722i	$0.0128862\pi$
$354$	−4.41421	+	7.64564i	−0.234613	+	0.406361i
$355$	−2.82843	−	4.89898i	−0.150117	−	0.260011i
$356$	−35.1127			−1.86097
$357$	5.17157	+	8.95743i	0.273709	+	0.474077i
$358$	0.828427	+	1.43488i	0.0437837	+	0.0758357i
$359$	−1.02944			−0.0543316			−0.0271658	−	0.999631i	$-0.508648\pi$
$359$	−1.02944			−0.0543316			−0.0271658	+	0.999631i	$0.508648\pi$
$360$	6.24264	+	10.8126i	0.329016	+	0.569873i
$361$	5.50000	−	9.52628i	0.289474	−	0.501383i
$362$	−16.8995	+	29.2708i	−0.888218	+	1.53844i
$363$	−7.00000			−0.367405
$364$		0			0
$365$	32.9706			1.72576
$366$	11.2426	−	19.4728i	0.587662	−	1.01786i
$367$	12.0000	−	20.7846i	0.626395	−	1.08495i	−0.361874	−	0.932227i	$-0.617863\pi$
$367$	12.0000	−	20.7846i	0.626395	−	1.08495i	0.988269	−	0.152721i	$-0.0488036\pi$
$368$	6.00000	+	10.3923i	0.312772	+	0.541736i
$369$	−10.8284			−0.563705
$370$	−12.4853	−	21.6251i	−0.649079	−	1.12424i
$371$	2.82843	+	4.89898i	0.146845	+	0.254342i
$372$	26.1421			1.35541
$373$	−5.00000	−	8.66025i	−0.258890	−	0.448411i	0.707055	−	0.707159i	$-0.250023\pi$
$373$	−5.00000	−	8.66025i	−0.258890	−	0.448411i	−0.965945	+	0.258748i	$0.916690\pi$
$374$	8.82843	−	15.2913i	0.456507	−	0.790693i
$375$	−2.82843	+	4.89898i	−0.146059	+	0.252982i
$376$	1.51472			0.0781156
$377$		0			0
$378$	6.82843			0.351216
$379$	−8.24264	+	14.2767i	−0.423396	+	0.733343i	−0.996269	−	0.0863007i	$-0.972495\pi$
$379$	−8.24264	+	14.2767i	−0.423396	+	0.733343i	0.572873	+	0.819644i	$0.305829\pi$
$380$	−15.3137	+	26.5241i	−0.785577	+	1.36066i
$381$	2.82843	+	4.89898i	0.144905	+	0.250982i
$382$	−46.6274			−2.38567
$383$	−1.48528	−	2.57258i	−0.0758943	−	0.131453i	0.825581	−	0.564284i	$-0.190848\pi$
$383$	−1.48528	−	2.57258i	−0.0758943	−	0.131453i	−0.901475	+	0.432832i	$0.857515\pi$
$384$	10.2782	+	17.8023i	0.524506	+	0.908471i
$385$	−16.0000			−0.815436
$386$	−20.8995	−	36.1990i	−1.06376	−	1.84248i
$387$	−4.82843	+	8.36308i	−0.245443	+	0.425119i
$388$	−14.6569	+	25.3864i	−0.744089	+	1.28880i
$389$	6.97056			0.353422			0.176711	−	0.984263i	$-0.443454\pi$
$389$	6.97056			0.353422			0.176711	+	0.984263i	$0.443454\pi$
$390$		0			0
$391$	14.6274			0.739740
$392$	−2.20711	+	3.82282i	−0.111476	+	0.193082i
$393$	4.00000	−	6.92820i	0.201773	−	0.349482i
$394$	−19.8995	−	34.4669i	−1.00252	−	1.73642i
$395$	−32.0000			−1.61009
$396$	−3.82843	−	6.63103i	−0.192386	−	0.333222i
$397$	−1.48528	−	2.57258i	−0.0745441	−	0.129114i	0.826344	−	0.563166i	$-0.190417\pi$
$397$	−1.48528	−	2.57258i	−0.0745441	−	0.129114i	−0.900888	+	0.434052i	$0.857083\pi$
$398$	24.9706			1.25166
$399$	4.00000	+	6.92820i	0.200250	+	0.346844i
$400$	−4.50000	+	7.79423i	−0.225000	+	0.389711i
$401$	−1.07107	+	1.85514i	−0.0534866	+	0.0926415i	−0.891529	−	0.452964i	$-0.850367\pi$
$401$	−1.07107	+	1.85514i	−0.0534866	+	0.0926415i	0.838042	+	0.545605i	$0.183700\pi$
$402$	−2.82843			−0.141069
$403$		0			0
$404$	−14.0000			−0.696526
$405$	1.41421	−	2.44949i	0.0702728	−	0.121716i
$406$	−6.82843	+	11.8272i	−0.338889	+	0.586973i
$407$	3.65685	+	6.33386i	0.181264	+	0.313958i
$408$	−16.1421			−0.799155
$409$	−0.514719	−	0.891519i	−0.0254512	−	0.0440828i	0.853019	−	0.521879i	$-0.174769\pi$
$409$	−0.514719	−	0.891519i	−0.0254512	−	0.0440828i	−0.878470	+	0.477797i	$0.841436\pi$
$410$	−36.9706	−	64.0349i	−1.82585	−	3.16246i
$411$	5.17157			0.255095
$412$	−26.1421	−	45.2795i	−1.28793	−	2.23076i
$413$	−5.17157	+	8.95743i	−0.254476	+	0.440766i
$414$	4.82843	−	8.36308i	0.237304	−	0.411023i
$415$	−21.6569			−1.06309
$416$		0			0
$417$	15.3137			0.749916
$418$	6.82843	−	11.8272i	0.333989	−	0.578486i
$419$	15.3137	−	26.5241i	0.748124	−	1.29579i	−0.200597	−	0.979674i	$-0.564288\pi$
$419$	15.3137	−	26.5241i	0.748124	−	1.29579i	0.948721	−	0.316114i	$-0.102378\pi$
$420$	15.3137	+	26.5241i	0.747232	+	1.29424i
$421$	−14.6863			−0.715766			−0.357883	−	0.933766i	$-0.616501\pi$
$421$	−14.6863			−0.715766			−0.357883	+	0.933766i	$0.616501\pi$
$422$	14.4853	+	25.0892i	0.705132	+	1.22133i
$423$	−0.171573	−	0.297173i	−0.00834216	−	0.0144490i
$424$	−8.82843			−0.428746
$425$	5.48528	+	9.50079i	0.266075	+	0.460856i
$426$	2.41421	−	4.18154i	0.116969	−	0.202596i
$427$	13.1716	−	22.8138i	0.637417	−	1.10404i
$428$	43.3137			2.09365
$429$		0			0
$430$	−65.9411			−3.17996
$431$	9.82843	−	17.0233i	0.473419	−	0.819985i	−0.526118	−	0.850411i	$-0.676353\pi$
$431$	9.82843	−	17.0233i	0.473419	−	0.819985i	0.999537	+	0.0304262i	$0.00968644\pi$
$432$	−1.50000	+	2.59808i	−0.0721688	+	0.125000i
$433$	−0.656854	−	1.13770i	−0.0315664	−	0.0546746i	0.849811	−	0.527088i	$-0.176716\pi$
$433$	−0.656854	−	1.13770i	−0.0315664	−	0.0546746i	−0.881377	+	0.472414i	$0.843383\pi$
$434$	46.6274			2.23819
$435$	2.82843	+	4.89898i	0.135613	+	0.234888i
$436$	−33.1421	−	57.4039i	−1.58722	−	2.74915i
$437$	11.3137			0.541208
$438$	14.0711	+	24.3718i	0.672342	+	1.16453i
$439$	8.48528	−	14.6969i	0.404980	−	0.701447i	−0.589339	−	0.807886i	$-0.700612\pi$
$439$	8.48528	−	14.6969i	0.404980	−	0.701447i	0.994319	+	0.106439i	$0.0339450\pi$
$440$	12.4853	−	21.6251i	0.595212	−	1.03094i
$441$	1.00000			0.0476190
$442$		0			0
$443$	41.9411			1.99268			0.996342	−	0.0854611i	$-0.0272364\pi$
$443$	41.9411			1.99268			0.996342	+	0.0854611i	$0.0272364\pi$
$444$	7.00000	−	12.1244i	0.332205	−	0.575396i
$445$	−12.9706	+	22.4657i	−0.614864	+	1.06498i
$446$	5.41421	+	9.37769i	0.256370	+	0.444047i
$447$	14.8284			0.701361
$448$	13.8995	+	24.0746i	0.656689	+	1.13742i
$449$	3.89949	+	6.75412i	0.184029	+	0.318747i	0.943249	−	0.332087i	$-0.107753\pi$
$449$	3.89949	+	6.75412i	0.184029	+	0.318747i	−0.759220	+	0.650834i	$0.774419\pi$
$450$	7.24264			0.341421
$451$	10.8284	+	18.7554i	0.509891	+	0.883157i
$452$	−33.1421	+	57.4039i	−1.55887	+	2.70005i
$453$	−10.2426	+	17.7408i	−0.481241	+	0.833534i
$454$	−12.8284			−0.602068
$455$		0			0
$456$	−12.4853			−0.584677
$457$	1.82843	−	3.16693i	0.0855302	−	0.148143i	−0.820087	−	0.572239i	$-0.806075\pi$
$457$	1.82843	−	3.16693i	0.0855302	−	0.148143i	0.905617	+	0.424096i	$0.139408\pi$
$458$	25.7279	−	44.5621i	1.20219	−	2.08225i
$459$	1.82843	+	3.16693i	0.0853437	+	0.147820i
$460$	43.3137			2.01951
$461$	5.41421	+	9.37769i	0.252165	+	0.436763i	0.964122	−	0.265461i	$-0.0855241\pi$
$461$	5.41421	+	9.37769i	0.252165	+	0.436763i	−0.711957	+	0.702223i	$0.752191\pi$
$462$	−6.82843	−	11.8272i	−0.317687	−	0.550250i
$463$	7.51472			0.349239			0.174619	−	0.984636i	$-0.444131\pi$
$463$	7.51472			0.349239			0.174619	+	0.984636i	$0.444131\pi$
$464$	−3.00000	−	5.19615i	−0.139272	−	0.241225i
$465$	9.65685	−	16.7262i	0.447826	−	0.775657i
$466$	32.5563	−	56.3893i	1.50814	−	2.61218i
$467$	−8.00000			−0.370196			−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000			−0.370196			−0.185098	+	0.982720i	$0.559260\pi$
$468$		0			0
$469$	−3.31371			−0.153013
$470$	1.17157	−	2.02922i	0.0540406	−	0.0936011i
$471$	5.00000	−	8.66025i	0.230388	−	0.399043i
$472$	−8.07107	−	13.9795i	−0.371501	−	0.643459i
$473$	19.3137			0.888045
$474$	−13.6569	−	23.6544i	−0.627280	−	1.08648i
$475$	4.24264	+	7.34847i	0.194666	+	0.337171i
$476$	−39.5980			−1.81497
$477$	1.00000	+	1.73205i	0.0457869	+	0.0793052i
$478$	2.41421	−	4.18154i	0.110424	−	0.191259i
$479$	1.34315	−	2.32640i	0.0613699	−	0.106296i	−0.833708	−	0.552205i	$-0.813786\pi$
$479$	1.34315	−	2.32640i	0.0613699	−	0.106296i	0.895078	+	0.445910i	$0.147120\pi$
$480$	4.48528			0.204724
$481$		0			0
$482$	−28.1421			−1.28184
$483$	5.65685	−	9.79796i	0.257396	−	0.445823i
$484$	13.3995	−	23.2086i	0.609068	−	1.05494i
$485$	10.8284	+	18.7554i	0.491694	+	0.851638i
$486$	2.41421			0.109511
$487$	15.8995	+	27.5387i	0.720475	+	1.24790i	0.960810	+	0.277209i	$0.0894095\pi$
$487$	15.8995	+	27.5387i	0.720475	+	1.24790i	−0.240335	+	0.970690i	$0.577257\pi$
$488$	20.5563	+	35.6046i	0.930542	+	1.61175i
$489$	−13.1716			−0.595639
$490$	3.41421	+	5.91359i	0.154238	+	0.267149i
$491$	7.31371	−	12.6677i	0.330063	−	0.571686i	−0.652461	−	0.757822i	$-0.726263\pi$
$491$	7.31371	−	12.6677i	0.330063	−	0.571686i	0.982524	+	0.186136i	$0.0595967\pi$
$492$	20.7279	−	35.9018i	0.934487	−	1.61858i
$493$	−7.31371			−0.329393
$494$		0			0
$495$	−5.65685			−0.254257
$496$	−10.2426	+	17.7408i	−0.459908	+	0.796584i
$497$	2.82843	−	4.89898i	0.126872	−	0.219749i
$498$	−9.24264	−	16.0087i	−0.414173	−	0.717368i
$499$	2.14214			0.0958952			0.0479476	−	0.998850i	$-0.484732\pi$
$499$	2.14214			0.0958952			0.0479476	+	0.998850i	$0.484732\pi$
$500$	−10.8284	−	18.7554i	−0.484262	−	0.838766i
$501$	3.82843	+	6.63103i	0.171042	+	0.296253i
$502$		0			0
$503$	−7.65685	−	13.2621i	−0.341402	−	0.591326i	0.643291	−	0.765622i	$-0.277569\pi$
$503$	−7.65685	−	13.2621i	−0.341402	−	0.591326i	−0.984693	+	0.174296i	$0.944235\pi$
$504$	−6.24264	+	10.8126i	−0.278069	+	0.481630i
$505$	−5.17157	+	8.95743i	−0.230132	+	0.398600i
$506$	−19.3137			−0.858599
$507$		0			0
$508$	−21.6569			−0.960868
$509$	−13.8995	+	24.0746i	−0.616084	+	1.06709i	0.374109	+	0.927385i	$0.377949\pi$
$509$	−13.8995	+	24.0746i	−0.616084	+	1.06709i	−0.990193	+	0.139705i	$0.955385\pi$
$510$	−12.4853	+	21.6251i	−0.552858	+	0.957577i
$511$	16.4853	+	28.5533i	0.729266	+	1.26313i
$512$	−31.2426			−1.38074
$513$	1.41421	+	2.44949i	0.0624391	+	0.108148i
$514$	18.8995	+	32.7349i	0.833621	+	1.44387i
$515$	−38.6274			−1.70213
$516$	−18.4853	−	32.0174i	−0.813769	−	1.40949i
$517$	−0.343146	+	0.594346i	−0.0150915	+	0.0261393i
$518$	12.4853	−	21.6251i	0.548572	−	0.950154i
$519$	−0.343146			−0.0150624
$520$		0			0
$521$	2.68629			0.117689			0.0588443	−	0.998267i	$-0.481258\pi$
$521$	2.68629			0.117689			0.0588443	+	0.998267i	$0.481258\pi$
$522$	−2.41421	+	4.18154i	−0.105667	+	0.183021i
$523$	−3.65685	+	6.33386i	−0.159903	+	0.276960i	−0.934834	−	0.355086i	$-0.884452\pi$
$523$	−3.65685	+	6.33386i	−0.159903	+	0.276960i	0.774930	+	0.632046i	$0.217785\pi$
$524$	15.3137	+	26.5241i	0.668982	+	1.15871i
$525$	8.48528			0.370328
$526$	−14.4853	−	25.0892i	−0.631588	−	1.09394i
$527$	12.4853	+	21.6251i	0.543867	+	0.942006i
$528$	6.00000			0.261116
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	−6.82843	+	11.8272i	−0.296608	+	0.513740i
$531$	−1.82843	+	3.16693i	−0.0793470	+	0.137433i
$532$	−30.6274			−1.32787
$533$		0			0
$534$	−22.1421			−0.958184
$535$	16.0000	−	27.7128i	0.691740	−	1.19813i
$536$	2.58579	−	4.47871i	0.111689	−	0.193451i
$537$	0.343146	+	0.594346i	0.0148078	+	0.0256479i
$538$	43.4558			1.87351
$539$	−1.00000	−	1.73205i	−0.0430730	−	0.0746047i
$540$	5.41421	+	9.37769i	0.232991	+	0.403552i
$541$	−10.0000			−0.429934			−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000			−0.429934			−0.214967	+	0.976621i	$0.568964\pi$
$542$	14.2426	+	24.6690i	0.611774	+	1.05962i
$543$	−7.00000	+	12.1244i	−0.300399	+	0.520306i
$544$	−2.89949	+	5.02207i	−0.124315	+	0.215320i
$545$	−48.9706			−2.09767
$546$		0			0
$547$	0.686292			0.0293437			0.0146719	−	0.999892i	$-0.495330\pi$
$547$	0.686292			0.0293437			0.0146719	+	0.999892i	$0.495330\pi$
$548$	−9.89949	+	17.1464i	−0.422885	+	0.732459i
$549$	4.65685	−	8.06591i	0.198750	−	0.344245i
$550$	−7.24264	−	12.5446i	−0.308827	−	0.534904i
$551$	−5.65685			−0.240990
$552$	8.82843	+	15.2913i	0.375763	+	0.650840i
$553$	−16.0000	−	27.7128i	−0.680389	−	1.17847i
$554$	−4.82843			−0.205140
$555$	−5.17157	−	8.95743i	−0.219521	−	0.380222i
$556$	−29.3137	+	50.7728i	−1.24318	+	2.15325i
$557$	15.8995	−	27.5387i	0.673683	−	1.16685i	−0.303169	−	0.952937i	$-0.598045\pi$
$557$	15.8995	−	27.5387i	0.673683	−	1.16685i	0.976852	−	0.213917i	$-0.0686221\pi$
$558$	16.4853			0.697878
$559$		0			0
$560$	−24.0000			−1.01419
$561$	3.65685	−	6.33386i	0.154393	−	0.267416i
$562$	32.3848	−	56.0921i	1.36607	−	2.36610i
$563$	−2.00000	−	3.46410i	−0.0842900	−	0.145994i	0.820798	−	0.571218i	$-0.193529\pi$
$563$	−2.00000	−	3.46410i	−0.0842900	−	0.145994i	−0.905088	+	0.425223i	$0.860196\pi$
$564$	1.31371			0.0553171
$565$	24.4853	+	42.4098i	1.03010	+	1.78419i
$566$	6.00000	+	10.3923i	0.252199	+	0.436821i
$567$	2.82843			0.118783
$568$	4.41421	+	7.64564i	0.185216	+	0.320804i
$569$	4.51472	−	7.81972i	0.189267	−	0.327820i	−0.755739	−	0.654873i	$-0.772722\pi$
$569$	4.51472	−	7.81972i	0.189267	−	0.327820i	0.945006	+	0.327053i	$0.106056\pi$
$570$	−9.65685	+	16.7262i	−0.404481	+	0.700582i
$571$	20.9706			0.877591			0.438795	−	0.898587i	$-0.355405\pi$
$571$	20.9706			0.877591			0.438795	+	0.898587i	$0.355405\pi$
$572$		0			0
$573$	−19.3137			−0.806842
$574$	36.9706	−	64.0349i	1.54312	−	2.67276i
$575$	6.00000	−	10.3923i	0.250217	−	0.433389i
$576$	4.91421	+	8.51167i	0.204759	+	0.354653i
$577$	−35.9411			−1.49625			−0.748124	−	0.663559i	$-0.769045\pi$
$577$	−35.9411			−1.49625			−0.748124	+	0.663559i	$0.769045\pi$
$578$	4.37868	+	7.58410i	0.182129	+	0.315457i
$579$	−8.65685	−	14.9941i	−0.359767	−	0.623134i
$580$	−21.6569			−0.899252
$581$	−10.8284	−	18.7554i	−0.449239	−	0.778105i
$582$	−9.24264	+	16.0087i	−0.383120	+	0.663583i
$583$	2.00000	−	3.46410i	0.0828315	−	0.143468i
$584$	−51.4558			−2.12926
$585$		0			0
$586$	63.1127			2.60716
$587$	11.4853	−	19.8931i	0.474048	−	0.821076i	−0.525510	−	0.850787i	$-0.676126\pi$
$587$	11.4853	−	19.8931i	0.474048	−	0.821076i	0.999559	+	0.0297116i	$0.00945887\pi$
$588$	−1.91421	+	3.31552i	−0.0789408	+	0.136730i
$589$	9.65685	+	16.7262i	0.397904	+	0.689190i
$590$	−24.9706			−1.02802
$591$	−8.24264	−	14.2767i	−0.339057	−	0.587264i
$592$	5.48528	+	9.50079i	0.225444	+	0.390480i
$593$	3.51472			0.144332			0.0721661	−	0.997393i	$-0.477009\pi$
$593$	3.51472			0.144332			0.0721661	+	0.997393i	$0.477009\pi$
$594$	−2.41421	−	4.18154i	−0.0990564	−	0.171571i
$595$	−14.6274	+	25.3354i	−0.599666	+	1.03865i
$596$	−28.3848	+	49.1639i	−1.16269	+	2.01383i
$597$	10.3431			0.423317
$598$		0			0
$599$	−0.686292			−0.0280411			−0.0140206	−	0.999902i	$-0.504463\pi$
$599$	−0.686292			−0.0280411			−0.0140206	+	0.999902i	$0.504463\pi$
$600$	−6.62132	+	11.4685i	−0.270314	+	0.468198i
$601$	−22.3137	+	38.6485i	−0.910195	+	1.57650i	−0.0964075	+	0.995342i	$0.530735\pi$
$601$	−22.3137	+	38.6485i	−0.910195	+	1.57650i	−0.813788	+	0.581162i	$0.802598\pi$
$602$	−32.9706	−	57.1067i	−1.34378	−	2.32749i
$603$	−1.17157			−0.0477101
$604$	−39.2132	−	67.9193i	−1.59556	−	2.76360i
$605$	−9.89949	−	17.1464i	−0.402472	−	0.697101i
$606$	−8.82843			−0.358630
$607$	12.9706	+	22.4657i	0.526459	+	0.911854i	0.999525	+	0.0308265i	$0.00981393\pi$
$607$	12.9706	+	22.4657i	0.526459	+	0.911854i	−0.473066	+	0.881027i	$0.656853\pi$
$608$	−2.24264	+	3.88437i	−0.0909511	+	0.157532i
$609$	−2.82843	+	4.89898i	−0.114614	+	0.198517i
$610$	63.5980			2.57501
$611$		0			0
$612$	−14.0000			−0.565916
$613$	−18.1716	+	31.4741i	−0.733943	+	1.27123i	0.221243	+	0.975219i	$0.428989\pi$
$613$	−18.1716	+	31.4741i	−0.733943	+	1.27123i	−0.955186	+	0.296008i	$0.904345\pi$
$614$	−20.7279	+	35.9018i	−0.836511	+	1.44888i
$615$	−15.3137	−	26.5241i	−0.617508	−	1.06956i
$616$	24.9706			1.00609
$617$	−14.5858	−	25.2633i	−0.587202	−	1.01706i	−0.994597	−	0.103811i	$-0.966896\pi$
$617$	−14.5858	−	25.2633i	−0.587202	−	1.01706i	0.407395	−	0.913252i	$-0.366437\pi$
$618$	−16.4853	−	28.5533i	−0.663135	−	1.14858i
$619$	15.7990			0.635015			0.317508	−	0.948256i	$-0.397154\pi$
$619$	15.7990			0.635015			0.317508	+	0.948256i	$0.397154\pi$
$620$	36.9706	+	64.0349i	1.48477	+	2.57170i
$621$	2.00000	−	3.46410i	0.0802572	−	0.139010i
$622$	−41.7990	+	72.3980i	−1.67599	+	2.90289i
$623$	−25.9411			−1.03931
$624$		0			0
$625$	−31.0000			−1.24000
$626$	−7.24264	+	12.5446i	−0.289474	+	0.501384i
$627$	2.82843	−	4.89898i	0.112956	−	0.195646i
$628$	19.1421	+	33.1552i	0.763854	+	1.32303i
$629$	13.3726			0.533200
$630$	9.65685	+	16.7262i	0.384738	+	0.666386i
$631$	−9.55635	−	16.5521i	−0.380432	−	0.658928i	0.610692	−	0.791868i	$-0.290891\pi$
$631$	−9.55635	−	16.5521i	−0.380432	−	0.658928i	−0.991124	+	0.132940i	$0.957558\pi$
$632$	49.9411			1.98655
$633$	6.00000	+	10.3923i	0.238479	+	0.413057i
$634$	−10.2426	+	17.7408i	−0.406787	+	0.704576i
$635$	−8.00000	+	13.8564i	−0.317470	+	0.549875i
$636$	−7.65685			−0.303614
$637$		0			0
$638$	9.65685			0.382319
$639$	1.00000	−	1.73205i	0.0395594	−	0.0685189i
$640$	−29.0711	+	50.3526i	−1.14913	+	1.99036i
$641$	13.1421	+	22.7628i	0.519083	+	0.899078i	0.999754	+	0.0221773i	$0.00705984\pi$
$641$	13.1421	+	22.7628i	0.519083	+	0.899078i	−0.480671	+	0.876901i	$0.659607\pi$
$642$	27.3137			1.07799
$643$	8.58579	+	14.8710i	0.338590	+	0.586456i	0.984168	−	0.177239i	$-0.0567166\pi$
$643$	8.58579	+	14.8710i	0.338590	+	0.586456i	−0.645577	+	0.763695i	$0.723383\pi$
$644$	21.6569	+	37.5108i	0.853400	+	1.47813i
$645$	−27.3137			−1.07548
$646$	−12.4853	−	21.6251i	−0.491227	−	0.850830i
$647$	5.65685	−	9.79796i	0.222394	−	0.385198i	−0.733140	−	0.680077i	$-0.761946\pi$
$647$	5.65685	−	9.79796i	0.222394	−	0.385198i	0.955534	+	0.294880i	$0.0952796\pi$
$648$	−2.20711	+	3.82282i	−0.0867033	+	0.150175i
$649$	7.31371			0.287088
$650$		0			0
$651$	19.3137			0.756964
$652$	25.2132	−	43.6705i	0.987425	−	1.71027i
$653$	1.34315	−	2.32640i	0.0525614	−	0.0910389i	−0.838548	−	0.544828i	$-0.816595\pi$
$653$	1.34315	−	2.32640i	0.0525614	−	0.0910389i	0.891109	+	0.453789i	$0.149928\pi$
$654$	−20.8995	−	36.1990i	−0.817235	−	1.41549i
$655$	22.6274			0.884126
$656$	16.2426	+	28.1331i	0.634169	+	1.09841i
$657$	5.82843	+	10.0951i	0.227389	+	0.393849i
$658$	2.34315			0.0913453
$659$	12.3431	+	21.3790i	0.480821	+	0.832806i	0.999758	−	0.0220065i	$-0.00700546\pi$
$659$	12.3431	+	21.3790i	0.480821	+	0.832806i	−0.518937	+	0.854812i	$0.673672\pi$
$660$	10.8284	−	18.7554i	0.421496	−	0.730052i
$661$	−0.514719	+	0.891519i	−0.0200202	+	0.0346761i	−0.875862	−	0.482562i	$-0.839706\pi$
$661$	−0.514719	+	0.891519i	−0.0200202	+	0.0346761i	0.855842	+	0.517238i	$0.173040\pi$
$662$	5.17157			0.200999
$663$		0			0
$664$	33.7990			1.31166
$665$	−11.3137	+	19.5959i	−0.438727	+	0.759897i
$666$	4.41421	−	7.64564i	0.171047	−	0.296263i
$667$	4.00000	+	6.92820i	0.154881	+	0.268261i
$668$	−29.3137			−1.13418
$669$	2.24264	+	3.88437i	0.0867055	+	0.150178i
$670$	−4.00000	−	6.92820i	−0.154533	−	0.267660i
$671$	−18.6274			−0.719103
$672$	2.24264	+	3.88437i	0.0865117	+	0.149843i
$673$	14.3137	−	24.7921i	0.551753	−	0.955664i	−0.446395	−	0.894836i	$-0.647292\pi$
$673$	14.3137	−	24.7921i	0.551753	−	0.955664i	0.998148	−	0.0608282i	$-0.0193742\pi$
$674$	16.0711	−	27.8359i	0.619034	−	1.07220i
$675$	3.00000			0.115470
$676$		0			0
$677$	49.3137			1.89528			0.947640	−	0.319341i	$-0.103462\pi$
$677$	49.3137			1.89528			0.947640	+	0.319341i	$0.103462\pi$
$678$	−20.8995	+	36.1990i	−0.802640	+	1.39021i
$679$	−10.8284	+	18.7554i	−0.415557	+	0.719766i
$680$	−22.8284	−	39.5400i	−0.875430	−	1.51629i
$681$	−5.31371			−0.203622
$682$	−16.4853	−	28.5533i	−0.631254	−	1.09336i
$683$	−9.97056	−	17.2695i	−0.381513	−	0.660800i	0.609766	−	0.792582i	$-0.291264\pi$
$683$	−9.97056	−	17.2695i	−0.381513	−	0.660800i	−0.991279	+	0.131782i	$0.957930\pi$
$684$	−10.8284			−0.414035
$685$	7.31371	+	12.6677i	0.279442	+	0.484008i
$686$	20.4853	−	35.4815i	0.782132	−	1.35469i
$687$	10.6569	−	18.4582i	0.406584	−	0.704225i
$688$	28.9706			1.10449
$689$		0			0
$690$	27.3137			1.03982
$691$	−17.0711	+	29.5680i	−0.649414	+	1.12482i	0.333849	+	0.942627i	$0.391652\pi$
$691$	−17.0711	+	29.5680i	−0.649414	+	1.12482i	−0.983263	+	0.182192i	$0.941681\pi$
$692$	0.656854	−	1.13770i	0.0249699	−	0.0432491i
$693$	−2.82843	−	4.89898i	−0.107443	−	0.186097i
$694$	−75.5980			−2.86966
$695$	21.6569	+	37.5108i	0.821491	+	1.42286i
$696$	−4.41421	−	7.64564i	−0.167320	−	0.289807i
$697$	39.5980			1.49988
$698$	−9.24264	−	16.0087i	−0.349839	−	0.605939i
$699$	13.4853	−	23.3572i	0.510060	−	0.883450i
$700$	−16.2426	+	28.1331i	−0.613914	+	1.06333i
$701$	38.9706			1.47190			0.735949	−	0.677037i	$-0.236736\pi$
$701$	38.9706			1.47190			0.735949	+	0.677037i	$0.236736\pi$
$702$		0			0
$703$	10.3431			0.390099
$704$	9.82843	−	17.0233i	0.370423	−	0.641591i
$705$	0.485281	−	0.840532i	0.0182768	−	0.0316563i
$706$	21.0711	+	36.4962i	0.793020	+	1.37355i
$707$	−10.3431			−0.388994
$708$	−7.00000	−	12.1244i	−0.263076	−	0.455661i
$709$	20.3137	+	35.1844i	0.762897	+	1.32138i	0.941351	+	0.337429i	$0.109557\pi$
$709$	20.3137	+	35.1844i	0.762897	+	1.32138i	−0.178454	+	0.983948i	$0.557109\pi$
$710$	13.6569			0.512533
$711$	−5.65685	−	9.79796i	−0.212149	−	0.367452i
$712$	20.2426	−	35.0613i	0.758625	−	1.31398i
$713$	13.6569	−	23.6544i	0.511453	−	0.885863i
$714$	−24.9706			−0.934500
$715$		0			0
$716$	−2.62742			−0.0981912
$717$	1.00000	−	1.73205i	0.0373457	−	0.0646846i
$718$	1.24264	−	2.15232i	0.0463749	−	0.0803237i
$719$	−18.9706	−	32.8580i	−0.707483	−	1.22540i	−0.965788	−	0.259333i	$-0.916497\pi$
$719$	−18.9706	−	32.8580i	−0.707483	−	1.22540i	0.258305	−	0.966063i	$-0.416836\pi$
$720$	−8.48528			−0.316228
$721$	−19.3137	−	33.4523i	−0.719280	−	1.24583i
$722$	13.2782	+	22.9985i	0.494162	+	0.855915i
$723$	−11.6569			−0.433523
$724$	−26.7990	−	46.4172i	−0.995977	−	1.72508i
$725$	−3.00000	+	5.19615i	−0.111417	+	0.192980i
$726$	8.44975	−	14.6354i	0.313600	−	0.543170i
$727$	−21.6569			−0.803208			−0.401604	−	0.915813i	$-0.631547\pi$
$727$	−21.6569			−0.803208			−0.401604	+	0.915813i	$0.631547\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−39.7990	+	68.9339i	−1.47303	+	2.55136i
$731$	17.6569	−	30.5826i	0.653062	−	1.13114i
$732$	17.8284	+	30.8797i	0.658958	+	1.14135i
$733$	−8.62742			−0.318661			−0.159330	−	0.987225i	$-0.550934\pi$
$733$	−8.62742			−0.318661			−0.159330	+	0.987225i	$0.550934\pi$
$734$	28.9706	+	50.1785i	1.06932	+	1.85212i
$735$	1.41421	+	2.44949i	0.0521641	+	0.0903508i
$736$	6.34315			0.233811
$737$	1.17157	+	2.02922i	0.0431554	+	0.0747474i
$738$	13.0711	−	22.6398i	0.481153	−	0.833381i
$739$	5.07107	−	8.78335i	0.186542	−	0.323101i	−0.757553	−	0.652774i	$-0.773605\pi$
$739$	5.07107	−	8.78335i	0.186542	−	0.323101i	0.944095	+	0.329673i	$0.106939\pi$
$740$	39.5980			1.45565
$741$		0			0
$742$	−13.6569			−0.501359
$743$	1.00000	−	1.73205i	0.0366864	−	0.0635428i	−0.847099	−	0.531435i	$-0.821653\pi$
$743$	1.00000	−	1.73205i	0.0366864	−	0.0635428i	0.883786	+	0.467892i	$0.154986\pi$
$744$	−15.0711	+	26.1039i	−0.552532	+	0.957014i
$745$	20.9706	+	36.3221i	0.768302	+	1.33074i
$746$	24.1421			0.883906
$747$	−3.82843	−	6.63103i	−0.140075	−	0.242617i
$748$	14.0000	+	24.2487i	0.511891	+	0.886621i
$749$	32.0000			1.16925
$750$	−6.82843	−	11.8272i	−0.249339	−	0.431868i
$751$	−16.4853	+	28.5533i	−0.601556	+	1.04193i	0.391029	+	0.920378i	$0.372119\pi$
$751$	−16.4853	+	28.5533i	−0.601556	+	1.04193i	−0.992586	+	0.121548i	$0.961214\pi$
$752$	−0.514719	+	0.891519i	−0.0187699	+	0.0325103i
$753$		0			0
$754$		0			0
$755$	−57.9411			−2.10869
$756$	−5.41421	+	9.37769i	−0.196913	+	0.341063i
$757$	7.97056	−	13.8054i	0.289695	−	0.501767i	−0.684042	−	0.729443i	$-0.739779\pi$
$757$	7.97056	−	13.8054i	0.289695	−	0.501767i	0.973737	+	0.227676i	$0.0731128\pi$
$758$	−19.8995	−	34.4669i	−0.722782	−	1.25190i
$759$	−8.00000			−0.290382
$760$	−17.6569	−	30.5826i	−0.640481	−	1.10935i
$761$	7.75736	+	13.4361i	0.281204	+	0.487060i	0.971682	−	0.236294i	$-0.0759329\pi$
$761$	7.75736	+	13.4361i	0.281204	+	0.487060i	−0.690478	+	0.723354i	$0.742600\pi$
$762$	−13.6569			−0.494736
$763$	−24.4853	−	42.4098i	−0.886427	−	1.53534i
$764$	36.9706	−	64.0349i	1.33755	−	2.31670i
$765$	−5.17157	+	8.95743i	−0.186979	+	0.323856i
$766$	7.17157			0.259119
$767$		0			0
$768$	−29.9706			−1.08147
$769$	21.0000	−	36.3731i	0.757279	−	1.31165i	−0.186954	−	0.982369i	$-0.559861\pi$
$769$	21.0000	−	36.3731i	0.757279	−	1.31165i	0.944233	−	0.329278i	$-0.106805\pi$
$770$	19.3137	−	33.4523i	0.696018	−	1.20554i
$771$	7.82843	+	13.5592i	0.281934	+	0.488324i
$772$	66.2843			2.38562
$773$	2.92893	+	5.07306i	0.105346	+	0.182465i	0.913880	−	0.405985i	$-0.133072\pi$
$773$	2.92893	+	5.07306i	0.105346	+	0.182465i	−0.808533	+	0.588450i	$0.799738\pi$
$774$	−11.6569	−	20.1903i	−0.418997	−	0.725724i
$775$	20.4853			0.735853
$776$	−16.8995	−	29.2708i	−0.606657	−	1.05076i
$777$	5.17157	−	8.95743i	0.185529	−	0.321346i
$778$	−8.41421	+	14.5738i	−0.301664	+	0.522498i
$779$	30.6274			1.09734
$780$		0			0
$781$	−4.00000			−0.143131
$782$	−17.6569	+	30.5826i	−0.631408	+	1.09363i
$783$	−1.00000	+	1.73205i	−0.0357371	+	0.0618984i
$784$	−1.50000	−	2.59808i	−0.0535714	−	0.0927884i
$785$	28.2843			1.00951
$786$	9.65685	+	16.7262i	0.344449	+	0.596602i
$787$	16.3848	+	28.3793i	0.584054	+	1.01161i	0.994993	+	0.0999484i	$0.0318678\pi$
$787$	16.3848	+	28.3793i	0.584054	+	1.01161i	−0.410938	+	0.911663i	$0.634799\pi$
$788$	63.1127			2.24830
$789$	−6.00000	−	10.3923i	−0.213606	−	0.369976i
$790$	38.6274	−	66.9046i	1.37430	−	2.38036i
$791$	−24.4853	+	42.4098i	−0.870596	+	1.50792i
$792$	8.82843			0.313704
$793$		0			0
$794$	7.17157			0.254510
$795$	−2.82843	+	4.89898i	−0.100314	+	0.173749i
$796$	−19.7990	+	34.2929i	−0.701757	+	1.21548i
$797$	−17.8284	−	30.8797i	−0.631515	−	1.09382i	−0.987242	−	0.159227i	$-0.949100\pi$
$797$	−17.8284	−	30.8797i	−0.631515	−	1.09382i	0.355727	−	0.934590i	$-0.384233\pi$
$798$	−19.3137			−0.683698
$799$	0.627417	+	1.08672i	0.0221964	+	0.0384453i
$800$	2.37868	+	4.11999i	0.0840990	+	0.145664i
$801$	−9.17157			−0.324062
$802$	−2.58579	−	4.47871i	−0.0913073	−	0.158149i
$803$	11.6569	−	20.1903i	0.411361	−	0.712499i
$804$	2.24264	−	3.88437i	0.0790918	−	0.136991i
$805$	32.0000			1.12785
$806$		0			0
$807$	18.0000			0.633630
$808$	8.07107	−	13.9795i	0.283939	−	0.491797i
$809$	−20.6569	+	35.7787i	−0.726256	+	1.25791i	0.232198	+	0.972668i	$0.425408\pi$
$809$	−20.6569	+	35.7787i	−0.726256	+	1.25791i	−0.958455	+	0.285244i	$0.907925\pi$
$810$	3.41421	+	5.91359i	0.119963	+	0.207782i
$811$	1.85786			0.0652384			0.0326192	−	0.999468i	$-0.489615\pi$
$811$	1.85786			0.0652384			0.0326192	+	0.999468i	$0.489615\pi$
$812$	−10.8284	−	18.7554i	−0.380003	−	0.658185i
$813$	5.89949	+	10.2182i	0.206904	+	0.358369i
$814$	−17.6569			−0.618872
$815$	−18.6274	−	32.2636i	−0.652490	−	1.13015i
$816$	5.48528	−	9.50079i	0.192023	−	0.332594i
$817$	13.6569	−	23.6544i	0.477793	−	0.827561i
$818$	2.48528			0.0868958
$819$		0			0
$820$	117.255			4.09472
$821$	7.89949	−	13.6823i	0.275694	−	0.477516i	−0.694616	−	0.719381i	$-0.744426\pi$
$821$	7.89949	−	13.6823i	0.275694	−	0.477516i	0.970310	+	0.241864i	$0.0777589\pi$
$822$	−6.24264	+	10.8126i	−0.217737	+	0.377132i
$823$	−24.4853	−	42.4098i	−0.853503	−	1.47831i	−0.878027	−	0.478612i	$-0.841140\pi$
$823$	−24.4853	−	42.4098i	−0.853503	−	1.47831i	0.0245234	−	0.999699i	$-0.492193\pi$
$824$	60.2843			2.10010
$825$	−3.00000	−	5.19615i	−0.104447	−	0.180907i
$826$	−12.4853	−	21.6251i	−0.434418	−	0.752435i
$827$	26.0000			0.904109			0.452054	−	0.891990i	$-0.350691\pi$
$827$	26.0000			0.904109			0.452054	+	0.891990i	$0.350691\pi$
$828$	7.65685	+	13.2621i	0.266094	+	0.460888i
$829$	−2.65685	+	4.60181i	−0.0922764	+	0.159827i	−0.908469	−	0.417953i	$-0.862748\pi$
$829$	−2.65685	+	4.60181i	−0.0922764	+	0.159827i	0.816192	+	0.577780i	$0.196081\pi$
$830$	26.1421	−	45.2795i	0.907407	−	1.57167i
$831$	−2.00000			−0.0693792
$832$		0			0
$833$	−3.65685			−0.126702
$834$	−18.4853	+	32.0174i	−0.640093	+	1.10867i
$835$	−10.8284	+	18.7554i	−0.374733	+	0.649057i
$836$	10.8284	+	18.7554i	0.374509	+	0.648669i
$837$	6.82843			0.236025
$838$	36.9706	+	64.0349i	1.27713	+	2.21205i
$839$	−23.6274	−	40.9239i	−0.815709	−	1.41285i	−0.908818	−	0.417194i	$-0.863014\pi$
$839$	−23.6274	−	40.9239i	−0.815709	−	1.41285i	0.0931087	−	0.995656i	$-0.470320\pi$
$840$	−35.3137			−1.21844
$841$	12.5000	+	21.6506i	0.431034	+	0.746574i
$842$	17.7279	−	30.7057i	0.610945	−	1.05819i
$843$	13.4142	−	23.2341i	0.462010	−	0.800225i
$844$	−45.9411			−1.58136
$845$		0			0
$846$	0.828427			0.0284819
$847$	9.89949	−	17.1464i	0.340151	−	0.589158i
$848$	3.00000	−	5.19615i	0.103020	−	0.178437i
$849$	2.48528	+	4.30463i	0.0852946	+	0.147735i
$850$	−26.4853			−0.908438
$851$	−7.31371	−	12.6677i	−0.250711	−	0.434244i
$852$	3.82843	+	6.63103i	0.131160	+	0.227175i
$853$	7.65685			0.262166			0.131083	−	0.991371i	$-0.458155\pi$
$853$	7.65685			0.262166			0.131083	+	0.991371i	$0.458155\pi$
$854$	31.7990	+	55.0775i	1.08814	+	1.88471i
$855$	−4.00000	+	6.92820i	−0.136797	+	0.236940i
$856$	−24.9706	+	43.2503i	−0.853476	+	1.47826i
$857$	29.5980			1.01105			0.505524	−	0.862813i	$-0.331299\pi$
$857$	29.5980			1.01105			0.505524	+	0.862813i	$0.331299\pi$
$858$		0			0
$859$	−23.3137			−0.795453			−0.397727	−	0.917504i	$-0.630201\pi$
$859$	−23.3137			−0.795453			−0.397727	+	0.917504i	$0.630201\pi$
$860$	52.2843	−	90.5590i	1.78288	−	3.08804i
$861$	15.3137	−	26.5241i	0.521890	−	0.903940i
$862$	23.7279	+	41.0980i	0.808176	+	1.39980i
$863$	39.6569			1.34994			0.674968	−	0.737847i	$-0.264158\pi$
$863$	39.6569			1.34994			0.674968	+	0.737847i	$0.264158\pi$
$864$	0.792893	+	1.37333i	0.0269748	+	0.0467217i
$865$	−0.485281	−	0.840532i	−0.0165001	−	0.0285789i
$866$	3.17157			0.107774
$867$	1.81371	+	3.14144i	0.0615968	+	0.106689i
$868$	−36.9706	+	64.0349i	−1.25486	+	2.17349i
$869$	−11.3137	+	19.5959i	−0.383791	+	0.664746i
$870$	−13.6569			−0.463011
$871$		0			0
$872$	76.4264			2.58812
$873$	−3.82843	+	6.63103i	−0.129573	+	0.224426i
$874$	−13.6569	+	23.6544i	−0.461950	+	0.800121i
$875$	−8.00000	−	13.8564i	−0.270449	−	0.468432i
$876$	−44.6274			−1.50782
$877$	−7.14214	−	12.3705i	−0.241173	−	0.417724i	0.719876	−	0.694103i	$-0.244199\pi$
$877$	−7.14214	−	12.3705i	−0.241173	−	0.417724i	−0.961049	+	0.276379i	$0.910865\pi$
$878$	20.4853	+	35.4815i	0.691345	+	1.19744i
$879$	26.1421			0.881752
$880$	8.48528	+	14.6969i	0.286039	+	0.495434i
$881$	−26.7990	+	46.4172i	−0.902881	+	1.56384i	−0.0791441	+	0.996863i	$0.525219\pi$
$881$	−26.7990	+	46.4172i	−0.902881	+	1.56384i	−0.823737	+	0.566972i	$0.808115\pi$
$882$	−1.20711	+	2.09077i	−0.0406454	+	0.0703999i
$883$	−51.5980			−1.73641			−0.868205	−	0.496205i	$-0.834726\pi$
$883$	−51.5980			−1.73641			−0.868205	+	0.496205i	$0.834726\pi$
$884$		0			0
$885$	−10.3431			−0.347681
$886$	−50.6274	+	87.6893i	−1.70086	+	2.94598i
$887$	4.00000	−	6.92820i	0.134307	−	0.232626i	−0.791026	−	0.611783i	$-0.790453\pi$
$887$	4.00000	−	6.92820i	0.134307	−	0.232626i	0.925332	+	0.379157i	$0.123786\pi$
$888$	8.07107	+	13.9795i	0.270847	+	0.469121i
$889$	−16.0000			−0.536623
$890$	−31.3137	−	54.2369i	−1.04964	−	1.81803i
$891$	−1.00000	−	1.73205i	−0.0335013	−	0.0580259i
$892$	−17.1716			−0.574947
$893$	0.485281	+	0.840532i	0.0162393	+	0.0281273i
$894$	−17.8995	+	31.0028i	−0.598649	+	1.03689i
$895$	−0.970563	+	1.68106i	−0.0324423	+	0.0561918i
$896$	−58.1421			−1.94239
$897$		0			0
$898$	−18.8284			−0.628313
$899$	−6.82843	+	11.8272i	−0.227741	+	0.394459i
$900$	−5.74264	+	9.94655i	−0.191421	+	0.331552i
$901$	−3.65685	−	6.33386i	−0.121827	−	0.211011i
$902$	−52.2843			−1.74088
$903$	−13.6569	−	23.6544i	−0.454472	−	0.787168i
$904$	−38.2132	−	66.1872i	−1.27095	−	2.20135i
$905$	−39.5980			−1.31628
$906$	−24.7279	−	42.8300i	−0.821530	−	1.42293i
$907$	−10.4853	+	18.1610i	−0.348158	+	0.603027i	−0.985922	−	0.167204i	$-0.946526\pi$
$907$	−10.4853	+	18.1610i	−0.348158	+	0.603027i	0.637764	+	0.770232i	$0.279859\pi$
$908$	10.1716	−	17.6177i	0.337556	−	0.584663i
$909$	−3.65685			−0.121290
$910$		0			0
$911$	−40.0000			−1.32526			−0.662630	−	0.748947i	$-0.730560\pi$
$911$	−40.0000			−1.32526			−0.662630	+	0.748947i	$0.730560\pi$
$912$	4.24264	−	7.34847i	0.140488	−	0.243332i
$913$	−7.65685	+	13.2621i	−0.253405	+	0.438910i
$914$	4.41421	+	7.64564i	0.146009	+	0.252895i
$915$	26.3431			0.870878
$916$	40.7990	+	70.6659i	1.34804	+	2.33487i
$917$	11.3137	+	19.5959i	0.373612	+	0.647114i
$918$	−8.82843			−0.291382
$919$	9.65685	+	16.7262i	0.318550	+	0.551745i	0.980186	−	0.198080i	$-0.0634707\pi$
$919$	9.65685	+	16.7262i	0.318550	+	0.551745i	−0.661636	+	0.749826i	$0.730137\pi$
$920$	−24.9706	+	43.2503i	−0.823255	+	1.42592i
$921$	−8.58579	+	14.8710i	−0.282911	+	0.490017i
$922$	−26.1421			−0.860945
$923$		0			0
$924$	21.6569			0.712458
$925$	5.48528	−	9.50079i	0.180355	−	0.312384i
$926$	−9.07107	+	15.7116i	−0.298094	+	0.516314i
$927$	−6.82843	−	11.8272i	−0.224275	−	0.388456i
$928$	−3.17157			−0.104112
$929$	−13.8995	−	24.0746i	−0.456028	−	0.789863i	0.542719	−	0.839914i	$-0.317395\pi$
$929$	−13.8995	−	24.0746i	−0.456028	−	0.789863i	−0.998747	+	0.0500513i	$0.984062\pi$
$930$	23.3137	+	40.3805i	0.764487	+	1.32413i
$931$	−2.82843			−0.0926980
$932$	51.6274	+	89.4213i	1.69111	+	2.92909i
$933$	−17.3137	+	29.9882i	−0.566825	+	0.981770i
$934$	9.65685	−	16.7262i	0.315982	−	0.547297i
$935$	20.6863			0.676514
$936$		0			0
$937$	1.31371			0.0429170			0.0214585	−	0.999770i	$-0.493169\pi$
$937$	1.31371			0.0429170			0.0214585	+	0.999770i	$0.493169\pi$
$938$	4.00000	−	6.92820i	0.130605	−	0.226214i
$939$	−3.00000	+	5.19615i	−0.0979013	+	0.169570i
$940$	1.85786	+	3.21792i	0.0605969	+	0.104957i
$941$	−5.85786			−0.190961			−0.0954805	−	0.995431i	$-0.530439\pi$
$941$	−5.85786			−0.190961			−0.0954805	+	0.995431i	$0.530439\pi$
$942$	12.0711	+	20.9077i	0.393297	+	0.681210i
$943$	−21.6569	−	37.5108i	−0.705244	−	1.22152i
$944$	10.9706			0.357061
$945$	4.00000	+	6.92820i	0.130120	+	0.225374i
$946$	−23.3137	+	40.3805i	−0.757994	+	1.31288i
$947$	−27.4853	+	47.6059i	−0.893152	+	1.54698i	−0.0570760	+	0.998370i	$0.518178\pi$
$947$	−27.4853	+	47.6059i	−0.893152	+	1.54698i	−0.836076	+	0.548614i	$0.815156\pi$
$948$	43.3137			1.40676
$949$		0			0
$950$	−20.4853			−0.664630
$951$	−4.24264	+	7.34847i	−0.137577	+	0.238290i
$952$	22.8284	−	39.5400i	0.739874	−	1.28150i
$953$	−25.8284	−	44.7361i	−0.836665	−	1.44915i	−0.892668	−	0.450715i	$-0.851169\pi$
$953$	−25.8284	−	44.7361i	−0.836665	−	1.44915i	0.0560029	−	0.998431i	$-0.482164\pi$
$954$	−4.82843			−0.156326
$955$	−27.3137	−	47.3087i	−0.883851	−	1.53087i
$956$	3.82843	+	6.63103i	0.123820	+	0.214463i
$957$	4.00000			0.129302
$958$	3.24264	+	5.61642i	0.104765	+	0.181458i
$959$	−7.31371	+	12.6677i	−0.236172	+	0.409062i
$960$	−13.8995	+	24.0746i	−0.448604	+	0.777005i
$961$	15.6274			0.504110
$962$		0			0
$963$	11.3137			0.364579
$964$	22.3137	−	38.6485i	0.718676	−	1.24478i
$965$	24.4853	−	42.4098i	0.788209	−	1.36522i
$966$	13.6569	+	23.6544i	0.439402	+	0.761067i
$967$	10.1421			0.326149			0.163075	−	0.986614i	$-0.447859\pi$
$967$	10.1421			0.326149			0.163075	+	0.986614i	$0.447859\pi$
$968$	15.4497	+	26.7597i	0.496574	+	0.860091i
$969$	−5.17157	−	8.95743i	−0.166135	−	0.287754i
$970$	−52.2843			−1.67875
$971$	−3.65685	−	6.33386i	−0.117354	−	0.203263i	0.801364	−	0.598177i	$-0.204108\pi$
$971$	−3.65685	−	6.33386i	−0.117354	−	0.203263i	−0.918718	+	0.394913i	$0.870775\pi$
$972$	−1.91421	+	3.31552i	−0.0613984	+	0.106345i
$973$	−21.6569	+	37.5108i	−0.694287	+	1.20254i
$974$	−76.7696			−2.45986
$975$		0			0
$976$	−27.9411			−0.894374
$977$	6.92893	−	12.0013i	0.221676	−	0.383954i	−0.733641	−	0.679537i	$-0.762181\pi$
$977$	6.92893	−	12.0013i	0.221676	−	0.383954i	0.955317	+	0.295583i	$0.0955139\pi$
$978$	15.8995	−	27.5387i	0.508410	−	0.880592i
$979$	9.17157	+	15.8856i	0.293125	+	0.507707i
$980$	−10.8284			−0.345901
$981$	−8.65685	−	14.9941i	−0.276392	−	0.478725i
$982$	17.6569	+	30.5826i	0.563453	+	0.975929i
$983$	−2.68629			−0.0856794			−0.0428397	−	0.999082i	$-0.513640\pi$
$983$	−2.68629			−0.0856794			−0.0428397	+	0.999082i	$0.513640\pi$
$984$	23.8995	+	41.3951i	0.761888	+	1.31963i
$985$	23.3137	−	40.3805i	0.742837	−	1.28663i
$986$	8.82843	−	15.2913i	0.281154	−	0.486974i
$987$	0.970563			0.0308934
$988$		0			0
$989$	−38.6274			−1.22828
$990$	6.82843	−	11.8272i	0.217022	−	0.375893i
$991$	−13.6569	+	23.6544i	−0.433824	+	0.751406i	−0.997199	−	0.0747959i	$-0.976169\pi$
$991$	−13.6569	+	23.6544i	−0.433824	+	0.751406i	0.563375	+	0.826202i	$0.309503\pi$
$992$	5.41421	+	9.37769i	0.171901	+	0.297742i
$993$	2.14214			0.0679786
$994$	6.82843	+	11.8272i	0.216585	+	0.375135i
$995$	14.6274	+	25.3354i	0.463720	+	0.803187i
$996$	29.3137			0.928840
$997$	−25.6274	−	44.3880i	−0.811628	−	1.40578i	−0.911724	−	0.410804i	$-0.865248\pi$
$997$	−25.6274	−	44.3880i	−0.811628	−	1.40578i	0.100095	−	0.994978i	$-0.468085\pi$
$998$	−2.58579	+	4.47871i	−0.0818516	+	0.141771i
$999$	1.82843	−	3.16693i	0.0578489	−	0.100197i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.e.d.22.1		4
13.2	odd	12		507.2.j.f.361.1		8
13.3	even	3	inner	507.2.e.d.484.1		4
13.4	even	6		39.2.a.b.1.1	✓	2
13.5	odd	4		507.2.j.f.316.4		8
13.6	odd	12		507.2.b.e.337.1		4
13.7	odd	12		507.2.b.e.337.4		4
13.8	odd	4		507.2.j.f.316.1		8
13.9	even	3		507.2.a.h.1.2		2
13.10	even	6		507.2.e.h.484.2		4
13.11	odd	12		507.2.j.f.361.4		8
13.12	even	2		507.2.e.h.22.2		4
39.17	odd	6		117.2.a.c.1.2		2
39.20	even	12		1521.2.b.j.1351.1		4
39.32	even	12		1521.2.b.j.1351.4		4
39.35	odd	6		1521.2.a.f.1.1		2
52.35	odd	6		8112.2.a.bm.1.1		2
52.43	odd	6		624.2.a.k.1.2		2
65.4	even	6		975.2.a.l.1.2		2
65.17	odd	12		975.2.c.h.274.1		4
65.43	odd	12		975.2.c.h.274.4		4
91.69	odd	6		1911.2.a.h.1.1		2
104.43	odd	6		2496.2.a.bi.1.1		2
104.69	even	6		2496.2.a.bf.1.1		2
117.4	even	6		1053.2.e.m.703.2		4
117.43	even	6		1053.2.e.m.352.2		4
117.56	odd	6		1053.2.e.e.352.1		4
117.95	odd	6		1053.2.e.e.703.1		4
143.43	odd	6		4719.2.a.p.1.2		2
156.95	even	6		1872.2.a.w.1.1		2
195.17	even	12		2925.2.c.u.2224.4		4
195.134	odd	6		2925.2.a.v.1.1		2
195.173	even	12		2925.2.c.u.2224.1		4
273.251	even	6		5733.2.a.u.1.2		2
312.173	odd	6		7488.2.a.cl.1.2		2
312.251	even	6		7488.2.a.co.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.2.a.b.1.1	✓	2	13.4	even	6
117.2.a.c.1.2		2	39.17	odd	6
507.2.a.h.1.2		2	13.9	even	3
507.2.b.e.337.1		4	13.6	odd	12
507.2.b.e.337.4		4	13.7	odd	12
507.2.e.d.22.1		4	1.1	even	1	trivial
507.2.e.d.484.1		4	13.3	even	3	inner
507.2.e.h.22.2		4	13.12	even	2
507.2.e.h.484.2		4	13.10	even	6
507.2.j.f.316.1		8	13.8	odd	4
507.2.j.f.316.4		8	13.5	odd	4
507.2.j.f.361.1		8	13.2	odd	12
507.2.j.f.361.4		8	13.11	odd	12
624.2.a.k.1.2		2	52.43	odd	6
975.2.a.l.1.2		2	65.4	even	6
975.2.c.h.274.1		4	65.17	odd	12
975.2.c.h.274.4		4	65.43	odd	12
1053.2.e.e.352.1		4	117.56	odd	6
1053.2.e.e.703.1		4	117.95	odd	6
1053.2.e.m.352.2		4	117.43	even	6
1053.2.e.m.703.2		4	117.4	even	6
1521.2.a.f.1.1		2	39.35	odd	6
1521.2.b.j.1351.1		4	39.20	even	12
1521.2.b.j.1351.4		4	39.32	even	12
1872.2.a.w.1.1		2	156.95	even	6
1911.2.a.h.1.1		2	91.69	odd	6
2496.2.a.bf.1.1		2	104.69	even	6
2496.2.a.bi.1.1		2	104.43	odd	6
2925.2.a.v.1.1		2	195.134	odd	6
2925.2.c.u.2224.1		4	195.173	even	12
2925.2.c.u.2224.4		4	195.17	even	12
4719.2.a.p.1.2		2	143.43	odd	6
5733.2.a.u.1.2		2	273.251	even	6
7488.2.a.cl.1.2		2	312.173	odd	6
7488.2.a.co.1.2		2	312.251	even	6
8112.2.a.bm.1.1		2	52.35	odd	6

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.20711 + 2.09077i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-1.91421 - 3.31552i) q^{4} -2.82843 q^{5} +(-1.20711 - 2.09077i) q^{6} +(-1.41421 - 2.44949i) q^{7} +4.41421 q^{8} +(-0.500000 - 0.866025i) q^{9} +(3.41421 - 5.91359i) q^{10} +(-1.00000 + 1.73205i) q^{11} +3.82843 q^{12} +6.82843 q^{14} +(1.41421 - 2.44949i) q^{15} +(-1.50000 + 2.59808i) q^{16} +(1.82843 + 3.16693i) q^{17} +2.41421 q^{18} +(1.41421 + 2.44949i) q^{19} +(5.41421 + 9.37769i) q^{20} +2.82843 q^{21} +(-2.41421 - 4.18154i) q^{22} +(2.00000 - 3.46410i) q^{23} +(-2.20711 + 3.82282i) q^{24} +3.00000 q^{25} +1.00000 q^{27} +(-5.41421 + 9.37769i) q^{28} +(-1.00000 + 1.73205i) q^{29} +(3.41421 + 5.91359i) q^{30} +6.82843 q^{31} +(0.792893 + 1.37333i) q^{32} +(-1.00000 - 1.73205i) q^{33} -8.82843 q^{34} +(4.00000 + 6.92820i) q^{35} +(-1.91421 + 3.31552i) q^{36} +(1.82843 - 3.16693i) q^{37} -6.82843 q^{38} -12.4853 q^{40} +(5.41421 - 9.37769i) q^{41} +(-3.41421 + 5.91359i) q^{42} +(-4.82843 - 8.36308i) q^{43} +7.65685 q^{44} +(1.41421 + 2.44949i) q^{45} +(4.82843 + 8.36308i) q^{46} +0.343146 q^{47} +(-1.50000 - 2.59808i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-3.62132 + 6.27231i) q^{50} -3.65685 q^{51} -2.00000 q^{53} +(-1.20711 + 2.09077i) q^{54} +(2.82843 - 4.89898i) q^{55} +(-6.24264 - 10.8126i) q^{56} -2.82843 q^{57} +(-2.41421 - 4.18154i) q^{58} +(-1.82843 - 3.16693i) q^{59} -10.8284 q^{60} +(4.65685 + 8.06591i) q^{61} +(-8.24264 + 14.2767i) q^{62} +(-1.41421 + 2.44949i) q^{63} -9.82843 q^{64} +4.82843 q^{66} +(0.585786 - 1.01461i) q^{67} +(7.00000 - 12.1244i) q^{68} +(2.00000 + 3.46410i) q^{69} -19.3137 q^{70} +(1.00000 + 1.73205i) q^{71} +(-2.20711 - 3.82282i) q^{72} -11.6569 q^{73} +(4.41421 + 7.64564i) q^{74} +(-1.50000 + 2.59808i) q^{75} +(5.41421 - 9.37769i) q^{76} +5.65685 q^{77} +11.3137 q^{79} +(4.24264 - 7.34847i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(13.0711 + 22.6398i) q^{82} +7.65685 q^{83} +(-5.41421 - 9.37769i) q^{84} +(-5.17157 - 8.95743i) q^{85} +23.3137 q^{86} +(-1.00000 - 1.73205i) q^{87} +(-4.41421 + 7.64564i) q^{88} +(4.58579 - 7.94282i) q^{89} -6.82843 q^{90} -15.3137 q^{92} +(-3.41421 + 5.91359i) q^{93} +(-0.414214 + 0.717439i) q^{94} +(-4.00000 - 6.92820i) q^{95} -1.58579 q^{96} +(-3.82843 - 6.63103i) q^{97} +(-1.20711 - 2.09077i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 2 q^{6} + 12 q^{8} - 2 q^{9} + 8 q^{10} - 4 q^{11} + 4 q^{12} + 16 q^{14} - 6 q^{16} - 4 q^{17} + 4 q^{18} + 16 q^{20} - 4 q^{22} + 8 q^{23} - 6 q^{24} + 12 q^{25} + 4 q^{27}+ \cdots + 8 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 2 * q^6 + 12 * q^8 - 2 * q^9 + 8 * q^10 - 4 * q^11 + 4 * q^12 + 16 * q^14 - 6 * q^16 - 4 * q^17 + 4 * q^18 + 16 * q^20 - 4 * q^22 + 8 * q^23 - 6 * q^24 + 12 * q^25 + 4 * q^27 - 16 * q^28 - 4 * q^29 + 8 * q^30 + 16 * q^31 + 6 * q^32 - 4 * q^33 - 24 * q^34 + 16 * q^35 - 2 * q^36 - 4 * q^37 - 16 * q^38 - 16 * q^40 + 16 * q^41 - 8 * q^42 - 8 * q^43 + 8 * q^44 + 8 * q^46 + 24 * q^47 - 6 * q^48 - 2 * q^49 - 6 * q^50 + 8 * q^51 - 8 * q^53 - 2 * q^54 - 8 * q^56 - 4 * q^58 + 4 * q^59 - 32 * q^60 - 4 * q^61 - 16 * q^62 - 28 * q^64 + 8 * q^66 + 8 * q^67 + 28 * q^68 + 8 * q^69 - 32 * q^70 + 4 * q^71 - 6 * q^72 - 24 * q^73 + 12 * q^74 - 6 * q^75 + 16 * q^76 - 2 * q^81 + 24 * q^82 + 8 * q^83 - 16 * q^84 - 32 * q^85 + 48 * q^86 - 4 * q^87 - 12 * q^88 + 24 * q^89 - 16 * q^90 - 16 * q^92 - 8 * q^93 + 4 * q^94 - 16 * q^95 - 12 * q^96 - 4 * q^97 - 2 * q^98 + 8 * q^99

Introduction

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